Properties

Label 2925.1.er.a.1117.4
Level $2925$
Weight $1$
Character 2925.1117
Analytic conductor $1.460$
Analytic rank $0$
Dimension $32$
Projective image $D_{40}$
CM discriminant -39
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2925,1,Mod(298,2925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2925, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 11, 10]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2925.298");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2925.er (of order \(20\), degree \(8\), 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: \(1.45976516195\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(4\) over \(\Q(\zeta_{20})\)
Coefficient field: \(\Q(\zeta_{80})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{32} - x^{24} + x^{16} - x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{40}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{40} + \cdots)\)

Embedding invariants

Embedding label 1117.4
Root \(0.0784591 - 0.996917i\) of defining polynomial
Character \(\chi\) \(=\) 2925.1117
Dual form 2925.1.er.a.2053.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35505 + 0.690434i) q^{2} +(0.771685 + 1.06213i) q^{4} +(0.852640 - 0.522499i) q^{5} +(0.0744338 + 0.469957i) q^{8} +O(q^{10})\) \(q+(1.35505 + 0.690434i) q^{2} +(0.771685 + 1.06213i) q^{4} +(0.852640 - 0.522499i) q^{5} +(0.0744338 + 0.469957i) q^{8} +(1.51612 - 0.119322i) q^{10} +(-0.444039 + 0.144277i) q^{11} +(0.453990 + 0.891007i) q^{13} +(0.182086 - 0.560404i) q^{16} +(1.21293 + 0.502413i) q^{20} +(-0.701311 - 0.111077i) q^{22} +(0.453990 - 0.891007i) q^{25} +1.52081i q^{26} +(0.970111 - 0.970111i) q^{32} +(0.309017 + 0.361812i) q^{40} +(-0.149238 - 0.0484904i) q^{41} +(-1.26007 + 1.26007i) q^{43} +(-0.495900 - 0.360293i) q^{44} +(0.0245474 - 0.154986i) q^{47} +1.00000i q^{49} +(1.23036 - 0.893911i) q^{50} +(-0.596030 + 1.16977i) q^{52} +(-0.303221 + 0.355026i) q^{55} +(-0.322922 + 0.993851i) q^{59} +(-0.610425 - 1.87869i) q^{61} +(1.42395 - 0.462668i) q^{64} +(0.852640 + 0.522499i) q^{65} +(-1.14309 - 1.57333i) q^{71} +(0.831254 + 1.14412i) q^{79} +(-0.137556 - 0.572963i) q^{80} +(-0.168746 - 0.168746i) q^{82} +(-0.203192 - 1.28290i) q^{83} +(-2.57746 + 0.837469i) q^{86} +(-0.100856 - 0.197940i) q^{88} +(-0.236511 - 0.727907i) q^{89} +(0.140271 - 0.193066i) q^{94} +(-0.690434 + 1.35505i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 8 q^{10} + 8 q^{16} - 8 q^{22} - 8 q^{40} + 8 q^{43} + 8 q^{52} + 40 q^{64} - 32 q^{82} + 24 q^{88} - 40 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(2251\)
\(\chi(n)\) \(1\) \(e\left(\frac{13}{20}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35505 + 0.690434i 1.35505 + 0.690434i 0.972370 0.233445i \(-0.0750000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(3\) 0 0
\(4\) 0.771685 + 1.06213i 0.771685 + 1.06213i
\(5\) 0.852640 0.522499i 0.852640 0.522499i
\(6\) 0 0
\(7\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(8\) 0.0744338 + 0.469957i 0.0744338 + 0.469957i
\(9\) 0 0
\(10\) 1.51612 0.119322i 1.51612 0.119322i
\(11\) −0.444039 + 0.144277i −0.444039 + 0.144277i −0.522499 0.852640i \(-0.675000\pi\)
0.0784591 + 0.996917i \(0.475000\pi\)
\(12\) 0 0
\(13\) 0.453990 + 0.891007i 0.453990 + 0.891007i
\(14\) 0 0
\(15\) 0 0
\(16\) 0.182086 0.560404i 0.182086 0.560404i
\(17\) 0 0 0.987688 0.156434i \(-0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(18\) 0 0
\(19\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(20\) 1.21293 + 0.502413i 1.21293 + 0.502413i
\(21\) 0 0
\(22\) −0.701311 0.111077i −0.701311 0.111077i
\(23\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(24\) 0 0
\(25\) 0.453990 0.891007i 0.453990 0.891007i
\(26\) 1.52081i 1.52081i
\(27\) 0 0
\(28\) 0 0
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(32\) 0.970111 0.970111i 0.970111 0.970111i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.309017 + 0.361812i 0.309017 + 0.361812i
\(41\) −0.149238 0.0484904i −0.149238 0.0484904i 0.233445 0.972370i \(-0.425000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(42\) 0 0
\(43\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(44\) −0.495900 0.360293i −0.495900 0.360293i
\(45\) 0 0
\(46\) 0 0
\(47\) 0.0245474 0.154986i 0.0245474 0.154986i −0.972370 0.233445i \(-0.925000\pi\)
0.996917 + 0.0784591i \(0.0250000\pi\)
\(48\) 0 0
\(49\) 1.00000i 1.00000i
\(50\) 1.23036 0.893911i 1.23036 0.893911i
\(51\) 0 0
\(52\) −0.596030 + 1.16977i −0.596030 + 1.16977i
\(53\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(54\) 0 0
\(55\) −0.303221 + 0.355026i −0.303221 + 0.355026i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −0.322922 + 0.993851i −0.322922 + 0.993851i 0.649448 + 0.760406i \(0.275000\pi\)
−0.972370 + 0.233445i \(0.925000\pi\)
\(60\) 0 0
\(61\) −0.610425 1.87869i −0.610425 1.87869i −0.453990 0.891007i \(-0.650000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.42395 0.462668i 1.42395 0.462668i
\(65\) 0.852640 + 0.522499i 0.852640 + 0.522499i
\(66\) 0 0
\(67\) 0 0 −0.156434 0.987688i \(-0.550000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.14309 1.57333i −1.14309 1.57333i −0.760406 0.649448i \(-0.775000\pi\)
−0.382683 0.923880i \(-0.625000\pi\)
\(72\) 0 0
\(73\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0.831254 + 1.14412i 0.831254 + 1.14412i 0.987688 + 0.156434i \(0.0500000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(80\) −0.137556 0.572963i −0.137556 0.572963i
\(81\) 0 0
\(82\) −0.168746 0.168746i −0.168746 0.168746i
\(83\) −0.203192 1.28290i −0.203192 1.28290i −0.852640 0.522499i \(-0.825000\pi\)
0.649448 0.760406i \(-0.275000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.57746 + 0.837469i −2.57746 + 0.837469i
\(87\) 0 0
\(88\) −0.100856 0.197940i −0.100856 0.197940i
\(89\) −0.236511 0.727907i −0.236511 0.727907i −0.996917 0.0784591i \(-0.975000\pi\)
0.760406 0.649448i \(-0.225000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.140271 0.193066i 0.140271 0.193066i
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(98\) −0.690434 + 1.35505i −0.690434 + 1.35505i
\(99\) 0 0
\(100\) 1.29671 0.205378i 1.29671 0.205378i
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −0.221232 + 1.39680i −0.221232 + 1.39680i 0.587785 + 0.809017i \(0.300000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −0.384942 + 0.279677i −0.384942 + 0.279677i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(108\) 0 0
\(109\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(110\) −0.656003 + 0.271726i −0.656003 + 0.271726i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.12377 + 1.12377i −1.12377 + 1.12377i
\(119\) 0 0
\(120\) 0 0
\(121\) −0.632662 + 0.459656i −0.632662 + 0.459656i
\(122\) 0.469957 2.96719i 0.469957 2.96719i
\(123\) 0 0
\(124\) 0 0
\(125\) −0.0784591 0.996917i −0.0784591 0.996917i
\(126\) 0 0
\(127\) −0.280582 + 0.550672i −0.280582 + 0.550672i −0.987688 0.156434i \(-0.950000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(128\) 0.893911 + 0.141582i 0.893911 + 0.141582i
\(129\) 0 0
\(130\) 0.794622 + 1.29671i 0.794622 + 1.29671i
\(131\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.347469 + 0.681947i 0.347469 + 0.681947i 0.996917 0.0784591i \(-0.0250000\pi\)
−0.649448 + 0.760406i \(0.725000\pi\)
\(138\) 0 0
\(139\) −1.11803 + 0.363271i −1.11803 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.462668 2.92117i −0.462668 2.92117i
\(143\) −0.330142 0.330142i −0.330142 0.330142i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.84776 −1.84776 −0.923880 0.382683i \(-0.875000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i \(-0.200000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(158\) 0.336452 + 2.12427i 0.336452 + 2.12427i
\(159\) 0 0
\(160\) 0.320274 1.33404i 0.320274 1.33404i
\(161\) 0 0
\(162\) 0 0
\(163\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(164\) −0.0636615 0.195930i −0.0636615 0.195930i
\(165\) 0 0
\(166\) 0.610425 1.87869i 0.610425 1.87869i
\(167\) −1.68429 + 0.266765i −1.68429 + 0.266765i −0.923880 0.382683i \(-0.875000\pi\)
−0.760406 + 0.649448i \(0.775000\pi\)
\(168\) 0 0
\(169\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(170\) 0 0
\(171\) 0 0
\(172\) −2.31075 0.365986i −2.31075 0.365986i
\(173\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0.275113i 0.275113i
\(177\) 0 0
\(178\) 0.182086 1.14965i 0.182086 1.14965i
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) 0 0
\(181\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0.183559 0.0935280i 0.183559 0.0935280i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(192\) 0 0
\(193\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −1.06213 + 0.771685i −1.06213 + 0.771685i
\(197\) 0.289053 1.82501i 0.289053 1.82501i −0.233445 0.972370i \(-0.575000\pi\)
0.522499 0.852640i \(-0.325000\pi\)
\(198\) 0 0
\(199\) 0.907981i 0.907981i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(200\) 0.452527 + 0.147035i 0.452527 + 0.147035i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −0.152583 + 0.0366318i −0.152583 + 0.0366318i
\(206\) −1.26418 + 1.74000i −1.26418 + 1.74000i
\(207\) 0 0
\(208\) 0.581990 0.0921781i 0.581990 0.0921781i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.550672 1.69480i −0.550672 1.69480i −0.707107 0.707107i \(-0.750000\pi\)
0.156434 0.987688i \(-0.450000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −0.416003 + 1.73278i −0.416003 + 1.73278i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) −0.611077 0.0480928i −0.611077 0.0480928i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0.681947 + 0.347469i 0.681947 + 0.347469i 0.760406 0.649448i \(-0.225000\pi\)
−0.0784591 + 0.996917i \(0.525000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.156434 0.987688i \(-0.550000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(234\) 0 0
\(235\) −0.0600500 0.144974i −0.0600500 0.144974i
\(236\) −1.30480 + 0.423954i −1.30480 + 0.423954i
\(237\) 0 0
\(238\) 0 0
\(239\) −0.570989 1.75732i −0.570989 1.75732i −0.649448 0.760406i \(-0.725000\pi\)
0.0784591 0.996917i \(-0.475000\pi\)
\(240\) 0 0
\(241\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(242\) −1.17465 + 0.186047i −1.17465 + 0.186047i
\(243\) 0 0
\(244\) 1.52437 2.09811i 1.52437 2.09811i
\(245\) 0.522499 + 0.852640i 0.522499 + 0.852640i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.581990 1.40505i 0.581990 1.40505i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −0.760406 + 0.552467i −0.760406 + 0.552467i
\(255\) 0 0
\(256\) −0.0977364 0.0710097i −0.0977364 0.0710097i
\(257\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.103007 + 1.30882i 0.103007 + 1.30882i
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(270\) 0 0
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.16398i 1.16398i
\(275\) −0.0730378 + 0.461143i −0.0730378 + 0.461143i
\(276\) 0 0
\(277\) 0.412215 0.809017i 0.412215 0.809017i −0.587785 0.809017i \(-0.700000\pi\)
1.00000 \(0\)
\(278\) −1.76581 0.279677i −1.76581 0.279677i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.00234 1.37960i 1.00234 1.37960i 0.0784591 0.996917i \(-0.475000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(282\) 0 0
\(283\) 1.59811 0.253116i 1.59811 0.253116i 0.707107 0.707107i \(-0.250000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(284\) 0.788979 2.42823i 0.788979 2.42823i
\(285\) 0 0
\(286\) −0.219418 0.675301i −0.219418 0.675301i
\(287\) 0 0
\(288\) 0 0
\(289\) 0.951057 0.309017i 0.951057 0.309017i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.40985 + 1.40985i 1.40985 + 1.40985i 0.760406 + 0.649448i \(0.225000\pi\)
0.649448 + 0.760406i \(0.275000\pi\)
\(294\) 0 0
\(295\) 0.243950 + 1.01612i 0.243950 + 1.01612i
\(296\) 0 0
\(297\) 0 0
\(298\) −2.50381 1.27576i −2.50381 1.27576i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.50209 1.28290i −1.50209 1.28290i
\(306\) 0 0
\(307\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(312\) 0 0
\(313\) 0.280582 + 0.550672i 0.280582 + 0.550672i 0.987688 0.156434i \(-0.0500000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 0.147035 + 0.452527i 0.147035 + 0.452527i
\(315\) 0 0
\(316\) −0.573745 + 1.76580i −0.573745 + 1.76580i
\(317\) −1.28290 + 0.203192i −1.28290 + 0.203192i −0.760406 0.649448i \(-0.775000\pi\)
−0.522499 + 0.852640i \(0.675000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.972370 1.13850i 0.972370 1.13850i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 1.00000 1.00000
\(326\) 0 0
\(327\) 0 0
\(328\) 0.0116800 0.0737448i 0.0116800 0.0737448i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(332\) 1.20582 1.20582i 1.20582 1.20582i
\(333\) 0 0
\(334\) −2.46648 0.801408i −2.46648 0.801408i
\(335\) 0 0
\(336\) 0 0
\(337\) 1.69480 0.863541i 1.69480 0.863541i 0.707107 0.707107i \(-0.250000\pi\)
0.987688 0.156434i \(-0.0500000\pi\)
\(338\) −1.35505 + 0.690434i −1.35505 + 0.690434i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) −0.685972 0.498388i −0.685972 0.498388i
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 0.156434 0.987688i \(-0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.290803 + 0.570732i −0.290803 + 0.570732i
\(353\) 1.96929 + 0.311904i 1.96929 + 0.311904i 0.996917 + 0.0784591i \(0.0250000\pi\)
0.972370 + 0.233445i \(0.0750000\pi\)
\(354\) 0 0
\(355\) −1.79671 0.744220i −1.79671 0.744220i
\(356\) 0.590622 0.812922i 0.590622 0.812922i
\(357\) 0 0
\(358\) 0 0
\(359\) 0.616129 1.89625i 0.616129 1.89625i 0.233445 0.972370i \(-0.425000\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(360\) 0 0
\(361\) −0.309017 0.951057i −0.309017 0.951057i
\(362\) 0.811654 + 1.59296i 0.811654 + 1.59296i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0.142040 + 0.896802i 0.142040 + 0.896802i 0.951057 + 0.309017i \(0.100000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.04744 + 0.533698i 1.04744 + 0.533698i 0.891007 0.453990i \(-0.150000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.0746640 0.0746640
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0.289053 + 1.82501i 0.289053 + 1.82501i 0.522499 + 0.852640i \(0.325000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.469957 + 0.0744338i −0.469957 + 0.0744338i
\(393\) 0 0
\(394\) 1.65173 2.27341i 1.65173 2.27341i
\(395\) 1.30656 + 0.541196i 1.30656 + 0.541196i
\(396\) 0 0
\(397\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(398\) −0.626901 + 1.23036i −0.626901 + 1.23036i
\(399\) 0 0
\(400\) −0.416659 0.416659i −0.416659 0.416659i
\(401\) 1.94474i 1.94474i 0.233445 + 0.972370i \(0.425000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(410\) −0.232049 0.0557101i −0.232049 0.0557101i
\(411\) 0 0
\(412\) −1.65431 + 0.842914i −1.65431 + 0.842914i
\(413\) 0 0
\(414\) 0 0
\(415\) −0.843566 0.987688i −0.843566 0.987688i
\(416\) 1.30480 + 0.423954i 1.30480 + 0.423954i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(420\) 0 0
\(421\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(422\) 0.423954 2.67674i 0.423954 2.67674i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) −1.76007 + 2.06078i −1.76007 + 2.06078i
\(431\) 0.893911 1.23036i 0.893911 1.23036i −0.0784591 0.996917i \(-0.525000\pi\)
0.972370 0.233445i \(-0.0750000\pi\)
\(432\) 0 0
\(433\) −1.16110 + 0.183900i −1.16110 + 0.183900i −0.707107 0.707107i \(-0.750000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.80902 + 0.587785i −1.80902 + 0.587785i −0.809017 + 0.587785i \(0.800000\pi\)
−1.00000 \(\pi\)
\(440\) −0.189417 0.116075i −0.189417 0.116075i
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(444\) 0 0
\(445\) −0.581990 0.497066i −0.581990 0.497066i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.04500 −1.04500 −0.522499 0.852640i \(-0.675000\pi\)
−0.522499 + 0.852640i \(0.675000\pi\)
\(450\) 0 0
\(451\) 0.0732636 0.0732636
\(452\) 0 0
\(453\) 0 0
\(454\) 0.684170 + 0.941679i 0.684170 + 0.941679i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.62182 0.526961i 1.62182 0.526961i 0.649448 0.760406i \(-0.275000\pi\)
0.972370 + 0.233445i \(0.0750000\pi\)
\(462\) 0 0
\(463\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.987688 0.156434i \(-0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.0187237 0.237907i 0.0187237 0.237907i
\(471\) 0 0
\(472\) −0.491103 0.0777831i −0.491103 0.0777831i
\(473\) 0.377723 0.741322i 0.377723 0.741322i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.439596 2.77550i 0.439596 2.77550i
\(479\) 1.37960 1.00234i 1.37960 1.00234i 0.382683 0.923880i \(-0.375000\pi\)
0.996917 0.0784591i \(-0.0250000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.976431 0.317262i −0.976431 0.317262i
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(488\) 0.837469 0.426712i 0.837469 0.426712i
\(489\) 0 0
\(490\) 0.119322 + 1.51612i 0.119322 + 1.51612i
\(491\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0.998313 0.852640i 0.998313 0.852640i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −0.801408 + 0.126931i −0.801408 + 0.126931i
\(509\) −0.469957 + 1.44638i −0.469957 + 1.44638i 0.382683 + 0.923880i \(0.375000\pi\)
−0.852640 + 0.522499i \(0.825000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.494296 0.970111i −0.494296 0.970111i
\(513\) 0 0
\(514\) 0 0
\(515\) 0.541196 + 1.30656i 0.541196 + 1.30656i
\(516\) 0 0
\(517\) 0.0114610 + 0.0723617i 0.0114610 + 0.0723617i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.182086 + 0.439596i −0.182086 + 0.439596i
\(521\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(522\) 0 0
\(523\) −1.76007 0.896802i −1.76007 0.896802i −0.951057 0.309017i \(-0.900000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.587785 0.809017i −0.587785 0.809017i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −0.0245474 0.154986i −0.0245474 0.154986i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.144277 0.444039i −0.144277 0.444039i
\(540\) 0 0
\(541\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.309017 0.0489435i −0.309017 0.0489435i 1.00000i \(-0.5\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(548\) −0.456182 + 0.895307i −0.456182 + 0.895307i
\(549\) 0 0
\(550\) −0.417359 + 0.574445i −0.417359 + 0.574445i
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 1.11715 0.811654i 1.11715 0.811654i
\(555\) 0 0
\(556\) −1.24861 0.907170i −1.24861 0.907170i
\(557\) −1.20582 + 1.20582i −1.20582 + 1.20582i −0.233445 + 0.972370i \(0.575000\pi\)
−0.972370 + 0.233445i \(0.925000\pi\)
\(558\) 0 0
\(559\) −1.69480 0.550672i −1.69480 0.550672i
\(560\) 0 0
\(561\) 0 0
\(562\) 2.31075 1.17738i 2.31075 1.17738i
\(563\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 2.34029 + 0.760406i 2.34029 + 0.760406i
\(567\) 0 0
\(568\) 0.654311 0.654311i 0.654311 0.654311i
\(569\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) −0.734572 + 0.533698i −0.734572 + 0.533698i −0.891007 0.453990i \(-0.850000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(572\) 0.0958891 0.605420i 0.0958891 0.605420i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(578\) 1.50209 + 0.237907i 1.50209 + 0.237907i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0.937016 + 2.88384i 0.937016 + 2.88384i
\(587\) 0.774181 + 1.51942i 0.774181 + 1.51942i 0.852640 + 0.522499i \(0.175000\pi\)
−0.0784591 + 0.996917i \(0.525000\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −0.371002 + 1.54533i −0.371002 + 1.54533i
\(591\) 0 0
\(592\) 0 0
\(593\) 1.30656 + 1.30656i 1.30656 + 1.30656i 0.923880 + 0.382683i \(0.125000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.42589 1.96257i −1.42589 1.96257i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 1.41421 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.299263 + 0.722486i −0.299263 + 0.722486i
\(606\) 0 0
\(607\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.14965 2.77550i −1.14965 2.77550i
\(611\) 0.149238 0.0484904i 0.149238 0.0484904i
\(612\) 0 0
\(613\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.154986 + 0.0245474i −0.154986 + 0.0245474i −0.233445 0.972370i \(-0.575000\pi\)
0.0784591 + 0.996917i \(0.475000\pi\)
\(618\) 0 0
\(619\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.587785 0.809017i −0.587785 0.809017i
\(626\) 0.939913i 0.939913i
\(627\) 0 0
\(628\) −0.0642564 + 0.405699i −0.0642564 + 0.405699i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) −0.475815 + 0.475815i −0.475815 + 0.475815i
\(633\) 0 0
\(634\) −1.87869 0.610425i −1.87869 0.610425i
\(635\) 0.0484904 + 0.616129i 0.0484904 + 0.616129i
\(636\) 0 0
\(637\) −0.891007 + 0.453990i −0.891007 + 0.453990i
\(638\) 0 0
\(639\) 0 0
\(640\) 0.836160 0.346349i 0.836160 0.346349i
\(641\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.156434 0.987688i \(-0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(648\) 0 0
\(649\) 0.487899i 0.487899i
\(650\) 1.35505 + 0.690434i 1.35505 + 0.690434i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.0543485 + 0.0748042i −0.0543485 + 0.0748042i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(660\) 0 0
\(661\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.587785 0.190983i 0.587785 0.190983i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.58308 1.58308i −1.58308 1.58308i
\(669\) 0 0
\(670\) 0 0
\(671\) 0.542106 + 0.746144i 0.542106 + 0.746144i
\(672\) 0 0
\(673\) 1.26007 + 0.642040i 1.26007 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 2.89276 2.89276
\(675\) 0 0
\(676\) −1.31287 −1.31287
\(677\) 0 0 −0.891007 0.453990i \(-0.850000\pi\)
0.891007 + 0.453990i \(0.150000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.0730378 0.461143i −0.0730378 0.461143i −0.996917 0.0784591i \(-0.975000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(684\) 0 0
\(685\) 0.652583 + 0.399903i 0.652583 + 0.399903i
\(686\) 0 0
\(687\) 0 0
\(688\) 0.476708 + 0.935593i 0.476708 + 0.935593i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.763472 + 0.893911i −0.763472 + 0.893911i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.565536 + 0.410886i −0.565536 + 0.410886i
\(705\) 0 0
\(706\) 2.45314 + 1.78231i 2.45314 + 1.78231i
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(710\) −1.92080 2.24896i −1.92080 2.24896i
\(711\) 0 0
\(712\) 0.324480 0.165331i 0.324480 0.165331i
\(713\) 0 0
\(714\) 0 0
\(715\) −0.453990 0.108993i −0.453990 0.108993i
\(716\) 0 0
\(717\) 0 0
\(718\) 2.14412 2.14412i 2.14412 2.14412i
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.237907 1.50209i 0.237907 1.50209i
\(723\) 0 0
\(724\) 1.54337i 1.54337i
\(725\) 0 0
\(726\) 0 0
\(727\) 0.734572 1.44168i 0.734572 1.44168i −0.156434 0.987688i \(-0.550000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.987688 0.156434i \(-0.0500000\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(734\) −0.426712 + 1.31328i −0.426712 + 1.31328i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 1.37514 + 1.37514i 1.37514 + 1.37514i 0.852640 + 0.522499i \(0.175000\pi\)
0.522499 + 0.852640i \(0.325000\pi\)
\(744\) 0 0
\(745\) −1.57547 + 0.965451i −1.57547 + 0.965451i
\(746\) 1.05086 + 1.44638i 1.05086 + 1.44638i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(752\) −0.0823852 0.0419774i −0.0823852 0.0419774i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.34500 + 1.34500i 1.34500 + 1.34500i 0.891007 + 0.453990i \(0.150000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.89625 + 0.616129i −1.89625 + 0.616129i −0.923880 + 0.382683i \(0.875000\pi\)
−0.972370 + 0.233445i \(0.925000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −0.868367 + 2.67256i −0.868367 + 2.67256i
\(767\) −1.03213 + 0.163474i −1.03213 + 0.163474i
\(768\) 0 0
\(769\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0.474419 0.931099i 0.474419 0.931099i −0.522499 0.852640i \(-0.675000\pi\)
0.996917 0.0784591i \(-0.0250000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0.734572 + 0.533698i 0.734572 + 0.533698i
\(782\) 0 0
\(783\) 0 0
\(784\) 0.560404 + 0.182086i 0.560404 + 0.182086i
\(785\) 0.304224 + 0.0730378i 0.304224 + 0.0730378i
\(786\) 0 0
\(787\) 0 0 0.891007 0.453990i \(-0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(788\) 2.16146 1.10132i 2.16146 1.10132i
\(789\) 0 0
\(790\) 1.39680 + 1.63545i 1.39680 + 1.63545i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.39680 1.39680i 1.39680 1.39680i
\(794\) 0 0
\(795\) 0 0
\(796\) −0.964397 + 0.700675i −0.964397 + 0.700675i
\(797\) 0 0 0.156434 0.987688i \(-0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.423954 1.30480i −0.423954 1.30480i
\(801\) 0 0
\(802\) −1.34271 + 2.63523i −1.34271 + 2.63523i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(810\) 0 0
\(811\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) −0.156654 0.133795i −0.156654 0.133795i
\(821\) −0.893911 1.23036i −0.893911 1.23036i −0.972370 0.233445i \(-0.925000\pi\)
0.0784591 0.996917i \(-0.475000\pi\)
\(822\) 0 0
\(823\) 1.76007 + 0.896802i 1.76007 + 0.896802i 0.951057 + 0.309017i \(0.100000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(824\) −0.672904 −0.672904
\(825\) 0 0
\(826\) 0 0
\(827\) 1.73278 + 0.882893i 1.73278 + 0.882893i 0.972370 + 0.233445i \(0.0750000\pi\)
0.760406 + 0.649448i \(0.225000\pi\)
\(828\) 0 0
\(829\) −1.04744 1.44168i −1.04744 1.44168i −0.891007 0.453990i \(-0.850000\pi\)
−0.156434 0.987688i \(-0.550000\pi\)
\(830\) −0.461143 1.92080i −0.461143 1.92080i
\(831\) 0 0
\(832\) 1.05870 + 1.05870i 1.05870 + 1.05870i
\(833\) 0 0
\(834\) 0 0
\(835\) −1.29671 + 1.10749i −1.29671 + 1.10749i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0.526961 + 1.62182i 0.526961 + 1.62182i 0.760406 + 0.649448i \(0.225000\pi\)
−0.233445 + 0.972370i \(0.575000\pi\)
\(840\) 0 0
\(841\) 0.309017 0.951057i 0.309017 0.951057i
\(842\) 0 0
\(843\) 0 0
\(844\) 1.37515 1.89274i 1.37515 1.89274i
\(845\) −0.0784591 + 0.996917i −0.0784591 + 0.996917i
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 0.156434 0.987688i \(-0.450000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(858\) 0 0
\(859\) −0.863541 0.280582i −0.863541 0.280582i −0.156434 0.987688i \(-0.550000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(860\) −2.16146 + 0.895307i −2.16146 + 0.895307i
\(861\) 0 0
\(862\) 2.06078 1.05002i 2.06078 1.05002i
\(863\) −1.77652 + 0.905182i −1.77652 + 0.905182i −0.852640 + 0.522499i \(0.825000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −1.70032 0.552467i −1.70032 0.552467i
\(867\) 0 0
\(868\) 0 0
\(869\) −0.534180 0.388105i −0.534180 0.388105i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.453990 0.891007i \(-0.350000\pi\)
−0.453990 + 0.891007i \(0.650000\pi\)
\(878\) −2.85714 0.452527i −2.85714 0.452527i
\(879\) 0 0
\(880\) 0.143746 + 0.234572i 0.143746 + 0.234572i
\(881\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(882\) 0 0
\(883\) −0.610425 + 0.0966818i −0.610425 + 0.0966818i −0.453990 0.891007i \(-0.650000\pi\)
−0.156434 + 0.987688i \(0.550000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.453990 0.891007i \(-0.650000\pi\)
0.453990 + 0.891007i \(0.350000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) −0.445436 1.07538i −0.445436 1.07538i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.41603 0.721502i −1.41603 0.721502i
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0.0992762 + 0.0505837i 0.0992762 + 0.0505837i
\(903\) 0 0
\(904\) 0 0
\(905\) 1.17195 + 0.0922342i 1.17195 + 0.0922342i
\(906\) 0 0
\(907\) −0.437016 0.437016i −0.437016 0.437016i 0.453990 0.891007i \(-0.350000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(908\) 0.157189 + 0.992455i 0.157189 + 0.992455i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(912\) 0 0
\(913\) 0.275319 + 0.540344i 0.275319 + 0.540344i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.16110 1.59811i 1.16110 1.59811i 0.453990 0.891007i \(-0.350000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 2.56148 + 0.405699i 2.56148 + 0.405699i
\(923\) 0.882893 1.73278i 0.882893 1.73278i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.61305 + 1.17195i −1.61305 + 1.17195i −0.760406 + 0.649448i \(0.775000\pi\)
−0.852640 + 0.522499i \(0.825000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 1.44168 0.734572i 1.44168 0.734572i 0.453990 0.891007i \(-0.350000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.107642 0.175655i 0.107642 0.175655i
\(941\) 1.84956 + 0.600958i 1.84956 + 0.600958i 0.996917 + 0.0784591i \(0.0250000\pi\)
0.852640 + 0.522499i \(0.175000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.498159 + 0.361934i 0.498159 + 0.361934i
\(945\) 0 0
\(946\) 1.02367 0.743739i 1.02367 0.743739i
\(947\) −0.163474 + 1.03213i −0.163474 + 1.03213i 0.760406 + 0.649448i \(0.225000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 −0.987688 0.156434i \(-0.950000\pi\)
0.987688 + 0.156434i \(0.0500000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 1.42589 1.96257i 1.42589 1.96257i
\(957\) 0 0
\(958\) 2.56148 0.405699i 2.56148 0.405699i
\(959\) 0 0
\(960\) 0 0
\(961\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.156434 0.987688i \(-0.550000\pi\)
0.156434 + 0.987688i \(0.450000\pi\)
\(968\) −0.263110 0.263110i −0.263110 0.263110i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −1.16398 −1.16398
\(977\) −0.931099 0.474419i −0.931099 0.474419i −0.0784591 0.996917i \(-0.525000\pi\)
−0.852640 + 0.522499i \(0.825000\pi\)
\(978\) 0 0
\(979\) 0.210041 + 0.289096i 0.210041 + 0.289096i
\(980\) −0.502413 + 1.21293i −0.502413 + 1.21293i
\(981\) 0 0
\(982\) 0 0
\(983\) −0.311904 1.96929i −0.311904 1.96929i −0.233445 0.972370i \(-0.575000\pi\)
−0.0784591 0.996917i \(-0.525000\pi\)
\(984\) 0 0
\(985\) −0.707107 1.70711i −0.707107 1.70711i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.474419 + 0.774181i 0.474419 + 0.774181i
\(996\) 0 0
\(997\) 1.76007 + 0.278768i 1.76007 + 0.278768i 0.951057 0.309017i \(-0.100000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(998\) 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 2925.1.er.a.1117.4 yes 32
3.2 odd 2 inner 2925.1.er.a.1117.1 32
13.12 even 2 inner 2925.1.er.a.1117.1 32
25.3 odd 20 inner 2925.1.er.a.2053.1 yes 32
39.38 odd 2 CM 2925.1.er.a.1117.4 yes 32
75.53 even 20 inner 2925.1.er.a.2053.4 yes 32
325.103 odd 20 inner 2925.1.er.a.2053.4 yes 32
975.428 even 20 inner 2925.1.er.a.2053.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2925.1.er.a.1117.1 32 3.2 odd 2 inner
2925.1.er.a.1117.1 32 13.12 even 2 inner
2925.1.er.a.1117.4 yes 32 1.1 even 1 trivial
2925.1.er.a.1117.4 yes 32 39.38 odd 2 CM
2925.1.er.a.2053.1 yes 32 25.3 odd 20 inner
2925.1.er.a.2053.1 yes 32 975.428 even 20 inner
2925.1.er.a.2053.4 yes 32 75.53 even 20 inner
2925.1.er.a.2053.4 yes 32 325.103 odd 20 inner