Properties

Label 4032.2.h.h.575.3
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 575.3
Root \(0.892524 - 1.09700i\)
Character \(\chi\) = 4032.575
Dual form 4032.2.h.h.575.10

$q$-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 \(-0.805580\pi\)
0.819197 0.573513i \(-0.194420\pi\)
\(6\) 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 \(-0.555495\pi\)
−0.173461 + 0.984841i \(0.555495\pi\)
\(12\) 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 \(0.226922\pi\)
−0.756470 + 0.654028i \(0.773078\pi\)
\(18\) 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 \(-0.207471\pi\)
0.794999 + 0.606611i \(0.207471\pi\)
\(24\) 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 \(0.0419172\pi\)
−0.991342 + 0.131306i \(0.958083\pi\)
\(30\) 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 \(-0.838816\pi\)
0.874509 0.485009i \(-0.161184\pi\)
\(42\) 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 \(-0.799389\pi\)
−0.807888 + 0.589336i \(0.799389\pi\)
\(48\) 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 \(0.100781\pi\)
−0.950295 + 0.311351i \(0.899219\pi\)
\(54\) 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 \(-0.397999\pi\)
0.314990 + 0.949095i \(0.397999\pi\)
\(60\) 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 \(-0.429765\pi\)
0.218863 + 0.975756i \(0.429765\pi\)
\(72\) 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 \(-0.340040\pi\)
0.481644 + 0.876367i \(0.340040\pi\)
\(84\) 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 \(0.0974034\pi\)
−0.953546 + 0.301249i \(0.902597\pi\)
\(90\) 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 \(0.0598574\pi\)
−0.982371 + 0.186941i \(0.940143\pi\)
\(102\) 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 \(-0.336540\pi\)
0.491252 + 0.871018i \(0.336540\pi\)
\(108\) 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 \(-0.923499\pi\)
0.971258 0.238027i \(-0.0765008\pi\)
\(114\) 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 \(-0.255271\pi\)
0.695301 + 0.718719i \(0.255271\pi\)
\(132\) 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 \(-0.880923\pi\)
0.930840 0.365426i \(-0.119077\pi\)
\(138\) 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 \(-0.758364\pi\)
0.725441 0.688285i \(-0.241636\pi\)
\(150\) 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 \(-0.203215\pi\)
0.803040 + 0.595925i \(0.203215\pi\)
\(168\) 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 \(0.181059\pi\)
−0.842540 + 0.538633i \(0.818941\pi\)
\(174\) 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 \(-0.513692\pi\)
−0.0430004 + 0.999075i \(0.513692\pi\)
\(180\) 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 \(-0.616927\pi\)
−0.359131 + 0.933287i \(0.616927\pi\)
\(192\) 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 \(0.0193444\pi\)
−0.998154 + 0.0607347i \(0.980656\pi\)
\(198\) 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 \(-0.398557\pi\)
0.313324 + 0.949646i \(0.398557\pi\)
\(228\) 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 \(0.00318673\pi\)
−0.999950 + 0.0100112i \(0.996813\pi\)
\(234\) 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 \(-0.395965\pi\)
0.321049 + 0.947063i \(0.395965\pi\)
\(240\) 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 \(-0.539653\pi\)
−0.124251 + 0.992251i \(0.539653\pi\)
\(252\) 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 \(0.165040\pi\)
−0.868570 + 0.495566i \(0.834960\pi\)
\(258\) 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 \(-0.486383\pi\)
0.0427668 + 0.999085i \(0.486383\pi\)
\(264\) 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 \(0.0156168\pi\)
−0.998797 + 0.0490419i \(0.984383\pi\)
\(270\) 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 \(-0.668550\pi\)
0.505115 0.863052i \(-0.331450\pi\)
\(282\) 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 \(0.0468305\pi\)
−0.989197 + 0.146592i \(0.953170\pi\)
\(294\) 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 \(-0.456191\pi\)
0.137196 + 0.990544i \(0.456191\pi\)
\(312\) 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 \(0.0535511\pi\)
−0.985882 + 0.167443i \(0.946449\pi\)
\(318\) 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 \(-0.354895\pi\)
0.440235 + 0.897883i \(0.354895\pi\)
\(348\) 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 \(0.231198\pi\)
−0.747617 + 0.664130i \(0.768802\pi\)
\(354\) 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 \(-0.488346\pi\)
0.0366048 + 0.999330i \(0.488346\pi\)
\(360\) 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 \(-0.410671\pi\)
0.276967 + 0.960880i \(0.410671\pi\)
\(384\) 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 \(-0.805683\pi\)
0.819381 0.573249i \(-0.194317\pi\)
\(390\) 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 \(-0.989970\pi\)
0.999504 0.0315047i \(-0.0100299\pi\)
\(402\) 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 \(-0.632740\pi\)
−0.405032 + 0.914302i \(0.632740\pi\)
\(420\) 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 \(-0.852740\pi\)
−0.894882 + 0.446303i \(0.852740\pi\)
\(432\) 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 \(-0.595686\pi\)
−0.296099 + 0.955157i \(0.595686\pi\)
\(444\) 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 \(-0.943783\pi\)
0.984445 0.175695i \(-0.0562172\pi\)
\(450\) 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 \(-0.994138\pi\)
0.999830 0.0184156i \(-0.00586221\pi\)
\(462\) 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 \(-0.893974\pi\)
−0.945036 + 0.326966i \(0.893974\pi\)
\(468\) 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 \(-0.613279\pi\)
−0.348412 + 0.937342i \(0.613279\pi\)
\(480\) 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 \(-0.249896\pi\)
0.707339 + 0.706875i \(0.249896\pi\)
\(492\) 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 \(-0.711500\pi\)
−0.616623 + 0.787259i \(0.711500\pi\)
\(504\) 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 \(0.229577\pi\)
−0.750990 + 0.660313i \(0.770423\pi\)
\(510\) 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 \(0.0128696\pi\)
−0.999183 + 0.0404199i \(0.987130\pi\)
\(522\) 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 \(-0.897836\pi\)
0.948934 0.315474i \(-0.102164\pi\)
\(558\) 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 \(-0.867163\pi\)
−0.914178 + 0.405313i \(0.867163\pi\)
\(564\) 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 \(0.151649\pi\)
−0.888643 + 0.458600i \(0.848351\pi\)
\(570\) 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 \(-0.391822\pi\)
0.333346 + 0.942805i \(0.391822\pi\)
\(588\) 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 \(0.0422641\pi\)
−0.991198 + 0.132387i \(0.957736\pi\)
\(594\) 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 \(-0.373541\pi\)
0.386915 + 0.922116i \(0.373541\pi\)
\(600\) 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 \(-0.966978\pi\)
0.994624 0.103557i \(-0.0330223\pi\)
\(618\) 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 \(-0.866044\pi\)
0.912748 0.408524i \(-0.133956\pi\)
\(642\) 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 \(-0.354929\pi\)
0.440139 + 0.897930i \(0.354929\pi\)
\(648\) 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 \(-0.791782\pi\)
0.793573 0.608475i \(-0.208218\pi\)
\(654\) 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 \(-0.563428\pi\)
−0.197949 + 0.980212i \(0.563428\pi\)
\(660\) 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 \(-0.936138\pi\)
0.979942 0.199285i \(-0.0638618\pi\)
\(678\) 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 \(-0.443724\pi\)
0.175875 + 0.984412i \(0.443724\pi\)
\(684\) 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 \(-0.882510\pi\)
0.932650 0.360782i \(-0.117490\pi\)
\(702\) 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 \(-0.692575\pi\)
−0.568756 + 0.822506i \(0.692575\pi\)
\(720\) 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 \(-0.713500\pi\)
−0.621558 + 0.783368i \(0.713500\pi\)
\(744\) 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 \(0.0781232\pi\)
−0.970033 + 0.242975i \(0.921877\pi\)
\(762\) 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 \(0.171613\pi\)
−0.858151 + 0.513398i \(0.828387\pi\)
\(774\) 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 \(0.135861\pi\)
−0.910287 + 0.413977i \(0.864139\pi\)
\(798\) 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 \(0.117962\pi\)
−0.932115 + 0.362163i \(0.882038\pi\)
\(810\) 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 \(0.274522\pi\)
−0.650589 + 0.759430i \(0.725478\pi\)
\(822\) 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 \(-0.521738\pi\)
−0.0682403 + 0.997669i \(0.521738\pi\)
\(828\) 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 \(-0.431987\pi\)
0.212046 + 0.977260i \(0.431987\pi\)
\(840\) 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 \(0.0880353\pi\)
−0.961997 + 0.273059i \(0.911965\pi\)
\(858\) 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 \(-0.269059\pi\)
0.663527 + 0.748153i \(0.269059\pi\)
\(864\) 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 \(0.0866305\pi\)
−0.963193 + 0.268810i \(0.913370\pi\)
\(882\) 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 \(-0.782404\pi\)
−0.775305 + 0.631587i \(0.782404\pi\)
\(888\) 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 \(-0.715533\pi\)
−0.626548 + 0.779383i \(0.715533\pi\)
\(912\) 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 \(-0.937342\pi\)
0.980688 0.195577i \(-0.0626580\pi\)
\(930\) 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 \(0.341544\pi\)
−0.477496 + 0.878634i \(0.658456\pi\)
\(942\) 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 \(-0.703538\pi\)
−0.596742 + 0.802433i \(0.703538\pi\)
\(948\) 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 \(-0.596789\pi\)
0.299408 0.954125i \(-0.403211\pi\)
\(954\) 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 \(-0.0909317\pi\)
0.959473 + 0.281801i \(0.0909317\pi\)
\(972\) 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 \(-0.768380\pi\)
0.746736 0.665121i \(-0.231620\pi\)
\(978\) 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 \(-0.497823\pi\)
0.00684043 + 0.999977i \(0.497823\pi\)
\(984\) 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.575.3 12
3.2 odd 2 inner 4032.2.h.h.575.9 12
4.3 odd 2 inner 4032.2.h.h.575.4 12
8.3 odd 2 252.2.e.a.71.6 yes 12
8.5 even 2 252.2.e.a.71.8 yes 12
12.11 even 2 inner 4032.2.h.h.575.10 12
24.5 odd 2 252.2.e.a.71.5 12
24.11 even 2 252.2.e.a.71.7 yes 12
56.13 odd 2 1764.2.e.g.1079.8 12
56.27 even 2 1764.2.e.g.1079.6 12
168.83 odd 2 1764.2.e.g.1079.7 12
168.125 even 2 1764.2.e.g.1079.5 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.e.a.71.5 12 24.5 odd 2
252.2.e.a.71.6 yes 12 8.3 odd 2
252.2.e.a.71.7 yes 12 24.11 even 2
252.2.e.a.71.8 yes 12 8.5 even 2
1764.2.e.g.1079.5 12 168.125 even 2
1764.2.e.g.1079.6 12 56.27 even 2
1764.2.e.g.1079.7 12 168.83 odd 2
1764.2.e.g.1079.8 12 56.13 odd 2
4032.2.h.h.575.3 12 1.1 even 1 trivial
4032.2.h.h.575.4 12 4.3 odd 2 inner
4032.2.h.h.575.9 12 3.2 odd 2 inner
4032.2.h.h.575.10 12 12.11 even 2 inner