Properties

Label 2151.4.a.h.1.11
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 1.11
Character \(\chi\) \(=\) 2151.1

$q$-expansion

\(f(q)\) \(=\) \(q-3.99709 q^{2} +7.97675 q^{4} -4.04840 q^{5} -1.10463 q^{7} +0.0929295 q^{8} +O(q^{10})\) \(q-3.99709 q^{2} +7.97675 q^{4} -4.04840 q^{5} -1.10463 q^{7} +0.0929295 q^{8} +16.1818 q^{10} +47.9991 q^{11} +50.4246 q^{13} +4.41533 q^{14} -64.1855 q^{16} -51.1190 q^{17} -87.9833 q^{19} -32.2931 q^{20} -191.857 q^{22} -141.821 q^{23} -108.610 q^{25} -201.552 q^{26} -8.81139 q^{28} +88.7250 q^{29} +242.373 q^{31} +255.812 q^{32} +204.328 q^{34} +4.47200 q^{35} +93.5246 q^{37} +351.677 q^{38} -0.376216 q^{40} +437.766 q^{41} +173.062 q^{43} +382.877 q^{44} +566.870 q^{46} +147.320 q^{47} -341.780 q^{49} +434.126 q^{50} +402.224 q^{52} +118.071 q^{53} -194.320 q^{55} -0.102653 q^{56} -354.642 q^{58} +674.993 q^{59} +122.013 q^{61} -968.787 q^{62} -509.020 q^{64} -204.139 q^{65} -711.424 q^{67} -407.764 q^{68} -17.8750 q^{70} +1026.79 q^{71} -1224.17 q^{73} -373.827 q^{74} -701.821 q^{76} -53.0214 q^{77} -13.8124 q^{79} +259.849 q^{80} -1749.79 q^{82} -113.011 q^{83} +206.950 q^{85} -691.743 q^{86} +4.46053 q^{88} -1140.93 q^{89} -55.7007 q^{91} -1131.27 q^{92} -588.853 q^{94} +356.192 q^{95} -476.494 q^{97} +1366.13 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} + O(q^{10}) \) \( 59q + 8q^{2} + 238q^{4} + 80q^{5} - 10q^{7} + 96q^{8} - 36q^{10} + 132q^{11} + 104q^{13} + 280q^{14} + 822q^{16} + 408q^{17} + 20q^{19} + 800q^{20} - 2q^{22} + 276q^{23} + 1477q^{25} + 780q^{26} + 224q^{28} + 696q^{29} - 380q^{31} + 896q^{32} - 72q^{34} + 700q^{35} + 224q^{37} + 988q^{38} - 258q^{40} + 2706q^{41} - 156q^{43} + 1584q^{44} + 428q^{46} + 1316q^{47} + 2135q^{49} + 1400q^{50} + 1092q^{52} + 1484q^{53} - 992q^{55} + 3360q^{56} - 120q^{58} + 3186q^{59} - 254q^{61} + 1240q^{62} + 3054q^{64} + 5120q^{65} + 288q^{67} + 9420q^{68} + 1108q^{70} + 4468q^{71} - 1770q^{73} + 6214q^{74} + 720q^{76} + 6352q^{77} - 746q^{79} + 7040q^{80} + 276q^{82} + 5484q^{83} + 588q^{85} + 10152q^{86} + 1186q^{88} + 11570q^{89} + 1768q^{91} + 15366q^{92} - 2142q^{94} + 5736q^{95} + 2390q^{97} + 6912q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.99709 −1.41319 −0.706593 0.707620i \(-0.749769\pi\)
−0.706593 + 0.707620i \(0.749769\pi\)
\(3\) 0 0
\(4\) 7.97675 0.997094
\(5\) −4.04840 −0.362100 −0.181050 0.983474i \(-0.557950\pi\)
−0.181050 + 0.983474i \(0.557950\pi\)
\(6\) 0 0
\(7\) −1.10463 −0.0596446 −0.0298223 0.999555i \(-0.509494\pi\)
−0.0298223 + 0.999555i \(0.509494\pi\)
\(8\) 0.0929295 0.00410694
\(9\) 0 0
\(10\) 16.1818 0.511715
\(11\) 47.9991 1.31566 0.657830 0.753166i \(-0.271474\pi\)
0.657830 + 0.753166i \(0.271474\pi\)
\(12\) 0 0
\(13\) 50.4246 1.07579 0.537894 0.843012i \(-0.319220\pi\)
0.537894 + 0.843012i \(0.319220\pi\)
\(14\) 4.41533 0.0842890
\(15\) 0 0
\(16\) −64.1855 −1.00290
\(17\) −51.1190 −0.729305 −0.364653 0.931144i \(-0.618812\pi\)
−0.364653 + 0.931144i \(0.618812\pi\)
\(18\) 0 0
\(19\) −87.9833 −1.06235 −0.531177 0.847261i \(-0.678250\pi\)
−0.531177 + 0.847261i \(0.678250\pi\)
\(20\) −32.2931 −0.361048
\(21\) 0 0
\(22\) −191.857 −1.85927
\(23\) −141.821 −1.28572 −0.642862 0.765982i \(-0.722253\pi\)
−0.642862 + 0.765982i \(0.722253\pi\)
\(24\) 0 0
\(25\) −108.610 −0.868884
\(26\) −201.552 −1.52029
\(27\) 0 0
\(28\) −8.81139 −0.0594713
\(29\) 88.7250 0.568132 0.284066 0.958805i \(-0.408317\pi\)
0.284066 + 0.958805i \(0.408317\pi\)
\(30\) 0 0
\(31\) 242.373 1.40424 0.702120 0.712058i \(-0.252237\pi\)
0.702120 + 0.712058i \(0.252237\pi\)
\(32\) 255.812 1.41317
\(33\) 0 0
\(34\) 204.328 1.03064
\(35\) 4.47200 0.0215973
\(36\) 0 0
\(37\) 93.5246 0.415550 0.207775 0.978177i \(-0.433378\pi\)
0.207775 + 0.978177i \(0.433378\pi\)
\(38\) 351.677 1.50130
\(39\) 0 0
\(40\) −0.376216 −0.00148712
\(41\) 437.766 1.66750 0.833750 0.552142i \(-0.186189\pi\)
0.833750 + 0.552142i \(0.186189\pi\)
\(42\) 0 0
\(43\) 173.062 0.613759 0.306880 0.951748i \(-0.400715\pi\)
0.306880 + 0.951748i \(0.400715\pi\)
\(44\) 382.877 1.31184
\(45\) 0 0
\(46\) 566.870 1.81697
\(47\) 147.320 0.457210 0.228605 0.973519i \(-0.426584\pi\)
0.228605 + 0.973519i \(0.426584\pi\)
\(48\) 0 0
\(49\) −341.780 −0.996443
\(50\) 434.126 1.22789
\(51\) 0 0
\(52\) 402.224 1.07266
\(53\) 118.071 0.306006 0.153003 0.988226i \(-0.451106\pi\)
0.153003 + 0.988226i \(0.451106\pi\)
\(54\) 0 0
\(55\) −194.320 −0.476401
\(56\) −0.102653 −0.000244957 0
\(57\) 0 0
\(58\) −354.642 −0.802875
\(59\) 674.993 1.48943 0.744717 0.667381i \(-0.232585\pi\)
0.744717 + 0.667381i \(0.232585\pi\)
\(60\) 0 0
\(61\) 122.013 0.256101 0.128050 0.991768i \(-0.459128\pi\)
0.128050 + 0.991768i \(0.459128\pi\)
\(62\) −968.787 −1.98445
\(63\) 0 0
\(64\) −509.020 −0.994179
\(65\) −204.139 −0.389543
\(66\) 0 0
\(67\) −711.424 −1.29723 −0.648614 0.761117i \(-0.724651\pi\)
−0.648614 + 0.761117i \(0.724651\pi\)
\(68\) −407.764 −0.727186
\(69\) 0 0
\(70\) −17.8750 −0.0305210
\(71\) 1026.79 1.71631 0.858155 0.513391i \(-0.171611\pi\)
0.858155 + 0.513391i \(0.171611\pi\)
\(72\) 0 0
\(73\) −1224.17 −1.96272 −0.981358 0.192190i \(-0.938441\pi\)
−0.981358 + 0.192190i \(0.938441\pi\)
\(74\) −373.827 −0.587250
\(75\) 0 0
\(76\) −701.821 −1.05927
\(77\) −53.0214 −0.0784721
\(78\) 0 0
\(79\) −13.8124 −0.0196711 −0.00983556 0.999952i \(-0.503131\pi\)
−0.00983556 + 0.999952i \(0.503131\pi\)
\(80\) 259.849 0.363149
\(81\) 0 0
\(82\) −1749.79 −2.35649
\(83\) −113.011 −0.149452 −0.0747262 0.997204i \(-0.523808\pi\)
−0.0747262 + 0.997204i \(0.523808\pi\)
\(84\) 0 0
\(85\) 206.950 0.264081
\(86\) −691.743 −0.867356
\(87\) 0 0
\(88\) 4.46053 0.00540334
\(89\) −1140.93 −1.35886 −0.679431 0.733739i \(-0.737773\pi\)
−0.679431 + 0.733739i \(0.737773\pi\)
\(90\) 0 0
\(91\) −55.7007 −0.0641651
\(92\) −1131.27 −1.28199
\(93\) 0 0
\(94\) −588.853 −0.646122
\(95\) 356.192 0.384679
\(96\) 0 0
\(97\) −476.494 −0.498770 −0.249385 0.968404i \(-0.580228\pi\)
−0.249385 + 0.968404i \(0.580228\pi\)
\(98\) 1366.13 1.40816
\(99\) 0 0
\(100\) −866.358 −0.866358
\(101\) 27.6630 0.0272532 0.0136266 0.999907i \(-0.495662\pi\)
0.0136266 + 0.999907i \(0.495662\pi\)
\(102\) 0 0
\(103\) 535.926 0.512683 0.256341 0.966586i \(-0.417483\pi\)
0.256341 + 0.966586i \(0.417483\pi\)
\(104\) 4.68593 0.00441820
\(105\) 0 0
\(106\) −471.941 −0.432443
\(107\) 507.713 0.458715 0.229357 0.973342i \(-0.426338\pi\)
0.229357 + 0.973342i \(0.426338\pi\)
\(108\) 0 0
\(109\) −468.604 −0.411781 −0.205890 0.978575i \(-0.566009\pi\)
−0.205890 + 0.978575i \(0.566009\pi\)
\(110\) 776.713 0.673243
\(111\) 0 0
\(112\) 70.9015 0.0598175
\(113\) −275.943 −0.229722 −0.114861 0.993382i \(-0.536642\pi\)
−0.114861 + 0.993382i \(0.536642\pi\)
\(114\) 0 0
\(115\) 574.147 0.465561
\(116\) 707.737 0.566480
\(117\) 0 0
\(118\) −2698.01 −2.10485
\(119\) 56.4678 0.0434991
\(120\) 0 0
\(121\) 972.912 0.730963
\(122\) −487.697 −0.361918
\(123\) 0 0
\(124\) 1933.35 1.40016
\(125\) 945.749 0.676723
\(126\) 0 0
\(127\) 1511.06 1.05578 0.527892 0.849311i \(-0.322982\pi\)
0.527892 + 0.849311i \(0.322982\pi\)
\(128\) −11.8949 −0.00821385
\(129\) 0 0
\(130\) 815.962 0.550497
\(131\) −1892.47 −1.26218 −0.631091 0.775709i \(-0.717393\pi\)
−0.631091 + 0.775709i \(0.717393\pi\)
\(132\) 0 0
\(133\) 97.1893 0.0633638
\(134\) 2843.63 1.83322
\(135\) 0 0
\(136\) −4.75046 −0.00299521
\(137\) 426.762 0.266137 0.133069 0.991107i \(-0.457517\pi\)
0.133069 + 0.991107i \(0.457517\pi\)
\(138\) 0 0
\(139\) −1346.23 −0.821479 −0.410739 0.911753i \(-0.634729\pi\)
−0.410739 + 0.911753i \(0.634729\pi\)
\(140\) 35.6721 0.0215346
\(141\) 0 0
\(142\) −4104.19 −2.42546
\(143\) 2420.33 1.41537
\(144\) 0 0
\(145\) −359.194 −0.205720
\(146\) 4893.12 2.77368
\(147\) 0 0
\(148\) 746.023 0.414343
\(149\) 2819.32 1.55012 0.775060 0.631887i \(-0.217719\pi\)
0.775060 + 0.631887i \(0.217719\pi\)
\(150\) 0 0
\(151\) −1597.84 −0.861129 −0.430564 0.902560i \(-0.641685\pi\)
−0.430564 + 0.902560i \(0.641685\pi\)
\(152\) −8.17624 −0.00436303
\(153\) 0 0
\(154\) 211.932 0.110896
\(155\) −981.223 −0.508476
\(156\) 0 0
\(157\) 1731.97 0.880422 0.440211 0.897894i \(-0.354904\pi\)
0.440211 + 0.897894i \(0.354904\pi\)
\(158\) 55.2095 0.0277990
\(159\) 0 0
\(160\) −1035.63 −0.511710
\(161\) 156.660 0.0766865
\(162\) 0 0
\(163\) −2310.95 −1.11048 −0.555238 0.831692i \(-0.687373\pi\)
−0.555238 + 0.831692i \(0.687373\pi\)
\(164\) 3491.95 1.66265
\(165\) 0 0
\(166\) 451.715 0.211204
\(167\) −1880.73 −0.871469 −0.435734 0.900075i \(-0.643511\pi\)
−0.435734 + 0.900075i \(0.643511\pi\)
\(168\) 0 0
\(169\) 345.636 0.157322
\(170\) −827.200 −0.373196
\(171\) 0 0
\(172\) 1380.47 0.611976
\(173\) 419.954 0.184558 0.0922789 0.995733i \(-0.470585\pi\)
0.0922789 + 0.995733i \(0.470585\pi\)
\(174\) 0 0
\(175\) 119.975 0.0518243
\(176\) −3080.84 −1.31947
\(177\) 0 0
\(178\) 4560.42 1.92032
\(179\) −1980.03 −0.826783 −0.413391 0.910553i \(-0.635656\pi\)
−0.413391 + 0.910553i \(0.635656\pi\)
\(180\) 0 0
\(181\) 1301.87 0.534627 0.267313 0.963610i \(-0.413864\pi\)
0.267313 + 0.963610i \(0.413864\pi\)
\(182\) 222.641 0.0906771
\(183\) 0 0
\(184\) −13.1793 −0.00528039
\(185\) −378.625 −0.150471
\(186\) 0 0
\(187\) −2453.67 −0.959518
\(188\) 1175.14 0.455881
\(189\) 0 0
\(190\) −1423.73 −0.543623
\(191\) 2560.05 0.969836 0.484918 0.874560i \(-0.338849\pi\)
0.484918 + 0.874560i \(0.338849\pi\)
\(192\) 0 0
\(193\) −974.394 −0.363411 −0.181706 0.983353i \(-0.558162\pi\)
−0.181706 + 0.983353i \(0.558162\pi\)
\(194\) 1904.59 0.704854
\(195\) 0 0
\(196\) −2726.29 −0.993547
\(197\) 757.309 0.273889 0.136944 0.990579i \(-0.456272\pi\)
0.136944 + 0.990579i \(0.456272\pi\)
\(198\) 0 0
\(199\) −1792.51 −0.638533 −0.319266 0.947665i \(-0.603436\pi\)
−0.319266 + 0.947665i \(0.603436\pi\)
\(200\) −10.0931 −0.00356845
\(201\) 0 0
\(202\) −110.572 −0.0385138
\(203\) −98.0087 −0.0338860
\(204\) 0 0
\(205\) −1772.25 −0.603802
\(206\) −2142.15 −0.724516
\(207\) 0 0
\(208\) −3236.52 −1.07891
\(209\) −4223.12 −1.39770
\(210\) 0 0
\(211\) −2277.10 −0.742947 −0.371474 0.928444i \(-0.621147\pi\)
−0.371474 + 0.928444i \(0.621147\pi\)
\(212\) 941.823 0.305116
\(213\) 0 0
\(214\) −2029.38 −0.648249
\(215\) −700.623 −0.222242
\(216\) 0 0
\(217\) −267.733 −0.0837554
\(218\) 1873.05 0.581923
\(219\) 0 0
\(220\) −1550.04 −0.475016
\(221\) −2577.65 −0.784578
\(222\) 0 0
\(223\) 2554.41 0.767066 0.383533 0.923527i \(-0.374707\pi\)
0.383533 + 0.923527i \(0.374707\pi\)
\(224\) −282.578 −0.0842883
\(225\) 0 0
\(226\) 1102.97 0.324639
\(227\) −2642.83 −0.772735 −0.386367 0.922345i \(-0.626270\pi\)
−0.386367 + 0.922345i \(0.626270\pi\)
\(228\) 0 0
\(229\) 4665.27 1.34624 0.673122 0.739531i \(-0.264953\pi\)
0.673122 + 0.739531i \(0.264953\pi\)
\(230\) −2294.92 −0.657924
\(231\) 0 0
\(232\) 8.24516 0.00233328
\(233\) 949.475 0.266962 0.133481 0.991051i \(-0.457384\pi\)
0.133481 + 0.991051i \(0.457384\pi\)
\(234\) 0 0
\(235\) −596.411 −0.165556
\(236\) 5384.25 1.48511
\(237\) 0 0
\(238\) −225.707 −0.0614724
\(239\) −239.000 −0.0646846
\(240\) 0 0
\(241\) 5411.45 1.44640 0.723200 0.690639i \(-0.242671\pi\)
0.723200 + 0.690639i \(0.242671\pi\)
\(242\) −3888.82 −1.03299
\(243\) 0 0
\(244\) 973.267 0.255357
\(245\) 1383.66 0.360812
\(246\) 0 0
\(247\) −4436.52 −1.14287
\(248\) 22.5236 0.00576713
\(249\) 0 0
\(250\) −3780.25 −0.956335
\(251\) 6171.16 1.55187 0.775936 0.630811i \(-0.217278\pi\)
0.775936 + 0.630811i \(0.217278\pi\)
\(252\) 0 0
\(253\) −6807.26 −1.69158
\(254\) −6039.84 −1.49202
\(255\) 0 0
\(256\) 4119.70 1.00579
\(257\) −1152.39 −0.279704 −0.139852 0.990172i \(-0.544663\pi\)
−0.139852 + 0.990172i \(0.544663\pi\)
\(258\) 0 0
\(259\) −103.311 −0.0247853
\(260\) −1628.36 −0.388411
\(261\) 0 0
\(262\) 7564.38 1.78370
\(263\) 3770.83 0.884103 0.442052 0.896990i \(-0.354251\pi\)
0.442052 + 0.896990i \(0.354251\pi\)
\(264\) 0 0
\(265\) −477.999 −0.110805
\(266\) −388.475 −0.0895448
\(267\) 0 0
\(268\) −5674.85 −1.29346
\(269\) 4716.65 1.06907 0.534534 0.845147i \(-0.320487\pi\)
0.534534 + 0.845147i \(0.320487\pi\)
\(270\) 0 0
\(271\) 10.3194 0.00231313 0.00115656 0.999999i \(-0.499632\pi\)
0.00115656 + 0.999999i \(0.499632\pi\)
\(272\) 3281.10 0.731418
\(273\) 0 0
\(274\) −1705.81 −0.376101
\(275\) −5213.20 −1.14316
\(276\) 0 0
\(277\) 7671.93 1.66412 0.832060 0.554685i \(-0.187161\pi\)
0.832060 + 0.554685i \(0.187161\pi\)
\(278\) 5381.00 1.16090
\(279\) 0 0
\(280\) 0.415581 8.86990e−5 0
\(281\) 62.9370 0.0133612 0.00668061 0.999978i \(-0.497873\pi\)
0.00668061 + 0.999978i \(0.497873\pi\)
\(282\) 0 0
\(283\) 7377.75 1.54969 0.774844 0.632152i \(-0.217828\pi\)
0.774844 + 0.632152i \(0.217828\pi\)
\(284\) 8190.48 1.71132
\(285\) 0 0
\(286\) −9674.29 −2.00019
\(287\) −483.571 −0.0994575
\(288\) 0 0
\(289\) −2299.84 −0.468114
\(290\) 1435.73 0.290721
\(291\) 0 0
\(292\) −9764.90 −1.95701
\(293\) 2769.63 0.552231 0.276115 0.961125i \(-0.410953\pi\)
0.276115 + 0.961125i \(0.410953\pi\)
\(294\) 0 0
\(295\) −2732.64 −0.539324
\(296\) 8.69119 0.00170664
\(297\) 0 0
\(298\) −11269.1 −2.19061
\(299\) −7151.24 −1.38317
\(300\) 0 0
\(301\) −191.170 −0.0366075
\(302\) 6386.72 1.21693
\(303\) 0 0
\(304\) 5647.25 1.06543
\(305\) −493.957 −0.0927342
\(306\) 0 0
\(307\) 9496.98 1.76554 0.882771 0.469804i \(-0.155675\pi\)
0.882771 + 0.469804i \(0.155675\pi\)
\(308\) −422.939 −0.0782441
\(309\) 0 0
\(310\) 3922.04 0.718570
\(311\) −6132.04 −1.11806 −0.559029 0.829148i \(-0.688826\pi\)
−0.559029 + 0.829148i \(0.688826\pi\)
\(312\) 0 0
\(313\) −7597.42 −1.37199 −0.685993 0.727608i \(-0.740632\pi\)
−0.685993 + 0.727608i \(0.740632\pi\)
\(314\) −6922.84 −1.24420
\(315\) 0 0
\(316\) −110.178 −0.0196140
\(317\) −3010.40 −0.533378 −0.266689 0.963783i \(-0.585930\pi\)
−0.266689 + 0.963783i \(0.585930\pi\)
\(318\) 0 0
\(319\) 4258.72 0.747468
\(320\) 2060.72 0.359992
\(321\) 0 0
\(322\) −626.184 −0.108372
\(323\) 4497.62 0.774781
\(324\) 0 0
\(325\) −5476.63 −0.934735
\(326\) 9237.08 1.56931
\(327\) 0 0
\(328\) 40.6813 0.00684833
\(329\) −162.735 −0.0272701
\(330\) 0 0
\(331\) 3742.19 0.621418 0.310709 0.950505i \(-0.399434\pi\)
0.310709 + 0.950505i \(0.399434\pi\)
\(332\) −901.460 −0.149018
\(333\) 0 0
\(334\) 7517.45 1.23155
\(335\) 2880.13 0.469726
\(336\) 0 0
\(337\) −2950.76 −0.476968 −0.238484 0.971146i \(-0.576651\pi\)
−0.238484 + 0.971146i \(0.576651\pi\)
\(338\) −1381.54 −0.222325
\(339\) 0 0
\(340\) 1650.79 0.263314
\(341\) 11633.7 1.84750
\(342\) 0 0
\(343\) 756.431 0.119077
\(344\) 16.0825 0.00252067
\(345\) 0 0
\(346\) −1678.59 −0.260814
\(347\) 8511.49 1.31677 0.658387 0.752679i \(-0.271239\pi\)
0.658387 + 0.752679i \(0.271239\pi\)
\(348\) 0 0
\(349\) −8812.19 −1.35159 −0.675796 0.737088i \(-0.736200\pi\)
−0.675796 + 0.737088i \(0.736200\pi\)
\(350\) −479.551 −0.0732373
\(351\) 0 0
\(352\) 12278.7 1.85926
\(353\) −8301.38 −1.25167 −0.625833 0.779957i \(-0.715241\pi\)
−0.625833 + 0.779957i \(0.715241\pi\)
\(354\) 0 0
\(355\) −4156.87 −0.621476
\(356\) −9100.94 −1.35491
\(357\) 0 0
\(358\) 7914.35 1.16840
\(359\) −5375.68 −0.790300 −0.395150 0.918617i \(-0.629307\pi\)
−0.395150 + 0.918617i \(0.629307\pi\)
\(360\) 0 0
\(361\) 882.055 0.128598
\(362\) −5203.71 −0.755527
\(363\) 0 0
\(364\) −444.311 −0.0639786
\(365\) 4955.93 0.710699
\(366\) 0 0
\(367\) 7875.44 1.12015 0.560075 0.828442i \(-0.310772\pi\)
0.560075 + 0.828442i \(0.310772\pi\)
\(368\) 9102.82 1.28945
\(369\) 0 0
\(370\) 1513.40 0.212643
\(371\) −130.425 −0.0182516
\(372\) 0 0
\(373\) −523.441 −0.0726615 −0.0363308 0.999340i \(-0.511567\pi\)
−0.0363308 + 0.999340i \(0.511567\pi\)
\(374\) 9807.53 1.35598
\(375\) 0 0
\(376\) 13.6904 0.00187773
\(377\) 4473.92 0.611190
\(378\) 0 0
\(379\) 854.837 0.115858 0.0579288 0.998321i \(-0.481550\pi\)
0.0579288 + 0.998321i \(0.481550\pi\)
\(380\) 2841.25 0.383561
\(381\) 0 0
\(382\) −10232.8 −1.37056
\(383\) −2973.40 −0.396694 −0.198347 0.980132i \(-0.563557\pi\)
−0.198347 + 0.980132i \(0.563557\pi\)
\(384\) 0 0
\(385\) 214.652 0.0284148
\(386\) 3894.74 0.513568
\(387\) 0 0
\(388\) −3800.88 −0.497320
\(389\) 8861.43 1.15499 0.577497 0.816393i \(-0.304030\pi\)
0.577497 + 0.816393i \(0.304030\pi\)
\(390\) 0 0
\(391\) 7249.73 0.937685
\(392\) −31.7614 −0.00409233
\(393\) 0 0
\(394\) −3027.04 −0.387055
\(395\) 55.9182 0.00712292
\(396\) 0 0
\(397\) −373.265 −0.0471879 −0.0235940 0.999722i \(-0.507511\pi\)
−0.0235940 + 0.999722i \(0.507511\pi\)
\(398\) 7164.85 0.902365
\(399\) 0 0
\(400\) 6971.21 0.871401
\(401\) −844.656 −0.105187 −0.0525936 0.998616i \(-0.516749\pi\)
−0.0525936 + 0.998616i \(0.516749\pi\)
\(402\) 0 0
\(403\) 12221.5 1.51067
\(404\) 220.661 0.0271740
\(405\) 0 0
\(406\) 391.750 0.0478872
\(407\) 4489.10 0.546723
\(408\) 0 0
\(409\) −2089.86 −0.252657 −0.126328 0.991988i \(-0.540319\pi\)
−0.126328 + 0.991988i \(0.540319\pi\)
\(410\) 7083.86 0.853285
\(411\) 0 0
\(412\) 4274.95 0.511193
\(413\) −745.620 −0.0888367
\(414\) 0 0
\(415\) 457.513 0.0541168
\(416\) 12899.2 1.52028
\(417\) 0 0
\(418\) 16880.2 1.97521
\(419\) −11396.1 −1.32873 −0.664363 0.747410i \(-0.731297\pi\)
−0.664363 + 0.747410i \(0.731297\pi\)
\(420\) 0 0
\(421\) −4878.55 −0.564765 −0.282383 0.959302i \(-0.591125\pi\)
−0.282383 + 0.959302i \(0.591125\pi\)
\(422\) 9101.77 1.04992
\(423\) 0 0
\(424\) 10.9723 0.00125675
\(425\) 5552.06 0.633681
\(426\) 0 0
\(427\) −134.780 −0.0152750
\(428\) 4049.90 0.457382
\(429\) 0 0
\(430\) 2800.46 0.314070
\(431\) 13782.1 1.54028 0.770139 0.637876i \(-0.220187\pi\)
0.770139 + 0.637876i \(0.220187\pi\)
\(432\) 0 0
\(433\) 2146.21 0.238199 0.119099 0.992882i \(-0.461999\pi\)
0.119099 + 0.992882i \(0.461999\pi\)
\(434\) 1070.16 0.118362
\(435\) 0 0
\(436\) −3737.94 −0.410584
\(437\) 12477.8 1.36590
\(438\) 0 0
\(439\) 8338.78 0.906579 0.453289 0.891363i \(-0.350250\pi\)
0.453289 + 0.891363i \(0.350250\pi\)
\(440\) −18.0580 −0.00195655
\(441\) 0 0
\(442\) 10303.1 1.10875
\(443\) −12614.7 −1.35292 −0.676461 0.736479i \(-0.736487\pi\)
−0.676461 + 0.736479i \(0.736487\pi\)
\(444\) 0 0
\(445\) 4618.96 0.492044
\(446\) −10210.2 −1.08401
\(447\) 0 0
\(448\) 562.281 0.0592975
\(449\) 7675.63 0.806761 0.403380 0.915032i \(-0.367835\pi\)
0.403380 + 0.915032i \(0.367835\pi\)
\(450\) 0 0
\(451\) 21012.4 2.19387
\(452\) −2201.13 −0.229054
\(453\) 0 0
\(454\) 10563.6 1.09202
\(455\) 225.499 0.0232342
\(456\) 0 0
\(457\) −320.495 −0.0328055 −0.0164028 0.999865i \(-0.505221\pi\)
−0.0164028 + 0.999865i \(0.505221\pi\)
\(458\) −18647.5 −1.90249
\(459\) 0 0
\(460\) 4579.83 0.464208
\(461\) 11008.9 1.11223 0.556113 0.831107i \(-0.312292\pi\)
0.556113 + 0.831107i \(0.312292\pi\)
\(462\) 0 0
\(463\) −6268.55 −0.629210 −0.314605 0.949223i \(-0.601872\pi\)
−0.314605 + 0.949223i \(0.601872\pi\)
\(464\) −5694.85 −0.569778
\(465\) 0 0
\(466\) −3795.14 −0.377267
\(467\) 5453.97 0.540427 0.270214 0.962800i \(-0.412906\pi\)
0.270214 + 0.962800i \(0.412906\pi\)
\(468\) 0 0
\(469\) 785.863 0.0773727
\(470\) 2383.91 0.233961
\(471\) 0 0
\(472\) 62.7267 0.00611702
\(473\) 8306.80 0.807499
\(474\) 0 0
\(475\) 9555.90 0.923063
\(476\) 450.430 0.0433727
\(477\) 0 0
\(478\) 955.305 0.0914114
\(479\) −15898.3 −1.51652 −0.758260 0.651952i \(-0.773950\pi\)
−0.758260 + 0.651952i \(0.773950\pi\)
\(480\) 0 0
\(481\) 4715.94 0.447044
\(482\) −21630.1 −2.04403
\(483\) 0 0
\(484\) 7760.68 0.728839
\(485\) 1929.04 0.180605
\(486\) 0 0
\(487\) −15727.9 −1.46345 −0.731726 0.681599i \(-0.761285\pi\)
−0.731726 + 0.681599i \(0.761285\pi\)
\(488\) 11.3386 0.00105179
\(489\) 0 0
\(490\) −5530.63 −0.509894
\(491\) 10116.1 0.929802 0.464901 0.885363i \(-0.346090\pi\)
0.464901 + 0.885363i \(0.346090\pi\)
\(492\) 0 0
\(493\) −4535.54 −0.414341
\(494\) 17733.2 1.61509
\(495\) 0 0
\(496\) −15556.8 −1.40831
\(497\) −1134.23 −0.102369
\(498\) 0 0
\(499\) −1710.86 −0.153484 −0.0767420 0.997051i \(-0.524452\pi\)
−0.0767420 + 0.997051i \(0.524452\pi\)
\(500\) 7544.00 0.674756
\(501\) 0 0
\(502\) −24666.7 −2.19308
\(503\) 14432.0 1.27930 0.639652 0.768664i \(-0.279078\pi\)
0.639652 + 0.768664i \(0.279078\pi\)
\(504\) 0 0
\(505\) −111.991 −0.00986838
\(506\) 27209.3 2.39051
\(507\) 0 0
\(508\) 12053.3 1.05272
\(509\) −3625.68 −0.315728 −0.157864 0.987461i \(-0.550461\pi\)
−0.157864 + 0.987461i \(0.550461\pi\)
\(510\) 0 0
\(511\) 1352.26 0.117065
\(512\) −16371.7 −1.41315
\(513\) 0 0
\(514\) 4606.20 0.395274
\(515\) −2169.64 −0.185643
\(516\) 0 0
\(517\) 7071.24 0.601533
\(518\) 412.942 0.0350263
\(519\) 0 0
\(520\) −18.9705 −0.00159983
\(521\) −6058.73 −0.509478 −0.254739 0.967010i \(-0.581989\pi\)
−0.254739 + 0.967010i \(0.581989\pi\)
\(522\) 0 0
\(523\) 17176.8 1.43612 0.718058 0.695983i \(-0.245031\pi\)
0.718058 + 0.695983i \(0.245031\pi\)
\(524\) −15095.8 −1.25851
\(525\) 0 0
\(526\) −15072.3 −1.24940
\(527\) −12389.9 −1.02412
\(528\) 0 0
\(529\) 7946.09 0.653086
\(530\) 1910.61 0.156588
\(531\) 0 0
\(532\) 775.255 0.0631796
\(533\) 22074.1 1.79388
\(534\) 0 0
\(535\) −2055.43 −0.166101
\(536\) −66.1122 −0.00532764
\(537\) 0 0
\(538\) −18852.9 −1.51079
\(539\) −16405.1 −1.31098
\(540\) 0 0
\(541\) −3891.14 −0.309230 −0.154615 0.987975i \(-0.549414\pi\)
−0.154615 + 0.987975i \(0.549414\pi\)
\(542\) −41.2475 −0.00326888
\(543\) 0 0
\(544\) −13076.9 −1.03063
\(545\) 1897.10 0.149106
\(546\) 0 0
\(547\) 13449.8 1.05132 0.525659 0.850695i \(-0.323819\pi\)
0.525659 + 0.850695i \(0.323819\pi\)
\(548\) 3404.18 0.265364
\(549\) 0 0
\(550\) 20837.7 1.61549
\(551\) −7806.31 −0.603557
\(552\) 0 0
\(553\) 15.2577 0.00117328
\(554\) −30665.4 −2.35171
\(555\) 0 0
\(556\) −10738.5 −0.819091
\(557\) 18563.3 1.41212 0.706062 0.708150i \(-0.250470\pi\)
0.706062 + 0.708150i \(0.250470\pi\)
\(558\) 0 0
\(559\) 8726.56 0.660275
\(560\) −287.038 −0.0216599
\(561\) 0 0
\(562\) −251.565 −0.0188819
\(563\) 1625.00 0.121644 0.0608219 0.998149i \(-0.480628\pi\)
0.0608219 + 0.998149i \(0.480628\pi\)
\(564\) 0 0
\(565\) 1117.13 0.0831822
\(566\) −29489.6 −2.19000
\(567\) 0 0
\(568\) 95.4194 0.00704878
\(569\) 3009.34 0.221719 0.110859 0.993836i \(-0.464640\pi\)
0.110859 + 0.993836i \(0.464640\pi\)
\(570\) 0 0
\(571\) 16739.6 1.22685 0.613424 0.789754i \(-0.289792\pi\)
0.613424 + 0.789754i \(0.289792\pi\)
\(572\) 19306.4 1.41126
\(573\) 0 0
\(574\) 1932.88 0.140552
\(575\) 15403.2 1.11714
\(576\) 0 0
\(577\) −11635.1 −0.839471 −0.419735 0.907647i \(-0.637877\pi\)
−0.419735 + 0.907647i \(0.637877\pi\)
\(578\) 9192.69 0.661532
\(579\) 0 0
\(580\) −2865.20 −0.205123
\(581\) 124.836 0.00891404
\(582\) 0 0
\(583\) 5667.30 0.402599
\(584\) −113.761 −0.00806076
\(585\) 0 0
\(586\) −11070.5 −0.780405
\(587\) 20826.5 1.46440 0.732198 0.681092i \(-0.238495\pi\)
0.732198 + 0.681092i \(0.238495\pi\)
\(588\) 0 0
\(589\) −21324.8 −1.49180
\(590\) 10922.6 0.762165
\(591\) 0 0
\(592\) −6002.92 −0.416754
\(593\) 2889.49 0.200097 0.100048 0.994983i \(-0.468100\pi\)
0.100048 + 0.994983i \(0.468100\pi\)
\(594\) 0 0
\(595\) −228.605 −0.0157510
\(596\) 22489.0 1.54562
\(597\) 0 0
\(598\) 28584.2 1.95467
\(599\) 10424.7 0.711085 0.355543 0.934660i \(-0.384296\pi\)
0.355543 + 0.934660i \(0.384296\pi\)
\(600\) 0 0
\(601\) 10091.1 0.684899 0.342449 0.939536i \(-0.388743\pi\)
0.342449 + 0.939536i \(0.388743\pi\)
\(602\) 764.123 0.0517331
\(603\) 0 0
\(604\) −12745.6 −0.858626
\(605\) −3938.74 −0.264682
\(606\) 0 0
\(607\) 6410.41 0.428650 0.214325 0.976762i \(-0.431245\pi\)
0.214325 + 0.976762i \(0.431245\pi\)
\(608\) −22507.2 −1.50129
\(609\) 0 0
\(610\) 1974.39 0.131051
\(611\) 7428.56 0.491861
\(612\) 0 0
\(613\) 10238.7 0.674611 0.337306 0.941395i \(-0.390484\pi\)
0.337306 + 0.941395i \(0.390484\pi\)
\(614\) −37960.3 −2.49504
\(615\) 0 0
\(616\) −4.92725 −0.000322280 0
\(617\) 5867.50 0.382847 0.191424 0.981508i \(-0.438690\pi\)
0.191424 + 0.981508i \(0.438690\pi\)
\(618\) 0 0
\(619\) 15855.6 1.02955 0.514775 0.857325i \(-0.327875\pi\)
0.514775 + 0.857325i \(0.327875\pi\)
\(620\) −7826.97 −0.506998
\(621\) 0 0
\(622\) 24510.3 1.58002
\(623\) 1260.31 0.0810488
\(624\) 0 0
\(625\) 9747.53 0.623842
\(626\) 30367.6 1.93887
\(627\) 0 0
\(628\) 13815.5 0.877863
\(629\) −4780.89 −0.303063
\(630\) 0 0
\(631\) 31300.6 1.97473 0.987367 0.158451i \(-0.0506499\pi\)
0.987367 + 0.158451i \(0.0506499\pi\)
\(632\) −1.28358 −8.07882e−5 0
\(633\) 0 0
\(634\) 12032.8 0.753762
\(635\) −6117.37 −0.382300
\(636\) 0 0
\(637\) −17234.1 −1.07196
\(638\) −17022.5 −1.05631
\(639\) 0 0
\(640\) 48.1554 0.00297423
\(641\) −4920.23 −0.303178 −0.151589 0.988444i \(-0.548439\pi\)
−0.151589 + 0.988444i \(0.548439\pi\)
\(642\) 0 0
\(643\) −26573.3 −1.62978 −0.814889 0.579617i \(-0.803202\pi\)
−0.814889 + 0.579617i \(0.803202\pi\)
\(644\) 1249.64 0.0764637
\(645\) 0 0
\(646\) −17977.4 −1.09491
\(647\) −14348.5 −0.871870 −0.435935 0.899978i \(-0.643582\pi\)
−0.435935 + 0.899978i \(0.643582\pi\)
\(648\) 0 0
\(649\) 32399.0 1.95959
\(650\) 21890.6 1.32095
\(651\) 0 0
\(652\) −18433.9 −1.10725
\(653\) −22712.9 −1.36114 −0.680569 0.732684i \(-0.738268\pi\)
−0.680569 + 0.732684i \(0.738268\pi\)
\(654\) 0 0
\(655\) 7661.48 0.457036
\(656\) −28098.2 −1.67233
\(657\) 0 0
\(658\) 650.467 0.0385377
\(659\) −5250.90 −0.310389 −0.155194 0.987884i \(-0.549600\pi\)
−0.155194 + 0.987884i \(0.549600\pi\)
\(660\) 0 0
\(661\) 30600.4 1.80063 0.900315 0.435238i \(-0.143336\pi\)
0.900315 + 0.435238i \(0.143336\pi\)
\(662\) −14957.9 −0.878178
\(663\) 0 0
\(664\) −10.5020 −0.000613792 0
\(665\) −393.461 −0.0229440
\(666\) 0 0
\(667\) −12583.0 −0.730460
\(668\) −15002.1 −0.868936
\(669\) 0 0
\(670\) −11512.1 −0.663811
\(671\) 5856.51 0.336942
\(672\) 0 0
\(673\) 4580.09 0.262332 0.131166 0.991360i \(-0.458128\pi\)
0.131166 + 0.991360i \(0.458128\pi\)
\(674\) 11794.5 0.674045
\(675\) 0 0
\(676\) 2757.05 0.156865
\(677\) 11317.7 0.642505 0.321252 0.946994i \(-0.395896\pi\)
0.321252 + 0.946994i \(0.395896\pi\)
\(678\) 0 0
\(679\) 526.352 0.0297489
\(680\) 19.2318 0.00108457
\(681\) 0 0
\(682\) −46500.9 −2.61087
\(683\) −6562.83 −0.367671 −0.183836 0.982957i \(-0.558851\pi\)
−0.183836 + 0.982957i \(0.558851\pi\)
\(684\) 0 0
\(685\) −1727.71 −0.0963682
\(686\) −3023.53 −0.168278
\(687\) 0 0
\(688\) −11108.0 −0.615538
\(689\) 5953.68 0.329197
\(690\) 0 0
\(691\) 30308.7 1.66859 0.834295 0.551318i \(-0.185875\pi\)
0.834295 + 0.551318i \(0.185875\pi\)
\(692\) 3349.87 0.184021
\(693\) 0 0
\(694\) −34021.2 −1.86085
\(695\) 5450.07 0.297458
\(696\) 0 0
\(697\) −22378.2 −1.21612
\(698\) 35223.1 1.91005
\(699\) 0 0
\(700\) 957.009 0.0516736
\(701\) 8394.73 0.452303 0.226152 0.974092i \(-0.427385\pi\)
0.226152 + 0.974092i \(0.427385\pi\)
\(702\) 0 0
\(703\) −8228.60 −0.441462
\(704\) −24432.5 −1.30800
\(705\) 0 0
\(706\) 33181.4 1.76884
\(707\) −30.5575 −0.00162551
\(708\) 0 0
\(709\) 24500.7 1.29780 0.648902 0.760872i \(-0.275229\pi\)
0.648902 + 0.760872i \(0.275229\pi\)
\(710\) 16615.4 0.878261
\(711\) 0 0
\(712\) −106.026 −0.00558077
\(713\) −34373.5 −1.80547
\(714\) 0 0
\(715\) −9798.48 −0.512507
\(716\) −15794.2 −0.824380
\(717\) 0 0
\(718\) 21487.1 1.11684
\(719\) 2682.97 0.139163 0.0695814 0.997576i \(-0.477834\pi\)
0.0695814 + 0.997576i \(0.477834\pi\)
\(720\) 0 0
\(721\) −592.002 −0.0305788
\(722\) −3525.65 −0.181733
\(723\) 0 0
\(724\) 10384.7 0.533073
\(725\) −9636.46 −0.493640
\(726\) 0 0
\(727\) 15504.9 0.790981 0.395491 0.918470i \(-0.370575\pi\)
0.395491 + 0.918470i \(0.370575\pi\)
\(728\) −5.17624 −0.000263522 0
\(729\) 0 0
\(730\) −19809.3 −1.00435
\(731\) −8846.74 −0.447618
\(732\) 0 0
\(733\) −31040.9 −1.56415 −0.782074 0.623185i \(-0.785838\pi\)
−0.782074 + 0.623185i \(0.785838\pi\)
\(734\) −31478.9 −1.58298
\(735\) 0 0
\(736\) −36279.4 −1.81695
\(737\) −34147.7 −1.70671
\(738\) 0 0
\(739\) 34245.2 1.70464 0.852320 0.523021i \(-0.175195\pi\)
0.852320 + 0.523021i \(0.175195\pi\)
\(740\) −3020.20 −0.150033
\(741\) 0 0
\(742\) 521.322 0.0257929
\(743\) 26315.7 1.29937 0.649684 0.760204i \(-0.274901\pi\)
0.649684 + 0.760204i \(0.274901\pi\)
\(744\) 0 0
\(745\) −11413.8 −0.561299
\(746\) 2092.24 0.102684
\(747\) 0 0
\(748\) −19572.3 −0.956730
\(749\) −560.837 −0.0273599
\(750\) 0 0
\(751\) −13876.1 −0.674229 −0.337114 0.941464i \(-0.609451\pi\)
−0.337114 + 0.941464i \(0.609451\pi\)
\(752\) −9455.81 −0.458535
\(753\) 0 0
\(754\) −17882.7 −0.863724
\(755\) 6468.70 0.311815
\(756\) 0 0
\(757\) 5912.49 0.283875 0.141937 0.989876i \(-0.454667\pi\)
0.141937 + 0.989876i \(0.454667\pi\)
\(758\) −3416.86 −0.163728
\(759\) 0 0
\(760\) 33.1007 0.00157985
\(761\) −19059.5 −0.907891 −0.453945 0.891030i \(-0.649984\pi\)
−0.453945 + 0.891030i \(0.649984\pi\)
\(762\) 0 0
\(763\) 517.636 0.0245605
\(764\) 20420.9 0.967018
\(765\) 0 0
\(766\) 11885.0 0.560602
\(767\) 34036.2 1.60232
\(768\) 0 0
\(769\) 25233.6 1.18329 0.591644 0.806200i \(-0.298479\pi\)
0.591644 + 0.806200i \(0.298479\pi\)
\(770\) −857.984 −0.0401553
\(771\) 0 0
\(772\) −7772.50 −0.362355
\(773\) 919.765 0.0427965 0.0213982 0.999771i \(-0.493188\pi\)
0.0213982 + 0.999771i \(0.493188\pi\)
\(774\) 0 0
\(775\) −26324.2 −1.22012
\(776\) −44.2804 −0.00204842
\(777\) 0 0
\(778\) −35420.0 −1.63222
\(779\) −38516.1 −1.77148
\(780\) 0 0
\(781\) 49285.2 2.25808
\(782\) −28977.9 −1.32512
\(783\) 0 0
\(784\) 21937.3 0.999330
\(785\) −7011.71 −0.318801
\(786\) 0 0
\(787\) −27714.4 −1.25529 −0.627643 0.778501i \(-0.715980\pi\)
−0.627643 + 0.778501i \(0.715980\pi\)
\(788\) 6040.87 0.273093
\(789\) 0 0
\(790\) −223.510 −0.0100660
\(791\) 304.816 0.0137017
\(792\) 0 0
\(793\) 6152.45 0.275511
\(794\) 1491.97 0.0666853
\(795\) 0 0
\(796\) −14298.4 −0.636677
\(797\) 17889.7 0.795091 0.397545 0.917583i \(-0.369862\pi\)
0.397545 + 0.917583i \(0.369862\pi\)
\(798\) 0 0
\(799\) −7530.87 −0.333445
\(800\) −27783.8 −1.22788
\(801\) 0 0
\(802\) 3376.17 0.148649
\(803\) −58759.0 −2.58227
\(804\) 0 0
\(805\) −634.222 −0.0277682
\(806\) −48850.6 −2.13485
\(807\) 0 0
\(808\) 2.57071 0.000111927 0
\(809\) 41008.0 1.78216 0.891078 0.453849i \(-0.149950\pi\)
0.891078 + 0.453849i \(0.149950\pi\)
\(810\) 0 0
\(811\) 37353.0 1.61732 0.808658 0.588279i \(-0.200195\pi\)
0.808658 + 0.588279i \(0.200195\pi\)
\(812\) −781.791 −0.0337875
\(813\) 0 0
\(814\) −17943.3 −0.772621
\(815\) 9355.65 0.402103
\(816\) 0 0
\(817\) −15226.5 −0.652030
\(818\) 8353.35 0.357051
\(819\) 0 0
\(820\) −14136.8 −0.602047
\(821\) −10694.8 −0.454628 −0.227314 0.973821i \(-0.572994\pi\)
−0.227314 + 0.973821i \(0.572994\pi\)
\(822\) 0 0
\(823\) −9279.81 −0.393042 −0.196521 0.980500i \(-0.562964\pi\)
−0.196521 + 0.980500i \(0.562964\pi\)
\(824\) 49.8033 0.00210556
\(825\) 0 0
\(826\) 2980.31 0.125543
\(827\) 3262.63 0.137186 0.0685930 0.997645i \(-0.478149\pi\)
0.0685930 + 0.997645i \(0.478149\pi\)
\(828\) 0 0
\(829\) 31780.5 1.33146 0.665732 0.746191i \(-0.268119\pi\)
0.665732 + 0.746191i \(0.268119\pi\)
\(830\) −1828.72 −0.0764770
\(831\) 0 0
\(832\) −25667.1 −1.06953
\(833\) 17471.5 0.726711
\(834\) 0 0
\(835\) 7613.95 0.315559
\(836\) −33686.7 −1.39364
\(837\) 0 0
\(838\) 45551.3 1.87774
\(839\) −32049.1 −1.31878 −0.659390 0.751801i \(-0.729186\pi\)
−0.659390 + 0.751801i \(0.729186\pi\)
\(840\) 0 0
\(841\) −16516.9 −0.677227
\(842\) 19500.0 0.798118
\(843\) 0 0
\(844\) −18163.8 −0.740788
\(845\) −1399.27 −0.0569662
\(846\) 0 0
\(847\) −1074.71 −0.0435980
\(848\) −7578.44 −0.306892
\(849\) 0 0
\(850\) −22192.1 −0.895509
\(851\) −13263.7 −0.534283
\(852\) 0 0
\(853\) −29521.1 −1.18497 −0.592487 0.805580i \(-0.701854\pi\)
−0.592487 + 0.805580i \(0.701854\pi\)
\(854\) 538.727 0.0215865
\(855\) 0 0
\(856\) 47.1815 0.00188391
\(857\) −17125.3 −0.682602 −0.341301 0.939954i \(-0.610868\pi\)
−0.341301 + 0.939954i \(0.610868\pi\)
\(858\) 0 0
\(859\) −8707.51 −0.345863 −0.172932 0.984934i \(-0.555324\pi\)
−0.172932 + 0.984934i \(0.555324\pi\)
\(860\) −5588.70 −0.221596
\(861\) 0 0
\(862\) −55088.3 −2.17670
\(863\) 21710.8 0.856366 0.428183 0.903692i \(-0.359154\pi\)
0.428183 + 0.903692i \(0.359154\pi\)
\(864\) 0 0
\(865\) −1700.14 −0.0668284
\(866\) −8578.58 −0.336619
\(867\) 0 0
\(868\) −2135.64 −0.0835120
\(869\) −662.984 −0.0258805
\(870\) 0 0
\(871\) −35873.2 −1.39554
\(872\) −43.5471 −0.00169116
\(873\) 0 0
\(874\) −49875.1 −1.93026
\(875\) −1044.71 −0.0403629
\(876\) 0 0
\(877\) 8646.67 0.332927 0.166464 0.986048i \(-0.446765\pi\)
0.166464 + 0.986048i \(0.446765\pi\)
\(878\) −33330.9 −1.28116
\(879\) 0 0
\(880\) 12472.5 0.477781
\(881\) 14872.3 0.568740 0.284370 0.958715i \(-0.408216\pi\)
0.284370 + 0.958715i \(0.408216\pi\)
\(882\) 0 0
\(883\) 30906.4 1.17790 0.588949 0.808170i \(-0.299542\pi\)
0.588949 + 0.808170i \(0.299542\pi\)
\(884\) −20561.3 −0.782298
\(885\) 0 0
\(886\) 50422.3 1.91193
\(887\) 16725.2 0.633122 0.316561 0.948572i \(-0.397472\pi\)
0.316561 + 0.948572i \(0.397472\pi\)
\(888\) 0 0
\(889\) −1669.17 −0.0629719
\(890\) −18462.4 −0.695350
\(891\) 0 0
\(892\) 20375.9 0.764837
\(893\) −12961.7 −0.485719
\(894\) 0 0
\(895\) 8015.94 0.299378
\(896\) 13.1395 0.000489912 0
\(897\) 0 0
\(898\) −30680.2 −1.14010
\(899\) 21504.5 0.797793
\(900\) 0 0
\(901\) −6035.67 −0.223171
\(902\) −83988.3 −3.10034
\(903\) 0 0
\(904\) −25.6433 −0.000943453 0
\(905\) −5270.50 −0.193588
\(906\) 0 0
\(907\) −8883.30 −0.325210 −0.162605 0.986691i \(-0.551990\pi\)
−0.162605 + 0.986691i \(0.551990\pi\)
\(908\) −21081.2 −0.770489
\(909\) 0 0
\(910\) −901.340 −0.0328342
\(911\) 5440.31 0.197855 0.0989274 0.995095i \(-0.468459\pi\)
0.0989274 + 0.995095i \(0.468459\pi\)
\(912\) 0 0
\(913\) −5424.42 −0.196629
\(914\) 1281.05 0.0463603
\(915\) 0 0
\(916\) 37213.7 1.34233
\(917\) 2090.49 0.0752824
\(918\) 0 0
\(919\) 29325.4 1.05262 0.526309 0.850294i \(-0.323576\pi\)
0.526309 + 0.850294i \(0.323576\pi\)
\(920\) 53.3552 0.00191203
\(921\) 0 0
\(922\) −44003.6 −1.57178
\(923\) 51775.6 1.84639
\(924\) 0 0
\(925\) −10157.8 −0.361065
\(926\) 25056.0 0.889191
\(927\) 0 0
\(928\) 22696.9 0.802869
\(929\) 50671.0 1.78952 0.894759 0.446549i \(-0.147347\pi\)
0.894759 + 0.446549i \(0.147347\pi\)
\(930\) 0 0
\(931\) 30070.9 1.05858
\(932\) 7573.73 0.266186
\(933\) 0 0
\(934\) −21800.0 −0.763724
\(935\) 9933.43 0.347442
\(936\) 0 0
\(937\) −13209.3 −0.460543 −0.230271 0.973126i \(-0.573961\pi\)
−0.230271 + 0.973126i \(0.573961\pi\)
\(938\) −3141.17 −0.109342
\(939\) 0 0
\(940\) −4757.43 −0.165075
\(941\) −45678.9 −1.58246 −0.791228 0.611521i \(-0.790558\pi\)
−0.791228 + 0.611521i \(0.790558\pi\)
\(942\) 0 0
\(943\) −62084.2 −2.14395
\(944\) −43324.7 −1.49375
\(945\) 0 0
\(946\) −33203.0 −1.14115
\(947\) 42368.9 1.45386 0.726930 0.686712i \(-0.240947\pi\)
0.726930 + 0.686712i \(0.240947\pi\)
\(948\) 0 0
\(949\) −61728.2 −2.11147
\(950\) −38195.8 −1.30446
\(951\) 0 0
\(952\) 5.24753 0.000178648 0
\(953\) −32335.5 −1.09911 −0.549553 0.835459i \(-0.685202\pi\)
−0.549553 + 0.835459i \(0.685202\pi\)
\(954\) 0 0
\(955\) −10364.1 −0.351178
\(956\) −1906.44 −0.0644966
\(957\) 0 0
\(958\) 63547.1 2.14312
\(959\) −471.416 −0.0158736
\(960\) 0 0
\(961\) 28953.6 0.971891
\(962\) −18850.0 −0.631757
\(963\) 0 0
\(964\) 43165.8 1.44220
\(965\) 3944.74 0.131591
\(966\) 0 0
\(967\) −35204.6 −1.17074 −0.585368 0.810768i \(-0.699050\pi\)
−0.585368 + 0.810768i \(0.699050\pi\)
\(968\) 90.4122 0.00300202
\(969\) 0 0
\(970\) −7710.55 −0.255228
\(971\) −18320.8 −0.605501 −0.302751 0.953070i \(-0.597905\pi\)
−0.302751 + 0.953070i \(0.597905\pi\)
\(972\) 0 0
\(973\) 1487.09 0.0489968
\(974\) 62866.0 2.06813
\(975\) 0 0
\(976\) −7831.46 −0.256843
\(977\) −8044.38 −0.263421 −0.131711 0.991288i \(-0.542047\pi\)
−0.131711 + 0.991288i \(0.542047\pi\)
\(978\) 0 0
\(979\) −54763.8 −1.78780
\(980\) 11037.1 0.359763
\(981\) 0 0
\(982\) −40435.0 −1.31398
\(983\) 2326.32 0.0754812 0.0377406 0.999288i \(-0.487984\pi\)
0.0377406 + 0.999288i \(0.487984\pi\)
\(984\) 0 0
\(985\) −3065.89 −0.0991751
\(986\) 18129.0 0.585541
\(987\) 0 0
\(988\) −35389.0 −1.13955
\(989\) −24543.7 −0.789125
\(990\) 0 0
\(991\) −40978.0 −1.31353 −0.656766 0.754094i \(-0.728076\pi\)
−0.656766 + 0.754094i \(0.728076\pi\)
\(992\) 62001.8 1.98444
\(993\) 0 0
\(994\) 4533.63 0.144666
\(995\) 7256.82 0.231213
\(996\) 0 0
\(997\) −10403.3 −0.330467 −0.165233 0.986255i \(-0.552838\pi\)
−0.165233 + 0.986255i \(0.552838\pi\)
\(998\) 6838.46 0.216901
\(999\) 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.1.11 yes 59
3.2 odd 2 2151.4.a.g.1.49 59
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2151.4.a.g.1.49 59 3.2 odd 2
2151.4.a.h.1.11 yes 59 1.1 even 1 trivial