Properties

Label 4840.2.a.bh.1.4
Level $4840$
Weight $2$
Character 4840.1
Self dual yes
Analytic conductor $38.648$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4840,2,Mod(1,4840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4840, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4840.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4840.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: \(38.6475945783\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 21x^{6} + 15x^{5} + 140x^{4} - 60x^{3} - 295x^{2} + 50x + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 440)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.569801\) of defining polynomial
Character \(\chi\) \(=\) 4840.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.569801 q^{3} +1.00000 q^{5} +1.82111 q^{7} -2.67533 q^{9} +O(q^{10})\) \(q-0.569801 q^{3} +1.00000 q^{5} +1.82111 q^{7} -2.67533 q^{9} +3.92663 q^{13} -0.569801 q^{15} +3.18309 q^{17} +8.21268 q^{19} -1.03767 q^{21} +0.734122 q^{23} +1.00000 q^{25} +3.23381 q^{27} +4.42950 q^{29} -0.396984 q^{31} +1.82111 q^{35} +2.99377 q^{37} -2.23740 q^{39} -12.0514 q^{41} -8.72957 q^{43} -2.67533 q^{45} -10.5107 q^{47} -3.68356 q^{49} -1.81373 q^{51} +9.84643 q^{53} -4.67959 q^{57} +10.0121 q^{59} -8.50878 q^{61} -4.87206 q^{63} +3.92663 q^{65} +1.11105 q^{67} -0.418304 q^{69} +5.87172 q^{71} -4.03588 q^{73} -0.569801 q^{75} -3.26768 q^{79} +6.18335 q^{81} +11.8570 q^{83} +3.18309 q^{85} -2.52394 q^{87} -6.56220 q^{89} +7.15083 q^{91} +0.226202 q^{93} +8.21268 q^{95} +14.5430 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{3} + 8 q^{5} + 6 q^{7} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{3} + 8 q^{5} + 6 q^{7} + 19 q^{9} - 12 q^{13} + q^{15} - 2 q^{17} + 6 q^{19} - 6 q^{21} + 10 q^{23} + 8 q^{25} + 13 q^{27} - 8 q^{29} + 19 q^{31} + 6 q^{35} + 12 q^{37} + 21 q^{39} + 3 q^{41} + 8 q^{43} + 19 q^{45} + 10 q^{47} + 22 q^{49} + 7 q^{51} + 28 q^{53} - 25 q^{57} + 25 q^{59} - 10 q^{61} + 64 q^{63} - 12 q^{65} - 2 q^{67} + 18 q^{69} + 25 q^{71} - 38 q^{73} + q^{75} + 38 q^{79} + 32 q^{81} + 28 q^{83} - 2 q^{85} - 15 q^{87} + 12 q^{89} + 8 q^{91} - 15 q^{93} + 6 q^{95} + 21 q^{97}+O(q^{100}) \) 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
\(3\) −0.569801 −0.328975 −0.164487 0.986379i \(-0.552597\pi\)
−0.164487 + 0.986379i \(0.552597\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.82111 0.688314 0.344157 0.938912i \(-0.388165\pi\)
0.344157 + 0.938912i \(0.388165\pi\)
\(8\) 0 0
\(9\) −2.67533 −0.891776
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 3.92663 1.08905 0.544526 0.838744i \(-0.316709\pi\)
0.544526 + 0.838744i \(0.316709\pi\)
\(14\) 0 0
\(15\) −0.569801 −0.147122
\(16\) 0 0
\(17\) 3.18309 0.772014 0.386007 0.922496i \(-0.373854\pi\)
0.386007 + 0.922496i \(0.373854\pi\)
\(18\) 0 0
\(19\) 8.21268 1.88412 0.942059 0.335447i \(-0.108887\pi\)
0.942059 + 0.335447i \(0.108887\pi\)
\(20\) 0 0
\(21\) −1.03767 −0.226438
\(22\) 0 0
\(23\) 0.734122 0.153075 0.0765376 0.997067i \(-0.475613\pi\)
0.0765376 + 0.997067i \(0.475613\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 3.23381 0.622346
\(28\) 0 0
\(29\) 4.42950 0.822538 0.411269 0.911514i \(-0.365086\pi\)
0.411269 + 0.911514i \(0.365086\pi\)
\(30\) 0 0
\(31\) −0.396984 −0.0713004 −0.0356502 0.999364i \(-0.511350\pi\)
−0.0356502 + 0.999364i \(0.511350\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.82111 0.307824
\(36\) 0 0
\(37\) 2.99377 0.492172 0.246086 0.969248i \(-0.420855\pi\)
0.246086 + 0.969248i \(0.420855\pi\)
\(38\) 0 0
\(39\) −2.23740 −0.358271
\(40\) 0 0
\(41\) −12.0514 −1.88212 −0.941060 0.338240i \(-0.890168\pi\)
−0.941060 + 0.338240i \(0.890168\pi\)
\(42\) 0 0
\(43\) −8.72957 −1.33125 −0.665624 0.746288i \(-0.731834\pi\)
−0.665624 + 0.746288i \(0.731834\pi\)
\(44\) 0 0
\(45\) −2.67533 −0.398814
\(46\) 0 0
\(47\) −10.5107 −1.53314 −0.766570 0.642160i \(-0.778038\pi\)
−0.766570 + 0.642160i \(0.778038\pi\)
\(48\) 0 0
\(49\) −3.68356 −0.526223
\(50\) 0 0
\(51\) −1.81373 −0.253973
\(52\) 0 0
\(53\) 9.84643 1.35251 0.676256 0.736667i \(-0.263602\pi\)
0.676256 + 0.736667i \(0.263602\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −4.67959 −0.619827
\(58\) 0 0
\(59\) 10.0121 1.30347 0.651734 0.758448i \(-0.274042\pi\)
0.651734 + 0.758448i \(0.274042\pi\)
\(60\) 0 0
\(61\) −8.50878 −1.08944 −0.544719 0.838619i \(-0.683364\pi\)
−0.544719 + 0.838619i \(0.683364\pi\)
\(62\) 0 0
\(63\) −4.87206 −0.613822
\(64\) 0 0
\(65\) 3.92663 0.487039
\(66\) 0 0
\(67\) 1.11105 0.135737 0.0678684 0.997694i \(-0.478380\pi\)
0.0678684 + 0.997694i \(0.478380\pi\)
\(68\) 0 0
\(69\) −0.418304 −0.0503579
\(70\) 0 0
\(71\) 5.87172 0.696845 0.348422 0.937338i \(-0.386717\pi\)
0.348422 + 0.937338i \(0.386717\pi\)
\(72\) 0 0
\(73\) −4.03588 −0.472364 −0.236182 0.971709i \(-0.575896\pi\)
−0.236182 + 0.971709i \(0.575896\pi\)
\(74\) 0 0
\(75\) −0.569801 −0.0657950
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −3.26768 −0.367643 −0.183821 0.982960i \(-0.558847\pi\)
−0.183821 + 0.982960i \(0.558847\pi\)
\(80\) 0 0
\(81\) 6.18335 0.687039
\(82\) 0 0
\(83\) 11.8570 1.30148 0.650739 0.759302i \(-0.274459\pi\)
0.650739 + 0.759302i \(0.274459\pi\)
\(84\) 0 0
\(85\) 3.18309 0.345255
\(86\) 0 0
\(87\) −2.52394 −0.270594
\(88\) 0 0
\(89\) −6.56220 −0.695592 −0.347796 0.937570i \(-0.613070\pi\)
−0.347796 + 0.937570i \(0.613070\pi\)
\(90\) 0 0
\(91\) 7.15083 0.749610
\(92\) 0 0
\(93\) 0.226202 0.0234560
\(94\) 0 0
\(95\) 8.21268 0.842603
\(96\) 0 0
\(97\) 14.5430 1.47662 0.738310 0.674462i \(-0.235624\pi\)
0.738310 + 0.674462i \(0.235624\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.89649 0.984737 0.492369 0.870387i \(-0.336131\pi\)
0.492369 + 0.870387i \(0.336131\pi\)
\(102\) 0 0
\(103\) 7.21119 0.710539 0.355270 0.934764i \(-0.384389\pi\)
0.355270 + 0.934764i \(0.384389\pi\)
\(104\) 0 0
\(105\) −1.03767 −0.101266
\(106\) 0 0
\(107\) 9.77736 0.945213 0.472606 0.881274i \(-0.343313\pi\)
0.472606 + 0.881274i \(0.343313\pi\)
\(108\) 0 0
\(109\) −18.7329 −1.79429 −0.897143 0.441741i \(-0.854361\pi\)
−0.897143 + 0.441741i \(0.854361\pi\)
\(110\) 0 0
\(111\) −1.70585 −0.161912
\(112\) 0 0
\(113\) 12.8614 1.20990 0.604948 0.796265i \(-0.293194\pi\)
0.604948 + 0.796265i \(0.293194\pi\)
\(114\) 0 0
\(115\) 0.734122 0.0684573
\(116\) 0 0
\(117\) −10.5050 −0.971190
\(118\) 0 0
\(119\) 5.79676 0.531388
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 6.86693 0.619170
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.84780 0.252701 0.126350 0.991986i \(-0.459674\pi\)
0.126350 + 0.991986i \(0.459674\pi\)
\(128\) 0 0
\(129\) 4.97412 0.437947
\(130\) 0 0
\(131\) 9.49411 0.829504 0.414752 0.909934i \(-0.363868\pi\)
0.414752 + 0.909934i \(0.363868\pi\)
\(132\) 0 0
\(133\) 14.9562 1.29687
\(134\) 0 0
\(135\) 3.23381 0.278322
\(136\) 0 0
\(137\) −7.03836 −0.601328 −0.300664 0.953730i \(-0.597208\pi\)
−0.300664 + 0.953730i \(0.597208\pi\)
\(138\) 0 0
\(139\) −3.73184 −0.316531 −0.158265 0.987397i \(-0.550590\pi\)
−0.158265 + 0.987397i \(0.550590\pi\)
\(140\) 0 0
\(141\) 5.98900 0.504365
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 4.42950 0.367850
\(146\) 0 0
\(147\) 2.09890 0.173114
\(148\) 0 0
\(149\) −12.2751 −1.00561 −0.502806 0.864399i \(-0.667699\pi\)
−0.502806 + 0.864399i \(0.667699\pi\)
\(150\) 0 0
\(151\) 5.80255 0.472205 0.236102 0.971728i \(-0.424130\pi\)
0.236102 + 0.971728i \(0.424130\pi\)
\(152\) 0 0
\(153\) −8.51581 −0.688463
\(154\) 0 0
\(155\) −0.396984 −0.0318865
\(156\) 0 0
\(157\) −20.7356 −1.65488 −0.827440 0.561553i \(-0.810204\pi\)
−0.827440 + 0.561553i \(0.810204\pi\)
\(158\) 0 0
\(159\) −5.61051 −0.444942
\(160\) 0 0
\(161\) 1.33692 0.105364
\(162\) 0 0
\(163\) −11.8323 −0.926778 −0.463389 0.886155i \(-0.653367\pi\)
−0.463389 + 0.886155i \(0.653367\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.1848 1.40718 0.703592 0.710604i \(-0.251578\pi\)
0.703592 + 0.710604i \(0.251578\pi\)
\(168\) 0 0
\(169\) 2.41846 0.186035
\(170\) 0 0
\(171\) −21.9716 −1.68021
\(172\) 0 0
\(173\) 10.2152 0.776649 0.388324 0.921523i \(-0.373054\pi\)
0.388324 + 0.921523i \(0.373054\pi\)
\(174\) 0 0
\(175\) 1.82111 0.137663
\(176\) 0 0
\(177\) −5.70492 −0.428808
\(178\) 0 0
\(179\) 1.72353 0.128823 0.0644114 0.997923i \(-0.479483\pi\)
0.0644114 + 0.997923i \(0.479483\pi\)
\(180\) 0 0
\(181\) 13.9521 1.03705 0.518525 0.855062i \(-0.326481\pi\)
0.518525 + 0.855062i \(0.326481\pi\)
\(182\) 0 0
\(183\) 4.84831 0.358398
\(184\) 0 0
\(185\) 2.99377 0.220106
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 5.88911 0.428370
\(190\) 0 0
\(191\) 24.6929 1.78672 0.893359 0.449344i \(-0.148342\pi\)
0.893359 + 0.449344i \(0.148342\pi\)
\(192\) 0 0
\(193\) −2.66652 −0.191940 −0.0959702 0.995384i \(-0.530595\pi\)
−0.0959702 + 0.995384i \(0.530595\pi\)
\(194\) 0 0
\(195\) −2.23740 −0.160224
\(196\) 0 0
\(197\) −21.4277 −1.52666 −0.763330 0.646009i \(-0.776437\pi\)
−0.763330 + 0.646009i \(0.776437\pi\)
\(198\) 0 0
\(199\) −5.78067 −0.409781 −0.204891 0.978785i \(-0.565684\pi\)
−0.204891 + 0.978785i \(0.565684\pi\)
\(200\) 0 0
\(201\) −0.633079 −0.0446540
\(202\) 0 0
\(203\) 8.06661 0.566165
\(204\) 0 0
\(205\) −12.0514 −0.841709
\(206\) 0 0
\(207\) −1.96402 −0.136509
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 11.5772 0.797006 0.398503 0.917167i \(-0.369530\pi\)
0.398503 + 0.917167i \(0.369530\pi\)
\(212\) 0 0
\(213\) −3.34571 −0.229244
\(214\) 0 0
\(215\) −8.72957 −0.595352
\(216\) 0 0
\(217\) −0.722951 −0.0490771
\(218\) 0 0
\(219\) 2.29965 0.155396
\(220\) 0 0
\(221\) 12.4988 0.840763
\(222\) 0 0
\(223\) −11.8308 −0.792252 −0.396126 0.918196i \(-0.629646\pi\)
−0.396126 + 0.918196i \(0.629646\pi\)
\(224\) 0 0
\(225\) −2.67533 −0.178355
\(226\) 0 0
\(227\) 6.18986 0.410835 0.205418 0.978674i \(-0.434145\pi\)
0.205418 + 0.978674i \(0.434145\pi\)
\(228\) 0 0
\(229\) 17.7699 1.17427 0.587133 0.809491i \(-0.300257\pi\)
0.587133 + 0.809491i \(0.300257\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 17.0269 1.11547 0.557733 0.830020i \(-0.311671\pi\)
0.557733 + 0.830020i \(0.311671\pi\)
\(234\) 0 0
\(235\) −10.5107 −0.685641
\(236\) 0 0
\(237\) 1.86193 0.120945
\(238\) 0 0
\(239\) −1.18624 −0.0767313 −0.0383656 0.999264i \(-0.512215\pi\)
−0.0383656 + 0.999264i \(0.512215\pi\)
\(240\) 0 0
\(241\) −10.3606 −0.667388 −0.333694 0.942682i \(-0.608295\pi\)
−0.333694 + 0.942682i \(0.608295\pi\)
\(242\) 0 0
\(243\) −13.2247 −0.848365
\(244\) 0 0
\(245\) −3.68356 −0.235334
\(246\) 0 0
\(247\) 32.2482 2.05190
\(248\) 0 0
\(249\) −6.75614 −0.428153
\(250\) 0 0
\(251\) 19.6814 1.24228 0.621139 0.783701i \(-0.286670\pi\)
0.621139 + 0.783701i \(0.286670\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −1.81373 −0.113580
\(256\) 0 0
\(257\) 13.4421 0.838496 0.419248 0.907872i \(-0.362294\pi\)
0.419248 + 0.907872i \(0.362294\pi\)
\(258\) 0 0
\(259\) 5.45197 0.338769
\(260\) 0 0
\(261\) −11.8504 −0.733519
\(262\) 0 0
\(263\) 1.60780 0.0991410 0.0495705 0.998771i \(-0.484215\pi\)
0.0495705 + 0.998771i \(0.484215\pi\)
\(264\) 0 0
\(265\) 9.84643 0.604861
\(266\) 0 0
\(267\) 3.73915 0.228832
\(268\) 0 0
\(269\) 9.01686 0.549767 0.274884 0.961477i \(-0.411361\pi\)
0.274884 + 0.961477i \(0.411361\pi\)
\(270\) 0 0
\(271\) 19.3857 1.17759 0.588797 0.808281i \(-0.299602\pi\)
0.588797 + 0.808281i \(0.299602\pi\)
\(272\) 0 0
\(273\) −4.07455 −0.246603
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.92697 −0.115781 −0.0578903 0.998323i \(-0.518437\pi\)
−0.0578903 + 0.998323i \(0.518437\pi\)
\(278\) 0 0
\(279\) 1.06206 0.0635840
\(280\) 0 0
\(281\) 2.19286 0.130815 0.0654076 0.997859i \(-0.479165\pi\)
0.0654076 + 0.997859i \(0.479165\pi\)
\(282\) 0 0
\(283\) 28.9913 1.72335 0.861677 0.507458i \(-0.169415\pi\)
0.861677 + 0.507458i \(0.169415\pi\)
\(284\) 0 0
\(285\) −4.67959 −0.277195
\(286\) 0 0
\(287\) −21.9470 −1.29549
\(288\) 0 0
\(289\) −6.86792 −0.403995
\(290\) 0 0
\(291\) −8.28662 −0.485770
\(292\) 0 0
\(293\) −6.09890 −0.356301 −0.178151 0.984003i \(-0.557011\pi\)
−0.178151 + 0.984003i \(0.557011\pi\)
\(294\) 0 0
\(295\) 10.0121 0.582929
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.88263 0.166707
\(300\) 0 0
\(301\) −15.8975 −0.916317
\(302\) 0 0
\(303\) −5.63903 −0.323954
\(304\) 0 0
\(305\) −8.50878 −0.487212
\(306\) 0 0
\(307\) −15.2560 −0.870706 −0.435353 0.900260i \(-0.643376\pi\)
−0.435353 + 0.900260i \(0.643376\pi\)
\(308\) 0 0
\(309\) −4.10894 −0.233750
\(310\) 0 0
\(311\) −3.46576 −0.196525 −0.0982627 0.995161i \(-0.531329\pi\)
−0.0982627 + 0.995161i \(0.531329\pi\)
\(312\) 0 0
\(313\) 13.0464 0.737428 0.368714 0.929543i \(-0.379798\pi\)
0.368714 + 0.929543i \(0.379798\pi\)
\(314\) 0 0
\(315\) −4.87206 −0.274510
\(316\) 0 0
\(317\) −30.2860 −1.70103 −0.850517 0.525948i \(-0.823711\pi\)
−0.850517 + 0.525948i \(0.823711\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −5.57115 −0.310951
\(322\) 0 0
\(323\) 26.1417 1.45456
\(324\) 0 0
\(325\) 3.92663 0.217810
\(326\) 0 0
\(327\) 10.6740 0.590275
\(328\) 0 0
\(329\) −19.1411 −1.05528
\(330\) 0 0
\(331\) 4.19183 0.230404 0.115202 0.993342i \(-0.463248\pi\)
0.115202 + 0.993342i \(0.463248\pi\)
\(332\) 0 0
\(333\) −8.00930 −0.438907
\(334\) 0 0
\(335\) 1.11105 0.0607033
\(336\) 0 0
\(337\) −26.5352 −1.44546 −0.722731 0.691129i \(-0.757113\pi\)
−0.722731 + 0.691129i \(0.757113\pi\)
\(338\) 0 0
\(339\) −7.32842 −0.398025
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −19.4559 −1.05052
\(344\) 0 0
\(345\) −0.418304 −0.0225207
\(346\) 0 0
\(347\) −1.13932 −0.0611619 −0.0305809 0.999532i \(-0.509736\pi\)
−0.0305809 + 0.999532i \(0.509736\pi\)
\(348\) 0 0
\(349\) −16.2421 −0.869420 −0.434710 0.900571i \(-0.643149\pi\)
−0.434710 + 0.900571i \(0.643149\pi\)
\(350\) 0 0
\(351\) 12.6980 0.677768
\(352\) 0 0
\(353\) −0.432655 −0.0230279 −0.0115140 0.999934i \(-0.503665\pi\)
−0.0115140 + 0.999934i \(0.503665\pi\)
\(354\) 0 0
\(355\) 5.87172 0.311638
\(356\) 0 0
\(357\) −3.30300 −0.174813
\(358\) 0 0
\(359\) −0.0977164 −0.00515727 −0.00257864 0.999997i \(-0.500821\pi\)
−0.00257864 + 0.999997i \(0.500821\pi\)
\(360\) 0 0
\(361\) 48.4481 2.54990
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.03588 −0.211248
\(366\) 0 0
\(367\) 14.3906 0.751185 0.375592 0.926785i \(-0.377439\pi\)
0.375592 + 0.926785i \(0.377439\pi\)
\(368\) 0 0
\(369\) 32.2416 1.67843
\(370\) 0 0
\(371\) 17.9314 0.930953
\(372\) 0 0
\(373\) 13.8834 0.718855 0.359428 0.933173i \(-0.382972\pi\)
0.359428 + 0.933173i \(0.382972\pi\)
\(374\) 0 0
\(375\) −0.569801 −0.0294244
\(376\) 0 0
\(377\) 17.3930 0.895787
\(378\) 0 0
\(379\) 17.8304 0.915885 0.457943 0.888982i \(-0.348586\pi\)
0.457943 + 0.888982i \(0.348586\pi\)
\(380\) 0 0
\(381\) −1.62268 −0.0831322
\(382\) 0 0
\(383\) 8.39655 0.429044 0.214522 0.976719i \(-0.431181\pi\)
0.214522 + 0.976719i \(0.431181\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 23.3545 1.18717
\(388\) 0 0
\(389\) −7.89641 −0.400364 −0.200182 0.979759i \(-0.564153\pi\)
−0.200182 + 0.979759i \(0.564153\pi\)
\(390\) 0 0
\(391\) 2.33678 0.118176
\(392\) 0 0
\(393\) −5.40975 −0.272886
\(394\) 0 0
\(395\) −3.26768 −0.164415
\(396\) 0 0
\(397\) −36.2170 −1.81768 −0.908840 0.417146i \(-0.863030\pi\)
−0.908840 + 0.417146i \(0.863030\pi\)
\(398\) 0 0
\(399\) −8.52205 −0.426636
\(400\) 0 0
\(401\) −12.4872 −0.623582 −0.311791 0.950151i \(-0.600929\pi\)
−0.311791 + 0.950151i \(0.600929\pi\)
\(402\) 0 0
\(403\) −1.55881 −0.0776499
\(404\) 0 0
\(405\) 6.18335 0.307253
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 9.24803 0.457286 0.228643 0.973510i \(-0.426571\pi\)
0.228643 + 0.973510i \(0.426571\pi\)
\(410\) 0 0
\(411\) 4.01047 0.197822
\(412\) 0 0
\(413\) 18.2332 0.897196
\(414\) 0 0
\(415\) 11.8570 0.582038
\(416\) 0 0
\(417\) 2.12641 0.104131
\(418\) 0 0
\(419\) 28.9794 1.41574 0.707869 0.706344i \(-0.249657\pi\)
0.707869 + 0.706344i \(0.249657\pi\)
\(420\) 0 0
\(421\) 22.8185 1.11210 0.556052 0.831148i \(-0.312316\pi\)
0.556052 + 0.831148i \(0.312316\pi\)
\(422\) 0 0
\(423\) 28.1195 1.36722
\(424\) 0 0
\(425\) 3.18309 0.154403
\(426\) 0 0
\(427\) −15.4954 −0.749876
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −25.6107 −1.23362 −0.616811 0.787111i \(-0.711576\pi\)
−0.616811 + 0.787111i \(0.711576\pi\)
\(432\) 0 0
\(433\) 2.63416 0.126590 0.0632948 0.997995i \(-0.479839\pi\)
0.0632948 + 0.997995i \(0.479839\pi\)
\(434\) 0 0
\(435\) −2.52394 −0.121013
\(436\) 0 0
\(437\) 6.02911 0.288412
\(438\) 0 0
\(439\) 7.16551 0.341991 0.170996 0.985272i \(-0.445302\pi\)
0.170996 + 0.985272i \(0.445302\pi\)
\(440\) 0 0
\(441\) 9.85473 0.469273
\(442\) 0 0
\(443\) 15.3877 0.731092 0.365546 0.930793i \(-0.380882\pi\)
0.365546 + 0.930793i \(0.380882\pi\)
\(444\) 0 0
\(445\) −6.56220 −0.311078
\(446\) 0 0
\(447\) 6.99435 0.330821
\(448\) 0 0
\(449\) −4.63933 −0.218943 −0.109472 0.993990i \(-0.534916\pi\)
−0.109472 + 0.993990i \(0.534916\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −3.30630 −0.155344
\(454\) 0 0
\(455\) 7.15083 0.335236
\(456\) 0 0
\(457\) −12.8616 −0.601639 −0.300820 0.953681i \(-0.597260\pi\)
−0.300820 + 0.953681i \(0.597260\pi\)
\(458\) 0 0
\(459\) 10.2935 0.480460
\(460\) 0 0
\(461\) 19.6157 0.913594 0.456797 0.889571i \(-0.348997\pi\)
0.456797 + 0.889571i \(0.348997\pi\)
\(462\) 0 0
\(463\) −3.15807 −0.146768 −0.0733839 0.997304i \(-0.523380\pi\)
−0.0733839 + 0.997304i \(0.523380\pi\)
\(464\) 0 0
\(465\) 0.226202 0.0104899
\(466\) 0 0
\(467\) −28.9593 −1.34008 −0.670038 0.742327i \(-0.733722\pi\)
−0.670038 + 0.742327i \(0.733722\pi\)
\(468\) 0 0
\(469\) 2.02335 0.0934296
\(470\) 0 0
\(471\) 11.8152 0.544414
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 8.21268 0.376824
\(476\) 0 0
\(477\) −26.3424 −1.20614
\(478\) 0 0
\(479\) 21.2299 0.970021 0.485011 0.874508i \(-0.338816\pi\)
0.485011 + 0.874508i \(0.338816\pi\)
\(480\) 0 0
\(481\) 11.7554 0.536001
\(482\) 0 0
\(483\) −0.761777 −0.0346620
\(484\) 0 0
\(485\) 14.5430 0.660364
\(486\) 0 0
\(487\) −13.9771 −0.633365 −0.316682 0.948532i \(-0.602569\pi\)
−0.316682 + 0.948532i \(0.602569\pi\)
\(488\) 0 0
\(489\) 6.74206 0.304887
\(490\) 0 0
\(491\) 17.0953 0.771501 0.385751 0.922603i \(-0.373943\pi\)
0.385751 + 0.922603i \(0.373943\pi\)
\(492\) 0 0
\(493\) 14.0995 0.635010
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.6930 0.479648
\(498\) 0 0
\(499\) 40.9501 1.83318 0.916590 0.399828i \(-0.130930\pi\)
0.916590 + 0.399828i \(0.130930\pi\)
\(500\) 0 0
\(501\) −10.3617 −0.462928
\(502\) 0 0
\(503\) −13.4389 −0.599212 −0.299606 0.954063i \(-0.596855\pi\)
−0.299606 + 0.954063i \(0.596855\pi\)
\(504\) 0 0
\(505\) 9.89649 0.440388
\(506\) 0 0
\(507\) −1.37804 −0.0612009
\(508\) 0 0
\(509\) 18.3442 0.813094 0.406547 0.913630i \(-0.366733\pi\)
0.406547 + 0.913630i \(0.366733\pi\)
\(510\) 0 0
\(511\) −7.34978 −0.325135
\(512\) 0 0
\(513\) 26.5582 1.17257
\(514\) 0 0
\(515\) 7.21119 0.317763
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −5.82064 −0.255498
\(520\) 0 0
\(521\) 2.87412 0.125918 0.0629588 0.998016i \(-0.479946\pi\)
0.0629588 + 0.998016i \(0.479946\pi\)
\(522\) 0 0
\(523\) −37.6986 −1.64845 −0.824223 0.566266i \(-0.808387\pi\)
−0.824223 + 0.566266i \(0.808387\pi\)
\(524\) 0 0
\(525\) −1.03767 −0.0452876
\(526\) 0 0
\(527\) −1.26364 −0.0550449
\(528\) 0 0
\(529\) −22.4611 −0.976568
\(530\) 0 0
\(531\) −26.7857 −1.16240
\(532\) 0 0
\(533\) −47.3216 −2.04973
\(534\) 0 0
\(535\) 9.77736 0.422712
\(536\) 0 0
\(537\) −0.982071 −0.0423795
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −12.5509 −0.539605 −0.269802 0.962916i \(-0.586958\pi\)
−0.269802 + 0.962916i \(0.586958\pi\)
\(542\) 0 0
\(543\) −7.94992 −0.341164
\(544\) 0 0
\(545\) −18.7329 −0.802429
\(546\) 0 0
\(547\) −35.5307 −1.51918 −0.759592 0.650400i \(-0.774601\pi\)
−0.759592 + 0.650400i \(0.774601\pi\)
\(548\) 0 0
\(549\) 22.7638 0.971534
\(550\) 0 0
\(551\) 36.3781 1.54976
\(552\) 0 0
\(553\) −5.95080 −0.253054
\(554\) 0 0
\(555\) −1.70585 −0.0724093
\(556\) 0 0
\(557\) −39.8419 −1.68815 −0.844077 0.536222i \(-0.819851\pi\)
−0.844077 + 0.536222i \(0.819851\pi\)
\(558\) 0 0
\(559\) −34.2778 −1.44980
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −32.2632 −1.35973 −0.679866 0.733336i \(-0.737962\pi\)
−0.679866 + 0.733336i \(0.737962\pi\)
\(564\) 0 0
\(565\) 12.8614 0.541082
\(566\) 0 0
\(567\) 11.2606 0.472899
\(568\) 0 0
\(569\) −17.8955 −0.750216 −0.375108 0.926981i \(-0.622394\pi\)
−0.375108 + 0.926981i \(0.622394\pi\)
\(570\) 0 0
\(571\) 11.9435 0.499819 0.249910 0.968269i \(-0.419599\pi\)
0.249910 + 0.968269i \(0.419599\pi\)
\(572\) 0 0
\(573\) −14.0701 −0.587785
\(574\) 0 0
\(575\) 0.734122 0.0306150
\(576\) 0 0
\(577\) 11.9451 0.497282 0.248641 0.968596i \(-0.420016\pi\)
0.248641 + 0.968596i \(0.420016\pi\)
\(578\) 0 0
\(579\) 1.51939 0.0631435
\(580\) 0 0
\(581\) 21.5929 0.895825
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) −10.5050 −0.434330
\(586\) 0 0
\(587\) 15.8502 0.654208 0.327104 0.944988i \(-0.393927\pi\)
0.327104 + 0.944988i \(0.393927\pi\)
\(588\) 0 0
\(589\) −3.26030 −0.134338
\(590\) 0 0
\(591\) 12.2095 0.502233
\(592\) 0 0
\(593\) −40.0924 −1.64640 −0.823198 0.567754i \(-0.807812\pi\)
−0.823198 + 0.567754i \(0.807812\pi\)
\(594\) 0 0
\(595\) 5.79676 0.237644
\(596\) 0 0
\(597\) 3.29383 0.134808
\(598\) 0 0
\(599\) 32.5610 1.33041 0.665204 0.746662i \(-0.268345\pi\)
0.665204 + 0.746662i \(0.268345\pi\)
\(600\) 0 0
\(601\) −5.80180 −0.236660 −0.118330 0.992974i \(-0.537754\pi\)
−0.118330 + 0.992974i \(0.537754\pi\)
\(602\) 0 0
\(603\) −2.97243 −0.121047
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0588 0.570630 0.285315 0.958434i \(-0.407902\pi\)
0.285315 + 0.958434i \(0.407902\pi\)
\(608\) 0 0
\(609\) −4.59636 −0.186254
\(610\) 0 0
\(611\) −41.2716 −1.66967
\(612\) 0 0
\(613\) −30.8706 −1.24685 −0.623426 0.781882i \(-0.714260\pi\)
−0.623426 + 0.781882i \(0.714260\pi\)
\(614\) 0 0
\(615\) 6.86693 0.276901
\(616\) 0 0
\(617\) 35.9658 1.44793 0.723963 0.689838i \(-0.242318\pi\)
0.723963 + 0.689838i \(0.242318\pi\)
\(618\) 0 0
\(619\) 8.85192 0.355789 0.177894 0.984050i \(-0.443071\pi\)
0.177894 + 0.984050i \(0.443071\pi\)
\(620\) 0 0
\(621\) 2.37401 0.0952658
\(622\) 0 0
\(623\) −11.9505 −0.478786
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 9.52943 0.379963
\(630\) 0 0
\(631\) −45.5152 −1.81193 −0.905967 0.423349i \(-0.860854\pi\)
−0.905967 + 0.423349i \(0.860854\pi\)
\(632\) 0 0
\(633\) −6.59669 −0.262195
\(634\) 0 0
\(635\) 2.84780 0.113011
\(636\) 0 0
\(637\) −14.4640 −0.573085
\(638\) 0 0
\(639\) −15.7088 −0.621429
\(640\) 0 0
\(641\) 23.7684 0.938796 0.469398 0.882987i \(-0.344471\pi\)
0.469398 + 0.882987i \(0.344471\pi\)
\(642\) 0 0
\(643\) −26.6580 −1.05129 −0.525644 0.850705i \(-0.676176\pi\)
−0.525644 + 0.850705i \(0.676176\pi\)
\(644\) 0 0
\(645\) 4.97412 0.195856
\(646\) 0 0
\(647\) −38.0457 −1.49573 −0.747865 0.663851i \(-0.768921\pi\)
−0.747865 + 0.663851i \(0.768921\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0.411938 0.0161451
\(652\) 0 0
\(653\) −7.85962 −0.307571 −0.153785 0.988104i \(-0.549146\pi\)
−0.153785 + 0.988104i \(0.549146\pi\)
\(654\) 0 0
\(655\) 9.49411 0.370966
\(656\) 0 0
\(657\) 10.7973 0.421243
\(658\) 0 0
\(659\) −27.5518 −1.07327 −0.536633 0.843816i \(-0.680304\pi\)
−0.536633 + 0.843816i \(0.680304\pi\)
\(660\) 0 0
\(661\) 39.6062 1.54050 0.770251 0.637741i \(-0.220131\pi\)
0.770251 + 0.637741i \(0.220131\pi\)
\(662\) 0 0
\(663\) −7.12185 −0.276590
\(664\) 0 0
\(665\) 14.9562 0.579976
\(666\) 0 0
\(667\) 3.25180 0.125910
\(668\) 0 0
\(669\) 6.74123 0.260631
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 43.1226 1.66225 0.831127 0.556082i \(-0.187696\pi\)
0.831127 + 0.556082i \(0.187696\pi\)
\(674\) 0 0
\(675\) 3.23381 0.124469
\(676\) 0 0
\(677\) 21.6325 0.831406 0.415703 0.909500i \(-0.363536\pi\)
0.415703 + 0.909500i \(0.363536\pi\)
\(678\) 0 0
\(679\) 26.4844 1.01638
\(680\) 0 0
\(681\) −3.52699 −0.135154
\(682\) 0 0
\(683\) −1.01316 −0.0387675 −0.0193838 0.999812i \(-0.506170\pi\)
−0.0193838 + 0.999812i \(0.506170\pi\)
\(684\) 0 0
\(685\) −7.03836 −0.268922
\(686\) 0 0
\(687\) −10.1253 −0.386304
\(688\) 0 0
\(689\) 38.6633 1.47296
\(690\) 0 0
\(691\) −17.1815 −0.653616 −0.326808 0.945091i \(-0.605973\pi\)
−0.326808 + 0.945091i \(0.605973\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −3.73184 −0.141557
\(696\) 0 0
\(697\) −38.3609 −1.45302
\(698\) 0 0
\(699\) −9.70192 −0.366960
\(700\) 0 0
\(701\) −17.4446 −0.658875 −0.329437 0.944177i \(-0.606859\pi\)
−0.329437 + 0.944177i \(0.606859\pi\)
\(702\) 0 0
\(703\) 24.5868 0.927310
\(704\) 0 0
\(705\) 5.98900 0.225559
\(706\) 0 0
\(707\) 18.0226 0.677809
\(708\) 0 0
\(709\) −17.0730 −0.641191 −0.320595 0.947216i \(-0.603883\pi\)
−0.320595 + 0.947216i \(0.603883\pi\)
\(710\) 0 0
\(711\) 8.74212 0.327855
\(712\) 0 0
\(713\) −0.291435 −0.0109143
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0.675919 0.0252427
\(718\) 0 0
\(719\) −25.2508 −0.941695 −0.470848 0.882215i \(-0.656052\pi\)
−0.470848 + 0.882215i \(0.656052\pi\)
\(720\) 0 0
\(721\) 13.1324 0.489075
\(722\) 0 0
\(723\) 5.90351 0.219554
\(724\) 0 0
\(725\) 4.42950 0.164508
\(726\) 0 0
\(727\) −49.9360 −1.85202 −0.926012 0.377493i \(-0.876786\pi\)
−0.926012 + 0.377493i \(0.876786\pi\)
\(728\) 0 0
\(729\) −11.0146 −0.407949
\(730\) 0 0
\(731\) −27.7870 −1.02774
\(732\) 0 0
\(733\) −14.9515 −0.552246 −0.276123 0.961122i \(-0.589050\pi\)
−0.276123 + 0.961122i \(0.589050\pi\)
\(734\) 0 0
\(735\) 2.09890 0.0774190
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −8.68720 −0.319564 −0.159782 0.987152i \(-0.551079\pi\)
−0.159782 + 0.987152i \(0.551079\pi\)
\(740\) 0 0
\(741\) −18.3751 −0.675025
\(742\) 0 0
\(743\) 11.9221 0.437380 0.218690 0.975794i \(-0.429822\pi\)
0.218690 + 0.975794i \(0.429822\pi\)
\(744\) 0 0
\(745\) −12.2751 −0.449724
\(746\) 0 0
\(747\) −31.7214 −1.16063
\(748\) 0 0
\(749\) 17.8056 0.650604
\(750\) 0 0
\(751\) 52.3281 1.90948 0.954739 0.297444i \(-0.0961340\pi\)
0.954739 + 0.297444i \(0.0961340\pi\)
\(752\) 0 0
\(753\) −11.2145 −0.408678
\(754\) 0 0
\(755\) 5.80255 0.211176
\(756\) 0 0
\(757\) −45.0769 −1.63835 −0.819174 0.573545i \(-0.805568\pi\)
−0.819174 + 0.573545i \(0.805568\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −22.7150 −0.823417 −0.411708 0.911316i \(-0.635068\pi\)
−0.411708 + 0.911316i \(0.635068\pi\)
\(762\) 0 0
\(763\) −34.1146 −1.23503
\(764\) 0 0
\(765\) −8.51581 −0.307890
\(766\) 0 0
\(767\) 39.3140 1.41954
\(768\) 0 0
\(769\) 10.5711 0.381202 0.190601 0.981668i \(-0.438956\pi\)
0.190601 + 0.981668i \(0.438956\pi\)
\(770\) 0 0
\(771\) −7.65933 −0.275844
\(772\) 0 0
\(773\) −8.71357 −0.313405 −0.156703 0.987646i \(-0.550086\pi\)
−0.156703 + 0.987646i \(0.550086\pi\)
\(774\) 0 0
\(775\) −0.396984 −0.0142601
\(776\) 0 0
\(777\) −3.10654 −0.111446
\(778\) 0 0
\(779\) −98.9747 −3.54614
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 14.3242 0.511904
\(784\) 0 0
\(785\) −20.7356 −0.740085
\(786\) 0 0
\(787\) 52.0753 1.85629 0.928143 0.372225i \(-0.121405\pi\)
0.928143 + 0.372225i \(0.121405\pi\)
\(788\) 0 0
\(789\) −0.916124 −0.0326149
\(790\) 0 0
\(791\) 23.4220 0.832789
\(792\) 0 0
\(793\) −33.4109 −1.18646
\(794\) 0 0
\(795\) −5.61051 −0.198984
\(796\) 0 0
\(797\) 48.7161 1.72561 0.862806 0.505535i \(-0.168705\pi\)
0.862806 + 0.505535i \(0.168705\pi\)
\(798\) 0 0
\(799\) −33.4565 −1.18361
\(800\) 0 0
\(801\) 17.5560 0.620312
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 1.33692 0.0471201
\(806\) 0 0
\(807\) −5.13781 −0.180860
\(808\) 0 0
\(809\) 15.0005 0.527389 0.263695 0.964606i \(-0.415059\pi\)
0.263695 + 0.964606i \(0.415059\pi\)
\(810\) 0 0
\(811\) −37.2387 −1.30763 −0.653814 0.756656i \(-0.726832\pi\)
−0.653814 + 0.756656i \(0.726832\pi\)
\(812\) 0 0
\(813\) −11.0460 −0.387399
\(814\) 0 0
\(815\) −11.8323 −0.414468
\(816\) 0 0
\(817\) −71.6932 −2.50823
\(818\) 0 0
\(819\) −19.1308 −0.668484
\(820\) 0 0
\(821\) 17.9737 0.627285 0.313642 0.949541i \(-0.398451\pi\)
0.313642 + 0.949541i \(0.398451\pi\)
\(822\) 0 0
\(823\) −18.3732 −0.640449 −0.320224 0.947342i \(-0.603758\pi\)
−0.320224 + 0.947342i \(0.603758\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −38.6104 −1.34262 −0.671308 0.741178i \(-0.734267\pi\)
−0.671308 + 0.741178i \(0.734267\pi\)
\(828\) 0 0
\(829\) 52.7170 1.83094 0.915469 0.402388i \(-0.131820\pi\)
0.915469 + 0.402388i \(0.131820\pi\)
\(830\) 0 0
\(831\) 1.09799 0.0380889
\(832\) 0 0
\(833\) −11.7251 −0.406252
\(834\) 0 0
\(835\) 18.1848 0.629312
\(836\) 0 0
\(837\) −1.28377 −0.0443736
\(838\) 0 0
\(839\) −25.8498 −0.892435 −0.446217 0.894925i \(-0.647229\pi\)
−0.446217 + 0.894925i \(0.647229\pi\)
\(840\) 0 0
\(841\) −9.37951 −0.323431
\(842\) 0 0
\(843\) −1.24949 −0.0430349
\(844\) 0 0
\(845\) 2.41846 0.0831975
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −16.5193 −0.566940
\(850\) 0 0
\(851\) 2.19779 0.0753393
\(852\) 0 0
\(853\) 25.3912 0.869380 0.434690 0.900580i \(-0.356858\pi\)
0.434690 + 0.900580i \(0.356858\pi\)
\(854\) 0 0
\(855\) −21.9716 −0.751413
\(856\) 0 0
\(857\) −4.42328 −0.151096 −0.0755482 0.997142i \(-0.524071\pi\)
−0.0755482 + 0.997142i \(0.524071\pi\)
\(858\) 0 0
\(859\) −13.1491 −0.448643 −0.224321 0.974515i \(-0.572017\pi\)
−0.224321 + 0.974515i \(0.572017\pi\)
\(860\) 0 0
\(861\) 12.5054 0.426184
\(862\) 0 0
\(863\) 15.4387 0.525539 0.262770 0.964859i \(-0.415364\pi\)
0.262770 + 0.964859i \(0.415364\pi\)
\(864\) 0 0
\(865\) 10.2152 0.347328
\(866\) 0 0
\(867\) 3.91335 0.132904
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 4.36270 0.147824
\(872\) 0 0
\(873\) −38.9073 −1.31681
\(874\) 0 0
\(875\) 1.82111 0.0615647
\(876\) 0 0
\(877\) −7.02185 −0.237111 −0.118556 0.992947i \(-0.537826\pi\)
−0.118556 + 0.992947i \(0.537826\pi\)
\(878\) 0 0
\(879\) 3.47516 0.117214
\(880\) 0 0
\(881\) 22.0522 0.742958 0.371479 0.928441i \(-0.378851\pi\)
0.371479 + 0.928441i \(0.378851\pi\)
\(882\) 0 0
\(883\) 12.0558 0.405709 0.202855 0.979209i \(-0.434978\pi\)
0.202855 + 0.979209i \(0.434978\pi\)
\(884\) 0 0
\(885\) −5.70492 −0.191769
\(886\) 0 0
\(887\) 33.1393 1.11271 0.556354 0.830946i \(-0.312200\pi\)
0.556354 + 0.830946i \(0.312200\pi\)
\(888\) 0 0
\(889\) 5.18614 0.173938
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −86.3209 −2.88862
\(894\) 0 0
\(895\) 1.72353 0.0576113
\(896\) 0 0
\(897\) −1.64253 −0.0548423
\(898\) 0 0
\(899\) −1.75844 −0.0586473
\(900\) 0 0
\(901\) 31.3421 1.04416
\(902\) 0 0
\(903\) 9.05841 0.301445
\(904\) 0 0
\(905\) 13.9521 0.463783
\(906\) 0 0
\(907\) −21.2434 −0.705376 −0.352688 0.935741i \(-0.614732\pi\)
−0.352688 + 0.935741i \(0.614732\pi\)
\(908\) 0 0
\(909\) −26.4763 −0.878165
\(910\) 0 0
\(911\) 47.9763 1.58952 0.794762 0.606921i \(-0.207596\pi\)
0.794762 + 0.606921i \(0.207596\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 4.84831 0.160280
\(916\) 0 0
\(917\) 17.2898 0.570960
\(918\) 0 0
\(919\) 6.85646 0.226174 0.113087 0.993585i \(-0.463926\pi\)
0.113087 + 0.993585i \(0.463926\pi\)
\(920\) 0 0
\(921\) 8.69289 0.286440
\(922\) 0 0
\(923\) 23.0561 0.758901
\(924\) 0 0
\(925\) 2.99377 0.0984344
\(926\) 0 0
\(927\) −19.2923 −0.633642
\(928\) 0 0
\(929\) −40.2466 −1.32045 −0.660224 0.751069i \(-0.729538\pi\)
−0.660224 + 0.751069i \(0.729538\pi\)
\(930\) 0 0
\(931\) −30.2519 −0.991467
\(932\) 0 0
\(933\) 1.97480 0.0646519
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −47.4498 −1.55012 −0.775058 0.631890i \(-0.782279\pi\)
−0.775058 + 0.631890i \(0.782279\pi\)
\(938\) 0 0
\(939\) −7.43387 −0.242595
\(940\) 0 0
\(941\) −18.5398 −0.604382 −0.302191 0.953247i \(-0.597718\pi\)
−0.302191 + 0.953247i \(0.597718\pi\)
\(942\) 0 0
\(943\) −8.84724 −0.288106
\(944\) 0 0
\(945\) 5.88911 0.191573
\(946\) 0 0
\(947\) −57.2726 −1.86111 −0.930555 0.366153i \(-0.880675\pi\)
−0.930555 + 0.366153i \(0.880675\pi\)
\(948\) 0 0
\(949\) −15.8474 −0.514430
\(950\) 0 0
\(951\) 17.2570 0.559597
\(952\) 0 0
\(953\) −1.12981 −0.0365983 −0.0182991 0.999833i \(-0.505825\pi\)
−0.0182991 + 0.999833i \(0.505825\pi\)
\(954\) 0 0
\(955\) 24.6929 0.799044
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −12.8176 −0.413903
\(960\) 0 0
\(961\) −30.8424 −0.994916
\(962\) 0 0
\(963\) −26.1576 −0.842918
\(964\) 0 0
\(965\) −2.66652 −0.0858383
\(966\) 0 0
\(967\) 54.1275 1.74062 0.870311 0.492502i \(-0.163917\pi\)
0.870311 + 0.492502i \(0.163917\pi\)
\(968\) 0 0
\(969\) −14.8956 −0.478515
\(970\) 0 0
\(971\) 20.1605 0.646980 0.323490 0.946232i \(-0.395144\pi\)
0.323490 + 0.946232i \(0.395144\pi\)
\(972\) 0 0
\(973\) −6.79609 −0.217873
\(974\) 0 0
\(975\) −2.23740 −0.0716542
\(976\) 0 0
\(977\) −42.3633 −1.35532 −0.677662 0.735374i \(-0.737007\pi\)
−0.677662 + 0.735374i \(0.737007\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 50.1166 1.60010
\(982\) 0 0
\(983\) 52.7171 1.68141 0.840706 0.541491i \(-0.182140\pi\)
0.840706 + 0.541491i \(0.182140\pi\)
\(984\) 0 0
\(985\) −21.4277 −0.682743
\(986\) 0 0
\(987\) 10.9066 0.347162
\(988\) 0 0
\(989\) −6.40858 −0.203781
\(990\) 0 0
\(991\) 25.8605 0.821487 0.410744 0.911751i \(-0.365269\pi\)
0.410744 + 0.911751i \(0.365269\pi\)
\(992\) 0 0
\(993\) −2.38851 −0.0757971
\(994\) 0 0
\(995\) −5.78067 −0.183260
\(996\) 0 0
\(997\) −0.222068 −0.00703296 −0.00351648 0.999994i \(-0.501119\pi\)
−0.00351648 + 0.999994i \(0.501119\pi\)
\(998\) 0 0
\(999\) 9.68126 0.306301
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 4840.2.a.bh.1.4 8
4.3 odd 2 9680.2.a.de.1.5 8
11.7 odd 10 440.2.y.d.401.3 yes 16
11.8 odd 10 440.2.y.d.361.3 16
11.10 odd 2 4840.2.a.bg.1.4 8
44.7 even 10 880.2.bo.k.401.2 16
44.19 even 10 880.2.bo.k.801.2 16
44.43 even 2 9680.2.a.df.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
440.2.y.d.361.3 16 11.8 odd 10
440.2.y.d.401.3 yes 16 11.7 odd 10
880.2.bo.k.401.2 16 44.7 even 10
880.2.bo.k.801.2 16 44.19 even 10
4840.2.a.bg.1.4 8 11.10 odd 2
4840.2.a.bh.1.4 8 1.1 even 1 trivial
9680.2.a.de.1.5 8 4.3 odd 2
9680.2.a.df.1.5 8 44.43 even 2