Properties

Label 980.2.c.a.979.2
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $8$
CM discriminant -4
Inner twists $8$

Related objects

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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: \(\Q(\zeta_{16})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label 979.2
Root \(-0.382683 - 0.923880i\) of defining polynomial
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.a.979.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.41421i q^{2} -2.00000 q^{4} +(-0.158513 + 2.23044i) q^{5} +2.82843i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421i q^{2} -2.00000 q^{4} +(-0.158513 + 2.23044i) q^{5} +2.82843i q^{8} +3.00000 q^{9} +(3.15432 + 0.224171i) q^{10} -5.99162 q^{13} +4.00000 q^{16} -6.62567 q^{17} -4.24264i q^{18} +(0.317025 - 4.46088i) q^{20} +(-4.94975 - 0.707107i) q^{25} +8.47343i q^{26} -9.89949 q^{29} -5.65685i q^{32} +9.37011i q^{34} -6.00000 q^{36} -7.07107i q^{37} +(-6.30864 - 0.448342i) q^{40} +3.56420i q^{41} +(-0.475538 + 6.69133i) q^{45} +(-1.00000 + 7.00000i) q^{50} +11.9832 q^{52} +14.0000i q^{53} +14.0000i q^{58} +13.8310i q^{61} -8.00000 q^{64} +(0.949747 - 13.3640i) q^{65} +13.2513 q^{68} +8.48528i q^{72} -11.6662 q^{73} -10.0000 q^{74} +(-0.634051 + 8.92177i) q^{80} +9.00000 q^{81} +5.04054 q^{82} +(1.05025 - 14.7782i) q^{85} -3.11586i q^{89} +(9.46297 + 0.672512i) q^{90} +13.5684 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 16 q^{4} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 16 q^{4} + 24 q^{9} + 32 q^{16} - 48 q^{36} - 8 q^{50} - 64 q^{64} - 32 q^{65} - 80 q^{74} + 72 q^{81} + 48 q^{85}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 1.00000i
\(3\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(4\) −2.00000 −1.00000
\(5\) −0.158513 + 2.23044i −0.0708890 + 0.997484i
\(6\) 0 0
\(7\) 0 0
\(8\) 2.82843i 1.00000i
\(9\) 3.00000 1.00000
\(10\) 3.15432 + 0.224171i 0.997484 + 0.0708890i
\(11\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(12\) 0 0
\(13\) −5.99162 −1.66178 −0.830888 0.556440i \(-0.812167\pi\)
−0.830888 + 0.556440i \(0.812167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) −6.62567 −1.60696 −0.803480 0.595331i \(-0.797021\pi\)
−0.803480 + 0.595331i \(0.797021\pi\)
\(18\) 4.24264i 1.00000i
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0.317025 4.46088i 0.0708890 0.997484i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −4.94975 0.707107i −0.989949 0.141421i
\(26\) 8.47343i 1.66178i
\(27\) 0 0
\(28\) 0 0
\(29\) −9.89949 −1.83829 −0.919145 0.393919i \(-0.871119\pi\)
−0.919145 + 0.393919i \(0.871119\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) 9.37011i 1.60696i
\(35\) 0 0
\(36\) −6.00000 −1.00000
\(37\) 7.07107i 1.16248i −0.813733 0.581238i \(-0.802568\pi\)
0.813733 0.581238i \(-0.197432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) −6.30864 0.448342i −0.997484 0.0708890i
\(41\) 3.56420i 0.556635i 0.960489 + 0.278317i \(0.0897767\pi\)
−0.960489 + 0.278317i \(0.910223\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) −0.475538 + 6.69133i −0.0708890 + 0.997484i
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.00000 + 7.00000i −0.141421 + 0.989949i
\(51\) 0 0
\(52\) 11.9832 1.66178
\(53\) 14.0000i 1.92305i 0.274721 + 0.961524i \(0.411414\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 14.0000i 1.83829i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 13.8310i 1.77088i 0.464756 + 0.885439i \(0.346142\pi\)
−0.464756 + 0.885439i \(0.653858\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0.949747 13.3640i 0.117802 1.65760i
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 13.2513 1.60696
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 8.48528i 1.00000i
\(73\) −11.6662 −1.36543 −0.682713 0.730686i \(-0.739200\pi\)
−0.682713 + 0.730686i \(0.739200\pi\)
\(74\) −10.0000 −1.16248
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(80\) −0.634051 + 8.92177i −0.0708890 + 0.997484i
\(81\) 9.00000 1.00000
\(82\) 5.04054 0.556635
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 1.05025 14.7782i 0.113916 1.60292i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3.11586i 0.330281i −0.986270 0.165140i \(-0.947192\pi\)
0.986270 0.165140i \(-0.0528077\pi\)
\(90\) 9.46297 + 0.672512i 0.997484 + 0.0708890i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.5684 1.37766 0.688829 0.724924i \(-0.258125\pi\)
0.688829 + 0.724924i \(0.258125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 9.89949 + 1.41421i 0.989949 + 0.141421i
\(101\) 5.80591i 0.577710i −0.957373 0.288855i \(-0.906726\pi\)
0.957373 0.288855i \(-0.0932745\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 16.9469i 1.66178i
\(105\) 0 0
\(106\) 19.7990 1.92305
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −9.89949 −0.948200 −0.474100 0.880471i \(-0.657226\pi\)
−0.474100 + 0.880471i \(0.657226\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.0000i 1.31701i −0.752577 0.658505i \(-0.771189\pi\)
0.752577 0.658505i \(-0.228811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 19.7990 1.83829
\(117\) −17.9749 −1.66178
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 11.0000 1.00000
\(122\) 19.5600 1.77088
\(123\) 0 0
\(124\) 0 0
\(125\) 2.36176 10.9280i 0.211242 0.977434i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 11.3137i 1.00000i
\(129\) 0 0
\(130\) −18.8995 1.34315i −1.65760 0.117802i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 18.7402i 1.60696i
\(137\) 21.2132i 1.81237i 0.422885 + 0.906183i \(0.361017\pi\)
−0.422885 + 0.906183i \(0.638983\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 12.0000 1.00000
\(145\) 1.56920 22.0803i 0.130315 1.83367i
\(146\) 16.4985i 1.36543i
\(147\) 0 0
\(148\) 14.1421i 1.16248i
\(149\) −20.0000 −1.63846 −0.819232 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0 0
\(153\) −19.8770 −1.60696
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −24.9176 −1.98864 −0.994319 0.106446i \(-0.966053\pi\)
−0.994319 + 0.106446i \(0.966053\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 12.6173 + 0.896683i 0.997484 + 0.0708890i
\(161\) 0 0
\(162\) 12.7279i 1.00000i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 7.12840i 0.556635i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 22.8995 1.76150
\(170\) −20.8995 1.48528i −1.60292 0.113916i
\(171\) 0 0
\(172\) 0 0
\(173\) 25.5516 1.94265 0.971326 0.237751i \(-0.0764102\pi\)
0.971326 + 0.237751i \(0.0764102\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −4.40649 −0.330281
\(179\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(180\) 0.951076 13.3827i 0.0708890 0.997484i
\(181\) 11.5893i 0.861425i 0.902489 + 0.430713i \(0.141738\pi\)
−0.902489 + 0.430713i \(0.858262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 15.7716 + 1.12085i 1.15955 + 0.0824068i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 14.0000i 1.00774i −0.863779 0.503871i \(-0.831909\pi\)
0.863779 0.503871i \(-0.168091\pi\)
\(194\) 19.1886i 1.37766i
\(195\) 0 0
\(196\) 0 0
\(197\) 28.0000i 1.99492i 0.0712470 + 0.997459i \(0.477302\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 2.00000 14.0000i 0.141421 0.989949i
\(201\) 0 0
\(202\) −8.21080 −0.577710
\(203\) 0 0
\(204\) 0 0
\(205\) −7.94975 0.564971i −0.555234 0.0394593i
\(206\) 0 0
\(207\) 0 0
\(208\) −23.9665 −1.66178
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(212\) 28.0000i 1.92305i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 14.0000i 0.948200i
\(219\) 0 0
\(220\) 0 0
\(221\) 39.6985 2.67041
\(222\) 0 0
\(223\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(224\) 0 0
\(225\) −14.8492 2.12132i −0.989949 0.141421i
\(226\) −19.7990 −1.31701
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 15.1760i 1.00286i −0.865198 0.501430i \(-0.832808\pi\)
0.865198 0.501430i \(-0.167192\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 28.0000i 1.83829i
\(233\) 7.07107i 0.463241i 0.972806 + 0.231621i \(0.0744028\pi\)
−0.972806 + 0.231621i \(0.925597\pi\)
\(234\) 25.4203i 1.66178i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 30.7779i 1.98258i −0.131713 0.991288i \(-0.542048\pi\)
0.131713 0.991288i \(-0.457952\pi\)
\(242\) 15.5563i 1.00000i
\(243\) 0 0
\(244\) 27.6620i 1.77088i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) −15.4546 3.34003i −0.977434 0.211242i
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −10.3981 −0.648616 −0.324308 0.945951i \(-0.605131\pi\)
−0.324308 + 0.945951i \(0.605131\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −1.89949 + 26.7279i −0.117802 + 1.65760i
\(261\) −29.6985 −1.83829
\(262\) 0 0
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 0 0
\(265\) −31.2262 2.21918i −1.91821 0.136323i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 31.6745i 1.93123i 0.259975 + 0.965615i \(0.416286\pi\)
−0.259975 + 0.965615i \(0.583714\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) −26.5027 −1.60696
\(273\) 0 0
\(274\) 30.0000 1.81237
\(275\) 0 0
\(276\) 0 0
\(277\) 28.0000i 1.68236i −0.540758 0.841178i \(-0.681862\pi\)
0.540758 0.841178i \(-0.318138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 29.6985 1.77166 0.885832 0.464007i \(-0.153589\pi\)
0.885832 + 0.464007i \(0.153589\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 16.9706i 1.00000i
\(289\) 26.8995 1.58232
\(290\) −31.2262 2.21918i −1.83367 0.130315i
\(291\) 0 0
\(292\) 23.3324 1.36543
\(293\) 16.7068 0.976019 0.488010 0.872838i \(-0.337723\pi\)
0.488010 + 0.872838i \(0.337723\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 20.0000 1.16248
\(297\) 0 0
\(298\) 28.2843i 1.63846i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −30.8492 2.19239i −1.76642 0.125536i
\(306\) 28.1103i 1.60696i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −14.8365 −0.838607 −0.419303 0.907846i \(-0.637726\pi\)
−0.419303 + 0.907846i \(0.637726\pi\)
\(314\) 35.2387i 1.98864i
\(315\) 0 0
\(316\) 0 0
\(317\) 28.0000i 1.57264i 0.617822 + 0.786318i \(0.288015\pi\)
−0.617822 + 0.786318i \(0.711985\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 1.26810 17.8435i 0.0708890 0.997484i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −18.0000 −1.00000
\(325\) 29.6570 + 4.23671i 1.64507 + 0.235011i
\(326\) 0 0
\(327\) 0 0
\(328\) −10.0811 −0.556635
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 21.2132i 1.16248i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 35.3553i 1.92593i 0.269630 + 0.962964i \(0.413099\pi\)
−0.269630 + 0.962964i \(0.586901\pi\)
\(338\) 32.3848i 1.76150i
\(339\) 0 0
\(340\) −2.10051 + 29.5563i −0.113916 + 1.60292i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 36.1354i 1.94265i
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 29.4328i 1.57550i −0.615993 0.787752i \(-0.711245\pi\)
0.615993 0.787752i \(-0.288755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 37.5348 1.99778 0.998889 0.0471260i \(-0.0150062\pi\)
0.998889 + 0.0471260i \(0.0150062\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.23172i 0.330281i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) −18.9259 1.34502i −0.997484 0.0708890i
\(361\) −19.0000 −1.00000
\(362\) 16.3897 0.861425
\(363\) 0 0
\(364\) 0 0
\(365\) 1.84924 26.0208i 0.0967938 1.36199i
\(366\) 0 0
\(367\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 10.6926i 0.556635i
\(370\) 1.58513 22.3044i 0.0824068 1.15955i
\(371\) 0 0
\(372\) 0 0
\(373\) 14.0000i 0.724893i −0.932005 0.362446i \(-0.881942\pi\)
0.932005 0.362446i \(-0.118058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 59.3140 3.05483
\(378\) 0 0
\(379\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −19.7990 −1.00774
\(387\) 0 0
\(388\) −27.1367 −1.37766
\(389\) 9.89949 0.501924 0.250962 0.967997i \(-0.419253\pi\)
0.250962 + 0.967997i \(0.419253\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 39.5980 1.99492
\(395\) 0 0
\(396\) 0 0
\(397\) −3.45542 −0.173422 −0.0867112 0.996233i \(-0.527636\pi\)
−0.0867112 + 0.996233i \(0.527636\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −19.7990 2.82843i −0.989949 0.141421i
\(401\) 29.6985 1.48307 0.741536 0.670913i \(-0.234098\pi\)
0.741536 + 0.670913i \(0.234098\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 11.6118i 0.577710i
\(405\) −1.42661 + 20.0740i −0.0708890 + 0.997484i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 39.2513i 1.94085i −0.241401 0.970425i \(-0.577607\pi\)
0.241401 0.970425i \(-0.422393\pi\)
\(410\) −0.798990 + 11.2426i −0.0394593 + 0.555234i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 33.8937i 1.66178i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −30.0000 −1.46211 −0.731055 0.682318i \(-0.760972\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) −39.5980 −1.92305
\(425\) 32.7954 + 4.68506i 1.59081 + 0.227259i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(432\) 0 0
\(433\) 9.16187 0.440291 0.220146 0.975467i \(-0.429347\pi\)
0.220146 + 0.975467i \(0.429347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 19.7990 0.948200
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 56.1421i 2.67041i
\(443\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 0 0
\(445\) 6.94975 + 0.493903i 0.329450 + 0.0234133i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −40.0000 −1.88772 −0.943858 0.330350i \(-0.892833\pi\)
−0.943858 + 0.330350i \(0.892833\pi\)
\(450\) −3.00000 + 21.0000i −0.141421 + 0.989949i
\(451\) 0 0
\(452\) 28.0000i 1.31701i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 42.0000i 1.96468i 0.187112 + 0.982339i \(0.440087\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(458\) −21.4621 −1.00286
\(459\) 0 0
\(460\) 0 0
\(461\) 33.0196i 1.53787i 0.639324 + 0.768937i \(0.279214\pi\)
−0.639324 + 0.768937i \(0.720786\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) −39.5980 −1.83829
\(465\) 0 0
\(466\) 10.0000 0.463241
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 35.9497 1.66178
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 42.0000i 1.92305i
\(478\) 0 0
\(479\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 42.3671i 1.93178i
\(482\) −43.5265 −1.98258
\(483\) 0 0
\(484\) −22.0000 −1.00000
\(485\) −2.15076 + 30.2635i −0.0976609 + 1.37419i
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) −39.1200 −1.77088
\(489\) 0 0
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 65.5908 2.95406
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −4.72352 + 21.8561i −0.211242 + 0.977434i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 12.9497 + 0.920310i 0.576256 + 0.0409533i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 7.59928i 0.336832i 0.985716 + 0.168416i \(0.0538652\pi\)
−0.985716 + 0.168416i \(0.946135\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 22.6274i 1.00000i
\(513\) 0 0
\(514\) 14.7051i 0.648616i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 37.7990 + 2.68629i 1.65760 + 0.117802i
\(521\) 28.5361i 1.25019i 0.780548 + 0.625096i \(0.214940\pi\)
−0.780548 + 0.625096i \(0.785060\pi\)
\(522\) 42.0000i 1.83829i
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −3.13839 + 44.1605i −0.136323 + 1.91821i
\(531\) 0 0
\(532\) 0 0
\(533\) 21.3553i 0.925002i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 44.7946 1.93123
\(539\) 0 0
\(540\) 0 0
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 37.4804i 1.60696i
\(545\) 1.56920 22.0803i 0.0672169 0.945814i
\(546\) 0 0
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 42.4264i 1.81237i
\(549\) 41.4930i 1.77088i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −39.5980 −1.68236
\(555\) 0 0
\(556\) 0 0
\(557\) 28.0000i 1.18640i 0.805056 + 0.593199i \(0.202135\pi\)
−0.805056 + 0.593199i \(0.797865\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 42.0000i 1.77166i
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 31.2262 + 2.21918i 1.31370 + 0.0933615i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −9.89949 −0.415008 −0.207504 0.978234i \(-0.566534\pi\)
−0.207504 + 0.978234i \(0.566534\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) −24.0000 −1.00000
\(577\) −45.1116 −1.87802 −0.939010 0.343890i \(-0.888255\pi\)
−0.939010 + 0.343890i \(0.888255\pi\)
\(578\) 38.0416i 1.58232i
\(579\) 0 0
\(580\) −3.13839 + 44.1605i −0.130315 + 1.83367i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 32.9970i 1.36543i
\(585\) 2.84924 40.0919i 0.117802 1.65760i
\(586\) 23.6269i 0.976019i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 28.2843i 1.16248i
\(593\) 2.82137 0.115860 0.0579298 0.998321i \(-0.481550\pi\)
0.0579298 + 0.998321i \(0.481550\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 40.0000 1.63846
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 48.1731i 1.96502i −0.186210 0.982510i \(-0.559621\pi\)
0.186210 0.982510i \(-0.440379\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.74364 + 24.5349i −0.0708890 + 0.997484i
\(606\) 0 0
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −3.10051 + 43.6274i −0.125536 + 1.76642i
\(611\) 0 0
\(612\) 39.7540 1.60696
\(613\) 1.41421i 0.0571195i 0.999592 + 0.0285598i \(0.00909209\pi\)
−0.999592 + 0.0285598i \(0.990908\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.24264i 0.170802i 0.996347 + 0.0854011i \(0.0272172\pi\)
−0.996347 + 0.0854011i \(0.972783\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.0000 + 7.00000i 0.960000 + 0.280000i
\(626\) 20.9819i 0.838607i
\(627\) 0 0
\(628\) 49.8351 1.98864
\(629\) 46.8506i 1.86805i
\(630\) 0 0
\(631\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 39.5980 1.57264
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −25.2346 1.79337i −0.997484 0.0708890i
\(641\) −29.6985 −1.17302 −0.586510 0.809942i \(-0.699498\pi\)
−0.586510 + 0.809942i \(0.699498\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 25.4558i 1.00000i
\(649\) 0 0
\(650\) 5.99162 41.9413i 0.235011 1.64507i
\(651\) 0 0
\(652\) 0 0
\(653\) 12.7279i 0.498082i 0.968493 + 0.249041i \(0.0801154\pi\)
−0.968493 + 0.249041i \(0.919885\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 14.2568i 0.556635i
\(657\) −34.9986 −1.36543
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 8.04762i 0.313016i 0.987677 + 0.156508i \(0.0500237\pi\)
−0.987677 + 0.156508i \(0.949976\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −30.0000 −1.16248
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 15.5563i 0.599653i 0.953994 + 0.299827i \(0.0969288\pi\)
−0.953994 + 0.299827i \(0.903071\pi\)
\(674\) 50.0000 1.92593
\(675\) 0 0
\(676\) −45.7990 −1.76150
\(677\) −21.7473 −0.835817 −0.417908 0.908489i \(-0.637237\pi\)
−0.417908 + 0.908489i \(0.637237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 41.7990 + 2.97056i 1.60292 + 0.113916i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) −47.3148 3.36256i −1.80781 0.128477i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 83.8827i 3.19567i
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −51.1032 −1.94265
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 23.6152i 0.894490i
\(698\) −41.6243 −1.57550
\(699\) 0 0
\(700\) 0 0
\(701\) −29.6985 −1.12170 −0.560848 0.827919i \(-0.689525\pi\)
−0.560848 + 0.827919i \(0.689525\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 53.0823i 1.99778i
\(707\) 0 0
\(708\) 0 0
\(709\) −9.89949 −0.371783 −0.185892 0.982570i \(-0.559517\pi\)
−0.185892 + 0.982570i \(0.559517\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 8.81298 0.330281
\(713\) 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 \(0.5\pi\)
\(720\) −1.90215 + 26.7653i −0.0708890 + 0.997484i
\(721\) 0 0
\(722\) 26.8701i 1.00000i
\(723\) 0 0
\(724\) 23.1786i 0.861425i
\(725\) 49.0000 + 7.00000i 1.81981 + 0.259973i
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) −36.7990 2.61522i −1.36199 0.0967938i
\(731\) 0 0
\(732\) 0 0
\(733\) −51.4202 −1.89925 −0.949625 0.313389i \(-0.898536\pi\)
−0.949625 + 0.313389i \(0.898536\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 15.1216 0.556635
\(739\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(740\) −31.5432 2.24171i −1.15955 0.0824068i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0 0
\(745\) 3.17025 44.6088i 0.116149 1.63434i
\(746\) −19.7990 −0.724893
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 83.8827i 3.05483i
\(755\) 0 0
\(756\) 0 0
\(757\) 24.0416i 0.873808i 0.899508 + 0.436904i \(0.143925\pi\)
−0.899508 + 0.436904i \(0.856075\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 50.4148i 1.82753i −0.406239 0.913767i \(-0.633160\pi\)
0.406239 0.913767i \(-0.366840\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 3.15076 44.3345i 0.113916 1.60292i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 37.0096i 1.33460i 0.744789 + 0.667300i \(0.232550\pi\)
−0.744789 + 0.667300i \(0.767450\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 28.0000i 1.00774i
\(773\) −48.2500 −1.73543 −0.867715 0.497061i \(-0.834412\pi\)
−0.867715 + 0.497061i \(0.834412\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 38.3771i 1.37766i
\(777\) 0 0
\(778\) 14.0000i 0.501924i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.94975 55.5772i 0.140973 1.98363i
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 56.0000i 1.99492i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 82.8701i 2.94280i
\(794\) 4.88670i 0.173422i
\(795\) 0 0
\(796\) 0 0
\(797\) 56.4608 1.99994 0.999972 0.00754150i \(-0.00240056\pi\)
0.999972 + 0.00754150i \(0.00240056\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −4.00000 + 28.0000i −0.141421 + 0.989949i
\(801\) 9.34758i 0.330281i
\(802\) 42.0000i 1.48307i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 16.4216 0.577710
\(809\) −10.0000 −0.351581 −0.175791 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 28.3889 + 2.01754i 0.997484 + 0.0708890i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −55.5097 −1.94085
\(819\) 0 0
\(820\) 15.8995 + 1.12994i 0.555234 + 0.0394593i
\(821\) −50.0000 −1.74501 −0.872506 0.488603i \(-0.837507\pi\)
−0.872506 + 0.488603i \(0.837507\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(828\) 0 0
\(829\) 57.5432i 1.99856i 0.0379843 + 0.999278i \(0.487906\pi\)
−0.0379843 + 0.999278i \(0.512094\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 47.9329 1.66178
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 69.0000 2.37931
\(842\) 42.4264i 1.46211i
\(843\) 0 0
\(844\) 0 0
\(845\) −3.62986 + 51.0760i −0.124871 + 1.75707i
\(846\) 0 0
\(847\) 0 0
\(848\) 56.0000i 1.92305i
\(849\) 0 0
\(850\) 6.62567 46.3797i 0.227259 1.59081i
\(851\) 0 0
\(852\) 0 0
\(853\) −28.7219 −0.983418 −0.491709 0.870760i \(-0.663628\pi\)
−0.491709 + 0.870760i \(0.663628\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −14.8046 −0.505716 −0.252858 0.967503i \(-0.581370\pi\)
−0.252858 + 0.967503i \(0.581370\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) −4.05025 + 56.9914i −0.137713 + 1.93776i
\(866\) 12.9568i 0.440291i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 28.0000i 0.948200i
\(873\) 40.7051 1.37766
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 32.5269i 1.09836i −0.835705 0.549178i \(-0.814941\pi\)
0.835705 0.549178i \(-0.185059\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 58.4398i 1.96889i −0.175697 0.984444i \(-0.556218\pi\)
0.175697 0.984444i \(-0.443782\pi\)
\(882\) 0 0
\(883\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(884\) −79.3970 −2.67041
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0.698485 9.82843i 0.0234133 0.329450i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 56.5685i 1.88772i
\(899\) 0 0
\(900\) 29.6985 + 4.24264i 0.989949 + 0.141421i
\(901\) 92.7594i 3.09026i
\(902\) 0 0
\(903\) 0 0
\(904\) 39.5980 1.31701
\(905\) −25.8492 1.83705i −0.859258 0.0610656i
\(906\) 0 0
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0 0
\(909\) 17.4177i 0.577710i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 59.3970 1.96468
\(915\) 0 0
\(916\) 30.3520i 1.00286i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 46.6967 1.53787
\(923\) 0 0
\(924\) 0 0
\(925\) −5.00000 + 35.0000i −0.164399 + 1.15079i
\(926\) 0 0
\(927\) 0 0
\(928\) 56.0000i 1.83829i
\(929\) 27.1911i 0.892112i −0.895005 0.446056i \(-0.852828\pi\)
0.895005 0.446056i \(-0.147172\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 14.1421i 0.463241i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 50.8406i 1.66178i
\(937\) −16.7386 −0.546827 −0.273413 0.961897i \(-0.588153\pi\)
−0.273413 + 0.961897i \(0.588153\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 45.9313i 1.49732i 0.662955 + 0.748660i \(0.269302\pi\)
−0.662955 + 0.748660i \(0.730698\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 69.8995 2.26903
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 56.0000i 1.81402i −0.421111 0.907009i \(-0.638360\pi\)
0.421111 0.907009i \(-0.361640\pi\)
\(954\) 59.3970 1.92305
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 59.9162 1.93178
\(963\) 0 0
\(964\) 61.5557i 1.98258i
\(965\) 31.2262 + 2.21918i 1.00521 + 0.0714378i
\(966\) 0 0
\(967\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(968\) 31.1127i 1.00000i
\(969\) 0 0
\(970\) 42.7990 + 3.04163i 1.37419 + 0.0976609i
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 55.3240i 1.77088i
\(977\) 38.1838i 1.22161i 0.791782 + 0.610803i \(0.209153\pi\)
−0.791782 + 0.610803i \(0.790847\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −29.6985 −0.948200
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0 0
\(985\) −62.4524 4.43835i −1.98990 0.141418i
\(986\) 92.7594i 2.95406i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −52.6883 −1.66866 −0.834328 0.551268i \(-0.814144\pi\)
−0.834328 + 0.551268i \(0.814144\pi\)
\(998\) 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.a.979.2 8
4.3 odd 2 CM 980.2.c.a.979.2 8
5.4 even 2 inner 980.2.c.a.979.7 yes 8
7.2 even 3 980.2.s.c.619.4 16
7.3 odd 6 980.2.s.c.19.8 16
7.4 even 3 980.2.s.c.19.5 16
7.5 odd 6 980.2.s.c.619.1 16
7.6 odd 2 inner 980.2.c.a.979.3 yes 8
20.19 odd 2 inner 980.2.c.a.979.7 yes 8
28.3 even 6 980.2.s.c.19.8 16
28.11 odd 6 980.2.s.c.19.5 16
28.19 even 6 980.2.s.c.619.1 16
28.23 odd 6 980.2.s.c.619.4 16
28.27 even 2 inner 980.2.c.a.979.3 yes 8
35.4 even 6 980.2.s.c.19.1 16
35.9 even 6 980.2.s.c.619.8 16
35.19 odd 6 980.2.s.c.619.5 16
35.24 odd 6 980.2.s.c.19.4 16
35.34 odd 2 inner 980.2.c.a.979.6 yes 8
140.19 even 6 980.2.s.c.619.5 16
140.39 odd 6 980.2.s.c.19.1 16
140.59 even 6 980.2.s.c.19.4 16
140.79 odd 6 980.2.s.c.619.8 16
140.139 even 2 inner 980.2.c.a.979.6 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.2.c.a.979.2 8 1.1 even 1 trivial
980.2.c.a.979.2 8 4.3 odd 2 CM
980.2.c.a.979.3 yes 8 7.6 odd 2 inner
980.2.c.a.979.3 yes 8 28.27 even 2 inner
980.2.c.a.979.6 yes 8 35.34 odd 2 inner
980.2.c.a.979.6 yes 8 140.139 even 2 inner
980.2.c.a.979.7 yes 8 5.4 even 2 inner
980.2.c.a.979.7 yes 8 20.19 odd 2 inner
980.2.s.c.19.1 16 35.4 even 6
980.2.s.c.19.1 16 140.39 odd 6
980.2.s.c.19.4 16 35.24 odd 6
980.2.s.c.19.4 16 140.59 even 6
980.2.s.c.19.5 16 7.4 even 3
980.2.s.c.19.5 16 28.11 odd 6
980.2.s.c.19.8 16 7.3 odd 6
980.2.s.c.19.8 16 28.3 even 6
980.2.s.c.619.1 16 7.5 odd 6
980.2.s.c.619.1 16 28.19 even 6
980.2.s.c.619.4 16 7.2 even 3
980.2.s.c.619.4 16 28.23 odd 6
980.2.s.c.619.5 16 35.19 odd 6
980.2.s.c.619.5 16 140.19 even 6
980.2.s.c.619.8 16 35.9 even 6
980.2.s.c.619.8 16 140.79 odd 6