Properties

Label 4032.2.h.h.575.2
Level 4032
Weight 2
Character 4032.575
Analytic conductor 32.196
Analytic rank 0
Dimension 12
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4032.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: 12.0.653473922154496.1
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 575.2
Root \(-1.35489 + 0.405301i\)
Character \(\chi\) = 4032.575
Dual form 4032.2.h.h.575.11

$q$-expansion

\(f(q)\) \(=\) \(q-3.31339i q^{5} +1.00000i q^{7} +O(q^{10})\) \(q-3.31339i q^{5} +1.00000i q^{7} +4.72761 q^{11} +4.97858 q^{13} +0.484966i q^{17} -2.29273i q^{19} +7.97002 q^{23} -5.97858 q^{25} -1.41421i q^{29} +7.66442i q^{31} +3.31339 q^{35} +2.39312 q^{37} +6.55580i q^{41} +5.37169i q^{43} +6.21280 q^{47} -1.00000 q^{49} +1.00023i q^{53} -15.6644i q^{55} -1.38392 q^{59} -13.6644 q^{61} -16.4960i q^{65} +3.27131i q^{67} +3.34369 q^{71} -2.10038 q^{73} +4.72761i q^{77} +12.0575i q^{79} +3.24241 q^{83} +1.60688 q^{85} +5.72784i q^{89} +4.97858i q^{91} -7.59672 q^{95} +12.0575 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + O(q^{10}) \) \( 12q - 12q^{25} - 8q^{37} - 12q^{49} - 56q^{61} + 56q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(5\) − 3.31339i − 1.48179i −0.671618 0.740897i \(-0.734400\pi\)
0.671618 0.740897i \(-0.265600\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.72761 1.42543 0.712714 0.701455i \(-0.247466\pi\)
0.712714 + 0.701455i \(0.247466\pi\)
\(12\) 0 0
\(13\) 4.97858 1.38081 0.690404 0.723424i \(-0.257433\pi\)
0.690404 + 0.723424i \(0.257433\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.484966i 0.117622i 0.998269 + 0.0588108i \(0.0187309\pi\)
−0.998269 + 0.0588108i \(0.981269\pi\)
\(18\) 0 0
\(19\) − 2.29273i − 0.525989i −0.964797 0.262994i \(-0.915290\pi\)
0.964797 0.262994i \(-0.0847100\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.97002 1.66186 0.830932 0.556374i \(-0.187808\pi\)
0.830932 + 0.556374i \(0.187808\pi\)
\(24\) 0 0
\(25\) −5.97858 −1.19572
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) − 1.41421i − 0.262613i −0.991342 0.131306i \(-0.958083\pi\)
0.991342 0.131306i \(-0.0419172\pi\)
\(30\) 0 0
\(31\) 7.66442i 1.37657i 0.725440 + 0.688286i \(0.241636\pi\)
−0.725440 + 0.688286i \(0.758364\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.31339 0.560066
\(36\) 0 0
\(37\) 2.39312 0.393426 0.196713 0.980461i \(-0.436973\pi\)
0.196713 + 0.980461i \(0.436973\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.55580i 1.02384i 0.859032 + 0.511922i \(0.171066\pi\)
−0.859032 + 0.511922i \(0.828934\pi\)
\(42\) 0 0
\(43\) 5.37169i 0.819175i 0.912271 + 0.409588i \(0.134327\pi\)
−0.912271 + 0.409588i \(0.865673\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.21280 0.906230 0.453115 0.891452i \(-0.350313\pi\)
0.453115 + 0.891452i \(0.350313\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 1.00023i 0.137392i 0.997638 + 0.0686960i \(0.0218839\pi\)
−0.997638 + 0.0686960i \(0.978116\pi\)
\(54\) 0 0
\(55\) − 15.6644i − 2.11219i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.38392 −0.180171 −0.0900853 0.995934i \(-0.528714\pi\)
−0.0900853 + 0.995934i \(0.528714\pi\)
\(60\) 0 0
\(61\) −13.6644 −1.74955 −0.874775 0.484529i \(-0.838991\pi\)
−0.874775 + 0.484529i \(0.838991\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) − 16.4960i − 2.04608i
\(66\) 0 0
\(67\) 3.27131i 0.399654i 0.979831 + 0.199827i \(0.0640380\pi\)
−0.979831 + 0.199827i \(0.935962\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.34369 0.396823 0.198412 0.980119i \(-0.436422\pi\)
0.198412 + 0.980119i \(0.436422\pi\)
\(72\) 0 0
\(73\) −2.10038 −0.245831 −0.122916 0.992417i \(-0.539224\pi\)
−0.122916 + 0.992417i \(0.539224\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 4.72761i 0.538761i
\(78\) 0 0
\(79\) 12.0575i 1.35658i 0.734795 + 0.678290i \(0.237278\pi\)
−0.734795 + 0.678290i \(0.762722\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.24241 0.355901 0.177950 0.984039i \(-0.443053\pi\)
0.177950 + 0.984039i \(0.443053\pi\)
\(84\) 0 0
\(85\) 1.60688 0.174291
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 5.72784i 0.607149i 0.952808 + 0.303575i \(0.0981802\pi\)
−0.952808 + 0.303575i \(0.901820\pi\)
\(90\) 0 0
\(91\) 4.97858i 0.521897i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.59672 −0.779407
\(96\) 0 0
\(97\) 12.0575 1.22426 0.612129 0.790758i \(-0.290313\pi\)
0.612129 + 0.790758i \(0.290313\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 14.5665i 1.44942i 0.689053 + 0.724711i \(0.258027\pi\)
−0.689053 + 0.724711i \(0.741973\pi\)
\(102\) 0 0
\(103\) − 5.70727i − 0.562354i −0.959656 0.281177i \(-0.909275\pi\)
0.959656 0.281177i \(-0.0907248\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.0413 1.55077 0.775386 0.631487i \(-0.217555\pi\)
0.775386 + 0.631487i \(0.217555\pi\)
\(108\) 0 0
\(109\) −1.37169 −0.131384 −0.0656921 0.997840i \(-0.520926\pi\)
−0.0656921 + 0.997840i \(0.520926\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 11.2834i 1.06145i 0.847543 + 0.530727i \(0.178081\pi\)
−0.847543 + 0.530727i \(0.821919\pi\)
\(114\) 0 0
\(115\) − 26.4078i − 2.46254i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −0.484966 −0.0444568
\(120\) 0 0
\(121\) 11.3503 1.03184
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 3.24241i 0.290010i
\(126\) 0 0
\(127\) − 16.6430i − 1.47683i −0.674348 0.738414i \(-0.735575\pi\)
0.674348 0.738414i \(-0.264425\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.59672 −0.663729 −0.331864 0.943327i \(-0.607678\pi\)
−0.331864 + 0.943327i \(0.607678\pi\)
\(132\) 0 0
\(133\) 2.29273 0.198805
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 9.42492i − 0.805225i −0.915370 0.402613i \(-0.868102\pi\)
0.915370 0.402613i \(-0.131898\pi\)
\(138\) 0 0
\(139\) − 16.0000i − 1.35710i −0.734553 0.678551i \(-0.762608\pi\)
0.734553 0.678551i \(-0.237392\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 23.5368 1.96824
\(144\) 0 0
\(145\) −4.68585 −0.389138
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 18.4661i − 1.51281i −0.654106 0.756403i \(-0.726955\pi\)
0.654106 0.756403i \(-0.273045\pi\)
\(150\) 0 0
\(151\) − 23.3288i − 1.89847i −0.314561 0.949237i \(-0.601857\pi\)
0.314561 0.949237i \(-0.398143\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 25.3953 2.03980
\(156\) 0 0
\(157\) −22.2499 −1.77573 −0.887867 0.460100i \(-0.847814\pi\)
−0.887867 + 0.460100i \(0.847814\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.97002i 0.628125i
\(162\) 0 0
\(163\) − 16.6430i − 1.30358i −0.758399 0.651790i \(-0.774018\pi\)
0.758399 0.651790i \(-0.225982\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.98064 −0.694943 −0.347471 0.937691i \(-0.612960\pi\)
−0.347471 + 0.937691i \(0.612960\pi\)
\(168\) 0 0
\(169\) 11.7862 0.906633
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 2.75744i − 0.209645i −0.994491 0.104822i \(-0.966573\pi\)
0.994491 0.104822i \(-0.0334274\pi\)
\(174\) 0 0
\(175\) − 5.97858i − 0.451938i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.72761 0.353358 0.176679 0.984269i \(-0.443465\pi\)
0.176679 + 0.984269i \(0.443465\pi\)
\(180\) 0 0
\(181\) 8.39312 0.623855 0.311928 0.950106i \(-0.399025\pi\)
0.311928 + 0.950106i \(0.399025\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 7.92933i − 0.582976i
\(186\) 0 0
\(187\) 2.29273i 0.167661i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.48520 0.107465 0.0537325 0.998555i \(-0.482888\pi\)
0.0537325 + 0.998555i \(0.482888\pi\)
\(192\) 0 0
\(193\) −8.35027 −0.601066 −0.300533 0.953771i \(-0.597164\pi\)
−0.300533 + 0.953771i \(0.597164\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.82866i 0.272780i 0.990655 + 0.136390i \(0.0435501\pi\)
−0.990655 + 0.136390i \(0.956450\pi\)
\(198\) 0 0
\(199\) − 6.04285i − 0.428366i −0.976794 0.214183i \(-0.931291\pi\)
0.976794 0.214183i \(-0.0687089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.41421 0.0992583
\(204\) 0 0
\(205\) 21.7220 1.51713
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 10.8391i − 0.749758i
\(210\) 0 0
\(211\) 9.95715i 0.685479i 0.939431 + 0.342739i \(0.111355\pi\)
−0.939431 + 0.342739i \(0.888645\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 17.7985 1.21385
\(216\) 0 0
\(217\) −7.66442 −0.520295
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.41444i 0.162413i
\(222\) 0 0
\(223\) − 0.786230i − 0.0526499i −0.999653 0.0263249i \(-0.991620\pi\)
0.999653 0.0263249i \(-0.00838046\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −20.2943 −1.34698 −0.673492 0.739195i \(-0.735206\pi\)
−0.673492 + 0.739195i \(0.735206\pi\)
\(228\) 0 0
\(229\) 4.97858 0.328994 0.164497 0.986378i \(-0.447400\pi\)
0.164497 + 0.986378i \(0.447400\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0.383688i 0.0251362i 0.999921 + 0.0125681i \(0.00400066\pi\)
−0.999921 + 0.0125681i \(0.995999\pi\)
\(234\) 0 0
\(235\) − 20.5855i − 1.34285i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.48520 −0.0960693 −0.0480347 0.998846i \(-0.515296\pi\)
−0.0480347 + 0.998846i \(0.515296\pi\)
\(240\) 0 0
\(241\) −23.4721 −1.51197 −0.755985 0.654589i \(-0.772842\pi\)
−0.755985 + 0.654589i \(0.772842\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.31339i 0.211685i
\(246\) 0 0
\(247\) − 11.4145i − 0.726290i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −4.62633 −0.292011 −0.146006 0.989284i \(-0.546642\pi\)
−0.146006 + 0.989284i \(0.546642\pi\)
\(252\) 0 0
\(253\) 37.6791 2.36887
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 3.78797i − 0.236287i −0.992997 0.118144i \(-0.962306\pi\)
0.992997 0.118144i \(-0.0376943\pi\)
\(258\) 0 0
\(259\) 2.39312i 0.148701i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 12.7989 0.789214 0.394607 0.918850i \(-0.370881\pi\)
0.394607 + 0.918850i \(0.370881\pi\)
\(264\) 0 0
\(265\) 3.31415 0.203587
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 25.4662i − 1.55270i −0.630300 0.776352i \(-0.717068\pi\)
0.630300 0.776352i \(-0.282932\pi\)
\(270\) 0 0
\(271\) 21.0361i 1.27785i 0.769268 + 0.638927i \(0.220621\pi\)
−0.769268 + 0.638927i \(0.779379\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −28.2644 −1.70441
\(276\) 0 0
\(277\) −8.39312 −0.504293 −0.252147 0.967689i \(-0.581137\pi\)
−0.252147 + 0.967689i \(0.581137\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) − 0.111668i − 0.00666157i −0.999994 0.00333078i \(-0.998940\pi\)
0.999994 0.00333078i \(-0.00106022\pi\)
\(282\) 0 0
\(283\) − 11.4637i − 0.681444i −0.940164 0.340722i \(-0.889329\pi\)
0.940164 0.340722i \(-0.110671\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.55580 −0.386977
\(288\) 0 0
\(289\) 16.7648 0.986165
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 17.8089i − 1.04041i −0.854042 0.520204i \(-0.825856\pi\)
0.854042 0.520204i \(-0.174144\pi\)
\(294\) 0 0
\(295\) 4.58546i 0.266976i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 39.6794 2.29472
\(300\) 0 0
\(301\) −5.37169 −0.309619
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 45.2756i 2.59247i
\(306\) 0 0
\(307\) 20.2499i 1.15572i 0.816135 + 0.577861i \(0.196112\pi\)
−0.816135 + 0.577861i \(0.803888\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.38392 −0.0784747 −0.0392374 0.999230i \(-0.512493\pi\)
−0.0392374 + 0.999230i \(0.512493\pi\)
\(312\) 0 0
\(313\) −30.1151 −1.70220 −0.851102 0.525000i \(-0.824065\pi\)
−0.851102 + 0.525000i \(0.824065\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 5.27317i − 0.296171i −0.988975 0.148085i \(-0.952689\pi\)
0.988975 0.148085i \(-0.0473110\pi\)
\(318\) 0 0
\(319\) − 6.68585i − 0.374336i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.11190 0.0618676
\(324\) 0 0
\(325\) −29.7648 −1.65105
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.21280i 0.342523i
\(330\) 0 0
\(331\) 9.95715i 0.547295i 0.961830 + 0.273647i \(0.0882301\pi\)
−0.961830 + 0.273647i \(0.911770\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 10.8391 0.592205
\(336\) 0 0
\(337\) −13.3717 −0.728402 −0.364201 0.931320i \(-0.618658\pi\)
−0.364201 + 0.931320i \(0.618658\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 36.2344i 1.96220i
\(342\) 0 0
\(343\) − 1.00000i − 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.2124 0.601915 0.300957 0.953638i \(-0.402694\pi\)
0.300957 + 0.953638i \(0.402694\pi\)
\(348\) 0 0
\(349\) 4.29273 0.229785 0.114892 0.993378i \(-0.463348\pi\)
0.114892 + 0.993378i \(0.463348\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 1.78751i − 0.0951397i −0.998868 0.0475698i \(-0.984852\pi\)
0.998868 0.0475698i \(-0.0151477\pi\)
\(354\) 0 0
\(355\) − 11.0790i − 0.588010i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.7989 0.675500 0.337750 0.941236i \(-0.390334\pi\)
0.337750 + 0.941236i \(0.390334\pi\)
\(360\) 0 0
\(361\) 13.7434 0.723336
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6.95940i 0.364272i
\(366\) 0 0
\(367\) 30.1579i 1.57423i 0.616806 + 0.787115i \(0.288426\pi\)
−0.616806 + 0.787115i \(0.711574\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.00023 −0.0519293
\(372\) 0 0
\(373\) −5.21377 −0.269959 −0.134979 0.990848i \(-0.543097\pi\)
−0.134979 + 0.990848i \(0.543097\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 7.04077i − 0.362618i
\(378\) 0 0
\(379\) − 16.7862i − 0.862251i −0.902292 0.431125i \(-0.858117\pi\)
0.902292 0.431125i \(-0.141883\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −23.7393 −1.21302 −0.606511 0.795075i \(-0.707431\pi\)
−0.606511 + 0.795075i \(0.707431\pi\)
\(384\) 0 0
\(385\) 15.6644 0.798333
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 17.7682i 0.900885i 0.892805 + 0.450443i \(0.148734\pi\)
−0.892805 + 0.450443i \(0.851266\pi\)
\(390\) 0 0
\(391\) 3.86519i 0.195471i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 39.9514 2.01017
\(396\) 0 0
\(397\) −24.4078 −1.22499 −0.612496 0.790473i \(-0.709835\pi\)
−0.612496 + 0.790473i \(0.709835\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) − 29.1633i − 1.45635i −0.685393 0.728173i \(-0.740370\pi\)
0.685393 0.728173i \(-0.259630\pi\)
\(402\) 0 0
\(403\) 38.1579i 1.90078i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 11.3137 0.560800
\(408\) 0 0
\(409\) −10.4851 −0.518454 −0.259227 0.965816i \(-0.583468\pi\)
−0.259227 + 0.965816i \(0.583468\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 1.38392i − 0.0680981i
\(414\) 0 0
\(415\) − 10.7434i − 0.527372i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 31.1335 1.52097 0.760485 0.649356i \(-0.224961\pi\)
0.760485 + 0.649356i \(0.224961\pi\)
\(420\) 0 0
\(421\) −30.2646 −1.47501 −0.737503 0.675344i \(-0.763995\pi\)
−0.737503 + 0.675344i \(0.763995\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 2.89941i − 0.140642i
\(426\) 0 0
\(427\) − 13.6644i − 0.661268i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.23179 −0.107502 −0.0537508 0.998554i \(-0.517118\pi\)
−0.0537508 + 0.998554i \(0.517118\pi\)
\(432\) 0 0
\(433\) −8.54262 −0.410532 −0.205266 0.978706i \(-0.565806\pi\)
−0.205266 + 0.978706i \(0.565806\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 18.2731i − 0.874121i
\(438\) 0 0
\(439\) − 1.17092i − 0.0558851i −0.999610 0.0279426i \(-0.991104\pi\)
0.999610 0.0279426i \(-0.00889556\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.58610 −0.312915 −0.156458 0.987685i \(-0.550007\pi\)
−0.156458 + 0.987685i \(0.550007\pi\)
\(444\) 0 0
\(445\) 18.9786 0.899671
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) − 11.2228i − 0.529638i −0.964298 0.264819i \(-0.914688\pi\)
0.964298 0.264819i \(-0.0853121\pi\)
\(450\) 0 0
\(451\) 30.9933i 1.45942i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 16.4960 0.773344
\(456\) 0 0
\(457\) 11.9143 0.557328 0.278664 0.960389i \(-0.410108\pi\)
0.278664 + 0.960389i \(0.410108\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 18.4255i 0.858159i 0.903267 + 0.429080i \(0.141162\pi\)
−0.903267 + 0.429080i \(0.858838\pi\)
\(462\) 0 0
\(463\) 7.47208i 0.347257i 0.984811 + 0.173628i \(0.0555492\pi\)
−0.984811 + 0.173628i \(0.944451\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.57548 −0.258003 −0.129001 0.991644i \(-0.541177\pi\)
−0.129001 + 0.991644i \(0.541177\pi\)
\(468\) 0 0
\(469\) −3.27131 −0.151055
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 25.3953i 1.16767i
\(474\) 0 0
\(475\) 13.7073i 0.628933i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −15.9400 −0.728319 −0.364159 0.931337i \(-0.618644\pi\)
−0.364159 + 0.931337i \(0.618644\pi\)
\(480\) 0 0
\(481\) 11.9143 0.543246
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 39.9514i − 1.81410i
\(486\) 0 0
\(487\) 34.0722i 1.54396i 0.635647 + 0.771980i \(0.280734\pi\)
−0.635647 + 0.771980i \(0.719266\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −34.0026 −1.53452 −0.767258 0.641339i \(-0.778379\pi\)
−0.767258 + 0.641339i \(0.778379\pi\)
\(492\) 0 0
\(493\) 0.685846 0.0308890
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.34369i 0.149985i
\(498\) 0 0
\(499\) 5.37169i 0.240470i 0.992745 + 0.120235i \(0.0383648\pi\)
−0.992745 + 0.120235i \(0.961635\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 37.3463 1.66519 0.832594 0.553884i \(-0.186855\pi\)
0.832594 + 0.553884i \(0.186855\pi\)
\(504\) 0 0
\(505\) 48.2646 2.14775
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 0.403595i − 0.0178890i −0.999960 0.00894451i \(-0.997153\pi\)
0.999960 0.00894451i \(-0.00284716\pi\)
\(510\) 0 0
\(511\) − 2.10038i − 0.0929155i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −18.9104 −0.833293
\(516\) 0 0
\(517\) 29.3717 1.29177
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 42.9927i − 1.88355i −0.336249 0.941773i \(-0.609158\pi\)
0.336249 0.941773i \(-0.390842\pi\)
\(522\) 0 0
\(523\) − 16.0000i − 0.699631i −0.936819 0.349816i \(-0.886244\pi\)
0.936819 0.349816i \(-0.113756\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.71699 −0.161915
\(528\) 0 0
\(529\) 40.5212 1.76179
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 32.6386i 1.41373i
\(534\) 0 0
\(535\) − 53.1512i − 2.29793i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −4.72761 −0.203632
\(540\) 0 0
\(541\) −19.1365 −0.822742 −0.411371 0.911468i \(-0.634950\pi\)
−0.411371 + 0.911468i \(0.634950\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.54496i 0.194685i
\(546\) 0 0
\(547\) 8.14323i 0.348179i 0.984730 + 0.174090i \(0.0556983\pi\)
−0.984730 + 0.174090i \(0.944302\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.24241 −0.138131
\(552\) 0 0
\(553\) −12.0575 −0.512739
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 39.0931i 1.65643i 0.560412 + 0.828214i \(0.310643\pi\)
−0.560412 + 0.828214i \(0.689357\pi\)
\(558\) 0 0
\(559\) 26.7434i 1.13112i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −13.6468 −0.575143 −0.287572 0.957759i \(-0.592848\pi\)
−0.287572 + 0.957759i \(0.592848\pi\)
\(564\) 0 0
\(565\) 37.3864 1.57286
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.32355i 0.0974084i 0.998813 + 0.0487042i \(0.0155092\pi\)
−0.998813 + 0.0487042i \(0.984491\pi\)
\(570\) 0 0
\(571\) − 2.88661i − 0.120801i −0.998174 0.0604005i \(-0.980762\pi\)
0.998174 0.0604005i \(-0.0192378\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −47.6494 −1.98712
\(576\) 0 0
\(577\) −18.5855 −0.773723 −0.386861 0.922138i \(-0.626441\pi\)
−0.386861 + 0.922138i \(0.626441\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 3.24241i 0.134518i
\(582\) 0 0
\(583\) 4.72869i 0.195842i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.92979 0.409846 0.204923 0.978778i \(-0.434306\pi\)
0.204923 + 0.978778i \(0.434306\pi\)
\(588\) 0 0
\(589\) 17.5725 0.724061
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 24.0823i − 0.988942i −0.869194 0.494471i \(-0.835362\pi\)
0.869194 0.494471i \(-0.164638\pi\)
\(594\) 0 0
\(595\) 1.60688i 0.0658759i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 19.2837 0.787912 0.393956 0.919129i \(-0.371106\pi\)
0.393956 + 0.919129i \(0.371106\pi\)
\(600\) 0 0
\(601\) 10.5855 0.431790 0.215895 0.976417i \(-0.430733\pi\)
0.215895 + 0.976417i \(0.430733\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 37.6079i − 1.52898i
\(606\) 0 0
\(607\) − 34.0722i − 1.38295i −0.722401 0.691475i \(-0.756961\pi\)
0.722401 0.691475i \(-0.243039\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.9309 1.25133
\(612\) 0 0
\(613\) 17.3288 0.699906 0.349953 0.936767i \(-0.386198\pi\)
0.349953 + 0.936767i \(0.386198\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 1.76760i − 0.0711611i −0.999367 0.0355805i \(-0.988672\pi\)
0.999367 0.0355805i \(-0.0113280\pi\)
\(618\) 0 0
\(619\) 47.0424i 1.89079i 0.325922 + 0.945397i \(0.394325\pi\)
−0.325922 + 0.945397i \(0.605675\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.72784 −0.229481
\(624\) 0 0
\(625\) −19.1495 −0.765980
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.16058i 0.0462754i
\(630\) 0 0
\(631\) 14.0147i 0.557916i 0.960303 + 0.278958i \(0.0899890\pi\)
−0.960303 + 0.278958i \(0.910011\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −55.1448 −2.18836
\(636\) 0 0
\(637\) −4.97858 −0.197258
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.92956i 0.352696i 0.984328 + 0.176348i \(0.0564285\pi\)
−0.984328 + 0.176348i \(0.943572\pi\)
\(642\) 0 0
\(643\) 4.53635i 0.178896i 0.995991 + 0.0894480i \(0.0285103\pi\)
−0.995991 + 0.0894480i \(0.971490\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.10091 0.200537 0.100269 0.994960i \(-0.468030\pi\)
0.100269 + 0.994960i \(0.468030\pi\)
\(648\) 0 0
\(649\) −6.54262 −0.256820
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 26.2535i 1.02738i 0.857976 + 0.513690i \(0.171722\pi\)
−0.857976 + 0.513690i \(0.828278\pi\)
\(654\) 0 0
\(655\) 25.1709i 0.983509i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.0413 −0.624881 −0.312440 0.949937i \(-0.601146\pi\)
−0.312440 + 0.949937i \(0.601146\pi\)
\(660\) 0 0
\(661\) −29.8652 −1.16162 −0.580811 0.814039i \(-0.697264\pi\)
−0.580811 + 0.814039i \(0.697264\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 7.59672i − 0.294588i
\(666\) 0 0
\(667\) − 11.2713i − 0.436427i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −64.6000 −2.49386
\(672\) 0 0
\(673\) −35.0080 −1.34946 −0.674729 0.738066i \(-0.735739\pi\)
−0.674729 + 0.738066i \(0.735739\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 37.6893i − 1.44852i −0.689529 0.724258i \(-0.742182\pi\)
0.689529 0.724258i \(-0.257818\pi\)
\(678\) 0 0
\(679\) 12.0575i 0.462726i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −21.5770 −0.825620 −0.412810 0.910817i \(-0.635453\pi\)
−0.412810 + 0.910817i \(0.635453\pi\)
\(684\) 0 0
\(685\) −31.2285 −1.19318
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.97972i 0.189712i
\(690\) 0 0
\(691\) 14.0428i 0.534215i 0.963667 + 0.267108i \(0.0860679\pi\)
−0.963667 + 0.267108i \(0.913932\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −53.0143 −2.01095
\(696\) 0 0
\(697\) −3.17935 −0.120426
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 27.9214i − 1.05458i −0.849687 0.527288i \(-0.823209\pi\)
0.849687 0.527288i \(-0.176791\pi\)
\(702\) 0 0
\(703\) − 5.48677i − 0.206937i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −14.5665 −0.547830
\(708\) 0 0
\(709\) 10.5426 0.395936 0.197968 0.980208i \(-0.436566\pi\)
0.197968 + 0.980208i \(0.436566\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 61.0856i 2.28767i
\(714\) 0 0
\(715\) − 77.9865i − 2.91653i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −31.8801 −1.18893 −0.594463 0.804123i \(-0.702635\pi\)
−0.594463 + 0.804123i \(0.702635\pi\)
\(720\) 0 0
\(721\) 5.70727 0.212550
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 8.45498i 0.314010i
\(726\) 0 0
\(727\) 46.2070i 1.71372i 0.515546 + 0.856862i \(0.327589\pi\)
−0.515546 + 0.856862i \(0.672411\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.60509 −0.0963528
\(732\) 0 0
\(733\) −22.4360 −0.828691 −0.414346 0.910120i \(-0.635990\pi\)
−0.414346 + 0.910120i \(0.635990\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 15.4655i 0.569678i
\(738\) 0 0
\(739\) − 14.0147i − 0.515539i −0.966206 0.257769i \(-0.917013\pi\)
0.966206 0.257769i \(-0.0829875\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 25.9313 0.951327 0.475663 0.879627i \(-0.342208\pi\)
0.475663 + 0.879627i \(0.342208\pi\)
\(744\) 0 0
\(745\) −61.1856 −2.24167
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 16.0413i 0.586137i
\(750\) 0 0
\(751\) − 2.74338i − 0.100108i −0.998747 0.0500538i \(-0.984061\pi\)
0.998747 0.0500538i \(-0.0159393\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −77.2977 −2.81315
\(756\) 0 0
\(757\) 15.7992 0.574233 0.287116 0.957896i \(-0.407303\pi\)
0.287116 + 0.957896i \(0.407303\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.0527i 0.980660i 0.871537 + 0.490330i \(0.163124\pi\)
−0.871537 + 0.490330i \(0.836876\pi\)
\(762\) 0 0
\(763\) − 1.37169i − 0.0496586i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −6.88994 −0.248781
\(768\) 0 0
\(769\) 39.8715 1.43780 0.718901 0.695113i \(-0.244646\pi\)
0.718901 + 0.695113i \(0.244646\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 34.4261i − 1.23822i −0.785304 0.619110i \(-0.787493\pi\)
0.785304 0.619110i \(-0.212507\pi\)
\(774\) 0 0
\(775\) − 45.8223i − 1.64599i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 15.0307 0.538531
\(780\) 0 0
\(781\) 15.8077 0.565642
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 73.7226i 2.63127i
\(786\) 0 0
\(787\) 24.1151i 0.859610i 0.902922 + 0.429805i \(0.141418\pi\)
−0.902922 + 0.429805i \(0.858582\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −11.2834 −0.401192
\(792\) 0 0
\(793\) −68.0294 −2.41579
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 35.0634i 1.24201i 0.783807 + 0.621005i \(0.213275\pi\)
−0.783807 + 0.621005i \(0.786725\pi\)
\(798\) 0 0
\(799\) 3.01300i 0.106592i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −9.92979 −0.350415
\(804\) 0 0
\(805\) 26.4078 0.930753
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 21.9806i − 0.772796i −0.922332 0.386398i \(-0.873719\pi\)
0.922332 0.386398i \(-0.126281\pi\)
\(810\) 0 0
\(811\) − 44.7005i − 1.56965i −0.619719 0.784824i \(-0.712753\pi\)
0.619719 0.784824i \(-0.287247\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −55.1448 −1.93164
\(816\) 0 0
\(817\) 12.3158 0.430877
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 39.3651i − 1.37385i −0.726727 0.686926i \(-0.758960\pi\)
0.726727 0.686926i \(-0.241040\pi\)
\(822\) 0 0
\(823\) 31.9718i 1.11447i 0.830355 + 0.557234i \(0.188137\pi\)
−0.830355 + 0.557234i \(0.811863\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −20.8702 −0.725728 −0.362864 0.931842i \(-0.618201\pi\)
−0.362864 + 0.931842i \(0.618201\pi\)
\(828\) 0 0
\(829\) 32.2217 1.11911 0.559554 0.828794i \(-0.310973\pi\)
0.559554 + 0.828794i \(0.310973\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 0.484966i − 0.0168031i
\(834\) 0 0
\(835\) 29.7564i 1.02976i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 48.9320 1.68932 0.844660 0.535303i \(-0.179802\pi\)
0.844660 + 0.535303i \(0.179802\pi\)
\(840\) 0 0
\(841\) 27.0000 0.931034
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 39.0524i − 1.34344i
\(846\) 0 0
\(847\) 11.3503i 0.390000i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 19.0732 0.653820
\(852\) 0 0
\(853\) −12.2927 −0.420895 −0.210448 0.977605i \(-0.567492\pi\)
−0.210448 + 0.977605i \(0.567492\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 57.1349i − 1.95169i −0.218463 0.975845i \(-0.570104\pi\)
0.218463 0.975845i \(-0.429896\pi\)
\(858\) 0 0
\(859\) 21.8223i 0.744569i 0.928119 + 0.372284i \(0.121425\pi\)
−0.928119 + 0.372284i \(0.878575\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −42.2764 −1.43911 −0.719553 0.694437i \(-0.755653\pi\)
−0.719553 + 0.694437i \(0.755653\pi\)
\(864\) 0 0
\(865\) −9.13650 −0.310650
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 57.0033i 1.93370i
\(870\) 0 0
\(871\) 16.2865i 0.551846i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.24241 −0.109614
\(876\) 0 0
\(877\) −26.2008 −0.884737 −0.442369 0.896833i \(-0.645862\pi\)
−0.442369 + 0.896833i \(0.645862\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 47.4165i − 1.59750i −0.601661 0.798752i \(-0.705494\pi\)
0.601661 0.798752i \(-0.294506\pi\)
\(882\) 0 0
\(883\) 26.6283i 0.896114i 0.894005 + 0.448057i \(0.147884\pi\)
−0.894005 + 0.448057i \(0.852116\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −6.75684 −0.226873 −0.113436 0.993545i \(-0.536186\pi\)
−0.113436 + 0.993545i \(0.536186\pi\)
\(888\) 0 0
\(889\) 16.6430 0.558188
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 14.2443i − 0.476667i
\(894\) 0 0
\(895\) − 15.6644i − 0.523604i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 10.8391 0.361505
\(900\) 0 0
\(901\) −0.485078 −0.0161603
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 27.8097i − 0.924426i
\(906\) 0 0
\(907\) − 25.2860i − 0.839608i −0.907615 0.419804i \(-0.862099\pi\)
0.907615 0.419804i \(-0.137901\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 21.3050 0.705865 0.352932 0.935649i \(-0.385185\pi\)
0.352932 + 0.935649i \(0.385185\pi\)
\(912\) 0 0
\(913\) 15.3288 0.507311
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 7.59672i − 0.250866i
\(918\) 0 0
\(919\) − 48.4998i − 1.59986i −0.600093 0.799930i \(-0.704870\pi\)
0.600093 0.799930i \(-0.295130\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 16.6468 0.547937
\(924\) 0 0
\(925\) −14.3074 −0.470425
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) − 10.5567i − 0.346355i −0.984891 0.173177i \(-0.944597\pi\)
0.984891 0.173177i \(-0.0554034\pi\)
\(930\) 0 0
\(931\) 2.29273i 0.0751412i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 7.59672 0.248439
\(936\) 0 0
\(937\) −29.5296 −0.964690 −0.482345 0.875981i \(-0.660215\pi\)
−0.482345 + 0.875981i \(0.660215\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 6.53503i − 0.213036i −0.994311 0.106518i \(-0.966030\pi\)
0.994311 0.106518i \(-0.0339701\pi\)
\(942\) 0 0
\(943\) 52.2499i 1.70149i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −43.2951 −1.40690 −0.703450 0.710745i \(-0.748358\pi\)
−0.703450 + 0.710745i \(0.748358\pi\)
\(948\) 0 0
\(949\) −10.4569 −0.339446
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 19.4848i 0.631173i 0.948897 + 0.315587i \(0.102201\pi\)
−0.948897 + 0.315587i \(0.897799\pi\)
\(954\) 0 0
\(955\) − 4.92104i − 0.159241i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 9.42492 0.304346
\(960\) 0 0
\(961\) −27.7434 −0.894948
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 27.6677i 0.890656i
\(966\) 0 0
\(967\) − 28.4422i − 0.914641i −0.889302 0.457320i \(-0.848809\pi\)
0.889302 0.457320i \(-0.151191\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 8.61534 0.276479 0.138240 0.990399i \(-0.455856\pi\)
0.138240 + 0.990399i \(0.455856\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 35.8715i − 1.14763i −0.818985 0.573815i \(-0.805463\pi\)
0.818985 0.573815i \(-0.194537\pi\)
\(978\) 0 0
\(979\) 27.0790i 0.865447i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −41.0633 −1.30971 −0.654857 0.755752i \(-0.727271\pi\)
−0.654857 + 0.755752i \(0.727271\pi\)
\(984\) 0 0
\(985\) 12.6858 0.404205
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 42.8125i 1.36136i
\(990\) 0 0
\(991\) − 25.6707i − 0.815456i −0.913103 0.407728i \(-0.866321\pi\)
0.913103 0.407728i \(-0.133679\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −20.0223 −0.634750
\(996\) 0 0
\(997\) 2.45065 0.0776130 0.0388065 0.999247i \(-0.487644\pi\)
0.0388065 + 0.999247i \(0.487644\pi\)
\(998\) 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 4032.2.h.h.575.2 12
3.2 odd 2 inner 4032.2.h.h.575.12 12
4.3 odd 2 inner 4032.2.h.h.575.1 12
8.3 odd 2 252.2.e.a.71.11 yes 12
8.5 even 2 252.2.e.a.71.1 12
12.11 even 2 inner 4032.2.h.h.575.11 12
24.5 odd 2 252.2.e.a.71.12 yes 12
24.11 even 2 252.2.e.a.71.2 yes 12
56.13 odd 2 1764.2.e.g.1079.1 12
56.27 even 2 1764.2.e.g.1079.11 12
168.83 odd 2 1764.2.e.g.1079.2 12
168.125 even 2 1764.2.e.g.1079.12 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.e.a.71.1 12 8.5 even 2
252.2.e.a.71.2 yes 12 24.11 even 2
252.2.e.a.71.11 yes 12 8.3 odd 2
252.2.e.a.71.12 yes 12 24.5 odd 2
1764.2.e.g.1079.1 12 56.13 odd 2
1764.2.e.g.1079.2 12 168.83 odd 2
1764.2.e.g.1079.11 12 56.27 even 2
1764.2.e.g.1079.12 12 168.125 even 2
4032.2.h.h.575.1 12 4.3 odd 2 inner
4032.2.h.h.575.2 12 1.1 even 1 trivial
4032.2.h.h.575.11 12 12.11 even 2 inner
4032.2.h.h.575.12 12 3.2 odd 2 inner