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Properties

Label 9450.2.a.dh.1.1
Level $9450$
Weight $2$
Character 9450.1
Self dual yes
Analytic conductor $75.459$
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] = [9450,2,Mod(1,9450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9450, 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("9450.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9450.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: \(75.4586299101\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1890)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{11} -4.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +2.00000 q^{17} -2.00000 q^{19} -2.00000 q^{22} -2.00000 q^{23} -4.00000 q^{26} +1.00000 q^{28} -1.00000 q^{29} +3.00000 q^{31} +1.00000 q^{32} +2.00000 q^{34} +3.00000 q^{37} -2.00000 q^{38} -3.00000 q^{41} -8.00000 q^{43} -2.00000 q^{44} -2.00000 q^{46} -3.00000 q^{47} +1.00000 q^{49} -4.00000 q^{52} +2.00000 q^{53} +1.00000 q^{56} -1.00000 q^{58} +3.00000 q^{59} +5.00000 q^{61} +3.00000 q^{62} +1.00000 q^{64} -6.00000 q^{67} +2.00000 q^{68} +5.00000 q^{71} -7.00000 q^{73} +3.00000 q^{74} -2.00000 q^{76} -2.00000 q^{77} +4.00000 q^{79} -3.00000 q^{82} -12.0000 q^{83} -8.00000 q^{86} -2.00000 q^{88} -10.0000 q^{89} -4.00000 q^{91} -2.00000 q^{92} -3.00000 q^{94} -14.0000 q^{97} +1.00000 q^{98} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 − 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) −2.00000 −0.417029 −0.208514 − 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −1.00000 −0.185695 −0.0928477 − 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 3.00000 0.538816 0.269408 − 0.963026i \(-0.413172\pi\)
0.269408 + 0.963026i \(0.413172\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 0 0
\(37\) 3.00000 0.493197 0.246598 − 0.969118i \(-0.420687\pi\)
0.246598 + 0.969118i \(0.420687\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) 0 0
\(41\) −3.00000 −0.468521 −0.234261 − 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) −3.00000 −0.437595 −0.218797 − 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) 2.00000 0.274721 0.137361 − 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −1.00000 −0.131306
\(59\) 3.00000 0.390567 0.195283 − 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 − 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) 3.00000 0.381000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.00000 −0.733017 −0.366508 − 0.930415i \(-0.619447\pi\)
−0.366508 + 0.930415i \(0.619447\pi\)
\(68\) 2.00000 0.242536
\(69\) 0 0
\(70\) 0 0
\(71\) 5.00000 0.593391 0.296695 − 0.954972i \(-0.404115\pi\)
0.296695 + 0.954972i \(0.404115\pi\)
\(72\) 0 0
\(73\) −7.00000 −0.819288 −0.409644 − 0.912245i \(-0.634347\pi\)
−0.409644 + 0.912245i \(0.634347\pi\)
\(74\) 3.00000 0.348743
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 − 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −3.00000 −0.331295
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −8.00000 −0.862662
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) −10.0000 −1.06000 −0.529999 − 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) −2.00000 −0.208514
\(93\) 0 0
\(94\) −3.00000 −0.309426
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) −12.0000 −1.19404 −0.597022 − 0.802225i \(-0.703650\pi\)
−0.597022 + 0.802225i \(0.703650\pi\)
\(102\) 0 0
\(103\) −4.00000 −0.394132 −0.197066 − 0.980390i \(-0.563141\pi\)
−0.197066 + 0.980390i \(0.563141\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −9.00000 −0.870063 −0.435031 − 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 − 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −15.0000 −1.41108 −0.705541 − 0.708669i \(-0.749296\pi\)
−0.705541 + 0.708669i \(0.749296\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) 0 0
\(118\) 3.00000 0.276172
\(119\) 2.00000 0.183340
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 5.00000 0.452679
\(123\) 0 0
\(124\) 3.00000 0.269408
\(125\) 0 0
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 − 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 7.00000 0.611593 0.305796 − 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) 2.00000 0.171499
\(137\) −11.0000 −0.939793 −0.469897 − 0.882721i \(-0.655709\pi\)
−0.469897 + 0.882721i \(0.655709\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 − 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.00000 0.419591
\(143\) 8.00000 0.668994
\(144\) 0 0
\(145\) 0 0
\(146\) −7.00000 −0.579324
\(147\) 0 0
\(148\) 3.00000 0.246598
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 − 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) 0 0
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 − 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 4.00000 0.318223
\(159\) 0 0
\(160\) 0 0
\(161\) −2.00000 −0.157622
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −3.00000 −0.234261
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) −23.0000 −1.77979 −0.889897 − 0.456162i \(-0.849224\pi\)
−0.889897 + 0.456162i \(0.849224\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) −8.00000 −0.609994
\(173\) −9.00000 −0.684257 −0.342129 − 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) −10.0000 −0.749532
\(179\) 2.00000 0.149487 0.0747435 − 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) 3.00000 0.222988 0.111494 − 0.993765i \(-0.464436\pi\)
0.111494 + 0.993765i \(0.464436\pi\)
\(182\) −4.00000 −0.296500
\(183\) 0 0
\(184\) −2.00000 −0.147442
\(185\) 0 0
\(186\) 0 0
\(187\) −4.00000 −0.292509
\(188\) −3.00000 −0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −12.0000 −0.844317
\(203\) −1.00000 −0.0701862
\(204\) 0 0
\(205\) 0 0
\(206\) −4.00000 −0.278693
\(207\) 0 0
\(208\) −4.00000 −0.277350
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) −15.0000 −1.03264 −0.516321 − 0.856395i \(-0.672699\pi\)
−0.516321 + 0.856395i \(0.672699\pi\)
\(212\) 2.00000 0.137361
\(213\) 0 0
\(214\) −9.00000 −0.615227
\(215\) 0 0
\(216\) 0 0
\(217\) 3.00000 0.203653
\(218\) −4.00000 −0.270914
\(219\) 0 0
\(220\) 0 0
\(221\) −8.00000 −0.538138
\(222\) 0 0
\(223\) −26.0000 −1.74109 −0.870544 − 0.492090i \(-0.836233\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −15.0000 −0.997785
\(227\) −8.00000 −0.530979 −0.265489 − 0.964114i \(-0.585534\pi\)
−0.265489 + 0.964114i \(0.585534\pi\)
\(228\) 0 0
\(229\) 14.0000 0.925146 0.462573 − 0.886581i \(-0.346926\pi\)
0.462573 + 0.886581i \(0.346926\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.00000 −0.0656532
\(233\) 17.0000 1.11371 0.556854 − 0.830611i \(-0.312008\pi\)
0.556854 + 0.830611i \(0.312008\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.00000 0.195283
\(237\) 0 0
\(238\) 2.00000 0.129641
\(239\) 27.0000 1.74648 0.873242 − 0.487286i \(-0.162013\pi\)
0.873242 + 0.487286i \(0.162013\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 − 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) 5.00000 0.320092
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 3.00000 0.190500
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 4.00000 0.251478
\(254\) 13.0000 0.815693
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −20.0000 −1.24757 −0.623783 − 0.781598i \(-0.714405\pi\)
−0.623783 + 0.781598i \(0.714405\pi\)
\(258\) 0 0
\(259\) 3.00000 0.186411
\(260\) 0 0
\(261\) 0 0
\(262\) 7.00000 0.432461
\(263\) 8.00000 0.493301 0.246651 − 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −2.00000 −0.122628
\(267\) 0 0
\(268\) −6.00000 −0.366508
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −11.0000 −0.668202 −0.334101 − 0.942537i \(-0.608433\pi\)
−0.334101 + 0.942537i \(0.608433\pi\)
\(272\) 2.00000 0.121268
\(273\) 0 0
\(274\) −11.0000 −0.664534
\(275\) 0 0
\(276\) 0 0
\(277\) 2.00000 0.120168 0.0600842 − 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) 14.0000 0.839664
\(279\) 0 0
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 11.0000 0.653882 0.326941 − 0.945045i \(-0.393982\pi\)
0.326941 + 0.945045i \(0.393982\pi\)
\(284\) 5.00000 0.296695
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) −3.00000 −0.177084
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 0 0
\(292\) −7.00000 −0.409644
\(293\) −15.0000 −0.876309 −0.438155 − 0.898900i \(-0.644368\pi\)
−0.438155 + 0.898900i \(0.644368\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.00000 0.174371
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) −8.00000 −0.461112
\(302\) 4.00000 0.230174
\(303\) 0 0
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) 0 0
\(307\) 16.0000 0.913168 0.456584 − 0.889680i \(-0.349073\pi\)
0.456584 + 0.889680i \(0.349073\pi\)
\(308\) −2.00000 −0.113961
\(309\) 0 0
\(310\) 0 0
\(311\) −22.0000 −1.24751 −0.623753 − 0.781622i \(-0.714393\pi\)
−0.623753 + 0.781622i \(0.714393\pi\)
\(312\) 0 0
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) 34.0000 1.90963 0.954815 − 0.297200i \(-0.0960529\pi\)
0.954815 + 0.297200i \(0.0960529\pi\)
\(318\) 0 0
\(319\) 2.00000 0.111979
\(320\) 0 0
\(321\) 0 0
\(322\) −2.00000 −0.111456
\(323\) −4.00000 −0.222566
\(324\) 0 0
\(325\) 0 0
\(326\) 4.00000 0.221540
\(327\) 0 0
\(328\) −3.00000 −0.165647
\(329\) −3.00000 −0.165395
\(330\) 0 0
\(331\) −15.0000 −0.824475 −0.412237 − 0.911077i \(-0.635253\pi\)
−0.412237 + 0.911077i \(0.635253\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) −23.0000 −1.25850
\(335\) 0 0
\(336\) 0 0
\(337\) 36.0000 1.96104 0.980522 − 0.196407i \(-0.0629273\pi\)
0.980522 + 0.196407i \(0.0629273\pi\)
\(338\) 3.00000 0.163178
\(339\) 0 0
\(340\) 0 0
\(341\) −6.00000 −0.324918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −9.00000 −0.483843
\(347\) −7.00000 −0.375780 −0.187890 − 0.982190i \(-0.560165\pi\)
−0.187890 + 0.982190i \(0.560165\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 − 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −2.00000 −0.106449 −0.0532246 − 0.998583i \(-0.516950\pi\)
−0.0532246 + 0.998583i \(0.516950\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 2.00000 0.105703
\(359\) 24.0000 1.26667 0.633336 − 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 3.00000 0.157676
\(363\) 0 0
\(364\) −4.00000 −0.209657
\(365\) 0 0
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −2.00000 −0.104257
\(369\) 0 0
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) 31.0000 1.60512 0.802560 − 0.596572i \(-0.203471\pi\)
0.802560 + 0.596572i \(0.203471\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 4.00000 0.206010
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 − 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −8.00000 −0.409316
\(383\) −32.0000 −1.63512 −0.817562 − 0.575841i \(-0.804675\pi\)
−0.817562 + 0.575841i \(0.804675\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) 0 0
\(388\) −14.0000 −0.710742
\(389\) 23.0000 1.16615 0.583073 − 0.812420i \(-0.301850\pi\)
0.583073 + 0.812420i \(0.301850\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −18.0000 −0.906827
\(395\) 0 0
\(396\) 0 0
\(397\) 30.0000 1.50566 0.752828 − 0.658217i \(-0.228689\pi\)
0.752828 + 0.658217i \(0.228689\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −28.0000 −1.39825 −0.699127 − 0.714998i \(-0.746428\pi\)
−0.699127 + 0.714998i \(0.746428\pi\)
\(402\) 0 0
\(403\) −12.0000 −0.597763
\(404\) −12.0000 −0.597022
\(405\) 0 0
\(406\) −1.00000 −0.0496292
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −4.00000 −0.197066
\(413\) 3.00000 0.147620
\(414\) 0 0
\(415\) 0 0
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) 4.00000 0.195646
\(419\) 7.00000 0.341972 0.170986 − 0.985273i \(-0.445305\pi\)
0.170986 + 0.985273i \(0.445305\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 − 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) −15.0000 −0.730189
\(423\) 0 0
\(424\) 2.00000 0.0971286
\(425\) 0 0
\(426\) 0 0
\(427\) 5.00000 0.241967
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 0 0
\(431\) 15.0000 0.722525 0.361262 − 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 0 0
\(433\) −19.0000 −0.913082 −0.456541 − 0.889702i \(-0.650912\pi\)
−0.456541 + 0.889702i \(0.650912\pi\)
\(434\) 3.00000 0.144005
\(435\) 0 0
\(436\) −4.00000 −0.191565
\(437\) 4.00000 0.191346
\(438\) 0 0
\(439\) −32.0000 −1.52728 −0.763638 − 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −8.00000 −0.380521
\(443\) 15.0000 0.712672 0.356336 − 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −26.0000 −1.23114
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 16.0000 0.755087 0.377543 − 0.925992i \(-0.376769\pi\)
0.377543 + 0.925992i \(0.376769\pi\)
\(450\) 0 0
\(451\) 6.00000 0.282529
\(452\) −15.0000 −0.705541
\(453\) 0 0
\(454\) −8.00000 −0.375459
\(455\) 0 0
\(456\) 0 0
\(457\) 8.00000 0.374224 0.187112 − 0.982339i \(-0.440087\pi\)
0.187112 + 0.982339i \(0.440087\pi\)
\(458\) 14.0000 0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −20.0000 −0.931493 −0.465746 − 0.884918i \(-0.654214\pi\)
−0.465746 + 0.884918i \(0.654214\pi\)
\(462\) 0 0
\(463\) 27.0000 1.25480 0.627398 − 0.778699i \(-0.284120\pi\)
0.627398 + 0.778699i \(0.284120\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) 17.0000 0.787510
\(467\) −30.0000 −1.38823 −0.694117 − 0.719862i \(-0.744205\pi\)
−0.694117 + 0.719862i \(0.744205\pi\)
\(468\) 0 0
\(469\) −6.00000 −0.277054
\(470\) 0 0
\(471\) 0 0
\(472\) 3.00000 0.138086
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) 0 0
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) 27.0000 1.23495
\(479\) −20.0000 −0.913823 −0.456912 − 0.889512i \(-0.651044\pi\)
−0.456912 + 0.889512i \(0.651044\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) 0 0
\(487\) −1.00000 −0.0453143 −0.0226572 − 0.999743i \(-0.507213\pi\)
−0.0226572 + 0.999743i \(0.507213\pi\)
\(488\) 5.00000 0.226339
\(489\) 0 0
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 − 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 3.00000 0.134704
\(497\) 5.00000 0.224281
\(498\) 0 0
\(499\) 21.0000 0.940089 0.470045 − 0.882643i \(-0.344238\pi\)
0.470045 + 0.882643i \(0.344238\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 4.00000 0.178351 0.0891756 − 0.996016i \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 4.00000 0.177822
\(507\) 0 0
\(508\) 13.0000 0.576782
\(509\) −24.0000 −1.06378 −0.531891 − 0.846813i \(-0.678518\pi\)
−0.531891 + 0.846813i \(0.678518\pi\)
\(510\) 0 0
\(511\) −7.00000 −0.309662
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −20.0000 −0.882162
\(515\) 0 0
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 3.00000 0.131812
\(519\) 0 0
\(520\) 0 0
\(521\) −30.0000 −1.31432 −0.657162 − 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 0 0
\(523\) 20.0000 0.874539 0.437269 − 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 7.00000 0.305796
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 6.00000 0.261364
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 12.0000 0.519778
\(534\) 0 0
\(535\) 0 0
\(536\) −6.00000 −0.259161
\(537\) 0 0
\(538\) −6.00000 −0.258678
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) −11.0000 −0.472490
\(543\) 0 0
\(544\) 2.00000 0.0857493
\(545\) 0 0
\(546\) 0 0
\(547\) 24.0000 1.02617 0.513083 − 0.858339i \(-0.328503\pi\)
0.513083 + 0.858339i \(0.328503\pi\)
\(548\) −11.0000 −0.469897
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 0 0
\(559\) 32.0000 1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) −6.00000 −0.253095
\(563\) 8.00000 0.337160 0.168580 − 0.985688i \(-0.446082\pi\)
0.168580 + 0.985688i \(0.446082\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 11.0000 0.462364
\(567\) 0 0
\(568\) 5.00000 0.209795
\(569\) −14.0000 −0.586911 −0.293455 − 0.955973i \(-0.594805\pi\)
−0.293455 + 0.955973i \(0.594805\pi\)
\(570\) 0 0
\(571\) 31.0000 1.29731 0.648655 − 0.761083i \(-0.275332\pi\)
0.648655 + 0.761083i \(0.275332\pi\)
\(572\) 8.00000 0.334497
\(573\) 0 0
\(574\) −3.00000 −0.125218
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 − 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) −13.0000 −0.540729
\(579\) 0 0
\(580\) 0 0
\(581\) −12.0000 −0.497844
\(582\) 0 0
\(583\) −4.00000 −0.165663
\(584\) −7.00000 −0.289662
\(585\) 0 0
\(586\) −15.0000 −0.619644
\(587\) 24.0000 0.990586 0.495293 − 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −6.00000 −0.247226
\(590\) 0 0
\(591\) 0 0
\(592\) 3.00000 0.123299
\(593\) 36.0000 1.47834 0.739171 − 0.673517i \(-0.235217\pi\)
0.739171 + 0.673517i \(0.235217\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 0 0
\(598\) 8.00000 0.327144
\(599\) 9.00000 0.367730 0.183865 − 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) 0 0
\(601\) 4.00000 0.163163 0.0815817 − 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) −8.00000 −0.326056
\(603\) 0 0
\(604\) 4.00000 0.162758
\(605\) 0 0
\(606\) 0 0
\(607\) −28.0000 −1.13648 −0.568242 − 0.822861i \(-0.692376\pi\)
−0.568242 + 0.822861i \(0.692376\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −30.0000 −1.21169 −0.605844 − 0.795583i \(-0.707165\pi\)
−0.605844 + 0.795583i \(0.707165\pi\)
\(614\) 16.0000 0.645707
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) 29.0000 1.16750 0.583748 − 0.811935i \(-0.301586\pi\)
0.583748 + 0.811935i \(0.301586\pi\)
\(618\) 0 0
\(619\) 20.0000 0.803868 0.401934 − 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −22.0000 −0.882120
\(623\) −10.0000 −0.400642
\(624\) 0 0
\(625\) 0 0
\(626\) −6.00000 −0.239808
\(627\) 0 0
\(628\) 18.0000 0.718278
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) 38.0000 1.51276 0.756378 − 0.654135i \(-0.226967\pi\)
0.756378 + 0.654135i \(0.226967\pi\)
\(632\) 4.00000 0.159111
\(633\) 0 0
\(634\) 34.0000 1.35031
\(635\) 0 0
\(636\) 0 0
\(637\) −4.00000 −0.158486
\(638\) 2.00000 0.0791808
\(639\) 0 0
\(640\) 0 0
\(641\) −28.0000 −1.10593 −0.552967 − 0.833203i \(-0.686504\pi\)
−0.552967 + 0.833203i \(0.686504\pi\)
\(642\) 0 0
\(643\) 19.0000 0.749287 0.374643 − 0.927169i \(-0.377765\pi\)
0.374643 + 0.927169i \(0.377765\pi\)
\(644\) −2.00000 −0.0788110
\(645\) 0 0
\(646\) −4.00000 −0.157378
\(647\) −27.0000 −1.06148 −0.530740 − 0.847535i \(-0.678086\pi\)
−0.530740 + 0.847535i \(0.678086\pi\)
\(648\) 0 0
\(649\) −6.00000 −0.235521
\(650\) 0 0
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −22.0000 −0.860927 −0.430463 − 0.902608i \(-0.641650\pi\)
−0.430463 + 0.902608i \(0.641650\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −3.00000 −0.117130
\(657\) 0 0
\(658\) −3.00000 −0.116952
\(659\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(660\) 0 0
\(661\) 29.0000 1.12797 0.563985 − 0.825785i \(-0.309268\pi\)
0.563985 + 0.825785i \(0.309268\pi\)
\(662\) −15.0000 −0.582992
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 0 0
\(667\) 2.00000 0.0774403
\(668\) −23.0000 −0.889897
\(669\) 0 0
\(670\) 0 0
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) −6.00000 −0.231283 −0.115642 − 0.993291i \(-0.536892\pi\)
−0.115642 + 0.993291i \(0.536892\pi\)
\(674\) 36.0000 1.38667
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −11.0000 −0.422764 −0.211382 − 0.977403i \(-0.567796\pi\)
−0.211382 + 0.977403i \(0.567796\pi\)
\(678\) 0 0
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) 0 0
\(682\) −6.00000 −0.229752
\(683\) 39.0000 1.49229 0.746147 − 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −8.00000 −0.304997
\(689\) −8.00000 −0.304776
\(690\) 0 0
\(691\) −30.0000 −1.14125 −0.570627 − 0.821209i \(-0.693300\pi\)
−0.570627 + 0.821209i \(0.693300\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) −7.00000 −0.265716
\(695\) 0 0
\(696\) 0 0
\(697\) −6.00000 −0.227266
\(698\) 26.0000 0.984115
\(699\) 0 0
\(700\) 0 0
\(701\) 3.00000 0.113308 0.0566542 − 0.998394i \(-0.481957\pi\)
0.0566542 + 0.998394i \(0.481957\pi\)
\(702\) 0 0
\(703\) −6.00000 −0.226294
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) −2.00000 −0.0752710
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) −14.0000 −0.525781 −0.262891 − 0.964826i \(-0.584676\pi\)
−0.262891 + 0.964826i \(0.584676\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.0000 −0.374766
\(713\) −6.00000 −0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 2.00000 0.0747435
\(717\) 0 0
\(718\) 24.0000 0.895672
\(719\) 22.0000 0.820462 0.410231 − 0.911982i \(-0.365448\pi\)
0.410231 + 0.911982i \(0.365448\pi\)
\(720\) 0 0
\(721\) −4.00000 −0.148968
\(722\) −15.0000 −0.558242
\(723\) 0 0
\(724\) 3.00000 0.111494
\(725\) 0 0
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 − 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) −4.00000 −0.148250
\(729\) 0 0
\(730\) 0 0
\(731\) −16.0000 −0.591781
\(732\) 0 0
\(733\) −4.00000 −0.147743 −0.0738717 − 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) −2.00000 −0.0737210
\(737\) 12.0000 0.442026
\(738\) 0 0
\(739\) 29.0000 1.06678 0.533391 − 0.845869i \(-0.320917\pi\)
0.533391 + 0.845869i \(0.320917\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 2.00000 0.0734223
\(743\) −42.0000 −1.54083 −0.770415 − 0.637542i \(-0.779951\pi\)
−0.770415 + 0.637542i \(0.779951\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 31.0000 1.13499
\(747\) 0 0
\(748\) −4.00000 −0.146254
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) 22.0000 0.802791 0.401396 − 0.915905i \(-0.368525\pi\)
0.401396 + 0.915905i \(0.368525\pi\)
\(752\) −3.00000 −0.109399
\(753\) 0 0
\(754\) 4.00000 0.145671
\(755\) 0 0
\(756\) 0 0
\(757\) 17.0000 0.617876 0.308938 − 0.951082i \(-0.400027\pi\)
0.308938 + 0.951082i \(0.400027\pi\)
\(758\) −17.0000 −0.617468
\(759\) 0 0
\(760\) 0 0
\(761\) −13.0000 −0.471250 −0.235625 − 0.971844i \(-0.575714\pi\)
−0.235625 + 0.971844i \(0.575714\pi\)
\(762\) 0 0
\(763\) −4.00000 −0.144810
\(764\) −8.00000 −0.289430
\(765\) 0 0
\(766\) −32.0000 −1.15621
\(767\) −12.0000 −0.433295
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 − 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −14.0000 −0.503871
\(773\) 31.0000 1.11499 0.557496 − 0.830179i \(-0.311762\pi\)
0.557496 + 0.830179i \(0.311762\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −14.0000 −0.502571
\(777\) 0 0
\(778\) 23.0000 0.824590
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) −10.0000 −0.357828
\(782\) −4.00000 −0.143040
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 1.00000 0.0356462 0.0178231 − 0.999841i \(-0.494326\pi\)
0.0178231 + 0.999841i \(0.494326\pi\)
\(788\) −18.0000 −0.641223
\(789\) 0 0
\(790\) 0 0
\(791\) −15.0000 −0.533339
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) 30.0000 1.06466
\(795\) 0 0
\(796\) 0 0
\(797\) 15.0000 0.531327 0.265664 − 0.964066i \(-0.414409\pi\)
0.265664 + 0.964066i \(0.414409\pi\)
\(798\) 0 0
\(799\) −6.00000 −0.212265
\(800\) 0 0
\(801\) 0 0
\(802\) −28.0000 −0.988714
\(803\) 14.0000 0.494049
\(804\) 0 0
\(805\) 0 0
\(806\) −12.0000 −0.422682
\(807\) 0 0
\(808\) −12.0000 −0.422159
\(809\) −50.0000 −1.75791 −0.878953 − 0.476908i \(-0.841757\pi\)
−0.878953 + 0.476908i \(0.841757\pi\)
\(810\) 0 0
\(811\) 40.0000 1.40459 0.702295 − 0.711886i \(-0.252159\pi\)
0.702295 + 0.711886i \(0.252159\pi\)
\(812\) −1.00000 −0.0350931
\(813\) 0 0
\(814\) −6.00000 −0.210300
\(815\) 0 0
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 0 0
\(821\) −10.0000 −0.349002 −0.174501 − 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) 0 0
\(823\) −39.0000 −1.35945 −0.679727 − 0.733465i \(-0.737902\pi\)
−0.679727 + 0.733465i \(0.737902\pi\)
\(824\) −4.00000 −0.139347
\(825\) 0 0
\(826\) 3.00000 0.104383
\(827\) −17.0000 −0.591148 −0.295574 − 0.955320i \(-0.595511\pi\)
−0.295574 + 0.955320i \(0.595511\pi\)
\(828\) 0 0
\(829\) 30.0000 1.04194 0.520972 − 0.853574i \(-0.325570\pi\)
0.520972 + 0.853574i \(0.325570\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −4.00000 −0.138675
\(833\) 2.00000 0.0692959
\(834\) 0 0
\(835\) 0 0
\(836\) 4.00000 0.138343
\(837\) 0 0
\(838\) 7.00000 0.241811
\(839\) 16.0000 0.552381 0.276191 − 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) −2.00000 −0.0689246
\(843\) 0 0
\(844\) −15.0000 −0.516321
\(845\) 0 0
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 2.00000 0.0686803
\(849\) 0 0
\(850\) 0 0
\(851\) −6.00000 −0.205677
\(852\) 0 0
\(853\) −34.0000 −1.16414 −0.582069 − 0.813139i \(-0.697757\pi\)
−0.582069 + 0.813139i \(0.697757\pi\)
\(854\) 5.00000 0.171096
\(855\) 0 0
\(856\) −9.00000 −0.307614
\(857\) −40.0000 −1.36637 −0.683187 − 0.730243i \(-0.739407\pi\)
−0.683187 + 0.730243i \(0.739407\pi\)
\(858\) 0 0
\(859\) 10.0000 0.341196 0.170598 − 0.985341i \(-0.445430\pi\)
0.170598 + 0.985341i \(0.445430\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) −52.0000 −1.77010 −0.885050 − 0.465495i \(-0.845876\pi\)
−0.885050 + 0.465495i \(0.845876\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −19.0000 −0.645646
\(867\) 0 0
\(868\) 3.00000 0.101827
\(869\) −8.00000 −0.271381
\(870\) 0 0
\(871\) 24.0000 0.813209
\(872\) −4.00000 −0.135457
\(873\) 0 0
\(874\) 4.00000 0.135302
\(875\) 0 0
\(876\) 0 0
\(877\) −23.0000 −0.776655 −0.388327 − 0.921521i \(-0.626947\pi\)
−0.388327 + 0.921521i \(0.626947\pi\)
\(878\) −32.0000 −1.07995
\(879\) 0 0
\(880\) 0 0
\(881\) 37.0000 1.24656 0.623281 − 0.781998i \(-0.285799\pi\)
0.623281 + 0.781998i \(0.285799\pi\)
\(882\) 0 0
\(883\) 28.0000 0.942275 0.471138 − 0.882060i \(-0.343844\pi\)
0.471138 + 0.882060i \(0.343844\pi\)
\(884\) −8.00000 −0.269069
\(885\) 0 0
\(886\) 15.0000 0.503935
\(887\) −55.0000 −1.84672 −0.923360 − 0.383936i \(-0.874568\pi\)
−0.923360 + 0.383936i \(0.874568\pi\)
\(888\) 0 0
\(889\) 13.0000 0.436006
\(890\) 0 0
\(891\) 0 0
\(892\) −26.0000 −0.870544
\(893\) 6.00000 0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 16.0000 0.533927
\(899\) −3.00000 −0.100056
\(900\) 0 0
\(901\) 4.00000 0.133259
\(902\) 6.00000 0.199778
\(903\) 0 0
\(904\) −15.0000 −0.498893
\(905\) 0 0
\(906\) 0 0
\(907\) 32.0000 1.06254 0.531271 − 0.847202i \(-0.321714\pi\)
0.531271 + 0.847202i \(0.321714\pi\)
\(908\) −8.00000 −0.265489
\(909\) 0 0
\(910\) 0 0
\(911\) −11.0000 −0.364446 −0.182223 − 0.983257i \(-0.558329\pi\)
−0.182223 + 0.983257i \(0.558329\pi\)
\(912\) 0 0
\(913\) 24.0000 0.794284
\(914\) 8.00000 0.264616
\(915\) 0 0
\(916\) 14.0000 0.462573
\(917\) 7.00000 0.231160
\(918\) 0 0
\(919\) −14.0000 −0.461817 −0.230909 − 0.972975i \(-0.574170\pi\)
−0.230909 + 0.972975i \(0.574170\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −20.0000 −0.658665
\(923\) −20.0000 −0.658308
\(924\) 0 0
\(925\) 0 0
\(926\) 27.0000 0.887275
\(927\) 0 0
\(928\) −1.00000 −0.0328266
\(929\) 50.0000 1.64045 0.820223 − 0.572043i \(-0.193849\pi\)
0.820223 + 0.572043i \(0.193849\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 17.0000 0.556854
\(933\) 0 0
\(934\) −30.0000 −0.981630
\(935\) 0 0
\(936\) 0 0
\(937\) −43.0000 −1.40475 −0.702374 − 0.711808i \(-0.747877\pi\)
−0.702374 + 0.711808i \(0.747877\pi\)
\(938\) −6.00000 −0.195907
\(939\) 0 0
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 6.00000 0.195387
\(944\) 3.00000 0.0976417
\(945\) 0 0
\(946\) 16.0000 0.520205
\(947\) 52.0000 1.68977 0.844886 − 0.534946i \(-0.179668\pi\)
0.844886 + 0.534946i \(0.179668\pi\)
\(948\) 0 0
\(949\) 28.0000 0.908918
\(950\) 0 0
\(951\) 0 0
\(952\) 2.00000 0.0648204
\(953\) 38.0000 1.23094 0.615470 − 0.788160i \(-0.288966\pi\)
0.615470 + 0.788160i \(0.288966\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 27.0000 0.873242
\(957\) 0 0
\(958\) −20.0000 −0.646171
\(959\) −11.0000 −0.355209
\(960\) 0 0
\(961\) −22.0000 −0.709677
\(962\) −12.0000 −0.386896
\(963\) 0 0
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) 23.0000 0.739630 0.369815 − 0.929105i \(-0.379421\pi\)
0.369815 + 0.929105i \(0.379421\pi\)
\(968\) −7.00000 −0.224989
\(969\) 0 0
\(970\) 0 0
\(971\) 17.0000 0.545556 0.272778 − 0.962077i \(-0.412058\pi\)
0.272778 + 0.962077i \(0.412058\pi\)
\(972\) 0 0
\(973\) 14.0000 0.448819
\(974\) −1.00000 −0.0320421
\(975\) 0 0
\(976\) 5.00000 0.160046
\(977\) 18.0000 0.575871 0.287936 − 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) 20.0000 0.639203
\(980\) 0 0
\(981\) 0 0
\(982\) −24.0000 −0.765871
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −2.00000 −0.0636930
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 58.0000 1.84243 0.921215 − 0.389053i \(-0.127198\pi\)
0.921215 + 0.389053i \(0.127198\pi\)
\(992\) 3.00000 0.0952501
\(993\) 0 0
\(994\) 5.00000 0.158590
\(995\) 0 0
\(996\) 0 0
\(997\) −22.0000 −0.696747 −0.348373 − 0.937356i \(-0.613266\pi\)
−0.348373 + 0.937356i \(0.613266\pi\)
\(998\) 21.0000 0.664743
\(999\) 0 0
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 9450.2.a.dh.1.1 1
3.2 odd 2 9450.2.a.bs.1.1 1
5.4 even 2 1890.2.a.a.1.1 ✓ 1
15.14 odd 2 1890.2.a.v.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1890.2.a.a.1.1 ✓ 1 5.4 even 2
1890.2.a.v.1.1 yes 1 15.14 odd 2
9450.2.a.bs.1.1 1 3.2 odd 2
9450.2.a.dh.1.1 1 1.1 even 1 trivial