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Properties

Label 799.2.a.b.1.1
Level $799$
Weight $2$
Character 799.1
Self dual yes
Analytic conductor $6.380$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,2,Mod(1,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("799.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 799.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: \(6.38004712150\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 799.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.00000 q^{3} -1.00000 q^{4} +4.00000 q^{5} -2.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.00000 q^{3} -1.00000 q^{4} +4.00000 q^{5} -2.00000 q^{6} -2.00000 q^{7} +3.00000 q^{8} +1.00000 q^{9} -4.00000 q^{10} -2.00000 q^{12} +2.00000 q^{13} +2.00000 q^{14} +8.00000 q^{15} -1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.00000 q^{20} -4.00000 q^{21} -4.00000 q^{23} +6.00000 q^{24} +11.0000 q^{25} -2.00000 q^{26} -4.00000 q^{27} +2.00000 q^{28} +8.00000 q^{29} -8.00000 q^{30} +8.00000 q^{31} -5.00000 q^{32} -1.00000 q^{34} -8.00000 q^{35} -1.00000 q^{36} -2.00000 q^{37} -4.00000 q^{38} +4.00000 q^{39} +12.0000 q^{40} -8.00000 q^{41} +4.00000 q^{42} -4.00000 q^{43} +4.00000 q^{45} +4.00000 q^{46} -1.00000 q^{47} -2.00000 q^{48} -3.00000 q^{49} -11.0000 q^{50} +2.00000 q^{51} -2.00000 q^{52} +6.00000 q^{53} +4.00000 q^{54} -6.00000 q^{56} +8.00000 q^{57} -8.00000 q^{58} +4.00000 q^{59} -8.00000 q^{60} +6.00000 q^{61} -8.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} +8.00000 q^{65} -4.00000 q^{67} -1.00000 q^{68} -8.00000 q^{69} +8.00000 q^{70} -6.00000 q^{71} +3.00000 q^{72} +4.00000 q^{73} +2.00000 q^{74} +22.0000 q^{75} -4.00000 q^{76} -4.00000 q^{78} +2.00000 q^{79} -4.00000 q^{80} -11.0000 q^{81} +8.00000 q^{82} +4.00000 q^{84} +4.00000 q^{85} +4.00000 q^{86} +16.0000 q^{87} +6.00000 q^{89} -4.00000 q^{90} -4.00000 q^{91} +4.00000 q^{92} +16.0000 q^{93} +1.00000 q^{94} +16.0000 q^{95} -10.0000 q^{96} +10.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 − 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 2.00000 1.15470 0.577350 − 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) −1.00000 −0.500000
\(5\) 4.00000 1.78885 0.894427 − 0.447214i \(-0.147584\pi\)
0.894427 + 0.447214i \(0.147584\pi\)
\(6\) −2.00000 −0.816497
\(7\) −2.00000 −0.755929 −0.377964 − 0.925820i \(-0.623376\pi\)
−0.377964 + 0.925820i \(0.623376\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) −4.00000 −1.26491
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) −2.00000 −0.577350
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 2.00000 0.534522
\(15\) 8.00000 2.06559
\(16\) −1.00000 −0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −4.00000 −0.894427
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 6.00000 1.22474
\(25\) 11.0000 2.20000
\(26\) −2.00000 −0.392232
\(27\) −4.00000 −0.769800
\(28\) 2.00000 0.377964
\(29\) 8.00000 1.48556 0.742781 − 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) −8.00000 −1.46059
\(31\) 8.00000 1.43684 0.718421 − 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −1.00000 −0.171499
\(35\) −8.00000 −1.35225
\(36\) −1.00000 −0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −4.00000 −0.648886
\(39\) 4.00000 0.640513
\(40\) 12.0000 1.89737
\(41\) −8.00000 −1.24939 −0.624695 − 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 4.00000 0.617213
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) 4.00000 0.596285
\(46\) 4.00000 0.589768
\(47\) −1.00000 −0.145865
\(48\) −2.00000 −0.288675
\(49\) −3.00000 −0.428571
\(50\) −11.0000 −1.55563
\(51\) 2.00000 0.280056
\(52\) −2.00000 −0.277350
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 4.00000 0.544331
\(55\) 0 0
\(56\) −6.00000 −0.801784
\(57\) 8.00000 1.05963
\(58\) −8.00000 −1.05045
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −8.00000 −1.03280
\(61\) 6.00000 0.768221 0.384111 − 0.923287i \(-0.374508\pi\)
0.384111 + 0.923287i \(0.374508\pi\)
\(62\) −8.00000 −1.01600
\(63\) −2.00000 −0.251976
\(64\) 7.00000 0.875000
\(65\) 8.00000 0.992278
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 −0.121268
\(69\) −8.00000 −0.963087
\(70\) 8.00000 0.956183
\(71\) −6.00000 −0.712069 −0.356034 − 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 3.00000 0.353553
\(73\) 4.00000 0.468165 0.234082 − 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 2.00000 0.232495
\(75\) 22.0000 2.54034
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) −4.00000 −0.452911
\(79\) 2.00000 0.225018 0.112509 − 0.993651i \(-0.464111\pi\)
0.112509 + 0.993651i \(0.464111\pi\)
\(80\) −4.00000 −0.447214
\(81\) −11.0000 −1.22222
\(82\) 8.00000 0.883452
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 4.00000 0.436436
\(85\) 4.00000 0.433861
\(86\) 4.00000 0.431331
\(87\) 16.0000 1.71538
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 − 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) −4.00000 −0.421637
\(91\) −4.00000 −0.419314
\(92\) 4.00000 0.417029
\(93\) 16.0000 1.65912
\(94\) 1.00000 0.103142
\(95\) 16.0000 1.64157
\(96\) −10.0000 −1.02062
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) −11.0000 −1.10000
\(101\) −18.0000 −1.79107 −0.895533 − 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) −2.00000 −0.198030
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) 6.00000 0.588348
\(105\) −16.0000 −1.56144
\(106\) −6.00000 −0.582772
\(107\) −4.00000 −0.386695 −0.193347 − 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 4.00000 0.384900
\(109\) −4.00000 −0.383131 −0.191565 − 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 2.00000 0.188982
\(113\) 12.0000 1.12887 0.564433 − 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) −8.00000 −0.749269
\(115\) −16.0000 −1.49201
\(116\) −8.00000 −0.742781
\(117\) 2.00000 0.184900
\(118\) −4.00000 −0.368230
\(119\) −2.00000 −0.183340
\(120\) 24.0000 2.19089
\(121\) −11.0000 −1.00000
\(122\) −6.00000 −0.543214
\(123\) −16.0000 −1.44267
\(124\) −8.00000 −0.718421
\(125\) 24.0000 2.14663
\(126\) 2.00000 0.178174
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 3.00000 0.265165
\(129\) −8.00000 −0.704361
\(130\) −8.00000 −0.701646
\(131\) 6.00000 0.524222 0.262111 − 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) −8.00000 −0.693688
\(134\) 4.00000 0.345547
\(135\) −16.0000 −1.37706
\(136\) 3.00000 0.257248
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 8.00000 0.681005
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 8.00000 0.676123
\(141\) −2.00000 −0.168430
\(142\) 6.00000 0.503509
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) 32.0000 2.65746
\(146\) −4.00000 −0.331042
\(147\) −6.00000 −0.494872
\(148\) 2.00000 0.164399
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) −22.0000 −1.79629
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 12.0000 0.973329
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 32.0000 2.57030
\(156\) −4.00000 −0.320256
\(157\) 10.0000 0.798087 0.399043 − 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −2.00000 −0.159111
\(159\) 12.0000 0.951662
\(160\) −20.0000 −1.58114
\(161\) 8.00000 0.630488
\(162\) 11.0000 0.864242
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 8.00000 0.624695
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) −12.0000 −0.925820
\(169\) −9.00000 −0.692308
\(170\) −4.00000 −0.306786
\(171\) 4.00000 0.305888
\(172\) 4.00000 0.304997
\(173\) −26.0000 −1.97674 −0.988372 − 0.152057i \(-0.951410\pi\)
−0.988372 + 0.152057i \(0.951410\pi\)
\(174\) −16.0000 −1.21296
\(175\) −22.0000 −1.66304
\(176\) 0 0
\(177\) 8.00000 0.601317
\(178\) −6.00000 −0.449719
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −4.00000 −0.298142
\(181\) 16.0000 1.18927 0.594635 − 0.803996i \(-0.297296\pi\)
0.594635 + 0.803996i \(0.297296\pi\)
\(182\) 4.00000 0.296500
\(183\) 12.0000 0.887066
\(184\) −12.0000 −0.884652
\(185\) −8.00000 −0.588172
\(186\) −16.0000 −1.17318
\(187\) 0 0
\(188\) 1.00000 0.0729325
\(189\) 8.00000 0.581914
\(190\) −16.0000 −1.16076
\(191\) 12.0000 0.868290 0.434145 − 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 14.0000 1.01036
\(193\) −20.0000 −1.43963 −0.719816 − 0.694165i \(-0.755774\pi\)
−0.719816 + 0.694165i \(0.755774\pi\)
\(194\) −10.0000 −0.717958
\(195\) 16.0000 1.14578
\(196\) 3.00000 0.214286
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) 33.0000 2.33345
\(201\) −8.00000 −0.564276
\(202\) 18.0000 1.26648
\(203\) −16.0000 −1.12298
\(204\) −2.00000 −0.140028
\(205\) −32.0000 −2.23498
\(206\) 4.00000 0.278693
\(207\) −4.00000 −0.278019
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 16.0000 1.10410
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −6.00000 −0.412082
\(213\) −12.0000 −0.822226
\(214\) 4.00000 0.273434
\(215\) −16.0000 −1.09119
\(216\) −12.0000 −0.816497
\(217\) −16.0000 −1.08615
\(218\) 4.00000 0.270914
\(219\) 8.00000 0.540590
\(220\) 0 0
\(221\) 2.00000 0.134535
\(222\) 4.00000 0.268462
\(223\) −16.0000 −1.07144 −0.535720 − 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 10.0000 0.668153
\(225\) 11.0000 0.733333
\(226\) −12.0000 −0.798228
\(227\) −28.0000 −1.85843 −0.929213 − 0.369546i \(-0.879513\pi\)
−0.929213 + 0.369546i \(0.879513\pi\)
\(228\) −8.00000 −0.529813
\(229\) 14.0000 0.925146 0.462573 − 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 16.0000 1.05501
\(231\) 0 0
\(232\) 24.0000 1.57568
\(233\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(234\) −2.00000 −0.130744
\(235\) −4.00000 −0.260931
\(236\) −4.00000 −0.260378
\(237\) 4.00000 0.259828
\(238\) 2.00000 0.129641
\(239\) 8.00000 0.517477 0.258738 − 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) −8.00000 −0.516398
\(241\) −18.0000 −1.15948 −0.579741 − 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 11.0000 0.707107
\(243\) −10.0000 −0.641500
\(244\) −6.00000 −0.384111
\(245\) −12.0000 −0.766652
\(246\) 16.0000 1.02012
\(247\) 8.00000 0.509028
\(248\) 24.0000 1.52400
\(249\) 0 0
\(250\) −24.0000 −1.51789
\(251\) 16.0000 1.00991 0.504956 − 0.863145i \(-0.331509\pi\)
0.504956 + 0.863145i \(0.331509\pi\)
\(252\) 2.00000 0.125988
\(253\) 0 0
\(254\) 8.00000 0.501965
\(255\) 8.00000 0.500979
\(256\) −17.0000 −1.06250
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) 8.00000 0.498058
\(259\) 4.00000 0.248548
\(260\) −8.00000 −0.496139
\(261\) 8.00000 0.495188
\(262\) −6.00000 −0.370681
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 8.00000 0.490511
\(267\) 12.0000 0.734388
\(268\) 4.00000 0.244339
\(269\) 14.0000 0.853595 0.426798 − 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 16.0000 0.973729
\(271\) −28.0000 −1.70088 −0.850439 − 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −8.00000 −0.484182
\(274\) −6.00000 −0.362473
\(275\) 0 0
\(276\) 8.00000 0.481543
\(277\) 10.0000 0.600842 0.300421 − 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) 0 0
\(279\) 8.00000 0.478947
\(280\) −24.0000 −1.43427
\(281\) −26.0000 −1.55103 −0.775515 − 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 2.00000 0.119098
\(283\) 6.00000 0.356663 0.178331 − 0.983970i \(-0.442930\pi\)
0.178331 + 0.983970i \(0.442930\pi\)
\(284\) 6.00000 0.356034
\(285\) 32.0000 1.89552
\(286\) 0 0
\(287\) 16.0000 0.944450
\(288\) −5.00000 −0.294628
\(289\) 1.00000 0.0588235
\(290\) −32.0000 −1.87910
\(291\) 20.0000 1.17242
\(292\) −4.00000 −0.234082
\(293\) 30.0000 1.75262 0.876309 − 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 6.00000 0.349927
\(295\) 16.0000 0.931556
\(296\) −6.00000 −0.348743
\(297\) 0 0
\(298\) −10.0000 −0.579284
\(299\) −8.00000 −0.462652
\(300\) −22.0000 −1.27017
\(301\) 8.00000 0.461112
\(302\) 16.0000 0.920697
\(303\) −36.0000 −2.06815
\(304\) −4.00000 −0.229416
\(305\) 24.0000 1.37424
\(306\) −1.00000 −0.0571662
\(307\) 8.00000 0.456584 0.228292 − 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) −32.0000 −1.81748
\(311\) 12.0000 0.680458 0.340229 − 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 12.0000 0.679366
\(313\) 8.00000 0.452187 0.226093 − 0.974106i \(-0.427405\pi\)
0.226093 + 0.974106i \(0.427405\pi\)
\(314\) −10.0000 −0.564333
\(315\) −8.00000 −0.450749
\(316\) −2.00000 −0.112509
\(317\) −32.0000 −1.79730 −0.898650 − 0.438667i \(-0.855451\pi\)
−0.898650 + 0.438667i \(0.855451\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) 28.0000 1.56525
\(321\) −8.00000 −0.446516
\(322\) −8.00000 −0.445823
\(323\) 4.00000 0.222566
\(324\) 11.0000 0.611111
\(325\) 22.0000 1.22034
\(326\) 16.0000 0.886158
\(327\) −8.00000 −0.442401
\(328\) −24.0000 −1.32518
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 − 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 0 0
\(333\) −2.00000 −0.109599
\(334\) 8.00000 0.437741
\(335\) −16.0000 −0.874173
\(336\) 4.00000 0.218218
\(337\) 6.00000 0.326841 0.163420 − 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 9.00000 0.489535
\(339\) 24.0000 1.30350
\(340\) −4.00000 −0.216930
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) 20.0000 1.07990
\(344\) −12.0000 −0.646997
\(345\) −32.0000 −1.72282
\(346\) 26.0000 1.39777
\(347\) 30.0000 1.61048 0.805242 − 0.592946i \(-0.202035\pi\)
0.805242 + 0.592946i \(0.202035\pi\)
\(348\) −16.0000 −0.857690
\(349\) −30.0000 −1.60586 −0.802932 − 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 22.0000 1.17595
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) 14.0000 0.745145 0.372572 − 0.928003i \(-0.378476\pi\)
0.372572 + 0.928003i \(0.378476\pi\)
\(354\) −8.00000 −0.425195
\(355\) −24.0000 −1.27379
\(356\) −6.00000 −0.317999
\(357\) −4.00000 −0.211702
\(358\) 12.0000 0.634220
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 12.0000 0.632456
\(361\) −3.00000 −0.157895
\(362\) −16.0000 −0.840941
\(363\) −22.0000 −1.15470
\(364\) 4.00000 0.209657
\(365\) 16.0000 0.837478
\(366\) −12.0000 −0.627250
\(367\) −16.0000 −0.835193 −0.417597 − 0.908633i \(-0.637127\pi\)
−0.417597 + 0.908633i \(0.637127\pi\)
\(368\) 4.00000 0.208514
\(369\) −8.00000 −0.416463
\(370\) 8.00000 0.415900
\(371\) −12.0000 −0.623009
\(372\) −16.0000 −0.829561
\(373\) 26.0000 1.34623 0.673114 − 0.739538i \(-0.264956\pi\)
0.673114 + 0.739538i \(0.264956\pi\)
\(374\) 0 0
\(375\) 48.0000 2.47871
\(376\) −3.00000 −0.154713
\(377\) 16.0000 0.824042
\(378\) −8.00000 −0.411476
\(379\) 38.0000 1.95193 0.975964 − 0.217930i \(-0.0699304\pi\)
0.975964 + 0.217930i \(0.0699304\pi\)
\(380\) −16.0000 −0.820783
\(381\) −16.0000 −0.819705
\(382\) −12.0000 −0.613973
\(383\) −12.0000 −0.613171 −0.306586 − 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 6.00000 0.306186
\(385\) 0 0
\(386\) 20.0000 1.01797
\(387\) −4.00000 −0.203331
\(388\) −10.0000 −0.507673
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) −16.0000 −0.810191
\(391\) −4.00000 −0.202289
\(392\) −9.00000 −0.454569
\(393\) 12.0000 0.605320
\(394\) 22.0000 1.10834
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 22.0000 1.10415 0.552074 − 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) 20.0000 1.00251
\(399\) −16.0000 −0.801002
\(400\) −11.0000 −0.550000
\(401\) −18.0000 −0.898877 −0.449439 − 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 8.00000 0.399004
\(403\) 16.0000 0.797017
\(404\) 18.0000 0.895533
\(405\) −44.0000 −2.18638
\(406\) 16.0000 0.794067
\(407\) 0 0
\(408\) 6.00000 0.297044
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 32.0000 1.58037
\(411\) 12.0000 0.591916
\(412\) 4.00000 0.197066
\(413\) −8.00000 −0.393654
\(414\) 4.00000 0.196589
\(415\) 0 0
\(416\) −10.0000 −0.490290
\(417\) 0 0
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 − 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 16.0000 0.780720
\(421\) 26.0000 1.26716 0.633581 − 0.773676i \(-0.281584\pi\)
0.633581 + 0.773676i \(0.281584\pi\)
\(422\) 12.0000 0.584151
\(423\) −1.00000 −0.0486217
\(424\) 18.0000 0.874157
\(425\) 11.0000 0.533578
\(426\) 12.0000 0.581402
\(427\) −12.0000 −0.580721
\(428\) 4.00000 0.193347
\(429\) 0 0
\(430\) 16.0000 0.771589
\(431\) 10.0000 0.481683 0.240842 − 0.970564i \(-0.422577\pi\)
0.240842 + 0.970564i \(0.422577\pi\)
\(432\) 4.00000 0.192450
\(433\) −38.0000 −1.82616 −0.913082 − 0.407777i \(-0.866304\pi\)
−0.913082 + 0.407777i \(0.866304\pi\)
\(434\) 16.0000 0.768025
\(435\) 64.0000 3.06857
\(436\) 4.00000 0.191565
\(437\) −16.0000 −0.765384
\(438\) −8.00000 −0.382255
\(439\) 14.0000 0.668184 0.334092 − 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) −2.00000 −0.0951303
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) 4.00000 0.189832
\(445\) 24.0000 1.13771
\(446\) 16.0000 0.757622
\(447\) 20.0000 0.945968
\(448\) −14.0000 −0.661438
\(449\) 24.0000 1.13263 0.566315 − 0.824189i \(-0.308369\pi\)
0.566315 + 0.824189i \(0.308369\pi\)
\(450\) −11.0000 −0.518545
\(451\) 0 0
\(452\) −12.0000 −0.564433
\(453\) −32.0000 −1.50349
\(454\) 28.0000 1.31411
\(455\) −16.0000 −0.750092
\(456\) 24.0000 1.12390
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −14.0000 −0.654177
\(459\) −4.00000 −0.186704
\(460\) 16.0000 0.746004
\(461\) 10.0000 0.465746 0.232873 − 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 − 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) −8.00000 −0.371391
\(465\) 64.0000 2.96793
\(466\) 0 0
\(467\) 4.00000 0.185098 0.0925490 − 0.995708i \(-0.470499\pi\)
0.0925490 + 0.995708i \(0.470499\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 8.00000 0.369406
\(470\) 4.00000 0.184506
\(471\) 20.0000 0.921551
\(472\) 12.0000 0.552345
\(473\) 0 0
\(474\) −4.00000 −0.183726
\(475\) 44.0000 2.01886
\(476\) 2.00000 0.0916698
\(477\) 6.00000 0.274721
\(478\) −8.00000 −0.365911
\(479\) 6.00000 0.274147 0.137073 − 0.990561i \(-0.456230\pi\)
0.137073 + 0.990561i \(0.456230\pi\)
\(480\) −40.0000 −1.82574
\(481\) −4.00000 −0.182384
\(482\) 18.0000 0.819878
\(483\) 16.0000 0.728025
\(484\) 11.0000 0.500000
\(485\) 40.0000 1.81631
\(486\) 10.0000 0.453609
\(487\) −22.0000 −0.996915 −0.498458 − 0.866914i \(-0.666100\pi\)
−0.498458 + 0.866914i \(0.666100\pi\)
\(488\) 18.0000 0.814822
\(489\) −32.0000 −1.44709
\(490\) 12.0000 0.542105
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 16.0000 0.721336
\(493\) 8.00000 0.360302
\(494\) −8.00000 −0.359937
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) 40.0000 1.79065 0.895323 − 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) −24.0000 −1.07331
\(501\) −16.0000 −0.714827
\(502\) −16.0000 −0.714115
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) −6.00000 −0.267261
\(505\) −72.0000 −3.20396
\(506\) 0 0
\(507\) −18.0000 −0.799408
\(508\) 8.00000 0.354943
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −8.00000 −0.354246
\(511\) −8.00000 −0.353899
\(512\) 11.0000 0.486136
\(513\) −16.0000 −0.706417
\(514\) −18.0000 −0.793946
\(515\) −16.0000 −0.705044
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) −4.00000 −0.175750
\(519\) −52.0000 −2.28255
\(520\) 24.0000 1.05247
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −8.00000 −0.350150
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −6.00000 −0.262111
\(525\) −44.0000 −1.92032
\(526\) 16.0000 0.697633
\(527\) 8.00000 0.348485
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) −24.0000 −1.04249
\(531\) 4.00000 0.173585
\(532\) 8.00000 0.346844
\(533\) −16.0000 −0.693037
\(534\) −12.0000 −0.519291
\(535\) −16.0000 −0.691740
\(536\) −12.0000 −0.518321
\(537\) −24.0000 −1.03568
\(538\) −14.0000 −0.603583
\(539\) 0 0
\(540\) 16.0000 0.688530
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) 28.0000 1.20270
\(543\) 32.0000 1.37325
\(544\) −5.00000 −0.214373
\(545\) −16.0000 −0.685365
\(546\) 8.00000 0.342368
\(547\) 4.00000 0.171028 0.0855138 − 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) −6.00000 −0.256307
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) 32.0000 1.36325
\(552\) −24.0000 −1.02151
\(553\) −4.00000 −0.170097
\(554\) −10.0000 −0.424859
\(555\) −16.0000 −0.679162
\(556\) 0 0
\(557\) 42.0000 1.77960 0.889799 − 0.456354i \(-0.150845\pi\)
0.889799 + 0.456354i \(0.150845\pi\)
\(558\) −8.00000 −0.338667
\(559\) −8.00000 −0.338364
\(560\) 8.00000 0.338062
\(561\) 0 0
\(562\) 26.0000 1.09674
\(563\) 20.0000 0.842900 0.421450 − 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) 2.00000 0.0842152
\(565\) 48.0000 2.01938
\(566\) −6.00000 −0.252199
\(567\) 22.0000 0.923913
\(568\) −18.0000 −0.755263
\(569\) 14.0000 0.586911 0.293455 − 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) −32.0000 −1.34033
\(571\) 10.0000 0.418487 0.209243 − 0.977864i \(-0.432900\pi\)
0.209243 + 0.977864i \(0.432900\pi\)
\(572\) 0 0
\(573\) 24.0000 1.00261
\(574\) −16.0000 −0.667827
\(575\) −44.0000 −1.83493
\(576\) 7.00000 0.291667
\(577\) 22.0000 0.915872 0.457936 − 0.888985i \(-0.348589\pi\)
0.457936 + 0.888985i \(0.348589\pi\)
\(578\) −1.00000 −0.0415945
\(579\) −40.0000 −1.66234
\(580\) −32.0000 −1.32873
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) 0 0
\(584\) 12.0000 0.496564
\(585\) 8.00000 0.330759
\(586\) −30.0000 −1.23929
\(587\) −44.0000 −1.81607 −0.908037 − 0.418890i \(-0.862419\pi\)
−0.908037 + 0.418890i \(0.862419\pi\)
\(588\) 6.00000 0.247436
\(589\) 32.0000 1.31854
\(590\) −16.0000 −0.658710
\(591\) −44.0000 −1.80992
\(592\) 2.00000 0.0821995
\(593\) 6.00000 0.246390 0.123195 − 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −8.00000 −0.327968
\(596\) −10.0000 −0.409616
\(597\) −40.0000 −1.63709
\(598\) 8.00000 0.327144
\(599\) −16.0000 −0.653742 −0.326871 − 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 66.0000 2.69444
\(601\) 2.00000 0.0815817 0.0407909 − 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) −8.00000 −0.326056
\(603\) −4.00000 −0.162893
\(604\) 16.0000 0.651031
\(605\) −44.0000 −1.78885
\(606\) 36.0000 1.46240
\(607\) −32.0000 −1.29884 −0.649420 − 0.760430i \(-0.724988\pi\)
−0.649420 + 0.760430i \(0.724988\pi\)
\(608\) −20.0000 −0.811107
\(609\) −32.0000 −1.29671
\(610\) −24.0000 −0.971732
\(611\) −2.00000 −0.0809113
\(612\) −1.00000 −0.0404226
\(613\) −26.0000 −1.05013 −0.525065 − 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) −8.00000 −0.322854
\(615\) −64.0000 −2.58073
\(616\) 0 0
\(617\) −38.0000 −1.52982 −0.764911 − 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 8.00000 0.321807
\(619\) −42.0000 −1.68812 −0.844061 − 0.536247i \(-0.819842\pi\)
−0.844061 + 0.536247i \(0.819842\pi\)
\(620\) −32.0000 −1.28515
\(621\) 16.0000 0.642058
\(622\) −12.0000 −0.481156
\(623\) −12.0000 −0.480770
\(624\) −4.00000 −0.160128
\(625\) 41.0000 1.64000
\(626\) −8.00000 −0.319744
\(627\) 0 0
\(628\) −10.0000 −0.399043
\(629\) −2.00000 −0.0797452
\(630\) 8.00000 0.318728
\(631\) 32.0000 1.27390 0.636950 − 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 6.00000 0.238667
\(633\) −24.0000 −0.953914
\(634\) 32.0000 1.27088
\(635\) −32.0000 −1.26988
\(636\) −12.0000 −0.475831
\(637\) −6.00000 −0.237729
\(638\) 0 0
\(639\) −6.00000 −0.237356
\(640\) 12.0000 0.474342
\(641\) 24.0000 0.947943 0.473972 − 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) 8.00000 0.315735
\(643\) −6.00000 −0.236617 −0.118308 − 0.992977i \(-0.537747\pi\)
−0.118308 + 0.992977i \(0.537747\pi\)
\(644\) −8.00000 −0.315244
\(645\) −32.0000 −1.26000
\(646\) −4.00000 −0.157378
\(647\) −12.0000 −0.471769 −0.235884 − 0.971781i \(-0.575799\pi\)
−0.235884 + 0.971781i \(0.575799\pi\)
\(648\) −33.0000 −1.29636
\(649\) 0 0
\(650\) −22.0000 −0.862911
\(651\) −32.0000 −1.25418
\(652\) 16.0000 0.626608
\(653\) 46.0000 1.80012 0.900060 − 0.435767i \(-0.143523\pi\)
0.900060 + 0.435767i \(0.143523\pi\)
\(654\) 8.00000 0.312825
\(655\) 24.0000 0.937758
\(656\) 8.00000 0.312348
\(657\) 4.00000 0.156055
\(658\) −2.00000 −0.0779681
\(659\) −28.0000 −1.09073 −0.545363 − 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 10.0000 0.388955 0.194477 − 0.980907i \(-0.437699\pi\)
0.194477 + 0.980907i \(0.437699\pi\)
\(662\) −28.0000 −1.08825
\(663\) 4.00000 0.155347
\(664\) 0 0
\(665\) −32.0000 −1.24091
\(666\) 2.00000 0.0774984
\(667\) −32.0000 −1.23904
\(668\) 8.00000 0.309529
\(669\) −32.0000 −1.23719
\(670\) 16.0000 0.618134
\(671\) 0 0
\(672\) 20.0000 0.771517
\(673\) 44.0000 1.69608 0.848038 − 0.529936i \(-0.177784\pi\)
0.848038 + 0.529936i \(0.177784\pi\)
\(674\) −6.00000 −0.231111
\(675\) −44.0000 −1.69356
\(676\) 9.00000 0.346154
\(677\) −32.0000 −1.22986 −0.614930 − 0.788582i \(-0.710816\pi\)
−0.614930 + 0.788582i \(0.710816\pi\)
\(678\) −24.0000 −0.921714
\(679\) −20.0000 −0.767530
\(680\) 12.0000 0.460179
\(681\) −56.0000 −2.14592
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 − 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) −4.00000 −0.152944
\(685\) 24.0000 0.916993
\(686\) −20.0000 −0.763604
\(687\) 28.0000 1.06827
\(688\) 4.00000 0.152499
\(689\) 12.0000 0.457164
\(690\) 32.0000 1.21822
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 26.0000 0.988372
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 0 0
\(696\) 48.0000 1.81944
\(697\) −8.00000 −0.303022
\(698\) 30.0000 1.13552
\(699\) 0 0
\(700\) 22.0000 0.831522
\(701\) 10.0000 0.377695 0.188847 − 0.982006i \(-0.439525\pi\)
0.188847 + 0.982006i \(0.439525\pi\)
\(702\) 8.00000 0.301941
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) −8.00000 −0.301297
\(706\) −14.0000 −0.526897
\(707\) 36.0000 1.35392
\(708\) −8.00000 −0.300658
\(709\) 10.0000 0.375558 0.187779 − 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 24.0000 0.900704
\(711\) 2.00000 0.0750059
\(712\) 18.0000 0.674579
\(713\) −32.0000 −1.19841
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 16.0000 0.597531
\(718\) 0 0
\(719\) 42.0000 1.56634 0.783168 − 0.621810i \(-0.213603\pi\)
0.783168 + 0.621810i \(0.213603\pi\)
\(720\) −4.00000 −0.149071
\(721\) 8.00000 0.297936
\(722\) 3.00000 0.111648
\(723\) −36.0000 −1.33885
\(724\) −16.0000 −0.594635
\(725\) 88.0000 3.26824
\(726\) 22.0000 0.816497
\(727\) −40.0000 −1.48352 −0.741759 − 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) −12.0000 −0.444750
\(729\) 13.0000 0.481481
\(730\) −16.0000 −0.592187
\(731\) −4.00000 −0.147945
\(732\) −12.0000 −0.443533
\(733\) 34.0000 1.25582 0.627909 − 0.778287i \(-0.283911\pi\)
0.627909 + 0.778287i \(0.283911\pi\)
\(734\) 16.0000 0.590571
\(735\) −24.0000 −0.885253
\(736\) 20.0000 0.737210
\(737\) 0 0
\(738\) 8.00000 0.294484
\(739\) 32.0000 1.17714 0.588570 − 0.808447i \(-0.299691\pi\)
0.588570 + 0.808447i \(0.299691\pi\)
\(740\) 8.00000 0.294086
\(741\) 16.0000 0.587775
\(742\) 12.0000 0.440534
\(743\) −12.0000 −0.440237 −0.220119 − 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 48.0000 1.75977
\(745\) 40.0000 1.46549
\(746\) −26.0000 −0.951928
\(747\) 0 0
\(748\) 0 0
\(749\) 8.00000 0.292314
\(750\) −48.0000 −1.75271
\(751\) 4.00000 0.145962 0.0729810 − 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 1.00000 0.0364662
\(753\) 32.0000 1.16614
\(754\) −16.0000 −0.582686
\(755\) −64.0000 −2.32920
\(756\) −8.00000 −0.290957
\(757\) 22.0000 0.799604 0.399802 − 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −38.0000 −1.38022
\(759\) 0 0
\(760\) 48.0000 1.74114
\(761\) 50.0000 1.81250 0.906249 − 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) 16.0000 0.579619
\(763\) 8.00000 0.289619
\(764\) −12.0000 −0.434145
\(765\) 4.00000 0.144620
\(766\) 12.0000 0.433578
\(767\) 8.00000 0.288863
\(768\) −34.0000 −1.22687
\(769\) −2.00000 −0.0721218 −0.0360609 − 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) 36.0000 1.29651
\(772\) 20.0000 0.719816
\(773\) 6.00000 0.215805 0.107903 − 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 4.00000 0.143777
\(775\) 88.0000 3.16105
\(776\) 30.0000 1.07694
\(777\) 8.00000 0.286998
\(778\) 26.0000 0.932145
\(779\) −32.0000 −1.14652
\(780\) −16.0000 −0.572892
\(781\) 0 0
\(782\) 4.00000 0.143040
\(783\) −32.0000 −1.14359
\(784\) 3.00000 0.107143
\(785\) 40.0000 1.42766
\(786\) −12.0000 −0.428026
\(787\) 12.0000 0.427754 0.213877 − 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 22.0000 0.783718
\(789\) −32.0000 −1.13923
\(790\) −8.00000 −0.284627
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 12.0000 0.426132
\(794\) −22.0000 −0.780751
\(795\) 48.0000 1.70238
\(796\) 20.0000 0.708881
\(797\) −6.00000 −0.212531 −0.106265 − 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 16.0000 0.566394
\(799\) −1.00000 −0.0353775
\(800\) −55.0000 −1.94454
\(801\) 6.00000 0.212000
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 32.0000 1.12785
\(806\) −16.0000 −0.563576
\(807\) 28.0000 0.985647
\(808\) −54.0000 −1.89971
\(809\) 12.0000 0.421898 0.210949 − 0.977497i \(-0.432345\pi\)
0.210949 + 0.977497i \(0.432345\pi\)
\(810\) 44.0000 1.54600
\(811\) −50.0000 −1.75574 −0.877869 − 0.478901i \(-0.841035\pi\)
−0.877869 + 0.478901i \(0.841035\pi\)
\(812\) 16.0000 0.561490
\(813\) −56.0000 −1.96401
\(814\) 0 0
\(815\) −64.0000 −2.24182
\(816\) −2.00000 −0.0700140
\(817\) −16.0000 −0.559769
\(818\) 22.0000 0.769212
\(819\) −4.00000 −0.139771
\(820\) 32.0000 1.11749
\(821\) 32.0000 1.11681 0.558404 − 0.829569i \(-0.311414\pi\)
0.558404 + 0.829569i \(0.311414\pi\)
\(822\) −12.0000 −0.418548
\(823\) −30.0000 −1.04573 −0.522867 − 0.852414i \(-0.675138\pi\)
−0.522867 + 0.852414i \(0.675138\pi\)
\(824\) −12.0000 −0.418040
\(825\) 0 0
\(826\) 8.00000 0.278356
\(827\) 54.0000 1.87776 0.938882 − 0.344239i \(-0.111863\pi\)
0.938882 + 0.344239i \(0.111863\pi\)
\(828\) 4.00000 0.139010
\(829\) 6.00000 0.208389 0.104194 − 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(830\) 0 0
\(831\) 20.0000 0.693792
\(832\) 14.0000 0.485363
\(833\) −3.00000 −0.103944
\(834\) 0 0
\(835\) −32.0000 −1.10741
\(836\) 0 0
\(837\) −32.0000 −1.10608
\(838\) −28.0000 −0.967244
\(839\) 4.00000 0.138095 0.0690477 − 0.997613i \(-0.478004\pi\)
0.0690477 + 0.997613i \(0.478004\pi\)
\(840\) −48.0000 −1.65616
\(841\) 35.0000 1.20690
\(842\) −26.0000 −0.896019
\(843\) −52.0000 −1.79098
\(844\) 12.0000 0.413057
\(845\) −36.0000 −1.23844
\(846\) 1.00000 0.0343807
\(847\) 22.0000 0.755929
\(848\) −6.00000 −0.206041
\(849\) 12.0000 0.411839
\(850\) −11.0000 −0.377297
\(851\) 8.00000 0.274236
\(852\) 12.0000 0.411113
\(853\) −18.0000 −0.616308 −0.308154 − 0.951336i \(-0.599711\pi\)
−0.308154 + 0.951336i \(0.599711\pi\)
\(854\) 12.0000 0.410632
\(855\) 16.0000 0.547188
\(856\) −12.0000 −0.410152
\(857\) −36.0000 −1.22974 −0.614868 − 0.788630i \(-0.710791\pi\)
−0.614868 + 0.788630i \(0.710791\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 − 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 16.0000 0.545595
\(861\) 32.0000 1.09056
\(862\) −10.0000 −0.340601
\(863\) −24.0000 −0.816970 −0.408485 − 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 20.0000 0.680414
\(865\) −104.000 −3.53611
\(866\) 38.0000 1.29129
\(867\) 2.00000 0.0679236
\(868\) 16.0000 0.543075
\(869\) 0 0
\(870\) −64.0000 −2.16980
\(871\) −8.00000 −0.271070
\(872\) −12.0000 −0.406371
\(873\) 10.0000 0.338449
\(874\) 16.0000 0.541208
\(875\) −48.0000 −1.62270
\(876\) −8.00000 −0.270295
\(877\) 28.0000 0.945493 0.472746 − 0.881199i \(-0.343263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(878\) −14.0000 −0.472477
\(879\) 60.0000 2.02375
\(880\) 0 0
\(881\) 48.0000 1.61716 0.808581 − 0.588386i \(-0.200236\pi\)
0.808581 + 0.588386i \(0.200236\pi\)
\(882\) 3.00000 0.101015
\(883\) 16.0000 0.538443 0.269221 − 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 32.0000 1.07567
\(886\) −12.0000 −0.403148
\(887\) 28.0000 0.940148 0.470074 − 0.882627i \(-0.344227\pi\)
0.470074 + 0.882627i \(0.344227\pi\)
\(888\) −12.0000 −0.402694
\(889\) 16.0000 0.536623
\(890\) −24.0000 −0.804482
\(891\) 0 0
\(892\) 16.0000 0.535720
\(893\) −4.00000 −0.133855
\(894\) −20.0000 −0.668900
\(895\) −48.0000 −1.60446
\(896\) −6.00000 −0.200446
\(897\) −16.0000 −0.534224
\(898\) −24.0000 −0.800890
\(899\) 64.0000 2.13452
\(900\) −11.0000 −0.366667
\(901\) 6.00000 0.199889
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) 36.0000 1.19734
\(905\) 64.0000 2.12743
\(906\) 32.0000 1.06313
\(907\) 26.0000 0.863316 0.431658 − 0.902037i \(-0.357929\pi\)
0.431658 + 0.902037i \(0.357929\pi\)
\(908\) 28.0000 0.929213
\(909\) −18.0000 −0.597022
\(910\) 16.0000 0.530395
\(911\) −30.0000 −0.993944 −0.496972 − 0.867766i \(-0.665555\pi\)
−0.496972 + 0.867766i \(0.665555\pi\)
\(912\) −8.00000 −0.264906
\(913\) 0 0
\(914\) 10.0000 0.330771
\(915\) 48.0000 1.58683
\(916\) −14.0000 −0.462573
\(917\) −12.0000 −0.396275
\(918\) 4.00000 0.132020
\(919\) −8.00000 −0.263896 −0.131948 − 0.991257i \(-0.542123\pi\)
−0.131948 + 0.991257i \(0.542123\pi\)
\(920\) −48.0000 −1.58251
\(921\) 16.0000 0.527218
\(922\) −10.0000 −0.329332
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) −22.0000 −0.723356
\(926\) 8.00000 0.262896
\(927\) −4.00000 −0.131377
\(928\) −40.0000 −1.31306
\(929\) 46.0000 1.50921 0.754606 − 0.656179i \(-0.227828\pi\)
0.754606 + 0.656179i \(0.227828\pi\)
\(930\) −64.0000 −2.09864
\(931\) −12.0000 −0.393284
\(932\) 0 0
\(933\) 24.0000 0.785725
\(934\) −4.00000 −0.130884
\(935\) 0 0
\(936\) 6.00000 0.196116
\(937\) −58.0000 −1.89478 −0.947389 − 0.320085i \(-0.896288\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) −8.00000 −0.261209
\(939\) 16.0000 0.522140
\(940\) 4.00000 0.130466
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −20.0000 −0.651635
\(943\) 32.0000 1.04206
\(944\) −4.00000 −0.130189
\(945\) 32.0000 1.04096
\(946\) 0 0
\(947\) 38.0000 1.23483 0.617417 − 0.786636i \(-0.288179\pi\)
0.617417 + 0.786636i \(0.288179\pi\)
\(948\) −4.00000 −0.129914
\(949\) 8.00000 0.259691
\(950\) −44.0000 −1.42755
\(951\) −64.0000 −2.07534
\(952\) −6.00000 −0.194461
\(953\) 38.0000 1.23094 0.615470 − 0.788160i \(-0.288966\pi\)
0.615470 + 0.788160i \(0.288966\pi\)
\(954\) −6.00000 −0.194257
\(955\) 48.0000 1.55324
\(956\) −8.00000 −0.258738
\(957\) 0 0
\(958\) −6.00000 −0.193851
\(959\) −12.0000 −0.387500
\(960\) 56.0000 1.80739
\(961\) 33.0000 1.06452
\(962\) 4.00000 0.128965
\(963\) −4.00000 −0.128898
\(964\) 18.0000 0.579741
\(965\) −80.0000 −2.57529
\(966\) −16.0000 −0.514792
\(967\) −44.0000 −1.41494 −0.707472 − 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) −33.0000 −1.06066
\(969\) 8.00000 0.256997
\(970\) −40.0000 −1.28432
\(971\) −20.0000 −0.641831 −0.320915 − 0.947108i \(-0.603990\pi\)
−0.320915 + 0.947108i \(0.603990\pi\)
\(972\) 10.0000 0.320750
\(973\) 0 0
\(974\) 22.0000 0.704925
\(975\) 44.0000 1.40913
\(976\) −6.00000 −0.192055
\(977\) 30.0000 0.959785 0.479893 − 0.877327i \(-0.340676\pi\)
0.479893 + 0.877327i \(0.340676\pi\)
\(978\) 32.0000 1.02325
\(979\) 0 0
\(980\) 12.0000 0.383326
\(981\) −4.00000 −0.127710
\(982\) −24.0000 −0.765871
\(983\) −44.0000 −1.40338 −0.701691 − 0.712481i \(-0.747571\pi\)
−0.701691 + 0.712481i \(0.747571\pi\)
\(984\) −48.0000 −1.53018
\(985\) −88.0000 −2.80391
\(986\) −8.00000 −0.254772
\(987\) 4.00000 0.127321
\(988\) −8.00000 −0.254514
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 2.00000 0.0635321 0.0317660 − 0.999495i \(-0.489887\pi\)
0.0317660 + 0.999495i \(0.489887\pi\)
\(992\) −40.0000 −1.27000
\(993\) 56.0000 1.77711
\(994\) −12.0000 −0.380617
\(995\) −80.0000 −2.53617
\(996\) 0 0
\(997\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) −40.0000 −1.26618
\(999\) 8.00000 0.253109
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 799.2.a.b.1.1 ✓ 1
3.2 odd 2 7191.2.a.g.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.2.a.b.1.1 ✓ 1 1.1 even 1 trivial
7191.2.a.g.1.1 1 3.2 odd 2