Properties

Label 2352.4.a.bw.1.1
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(138.772492334\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.41421\) of defining polynomial
Character \(\chi\) \(=\) 2352.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} -7.41421 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} -7.41421 q^{5} +9.00000 q^{9} -10.4853 q^{11} -2.78680 q^{13} -22.2426 q^{15} -50.4437 q^{17} +125.054 q^{19} +182.250 q^{23} -70.0294 q^{25} +27.0000 q^{27} +156.132 q^{29} +139.632 q^{31} -31.4558 q^{33} -394.558 q^{37} -8.36039 q^{39} -197.605 q^{41} -343.294 q^{43} -66.7279 q^{45} -610.004 q^{47} -151.331 q^{51} -137.529 q^{53} +77.7401 q^{55} +375.161 q^{57} +589.436 q^{59} -247.217 q^{61} +20.6619 q^{65} +395.647 q^{67} +546.749 q^{69} -285.661 q^{71} +997.457 q^{73} -210.088 q^{75} +848.264 q^{79} +81.0000 q^{81} -210.863 q^{83} +374.000 q^{85} +468.396 q^{87} +553.487 q^{89} +418.897 q^{93} -927.176 q^{95} +903.910 q^{97} -94.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 6q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 2q + 6q^{3} - 12q^{5} + 18q^{9} - 4q^{11} - 48q^{13} - 36q^{15} - 132q^{17} + 120q^{19} + 76q^{23} - 174q^{25} + 54q^{27} - 112q^{29} + 432q^{31} - 12q^{33} - 280q^{37} - 144q^{39} - 36q^{41} + 128q^{43} - 108q^{45} - 264q^{47} - 396q^{51} + 268q^{53} + 48q^{55} + 360q^{57} + 336q^{59} + 504q^{61} + 228q^{65} + 384q^{67} + 228q^{69} + 396q^{71} + 312q^{73} - 522q^{75} + 848q^{79} + 162q^{81} - 648q^{83} + 748q^{85} - 336q^{87} + 612q^{89} + 1296q^{93} - 904q^{95} + 2184q^{97} - 36q^{99} + O(q^{100}) \)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) −7.41421 −0.663147 −0.331574 0.943429i \(-0.607580\pi\)
−0.331574 + 0.943429i \(0.607580\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) −10.4853 −0.287403 −0.143701 0.989621i \(-0.545900\pi\)
−0.143701 + 0.989621i \(0.545900\pi\)
\(12\) 0 0
\(13\) −2.78680 −0.0594553 −0.0297276 0.999558i \(-0.509464\pi\)
−0.0297276 + 0.999558i \(0.509464\pi\)
\(14\) 0 0
\(15\) −22.2426 −0.382868
\(16\) 0 0
\(17\) −50.4437 −0.719670 −0.359835 0.933016i \(-0.617167\pi\)
−0.359835 + 0.933016i \(0.617167\pi\)
\(18\) 0 0
\(19\) 125.054 1.50996 0.754982 0.655746i \(-0.227646\pi\)
0.754982 + 0.655746i \(0.227646\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 182.250 1.65225 0.826124 0.563488i \(-0.190541\pi\)
0.826124 + 0.563488i \(0.190541\pi\)
\(24\) 0 0
\(25\) −70.0294 −0.560235
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 156.132 0.999758 0.499879 0.866095i \(-0.333378\pi\)
0.499879 + 0.866095i \(0.333378\pi\)
\(30\) 0 0
\(31\) 139.632 0.808991 0.404496 0.914540i \(-0.367447\pi\)
0.404496 + 0.914540i \(0.367447\pi\)
\(32\) 0 0
\(33\) −31.4558 −0.165932
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −394.558 −1.75311 −0.876554 0.481303i \(-0.840164\pi\)
−0.876554 + 0.481303i \(0.840164\pi\)
\(38\) 0 0
\(39\) −8.36039 −0.0343265
\(40\) 0 0
\(41\) −197.605 −0.752701 −0.376350 0.926477i \(-0.622821\pi\)
−0.376350 + 0.926477i \(0.622821\pi\)
\(42\) 0 0
\(43\) −343.294 −1.21748 −0.608741 0.793369i \(-0.708325\pi\)
−0.608741 + 0.793369i \(0.708325\pi\)
\(44\) 0 0
\(45\) −66.7279 −0.221049
\(46\) 0 0
\(47\) −610.004 −1.89315 −0.946577 0.322477i \(-0.895484\pi\)
−0.946577 + 0.322477i \(0.895484\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −151.331 −0.415501
\(52\) 0 0
\(53\) −137.529 −0.356435 −0.178218 0.983991i \(-0.557033\pi\)
−0.178218 + 0.983991i \(0.557033\pi\)
\(54\) 0 0
\(55\) 77.7401 0.190590
\(56\) 0 0
\(57\) 375.161 0.871778
\(58\) 0 0
\(59\) 589.436 1.30064 0.650322 0.759659i \(-0.274634\pi\)
0.650322 + 0.759659i \(0.274634\pi\)
\(60\) 0 0
\(61\) −247.217 −0.518901 −0.259450 0.965756i \(-0.583541\pi\)
−0.259450 + 0.965756i \(0.583541\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 20.6619 0.0394276
\(66\) 0 0
\(67\) 395.647 0.721432 0.360716 0.932676i \(-0.382532\pi\)
0.360716 + 0.932676i \(0.382532\pi\)
\(68\) 0 0
\(69\) 546.749 0.953926
\(70\) 0 0
\(71\) −285.661 −0.477489 −0.238745 0.971082i \(-0.576736\pi\)
−0.238745 + 0.971082i \(0.576736\pi\)
\(72\) 0 0
\(73\) 997.457 1.59923 0.799613 0.600515i \(-0.205038\pi\)
0.799613 + 0.600515i \(0.205038\pi\)
\(74\) 0 0
\(75\) −210.088 −0.323452
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 848.264 1.20807 0.604033 0.796960i \(-0.293560\pi\)
0.604033 + 0.796960i \(0.293560\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −210.863 −0.278858 −0.139429 0.990232i \(-0.544527\pi\)
−0.139429 + 0.990232i \(0.544527\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) 0 0
\(87\) 468.396 0.577211
\(88\) 0 0
\(89\) 553.487 0.659208 0.329604 0.944119i \(-0.393085\pi\)
0.329604 + 0.944119i \(0.393085\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 418.897 0.467071
\(94\) 0 0
\(95\) −927.176 −1.00133
\(96\) 0 0
\(97\) 903.910 0.946166 0.473083 0.881018i \(-0.343141\pi\)
0.473083 + 0.881018i \(0.343141\pi\)
\(98\) 0 0
\(99\) −94.3675 −0.0958009
\(100\) 0 0
\(101\) 313.611 0.308965 0.154482 0.987996i \(-0.450629\pi\)
0.154482 + 0.987996i \(0.450629\pi\)
\(102\) 0 0
\(103\) 230.975 0.220957 0.110479 0.993878i \(-0.464762\pi\)
0.110479 + 0.993878i \(0.464762\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −125.486 −0.113376 −0.0566879 0.998392i \(-0.518054\pi\)
−0.0566879 + 0.998392i \(0.518054\pi\)
\(108\) 0 0
\(109\) 745.527 0.655124 0.327562 0.944830i \(-0.393773\pi\)
0.327562 + 0.944830i \(0.393773\pi\)
\(110\) 0 0
\(111\) −1183.68 −1.01216
\(112\) 0 0
\(113\) −1043.76 −0.868929 −0.434464 0.900689i \(-0.643062\pi\)
−0.434464 + 0.900689i \(0.643062\pi\)
\(114\) 0 0
\(115\) −1351.24 −1.09568
\(116\) 0 0
\(117\) −25.0812 −0.0198184
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1221.06 −0.917400
\(122\) 0 0
\(123\) −592.815 −0.434572
\(124\) 0 0
\(125\) 1445.99 1.03467
\(126\) 0 0
\(127\) 2080.17 1.45343 0.726715 0.686939i \(-0.241046\pi\)
0.726715 + 0.686939i \(0.241046\pi\)
\(128\) 0 0
\(129\) −1029.88 −0.702914
\(130\) 0 0
\(131\) −1269.53 −0.846711 −0.423355 0.905964i \(-0.639148\pi\)
−0.423355 + 0.905964i \(0.639148\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −200.184 −0.127623
\(136\) 0 0
\(137\) 3073.19 1.91650 0.958249 0.285935i \(-0.0923043\pi\)
0.958249 + 0.285935i \(0.0923043\pi\)
\(138\) 0 0
\(139\) 1013.60 0.618504 0.309252 0.950980i \(-0.399921\pi\)
0.309252 + 0.950980i \(0.399921\pi\)
\(140\) 0 0
\(141\) −1830.01 −1.09301
\(142\) 0 0
\(143\) 29.2203 0.0170876
\(144\) 0 0
\(145\) −1157.60 −0.662987
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1231.47 0.677087 0.338544 0.940951i \(-0.390066\pi\)
0.338544 + 0.940951i \(0.390066\pi\)
\(150\) 0 0
\(151\) 2244.74 1.20976 0.604881 0.796316i \(-0.293221\pi\)
0.604881 + 0.796316i \(0.293221\pi\)
\(152\) 0 0
\(153\) −453.993 −0.239890
\(154\) 0 0
\(155\) −1035.26 −0.536481
\(156\) 0 0
\(157\) 3787.16 1.92515 0.962573 0.271021i \(-0.0873614\pi\)
0.962573 + 0.271021i \(0.0873614\pi\)
\(158\) 0 0
\(159\) −412.587 −0.205788
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2108.56 1.01322 0.506611 0.862175i \(-0.330898\pi\)
0.506611 + 0.862175i \(0.330898\pi\)
\(164\) 0 0
\(165\) 233.220 0.110037
\(166\) 0 0
\(167\) 1502.41 0.696170 0.348085 0.937463i \(-0.386832\pi\)
0.348085 + 0.937463i \(0.386832\pi\)
\(168\) 0 0
\(169\) −2189.23 −0.996465
\(170\) 0 0
\(171\) 1125.48 0.503321
\(172\) 0 0
\(173\) −471.256 −0.207104 −0.103552 0.994624i \(-0.533021\pi\)
−0.103552 + 0.994624i \(0.533021\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1768.31 0.750927
\(178\) 0 0
\(179\) −1332.49 −0.556395 −0.278198 0.960524i \(-0.589737\pi\)
−0.278198 + 0.960524i \(0.589737\pi\)
\(180\) 0 0
\(181\) 997.727 0.409726 0.204863 0.978791i \(-0.434325\pi\)
0.204863 + 0.978791i \(0.434325\pi\)
\(182\) 0 0
\(183\) −741.652 −0.299587
\(184\) 0 0
\(185\) 2925.34 1.16257
\(186\) 0 0
\(187\) 528.916 0.206835
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1226.72 −0.464725 −0.232362 0.972629i \(-0.574646\pi\)
−0.232362 + 0.972629i \(0.574646\pi\)
\(192\) 0 0
\(193\) −3479.29 −1.29764 −0.648821 0.760941i \(-0.724738\pi\)
−0.648821 + 0.760941i \(0.724738\pi\)
\(194\) 0 0
\(195\) 61.9857 0.0227635
\(196\) 0 0
\(197\) 3193.47 1.15495 0.577476 0.816408i \(-0.304038\pi\)
0.577476 + 0.816408i \(0.304038\pi\)
\(198\) 0 0
\(199\) 1065.15 0.379429 0.189715 0.981839i \(-0.439244\pi\)
0.189715 + 0.981839i \(0.439244\pi\)
\(200\) 0 0
\(201\) 1186.94 0.416519
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 1465.09 0.499152
\(206\) 0 0
\(207\) 1640.25 0.550749
\(208\) 0 0
\(209\) −1311.22 −0.433968
\(210\) 0 0
\(211\) −2057.50 −0.671298 −0.335649 0.941987i \(-0.608956\pi\)
−0.335649 + 0.941987i \(0.608956\pi\)
\(212\) 0 0
\(213\) −856.983 −0.275678
\(214\) 0 0
\(215\) 2545.25 0.807371
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 2992.37 0.923314
\(220\) 0 0
\(221\) 140.576 0.0427881
\(222\) 0 0
\(223\) 2028.27 0.609071 0.304536 0.952501i \(-0.401499\pi\)
0.304536 + 0.952501i \(0.401499\pi\)
\(224\) 0 0
\(225\) −630.265 −0.186745
\(226\) 0 0
\(227\) 2423.96 0.708739 0.354369 0.935106i \(-0.384696\pi\)
0.354369 + 0.935106i \(0.384696\pi\)
\(228\) 0 0
\(229\) 1967.17 0.567660 0.283830 0.958875i \(-0.408395\pi\)
0.283830 + 0.958875i \(0.408395\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4478.33 1.25916 0.629582 0.776934i \(-0.283226\pi\)
0.629582 + 0.776934i \(0.283226\pi\)
\(234\) 0 0
\(235\) 4522.70 1.25544
\(236\) 0 0
\(237\) 2544.79 0.697477
\(238\) 0 0
\(239\) −6116.92 −1.65553 −0.827763 0.561078i \(-0.810387\pi\)
−0.827763 + 0.561078i \(0.810387\pi\)
\(240\) 0 0
\(241\) −6228.38 −1.66475 −0.832376 0.554211i \(-0.813020\pi\)
−0.832376 + 0.554211i \(0.813020\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −348.500 −0.0897753
\(248\) 0 0
\(249\) −632.589 −0.160999
\(250\) 0 0
\(251\) 5904.42 1.48479 0.742397 0.669960i \(-0.233689\pi\)
0.742397 + 0.669960i \(0.233689\pi\)
\(252\) 0 0
\(253\) −1910.94 −0.474861
\(254\) 0 0
\(255\) 1122.00 0.275539
\(256\) 0 0
\(257\) 408.223 0.0990827 0.0495414 0.998772i \(-0.484224\pi\)
0.0495414 + 0.998772i \(0.484224\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 1405.19 0.333253
\(262\) 0 0
\(263\) 4626.01 1.08461 0.542304 0.840182i \(-0.317552\pi\)
0.542304 + 0.840182i \(0.317552\pi\)
\(264\) 0 0
\(265\) 1019.67 0.236369
\(266\) 0 0
\(267\) 1660.46 0.380594
\(268\) 0 0
\(269\) 871.293 0.197486 0.0987429 0.995113i \(-0.468518\pi\)
0.0987429 + 0.995113i \(0.468518\pi\)
\(270\) 0 0
\(271\) 6472.35 1.45080 0.725401 0.688327i \(-0.241655\pi\)
0.725401 + 0.688327i \(0.241655\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 734.278 0.161013
\(276\) 0 0
\(277\) 4711.88 1.02206 0.511028 0.859564i \(-0.329265\pi\)
0.511028 + 0.859564i \(0.329265\pi\)
\(278\) 0 0
\(279\) 1256.69 0.269664
\(280\) 0 0
\(281\) −7165.66 −1.52124 −0.760618 0.649200i \(-0.775104\pi\)
−0.760618 + 0.649200i \(0.775104\pi\)
\(282\) 0 0
\(283\) 6347.00 1.33318 0.666590 0.745424i \(-0.267753\pi\)
0.666590 + 0.745424i \(0.267753\pi\)
\(284\) 0 0
\(285\) −2781.53 −0.578117
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −2368.44 −0.482076
\(290\) 0 0
\(291\) 2711.73 0.546269
\(292\) 0 0
\(293\) −9233.78 −1.84110 −0.920552 0.390621i \(-0.872260\pi\)
−0.920552 + 0.390621i \(0.872260\pi\)
\(294\) 0 0
\(295\) −4370.20 −0.862519
\(296\) 0 0
\(297\) −283.103 −0.0553107
\(298\) 0 0
\(299\) −507.893 −0.0982348
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 940.833 0.178381
\(304\) 0 0
\(305\) 1832.92 0.344108
\(306\) 0 0
\(307\) 6786.53 1.26165 0.630827 0.775923i \(-0.282716\pi\)
0.630827 + 0.775923i \(0.282716\pi\)
\(308\) 0 0
\(309\) 692.924 0.127570
\(310\) 0 0
\(311\) 5136.77 0.936590 0.468295 0.883572i \(-0.344868\pi\)
0.468295 + 0.883572i \(0.344868\pi\)
\(312\) 0 0
\(313\) 3763.56 0.679645 0.339822 0.940490i \(-0.389633\pi\)
0.339822 + 0.940490i \(0.389633\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1034.95 −0.183370 −0.0916851 0.995788i \(-0.529225\pi\)
−0.0916851 + 0.995788i \(0.529225\pi\)
\(318\) 0 0
\(319\) −1637.09 −0.287333
\(320\) 0 0
\(321\) −376.458 −0.0654575
\(322\) 0 0
\(323\) −6308.17 −1.08668
\(324\) 0 0
\(325\) 195.158 0.0333089
\(326\) 0 0
\(327\) 2236.58 0.378236
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −8800.06 −1.46131 −0.730657 0.682744i \(-0.760786\pi\)
−0.730657 + 0.682744i \(0.760786\pi\)
\(332\) 0 0
\(333\) −3551.03 −0.584369
\(334\) 0 0
\(335\) −2933.41 −0.478416
\(336\) 0 0
\(337\) −5859.78 −0.947189 −0.473595 0.880743i \(-0.657044\pi\)
−0.473595 + 0.880743i \(0.657044\pi\)
\(338\) 0 0
\(339\) −3131.29 −0.501676
\(340\) 0 0
\(341\) −1464.09 −0.232506
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −4053.72 −0.632593
\(346\) 0 0
\(347\) −7938.54 −1.22814 −0.614068 0.789253i \(-0.710468\pi\)
−0.614068 + 0.789253i \(0.710468\pi\)
\(348\) 0 0
\(349\) 9927.75 1.52269 0.761347 0.648344i \(-0.224538\pi\)
0.761347 + 0.648344i \(0.224538\pi\)
\(350\) 0 0
\(351\) −75.2435 −0.0114422
\(352\) 0 0
\(353\) 10103.0 1.52332 0.761658 0.647979i \(-0.224386\pi\)
0.761658 + 0.647979i \(0.224386\pi\)
\(354\) 0 0
\(355\) 2117.95 0.316646
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4825.27 0.709382 0.354691 0.934984i \(-0.384586\pi\)
0.354691 + 0.934984i \(0.384586\pi\)
\(360\) 0 0
\(361\) 8779.46 1.27999
\(362\) 0 0
\(363\) −3663.18 −0.529661
\(364\) 0 0
\(365\) −7395.36 −1.06052
\(366\) 0 0
\(367\) 6935.30 0.986430 0.493215 0.869907i \(-0.335822\pi\)
0.493215 + 0.869907i \(0.335822\pi\)
\(368\) 0 0
\(369\) −1778.45 −0.250900
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 14093.1 1.95634 0.978168 0.207816i \(-0.0666355\pi\)
0.978168 + 0.207816i \(0.0666355\pi\)
\(374\) 0 0
\(375\) 4337.97 0.597365
\(376\) 0 0
\(377\) −435.108 −0.0594409
\(378\) 0 0
\(379\) −5354.17 −0.725661 −0.362830 0.931855i \(-0.618190\pi\)
−0.362830 + 0.931855i \(0.618190\pi\)
\(380\) 0 0
\(381\) 6240.52 0.839138
\(382\) 0 0
\(383\) −8970.47 −1.19679 −0.598394 0.801202i \(-0.704194\pi\)
−0.598394 + 0.801202i \(0.704194\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3089.64 −0.405828
\(388\) 0 0
\(389\) −3702.58 −0.482592 −0.241296 0.970452i \(-0.577572\pi\)
−0.241296 + 0.970452i \(0.577572\pi\)
\(390\) 0 0
\(391\) −9193.34 −1.18907
\(392\) 0 0
\(393\) −3808.58 −0.488849
\(394\) 0 0
\(395\) −6289.21 −0.801125
\(396\) 0 0
\(397\) 2083.24 0.263362 0.131681 0.991292i \(-0.457963\pi\)
0.131681 + 0.991292i \(0.457963\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −10634.0 −1.32428 −0.662141 0.749379i \(-0.730352\pi\)
−0.662141 + 0.749379i \(0.730352\pi\)
\(402\) 0 0
\(403\) −389.127 −0.0480988
\(404\) 0 0
\(405\) −600.551 −0.0736830
\(406\) 0 0
\(407\) 4137.06 0.503848
\(408\) 0 0
\(409\) 6516.37 0.787808 0.393904 0.919152i \(-0.371124\pi\)
0.393904 + 0.919152i \(0.371124\pi\)
\(410\) 0 0
\(411\) 9219.56 1.10649
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 1563.38 0.184924
\(416\) 0 0
\(417\) 3040.79 0.357094
\(418\) 0 0
\(419\) 6079.92 0.708887 0.354443 0.935077i \(-0.384670\pi\)
0.354443 + 0.935077i \(0.384670\pi\)
\(420\) 0 0
\(421\) −5631.58 −0.651939 −0.325969 0.945380i \(-0.605691\pi\)
−0.325969 + 0.945380i \(0.605691\pi\)
\(422\) 0 0
\(423\) −5490.04 −0.631051
\(424\) 0 0
\(425\) 3532.54 0.403184
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 87.6610 0.00986554
\(430\) 0 0
\(431\) 3736.90 0.417633 0.208817 0.977955i \(-0.433039\pi\)
0.208817 + 0.977955i \(0.433039\pi\)
\(432\) 0 0
\(433\) 5757.46 0.638998 0.319499 0.947587i \(-0.396485\pi\)
0.319499 + 0.947587i \(0.396485\pi\)
\(434\) 0 0
\(435\) −3472.79 −0.382776
\(436\) 0 0
\(437\) 22791.0 2.49484
\(438\) 0 0
\(439\) −9812.76 −1.06683 −0.533414 0.845854i \(-0.679091\pi\)
−0.533414 + 0.845854i \(0.679091\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −5830.30 −0.625296 −0.312648 0.949869i \(-0.601216\pi\)
−0.312648 + 0.949869i \(0.601216\pi\)
\(444\) 0 0
\(445\) −4103.67 −0.437152
\(446\) 0 0
\(447\) 3694.41 0.390916
\(448\) 0 0
\(449\) −8674.94 −0.911794 −0.455897 0.890033i \(-0.650681\pi\)
−0.455897 + 0.890033i \(0.650681\pi\)
\(450\) 0 0
\(451\) 2071.95 0.216328
\(452\) 0 0
\(453\) 6734.21 0.698456
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9106.82 0.932165 0.466082 0.884741i \(-0.345665\pi\)
0.466082 + 0.884741i \(0.345665\pi\)
\(458\) 0 0
\(459\) −1361.98 −0.138500
\(460\) 0 0
\(461\) 8729.69 0.881957 0.440979 0.897518i \(-0.354631\pi\)
0.440979 + 0.897518i \(0.354631\pi\)
\(462\) 0 0
\(463\) 1795.62 0.180237 0.0901184 0.995931i \(-0.471275\pi\)
0.0901184 + 0.995931i \(0.471275\pi\)
\(464\) 0 0
\(465\) −3105.79 −0.309737
\(466\) 0 0
\(467\) 130.559 0.0129370 0.00646849 0.999979i \(-0.497941\pi\)
0.00646849 + 0.999979i \(0.497941\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 11361.5 1.11148
\(472\) 0 0
\(473\) 3599.53 0.349908
\(474\) 0 0
\(475\) −8757.45 −0.845935
\(476\) 0 0
\(477\) −1237.76 −0.118812
\(478\) 0 0
\(479\) 11845.8 1.12996 0.564978 0.825106i \(-0.308885\pi\)
0.564978 + 0.825106i \(0.308885\pi\)
\(480\) 0 0
\(481\) 1099.55 0.104232
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6701.78 −0.627448
\(486\) 0 0
\(487\) 4807.21 0.447301 0.223650 0.974669i \(-0.428203\pi\)
0.223650 + 0.974669i \(0.428203\pi\)
\(488\) 0 0
\(489\) 6325.68 0.584984
\(490\) 0 0
\(491\) −6068.04 −0.557733 −0.278866 0.960330i \(-0.589959\pi\)
−0.278866 + 0.960330i \(0.589959\pi\)
\(492\) 0 0
\(493\) −7875.87 −0.719496
\(494\) 0 0
\(495\) 699.661 0.0635302
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 15506.4 1.39111 0.695554 0.718474i \(-0.255159\pi\)
0.695554 + 0.718474i \(0.255159\pi\)
\(500\) 0 0
\(501\) 4507.24 0.401934
\(502\) 0 0
\(503\) −1496.79 −0.132681 −0.0663405 0.997797i \(-0.521132\pi\)
−0.0663405 + 0.997797i \(0.521132\pi\)
\(504\) 0 0
\(505\) −2325.18 −0.204889
\(506\) 0 0
\(507\) −6567.70 −0.575309
\(508\) 0 0
\(509\) 5053.74 0.440084 0.220042 0.975490i \(-0.429380\pi\)
0.220042 + 0.975490i \(0.429380\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 3376.45 0.290593
\(514\) 0 0
\(515\) −1712.50 −0.146527
\(516\) 0 0
\(517\) 6396.07 0.544098
\(518\) 0 0
\(519\) −1413.77 −0.119571
\(520\) 0 0
\(521\) −9736.73 −0.818760 −0.409380 0.912364i \(-0.634255\pi\)
−0.409380 + 0.912364i \(0.634255\pi\)
\(522\) 0 0
\(523\) −11796.7 −0.986295 −0.493148 0.869946i \(-0.664154\pi\)
−0.493148 + 0.869946i \(0.664154\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −7043.57 −0.582206
\(528\) 0 0
\(529\) 21048.0 1.72992
\(530\) 0 0
\(531\) 5304.92 0.433548
\(532\) 0 0
\(533\) 550.685 0.0447520
\(534\) 0 0
\(535\) 930.381 0.0751848
\(536\) 0 0
\(537\) −3997.46 −0.321235
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −4310.82 −0.342581 −0.171291 0.985221i \(-0.554794\pi\)
−0.171291 + 0.985221i \(0.554794\pi\)
\(542\) 0 0
\(543\) 2993.18 0.236556
\(544\) 0 0
\(545\) −5527.50 −0.434444
\(546\) 0 0
\(547\) −17015.9 −1.33007 −0.665034 0.746813i \(-0.731583\pi\)
−0.665034 + 0.746813i \(0.731583\pi\)
\(548\) 0 0
\(549\) −2224.96 −0.172967
\(550\) 0 0
\(551\) 19524.9 1.50960
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 8776.02 0.671210
\(556\) 0 0
\(557\) 1741.18 0.132452 0.0662262 0.997805i \(-0.478904\pi\)
0.0662262 + 0.997805i \(0.478904\pi\)
\(558\) 0 0
\(559\) 956.689 0.0723858
\(560\) 0 0
\(561\) 1586.75 0.119416
\(562\) 0 0
\(563\) 11346.8 0.849401 0.424700 0.905334i \(-0.360379\pi\)
0.424700 + 0.905334i \(0.360379\pi\)
\(564\) 0 0
\(565\) 7738.68 0.576228
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18417.4 −1.35694 −0.678470 0.734628i \(-0.737357\pi\)
−0.678470 + 0.734628i \(0.737357\pi\)
\(570\) 0 0
\(571\) −9998.49 −0.732791 −0.366396 0.930459i \(-0.619408\pi\)
−0.366396 + 0.930459i \(0.619408\pi\)
\(572\) 0 0
\(573\) −3680.16 −0.268309
\(574\) 0 0
\(575\) −12762.8 −0.925648
\(576\) 0 0
\(577\) 1401.71 0.101133 0.0505667 0.998721i \(-0.483897\pi\)
0.0505667 + 0.998721i \(0.483897\pi\)
\(578\) 0 0
\(579\) −10437.9 −0.749194
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 1442.03 0.102440
\(584\) 0 0
\(585\) 185.957 0.0131425
\(586\) 0 0
\(587\) −10851.3 −0.763001 −0.381500 0.924369i \(-0.624593\pi\)
−0.381500 + 0.924369i \(0.624593\pi\)
\(588\) 0 0
\(589\) 17461.6 1.22155
\(590\) 0 0
\(591\) 9580.42 0.666812
\(592\) 0 0
\(593\) −20462.0 −1.41699 −0.708493 0.705717i \(-0.750625\pi\)
−0.708493 + 0.705717i \(0.750625\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3195.45 0.219064
\(598\) 0 0
\(599\) −9990.42 −0.681465 −0.340733 0.940160i \(-0.610675\pi\)
−0.340733 + 0.940160i \(0.610675\pi\)
\(600\) 0 0
\(601\) −17435.9 −1.18341 −0.591703 0.806156i \(-0.701544\pi\)
−0.591703 + 0.806156i \(0.701544\pi\)
\(602\) 0 0
\(603\) 3560.82 0.240477
\(604\) 0 0
\(605\) 9053.19 0.608371
\(606\) 0 0
\(607\) 16700.3 1.11671 0.558356 0.829601i \(-0.311432\pi\)
0.558356 + 0.829601i \(0.311432\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1699.96 0.112558
\(612\) 0 0
\(613\) −26702.9 −1.75941 −0.879707 0.475515i \(-0.842262\pi\)
−0.879707 + 0.475515i \(0.842262\pi\)
\(614\) 0 0
\(615\) 4395.26 0.288185
\(616\) 0 0
\(617\) 27790.4 1.81329 0.906645 0.421894i \(-0.138635\pi\)
0.906645 + 0.421894i \(0.138635\pi\)
\(618\) 0 0
\(619\) 1736.08 0.112728 0.0563642 0.998410i \(-0.482049\pi\)
0.0563642 + 0.998410i \(0.482049\pi\)
\(620\) 0 0
\(621\) 4920.74 0.317975
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −1967.20 −0.125901
\(626\) 0 0
\(627\) −3933.67 −0.250552
\(628\) 0 0
\(629\) 19903.0 1.26166
\(630\) 0 0
\(631\) 8990.27 0.567190 0.283595 0.958944i \(-0.408473\pi\)
0.283595 + 0.958944i \(0.408473\pi\)
\(632\) 0 0
\(633\) −6172.49 −0.387574
\(634\) 0 0
\(635\) −15422.9 −0.963839
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −2570.95 −0.159163
\(640\) 0 0
\(641\) −13769.6 −0.848467 −0.424233 0.905553i \(-0.639456\pi\)
−0.424233 + 0.905553i \(0.639456\pi\)
\(642\) 0 0
\(643\) 26969.9 1.65411 0.827053 0.562124i \(-0.190015\pi\)
0.827053 + 0.562124i \(0.190015\pi\)
\(644\) 0 0
\(645\) 7635.75 0.466136
\(646\) 0 0
\(647\) 24401.7 1.48274 0.741368 0.671098i \(-0.234177\pi\)
0.741368 + 0.671098i \(0.234177\pi\)
\(648\) 0 0
\(649\) −6180.40 −0.373809
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 15969.6 0.957026 0.478513 0.878080i \(-0.341176\pi\)
0.478513 + 0.878080i \(0.341176\pi\)
\(654\) 0 0
\(655\) 9412.55 0.561494
\(656\) 0 0
\(657\) 8977.11 0.533075
\(658\) 0 0
\(659\) 11596.2 0.685467 0.342733 0.939433i \(-0.388647\pi\)
0.342733 + 0.939433i \(0.388647\pi\)
\(660\) 0 0
\(661\) −12602.2 −0.741558 −0.370779 0.928721i \(-0.620909\pi\)
−0.370779 + 0.928721i \(0.620909\pi\)
\(662\) 0 0
\(663\) 421.729 0.0247037
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28455.0 1.65185
\(668\) 0 0
\(669\) 6084.80 0.351647
\(670\) 0 0
\(671\) 2592.14 0.149134
\(672\) 0 0
\(673\) 2126.29 0.121787 0.0608934 0.998144i \(-0.480605\pi\)
0.0608934 + 0.998144i \(0.480605\pi\)
\(674\) 0 0
\(675\) −1890.79 −0.107817
\(676\) 0 0
\(677\) −2619.38 −0.148702 −0.0743508 0.997232i \(-0.523688\pi\)
−0.0743508 + 0.997232i \(0.523688\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 7271.87 0.409190
\(682\) 0 0
\(683\) 29929.8 1.67677 0.838383 0.545082i \(-0.183501\pi\)
0.838383 + 0.545082i \(0.183501\pi\)
\(684\) 0 0
\(685\) −22785.3 −1.27092
\(686\) 0 0
\(687\) 5901.51 0.327739
\(688\) 0 0
\(689\) 383.265 0.0211919
\(690\) 0 0
\(691\) 6760.90 0.372209 0.186105 0.982530i \(-0.440414\pi\)
0.186105 + 0.982530i \(0.440414\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −7515.02 −0.410160
\(696\) 0 0
\(697\) 9967.92 0.541696
\(698\) 0 0
\(699\) 13435.0 0.726979
\(700\) 0 0
\(701\) 467.205 0.0251727 0.0125864 0.999921i \(-0.495994\pi\)
0.0125864 + 0.999921i \(0.495994\pi\)
\(702\) 0 0
\(703\) −49341.0 −2.64713
\(704\) 0 0
\(705\) 13568.1 0.724829
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 8824.64 0.467442 0.233721 0.972304i \(-0.424910\pi\)
0.233721 + 0.972304i \(0.424910\pi\)
\(710\) 0 0
\(711\) 7634.38 0.402688
\(712\) 0 0
\(713\) 25448.0 1.33665
\(714\) 0 0
\(715\) −216.646 −0.0113316
\(716\) 0 0
\(717\) −18350.8 −0.955818
\(718\) 0 0
\(719\) −21098.9 −1.09438 −0.547188 0.837010i \(-0.684302\pi\)
−0.547188 + 0.837010i \(0.684302\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −18685.1 −0.961145
\(724\) 0 0
\(725\) −10933.8 −0.560100
\(726\) 0 0
\(727\) −4616.48 −0.235510 −0.117755 0.993043i \(-0.537570\pi\)
−0.117755 + 0.993043i \(0.537570\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 17317.0 0.876185
\(732\) 0 0
\(733\) 10688.1 0.538571 0.269285 0.963060i \(-0.413212\pi\)
0.269285 + 0.963060i \(0.413212\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −4148.47 −0.207342
\(738\) 0 0
\(739\) 15367.6 0.764959 0.382480 0.923964i \(-0.375070\pi\)
0.382480 + 0.923964i \(0.375070\pi\)
\(740\) 0 0
\(741\) −1045.50 −0.0518318
\(742\) 0 0
\(743\) −6502.58 −0.321072 −0.160536 0.987030i \(-0.551322\pi\)
−0.160536 + 0.987030i \(0.551322\pi\)
\(744\) 0 0
\(745\) −9130.38 −0.449009
\(746\) 0 0
\(747\) −1897.77 −0.0929527
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 19874.1 0.965670 0.482835 0.875711i \(-0.339607\pi\)
0.482835 + 0.875711i \(0.339607\pi\)
\(752\) 0 0
\(753\) 17713.2 0.857247
\(754\) 0 0
\(755\) −16642.9 −0.802250
\(756\) 0 0
\(757\) −15157.8 −0.727765 −0.363883 0.931445i \(-0.618549\pi\)
−0.363883 + 0.931445i \(0.618549\pi\)
\(758\) 0 0
\(759\) −5732.82 −0.274161
\(760\) 0 0
\(761\) −35219.8 −1.67768 −0.838842 0.544375i \(-0.816767\pi\)
−0.838842 + 0.544375i \(0.816767\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3366.00 0.159082
\(766\) 0 0
\(767\) −1642.64 −0.0773301
\(768\) 0 0
\(769\) 2264.35 0.106183 0.0530915 0.998590i \(-0.483093\pi\)
0.0530915 + 0.998590i \(0.483093\pi\)
\(770\) 0 0
\(771\) 1224.67 0.0572054
\(772\) 0 0
\(773\) 9532.79 0.443558 0.221779 0.975097i \(-0.428814\pi\)
0.221779 + 0.975097i \(0.428814\pi\)
\(774\) 0 0
\(775\) −9778.38 −0.453226
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24711.3 −1.13655
\(780\) 0 0
\(781\) 2995.24 0.137232
\(782\) 0 0
\(783\) 4215.56 0.192404
\(784\) 0 0
\(785\) −28078.8 −1.27666
\(786\) 0 0
\(787\) −33213.0 −1.50434 −0.752170 0.658969i \(-0.770993\pi\)
−0.752170 + 0.658969i \(0.770993\pi\)
\(788\) 0 0
\(789\) 13878.0 0.626199
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 688.945 0.0308514
\(794\) 0 0
\(795\) 3059.01 0.136468
\(796\) 0 0
\(797\) −42065.6 −1.86956 −0.934781 0.355223i \(-0.884405\pi\)
−0.934781 + 0.355223i \(0.884405\pi\)
\(798\) 0 0
\(799\) 30770.8 1.36245
\(800\) 0 0
\(801\) 4981.39 0.219736
\(802\) 0 0
\(803\) −10458.6 −0.459622
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 2613.88 0.114018
\(808\) 0 0
\(809\) −777.560 −0.0337918 −0.0168959 0.999857i \(-0.505378\pi\)
−0.0168959 + 0.999857i \(0.505378\pi\)
\(810\) 0 0
\(811\) 16559.4 0.716991 0.358496 0.933531i \(-0.383290\pi\)
0.358496 + 0.933531i \(0.383290\pi\)
\(812\) 0 0
\(813\) 19417.0 0.837620
\(814\) 0 0
\(815\) −15633.3 −0.671916
\(816\) 0 0
\(817\) −42930.2 −1.83836
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 231.224 0.00982921 0.00491460 0.999988i \(-0.498436\pi\)
0.00491460 + 0.999988i \(0.498436\pi\)
\(822\) 0 0
\(823\) 5222.86 0.221212 0.110606 0.993864i \(-0.464721\pi\)
0.110606 + 0.993864i \(0.464721\pi\)
\(824\) 0 0
\(825\) 2202.84 0.0929611
\(826\) 0 0
\(827\) 46225.5 1.94367 0.971836 0.235658i \(-0.0757246\pi\)
0.971836 + 0.235658i \(0.0757246\pi\)
\(828\) 0 0
\(829\) 39594.2 1.65882 0.829410 0.558640i \(-0.188677\pi\)
0.829410 + 0.558640i \(0.188677\pi\)
\(830\) 0 0
\(831\) 14135.6 0.590084
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −11139.2 −0.461663
\(836\) 0 0
\(837\) 3770.08 0.155690
\(838\) 0 0
\(839\) −45737.6 −1.88205 −0.941023 0.338344i \(-0.890133\pi\)
−0.941023 + 0.338344i \(0.890133\pi\)
\(840\) 0 0
\(841\) −11.7878 −0.000483326 0
\(842\) 0 0
\(843\) −21497.0 −0.878286
\(844\) 0 0
\(845\) 16231.4 0.660803
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 19041.0 0.769712
\(850\) 0 0
\(851\) −71908.2 −2.89657
\(852\) 0 0
\(853\) 8795.55 0.353053 0.176526 0.984296i \(-0.443514\pi\)
0.176526 + 0.984296i \(0.443514\pi\)
\(854\) 0 0
\(855\) −8344.58 −0.333776
\(856\) 0 0
\(857\) −30254.9 −1.20594 −0.602969 0.797764i \(-0.706016\pi\)
−0.602969 + 0.797764i \(0.706016\pi\)
\(858\) 0 0
\(859\) 44993.5 1.78715 0.893573 0.448918i \(-0.148191\pi\)
0.893573 + 0.448918i \(0.148191\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −44667.9 −1.76189 −0.880946 0.473217i \(-0.843093\pi\)
−0.880946 + 0.473217i \(0.843093\pi\)
\(864\) 0 0
\(865\) 3493.99 0.137340
\(866\) 0 0
\(867\) −7105.31 −0.278327
\(868\) 0 0
\(869\) −8894.29 −0.347201
\(870\) 0 0
\(871\) −1102.59 −0.0428929
\(872\) 0 0
\(873\) 8135.19 0.315389
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5986.84 0.230515 0.115257 0.993336i \(-0.463231\pi\)
0.115257 + 0.993336i \(0.463231\pi\)
\(878\) 0 0
\(879\) −27701.3 −1.06296
\(880\) 0 0
\(881\) −37911.8 −1.44981 −0.724904 0.688850i \(-0.758116\pi\)
−0.724904 + 0.688850i \(0.758116\pi\)
\(882\) 0 0
\(883\) 16293.6 0.620978 0.310489 0.950577i \(-0.399507\pi\)
0.310489 + 0.950577i \(0.399507\pi\)
\(884\) 0 0
\(885\) −13110.6 −0.497975
\(886\) 0 0
\(887\) 8853.41 0.335139 0.167570 0.985860i \(-0.446408\pi\)
0.167570 + 0.985860i \(0.446408\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −849.308 −0.0319336
\(892\) 0 0
\(893\) −76283.4 −2.85859
\(894\) 0 0
\(895\) 9879.34 0.368972
\(896\) 0 0
\(897\) −1523.68 −0.0567159
\(898\) 0 0
\(899\) 21801.1 0.808796
\(900\) 0 0
\(901\) 6937.47 0.256516
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −7397.36 −0.271709
\(906\) 0 0
\(907\) −16662.5 −0.609998 −0.304999 0.952353i \(-0.598656\pi\)
−0.304999 + 0.952353i \(0.598656\pi\)
\(908\) 0 0
\(909\) 2822.50 0.102988
\(910\) 0 0
\(911\) 29071.2 1.05727 0.528635 0.848849i \(-0.322704\pi\)
0.528635 + 0.848849i \(0.322704\pi\)
\(912\) 0 0
\(913\) 2210.96 0.0801446
\(914\) 0 0
\(915\) 5498.77 0.198671
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −7973.39 −0.286200 −0.143100 0.989708i \(-0.545707\pi\)
−0.143100 + 0.989708i \(0.545707\pi\)
\(920\) 0 0
\(921\) 20359.6 0.728416
\(922\) 0 0
\(923\) 796.079 0.0283892
\(924\) 0 0
\(925\) 27630.7 0.982154
\(926\) 0 0
\(927\) 2078.77 0.0736525
\(928\) 0 0
\(929\) −30141.5 −1.06449 −0.532244 0.846591i \(-0.678651\pi\)
−0.532244 + 0.846591i \(0.678651\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 15410.3 0.540740
\(934\) 0 0
\(935\) −3921.50 −0.137162
\(936\) 0 0
\(937\) −1126.37 −0.0392709 −0.0196354 0.999807i \(-0.506251\pi\)
−0.0196354 + 0.999807i \(0.506251\pi\)
\(938\) 0 0
\(939\) 11290.7 0.392393
\(940\) 0 0
\(941\) 10333.3 0.357976 0.178988 0.983851i \(-0.442718\pi\)
0.178988 + 0.983851i \(0.442718\pi\)
\(942\) 0 0
\(943\) −36013.5 −1.24365
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −24810.3 −0.851347 −0.425673 0.904877i \(-0.639963\pi\)
−0.425673 + 0.904877i \(0.639963\pi\)
\(948\) 0 0
\(949\) −2779.71 −0.0950824
\(950\) 0 0
\(951\) −3104.84 −0.105869
\(952\) 0 0
\(953\) −15048.6 −0.511513 −0.255757 0.966741i \(-0.582325\pi\)
−0.255757 + 0.966741i \(0.582325\pi\)
\(954\) 0 0
\(955\) 9095.17 0.308181
\(956\) 0 0
\(957\) −4911.26 −0.165892
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −10293.8 −0.345533
\(962\) 0 0
\(963\) −1129.38 −0.0377919
\(964\) 0 0
\(965\) 25796.2 0.860528
\(966\) 0 0
\(967\) 15619.9 0.519442 0.259721 0.965684i \(-0.416369\pi\)
0.259721 + 0.965684i \(0.416369\pi\)
\(968\) 0 0
\(969\) −18924.5 −0.627392
\(970\) 0 0
\(971\) −24833.0 −0.820730 −0.410365 0.911921i \(-0.634599\pi\)
−0.410365 + 0.911921i \(0.634599\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 585.473 0.0192309
\(976\) 0 0
\(977\) 38656.8 1.26586 0.632928 0.774211i \(-0.281853\pi\)
0.632928 + 0.774211i \(0.281853\pi\)
\(978\) 0 0
\(979\) −5803.47 −0.189458
\(980\) 0 0
\(981\) 6709.75 0.218375
\(982\) 0 0
\(983\) 26664.1 0.865162 0.432581 0.901595i \(-0.357603\pi\)
0.432581 + 0.901595i \(0.357603\pi\)
\(984\) 0 0
\(985\) −23677.1 −0.765903
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −62565.2 −2.01158
\(990\) 0 0
\(991\) −27228.2 −0.872786 −0.436393 0.899756i \(-0.643744\pi\)
−0.436393 + 0.899756i \(0.643744\pi\)
\(992\) 0 0
\(993\) −26400.2 −0.843690
\(994\) 0 0
\(995\) −7897.24 −0.251617
\(996\) 0 0
\(997\) −5162.91 −0.164003 −0.0820016 0.996632i \(-0.526131\pi\)
−0.0820016 + 0.996632i \(0.526131\pi\)
\(998\) 0 0
\(999\) −10653.1 −0.337386
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 2352.4.a.bw.1.1 2
4.3 odd 2 294.4.a.l.1.1 2
7.6 odd 2 2352.4.a.bu.1.2 2
12.11 even 2 882.4.a.bb.1.2 2
28.3 even 6 294.4.e.k.79.1 4
28.11 odd 6 294.4.e.m.79.2 4
28.19 even 6 294.4.e.k.67.1 4
28.23 odd 6 294.4.e.m.67.2 4
28.27 even 2 294.4.a.o.1.2 yes 2
84.11 even 6 882.4.g.be.667.1 4
84.23 even 6 882.4.g.be.361.1 4
84.47 odd 6 882.4.g.bk.361.2 4
84.59 odd 6 882.4.g.bk.667.2 4
84.83 odd 2 882.4.a.t.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.l.1.1 2 4.3 odd 2
294.4.a.o.1.2 yes 2 28.27 even 2
294.4.e.k.67.1 4 28.19 even 6
294.4.e.k.79.1 4 28.3 even 6
294.4.e.m.67.2 4 28.23 odd 6
294.4.e.m.79.2 4 28.11 odd 6
882.4.a.t.1.1 2 84.83 odd 2
882.4.a.bb.1.2 2 12.11 even 2
882.4.g.be.361.1 4 84.23 even 6
882.4.g.be.667.1 4 84.11 even 6
882.4.g.bk.361.2 4 84.47 odd 6
882.4.g.bk.667.2 4 84.59 odd 6
2352.4.a.bu.1.2 2 7.6 odd 2
2352.4.a.bw.1.1 2 1.1 even 1 trivial