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Properties

Label 1666.2.a.f.1.1
Level $1666$
Weight $2$
Character 1666.1
Self dual yes
Analytic conductor $13.303$
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] = [1666,2,Mod(1,1666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1666, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1666.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1666 = 2 \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1666.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: \(13.3030769767\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 238)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1666.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} -2.00000 q^{9} -2.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -5.00000 q^{13} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +2.00000 q^{18} -6.00000 q^{19} +2.00000 q^{20} +1.00000 q^{22} -1.00000 q^{24} -1.00000 q^{25} +5.00000 q^{26} -5.00000 q^{27} -6.00000 q^{29} -2.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.00000 q^{34} -2.00000 q^{36} +8.00000 q^{37} +6.00000 q^{38} -5.00000 q^{39} -2.00000 q^{40} -6.00000 q^{41} -12.0000 q^{43} -1.00000 q^{44} -4.00000 q^{45} +2.00000 q^{47} +1.00000 q^{48} +1.00000 q^{50} +1.00000 q^{51} -5.00000 q^{52} -7.00000 q^{53} +5.00000 q^{54} -2.00000 q^{55} -6.00000 q^{57} +6.00000 q^{58} +12.0000 q^{59} +2.00000 q^{60} +12.0000 q^{61} +4.00000 q^{62} +1.00000 q^{64} -10.0000 q^{65} +1.00000 q^{66} -2.00000 q^{67} +1.00000 q^{68} +7.00000 q^{71} +2.00000 q^{72} -2.00000 q^{73} -8.00000 q^{74} -1.00000 q^{75} -6.00000 q^{76} +5.00000 q^{78} +3.00000 q^{79} +2.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -4.00000 q^{83} +2.00000 q^{85} +12.0000 q^{86} -6.00000 q^{87} +1.00000 q^{88} -1.00000 q^{89} +4.00000 q^{90} -4.00000 q^{93} -2.00000 q^{94} -12.0000 q^{95} -1.00000 q^{96} +12.0000 q^{97} +2.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 1.00000 0.577350 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.00000 0.894427 0.447214 − 0.894427i \(-0.352416\pi\)
0.447214 + 0.894427i \(0.352416\pi\)
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −2.00000 −0.666667
\(10\) −2.00000 −0.632456
\(11\) −1.00000 −0.301511 −0.150756 − 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 1.00000 0.288675
\(13\) −5.00000 −1.38675 −0.693375 − 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 2.00000 0.471405
\(19\) −6.00000 −1.37649 −0.688247 − 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) 2.00000 0.447214
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) −1.00000 −0.200000
\(26\) 5.00000 0.980581
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 − 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) −2.00000 −0.365148
\(31\) −4.00000 −0.718421 −0.359211 − 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.00000 −0.174078
\(34\) −1.00000 −0.171499
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 6.00000 0.973329
\(39\) −5.00000 −0.800641
\(40\) −2.00000 −0.316228
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −12.0000 −1.82998 −0.914991 − 0.403473i \(-0.867803\pi\)
−0.914991 + 0.403473i \(0.867803\pi\)
\(44\) −1.00000 −0.150756
\(45\) −4.00000 −0.596285
\(46\) 0 0
\(47\) 2.00000 0.291730 0.145865 − 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 1.00000 0.144338
\(49\) 0 0
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) −5.00000 −0.693375
\(53\) −7.00000 −0.961524 −0.480762 − 0.876851i \(-0.659640\pi\)
−0.480762 + 0.876851i \(0.659640\pi\)
\(54\) 5.00000 0.680414
\(55\) −2.00000 −0.269680
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) 6.00000 0.787839
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 2.00000 0.258199
\(61\) 12.0000 1.53644 0.768221 − 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −10.0000 −1.24035
\(66\) 1.00000 0.123091
\(67\) −2.00000 −0.244339 −0.122169 − 0.992509i \(-0.538985\pi\)
−0.122169 + 0.992509i \(0.538985\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) 7.00000 0.830747 0.415374 − 0.909651i \(-0.363651\pi\)
0.415374 + 0.909651i \(0.363651\pi\)
\(72\) 2.00000 0.235702
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −8.00000 −0.929981
\(75\) −1.00000 −0.115470
\(76\) −6.00000 −0.688247
\(77\) 0 0
\(78\) 5.00000 0.566139
\(79\) 3.00000 0.337526 0.168763 − 0.985657i \(-0.446023\pi\)
0.168763 + 0.985657i \(0.446023\pi\)
\(80\) 2.00000 0.223607
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 0 0
\(85\) 2.00000 0.216930
\(86\) 12.0000 1.29399
\(87\) −6.00000 −0.643268
\(88\) 1.00000 0.106600
\(89\) −1.00000 −0.106000 −0.0529999 − 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 4.00000 0.421637
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 −0.414781
\(94\) −2.00000 −0.206284
\(95\) −12.0000 −1.23117
\(96\) −1.00000 −0.102062
\(97\) 12.0000 1.21842 0.609208 − 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 0 0
\(99\) 2.00000 0.201008
\(100\) −1.00000 −0.100000
\(101\) 2.00000 0.199007 0.0995037 − 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 10.0000 0.985329 0.492665 − 0.870219i \(-0.336023\pi\)
0.492665 + 0.870219i \(0.336023\pi\)
\(104\) 5.00000 0.490290
\(105\) 0 0
\(106\) 7.00000 0.679900
\(107\) 3.00000 0.290021 0.145010 − 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −5.00000 −0.481125
\(109\) 16.0000 1.53252 0.766261 − 0.642529i \(-0.222115\pi\)
0.766261 + 0.642529i \(0.222115\pi\)
\(110\) 2.00000 0.190693
\(111\) 8.00000 0.759326
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 − 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 6.00000 0.561951
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 10.0000 0.924500
\(118\) −12.0000 −1.10469
\(119\) 0 0
\(120\) −2.00000 −0.182574
\(121\) −10.0000 −0.909091
\(122\) −12.0000 −1.08643
\(123\) −6.00000 −0.541002
\(124\) −4.00000 −0.359211
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) −14.0000 −1.24230 −0.621150 − 0.783692i \(-0.713334\pi\)
−0.621150 + 0.783692i \(0.713334\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −12.0000 −1.05654
\(130\) 10.0000 0.877058
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 0 0
\(134\) 2.00000 0.172774
\(135\) −10.0000 −0.860663
\(136\) −1.00000 −0.0857493
\(137\) 5.00000 0.427179 0.213589 − 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(138\) 0 0
\(139\) 11.0000 0.933008 0.466504 − 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) 0 0
\(141\) 2.00000 0.168430
\(142\) −7.00000 −0.587427
\(143\) 5.00000 0.418121
\(144\) −2.00000 −0.166667
\(145\) −12.0000 −0.996546
\(146\) 2.00000 0.165521
\(147\) 0 0
\(148\) 8.00000 0.657596
\(149\) −17.0000 −1.39269 −0.696347 − 0.717705i \(-0.745193\pi\)
−0.696347 + 0.717705i \(0.745193\pi\)
\(150\) 1.00000 0.0816497
\(151\) −22.0000 −1.79033 −0.895167 − 0.445730i \(-0.852944\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(152\) 6.00000 0.486664
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −8.00000 −0.642575
\(156\) −5.00000 −0.400320
\(157\) 5.00000 0.399043 0.199522 − 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) −3.00000 −0.238667
\(159\) −7.00000 −0.555136
\(160\) −2.00000 −0.158114
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) 4.00000 0.313304 0.156652 − 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) −6.00000 −0.468521
\(165\) −2.00000 −0.155700
\(166\) 4.00000 0.310460
\(167\) −1.00000 −0.0773823 −0.0386912 − 0.999251i \(-0.512319\pi\)
−0.0386912 + 0.999251i \(0.512319\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −2.00000 −0.153393
\(171\) 12.0000 0.917663
\(172\) −12.0000 −0.914991
\(173\) −16.0000 −1.21646 −0.608229 − 0.793762i \(-0.708120\pi\)
−0.608229 + 0.793762i \(0.708120\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 12.0000 0.901975
\(178\) 1.00000 0.0749532
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) −4.00000 −0.298142
\(181\) 12.0000 0.891953 0.445976 − 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 0 0
\(185\) 16.0000 1.17634
\(186\) 4.00000 0.293294
\(187\) −1.00000 −0.0731272
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) 12.0000 0.870572
\(191\) −24.0000 −1.73658 −0.868290 − 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 1.00000 0.0721688
\(193\) 16.0000 1.15171 0.575853 − 0.817554i \(-0.304670\pi\)
0.575853 + 0.817554i \(0.304670\pi\)
\(194\) −12.0000 −0.861550
\(195\) −10.0000 −0.716115
\(196\) 0 0
\(197\) 14.0000 0.997459 0.498729 − 0.866758i \(-0.333800\pi\)
0.498729 + 0.866758i \(0.333800\pi\)
\(198\) −2.00000 −0.142134
\(199\) −13.0000 −0.921546 −0.460773 − 0.887518i \(-0.652428\pi\)
−0.460773 + 0.887518i \(0.652428\pi\)
\(200\) 1.00000 0.0707107
\(201\) −2.00000 −0.141069
\(202\) −2.00000 −0.140720
\(203\) 0 0
\(204\) 1.00000 0.0700140
\(205\) −12.0000 −0.838116
\(206\) −10.0000 −0.696733
\(207\) 0 0
\(208\) −5.00000 −0.346688
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) −7.00000 −0.480762
\(213\) 7.00000 0.479632
\(214\) −3.00000 −0.205076
\(215\) −24.0000 −1.63679
\(216\) 5.00000 0.340207
\(217\) 0 0
\(218\) −16.0000 −1.08366
\(219\) −2.00000 −0.135147
\(220\) −2.00000 −0.134840
\(221\) −5.00000 −0.336336
\(222\) −8.00000 −0.536925
\(223\) 12.0000 0.803579 0.401790 − 0.915732i \(-0.368388\pi\)
0.401790 + 0.915732i \(0.368388\pi\)
\(224\) 0 0
\(225\) 2.00000 0.133333
\(226\) 16.0000 1.06430
\(227\) −7.00000 −0.464606 −0.232303 − 0.972643i \(-0.574626\pi\)
−0.232303 + 0.972643i \(0.574626\pi\)
\(228\) −6.00000 −0.397360
\(229\) −2.00000 −0.132164 −0.0660819 − 0.997814i \(-0.521050\pi\)
−0.0660819 + 0.997814i \(0.521050\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 8.00000 0.524097 0.262049 − 0.965055i \(-0.415602\pi\)
0.262049 + 0.965055i \(0.415602\pi\)
\(234\) −10.0000 −0.653720
\(235\) 4.00000 0.260931
\(236\) 12.0000 0.781133
\(237\) 3.00000 0.194871
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 − 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 2.00000 0.129099
\(241\) 14.0000 0.901819 0.450910 − 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 10.0000 0.642824
\(243\) 16.0000 1.02640
\(244\) 12.0000 0.768221
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) 30.0000 1.90885
\(248\) 4.00000 0.254000
\(249\) −4.00000 −0.253490
\(250\) 12.0000 0.758947
\(251\) −26.0000 −1.64111 −0.820553 − 0.571571i \(-0.806334\pi\)
−0.820553 + 0.571571i \(0.806334\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 14.0000 0.878438
\(255\) 2.00000 0.125245
\(256\) 1.00000 0.0625000
\(257\) −15.0000 −0.935674 −0.467837 − 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) 12.0000 0.747087
\(259\) 0 0
\(260\) −10.0000 −0.620174
\(261\) 12.0000 0.742781
\(262\) −12.0000 −0.741362
\(263\) 6.00000 0.369976 0.184988 − 0.982741i \(-0.440775\pi\)
0.184988 + 0.982741i \(0.440775\pi\)
\(264\) 1.00000 0.0615457
\(265\) −14.0000 −0.860013
\(266\) 0 0
\(267\) −1.00000 −0.0611990
\(268\) −2.00000 −0.122169
\(269\) 30.0000 1.82913 0.914566 − 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 10.0000 0.608581
\(271\) −12.0000 −0.728948 −0.364474 − 0.931214i \(-0.618751\pi\)
−0.364474 + 0.931214i \(0.618751\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) −5.00000 −0.302061
\(275\) 1.00000 0.0603023
\(276\) 0 0
\(277\) 12.0000 0.721010 0.360505 − 0.932757i \(-0.382604\pi\)
0.360505 + 0.932757i \(0.382604\pi\)
\(278\) −11.0000 −0.659736
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 − 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) −2.00000 −0.119098
\(283\) −5.00000 −0.297219 −0.148610 − 0.988896i \(-0.547480\pi\)
−0.148610 + 0.988896i \(0.547480\pi\)
\(284\) 7.00000 0.415374
\(285\) −12.0000 −0.710819
\(286\) −5.00000 −0.295656
\(287\) 0 0
\(288\) 2.00000 0.117851
\(289\) 1.00000 0.0588235
\(290\) 12.0000 0.704664
\(291\) 12.0000 0.703452
\(292\) −2.00000 −0.117041
\(293\) −3.00000 −0.175262 −0.0876309 − 0.996153i \(-0.527930\pi\)
−0.0876309 + 0.996153i \(0.527930\pi\)
\(294\) 0 0
\(295\) 24.0000 1.39733
\(296\) −8.00000 −0.464991
\(297\) 5.00000 0.290129
\(298\) 17.0000 0.984784
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 22.0000 1.26596
\(303\) 2.00000 0.114897
\(304\) −6.00000 −0.344124
\(305\) 24.0000 1.37424
\(306\) 2.00000 0.114332
\(307\) 2.00000 0.114146 0.0570730 − 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 10.0000 0.568880
\(310\) 8.00000 0.454369
\(311\) −11.0000 −0.623753 −0.311876 − 0.950123i \(-0.600957\pi\)
−0.311876 + 0.950123i \(0.600957\pi\)
\(312\) 5.00000 0.283069
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −5.00000 −0.282166
\(315\) 0 0
\(316\) 3.00000 0.168763
\(317\) −4.00000 −0.224662 −0.112331 − 0.993671i \(-0.535832\pi\)
−0.112331 + 0.993671i \(0.535832\pi\)
\(318\) 7.00000 0.392541
\(319\) 6.00000 0.335936
\(320\) 2.00000 0.111803
\(321\) 3.00000 0.167444
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 1.00000 0.0555556
\(325\) 5.00000 0.277350
\(326\) −4.00000 −0.221540
\(327\) 16.0000 0.884802
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 2.00000 0.110096
\(331\) −24.0000 −1.31916 −0.659580 − 0.751635i \(-0.729266\pi\)
−0.659580 + 0.751635i \(0.729266\pi\)
\(332\) −4.00000 −0.219529
\(333\) −16.0000 −0.876795
\(334\) 1.00000 0.0547176
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −8.00000 −0.435788 −0.217894 − 0.975972i \(-0.569919\pi\)
−0.217894 + 0.975972i \(0.569919\pi\)
\(338\) −12.0000 −0.652714
\(339\) −16.0000 −0.869001
\(340\) 2.00000 0.108465
\(341\) 4.00000 0.216612
\(342\) −12.0000 −0.648886
\(343\) 0 0
\(344\) 12.0000 0.646997
\(345\) 0 0
\(346\) 16.0000 0.860165
\(347\) 12.0000 0.644194 0.322097 − 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) −6.00000 −0.321634
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 25.0000 1.33440
\(352\) 1.00000 0.0533002
\(353\) 1.00000 0.0532246 0.0266123 − 0.999646i \(-0.491528\pi\)
0.0266123 + 0.999646i \(0.491528\pi\)
\(354\) −12.0000 −0.637793
\(355\) 14.0000 0.743043
\(356\) −1.00000 −0.0529999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −12.0000 −0.633336 −0.316668 − 0.948536i \(-0.602564\pi\)
−0.316668 + 0.948536i \(0.602564\pi\)
\(360\) 4.00000 0.210819
\(361\) 17.0000 0.894737
\(362\) −12.0000 −0.630706
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) −12.0000 −0.627250
\(367\) −3.00000 −0.156599 −0.0782994 − 0.996930i \(-0.524949\pi\)
−0.0782994 + 0.996930i \(0.524949\pi\)
\(368\) 0 0
\(369\) 12.0000 0.624695
\(370\) −16.0000 −0.831800
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) 29.0000 1.50156 0.750782 − 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 1.00000 0.0517088
\(375\) −12.0000 −0.619677
\(376\) −2.00000 −0.103142
\(377\) 30.0000 1.54508
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 − 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) −12.0000 −0.615587
\(381\) −14.0000 −0.717242
\(382\) 24.0000 1.22795
\(383\) 20.0000 1.02195 0.510976 − 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −16.0000 −0.814379
\(387\) 24.0000 1.21999
\(388\) 12.0000 0.609208
\(389\) 39.0000 1.97738 0.988689 − 0.149979i \(-0.0479205\pi\)
0.988689 + 0.149979i \(0.0479205\pi\)
\(390\) 10.0000 0.506370
\(391\) 0 0
\(392\) 0 0
\(393\) 12.0000 0.605320
\(394\) −14.0000 −0.705310
\(395\) 6.00000 0.301893
\(396\) 2.00000 0.100504
\(397\) −32.0000 −1.60603 −0.803017 − 0.595956i \(-0.796773\pi\)
−0.803017 + 0.595956i \(0.796773\pi\)
\(398\) 13.0000 0.651631
\(399\) 0 0
\(400\) −1.00000 −0.0500000
\(401\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 2.00000 0.0997509
\(403\) 20.0000 0.996271
\(404\) 2.00000 0.0995037
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −8.00000 −0.396545
\(408\) −1.00000 −0.0495074
\(409\) −7.00000 −0.346128 −0.173064 − 0.984911i \(-0.555367\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 12.0000 0.592638
\(411\) 5.00000 0.246632
\(412\) 10.0000 0.492665
\(413\) 0 0
\(414\) 0 0
\(415\) −8.00000 −0.392705
\(416\) 5.00000 0.245145
\(417\) 11.0000 0.538672
\(418\) −6.00000 −0.293470
\(419\) 21.0000 1.02592 0.512959 − 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 0 0
\(421\) 30.0000 1.46211 0.731055 − 0.682318i \(-0.239028\pi\)
0.731055 + 0.682318i \(0.239028\pi\)
\(422\) 20.0000 0.973585
\(423\) −4.00000 −0.194487
\(424\) 7.00000 0.339950
\(425\) −1.00000 −0.0485071
\(426\) −7.00000 −0.339151
\(427\) 0 0
\(428\) 3.00000 0.145010
\(429\) 5.00000 0.241402
\(430\) 24.0000 1.15738
\(431\) −23.0000 −1.10787 −0.553936 − 0.832560i \(-0.686875\pi\)
−0.553936 + 0.832560i \(0.686875\pi\)
\(432\) −5.00000 −0.240563
\(433\) 34.0000 1.63394 0.816968 − 0.576683i \(-0.195653\pi\)
0.816968 + 0.576683i \(0.195653\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) 16.0000 0.766261
\(437\) 0 0
\(438\) 2.00000 0.0955637
\(439\) 29.0000 1.38409 0.692047 − 0.721852i \(-0.256709\pi\)
0.692047 + 0.721852i \(0.256709\pi\)
\(440\) 2.00000 0.0953463
\(441\) 0 0
\(442\) 5.00000 0.237826
\(443\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(444\) 8.00000 0.379663
\(445\) −2.00000 −0.0948091
\(446\) −12.0000 −0.568216
\(447\) −17.0000 −0.804072
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 − 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) −2.00000 −0.0942809
\(451\) 6.00000 0.282529
\(452\) −16.0000 −0.752577
\(453\) −22.0000 −1.03365
\(454\) 7.00000 0.328526
\(455\) 0 0
\(456\) 6.00000 0.280976
\(457\) 22.0000 1.02912 0.514558 − 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) 2.00000 0.0934539
\(459\) −5.00000 −0.233380
\(460\) 0 0
\(461\) −37.0000 −1.72326 −0.861631 − 0.507535i \(-0.830557\pi\)
−0.861631 + 0.507535i \(0.830557\pi\)
\(462\) 0 0
\(463\) −10.0000 −0.464739 −0.232370 − 0.972628i \(-0.574648\pi\)
−0.232370 + 0.972628i \(0.574648\pi\)
\(464\) −6.00000 −0.278543
\(465\) −8.00000 −0.370991
\(466\) −8.00000 −0.370593
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 10.0000 0.462250
\(469\) 0 0
\(470\) −4.00000 −0.184506
\(471\) 5.00000 0.230388
\(472\) −12.0000 −0.552345
\(473\) 12.0000 0.551761
\(474\) −3.00000 −0.137795
\(475\) 6.00000 0.275299
\(476\) 0 0
\(477\) 14.0000 0.641016
\(478\) 20.0000 0.914779
\(479\) 8.00000 0.365529 0.182765 − 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) −2.00000 −0.0912871
\(481\) −40.0000 −1.82384
\(482\) −14.0000 −0.637683
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 24.0000 1.08978
\(486\) −16.0000 −0.725775
\(487\) −17.0000 −0.770344 −0.385172 − 0.922845i \(-0.625858\pi\)
−0.385172 + 0.922845i \(0.625858\pi\)
\(488\) −12.0000 −0.543214
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 − 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −6.00000 −0.270501
\(493\) −6.00000 −0.270226
\(494\) −30.0000 −1.34976
\(495\) 4.00000 0.179787
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) −39.0000 −1.74588 −0.872940 − 0.487828i \(-0.837789\pi\)
−0.872940 + 0.487828i \(0.837789\pi\)
\(500\) −12.0000 −0.536656
\(501\) −1.00000 −0.0446767
\(502\) 26.0000 1.16044
\(503\) 19.0000 0.847168 0.423584 − 0.905857i \(-0.360772\pi\)
0.423584 + 0.905857i \(0.360772\pi\)
\(504\) 0 0
\(505\) 4.00000 0.177998
\(506\) 0 0
\(507\) 12.0000 0.532939
\(508\) −14.0000 −0.621150
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) −2.00000 −0.0885615
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 30.0000 1.32453
\(514\) 15.0000 0.661622
\(515\) 20.0000 0.881305
\(516\) −12.0000 −0.528271
\(517\) −2.00000 −0.0879599
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 10.0000 0.438529
\(521\) −2.00000 −0.0876216 −0.0438108 − 0.999040i \(-0.513950\pi\)
−0.0438108 + 0.999040i \(0.513950\pi\)
\(522\) −12.0000 −0.525226
\(523\) −16.0000 −0.699631 −0.349816 − 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) −6.00000 −0.261612
\(527\) −4.00000 −0.174243
\(528\) −1.00000 −0.0435194
\(529\) −23.0000 −1.00000
\(530\) 14.0000 0.608121
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 30.0000 1.29944
\(534\) 1.00000 0.0432742
\(535\) 6.00000 0.259403
\(536\) 2.00000 0.0863868
\(537\) −12.0000 −0.517838
\(538\) −30.0000 −1.29339
\(539\) 0 0
\(540\) −10.0000 −0.430331
\(541\) 8.00000 0.343947 0.171973 − 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) 12.0000 0.515444
\(543\) 12.0000 0.514969
\(544\) −1.00000 −0.0428746
\(545\) 32.0000 1.37073
\(546\) 0 0
\(547\) 17.0000 0.726868 0.363434 − 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 5.00000 0.213589
\(549\) −24.0000 −1.02430
\(550\) −1.00000 −0.0426401
\(551\) 36.0000 1.53365
\(552\) 0 0
\(553\) 0 0
\(554\) −12.0000 −0.509831
\(555\) 16.0000 0.679162
\(556\) 11.0000 0.466504
\(557\) −3.00000 −0.127114 −0.0635570 − 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) −8.00000 −0.338667
\(559\) 60.0000 2.53773
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) 27.0000 1.13893
\(563\) −32.0000 −1.34864 −0.674320 − 0.738440i \(-0.735563\pi\)
−0.674320 + 0.738440i \(0.735563\pi\)
\(564\) 2.00000 0.0842152
\(565\) −32.0000 −1.34625
\(566\) 5.00000 0.210166
\(567\) 0 0
\(568\) −7.00000 −0.293713
\(569\) 13.0000 0.544988 0.272494 − 0.962157i \(-0.412151\pi\)
0.272494 + 0.962157i \(0.412151\pi\)
\(570\) 12.0000 0.502625
\(571\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 5.00000 0.209061
\(573\) −24.0000 −1.00261
\(574\) 0 0
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) 19.0000 0.790980 0.395490 − 0.918470i \(-0.370575\pi\)
0.395490 + 0.918470i \(0.370575\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 16.0000 0.664937
\(580\) −12.0000 −0.498273
\(581\) 0 0
\(582\) −12.0000 −0.497416
\(583\) 7.00000 0.289910
\(584\) 2.00000 0.0827606
\(585\) 20.0000 0.826898
\(586\) 3.00000 0.123929
\(587\) −42.0000 −1.73353 −0.866763 − 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 24.0000 0.988903
\(590\) −24.0000 −0.988064
\(591\) 14.0000 0.575883
\(592\) 8.00000 0.328798
\(593\) 39.0000 1.60154 0.800769 − 0.598973i \(-0.204424\pi\)
0.800769 + 0.598973i \(0.204424\pi\)
\(594\) −5.00000 −0.205152
\(595\) 0 0
\(596\) −17.0000 −0.696347
\(597\) −13.0000 −0.532055
\(598\) 0 0
\(599\) −4.00000 −0.163436 −0.0817178 − 0.996656i \(-0.526041\pi\)
−0.0817178 + 0.996656i \(0.526041\pi\)
\(600\) 1.00000 0.0408248
\(601\) −2.00000 −0.0815817 −0.0407909 − 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) −22.0000 −0.895167
\(605\) −20.0000 −0.813116
\(606\) −2.00000 −0.0812444
\(607\) −1.00000 −0.0405887 −0.0202944 − 0.999794i \(-0.506460\pi\)
−0.0202944 + 0.999794i \(0.506460\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) −24.0000 −0.971732
\(611\) −10.0000 −0.404557
\(612\) −2.00000 −0.0808452
\(613\) −29.0000 −1.17130 −0.585649 − 0.810564i \(-0.699160\pi\)
−0.585649 + 0.810564i \(0.699160\pi\)
\(614\) −2.00000 −0.0807134
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 − 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) −10.0000 −0.402259
\(619\) 35.0000 1.40677 0.703384 − 0.710810i \(-0.251671\pi\)
0.703384 + 0.710810i \(0.251671\pi\)
\(620\) −8.00000 −0.321288
\(621\) 0 0
\(622\) 11.0000 0.441060
\(623\) 0 0
\(624\) −5.00000 −0.200160
\(625\) −19.0000 −0.760000
\(626\) 6.00000 0.239808
\(627\) 6.00000 0.239617
\(628\) 5.00000 0.199522
\(629\) 8.00000 0.318981
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 − 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) −3.00000 −0.119334
\(633\) −20.0000 −0.794929
\(634\) 4.00000 0.158860
\(635\) −28.0000 −1.11115
\(636\) −7.00000 −0.277568
\(637\) 0 0
\(638\) −6.00000 −0.237542
\(639\) −14.0000 −0.553831
\(640\) −2.00000 −0.0790569
\(641\) −30.0000 −1.18493 −0.592464 − 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) −3.00000 −0.118401
\(643\) −1.00000 −0.0394362 −0.0197181 − 0.999806i \(-0.506277\pi\)
−0.0197181 + 0.999806i \(0.506277\pi\)
\(644\) 0 0
\(645\) −24.0000 −0.944999
\(646\) 6.00000 0.236067
\(647\) 12.0000 0.471769 0.235884 − 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) −1.00000 −0.0392837
\(649\) −12.0000 −0.471041
\(650\) −5.00000 −0.196116
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) −40.0000 −1.56532 −0.782660 − 0.622449i \(-0.786138\pi\)
−0.782660 + 0.622449i \(0.786138\pi\)
\(654\) −16.0000 −0.625650
\(655\) 24.0000 0.937758
\(656\) −6.00000 −0.234261
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −48.0000 −1.86981 −0.934907 − 0.354892i \(-0.884518\pi\)
−0.934907 + 0.354892i \(0.884518\pi\)
\(660\) −2.00000 −0.0778499
\(661\) 18.0000 0.700119 0.350059 − 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) 24.0000 0.932786
\(663\) −5.00000 −0.194184
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) 16.0000 0.619987
\(667\) 0 0
\(668\) −1.00000 −0.0386912
\(669\) 12.0000 0.463947
\(670\) 4.00000 0.154533
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 42.0000 1.61898 0.809491 − 0.587133i \(-0.199743\pi\)
0.809491 + 0.587133i \(0.199743\pi\)
\(674\) 8.00000 0.308148
\(675\) 5.00000 0.192450
\(676\) 12.0000 0.461538
\(677\) 26.0000 0.999261 0.499631 − 0.866239i \(-0.333469\pi\)
0.499631 + 0.866239i \(0.333469\pi\)
\(678\) 16.0000 0.614476
\(679\) 0 0
\(680\) −2.00000 −0.0766965
\(681\) −7.00000 −0.268241
\(682\) −4.00000 −0.153168
\(683\) −31.0000 −1.18618 −0.593091 − 0.805135i \(-0.702093\pi\)
−0.593091 + 0.805135i \(0.702093\pi\)
\(684\) 12.0000 0.458831
\(685\) 10.0000 0.382080
\(686\) 0 0
\(687\) −2.00000 −0.0763048
\(688\) −12.0000 −0.457496
\(689\) 35.0000 1.33339
\(690\) 0 0
\(691\) 36.0000 1.36950 0.684752 − 0.728776i \(-0.259910\pi\)
0.684752 + 0.728776i \(0.259910\pi\)
\(692\) −16.0000 −0.608229
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 22.0000 0.834508
\(696\) 6.00000 0.227429
\(697\) −6.00000 −0.227266
\(698\) 14.0000 0.529908
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) −39.0000 −1.47301 −0.736505 − 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) −25.0000 −0.943564
\(703\) −48.0000 −1.81035
\(704\) −1.00000 −0.0376889
\(705\) 4.00000 0.150649
\(706\) −1.00000 −0.0376355
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) −14.0000 −0.525411
\(711\) −6.00000 −0.225018
\(712\) 1.00000 0.0374766
\(713\) 0 0
\(714\) 0 0
\(715\) 10.0000 0.373979
\(716\) −12.0000 −0.448461
\(717\) −20.0000 −0.746914
\(718\) 12.0000 0.447836
\(719\) 27.0000 1.00693 0.503465 − 0.864016i \(-0.332058\pi\)
0.503465 + 0.864016i \(0.332058\pi\)
\(720\) −4.00000 −0.149071
\(721\) 0 0
\(722\) −17.0000 −0.632674
\(723\) 14.0000 0.520666
\(724\) 12.0000 0.445976
\(725\) 6.00000 0.222834
\(726\) 10.0000 0.371135
\(727\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 4.00000 0.148047
\(731\) −12.0000 −0.443836
\(732\) 12.0000 0.443533
\(733\) 15.0000 0.554038 0.277019 − 0.960864i \(-0.410654\pi\)
0.277019 + 0.960864i \(0.410654\pi\)
\(734\) 3.00000 0.110732
\(735\) 0 0
\(736\) 0 0
\(737\) 2.00000 0.0736709
\(738\) −12.0000 −0.441726
\(739\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(740\) 16.0000 0.588172
\(741\) 30.0000 1.10208
\(742\) 0 0
\(743\) −51.0000 −1.87101 −0.935504 − 0.353315i \(-0.885054\pi\)
−0.935504 + 0.353315i \(0.885054\pi\)
\(744\) 4.00000 0.146647
\(745\) −34.0000 −1.24566
\(746\) −29.0000 −1.06177
\(747\) 8.00000 0.292705
\(748\) −1.00000 −0.0365636
\(749\) 0 0
\(750\) 12.0000 0.438178
\(751\) −13.0000 −0.474377 −0.237188 − 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 2.00000 0.0729325
\(753\) −26.0000 −0.947493
\(754\) −30.0000 −1.09254
\(755\) −44.0000 −1.60132
\(756\) 0 0
\(757\) 15.0000 0.545184 0.272592 − 0.962130i \(-0.412119\pi\)
0.272592 + 0.962130i \(0.412119\pi\)
\(758\) −23.0000 −0.835398
\(759\) 0 0
\(760\) 12.0000 0.435286
\(761\) −53.0000 −1.92125 −0.960624 − 0.277851i \(-0.910378\pi\)
−0.960624 + 0.277851i \(0.910378\pi\)
\(762\) 14.0000 0.507166
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) −4.00000 −0.144620
\(766\) −20.0000 −0.722629
\(767\) −60.0000 −2.16647
\(768\) 1.00000 0.0360844
\(769\) −1.00000 −0.0360609 −0.0180305 − 0.999837i \(-0.505740\pi\)
−0.0180305 + 0.999837i \(0.505740\pi\)
\(770\) 0 0
\(771\) −15.0000 −0.540212
\(772\) 16.0000 0.575853
\(773\) −11.0000 −0.395643 −0.197821 − 0.980238i \(-0.563387\pi\)
−0.197821 + 0.980238i \(0.563387\pi\)
\(774\) −24.0000 −0.862662
\(775\) 4.00000 0.143684
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) −39.0000 −1.39822
\(779\) 36.0000 1.28983
\(780\) −10.0000 −0.358057
\(781\) −7.00000 −0.250480
\(782\) 0 0
\(783\) 30.0000 1.07211
\(784\) 0 0
\(785\) 10.0000 0.356915
\(786\) −12.0000 −0.428026
\(787\) −20.0000 −0.712923 −0.356462 − 0.934310i \(-0.616017\pi\)
−0.356462 + 0.934310i \(0.616017\pi\)
\(788\) 14.0000 0.498729
\(789\) 6.00000 0.213606
\(790\) −6.00000 −0.213470
\(791\) 0 0
\(792\) −2.00000 −0.0710669
\(793\) −60.0000 −2.13066
\(794\) 32.0000 1.13564
\(795\) −14.0000 −0.496529
\(796\) −13.0000 −0.460773
\(797\) −17.0000 −0.602171 −0.301085 − 0.953597i \(-0.597349\pi\)
−0.301085 + 0.953597i \(0.597349\pi\)
\(798\) 0 0
\(799\) 2.00000 0.0707549
\(800\) 1.00000 0.0353553
\(801\) 2.00000 0.0706665
\(802\) 0 0
\(803\) 2.00000 0.0705785
\(804\) −2.00000 −0.0705346
\(805\) 0 0
\(806\) −20.0000 −0.704470
\(807\) 30.0000 1.05605
\(808\) −2.00000 −0.0703598
\(809\) 34.0000 1.19538 0.597688 − 0.801729i \(-0.296086\pi\)
0.597688 + 0.801729i \(0.296086\pi\)
\(810\) −2.00000 −0.0702728
\(811\) −7.00000 −0.245803 −0.122902 − 0.992419i \(-0.539220\pi\)
−0.122902 + 0.992419i \(0.539220\pi\)
\(812\) 0 0
\(813\) −12.0000 −0.420858
\(814\) 8.00000 0.280400
\(815\) 8.00000 0.280228
\(816\) 1.00000 0.0350070
\(817\) 72.0000 2.51896
\(818\) 7.00000 0.244749
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) −5.00000 −0.174395
\(823\) −31.0000 −1.08059 −0.540296 − 0.841475i \(-0.681688\pi\)
−0.540296 + 0.841475i \(0.681688\pi\)
\(824\) −10.0000 −0.348367
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) 55.0000 1.91254 0.956269 − 0.292490i \(-0.0944837\pi\)
0.956269 + 0.292490i \(0.0944837\pi\)
\(828\) 0 0
\(829\) −43.0000 −1.49345 −0.746726 − 0.665132i \(-0.768375\pi\)
−0.746726 + 0.665132i \(0.768375\pi\)
\(830\) 8.00000 0.277684
\(831\) 12.0000 0.416275
\(832\) −5.00000 −0.173344
\(833\) 0 0
\(834\) −11.0000 −0.380899
\(835\) −2.00000 −0.0692129
\(836\) 6.00000 0.207514
\(837\) 20.0000 0.691301
\(838\) −21.0000 −0.725433
\(839\) −28.0000 −0.966667 −0.483334 − 0.875436i \(-0.660574\pi\)
−0.483334 + 0.875436i \(0.660574\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −30.0000 −1.03387
\(843\) −27.0000 −0.929929
\(844\) −20.0000 −0.688428
\(845\) 24.0000 0.825625
\(846\) 4.00000 0.137523
\(847\) 0 0
\(848\) −7.00000 −0.240381
\(849\) −5.00000 −0.171600
\(850\) 1.00000 0.0342997
\(851\) 0 0
\(852\) 7.00000 0.239816
\(853\) 26.0000 0.890223 0.445112 − 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) 0 0
\(855\) 24.0000 0.820783
\(856\) −3.00000 −0.102538
\(857\) 36.0000 1.22974 0.614868 − 0.788630i \(-0.289209\pi\)
0.614868 + 0.788630i \(0.289209\pi\)
\(858\) −5.00000 −0.170697
\(859\) 54.0000 1.84246 0.921228 − 0.389023i \(-0.127187\pi\)
0.921228 + 0.389023i \(0.127187\pi\)
\(860\) −24.0000 −0.818393
\(861\) 0 0
\(862\) 23.0000 0.783383
\(863\) −32.0000 −1.08929 −0.544646 − 0.838666i \(-0.683336\pi\)
−0.544646 + 0.838666i \(0.683336\pi\)
\(864\) 5.00000 0.170103
\(865\) −32.0000 −1.08803
\(866\) −34.0000 −1.15537
\(867\) 1.00000 0.0339618
\(868\) 0 0
\(869\) −3.00000 −0.101768
\(870\) 12.0000 0.406838
\(871\) 10.0000 0.338837
\(872\) −16.0000 −0.541828
\(873\) −24.0000 −0.812277
\(874\) 0 0
\(875\) 0 0
\(876\) −2.00000 −0.0675737
\(877\) 58.0000 1.95852 0.979260 − 0.202606i \(-0.0649409\pi\)
0.979260 + 0.202606i \(0.0649409\pi\)
\(878\) −29.0000 −0.978703
\(879\) −3.00000 −0.101187
\(880\) −2.00000 −0.0674200
\(881\) 52.0000 1.75192 0.875962 − 0.482380i \(-0.160227\pi\)
0.875962 + 0.482380i \(0.160227\pi\)
\(882\) 0 0
\(883\) −4.00000 −0.134611 −0.0673054 − 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) −5.00000 −0.168168
\(885\) 24.0000 0.806751
\(886\) 0 0
\(887\) −9.00000 −0.302190 −0.151095 − 0.988519i \(-0.548280\pi\)
−0.151095 + 0.988519i \(0.548280\pi\)
\(888\) −8.00000 −0.268462
\(889\) 0 0
\(890\) 2.00000 0.0670402
\(891\) −1.00000 −0.0335013
\(892\) 12.0000 0.401790
\(893\) −12.0000 −0.401565
\(894\) 17.0000 0.568565
\(895\) −24.0000 −0.802232
\(896\) 0 0
\(897\) 0 0
\(898\) −10.0000 −0.333704
\(899\) 24.0000 0.800445
\(900\) 2.00000 0.0666667
\(901\) −7.00000 −0.233204
\(902\) −6.00000 −0.199778
\(903\) 0 0
\(904\) 16.0000 0.532152
\(905\) 24.0000 0.797787
\(906\) 22.0000 0.730901
\(907\) −8.00000 −0.265636 −0.132818 − 0.991140i \(-0.542403\pi\)
−0.132818 + 0.991140i \(0.542403\pi\)
\(908\) −7.00000 −0.232303
\(909\) −4.00000 −0.132672
\(910\) 0 0
\(911\) −60.0000 −1.98789 −0.993944 − 0.109885i \(-0.964952\pi\)
−0.993944 + 0.109885i \(0.964952\pi\)
\(912\) −6.00000 −0.198680
\(913\) 4.00000 0.132381
\(914\) −22.0000 −0.727695
\(915\) 24.0000 0.793416
\(916\) −2.00000 −0.0660819
\(917\) 0 0
\(918\) 5.00000 0.165025
\(919\) −26.0000 −0.857661 −0.428830 − 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) 0 0
\(921\) 2.00000 0.0659022
\(922\) 37.0000 1.21853
\(923\) −35.0000 −1.15204
\(924\) 0 0
\(925\) −8.00000 −0.263038
\(926\) 10.0000 0.328620
\(927\) −20.0000 −0.656886
\(928\) 6.00000 0.196960
\(929\) −46.0000 −1.50921 −0.754606 − 0.656179i \(-0.772172\pi\)
−0.754606 + 0.656179i \(0.772172\pi\)
\(930\) 8.00000 0.262330
\(931\) 0 0
\(932\) 8.00000 0.262049
\(933\) −11.0000 −0.360124
\(934\) 18.0000 0.588978
\(935\) −2.00000 −0.0654070
\(936\) −10.0000 −0.326860
\(937\) −34.0000 −1.11073 −0.555366 − 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 0 0
\(939\) −6.00000 −0.195803
\(940\) 4.00000 0.130466
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −5.00000 −0.162909
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) −12.0000 −0.390154
\(947\) 47.0000 1.52729 0.763647 − 0.645634i \(-0.223407\pi\)
0.763647 + 0.645634i \(0.223407\pi\)
\(948\) 3.00000 0.0974355
\(949\) 10.0000 0.324614
\(950\) −6.00000 −0.194666
\(951\) −4.00000 −0.129709
\(952\) 0 0
\(953\) 41.0000 1.32812 0.664060 − 0.747679i \(-0.268832\pi\)
0.664060 + 0.747679i \(0.268832\pi\)
\(954\) −14.0000 −0.453267
\(955\) −48.0000 −1.55324
\(956\) −20.0000 −0.646846
\(957\) 6.00000 0.193952
\(958\) −8.00000 −0.258468
\(959\) 0 0
\(960\) 2.00000 0.0645497
\(961\) −15.0000 −0.483871
\(962\) 40.0000 1.28965
\(963\) −6.00000 −0.193347
\(964\) 14.0000 0.450910
\(965\) 32.0000 1.03012
\(966\) 0 0
\(967\) −58.0000 −1.86515 −0.932577 − 0.360971i \(-0.882445\pi\)
−0.932577 + 0.360971i \(0.882445\pi\)
\(968\) 10.0000 0.321412
\(969\) −6.00000 −0.192748
\(970\) −24.0000 −0.770594
\(971\) −58.0000 −1.86131 −0.930654 − 0.365900i \(-0.880761\pi\)
−0.930654 + 0.365900i \(0.880761\pi\)
\(972\) 16.0000 0.513200
\(973\) 0 0
\(974\) 17.0000 0.544715
\(975\) 5.00000 0.160128
\(976\) 12.0000 0.384111
\(977\) 42.0000 1.34370 0.671850 − 0.740688i \(-0.265500\pi\)
0.671850 + 0.740688i \(0.265500\pi\)
\(978\) −4.00000 −0.127906
\(979\) 1.00000 0.0319601
\(980\) 0 0
\(981\) −32.0000 −1.02168
\(982\) −2.00000 −0.0638226
\(983\) 25.0000 0.797376 0.398688 − 0.917087i \(-0.369466\pi\)
0.398688 + 0.917087i \(0.369466\pi\)
\(984\) 6.00000 0.191273
\(985\) 28.0000 0.892154
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) 30.0000 0.954427
\(989\) 0 0
\(990\) −4.00000 −0.127128
\(991\) −3.00000 −0.0952981 −0.0476491 − 0.998864i \(-0.515173\pi\)
−0.0476491 + 0.998864i \(0.515173\pi\)
\(992\) 4.00000 0.127000
\(993\) −24.0000 −0.761617
\(994\) 0 0
\(995\) −26.0000 −0.824255
\(996\) −4.00000 −0.126745
\(997\) −2.00000 −0.0633406 −0.0316703 − 0.999498i \(-0.510083\pi\)
−0.0316703 + 0.999498i \(0.510083\pi\)
\(998\) 39.0000 1.23452
\(999\) −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 1666.2.a.f.1.1 1
7.3 odd 6 238.2.e.c.205.1 yes 2
7.5 odd 6 238.2.e.c.137.1 ✓ 2
7.6 odd 2 1666.2.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
238.2.e.c.137.1 ✓ 2 7.5 odd 6
238.2.e.c.205.1 yes 2 7.3 odd 6
1666.2.a.d.1.1 1 7.6 odd 2
1666.2.a.f.1.1 1 1.1 even 1 trivial