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Properties

Label 5166.2.a.h.1.1
Level $5166$
Weight $2$
Character 5166.1
Self dual yes
Analytic conductor $41.251$
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] = [5166,2,Mod(1,5166)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5166, 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("5166.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5166 = 2 \cdot 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5166.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: \(41.2507176842\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 574)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5166.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{10} -2.00000 q^{11} +4.00000 q^{13} -1.00000 q^{14} +1.00000 q^{16} -3.00000 q^{17} -1.00000 q^{20} +2.00000 q^{22} -4.00000 q^{23} -4.00000 q^{25} -4.00000 q^{26} +1.00000 q^{28} +5.00000 q^{29} +7.00000 q^{31} -1.00000 q^{32} +3.00000 q^{34} -1.00000 q^{35} -2.00000 q^{37} +1.00000 q^{40} -1.00000 q^{41} -1.00000 q^{43} -2.00000 q^{44} +4.00000 q^{46} +2.00000 q^{47} +1.00000 q^{49} +4.00000 q^{50} +4.00000 q^{52} +1.00000 q^{53} +2.00000 q^{55} -1.00000 q^{56} -5.00000 q^{58} -10.0000 q^{59} -13.0000 q^{61} -7.00000 q^{62} +1.00000 q^{64} -4.00000 q^{65} -2.00000 q^{67} -3.00000 q^{68} +1.00000 q^{70} +3.00000 q^{71} +4.00000 q^{73} +2.00000 q^{74} -2.00000 q^{77} -15.0000 q^{79} -1.00000 q^{80} +1.00000 q^{82} +6.00000 q^{83} +3.00000 q^{85} +1.00000 q^{86} +2.00000 q^{88} +15.0000 q^{89} +4.00000 q^{91} -4.00000 q^{92} -2.00000 q^{94} -7.00000 q^{97} -1.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214 −0.223607 − 0.974679i \(-0.571783\pi\)
−0.223607 + 0.974679i \(0.571783\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 1.00000 0.316228
\(11\) −2.00000 −0.603023 −0.301511 − 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 − 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −3.00000 −0.727607 −0.363803 − 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) 2.00000 0.426401
\(23\) −4.00000 −0.834058 −0.417029 − 0.908893i \(-0.636929\pi\)
−0.417029 + 0.908893i \(0.636929\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) 5.00000 0.928477 0.464238 − 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 7.00000 1.25724 0.628619 − 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 3.00000 0.514496
\(35\) −1.00000 −0.169031
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 − 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 4.00000 0.589768
\(47\) 2.00000 0.291730 0.145865 − 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.00000 0.565685
\(51\) 0 0
\(52\) 4.00000 0.554700
\(53\) 1.00000 0.137361 0.0686803 − 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0 0
\(55\) 2.00000 0.269680
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) −5.00000 −0.656532
\(59\) −10.0000 −1.30189 −0.650945 − 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) −13.0000 −1.66448 −0.832240 − 0.554416i \(-0.812942\pi\)
−0.832240 + 0.554416i \(0.812942\pi\)
\(62\) −7.00000 −0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) 0 0
\(67\) −2.00000 −0.244339 −0.122169 − 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) −3.00000 −0.363803
\(69\) 0 0
\(70\) 1.00000 0.119523
\(71\) 3.00000 0.356034 0.178017 − 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0 0
\(73\) 4.00000 0.468165 0.234082 − 0.972217i \(-0.424791\pi\)
0.234082 + 0.972217i \(0.424791\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) 0 0
\(77\) −2.00000 −0.227921
\(78\) 0 0
\(79\) −15.0000 −1.68763 −0.843816 − 0.536633i \(-0.819696\pi\)
−0.843816 + 0.536633i \(0.819696\pi\)
\(80\) −1.00000 −0.111803
\(81\) 0 0
\(82\) 1.00000 0.110432
\(83\) 6.00000 0.658586 0.329293 − 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 1.00000 0.107833
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) 15.0000 1.59000 0.794998 − 0.606612i \(-0.207472\pi\)
0.794998 + 0.606612i \(0.207472\pi\)
\(90\) 0 0
\(91\) 4.00000 0.419314
\(92\) −4.00000 −0.417029
\(93\) 0 0
\(94\) −2.00000 −0.206284
\(95\) 0 0
\(96\) 0 0
\(97\) −7.00000 −0.710742 −0.355371 − 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.00000 −0.400000
\(101\) −2.00000 −0.199007 −0.0995037 − 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) 0 0
\(103\) −1.00000 −0.0985329 −0.0492665 − 0.998786i \(-0.515688\pi\)
−0.0492665 + 0.998786i \(0.515688\pi\)
\(104\) −4.00000 −0.392232
\(105\) 0 0
\(106\) −1.00000 −0.0971286
\(107\) 17.0000 1.64345 0.821726 − 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) −2.00000 −0.190693
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −9.00000 −0.846649 −0.423324 − 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 4.00000 0.373002
\(116\) 5.00000 0.464238
\(117\) 0 0
\(118\) 10.0000 0.920575
\(119\) −3.00000 −0.275010
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 13.0000 1.17696
\(123\) 0 0
\(124\) 7.00000 0.628619
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) −2.00000 −0.177471 −0.0887357 − 0.996055i \(-0.528283\pi\)
−0.0887357 + 0.996055i \(0.528283\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 4.00000 0.350823
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) 12.0000 1.02523 0.512615 − 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) 10.0000 0.848189 0.424094 − 0.905618i \(-0.360592\pi\)
0.424094 + 0.905618i \(0.360592\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) −3.00000 −0.251754
\(143\) −8.00000 −0.668994
\(144\) 0 0
\(145\) −5.00000 −0.415227
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 5.00000 0.409616 0.204808 − 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) 7.00000 0.569652 0.284826 − 0.958579i \(-0.408064\pi\)
0.284826 + 0.958579i \(0.408064\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) −7.00000 −0.562254
\(156\) 0 0
\(157\) −12.0000 −0.957704 −0.478852 − 0.877896i \(-0.658947\pi\)
−0.478852 + 0.877896i \(0.658947\pi\)
\(158\) 15.0000 1.19334
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) −8.00000 −0.619059 −0.309529 − 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) −3.00000 −0.230089
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) −9.00000 −0.684257 −0.342129 − 0.939653i \(-0.611148\pi\)
−0.342129 + 0.939653i \(0.611148\pi\)
\(174\) 0 0
\(175\) −4.00000 −0.302372
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) −15.0000 −1.12430
\(179\) −20.0000 −1.49487 −0.747435 − 0.664335i \(-0.768715\pi\)
−0.747435 + 0.664335i \(0.768715\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 − 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) −4.00000 −0.296500
\(183\) 0 0
\(184\) 4.00000 0.294884
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) 6.00000 0.438763
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) −17.0000 −1.23008 −0.615038 − 0.788497i \(-0.710860\pi\)
−0.615038 + 0.788497i \(0.710860\pi\)
\(192\) 0 0
\(193\) −16.0000 −1.15171 −0.575853 − 0.817554i \(-0.695330\pi\)
−0.575853 + 0.817554i \(0.695330\pi\)
\(194\) 7.00000 0.502571
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −28.0000 −1.99492 −0.997459 − 0.0712470i \(-0.977302\pi\)
−0.997459 + 0.0712470i \(0.977302\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) 2.00000 0.140720
\(203\) 5.00000 0.350931
\(204\) 0 0
\(205\) 1.00000 0.0698430
\(206\) 1.00000 0.0696733
\(207\) 0 0
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 − 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 1.00000 0.0686803
\(213\) 0 0
\(214\) −17.0000 −1.16210
\(215\) 1.00000 0.0681994
\(216\) 0 0
\(217\) 7.00000 0.475191
\(218\) 10.0000 0.677285
\(219\) 0 0
\(220\) 2.00000 0.134840
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) −1.00000 −0.0669650 −0.0334825 − 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) −3.00000 −0.199117 −0.0995585 − 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) −4.00000 −0.263752
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −14.0000 −0.917170 −0.458585 − 0.888650i \(-0.651644\pi\)
−0.458585 + 0.888650i \(0.651644\pi\)
\(234\) 0 0
\(235\) −2.00000 −0.130466
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 3.00000 0.194461
\(239\) 20.0000 1.29369 0.646846 − 0.762620i \(-0.276088\pi\)
0.646846 + 0.762620i \(0.276088\pi\)
\(240\) 0 0
\(241\) 22.0000 1.41714 0.708572 − 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) −13.0000 −0.832240
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 0 0
\(248\) −7.00000 −0.444500
\(249\) 0 0
\(250\) −9.00000 −0.569210
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 8.00000 0.502956
\(254\) 2.00000 0.125491
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 17.0000 1.06043 0.530215 − 0.847863i \(-0.322111\pi\)
0.530215 + 0.847863i \(0.322111\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) 12.0000 0.741362
\(263\) 16.0000 0.986602 0.493301 − 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) 0 0
\(267\) 0 0
\(268\) −2.00000 −0.122169
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) −28.0000 −1.70088 −0.850439 − 0.526073i \(-0.823664\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) −3.00000 −0.181902
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) 8.00000 0.482418
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −10.0000 −0.599760
\(279\) 0 0
\(280\) 1.00000 0.0597614
\(281\) −2.00000 −0.119310 −0.0596550 − 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) 3.00000 0.178017
\(285\) 0 0
\(286\) 8.00000 0.473050
\(287\) −1.00000 −0.0590281
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 5.00000 0.293610
\(291\) 0 0
\(292\) 4.00000 0.234082
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 10.0000 0.582223
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −5.00000 −0.289642
\(299\) −16.0000 −0.925304
\(300\) 0 0
\(301\) −1.00000 −0.0576390
\(302\) −7.00000 −0.402805
\(303\) 0 0
\(304\) 0 0
\(305\) 13.0000 0.744378
\(306\) 0 0
\(307\) −12.0000 −0.684876 −0.342438 − 0.939540i \(-0.611253\pi\)
−0.342438 + 0.939540i \(0.611253\pi\)
\(308\) −2.00000 −0.113961
\(309\) 0 0
\(310\) 7.00000 0.397573
\(311\) −22.0000 −1.24751 −0.623753 − 0.781622i \(-0.714393\pi\)
−0.623753 + 0.781622i \(0.714393\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 12.0000 0.677199
\(315\) 0 0
\(316\) −15.0000 −0.843816
\(317\) 2.00000 0.112331 0.0561656 − 0.998421i \(-0.482113\pi\)
0.0561656 + 0.998421i \(0.482113\pi\)
\(318\) 0 0
\(319\) −10.0000 −0.559893
\(320\) −1.00000 −0.0559017
\(321\) 0 0
\(322\) 4.00000 0.222911
\(323\) 0 0
\(324\) 0 0
\(325\) −16.0000 −0.887520
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) 1.00000 0.0552158
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) 12.0000 0.659580 0.329790 − 0.944054i \(-0.393022\pi\)
0.329790 + 0.944054i \(0.393022\pi\)
\(332\) 6.00000 0.329293
\(333\) 0 0
\(334\) 8.00000 0.437741
\(335\) 2.00000 0.109272
\(336\) 0 0
\(337\) 13.0000 0.708155 0.354078 − 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) −3.00000 −0.163178
\(339\) 0 0
\(340\) 3.00000 0.162698
\(341\) −14.0000 −0.758143
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 9.00000 0.483843
\(347\) 12.0000 0.644194 0.322097 − 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 − 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 4.00000 0.213809
\(351\) 0 0
\(352\) 2.00000 0.106600
\(353\) −24.0000 −1.27739 −0.638696 − 0.769460i \(-0.720526\pi\)
−0.638696 + 0.769460i \(0.720526\pi\)
\(354\) 0 0
\(355\) −3.00000 −0.159223
\(356\) 15.0000 0.794998
\(357\) 0 0
\(358\) 20.0000 1.05703
\(359\) −20.0000 −1.05556 −0.527780 − 0.849381i \(-0.676975\pi\)
−0.527780 + 0.849381i \(0.676975\pi\)
\(360\) 0 0
\(361\) −19.0000 −1.00000
\(362\) −2.00000 −0.105118
\(363\) 0 0
\(364\) 4.00000 0.209657
\(365\) −4.00000 −0.209370
\(366\) 0 0
\(367\) −27.0000 −1.40939 −0.704694 − 0.709511i \(-0.748916\pi\)
−0.704694 + 0.709511i \(0.748916\pi\)
\(368\) −4.00000 −0.208514
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 1.00000 0.0519174
\(372\) 0 0
\(373\) 34.0000 1.76045 0.880227 − 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) −6.00000 −0.310253
\(375\) 0 0
\(376\) −2.00000 −0.103142
\(377\) 20.0000 1.03005
\(378\) 0 0
\(379\) 25.0000 1.28416 0.642082 − 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 17.0000 0.869796
\(383\) 6.00000 0.306586 0.153293 − 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 2.00000 0.101929
\(386\) 16.0000 0.814379
\(387\) 0 0
\(388\) −7.00000 −0.355371
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) 12.0000 0.606866
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 28.0000 1.41062
\(395\) 15.0000 0.754732
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 − 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −4.00000 −0.200000
\(401\) −7.00000 −0.349563 −0.174782 − 0.984607i \(-0.555922\pi\)
−0.174782 + 0.984607i \(0.555922\pi\)
\(402\) 0 0
\(403\) 28.0000 1.39478
\(404\) −2.00000 −0.0995037
\(405\) 0 0
\(406\) −5.00000 −0.248146
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −10.0000 −0.494468 −0.247234 − 0.968956i \(-0.579522\pi\)
−0.247234 + 0.968956i \(0.579522\pi\)
\(410\) −1.00000 −0.0493865
\(411\) 0 0
\(412\) −1.00000 −0.0492665
\(413\) −10.0000 −0.492068
\(414\) 0 0
\(415\) −6.00000 −0.294528
\(416\) −4.00000 −0.196116
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −3.00000 −0.146211 −0.0731055 − 0.997324i \(-0.523291\pi\)
−0.0731055 + 0.997324i \(0.523291\pi\)
\(422\) −12.0000 −0.584151
\(423\) 0 0
\(424\) −1.00000 −0.0485643
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) −13.0000 −0.629114
\(428\) 17.0000 0.821726
\(429\) 0 0
\(430\) −1.00000 −0.0482243
\(431\) −32.0000 −1.54139 −0.770693 − 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −7.00000 −0.336011
\(435\) 0 0
\(436\) −10.0000 −0.478913
\(437\) 0 0
\(438\) 0 0
\(439\) −10.0000 −0.477274 −0.238637 − 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) 21.0000 0.997740 0.498870 − 0.866677i \(-0.333748\pi\)
0.498870 + 0.866677i \(0.333748\pi\)
\(444\) 0 0
\(445\) −15.0000 −0.711068
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 25.0000 1.17982 0.589911 − 0.807468i \(-0.299163\pi\)
0.589911 + 0.807468i \(0.299163\pi\)
\(450\) 0 0
\(451\) 2.00000 0.0941763
\(452\) −9.00000 −0.423324
\(453\) 0 0
\(454\) 3.00000 0.140797
\(455\) −4.00000 −0.187523
\(456\) 0 0
\(457\) −22.0000 −1.02912 −0.514558 − 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 4.00000 0.186501
\(461\) −37.0000 −1.72326 −0.861631 − 0.507535i \(-0.830557\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 − 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) 14.0000 0.648537
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) −2.00000 −0.0923514
\(470\) 2.00000 0.0922531
\(471\) 0 0
\(472\) 10.0000 0.460287
\(473\) 2.00000 0.0919601
\(474\) 0 0
\(475\) 0 0
\(476\) −3.00000 −0.137505
\(477\) 0 0
\(478\) −20.0000 −0.914779
\(479\) 10.0000 0.456912 0.228456 − 0.973554i \(-0.426632\pi\)
0.228456 + 0.973554i \(0.426632\pi\)
\(480\) 0 0
\(481\) −8.00000 −0.364769
\(482\) −22.0000 −1.00207
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 7.00000 0.317854
\(486\) 0 0
\(487\) −32.0000 −1.45006 −0.725029 − 0.688718i \(-0.758174\pi\)
−0.725029 + 0.688718i \(0.758174\pi\)
\(488\) 13.0000 0.588482
\(489\) 0 0
\(490\) 1.00000 0.0451754
\(491\) −17.0000 −0.767199 −0.383600 − 0.923499i \(-0.625316\pi\)
−0.383600 + 0.923499i \(0.625316\pi\)
\(492\) 0 0
\(493\) −15.0000 −0.675566
\(494\) 0 0
\(495\) 0 0
\(496\) 7.00000 0.314309
\(497\) 3.00000 0.134568
\(498\) 0 0
\(499\) −30.0000 −1.34298 −0.671492 − 0.741012i \(-0.734346\pi\)
−0.671492 + 0.741012i \(0.734346\pi\)
\(500\) 9.00000 0.402492
\(501\) 0 0
\(502\) 12.0000 0.535586
\(503\) 16.0000 0.713405 0.356702 − 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 2.00000 0.0889988
\(506\) −8.00000 −0.355643
\(507\) 0 0
\(508\) −2.00000 −0.0887357
\(509\) 20.0000 0.886484 0.443242 − 0.896402i \(-0.353828\pi\)
0.443242 + 0.896402i \(0.353828\pi\)
\(510\) 0 0
\(511\) 4.00000 0.176950
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −17.0000 −0.749838
\(515\) 1.00000 0.0440653
\(516\) 0 0
\(517\) −4.00000 −0.175920
\(518\) 2.00000 0.0878750
\(519\) 0 0
\(520\) 4.00000 0.175412
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −36.0000 −1.57417 −0.787085 − 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −21.0000 −0.914774
\(528\) 0 0
\(529\) −7.00000 −0.304348
\(530\) 1.00000 0.0434372
\(531\) 0 0
\(532\) 0 0
\(533\) −4.00000 −0.173259
\(534\) 0 0
\(535\) −17.0000 −0.734974
\(536\) 2.00000 0.0863868
\(537\) 0 0
\(538\) 10.0000 0.431131
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 28.0000 1.20270
\(543\) 0 0
\(544\) 3.00000 0.128624
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) −22.0000 −0.940652 −0.470326 − 0.882493i \(-0.655864\pi\)
−0.470326 + 0.882493i \(0.655864\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) −8.00000 −0.341121
\(551\) 0 0
\(552\) 0 0
\(553\) −15.0000 −0.637865
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) 10.0000 0.424094
\(557\) −33.0000 −1.39825 −0.699127 − 0.714997i \(-0.746428\pi\)
−0.699127 + 0.714997i \(0.746428\pi\)
\(558\) 0 0
\(559\) −4.00000 −0.169182
\(560\) −1.00000 −0.0422577
\(561\) 0 0
\(562\) 2.00000 0.0843649
\(563\) −4.00000 −0.168580 −0.0842900 − 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 9.00000 0.378633
\(566\) −14.0000 −0.588464
\(567\) 0 0
\(568\) −3.00000 −0.125877
\(569\) −15.0000 −0.628833 −0.314416 − 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 0 0
\(571\) 12.0000 0.502184 0.251092 − 0.967963i \(-0.419210\pi\)
0.251092 + 0.967963i \(0.419210\pi\)
\(572\) −8.00000 −0.334497
\(573\) 0 0
\(574\) 1.00000 0.0417392
\(575\) 16.0000 0.667246
\(576\) 0 0
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 8.00000 0.332756
\(579\) 0 0
\(580\) −5.00000 −0.207614
\(581\) 6.00000 0.248922
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) −4.00000 −0.165521
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −33.0000 −1.36206 −0.681028 − 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −10.0000 −0.411693
\(591\) 0 0
\(592\) −2.00000 −0.0821995
\(593\) −19.0000 −0.780236 −0.390118 − 0.920765i \(-0.627566\pi\)
−0.390118 + 0.920765i \(0.627566\pi\)
\(594\) 0 0
\(595\) 3.00000 0.122988
\(596\) 5.00000 0.204808
\(597\) 0 0
\(598\) 16.0000 0.654289
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −13.0000 −0.530281 −0.265141 − 0.964210i \(-0.585418\pi\)
−0.265141 + 0.964210i \(0.585418\pi\)
\(602\) 1.00000 0.0407570
\(603\) 0 0
\(604\) 7.00000 0.284826
\(605\) 7.00000 0.284590
\(606\) 0 0
\(607\) 23.0000 0.933541 0.466771 − 0.884378i \(-0.345417\pi\)
0.466771 + 0.884378i \(0.345417\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −13.0000 −0.526355
\(611\) 8.00000 0.323645
\(612\) 0 0
\(613\) −36.0000 −1.45403 −0.727013 − 0.686624i \(-0.759092\pi\)
−0.727013 + 0.686624i \(0.759092\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 42.0000 1.69086 0.845428 − 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 0 0
\(619\) −20.0000 −0.803868 −0.401934 − 0.915669i \(-0.631662\pi\)
−0.401934 + 0.915669i \(0.631662\pi\)
\(620\) −7.00000 −0.281127
\(621\) 0 0
\(622\) 22.0000 0.882120
\(623\) 15.0000 0.600962
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) −12.0000 −0.478852
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) 42.0000 1.67199 0.835997 − 0.548734i \(-0.184890\pi\)
0.835997 + 0.548734i \(0.184890\pi\)
\(632\) 15.0000 0.596668
\(633\) 0 0
\(634\) −2.00000 −0.0794301
\(635\) 2.00000 0.0793676
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 10.0000 0.395904
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 0 0
\(643\) −21.0000 −0.828159 −0.414080 − 0.910241i \(-0.635896\pi\)
−0.414080 + 0.910241i \(0.635896\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) 0 0
\(647\) 17.0000 0.668339 0.334169 − 0.942513i \(-0.391544\pi\)
0.334169 + 0.942513i \(0.391544\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 16.0000 0.627572
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 21.0000 0.821794 0.410897 − 0.911682i \(-0.365216\pi\)
0.410897 + 0.911682i \(0.365216\pi\)
\(654\) 0 0
\(655\) 12.0000 0.468879
\(656\) −1.00000 −0.0390434
\(657\) 0 0
\(658\) −2.00000 −0.0779681
\(659\) 20.0000 0.779089 0.389545 − 0.921008i \(-0.372632\pi\)
0.389545 + 0.921008i \(0.372632\pi\)
\(660\) 0 0
\(661\) −18.0000 −0.700119 −0.350059 − 0.936727i \(-0.613839\pi\)
−0.350059 + 0.936727i \(0.613839\pi\)
\(662\) −12.0000 −0.466393
\(663\) 0 0
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) −20.0000 −0.774403
\(668\) −8.00000 −0.309529
\(669\) 0 0
\(670\) −2.00000 −0.0772667
\(671\) 26.0000 1.00372
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 − 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −13.0000 −0.500741
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −18.0000 −0.691796 −0.345898 − 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) 0 0
\(679\) −7.00000 −0.268635
\(680\) −3.00000 −0.115045
\(681\) 0 0
\(682\) 14.0000 0.536088
\(683\) 16.0000 0.612223 0.306111 − 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) 0 0
\(685\) −12.0000 −0.458496
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) −33.0000 −1.25538 −0.627690 − 0.778464i \(-0.715999\pi\)
−0.627690 + 0.778464i \(0.715999\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −10.0000 −0.379322
\(696\) 0 0
\(697\) 3.00000 0.113633
\(698\) −10.0000 −0.378506
\(699\) 0 0
\(700\) −4.00000 −0.151186
\(701\) 8.00000 0.302156 0.151078 − 0.988522i \(-0.451726\pi\)
0.151078 + 0.988522i \(0.451726\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) 24.0000 0.903252
\(707\) −2.00000 −0.0752177
\(708\) 0 0
\(709\) 35.0000 1.31445 0.657226 − 0.753693i \(-0.271730\pi\)
0.657226 + 0.753693i \(0.271730\pi\)
\(710\) 3.00000 0.112588
\(711\) 0 0
\(712\) −15.0000 −0.562149
\(713\) −28.0000 −1.04861
\(714\) 0 0
\(715\) 8.00000 0.299183
\(716\) −20.0000 −0.747435
\(717\) 0 0
\(718\) 20.0000 0.746393
\(719\) −20.0000 −0.745874 −0.372937 − 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 0 0
\(721\) −1.00000 −0.0372419
\(722\) 19.0000 0.707107
\(723\) 0 0
\(724\) 2.00000 0.0743294
\(725\) −20.0000 −0.742781
\(726\) 0 0
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) −4.00000 −0.148250
\(729\) 0 0
\(730\) 4.00000 0.148047
\(731\) 3.00000 0.110959
\(732\) 0 0
\(733\) −21.0000 −0.775653 −0.387826 − 0.921732i \(-0.626774\pi\)
−0.387826 + 0.921732i \(0.626774\pi\)
\(734\) 27.0000 0.996588
\(735\) 0 0
\(736\) 4.00000 0.147442
\(737\) 4.00000 0.147342
\(738\) 0 0
\(739\) 15.0000 0.551784 0.275892 − 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(740\) 2.00000 0.0735215
\(741\) 0 0
\(742\) −1.00000 −0.0367112
\(743\) 36.0000 1.32071 0.660356 − 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) −5.00000 −0.183186
\(746\) −34.0000 −1.24483
\(747\) 0 0
\(748\) 6.00000 0.219382
\(749\) 17.0000 0.621166
\(750\) 0 0
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 2.00000 0.0729325
\(753\) 0 0
\(754\) −20.0000 −0.728357
\(755\) −7.00000 −0.254756
\(756\) 0 0
\(757\) 43.0000 1.56286 0.781431 − 0.623992i \(-0.214490\pi\)
0.781431 + 0.623992i \(0.214490\pi\)
\(758\) −25.0000 −0.908041
\(759\) 0 0
\(760\) 0 0
\(761\) −22.0000 −0.797499 −0.398750 − 0.917060i \(-0.630556\pi\)
−0.398750 + 0.917060i \(0.630556\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) −17.0000 −0.615038
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) −40.0000 −1.44432
\(768\) 0 0
\(769\) −10.0000 −0.360609 −0.180305 − 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) −2.00000 −0.0720750
\(771\) 0 0
\(772\) −16.0000 −0.575853
\(773\) −34.0000 −1.22290 −0.611448 − 0.791285i \(-0.709412\pi\)
−0.611448 + 0.791285i \(0.709412\pi\)
\(774\) 0 0
\(775\) −28.0000 −1.00579
\(776\) 7.00000 0.251285
\(777\) 0 0
\(778\) 30.0000 1.07555
\(779\) 0 0
\(780\) 0 0
\(781\) −6.00000 −0.214697
\(782\) −12.0000 −0.429119
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) −28.0000 −0.997459
\(789\) 0 0
\(790\) −15.0000 −0.533676
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) −52.0000 −1.84657
\(794\) −8.00000 −0.283909
\(795\) 0 0
\(796\) 0 0
\(797\) −43.0000 −1.52314 −0.761569 − 0.648084i \(-0.775571\pi\)
−0.761569 + 0.648084i \(0.775571\pi\)
\(798\) 0 0
\(799\) −6.00000 −0.212265
\(800\) 4.00000 0.141421
\(801\) 0 0
\(802\) 7.00000 0.247179
\(803\) −8.00000 −0.282314
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) −28.0000 −0.986258
\(807\) 0 0
\(808\) 2.00000 0.0703598
\(809\) −10.0000 −0.351581 −0.175791 − 0.984428i \(-0.556248\pi\)
−0.175791 + 0.984428i \(0.556248\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 − 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 5.00000 0.175466
\(813\) 0 0
\(814\) −4.00000 −0.140200
\(815\) −4.00000 −0.140114
\(816\) 0 0
\(817\) 0 0
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) 1.00000 0.0349215
\(821\) −32.0000 −1.11681 −0.558404 − 0.829569i \(-0.688586\pi\)
−0.558404 + 0.829569i \(0.688586\pi\)
\(822\) 0 0
\(823\) 49.0000 1.70803 0.854016 − 0.520246i \(-0.174160\pi\)
0.854016 + 0.520246i \(0.174160\pi\)
\(824\) 1.00000 0.0348367
\(825\) 0 0
\(826\) 10.0000 0.347945
\(827\) 42.0000 1.46048 0.730242 − 0.683189i \(-0.239408\pi\)
0.730242 + 0.683189i \(0.239408\pi\)
\(828\) 0 0
\(829\) 45.0000 1.56291 0.781457 − 0.623959i \(-0.214477\pi\)
0.781457 + 0.623959i \(0.214477\pi\)
\(830\) 6.00000 0.208263
\(831\) 0 0
\(832\) 4.00000 0.138675
\(833\) −3.00000 −0.103944
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −10.0000 −0.345238 −0.172619 − 0.984989i \(-0.555223\pi\)
−0.172619 + 0.984989i \(0.555223\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 3.00000 0.103387
\(843\) 0 0
\(844\) 12.0000 0.413057
\(845\) −3.00000 −0.103203
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 1.00000 0.0343401
\(849\) 0 0
\(850\) −12.0000 −0.411597
\(851\) 8.00000 0.274236
\(852\) 0 0
\(853\) −11.0000 −0.376633 −0.188316 − 0.982108i \(-0.560303\pi\)
−0.188316 + 0.982108i \(0.560303\pi\)
\(854\) 13.0000 0.444851
\(855\) 0 0
\(856\) −17.0000 −0.581048
\(857\) 2.00000 0.0683187 0.0341593 − 0.999416i \(-0.489125\pi\)
0.0341593 + 0.999416i \(0.489125\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 1.00000 0.0340997
\(861\) 0 0
\(862\) 32.0000 1.08992
\(863\) 36.0000 1.22545 0.612727 − 0.790295i \(-0.290072\pi\)
0.612727 + 0.790295i \(0.290072\pi\)
\(864\) 0 0
\(865\) 9.00000 0.306009
\(866\) 16.0000 0.543702
\(867\) 0 0
\(868\) 7.00000 0.237595
\(869\) 30.0000 1.01768
\(870\) 0 0
\(871\) −8.00000 −0.271070
\(872\) 10.0000 0.338643
\(873\) 0 0
\(874\) 0 0
\(875\) 9.00000 0.304256
\(876\) 0 0
\(877\) 8.00000 0.270141 0.135070 − 0.990836i \(-0.456874\pi\)
0.135070 + 0.990836i \(0.456874\pi\)
\(878\) 10.0000 0.337484
\(879\) 0 0
\(880\) 2.00000 0.0674200
\(881\) 28.0000 0.943344 0.471672 − 0.881774i \(-0.343651\pi\)
0.471672 + 0.881774i \(0.343651\pi\)
\(882\) 0 0
\(883\) −26.0000 −0.874970 −0.437485 − 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) −12.0000 −0.403604
\(885\) 0 0
\(886\) −21.0000 −0.705509
\(887\) −28.0000 −0.940148 −0.470074 − 0.882627i \(-0.655773\pi\)
−0.470074 + 0.882627i \(0.655773\pi\)
\(888\) 0 0
\(889\) −2.00000 −0.0670778
\(890\) 15.0000 0.502801
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) 0 0
\(894\) 0 0
\(895\) 20.0000 0.668526
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −25.0000 −0.834261
\(899\) 35.0000 1.16732
\(900\) 0 0
\(901\) −3.00000 −0.0999445
\(902\) −2.00000 −0.0665927
\(903\) 0 0
\(904\) 9.00000 0.299336
\(905\) −2.00000 −0.0664822
\(906\) 0 0
\(907\) 23.0000 0.763702 0.381851 − 0.924224i \(-0.375287\pi\)
0.381851 + 0.924224i \(0.375287\pi\)
\(908\) −3.00000 −0.0995585
\(909\) 0 0
\(910\) 4.00000 0.132599
\(911\) 38.0000 1.25900 0.629498 − 0.777002i \(-0.283261\pi\)
0.629498 + 0.777002i \(0.283261\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 22.0000 0.727695
\(915\) 0 0
\(916\) 0 0
\(917\) −12.0000 −0.396275
\(918\) 0 0
\(919\) −25.0000 −0.824674 −0.412337 − 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) −4.00000 −0.131876
\(921\) 0 0
\(922\) 37.0000 1.21853
\(923\) 12.0000 0.394985
\(924\) 0 0
\(925\) 8.00000 0.263038
\(926\) 16.0000 0.525793
\(927\) 0 0
\(928\) −5.00000 −0.164133
\(929\) −10.0000 −0.328089 −0.164045 − 0.986453i \(-0.552454\pi\)
−0.164045 + 0.986453i \(0.552454\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −14.0000 −0.458585
\(933\) 0 0
\(934\) 18.0000 0.588978
\(935\) −6.00000 −0.196221
\(936\) 0 0
\(937\) 33.0000 1.07806 0.539032 − 0.842286i \(-0.318790\pi\)
0.539032 + 0.842286i \(0.318790\pi\)
\(938\) 2.00000 0.0653023
\(939\) 0 0
\(940\) −2.00000 −0.0652328
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) 0 0
\(943\) 4.00000 0.130258
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) −2.00000 −0.0650256
\(947\) 12.0000 0.389948 0.194974 − 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 0 0
\(949\) 16.0000 0.519382
\(950\) 0 0
\(951\) 0 0
\(952\) 3.00000 0.0972306
\(953\) −54.0000 −1.74923 −0.874616 − 0.484817i \(-0.838886\pi\)
−0.874616 + 0.484817i \(0.838886\pi\)
\(954\) 0 0
\(955\) 17.0000 0.550107
\(956\) 20.0000 0.646846
\(957\) 0 0
\(958\) −10.0000 −0.323085
\(959\) 12.0000 0.387500
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 8.00000 0.257930
\(963\) 0 0
\(964\) 22.0000 0.708572
\(965\) 16.0000 0.515058
\(966\) 0 0
\(967\) 13.0000 0.418052 0.209026 − 0.977910i \(-0.432971\pi\)
0.209026 + 0.977910i \(0.432971\pi\)
\(968\) 7.00000 0.224989
\(969\) 0 0
\(970\) −7.00000 −0.224756
\(971\) −47.0000 −1.50830 −0.754151 − 0.656701i \(-0.771951\pi\)
−0.754151 + 0.656701i \(0.771951\pi\)
\(972\) 0 0
\(973\) 10.0000 0.320585
\(974\) 32.0000 1.02535
\(975\) 0 0
\(976\) −13.0000 −0.416120
\(977\) 2.00000 0.0639857 0.0319928 − 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 0 0
\(979\) −30.0000 −0.958804
\(980\) −1.00000 −0.0319438
\(981\) 0 0
\(982\) 17.0000 0.542492
\(983\) 1.00000 0.0318950 0.0159475 − 0.999873i \(-0.494924\pi\)
0.0159475 + 0.999873i \(0.494924\pi\)
\(984\) 0 0
\(985\) 28.0000 0.892154
\(986\) 15.0000 0.477697
\(987\) 0 0
\(988\) 0 0
\(989\) 4.00000 0.127193
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 − 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −7.00000 −0.222250
\(993\) 0 0
\(994\) −3.00000 −0.0951542
\(995\) 0 0
\(996\) 0 0
\(997\) 28.0000 0.886769 0.443384 − 0.896332i \(-0.353778\pi\)
0.443384 + 0.896332i \(0.353778\pi\)
\(998\) 30.0000 0.949633
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 5166.2.a.h.1.1 1
3.2 odd 2 574.2.a.i.1.1 ✓ 1
12.11 even 2 4592.2.a.i.1.1 1
21.20 even 2 4018.2.a.o.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
574.2.a.i.1.1 ✓ 1 3.2 odd 2
4018.2.a.o.1.1 1 21.20 even 2
4592.2.a.i.1.1 1 12.11 even 2
5166.2.a.h.1.1 1 1.1 even 1 trivial