Properties

Label 232.2.a.d.1.2
Level $232$
Weight $2$
Character 232.1
Self dual yes
Analytic conductor $1.853$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [232,2,Mod(1,232)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(232, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("232.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 232 = 2^{3} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 232.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(1.85252932689\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 6x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 232.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.36333 q^{3} +4.14134 q^{5} -1.14134 q^{9} +O(q^{10})\) \(q+1.36333 q^{3} +4.14134 q^{5} -1.14134 q^{9} -5.64600 q^{11} -2.86799 q^{13} +5.64600 q^{15} +2.00000 q^{17} +4.28267 q^{19} -2.72666 q^{23} +12.1507 q^{25} -5.64600 q^{27} +1.00000 q^{29} -5.36333 q^{31} -7.69735 q^{33} -6.28267 q^{37} -3.91002 q^{39} +11.7360 q^{41} +2.91934 q^{43} -4.72666 q^{45} -4.19269 q^{47} -7.00000 q^{49} +2.72666 q^{51} +1.41468 q^{53} -23.3820 q^{55} +5.83869 q^{57} +1.27334 q^{59} +3.45331 q^{61} -11.8773 q^{65} +9.45331 q^{67} -3.71733 q^{69} +13.8387 q^{71} -7.73599 q^{73} +16.5653 q^{75} -14.9193 q^{79} -4.27334 q^{81} +9.27334 q^{83} +8.28267 q^{85} +1.36333 q^{87} -16.3013 q^{89} -7.31198 q^{93} +17.7360 q^{95} -10.2827 q^{97} +6.44398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 4 q^{5} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} + 4 q^{5} + 5 q^{9} + 2 q^{11} + 4 q^{13} - 2 q^{15} + 6 q^{17} - 4 q^{19} - 4 q^{23} + 7 q^{25} + 2 q^{27} + 3 q^{29} - 14 q^{31} - 2 q^{33} - 2 q^{37} - 18 q^{39} + 10 q^{41} - 6 q^{43} - 10 q^{45} - 2 q^{47} - 21 q^{49} + 4 q^{51} - 26 q^{55} - 12 q^{57} + 8 q^{59} + 2 q^{61} - 2 q^{65} + 20 q^{67} - 28 q^{69} + 12 q^{71} + 2 q^{73} + 16 q^{75} - 30 q^{79} - 17 q^{81} + 32 q^{83} + 8 q^{85} + 2 q^{87} + 10 q^{89} - 22 q^{93} + 28 q^{95} - 14 q^{97} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.36333 0.787118 0.393559 0.919299i \(-0.371244\pi\)
0.393559 + 0.919299i \(0.371244\pi\)
\(4\) 0 0
\(5\) 4.14134 1.85206 0.926031 0.377448i \(-0.123198\pi\)
0.926031 + 0.377448i \(0.123198\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) −1.14134 −0.380445
\(10\) 0 0
\(11\) −5.64600 −1.70233 −0.851167 0.524896i \(-0.824104\pi\)
−0.851167 + 0.524896i \(0.824104\pi\)
\(12\) 0 0
\(13\) −2.86799 −0.795438 −0.397719 0.917507i \(-0.630198\pi\)
−0.397719 + 0.917507i \(0.630198\pi\)
\(14\) 0 0
\(15\) 5.64600 1.45779
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 4.28267 0.982512 0.491256 0.871015i \(-0.336538\pi\)
0.491256 + 0.871015i \(0.336538\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.72666 −0.568547 −0.284274 0.958743i \(-0.591752\pi\)
−0.284274 + 0.958743i \(0.591752\pi\)
\(24\) 0 0
\(25\) 12.1507 2.43013
\(26\) 0 0
\(27\) −5.64600 −1.08657
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −5.36333 −0.963282 −0.481641 0.876369i \(-0.659959\pi\)
−0.481641 + 0.876369i \(0.659959\pi\)
\(32\) 0 0
\(33\) −7.69735 −1.33994
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.28267 −1.03286 −0.516432 0.856328i \(-0.672740\pi\)
−0.516432 + 0.856328i \(0.672740\pi\)
\(38\) 0 0
\(39\) −3.91002 −0.626104
\(40\) 0 0
\(41\) 11.7360 1.83285 0.916426 0.400203i \(-0.131060\pi\)
0.916426 + 0.400203i \(0.131060\pi\)
\(42\) 0 0
\(43\) 2.91934 0.445196 0.222598 0.974910i \(-0.428546\pi\)
0.222598 + 0.974910i \(0.428546\pi\)
\(44\) 0 0
\(45\) −4.72666 −0.704608
\(46\) 0 0
\(47\) −4.19269 −0.611566 −0.305783 0.952101i \(-0.598918\pi\)
−0.305783 + 0.952101i \(0.598918\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 2.72666 0.381808
\(52\) 0 0
\(53\) 1.41468 0.194321 0.0971606 0.995269i \(-0.469024\pi\)
0.0971606 + 0.995269i \(0.469024\pi\)
\(54\) 0 0
\(55\) −23.3820 −3.15283
\(56\) 0 0
\(57\) 5.83869 0.773353
\(58\) 0 0
\(59\) 1.27334 0.165775 0.0828876 0.996559i \(-0.473586\pi\)
0.0828876 + 0.996559i \(0.473586\pi\)
\(60\) 0 0
\(61\) 3.45331 0.442151 0.221076 0.975257i \(-0.429043\pi\)
0.221076 + 0.975257i \(0.429043\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −11.8773 −1.47320
\(66\) 0 0
\(67\) 9.45331 1.15491 0.577453 0.816424i \(-0.304047\pi\)
0.577453 + 0.816424i \(0.304047\pi\)
\(68\) 0 0
\(69\) −3.71733 −0.447514
\(70\) 0 0
\(71\) 13.8387 1.64235 0.821175 0.570676i \(-0.193319\pi\)
0.821175 + 0.570676i \(0.193319\pi\)
\(72\) 0 0
\(73\) −7.73599 −0.905429 −0.452714 0.891656i \(-0.649544\pi\)
−0.452714 + 0.891656i \(0.649544\pi\)
\(74\) 0 0
\(75\) 16.5653 1.91280
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −14.9193 −1.67856 −0.839279 0.543701i \(-0.817022\pi\)
−0.839279 + 0.543701i \(0.817022\pi\)
\(80\) 0 0
\(81\) −4.27334 −0.474816
\(82\) 0 0
\(83\) 9.27334 1.01788 0.508941 0.860801i \(-0.330037\pi\)
0.508941 + 0.860801i \(0.330037\pi\)
\(84\) 0 0
\(85\) 8.28267 0.898382
\(86\) 0 0
\(87\) 1.36333 0.146164
\(88\) 0 0
\(89\) −16.3013 −1.72794 −0.863969 0.503545i \(-0.832029\pi\)
−0.863969 + 0.503545i \(0.832029\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −7.31198 −0.758217
\(94\) 0 0
\(95\) 17.7360 1.81967
\(96\) 0 0
\(97\) −10.2827 −1.04405 −0.522024 0.852931i \(-0.674823\pi\)
−0.522024 + 0.852931i \(0.674823\pi\)
\(98\) 0 0
\(99\) 6.44398 0.647645
\(100\) 0 0
\(101\) −0.829359 −0.0825243 −0.0412622 0.999148i \(-0.513138\pi\)
−0.0412622 + 0.999148i \(0.513138\pi\)
\(102\) 0 0
\(103\) −2.72666 −0.268665 −0.134333 0.990936i \(-0.542889\pi\)
−0.134333 + 0.990936i \(0.542889\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.0187 1.74193 0.870965 0.491346i \(-0.163495\pi\)
0.870965 + 0.491346i \(0.163495\pi\)
\(108\) 0 0
\(109\) −6.97070 −0.667672 −0.333836 0.942631i \(-0.608343\pi\)
−0.333836 + 0.942631i \(0.608343\pi\)
\(110\) 0 0
\(111\) −8.56534 −0.812987
\(112\) 0 0
\(113\) 10.5653 0.993904 0.496952 0.867778i \(-0.334452\pi\)
0.496952 + 0.867778i \(0.334452\pi\)
\(114\) 0 0
\(115\) −11.2920 −1.05298
\(116\) 0 0
\(117\) 3.27334 0.302621
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 20.8773 1.89794
\(122\) 0 0
\(123\) 16.0000 1.44267
\(124\) 0 0
\(125\) 29.6133 2.64869
\(126\) 0 0
\(127\) 5.73599 0.508986 0.254493 0.967075i \(-0.418091\pi\)
0.254493 + 0.967075i \(0.418091\pi\)
\(128\) 0 0
\(129\) 3.98002 0.350422
\(130\) 0 0
\(131\) 3.71733 0.324784 0.162392 0.986726i \(-0.448079\pi\)
0.162392 + 0.986726i \(0.448079\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −23.3820 −2.01240
\(136\) 0 0
\(137\) 6.28267 0.536765 0.268382 0.963312i \(-0.413511\pi\)
0.268382 + 0.963312i \(0.413511\pi\)
\(138\) 0 0
\(139\) −4.17997 −0.354540 −0.177270 0.984162i \(-0.556727\pi\)
−0.177270 + 0.984162i \(0.556727\pi\)
\(140\) 0 0
\(141\) −5.71601 −0.481375
\(142\) 0 0
\(143\) 16.1927 1.35410
\(144\) 0 0
\(145\) 4.14134 0.343919
\(146\) 0 0
\(147\) −9.54330 −0.787118
\(148\) 0 0
\(149\) 8.60398 0.704865 0.352433 0.935837i \(-0.385355\pi\)
0.352433 + 0.935837i \(0.385355\pi\)
\(150\) 0 0
\(151\) 6.01866 0.489791 0.244896 0.969549i \(-0.421246\pi\)
0.244896 + 0.969549i \(0.421246\pi\)
\(152\) 0 0
\(153\) −2.28267 −0.184543
\(154\) 0 0
\(155\) −22.2113 −1.78406
\(156\) 0 0
\(157\) 1.71733 0.137058 0.0685288 0.997649i \(-0.478169\pi\)
0.0685288 + 0.997649i \(0.478169\pi\)
\(158\) 0 0
\(159\) 1.92867 0.152954
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 10.1086 0.791770 0.395885 0.918300i \(-0.370438\pi\)
0.395885 + 0.918300i \(0.370438\pi\)
\(164\) 0 0
\(165\) −31.8773 −2.48165
\(166\) 0 0
\(167\) 13.8387 1.07087 0.535435 0.844576i \(-0.320148\pi\)
0.535435 + 0.844576i \(0.320148\pi\)
\(168\) 0 0
\(169\) −4.77462 −0.367278
\(170\) 0 0
\(171\) −4.88797 −0.373792
\(172\) 0 0
\(173\) −10.5653 −0.803268 −0.401634 0.915800i \(-0.631558\pi\)
−0.401634 + 0.915800i \(0.631558\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 1.73599 0.130485
\(178\) 0 0
\(179\) −17.8387 −1.33333 −0.666663 0.745359i \(-0.732278\pi\)
−0.666663 + 0.745359i \(0.732278\pi\)
\(180\) 0 0
\(181\) 10.9707 0.815445 0.407723 0.913106i \(-0.366323\pi\)
0.407723 + 0.913106i \(0.366323\pi\)
\(182\) 0 0
\(183\) 4.70800 0.348025
\(184\) 0 0
\(185\) −26.0187 −1.91293
\(186\) 0 0
\(187\) −11.2920 −0.825753
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −22.3013 −1.61367 −0.806834 0.590778i \(-0.798821\pi\)
−0.806834 + 0.590778i \(0.798821\pi\)
\(192\) 0 0
\(193\) −4.82936 −0.347625 −0.173812 0.984779i \(-0.555609\pi\)
−0.173812 + 0.984779i \(0.555609\pi\)
\(194\) 0 0
\(195\) −16.1927 −1.15958
\(196\) 0 0
\(197\) −18.5653 −1.32273 −0.661363 0.750066i \(-0.730022\pi\)
−0.661363 + 0.750066i \(0.730022\pi\)
\(198\) 0 0
\(199\) −1.98134 −0.140454 −0.0702268 0.997531i \(-0.522372\pi\)
−0.0702268 + 0.997531i \(0.522372\pi\)
\(200\) 0 0
\(201\) 12.8880 0.909047
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 48.6027 3.39456
\(206\) 0 0
\(207\) 3.11203 0.216301
\(208\) 0 0
\(209\) −24.1800 −1.67256
\(210\) 0 0
\(211\) 20.6553 1.42197 0.710986 0.703206i \(-0.248249\pi\)
0.710986 + 0.703206i \(0.248249\pi\)
\(212\) 0 0
\(213\) 18.8667 1.29272
\(214\) 0 0
\(215\) 12.0900 0.824530
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −10.5467 −0.712679
\(220\) 0 0
\(221\) −5.73599 −0.385844
\(222\) 0 0
\(223\) −22.4040 −1.50028 −0.750142 0.661276i \(-0.770015\pi\)
−0.750142 + 0.661276i \(0.770015\pi\)
\(224\) 0 0
\(225\) −13.8680 −0.924533
\(226\) 0 0
\(227\) 26.7640 1.77639 0.888194 0.459469i \(-0.151960\pi\)
0.888194 + 0.459469i \(0.151960\pi\)
\(228\) 0 0
\(229\) −0.829359 −0.0548056 −0.0274028 0.999624i \(-0.508724\pi\)
−0.0274028 + 0.999624i \(0.508724\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 23.1507 1.51665 0.758325 0.651876i \(-0.226018\pi\)
0.758325 + 0.651876i \(0.226018\pi\)
\(234\) 0 0
\(235\) −17.3633 −1.13266
\(236\) 0 0
\(237\) −20.3400 −1.32122
\(238\) 0 0
\(239\) 10.7267 0.693850 0.346925 0.937893i \(-0.387226\pi\)
0.346925 + 0.937893i \(0.387226\pi\)
\(240\) 0 0
\(241\) −0.603978 −0.0389056 −0.0194528 0.999811i \(-0.506192\pi\)
−0.0194528 + 0.999811i \(0.506192\pi\)
\(242\) 0 0
\(243\) 11.1120 0.712837
\(244\) 0 0
\(245\) −28.9894 −1.85206
\(246\) 0 0
\(247\) −12.2827 −0.781528
\(248\) 0 0
\(249\) 12.6426 0.801193
\(250\) 0 0
\(251\) 1.92867 0.121737 0.0608684 0.998146i \(-0.480613\pi\)
0.0608684 + 0.998146i \(0.480613\pi\)
\(252\) 0 0
\(253\) 15.3947 0.967857
\(254\) 0 0
\(255\) 11.2920 0.707133
\(256\) 0 0
\(257\) 21.5946 1.34704 0.673519 0.739170i \(-0.264782\pi\)
0.673519 + 0.739170i \(0.264782\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.14134 −0.0706469
\(262\) 0 0
\(263\) 8.08998 0.498850 0.249425 0.968394i \(-0.419758\pi\)
0.249425 + 0.968394i \(0.419758\pi\)
\(264\) 0 0
\(265\) 5.85866 0.359895
\(266\) 0 0
\(267\) −22.2241 −1.36009
\(268\) 0 0
\(269\) 11.6587 0.710845 0.355422 0.934706i \(-0.384337\pi\)
0.355422 + 0.934706i \(0.384337\pi\)
\(270\) 0 0
\(271\) −2.07133 −0.125824 −0.0629121 0.998019i \(-0.520039\pi\)
−0.0629121 + 0.998019i \(0.520039\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −68.6027 −4.13690
\(276\) 0 0
\(277\) −13.4720 −0.809452 −0.404726 0.914438i \(-0.632633\pi\)
−0.404726 + 0.914438i \(0.632633\pi\)
\(278\) 0 0
\(279\) 6.12136 0.366476
\(280\) 0 0
\(281\) −22.8680 −1.36419 −0.682095 0.731264i \(-0.738931\pi\)
−0.682095 + 0.731264i \(0.738931\pi\)
\(282\) 0 0
\(283\) 0.707999 0.0420862 0.0210431 0.999779i \(-0.493301\pi\)
0.0210431 + 0.999779i \(0.493301\pi\)
\(284\) 0 0
\(285\) 24.1800 1.43230
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −14.0187 −0.821788
\(292\) 0 0
\(293\) −18.5653 −1.08460 −0.542300 0.840185i \(-0.682446\pi\)
−0.542300 + 0.840185i \(0.682446\pi\)
\(294\) 0 0
\(295\) 5.27334 0.307026
\(296\) 0 0
\(297\) 31.8773 1.84971
\(298\) 0 0
\(299\) 7.82003 0.452244
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −1.13069 −0.0649564
\(304\) 0 0
\(305\) 14.3013 0.818892
\(306\) 0 0
\(307\) −8.55263 −0.488124 −0.244062 0.969760i \(-0.578480\pi\)
−0.244062 + 0.969760i \(0.578480\pi\)
\(308\) 0 0
\(309\) −3.71733 −0.211471
\(310\) 0 0
\(311\) −13.1706 −0.746839 −0.373419 0.927663i \(-0.621815\pi\)
−0.373419 + 0.927663i \(0.621815\pi\)
\(312\) 0 0
\(313\) 8.14134 0.460176 0.230088 0.973170i \(-0.426099\pi\)
0.230088 + 0.973170i \(0.426099\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 17.1120 0.961107 0.480554 0.876965i \(-0.340436\pi\)
0.480554 + 0.876965i \(0.340436\pi\)
\(318\) 0 0
\(319\) −5.64600 −0.316115
\(320\) 0 0
\(321\) 24.5653 1.37110
\(322\) 0 0
\(323\) 8.56534 0.476589
\(324\) 0 0
\(325\) −34.8480 −1.93302
\(326\) 0 0
\(327\) −9.50335 −0.525536
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.7487 0.975557 0.487778 0.872967i \(-0.337807\pi\)
0.487778 + 0.872967i \(0.337807\pi\)
\(332\) 0 0
\(333\) 7.17064 0.392949
\(334\) 0 0
\(335\) 39.1493 2.13896
\(336\) 0 0
\(337\) 12.5467 0.683462 0.341731 0.939798i \(-0.388987\pi\)
0.341731 + 0.939798i \(0.388987\pi\)
\(338\) 0 0
\(339\) 14.4040 0.782320
\(340\) 0 0
\(341\) 30.2814 1.63983
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −15.3947 −0.828823
\(346\) 0 0
\(347\) 21.3107 1.14402 0.572008 0.820248i \(-0.306165\pi\)
0.572008 + 0.820248i \(0.306165\pi\)
\(348\) 0 0
\(349\) 20.3213 1.08777 0.543887 0.839158i \(-0.316952\pi\)
0.543887 + 0.839158i \(0.316952\pi\)
\(350\) 0 0
\(351\) 16.1927 0.864302
\(352\) 0 0
\(353\) −3.09337 −0.164644 −0.0823218 0.996606i \(-0.526234\pi\)
−0.0823218 + 0.996606i \(0.526234\pi\)
\(354\) 0 0
\(355\) 57.3107 3.04173
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −15.4847 −0.817251 −0.408625 0.912702i \(-0.633992\pi\)
−0.408625 + 0.912702i \(0.633992\pi\)
\(360\) 0 0
\(361\) −0.658719 −0.0346694
\(362\) 0 0
\(363\) 28.4626 1.49390
\(364\) 0 0
\(365\) −32.0373 −1.67691
\(366\) 0 0
\(367\) −32.8480 −1.71465 −0.857326 0.514773i \(-0.827876\pi\)
−0.857326 + 0.514773i \(0.827876\pi\)
\(368\) 0 0
\(369\) −13.3947 −0.697300
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.706681 −0.0365905 −0.0182953 0.999833i \(-0.505824\pi\)
−0.0182953 + 0.999833i \(0.505824\pi\)
\(374\) 0 0
\(375\) 40.3727 2.08484
\(376\) 0 0
\(377\) −2.86799 −0.147709
\(378\) 0 0
\(379\) −15.3947 −0.790773 −0.395386 0.918515i \(-0.629389\pi\)
−0.395386 + 0.918515i \(0.629389\pi\)
\(380\) 0 0
\(381\) 7.82003 0.400632
\(382\) 0 0
\(383\) 7.43466 0.379893 0.189947 0.981794i \(-0.439169\pi\)
0.189947 + 0.981794i \(0.439169\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −3.33195 −0.169373
\(388\) 0 0
\(389\) −33.1893 −1.68276 −0.841382 0.540441i \(-0.818258\pi\)
−0.841382 + 0.540441i \(0.818258\pi\)
\(390\) 0 0
\(391\) −5.45331 −0.275786
\(392\) 0 0
\(393\) 5.06794 0.255644
\(394\) 0 0
\(395\) −61.7860 −3.10879
\(396\) 0 0
\(397\) 6.44267 0.323348 0.161674 0.986844i \(-0.448311\pi\)
0.161674 + 0.986844i \(0.448311\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.32131 −0.215796 −0.107898 0.994162i \(-0.534412\pi\)
−0.107898 + 0.994162i \(0.534412\pi\)
\(402\) 0 0
\(403\) 15.3820 0.766231
\(404\) 0 0
\(405\) −17.6974 −0.879388
\(406\) 0 0
\(407\) 35.4720 1.75828
\(408\) 0 0
\(409\) −22.3599 −1.10563 −0.552814 0.833305i \(-0.686446\pi\)
−0.552814 + 0.833305i \(0.686446\pi\)
\(410\) 0 0
\(411\) 8.56534 0.422497
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 38.4040 1.88518
\(416\) 0 0
\(417\) −5.69867 −0.279065
\(418\) 0 0
\(419\) 1.63328 0.0797911 0.0398955 0.999204i \(-0.487297\pi\)
0.0398955 + 0.999204i \(0.487297\pi\)
\(420\) 0 0
\(421\) 14.5653 0.709871 0.354936 0.934891i \(-0.384503\pi\)
0.354936 + 0.934891i \(0.384503\pi\)
\(422\) 0 0
\(423\) 4.78527 0.232668
\(424\) 0 0
\(425\) 24.3013 1.17879
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 22.0759 1.06584
\(430\) 0 0
\(431\) −38.7640 −1.86719 −0.933597 0.358324i \(-0.883348\pi\)
−0.933597 + 0.358324i \(0.883348\pi\)
\(432\) 0 0
\(433\) 3.73599 0.179540 0.0897700 0.995963i \(-0.471387\pi\)
0.0897700 + 0.995963i \(0.471387\pi\)
\(434\) 0 0
\(435\) 5.64600 0.270705
\(436\) 0 0
\(437\) −11.6774 −0.558605
\(438\) 0 0
\(439\) −33.3107 −1.58983 −0.794915 0.606720i \(-0.792485\pi\)
−0.794915 + 0.606720i \(0.792485\pi\)
\(440\) 0 0
\(441\) 7.98935 0.380445
\(442\) 0 0
\(443\) 12.8480 0.610428 0.305214 0.952284i \(-0.401272\pi\)
0.305214 + 0.952284i \(0.401272\pi\)
\(444\) 0 0
\(445\) −67.5093 −3.20025
\(446\) 0 0
\(447\) 11.7300 0.554812
\(448\) 0 0
\(449\) −0.341281 −0.0161061 −0.00805303 0.999968i \(-0.502563\pi\)
−0.00805303 + 0.999968i \(0.502563\pi\)
\(450\) 0 0
\(451\) −66.2614 −3.12013
\(452\) 0 0
\(453\) 8.20541 0.385524
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −16.9066 −0.790859 −0.395429 0.918496i \(-0.629404\pi\)
−0.395429 + 0.918496i \(0.629404\pi\)
\(458\) 0 0
\(459\) −11.2920 −0.527065
\(460\) 0 0
\(461\) 26.0373 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(462\) 0 0
\(463\) 41.3107 1.91987 0.959935 0.280224i \(-0.0904088\pi\)
0.959935 + 0.280224i \(0.0904088\pi\)
\(464\) 0 0
\(465\) −30.2814 −1.40426
\(466\) 0 0
\(467\) −33.1180 −1.53252 −0.766258 0.642532i \(-0.777884\pi\)
−0.766258 + 0.642532i \(0.777884\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 2.34128 0.107881
\(472\) 0 0
\(473\) −16.4826 −0.757872
\(474\) 0 0
\(475\) 52.0373 2.38764
\(476\) 0 0
\(477\) −1.61462 −0.0739286
\(478\) 0 0
\(479\) −24.6553 −1.12653 −0.563265 0.826276i \(-0.690455\pi\)
−0.563265 + 0.826276i \(0.690455\pi\)
\(480\) 0 0
\(481\) 18.0187 0.821580
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −42.5840 −1.93364
\(486\) 0 0
\(487\) 5.45331 0.247113 0.123557 0.992338i \(-0.460570\pi\)
0.123557 + 0.992338i \(0.460570\pi\)
\(488\) 0 0
\(489\) 13.7814 0.623216
\(490\) 0 0
\(491\) −16.3727 −0.738888 −0.369444 0.929253i \(-0.620452\pi\)
−0.369444 + 0.929253i \(0.620452\pi\)
\(492\) 0 0
\(493\) 2.00000 0.0900755
\(494\) 0 0
\(495\) 26.6867 1.19948
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −25.6333 −1.14750 −0.573752 0.819029i \(-0.694513\pi\)
−0.573752 + 0.819029i \(0.694513\pi\)
\(500\) 0 0
\(501\) 18.8667 0.842901
\(502\) 0 0
\(503\) 0.475360 0.0211952 0.0105976 0.999944i \(-0.496627\pi\)
0.0105976 + 0.999944i \(0.496627\pi\)
\(504\) 0 0
\(505\) −3.43466 −0.152840
\(506\) 0 0
\(507\) −6.50937 −0.289091
\(508\) 0 0
\(509\) 31.9987 1.41832 0.709158 0.705049i \(-0.249075\pi\)
0.709158 + 0.705049i \(0.249075\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −24.1800 −1.06757
\(514\) 0 0
\(515\) −11.2920 −0.497585
\(516\) 0 0
\(517\) 23.6719 1.04109
\(518\) 0 0
\(519\) −14.4040 −0.632267
\(520\) 0 0
\(521\) −26.7253 −1.17086 −0.585429 0.810724i \(-0.699074\pi\)
−0.585429 + 0.810724i \(0.699074\pi\)
\(522\) 0 0
\(523\) 9.45331 0.413365 0.206682 0.978408i \(-0.433733\pi\)
0.206682 + 0.978408i \(0.433733\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −10.7267 −0.467260
\(528\) 0 0
\(529\) −15.5653 −0.676754
\(530\) 0 0
\(531\) −1.45331 −0.0630684
\(532\) 0 0
\(533\) −33.6587 −1.45792
\(534\) 0 0
\(535\) 74.6213 3.22616
\(536\) 0 0
\(537\) −24.3200 −1.04948
\(538\) 0 0
\(539\) 39.5220 1.70233
\(540\) 0 0
\(541\) −20.8667 −0.897128 −0.448564 0.893751i \(-0.648064\pi\)
−0.448564 + 0.893751i \(0.648064\pi\)
\(542\) 0 0
\(543\) 14.9567 0.641852
\(544\) 0 0
\(545\) −28.8680 −1.23657
\(546\) 0 0
\(547\) −12.5653 −0.537255 −0.268628 0.963244i \(-0.586570\pi\)
−0.268628 + 0.963244i \(0.586570\pi\)
\(548\) 0 0
\(549\) −3.94139 −0.168214
\(550\) 0 0
\(551\) 4.28267 0.182448
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −35.4720 −1.50570
\(556\) 0 0
\(557\) 28.3786 1.20244 0.601220 0.799084i \(-0.294682\pi\)
0.601220 + 0.799084i \(0.294682\pi\)
\(558\) 0 0
\(559\) −8.37266 −0.354126
\(560\) 0 0
\(561\) −15.3947 −0.649965
\(562\) 0 0
\(563\) 3.16470 0.133376 0.0666881 0.997774i \(-0.478757\pi\)
0.0666881 + 0.997774i \(0.478757\pi\)
\(564\) 0 0
\(565\) 43.7546 1.84077
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.3599 0.434311 0.217156 0.976137i \(-0.430322\pi\)
0.217156 + 0.976137i \(0.430322\pi\)
\(570\) 0 0
\(571\) −18.5840 −0.777716 −0.388858 0.921298i \(-0.627130\pi\)
−0.388858 + 0.921298i \(0.627130\pi\)
\(572\) 0 0
\(573\) −30.4040 −1.27015
\(574\) 0 0
\(575\) −33.1307 −1.38165
\(576\) 0 0
\(577\) −28.0187 −1.16643 −0.583216 0.812317i \(-0.698206\pi\)
−0.583216 + 0.812317i \(0.698206\pi\)
\(578\) 0 0
\(579\) −6.58400 −0.273622
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −7.98728 −0.330799
\(584\) 0 0
\(585\) 13.5560 0.560472
\(586\) 0 0
\(587\) −45.8760 −1.89351 −0.946753 0.321962i \(-0.895658\pi\)
−0.946753 + 0.321962i \(0.895658\pi\)
\(588\) 0 0
\(589\) −22.9694 −0.946437
\(590\) 0 0
\(591\) −25.3107 −1.04114
\(592\) 0 0
\(593\) 42.8026 1.75769 0.878846 0.477105i \(-0.158314\pi\)
0.878846 + 0.477105i \(0.158314\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −2.70122 −0.110554
\(598\) 0 0
\(599\) −8.90069 −0.363672 −0.181836 0.983329i \(-0.558204\pi\)
−0.181836 + 0.983329i \(0.558204\pi\)
\(600\) 0 0
\(601\) 13.7173 0.559541 0.279771 0.960067i \(-0.409742\pi\)
0.279771 + 0.960067i \(0.409742\pi\)
\(602\) 0 0
\(603\) −10.7894 −0.439379
\(604\) 0 0
\(605\) 86.4600 3.51510
\(606\) 0 0
\(607\) 24.4754 0.993424 0.496712 0.867915i \(-0.334540\pi\)
0.496712 + 0.867915i \(0.334540\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0246 0.486463
\(612\) 0 0
\(613\) −8.74663 −0.353273 −0.176637 0.984276i \(-0.556522\pi\)
−0.176637 + 0.984276i \(0.556522\pi\)
\(614\) 0 0
\(615\) 66.2614 2.67192
\(616\) 0 0
\(617\) 22.2827 0.897067 0.448533 0.893766i \(-0.351947\pi\)
0.448533 + 0.893766i \(0.351947\pi\)
\(618\) 0 0
\(619\) 14.9966 0.602765 0.301382 0.953503i \(-0.402552\pi\)
0.301382 + 0.953503i \(0.402552\pi\)
\(620\) 0 0
\(621\) 15.3947 0.617768
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 61.8853 2.47541
\(626\) 0 0
\(627\) −32.9652 −1.31650
\(628\) 0 0
\(629\) −12.5653 −0.501013
\(630\) 0 0
\(631\) −10.7267 −0.427021 −0.213511 0.976941i \(-0.568490\pi\)
−0.213511 + 0.976941i \(0.568490\pi\)
\(632\) 0 0
\(633\) 28.1600 1.11926
\(634\) 0 0
\(635\) 23.7546 0.942674
\(636\) 0 0
\(637\) 20.0759 0.795438
\(638\) 0 0
\(639\) −15.7946 −0.624824
\(640\) 0 0
\(641\) −22.9253 −0.905494 −0.452747 0.891639i \(-0.649556\pi\)
−0.452747 + 0.891639i \(0.649556\pi\)
\(642\) 0 0
\(643\) 30.5467 1.20464 0.602322 0.798253i \(-0.294242\pi\)
0.602322 + 0.798253i \(0.294242\pi\)
\(644\) 0 0
\(645\) 16.4826 0.649002
\(646\) 0 0
\(647\) 24.7453 0.972839 0.486419 0.873725i \(-0.338303\pi\)
0.486419 + 0.873725i \(0.338303\pi\)
\(648\) 0 0
\(649\) −7.18930 −0.282205
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −15.4134 −0.603171 −0.301586 0.953439i \(-0.597516\pi\)
−0.301586 + 0.953439i \(0.597516\pi\)
\(654\) 0 0
\(655\) 15.3947 0.601521
\(656\) 0 0
\(657\) 8.82936 0.344466
\(658\) 0 0
\(659\) 18.1341 0.706403 0.353202 0.935547i \(-0.385093\pi\)
0.353202 + 0.935547i \(0.385093\pi\)
\(660\) 0 0
\(661\) 11.0934 0.431482 0.215741 0.976451i \(-0.430783\pi\)
0.215741 + 0.976451i \(0.430783\pi\)
\(662\) 0 0
\(663\) −7.82003 −0.303705
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.72666 −0.105577
\(668\) 0 0
\(669\) −30.5441 −1.18090
\(670\) 0 0
\(671\) −19.4974 −0.752689
\(672\) 0 0
\(673\) −35.7160 −1.37675 −0.688375 0.725355i \(-0.741676\pi\)
−0.688375 + 0.725355i \(0.741676\pi\)
\(674\) 0 0
\(675\) −68.6027 −2.64052
\(676\) 0 0
\(677\) 5.64006 0.216765 0.108383 0.994109i \(-0.465433\pi\)
0.108383 + 0.994109i \(0.465433\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 36.4881 1.39823
\(682\) 0 0
\(683\) −26.0187 −0.995576 −0.497788 0.867299i \(-0.665854\pi\)
−0.497788 + 0.867299i \(0.665854\pi\)
\(684\) 0 0
\(685\) 26.0187 0.994122
\(686\) 0 0
\(687\) −1.13069 −0.0431385
\(688\) 0 0
\(689\) −4.05729 −0.154570
\(690\) 0 0
\(691\) 9.65872 0.367435 0.183717 0.982979i \(-0.441187\pi\)
0.183717 + 0.982979i \(0.441187\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −17.3107 −0.656631
\(696\) 0 0
\(697\) 23.4720 0.889064
\(698\) 0 0
\(699\) 31.5620 1.19378
\(700\) 0 0
\(701\) −16.8867 −0.637800 −0.318900 0.947788i \(-0.603313\pi\)
−0.318900 + 0.947788i \(0.603313\pi\)
\(702\) 0 0
\(703\) −26.9066 −1.01480
\(704\) 0 0
\(705\) −23.6719 −0.891536
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 36.2814 1.36257 0.681287 0.732016i \(-0.261420\pi\)
0.681287 + 0.732016i \(0.261420\pi\)
\(710\) 0 0
\(711\) 17.0280 0.638599
\(712\) 0 0
\(713\) 14.6240 0.547671
\(714\) 0 0
\(715\) 67.0594 2.50788
\(716\) 0 0
\(717\) 14.6240 0.546142
\(718\) 0 0
\(719\) −47.3293 −1.76509 −0.882543 0.470232i \(-0.844170\pi\)
−0.882543 + 0.470232i \(0.844170\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −0.823420 −0.0306233
\(724\) 0 0
\(725\) 12.1507 0.451264
\(726\) 0 0
\(727\) −52.5254 −1.94806 −0.974029 0.226421i \(-0.927297\pi\)
−0.974029 + 0.226421i \(0.927297\pi\)
\(728\) 0 0
\(729\) 27.9694 1.03590
\(730\) 0 0
\(731\) 5.83869 0.215952
\(732\) 0 0
\(733\) −29.4320 −1.08710 −0.543548 0.839378i \(-0.682919\pi\)
−0.543548 + 0.839378i \(0.682919\pi\)
\(734\) 0 0
\(735\) −39.5220 −1.45779
\(736\) 0 0
\(737\) −53.3734 −1.96603
\(738\) 0 0
\(739\) −4.08998 −0.150453 −0.0752263 0.997166i \(-0.523968\pi\)
−0.0752263 + 0.997166i \(0.523968\pi\)
\(740\) 0 0
\(741\) −16.7453 −0.615154
\(742\) 0 0
\(743\) −18.8294 −0.690782 −0.345391 0.938459i \(-0.612254\pi\)
−0.345391 + 0.938459i \(0.612254\pi\)
\(744\) 0 0
\(745\) 35.6320 1.30545
\(746\) 0 0
\(747\) −10.5840 −0.387248
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 22.6613 0.826921 0.413461 0.910522i \(-0.364320\pi\)
0.413461 + 0.910522i \(0.364320\pi\)
\(752\) 0 0
\(753\) 2.62941 0.0958212
\(754\) 0 0
\(755\) 24.9253 0.907124
\(756\) 0 0
\(757\) 35.1680 1.27820 0.639101 0.769122i \(-0.279306\pi\)
0.639101 + 0.769122i \(0.279306\pi\)
\(758\) 0 0
\(759\) 20.9880 0.761817
\(760\) 0 0
\(761\) 13.4720 0.488359 0.244179 0.969730i \(-0.421481\pi\)
0.244179 + 0.969730i \(0.421481\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −9.45331 −0.341785
\(766\) 0 0
\(767\) −3.65194 −0.131864
\(768\) 0 0
\(769\) 44.0560 1.58870 0.794349 0.607461i \(-0.207812\pi\)
0.794349 + 0.607461i \(0.207812\pi\)
\(770\) 0 0
\(771\) 29.4406 1.06028
\(772\) 0 0
\(773\) 4.26401 0.153366 0.0766830 0.997056i \(-0.475567\pi\)
0.0766830 + 0.997056i \(0.475567\pi\)
\(774\) 0 0
\(775\) −65.1680 −2.34090
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 50.2614 1.80080
\(780\) 0 0
\(781\) −78.1332 −2.79583
\(782\) 0 0
\(783\) −5.64600 −0.201772
\(784\) 0 0
\(785\) 7.11203 0.253839
\(786\) 0 0
\(787\) 7.08660 0.252610 0.126305 0.991991i \(-0.459688\pi\)
0.126305 + 0.991991i \(0.459688\pi\)
\(788\) 0 0
\(789\) 11.0293 0.392654
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −9.90408 −0.351704
\(794\) 0 0
\(795\) 7.98728 0.283280
\(796\) 0 0
\(797\) 19.4533 0.689072 0.344536 0.938773i \(-0.388036\pi\)
0.344536 + 0.938773i \(0.388036\pi\)
\(798\) 0 0
\(799\) −8.38538 −0.296653
\(800\) 0 0
\(801\) 18.6053 0.657386
\(802\) 0 0
\(803\) 43.6774 1.54134
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 15.8947 0.559519
\(808\) 0 0
\(809\) −14.3200 −0.503464 −0.251732 0.967797i \(-0.581000\pi\)
−0.251732 + 0.967797i \(0.581000\pi\)
\(810\) 0 0
\(811\) 3.43466 0.120607 0.0603035 0.998180i \(-0.480793\pi\)
0.0603035 + 0.998180i \(0.480793\pi\)
\(812\) 0 0
\(813\) −2.82390 −0.0990385
\(814\) 0 0
\(815\) 41.8633 1.46641
\(816\) 0 0
\(817\) 12.5026 0.437410
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −33.0921 −1.15492 −0.577460 0.816419i \(-0.695956\pi\)
−0.577460 + 0.816419i \(0.695956\pi\)
\(822\) 0 0
\(823\) −9.20796 −0.320969 −0.160485 0.987038i \(-0.551306\pi\)
−0.160485 + 0.987038i \(0.551306\pi\)
\(824\) 0 0
\(825\) −93.5279 −3.25623
\(826\) 0 0
\(827\) 20.8607 0.725399 0.362699 0.931906i \(-0.381855\pi\)
0.362699 + 0.931906i \(0.381855\pi\)
\(828\) 0 0
\(829\) −11.4160 −0.396494 −0.198247 0.980152i \(-0.563525\pi\)
−0.198247 + 0.980152i \(0.563525\pi\)
\(830\) 0 0
\(831\) −18.3667 −0.637134
\(832\) 0 0
\(833\) −14.0000 −0.485071
\(834\) 0 0
\(835\) 57.3107 1.98332
\(836\) 0 0
\(837\) 30.2814 1.04668
\(838\) 0 0
\(839\) 33.8260 1.16780 0.583901 0.811825i \(-0.301526\pi\)
0.583901 + 0.811825i \(0.301526\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −31.1766 −1.07378
\(844\) 0 0
\(845\) −19.7733 −0.680222
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0.965235 0.0331268
\(850\) 0 0
\(851\) 17.1307 0.587232
\(852\) 0 0
\(853\) −17.4347 −0.596951 −0.298476 0.954417i \(-0.596478\pi\)
−0.298476 + 0.954417i \(0.596478\pi\)
\(854\) 0 0
\(855\) −20.2427 −0.692286
\(856\) 0 0
\(857\) −8.98935 −0.307070 −0.153535 0.988143i \(-0.549066\pi\)
−0.153535 + 0.988143i \(0.549066\pi\)
\(858\) 0 0
\(859\) −3.48469 −0.118896 −0.0594480 0.998231i \(-0.518934\pi\)
−0.0594480 + 0.998231i \(0.518934\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 31.8947 1.08571 0.542853 0.839827i \(-0.317344\pi\)
0.542853 + 0.839827i \(0.317344\pi\)
\(864\) 0 0
\(865\) −43.7546 −1.48770
\(866\) 0 0
\(867\) −17.7233 −0.601914
\(868\) 0 0
\(869\) 84.2346 2.85746
\(870\) 0 0
\(871\) −27.1120 −0.918656
\(872\) 0 0
\(873\) 11.7360 0.397203
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −38.5853 −1.30293 −0.651467 0.758677i \(-0.725846\pi\)
−0.651467 + 0.758677i \(0.725846\pi\)
\(878\) 0 0
\(879\) −25.3107 −0.853707
\(880\) 0 0
\(881\) −8.54669 −0.287945 −0.143973 0.989582i \(-0.545988\pi\)
−0.143973 + 0.989582i \(0.545988\pi\)
\(882\) 0 0
\(883\) −20.9253 −0.704192 −0.352096 0.935964i \(-0.614531\pi\)
−0.352096 + 0.935964i \(0.614531\pi\)
\(884\) 0 0
\(885\) 7.18930 0.241666
\(886\) 0 0
\(887\) −38.2886 −1.28561 −0.642803 0.766032i \(-0.722229\pi\)
−0.642803 + 0.766032i \(0.722229\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 24.1273 0.808295
\(892\) 0 0
\(893\) −17.9559 −0.600871
\(894\) 0 0
\(895\) −73.8760 −2.46940
\(896\) 0 0
\(897\) 10.6613 0.355969
\(898\) 0 0
\(899\) −5.36333 −0.178877
\(900\) 0 0
\(901\) 2.82936 0.0942596
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 45.4333 1.51026
\(906\) 0 0
\(907\) −4.28267 −0.142204 −0.0711019 0.997469i \(-0.522652\pi\)
−0.0711019 + 0.997469i \(0.522652\pi\)
\(908\) 0 0
\(909\) 0.946578 0.0313960
\(910\) 0 0
\(911\) 41.9660 1.39040 0.695198 0.718819i \(-0.255317\pi\)
0.695198 + 0.718819i \(0.255317\pi\)
\(912\) 0 0
\(913\) −52.3573 −1.73277
\(914\) 0 0
\(915\) 19.4974 0.644564
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −5.06794 −0.167176 −0.0835879 0.996500i \(-0.526638\pi\)
−0.0835879 + 0.996500i \(0.526638\pi\)
\(920\) 0 0
\(921\) −11.6600 −0.384211
\(922\) 0 0
\(923\) −39.6893 −1.30639
\(924\) 0 0
\(925\) −76.3386 −2.51000
\(926\) 0 0
\(927\) 3.11203 0.102213
\(928\) 0 0
\(929\) 27.6960 0.908677 0.454339 0.890829i \(-0.349876\pi\)
0.454339 + 0.890829i \(0.349876\pi\)
\(930\) 0 0
\(931\) −29.9787 −0.982512
\(932\) 0 0
\(933\) −17.9559 −0.587850
\(934\) 0 0
\(935\) −46.7640 −1.52935
\(936\) 0 0
\(937\) 14.6027 0.477048 0.238524 0.971137i \(-0.423336\pi\)
0.238524 + 0.971137i \(0.423336\pi\)
\(938\) 0 0
\(939\) 11.0993 0.362212
\(940\) 0 0
\(941\) 10.1600 0.331206 0.165603 0.986192i \(-0.447043\pi\)
0.165603 + 0.986192i \(0.447043\pi\)
\(942\) 0 0
\(943\) −32.0000 −1.04206
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.2487 −0.593002 −0.296501 0.955033i \(-0.595820\pi\)
−0.296501 + 0.955033i \(0.595820\pi\)
\(948\) 0 0
\(949\) 22.1867 0.720212
\(950\) 0 0
\(951\) 23.3293 0.756505
\(952\) 0 0
\(953\) −32.5640 −1.05485 −0.527426 0.849601i \(-0.676843\pi\)
−0.527426 + 0.849601i \(0.676843\pi\)
\(954\) 0 0
\(955\) −92.3573 −2.98861
\(956\) 0 0
\(957\) −7.69735 −0.248820
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −2.23471 −0.0720874
\(962\) 0 0
\(963\) −20.5653 −0.662709
\(964\) 0 0
\(965\) −20.0000 −0.643823
\(966\) 0 0
\(967\) 15.1247 0.486379 0.243190 0.969979i \(-0.421806\pi\)
0.243190 + 0.969979i \(0.421806\pi\)
\(968\) 0 0
\(969\) 11.6774 0.375131
\(970\) 0 0
\(971\) −8.81070 −0.282749 −0.141374 0.989956i \(-0.545152\pi\)
−0.141374 + 0.989956i \(0.545152\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) −47.5093 −1.52151
\(976\) 0 0
\(977\) −6.08273 −0.194604 −0.0973018 0.995255i \(-0.531021\pi\)
−0.0973018 + 0.995255i \(0.531021\pi\)
\(978\) 0 0
\(979\) 92.0373 2.94153
\(980\) 0 0
\(981\) 7.95591 0.254013
\(982\) 0 0
\(983\) 0.335342 0.0106958 0.00534788 0.999986i \(-0.498298\pi\)
0.00534788 + 0.999986i \(0.498298\pi\)
\(984\) 0 0
\(985\) −76.8853 −2.44977
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.96005 −0.253115
\(990\) 0 0
\(991\) 22.1986 0.705163 0.352581 0.935781i \(-0.385304\pi\)
0.352581 + 0.935781i \(0.385304\pi\)
\(992\) 0 0
\(993\) 24.1973 0.767878
\(994\) 0 0
\(995\) −8.20541 −0.260129
\(996\) 0 0
\(997\) 29.1893 0.924434 0.462217 0.886767i \(-0.347054\pi\)
0.462217 + 0.886767i \(0.347054\pi\)
\(998\) 0 0
\(999\) 35.4720 1.12228
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 232.2.a.d.1.2 3
3.2 odd 2 2088.2.a.s.1.1 3
4.3 odd 2 464.2.a.j.1.2 3
5.4 even 2 5800.2.a.p.1.2 3
8.3 odd 2 1856.2.a.y.1.2 3
8.5 even 2 1856.2.a.x.1.2 3
12.11 even 2 4176.2.a.bu.1.1 3
29.28 even 2 6728.2.a.j.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
232.2.a.d.1.2 3 1.1 even 1 trivial
464.2.a.j.1.2 3 4.3 odd 2
1856.2.a.x.1.2 3 8.5 even 2
1856.2.a.y.1.2 3 8.3 odd 2
2088.2.a.s.1.1 3 3.2 odd 2
4176.2.a.bu.1.1 3 12.11 even 2
5800.2.a.p.1.2 3 5.4 even 2
6728.2.a.j.1.2 3 29.28 even 2