Properties

Label 980.2.c.b.979.2
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $8$
CM discriminant -20
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(979,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.979");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3317760000.3
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 979.2
Root \(1.72286 - 0.178197i\) of defining polynomial
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.b.979.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421 q^{2} -0.356394i q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.504017i q^{6} -2.82843 q^{8} +2.87298 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -0.356394i q^{3} +2.00000 q^{4} +2.23607i q^{5} +0.504017i q^{6} -2.82843 q^{8} +2.87298 q^{9} -3.16228i q^{10} -0.712788i q^{12} +0.796921 q^{15} +4.00000 q^{16} -4.06301 q^{18} +4.47214i q^{20} +7.50873 q^{23} +1.00803i q^{24} -5.00000 q^{25} -2.09310i q^{27} +4.74597 q^{29} -1.12702 q^{30} -5.65685 q^{32} +5.74597 q^{36} -6.32456i q^{40} +12.6284i q^{41} -9.10257 q^{43} +6.42419i q^{45} -10.6190 q^{46} +9.48683i q^{47} -1.42558i q^{48} +7.07107 q^{50} +2.96008i q^{54} -6.71181 q^{58} +1.59384 q^{60} -13.6364i q^{61} +8.00000 q^{64} +15.8144 q^{67} -2.67607i q^{69} -8.12602 q^{72} +1.78197i q^{75} +8.94427i q^{80} +7.87298 q^{81} -17.8592i q^{82} +18.2156i q^{83} +12.8730 q^{86} -1.69143i q^{87} +14.1404i q^{89} -9.08517i q^{90} +15.0175 q^{92} -13.4164i q^{94} +2.01607i q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 16 q^{4} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 16 q^{4} - 8 q^{9} + 32 q^{16} - 40 q^{25} - 24 q^{29} - 40 q^{30} - 16 q^{36} + 8 q^{46} + 64 q^{64} + 32 q^{81} + 72 q^{86}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −1.00000
\(3\) − 0.356394i − 0.205764i −0.994694 0.102882i \(-0.967194\pi\)
0.994694 0.102882i \(-0.0328064\pi\)
\(4\) 2.00000 1.00000
\(5\) 2.23607i 1.00000i
\(6\) 0.504017i 0.205764i
\(7\) 0 0
\(8\) −2.82843 −1.00000
\(9\) 2.87298 0.957661
\(10\) − 3.16228i − 1.00000i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) − 0.712788i − 0.205764i
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0.796921 0.205764
\(16\) 4.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −4.06301 −0.957661
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 4.47214i 1.00000i
\(21\) 0 0
\(22\) 0 0
\(23\) 7.50873 1.56568 0.782839 0.622224i \(-0.213771\pi\)
0.782839 + 0.622224i \(0.213771\pi\)
\(24\) 1.00803i 0.205764i
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) − 2.09310i − 0.402816i
\(28\) 0 0
\(29\) 4.74597 0.881304 0.440652 0.897678i \(-0.354747\pi\)
0.440652 + 0.897678i \(0.354747\pi\)
\(30\) −1.12702 −0.205764
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.65685 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 5.74597 0.957661
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) − 6.32456i − 1.00000i
\(41\) 12.6284i 1.97222i 0.166092 + 0.986110i \(0.446885\pi\)
−0.166092 + 0.986110i \(0.553115\pi\)
\(42\) 0 0
\(43\) −9.10257 −1.38813 −0.694065 0.719913i \(-0.744182\pi\)
−0.694065 + 0.719913i \(0.744182\pi\)
\(44\) 0 0
\(45\) 6.42419i 0.957661i
\(46\) −10.6190 −1.56568
\(47\) 9.48683i 1.38380i 0.721995 + 0.691898i \(0.243225\pi\)
−0.721995 + 0.691898i \(0.756775\pi\)
\(48\) − 1.42558i − 0.205764i
\(49\) 0 0
\(50\) 7.07107 1.00000
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 2.96008i 0.402816i
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −6.71181 −0.881304
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.59384 0.205764
\(61\) − 13.6364i − 1.74596i −0.487753 0.872982i \(-0.662183\pi\)
0.487753 0.872982i \(-0.337817\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 15.8144 1.93203 0.966017 0.258478i \(-0.0832208\pi\)
0.966017 + 0.258478i \(0.0832208\pi\)
\(68\) 0 0
\(69\) − 2.67607i − 0.322161i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −8.12602 −0.957661
\(73\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 1.78197i 0.205764i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) 8.94427i 1.00000i
\(81\) 7.87298 0.874776
\(82\) − 17.8592i − 1.97222i
\(83\) 18.2156i 1.99942i 0.0240199 + 0.999711i \(0.492353\pi\)
−0.0240199 + 0.999711i \(0.507647\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 12.8730 1.38813
\(87\) − 1.69143i − 0.181341i
\(88\) 0 0
\(89\) 14.1404i 1.49888i 0.662071 + 0.749441i \(0.269678\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) − 9.08517i − 0.957661i
\(91\) 0 0
\(92\) 15.0175 1.56568
\(93\) 0 0
\(94\) − 13.4164i − 1.38380i
\(95\) 0 0
\(96\) 2.01607i 0.205764i
\(97\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −10.0000 −1.00000
\(101\) − 11.1163i − 1.10612i −0.833143 0.553058i \(-0.813461\pi\)
0.833143 0.553058i \(-0.186539\pi\)
\(102\) 0 0
\(103\) 18.9284i 1.86507i 0.361079 + 0.932535i \(0.382408\pi\)
−0.361079 + 0.932535i \(0.617592\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 17.4082 1.68292 0.841458 0.540322i \(-0.181698\pi\)
0.841458 + 0.540322i \(0.181698\pi\)
\(108\) − 4.18619i − 0.402816i
\(109\) −3.61895 −0.346633 −0.173316 0.984866i \(-0.555448\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 16.7900i 1.56568i
\(116\) 9.49193 0.881304
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) −2.25403 −0.205764
\(121\) 11.0000 1.00000
\(122\) 19.2848i 1.74596i
\(123\) 4.50068 0.405812
\(124\) 0 0
\(125\) − 11.1803i − 1.00000i
\(126\) 0 0
\(127\) 4.24264 0.376473 0.188237 0.982124i \(-0.439723\pi\)
0.188237 + 0.982124i \(0.439723\pi\)
\(128\) −11.3137 −1.00000
\(129\) 3.24410i 0.285627i
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −22.3649 −1.93203
\(135\) 4.68030 0.402816
\(136\) 0 0
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 3.78453i 0.322161i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 3.38105 0.284736
\(142\) 0 0
\(143\) 0 0
\(144\) 11.4919 0.957661
\(145\) 10.6123i 0.881304i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −8.12702 −0.665791 −0.332896 0.942964i \(-0.608026\pi\)
−0.332896 + 0.942964i \(0.608026\pi\)
\(150\) − 2.52009i − 0.205764i
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) − 12.6491i − 1.00000i
\(161\) 0 0
\(162\) −11.1341 −0.874776
\(163\) −12.7279 −0.996928 −0.498464 0.866910i \(-0.666102\pi\)
−0.498464 + 0.866910i \(0.666102\pi\)
\(164\) 25.2567i 1.97222i
\(165\) 0 0
\(166\) − 25.7608i − 1.99942i
\(167\) − 16.0772i − 1.24409i −0.782980 0.622047i \(-0.786301\pi\)
0.782980 0.622047i \(-0.213699\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) −18.2051 −1.38813
\(173\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(174\) 2.39205i 0.181341i
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) − 19.9976i − 1.49888i
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 12.8484i 0.957661i
\(181\) − 15.1485i − 1.12598i −0.826465 0.562988i \(-0.809652\pi\)
0.826465 0.562988i \(-0.190348\pi\)
\(182\) 0 0
\(183\) −4.85993 −0.359257
\(184\) −21.2379 −1.56568
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 18.9737i 1.38380i
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) − 2.85115i − 0.205764i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 14.1421 1.00000
\(201\) − 5.63615i − 0.397543i
\(202\) 15.7209i 1.10612i
\(203\) 0 0
\(204\) 0 0
\(205\) −28.2379 −1.97222
\(206\) − 26.7688i − 1.86507i
\(207\) 21.5725 1.49939
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −24.6190 −1.68292
\(215\) − 20.3540i − 1.38813i
\(216\) 5.92017i 0.402816i
\(217\) 0 0
\(218\) 5.11797 0.346633
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) − 3.16228i − 0.211762i −0.994379 0.105881i \(-0.966234\pi\)
0.994379 0.105881i \(-0.0337662\pi\)
\(224\) 0 0
\(225\) −14.3649 −0.957661
\(226\) 0 0
\(227\) − 28.4605i − 1.88899i −0.328526 0.944495i \(-0.606552\pi\)
0.328526 0.944495i \(-0.393448\pi\)
\(228\) 0 0
\(229\) − 26.8328i − 1.77316i −0.462573 0.886581i \(-0.653074\pi\)
0.462573 0.886581i \(-0.346926\pi\)
\(230\) − 23.7447i − 1.56568i
\(231\) 0 0
\(232\) −13.4236 −0.881304
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) −21.2132 −1.38380
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 3.18768 0.205764
\(241\) − 13.4164i − 0.864227i −0.901819 0.432113i \(-0.857768\pi\)
0.901819 0.432113i \(-0.142232\pi\)
\(242\) −15.5563 −1.00000
\(243\) − 9.08517i − 0.582814i
\(244\) − 27.2728i − 1.74596i
\(245\) 0 0
\(246\) −6.36492 −0.405812
\(247\) 0 0
\(248\) 0 0
\(249\) 6.49193 0.411410
\(250\) 15.8114i 1.00000i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −6.00000 −0.376473
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) − 4.58785i − 0.285627i
\(259\) 0 0
\(260\) 0 0
\(261\) 13.6351 0.843990
\(262\) 0 0
\(263\) −32.4257 −1.99945 −0.999727 0.0233719i \(-0.992560\pi\)
−0.999727 + 0.0233719i \(0.992560\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 5.03956 0.308416
\(268\) 31.6288 1.93203
\(269\) 9.60427i 0.585583i 0.956176 + 0.292791i \(0.0945841\pi\)
−0.956176 + 0.292791i \(0.905416\pi\)
\(270\) −6.61895 −0.402816
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) − 5.35213i − 0.322161i
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) −4.78153 −0.284736
\(283\) 15.8114i 0.939889i 0.882696 + 0.469945i \(0.155726\pi\)
−0.882696 + 0.469945i \(0.844274\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −16.2520 −0.957661
\(289\) −17.0000 −1.00000
\(290\) − 15.0081i − 0.881304i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 11.4933 0.665791
\(299\) 0 0
\(300\) 3.56394i 0.205764i
\(301\) 0 0
\(302\) 0 0
\(303\) −3.96179 −0.227599
\(304\) 0 0
\(305\) 30.4919 1.74596
\(306\) 0 0
\(307\) − 21.0668i − 1.20234i −0.799120 0.601172i \(-0.794701\pi\)
0.799120 0.601172i \(-0.205299\pi\)
\(308\) 0 0
\(309\) 6.74597 0.383765
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 17.8885i 1.00000i
\(321\) − 6.20419i − 0.346284i
\(322\) 0 0
\(323\) 0 0
\(324\) 15.7460 0.874776
\(325\) 0 0
\(326\) 18.0000 0.996928
\(327\) 1.28977i 0.0713246i
\(328\) − 35.7184i − 1.97222i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 36.4312i 1.99942i
\(333\) 0 0
\(334\) 22.7367i 1.24409i
\(335\) 35.3620i 1.93203i
\(336\) 0 0
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 18.3848 1.00000
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 25.7460 1.38813
\(345\) 5.98387 0.322161
\(346\) 0 0
\(347\) −12.6267 −0.677837 −0.338918 0.940816i \(-0.610061\pi\)
−0.338918 + 0.940816i \(0.610061\pi\)
\(348\) − 3.38287i − 0.181341i
\(349\) 9.10025i 0.487125i 0.969885 + 0.243563i \(0.0783162\pi\)
−0.969885 + 0.243563i \(0.921684\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 28.2808i 1.49888i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) − 18.1703i − 0.957661i
\(361\) −19.0000 −1.00000
\(362\) 21.4232i 1.12598i
\(363\) − 3.92033i − 0.205764i
\(364\) 0 0
\(365\) 0 0
\(366\) 6.87298 0.359257
\(367\) − 34.6493i − 1.80868i −0.426817 0.904338i \(-0.640365\pi\)
0.426817 0.904338i \(-0.359635\pi\)
\(368\) 30.0349 1.56568
\(369\) 36.2811i 1.88872i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) −3.98461 −0.205764
\(376\) − 26.8328i − 1.38380i
\(377\) 0 0
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) − 1.51205i − 0.0774647i
\(382\) 0 0
\(383\) − 37.5004i − 1.91618i −0.286466 0.958091i \(-0.592480\pi\)
0.286466 0.958091i \(-0.407520\pi\)
\(384\) 4.03214i 0.205764i
\(385\) 0 0
\(386\) 0 0
\(387\) −26.1515 −1.32936
\(388\) 0 0
\(389\) −24.0000 −1.21685 −0.608424 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −20.0000 −1.00000
\(401\) 39.9839 1.99670 0.998350 0.0574304i \(-0.0182907\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 7.97072i 0.397543i
\(403\) 0 0
\(404\) − 22.2326i − 1.10612i
\(405\) 17.6045i 0.874776i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 16.6605i 0.823809i 0.911227 + 0.411905i \(0.135136\pi\)
−0.911227 + 0.411905i \(0.864864\pi\)
\(410\) 39.9344 1.97222
\(411\) 0 0
\(412\) 37.8568i 1.86507i
\(413\) 0 0
\(414\) −30.5081 −1.49939
\(415\) −40.7313 −1.99942
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 38.8569 1.89377 0.946883 0.321577i \(-0.104213\pi\)
0.946883 + 0.321577i \(0.104213\pi\)
\(422\) 0 0
\(423\) 27.2555i 1.32521i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 34.8165 1.68292
\(429\) 0 0
\(430\) 28.7849i 1.38813i
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) − 8.37238i − 0.402816i
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 3.78216 0.181341
\(436\) −7.23790 −0.346633
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.2903 −0.583928 −0.291964 0.956429i \(-0.594309\pi\)
−0.291964 + 0.956429i \(0.594309\pi\)
\(444\) 0 0
\(445\) −31.6190 −1.49888
\(446\) 4.47214i 0.211762i
\(447\) 2.89642i 0.136996i
\(448\) 0 0
\(449\) −1.36492 −0.0644144 −0.0322072 0.999481i \(-0.510254\pi\)
−0.0322072 + 0.999481i \(0.510254\pi\)
\(450\) 20.3151 0.957661
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 40.2492i 1.88899i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 37.9473i 1.77316i
\(459\) 0 0
\(460\) 33.5801i 1.56568i
\(461\) 8.94427i 0.416576i 0.978068 + 0.208288i \(0.0667892\pi\)
−0.978068 + 0.208288i \(0.933211\pi\)
\(462\) 0 0
\(463\) 29.2380 1.35881 0.679403 0.733766i \(-0.262239\pi\)
0.679403 + 0.733766i \(0.262239\pi\)
\(464\) 18.9839 0.881304
\(465\) 0 0
\(466\) 0 0
\(467\) 13.9389i 0.645015i 0.946567 + 0.322507i \(0.104526\pi\)
−0.946567 + 0.322507i \(0.895474\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 30.0000 1.38380
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −4.50807 −0.205764
\(481\) 0 0
\(482\) 18.9737i 0.864227i
\(483\) 0 0
\(484\) 22.0000 1.00000
\(485\) 0 0
\(486\) 12.8484i 0.582814i
\(487\) 38.1838 1.73027 0.865136 0.501538i \(-0.167232\pi\)
0.865136 + 0.501538i \(0.167232\pi\)
\(488\) 38.5696i 1.74596i
\(489\) 4.53615i 0.205132i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 9.00135 0.405812
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −9.18098 −0.411410
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) − 22.3607i − 1.00000i
\(501\) −5.72983 −0.255990
\(502\) 0 0
\(503\) − 33.2237i − 1.48137i −0.671852 0.740685i \(-0.734501\pi\)
0.671852 0.740685i \(-0.265499\pi\)
\(504\) 0 0
\(505\) 24.8569 1.10612
\(506\) 0 0
\(507\) 4.63312i 0.205764i
\(508\) 8.48528 0.376473
\(509\) − 17.1645i − 0.760804i −0.924821 0.380402i \(-0.875786\pi\)
0.924821 0.380402i \(-0.124214\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −22.6274 −1.00000
\(513\) 0 0
\(514\) 0 0
\(515\) −42.3252 −1.86507
\(516\) 6.48820i 0.285627i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17.8885i 0.783711i 0.920027 + 0.391856i \(0.128167\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) −19.2829 −0.843990
\(523\) − 34.7851i − 1.52104i −0.649312 0.760522i \(-0.724943\pi\)
0.649312 0.760522i \(-0.275057\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 45.8569 1.99945
\(527\) 0 0
\(528\) 0 0
\(529\) 33.3810 1.45135
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −7.12702 −0.308416
\(535\) 38.9260i 1.68292i
\(536\) −44.7298 −1.93203
\(537\) 0 0
\(538\) − 13.5825i − 0.585583i
\(539\) 0 0
\(540\) 9.36061 0.402816
\(541\) −42.2379 −1.81595 −0.907975 0.419025i \(-0.862372\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) 0 0
\(543\) −5.39882 −0.231686
\(544\) 0 0
\(545\) − 8.09222i − 0.346633i
\(546\) 0 0
\(547\) 20.5959 0.880618 0.440309 0.897846i \(-0.354869\pi\)
0.440309 + 0.897846i \(0.354869\pi\)
\(548\) 0 0
\(549\) − 39.1772i − 1.67204i
\(550\) 0 0
\(551\) 0 0
\(552\) 7.56906i 0.322161i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 16.9706 0.715860
\(563\) − 22.4923i − 0.947939i −0.880541 0.473970i \(-0.842821\pi\)
0.880541 0.473970i \(-0.157179\pi\)
\(564\) 6.76210 0.284736
\(565\) 0 0
\(566\) − 22.3607i − 0.939889i
\(567\) 0 0
\(568\) 0 0
\(569\) 36.0000 1.50920 0.754599 0.656186i \(-0.227831\pi\)
0.754599 + 0.656186i \(0.227831\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −37.5437 −1.56568
\(576\) 22.9839 0.957661
\(577\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(578\) 24.0416 1.00000
\(579\) 0 0
\(580\) 21.2246i 0.881304i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 47.4342i − 1.95782i −0.204298 0.978909i \(-0.565491\pi\)
0.204298 0.978909i \(-0.434509\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.2540 −0.665791
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) − 5.04017i − 0.205764i
\(601\) 40.2492i 1.64180i 0.571072 + 0.820900i \(0.306528\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 0 0
\(603\) 45.4345 1.85023
\(604\) 0 0
\(605\) 24.5967i 1.00000i
\(606\) 5.60282 0.227599
\(607\) − 32.5109i − 1.31958i −0.751452 0.659788i \(-0.770646\pi\)
0.751452 0.659788i \(-0.229354\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −43.1221 −1.74596
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 29.7929i 1.20234i
\(615\) 10.0638i 0.405812i
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −9.54024 −0.383765
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) − 15.7165i − 0.630681i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 9.48683i 0.376473i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) − 25.2982i − 1.00000i
\(641\) 36.6028 1.44572 0.722862 0.690992i \(-0.242826\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 8.77405i 0.346284i
\(643\) 41.1096i 1.62120i 0.585597 + 0.810602i \(0.300860\pi\)
−0.585597 + 0.810602i \(0.699140\pi\)
\(644\) 0 0
\(645\) −7.25403 −0.285627
\(646\) 0 0
\(647\) − 39.6388i − 1.55836i −0.626800 0.779180i \(-0.715636\pi\)
0.626800 0.779180i \(-0.284364\pi\)
\(648\) −22.2682 −0.874776
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −25.4558 −0.996928
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) − 1.82401i − 0.0713246i
\(655\) 0 0
\(656\) 50.5135i 1.97222i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) − 7.58820i − 0.295147i −0.989051 0.147573i \(-0.952854\pi\)
0.989051 0.147573i \(-0.0471463\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) − 51.5215i − 1.99942i
\(665\) 0 0
\(666\) 0 0
\(667\) 35.6362 1.37984
\(668\) − 32.1545i − 1.24409i
\(669\) −1.12702 −0.0435730
\(670\) − 50.0095i − 1.93203i
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 10.4655i 0.402816i
\(676\) −26.0000 −1.00000
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −10.1431 −0.388686
\(682\) 0 0
\(683\) −2.72720 −0.104354 −0.0521768 0.998638i \(-0.516616\pi\)
−0.0521768 + 0.998638i \(0.516616\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −9.56305 −0.364853
\(688\) −36.4103 −1.38813
\(689\) 0 0
\(690\) −8.46247 −0.322161
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 17.8569 0.677837
\(695\) 0 0
\(696\) 4.78410i 0.181341i
\(697\) 0 0
\(698\) − 12.8697i − 0.487125i
\(699\) 0 0
\(700\) 0 0
\(701\) −43.3649 −1.63787 −0.818935 0.573886i \(-0.805435\pi\)
−0.818935 + 0.573886i \(0.805435\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 7.56026i 0.284736i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.237900 −0.00893452 −0.00446726 0.999990i \(-0.501422\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) − 39.9952i − 1.49888i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 25.6967i 0.957661i
\(721\) 0 0
\(722\) 26.8701 1.00000
\(723\) −4.78153 −0.177827
\(724\) − 30.2969i − 1.12598i
\(725\) −23.7298 −0.881304
\(726\) 5.54419i 0.205764i
\(727\) 23.2051i 0.860630i 0.902679 + 0.430315i \(0.141598\pi\)
−0.902679 + 0.430315i \(0.858402\pi\)
\(728\) 0 0
\(729\) 20.3810 0.754854
\(730\) 0 0
\(731\) 0 0
\(732\) −9.71987 −0.359257
\(733\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(734\) 49.0014i 1.80868i
\(735\) 0 0
\(736\) −42.4758 −1.56568
\(737\) 0 0
\(738\) − 51.3092i − 1.88872i
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −27.6442 −1.01417 −0.507083 0.861897i \(-0.669276\pi\)
−0.507083 + 0.861897i \(0.669276\pi\)
\(744\) 0 0
\(745\) − 18.1726i − 0.665791i
\(746\) 0 0
\(747\) 52.3331i 1.91477i
\(748\) 0 0
\(749\) 0 0
\(750\) 5.63508 0.205764
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 37.9473i 1.38380i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 35.7771i 1.29692i 0.761249 + 0.648459i \(0.224586\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 2.13836i 0.0774647i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 53.0336i 1.91618i
\(767\) 0 0
\(768\) − 5.70230i − 0.205764i
\(769\) − 53.6656i − 1.93523i −0.252426 0.967616i \(-0.581229\pi\)
0.252426 0.967616i \(-0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) 36.9839 1.32936
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 33.9411 1.21685
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) − 9.93376i − 0.355004i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 12.5133i − 0.446051i −0.974813 0.223026i \(-0.928407\pi\)
0.974813 0.223026i \(-0.0715934\pi\)
\(788\) 0 0
\(789\) 11.5563i 0.411416i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 28.2843 1.00000
\(801\) 40.6252i 1.43542i
\(802\) −56.5457 −1.99670
\(803\) 0 0
\(804\) − 11.2723i − 0.397543i
\(805\) 0 0
\(806\) 0 0
\(807\) 3.42290 0.120492
\(808\) 31.4417i 1.10612i
\(809\) −11.5081 −0.404602 −0.202301 0.979323i \(-0.564842\pi\)
−0.202301 + 0.979323i \(0.564842\pi\)
\(810\) − 24.8966i − 0.874776i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) − 28.4605i − 0.996928i
\(816\) 0 0
\(817\) 0 0
\(818\) − 23.5615i − 0.823809i
\(819\) 0 0
\(820\) −56.4758 −1.97222
\(821\) −48.0000 −1.67521 −0.837606 0.546275i \(-0.816045\pi\)
−0.837606 + 0.546275i \(0.816045\pi\)
\(822\) 0 0
\(823\) −13.8841 −0.483969 −0.241985 0.970280i \(-0.577798\pi\)
−0.241985 + 0.970280i \(0.577798\pi\)
\(824\) − 53.5376i − 1.86507i
\(825\) 0 0
\(826\) 0 0
\(827\) −57.3426 −1.99400 −0.997000 0.0774065i \(-0.975336\pi\)
−0.997000 + 0.0774065i \(0.975336\pi\)
\(828\) 43.1449 1.49939
\(829\) − 13.4164i − 0.465971i −0.972480 0.232986i \(-0.925151\pi\)
0.972480 0.232986i \(-0.0748495\pi\)
\(830\) 57.6028 1.99942
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 35.9498 1.24409
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) −6.47580 −0.223303
\(842\) −54.9519 −1.89377
\(843\) 4.27673i 0.147298i
\(844\) 0 0
\(845\) − 29.0689i − 1.00000i
\(846\) − 38.5451i − 1.32521i
\(847\) 0 0
\(848\) 0 0
\(849\) 5.63508 0.193396
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −49.2379 −1.68292
\(857\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) − 40.7079i − 1.38813i
\(861\) 0 0
\(862\) 0 0
\(863\) 37.2072 1.26655 0.633274 0.773928i \(-0.281711\pi\)
0.633274 + 0.773928i \(0.281711\pi\)
\(864\) 11.8403i 0.402816i
\(865\) 0 0
\(866\) 0 0
\(867\) 6.05870i 0.205764i
\(868\) 0 0
\(869\) 0 0
\(870\) −5.34878 −0.181341
\(871\) 0 0
\(872\) 10.2359 0.346633
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 18.6766i − 0.629230i −0.949219 0.314615i \(-0.898125\pi\)
0.949219 0.314615i \(-0.101875\pi\)
\(882\) 0 0
\(883\) −55.1543 −1.85609 −0.928045 0.372467i \(-0.878512\pi\)
−0.928045 + 0.372467i \(0.878512\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 17.3810 0.583928
\(887\) 31.0853i 1.04374i 0.853024 + 0.521871i \(0.174766\pi\)
−0.853024 + 0.521871i \(0.825234\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 44.7159 1.49888
\(891\) 0 0
\(892\) − 6.32456i − 0.211762i
\(893\) 0 0
\(894\) − 4.09616i − 0.136996i
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 1.93028 0.0644144
\(899\) 0 0
\(900\) −28.7298 −0.957661
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 33.8730 1.12598
\(906\) 0 0
\(907\) 54.1550 1.79819 0.899093 0.437758i \(-0.144227\pi\)
0.899093 + 0.437758i \(0.144227\pi\)
\(908\) − 56.9210i − 1.88899i
\(909\) − 31.9370i − 1.05928i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) − 10.8671i − 0.359257i
\(916\) − 53.6656i − 1.77316i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) − 47.4894i − 1.56568i
\(921\) −7.50807 −0.247399
\(922\) − 12.6491i − 0.416576i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −41.3488 −1.35881
\(927\) 54.3810i 1.78611i
\(928\) −26.8472 −0.881304
\(929\) − 6.58017i − 0.215888i −0.994157 0.107944i \(-0.965573\pi\)
0.994157 0.107944i \(-0.0344268\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) − 19.7126i − 0.645015i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −42.4264 −1.38380
\(941\) − 44.7214i − 1.45787i −0.684580 0.728937i \(-0.740015\pi\)
0.684580 0.728937i \(-0.259985\pi\)
\(942\) 0 0
\(943\) 94.8231i 3.08786i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −22.1898 −0.721070 −0.360535 0.932746i \(-0.617406\pi\)
−0.360535 + 0.932746i \(0.617406\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 6.37537 0.205764
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 50.0135 1.61166
\(964\) − 26.8328i − 0.864227i
\(965\) 0 0
\(966\) 0 0
\(967\) 58.9365 1.89527 0.947635 0.319356i \(-0.103467\pi\)
0.947635 + 0.319356i \(0.103467\pi\)
\(968\) −31.1127 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) − 18.1703i − 0.582814i
\(973\) 0 0
\(974\) −54.0000 −1.73027
\(975\) 0 0
\(976\) − 54.5456i − 1.74596i
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) − 6.41509i − 0.205132i
\(979\) 0 0
\(980\) 0 0
\(981\) −10.3972 −0.331957
\(982\) 0 0
\(983\) 11.8005i 0.376378i 0.982133 + 0.188189i \(0.0602618\pi\)
−0.982133 + 0.188189i \(0.939738\pi\)
\(984\) −12.7298 −0.405812
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −68.3488 −2.17336
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 12.9839 0.411410
\(997\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(998\) 0 0
\(999\) 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 980.2.c.b.979.2 8
4.3 odd 2 inner 980.2.c.b.979.7 8
5.4 even 2 inner 980.2.c.b.979.7 8
7.2 even 3 140.2.s.a.59.4 yes 8
7.3 odd 6 140.2.s.a.19.4 yes 8
7.4 even 3 980.2.s.a.19.3 8
7.5 odd 6 980.2.s.a.619.3 8
7.6 odd 2 inner 980.2.c.b.979.3 8
20.19 odd 2 CM 980.2.c.b.979.2 8
28.3 even 6 140.2.s.a.19.1 8
28.11 odd 6 980.2.s.a.19.2 8
28.19 even 6 980.2.s.a.619.2 8
28.23 odd 6 140.2.s.a.59.1 yes 8
28.27 even 2 inner 980.2.c.b.979.6 8
35.2 odd 12 700.2.p.b.451.2 8
35.3 even 12 700.2.p.b.551.2 8
35.4 even 6 980.2.s.a.19.2 8
35.9 even 6 140.2.s.a.59.1 yes 8
35.17 even 12 700.2.p.b.551.3 8
35.19 odd 6 980.2.s.a.619.2 8
35.23 odd 12 700.2.p.b.451.3 8
35.24 odd 6 140.2.s.a.19.1 8
35.34 odd 2 inner 980.2.c.b.979.6 8
140.3 odd 12 700.2.p.b.551.3 8
140.19 even 6 980.2.s.a.619.3 8
140.23 even 12 700.2.p.b.451.2 8
140.39 odd 6 980.2.s.a.19.3 8
140.59 even 6 140.2.s.a.19.4 yes 8
140.79 odd 6 140.2.s.a.59.4 yes 8
140.87 odd 12 700.2.p.b.551.2 8
140.107 even 12 700.2.p.b.451.3 8
140.139 even 2 inner 980.2.c.b.979.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.s.a.19.1 8 28.3 even 6
140.2.s.a.19.1 8 35.24 odd 6
140.2.s.a.19.4 yes 8 7.3 odd 6
140.2.s.a.19.4 yes 8 140.59 even 6
140.2.s.a.59.1 yes 8 28.23 odd 6
140.2.s.a.59.1 yes 8 35.9 even 6
140.2.s.a.59.4 yes 8 7.2 even 3
140.2.s.a.59.4 yes 8 140.79 odd 6
700.2.p.b.451.2 8 35.2 odd 12
700.2.p.b.451.2 8 140.23 even 12
700.2.p.b.451.3 8 35.23 odd 12
700.2.p.b.451.3 8 140.107 even 12
700.2.p.b.551.2 8 35.3 even 12
700.2.p.b.551.2 8 140.87 odd 12
700.2.p.b.551.3 8 35.17 even 12
700.2.p.b.551.3 8 140.3 odd 12
980.2.c.b.979.2 8 1.1 even 1 trivial
980.2.c.b.979.2 8 20.19 odd 2 CM
980.2.c.b.979.3 8 7.6 odd 2 inner
980.2.c.b.979.3 8 140.139 even 2 inner
980.2.c.b.979.6 8 28.27 even 2 inner
980.2.c.b.979.6 8 35.34 odd 2 inner
980.2.c.b.979.7 8 4.3 odd 2 inner
980.2.c.b.979.7 8 5.4 even 2 inner
980.2.s.a.19.2 8 28.11 odd 6
980.2.s.a.19.2 8 35.4 even 6
980.2.s.a.19.3 8 7.4 even 3
980.2.s.a.19.3 8 140.39 odd 6
980.2.s.a.619.2 8 28.19 even 6
980.2.s.a.619.2 8 35.19 odd 6
980.2.s.a.619.3 8 7.5 odd 6
980.2.s.a.619.3 8 140.19 even 6