Properties

Label 5700.2.f.q.3649.1
Level $5700$
Weight $2$
Character 5700.3649
Analytic conductor $45.515$
Analytic rank $0$
Dimension $6$
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] = [5700,2,Mod(3649,5700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5700.3649");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5700.f (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: \(45.5147291521\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.5089536.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3649.1
Root \(1.66044 - 1.66044i\) of defining polynomial
Character \(\chi\) \(=\) 5700.3649
Dual form 5700.2.f.q.3649.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{3} -1.32088i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{3} -1.32088i q^{7} -1.00000 q^{9} +3.70739 q^{11} -3.32088i q^{13} +1.61350i q^{17} +1.00000 q^{19} -1.32088 q^{21} +7.67004i q^{23} +1.00000i q^{27} +1.70739 q^{29} +9.67004 q^{31} -3.70739i q^{33} +5.96265i q^{37} -3.32088 q^{39} +2.29261 q^{41} +8.73566i q^{43} +11.6700i q^{47} +5.25526 q^{49} +1.61350 q^{51} -10.4431i q^{53} -1.00000i q^{57} -12.6983 q^{59} +9.02827 q^{61} +1.32088i q^{63} -13.2835i q^{67} +7.67004 q^{69} -8.69832 q^{71} +12.0565i q^{73} -4.89703i q^{77} +14.0565 q^{79} +1.00000 q^{81} -5.02827i q^{83} -1.70739i q^{87} +1.70739 q^{89} -4.38650 q^{91} -9.67004i q^{93} -0.679116i q^{97} -3.70739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{9} + 12 q^{11} + 6 q^{19} + 8 q^{21} - 4 q^{39} + 24 q^{41} - 6 q^{49} + 4 q^{51} + 8 q^{59} + 28 q^{61} - 12 q^{69} + 32 q^{71} + 32 q^{79} + 6 q^{81} - 32 q^{91} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5700\mathbb{Z}\right)^\times\).

\(n\) \(1901\) \(2851\) \(3877\) \(4201\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(1\)

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
\(3\) − 1.00000i − 0.577350i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 1.32088i − 0.499247i −0.968343 0.249624i \(-0.919693\pi\)
0.968343 0.249624i \(-0.0803069\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) 0 0
\(11\) 3.70739 1.11782 0.558910 0.829228i \(-0.311220\pi\)
0.558910 + 0.829228i \(0.311220\pi\)
\(12\) 0 0
\(13\) − 3.32088i − 0.921048i −0.887647 0.460524i \(-0.847662\pi\)
0.887647 0.460524i \(-0.152338\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.61350i 0.391330i 0.980671 + 0.195665i \(0.0626865\pi\)
−0.980671 + 0.195665i \(0.937313\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −1.32088 −0.288241
\(22\) 0 0
\(23\) 7.67004i 1.59931i 0.600457 + 0.799657i \(0.294985\pi\)
−0.600457 + 0.799657i \(0.705015\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 1.70739 0.317054 0.158527 0.987355i \(-0.449325\pi\)
0.158527 + 0.987355i \(0.449325\pi\)
\(30\) 0 0
\(31\) 9.67004 1.73679 0.868395 0.495872i \(-0.165152\pi\)
0.868395 + 0.495872i \(0.165152\pi\)
\(32\) 0 0
\(33\) − 3.70739i − 0.645374i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 5.96265i 0.980254i 0.871651 + 0.490127i \(0.163050\pi\)
−0.871651 + 0.490127i \(0.836950\pi\)
\(38\) 0 0
\(39\) −3.32088 −0.531767
\(40\) 0 0
\(41\) 2.29261 0.358046 0.179023 0.983845i \(-0.442706\pi\)
0.179023 + 0.983845i \(0.442706\pi\)
\(42\) 0 0
\(43\) 8.73566i 1.33218i 0.745873 + 0.666088i \(0.232033\pi\)
−0.745873 + 0.666088i \(0.767967\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.6700i 1.70225i 0.524963 + 0.851125i \(0.324079\pi\)
−0.524963 + 0.851125i \(0.675921\pi\)
\(48\) 0 0
\(49\) 5.25526 0.750752
\(50\) 0 0
\(51\) 1.61350 0.225935
\(52\) 0 0
\(53\) − 10.4431i − 1.43446i −0.696835 0.717232i \(-0.745409\pi\)
0.696835 0.717232i \(-0.254591\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) − 1.00000i − 0.132453i
\(58\) 0 0
\(59\) −12.6983 −1.65318 −0.826590 0.562805i \(-0.809722\pi\)
−0.826590 + 0.562805i \(0.809722\pi\)
\(60\) 0 0
\(61\) 9.02827 1.15595 0.577976 0.816054i \(-0.303843\pi\)
0.577976 + 0.816054i \(0.303843\pi\)
\(62\) 0 0
\(63\) 1.32088i 0.166416i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 13.2835i − 1.62284i −0.584462 0.811421i \(-0.698694\pi\)
0.584462 0.811421i \(-0.301306\pi\)
\(68\) 0 0
\(69\) 7.67004 0.923365
\(70\) 0 0
\(71\) −8.69832 −1.03230 −0.516150 0.856498i \(-0.672635\pi\)
−0.516150 + 0.856498i \(0.672635\pi\)
\(72\) 0 0
\(73\) 12.0565i 1.41111i 0.708654 + 0.705556i \(0.249303\pi\)
−0.708654 + 0.705556i \(0.750697\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 4.89703i − 0.558069i
\(78\) 0 0
\(79\) 14.0565 1.58149 0.790743 0.612149i \(-0.209695\pi\)
0.790743 + 0.612149i \(0.209695\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) − 5.02827i − 0.551925i −0.961168 0.275962i \(-0.911003\pi\)
0.961168 0.275962i \(-0.0889965\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) − 1.70739i − 0.183051i
\(88\) 0 0
\(89\) 1.70739 0.180983 0.0904915 0.995897i \(-0.471156\pi\)
0.0904915 + 0.995897i \(0.471156\pi\)
\(90\) 0 0
\(91\) −4.38650 −0.459831
\(92\) 0 0
\(93\) − 9.67004i − 1.00274i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) − 0.679116i − 0.0689537i −0.999405 0.0344769i \(-0.989023\pi\)
0.999405 0.0344769i \(-0.0109765\pi\)
\(98\) 0 0
\(99\) −3.70739 −0.372607
\(100\) 0 0
\(101\) 12.6418 1.25790 0.628952 0.777445i \(-0.283484\pi\)
0.628952 + 0.777445i \(0.283484\pi\)
\(102\) 0 0
\(103\) − 6.05655i − 0.596769i −0.954446 0.298385i \(-0.903552\pi\)
0.954446 0.298385i \(-0.0964478\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) −10.6983 −1.02471 −0.512356 0.858773i \(-0.671227\pi\)
−0.512356 + 0.858773i \(0.671227\pi\)
\(110\) 0 0
\(111\) 5.96265 0.565950
\(112\) 0 0
\(113\) 16.3118i 1.53449i 0.641356 + 0.767243i \(0.278372\pi\)
−0.641356 + 0.767243i \(0.721628\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 3.32088i 0.307016i
\(118\) 0 0
\(119\) 2.13124 0.195371
\(120\) 0 0
\(121\) 2.74474 0.249521
\(122\) 0 0
\(123\) − 2.29261i − 0.206718i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 4.00000i − 0.354943i −0.984126 0.177471i \(-0.943208\pi\)
0.984126 0.177471i \(-0.0567917\pi\)
\(128\) 0 0
\(129\) 8.73566 0.769132
\(130\) 0 0
\(131\) 4.29261 0.375047 0.187524 0.982260i \(-0.439954\pi\)
0.187524 + 0.982260i \(0.439954\pi\)
\(132\) 0 0
\(133\) − 1.32088i − 0.114535i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.00000i 0.170872i 0.996344 + 0.0854358i \(0.0272282\pi\)
−0.996344 + 0.0854358i \(0.972772\pi\)
\(138\) 0 0
\(139\) 8.58522 0.728189 0.364094 0.931362i \(-0.381379\pi\)
0.364094 + 0.931362i \(0.381379\pi\)
\(140\) 0 0
\(141\) 11.6700 0.982795
\(142\) 0 0
\(143\) − 12.3118i − 1.02957i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 5.25526i − 0.433447i
\(148\) 0 0
\(149\) −12.0565 −0.987711 −0.493855 0.869544i \(-0.664413\pi\)
−0.493855 + 0.869544i \(0.664413\pi\)
\(150\) 0 0
\(151\) −22.9536 −1.86794 −0.933968 0.357357i \(-0.883678\pi\)
−0.933968 + 0.357357i \(0.883678\pi\)
\(152\) 0 0
\(153\) − 1.61350i − 0.130443i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 11.8688i − 0.947230i −0.880732 0.473615i \(-0.842949\pi\)
0.880732 0.473615i \(-0.157051\pi\)
\(158\) 0 0
\(159\) −10.4431 −0.828188
\(160\) 0 0
\(161\) 10.1312 0.798454
\(162\) 0 0
\(163\) 0.0373465i 0.00292520i 0.999999 + 0.00146260i \(0.000465561\pi\)
−0.999999 + 0.00146260i \(0.999534\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 11.0283i − 0.853393i −0.904395 0.426697i \(-0.859677\pi\)
0.904395 0.426697i \(-0.140323\pi\)
\(168\) 0 0
\(169\) 1.97173 0.151671
\(170\) 0 0
\(171\) −1.00000 −0.0764719
\(172\) 0 0
\(173\) 17.8578i 1.35771i 0.734274 + 0.678853i \(0.237523\pi\)
−0.734274 + 0.678853i \(0.762477\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 12.6983i 0.954464i
\(178\) 0 0
\(179\) 19.9253 1.48929 0.744644 0.667462i \(-0.232619\pi\)
0.744644 + 0.667462i \(0.232619\pi\)
\(180\) 0 0
\(181\) −15.4713 −1.14997 −0.574987 0.818162i \(-0.694993\pi\)
−0.574987 + 0.818162i \(0.694993\pi\)
\(182\) 0 0
\(183\) − 9.02827i − 0.667389i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 5.98185i 0.437437i
\(188\) 0 0
\(189\) 1.32088 0.0960802
\(190\) 0 0
\(191\) 18.3492 1.32770 0.663849 0.747866i \(-0.268922\pi\)
0.663849 + 0.747866i \(0.268922\pi\)
\(192\) 0 0
\(193\) − 12.0192i − 0.865161i −0.901595 0.432581i \(-0.857603\pi\)
0.901595 0.432581i \(-0.142397\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.84049i 0.344870i 0.985021 + 0.172435i \(0.0551635\pi\)
−0.985021 + 0.172435i \(0.944836\pi\)
\(198\) 0 0
\(199\) 20.6983 1.46726 0.733632 0.679547i \(-0.237823\pi\)
0.733632 + 0.679547i \(0.237823\pi\)
\(200\) 0 0
\(201\) −13.2835 −0.936949
\(202\) 0 0
\(203\) − 2.25526i − 0.158289i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 7.67004i − 0.533105i
\(208\) 0 0
\(209\) 3.70739 0.256445
\(210\) 0 0
\(211\) 2.05655 0.141579 0.0707893 0.997491i \(-0.477448\pi\)
0.0707893 + 0.997491i \(0.477448\pi\)
\(212\) 0 0
\(213\) 8.69832i 0.595999i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 12.7730i − 0.867088i
\(218\) 0 0
\(219\) 12.0565 0.814706
\(220\) 0 0
\(221\) 5.35823 0.360434
\(222\) 0 0
\(223\) − 6.05655i − 0.405576i −0.979223 0.202788i \(-0.935000\pi\)
0.979223 0.202788i \(-0.0650003\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) − 28.3118i − 1.87912i −0.342383 0.939560i \(-0.611234\pi\)
0.342383 0.939560i \(-0.388766\pi\)
\(228\) 0 0
\(229\) 1.80128 0.119032 0.0595161 0.998227i \(-0.481044\pi\)
0.0595161 + 0.998227i \(0.481044\pi\)
\(230\) 0 0
\(231\) −4.89703 −0.322201
\(232\) 0 0
\(233\) 3.94345i 0.258344i 0.991622 + 0.129172i \(0.0412320\pi\)
−0.991622 + 0.129172i \(0.958768\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) − 14.0565i − 0.913071i
\(238\) 0 0
\(239\) 16.8031 1.08690 0.543452 0.839440i \(-0.317117\pi\)
0.543452 + 0.839440i \(0.317117\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) − 1.00000i − 0.0641500i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 3.32088i − 0.211303i
\(248\) 0 0
\(249\) −5.02827 −0.318654
\(250\) 0 0
\(251\) 24.9909 1.57741 0.788707 0.614770i \(-0.210751\pi\)
0.788707 + 0.614770i \(0.210751\pi\)
\(252\) 0 0
\(253\) 28.4358i 1.78775i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 2.91518i − 0.181844i −0.995858 0.0909219i \(-0.971019\pi\)
0.995858 0.0909219i \(-0.0289814\pi\)
\(258\) 0 0
\(259\) 7.87598 0.489389
\(260\) 0 0
\(261\) −1.70739 −0.105685
\(262\) 0 0
\(263\) 22.3118i 1.37581i 0.725803 + 0.687903i \(0.241468\pi\)
−0.725803 + 0.687903i \(0.758532\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) − 1.70739i − 0.104491i
\(268\) 0 0
\(269\) −15.0656 −0.918567 −0.459284 0.888290i \(-0.651894\pi\)
−0.459284 + 0.888290i \(0.651894\pi\)
\(270\) 0 0
\(271\) 5.47133 0.332359 0.166180 0.986095i \(-0.446857\pi\)
0.166180 + 0.986095i \(0.446857\pi\)
\(272\) 0 0
\(273\) 4.38650i 0.265483i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 10.7730i − 0.647287i −0.946179 0.323644i \(-0.895092\pi\)
0.946179 0.323644i \(-0.104908\pi\)
\(278\) 0 0
\(279\) −9.67004 −0.578930
\(280\) 0 0
\(281\) 17.8205 1.06308 0.531540 0.847033i \(-0.321613\pi\)
0.531540 + 0.847033i \(0.321613\pi\)
\(282\) 0 0
\(283\) 30.2070i 1.79562i 0.440384 + 0.897810i \(0.354842\pi\)
−0.440384 + 0.897810i \(0.645158\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 3.02827i − 0.178753i
\(288\) 0 0
\(289\) 14.3966 0.846861
\(290\) 0 0
\(291\) −0.679116 −0.0398105
\(292\) 0 0
\(293\) 18.2553i 1.06648i 0.845963 + 0.533242i \(0.179026\pi\)
−0.845963 + 0.533242i \(0.820974\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.70739i 0.215125i
\(298\) 0 0
\(299\) 25.4713 1.47304
\(300\) 0 0
\(301\) 11.5388 0.665085
\(302\) 0 0
\(303\) − 12.6418i − 0.726251i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 16.5852i − 0.946569i −0.880910 0.473284i \(-0.843068\pi\)
0.880910 0.473284i \(-0.156932\pi\)
\(308\) 0 0
\(309\) −6.05655 −0.344545
\(310\) 0 0
\(311\) 11.5196 0.653217 0.326608 0.945160i \(-0.394094\pi\)
0.326608 + 0.945160i \(0.394094\pi\)
\(312\) 0 0
\(313\) − 32.7549i − 1.85141i −0.378241 0.925707i \(-0.623471\pi\)
0.378241 0.925707i \(-0.376529\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.2161i 0.854619i 0.904105 + 0.427310i \(0.140539\pi\)
−0.904105 + 0.427310i \(0.859461\pi\)
\(318\) 0 0
\(319\) 6.32996 0.354410
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.61350i 0.0897773i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 10.6983i 0.591618i
\(328\) 0 0
\(329\) 15.4148 0.849844
\(330\) 0 0
\(331\) −26.9536 −1.48150 −0.740751 0.671779i \(-0.765530\pi\)
−0.740751 + 0.671779i \(0.765530\pi\)
\(332\) 0 0
\(333\) − 5.96265i − 0.326751i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 17.5652i − 0.956839i −0.878132 0.478419i \(-0.841210\pi\)
0.878132 0.478419i \(-0.158790\pi\)
\(338\) 0 0
\(339\) 16.3118 0.885936
\(340\) 0 0
\(341\) 35.8506 1.94142
\(342\) 0 0
\(343\) − 16.1878i − 0.874058i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) − 34.3118i − 1.84195i −0.389616 0.920977i \(-0.627392\pi\)
0.389616 0.920977i \(-0.372608\pi\)
\(348\) 0 0
\(349\) −35.2835 −1.88868 −0.944342 0.328965i \(-0.893300\pi\)
−0.944342 + 0.328965i \(0.893300\pi\)
\(350\) 0 0
\(351\) 3.32088 0.177256
\(352\) 0 0
\(353\) 8.71646i 0.463930i 0.972724 + 0.231965i \(0.0745156\pi\)
−0.972724 + 0.231965i \(0.925484\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 2.13124i − 0.112797i
\(358\) 0 0
\(359\) −30.4623 −1.60774 −0.803868 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) − 2.74474i − 0.144061i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 27.5652i − 1.43889i −0.694548 0.719446i \(-0.744396\pi\)
0.694548 0.719446i \(-0.255604\pi\)
\(368\) 0 0
\(369\) −2.29261 −0.119349
\(370\) 0 0
\(371\) −13.7941 −0.716152
\(372\) 0 0
\(373\) − 16.0939i − 0.833310i −0.909065 0.416655i \(-0.863202\pi\)
0.909065 0.416655i \(-0.136798\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 5.67004i − 0.292022i
\(378\) 0 0
\(379\) −9.01013 −0.462819 −0.231410 0.972856i \(-0.574334\pi\)
−0.231410 + 0.972856i \(0.574334\pi\)
\(380\) 0 0
\(381\) −4.00000 −0.204926
\(382\) 0 0
\(383\) 23.3401i 1.19262i 0.802753 + 0.596311i \(0.203368\pi\)
−0.802753 + 0.596311i \(0.796632\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) − 8.73566i − 0.444059i
\(388\) 0 0
\(389\) −20.0565 −1.01691 −0.508454 0.861089i \(-0.669783\pi\)
−0.508454 + 0.861089i \(0.669783\pi\)
\(390\) 0 0
\(391\) −12.3756 −0.625860
\(392\) 0 0
\(393\) − 4.29261i − 0.216534i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) − 21.7375i − 1.09097i −0.838119 0.545487i \(-0.816345\pi\)
0.838119 0.545487i \(-0.183655\pi\)
\(398\) 0 0
\(399\) −1.32088 −0.0661269
\(400\) 0 0
\(401\) −7.17872 −0.358488 −0.179244 0.983805i \(-0.557365\pi\)
−0.179244 + 0.983805i \(0.557365\pi\)
\(402\) 0 0
\(403\) − 32.1131i − 1.59967i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 22.1059i 1.09575i
\(408\) 0 0
\(409\) −16.2443 −0.803231 −0.401615 0.915808i \(-0.631551\pi\)
−0.401615 + 0.915808i \(0.631551\pi\)
\(410\) 0 0
\(411\) 2.00000 0.0986527
\(412\) 0 0
\(413\) 16.7730i 0.825346i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 8.58522i − 0.420420i
\(418\) 0 0
\(419\) −16.9909 −0.830061 −0.415031 0.909807i \(-0.636229\pi\)
−0.415031 + 0.909807i \(0.636229\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) − 11.6700i − 0.567417i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) − 11.9253i − 0.577106i
\(428\) 0 0
\(429\) −12.3118 −0.594420
\(430\) 0 0
\(431\) 22.6418 1.09062 0.545308 0.838236i \(-0.316413\pi\)
0.545308 + 0.838236i \(0.316413\pi\)
\(432\) 0 0
\(433\) 12.2070i 0.586630i 0.956016 + 0.293315i \(0.0947586\pi\)
−0.956016 + 0.293315i \(0.905241\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.67004i 0.366908i
\(438\) 0 0
\(439\) 31.8506 1.52015 0.760073 0.649837i \(-0.225163\pi\)
0.760073 + 0.649837i \(0.225163\pi\)
\(440\) 0 0
\(441\) −5.25526 −0.250251
\(442\) 0 0
\(443\) − 8.95358i − 0.425397i −0.977118 0.212699i \(-0.931775\pi\)
0.977118 0.212699i \(-0.0682253\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0565i 0.570255i
\(448\) 0 0
\(449\) −5.51960 −0.260486 −0.130243 0.991482i \(-0.541576\pi\)
−0.130243 + 0.991482i \(0.541576\pi\)
\(450\) 0 0
\(451\) 8.49960 0.400231
\(452\) 0 0
\(453\) 22.9536i 1.07845i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.131241i 0.00613918i 0.999995 + 0.00306959i \(0.000977083\pi\)
−0.999995 + 0.00306959i \(0.999023\pi\)
\(458\) 0 0
\(459\) −1.61350 −0.0753115
\(460\) 0 0
\(461\) −14.1131 −0.657312 −0.328656 0.944450i \(-0.606596\pi\)
−0.328656 + 0.944450i \(0.606596\pi\)
\(462\) 0 0
\(463\) − 5.98080i − 0.277951i −0.990296 0.138976i \(-0.955619\pi\)
0.990296 0.138976i \(-0.0443810\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 6.38650i − 0.295532i −0.989022 0.147766i \(-0.952792\pi\)
0.989022 0.147766i \(-0.0472083\pi\)
\(468\) 0 0
\(469\) −17.5460 −0.810200
\(470\) 0 0
\(471\) −11.8688 −0.546884
\(472\) 0 0
\(473\) 32.3865i 1.48913i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 10.4431i 0.478155i
\(478\) 0 0
\(479\) −18.8597 −0.861721 −0.430861 0.902419i \(-0.641790\pi\)
−0.430861 + 0.902419i \(0.641790\pi\)
\(480\) 0 0
\(481\) 19.8013 0.902861
\(482\) 0 0
\(483\) − 10.1312i − 0.460987i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 10.1312i 0.459090i 0.973298 + 0.229545i \(0.0737239\pi\)
−0.973298 + 0.229545i \(0.926276\pi\)
\(488\) 0 0
\(489\) 0.0373465 0.00168887
\(490\) 0 0
\(491\) 1.06562 0.0480908 0.0240454 0.999711i \(-0.492345\pi\)
0.0240454 + 0.999711i \(0.492345\pi\)
\(492\) 0 0
\(493\) 2.75486i 0.124073i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 11.4895i 0.515373i
\(498\) 0 0
\(499\) 14.2443 0.637664 0.318832 0.947811i \(-0.396709\pi\)
0.318832 + 0.947811i \(0.396709\pi\)
\(500\) 0 0
\(501\) −11.0283 −0.492707
\(502\) 0 0
\(503\) − 30.9717i − 1.38096i −0.723351 0.690481i \(-0.757399\pi\)
0.723351 0.690481i \(-0.242601\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) − 1.97173i − 0.0875674i
\(508\) 0 0
\(509\) 30.4057 1.34771 0.673855 0.738864i \(-0.264637\pi\)
0.673855 + 0.738864i \(0.264637\pi\)
\(510\) 0 0
\(511\) 15.9253 0.704494
\(512\) 0 0
\(513\) 1.00000i 0.0441511i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 43.2654i 1.90281i
\(518\) 0 0
\(519\) 17.8578 0.783872
\(520\) 0 0
\(521\) −4.34916 −0.190540 −0.0952700 0.995451i \(-0.530371\pi\)
−0.0952700 + 0.995451i \(0.530371\pi\)
\(522\) 0 0
\(523\) 8.69832i 0.380351i 0.981750 + 0.190175i \(0.0609057\pi\)
−0.981750 + 0.190175i \(0.939094\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 15.6026i 0.679659i
\(528\) 0 0
\(529\) −35.8296 −1.55781
\(530\) 0 0
\(531\) 12.6983 0.551060
\(532\) 0 0
\(533\) − 7.61350i − 0.329777i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 19.9253i − 0.859840i
\(538\) 0 0
\(539\) 19.4833 0.839206
\(540\) 0 0
\(541\) 8.45398 0.363465 0.181733 0.983348i \(-0.441830\pi\)
0.181733 + 0.983348i \(0.441830\pi\)
\(542\) 0 0
\(543\) 15.4713i 0.663938i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 11.5279i 0.492896i 0.969156 + 0.246448i \(0.0792635\pi\)
−0.969156 + 0.246448i \(0.920736\pi\)
\(548\) 0 0
\(549\) −9.02827 −0.385317
\(550\) 0 0
\(551\) 1.70739 0.0727372
\(552\) 0 0
\(553\) − 18.5671i − 0.789552i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.22699i 0.0519892i 0.999662 + 0.0259946i \(0.00827528\pi\)
−0.999662 + 0.0259946i \(0.991725\pi\)
\(558\) 0 0
\(559\) 29.0101 1.22700
\(560\) 0 0
\(561\) 5.98185 0.252554
\(562\) 0 0
\(563\) − 19.9144i − 0.839291i −0.907688 0.419646i \(-0.862154\pi\)
0.907688 0.419646i \(-0.137846\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 1.32088i − 0.0554719i
\(568\) 0 0
\(569\) 27.5015 1.15292 0.576460 0.817125i \(-0.304433\pi\)
0.576460 + 0.817125i \(0.304433\pi\)
\(570\) 0 0
\(571\) −9.47133 −0.396363 −0.198181 0.980165i \(-0.563503\pi\)
−0.198181 + 0.980165i \(0.563503\pi\)
\(572\) 0 0
\(573\) − 18.3492i − 0.766547i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 36.6418i 1.52542i 0.646743 + 0.762708i \(0.276131\pi\)
−0.646743 + 0.762708i \(0.723869\pi\)
\(578\) 0 0
\(579\) −12.0192 −0.499501
\(580\) 0 0
\(581\) −6.64177 −0.275547
\(582\) 0 0
\(583\) − 38.7165i − 1.60347i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) − 3.67004i − 0.151479i −0.997128 0.0757394i \(-0.975868\pi\)
0.997128 0.0757394i \(-0.0241317\pi\)
\(588\) 0 0
\(589\) 9.67004 0.398447
\(590\) 0 0
\(591\) 4.84049 0.199111
\(592\) 0 0
\(593\) 17.2270i 0.707428i 0.935354 + 0.353714i \(0.115081\pi\)
−0.935354 + 0.353714i \(0.884919\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) − 20.6983i − 0.847126i
\(598\) 0 0
\(599\) 8.11310 0.331492 0.165746 0.986168i \(-0.446997\pi\)
0.165746 + 0.986168i \(0.446997\pi\)
\(600\) 0 0
\(601\) 7.35823 0.300149 0.150074 0.988675i \(-0.452049\pi\)
0.150074 + 0.988675i \(0.452049\pi\)
\(602\) 0 0
\(603\) 13.2835i 0.540947i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 19.9253i 0.808743i 0.914595 + 0.404372i \(0.132510\pi\)
−0.914595 + 0.404372i \(0.867490\pi\)
\(608\) 0 0
\(609\) −2.25526 −0.0913879
\(610\) 0 0
\(611\) 38.7549 1.56785
\(612\) 0 0
\(613\) − 39.3219i − 1.58820i −0.607788 0.794099i \(-0.707943\pi\)
0.607788 0.794099i \(-0.292057\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.0674757i 0.00271647i 0.999999 + 0.00135823i \(0.000432340\pi\)
−0.999999 + 0.00135823i \(0.999568\pi\)
\(618\) 0 0
\(619\) −38.8680 −1.56224 −0.781118 0.624384i \(-0.785350\pi\)
−0.781118 + 0.624384i \(0.785350\pi\)
\(620\) 0 0
\(621\) −7.67004 −0.307788
\(622\) 0 0
\(623\) − 2.25526i − 0.0903552i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) − 3.70739i − 0.148059i
\(628\) 0 0
\(629\) −9.62071 −0.383603
\(630\) 0 0
\(631\) 29.2835 1.16576 0.582880 0.812559i \(-0.301926\pi\)
0.582880 + 0.812559i \(0.301926\pi\)
\(632\) 0 0
\(633\) − 2.05655i − 0.0817404i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 17.4521i − 0.691478i
\(638\) 0 0
\(639\) 8.69832 0.344100
\(640\) 0 0
\(641\) 10.4057 0.411001 0.205500 0.978657i \(-0.434118\pi\)
0.205500 + 0.978657i \(0.434118\pi\)
\(642\) 0 0
\(643\) 11.3774i 0.448682i 0.974511 + 0.224341i \(0.0720230\pi\)
−0.974511 + 0.224341i \(0.927977\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 45.5388i 1.79032i 0.445750 + 0.895158i \(0.352937\pi\)
−0.445750 + 0.895158i \(0.647063\pi\)
\(648\) 0 0
\(649\) −47.0776 −1.84796
\(650\) 0 0
\(651\) −12.7730 −0.500614
\(652\) 0 0
\(653\) 2.27341i 0.0889654i 0.999010 + 0.0444827i \(0.0141640\pi\)
−0.999010 + 0.0444827i \(0.985836\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 12.0565i − 0.470371i
\(658\) 0 0
\(659\) 8.77301 0.341748 0.170874 0.985293i \(-0.445341\pi\)
0.170874 + 0.985293i \(0.445341\pi\)
\(660\) 0 0
\(661\) −44.4924 −1.73055 −0.865277 0.501295i \(-0.832857\pi\)
−0.865277 + 0.501295i \(0.832857\pi\)
\(662\) 0 0
\(663\) − 5.35823i − 0.208096i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 13.0957i 0.507069i
\(668\) 0 0
\(669\) −6.05655 −0.234160
\(670\) 0 0
\(671\) 33.4713 1.29215
\(672\) 0 0
\(673\) 5.96265i 0.229843i 0.993375 + 0.114922i \(0.0366617\pi\)
−0.993375 + 0.114922i \(0.963338\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 6.32996i 0.243280i 0.992574 + 0.121640i \(0.0388153\pi\)
−0.992574 + 0.121640i \(0.961185\pi\)
\(678\) 0 0
\(679\) −0.897033 −0.0344250
\(680\) 0 0
\(681\) −28.3118 −1.08491
\(682\) 0 0
\(683\) − 39.8506i − 1.52484i −0.647082 0.762421i \(-0.724011\pi\)
0.647082 0.762421i \(-0.275989\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 1.80128i − 0.0687233i
\(688\) 0 0
\(689\) −34.6802 −1.32121
\(690\) 0 0
\(691\) 8.07469 0.307176 0.153588 0.988135i \(-0.450917\pi\)
0.153588 + 0.988135i \(0.450917\pi\)
\(692\) 0 0
\(693\) 4.89703i 0.186023i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 3.69912i 0.140114i
\(698\) 0 0
\(699\) 3.94345 0.149155
\(700\) 0 0
\(701\) −2.77301 −0.104735 −0.0523676 0.998628i \(-0.516677\pi\)
−0.0523676 + 0.998628i \(0.516677\pi\)
\(702\) 0 0
\(703\) 5.96265i 0.224886i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 16.6983i − 0.628005i
\(708\) 0 0
\(709\) −10.1987 −0.383021 −0.191510 0.981491i \(-0.561339\pi\)
−0.191510 + 0.981491i \(0.561339\pi\)
\(710\) 0 0
\(711\) −14.0565 −0.527162
\(712\) 0 0
\(713\) 74.1696i 2.77767i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) − 16.8031i − 0.627525i
\(718\) 0 0
\(719\) −34.2745 −1.27822 −0.639111 0.769115i \(-0.720698\pi\)
−0.639111 + 0.769115i \(0.720698\pi\)
\(720\) 0 0
\(721\) −8.00000 −0.297936
\(722\) 0 0
\(723\) − 14.0000i − 0.520666i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 22.0939i 0.819417i 0.912216 + 0.409709i \(0.134370\pi\)
−0.912216 + 0.409709i \(0.865630\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −14.0950 −0.521321
\(732\) 0 0
\(733\) 13.3401i 0.492727i 0.969177 + 0.246364i \(0.0792358\pi\)
−0.969177 + 0.246364i \(0.920764\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 49.2472i − 1.81405i
\(738\) 0 0
\(739\) 28.0000 1.03000 0.514998 0.857191i \(-0.327793\pi\)
0.514998 + 0.857191i \(0.327793\pi\)
\(740\) 0 0
\(741\) −3.32088 −0.121996
\(742\) 0 0
\(743\) − 32.8861i − 1.20647i −0.797562 0.603237i \(-0.793877\pi\)
0.797562 0.603237i \(-0.206123\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 5.02827i 0.183975i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 16.4996 0.602079 0.301039 0.953612i \(-0.402666\pi\)
0.301039 + 0.953612i \(0.402666\pi\)
\(752\) 0 0
\(753\) − 24.9909i − 0.910720i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 42.5489i − 1.54647i −0.634121 0.773234i \(-0.718638\pi\)
0.634121 0.773234i \(-0.281362\pi\)
\(758\) 0 0
\(759\) 28.4358 1.03216
\(760\) 0 0
\(761\) 5.34009 0.193578 0.0967890 0.995305i \(-0.469143\pi\)
0.0967890 + 0.995305i \(0.469143\pi\)
\(762\) 0 0
\(763\) 14.1312i 0.511585i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 42.1696i 1.52266i
\(768\) 0 0
\(769\) 7.28354 0.262651 0.131326 0.991339i \(-0.458077\pi\)
0.131326 + 0.991339i \(0.458077\pi\)
\(770\) 0 0
\(771\) −2.91518 −0.104988
\(772\) 0 0
\(773\) 18.1806i 0.653910i 0.945040 + 0.326955i \(0.106023\pi\)
−0.945040 + 0.326955i \(0.893977\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) − 7.87598i − 0.282549i
\(778\) 0 0
\(779\) 2.29261 0.0821413
\(780\) 0 0
\(781\) −32.2480 −1.15393
\(782\) 0 0
\(783\) 1.70739i 0.0610171i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 20.8114i 0.741847i 0.928663 + 0.370923i \(0.120959\pi\)
−0.928663 + 0.370923i \(0.879041\pi\)
\(788\) 0 0
\(789\) 22.3118 0.794322
\(790\) 0 0
\(791\) 21.5460 0.766088
\(792\) 0 0
\(793\) − 29.9819i − 1.06469i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 40.9354i 1.45001i 0.688745 + 0.725004i \(0.258162\pi\)
−0.688745 + 0.725004i \(0.741838\pi\)
\(798\) 0 0
\(799\) −18.8296 −0.666142
\(800\) 0 0
\(801\) −1.70739 −0.0603276
\(802\) 0 0
\(803\) 44.6983i 1.57737i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 15.0656i 0.530335i
\(808\) 0 0
\(809\) 1.48947 0.0523670 0.0261835 0.999657i \(-0.491665\pi\)
0.0261835 + 0.999657i \(0.491665\pi\)
\(810\) 0 0
\(811\) 21.5460 0.756583 0.378292 0.925687i \(-0.376512\pi\)
0.378292 + 0.925687i \(0.376512\pi\)
\(812\) 0 0
\(813\) − 5.47133i − 0.191888i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 8.73566i 0.305622i
\(818\) 0 0
\(819\) 4.38650 0.153277
\(820\) 0 0
\(821\) −35.9819 −1.25578 −0.627888 0.778304i \(-0.716080\pi\)
−0.627888 + 0.778304i \(0.716080\pi\)
\(822\) 0 0
\(823\) − 15.8880i − 0.553819i −0.960896 0.276910i \(-0.910690\pi\)
0.960896 0.276910i \(-0.0893103\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 26.8789i 0.934671i 0.884080 + 0.467335i \(0.154786\pi\)
−0.884080 + 0.467335i \(0.845214\pi\)
\(828\) 0 0
\(829\) −17.9253 −0.622572 −0.311286 0.950316i \(-0.600760\pi\)
−0.311286 + 0.950316i \(0.600760\pi\)
\(830\) 0 0
\(831\) −10.7730 −0.373712
\(832\) 0 0
\(833\) 8.47934i 0.293792i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 9.67004i 0.334246i
\(838\) 0 0
\(839\) −7.30168 −0.252082 −0.126041 0.992025i \(-0.540227\pi\)
−0.126041 + 0.992025i \(0.540227\pi\)
\(840\) 0 0
\(841\) −26.0848 −0.899477
\(842\) 0 0
\(843\) − 17.8205i − 0.613770i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 3.62548i − 0.124573i
\(848\) 0 0
\(849\) 30.2070 1.03670
\(850\) 0 0
\(851\) −45.7338 −1.56773
\(852\) 0 0
\(853\) 37.4148i 1.28106i 0.767934 + 0.640529i \(0.221285\pi\)
−0.767934 + 0.640529i \(0.778715\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) − 10.1806i − 0.347762i −0.984767 0.173881i \(-0.944369\pi\)
0.984767 0.173881i \(-0.0556308\pi\)
\(858\) 0 0
\(859\) 40.7367 1.38992 0.694959 0.719049i \(-0.255422\pi\)
0.694959 + 0.719049i \(0.255422\pi\)
\(860\) 0 0
\(861\) −3.02827 −0.103203
\(862\) 0 0
\(863\) 8.11310i 0.276173i 0.990420 + 0.138086i \(0.0440952\pi\)
−0.990420 + 0.138086i \(0.955905\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) − 14.3966i − 0.488935i
\(868\) 0 0
\(869\) 52.1131 1.76782
\(870\) 0 0
\(871\) −44.1131 −1.49472
\(872\) 0 0
\(873\) 0.679116i 0.0229846i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 29.8880i 1.00924i 0.863340 + 0.504622i \(0.168368\pi\)
−0.863340 + 0.504622i \(0.831632\pi\)
\(878\) 0 0
\(879\) 18.2553 0.615735
\(880\) 0 0
\(881\) 34.8114 1.17283 0.586413 0.810012i \(-0.300540\pi\)
0.586413 + 0.810012i \(0.300540\pi\)
\(882\) 0 0
\(883\) − 27.8496i − 0.937212i −0.883407 0.468606i \(-0.844756\pi\)
0.883407 0.468606i \(-0.155244\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 50.7933i − 1.70547i −0.522343 0.852735i \(-0.674942\pi\)
0.522343 0.852735i \(-0.325058\pi\)
\(888\) 0 0
\(889\) −5.28354 −0.177204
\(890\) 0 0
\(891\) 3.70739 0.124202
\(892\) 0 0
\(893\) 11.6700i 0.390523i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 25.4713i − 0.850463i
\(898\) 0 0
\(899\) 16.5105 0.550657
\(900\) 0 0
\(901\) 16.8498 0.561349
\(902\) 0 0
\(903\) − 11.5388i − 0.383987i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 32.3009i − 1.07253i −0.844049 0.536267i \(-0.819834\pi\)
0.844049 0.536267i \(-0.180166\pi\)
\(908\) 0 0
\(909\) −12.6418 −0.419301
\(910\) 0 0
\(911\) −52.7367 −1.74725 −0.873623 0.486604i \(-0.838236\pi\)
−0.873623 + 0.486604i \(0.838236\pi\)
\(912\) 0 0
\(913\) − 18.6418i − 0.616953i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 5.67004i − 0.187241i
\(918\) 0 0
\(919\) −52.5105 −1.73216 −0.866081 0.499903i \(-0.833369\pi\)
−0.866081 + 0.499903i \(0.833369\pi\)
\(920\) 0 0
\(921\) −16.5852 −0.546502
\(922\) 0 0
\(923\) 28.8861i 0.950798i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 6.05655i 0.198923i
\(928\) 0 0
\(929\) 35.8688 1.17682 0.588408 0.808564i \(-0.299755\pi\)
0.588408 + 0.808564i \(0.299755\pi\)
\(930\) 0 0
\(931\) 5.25526 0.172234
\(932\) 0 0
\(933\) − 11.5196i − 0.377135i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 10.6983i 0.349499i 0.984613 + 0.174749i \(0.0559115\pi\)
−0.984613 + 0.174749i \(0.944088\pi\)
\(938\) 0 0
\(939\) −32.7549 −1.06891
\(940\) 0 0
\(941\) −22.3673 −0.729153 −0.364577 0.931173i \(-0.618786\pi\)
−0.364577 + 0.931173i \(0.618786\pi\)
\(942\) 0 0
\(943\) 17.5844i 0.572628i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 34.8223i 1.13157i 0.824551 + 0.565787i \(0.191428\pi\)
−0.824551 + 0.565787i \(0.808572\pi\)
\(948\) 0 0
\(949\) 40.0384 1.29970
\(950\) 0 0
\(951\) 15.2161 0.493415
\(952\) 0 0
\(953\) 29.4823i 0.955024i 0.878625 + 0.477512i \(0.158461\pi\)
−0.878625 + 0.477512i \(0.841539\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) − 6.32996i − 0.204618i
\(958\) 0 0
\(959\) 2.64177 0.0853072
\(960\) 0 0
\(961\) 62.5097 2.01644
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 18.8669i 0.606719i 0.952876 + 0.303359i \(0.0981083\pi\)
−0.952876 + 0.303359i \(0.901892\pi\)
\(968\) 0 0
\(969\) 1.61350 0.0518329
\(970\) 0 0
\(971\) 31.2270 1.00212 0.501061 0.865412i \(-0.332943\pi\)
0.501061 + 0.865412i \(0.332943\pi\)
\(972\) 0 0
\(973\) − 11.3401i − 0.363546i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 6.44305i 0.206132i 0.994675 + 0.103066i \(0.0328652\pi\)
−0.994675 + 0.103066i \(0.967135\pi\)
\(978\) 0 0
\(979\) 6.32996 0.202306
\(980\) 0 0
\(981\) 10.6983 0.341571
\(982\) 0 0
\(983\) − 4.57429i − 0.145897i −0.997336 0.0729486i \(-0.976759\pi\)
0.997336 0.0729486i \(-0.0232409\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) − 15.4148i − 0.490658i
\(988\) 0 0
\(989\) −67.0029 −2.13057
\(990\) 0 0
\(991\) −38.8296 −1.23346 −0.616731 0.787174i \(-0.711543\pi\)
−0.616731 + 0.787174i \(0.711543\pi\)
\(992\) 0 0
\(993\) 26.9536i 0.855346i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 54.9245i 1.73948i 0.493513 + 0.869738i \(0.335712\pi\)
−0.493513 + 0.869738i \(0.664288\pi\)
\(998\) 0 0
\(999\) −5.96265 −0.188650
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 5700.2.f.q.3649.1 6
5.2 odd 4 5700.2.a.w.1.3 3
5.3 odd 4 1140.2.a.g.1.1 3
5.4 even 2 inner 5700.2.f.q.3649.6 6
15.8 even 4 3420.2.a.m.1.1 3
20.3 even 4 4560.2.a.br.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1140.2.a.g.1.1 3 5.3 odd 4
3420.2.a.m.1.1 3 15.8 even 4
4560.2.a.br.1.3 3 20.3 even 4
5700.2.a.w.1.3 3 5.2 odd 4
5700.2.f.q.3649.1 6 1.1 even 1 trivial
5700.2.f.q.3649.6 6 5.4 even 2 inner