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Properties

Label 5610.2.a.g.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $0$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +1.00000 q^{22} +8.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} -2.00000 q^{39} -1.00000 q^{40} +2.00000 q^{41} -8.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -8.00000 q^{46} -1.00000 q^{48} -7.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +2.00000 q^{52} +2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{57} -6.00000 q^{58} -1.00000 q^{60} +2.00000 q^{61} -4.00000 q^{62} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -8.00000 q^{69} +8.00000 q^{71} -1.00000 q^{72} +6.00000 q^{73} +6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +4.00000 q^{83} -1.00000 q^{85} +8.00000 q^{86} -6.00000 q^{87} +1.00000 q^{88} +2.00000 q^{89} -1.00000 q^{90} +8.00000 q^{92} -4.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} +7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) 1.00000 0.408248
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) −1.00000 −0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) −1.00000 −0.235702
\(19\) 4.00000 0.917663 0.458831 − 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 8.00000 1.66812 0.834058 − 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 − 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 1.00000 0.182574
\(31\) 4.00000 0.718421 0.359211 − 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −4.00000 −0.648886
\(39\) −2.00000 −0.320256
\(40\) −1.00000 −0.158114
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 − 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) −8.00000 −1.17954
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) 2.00000 0.277350
\(53\) 2.00000 0.274721 0.137361 − 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −6.00000 −0.787839
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 − 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) −1.00000 −0.123091
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 −0.121268
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 − 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.00000 −0.117851
\(73\) 6.00000 0.702247 0.351123 − 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 6.00000 0.697486
\(75\) −1.00000 −0.115470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) −8.00000 −0.900070 −0.450035 − 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −2.00000 −0.220863
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 8.00000 0.862662
\(87\) −6.00000 −0.643268
\(88\) 1.00000 0.106600
\(89\) 2.00000 0.212000 0.106000 − 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) 8.00000 0.834058
\(93\) −4.00000 −0.414781
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) 1.00000 0.102062
\(97\) −10.0000 −1.01535 −0.507673 − 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 7.00000 0.707107
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 16.0000 1.57653 0.788263 − 0.615338i \(-0.210980\pi\)
0.788263 + 0.615338i \(0.210980\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) 8.00000 0.773389 0.386695 − 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 2.00000 0.191565 0.0957826 − 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 1.00000 0.0953463
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 − 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 4.00000 0.374634
\(115\) 8.00000 0.746004
\(116\) 6.00000 0.557086
\(117\) 2.00000 0.184900
\(118\) 0 0
\(119\) 0 0
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) −2.00000 −0.181071
\(123\) −2.00000 −0.180334
\(124\) 4.00000 0.359211
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 − 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 8.00000 0.704361
\(130\) −2.00000 −0.175412
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) −10.0000 −0.854358 −0.427179 − 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 8.00000 0.681005
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) −2.00000 −0.167248
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −6.00000 −0.496564
\(147\) 7.00000 0.577350
\(148\) −6.00000 −0.493197
\(149\) 10.0000 0.819232 0.409616 − 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 1.00000 0.0816497
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −4.00000 −0.324443
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) −2.00000 −0.160128
\(157\) 6.00000 0.478852 0.239426 − 0.970915i \(-0.423041\pi\)
0.239426 + 0.970915i \(0.423041\pi\)
\(158\) 8.00000 0.636446
\(159\) −2.00000 −0.158610
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −1.00000 −0.0785674
\(163\) −12.0000 −0.939913 −0.469956 − 0.882690i \(-0.655730\pi\)
−0.469956 + 0.882690i \(0.655730\pi\)
\(164\) 2.00000 0.156174
\(165\) 1.00000 0.0778499
\(166\) −4.00000 −0.310460
\(167\) −12.0000 −0.928588 −0.464294 − 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 1.00000 0.0766965
\(171\) 4.00000 0.305888
\(172\) −8.00000 −0.609994
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 6.00000 0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −2.00000 −0.149906
\(179\) 24.0000 1.79384 0.896922 − 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 1.00000 0.0745356
\(181\) −2.00000 −0.148659 −0.0743294 − 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −2.00000 −0.147844
\(184\) −8.00000 −0.589768
\(185\) −6.00000 −0.441129
\(186\) 4.00000 0.293294
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) −12.0000 −0.868290 −0.434145 − 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −18.0000 −1.29567 −0.647834 − 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) 10.0000 0.717958
\(195\) −2.00000 −0.143223
\(196\) −7.00000 −0.500000
\(197\) 18.0000 1.28245 0.641223 − 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 1.00000 0.0710669
\(199\) −4.00000 −0.283552 −0.141776 − 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 4.00000 0.282138
\(202\) −10.0000 −0.703598
\(203\) 0 0
\(204\) 1.00000 0.0700140
\(205\) 2.00000 0.139686
\(206\) −16.0000 −1.11477
\(207\) 8.00000 0.556038
\(208\) 2.00000 0.138675
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −12.0000 −0.826114 −0.413057 − 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) 2.00000 0.137361
\(213\) −8.00000 −0.548151
\(214\) −8.00000 −0.546869
\(215\) −8.00000 −0.545595
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) −6.00000 −0.405442
\(220\) −1.00000 −0.0674200
\(221\) −2.00000 −0.134535
\(222\) −6.00000 −0.402694
\(223\) 8.00000 0.535720 0.267860 − 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 14.0000 0.931266
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −4.00000 −0.264906
\(229\) 6.00000 0.396491 0.198246 − 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 14.0000 0.917170 0.458585 − 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 6.00000 0.386494 0.193247 − 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) 2.00000 0.128037
\(245\) −7.00000 −0.447214
\(246\) 2.00000 0.127515
\(247\) 8.00000 0.509028
\(248\) −4.00000 −0.254000
\(249\) −4.00000 −0.253490
\(250\) −1.00000 −0.0632456
\(251\) 24.0000 1.51487 0.757433 − 0.652913i \(-0.226453\pi\)
0.757433 + 0.652913i \(0.226453\pi\)
\(252\) 0 0
\(253\) −8.00000 −0.502956
\(254\) −12.0000 −0.752947
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −26.0000 −1.62184 −0.810918 − 0.585160i \(-0.801032\pi\)
−0.810918 + 0.585160i \(0.801032\pi\)
\(258\) −8.00000 −0.498058
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 12.0000 0.741362
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 2.00000 0.122859
\(266\) 0 0
\(267\) −2.00000 −0.122398
\(268\) −4.00000 −0.244339
\(269\) 14.0000 0.853595 0.426798 − 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 1.00000 0.0608581
\(271\) 8.00000 0.485965 0.242983 − 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) −1.00000 −0.0606339
\(273\) 0 0
\(274\) 10.0000 0.604122
\(275\) −1.00000 −0.0603023
\(276\) −8.00000 −0.481543
\(277\) 10.0000 0.600842 0.300421 − 0.953807i \(-0.402873\pi\)
0.300421 + 0.953807i \(0.402873\pi\)
\(278\) −4.00000 −0.239904
\(279\) 4.00000 0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 − 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) 4.00000 0.237775 0.118888 − 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 8.00000 0.474713
\(285\) −4.00000 −0.236940
\(286\) 2.00000 0.118262
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −6.00000 −0.352332
\(291\) 10.0000 0.586210
\(292\) 6.00000 0.351123
\(293\) −6.00000 −0.350524 −0.175262 − 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) −7.00000 −0.408248
\(295\) 0 0
\(296\) 6.00000 0.348743
\(297\) 1.00000 0.0580259
\(298\) −10.0000 −0.579284
\(299\) 16.0000 0.925304
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) 0 0
\(303\) −10.0000 −0.574485
\(304\) 4.00000 0.229416
\(305\) 2.00000 0.114520
\(306\) 1.00000 0.0571662
\(307\) 8.00000 0.456584 0.228292 − 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) −4.00000 −0.227185
\(311\) 24.0000 1.36092 0.680458 − 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 2.00000 0.113228
\(313\) 14.0000 0.791327 0.395663 − 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) −6.00000 −0.338600
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 14.0000 0.786318 0.393159 − 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(318\) 2.00000 0.112154
\(319\) −6.00000 −0.335936
\(320\) 1.00000 0.0559017
\(321\) −8.00000 −0.446516
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) 12.0000 0.664619
\(327\) −2.00000 −0.110600
\(328\) −2.00000 −0.110432
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 4.00000 0.219860 0.109930 − 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 4.00000 0.219529
\(333\) −6.00000 −0.328798
\(334\) 12.0000 0.656611
\(335\) −4.00000 −0.218543
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 9.00000 0.489535
\(339\) 14.0000 0.760376
\(340\) −1.00000 −0.0542326
\(341\) −4.00000 −0.216612
\(342\) −4.00000 −0.216295
\(343\) 0 0
\(344\) 8.00000 0.431331
\(345\) −8.00000 −0.430706
\(346\) 6.00000 0.322562
\(347\) 24.0000 1.28839 0.644194 − 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) −6.00000 −0.321634
\(349\) 14.0000 0.749403 0.374701 − 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 1.00000 0.0533002
\(353\) −2.00000 −0.106449 −0.0532246 − 0.998583i \(-0.516950\pi\)
−0.0532246 + 0.998583i \(0.516950\pi\)
\(354\) 0 0
\(355\) 8.00000 0.424596
\(356\) 2.00000 0.106000
\(357\) 0 0
\(358\) −24.0000 −1.26844
\(359\) 32.0000 1.68890 0.844448 − 0.535638i \(-0.179929\pi\)
0.844448 + 0.535638i \(0.179929\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 2.00000 0.105118
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) 6.00000 0.314054
\(366\) 2.00000 0.104542
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 8.00000 0.417029
\(369\) 2.00000 0.104116
\(370\) 6.00000 0.311925
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) −14.0000 −0.724893 −0.362446 − 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) −1.00000 −0.0517088
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 16.0000 0.821865 0.410932 − 0.911666i \(-0.365203\pi\)
0.410932 + 0.911666i \(0.365203\pi\)
\(380\) 4.00000 0.205196
\(381\) −12.0000 −0.614779
\(382\) 12.0000 0.613973
\(383\) 8.00000 0.408781 0.204390 − 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) −8.00000 −0.406663
\(388\) −10.0000 −0.507673
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 2.00000 0.101274
\(391\) −8.00000 −0.404577
\(392\) 7.00000 0.353553
\(393\) 12.0000 0.605320
\(394\) −18.0000 −0.906827
\(395\) −8.00000 −0.402524
\(396\) −1.00000 −0.0502519
\(397\) −30.0000 −1.50566 −0.752828 − 0.658217i \(-0.771311\pi\)
−0.752828 + 0.658217i \(0.771311\pi\)
\(398\) 4.00000 0.200502
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 18.0000 0.898877 0.449439 − 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −4.00000 −0.199502
\(403\) 8.00000 0.398508
\(404\) 10.0000 0.497519
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) −1.00000 −0.0495074
\(409\) 2.00000 0.0988936 0.0494468 − 0.998777i \(-0.484254\pi\)
0.0494468 + 0.998777i \(0.484254\pi\)
\(410\) −2.00000 −0.0987730
\(411\) 10.0000 0.493264
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) −8.00000 −0.393179
\(415\) 4.00000 0.196352
\(416\) −2.00000 −0.0980581
\(417\) −4.00000 −0.195881
\(418\) 4.00000 0.195646
\(419\) 4.00000 0.195413 0.0977064 − 0.995215i \(-0.468849\pi\)
0.0977064 + 0.995215i \(0.468849\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 − 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 12.0000 0.584151
\(423\) 0 0
\(424\) −2.00000 −0.0971286
\(425\) −1.00000 −0.0485071
\(426\) 8.00000 0.387601
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) 2.00000 0.0965609
\(430\) 8.00000 0.385794
\(431\) 32.0000 1.54139 0.770693 − 0.637207i \(-0.219910\pi\)
0.770693 + 0.637207i \(0.219910\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −6.00000 −0.288342 −0.144171 − 0.989553i \(-0.546051\pi\)
−0.144171 + 0.989553i \(0.546051\pi\)
\(434\) 0 0
\(435\) −6.00000 −0.287678
\(436\) 2.00000 0.0957826
\(437\) 32.0000 1.53077
\(438\) 6.00000 0.286691
\(439\) 32.0000 1.52728 0.763638 − 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 1.00000 0.0476731
\(441\) −7.00000 −0.333333
\(442\) 2.00000 0.0951303
\(443\) −20.0000 −0.950229 −0.475114 − 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 6.00000 0.284747
\(445\) 2.00000 0.0948091
\(446\) −8.00000 −0.378811
\(447\) −10.0000 −0.472984
\(448\) 0 0
\(449\) 2.00000 0.0943858 0.0471929 − 0.998886i \(-0.484972\pi\)
0.0471929 + 0.998886i \(0.484972\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −2.00000 −0.0941763
\(452\) −14.0000 −0.658505
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) −34.0000 −1.59045 −0.795226 − 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) −6.00000 −0.280362
\(459\) 1.00000 0.0466760
\(460\) 8.00000 0.373002
\(461\) 10.0000 0.465746 0.232873 − 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 6.00000 0.278543
\(465\) −4.00000 −0.185496
\(466\) −14.0000 −0.648537
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 2.00000 0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) −6.00000 −0.276465
\(472\) 0 0
\(473\) 8.00000 0.367840
\(474\) −8.00000 −0.367452
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 2.00000 0.0915737
\(478\) −24.0000 −1.09773
\(479\) 32.0000 1.46212 0.731059 − 0.682315i \(-0.239027\pi\)
0.731059 + 0.682315i \(0.239027\pi\)
\(480\) 1.00000 0.0456435
\(481\) −12.0000 −0.547153
\(482\) −6.00000 −0.273293
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −10.0000 −0.454077
\(486\) 1.00000 0.0453609
\(487\) 32.0000 1.45006 0.725029 − 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) −2.00000 −0.0905357
\(489\) 12.0000 0.542659
\(490\) 7.00000 0.316228
\(491\) −28.0000 −1.26362 −0.631811 − 0.775122i \(-0.717688\pi\)
−0.631811 + 0.775122i \(0.717688\pi\)
\(492\) −2.00000 −0.0901670
\(493\) −6.00000 −0.270226
\(494\) −8.00000 −0.359937
\(495\) −1.00000 −0.0449467
\(496\) 4.00000 0.179605
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 16.0000 0.716258 0.358129 − 0.933672i \(-0.383415\pi\)
0.358129 + 0.933672i \(0.383415\pi\)
\(500\) 1.00000 0.0447214
\(501\) 12.0000 0.536120
\(502\) −24.0000 −1.07117
\(503\) 28.0000 1.24846 0.624229 − 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 8.00000 0.355643
\(507\) 9.00000 0.399704
\(508\) 12.0000 0.532414
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) 26.0000 1.14681
\(515\) 16.0000 0.705044
\(516\) 8.00000 0.352180
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) −2.00000 −0.0877058
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) −6.00000 −0.262613
\(523\) 16.0000 0.699631 0.349816 − 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) −12.0000 −0.524222
\(525\) 0 0
\(526\) 16.0000 0.697633
\(527\) −4.00000 −0.174243
\(528\) 1.00000 0.0435194
\(529\) 41.0000 1.78261
\(530\) −2.00000 −0.0868744
\(531\) 0 0
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 2.00000 0.0865485
\(535\) 8.00000 0.345870
\(536\) 4.00000 0.172774
\(537\) −24.0000 −1.03568
\(538\) −14.0000 −0.603583
\(539\) 7.00000 0.301511
\(540\) −1.00000 −0.0430331
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) −8.00000 −0.343629
\(543\) 2.00000 0.0858282
\(544\) 1.00000 0.0428746
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 − 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −10.0000 −0.427179
\(549\) 2.00000 0.0853579
\(550\) 1.00000 0.0426401
\(551\) 24.0000 1.02243
\(552\) 8.00000 0.340503
\(553\) 0 0
\(554\) −10.0000 −0.424859
\(555\) 6.00000 0.254686
\(556\) 4.00000 0.169638
\(557\) 34.0000 1.44063 0.720313 − 0.693649i \(-0.243998\pi\)
0.720313 + 0.693649i \(0.243998\pi\)
\(558\) −4.00000 −0.169334
\(559\) −16.0000 −0.676728
\(560\) 0 0
\(561\) −1.00000 −0.0422200
\(562\) −6.00000 −0.253095
\(563\) 36.0000 1.51722 0.758610 − 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) −14.0000 −0.588984
\(566\) −4.00000 −0.168133
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) −2.00000 −0.0838444 −0.0419222 − 0.999121i \(-0.513348\pi\)
−0.0419222 + 0.999121i \(0.513348\pi\)
\(570\) 4.00000 0.167542
\(571\) 20.0000 0.836974 0.418487 − 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 12.0000 0.501307
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 1.00000 0.0416667
\(577\) 2.00000 0.0832611 0.0416305 − 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 18.0000 0.748054
\(580\) 6.00000 0.249136
\(581\) 0 0
\(582\) −10.0000 −0.414513
\(583\) −2.00000 −0.0828315
\(584\) −6.00000 −0.248282
\(585\) 2.00000 0.0826898
\(586\) 6.00000 0.247858
\(587\) −36.0000 −1.48588 −0.742940 − 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 7.00000 0.288675
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −18.0000 −0.740421
\(592\) −6.00000 −0.246598
\(593\) −18.0000 −0.739171 −0.369586 − 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 0 0
\(596\) 10.0000 0.409616
\(597\) 4.00000 0.163709
\(598\) −16.0000 −0.654289
\(599\) 28.0000 1.14405 0.572024 − 0.820237i \(-0.306158\pi\)
0.572024 + 0.820237i \(0.306158\pi\)
\(600\) 1.00000 0.0408248
\(601\) 14.0000 0.571072 0.285536 − 0.958368i \(-0.407828\pi\)
0.285536 + 0.958368i \(0.407828\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) 0 0
\(605\) 1.00000 0.0406558
\(606\) 10.0000 0.406222
\(607\) −8.00000 −0.324710 −0.162355 − 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −4.00000 −0.162221
\(609\) 0 0
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) −1.00000 −0.0404226
\(613\) 34.0000 1.37325 0.686624 − 0.727013i \(-0.259092\pi\)
0.686624 + 0.727013i \(0.259092\pi\)
\(614\) −8.00000 −0.322854
\(615\) −2.00000 −0.0806478
\(616\) 0 0
\(617\) −30.0000 −1.20775 −0.603877 − 0.797077i \(-0.706378\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 16.0000 0.643614
\(619\) −40.0000 −1.60774 −0.803868 − 0.594808i \(-0.797228\pi\)
−0.803868 + 0.594808i \(0.797228\pi\)
\(620\) 4.00000 0.160644
\(621\) −8.00000 −0.321029
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −2.00000 −0.0800641
\(625\) 1.00000 0.0400000
\(626\) −14.0000 −0.559553
\(627\) 4.00000 0.159745
\(628\) 6.00000 0.239426
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 − 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 8.00000 0.318223
\(633\) 12.0000 0.476957
\(634\) −14.0000 −0.556011
\(635\) 12.0000 0.476205
\(636\) −2.00000 −0.0793052
\(637\) −14.0000 −0.554700
\(638\) 6.00000 0.237542
\(639\) 8.00000 0.316475
\(640\) −1.00000 −0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) 8.00000 0.315735
\(643\) −4.00000 −0.157745 −0.0788723 − 0.996885i \(-0.525132\pi\)
−0.0788723 + 0.996885i \(0.525132\pi\)
\(644\) 0 0
\(645\) 8.00000 0.315000
\(646\) 4.00000 0.157378
\(647\) 40.0000 1.57256 0.786281 − 0.617869i \(-0.212004\pi\)
0.786281 + 0.617869i \(0.212004\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) −2.00000 −0.0784465
\(651\) 0 0
\(652\) −12.0000 −0.469956
\(653\) 6.00000 0.234798 0.117399 − 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 2.00000 0.0782062
\(655\) −12.0000 −0.468879
\(656\) 2.00000 0.0780869
\(657\) 6.00000 0.234082
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 − 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 1.00000 0.0389249
\(661\) −10.0000 −0.388955 −0.194477 − 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) −4.00000 −0.155464
\(663\) 2.00000 0.0776736
\(664\) −4.00000 −0.155230
\(665\) 0 0
\(666\) 6.00000 0.232495
\(667\) 48.0000 1.85857
\(668\) −12.0000 −0.464294
\(669\) −8.00000 −0.309298
\(670\) 4.00000 0.154533
\(671\) −2.00000 −0.0772091
\(672\) 0 0
\(673\) −2.00000 −0.0770943 −0.0385472 − 0.999257i \(-0.512273\pi\)
−0.0385472 + 0.999257i \(0.512273\pi\)
\(674\) 18.0000 0.693334
\(675\) −1.00000 −0.0384900
\(676\) −9.00000 −0.346154
\(677\) −6.00000 −0.230599 −0.115299 − 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) −14.0000 −0.537667
\(679\) 0 0
\(680\) 1.00000 0.0383482
\(681\) 0 0
\(682\) 4.00000 0.153168
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 4.00000 0.152944
\(685\) −10.0000 −0.382080
\(686\) 0 0
\(687\) −6.00000 −0.228914
\(688\) −8.00000 −0.304997
\(689\) 4.00000 0.152388
\(690\) 8.00000 0.304555
\(691\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −24.0000 −0.911028
\(695\) 4.00000 0.151729
\(696\) 6.00000 0.227429
\(697\) −2.00000 −0.0757554
\(698\) −14.0000 −0.529908
\(699\) −14.0000 −0.529529
\(700\) 0 0
\(701\) −38.0000 −1.43524 −0.717620 − 0.696435i \(-0.754769\pi\)
−0.717620 + 0.696435i \(0.754769\pi\)
\(702\) 2.00000 0.0754851
\(703\) −24.0000 −0.905177
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 2.00000 0.0752710
\(707\) 0 0
\(708\) 0 0
\(709\) 38.0000 1.42712 0.713560 − 0.700594i \(-0.247082\pi\)
0.713560 + 0.700594i \(0.247082\pi\)
\(710\) −8.00000 −0.300235
\(711\) −8.00000 −0.300023
\(712\) −2.00000 −0.0749532
\(713\) 32.0000 1.19841
\(714\) 0 0
\(715\) −2.00000 −0.0747958
\(716\) 24.0000 0.896922
\(717\) −24.0000 −0.896296
\(718\) −32.0000 −1.19423
\(719\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) 3.00000 0.111648
\(723\) −6.00000 −0.223142
\(724\) −2.00000 −0.0743294
\(725\) 6.00000 0.222834
\(726\) 1.00000 0.0371135
\(727\) 8.00000 0.296704 0.148352 − 0.988935i \(-0.452603\pi\)
0.148352 + 0.988935i \(0.452603\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.00000 −0.222070
\(731\) 8.00000 0.295891
\(732\) −2.00000 −0.0739221
\(733\) −22.0000 −0.812589 −0.406294 − 0.913742i \(-0.633179\pi\)
−0.406294 + 0.913742i \(0.633179\pi\)
\(734\) 8.00000 0.295285
\(735\) 7.00000 0.258199
\(736\) −8.00000 −0.294884
\(737\) 4.00000 0.147342
\(738\) −2.00000 −0.0736210
\(739\) −28.0000 −1.03000 −0.514998 − 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) −6.00000 −0.220564
\(741\) −8.00000 −0.293887
\(742\) 0 0
\(743\) 44.0000 1.61420 0.807102 − 0.590412i \(-0.201035\pi\)
0.807102 + 0.590412i \(0.201035\pi\)
\(744\) 4.00000 0.146647
\(745\) 10.0000 0.366372
\(746\) 14.0000 0.512576
\(747\) 4.00000 0.146352
\(748\) 1.00000 0.0365636
\(749\) 0 0
\(750\) 1.00000 0.0365148
\(751\) 12.0000 0.437886 0.218943 − 0.975738i \(-0.429739\pi\)
0.218943 + 0.975738i \(0.429739\pi\)
\(752\) 0 0
\(753\) −24.0000 −0.874609
\(754\) −12.0000 −0.437014
\(755\) 0 0
\(756\) 0 0
\(757\) 22.0000 0.799604 0.399802 − 0.916602i \(-0.369079\pi\)
0.399802 + 0.916602i \(0.369079\pi\)
\(758\) −16.0000 −0.581146
\(759\) 8.00000 0.290382
\(760\) −4.00000 −0.145095
\(761\) −18.0000 −0.652499 −0.326250 − 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 12.0000 0.434714
\(763\) 0 0
\(764\) −12.0000 −0.434145
\(765\) −1.00000 −0.0361551
\(766\) −8.00000 −0.289052
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 2.00000 0.0721218 0.0360609 − 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) 26.0000 0.936367
\(772\) −18.0000 −0.647834
\(773\) −6.00000 −0.215805 −0.107903 − 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 8.00000 0.287554
\(775\) 4.00000 0.143684
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 26.0000 0.932145
\(779\) 8.00000 0.286630
\(780\) −2.00000 −0.0716115
\(781\) −8.00000 −0.286263
\(782\) 8.00000 0.286079
\(783\) −6.00000 −0.214423
\(784\) −7.00000 −0.250000
\(785\) 6.00000 0.214149
\(786\) −12.0000 −0.428026
\(787\) 12.0000 0.427754 0.213877 − 0.976861i \(-0.431391\pi\)
0.213877 + 0.976861i \(0.431391\pi\)
\(788\) 18.0000 0.641223
\(789\) 16.0000 0.569615
\(790\) 8.00000 0.284627
\(791\) 0 0
\(792\) 1.00000 0.0355335
\(793\) 4.00000 0.142044
\(794\) 30.0000 1.06466
\(795\) −2.00000 −0.0709327
\(796\) −4.00000 −0.141776
\(797\) 2.00000 0.0708436 0.0354218 − 0.999372i \(-0.488723\pi\)
0.0354218 + 0.999372i \(0.488723\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) 2.00000 0.0706665
\(802\) −18.0000 −0.635602
\(803\) −6.00000 −0.211735
\(804\) 4.00000 0.141069
\(805\) 0 0
\(806\) −8.00000 −0.281788
\(807\) −14.0000 −0.492823
\(808\) −10.0000 −0.351799
\(809\) 18.0000 0.632846 0.316423 − 0.948618i \(-0.397518\pi\)
0.316423 + 0.948618i \(0.397518\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 44.0000 1.54505 0.772524 − 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) 0 0
\(813\) −8.00000 −0.280572
\(814\) −6.00000 −0.210300
\(815\) −12.0000 −0.420342
\(816\) 1.00000 0.0350070
\(817\) −32.0000 −1.11954
\(818\) −2.00000 −0.0699284
\(819\) 0 0
\(820\) 2.00000 0.0698430
\(821\) 6.00000 0.209401 0.104701 − 0.994504i \(-0.466612\pi\)
0.104701 + 0.994504i \(0.466612\pi\)
\(822\) −10.0000 −0.348790
\(823\) 16.0000 0.557725 0.278862 − 0.960331i \(-0.410043\pi\)
0.278862 + 0.960331i \(0.410043\pi\)
\(824\) −16.0000 −0.557386
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) 8.00000 0.278187 0.139094 − 0.990279i \(-0.455581\pi\)
0.139094 + 0.990279i \(0.455581\pi\)
\(828\) 8.00000 0.278019
\(829\) −2.00000 −0.0694629 −0.0347314 − 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) −4.00000 −0.138842
\(831\) −10.0000 −0.346896
\(832\) 2.00000 0.0693375
\(833\) 7.00000 0.242536
\(834\) 4.00000 0.138509
\(835\) −12.0000 −0.415277
\(836\) −4.00000 −0.138343
\(837\) −4.00000 −0.138260
\(838\) −4.00000 −0.138178
\(839\) 24.0000 0.828572 0.414286 − 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 10.0000 0.344623
\(843\) −6.00000 −0.206651
\(844\) −12.0000 −0.413057
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) −4.00000 −0.137280
\(850\) 1.00000 0.0342997
\(851\) −48.0000 −1.64542
\(852\) −8.00000 −0.274075
\(853\) −6.00000 −0.205436 −0.102718 − 0.994711i \(-0.532754\pi\)
−0.102718 + 0.994711i \(0.532754\pi\)
\(854\) 0 0
\(855\) 4.00000 0.136797
\(856\) −8.00000 −0.273434
\(857\) 38.0000 1.29806 0.649028 − 0.760765i \(-0.275176\pi\)
0.649028 + 0.760765i \(0.275176\pi\)
\(858\) −2.00000 −0.0682789
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) −8.00000 −0.272798
\(861\) 0 0
\(862\) −32.0000 −1.08992
\(863\) −40.0000 −1.36162 −0.680808 − 0.732462i \(-0.738371\pi\)
−0.680808 + 0.732462i \(0.738371\pi\)
\(864\) 1.00000 0.0340207
\(865\) −6.00000 −0.204006
\(866\) 6.00000 0.203888
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 6.00000 0.203419
\(871\) −8.00000 −0.271070
\(872\) −2.00000 −0.0677285
\(873\) −10.0000 −0.338449
\(874\) −32.0000 −1.08242
\(875\) 0 0
\(876\) −6.00000 −0.202721
\(877\) −14.0000 −0.472746 −0.236373 − 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) −32.0000 −1.07995
\(879\) 6.00000 0.202375
\(880\) −1.00000 −0.0337100
\(881\) −14.0000 −0.471672 −0.235836 − 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 7.00000 0.235702
\(883\) 12.0000 0.403832 0.201916 − 0.979403i \(-0.435283\pi\)
0.201916 + 0.979403i \(0.435283\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) 20.0000 0.671913
\(887\) −12.0000 −0.402921 −0.201460 − 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) −6.00000 −0.201347
\(889\) 0 0
\(890\) −2.00000 −0.0670402
\(891\) −1.00000 −0.0335013
\(892\) 8.00000 0.267860
\(893\) 0 0
\(894\) 10.0000 0.334450
\(895\) 24.0000 0.802232
\(896\) 0 0
\(897\) −16.0000 −0.534224
\(898\) −2.00000 −0.0667409
\(899\) 24.0000 0.800445
\(900\) 1.00000 0.0333333
\(901\) −2.00000 −0.0666297
\(902\) 2.00000 0.0665927
\(903\) 0 0
\(904\) 14.0000 0.465633
\(905\) −2.00000 −0.0664822
\(906\) 0 0
\(907\) −28.0000 −0.929725 −0.464862 − 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 0 0
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) −56.0000 −1.85536 −0.927681 − 0.373373i \(-0.878201\pi\)
−0.927681 + 0.373373i \(0.878201\pi\)
\(912\) −4.00000 −0.132453
\(913\) −4.00000 −0.132381
\(914\) 34.0000 1.12462
\(915\) −2.00000 −0.0661180
\(916\) 6.00000 0.198246
\(917\) 0 0
\(918\) −1.00000 −0.0330049
\(919\) −32.0000 −1.05558 −0.527791 − 0.849374i \(-0.676980\pi\)
−0.527791 + 0.849374i \(0.676980\pi\)
\(920\) −8.00000 −0.263752
\(921\) −8.00000 −0.263609
\(922\) −10.0000 −0.329332
\(923\) 16.0000 0.526646
\(924\) 0 0
\(925\) −6.00000 −0.197279
\(926\) 0 0
\(927\) 16.0000 0.525509
\(928\) −6.00000 −0.196960
\(929\) −46.0000 −1.50921 −0.754606 − 0.656179i \(-0.772172\pi\)
−0.754606 + 0.656179i \(0.772172\pi\)
\(930\) 4.00000 0.131165
\(931\) −28.0000 −0.917663
\(932\) 14.0000 0.458585
\(933\) −24.0000 −0.785725
\(934\) 12.0000 0.392652
\(935\) 1.00000 0.0327035
\(936\) −2.00000 −0.0653720
\(937\) −2.00000 −0.0653372 −0.0326686 − 0.999466i \(-0.510401\pi\)
−0.0326686 + 0.999466i \(0.510401\pi\)
\(938\) 0 0
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) −50.0000 −1.62995 −0.814977 − 0.579494i \(-0.803250\pi\)
−0.814977 + 0.579494i \(0.803250\pi\)
\(942\) 6.00000 0.195491
\(943\) 16.0000 0.521032
\(944\) 0 0
\(945\) 0 0
\(946\) −8.00000 −0.260102
\(947\) 12.0000 0.389948 0.194974 − 0.980808i \(-0.437538\pi\)
0.194974 + 0.980808i \(0.437538\pi\)
\(948\) 8.00000 0.259828
\(949\) 12.0000 0.389536
\(950\) −4.00000 −0.129777
\(951\) −14.0000 −0.453981
\(952\) 0 0
\(953\) 22.0000 0.712650 0.356325 − 0.934362i \(-0.384030\pi\)
0.356325 + 0.934362i \(0.384030\pi\)
\(954\) −2.00000 −0.0647524
\(955\) −12.0000 −0.388311
\(956\) 24.0000 0.776215
\(957\) 6.00000 0.193952
\(958\) −32.0000 −1.03387
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) 12.0000 0.386896
\(963\) 8.00000 0.257796
\(964\) 6.00000 0.193247
\(965\) −18.0000 −0.579441
\(966\) 0 0
\(967\) 12.0000 0.385894 0.192947 − 0.981209i \(-0.438195\pi\)
0.192947 + 0.981209i \(0.438195\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 4.00000 0.128499
\(970\) 10.0000 0.321081
\(971\) −48.0000 −1.54039 −0.770197 − 0.637806i \(-0.779842\pi\)
−0.770197 + 0.637806i \(0.779842\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −32.0000 −1.02535
\(975\) −2.00000 −0.0640513
\(976\) 2.00000 0.0640184
\(977\) −58.0000 −1.85558 −0.927792 − 0.373097i \(-0.878296\pi\)
−0.927792 + 0.373097i \(0.878296\pi\)
\(978\) −12.0000 −0.383718
\(979\) −2.00000 −0.0639203
\(980\) −7.00000 −0.223607
\(981\) 2.00000 0.0638551
\(982\) 28.0000 0.893516
\(983\) 40.0000 1.27580 0.637901 − 0.770118i \(-0.279803\pi\)
0.637901 + 0.770118i \(0.279803\pi\)
\(984\) 2.00000 0.0637577
\(985\) 18.0000 0.573528
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) −64.0000 −2.03508
\(990\) 1.00000 0.0317821
\(991\) −44.0000 −1.39771 −0.698853 − 0.715265i \(-0.746306\pi\)
−0.698853 + 0.715265i \(0.746306\pi\)
\(992\) −4.00000 −0.127000
\(993\) −4.00000 −0.126936
\(994\) 0 0
\(995\) −4.00000 −0.126809
\(996\) −4.00000 −0.126745
\(997\) 10.0000 0.316703 0.158352 − 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) −16.0000 −0.506471
\(999\) 6.00000 0.189832
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 5610.2.a.g.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.g.1.1 ✓ 1 1.1 even 1 trivial