Properties

Label 4032.2.h.h.575.9
Level 4032
Weight 2
Character 4032.575
Analytic conductor 32.196
Analytic rank 0
Dimension 12
CM no
Inner twists 4

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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 575.9
Root \(-0.892524 + 1.09700i\)
Character \(\chi\) = 4032.575
Dual form 4032.2.h.h.575.4

$q$-expansion

\(f(q)\) \(=\) \(q+2.56483i q^{5} -1.00000i q^{7} +O(q^{10})\) \(q+2.56483i q^{5} -1.00000i q^{7} +1.15061 q^{11} +0.578337 q^{13} -5.39325i q^{17} +6.20555i q^{19} -7.62536 q^{23} -1.57834 q^{25} -1.41421i q^{29} +5.04888i q^{31} +2.56483 q^{35} -9.83276 q^{37} +6.21115i q^{41} +11.2544i q^{43} +11.0772 q^{47} -1.00000 q^{49} -4.53333i q^{53} +2.95112i q^{55} -4.83896 q^{59} -0.951124 q^{61} +1.48333i q^{65} -2.78389i q^{67} -3.68835 q^{71} +14.0383 q^{73} -1.15061i q^{77} +12.8816i q^{79} -8.77597 q^{83} +13.8328 q^{85} -5.68395i q^{89} -0.578337i q^{91} -15.9162 q^{95} -12.8816 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + O(q^{10}) \) \( 12q - 12q^{25} - 8q^{37} - 12q^{49} - 56q^{61} + 56q^{85} + O(q^{100}) \)

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
\(5\) 2.56483i 1.14703i 0.819197 + 0.573513i \(0.194420\pi\)
−0.819197 + 0.573513i \(0.805580\pi\)
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.15061 0.346923 0.173461 0.984841i \(-0.444505\pi\)
0.173461 + 0.984841i \(0.444505\pi\)
\(12\) 0 0
\(13\) 0.578337 0.160402 0.0802009 0.996779i \(-0.474444\pi\)
0.0802009 + 0.996779i \(0.474444\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 5.39325i − 1.30806i −0.756470 0.654028i \(-0.773078\pi\)
0.756470 0.654028i \(-0.226922\pi\)
\(18\) 0 0
\(19\) 6.20555i 1.42365i 0.702356 + 0.711825i \(0.252131\pi\)
−0.702356 + 0.711825i \(0.747869\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −7.62536 −1.59000 −0.794999 0.606611i \(-0.792529\pi\)
−0.794999 + 0.606611i \(0.792529\pi\)
\(24\) 0 0
\(25\) −1.57834 −0.315667
\(26\) 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
\(31\) 5.04888i 0.906805i 0.891306 + 0.453402i \(0.149790\pi\)
−0.891306 + 0.453402i \(0.850210\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.56483 0.433535
\(36\) 0 0
\(37\) −9.83276 −1.61650 −0.808248 0.588842i \(-0.799584\pi\)
−0.808248 + 0.588842i \(0.799584\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.21115i 0.970018i 0.874509 + 0.485009i \(0.161184\pi\)
−0.874509 + 0.485009i \(0.838816\pi\)
\(42\) 0 0
\(43\) 11.2544i 1.71628i 0.513413 + 0.858142i \(0.328381\pi\)
−0.513413 + 0.858142i \(0.671619\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.0772 1.61578 0.807888 0.589336i \(-0.200611\pi\)
0.807888 + 0.589336i \(0.200611\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) − 4.53333i − 0.622701i −0.950295 0.311351i \(-0.899219\pi\)
0.950295 0.311351i \(-0.100781\pi\)
\(54\) 0 0
\(55\) 2.95112i 0.397929i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.83896 −0.629979 −0.314990 0.949095i \(-0.602001\pi\)
−0.314990 + 0.949095i \(0.602001\pi\)
\(60\) 0 0
\(61\) −0.951124 −0.121779 −0.0608895 0.998145i \(-0.519394\pi\)
−0.0608895 + 0.998145i \(0.519394\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.48333i 0.183985i
\(66\) 0 0
\(67\) − 2.78389i − 0.340106i −0.985435 0.170053i \(-0.945606\pi\)
0.985435 0.170053i \(-0.0543939\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.68835 −0.437726 −0.218863 0.975756i \(-0.570235\pi\)
−0.218863 + 0.975756i \(0.570235\pi\)
\(72\) 0 0
\(73\) 14.0383 1.64306 0.821530 0.570165i \(-0.193121\pi\)
0.821530 + 0.570165i \(0.193121\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 1.15061i − 0.131125i
\(78\) 0 0
\(79\) 12.8816i 1.44930i 0.689118 + 0.724649i \(0.257998\pi\)
−0.689118 + 0.724649i \(0.742002\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −8.77597 −0.963288 −0.481644 0.876367i \(-0.659960\pi\)
−0.481644 + 0.876367i \(0.659960\pi\)
\(84\) 0 0
\(85\) 13.8328 1.50037
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) − 5.68395i − 0.602497i −0.953546 0.301249i \(-0.902597\pi\)
0.953546 0.301249i \(-0.0974034\pi\)
\(90\) 0 0
\(91\) − 0.578337i − 0.0606262i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −15.9162 −1.63296
\(96\) 0 0
\(97\) −12.8816 −1.30793 −0.653966 0.756524i \(-0.726896\pi\)
−0.653966 + 0.756524i \(0.726896\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) − 3.75747i − 0.373882i −0.982371 0.186941i \(-0.940143\pi\)
0.982371 0.186941i \(-0.0598574\pi\)
\(102\) 0 0
\(103\) 1.79445i 0.176812i 0.996085 + 0.0884062i \(0.0281774\pi\)
−0.996085 + 0.0884062i \(0.971823\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.1631 −0.982503 −0.491252 0.871018i \(-0.663460\pi\)
−0.491252 + 0.871018i \(0.663460\pi\)
\(108\) 0 0
\(109\) 15.2544 1.46111 0.730555 0.682854i \(-0.239262\pi\)
0.730555 + 0.682854i \(0.239262\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.06053i 0.476055i 0.971258 + 0.238027i \(0.0765008\pi\)
−0.971258 + 0.238027i \(0.923499\pi\)
\(114\) 0 0
\(115\) − 19.5577i − 1.82377i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −5.39325 −0.494399
\(120\) 0 0
\(121\) −9.67609 −0.879644
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 8.77597i 0.784947i
\(126\) 0 0
\(127\) − 0.470539i − 0.0417536i −0.999782 0.0208768i \(-0.993354\pi\)
0.999782 0.0208768i \(-0.00664577\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −15.9162 −1.39060 −0.695301 0.718719i \(-0.744729\pi\)
−0.695301 + 0.718719i \(0.744729\pi\)
\(132\) 0 0
\(133\) 6.20555 0.538089
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.55440i 0.730852i 0.930840 + 0.365426i \(0.119077\pi\)
−0.930840 + 0.365426i \(0.880923\pi\)
\(138\) 0 0
\(139\) 16.0000i 1.35710i 0.734553 + 0.678551i \(0.237392\pi\)
−0.734553 + 0.678551i \(0.762608\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0.665442 0.0556471
\(144\) 0 0
\(145\) 3.62721 0.301224
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 16.8032i 1.37657i 0.725441 + 0.688285i \(0.241636\pi\)
−0.725441 + 0.688285i \(0.758364\pi\)
\(150\) 0 0
\(151\) − 2.09775i − 0.170713i −0.996350 0.0853563i \(-0.972797\pi\)
0.996350 0.0853563i \(-0.0272029\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −12.9495 −1.04013
\(156\) 0 0
\(157\) −17.3622 −1.38566 −0.692828 0.721103i \(-0.743636\pi\)
−0.692828 + 0.721103i \(0.743636\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.62536i 0.600963i
\(162\) 0 0
\(163\) − 0.470539i − 0.0368554i −0.999830 0.0184277i \(-0.994134\pi\)
0.999830 0.0184277i \(-0.00586606\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −20.7551 −1.60608 −0.803040 0.595925i \(-0.796785\pi\)
−0.803040 + 0.595925i \(0.796785\pi\)
\(168\) 0 0
\(169\) −12.6655 −0.974271
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 14.1692i − 1.07727i −0.842540 0.538633i \(-0.818941\pi\)
0.842540 0.538633i \(-0.181059\pi\)
\(174\) 0 0
\(175\) 1.57834i 0.119311i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.15061 0.0860009 0.0430004 0.999075i \(-0.486308\pi\)
0.0430004 + 0.999075i \(0.486308\pi\)
\(180\) 0 0
\(181\) −3.83276 −0.284887 −0.142444 0.989803i \(-0.545496\pi\)
−0.142444 + 0.989803i \(0.545496\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) − 25.2193i − 1.85416i
\(186\) 0 0
\(187\) − 6.20555i − 0.453795i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 9.92659 0.718263 0.359131 0.933287i \(-0.383073\pi\)
0.359131 + 0.933287i \(0.383073\pi\)
\(192\) 0 0
\(193\) 12.6761 0.912445 0.456222 0.889866i \(-0.349202\pi\)
0.456222 + 0.889866i \(0.349202\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 1.70491i − 0.121469i −0.998154 0.0607347i \(-0.980656\pi\)
0.998154 0.0607347i \(-0.0193444\pi\)
\(198\) 0 0
\(199\) 14.8433i 1.05222i 0.850418 + 0.526108i \(0.176349\pi\)
−0.850418 + 0.526108i \(0.823651\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.41421 −0.0992583
\(204\) 0 0
\(205\) −15.9305 −1.11264
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 7.14019i 0.493897i
\(210\) 0 0
\(211\) − 1.15667i − 0.0796287i −0.999207 0.0398144i \(-0.987323\pi\)
0.999207 0.0398144i \(-0.0126767\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −28.8657 −1.96862
\(216\) 0 0
\(217\) 5.04888 0.342740
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) − 3.11912i − 0.209815i
\(222\) 0 0
\(223\) − 23.6655i − 1.58476i −0.610027 0.792380i \(-0.708842\pi\)
0.610027 0.792380i \(-0.291158\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.44142 −0.626649 −0.313324 0.949646i \(-0.601443\pi\)
−0.313324 + 0.949646i \(0.601443\pi\)
\(228\) 0 0
\(229\) 0.578337 0.0382176 0.0191088 0.999817i \(-0.493917\pi\)
0.0191088 + 0.999817i \(0.493917\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 0.305630i − 0.0200225i −0.999950 0.0100112i \(-0.996813\pi\)
0.999950 0.0100112i \(-0.00318673\pi\)
\(234\) 0 0
\(235\) 28.4111i 1.85334i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.92659 −0.642098 −0.321049 0.947063i \(-0.604035\pi\)
−0.321049 + 0.947063i \(0.604035\pi\)
\(240\) 0 0
\(241\) 9.29274 0.598598 0.299299 0.954159i \(-0.403247\pi\)
0.299299 + 0.954159i \(0.403247\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 2.56483i − 0.163861i
\(246\) 0 0
\(247\) 3.58890i 0.228356i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.93701 0.248502 0.124251 0.992251i \(-0.460347\pi\)
0.124251 + 0.992251i \(0.460347\pi\)
\(252\) 0 0
\(253\) −8.77384 −0.551607
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 15.8891i − 0.991133i −0.868570 0.495566i \(-0.834960\pi\)
0.868570 0.495566i \(-0.165040\pi\)
\(258\) 0 0
\(259\) 9.83276i 0.610978i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.38712 −0.0855336 −0.0427668 0.999085i \(-0.513617\pi\)
−0.0427668 + 0.999085i \(0.513617\pi\)
\(264\) 0 0
\(265\) 11.6272 0.714254
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 1.60869i − 0.0980837i −0.998797 0.0490419i \(-0.984383\pi\)
0.998797 0.0490419i \(-0.0156168\pi\)
\(270\) 0 0
\(271\) 8.30330i 0.504390i 0.967676 + 0.252195i \(0.0811524\pi\)
−0.967676 + 0.252195i \(0.918848\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.81606 −0.109512
\(276\) 0 0
\(277\) 3.83276 0.230288 0.115144 0.993349i \(-0.463267\pi\)
0.115144 + 0.993349i \(0.463267\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 28.9348i 1.72610i 0.505115 + 0.863052i \(0.331450\pi\)
−0.505115 + 0.863052i \(0.668550\pi\)
\(282\) 0 0
\(283\) 31.0278i 1.84441i 0.386703 + 0.922204i \(0.373614\pi\)
−0.386703 + 0.922204i \(0.626386\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.21115 0.366632
\(288\) 0 0
\(289\) −12.0872 −0.711011
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 5.01850i − 0.293184i −0.989197 0.146592i \(-0.953170\pi\)
0.989197 0.146592i \(-0.0468305\pi\)
\(294\) 0 0
\(295\) − 12.4111i − 0.722602i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.41003 −0.255039
\(300\) 0 0
\(301\) 11.2544 0.648694
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) − 2.43947i − 0.139684i
\(306\) 0 0
\(307\) − 15.3622i − 0.876768i −0.898788 0.438384i \(-0.855551\pi\)
0.898788 0.438384i \(-0.144449\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.83896 −0.274392 −0.137196 0.990544i \(-0.543809\pi\)
−0.137196 + 0.990544i \(0.543809\pi\)
\(312\) 0 0
\(313\) 19.7633 1.11709 0.558543 0.829475i \(-0.311360\pi\)
0.558543 + 0.829475i \(0.311360\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 5.96248i − 0.334886i −0.985882 0.167443i \(-0.946449\pi\)
0.985882 0.167443i \(-0.0535511\pi\)
\(318\) 0 0
\(319\) − 1.62721i − 0.0911064i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 33.4681 1.86222
\(324\) 0 0
\(325\) −0.912811 −0.0506336
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 11.0772i − 0.610706i
\(330\) 0 0
\(331\) − 1.15667i − 0.0635766i −0.999495 0.0317883i \(-0.989880\pi\)
0.999495 0.0317883i \(-0.0101202\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.14019 0.390110
\(336\) 0 0
\(337\) 3.25443 0.177280 0.0886399 0.996064i \(-0.471748\pi\)
0.0886399 + 0.996064i \(0.471748\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 5.80930i 0.314591i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −16.4013 −0.880470 −0.440235 0.897883i \(-0.645105\pi\)
−0.440235 + 0.897883i \(0.645105\pi\)
\(348\) 0 0
\(349\) 8.20555 0.439233 0.219617 0.975586i \(-0.429519\pi\)
0.219617 + 0.975586i \(0.429519\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) − 24.9557i − 1.32826i −0.747617 0.664130i \(-0.768802\pi\)
0.747617 0.664130i \(-0.231198\pi\)
\(354\) 0 0
\(355\) − 9.45998i − 0.502083i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.38712 −0.0732095 −0.0366048 0.999330i \(-0.511654\pi\)
−0.0366048 + 0.999330i \(0.511654\pi\)
\(360\) 0 0
\(361\) −19.5089 −1.02678
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 36.0058i 1.88463i
\(366\) 0 0
\(367\) 10.9200i 0.570017i 0.958525 + 0.285008i \(0.0919964\pi\)
−0.958525 + 0.285008i \(0.908004\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −4.53333 −0.235359
\(372\) 0 0
\(373\) −29.6655 −1.53602 −0.768011 0.640436i \(-0.778754\pi\)
−0.768011 + 0.640436i \(0.778754\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 0.817892i − 0.0421236i
\(378\) 0 0
\(379\) − 7.66553i − 0.393752i −0.980428 0.196876i \(-0.936920\pi\)
0.980428 0.196876i \(-0.0630796\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10.8407 −0.553933 −0.276967 0.960880i \(-0.589329\pi\)
−0.276967 + 0.960880i \(0.589329\pi\)
\(384\) 0 0
\(385\) 2.95112 0.150403
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 22.6125i 1.14650i 0.819381 + 0.573249i \(0.194317\pi\)
−0.819381 + 0.573249i \(0.805683\pi\)
\(390\) 0 0
\(391\) 41.1255i 2.07981i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −33.0392 −1.66238
\(396\) 0 0
\(397\) 21.5577 1.08195 0.540976 0.841038i \(-0.318055\pi\)
0.540976 + 0.841038i \(0.318055\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.26176i 0.0630095i 0.999504 + 0.0315047i \(0.0100299\pi\)
−0.999504 + 0.0315047i \(0.989970\pi\)
\(402\) 0 0
\(403\) 2.91995i 0.145453i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.3137 −0.560800
\(408\) 0 0
\(409\) −34.4494 −1.70341 −0.851707 0.524018i \(-0.824432\pi\)
−0.851707 + 0.524018i \(0.824432\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 4.83896i 0.238110i
\(414\) 0 0
\(415\) − 22.5089i − 1.10492i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 16.5816 0.810064 0.405032 0.914302i \(-0.367260\pi\)
0.405032 + 0.914302i \(0.367260\pi\)
\(420\) 0 0
\(421\) 8.36274 0.407575 0.203788 0.979015i \(-0.434675\pi\)
0.203788 + 0.979015i \(0.434675\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.51237i 0.412911i
\(426\) 0 0
\(427\) 0.951124i 0.0460281i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 37.1565 1.78976 0.894882 0.446303i \(-0.147260\pi\)
0.894882 + 0.446303i \(0.147260\pi\)
\(432\) 0 0
\(433\) −7.56777 −0.363684 −0.181842 0.983328i \(-0.558206\pi\)
−0.181842 + 0.983328i \(0.558206\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 47.3196i − 2.26360i
\(438\) 0 0
\(439\) 16.8222i 0.802880i 0.915885 + 0.401440i \(0.131490\pi\)
−0.915885 + 0.401440i \(0.868510\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 12.4643 0.592198 0.296099 0.955157i \(-0.404314\pi\)
0.296099 + 0.955157i \(0.404314\pi\)
\(444\) 0 0
\(445\) 14.5783 0.691079
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 7.44582i 0.351390i 0.984445 + 0.175695i \(0.0562172\pi\)
−0.984445 + 0.175695i \(0.943783\pi\)
\(450\) 0 0
\(451\) 7.14663i 0.336522i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.48333 0.0695398
\(456\) 0 0
\(457\) −5.68665 −0.266010 −0.133005 0.991115i \(-0.542463\pi\)
−0.133005 + 0.991115i \(0.542463\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0.790801i 0.0368313i 0.999830 + 0.0184156i \(0.00586221\pi\)
−0.999830 + 0.0184156i \(0.994138\pi\)
\(462\) 0 0
\(463\) 25.2927i 1.17545i 0.809060 + 0.587727i \(0.199977\pi\)
−0.809060 + 0.587727i \(0.800023\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 40.8448 1.89007 0.945036 0.326966i \(-0.106026\pi\)
0.945036 + 0.326966i \(0.106026\pi\)
\(468\) 0 0
\(469\) −2.78389 −0.128548
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 12.9495i 0.595418i
\(474\) 0 0
\(475\) − 9.79445i − 0.449400i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 15.2507 0.696823 0.348412 0.937342i \(-0.386721\pi\)
0.348412 + 0.937342i \(0.386721\pi\)
\(480\) 0 0
\(481\) −5.68665 −0.259289
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) − 33.0392i − 1.50023i
\(486\) 0 0
\(487\) 24.6066i 1.11503i 0.830166 + 0.557516i \(0.188245\pi\)
−0.830166 + 0.557516i \(0.811755\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −31.3472 −1.41468 −0.707339 0.706875i \(-0.750104\pi\)
−0.707339 + 0.706875i \(0.750104\pi\)
\(492\) 0 0
\(493\) −7.62721 −0.343512
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.68835i 0.165445i
\(498\) 0 0
\(499\) 11.2544i 0.503817i 0.967751 + 0.251909i \(0.0810583\pi\)
−0.967751 + 0.251909i \(0.918942\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.6588 1.23325 0.616623 0.787259i \(-0.288500\pi\)
0.616623 + 0.787259i \(0.288500\pi\)
\(504\) 0 0
\(505\) 9.63726 0.428852
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 29.7947i − 1.32063i −0.750990 0.660313i \(-0.770423\pi\)
0.750990 0.660313i \(-0.229577\pi\)
\(510\) 0 0
\(511\) − 14.0383i − 0.621018i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.60245 −0.202808
\(516\) 0 0
\(517\) 12.7456 0.560550
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 1.84520i − 0.0808397i −0.999183 0.0404199i \(-0.987130\pi\)
0.999183 0.0404199i \(-0.0128696\pi\)
\(522\) 0 0
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 27.2299 1.18615
\(528\) 0 0
\(529\) 35.1461 1.52809
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.59214i 0.155593i
\(534\) 0 0
\(535\) − 26.0666i − 1.12696i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.15061 −0.0495604
\(540\) 0 0
\(541\) 26.3416 1.13251 0.566257 0.824229i \(-0.308391\pi\)
0.566257 + 0.824229i \(0.308391\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 39.1250i 1.67593i
\(546\) 0 0
\(547\) − 0.805013i − 0.0344199i −0.999852 0.0172099i \(-0.994522\pi\)
0.999852 0.0172099i \(-0.00547836\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8.77597 0.373869
\(552\) 0 0
\(553\) 12.8816 0.547783
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.8909i 0.630948i 0.948934 + 0.315474i \(0.102164\pi\)
−0.948934 + 0.315474i \(0.897836\pi\)
\(558\) 0 0
\(559\) 6.50885i 0.275295i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 43.3825 1.82836 0.914178 0.405313i \(-0.132837\pi\)
0.914178 + 0.405313i \(0.132837\pi\)
\(564\) 0 0
\(565\) −12.9794 −0.546047
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 21.8786i − 0.917201i −0.888643 0.458600i \(-0.848351\pi\)
0.888643 0.458600i \(-0.151649\pi\)
\(570\) 0 0
\(571\) − 37.7038i − 1.57786i −0.614485 0.788928i \(-0.710636\pi\)
0.614485 0.788928i \(-0.289364\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 12.0354 0.501910
\(576\) 0 0
\(577\) −26.4111 −1.09951 −0.549754 0.835326i \(-0.685279\pi\)
−0.549754 + 0.835326i \(0.685279\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.77597i 0.364089i
\(582\) 0 0
\(583\) − 5.21611i − 0.216029i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −16.1527 −0.666692 −0.333346 0.942805i \(-0.608178\pi\)
−0.333346 + 0.942805i \(0.608178\pi\)
\(588\) 0 0
\(589\) −31.3311 −1.29097
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 6.44765i − 0.264773i −0.991198 0.132387i \(-0.957736\pi\)
0.991198 0.132387i \(-0.0422641\pi\)
\(594\) 0 0
\(595\) − 13.8328i − 0.567088i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −18.9391 −0.773829 −0.386915 0.922116i \(-0.626459\pi\)
−0.386915 + 0.922116i \(0.626459\pi\)
\(600\) 0 0
\(601\) 18.4111 0.751004 0.375502 0.926821i \(-0.377470\pi\)
0.375502 + 0.926821i \(0.377470\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 24.8175i − 1.00897i
\(606\) 0 0
\(607\) − 24.6066i − 0.998751i −0.866386 0.499376i \(-0.833563\pi\)
0.866386 0.499376i \(-0.166437\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.40636 0.259173
\(612\) 0 0
\(613\) −8.09775 −0.327065 −0.163533 0.986538i \(-0.552289\pi\)
−0.163533 + 0.986538i \(0.552289\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.14459i 0.207113i 0.994624 + 0.103557i \(0.0330223\pi\)
−0.994624 + 0.103557i \(0.966978\pi\)
\(618\) 0 0
\(619\) − 36.2922i − 1.45871i −0.684137 0.729354i \(-0.739821\pi\)
0.684137 0.729354i \(-0.260179\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −5.68395 −0.227722
\(624\) 0 0
\(625\) −30.4005 −1.21602
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 53.0306i 2.11447i
\(630\) 0 0
\(631\) 19.7250i 0.785238i 0.919701 + 0.392619i \(0.128431\pi\)
−0.919701 + 0.392619i \(0.871569\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.20685 0.0478924
\(636\) 0 0
\(637\) −0.578337 −0.0229145
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.6860i 0.817048i 0.912748 + 0.408524i \(0.133956\pi\)
−0.912748 + 0.408524i \(0.866044\pi\)
\(642\) 0 0
\(643\) 15.0278i 0.592637i 0.955089 + 0.296318i \(0.0957589\pi\)
−0.955089 + 0.296318i \(0.904241\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.3909 −0.880277 −0.440139 0.897930i \(-0.645071\pi\)
−0.440139 + 0.897930i \(0.645071\pi\)
\(648\) 0 0
\(649\) −5.56777 −0.218554
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31.0978i 1.21695i 0.793573 + 0.608475i \(0.208218\pi\)
−0.793573 + 0.608475i \(0.791782\pi\)
\(654\) 0 0
\(655\) − 40.8222i − 1.59506i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.1631 0.395898 0.197949 0.980212i \(-0.436572\pi\)
0.197949 + 0.980212i \(0.436572\pi\)
\(660\) 0 0
\(661\) 15.1255 0.588314 0.294157 0.955757i \(-0.404961\pi\)
0.294157 + 0.955757i \(0.404961\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 15.9162i 0.617202i
\(666\) 0 0
\(667\) 10.7839i 0.417554i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.09438 −0.0422479
\(672\) 0 0
\(673\) 36.8716 1.42130 0.710648 0.703548i \(-0.248402\pi\)
0.710648 + 0.703548i \(0.248402\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.3705i 0.398569i 0.979942 + 0.199285i \(0.0638618\pi\)
−0.979942 + 0.199285i \(0.936138\pi\)
\(678\) 0 0
\(679\) 12.8816i 0.494352i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.19275 −0.351751 −0.175875 0.984412i \(-0.556276\pi\)
−0.175875 + 0.984412i \(0.556276\pi\)
\(684\) 0 0
\(685\) −21.9406 −0.838306
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) − 2.62179i − 0.0998824i
\(690\) 0 0
\(691\) − 22.8433i − 0.869001i −0.900672 0.434501i \(-0.856925\pi\)
0.900672 0.434501i \(-0.143075\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −41.0372 −1.55663
\(696\) 0 0
\(697\) 33.4983 1.26884
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 19.1044i 0.721563i 0.932650 + 0.360782i \(0.117490\pi\)
−0.932650 + 0.360782i \(0.882510\pi\)
\(702\) 0 0
\(703\) − 61.0177i − 2.30133i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.75747 −0.141314
\(708\) 0 0
\(709\) 9.56777 0.359325 0.179663 0.983728i \(-0.442499\pi\)
0.179663 + 0.983728i \(0.442499\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) − 38.4995i − 1.44182i
\(714\) 0 0
\(715\) 1.70674i 0.0638286i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 30.5014 1.13751 0.568756 0.822506i \(-0.307425\pi\)
0.568756 + 0.822506i \(0.307425\pi\)
\(720\) 0 0
\(721\) 1.79445 0.0668288
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 2.23211i 0.0828983i
\(726\) 0 0
\(727\) − 32.5189i − 1.20606i −0.797719 0.603030i \(-0.793960\pi\)
0.797719 0.603030i \(-0.206040\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 60.6980 2.24500
\(732\) 0 0
\(733\) −19.0106 −0.702171 −0.351086 0.936343i \(-0.614187\pi\)
−0.351086 + 0.936343i \(0.614187\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 3.20318i − 0.117991i
\(738\) 0 0
\(739\) − 19.7250i − 0.725595i −0.931868 0.362797i \(-0.881822\pi\)
0.931868 0.362797i \(-0.118178\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33.8849 1.24312 0.621558 0.783368i \(-0.286500\pi\)
0.621558 + 0.783368i \(0.286500\pi\)
\(744\) 0 0
\(745\) −43.0972 −1.57896
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.1631i 0.371351i
\(750\) 0 0
\(751\) − 30.5089i − 1.11328i −0.830753 0.556642i \(-0.812090\pi\)
0.830753 0.556642i \(-0.187910\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.38037 0.195812
\(756\) 0 0
\(757\) 48.0766 1.74737 0.873687 0.486488i \(-0.161722\pi\)
0.873687 + 0.486488i \(0.161722\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 13.4055i − 0.485950i −0.970033 0.242975i \(-0.921877\pi\)
0.970033 0.242975i \(-0.0781232\pi\)
\(762\) 0 0
\(763\) − 15.2544i − 0.552247i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.79855 −0.101050
\(768\) 0 0
\(769\) 13.4700 0.485741 0.242871 0.970059i \(-0.421911\pi\)
0.242871 + 0.970059i \(0.421911\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 28.5479i − 1.02680i −0.858151 0.513398i \(-0.828387\pi\)
0.858151 0.513398i \(-0.171613\pi\)
\(774\) 0 0
\(775\) − 7.96883i − 0.286249i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −38.5436 −1.38097
\(780\) 0 0
\(781\) −4.24386 −0.151857
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) − 44.5311i − 1.58938i
\(786\) 0 0
\(787\) 25.7633i 0.918362i 0.888343 + 0.459181i \(0.151857\pi\)
−0.888343 + 0.459181i \(0.848143\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 5.06053 0.179932
\(792\) 0 0
\(793\) −0.550070 −0.0195336
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 23.3741i − 0.827954i −0.910287 0.413977i \(-0.864139\pi\)
0.910287 0.413977i \(-0.135861\pi\)
\(798\) 0 0
\(799\) − 59.7422i − 2.11353i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 16.1527 0.570015
\(804\) 0 0
\(805\) −19.5577 −0.689319
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) − 20.6019i − 0.724326i −0.932115 0.362163i \(-0.882038\pi\)
0.932115 0.362163i \(-0.117962\pi\)
\(810\) 0 0
\(811\) 2.64782i 0.0929776i 0.998919 + 0.0464888i \(0.0148032\pi\)
−0.998919 + 0.0464888i \(0.985197\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.20685 0.0422741
\(816\) 0 0
\(817\) −69.8399 −2.44339
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) − 43.5201i − 1.51886i −0.650589 0.759430i \(-0.725478\pi\)
0.650589 0.759430i \(-0.274522\pi\)
\(822\) 0 0
\(823\) 10.5683i 0.368387i 0.982890 + 0.184194i \(0.0589674\pi\)
−0.982890 + 0.184194i \(0.941033\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.92486 0.136481 0.0682403 0.997669i \(-0.478262\pi\)
0.0682403 + 0.997669i \(0.478262\pi\)
\(828\) 0 0
\(829\) −15.2061 −0.528129 −0.264064 0.964505i \(-0.585063\pi\)
−0.264064 + 0.964505i \(0.585063\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.39325i 0.186865i
\(834\) 0 0
\(835\) − 53.2333i − 1.84221i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −12.2841 −0.424093 −0.212046 0.977260i \(-0.568013\pi\)
−0.212046 + 0.977260i \(0.568013\pi\)
\(840\) 0 0
\(841\) 27.0000 0.931034
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) − 32.4849i − 1.11751i
\(846\) 0 0
\(847\) 9.67609i 0.332474i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 74.9784 2.57022
\(852\) 0 0
\(853\) −16.2056 −0.554867 −0.277434 0.960745i \(-0.589484\pi\)
−0.277434 + 0.960745i \(0.589484\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 15.9873i − 0.546117i −0.961997 0.273059i \(-0.911965\pi\)
0.961997 0.273059i \(-0.0880353\pi\)
\(858\) 0 0
\(859\) 31.9688i 1.09076i 0.838188 + 0.545381i \(0.183615\pi\)
−0.838188 + 0.545381i \(0.816385\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −38.9847 −1.32705 −0.663527 0.748153i \(-0.730941\pi\)
−0.663527 + 0.748153i \(0.730941\pi\)
\(864\) 0 0
\(865\) 36.3416 1.23565
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 14.8218i 0.502795i
\(870\) 0 0
\(871\) − 1.61003i − 0.0545536i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 8.77597 0.296682
\(876\) 0 0
\(877\) 6.07663 0.205193 0.102597 0.994723i \(-0.467285\pi\)
0.102597 + 0.994723i \(0.467285\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 15.9575i − 0.537621i −0.963193 0.268810i \(-0.913370\pi\)
0.963193 0.268810i \(-0.0866305\pi\)
\(882\) 0 0
\(883\) − 43.2544i − 1.45563i −0.685775 0.727814i \(-0.740537\pi\)
0.685775 0.727814i \(-0.259463\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 46.1811 1.55061 0.775305 0.631587i \(-0.217596\pi\)
0.775305 + 0.631587i \(0.217596\pi\)
\(888\) 0 0
\(889\) −0.470539 −0.0157814
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 68.7401i 2.30030i
\(894\) 0 0
\(895\) 2.95112i 0.0986452i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 7.14019 0.238139
\(900\) 0 0
\(901\) −24.4494 −0.814528
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 9.83037i − 0.326773i
\(906\) 0 0
\(907\) − 8.94108i − 0.296884i −0.988921 0.148442i \(-0.952574\pi\)
0.988921 0.148442i \(-0.0474258\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 37.8219 1.25310 0.626548 0.779383i \(-0.284467\pi\)
0.626548 + 0.779383i \(0.284467\pi\)
\(912\) 0 0
\(913\) −10.0978 −0.334187
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 15.9162i 0.525598i
\(918\) 0 0
\(919\) 38.7244i 1.27740i 0.769455 + 0.638701i \(0.220528\pi\)
−0.769455 + 0.638701i \(0.779472\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.13311 −0.0702121
\(924\) 0 0
\(925\) 15.5194 0.510275
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 11.9222i 0.391154i 0.980688 + 0.195577i \(0.0626580\pi\)
−0.980688 + 0.195577i \(0.937342\pi\)
\(930\) 0 0
\(931\) − 6.20555i − 0.203379i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 15.9162 0.520514
\(936\) 0 0
\(937\) 28.1744 0.920417 0.460208 0.887811i \(-0.347775\pi\)
0.460208 + 0.887811i \(0.347775\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 53.9054i − 1.75727i −0.477496 0.878634i \(-0.658456\pi\)
0.477496 0.878634i \(-0.341544\pi\)
\(942\) 0 0
\(943\) − 47.3622i − 1.54233i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.7275 1.19348 0.596742 0.802433i \(-0.296462\pi\)
0.596742 + 0.802433i \(0.296462\pi\)
\(948\) 0 0
\(949\) 8.11888 0.263550
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 58.9090i 1.90825i 0.299408 + 0.954125i \(0.403211\pi\)
−0.299408 + 0.954125i \(0.596789\pi\)
\(954\) 0 0
\(955\) 25.4600i 0.823865i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 8.55440 0.276236
\(960\) 0 0
\(961\) 5.50885 0.177705
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 32.5120i 1.04660i
\(966\) 0 0
\(967\) 43.6061i 1.40228i 0.713025 + 0.701139i \(0.247325\pi\)
−0.713025 + 0.701139i \(0.752675\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −59.7960 −1.91895 −0.959473 0.281801i \(-0.909068\pi\)
−0.959473 + 0.281801i \(0.909068\pi\)
\(972\) 0 0
\(973\) 16.0000 0.512936
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 41.5794i 1.33024i 0.746736 + 0.665121i \(0.231620\pi\)
−0.746736 + 0.665121i \(0.768380\pi\)
\(978\) 0 0
\(979\) − 6.54002i − 0.209020i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −0.428934 −0.0136809 −0.00684043 0.999977i \(-0.502177\pi\)
−0.00684043 + 0.999977i \(0.502177\pi\)
\(984\) 0 0
\(985\) 4.37279 0.139329
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) − 85.8190i − 2.72889i
\(990\) 0 0
\(991\) 31.5466i 1.00211i 0.865415 + 0.501056i \(0.167055\pi\)
−0.865415 + 0.501056i \(0.832945\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −38.0706 −1.20692
\(996\) 0 0
\(997\) −34.7144 −1.09942 −0.549708 0.835357i \(-0.685261\pi\)
−0.549708 + 0.835357i \(0.685261\pi\)
\(998\) 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.575.9 12
3.2 odd 2 inner 4032.2.h.h.575.3 12
4.3 odd 2 inner 4032.2.h.h.575.10 12
8.3 odd 2 252.2.e.a.71.7 yes 12
8.5 even 2 252.2.e.a.71.5 12
12.11 even 2 inner 4032.2.h.h.575.4 12
24.5 odd 2 252.2.e.a.71.8 yes 12
24.11 even 2 252.2.e.a.71.6 yes 12
56.13 odd 2 1764.2.e.g.1079.5 12
56.27 even 2 1764.2.e.g.1079.7 12
168.83 odd 2 1764.2.e.g.1079.6 12
168.125 even 2 1764.2.e.g.1079.8 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.e.a.71.5 12 8.5 even 2
252.2.e.a.71.6 yes 12 24.11 even 2
252.2.e.a.71.7 yes 12 8.3 odd 2
252.2.e.a.71.8 yes 12 24.5 odd 2
1764.2.e.g.1079.5 12 56.13 odd 2
1764.2.e.g.1079.6 12 168.83 odd 2
1764.2.e.g.1079.7 12 56.27 even 2
1764.2.e.g.1079.8 12 168.125 even 2
4032.2.h.h.575.3 12 3.2 odd 2 inner
4032.2.h.h.575.4 12 12.11 even 2 inner
4032.2.h.h.575.9 12 1.1 even 1 trivial
4032.2.h.h.575.10 12 4.3 odd 2 inner