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Properties

Label 9438.2.a.d.1.1
Level $9438$
Weight $2$
Character 9438.1
Self dual yes
Analytic conductor $75.363$
Analytic rank $1$
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] = [9438,2,Mod(1,9438)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9438, 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("9438.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9438 = 2 \cdot 3 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9438.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: \(75.3628094277\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 858)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9438.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +1.00000 q^{13} -3.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +2.00000 q^{19} -1.00000 q^{20} -3.00000 q^{21} -1.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} -1.00000 q^{26} -1.00000 q^{27} +3.00000 q^{28} +9.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -4.00000 q^{34} -3.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -2.00000 q^{38} -1.00000 q^{39} +1.00000 q^{40} -1.00000 q^{41} +3.00000 q^{42} -11.0000 q^{43} -1.00000 q^{45} +1.00000 q^{46} -1.00000 q^{48} +2.00000 q^{49} +4.00000 q^{50} -4.00000 q^{51} +1.00000 q^{52} -10.0000 q^{53} +1.00000 q^{54} -3.00000 q^{56} -2.00000 q^{57} -9.00000 q^{58} -3.00000 q^{59} +1.00000 q^{60} -5.00000 q^{61} +4.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} +3.00000 q^{67} +4.00000 q^{68} +1.00000 q^{69} +3.00000 q^{70} +10.0000 q^{71} -1.00000 q^{72} -9.00000 q^{73} +6.00000 q^{74} +4.00000 q^{75} +2.00000 q^{76} +1.00000 q^{78} -10.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.00000 q^{82} +6.00000 q^{83} -3.00000 q^{84} -4.00000 q^{85} +11.0000 q^{86} -9.00000 q^{87} -8.00000 q^{89} +1.00000 q^{90} +3.00000 q^{91} -1.00000 q^{92} +4.00000 q^{93} -2.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 1.00000 0.408248
\(7\) 3.00000 1.13389 0.566947 − 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 0 0
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) −3.00000 −0.801784
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 − 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) −1.00000 −0.235702
\(19\) 2.00000 0.458831 0.229416 − 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −1.00000 −0.223607
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.00000 −0.800000
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) 3.00000 0.566947
\(29\) 9.00000 1.67126 0.835629 − 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −1.00000 −0.182574
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) −3.00000 −0.507093
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −2.00000 −0.324443
\(39\) −1.00000 −0.160128
\(40\) 1.00000 0.158114
\(41\) −1.00000 −0.156174 −0.0780869 − 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 3.00000 0.462910
\(43\) −11.0000 −1.67748 −0.838742 − 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 1.00000 0.147442
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) 4.00000 0.565685
\(51\) −4.00000 −0.560112
\(52\) 1.00000 0.138675
\(53\) −10.0000 −1.37361 −0.686803 − 0.726844i \(-0.740986\pi\)
−0.686803 + 0.726844i \(0.740986\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −3.00000 −0.400892
\(57\) −2.00000 −0.264906
\(58\) −9.00000 −1.18176
\(59\) −3.00000 −0.390567 −0.195283 − 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) 1.00000 0.129099
\(61\) −5.00000 −0.640184 −0.320092 − 0.947386i \(-0.603714\pi\)
−0.320092 + 0.947386i \(0.603714\pi\)
\(62\) 4.00000 0.508001
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 − 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 4.00000 0.485071
\(69\) 1.00000 0.120386
\(70\) 3.00000 0.358569
\(71\) 10.0000 1.18678 0.593391 − 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) −1.00000 −0.117851
\(73\) −9.00000 −1.05337 −0.526685 − 0.850060i \(-0.676565\pi\)
−0.526685 + 0.850060i \(0.676565\pi\)
\(74\) 6.00000 0.697486
\(75\) 4.00000 0.461880
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) −10.0000 −1.12509 −0.562544 − 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 1.00000 0.110432
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) −3.00000 −0.327327
\(85\) −4.00000 −0.433861
\(86\) 11.0000 1.18616
\(87\) −9.00000 −0.964901
\(88\) 0 0
\(89\) −8.00000 −0.847998 −0.423999 − 0.905663i \(-0.639374\pi\)
−0.423999 + 0.905663i \(0.639374\pi\)
\(90\) 1.00000 0.105409
\(91\) 3.00000 0.314485
\(92\) −1.00000 −0.104257
\(93\) 4.00000 0.414781
\(94\) 0 0
\(95\) −2.00000 −0.205196
\(96\) 1.00000 0.102062
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 4.00000 0.396059
\(103\) −11.0000 −1.08386 −0.541931 − 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 3.00000 0.292770
\(106\) 10.0000 0.971286
\(107\) −7.00000 −0.676716 −0.338358 − 0.941018i \(-0.609871\pi\)
−0.338358 + 0.941018i \(0.609871\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −16.0000 −1.53252 −0.766261 − 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 3.00000 0.283473
\(113\) 5.00000 0.470360 0.235180 − 0.971952i \(-0.424432\pi\)
0.235180 + 0.971952i \(0.424432\pi\)
\(114\) 2.00000 0.187317
\(115\) 1.00000 0.0932505
\(116\) 9.00000 0.835629
\(117\) 1.00000 0.0924500
\(118\) 3.00000 0.276172
\(119\) 12.0000 1.10004
\(120\) −1.00000 −0.0912871
\(121\) 0 0
\(122\) 5.00000 0.452679
\(123\) 1.00000 0.0901670
\(124\) −4.00000 −0.359211
\(125\) 9.00000 0.804984
\(126\) −3.00000 −0.267261
\(127\) 14.0000 1.24230 0.621150 − 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 11.0000 0.968496
\(130\) 1.00000 0.0877058
\(131\) 3.00000 0.262111 0.131056 − 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) 0 0
\(133\) 6.00000 0.520266
\(134\) −3.00000 −0.259161
\(135\) 1.00000 0.0860663
\(136\) −4.00000 −0.342997
\(137\) −18.0000 −1.53784 −0.768922 − 0.639343i \(-0.779207\pi\)
−0.768922 + 0.639343i \(0.779207\pi\)
\(138\) −1.00000 −0.0851257
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) −10.0000 −0.839181
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −9.00000 −0.747409
\(146\) 9.00000 0.744845
\(147\) −2.00000 −0.164957
\(148\) −6.00000 −0.493197
\(149\) −4.00000 −0.327693 −0.163846 − 0.986486i \(-0.552390\pi\)
−0.163846 + 0.986486i \(0.552390\pi\)
\(150\) −4.00000 −0.326599
\(151\) −24.0000 −1.95309 −0.976546 − 0.215308i \(-0.930924\pi\)
−0.976546 + 0.215308i \(0.930924\pi\)
\(152\) −2.00000 −0.162221
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) −1.00000 −0.0800641
\(157\) −22.0000 −1.75579 −0.877896 − 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 10.0000 0.795557
\(159\) 10.0000 0.793052
\(160\) 1.00000 0.0790569
\(161\) −3.00000 −0.236433
\(162\) −1.00000 −0.0785674
\(163\) 9.00000 0.704934 0.352467 − 0.935824i \(-0.385343\pi\)
0.352467 + 0.935824i \(0.385343\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 3.00000 0.232147 0.116073 − 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 3.00000 0.231455
\(169\) 1.00000 0.0769231
\(170\) 4.00000 0.306786
\(171\) 2.00000 0.152944
\(172\) −11.0000 −0.838742
\(173\) 19.0000 1.44454 0.722272 − 0.691609i \(-0.243098\pi\)
0.722272 + 0.691609i \(0.243098\pi\)
\(174\) 9.00000 0.682288
\(175\) −12.0000 −0.907115
\(176\) 0 0
\(177\) 3.00000 0.225494
\(178\) 8.00000 0.599625
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −3.00000 −0.222375
\(183\) 5.00000 0.369611
\(184\) 1.00000 0.0737210
\(185\) 6.00000 0.441129
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 0 0
\(189\) −3.00000 −0.218218
\(190\) 2.00000 0.145095
\(191\) −15.0000 −1.08536 −0.542681 − 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) −2.00000 −0.143592
\(195\) 1.00000 0.0716115
\(196\) 2.00000 0.142857
\(197\) −12.0000 −0.854965 −0.427482 − 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) 3.00000 0.212664 0.106332 − 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) 4.00000 0.282843
\(201\) −3.00000 −0.211604
\(202\) −10.0000 −0.703598
\(203\) 27.0000 1.89503
\(204\) −4.00000 −0.280056
\(205\) 1.00000 0.0698430
\(206\) 11.0000 0.766406
\(207\) −1.00000 −0.0695048
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) −3.00000 −0.207020
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −10.0000 −0.686803
\(213\) −10.0000 −0.685189
\(214\) 7.00000 0.478510
\(215\) 11.0000 0.750194
\(216\) 1.00000 0.0680414
\(217\) −12.0000 −0.814613
\(218\) 16.0000 1.08366
\(219\) 9.00000 0.608164
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) −6.00000 −0.402694
\(223\) −20.0000 −1.33930 −0.669650 − 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) −3.00000 −0.200446
\(225\) −4.00000 −0.266667
\(226\) −5.00000 −0.332595
\(227\) −8.00000 −0.530979 −0.265489 − 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) −2.00000 −0.132453
\(229\) 25.0000 1.65205 0.826023 − 0.563636i \(-0.190598\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(230\) −1.00000 −0.0659380
\(231\) 0 0
\(232\) −9.00000 −0.590879
\(233\) −14.0000 −0.917170 −0.458585 − 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 0 0
\(236\) −3.00000 −0.195283
\(237\) 10.0000 0.649570
\(238\) −12.0000 −0.777844
\(239\) 5.00000 0.323423 0.161712 − 0.986838i \(-0.448299\pi\)
0.161712 + 0.986838i \(0.448299\pi\)
\(240\) 1.00000 0.0645497
\(241\) −2.00000 −0.128831 −0.0644157 − 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) −5.00000 −0.320092
\(245\) −2.00000 −0.127775
\(246\) −1.00000 −0.0637577
\(247\) 2.00000 0.127257
\(248\) 4.00000 0.254000
\(249\) −6.00000 −0.380235
\(250\) −9.00000 −0.569210
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 3.00000 0.188982
\(253\) 0 0
\(254\) −14.0000 −0.878438
\(255\) 4.00000 0.250490
\(256\) 1.00000 0.0625000
\(257\) −25.0000 −1.55946 −0.779729 − 0.626118i \(-0.784643\pi\)
−0.779729 + 0.626118i \(0.784643\pi\)
\(258\) −11.0000 −0.684830
\(259\) −18.0000 −1.11847
\(260\) −1.00000 −0.0620174
\(261\) 9.00000 0.557086
\(262\) −3.00000 −0.185341
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) 10.0000 0.614295
\(266\) −6.00000 −0.367884
\(267\) 8.00000 0.489592
\(268\) 3.00000 0.183254
\(269\) −4.00000 −0.243884 −0.121942 − 0.992537i \(-0.538912\pi\)
−0.121942 + 0.992537i \(0.538912\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 16.0000 0.971931 0.485965 − 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 4.00000 0.242536
\(273\) −3.00000 −0.181568
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) −5.00000 −0.300421 −0.150210 − 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 3.00000 0.179284
\(281\) 29.0000 1.72999 0.864997 − 0.501776i \(-0.167320\pi\)
0.864997 + 0.501776i \(0.167320\pi\)
\(282\) 0 0
\(283\) 9.00000 0.534994 0.267497 − 0.963559i \(-0.413803\pi\)
0.267497 + 0.963559i \(0.413803\pi\)
\(284\) 10.0000 0.593391
\(285\) 2.00000 0.118470
\(286\) 0 0
\(287\) −3.00000 −0.177084
\(288\) −1.00000 −0.0589256
\(289\) −1.00000 −0.0588235
\(290\) 9.00000 0.528498
\(291\) −2.00000 −0.117242
\(292\) −9.00000 −0.526685
\(293\) 18.0000 1.05157 0.525786 − 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 2.00000 0.116642
\(295\) 3.00000 0.174667
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) 4.00000 0.231714
\(299\) −1.00000 −0.0578315
\(300\) 4.00000 0.230940
\(301\) −33.0000 −1.90209
\(302\) 24.0000 1.38104
\(303\) −10.0000 −0.574485
\(304\) 2.00000 0.114708
\(305\) 5.00000 0.286299
\(306\) −4.00000 −0.228665
\(307\) 10.0000 0.570730 0.285365 − 0.958419i \(-0.407885\pi\)
0.285365 + 0.958419i \(0.407885\pi\)
\(308\) 0 0
\(309\) 11.0000 0.625768
\(310\) −4.00000 −0.227185
\(311\) −8.00000 −0.453638 −0.226819 − 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 1.00000 0.0566139
\(313\) 19.0000 1.07394 0.536972 − 0.843600i \(-0.319568\pi\)
0.536972 + 0.843600i \(0.319568\pi\)
\(314\) 22.0000 1.24153
\(315\) −3.00000 −0.169031
\(316\) −10.0000 −0.562544
\(317\) −3.00000 −0.168497 −0.0842484 − 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) −10.0000 −0.560772
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) 7.00000 0.390702
\(322\) 3.00000 0.167183
\(323\) 8.00000 0.445132
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) −9.00000 −0.498464
\(327\) 16.0000 0.884802
\(328\) 1.00000 0.0552158
\(329\) 0 0
\(330\) 0 0
\(331\) 19.0000 1.04433 0.522167 − 0.852843i \(-0.325124\pi\)
0.522167 + 0.852843i \(0.325124\pi\)
\(332\) 6.00000 0.329293
\(333\) −6.00000 −0.328798
\(334\) −3.00000 −0.164153
\(335\) −3.00000 −0.163908
\(336\) −3.00000 −0.163663
\(337\) −2.00000 −0.108947 −0.0544735 − 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −1.00000 −0.0543928
\(339\) −5.00000 −0.271563
\(340\) −4.00000 −0.216930
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) −15.0000 −0.809924
\(344\) 11.0000 0.593080
\(345\) −1.00000 −0.0538382
\(346\) −19.0000 −1.02145
\(347\) 12.0000 0.644194 0.322097 − 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −9.00000 −0.482451
\(349\) 20.0000 1.07058 0.535288 − 0.844670i \(-0.320203\pi\)
0.535288 + 0.844670i \(0.320203\pi\)
\(350\) 12.0000 0.641427
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −3.00000 −0.159448
\(355\) −10.0000 −0.530745
\(356\) −8.00000 −0.423999
\(357\) −12.0000 −0.635107
\(358\) −12.0000 −0.634220
\(359\) −13.0000 −0.686114 −0.343057 − 0.939315i \(-0.611462\pi\)
−0.343057 + 0.939315i \(0.611462\pi\)
\(360\) 1.00000 0.0527046
\(361\) −15.0000 −0.789474
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) 9.00000 0.471082
\(366\) −5.00000 −0.261354
\(367\) −32.0000 −1.67039 −0.835193 − 0.549957i \(-0.814644\pi\)
−0.835193 + 0.549957i \(0.814644\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −1.00000 −0.0520579
\(370\) −6.00000 −0.311925
\(371\) −30.0000 −1.55752
\(372\) 4.00000 0.207390
\(373\) 11.0000 0.569558 0.284779 − 0.958593i \(-0.408080\pi\)
0.284779 + 0.958593i \(0.408080\pi\)
\(374\) 0 0
\(375\) −9.00000 −0.464758
\(376\) 0 0
\(377\) 9.00000 0.463524
\(378\) 3.00000 0.154303
\(379\) 24.0000 1.23280 0.616399 − 0.787434i \(-0.288591\pi\)
0.616399 + 0.787434i \(0.288591\pi\)
\(380\) −2.00000 −0.102598
\(381\) −14.0000 −0.717242
\(382\) 15.0000 0.767467
\(383\) 14.0000 0.715367 0.357683 − 0.933843i \(-0.383567\pi\)
0.357683 + 0.933843i \(0.383567\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −6.00000 −0.305392
\(387\) −11.0000 −0.559161
\(388\) 2.00000 0.101535
\(389\) −18.0000 −0.912636 −0.456318 − 0.889817i \(-0.650832\pi\)
−0.456318 + 0.889817i \(0.650832\pi\)
\(390\) −1.00000 −0.0506370
\(391\) −4.00000 −0.202289
\(392\) −2.00000 −0.101015
\(393\) −3.00000 −0.151330
\(394\) 12.0000 0.604551
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) −19.0000 −0.953583 −0.476791 − 0.879017i \(-0.658200\pi\)
−0.476791 + 0.879017i \(0.658200\pi\)
\(398\) −3.00000 −0.150376
\(399\) −6.00000 −0.300376
\(400\) −4.00000 −0.200000
\(401\) −24.0000 −1.19850 −0.599251 − 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 3.00000 0.149626
\(403\) −4.00000 −0.199254
\(404\) 10.0000 0.497519
\(405\) −1.00000 −0.0496904
\(406\) −27.0000 −1.33999
\(407\) 0 0
\(408\) 4.00000 0.198030
\(409\) −7.00000 −0.346128 −0.173064 − 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) −1.00000 −0.0493865
\(411\) 18.0000 0.887875
\(412\) −11.0000 −0.541931
\(413\) −9.00000 −0.442861
\(414\) 1.00000 0.0491473
\(415\) −6.00000 −0.294528
\(416\) −1.00000 −0.0490290
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 3.00000 0.146385
\(421\) 5.00000 0.243685 0.121843 − 0.992549i \(-0.461120\pi\)
0.121843 + 0.992549i \(0.461120\pi\)
\(422\) 20.0000 0.973585
\(423\) 0 0
\(424\) 10.0000 0.485643
\(425\) −16.0000 −0.776114
\(426\) 10.0000 0.484502
\(427\) −15.0000 −0.725901
\(428\) −7.00000 −0.338358
\(429\) 0 0
\(430\) −11.0000 −0.530467
\(431\) −16.0000 −0.770693 −0.385346 − 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 5.00000 0.240285 0.120142 − 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 12.0000 0.576018
\(435\) 9.00000 0.431517
\(436\) −16.0000 −0.766261
\(437\) −2.00000 −0.0956730
\(438\) −9.00000 −0.430037
\(439\) 8.00000 0.381819 0.190910 − 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) −4.00000 −0.190261
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 6.00000 0.284747
\(445\) 8.00000 0.379236
\(446\) 20.0000 0.947027
\(447\) 4.00000 0.189194
\(448\) 3.00000 0.141737
\(449\) −36.0000 −1.69895 −0.849473 − 0.527633i \(-0.823080\pi\)
−0.849473 + 0.527633i \(0.823080\pi\)
\(450\) 4.00000 0.188562
\(451\) 0 0
\(452\) 5.00000 0.235180
\(453\) 24.0000 1.12762
\(454\) 8.00000 0.375459
\(455\) −3.00000 −0.140642
\(456\) 2.00000 0.0936586
\(457\) 37.0000 1.73079 0.865393 − 0.501093i \(-0.167069\pi\)
0.865393 + 0.501093i \(0.167069\pi\)
\(458\) −25.0000 −1.16817
\(459\) −4.00000 −0.186704
\(460\) 1.00000 0.0466252
\(461\) −24.0000 −1.11779 −0.558896 − 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 0 0
\(463\) −34.0000 −1.58011 −0.790057 − 0.613033i \(-0.789949\pi\)
−0.790057 + 0.613033i \(0.789949\pi\)
\(464\) 9.00000 0.417815
\(465\) −4.00000 −0.185496
\(466\) 14.0000 0.648537
\(467\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 1.00000 0.0462250
\(469\) 9.00000 0.415581
\(470\) 0 0
\(471\) 22.0000 1.01371
\(472\) 3.00000 0.138086
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) −8.00000 −0.367065
\(476\) 12.0000 0.550019
\(477\) −10.0000 −0.457869
\(478\) −5.00000 −0.228695
\(479\) 31.0000 1.41643 0.708213 − 0.705999i \(-0.249502\pi\)
0.708213 + 0.705999i \(0.249502\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −6.00000 −0.273576
\(482\) 2.00000 0.0910975
\(483\) 3.00000 0.136505
\(484\) 0 0
\(485\) −2.00000 −0.0908153
\(486\) 1.00000 0.0453609
\(487\) −2.00000 −0.0906287 −0.0453143 − 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 5.00000 0.226339
\(489\) −9.00000 −0.406994
\(490\) 2.00000 0.0903508
\(491\) −29.0000 −1.30875 −0.654376 − 0.756169i \(-0.727069\pi\)
−0.654376 + 0.756169i \(0.727069\pi\)
\(492\) 1.00000 0.0450835
\(493\) 36.0000 1.62136
\(494\) −2.00000 −0.0899843
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 30.0000 1.34568
\(498\) 6.00000 0.268866
\(499\) 17.0000 0.761025 0.380512 − 0.924776i \(-0.375748\pi\)
0.380512 + 0.924776i \(0.375748\pi\)
\(500\) 9.00000 0.402492
\(501\) −3.00000 −0.134030
\(502\) 6.00000 0.267793
\(503\) −36.0000 −1.60516 −0.802580 − 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) −3.00000 −0.133631
\(505\) −10.0000 −0.444994
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 14.0000 0.621150
\(509\) 34.0000 1.50702 0.753512 − 0.657434i \(-0.228358\pi\)
0.753512 + 0.657434i \(0.228358\pi\)
\(510\) −4.00000 −0.177123
\(511\) −27.0000 −1.19441
\(512\) −1.00000 −0.0441942
\(513\) −2.00000 −0.0883022
\(514\) 25.0000 1.10270
\(515\) 11.0000 0.484718
\(516\) 11.0000 0.484248
\(517\) 0 0
\(518\) 18.0000 0.790875
\(519\) −19.0000 −0.834007
\(520\) 1.00000 0.0438529
\(521\) −37.0000 −1.62100 −0.810500 − 0.585739i \(-0.800804\pi\)
−0.810500 + 0.585739i \(0.800804\pi\)
\(522\) −9.00000 −0.393919
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) 3.00000 0.131056
\(525\) 12.0000 0.523723
\(526\) −24.0000 −1.04645
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) −10.0000 −0.434372
\(531\) −3.00000 −0.130189
\(532\) 6.00000 0.260133
\(533\) −1.00000 −0.0433148
\(534\) −8.00000 −0.346194
\(535\) 7.00000 0.302636
\(536\) −3.00000 −0.129580
\(537\) −12.0000 −0.517838
\(538\) 4.00000 0.172452
\(539\) 0 0
\(540\) 1.00000 0.0430331
\(541\) 18.0000 0.773880 0.386940 − 0.922105i \(-0.373532\pi\)
0.386940 + 0.922105i \(0.373532\pi\)
\(542\) −16.0000 −0.687259
\(543\) −14.0000 −0.600798
\(544\) −4.00000 −0.171499
\(545\) 16.0000 0.685365
\(546\) 3.00000 0.128388
\(547\) 5.00000 0.213785 0.106892 − 0.994271i \(-0.465910\pi\)
0.106892 + 0.994271i \(0.465910\pi\)
\(548\) −18.0000 −0.768922
\(549\) −5.00000 −0.213395
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) −1.00000 −0.0425628
\(553\) −30.0000 −1.27573
\(554\) 5.00000 0.212430
\(555\) −6.00000 −0.254686
\(556\) 0 0
\(557\) 14.0000 0.593199 0.296600 − 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 4.00000 0.169334
\(559\) −11.0000 −0.465250
\(560\) −3.00000 −0.126773
\(561\) 0 0
\(562\) −29.0000 −1.22329
\(563\) −32.0000 −1.34864 −0.674320 − 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(564\) 0 0
\(565\) −5.00000 −0.210352
\(566\) −9.00000 −0.378298
\(567\) 3.00000 0.125988
\(568\) −10.0000 −0.419591
\(569\) −30.0000 −1.25767 −0.628833 − 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −2.00000 −0.0837708
\(571\) 29.0000 1.21361 0.606806 − 0.794850i \(-0.292450\pi\)
0.606806 + 0.794850i \(0.292450\pi\)
\(572\) 0 0
\(573\) 15.0000 0.626634
\(574\) 3.00000 0.125218
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 4.00000 0.166522 0.0832611 − 0.996528i \(-0.473466\pi\)
0.0832611 + 0.996528i \(0.473466\pi\)
\(578\) 1.00000 0.0415945
\(579\) −6.00000 −0.249351
\(580\) −9.00000 −0.373705
\(581\) 18.0000 0.746766
\(582\) 2.00000 0.0829027
\(583\) 0 0
\(584\) 9.00000 0.372423
\(585\) −1.00000 −0.0413449
\(586\) −18.0000 −0.743573
\(587\) −37.0000 −1.52715 −0.763577 − 0.645717i \(-0.776559\pi\)
−0.763577 + 0.645717i \(0.776559\pi\)
\(588\) −2.00000 −0.0824786
\(589\) −8.00000 −0.329634
\(590\) −3.00000 −0.123508
\(591\) 12.0000 0.493614
\(592\) −6.00000 −0.246598
\(593\) −26.0000 −1.06769 −0.533846 − 0.845582i \(-0.679254\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) −4.00000 −0.163846
\(597\) −3.00000 −0.122782
\(598\) 1.00000 0.0408930
\(599\) −13.0000 −0.531166 −0.265583 − 0.964088i \(-0.585564\pi\)
−0.265583 + 0.964088i \(0.585564\pi\)
\(600\) −4.00000 −0.163299
\(601\) 24.0000 0.978980 0.489490 − 0.872009i \(-0.337183\pi\)
0.489490 + 0.872009i \(0.337183\pi\)
\(602\) 33.0000 1.34498
\(603\) 3.00000 0.122169
\(604\) −24.0000 −0.976546
\(605\) 0 0
\(606\) 10.0000 0.406222
\(607\) −10.0000 −0.405887 −0.202944 − 0.979190i \(-0.565051\pi\)
−0.202944 + 0.979190i \(0.565051\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −27.0000 −1.09410
\(610\) −5.00000 −0.202444
\(611\) 0 0
\(612\) 4.00000 0.161690
\(613\) −24.0000 −0.969351 −0.484675 − 0.874694i \(-0.661062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(614\) −10.0000 −0.403567
\(615\) −1.00000 −0.0403239
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 − 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −11.0000 −0.442485
\(619\) 11.0000 0.442127 0.221064 − 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) 4.00000 0.160644
\(621\) 1.00000 0.0401286
\(622\) 8.00000 0.320771
\(623\) −24.0000 −0.961540
\(624\) −1.00000 −0.0400320
\(625\) 11.0000 0.440000
\(626\) −19.0000 −0.759393
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −24.0000 −0.956943
\(630\) 3.00000 0.119523
\(631\) 30.0000 1.19428 0.597141 − 0.802137i \(-0.296303\pi\)
0.597141 + 0.802137i \(0.296303\pi\)
\(632\) 10.0000 0.397779
\(633\) 20.0000 0.794929
\(634\) 3.00000 0.119145
\(635\) −14.0000 −0.555573
\(636\) 10.0000 0.396526
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 10.0000 0.395594
\(640\) 1.00000 0.0395285
\(641\) 35.0000 1.38242 0.691208 − 0.722655i \(-0.257079\pi\)
0.691208 + 0.722655i \(0.257079\pi\)
\(642\) −7.00000 −0.276268
\(643\) −36.0000 −1.41970 −0.709851 − 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) −3.00000 −0.118217
\(645\) −11.0000 −0.433125
\(646\) −8.00000 −0.314756
\(647\) −24.0000 −0.943537 −0.471769 − 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 4.00000 0.156893
\(651\) 12.0000 0.470317
\(652\) 9.00000 0.352467
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) −16.0000 −0.625650
\(655\) −3.00000 −0.117220
\(656\) −1.00000 −0.0390434
\(657\) −9.00000 −0.351123
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 − 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 − 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) −19.0000 −0.738456
\(663\) −4.00000 −0.155347
\(664\) −6.00000 −0.232845
\(665\) −6.00000 −0.232670
\(666\) 6.00000 0.232495
\(667\) −9.00000 −0.348481
\(668\) 3.00000 0.116073
\(669\) 20.0000 0.773245
\(670\) 3.00000 0.115900
\(671\) 0 0
\(672\) 3.00000 0.115728
\(673\) 16.0000 0.616755 0.308377 − 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 2.00000 0.0770371
\(675\) 4.00000 0.153960
\(676\) 1.00000 0.0384615
\(677\) 22.0000 0.845529 0.422764 − 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 5.00000 0.192024
\(679\) 6.00000 0.230259
\(680\) 4.00000 0.153393
\(681\) 8.00000 0.306561
\(682\) 0 0
\(683\) 29.0000 1.10965 0.554827 − 0.831966i \(-0.312784\pi\)
0.554827 + 0.831966i \(0.312784\pi\)
\(684\) 2.00000 0.0764719
\(685\) 18.0000 0.687745
\(686\) 15.0000 0.572703
\(687\) −25.0000 −0.953809
\(688\) −11.0000 −0.419371
\(689\) −10.0000 −0.380970
\(690\) 1.00000 0.0380693
\(691\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 19.0000 0.722272
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 9.00000 0.341144
\(697\) −4.00000 −0.151511
\(698\) −20.0000 −0.757011
\(699\) 14.0000 0.529529
\(700\) −12.0000 −0.453557
\(701\) −35.0000 −1.32193 −0.660966 − 0.750416i \(-0.729853\pi\)
−0.660966 + 0.750416i \(0.729853\pi\)
\(702\) 1.00000 0.0377426
\(703\) −12.0000 −0.452589
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 30.0000 1.12827
\(708\) 3.00000 0.112747
\(709\) −39.0000 −1.46468 −0.732338 − 0.680941i \(-0.761571\pi\)
−0.732338 + 0.680941i \(0.761571\pi\)
\(710\) 10.0000 0.375293
\(711\) −10.0000 −0.375029
\(712\) 8.00000 0.299813
\(713\) 4.00000 0.149801
\(714\) 12.0000 0.449089
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) −5.00000 −0.186728
\(718\) 13.0000 0.485156
\(719\) −15.0000 −0.559406 −0.279703 − 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) −1.00000 −0.0372678
\(721\) −33.0000 −1.22898
\(722\) 15.0000 0.558242
\(723\) 2.00000 0.0743808
\(724\) 14.0000 0.520306
\(725\) −36.0000 −1.33701
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 − 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) −3.00000 −0.111187
\(729\) 1.00000 0.0370370
\(730\) −9.00000 −0.333105
\(731\) −44.0000 −1.62740
\(732\) 5.00000 0.184805
\(733\) 2.00000 0.0738717 0.0369358 − 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 32.0000 1.18114
\(735\) 2.00000 0.0737711
\(736\) 1.00000 0.0368605
\(737\) 0 0
\(738\) 1.00000 0.0368105
\(739\) 24.0000 0.882854 0.441427 − 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) 6.00000 0.220564
\(741\) −2.00000 −0.0734718
\(742\) 30.0000 1.10133
\(743\) −29.0000 −1.06391 −0.531953 − 0.846774i \(-0.678542\pi\)
−0.531953 + 0.846774i \(0.678542\pi\)
\(744\) −4.00000 −0.146647
\(745\) 4.00000 0.146549
\(746\) −11.0000 −0.402739
\(747\) 6.00000 0.219529
\(748\) 0 0
\(749\) −21.0000 −0.767323
\(750\) 9.00000 0.328634
\(751\) −53.0000 −1.93400 −0.966999 − 0.254781i \(-0.917997\pi\)
−0.966999 + 0.254781i \(0.917997\pi\)
\(752\) 0 0
\(753\) 6.00000 0.218652
\(754\) −9.00000 −0.327761
\(755\) 24.0000 0.873449
\(756\) −3.00000 −0.109109
\(757\) −2.00000 −0.0726912 −0.0363456 − 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −24.0000 −0.871719
\(759\) 0 0
\(760\) 2.00000 0.0725476
\(761\) −35.0000 −1.26875 −0.634375 − 0.773026i \(-0.718742\pi\)
−0.634375 + 0.773026i \(0.718742\pi\)
\(762\) 14.0000 0.507166
\(763\) −48.0000 −1.73772
\(764\) −15.0000 −0.542681
\(765\) −4.00000 −0.144620
\(766\) −14.0000 −0.505841
\(767\) −3.00000 −0.108324
\(768\) −1.00000 −0.0360844
\(769\) −49.0000 −1.76699 −0.883493 − 0.468445i \(-0.844814\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 25.0000 0.900353
\(772\) 6.00000 0.215945
\(773\) −2.00000 −0.0719350 −0.0359675 − 0.999353i \(-0.511451\pi\)
−0.0359675 + 0.999353i \(0.511451\pi\)
\(774\) 11.0000 0.395387
\(775\) 16.0000 0.574737
\(776\) −2.00000 −0.0717958
\(777\) 18.0000 0.645746
\(778\) 18.0000 0.645331
\(779\) −2.00000 −0.0716574
\(780\) 1.00000 0.0358057
\(781\) 0 0
\(782\) 4.00000 0.143040
\(783\) −9.00000 −0.321634
\(784\) 2.00000 0.0714286
\(785\) 22.0000 0.785214
\(786\) 3.00000 0.107006
\(787\) −44.0000 −1.56843 −0.784215 − 0.620489i \(-0.786934\pi\)
−0.784215 + 0.620489i \(0.786934\pi\)
\(788\) −12.0000 −0.427482
\(789\) −24.0000 −0.854423
\(790\) −10.0000 −0.355784
\(791\) 15.0000 0.533339
\(792\) 0 0
\(793\) −5.00000 −0.177555
\(794\) 19.0000 0.674285
\(795\) −10.0000 −0.354663
\(796\) 3.00000 0.106332
\(797\) 28.0000 0.991811 0.495905 − 0.868377i \(-0.334836\pi\)
0.495905 + 0.868377i \(0.334836\pi\)
\(798\) 6.00000 0.212398
\(799\) 0 0
\(800\) 4.00000 0.141421
\(801\) −8.00000 −0.282666
\(802\) 24.0000 0.847469
\(803\) 0 0
\(804\) −3.00000 −0.105802
\(805\) 3.00000 0.105736
\(806\) 4.00000 0.140894
\(807\) 4.00000 0.140807
\(808\) −10.0000 −0.351799
\(809\) 50.0000 1.75791 0.878953 − 0.476908i \(-0.158243\pi\)
0.878953 + 0.476908i \(0.158243\pi\)
\(810\) 1.00000 0.0351364
\(811\) −56.0000 −1.96643 −0.983213 − 0.182462i \(-0.941593\pi\)
−0.983213 + 0.182462i \(0.941593\pi\)
\(812\) 27.0000 0.947514
\(813\) −16.0000 −0.561144
\(814\) 0 0
\(815\) −9.00000 −0.315256
\(816\) −4.00000 −0.140028
\(817\) −22.0000 −0.769683
\(818\) 7.00000 0.244749
\(819\) 3.00000 0.104828
\(820\) 1.00000 0.0349215
\(821\) −34.0000 −1.18661 −0.593304 − 0.804978i \(-0.702177\pi\)
−0.593304 + 0.804978i \(0.702177\pi\)
\(822\) −18.0000 −0.627822
\(823\) 7.00000 0.244005 0.122002 − 0.992530i \(-0.461068\pi\)
0.122002 + 0.992530i \(0.461068\pi\)
\(824\) 11.0000 0.383203
\(825\) 0 0
\(826\) 9.00000 0.313150
\(827\) −28.0000 −0.973655 −0.486828 − 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −6.00000 −0.208389 −0.104194 − 0.994557i \(-0.533226\pi\)
−0.104194 + 0.994557i \(0.533226\pi\)
\(830\) 6.00000 0.208263
\(831\) 5.00000 0.173448
\(832\) 1.00000 0.0346688
\(833\) 8.00000 0.277184
\(834\) 0 0
\(835\) −3.00000 −0.103819
\(836\) 0 0
\(837\) 4.00000 0.138260
\(838\) 0 0
\(839\) 14.0000 0.483334 0.241667 − 0.970359i \(-0.422306\pi\)
0.241667 + 0.970359i \(0.422306\pi\)
\(840\) −3.00000 −0.103510
\(841\) 52.0000 1.79310
\(842\) −5.00000 −0.172311
\(843\) −29.0000 −0.998813
\(844\) −20.0000 −0.688428
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 0 0
\(848\) −10.0000 −0.343401
\(849\) −9.00000 −0.308879
\(850\) 16.0000 0.548795
\(851\) 6.00000 0.205677
\(852\) −10.0000 −0.342594
\(853\) −16.0000 −0.547830 −0.273915 − 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(854\) 15.0000 0.513289
\(855\) −2.00000 −0.0683986
\(856\) 7.00000 0.239255
\(857\) 12.0000 0.409912 0.204956 − 0.978771i \(-0.434295\pi\)
0.204956 + 0.978771i \(0.434295\pi\)
\(858\) 0 0
\(859\) 32.0000 1.09183 0.545913 − 0.837842i \(-0.316183\pi\)
0.545913 + 0.837842i \(0.316183\pi\)
\(860\) 11.0000 0.375097
\(861\) 3.00000 0.102240
\(862\) 16.0000 0.544962
\(863\) 32.0000 1.08929 0.544646 − 0.838666i \(-0.316664\pi\)
0.544646 + 0.838666i \(0.316664\pi\)
\(864\) 1.00000 0.0340207
\(865\) −19.0000 −0.646019
\(866\) −5.00000 −0.169907
\(867\) 1.00000 0.0339618
\(868\) −12.0000 −0.407307
\(869\) 0 0
\(870\) −9.00000 −0.305129
\(871\) 3.00000 0.101651
\(872\) 16.0000 0.541828
\(873\) 2.00000 0.0676897
\(874\) 2.00000 0.0676510
\(875\) 27.0000 0.912767
\(876\) 9.00000 0.304082
\(877\) −36.0000 −1.21563 −0.607817 − 0.794077i \(-0.707955\pi\)
−0.607817 + 0.794077i \(0.707955\pi\)
\(878\) −8.00000 −0.269987
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) 9.00000 0.303218 0.151609 − 0.988441i \(-0.451555\pi\)
0.151609 + 0.988441i \(0.451555\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 26.0000 0.874970 0.437485 − 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 4.00000 0.134535
\(885\) −3.00000 −0.100844
\(886\) 0 0
\(887\) 32.0000 1.07445 0.537227 − 0.843437i \(-0.319472\pi\)
0.537227 + 0.843437i \(0.319472\pi\)
\(888\) −6.00000 −0.201347
\(889\) 42.0000 1.40863
\(890\) −8.00000 −0.268161
\(891\) 0 0
\(892\) −20.0000 −0.669650
\(893\) 0 0
\(894\) −4.00000 −0.133780
\(895\) −12.0000 −0.401116
\(896\) −3.00000 −0.100223
\(897\) 1.00000 0.0333890
\(898\) 36.0000 1.20134
\(899\) −36.0000 −1.20067
\(900\) −4.00000 −0.133333
\(901\) −40.0000 −1.33259
\(902\) 0 0
\(903\) 33.0000 1.09817
\(904\) −5.00000 −0.166298
\(905\) −14.0000 −0.465376
\(906\) −24.0000 −0.797347
\(907\) −20.0000 −0.664089 −0.332045 − 0.943264i \(-0.607738\pi\)
−0.332045 + 0.943264i \(0.607738\pi\)
\(908\) −8.00000 −0.265489
\(909\) 10.0000 0.331679
\(910\) 3.00000 0.0994490
\(911\) −16.0000 −0.530104 −0.265052 − 0.964234i \(-0.585389\pi\)
−0.265052 + 0.964234i \(0.585389\pi\)
\(912\) −2.00000 −0.0662266
\(913\) 0 0
\(914\) −37.0000 −1.22385
\(915\) −5.00000 −0.165295
\(916\) 25.0000 0.826023
\(917\) 9.00000 0.297206
\(918\) 4.00000 0.132020
\(919\) −20.0000 −0.659739 −0.329870 − 0.944027i \(-0.607005\pi\)
−0.329870 + 0.944027i \(0.607005\pi\)
\(920\) −1.00000 −0.0329690
\(921\) −10.0000 −0.329511
\(922\) 24.0000 0.790398
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) 24.0000 0.789115
\(926\) 34.0000 1.11731
\(927\) −11.0000 −0.361287
\(928\) −9.00000 −0.295439
\(929\) −12.0000 −0.393707 −0.196854 − 0.980433i \(-0.563072\pi\)
−0.196854 + 0.980433i \(0.563072\pi\)
\(930\) 4.00000 0.131165
\(931\) 4.00000 0.131095
\(932\) −14.0000 −0.458585
\(933\) 8.00000 0.261908
\(934\) 0 0
\(935\) 0 0
\(936\) −1.00000 −0.0326860
\(937\) −20.0000 −0.653372 −0.326686 − 0.945133i \(-0.605932\pi\)
−0.326686 + 0.945133i \(0.605932\pi\)
\(938\) −9.00000 −0.293860
\(939\) −19.0000 −0.620042
\(940\) 0 0
\(941\) −24.0000 −0.782378 −0.391189 − 0.920310i \(-0.627936\pi\)
−0.391189 + 0.920310i \(0.627936\pi\)
\(942\) −22.0000 −0.716799
\(943\) 1.00000 0.0325645
\(944\) −3.00000 −0.0976417
\(945\) 3.00000 0.0975900
\(946\) 0 0
\(947\) 4.00000 0.129983 0.0649913 − 0.997886i \(-0.479298\pi\)
0.0649913 + 0.997886i \(0.479298\pi\)
\(948\) 10.0000 0.324785
\(949\) −9.00000 −0.292152
\(950\) 8.00000 0.259554
\(951\) 3.00000 0.0972817
\(952\) −12.0000 −0.388922
\(953\) −44.0000 −1.42530 −0.712650 − 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) 10.0000 0.323762
\(955\) 15.0000 0.485389
\(956\) 5.00000 0.161712
\(957\) 0 0
\(958\) −31.0000 −1.00156
\(959\) −54.0000 −1.74375
\(960\) 1.00000 0.0322749
\(961\) −15.0000 −0.483871
\(962\) 6.00000 0.193448
\(963\) −7.00000 −0.225572
\(964\) −2.00000 −0.0644157
\(965\) −6.00000 −0.193147
\(966\) −3.00000 −0.0965234
\(967\) 13.0000 0.418052 0.209026 − 0.977910i \(-0.432971\pi\)
0.209026 + 0.977910i \(0.432971\pi\)
\(968\) 0 0
\(969\) −8.00000 −0.256997
\(970\) 2.00000 0.0642161
\(971\) 34.0000 1.09111 0.545556 − 0.838074i \(-0.316319\pi\)
0.545556 + 0.838074i \(0.316319\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) 2.00000 0.0640841
\(975\) 4.00000 0.128103
\(976\) −5.00000 −0.160046
\(977\) −48.0000 −1.53566 −0.767828 − 0.640656i \(-0.778662\pi\)
−0.767828 + 0.640656i \(0.778662\pi\)
\(978\) 9.00000 0.287788
\(979\) 0 0
\(980\) −2.00000 −0.0638877
\(981\) −16.0000 −0.510841
\(982\) 29.0000 0.925427
\(983\) 38.0000 1.21201 0.606006 − 0.795460i \(-0.292771\pi\)
0.606006 + 0.795460i \(0.292771\pi\)
\(984\) −1.00000 −0.0318788
\(985\) 12.0000 0.382352
\(986\) −36.0000 −1.14647
\(987\) 0 0
\(988\) 2.00000 0.0636285
\(989\) 11.0000 0.349780
\(990\) 0 0
\(991\) −47.0000 −1.49300 −0.746502 − 0.665383i \(-0.768268\pi\)
−0.746502 + 0.665383i \(0.768268\pi\)
\(992\) 4.00000 0.127000
\(993\) −19.0000 −0.602947
\(994\) −30.0000 −0.951542
\(995\) −3.00000 −0.0951064
\(996\) −6.00000 −0.190117
\(997\) 37.0000 1.17180 0.585901 − 0.810383i \(-0.300741\pi\)
0.585901 + 0.810383i \(0.300741\pi\)
\(998\) −17.0000 −0.538126
\(999\) 6.00000 0.189832
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 9438.2.a.d.1.1 1
11.10 odd 2 858.2.a.g.1.1 ✓ 1
33.32 even 2 2574.2.a.i.1.1 1
44.43 even 2 6864.2.a.u.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
858.2.a.g.1.1 ✓ 1 11.10 odd 2
2574.2.a.i.1.1 1 33.32 even 2
6864.2.a.u.1.1 1 44.43 even 2
9438.2.a.d.1.1 1 1.1 even 1 trivial