Properties

Label 1521.4.a.bm.1.13
Level $1521$
Weight $4$
Character 1521.1
Self dual yes
Analytic conductor $89.742$
Analytic rank $1$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1521.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(89.7419051187\)
Analytic rank: \(1\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \( x^{18} - 100 x^{16} + 4066 x^{14} - 86197 x^{12} + 1016064 x^{10} - 6594119 x^{8} + 22251817 x^{6} - 37096332 x^{4} + 27824160 x^{2} - 6889792 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3}\cdot 7\cdot 13^{4} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Root \(1.86163\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.86163 q^{2} -4.53433 q^{4} -3.46613 q^{5} +21.2285 q^{7} -23.3343 q^{8} +O(q^{10})\) \(q+1.86163 q^{2} -4.53433 q^{4} -3.46613 q^{5} +21.2285 q^{7} -23.3343 q^{8} -6.45265 q^{10} -54.1559 q^{11} +39.5196 q^{14} -7.16523 q^{16} +99.0529 q^{17} +64.1160 q^{19} +15.7166 q^{20} -100.818 q^{22} +153.983 q^{23} -112.986 q^{25} -96.2569 q^{28} -22.5438 q^{29} -241.319 q^{31} +173.335 q^{32} +184.400 q^{34} -73.5806 q^{35} +34.5346 q^{37} +119.360 q^{38} +80.8796 q^{40} -117.778 q^{41} -101.468 q^{43} +245.561 q^{44} +286.660 q^{46} +451.273 q^{47} +107.649 q^{49} -210.338 q^{50} +6.41346 q^{53} +187.711 q^{55} -495.352 q^{56} -41.9682 q^{58} -303.502 q^{59} -622.411 q^{61} -449.248 q^{62} +380.008 q^{64} +289.575 q^{67} -449.138 q^{68} -136.980 q^{70} -949.340 q^{71} -56.4739 q^{73} +64.2906 q^{74} -290.723 q^{76} -1149.65 q^{77} -968.723 q^{79} +24.8356 q^{80} -219.259 q^{82} +480.985 q^{83} -343.330 q^{85} -188.897 q^{86} +1263.69 q^{88} -240.037 q^{89} -698.210 q^{92} +840.104 q^{94} -222.234 q^{95} -1871.81 q^{97} +200.402 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 56 q^{4} - 94 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 56 q^{4} - 94 q^{7} + 156 q^{10} + 88 q^{16} - 448 q^{19} - 256 q^{22} - 16 q^{25} - 1300 q^{28} - 818 q^{31} - 900 q^{34} - 524 q^{37} + 800 q^{40} + 752 q^{43} - 1650 q^{46} + 2948 q^{49} - 464 q^{55} - 1626 q^{58} - 1784 q^{61} - 4274 q^{64} - 2872 q^{67} - 5772 q^{70} - 3078 q^{73} - 5726 q^{76} + 3326 q^{79} - 1038 q^{82} - 2340 q^{85} + 780 q^{88} + 1220 q^{94} - 4630 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86163 0.658186 0.329093 0.944298i \(-0.393257\pi\)
0.329093 + 0.944298i \(0.393257\pi\)
\(3\) 0 0
\(4\) −4.53433 −0.566791
\(5\) −3.46613 −0.310020 −0.155010 0.987913i \(-0.549541\pi\)
−0.155010 + 0.987913i \(0.549541\pi\)
\(6\) 0 0
\(7\) 21.2285 1.14623 0.573115 0.819475i \(-0.305735\pi\)
0.573115 + 0.819475i \(0.305735\pi\)
\(8\) −23.3343 −1.03124
\(9\) 0 0
\(10\) −6.45265 −0.204051
\(11\) −54.1559 −1.48442 −0.742210 0.670168i \(-0.766222\pi\)
−0.742210 + 0.670168i \(0.766222\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 39.5196 0.754433
\(15\) 0 0
\(16\) −7.16523 −0.111957
\(17\) 99.0529 1.41317 0.706584 0.707629i \(-0.250235\pi\)
0.706584 + 0.707629i \(0.250235\pi\)
\(18\) 0 0
\(19\) 64.1160 0.774169 0.387085 0.922044i \(-0.373482\pi\)
0.387085 + 0.922044i \(0.373482\pi\)
\(20\) 15.7166 0.175716
\(21\) 0 0
\(22\) −100.818 −0.977024
\(23\) 153.983 1.39599 0.697994 0.716104i \(-0.254076\pi\)
0.697994 + 0.716104i \(0.254076\pi\)
\(24\) 0 0
\(25\) −112.986 −0.903888
\(26\) 0 0
\(27\) 0 0
\(28\) −96.2569 −0.649673
\(29\) −22.5438 −0.144354 −0.0721771 0.997392i \(-0.522995\pi\)
−0.0721771 + 0.997392i \(0.522995\pi\)
\(30\) 0 0
\(31\) −241.319 −1.39814 −0.699068 0.715055i \(-0.746402\pi\)
−0.699068 + 0.715055i \(0.746402\pi\)
\(32\) 173.335 0.957552
\(33\) 0 0
\(34\) 184.400 0.930128
\(35\) −73.5806 −0.355354
\(36\) 0 0
\(37\) 34.5346 0.153444 0.0767222 0.997053i \(-0.475555\pi\)
0.0767222 + 0.997053i \(0.475555\pi\)
\(38\) 119.360 0.509547
\(39\) 0 0
\(40\) 80.8796 0.319705
\(41\) −117.778 −0.448630 −0.224315 0.974517i \(-0.572014\pi\)
−0.224315 + 0.974517i \(0.572014\pi\)
\(42\) 0 0
\(43\) −101.468 −0.359856 −0.179928 0.983680i \(-0.557586\pi\)
−0.179928 + 0.983680i \(0.557586\pi\)
\(44\) 245.561 0.841356
\(45\) 0 0
\(46\) 286.660 0.918819
\(47\) 451.273 1.40053 0.700265 0.713883i \(-0.253065\pi\)
0.700265 + 0.713883i \(0.253065\pi\)
\(48\) 0 0
\(49\) 107.649 0.313844
\(50\) −210.338 −0.594926
\(51\) 0 0
\(52\) 0 0
\(53\) 6.41346 0.0166218 0.00831091 0.999965i \(-0.497355\pi\)
0.00831091 + 0.999965i \(0.497355\pi\)
\(54\) 0 0
\(55\) 187.711 0.460199
\(56\) −495.352 −1.18204
\(57\) 0 0
\(58\) −41.9682 −0.0950119
\(59\) −303.502 −0.669704 −0.334852 0.942271i \(-0.608686\pi\)
−0.334852 + 0.942271i \(0.608686\pi\)
\(60\) 0 0
\(61\) −622.411 −1.30642 −0.653210 0.757177i \(-0.726578\pi\)
−0.653210 + 0.757177i \(0.726578\pi\)
\(62\) −449.248 −0.920234
\(63\) 0 0
\(64\) 380.008 0.742204
\(65\) 0 0
\(66\) 0 0
\(67\) 289.575 0.528018 0.264009 0.964520i \(-0.414955\pi\)
0.264009 + 0.964520i \(0.414955\pi\)
\(68\) −449.138 −0.800971
\(69\) 0 0
\(70\) −136.980 −0.233889
\(71\) −949.340 −1.58684 −0.793422 0.608671i \(-0.791703\pi\)
−0.793422 + 0.608671i \(0.791703\pi\)
\(72\) 0 0
\(73\) −56.4739 −0.0905448 −0.0452724 0.998975i \(-0.514416\pi\)
−0.0452724 + 0.998975i \(0.514416\pi\)
\(74\) 64.2906 0.100995
\(75\) 0 0
\(76\) −290.723 −0.438792
\(77\) −1149.65 −1.70149
\(78\) 0 0
\(79\) −968.723 −1.37962 −0.689809 0.723991i \(-0.742306\pi\)
−0.689809 + 0.723991i \(0.742306\pi\)
\(80\) 24.8356 0.0347088
\(81\) 0 0
\(82\) −219.259 −0.295282
\(83\) 480.985 0.636084 0.318042 0.948077i \(-0.396975\pi\)
0.318042 + 0.948077i \(0.396975\pi\)
\(84\) 0 0
\(85\) −343.330 −0.438110
\(86\) −188.897 −0.236852
\(87\) 0 0
\(88\) 1263.69 1.53079
\(89\) −240.037 −0.285887 −0.142943 0.989731i \(-0.545657\pi\)
−0.142943 + 0.989731i \(0.545657\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −698.210 −0.791233
\(93\) 0 0
\(94\) 840.104 0.921810
\(95\) −222.234 −0.240008
\(96\) 0 0
\(97\) −1871.81 −1.95931 −0.979657 0.200680i \(-0.935685\pi\)
−0.979657 + 0.200680i \(0.935685\pi\)
\(98\) 200.402 0.206568
\(99\) 0 0
\(100\) 512.316 0.512316
\(101\) 1798.53 1.77189 0.885944 0.463792i \(-0.153511\pi\)
0.885944 + 0.463792i \(0.153511\pi\)
\(102\) 0 0
\(103\) 723.429 0.692054 0.346027 0.938225i \(-0.387531\pi\)
0.346027 + 0.938225i \(0.387531\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 11.9395 0.0109403
\(107\) −1767.01 −1.59648 −0.798241 0.602338i \(-0.794236\pi\)
−0.798241 + 0.602338i \(0.794236\pi\)
\(108\) 0 0
\(109\) −401.486 −0.352801 −0.176401 0.984318i \(-0.556445\pi\)
−0.176401 + 0.984318i \(0.556445\pi\)
\(110\) 349.449 0.302897
\(111\) 0 0
\(112\) −152.107 −0.128328
\(113\) −1042.23 −0.867649 −0.433824 0.900997i \(-0.642836\pi\)
−0.433824 + 0.900997i \(0.642836\pi\)
\(114\) 0 0
\(115\) −533.725 −0.432784
\(116\) 102.221 0.0818187
\(117\) 0 0
\(118\) −565.008 −0.440790
\(119\) 2102.74 1.61982
\(120\) 0 0
\(121\) 1601.86 1.20350
\(122\) −1158.70 −0.859867
\(123\) 0 0
\(124\) 1094.22 0.792452
\(125\) 824.889 0.590243
\(126\) 0 0
\(127\) 818.340 0.571779 0.285889 0.958263i \(-0.407711\pi\)
0.285889 + 0.958263i \(0.407711\pi\)
\(128\) −679.248 −0.469044
\(129\) 0 0
\(130\) 0 0
\(131\) 1359.91 0.906993 0.453496 0.891258i \(-0.350176\pi\)
0.453496 + 0.891258i \(0.350176\pi\)
\(132\) 0 0
\(133\) 1361.09 0.887376
\(134\) 539.082 0.347534
\(135\) 0 0
\(136\) −2311.33 −1.45732
\(137\) −2233.38 −1.39278 −0.696390 0.717664i \(-0.745211\pi\)
−0.696390 + 0.717664i \(0.745211\pi\)
\(138\) 0 0
\(139\) −3119.54 −1.90357 −0.951784 0.306768i \(-0.900752\pi\)
−0.951784 + 0.306768i \(0.900752\pi\)
\(140\) 333.639 0.201412
\(141\) 0 0
\(142\) −1767.32 −1.04444
\(143\) 0 0
\(144\) 0 0
\(145\) 78.1395 0.0447527
\(146\) −105.134 −0.0595953
\(147\) 0 0
\(148\) −156.591 −0.0869710
\(149\) 2157.72 1.18636 0.593180 0.805070i \(-0.297872\pi\)
0.593180 + 0.805070i \(0.297872\pi\)
\(150\) 0 0
\(151\) −2588.04 −1.39478 −0.697391 0.716691i \(-0.745656\pi\)
−0.697391 + 0.716691i \(0.745656\pi\)
\(152\) −1496.10 −0.798354
\(153\) 0 0
\(154\) −2140.22 −1.11989
\(155\) 836.443 0.433450
\(156\) 0 0
\(157\) −1535.63 −0.780614 −0.390307 0.920685i \(-0.627631\pi\)
−0.390307 + 0.920685i \(0.627631\pi\)
\(158\) −1803.40 −0.908046
\(159\) 0 0
\(160\) −600.802 −0.296860
\(161\) 3268.83 1.60012
\(162\) 0 0
\(163\) 2318.00 1.11386 0.556931 0.830559i \(-0.311979\pi\)
0.556931 + 0.830559i \(0.311979\pi\)
\(164\) 534.044 0.254280
\(165\) 0 0
\(166\) 895.417 0.418662
\(167\) −1684.04 −0.780327 −0.390163 0.920746i \(-0.627581\pi\)
−0.390163 + 0.920746i \(0.627581\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −639.154 −0.288358
\(171\) 0 0
\(172\) 460.091 0.203963
\(173\) 1269.76 0.558021 0.279011 0.960288i \(-0.409993\pi\)
0.279011 + 0.960288i \(0.409993\pi\)
\(174\) 0 0
\(175\) −2398.52 −1.03606
\(176\) 388.039 0.166191
\(177\) 0 0
\(178\) −446.861 −0.188167
\(179\) −2236.72 −0.933967 −0.466984 0.884266i \(-0.654659\pi\)
−0.466984 + 0.884266i \(0.654659\pi\)
\(180\) 0 0
\(181\) −3560.87 −1.46230 −0.731152 0.682214i \(-0.761017\pi\)
−0.731152 + 0.682214i \(0.761017\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3593.09 −1.43960
\(185\) −119.701 −0.0475708
\(186\) 0 0
\(187\) −5364.30 −2.09773
\(188\) −2046.22 −0.793808
\(189\) 0 0
\(190\) −413.718 −0.157970
\(191\) 859.826 0.325732 0.162866 0.986648i \(-0.447926\pi\)
0.162866 + 0.986648i \(0.447926\pi\)
\(192\) 0 0
\(193\) −4824.95 −1.79952 −0.899761 0.436383i \(-0.856259\pi\)
−0.899761 + 0.436383i \(0.856259\pi\)
\(194\) −3484.62 −1.28959
\(195\) 0 0
\(196\) −488.114 −0.177884
\(197\) −2722.78 −0.984721 −0.492360 0.870392i \(-0.663866\pi\)
−0.492360 + 0.870392i \(0.663866\pi\)
\(198\) 0 0
\(199\) 1752.86 0.624405 0.312203 0.950016i \(-0.398933\pi\)
0.312203 + 0.950016i \(0.398933\pi\)
\(200\) 2636.45 0.932125
\(201\) 0 0
\(202\) 3348.21 1.16623
\(203\) −478.570 −0.165463
\(204\) 0 0
\(205\) 408.233 0.139084
\(206\) 1346.76 0.455500
\(207\) 0 0
\(208\) 0 0
\(209\) −3472.26 −1.14919
\(210\) 0 0
\(211\) 3839.73 1.25279 0.626393 0.779508i \(-0.284531\pi\)
0.626393 + 0.779508i \(0.284531\pi\)
\(212\) −29.0807 −0.00942110
\(213\) 0 0
\(214\) −3289.53 −1.05078
\(215\) 351.703 0.111562
\(216\) 0 0
\(217\) −5122.84 −1.60259
\(218\) −747.418 −0.232209
\(219\) 0 0
\(220\) −851.144 −0.260837
\(221\) 0 0
\(222\) 0 0
\(223\) 1070.50 0.321461 0.160730 0.986998i \(-0.448615\pi\)
0.160730 + 0.986998i \(0.448615\pi\)
\(224\) 3679.65 1.09757
\(225\) 0 0
\(226\) −1940.24 −0.571074
\(227\) −2762.09 −0.807606 −0.403803 0.914846i \(-0.632312\pi\)
−0.403803 + 0.914846i \(0.632312\pi\)
\(228\) 0 0
\(229\) −443.465 −0.127969 −0.0639847 0.997951i \(-0.520381\pi\)
−0.0639847 + 0.997951i \(0.520381\pi\)
\(230\) −993.599 −0.284852
\(231\) 0 0
\(232\) 526.043 0.148864
\(233\) 4535.09 1.27512 0.637561 0.770399i \(-0.279943\pi\)
0.637561 + 0.770399i \(0.279943\pi\)
\(234\) 0 0
\(235\) −1564.17 −0.434192
\(236\) 1376.18 0.379582
\(237\) 0 0
\(238\) 3914.53 1.06614
\(239\) −6158.94 −1.66690 −0.833449 0.552596i \(-0.813637\pi\)
−0.833449 + 0.552596i \(0.813637\pi\)
\(240\) 0 0
\(241\) 794.221 0.212283 0.106142 0.994351i \(-0.466150\pi\)
0.106142 + 0.994351i \(0.466150\pi\)
\(242\) 2982.07 0.792128
\(243\) 0 0
\(244\) 2822.22 0.740467
\(245\) −373.123 −0.0972978
\(246\) 0 0
\(247\) 0 0
\(248\) 5631.02 1.44181
\(249\) 0 0
\(250\) 1535.64 0.388490
\(251\) −5736.65 −1.44261 −0.721303 0.692620i \(-0.756456\pi\)
−0.721303 + 0.692620i \(0.756456\pi\)
\(252\) 0 0
\(253\) −8339.09 −2.07223
\(254\) 1523.45 0.376337
\(255\) 0 0
\(256\) −4304.58 −1.05092
\(257\) 3815.47 0.926080 0.463040 0.886337i \(-0.346759\pi\)
0.463040 + 0.886337i \(0.346759\pi\)
\(258\) 0 0
\(259\) 733.116 0.175883
\(260\) 0 0
\(261\) 0 0
\(262\) 2531.65 0.596970
\(263\) −1307.88 −0.306644 −0.153322 0.988176i \(-0.548997\pi\)
−0.153322 + 0.988176i \(0.548997\pi\)
\(264\) 0 0
\(265\) −22.2299 −0.00515309
\(266\) 2533.84 0.584059
\(267\) 0 0
\(268\) −1313.03 −0.299276
\(269\) 4631.27 1.04972 0.524858 0.851190i \(-0.324118\pi\)
0.524858 + 0.851190i \(0.324118\pi\)
\(270\) 0 0
\(271\) −3912.21 −0.876937 −0.438468 0.898747i \(-0.644479\pi\)
−0.438468 + 0.898747i \(0.644479\pi\)
\(272\) −709.736 −0.158214
\(273\) 0 0
\(274\) −4157.73 −0.916708
\(275\) 6118.86 1.34175
\(276\) 0 0
\(277\) −7619.61 −1.65277 −0.826387 0.563103i \(-0.809607\pi\)
−0.826387 + 0.563103i \(0.809607\pi\)
\(278\) −5807.43 −1.25290
\(279\) 0 0
\(280\) 1716.95 0.366455
\(281\) −7136.58 −1.51506 −0.757531 0.652799i \(-0.773595\pi\)
−0.757531 + 0.652799i \(0.773595\pi\)
\(282\) 0 0
\(283\) 8223.69 1.72738 0.863689 0.504025i \(-0.168148\pi\)
0.863689 + 0.504025i \(0.168148\pi\)
\(284\) 4304.62 0.899410
\(285\) 0 0
\(286\) 0 0
\(287\) −2500.25 −0.514233
\(288\) 0 0
\(289\) 4898.48 0.997044
\(290\) 145.467 0.0294556
\(291\) 0 0
\(292\) 256.071 0.0513200
\(293\) 6094.65 1.21520 0.607600 0.794243i \(-0.292133\pi\)
0.607600 + 0.794243i \(0.292133\pi\)
\(294\) 0 0
\(295\) 1051.97 0.207621
\(296\) −805.840 −0.158238
\(297\) 0 0
\(298\) 4016.89 0.780846
\(299\) 0 0
\(300\) 0 0
\(301\) −2154.02 −0.412478
\(302\) −4817.99 −0.918026
\(303\) 0 0
\(304\) −459.406 −0.0866734
\(305\) 2157.36 0.405016
\(306\) 0 0
\(307\) 189.227 0.0351783 0.0175892 0.999845i \(-0.494401\pi\)
0.0175892 + 0.999845i \(0.494401\pi\)
\(308\) 5212.88 0.964388
\(309\) 0 0
\(310\) 1557.15 0.285291
\(311\) 2282.65 0.416196 0.208098 0.978108i \(-0.433273\pi\)
0.208098 + 0.978108i \(0.433273\pi\)
\(312\) 0 0
\(313\) −5417.71 −0.978361 −0.489180 0.872183i \(-0.662704\pi\)
−0.489180 + 0.872183i \(0.662704\pi\)
\(314\) −2858.77 −0.513789
\(315\) 0 0
\(316\) 4392.51 0.781955
\(317\) 2033.88 0.360360 0.180180 0.983634i \(-0.442332\pi\)
0.180180 + 0.983634i \(0.442332\pi\)
\(318\) 0 0
\(319\) 1220.88 0.214282
\(320\) −1317.16 −0.230098
\(321\) 0 0
\(322\) 6085.35 1.05318
\(323\) 6350.88 1.09403
\(324\) 0 0
\(325\) 0 0
\(326\) 4315.26 0.733128
\(327\) 0 0
\(328\) 2748.27 0.462645
\(329\) 9579.84 1.60533
\(330\) 0 0
\(331\) −6413.08 −1.06494 −0.532469 0.846449i \(-0.678736\pi\)
−0.532469 + 0.846449i \(0.678736\pi\)
\(332\) −2180.95 −0.360527
\(333\) 0 0
\(334\) −3135.05 −0.513600
\(335\) −1003.70 −0.163696
\(336\) 0 0
\(337\) 10577.9 1.70984 0.854922 0.518756i \(-0.173605\pi\)
0.854922 + 0.518756i \(0.173605\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 1556.77 0.248317
\(341\) 13068.9 2.07542
\(342\) 0 0
\(343\) −4996.16 −0.786493
\(344\) 2367.70 0.371098
\(345\) 0 0
\(346\) 2363.82 0.367282
\(347\) 5339.55 0.826058 0.413029 0.910718i \(-0.364471\pi\)
0.413029 + 0.910718i \(0.364471\pi\)
\(348\) 0 0
\(349\) −2188.63 −0.335687 −0.167843 0.985814i \(-0.553680\pi\)
−0.167843 + 0.985814i \(0.553680\pi\)
\(350\) −4465.16 −0.681923
\(351\) 0 0
\(352\) −9387.13 −1.42141
\(353\) −5534.31 −0.834452 −0.417226 0.908803i \(-0.636998\pi\)
−0.417226 + 0.908803i \(0.636998\pi\)
\(354\) 0 0
\(355\) 3290.53 0.491953
\(356\) 1088.41 0.162038
\(357\) 0 0
\(358\) −4163.94 −0.614724
\(359\) −4937.93 −0.725945 −0.362972 0.931800i \(-0.618238\pi\)
−0.362972 + 0.931800i \(0.618238\pi\)
\(360\) 0 0
\(361\) −2748.14 −0.400662
\(362\) −6629.02 −0.962468
\(363\) 0 0
\(364\) 0 0
\(365\) 195.746 0.0280707
\(366\) 0 0
\(367\) −451.014 −0.0641492 −0.0320746 0.999485i \(-0.510211\pi\)
−0.0320746 + 0.999485i \(0.510211\pi\)
\(368\) −1103.32 −0.156290
\(369\) 0 0
\(370\) −222.839 −0.0313104
\(371\) 136.148 0.0190524
\(372\) 0 0
\(373\) −3759.18 −0.521831 −0.260915 0.965362i \(-0.584024\pi\)
−0.260915 + 0.965362i \(0.584024\pi\)
\(374\) −9986.35 −1.38070
\(375\) 0 0
\(376\) −10530.1 −1.44428
\(377\) 0 0
\(378\) 0 0
\(379\) 6247.82 0.846778 0.423389 0.905948i \(-0.360840\pi\)
0.423389 + 0.905948i \(0.360840\pi\)
\(380\) 1007.68 0.136034
\(381\) 0 0
\(382\) 1600.68 0.214392
\(383\) −7950.94 −1.06077 −0.530384 0.847757i \(-0.677952\pi\)
−0.530384 + 0.847757i \(0.677952\pi\)
\(384\) 0 0
\(385\) 3984.82 0.527495
\(386\) −8982.28 −1.18442
\(387\) 0 0
\(388\) 8487.40 1.11052
\(389\) 11176.0 1.45668 0.728338 0.685218i \(-0.240293\pi\)
0.728338 + 0.685218i \(0.240293\pi\)
\(390\) 0 0
\(391\) 15252.5 1.97276
\(392\) −2511.90 −0.323649
\(393\) 0 0
\(394\) −5068.81 −0.648129
\(395\) 3357.72 0.427709
\(396\) 0 0
\(397\) 7407.12 0.936404 0.468202 0.883621i \(-0.344902\pi\)
0.468202 + 0.883621i \(0.344902\pi\)
\(398\) 3263.17 0.410975
\(399\) 0 0
\(400\) 809.570 0.101196
\(401\) 4464.87 0.556022 0.278011 0.960578i \(-0.410325\pi\)
0.278011 + 0.960578i \(0.410325\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −8155.14 −1.00429
\(405\) 0 0
\(406\) −890.921 −0.108906
\(407\) −1870.25 −0.227776
\(408\) 0 0
\(409\) 2362.97 0.285676 0.142838 0.989746i \(-0.454377\pi\)
0.142838 + 0.989746i \(0.454377\pi\)
\(410\) 759.980 0.0915433
\(411\) 0 0
\(412\) −3280.26 −0.392250
\(413\) −6442.88 −0.767635
\(414\) 0 0
\(415\) −1667.16 −0.197199
\(416\) 0 0
\(417\) 0 0
\(418\) −6464.07 −0.756382
\(419\) 15637.3 1.82323 0.911614 0.411048i \(-0.134837\pi\)
0.911614 + 0.411048i \(0.134837\pi\)
\(420\) 0 0
\(421\) −4087.68 −0.473210 −0.236605 0.971606i \(-0.576035\pi\)
−0.236605 + 0.971606i \(0.576035\pi\)
\(422\) 7148.16 0.824566
\(423\) 0 0
\(424\) −149.654 −0.0171411
\(425\) −11191.6 −1.27735
\(426\) 0 0
\(427\) −13212.8 −1.49746
\(428\) 8012.22 0.904872
\(429\) 0 0
\(430\) 654.740 0.0734288
\(431\) −1822.93 −0.203730 −0.101865 0.994798i \(-0.532481\pi\)
−0.101865 + 0.994798i \(0.532481\pi\)
\(432\) 0 0
\(433\) −6100.85 −0.677109 −0.338555 0.940947i \(-0.609938\pi\)
−0.338555 + 0.940947i \(0.609938\pi\)
\(434\) −9536.85 −1.05480
\(435\) 0 0
\(436\) 1820.47 0.199965
\(437\) 9872.78 1.08073
\(438\) 0 0
\(439\) −2269.61 −0.246749 −0.123374 0.992360i \(-0.539372\pi\)
−0.123374 + 0.992360i \(0.539372\pi\)
\(440\) −4380.11 −0.474576
\(441\) 0 0
\(442\) 0 0
\(443\) −1508.03 −0.161735 −0.0808674 0.996725i \(-0.525769\pi\)
−0.0808674 + 0.996725i \(0.525769\pi\)
\(444\) 0 0
\(445\) 832.000 0.0886305
\(446\) 1992.87 0.211581
\(447\) 0 0
\(448\) 8067.00 0.850737
\(449\) −4573.69 −0.480725 −0.240363 0.970683i \(-0.577266\pi\)
−0.240363 + 0.970683i \(0.577266\pi\)
\(450\) 0 0
\(451\) 6378.37 0.665955
\(452\) 4725.79 0.491776
\(453\) 0 0
\(454\) −5142.00 −0.531555
\(455\) 0 0
\(456\) 0 0
\(457\) −8999.57 −0.921186 −0.460593 0.887611i \(-0.652363\pi\)
−0.460593 + 0.887611i \(0.652363\pi\)
\(458\) −825.569 −0.0842277
\(459\) 0 0
\(460\) 2420.08 0.245298
\(461\) 4945.51 0.499643 0.249821 0.968292i \(-0.419628\pi\)
0.249821 + 0.968292i \(0.419628\pi\)
\(462\) 0 0
\(463\) −3371.96 −0.338463 −0.169231 0.985576i \(-0.554128\pi\)
−0.169231 + 0.985576i \(0.554128\pi\)
\(464\) 161.531 0.0161614
\(465\) 0 0
\(466\) 8442.67 0.839268
\(467\) −6411.64 −0.635322 −0.317661 0.948204i \(-0.602897\pi\)
−0.317661 + 0.948204i \(0.602897\pi\)
\(468\) 0 0
\(469\) 6147.24 0.605230
\(470\) −2911.91 −0.285779
\(471\) 0 0
\(472\) 7082.00 0.690626
\(473\) 5495.12 0.534177
\(474\) 0 0
\(475\) −7244.21 −0.699762
\(476\) −9534.53 −0.918098
\(477\) 0 0
\(478\) −11465.7 −1.09713
\(479\) 13472.4 1.28512 0.642559 0.766237i \(-0.277873\pi\)
0.642559 + 0.766237i \(0.277873\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1478.55 0.139722
\(483\) 0 0
\(484\) −7263.37 −0.682134
\(485\) 6487.93 0.607426
\(486\) 0 0
\(487\) 14439.2 1.34354 0.671770 0.740760i \(-0.265534\pi\)
0.671770 + 0.740760i \(0.265534\pi\)
\(488\) 14523.5 1.34723
\(489\) 0 0
\(490\) −694.618 −0.0640401
\(491\) 12856.5 1.18168 0.590842 0.806787i \(-0.298796\pi\)
0.590842 + 0.806787i \(0.298796\pi\)
\(492\) 0 0
\(493\) −2233.03 −0.203997
\(494\) 0 0
\(495\) 0 0
\(496\) 1729.11 0.156531
\(497\) −20153.1 −1.81889
\(498\) 0 0
\(499\) −2996.45 −0.268817 −0.134409 0.990926i \(-0.542913\pi\)
−0.134409 + 0.990926i \(0.542913\pi\)
\(500\) −3740.32 −0.334544
\(501\) 0 0
\(502\) −10679.5 −0.949503
\(503\) 20295.0 1.79902 0.899511 0.436899i \(-0.143923\pi\)
0.899511 + 0.436899i \(0.143923\pi\)
\(504\) 0 0
\(505\) −6233.94 −0.549320
\(506\) −15524.3 −1.36391
\(507\) 0 0
\(508\) −3710.62 −0.324079
\(509\) 16270.4 1.41684 0.708421 0.705790i \(-0.249408\pi\)
0.708421 + 0.705790i \(0.249408\pi\)
\(510\) 0 0
\(511\) −1198.86 −0.103785
\(512\) −2579.55 −0.222658
\(513\) 0 0
\(514\) 7103.00 0.609533
\(515\) −2507.50 −0.214550
\(516\) 0 0
\(517\) −24439.1 −2.07897
\(518\) 1364.79 0.115764
\(519\) 0 0
\(520\) 0 0
\(521\) 10390.5 0.873734 0.436867 0.899526i \(-0.356088\pi\)
0.436867 + 0.899526i \(0.356088\pi\)
\(522\) 0 0
\(523\) −14355.4 −1.20023 −0.600113 0.799916i \(-0.704878\pi\)
−0.600113 + 0.799916i \(0.704878\pi\)
\(524\) −6166.29 −0.514076
\(525\) 0 0
\(526\) −2434.79 −0.201829
\(527\) −23903.4 −1.97580
\(528\) 0 0
\(529\) 11543.8 0.948780
\(530\) −41.3838 −0.00339169
\(531\) 0 0
\(532\) −6171.61 −0.502957
\(533\) 0 0
\(534\) 0 0
\(535\) 6124.69 0.494941
\(536\) −6757.03 −0.544513
\(537\) 0 0
\(538\) 8621.72 0.690909
\(539\) −5829.80 −0.465876
\(540\) 0 0
\(541\) 14187.5 1.12748 0.563741 0.825951i \(-0.309362\pi\)
0.563741 + 0.825951i \(0.309362\pi\)
\(542\) −7283.09 −0.577188
\(543\) 0 0
\(544\) 17169.4 1.35318
\(545\) 1391.60 0.109375
\(546\) 0 0
\(547\) 8864.63 0.692915 0.346457 0.938066i \(-0.387385\pi\)
0.346457 + 0.938066i \(0.387385\pi\)
\(548\) 10126.9 0.789415
\(549\) 0 0
\(550\) 11391.1 0.883120
\(551\) −1445.42 −0.111755
\(552\) 0 0
\(553\) −20564.5 −1.58136
\(554\) −14184.9 −1.08783
\(555\) 0 0
\(556\) 14145.0 1.07893
\(557\) −16846.3 −1.28151 −0.640755 0.767746i \(-0.721378\pi\)
−0.640755 + 0.767746i \(0.721378\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 527.222 0.0397842
\(561\) 0 0
\(562\) −13285.7 −0.997193
\(563\) −4754.01 −0.355875 −0.177938 0.984042i \(-0.556943\pi\)
−0.177938 + 0.984042i \(0.556943\pi\)
\(564\) 0 0
\(565\) 3612.49 0.268988
\(566\) 15309.5 1.13694
\(567\) 0 0
\(568\) 22152.2 1.63642
\(569\) −8299.82 −0.611506 −0.305753 0.952111i \(-0.598908\pi\)
−0.305753 + 0.952111i \(0.598908\pi\)
\(570\) 0 0
\(571\) 9383.57 0.687723 0.343862 0.939020i \(-0.388265\pi\)
0.343862 + 0.939020i \(0.388265\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −4654.54 −0.338461
\(575\) −17397.9 −1.26182
\(576\) 0 0
\(577\) 24230.2 1.74821 0.874105 0.485736i \(-0.161449\pi\)
0.874105 + 0.485736i \(0.161449\pi\)
\(578\) 9119.16 0.656241
\(579\) 0 0
\(580\) −354.310 −0.0253654
\(581\) 10210.6 0.729099
\(582\) 0 0
\(583\) −347.327 −0.0246738
\(584\) 1317.78 0.0933735
\(585\) 0 0
\(586\) 11346.0 0.799827
\(587\) −446.729 −0.0314113 −0.0157057 0.999877i \(-0.504999\pi\)
−0.0157057 + 0.999877i \(0.504999\pi\)
\(588\) 0 0
\(589\) −15472.4 −1.08239
\(590\) 1958.39 0.136654
\(591\) 0 0
\(592\) −247.448 −0.0171791
\(593\) 9449.99 0.654409 0.327205 0.944954i \(-0.393893\pi\)
0.327205 + 0.944954i \(0.393893\pi\)
\(594\) 0 0
\(595\) −7288.37 −0.502175
\(596\) −9783.83 −0.672418
\(597\) 0 0
\(598\) 0 0
\(599\) −3273.52 −0.223293 −0.111646 0.993748i \(-0.535612\pi\)
−0.111646 + 0.993748i \(0.535612\pi\)
\(600\) 0 0
\(601\) 15211.4 1.03242 0.516211 0.856462i \(-0.327342\pi\)
0.516211 + 0.856462i \(0.327342\pi\)
\(602\) −4009.99 −0.271487
\(603\) 0 0
\(604\) 11735.0 0.790550
\(605\) −5552.25 −0.373109
\(606\) 0 0
\(607\) 14322.4 0.957705 0.478852 0.877895i \(-0.341053\pi\)
0.478852 + 0.877895i \(0.341053\pi\)
\(608\) 11113.6 0.741307
\(609\) 0 0
\(610\) 4016.20 0.266576
\(611\) 0 0
\(612\) 0 0
\(613\) 17695.5 1.16593 0.582966 0.812497i \(-0.301892\pi\)
0.582966 + 0.812497i \(0.301892\pi\)
\(614\) 352.271 0.0231539
\(615\) 0 0
\(616\) 26826.2 1.75464
\(617\) −24230.3 −1.58100 −0.790499 0.612463i \(-0.790179\pi\)
−0.790499 + 0.612463i \(0.790179\pi\)
\(618\) 0 0
\(619\) −16761.3 −1.08836 −0.544178 0.838970i \(-0.683158\pi\)
−0.544178 + 0.838970i \(0.683158\pi\)
\(620\) −3792.71 −0.245676
\(621\) 0 0
\(622\) 4249.45 0.273935
\(623\) −5095.63 −0.327692
\(624\) 0 0
\(625\) 11264.1 0.720901
\(626\) −10085.8 −0.643943
\(627\) 0 0
\(628\) 6963.04 0.442445
\(629\) 3420.75 0.216843
\(630\) 0 0
\(631\) −26812.2 −1.69156 −0.845780 0.533531i \(-0.820865\pi\)
−0.845780 + 0.533531i \(0.820865\pi\)
\(632\) 22604.5 1.42272
\(633\) 0 0
\(634\) 3786.33 0.237184
\(635\) −2836.47 −0.177263
\(636\) 0 0
\(637\) 0 0
\(638\) 2272.82 0.141038
\(639\) 0 0
\(640\) 2354.36 0.145413
\(641\) −23803.2 −1.46673 −0.733363 0.679838i \(-0.762050\pi\)
−0.733363 + 0.679838i \(0.762050\pi\)
\(642\) 0 0
\(643\) 9688.90 0.594235 0.297117 0.954841i \(-0.403975\pi\)
0.297117 + 0.954841i \(0.403975\pi\)
\(644\) −14821.9 −0.906935
\(645\) 0 0
\(646\) 11823.0 0.720076
\(647\) 14666.7 0.891204 0.445602 0.895231i \(-0.352990\pi\)
0.445602 + 0.895231i \(0.352990\pi\)
\(648\) 0 0
\(649\) 16436.4 0.994122
\(650\) 0 0
\(651\) 0 0
\(652\) −10510.6 −0.631327
\(653\) 16774.9 1.00528 0.502642 0.864494i \(-0.332361\pi\)
0.502642 + 0.864494i \(0.332361\pi\)
\(654\) 0 0
\(655\) −4713.63 −0.281186
\(656\) 843.906 0.0502271
\(657\) 0 0
\(658\) 17834.1 1.05661
\(659\) −33153.6 −1.95976 −0.979880 0.199587i \(-0.936040\pi\)
−0.979880 + 0.199587i \(0.936040\pi\)
\(660\) 0 0
\(661\) 26998.6 1.58869 0.794343 0.607469i \(-0.207815\pi\)
0.794343 + 0.607469i \(0.207815\pi\)
\(662\) −11938.8 −0.700928
\(663\) 0 0
\(664\) −11223.5 −0.655956
\(665\) −4717.69 −0.275104
\(666\) 0 0
\(667\) −3471.36 −0.201517
\(668\) 7635.97 0.442282
\(669\) 0 0
\(670\) −1868.52 −0.107742
\(671\) 33707.2 1.93928
\(672\) 0 0
\(673\) −31725.4 −1.81713 −0.908563 0.417749i \(-0.862819\pi\)
−0.908563 + 0.417749i \(0.862819\pi\)
\(674\) 19692.2 1.12540
\(675\) 0 0
\(676\) 0 0
\(677\) −28609.6 −1.62416 −0.812081 0.583544i \(-0.801665\pi\)
−0.812081 + 0.583544i \(0.801665\pi\)
\(678\) 0 0
\(679\) −39735.7 −2.24582
\(680\) 8011.36 0.451797
\(681\) 0 0
\(682\) 24329.4 1.36601
\(683\) 16876.6 0.945482 0.472741 0.881201i \(-0.343265\pi\)
0.472741 + 0.881201i \(0.343265\pi\)
\(684\) 0 0
\(685\) 7741.18 0.431789
\(686\) −9301.00 −0.517659
\(687\) 0 0
\(688\) 727.045 0.0402882
\(689\) 0 0
\(690\) 0 0
\(691\) 14682.7 0.808329 0.404165 0.914686i \(-0.367562\pi\)
0.404165 + 0.914686i \(0.367562\pi\)
\(692\) −5757.49 −0.316282
\(693\) 0 0
\(694\) 9940.27 0.543700
\(695\) 10812.7 0.590144
\(696\) 0 0
\(697\) −11666.3 −0.633990
\(698\) −4074.42 −0.220944
\(699\) 0 0
\(700\) 10875.7 0.587232
\(701\) 12377.6 0.666898 0.333449 0.942768i \(-0.391787\pi\)
0.333449 + 0.942768i \(0.391787\pi\)
\(702\) 0 0
\(703\) 2214.22 0.118792
\(704\) −20579.7 −1.10174
\(705\) 0 0
\(706\) −10302.8 −0.549224
\(707\) 38180.1 2.03099
\(708\) 0 0
\(709\) −25093.4 −1.32920 −0.664599 0.747200i \(-0.731398\pi\)
−0.664599 + 0.747200i \(0.731398\pi\)
\(710\) 6125.76 0.323797
\(711\) 0 0
\(712\) 5601.10 0.294818
\(713\) −37159.1 −1.95178
\(714\) 0 0
\(715\) 0 0
\(716\) 10142.0 0.529364
\(717\) 0 0
\(718\) −9192.61 −0.477807
\(719\) 19834.1 1.02877 0.514385 0.857559i \(-0.328020\pi\)
0.514385 + 0.857559i \(0.328020\pi\)
\(720\) 0 0
\(721\) 15357.3 0.793253
\(722\) −5116.02 −0.263710
\(723\) 0 0
\(724\) 16146.1 0.828821
\(725\) 2547.13 0.130480
\(726\) 0 0
\(727\) 26992.7 1.37703 0.688517 0.725221i \(-0.258262\pi\)
0.688517 + 0.725221i \(0.258262\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 364.406 0.0184757
\(731\) −10050.7 −0.508537
\(732\) 0 0
\(733\) −12248.4 −0.617195 −0.308597 0.951193i \(-0.599860\pi\)
−0.308597 + 0.951193i \(0.599860\pi\)
\(734\) −839.622 −0.0422221
\(735\) 0 0
\(736\) 26690.7 1.33673
\(737\) −15682.2 −0.783800
\(738\) 0 0
\(739\) −13980.0 −0.695889 −0.347945 0.937515i \(-0.613120\pi\)
−0.347945 + 0.937515i \(0.613120\pi\)
\(740\) 542.764 0.0269627
\(741\) 0 0
\(742\) 253.458 0.0125401
\(743\) −13730.3 −0.677949 −0.338975 0.940795i \(-0.610080\pi\)
−0.338975 + 0.940795i \(0.610080\pi\)
\(744\) 0 0
\(745\) −7478.94 −0.367795
\(746\) −6998.20 −0.343462
\(747\) 0 0
\(748\) 24323.5 1.18898
\(749\) −37511.0 −1.82994
\(750\) 0 0
\(751\) −16795.7 −0.816092 −0.408046 0.912961i \(-0.633790\pi\)
−0.408046 + 0.912961i \(0.633790\pi\)
\(752\) −3233.47 −0.156799
\(753\) 0 0
\(754\) 0 0
\(755\) 8970.49 0.432410
\(756\) 0 0
\(757\) −3680.42 −0.176707 −0.0883533 0.996089i \(-0.528160\pi\)
−0.0883533 + 0.996089i \(0.528160\pi\)
\(758\) 11631.1 0.557338
\(759\) 0 0
\(760\) 5185.68 0.247506
\(761\) −17732.8 −0.844695 −0.422347 0.906434i \(-0.638794\pi\)
−0.422347 + 0.906434i \(0.638794\pi\)
\(762\) 0 0
\(763\) −8522.93 −0.404392
\(764\) −3898.74 −0.184622
\(765\) 0 0
\(766\) −14801.7 −0.698183
\(767\) 0 0
\(768\) 0 0
\(769\) 5198.88 0.243792 0.121896 0.992543i \(-0.461103\pi\)
0.121896 + 0.992543i \(0.461103\pi\)
\(770\) 7418.27 0.347190
\(771\) 0 0
\(772\) 21877.9 1.01995
\(773\) 10049.6 0.467605 0.233802 0.972284i \(-0.424883\pi\)
0.233802 + 0.972284i \(0.424883\pi\)
\(774\) 0 0
\(775\) 27265.7 1.26376
\(776\) 43677.4 2.02052
\(777\) 0 0
\(778\) 20805.6 0.958764
\(779\) −7551.45 −0.347316
\(780\) 0 0
\(781\) 51412.4 2.35554
\(782\) 28394.5 1.29845
\(783\) 0 0
\(784\) −771.326 −0.0351369
\(785\) 5322.68 0.242006
\(786\) 0 0
\(787\) −2283.57 −0.103431 −0.0517157 0.998662i \(-0.516469\pi\)
−0.0517157 + 0.998662i \(0.516469\pi\)
\(788\) 12346.0 0.558131
\(789\) 0 0
\(790\) 6250.83 0.281512
\(791\) −22124.9 −0.994526
\(792\) 0 0
\(793\) 0 0
\(794\) 13789.3 0.616328
\(795\) 0 0
\(796\) −7948.02 −0.353907
\(797\) −15767.9 −0.700787 −0.350394 0.936603i \(-0.613952\pi\)
−0.350394 + 0.936603i \(0.613952\pi\)
\(798\) 0 0
\(799\) 44699.9 1.97918
\(800\) −19584.5 −0.865519
\(801\) 0 0
\(802\) 8311.94 0.365966
\(803\) 3058.40 0.134407
\(804\) 0 0
\(805\) −11330.2 −0.496070
\(806\) 0 0
\(807\) 0 0
\(808\) −41967.5 −1.82724
\(809\) −35014.4 −1.52168 −0.760842 0.648937i \(-0.775214\pi\)
−0.760842 + 0.648937i \(0.775214\pi\)
\(810\) 0 0
\(811\) −15741.1 −0.681561 −0.340780 0.940143i \(-0.610691\pi\)
−0.340780 + 0.940143i \(0.610691\pi\)
\(812\) 2169.99 0.0937831
\(813\) 0 0
\(814\) −3481.72 −0.149919
\(815\) −8034.47 −0.345319
\(816\) 0 0
\(817\) −6505.75 −0.278589
\(818\) 4398.98 0.188028
\(819\) 0 0
\(820\) −1851.06 −0.0788317
\(821\) 28093.1 1.19422 0.597111 0.802158i \(-0.296315\pi\)
0.597111 + 0.802158i \(0.296315\pi\)
\(822\) 0 0
\(823\) −17076.7 −0.723276 −0.361638 0.932319i \(-0.617782\pi\)
−0.361638 + 0.932319i \(0.617782\pi\)
\(824\) −16880.7 −0.713674
\(825\) 0 0
\(826\) −11994.3 −0.505247
\(827\) −21398.3 −0.899748 −0.449874 0.893092i \(-0.648531\pi\)
−0.449874 + 0.893092i \(0.648531\pi\)
\(828\) 0 0
\(829\) −34951.3 −1.46430 −0.732152 0.681141i \(-0.761484\pi\)
−0.732152 + 0.681141i \(0.761484\pi\)
\(830\) −3103.63 −0.129793
\(831\) 0 0
\(832\) 0 0
\(833\) 10662.9 0.443514
\(834\) 0 0
\(835\) 5837.08 0.241917
\(836\) 15744.4 0.651352
\(837\) 0 0
\(838\) 29110.9 1.20002
\(839\) 14168.0 0.582996 0.291498 0.956571i \(-0.405846\pi\)
0.291498 + 0.956571i \(0.405846\pi\)
\(840\) 0 0
\(841\) −23880.8 −0.979162
\(842\) −7609.76 −0.311460
\(843\) 0 0
\(844\) −17410.6 −0.710068
\(845\) 0 0
\(846\) 0 0
\(847\) 34005.1 1.37949
\(848\) −45.9539 −0.00186092
\(849\) 0 0
\(850\) −20834.6 −0.840731
\(851\) 5317.74 0.214206
\(852\) 0 0
\(853\) 2604.09 0.104528 0.0522639 0.998633i \(-0.483356\pi\)
0.0522639 + 0.998633i \(0.483356\pi\)
\(854\) −24597.5 −0.985606
\(855\) 0 0
\(856\) 41232.0 1.64636
\(857\) −7726.51 −0.307973 −0.153986 0.988073i \(-0.549211\pi\)
−0.153986 + 0.988073i \(0.549211\pi\)
\(858\) 0 0
\(859\) 16487.4 0.654883 0.327441 0.944872i \(-0.393814\pi\)
0.327441 + 0.944872i \(0.393814\pi\)
\(860\) −1594.74 −0.0632326
\(861\) 0 0
\(862\) −3393.63 −0.134092
\(863\) −19510.7 −0.769585 −0.384792 0.923003i \(-0.625727\pi\)
−0.384792 + 0.923003i \(0.625727\pi\)
\(864\) 0 0
\(865\) −4401.13 −0.172998
\(866\) −11357.5 −0.445664
\(867\) 0 0
\(868\) 23228.7 0.908332
\(869\) 52462.1 2.04793
\(870\) 0 0
\(871\) 0 0
\(872\) 9368.39 0.363823
\(873\) 0 0
\(874\) 18379.5 0.711322
\(875\) 17511.1 0.676554
\(876\) 0 0
\(877\) −8989.31 −0.346120 −0.173060 0.984911i \(-0.555365\pi\)
−0.173060 + 0.984911i \(0.555365\pi\)
\(878\) −4225.18 −0.162407
\(879\) 0 0
\(880\) −1344.99 −0.0515224
\(881\) 36597.1 1.39953 0.699766 0.714372i \(-0.253287\pi\)
0.699766 + 0.714372i \(0.253287\pi\)
\(882\) 0 0
\(883\) −5749.48 −0.219123 −0.109561 0.993980i \(-0.534945\pi\)
−0.109561 + 0.993980i \(0.534945\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −2807.39 −0.106452
\(887\) 14331.4 0.542503 0.271252 0.962508i \(-0.412562\pi\)
0.271252 + 0.962508i \(0.412562\pi\)
\(888\) 0 0
\(889\) 17372.1 0.655390
\(890\) 1548.88 0.0583353
\(891\) 0 0
\(892\) −4853.98 −0.182201
\(893\) 28933.8 1.08425
\(894\) 0 0
\(895\) 7752.75 0.289548
\(896\) −14419.4 −0.537632
\(897\) 0 0
\(898\) −8514.52 −0.316407
\(899\) 5440.25 0.201827
\(900\) 0 0
\(901\) 635.272 0.0234894
\(902\) 11874.2 0.438323
\(903\) 0 0
\(904\) 24319.6 0.894754
\(905\) 12342.4 0.453343
\(906\) 0 0
\(907\) −25035.2 −0.916516 −0.458258 0.888819i \(-0.651526\pi\)
−0.458258 + 0.888819i \(0.651526\pi\)
\(908\) 12524.2 0.457744
\(909\) 0 0
\(910\) 0 0
\(911\) −41464.5 −1.50799 −0.753996 0.656879i \(-0.771876\pi\)
−0.753996 + 0.656879i \(0.771876\pi\)
\(912\) 0 0
\(913\) −26048.2 −0.944216
\(914\) −16753.9 −0.606312
\(915\) 0 0
\(916\) 2010.82 0.0725319
\(917\) 28868.9 1.03962
\(918\) 0 0
\(919\) 6761.65 0.242705 0.121353 0.992609i \(-0.461277\pi\)
0.121353 + 0.992609i \(0.461277\pi\)
\(920\) 12454.1 0.446304
\(921\) 0 0
\(922\) 9206.71 0.328858
\(923\) 0 0
\(924\) 0 0
\(925\) −3901.92 −0.138697
\(926\) −6277.34 −0.222771
\(927\) 0 0
\(928\) −3907.63 −0.138227
\(929\) −1309.62 −0.0462512 −0.0231256 0.999733i \(-0.507362\pi\)
−0.0231256 + 0.999733i \(0.507362\pi\)
\(930\) 0 0
\(931\) 6901.99 0.242968
\(932\) −20563.6 −0.722728
\(933\) 0 0
\(934\) −11936.1 −0.418160
\(935\) 18593.3 0.650339
\(936\) 0 0
\(937\) −31660.7 −1.10385 −0.551926 0.833893i \(-0.686107\pi\)
−0.551926 + 0.833893i \(0.686107\pi\)
\(938\) 11443.9 0.398354
\(939\) 0 0
\(940\) 7092.46 0.246096
\(941\) −54545.0 −1.88960 −0.944802 0.327643i \(-0.893746\pi\)
−0.944802 + 0.327643i \(0.893746\pi\)
\(942\) 0 0
\(943\) −18135.8 −0.626282
\(944\) 2174.66 0.0749778
\(945\) 0 0
\(946\) 10229.9 0.351588
\(947\) 25624.5 0.879286 0.439643 0.898173i \(-0.355105\pi\)
0.439643 + 0.898173i \(0.355105\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −13486.0 −0.460574
\(951\) 0 0
\(952\) −49066.0 −1.67042
\(953\) −44620.8 −1.51670 −0.758348 0.651850i \(-0.773993\pi\)
−0.758348 + 0.651850i \(0.773993\pi\)
\(954\) 0 0
\(955\) −2980.27 −0.100983
\(956\) 27926.7 0.944783
\(957\) 0 0
\(958\) 25080.7 0.845846
\(959\) −47411.3 −1.59645
\(960\) 0 0
\(961\) 28444.0 0.954786
\(962\) 0 0
\(963\) 0 0
\(964\) −3601.26 −0.120320
\(965\) 16723.9 0.557887
\(966\) 0 0
\(967\) −13882.9 −0.461679 −0.230839 0.972992i \(-0.574147\pi\)
−0.230839 + 0.972992i \(0.574147\pi\)
\(968\) −37378.3 −1.24110
\(969\) 0 0
\(970\) 12078.1 0.399799
\(971\) 13687.2 0.452363 0.226181 0.974085i \(-0.427376\pi\)
0.226181 + 0.974085i \(0.427376\pi\)
\(972\) 0 0
\(973\) −66223.1 −2.18193
\(974\) 26880.5 0.884299
\(975\) 0 0
\(976\) 4459.72 0.146262
\(977\) −23474.5 −0.768694 −0.384347 0.923189i \(-0.625573\pi\)
−0.384347 + 0.923189i \(0.625573\pi\)
\(978\) 0 0
\(979\) 12999.4 0.424376
\(980\) 1691.86 0.0551476
\(981\) 0 0
\(982\) 23934.1 0.777768
\(983\) −528.996 −0.0171641 −0.00858207 0.999963i \(-0.502732\pi\)
−0.00858207 + 0.999963i \(0.502732\pi\)
\(984\) 0 0
\(985\) 9437.49 0.305283
\(986\) −4157.07 −0.134268
\(987\) 0 0
\(988\) 0 0
\(989\) −15624.4 −0.502354
\(990\) 0 0
\(991\) 52472.4 1.68198 0.840989 0.541052i \(-0.181974\pi\)
0.840989 + 0.541052i \(0.181974\pi\)
\(992\) −41829.2 −1.33879
\(993\) 0 0
\(994\) −37517.6 −1.19717
\(995\) −6075.62 −0.193578
\(996\) 0 0
\(997\) −5163.27 −0.164015 −0.0820073 0.996632i \(-0.526133\pi\)
−0.0820073 + 0.996632i \(0.526133\pi\)
\(998\) −5578.29 −0.176932
\(999\) 0 0
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 1521.4.a.bm.1.13 yes 18
3.2 odd 2 inner 1521.4.a.bm.1.6 18
13.12 even 2 1521.4.a.bn.1.6 yes 18
39.38 odd 2 1521.4.a.bn.1.13 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.4.a.bm.1.6 18 3.2 odd 2 inner
1521.4.a.bm.1.13 yes 18 1.1 even 1 trivial
1521.4.a.bn.1.6 yes 18 13.12 even 2
1521.4.a.bn.1.13 yes 18 39.38 odd 2