Properties

Label 1521.1.bm.a.1360.1
Level $1521$
Weight $1$
Character 1521.1360
Analytic conductor $0.759$
Analytic rank $0$
Dimension $24$
Projective image $D_{52}$
CM discriminant -3
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1521,1,Mod(73,1521)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1521, base_ring=CyclotomicField(52))
 
chi = DirichletCharacter(H, H._module([0, 17]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1521.73");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1521 = 3^{2} \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1521.bm (of order \(52\), degree \(24\), 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: \(0.759077884215\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient field: \(\Q(\zeta_{52})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{24} - x^{22} + x^{20} - x^{18} + x^{16} - x^{14} + x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{52}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{52} - \cdots)\)

Embedding invariants

Embedding label 1360.1
Root \(-0.935016 + 0.354605i\) of defining polynomial
Character \(\chi\) \(=\) 1521.1360
Dual form 1521.1.bm.a.1162.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.992709 - 0.120537i) q^{4} +(-0.807380 - 0.147958i) q^{7} +O(q^{10})\) \(q+(-0.992709 - 0.120537i) q^{4} +(-0.807380 - 0.147958i) q^{7} +1.00000i q^{13} +(0.970942 + 0.239316i) q^{16} +(1.41163 + 1.41163i) q^{19} +(-0.464723 - 0.885456i) q^{25} +(0.783659 + 0.244198i) q^{28} +(0.468379 + 1.50308i) q^{31} +(1.87816 - 0.585260i) q^{37} +(0.764919 + 1.45743i) q^{43} +(-0.305045 - 0.115688i) q^{49} +(0.120537 - 0.992709i) q^{52} +(-1.12785 + 1.63397i) q^{61} +(-0.935016 - 0.354605i) q^{64} +(1.17759 - 1.50308i) q^{67} +(-1.70844 + 0.103342i) q^{73} +(-1.23119 - 1.57149i) q^{76} +(0.225408 + 1.85640i) q^{79} +(0.147958 - 0.807380i) q^{91} +(-0.731626 - 1.21026i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 2 q^{7} + 2 q^{16} + 2 q^{19} - 2 q^{28} - 2 q^{31} - 2 q^{37} - 2 q^{52} + 2 q^{67} + 2 q^{73} + 2 q^{76} + 2 q^{91} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1521\mathbb{Z}\right)^\times\).

\(n\) \(677\) \(847\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{52}\right)\)

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 0.0603785 0.998176i \(-0.480769\pi\)
−0.0603785 + 0.998176i \(0.519231\pi\)
\(3\) 0 0
\(4\) −0.992709 0.120537i −0.992709 0.120537i
\(5\) 0 0 0.517338 0.855781i \(-0.326923\pi\)
−0.517338 + 0.855781i \(0.673077\pi\)
\(6\) 0 0
\(7\) −0.807380 0.147958i −0.807380 0.147958i −0.239316 0.970942i \(-0.576923\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 −0.0603785 0.998176i \(-0.519231\pi\)
0.0603785 + 0.998176i \(0.480769\pi\)
\(12\) 0 0
\(13\) 1.00000i 1.00000i
\(14\) 0 0
\(15\) 0 0
\(16\) 0.970942 + 0.239316i 0.970942 + 0.239316i
\(17\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(18\) 0 0
\(19\) 1.41163 + 1.41163i 1.41163 + 1.41163i 0.748511 + 0.663123i \(0.230769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) 0 0
\(25\) −0.464723 0.885456i −0.464723 0.885456i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.783659 + 0.244198i 0.783659 + 0.244198i
\(29\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(30\) 0 0
\(31\) 0.468379 + 1.50308i 0.468379 + 1.50308i 0.822984 + 0.568065i \(0.192308\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.87816 0.585260i 1.87816 0.585260i 0.885456 0.464723i \(-0.153846\pi\)
0.992709 0.120537i \(-0.0384615\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.911900 0.410413i \(-0.865385\pi\)
0.911900 + 0.410413i \(0.134615\pi\)
\(42\) 0 0
\(43\) 0.764919 + 1.45743i 0.764919 + 1.45743i 0.885456 + 0.464723i \(0.153846\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.616719 0.787183i \(-0.288462\pi\)
−0.616719 + 0.787183i \(0.711538\pi\)
\(48\) 0 0
\(49\) −0.305045 0.115688i −0.305045 0.115688i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.120537 0.992709i 0.120537 0.992709i
\(53\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.855781 0.517338i \(-0.826923\pi\)
0.855781 + 0.517338i \(0.173077\pi\)
\(60\) 0 0
\(61\) −1.12785 + 1.63397i −1.12785 + 1.63397i −0.464723 + 0.885456i \(0.653846\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.935016 0.354605i −0.935016 0.354605i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.17759 1.50308i 1.17759 1.50308i 0.354605 0.935016i \(-0.384615\pi\)
0.822984 0.568065i \(-0.192308\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.911900 0.410413i \(-0.865385\pi\)
0.911900 + 0.410413i \(0.134615\pi\)
\(72\) 0 0
\(73\) −1.70844 + 0.103342i −1.70844 + 0.103342i −0.885456 0.464723i \(-0.846154\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.23119 1.57149i −1.23119 1.57149i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.225408 + 1.85640i 0.225408 + 1.85640i 0.464723 + 0.885456i \(0.346154\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 −0.410413 0.911900i \(-0.634615\pi\)
0.410413 + 0.911900i \(0.365385\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(90\) 0 0
\(91\) 0.147958 0.807380i 0.147958 0.807380i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.731626 1.21026i −0.731626 1.21026i −0.970942 0.239316i \(-0.923077\pi\)
0.239316 0.970942i \(-0.423077\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.354605 + 0.935016i 0.354605 + 0.935016i
\(101\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(102\) 0 0
\(103\) 0.447528 0.169725i 0.447528 0.169725i −0.120537 0.992709i \(-0.538462\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.239316 0.970942i \(-0.576923\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(108\) 0 0
\(109\) 0.987826 + 0.307819i 0.987826 + 0.307819i 0.748511 0.663123i \(-0.230769\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.748511 0.336877i −0.748511 0.336877i
\(113\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.992709 + 0.120537i −0.992709 + 0.120537i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.283788 1.54858i −0.283788 1.54858i
\(125\) 0 0
\(126\) 0 0
\(127\) 1.92773 0.234068i 1.92773 0.234068i 0.935016 0.354605i \(-0.115385\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(132\) 0 0
\(133\) −0.930863 1.34859i −0.930863 1.34859i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 −0.954721 0.297503i \(-0.903846\pi\)
0.954721 + 0.297503i \(0.0961538\pi\)
\(138\) 0 0
\(139\) −1.71945 0.423807i −1.71945 0.423807i −0.748511 0.663123i \(-0.769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −1.93502 + 0.354605i −1.93502 + 0.354605i
\(149\) 0 0 −0.787183 0.616719i \(-0.788462\pi\)
0.787183 + 0.616719i \(0.211538\pi\)
\(150\) 0 0
\(151\) −0.366951 0.468379i −0.366951 0.468379i 0.568065 0.822984i \(-0.307692\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.234068 0.0576926i 0.234068 0.0576926i −0.120537 0.992709i \(-0.538462\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 0.568065 0.177016i 0.568065 0.177016i 1.00000i \(-0.5\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.998176 0.0603785i \(-0.980769\pi\)
0.998176 + 0.0603785i \(0.0192308\pi\)
\(168\) 0 0
\(169\) −1.00000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −0.583668 1.53901i −0.583668 1.53901i
\(173\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(174\) 0 0
\(175\) 0.244198 + 0.783659i 0.244198 + 0.783659i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(180\) 0 0
\(181\) −0.222431 0.902438i −0.222431 0.902438i −0.970942 0.239316i \(-0.923077\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0 0
\(193\) −0.0649838 0.354605i −0.0649838 0.354605i 0.935016 0.354605i \(-0.115385\pi\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.288876 + 0.151614i 0.288876 + 0.151614i
\(197\) 0 0 0.297503 0.954721i \(-0.403846\pi\)
−0.297503 + 0.954721i \(0.596154\pi\)
\(198\) 0 0
\(199\) −0.358261 + 1.45352i −0.358261 + 1.45352i 0.464723 + 0.885456i \(0.346154\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.239316 + 0.970942i −0.239316 + 0.970942i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.112032 0.922670i −0.112032 0.922670i −0.935016 0.354605i \(-0.884615\pi\)
0.822984 0.568065i \(-0.192308\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −0.155767 1.28286i −0.155767 1.28286i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.21026 + 0.731626i 1.21026 + 0.731626i 0.970942 0.239316i \(-0.0769231\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 −0.616719 0.787183i \(-0.711538\pi\)
0.616719 + 0.787183i \(0.288462\pi\)
\(228\) 0 0
\(229\) 0.307819 0.987826i 0.307819 0.987826i −0.663123 0.748511i \(-0.730769\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(240\) 0 0
\(241\) 1.05555 0.638104i 1.05555 0.638104i 0.120537 0.992709i \(-0.461538\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 1.31658 1.48611i 1.31658 1.48611i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.41163 + 1.41163i −1.41163 + 1.41163i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.885456 + 0.464723i 0.885456 + 0.464723i
\(257\) 0 0 0.120537 0.992709i \(-0.461538\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(258\) 0 0
\(259\) −1.60299 + 0.194638i −1.60299 + 0.194638i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.663123 0.748511i \(-0.269231\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.35018 + 1.35018i −1.35018 + 1.35018i
\(269\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(270\) 0 0
\(271\) −0.970942 0.760684i −0.970942 0.760684i 1.00000i \(-0.5\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.53901 1.06230i −1.53901 1.06230i −0.970942 0.239316i \(-0.923077\pi\)
−0.568065 0.822984i \(-0.692308\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.410413 0.911900i \(-0.365385\pi\)
−0.410413 + 0.911900i \(0.634615\pi\)
\(282\) 0 0
\(283\) −0.902438 + 1.71945i −0.902438 + 1.71945i −0.239316 + 0.970942i \(0.576923\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.354605 + 0.935016i −0.354605 + 0.935016i
\(290\) 0 0
\(291\) 0 0
\(292\) 1.70844 + 0.103342i 1.70844 + 0.103342i
\(293\) 0 0 0.983620 0.180255i \(-0.0576923\pi\)
−0.983620 + 0.180255i \(0.942308\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −0.401942 1.28988i −0.401942 1.28988i
\(302\) 0 0
\(303\) 0 0
\(304\) 1.03279 + 1.70844i 1.03279 + 1.70844i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.344186 + 0.107253i −0.344186 + 0.107253i −0.464723 0.885456i \(-0.653846\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.885456 0.464723i \(-0.846154\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(312\) 0 0
\(313\) 1.65583 0.869047i 1.65583 0.869047i 0.663123 0.748511i \(-0.269231\pi\)
0.992709 0.120537i \(-0.0384615\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.87003i 1.87003i
\(317\) 0 0 −0.180255 0.983620i \(-0.557692\pi\)
0.180255 + 0.983620i \(0.442308\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.885456 0.464723i 0.885456 0.464723i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.344186 1.87816i 0.344186 1.87816i −0.120537 0.992709i \(-0.538462\pi\)
0.464723 0.885456i \(-0.346154\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 1.13613i 1.13613i −0.822984 0.568065i \(-0.807692\pi\)
0.822984 0.568065i \(-0.192308\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.931617 + 0.563182i 0.931617 + 0.563182i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0 0 −0.663123 0.748511i \(-0.730769\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(348\) 0 0
\(349\) 1.41163 0.0853881i 1.41163 0.0853881i 0.663123 0.748511i \(-0.269231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.983620 0.180255i \(-0.942308\pi\)
0.983620 + 0.180255i \(0.0576923\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 0.983620 0.180255i \(-0.0576923\pi\)
−0.983620 + 0.180255i \(0.942308\pi\)
\(360\) 0 0
\(361\) 2.98542i 2.98542i
\(362\) 0 0
\(363\) 0 0
\(364\) −0.244198 + 0.783659i −0.244198 + 0.783659i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.530851 + 0.470293i −0.530851 + 0.470293i −0.885456 0.464723i \(-0.846154\pi\)
0.354605 + 0.935016i \(0.384615\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 1.48611 + 1.31658i 1.48611 + 1.31658i 0.822984 + 0.568065i \(0.192308\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.0495602 + 0.110118i −0.0495602 + 0.110118i −0.935016 0.354605i \(-0.884615\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.180255 0.983620i \(-0.557692\pi\)
0.180255 + 0.983620i \(0.442308\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0.580411 + 1.28962i 0.580411 + 1.28962i
\(389\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.638104 + 1.05555i −0.638104 + 1.05555i 0.354605 + 0.935016i \(0.384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.239316 0.970942i −0.239316 0.970942i
\(401\) 0 0 −0.517338 0.855781i \(-0.673077\pi\)
0.517338 + 0.855781i \(0.326923\pi\)
\(402\) 0 0
\(403\) −1.50308 + 0.468379i −1.50308 + 0.468379i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.0495602 0.110118i 0.0495602 0.110118i −0.885456 0.464723i \(-0.846154\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.464723 + 0.114544i −0.464723 + 0.114544i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(420\) 0 0
\(421\) −1.56077 + 0.702447i −1.56077 + 0.702447i −0.992709 0.120537i \(-0.961538\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.15236 1.15236i 1.15236 1.15236i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.616719 0.787183i \(-0.711538\pi\)
0.616719 + 0.787183i \(0.288462\pi\)
\(432\) 0 0
\(433\) −0.358261 1.45352i −0.358261 1.45352i −0.822984 0.568065i \(-0.807692\pi\)
0.464723 0.885456i \(-0.346154\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.943521 0.424644i −0.943521 0.424644i
\(437\) 0 0
\(438\) 0 0
\(439\) 0.616337 + 1.17433i 0.616337 + 1.17433i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0 0 −0.935016 0.354605i \(-0.884615\pi\)
0.935016 + 0.354605i \(0.115385\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.702447 + 0.424644i 0.702447 + 0.424644i
\(449\) 0 0 0.787183 0.616719i \(-0.211538\pi\)
−0.787183 + 0.616719i \(0.788462\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.943521 0.424644i 0.943521 0.424644i 0.120537 0.992709i \(-0.461538\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.0603785 0.998176i \(-0.480769\pi\)
−0.0603785 + 0.998176i \(0.519231\pi\)
\(462\) 0 0
\(463\) 0.00729113 0.120537i 0.00729113 0.120537i −0.992709 0.120537i \(-0.961538\pi\)
1.00000 \(0\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(468\) 0 0
\(469\) −1.17315 + 1.03932i −1.17315 + 1.03932i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0.593921 1.90596i 0.593921 1.90596i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.954721 0.297503i \(-0.903846\pi\)
0.954721 + 0.297503i \(0.0961538\pi\)
\(480\) 0 0
\(481\) 0.585260 + 1.87816i 0.585260 + 1.87816i
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 1.00000
\(485\) 0 0
\(486\) 0 0
\(487\) 0.760684 0.970942i 0.760684 0.970942i −0.239316 0.970942i \(-0.576923\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 −0.970942 0.239316i \(-0.923077\pi\)
0.970942 + 0.239316i \(0.0769231\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.0950579 + 1.57149i 0.0950579 + 1.57149i
\(497\) 0 0
\(498\) 0 0
\(499\) 0.308518 1.68353i 0.308518 1.68353i −0.354605 0.935016i \(-0.615385\pi\)
0.663123 0.748511i \(-0.269231\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) −1.94188 −1.94188
\(509\) 0 0 0.0603785 0.998176i \(-0.480769\pi\)
−0.0603785 + 0.998176i \(0.519231\pi\)
\(510\) 0 0
\(511\) 1.39465 + 0.169341i 1.39465 + 0.169341i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.239316 0.970942i \(-0.423077\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(522\) 0 0
\(523\) −1.45352 0.358261i −1.45352 0.358261i −0.568065 0.822984i \(-0.692308\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0.761521 + 1.45096i 0.761521 + 1.45096i
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 0.509195 0.307819i 0.509195 0.307819i −0.239316 0.970942i \(-0.576923\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.180446 0.159861i −0.180446 0.159861i 0.568065 0.822984i \(-0.307692\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0.0926792 1.53217i 0.0926792 1.53217i
\(554\) 0 0
\(555\) 0 0
\(556\) 1.65583 + 0.627974i 1.65583 + 0.627974i
\(557\) 0 0 0.911900 0.410413i \(-0.134615\pi\)
−0.911900 + 0.410413i \(0.865385\pi\)
\(558\) 0 0
\(559\) −1.45743 + 0.764919i −1.45743 + 0.764919i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 0.354605 0.935016i \(-0.384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(570\) 0 0
\(571\) 0.663123 + 0.251489i 0.663123 + 0.251489i 0.663123 0.748511i \(-0.269231\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0.420733 + 0.420733i 0.420733 + 0.420733i 0.885456 0.464723i \(-0.153846\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(588\) 0 0
\(589\) −1.46062 + 2.78298i −1.46062 + 2.78298i
\(590\) 0 0
\(591\) 0 0
\(592\) 1.96365 0.118779i 1.96365 0.118779i
\(593\) 0 0 0.911900 0.410413i \(-0.134615\pi\)
−0.911900 + 0.410413i \(0.865385\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.992709 0.120537i \(-0.961538\pi\)
0.992709 + 0.120537i \(0.0384615\pi\)
\(600\) 0 0
\(601\) −1.23202 1.09148i −1.23202 1.09148i −0.992709 0.120537i \(-0.961538\pi\)
−0.239316 0.970942i \(-0.576923\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.307819 + 0.509195i 0.307819 + 0.509195i
\(605\) 0 0
\(606\) 0 0
\(607\) 0.402877 + 1.06230i 0.402877 + 1.06230i 0.970942 + 0.239316i \(0.0769231\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.01773 1.68353i −1.01773 1.68353i −0.663123 0.748511i \(-0.730769\pi\)
−0.354605 0.935016i \(-0.615385\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 0.517338 0.855781i \(-0.326923\pi\)
−0.517338 + 0.855781i \(0.673077\pi\)
\(618\) 0 0
\(619\) 1.79393 + 0.807380i 1.79393 + 0.807380i 0.970942 + 0.239316i \(0.0769231\pi\)
0.822984 + 0.568065i \(0.192308\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.568065 + 0.822984i −0.568065 + 0.822984i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.239316 + 0.0290582i −0.239316 + 0.0290582i
\(629\) 0 0
\(630\) 0 0
\(631\) −0.0649838 0.354605i −0.0649838 0.354605i 0.935016 0.354605i \(-0.115385\pi\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.115688 0.305045i 0.115688 0.305045i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.748511 0.663123i \(-0.769231\pi\)
0.748511 + 0.663123i \(0.230769\pi\)
\(642\) 0 0
\(643\) −0.328749 + 0.147958i −0.328749 + 0.147958i −0.568065 0.822984i \(-0.692308\pi\)
0.239316 + 0.970942i \(0.423077\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.748511 0.663123i \(-0.230769\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.585260 + 0.107253i −0.585260 + 0.107253i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(660\) 0 0
\(661\) −0.118779 0.0217671i −0.118779 0.0217671i 0.120537 0.992709i \(-0.461538\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 1.24006 0.470293i 1.24006 0.470293i 0.354605 0.935016i \(-0.384615\pi\)
0.885456 + 0.464723i \(0.153846\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0.992709 + 0.120537i 0.992709 + 0.120537i
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0.411633 + 1.08539i 0.411633 + 1.08539i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.180255 0.983620i \(-0.442308\pi\)
−0.180255 + 0.983620i \(0.557692\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.393906 + 1.59814i 0.393906 + 1.59814i
\(689\) 0 0
\(690\) 0 0
\(691\) −0.283788 + 1.54858i −0.283788 + 1.54858i 0.464723 + 0.885456i \(0.346154\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.147958 0.807380i −0.147958 0.807380i
\(701\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(702\) 0 0
\(703\) 3.47745 + 1.82511i 3.47745 + 1.82511i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0.783659 + 1.74122i 0.783659 + 1.74122i 0.663123 + 0.748511i \(0.269231\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.885456 0.464723i \(-0.153846\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(720\) 0 0
\(721\) −0.386438 + 0.0708173i −0.386438 + 0.0708173i
\(722\) 0 0
\(723\) 0 0
\(724\) 0.112032 + 0.922670i 0.112032 + 0.922670i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.935016 0.645395i −0.935016 0.645395i 1.00000i \(-0.5\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0.807380 1.79393i 0.807380 1.79393i 0.239316 0.970942i \(-0.423077\pi\)
0.568065 0.822984i \(-0.307692\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −1.05555 + 0.638104i −1.05555 + 0.638104i −0.935016 0.354605i \(-0.884615\pi\)
−0.120537 + 0.992709i \(0.538462\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.787183 0.616719i \(-0.788462\pi\)
0.787183 + 0.616719i \(0.211538\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −0.317391 + 0.358261i −0.317391 + 0.358261i −0.885456 0.464723i \(-0.846154\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.198399 1.63397i 0.198399 1.63397i −0.464723 0.885456i \(-0.653846\pi\)
0.663123 0.748511i \(-0.269231\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.0603785 0.998176i \(-0.519231\pi\)
0.0603785 + 0.998176i \(0.480769\pi\)
\(762\) 0 0
\(763\) −0.752007 0.394684i −0.752007 0.394684i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 1.50308 1.17759i 1.50308 1.17759i 0.568065 0.822984i \(-0.307692\pi\)
0.935016 0.354605i \(-0.115385\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.0217671 + 0.359852i 0.0217671 + 0.359852i
\(773\) 0 0 0.855781 0.517338i \(-0.173077\pi\)
−0.855781 + 0.517338i \(0.826923\pi\)
\(774\) 0 0
\(775\) 1.11325 1.11325i 1.11325 1.11325i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.268495 0.185328i −0.268495 0.185328i
\(785\) 0 0
\(786\) 0 0
\(787\) 0.638104 + 0.814480i 0.638104 + 0.814480i 0.992709 0.120537i \(-0.0384615\pi\)
−0.354605 + 0.935016i \(0.615385\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −1.63397 1.12785i −1.63397 1.12785i
\(794\) 0 0
\(795\) 0 0
\(796\) 0.530851 1.39974i 0.530851 1.39974i
\(797\) 0 0 −0.120537 0.992709i \(-0.538462\pi\)
0.120537 + 0.992709i \(0.461538\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 0.822984 0.568065i \(-0.192308\pi\)
−0.822984 + 0.568065i \(0.807692\pi\)
\(810\) 0 0
\(811\) −0.0624722 0.103342i −0.0624722 0.103342i 0.822984 0.568065i \(-0.192308\pi\)
−0.885456 + 0.464723i \(0.846154\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −0.977574 + 3.13715i −0.977574 + 3.13715i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.180255 0.983620i \(-0.557692\pi\)
0.180255 + 0.983620i \(0.442308\pi\)
\(822\) 0 0
\(823\) 1.32625i 1.32625i −0.748511 0.663123i \(-0.769231\pi\)
0.748511 0.663123i \(-0.230769\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.787183 0.616719i \(-0.211538\pi\)
−0.787183 + 0.616719i \(0.788462\pi\)
\(828\) 0 0
\(829\) 0.464723 1.88546i 0.464723 1.88546i 1.00000i \(-0.5\pi\)
0.464723 0.885456i \(-0.346154\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.354605 0.935016i 0.354605 0.935016i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.297503 0.954721i \(-0.596154\pi\)
0.297503 + 0.954721i \(0.403846\pi\)
\(840\) 0 0
\(841\) −0.120537 + 0.992709i −0.120537 + 0.992709i
\(842\) 0 0
\(843\) 0 0
\(844\) 0.929446i 0.929446i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.819328 + 0.0495602i 0.819328 + 0.0495602i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −1.01773 0.186505i −1.01773 0.186505i −0.354605 0.935016i \(-0.615385\pi\)
−0.663123 + 0.748511i \(0.730769\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.970942 0.239316i \(-0.0769231\pi\)
−0.970942 + 0.239316i \(0.923077\pi\)
\(858\) 0 0
\(859\) −1.81569 0.447528i −1.81569 0.447528i −0.822984 0.568065i \(-0.807692\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 −0.616719 0.787183i \(-0.711538\pi\)
0.616719 + 0.787183i \(0.288462\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 1.29228i 1.29228i
\(869\) 0 0
\(870\) 0 0
\(871\) 1.50308 + 1.17759i 1.50308 + 1.17759i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.344186 0.107253i −0.344186 0.107253i 0.120537 0.992709i \(-0.461538\pi\)
−0.464723 + 0.885456i \(0.653846\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.568065 0.822984i \(-0.692308\pi\)
0.568065 + 0.822984i \(0.307692\pi\)
\(882\) 0 0
\(883\) −0.753393 0.850405i −0.753393 0.850405i 0.239316 0.970942i \(-0.423077\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 0.992709 0.120537i \(-0.0384615\pi\)
−0.992709 + 0.120537i \(0.961538\pi\)
\(888\) 0 0
\(889\) −1.59104 0.0962402i −1.59104 0.0962402i
\(890\) 0 0
\(891\) 0 0
\(892\) −1.11325 0.872172i −1.11325 0.872172i
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.423807 1.71945i −0.423807 1.71945i −0.663123 0.748511i \(-0.730769\pi\)
0.239316 0.970942i \(-0.423077\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.935016 0.354605i \(-0.115385\pi\)
−0.935016 + 0.354605i \(0.884615\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) −0.424644 + 0.943521i −0.424644 + 0.943521i
\(917\) 0 0
\(918\) 0 0
\(919\) −0.902438 + 0.222431i −0.902438 + 0.222431i −0.663123 0.748511i \(-0.730769\pi\)
−0.239316 + 0.970942i \(0.576923\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.39105 1.39105i −1.39105 1.39105i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.998176 0.0603785i \(-0.0192308\pi\)
−0.998176 + 0.0603785i \(0.980769\pi\)
\(930\) 0 0
\(931\) −0.267302 0.593921i −0.267302 0.593921i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0.159861 1.31658i 0.159861 1.31658i −0.663123 0.748511i \(-0.730769\pi\)
0.822984 0.568065i \(-0.192308\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.998176 0.0603785i \(-0.0192308\pi\)
−0.998176 + 0.0603785i \(0.980769\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.616719 0.787183i \(-0.288462\pi\)
−0.616719 + 0.787183i \(0.711538\pi\)
\(948\) 0 0
\(949\) −0.103342 1.70844i −0.103342 1.70844i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.568065 0.822984i \(-0.307692\pi\)
−0.568065 + 0.822984i \(0.692308\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −1.21689 + 0.839958i −1.21689 + 0.839958i
\(962\) 0 0
\(963\) 0 0
\(964\) −1.12477 + 0.506219i −1.12477 + 0.506219i
\(965\) 0 0
\(966\) 0 0
\(967\) 0.970942 1.23932i 0.970942 1.23932i 1.00000i \(-0.5\pi\)
0.970942 0.239316i \(-0.0769231\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.464723 0.885456i \(-0.653846\pi\)
0.464723 + 0.885456i \(0.346154\pi\)
\(972\) 0 0
\(973\) 1.32555 + 0.596580i 1.32555 + 0.596580i
\(974\) 0 0
\(975\) 0 0
\(976\) −1.48611 + 1.31658i −1.48611 + 1.31658i
\(977\) 0 0 0.954721 0.297503i \(-0.0961538\pi\)
−0.954721 + 0.297503i \(0.903846\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 −0.297503 0.954721i \(-0.596154\pi\)
0.297503 + 0.954721i \(0.403846\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.57149 1.23119i 1.57149 1.23119i
\(989\) 0 0
\(990\) 0 0
\(991\) −1.49702 −1.49702 −0.748511 0.663123i \(-0.769231\pi\)
−0.748511 + 0.663123i \(0.769231\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.00599 1.45743i −1.00599 1.45743i −0.885456 0.464723i \(-0.846154\pi\)
−0.120537 0.992709i \(-0.538462\pi\)
\(998\) 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 1521.1.bm.a.1360.1 yes 24
3.2 odd 2 CM 1521.1.bm.a.1360.1 yes 24
169.148 odd 52 inner 1521.1.bm.a.1162.1 24
507.317 even 52 inner 1521.1.bm.a.1162.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1521.1.bm.a.1162.1 24 169.148 odd 52 inner
1521.1.bm.a.1162.1 24 507.317 even 52 inner
1521.1.bm.a.1360.1 yes 24 1.1 even 1 trivial
1521.1.bm.a.1360.1 yes 24 3.2 odd 2 CM