Properties

Label 1078.4.a.h.1.1
Level $1078$
Weight $4$
Character 1078.1
Self dual yes
Analytic conductor $63.604$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1078.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.6040589862\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 154)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1078.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} +14.0000 q^{5} +20.0000 q^{6} +8.00000 q^{8} +73.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +10.0000 q^{3} +4.00000 q^{4} +14.0000 q^{5} +20.0000 q^{6} +8.00000 q^{8} +73.0000 q^{9} +28.0000 q^{10} -11.0000 q^{11} +40.0000 q^{12} +16.0000 q^{13} +140.000 q^{15} +16.0000 q^{16} -108.000 q^{17} +146.000 q^{18} -116.000 q^{19} +56.0000 q^{20} -22.0000 q^{22} +68.0000 q^{23} +80.0000 q^{24} +71.0000 q^{25} +32.0000 q^{26} +460.000 q^{27} +122.000 q^{29} +280.000 q^{30} +262.000 q^{31} +32.0000 q^{32} -110.000 q^{33} -216.000 q^{34} +292.000 q^{36} +130.000 q^{37} -232.000 q^{38} +160.000 q^{39} +112.000 q^{40} -204.000 q^{41} -396.000 q^{43} -44.0000 q^{44} +1022.00 q^{45} +136.000 q^{46} -166.000 q^{47} +160.000 q^{48} +142.000 q^{50} -1080.00 q^{51} +64.0000 q^{52} +442.000 q^{53} +920.000 q^{54} -154.000 q^{55} -1160.00 q^{57} +244.000 q^{58} -702.000 q^{59} +560.000 q^{60} -196.000 q^{61} +524.000 q^{62} +64.0000 q^{64} +224.000 q^{65} -220.000 q^{66} -416.000 q^{67} -432.000 q^{68} +680.000 q^{69} +492.000 q^{71} +584.000 q^{72} -408.000 q^{73} +260.000 q^{74} +710.000 q^{75} -464.000 q^{76} +320.000 q^{78} +600.000 q^{79} +224.000 q^{80} +2629.00 q^{81} -408.000 q^{82} +1212.00 q^{83} -1512.00 q^{85} -792.000 q^{86} +1220.00 q^{87} -88.0000 q^{88} -1146.00 q^{89} +2044.00 q^{90} +272.000 q^{92} +2620.00 q^{93} -332.000 q^{94} -1624.00 q^{95} +320.000 q^{96} +482.000 q^{97} -803.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.707107
\(3\) 10.0000 1.92450 0.962250 0.272166i \(-0.0877398\pi\)
0.962250 + 0.272166i \(0.0877398\pi\)
\(4\) 4.00000 0.500000
\(5\) 14.0000 1.25220 0.626099 0.779744i \(-0.284651\pi\)
0.626099 + 0.779744i \(0.284651\pi\)
\(6\) 20.0000 1.36083
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) 73.0000 2.70370
\(10\) 28.0000 0.885438
\(11\) −11.0000 −0.301511
\(12\) 40.0000 0.962250
\(13\) 16.0000 0.341354 0.170677 0.985327i \(-0.445405\pi\)
0.170677 + 0.985327i \(0.445405\pi\)
\(14\) 0 0
\(15\) 140.000 2.40986
\(16\) 16.0000 0.250000
\(17\) −108.000 −1.54081 −0.770407 0.637552i \(-0.779947\pi\)
−0.770407 + 0.637552i \(0.779947\pi\)
\(18\) 146.000 1.91181
\(19\) −116.000 −1.40064 −0.700322 0.713827i \(-0.746960\pi\)
−0.700322 + 0.713827i \(0.746960\pi\)
\(20\) 56.0000 0.626099
\(21\) 0 0
\(22\) −22.0000 −0.213201
\(23\) 68.0000 0.616477 0.308239 0.951309i \(-0.400260\pi\)
0.308239 + 0.951309i \(0.400260\pi\)
\(24\) 80.0000 0.680414
\(25\) 71.0000 0.568000
\(26\) 32.0000 0.241374
\(27\) 460.000 3.27878
\(28\) 0 0
\(29\) 122.000 0.781201 0.390601 0.920560i \(-0.372267\pi\)
0.390601 + 0.920560i \(0.372267\pi\)
\(30\) 280.000 1.70403
\(31\) 262.000 1.51795 0.758977 0.651117i \(-0.225699\pi\)
0.758977 + 0.651117i \(0.225699\pi\)
\(32\) 32.0000 0.176777
\(33\) −110.000 −0.580259
\(34\) −216.000 −1.08952
\(35\) 0 0
\(36\) 292.000 1.35185
\(37\) 130.000 0.577618 0.288809 0.957387i \(-0.406741\pi\)
0.288809 + 0.957387i \(0.406741\pi\)
\(38\) −232.000 −0.990404
\(39\) 160.000 0.656936
\(40\) 112.000 0.442719
\(41\) −204.000 −0.777060 −0.388530 0.921436i \(-0.627017\pi\)
−0.388530 + 0.921436i \(0.627017\pi\)
\(42\) 0 0
\(43\) −396.000 −1.40441 −0.702203 0.711977i \(-0.747800\pi\)
−0.702203 + 0.711977i \(0.747800\pi\)
\(44\) −44.0000 −0.150756
\(45\) 1022.00 3.38557
\(46\) 136.000 0.435915
\(47\) −166.000 −0.515183 −0.257591 0.966254i \(-0.582929\pi\)
−0.257591 + 0.966254i \(0.582929\pi\)
\(48\) 160.000 0.481125
\(49\) 0 0
\(50\) 142.000 0.401637
\(51\) −1080.00 −2.96530
\(52\) 64.0000 0.170677
\(53\) 442.000 1.14554 0.572768 0.819718i \(-0.305870\pi\)
0.572768 + 0.819718i \(0.305870\pi\)
\(54\) 920.000 2.31845
\(55\) −154.000 −0.377552
\(56\) 0 0
\(57\) −1160.00 −2.69554
\(58\) 244.000 0.552393
\(59\) −702.000 −1.54903 −0.774514 0.632557i \(-0.782005\pi\)
−0.774514 + 0.632557i \(0.782005\pi\)
\(60\) 560.000 1.20493
\(61\) −196.000 −0.411397 −0.205699 0.978615i \(-0.565947\pi\)
−0.205699 + 0.978615i \(0.565947\pi\)
\(62\) 524.000 1.07336
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 224.000 0.427443
\(66\) −220.000 −0.410305
\(67\) −416.000 −0.758545 −0.379272 0.925285i \(-0.623826\pi\)
−0.379272 + 0.925285i \(0.623826\pi\)
\(68\) −432.000 −0.770407
\(69\) 680.000 1.18641
\(70\) 0 0
\(71\) 492.000 0.822390 0.411195 0.911548i \(-0.365112\pi\)
0.411195 + 0.911548i \(0.365112\pi\)
\(72\) 584.000 0.955904
\(73\) −408.000 −0.654148 −0.327074 0.944999i \(-0.606063\pi\)
−0.327074 + 0.944999i \(0.606063\pi\)
\(74\) 260.000 0.408438
\(75\) 710.000 1.09312
\(76\) −464.000 −0.700322
\(77\) 0 0
\(78\) 320.000 0.464524
\(79\) 600.000 0.854497 0.427249 0.904134i \(-0.359483\pi\)
0.427249 + 0.904134i \(0.359483\pi\)
\(80\) 224.000 0.313050
\(81\) 2629.00 3.60631
\(82\) −408.000 −0.549464
\(83\) 1212.00 1.60282 0.801411 0.598114i \(-0.204083\pi\)
0.801411 + 0.598114i \(0.204083\pi\)
\(84\) 0 0
\(85\) −1512.00 −1.92941
\(86\) −792.000 −0.993065
\(87\) 1220.00 1.50342
\(88\) −88.0000 −0.106600
\(89\) −1146.00 −1.36490 −0.682448 0.730934i \(-0.739085\pi\)
−0.682448 + 0.730934i \(0.739085\pi\)
\(90\) 2044.00 2.39396
\(91\) 0 0
\(92\) 272.000 0.308239
\(93\) 2620.00 2.92130
\(94\) −332.000 −0.364289
\(95\) −1624.00 −1.75388
\(96\) 320.000 0.340207
\(97\) 482.000 0.504533 0.252266 0.967658i \(-0.418824\pi\)
0.252266 + 0.967658i \(0.418824\pi\)
\(98\) 0 0
\(99\) −803.000 −0.815197
\(100\) 284.000 0.284000
\(101\) −1216.00 −1.19799 −0.598993 0.800754i \(-0.704432\pi\)
−0.598993 + 0.800754i \(0.704432\pi\)
\(102\) −2160.00 −2.09678
\(103\) −1406.00 −1.34502 −0.672511 0.740087i \(-0.734784\pi\)
−0.672511 + 0.740087i \(0.734784\pi\)
\(104\) 128.000 0.120687
\(105\) 0 0
\(106\) 884.000 0.810016
\(107\) −588.000 −0.531253 −0.265627 0.964076i \(-0.585579\pi\)
−0.265627 + 0.964076i \(0.585579\pi\)
\(108\) 1840.00 1.63939
\(109\) 154.000 0.135326 0.0676630 0.997708i \(-0.478446\pi\)
0.0676630 + 0.997708i \(0.478446\pi\)
\(110\) −308.000 −0.266970
\(111\) 1300.00 1.11163
\(112\) 0 0
\(113\) −1902.00 −1.58341 −0.791704 0.610905i \(-0.790806\pi\)
−0.791704 + 0.610905i \(0.790806\pi\)
\(114\) −2320.00 −1.90603
\(115\) 952.000 0.771952
\(116\) 488.000 0.390601
\(117\) 1168.00 0.922920
\(118\) −1404.00 −1.09533
\(119\) 0 0
\(120\) 1120.00 0.852013
\(121\) 121.000 0.0909091
\(122\) −392.000 −0.290902
\(123\) −2040.00 −1.49545
\(124\) 1048.00 0.758977
\(125\) −756.000 −0.540950
\(126\) 0 0
\(127\) 64.0000 0.0447172 0.0223586 0.999750i \(-0.492882\pi\)
0.0223586 + 0.999750i \(0.492882\pi\)
\(128\) 128.000 0.0883883
\(129\) −3960.00 −2.70278
\(130\) 448.000 0.302248
\(131\) 1584.00 1.05645 0.528224 0.849105i \(-0.322858\pi\)
0.528224 + 0.849105i \(0.322858\pi\)
\(132\) −440.000 −0.290129
\(133\) 0 0
\(134\) −832.000 −0.536372
\(135\) 6440.00 4.10568
\(136\) −864.000 −0.544760
\(137\) 998.000 0.622371 0.311186 0.950349i \(-0.399274\pi\)
0.311186 + 0.950349i \(0.399274\pi\)
\(138\) 1360.00 0.838919
\(139\) −276.000 −0.168417 −0.0842087 0.996448i \(-0.526836\pi\)
−0.0842087 + 0.996448i \(0.526836\pi\)
\(140\) 0 0
\(141\) −1660.00 −0.991470
\(142\) 984.000 0.581517
\(143\) −176.000 −0.102922
\(144\) 1168.00 0.675926
\(145\) 1708.00 0.978218
\(146\) −816.000 −0.462552
\(147\) 0 0
\(148\) 520.000 0.288809
\(149\) 1318.00 0.724663 0.362331 0.932049i \(-0.381981\pi\)
0.362331 + 0.932049i \(0.381981\pi\)
\(150\) 1420.00 0.772950
\(151\) −984.000 −0.530310 −0.265155 0.964206i \(-0.585423\pi\)
−0.265155 + 0.964206i \(0.585423\pi\)
\(152\) −928.000 −0.495202
\(153\) −7884.00 −4.16591
\(154\) 0 0
\(155\) 3668.00 1.90078
\(156\) 640.000 0.328468
\(157\) −1706.00 −0.867221 −0.433610 0.901101i \(-0.642761\pi\)
−0.433610 + 0.901101i \(0.642761\pi\)
\(158\) 1200.00 0.604221
\(159\) 4420.00 2.20458
\(160\) 448.000 0.221359
\(161\) 0 0
\(162\) 5258.00 2.55005
\(163\) 1168.00 0.561257 0.280628 0.959817i \(-0.409457\pi\)
0.280628 + 0.959817i \(0.409457\pi\)
\(164\) −816.000 −0.388530
\(165\) −1540.00 −0.726599
\(166\) 2424.00 1.13337
\(167\) −72.0000 −0.0333624 −0.0166812 0.999861i \(-0.505310\pi\)
−0.0166812 + 0.999861i \(0.505310\pi\)
\(168\) 0 0
\(169\) −1941.00 −0.883477
\(170\) −3024.00 −1.36430
\(171\) −8468.00 −3.78692
\(172\) −1584.00 −0.702203
\(173\) 4328.00 1.90203 0.951017 0.309140i \(-0.100041\pi\)
0.951017 + 0.309140i \(0.100041\pi\)
\(174\) 2440.00 1.06308
\(175\) 0 0
\(176\) −176.000 −0.0753778
\(177\) −7020.00 −2.98110
\(178\) −2292.00 −0.965127
\(179\) −1924.00 −0.803388 −0.401694 0.915774i \(-0.631579\pi\)
−0.401694 + 0.915774i \(0.631579\pi\)
\(180\) 4088.00 1.69279
\(181\) −2230.00 −0.915771 −0.457886 0.889011i \(-0.651393\pi\)
−0.457886 + 0.889011i \(0.651393\pi\)
\(182\) 0 0
\(183\) −1960.00 −0.791734
\(184\) 544.000 0.217958
\(185\) 1820.00 0.723292
\(186\) 5240.00 2.06567
\(187\) 1188.00 0.464573
\(188\) −664.000 −0.257591
\(189\) 0 0
\(190\) −3248.00 −1.24018
\(191\) 2176.00 0.824345 0.412172 0.911106i \(-0.364770\pi\)
0.412172 + 0.911106i \(0.364770\pi\)
\(192\) 640.000 0.240563
\(193\) −3126.00 −1.16588 −0.582939 0.812516i \(-0.698097\pi\)
−0.582939 + 0.812516i \(0.698097\pi\)
\(194\) 964.000 0.356759
\(195\) 2240.00 0.822614
\(196\) 0 0
\(197\) −1122.00 −0.405783 −0.202891 0.979201i \(-0.565034\pi\)
−0.202891 + 0.979201i \(0.565034\pi\)
\(198\) −1606.00 −0.576432
\(199\) 5586.00 1.98985 0.994927 0.100597i \(-0.0320753\pi\)
0.994927 + 0.100597i \(0.0320753\pi\)
\(200\) 568.000 0.200818
\(201\) −4160.00 −1.45982
\(202\) −2432.00 −0.847104
\(203\) 0 0
\(204\) −4320.00 −1.48265
\(205\) −2856.00 −0.973033
\(206\) −2812.00 −0.951074
\(207\) 4964.00 1.66677
\(208\) 256.000 0.0853385
\(209\) 1276.00 0.422310
\(210\) 0 0
\(211\) 3372.00 1.10018 0.550090 0.835105i \(-0.314593\pi\)
0.550090 + 0.835105i \(0.314593\pi\)
\(212\) 1768.00 0.572768
\(213\) 4920.00 1.58269
\(214\) −1176.00 −0.375653
\(215\) −5544.00 −1.75859
\(216\) 3680.00 1.15922
\(217\) 0 0
\(218\) 308.000 0.0956899
\(219\) −4080.00 −1.25891
\(220\) −616.000 −0.188776
\(221\) −1728.00 −0.525963
\(222\) 2600.00 0.786039
\(223\) −606.000 −0.181977 −0.0909883 0.995852i \(-0.529003\pi\)
−0.0909883 + 0.995852i \(0.529003\pi\)
\(224\) 0 0
\(225\) 5183.00 1.53570
\(226\) −3804.00 −1.11964
\(227\) −144.000 −0.0421040 −0.0210520 0.999778i \(-0.506702\pi\)
−0.0210520 + 0.999778i \(0.506702\pi\)
\(228\) −4640.00 −1.34777
\(229\) 1010.00 0.291453 0.145726 0.989325i \(-0.453448\pi\)
0.145726 + 0.989325i \(0.453448\pi\)
\(230\) 1904.00 0.545852
\(231\) 0 0
\(232\) 976.000 0.276196
\(233\) 3790.00 1.06563 0.532814 0.846233i \(-0.321135\pi\)
0.532814 + 0.846233i \(0.321135\pi\)
\(234\) 2336.00 0.652603
\(235\) −2324.00 −0.645111
\(236\) −2808.00 −0.774514
\(237\) 6000.00 1.64448
\(238\) 0 0
\(239\) 2184.00 0.591093 0.295546 0.955328i \(-0.404498\pi\)
0.295546 + 0.955328i \(0.404498\pi\)
\(240\) 2240.00 0.602464
\(241\) 4268.00 1.14077 0.570386 0.821377i \(-0.306794\pi\)
0.570386 + 0.821377i \(0.306794\pi\)
\(242\) 242.000 0.0642824
\(243\) 13870.0 3.66157
\(244\) −784.000 −0.205699
\(245\) 0 0
\(246\) −4080.00 −1.05744
\(247\) −1856.00 −0.478115
\(248\) 2096.00 0.536678
\(249\) 12120.0 3.08463
\(250\) −1512.00 −0.382509
\(251\) −7922.00 −1.99216 −0.996080 0.0884559i \(-0.971807\pi\)
−0.996080 + 0.0884559i \(0.971807\pi\)
\(252\) 0 0
\(253\) −748.000 −0.185875
\(254\) 128.000 0.0316198
\(255\) −15120.0 −3.71314
\(256\) 256.000 0.0625000
\(257\) −4002.00 −0.971354 −0.485677 0.874138i \(-0.661427\pi\)
−0.485677 + 0.874138i \(0.661427\pi\)
\(258\) −7920.00 −1.91115
\(259\) 0 0
\(260\) 896.000 0.213721
\(261\) 8906.00 2.11214
\(262\) 3168.00 0.747022
\(263\) −3960.00 −0.928457 −0.464228 0.885716i \(-0.653668\pi\)
−0.464228 + 0.885716i \(0.653668\pi\)
\(264\) −880.000 −0.205152
\(265\) 6188.00 1.43444
\(266\) 0 0
\(267\) −11460.0 −2.62674
\(268\) −1664.00 −0.379272
\(269\) −1878.00 −0.425664 −0.212832 0.977089i \(-0.568269\pi\)
−0.212832 + 0.977089i \(0.568269\pi\)
\(270\) 12880.0 2.90315
\(271\) 4740.00 1.06249 0.531244 0.847219i \(-0.321725\pi\)
0.531244 + 0.847219i \(0.321725\pi\)
\(272\) −1728.00 −0.385204
\(273\) 0 0
\(274\) 1996.00 0.440083
\(275\) −781.000 −0.171258
\(276\) 2720.00 0.593206
\(277\) 710.000 0.154006 0.0770032 0.997031i \(-0.475465\pi\)
0.0770032 + 0.997031i \(0.475465\pi\)
\(278\) −552.000 −0.119089
\(279\) 19126.0 4.10410
\(280\) 0 0
\(281\) −90.0000 −0.0191066 −0.00955329 0.999954i \(-0.503041\pi\)
−0.00955329 + 0.999954i \(0.503041\pi\)
\(282\) −3320.00 −0.701075
\(283\) 3448.00 0.724248 0.362124 0.932130i \(-0.382052\pi\)
0.362124 + 0.932130i \(0.382052\pi\)
\(284\) 1968.00 0.411195
\(285\) −16240.0 −3.37535
\(286\) −352.000 −0.0727769
\(287\) 0 0
\(288\) 2336.00 0.477952
\(289\) 6751.00 1.37411
\(290\) 3416.00 0.691705
\(291\) 4820.00 0.970974
\(292\) −1632.00 −0.327074
\(293\) 2804.00 0.559083 0.279542 0.960134i \(-0.409817\pi\)
0.279542 + 0.960134i \(0.409817\pi\)
\(294\) 0 0
\(295\) −9828.00 −1.93969
\(296\) 1040.00 0.204219
\(297\) −5060.00 −0.988589
\(298\) 2636.00 0.512414
\(299\) 1088.00 0.210437
\(300\) 2840.00 0.546558
\(301\) 0 0
\(302\) −1968.00 −0.374986
\(303\) −12160.0 −2.30552
\(304\) −1856.00 −0.350161
\(305\) −2744.00 −0.515151
\(306\) −15768.0 −2.94574
\(307\) −1320.00 −0.245395 −0.122698 0.992444i \(-0.539155\pi\)
−0.122698 + 0.992444i \(0.539155\pi\)
\(308\) 0 0
\(309\) −14060.0 −2.58850
\(310\) 7336.00 1.34405
\(311\) 1066.00 0.194364 0.0971822 0.995267i \(-0.469017\pi\)
0.0971822 + 0.995267i \(0.469017\pi\)
\(312\) 1280.00 0.232262
\(313\) 9254.00 1.67114 0.835570 0.549384i \(-0.185137\pi\)
0.835570 + 0.549384i \(0.185137\pi\)
\(314\) −3412.00 −0.613218
\(315\) 0 0
\(316\) 2400.00 0.427249
\(317\) −9722.00 −1.72253 −0.861265 0.508156i \(-0.830327\pi\)
−0.861265 + 0.508156i \(0.830327\pi\)
\(318\) 8840.00 1.55888
\(319\) −1342.00 −0.235541
\(320\) 896.000 0.156525
\(321\) −5880.00 −1.02240
\(322\) 0 0
\(323\) 12528.0 2.15813
\(324\) 10516.0 1.80316
\(325\) 1136.00 0.193889
\(326\) 2336.00 0.396868
\(327\) 1540.00 0.260435
\(328\) −1632.00 −0.274732
\(329\) 0 0
\(330\) −3080.00 −0.513783
\(331\) 2620.00 0.435070 0.217535 0.976053i \(-0.430198\pi\)
0.217535 + 0.976053i \(0.430198\pi\)
\(332\) 4848.00 0.801411
\(333\) 9490.00 1.56171
\(334\) −144.000 −0.0235908
\(335\) −5824.00 −0.949848
\(336\) 0 0
\(337\) 2806.00 0.453568 0.226784 0.973945i \(-0.427179\pi\)
0.226784 + 0.973945i \(0.427179\pi\)
\(338\) −3882.00 −0.624713
\(339\) −19020.0 −3.04727
\(340\) −6048.00 −0.964703
\(341\) −2882.00 −0.457680
\(342\) −16936.0 −2.67776
\(343\) 0 0
\(344\) −3168.00 −0.496532
\(345\) 9520.00 1.48562
\(346\) 8656.00 1.34494
\(347\) 5564.00 0.860781 0.430391 0.902643i \(-0.358376\pi\)
0.430391 + 0.902643i \(0.358376\pi\)
\(348\) 4880.00 0.751711
\(349\) −10060.0 −1.54298 −0.771489 0.636242i \(-0.780488\pi\)
−0.771489 + 0.636242i \(0.780488\pi\)
\(350\) 0 0
\(351\) 7360.00 1.11922
\(352\) −352.000 −0.0533002
\(353\) 5102.00 0.769269 0.384635 0.923069i \(-0.374327\pi\)
0.384635 + 0.923069i \(0.374327\pi\)
\(354\) −14040.0 −2.10796
\(355\) 6888.00 1.02979
\(356\) −4584.00 −0.682448
\(357\) 0 0
\(358\) −3848.00 −0.568081
\(359\) 7976.00 1.17258 0.586291 0.810100i \(-0.300587\pi\)
0.586291 + 0.810100i \(0.300587\pi\)
\(360\) 8176.00 1.19698
\(361\) 6597.00 0.961802
\(362\) −4460.00 −0.647548
\(363\) 1210.00 0.174955
\(364\) 0 0
\(365\) −5712.00 −0.819123
\(366\) −3920.00 −0.559841
\(367\) 1234.00 0.175516 0.0877579 0.996142i \(-0.472030\pi\)
0.0877579 + 0.996142i \(0.472030\pi\)
\(368\) 1088.00 0.154119
\(369\) −14892.0 −2.10094
\(370\) 3640.00 0.511445
\(371\) 0 0
\(372\) 10480.0 1.46065
\(373\) 8030.00 1.11469 0.557343 0.830283i \(-0.311821\pi\)
0.557343 + 0.830283i \(0.311821\pi\)
\(374\) 2376.00 0.328503
\(375\) −7560.00 −1.04106
\(376\) −1328.00 −0.182145
\(377\) 1952.00 0.266666
\(378\) 0 0
\(379\) −5184.00 −0.702597 −0.351298 0.936264i \(-0.614260\pi\)
−0.351298 + 0.936264i \(0.614260\pi\)
\(380\) −6496.00 −0.876941
\(381\) 640.000 0.0860583
\(382\) 4352.00 0.582900
\(383\) −7570.00 −1.00994 −0.504972 0.863135i \(-0.668497\pi\)
−0.504972 + 0.863135i \(0.668497\pi\)
\(384\) 1280.00 0.170103
\(385\) 0 0
\(386\) −6252.00 −0.824400
\(387\) −28908.0 −3.79710
\(388\) 1928.00 0.252266
\(389\) −5370.00 −0.699922 −0.349961 0.936764i \(-0.613805\pi\)
−0.349961 + 0.936764i \(0.613805\pi\)
\(390\) 4480.00 0.581676
\(391\) −7344.00 −0.949877
\(392\) 0 0
\(393\) 15840.0 2.03314
\(394\) −2244.00 −0.286932
\(395\) 8400.00 1.07000
\(396\) −3212.00 −0.407599
\(397\) −11442.0 −1.44649 −0.723246 0.690590i \(-0.757351\pi\)
−0.723246 + 0.690590i \(0.757351\pi\)
\(398\) 11172.0 1.40704
\(399\) 0 0
\(400\) 1136.00 0.142000
\(401\) 2362.00 0.294146 0.147073 0.989126i \(-0.453015\pi\)
0.147073 + 0.989126i \(0.453015\pi\)
\(402\) −8320.00 −1.03225
\(403\) 4192.00 0.518160
\(404\) −4864.00 −0.598993
\(405\) 36806.0 4.51581
\(406\) 0 0
\(407\) −1430.00 −0.174158
\(408\) −8640.00 −1.04839
\(409\) 16.0000 0.00193435 0.000967175 1.00000i \(-0.499692\pi\)
0.000967175 1.00000i \(0.499692\pi\)
\(410\) −5712.00 −0.688038
\(411\) 9980.00 1.19775
\(412\) −5624.00 −0.672511
\(413\) 0 0
\(414\) 9928.00 1.17859
\(415\) 16968.0 2.00705
\(416\) 512.000 0.0603434
\(417\) −2760.00 −0.324119
\(418\) 2552.00 0.298618
\(419\) −9462.00 −1.10322 −0.551610 0.834102i \(-0.685986\pi\)
−0.551610 + 0.834102i \(0.685986\pi\)
\(420\) 0 0
\(421\) −6302.00 −0.729550 −0.364775 0.931096i \(-0.618854\pi\)
−0.364775 + 0.931096i \(0.618854\pi\)
\(422\) 6744.00 0.777945
\(423\) −12118.0 −1.39290
\(424\) 3536.00 0.405008
\(425\) −7668.00 −0.875183
\(426\) 9840.00 1.11913
\(427\) 0 0
\(428\) −2352.00 −0.265627
\(429\) −1760.00 −0.198074
\(430\) −11088.0 −1.24351
\(431\) 7816.00 0.873512 0.436756 0.899580i \(-0.356127\pi\)
0.436756 + 0.899580i \(0.356127\pi\)
\(432\) 7360.00 0.819695
\(433\) 9506.00 1.05503 0.527516 0.849545i \(-0.323123\pi\)
0.527516 + 0.849545i \(0.323123\pi\)
\(434\) 0 0
\(435\) 17080.0 1.88258
\(436\) 616.000 0.0676630
\(437\) −7888.00 −0.863465
\(438\) −8160.00 −0.890182
\(439\) 8228.00 0.894535 0.447268 0.894400i \(-0.352397\pi\)
0.447268 + 0.894400i \(0.352397\pi\)
\(440\) −1232.00 −0.133485
\(441\) 0 0
\(442\) −3456.00 −0.371912
\(443\) 7668.00 0.822388 0.411194 0.911548i \(-0.365112\pi\)
0.411194 + 0.911548i \(0.365112\pi\)
\(444\) 5200.00 0.555813
\(445\) −16044.0 −1.70912
\(446\) −1212.00 −0.128677
\(447\) 13180.0 1.39461
\(448\) 0 0
\(449\) −922.000 −0.0969084 −0.0484542 0.998825i \(-0.515429\pi\)
−0.0484542 + 0.998825i \(0.515429\pi\)
\(450\) 10366.0 1.08591
\(451\) 2244.00 0.234292
\(452\) −7608.00 −0.791704
\(453\) −9840.00 −1.02058
\(454\) −288.000 −0.0297720
\(455\) 0 0
\(456\) −9280.00 −0.953017
\(457\) 3386.00 0.346587 0.173294 0.984870i \(-0.444559\pi\)
0.173294 + 0.984870i \(0.444559\pi\)
\(458\) 2020.00 0.206088
\(459\) −49680.0 −5.05199
\(460\) 3808.00 0.385976
\(461\) 3300.00 0.333398 0.166699 0.986008i \(-0.446689\pi\)
0.166699 + 0.986008i \(0.446689\pi\)
\(462\) 0 0
\(463\) 14236.0 1.42895 0.714474 0.699662i \(-0.246666\pi\)
0.714474 + 0.699662i \(0.246666\pi\)
\(464\) 1952.00 0.195300
\(465\) 36680.0 3.65805
\(466\) 7580.00 0.753512
\(467\) −3770.00 −0.373565 −0.186782 0.982401i \(-0.559806\pi\)
−0.186782 + 0.982401i \(0.559806\pi\)
\(468\) 4672.00 0.461460
\(469\) 0 0
\(470\) −4648.00 −0.456162
\(471\) −17060.0 −1.66897
\(472\) −5616.00 −0.547664
\(473\) 4356.00 0.423444
\(474\) 12000.0 1.16282
\(475\) −8236.00 −0.795565
\(476\) 0 0
\(477\) 32266.0 3.09719
\(478\) 4368.00 0.417966
\(479\) −17796.0 −1.69754 −0.848768 0.528765i \(-0.822655\pi\)
−0.848768 + 0.528765i \(0.822655\pi\)
\(480\) 4480.00 0.426006
\(481\) 2080.00 0.197172
\(482\) 8536.00 0.806648
\(483\) 0 0
\(484\) 484.000 0.0454545
\(485\) 6748.00 0.631775
\(486\) 27740.0 2.58912
\(487\) −3684.00 −0.342788 −0.171394 0.985203i \(-0.554827\pi\)
−0.171394 + 0.985203i \(0.554827\pi\)
\(488\) −1568.00 −0.145451
\(489\) 11680.0 1.08014
\(490\) 0 0
\(491\) −17236.0 −1.58422 −0.792108 0.610381i \(-0.791016\pi\)
−0.792108 + 0.610381i \(0.791016\pi\)
\(492\) −8160.00 −0.747726
\(493\) −13176.0 −1.20369
\(494\) −3712.00 −0.338078
\(495\) −11242.0 −1.02079
\(496\) 4192.00 0.379489
\(497\) 0 0
\(498\) 24240.0 2.18117
\(499\) 13176.0 1.18204 0.591021 0.806656i \(-0.298725\pi\)
0.591021 + 0.806656i \(0.298725\pi\)
\(500\) −3024.00 −0.270475
\(501\) −720.000 −0.0642060
\(502\) −15844.0 −1.40867
\(503\) −15428.0 −1.36760 −0.683798 0.729672i \(-0.739673\pi\)
−0.683798 + 0.729672i \(0.739673\pi\)
\(504\) 0 0
\(505\) −17024.0 −1.50011
\(506\) −1496.00 −0.131433
\(507\) −19410.0 −1.70025
\(508\) 256.000 0.0223586
\(509\) 7842.00 0.682889 0.341445 0.939902i \(-0.389084\pi\)
0.341445 + 0.939902i \(0.389084\pi\)
\(510\) −30240.0 −2.62559
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) −53360.0 −4.59240
\(514\) −8004.00 −0.686851
\(515\) −19684.0 −1.68423
\(516\) −15840.0 −1.35139
\(517\) 1826.00 0.155333
\(518\) 0 0
\(519\) 43280.0 3.66046
\(520\) 1792.00 0.151124
\(521\) 17250.0 1.45055 0.725275 0.688460i \(-0.241713\pi\)
0.725275 + 0.688460i \(0.241713\pi\)
\(522\) 17812.0 1.49351
\(523\) −1032.00 −0.0862834 −0.0431417 0.999069i \(-0.513737\pi\)
−0.0431417 + 0.999069i \(0.513737\pi\)
\(524\) 6336.00 0.528224
\(525\) 0 0
\(526\) −7920.00 −0.656518
\(527\) −28296.0 −2.33889
\(528\) −1760.00 −0.145065
\(529\) −7543.00 −0.619956
\(530\) 12376.0 1.01430
\(531\) −51246.0 −4.18811
\(532\) 0 0
\(533\) −3264.00 −0.265252
\(534\) −22920.0 −1.85739
\(535\) −8232.00 −0.665234
\(536\) −3328.00 −0.268186
\(537\) −19240.0 −1.54612
\(538\) −3756.00 −0.300990
\(539\) 0 0
\(540\) 25760.0 2.05284
\(541\) 94.0000 0.00747020 0.00373510 0.999993i \(-0.498811\pi\)
0.00373510 + 0.999993i \(0.498811\pi\)
\(542\) 9480.00 0.751293
\(543\) −22300.0 −1.76240
\(544\) −3456.00 −0.272380
\(545\) 2156.00 0.169455
\(546\) 0 0
\(547\) −11676.0 −0.912669 −0.456334 0.889808i \(-0.650838\pi\)
−0.456334 + 0.889808i \(0.650838\pi\)
\(548\) 3992.00 0.311186
\(549\) −14308.0 −1.11230
\(550\) −1562.00 −0.121098
\(551\) −14152.0 −1.09418
\(552\) 5440.00 0.419460
\(553\) 0 0
\(554\) 1420.00 0.108899
\(555\) 18200.0 1.39198
\(556\) −1104.00 −0.0842087
\(557\) −1858.00 −0.141339 −0.0706696 0.997500i \(-0.522514\pi\)
−0.0706696 + 0.997500i \(0.522514\pi\)
\(558\) 38252.0 2.90204
\(559\) −6336.00 −0.479399
\(560\) 0 0
\(561\) 11880.0 0.894071
\(562\) −180.000 −0.0135104
\(563\) 23028.0 1.72383 0.861913 0.507056i \(-0.169266\pi\)
0.861913 + 0.507056i \(0.169266\pi\)
\(564\) −6640.00 −0.495735
\(565\) −26628.0 −1.98274
\(566\) 6896.00 0.512121
\(567\) 0 0
\(568\) 3936.00 0.290759
\(569\) −17066.0 −1.25737 −0.628685 0.777660i \(-0.716407\pi\)
−0.628685 + 0.777660i \(0.716407\pi\)
\(570\) −32480.0 −2.38673
\(571\) −10252.0 −0.751371 −0.375686 0.926747i \(-0.622593\pi\)
−0.375686 + 0.926747i \(0.622593\pi\)
\(572\) −704.000 −0.0514610
\(573\) 21760.0 1.58645
\(574\) 0 0
\(575\) 4828.00 0.350159
\(576\) 4672.00 0.337963
\(577\) −2142.00 −0.154545 −0.0772726 0.997010i \(-0.524621\pi\)
−0.0772726 + 0.997010i \(0.524621\pi\)
\(578\) 13502.0 0.971642
\(579\) −31260.0 −2.24373
\(580\) 6832.00 0.489109
\(581\) 0 0
\(582\) 9640.00 0.686582
\(583\) −4862.00 −0.345392
\(584\) −3264.00 −0.231276
\(585\) 16352.0 1.15568
\(586\) 5608.00 0.395332
\(587\) −3474.00 −0.244271 −0.122136 0.992513i \(-0.538974\pi\)
−0.122136 + 0.992513i \(0.538974\pi\)
\(588\) 0 0
\(589\) −30392.0 −2.12611
\(590\) −19656.0 −1.37157
\(591\) −11220.0 −0.780929
\(592\) 2080.00 0.144405
\(593\) 17424.0 1.20661 0.603303 0.797512i \(-0.293851\pi\)
0.603303 + 0.797512i \(0.293851\pi\)
\(594\) −10120.0 −0.699038
\(595\) 0 0
\(596\) 5272.00 0.362331
\(597\) 55860.0 3.82948
\(598\) 2176.00 0.148801
\(599\) 6916.00 0.471753 0.235877 0.971783i \(-0.424204\pi\)
0.235877 + 0.971783i \(0.424204\pi\)
\(600\) 5680.00 0.386475
\(601\) −16468.0 −1.11771 −0.558855 0.829265i \(-0.688759\pi\)
−0.558855 + 0.829265i \(0.688759\pi\)
\(602\) 0 0
\(603\) −30368.0 −2.05088
\(604\) −3936.00 −0.265155
\(605\) 1694.00 0.113836
\(606\) −24320.0 −1.63025
\(607\) 17176.0 1.14852 0.574261 0.818673i \(-0.305290\pi\)
0.574261 + 0.818673i \(0.305290\pi\)
\(608\) −3712.00 −0.247601
\(609\) 0 0
\(610\) −5488.00 −0.364267
\(611\) −2656.00 −0.175860
\(612\) −31536.0 −2.08295
\(613\) 11402.0 0.751260 0.375630 0.926770i \(-0.377426\pi\)
0.375630 + 0.926770i \(0.377426\pi\)
\(614\) −2640.00 −0.173521
\(615\) −28560.0 −1.87260
\(616\) 0 0
\(617\) 3654.00 0.238419 0.119209 0.992869i \(-0.461964\pi\)
0.119209 + 0.992869i \(0.461964\pi\)
\(618\) −28120.0 −1.83034
\(619\) 11318.0 0.734909 0.367455 0.930041i \(-0.380229\pi\)
0.367455 + 0.930041i \(0.380229\pi\)
\(620\) 14672.0 0.950390
\(621\) 31280.0 2.02129
\(622\) 2132.00 0.137436
\(623\) 0 0
\(624\) 2560.00 0.164234
\(625\) −19459.0 −1.24538
\(626\) 18508.0 1.18167
\(627\) 12760.0 0.812736
\(628\) −6824.00 −0.433610
\(629\) −14040.0 −0.890002
\(630\) 0 0
\(631\) −23872.0 −1.50607 −0.753034 0.657981i \(-0.771411\pi\)
−0.753034 + 0.657981i \(0.771411\pi\)
\(632\) 4800.00 0.302110
\(633\) 33720.0 2.11730
\(634\) −19444.0 −1.21801
\(635\) 896.000 0.0559948
\(636\) 17680.0 1.10229
\(637\) 0 0
\(638\) −2684.00 −0.166553
\(639\) 35916.0 2.22350
\(640\) 1792.00 0.110680
\(641\) −27026.0 −1.66531 −0.832654 0.553793i \(-0.813180\pi\)
−0.832654 + 0.553793i \(0.813180\pi\)
\(642\) −11760.0 −0.722944
\(643\) −6498.00 −0.398532 −0.199266 0.979945i \(-0.563856\pi\)
−0.199266 + 0.979945i \(0.563856\pi\)
\(644\) 0 0
\(645\) −55440.0 −3.38442
\(646\) 25056.0 1.52603
\(647\) 6422.00 0.390224 0.195112 0.980781i \(-0.437493\pi\)
0.195112 + 0.980781i \(0.437493\pi\)
\(648\) 21032.0 1.27502
\(649\) 7722.00 0.467049
\(650\) 2272.00 0.137100
\(651\) 0 0
\(652\) 4672.00 0.280628
\(653\) 23670.0 1.41850 0.709249 0.704958i \(-0.249034\pi\)
0.709249 + 0.704958i \(0.249034\pi\)
\(654\) 3080.00 0.184155
\(655\) 22176.0 1.32288
\(656\) −3264.00 −0.194265
\(657\) −29784.0 −1.76862
\(658\) 0 0
\(659\) −9812.00 −0.580002 −0.290001 0.957026i \(-0.593656\pi\)
−0.290001 + 0.957026i \(0.593656\pi\)
\(660\) −6160.00 −0.363300
\(661\) 5190.00 0.305397 0.152699 0.988273i \(-0.451204\pi\)
0.152699 + 0.988273i \(0.451204\pi\)
\(662\) 5240.00 0.307641
\(663\) −17280.0 −1.01222
\(664\) 9696.00 0.566683
\(665\) 0 0
\(666\) 18980.0 1.10429
\(667\) 8296.00 0.481593
\(668\) −288.000 −0.0166812
\(669\) −6060.00 −0.350214
\(670\) −11648.0 −0.671644
\(671\) 2156.00 0.124041
\(672\) 0 0
\(673\) 94.0000 0.00538400 0.00269200 0.999996i \(-0.499143\pi\)
0.00269200 + 0.999996i \(0.499143\pi\)
\(674\) 5612.00 0.320721
\(675\) 32660.0 1.86235
\(676\) −7764.00 −0.441739
\(677\) 12432.0 0.705762 0.352881 0.935668i \(-0.385202\pi\)
0.352881 + 0.935668i \(0.385202\pi\)
\(678\) −38040.0 −2.15475
\(679\) 0 0
\(680\) −12096.0 −0.682148
\(681\) −1440.00 −0.0810293
\(682\) −5764.00 −0.323629
\(683\) −2308.00 −0.129302 −0.0646509 0.997908i \(-0.520593\pi\)
−0.0646509 + 0.997908i \(0.520593\pi\)
\(684\) −33872.0 −1.89346
\(685\) 13972.0 0.779332
\(686\) 0 0
\(687\) 10100.0 0.560901
\(688\) −6336.00 −0.351101
\(689\) 7072.00 0.391033
\(690\) 19040.0 1.05049
\(691\) −26446.0 −1.45594 −0.727969 0.685610i \(-0.759536\pi\)
−0.727969 + 0.685610i \(0.759536\pi\)
\(692\) 17312.0 0.951017
\(693\) 0 0
\(694\) 11128.0 0.608664
\(695\) −3864.00 −0.210892
\(696\) 9760.00 0.531540
\(697\) 22032.0 1.19730
\(698\) −20120.0 −1.09105
\(699\) 37900.0 2.05080
\(700\) 0 0
\(701\) 26450.0 1.42511 0.712555 0.701616i \(-0.247538\pi\)
0.712555 + 0.701616i \(0.247538\pi\)
\(702\) 14720.0 0.791411
\(703\) −15080.0 −0.809037
\(704\) −704.000 −0.0376889
\(705\) −23240.0 −1.24152
\(706\) 10204.0 0.543956
\(707\) 0 0
\(708\) −28080.0 −1.49055
\(709\) 17102.0 0.905894 0.452947 0.891537i \(-0.350373\pi\)
0.452947 + 0.891537i \(0.350373\pi\)
\(710\) 13776.0 0.728175
\(711\) 43800.0 2.31031
\(712\) −9168.00 −0.482564
\(713\) 17816.0 0.935785
\(714\) 0 0
\(715\) −2464.00 −0.128879
\(716\) −7696.00 −0.401694
\(717\) 21840.0 1.13756
\(718\) 15952.0 0.829141
\(719\) 16854.0 0.874198 0.437099 0.899413i \(-0.356006\pi\)
0.437099 + 0.899413i \(0.356006\pi\)
\(720\) 16352.0 0.846393
\(721\) 0 0
\(722\) 13194.0 0.680097
\(723\) 42680.0 2.19542
\(724\) −8920.00 −0.457886
\(725\) 8662.00 0.443722
\(726\) 2420.00 0.123712
\(727\) 34670.0 1.76869 0.884346 0.466832i \(-0.154605\pi\)
0.884346 + 0.466832i \(0.154605\pi\)
\(728\) 0 0
\(729\) 67717.0 3.44038
\(730\) −11424.0 −0.579207
\(731\) 42768.0 2.16393
\(732\) −7840.00 −0.395867
\(733\) −11716.0 −0.590369 −0.295184 0.955440i \(-0.595381\pi\)
−0.295184 + 0.955440i \(0.595381\pi\)
\(734\) 2468.00 0.124108
\(735\) 0 0
\(736\) 2176.00 0.108979
\(737\) 4576.00 0.228710
\(738\) −29784.0 −1.48559
\(739\) 29772.0 1.48198 0.740988 0.671518i \(-0.234357\pi\)
0.740988 + 0.671518i \(0.234357\pi\)
\(740\) 7280.00 0.361646
\(741\) −18560.0 −0.920133
\(742\) 0 0
\(743\) −24928.0 −1.23085 −0.615424 0.788196i \(-0.711015\pi\)
−0.615424 + 0.788196i \(0.711015\pi\)
\(744\) 20960.0 1.03284
\(745\) 18452.0 0.907421
\(746\) 16060.0 0.788202
\(747\) 88476.0 4.33356
\(748\) 4752.00 0.232287
\(749\) 0 0
\(750\) −15120.0 −0.736139
\(751\) −4652.00 −0.226037 −0.113019 0.993593i \(-0.536052\pi\)
−0.113019 + 0.993593i \(0.536052\pi\)
\(752\) −2656.00 −0.128796
\(753\) −79220.0 −3.83391
\(754\) 3904.00 0.188561
\(755\) −13776.0 −0.664053
\(756\) 0 0
\(757\) −1802.00 −0.0865189 −0.0432594 0.999064i \(-0.513774\pi\)
−0.0432594 + 0.999064i \(0.513774\pi\)
\(758\) −10368.0 −0.496811
\(759\) −7480.00 −0.357716
\(760\) −12992.0 −0.620091
\(761\) 808.000 0.0384888 0.0192444 0.999815i \(-0.493874\pi\)
0.0192444 + 0.999815i \(0.493874\pi\)
\(762\) 1280.00 0.0608524
\(763\) 0 0
\(764\) 8704.00 0.412172
\(765\) −110376. −5.21654
\(766\) −15140.0 −0.714139
\(767\) −11232.0 −0.528767
\(768\) 2560.00 0.120281
\(769\) −23144.0 −1.08530 −0.542649 0.839960i \(-0.682579\pi\)
−0.542649 + 0.839960i \(0.682579\pi\)
\(770\) 0 0
\(771\) −40020.0 −1.86937
\(772\) −12504.0 −0.582939
\(773\) 27466.0 1.27799 0.638993 0.769212i \(-0.279351\pi\)
0.638993 + 0.769212i \(0.279351\pi\)
\(774\) −57816.0 −2.68495
\(775\) 18602.0 0.862198
\(776\) 3856.00 0.178379
\(777\) 0 0
\(778\) −10740.0 −0.494920
\(779\) 23664.0 1.08838
\(780\) 8960.00 0.411307
\(781\) −5412.00 −0.247960
\(782\) −14688.0 −0.671665
\(783\) 56120.0 2.56139
\(784\) 0 0
\(785\) −23884.0 −1.08593
\(786\) 31680.0 1.43764
\(787\) −23604.0 −1.06911 −0.534556 0.845133i \(-0.679521\pi\)
−0.534556 + 0.845133i \(0.679521\pi\)
\(788\) −4488.00 −0.202891
\(789\) −39600.0 −1.78682
\(790\) 16800.0 0.756604
\(791\) 0 0
\(792\) −6424.00 −0.288216
\(793\) −3136.00 −0.140432
\(794\) −22884.0 −1.02282
\(795\) 61880.0 2.76058
\(796\) 22344.0 0.994927
\(797\) −4122.00 −0.183198 −0.0915990 0.995796i \(-0.529198\pi\)
−0.0915990 + 0.995796i \(0.529198\pi\)
\(798\) 0 0
\(799\) 17928.0 0.793801
\(800\) 2272.00 0.100409
\(801\) −83658.0 −3.69027
\(802\) 4724.00 0.207993
\(803\) 4488.00 0.197233
\(804\) −16640.0 −0.729910
\(805\) 0 0
\(806\) 8384.00 0.366394
\(807\) −18780.0 −0.819191
\(808\) −9728.00 −0.423552
\(809\) −9110.00 −0.395909 −0.197955 0.980211i \(-0.563430\pi\)
−0.197955 + 0.980211i \(0.563430\pi\)
\(810\) 73612.0 3.19316
\(811\) 28352.0 1.22759 0.613794 0.789466i \(-0.289643\pi\)
0.613794 + 0.789466i \(0.289643\pi\)
\(812\) 0 0
\(813\) 47400.0 2.04476
\(814\) −2860.00 −0.123149
\(815\) 16352.0 0.702804
\(816\) −17280.0 −0.741325
\(817\) 45936.0 1.96707
\(818\) 32.0000 0.00136779
\(819\) 0 0
\(820\) −11424.0 −0.486516
\(821\) −14002.0 −0.595217 −0.297609 0.954688i \(-0.596189\pi\)
−0.297609 + 0.954688i \(0.596189\pi\)
\(822\) 19960.0 0.846940
\(823\) −14848.0 −0.628881 −0.314440 0.949277i \(-0.601817\pi\)
−0.314440 + 0.949277i \(0.601817\pi\)
\(824\) −11248.0 −0.475537
\(825\) −7810.00 −0.329587
\(826\) 0 0
\(827\) 10500.0 0.441500 0.220750 0.975330i \(-0.429149\pi\)
0.220750 + 0.975330i \(0.429149\pi\)
\(828\) 19856.0 0.833386
\(829\) −23890.0 −1.00089 −0.500443 0.865770i \(-0.666829\pi\)
−0.500443 + 0.865770i \(0.666829\pi\)
\(830\) 33936.0 1.41920
\(831\) 7100.00 0.296385
\(832\) 1024.00 0.0426692
\(833\) 0 0
\(834\) −5520.00 −0.229187
\(835\) −1008.00 −0.0417764
\(836\) 5104.00 0.211155
\(837\) 120520. 4.97704
\(838\) −18924.0 −0.780094
\(839\) 670.000 0.0275697 0.0137848 0.999905i \(-0.495612\pi\)
0.0137848 + 0.999905i \(0.495612\pi\)
\(840\) 0 0
\(841\) −9505.00 −0.389725
\(842\) −12604.0 −0.515870
\(843\) −900.000 −0.0367706
\(844\) 13488.0 0.550090
\(845\) −27174.0 −1.10629
\(846\) −24236.0 −0.984930
\(847\) 0 0
\(848\) 7072.00 0.286384
\(849\) 34480.0 1.39382
\(850\) −15336.0 −0.618848
\(851\) 8840.00 0.356088
\(852\) 19680.0 0.791345
\(853\) 4776.00 0.191708 0.0958541 0.995395i \(-0.469442\pi\)
0.0958541 + 0.995395i \(0.469442\pi\)
\(854\) 0 0
\(855\) −118552. −4.74198
\(856\) −4704.00 −0.187826
\(857\) 13024.0 0.519126 0.259563 0.965726i \(-0.416421\pi\)
0.259563 + 0.965726i \(0.416421\pi\)
\(858\) −3520.00 −0.140059
\(859\) 32998.0 1.31068 0.655342 0.755332i \(-0.272525\pi\)
0.655342 + 0.755332i \(0.272525\pi\)
\(860\) −22176.0 −0.879297
\(861\) 0 0
\(862\) 15632.0 0.617666
\(863\) 22272.0 0.878503 0.439251 0.898364i \(-0.355244\pi\)
0.439251 + 0.898364i \(0.355244\pi\)
\(864\) 14720.0 0.579612
\(865\) 60592.0 2.38172
\(866\) 19012.0 0.746021
\(867\) 67510.0 2.64447
\(868\) 0 0
\(869\) −6600.00 −0.257641
\(870\) 34160.0 1.33119
\(871\) −6656.00 −0.258932
\(872\) 1232.00 0.0478449
\(873\) 35186.0 1.36411
\(874\) −15776.0 −0.610562
\(875\) 0 0
\(876\) −16320.0 −0.629454
\(877\) −30398.0 −1.17043 −0.585215 0.810878i \(-0.698990\pi\)
−0.585215 + 0.810878i \(0.698990\pi\)
\(878\) 16456.0 0.632532
\(879\) 28040.0 1.07596
\(880\) −2464.00 −0.0943880
\(881\) −1630.00 −0.0623338 −0.0311669 0.999514i \(-0.509922\pi\)
−0.0311669 + 0.999514i \(0.509922\pi\)
\(882\) 0 0
\(883\) −20228.0 −0.770925 −0.385462 0.922724i \(-0.625958\pi\)
−0.385462 + 0.922724i \(0.625958\pi\)
\(884\) −6912.00 −0.262982
\(885\) −98280.0 −3.73293
\(886\) 15336.0 0.581516
\(887\) −38908.0 −1.47283 −0.736416 0.676528i \(-0.763484\pi\)
−0.736416 + 0.676528i \(0.763484\pi\)
\(888\) 10400.0 0.393019
\(889\) 0 0
\(890\) −32088.0 −1.20853
\(891\) −28919.0 −1.08734
\(892\) −2424.00 −0.0909883
\(893\) 19256.0 0.721587
\(894\) 26360.0 0.986141
\(895\) −26936.0 −1.00600
\(896\) 0 0
\(897\) 10880.0 0.404986
\(898\) −1844.00 −0.0685246
\(899\) 31964.0 1.18583
\(900\) 20732.0 0.767852
\(901\) −47736.0 −1.76506
\(902\) 4488.00 0.165670
\(903\) 0 0
\(904\) −15216.0 −0.559819
\(905\) −31220.0 −1.14673
\(906\) −19680.0 −0.721660
\(907\) −20936.0 −0.766448 −0.383224 0.923655i \(-0.625186\pi\)
−0.383224 + 0.923655i \(0.625186\pi\)
\(908\) −576.000 −0.0210520
\(909\) −88768.0 −3.23900
\(910\) 0 0
\(911\) 48204.0 1.75310 0.876548 0.481315i \(-0.159841\pi\)
0.876548 + 0.481315i \(0.159841\pi\)
\(912\) −18560.0 −0.673885
\(913\) −13332.0 −0.483269
\(914\) 6772.00 0.245074
\(915\) −27440.0 −0.991408
\(916\) 4040.00 0.145726
\(917\) 0 0
\(918\) −99360.0 −3.57230
\(919\) −27304.0 −0.980061 −0.490030 0.871705i \(-0.663014\pi\)
−0.490030 + 0.871705i \(0.663014\pi\)
\(920\) 7616.00 0.272926
\(921\) −13200.0 −0.472264
\(922\) 6600.00 0.235748
\(923\) 7872.00 0.280726
\(924\) 0 0
\(925\) 9230.00 0.328087
\(926\) 28472.0 1.01042
\(927\) −102638. −3.63654
\(928\) 3904.00 0.138098
\(929\) −30.0000 −0.00105949 −0.000529746 1.00000i \(-0.500169\pi\)
−0.000529746 1.00000i \(0.500169\pi\)
\(930\) 73360.0 2.58663
\(931\) 0 0
\(932\) 15160.0 0.532814
\(933\) 10660.0 0.374054
\(934\) −7540.00 −0.264150
\(935\) 16632.0 0.581737
\(936\) 9344.00 0.326301
\(937\) −4736.00 −0.165121 −0.0825605 0.996586i \(-0.526310\pi\)
−0.0825605 + 0.996586i \(0.526310\pi\)
\(938\) 0 0
\(939\) 92540.0 3.21611
\(940\) −9296.00 −0.322555
\(941\) −19996.0 −0.692722 −0.346361 0.938101i \(-0.612583\pi\)
−0.346361 + 0.938101i \(0.612583\pi\)
\(942\) −34120.0 −1.18014
\(943\) −13872.0 −0.479040
\(944\) −11232.0 −0.387257
\(945\) 0 0
\(946\) 8712.00 0.299420
\(947\) −1252.00 −0.0429615 −0.0214807 0.999769i \(-0.506838\pi\)
−0.0214807 + 0.999769i \(0.506838\pi\)
\(948\) 24000.0 0.822240
\(949\) −6528.00 −0.223296
\(950\) −16472.0 −0.562550
\(951\) −97220.0 −3.31501
\(952\) 0 0
\(953\) 17986.0 0.611357 0.305679 0.952135i \(-0.401117\pi\)
0.305679 + 0.952135i \(0.401117\pi\)
\(954\) 64532.0 2.19004
\(955\) 30464.0 1.03224
\(956\) 8736.00 0.295546
\(957\) −13420.0 −0.453299
\(958\) −35592.0 −1.20034
\(959\) 0 0
\(960\) 8960.00 0.301232
\(961\) 38853.0 1.30419
\(962\) 4160.00 0.139422
\(963\) −42924.0 −1.43635
\(964\) 17072.0 0.570386
\(965\) −43764.0 −1.45991
\(966\) 0 0
\(967\) 14256.0 0.474087 0.237043 0.971499i \(-0.423822\pi\)
0.237043 + 0.971499i \(0.423822\pi\)
\(968\) 968.000 0.0321412
\(969\) 125280. 4.15333
\(970\) 13496.0 0.446732
\(971\) 50214.0 1.65957 0.829786 0.558082i \(-0.188463\pi\)
0.829786 + 0.558082i \(0.188463\pi\)
\(972\) 55480.0 1.83078
\(973\) 0 0
\(974\) −7368.00 −0.242388
\(975\) 11360.0 0.373140
\(976\) −3136.00 −0.102849
\(977\) −35814.0 −1.17276 −0.586382 0.810034i \(-0.699448\pi\)
−0.586382 + 0.810034i \(0.699448\pi\)
\(978\) 23360.0 0.763773
\(979\) 12606.0 0.411532
\(980\) 0 0
\(981\) 11242.0 0.365881
\(982\) −34472.0 −1.12021
\(983\) 19274.0 0.625377 0.312688 0.949856i \(-0.398770\pi\)
0.312688 + 0.949856i \(0.398770\pi\)
\(984\) −16320.0 −0.528722
\(985\) −15708.0 −0.508120
\(986\) −26352.0 −0.851135
\(987\) 0 0
\(988\) −7424.00 −0.239058
\(989\) −26928.0 −0.865784
\(990\) −22484.0 −0.721806
\(991\) 59996.0 1.92314 0.961572 0.274553i \(-0.0885298\pi\)
0.961572 + 0.274553i \(0.0885298\pi\)
\(992\) 8384.00 0.268339
\(993\) 26200.0 0.837293
\(994\) 0 0
\(995\) 78204.0 2.49169
\(996\) 48480.0 1.54232
\(997\) −24344.0 −0.773302 −0.386651 0.922226i \(-0.626368\pi\)
−0.386651 + 0.922226i \(0.626368\pi\)
\(998\) 26352.0 0.835830
\(999\) 59800.0 1.89388
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 1078.4.a.h.1.1 1
7.6 odd 2 154.4.a.c.1.1 1
21.20 even 2 1386.4.a.g.1.1 1
28.27 even 2 1232.4.a.i.1.1 1
77.76 even 2 1694.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
154.4.a.c.1.1 1 7.6 odd 2
1078.4.a.h.1.1 1 1.1 even 1 trivial
1232.4.a.i.1.1 1 28.27 even 2
1386.4.a.g.1.1 1 21.20 even 2
1694.4.a.a.1.1 1 77.76 even 2