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Properties

Label 7007.2.a.c.1.1
Level $7007$
Weight $2$
Character 7007.1
Self dual yes
Analytic conductor $55.951$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7007,2,Mod(1,7007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7007, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7007 = 7^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7007.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(55.9511766963\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 7007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +1.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} +1.00000 q^{9} -1.00000 q^{11} +4.00000 q^{12} +1.00000 q^{13} -2.00000 q^{15} +4.00000 q^{16} -2.00000 q^{17} +1.00000 q^{19} -2.00000 q^{20} -5.00000 q^{23} -4.00000 q^{25} +4.00000 q^{27} -5.00000 q^{29} +9.00000 q^{31} +2.00000 q^{33} -2.00000 q^{36} +10.0000 q^{37} -2.00000 q^{39} +2.00000 q^{41} -13.0000 q^{43} +2.00000 q^{44} +1.00000 q^{45} +7.00000 q^{47} -8.00000 q^{48} +4.00000 q^{51} -2.00000 q^{52} -1.00000 q^{53} -1.00000 q^{55} -2.00000 q^{57} -8.00000 q^{59} +4.00000 q^{60} +2.00000 q^{61} -8.00000 q^{64} +1.00000 q^{65} +2.00000 q^{67} +4.00000 q^{68} +10.0000 q^{69} +6.00000 q^{71} -5.00000 q^{73} +8.00000 q^{75} -2.00000 q^{76} +11.0000 q^{79} +4.00000 q^{80} -11.0000 q^{81} +3.00000 q^{83} -2.00000 q^{85} +10.0000 q^{87} -5.00000 q^{89} +10.0000 q^{92} -18.0000 q^{93} +1.00000 q^{95} -5.00000 q^{97} -1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) −2.00000 −1.15470 −0.577350 − 0.816497i \(-0.695913\pi\)
−0.577350 + 0.816497i \(0.695913\pi\)
\(4\) −2.00000 −1.00000
\(5\) 1.00000 0.447214 0.223607 − 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 4.00000 1.15470
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 4.00000 1.00000
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 − 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) −2.00000 −0.447214
\(21\) 0 0
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 − 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) −5.00000 −0.928477 −0.464238 − 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) 9.00000 1.61645 0.808224 − 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) 0 0
\(33\) 2.00000 0.348155
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 10.0000 1.64399 0.821995 − 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) −2.00000 −0.320256
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −13.0000 −1.98248 −0.991241 − 0.132068i \(-0.957838\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 2.00000 0.301511
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) 7.00000 1.02105 0.510527 − 0.859861i \(-0.329450\pi\)
0.510527 + 0.859861i \(0.329450\pi\)
\(48\) −8.00000 −1.15470
\(49\) 0 0
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) −2.00000 −0.277350
\(53\) −1.00000 −0.137361 −0.0686803 − 0.997639i \(-0.521879\pi\)
−0.0686803 + 0.997639i \(0.521879\pi\)
\(54\) 0 0
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) −2.00000 −0.264906
\(58\) 0 0
\(59\) −8.00000 −1.04151 −0.520756 − 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 4.00000 0.516398
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 − 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 4.00000 0.485071
\(69\) 10.0000 1.20386
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 − 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −5.00000 −0.585206 −0.292603 − 0.956234i \(-0.594521\pi\)
−0.292603 + 0.956234i \(0.594521\pi\)
\(74\) 0 0
\(75\) 8.00000 0.923760
\(76\) −2.00000 −0.229416
\(77\) 0 0
\(78\) 0 0
\(79\) 11.0000 1.23760 0.618798 − 0.785550i \(-0.287620\pi\)
0.618798 + 0.785550i \(0.287620\pi\)
\(80\) 4.00000 0.447214
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) 3.00000 0.329293 0.164646 − 0.986353i \(-0.447352\pi\)
0.164646 + 0.986353i \(0.447352\pi\)
\(84\) 0 0
\(85\) −2.00000 −0.216930
\(86\) 0 0
\(87\) 10.0000 1.07211
\(88\) 0 0
\(89\) −5.00000 −0.529999 −0.264999 − 0.964249i \(-0.585372\pi\)
−0.264999 + 0.964249i \(0.585372\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 10.0000 1.04257
\(93\) −18.0000 −1.86651
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) −5.00000 −0.507673 −0.253837 − 0.967247i \(-0.581693\pi\)
−0.253837 + 0.967247i \(0.581693\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 8.00000 0.800000
\(101\) 12.0000 1.19404 0.597022 − 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.0000 1.93347 0.966736 − 0.255774i \(-0.0823304\pi\)
0.966736 + 0.255774i \(0.0823304\pi\)
\(108\) −8.00000 −0.769800
\(109\) 4.00000 0.383131 0.191565 − 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) −20.0000 −1.89832
\(112\) 0 0
\(113\) 1.00000 0.0940721 0.0470360 − 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) −5.00000 −0.466252
\(116\) 10.0000 0.928477
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) −4.00000 −0.360668
\(124\) −18.0000 −1.61645
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) 26.0000 2.28917
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −4.00000 −0.348155
\(133\) 0 0
\(134\) 0 0
\(135\) 4.00000 0.344265
\(136\) 0 0
\(137\) 22.0000 1.87959 0.939793 − 0.341743i \(-0.111017\pi\)
0.939793 + 0.341743i \(0.111017\pi\)
\(138\) 0 0
\(139\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −14.0000 −1.17901
\(142\) 0 0
\(143\) −1.00000 −0.0836242
\(144\) 4.00000 0.333333
\(145\) −5.00000 −0.415227
\(146\) 0 0
\(147\) 0 0
\(148\) −20.0000 −1.64399
\(149\) 8.00000 0.655386 0.327693 − 0.944784i \(-0.393729\pi\)
0.327693 + 0.944784i \(0.393729\pi\)
\(150\) 0 0
\(151\) −14.0000 −1.13930 −0.569652 − 0.821886i \(-0.692922\pi\)
−0.569652 + 0.821886i \(0.692922\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) 9.00000 0.722897
\(156\) 4.00000 0.320256
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 2.00000 0.158610
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −4.00000 −0.312348
\(165\) 2.00000 0.155700
\(166\) 0 0
\(167\) 17.0000 1.31550 0.657750 − 0.753237i \(-0.271508\pi\)
0.657750 + 0.753237i \(0.271508\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 26.0000 1.98248
\(173\) 14.0000 1.06440 0.532200 − 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 16.0000 1.20263
\(178\) 0 0
\(179\) −9.00000 −0.672692 −0.336346 − 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) −2.00000 −0.149071
\(181\) 20.0000 1.48659 0.743294 − 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) −4.00000 −0.295689
\(184\) 0 0
\(185\) 10.0000 0.735215
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) −14.0000 −1.02105
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 16.0000 1.15470
\(193\) −6.00000 −0.431889 −0.215945 − 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 0 0
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) −22.0000 −1.56744 −0.783718 − 0.621117i \(-0.786679\pi\)
−0.783718 + 0.621117i \(0.786679\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 − 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) −4.00000 −0.282138
\(202\) 0 0
\(203\) 0 0
\(204\) −8.00000 −0.560112
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) −5.00000 −0.347524
\(208\) 4.00000 0.277350
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 3.00000 0.206529 0.103264 − 0.994654i \(-0.467071\pi\)
0.103264 + 0.994654i \(0.467071\pi\)
\(212\) 2.00000 0.137361
\(213\) −12.0000 −0.822226
\(214\) 0 0
\(215\) −13.0000 −0.886593
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 10.0000 0.675737
\(220\) 2.00000 0.134840
\(221\) −2.00000 −0.134535
\(222\) 0 0
\(223\) 19.0000 1.27233 0.636167 − 0.771551i \(-0.280519\pi\)
0.636167 + 0.771551i \(0.280519\pi\)
\(224\) 0 0
\(225\) −4.00000 −0.266667
\(226\) 0 0
\(227\) −24.0000 −1.59294 −0.796468 − 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 4.00000 0.264906
\(229\) −18.0000 −1.18947 −0.594737 − 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.0000 0.720634 0.360317 − 0.932830i \(-0.382669\pi\)
0.360317 + 0.932830i \(0.382669\pi\)
\(234\) 0 0
\(235\) 7.00000 0.456630
\(236\) 16.0000 1.04151
\(237\) −22.0000 −1.42905
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −8.00000 −0.516398
\(241\) 7.00000 0.450910 0.225455 − 0.974254i \(-0.427613\pi\)
0.225455 + 0.974254i \(0.427613\pi\)
\(242\) 0 0
\(243\) 10.0000 0.641500
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 0.0636285
\(248\) 0 0
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) −24.0000 −1.51487 −0.757433 − 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 0 0
\(255\) 4.00000 0.250490
\(256\) 16.0000 1.00000
\(257\) −24.0000 −1.49708 −0.748539 − 0.663090i \(-0.769245\pi\)
−0.748539 + 0.663090i \(0.769245\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2.00000 −0.124035
\(261\) −5.00000 −0.309492
\(262\) 0 0
\(263\) −27.0000 −1.66489 −0.832446 − 0.554107i \(-0.813060\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) −4.00000 −0.244339
\(269\) −12.0000 −0.731653 −0.365826 − 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) −16.0000 −0.971931 −0.485965 − 0.873978i \(-0.661532\pi\)
−0.485965 + 0.873978i \(0.661532\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) 0 0
\(275\) 4.00000 0.241209
\(276\) −20.0000 −1.20386
\(277\) −31.0000 −1.86261 −0.931305 − 0.364241i \(-0.881328\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 0 0
\(279\) 9.00000 0.538816
\(280\) 0 0
\(281\) −24.0000 −1.43172 −0.715860 − 0.698244i \(-0.753965\pi\)
−0.715860 + 0.698244i \(0.753965\pi\)
\(282\) 0 0
\(283\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) −12.0000 −0.712069
\(285\) −2.00000 −0.118470
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) 10.0000 0.585206
\(293\) 1.00000 0.0584206 0.0292103 − 0.999573i \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) −5.00000 −0.289157
\(300\) −16.0000 −0.923760
\(301\) 0 0
\(302\) 0 0
\(303\) −24.0000 −1.37876
\(304\) 4.00000 0.229416
\(305\) 2.00000 0.114520
\(306\) 0 0
\(307\) 3.00000 0.171219 0.0856095 − 0.996329i \(-0.472716\pi\)
0.0856095 + 0.996329i \(0.472716\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) −8.00000 −0.453638 −0.226819 − 0.973937i \(-0.572833\pi\)
−0.226819 + 0.973937i \(0.572833\pi\)
\(312\) 0 0
\(313\) −12.0000 −0.678280 −0.339140 − 0.940736i \(-0.610136\pi\)
−0.339140 + 0.940736i \(0.610136\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −22.0000 −1.23760
\(317\) −16.0000 −0.898650 −0.449325 − 0.893368i \(-0.648335\pi\)
−0.449325 + 0.893368i \(0.648335\pi\)
\(318\) 0 0
\(319\) 5.00000 0.279946
\(320\) −8.00000 −0.447214
\(321\) −40.0000 −2.23258
\(322\) 0 0
\(323\) −2.00000 −0.111283
\(324\) 22.0000 1.22222
\(325\) −4.00000 −0.221880
\(326\) 0 0
\(327\) −8.00000 −0.442401
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −2.00000 −0.109930 −0.0549650 − 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) −6.00000 −0.329293
\(333\) 10.0000 0.547997
\(334\) 0 0
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 − 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) 0 0
\(339\) −2.00000 −0.108625
\(340\) 4.00000 0.216930
\(341\) −9.00000 −0.487377
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 10.0000 0.538382
\(346\) 0 0
\(347\) 24.0000 1.28839 0.644194 − 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) −20.0000 −1.07211
\(349\) −1.00000 −0.0535288 −0.0267644 − 0.999642i \(-0.508520\pi\)
−0.0267644 + 0.999642i \(0.508520\pi\)
\(350\) 0 0
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 6.00000 0.318447
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 0 0
\(359\) −2.00000 −0.105556 −0.0527780 − 0.998606i \(-0.516808\pi\)
−0.0527780 + 0.998606i \(0.516808\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) −5.00000 −0.261712
\(366\) 0 0
\(367\) 36.0000 1.87918 0.939592 − 0.342296i \(-0.111204\pi\)
0.939592 + 0.342296i \(0.111204\pi\)
\(368\) −20.0000 −1.04257
\(369\) 2.00000 0.104116
\(370\) 0 0
\(371\) 0 0
\(372\) 36.0000 1.86651
\(373\) −34.0000 −1.76045 −0.880227 − 0.474554i \(-0.842610\pi\)
−0.880227 + 0.474554i \(0.842610\pi\)
\(374\) 0 0
\(375\) 18.0000 0.929516
\(376\) 0 0
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 − 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) −2.00000 −0.102598
\(381\) 16.0000 0.819705
\(382\) 0 0
\(383\) −32.0000 −1.63512 −0.817562 − 0.575841i \(-0.804675\pi\)
−0.817562 + 0.575841i \(0.804675\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.0000 −0.660827
\(388\) 10.0000 0.507673
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 10.0000 0.505722
\(392\) 0 0
\(393\) −24.0000 −1.21064
\(394\) 0 0
\(395\) 11.0000 0.553470
\(396\) 2.00000 0.100504
\(397\) −33.0000 −1.65622 −0.828111 − 0.560564i \(-0.810584\pi\)
−0.828111 + 0.560564i \(0.810584\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −16.0000 −0.800000
\(401\) 24.0000 1.19850 0.599251 − 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 0 0
\(403\) 9.00000 0.448322
\(404\) −24.0000 −1.19404
\(405\) −11.0000 −0.546594
\(406\) 0 0
\(407\) −10.0000 −0.495682
\(408\) 0 0
\(409\) −9.00000 −0.445021 −0.222511 − 0.974930i \(-0.571425\pi\)
−0.222511 + 0.974930i \(0.571425\pi\)
\(410\) 0 0
\(411\) −44.0000 −2.17036
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) 3.00000 0.147264
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 4.00000 0.195413 0.0977064 − 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 − 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 0 0
\(423\) 7.00000 0.340352
\(424\) 0 0
\(425\) 8.00000 0.388057
\(426\) 0 0
\(427\) 0 0
\(428\) −40.0000 −1.93347
\(429\) 2.00000 0.0965609
\(430\) 0 0
\(431\) −10.0000 −0.481683 −0.240842 − 0.970564i \(-0.577423\pi\)
−0.240842 + 0.970564i \(0.577423\pi\)
\(432\) 16.0000 0.769800
\(433\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 10.0000 0.479463
\(436\) −8.00000 −0.383131
\(437\) −5.00000 −0.239182
\(438\) 0 0
\(439\) −6.00000 −0.286364 −0.143182 − 0.989696i \(-0.545733\pi\)
−0.143182 + 0.989696i \(0.545733\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 31.0000 1.47285 0.736427 − 0.676517i \(-0.236511\pi\)
0.736427 + 0.676517i \(0.236511\pi\)
\(444\) 40.0000 1.89832
\(445\) −5.00000 −0.237023
\(446\) 0 0
\(447\) −16.0000 −0.756774
\(448\) 0 0
\(449\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) −2.00000 −0.0941763
\(452\) −2.00000 −0.0940721
\(453\) 28.0000 1.31555
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 − 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) −8.00000 −0.373408
\(460\) 10.0000 0.466252
\(461\) 2.00000 0.0931493 0.0465746 − 0.998915i \(-0.485169\pi\)
0.0465746 + 0.998915i \(0.485169\pi\)
\(462\) 0 0
\(463\) −12.0000 −0.557687 −0.278844 − 0.960337i \(-0.589951\pi\)
−0.278844 + 0.960337i \(0.589951\pi\)
\(464\) −20.0000 −0.928477
\(465\) −18.0000 −0.834730
\(466\) 0 0
\(467\) 32.0000 1.48078 0.740392 − 0.672176i \(-0.234640\pi\)
0.740392 + 0.672176i \(0.234640\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 4.00000 0.184310
\(472\) 0 0
\(473\) 13.0000 0.597741
\(474\) 0 0
\(475\) −4.00000 −0.183533
\(476\) 0 0
\(477\) −1.00000 −0.0457869
\(478\) 0 0
\(479\) 33.0000 1.50781 0.753904 − 0.656984i \(-0.228168\pi\)
0.753904 + 0.656984i \(0.228168\pi\)
\(480\) 0 0
\(481\) 10.0000 0.455961
\(482\) 0 0
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) −5.00000 −0.227038
\(486\) 0 0
\(487\) −38.0000 −1.72194 −0.860972 − 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) 32.0000 1.44709
\(490\) 0 0
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 8.00000 0.360668
\(493\) 10.0000 0.450377
\(494\) 0 0
\(495\) −1.00000 −0.0449467
\(496\) 36.0000 1.61645
\(497\) 0 0
\(498\) 0 0
\(499\) −26.0000 −1.16392 −0.581960 − 0.813217i \(-0.697714\pi\)
−0.581960 + 0.813217i \(0.697714\pi\)
\(500\) 18.0000 0.804984
\(501\) −34.0000 −1.51901
\(502\) 0 0
\(503\) 30.0000 1.33763 0.668817 − 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) −2.00000 −0.0888231
\(508\) 16.0000 0.709885
\(509\) −39.0000 −1.72864 −0.864322 − 0.502938i \(-0.832252\pi\)
−0.864322 + 0.502938i \(0.832252\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 4.00000 0.176604
\(514\) 0 0
\(515\) −8.00000 −0.352522
\(516\) −52.0000 −2.28917
\(517\) −7.00000 −0.307860
\(518\) 0 0
\(519\) −28.0000 −1.22906
\(520\) 0 0
\(521\) −32.0000 −1.40195 −0.700973 − 0.713188i \(-0.747251\pi\)
−0.700973 + 0.713188i \(0.747251\pi\)
\(522\) 0 0
\(523\) 38.0000 1.66162 0.830812 − 0.556553i \(-0.187876\pi\)
0.830812 + 0.556553i \(0.187876\pi\)
\(524\) −24.0000 −1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) −18.0000 −0.784092
\(528\) 8.00000 0.348155
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −8.00000 −0.347170
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) 20.0000 0.864675
\(536\) 0 0
\(537\) 18.0000 0.776757
\(538\) 0 0
\(539\) 0 0
\(540\) −8.00000 −0.344265
\(541\) −18.0000 −0.773880 −0.386940 − 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 0 0
\(543\) −40.0000 −1.71656
\(544\) 0 0
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −19.0000 −0.812381 −0.406191 − 0.913788i \(-0.633143\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(548\) −44.0000 −1.87959
\(549\) 2.00000 0.0853579
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −20.0000 −0.848953
\(556\) 0 0
\(557\) 24.0000 1.01691 0.508456 − 0.861088i \(-0.330216\pi\)
0.508456 + 0.861088i \(0.330216\pi\)
\(558\) 0 0
\(559\) −13.0000 −0.549841
\(560\) 0 0
\(561\) −4.00000 −0.168880
\(562\) 0 0
\(563\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 28.0000 1.17901
\(565\) 1.00000 0.0420703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.00000 0.293455 0.146728 − 0.989177i \(-0.453126\pi\)
0.146728 + 0.989177i \(0.453126\pi\)
\(570\) 0 0
\(571\) −5.00000 −0.209243 −0.104622 − 0.994512i \(-0.533363\pi\)
−0.104622 + 0.994512i \(0.533363\pi\)
\(572\) 2.00000 0.0836242
\(573\) 0 0
\(574\) 0 0
\(575\) 20.0000 0.834058
\(576\) −8.00000 −0.333333
\(577\) −10.0000 −0.416305 −0.208153 − 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 0 0
\(579\) 12.0000 0.498703
\(580\) 10.0000 0.415227
\(581\) 0 0
\(582\) 0 0
\(583\) 1.00000 0.0414158
\(584\) 0 0
\(585\) 1.00000 0.0413449
\(586\) 0 0
\(587\) −21.0000 −0.866763 −0.433381 − 0.901211i \(-0.642680\pi\)
−0.433381 + 0.901211i \(0.642680\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 0 0
\(591\) 44.0000 1.80992
\(592\) 40.0000 1.64399
\(593\) −15.0000 −0.615976 −0.307988 − 0.951390i \(-0.599656\pi\)
−0.307988 + 0.951390i \(0.599656\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.0000 −0.655386
\(597\) 4.00000 0.163709
\(598\) 0 0
\(599\) −33.0000 −1.34834 −0.674172 − 0.738575i \(-0.735499\pi\)
−0.674172 + 0.738575i \(0.735499\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 − 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) 28.0000 1.13930
\(605\) 1.00000 0.0406558
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 − 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.00000 0.283190
\(612\) 4.00000 0.161690
\(613\) −44.0000 −1.77714 −0.888572 − 0.458738i \(-0.848302\pi\)
−0.888572 + 0.458738i \(0.848302\pi\)
\(614\) 0 0
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) 30.0000 1.20775 0.603877 − 0.797077i \(-0.293622\pi\)
0.603877 + 0.797077i \(0.293622\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 − 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) −18.0000 −0.722897
\(621\) −20.0000 −0.802572
\(622\) 0 0
\(623\) 0 0
\(624\) −8.00000 −0.320256
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 2.00000 0.0798723
\(628\) 4.00000 0.159617
\(629\) −20.0000 −0.797452
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 − 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 0 0
\(633\) −6.00000 −0.238479
\(634\) 0 0
\(635\) −8.00000 −0.317470
\(636\) −4.00000 −0.158610
\(637\) 0 0
\(638\) 0 0
\(639\) 6.00000 0.237356
\(640\) 0 0
\(641\) −15.0000 −0.592464 −0.296232 − 0.955116i \(-0.595730\pi\)
−0.296232 + 0.955116i \(0.595730\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 26.0000 1.02375
\(646\) 0 0
\(647\) −24.0000 −0.943537 −0.471769 − 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 32.0000 1.25322
\(653\) −22.0000 −0.860927 −0.430463 − 0.902608i \(-0.641650\pi\)
−0.430463 + 0.902608i \(0.641650\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) 8.00000 0.312348
\(657\) −5.00000 −0.195069
\(658\) 0 0
\(659\) −47.0000 −1.83086 −0.915430 − 0.402477i \(-0.868149\pi\)
−0.915430 + 0.402477i \(0.868149\pi\)
\(660\) −4.00000 −0.155700
\(661\) −25.0000 −0.972387 −0.486194 − 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) 0 0
\(663\) 4.00000 0.155347
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.0000 0.968004
\(668\) −34.0000 −1.31550
\(669\) −38.0000 −1.46916
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) 0 0
\(673\) 49.0000 1.88881 0.944406 − 0.328783i \(-0.106638\pi\)
0.944406 + 0.328783i \(0.106638\pi\)
\(674\) 0 0
\(675\) −16.0000 −0.615840
\(676\) −2.00000 −0.0769231
\(677\) 12.0000 0.461197 0.230599 − 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 48.0000 1.83936
\(682\) 0 0
\(683\) −28.0000 −1.07139 −0.535695 − 0.844411i \(-0.679950\pi\)
−0.535695 + 0.844411i \(0.679950\pi\)
\(684\) −2.00000 −0.0764719
\(685\) 22.0000 0.840577
\(686\) 0 0
\(687\) 36.0000 1.37349
\(688\) −52.0000 −1.98248
\(689\) −1.00000 −0.0380970
\(690\) 0 0
\(691\) 15.0000 0.570627 0.285313 − 0.958434i \(-0.407902\pi\)
0.285313 + 0.958434i \(0.407902\pi\)
\(692\) −28.0000 −1.06440
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −4.00000 −0.151511
\(698\) 0 0
\(699\) −22.0000 −0.832116
\(700\) 0 0
\(701\) 5.00000 0.188847 0.0944237 − 0.995532i \(-0.469899\pi\)
0.0944237 + 0.995532i \(0.469899\pi\)
\(702\) 0 0
\(703\) 10.0000 0.377157
\(704\) 8.00000 0.301511
\(705\) −14.0000 −0.527271
\(706\) 0 0
\(707\) 0 0
\(708\) −32.0000 −1.20263
\(709\) 4.00000 0.150223 0.0751116 − 0.997175i \(-0.476069\pi\)
0.0751116 + 0.997175i \(0.476069\pi\)
\(710\) 0 0
\(711\) 11.0000 0.412532
\(712\) 0 0
\(713\) −45.0000 −1.68526
\(714\) 0 0
\(715\) −1.00000 −0.0373979
\(716\) 18.0000 0.672692
\(717\) −48.0000 −1.79259
\(718\) 0 0
\(719\) −4.00000 −0.149175 −0.0745874 − 0.997214i \(-0.523764\pi\)
−0.0745874 + 0.997214i \(0.523764\pi\)
\(720\) 4.00000 0.149071
\(721\) 0 0
\(722\) 0 0
\(723\) −14.0000 −0.520666
\(724\) −40.0000 −1.48659
\(725\) 20.0000 0.742781
\(726\) 0 0
\(727\) 14.0000 0.519231 0.259616 − 0.965712i \(-0.416404\pi\)
0.259616 + 0.965712i \(0.416404\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 26.0000 0.961645
\(732\) 8.00000 0.295689
\(733\) −41.0000 −1.51437 −0.757185 − 0.653201i \(-0.773426\pi\)
−0.757185 + 0.653201i \(0.773426\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.00000 −0.0736709
\(738\) 0 0
\(739\) −8.00000 −0.294285 −0.147142 − 0.989115i \(-0.547008\pi\)
−0.147142 + 0.989115i \(0.547008\pi\)
\(740\) −20.0000 −0.735215
\(741\) −2.00000 −0.0734718
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 8.00000 0.293097
\(746\) 0 0
\(747\) 3.00000 0.109764
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) 0 0
\(751\) 27.0000 0.985244 0.492622 − 0.870243i \(-0.336039\pi\)
0.492622 + 0.870243i \(0.336039\pi\)
\(752\) 28.0000 1.02105
\(753\) 48.0000 1.74922
\(754\) 0 0
\(755\) −14.0000 −0.509512
\(756\) 0 0
\(757\) −27.0000 −0.981332 −0.490666 − 0.871348i \(-0.663246\pi\)
−0.490666 + 0.871348i \(0.663246\pi\)
\(758\) 0 0
\(759\) −10.0000 −0.362977
\(760\) 0 0
\(761\) 13.0000 0.471250 0.235625 − 0.971844i \(-0.424286\pi\)
0.235625 + 0.971844i \(0.424286\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −2.00000 −0.0723102
\(766\) 0 0
\(767\) −8.00000 −0.288863
\(768\) −32.0000 −1.15470
\(769\) 45.0000 1.62274 0.811371 − 0.584532i \(-0.198722\pi\)
0.811371 + 0.584532i \(0.198722\pi\)
\(770\) 0 0
\(771\) 48.0000 1.72868
\(772\) 12.0000 0.431889
\(773\) 6.00000 0.215805 0.107903 − 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) −36.0000 −1.29316
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.00000 0.0716574
\(780\) 4.00000 0.143223
\(781\) −6.00000 −0.214697
\(782\) 0 0
\(783\) −20.0000 −0.714742
\(784\) 0 0
\(785\) −2.00000 −0.0713831
\(786\) 0 0
\(787\) −3.00000 −0.106938 −0.0534692 − 0.998569i \(-0.517028\pi\)
−0.0534692 + 0.998569i \(0.517028\pi\)
\(788\) 44.0000 1.56744
\(789\) 54.0000 1.92245
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 2.00000 0.0710221
\(794\) 0 0
\(795\) 2.00000 0.0709327
\(796\) 4.00000 0.141776
\(797\) 22.0000 0.779280 0.389640 − 0.920967i \(-0.372599\pi\)
0.389640 + 0.920967i \(0.372599\pi\)
\(798\) 0 0
\(799\) −14.0000 −0.495284
\(800\) 0 0
\(801\) −5.00000 −0.176666
\(802\) 0 0
\(803\) 5.00000 0.176446
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) 0 0
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) −15.0000 −0.527372 −0.263686 − 0.964609i \(-0.584938\pi\)
−0.263686 + 0.964609i \(0.584938\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 − 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) 32.0000 1.12229
\(814\) 0 0
\(815\) −16.0000 −0.560456
\(816\) 16.0000 0.560112
\(817\) −13.0000 −0.454812
\(818\) 0 0
\(819\) 0 0
\(820\) −4.00000 −0.139686
\(821\) 18.0000 0.628204 0.314102 − 0.949389i \(-0.398297\pi\)
0.314102 + 0.949389i \(0.398297\pi\)
\(822\) 0 0
\(823\) 40.0000 1.39431 0.697156 − 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) 0 0
\(825\) −8.00000 −0.278524
\(826\) 0 0
\(827\) 20.0000 0.695468 0.347734 − 0.937593i \(-0.386951\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(828\) 10.0000 0.347524
\(829\) 4.00000 0.138926 0.0694629 − 0.997585i \(-0.477871\pi\)
0.0694629 + 0.997585i \(0.477871\pi\)
\(830\) 0 0
\(831\) 62.0000 2.15076
\(832\) −8.00000 −0.277350
\(833\) 0 0
\(834\) 0 0
\(835\) 17.0000 0.588309
\(836\) 2.00000 0.0691714
\(837\) 36.0000 1.24434
\(838\) 0 0
\(839\) −20.0000 −0.690477 −0.345238 − 0.938515i \(-0.612202\pi\)
−0.345238 + 0.938515i \(0.612202\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) 48.0000 1.65321
\(844\) −6.00000 −0.206529
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) 0 0
\(848\) −4.00000 −0.137361
\(849\) 0 0
\(850\) 0 0
\(851\) −50.0000 −1.71398
\(852\) 24.0000 0.822226
\(853\) −31.0000 −1.06142 −0.530710 − 0.847554i \(-0.678075\pi\)
−0.530710 + 0.847554i \(0.678075\pi\)
\(854\) 0 0
\(855\) 1.00000 0.0341993
\(856\) 0 0
\(857\) −22.0000 −0.751506 −0.375753 − 0.926720i \(-0.622616\pi\)
−0.375753 + 0.926720i \(0.622616\pi\)
\(858\) 0 0
\(859\) 50.0000 1.70598 0.852989 − 0.521929i \(-0.174787\pi\)
0.852989 + 0.521929i \(0.174787\pi\)
\(860\) 26.0000 0.886593
\(861\) 0 0
\(862\) 0 0
\(863\) 12.0000 0.408485 0.204242 − 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 0 0
\(865\) 14.0000 0.476014
\(866\) 0 0
\(867\) 26.0000 0.883006
\(868\) 0 0
\(869\) −11.0000 −0.373149
\(870\) 0 0
\(871\) 2.00000 0.0677674
\(872\) 0 0
\(873\) −5.00000 −0.169224
\(874\) 0 0
\(875\) 0 0
\(876\) −20.0000 −0.675737
\(877\) 2.00000 0.0675352 0.0337676 − 0.999430i \(-0.489249\pi\)
0.0337676 + 0.999430i \(0.489249\pi\)
\(878\) 0 0
\(879\) −2.00000 −0.0674583
\(880\) −4.00000 −0.134840
\(881\) −42.0000 −1.41502 −0.707508 − 0.706705i \(-0.750181\pi\)
−0.707508 + 0.706705i \(0.750181\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 − 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 4.00000 0.134535
\(885\) 16.0000 0.537834
\(886\) 0 0
\(887\) 12.0000 0.402921 0.201460 − 0.979497i \(-0.435431\pi\)
0.201460 + 0.979497i \(0.435431\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 11.0000 0.368514
\(892\) −38.0000 −1.27233
\(893\) 7.00000 0.234246
\(894\) 0 0
\(895\) −9.00000 −0.300837
\(896\) 0 0
\(897\) 10.0000 0.333890
\(898\) 0 0
\(899\) −45.0000 −1.50083
\(900\) 8.00000 0.266667
\(901\) 2.00000 0.0666297
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 20.0000 0.664822
\(906\) 0 0
\(907\) −5.00000 −0.166022 −0.0830111 − 0.996549i \(-0.526454\pi\)
−0.0830111 + 0.996549i \(0.526454\pi\)
\(908\) 48.0000 1.59294
\(909\) 12.0000 0.398015
\(910\) 0 0
\(911\) 25.0000 0.828287 0.414143 − 0.910212i \(-0.364081\pi\)
0.414143 + 0.910212i \(0.364081\pi\)
\(912\) −8.00000 −0.264906
\(913\) −3.00000 −0.0992855
\(914\) 0 0
\(915\) −4.00000 −0.132236
\(916\) 36.0000 1.18947
\(917\) 0 0
\(918\) 0 0
\(919\) −32.0000 −1.05558 −0.527791 − 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) 0 0
\(921\) −6.00000 −0.197707
\(922\) 0 0
\(923\) 6.00000 0.197492
\(924\) 0 0
\(925\) −40.0000 −1.31519
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) −15.0000 −0.492134 −0.246067 − 0.969253i \(-0.579138\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −22.0000 −0.720634
\(933\) 16.0000 0.523816
\(934\) 0 0
\(935\) 2.00000 0.0654070
\(936\) 0 0
\(937\) −6.00000 −0.196011 −0.0980057 − 0.995186i \(-0.531246\pi\)
−0.0980057 + 0.995186i \(0.531246\pi\)
\(938\) 0 0
\(939\) 24.0000 0.783210
\(940\) −14.0000 −0.456630
\(941\) −33.0000 −1.07577 −0.537885 − 0.843018i \(-0.680776\pi\)
−0.537885 + 0.843018i \(0.680776\pi\)
\(942\) 0 0
\(943\) −10.0000 −0.325645
\(944\) −32.0000 −1.04151
\(945\) 0 0
\(946\) 0 0
\(947\) 30.0000 0.974869 0.487435 − 0.873160i \(-0.337933\pi\)
0.487435 + 0.873160i \(0.337933\pi\)
\(948\) 44.0000 1.42905
\(949\) −5.00000 −0.162307
\(950\) 0 0
\(951\) 32.0000 1.03767
\(952\) 0 0
\(953\) 9.00000 0.291539 0.145769 − 0.989319i \(-0.453434\pi\)
0.145769 + 0.989319i \(0.453434\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −48.0000 −1.55243
\(957\) −10.0000 −0.323254
\(958\) 0 0
\(959\) 0 0
\(960\) 16.0000 0.516398
\(961\) 50.0000 1.61290
\(962\) 0 0
\(963\) 20.0000 0.644491
\(964\) −14.0000 −0.450910
\(965\) −6.00000 −0.193147
\(966\) 0 0
\(967\) −44.0000 −1.41494 −0.707472 − 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) 0 0
\(969\) 4.00000 0.128499
\(970\) 0 0
\(971\) −14.0000 −0.449281 −0.224641 − 0.974442i \(-0.572121\pi\)
−0.224641 + 0.974442i \(0.572121\pi\)
\(972\) −20.0000 −0.641500
\(973\) 0 0
\(974\) 0 0
\(975\) 8.00000 0.256205
\(976\) 8.00000 0.256074
\(977\) −36.0000 −1.15174 −0.575871 − 0.817541i \(-0.695337\pi\)
−0.575871 + 0.817541i \(0.695337\pi\)
\(978\) 0 0
\(979\) 5.00000 0.159801
\(980\) 0 0
\(981\) 4.00000 0.127710
\(982\) 0 0
\(983\) 37.0000 1.18012 0.590058 − 0.807361i \(-0.299105\pi\)
0.590058 + 0.807361i \(0.299105\pi\)
\(984\) 0 0
\(985\) −22.0000 −0.700978
\(986\) 0 0
\(987\) 0 0
\(988\) −2.00000 −0.0636285
\(989\) 65.0000 2.06688
\(990\) 0 0
\(991\) 8.00000 0.254128 0.127064 − 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) 0 0
\(993\) 4.00000 0.126936
\(994\) 0 0
\(995\) −2.00000 −0.0634043
\(996\) 12.0000 0.380235
\(997\) −48.0000 −1.52018 −0.760088 − 0.649821i \(-0.774844\pi\)
−0.760088 + 0.649821i \(0.774844\pi\)
\(998\) 0 0
\(999\) 40.0000 1.26554
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 7007.2.a.c.1.1 1
7.6 odd 2 1001.2.a.c.1.1 ✓ 1
21.20 even 2 9009.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1001.2.a.c.1.1 ✓ 1 7.6 odd 2
7007.2.a.c.1.1 1 1.1 even 1 trivial
9009.2.a.h.1.1 1 21.20 even 2