Properties

Label 2916.3.c.b.1457.4
Level $2916$
Weight $3$
Character 2916.1457
Analytic conductor $79.455$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2916,3,Mod(1457,2916)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2916, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2916.1457");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2916.c (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(79.4552450875\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: no (minimal twist has level 108)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1457.4
Character \(\chi\) \(=\) 2916.1457
Dual form 2916.3.c.b.1457.33

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-7.77099i q^{5} +13.6742 q^{7} +O(q^{10})\) \(q-7.77099i q^{5} +13.6742 q^{7} -2.59394i q^{11} +8.76827 q^{13} -17.6544i q^{17} -2.93881 q^{19} +18.5107i q^{23} -35.3882 q^{25} +3.09899i q^{29} +40.0195 q^{31} -106.262i q^{35} +25.6409 q^{37} -62.1311i q^{41} +32.9177 q^{43} -52.0015i q^{47} +137.983 q^{49} -53.2686i q^{53} -20.1575 q^{55} +103.991i q^{59} -5.95342 q^{61} -68.1381i q^{65} +47.3318 q^{67} +89.5061i q^{71} -67.2043 q^{73} -35.4700i q^{77} -36.3221 q^{79} +20.2994i q^{83} -137.192 q^{85} +96.6488i q^{89} +119.899 q^{91} +22.8375i q^{95} -67.2509 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 180 q^{25} + 252 q^{49} + 18 q^{61} - 90 q^{67} + 126 q^{73} - 198 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times\).

\(n\) \(1459\) \(2189\)
\(\chi(n)\) \(1\) \(-1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) − 7.77099i − 1.55420i −0.629379 0.777099i \(-0.716691\pi\)
0.629379 0.777099i \(-0.283309\pi\)
\(6\) 0 0
\(7\) 13.6742 1.95345 0.976727 0.214485i \(-0.0688072\pi\)
0.976727 + 0.214485i \(0.0688072\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) − 2.59394i − 0.235813i −0.993025 0.117906i \(-0.962382\pi\)
0.993025 0.117906i \(-0.0376183\pi\)
\(12\) 0 0
\(13\) 8.76827 0.674482 0.337241 0.941418i \(-0.390506\pi\)
0.337241 + 0.941418i \(0.390506\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 17.6544i − 1.03849i −0.854624 0.519247i \(-0.826213\pi\)
0.854624 0.519247i \(-0.173787\pi\)
\(18\) 0 0
\(19\) −2.93881 −0.154674 −0.0773372 0.997005i \(-0.524642\pi\)
−0.0773372 + 0.997005i \(0.524642\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 18.5107i 0.804814i 0.915461 + 0.402407i \(0.131826\pi\)
−0.915461 + 0.402407i \(0.868174\pi\)
\(24\) 0 0
\(25\) −35.3882 −1.41553
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.09899i 0.106862i 0.998572 + 0.0534308i \(0.0170157\pi\)
−0.998572 + 0.0534308i \(0.982984\pi\)
\(30\) 0 0
\(31\) 40.0195 1.29095 0.645476 0.763781i \(-0.276659\pi\)
0.645476 + 0.763781i \(0.276659\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) − 106.262i − 3.03605i
\(36\) 0 0
\(37\) 25.6409 0.692998 0.346499 0.938050i \(-0.387370\pi\)
0.346499 + 0.938050i \(0.387370\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) − 62.1311i − 1.51539i −0.652608 0.757696i \(-0.726325\pi\)
0.652608 0.757696i \(-0.273675\pi\)
\(42\) 0 0
\(43\) 32.9177 0.765529 0.382764 0.923846i \(-0.374972\pi\)
0.382764 + 0.923846i \(0.374972\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 52.0015i − 1.10641i −0.833044 0.553207i \(-0.813404\pi\)
0.833044 0.553207i \(-0.186596\pi\)
\(48\) 0 0
\(49\) 137.983 2.81599
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 53.2686i − 1.00507i −0.864557 0.502534i \(-0.832401\pi\)
0.864557 0.502534i \(-0.167599\pi\)
\(54\) 0 0
\(55\) −20.1575 −0.366500
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 103.991i 1.76255i 0.472601 + 0.881277i \(0.343315\pi\)
−0.472601 + 0.881277i \(0.656685\pi\)
\(60\) 0 0
\(61\) −5.95342 −0.0975970 −0.0487985 0.998809i \(-0.515539\pi\)
−0.0487985 + 0.998809i \(0.515539\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 68.1381i − 1.04828i
\(66\) 0 0
\(67\) 47.3318 0.706445 0.353222 0.935539i \(-0.385086\pi\)
0.353222 + 0.935539i \(0.385086\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 89.5061i 1.26065i 0.776331 + 0.630325i \(0.217078\pi\)
−0.776331 + 0.630325i \(0.782922\pi\)
\(72\) 0 0
\(73\) −67.2043 −0.920607 −0.460303 0.887762i \(-0.652259\pi\)
−0.460303 + 0.887762i \(0.652259\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 35.4700i − 0.460650i
\(78\) 0 0
\(79\) −36.3221 −0.459774 −0.229887 0.973217i \(-0.573836\pi\)
−0.229887 + 0.973217i \(0.573836\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 20.2994i 0.244571i 0.992495 + 0.122286i \(0.0390224\pi\)
−0.992495 + 0.122286i \(0.960978\pi\)
\(84\) 0 0
\(85\) −137.192 −1.61402
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 96.6488i 1.08594i 0.839752 + 0.542971i \(0.182701\pi\)
−0.839752 + 0.542971i \(0.817299\pi\)
\(90\) 0 0
\(91\) 119.899 1.31757
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 22.8375i 0.240395i
\(96\) 0 0
\(97\) −67.2509 −0.693308 −0.346654 0.937993i \(-0.612682\pi\)
−0.346654 + 0.937993i \(0.612682\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 93.9271i − 0.929971i −0.885318 0.464985i \(-0.846060\pi\)
0.885318 0.464985i \(-0.153940\pi\)
\(102\) 0 0
\(103\) 16.0359 0.155688 0.0778442 0.996966i \(-0.475196\pi\)
0.0778442 + 0.996966i \(0.475196\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 96.4400i 0.901308i 0.892699 + 0.450654i \(0.148809\pi\)
−0.892699 + 0.450654i \(0.851191\pi\)
\(108\) 0 0
\(109\) −141.184 −1.29527 −0.647635 0.761951i \(-0.724242\pi\)
−0.647635 + 0.761951i \(0.724242\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) − 26.3337i − 0.233042i −0.993188 0.116521i \(-0.962826\pi\)
0.993188 0.116521i \(-0.0371742\pi\)
\(114\) 0 0
\(115\) 143.847 1.25084
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) − 241.409i − 2.02865i
\(120\) 0 0
\(121\) 114.271 0.944392
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 80.7268i 0.645814i
\(126\) 0 0
\(127\) 102.490 0.807010 0.403505 0.914977i \(-0.367792\pi\)
0.403505 + 0.914977i \(0.367792\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 78.0185i 0.595561i 0.954634 + 0.297781i \(0.0962464\pi\)
−0.954634 + 0.297781i \(0.903754\pi\)
\(132\) 0 0
\(133\) −40.1859 −0.302149
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 54.9068i 0.400779i 0.979716 + 0.200390i \(0.0642208\pi\)
−0.979716 + 0.200390i \(0.935779\pi\)
\(138\) 0 0
\(139\) −40.5682 −0.291857 −0.145929 0.989295i \(-0.546617\pi\)
−0.145929 + 0.989295i \(0.546617\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 22.7444i − 0.159051i
\(144\) 0 0
\(145\) 24.0822 0.166084
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 167.504i − 1.12419i −0.827073 0.562094i \(-0.809996\pi\)
0.827073 0.562094i \(-0.190004\pi\)
\(150\) 0 0
\(151\) 275.526 1.82467 0.912336 0.409441i \(-0.134276\pi\)
0.912336 + 0.409441i \(0.134276\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) − 310.991i − 2.00639i
\(156\) 0 0
\(157\) −206.161 −1.31313 −0.656565 0.754270i \(-0.727991\pi\)
−0.656565 + 0.754270i \(0.727991\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 253.119i 1.57217i
\(162\) 0 0
\(163\) −85.6172 −0.525259 −0.262629 0.964897i \(-0.584590\pi\)
−0.262629 + 0.964897i \(0.584590\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 44.9509i 0.269167i 0.990902 + 0.134584i \(0.0429697\pi\)
−0.990902 + 0.134584i \(0.957030\pi\)
\(168\) 0 0
\(169\) −92.1175 −0.545074
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 169.446i − 0.979456i −0.871875 0.489728i \(-0.837096\pi\)
0.871875 0.489728i \(-0.162904\pi\)
\(174\) 0 0
\(175\) −483.905 −2.76517
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 140.618i 0.785577i 0.919629 + 0.392789i \(0.128490\pi\)
−0.919629 + 0.392789i \(0.871510\pi\)
\(180\) 0 0
\(181\) 69.3731 0.383277 0.191638 0.981466i \(-0.438620\pi\)
0.191638 + 0.981466i \(0.438620\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 199.255i − 1.07706i
\(186\) 0 0
\(187\) −45.7944 −0.244890
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) − 294.098i − 1.53978i −0.638175 0.769891i \(-0.720310\pi\)
0.638175 0.769891i \(-0.279690\pi\)
\(192\) 0 0
\(193\) −104.946 −0.543762 −0.271881 0.962331i \(-0.587646\pi\)
−0.271881 + 0.962331i \(0.587646\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 66.6479i 0.338314i 0.985589 + 0.169157i \(0.0541045\pi\)
−0.985589 + 0.169157i \(0.945895\pi\)
\(198\) 0 0
\(199\) −185.725 −0.933294 −0.466647 0.884444i \(-0.654538\pi\)
−0.466647 + 0.884444i \(0.654538\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 42.3761i 0.208749i
\(204\) 0 0
\(205\) −482.820 −2.35522
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7.62311i 0.0364742i
\(210\) 0 0
\(211\) 23.3483 0.110655 0.0553276 0.998468i \(-0.482380\pi\)
0.0553276 + 0.998468i \(0.482380\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) − 255.803i − 1.18978i
\(216\) 0 0
\(217\) 547.234 2.52181
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 154.798i − 0.700445i
\(222\) 0 0
\(223\) −184.646 −0.828008 −0.414004 0.910275i \(-0.635870\pi\)
−0.414004 + 0.910275i \(0.635870\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 198.608i 0.874925i 0.899237 + 0.437463i \(0.144123\pi\)
−0.899237 + 0.437463i \(0.855877\pi\)
\(228\) 0 0
\(229\) −62.2729 −0.271934 −0.135967 0.990713i \(-0.543414\pi\)
−0.135967 + 0.990713i \(0.543414\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 138.893i − 0.596108i −0.954549 0.298054i \(-0.903662\pi\)
0.954549 0.298054i \(-0.0963375\pi\)
\(234\) 0 0
\(235\) −404.103 −1.71959
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 394.203i 1.64938i 0.565583 + 0.824692i \(0.308651\pi\)
−0.565583 + 0.824692i \(0.691349\pi\)
\(240\) 0 0
\(241\) −14.0515 −0.0583051 −0.0291526 0.999575i \(-0.509281\pi\)
−0.0291526 + 0.999575i \(0.509281\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 1072.27i − 4.37660i
\(246\) 0 0
\(247\) −25.7683 −0.104325
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) − 137.653i − 0.548417i −0.961670 0.274208i \(-0.911584\pi\)
0.961670 0.274208i \(-0.0884158\pi\)
\(252\) 0 0
\(253\) 48.0157 0.189786
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 449.614i 1.74947i 0.484600 + 0.874736i \(0.338965\pi\)
−0.484600 + 0.874736i \(0.661035\pi\)
\(258\) 0 0
\(259\) 350.619 1.35374
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) − 5.84301i − 0.0222168i −0.999938 0.0111084i \(-0.996464\pi\)
0.999938 0.0111084i \(-0.00353598\pi\)
\(264\) 0 0
\(265\) −413.950 −1.56207
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 382.562i − 1.42216i −0.703109 0.711082i \(-0.748206\pi\)
0.703109 0.711082i \(-0.251794\pi\)
\(270\) 0 0
\(271\) 41.5492 0.153318 0.0766591 0.997057i \(-0.475575\pi\)
0.0766591 + 0.997057i \(0.475575\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 91.7950i 0.333800i
\(276\) 0 0
\(277\) 269.629 0.973391 0.486695 0.873572i \(-0.338202\pi\)
0.486695 + 0.873572i \(0.338202\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 280.532i − 0.998335i −0.866506 0.499167i \(-0.833639\pi\)
0.866506 0.499167i \(-0.166361\pi\)
\(282\) 0 0
\(283\) 229.103 0.809553 0.404776 0.914416i \(-0.367349\pi\)
0.404776 + 0.914416i \(0.367349\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 849.591i − 2.96025i
\(288\) 0 0
\(289\) −22.6772 −0.0784679
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 134.836i − 0.460191i −0.973168 0.230095i \(-0.926096\pi\)
0.973168 0.230095i \(-0.0739038\pi\)
\(294\) 0 0
\(295\) 808.110 2.73936
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 162.307i 0.542833i
\(300\) 0 0
\(301\) 450.123 1.49543
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 46.2639i 0.151685i
\(306\) 0 0
\(307\) −394.389 −1.28465 −0.642327 0.766431i \(-0.722031\pi\)
−0.642327 + 0.766431i \(0.722031\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) − 173.275i − 0.557154i −0.960414 0.278577i \(-0.910137\pi\)
0.960414 0.278577i \(-0.0898627\pi\)
\(312\) 0 0
\(313\) −42.7576 −0.136606 −0.0683028 0.997665i \(-0.521758\pi\)
−0.0683028 + 0.997665i \(0.521758\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 233.172i − 0.735560i −0.929913 0.367780i \(-0.880118\pi\)
0.929913 0.367780i \(-0.119882\pi\)
\(318\) 0 0
\(319\) 8.03859 0.0251993
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 51.8829i 0.160628i
\(324\) 0 0
\(325\) −310.293 −0.954749
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 711.078i − 2.16133i
\(330\) 0 0
\(331\) −373.782 −1.12925 −0.564626 0.825347i \(-0.690979\pi\)
−0.564626 + 0.825347i \(0.690979\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) − 367.815i − 1.09795i
\(336\) 0 0
\(337\) 204.899 0.608010 0.304005 0.952670i \(-0.401676\pi\)
0.304005 + 0.952670i \(0.401676\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) − 103.808i − 0.304423i
\(342\) 0 0
\(343\) 1216.77 3.54744
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 535.122i − 1.54214i −0.636751 0.771070i \(-0.719722\pi\)
0.636751 0.771070i \(-0.280278\pi\)
\(348\) 0 0
\(349\) −478.052 −1.36978 −0.684888 0.728648i \(-0.740149\pi\)
−0.684888 + 0.728648i \(0.740149\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 77.0832i 0.218366i 0.994022 + 0.109183i \(0.0348235\pi\)
−0.994022 + 0.109183i \(0.965177\pi\)
\(354\) 0 0
\(355\) 695.551 1.95930
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) − 203.832i − 0.567777i −0.958857 0.283889i \(-0.908375\pi\)
0.958857 0.283889i \(-0.0916246\pi\)
\(360\) 0 0
\(361\) −352.363 −0.976076
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 522.244i 1.43080i
\(366\) 0 0
\(367\) −407.785 −1.11113 −0.555566 0.831473i \(-0.687498\pi\)
−0.555566 + 0.831473i \(0.687498\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) − 728.405i − 1.96335i
\(372\) 0 0
\(373\) 345.500 0.926274 0.463137 0.886287i \(-0.346724\pi\)
0.463137 + 0.886287i \(0.346724\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 27.1728i 0.0720763i
\(378\) 0 0
\(379\) −63.5579 −0.167699 −0.0838495 0.996478i \(-0.526722\pi\)
−0.0838495 + 0.996478i \(0.526722\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 490.175i 1.27983i 0.768446 + 0.639915i \(0.221030\pi\)
−0.768446 + 0.639915i \(0.778970\pi\)
\(384\) 0 0
\(385\) −275.637 −0.715940
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 86.6934i − 0.222862i −0.993772 0.111431i \(-0.964457\pi\)
0.993772 0.111431i \(-0.0355435\pi\)
\(390\) 0 0
\(391\) 326.795 0.835794
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 282.259i 0.714579i
\(396\) 0 0
\(397\) −531.427 −1.33861 −0.669304 0.742989i \(-0.733408\pi\)
−0.669304 + 0.742989i \(0.733408\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 531.451i 1.32531i 0.748923 + 0.662657i \(0.230571\pi\)
−0.748923 + 0.662657i \(0.769429\pi\)
\(402\) 0 0
\(403\) 350.902 0.870723
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 66.5110i − 0.163418i
\(408\) 0 0
\(409\) −212.013 −0.518370 −0.259185 0.965828i \(-0.583454\pi\)
−0.259185 + 0.965828i \(0.583454\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1421.99i 3.44307i
\(414\) 0 0
\(415\) 157.746 0.380112
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) − 9.74283i − 0.0232526i −0.999932 0.0116263i \(-0.996299\pi\)
0.999932 0.0116263i \(-0.00370085\pi\)
\(420\) 0 0
\(421\) −10.7083 −0.0254354 −0.0127177 0.999919i \(-0.504048\pi\)
−0.0127177 + 0.999919i \(0.504048\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 624.757i 1.47002i
\(426\) 0 0
\(427\) −81.4082 −0.190651
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 65.8369i 0.152754i 0.997079 + 0.0763769i \(0.0243352\pi\)
−0.997079 + 0.0763769i \(0.975665\pi\)
\(432\) 0 0
\(433\) 6.63250 0.0153176 0.00765878 0.999971i \(-0.497562\pi\)
0.00765878 + 0.999971i \(0.497562\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 54.3996i − 0.124484i
\(438\) 0 0
\(439\) 87.6058 0.199558 0.0997788 0.995010i \(-0.468186\pi\)
0.0997788 + 0.995010i \(0.468186\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 587.210i − 1.32553i −0.748827 0.662765i \(-0.769383\pi\)
0.748827 0.662765i \(-0.230617\pi\)
\(444\) 0 0
\(445\) 751.056 1.68777
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 235.351i 0.524168i 0.965045 + 0.262084i \(0.0844097\pi\)
−0.965045 + 0.262084i \(0.915590\pi\)
\(450\) 0 0
\(451\) −161.164 −0.357349
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) − 931.733i − 2.04776i
\(456\) 0 0
\(457\) 609.689 1.33411 0.667056 0.745008i \(-0.267554\pi\)
0.667056 + 0.745008i \(0.267554\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) − 904.652i − 1.96237i −0.193071 0.981185i \(-0.561845\pi\)
0.193071 0.981185i \(-0.438155\pi\)
\(462\) 0 0
\(463\) −69.6790 −0.150495 −0.0752473 0.997165i \(-0.523975\pi\)
−0.0752473 + 0.997165i \(0.523975\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 110.122i − 0.235808i −0.993025 0.117904i \(-0.962383\pi\)
0.993025 0.117904i \(-0.0376175\pi\)
\(468\) 0 0
\(469\) 647.224 1.38001
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) − 85.3867i − 0.180522i
\(474\) 0 0
\(475\) 103.999 0.218946
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 166.090i 0.346744i 0.984856 + 0.173372i \(0.0554663\pi\)
−0.984856 + 0.173372i \(0.944534\pi\)
\(480\) 0 0
\(481\) 224.826 0.467415
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 522.606i 1.07754i
\(486\) 0 0
\(487\) 492.594 1.01149 0.505743 0.862684i \(-0.331218\pi\)
0.505743 + 0.862684i \(0.331218\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) − 601.147i − 1.22433i −0.790730 0.612166i \(-0.790299\pi\)
0.790730 0.612166i \(-0.209701\pi\)
\(492\) 0 0
\(493\) 54.7107 0.110975
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1223.92i 2.46262i
\(498\) 0 0
\(499\) −577.732 −1.15778 −0.578889 0.815406i \(-0.696514\pi\)
−0.578889 + 0.815406i \(0.696514\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 463.653i 0.921775i 0.887459 + 0.460887i \(0.152469\pi\)
−0.887459 + 0.460887i \(0.847531\pi\)
\(504\) 0 0
\(505\) −729.906 −1.44536
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 762.823i 1.49867i 0.662191 + 0.749335i \(0.269627\pi\)
−0.662191 + 0.749335i \(0.730373\pi\)
\(510\) 0 0
\(511\) −918.964 −1.79836
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) − 124.615i − 0.241971i
\(516\) 0 0
\(517\) −134.889 −0.260907
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 275.133i − 0.528086i −0.964511 0.264043i \(-0.914944\pi\)
0.964511 0.264043i \(-0.0850561\pi\)
\(522\) 0 0
\(523\) −185.838 −0.355331 −0.177665 0.984091i \(-0.556854\pi\)
−0.177665 + 0.984091i \(0.556854\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 706.519i − 1.34064i
\(528\) 0 0
\(529\) 186.353 0.352274
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) − 544.782i − 1.02210i
\(534\) 0 0
\(535\) 749.434 1.40081
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) − 357.920i − 0.664045i
\(540\) 0 0
\(541\) 745.728 1.37843 0.689213 0.724559i \(-0.257956\pi\)
0.689213 + 0.724559i \(0.257956\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1097.14i 2.01310i
\(546\) 0 0
\(547\) 44.4985 0.0813502 0.0406751 0.999172i \(-0.487049\pi\)
0.0406751 + 0.999172i \(0.487049\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) − 9.10735i − 0.0165288i
\(552\) 0 0
\(553\) −496.675 −0.898147
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 973.545i 1.74784i 0.486073 + 0.873918i \(0.338429\pi\)
−0.486073 + 0.873918i \(0.661571\pi\)
\(558\) 0 0
\(559\) 288.632 0.516335
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 180.589i 0.320763i 0.987055 + 0.160381i \(0.0512724\pi\)
−0.987055 + 0.160381i \(0.948728\pi\)
\(564\) 0 0
\(565\) −204.639 −0.362193
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 913.212i 1.60494i 0.596691 + 0.802471i \(0.296482\pi\)
−0.596691 + 0.802471i \(0.703518\pi\)
\(570\) 0 0
\(571\) −25.3524 −0.0444000 −0.0222000 0.999754i \(-0.507067\pi\)
−0.0222000 + 0.999754i \(0.507067\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) − 655.062i − 1.13924i
\(576\) 0 0
\(577\) −208.508 −0.361365 −0.180683 0.983541i \(-0.557831\pi\)
−0.180683 + 0.983541i \(0.557831\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 277.578i 0.477759i
\(582\) 0 0
\(583\) −138.176 −0.237008
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 573.400i 0.976831i 0.872611 + 0.488416i \(0.162425\pi\)
−0.872611 + 0.488416i \(0.837575\pi\)
\(588\) 0 0
\(589\) −117.610 −0.199677
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 875.654i 1.47665i 0.674445 + 0.738325i \(0.264383\pi\)
−0.674445 + 0.738325i \(0.735617\pi\)
\(594\) 0 0
\(595\) −1875.99 −3.15292
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 474.655i 0.792413i 0.918161 + 0.396206i \(0.129674\pi\)
−0.918161 + 0.396206i \(0.870326\pi\)
\(600\) 0 0
\(601\) 618.401 1.02895 0.514476 0.857505i \(-0.327986\pi\)
0.514476 + 0.857505i \(0.327986\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 888.002i − 1.46777i
\(606\) 0 0
\(607\) −370.800 −0.610873 −0.305437 0.952212i \(-0.598802\pi\)
−0.305437 + 0.952212i \(0.598802\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) − 455.963i − 0.746256i
\(612\) 0 0
\(613\) 330.774 0.539598 0.269799 0.962917i \(-0.413043\pi\)
0.269799 + 0.962917i \(0.413043\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 545.705i 0.884449i 0.896904 + 0.442224i \(0.145810\pi\)
−0.896904 + 0.442224i \(0.854190\pi\)
\(618\) 0 0
\(619\) −959.199 −1.54959 −0.774797 0.632210i \(-0.782148\pi\)
−0.774797 + 0.632210i \(0.782148\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1321.59i 2.12134i
\(624\) 0 0
\(625\) −257.379 −0.411806
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) − 452.675i − 0.719674i
\(630\) 0 0
\(631\) 573.390 0.908700 0.454350 0.890823i \(-0.349872\pi\)
0.454350 + 0.890823i \(0.349872\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) − 796.451i − 1.25425i
\(636\) 0 0
\(637\) 1209.87 1.89933
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 895.044i − 1.39633i −0.715939 0.698163i \(-0.754001\pi\)
0.715939 0.698163i \(-0.245999\pi\)
\(642\) 0 0
\(643\) −474.571 −0.738058 −0.369029 0.929418i \(-0.620310\pi\)
−0.369029 + 0.929418i \(0.620310\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 459.625i 0.710394i 0.934792 + 0.355197i \(0.115586\pi\)
−0.934792 + 0.355197i \(0.884414\pi\)
\(648\) 0 0
\(649\) 269.746 0.415633
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) − 27.2561i − 0.0417398i −0.999782 0.0208699i \(-0.993356\pi\)
0.999782 0.0208699i \(-0.00664357\pi\)
\(654\) 0 0
\(655\) 606.281 0.925619
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 50.4027i 0.0764836i 0.999269 + 0.0382418i \(0.0121757\pi\)
−0.999269 + 0.0382418i \(0.987824\pi\)
\(660\) 0 0
\(661\) −928.837 −1.40520 −0.702600 0.711585i \(-0.747978\pi\)
−0.702600 + 0.711585i \(0.747978\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 312.284i 0.469600i
\(666\) 0 0
\(667\) −57.3645 −0.0860038
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.4428i 0.0230146i
\(672\) 0 0
\(673\) 212.941 0.316406 0.158203 0.987407i \(-0.449430\pi\)
0.158203 + 0.987407i \(0.449430\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 879.368i 1.29892i 0.760396 + 0.649459i \(0.225005\pi\)
−0.760396 + 0.649459i \(0.774995\pi\)
\(678\) 0 0
\(679\) −919.601 −1.35435
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 1189.08i − 1.74097i −0.492199 0.870483i \(-0.663807\pi\)
0.492199 0.870483i \(-0.336193\pi\)
\(684\) 0 0
\(685\) 426.680 0.622890
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 467.073i − 0.677900i
\(690\) 0 0
\(691\) 165.918 0.240114 0.120057 0.992767i \(-0.461692\pi\)
0.120057 + 0.992767i \(0.461692\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 315.255i 0.453604i
\(696\) 0 0
\(697\) −1096.89 −1.57372
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 256.999i − 0.366617i −0.983055 0.183309i \(-0.941319\pi\)
0.983055 0.183309i \(-0.0586808\pi\)
\(702\) 0 0
\(703\) −75.3539 −0.107189
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 1284.38i − 1.81666i
\(708\) 0 0
\(709\) 1096.94 1.54716 0.773581 0.633698i \(-0.218464\pi\)
0.773581 + 0.633698i \(0.218464\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 740.790i 1.03898i
\(714\) 0 0
\(715\) −176.746 −0.247197
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) − 997.306i − 1.38707i −0.720421 0.693537i \(-0.756051\pi\)
0.720421 0.693537i \(-0.243949\pi\)
\(720\) 0 0
\(721\) 219.278 0.304130
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) − 109.668i − 0.151266i
\(726\) 0 0
\(727\) −994.798 −1.36836 −0.684180 0.729313i \(-0.739840\pi\)
−0.684180 + 0.729313i \(0.739840\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) − 581.142i − 0.794996i
\(732\) 0 0
\(733\) −1203.78 −1.64226 −0.821131 0.570740i \(-0.806656\pi\)
−0.821131 + 0.570740i \(0.806656\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 122.776i − 0.166589i
\(738\) 0 0
\(739\) 266.460 0.360568 0.180284 0.983615i \(-0.442298\pi\)
0.180284 + 0.983615i \(0.442298\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 349.670i 0.470619i 0.971921 + 0.235309i \(0.0756103\pi\)
−0.971921 + 0.235309i \(0.924390\pi\)
\(744\) 0 0
\(745\) −1301.67 −1.74721
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1318.74i 1.76066i
\(750\) 0 0
\(751\) −313.122 −0.416940 −0.208470 0.978029i \(-0.566848\pi\)
−0.208470 + 0.978029i \(0.566848\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) − 2141.11i − 2.83590i
\(756\) 0 0
\(757\) −806.976 −1.06602 −0.533009 0.846109i \(-0.678939\pi\)
−0.533009 + 0.846109i \(0.678939\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 866.633i 1.13881i 0.822058 + 0.569404i \(0.192826\pi\)
−0.822058 + 0.569404i \(0.807174\pi\)
\(762\) 0 0
\(763\) −1930.58 −2.53025
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 911.818i 1.18881i
\(768\) 0 0
\(769\) 1254.03 1.63073 0.815365 0.578947i \(-0.196536\pi\)
0.815365 + 0.578947i \(0.196536\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 1013.11i − 1.31062i −0.755361 0.655309i \(-0.772538\pi\)
0.755361 0.655309i \(-0.227462\pi\)
\(774\) 0 0
\(775\) −1416.22 −1.82738
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 182.592i 0.234392i
\(780\) 0 0
\(781\) 232.174 0.297277
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1602.08i 2.04086i
\(786\) 0 0
\(787\) −1225.56 −1.55726 −0.778630 0.627484i \(-0.784085\pi\)
−0.778630 + 0.627484i \(0.784085\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) − 360.092i − 0.455237i
\(792\) 0 0
\(793\) −52.2012 −0.0658275
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 369.326i − 0.463395i −0.972788 0.231697i \(-0.925572\pi\)
0.972788 0.231697i \(-0.0744279\pi\)
\(798\) 0 0
\(799\) −918.054 −1.14900
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 174.324i 0.217091i
\(804\) 0 0
\(805\) 1966.98 2.44346
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 622.873i − 0.769930i −0.922931 0.384965i \(-0.874214\pi\)
0.922931 0.384965i \(-0.125786\pi\)
\(810\) 0 0
\(811\) 899.290 1.10887 0.554433 0.832228i \(-0.312935\pi\)
0.554433 + 0.832228i \(0.312935\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 665.330i 0.816356i
\(816\) 0 0
\(817\) −96.7391 −0.118408
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 965.532i − 1.17604i −0.808845 0.588022i \(-0.799907\pi\)
0.808845 0.588022i \(-0.200093\pi\)
\(822\) 0 0
\(823\) 486.562 0.591205 0.295602 0.955311i \(-0.404480\pi\)
0.295602 + 0.955311i \(0.404480\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 237.282i 0.286919i 0.989656 + 0.143460i \(0.0458227\pi\)
−0.989656 + 0.143460i \(0.954177\pi\)
\(828\) 0 0
\(829\) 414.083 0.499497 0.249748 0.968311i \(-0.419652\pi\)
0.249748 + 0.968311i \(0.419652\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 2436.01i − 2.92438i
\(834\) 0 0
\(835\) 349.313 0.418339
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 315.279i 0.375779i 0.982190 + 0.187890i \(0.0601647\pi\)
−0.982190 + 0.187890i \(0.939835\pi\)
\(840\) 0 0
\(841\) 831.396 0.988581
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 715.844i 0.847153i
\(846\) 0 0
\(847\) 1562.57 1.84483
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 474.632i 0.557735i
\(852\) 0 0
\(853\) 1084.36 1.27123 0.635615 0.772006i \(-0.280746\pi\)
0.635615 + 0.772006i \(0.280746\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1451.35i 1.69353i 0.531969 + 0.846764i \(0.321452\pi\)
−0.531969 + 0.846764i \(0.678548\pi\)
\(858\) 0 0
\(859\) 59.3435 0.0690844 0.0345422 0.999403i \(-0.489003\pi\)
0.0345422 + 0.999403i \(0.489003\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) − 617.264i − 0.715254i −0.933865 0.357627i \(-0.883586\pi\)
0.933865 0.357627i \(-0.116414\pi\)
\(864\) 0 0
\(865\) −1316.76 −1.52227
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 94.2174i 0.108420i
\(870\) 0 0
\(871\) 415.018 0.476484
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1103.87i 1.26157i
\(876\) 0 0
\(877\) −926.943 −1.05695 −0.528474 0.848950i \(-0.677236\pi\)
−0.528474 + 0.848950i \(0.677236\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1539.43i 1.74737i 0.486491 + 0.873686i \(0.338277\pi\)
−0.486491 + 0.873686i \(0.661723\pi\)
\(882\) 0 0
\(883\) −39.0095 −0.0441784 −0.0220892 0.999756i \(-0.507032\pi\)
−0.0220892 + 0.999756i \(0.507032\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 766.276i 0.863897i 0.901898 + 0.431948i \(0.142174\pi\)
−0.901898 + 0.431948i \(0.857826\pi\)
\(888\) 0 0
\(889\) 1401.47 1.57646
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 152.823i 0.171134i
\(894\) 0 0
\(895\) 1092.74 1.22094
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 124.020i 0.137953i
\(900\) 0 0
\(901\) −940.424 −1.04376
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 539.097i − 0.595687i
\(906\) 0 0
\(907\) 463.758 0.511310 0.255655 0.966768i \(-0.417709\pi\)
0.255655 + 0.966768i \(0.417709\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) − 1237.16i − 1.35802i −0.734128 0.679011i \(-0.762409\pi\)
0.734128 0.679011i \(-0.237591\pi\)
\(912\) 0 0
\(913\) 52.6555 0.0576730
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1066.84i 1.16340i
\(918\) 0 0
\(919\) 1781.60 1.93863 0.969315 0.245823i \(-0.0790581\pi\)
0.969315 + 0.245823i \(0.0790581\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 784.814i 0.850286i
\(924\) 0 0
\(925\) −907.387 −0.980959
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 1101.20i 1.18536i 0.805439 + 0.592678i \(0.201929\pi\)
−0.805439 + 0.592678i \(0.798071\pi\)
\(930\) 0 0
\(931\) −405.507 −0.435561
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 355.868i 0.380607i
\(936\) 0 0
\(937\) 1408.82 1.50354 0.751771 0.659425i \(-0.229200\pi\)
0.751771 + 0.659425i \(0.229200\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 169.230i 0.179841i 0.995949 + 0.0899203i \(0.0286612\pi\)
−0.995949 + 0.0899203i \(0.971339\pi\)
\(942\) 0 0
\(943\) 1150.09 1.21961
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1377.82i 1.45494i 0.686141 + 0.727468i \(0.259303\pi\)
−0.686141 + 0.727468i \(0.740697\pi\)
\(948\) 0 0
\(949\) −589.265 −0.620933
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 810.833i 0.850821i 0.905000 + 0.425411i \(0.139870\pi\)
−0.905000 + 0.425411i \(0.860130\pi\)
\(954\) 0 0
\(955\) −2285.44 −2.39313
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 750.805i 0.782904i
\(960\) 0 0
\(961\) 640.559 0.666555
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 815.534i 0.845113i
\(966\) 0 0
\(967\) 947.710 0.980051 0.490026 0.871708i \(-0.336987\pi\)
0.490026 + 0.871708i \(0.336987\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1197.72i 1.23349i 0.787162 + 0.616747i \(0.211550\pi\)
−0.787162 + 0.616747i \(0.788450\pi\)
\(972\) 0 0
\(973\) −554.737 −0.570130
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 233.702i 0.239204i 0.992822 + 0.119602i \(0.0381619\pi\)
−0.992822 + 0.119602i \(0.961838\pi\)
\(978\) 0 0
\(979\) 250.701 0.256079
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1128.07i 1.14758i 0.819003 + 0.573789i \(0.194527\pi\)
−0.819003 + 0.573789i \(0.805473\pi\)
\(984\) 0 0
\(985\) 517.920 0.525807
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 609.331i 0.616109i
\(990\) 0 0
\(991\) 550.092 0.555088 0.277544 0.960713i \(-0.410480\pi\)
0.277544 + 0.960713i \(0.410480\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1443.27i 1.45052i
\(996\) 0 0
\(997\) −999.986 −1.00299 −0.501497 0.865159i \(-0.667217\pi\)
−0.501497 + 0.865159i \(0.667217\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2916.3.c.b.1457.4 36
3.2 odd 2 inner 2916.3.c.b.1457.33 36
27.2 odd 18 324.3.k.a.17.6 36
27.13 even 9 324.3.k.a.305.6 36
27.14 odd 18 108.3.k.a.101.6 yes 36
27.25 even 9 108.3.k.a.77.6 36
108.79 odd 18 432.3.bc.b.401.1 36
108.95 even 18 432.3.bc.b.209.1 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.k.a.77.6 36 27.25 even 9
108.3.k.a.101.6 yes 36 27.14 odd 18
324.3.k.a.17.6 36 27.2 odd 18
324.3.k.a.305.6 36 27.13 even 9
432.3.bc.b.209.1 36 108.95 even 18
432.3.bc.b.401.1 36 108.79 odd 18
2916.3.c.b.1457.4 36 1.1 even 1 trivial
2916.3.c.b.1457.33 36 3.2 odd 2 inner