Properties

Label 2352.4.a.u.1.1
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2352.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(138.772492334\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2352.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} -15.0000 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} -15.0000 q^{5} +9.00000 q^{9} +9.00000 q^{11} -88.0000 q^{13} -45.0000 q^{15} -84.0000 q^{17} -104.000 q^{19} +84.0000 q^{23} +100.000 q^{25} +27.0000 q^{27} +51.0000 q^{29} -185.000 q^{31} +27.0000 q^{33} +44.0000 q^{37} -264.000 q^{39} -168.000 q^{41} -326.000 q^{43} -135.000 q^{45} +138.000 q^{47} -252.000 q^{51} +639.000 q^{53} -135.000 q^{55} -312.000 q^{57} -159.000 q^{59} +722.000 q^{61} +1320.00 q^{65} +166.000 q^{67} +252.000 q^{69} -1086.00 q^{71} +218.000 q^{73} +300.000 q^{75} +583.000 q^{79} +81.0000 q^{81} +597.000 q^{83} +1260.00 q^{85} +153.000 q^{87} -1038.00 q^{89} -555.000 q^{93} +1560.00 q^{95} -169.000 q^{97} +81.0000 q^{99} +O(q^{100})\)

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
\(3\) 3.00000 0.577350
\(4\) 0 0
\(5\) −15.0000 −1.34164 −0.670820 0.741620i \(-0.734058\pi\)
−0.670820 + 0.741620i \(0.734058\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 9.00000 0.246691 0.123346 0.992364i \(-0.460638\pi\)
0.123346 + 0.992364i \(0.460638\pi\)
\(12\) 0 0
\(13\) −88.0000 −1.87745 −0.938723 0.344671i \(-0.887990\pi\)
−0.938723 + 0.344671i \(0.887990\pi\)
\(14\) 0 0
\(15\) −45.0000 −0.774597
\(16\) 0 0
\(17\) −84.0000 −1.19841 −0.599206 0.800595i \(-0.704517\pi\)
−0.599206 + 0.800595i \(0.704517\pi\)
\(18\) 0 0
\(19\) −104.000 −1.25575 −0.627875 0.778314i \(-0.716075\pi\)
−0.627875 + 0.778314i \(0.716075\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 84.0000 0.761531 0.380765 0.924672i \(-0.375661\pi\)
0.380765 + 0.924672i \(0.375661\pi\)
\(24\) 0 0
\(25\) 100.000 0.800000
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) 51.0000 0.326568 0.163284 0.986579i \(-0.447791\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(30\) 0 0
\(31\) −185.000 −1.07184 −0.535919 0.844269i \(-0.680035\pi\)
−0.535919 + 0.844269i \(0.680035\pi\)
\(32\) 0 0
\(33\) 27.0000 0.142427
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 44.0000 0.195501 0.0977507 0.995211i \(-0.468835\pi\)
0.0977507 + 0.995211i \(0.468835\pi\)
\(38\) 0 0
\(39\) −264.000 −1.08394
\(40\) 0 0
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 0 0
\(43\) −326.000 −1.15615 −0.578076 0.815983i \(-0.696196\pi\)
−0.578076 + 0.815983i \(0.696196\pi\)
\(44\) 0 0
\(45\) −135.000 −0.447214
\(46\) 0 0
\(47\) 138.000 0.428284 0.214142 0.976802i \(-0.431304\pi\)
0.214142 + 0.976802i \(0.431304\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −252.000 −0.691903
\(52\) 0 0
\(53\) 639.000 1.65610 0.828051 0.560653i \(-0.189450\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(54\) 0 0
\(55\) −135.000 −0.330971
\(56\) 0 0
\(57\) −312.000 −0.725007
\(58\) 0 0
\(59\) −159.000 −0.350848 −0.175424 0.984493i \(-0.556130\pi\)
−0.175424 + 0.984493i \(0.556130\pi\)
\(60\) 0 0
\(61\) 722.000 1.51545 0.757726 0.652572i \(-0.226310\pi\)
0.757726 + 0.652572i \(0.226310\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1320.00 2.51886
\(66\) 0 0
\(67\) 166.000 0.302688 0.151344 0.988481i \(-0.451640\pi\)
0.151344 + 0.988481i \(0.451640\pi\)
\(68\) 0 0
\(69\) 252.000 0.439670
\(70\) 0 0
\(71\) −1086.00 −1.81527 −0.907637 0.419755i \(-0.862116\pi\)
−0.907637 + 0.419755i \(0.862116\pi\)
\(72\) 0 0
\(73\) 218.000 0.349520 0.174760 0.984611i \(-0.444085\pi\)
0.174760 + 0.984611i \(0.444085\pi\)
\(74\) 0 0
\(75\) 300.000 0.461880
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 583.000 0.830286 0.415143 0.909756i \(-0.363731\pi\)
0.415143 + 0.909756i \(0.363731\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) 597.000 0.789509 0.394755 0.918787i \(-0.370830\pi\)
0.394755 + 0.918787i \(0.370830\pi\)
\(84\) 0 0
\(85\) 1260.00 1.60784
\(86\) 0 0
\(87\) 153.000 0.188544
\(88\) 0 0
\(89\) −1038.00 −1.23627 −0.618134 0.786073i \(-0.712111\pi\)
−0.618134 + 0.786073i \(0.712111\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −555.000 −0.618826
\(94\) 0 0
\(95\) 1560.00 1.68476
\(96\) 0 0
\(97\) −169.000 −0.176901 −0.0884503 0.996081i \(-0.528191\pi\)
−0.0884503 + 0.996081i \(0.528191\pi\)
\(98\) 0 0
\(99\) 81.0000 0.0822304
\(100\) 0 0
\(101\) 642.000 0.632489 0.316244 0.948678i \(-0.397578\pi\)
0.316244 + 0.948678i \(0.397578\pi\)
\(102\) 0 0
\(103\) −464.000 −0.443876 −0.221938 0.975061i \(-0.571238\pi\)
−0.221938 + 0.975061i \(0.571238\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −393.000 −0.355072 −0.177536 0.984114i \(-0.556813\pi\)
−0.177536 + 0.984114i \(0.556813\pi\)
\(108\) 0 0
\(109\) 14.0000 0.0123024 0.00615118 0.999981i \(-0.498042\pi\)
0.00615118 + 0.999981i \(0.498042\pi\)
\(110\) 0 0
\(111\) 132.000 0.112873
\(112\) 0 0
\(113\) −2184.00 −1.81817 −0.909086 0.416608i \(-0.863219\pi\)
−0.909086 + 0.416608i \(0.863219\pi\)
\(114\) 0 0
\(115\) −1260.00 −1.02170
\(116\) 0 0
\(117\) −792.000 −0.625816
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1250.00 −0.939144
\(122\) 0 0
\(123\) −504.000 −0.369465
\(124\) 0 0
\(125\) 375.000 0.268328
\(126\) 0 0
\(127\) 373.000 0.260617 0.130309 0.991473i \(-0.458403\pi\)
0.130309 + 0.991473i \(0.458403\pi\)
\(128\) 0 0
\(129\) −978.000 −0.667505
\(130\) 0 0
\(131\) 1173.00 0.782332 0.391166 0.920320i \(-0.372072\pi\)
0.391166 + 0.920320i \(0.372072\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −405.000 −0.258199
\(136\) 0 0
\(137\) 30.0000 0.0187086 0.00935428 0.999956i \(-0.497022\pi\)
0.00935428 + 0.999956i \(0.497022\pi\)
\(138\) 0 0
\(139\) 82.0000 0.0500370 0.0250185 0.999687i \(-0.492036\pi\)
0.0250185 + 0.999687i \(0.492036\pi\)
\(140\) 0 0
\(141\) 414.000 0.247270
\(142\) 0 0
\(143\) −792.000 −0.463149
\(144\) 0 0
\(145\) −765.000 −0.438136
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1434.00 −0.788442 −0.394221 0.919016i \(-0.628986\pi\)
−0.394221 + 0.919016i \(0.628986\pi\)
\(150\) 0 0
\(151\) 2671.00 1.43949 0.719745 0.694239i \(-0.244259\pi\)
0.719745 + 0.694239i \(0.244259\pi\)
\(152\) 0 0
\(153\) −756.000 −0.399470
\(154\) 0 0
\(155\) 2775.00 1.43802
\(156\) 0 0
\(157\) 2252.00 1.14477 0.572386 0.819984i \(-0.306018\pi\)
0.572386 + 0.819984i \(0.306018\pi\)
\(158\) 0 0
\(159\) 1917.00 0.956151
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1676.00 −0.805365 −0.402682 0.915340i \(-0.631922\pi\)
−0.402682 + 0.915340i \(0.631922\pi\)
\(164\) 0 0
\(165\) −405.000 −0.191086
\(166\) 0 0
\(167\) −3030.00 −1.40400 −0.702001 0.712176i \(-0.747710\pi\)
−0.702001 + 0.712176i \(0.747710\pi\)
\(168\) 0 0
\(169\) 5547.00 2.52481
\(170\) 0 0
\(171\) −936.000 −0.418583
\(172\) 0 0
\(173\) 3438.00 1.51090 0.755452 0.655204i \(-0.227417\pi\)
0.755452 + 0.655204i \(0.227417\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −477.000 −0.202562
\(178\) 0 0
\(179\) 1212.00 0.506085 0.253042 0.967455i \(-0.418569\pi\)
0.253042 + 0.967455i \(0.418569\pi\)
\(180\) 0 0
\(181\) 3032.00 1.24512 0.622560 0.782572i \(-0.286093\pi\)
0.622560 + 0.782572i \(0.286093\pi\)
\(182\) 0 0
\(183\) 2166.00 0.874947
\(184\) 0 0
\(185\) −660.000 −0.262293
\(186\) 0 0
\(187\) −756.000 −0.295637
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −2520.00 −0.954664 −0.477332 0.878723i \(-0.658396\pi\)
−0.477332 + 0.878723i \(0.658396\pi\)
\(192\) 0 0
\(193\) 365.000 0.136131 0.0680655 0.997681i \(-0.478317\pi\)
0.0680655 + 0.997681i \(0.478317\pi\)
\(194\) 0 0
\(195\) 3960.00 1.45426
\(196\) 0 0
\(197\) −1590.00 −0.575040 −0.287520 0.957775i \(-0.592831\pi\)
−0.287520 + 0.957775i \(0.592831\pi\)
\(198\) 0 0
\(199\) 5380.00 1.91647 0.958236 0.285977i \(-0.0923182\pi\)
0.958236 + 0.285977i \(0.0923182\pi\)
\(200\) 0 0
\(201\) 498.000 0.174757
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 2520.00 0.858558
\(206\) 0 0
\(207\) 756.000 0.253844
\(208\) 0 0
\(209\) −936.000 −0.309782
\(210\) 0 0
\(211\) 5362.00 1.74946 0.874728 0.484614i \(-0.161040\pi\)
0.874728 + 0.484614i \(0.161040\pi\)
\(212\) 0 0
\(213\) −3258.00 −1.04805
\(214\) 0 0
\(215\) 4890.00 1.55114
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 654.000 0.201796
\(220\) 0 0
\(221\) 7392.00 2.24995
\(222\) 0 0
\(223\) 1573.00 0.472358 0.236179 0.971710i \(-0.424105\pi\)
0.236179 + 0.971710i \(0.424105\pi\)
\(224\) 0 0
\(225\) 900.000 0.266667
\(226\) 0 0
\(227\) −921.000 −0.269290 −0.134645 0.990894i \(-0.542989\pi\)
−0.134645 + 0.990894i \(0.542989\pi\)
\(228\) 0 0
\(229\) 4052.00 1.16927 0.584637 0.811295i \(-0.301237\pi\)
0.584637 + 0.811295i \(0.301237\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −468.000 −0.131587 −0.0657933 0.997833i \(-0.520958\pi\)
−0.0657933 + 0.997833i \(0.520958\pi\)
\(234\) 0 0
\(235\) −2070.00 −0.574604
\(236\) 0 0
\(237\) 1749.00 0.479366
\(238\) 0 0
\(239\) −4932.00 −1.33483 −0.667415 0.744686i \(-0.732599\pi\)
−0.667415 + 0.744686i \(0.732599\pi\)
\(240\) 0 0
\(241\) −1537.00 −0.410817 −0.205408 0.978676i \(-0.565852\pi\)
−0.205408 + 0.978676i \(0.565852\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 9152.00 2.35760
\(248\) 0 0
\(249\) 1791.00 0.455823
\(250\) 0 0
\(251\) −5319.00 −1.33758 −0.668789 0.743452i \(-0.733187\pi\)
−0.668789 + 0.743452i \(0.733187\pi\)
\(252\) 0 0
\(253\) 756.000 0.187863
\(254\) 0 0
\(255\) 3780.00 0.928285
\(256\) 0 0
\(257\) 5346.00 1.29757 0.648783 0.760974i \(-0.275278\pi\)
0.648783 + 0.760974i \(0.275278\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 459.000 0.108856
\(262\) 0 0
\(263\) −774.000 −0.181471 −0.0907355 0.995875i \(-0.528922\pi\)
−0.0907355 + 0.995875i \(0.528922\pi\)
\(264\) 0 0
\(265\) −9585.00 −2.22189
\(266\) 0 0
\(267\) −3114.00 −0.713759
\(268\) 0 0
\(269\) 2415.00 0.547380 0.273690 0.961818i \(-0.411756\pi\)
0.273690 + 0.961818i \(0.411756\pi\)
\(270\) 0 0
\(271\) 475.000 0.106473 0.0532365 0.998582i \(-0.483046\pi\)
0.0532365 + 0.998582i \(0.483046\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 900.000 0.197353
\(276\) 0 0
\(277\) 3728.00 0.808642 0.404321 0.914617i \(-0.367508\pi\)
0.404321 + 0.914617i \(0.367508\pi\)
\(278\) 0 0
\(279\) −1665.00 −0.357279
\(280\) 0 0
\(281\) 1602.00 0.340097 0.170049 0.985436i \(-0.445608\pi\)
0.170049 + 0.985436i \(0.445608\pi\)
\(282\) 0 0
\(283\) −686.000 −0.144094 −0.0720468 0.997401i \(-0.522953\pi\)
−0.0720468 + 0.997401i \(0.522953\pi\)
\(284\) 0 0
\(285\) 4680.00 0.972699
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 2143.00 0.436190
\(290\) 0 0
\(291\) −507.000 −0.102134
\(292\) 0 0
\(293\) −1101.00 −0.219526 −0.109763 0.993958i \(-0.535009\pi\)
−0.109763 + 0.993958i \(0.535009\pi\)
\(294\) 0 0
\(295\) 2385.00 0.470712
\(296\) 0 0
\(297\) 243.000 0.0474757
\(298\) 0 0
\(299\) −7392.00 −1.42973
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1926.00 0.365168
\(304\) 0 0
\(305\) −10830.0 −2.03319
\(306\) 0 0
\(307\) −2780.00 −0.516818 −0.258409 0.966036i \(-0.583198\pi\)
−0.258409 + 0.966036i \(0.583198\pi\)
\(308\) 0 0
\(309\) −1392.00 −0.256272
\(310\) 0 0
\(311\) −4296.00 −0.783292 −0.391646 0.920116i \(-0.628094\pi\)
−0.391646 + 0.920116i \(0.628094\pi\)
\(312\) 0 0
\(313\) 5489.00 0.991235 0.495618 0.868541i \(-0.334942\pi\)
0.495618 + 0.868541i \(0.334942\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 4491.00 0.795709 0.397854 0.917449i \(-0.369755\pi\)
0.397854 + 0.917449i \(0.369755\pi\)
\(318\) 0 0
\(319\) 459.000 0.0805613
\(320\) 0 0
\(321\) −1179.00 −0.205001
\(322\) 0 0
\(323\) 8736.00 1.50490
\(324\) 0 0
\(325\) −8800.00 −1.50196
\(326\) 0 0
\(327\) 42.0000 0.00710277
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 3964.00 0.658251 0.329126 0.944286i \(-0.393246\pi\)
0.329126 + 0.944286i \(0.393246\pi\)
\(332\) 0 0
\(333\) 396.000 0.0651672
\(334\) 0 0
\(335\) −2490.00 −0.406099
\(336\) 0 0
\(337\) 161.000 0.0260244 0.0130122 0.999915i \(-0.495858\pi\)
0.0130122 + 0.999915i \(0.495858\pi\)
\(338\) 0 0
\(339\) −6552.00 −1.04972
\(340\) 0 0
\(341\) −1665.00 −0.264413
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −3780.00 −0.589879
\(346\) 0 0
\(347\) 5916.00 0.915238 0.457619 0.889148i \(-0.348702\pi\)
0.457619 + 0.889148i \(0.348702\pi\)
\(348\) 0 0
\(349\) −142.000 −0.0217796 −0.0108898 0.999941i \(-0.503466\pi\)
−0.0108898 + 0.999941i \(0.503466\pi\)
\(350\) 0 0
\(351\) −2376.00 −0.361315
\(352\) 0 0
\(353\) −4440.00 −0.669454 −0.334727 0.942315i \(-0.608644\pi\)
−0.334727 + 0.942315i \(0.608644\pi\)
\(354\) 0 0
\(355\) 16290.0 2.43545
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2286.00 −0.336074 −0.168037 0.985781i \(-0.553743\pi\)
−0.168037 + 0.985781i \(0.553743\pi\)
\(360\) 0 0
\(361\) 3957.00 0.576906
\(362\) 0 0
\(363\) −3750.00 −0.542215
\(364\) 0 0
\(365\) −3270.00 −0.468930
\(366\) 0 0
\(367\) 2869.00 0.408067 0.204033 0.978964i \(-0.434595\pi\)
0.204033 + 0.978964i \(0.434595\pi\)
\(368\) 0 0
\(369\) −1512.00 −0.213311
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −3064.00 −0.425330 −0.212665 0.977125i \(-0.568214\pi\)
−0.212665 + 0.977125i \(0.568214\pi\)
\(374\) 0 0
\(375\) 1125.00 0.154919
\(376\) 0 0
\(377\) −4488.00 −0.613113
\(378\) 0 0
\(379\) 6040.00 0.818612 0.409306 0.912397i \(-0.365771\pi\)
0.409306 + 0.912397i \(0.365771\pi\)
\(380\) 0 0
\(381\) 1119.00 0.150467
\(382\) 0 0
\(383\) −1842.00 −0.245749 −0.122874 0.992422i \(-0.539211\pi\)
−0.122874 + 0.992422i \(0.539211\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −2934.00 −0.385384
\(388\) 0 0
\(389\) 7830.00 1.02056 0.510279 0.860009i \(-0.329542\pi\)
0.510279 + 0.860009i \(0.329542\pi\)
\(390\) 0 0
\(391\) −7056.00 −0.912627
\(392\) 0 0
\(393\) 3519.00 0.451680
\(394\) 0 0
\(395\) −8745.00 −1.11395
\(396\) 0 0
\(397\) −14764.0 −1.86646 −0.933229 0.359282i \(-0.883022\pi\)
−0.933229 + 0.359282i \(0.883022\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6264.00 0.780073 0.390036 0.920799i \(-0.372462\pi\)
0.390036 + 0.920799i \(0.372462\pi\)
\(402\) 0 0
\(403\) 16280.0 2.01232
\(404\) 0 0
\(405\) −1215.00 −0.149071
\(406\) 0 0
\(407\) 396.000 0.0482285
\(408\) 0 0
\(409\) 4751.00 0.574381 0.287191 0.957873i \(-0.407279\pi\)
0.287191 + 0.957873i \(0.407279\pi\)
\(410\) 0 0
\(411\) 90.0000 0.0108014
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −8955.00 −1.05924
\(416\) 0 0
\(417\) 246.000 0.0288889
\(418\) 0 0
\(419\) 4704.00 0.548462 0.274231 0.961664i \(-0.411577\pi\)
0.274231 + 0.961664i \(0.411577\pi\)
\(420\) 0 0
\(421\) −4474.00 −0.517932 −0.258966 0.965886i \(-0.583382\pi\)
−0.258966 + 0.965886i \(0.583382\pi\)
\(422\) 0 0
\(423\) 1242.00 0.142761
\(424\) 0 0
\(425\) −8400.00 −0.958729
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −2376.00 −0.267399
\(430\) 0 0
\(431\) 12804.0 1.43097 0.715484 0.698629i \(-0.246206\pi\)
0.715484 + 0.698629i \(0.246206\pi\)
\(432\) 0 0
\(433\) −5074.00 −0.563143 −0.281571 0.959540i \(-0.590856\pi\)
−0.281571 + 0.959540i \(0.590856\pi\)
\(434\) 0 0
\(435\) −2295.00 −0.252958
\(436\) 0 0
\(437\) −8736.00 −0.956292
\(438\) 0 0
\(439\) 1267.00 0.137746 0.0688731 0.997625i \(-0.478060\pi\)
0.0688731 + 0.997625i \(0.478060\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 6933.00 0.743559 0.371780 0.928321i \(-0.378748\pi\)
0.371780 + 0.928321i \(0.378748\pi\)
\(444\) 0 0
\(445\) 15570.0 1.65863
\(446\) 0 0
\(447\) −4302.00 −0.455207
\(448\) 0 0
\(449\) 11688.0 1.22849 0.614244 0.789116i \(-0.289461\pi\)
0.614244 + 0.789116i \(0.289461\pi\)
\(450\) 0 0
\(451\) −1512.00 −0.157865
\(452\) 0 0
\(453\) 8013.00 0.831090
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 551.000 0.0563998 0.0281999 0.999602i \(-0.491023\pi\)
0.0281999 + 0.999602i \(0.491023\pi\)
\(458\) 0 0
\(459\) −2268.00 −0.230634
\(460\) 0 0
\(461\) 13386.0 1.35238 0.676191 0.736726i \(-0.263629\pi\)
0.676191 + 0.736726i \(0.263629\pi\)
\(462\) 0 0
\(463\) 6376.00 0.639995 0.319998 0.947418i \(-0.396318\pi\)
0.319998 + 0.947418i \(0.396318\pi\)
\(464\) 0 0
\(465\) 8325.00 0.830242
\(466\) 0 0
\(467\) −5700.00 −0.564806 −0.282403 0.959296i \(-0.591132\pi\)
−0.282403 + 0.959296i \(0.591132\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 6756.00 0.660934
\(472\) 0 0
\(473\) −2934.00 −0.285212
\(474\) 0 0
\(475\) −10400.0 −1.00460
\(476\) 0 0
\(477\) 5751.00 0.552034
\(478\) 0 0
\(479\) −19794.0 −1.88812 −0.944062 0.329769i \(-0.893029\pi\)
−0.944062 + 0.329769i \(0.893029\pi\)
\(480\) 0 0
\(481\) −3872.00 −0.367044
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2535.00 0.237337
\(486\) 0 0
\(487\) −15935.0 −1.48272 −0.741359 0.671109i \(-0.765818\pi\)
−0.741359 + 0.671109i \(0.765818\pi\)
\(488\) 0 0
\(489\) −5028.00 −0.464978
\(490\) 0 0
\(491\) −9963.00 −0.915731 −0.457865 0.889021i \(-0.651386\pi\)
−0.457865 + 0.889021i \(0.651386\pi\)
\(492\) 0 0
\(493\) −4284.00 −0.391362
\(494\) 0 0
\(495\) −1215.00 −0.110324
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −19142.0 −1.71726 −0.858631 0.512594i \(-0.828684\pi\)
−0.858631 + 0.512594i \(0.828684\pi\)
\(500\) 0 0
\(501\) −9090.00 −0.810601
\(502\) 0 0
\(503\) 12192.0 1.08074 0.540372 0.841426i \(-0.318283\pi\)
0.540372 + 0.841426i \(0.318283\pi\)
\(504\) 0 0
\(505\) −9630.00 −0.848573
\(506\) 0 0
\(507\) 16641.0 1.45770
\(508\) 0 0
\(509\) −19809.0 −1.72499 −0.862494 0.506068i \(-0.831098\pi\)
−0.862494 + 0.506068i \(0.831098\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −2808.00 −0.241669
\(514\) 0 0
\(515\) 6960.00 0.595523
\(516\) 0 0
\(517\) 1242.00 0.105654
\(518\) 0 0
\(519\) 10314.0 0.872321
\(520\) 0 0
\(521\) −1794.00 −0.150857 −0.0754286 0.997151i \(-0.524032\pi\)
−0.0754286 + 0.997151i \(0.524032\pi\)
\(522\) 0 0
\(523\) 6448.00 0.539104 0.269552 0.962986i \(-0.413124\pi\)
0.269552 + 0.962986i \(0.413124\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15540.0 1.28450
\(528\) 0 0
\(529\) −5111.00 −0.420071
\(530\) 0 0
\(531\) −1431.00 −0.116949
\(532\) 0 0
\(533\) 14784.0 1.20144
\(534\) 0 0
\(535\) 5895.00 0.476380
\(536\) 0 0
\(537\) 3636.00 0.292188
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 7262.00 0.577112 0.288556 0.957463i \(-0.406825\pi\)
0.288556 + 0.957463i \(0.406825\pi\)
\(542\) 0 0
\(543\) 9096.00 0.718871
\(544\) 0 0
\(545\) −210.000 −0.0165053
\(546\) 0 0
\(547\) −14204.0 −1.11027 −0.555136 0.831759i \(-0.687334\pi\)
−0.555136 + 0.831759i \(0.687334\pi\)
\(548\) 0 0
\(549\) 6498.00 0.505151
\(550\) 0 0
\(551\) −5304.00 −0.410087
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1980.00 −0.151435
\(556\) 0 0
\(557\) 15825.0 1.20382 0.601909 0.798565i \(-0.294407\pi\)
0.601909 + 0.798565i \(0.294407\pi\)
\(558\) 0 0
\(559\) 28688.0 2.17061
\(560\) 0 0
\(561\) −2268.00 −0.170686
\(562\) 0 0
\(563\) −1059.00 −0.0792745 −0.0396372 0.999214i \(-0.512620\pi\)
−0.0396372 + 0.999214i \(0.512620\pi\)
\(564\) 0 0
\(565\) 32760.0 2.43933
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3960.00 0.291761 0.145880 0.989302i \(-0.453399\pi\)
0.145880 + 0.989302i \(0.453399\pi\)
\(570\) 0 0
\(571\) 2530.00 0.185424 0.0927121 0.995693i \(-0.470446\pi\)
0.0927121 + 0.995693i \(0.470446\pi\)
\(572\) 0 0
\(573\) −7560.00 −0.551175
\(574\) 0 0
\(575\) 8400.00 0.609225
\(576\) 0 0
\(577\) 11831.0 0.853607 0.426803 0.904344i \(-0.359640\pi\)
0.426803 + 0.904344i \(0.359640\pi\)
\(578\) 0 0
\(579\) 1095.00 0.0785952
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 5751.00 0.408546
\(584\) 0 0
\(585\) 11880.0 0.839620
\(586\) 0 0
\(587\) −4809.00 −0.338141 −0.169070 0.985604i \(-0.554077\pi\)
−0.169070 + 0.985604i \(0.554077\pi\)
\(588\) 0 0
\(589\) 19240.0 1.34596
\(590\) 0 0
\(591\) −4770.00 −0.331999
\(592\) 0 0
\(593\) 21804.0 1.50992 0.754960 0.655770i \(-0.227656\pi\)
0.754960 + 0.655770i \(0.227656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 16140.0 1.10648
\(598\) 0 0
\(599\) −14166.0 −0.966289 −0.483144 0.875541i \(-0.660505\pi\)
−0.483144 + 0.875541i \(0.660505\pi\)
\(600\) 0 0
\(601\) 5891.00 0.399832 0.199916 0.979813i \(-0.435933\pi\)
0.199916 + 0.979813i \(0.435933\pi\)
\(602\) 0 0
\(603\) 1494.00 0.100896
\(604\) 0 0
\(605\) 18750.0 1.25999
\(606\) 0 0
\(607\) 2737.00 0.183017 0.0915086 0.995804i \(-0.470831\pi\)
0.0915086 + 0.995804i \(0.470831\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −12144.0 −0.804081
\(612\) 0 0
\(613\) −26188.0 −1.72549 −0.862743 0.505642i \(-0.831256\pi\)
−0.862743 + 0.505642i \(0.831256\pi\)
\(614\) 0 0
\(615\) 7560.00 0.495689
\(616\) 0 0
\(617\) −2358.00 −0.153857 −0.0769283 0.997037i \(-0.524511\pi\)
−0.0769283 + 0.997037i \(0.524511\pi\)
\(618\) 0 0
\(619\) −13766.0 −0.893865 −0.446932 0.894568i \(-0.647484\pi\)
−0.446932 + 0.894568i \(0.647484\pi\)
\(620\) 0 0
\(621\) 2268.00 0.146557
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −18125.0 −1.16000
\(626\) 0 0
\(627\) −2808.00 −0.178853
\(628\) 0 0
\(629\) −3696.00 −0.234291
\(630\) 0 0
\(631\) −21287.0 −1.34298 −0.671491 0.741012i \(-0.734346\pi\)
−0.671491 + 0.741012i \(0.734346\pi\)
\(632\) 0 0
\(633\) 16086.0 1.01005
\(634\) 0 0
\(635\) −5595.00 −0.349655
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −9774.00 −0.605091
\(640\) 0 0
\(641\) 21426.0 1.32024 0.660122 0.751159i \(-0.270505\pi\)
0.660122 + 0.751159i \(0.270505\pi\)
\(642\) 0 0
\(643\) −9962.00 −0.610984 −0.305492 0.952195i \(-0.598821\pi\)
−0.305492 + 0.952195i \(0.598821\pi\)
\(644\) 0 0
\(645\) 14670.0 0.895551
\(646\) 0 0
\(647\) 18174.0 1.10432 0.552159 0.833739i \(-0.313804\pi\)
0.552159 + 0.833739i \(0.313804\pi\)
\(648\) 0 0
\(649\) −1431.00 −0.0865511
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19167.0 −1.14864 −0.574321 0.818630i \(-0.694734\pi\)
−0.574321 + 0.818630i \(0.694734\pi\)
\(654\) 0 0
\(655\) −17595.0 −1.04961
\(656\) 0 0
\(657\) 1962.00 0.116507
\(658\) 0 0
\(659\) −13080.0 −0.773178 −0.386589 0.922252i \(-0.626347\pi\)
−0.386589 + 0.922252i \(0.626347\pi\)
\(660\) 0 0
\(661\) −15190.0 −0.893831 −0.446916 0.894576i \(-0.647478\pi\)
−0.446916 + 0.894576i \(0.647478\pi\)
\(662\) 0 0
\(663\) 22176.0 1.29901
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 4284.00 0.248691
\(668\) 0 0
\(669\) 4719.00 0.272716
\(670\) 0 0
\(671\) 6498.00 0.373849
\(672\) 0 0
\(673\) 4397.00 0.251845 0.125923 0.992040i \(-0.459811\pi\)
0.125923 + 0.992040i \(0.459811\pi\)
\(674\) 0 0
\(675\) 2700.00 0.153960
\(676\) 0 0
\(677\) 4029.00 0.228725 0.114363 0.993439i \(-0.463517\pi\)
0.114363 + 0.993439i \(0.463517\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2763.00 −0.155475
\(682\) 0 0
\(683\) −15021.0 −0.841526 −0.420763 0.907170i \(-0.638238\pi\)
−0.420763 + 0.907170i \(0.638238\pi\)
\(684\) 0 0
\(685\) −450.000 −0.0251002
\(686\) 0 0
\(687\) 12156.0 0.675081
\(688\) 0 0
\(689\) −56232.0 −3.10924
\(690\) 0 0
\(691\) 13984.0 0.769865 0.384932 0.922945i \(-0.374225\pi\)
0.384932 + 0.922945i \(0.374225\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −1230.00 −0.0671317
\(696\) 0 0
\(697\) 14112.0 0.766901
\(698\) 0 0
\(699\) −1404.00 −0.0759716
\(700\) 0 0
\(701\) −31053.0 −1.67312 −0.836559 0.547877i \(-0.815436\pi\)
−0.836559 + 0.547877i \(0.815436\pi\)
\(702\) 0 0
\(703\) −4576.00 −0.245501
\(704\) 0 0
\(705\) −6210.00 −0.331748
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 15086.0 0.799107 0.399553 0.916710i \(-0.369165\pi\)
0.399553 + 0.916710i \(0.369165\pi\)
\(710\) 0 0
\(711\) 5247.00 0.276762
\(712\) 0 0
\(713\) −15540.0 −0.816238
\(714\) 0 0
\(715\) 11880.0 0.621380
\(716\) 0 0
\(717\) −14796.0 −0.770665
\(718\) 0 0
\(719\) 6378.00 0.330820 0.165410 0.986225i \(-0.447105\pi\)
0.165410 + 0.986225i \(0.447105\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −4611.00 −0.237185
\(724\) 0 0
\(725\) 5100.00 0.261254
\(726\) 0 0
\(727\) 7363.00 0.375624 0.187812 0.982205i \(-0.439860\pi\)
0.187812 + 0.982205i \(0.439860\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) 27384.0 1.38555
\(732\) 0 0
\(733\) 32810.0 1.65329 0.826647 0.562720i \(-0.190245\pi\)
0.826647 + 0.562720i \(0.190245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1494.00 0.0746706
\(738\) 0 0
\(739\) 24034.0 1.19635 0.598177 0.801364i \(-0.295892\pi\)
0.598177 + 0.801364i \(0.295892\pi\)
\(740\) 0 0
\(741\) 27456.0 1.36116
\(742\) 0 0
\(743\) 8022.00 0.396095 0.198048 0.980192i \(-0.436540\pi\)
0.198048 + 0.980192i \(0.436540\pi\)
\(744\) 0 0
\(745\) 21510.0 1.05781
\(746\) 0 0
\(747\) 5373.00 0.263170
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −29519.0 −1.43431 −0.717153 0.696916i \(-0.754555\pi\)
−0.717153 + 0.696916i \(0.754555\pi\)
\(752\) 0 0
\(753\) −15957.0 −0.772252
\(754\) 0 0
\(755\) −40065.0 −1.93128
\(756\) 0 0
\(757\) −3742.00 −0.179664 −0.0898318 0.995957i \(-0.528633\pi\)
−0.0898318 + 0.995957i \(0.528633\pi\)
\(758\) 0 0
\(759\) 2268.00 0.108463
\(760\) 0 0
\(761\) −10896.0 −0.519027 −0.259514 0.965739i \(-0.583562\pi\)
−0.259514 + 0.965739i \(0.583562\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 11340.0 0.535946
\(766\) 0 0
\(767\) 13992.0 0.658699
\(768\) 0 0
\(769\) 17285.0 0.810550 0.405275 0.914195i \(-0.367176\pi\)
0.405275 + 0.914195i \(0.367176\pi\)
\(770\) 0 0
\(771\) 16038.0 0.749150
\(772\) 0 0
\(773\) 11826.0 0.550261 0.275130 0.961407i \(-0.411279\pi\)
0.275130 + 0.961407i \(0.411279\pi\)
\(774\) 0 0
\(775\) −18500.0 −0.857470
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 17472.0 0.803594
\(780\) 0 0
\(781\) −9774.00 −0.447812
\(782\) 0 0
\(783\) 1377.00 0.0628480
\(784\) 0 0
\(785\) −33780.0 −1.53587
\(786\) 0 0
\(787\) −17714.0 −0.802333 −0.401166 0.916005i \(-0.631395\pi\)
−0.401166 + 0.916005i \(0.631395\pi\)
\(788\) 0 0
\(789\) −2322.00 −0.104772
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −63536.0 −2.84518
\(794\) 0 0
\(795\) −28755.0 −1.28281
\(796\) 0 0
\(797\) −24939.0 −1.10839 −0.554194 0.832388i \(-0.686973\pi\)
−0.554194 + 0.832388i \(0.686973\pi\)
\(798\) 0 0
\(799\) −11592.0 −0.513261
\(800\) 0 0
\(801\) −9342.00 −0.412089
\(802\) 0 0
\(803\) 1962.00 0.0862235
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7245.00 0.316030
\(808\) 0 0
\(809\) −29064.0 −1.26309 −0.631543 0.775341i \(-0.717578\pi\)
−0.631543 + 0.775341i \(0.717578\pi\)
\(810\) 0 0
\(811\) 15370.0 0.665492 0.332746 0.943017i \(-0.392025\pi\)
0.332746 + 0.943017i \(0.392025\pi\)
\(812\) 0 0
\(813\) 1425.00 0.0614722
\(814\) 0 0
\(815\) 25140.0 1.08051
\(816\) 0 0
\(817\) 33904.0 1.45184
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 44031.0 1.87173 0.935866 0.352355i \(-0.114619\pi\)
0.935866 + 0.352355i \(0.114619\pi\)
\(822\) 0 0
\(823\) 4192.00 0.177550 0.0887752 0.996052i \(-0.471705\pi\)
0.0887752 + 0.996052i \(0.471705\pi\)
\(824\) 0 0
\(825\) 2700.00 0.113942
\(826\) 0 0
\(827\) −33195.0 −1.39577 −0.697886 0.716209i \(-0.745876\pi\)
−0.697886 + 0.716209i \(0.745876\pi\)
\(828\) 0 0
\(829\) 16448.0 0.689098 0.344549 0.938768i \(-0.388032\pi\)
0.344549 + 0.938768i \(0.388032\pi\)
\(830\) 0 0
\(831\) 11184.0 0.466870
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 45450.0 1.88367
\(836\) 0 0
\(837\) −4995.00 −0.206275
\(838\) 0 0
\(839\) −16860.0 −0.693769 −0.346884 0.937908i \(-0.612760\pi\)
−0.346884 + 0.937908i \(0.612760\pi\)
\(840\) 0 0
\(841\) −21788.0 −0.893354
\(842\) 0 0
\(843\) 4806.00 0.196355
\(844\) 0 0
\(845\) −83205.0 −3.38738
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −2058.00 −0.0831924
\(850\) 0 0
\(851\) 3696.00 0.148880
\(852\) 0 0
\(853\) 29054.0 1.16623 0.583113 0.812391i \(-0.301835\pi\)
0.583113 + 0.812391i \(0.301835\pi\)
\(854\) 0 0
\(855\) 14040.0 0.561588
\(856\) 0 0
\(857\) 41958.0 1.67241 0.836207 0.548415i \(-0.184768\pi\)
0.836207 + 0.548415i \(0.184768\pi\)
\(858\) 0 0
\(859\) −5546.00 −0.220288 −0.110144 0.993916i \(-0.535131\pi\)
−0.110144 + 0.993916i \(0.535131\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 32538.0 1.28344 0.641719 0.766940i \(-0.278222\pi\)
0.641719 + 0.766940i \(0.278222\pi\)
\(864\) 0 0
\(865\) −51570.0 −2.02709
\(866\) 0 0
\(867\) 6429.00 0.251834
\(868\) 0 0
\(869\) 5247.00 0.204824
\(870\) 0 0
\(871\) −14608.0 −0.568282
\(872\) 0 0
\(873\) −1521.00 −0.0589668
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 32096.0 1.23581 0.617905 0.786253i \(-0.287982\pi\)
0.617905 + 0.786253i \(0.287982\pi\)
\(878\) 0 0
\(879\) −3303.00 −0.126743
\(880\) 0 0
\(881\) −8490.00 −0.324671 −0.162336 0.986736i \(-0.551903\pi\)
−0.162336 + 0.986736i \(0.551903\pi\)
\(882\) 0 0
\(883\) 48352.0 1.84278 0.921390 0.388640i \(-0.127055\pi\)
0.921390 + 0.388640i \(0.127055\pi\)
\(884\) 0 0
\(885\) 7155.00 0.271766
\(886\) 0 0
\(887\) −15492.0 −0.586438 −0.293219 0.956045i \(-0.594726\pi\)
−0.293219 + 0.956045i \(0.594726\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 729.000 0.0274101
\(892\) 0 0
\(893\) −14352.0 −0.537818
\(894\) 0 0
\(895\) −18180.0 −0.678984
\(896\) 0 0
\(897\) −22176.0 −0.825457
\(898\) 0 0
\(899\) −9435.00 −0.350028
\(900\) 0 0
\(901\) −53676.0 −1.98469
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −45480.0 −1.67050
\(906\) 0 0
\(907\) 8116.00 0.297119 0.148560 0.988903i \(-0.452536\pi\)
0.148560 + 0.988903i \(0.452536\pi\)
\(908\) 0 0
\(909\) 5778.00 0.210830
\(910\) 0 0
\(911\) 4446.00 0.161693 0.0808466 0.996727i \(-0.474238\pi\)
0.0808466 + 0.996727i \(0.474238\pi\)
\(912\) 0 0
\(913\) 5373.00 0.194765
\(914\) 0 0
\(915\) −32490.0 −1.17386
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −26504.0 −0.951345 −0.475673 0.879622i \(-0.657795\pi\)
−0.475673 + 0.879622i \(0.657795\pi\)
\(920\) 0 0
\(921\) −8340.00 −0.298385
\(922\) 0 0
\(923\) 95568.0 3.40808
\(924\) 0 0
\(925\) 4400.00 0.156401
\(926\) 0 0
\(927\) −4176.00 −0.147959
\(928\) 0 0
\(929\) −5430.00 −0.191768 −0.0958840 0.995393i \(-0.530568\pi\)
−0.0958840 + 0.995393i \(0.530568\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −12888.0 −0.452234
\(934\) 0 0
\(935\) 11340.0 0.396639
\(936\) 0 0
\(937\) 33803.0 1.17854 0.589272 0.807935i \(-0.299415\pi\)
0.589272 + 0.807935i \(0.299415\pi\)
\(938\) 0 0
\(939\) 16467.0 0.572290
\(940\) 0 0
\(941\) −48483.0 −1.67960 −0.839798 0.542898i \(-0.817327\pi\)
−0.839798 + 0.542898i \(0.817327\pi\)
\(942\) 0 0
\(943\) −14112.0 −0.487328
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −37296.0 −1.27979 −0.639893 0.768464i \(-0.721021\pi\)
−0.639893 + 0.768464i \(0.721021\pi\)
\(948\) 0 0
\(949\) −19184.0 −0.656205
\(950\) 0 0
\(951\) 13473.0 0.459403
\(952\) 0 0
\(953\) −38478.0 −1.30790 −0.653948 0.756540i \(-0.726888\pi\)
−0.653948 + 0.756540i \(0.726888\pi\)
\(954\) 0 0
\(955\) 37800.0 1.28082
\(956\) 0 0
\(957\) 1377.00 0.0465121
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 4434.00 0.148837
\(962\) 0 0
\(963\) −3537.00 −0.118357
\(964\) 0 0
\(965\) −5475.00 −0.182639
\(966\) 0 0
\(967\) −27257.0 −0.906438 −0.453219 0.891399i \(-0.649725\pi\)
−0.453219 + 0.891399i \(0.649725\pi\)
\(968\) 0 0
\(969\) 26208.0 0.868857
\(970\) 0 0
\(971\) −34341.0 −1.13497 −0.567485 0.823384i \(-0.692083\pi\)
−0.567485 + 0.823384i \(0.692083\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −26400.0 −0.867156
\(976\) 0 0
\(977\) 27426.0 0.898092 0.449046 0.893509i \(-0.351764\pi\)
0.449046 + 0.893509i \(0.351764\pi\)
\(978\) 0 0
\(979\) −9342.00 −0.304976
\(980\) 0 0
\(981\) 126.000 0.00410079
\(982\) 0 0
\(983\) −12324.0 −0.399872 −0.199936 0.979809i \(-0.564073\pi\)
−0.199936 + 0.979809i \(0.564073\pi\)
\(984\) 0 0
\(985\) 23850.0 0.771497
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −27384.0 −0.880445
\(990\) 0 0
\(991\) −47597.0 −1.52570 −0.762850 0.646576i \(-0.776200\pi\)
−0.762850 + 0.646576i \(0.776200\pi\)
\(992\) 0 0
\(993\) 11892.0 0.380042
\(994\) 0 0
\(995\) −80700.0 −2.57122
\(996\) 0 0
\(997\) −11242.0 −0.357109 −0.178555 0.983930i \(-0.557142\pi\)
−0.178555 + 0.983930i \(0.557142\pi\)
\(998\) 0 0
\(999\) 1188.00 0.0376243
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 2352.4.a.u.1.1 1
4.3 odd 2 294.4.a.a.1.1 1
7.2 even 3 336.4.q.d.193.1 2
7.4 even 3 336.4.q.d.289.1 2
7.6 odd 2 2352.4.a.q.1.1 1
12.11 even 2 882.4.a.r.1.1 1
28.3 even 6 294.4.e.e.79.1 2
28.11 odd 6 42.4.e.b.37.1 yes 2
28.19 even 6 294.4.e.e.67.1 2
28.23 odd 6 42.4.e.b.25.1 2
28.27 even 2 294.4.a.g.1.1 1
84.11 even 6 126.4.g.a.37.1 2
84.23 even 6 126.4.g.a.109.1 2
84.47 odd 6 882.4.g.l.361.1 2
84.59 odd 6 882.4.g.l.667.1 2
84.83 odd 2 882.4.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.b.25.1 2 28.23 odd 6
42.4.e.b.37.1 yes 2 28.11 odd 6
126.4.g.a.37.1 2 84.11 even 6
126.4.g.a.109.1 2 84.23 even 6
294.4.a.a.1.1 1 4.3 odd 2
294.4.a.g.1.1 1 28.27 even 2
294.4.e.e.67.1 2 28.19 even 6
294.4.e.e.79.1 2 28.3 even 6
336.4.q.d.193.1 2 7.2 even 3
336.4.q.d.289.1 2 7.4 even 3
882.4.a.h.1.1 1 84.83 odd 2
882.4.a.r.1.1 1 12.11 even 2
882.4.g.l.361.1 2 84.47 odd 6
882.4.g.l.667.1 2 84.59 odd 6
2352.4.a.q.1.1 1 7.6 odd 2
2352.4.a.u.1.1 1 1.1 even 1 trivial