Properties

Label 1008.4.a.ba.1.1
Level $1008$
Weight $4$
Character 1008.1
Self dual yes
Analytic conductor $59.474$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,4,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(59.4739252858\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{57}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.27492\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.5498 q^{5} -7.00000 q^{7} +O(q^{10})\) \(q-10.5498 q^{5} -7.00000 q^{7} +34.7492 q^{11} -37.2990 q^{13} +10.5498 q^{17} +58.5980 q^{19} -125.347 q^{23} -13.7010 q^{25} +35.4020 q^{29} -291.794 q^{31} +73.8488 q^{35} -259.897 q^{37} +338.248 q^{41} -6.80397 q^{43} +250.694 q^{47} +49.0000 q^{49} +536.900 q^{53} -366.598 q^{55} -35.8904 q^{59} +57.7940 q^{61} +393.498 q^{65} -481.691 q^{67} +363.752 q^{71} +581.299 q^{73} -243.244 q^{77} +693.691 q^{79} +1334.39 q^{83} -111.299 q^{85} +353.038 q^{89} +261.093 q^{91} -618.199 q^{95} +1445.88 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{5} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 6 q^{5} - 14 q^{7} - 6 q^{11} + 16 q^{13} + 6 q^{17} - 64 q^{19} + 6 q^{23} - 118 q^{25} + 252 q^{29} - 40 q^{31} + 42 q^{35} - 248 q^{37} + 450 q^{41} - 376 q^{43} - 12 q^{47} + 98 q^{49} + 1104 q^{53} - 552 q^{55} + 804 q^{59} - 428 q^{61} + 636 q^{65} - 148 q^{67} + 954 q^{71} + 1072 q^{73} + 42 q^{77} + 572 q^{79} + 1944 q^{83} - 132 q^{85} - 366 q^{89} - 112 q^{91} - 1176 q^{95} + 808 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −10.5498 −0.943606 −0.471803 0.881704i \(-0.656397\pi\)
−0.471803 + 0.881704i \(0.656397\pi\)
\(6\) 0 0
\(7\) −7.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 34.7492 0.952479 0.476240 0.879316i \(-0.342000\pi\)
0.476240 + 0.879316i \(0.342000\pi\)
\(12\) 0 0
\(13\) −37.2990 −0.795760 −0.397880 0.917437i \(-0.630254\pi\)
−0.397880 + 0.917437i \(0.630254\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 10.5498 0.150512 0.0752562 0.997164i \(-0.476023\pi\)
0.0752562 + 0.997164i \(0.476023\pi\)
\(18\) 0 0
\(19\) 58.5980 0.707542 0.353771 0.935332i \(-0.384899\pi\)
0.353771 + 0.935332i \(0.384899\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −125.347 −1.13638 −0.568189 0.822898i \(-0.692356\pi\)
−0.568189 + 0.822898i \(0.692356\pi\)
\(24\) 0 0
\(25\) −13.7010 −0.109608
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 35.4020 0.226689 0.113345 0.993556i \(-0.463844\pi\)
0.113345 + 0.993556i \(0.463844\pi\)
\(30\) 0 0
\(31\) −291.794 −1.69057 −0.845286 0.534313i \(-0.820570\pi\)
−0.845286 + 0.534313i \(0.820570\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 73.8488 0.356649
\(36\) 0 0
\(37\) −259.897 −1.15478 −0.577389 0.816469i \(-0.695928\pi\)
−0.577389 + 0.816469i \(0.695928\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 338.248 1.28842 0.644212 0.764847i \(-0.277185\pi\)
0.644212 + 0.764847i \(0.277185\pi\)
\(42\) 0 0
\(43\) −6.80397 −0.0241301 −0.0120651 0.999927i \(-0.503841\pi\)
−0.0120651 + 0.999927i \(0.503841\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 250.694 0.778033 0.389016 0.921231i \(-0.372815\pi\)
0.389016 + 0.921231i \(0.372815\pi\)
\(48\) 0 0
\(49\) 49.0000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 536.900 1.39149 0.695745 0.718289i \(-0.255075\pi\)
0.695745 + 0.718289i \(0.255075\pi\)
\(54\) 0 0
\(55\) −366.598 −0.898765
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −35.8904 −0.0791955 −0.0395977 0.999216i \(-0.512608\pi\)
−0.0395977 + 0.999216i \(0.512608\pi\)
\(60\) 0 0
\(61\) 57.7940 0.121308 0.0606538 0.998159i \(-0.480681\pi\)
0.0606538 + 0.998159i \(0.480681\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 393.498 0.750884
\(66\) 0 0
\(67\) −481.691 −0.878327 −0.439164 0.898407i \(-0.644725\pi\)
−0.439164 + 0.898407i \(0.644725\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 363.752 0.608021 0.304010 0.952669i \(-0.401674\pi\)
0.304010 + 0.952669i \(0.401674\pi\)
\(72\) 0 0
\(73\) 581.299 0.931999 0.465999 0.884785i \(-0.345695\pi\)
0.465999 + 0.884785i \(0.345695\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −243.244 −0.360003
\(78\) 0 0
\(79\) 693.691 0.987928 0.493964 0.869482i \(-0.335547\pi\)
0.493964 + 0.869482i \(0.335547\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1334.39 1.76468 0.882341 0.470611i \(-0.155967\pi\)
0.882341 + 0.470611i \(0.155967\pi\)
\(84\) 0 0
\(85\) −111.299 −0.142024
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 353.038 0.420472 0.210236 0.977651i \(-0.432577\pi\)
0.210236 + 0.977651i \(0.432577\pi\)
\(90\) 0 0
\(91\) 261.093 0.300769
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −618.199 −0.667641
\(96\) 0 0
\(97\) 1445.88 1.51347 0.756735 0.653722i \(-0.226793\pi\)
0.756735 + 0.653722i \(0.226793\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −474.852 −0.467817 −0.233909 0.972259i \(-0.575152\pi\)
−0.233909 + 0.972259i \(0.575152\pi\)
\(102\) 0 0
\(103\) 1999.59 1.91287 0.956433 0.291951i \(-0.0943044\pi\)
0.956433 + 0.291951i \(0.0943044\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1166.74 1.05414 0.527068 0.849823i \(-0.323291\pi\)
0.527068 + 0.849823i \(0.323291\pi\)
\(108\) 0 0
\(109\) −1337.18 −1.17503 −0.587515 0.809213i \(-0.699894\pi\)
−0.587515 + 0.809213i \(0.699894\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −906.578 −0.754723 −0.377361 0.926066i \(-0.623169\pi\)
−0.377361 + 0.926066i \(0.623169\pi\)
\(114\) 0 0
\(115\) 1322.39 1.07229
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −73.8488 −0.0568883
\(120\) 0 0
\(121\) −123.495 −0.0927836
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1463.27 1.04703
\(126\) 0 0
\(127\) 1714.89 1.19820 0.599101 0.800674i \(-0.295525\pi\)
0.599101 + 0.800674i \(0.295525\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 470.611 0.313874 0.156937 0.987609i \(-0.449838\pi\)
0.156937 + 0.987609i \(0.449838\pi\)
\(132\) 0 0
\(133\) −410.186 −0.267426
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 443.910 0.276831 0.138415 0.990374i \(-0.455799\pi\)
0.138415 + 0.990374i \(0.455799\pi\)
\(138\) 0 0
\(139\) −1669.98 −1.01904 −0.509518 0.860460i \(-0.670176\pi\)
−0.509518 + 0.860460i \(0.670176\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1296.11 −0.757945
\(144\) 0 0
\(145\) −373.485 −0.213905
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −743.871 −0.408995 −0.204497 0.978867i \(-0.565556\pi\)
−0.204497 + 0.978867i \(0.565556\pi\)
\(150\) 0 0
\(151\) −606.764 −0.327005 −0.163503 0.986543i \(-0.552279\pi\)
−0.163503 + 0.986543i \(0.552279\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 3078.38 1.59523
\(156\) 0 0
\(157\) 3114.78 1.58336 0.791678 0.610939i \(-0.209208\pi\)
0.791678 + 0.610939i \(0.209208\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 877.430 0.429511
\(162\) 0 0
\(163\) −2413.07 −1.15955 −0.579774 0.814777i \(-0.696859\pi\)
−0.579774 + 0.814777i \(0.696859\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −610.475 −0.282874 −0.141437 0.989947i \(-0.545172\pi\)
−0.141437 + 0.989947i \(0.545172\pi\)
\(168\) 0 0
\(169\) −805.784 −0.366766
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −3793.81 −1.66727 −0.833636 0.552315i \(-0.813745\pi\)
−0.833636 + 0.552315i \(0.813745\pi\)
\(174\) 0 0
\(175\) 95.9070 0.0414279
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −2804.68 −1.17112 −0.585562 0.810627i \(-0.699126\pi\)
−0.585562 + 0.810627i \(0.699126\pi\)
\(180\) 0 0
\(181\) 3106.04 1.27553 0.637763 0.770232i \(-0.279860\pi\)
0.637763 + 0.770232i \(0.279860\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2741.87 1.08966
\(186\) 0 0
\(187\) 366.598 0.143360
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 261.952 0.0992365 0.0496182 0.998768i \(-0.484200\pi\)
0.0496182 + 0.998768i \(0.484200\pi\)
\(192\) 0 0
\(193\) 4051.07 1.51089 0.755447 0.655210i \(-0.227420\pi\)
0.755447 + 0.655210i \(0.227420\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2874.83 1.03971 0.519855 0.854254i \(-0.325986\pi\)
0.519855 + 0.854254i \(0.325986\pi\)
\(198\) 0 0
\(199\) 3066.97 1.09252 0.546261 0.837615i \(-0.316051\pi\)
0.546261 + 0.837615i \(0.316051\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −247.814 −0.0856804
\(204\) 0 0
\(205\) −3568.46 −1.21576
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 2036.23 0.673919
\(210\) 0 0
\(211\) −595.422 −0.194268 −0.0971340 0.995271i \(-0.530968\pi\)
−0.0971340 + 0.995271i \(0.530968\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 71.7808 0.0227693
\(216\) 0 0
\(217\) 2042.56 0.638976
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −393.498 −0.119772
\(222\) 0 0
\(223\) 3779.79 1.13504 0.567520 0.823360i \(-0.307903\pi\)
0.567520 + 0.823360i \(0.307903\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1827.62 0.534376 0.267188 0.963644i \(-0.413906\pi\)
0.267188 + 0.963644i \(0.413906\pi\)
\(228\) 0 0
\(229\) −850.249 −0.245354 −0.122677 0.992447i \(-0.539148\pi\)
−0.122677 + 0.992447i \(0.539148\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 6591.10 1.85321 0.926604 0.376039i \(-0.122714\pi\)
0.926604 + 0.376039i \(0.122714\pi\)
\(234\) 0 0
\(235\) −2644.78 −0.734156
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −182.556 −0.0494083 −0.0247042 0.999695i \(-0.507864\pi\)
−0.0247042 + 0.999695i \(0.507864\pi\)
\(240\) 0 0
\(241\) 1523.90 0.407315 0.203657 0.979042i \(-0.434717\pi\)
0.203657 + 0.979042i \(0.434717\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −516.942 −0.134801
\(246\) 0 0
\(247\) −2185.65 −0.563034
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2357.73 0.592903 0.296451 0.955048i \(-0.404197\pi\)
0.296451 + 0.955048i \(0.404197\pi\)
\(252\) 0 0
\(253\) −4355.71 −1.08238
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2782.55 −0.675372 −0.337686 0.941259i \(-0.609644\pi\)
−0.337686 + 0.941259i \(0.609644\pi\)
\(258\) 0 0
\(259\) 1819.28 0.436465
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2043.78 0.479183 0.239591 0.970874i \(-0.422987\pi\)
0.239591 + 0.970874i \(0.422987\pi\)
\(264\) 0 0
\(265\) −5664.21 −1.31302
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −3452.84 −0.782614 −0.391307 0.920260i \(-0.627977\pi\)
−0.391307 + 0.920260i \(0.627977\pi\)
\(270\) 0 0
\(271\) −2644.29 −0.592728 −0.296364 0.955075i \(-0.595774\pi\)
−0.296364 + 0.955075i \(0.595774\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −476.098 −0.104399
\(276\) 0 0
\(277\) 2679.49 0.581208 0.290604 0.956843i \(-0.406144\pi\)
0.290604 + 0.956843i \(0.406144\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1019.69 0.216476 0.108238 0.994125i \(-0.465479\pi\)
0.108238 + 0.994125i \(0.465479\pi\)
\(282\) 0 0
\(283\) −432.206 −0.0907844 −0.0453922 0.998969i \(-0.514454\pi\)
−0.0453922 + 0.998969i \(0.514454\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2367.73 −0.486979
\(288\) 0 0
\(289\) −4801.70 −0.977346
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2245.92 0.447809 0.223904 0.974611i \(-0.428120\pi\)
0.223904 + 0.974611i \(0.428120\pi\)
\(294\) 0 0
\(295\) 378.638 0.0747293
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4675.33 0.904284
\(300\) 0 0
\(301\) 47.6278 0.00912034
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −609.718 −0.114467
\(306\) 0 0
\(307\) 3197.08 0.594354 0.297177 0.954822i \(-0.403955\pi\)
0.297177 + 0.954822i \(0.403955\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3355.60 −0.611829 −0.305915 0.952059i \(-0.598962\pi\)
−0.305915 + 0.952059i \(0.598962\pi\)
\(312\) 0 0
\(313\) −2256.39 −0.407472 −0.203736 0.979026i \(-0.565308\pi\)
−0.203736 + 0.979026i \(0.565308\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6139.19 1.08773 0.543866 0.839172i \(-0.316960\pi\)
0.543866 + 0.839172i \(0.316960\pi\)
\(318\) 0 0
\(319\) 1230.19 0.215917
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 618.199 0.106494
\(324\) 0 0
\(325\) 511.033 0.0872216
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1754.86 −0.294069
\(330\) 0 0
\(331\) −7029.81 −1.16735 −0.583676 0.811987i \(-0.698386\pi\)
−0.583676 + 0.811987i \(0.698386\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 5081.76 0.828795
\(336\) 0 0
\(337\) 10328.4 1.66951 0.834757 0.550619i \(-0.185608\pi\)
0.834757 + 0.550619i \(0.185608\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −10139.6 −1.61024
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1967.54 0.304389 0.152194 0.988351i \(-0.451366\pi\)
0.152194 + 0.988351i \(0.451366\pi\)
\(348\) 0 0
\(349\) −4365.46 −0.669564 −0.334782 0.942296i \(-0.608663\pi\)
−0.334782 + 0.942296i \(0.608663\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 6071.59 0.915462 0.457731 0.889091i \(-0.348662\pi\)
0.457731 + 0.889091i \(0.348662\pi\)
\(354\) 0 0
\(355\) −3837.53 −0.573732
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9638.04 1.41693 0.708463 0.705748i \(-0.249389\pi\)
0.708463 + 0.705748i \(0.249389\pi\)
\(360\) 0 0
\(361\) −3425.27 −0.499384
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −6132.61 −0.879439
\(366\) 0 0
\(367\) −522.725 −0.0743488 −0.0371744 0.999309i \(-0.511836\pi\)
−0.0371744 + 0.999309i \(0.511836\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3758.30 −0.525934
\(372\) 0 0
\(373\) 3229.84 0.448351 0.224175 0.974549i \(-0.428031\pi\)
0.224175 + 0.974549i \(0.428031\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1320.46 −0.180390
\(378\) 0 0
\(379\) −6639.71 −0.899892 −0.449946 0.893056i \(-0.648557\pi\)
−0.449946 + 0.893056i \(0.648557\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14224.4 −1.89774 −0.948871 0.315664i \(-0.897773\pi\)
−0.948871 + 0.315664i \(0.897773\pi\)
\(384\) 0 0
\(385\) 2566.19 0.339701
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −2921.82 −0.380828 −0.190414 0.981704i \(-0.560983\pi\)
−0.190414 + 0.981704i \(0.560983\pi\)
\(390\) 0 0
\(391\) −1322.39 −0.171039
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −7318.33 −0.932215
\(396\) 0 0
\(397\) 811.940 0.102645 0.0513226 0.998682i \(-0.483656\pi\)
0.0513226 + 0.998682i \(0.483656\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2338.63 −0.291237 −0.145618 0.989341i \(-0.546517\pi\)
−0.145618 + 0.989341i \(0.546517\pi\)
\(402\) 0 0
\(403\) 10883.6 1.34529
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9031.21 −1.09990
\(408\) 0 0
\(409\) −2727.57 −0.329755 −0.164877 0.986314i \(-0.552723\pi\)
−0.164877 + 0.986314i \(0.552723\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 251.233 0.0299331
\(414\) 0 0
\(415\) −14077.6 −1.66516
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 13306.3 1.55144 0.775721 0.631076i \(-0.217386\pi\)
0.775721 + 0.631076i \(0.217386\pi\)
\(420\) 0 0
\(421\) −11007.5 −1.27428 −0.637138 0.770750i \(-0.719882\pi\)
−0.637138 + 0.770750i \(0.719882\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −144.543 −0.0164974
\(426\) 0 0
\(427\) −404.558 −0.0458500
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6525.62 −0.729300 −0.364650 0.931145i \(-0.618811\pi\)
−0.364650 + 0.931145i \(0.618811\pi\)
\(432\) 0 0
\(433\) −11716.3 −1.30034 −0.650171 0.759788i \(-0.725303\pi\)
−0.650171 + 0.759788i \(0.725303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7345.10 −0.804036
\(438\) 0 0
\(439\) 14611.4 1.58853 0.794264 0.607573i \(-0.207857\pi\)
0.794264 + 0.607573i \(0.207857\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −15239.8 −1.63446 −0.817228 0.576314i \(-0.804490\pi\)
−0.817228 + 0.576314i \(0.804490\pi\)
\(444\) 0 0
\(445\) −3724.50 −0.396760
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −10678.8 −1.12241 −0.561206 0.827676i \(-0.689662\pi\)
−0.561206 + 0.827676i \(0.689662\pi\)
\(450\) 0 0
\(451\) 11753.8 1.22720
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2754.49 −0.283807
\(456\) 0 0
\(457\) 4228.23 0.432797 0.216399 0.976305i \(-0.430569\pi\)
0.216399 + 0.976305i \(0.430569\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −910.121 −0.0919492 −0.0459746 0.998943i \(-0.514639\pi\)
−0.0459746 + 0.998943i \(0.514639\pi\)
\(462\) 0 0
\(463\) −4456.16 −0.447290 −0.223645 0.974671i \(-0.571796\pi\)
−0.223645 + 0.974671i \(0.571796\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4429.42 −0.438907 −0.219453 0.975623i \(-0.570427\pi\)
−0.219453 + 0.975623i \(0.570427\pi\)
\(468\) 0 0
\(469\) 3371.84 0.331977
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −236.432 −0.0229835
\(474\) 0 0
\(475\) −802.851 −0.0775523
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2752.85 0.262591 0.131296 0.991343i \(-0.458086\pi\)
0.131296 + 0.991343i \(0.458086\pi\)
\(480\) 0 0
\(481\) 9693.90 0.918927
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −15253.8 −1.42812
\(486\) 0 0
\(487\) 670.598 0.0623977 0.0311989 0.999513i \(-0.490067\pi\)
0.0311989 + 0.999513i \(0.490067\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −8244.70 −0.757797 −0.378898 0.925438i \(-0.623697\pi\)
−0.378898 + 0.925438i \(0.623697\pi\)
\(492\) 0 0
\(493\) 373.485 0.0341195
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2546.27 −0.229810
\(498\) 0 0
\(499\) −8164.91 −0.732488 −0.366244 0.930519i \(-0.619356\pi\)
−0.366244 + 0.930519i \(0.619356\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8175.59 0.724715 0.362357 0.932039i \(-0.381972\pi\)
0.362357 + 0.932039i \(0.381972\pi\)
\(504\) 0 0
\(505\) 5009.61 0.441435
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 878.448 0.0764961 0.0382480 0.999268i \(-0.487822\pi\)
0.0382480 + 0.999268i \(0.487822\pi\)
\(510\) 0 0
\(511\) −4069.09 −0.352262
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −21095.3 −1.80499
\(516\) 0 0
\(517\) 8711.42 0.741060
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −11712.6 −0.984910 −0.492455 0.870338i \(-0.663900\pi\)
−0.492455 + 0.870338i \(0.663900\pi\)
\(522\) 0 0
\(523\) 7341.82 0.613834 0.306917 0.951736i \(-0.400703\pi\)
0.306917 + 0.951736i \(0.400703\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3078.38 −0.254452
\(528\) 0 0
\(529\) 3544.92 0.291355
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −12616.3 −1.02528
\(534\) 0 0
\(535\) −12308.9 −0.994690
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1702.71 0.136068
\(540\) 0 0
\(541\) −15868.7 −1.26109 −0.630545 0.776153i \(-0.717169\pi\)
−0.630545 + 0.776153i \(0.717169\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 14107.0 1.10877
\(546\) 0 0
\(547\) −2315.26 −0.180975 −0.0904875 0.995898i \(-0.528843\pi\)
−0.0904875 + 0.995898i \(0.528843\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2074.49 0.160392
\(552\) 0 0
\(553\) −4855.84 −0.373402
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 4819.05 0.366588 0.183294 0.983058i \(-0.441324\pi\)
0.183294 + 0.983058i \(0.441324\pi\)
\(558\) 0 0
\(559\) 253.781 0.0192018
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2540.86 0.190203 0.0951017 0.995468i \(-0.469682\pi\)
0.0951017 + 0.995468i \(0.469682\pi\)
\(564\) 0 0
\(565\) 9564.25 0.712161
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 24220.0 1.78445 0.892227 0.451587i \(-0.149142\pi\)
0.892227 + 0.451587i \(0.149142\pi\)
\(570\) 0 0
\(571\) 11772.1 0.862778 0.431389 0.902166i \(-0.358024\pi\)
0.431389 + 0.902166i \(0.358024\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1717.38 0.124556
\(576\) 0 0
\(577\) 10584.3 0.763655 0.381827 0.924234i \(-0.375295\pi\)
0.381827 + 0.924234i \(0.375295\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9340.74 −0.666987
\(582\) 0 0
\(583\) 18656.8 1.32536
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −8712.63 −0.612621 −0.306311 0.951932i \(-0.599095\pi\)
−0.306311 + 0.951932i \(0.599095\pi\)
\(588\) 0 0
\(589\) −17098.6 −1.19615
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 15362.9 1.06387 0.531937 0.846784i \(-0.321464\pi\)
0.531937 + 0.846784i \(0.321464\pi\)
\(594\) 0 0
\(595\) 779.093 0.0536802
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 26003.8 1.77377 0.886883 0.461994i \(-0.152866\pi\)
0.886883 + 0.461994i \(0.152866\pi\)
\(600\) 0 0
\(601\) 20567.7 1.39596 0.697982 0.716115i \(-0.254082\pi\)
0.697982 + 0.716115i \(0.254082\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1302.85 0.0875512
\(606\) 0 0
\(607\) −19642.1 −1.31342 −0.656711 0.754142i \(-0.728053\pi\)
−0.656711 + 0.754142i \(0.728053\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −9350.65 −0.619127
\(612\) 0 0
\(613\) 8454.59 0.557060 0.278530 0.960428i \(-0.410153\pi\)
0.278530 + 0.960428i \(0.410153\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24168.4 1.57696 0.788479 0.615061i \(-0.210869\pi\)
0.788479 + 0.615061i \(0.210869\pi\)
\(618\) 0 0
\(619\) 2037.56 0.132305 0.0661523 0.997810i \(-0.478928\pi\)
0.0661523 + 0.997810i \(0.478928\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2471.27 −0.158923
\(624\) 0 0
\(625\) −13724.7 −0.878378
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2741.87 −0.173808
\(630\) 0 0
\(631\) −12339.5 −0.778489 −0.389244 0.921135i \(-0.627264\pi\)
−0.389244 + 0.921135i \(0.627264\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −18091.8 −1.13063
\(636\) 0 0
\(637\) −1827.65 −0.113680
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 10222.6 0.629906 0.314953 0.949107i \(-0.398011\pi\)
0.314953 + 0.949107i \(0.398011\pi\)
\(642\) 0 0
\(643\) 1211.75 0.0743187 0.0371594 0.999309i \(-0.488169\pi\)
0.0371594 + 0.999309i \(0.488169\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2817.22 −0.171184 −0.0855922 0.996330i \(-0.527278\pi\)
−0.0855922 + 0.996330i \(0.527278\pi\)
\(648\) 0 0
\(649\) −1247.16 −0.0754320
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −20986.2 −1.25766 −0.628831 0.777542i \(-0.716466\pi\)
−0.628831 + 0.777542i \(0.716466\pi\)
\(654\) 0 0
\(655\) −4964.87 −0.296173
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2384.09 −0.140927 −0.0704635 0.997514i \(-0.522448\pi\)
−0.0704635 + 0.997514i \(0.522448\pi\)
\(660\) 0 0
\(661\) −7577.10 −0.445862 −0.222931 0.974834i \(-0.571562\pi\)
−0.222931 + 0.974834i \(0.571562\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 4327.40 0.252345
\(666\) 0 0
\(667\) −4437.54 −0.257605
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2008.30 0.115543
\(672\) 0 0
\(673\) 11724.6 0.671547 0.335774 0.941943i \(-0.391002\pi\)
0.335774 + 0.941943i \(0.391002\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32304.3 −1.83390 −0.916952 0.398997i \(-0.869358\pi\)
−0.916952 + 0.398997i \(0.869358\pi\)
\(678\) 0 0
\(679\) −10121.1 −0.572038
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 33367.1 1.86934 0.934669 0.355519i \(-0.115696\pi\)
0.934669 + 0.355519i \(0.115696\pi\)
\(684\) 0 0
\(685\) −4683.18 −0.261219
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −20025.8 −1.10729
\(690\) 0 0
\(691\) 1043.67 0.0574577 0.0287288 0.999587i \(-0.490854\pi\)
0.0287288 + 0.999587i \(0.490854\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 17618.0 0.961567
\(696\) 0 0
\(697\) 3568.46 0.193924
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 11305.7 0.609143 0.304572 0.952489i \(-0.401487\pi\)
0.304572 + 0.952489i \(0.401487\pi\)
\(702\) 0 0
\(703\) −15229.4 −0.817055
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3323.97 0.176818
\(708\) 0 0
\(709\) −13306.8 −0.704860 −0.352430 0.935838i \(-0.614645\pi\)
−0.352430 + 0.935838i \(0.614645\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 36575.6 1.92113
\(714\) 0 0
\(715\) 13673.7 0.715201
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 10701.2 0.555062 0.277531 0.960717i \(-0.410484\pi\)
0.277531 + 0.960717i \(0.410484\pi\)
\(720\) 0 0
\(721\) −13997.1 −0.722996
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −485.042 −0.0248469
\(726\) 0 0
\(727\) 2121.14 0.108210 0.0541051 0.998535i \(-0.482769\pi\)
0.0541051 + 0.998535i \(0.482769\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −71.7808 −0.00363189
\(732\) 0 0
\(733\) −21584.0 −1.08762 −0.543809 0.839209i \(-0.683019\pi\)
−0.543809 + 0.839209i \(0.683019\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −16738.4 −0.836588
\(738\) 0 0
\(739\) 9945.21 0.495048 0.247524 0.968882i \(-0.420383\pi\)
0.247524 + 0.968882i \(0.420383\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2867.01 0.141562 0.0707808 0.997492i \(-0.477451\pi\)
0.0707808 + 0.997492i \(0.477451\pi\)
\(744\) 0 0
\(745\) 7847.71 0.385930
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −8167.15 −0.398426
\(750\) 0 0
\(751\) 10824.1 0.525934 0.262967 0.964805i \(-0.415299\pi\)
0.262967 + 0.964805i \(0.415299\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6401.26 0.308564
\(756\) 0 0
\(757\) −14512.0 −0.696761 −0.348381 0.937353i \(-0.613268\pi\)
−0.348381 + 0.937353i \(0.613268\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 33075.8 1.57556 0.787778 0.615959i \(-0.211231\pi\)
0.787778 + 0.615959i \(0.211231\pi\)
\(762\) 0 0
\(763\) 9360.23 0.444120
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1338.68 0.0630206
\(768\) 0 0
\(769\) 6728.44 0.315518 0.157759 0.987478i \(-0.449573\pi\)
0.157759 + 0.987478i \(0.449573\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 24233.3 1.12757 0.563784 0.825922i \(-0.309345\pi\)
0.563784 + 0.825922i \(0.309345\pi\)
\(774\) 0 0
\(775\) 3997.87 0.185300
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 19820.6 0.911615
\(780\) 0 0
\(781\) 12640.1 0.579127
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −32860.5 −1.49406
\(786\) 0 0
\(787\) 17200.4 0.779069 0.389535 0.921012i \(-0.372636\pi\)
0.389535 + 0.921012i \(0.372636\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 6346.05 0.285258
\(792\) 0 0
\(793\) −2155.66 −0.0965318
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 4208.87 0.187059 0.0935295 0.995617i \(-0.470185\pi\)
0.0935295 + 0.995617i \(0.470185\pi\)
\(798\) 0 0
\(799\) 2644.78 0.117104
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 20199.7 0.887709
\(804\) 0 0
\(805\) −9256.74 −0.405289
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 23632.1 1.02702 0.513511 0.858083i \(-0.328344\pi\)
0.513511 + 0.858083i \(0.328344\pi\)
\(810\) 0 0
\(811\) −28425.1 −1.23075 −0.615377 0.788233i \(-0.710996\pi\)
−0.615377 + 0.788233i \(0.710996\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 25457.5 1.09416
\(816\) 0 0
\(817\) −398.699 −0.0170731
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −39409.6 −1.67528 −0.837640 0.546223i \(-0.816065\pi\)
−0.837640 + 0.546223i \(0.816065\pi\)
\(822\) 0 0
\(823\) −16346.6 −0.692352 −0.346176 0.938170i \(-0.612520\pi\)
−0.346176 + 0.938170i \(0.612520\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3738.87 −0.157211 −0.0786054 0.996906i \(-0.525047\pi\)
−0.0786054 + 0.996906i \(0.525047\pi\)
\(828\) 0 0
\(829\) −45196.2 −1.89352 −0.946761 0.321937i \(-0.895666\pi\)
−0.946761 + 0.321937i \(0.895666\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 516.942 0.0215018
\(834\) 0 0
\(835\) 6440.41 0.266922
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 15899.7 0.654254 0.327127 0.944980i \(-0.393920\pi\)
0.327127 + 0.944980i \(0.393920\pi\)
\(840\) 0 0
\(841\) −23135.7 −0.948612
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8500.89 0.346082
\(846\) 0 0
\(847\) 864.465 0.0350689
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 32577.4 1.31227
\(852\) 0 0
\(853\) 33926.7 1.36182 0.680908 0.732369i \(-0.261585\pi\)
0.680908 + 0.732369i \(0.261585\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 35432.4 1.41231 0.706154 0.708058i \(-0.250428\pi\)
0.706154 + 0.708058i \(0.250428\pi\)
\(858\) 0 0
\(859\) 6780.17 0.269309 0.134655 0.990893i \(-0.457008\pi\)
0.134655 + 0.990893i \(0.457008\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −30675.1 −1.20995 −0.604977 0.796243i \(-0.706818\pi\)
−0.604977 + 0.796243i \(0.706818\pi\)
\(864\) 0 0
\(865\) 40024.1 1.57325
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 24105.2 0.940981
\(870\) 0 0
\(871\) 17966.6 0.698938
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10242.9 −0.395741
\(876\) 0 0
\(877\) 40861.3 1.57330 0.786652 0.617397i \(-0.211813\pi\)
0.786652 + 0.617397i \(0.211813\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 43839.0 1.67647 0.838236 0.545308i \(-0.183587\pi\)
0.838236 + 0.545308i \(0.183587\pi\)
\(882\) 0 0
\(883\) −44625.1 −1.70074 −0.850371 0.526183i \(-0.823623\pi\)
−0.850371 + 0.526183i \(0.823623\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −43967.5 −1.66436 −0.832178 0.554509i \(-0.812906\pi\)
−0.832178 + 0.554509i \(0.812906\pi\)
\(888\) 0 0
\(889\) −12004.2 −0.452878
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 14690.2 0.550491
\(894\) 0 0
\(895\) 29588.9 1.10508
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −10330.1 −0.383234
\(900\) 0 0
\(901\) 5664.21 0.209436
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −32768.2 −1.20359
\(906\) 0 0
\(907\) 13584.3 0.497309 0.248654 0.968592i \(-0.420012\pi\)
0.248654 + 0.968592i \(0.420012\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −16421.6 −0.597226 −0.298613 0.954374i \(-0.596524\pi\)
−0.298613 + 0.954374i \(0.596524\pi\)
\(912\) 0 0
\(913\) 46369.0 1.68082
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3294.28 −0.118633
\(918\) 0 0
\(919\) 29487.3 1.05843 0.529214 0.848488i \(-0.322487\pi\)
0.529214 + 0.848488i \(0.322487\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −13567.6 −0.483839
\(924\) 0 0
\(925\) 3560.85 0.126573
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3441.85 −0.121554 −0.0607769 0.998151i \(-0.519358\pi\)
−0.0607769 + 0.998151i \(0.519358\pi\)
\(930\) 0 0
\(931\) 2871.30 0.101077
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3867.55 −0.135275
\(936\) 0 0
\(937\) 5646.60 0.196869 0.0984346 0.995144i \(-0.468616\pi\)
0.0984346 + 0.995144i \(0.468616\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 44680.1 1.54785 0.773927 0.633275i \(-0.218290\pi\)
0.773927 + 0.633275i \(0.218290\pi\)
\(942\) 0 0
\(943\) −42398.4 −1.46414
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −48924.6 −1.67881 −0.839406 0.543505i \(-0.817097\pi\)
−0.839406 + 0.543505i \(0.817097\pi\)
\(948\) 0 0
\(949\) −21681.9 −0.741647
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −52014.3 −1.76801 −0.884003 0.467482i \(-0.845161\pi\)
−0.884003 + 0.467482i \(0.845161\pi\)
\(954\) 0 0
\(955\) −2763.55 −0.0936401
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3107.37 −0.104632
\(960\) 0 0
\(961\) 55352.8 1.85804
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −42738.2 −1.42569
\(966\) 0 0
\(967\) 47117.7 1.56691 0.783456 0.621448i \(-0.213455\pi\)
0.783456 + 0.621448i \(0.213455\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −8195.04 −0.270846 −0.135423 0.990788i \(-0.543239\pi\)
−0.135423 + 0.990788i \(0.543239\pi\)
\(972\) 0 0
\(973\) 11689.9 0.385159
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −4643.51 −0.152056 −0.0760282 0.997106i \(-0.524224\pi\)
−0.0760282 + 0.997106i \(0.524224\pi\)
\(978\) 0 0
\(979\) 12267.8 0.400490
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 43986.5 1.42721 0.713607 0.700546i \(-0.247060\pi\)
0.713607 + 0.700546i \(0.247060\pi\)
\(984\) 0 0
\(985\) −30329.0 −0.981077
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 852.859 0.0274210
\(990\) 0 0
\(991\) −1595.21 −0.0511337 −0.0255668 0.999673i \(-0.508139\pi\)
−0.0255668 + 0.999673i \(0.508139\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −32356.0 −1.03091
\(996\) 0 0
\(997\) 21501.2 0.682998 0.341499 0.939882i \(-0.389065\pi\)
0.341499 + 0.939882i \(0.389065\pi\)
\(998\) 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 1008.4.a.ba.1.1 2
3.2 odd 2 336.4.a.m.1.2 2
4.3 odd 2 63.4.a.e.1.2 2
12.11 even 2 21.4.a.c.1.1 2
20.19 odd 2 1575.4.a.p.1.1 2
21.20 even 2 2352.4.a.bz.1.1 2
24.5 odd 2 1344.4.a.bo.1.1 2
24.11 even 2 1344.4.a.bg.1.1 2
28.3 even 6 441.4.e.p.226.1 4
28.11 odd 6 441.4.e.q.226.1 4
28.19 even 6 441.4.e.p.361.1 4
28.23 odd 6 441.4.e.q.361.1 4
28.27 even 2 441.4.a.r.1.2 2
60.23 odd 4 525.4.d.g.274.4 4
60.47 odd 4 525.4.d.g.274.1 4
60.59 even 2 525.4.a.n.1.2 2
84.11 even 6 147.4.e.l.79.2 4
84.23 even 6 147.4.e.l.67.2 4
84.47 odd 6 147.4.e.m.67.2 4
84.59 odd 6 147.4.e.m.79.2 4
84.83 odd 2 147.4.a.i.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.4.a.c.1.1 2 12.11 even 2
63.4.a.e.1.2 2 4.3 odd 2
147.4.a.i.1.1 2 84.83 odd 2
147.4.e.l.67.2 4 84.23 even 6
147.4.e.l.79.2 4 84.11 even 6
147.4.e.m.67.2 4 84.47 odd 6
147.4.e.m.79.2 4 84.59 odd 6
336.4.a.m.1.2 2 3.2 odd 2
441.4.a.r.1.2 2 28.27 even 2
441.4.e.p.226.1 4 28.3 even 6
441.4.e.p.361.1 4 28.19 even 6
441.4.e.q.226.1 4 28.11 odd 6
441.4.e.q.361.1 4 28.23 odd 6
525.4.a.n.1.2 2 60.59 even 2
525.4.d.g.274.1 4 60.47 odd 4
525.4.d.g.274.4 4 60.23 odd 4
1008.4.a.ba.1.1 2 1.1 even 1 trivial
1344.4.a.bg.1.1 2 24.11 even 2
1344.4.a.bo.1.1 2 24.5 odd 2
1575.4.a.p.1.1 2 20.19 odd 2
2352.4.a.bz.1.1 2 21.20 even 2