Properties

Label 3380.2.a.r.1.5
Level $3380$
Weight $2$
Character 3380.1
Self dual yes
Analytic conductor $26.989$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.9894358832\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 19 x^{7} + 16 x^{6} + 106 x^{5} - 87 x^{4} - 153 x^{3} + 149 x^{2} - 26 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(0.161999\) of defining polynomial
Character \(\chi\) \(=\) 3380.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.161999 q^{3} -1.00000 q^{5} -1.89771 q^{7} -2.97376 q^{9} +O(q^{10})\) \(q-0.161999 q^{3} -1.00000 q^{5} -1.89771 q^{7} -2.97376 q^{9} -5.35728 q^{11} +0.161999 q^{15} +7.71387 q^{17} -0.553719 q^{19} +0.307427 q^{21} -3.14988 q^{23} +1.00000 q^{25} +0.967741 q^{27} -3.54250 q^{29} -6.01423 q^{31} +0.867873 q^{33} +1.89771 q^{35} +10.8657 q^{37} -8.74983 q^{41} -3.25198 q^{43} +2.97376 q^{45} -9.81442 q^{47} -3.39868 q^{49} -1.24964 q^{51} +8.87818 q^{53} +5.35728 q^{55} +0.0897018 q^{57} +13.4174 q^{59} -0.551418 q^{61} +5.64334 q^{63} -4.46051 q^{67} +0.510276 q^{69} +8.17861 q^{71} +12.6129 q^{73} -0.161999 q^{75} +10.1666 q^{77} +13.4130 q^{79} +8.76450 q^{81} -5.42318 q^{83} -7.71387 q^{85} +0.573881 q^{87} +1.46756 q^{89} +0.974297 q^{93} +0.553719 q^{95} +5.69045 q^{97} +15.9313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - q^{3} - 9 q^{5} - q^{7} + 12 q^{9} + O(q^{10}) \) \( 9 q - q^{3} - 9 q^{5} - q^{7} + 12 q^{9} + 7 q^{11} + q^{15} + 13 q^{17} + 4 q^{19} + 3 q^{21} + 12 q^{23} + 9 q^{25} - 4 q^{27} + 16 q^{29} - 13 q^{31} - 34 q^{33} + q^{35} - q^{37} + 6 q^{41} + q^{43} - 12 q^{45} + 2 q^{47} + 20 q^{49} + 11 q^{51} + 30 q^{53} - 7 q^{55} - 38 q^{57} - 15 q^{59} + 21 q^{61} + 17 q^{63} + 7 q^{67} + 15 q^{69} + 7 q^{71} + 28 q^{73} - q^{75} + 46 q^{77} + 31 q^{79} + 41 q^{81} - 45 q^{83} - 13 q^{85} + 28 q^{87} + 41 q^{89} + 11 q^{93} - 4 q^{95} - 8 q^{97} + 81 q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.161999 −0.0935300 −0.0467650 0.998906i \(-0.514891\pi\)
−0.0467650 + 0.998906i \(0.514891\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.89771 −0.717268 −0.358634 0.933478i \(-0.616757\pi\)
−0.358634 + 0.933478i \(0.616757\pi\)
\(8\) 0 0
\(9\) −2.97376 −0.991252
\(10\) 0 0
\(11\) −5.35728 −1.61528 −0.807641 0.589674i \(-0.799256\pi\)
−0.807641 + 0.589674i \(0.799256\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 0.161999 0.0418279
\(16\) 0 0
\(17\) 7.71387 1.87089 0.935445 0.353473i \(-0.114999\pi\)
0.935445 + 0.353473i \(0.114999\pi\)
\(18\) 0 0
\(19\) −0.553719 −0.127032 −0.0635160 0.997981i \(-0.520231\pi\)
−0.0635160 + 0.997981i \(0.520231\pi\)
\(20\) 0 0
\(21\) 0.307427 0.0670861
\(22\) 0 0
\(23\) −3.14988 −0.656795 −0.328398 0.944540i \(-0.606509\pi\)
−0.328398 + 0.944540i \(0.606509\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 0.967741 0.186242
\(28\) 0 0
\(29\) −3.54250 −0.657826 −0.328913 0.944360i \(-0.606682\pi\)
−0.328913 + 0.944360i \(0.606682\pi\)
\(30\) 0 0
\(31\) −6.01423 −1.08019 −0.540094 0.841605i \(-0.681611\pi\)
−0.540094 + 0.841605i \(0.681611\pi\)
\(32\) 0 0
\(33\) 0.867873 0.151077
\(34\) 0 0
\(35\) 1.89771 0.320772
\(36\) 0 0
\(37\) 10.8657 1.78631 0.893157 0.449746i \(-0.148485\pi\)
0.893157 + 0.449746i \(0.148485\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.74983 −1.36649 −0.683247 0.730187i \(-0.739433\pi\)
−0.683247 + 0.730187i \(0.739433\pi\)
\(42\) 0 0
\(43\) −3.25198 −0.495923 −0.247961 0.968770i \(-0.579761\pi\)
−0.247961 + 0.968770i \(0.579761\pi\)
\(44\) 0 0
\(45\) 2.97376 0.443301
\(46\) 0 0
\(47\) −9.81442 −1.43158 −0.715790 0.698315i \(-0.753933\pi\)
−0.715790 + 0.698315i \(0.753933\pi\)
\(48\) 0 0
\(49\) −3.39868 −0.485526
\(50\) 0 0
\(51\) −1.24964 −0.174984
\(52\) 0 0
\(53\) 8.87818 1.21951 0.609756 0.792590i \(-0.291268\pi\)
0.609756 + 0.792590i \(0.291268\pi\)
\(54\) 0 0
\(55\) 5.35728 0.722376
\(56\) 0 0
\(57\) 0.0897018 0.0118813
\(58\) 0 0
\(59\) 13.4174 1.74680 0.873401 0.487002i \(-0.161909\pi\)
0.873401 + 0.487002i \(0.161909\pi\)
\(60\) 0 0
\(61\) −0.551418 −0.0706018 −0.0353009 0.999377i \(-0.511239\pi\)
−0.0353009 + 0.999377i \(0.511239\pi\)
\(62\) 0 0
\(63\) 5.64334 0.710994
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.46051 −0.544938 −0.272469 0.962165i \(-0.587840\pi\)
−0.272469 + 0.962165i \(0.587840\pi\)
\(68\) 0 0
\(69\) 0.510276 0.0614301
\(70\) 0 0
\(71\) 8.17861 0.970623 0.485311 0.874341i \(-0.338706\pi\)
0.485311 + 0.874341i \(0.338706\pi\)
\(72\) 0 0
\(73\) 12.6129 1.47623 0.738113 0.674677i \(-0.235717\pi\)
0.738113 + 0.674677i \(0.235717\pi\)
\(74\) 0 0
\(75\) −0.161999 −0.0187060
\(76\) 0 0
\(77\) 10.1666 1.15859
\(78\) 0 0
\(79\) 13.4130 1.50908 0.754540 0.656255i \(-0.227860\pi\)
0.754540 + 0.656255i \(0.227860\pi\)
\(80\) 0 0
\(81\) 8.76450 0.973833
\(82\) 0 0
\(83\) −5.42318 −0.595271 −0.297636 0.954680i \(-0.596198\pi\)
−0.297636 + 0.954680i \(0.596198\pi\)
\(84\) 0 0
\(85\) −7.71387 −0.836687
\(86\) 0 0
\(87\) 0.573881 0.0615265
\(88\) 0 0
\(89\) 1.46756 0.155561 0.0777804 0.996971i \(-0.475217\pi\)
0.0777804 + 0.996971i \(0.475217\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.974297 0.101030
\(94\) 0 0
\(95\) 0.553719 0.0568104
\(96\) 0 0
\(97\) 5.69045 0.577777 0.288889 0.957363i \(-0.406714\pi\)
0.288889 + 0.957363i \(0.406714\pi\)
\(98\) 0 0
\(99\) 15.9313 1.60115
\(100\) 0 0
\(101\) 6.80029 0.676654 0.338327 0.941029i \(-0.390139\pi\)
0.338327 + 0.941029i \(0.390139\pi\)
\(102\) 0 0
\(103\) 12.9081 1.27187 0.635936 0.771742i \(-0.280614\pi\)
0.635936 + 0.771742i \(0.280614\pi\)
\(104\) 0 0
\(105\) −0.307427 −0.0300018
\(106\) 0 0
\(107\) −4.23968 −0.409865 −0.204933 0.978776i \(-0.565697\pi\)
−0.204933 + 0.978776i \(0.565697\pi\)
\(108\) 0 0
\(109\) −7.00088 −0.670563 −0.335281 0.942118i \(-0.608831\pi\)
−0.335281 + 0.942118i \(0.608831\pi\)
\(110\) 0 0
\(111\) −1.76023 −0.167074
\(112\) 0 0
\(113\) 2.29176 0.215590 0.107795 0.994173i \(-0.465621\pi\)
0.107795 + 0.994173i \(0.465621\pi\)
\(114\) 0 0
\(115\) 3.14988 0.293728
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −14.6387 −1.34193
\(120\) 0 0
\(121\) 17.7005 1.60914
\(122\) 0 0
\(123\) 1.41746 0.127808
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −0.526702 −0.0467372 −0.0233686 0.999727i \(-0.507439\pi\)
−0.0233686 + 0.999727i \(0.507439\pi\)
\(128\) 0 0
\(129\) 0.526817 0.0463837
\(130\) 0 0
\(131\) 17.8745 1.56171 0.780853 0.624715i \(-0.214785\pi\)
0.780853 + 0.624715i \(0.214785\pi\)
\(132\) 0 0
\(133\) 1.05080 0.0911159
\(134\) 0 0
\(135\) −0.967741 −0.0832899
\(136\) 0 0
\(137\) −8.58940 −0.733842 −0.366921 0.930252i \(-0.619588\pi\)
−0.366921 + 0.930252i \(0.619588\pi\)
\(138\) 0 0
\(139\) 2.68254 0.227530 0.113765 0.993508i \(-0.463709\pi\)
0.113765 + 0.993508i \(0.463709\pi\)
\(140\) 0 0
\(141\) 1.58992 0.133896
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 3.54250 0.294189
\(146\) 0 0
\(147\) 0.550583 0.0454113
\(148\) 0 0
\(149\) 4.22172 0.345857 0.172929 0.984934i \(-0.444677\pi\)
0.172929 + 0.984934i \(0.444677\pi\)
\(150\) 0 0
\(151\) 7.26015 0.590822 0.295411 0.955370i \(-0.404543\pi\)
0.295411 + 0.955370i \(0.404543\pi\)
\(152\) 0 0
\(153\) −22.9392 −1.85452
\(154\) 0 0
\(155\) 6.01423 0.483074
\(156\) 0 0
\(157\) −10.7458 −0.857609 −0.428805 0.903397i \(-0.641065\pi\)
−0.428805 + 0.903397i \(0.641065\pi\)
\(158\) 0 0
\(159\) −1.43825 −0.114061
\(160\) 0 0
\(161\) 5.97757 0.471098
\(162\) 0 0
\(163\) 8.75744 0.685935 0.342968 0.939347i \(-0.388568\pi\)
0.342968 + 0.939347i \(0.388568\pi\)
\(164\) 0 0
\(165\) −0.867873 −0.0675639
\(166\) 0 0
\(167\) 3.29670 0.255106 0.127553 0.991832i \(-0.459288\pi\)
0.127553 + 0.991832i \(0.459288\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 1.64663 0.125921
\(172\) 0 0
\(173\) 20.6617 1.57088 0.785440 0.618938i \(-0.212437\pi\)
0.785440 + 0.618938i \(0.212437\pi\)
\(174\) 0 0
\(175\) −1.89771 −0.143454
\(176\) 0 0
\(177\) −2.17361 −0.163378
\(178\) 0 0
\(179\) −19.5721 −1.46289 −0.731446 0.681900i \(-0.761154\pi\)
−0.731446 + 0.681900i \(0.761154\pi\)
\(180\) 0 0
\(181\) 10.7679 0.800369 0.400185 0.916435i \(-0.368946\pi\)
0.400185 + 0.916435i \(0.368946\pi\)
\(182\) 0 0
\(183\) 0.0893290 0.00660339
\(184\) 0 0
\(185\) −10.8657 −0.798863
\(186\) 0 0
\(187\) −41.3254 −3.02201
\(188\) 0 0
\(189\) −1.83649 −0.133585
\(190\) 0 0
\(191\) −13.3596 −0.966667 −0.483334 0.875436i \(-0.660574\pi\)
−0.483334 + 0.875436i \(0.660574\pi\)
\(192\) 0 0
\(193\) −3.69764 −0.266162 −0.133081 0.991105i \(-0.542487\pi\)
−0.133081 + 0.991105i \(0.542487\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.5498 −1.25037 −0.625187 0.780475i \(-0.714977\pi\)
−0.625187 + 0.780475i \(0.714977\pi\)
\(198\) 0 0
\(199\) 19.2570 1.36510 0.682548 0.730841i \(-0.260872\pi\)
0.682548 + 0.730841i \(0.260872\pi\)
\(200\) 0 0
\(201\) 0.722597 0.0509681
\(202\) 0 0
\(203\) 6.72265 0.471838
\(204\) 0 0
\(205\) 8.74983 0.611115
\(206\) 0 0
\(207\) 9.36697 0.651050
\(208\) 0 0
\(209\) 2.96643 0.205192
\(210\) 0 0
\(211\) −26.0925 −1.79628 −0.898142 0.439705i \(-0.855083\pi\)
−0.898142 + 0.439705i \(0.855083\pi\)
\(212\) 0 0
\(213\) −1.32492 −0.0907824
\(214\) 0 0
\(215\) 3.25198 0.221783
\(216\) 0 0
\(217\) 11.4133 0.774784
\(218\) 0 0
\(219\) −2.04327 −0.138071
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −9.30627 −0.623194 −0.311597 0.950214i \(-0.600864\pi\)
−0.311597 + 0.950214i \(0.600864\pi\)
\(224\) 0 0
\(225\) −2.97376 −0.198250
\(226\) 0 0
\(227\) 1.77639 0.117903 0.0589515 0.998261i \(-0.481224\pi\)
0.0589515 + 0.998261i \(0.481224\pi\)
\(228\) 0 0
\(229\) −12.8216 −0.847272 −0.423636 0.905833i \(-0.639246\pi\)
−0.423636 + 0.905833i \(0.639246\pi\)
\(230\) 0 0
\(231\) −1.64697 −0.108363
\(232\) 0 0
\(233\) −16.8823 −1.10599 −0.552997 0.833183i \(-0.686516\pi\)
−0.552997 + 0.833183i \(0.686516\pi\)
\(234\) 0 0
\(235\) 9.81442 0.640222
\(236\) 0 0
\(237\) −2.17289 −0.141144
\(238\) 0 0
\(239\) 20.5027 1.32621 0.663106 0.748526i \(-0.269238\pi\)
0.663106 + 0.748526i \(0.269238\pi\)
\(240\) 0 0
\(241\) 11.0766 0.713504 0.356752 0.934199i \(-0.383884\pi\)
0.356752 + 0.934199i \(0.383884\pi\)
\(242\) 0 0
\(243\) −4.32306 −0.277324
\(244\) 0 0
\(245\) 3.39868 0.217134
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0.878548 0.0556757
\(250\) 0 0
\(251\) −1.61833 −0.102148 −0.0510740 0.998695i \(-0.516264\pi\)
−0.0510740 + 0.998695i \(0.516264\pi\)
\(252\) 0 0
\(253\) 16.8748 1.06091
\(254\) 0 0
\(255\) 1.24964 0.0782554
\(256\) 0 0
\(257\) 13.6190 0.849532 0.424766 0.905303i \(-0.360356\pi\)
0.424766 + 0.905303i \(0.360356\pi\)
\(258\) 0 0
\(259\) −20.6200 −1.28127
\(260\) 0 0
\(261\) 10.5345 0.652071
\(262\) 0 0
\(263\) 11.1385 0.686828 0.343414 0.939184i \(-0.388417\pi\)
0.343414 + 0.939184i \(0.388417\pi\)
\(264\) 0 0
\(265\) −8.87818 −0.545382
\(266\) 0 0
\(267\) −0.237743 −0.0145496
\(268\) 0 0
\(269\) 18.2455 1.11245 0.556223 0.831033i \(-0.312250\pi\)
0.556223 + 0.831033i \(0.312250\pi\)
\(270\) 0 0
\(271\) 17.2410 1.04732 0.523658 0.851929i \(-0.324567\pi\)
0.523658 + 0.851929i \(0.324567\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −5.35728 −0.323056
\(276\) 0 0
\(277\) −16.7759 −1.00797 −0.503983 0.863713i \(-0.668133\pi\)
−0.503983 + 0.863713i \(0.668133\pi\)
\(278\) 0 0
\(279\) 17.8849 1.07074
\(280\) 0 0
\(281\) 3.71383 0.221549 0.110774 0.993846i \(-0.464667\pi\)
0.110774 + 0.993846i \(0.464667\pi\)
\(282\) 0 0
\(283\) 29.2742 1.74017 0.870086 0.492900i \(-0.164063\pi\)
0.870086 + 0.492900i \(0.164063\pi\)
\(284\) 0 0
\(285\) −0.0897018 −0.00531348
\(286\) 0 0
\(287\) 16.6047 0.980143
\(288\) 0 0
\(289\) 42.5039 2.50023
\(290\) 0 0
\(291\) −0.921845 −0.0540395
\(292\) 0 0
\(293\) −7.58006 −0.442832 −0.221416 0.975179i \(-0.571068\pi\)
−0.221416 + 0.975179i \(0.571068\pi\)
\(294\) 0 0
\(295\) −13.4174 −0.781194
\(296\) 0 0
\(297\) −5.18446 −0.300833
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 6.17133 0.355710
\(302\) 0 0
\(303\) −1.10164 −0.0632875
\(304\) 0 0
\(305\) 0.551418 0.0315741
\(306\) 0 0
\(307\) 2.94812 0.168258 0.0841292 0.996455i \(-0.473189\pi\)
0.0841292 + 0.996455i \(0.473189\pi\)
\(308\) 0 0
\(309\) −2.09110 −0.118958
\(310\) 0 0
\(311\) −5.64858 −0.320302 −0.160151 0.987093i \(-0.551198\pi\)
−0.160151 + 0.987093i \(0.551198\pi\)
\(312\) 0 0
\(313\) 16.4132 0.927726 0.463863 0.885907i \(-0.346463\pi\)
0.463863 + 0.885907i \(0.346463\pi\)
\(314\) 0 0
\(315\) −5.64334 −0.317966
\(316\) 0 0
\(317\) −25.3498 −1.42378 −0.711892 0.702289i \(-0.752162\pi\)
−0.711892 + 0.702289i \(0.752162\pi\)
\(318\) 0 0
\(319\) 18.9782 1.06257
\(320\) 0 0
\(321\) 0.686822 0.0383347
\(322\) 0 0
\(323\) −4.27132 −0.237663
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 1.13413 0.0627178
\(328\) 0 0
\(329\) 18.6250 1.02683
\(330\) 0 0
\(331\) −16.8750 −0.927534 −0.463767 0.885957i \(-0.653503\pi\)
−0.463767 + 0.885957i \(0.653503\pi\)
\(332\) 0 0
\(333\) −32.3120 −1.77069
\(334\) 0 0
\(335\) 4.46051 0.243704
\(336\) 0 0
\(337\) 33.2141 1.80929 0.904643 0.426170i \(-0.140138\pi\)
0.904643 + 0.426170i \(0.140138\pi\)
\(338\) 0 0
\(339\) −0.371261 −0.0201642
\(340\) 0 0
\(341\) 32.2199 1.74481
\(342\) 0 0
\(343\) 19.7337 1.06552
\(344\) 0 0
\(345\) −0.510276 −0.0274724
\(346\) 0 0
\(347\) −32.1558 −1.72621 −0.863107 0.505021i \(-0.831485\pi\)
−0.863107 + 0.505021i \(0.831485\pi\)
\(348\) 0 0
\(349\) 2.18315 0.116861 0.0584307 0.998291i \(-0.481390\pi\)
0.0584307 + 0.998291i \(0.481390\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −10.8132 −0.575529 −0.287764 0.957701i \(-0.592912\pi\)
−0.287764 + 0.957701i \(0.592912\pi\)
\(354\) 0 0
\(355\) −8.17861 −0.434076
\(356\) 0 0
\(357\) 2.37145 0.125511
\(358\) 0 0
\(359\) 20.4897 1.08140 0.540702 0.841214i \(-0.318159\pi\)
0.540702 + 0.841214i \(0.318159\pi\)
\(360\) 0 0
\(361\) −18.6934 −0.983863
\(362\) 0 0
\(363\) −2.86746 −0.150503
\(364\) 0 0
\(365\) −12.6129 −0.660188
\(366\) 0 0
\(367\) −32.5527 −1.69924 −0.849619 0.527398i \(-0.823168\pi\)
−0.849619 + 0.527398i \(0.823168\pi\)
\(368\) 0 0
\(369\) 26.0199 1.35454
\(370\) 0 0
\(371\) −16.8482 −0.874717
\(372\) 0 0
\(373\) 18.8558 0.976317 0.488159 0.872755i \(-0.337669\pi\)
0.488159 + 0.872755i \(0.337669\pi\)
\(374\) 0 0
\(375\) 0.161999 0.00836558
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 13.3031 0.683332 0.341666 0.939821i \(-0.389009\pi\)
0.341666 + 0.939821i \(0.389009\pi\)
\(380\) 0 0
\(381\) 0.0853250 0.00437133
\(382\) 0 0
\(383\) −28.3902 −1.45067 −0.725336 0.688395i \(-0.758315\pi\)
−0.725336 + 0.688395i \(0.758315\pi\)
\(384\) 0 0
\(385\) −10.1666 −0.518137
\(386\) 0 0
\(387\) 9.67061 0.491585
\(388\) 0 0
\(389\) −7.38713 −0.374543 −0.187271 0.982308i \(-0.559964\pi\)
−0.187271 + 0.982308i \(0.559964\pi\)
\(390\) 0 0
\(391\) −24.2978 −1.22879
\(392\) 0 0
\(393\) −2.89565 −0.146066
\(394\) 0 0
\(395\) −13.4130 −0.674881
\(396\) 0 0
\(397\) −16.1613 −0.811114 −0.405557 0.914070i \(-0.632922\pi\)
−0.405557 + 0.914070i \(0.632922\pi\)
\(398\) 0 0
\(399\) −0.170228 −0.00852208
\(400\) 0 0
\(401\) 8.05887 0.402441 0.201220 0.979546i \(-0.435509\pi\)
0.201220 + 0.979546i \(0.435509\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) −8.76450 −0.435511
\(406\) 0 0
\(407\) −58.2107 −2.88540
\(408\) 0 0
\(409\) −24.9429 −1.23335 −0.616674 0.787219i \(-0.711520\pi\)
−0.616674 + 0.787219i \(0.711520\pi\)
\(410\) 0 0
\(411\) 1.39147 0.0686363
\(412\) 0 0
\(413\) −25.4625 −1.25293
\(414\) 0 0
\(415\) 5.42318 0.266213
\(416\) 0 0
\(417\) −0.434568 −0.0212809
\(418\) 0 0
\(419\) −0.758173 −0.0370392 −0.0185196 0.999828i \(-0.505895\pi\)
−0.0185196 + 0.999828i \(0.505895\pi\)
\(420\) 0 0
\(421\) −1.20278 −0.0586199 −0.0293099 0.999570i \(-0.509331\pi\)
−0.0293099 + 0.999570i \(0.509331\pi\)
\(422\) 0 0
\(423\) 29.1857 1.41906
\(424\) 0 0
\(425\) 7.71387 0.374178
\(426\) 0 0
\(427\) 1.04643 0.0506404
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.55978 0.171469 0.0857344 0.996318i \(-0.472676\pi\)
0.0857344 + 0.996318i \(0.472676\pi\)
\(432\) 0 0
\(433\) 37.2920 1.79214 0.896070 0.443913i \(-0.146410\pi\)
0.896070 + 0.443913i \(0.146410\pi\)
\(434\) 0 0
\(435\) −0.573881 −0.0275155
\(436\) 0 0
\(437\) 1.74415 0.0834339
\(438\) 0 0
\(439\) −13.0813 −0.624336 −0.312168 0.950027i \(-0.601055\pi\)
−0.312168 + 0.950027i \(0.601055\pi\)
\(440\) 0 0
\(441\) 10.1069 0.481279
\(442\) 0 0
\(443\) −22.1758 −1.05360 −0.526802 0.849988i \(-0.676609\pi\)
−0.526802 + 0.849988i \(0.676609\pi\)
\(444\) 0 0
\(445\) −1.46756 −0.0695689
\(446\) 0 0
\(447\) −0.683914 −0.0323480
\(448\) 0 0
\(449\) 3.92762 0.185356 0.0926778 0.995696i \(-0.470457\pi\)
0.0926778 + 0.995696i \(0.470457\pi\)
\(450\) 0 0
\(451\) 46.8753 2.20727
\(452\) 0 0
\(453\) −1.17613 −0.0552596
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 29.1786 1.36492 0.682458 0.730925i \(-0.260911\pi\)
0.682458 + 0.730925i \(0.260911\pi\)
\(458\) 0 0
\(459\) 7.46503 0.348438
\(460\) 0 0
\(461\) 13.8570 0.645384 0.322692 0.946504i \(-0.395412\pi\)
0.322692 + 0.946504i \(0.395412\pi\)
\(462\) 0 0
\(463\) 28.0020 1.30136 0.650682 0.759351i \(-0.274483\pi\)
0.650682 + 0.759351i \(0.274483\pi\)
\(464\) 0 0
\(465\) −0.974297 −0.0451820
\(466\) 0 0
\(467\) 7.17194 0.331878 0.165939 0.986136i \(-0.446935\pi\)
0.165939 + 0.986136i \(0.446935\pi\)
\(468\) 0 0
\(469\) 8.46477 0.390867
\(470\) 0 0
\(471\) 1.74081 0.0802122
\(472\) 0 0
\(473\) 17.4218 0.801056
\(474\) 0 0
\(475\) −0.553719 −0.0254064
\(476\) 0 0
\(477\) −26.4015 −1.20884
\(478\) 0 0
\(479\) −15.4839 −0.707478 −0.353739 0.935344i \(-0.615090\pi\)
−0.353739 + 0.935344i \(0.615090\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −0.968358 −0.0440618
\(484\) 0 0
\(485\) −5.69045 −0.258390
\(486\) 0 0
\(487\) −34.4727 −1.56211 −0.781054 0.624464i \(-0.785317\pi\)
−0.781054 + 0.624464i \(0.785317\pi\)
\(488\) 0 0
\(489\) −1.41869 −0.0641555
\(490\) 0 0
\(491\) −31.8837 −1.43889 −0.719446 0.694548i \(-0.755604\pi\)
−0.719446 + 0.694548i \(0.755604\pi\)
\(492\) 0 0
\(493\) −27.3264 −1.23072
\(494\) 0 0
\(495\) −15.9313 −0.716057
\(496\) 0 0
\(497\) −15.5207 −0.696197
\(498\) 0 0
\(499\) 4.94343 0.221298 0.110649 0.993860i \(-0.464707\pi\)
0.110649 + 0.993860i \(0.464707\pi\)
\(500\) 0 0
\(501\) −0.534061 −0.0238601
\(502\) 0 0
\(503\) −30.1426 −1.34399 −0.671996 0.740555i \(-0.734563\pi\)
−0.671996 + 0.740555i \(0.734563\pi\)
\(504\) 0 0
\(505\) −6.80029 −0.302609
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 28.3768 1.25778 0.628889 0.777495i \(-0.283510\pi\)
0.628889 + 0.777495i \(0.283510\pi\)
\(510\) 0 0
\(511\) −23.9356 −1.05885
\(512\) 0 0
\(513\) −0.535857 −0.0236587
\(514\) 0 0
\(515\) −12.9081 −0.568799
\(516\) 0 0
\(517\) 52.5787 2.31241
\(518\) 0 0
\(519\) −3.34717 −0.146924
\(520\) 0 0
\(521\) −24.8552 −1.08893 −0.544463 0.838785i \(-0.683267\pi\)
−0.544463 + 0.838785i \(0.683267\pi\)
\(522\) 0 0
\(523\) 3.95417 0.172904 0.0864520 0.996256i \(-0.472447\pi\)
0.0864520 + 0.996256i \(0.472447\pi\)
\(524\) 0 0
\(525\) 0.307427 0.0134172
\(526\) 0 0
\(527\) −46.3930 −2.02091
\(528\) 0 0
\(529\) −13.0783 −0.568620
\(530\) 0 0
\(531\) −39.9002 −1.73152
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 4.23968 0.183297
\(536\) 0 0
\(537\) 3.17066 0.136824
\(538\) 0 0
\(539\) 18.2077 0.784262
\(540\) 0 0
\(541\) −11.8032 −0.507461 −0.253731 0.967275i \(-0.581658\pi\)
−0.253731 + 0.967275i \(0.581658\pi\)
\(542\) 0 0
\(543\) −1.74438 −0.0748585
\(544\) 0 0
\(545\) 7.00088 0.299885
\(546\) 0 0
\(547\) −22.2805 −0.952644 −0.476322 0.879271i \(-0.658030\pi\)
−0.476322 + 0.879271i \(0.658030\pi\)
\(548\) 0 0
\(549\) 1.63978 0.0699842
\(550\) 0 0
\(551\) 1.96155 0.0835649
\(552\) 0 0
\(553\) −25.4540 −1.08241
\(554\) 0 0
\(555\) 1.76023 0.0747177
\(556\) 0 0
\(557\) 34.7144 1.47090 0.735448 0.677581i \(-0.236972\pi\)
0.735448 + 0.677581i \(0.236972\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 6.69467 0.282649
\(562\) 0 0
\(563\) −20.0781 −0.846191 −0.423095 0.906085i \(-0.639056\pi\)
−0.423095 + 0.906085i \(0.639056\pi\)
\(564\) 0 0
\(565\) −2.29176 −0.0964149
\(566\) 0 0
\(567\) −16.6325 −0.698499
\(568\) 0 0
\(569\) −11.2353 −0.471010 −0.235505 0.971873i \(-0.575674\pi\)
−0.235505 + 0.971873i \(0.575674\pi\)
\(570\) 0 0
\(571\) −25.7673 −1.07833 −0.539164 0.842201i \(-0.681260\pi\)
−0.539164 + 0.842201i \(0.681260\pi\)
\(572\) 0 0
\(573\) 2.16424 0.0904124
\(574\) 0 0
\(575\) −3.14988 −0.131359
\(576\) 0 0
\(577\) −1.07927 −0.0449307 −0.0224654 0.999748i \(-0.507152\pi\)
−0.0224654 + 0.999748i \(0.507152\pi\)
\(578\) 0 0
\(579\) 0.599014 0.0248942
\(580\) 0 0
\(581\) 10.2916 0.426969
\(582\) 0 0
\(583\) −47.5629 −1.96985
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 29.9803 1.23742 0.618710 0.785620i \(-0.287656\pi\)
0.618710 + 0.785620i \(0.287656\pi\)
\(588\) 0 0
\(589\) 3.33019 0.137218
\(590\) 0 0
\(591\) 2.84305 0.116947
\(592\) 0 0
\(593\) −7.87304 −0.323307 −0.161653 0.986848i \(-0.551683\pi\)
−0.161653 + 0.986848i \(0.551683\pi\)
\(594\) 0 0
\(595\) 14.6387 0.600129
\(596\) 0 0
\(597\) −3.11962 −0.127677
\(598\) 0 0
\(599\) 19.7409 0.806590 0.403295 0.915070i \(-0.367865\pi\)
0.403295 + 0.915070i \(0.367865\pi\)
\(600\) 0 0
\(601\) −3.33925 −0.136211 −0.0681054 0.997678i \(-0.521695\pi\)
−0.0681054 + 0.997678i \(0.521695\pi\)
\(602\) 0 0
\(603\) 13.2645 0.540171
\(604\) 0 0
\(605\) −17.7005 −0.719628
\(606\) 0 0
\(607\) 22.2968 0.904998 0.452499 0.891765i \(-0.350533\pi\)
0.452499 + 0.891765i \(0.350533\pi\)
\(608\) 0 0
\(609\) −1.08906 −0.0441310
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 21.6710 0.875285 0.437643 0.899149i \(-0.355814\pi\)
0.437643 + 0.899149i \(0.355814\pi\)
\(614\) 0 0
\(615\) −1.41746 −0.0571576
\(616\) 0 0
\(617\) 29.1369 1.17301 0.586504 0.809946i \(-0.300504\pi\)
0.586504 + 0.809946i \(0.300504\pi\)
\(618\) 0 0
\(619\) 33.1986 1.33437 0.667183 0.744894i \(-0.267500\pi\)
0.667183 + 0.744894i \(0.267500\pi\)
\(620\) 0 0
\(621\) −3.04827 −0.122323
\(622\) 0 0
\(623\) −2.78500 −0.111579
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −0.480558 −0.0191916
\(628\) 0 0
\(629\) 83.8168 3.34199
\(630\) 0 0
\(631\) 46.5904 1.85473 0.927366 0.374155i \(-0.122067\pi\)
0.927366 + 0.374155i \(0.122067\pi\)
\(632\) 0 0
\(633\) 4.22696 0.168006
\(634\) 0 0
\(635\) 0.526702 0.0209015
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −24.3212 −0.962132
\(640\) 0 0
\(641\) −30.9608 −1.22288 −0.611438 0.791292i \(-0.709409\pi\)
−0.611438 + 0.791292i \(0.709409\pi\)
\(642\) 0 0
\(643\) 24.0391 0.948010 0.474005 0.880522i \(-0.342808\pi\)
0.474005 + 0.880522i \(0.342808\pi\)
\(644\) 0 0
\(645\) −0.526817 −0.0207434
\(646\) 0 0
\(647\) 41.9606 1.64964 0.824822 0.565393i \(-0.191275\pi\)
0.824822 + 0.565393i \(0.191275\pi\)
\(648\) 0 0
\(649\) −71.8811 −2.82158
\(650\) 0 0
\(651\) −1.84894 −0.0724656
\(652\) 0 0
\(653\) −1.92478 −0.0753223 −0.0376612 0.999291i \(-0.511991\pi\)
−0.0376612 + 0.999291i \(0.511991\pi\)
\(654\) 0 0
\(655\) −17.8745 −0.698416
\(656\) 0 0
\(657\) −37.5076 −1.46331
\(658\) 0 0
\(659\) 2.78444 0.108466 0.0542332 0.998528i \(-0.482729\pi\)
0.0542332 + 0.998528i \(0.482729\pi\)
\(660\) 0 0
\(661\) 12.5553 0.488346 0.244173 0.969732i \(-0.421484\pi\)
0.244173 + 0.969732i \(0.421484\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.05080 −0.0407483
\(666\) 0 0
\(667\) 11.1584 0.432057
\(668\) 0 0
\(669\) 1.50760 0.0582874
\(670\) 0 0
\(671\) 2.95410 0.114042
\(672\) 0 0
\(673\) 46.3999 1.78859 0.894293 0.447481i \(-0.147679\pi\)
0.894293 + 0.447481i \(0.147679\pi\)
\(674\) 0 0
\(675\) 0.967741 0.0372484
\(676\) 0 0
\(677\) −45.7333 −1.75767 −0.878837 0.477123i \(-0.841680\pi\)
−0.878837 + 0.477123i \(0.841680\pi\)
\(678\) 0 0
\(679\) −10.7988 −0.414421
\(680\) 0 0
\(681\) −0.287773 −0.0110275
\(682\) 0 0
\(683\) 40.5600 1.55198 0.775992 0.630743i \(-0.217250\pi\)
0.775992 + 0.630743i \(0.217250\pi\)
\(684\) 0 0
\(685\) 8.58940 0.328184
\(686\) 0 0
\(687\) 2.07708 0.0792454
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) −17.9242 −0.681868 −0.340934 0.940087i \(-0.610743\pi\)
−0.340934 + 0.940087i \(0.610743\pi\)
\(692\) 0 0
\(693\) −30.2330 −1.14846
\(694\) 0 0
\(695\) −2.68254 −0.101755
\(696\) 0 0
\(697\) −67.4951 −2.55656
\(698\) 0 0
\(699\) 2.73491 0.103444
\(700\) 0 0
\(701\) −19.5457 −0.738230 −0.369115 0.929384i \(-0.620339\pi\)
−0.369115 + 0.929384i \(0.620339\pi\)
\(702\) 0 0
\(703\) −6.01656 −0.226919
\(704\) 0 0
\(705\) −1.58992 −0.0598800
\(706\) 0 0
\(707\) −12.9050 −0.485343
\(708\) 0 0
\(709\) 46.6490 1.75194 0.875970 0.482366i \(-0.160222\pi\)
0.875970 + 0.482366i \(0.160222\pi\)
\(710\) 0 0
\(711\) −39.8870 −1.49588
\(712\) 0 0
\(713\) 18.9441 0.709462
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −3.32142 −0.124041
\(718\) 0 0
\(719\) −40.4882 −1.50995 −0.754977 0.655751i \(-0.772352\pi\)
−0.754977 + 0.655751i \(0.772352\pi\)
\(720\) 0 0
\(721\) −24.4959 −0.912274
\(722\) 0 0
\(723\) −1.79439 −0.0667341
\(724\) 0 0
\(725\) −3.54250 −0.131565
\(726\) 0 0
\(727\) 22.9582 0.851471 0.425736 0.904848i \(-0.360015\pi\)
0.425736 + 0.904848i \(0.360015\pi\)
\(728\) 0 0
\(729\) −25.5932 −0.947895
\(730\) 0 0
\(731\) −25.0854 −0.927817
\(732\) 0 0
\(733\) 21.3753 0.789513 0.394757 0.918786i \(-0.370829\pi\)
0.394757 + 0.918786i \(0.370829\pi\)
\(734\) 0 0
\(735\) −0.550583 −0.0203085
\(736\) 0 0
\(737\) 23.8962 0.880229
\(738\) 0 0
\(739\) −35.1671 −1.29364 −0.646821 0.762642i \(-0.723902\pi\)
−0.646821 + 0.762642i \(0.723902\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19.9324 0.731249 0.365625 0.930762i \(-0.380855\pi\)
0.365625 + 0.930762i \(0.380855\pi\)
\(744\) 0 0
\(745\) −4.22172 −0.154672
\(746\) 0 0
\(747\) 16.1272 0.590064
\(748\) 0 0
\(749\) 8.04569 0.293983
\(750\) 0 0
\(751\) 33.7277 1.23074 0.615370 0.788238i \(-0.289006\pi\)
0.615370 + 0.788238i \(0.289006\pi\)
\(752\) 0 0
\(753\) 0.262167 0.00955390
\(754\) 0 0
\(755\) −7.26015 −0.264224
\(756\) 0 0
\(757\) 23.3007 0.846877 0.423439 0.905925i \(-0.360823\pi\)
0.423439 + 0.905925i \(0.360823\pi\)
\(758\) 0 0
\(759\) −2.73370 −0.0992269
\(760\) 0 0
\(761\) 7.72440 0.280009 0.140005 0.990151i \(-0.455288\pi\)
0.140005 + 0.990151i \(0.455288\pi\)
\(762\) 0 0
\(763\) 13.2857 0.480973
\(764\) 0 0
\(765\) 22.9392 0.829368
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 6.44221 0.232312 0.116156 0.993231i \(-0.462943\pi\)
0.116156 + 0.993231i \(0.462943\pi\)
\(770\) 0 0
\(771\) −2.20627 −0.0794568
\(772\) 0 0
\(773\) −39.1922 −1.40964 −0.704822 0.709384i \(-0.748973\pi\)
−0.704822 + 0.709384i \(0.748973\pi\)
\(774\) 0 0
\(775\) −6.01423 −0.216037
\(776\) 0 0
\(777\) 3.34042 0.119837
\(778\) 0 0
\(779\) 4.84495 0.173588
\(780\) 0 0
\(781\) −43.8152 −1.56783
\(782\) 0 0
\(783\) −3.42822 −0.122515
\(784\) 0 0
\(785\) 10.7458 0.383535
\(786\) 0 0
\(787\) −27.0865 −0.965529 −0.482765 0.875750i \(-0.660367\pi\)
−0.482765 + 0.875750i \(0.660367\pi\)
\(788\) 0 0
\(789\) −1.80442 −0.0642390
\(790\) 0 0
\(791\) −4.34909 −0.154636
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.43825 0.0510096
\(796\) 0 0
\(797\) 3.49750 0.123888 0.0619440 0.998080i \(-0.480270\pi\)
0.0619440 + 0.998080i \(0.480270\pi\)
\(798\) 0 0
\(799\) −75.7072 −2.67833
\(800\) 0 0
\(801\) −4.36416 −0.154200
\(802\) 0 0
\(803\) −67.5708 −2.38452
\(804\) 0 0
\(805\) −5.97757 −0.210682
\(806\) 0 0
\(807\) −2.95574 −0.104047
\(808\) 0 0
\(809\) 12.6258 0.443898 0.221949 0.975058i \(-0.428758\pi\)
0.221949 + 0.975058i \(0.428758\pi\)
\(810\) 0 0
\(811\) 40.7350 1.43040 0.715200 0.698920i \(-0.246336\pi\)
0.715200 + 0.698920i \(0.246336\pi\)
\(812\) 0 0
\(813\) −2.79302 −0.0979554
\(814\) 0 0
\(815\) −8.75744 −0.306760
\(816\) 0 0
\(817\) 1.80069 0.0629980
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26.0805 0.910214 0.455107 0.890437i \(-0.349601\pi\)
0.455107 + 0.890437i \(0.349601\pi\)
\(822\) 0 0
\(823\) −4.24240 −0.147881 −0.0739404 0.997263i \(-0.523557\pi\)
−0.0739404 + 0.997263i \(0.523557\pi\)
\(824\) 0 0
\(825\) 0.867873 0.0302155
\(826\) 0 0
\(827\) −41.1905 −1.43234 −0.716168 0.697928i \(-0.754105\pi\)
−0.716168 + 0.697928i \(0.754105\pi\)
\(828\) 0 0
\(829\) −26.2757 −0.912591 −0.456296 0.889828i \(-0.650824\pi\)
−0.456296 + 0.889828i \(0.650824\pi\)
\(830\) 0 0
\(831\) 2.71768 0.0942752
\(832\) 0 0
\(833\) −26.2170 −0.908366
\(834\) 0 0
\(835\) −3.29670 −0.114087
\(836\) 0 0
\(837\) −5.82022 −0.201176
\(838\) 0 0
\(839\) 29.6372 1.02319 0.511594 0.859227i \(-0.329055\pi\)
0.511594 + 0.859227i \(0.329055\pi\)
\(840\) 0 0
\(841\) −16.4507 −0.567265
\(842\) 0 0
\(843\) −0.601637 −0.0207215
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −33.5905 −1.15418
\(848\) 0 0
\(849\) −4.74239 −0.162758
\(850\) 0 0
\(851\) −34.2257 −1.17324
\(852\) 0 0
\(853\) 37.5743 1.28652 0.643259 0.765648i \(-0.277582\pi\)
0.643259 + 0.765648i \(0.277582\pi\)
\(854\) 0 0
\(855\) −1.64663 −0.0563134
\(856\) 0 0
\(857\) 41.4208 1.41491 0.707453 0.706760i \(-0.249844\pi\)
0.707453 + 0.706760i \(0.249844\pi\)
\(858\) 0 0
\(859\) −6.17985 −0.210854 −0.105427 0.994427i \(-0.533621\pi\)
−0.105427 + 0.994427i \(0.533621\pi\)
\(860\) 0 0
\(861\) −2.68994 −0.0916728
\(862\) 0 0
\(863\) 18.0410 0.614124 0.307062 0.951690i \(-0.400654\pi\)
0.307062 + 0.951690i \(0.400654\pi\)
\(864\) 0 0
\(865\) −20.6617 −0.702519
\(866\) 0 0
\(867\) −6.88557 −0.233846
\(868\) 0 0
\(869\) −71.8572 −2.43759
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −16.9220 −0.572723
\(874\) 0 0
\(875\) 1.89771 0.0641544
\(876\) 0 0
\(877\) −15.3180 −0.517251 −0.258625 0.965978i \(-0.583270\pi\)
−0.258625 + 0.965978i \(0.583270\pi\)
\(878\) 0 0
\(879\) 1.22796 0.0414181
\(880\) 0 0
\(881\) 38.9448 1.31208 0.656042 0.754725i \(-0.272230\pi\)
0.656042 + 0.754725i \(0.272230\pi\)
\(882\) 0 0
\(883\) −53.4157 −1.79758 −0.898791 0.438376i \(-0.855554\pi\)
−0.898791 + 0.438376i \(0.855554\pi\)
\(884\) 0 0
\(885\) 2.17361 0.0730651
\(886\) 0 0
\(887\) 15.9682 0.536161 0.268080 0.963397i \(-0.413611\pi\)
0.268080 + 0.963397i \(0.413611\pi\)
\(888\) 0 0
\(889\) 0.999529 0.0335231
\(890\) 0 0
\(891\) −46.9539 −1.57302
\(892\) 0 0
\(893\) 5.43444 0.181856
\(894\) 0 0
\(895\) 19.5721 0.654225
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 21.3054 0.710575
\(900\) 0 0
\(901\) 68.4851 2.28157
\(902\) 0 0
\(903\) −0.999748 −0.0332695
\(904\) 0 0
\(905\) −10.7679 −0.357936
\(906\) 0 0
\(907\) 9.85604 0.327265 0.163632 0.986521i \(-0.447679\pi\)
0.163632 + 0.986521i \(0.447679\pi\)
\(908\) 0 0
\(909\) −20.2224 −0.670735
\(910\) 0 0
\(911\) 46.1345 1.52850 0.764252 0.644918i \(-0.223109\pi\)
0.764252 + 0.644918i \(0.223109\pi\)
\(912\) 0 0
\(913\) 29.0535 0.961531
\(914\) 0 0
\(915\) −0.0893290 −0.00295312
\(916\) 0 0
\(917\) −33.9208 −1.12016
\(918\) 0 0
\(919\) 15.6260 0.515455 0.257727 0.966218i \(-0.417026\pi\)
0.257727 + 0.966218i \(0.417026\pi\)
\(920\) 0 0
\(921\) −0.477592 −0.0157372
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 10.8657 0.357263
\(926\) 0 0
\(927\) −38.3855 −1.26075
\(928\) 0 0
\(929\) 18.2052 0.597294 0.298647 0.954364i \(-0.403465\pi\)
0.298647 + 0.954364i \(0.403465\pi\)
\(930\) 0 0
\(931\) 1.88192 0.0616773
\(932\) 0 0
\(933\) 0.915063 0.0299578
\(934\) 0 0
\(935\) 41.3254 1.35149
\(936\) 0 0
\(937\) −41.4735 −1.35488 −0.677440 0.735578i \(-0.736911\pi\)
−0.677440 + 0.735578i \(0.736911\pi\)
\(938\) 0 0
\(939\) −2.65891 −0.0867702
\(940\) 0 0
\(941\) 25.1745 0.820665 0.410333 0.911936i \(-0.365413\pi\)
0.410333 + 0.911936i \(0.365413\pi\)
\(942\) 0 0
\(943\) 27.5609 0.897507
\(944\) 0 0
\(945\) 1.83649 0.0597412
\(946\) 0 0
\(947\) −27.6232 −0.897634 −0.448817 0.893624i \(-0.648155\pi\)
−0.448817 + 0.893624i \(0.648155\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 4.10663 0.133167
\(952\) 0 0
\(953\) −35.7517 −1.15811 −0.579055 0.815289i \(-0.696578\pi\)
−0.579055 + 0.815289i \(0.696578\pi\)
\(954\) 0 0
\(955\) 13.3596 0.432307
\(956\) 0 0
\(957\) −3.07444 −0.0993826
\(958\) 0 0
\(959\) 16.3002 0.526362
\(960\) 0 0
\(961\) 5.17095 0.166805
\(962\) 0 0
\(963\) 12.6078 0.406280
\(964\) 0 0
\(965\) 3.69764 0.119031
\(966\) 0 0
\(967\) −47.4240 −1.52505 −0.762527 0.646957i \(-0.776041\pi\)
−0.762527 + 0.646957i \(0.776041\pi\)
\(968\) 0 0
\(969\) 0.691949 0.0222286
\(970\) 0 0
\(971\) −19.7029 −0.632295 −0.316147 0.948710i \(-0.602389\pi\)
−0.316147 + 0.948710i \(0.602389\pi\)
\(972\) 0 0
\(973\) −5.09069 −0.163200
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.0105702 0.000338172 0 0.000169086 1.00000i \(-0.499946\pi\)
0.000169086 1.00000i \(0.499946\pi\)
\(978\) 0 0
\(979\) −7.86213 −0.251275
\(980\) 0 0
\(981\) 20.8189 0.664697
\(982\) 0 0
\(983\) 17.7240 0.565306 0.282653 0.959222i \(-0.408785\pi\)
0.282653 + 0.959222i \(0.408785\pi\)
\(984\) 0 0
\(985\) 17.5498 0.559184
\(986\) 0 0
\(987\) −3.01722 −0.0960392
\(988\) 0 0
\(989\) 10.2434 0.325720
\(990\) 0 0
\(991\) 6.89901 0.219154 0.109577 0.993978i \(-0.465050\pi\)
0.109577 + 0.993978i \(0.465050\pi\)
\(992\) 0 0
\(993\) 2.73373 0.0867523
\(994\) 0 0
\(995\) −19.2570 −0.610489
\(996\) 0 0
\(997\) −4.36107 −0.138117 −0.0690583 0.997613i \(-0.521999\pi\)
−0.0690583 + 0.997613i \(0.521999\pi\)
\(998\) 0 0
\(999\) 10.5152 0.332686
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 3380.2.a.r.1.5 9
13.5 odd 4 3380.2.f.j.3041.10 18
13.8 odd 4 3380.2.f.j.3041.9 18
13.12 even 2 3380.2.a.s.1.5 yes 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3380.2.a.r.1.5 9 1.1 even 1 trivial
3380.2.a.s.1.5 yes 9 13.12 even 2
3380.2.f.j.3041.9 18 13.8 odd 4
3380.2.f.j.3041.10 18 13.5 odd 4