Properties

Label 1449.1.bu.a.125.3
Level $1449$
Weight $1$
Character 1449.125
Analytic conductor $0.723$
Analytic rank $0$
Dimension $40$
Projective image $D_{44}$
CM discriminant -7
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1449,1,Mod(125,1449)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1449, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 3]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1449.125");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1449 = 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1449.bu (of order \(22\), degree \(10\), 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: \(0.723145203305\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(4\) over \(\Q(\zeta_{22})\)
Coefficient field: \(\Q(\zeta_{88})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{40} - x^{36} + x^{32} - x^{28} + x^{24} - x^{20} + x^{16} - x^{12} + x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{44}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{44} - \cdots)\)

Embedding invariants

Embedding label 125.3
Root \(-0.599278 - 0.800541i\) of defining polynomial
Character \(\chi\) \(=\) 1449.125
Dual form 1449.1.bu.a.881.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.905808 - 0.784887i) q^{2} +(0.0621254 - 0.432092i) q^{4} +(0.281733 - 0.959493i) q^{7} +(0.365119 + 0.568136i) q^{8} +O(q^{10})\) \(q+(0.905808 - 0.784887i) q^{2} +(0.0621254 - 0.432092i) q^{4} +(0.281733 - 0.959493i) q^{7} +(0.365119 + 0.568136i) q^{8} +(0.278401 - 0.321292i) q^{11} +(-0.497898 - 1.09024i) q^{14} +(1.19550 + 0.351031i) q^{16} -0.509543i q^{22} +(0.349464 + 0.936950i) q^{23} +(-0.654861 - 0.755750i) q^{25} +(-0.397086 - 0.181343i) q^{28} +(-1.97460 + 0.283904i) q^{29} +(0.744099 - 0.339819i) q^{32} +(1.74557 - 0.797176i) q^{37} +(0.449181 - 0.698939i) q^{43} +(-0.121532 - 0.140255i) q^{44} +(1.05195 + 0.574406i) q^{46} +(-0.841254 - 0.540641i) q^{49} +(-1.18636 - 0.170572i) q^{50} +(-0.136899 - 0.0401971i) q^{53} +(0.647988 - 0.190266i) q^{56} +(-1.56577 + 1.80700i) q^{58} +(-0.110304 + 0.241532i) q^{64} +(-1.49611 + 1.29639i) q^{67} +(-1.47696 + 1.27979i) q^{71} +(0.955459 - 2.09216i) q^{74} +(-0.229843 - 0.357643i) q^{77} +(0.425839 + 1.45027i) q^{79} +(-0.141717 - 0.985660i) q^{86} +(0.284187 + 0.0408599i) q^{88} +(0.426559 - 0.0927922i) q^{92} +(-1.18636 + 0.170572i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 4 q^{4} + 4 q^{16} - 4 q^{25} + 4 q^{46} + 4 q^{49} - 36 q^{58} - 4 q^{64}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1449\mathbb{Z}\right)^\times\).

\(n\) \(442\) \(829\) \(1289\)
\(\chi(n)\) \(e\left(\frac{3}{22}\right)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.905808 0.784887i 0.905808 0.784887i −0.0713392 0.997452i \(-0.522727\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(3\) 0 0
\(4\) 0.0621254 0.432092i 0.0621254 0.432092i
\(5\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(6\) 0 0
\(7\) 0.281733 0.959493i 0.281733 0.959493i
\(8\) 0.365119 + 0.568136i 0.365119 + 0.568136i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.278401 0.321292i 0.278401 0.321292i −0.599278 0.800541i \(-0.704545\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(12\) 0 0
\(13\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(14\) −0.497898 1.09024i −0.497898 1.09024i
\(15\) 0 0
\(16\) 1.19550 + 0.351031i 1.19550 + 0.351031i
\(17\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(18\) 0 0
\(19\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.509543i 0.509543i
\(23\) 0.349464 + 0.936950i 0.349464 + 0.936950i
\(24\) 0 0
\(25\) −0.654861 0.755750i −0.654861 0.755750i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.397086 0.181343i −0.397086 0.181343i
\(29\) −1.97460 + 0.283904i −1.97460 + 0.283904i −0.977147 + 0.212565i \(0.931818\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(30\) 0 0
\(31\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(32\) 0.744099 0.339819i 0.744099 0.339819i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 1.74557 0.797176i 1.74557 0.797176i 0.755750 0.654861i \(-0.227273\pi\)
0.989821 0.142315i \(-0.0454545\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(42\) 0 0
\(43\) 0.449181 0.698939i 0.449181 0.698939i −0.540641 0.841254i \(-0.681818\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(44\) −0.121532 0.140255i −0.121532 0.140255i
\(45\) 0 0
\(46\) 1.05195 + 0.574406i 1.05195 + 0.574406i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −0.841254 0.540641i −0.841254 0.540641i
\(50\) −1.18636 0.170572i −1.18636 0.170572i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.136899 0.0401971i −0.136899 0.0401971i 0.212565 0.977147i \(-0.431818\pi\)
−0.349464 + 0.936950i \(0.613636\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0.647988 0.190266i 0.647988 0.190266i
\(57\) 0 0
\(58\) −1.56577 + 1.80700i −1.56577 + 1.80700i
\(59\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(60\) 0 0
\(61\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −0.110304 + 0.241532i −0.110304 + 0.241532i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.49611 + 1.29639i −1.49611 + 1.29639i −0.654861 + 0.755750i \(0.727273\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.47696 + 1.27979i −1.47696 + 1.27979i −0.599278 + 0.800541i \(0.704545\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(72\) 0 0
\(73\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(74\) 0.955459 2.09216i 0.955459 2.09216i
\(75\) 0 0
\(76\) 0 0
\(77\) −0.229843 0.357643i −0.229843 0.357643i
\(78\) 0 0
\(79\) 0.425839 + 1.45027i 0.425839 + 1.45027i 0.841254 + 0.540641i \(0.181818\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.141717 0.985660i −0.141717 0.985660i
\(87\) 0 0
\(88\) 0.284187 + 0.0408599i 0.284187 + 0.0408599i
\(89\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.426559 0.0927922i 0.426559 0.0927922i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(98\) −1.18636 + 0.170572i −1.18636 + 0.170572i
\(99\) 0 0
\(100\) −0.367237 + 0.236009i −0.367237 + 0.236009i
\(101\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(102\) 0 0
\(103\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −0.155554 + 0.0710393i −0.155554 + 0.0710393i
\(107\) −0.806340 + 0.518203i −0.806340 + 0.518203i −0.877679 0.479249i \(-0.840909\pi\)
0.0713392 + 0.997452i \(0.477273\pi\)
\(108\) 0 0
\(109\) −0.281733 + 0.0405070i −0.281733 + 0.0405070i −0.281733 0.959493i \(-0.590909\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.673623 1.04818i 0.673623 1.04818i
\(113\) 0.457701 + 0.528215i 0.457701 + 0.528215i 0.936950 0.349464i \(-0.113636\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.870845i 0.870845i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0.116593 + 0.810925i 0.116593 + 0.810925i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −0.544078 + 0.627899i −0.544078 + 0.627899i −0.959493 0.281733i \(-0.909091\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(128\) 0.320125 + 1.09024i 0.320125 + 1.09024i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −0.337672 + 2.34856i −0.337672 + 2.34856i
\(135\) 0 0
\(136\) 0 0
\(137\) −1.60108 −1.60108 −0.800541 0.599278i \(-0.795455\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −0.333348 + 2.31849i −0.333348 + 2.31849i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −0.236009 0.803771i −0.236009 0.803771i
\(149\) 1.22714 1.41620i 1.22714 1.41620i 0.349464 0.936950i \(-0.386364\pi\)
0.877679 0.479249i \(-0.159091\pi\)
\(150\) 0 0
\(151\) −1.45027 + 0.425839i −1.45027 + 0.425839i −0.909632 0.415415i \(-0.863636\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.488902 0.143555i −0.488902 0.143555i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(158\) 1.52403 + 0.979433i 1.52403 + 0.979433i
\(159\) 0 0
\(160\) 0 0
\(161\) 0.997452 0.0713392i 0.997452 0.0713392i
\(162\) 0 0
\(163\) −0.857685 0.989821i −0.857685 0.989821i 0.142315 0.989821i \(-0.454545\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(168\) 0 0
\(169\) 0.841254 0.540641i 0.841254 0.540641i
\(170\) 0 0
\(171\) 0 0
\(172\) −0.274100 0.237509i −0.274100 0.237509i
\(173\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(174\) 0 0
\(175\) −0.909632 + 0.415415i −0.909632 + 0.415415i
\(176\) 0.445613 0.286378i 0.445613 0.286378i
\(177\) 0 0
\(178\) 0 0
\(179\) −0.635768 0.290345i −0.635768 0.290345i 0.0713392 0.997452i \(-0.477273\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(180\) 0 0
\(181\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.404719 + 0.540641i −0.404719 + 0.540641i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 1.68425 + 0.494541i 1.68425 + 0.494541i 0.977147 0.212565i \(-0.0681818\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(192\) 0 0
\(193\) −0.449181 0.983568i −0.449181 0.983568i −0.989821 0.142315i \(-0.954545\pi\)
0.540641 0.841254i \(-0.318182\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.285870 + 0.329911i −0.285870 + 0.329911i
\(197\) −0.196911 0.670617i −0.196911 0.670617i −0.997452 0.0713392i \(-0.977273\pi\)
0.800541 0.599278i \(-0.204545\pi\)
\(198\) 0 0
\(199\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(200\) 0.190266 0.647988i 0.190266 0.647988i
\(201\) 0 0
\(202\) 0 0
\(203\) −0.283904 + 1.97460i −0.283904 + 1.97460i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.153882 1.07028i 0.153882 1.07028i −0.755750 0.654861i \(-0.772727\pi\)
0.909632 0.415415i \(-0.136364\pi\)
\(212\) −0.0258737 + 0.0566556i −0.0258737 + 0.0566556i
\(213\) 0 0
\(214\) −0.323658 + 1.10228i −0.323658 + 1.10228i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −0.223402 + 0.257820i −0.223402 + 0.257820i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(224\) −0.116417 0.809696i −0.116417 0.809696i
\(225\) 0 0
\(226\) 0.829178 + 0.119218i 0.829178 + 0.119218i
\(227\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.882259 1.01818i −0.882259 1.01818i
\(233\) −0.518203 + 0.806340i −0.518203 + 0.806340i −0.997452 0.0713392i \(-0.977273\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.59673 0.729202i 1.59673 0.729202i 0.599278 0.800541i \(-0.295455\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(240\) 0 0
\(241\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(242\) 0.742096 + 0.643030i 0.742096 + 0.643030i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(252\) 0 0
\(253\) 0.398326 + 0.148568i 0.398326 + 0.148568i
\(254\) 0.995796i 0.995796i
\(255\) 0 0
\(256\) 0.922314 + 0.592735i 0.922314 + 0.592735i
\(257\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(258\) 0 0
\(259\) −0.273100 1.89945i −0.273100 1.89945i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.53623 0.451077i 1.53623 0.451077i 0.599278 0.800541i \(-0.295455\pi\)
0.936950 + 0.349464i \(0.113636\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0.467213 + 0.726997i 0.467213 + 0.726997i
\(269\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(270\) 0 0
\(271\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −1.45027 + 1.25667i −1.45027 + 1.25667i
\(275\) −0.425131 −0.425131
\(276\) 0 0
\(277\) 1.91899 1.91899 0.959493 0.281733i \(-0.0909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.828713 1.81463i 0.828713 1.81463i 0.349464 0.936950i \(-0.386364\pi\)
0.479249 0.877679i \(-0.340909\pi\)
\(282\) 0 0
\(283\) 0 0 0.281733 0.959493i \(-0.409091\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(284\) 0.461230 + 0.717688i 0.461230 + 0.717688i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.959493 + 0.281733i −0.959493 + 0.281733i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.09024 + 0.700657i 1.09024 + 0.700657i
\(297\) 0 0
\(298\) 2.24597i 2.24597i
\(299\) 0 0
\(300\) 0 0
\(301\) −0.544078 0.627899i −0.544078 0.627899i
\(302\) −0.979433 + 1.52403i −0.979433 + 1.52403i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(308\) −0.168813 + 0.0770945i −0.168813 + 0.0770945i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(312\) 0 0
\(313\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.653106 0.0939025i 0.653106 0.0939025i
\(317\) 1.59673 + 0.729202i 1.59673 + 0.729202i 0.997452 0.0713392i \(-0.0227273\pi\)
0.599278 + 0.800541i \(0.295455\pi\)
\(318\) 0 0
\(319\) −0.458515 + 0.713463i −0.458515 + 0.713463i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.847507 0.847507i 0.847507 0.847507i
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) −1.55380 0.223402i −1.55380 0.223402i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.755750 1.65486i −0.755750 1.65486i −0.755750 0.654861i \(-0.772727\pi\)
1.00000i \(-0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.909632 + 1.41542i 0.909632 + 1.41542i 0.909632 + 0.415415i \(0.136364\pi\)
1.00000i \(0.5\pi\)
\(338\) 0.337672 1.15001i 0.337672 1.15001i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(344\) 0.561096 0.561096
\(345\) 0 0
\(346\) 0 0
\(347\) −0.724384 + 0.627683i −0.724384 + 0.627683i −0.936950 0.349464i \(-0.886364\pi\)
0.212565 + 0.977147i \(0.431818\pi\)
\(348\) 0 0
\(349\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(350\) −0.497898 + 1.09024i −0.497898 + 1.09024i
\(351\) 0 0
\(352\) 0.0979771 0.333679i 0.0979771 0.333679i
\(353\) 0 0 −0.540641 0.841254i \(-0.681818\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.803771 + 0.236009i −0.803771 + 0.236009i
\(359\) −0.778446 1.70456i −0.778446 1.70456i −0.707107 0.707107i \(-0.750000\pi\)
−0.0713392 0.997452i \(-0.522727\pi\)
\(360\) 0 0
\(361\) 0.959493 + 0.281733i 0.959493 + 0.281733i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 0.0888866 + 1.24280i 0.0888866 + 1.24280i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.0771377 + 0.120029i −0.0771377 + 0.120029i
\(372\) 0 0
\(373\) 0.983568 + 0.449181i 0.983568 + 0.449181i 0.841254 0.540641i \(-0.181818\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −0.989821 0.857685i −0.989821 0.857685i 1.00000i \(-0.5\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 1.91377 0.873989i 1.91377 0.873989i
\(383\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −1.17886 0.538368i −1.17886 0.538368i
\(387\) 0 0
\(388\) 0 0
\(389\) −1.27979 1.47696i −1.27979 1.47696i −0.800541 0.599278i \(-0.795455\pi\)
−0.479249 0.877679i \(-0.659091\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.675344i 0.675344i
\(393\) 0 0
\(394\) −0.704722 0.452897i −0.704722 0.452897i
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.517596 1.13338i −0.517596 1.13338i
\(401\) 1.68425 0.494541i 1.68425 0.494541i 0.707107 0.707107i \(-0.250000\pi\)
0.977147 + 0.212565i \(0.0681818\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.29267 + 2.01144i 1.29267 + 2.01144i
\(407\) 0.229843 0.782773i 0.229843 0.782773i
\(408\) 0 0
\(409\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(420\) 0 0
\(421\) 0.512546 1.74557i 0.512546 1.74557i −0.142315 0.989821i \(-0.545455\pi\)
0.654861 0.755750i \(-0.272727\pi\)
\(422\) −0.700657 1.09024i −0.700657 1.09024i
\(423\) 0 0
\(424\) −0.0271469 0.0924539i −0.0271469 0.0924539i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0.173817 + 0.380606i 0.173817 + 0.380606i
\(429\) 0 0
\(430\) 0 0
\(431\) 0.0994679 + 0.691814i 0.0994679 + 0.691814i 0.977147 + 0.212565i \(0.0681818\pi\)
−0.877679 + 0.479249i \(0.840909\pi\)
\(432\) 0 0
\(433\) 0 0 −0.989821 0.142315i \(-0.954545\pi\)
0.989821 + 0.142315i \(0.0454545\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0.124251i 0.124251i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −0.420803 + 0.0605024i −0.420803 + 0.0605024i −0.349464 0.936950i \(-0.613636\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.200672 + 0.173883i 0.200672 + 0.173883i
\(449\) −1.32661 1.14952i −1.32661 1.14952i −0.977147 0.212565i \(-0.931818\pi\)
−0.349464 0.936950i \(-0.613636\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0.256672 0.164953i 0.256672 0.164953i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −0.708089 + 1.10181i −0.708089 + 1.10181i 0.281733 + 0.959493i \(0.409091\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0.239446 + 0.153882i 0.239446 + 0.153882i 0.654861 0.755750i \(-0.272727\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(464\) −2.46030 0.353737i −2.46030 0.353737i
\(465\) 0 0
\(466\) 0.163493 + 1.13712i 0.163493 + 1.13712i
\(467\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(468\) 0 0
\(469\) 0.822373 + 1.80075i 0.822373 + 1.80075i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −0.0995111 0.338904i −0.0995111 0.338904i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.873989 1.91377i 0.873989 1.91377i
\(479\) 0 0 0.142315 0.989821i \(-0.454545\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0.357637 0.357637
\(485\) 0 0
\(486\) 0 0
\(487\) −0.258908 + 1.80075i −0.258908 + 1.80075i 0.281733 + 0.959493i \(0.409091\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.865611 1.34692i −0.865611 1.34692i −0.936950 0.349464i \(-0.886364\pi\)
0.0713392 0.997452i \(-0.477273\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.811843 + 1.77769i 0.811843 + 1.77769i
\(498\) 0 0
\(499\) 1.89945 + 0.557730i 1.89945 + 0.557730i 0.989821 + 0.142315i \(0.0454545\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.477416 0.178067i 0.477416 0.178067i
\(507\) 0 0
\(508\) 0.237509 + 0.274100i 0.237509 + 0.274100i
\(509\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.175964 0.0252998i 0.175964 0.0252998i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −1.73823 1.50619i −1.73823 1.50619i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(522\) 0 0
\(523\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.03748 1.61435i 1.03748 1.61435i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.755750 + 0.654861i −0.755750 + 0.654861i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) −1.28278 0.376660i −1.28278 0.376660i
\(537\) 0 0
\(538\) 0 0
\(539\) −0.407910 + 0.119773i −0.407910 + 0.119773i
\(540\) 0 0
\(541\) −0.186393 + 0.215109i −0.186393 + 0.215109i −0.841254 0.540641i \(-0.818182\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.698939 + 1.53046i −0.698939 + 1.53046i 0.142315 + 0.989821i \(0.454545\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(548\) −0.0994679 + 0.691814i −0.0994679 + 0.691814i
\(549\) 0 0
\(550\) −0.385087 + 0.333679i −0.385087 + 0.333679i
\(551\) 0 0
\(552\) 0 0
\(553\) 1.51150 1.51150
\(554\) 1.73823 1.50619i 1.73823 1.50619i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.587486 1.28641i 0.587486 1.28641i −0.349464 0.936950i \(-0.613636\pi\)
0.936950 0.349464i \(-0.113636\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −0.673623 2.29415i −0.673623 2.29415i
\(563\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −1.26636 0.371836i −1.26636 0.371836i
\(569\) −0.136408 0.948742i −0.136408 0.948742i −0.936950 0.349464i \(-0.886364\pi\)
0.800541 0.599278i \(-0.204545\pi\)
\(570\) 0 0
\(571\) 0.557730 + 0.0801894i 0.557730 + 0.0801894i 0.415415 0.909632i \(-0.363636\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.479249 0.877679i 0.479249 0.877679i
\(576\) 0 0
\(577\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(578\) −0.647988 + 1.00829i −0.647988 + 1.00829i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.0510279 + 0.0327936i −0.0510279 + 0.0327936i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 −0.755750 0.654861i \(-0.772727\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 2.36667 0.340275i 2.36667 0.340275i
\(593\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.535691 0.618220i −0.535691 0.618220i
\(597\) 0 0
\(598\) 0 0
\(599\) 1.60108i 1.60108i 0.599278 + 0.800541i \(0.295455\pi\)
−0.599278 + 0.800541i \(0.704545\pi\)
\(600\) 0 0
\(601\) 0 0 −0.841254 0.540641i \(-0.818182\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(602\) −0.985660 0.141717i −0.985660 0.141717i
\(603\) 0 0
\(604\) 0.0939025 + 0.653106i 0.0939025 + 0.653106i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −1.07028 1.66538i −1.07028 1.66538i −0.654861 0.755750i \(-0.727273\pi\)
−0.415415 0.909632i \(-0.636364\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.119270 0.261164i 0.119270 0.261164i
\(617\) 0.170572 1.18636i 0.170572 1.18636i −0.707107 0.707107i \(-0.750000\pi\)
0.877679 0.479249i \(-0.159091\pi\)
\(618\) 0 0
\(619\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.142315 + 0.989821i −0.142315 + 0.989821i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.512546 + 1.74557i 0.512546 + 1.74557i 0.654861 + 0.755750i \(0.272727\pi\)
−0.142315 + 0.989821i \(0.545455\pi\)
\(632\) −0.668470 + 0.771456i −0.668470 + 0.771456i
\(633\) 0 0
\(634\) 2.01867 0.592735i 2.01867 0.592735i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.144661 + 1.00614i 0.144661 + 1.00614i
\(639\) 0 0
\(640\) 0 0
\(641\) −1.18971 0.764582i −1.18971 0.764582i −0.212565 0.977147i \(-0.568182\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0.0311420 0.435423i 0.0311420 0.435423i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.480978 + 0.309106i −0.480978 + 0.309106i
\(653\) −1.45640 + 0.665114i −1.45640 + 0.665114i −0.977147 0.212565i \(-0.931818\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.120029 + 0.0771377i −0.120029 + 0.0771377i −0.599278 0.800541i \(-0.704545\pi\)
0.479249 + 0.877679i \(0.340909\pi\)
\(660\) 0 0
\(661\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(662\) −1.98344 0.905808i −1.98344 0.905808i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.956056 1.75089i −0.956056 1.75089i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.281733 1.95949i −0.281733 1.95949i −0.281733 0.959493i \(-0.590909\pi\)
1.00000i \(-0.5\pi\)
\(674\) 1.93489 + 0.568136i 1.93489 + 0.568136i
\(675\) 0 0
\(676\) −0.181343 0.397086i −0.181343 0.397086i
\(677\) 0 0 0.959493 0.281733i \(-0.0909091\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.494541 + 1.68425i −0.494541 + 1.68425i 0.212565 + 0.977147i \(0.431818\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.170572 + 1.18636i −0.170572 + 1.18636i
\(687\) 0 0
\(688\) 0.782345 0.677906i 0.782345 0.677906i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.163493 + 1.13712i −0.163493 + 1.13712i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.122986 + 0.418852i 0.122986 + 0.418852i
\(701\) 0.784887 0.905808i 0.784887 0.905808i −0.212565 0.977147i \(-0.568182\pi\)
0.997452 + 0.0713392i \(0.0227273\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0.0468936 + 0.102683i 0.0468936 + 0.102683i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 1.66538 + 0.239446i 1.66538 + 0.239446i 0.909632 0.415415i \(-0.136364\pi\)
0.755750 + 0.654861i \(0.227273\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.164953 + 0.256672i −0.164953 + 0.256672i
\(717\) 0 0
\(718\) −2.04301 0.933011i −2.04301 0.933011i
\(719\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.09024 0.497898i 1.09024 0.497898i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.50765 + 1.30638i 1.50765 + 1.30638i
\(726\) 0 0
\(727\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.540641 0.841254i \(-0.318182\pi\)
−0.540641 + 0.841254i \(0.681818\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0.578429 + 0.578429i 0.578429 + 0.578429i
\(737\) 0.841607i 0.841607i
\(738\) 0 0
\(739\) −0.239446 0.153882i −0.239446 0.153882i 0.415415 0.909632i \(-0.363636\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.0243370 + 0.169267i 0.0243370 + 0.169267i
\(743\) 1.15001 + 0.337672i 1.15001 + 0.337672i 0.800541 0.599278i \(-0.204545\pi\)
0.349464 + 0.936950i \(0.386364\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 1.24348 0.365119i 1.24348 0.365119i
\(747\) 0 0
\(748\) 0 0
\(749\) 0.270040 + 0.919672i 0.270040 + 0.919672i
\(750\) 0 0
\(751\) −0.708089 1.10181i −0.708089 1.10181i −0.989821 0.142315i \(-0.954545\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −1.27155 + 1.10181i −1.27155 + 1.10181i −0.281733 + 0.959493i \(0.590909\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(758\) −1.56977 −1.56977
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.755750 0.654861i \(-0.227273\pi\)
−0.755750 + 0.654861i \(0.772727\pi\)
\(762\) 0 0
\(763\) −0.0405070 + 0.281733i −0.0405070 + 0.281733i
\(764\) 0.318322 0.697028i 0.318322 0.697028i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.452897 + 0.132983i −0.452897 + 0.132983i
\(773\) 0 0 −0.415415 0.909632i \(-0.636364\pi\)
0.415415 + 0.909632i \(0.363636\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −2.31849 0.333348i −2.31849 0.333348i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.830830i 0.830830i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.815938 0.941643i −0.815938 0.941643i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.909632 0.415415i \(-0.863636\pi\)
0.909632 + 0.415415i \(0.136364\pi\)
\(788\) −0.302001 + 0.0434212i −0.302001 + 0.0434212i
\(789\) 0 0
\(790\) 0 0
\(791\) 0.635768 0.290345i 0.635768 0.290345i
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.744099 0.339819i −0.744099 0.339819i
\(801\) 0 0
\(802\) 1.13745 1.76991i 1.13745 1.76991i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0.141226 + 0.0203052i 0.141226 + 0.0203052i 0.212565 0.977147i \(-0.431818\pi\)
−0.0713392 + 0.997452i \(0.522727\pi\)
\(810\) 0 0
\(811\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(812\) 0.835570 + 0.245345i 0.835570 + 0.245345i
\(813\) 0 0
\(814\) −0.406195 0.889443i −0.406195 0.889443i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.550588 1.87513i 0.550588 1.87513i 0.0713392 0.997452i \(-0.477273\pi\)
0.479249 0.877679i \(-0.340909\pi\)
\(822\) 0 0
\(823\) −0.544078 + 1.19136i −0.544078 + 1.19136i 0.415415 + 0.909632i \(0.363636\pi\)
−0.959493 + 0.281733i \(0.909091\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.75536 1.75536 0.877679 0.479249i \(-0.159091\pi\)
0.877679 + 0.479249i \(0.159091\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.654861 0.755750i \(-0.272727\pi\)
−0.654861 + 0.755750i \(0.727273\pi\)
\(840\) 0 0
\(841\) 2.85895 0.839462i 2.85895 0.839462i
\(842\) −0.905808 1.98344i −0.905808 1.98344i
\(843\) 0 0
\(844\) −0.452897 0.132983i −0.452897 0.132983i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.810925 + 0.116593i 0.810925 + 0.116593i
\(848\) −0.149552 0.0961115i −0.149552 0.0961115i
\(849\) 0 0
\(850\) 0 0
\(851\) 1.35693 + 1.35693i 1.35693 + 1.35693i
\(852\) 0 0
\(853\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.588819 0.268905i −0.588819 0.268905i
\(857\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(858\) 0 0
\(859\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.633095 + 0.548580i 0.633095 + 0.548580i
\(863\) −0.321292 0.278401i −0.321292 0.278401i 0.479249 0.877679i \(-0.340909\pi\)
−0.800541 + 0.599278i \(0.795455\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.584515 + 0.266939i 0.584515 + 0.266939i
\(870\) 0 0
\(871\) 0 0
\(872\) −0.125879 0.145272i −0.125879 0.145272i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.41542 + 0.909632i 1.41542 + 0.909632i 1.00000 \(0\)
0.415415 + 0.909632i \(0.363636\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.959493 0.281733i \(-0.909091\pi\)
0.959493 + 0.281733i \(0.0909091\pi\)
\(882\) 0 0
\(883\) 0.627899 + 1.37491i 0.627899 + 1.37491i 0.909632 + 0.415415i \(0.136364\pi\)
−0.281733 + 0.959493i \(0.590909\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.333679 + 0.385087i −0.333679 + 0.385087i
\(887\) 0 0 −0.281733 0.959493i \(-0.590909\pi\)
0.281733 + 0.959493i \(0.409091\pi\)
\(888\) 0 0
\(889\) 0.449181 + 0.698939i 0.449181 + 0.698939i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 1.13627 1.13627
\(897\) 0 0
\(898\) −2.10389 −2.10389
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.132983 + 0.452897i −0.132983 + 0.452897i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.0801894 0.273100i −0.0801894 0.273100i 0.909632 0.415415i \(-0.136364\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.497898 + 1.09024i 0.497898 + 1.09024i 0.977147 + 0.212565i \(0.0681818\pi\)
−0.479249 + 0.877679i \(0.659091\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.223402 + 1.55380i 0.223402 + 1.55380i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.91899i 1.91899i −0.281733 0.959493i \(-0.590909\pi\)
0.281733 0.959493i \(-0.409091\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.74557 0.797176i −1.74557 0.797176i
\(926\) 0.337672 0.0485499i 0.337672 0.0485499i
\(927\) 0 0
\(928\) −1.37282 + 0.882259i −1.37282 + 0.882259i
\(929\) 0 0 0.909632 0.415415i \(-0.136364\pi\)
−0.909632 + 0.415415i \(0.863636\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.316219 + 0.274005i 0.316219 + 0.274005i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.989821 0.142315i \(-0.0454545\pi\)
−0.989821 + 0.142315i \(0.954545\pi\)
\(938\) 2.15829 + 0.985660i 2.15829 + 0.985660i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.654861 0.755750i \(-0.727273\pi\)
0.654861 + 0.755750i \(0.272727\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.356139 0.228877i −0.356139 0.228877i
\(947\) 1.73749 + 0.249813i 1.73749 + 0.249813i 0.936950 0.349464i \(-0.113636\pi\)
0.800541 + 0.599278i \(0.204545\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.919672 0.270040i 0.919672 0.270040i 0.212565 0.977147i \(-0.431818\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −0.215885 0.735235i −0.215885 0.735235i
\(957\) 0 0
\(958\) 0 0
\(959\) −0.451077 + 1.53623i −0.451077 + 1.53623i
\(960\) 0 0
\(961\) 0.415415 0.909632i 0.415415 0.909632i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.68251 1.68251 0.841254 0.540641i \(-0.181818\pi\)
0.841254 + 0.540641i \(0.181818\pi\)
\(968\) −0.418145 + 0.362325i −0.418145 + 0.362325i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.415415 0.909632i \(-0.363636\pi\)
−0.415415 + 0.909632i \(0.636364\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 1.17886 + 1.83434i 1.17886 + 1.83434i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.926113 + 1.06879i −0.926113 + 1.06879i 0.0713392 + 0.997452i \(0.477273\pi\)
−0.997452 + 0.0713392i \(0.977273\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −1.84125 0.540641i −1.84125 0.540641i
\(983\) 0 0 −0.142315 0.989821i \(-0.545455\pi\)
0.142315 + 0.989821i \(0.454545\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.811843 + 0.176606i 0.811843 + 0.176606i
\(990\) 0 0
\(991\) 1.29639 + 1.49611i 1.29639 + 1.49611i 0.755750 + 0.654861i \(0.227273\pi\)
0.540641 + 0.841254i \(0.318182\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 2.13066 + 0.973039i 2.13066 + 0.973039i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.841254 0.540641i \(-0.181818\pi\)
−0.841254 + 0.540641i \(0.818182\pi\)
\(998\) 2.15829 0.985660i 2.15829 0.985660i
\(999\) 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 1449.1.bu.a.125.3 yes 40
3.2 odd 2 inner 1449.1.bu.a.125.2 40
7.6 odd 2 CM 1449.1.bu.a.125.3 yes 40
21.20 even 2 inner 1449.1.bu.a.125.2 40
23.7 odd 22 inner 1449.1.bu.a.881.2 yes 40
69.53 even 22 inner 1449.1.bu.a.881.3 yes 40
161.76 even 22 inner 1449.1.bu.a.881.2 yes 40
483.398 odd 22 inner 1449.1.bu.a.881.3 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1449.1.bu.a.125.2 40 3.2 odd 2 inner
1449.1.bu.a.125.2 40 21.20 even 2 inner
1449.1.bu.a.125.3 yes 40 1.1 even 1 trivial
1449.1.bu.a.125.3 yes 40 7.6 odd 2 CM
1449.1.bu.a.881.2 yes 40 23.7 odd 22 inner
1449.1.bu.a.881.2 yes 40 161.76 even 22 inner
1449.1.bu.a.881.3 yes 40 69.53 even 22 inner
1449.1.bu.a.881.3 yes 40 483.398 odd 22 inner