Properties

Label 2352.4.a.bw.1.2
Level $2352$
Weight $4$
Character 2352.1
Self dual yes
Analytic conductor $138.772$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \(x^{2} - 2\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 2352.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.00000 q^{3} -4.58579 q^{5} +9.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} -4.58579 q^{5} +9.00000 q^{9} +6.48528 q^{11} -45.2132 q^{13} -13.7574 q^{15} -81.5563 q^{17} -5.05382 q^{19} -106.250 q^{23} -103.971 q^{25} +27.0000 q^{27} -268.132 q^{29} +292.368 q^{31} +19.4558 q^{33} +114.558 q^{37} -135.640 q^{39} +161.605 q^{41} +471.294 q^{43} -41.2721 q^{45} +346.004 q^{47} -244.669 q^{51} +405.529 q^{53} -29.7401 q^{55} -15.1615 q^{57} -253.436 q^{59} +751.217 q^{61} +207.338 q^{65} -11.6468 q^{67} -318.749 q^{69} +681.661 q^{71} -685.457 q^{73} -311.912 q^{75} -0.264069 q^{79} +81.0000 q^{81} -437.137 q^{83} +374.000 q^{85} -804.396 q^{87} +58.5126 q^{89} +877.103 q^{93} +23.1758 q^{95} +1280.09 q^{97} +58.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 6q^{3} - 12q^{5} + 18q^{9} + O(q^{10}) \) \( 2q + 6q^{3} - 12q^{5} + 18q^{9} - 4q^{11} - 48q^{13} - 36q^{15} - 132q^{17} + 120q^{19} + 76q^{23} - 174q^{25} + 54q^{27} - 112q^{29} + 432q^{31} - 12q^{33} - 280q^{37} - 144q^{39} - 36q^{41} + 128q^{43} - 108q^{45} - 264q^{47} - 396q^{51} + 268q^{53} + 48q^{55} + 360q^{57} + 336q^{59} + 504q^{61} + 228q^{65} + 384q^{67} + 228q^{69} + 396q^{71} + 312q^{73} - 522q^{75} + 848q^{79} + 162q^{81} - 648q^{83} + 748q^{85} - 336q^{87} + 612q^{89} + 1296q^{93} - 904q^{95} + 2184q^{97} - 36q^{99} + O(q^{100}) \)

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
\(5\) −4.58579 −0.410165 −0.205083 0.978745i \(-0.565746\pi\)
−0.205083 + 0.978745i \(0.565746\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 9.00000 0.333333
\(10\) 0 0
\(11\) 6.48528 0.177762 0.0888812 0.996042i \(-0.471671\pi\)
0.0888812 + 0.996042i \(0.471671\pi\)
\(12\) 0 0
\(13\) −45.2132 −0.964607 −0.482303 0.876004i \(-0.660200\pi\)
−0.482303 + 0.876004i \(0.660200\pi\)
\(14\) 0 0
\(15\) −13.7574 −0.236809
\(16\) 0 0
\(17\) −81.5563 −1.16355 −0.581774 0.813350i \(-0.697641\pi\)
−0.581774 + 0.813350i \(0.697641\pi\)
\(18\) 0 0
\(19\) −5.05382 −0.0610225 −0.0305112 0.999534i \(-0.509714\pi\)
−0.0305112 + 0.999534i \(0.509714\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −106.250 −0.963244 −0.481622 0.876379i \(-0.659952\pi\)
−0.481622 + 0.876379i \(0.659952\pi\)
\(24\) 0 0
\(25\) −103.971 −0.831765
\(26\) 0 0
\(27\) 27.0000 0.192450
\(28\) 0 0
\(29\) −268.132 −1.71693 −0.858463 0.512875i \(-0.828580\pi\)
−0.858463 + 0.512875i \(0.828580\pi\)
\(30\) 0 0
\(31\) 292.368 1.69390 0.846948 0.531676i \(-0.178438\pi\)
0.846948 + 0.531676i \(0.178438\pi\)
\(32\) 0 0
\(33\) 19.4558 0.102631
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 114.558 0.509008 0.254504 0.967072i \(-0.418088\pi\)
0.254504 + 0.967072i \(0.418088\pi\)
\(38\) 0 0
\(39\) −135.640 −0.556916
\(40\) 0 0
\(41\) 161.605 0.615573 0.307786 0.951456i \(-0.400412\pi\)
0.307786 + 0.951456i \(0.400412\pi\)
\(42\) 0 0
\(43\) 471.294 1.67143 0.835716 0.549162i \(-0.185053\pi\)
0.835716 + 0.549162i \(0.185053\pi\)
\(44\) 0 0
\(45\) −41.2721 −0.136722
\(46\) 0 0
\(47\) 346.004 1.07383 0.536914 0.843637i \(-0.319590\pi\)
0.536914 + 0.843637i \(0.319590\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −244.669 −0.671775
\(52\) 0 0
\(53\) 405.529 1.05101 0.525507 0.850790i \(-0.323876\pi\)
0.525507 + 0.850790i \(0.323876\pi\)
\(54\) 0 0
\(55\) −29.7401 −0.0729119
\(56\) 0 0
\(57\) −15.1615 −0.0352313
\(58\) 0 0
\(59\) −253.436 −0.559229 −0.279614 0.960112i \(-0.590207\pi\)
−0.279614 + 0.960112i \(0.590207\pi\)
\(60\) 0 0
\(61\) 751.217 1.57678 0.788390 0.615176i \(-0.210915\pi\)
0.788390 + 0.615176i \(0.210915\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 207.338 0.395648
\(66\) 0 0
\(67\) −11.6468 −0.0212370 −0.0106185 0.999944i \(-0.503380\pi\)
−0.0106185 + 0.999944i \(0.503380\pi\)
\(68\) 0 0
\(69\) −318.749 −0.556129
\(70\) 0 0
\(71\) 681.661 1.13941 0.569706 0.821848i \(-0.307057\pi\)
0.569706 + 0.821848i \(0.307057\pi\)
\(72\) 0 0
\(73\) −685.457 −1.09900 −0.549498 0.835495i \(-0.685181\pi\)
−0.549498 + 0.835495i \(0.685181\pi\)
\(74\) 0 0
\(75\) −311.912 −0.480219
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.264069 −0.000376077 0 −0.000188038 1.00000i \(-0.500060\pi\)
−0.000188038 1.00000i \(0.500060\pi\)
\(80\) 0 0
\(81\) 81.0000 0.111111
\(82\) 0 0
\(83\) −437.137 −0.578097 −0.289048 0.957314i \(-0.593339\pi\)
−0.289048 + 0.957314i \(0.593339\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) 0 0
\(87\) −804.396 −0.991268
\(88\) 0 0
\(89\) 58.5126 0.0696891 0.0348445 0.999393i \(-0.488906\pi\)
0.0348445 + 0.999393i \(0.488906\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 877.103 0.977971
\(94\) 0 0
\(95\) 23.1758 0.0250293
\(96\) 0 0
\(97\) 1280.09 1.33993 0.669966 0.742391i \(-0.266308\pi\)
0.669966 + 0.742391i \(0.266308\pi\)
\(98\) 0 0
\(99\) 58.3675 0.0592541
\(100\) 0 0
\(101\) 1306.39 1.28704 0.643518 0.765431i \(-0.277474\pi\)
0.643518 + 0.765431i \(0.277474\pi\)
\(102\) 0 0
\(103\) −758.975 −0.726058 −0.363029 0.931778i \(-0.618257\pi\)
−0.363029 + 0.931778i \(0.618257\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1262.51 −1.14067 −0.570336 0.821412i \(-0.693187\pi\)
−0.570336 + 0.821412i \(0.693187\pi\)
\(108\) 0 0
\(109\) −2105.53 −1.85021 −0.925105 0.379711i \(-0.876023\pi\)
−0.925105 + 0.379711i \(0.876023\pi\)
\(110\) 0 0
\(111\) 343.675 0.293876
\(112\) 0 0
\(113\) 1535.76 1.27852 0.639258 0.768992i \(-0.279241\pi\)
0.639258 + 0.768992i \(0.279241\pi\)
\(114\) 0 0
\(115\) 487.239 0.395089
\(116\) 0 0
\(117\) −406.919 −0.321536
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1288.94 −0.968401
\(122\) 0 0
\(123\) 484.815 0.355401
\(124\) 0 0
\(125\) 1050.01 0.751326
\(126\) 0 0
\(127\) −24.1749 −0.0168911 −0.00844557 0.999964i \(-0.502688\pi\)
−0.00844557 + 0.999964i \(0.502688\pi\)
\(128\) 0 0
\(129\) 1413.88 0.965002
\(130\) 0 0
\(131\) 1581.53 1.05480 0.527400 0.849617i \(-0.323167\pi\)
0.527400 + 0.849617i \(0.323167\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −123.816 −0.0789363
\(136\) 0 0
\(137\) −745.188 −0.464713 −0.232357 0.972631i \(-0.574644\pi\)
−0.232357 + 0.972631i \(0.574644\pi\)
\(138\) 0 0
\(139\) −1373.60 −0.838179 −0.419090 0.907945i \(-0.637651\pi\)
−0.419090 + 0.907945i \(0.637651\pi\)
\(140\) 0 0
\(141\) 1038.01 0.619975
\(142\) 0 0
\(143\) −293.220 −0.171471
\(144\) 0 0
\(145\) 1229.60 0.704224
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 620.530 0.341180 0.170590 0.985342i \(-0.445433\pi\)
0.170590 + 0.985342i \(0.445433\pi\)
\(150\) 0 0
\(151\) 1939.26 1.04513 0.522567 0.852598i \(-0.324975\pi\)
0.522567 + 0.852598i \(0.324975\pi\)
\(152\) 0 0
\(153\) −734.007 −0.387849
\(154\) 0 0
\(155\) −1340.74 −0.694777
\(156\) 0 0
\(157\) 412.843 0.209863 0.104931 0.994479i \(-0.466538\pi\)
0.104931 + 0.994479i \(0.466538\pi\)
\(158\) 0 0
\(159\) 1216.59 0.606803
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3907.44 1.87763 0.938817 0.344417i \(-0.111923\pi\)
0.938817 + 0.344417i \(0.111923\pi\)
\(164\) 0 0
\(165\) −89.2203 −0.0420957
\(166\) 0 0
\(167\) −1286.41 −0.596082 −0.298041 0.954553i \(-0.596333\pi\)
−0.298041 + 0.954553i \(0.596333\pi\)
\(168\) 0 0
\(169\) −152.766 −0.0695340
\(170\) 0 0
\(171\) −45.4844 −0.0203408
\(172\) 0 0
\(173\) 1251.26 0.549892 0.274946 0.961460i \(-0.411340\pi\)
0.274946 + 0.961460i \(0.411340\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −760.307 −0.322871
\(178\) 0 0
\(179\) −3623.51 −1.51304 −0.756520 0.653971i \(-0.773102\pi\)
−0.756520 + 0.653971i \(0.773102\pi\)
\(180\) 0 0
\(181\) −181.727 −0.0746280 −0.0373140 0.999304i \(-0.511880\pi\)
−0.0373140 + 0.999304i \(0.511880\pi\)
\(182\) 0 0
\(183\) 2253.65 0.910354
\(184\) 0 0
\(185\) −525.341 −0.208777
\(186\) 0 0
\(187\) −528.916 −0.206835
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1481.28 −0.561160 −0.280580 0.959831i \(-0.590527\pi\)
−0.280580 + 0.959831i \(0.590527\pi\)
\(192\) 0 0
\(193\) −356.708 −0.133038 −0.0665192 0.997785i \(-0.521189\pi\)
−0.0665192 + 0.997785i \(0.521189\pi\)
\(194\) 0 0
\(195\) 622.014 0.228428
\(196\) 0 0
\(197\) 4890.53 1.76871 0.884355 0.466816i \(-0.154599\pi\)
0.884355 + 0.466816i \(0.154599\pi\)
\(198\) 0 0
\(199\) 3542.85 1.26204 0.631020 0.775766i \(-0.282636\pi\)
0.631020 + 0.775766i \(0.282636\pi\)
\(200\) 0 0
\(201\) −34.9403 −0.0122612
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −741.087 −0.252486
\(206\) 0 0
\(207\) −956.248 −0.321081
\(208\) 0 0
\(209\) −32.7755 −0.0108475
\(210\) 0 0
\(211\) 4289.50 1.39953 0.699765 0.714373i \(-0.253288\pi\)
0.699765 + 0.714373i \(0.253288\pi\)
\(212\) 0 0
\(213\) 2044.98 0.657840
\(214\) 0 0
\(215\) −2161.25 −0.685563
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2056.37 −0.634505
\(220\) 0 0
\(221\) 3687.42 1.12237
\(222\) 0 0
\(223\) 5795.73 1.74041 0.870204 0.492692i \(-0.163987\pi\)
0.870204 + 0.492692i \(0.163987\pi\)
\(224\) 0 0
\(225\) −935.735 −0.277255
\(226\) 0 0
\(227\) 4104.04 1.19998 0.599989 0.800008i \(-0.295172\pi\)
0.599989 + 0.800008i \(0.295172\pi\)
\(228\) 0 0
\(229\) 1296.83 0.374223 0.187111 0.982339i \(-0.440087\pi\)
0.187111 + 0.982339i \(0.440087\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1478.33 −0.415660 −0.207830 0.978165i \(-0.566640\pi\)
−0.207830 + 0.978165i \(0.566640\pi\)
\(234\) 0 0
\(235\) −1586.70 −0.440447
\(236\) 0 0
\(237\) −0.792206 −0.000217128 0
\(238\) 0 0
\(239\) 3776.92 1.02221 0.511106 0.859518i \(-0.329236\pi\)
0.511106 + 0.859518i \(0.329236\pi\)
\(240\) 0 0
\(241\) 3996.38 1.06817 0.534086 0.845430i \(-0.320656\pi\)
0.534086 + 0.845430i \(0.320656\pi\)
\(242\) 0 0
\(243\) 243.000 0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 228.500 0.0588627
\(248\) 0 0
\(249\) −1311.41 −0.333764
\(250\) 0 0
\(251\) 5423.58 1.36388 0.681939 0.731409i \(-0.261137\pi\)
0.681939 + 0.731409i \(0.261137\pi\)
\(252\) 0 0
\(253\) −689.060 −0.171229
\(254\) 0 0
\(255\) 1122.00 0.275539
\(256\) 0 0
\(257\) −5964.22 −1.44762 −0.723809 0.690000i \(-0.757611\pi\)
−0.723809 + 0.690000i \(0.757611\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −2413.19 −0.572309
\(262\) 0 0
\(263\) −5166.01 −1.21122 −0.605608 0.795763i \(-0.707070\pi\)
−0.605608 + 0.795763i \(0.707070\pi\)
\(264\) 0 0
\(265\) −1859.67 −0.431089
\(266\) 0 0
\(267\) 175.538 0.0402350
\(268\) 0 0
\(269\) −3883.29 −0.880180 −0.440090 0.897954i \(-0.645054\pi\)
−0.440090 + 0.897954i \(0.645054\pi\)
\(270\) 0 0
\(271\) 5527.65 1.23904 0.619522 0.784979i \(-0.287326\pi\)
0.619522 + 0.784979i \(0.287326\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −674.278 −0.147856
\(276\) 0 0
\(277\) 2268.12 0.491979 0.245989 0.969273i \(-0.420887\pi\)
0.245989 + 0.969273i \(0.420887\pi\)
\(278\) 0 0
\(279\) 2631.31 0.564632
\(280\) 0 0
\(281\) 725.656 0.154053 0.0770267 0.997029i \(-0.475457\pi\)
0.0770267 + 0.997029i \(0.475457\pi\)
\(282\) 0 0
\(283\) 4237.00 0.889976 0.444988 0.895536i \(-0.353208\pi\)
0.444988 + 0.895536i \(0.353208\pi\)
\(284\) 0 0
\(285\) 69.5273 0.0144507
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1738.44 0.353845
\(290\) 0 0
\(291\) 3840.27 0.773611
\(292\) 0 0
\(293\) 4373.78 0.872079 0.436039 0.899928i \(-0.356381\pi\)
0.436039 + 0.899928i \(0.356381\pi\)
\(294\) 0 0
\(295\) 1162.20 0.229376
\(296\) 0 0
\(297\) 175.103 0.0342104
\(298\) 0 0
\(299\) 4803.89 0.929152
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 3919.17 0.743070
\(304\) 0 0
\(305\) −3444.92 −0.646740
\(306\) 0 0
\(307\) 4133.47 0.768435 0.384217 0.923243i \(-0.374471\pi\)
0.384217 + 0.923243i \(0.374471\pi\)
\(308\) 0 0
\(309\) −2276.92 −0.419190
\(310\) 0 0
\(311\) 5063.23 0.923182 0.461591 0.887093i \(-0.347279\pi\)
0.461591 + 0.887093i \(0.347279\pi\)
\(312\) 0 0
\(313\) −7411.56 −1.33842 −0.669211 0.743073i \(-0.733368\pi\)
−0.669211 + 0.743073i \(0.733368\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −6737.05 −1.19366 −0.596831 0.802367i \(-0.703574\pi\)
−0.596831 + 0.802367i \(0.703574\pi\)
\(318\) 0 0
\(319\) −1738.91 −0.305205
\(320\) 0 0
\(321\) −3787.54 −0.658567
\(322\) 0 0
\(323\) 412.171 0.0710026
\(324\) 0 0
\(325\) 4700.84 0.802326
\(326\) 0 0
\(327\) −6316.58 −1.06822
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11175.9 −1.85585 −0.927923 0.372771i \(-0.878408\pi\)
−0.927923 + 0.372771i \(0.878408\pi\)
\(332\) 0 0
\(333\) 1031.03 0.169669
\(334\) 0 0
\(335\) 53.4095 0.00871067
\(336\) 0 0
\(337\) 9379.78 1.51617 0.758085 0.652156i \(-0.226135\pi\)
0.758085 + 0.652156i \(0.226135\pi\)
\(338\) 0 0
\(339\) 4607.29 0.738152
\(340\) 0 0
\(341\) 1896.09 0.301111
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 1461.72 0.228105
\(346\) 0 0
\(347\) −5681.46 −0.878953 −0.439476 0.898254i \(-0.644836\pi\)
−0.439476 + 0.898254i \(0.644836\pi\)
\(348\) 0 0
\(349\) 704.250 0.108016 0.0540080 0.998541i \(-0.482800\pi\)
0.0540080 + 0.998541i \(0.482800\pi\)
\(350\) 0 0
\(351\) −1220.76 −0.185639
\(352\) 0 0
\(353\) 4284.96 0.646078 0.323039 0.946386i \(-0.395295\pi\)
0.323039 + 0.946386i \(0.395295\pi\)
\(354\) 0 0
\(355\) −3125.95 −0.467347
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −4661.27 −0.685272 −0.342636 0.939468i \(-0.611320\pi\)
−0.342636 + 0.939468i \(0.611320\pi\)
\(360\) 0 0
\(361\) −6833.46 −0.996276
\(362\) 0 0
\(363\) −3866.82 −0.559106
\(364\) 0 0
\(365\) 3143.36 0.450770
\(366\) 0 0
\(367\) −6935.30 −0.986430 −0.493215 0.869907i \(-0.664178\pi\)
−0.493215 + 0.869907i \(0.664178\pi\)
\(368\) 0 0
\(369\) 1454.45 0.205191
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −3081.10 −0.427704 −0.213852 0.976866i \(-0.568601\pi\)
−0.213852 + 0.976866i \(0.568601\pi\)
\(374\) 0 0
\(375\) 3150.03 0.433778
\(376\) 0 0
\(377\) 12123.1 1.65616
\(378\) 0 0
\(379\) −941.827 −0.127647 −0.0638237 0.997961i \(-0.520330\pi\)
−0.0638237 + 0.997961i \(0.520330\pi\)
\(380\) 0 0
\(381\) −72.5247 −0.00975210
\(382\) 0 0
\(383\) −677.526 −0.0903915 −0.0451958 0.998978i \(-0.514391\pi\)
−0.0451958 + 0.998978i \(0.514391\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 4241.64 0.557144
\(388\) 0 0
\(389\) −11865.4 −1.54653 −0.773266 0.634082i \(-0.781378\pi\)
−0.773266 + 0.634082i \(0.781378\pi\)
\(390\) 0 0
\(391\) 8665.34 1.12078
\(392\) 0 0
\(393\) 4744.58 0.608989
\(394\) 0 0
\(395\) 1.21096 0.000154254 0
\(396\) 0 0
\(397\) 5140.76 0.649893 0.324947 0.945732i \(-0.394654\pi\)
0.324947 + 0.945732i \(0.394654\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −12382.0 −1.54196 −0.770981 0.636858i \(-0.780234\pi\)
−0.770981 + 0.636858i \(0.780234\pi\)
\(402\) 0 0
\(403\) −13218.9 −1.63394
\(404\) 0 0
\(405\) −371.449 −0.0455739
\(406\) 0 0
\(407\) 742.944 0.0904824
\(408\) 0 0
\(409\) 15875.6 1.91931 0.959657 0.281173i \(-0.0907235\pi\)
0.959657 + 0.281173i \(0.0907235\pi\)
\(410\) 0 0
\(411\) −2235.56 −0.268302
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 2004.62 0.237115
\(416\) 0 0
\(417\) −4120.79 −0.483923
\(418\) 0 0
\(419\) −16111.9 −1.87857 −0.939283 0.343145i \(-0.888508\pi\)
−0.939283 + 0.343145i \(0.888508\pi\)
\(420\) 0 0
\(421\) 8691.58 1.00618 0.503090 0.864234i \(-0.332197\pi\)
0.503090 + 0.864234i \(0.332197\pi\)
\(422\) 0 0
\(423\) 3114.04 0.357943
\(424\) 0 0
\(425\) 8479.46 0.967798
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −879.661 −0.0989987
\(430\) 0 0
\(431\) 4195.10 0.468842 0.234421 0.972135i \(-0.424681\pi\)
0.234421 + 0.972135i \(0.424681\pi\)
\(432\) 0 0
\(433\) 5426.54 0.602270 0.301135 0.953582i \(-0.402635\pi\)
0.301135 + 0.953582i \(0.402635\pi\)
\(434\) 0 0
\(435\) 3688.79 0.406584
\(436\) 0 0
\(437\) 536.968 0.0587795
\(438\) 0 0
\(439\) −3771.24 −0.410003 −0.205002 0.978762i \(-0.565720\pi\)
−0.205002 + 0.978762i \(0.565720\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5930.30 0.636020 0.318010 0.948087i \(-0.396985\pi\)
0.318010 + 0.948087i \(0.396985\pi\)
\(444\) 0 0
\(445\) −268.326 −0.0285840
\(446\) 0 0
\(447\) 1861.59 0.196980
\(448\) 0 0
\(449\) −529.065 −0.0556083 −0.0278041 0.999613i \(-0.508851\pi\)
−0.0278041 + 0.999613i \(0.508851\pi\)
\(450\) 0 0
\(451\) 1048.05 0.109426
\(452\) 0 0
\(453\) 5817.79 0.603408
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 10057.2 1.02944 0.514721 0.857358i \(-0.327896\pi\)
0.514721 + 0.857358i \(0.327896\pi\)
\(458\) 0 0
\(459\) −2202.02 −0.223925
\(460\) 0 0
\(461\) 5010.31 0.506190 0.253095 0.967441i \(-0.418552\pi\)
0.253095 + 0.967441i \(0.418552\pi\)
\(462\) 0 0
\(463\) 7124.38 0.715114 0.357557 0.933891i \(-0.383610\pi\)
0.357557 + 0.933891i \(0.383610\pi\)
\(464\) 0 0
\(465\) −4022.21 −0.401130
\(466\) 0 0
\(467\) 7501.44 0.743309 0.371654 0.928371i \(-0.378791\pi\)
0.371654 + 0.928371i \(0.378791\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 1238.53 0.121164
\(472\) 0 0
\(473\) 3056.47 0.297118
\(474\) 0 0
\(475\) 525.449 0.0507563
\(476\) 0 0
\(477\) 3649.76 0.350338
\(478\) 0 0
\(479\) −8173.80 −0.779688 −0.389844 0.920881i \(-0.627471\pi\)
−0.389844 + 0.920881i \(0.627471\pi\)
\(480\) 0 0
\(481\) −5179.55 −0.490992
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −5870.22 −0.549594
\(486\) 0 0
\(487\) 11968.8 1.11367 0.556835 0.830623i \(-0.312015\pi\)
0.556835 + 0.830623i \(0.312015\pi\)
\(488\) 0 0
\(489\) 11722.3 1.08405
\(490\) 0 0
\(491\) −2079.96 −0.191176 −0.0955878 0.995421i \(-0.530473\pi\)
−0.0955878 + 0.995421i \(0.530473\pi\)
\(492\) 0 0
\(493\) 21867.9 1.99773
\(494\) 0 0
\(495\) −267.661 −0.0243040
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −12834.4 −1.15140 −0.575699 0.817662i \(-0.695270\pi\)
−0.575699 + 0.817662i \(0.695270\pi\)
\(500\) 0 0
\(501\) −3859.24 −0.344148
\(502\) 0 0
\(503\) 16808.8 1.48999 0.744997 0.667068i \(-0.232451\pi\)
0.744997 + 0.667068i \(0.232451\pi\)
\(504\) 0 0
\(505\) −5990.82 −0.527897
\(506\) 0 0
\(507\) −458.299 −0.0401455
\(508\) 0 0
\(509\) 4270.26 0.371859 0.185929 0.982563i \(-0.440470\pi\)
0.185929 + 0.982563i \(0.440470\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −136.453 −0.0117438
\(514\) 0 0
\(515\) 3480.50 0.297804
\(516\) 0 0
\(517\) 2243.93 0.190886
\(518\) 0 0
\(519\) 3753.77 0.317480
\(520\) 0 0
\(521\) −15283.3 −1.28517 −0.642584 0.766215i \(-0.722138\pi\)
−0.642584 + 0.766215i \(0.722138\pi\)
\(522\) 0 0
\(523\) −4499.33 −0.376180 −0.188090 0.982152i \(-0.560230\pi\)
−0.188090 + 0.982152i \(0.560230\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −23844.4 −1.97093
\(528\) 0 0
\(529\) −877.984 −0.0721611
\(530\) 0 0
\(531\) −2280.92 −0.186410
\(532\) 0 0
\(533\) −7306.69 −0.593785
\(534\) 0 0
\(535\) 5789.62 0.467864
\(536\) 0 0
\(537\) −10870.5 −0.873554
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 3970.82 0.315561 0.157781 0.987474i \(-0.449566\pi\)
0.157781 + 0.987474i \(0.449566\pi\)
\(542\) 0 0
\(543\) −545.181 −0.0430865
\(544\) 0 0
\(545\) 9655.50 0.758892
\(546\) 0 0
\(547\) 2703.90 0.211353 0.105677 0.994401i \(-0.466299\pi\)
0.105677 + 0.994401i \(0.466299\pi\)
\(548\) 0 0
\(549\) 6760.96 0.525593
\(550\) 0 0
\(551\) 1355.09 0.104771
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −1576.02 −0.120538
\(556\) 0 0
\(557\) 790.824 0.0601585 0.0300793 0.999548i \(-0.490424\pi\)
0.0300793 + 0.999548i \(0.490424\pi\)
\(558\) 0 0
\(559\) −21308.7 −1.61227
\(560\) 0 0
\(561\) −1586.75 −0.119416
\(562\) 0 0
\(563\) 7517.15 0.562718 0.281359 0.959603i \(-0.409215\pi\)
0.281359 + 0.959603i \(0.409215\pi\)
\(564\) 0 0
\(565\) −7042.68 −0.524403
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13945.4 1.02746 0.513728 0.857953i \(-0.328264\pi\)
0.513728 + 0.857953i \(0.328264\pi\)
\(570\) 0 0
\(571\) 2118.49 0.155265 0.0776323 0.996982i \(-0.475264\pi\)
0.0776323 + 0.996982i \(0.475264\pi\)
\(572\) 0 0
\(573\) −4443.84 −0.323986
\(574\) 0 0
\(575\) 11046.8 0.801192
\(576\) 0 0
\(577\) −22857.7 −1.64918 −0.824592 0.565728i \(-0.808595\pi\)
−0.824592 + 0.565728i \(0.808595\pi\)
\(578\) 0 0
\(579\) −1070.12 −0.0768098
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 2629.97 0.186831
\(584\) 0 0
\(585\) 1866.04 0.131883
\(586\) 0 0
\(587\) 23955.3 1.68440 0.842199 0.539167i \(-0.181261\pi\)
0.842199 + 0.539167i \(0.181261\pi\)
\(588\) 0 0
\(589\) −1477.57 −0.103366
\(590\) 0 0
\(591\) 14671.6 1.02116
\(592\) 0 0
\(593\) 10778.0 0.746373 0.373186 0.927756i \(-0.378265\pi\)
0.373186 + 0.927756i \(0.378265\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10628.6 0.728639
\(598\) 0 0
\(599\) −7597.58 −0.518245 −0.259122 0.965845i \(-0.583433\pi\)
−0.259122 + 0.965845i \(0.583433\pi\)
\(600\) 0 0
\(601\) −19956.1 −1.35445 −0.677225 0.735776i \(-0.736818\pi\)
−0.677225 + 0.735776i \(0.736818\pi\)
\(602\) 0 0
\(603\) −104.821 −0.00707899
\(604\) 0 0
\(605\) 5910.81 0.397204
\(606\) 0 0
\(607\) −236.311 −0.0158016 −0.00790079 0.999969i \(-0.502515\pi\)
−0.00790079 + 0.999969i \(0.502515\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −15644.0 −1.03582
\(612\) 0 0
\(613\) 26414.9 1.74044 0.870219 0.492664i \(-0.163977\pi\)
0.870219 + 0.492664i \(0.163977\pi\)
\(614\) 0 0
\(615\) −2223.26 −0.145773
\(616\) 0 0
\(617\) 18473.6 1.20538 0.602689 0.797976i \(-0.294096\pi\)
0.602689 + 0.797976i \(0.294096\pi\)
\(618\) 0 0
\(619\) 16047.9 1.04204 0.521018 0.853546i \(-0.325552\pi\)
0.521018 + 0.853546i \(0.325552\pi\)
\(620\) 0 0
\(621\) −2868.74 −0.185376
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 8181.20 0.523597
\(626\) 0 0
\(627\) −98.3264 −0.00626280
\(628\) 0 0
\(629\) −9342.97 −0.592255
\(630\) 0 0
\(631\) 15065.7 0.950487 0.475243 0.879854i \(-0.342360\pi\)
0.475243 + 0.879854i \(0.342360\pi\)
\(632\) 0 0
\(633\) 12868.5 0.808020
\(634\) 0 0
\(635\) 110.861 0.00692816
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 6134.95 0.379804
\(640\) 0 0
\(641\) −31198.4 −1.92241 −0.961203 0.275842i \(-0.911043\pi\)
−0.961203 + 0.275842i \(0.911043\pi\)
\(642\) 0 0
\(643\) −12497.9 −0.766517 −0.383259 0.923641i \(-0.625198\pi\)
−0.383259 + 0.923641i \(0.625198\pi\)
\(644\) 0 0
\(645\) −6483.75 −0.395810
\(646\) 0 0
\(647\) −9929.72 −0.603366 −0.301683 0.953408i \(-0.597548\pi\)
−0.301683 + 0.953408i \(0.597548\pi\)
\(648\) 0 0
\(649\) −1643.60 −0.0994099
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8145.58 −0.488149 −0.244075 0.969756i \(-0.578484\pi\)
−0.244075 + 0.969756i \(0.578484\pi\)
\(654\) 0 0
\(655\) −7252.55 −0.432642
\(656\) 0 0
\(657\) −6169.11 −0.366332
\(658\) 0 0
\(659\) 16975.8 1.00347 0.501733 0.865022i \(-0.332696\pi\)
0.501733 + 0.865022i \(0.332696\pi\)
\(660\) 0 0
\(661\) −20637.8 −1.21440 −0.607199 0.794550i \(-0.707707\pi\)
−0.607199 + 0.794550i \(0.707707\pi\)
\(662\) 0 0
\(663\) 11062.3 0.647999
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 28489.0 1.65382
\(668\) 0 0
\(669\) 17387.2 1.00482
\(670\) 0 0
\(671\) 4871.86 0.280292
\(672\) 0 0
\(673\) −2150.29 −0.123161 −0.0615807 0.998102i \(-0.519614\pi\)
−0.0615807 + 0.998102i \(0.519614\pi\)
\(674\) 0 0
\(675\) −2807.21 −0.160073
\(676\) 0 0
\(677\) 27783.4 1.57726 0.788628 0.614871i \(-0.210792\pi\)
0.788628 + 0.614871i \(0.210792\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 12312.1 0.692807
\(682\) 0 0
\(683\) −18181.8 −1.01860 −0.509302 0.860588i \(-0.670096\pi\)
−0.509302 + 0.860588i \(0.670096\pi\)
\(684\) 0 0
\(685\) 3417.27 0.190609
\(686\) 0 0
\(687\) 3890.49 0.216058
\(688\) 0 0
\(689\) −18335.3 −1.01381
\(690\) 0 0
\(691\) 23935.1 1.31771 0.658853 0.752272i \(-0.271042\pi\)
0.658853 + 0.752272i \(0.271042\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6299.02 0.343792
\(696\) 0 0
\(697\) −13179.9 −0.716249
\(698\) 0 0
\(699\) −4435.00 −0.239982
\(700\) 0 0
\(701\) −20627.2 −1.11138 −0.555691 0.831389i \(-0.687546\pi\)
−0.555691 + 0.831389i \(0.687546\pi\)
\(702\) 0 0
\(703\) −578.958 −0.0310609
\(704\) 0 0
\(705\) −4760.10 −0.254292
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −6584.64 −0.348789 −0.174394 0.984676i \(-0.555797\pi\)
−0.174394 + 0.984676i \(0.555797\pi\)
\(710\) 0 0
\(711\) −2.37662 −0.000125359 0
\(712\) 0 0
\(713\) −31064.0 −1.63163
\(714\) 0 0
\(715\) 1344.65 0.0703313
\(716\) 0 0
\(717\) 11330.8 0.590174
\(718\) 0 0
\(719\) 170.886 0.00886366 0.00443183 0.999990i \(-0.498589\pi\)
0.00443183 + 0.999990i \(0.498589\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 11989.1 0.616710
\(724\) 0 0
\(725\) 27877.8 1.42808
\(726\) 0 0
\(727\) −11127.5 −0.567671 −0.283836 0.958873i \(-0.591607\pi\)
−0.283836 + 0.958873i \(0.591607\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 0 0
\(731\) −38437.0 −1.94479
\(732\) 0 0
\(733\) 22575.9 1.13760 0.568800 0.822476i \(-0.307408\pi\)
0.568800 + 0.822476i \(0.307408\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −75.5325 −0.00377513
\(738\) 0 0
\(739\) 22936.4 1.14172 0.570860 0.821048i \(-0.306610\pi\)
0.570860 + 0.821048i \(0.306610\pi\)
\(740\) 0 0
\(741\) 685.499 0.0339844
\(742\) 0 0
\(743\) −16973.4 −0.838081 −0.419041 0.907967i \(-0.637634\pi\)
−0.419041 + 0.907967i \(0.637634\pi\)
\(744\) 0 0
\(745\) −2845.62 −0.139940
\(746\) 0 0
\(747\) −3934.23 −0.192699
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 21197.9 1.02999 0.514994 0.857194i \(-0.327794\pi\)
0.514994 + 0.857194i \(0.327794\pi\)
\(752\) 0 0
\(753\) 16270.8 0.787436
\(754\) 0 0
\(755\) −8893.05 −0.428677
\(756\) 0 0
\(757\) −7962.24 −0.382289 −0.191144 0.981562i \(-0.561220\pi\)
−0.191144 + 0.981562i \(0.561220\pi\)
\(758\) 0 0
\(759\) −2067.18 −0.0988588
\(760\) 0 0
\(761\) −26856.2 −1.27928 −0.639642 0.768673i \(-0.720917\pi\)
−0.639642 + 0.768673i \(0.720917\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3366.00 0.159082
\(766\) 0 0
\(767\) 11458.6 0.539436
\(768\) 0 0
\(769\) 12183.6 0.571331 0.285666 0.958329i \(-0.407785\pi\)
0.285666 + 0.958329i \(0.407785\pi\)
\(770\) 0 0
\(771\) −17892.7 −0.835783
\(772\) 0 0
\(773\) 17455.2 0.812187 0.406093 0.913832i \(-0.366891\pi\)
0.406093 + 0.913832i \(0.366891\pi\)
\(774\) 0 0
\(775\) −30397.6 −1.40892
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −816.724 −0.0375638
\(780\) 0 0
\(781\) 4420.76 0.202545
\(782\) 0 0
\(783\) −7239.56 −0.330423
\(784\) 0 0
\(785\) −1893.21 −0.0860785
\(786\) 0 0
\(787\) 30981.0 1.40324 0.701622 0.712549i \(-0.252460\pi\)
0.701622 + 0.712549i \(0.252460\pi\)
\(788\) 0 0
\(789\) −15498.0 −0.699296
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −33964.9 −1.52097
\(794\) 0 0
\(795\) −5579.01 −0.248889
\(796\) 0 0
\(797\) 10517.6 0.467446 0.233723 0.972303i \(-0.424909\pi\)
0.233723 + 0.972303i \(0.424909\pi\)
\(798\) 0 0
\(799\) −28218.8 −1.24945
\(800\) 0 0
\(801\) 526.614 0.0232297
\(802\) 0 0
\(803\) −4445.38 −0.195360
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −11649.9 −0.508172
\(808\) 0 0
\(809\) −41778.4 −1.81564 −0.907819 0.419361i \(-0.862254\pi\)
−0.907819 + 0.419361i \(0.862254\pi\)
\(810\) 0 0
\(811\) −12935.4 −0.560079 −0.280039 0.959988i \(-0.590348\pi\)
−0.280039 + 0.959988i \(0.590348\pi\)
\(812\) 0 0
\(813\) 16583.0 0.715363
\(814\) 0 0
\(815\) −17918.7 −0.770140
\(816\) 0 0
\(817\) −2381.83 −0.101995
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −14499.2 −0.616354 −0.308177 0.951329i \(-0.599719\pi\)
−0.308177 + 0.951329i \(0.599719\pi\)
\(822\) 0 0
\(823\) 11977.1 0.507287 0.253643 0.967298i \(-0.418371\pi\)
0.253643 + 0.967298i \(0.418371\pi\)
\(824\) 0 0
\(825\) −2022.84 −0.0853649
\(826\) 0 0
\(827\) −27613.5 −1.16108 −0.580541 0.814231i \(-0.697159\pi\)
−0.580541 + 0.814231i \(0.697159\pi\)
\(828\) 0 0
\(829\) 677.836 0.0283983 0.0141992 0.999899i \(-0.495480\pi\)
0.0141992 + 0.999899i \(0.495480\pi\)
\(830\) 0 0
\(831\) 6804.36 0.284044
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 5899.22 0.244492
\(836\) 0 0
\(837\) 7893.92 0.325990
\(838\) 0 0
\(839\) 42209.6 1.73687 0.868436 0.495801i \(-0.165126\pi\)
0.868436 + 0.495801i \(0.165126\pi\)
\(840\) 0 0
\(841\) 47505.8 1.94784
\(842\) 0 0
\(843\) 2176.97 0.0889428
\(844\) 0 0
\(845\) 700.553 0.0285204
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 12711.0 0.513828
\(850\) 0 0
\(851\) −12171.8 −0.490299
\(852\) 0 0
\(853\) 2796.45 0.112249 0.0561247 0.998424i \(-0.482126\pi\)
0.0561247 + 0.998424i \(0.482126\pi\)
\(854\) 0 0
\(855\) 208.582 0.00834310
\(856\) 0 0
\(857\) −23181.1 −0.923979 −0.461989 0.886886i \(-0.652864\pi\)
−0.461989 + 0.886886i \(0.652864\pi\)
\(858\) 0 0
\(859\) −11897.5 −0.472569 −0.236285 0.971684i \(-0.575930\pi\)
−0.236285 + 0.971684i \(0.575930\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 29815.9 1.17607 0.588033 0.808837i \(-0.299902\pi\)
0.588033 + 0.808837i \(0.299902\pi\)
\(864\) 0 0
\(865\) −5737.99 −0.225546
\(866\) 0 0
\(867\) 5215.31 0.204292
\(868\) 0 0
\(869\) −1.71256 −6.68523e−5 0
\(870\) 0 0
\(871\) 526.587 0.0204853
\(872\) 0 0
\(873\) 11520.8 0.446644
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −10338.8 −0.398082 −0.199041 0.979991i \(-0.563783\pi\)
−0.199041 + 0.979991i \(0.563783\pi\)
\(878\) 0 0
\(879\) 13121.3 0.503495
\(880\) 0 0
\(881\) −24140.2 −0.923160 −0.461580 0.887099i \(-0.652717\pi\)
−0.461580 + 0.887099i \(0.652717\pi\)
\(882\) 0 0
\(883\) −12997.6 −0.495361 −0.247681 0.968842i \(-0.579668\pi\)
−0.247681 + 0.968842i \(0.579668\pi\)
\(884\) 0 0
\(885\) 3486.61 0.132430
\(886\) 0 0
\(887\) 45266.6 1.71353 0.856766 0.515705i \(-0.172470\pi\)
0.856766 + 0.515705i \(0.172470\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 525.308 0.0197514
\(892\) 0 0
\(893\) −1748.64 −0.0655276
\(894\) 0 0
\(895\) 16616.7 0.620596
\(896\) 0 0
\(897\) 14411.7 0.536446
\(898\) 0 0
\(899\) −78393.1 −2.90829
\(900\) 0 0
\(901\) −33073.5 −1.22290
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 833.361 0.0306098
\(906\) 0 0
\(907\) 27766.5 1.01651 0.508253 0.861208i \(-0.330292\pi\)
0.508253 + 0.861208i \(0.330292\pi\)
\(908\) 0 0
\(909\) 11757.5 0.429012
\(910\) 0 0
\(911\) −18531.2 −0.673948 −0.336974 0.941514i \(-0.609403\pi\)
−0.336974 + 0.941514i \(0.609403\pi\)
\(912\) 0 0
\(913\) −2834.96 −0.102764
\(914\) 0 0
\(915\) −10334.8 −0.373395
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 18093.4 0.649452 0.324726 0.945808i \(-0.394728\pi\)
0.324726 + 0.945808i \(0.394728\pi\)
\(920\) 0 0
\(921\) 12400.4 0.443656
\(922\) 0 0
\(923\) −30820.1 −1.09908
\(924\) 0 0
\(925\) −11910.7 −0.423375
\(926\) 0 0
\(927\) −6830.77 −0.242019
\(928\) 0 0
\(929\) −10622.5 −0.375149 −0.187574 0.982250i \(-0.560063\pi\)
−0.187574 + 0.982250i \(0.560063\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 15189.7 0.532999
\(934\) 0 0
\(935\) 2425.50 0.0848366
\(936\) 0 0
\(937\) −16057.6 −0.559851 −0.279925 0.960022i \(-0.590310\pi\)
−0.279925 + 0.960022i \(0.590310\pi\)
\(938\) 0 0
\(939\) −22234.7 −0.772738
\(940\) 0 0
\(941\) −55153.3 −1.91068 −0.955338 0.295516i \(-0.904508\pi\)
−0.955338 + 0.295516i \(0.904508\pi\)
\(942\) 0 0
\(943\) −17170.5 −0.592947
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18785.7 −0.644619 −0.322309 0.946634i \(-0.604459\pi\)
−0.322309 + 0.946634i \(0.604459\pi\)
\(948\) 0 0
\(949\) 30991.7 1.06010
\(950\) 0 0
\(951\) −20211.2 −0.689161
\(952\) 0 0
\(953\) −36499.4 −1.24064 −0.620321 0.784348i \(-0.712998\pi\)
−0.620321 + 0.784348i \(0.712998\pi\)
\(954\) 0 0
\(955\) 6792.83 0.230168
\(956\) 0 0
\(957\) −5216.74 −0.176210
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 55687.8 1.86928
\(962\) 0 0
\(963\) −11362.6 −0.380224
\(964\) 0 0
\(965\) 1635.79 0.0545677
\(966\) 0 0
\(967\) −26059.9 −0.866627 −0.433314 0.901243i \(-0.642656\pi\)
−0.433314 + 0.901243i \(0.642656\pi\)
\(968\) 0 0
\(969\) 1236.51 0.0409934
\(970\) 0 0
\(971\) 21689.0 0.716820 0.358410 0.933564i \(-0.383319\pi\)
0.358410 + 0.933564i \(0.383319\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 14102.5 0.463223
\(976\) 0 0
\(977\) 2119.19 0.0693950 0.0346975 0.999398i \(-0.488953\pi\)
0.0346975 + 0.999398i \(0.488953\pi\)
\(978\) 0 0
\(979\) 379.471 0.0123881
\(980\) 0 0
\(981\) −18949.7 −0.616737
\(982\) 0 0
\(983\) −48504.1 −1.57380 −0.786898 0.617083i \(-0.788314\pi\)
−0.786898 + 0.617083i \(0.788314\pi\)
\(984\) 0 0
\(985\) −22426.9 −0.725463
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −50074.8 −1.61000
\(990\) 0 0
\(991\) −2043.84 −0.0655144 −0.0327572 0.999463i \(-0.510429\pi\)
−0.0327572 + 0.999463i \(0.510429\pi\)
\(992\) 0 0
\(993\) −33527.8 −1.07147
\(994\) 0 0
\(995\) −16246.8 −0.517645
\(996\) 0 0
\(997\) 26738.9 0.849378 0.424689 0.905339i \(-0.360383\pi\)
0.424689 + 0.905339i \(0.360383\pi\)
\(998\) 0 0
\(999\) 3093.08 0.0979586
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.bw.1.2 2
4.3 odd 2 294.4.a.l.1.2 2
7.6 odd 2 2352.4.a.bu.1.1 2
12.11 even 2 882.4.a.bb.1.1 2
28.3 even 6 294.4.e.k.79.2 4
28.11 odd 6 294.4.e.m.79.1 4
28.19 even 6 294.4.e.k.67.2 4
28.23 odd 6 294.4.e.m.67.1 4
28.27 even 2 294.4.a.o.1.1 yes 2
84.11 even 6 882.4.g.be.667.2 4
84.23 even 6 882.4.g.be.361.2 4
84.47 odd 6 882.4.g.bk.361.1 4
84.59 odd 6 882.4.g.bk.667.1 4
84.83 odd 2 882.4.a.t.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
294.4.a.l.1.2 2 4.3 odd 2
294.4.a.o.1.1 yes 2 28.27 even 2
294.4.e.k.67.2 4 28.19 even 6
294.4.e.k.79.2 4 28.3 even 6
294.4.e.m.67.1 4 28.23 odd 6
294.4.e.m.79.1 4 28.11 odd 6
882.4.a.t.1.2 2 84.83 odd 2
882.4.a.bb.1.1 2 12.11 even 2
882.4.g.be.361.2 4 84.23 even 6
882.4.g.be.667.2 4 84.11 even 6
882.4.g.bk.361.1 4 84.47 odd 6
882.4.g.bk.667.1 4 84.59 odd 6
2352.4.a.bu.1.1 2 7.6 odd 2
2352.4.a.bw.1.2 2 1.1 even 1 trivial