Properties

Label 9075.2.a.di.1.3
Level $9075$
Weight $2$
Character 9075.1
Self dual yes
Analytic conductor $72.464$
Analytic rank $1$
Dimension $4$
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] = [9075,2,Mod(1,9075)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9075, 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("9075.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9075 = 3 \cdot 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9075.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: \(72.4642398343\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: 4.4.725.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 3x^{2} + x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-0.477260\) of defining polynomial
Character \(\chi\) \(=\) 9075.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.47726 q^{2} -1.00000 q^{3} +0.182297 q^{4} -1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.47726 q^{2} -1.00000 q^{3} +0.182297 q^{4} -1.47726 q^{6} +2.29496 q^{7} -2.68522 q^{8} +1.00000 q^{9} -0.182297 q^{12} +2.14077 q^{13} +3.39026 q^{14} -4.33136 q^{16} -0.544446 q^{17} +1.47726 q^{18} -2.18230 q^{19} -2.29496 q^{21} -2.03908 q^{23} +2.68522 q^{24} +3.16248 q^{26} -1.00000 q^{27} +0.418365 q^{28} -9.94544 q^{29} +6.77143 q^{31} -1.02811 q^{32} -0.804288 q^{34} +0.182297 q^{36} +8.81959 q^{37} -3.22382 q^{38} -2.14077 q^{39} -1.82283 q^{41} -3.39026 q^{42} +0.620713 q^{43} -3.01225 q^{46} +0.378009 q^{47} +4.33136 q^{48} -1.73315 q^{49} +0.544446 q^{51} +0.390257 q^{52} -11.5931 q^{53} -1.47726 q^{54} -6.16248 q^{56} +2.18230 q^{57} -14.6920 q^{58} -8.07792 q^{59} +8.72595 q^{61} +10.0032 q^{62} +2.29496 q^{63} +7.14394 q^{64} +9.75802 q^{67} -0.0992509 q^{68} +2.03908 q^{69} -14.9968 q^{71} -2.68522 q^{72} -7.85844 q^{73} +13.0288 q^{74} -0.397826 q^{76} -3.16248 q^{78} -9.22454 q^{79} +1.00000 q^{81} -2.69279 q^{82} +9.45232 q^{83} -0.418365 q^{84} +0.916954 q^{86} +9.94544 q^{87} +0.583290 q^{89} +4.91300 q^{91} -0.371718 q^{92} -6.77143 q^{93} +0.558418 q^{94} +1.02811 q^{96} +5.37801 q^{97} -2.56031 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - 4 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 3 q^{8} + 4 q^{9} - q^{12} + 7 q^{13} + 3 q^{14} - q^{16} + 10 q^{17} + 3 q^{18} - 9 q^{19} - 6 q^{21} + 3 q^{23} - 3 q^{24} - 4 q^{26} - 4 q^{27} - 7 q^{28} - 15 q^{29} - 13 q^{31} - 6 q^{32} - 3 q^{34} + q^{36} + 3 q^{37} - 15 q^{38} - 7 q^{39} - 22 q^{41} - 3 q^{42} - q^{46} + 2 q^{47} + q^{48} - 12 q^{49} - 10 q^{51} - 9 q^{52} - 10 q^{53} - 3 q^{54} - 8 q^{56} + 9 q^{57} - 39 q^{58} - 21 q^{59} - 11 q^{61} + 10 q^{62} + 6 q^{63} - 3 q^{64} - q^{67} + 3 q^{68} - 3 q^{69} - 13 q^{71} + 3 q^{72} + q^{73} + 11 q^{74} - 19 q^{76} + 4 q^{78} + 4 q^{79} + 4 q^{81} - 25 q^{82} + 3 q^{83} + 7 q^{84} + 15 q^{87} - 10 q^{89} + 12 q^{91} + 24 q^{92} + 13 q^{93} + 35 q^{94} + 6 q^{96} + 22 q^{97} - 11 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.47726 1.04458 0.522290 0.852768i \(-0.325078\pi\)
0.522290 + 0.852768i \(0.325078\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.182297 0.0911485
\(5\) 0 0
\(6\) −1.47726 −0.603089
\(7\) 2.29496 0.867414 0.433707 0.901054i \(-0.357205\pi\)
0.433707 + 0.901054i \(0.357205\pi\)
\(8\) −2.68522 −0.949369
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 0 0
\(12\) −0.182297 −0.0526246
\(13\) 2.14077 0.593744 0.296872 0.954917i \(-0.404057\pi\)
0.296872 + 0.954917i \(0.404057\pi\)
\(14\) 3.39026 0.906084
\(15\) 0 0
\(16\) −4.33136 −1.08284
\(17\) −0.544446 −0.132048 −0.0660238 0.997818i \(-0.521031\pi\)
−0.0660238 + 0.997818i \(0.521031\pi\)
\(18\) 1.47726 0.348194
\(19\) −2.18230 −0.500653 −0.250327 0.968161i \(-0.580538\pi\)
−0.250327 + 0.968161i \(0.580538\pi\)
\(20\) 0 0
\(21\) −2.29496 −0.500802
\(22\) 0 0
\(23\) −2.03908 −0.425177 −0.212589 0.977142i \(-0.568189\pi\)
−0.212589 + 0.977142i \(0.568189\pi\)
\(24\) 2.68522 0.548118
\(25\) 0 0
\(26\) 3.16248 0.620213
\(27\) −1.00000 −0.192450
\(28\) 0.418365 0.0790636
\(29\) −9.94544 −1.84682 −0.923411 0.383813i \(-0.874611\pi\)
−0.923411 + 0.383813i \(0.874611\pi\)
\(30\) 0 0
\(31\) 6.77143 1.21619 0.608093 0.793866i \(-0.291935\pi\)
0.608093 + 0.793866i \(0.291935\pi\)
\(32\) −1.02811 −0.181746
\(33\) 0 0
\(34\) −0.804288 −0.137934
\(35\) 0 0
\(36\) 0.182297 0.0303828
\(37\) 8.81959 1.44993 0.724966 0.688785i \(-0.241855\pi\)
0.724966 + 0.688785i \(0.241855\pi\)
\(38\) −3.22382 −0.522973
\(39\) −2.14077 −0.342798
\(40\) 0 0
\(41\) −1.82283 −0.284678 −0.142339 0.989818i \(-0.545462\pi\)
−0.142339 + 0.989818i \(0.545462\pi\)
\(42\) −3.39026 −0.523128
\(43\) 0.620713 0.0946578 0.0473289 0.998879i \(-0.484929\pi\)
0.0473289 + 0.998879i \(0.484929\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −3.01225 −0.444132
\(47\) 0.378009 0.0551383 0.0275691 0.999620i \(-0.491223\pi\)
0.0275691 + 0.999620i \(0.491223\pi\)
\(48\) 4.33136 0.625178
\(49\) −1.73315 −0.247592
\(50\) 0 0
\(51\) 0.544446 0.0762377
\(52\) 0.390257 0.0541189
\(53\) −11.5931 −1.59243 −0.796217 0.605011i \(-0.793169\pi\)
−0.796217 + 0.605011i \(0.793169\pi\)
\(54\) −1.47726 −0.201030
\(55\) 0 0
\(56\) −6.16248 −0.823496
\(57\) 2.18230 0.289052
\(58\) −14.6920 −1.92915
\(59\) −8.07792 −1.05166 −0.525828 0.850591i \(-0.676244\pi\)
−0.525828 + 0.850591i \(0.676244\pi\)
\(60\) 0 0
\(61\) 8.72595 1.11724 0.558622 0.829422i \(-0.311330\pi\)
0.558622 + 0.829422i \(0.311330\pi\)
\(62\) 10.0032 1.27040
\(63\) 2.29496 0.289138
\(64\) 7.14394 0.892993
\(65\) 0 0
\(66\) 0 0
\(67\) 9.75802 1.19213 0.596066 0.802936i \(-0.296730\pi\)
0.596066 + 0.802936i \(0.296730\pi\)
\(68\) −0.0992509 −0.0120359
\(69\) 2.03908 0.245476
\(70\) 0 0
\(71\) −14.9968 −1.77979 −0.889894 0.456167i \(-0.849222\pi\)
−0.889894 + 0.456167i \(0.849222\pi\)
\(72\) −2.68522 −0.316456
\(73\) −7.85844 −0.919760 −0.459880 0.887981i \(-0.652108\pi\)
−0.459880 + 0.887981i \(0.652108\pi\)
\(74\) 13.0288 1.51457
\(75\) 0 0
\(76\) −0.397826 −0.0456338
\(77\) 0 0
\(78\) −3.16248 −0.358080
\(79\) −9.22454 −1.03784 −0.518921 0.854822i \(-0.673666\pi\)
−0.518921 + 0.854822i \(0.673666\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −2.69279 −0.297369
\(83\) 9.45232 1.03753 0.518763 0.854918i \(-0.326393\pi\)
0.518763 + 0.854918i \(0.326393\pi\)
\(84\) −0.418365 −0.0456474
\(85\) 0 0
\(86\) 0.916954 0.0988777
\(87\) 9.94544 1.06626
\(88\) 0 0
\(89\) 0.583290 0.0618287 0.0309143 0.999522i \(-0.490158\pi\)
0.0309143 + 0.999522i \(0.490158\pi\)
\(90\) 0 0
\(91\) 4.91300 0.515022
\(92\) −0.371718 −0.0387543
\(93\) −6.77143 −0.702165
\(94\) 0.558418 0.0575964
\(95\) 0 0
\(96\) 1.02811 0.104931
\(97\) 5.37801 0.546054 0.273027 0.962006i \(-0.411975\pi\)
0.273027 + 0.962006i \(0.411975\pi\)
\(98\) −2.56031 −0.258630
\(99\) 0 0
\(100\) 0 0
\(101\) −19.5291 −1.94322 −0.971608 0.236598i \(-0.923968\pi\)
−0.971608 + 0.236598i \(0.923968\pi\)
\(102\) 0.804288 0.0796364
\(103\) −13.0062 −1.28154 −0.640771 0.767732i \(-0.721385\pi\)
−0.640771 + 0.767732i \(0.721385\pi\)
\(104\) −5.74845 −0.563682
\(105\) 0 0
\(106\) −17.1260 −1.66343
\(107\) −1.97355 −0.190790 −0.0953950 0.995439i \(-0.530411\pi\)
−0.0953950 + 0.995439i \(0.530411\pi\)
\(108\) −0.182297 −0.0175415
\(109\) 10.6212 1.01733 0.508663 0.860966i \(-0.330140\pi\)
0.508663 + 0.860966i \(0.330140\pi\)
\(110\) 0 0
\(111\) −8.81959 −0.837119
\(112\) −9.94032 −0.939271
\(113\) 16.8956 1.58940 0.794700 0.607002i \(-0.207628\pi\)
0.794700 + 0.607002i \(0.207628\pi\)
\(114\) 3.22382 0.301938
\(115\) 0 0
\(116\) −1.81302 −0.168335
\(117\) 2.14077 0.197915
\(118\) −11.9332 −1.09854
\(119\) −1.24948 −0.114540
\(120\) 0 0
\(121\) 0 0
\(122\) 12.8905 1.16705
\(123\) 1.82283 0.164359
\(124\) 1.23441 0.110854
\(125\) 0 0
\(126\) 3.39026 0.302028
\(127\) −4.13248 −0.366699 −0.183349 0.983048i \(-0.558694\pi\)
−0.183349 + 0.983048i \(0.558694\pi\)
\(128\) 12.6097 1.11455
\(129\) −0.620713 −0.0546507
\(130\) 0 0
\(131\) −0.436527 −0.0381395 −0.0190698 0.999818i \(-0.506070\pi\)
−0.0190698 + 0.999818i \(0.506070\pi\)
\(132\) 0 0
\(133\) −5.00829 −0.434274
\(134\) 14.4151 1.24528
\(135\) 0 0
\(136\) 1.46196 0.125362
\(137\) 7.86789 0.672200 0.336100 0.941826i \(-0.390892\pi\)
0.336100 + 0.941826i \(0.390892\pi\)
\(138\) 3.01225 0.256420
\(139\) 17.6431 1.49647 0.748236 0.663433i \(-0.230901\pi\)
0.748236 + 0.663433i \(0.230901\pi\)
\(140\) 0 0
\(141\) −0.378009 −0.0318341
\(142\) −22.1541 −1.85913
\(143\) 0 0
\(144\) −4.33136 −0.360947
\(145\) 0 0
\(146\) −11.6090 −0.960764
\(147\) 1.73315 0.142947
\(148\) 1.60779 0.132159
\(149\) −10.9601 −0.897889 −0.448945 0.893560i \(-0.648200\pi\)
−0.448945 + 0.893560i \(0.648200\pi\)
\(150\) 0 0
\(151\) −20.0324 −1.63021 −0.815106 0.579312i \(-0.803321\pi\)
−0.815106 + 0.579312i \(0.803321\pi\)
\(152\) 5.85995 0.475304
\(153\) −0.544446 −0.0440158
\(154\) 0 0
\(155\) 0 0
\(156\) −0.390257 −0.0312456
\(157\) −9.15468 −0.730623 −0.365311 0.930885i \(-0.619037\pi\)
−0.365311 + 0.930885i \(0.619037\pi\)
\(158\) −13.6270 −1.08411
\(159\) 11.5931 0.919392
\(160\) 0 0
\(161\) −4.67961 −0.368805
\(162\) 1.47726 0.116065
\(163\) 11.3321 0.887597 0.443799 0.896127i \(-0.353631\pi\)
0.443799 + 0.896127i \(0.353631\pi\)
\(164\) −0.332296 −0.0259480
\(165\) 0 0
\(166\) 13.9635 1.08378
\(167\) −15.1001 −1.16848 −0.584241 0.811580i \(-0.698608\pi\)
−0.584241 + 0.811580i \(0.698608\pi\)
\(168\) 6.16248 0.475446
\(169\) −8.41709 −0.647468
\(170\) 0 0
\(171\) −2.18230 −0.166884
\(172\) 0.113154 0.00862792
\(173\) −18.2641 −1.38859 −0.694297 0.719688i \(-0.744285\pi\)
−0.694297 + 0.719688i \(0.744285\pi\)
\(174\) 14.6920 1.11380
\(175\) 0 0
\(176\) 0 0
\(177\) 8.07792 0.607174
\(178\) 0.861672 0.0645850
\(179\) −0.525419 −0.0392716 −0.0196358 0.999807i \(-0.506251\pi\)
−0.0196358 + 0.999807i \(0.506251\pi\)
\(180\) 0 0
\(181\) −17.7106 −1.31642 −0.658211 0.752833i \(-0.728687\pi\)
−0.658211 + 0.752833i \(0.728687\pi\)
\(182\) 7.25777 0.537982
\(183\) −8.72595 −0.645041
\(184\) 5.47537 0.403650
\(185\) 0 0
\(186\) −10.0032 −0.733468
\(187\) 0 0
\(188\) 0.0689100 0.00502578
\(189\) −2.29496 −0.166934
\(190\) 0 0
\(191\) −16.5519 −1.19766 −0.598828 0.800877i \(-0.704367\pi\)
−0.598828 + 0.800877i \(0.704367\pi\)
\(192\) −7.14394 −0.515570
\(193\) 24.5032 1.76378 0.881891 0.471454i \(-0.156271\pi\)
0.881891 + 0.471454i \(0.156271\pi\)
\(194\) 7.94472 0.570397
\(195\) 0 0
\(196\) −0.315947 −0.0225677
\(197\) 7.50877 0.534978 0.267489 0.963561i \(-0.413806\pi\)
0.267489 + 0.963561i \(0.413806\pi\)
\(198\) 0 0
\(199\) −20.0956 −1.42454 −0.712270 0.701906i \(-0.752333\pi\)
−0.712270 + 0.701906i \(0.752333\pi\)
\(200\) 0 0
\(201\) −9.75802 −0.688278
\(202\) −28.8495 −2.02985
\(203\) −22.8244 −1.60196
\(204\) 0.0992509 0.00694895
\(205\) 0 0
\(206\) −19.2136 −1.33867
\(207\) −2.03908 −0.141726
\(208\) −9.27247 −0.642930
\(209\) 0 0
\(210\) 0 0
\(211\) 5.41860 0.373032 0.186516 0.982452i \(-0.440280\pi\)
0.186516 + 0.982452i \(0.440280\pi\)
\(212\) −2.11339 −0.145148
\(213\) 14.9968 1.02756
\(214\) −2.91544 −0.199296
\(215\) 0 0
\(216\) 2.68522 0.182706
\(217\) 15.5402 1.05494
\(218\) 15.6903 1.06268
\(219\) 7.85844 0.531024
\(220\) 0 0
\(221\) −1.16554 −0.0784024
\(222\) −13.0288 −0.874438
\(223\) −15.7074 −1.05185 −0.525923 0.850532i \(-0.676280\pi\)
−0.525923 + 0.850532i \(0.676280\pi\)
\(224\) −2.35947 −0.157649
\(225\) 0 0
\(226\) 24.9591 1.66026
\(227\) 1.47141 0.0976612 0.0488306 0.998807i \(-0.484451\pi\)
0.0488306 + 0.998807i \(0.484451\pi\)
\(228\) 0.397826 0.0263467
\(229\) −15.9751 −1.05566 −0.527831 0.849350i \(-0.676994\pi\)
−0.527831 + 0.849350i \(0.676994\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 26.7057 1.75331
\(233\) 25.6382 1.67961 0.839806 0.542887i \(-0.182669\pi\)
0.839806 + 0.542887i \(0.182669\pi\)
\(234\) 3.16248 0.206738
\(235\) 0 0
\(236\) −1.47258 −0.0958569
\(237\) 9.22454 0.599198
\(238\) −1.84581 −0.119646
\(239\) −4.18206 −0.270515 −0.135258 0.990810i \(-0.543186\pi\)
−0.135258 + 0.990810i \(0.543186\pi\)
\(240\) 0 0
\(241\) −3.29180 −0.212043 −0.106022 0.994364i \(-0.533811\pi\)
−0.106022 + 0.994364i \(0.533811\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 1.59072 0.101835
\(245\) 0 0
\(246\) 2.69279 0.171686
\(247\) −4.67180 −0.297260
\(248\) −18.1828 −1.15461
\(249\) −9.45232 −0.599016
\(250\) 0 0
\(251\) −9.36459 −0.591088 −0.295544 0.955329i \(-0.595501\pi\)
−0.295544 + 0.955329i \(0.595501\pi\)
\(252\) 0.418365 0.0263545
\(253\) 0 0
\(254\) −6.10475 −0.383046
\(255\) 0 0
\(256\) 4.33989 0.271243
\(257\) 12.5714 0.784182 0.392091 0.919927i \(-0.371752\pi\)
0.392091 + 0.919927i \(0.371752\pi\)
\(258\) −0.916954 −0.0570870
\(259\) 20.2406 1.25769
\(260\) 0 0
\(261\) −9.94544 −0.615607
\(262\) −0.644864 −0.0398398
\(263\) −4.82946 −0.297797 −0.148899 0.988852i \(-0.547573\pi\)
−0.148899 + 0.988852i \(0.547573\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −7.39855 −0.453634
\(267\) −0.583290 −0.0356968
\(268\) 1.77886 0.108661
\(269\) −5.22929 −0.318835 −0.159418 0.987211i \(-0.550962\pi\)
−0.159418 + 0.987211i \(0.550962\pi\)
\(270\) 0 0
\(271\) 30.3311 1.84248 0.921240 0.388994i \(-0.127177\pi\)
0.921240 + 0.388994i \(0.127177\pi\)
\(272\) 2.35819 0.142986
\(273\) −4.91300 −0.297348
\(274\) 11.6229 0.702167
\(275\) 0 0
\(276\) 0.371718 0.0223748
\(277\) −15.9694 −0.959511 −0.479756 0.877402i \(-0.659275\pi\)
−0.479756 + 0.877402i \(0.659275\pi\)
\(278\) 26.0635 1.56319
\(279\) 6.77143 0.405395
\(280\) 0 0
\(281\) −1.39067 −0.0829604 −0.0414802 0.999139i \(-0.513207\pi\)
−0.0414802 + 0.999139i \(0.513207\pi\)
\(282\) −0.558418 −0.0332533
\(283\) −5.87453 −0.349205 −0.174602 0.984639i \(-0.555864\pi\)
−0.174602 + 0.984639i \(0.555864\pi\)
\(284\) −2.73387 −0.162225
\(285\) 0 0
\(286\) 0 0
\(287\) −4.18332 −0.246934
\(288\) −1.02811 −0.0605819
\(289\) −16.7036 −0.982563
\(290\) 0 0
\(291\) −5.37801 −0.315264
\(292\) −1.43257 −0.0838348
\(293\) −19.9745 −1.16692 −0.583461 0.812141i \(-0.698302\pi\)
−0.583461 + 0.812141i \(0.698302\pi\)
\(294\) 2.56031 0.149320
\(295\) 0 0
\(296\) −23.6825 −1.37652
\(297\) 0 0
\(298\) −16.1910 −0.937917
\(299\) −4.36520 −0.252446
\(300\) 0 0
\(301\) 1.42451 0.0821075
\(302\) −29.5930 −1.70289
\(303\) 19.5291 1.12192
\(304\) 9.45232 0.542128
\(305\) 0 0
\(306\) −0.804288 −0.0459781
\(307\) −19.4372 −1.10934 −0.554671 0.832070i \(-0.687156\pi\)
−0.554671 + 0.832070i \(0.687156\pi\)
\(308\) 0 0
\(309\) 13.0062 0.739898
\(310\) 0 0
\(311\) 6.02182 0.341466 0.170733 0.985317i \(-0.445386\pi\)
0.170733 + 0.985317i \(0.445386\pi\)
\(312\) 5.74845 0.325442
\(313\) 5.10833 0.288740 0.144370 0.989524i \(-0.453884\pi\)
0.144370 + 0.989524i \(0.453884\pi\)
\(314\) −13.5238 −0.763194
\(315\) 0 0
\(316\) −1.68161 −0.0945978
\(317\) −13.6788 −0.768279 −0.384139 0.923275i \(-0.625502\pi\)
−0.384139 + 0.923275i \(0.625502\pi\)
\(318\) 17.1260 0.960379
\(319\) 0 0
\(320\) 0 0
\(321\) 1.97355 0.110153
\(322\) −6.91300 −0.385246
\(323\) 1.18814 0.0661100
\(324\) 0.182297 0.0101276
\(325\) 0 0
\(326\) 16.7404 0.927167
\(327\) −10.6212 −0.587354
\(328\) 4.89469 0.270264
\(329\) 0.867517 0.0478278
\(330\) 0 0
\(331\) 11.4695 0.630418 0.315209 0.949022i \(-0.397925\pi\)
0.315209 + 0.949022i \(0.397925\pi\)
\(332\) 1.72313 0.0945691
\(333\) 8.81959 0.483311
\(334\) −22.3068 −1.22057
\(335\) 0 0
\(336\) 9.94032 0.542289
\(337\) −3.76404 −0.205041 −0.102520 0.994731i \(-0.532691\pi\)
−0.102520 + 0.994731i \(0.532691\pi\)
\(338\) −12.4342 −0.676333
\(339\) −16.8956 −0.917641
\(340\) 0 0
\(341\) 0 0
\(342\) −3.22382 −0.174324
\(343\) −20.0422 −1.08218
\(344\) −1.66675 −0.0898651
\(345\) 0 0
\(346\) −26.9808 −1.45050
\(347\) 0.395980 0.0212573 0.0106287 0.999944i \(-0.496617\pi\)
0.0106287 + 0.999944i \(0.496617\pi\)
\(348\) 1.81302 0.0971883
\(349\) −13.1708 −0.705015 −0.352508 0.935809i \(-0.614671\pi\)
−0.352508 + 0.935809i \(0.614671\pi\)
\(350\) 0 0
\(351\) −2.14077 −0.114266
\(352\) 0 0
\(353\) −11.3853 −0.605977 −0.302989 0.952994i \(-0.597984\pi\)
−0.302989 + 0.952994i \(0.597984\pi\)
\(354\) 11.9332 0.634242
\(355\) 0 0
\(356\) 0.106332 0.00563559
\(357\) 1.24948 0.0661296
\(358\) −0.776180 −0.0410224
\(359\) −14.3682 −0.758326 −0.379163 0.925330i \(-0.623788\pi\)
−0.379163 + 0.925330i \(0.623788\pi\)
\(360\) 0 0
\(361\) −14.2376 −0.749346
\(362\) −26.1632 −1.37511
\(363\) 0 0
\(364\) 0.895625 0.0469435
\(365\) 0 0
\(366\) −12.8905 −0.673797
\(367\) 26.2640 1.37097 0.685485 0.728087i \(-0.259590\pi\)
0.685485 + 0.728087i \(0.259590\pi\)
\(368\) 8.83198 0.460399
\(369\) −1.82283 −0.0948926
\(370\) 0 0
\(371\) −26.6057 −1.38130
\(372\) −1.23441 −0.0640013
\(373\) −21.8951 −1.13368 −0.566842 0.823827i \(-0.691835\pi\)
−0.566842 + 0.823827i \(0.691835\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −1.01504 −0.0523466
\(377\) −21.2909 −1.09654
\(378\) −3.39026 −0.174376
\(379\) 25.5596 1.31291 0.656455 0.754365i \(-0.272055\pi\)
0.656455 + 0.754365i \(0.272055\pi\)
\(380\) 0 0
\(381\) 4.13248 0.211714
\(382\) −24.4515 −1.25105
\(383\) −19.0519 −0.973508 −0.486754 0.873539i \(-0.661819\pi\)
−0.486754 + 0.873539i \(0.661819\pi\)
\(384\) −12.6097 −0.643485
\(385\) 0 0
\(386\) 36.1976 1.84241
\(387\) 0.620713 0.0315526
\(388\) 0.980395 0.0497720
\(389\) 16.3925 0.831134 0.415567 0.909563i \(-0.363583\pi\)
0.415567 + 0.909563i \(0.363583\pi\)
\(390\) 0 0
\(391\) 1.11017 0.0561436
\(392\) 4.65388 0.235056
\(393\) 0.436527 0.0220199
\(394\) 11.0924 0.558827
\(395\) 0 0
\(396\) 0 0
\(397\) −30.9826 −1.55497 −0.777485 0.628901i \(-0.783505\pi\)
−0.777485 + 0.628901i \(0.783505\pi\)
\(398\) −29.6864 −1.48805
\(399\) 5.00829 0.250728
\(400\) 0 0
\(401\) −6.36611 −0.317908 −0.158954 0.987286i \(-0.550812\pi\)
−0.158954 + 0.987286i \(0.550812\pi\)
\(402\) −14.4151 −0.718961
\(403\) 14.4961 0.722103
\(404\) −3.56009 −0.177121
\(405\) 0 0
\(406\) −33.7176 −1.67338
\(407\) 0 0
\(408\) −1.46196 −0.0723776
\(409\) −6.26874 −0.309969 −0.154985 0.987917i \(-0.549533\pi\)
−0.154985 + 0.987917i \(0.549533\pi\)
\(410\) 0 0
\(411\) −7.86789 −0.388095
\(412\) −2.37100 −0.116811
\(413\) −18.5385 −0.912222
\(414\) −3.01225 −0.148044
\(415\) 0 0
\(416\) −2.20095 −0.107910
\(417\) −17.6431 −0.863988
\(418\) 0 0
\(419\) 3.90332 0.190689 0.0953447 0.995444i \(-0.469605\pi\)
0.0953447 + 0.995444i \(0.469605\pi\)
\(420\) 0 0
\(421\) 17.3715 0.846637 0.423318 0.905981i \(-0.360865\pi\)
0.423318 + 0.905981i \(0.360865\pi\)
\(422\) 8.00468 0.389662
\(423\) 0.378009 0.0183794
\(424\) 31.1300 1.51181
\(425\) 0 0
\(426\) 22.1541 1.07337
\(427\) 20.0257 0.969113
\(428\) −0.359772 −0.0173902
\(429\) 0 0
\(430\) 0 0
\(431\) −7.03651 −0.338937 −0.169468 0.985536i \(-0.554205\pi\)
−0.169468 + 0.985536i \(0.554205\pi\)
\(432\) 4.33136 0.208393
\(433\) −2.75229 −0.132267 −0.0661334 0.997811i \(-0.521066\pi\)
−0.0661334 + 0.997811i \(0.521066\pi\)
\(434\) 22.9569 1.10197
\(435\) 0 0
\(436\) 1.93621 0.0927278
\(437\) 4.44987 0.212866
\(438\) 11.6090 0.554697
\(439\) −2.73703 −0.130631 −0.0653157 0.997865i \(-0.520805\pi\)
−0.0653157 + 0.997865i \(0.520805\pi\)
\(440\) 0 0
\(441\) −1.73315 −0.0825307
\(442\) −1.72180 −0.0818976
\(443\) −11.1042 −0.527576 −0.263788 0.964581i \(-0.584972\pi\)
−0.263788 + 0.964581i \(0.584972\pi\)
\(444\) −1.60779 −0.0763021
\(445\) 0 0
\(446\) −23.2039 −1.09874
\(447\) 10.9601 0.518396
\(448\) 16.3951 0.774595
\(449\) 14.8268 0.699722 0.349861 0.936802i \(-0.386229\pi\)
0.349861 + 0.936802i \(0.386229\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 3.08001 0.144872
\(453\) 20.0324 0.941203
\(454\) 2.17366 0.102015
\(455\) 0 0
\(456\) −5.85995 −0.274417
\(457\) −29.1825 −1.36510 −0.682549 0.730840i \(-0.739129\pi\)
−0.682549 + 0.730840i \(0.739129\pi\)
\(458\) −23.5993 −1.10272
\(459\) 0.544446 0.0254126
\(460\) 0 0
\(461\) −31.1798 −1.45219 −0.726094 0.687595i \(-0.758666\pi\)
−0.726094 + 0.687595i \(0.758666\pi\)
\(462\) 0 0
\(463\) −41.1642 −1.91306 −0.956531 0.291631i \(-0.905802\pi\)
−0.956531 + 0.291631i \(0.905802\pi\)
\(464\) 43.0773 1.99981
\(465\) 0 0
\(466\) 37.8742 1.75449
\(467\) −38.7766 −1.79437 −0.897184 0.441656i \(-0.854391\pi\)
−0.897184 + 0.441656i \(0.854391\pi\)
\(468\) 0.390257 0.0180396
\(469\) 22.3943 1.03407
\(470\) 0 0
\(471\) 9.15468 0.421825
\(472\) 21.6910 0.998409
\(473\) 0 0
\(474\) 13.6270 0.625911
\(475\) 0 0
\(476\) −0.227777 −0.0104401
\(477\) −11.5931 −0.530811
\(478\) −6.17800 −0.282575
\(479\) 16.6876 0.762476 0.381238 0.924477i \(-0.375498\pi\)
0.381238 + 0.924477i \(0.375498\pi\)
\(480\) 0 0
\(481\) 18.8808 0.860888
\(482\) −4.86284 −0.221496
\(483\) 4.67961 0.212930
\(484\) 0 0
\(485\) 0 0
\(486\) −1.47726 −0.0670099
\(487\) −2.51193 −0.113827 −0.0569133 0.998379i \(-0.518126\pi\)
−0.0569133 + 0.998379i \(0.518126\pi\)
\(488\) −23.4311 −1.06068
\(489\) −11.3321 −0.512455
\(490\) 0 0
\(491\) −7.55865 −0.341117 −0.170559 0.985348i \(-0.554557\pi\)
−0.170559 + 0.985348i \(0.554557\pi\)
\(492\) 0.332296 0.0149811
\(493\) 5.41475 0.243868
\(494\) −6.90147 −0.310512
\(495\) 0 0
\(496\) −29.3295 −1.31693
\(497\) −34.4170 −1.54381
\(498\) −13.9635 −0.625721
\(499\) 16.7964 0.751911 0.375955 0.926638i \(-0.377315\pi\)
0.375955 + 0.926638i \(0.377315\pi\)
\(500\) 0 0
\(501\) 15.1001 0.674623
\(502\) −13.8339 −0.617439
\(503\) −7.63258 −0.340320 −0.170160 0.985416i \(-0.554428\pi\)
−0.170160 + 0.985416i \(0.554428\pi\)
\(504\) −6.16248 −0.274499
\(505\) 0 0
\(506\) 0 0
\(507\) 8.41709 0.373816
\(508\) −0.753340 −0.0334240
\(509\) 32.9039 1.45844 0.729219 0.684280i \(-0.239883\pi\)
0.729219 + 0.684280i \(0.239883\pi\)
\(510\) 0 0
\(511\) −18.0348 −0.797813
\(512\) −18.8082 −0.831213
\(513\) 2.18230 0.0963508
\(514\) 18.5712 0.819141
\(515\) 0 0
\(516\) −0.113154 −0.00498133
\(517\) 0 0
\(518\) 29.9007 1.31376
\(519\) 18.2641 0.801705
\(520\) 0 0
\(521\) 0.797954 0.0349590 0.0174795 0.999847i \(-0.494436\pi\)
0.0174795 + 0.999847i \(0.494436\pi\)
\(522\) −14.6920 −0.643051
\(523\) −4.30514 −0.188251 −0.0941254 0.995560i \(-0.530005\pi\)
−0.0941254 + 0.995560i \(0.530005\pi\)
\(524\) −0.0795776 −0.00347636
\(525\) 0 0
\(526\) −7.13437 −0.311073
\(527\) −3.68668 −0.160594
\(528\) 0 0
\(529\) −18.8422 −0.819224
\(530\) 0 0
\(531\) −8.07792 −0.350552
\(532\) −0.912997 −0.0395834
\(533\) −3.90226 −0.169026
\(534\) −0.861672 −0.0372882
\(535\) 0 0
\(536\) −26.2024 −1.13177
\(537\) 0.525419 0.0226735
\(538\) −7.72502 −0.333049
\(539\) 0 0
\(540\) 0 0
\(541\) −22.7081 −0.976299 −0.488149 0.872760i \(-0.662328\pi\)
−0.488149 + 0.872760i \(0.662328\pi\)
\(542\) 44.8069 1.92462
\(543\) 17.7106 0.760037
\(544\) 0.559749 0.0239990
\(545\) 0 0
\(546\) −7.25777 −0.310604
\(547\) −32.1551 −1.37485 −0.687425 0.726255i \(-0.741259\pi\)
−0.687425 + 0.726255i \(0.741259\pi\)
\(548\) 1.43429 0.0612700
\(549\) 8.72595 0.372415
\(550\) 0 0
\(551\) 21.7039 0.924617
\(552\) −5.47537 −0.233047
\(553\) −21.1700 −0.900239
\(554\) −23.5910 −1.00229
\(555\) 0 0
\(556\) 3.21629 0.136401
\(557\) −37.7151 −1.59804 −0.799021 0.601303i \(-0.794648\pi\)
−0.799021 + 0.601303i \(0.794648\pi\)
\(558\) 10.0032 0.423468
\(559\) 1.32881 0.0562025
\(560\) 0 0
\(561\) 0 0
\(562\) −2.05438 −0.0866588
\(563\) −21.9871 −0.926645 −0.463322 0.886190i \(-0.653343\pi\)
−0.463322 + 0.886190i \(0.653343\pi\)
\(564\) −0.0689100 −0.00290163
\(565\) 0 0
\(566\) −8.67821 −0.364772
\(567\) 2.29496 0.0963794
\(568\) 40.2696 1.68968
\(569\) −20.4804 −0.858584 −0.429292 0.903166i \(-0.641237\pi\)
−0.429292 + 0.903166i \(0.641237\pi\)
\(570\) 0 0
\(571\) 17.4373 0.729728 0.364864 0.931061i \(-0.381116\pi\)
0.364864 + 0.931061i \(0.381116\pi\)
\(572\) 0 0
\(573\) 16.5519 0.691467
\(574\) −6.17985 −0.257942
\(575\) 0 0
\(576\) 7.14394 0.297664
\(577\) 33.2349 1.38359 0.691793 0.722096i \(-0.256821\pi\)
0.691793 + 0.722096i \(0.256821\pi\)
\(578\) −24.6755 −1.02637
\(579\) −24.5032 −1.01832
\(580\) 0 0
\(581\) 21.6927 0.899966
\(582\) −7.94472 −0.329319
\(583\) 0 0
\(584\) 21.1016 0.873192
\(585\) 0 0
\(586\) −29.5075 −1.21894
\(587\) 42.7954 1.76635 0.883177 0.469040i \(-0.155400\pi\)
0.883177 + 0.469040i \(0.155400\pi\)
\(588\) 0.315947 0.0130294
\(589\) −14.7773 −0.608887
\(590\) 0 0
\(591\) −7.50877 −0.308869
\(592\) −38.2008 −1.57004
\(593\) 42.6570 1.75171 0.875857 0.482570i \(-0.160297\pi\)
0.875857 + 0.482570i \(0.160297\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.99800 −0.0818413
\(597\) 20.0956 0.822458
\(598\) −6.44854 −0.263700
\(599\) 28.3204 1.15714 0.578570 0.815633i \(-0.303611\pi\)
0.578570 + 0.815633i \(0.303611\pi\)
\(600\) 0 0
\(601\) −7.65458 −0.312237 −0.156118 0.987738i \(-0.549898\pi\)
−0.156118 + 0.987738i \(0.549898\pi\)
\(602\) 2.10437 0.0857679
\(603\) 9.75802 0.397377
\(604\) −3.65184 −0.148591
\(605\) 0 0
\(606\) 28.8495 1.17193
\(607\) −11.5986 −0.470771 −0.235386 0.971902i \(-0.575635\pi\)
−0.235386 + 0.971902i \(0.575635\pi\)
\(608\) 2.24364 0.0909915
\(609\) 22.8244 0.924892
\(610\) 0 0
\(611\) 0.809232 0.0327380
\(612\) −0.0992509 −0.00401198
\(613\) 32.1077 1.29682 0.648410 0.761292i \(-0.275434\pi\)
0.648410 + 0.761292i \(0.275434\pi\)
\(614\) −28.7139 −1.15880
\(615\) 0 0
\(616\) 0 0
\(617\) 18.7392 0.754414 0.377207 0.926129i \(-0.376885\pi\)
0.377207 + 0.926129i \(0.376885\pi\)
\(618\) 19.2136 0.772883
\(619\) −39.0600 −1.56995 −0.784977 0.619525i \(-0.787325\pi\)
−0.784977 + 0.619525i \(0.787325\pi\)
\(620\) 0 0
\(621\) 2.03908 0.0818254
\(622\) 8.89579 0.356689
\(623\) 1.33863 0.0536311
\(624\) 9.27247 0.371196
\(625\) 0 0
\(626\) 7.54633 0.301612
\(627\) 0 0
\(628\) −1.66887 −0.0665952
\(629\) −4.80179 −0.191460
\(630\) 0 0
\(631\) 45.0561 1.79366 0.896828 0.442380i \(-0.145866\pi\)
0.896828 + 0.442380i \(0.145866\pi\)
\(632\) 24.7699 0.985295
\(633\) −5.41860 −0.215370
\(634\) −20.2072 −0.802529
\(635\) 0 0
\(636\) 2.11339 0.0838013
\(637\) −3.71027 −0.147006
\(638\) 0 0
\(639\) −14.9968 −0.593263
\(640\) 0 0
\(641\) 25.8928 1.02270 0.511351 0.859372i \(-0.329145\pi\)
0.511351 + 0.859372i \(0.329145\pi\)
\(642\) 2.91544 0.115063
\(643\) −30.6381 −1.20825 −0.604125 0.796890i \(-0.706477\pi\)
−0.604125 + 0.796890i \(0.706477\pi\)
\(644\) −0.853079 −0.0336160
\(645\) 0 0
\(646\) 1.75520 0.0690572
\(647\) 15.1084 0.593972 0.296986 0.954882i \(-0.404019\pi\)
0.296986 + 0.954882i \(0.404019\pi\)
\(648\) −2.68522 −0.105485
\(649\) 0 0
\(650\) 0 0
\(651\) −15.5402 −0.609068
\(652\) 2.06581 0.0809032
\(653\) 5.23528 0.204872 0.102436 0.994740i \(-0.467336\pi\)
0.102436 + 0.994740i \(0.467336\pi\)
\(654\) −15.6903 −0.613538
\(655\) 0 0
\(656\) 7.89532 0.308261
\(657\) −7.85844 −0.306587
\(658\) 1.28155 0.0499599
\(659\) 14.9207 0.581229 0.290615 0.956840i \(-0.406140\pi\)
0.290615 + 0.956840i \(0.406140\pi\)
\(660\) 0 0
\(661\) 45.7403 1.77909 0.889545 0.456847i \(-0.151021\pi\)
0.889545 + 0.456847i \(0.151021\pi\)
\(662\) 16.9434 0.658523
\(663\) 1.16554 0.0452656
\(664\) −25.3816 −0.984995
\(665\) 0 0
\(666\) 13.0288 0.504857
\(667\) 20.2795 0.785226
\(668\) −2.75271 −0.106505
\(669\) 15.7074 0.607284
\(670\) 0 0
\(671\) 0 0
\(672\) 2.35947 0.0910185
\(673\) −21.1087 −0.813680 −0.406840 0.913500i \(-0.633369\pi\)
−0.406840 + 0.913500i \(0.633369\pi\)
\(674\) −5.56047 −0.214181
\(675\) 0 0
\(676\) −1.53441 −0.0590158
\(677\) 44.0695 1.69373 0.846863 0.531810i \(-0.178488\pi\)
0.846863 + 0.531810i \(0.178488\pi\)
\(678\) −24.9591 −0.958550
\(679\) 12.3423 0.473655
\(680\) 0 0
\(681\) −1.47141 −0.0563847
\(682\) 0 0
\(683\) 42.5318 1.62743 0.813717 0.581261i \(-0.197440\pi\)
0.813717 + 0.581261i \(0.197440\pi\)
\(684\) −0.397826 −0.0152113
\(685\) 0 0
\(686\) −29.6076 −1.13042
\(687\) 15.9751 0.609487
\(688\) −2.68853 −0.102499
\(689\) −24.8182 −0.945498
\(690\) 0 0
\(691\) −5.74570 −0.218577 −0.109288 0.994010i \(-0.534857\pi\)
−0.109288 + 0.994010i \(0.534857\pi\)
\(692\) −3.32949 −0.126568
\(693\) 0 0
\(694\) 0.584966 0.0222050
\(695\) 0 0
\(696\) −26.7057 −1.01228
\(697\) 0.992430 0.0375910
\(698\) −19.4567 −0.736445
\(699\) −25.6382 −0.969724
\(700\) 0 0
\(701\) −1.21594 −0.0459255 −0.0229628 0.999736i \(-0.507310\pi\)
−0.0229628 + 0.999736i \(0.507310\pi\)
\(702\) −3.16248 −0.119360
\(703\) −19.2470 −0.725913
\(704\) 0 0
\(705\) 0 0
\(706\) −16.8190 −0.632992
\(707\) −44.8185 −1.68557
\(708\) 1.47258 0.0553430
\(709\) −26.4100 −0.991850 −0.495925 0.868365i \(-0.665171\pi\)
−0.495925 + 0.868365i \(0.665171\pi\)
\(710\) 0 0
\(711\) −9.22454 −0.345947
\(712\) −1.56626 −0.0586982
\(713\) −13.8075 −0.517094
\(714\) 1.84581 0.0690777
\(715\) 0 0
\(716\) −0.0957823 −0.00357955
\(717\) 4.18206 0.156182
\(718\) −21.2256 −0.792133
\(719\) 49.4435 1.84393 0.921967 0.387269i \(-0.126582\pi\)
0.921967 + 0.387269i \(0.126582\pi\)
\(720\) 0 0
\(721\) −29.8488 −1.11163
\(722\) −21.0326 −0.782753
\(723\) 3.29180 0.122423
\(724\) −3.22860 −0.119990
\(725\) 0 0
\(726\) 0 0
\(727\) 39.2447 1.45551 0.727753 0.685839i \(-0.240565\pi\)
0.727753 + 0.685839i \(0.240565\pi\)
\(728\) −13.1925 −0.488946
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.337944 −0.0124993
\(732\) −1.59072 −0.0587946
\(733\) −5.19920 −0.192037 −0.0960185 0.995380i \(-0.530611\pi\)
−0.0960185 + 0.995380i \(0.530611\pi\)
\(734\) 38.7988 1.43209
\(735\) 0 0
\(736\) 2.09639 0.0772740
\(737\) 0 0
\(738\) −2.69279 −0.0991229
\(739\) 29.0090 1.06711 0.533557 0.845764i \(-0.320855\pi\)
0.533557 + 0.845764i \(0.320855\pi\)
\(740\) 0 0
\(741\) 4.67180 0.171623
\(742\) −39.3036 −1.44288
\(743\) −8.50677 −0.312083 −0.156042 0.987750i \(-0.549873\pi\)
−0.156042 + 0.987750i \(0.549873\pi\)
\(744\) 18.1828 0.666613
\(745\) 0 0
\(746\) −32.3447 −1.18422
\(747\) 9.45232 0.345842
\(748\) 0 0
\(749\) −4.52922 −0.165494
\(750\) 0 0
\(751\) −35.1051 −1.28100 −0.640502 0.767957i \(-0.721274\pi\)
−0.640502 + 0.767957i \(0.721274\pi\)
\(752\) −1.63729 −0.0597060
\(753\) 9.36459 0.341265
\(754\) −31.4522 −1.14542
\(755\) 0 0
\(756\) −0.418365 −0.0152158
\(757\) 7.18316 0.261076 0.130538 0.991443i \(-0.458329\pi\)
0.130538 + 0.991443i \(0.458329\pi\)
\(758\) 37.7582 1.37144
\(759\) 0 0
\(760\) 0 0
\(761\) −43.3866 −1.57276 −0.786382 0.617741i \(-0.788048\pi\)
−0.786382 + 0.617741i \(0.788048\pi\)
\(762\) 6.10475 0.221152
\(763\) 24.3753 0.882444
\(764\) −3.01737 −0.109165
\(765\) 0 0
\(766\) −28.1447 −1.01691
\(767\) −17.2930 −0.624414
\(768\) −4.33989 −0.156602
\(769\) −19.6548 −0.708771 −0.354385 0.935099i \(-0.615310\pi\)
−0.354385 + 0.935099i \(0.615310\pi\)
\(770\) 0 0
\(771\) −12.5714 −0.452747
\(772\) 4.46687 0.160766
\(773\) 24.4359 0.878899 0.439450 0.898267i \(-0.355174\pi\)
0.439450 + 0.898267i \(0.355174\pi\)
\(774\) 0.916954 0.0329592
\(775\) 0 0
\(776\) −14.4411 −0.518407
\(777\) −20.2406 −0.726129
\(778\) 24.2160 0.868186
\(779\) 3.97795 0.142525
\(780\) 0 0
\(781\) 0 0
\(782\) 1.64001 0.0586465
\(783\) 9.94544 0.355421
\(784\) 7.50688 0.268103
\(785\) 0 0
\(786\) 0.644864 0.0230015
\(787\) 34.1432 1.21707 0.608536 0.793526i \(-0.291757\pi\)
0.608536 + 0.793526i \(0.291757\pi\)
\(788\) 1.36883 0.0487624
\(789\) 4.82946 0.171933
\(790\) 0 0
\(791\) 38.7747 1.37867
\(792\) 0 0
\(793\) 18.6803 0.663357
\(794\) −45.7693 −1.62429
\(795\) 0 0
\(796\) −3.66337 −0.129845
\(797\) 3.04303 0.107790 0.0538949 0.998547i \(-0.482836\pi\)
0.0538949 + 0.998547i \(0.482836\pi\)
\(798\) 7.39855 0.261906
\(799\) −0.205805 −0.00728087
\(800\) 0 0
\(801\) 0.583290 0.0206096
\(802\) −9.40439 −0.332081
\(803\) 0 0
\(804\) −1.77886 −0.0627355
\(805\) 0 0
\(806\) 21.4145 0.754294
\(807\) 5.22929 0.184080
\(808\) 52.4399 1.84483
\(809\) −11.1011 −0.390294 −0.195147 0.980774i \(-0.562518\pi\)
−0.195147 + 0.980774i \(0.562518\pi\)
\(810\) 0 0
\(811\) 41.3262 1.45116 0.725579 0.688139i \(-0.241572\pi\)
0.725579 + 0.688139i \(0.241572\pi\)
\(812\) −4.16082 −0.146016
\(813\) −30.3311 −1.06376
\(814\) 0 0
\(815\) 0 0
\(816\) −2.35819 −0.0825532
\(817\) −1.35458 −0.0473907
\(818\) −9.26056 −0.323788
\(819\) 4.91300 0.171674
\(820\) 0 0
\(821\) 8.17883 0.285443 0.142722 0.989763i \(-0.454415\pi\)
0.142722 + 0.989763i \(0.454415\pi\)
\(822\) −11.6229 −0.405396
\(823\) −13.1973 −0.460029 −0.230014 0.973187i \(-0.573877\pi\)
−0.230014 + 0.973187i \(0.573877\pi\)
\(824\) 34.9246 1.21665
\(825\) 0 0
\(826\) −27.3862 −0.952889
\(827\) 30.7370 1.06883 0.534415 0.845222i \(-0.320532\pi\)
0.534415 + 0.845222i \(0.320532\pi\)
\(828\) −0.371718 −0.0129181
\(829\) 3.68790 0.128086 0.0640430 0.997947i \(-0.479601\pi\)
0.0640430 + 0.997947i \(0.479601\pi\)
\(830\) 0 0
\(831\) 15.9694 0.553974
\(832\) 15.2936 0.530209
\(833\) 0.943604 0.0326939
\(834\) −26.0635 −0.902505
\(835\) 0 0
\(836\) 0 0
\(837\) −6.77143 −0.234055
\(838\) 5.76621 0.199191
\(839\) 43.5517 1.50357 0.751786 0.659407i \(-0.229192\pi\)
0.751786 + 0.659407i \(0.229192\pi\)
\(840\) 0 0
\(841\) 69.9118 2.41075
\(842\) 25.6623 0.884381
\(843\) 1.39067 0.0478972
\(844\) 0.987795 0.0340013
\(845\) 0 0
\(846\) 0.558418 0.0191988
\(847\) 0 0
\(848\) 50.2139 1.72435
\(849\) 5.87453 0.201613
\(850\) 0 0
\(851\) −17.9838 −0.616478
\(852\) 2.73387 0.0936607
\(853\) 30.3434 1.03894 0.519469 0.854489i \(-0.326130\pi\)
0.519469 + 0.854489i \(0.326130\pi\)
\(854\) 29.5832 1.01232
\(855\) 0 0
\(856\) 5.29941 0.181130
\(857\) −12.5402 −0.428365 −0.214182 0.976794i \(-0.568709\pi\)
−0.214182 + 0.976794i \(0.568709\pi\)
\(858\) 0 0
\(859\) −8.67783 −0.296084 −0.148042 0.988981i \(-0.547297\pi\)
−0.148042 + 0.988981i \(0.547297\pi\)
\(860\) 0 0
\(861\) 4.18332 0.142567
\(862\) −10.3948 −0.354047
\(863\) 38.3918 1.30687 0.653437 0.756981i \(-0.273327\pi\)
0.653437 + 0.756981i \(0.273327\pi\)
\(864\) 1.02811 0.0349770
\(865\) 0 0
\(866\) −4.06585 −0.138163
\(867\) 16.7036 0.567283
\(868\) 2.83293 0.0961559
\(869\) 0 0
\(870\) 0 0
\(871\) 20.8897 0.707821
\(872\) −28.5203 −0.965818
\(873\) 5.37801 0.182018
\(874\) 6.57362 0.222356
\(875\) 0 0
\(876\) 1.43257 0.0484021
\(877\) −31.2898 −1.05658 −0.528291 0.849064i \(-0.677167\pi\)
−0.528291 + 0.849064i \(0.677167\pi\)
\(878\) −4.04331 −0.136455
\(879\) 19.9745 0.673723
\(880\) 0 0
\(881\) 49.2703 1.65996 0.829979 0.557795i \(-0.188353\pi\)
0.829979 + 0.557795i \(0.188353\pi\)
\(882\) −2.56031 −0.0862100
\(883\) −28.1861 −0.948539 −0.474270 0.880380i \(-0.657288\pi\)
−0.474270 + 0.880380i \(0.657288\pi\)
\(884\) −0.212474 −0.00714626
\(885\) 0 0
\(886\) −16.4038 −0.551096
\(887\) 25.4943 0.856016 0.428008 0.903775i \(-0.359216\pi\)
0.428008 + 0.903775i \(0.359216\pi\)
\(888\) 23.6825 0.794734
\(889\) −9.48390 −0.318080
\(890\) 0 0
\(891\) 0 0
\(892\) −2.86342 −0.0958743
\(893\) −0.824928 −0.0276052
\(894\) 16.1910 0.541507
\(895\) 0 0
\(896\) 28.9387 0.966775
\(897\) 4.36520 0.145750
\(898\) 21.9031 0.730916
\(899\) −67.3449 −2.24608
\(900\) 0 0
\(901\) 6.31181 0.210277
\(902\) 0 0
\(903\) −1.42451 −0.0474048
\(904\) −45.3683 −1.50893
\(905\) 0 0
\(906\) 29.5930 0.983162
\(907\) −2.48054 −0.0823649 −0.0411825 0.999152i \(-0.513112\pi\)
−0.0411825 + 0.999152i \(0.513112\pi\)
\(908\) 0.268235 0.00890168
\(909\) −19.5291 −0.647738
\(910\) 0 0
\(911\) 2.71559 0.0899716 0.0449858 0.998988i \(-0.485676\pi\)
0.0449858 + 0.998988i \(0.485676\pi\)
\(912\) −9.45232 −0.312998
\(913\) 0 0
\(914\) −43.1101 −1.42595
\(915\) 0 0
\(916\) −2.91221 −0.0962220
\(917\) −1.00181 −0.0330828
\(918\) 0.804288 0.0265455
\(919\) 3.23900 0.106845 0.0534224 0.998572i \(-0.482987\pi\)
0.0534224 + 0.998572i \(0.482987\pi\)
\(920\) 0 0
\(921\) 19.4372 0.640479
\(922\) −46.0607 −1.51693
\(923\) −32.1047 −1.05674
\(924\) 0 0
\(925\) 0 0
\(926\) −60.8102 −1.99835
\(927\) −13.0062 −0.427180
\(928\) 10.2250 0.335652
\(929\) 7.18207 0.235636 0.117818 0.993035i \(-0.462410\pi\)
0.117818 + 0.993035i \(0.462410\pi\)
\(930\) 0 0
\(931\) 3.78224 0.123958
\(932\) 4.67376 0.153094
\(933\) −6.02182 −0.197145
\(934\) −57.2832 −1.87436
\(935\) 0 0
\(936\) −5.74845 −0.187894
\(937\) −20.3127 −0.663586 −0.331793 0.943352i \(-0.607654\pi\)
−0.331793 + 0.943352i \(0.607654\pi\)
\(938\) 33.0822 1.08017
\(939\) −5.10833 −0.166704
\(940\) 0 0
\(941\) −25.4246 −0.828818 −0.414409 0.910091i \(-0.636012\pi\)
−0.414409 + 0.910091i \(0.636012\pi\)
\(942\) 13.5238 0.440630
\(943\) 3.71689 0.121038
\(944\) 34.9884 1.13878
\(945\) 0 0
\(946\) 0 0
\(947\) 4.55536 0.148029 0.0740147 0.997257i \(-0.476419\pi\)
0.0740147 + 0.997257i \(0.476419\pi\)
\(948\) 1.68161 0.0546161
\(949\) −16.8231 −0.546102
\(950\) 0 0
\(951\) 13.6788 0.443566
\(952\) 3.35514 0.108741
\(953\) 41.5855 1.34709 0.673543 0.739148i \(-0.264772\pi\)
0.673543 + 0.739148i \(0.264772\pi\)
\(954\) −17.1260 −0.554475
\(955\) 0 0
\(956\) −0.762378 −0.0246571
\(957\) 0 0
\(958\) 24.6519 0.796467
\(959\) 18.0565 0.583076
\(960\) 0 0
\(961\) 14.8523 0.479107
\(962\) 27.8918 0.899267
\(963\) −1.97355 −0.0635967
\(964\) −0.600085 −0.0193274
\(965\) 0 0
\(966\) 6.91300 0.222422
\(967\) 16.2161 0.521476 0.260738 0.965410i \(-0.416034\pi\)
0.260738 + 0.965410i \(0.416034\pi\)
\(968\) 0 0
\(969\) −1.18814 −0.0381686
\(970\) 0 0
\(971\) −13.4705 −0.432290 −0.216145 0.976361i \(-0.569348\pi\)
−0.216145 + 0.976361i \(0.569348\pi\)
\(972\) −0.182297 −0.00584718
\(973\) 40.4904 1.29806
\(974\) −3.71078 −0.118901
\(975\) 0 0
\(976\) −37.7953 −1.20980
\(977\) 14.5400 0.465177 0.232588 0.972575i \(-0.425281\pi\)
0.232588 + 0.972575i \(0.425281\pi\)
\(978\) −16.7404 −0.535300
\(979\) 0 0
\(980\) 0 0
\(981\) 10.6212 0.339109
\(982\) −11.1661 −0.356324
\(983\) 24.5938 0.784422 0.392211 0.919875i \(-0.371710\pi\)
0.392211 + 0.919875i \(0.371710\pi\)
\(984\) −4.89469 −0.156037
\(985\) 0 0
\(986\) 7.99900 0.254740
\(987\) −0.867517 −0.0276134
\(988\) −0.851656 −0.0270948
\(989\) −1.26568 −0.0402463
\(990\) 0 0
\(991\) 4.43775 0.140970 0.0704848 0.997513i \(-0.477545\pi\)
0.0704848 + 0.997513i \(0.477545\pi\)
\(992\) −6.96177 −0.221036
\(993\) −11.4695 −0.363972
\(994\) −50.8429 −1.61264
\(995\) 0 0
\(996\) −1.72313 −0.0545995
\(997\) −0.0104705 −0.000331605 0 −0.000165802 1.00000i \(-0.500053\pi\)
−0.000165802 1.00000i \(0.500053\pi\)
\(998\) 24.8127 0.785431
\(999\) −8.81959 −0.279040
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 9075.2.a.di.1.3 4
5.4 even 2 1815.2.a.p.1.2 4
11.3 even 5 825.2.n.g.526.2 8
11.4 even 5 825.2.n.g.676.2 8
11.10 odd 2 9075.2.a.cm.1.2 4
15.14 odd 2 5445.2.a.bt.1.3 4
55.3 odd 20 825.2.bx.f.724.1 16
55.4 even 10 165.2.m.d.16.1 8
55.14 even 10 165.2.m.d.31.1 yes 8
55.37 odd 20 825.2.bx.f.49.1 16
55.47 odd 20 825.2.bx.f.724.4 16
55.48 odd 20 825.2.bx.f.49.4 16
55.54 odd 2 1815.2.a.w.1.3 4
165.14 odd 10 495.2.n.a.361.2 8
165.59 odd 10 495.2.n.a.181.2 8
165.164 even 2 5445.2.a.bf.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
165.2.m.d.16.1 8 55.4 even 10
165.2.m.d.31.1 yes 8 55.14 even 10
495.2.n.a.181.2 8 165.59 odd 10
495.2.n.a.361.2 8 165.14 odd 10
825.2.n.g.526.2 8 11.3 even 5
825.2.n.g.676.2 8 11.4 even 5
825.2.bx.f.49.1 16 55.37 odd 20
825.2.bx.f.49.4 16 55.48 odd 20
825.2.bx.f.724.1 16 55.3 odd 20
825.2.bx.f.724.4 16 55.47 odd 20
1815.2.a.p.1.2 4 5.4 even 2
1815.2.a.w.1.3 4 55.54 odd 2
5445.2.a.bf.1.2 4 165.164 even 2
5445.2.a.bt.1.3 4 15.14 odd 2
9075.2.a.cm.1.2 4 11.10 odd 2
9075.2.a.di.1.3 4 1.1 even 1 trivial