Properties

Label 928.4.a.a.1.1
Level $928$
Weight $4$
Character 928.1
Self dual yes
Analytic conductor $54.754$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 928 = 2^{5} \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 928.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(54.7537724853\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 928.1

$q$-expansion

\(f(q)\) \(=\) \(q-7.00000 q^{3} -13.0000 q^{5} +16.0000 q^{7} +22.0000 q^{9} +O(q^{10})\) \(q-7.00000 q^{3} -13.0000 q^{5} +16.0000 q^{7} +22.0000 q^{9} -45.0000 q^{11} +61.0000 q^{13} +91.0000 q^{15} -102.000 q^{17} -68.0000 q^{19} -112.000 q^{21} +194.000 q^{23} +44.0000 q^{25} +35.0000 q^{27} -29.0000 q^{29} +149.000 q^{31} +315.000 q^{33} -208.000 q^{35} +400.000 q^{37} -427.000 q^{39} +280.000 q^{41} +263.000 q^{43} -286.000 q^{45} +509.000 q^{47} -87.0000 q^{49} +714.000 q^{51} -605.000 q^{53} +585.000 q^{55} +476.000 q^{57} -578.000 q^{59} -718.000 q^{61} +352.000 q^{63} -793.000 q^{65} -260.000 q^{67} -1358.00 q^{69} +738.000 q^{71} +652.000 q^{73} -308.000 q^{75} -720.000 q^{77} -917.000 q^{79} -839.000 q^{81} +678.000 q^{83} +1326.00 q^{85} +203.000 q^{87} -1008.00 q^{89} +976.000 q^{91} -1043.00 q^{93} +884.000 q^{95} -1764.00 q^{97} -990.000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −7.00000 −1.34715 −0.673575 0.739119i \(-0.735242\pi\)
−0.673575 + 0.739119i \(0.735242\pi\)
\(4\) 0 0
\(5\) −13.0000 −1.16276 −0.581378 0.813634i \(-0.697486\pi\)
−0.581378 + 0.813634i \(0.697486\pi\)
\(6\) 0 0
\(7\) 16.0000 0.863919 0.431959 0.901893i \(-0.357822\pi\)
0.431959 + 0.901893i \(0.357822\pi\)
\(8\) 0 0
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) −45.0000 −1.23346 −0.616728 0.787177i \(-0.711542\pi\)
−0.616728 + 0.787177i \(0.711542\pi\)
\(12\) 0 0
\(13\) 61.0000 1.30141 0.650706 0.759330i \(-0.274473\pi\)
0.650706 + 0.759330i \(0.274473\pi\)
\(14\) 0 0
\(15\) 91.0000 1.56641
\(16\) 0 0
\(17\) −102.000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) −68.0000 −0.821067 −0.410533 0.911846i \(-0.634657\pi\)
−0.410533 + 0.911846i \(0.634657\pi\)
\(20\) 0 0
\(21\) −112.000 −1.16383
\(22\) 0 0
\(23\) 194.000 1.75877 0.879387 0.476108i \(-0.157953\pi\)
0.879387 + 0.476108i \(0.157953\pi\)
\(24\) 0 0
\(25\) 44.0000 0.352000
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) 0 0
\(29\) −29.0000 −0.185695
\(30\) 0 0
\(31\) 149.000 0.863264 0.431632 0.902050i \(-0.357938\pi\)
0.431632 + 0.902050i \(0.357938\pi\)
\(32\) 0 0
\(33\) 315.000 1.66165
\(34\) 0 0
\(35\) −208.000 −1.00453
\(36\) 0 0
\(37\) 400.000 1.77729 0.888643 0.458599i \(-0.151649\pi\)
0.888643 + 0.458599i \(0.151649\pi\)
\(38\) 0 0
\(39\) −427.000 −1.75320
\(40\) 0 0
\(41\) 280.000 1.06655 0.533276 0.845941i \(-0.320961\pi\)
0.533276 + 0.845941i \(0.320961\pi\)
\(42\) 0 0
\(43\) 263.000 0.932724 0.466362 0.884594i \(-0.345564\pi\)
0.466362 + 0.884594i \(0.345564\pi\)
\(44\) 0 0
\(45\) −286.000 −0.947430
\(46\) 0 0
\(47\) 509.000 1.57969 0.789843 0.613309i \(-0.210162\pi\)
0.789843 + 0.613309i \(0.210162\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) 0 0
\(51\) 714.000 1.96039
\(52\) 0 0
\(53\) −605.000 −1.56798 −0.783992 0.620771i \(-0.786820\pi\)
−0.783992 + 0.620771i \(0.786820\pi\)
\(54\) 0 0
\(55\) 585.000 1.43421
\(56\) 0 0
\(57\) 476.000 1.10610
\(58\) 0 0
\(59\) −578.000 −1.27541 −0.637705 0.770281i \(-0.720116\pi\)
−0.637705 + 0.770281i \(0.720116\pi\)
\(60\) 0 0
\(61\) −718.000 −1.50706 −0.753529 0.657415i \(-0.771650\pi\)
−0.753529 + 0.657415i \(0.771650\pi\)
\(62\) 0 0
\(63\) 352.000 0.703934
\(64\) 0 0
\(65\) −793.000 −1.51322
\(66\) 0 0
\(67\) −260.000 −0.474090 −0.237045 0.971499i \(-0.576179\pi\)
−0.237045 + 0.971499i \(0.576179\pi\)
\(68\) 0 0
\(69\) −1358.00 −2.36933
\(70\) 0 0
\(71\) 738.000 1.23358 0.616792 0.787126i \(-0.288432\pi\)
0.616792 + 0.787126i \(0.288432\pi\)
\(72\) 0 0
\(73\) 652.000 1.04535 0.522677 0.852531i \(-0.324933\pi\)
0.522677 + 0.852531i \(0.324933\pi\)
\(74\) 0 0
\(75\) −308.000 −0.474197
\(76\) 0 0
\(77\) −720.000 −1.06561
\(78\) 0 0
\(79\) −917.000 −1.30596 −0.652978 0.757377i \(-0.726481\pi\)
−0.652978 + 0.757377i \(0.726481\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 0 0
\(83\) 678.000 0.896629 0.448314 0.893876i \(-0.352025\pi\)
0.448314 + 0.893876i \(0.352025\pi\)
\(84\) 0 0
\(85\) 1326.00 1.69206
\(86\) 0 0
\(87\) 203.000 0.250160
\(88\) 0 0
\(89\) −1008.00 −1.20054 −0.600268 0.799799i \(-0.704940\pi\)
−0.600268 + 0.799799i \(0.704940\pi\)
\(90\) 0 0
\(91\) 976.000 1.12431
\(92\) 0 0
\(93\) −1043.00 −1.16295
\(94\) 0 0
\(95\) 884.000 0.954700
\(96\) 0 0
\(97\) −1764.00 −1.84646 −0.923232 0.384242i \(-0.874463\pi\)
−0.923232 + 0.384242i \(0.874463\pi\)
\(98\) 0 0
\(99\) −990.000 −1.00504
\(100\) 0 0
\(101\) −1360.00 −1.33985 −0.669926 0.742428i \(-0.733674\pi\)
−0.669926 + 0.742428i \(0.733674\pi\)
\(102\) 0 0
\(103\) 1498.00 1.43303 0.716516 0.697571i \(-0.245736\pi\)
0.716516 + 0.697571i \(0.245736\pi\)
\(104\) 0 0
\(105\) 1456.00 1.35325
\(106\) 0 0
\(107\) −772.000 −0.697496 −0.348748 0.937217i \(-0.613393\pi\)
−0.348748 + 0.937217i \(0.613393\pi\)
\(108\) 0 0
\(109\) 763.000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) −2800.00 −2.39427
\(112\) 0 0
\(113\) −1218.00 −1.01398 −0.506990 0.861952i \(-0.669242\pi\)
−0.506990 + 0.861952i \(0.669242\pi\)
\(114\) 0 0
\(115\) −2522.00 −2.04502
\(116\) 0 0
\(117\) 1342.00 1.06041
\(118\) 0 0
\(119\) −1632.00 −1.25719
\(120\) 0 0
\(121\) 694.000 0.521412
\(122\) 0 0
\(123\) −1960.00 −1.43681
\(124\) 0 0
\(125\) 1053.00 0.753465
\(126\) 0 0
\(127\) 1544.00 1.07880 0.539401 0.842049i \(-0.318651\pi\)
0.539401 + 0.842049i \(0.318651\pi\)
\(128\) 0 0
\(129\) −1841.00 −1.25652
\(130\) 0 0
\(131\) −1916.00 −1.27788 −0.638938 0.769258i \(-0.720626\pi\)
−0.638938 + 0.769258i \(0.720626\pi\)
\(132\) 0 0
\(133\) −1088.00 −0.709335
\(134\) 0 0
\(135\) −455.000 −0.290075
\(136\) 0 0
\(137\) 72.0000 0.0449005 0.0224503 0.999748i \(-0.492853\pi\)
0.0224503 + 0.999748i \(0.492853\pi\)
\(138\) 0 0
\(139\) 1394.00 0.850630 0.425315 0.905045i \(-0.360163\pi\)
0.425315 + 0.905045i \(0.360163\pi\)
\(140\) 0 0
\(141\) −3563.00 −2.12808
\(142\) 0 0
\(143\) −2745.00 −1.60523
\(144\) 0 0
\(145\) 377.000 0.215918
\(146\) 0 0
\(147\) 609.000 0.341697
\(148\) 0 0
\(149\) −135.000 −0.0742257 −0.0371129 0.999311i \(-0.511816\pi\)
−0.0371129 + 0.999311i \(0.511816\pi\)
\(150\) 0 0
\(151\) −1708.00 −0.920497 −0.460249 0.887790i \(-0.652240\pi\)
−0.460249 + 0.887790i \(0.652240\pi\)
\(152\) 0 0
\(153\) −2244.00 −1.18573
\(154\) 0 0
\(155\) −1937.00 −1.00377
\(156\) 0 0
\(157\) 128.000 0.0650670 0.0325335 0.999471i \(-0.489642\pi\)
0.0325335 + 0.999471i \(0.489642\pi\)
\(158\) 0 0
\(159\) 4235.00 2.11231
\(160\) 0 0
\(161\) 3104.00 1.51944
\(162\) 0 0
\(163\) 1235.00 0.593452 0.296726 0.954963i \(-0.404105\pi\)
0.296726 + 0.954963i \(0.404105\pi\)
\(164\) 0 0
\(165\) −4095.00 −1.93209
\(166\) 0 0
\(167\) −2398.00 −1.11115 −0.555577 0.831465i \(-0.687503\pi\)
−0.555577 + 0.831465i \(0.687503\pi\)
\(168\) 0 0
\(169\) 1524.00 0.693673
\(170\) 0 0
\(171\) −1496.00 −0.669017
\(172\) 0 0
\(173\) −1258.00 −0.552855 −0.276428 0.961035i \(-0.589151\pi\)
−0.276428 + 0.961035i \(0.589151\pi\)
\(174\) 0 0
\(175\) 704.000 0.304099
\(176\) 0 0
\(177\) 4046.00 1.71817
\(178\) 0 0
\(179\) 154.000 0.0643045 0.0321522 0.999483i \(-0.489764\pi\)
0.0321522 + 0.999483i \(0.489764\pi\)
\(180\) 0 0
\(181\) 3089.00 1.26853 0.634264 0.773117i \(-0.281303\pi\)
0.634264 + 0.773117i \(0.281303\pi\)
\(182\) 0 0
\(183\) 5026.00 2.03023
\(184\) 0 0
\(185\) −5200.00 −2.06655
\(186\) 0 0
\(187\) 4590.00 1.79494
\(188\) 0 0
\(189\) 560.000 0.215524
\(190\) 0 0
\(191\) −1088.00 −0.412172 −0.206086 0.978534i \(-0.566073\pi\)
−0.206086 + 0.978534i \(0.566073\pi\)
\(192\) 0 0
\(193\) −228.000 −0.0850352 −0.0425176 0.999096i \(-0.513538\pi\)
−0.0425176 + 0.999096i \(0.513538\pi\)
\(194\) 0 0
\(195\) 5551.00 2.03854
\(196\) 0 0
\(197\) 2226.00 0.805055 0.402528 0.915408i \(-0.368132\pi\)
0.402528 + 0.915408i \(0.368132\pi\)
\(198\) 0 0
\(199\) −1908.00 −0.679671 −0.339836 0.940485i \(-0.610371\pi\)
−0.339836 + 0.940485i \(0.610371\pi\)
\(200\) 0 0
\(201\) 1820.00 0.638671
\(202\) 0 0
\(203\) −464.000 −0.160426
\(204\) 0 0
\(205\) −3640.00 −1.24014
\(206\) 0 0
\(207\) 4268.00 1.43307
\(208\) 0 0
\(209\) 3060.00 1.01275
\(210\) 0 0
\(211\) 583.000 0.190215 0.0951075 0.995467i \(-0.469681\pi\)
0.0951075 + 0.995467i \(0.469681\pi\)
\(212\) 0 0
\(213\) −5166.00 −1.66182
\(214\) 0 0
\(215\) −3419.00 −1.08453
\(216\) 0 0
\(217\) 2384.00 0.745790
\(218\) 0 0
\(219\) −4564.00 −1.40825
\(220\) 0 0
\(221\) −6222.00 −1.89383
\(222\) 0 0
\(223\) −1594.00 −0.478664 −0.239332 0.970938i \(-0.576928\pi\)
−0.239332 + 0.970938i \(0.576928\pi\)
\(224\) 0 0
\(225\) 968.000 0.286815
\(226\) 0 0
\(227\) 2682.00 0.784188 0.392094 0.919925i \(-0.371751\pi\)
0.392094 + 0.919925i \(0.371751\pi\)
\(228\) 0 0
\(229\) −960.000 −0.277024 −0.138512 0.990361i \(-0.544232\pi\)
−0.138512 + 0.990361i \(0.544232\pi\)
\(230\) 0 0
\(231\) 5040.00 1.43553
\(232\) 0 0
\(233\) −1225.00 −0.344431 −0.172215 0.985059i \(-0.555093\pi\)
−0.172215 + 0.985059i \(0.555093\pi\)
\(234\) 0 0
\(235\) −6617.00 −1.83679
\(236\) 0 0
\(237\) 6419.00 1.75932
\(238\) 0 0
\(239\) −1650.00 −0.446567 −0.223284 0.974753i \(-0.571678\pi\)
−0.223284 + 0.974753i \(0.571678\pi\)
\(240\) 0 0
\(241\) −3503.00 −0.936299 −0.468150 0.883649i \(-0.655079\pi\)
−0.468150 + 0.883649i \(0.655079\pi\)
\(242\) 0 0
\(243\) 4928.00 1.30095
\(244\) 0 0
\(245\) 1131.00 0.294926
\(246\) 0 0
\(247\) −4148.00 −1.06855
\(248\) 0 0
\(249\) −4746.00 −1.20789
\(250\) 0 0
\(251\) −5571.00 −1.40095 −0.700475 0.713677i \(-0.747028\pi\)
−0.700475 + 0.713677i \(0.747028\pi\)
\(252\) 0 0
\(253\) −8730.00 −2.16937
\(254\) 0 0
\(255\) −9282.00 −2.27946
\(256\) 0 0
\(257\) −4891.00 −1.18713 −0.593565 0.804786i \(-0.702280\pi\)
−0.593565 + 0.804786i \(0.702280\pi\)
\(258\) 0 0
\(259\) 6400.00 1.53543
\(260\) 0 0
\(261\) −638.000 −0.151307
\(262\) 0 0
\(263\) −1287.00 −0.301748 −0.150874 0.988553i \(-0.548209\pi\)
−0.150874 + 0.988553i \(0.548209\pi\)
\(264\) 0 0
\(265\) 7865.00 1.82318
\(266\) 0 0
\(267\) 7056.00 1.61730
\(268\) 0 0
\(269\) −3826.00 −0.867195 −0.433597 0.901107i \(-0.642756\pi\)
−0.433597 + 0.901107i \(0.642756\pi\)
\(270\) 0 0
\(271\) −1713.00 −0.383975 −0.191988 0.981397i \(-0.561493\pi\)
−0.191988 + 0.981397i \(0.561493\pi\)
\(272\) 0 0
\(273\) −6832.00 −1.51462
\(274\) 0 0
\(275\) −1980.00 −0.434176
\(276\) 0 0
\(277\) 7086.00 1.53703 0.768513 0.639834i \(-0.220997\pi\)
0.768513 + 0.639834i \(0.220997\pi\)
\(278\) 0 0
\(279\) 3278.00 0.703400
\(280\) 0 0
\(281\) 7063.00 1.49944 0.749721 0.661754i \(-0.230188\pi\)
0.749721 + 0.661754i \(0.230188\pi\)
\(282\) 0 0
\(283\) −5002.00 −1.05066 −0.525332 0.850897i \(-0.676059\pi\)
−0.525332 + 0.850897i \(0.676059\pi\)
\(284\) 0 0
\(285\) −6188.00 −1.28612
\(286\) 0 0
\(287\) 4480.00 0.921415
\(288\) 0 0
\(289\) 5491.00 1.11765
\(290\) 0 0
\(291\) 12348.0 2.48747
\(292\) 0 0
\(293\) 4086.00 0.814699 0.407349 0.913272i \(-0.366453\pi\)
0.407349 + 0.913272i \(0.366453\pi\)
\(294\) 0 0
\(295\) 7514.00 1.48299
\(296\) 0 0
\(297\) −1575.00 −0.307713
\(298\) 0 0
\(299\) 11834.0 2.28889
\(300\) 0 0
\(301\) 4208.00 0.805798
\(302\) 0 0
\(303\) 9520.00 1.80498
\(304\) 0 0
\(305\) 9334.00 1.75234
\(306\) 0 0
\(307\) −1909.00 −0.354894 −0.177447 0.984130i \(-0.556784\pi\)
−0.177447 + 0.984130i \(0.556784\pi\)
\(308\) 0 0
\(309\) −10486.0 −1.93051
\(310\) 0 0
\(311\) −5808.00 −1.05898 −0.529488 0.848317i \(-0.677616\pi\)
−0.529488 + 0.848317i \(0.677616\pi\)
\(312\) 0 0
\(313\) −6783.00 −1.22491 −0.612457 0.790504i \(-0.709819\pi\)
−0.612457 + 0.790504i \(0.709819\pi\)
\(314\) 0 0
\(315\) −4576.00 −0.818503
\(316\) 0 0
\(317\) −6090.00 −1.07902 −0.539509 0.841980i \(-0.681390\pi\)
−0.539509 + 0.841980i \(0.681390\pi\)
\(318\) 0 0
\(319\) 1305.00 0.229047
\(320\) 0 0
\(321\) 5404.00 0.939632
\(322\) 0 0
\(323\) 6936.00 1.19483
\(324\) 0 0
\(325\) 2684.00 0.458097
\(326\) 0 0
\(327\) −5341.00 −0.903235
\(328\) 0 0
\(329\) 8144.00 1.36472
\(330\) 0 0
\(331\) −3801.00 −0.631184 −0.315592 0.948895i \(-0.602203\pi\)
−0.315592 + 0.948895i \(0.602203\pi\)
\(332\) 0 0
\(333\) 8800.00 1.44816
\(334\) 0 0
\(335\) 3380.00 0.551251
\(336\) 0 0
\(337\) −2374.00 −0.383739 −0.191869 0.981420i \(-0.561455\pi\)
−0.191869 + 0.981420i \(0.561455\pi\)
\(338\) 0 0
\(339\) 8526.00 1.36598
\(340\) 0 0
\(341\) −6705.00 −1.06480
\(342\) 0 0
\(343\) −6880.00 −1.08305
\(344\) 0 0
\(345\) 17654.0 2.75495
\(346\) 0 0
\(347\) −5346.00 −0.827056 −0.413528 0.910491i \(-0.635704\pi\)
−0.413528 + 0.910491i \(0.635704\pi\)
\(348\) 0 0
\(349\) 9003.00 1.38086 0.690429 0.723400i \(-0.257422\pi\)
0.690429 + 0.723400i \(0.257422\pi\)
\(350\) 0 0
\(351\) 2135.00 0.324666
\(352\) 0 0
\(353\) 10222.0 1.54125 0.770626 0.637287i \(-0.219944\pi\)
0.770626 + 0.637287i \(0.219944\pi\)
\(354\) 0 0
\(355\) −9594.00 −1.43436
\(356\) 0 0
\(357\) 11424.0 1.69362
\(358\) 0 0
\(359\) 719.000 0.105703 0.0528515 0.998602i \(-0.483169\pi\)
0.0528515 + 0.998602i \(0.483169\pi\)
\(360\) 0 0
\(361\) −2235.00 −0.325849
\(362\) 0 0
\(363\) −4858.00 −0.702421
\(364\) 0 0
\(365\) −8476.00 −1.21549
\(366\) 0 0
\(367\) −6084.00 −0.865347 −0.432673 0.901551i \(-0.642430\pi\)
−0.432673 + 0.901551i \(0.642430\pi\)
\(368\) 0 0
\(369\) 6160.00 0.869043
\(370\) 0 0
\(371\) −9680.00 −1.35461
\(372\) 0 0
\(373\) −1451.00 −0.201421 −0.100710 0.994916i \(-0.532112\pi\)
−0.100710 + 0.994916i \(0.532112\pi\)
\(374\) 0 0
\(375\) −7371.00 −1.01503
\(376\) 0 0
\(377\) −1769.00 −0.241666
\(378\) 0 0
\(379\) 896.000 0.121436 0.0607182 0.998155i \(-0.480661\pi\)
0.0607182 + 0.998155i \(0.480661\pi\)
\(380\) 0 0
\(381\) −10808.0 −1.45331
\(382\) 0 0
\(383\) 13016.0 1.73652 0.868259 0.496111i \(-0.165239\pi\)
0.868259 + 0.496111i \(0.165239\pi\)
\(384\) 0 0
\(385\) 9360.00 1.23904
\(386\) 0 0
\(387\) 5786.00 0.759997
\(388\) 0 0
\(389\) −6560.00 −0.855026 −0.427513 0.904009i \(-0.640610\pi\)
−0.427513 + 0.904009i \(0.640610\pi\)
\(390\) 0 0
\(391\) −19788.0 −2.55939
\(392\) 0 0
\(393\) 13412.0 1.72149
\(394\) 0 0
\(395\) 11921.0 1.51851
\(396\) 0 0
\(397\) 2757.00 0.348539 0.174269 0.984698i \(-0.444244\pi\)
0.174269 + 0.984698i \(0.444244\pi\)
\(398\) 0 0
\(399\) 7616.00 0.955581
\(400\) 0 0
\(401\) 4995.00 0.622041 0.311020 0.950403i \(-0.399329\pi\)
0.311020 + 0.950403i \(0.399329\pi\)
\(402\) 0 0
\(403\) 9089.00 1.12346
\(404\) 0 0
\(405\) 10907.0 1.33821
\(406\) 0 0
\(407\) −18000.0 −2.19220
\(408\) 0 0
\(409\) 3930.00 0.475125 0.237562 0.971372i \(-0.423652\pi\)
0.237562 + 0.971372i \(0.423652\pi\)
\(410\) 0 0
\(411\) −504.000 −0.0604878
\(412\) 0 0
\(413\) −9248.00 −1.10185
\(414\) 0 0
\(415\) −8814.00 −1.04256
\(416\) 0 0
\(417\) −9758.00 −1.14593
\(418\) 0 0
\(419\) −3230.00 −0.376601 −0.188301 0.982111i \(-0.560298\pi\)
−0.188301 + 0.982111i \(0.560298\pi\)
\(420\) 0 0
\(421\) 6110.00 0.707323 0.353662 0.935373i \(-0.384936\pi\)
0.353662 + 0.935373i \(0.384936\pi\)
\(422\) 0 0
\(423\) 11198.0 1.28715
\(424\) 0 0
\(425\) −4488.00 −0.512235
\(426\) 0 0
\(427\) −11488.0 −1.30197
\(428\) 0 0
\(429\) 19215.0 2.16249
\(430\) 0 0
\(431\) 14218.0 1.58900 0.794498 0.607267i \(-0.207734\pi\)
0.794498 + 0.607267i \(0.207734\pi\)
\(432\) 0 0
\(433\) −10008.0 −1.11075 −0.555374 0.831601i \(-0.687425\pi\)
−0.555374 + 0.831601i \(0.687425\pi\)
\(434\) 0 0
\(435\) −2639.00 −0.290874
\(436\) 0 0
\(437\) −13192.0 −1.44407
\(438\) 0 0
\(439\) −11338.0 −1.23265 −0.616325 0.787492i \(-0.711379\pi\)
−0.616325 + 0.787492i \(0.711379\pi\)
\(440\) 0 0
\(441\) −1914.00 −0.206673
\(442\) 0 0
\(443\) 10180.0 1.09180 0.545899 0.837851i \(-0.316188\pi\)
0.545899 + 0.837851i \(0.316188\pi\)
\(444\) 0 0
\(445\) 13104.0 1.39593
\(446\) 0 0
\(447\) 945.000 0.0999932
\(448\) 0 0
\(449\) −90.0000 −0.00945960 −0.00472980 0.999989i \(-0.501506\pi\)
−0.00472980 + 0.999989i \(0.501506\pi\)
\(450\) 0 0
\(451\) −12600.0 −1.31555
\(452\) 0 0
\(453\) 11956.0 1.24005
\(454\) 0 0
\(455\) −12688.0 −1.30730
\(456\) 0 0
\(457\) −8906.00 −0.911609 −0.455804 0.890080i \(-0.650648\pi\)
−0.455804 + 0.890080i \(0.650648\pi\)
\(458\) 0 0
\(459\) −3570.00 −0.363036
\(460\) 0 0
\(461\) −9646.00 −0.974531 −0.487266 0.873254i \(-0.662006\pi\)
−0.487266 + 0.873254i \(0.662006\pi\)
\(462\) 0 0
\(463\) 11578.0 1.16215 0.581075 0.813850i \(-0.302632\pi\)
0.581075 + 0.813850i \(0.302632\pi\)
\(464\) 0 0
\(465\) 13559.0 1.35222
\(466\) 0 0
\(467\) 4671.00 0.462844 0.231422 0.972853i \(-0.425662\pi\)
0.231422 + 0.972853i \(0.425662\pi\)
\(468\) 0 0
\(469\) −4160.00 −0.409576
\(470\) 0 0
\(471\) −896.000 −0.0876550
\(472\) 0 0
\(473\) −11835.0 −1.15047
\(474\) 0 0
\(475\) −2992.00 −0.289016
\(476\) 0 0
\(477\) −13310.0 −1.27762
\(478\) 0 0
\(479\) 195.000 0.0186008 0.00930039 0.999957i \(-0.497040\pi\)
0.00930039 + 0.999957i \(0.497040\pi\)
\(480\) 0 0
\(481\) 24400.0 2.31298
\(482\) 0 0
\(483\) −21728.0 −2.04691
\(484\) 0 0
\(485\) 22932.0 2.14699
\(486\) 0 0
\(487\) 15604.0 1.45192 0.725960 0.687737i \(-0.241396\pi\)
0.725960 + 0.687737i \(0.241396\pi\)
\(488\) 0 0
\(489\) −8645.00 −0.799469
\(490\) 0 0
\(491\) −18507.0 −1.70104 −0.850519 0.525945i \(-0.823712\pi\)
−0.850519 + 0.525945i \(0.823712\pi\)
\(492\) 0 0
\(493\) 2958.00 0.270226
\(494\) 0 0
\(495\) 12870.0 1.16861
\(496\) 0 0
\(497\) 11808.0 1.06572
\(498\) 0 0
\(499\) −1882.00 −0.168837 −0.0844187 0.996430i \(-0.526903\pi\)
−0.0844187 + 0.996430i \(0.526903\pi\)
\(500\) 0 0
\(501\) 16786.0 1.49689
\(502\) 0 0
\(503\) −7645.00 −0.677681 −0.338841 0.940844i \(-0.610035\pi\)
−0.338841 + 0.940844i \(0.610035\pi\)
\(504\) 0 0
\(505\) 17680.0 1.55792
\(506\) 0 0
\(507\) −10668.0 −0.934482
\(508\) 0 0
\(509\) 1255.00 0.109287 0.0546433 0.998506i \(-0.482598\pi\)
0.0546433 + 0.998506i \(0.482598\pi\)
\(510\) 0 0
\(511\) 10432.0 0.903101
\(512\) 0 0
\(513\) −2380.00 −0.204833
\(514\) 0 0
\(515\) −19474.0 −1.66627
\(516\) 0 0
\(517\) −22905.0 −1.94847
\(518\) 0 0
\(519\) 8806.00 0.744779
\(520\) 0 0
\(521\) −873.000 −0.0734104 −0.0367052 0.999326i \(-0.511686\pi\)
−0.0367052 + 0.999326i \(0.511686\pi\)
\(522\) 0 0
\(523\) 14996.0 1.25378 0.626892 0.779106i \(-0.284327\pi\)
0.626892 + 0.779106i \(0.284327\pi\)
\(524\) 0 0
\(525\) −4928.00 −0.409668
\(526\) 0 0
\(527\) −15198.0 −1.25623
\(528\) 0 0
\(529\) 25469.0 2.09329
\(530\) 0 0
\(531\) −12716.0 −1.03922
\(532\) 0 0
\(533\) 17080.0 1.38802
\(534\) 0 0
\(535\) 10036.0 0.811017
\(536\) 0 0
\(537\) −1078.00 −0.0866278
\(538\) 0 0
\(539\) 3915.00 0.312859
\(540\) 0 0
\(541\) 2672.00 0.212344 0.106172 0.994348i \(-0.466141\pi\)
0.106172 + 0.994348i \(0.466141\pi\)
\(542\) 0 0
\(543\) −21623.0 −1.70890
\(544\) 0 0
\(545\) −9919.00 −0.779602
\(546\) 0 0
\(547\) −4776.00 −0.373322 −0.186661 0.982424i \(-0.559767\pi\)
−0.186661 + 0.982424i \(0.559767\pi\)
\(548\) 0 0
\(549\) −15796.0 −1.22797
\(550\) 0 0
\(551\) 1972.00 0.152468
\(552\) 0 0
\(553\) −14672.0 −1.12824
\(554\) 0 0
\(555\) 36400.0 2.78395
\(556\) 0 0
\(557\) −134.000 −0.0101935 −0.00509673 0.999987i \(-0.501622\pi\)
−0.00509673 + 0.999987i \(0.501622\pi\)
\(558\) 0 0
\(559\) 16043.0 1.21386
\(560\) 0 0
\(561\) −32130.0 −2.41806
\(562\) 0 0
\(563\) −437.000 −0.0327129 −0.0163564 0.999866i \(-0.505207\pi\)
−0.0163564 + 0.999866i \(0.505207\pi\)
\(564\) 0 0
\(565\) 15834.0 1.17901
\(566\) 0 0
\(567\) −13424.0 −0.994277
\(568\) 0 0
\(569\) −23990.0 −1.76751 −0.883755 0.467950i \(-0.844993\pi\)
−0.883755 + 0.467950i \(0.844993\pi\)
\(570\) 0 0
\(571\) −100.000 −0.00732902 −0.00366451 0.999993i \(-0.501166\pi\)
−0.00366451 + 0.999993i \(0.501166\pi\)
\(572\) 0 0
\(573\) 7616.00 0.555258
\(574\) 0 0
\(575\) 8536.00 0.619088
\(576\) 0 0
\(577\) 6078.00 0.438528 0.219264 0.975666i \(-0.429634\pi\)
0.219264 + 0.975666i \(0.429634\pi\)
\(578\) 0 0
\(579\) 1596.00 0.114555
\(580\) 0 0
\(581\) 10848.0 0.774614
\(582\) 0 0
\(583\) 27225.0 1.93404
\(584\) 0 0
\(585\) −17446.0 −1.23300
\(586\) 0 0
\(587\) −4214.00 −0.296304 −0.148152 0.988965i \(-0.547332\pi\)
−0.148152 + 0.988965i \(0.547332\pi\)
\(588\) 0 0
\(589\) −10132.0 −0.708798
\(590\) 0 0
\(591\) −15582.0 −1.08453
\(592\) 0 0
\(593\) −28293.0 −1.95928 −0.979641 0.200757i \(-0.935660\pi\)
−0.979641 + 0.200757i \(0.935660\pi\)
\(594\) 0 0
\(595\) 21216.0 1.46180
\(596\) 0 0
\(597\) 13356.0 0.915619
\(598\) 0 0
\(599\) 8843.00 0.603197 0.301599 0.953435i \(-0.402480\pi\)
0.301599 + 0.953435i \(0.402480\pi\)
\(600\) 0 0
\(601\) −22548.0 −1.53037 −0.765185 0.643811i \(-0.777352\pi\)
−0.765185 + 0.643811i \(0.777352\pi\)
\(602\) 0 0
\(603\) −5720.00 −0.386296
\(604\) 0 0
\(605\) −9022.00 −0.606275
\(606\) 0 0
\(607\) −17061.0 −1.14083 −0.570416 0.821356i \(-0.693218\pi\)
−0.570416 + 0.821356i \(0.693218\pi\)
\(608\) 0 0
\(609\) 3248.00 0.216118
\(610\) 0 0
\(611\) 31049.0 2.05582
\(612\) 0 0
\(613\) 21251.0 1.40020 0.700098 0.714047i \(-0.253140\pi\)
0.700098 + 0.714047i \(0.253140\pi\)
\(614\) 0 0
\(615\) 25480.0 1.67065
\(616\) 0 0
\(617\) 200.000 0.0130498 0.00652488 0.999979i \(-0.497923\pi\)
0.00652488 + 0.999979i \(0.497923\pi\)
\(618\) 0 0
\(619\) −19533.0 −1.26833 −0.634166 0.773197i \(-0.718656\pi\)
−0.634166 + 0.773197i \(0.718656\pi\)
\(620\) 0 0
\(621\) 6790.00 0.438765
\(622\) 0 0
\(623\) −16128.0 −1.03717
\(624\) 0 0
\(625\) −19189.0 −1.22810
\(626\) 0 0
\(627\) −21420.0 −1.36433
\(628\) 0 0
\(629\) −40800.0 −2.58633
\(630\) 0 0
\(631\) 12570.0 0.793033 0.396516 0.918028i \(-0.370219\pi\)
0.396516 + 0.918028i \(0.370219\pi\)
\(632\) 0 0
\(633\) −4081.00 −0.256248
\(634\) 0 0
\(635\) −20072.0 −1.25438
\(636\) 0 0
\(637\) −5307.00 −0.330096
\(638\) 0 0
\(639\) 16236.0 1.00514
\(640\) 0 0
\(641\) 17446.0 1.07500 0.537500 0.843263i \(-0.319369\pi\)
0.537500 + 0.843263i \(0.319369\pi\)
\(642\) 0 0
\(643\) −11324.0 −0.694518 −0.347259 0.937769i \(-0.612887\pi\)
−0.347259 + 0.937769i \(0.612887\pi\)
\(644\) 0 0
\(645\) 23933.0 1.46102
\(646\) 0 0
\(647\) 2922.00 0.177551 0.0887756 0.996052i \(-0.471705\pi\)
0.0887756 + 0.996052i \(0.471705\pi\)
\(648\) 0 0
\(649\) 26010.0 1.57316
\(650\) 0 0
\(651\) −16688.0 −1.00469
\(652\) 0 0
\(653\) 23120.0 1.38554 0.692768 0.721160i \(-0.256391\pi\)
0.692768 + 0.721160i \(0.256391\pi\)
\(654\) 0 0
\(655\) 24908.0 1.48586
\(656\) 0 0
\(657\) 14344.0 0.851770
\(658\) 0 0
\(659\) 32901.0 1.94483 0.972414 0.233264i \(-0.0749406\pi\)
0.972414 + 0.233264i \(0.0749406\pi\)
\(660\) 0 0
\(661\) −18494.0 −1.08825 −0.544125 0.839004i \(-0.683138\pi\)
−0.544125 + 0.839004i \(0.683138\pi\)
\(662\) 0 0
\(663\) 43554.0 2.55128
\(664\) 0 0
\(665\) 14144.0 0.824783
\(666\) 0 0
\(667\) −5626.00 −0.326596
\(668\) 0 0
\(669\) 11158.0 0.644833
\(670\) 0 0
\(671\) 32310.0 1.85889
\(672\) 0 0
\(673\) −15119.0 −0.865965 −0.432983 0.901402i \(-0.642539\pi\)
−0.432983 + 0.901402i \(0.642539\pi\)
\(674\) 0 0
\(675\) 1540.00 0.0878143
\(676\) 0 0
\(677\) 6946.00 0.394323 0.197161 0.980371i \(-0.436828\pi\)
0.197161 + 0.980371i \(0.436828\pi\)
\(678\) 0 0
\(679\) −28224.0 −1.59520
\(680\) 0 0
\(681\) −18774.0 −1.05642
\(682\) 0 0
\(683\) 31124.0 1.74367 0.871835 0.489799i \(-0.162930\pi\)
0.871835 + 0.489799i \(0.162930\pi\)
\(684\) 0 0
\(685\) −936.000 −0.0522084
\(686\) 0 0
\(687\) 6720.00 0.373194
\(688\) 0 0
\(689\) −36905.0 −2.04059
\(690\) 0 0
\(691\) 12664.0 0.697194 0.348597 0.937273i \(-0.386658\pi\)
0.348597 + 0.937273i \(0.386658\pi\)
\(692\) 0 0
\(693\) −15840.0 −0.868271
\(694\) 0 0
\(695\) −18122.0 −0.989074
\(696\) 0 0
\(697\) −28560.0 −1.55206
\(698\) 0 0
\(699\) 8575.00 0.464000
\(700\) 0 0
\(701\) −18715.0 −1.00835 −0.504177 0.863600i \(-0.668204\pi\)
−0.504177 + 0.863600i \(0.668204\pi\)
\(702\) 0 0
\(703\) −27200.0 −1.45927
\(704\) 0 0
\(705\) 46319.0 2.47443
\(706\) 0 0
\(707\) −21760.0 −1.15752
\(708\) 0 0
\(709\) −7531.00 −0.398918 −0.199459 0.979906i \(-0.563918\pi\)
−0.199459 + 0.979906i \(0.563918\pi\)
\(710\) 0 0
\(711\) −20174.0 −1.06411
\(712\) 0 0
\(713\) 28906.0 1.51829
\(714\) 0 0
\(715\) 35685.0 1.86649
\(716\) 0 0
\(717\) 11550.0 0.601594
\(718\) 0 0
\(719\) 35338.0 1.83294 0.916471 0.400102i \(-0.131025\pi\)
0.916471 + 0.400102i \(0.131025\pi\)
\(720\) 0 0
\(721\) 23968.0 1.23802
\(722\) 0 0
\(723\) 24521.0 1.26134
\(724\) 0 0
\(725\) −1276.00 −0.0653648
\(726\) 0 0
\(727\) −13976.0 −0.712986 −0.356493 0.934298i \(-0.616028\pi\)
−0.356493 + 0.934298i \(0.616028\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) −26826.0 −1.35731
\(732\) 0 0
\(733\) 7172.00 0.361397 0.180698 0.983539i \(-0.442164\pi\)
0.180698 + 0.983539i \(0.442164\pi\)
\(734\) 0 0
\(735\) −7917.00 −0.397310
\(736\) 0 0
\(737\) 11700.0 0.584769
\(738\) 0 0
\(739\) −35091.0 −1.74674 −0.873372 0.487054i \(-0.838071\pi\)
−0.873372 + 0.487054i \(0.838071\pi\)
\(740\) 0 0
\(741\) 29036.0 1.43949
\(742\) 0 0
\(743\) −10992.0 −0.542742 −0.271371 0.962475i \(-0.587477\pi\)
−0.271371 + 0.962475i \(0.587477\pi\)
\(744\) 0 0
\(745\) 1755.00 0.0863063
\(746\) 0 0
\(747\) 14916.0 0.730586
\(748\) 0 0
\(749\) −12352.0 −0.602580
\(750\) 0 0
\(751\) −20988.0 −1.01979 −0.509895 0.860236i \(-0.670316\pi\)
−0.509895 + 0.860236i \(0.670316\pi\)
\(752\) 0 0
\(753\) 38997.0 1.88729
\(754\) 0 0
\(755\) 22204.0 1.07031
\(756\) 0 0
\(757\) −39094.0 −1.87701 −0.938504 0.345267i \(-0.887788\pi\)
−0.938504 + 0.345267i \(0.887788\pi\)
\(758\) 0 0
\(759\) 61110.0 2.92247
\(760\) 0 0
\(761\) −27270.0 −1.29900 −0.649499 0.760363i \(-0.725021\pi\)
−0.649499 + 0.760363i \(0.725021\pi\)
\(762\) 0 0
\(763\) 12208.0 0.579239
\(764\) 0 0
\(765\) 29172.0 1.37871
\(766\) 0 0
\(767\) −35258.0 −1.65983
\(768\) 0 0
\(769\) 3462.00 0.162344 0.0811722 0.996700i \(-0.474134\pi\)
0.0811722 + 0.996700i \(0.474134\pi\)
\(770\) 0 0
\(771\) 34237.0 1.59924
\(772\) 0 0
\(773\) −10632.0 −0.494704 −0.247352 0.968926i \(-0.579560\pi\)
−0.247352 + 0.968926i \(0.579560\pi\)
\(774\) 0 0
\(775\) 6556.00 0.303869
\(776\) 0 0
\(777\) −44800.0 −2.06846
\(778\) 0 0
\(779\) −19040.0 −0.875711
\(780\) 0 0
\(781\) −33210.0 −1.52157
\(782\) 0 0
\(783\) −1015.00 −0.0463259
\(784\) 0 0
\(785\) −1664.00 −0.0756570
\(786\) 0 0
\(787\) −3754.00 −0.170033 −0.0850163 0.996380i \(-0.527094\pi\)
−0.0850163 + 0.996380i \(0.527094\pi\)
\(788\) 0 0
\(789\) 9009.00 0.406500
\(790\) 0 0
\(791\) −19488.0 −0.875997
\(792\) 0 0
\(793\) −43798.0 −1.96130
\(794\) 0 0
\(795\) −55055.0 −2.45610
\(796\) 0 0
\(797\) 9378.00 0.416795 0.208398 0.978044i \(-0.433175\pi\)
0.208398 + 0.978044i \(0.433175\pi\)
\(798\) 0 0
\(799\) −51918.0 −2.29878
\(800\) 0 0
\(801\) −22176.0 −0.978215
\(802\) 0 0
\(803\) −29340.0 −1.28940
\(804\) 0 0
\(805\) −40352.0 −1.76673
\(806\) 0 0
\(807\) 26782.0 1.16824
\(808\) 0 0
\(809\) −3708.00 −0.161145 −0.0805725 0.996749i \(-0.525675\pi\)
−0.0805725 + 0.996749i \(0.525675\pi\)
\(810\) 0 0
\(811\) 13232.0 0.572920 0.286460 0.958092i \(-0.407521\pi\)
0.286460 + 0.958092i \(0.407521\pi\)
\(812\) 0 0
\(813\) 11991.0 0.517273
\(814\) 0 0
\(815\) −16055.0 −0.690039
\(816\) 0 0
\(817\) −17884.0 −0.765829
\(818\) 0 0
\(819\) 21472.0 0.916108
\(820\) 0 0
\(821\) 5445.00 0.231464 0.115732 0.993280i \(-0.463079\pi\)
0.115732 + 0.993280i \(0.463079\pi\)
\(822\) 0 0
\(823\) −17576.0 −0.744424 −0.372212 0.928148i \(-0.621401\pi\)
−0.372212 + 0.928148i \(0.621401\pi\)
\(824\) 0 0
\(825\) 13860.0 0.584901
\(826\) 0 0
\(827\) 10143.0 0.426489 0.213245 0.976999i \(-0.431597\pi\)
0.213245 + 0.976999i \(0.431597\pi\)
\(828\) 0 0
\(829\) −8558.00 −0.358542 −0.179271 0.983800i \(-0.557374\pi\)
−0.179271 + 0.983800i \(0.557374\pi\)
\(830\) 0 0
\(831\) −49602.0 −2.07061
\(832\) 0 0
\(833\) 8874.00 0.369107
\(834\) 0 0
\(835\) 31174.0 1.29200
\(836\) 0 0
\(837\) 5215.00 0.215361
\(838\) 0 0
\(839\) −30467.0 −1.25368 −0.626840 0.779148i \(-0.715652\pi\)
−0.626840 + 0.779148i \(0.715652\pi\)
\(840\) 0 0
\(841\) 841.000 0.0344828
\(842\) 0 0
\(843\) −49441.0 −2.01997
\(844\) 0 0
\(845\) −19812.0 −0.806572
\(846\) 0 0
\(847\) 11104.0 0.450458
\(848\) 0 0
\(849\) 35014.0 1.41540
\(850\) 0 0
\(851\) 77600.0 3.12584
\(852\) 0 0
\(853\) −154.000 −0.00618155 −0.00309077 0.999995i \(-0.500984\pi\)
−0.00309077 + 0.999995i \(0.500984\pi\)
\(854\) 0 0
\(855\) 19448.0 0.777904
\(856\) 0 0
\(857\) −10463.0 −0.417047 −0.208523 0.978017i \(-0.566866\pi\)
−0.208523 + 0.978017i \(0.566866\pi\)
\(858\) 0 0
\(859\) 24749.0 0.983033 0.491516 0.870868i \(-0.336443\pi\)
0.491516 + 0.870868i \(0.336443\pi\)
\(860\) 0 0
\(861\) −31360.0 −1.24128
\(862\) 0 0
\(863\) −20586.0 −0.812000 −0.406000 0.913873i \(-0.633077\pi\)
−0.406000 + 0.913873i \(0.633077\pi\)
\(864\) 0 0
\(865\) 16354.0 0.642835
\(866\) 0 0
\(867\) −38437.0 −1.50564
\(868\) 0 0
\(869\) 41265.0 1.61084
\(870\) 0 0
\(871\) −15860.0 −0.616987
\(872\) 0 0
\(873\) −38808.0 −1.50453
\(874\) 0 0
\(875\) 16848.0 0.650933
\(876\) 0 0
\(877\) 5051.00 0.194481 0.0972407 0.995261i \(-0.468998\pi\)
0.0972407 + 0.995261i \(0.468998\pi\)
\(878\) 0 0
\(879\) −28602.0 −1.09752
\(880\) 0 0
\(881\) −38990.0 −1.49104 −0.745520 0.666483i \(-0.767799\pi\)
−0.745520 + 0.666483i \(0.767799\pi\)
\(882\) 0 0
\(883\) −27180.0 −1.03588 −0.517939 0.855418i \(-0.673300\pi\)
−0.517939 + 0.855418i \(0.673300\pi\)
\(884\) 0 0
\(885\) −52598.0 −1.99781
\(886\) 0 0
\(887\) −17435.0 −0.659989 −0.329994 0.943983i \(-0.607047\pi\)
−0.329994 + 0.943983i \(0.607047\pi\)
\(888\) 0 0
\(889\) 24704.0 0.931997
\(890\) 0 0
\(891\) 37755.0 1.41957
\(892\) 0 0
\(893\) −34612.0 −1.29703
\(894\) 0 0
\(895\) −2002.00 −0.0747704
\(896\) 0 0
\(897\) −82838.0 −3.08348
\(898\) 0 0
\(899\) −4321.00 −0.160304
\(900\) 0 0
\(901\) 61710.0 2.28175
\(902\) 0 0
\(903\) −29456.0 −1.08553
\(904\) 0 0
\(905\) −40157.0 −1.47499
\(906\) 0 0
\(907\) −11500.0 −0.421005 −0.210502 0.977593i \(-0.567510\pi\)
−0.210502 + 0.977593i \(0.567510\pi\)
\(908\) 0 0
\(909\) −29920.0 −1.09173
\(910\) 0 0
\(911\) −7969.00 −0.289819 −0.144909 0.989445i \(-0.546289\pi\)
−0.144909 + 0.989445i \(0.546289\pi\)
\(912\) 0 0
\(913\) −30510.0 −1.10595
\(914\) 0 0
\(915\) −65338.0 −2.36066
\(916\) 0 0
\(917\) −30656.0 −1.10398
\(918\) 0 0
\(919\) −24414.0 −0.876326 −0.438163 0.898896i \(-0.644371\pi\)
−0.438163 + 0.898896i \(0.644371\pi\)
\(920\) 0 0
\(921\) 13363.0 0.478095
\(922\) 0 0
\(923\) 45018.0 1.60540
\(924\) 0 0
\(925\) 17600.0 0.625605
\(926\) 0 0
\(927\) 32956.0 1.16766
\(928\) 0 0
\(929\) −18694.0 −0.660205 −0.330102 0.943945i \(-0.607083\pi\)
−0.330102 + 0.943945i \(0.607083\pi\)
\(930\) 0 0
\(931\) 5916.00 0.208259
\(932\) 0 0
\(933\) 40656.0 1.42660
\(934\) 0 0
\(935\) −59670.0 −2.08708
\(936\) 0 0
\(937\) 14394.0 0.501848 0.250924 0.968007i \(-0.419266\pi\)
0.250924 + 0.968007i \(0.419266\pi\)
\(938\) 0 0
\(939\) 47481.0 1.65014
\(940\) 0 0
\(941\) −11925.0 −0.413118 −0.206559 0.978434i \(-0.566227\pi\)
−0.206559 + 0.978434i \(0.566227\pi\)
\(942\) 0 0
\(943\) 54320.0 1.87582
\(944\) 0 0
\(945\) −7280.00 −0.250602
\(946\) 0 0
\(947\) −53321.0 −1.82967 −0.914836 0.403825i \(-0.867680\pi\)
−0.914836 + 0.403825i \(0.867680\pi\)
\(948\) 0 0
\(949\) 39772.0 1.36044
\(950\) 0 0
\(951\) 42630.0 1.45360
\(952\) 0 0
\(953\) −38301.0 −1.30188 −0.650940 0.759129i \(-0.725625\pi\)
−0.650940 + 0.759129i \(0.725625\pi\)
\(954\) 0 0
\(955\) 14144.0 0.479256
\(956\) 0 0
\(957\) −9135.00 −0.308561
\(958\) 0 0
\(959\) 1152.00 0.0387904
\(960\) 0 0
\(961\) −7590.00 −0.254775
\(962\) 0 0
\(963\) −16984.0 −0.568330
\(964\) 0 0
\(965\) 2964.00 0.0988752
\(966\) 0 0
\(967\) −40011.0 −1.33058 −0.665288 0.746587i \(-0.731691\pi\)
−0.665288 + 0.746587i \(0.731691\pi\)
\(968\) 0 0
\(969\) −48552.0 −1.60961
\(970\) 0 0
\(971\) −53500.0 −1.76817 −0.884087 0.467323i \(-0.845219\pi\)
−0.884087 + 0.467323i \(0.845219\pi\)
\(972\) 0 0
\(973\) 22304.0 0.734875
\(974\) 0 0
\(975\) −18788.0 −0.617126
\(976\) 0 0
\(977\) 28449.0 0.931591 0.465795 0.884892i \(-0.345768\pi\)
0.465795 + 0.884892i \(0.345768\pi\)
\(978\) 0 0
\(979\) 45360.0 1.48081
\(980\) 0 0
\(981\) 16786.0 0.546316
\(982\) 0 0
\(983\) 48529.0 1.57460 0.787301 0.616568i \(-0.211478\pi\)
0.787301 + 0.616568i \(0.211478\pi\)
\(984\) 0 0
\(985\) −28938.0 −0.936083
\(986\) 0 0
\(987\) −57008.0 −1.83848
\(988\) 0 0
\(989\) 51022.0 1.64045
\(990\) 0 0
\(991\) 8142.00 0.260988 0.130494 0.991449i \(-0.458344\pi\)
0.130494 + 0.991449i \(0.458344\pi\)
\(992\) 0 0
\(993\) 26607.0 0.850300
\(994\) 0 0
\(995\) 24804.0 0.790291
\(996\) 0 0
\(997\) −30572.0 −0.971138 −0.485569 0.874198i \(-0.661388\pi\)
−0.485569 + 0.874198i \(0.661388\pi\)
\(998\) 0 0
\(999\) 14000.0 0.443384
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 928.4.a.a.1.1 1
4.3 odd 2 928.4.a.b.1.1 yes 1
8.3 odd 2 1856.4.a.b.1.1 1
8.5 even 2 1856.4.a.e.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
928.4.a.a.1.1 1 1.1 even 1 trivial
928.4.a.b.1.1 yes 1 4.3 odd 2
1856.4.a.b.1.1 1 8.3 odd 2
1856.4.a.e.1.1 1 8.5 even 2