Properties

Label 1280.4.d.c.641.2
Level $1280$
Weight $4$
Character 1280.641
Analytic conductor $75.522$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1280 = 2^{8} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1280.d (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(75.5224448073\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 20)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 641.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1280.641
Dual form 1280.4.d.c.641.1

$q$-expansion

\(f(q)\) \(=\) \(q+4.00000i q^{3} +5.00000i q^{5} -16.0000 q^{7} +11.0000 q^{9} +O(q^{10})\) \(q+4.00000i q^{3} +5.00000i q^{5} -16.0000 q^{7} +11.0000 q^{9} +60.0000i q^{11} -86.0000i q^{13} -20.0000 q^{15} +18.0000 q^{17} +44.0000i q^{19} -64.0000i q^{21} +48.0000 q^{23} -25.0000 q^{25} +152.000i q^{27} +186.000i q^{29} -176.000 q^{31} -240.000 q^{33} -80.0000i q^{35} +254.000i q^{37} +344.000 q^{39} -186.000 q^{41} +100.000i q^{43} +55.0000i q^{45} -168.000 q^{47} -87.0000 q^{49} +72.0000i q^{51} -498.000i q^{53} -300.000 q^{55} -176.000 q^{57} +252.000i q^{59} +58.0000i q^{61} -176.000 q^{63} +430.000 q^{65} -1036.00i q^{67} +192.000i q^{69} +168.000 q^{71} -506.000 q^{73} -100.000i q^{75} -960.000i q^{77} -272.000 q^{79} -311.000 q^{81} +948.000i q^{83} +90.0000i q^{85} -744.000 q^{87} +1014.00 q^{89} +1376.00i q^{91} -704.000i q^{93} -220.000 q^{95} -766.000 q^{97} +660.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 32 q^{7} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 32 q^{7} + 22 q^{9} - 40 q^{15} + 36 q^{17} + 96 q^{23} - 50 q^{25} - 352 q^{31} - 480 q^{33} + 688 q^{39} - 372 q^{41} - 336 q^{47} - 174 q^{49} - 600 q^{55} - 352 q^{57} - 352 q^{63} + 860 q^{65} + 336 q^{71} - 1012 q^{73} - 544 q^{79} - 622 q^{81} - 1488 q^{87} + 2028 q^{89} - 440 q^{95} - 1532 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1280\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(261\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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
\(3\) 4.00000i 0.769800i 0.922958 + 0.384900i \(0.125764\pi\)
−0.922958 + 0.384900i \(0.874236\pi\)
\(4\) 0 0
\(5\) 5.00000i 0.447214i
\(6\) 0 0
\(7\) −16.0000 −0.863919 −0.431959 0.901893i \(-0.642178\pi\)
−0.431959 + 0.901893i \(0.642178\pi\)
\(8\) 0 0
\(9\) 11.0000 0.407407
\(10\) 0 0
\(11\) 60.0000i 1.64461i 0.569049 + 0.822304i \(0.307311\pi\)
−0.569049 + 0.822304i \(0.692689\pi\)
\(12\) 0 0
\(13\) − 86.0000i − 1.83478i −0.397992 0.917389i \(-0.630293\pi\)
0.397992 0.917389i \(-0.369707\pi\)
\(14\) 0 0
\(15\) −20.0000 −0.344265
\(16\) 0 0
\(17\) 18.0000 0.256802 0.128401 0.991722i \(-0.459015\pi\)
0.128401 + 0.991722i \(0.459015\pi\)
\(18\) 0 0
\(19\) 44.0000i 0.531279i 0.964072 + 0.265639i \(0.0855830\pi\)
−0.964072 + 0.265639i \(0.914417\pi\)
\(20\) 0 0
\(21\) − 64.0000i − 0.665045i
\(22\) 0 0
\(23\) 48.0000 0.435161 0.217580 0.976042i \(-0.430184\pi\)
0.217580 + 0.976042i \(0.430184\pi\)
\(24\) 0 0
\(25\) −25.0000 −0.200000
\(26\) 0 0
\(27\) 152.000i 1.08342i
\(28\) 0 0
\(29\) 186.000i 1.19101i 0.803351 + 0.595506i \(0.203048\pi\)
−0.803351 + 0.595506i \(0.796952\pi\)
\(30\) 0 0
\(31\) −176.000 −1.01969 −0.509847 0.860265i \(-0.670298\pi\)
−0.509847 + 0.860265i \(0.670298\pi\)
\(32\) 0 0
\(33\) −240.000 −1.26602
\(34\) 0 0
\(35\) − 80.0000i − 0.386356i
\(36\) 0 0
\(37\) 254.000i 1.12858i 0.825578 + 0.564288i \(0.190849\pi\)
−0.825578 + 0.564288i \(0.809151\pi\)
\(38\) 0 0
\(39\) 344.000 1.41241
\(40\) 0 0
\(41\) −186.000 −0.708496 −0.354248 0.935152i \(-0.615263\pi\)
−0.354248 + 0.935152i \(0.615263\pi\)
\(42\) 0 0
\(43\) 100.000i 0.354648i 0.984153 + 0.177324i \(0.0567440\pi\)
−0.984153 + 0.177324i \(0.943256\pi\)
\(44\) 0 0
\(45\) 55.0000i 0.182198i
\(46\) 0 0
\(47\) −168.000 −0.521390 −0.260695 0.965421i \(-0.583952\pi\)
−0.260695 + 0.965421i \(0.583952\pi\)
\(48\) 0 0
\(49\) −87.0000 −0.253644
\(50\) 0 0
\(51\) 72.0000i 0.197687i
\(52\) 0 0
\(53\) − 498.000i − 1.29067i −0.763899 0.645335i \(-0.776718\pi\)
0.763899 0.645335i \(-0.223282\pi\)
\(54\) 0 0
\(55\) −300.000 −0.735491
\(56\) 0 0
\(57\) −176.000 −0.408978
\(58\) 0 0
\(59\) 252.000i 0.556061i 0.960572 + 0.278031i \(0.0896817\pi\)
−0.960572 + 0.278031i \(0.910318\pi\)
\(60\) 0 0
\(61\) 58.0000i 0.121740i 0.998146 + 0.0608700i \(0.0193875\pi\)
−0.998146 + 0.0608700i \(0.980612\pi\)
\(62\) 0 0
\(63\) −176.000 −0.351967
\(64\) 0 0
\(65\) 430.000 0.820537
\(66\) 0 0
\(67\) − 1036.00i − 1.88907i −0.328414 0.944534i \(-0.606514\pi\)
0.328414 0.944534i \(-0.393486\pi\)
\(68\) 0 0
\(69\) 192.000i 0.334987i
\(70\) 0 0
\(71\) 168.000 0.280816 0.140408 0.990094i \(-0.455159\pi\)
0.140408 + 0.990094i \(0.455159\pi\)
\(72\) 0 0
\(73\) −506.000 −0.811272 −0.405636 0.914035i \(-0.632950\pi\)
−0.405636 + 0.914035i \(0.632950\pi\)
\(74\) 0 0
\(75\) − 100.000i − 0.153960i
\(76\) 0 0
\(77\) − 960.000i − 1.42081i
\(78\) 0 0
\(79\) −272.000 −0.387372 −0.193686 0.981064i \(-0.562044\pi\)
−0.193686 + 0.981064i \(0.562044\pi\)
\(80\) 0 0
\(81\) −311.000 −0.426612
\(82\) 0 0
\(83\) 948.000i 1.25369i 0.779143 + 0.626846i \(0.215655\pi\)
−0.779143 + 0.626846i \(0.784345\pi\)
\(84\) 0 0
\(85\) 90.0000i 0.114846i
\(86\) 0 0
\(87\) −744.000 −0.916841
\(88\) 0 0
\(89\) 1014.00 1.20768 0.603841 0.797104i \(-0.293636\pi\)
0.603841 + 0.797104i \(0.293636\pi\)
\(90\) 0 0
\(91\) 1376.00i 1.58510i
\(92\) 0 0
\(93\) − 704.000i − 0.784961i
\(94\) 0 0
\(95\) −220.000 −0.237595
\(96\) 0 0
\(97\) −766.000 −0.801809 −0.400905 0.916120i \(-0.631304\pi\)
−0.400905 + 0.916120i \(0.631304\pi\)
\(98\) 0 0
\(99\) 660.000i 0.670025i
\(100\) 0 0
\(101\) − 1314.00i − 1.29453i −0.762264 0.647267i \(-0.775912\pi\)
0.762264 0.647267i \(-0.224088\pi\)
\(102\) 0 0
\(103\) −448.000 −0.428570 −0.214285 0.976771i \(-0.568742\pi\)
−0.214285 + 0.976771i \(0.568742\pi\)
\(104\) 0 0
\(105\) 320.000 0.297417
\(106\) 0 0
\(107\) − 1548.00i − 1.39861i −0.714826 0.699303i \(-0.753494\pi\)
0.714826 0.699303i \(-0.246506\pi\)
\(108\) 0 0
\(109\) − 278.000i − 0.244290i −0.992512 0.122145i \(-0.961023\pi\)
0.992512 0.122145i \(-0.0389772\pi\)
\(110\) 0 0
\(111\) −1016.00 −0.868779
\(112\) 0 0
\(113\) −558.000 −0.464533 −0.232266 0.972652i \(-0.574614\pi\)
−0.232266 + 0.972652i \(0.574614\pi\)
\(114\) 0 0
\(115\) 240.000i 0.194610i
\(116\) 0 0
\(117\) − 946.000i − 0.747502i
\(118\) 0 0
\(119\) −288.000 −0.221856
\(120\) 0 0
\(121\) −2269.00 −1.70473
\(122\) 0 0
\(123\) − 744.000i − 0.545400i
\(124\) 0 0
\(125\) − 125.000i − 0.0894427i
\(126\) 0 0
\(127\) −344.000 −0.240355 −0.120177 0.992752i \(-0.538346\pi\)
−0.120177 + 0.992752i \(0.538346\pi\)
\(128\) 0 0
\(129\) −400.000 −0.273008
\(130\) 0 0
\(131\) 780.000i 0.520221i 0.965579 + 0.260110i \(0.0837590\pi\)
−0.965579 + 0.260110i \(0.916241\pi\)
\(132\) 0 0
\(133\) − 704.000i − 0.458982i
\(134\) 0 0
\(135\) −760.000 −0.484521
\(136\) 0 0
\(137\) −666.000 −0.415330 −0.207665 0.978200i \(-0.566586\pi\)
−0.207665 + 0.978200i \(0.566586\pi\)
\(138\) 0 0
\(139\) − 884.000i − 0.539424i −0.962941 0.269712i \(-0.913072\pi\)
0.962941 0.269712i \(-0.0869285\pi\)
\(140\) 0 0
\(141\) − 672.000i − 0.401366i
\(142\) 0 0
\(143\) 5160.00 3.01749
\(144\) 0 0
\(145\) −930.000 −0.532637
\(146\) 0 0
\(147\) − 348.000i − 0.195255i
\(148\) 0 0
\(149\) − 114.000i − 0.0626795i −0.999509 0.0313397i \(-0.990023\pi\)
0.999509 0.0313397i \(-0.00997738\pi\)
\(150\) 0 0
\(151\) −40.0000 −0.0215573 −0.0107787 0.999942i \(-0.503431\pi\)
−0.0107787 + 0.999942i \(0.503431\pi\)
\(152\) 0 0
\(153\) 198.000 0.104623
\(154\) 0 0
\(155\) − 880.000i − 0.456021i
\(156\) 0 0
\(157\) 154.000i 0.0782837i 0.999234 + 0.0391418i \(0.0124624\pi\)
−0.999234 + 0.0391418i \(0.987538\pi\)
\(158\) 0 0
\(159\) 1992.00 0.993559
\(160\) 0 0
\(161\) −768.000 −0.375943
\(162\) 0 0
\(163\) 2180.00i 1.04755i 0.851856 + 0.523775i \(0.175477\pi\)
−0.851856 + 0.523775i \(0.824523\pi\)
\(164\) 0 0
\(165\) − 1200.00i − 0.566181i
\(166\) 0 0
\(167\) 3696.00 1.71261 0.856303 0.516474i \(-0.172756\pi\)
0.856303 + 0.516474i \(0.172756\pi\)
\(168\) 0 0
\(169\) −5199.00 −2.36641
\(170\) 0 0
\(171\) 484.000i 0.216447i
\(172\) 0 0
\(173\) − 1302.00i − 0.572192i −0.958201 0.286096i \(-0.907642\pi\)
0.958201 0.286096i \(-0.0923576\pi\)
\(174\) 0 0
\(175\) 400.000 0.172784
\(176\) 0 0
\(177\) −1008.00 −0.428056
\(178\) 0 0
\(179\) − 4308.00i − 1.79885i −0.437070 0.899427i \(-0.643984\pi\)
0.437070 0.899427i \(-0.356016\pi\)
\(180\) 0 0
\(181\) 1550.00i 0.636523i 0.948003 + 0.318261i \(0.103099\pi\)
−0.948003 + 0.318261i \(0.896901\pi\)
\(182\) 0 0
\(183\) −232.000 −0.0937155
\(184\) 0 0
\(185\) −1270.00 −0.504715
\(186\) 0 0
\(187\) 1080.00i 0.422339i
\(188\) 0 0
\(189\) − 2432.00i − 0.935989i
\(190\) 0 0
\(191\) −48.0000 −0.0181841 −0.00909204 0.999959i \(-0.502894\pi\)
−0.00909204 + 0.999959i \(0.502894\pi\)
\(192\) 0 0
\(193\) 1058.00 0.394593 0.197297 0.980344i \(-0.436784\pi\)
0.197297 + 0.980344i \(0.436784\pi\)
\(194\) 0 0
\(195\) 1720.00i 0.631650i
\(196\) 0 0
\(197\) − 3714.00i − 1.34321i −0.740911 0.671603i \(-0.765606\pi\)
0.740911 0.671603i \(-0.234394\pi\)
\(198\) 0 0
\(199\) −1768.00 −0.629800 −0.314900 0.949125i \(-0.601971\pi\)
−0.314900 + 0.949125i \(0.601971\pi\)
\(200\) 0 0
\(201\) 4144.00 1.45421
\(202\) 0 0
\(203\) − 2976.00i − 1.02894i
\(204\) 0 0
\(205\) − 930.000i − 0.316849i
\(206\) 0 0
\(207\) 528.000 0.177288
\(208\) 0 0
\(209\) −2640.00 −0.873745
\(210\) 0 0
\(211\) − 4036.00i − 1.31682i −0.752658 0.658412i \(-0.771229\pi\)
0.752658 0.658412i \(-0.228771\pi\)
\(212\) 0 0
\(213\) 672.000i 0.216172i
\(214\) 0 0
\(215\) −500.000 −0.158603
\(216\) 0 0
\(217\) 2816.00 0.880933
\(218\) 0 0
\(219\) − 2024.00i − 0.624517i
\(220\) 0 0
\(221\) − 1548.00i − 0.471175i
\(222\) 0 0
\(223\) −680.000 −0.204198 −0.102099 0.994774i \(-0.532556\pi\)
−0.102099 + 0.994774i \(0.532556\pi\)
\(224\) 0 0
\(225\) −275.000 −0.0814815
\(226\) 0 0
\(227\) 2388.00i 0.698225i 0.937081 + 0.349113i \(0.113517\pi\)
−0.937081 + 0.349113i \(0.886483\pi\)
\(228\) 0 0
\(229\) − 3874.00i − 1.11791i −0.829198 0.558954i \(-0.811203\pi\)
0.829198 0.558954i \(-0.188797\pi\)
\(230\) 0 0
\(231\) 3840.00 1.09374
\(232\) 0 0
\(233\) −3162.00 −0.889054 −0.444527 0.895766i \(-0.646628\pi\)
−0.444527 + 0.895766i \(0.646628\pi\)
\(234\) 0 0
\(235\) − 840.000i − 0.233173i
\(236\) 0 0
\(237\) − 1088.00i − 0.298199i
\(238\) 0 0
\(239\) −5424.00 −1.46799 −0.733995 0.679155i \(-0.762346\pi\)
−0.733995 + 0.679155i \(0.762346\pi\)
\(240\) 0 0
\(241\) −3886.00 −1.03867 −0.519335 0.854571i \(-0.673820\pi\)
−0.519335 + 0.854571i \(0.673820\pi\)
\(242\) 0 0
\(243\) 2860.00i 0.755017i
\(244\) 0 0
\(245\) − 435.000i − 0.113433i
\(246\) 0 0
\(247\) 3784.00 0.974778
\(248\) 0 0
\(249\) −3792.00 −0.965093
\(250\) 0 0
\(251\) 5100.00i 1.28251i 0.767329 + 0.641253i \(0.221585\pi\)
−0.767329 + 0.641253i \(0.778415\pi\)
\(252\) 0 0
\(253\) 2880.00i 0.715668i
\(254\) 0 0
\(255\) −360.000 −0.0884081
\(256\) 0 0
\(257\) 2178.00 0.528638 0.264319 0.964435i \(-0.414853\pi\)
0.264319 + 0.964435i \(0.414853\pi\)
\(258\) 0 0
\(259\) − 4064.00i − 0.974999i
\(260\) 0 0
\(261\) 2046.00i 0.485227i
\(262\) 0 0
\(263\) −6144.00 −1.44051 −0.720257 0.693707i \(-0.755976\pi\)
−0.720257 + 0.693707i \(0.755976\pi\)
\(264\) 0 0
\(265\) 2490.00 0.577206
\(266\) 0 0
\(267\) 4056.00i 0.929675i
\(268\) 0 0
\(269\) − 822.000i − 0.186313i −0.995651 0.0931566i \(-0.970304\pi\)
0.995651 0.0931566i \(-0.0296957\pi\)
\(270\) 0 0
\(271\) −8480.00 −1.90082 −0.950412 0.310994i \(-0.899338\pi\)
−0.950412 + 0.310994i \(0.899338\pi\)
\(272\) 0 0
\(273\) −5504.00 −1.22021
\(274\) 0 0
\(275\) − 1500.00i − 0.328921i
\(276\) 0 0
\(277\) − 1138.00i − 0.246844i −0.992354 0.123422i \(-0.960613\pi\)
0.992354 0.123422i \(-0.0393869\pi\)
\(278\) 0 0
\(279\) −1936.00 −0.415431
\(280\) 0 0
\(281\) −5706.00 −1.21136 −0.605679 0.795709i \(-0.707098\pi\)
−0.605679 + 0.795709i \(0.707098\pi\)
\(282\) 0 0
\(283\) 3028.00i 0.636028i 0.948086 + 0.318014i \(0.103016\pi\)
−0.948086 + 0.318014i \(0.896984\pi\)
\(284\) 0 0
\(285\) − 880.000i − 0.182901i
\(286\) 0 0
\(287\) 2976.00 0.612083
\(288\) 0 0
\(289\) −4589.00 −0.934053
\(290\) 0 0
\(291\) − 3064.00i − 0.617233i
\(292\) 0 0
\(293\) 3390.00i 0.675925i 0.941160 + 0.337962i \(0.109738\pi\)
−0.941160 + 0.337962i \(0.890262\pi\)
\(294\) 0 0
\(295\) −1260.00 −0.248678
\(296\) 0 0
\(297\) −9120.00 −1.78180
\(298\) 0 0
\(299\) − 4128.00i − 0.798423i
\(300\) 0 0
\(301\) − 1600.00i − 0.306387i
\(302\) 0 0
\(303\) 5256.00 0.996532
\(304\) 0 0
\(305\) −290.000 −0.0544438
\(306\) 0 0
\(307\) − 4156.00i − 0.772624i −0.922368 0.386312i \(-0.873749\pi\)
0.922368 0.386312i \(-0.126251\pi\)
\(308\) 0 0
\(309\) − 1792.00i − 0.329914i
\(310\) 0 0
\(311\) 6552.00 1.19463 0.597315 0.802007i \(-0.296234\pi\)
0.597315 + 0.802007i \(0.296234\pi\)
\(312\) 0 0
\(313\) 1366.00 0.246680 0.123340 0.992364i \(-0.460639\pi\)
0.123340 + 0.992364i \(0.460639\pi\)
\(314\) 0 0
\(315\) − 880.000i − 0.157404i
\(316\) 0 0
\(317\) − 2598.00i − 0.460310i −0.973154 0.230155i \(-0.926077\pi\)
0.973154 0.230155i \(-0.0739233\pi\)
\(318\) 0 0
\(319\) −11160.0 −1.95875
\(320\) 0 0
\(321\) 6192.00 1.07665
\(322\) 0 0
\(323\) 792.000i 0.136434i
\(324\) 0 0
\(325\) 2150.00i 0.366956i
\(326\) 0 0
\(327\) 1112.00 0.188054
\(328\) 0 0
\(329\) 2688.00 0.450438
\(330\) 0 0
\(331\) 3292.00i 0.546661i 0.961920 + 0.273330i \(0.0881252\pi\)
−0.961920 + 0.273330i \(0.911875\pi\)
\(332\) 0 0
\(333\) 2794.00i 0.459791i
\(334\) 0 0
\(335\) 5180.00 0.844817
\(336\) 0 0
\(337\) 6194.00 1.00121 0.500606 0.865675i \(-0.333110\pi\)
0.500606 + 0.865675i \(0.333110\pi\)
\(338\) 0 0
\(339\) − 2232.00i − 0.357598i
\(340\) 0 0
\(341\) − 10560.0i − 1.67700i
\(342\) 0 0
\(343\) 6880.00 1.08305
\(344\) 0 0
\(345\) −960.000 −0.149811
\(346\) 0 0
\(347\) 10020.0i 1.55015i 0.631870 + 0.775075i \(0.282288\pi\)
−0.631870 + 0.775075i \(0.717712\pi\)
\(348\) 0 0
\(349\) 3130.00i 0.480072i 0.970764 + 0.240036i \(0.0771592\pi\)
−0.970764 + 0.240036i \(0.922841\pi\)
\(350\) 0 0
\(351\) 13072.0 1.98784
\(352\) 0 0
\(353\) 4194.00 0.632363 0.316181 0.948699i \(-0.397599\pi\)
0.316181 + 0.948699i \(0.397599\pi\)
\(354\) 0 0
\(355\) 840.000i 0.125585i
\(356\) 0 0
\(357\) − 1152.00i − 0.170785i
\(358\) 0 0
\(359\) −4104.00 −0.603345 −0.301672 0.953412i \(-0.597545\pi\)
−0.301672 + 0.953412i \(0.597545\pi\)
\(360\) 0 0
\(361\) 4923.00 0.717743
\(362\) 0 0
\(363\) − 9076.00i − 1.31230i
\(364\) 0 0
\(365\) − 2530.00i − 0.362812i
\(366\) 0 0
\(367\) −7496.00 −1.06618 −0.533090 0.846059i \(-0.678969\pi\)
−0.533090 + 0.846059i \(0.678969\pi\)
\(368\) 0 0
\(369\) −2046.00 −0.288646
\(370\) 0 0
\(371\) 7968.00i 1.11503i
\(372\) 0 0
\(373\) − 5842.00i − 0.810958i −0.914104 0.405479i \(-0.867105\pi\)
0.914104 0.405479i \(-0.132895\pi\)
\(374\) 0 0
\(375\) 500.000 0.0688530
\(376\) 0 0
\(377\) 15996.0 2.18524
\(378\) 0 0
\(379\) 412.000i 0.0558391i 0.999610 + 0.0279195i \(0.00888822\pi\)
−0.999610 + 0.0279195i \(0.991112\pi\)
\(380\) 0 0
\(381\) − 1376.00i − 0.185025i
\(382\) 0 0
\(383\) −2568.00 −0.342607 −0.171304 0.985218i \(-0.554798\pi\)
−0.171304 + 0.985218i \(0.554798\pi\)
\(384\) 0 0
\(385\) 4800.00 0.635404
\(386\) 0 0
\(387\) 1100.00i 0.144486i
\(388\) 0 0
\(389\) 13086.0i 1.70562i 0.522221 + 0.852810i \(0.325104\pi\)
−0.522221 + 0.852810i \(0.674896\pi\)
\(390\) 0 0
\(391\) 864.000 0.111750
\(392\) 0 0
\(393\) −3120.00 −0.400466
\(394\) 0 0
\(395\) − 1360.00i − 0.173238i
\(396\) 0 0
\(397\) − 10454.0i − 1.32159i −0.750566 0.660795i \(-0.770219\pi\)
0.750566 0.660795i \(-0.229781\pi\)
\(398\) 0 0
\(399\) 2816.00 0.353324
\(400\) 0 0
\(401\) −10830.0 −1.34869 −0.674345 0.738417i \(-0.735574\pi\)
−0.674345 + 0.738417i \(0.735574\pi\)
\(402\) 0 0
\(403\) 15136.0i 1.87091i
\(404\) 0 0
\(405\) − 1555.00i − 0.190787i
\(406\) 0 0
\(407\) −15240.0 −1.85607
\(408\) 0 0
\(409\) 8566.00 1.03560 0.517801 0.855501i \(-0.326751\pi\)
0.517801 + 0.855501i \(0.326751\pi\)
\(410\) 0 0
\(411\) − 2664.00i − 0.319721i
\(412\) 0 0
\(413\) − 4032.00i − 0.480392i
\(414\) 0 0
\(415\) −4740.00 −0.560669
\(416\) 0 0
\(417\) 3536.00 0.415249
\(418\) 0 0
\(419\) 13884.0i 1.61880i 0.587257 + 0.809401i \(0.300208\pi\)
−0.587257 + 0.809401i \(0.699792\pi\)
\(420\) 0 0
\(421\) 4286.00i 0.496168i 0.968738 + 0.248084i \(0.0798010\pi\)
−0.968738 + 0.248084i \(0.920199\pi\)
\(422\) 0 0
\(423\) −1848.00 −0.212418
\(424\) 0 0
\(425\) −450.000 −0.0513605
\(426\) 0 0
\(427\) − 928.000i − 0.105173i
\(428\) 0 0
\(429\) 20640.0i 2.32286i
\(430\) 0 0
\(431\) −6336.00 −0.708108 −0.354054 0.935225i \(-0.615197\pi\)
−0.354054 + 0.935225i \(0.615197\pi\)
\(432\) 0 0
\(433\) −8974.00 −0.995988 −0.497994 0.867180i \(-0.665930\pi\)
−0.497994 + 0.867180i \(0.665930\pi\)
\(434\) 0 0
\(435\) − 3720.00i − 0.410024i
\(436\) 0 0
\(437\) 2112.00i 0.231191i
\(438\) 0 0
\(439\) −2968.00 −0.322676 −0.161338 0.986899i \(-0.551581\pi\)
−0.161338 + 0.986899i \(0.551581\pi\)
\(440\) 0 0
\(441\) −957.000 −0.103337
\(442\) 0 0
\(443\) 12372.0i 1.32689i 0.748226 + 0.663444i \(0.230906\pi\)
−0.748226 + 0.663444i \(0.769094\pi\)
\(444\) 0 0
\(445\) 5070.00i 0.540092i
\(446\) 0 0
\(447\) 456.000 0.0482507
\(448\) 0 0
\(449\) 11394.0 1.19759 0.598793 0.800904i \(-0.295647\pi\)
0.598793 + 0.800904i \(0.295647\pi\)
\(450\) 0 0
\(451\) − 11160.0i − 1.16520i
\(452\) 0 0
\(453\) − 160.000i − 0.0165948i
\(454\) 0 0
\(455\) −6880.00 −0.708878
\(456\) 0 0
\(457\) 358.000 0.0366445 0.0183222 0.999832i \(-0.494168\pi\)
0.0183222 + 0.999832i \(0.494168\pi\)
\(458\) 0 0
\(459\) 2736.00i 0.278226i
\(460\) 0 0
\(461\) 7530.00i 0.760753i 0.924832 + 0.380376i \(0.124206\pi\)
−0.924832 + 0.380376i \(0.875794\pi\)
\(462\) 0 0
\(463\) 13768.0 1.38197 0.690986 0.722868i \(-0.257177\pi\)
0.690986 + 0.722868i \(0.257177\pi\)
\(464\) 0 0
\(465\) 3520.00 0.351045
\(466\) 0 0
\(467\) 13380.0i 1.32581i 0.748704 + 0.662904i \(0.230676\pi\)
−0.748704 + 0.662904i \(0.769324\pi\)
\(468\) 0 0
\(469\) 16576.0i 1.63200i
\(470\) 0 0
\(471\) −616.000 −0.0602628
\(472\) 0 0
\(473\) −6000.00 −0.583256
\(474\) 0 0
\(475\) − 1100.00i − 0.106256i
\(476\) 0 0
\(477\) − 5478.00i − 0.525829i
\(478\) 0 0
\(479\) 6336.00 0.604383 0.302191 0.953247i \(-0.402282\pi\)
0.302191 + 0.953247i \(0.402282\pi\)
\(480\) 0 0
\(481\) 21844.0 2.07069
\(482\) 0 0
\(483\) − 3072.00i − 0.289401i
\(484\) 0 0
\(485\) − 3830.00i − 0.358580i
\(486\) 0 0
\(487\) −5008.00 −0.465984 −0.232992 0.972479i \(-0.574852\pi\)
−0.232992 + 0.972479i \(0.574852\pi\)
\(488\) 0 0
\(489\) −8720.00 −0.806405
\(490\) 0 0
\(491\) − 12900.0i − 1.18568i −0.805320 0.592840i \(-0.798007\pi\)
0.805320 0.592840i \(-0.201993\pi\)
\(492\) 0 0
\(493\) 3348.00i 0.305855i
\(494\) 0 0
\(495\) −3300.00 −0.299644
\(496\) 0 0
\(497\) −2688.00 −0.242602
\(498\) 0 0
\(499\) − 8116.00i − 0.728100i −0.931379 0.364050i \(-0.881394\pi\)
0.931379 0.364050i \(-0.118606\pi\)
\(500\) 0 0
\(501\) 14784.0i 1.31836i
\(502\) 0 0
\(503\) −4944.00 −0.438255 −0.219127 0.975696i \(-0.570321\pi\)
−0.219127 + 0.975696i \(0.570321\pi\)
\(504\) 0 0
\(505\) 6570.00 0.578933
\(506\) 0 0
\(507\) − 20796.0i − 1.82166i
\(508\) 0 0
\(509\) 5466.00i 0.475985i 0.971267 + 0.237992i \(0.0764893\pi\)
−0.971267 + 0.237992i \(0.923511\pi\)
\(510\) 0 0
\(511\) 8096.00 0.700873
\(512\) 0 0
\(513\) −6688.00 −0.575599
\(514\) 0 0
\(515\) − 2240.00i − 0.191663i
\(516\) 0 0
\(517\) − 10080.0i − 0.857481i
\(518\) 0 0
\(519\) 5208.00 0.440474
\(520\) 0 0
\(521\) −10074.0 −0.847121 −0.423560 0.905868i \(-0.639220\pi\)
−0.423560 + 0.905868i \(0.639220\pi\)
\(522\) 0 0
\(523\) 13828.0i 1.15613i 0.815991 + 0.578065i \(0.196192\pi\)
−0.815991 + 0.578065i \(0.803808\pi\)
\(524\) 0 0
\(525\) 1600.00i 0.133009i
\(526\) 0 0
\(527\) −3168.00 −0.261860
\(528\) 0 0
\(529\) −9863.00 −0.810635
\(530\) 0 0
\(531\) 2772.00i 0.226543i
\(532\) 0 0
\(533\) 15996.0i 1.29993i
\(534\) 0 0
\(535\) 7740.00 0.625475
\(536\) 0 0
\(537\) 17232.0 1.38476
\(538\) 0 0
\(539\) − 5220.00i − 0.417145i
\(540\) 0 0
\(541\) 15226.0i 1.21001i 0.796221 + 0.605006i \(0.206829\pi\)
−0.796221 + 0.605006i \(0.793171\pi\)
\(542\) 0 0
\(543\) −6200.00 −0.489995
\(544\) 0 0
\(545\) 1390.00 0.109250
\(546\) 0 0
\(547\) − 13228.0i − 1.03398i −0.855991 0.516991i \(-0.827052\pi\)
0.855991 0.516991i \(-0.172948\pi\)
\(548\) 0 0
\(549\) 638.000i 0.0495978i
\(550\) 0 0
\(551\) −8184.00 −0.632759
\(552\) 0 0
\(553\) 4352.00 0.334658
\(554\) 0 0
\(555\) − 5080.00i − 0.388530i
\(556\) 0 0
\(557\) 8490.00i 0.645840i 0.946426 + 0.322920i \(0.104664\pi\)
−0.946426 + 0.322920i \(0.895336\pi\)
\(558\) 0 0
\(559\) 8600.00 0.650700
\(560\) 0 0
\(561\) −4320.00 −0.325117
\(562\) 0 0
\(563\) − 10284.0i − 0.769838i −0.922950 0.384919i \(-0.874229\pi\)
0.922950 0.384919i \(-0.125771\pi\)
\(564\) 0 0
\(565\) − 2790.00i − 0.207745i
\(566\) 0 0
\(567\) 4976.00 0.368558
\(568\) 0 0
\(569\) −1770.00 −0.130408 −0.0652041 0.997872i \(-0.520770\pi\)
−0.0652041 + 0.997872i \(0.520770\pi\)
\(570\) 0 0
\(571\) − 6068.00i − 0.444725i −0.974964 0.222362i \(-0.928623\pi\)
0.974964 0.222362i \(-0.0713768\pi\)
\(572\) 0 0
\(573\) − 192.000i − 0.0139981i
\(574\) 0 0
\(575\) −1200.00 −0.0870321
\(576\) 0 0
\(577\) 21506.0 1.55166 0.775829 0.630943i \(-0.217332\pi\)
0.775829 + 0.630943i \(0.217332\pi\)
\(578\) 0 0
\(579\) 4232.00i 0.303758i
\(580\) 0 0
\(581\) − 15168.0i − 1.08309i
\(582\) 0 0
\(583\) 29880.0 2.12265
\(584\) 0 0
\(585\) 4730.00 0.334293
\(586\) 0 0
\(587\) − 12108.0i − 0.851364i −0.904873 0.425682i \(-0.860034\pi\)
0.904873 0.425682i \(-0.139966\pi\)
\(588\) 0 0
\(589\) − 7744.00i − 0.541742i
\(590\) 0 0
\(591\) 14856.0 1.03400
\(592\) 0 0
\(593\) 15474.0 1.07157 0.535785 0.844354i \(-0.320016\pi\)
0.535785 + 0.844354i \(0.320016\pi\)
\(594\) 0 0
\(595\) − 1440.00i − 0.0992172i
\(596\) 0 0
\(597\) − 7072.00i − 0.484820i
\(598\) 0 0
\(599\) −2520.00 −0.171894 −0.0859469 0.996300i \(-0.527392\pi\)
−0.0859469 + 0.996300i \(0.527392\pi\)
\(600\) 0 0
\(601\) 12790.0 0.868078 0.434039 0.900894i \(-0.357088\pi\)
0.434039 + 0.900894i \(0.357088\pi\)
\(602\) 0 0
\(603\) − 11396.0i − 0.769620i
\(604\) 0 0
\(605\) − 11345.0i − 0.762380i
\(606\) 0 0
\(607\) −11576.0 −0.774062 −0.387031 0.922067i \(-0.626499\pi\)
−0.387031 + 0.922067i \(0.626499\pi\)
\(608\) 0 0
\(609\) 11904.0 0.792076
\(610\) 0 0
\(611\) 14448.0i 0.956634i
\(612\) 0 0
\(613\) 20126.0i 1.32607i 0.748588 + 0.663035i \(0.230732\pi\)
−0.748588 + 0.663035i \(0.769268\pi\)
\(614\) 0 0
\(615\) 3720.00 0.243910
\(616\) 0 0
\(617\) 27942.0 1.82318 0.911590 0.411100i \(-0.134855\pi\)
0.911590 + 0.411100i \(0.134855\pi\)
\(618\) 0 0
\(619\) 22540.0i 1.46358i 0.681528 + 0.731792i \(0.261316\pi\)
−0.681528 + 0.731792i \(0.738684\pi\)
\(620\) 0 0
\(621\) 7296.00i 0.471463i
\(622\) 0 0
\(623\) −16224.0 −1.04334
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) − 10560.0i − 0.672609i
\(628\) 0 0
\(629\) 4572.00i 0.289821i
\(630\) 0 0
\(631\) −5128.00 −0.323522 −0.161761 0.986830i \(-0.551717\pi\)
−0.161761 + 0.986830i \(0.551717\pi\)
\(632\) 0 0
\(633\) 16144.0 1.01369
\(634\) 0 0
\(635\) − 1720.00i − 0.107490i
\(636\) 0 0
\(637\) 7482.00i 0.465381i
\(638\) 0 0
\(639\) 1848.00 0.114406
\(640\) 0 0
\(641\) −12798.0 −0.788597 −0.394298 0.918982i \(-0.629012\pi\)
−0.394298 + 0.918982i \(0.629012\pi\)
\(642\) 0 0
\(643\) − 21148.0i − 1.29704i −0.761198 0.648519i \(-0.775389\pi\)
0.761198 0.648519i \(-0.224611\pi\)
\(644\) 0 0
\(645\) − 2000.00i − 0.122093i
\(646\) 0 0
\(647\) 16464.0 1.00041 0.500206 0.865906i \(-0.333258\pi\)
0.500206 + 0.865906i \(0.333258\pi\)
\(648\) 0 0
\(649\) −15120.0 −0.914502
\(650\) 0 0
\(651\) 11264.0i 0.678143i
\(652\) 0 0
\(653\) 24234.0i 1.45230i 0.687538 + 0.726148i \(0.258691\pi\)
−0.687538 + 0.726148i \(0.741309\pi\)
\(654\) 0 0
\(655\) −3900.00 −0.232650
\(656\) 0 0
\(657\) −5566.00 −0.330518
\(658\) 0 0
\(659\) − 22836.0i − 1.34987i −0.737877 0.674935i \(-0.764172\pi\)
0.737877 0.674935i \(-0.235828\pi\)
\(660\) 0 0
\(661\) 26318.0i 1.54864i 0.632794 + 0.774320i \(0.281908\pi\)
−0.632794 + 0.774320i \(0.718092\pi\)
\(662\) 0 0
\(663\) 6192.00 0.362711
\(664\) 0 0
\(665\) 3520.00 0.205263
\(666\) 0 0
\(667\) 8928.00i 0.518281i
\(668\) 0 0
\(669\) − 2720.00i − 0.157192i
\(670\) 0 0
\(671\) −3480.00 −0.200214
\(672\) 0 0
\(673\) 28802.0 1.64968 0.824841 0.565365i \(-0.191265\pi\)
0.824841 + 0.565365i \(0.191265\pi\)
\(674\) 0 0
\(675\) − 3800.00i − 0.216685i
\(676\) 0 0
\(677\) 2526.00i 0.143400i 0.997426 + 0.0717002i \(0.0228425\pi\)
−0.997426 + 0.0717002i \(0.977158\pi\)
\(678\) 0 0
\(679\) 12256.0 0.692698
\(680\) 0 0
\(681\) −9552.00 −0.537494
\(682\) 0 0
\(683\) 23076.0i 1.29279i 0.763001 + 0.646397i \(0.223725\pi\)
−0.763001 + 0.646397i \(0.776275\pi\)
\(684\) 0 0
\(685\) − 3330.00i − 0.185741i
\(686\) 0 0
\(687\) 15496.0 0.860567
\(688\) 0 0
\(689\) −42828.0 −2.36809
\(690\) 0 0
\(691\) 7868.00i 0.433159i 0.976265 + 0.216579i \(0.0694900\pi\)
−0.976265 + 0.216579i \(0.930510\pi\)
\(692\) 0 0
\(693\) − 10560.0i − 0.578847i
\(694\) 0 0
\(695\) 4420.00 0.241238
\(696\) 0 0
\(697\) −3348.00 −0.181943
\(698\) 0 0
\(699\) − 12648.0i − 0.684394i
\(700\) 0 0
\(701\) − 21510.0i − 1.15895i −0.814991 0.579473i \(-0.803258\pi\)
0.814991 0.579473i \(-0.196742\pi\)
\(702\) 0 0
\(703\) −11176.0 −0.599589
\(704\) 0 0
\(705\) 3360.00 0.179496
\(706\) 0 0
\(707\) 21024.0i 1.11837i
\(708\) 0 0
\(709\) 30014.0i 1.58984i 0.606712 + 0.794922i \(0.292488\pi\)
−0.606712 + 0.794922i \(0.707512\pi\)
\(710\) 0 0
\(711\) −2992.00 −0.157818
\(712\) 0 0
\(713\) −8448.00 −0.443731
\(714\) 0 0
\(715\) 25800.0i 1.34946i
\(716\) 0 0
\(717\) − 21696.0i − 1.13006i
\(718\) 0 0
\(719\) 816.000 0.0423250 0.0211625 0.999776i \(-0.493263\pi\)
0.0211625 + 0.999776i \(0.493263\pi\)
\(720\) 0 0
\(721\) 7168.00 0.370250
\(722\) 0 0
\(723\) − 15544.0i − 0.799568i
\(724\) 0 0
\(725\) − 4650.00i − 0.238202i
\(726\) 0 0
\(727\) −9952.00 −0.507702 −0.253851 0.967243i \(-0.581697\pi\)
−0.253851 + 0.967243i \(0.581697\pi\)
\(728\) 0 0
\(729\) −19837.0 −1.00782
\(730\) 0 0
\(731\) 1800.00i 0.0910744i
\(732\) 0 0
\(733\) 33946.0i 1.71054i 0.518185 + 0.855269i \(0.326608\pi\)
−0.518185 + 0.855269i \(0.673392\pi\)
\(734\) 0 0
\(735\) 1740.00 0.0873209
\(736\) 0 0
\(737\) 62160.0 3.10677
\(738\) 0 0
\(739\) 23420.0i 1.16579i 0.812548 + 0.582895i \(0.198080\pi\)
−0.812548 + 0.582895i \(0.801920\pi\)
\(740\) 0 0
\(741\) 15136.0i 0.750384i
\(742\) 0 0
\(743\) −14592.0 −0.720496 −0.360248 0.932857i \(-0.617308\pi\)
−0.360248 + 0.932857i \(0.617308\pi\)
\(744\) 0 0
\(745\) 570.000 0.0280311
\(746\) 0 0
\(747\) 10428.0i 0.510764i
\(748\) 0 0
\(749\) 24768.0i 1.20828i
\(750\) 0 0
\(751\) −9056.00 −0.440024 −0.220012 0.975497i \(-0.570610\pi\)
−0.220012 + 0.975497i \(0.570610\pi\)
\(752\) 0 0
\(753\) −20400.0 −0.987274
\(754\) 0 0
\(755\) − 200.000i − 0.00964072i
\(756\) 0 0
\(757\) − 17554.0i − 0.842815i −0.906871 0.421408i \(-0.861536\pi\)
0.906871 0.421408i \(-0.138464\pi\)
\(758\) 0 0
\(759\) −11520.0 −0.550922
\(760\) 0 0
\(761\) 36438.0 1.73571 0.867856 0.496816i \(-0.165498\pi\)
0.867856 + 0.496816i \(0.165498\pi\)
\(762\) 0 0
\(763\) 4448.00i 0.211046i
\(764\) 0 0
\(765\) 990.000i 0.0467889i
\(766\) 0 0
\(767\) 21672.0 1.02025
\(768\) 0 0
\(769\) −9022.00 −0.423071 −0.211536 0.977370i \(-0.567846\pi\)
−0.211536 + 0.977370i \(0.567846\pi\)
\(770\) 0 0
\(771\) 8712.00i 0.406946i
\(772\) 0 0
\(773\) 1470.00i 0.0683987i 0.999415 + 0.0341994i \(0.0108881\pi\)
−0.999415 + 0.0341994i \(0.989112\pi\)
\(774\) 0 0
\(775\) 4400.00 0.203939
\(776\) 0 0
\(777\) 16256.0 0.750554
\(778\) 0 0
\(779\) − 8184.00i − 0.376409i
\(780\) 0 0
\(781\) 10080.0i 0.461832i
\(782\) 0 0
\(783\) −28272.0 −1.29037
\(784\) 0 0
\(785\) −770.000 −0.0350095
\(786\) 0 0
\(787\) 5252.00i 0.237883i 0.992901 + 0.118941i \(0.0379500\pi\)
−0.992901 + 0.118941i \(0.962050\pi\)
\(788\) 0 0
\(789\) − 24576.0i − 1.10891i
\(790\) 0 0
\(791\) 8928.00 0.401319
\(792\) 0 0
\(793\) 4988.00 0.223366
\(794\) 0 0
\(795\) 9960.00i 0.444333i
\(796\) 0 0
\(797\) − 12294.0i − 0.546394i −0.961958 0.273197i \(-0.911919\pi\)
0.961958 0.273197i \(-0.0880810\pi\)
\(798\) 0 0
\(799\) −3024.00 −0.133894
\(800\) 0 0
\(801\) 11154.0 0.492019
\(802\) 0 0
\(803\) − 30360.0i − 1.33422i
\(804\) 0 0
\(805\) − 3840.00i − 0.168127i
\(806\) 0 0
\(807\) 3288.00 0.143424
\(808\) 0 0
\(809\) −15546.0 −0.675610 −0.337805 0.941216i \(-0.609684\pi\)
−0.337805 + 0.941216i \(0.609684\pi\)
\(810\) 0 0
\(811\) − 19364.0i − 0.838424i −0.907888 0.419212i \(-0.862306\pi\)
0.907888 0.419212i \(-0.137694\pi\)
\(812\) 0 0
\(813\) − 33920.0i − 1.46326i
\(814\) 0 0
\(815\) −10900.0 −0.468479
\(816\) 0 0
\(817\) −4400.00 −0.188417
\(818\) 0 0
\(819\) 15136.0i 0.645781i
\(820\) 0 0
\(821\) − 7314.00i − 0.310914i −0.987843 0.155457i \(-0.950315\pi\)
0.987843 0.155457i \(-0.0496850\pi\)
\(822\) 0 0
\(823\) 11984.0 0.507577 0.253789 0.967260i \(-0.418323\pi\)
0.253789 + 0.967260i \(0.418323\pi\)
\(824\) 0 0
\(825\) 6000.00 0.253204
\(826\) 0 0
\(827\) − 13500.0i − 0.567643i −0.958877 0.283822i \(-0.908398\pi\)
0.958877 0.283822i \(-0.0916024\pi\)
\(828\) 0 0
\(829\) 44602.0i 1.86863i 0.356453 + 0.934313i \(0.383986\pi\)
−0.356453 + 0.934313i \(0.616014\pi\)
\(830\) 0 0
\(831\) 4552.00 0.190021
\(832\) 0 0
\(833\) −1566.00 −0.0651365
\(834\) 0 0
\(835\) 18480.0i 0.765900i
\(836\) 0 0
\(837\) − 26752.0i − 1.10476i
\(838\) 0 0
\(839\) 35448.0 1.45864 0.729321 0.684172i \(-0.239836\pi\)
0.729321 + 0.684172i \(0.239836\pi\)
\(840\) 0 0
\(841\) −10207.0 −0.418508
\(842\) 0 0
\(843\) − 22824.0i − 0.932503i
\(844\) 0 0
\(845\) − 25995.0i − 1.05829i
\(846\) 0 0
\(847\) 36304.0 1.47275
\(848\) 0 0
\(849\) −12112.0 −0.489615
\(850\) 0 0
\(851\) 12192.0i 0.491112i
\(852\) 0 0
\(853\) 12590.0i 0.505362i 0.967550 + 0.252681i \(0.0813122\pi\)
−0.967550 + 0.252681i \(0.918688\pi\)
\(854\) 0 0
\(855\) −2420.00 −0.0967980
\(856\) 0 0
\(857\) −24906.0 −0.992734 −0.496367 0.868113i \(-0.665333\pi\)
−0.496367 + 0.868113i \(0.665333\pi\)
\(858\) 0 0
\(859\) − 23204.0i − 0.921665i −0.887487 0.460833i \(-0.847551\pi\)
0.887487 0.460833i \(-0.152449\pi\)
\(860\) 0 0
\(861\) 11904.0i 0.471181i
\(862\) 0 0
\(863\) −19848.0 −0.782890 −0.391445 0.920202i \(-0.628025\pi\)
−0.391445 + 0.920202i \(0.628025\pi\)
\(864\) 0 0
\(865\) 6510.00 0.255892
\(866\) 0 0
\(867\) − 18356.0i − 0.719034i
\(868\) 0 0
\(869\) − 16320.0i − 0.637075i
\(870\) 0 0
\(871\) −89096.0 −3.46602
\(872\) 0 0
\(873\) −8426.00 −0.326663
\(874\) 0 0
\(875\) 2000.00i 0.0772712i
\(876\) 0 0
\(877\) − 27542.0i − 1.06046i −0.847852 0.530232i \(-0.822105\pi\)
0.847852 0.530232i \(-0.177895\pi\)
\(878\) 0 0
\(879\) −13560.0 −0.520327
\(880\) 0 0
\(881\) −20718.0 −0.792290 −0.396145 0.918188i \(-0.629652\pi\)
−0.396145 + 0.918188i \(0.629652\pi\)
\(882\) 0 0
\(883\) 25172.0i 0.959349i 0.877446 + 0.479675i \(0.159245\pi\)
−0.877446 + 0.479675i \(0.840755\pi\)
\(884\) 0 0
\(885\) − 5040.00i − 0.191432i
\(886\) 0 0
\(887\) −12864.0 −0.486957 −0.243478 0.969906i \(-0.578289\pi\)
−0.243478 + 0.969906i \(0.578289\pi\)
\(888\) 0 0
\(889\) 5504.00 0.207647
\(890\) 0 0
\(891\) − 18660.0i − 0.701609i
\(892\) 0 0
\(893\) − 7392.00i − 0.277003i
\(894\) 0 0
\(895\) 21540.0 0.804472
\(896\) 0 0
\(897\) 16512.0 0.614626
\(898\) 0 0
\(899\) − 32736.0i − 1.21447i
\(900\) 0 0
\(901\) − 8964.00i − 0.331447i
\(902\) 0 0
\(903\) 6400.00 0.235857
\(904\) 0 0
\(905\) −7750.00 −0.284662
\(906\) 0 0
\(907\) 23092.0i 0.845377i 0.906275 + 0.422689i \(0.138914\pi\)
−0.906275 + 0.422689i \(0.861086\pi\)
\(908\) 0 0
\(909\) − 14454.0i − 0.527403i
\(910\) 0 0
\(911\) 14208.0 0.516720 0.258360 0.966049i \(-0.416818\pi\)
0.258360 + 0.966049i \(0.416818\pi\)
\(912\) 0 0
\(913\) −56880.0 −2.06183
\(914\) 0 0
\(915\) − 1160.00i − 0.0419108i
\(916\) 0 0
\(917\) − 12480.0i − 0.449428i
\(918\) 0 0
\(919\) −26584.0 −0.954217 −0.477108 0.878844i \(-0.658315\pi\)
−0.477108 + 0.878844i \(0.658315\pi\)
\(920\) 0 0
\(921\) 16624.0 0.594766
\(922\) 0 0
\(923\) − 14448.0i − 0.515235i
\(924\) 0 0
\(925\) − 6350.00i − 0.225715i
\(926\) 0 0
\(927\) −4928.00 −0.174603
\(928\) 0 0
\(929\) 162.000 0.00572126 0.00286063 0.999996i \(-0.499089\pi\)
0.00286063 + 0.999996i \(0.499089\pi\)
\(930\) 0 0
\(931\) − 3828.00i − 0.134756i
\(932\) 0 0
\(933\) 26208.0i 0.919626i
\(934\) 0 0
\(935\) −5400.00 −0.188876
\(936\) 0 0
\(937\) 29734.0 1.03668 0.518339 0.855175i \(-0.326551\pi\)
0.518339 + 0.855175i \(0.326551\pi\)
\(938\) 0 0
\(939\) 5464.00i 0.189894i
\(940\) 0 0
\(941\) − 17142.0i − 0.593850i −0.954901 0.296925i \(-0.904039\pi\)
0.954901 0.296925i \(-0.0959612\pi\)
\(942\) 0 0
\(943\) −8928.00 −0.308309
\(944\) 0 0
\(945\) 12160.0 0.418587
\(946\) 0 0
\(947\) 26436.0i 0.907133i 0.891223 + 0.453566i \(0.149848\pi\)
−0.891223 + 0.453566i \(0.850152\pi\)
\(948\) 0 0
\(949\) 43516.0i 1.48850i
\(950\) 0 0
\(951\) 10392.0 0.354347
\(952\) 0 0
\(953\) −27882.0 −0.947730 −0.473865 0.880598i \(-0.657142\pi\)
−0.473865 + 0.880598i \(0.657142\pi\)
\(954\) 0 0
\(955\) − 240.000i − 0.00813217i
\(956\) 0 0
\(957\) − 44640.0i − 1.50784i
\(958\) 0 0
\(959\) 10656.0 0.358811
\(960\) 0 0
\(961\) 1185.00 0.0397771
\(962\) 0 0
\(963\) − 17028.0i − 0.569802i
\(964\) 0 0
\(965\) 5290.00i 0.176467i
\(966\) 0 0
\(967\) 12656.0 0.420879 0.210439 0.977607i \(-0.432511\pi\)
0.210439 + 0.977607i \(0.432511\pi\)
\(968\) 0 0
\(969\) −3168.00 −0.105027
\(970\) 0 0
\(971\) − 2916.00i − 0.0963737i −0.998838 0.0481869i \(-0.984656\pi\)
0.998838 0.0481869i \(-0.0153443\pi\)
\(972\) 0 0
\(973\) 14144.0i 0.466018i
\(974\) 0 0
\(975\) −8600.00 −0.282482
\(976\) 0 0
\(977\) −6894.00 −0.225751 −0.112875 0.993609i \(-0.536006\pi\)
−0.112875 + 0.993609i \(0.536006\pi\)
\(978\) 0 0
\(979\) 60840.0i 1.98616i
\(980\) 0 0
\(981\) − 3058.00i − 0.0995254i
\(982\) 0 0
\(983\) −45264.0 −1.46866 −0.734332 0.678790i \(-0.762505\pi\)
−0.734332 + 0.678790i \(0.762505\pi\)
\(984\) 0 0
\(985\) 18570.0 0.600700
\(986\) 0 0
\(987\) 10752.0i 0.346748i
\(988\) 0 0
\(989\) 4800.00i 0.154329i
\(990\) 0 0
\(991\) −52016.0 −1.66735 −0.833674 0.552256i \(-0.813767\pi\)
−0.833674 + 0.552256i \(0.813767\pi\)
\(992\) 0 0
\(993\) −13168.0 −0.420820
\(994\) 0 0
\(995\) − 8840.00i − 0.281655i
\(996\) 0 0
\(997\) − 13858.0i − 0.440208i −0.975476 0.220104i \(-0.929360\pi\)
0.975476 0.220104i \(-0.0706397\pi\)
\(998\) 0 0
\(999\) −38608.0 −1.22273
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 1280.4.d.c.641.2 2
4.3 odd 2 1280.4.d.n.641.1 2
8.3 odd 2 1280.4.d.n.641.2 2
8.5 even 2 inner 1280.4.d.c.641.1 2
16.3 odd 4 20.4.a.a.1.1 1
16.5 even 4 320.4.a.k.1.1 1
16.11 odd 4 320.4.a.d.1.1 1
16.13 even 4 80.4.a.c.1.1 1
48.29 odd 4 720.4.a.k.1.1 1
48.35 even 4 180.4.a.a.1.1 1
80.3 even 4 100.4.c.a.49.2 2
80.13 odd 4 400.4.c.j.49.1 2
80.19 odd 4 100.4.a.a.1.1 1
80.29 even 4 400.4.a.o.1.1 1
80.59 odd 4 1600.4.a.bl.1.1 1
80.67 even 4 100.4.c.a.49.1 2
80.69 even 4 1600.4.a.p.1.1 1
80.77 odd 4 400.4.c.j.49.2 2
112.3 even 12 980.4.i.n.961.1 2
112.19 even 12 980.4.i.n.361.1 2
112.51 odd 12 980.4.i.e.361.1 2
112.67 odd 12 980.4.i.e.961.1 2
112.83 even 4 980.4.a.c.1.1 1
144.67 odd 12 1620.4.i.d.541.1 2
144.83 even 12 1620.4.i.j.1081.1 2
144.115 odd 12 1620.4.i.d.1081.1 2
144.131 even 12 1620.4.i.j.541.1 2
176.131 even 4 2420.4.a.d.1.1 1
240.83 odd 4 900.4.d.k.649.2 2
240.179 even 4 900.4.a.m.1.1 1
240.227 odd 4 900.4.d.k.649.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
20.4.a.a.1.1 1 16.3 odd 4
80.4.a.c.1.1 1 16.13 even 4
100.4.a.a.1.1 1 80.19 odd 4
100.4.c.a.49.1 2 80.67 even 4
100.4.c.a.49.2 2 80.3 even 4
180.4.a.a.1.1 1 48.35 even 4
320.4.a.d.1.1 1 16.11 odd 4
320.4.a.k.1.1 1 16.5 even 4
400.4.a.o.1.1 1 80.29 even 4
400.4.c.j.49.1 2 80.13 odd 4
400.4.c.j.49.2 2 80.77 odd 4
720.4.a.k.1.1 1 48.29 odd 4
900.4.a.m.1.1 1 240.179 even 4
900.4.d.k.649.1 2 240.227 odd 4
900.4.d.k.649.2 2 240.83 odd 4
980.4.a.c.1.1 1 112.83 even 4
980.4.i.e.361.1 2 112.51 odd 12
980.4.i.e.961.1 2 112.67 odd 12
980.4.i.n.361.1 2 112.19 even 12
980.4.i.n.961.1 2 112.3 even 12
1280.4.d.c.641.1 2 8.5 even 2 inner
1280.4.d.c.641.2 2 1.1 even 1 trivial
1280.4.d.n.641.1 2 4.3 odd 2
1280.4.d.n.641.2 2 8.3 odd 2
1600.4.a.p.1.1 1 80.69 even 4
1600.4.a.bl.1.1 1 80.59 odd 4
1620.4.i.d.541.1 2 144.67 odd 12
1620.4.i.d.1081.1 2 144.115 odd 12
1620.4.i.j.541.1 2 144.131 even 12
1620.4.i.j.1081.1 2 144.83 even 12
2420.4.a.d.1.1 1 176.131 even 4