Properties

Label 576.5.m.a.271.6
Level $576$
Weight $5$
Character 576.271
Analytic conductor $59.541$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,5,Mod(271,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.271");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 576.m (of order \(4\), degree \(2\), not minimal)

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: no
Analytic conductor: \(59.5410987363\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 271.6
Root \(1.03712 - 2.63142i\) of defining polynomial
Character \(\chi\) \(=\) 576.271
Dual form 576.5.m.a.559.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(14.6016 + 14.6016i) q^{5} +24.0210 q^{7} +O(q^{10})\) \(q+(14.6016 + 14.6016i) q^{5} +24.0210 q^{7} +(61.7287 - 61.7287i) q^{11} +(-37.5611 + 37.5611i) q^{13} -96.8718 q^{17} +(156.751 + 156.751i) q^{19} +959.783 q^{23} -198.587i q^{25} +(350.180 - 350.180i) q^{29} +237.885i q^{31} +(350.744 + 350.744i) q^{35} +(-560.815 - 560.815i) q^{37} -1802.95i q^{41} +(-206.090 + 206.090i) q^{43} +1599.92i q^{47} -1823.99 q^{49} +(2234.17 + 2234.17i) q^{53} +1802.67 q^{55} +(2353.11 - 2353.11i) q^{59} +(-4443.45 + 4443.45i) q^{61} -1096.90 q^{65} +(3995.40 + 3995.40i) q^{67} +4929.25 q^{71} +2651.57i q^{73} +(1482.78 - 1482.78i) q^{77} -8792.34i q^{79} +(-228.231 - 228.231i) q^{83} +(-1414.48 - 1414.48i) q^{85} +10596.7i q^{89} +(-902.254 + 902.254i) q^{91} +4577.63i q^{95} +11048.3 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 2 q^{5} + 4 q^{7} + 94 q^{11} - 2 q^{13} + 4 q^{17} + 706 q^{19} + 1148 q^{23} - 862 q^{29} + 1340 q^{35} - 1826 q^{37} - 1694 q^{43} + 682 q^{49} + 482 q^{53} + 11780 q^{55} - 2786 q^{59} - 3778 q^{61} + 2020 q^{65} - 7998 q^{67} + 19964 q^{71} + 9508 q^{77} - 17282 q^{83} + 9948 q^{85} + 28036 q^{91} - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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
\(5\) 14.6016 + 14.6016i 0.584063 + 0.584063i 0.936017 0.351954i \(-0.114483\pi\)
−0.351954 + 0.936017i \(0.614483\pi\)
\(6\) 0 0
\(7\) 24.0210 0.490224 0.245112 0.969495i \(-0.421175\pi\)
0.245112 + 0.969495i \(0.421175\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 61.7287 61.7287i 0.510154 0.510154i −0.404419 0.914574i \(-0.632526\pi\)
0.914574 + 0.404419i \(0.132526\pi\)
\(12\) 0 0
\(13\) −37.5611 + 37.5611i −0.222255 + 0.222255i −0.809447 0.587192i \(-0.800233\pi\)
0.587192 + 0.809447i \(0.300233\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −96.8718 −0.335197 −0.167598 0.985855i \(-0.553601\pi\)
−0.167598 + 0.985855i \(0.553601\pi\)
\(18\) 0 0
\(19\) 156.751 + 156.751i 0.434214 + 0.434214i 0.890059 0.455845i \(-0.150663\pi\)
−0.455845 + 0.890059i \(0.650663\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 959.783 1.81433 0.907167 0.420770i \(-0.138240\pi\)
0.907167 + 0.420770i \(0.138240\pi\)
\(24\) 0 0
\(25\) 198.587i 0.317740i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 350.180 350.180i 0.416385 0.416385i −0.467571 0.883956i \(-0.654871\pi\)
0.883956 + 0.467571i \(0.154871\pi\)
\(30\) 0 0
\(31\) 237.885i 0.247539i 0.992311 + 0.123769i \(0.0394983\pi\)
−0.992311 + 0.123769i \(0.960502\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 350.744 + 350.744i 0.286322 + 0.286322i
\(36\) 0 0
\(37\) −560.815 560.815i −0.409653 0.409653i 0.471965 0.881617i \(-0.343545\pi\)
−0.881617 + 0.471965i \(0.843545\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1802.95i 1.07255i −0.844044 0.536274i \(-0.819831\pi\)
0.844044 0.536274i \(-0.180169\pi\)
\(42\) 0 0
\(43\) −206.090 + 206.090i −0.111460 + 0.111460i −0.760637 0.649177i \(-0.775113\pi\)
0.649177 + 0.760637i \(0.275113\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1599.92i 0.724274i 0.932125 + 0.362137i \(0.117953\pi\)
−0.932125 + 0.362137i \(0.882047\pi\)
\(48\) 0 0
\(49\) −1823.99 −0.759681
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2234.17 + 2234.17i 0.795360 + 0.795360i 0.982360 0.187000i \(-0.0598765\pi\)
−0.187000 + 0.982360i \(0.559876\pi\)
\(54\) 0 0
\(55\) 1802.67 0.595925
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2353.11 2353.11i 0.675988 0.675988i −0.283102 0.959090i \(-0.591364\pi\)
0.959090 + 0.283102i \(0.0913636\pi\)
\(60\) 0 0
\(61\) −4443.45 + 4443.45i −1.19415 + 1.19415i −0.218264 + 0.975890i \(0.570039\pi\)
−0.975890 + 0.218264i \(0.929961\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1096.90 −0.259622
\(66\) 0 0
\(67\) 3995.40 + 3995.40i 0.890042 + 0.890042i 0.994527 0.104485i \(-0.0333193\pi\)
−0.104485 + 0.994527i \(0.533319\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4929.25 0.977832 0.488916 0.872331i \(-0.337392\pi\)
0.488916 + 0.872331i \(0.337392\pi\)
\(72\) 0 0
\(73\) 2651.57i 0.497574i 0.968558 + 0.248787i \(0.0800319\pi\)
−0.968558 + 0.248787i \(0.919968\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1482.78 1482.78i 0.250090 0.250090i
\(78\) 0 0
\(79\) 8792.34i 1.40880i −0.709801 0.704402i \(-0.751215\pi\)
0.709801 0.704402i \(-0.248785\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −228.231 228.231i −0.0331298 0.0331298i 0.690348 0.723478i \(-0.257458\pi\)
−0.723478 + 0.690348i \(0.757458\pi\)
\(84\) 0 0
\(85\) −1414.48 1414.48i −0.195776 0.195776i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 10596.7i 1.33780i 0.743353 + 0.668899i \(0.233234\pi\)
−0.743353 + 0.668899i \(0.766766\pi\)
\(90\) 0 0
\(91\) −902.254 + 902.254i −0.108955 + 0.108955i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4577.63i 0.507217i
\(96\) 0 0
\(97\) 11048.3 1.17422 0.587111 0.809506i \(-0.300265\pi\)
0.587111 + 0.809506i \(0.300265\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7543.12 + 7543.12i 0.739449 + 0.739449i 0.972471 0.233022i \(-0.0748615\pi\)
−0.233022 + 0.972471i \(0.574861\pi\)
\(102\) 0 0
\(103\) 6124.81 0.577322 0.288661 0.957431i \(-0.406790\pi\)
0.288661 + 0.957431i \(0.406790\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4636.79 4636.79i 0.404995 0.404995i −0.474994 0.879989i \(-0.657550\pi\)
0.879989 + 0.474994i \(0.157550\pi\)
\(108\) 0 0
\(109\) 15235.6 15235.6i 1.28235 1.28235i 0.343022 0.939327i \(-0.388549\pi\)
0.939327 0.343022i \(-0.111451\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2902.13 −0.227279 −0.113639 0.993522i \(-0.536251\pi\)
−0.113639 + 0.993522i \(0.536251\pi\)
\(114\) 0 0
\(115\) 14014.4 + 14014.4i 1.05969 + 1.05969i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2326.95 −0.164321
\(120\) 0 0
\(121\) 7020.14i 0.479485i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12025.7 12025.7i 0.769644 0.769644i
\(126\) 0 0
\(127\) 3992.46i 0.247533i −0.992311 0.123766i \(-0.960503\pi\)
0.992311 0.123766i \(-0.0394974\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16640.1 + 16640.1i 0.969645 + 0.969645i 0.999553 0.0299081i \(-0.00952147\pi\)
−0.0299081 + 0.999553i \(0.509521\pi\)
\(132\) 0 0
\(133\) 3765.31 + 3765.31i 0.212862 + 0.212862i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10746.6i 0.572573i 0.958144 + 0.286286i \(0.0924209\pi\)
−0.958144 + 0.286286i \(0.907579\pi\)
\(138\) 0 0
\(139\) 7583.76 7583.76i 0.392514 0.392514i −0.483069 0.875582i \(-0.660478\pi\)
0.875582 + 0.483069i \(0.160478\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4637.20i 0.226769i
\(144\) 0 0
\(145\) 10226.4 0.486390
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3385.37 3385.37i −0.152487 0.152487i 0.626741 0.779228i \(-0.284389\pi\)
−0.779228 + 0.626741i \(0.784389\pi\)
\(150\) 0 0
\(151\) −21697.8 −0.951617 −0.475809 0.879549i \(-0.657845\pi\)
−0.475809 + 0.879549i \(0.657845\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3473.49 + 3473.49i −0.144578 + 0.144578i
\(156\) 0 0
\(157\) 14212.7 14212.7i 0.576603 0.576603i −0.357363 0.933966i \(-0.616324\pi\)
0.933966 + 0.357363i \(0.116324\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 23054.9 0.889430
\(162\) 0 0
\(163\) 7450.28 + 7450.28i 0.280412 + 0.280412i 0.833273 0.552861i \(-0.186464\pi\)
−0.552861 + 0.833273i \(0.686464\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3997.25 −0.143327 −0.0716635 0.997429i \(-0.522831\pi\)
−0.0716635 + 0.997429i \(0.522831\pi\)
\(168\) 0 0
\(169\) 25739.3i 0.901205i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 16996.8 16996.8i 0.567903 0.567903i −0.363638 0.931540i \(-0.618465\pi\)
0.931540 + 0.363638i \(0.118465\pi\)
\(174\) 0 0
\(175\) 4770.26i 0.155764i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 24121.3 + 24121.3i 0.752826 + 0.752826i 0.975006 0.222180i \(-0.0713173\pi\)
−0.222180 + 0.975006i \(0.571317\pi\)
\(180\) 0 0
\(181\) 13837.8 + 13837.8i 0.422386 + 0.422386i 0.886025 0.463638i \(-0.153456\pi\)
−0.463638 + 0.886025i \(0.653456\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 16377.6i 0.478526i
\(186\) 0 0
\(187\) −5979.77 + 5979.77i −0.171002 + 0.171002i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 11717.4i 0.321193i −0.987020 0.160596i \(-0.948658\pi\)
0.987020 0.160596i \(-0.0513417\pi\)
\(192\) 0 0
\(193\) −68633.2 −1.84255 −0.921276 0.388910i \(-0.872852\pi\)
−0.921276 + 0.388910i \(0.872852\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22885.3 + 22885.3i 0.589689 + 0.589689i 0.937547 0.347858i \(-0.113091\pi\)
−0.347858 + 0.937547i \(0.613091\pi\)
\(198\) 0 0
\(199\) −59936.9 −1.51352 −0.756761 0.653692i \(-0.773219\pi\)
−0.756761 + 0.653692i \(0.773219\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8411.65 8411.65i 0.204122 0.204122i
\(204\) 0 0
\(205\) 26326.0 26326.0i 0.626436 0.626436i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 19352.1 0.443032
\(210\) 0 0
\(211\) 12558.8 + 12558.8i 0.282086 + 0.282086i 0.833941 0.551854i \(-0.186080\pi\)
−0.551854 + 0.833941i \(0.686080\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −6018.47 −0.130199
\(216\) 0 0
\(217\) 5714.22i 0.121349i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 3638.61 3638.61i 0.0744992 0.0744992i
\(222\) 0 0
\(223\) 22761.5i 0.457711i 0.973460 + 0.228856i \(0.0734983\pi\)
−0.973460 + 0.228856i \(0.926502\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6480.30 + 6480.30i 0.125760 + 0.125760i 0.767186 0.641425i \(-0.221657\pi\)
−0.641425 + 0.767186i \(0.721657\pi\)
\(228\) 0 0
\(229\) 36068.6 + 36068.6i 0.687795 + 0.687795i 0.961744 0.273949i \(-0.0883301\pi\)
−0.273949 + 0.961744i \(0.588330\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 68226.4i 1.25673i 0.777920 + 0.628363i \(0.216275\pi\)
−0.777920 + 0.628363i \(0.783725\pi\)
\(234\) 0 0
\(235\) −23361.4 + 23361.4i −0.423022 + 0.423022i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 100556.i 1.76040i −0.474599 0.880202i \(-0.657407\pi\)
0.474599 0.880202i \(-0.342593\pi\)
\(240\) 0 0
\(241\) −35563.1 −0.612302 −0.306151 0.951983i \(-0.599041\pi\)
−0.306151 + 0.951983i \(0.599041\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −26633.2 26633.2i −0.443702 0.443702i
\(246\) 0 0
\(247\) −11775.5 −0.193013
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −29206.3 + 29206.3i −0.463585 + 0.463585i −0.899829 0.436244i \(-0.856309\pi\)
0.436244 + 0.899829i \(0.356309\pi\)
\(252\) 0 0
\(253\) 59246.1 59246.1i 0.925591 0.925591i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2932.77 −0.0444029 −0.0222015 0.999754i \(-0.507068\pi\)
−0.0222015 + 0.999754i \(0.507068\pi\)
\(258\) 0 0
\(259\) −13471.3 13471.3i −0.200821 0.200821i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 23253.5 0.336184 0.168092 0.985771i \(-0.446239\pi\)
0.168092 + 0.985771i \(0.446239\pi\)
\(264\) 0 0
\(265\) 65244.7i 0.929081i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −56836.3 + 56836.3i −0.785455 + 0.785455i −0.980745 0.195290i \(-0.937435\pi\)
0.195290 + 0.980745i \(0.437435\pi\)
\(270\) 0 0
\(271\) 91679.6i 1.24834i −0.781287 0.624172i \(-0.785436\pi\)
0.781287 0.624172i \(-0.214564\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −12258.5 12258.5i −0.162096 0.162096i
\(276\) 0 0
\(277\) −75831.0 75831.0i −0.988297 0.988297i 0.0116353 0.999932i \(-0.496296\pi\)
−0.999932 + 0.0116353i \(0.996296\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 77682.2i 0.983805i −0.870650 0.491903i \(-0.836302\pi\)
0.870650 0.491903i \(-0.163698\pi\)
\(282\) 0 0
\(283\) 43834.7 43834.7i 0.547325 0.547325i −0.378341 0.925666i \(-0.623505\pi\)
0.925666 + 0.378341i \(0.123505\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 43308.7i 0.525788i
\(288\) 0 0
\(289\) −74136.9 −0.887643
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −61916.9 61916.9i −0.721231 0.721231i 0.247625 0.968856i \(-0.420350\pi\)
−0.968856 + 0.247625i \(0.920350\pi\)
\(294\) 0 0
\(295\) 68718.4 0.789639
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −36050.5 + 36050.5i −0.403245 + 0.403245i
\(300\) 0 0
\(301\) −4950.47 + 4950.47i −0.0546404 + 0.0546404i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −129763. −1.39492
\(306\) 0 0
\(307\) 99698.5 + 99698.5i 1.05782 + 1.05782i 0.998223 + 0.0595972i \(0.0189816\pi\)
0.0595972 + 0.998223i \(0.481018\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −127678. −1.32006 −0.660031 0.751238i \(-0.729457\pi\)
−0.660031 + 0.751238i \(0.729457\pi\)
\(312\) 0 0
\(313\) 24132.5i 0.246328i 0.992386 + 0.123164i \(0.0393042\pi\)
−0.992386 + 0.123164i \(0.960696\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 63739.0 63739.0i 0.634289 0.634289i −0.314852 0.949141i \(-0.601955\pi\)
0.949141 + 0.314852i \(0.101955\pi\)
\(318\) 0 0
\(319\) 43232.3i 0.424841i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −15184.8 15184.8i −0.145547 0.145547i
\(324\) 0 0
\(325\) 7459.16 + 7459.16i 0.0706193 + 0.0706193i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 38431.6i 0.355056i
\(330\) 0 0
\(331\) 111266. 111266.i 1.01556 1.01556i 0.0156868 0.999877i \(-0.495007\pi\)
0.999877 0.0156868i \(-0.00499346\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 116678.i 1.03968i
\(336\) 0 0
\(337\) −89183.5 −0.785280 −0.392640 0.919692i \(-0.628438\pi\)
−0.392640 + 0.919692i \(0.628438\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 14684.3 + 14684.3i 0.126283 + 0.126283i
\(342\) 0 0
\(343\) −101488. −0.862637
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17075.7 + 17075.7i −0.141814 + 0.141814i −0.774450 0.632635i \(-0.781973\pi\)
0.632635 + 0.774450i \(0.281973\pi\)
\(348\) 0 0
\(349\) −25961.7 + 25961.7i −0.213149 + 0.213149i −0.805604 0.592455i \(-0.798159\pi\)
0.592455 + 0.805604i \(0.298159\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −221897. −1.78075 −0.890374 0.455230i \(-0.849557\pi\)
−0.890374 + 0.455230i \(0.849557\pi\)
\(354\) 0 0
\(355\) 71974.9 + 71974.9i 0.571116 + 0.571116i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −106831. −0.828908 −0.414454 0.910070i \(-0.636027\pi\)
−0.414454 + 0.910070i \(0.636027\pi\)
\(360\) 0 0
\(361\) 81179.1i 0.622917i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −38717.2 + 38717.2i −0.290615 + 0.290615i
\(366\) 0 0
\(367\) 79074.9i 0.587093i −0.955945 0.293546i \(-0.905164\pi\)
0.955945 0.293546i \(-0.0948355\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 53666.8 + 53666.8i 0.389904 + 0.389904i
\(372\) 0 0
\(373\) −86341.4 86341.4i −0.620585 0.620585i 0.325096 0.945681i \(-0.394603\pi\)
−0.945681 + 0.325096i \(0.894603\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 26306.3i 0.185087i
\(378\) 0 0
\(379\) −168223. + 168223.i −1.17114 + 1.17114i −0.189199 + 0.981939i \(0.560589\pi\)
−0.981939 + 0.189199i \(0.939411\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 22177.8i 0.151189i 0.997139 + 0.0755946i \(0.0240855\pi\)
−0.997139 + 0.0755946i \(0.975915\pi\)
\(384\) 0 0
\(385\) 43301.9 0.292137
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −163109. 163109.i −1.07790 1.07790i −0.996698 0.0812004i \(-0.974125\pi\)
−0.0812004 0.996698i \(-0.525875\pi\)
\(390\) 0 0
\(391\) −92975.9 −0.608159
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 128382. 128382.i 0.822831 0.822831i
\(396\) 0 0
\(397\) 110463. 110463.i 0.700868 0.700868i −0.263729 0.964597i \(-0.584953\pi\)
0.964597 + 0.263729i \(0.0849525\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −43913.8 −0.273094 −0.136547 0.990634i \(-0.543601\pi\)
−0.136547 + 0.990634i \(0.543601\pi\)
\(402\) 0 0
\(403\) −8935.22 8935.22i −0.0550168 0.0550168i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −69236.7 −0.417972
\(408\) 0 0
\(409\) 188666.i 1.12784i 0.825830 + 0.563919i \(0.190707\pi\)
−0.825830 + 0.563919i \(0.809293\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 56524.0 56524.0i 0.331385 0.331385i
\(414\) 0 0
\(415\) 6665.07i 0.0386998i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −88556.3 88556.3i −0.504419 0.504419i 0.408389 0.912808i \(-0.366091\pi\)
−0.912808 + 0.408389i \(0.866091\pi\)
\(420\) 0 0
\(421\) −42983.4 42983.4i −0.242514 0.242514i 0.575375 0.817889i \(-0.304856\pi\)
−0.817889 + 0.575375i \(0.804856\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 19237.5i 0.106505i
\(426\) 0 0
\(427\) −106736. + 106736.i −0.585403 + 0.585403i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 163696.i 0.881219i −0.897699 0.440609i \(-0.854762\pi\)
0.897699 0.440609i \(-0.145238\pi\)
\(432\) 0 0
\(433\) 49710.2 0.265137 0.132568 0.991174i \(-0.457678\pi\)
0.132568 + 0.991174i \(0.457678\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 150447. + 150447.i 0.787809 + 0.787809i
\(438\) 0 0
\(439\) −182166. −0.945233 −0.472617 0.881268i \(-0.656690\pi\)
−0.472617 + 0.881268i \(0.656690\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3141.28 + 3141.28i −0.0160066 + 0.0160066i −0.715065 0.699058i \(-0.753603\pi\)
0.699058 + 0.715065i \(0.253603\pi\)
\(444\) 0 0
\(445\) −154729. + 154729.i −0.781359 + 0.781359i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 108328. 0.537341 0.268670 0.963232i \(-0.413416\pi\)
0.268670 + 0.963232i \(0.413416\pi\)
\(450\) 0 0
\(451\) −111294. 111294.i −0.547165 0.547165i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −26348.7 −0.127273
\(456\) 0 0
\(457\) 220908.i 1.05774i −0.848703 0.528870i \(-0.822616\pi\)
0.848703 0.528870i \(-0.177384\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 137539. 137539.i 0.647176 0.647176i −0.305133 0.952310i \(-0.598701\pi\)
0.952310 + 0.305133i \(0.0987010\pi\)
\(462\) 0 0
\(463\) 53332.6i 0.248789i −0.992233 0.124394i \(-0.960301\pi\)
0.992233 0.124394i \(-0.0396988\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −207164. 207164.i −0.949908 0.949908i 0.0488961 0.998804i \(-0.484430\pi\)
−0.998804 + 0.0488961i \(0.984430\pi\)
\(468\) 0 0
\(469\) 95973.3 + 95973.3i 0.436320 + 0.436320i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 25443.3i 0.113724i
\(474\) 0 0
\(475\) 31128.8 31128.8i 0.137967 0.137967i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 269434.i 1.17430i 0.809477 + 0.587152i \(0.199751\pi\)
−0.809477 + 0.587152i \(0.800249\pi\)
\(480\) 0 0
\(481\) 42129.6 0.182095
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 161322. + 161322.i 0.685821 + 0.685821i
\(486\) 0 0
\(487\) 114893. 0.484436 0.242218 0.970222i \(-0.422125\pi\)
0.242218 + 0.970222i \(0.422125\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 83485.8 83485.8i 0.346298 0.346298i −0.512431 0.858728i \(-0.671255\pi\)
0.858728 + 0.512431i \(0.171255\pi\)
\(492\) 0 0
\(493\) −33922.5 + 33922.5i −0.139571 + 0.139571i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 118405. 0.479356
\(498\) 0 0
\(499\) 8291.04 + 8291.04i 0.0332972 + 0.0332972i 0.723559 0.690262i \(-0.242505\pi\)
−0.690262 + 0.723559i \(0.742505\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 302384. 1.19515 0.597575 0.801813i \(-0.296131\pi\)
0.597575 + 0.801813i \(0.296131\pi\)
\(504\) 0 0
\(505\) 220283.i 0.863770i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 41954.6 41954.6i 0.161936 0.161936i −0.621488 0.783424i \(-0.713471\pi\)
0.783424 + 0.621488i \(0.213471\pi\)
\(510\) 0 0
\(511\) 63693.3i 0.243923i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 89431.9 + 89431.9i 0.337193 + 0.337193i
\(516\) 0 0
\(517\) 98761.0 + 98761.0i 0.369492 + 0.369492i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 16852.7i 0.0620860i 0.999518 + 0.0310430i \(0.00988289\pi\)
−0.999518 + 0.0310430i \(0.990117\pi\)
\(522\) 0 0
\(523\) 92911.9 92911.9i 0.339678 0.339678i −0.516568 0.856246i \(-0.672791\pi\)
0.856246 + 0.516568i \(0.172791\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23044.3i 0.0829741i
\(528\) 0 0
\(529\) 641343. 2.29181
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 67720.9 + 67720.9i 0.238379 + 0.238379i
\(534\) 0 0
\(535\) 135409. 0.473086
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −112593. + 112593.i −0.387554 + 0.387554i
\(540\) 0 0
\(541\) −40690.8 + 40690.8i −0.139028 + 0.139028i −0.773196 0.634168i \(-0.781343\pi\)
0.634168 + 0.773196i \(0.281343\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 444928. 1.49795
\(546\) 0 0
\(547\) −222264. 222264.i −0.742839 0.742839i 0.230284 0.973123i \(-0.426034\pi\)
−0.973123 + 0.230284i \(0.926034\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 109782. 0.361600
\(552\) 0 0
\(553\) 211201.i 0.690629i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −223795. + 223795.i −0.721341 + 0.721341i −0.968878 0.247537i \(-0.920379\pi\)
0.247537 + 0.968878i \(0.420379\pi\)
\(558\) 0 0
\(559\) 15481.9i 0.0495451i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 201474. + 201474.i 0.635626 + 0.635626i 0.949474 0.313847i \(-0.101618\pi\)
−0.313847 + 0.949474i \(0.601618\pi\)
\(564\) 0 0
\(565\) −42375.6 42375.6i −0.132745 0.132745i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 473995.i 1.46403i −0.681289 0.732014i \(-0.738580\pi\)
0.681289 0.732014i \(-0.261420\pi\)
\(570\) 0 0
\(571\) −303262. + 303262.i −0.930133 + 0.930133i −0.997714 0.0675806i \(-0.978472\pi\)
0.0675806 + 0.997714i \(0.478472\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 190601.i 0.576486i
\(576\) 0 0
\(577\) −340809. −1.02367 −0.511834 0.859084i \(-0.671034\pi\)
−0.511834 + 0.859084i \(0.671034\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5482.33 5482.33i −0.0162410 0.0162410i
\(582\) 0 0
\(583\) 275824. 0.811512
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −253433. + 253433.i −0.735507 + 0.735507i −0.971705 0.236198i \(-0.924099\pi\)
0.236198 + 0.971705i \(0.424099\pi\)
\(588\) 0 0
\(589\) −37288.7 + 37288.7i −0.107485 + 0.107485i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −117236. −0.333390 −0.166695 0.986009i \(-0.553309\pi\)
−0.166695 + 0.986009i \(0.553309\pi\)
\(594\) 0 0
\(595\) −33977.2 33977.2i −0.0959741 0.0959741i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 277087. 0.772257 0.386129 0.922445i \(-0.373812\pi\)
0.386129 + 0.922445i \(0.373812\pi\)
\(600\) 0 0
\(601\) 323876.i 0.896665i −0.893867 0.448333i \(-0.852018\pi\)
0.893867 0.448333i \(-0.147982\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −102505. + 102505.i −0.280050 + 0.280050i
\(606\) 0 0
\(607\) 715467.i 1.94184i 0.239414 + 0.970918i \(0.423045\pi\)
−0.239414 + 0.970918i \(0.576955\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −60094.8 60094.8i −0.160974 0.160974i
\(612\) 0 0
\(613\) 137200. + 137200.i 0.365117 + 0.365117i 0.865693 0.500576i \(-0.166878\pi\)
−0.500576 + 0.865693i \(0.666878\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 106650.i 0.280149i 0.990141 + 0.140074i \(0.0447342\pi\)
−0.990141 + 0.140074i \(0.955266\pi\)
\(618\) 0 0
\(619\) 373667. 373667.i 0.975221 0.975221i −0.0244790 0.999700i \(-0.507793\pi\)
0.999700 + 0.0244790i \(0.00779267\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 254543.i 0.655820i
\(624\) 0 0
\(625\) 227071. 0.581302
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 54327.1 + 54327.1i 0.137314 + 0.137314i
\(630\) 0 0
\(631\) 445762. 1.11955 0.559777 0.828644i \(-0.310887\pi\)
0.559777 + 0.828644i \(0.310887\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 58296.2 58296.2i 0.144575 0.144575i
\(636\) 0 0
\(637\) 68511.2 68511.2i 0.168843 0.168843i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 412550. 1.00406 0.502031 0.864850i \(-0.332586\pi\)
0.502031 + 0.864850i \(0.332586\pi\)
\(642\) 0 0
\(643\) 71290.0 + 71290.0i 0.172428 + 0.172428i 0.788045 0.615617i \(-0.211093\pi\)
−0.615617 + 0.788045i \(0.711093\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 138722. 0.331388 0.165694 0.986177i \(-0.447014\pi\)
0.165694 + 0.986177i \(0.447014\pi\)
\(648\) 0 0
\(649\) 290509.i 0.689716i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −467444. + 467444.i −1.09623 + 1.09623i −0.101387 + 0.994847i \(0.532328\pi\)
−0.994847 + 0.101387i \(0.967672\pi\)
\(654\) 0 0
\(655\) 485943.i 1.13267i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 180573. + 180573.i 0.415797 + 0.415797i 0.883752 0.467955i \(-0.155009\pi\)
−0.467955 + 0.883752i \(0.655009\pi\)
\(660\) 0 0
\(661\) 142726. + 142726.i 0.326664 + 0.326664i 0.851317 0.524652i \(-0.175805\pi\)
−0.524652 + 0.851317i \(0.675805\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 109959.i 0.248650i
\(666\) 0 0
\(667\) 336097. 336097.i 0.755462 0.755462i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 548576.i 1.21841i
\(672\) 0 0
\(673\) −272445. −0.601517 −0.300759 0.953700i \(-0.597240\pi\)
−0.300759 + 0.953700i \(0.597240\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −285404. 285404.i −0.622706 0.622706i 0.323517 0.946222i \(-0.395135\pi\)
−0.946222 + 0.323517i \(0.895135\pi\)
\(678\) 0 0
\(679\) 265390. 0.575632
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 186551. 186551.i 0.399904 0.399904i −0.478295 0.878199i \(-0.658745\pi\)
0.878199 + 0.478295i \(0.158745\pi\)
\(684\) 0 0
\(685\) −156918. + 156918.i −0.334419 + 0.334419i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −167836. −0.353546
\(690\) 0 0
\(691\) −544261. 544261.i −1.13986 1.13986i −0.988475 0.151383i \(-0.951627\pi\)
−0.151383 0.988475i \(-0.548373\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 221470. 0.458506
\(696\) 0 0
\(697\) 174655.i 0.359514i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 69213.2 69213.2i 0.140849 0.140849i −0.633167 0.774015i \(-0.718245\pi\)
0.774015 + 0.633167i \(0.218245\pi\)
\(702\) 0 0
\(703\) 175817.i 0.355754i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 181193. + 181193.i 0.362496 + 0.362496i
\(708\) 0 0
\(709\) 133745. + 133745.i 0.266063 + 0.266063i 0.827512 0.561448i \(-0.189756\pi\)
−0.561448 + 0.827512i \(0.689756\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 228318.i 0.449118i
\(714\) 0 0
\(715\) −67710.4 + 67710.4i −0.132447 + 0.132447i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 762270.i 1.47452i −0.675609 0.737261i \(-0.736119\pi\)
0.675609 0.737261i \(-0.263881\pi\)
\(720\) 0 0
\(721\) 147124. 0.283017
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −69541.2 69541.2i −0.132302 0.132302i
\(726\) 0 0
\(727\) 664888. 1.25800 0.628999 0.777406i \(-0.283465\pi\)
0.628999 + 0.777406i \(0.283465\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 19964.3 19964.3i 0.0373610 0.0373610i
\(732\) 0 0
\(733\) −616942. + 616942.i −1.14825 + 1.14825i −0.161352 + 0.986897i \(0.551586\pi\)
−0.986897 + 0.161352i \(0.948414\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 493261. 0.908117
\(738\) 0 0
\(739\) 204895. + 204895.i 0.375182 + 0.375182i 0.869360 0.494179i \(-0.164531\pi\)
−0.494179 + 0.869360i \(0.664531\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 183598. 0.332576 0.166288 0.986077i \(-0.446822\pi\)
0.166288 + 0.986077i \(0.446822\pi\)
\(744\) 0 0
\(745\) 98863.7i 0.178125i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 111380. 111380.i 0.198538 0.198538i
\(750\) 0 0
\(751\) 167996.i 0.297864i 0.988847 + 0.148932i \(0.0475836\pi\)
−0.988847 + 0.148932i \(0.952416\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −316823. 316823.i −0.555805 0.555805i
\(756\) 0 0
\(757\) −414105. 414105.i −0.722634 0.722634i 0.246507 0.969141i \(-0.420717\pi\)
−0.969141 + 0.246507i \(0.920717\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 315375.i 0.544575i 0.962216 + 0.272287i \(0.0877801\pi\)
−0.962216 + 0.272287i \(0.912220\pi\)
\(762\) 0 0
\(763\) 365974. 365974.i 0.628638 0.628638i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 176771.i 0.300483i
\(768\) 0 0
\(769\) 156016. 0.263825 0.131913 0.991261i \(-0.457888\pi\)
0.131913 + 0.991261i \(0.457888\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 151026. + 151026.i 0.252751 + 0.252751i 0.822098 0.569347i \(-0.192804\pi\)
−0.569347 + 0.822098i \(0.692804\pi\)
\(774\) 0 0
\(775\) 47240.9 0.0786529
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 282615. 282615.i 0.465715 0.465715i
\(780\) 0 0
\(781\) 304276. 304276.i 0.498845 0.498845i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 415056. 0.673546
\(786\) 0 0
\(787\) −95574.5 95574.5i −0.154310 0.154310i 0.625730 0.780040i \(-0.284801\pi\)
−0.780040 + 0.625730i \(0.784801\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −69711.8 −0.111418
\(792\) 0 0
\(793\) 333802.i 0.530814i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 497721. 497721.i 0.783555 0.783555i −0.196874 0.980429i \(-0.563079\pi\)
0.980429 + 0.196874i \(0.0630790\pi\)
\(798\) 0 0
\(799\) 154987.i 0.242774i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 163678. + 163678.i 0.253840 + 0.253840i
\(804\) 0 0
\(805\) 336638. + 336638.i 0.519484 + 0.519484i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 363878.i 0.555979i −0.960584 0.277990i \(-0.910332\pi\)
0.960584 0.277990i \(-0.0896681\pi\)
\(810\) 0 0
\(811\) 53046.1 53046.1i 0.0806513 0.0806513i −0.665630 0.746282i \(-0.731837\pi\)
0.746282 + 0.665630i \(0.231837\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 217572.i 0.327557i
\(816\) 0 0
\(817\) −64609.6 −0.0967950
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 540562. + 540562.i 0.801972 + 0.801972i 0.983404 0.181432i \(-0.0580731\pi\)
−0.181432 + 0.983404i \(0.558073\pi\)
\(822\) 0 0
\(823\) −956590. −1.41230 −0.706148 0.708064i \(-0.749569\pi\)
−0.706148 + 0.708064i \(0.749569\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −83207.7 + 83207.7i −0.121661 + 0.121661i −0.765316 0.643655i \(-0.777417\pi\)
0.643655 + 0.765316i \(0.277417\pi\)
\(828\) 0 0
\(829\) −673529. + 673529.i −0.980048 + 0.980048i −0.999805 0.0197565i \(-0.993711\pi\)
0.0197565 + 0.999805i \(0.493711\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 176694. 0.254642
\(834\) 0 0
\(835\) −58366.2 58366.2i −0.0837121 0.0837121i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −488503. −0.693975 −0.346987 0.937870i \(-0.612795\pi\)
−0.346987 + 0.937870i \(0.612795\pi\)
\(840\) 0 0
\(841\) 462029.i 0.653247i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −375835. + 375835.i −0.526361 + 0.526361i
\(846\) 0 0
\(847\) 168631.i 0.235055i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −538260. 538260.i −0.743247 0.743247i
\(852\) 0 0
\(853\) −462565. 462565.i −0.635733 0.635733i 0.313767 0.949500i \(-0.398409\pi\)
−0.949500 + 0.313767i \(0.898409\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.08100e6i 1.47185i −0.677064 0.735924i \(-0.736748\pi\)
0.677064 0.735924i \(-0.263252\pi\)
\(858\) 0 0
\(859\) −911196. + 911196.i −1.23488 + 1.23488i −0.272816 + 0.962066i \(0.587955\pi\)
−0.962066 + 0.272816i \(0.912045\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 35108.9i 0.0471406i 0.999722 + 0.0235703i \(0.00750335\pi\)
−0.999722 + 0.0235703i \(0.992497\pi\)
\(864\) 0 0
\(865\) 496359. 0.663382
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −542740. 542740.i −0.718707 0.718707i
\(870\) 0 0
\(871\) −300143. −0.395633
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 288868. 288868.i 0.377298 0.377298i
\(876\) 0 0
\(877\) 134545. 134545.i 0.174931 0.174931i −0.614211 0.789142i \(-0.710526\pi\)
0.789142 + 0.614211i \(0.210526\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.27287e6 −1.63995 −0.819975 0.572399i \(-0.806013\pi\)
−0.819975 + 0.572399i \(0.806013\pi\)
\(882\) 0 0
\(883\) −484264. 484264.i −0.621098 0.621098i 0.324714 0.945812i \(-0.394732\pi\)
−0.945812 + 0.324714i \(0.894732\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −66348.3 −0.0843301 −0.0421650 0.999111i \(-0.513426\pi\)
−0.0421650 + 0.999111i \(0.513426\pi\)
\(888\) 0 0
\(889\) 95902.7i 0.121347i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −250790. + 250790.i −0.314490 + 0.314490i
\(894\) 0 0
\(895\) 704418.i 0.879396i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 83302.4 + 83302.4i 0.103071 + 0.103071i
\(900\) 0 0
\(901\) −216428. 216428.i −0.266602 0.266602i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 404107.i 0.493401i
\(906\) 0 0
\(907\) −846133. + 846133.i −1.02855 + 1.02855i −0.0289661 + 0.999580i \(0.509221\pi\)
−0.999580 + 0.0289661i \(0.990779\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 133938.i 0.161386i −0.996739 0.0806932i \(-0.974287\pi\)
0.996739 0.0806932i \(-0.0257134\pi\)
\(912\) 0 0
\(913\) −28176.8 −0.0338026
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 399711. + 399711.i 0.475343 + 0.475343i
\(918\) 0 0
\(919\) 469228. 0.555589 0.277794 0.960641i \(-0.410397\pi\)
0.277794 + 0.960641i \(0.410397\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −185148. + 185148.i −0.217328 + 0.217328i
\(924\) 0 0
\(925\) −111371. + 111371.i −0.130163 + 0.130163i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −728330. −0.843911 −0.421955 0.906617i \(-0.638656\pi\)
−0.421955 + 0.906617i \(0.638656\pi\)
\(930\) 0 0
\(931\) −285913. 285913.i −0.329864 0.329864i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −174628. −0.199752
\(936\) 0 0
\(937\) 572084.i 0.651599i −0.945439 0.325800i \(-0.894366\pi\)
0.945439 0.325800i \(-0.105634\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 270062. 270062.i 0.304989 0.304989i −0.537973 0.842962i \(-0.680810\pi\)
0.842962 + 0.537973i \(0.180810\pi\)
\(942\) 0 0
\(943\) 1.73044e6i 1.94596i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −803359. 803359.i −0.895797 0.895797i 0.0992642 0.995061i \(-0.468351\pi\)
−0.995061 + 0.0992642i \(0.968351\pi\)
\(948\) 0 0
\(949\) −99596.1 99596.1i −0.110588 0.110588i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 188445.i 0.207491i 0.994604 + 0.103746i \(0.0330827\pi\)
−0.994604 + 0.103746i \(0.966917\pi\)
\(954\) 0 0
\(955\) 171093. 171093.i 0.187597 0.187597i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 258144.i 0.280689i
\(960\) 0 0
\(961\) 866932. 0.938725
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.00215e6 1.00215e6i −1.07617 1.07617i
\(966\) 0 0
\(967\) −1.17554e6 −1.25715 −0.628573 0.777751i \(-0.716361\pi\)
−0.628573 + 0.777751i \(0.716361\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −784226. + 784226.i −0.831769 + 0.831769i −0.987759 0.155989i \(-0.950143\pi\)
0.155989 + 0.987759i \(0.450143\pi\)
\(972\) 0 0
\(973\) 182169. 182169.i 0.192420 0.192420i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −710097. −0.743924 −0.371962 0.928248i \(-0.621315\pi\)
−0.371962 + 0.928248i \(0.621315\pi\)
\(978\) 0 0
\(979\) 654120. + 654120.i 0.682483 + 0.682483i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 471799. 0.488259 0.244129 0.969743i \(-0.421498\pi\)
0.244129 + 0.969743i \(0.421498\pi\)
\(984\) 0 0
\(985\) 668322.i 0.688832i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −197801. + 197801.i −0.202226 + 0.202226i
\(990\) 0 0
\(991\) 1.06681e6i 1.08627i −0.839644 0.543137i \(-0.817237\pi\)
0.839644 0.543137i \(-0.182763\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −875175. 875175.i −0.883992 0.883992i
\(996\) 0 0
\(997\) −303115. 303115.i −0.304942 0.304942i 0.538002 0.842944i \(-0.319179\pi\)
−0.842944 + 0.538002i \(0.819179\pi\)
\(998\) 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 576.5.m.a.271.6 14
3.2 odd 2 64.5.f.a.15.1 14
4.3 odd 2 144.5.m.a.91.3 14
12.11 even 2 16.5.f.a.11.5 yes 14
16.3 odd 4 inner 576.5.m.a.559.6 14
16.13 even 4 144.5.m.a.19.3 14
24.5 odd 2 128.5.f.a.31.7 14
24.11 even 2 128.5.f.b.31.1 14
48.5 odd 4 128.5.f.b.95.1 14
48.11 even 4 128.5.f.a.95.7 14
48.29 odd 4 16.5.f.a.3.5 14
48.35 even 4 64.5.f.a.47.1 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.5.f.a.3.5 14 48.29 odd 4
16.5.f.a.11.5 yes 14 12.11 even 2
64.5.f.a.15.1 14 3.2 odd 2
64.5.f.a.47.1 14 48.35 even 4
128.5.f.a.31.7 14 24.5 odd 2
128.5.f.a.95.7 14 48.11 even 4
128.5.f.b.31.1 14 24.11 even 2
128.5.f.b.95.1 14 48.5 odd 4
144.5.m.a.19.3 14 16.13 even 4
144.5.m.a.91.3 14 4.3 odd 2
576.5.m.a.271.6 14 1.1 even 1 trivial
576.5.m.a.559.6 14 16.3 odd 4 inner