Properties

Label 700.2.e.b.449.1
Level $700$
Weight $2$
Character 700.449
Analytic conductor $5.590$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,2,Mod(449,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.449");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.e (of order \(2\), degree \(1\), not 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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 700.449
Dual form 700.2.e.b.449.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000i q^{3} -1.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{3} -1.00000i q^{7} -1.00000 q^{9} +3.00000 q^{11} -4.00000i q^{13} -2.00000 q^{19} -2.00000 q^{21} -3.00000i q^{23} -4.00000i q^{27} -9.00000 q^{29} +8.00000 q^{31} -6.00000i q^{33} -5.00000i q^{37} -8.00000 q^{39} -6.00000 q^{41} +11.0000i q^{43} -6.00000i q^{47} -1.00000 q^{49} +6.00000i q^{53} +4.00000i q^{57} -10.0000 q^{61} +1.00000i q^{63} -5.00000i q^{67} -6.00000 q^{69} +15.0000 q^{71} -10.0000i q^{73} -3.00000i q^{77} +7.00000 q^{79} -11.0000 q^{81} +12.0000i q^{83} +18.0000i q^{87} +12.0000 q^{89} -4.00000 q^{91} -16.0000i q^{93} -8.00000i q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{9} + 6 q^{11} - 4 q^{19} - 4 q^{21} - 18 q^{29} + 16 q^{31} - 16 q^{39} - 12 q^{41} - 2 q^{49} - 20 q^{61} - 12 q^{69} + 30 q^{71} + 14 q^{79} - 22 q^{81} + 24 q^{89} - 8 q^{91} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) − 2.00000i − 1.15470i −0.816497 0.577350i \(-0.804087\pi\)
0.816497 0.577350i \(-0.195913\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 1.00000i − 0.377964i
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) − 4.00000i − 1.10940i −0.832050 0.554700i \(-0.812833\pi\)
0.832050 0.554700i \(-0.187167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) − 3.00000i − 0.625543i −0.949828 0.312772i \(-0.898743\pi\)
0.949828 0.312772i \(-0.101257\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 4.00000i − 0.769800i
\(28\) 0 0
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) − 6.00000i − 1.04447i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) − 5.00000i − 0.821995i −0.911636 0.410997i \(-0.865181\pi\)
0.911636 0.410997i \(-0.134819\pi\)
\(38\) 0 0
\(39\) −8.00000 −1.28103
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) 11.0000i 1.67748i 0.544529 + 0.838742i \(0.316708\pi\)
−0.544529 + 0.838742i \(0.683292\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 6.00000i − 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000i 0.824163i 0.911147 + 0.412082i \(0.135198\pi\)
−0.911147 + 0.412082i \(0.864802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000i 0.529813i
\(58\) 0 0
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) 1.00000i 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 5.00000i − 0.610847i −0.952217 0.305424i \(-0.901202\pi\)
0.952217 0.305424i \(-0.0987981\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) − 10.0000i − 1.17041i −0.810885 0.585206i \(-0.801014\pi\)
0.810885 0.585206i \(-0.198986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 3.00000i − 0.341882i
\(78\) 0 0
\(79\) 7.00000 0.787562 0.393781 0.919204i \(-0.371167\pi\)
0.393781 + 0.919204i \(0.371167\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) 12.0000i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 18.0000i 1.92980i
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) − 16.0000i − 1.65912i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 8.00000i − 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) 0 0
\(101\) 18.0000 1.79107 0.895533 0.444994i \(-0.146794\pi\)
0.895533 + 0.444994i \(0.146794\pi\)
\(102\) 0 0
\(103\) − 10.0000i − 0.985329i −0.870219 0.492665i \(-0.836023\pi\)
0.870219 0.492665i \(-0.163977\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 0 0
\(109\) 7.00000 0.670478 0.335239 0.942133i \(-0.391183\pi\)
0.335239 + 0.942133i \(0.391183\pi\)
\(110\) 0 0
\(111\) −10.0000 −0.949158
\(112\) 0 0
\(113\) 15.0000i 1.41108i 0.708669 + 0.705541i \(0.249296\pi\)
−0.708669 + 0.705541i \(0.750704\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 4.00000i 0.369800i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 12.0000i 1.08200i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 7.00000i 0.621150i 0.950549 + 0.310575i \(0.100522\pi\)
−0.950549 + 0.310575i \(0.899478\pi\)
\(128\) 0 0
\(129\) 22.0000 1.93699
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 2.00000i 0.173422i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000i 0.512615i 0.966595 + 0.256307i \(0.0825059\pi\)
−0.966595 + 0.256307i \(0.917494\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) 0 0
\(141\) −12.0000 −1.01058
\(142\) 0 0
\(143\) − 12.0000i − 1.00349i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2.00000i 0.164957i
\(148\) 0 0
\(149\) 21.0000 1.72039 0.860194 0.509968i \(-0.170343\pi\)
0.860194 + 0.509968i \(0.170343\pi\)
\(150\) 0 0
\(151\) −1.00000 −0.0813788 −0.0406894 0.999172i \(-0.512955\pi\)
−0.0406894 + 0.999172i \(0.512955\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 2.00000i − 0.159617i −0.996810 0.0798087i \(-0.974569\pi\)
0.996810 0.0798087i \(-0.0254309\pi\)
\(158\) 0 0
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 0 0
\(163\) − 4.00000i − 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) 0 0
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −24.0000 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 20.0000i 1.47844i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −4.00000 −0.290957
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 23.0000i 1.65558i 0.561041 + 0.827788i \(0.310401\pi\)
−0.561041 + 0.827788i \(0.689599\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 15.0000i − 1.06871i −0.845262 0.534353i \(-0.820555\pi\)
0.845262 0.534353i \(-0.179445\pi\)
\(198\) 0 0
\(199\) 22.0000 1.55954 0.779769 0.626067i \(-0.215336\pi\)
0.779769 + 0.626067i \(0.215336\pi\)
\(200\) 0 0
\(201\) −10.0000 −0.705346
\(202\) 0 0
\(203\) 9.00000i 0.631676i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.00000i 0.208514i
\(208\) 0 0
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 0 0
\(213\) − 30.0000i − 2.05557i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 8.00000i − 0.543075i
\(218\) 0 0
\(219\) −20.0000 −1.35147
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 14.0000i 0.937509i 0.883328 + 0.468755i \(0.155297\pi\)
−0.883328 + 0.468755i \(0.844703\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.0000i 1.19470i 0.801980 + 0.597351i \(0.203780\pi\)
−0.801980 + 0.597351i \(0.796220\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) 21.0000i 1.37576i 0.725826 + 0.687878i \(0.241458\pi\)
−0.725826 + 0.687878i \(0.758542\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 14.0000i − 0.909398i
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 10.0000i 0.641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 8.00000i 0.509028i
\(248\) 0 0
\(249\) 24.0000 1.52094
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) − 9.00000i − 0.565825i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 24.0000i 1.49708i 0.663090 + 0.748539i \(0.269245\pi\)
−0.663090 + 0.748539i \(0.730755\pi\)
\(258\) 0 0
\(259\) −5.00000 −0.310685
\(260\) 0 0
\(261\) 9.00000 0.557086
\(262\) 0 0
\(263\) − 9.00000i − 0.554964i −0.960731 0.277482i \(-0.910500\pi\)
0.960731 0.277482i \(-0.0894999\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 24.0000i − 1.46878i
\(268\) 0 0
\(269\) −12.0000 −0.731653 −0.365826 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 0 0
\(273\) 8.00000i 0.484182i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 26.0000i − 1.56219i −0.624413 0.781094i \(-0.714662\pi\)
0.624413 0.781094i \(-0.285338\pi\)
\(278\) 0 0
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −15.0000 −0.894825 −0.447412 0.894328i \(-0.647654\pi\)
−0.447412 + 0.894328i \(0.647654\pi\)
\(282\) 0 0
\(283\) − 22.0000i − 1.30776i −0.756596 0.653882i \(-0.773139\pi\)
0.756596 0.653882i \(-0.226861\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.00000i 0.354169i
\(288\) 0 0
\(289\) 17.0000 1.00000
\(290\) 0 0
\(291\) −16.0000 −0.937937
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) − 12.0000i − 0.696311i
\(298\) 0 0
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) 11.0000 0.634029
\(302\) 0 0
\(303\) − 36.0000i − 2.06815i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 0 0
\(309\) −20.0000 −1.13776
\(310\) 0 0
\(311\) 12.0000 0.680458 0.340229 0.940343i \(-0.389495\pi\)
0.340229 + 0.940343i \(0.389495\pi\)
\(312\) 0 0
\(313\) − 22.0000i − 1.24351i −0.783210 0.621757i \(-0.786419\pi\)
0.783210 0.621757i \(-0.213581\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 3.00000i − 0.168497i −0.996445 0.0842484i \(-0.973151\pi\)
0.996445 0.0842484i \(-0.0268489\pi\)
\(318\) 0 0
\(319\) −27.0000 −1.51171
\(320\) 0 0
\(321\) 24.0000 1.33955
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) − 14.0000i − 0.774202i
\(328\) 0 0
\(329\) −6.00000 −0.330791
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 0 0
\(333\) 5.00000i 0.273998i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 2.00000i − 0.108947i −0.998515 0.0544735i \(-0.982652\pi\)
0.998515 0.0544735i \(-0.0173480\pi\)
\(338\) 0 0
\(339\) 30.0000 1.62938
\(340\) 0 0
\(341\) 24.0000 1.29967
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 3.00000i − 0.161048i −0.996753 0.0805242i \(-0.974341\pi\)
0.996753 0.0805242i \(-0.0256594\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) − 24.0000i − 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 4.00000i 0.209946i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 14.0000i − 0.730794i −0.930852 0.365397i \(-0.880933\pi\)
0.930852 0.365397i \(-0.119067\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) − 13.0000i − 0.673114i −0.941663 0.336557i \(-0.890737\pi\)
0.941663 0.336557i \(-0.109263\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 36.0000i 1.85409i
\(378\) 0 0
\(379\) 7.00000 0.359566 0.179783 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 0 0
\(381\) 14.0000 0.717242
\(382\) 0 0
\(383\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 11.0000i − 0.559161i
\(388\) 0 0
\(389\) −9.00000 −0.456318 −0.228159 0.973624i \(-0.573271\pi\)
−0.228159 + 0.973624i \(0.573271\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) − 24.0000i − 1.21064i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 22.0000i 1.10415i 0.833795 + 0.552074i \(0.186163\pi\)
−0.833795 + 0.552074i \(0.813837\pi\)
\(398\) 0 0
\(399\) 4.00000 0.200250
\(400\) 0 0
\(401\) 33.0000 1.64794 0.823971 0.566632i \(-0.191754\pi\)
0.823971 + 0.566632i \(0.191754\pi\)
\(402\) 0 0
\(403\) − 32.0000i − 1.59403i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 15.0000i − 0.743522i
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 20.0000i − 0.979404i
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) −13.0000 −0.633581 −0.316791 0.948495i \(-0.602605\pi\)
−0.316791 + 0.948495i \(0.602605\pi\)
\(422\) 0 0
\(423\) 6.00000i 0.291730i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 10.0000i 0.483934i
\(428\) 0 0
\(429\) −24.0000 −1.15873
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) 32.0000i 1.53782i 0.639356 + 0.768911i \(0.279201\pi\)
−0.639356 + 0.768911i \(0.720799\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.00000i 0.287019i
\(438\) 0 0
\(439\) 4.00000 0.190910 0.0954548 0.995434i \(-0.469569\pi\)
0.0954548 + 0.995434i \(0.469569\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 12.0000i 0.570137i 0.958507 + 0.285069i \(0.0920164\pi\)
−0.958507 + 0.285069i \(0.907984\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 42.0000i − 1.98653i
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) −18.0000 −0.847587
\(452\) 0 0
\(453\) 2.00000i 0.0939682i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 37.0000i 1.73079i 0.501093 + 0.865393i \(0.332931\pi\)
−0.501093 + 0.865393i \(0.667069\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) − 16.0000i − 0.743583i −0.928316 0.371792i \(-0.878744\pi\)
0.928316 0.371792i \(-0.121256\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 42.0000i − 1.94353i −0.235954 0.971764i \(-0.575822\pi\)
0.235954 0.971764i \(-0.424178\pi\)
\(468\) 0 0
\(469\) −5.00000 −0.230879
\(470\) 0 0
\(471\) −4.00000 −0.184310
\(472\) 0 0
\(473\) 33.0000i 1.51734i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 6.00000i − 0.274721i
\(478\) 0 0
\(479\) −12.0000 −0.548294 −0.274147 0.961688i \(-0.588395\pi\)
−0.274147 + 0.961688i \(0.588395\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 0 0
\(483\) 6.00000i 0.273009i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 1.00000i 0.0453143i 0.999743 + 0.0226572i \(0.00721262\pi\)
−0.999743 + 0.0226572i \(0.992787\pi\)
\(488\) 0 0
\(489\) −8.00000 −0.361773
\(490\) 0 0
\(491\) 3.00000 0.135388 0.0676941 0.997706i \(-0.478436\pi\)
0.0676941 + 0.997706i \(0.478436\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 15.0000i − 0.672842i
\(498\) 0 0
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 0 0
\(501\) 24.0000 1.07224
\(502\) 0 0
\(503\) 6.00000i 0.267527i 0.991013 + 0.133763i \(0.0427062\pi\)
−0.991013 + 0.133763i \(0.957294\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.00000i 0.266469i
\(508\) 0 0
\(509\) −36.0000 −1.59567 −0.797836 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) 0 0
\(511\) −10.0000 −0.442374
\(512\) 0 0
\(513\) 8.00000i 0.353209i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) − 18.0000i − 0.791639i
\(518\) 0 0
\(519\) 12.0000 0.526742
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 0 0
\(523\) 20.0000i 0.874539i 0.899331 + 0.437269i \(0.144054\pi\)
−0.899331 + 0.437269i \(0.855946\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 14.0000 0.608696
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 24.0000i 1.03956i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 48.0000i 2.07135i
\(538\) 0 0
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) −25.0000 −1.07483 −0.537417 0.843317i \(-0.680600\pi\)
−0.537417 + 0.843317i \(0.680600\pi\)
\(542\) 0 0
\(543\) 20.0000i 0.858282i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 17.0000i − 0.726868i −0.931620 0.363434i \(-0.881604\pi\)
0.931620 0.363434i \(-0.118396\pi\)
\(548\) 0 0
\(549\) 10.0000 0.426790
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) 0 0
\(553\) − 7.00000i − 0.297670i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 45.0000i 1.90671i 0.301849 + 0.953356i \(0.402396\pi\)
−0.301849 + 0.953356i \(0.597604\pi\)
\(558\) 0 0
\(559\) 44.0000 1.86100
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 6.00000i − 0.252870i −0.991975 0.126435i \(-0.959647\pi\)
0.991975 0.126435i \(-0.0403535\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 11.0000i 0.461957i
\(568\) 0 0
\(569\) 27.0000 1.13190 0.565949 0.824440i \(-0.308510\pi\)
0.565949 + 0.824440i \(0.308510\pi\)
\(570\) 0 0
\(571\) 5.00000 0.209243 0.104622 0.994512i \(-0.466637\pi\)
0.104622 + 0.994512i \(0.466637\pi\)
\(572\) 0 0
\(573\) − 24.0000i − 1.00261i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 2.00000i − 0.0832611i −0.999133 0.0416305i \(-0.986745\pi\)
0.999133 0.0416305i \(-0.0132552\pi\)
\(578\) 0 0
\(579\) 46.0000 1.91169
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) 18.0000i 0.745484i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 42.0000i 1.73353i 0.498721 + 0.866763i \(0.333803\pi\)
−0.498721 + 0.866763i \(0.666197\pi\)
\(588\) 0 0
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) −30.0000 −1.23404
\(592\) 0 0
\(593\) 12.0000i 0.492781i 0.969171 + 0.246390i \(0.0792446\pi\)
−0.969171 + 0.246390i \(0.920755\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 44.0000i − 1.80080i
\(598\) 0 0
\(599\) −9.00000 −0.367730 −0.183865 0.982952i \(-0.558861\pi\)
−0.183865 + 0.982952i \(0.558861\pi\)
\(600\) 0 0
\(601\) 8.00000 0.326327 0.163163 0.986599i \(-0.447830\pi\)
0.163163 + 0.986599i \(0.447830\pi\)
\(602\) 0 0
\(603\) 5.00000i 0.203616i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 20.0000i − 0.811775i −0.913923 0.405887i \(-0.866962\pi\)
0.913923 0.405887i \(-0.133038\pi\)
\(608\) 0 0
\(609\) 18.0000 0.729397
\(610\) 0 0
\(611\) −24.0000 −0.970936
\(612\) 0 0
\(613\) − 7.00000i − 0.282727i −0.989958 0.141364i \(-0.954851\pi\)
0.989958 0.141364i \(-0.0451487\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 39.0000i 1.57008i 0.619445 + 0.785040i \(0.287358\pi\)
−0.619445 + 0.785040i \(0.712642\pi\)
\(618\) 0 0
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) −12.0000 −0.481543
\(622\) 0 0
\(623\) − 12.0000i − 0.480770i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 12.0000i 0.479234i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) 0 0
\(633\) 56.0000i 2.22580i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 4.00000i 0.158486i
\(638\) 0 0
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) 9.00000 0.355479 0.177739 0.984078i \(-0.443122\pi\)
0.177739 + 0.984078i \(0.443122\pi\)
\(642\) 0 0
\(643\) − 40.0000i − 1.57745i −0.614749 0.788723i \(-0.710743\pi\)
0.614749 0.788723i \(-0.289257\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 6.00000i − 0.235884i −0.993020 0.117942i \(-0.962370\pi\)
0.993020 0.117942i \(-0.0376297\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −16.0000 −0.627089
\(652\) 0 0
\(653\) 6.00000i 0.234798i 0.993085 + 0.117399i \(0.0374557\pi\)
−0.993085 + 0.117399i \(0.962544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 10.0000i 0.390137i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) 38.0000 1.47803 0.739014 0.673690i \(-0.235292\pi\)
0.739014 + 0.673690i \(0.235292\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 27.0000i 1.04544i
\(668\) 0 0
\(669\) 28.0000 1.08254
\(670\) 0 0
\(671\) −30.0000 −1.15814
\(672\) 0 0
\(673\) 14.0000i 0.539660i 0.962908 + 0.269830i \(0.0869676\pi\)
−0.962908 + 0.269830i \(0.913032\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.00000i 0.230599i 0.993331 + 0.115299i \(0.0367827\pi\)
−0.993331 + 0.115299i \(0.963217\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 36.0000 1.37952
\(682\) 0 0
\(683\) − 45.0000i − 1.72188i −0.508709 0.860939i \(-0.669877\pi\)
0.508709 0.860939i \(-0.330123\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 28.0000i 1.06827i
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) 3.00000i 0.113961i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 42.0000 1.58859
\(700\) 0 0
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 10.0000i 0.377157i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 18.0000i − 0.676960i
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) −7.00000 −0.262521
\(712\) 0 0
\(713\) − 24.0000i − 0.898807i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 18.0000 0.671287 0.335643 0.941989i \(-0.391046\pi\)
0.335643 + 0.941989i \(0.391046\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) − 4.00000i − 0.148762i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 8.00000i − 0.296704i −0.988935 0.148352i \(-0.952603\pi\)
0.988935 0.148352i \(-0.0473968\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) − 4.00000i − 0.147743i −0.997268 0.0738717i \(-0.976464\pi\)
0.997268 0.0738717i \(-0.0235355\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 15.0000i − 0.552532i
\(738\) 0 0
\(739\) 25.0000 0.919640 0.459820 0.888012i \(-0.347914\pi\)
0.459820 + 0.888012i \(0.347914\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) − 12.0000i − 0.439057i
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −52.0000 −1.89751 −0.948753 0.316017i \(-0.897654\pi\)
−0.948753 + 0.316017i \(0.897654\pi\)
\(752\) 0 0
\(753\) − 24.0000i − 0.874609i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 43.0000i 1.56286i 0.623992 + 0.781431i \(0.285510\pi\)
−0.623992 + 0.781431i \(0.714490\pi\)
\(758\) 0 0
\(759\) −18.0000 −0.653359
\(760\) 0 0
\(761\) −48.0000 −1.74000 −0.869999 0.493053i \(-0.835881\pi\)
−0.869999 + 0.493053i \(0.835881\pi\)
\(762\) 0 0
\(763\) − 7.00000i − 0.253417i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 48.0000 1.72868
\(772\) 0 0
\(773\) 48.0000i 1.72644i 0.504828 + 0.863220i \(0.331556\pi\)
−0.504828 + 0.863220i \(0.668444\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 10.0000i 0.358748i
\(778\) 0 0
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) 45.0000 1.61023
\(782\) 0 0
\(783\) 36.0000i 1.28654i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.0000i 0.784215i 0.919919 + 0.392108i \(0.128254\pi\)
−0.919919 + 0.392108i \(0.871746\pi\)
\(788\) 0 0
\(789\) −18.0000 −0.640817
\(790\) 0 0
\(791\) 15.0000 0.533339
\(792\) 0 0
\(793\) 40.0000i 1.42044i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.0000i 0.425062i 0.977154 + 0.212531i \(0.0681706\pi\)
−0.977154 + 0.212531i \(0.931829\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −12.0000 −0.423999
\(802\) 0 0
\(803\) − 30.0000i − 1.05868i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.0000i 0.844840i
\(808\) 0 0
\(809\) 21.0000 0.738321 0.369160 0.929366i \(-0.379645\pi\)
0.369160 + 0.929366i \(0.379645\pi\)
\(810\) 0 0
\(811\) 26.0000 0.912983 0.456492 0.889728i \(-0.349106\pi\)
0.456492 + 0.889728i \(0.349106\pi\)
\(812\) 0 0
\(813\) − 40.0000i − 1.40286i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 22.0000i − 0.769683i
\(818\) 0 0
\(819\) 4.00000 0.139771
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) 17.0000i 0.592583i 0.955098 + 0.296291i \(0.0957499\pi\)
−0.955098 + 0.296291i \(0.904250\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 3.00000i − 0.104320i −0.998639 0.0521601i \(-0.983389\pi\)
0.998639 0.0521601i \(-0.0166106\pi\)
\(828\) 0 0
\(829\) −44.0000 −1.52818 −0.764092 0.645108i \(-0.776812\pi\)
−0.764092 + 0.645108i \(0.776812\pi\)
\(830\) 0 0
\(831\) −52.0000 −1.80386
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 32.0000i − 1.10608i
\(838\) 0 0
\(839\) −54.0000 −1.86429 −0.932144 0.362089i \(-0.882064\pi\)
−0.932144 + 0.362089i \(0.882064\pi\)
\(840\) 0 0
\(841\) 52.0000 1.79310
\(842\) 0 0
\(843\) 30.0000i 1.03325i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.00000i 0.0687208i
\(848\) 0 0
\(849\) −44.0000 −1.51008
\(850\) 0 0
\(851\) −15.0000 −0.514193
\(852\) 0 0
\(853\) − 4.00000i − 0.136957i −0.997653 0.0684787i \(-0.978185\pi\)
0.997653 0.0684787i \(-0.0218145\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 18.0000i − 0.614868i −0.951569 0.307434i \(-0.900530\pi\)
0.951569 0.307434i \(-0.0994704\pi\)
\(858\) 0 0
\(859\) −14.0000 −0.477674 −0.238837 0.971060i \(-0.576766\pi\)
−0.238837 + 0.971060i \(0.576766\pi\)
\(860\) 0 0
\(861\) 12.0000 0.408959
\(862\) 0 0
\(863\) − 9.00000i − 0.306364i −0.988198 0.153182i \(-0.951048\pi\)
0.988198 0.153182i \(-0.0489520\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 34.0000i − 1.15470i
\(868\) 0 0
\(869\) 21.0000 0.712376
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) 0 0
\(873\) 8.00000i 0.270759i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 50.0000i − 1.68838i −0.536044 0.844190i \(-0.680082\pi\)
0.536044 0.844190i \(-0.319918\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −48.0000 −1.61716 −0.808581 0.588386i \(-0.799764\pi\)
−0.808581 + 0.588386i \(0.799764\pi\)
\(882\) 0 0
\(883\) 29.0000i 0.975928i 0.872864 + 0.487964i \(0.162260\pi\)
−0.872864 + 0.487964i \(0.837740\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 42.0000i − 1.41022i −0.709097 0.705111i \(-0.750897\pi\)
0.709097 0.705111i \(-0.249103\pi\)
\(888\) 0 0
\(889\) 7.00000 0.234772
\(890\) 0 0
\(891\) −33.0000 −1.10554
\(892\) 0 0
\(893\) 12.0000i 0.401565i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 24.0000i 0.801337i
\(898\) 0 0
\(899\) −72.0000 −2.40133
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) − 22.0000i − 0.732114i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 52.0000i 1.72663i 0.504664 + 0.863316i \(0.331616\pi\)
−0.504664 + 0.863316i \(0.668384\pi\)
\(908\) 0 0
\(909\) −18.0000 −0.597022
\(910\) 0 0
\(911\) 33.0000 1.09334 0.546669 0.837349i \(-0.315895\pi\)
0.546669 + 0.837349i \(0.315895\pi\)
\(912\) 0 0
\(913\) 36.0000i 1.19143i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 12.0000i − 0.396275i
\(918\) 0 0
\(919\) −5.00000 −0.164935 −0.0824674 0.996594i \(-0.526280\pi\)
−0.0824674 + 0.996594i \(0.526280\pi\)
\(920\) 0 0
\(921\) 8.00000 0.263609
\(922\) 0 0
\(923\) − 60.0000i − 1.97492i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 10.0000i 0.328443i
\(928\) 0 0
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 0 0
\(931\) 2.00000 0.0655474
\(932\) 0 0
\(933\) − 24.0000i − 0.785725i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 2.00000i − 0.0653372i −0.999466 0.0326686i \(-0.989599\pi\)
0.999466 0.0326686i \(-0.0104006\pi\)
\(938\) 0 0
\(939\) −44.0000 −1.43589
\(940\) 0 0
\(941\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(942\) 0 0
\(943\) 18.0000i 0.586161i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 36.0000i − 1.16984i −0.811090 0.584921i \(-0.801125\pi\)
0.811090 0.584921i \(-0.198875\pi\)
\(948\) 0 0
\(949\) −40.0000 −1.29845
\(950\) 0 0
\(951\) −6.00000 −0.194563
\(952\) 0 0
\(953\) 3.00000i 0.0971795i 0.998819 + 0.0485898i \(0.0154727\pi\)
−0.998819 + 0.0485898i \(0.984527\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 54.0000i 1.74557i
\(958\) 0 0
\(959\) 6.00000 0.193750
\(960\) 0 0
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) − 12.0000i − 0.386695i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 8.00000i − 0.257263i −0.991692 0.128631i \(-0.958942\pi\)
0.991692 0.128631i \(-0.0410584\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 18.0000 0.577647 0.288824 0.957382i \(-0.406736\pi\)
0.288824 + 0.957382i \(0.406736\pi\)
\(972\) 0 0
\(973\) − 10.0000i − 0.320585i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 45.0000i − 1.43968i −0.694141 0.719839i \(-0.744216\pi\)
0.694141 0.719839i \(-0.255784\pi\)
\(978\) 0 0
\(979\) 36.0000 1.15056
\(980\) 0 0
\(981\) −7.00000 −0.223493
\(982\) 0 0
\(983\) 48.0000i 1.53096i 0.643458 + 0.765481i \(0.277499\pi\)
−0.643458 + 0.765481i \(0.722501\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 12.0000i 0.381964i
\(988\) 0 0
\(989\) 33.0000 1.04934
\(990\) 0 0
\(991\) −7.00000 −0.222362 −0.111181 0.993800i \(-0.535463\pi\)
−0.111181 + 0.993800i \(0.535463\pi\)
\(992\) 0 0
\(993\) − 10.0000i − 0.317340i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) − 62.0000i − 1.96356i −0.190022 0.981780i \(-0.560856\pi\)
0.190022 0.981780i \(-0.439144\pi\)
\(998\) 0 0
\(999\) −20.0000 −0.632772
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 700.2.e.b.449.1 2
3.2 odd 2 6300.2.k.d.6049.1 2
4.3 odd 2 2800.2.g.e.449.2 2
5.2 odd 4 700.2.a.c.1.1 1
5.3 odd 4 700.2.a.i.1.1 yes 1
5.4 even 2 inner 700.2.e.b.449.2 2
7.6 odd 2 4900.2.e.g.2549.2 2
15.2 even 4 6300.2.a.s.1.1 1
15.8 even 4 6300.2.a.e.1.1 1
15.14 odd 2 6300.2.k.d.6049.2 2
20.3 even 4 2800.2.a.e.1.1 1
20.7 even 4 2800.2.a.ba.1.1 1
20.19 odd 2 2800.2.g.e.449.1 2
35.13 even 4 4900.2.a.f.1.1 1
35.27 even 4 4900.2.a.t.1.1 1
35.34 odd 2 4900.2.e.g.2549.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
700.2.a.c.1.1 1 5.2 odd 4
700.2.a.i.1.1 yes 1 5.3 odd 4
700.2.e.b.449.1 2 1.1 even 1 trivial
700.2.e.b.449.2 2 5.4 even 2 inner
2800.2.a.e.1.1 1 20.3 even 4
2800.2.a.ba.1.1 1 20.7 even 4
2800.2.g.e.449.1 2 20.19 odd 2
2800.2.g.e.449.2 2 4.3 odd 2
4900.2.a.f.1.1 1 35.13 even 4
4900.2.a.t.1.1 1 35.27 even 4
4900.2.e.g.2549.1 2 35.34 odd 2
4900.2.e.g.2549.2 2 7.6 odd 2
6300.2.a.e.1.1 1 15.8 even 4
6300.2.a.s.1.1 1 15.2 even 4
6300.2.k.d.6049.1 2 3.2 odd 2
6300.2.k.d.6049.2 2 15.14 odd 2