Properties

Label 1521.4.a.bm.1.6
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 1.6
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 \(-0.606743\pi\)
−0.329093 + 0.944298i \(0.606743\pi\)
\(3\) 0 0
\(4\) −4.53433 −0.566791
\(5\) 3.46613 0.310020 0.155010 0.987913i \(-0.450459\pi\)
0.155010 + 0.987913i \(0.450459\pi\)
\(6\) 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 \(-0.233778\pi\)
0.742210 + 0.670168i \(0.233778\pi\)
\(12\) 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 \(-0.749765\pi\)
−0.706584 + 0.707629i \(0.749765\pi\)
\(18\) 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 \(-0.745924\pi\)
−0.697994 + 0.716104i \(0.745924\pi\)
\(24\) 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 \(-0.477005\pi\)
0.0721771 + 0.997392i \(0.477005\pi\)
\(30\) 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 \(-0.427986\pi\)
0.224315 + 0.974517i \(0.427986\pi\)
\(42\) 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 \(-0.746935\pi\)
−0.700265 + 0.713883i \(0.746935\pi\)
\(48\) 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 \(-0.502645\pi\)
−0.00831091 + 0.999965i \(0.502645\pi\)
\(54\) 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 \(-0.391314\pi\)
0.334852 + 0.942271i \(0.391314\pi\)
\(60\) 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 \(-0.208297\pi\)
0.793422 + 0.608671i \(0.208297\pi\)
\(72\) 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 \(-0.603025\pi\)
−0.318042 + 0.948077i \(0.603025\pi\)
\(84\) 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 \(-0.454343\pi\)
0.142943 + 0.989731i \(0.454343\pi\)
\(90\) 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 \(-0.846489\pi\)
−0.885944 + 0.463792i \(0.846489\pi\)
\(102\) 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 \(-0.205764\pi\)
0.798241 + 0.602338i \(0.205764\pi\)
\(108\) 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 \(-0.357164\pi\)
0.433824 + 0.900997i \(0.357164\pi\)
\(114\) 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 \(-0.649824\pi\)
−0.453496 + 0.891258i \(0.649824\pi\)
\(132\) 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 \(-0.254789\pi\)
0.696390 + 0.717664i \(0.254789\pi\)
\(138\) 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 \(-0.702128\pi\)
−0.593180 + 0.805070i \(0.702128\pi\)
\(150\) 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 \(-0.372419\pi\)
0.390163 + 0.920746i \(0.372419\pi\)
\(168\) 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 \(-0.590007\pi\)
−0.279011 + 0.960288i \(0.590007\pi\)
\(174\) 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 \(-0.345341\pi\)
0.466984 + 0.884266i \(0.345341\pi\)
\(180\) 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 \(-0.552074\pi\)
−0.162866 + 0.986648i \(0.552074\pi\)
\(192\) 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 \(-0.336134\pi\)
0.492360 + 0.870392i \(0.336134\pi\)
\(198\) 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 \(-0.367688\pi\)
0.403803 + 0.914846i \(0.367688\pi\)
\(228\) 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 \(-0.720057\pi\)
−0.637561 + 0.770399i \(0.720057\pi\)
\(234\) 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 \(-0.186363\pi\)
0.833449 + 0.552596i \(0.186363\pi\)
\(240\) 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 \(-0.243544\pi\)
0.721303 + 0.692620i \(0.243544\pi\)
\(252\) 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 \(-0.653241\pi\)
−0.463040 + 0.886337i \(0.653241\pi\)
\(258\) 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 \(-0.451003\pi\)
0.153322 + 0.988176i \(0.451003\pi\)
\(264\) 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 \(-0.675882\pi\)
−0.524858 + 0.851190i \(0.675882\pi\)
\(270\) 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 \(-0.226405\pi\)
0.757531 + 0.652799i \(0.226405\pi\)
\(282\) 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 \(-0.707867\pi\)
−0.607600 + 0.794243i \(0.707867\pi\)
\(294\) 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 \(-0.566727\pi\)
−0.208098 + 0.978108i \(0.566727\pi\)
\(312\) 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 \(-0.557668\pi\)
−0.180180 + 0.983634i \(0.557668\pi\)
\(318\) 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 \(-0.635529\pi\)
−0.413029 + 0.910718i \(0.635529\pi\)
\(348\) 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 \(-0.363002\pi\)
0.417226 + 0.908803i \(0.363002\pi\)
\(354\) 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 \(-0.381762\pi\)
0.362972 + 0.931800i \(0.381762\pi\)
\(360\) 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 \(-0.322048\pi\)
0.530384 + 0.847757i \(0.322048\pi\)
\(384\) 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 \(-0.759707\pi\)
−0.728338 + 0.685218i \(0.759707\pi\)
\(390\) 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 \(-0.589675\pi\)
−0.278011 + 0.960578i \(0.589675\pi\)
\(402\) 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 \(-0.865163\pi\)
−0.911614 + 0.411048i \(0.865163\pi\)
\(420\) 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 \(-0.467519\pi\)
0.101865 + 0.994798i \(0.467519\pi\)
\(432\) 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 \(-0.474231\pi\)
0.0808674 + 0.996725i \(0.474231\pi\)
\(444\) 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 \(-0.422734\pi\)
0.240363 + 0.970683i \(0.422734\pi\)
\(450\) 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 \(-0.580372\pi\)
−0.249821 + 0.968292i \(0.580372\pi\)
\(462\) 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 \(-0.397103\pi\)
0.317661 + 0.948204i \(0.397103\pi\)
\(468\) 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 \(-0.722127\pi\)
−0.642559 + 0.766237i \(0.722127\pi\)
\(480\) 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 \(-0.701204\pi\)
−0.590842 + 0.806787i \(0.701204\pi\)
\(492\) 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 \(-0.856077\pi\)
−0.899511 + 0.436899i \(0.856077\pi\)
\(504\) 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 \(-0.750592\pi\)
−0.708421 + 0.705790i \(0.750592\pi\)
\(510\) 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 \(-0.643912\pi\)
−0.436867 + 0.899526i \(0.643912\pi\)
\(522\) 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 \(-0.278622\pi\)
0.640755 + 0.767746i \(0.278622\pi\)
\(558\) 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 \(-0.443057\pi\)
0.177938 + 0.984042i \(0.443057\pi\)
\(564\) 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 \(-0.401092\pi\)
0.305753 + 0.952111i \(0.401092\pi\)
\(570\) 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 \(-0.495001\pi\)
0.0157057 + 0.999877i \(0.495001\pi\)
\(588\) 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 \(-0.606107\pi\)
−0.327205 + 0.944954i \(0.606107\pi\)
\(594\) 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 \(-0.464388\pi\)
0.111646 + 0.993748i \(0.464388\pi\)
\(600\) 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 \(-0.209821\pi\)
0.790499 + 0.612463i \(0.209821\pi\)
\(618\) 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 \(-0.237950\pi\)
0.733363 + 0.679838i \(0.237950\pi\)
\(642\) 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 \(-0.647010\pi\)
−0.445602 + 0.895231i \(0.647010\pi\)
\(648\) 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 \(-0.667639\pi\)
−0.502642 + 0.864494i \(0.667639\pi\)
\(654\) 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 \(-0.0639599\pi\)
0.979880 + 0.199587i \(0.0639599\pi\)
\(660\) 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 \(-0.198335\pi\)
0.812081 + 0.583544i \(0.198335\pi\)
\(678\) 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 \(-0.656735\pi\)
−0.472741 + 0.881201i \(0.656735\pi\)
\(684\) 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 \(-0.608213\pi\)
−0.333449 + 0.942768i \(0.608213\pi\)
\(702\) 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 \(-0.671980\pi\)
−0.514385 + 0.857559i \(0.671980\pi\)
\(720\) 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 \(-0.389920\pi\)
0.338975 + 0.940795i \(0.389920\pi\)
\(744\) 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 \(-0.361206\pi\)
0.422347 + 0.906434i \(0.361206\pi\)
\(762\) 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 \(-0.575117\pi\)
−0.233802 + 0.972284i \(0.575117\pi\)
\(774\) 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 \(-0.386048\pi\)
0.350394 + 0.936603i \(0.386048\pi\)
\(798\) 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 \(-0.224786\pi\)
0.760842 + 0.648937i \(0.224786\pi\)
\(810\) 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 \(-0.703685\pi\)
−0.597111 + 0.802158i \(0.703685\pi\)
\(822\) 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 \(-0.351469\pi\)
0.449874 + 0.893092i \(0.351469\pi\)
\(828\) 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 \(-0.594154\pi\)
−0.291498 + 0.956571i \(0.594154\pi\)
\(840\) 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 \(-0.450789\pi\)
0.153986 + 0.988073i \(0.450789\pi\)
\(858\) 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 \(-0.374273\pi\)
0.384792 + 0.923003i \(0.374273\pi\)
\(864\) 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 \(-0.746713\pi\)
−0.699766 + 0.714372i \(0.746713\pi\)
\(882\) 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 \(-0.587438\pi\)
−0.271252 + 0.962508i \(0.587438\pi\)
\(888\) 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 \(-0.228124\pi\)
0.753996 + 0.656879i \(0.228124\pi\)
\(912\) 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 \(-0.492638\pi\)
0.0231256 + 0.999733i \(0.492638\pi\)
\(930\) 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 \(-0.106254\pi\)
0.944802 + 0.327643i \(0.106254\pi\)
\(942\) 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 \(-0.644895\pi\)
−0.439643 + 0.898173i \(0.644895\pi\)
\(948\) 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 \(-0.226007\pi\)
0.758348 + 0.651850i \(0.226007\pi\)
\(954\) 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 \(-0.572624\pi\)
−0.226181 + 0.974085i \(0.572624\pi\)
\(972\) 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 \(-0.374427\pi\)
0.384347 + 0.923189i \(0.374427\pi\)
\(978\) 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 \(-0.497268\pi\)
0.00858207 + 0.999963i \(0.497268\pi\)
\(984\) 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.1.6 18
3.2 odd 2 inner 1521.4.a.bm.1.13 yes 18
13.12 even 2 1521.4.a.bn.1.13 yes 18
39.38 odd 2 1521.4.a.bn.1.6 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.4.a.bm.1.6 18 1.1 even 1 trivial
1521.4.a.bm.1.13 yes 18 3.2 odd 2 inner
1521.4.a.bn.1.6 yes 18 39.38 odd 2
1521.4.a.bn.1.13 yes 18 13.12 even 2