Properties

Label 2151.4.a.h.1.9
Level $2151$
Weight $4$
Character 2151.1
Self dual yes
Analytic conductor $126.913$
Analytic rank $0$
Dimension $59$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2151 = 3^{2} \cdot 239 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2151.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(126.913108422\)
Analytic rank: \(0\)
Dimension: \(59\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-4.40394 q^{2} +11.3946 q^{4} +1.03938 q^{5} +0.641944 q^{7} -14.9498 q^{8} +O(q^{10})\) \(q-4.40394 q^{2} +11.3946 q^{4} +1.03938 q^{5} +0.641944 q^{7} -14.9498 q^{8} -4.57738 q^{10} -48.9987 q^{11} -36.7063 q^{13} -2.82708 q^{14} -25.3192 q^{16} +37.8766 q^{17} -135.430 q^{19} +11.8434 q^{20} +215.787 q^{22} -107.109 q^{23} -123.920 q^{25} +161.652 q^{26} +7.31473 q^{28} -164.716 q^{29} -178.114 q^{31} +231.103 q^{32} -166.806 q^{34} +0.667226 q^{35} -312.490 q^{37} +596.427 q^{38} -15.5386 q^{40} -128.393 q^{41} -167.661 q^{43} -558.323 q^{44} +471.700 q^{46} -59.1103 q^{47} -342.588 q^{49} +545.734 q^{50} -418.255 q^{52} +261.864 q^{53} -50.9285 q^{55} -9.59694 q^{56} +725.399 q^{58} -716.904 q^{59} +900.978 q^{61} +784.401 q^{62} -815.207 q^{64} -38.1519 q^{65} -397.047 q^{67} +431.590 q^{68} -2.93842 q^{70} +360.948 q^{71} +145.439 q^{73} +1376.18 q^{74} -1543.18 q^{76} -31.4545 q^{77} -227.148 q^{79} -26.3163 q^{80} +565.437 q^{82} +994.304 q^{83} +39.3683 q^{85} +738.368 q^{86} +732.522 q^{88} +323.348 q^{89} -23.5634 q^{91} -1220.47 q^{92} +260.318 q^{94} -140.764 q^{95} -198.509 q^{97} +1508.74 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.40394 −1.55703 −0.778513 0.627628i \(-0.784026\pi\)
−0.778513 + 0.627628i \(0.784026\pi\)
\(3\) 0 0
\(4\) 11.3946 1.42433
\(5\) 1.03938 0.0929653 0.0464826 0.998919i \(-0.485199\pi\)
0.0464826 + 0.998919i \(0.485199\pi\)
\(6\) 0 0
\(7\) 0.641944 0.0346617 0.0173309 0.999850i \(-0.494483\pi\)
0.0173309 + 0.999850i \(0.494483\pi\)
\(8\) −14.9498 −0.660694
\(9\) 0 0
\(10\) −4.57738 −0.144749
\(11\) −48.9987 −1.34306 −0.671531 0.740977i \(-0.734363\pi\)
−0.671531 + 0.740977i \(0.734363\pi\)
\(12\) 0 0
\(13\) −36.7063 −0.783115 −0.391557 0.920154i \(-0.628064\pi\)
−0.391557 + 0.920154i \(0.628064\pi\)
\(14\) −2.82708 −0.0539692
\(15\) 0 0
\(16\) −25.3192 −0.395612
\(17\) 37.8766 0.540378 0.270189 0.962807i \(-0.412914\pi\)
0.270189 + 0.962807i \(0.412914\pi\)
\(18\) 0 0
\(19\) −135.430 −1.63526 −0.817629 0.575746i \(-0.804712\pi\)
−0.817629 + 0.575746i \(0.804712\pi\)
\(20\) 11.8434 0.132413
\(21\) 0 0
\(22\) 215.787 2.09118
\(23\) −107.109 −0.971031 −0.485516 0.874228i \(-0.661368\pi\)
−0.485516 + 0.874228i \(0.661368\pi\)
\(24\) 0 0
\(25\) −123.920 −0.991357
\(26\) 161.652 1.21933
\(27\) 0 0
\(28\) 7.31473 0.0493698
\(29\) −164.716 −1.05473 −0.527363 0.849640i \(-0.676819\pi\)
−0.527363 + 0.849640i \(0.676819\pi\)
\(30\) 0 0
\(31\) −178.114 −1.03194 −0.515970 0.856606i \(-0.672569\pi\)
−0.515970 + 0.856606i \(0.672569\pi\)
\(32\) 231.103 1.27667
\(33\) 0 0
\(34\) −166.806 −0.841382
\(35\) 0.667226 0.00322234
\(36\) 0 0
\(37\) −312.490 −1.38846 −0.694229 0.719754i \(-0.744255\pi\)
−0.694229 + 0.719754i \(0.744255\pi\)
\(38\) 596.427 2.54614
\(39\) 0 0
\(40\) −15.5386 −0.0614216
\(41\) −128.393 −0.489066 −0.244533 0.969641i \(-0.578635\pi\)
−0.244533 + 0.969641i \(0.578635\pi\)
\(42\) 0 0
\(43\) −167.661 −0.594606 −0.297303 0.954783i \(-0.596087\pi\)
−0.297303 + 0.954783i \(0.596087\pi\)
\(44\) −558.323 −1.91296
\(45\) 0 0
\(46\) 471.700 1.51192
\(47\) −59.1103 −0.183449 −0.0917247 0.995784i \(-0.529238\pi\)
−0.0917247 + 0.995784i \(0.529238\pi\)
\(48\) 0 0
\(49\) −342.588 −0.998799
\(50\) 545.734 1.54357
\(51\) 0 0
\(52\) −418.255 −1.11541
\(53\) 261.864 0.678676 0.339338 0.940665i \(-0.389797\pi\)
0.339338 + 0.940665i \(0.389797\pi\)
\(54\) 0 0
\(55\) −50.9285 −0.124858
\(56\) −9.59694 −0.0229008
\(57\) 0 0
\(58\) 725.399 1.64223
\(59\) −716.904 −1.58191 −0.790957 0.611872i \(-0.790417\pi\)
−0.790957 + 0.611872i \(0.790417\pi\)
\(60\) 0 0
\(61\) 900.978 1.89112 0.945561 0.325446i \(-0.105514\pi\)
0.945561 + 0.325446i \(0.105514\pi\)
\(62\) 784.401 1.60676
\(63\) 0 0
\(64\) −815.207 −1.59220
\(65\) −38.1519 −0.0728024
\(66\) 0 0
\(67\) −397.047 −0.723986 −0.361993 0.932181i \(-0.617904\pi\)
−0.361993 + 0.932181i \(0.617904\pi\)
\(68\) 431.590 0.769677
\(69\) 0 0
\(70\) −2.93842 −0.00501726
\(71\) 360.948 0.603333 0.301666 0.953414i \(-0.402457\pi\)
0.301666 + 0.953414i \(0.402457\pi\)
\(72\) 0 0
\(73\) 145.439 0.233183 0.116592 0.993180i \(-0.462803\pi\)
0.116592 + 0.993180i \(0.462803\pi\)
\(74\) 1376.18 2.16187
\(75\) 0 0
\(76\) −1543.18 −2.32915
\(77\) −31.4545 −0.0465529
\(78\) 0 0
\(79\) −227.148 −0.323496 −0.161748 0.986832i \(-0.551713\pi\)
−0.161748 + 0.986832i \(0.551713\pi\)
\(80\) −26.3163 −0.0367782
\(81\) 0 0
\(82\) 565.437 0.761488
\(83\) 994.304 1.31493 0.657464 0.753486i \(-0.271629\pi\)
0.657464 + 0.753486i \(0.271629\pi\)
\(84\) 0 0
\(85\) 39.3683 0.0502363
\(86\) 738.368 0.925817
\(87\) 0 0
\(88\) 732.522 0.887353
\(89\) 323.348 0.385111 0.192555 0.981286i \(-0.438323\pi\)
0.192555 + 0.981286i \(0.438323\pi\)
\(90\) 0 0
\(91\) −23.5634 −0.0271441
\(92\) −1220.47 −1.38307
\(93\) 0 0
\(94\) 260.318 0.285636
\(95\) −140.764 −0.152022
\(96\) 0 0
\(97\) −198.509 −0.207789 −0.103895 0.994588i \(-0.533130\pi\)
−0.103895 + 0.994588i \(0.533130\pi\)
\(98\) 1508.74 1.55516
\(99\) 0 0
\(100\) −1412.02 −1.41202
\(101\) 1377.89 1.35748 0.678738 0.734380i \(-0.262527\pi\)
0.678738 + 0.734380i \(0.262527\pi\)
\(102\) 0 0
\(103\) −134.668 −0.128828 −0.0644140 0.997923i \(-0.520518\pi\)
−0.0644140 + 0.997923i \(0.520518\pi\)
\(104\) 548.752 0.517399
\(105\) 0 0
\(106\) −1153.23 −1.05672
\(107\) 288.843 0.260967 0.130484 0.991450i \(-0.458347\pi\)
0.130484 + 0.991450i \(0.458347\pi\)
\(108\) 0 0
\(109\) −885.572 −0.778187 −0.389094 0.921198i \(-0.627212\pi\)
−0.389094 + 0.921198i \(0.627212\pi\)
\(110\) 224.286 0.194407
\(111\) 0 0
\(112\) −16.2535 −0.0137126
\(113\) 23.9012 0.0198976 0.00994882 0.999951i \(-0.496833\pi\)
0.00994882 + 0.999951i \(0.496833\pi\)
\(114\) 0 0
\(115\) −111.327 −0.0902722
\(116\) −1876.88 −1.50228
\(117\) 0 0
\(118\) 3157.20 2.46308
\(119\) 24.3147 0.0187304
\(120\) 0 0
\(121\) 1069.88 0.803815
\(122\) −3967.85 −2.94453
\(123\) 0 0
\(124\) −2029.54 −1.46983
\(125\) −258.723 −0.185127
\(126\) 0 0
\(127\) 857.709 0.599286 0.299643 0.954051i \(-0.403132\pi\)
0.299643 + 0.954051i \(0.403132\pi\)
\(128\) 1741.30 1.20243
\(129\) 0 0
\(130\) 168.018 0.113355
\(131\) −1472.96 −0.982392 −0.491196 0.871049i \(-0.663440\pi\)
−0.491196 + 0.871049i \(0.663440\pi\)
\(132\) 0 0
\(133\) −86.9388 −0.0566809
\(134\) 1748.57 1.12727
\(135\) 0 0
\(136\) −566.247 −0.357024
\(137\) 1390.34 0.867041 0.433520 0.901144i \(-0.357271\pi\)
0.433520 + 0.901144i \(0.357271\pi\)
\(138\) 0 0
\(139\) −27.7276 −0.0169196 −0.00845981 0.999964i \(-0.502693\pi\)
−0.00845981 + 0.999964i \(0.502693\pi\)
\(140\) 7.60281 0.00458967
\(141\) 0 0
\(142\) −1589.59 −0.939405
\(143\) 1798.56 1.05177
\(144\) 0 0
\(145\) −171.203 −0.0980528
\(146\) −640.505 −0.363072
\(147\) 0 0
\(148\) −3560.71 −1.97762
\(149\) −995.083 −0.547116 −0.273558 0.961855i \(-0.588201\pi\)
−0.273558 + 0.961855i \(0.588201\pi\)
\(150\) 0 0
\(151\) −659.208 −0.355269 −0.177634 0.984097i \(-0.556844\pi\)
−0.177634 + 0.984097i \(0.556844\pi\)
\(152\) 2024.66 1.08041
\(153\) 0 0
\(154\) 138.523 0.0724840
\(155\) −185.128 −0.0959346
\(156\) 0 0
\(157\) −741.441 −0.376901 −0.188450 0.982083i \(-0.560346\pi\)
−0.188450 + 0.982083i \(0.560346\pi\)
\(158\) 1000.35 0.503692
\(159\) 0 0
\(160\) 240.204 0.118686
\(161\) −68.7579 −0.0336576
\(162\) 0 0
\(163\) −181.036 −0.0869926 −0.0434963 0.999054i \(-0.513850\pi\)
−0.0434963 + 0.999054i \(0.513850\pi\)
\(164\) −1463.00 −0.696591
\(165\) 0 0
\(166\) −4378.85 −2.04738
\(167\) 882.972 0.409140 0.204570 0.978852i \(-0.434420\pi\)
0.204570 + 0.978852i \(0.434420\pi\)
\(168\) 0 0
\(169\) −849.649 −0.386732
\(170\) −173.375 −0.0782193
\(171\) 0 0
\(172\) −1910.44 −0.846916
\(173\) 589.731 0.259170 0.129585 0.991568i \(-0.458635\pi\)
0.129585 + 0.991568i \(0.458635\pi\)
\(174\) 0 0
\(175\) −79.5495 −0.0343622
\(176\) 1240.61 0.531332
\(177\) 0 0
\(178\) −1424.00 −0.599627
\(179\) −2060.21 −0.860263 −0.430132 0.902766i \(-0.641533\pi\)
−0.430132 + 0.902766i \(0.641533\pi\)
\(180\) 0 0
\(181\) −1514.84 −0.622083 −0.311041 0.950396i \(-0.600678\pi\)
−0.311041 + 0.950396i \(0.600678\pi\)
\(182\) 103.772 0.0422641
\(183\) 0 0
\(184\) 1601.26 0.641555
\(185\) −324.796 −0.129078
\(186\) 0 0
\(187\) −1855.90 −0.725760
\(188\) −673.541 −0.261293
\(189\) 0 0
\(190\) 619.916 0.236702
\(191\) 1934.29 0.732777 0.366388 0.930462i \(-0.380594\pi\)
0.366388 + 0.930462i \(0.380594\pi\)
\(192\) 0 0
\(193\) 4952.41 1.84706 0.923530 0.383526i \(-0.125290\pi\)
0.923530 + 0.383526i \(0.125290\pi\)
\(194\) 874.222 0.323534
\(195\) 0 0
\(196\) −3903.67 −1.42262
\(197\) −1761.04 −0.636899 −0.318449 0.947940i \(-0.603162\pi\)
−0.318449 + 0.947940i \(0.603162\pi\)
\(198\) 0 0
\(199\) −3690.29 −1.31456 −0.657281 0.753645i \(-0.728294\pi\)
−0.657281 + 0.753645i \(0.728294\pi\)
\(200\) 1852.58 0.654984
\(201\) 0 0
\(202\) −6068.14 −2.11363
\(203\) −105.739 −0.0365586
\(204\) 0 0
\(205\) −133.450 −0.0454661
\(206\) 593.071 0.200588
\(207\) 0 0
\(208\) 929.373 0.309810
\(209\) 6635.92 2.19625
\(210\) 0 0
\(211\) −5426.38 −1.77046 −0.885231 0.465151i \(-0.846000\pi\)
−0.885231 + 0.465151i \(0.846000\pi\)
\(212\) 2983.85 0.966659
\(213\) 0 0
\(214\) −1272.04 −0.406333
\(215\) −174.264 −0.0552777
\(216\) 0 0
\(217\) −114.339 −0.0357689
\(218\) 3900.00 1.21166
\(219\) 0 0
\(220\) −580.312 −0.177839
\(221\) −1390.31 −0.423178
\(222\) 0 0
\(223\) 2368.65 0.711286 0.355643 0.934622i \(-0.384262\pi\)
0.355643 + 0.934622i \(0.384262\pi\)
\(224\) 148.355 0.0442517
\(225\) 0 0
\(226\) −105.259 −0.0309812
\(227\) 4653.98 1.36077 0.680387 0.732853i \(-0.261812\pi\)
0.680387 + 0.732853i \(0.261812\pi\)
\(228\) 0 0
\(229\) −2760.19 −0.796500 −0.398250 0.917277i \(-0.630382\pi\)
−0.398250 + 0.917277i \(0.630382\pi\)
\(230\) 490.277 0.140556
\(231\) 0 0
\(232\) 2462.48 0.696851
\(233\) −4125.32 −1.15991 −0.579955 0.814649i \(-0.696930\pi\)
−0.579955 + 0.814649i \(0.696930\pi\)
\(234\) 0 0
\(235\) −61.4382 −0.0170544
\(236\) −8168.87 −2.25317
\(237\) 0 0
\(238\) −107.080 −0.0291638
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) −3229.52 −0.863202 −0.431601 0.902065i \(-0.642051\pi\)
−0.431601 + 0.902065i \(0.642051\pi\)
\(242\) −4711.67 −1.25156
\(243\) 0 0
\(244\) 10266.3 2.69358
\(245\) −356.080 −0.0928536
\(246\) 0 0
\(247\) 4971.15 1.28059
\(248\) 2662.77 0.681797
\(249\) 0 0
\(250\) 1139.40 0.288248
\(251\) 1164.25 0.292777 0.146389 0.989227i \(-0.453235\pi\)
0.146389 + 0.989227i \(0.453235\pi\)
\(252\) 0 0
\(253\) 5248.20 1.30416
\(254\) −3777.29 −0.933105
\(255\) 0 0
\(256\) −1146.91 −0.280008
\(257\) −7690.46 −1.86661 −0.933303 0.359090i \(-0.883087\pi\)
−0.933303 + 0.359090i \(0.883087\pi\)
\(258\) 0 0
\(259\) −200.601 −0.0481264
\(260\) −434.727 −0.103695
\(261\) 0 0
\(262\) 6486.83 1.52961
\(263\) −3236.93 −0.758927 −0.379463 0.925207i \(-0.623891\pi\)
−0.379463 + 0.925207i \(0.623891\pi\)
\(264\) 0 0
\(265\) 272.177 0.0630933
\(266\) 382.873 0.0882536
\(267\) 0 0
\(268\) −4524.22 −1.03120
\(269\) −709.861 −0.160896 −0.0804479 0.996759i \(-0.525635\pi\)
−0.0804479 + 0.996759i \(0.525635\pi\)
\(270\) 0 0
\(271\) −6243.22 −1.39944 −0.699721 0.714416i \(-0.746692\pi\)
−0.699721 + 0.714416i \(0.746692\pi\)
\(272\) −959.005 −0.213780
\(273\) 0 0
\(274\) −6122.96 −1.35001
\(275\) 6071.91 1.33145
\(276\) 0 0
\(277\) 5525.13 1.19846 0.599229 0.800578i \(-0.295474\pi\)
0.599229 + 0.800578i \(0.295474\pi\)
\(278\) 122.111 0.0263443
\(279\) 0 0
\(280\) −9.97490 −0.00212898
\(281\) −148.471 −0.0315197 −0.0157598 0.999876i \(-0.505017\pi\)
−0.0157598 + 0.999876i \(0.505017\pi\)
\(282\) 0 0
\(283\) −2136.10 −0.448685 −0.224342 0.974510i \(-0.572023\pi\)
−0.224342 + 0.974510i \(0.572023\pi\)
\(284\) 4112.87 0.859346
\(285\) 0 0
\(286\) −7920.75 −1.63764
\(287\) −82.4215 −0.0169519
\(288\) 0 0
\(289\) −3478.36 −0.707992
\(290\) 753.968 0.152671
\(291\) 0 0
\(292\) 1657.23 0.332130
\(293\) 5523.29 1.10128 0.550639 0.834744i \(-0.314384\pi\)
0.550639 + 0.834744i \(0.314384\pi\)
\(294\) 0 0
\(295\) −745.138 −0.147063
\(296\) 4671.66 0.917347
\(297\) 0 0
\(298\) 4382.28 0.851875
\(299\) 3931.56 0.760429
\(300\) 0 0
\(301\) −107.629 −0.0206101
\(302\) 2903.11 0.553163
\(303\) 0 0
\(304\) 3428.99 0.646928
\(305\) 936.461 0.175809
\(306\) 0 0
\(307\) −1415.87 −0.263218 −0.131609 0.991302i \(-0.542014\pi\)
−0.131609 + 0.991302i \(0.542014\pi\)
\(308\) −358.413 −0.0663067
\(309\) 0 0
\(310\) 815.293 0.149373
\(311\) −6245.37 −1.13872 −0.569361 0.822088i \(-0.692809\pi\)
−0.569361 + 0.822088i \(0.692809\pi\)
\(312\) 0 0
\(313\) −3634.14 −0.656273 −0.328137 0.944630i \(-0.606421\pi\)
−0.328137 + 0.944630i \(0.606421\pi\)
\(314\) 3265.26 0.586844
\(315\) 0 0
\(316\) −2588.27 −0.460765
\(317\) 1405.97 0.249107 0.124553 0.992213i \(-0.460250\pi\)
0.124553 + 0.992213i \(0.460250\pi\)
\(318\) 0 0
\(319\) 8070.89 1.41656
\(320\) −847.313 −0.148019
\(321\) 0 0
\(322\) 302.805 0.0524058
\(323\) −5129.64 −0.883656
\(324\) 0 0
\(325\) 4548.63 0.776346
\(326\) 797.269 0.135450
\(327\) 0 0
\(328\) 1919.46 0.323123
\(329\) −37.9455 −0.00635867
\(330\) 0 0
\(331\) 9057.14 1.50400 0.752002 0.659161i \(-0.229088\pi\)
0.752002 + 0.659161i \(0.229088\pi\)
\(332\) 11329.7 1.87289
\(333\) 0 0
\(334\) −3888.55 −0.637042
\(335\) −412.684 −0.0673056
\(336\) 0 0
\(337\) 1855.81 0.299977 0.149988 0.988688i \(-0.452076\pi\)
0.149988 + 0.988688i \(0.452076\pi\)
\(338\) 3741.80 0.602151
\(339\) 0 0
\(340\) 448.588 0.0715532
\(341\) 8727.35 1.38596
\(342\) 0 0
\(343\) −440.109 −0.0692818
\(344\) 2506.50 0.392853
\(345\) 0 0
\(346\) −2597.14 −0.403535
\(347\) −11986.1 −1.85432 −0.927161 0.374663i \(-0.877759\pi\)
−0.927161 + 0.374663i \(0.877759\pi\)
\(348\) 0 0
\(349\) 6042.16 0.926732 0.463366 0.886167i \(-0.346641\pi\)
0.463366 + 0.886167i \(0.346641\pi\)
\(350\) 350.331 0.0535028
\(351\) 0 0
\(352\) −11323.7 −1.71465
\(353\) −5817.21 −0.877107 −0.438554 0.898705i \(-0.644509\pi\)
−0.438554 + 0.898705i \(0.644509\pi\)
\(354\) 0 0
\(355\) 375.163 0.0560890
\(356\) 3684.44 0.548525
\(357\) 0 0
\(358\) 9073.02 1.33945
\(359\) 3414.05 0.501912 0.250956 0.967998i \(-0.419255\pi\)
0.250956 + 0.967998i \(0.419255\pi\)
\(360\) 0 0
\(361\) 11482.4 1.67407
\(362\) 6671.25 0.968599
\(363\) 0 0
\(364\) −268.496 −0.0386622
\(365\) 151.167 0.0216779
\(366\) 0 0
\(367\) 6466.51 0.919753 0.459876 0.887983i \(-0.347894\pi\)
0.459876 + 0.887983i \(0.347894\pi\)
\(368\) 2711.91 0.384152
\(369\) 0 0
\(370\) 1430.38 0.200978
\(371\) 168.102 0.0235241
\(372\) 0 0
\(373\) 6467.86 0.897836 0.448918 0.893573i \(-0.351810\pi\)
0.448918 + 0.893573i \(0.351810\pi\)
\(374\) 8173.29 1.13003
\(375\) 0 0
\(376\) 883.687 0.121204
\(377\) 6046.12 0.825971
\(378\) 0 0
\(379\) −4816.72 −0.652818 −0.326409 0.945229i \(-0.605839\pi\)
−0.326409 + 0.945229i \(0.605839\pi\)
\(380\) −1603.96 −0.216530
\(381\) 0 0
\(382\) −8518.49 −1.14095
\(383\) −2548.11 −0.339954 −0.169977 0.985448i \(-0.554369\pi\)
−0.169977 + 0.985448i \(0.554369\pi\)
\(384\) 0 0
\(385\) −32.6932 −0.00432780
\(386\) −21810.1 −2.87592
\(387\) 0 0
\(388\) −2261.94 −0.295961
\(389\) 526.077 0.0685685 0.0342843 0.999412i \(-0.489085\pi\)
0.0342843 + 0.999412i \(0.489085\pi\)
\(390\) 0 0
\(391\) −4056.91 −0.524724
\(392\) 5121.62 0.659901
\(393\) 0 0
\(394\) 7755.52 0.991668
\(395\) −236.094 −0.0300739
\(396\) 0 0
\(397\) 385.566 0.0487431 0.0243715 0.999703i \(-0.492242\pi\)
0.0243715 + 0.999703i \(0.492242\pi\)
\(398\) 16251.8 2.04681
\(399\) 0 0
\(400\) 3137.55 0.392193
\(401\) −3502.48 −0.436173 −0.218087 0.975929i \(-0.569982\pi\)
−0.218087 + 0.975929i \(0.569982\pi\)
\(402\) 0 0
\(403\) 6537.89 0.808128
\(404\) 15700.6 1.93350
\(405\) 0 0
\(406\) 465.666 0.0569227
\(407\) 15311.6 1.86479
\(408\) 0 0
\(409\) 14696.0 1.77670 0.888352 0.459163i \(-0.151851\pi\)
0.888352 + 0.459163i \(0.151851\pi\)
\(410\) 587.705 0.0707919
\(411\) 0 0
\(412\) −1534.50 −0.183494
\(413\) −460.212 −0.0548319
\(414\) 0 0
\(415\) 1033.46 0.122243
\(416\) −8482.91 −0.999781
\(417\) 0 0
\(418\) −29224.2 −3.41962
\(419\) −4073.53 −0.474952 −0.237476 0.971393i \(-0.576320\pi\)
−0.237476 + 0.971393i \(0.576320\pi\)
\(420\) 0 0
\(421\) 16058.5 1.85901 0.929503 0.368814i \(-0.120236\pi\)
0.929503 + 0.368814i \(0.120236\pi\)
\(422\) 23897.4 2.75666
\(423\) 0 0
\(424\) −3914.82 −0.448397
\(425\) −4693.65 −0.535707
\(426\) 0 0
\(427\) 578.378 0.0655496
\(428\) 3291.26 0.371703
\(429\) 0 0
\(430\) 767.447 0.0860688
\(431\) 92.4432 0.0103314 0.00516570 0.999987i \(-0.498356\pi\)
0.00516570 + 0.999987i \(0.498356\pi\)
\(432\) 0 0
\(433\) −3712.65 −0.412053 −0.206026 0.978546i \(-0.566053\pi\)
−0.206026 + 0.978546i \(0.566053\pi\)
\(434\) 503.542 0.0556931
\(435\) 0 0
\(436\) −10090.8 −1.10840
\(437\) 14505.8 1.58789
\(438\) 0 0
\(439\) −12513.8 −1.36048 −0.680241 0.732989i \(-0.738125\pi\)
−0.680241 + 0.732989i \(0.738125\pi\)
\(440\) 761.371 0.0824930
\(441\) 0 0
\(442\) 6122.83 0.658899
\(443\) −9236.58 −0.990617 −0.495308 0.868717i \(-0.664945\pi\)
−0.495308 + 0.868717i \(0.664945\pi\)
\(444\) 0 0
\(445\) 336.083 0.0358019
\(446\) −10431.4 −1.10749
\(447\) 0 0
\(448\) −523.318 −0.0551885
\(449\) −1911.77 −0.200939 −0.100470 0.994940i \(-0.532035\pi\)
−0.100470 + 0.994940i \(0.532035\pi\)
\(450\) 0 0
\(451\) 6291.12 0.656845
\(452\) 272.345 0.0283408
\(453\) 0 0
\(454\) −20495.8 −2.11876
\(455\) −24.4914 −0.00252346
\(456\) 0 0
\(457\) 11969.9 1.22523 0.612615 0.790381i \(-0.290117\pi\)
0.612615 + 0.790381i \(0.290117\pi\)
\(458\) 12155.7 1.24017
\(459\) 0 0
\(460\) −1268.53 −0.128577
\(461\) 1178.25 0.119038 0.0595190 0.998227i \(-0.481043\pi\)
0.0595190 + 0.998227i \(0.481043\pi\)
\(462\) 0 0
\(463\) −13223.2 −1.32729 −0.663643 0.748050i \(-0.730990\pi\)
−0.663643 + 0.748050i \(0.730990\pi\)
\(464\) 4170.48 0.417262
\(465\) 0 0
\(466\) 18167.7 1.80601
\(467\) 3290.43 0.326045 0.163022 0.986622i \(-0.447876\pi\)
0.163022 + 0.986622i \(0.447876\pi\)
\(468\) 0 0
\(469\) −254.882 −0.0250946
\(470\) 270.570 0.0265542
\(471\) 0 0
\(472\) 10717.6 1.04516
\(473\) 8215.18 0.798592
\(474\) 0 0
\(475\) 16782.5 1.62112
\(476\) 277.057 0.0266783
\(477\) 0 0
\(478\) 1052.54 0.100716
\(479\) 11053.9 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(480\) 0 0
\(481\) 11470.3 1.08732
\(482\) 14222.6 1.34403
\(483\) 0 0
\(484\) 12190.9 1.14490
\(485\) −206.327 −0.0193172
\(486\) 0 0
\(487\) 16349.3 1.52127 0.760635 0.649180i \(-0.224888\pi\)
0.760635 + 0.649180i \(0.224888\pi\)
\(488\) −13469.4 −1.24945
\(489\) 0 0
\(490\) 1568.15 0.144575
\(491\) 2008.83 0.184638 0.0923189 0.995729i \(-0.470572\pi\)
0.0923189 + 0.995729i \(0.470572\pi\)
\(492\) 0 0
\(493\) −6238.89 −0.569950
\(494\) −21892.6 −1.99392
\(495\) 0 0
\(496\) 4509.70 0.408249
\(497\) 231.708 0.0209126
\(498\) 0 0
\(499\) 15817.0 1.41897 0.709486 0.704719i \(-0.248927\pi\)
0.709486 + 0.704719i \(0.248927\pi\)
\(500\) −2948.06 −0.263682
\(501\) 0 0
\(502\) −5127.30 −0.455862
\(503\) −8353.62 −0.740496 −0.370248 0.928933i \(-0.620727\pi\)
−0.370248 + 0.928933i \(0.620727\pi\)
\(504\) 0 0
\(505\) 1432.15 0.126198
\(506\) −23112.7 −2.03060
\(507\) 0 0
\(508\) 9773.29 0.853582
\(509\) 21578.9 1.87911 0.939557 0.342394i \(-0.111238\pi\)
0.939557 + 0.342394i \(0.111238\pi\)
\(510\) 0 0
\(511\) 93.3639 0.00808253
\(512\) −8879.47 −0.766447
\(513\) 0 0
\(514\) 33868.3 2.90635
\(515\) −139.972 −0.0119765
\(516\) 0 0
\(517\) 2896.33 0.246384
\(518\) 883.433 0.0749340
\(519\) 0 0
\(520\) 570.363 0.0481002
\(521\) 8204.63 0.689926 0.344963 0.938616i \(-0.387891\pi\)
0.344963 + 0.938616i \(0.387891\pi\)
\(522\) 0 0
\(523\) −2955.61 −0.247112 −0.123556 0.992338i \(-0.539430\pi\)
−0.123556 + 0.992338i \(0.539430\pi\)
\(524\) −16783.9 −1.39925
\(525\) 0 0
\(526\) 14255.2 1.18167
\(527\) −6746.34 −0.557638
\(528\) 0 0
\(529\) −694.712 −0.0570980
\(530\) −1198.65 −0.0982379
\(531\) 0 0
\(532\) −990.637 −0.0807323
\(533\) 4712.85 0.382994
\(534\) 0 0
\(535\) 300.218 0.0242609
\(536\) 5935.78 0.478334
\(537\) 0 0
\(538\) 3126.18 0.250519
\(539\) 16786.4 1.34145
\(540\) 0 0
\(541\) 6432.08 0.511158 0.255579 0.966788i \(-0.417734\pi\)
0.255579 + 0.966788i \(0.417734\pi\)
\(542\) 27494.8 2.17897
\(543\) 0 0
\(544\) 8753.37 0.689886
\(545\) −920.449 −0.0723444
\(546\) 0 0
\(547\) −16502.9 −1.28997 −0.644983 0.764197i \(-0.723135\pi\)
−0.644983 + 0.764197i \(0.723135\pi\)
\(548\) 15842.4 1.23495
\(549\) 0 0
\(550\) −26740.3 −2.07311
\(551\) 22307.6 1.72475
\(552\) 0 0
\(553\) −145.817 −0.0112129
\(554\) −24332.3 −1.86603
\(555\) 0 0
\(556\) −315.947 −0.0240991
\(557\) −1129.33 −0.0859092 −0.0429546 0.999077i \(-0.513677\pi\)
−0.0429546 + 0.999077i \(0.513677\pi\)
\(558\) 0 0
\(559\) 6154.21 0.465645
\(560\) −16.8936 −0.00127480
\(561\) 0 0
\(562\) 653.856 0.0490770
\(563\) −2308.16 −0.172784 −0.0863920 0.996261i \(-0.527534\pi\)
−0.0863920 + 0.996261i \(0.527534\pi\)
\(564\) 0 0
\(565\) 24.8425 0.00184979
\(566\) 9407.24 0.698614
\(567\) 0 0
\(568\) −5396.10 −0.398619
\(569\) −7530.78 −0.554845 −0.277423 0.960748i \(-0.589480\pi\)
−0.277423 + 0.960748i \(0.589480\pi\)
\(570\) 0 0
\(571\) −873.313 −0.0640053 −0.0320026 0.999488i \(-0.510188\pi\)
−0.0320026 + 0.999488i \(0.510188\pi\)
\(572\) 20494.0 1.49807
\(573\) 0 0
\(574\) 362.979 0.0263945
\(575\) 13272.9 0.962639
\(576\) 0 0
\(577\) −6904.84 −0.498184 −0.249092 0.968480i \(-0.580132\pi\)
−0.249092 + 0.968480i \(0.580132\pi\)
\(578\) 15318.5 1.10236
\(579\) 0 0
\(580\) −1950.80 −0.139660
\(581\) 638.288 0.0455777
\(582\) 0 0
\(583\) −12831.0 −0.911503
\(584\) −2174.29 −0.154063
\(585\) 0 0
\(586\) −24324.2 −1.71472
\(587\) 16415.9 1.15427 0.577134 0.816649i \(-0.304171\pi\)
0.577134 + 0.816649i \(0.304171\pi\)
\(588\) 0 0
\(589\) 24122.0 1.68749
\(590\) 3281.54 0.228981
\(591\) 0 0
\(592\) 7911.98 0.549291
\(593\) 15126.7 1.04752 0.523761 0.851865i \(-0.324528\pi\)
0.523761 + 0.851865i \(0.324528\pi\)
\(594\) 0 0
\(595\) 25.2722 0.00174128
\(596\) −11338.6 −0.779275
\(597\) 0 0
\(598\) −17314.4 −1.18401
\(599\) −2800.89 −0.191054 −0.0955270 0.995427i \(-0.530454\pi\)
−0.0955270 + 0.995427i \(0.530454\pi\)
\(600\) 0 0
\(601\) 751.290 0.0509913 0.0254956 0.999675i \(-0.491884\pi\)
0.0254956 + 0.999675i \(0.491884\pi\)
\(602\) 473.991 0.0320904
\(603\) 0 0
\(604\) −7511.44 −0.506020
\(605\) 1112.01 0.0747268
\(606\) 0 0
\(607\) −13057.4 −0.873118 −0.436559 0.899676i \(-0.643803\pi\)
−0.436559 + 0.899676i \(0.643803\pi\)
\(608\) −31298.3 −2.08769
\(609\) 0 0
\(610\) −4124.12 −0.273739
\(611\) 2169.72 0.143662
\(612\) 0 0
\(613\) −10446.0 −0.688270 −0.344135 0.938920i \(-0.611828\pi\)
−0.344135 + 0.938920i \(0.611828\pi\)
\(614\) 6235.39 0.409837
\(615\) 0 0
\(616\) 470.238 0.0307572
\(617\) −23077.9 −1.50580 −0.752902 0.658133i \(-0.771346\pi\)
−0.752902 + 0.658133i \(0.771346\pi\)
\(618\) 0 0
\(619\) −15208.7 −0.987541 −0.493771 0.869592i \(-0.664382\pi\)
−0.493771 + 0.869592i \(0.664382\pi\)
\(620\) −2109.47 −0.136643
\(621\) 0 0
\(622\) 27504.2 1.77302
\(623\) 207.572 0.0133486
\(624\) 0 0
\(625\) 15221.0 0.974147
\(626\) 16004.5 1.02184
\(627\) 0 0
\(628\) −8448.46 −0.536831
\(629\) −11836.0 −0.750292
\(630\) 0 0
\(631\) 12789.5 0.806881 0.403440 0.915006i \(-0.367814\pi\)
0.403440 + 0.915006i \(0.367814\pi\)
\(632\) 3395.82 0.213732
\(633\) 0 0
\(634\) −6191.78 −0.387866
\(635\) 891.488 0.0557128
\(636\) 0 0
\(637\) 12575.1 0.782174
\(638\) −35543.7 −2.20562
\(639\) 0 0
\(640\) 1809.88 0.111784
\(641\) 26876.5 1.65610 0.828048 0.560657i \(-0.189451\pi\)
0.828048 + 0.560657i \(0.189451\pi\)
\(642\) 0 0
\(643\) −19135.9 −1.17363 −0.586816 0.809720i \(-0.699619\pi\)
−0.586816 + 0.809720i \(0.699619\pi\)
\(644\) −783.472 −0.0479396
\(645\) 0 0
\(646\) 22590.6 1.37588
\(647\) 21262.7 1.29200 0.645999 0.763338i \(-0.276441\pi\)
0.645999 + 0.763338i \(0.276441\pi\)
\(648\) 0 0
\(649\) 35127.4 2.12461
\(650\) −20031.9 −1.20879
\(651\) 0 0
\(652\) −2062.84 −0.123906
\(653\) −20411.0 −1.22319 −0.611597 0.791169i \(-0.709473\pi\)
−0.611597 + 0.791169i \(0.709473\pi\)
\(654\) 0 0
\(655\) −1530.97 −0.0913283
\(656\) 3250.82 0.193480
\(657\) 0 0
\(658\) 167.110 0.00990062
\(659\) 9829.73 0.581050 0.290525 0.956867i \(-0.406170\pi\)
0.290525 + 0.956867i \(0.406170\pi\)
\(660\) 0 0
\(661\) −12394.9 −0.729355 −0.364678 0.931134i \(-0.618821\pi\)
−0.364678 + 0.931134i \(0.618821\pi\)
\(662\) −39887.1 −2.34177
\(663\) 0 0
\(664\) −14864.7 −0.868766
\(665\) −90.3628 −0.00526935
\(666\) 0 0
\(667\) 17642.5 1.02417
\(668\) 10061.2 0.582751
\(669\) 0 0
\(670\) 1817.44 0.104797
\(671\) −44146.8 −2.53989
\(672\) 0 0
\(673\) 24772.1 1.41886 0.709430 0.704776i \(-0.248952\pi\)
0.709430 + 0.704776i \(0.248952\pi\)
\(674\) −8172.85 −0.467072
\(675\) 0 0
\(676\) −9681.46 −0.550834
\(677\) −25646.0 −1.45592 −0.727959 0.685621i \(-0.759531\pi\)
−0.727959 + 0.685621i \(0.759531\pi\)
\(678\) 0 0
\(679\) −127.432 −0.00720234
\(680\) −588.548 −0.0331909
\(681\) 0 0
\(682\) −38434.7 −2.15798
\(683\) −31682.3 −1.77495 −0.887475 0.460857i \(-0.847542\pi\)
−0.887475 + 0.460857i \(0.847542\pi\)
\(684\) 0 0
\(685\) 1445.09 0.0806047
\(686\) 1938.21 0.107874
\(687\) 0 0
\(688\) 4245.04 0.235233
\(689\) −9612.06 −0.531481
\(690\) 0 0
\(691\) −26145.5 −1.43939 −0.719696 0.694289i \(-0.755719\pi\)
−0.719696 + 0.694289i \(0.755719\pi\)
\(692\) 6719.78 0.369144
\(693\) 0 0
\(694\) 52786.2 2.88723
\(695\) −28.8196 −0.00157294
\(696\) 0 0
\(697\) −4863.10 −0.264280
\(698\) −26609.3 −1.44295
\(699\) 0 0
\(700\) −906.439 −0.0489431
\(701\) −14749.5 −0.794694 −0.397347 0.917668i \(-0.630069\pi\)
−0.397347 + 0.917668i \(0.630069\pi\)
\(702\) 0 0
\(703\) 42320.6 2.27049
\(704\) 39944.1 2.13842
\(705\) 0 0
\(706\) 25618.6 1.36568
\(707\) 884.528 0.0470525
\(708\) 0 0
\(709\) −17166.5 −0.909313 −0.454657 0.890667i \(-0.650238\pi\)
−0.454657 + 0.890667i \(0.650238\pi\)
\(710\) −1652.19 −0.0873320
\(711\) 0 0
\(712\) −4833.99 −0.254440
\(713\) 19077.5 1.00205
\(714\) 0 0
\(715\) 1869.39 0.0977782
\(716\) −23475.3 −1.22530
\(717\) 0 0
\(718\) −15035.2 −0.781491
\(719\) −7064.10 −0.366407 −0.183203 0.983075i \(-0.558647\pi\)
−0.183203 + 0.983075i \(0.558647\pi\)
\(720\) 0 0
\(721\) −86.4496 −0.00446540
\(722\) −50567.8 −2.60656
\(723\) 0 0
\(724\) −17261.0 −0.886052
\(725\) 20411.6 1.04561
\(726\) 0 0
\(727\) 5129.92 0.261703 0.130852 0.991402i \(-0.458229\pi\)
0.130852 + 0.991402i \(0.458229\pi\)
\(728\) 352.268 0.0179340
\(729\) 0 0
\(730\) −665.730 −0.0337531
\(731\) −6350.42 −0.321312
\(732\) 0 0
\(733\) −36422.5 −1.83533 −0.917664 0.397357i \(-0.869928\pi\)
−0.917664 + 0.397357i \(0.869928\pi\)
\(734\) −28478.1 −1.43208
\(735\) 0 0
\(736\) −24753.1 −1.23969
\(737\) 19454.8 0.972358
\(738\) 0 0
\(739\) 2073.74 0.103226 0.0516129 0.998667i \(-0.483564\pi\)
0.0516129 + 0.998667i \(0.483564\pi\)
\(740\) −3700.94 −0.183850
\(741\) 0 0
\(742\) −740.311 −0.0366276
\(743\) 24869.6 1.22797 0.613983 0.789319i \(-0.289566\pi\)
0.613983 + 0.789319i \(0.289566\pi\)
\(744\) 0 0
\(745\) −1034.27 −0.0508628
\(746\) −28484.0 −1.39795
\(747\) 0 0
\(748\) −21147.4 −1.03372
\(749\) 185.421 0.00904557
\(750\) 0 0
\(751\) −3087.87 −0.150037 −0.0750187 0.997182i \(-0.523902\pi\)
−0.0750187 + 0.997182i \(0.523902\pi\)
\(752\) 1496.62 0.0725749
\(753\) 0 0
\(754\) −26626.7 −1.28606
\(755\) −685.170 −0.0330277
\(756\) 0 0
\(757\) 536.550 0.0257612 0.0128806 0.999917i \(-0.495900\pi\)
0.0128806 + 0.999917i \(0.495900\pi\)
\(758\) 21212.5 1.01646
\(759\) 0 0
\(760\) 2104.40 0.100440
\(761\) −35832.5 −1.70687 −0.853435 0.521199i \(-0.825485\pi\)
−0.853435 + 0.521199i \(0.825485\pi\)
\(762\) 0 0
\(763\) −568.488 −0.0269733
\(764\) 22040.6 1.04372
\(765\) 0 0
\(766\) 11221.7 0.529317
\(767\) 26314.9 1.23882
\(768\) 0 0
\(769\) −2680.19 −0.125683 −0.0628415 0.998024i \(-0.520016\pi\)
−0.0628415 + 0.998024i \(0.520016\pi\)
\(770\) 143.979 0.00673849
\(771\) 0 0
\(772\) 56431.0 2.63082
\(773\) −29716.1 −1.38268 −0.691342 0.722528i \(-0.742980\pi\)
−0.691342 + 0.722528i \(0.742980\pi\)
\(774\) 0 0
\(775\) 22071.8 1.02302
\(776\) 2967.68 0.137285
\(777\) 0 0
\(778\) −2316.81 −0.106763
\(779\) 17388.4 0.799748
\(780\) 0 0
\(781\) −17686.0 −0.810313
\(782\) 17866.4 0.817008
\(783\) 0 0
\(784\) 8674.05 0.395137
\(785\) −770.641 −0.0350387
\(786\) 0 0
\(787\) −24465.5 −1.10813 −0.554067 0.832472i \(-0.686925\pi\)
−0.554067 + 0.832472i \(0.686925\pi\)
\(788\) −20066.5 −0.907155
\(789\) 0 0
\(790\) 1039.74 0.0468258
\(791\) 15.3432 0.000689687 0
\(792\) 0 0
\(793\) −33071.5 −1.48096
\(794\) −1698.01 −0.0758942
\(795\) 0 0
\(796\) −42049.6 −1.87237
\(797\) −40634.3 −1.80595 −0.902974 0.429695i \(-0.858621\pi\)
−0.902974 + 0.429695i \(0.858621\pi\)
\(798\) 0 0
\(799\) −2238.90 −0.0991319
\(800\) −28638.2 −1.26564
\(801\) 0 0
\(802\) 15424.7 0.679133
\(803\) −7126.34 −0.313179
\(804\) 0 0
\(805\) −71.4658 −0.00312899
\(806\) −28792.4 −1.25828
\(807\) 0 0
\(808\) −20599.2 −0.896877
\(809\) 29160.3 1.26727 0.633636 0.773631i \(-0.281562\pi\)
0.633636 + 0.773631i \(0.281562\pi\)
\(810\) 0 0
\(811\) −30266.4 −1.31048 −0.655239 0.755422i \(-0.727432\pi\)
−0.655239 + 0.755422i \(0.727432\pi\)
\(812\) −1204.85 −0.0520715
\(813\) 0 0
\(814\) −67431.3 −2.90352
\(815\) −188.165 −0.00808729
\(816\) 0 0
\(817\) 22706.4 0.972334
\(818\) −64720.4 −2.76637
\(819\) 0 0
\(820\) −1520.62 −0.0647588
\(821\) −6700.52 −0.284835 −0.142418 0.989807i \(-0.545488\pi\)
−0.142418 + 0.989807i \(0.545488\pi\)
\(822\) 0 0
\(823\) 26517.6 1.12314 0.561570 0.827429i \(-0.310198\pi\)
0.561570 + 0.827429i \(0.310198\pi\)
\(824\) 2013.27 0.0851159
\(825\) 0 0
\(826\) 2026.75 0.0853747
\(827\) −30173.6 −1.26873 −0.634364 0.773034i \(-0.718738\pi\)
−0.634364 + 0.773034i \(0.718738\pi\)
\(828\) 0 0
\(829\) −3774.02 −0.158115 −0.0790573 0.996870i \(-0.525191\pi\)
−0.0790573 + 0.996870i \(0.525191\pi\)
\(830\) −4551.30 −0.190335
\(831\) 0 0
\(832\) 29923.2 1.24688
\(833\) −12976.1 −0.539728
\(834\) 0 0
\(835\) 917.747 0.0380358
\(836\) 75614.0 3.12819
\(837\) 0 0
\(838\) 17939.6 0.739513
\(839\) −8724.67 −0.359010 −0.179505 0.983757i \(-0.557450\pi\)
−0.179505 + 0.983757i \(0.557450\pi\)
\(840\) 0 0
\(841\) 2742.42 0.112445
\(842\) −70720.4 −2.89452
\(843\) 0 0
\(844\) −61831.7 −2.52172
\(845\) −883.111 −0.0359526
\(846\) 0 0
\(847\) 686.802 0.0278616
\(848\) −6630.19 −0.268493
\(849\) 0 0
\(850\) 20670.5 0.834110
\(851\) 33470.4 1.34824
\(852\) 0 0
\(853\) −26434.7 −1.06109 −0.530543 0.847658i \(-0.678012\pi\)
−0.530543 + 0.847658i \(0.678012\pi\)
\(854\) −2547.14 −0.102062
\(855\) 0 0
\(856\) −4318.14 −0.172419
\(857\) −927.595 −0.0369732 −0.0184866 0.999829i \(-0.505885\pi\)
−0.0184866 + 0.999829i \(0.505885\pi\)
\(858\) 0 0
\(859\) 45670.7 1.81405 0.907023 0.421081i \(-0.138349\pi\)
0.907023 + 0.421081i \(0.138349\pi\)
\(860\) −1985.68 −0.0787337
\(861\) 0 0
\(862\) −407.114 −0.0160863
\(863\) 4030.68 0.158987 0.0794936 0.996835i \(-0.474670\pi\)
0.0794936 + 0.996835i \(0.474670\pi\)
\(864\) 0 0
\(865\) 612.957 0.0240938
\(866\) 16350.3 0.641577
\(867\) 0 0
\(868\) −1302.85 −0.0509467
\(869\) 11130.0 0.434475
\(870\) 0 0
\(871\) 14574.1 0.566964
\(872\) 13239.1 0.514144
\(873\) 0 0
\(874\) −63882.6 −2.47238
\(875\) −166.086 −0.00641682
\(876\) 0 0
\(877\) −28143.7 −1.08363 −0.541816 0.840497i \(-0.682263\pi\)
−0.541816 + 0.840497i \(0.682263\pi\)
\(878\) 55110.0 2.11831
\(879\) 0 0
\(880\) 1289.47 0.0493954
\(881\) −2213.18 −0.0846354 −0.0423177 0.999104i \(-0.513474\pi\)
−0.0423177 + 0.999104i \(0.513474\pi\)
\(882\) 0 0
\(883\) 35722.9 1.36146 0.680732 0.732533i \(-0.261662\pi\)
0.680732 + 0.732533i \(0.261662\pi\)
\(884\) −15842.1 −0.602745
\(885\) 0 0
\(886\) 40677.3 1.54242
\(887\) 10710.8 0.405449 0.202725 0.979236i \(-0.435020\pi\)
0.202725 + 0.979236i \(0.435020\pi\)
\(888\) 0 0
\(889\) 550.601 0.0207723
\(890\) −1480.09 −0.0557445
\(891\) 0 0
\(892\) 26990.0 1.01311
\(893\) 8005.33 0.299987
\(894\) 0 0
\(895\) −2141.34 −0.0799746
\(896\) 1117.82 0.0416782
\(897\) 0 0
\(898\) 8419.29 0.312868
\(899\) 29338.2 1.08841
\(900\) 0 0
\(901\) 9918.52 0.366741
\(902\) −27705.7 −1.02273
\(903\) 0 0
\(904\) −357.318 −0.0131463
\(905\) −1574.50 −0.0578321
\(906\) 0 0
\(907\) 1897.49 0.0694655 0.0347327 0.999397i \(-0.488942\pi\)
0.0347327 + 0.999397i \(0.488942\pi\)
\(908\) 53030.5 1.93819
\(909\) 0 0
\(910\) 107.858 0.00392909
\(911\) 29031.1 1.05581 0.527905 0.849303i \(-0.322978\pi\)
0.527905 + 0.849303i \(0.322978\pi\)
\(912\) 0 0
\(913\) −48719.7 −1.76603
\(914\) −52714.9 −1.90772
\(915\) 0 0
\(916\) −31451.4 −1.13448
\(917\) −945.560 −0.0340514
\(918\) 0 0
\(919\) −28486.3 −1.02250 −0.511249 0.859433i \(-0.670817\pi\)
−0.511249 + 0.859433i \(0.670817\pi\)
\(920\) 1664.32 0.0596423
\(921\) 0 0
\(922\) −5188.93 −0.185345
\(923\) −13249.1 −0.472479
\(924\) 0 0
\(925\) 38723.6 1.37646
\(926\) 58234.0 2.06662
\(927\) 0 0
\(928\) −38066.3 −1.34654
\(929\) −10167.6 −0.359084 −0.179542 0.983750i \(-0.557462\pi\)
−0.179542 + 0.983750i \(0.557462\pi\)
\(930\) 0 0
\(931\) 46396.8 1.63329
\(932\) −47006.6 −1.65209
\(933\) 0 0
\(934\) −14490.8 −0.507660
\(935\) −1929.00 −0.0674705
\(936\) 0 0
\(937\) −19728.5 −0.687835 −0.343917 0.939000i \(-0.611754\pi\)
−0.343917 + 0.939000i \(0.611754\pi\)
\(938\) 1122.49 0.0390730
\(939\) 0 0
\(940\) −700.067 −0.0242911
\(941\) 7614.04 0.263773 0.131887 0.991265i \(-0.457897\pi\)
0.131887 + 0.991265i \(0.457897\pi\)
\(942\) 0 0
\(943\) 13752.1 0.474898
\(944\) 18151.4 0.625825
\(945\) 0 0
\(946\) −36179.1 −1.24343
\(947\) −5187.12 −0.177992 −0.0889962 0.996032i \(-0.528366\pi\)
−0.0889962 + 0.996032i \(0.528366\pi\)
\(948\) 0 0
\(949\) −5338.53 −0.182609
\(950\) −73909.1 −2.52413
\(951\) 0 0
\(952\) −363.499 −0.0123751
\(953\) 4786.50 0.162697 0.0813483 0.996686i \(-0.474077\pi\)
0.0813483 + 0.996686i \(0.474077\pi\)
\(954\) 0 0
\(955\) 2010.47 0.0681228
\(956\) −2723.32 −0.0921323
\(957\) 0 0
\(958\) −48680.5 −1.64175
\(959\) 892.519 0.0300531
\(960\) 0 0
\(961\) 1933.49 0.0649018
\(962\) −50514.6 −1.69299
\(963\) 0 0
\(964\) −36799.2 −1.22949
\(965\) 5147.46 0.171712
\(966\) 0 0
\(967\) −26758.4 −0.889858 −0.444929 0.895566i \(-0.646771\pi\)
−0.444929 + 0.895566i \(0.646771\pi\)
\(968\) −15994.5 −0.531076
\(969\) 0 0
\(970\) 908.652 0.0300774
\(971\) 151.922 0.00502102 0.00251051 0.999997i \(-0.499201\pi\)
0.00251051 + 0.999997i \(0.499201\pi\)
\(972\) 0 0
\(973\) −17.7996 −0.000586464 0
\(974\) −72001.3 −2.36866
\(975\) 0 0
\(976\) −22812.0 −0.748151
\(977\) −49782.9 −1.63019 −0.815096 0.579326i \(-0.803316\pi\)
−0.815096 + 0.579326i \(0.803316\pi\)
\(978\) 0 0
\(979\) −15843.7 −0.517227
\(980\) −4057.41 −0.132254
\(981\) 0 0
\(982\) −8846.75 −0.287486
\(983\) 14715.5 0.477469 0.238734 0.971085i \(-0.423268\pi\)
0.238734 + 0.971085i \(0.423268\pi\)
\(984\) 0 0
\(985\) −1830.40 −0.0592095
\(986\) 27475.6 0.887427
\(987\) 0 0
\(988\) 56644.5 1.82399
\(989\) 17958.0 0.577381
\(990\) 0 0
\(991\) −30000.8 −0.961662 −0.480831 0.876813i \(-0.659665\pi\)
−0.480831 + 0.876813i \(0.659665\pi\)
\(992\) −41162.5 −1.31745
\(993\) 0 0
\(994\) −1020.43 −0.0325614
\(995\) −3835.63 −0.122209
\(996\) 0 0
\(997\) −48254.9 −1.53285 −0.766424 0.642335i \(-0.777966\pi\)
−0.766424 + 0.642335i \(0.777966\pi\)
\(998\) −69657.2 −2.20938
\(999\) 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 2151.4.a.h.1.9 yes 59
3.2 odd 2 2151.4.a.g.1.51 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.51 59 3.2 odd 2
2151.4.a.h.1.9 yes 59 1.1 even 1 trivial