Properties

Label 1521.4.a.bm.1.4
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 1.4
Root \(-3.66578\) of defining polynomial
Character \(\chi\) \(=\) 1521.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.66578 q^{2} +5.43796 q^{4} +9.45496 q^{5} +15.4112 q^{7} +9.39187 q^{8} +O(q^{10})\) \(q-3.66578 q^{2} +5.43796 q^{4} +9.45496 q^{5} +15.4112 q^{7} +9.39187 q^{8} -34.6598 q^{10} -12.7273 q^{11} -56.4943 q^{14} -77.9323 q^{16} -18.9954 q^{17} +95.4839 q^{19} +51.4157 q^{20} +46.6556 q^{22} +104.290 q^{23} -35.6037 q^{25} +83.8058 q^{28} +23.3225 q^{29} -177.018 q^{31} +210.548 q^{32} +69.6329 q^{34} +145.713 q^{35} -350.533 q^{37} -350.023 q^{38} +88.7998 q^{40} -348.495 q^{41} +60.8686 q^{43} -69.2107 q^{44} -382.304 q^{46} -226.920 q^{47} -105.494 q^{49} +130.516 q^{50} -294.134 q^{53} -120.336 q^{55} +144.740 q^{56} -85.4954 q^{58} -596.423 q^{59} -487.247 q^{61} +648.908 q^{62} -148.364 q^{64} -943.554 q^{67} -103.296 q^{68} -534.151 q^{70} +1044.76 q^{71} -554.083 q^{73} +1284.98 q^{74} +519.238 q^{76} -196.144 q^{77} +126.990 q^{79} -736.846 q^{80} +1277.51 q^{82} +1448.23 q^{83} -179.601 q^{85} -223.131 q^{86} -119.533 q^{88} -247.561 q^{89} +567.125 q^{92} +831.840 q^{94} +902.797 q^{95} +136.799 q^{97} +386.716 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 56 q^{4} - 94 q^{7}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.66578 −1.29605 −0.648025 0.761619i \(-0.724405\pi\)
−0.648025 + 0.761619i \(0.724405\pi\)
\(3\) 0 0
\(4\) 5.43796 0.679745
\(5\) 9.45496 0.845677 0.422839 0.906205i \(-0.361034\pi\)
0.422839 + 0.906205i \(0.361034\pi\)
\(6\) 0 0
\(7\) 15.4112 0.832129 0.416065 0.909335i \(-0.363409\pi\)
0.416065 + 0.909335i \(0.363409\pi\)
\(8\) 9.39187 0.415066
\(9\) 0 0
\(10\) −34.6598 −1.09604
\(11\) −12.7273 −0.348858 −0.174429 0.984670i \(-0.555808\pi\)
−0.174429 + 0.984670i \(0.555808\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) −56.4943 −1.07848
\(15\) 0 0
\(16\) −77.9323 −1.21769
\(17\) −18.9954 −0.271003 −0.135502 0.990777i \(-0.543265\pi\)
−0.135502 + 0.990777i \(0.543265\pi\)
\(18\) 0 0
\(19\) 95.4839 1.15292 0.576461 0.817125i \(-0.304433\pi\)
0.576461 + 0.817125i \(0.304433\pi\)
\(20\) 51.4157 0.574845
\(21\) 0 0
\(22\) 46.6556 0.452137
\(23\) 104.290 0.945476 0.472738 0.881203i \(-0.343266\pi\)
0.472738 + 0.881203i \(0.343266\pi\)
\(24\) 0 0
\(25\) −35.6037 −0.284830
\(26\) 0 0
\(27\) 0 0
\(28\) 83.8058 0.565636
\(29\) 23.3225 0.149341 0.0746705 0.997208i \(-0.476210\pi\)
0.0746705 + 0.997208i \(0.476210\pi\)
\(30\) 0 0
\(31\) −177.018 −1.02559 −0.512795 0.858511i \(-0.671390\pi\)
−0.512795 + 0.858511i \(0.671390\pi\)
\(32\) 210.548 1.16312
\(33\) 0 0
\(34\) 69.6329 0.351234
\(35\) 145.713 0.703713
\(36\) 0 0
\(37\) −350.533 −1.55750 −0.778748 0.627337i \(-0.784145\pi\)
−0.778748 + 0.627337i \(0.784145\pi\)
\(38\) −350.023 −1.49424
\(39\) 0 0
\(40\) 88.7998 0.351012
\(41\) −348.495 −1.32746 −0.663729 0.747973i \(-0.731027\pi\)
−0.663729 + 0.747973i \(0.731027\pi\)
\(42\) 0 0
\(43\) 60.8686 0.215869 0.107935 0.994158i \(-0.465576\pi\)
0.107935 + 0.994158i \(0.465576\pi\)
\(44\) −69.2107 −0.237134
\(45\) 0 0
\(46\) −382.304 −1.22538
\(47\) −226.920 −0.704249 −0.352124 0.935953i \(-0.614541\pi\)
−0.352124 + 0.935953i \(0.614541\pi\)
\(48\) 0 0
\(49\) −105.494 −0.307561
\(50\) 130.516 0.369154
\(51\) 0 0
\(52\) 0 0
\(53\) −294.134 −0.762311 −0.381155 0.924511i \(-0.624474\pi\)
−0.381155 + 0.924511i \(0.624474\pi\)
\(54\) 0 0
\(55\) −120.336 −0.295021
\(56\) 144.740 0.345388
\(57\) 0 0
\(58\) −85.4954 −0.193553
\(59\) −596.423 −1.31606 −0.658031 0.752991i \(-0.728610\pi\)
−0.658031 + 0.752991i \(0.728610\pi\)
\(60\) 0 0
\(61\) −487.247 −1.02271 −0.511357 0.859368i \(-0.670857\pi\)
−0.511357 + 0.859368i \(0.670857\pi\)
\(62\) 648.908 1.32922
\(63\) 0 0
\(64\) −148.364 −0.289774
\(65\) 0 0
\(66\) 0 0
\(67\) −943.554 −1.72050 −0.860250 0.509873i \(-0.829693\pi\)
−0.860250 + 0.509873i \(0.829693\pi\)
\(68\) −103.296 −0.184213
\(69\) 0 0
\(70\) −534.151 −0.912047
\(71\) 1044.76 1.74633 0.873167 0.487422i \(-0.162063\pi\)
0.873167 + 0.487422i \(0.162063\pi\)
\(72\) 0 0
\(73\) −554.083 −0.888364 −0.444182 0.895937i \(-0.646506\pi\)
−0.444182 + 0.895937i \(0.646506\pi\)
\(74\) 1284.98 2.01859
\(75\) 0 0
\(76\) 519.238 0.783693
\(77\) −196.144 −0.290295
\(78\) 0 0
\(79\) 126.990 0.180855 0.0904275 0.995903i \(-0.471177\pi\)
0.0904275 + 0.995903i \(0.471177\pi\)
\(80\) −736.846 −1.02977
\(81\) 0 0
\(82\) 1277.51 1.72045
\(83\) 1448.23 1.91523 0.957613 0.288058i \(-0.0930096\pi\)
0.957613 + 0.288058i \(0.0930096\pi\)
\(84\) 0 0
\(85\) −179.601 −0.229181
\(86\) −223.131 −0.279777
\(87\) 0 0
\(88\) −119.533 −0.144799
\(89\) −247.561 −0.294847 −0.147424 0.989073i \(-0.547098\pi\)
−0.147424 + 0.989073i \(0.547098\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 567.125 0.642683
\(93\) 0 0
\(94\) 831.840 0.912742
\(95\) 902.797 0.975000
\(96\) 0 0
\(97\) 136.799 0.143194 0.0715970 0.997434i \(-0.477190\pi\)
0.0715970 + 0.997434i \(0.477190\pi\)
\(98\) 386.716 0.398615
\(99\) 0 0
\(100\) −193.612 −0.193612
\(101\) 1674.46 1.64965 0.824826 0.565386i \(-0.191273\pi\)
0.824826 + 0.565386i \(0.191273\pi\)
\(102\) 0 0
\(103\) −531.415 −0.508368 −0.254184 0.967156i \(-0.581807\pi\)
−0.254184 + 0.967156i \(0.581807\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1078.23 0.987993
\(107\) −515.773 −0.465997 −0.232998 0.972477i \(-0.574854\pi\)
−0.232998 + 0.972477i \(0.574854\pi\)
\(108\) 0 0
\(109\) −1604.26 −1.40973 −0.704864 0.709343i \(-0.748992\pi\)
−0.704864 + 0.709343i \(0.748992\pi\)
\(110\) 441.127 0.382362
\(111\) 0 0
\(112\) −1201.03 −1.01328
\(113\) 1907.87 1.58830 0.794149 0.607724i \(-0.207917\pi\)
0.794149 + 0.607724i \(0.207917\pi\)
\(114\) 0 0
\(115\) 986.057 0.799568
\(116\) 126.827 0.101514
\(117\) 0 0
\(118\) 2186.36 1.70568
\(119\) −292.742 −0.225510
\(120\) 0 0
\(121\) −1169.02 −0.878298
\(122\) 1786.14 1.32549
\(123\) 0 0
\(124\) −962.615 −0.697140
\(125\) −1518.50 −1.08655
\(126\) 0 0
\(127\) −771.937 −0.539357 −0.269678 0.962950i \(-0.586917\pi\)
−0.269678 + 0.962950i \(0.586917\pi\)
\(128\) −1140.51 −0.787562
\(129\) 0 0
\(130\) 0 0
\(131\) 765.560 0.510590 0.255295 0.966863i \(-0.417827\pi\)
0.255295 + 0.966863i \(0.417827\pi\)
\(132\) 0 0
\(133\) 1471.53 0.959380
\(134\) 3458.86 2.22985
\(135\) 0 0
\(136\) −178.402 −0.112484
\(137\) −2654.87 −1.65562 −0.827812 0.561006i \(-0.810415\pi\)
−0.827812 + 0.561006i \(0.810415\pi\)
\(138\) 0 0
\(139\) 2879.66 1.75719 0.878596 0.477565i \(-0.158481\pi\)
0.878596 + 0.477565i \(0.158481\pi\)
\(140\) 792.380 0.478345
\(141\) 0 0
\(142\) −3829.85 −2.26334
\(143\) 0 0
\(144\) 0 0
\(145\) 220.514 0.126294
\(146\) 2031.15 1.15136
\(147\) 0 0
\(148\) −1906.19 −1.05870
\(149\) 2004.35 1.10203 0.551017 0.834494i \(-0.314240\pi\)
0.551017 + 0.834494i \(0.314240\pi\)
\(150\) 0 0
\(151\) −370.126 −0.199473 −0.0997365 0.995014i \(-0.531800\pi\)
−0.0997365 + 0.995014i \(0.531800\pi\)
\(152\) 896.773 0.478539
\(153\) 0 0
\(154\) 719.021 0.376236
\(155\) −1673.69 −0.867319
\(156\) 0 0
\(157\) −1148.00 −0.583568 −0.291784 0.956484i \(-0.594249\pi\)
−0.291784 + 0.956484i \(0.594249\pi\)
\(158\) −465.519 −0.234397
\(159\) 0 0
\(160\) 1990.72 0.983627
\(161\) 1607.24 0.786758
\(162\) 0 0
\(163\) −2043.17 −0.981798 −0.490899 0.871217i \(-0.663332\pi\)
−0.490899 + 0.871217i \(0.663332\pi\)
\(164\) −1895.10 −0.902333
\(165\) 0 0
\(166\) −5308.89 −2.48223
\(167\) −813.252 −0.376834 −0.188417 0.982089i \(-0.560336\pi\)
−0.188417 + 0.982089i \(0.560336\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 658.377 0.297031
\(171\) 0 0
\(172\) 331.001 0.146736
\(173\) −303.878 −0.133546 −0.0667728 0.997768i \(-0.521270\pi\)
−0.0667728 + 0.997768i \(0.521270\pi\)
\(174\) 0 0
\(175\) −548.698 −0.237015
\(176\) 991.869 0.424801
\(177\) 0 0
\(178\) 907.504 0.382137
\(179\) −1829.37 −0.763874 −0.381937 0.924188i \(-0.624743\pi\)
−0.381937 + 0.924188i \(0.624743\pi\)
\(180\) 0 0
\(181\) −1186.50 −0.487249 −0.243624 0.969870i \(-0.578336\pi\)
−0.243624 + 0.969870i \(0.578336\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 979.478 0.392435
\(185\) −3314.28 −1.31714
\(186\) 0 0
\(187\) 241.760 0.0945416
\(188\) −1233.98 −0.478710
\(189\) 0 0
\(190\) −3309.46 −1.26365
\(191\) 1191.17 0.451256 0.225628 0.974214i \(-0.427557\pi\)
0.225628 + 0.974214i \(0.427557\pi\)
\(192\) 0 0
\(193\) 4000.67 1.49210 0.746048 0.665892i \(-0.231949\pi\)
0.746048 + 0.665892i \(0.231949\pi\)
\(194\) −501.475 −0.185586
\(195\) 0 0
\(196\) −573.670 −0.209063
\(197\) 1676.21 0.606220 0.303110 0.952956i \(-0.401975\pi\)
0.303110 + 0.952956i \(0.401975\pi\)
\(198\) 0 0
\(199\) 3048.89 1.08608 0.543040 0.839707i \(-0.317273\pi\)
0.543040 + 0.839707i \(0.317273\pi\)
\(200\) −334.386 −0.118223
\(201\) 0 0
\(202\) −6138.20 −2.13803
\(203\) 359.429 0.124271
\(204\) 0 0
\(205\) −3295.00 −1.12260
\(206\) 1948.05 0.658870
\(207\) 0 0
\(208\) 0 0
\(209\) −1215.26 −0.402206
\(210\) 0 0
\(211\) 3454.40 1.12707 0.563533 0.826093i \(-0.309442\pi\)
0.563533 + 0.826093i \(0.309442\pi\)
\(212\) −1599.49 −0.518177
\(213\) 0 0
\(214\) 1890.71 0.603955
\(215\) 575.510 0.182556
\(216\) 0 0
\(217\) −2728.06 −0.853424
\(218\) 5880.87 1.82708
\(219\) 0 0
\(220\) −654.385 −0.200539
\(221\) 0 0
\(222\) 0 0
\(223\) −467.158 −0.140283 −0.0701417 0.997537i \(-0.522345\pi\)
−0.0701417 + 0.997537i \(0.522345\pi\)
\(224\) 3244.80 0.967868
\(225\) 0 0
\(226\) −6993.85 −2.05851
\(227\) 2265.23 0.662329 0.331165 0.943573i \(-0.392558\pi\)
0.331165 + 0.943573i \(0.392558\pi\)
\(228\) 0 0
\(229\) −102.372 −0.0295410 −0.0147705 0.999891i \(-0.504702\pi\)
−0.0147705 + 0.999891i \(0.504702\pi\)
\(230\) −3614.67 −1.03628
\(231\) 0 0
\(232\) 219.042 0.0619864
\(233\) 2570.39 0.722713 0.361356 0.932428i \(-0.382314\pi\)
0.361356 + 0.932428i \(0.382314\pi\)
\(234\) 0 0
\(235\) −2145.52 −0.595567
\(236\) −3243.32 −0.894586
\(237\) 0 0
\(238\) 1073.13 0.292272
\(239\) −867.428 −0.234767 −0.117383 0.993087i \(-0.537451\pi\)
−0.117383 + 0.993087i \(0.537451\pi\)
\(240\) 0 0
\(241\) −5242.46 −1.40123 −0.700615 0.713540i \(-0.747091\pi\)
−0.700615 + 0.713540i \(0.747091\pi\)
\(242\) 4285.36 1.13832
\(243\) 0 0
\(244\) −2649.63 −0.695185
\(245\) −997.437 −0.260098
\(246\) 0 0
\(247\) 0 0
\(248\) −1662.53 −0.425688
\(249\) 0 0
\(250\) 5566.50 1.40822
\(251\) −5721.44 −1.43878 −0.719390 0.694606i \(-0.755579\pi\)
−0.719390 + 0.694606i \(0.755579\pi\)
\(252\) 0 0
\(253\) −1327.33 −0.329837
\(254\) 2829.75 0.699034
\(255\) 0 0
\(256\) 5367.78 1.31049
\(257\) −7263.31 −1.76293 −0.881465 0.472250i \(-0.843442\pi\)
−0.881465 + 0.472250i \(0.843442\pi\)
\(258\) 0 0
\(259\) −5402.16 −1.29604
\(260\) 0 0
\(261\) 0 0
\(262\) −2806.38 −0.661750
\(263\) −3168.26 −0.742827 −0.371413 0.928468i \(-0.621127\pi\)
−0.371413 + 0.928468i \(0.621127\pi\)
\(264\) 0 0
\(265\) −2781.03 −0.644669
\(266\) −5394.30 −1.24340
\(267\) 0 0
\(268\) −5131.01 −1.16950
\(269\) −3738.01 −0.847251 −0.423626 0.905837i \(-0.639243\pi\)
−0.423626 + 0.905837i \(0.639243\pi\)
\(270\) 0 0
\(271\) −2397.74 −0.537462 −0.268731 0.963215i \(-0.586604\pi\)
−0.268731 + 0.963215i \(0.586604\pi\)
\(272\) 1480.35 0.329998
\(273\) 0 0
\(274\) 9732.16 2.14577
\(275\) 453.140 0.0993651
\(276\) 0 0
\(277\) 2325.17 0.504353 0.252177 0.967681i \(-0.418854\pi\)
0.252177 + 0.967681i \(0.418854\pi\)
\(278\) −10556.2 −2.27741
\(279\) 0 0
\(280\) 1368.52 0.292087
\(281\) 4700.23 0.997838 0.498919 0.866649i \(-0.333731\pi\)
0.498919 + 0.866649i \(0.333731\pi\)
\(282\) 0 0
\(283\) 3110.96 0.653454 0.326727 0.945119i \(-0.394054\pi\)
0.326727 + 0.945119i \(0.394054\pi\)
\(284\) 5681.34 1.18706
\(285\) 0 0
\(286\) 0 0
\(287\) −5370.74 −1.10462
\(288\) 0 0
\(289\) −4552.18 −0.926557
\(290\) −808.355 −0.163684
\(291\) 0 0
\(292\) −3013.09 −0.603861
\(293\) −2367.81 −0.472113 −0.236057 0.971739i \(-0.575855\pi\)
−0.236057 + 0.971739i \(0.575855\pi\)
\(294\) 0 0
\(295\) −5639.15 −1.11296
\(296\) −3292.17 −0.646464
\(297\) 0 0
\(298\) −7347.52 −1.42829
\(299\) 0 0
\(300\) 0 0
\(301\) 938.061 0.179631
\(302\) 1356.80 0.258527
\(303\) 0 0
\(304\) −7441.28 −1.40390
\(305\) −4606.90 −0.864886
\(306\) 0 0
\(307\) −3696.56 −0.687210 −0.343605 0.939114i \(-0.611648\pi\)
−0.343605 + 0.939114i \(0.611648\pi\)
\(308\) −1066.62 −0.197326
\(309\) 0 0
\(310\) 6135.40 1.12409
\(311\) −2806.06 −0.511630 −0.255815 0.966726i \(-0.582344\pi\)
−0.255815 + 0.966726i \(0.582344\pi\)
\(312\) 0 0
\(313\) 8168.52 1.47512 0.737559 0.675283i \(-0.235978\pi\)
0.737559 + 0.675283i \(0.235978\pi\)
\(314\) 4208.31 0.756333
\(315\) 0 0
\(316\) 690.569 0.122935
\(317\) −6882.13 −1.21937 −0.609683 0.792646i \(-0.708703\pi\)
−0.609683 + 0.792646i \(0.708703\pi\)
\(318\) 0 0
\(319\) −296.834 −0.0520987
\(320\) −1402.78 −0.245055
\(321\) 0 0
\(322\) −5891.79 −1.01968
\(323\) −1813.75 −0.312446
\(324\) 0 0
\(325\) 0 0
\(326\) 7489.80 1.27246
\(327\) 0 0
\(328\) −3273.02 −0.550982
\(329\) −3497.12 −0.586026
\(330\) 0 0
\(331\) 2835.07 0.470784 0.235392 0.971900i \(-0.424363\pi\)
0.235392 + 0.971900i \(0.424363\pi\)
\(332\) 7875.41 1.30187
\(333\) 0 0
\(334\) 2981.20 0.488396
\(335\) −8921.27 −1.45499
\(336\) 0 0
\(337\) 1948.43 0.314948 0.157474 0.987523i \(-0.449665\pi\)
0.157474 + 0.987523i \(0.449665\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) −976.661 −0.155785
\(341\) 2252.96 0.357785
\(342\) 0 0
\(343\) −6911.84 −1.08806
\(344\) 571.670 0.0896000
\(345\) 0 0
\(346\) 1113.95 0.173082
\(347\) −8797.96 −1.36109 −0.680546 0.732705i \(-0.738257\pi\)
−0.680546 + 0.732705i \(0.738257\pi\)
\(348\) 0 0
\(349\) −2479.39 −0.380282 −0.190141 0.981757i \(-0.560895\pi\)
−0.190141 + 0.981757i \(0.560895\pi\)
\(350\) 2011.41 0.307184
\(351\) 0 0
\(352\) −2679.71 −0.405764
\(353\) 8819.59 1.32980 0.664900 0.746933i \(-0.268474\pi\)
0.664900 + 0.746933i \(0.268474\pi\)
\(354\) 0 0
\(355\) 9878.12 1.47683
\(356\) −1346.23 −0.200421
\(357\) 0 0
\(358\) 6706.07 0.990019
\(359\) 8233.51 1.21044 0.605220 0.796058i \(-0.293085\pi\)
0.605220 + 0.796058i \(0.293085\pi\)
\(360\) 0 0
\(361\) 2258.18 0.329229
\(362\) 4349.46 0.631499
\(363\) 0 0
\(364\) 0 0
\(365\) −5238.84 −0.751269
\(366\) 0 0
\(367\) 6269.59 0.891744 0.445872 0.895097i \(-0.352894\pi\)
0.445872 + 0.895097i \(0.352894\pi\)
\(368\) −8127.55 −1.15130
\(369\) 0 0
\(370\) 12149.4 1.70708
\(371\) −4532.98 −0.634341
\(372\) 0 0
\(373\) −4222.06 −0.586086 −0.293043 0.956099i \(-0.594668\pi\)
−0.293043 + 0.956099i \(0.594668\pi\)
\(374\) −886.241 −0.122531
\(375\) 0 0
\(376\) −2131.20 −0.292310
\(377\) 0 0
\(378\) 0 0
\(379\) −2627.37 −0.356092 −0.178046 0.984022i \(-0.556978\pi\)
−0.178046 + 0.984022i \(0.556978\pi\)
\(380\) 4909.38 0.662752
\(381\) 0 0
\(382\) −4366.56 −0.584850
\(383\) −12709.7 −1.69566 −0.847829 0.530270i \(-0.822091\pi\)
−0.847829 + 0.530270i \(0.822091\pi\)
\(384\) 0 0
\(385\) −1854.53 −0.245496
\(386\) −14665.6 −1.93383
\(387\) 0 0
\(388\) 743.907 0.0973354
\(389\) 13138.4 1.71245 0.856223 0.516607i \(-0.172805\pi\)
0.856223 + 0.516607i \(0.172805\pi\)
\(390\) 0 0
\(391\) −1981.03 −0.256227
\(392\) −990.782 −0.127658
\(393\) 0 0
\(394\) −6144.64 −0.785691
\(395\) 1200.69 0.152945
\(396\) 0 0
\(397\) −10395.1 −1.31414 −0.657069 0.753830i \(-0.728204\pi\)
−0.657069 + 0.753830i \(0.728204\pi\)
\(398\) −11176.6 −1.40761
\(399\) 0 0
\(400\) 2774.68 0.346835
\(401\) −6784.67 −0.844913 −0.422457 0.906383i \(-0.638832\pi\)
−0.422457 + 0.906383i \(0.638832\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 9105.65 1.12134
\(405\) 0 0
\(406\) −1317.59 −0.161061
\(407\) 4461.35 0.543344
\(408\) 0 0
\(409\) −8002.13 −0.967432 −0.483716 0.875225i \(-0.660713\pi\)
−0.483716 + 0.875225i \(0.660713\pi\)
\(410\) 12078.8 1.45495
\(411\) 0 0
\(412\) −2889.82 −0.345561
\(413\) −9191.61 −1.09513
\(414\) 0 0
\(415\) 13692.9 1.61966
\(416\) 0 0
\(417\) 0 0
\(418\) 4454.86 0.521279
\(419\) −12879.7 −1.50170 −0.750852 0.660470i \(-0.770357\pi\)
−0.750852 + 0.660470i \(0.770357\pi\)
\(420\) 0 0
\(421\) 12575.3 1.45577 0.727887 0.685697i \(-0.240502\pi\)
0.727887 + 0.685697i \(0.240502\pi\)
\(422\) −12663.1 −1.46073
\(423\) 0 0
\(424\) −2762.47 −0.316409
\(425\) 676.306 0.0771898
\(426\) 0 0
\(427\) −7509.08 −0.851030
\(428\) −2804.75 −0.316759
\(429\) 0 0
\(430\) −2109.70 −0.236601
\(431\) 7839.30 0.876116 0.438058 0.898947i \(-0.355666\pi\)
0.438058 + 0.898947i \(0.355666\pi\)
\(432\) 0 0
\(433\) 878.419 0.0974922 0.0487461 0.998811i \(-0.484477\pi\)
0.0487461 + 0.998811i \(0.484477\pi\)
\(434\) 10000.5 1.10608
\(435\) 0 0
\(436\) −8723.91 −0.958256
\(437\) 9958.02 1.09006
\(438\) 0 0
\(439\) −8427.48 −0.916222 −0.458111 0.888895i \(-0.651474\pi\)
−0.458111 + 0.888895i \(0.651474\pi\)
\(440\) −1130.18 −0.122453
\(441\) 0 0
\(442\) 0 0
\(443\) −9616.41 −1.03135 −0.515677 0.856783i \(-0.672459\pi\)
−0.515677 + 0.856783i \(0.672459\pi\)
\(444\) 0 0
\(445\) −2340.68 −0.249346
\(446\) 1712.50 0.181814
\(447\) 0 0
\(448\) −2286.48 −0.241129
\(449\) −6147.42 −0.646136 −0.323068 0.946376i \(-0.604714\pi\)
−0.323068 + 0.946376i \(0.604714\pi\)
\(450\) 0 0
\(451\) 4435.41 0.463094
\(452\) 10374.9 1.07964
\(453\) 0 0
\(454\) −8303.85 −0.858411
\(455\) 0 0
\(456\) 0 0
\(457\) −10966.2 −1.12248 −0.561242 0.827652i \(-0.689676\pi\)
−0.561242 + 0.827652i \(0.689676\pi\)
\(458\) 375.272 0.0382867
\(459\) 0 0
\(460\) 5362.14 0.543503
\(461\) 19458.5 1.96588 0.982942 0.183916i \(-0.0588775\pi\)
0.982942 + 0.183916i \(0.0588775\pi\)
\(462\) 0 0
\(463\) 10607.1 1.06469 0.532346 0.846527i \(-0.321310\pi\)
0.532346 + 0.846527i \(0.321310\pi\)
\(464\) −1817.58 −0.181851
\(465\) 0 0
\(466\) −9422.51 −0.936672
\(467\) 958.675 0.0949940 0.0474970 0.998871i \(-0.484876\pi\)
0.0474970 + 0.998871i \(0.484876\pi\)
\(468\) 0 0
\(469\) −14541.3 −1.43168
\(470\) 7865.01 0.771885
\(471\) 0 0
\(472\) −5601.52 −0.546252
\(473\) −774.695 −0.0753076
\(474\) 0 0
\(475\) −3399.58 −0.328387
\(476\) −1591.92 −0.153289
\(477\) 0 0
\(478\) 3179.80 0.304269
\(479\) −10862.3 −1.03614 −0.518071 0.855338i \(-0.673350\pi\)
−0.518071 + 0.855338i \(0.673350\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 19217.7 1.81606
\(483\) 0 0
\(484\) −6357.06 −0.597019
\(485\) 1293.43 0.121096
\(486\) 0 0
\(487\) −17700.1 −1.64695 −0.823477 0.567350i \(-0.807969\pi\)
−0.823477 + 0.567350i \(0.807969\pi\)
\(488\) −4576.16 −0.424494
\(489\) 0 0
\(490\) 3656.39 0.337100
\(491\) −16743.5 −1.53895 −0.769476 0.638675i \(-0.779483\pi\)
−0.769476 + 0.638675i \(0.779483\pi\)
\(492\) 0 0
\(493\) −443.021 −0.0404719
\(494\) 0 0
\(495\) 0 0
\(496\) 13795.4 1.24885
\(497\) 16101.0 1.45317
\(498\) 0 0
\(499\) 8847.23 0.793700 0.396850 0.917884i \(-0.370103\pi\)
0.396850 + 0.917884i \(0.370103\pi\)
\(500\) −8257.56 −0.738578
\(501\) 0 0
\(502\) 20973.6 1.86473
\(503\) 13132.5 1.16411 0.582056 0.813149i \(-0.302249\pi\)
0.582056 + 0.813149i \(0.302249\pi\)
\(504\) 0 0
\(505\) 15831.9 1.39507
\(506\) 4865.71 0.427485
\(507\) 0 0
\(508\) −4197.76 −0.366625
\(509\) −6678.39 −0.581561 −0.290780 0.956790i \(-0.593915\pi\)
−0.290780 + 0.956790i \(0.593915\pi\)
\(510\) 0 0
\(511\) −8539.12 −0.739233
\(512\) −10553.0 −0.910903
\(513\) 0 0
\(514\) 26625.7 2.28484
\(515\) −5024.51 −0.429915
\(516\) 0 0
\(517\) 2888.09 0.245683
\(518\) 19803.1 1.67973
\(519\) 0 0
\(520\) 0 0
\(521\) −1463.98 −0.123105 −0.0615527 0.998104i \(-0.519605\pi\)
−0.0615527 + 0.998104i \(0.519605\pi\)
\(522\) 0 0
\(523\) 8812.25 0.736774 0.368387 0.929673i \(-0.379910\pi\)
0.368387 + 0.929673i \(0.379910\pi\)
\(524\) 4163.09 0.347071
\(525\) 0 0
\(526\) 11614.2 0.962740
\(527\) 3362.52 0.277938
\(528\) 0 0
\(529\) −1290.61 −0.106074
\(530\) 10194.6 0.835523
\(531\) 0 0
\(532\) 8002.11 0.652134
\(533\) 0 0
\(534\) 0 0
\(535\) −4876.61 −0.394083
\(536\) −8861.74 −0.714121
\(537\) 0 0
\(538\) 13702.7 1.09808
\(539\) 1342.65 0.107295
\(540\) 0 0
\(541\) −15404.2 −1.22418 −0.612088 0.790790i \(-0.709670\pi\)
−0.612088 + 0.790790i \(0.709670\pi\)
\(542\) 8789.59 0.696578
\(543\) 0 0
\(544\) −3999.44 −0.315210
\(545\) −15168.2 −1.19217
\(546\) 0 0
\(547\) −1332.47 −0.104154 −0.0520769 0.998643i \(-0.516584\pi\)
−0.0520769 + 0.998643i \(0.516584\pi\)
\(548\) −14437.1 −1.12540
\(549\) 0 0
\(550\) −1661.11 −0.128782
\(551\) 2226.93 0.172179
\(552\) 0 0
\(553\) 1957.08 0.150495
\(554\) −8523.56 −0.653667
\(555\) 0 0
\(556\) 15659.5 1.19444
\(557\) −8485.98 −0.645534 −0.322767 0.946478i \(-0.604613\pi\)
−0.322767 + 0.946478i \(0.604613\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −11355.7 −0.856905
\(561\) 0 0
\(562\) −17230.0 −1.29325
\(563\) 17985.2 1.34633 0.673166 0.739491i \(-0.264934\pi\)
0.673166 + 0.739491i \(0.264934\pi\)
\(564\) 0 0
\(565\) 18038.9 1.34319
\(566\) −11404.1 −0.846909
\(567\) 0 0
\(568\) 9812.21 0.724844
\(569\) 16723.5 1.23214 0.616068 0.787693i \(-0.288725\pi\)
0.616068 + 0.787693i \(0.288725\pi\)
\(570\) 0 0
\(571\) 16036.9 1.17535 0.587674 0.809097i \(-0.300044\pi\)
0.587674 + 0.809097i \(0.300044\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 19688.0 1.43164
\(575\) −3713.11 −0.269300
\(576\) 0 0
\(577\) 20293.1 1.46415 0.732074 0.681225i \(-0.238553\pi\)
0.732074 + 0.681225i \(0.238553\pi\)
\(578\) 16687.3 1.20086
\(579\) 0 0
\(580\) 1199.15 0.0858479
\(581\) 22319.0 1.59372
\(582\) 0 0
\(583\) 3743.54 0.265938
\(584\) −5203.88 −0.368730
\(585\) 0 0
\(586\) 8679.89 0.611882
\(587\) −9014.69 −0.633860 −0.316930 0.948449i \(-0.602652\pi\)
−0.316930 + 0.948449i \(0.602652\pi\)
\(588\) 0 0
\(589\) −16902.3 −1.18243
\(590\) 20671.9 1.44246
\(591\) 0 0
\(592\) 27317.9 1.89655
\(593\) 2114.55 0.146432 0.0732161 0.997316i \(-0.476674\pi\)
0.0732161 + 0.997316i \(0.476674\pi\)
\(594\) 0 0
\(595\) −2767.87 −0.190708
\(596\) 10899.6 0.749102
\(597\) 0 0
\(598\) 0 0
\(599\) −6336.81 −0.432245 −0.216123 0.976366i \(-0.569341\pi\)
−0.216123 + 0.976366i \(0.569341\pi\)
\(600\) 0 0
\(601\) 14789.6 1.00379 0.501896 0.864928i \(-0.332636\pi\)
0.501896 + 0.864928i \(0.332636\pi\)
\(602\) −3438.73 −0.232811
\(603\) 0 0
\(604\) −2012.73 −0.135591
\(605\) −11053.0 −0.742757
\(606\) 0 0
\(607\) −4865.13 −0.325320 −0.162660 0.986682i \(-0.552007\pi\)
−0.162660 + 0.986682i \(0.552007\pi\)
\(608\) 20103.9 1.34099
\(609\) 0 0
\(610\) 16887.9 1.12094
\(611\) 0 0
\(612\) 0 0
\(613\) 7699.32 0.507296 0.253648 0.967297i \(-0.418369\pi\)
0.253648 + 0.967297i \(0.418369\pi\)
\(614\) 13550.8 0.890659
\(615\) 0 0
\(616\) −1842.16 −0.120491
\(617\) 12024.2 0.784562 0.392281 0.919845i \(-0.371686\pi\)
0.392281 + 0.919845i \(0.371686\pi\)
\(618\) 0 0
\(619\) 10305.6 0.669170 0.334585 0.942366i \(-0.391404\pi\)
0.334585 + 0.942366i \(0.391404\pi\)
\(620\) −9101.49 −0.589556
\(621\) 0 0
\(622\) 10286.4 0.663098
\(623\) −3815.22 −0.245351
\(624\) 0 0
\(625\) −9906.91 −0.634042
\(626\) −29944.0 −1.91183
\(627\) 0 0
\(628\) −6242.77 −0.396678
\(629\) 6658.52 0.422087
\(630\) 0 0
\(631\) 15380.2 0.970326 0.485163 0.874424i \(-0.338760\pi\)
0.485163 + 0.874424i \(0.338760\pi\)
\(632\) 1192.68 0.0750668
\(633\) 0 0
\(634\) 25228.4 1.58036
\(635\) −7298.63 −0.456122
\(636\) 0 0
\(637\) 0 0
\(638\) 1088.13 0.0675226
\(639\) 0 0
\(640\) −10783.5 −0.666023
\(641\) −11443.0 −0.705101 −0.352551 0.935793i \(-0.614686\pi\)
−0.352551 + 0.935793i \(0.614686\pi\)
\(642\) 0 0
\(643\) −20154.3 −1.23609 −0.618046 0.786142i \(-0.712076\pi\)
−0.618046 + 0.786142i \(0.712076\pi\)
\(644\) 8740.10 0.534795
\(645\) 0 0
\(646\) 6648.83 0.404945
\(647\) 8876.33 0.539358 0.269679 0.962950i \(-0.413082\pi\)
0.269679 + 0.962950i \(0.413082\pi\)
\(648\) 0 0
\(649\) 7590.87 0.459118
\(650\) 0 0
\(651\) 0 0
\(652\) −11110.7 −0.667372
\(653\) −22064.9 −1.32230 −0.661152 0.750252i \(-0.729932\pi\)
−0.661152 + 0.750252i \(0.729932\pi\)
\(654\) 0 0
\(655\) 7238.34 0.431794
\(656\) 27159.0 1.61643
\(657\) 0 0
\(658\) 12819.7 0.759519
\(659\) 30027.8 1.77499 0.887495 0.460817i \(-0.152444\pi\)
0.887495 + 0.460817i \(0.152444\pi\)
\(660\) 0 0
\(661\) −24272.9 −1.42830 −0.714149 0.699994i \(-0.753186\pi\)
−0.714149 + 0.699994i \(0.753186\pi\)
\(662\) −10392.8 −0.610160
\(663\) 0 0
\(664\) 13601.6 0.794945
\(665\) 13913.2 0.811326
\(666\) 0 0
\(667\) 2432.31 0.141198
\(668\) −4422.43 −0.256151
\(669\) 0 0
\(670\) 32703.4 1.88574
\(671\) 6201.35 0.356782
\(672\) 0 0
\(673\) 30335.7 1.73752 0.868762 0.495230i \(-0.164916\pi\)
0.868762 + 0.495230i \(0.164916\pi\)
\(674\) −7142.51 −0.408189
\(675\) 0 0
\(676\) 0 0
\(677\) −9984.71 −0.566829 −0.283415 0.958997i \(-0.591467\pi\)
−0.283415 + 0.958997i \(0.591467\pi\)
\(678\) 0 0
\(679\) 2108.24 0.119156
\(680\) −1686.79 −0.0951254
\(681\) 0 0
\(682\) −8258.87 −0.463707
\(683\) 3099.24 0.173629 0.0868147 0.996224i \(-0.472331\pi\)
0.0868147 + 0.996224i \(0.472331\pi\)
\(684\) 0 0
\(685\) −25101.6 −1.40012
\(686\) 25337.3 1.41018
\(687\) 0 0
\(688\) −4743.63 −0.262862
\(689\) 0 0
\(690\) 0 0
\(691\) −33108.4 −1.82273 −0.911363 0.411604i \(-0.864969\pi\)
−0.911363 + 0.411604i \(0.864969\pi\)
\(692\) −1652.48 −0.0907770
\(693\) 0 0
\(694\) 32251.4 1.76404
\(695\) 27227.1 1.48602
\(696\) 0 0
\(697\) 6619.79 0.359745
\(698\) 9088.89 0.492865
\(699\) 0 0
\(700\) −2983.80 −0.161110
\(701\) 886.423 0.0477600 0.0238800 0.999715i \(-0.492398\pi\)
0.0238800 + 0.999715i \(0.492398\pi\)
\(702\) 0 0
\(703\) −33470.3 −1.79567
\(704\) 1888.28 0.101090
\(705\) 0 0
\(706\) −32330.7 −1.72349
\(707\) 25805.5 1.37272
\(708\) 0 0
\(709\) −31368.8 −1.66161 −0.830803 0.556566i \(-0.812119\pi\)
−0.830803 + 0.556566i \(0.812119\pi\)
\(710\) −36211.0 −1.91405
\(711\) 0 0
\(712\) −2325.06 −0.122381
\(713\) −18461.2 −0.969672
\(714\) 0 0
\(715\) 0 0
\(716\) −9948.04 −0.519240
\(717\) 0 0
\(718\) −30182.2 −1.56879
\(719\) 16101.2 0.835152 0.417576 0.908642i \(-0.362880\pi\)
0.417576 + 0.908642i \(0.362880\pi\)
\(720\) 0 0
\(721\) −8189.77 −0.423028
\(722\) −8278.01 −0.426698
\(723\) 0 0
\(724\) −6452.16 −0.331205
\(725\) −830.370 −0.0425368
\(726\) 0 0
\(727\) −2103.83 −0.107327 −0.0536635 0.998559i \(-0.517090\pi\)
−0.0536635 + 0.998559i \(0.517090\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 19204.4 0.973682
\(731\) −1156.22 −0.0585013
\(732\) 0 0
\(733\) 8104.43 0.408382 0.204191 0.978931i \(-0.434544\pi\)
0.204191 + 0.978931i \(0.434544\pi\)
\(734\) −22983.0 −1.15574
\(735\) 0 0
\(736\) 21958.0 1.09971
\(737\) 12008.9 0.600209
\(738\) 0 0
\(739\) −6096.91 −0.303489 −0.151745 0.988420i \(-0.548489\pi\)
−0.151745 + 0.988420i \(0.548489\pi\)
\(740\) −18022.9 −0.895319
\(741\) 0 0
\(742\) 16616.9 0.822137
\(743\) −37762.3 −1.86455 −0.932277 0.361745i \(-0.882181\pi\)
−0.932277 + 0.361745i \(0.882181\pi\)
\(744\) 0 0
\(745\) 18951.1 0.931964
\(746\) 15477.2 0.759596
\(747\) 0 0
\(748\) 1314.68 0.0642642
\(749\) −7948.71 −0.387770
\(750\) 0 0
\(751\) 18803.3 0.913637 0.456818 0.889560i \(-0.348989\pi\)
0.456818 + 0.889560i \(0.348989\pi\)
\(752\) 17684.4 0.857558
\(753\) 0 0
\(754\) 0 0
\(755\) −3499.52 −0.168690
\(756\) 0 0
\(757\) −19451.0 −0.933893 −0.466947 0.884286i \(-0.654646\pi\)
−0.466947 + 0.884286i \(0.654646\pi\)
\(758\) 9631.37 0.461513
\(759\) 0 0
\(760\) 8478.95 0.404689
\(761\) −7000.32 −0.333458 −0.166729 0.986003i \(-0.553320\pi\)
−0.166729 + 0.986003i \(0.553320\pi\)
\(762\) 0 0
\(763\) −24723.7 −1.17308
\(764\) 6477.53 0.306739
\(765\) 0 0
\(766\) 46591.1 2.19766
\(767\) 0 0
\(768\) 0 0
\(769\) −21957.7 −1.02967 −0.514834 0.857290i \(-0.672146\pi\)
−0.514834 + 0.857290i \(0.672146\pi\)
\(770\) 6798.32 0.318174
\(771\) 0 0
\(772\) 21755.5 1.01425
\(773\) 15048.7 0.700213 0.350107 0.936710i \(-0.386145\pi\)
0.350107 + 0.936710i \(0.386145\pi\)
\(774\) 0 0
\(775\) 6302.49 0.292119
\(776\) 1284.80 0.0594349
\(777\) 0 0
\(778\) −48162.4 −2.21942
\(779\) −33275.7 −1.53046
\(780\) 0 0
\(781\) −13296.9 −0.609222
\(782\) 7262.02 0.332083
\(783\) 0 0
\(784\) 8221.35 0.374515
\(785\) −10854.3 −0.493510
\(786\) 0 0
\(787\) 132.925 0.00602068 0.00301034 0.999995i \(-0.499042\pi\)
0.00301034 + 0.999995i \(0.499042\pi\)
\(788\) 9115.19 0.412075
\(789\) 0 0
\(790\) −4401.47 −0.198224
\(791\) 29402.7 1.32167
\(792\) 0 0
\(793\) 0 0
\(794\) 38106.0 1.70319
\(795\) 0 0
\(796\) 16579.7 0.738258
\(797\) 35040.6 1.55734 0.778672 0.627431i \(-0.215894\pi\)
0.778672 + 0.627431i \(0.215894\pi\)
\(798\) 0 0
\(799\) 4310.43 0.190854
\(800\) −7496.29 −0.331292
\(801\) 0 0
\(802\) 24871.1 1.09505
\(803\) 7052.00 0.309912
\(804\) 0 0
\(805\) 15196.4 0.665344
\(806\) 0 0
\(807\) 0 0
\(808\) 15726.3 0.684715
\(809\) 25088.1 1.09030 0.545149 0.838339i \(-0.316473\pi\)
0.545149 + 0.838339i \(0.316473\pi\)
\(810\) 0 0
\(811\) −16450.7 −0.712286 −0.356143 0.934432i \(-0.615908\pi\)
−0.356143 + 0.934432i \(0.615908\pi\)
\(812\) 1954.56 0.0844726
\(813\) 0 0
\(814\) −16354.4 −0.704201
\(815\) −19318.0 −0.830284
\(816\) 0 0
\(817\) 5811.97 0.248880
\(818\) 29334.1 1.25384
\(819\) 0 0
\(820\) −17918.1 −0.763083
\(821\) 27895.9 1.18584 0.592919 0.805262i \(-0.297976\pi\)
0.592919 + 0.805262i \(0.297976\pi\)
\(822\) 0 0
\(823\) 3885.73 0.164578 0.0822892 0.996608i \(-0.473777\pi\)
0.0822892 + 0.996608i \(0.473777\pi\)
\(824\) −4990.98 −0.211006
\(825\) 0 0
\(826\) 33694.5 1.41935
\(827\) −2853.98 −0.120003 −0.0600016 0.998198i \(-0.519111\pi\)
−0.0600016 + 0.998198i \(0.519111\pi\)
\(828\) 0 0
\(829\) 8704.35 0.364674 0.182337 0.983236i \(-0.441634\pi\)
0.182337 + 0.983236i \(0.441634\pi\)
\(830\) −50195.4 −2.09916
\(831\) 0 0
\(832\) 0 0
\(833\) 2003.89 0.0833501
\(834\) 0 0
\(835\) −7689.26 −0.318680
\(836\) −6608.51 −0.273397
\(837\) 0 0
\(838\) 47214.1 1.94628
\(839\) −21730.7 −0.894194 −0.447097 0.894485i \(-0.647542\pi\)
−0.447097 + 0.894485i \(0.647542\pi\)
\(840\) 0 0
\(841\) −23845.1 −0.977697
\(842\) −46098.2 −1.88676
\(843\) 0 0
\(844\) 18784.9 0.766118
\(845\) 0 0
\(846\) 0 0
\(847\) −18016.0 −0.730858
\(848\) 22922.6 0.928259
\(849\) 0 0
\(850\) −2479.19 −0.100042
\(851\) −36557.1 −1.47258
\(852\) 0 0
\(853\) 36279.1 1.45624 0.728120 0.685450i \(-0.240394\pi\)
0.728120 + 0.685450i \(0.240394\pi\)
\(854\) 27526.7 1.10298
\(855\) 0 0
\(856\) −4844.07 −0.193419
\(857\) 45276.5 1.80469 0.902343 0.431018i \(-0.141845\pi\)
0.902343 + 0.431018i \(0.141845\pi\)
\(858\) 0 0
\(859\) −19162.8 −0.761149 −0.380575 0.924750i \(-0.624274\pi\)
−0.380575 + 0.924750i \(0.624274\pi\)
\(860\) 3129.60 0.124091
\(861\) 0 0
\(862\) −28737.2 −1.13549
\(863\) 11531.7 0.454860 0.227430 0.973794i \(-0.426968\pi\)
0.227430 + 0.973794i \(0.426968\pi\)
\(864\) 0 0
\(865\) −2873.15 −0.112937
\(866\) −3220.09 −0.126355
\(867\) 0 0
\(868\) −14835.1 −0.580111
\(869\) −1616.25 −0.0630926
\(870\) 0 0
\(871\) 0 0
\(872\) −15067.0 −0.585130
\(873\) 0 0
\(874\) −36503.9 −1.41277
\(875\) −23402.0 −0.904151
\(876\) 0 0
\(877\) −5495.83 −0.211609 −0.105804 0.994387i \(-0.533742\pi\)
−0.105804 + 0.994387i \(0.533742\pi\)
\(878\) 30893.3 1.18747
\(879\) 0 0
\(880\) 9378.09 0.359245
\(881\) 9701.52 0.371002 0.185501 0.982644i \(-0.440609\pi\)
0.185501 + 0.982644i \(0.440609\pi\)
\(882\) 0 0
\(883\) 15919.0 0.606702 0.303351 0.952879i \(-0.401895\pi\)
0.303351 + 0.952879i \(0.401895\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 35251.7 1.33669
\(887\) −42705.2 −1.61657 −0.808287 0.588789i \(-0.799605\pi\)
−0.808287 + 0.588789i \(0.799605\pi\)
\(888\) 0 0
\(889\) −11896.5 −0.448815
\(890\) 8580.42 0.323164
\(891\) 0 0
\(892\) −2540.39 −0.0953570
\(893\) −21667.2 −0.811944
\(894\) 0 0
\(895\) −17296.6 −0.645991
\(896\) −17576.7 −0.655353
\(897\) 0 0
\(898\) 22535.1 0.837424
\(899\) −4128.50 −0.153163
\(900\) 0 0
\(901\) 5587.20 0.206589
\(902\) −16259.2 −0.600192
\(903\) 0 0
\(904\) 17918.5 0.659248
\(905\) −11218.3 −0.412055
\(906\) 0 0
\(907\) −3188.34 −0.116722 −0.0583611 0.998296i \(-0.518587\pi\)
−0.0583611 + 0.998296i \(0.518587\pi\)
\(908\) 12318.2 0.450215
\(909\) 0 0
\(910\) 0 0
\(911\) 29528.3 1.07389 0.536947 0.843616i \(-0.319577\pi\)
0.536947 + 0.843616i \(0.319577\pi\)
\(912\) 0 0
\(913\) −18432.1 −0.668141
\(914\) 40199.5 1.45479
\(915\) 0 0
\(916\) −556.692 −0.0200804
\(917\) 11798.2 0.424877
\(918\) 0 0
\(919\) −3132.67 −0.112445 −0.0562227 0.998418i \(-0.517906\pi\)
−0.0562227 + 0.998418i \(0.517906\pi\)
\(920\) 9260.92 0.331874
\(921\) 0 0
\(922\) −71330.6 −2.54788
\(923\) 0 0
\(924\) 0 0
\(925\) 12480.3 0.443621
\(926\) −38883.2 −1.37989
\(927\) 0 0
\(928\) 4910.51 0.173702
\(929\) −21825.6 −0.770803 −0.385401 0.922749i \(-0.625937\pi\)
−0.385401 + 0.922749i \(0.625937\pi\)
\(930\) 0 0
\(931\) −10072.9 −0.354594
\(932\) 13977.7 0.491261
\(933\) 0 0
\(934\) −3514.29 −0.123117
\(935\) 2285.84 0.0799517
\(936\) 0 0
\(937\) 11985.0 0.417857 0.208928 0.977931i \(-0.433002\pi\)
0.208928 + 0.977931i \(0.433002\pi\)
\(938\) 53305.4 1.85553
\(939\) 0 0
\(940\) −11667.3 −0.404834
\(941\) 18229.7 0.631531 0.315766 0.948837i \(-0.397739\pi\)
0.315766 + 0.948837i \(0.397739\pi\)
\(942\) 0 0
\(943\) −36344.5 −1.25508
\(944\) 46480.6 1.60256
\(945\) 0 0
\(946\) 2839.86 0.0976024
\(947\) −1762.07 −0.0604640 −0.0302320 0.999543i \(-0.509625\pi\)
−0.0302320 + 0.999543i \(0.509625\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 12462.1 0.425605
\(951\) 0 0
\(952\) −2749.40 −0.0936014
\(953\) −30840.5 −1.04829 −0.524146 0.851629i \(-0.675615\pi\)
−0.524146 + 0.851629i \(0.675615\pi\)
\(954\) 0 0
\(955\) 11262.4 0.381617
\(956\) −4717.04 −0.159582
\(957\) 0 0
\(958\) 39818.9 1.34289
\(959\) −40914.8 −1.37769
\(960\) 0 0
\(961\) 1544.24 0.0518359
\(962\) 0 0
\(963\) 0 0
\(964\) −28508.3 −0.952479
\(965\) 37826.2 1.26183
\(966\) 0 0
\(967\) 50612.3 1.68312 0.841562 0.540160i \(-0.181636\pi\)
0.841562 + 0.540160i \(0.181636\pi\)
\(968\) −10979.2 −0.364552
\(969\) 0 0
\(970\) −4741.42 −0.156946
\(971\) −46156.7 −1.52548 −0.762739 0.646707i \(-0.776146\pi\)
−0.762739 + 0.646707i \(0.776146\pi\)
\(972\) 0 0
\(973\) 44379.2 1.46221
\(974\) 64884.6 2.13453
\(975\) 0 0
\(976\) 37972.3 1.24535
\(977\) −12445.5 −0.407540 −0.203770 0.979019i \(-0.565319\pi\)
−0.203770 + 0.979019i \(0.565319\pi\)
\(978\) 0 0
\(979\) 3150.79 0.102860
\(980\) −5424.03 −0.176800
\(981\) 0 0
\(982\) 61378.2 1.99456
\(983\) 26127.4 0.847745 0.423873 0.905722i \(-0.360670\pi\)
0.423873 + 0.905722i \(0.360670\pi\)
\(984\) 0 0
\(985\) 15848.5 0.512667
\(986\) 1624.02 0.0524536
\(987\) 0 0
\(988\) 0 0
\(989\) 6347.98 0.204099
\(990\) 0 0
\(991\) 41054.6 1.31599 0.657993 0.753024i \(-0.271406\pi\)
0.657993 + 0.753024i \(0.271406\pi\)
\(992\) −37270.7 −1.19289
\(993\) 0 0
\(994\) −59022.7 −1.88339
\(995\) 28827.1 0.918474
\(996\) 0 0
\(997\) 12412.0 0.394276 0.197138 0.980376i \(-0.436835\pi\)
0.197138 + 0.980376i \(0.436835\pi\)
\(998\) −32432.0 −1.02867
\(999\) 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.1.4 18
3.2 odd 2 inner 1521.4.a.bm.1.15 yes 18
13.12 even 2 1521.4.a.bn.1.15 yes 18
39.38 odd 2 1521.4.a.bn.1.4 yes 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.4.a.bm.1.4 18 1.1 even 1 trivial
1521.4.a.bm.1.15 yes 18 3.2 odd 2 inner
1521.4.a.bn.1.4 yes 18 39.38 odd 2
1521.4.a.bn.1.15 yes 18 13.12 even 2