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Properties

Label 2550.2.a.t.1.1
Level $2550$
Weight $2$
Character 2550.1
Self dual yes
Analytic conductor $20.362$
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] = [2550,2,Mod(1,2550)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2550, 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("2550.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2550 = 2 \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2550.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: \(20.3618525154\)
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 \(\chi\) \(=\) 2550.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -4.00000 q^{14} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +8.00000 q^{19} +4.00000 q^{21} +2.00000 q^{22} -1.00000 q^{23} -1.00000 q^{24} -2.00000 q^{26} -1.00000 q^{27} -4.00000 q^{28} -4.00000 q^{29} -2.00000 q^{31} +1.00000 q^{32} -2.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -3.00000 q^{37} +8.00000 q^{38} +2.00000 q^{39} -1.00000 q^{41} +4.00000 q^{42} +6.00000 q^{43} +2.00000 q^{44} -1.00000 q^{46} -4.00000 q^{47} -1.00000 q^{48} +9.00000 q^{49} -1.00000 q^{51} -2.00000 q^{52} +13.0000 q^{53} -1.00000 q^{54} -4.00000 q^{56} -8.00000 q^{57} -4.00000 q^{58} +15.0000 q^{59} +5.00000 q^{61} -2.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -2.00000 q^{66} +10.0000 q^{67} +1.00000 q^{68} +1.00000 q^{69} -1.00000 q^{71} +1.00000 q^{72} +16.0000 q^{73} -3.00000 q^{74} +8.00000 q^{76} -8.00000 q^{77} +2.00000 q^{78} +12.0000 q^{79} +1.00000 q^{81} -1.00000 q^{82} +11.0000 q^{83} +4.00000 q^{84} +6.00000 q^{86} +4.00000 q^{87} +2.00000 q^{88} -2.00000 q^{89} +8.00000 q^{91} -1.00000 q^{92} +2.00000 q^{93} -4.00000 q^{94} -1.00000 q^{96} +9.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −1.00000 −0.408248
\(7\) −4.00000 −1.51186 −0.755929 − 0.654654i \(-0.772814\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 − 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 −0.554700 −0.277350 − 0.960769i \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −4.00000 −1.06904
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) 1.00000 0.235702
\(19\) 8.00000 1.83533 0.917663 − 0.397360i \(-0.130073\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 4.00000 0.872872
\(22\) 2.00000 0.426401
\(23\) −1.00000 −0.208514 −0.104257 − 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0 0
\(26\) −2.00000 −0.392232
\(27\) −1.00000 −0.192450
\(28\) −4.00000 −0.755929
\(29\) −4.00000 −0.742781 −0.371391 − 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 − 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 −0.348155
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −3.00000 −0.493197 −0.246598 − 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 8.00000 1.29777
\(39\) 2.00000 0.320256
\(40\) 0 0
\(41\) −1.00000 −0.156174 −0.0780869 − 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 4.00000 0.617213
\(43\) 6.00000 0.914991 0.457496 − 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) −1.00000 −0.147442
\(47\) −4.00000 −0.583460 −0.291730 − 0.956501i \(-0.594231\pi\)
−0.291730 + 0.956501i \(0.594231\pi\)
\(48\) −1.00000 −0.144338
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) −1.00000 −0.140028
\(52\) −2.00000 −0.277350
\(53\) 13.0000 1.78569 0.892844 − 0.450367i \(-0.148707\pi\)
0.892844 + 0.450367i \(0.148707\pi\)
\(54\) −1.00000 −0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) −8.00000 −1.05963
\(58\) −4.00000 −0.525226
\(59\) 15.0000 1.95283 0.976417 − 0.215894i \(-0.0692665\pi\)
0.976417 + 0.215894i \(0.0692665\pi\)
\(60\) 0 0
\(61\) 5.00000 0.640184 0.320092 − 0.947386i \(-0.396286\pi\)
0.320092 + 0.947386i \(0.396286\pi\)
\(62\) −2.00000 −0.254000
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −2.00000 −0.246183
\(67\) 10.0000 1.22169 0.610847 − 0.791748i \(-0.290829\pi\)
0.610847 + 0.791748i \(0.290829\pi\)
\(68\) 1.00000 0.121268
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −1.00000 −0.118678 −0.0593391 − 0.998238i \(-0.518899\pi\)
−0.0593391 + 0.998238i \(0.518899\pi\)
\(72\) 1.00000 0.117851
\(73\) 16.0000 1.87266 0.936329 − 0.351123i \(-0.114200\pi\)
0.936329 + 0.351123i \(0.114200\pi\)
\(74\) −3.00000 −0.348743
\(75\) 0 0
\(76\) 8.00000 0.917663
\(77\) −8.00000 −0.911685
\(78\) 2.00000 0.226455
\(79\) 12.0000 1.35011 0.675053 − 0.737769i \(-0.264121\pi\)
0.675053 + 0.737769i \(0.264121\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −1.00000 −0.110432
\(83\) 11.0000 1.20741 0.603703 − 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 4.00000 0.436436
\(85\) 0 0
\(86\) 6.00000 0.646997
\(87\) 4.00000 0.428845
\(88\) 2.00000 0.213201
\(89\) −2.00000 −0.212000 −0.106000 − 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 0 0
\(91\) 8.00000 0.838628
\(92\) −1.00000 −0.104257
\(93\) 2.00000 0.207390
\(94\) −4.00000 −0.412568
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(98\) 9.00000 0.909137
\(99\) 2.00000 0.201008
\(100\) 0 0
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −3.00000 −0.295599 −0.147799 − 0.989017i \(-0.547219\pi\)
−0.147799 + 0.989017i \(0.547219\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 13.0000 1.26267
\(107\) −12.0000 −1.16008 −0.580042 − 0.814587i \(-0.696964\pi\)
−0.580042 + 0.814587i \(0.696964\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −2.00000 −0.191565 −0.0957826 − 0.995402i \(-0.530535\pi\)
−0.0957826 + 0.995402i \(0.530535\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) −4.00000 −0.377964
\(113\) 15.0000 1.41108 0.705541 − 0.708669i \(-0.250704\pi\)
0.705541 + 0.708669i \(0.250704\pi\)
\(114\) −8.00000 −0.749269
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) −2.00000 −0.184900
\(118\) 15.0000 1.38086
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 5.00000 0.452679
\(123\) 1.00000 0.0901670
\(124\) −2.00000 −0.179605
\(125\) 0 0
\(126\) −4.00000 −0.356348
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) 8.00000 0.698963 0.349482 − 0.936943i \(-0.386358\pi\)
0.349482 + 0.936943i \(0.386358\pi\)
\(132\) −2.00000 −0.174078
\(133\) −32.0000 −2.77475
\(134\) 10.0000 0.863868
\(135\) 0 0
\(136\) 1.00000 0.0857493
\(137\) −12.0000 −1.02523 −0.512615 − 0.858619i \(-0.671323\pi\)
−0.512615 + 0.858619i \(0.671323\pi\)
\(138\) 1.00000 0.0851257
\(139\) 1.00000 0.0848189 0.0424094 − 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) 0 0
\(141\) 4.00000 0.336861
\(142\) −1.00000 −0.0839181
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 16.0000 1.32417
\(147\) −9.00000 −0.742307
\(148\) −3.00000 −0.246598
\(149\) 1.00000 0.0819232 0.0409616 − 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788 0.0406894 − 0.999172i \(-0.487045\pi\)
0.0406894 + 0.999172i \(0.487045\pi\)
\(152\) 8.00000 0.648886
\(153\) 1.00000 0.0808452
\(154\) −8.00000 −0.644658
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) 14.0000 1.11732 0.558661 − 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 12.0000 0.954669
\(159\) −13.0000 −1.03097
\(160\) 0 0
\(161\) 4.00000 0.315244
\(162\) 1.00000 0.0785674
\(163\) 7.00000 0.548282 0.274141 − 0.961689i \(-0.411606\pi\)
0.274141 + 0.961689i \(0.411606\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) 11.0000 0.853766
\(167\) 24.0000 1.85718 0.928588 − 0.371113i \(-0.121024\pi\)
0.928588 + 0.371113i \(0.121024\pi\)
\(168\) 4.00000 0.308607
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 8.00000 0.611775
\(172\) 6.00000 0.457496
\(173\) −8.00000 −0.608229 −0.304114 − 0.952636i \(-0.598361\pi\)
−0.304114 + 0.952636i \(0.598361\pi\)
\(174\) 4.00000 0.303239
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) −15.0000 −1.12747
\(178\) −2.00000 −0.149906
\(179\) 9.00000 0.672692 0.336346 − 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 − 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 8.00000 0.592999
\(183\) −5.00000 −0.369611
\(184\) −1.00000 −0.0737210
\(185\) 0 0
\(186\) 2.00000 0.146647
\(187\) 2.00000 0.146254
\(188\) −4.00000 −0.291730
\(189\) 4.00000 0.290957
\(190\) 0 0
\(191\) 10.0000 0.723575 0.361787 − 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −24.0000 −1.72756 −0.863779 − 0.503871i \(-0.831909\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 9.00000 0.642857
\(197\) −2.00000 −0.142494 −0.0712470 − 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 2.00000 0.142134
\(199\) 10.0000 0.708881 0.354441 − 0.935079i \(-0.384671\pi\)
0.354441 + 0.935079i \(0.384671\pi\)
\(200\) 0 0
\(201\) −10.0000 −0.705346
\(202\) −10.0000 −0.703598
\(203\) 16.0000 1.12298
\(204\) −1.00000 −0.0700140
\(205\) 0 0
\(206\) −3.00000 −0.209020
\(207\) −1.00000 −0.0695048
\(208\) −2.00000 −0.138675
\(209\) 16.0000 1.10674
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 − 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 13.0000 0.892844
\(213\) 1.00000 0.0685189
\(214\) −12.0000 −0.820303
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 8.00000 0.543075
\(218\) −2.00000 −0.135457
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) −2.00000 −0.134535
\(222\) 3.00000 0.201347
\(223\) −17.0000 −1.13840 −0.569202 − 0.822198i \(-0.692748\pi\)
−0.569202 + 0.822198i \(0.692748\pi\)
\(224\) −4.00000 −0.267261
\(225\) 0 0
\(226\) 15.0000 0.997785
\(227\) 22.0000 1.46019 0.730096 − 0.683345i \(-0.239475\pi\)
0.730096 + 0.683345i \(0.239475\pi\)
\(228\) −8.00000 −0.529813
\(229\) −18.0000 −1.18947 −0.594737 − 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 8.00000 0.526361
\(232\) −4.00000 −0.262613
\(233\) −3.00000 −0.196537 −0.0982683 − 0.995160i \(-0.531330\pi\)
−0.0982683 + 0.995160i \(0.531330\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 15.0000 0.976417
\(237\) −12.0000 −0.779484
\(238\) −4.00000 −0.259281
\(239\) 6.00000 0.388108 0.194054 − 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 − 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) −7.00000 −0.449977
\(243\) −1.00000 −0.0641500
\(244\) 5.00000 0.320092
\(245\) 0 0
\(246\) 1.00000 0.0637577
\(247\) −16.0000 −1.01806
\(248\) −2.00000 −0.127000
\(249\) −11.0000 −0.697097
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 − 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) −4.00000 −0.251976
\(253\) −2.00000 −0.125739
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −12.0000 −0.748539 −0.374270 − 0.927320i \(-0.622107\pi\)
−0.374270 + 0.927320i \(0.622107\pi\)
\(258\) −6.00000 −0.373544
\(259\) 12.0000 0.745644
\(260\) 0 0
\(261\) −4.00000 −0.247594
\(262\) 8.00000 0.494242
\(263\) −4.00000 −0.246651 −0.123325 − 0.992366i \(-0.539356\pi\)
−0.123325 + 0.992366i \(0.539356\pi\)
\(264\) −2.00000 −0.123091
\(265\) 0 0
\(266\) −32.0000 −1.96205
\(267\) 2.00000 0.122398
\(268\) 10.0000 0.610847
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −21.0000 −1.27566 −0.637830 − 0.770178i \(-0.720168\pi\)
−0.637830 + 0.770178i \(0.720168\pi\)
\(272\) 1.00000 0.0606339
\(273\) −8.00000 −0.484182
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) 1.00000 0.0601929
\(277\) −31.0000 −1.86261 −0.931305 − 0.364241i \(-0.881328\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 1.00000 0.0599760
\(279\) −2.00000 −0.119737
\(280\) 0 0
\(281\) −2.00000 −0.119310 −0.0596550 − 0.998219i \(-0.519000\pi\)
−0.0596550 + 0.998219i \(0.519000\pi\)
\(282\) 4.00000 0.238197
\(283\) 7.00000 0.416107 0.208053 − 0.978117i \(-0.433287\pi\)
0.208053 + 0.978117i \(0.433287\pi\)
\(284\) −1.00000 −0.0593391
\(285\) 0 0
\(286\) −4.00000 −0.236525
\(287\) 4.00000 0.236113
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 16.0000 0.936329
\(293\) 31.0000 1.81104 0.905520 − 0.424304i \(-0.139481\pi\)
0.905520 + 0.424304i \(0.139481\pi\)
\(294\) −9.00000 −0.524891
\(295\) 0 0
\(296\) −3.00000 −0.174371
\(297\) −2.00000 −0.116052
\(298\) 1.00000 0.0579284
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) −24.0000 −1.38334
\(302\) 1.00000 0.0575435
\(303\) 10.0000 0.574485
\(304\) 8.00000 0.458831
\(305\) 0 0
\(306\) 1.00000 0.0571662
\(307\) −22.0000 −1.25561 −0.627803 − 0.778372i \(-0.716046\pi\)
−0.627803 + 0.778372i \(0.716046\pi\)
\(308\) −8.00000 −0.455842
\(309\) 3.00000 0.170664
\(310\) 0 0
\(311\) 5.00000 0.283524 0.141762 − 0.989901i \(-0.454723\pi\)
0.141762 + 0.989901i \(0.454723\pi\)
\(312\) 2.00000 0.113228
\(313\) −20.0000 −1.13047 −0.565233 − 0.824931i \(-0.691214\pi\)
−0.565233 + 0.824931i \(0.691214\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 12.0000 0.675053
\(317\) −26.0000 −1.46031 −0.730153 − 0.683284i \(-0.760551\pi\)
−0.730153 + 0.683284i \(0.760551\pi\)
\(318\) −13.0000 −0.729004
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 4.00000 0.222911
\(323\) 8.00000 0.445132
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 7.00000 0.387694
\(327\) 2.00000 0.110600
\(328\) −1.00000 −0.0552158
\(329\) 16.0000 0.882109
\(330\) 0 0
\(331\) 10.0000 0.549650 0.274825 − 0.961494i \(-0.411380\pi\)
0.274825 + 0.961494i \(0.411380\pi\)
\(332\) 11.0000 0.603703
\(333\) −3.00000 −0.164399
\(334\) 24.0000 1.31322
\(335\) 0 0
\(336\) 4.00000 0.218218
\(337\) 26.0000 1.41631 0.708155 − 0.706057i \(-0.249528\pi\)
0.708155 + 0.706057i \(0.249528\pi\)
\(338\) −9.00000 −0.489535
\(339\) −15.0000 −0.814688
\(340\) 0 0
\(341\) −4.00000 −0.216612
\(342\) 8.00000 0.432590
\(343\) −8.00000 −0.431959
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) −8.00000 −0.430083
\(347\) −16.0000 −0.858925 −0.429463 − 0.903085i \(-0.641297\pi\)
−0.429463 + 0.903085i \(0.641297\pi\)
\(348\) 4.00000 0.214423
\(349\) −14.0000 −0.749403 −0.374701 − 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 2.00000 0.106752
\(352\) 2.00000 0.106600
\(353\) −16.0000 −0.851594 −0.425797 − 0.904819i \(-0.640006\pi\)
−0.425797 + 0.904819i \(0.640006\pi\)
\(354\) −15.0000 −0.797241
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 4.00000 0.211702
\(358\) 9.00000 0.475665
\(359\) 36.0000 1.90001 0.950004 − 0.312239i \(-0.101079\pi\)
0.950004 + 0.312239i \(0.101079\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 11.0000 0.578147
\(363\) 7.00000 0.367405
\(364\) 8.00000 0.419314
\(365\) 0 0
\(366\) −5.00000 −0.261354
\(367\) −2.00000 −0.104399 −0.0521996 − 0.998637i \(-0.516623\pi\)
−0.0521996 + 0.998637i \(0.516623\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −1.00000 −0.0520579
\(370\) 0 0
\(371\) −52.0000 −2.69971
\(372\) 2.00000 0.103695
\(373\) −4.00000 −0.207112 −0.103556 − 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 2.00000 0.103418
\(375\) 0 0
\(376\) −4.00000 −0.206284
\(377\) 8.00000 0.412021
\(378\) 4.00000 0.205738
\(379\) −1.00000 −0.0513665 −0.0256833 − 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) 16.0000 0.819705
\(382\) 10.0000 0.511645
\(383\) 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
\(386\) −24.0000 −1.22157
\(387\) 6.00000 0.304997
\(388\) 0 0
\(389\) 9.00000 0.456318 0.228159 − 0.973624i \(-0.426729\pi\)
0.228159 + 0.973624i \(0.426729\pi\)
\(390\) 0 0
\(391\) −1.00000 −0.0505722
\(392\) 9.00000 0.454569
\(393\) −8.00000 −0.403547
\(394\) −2.00000 −0.100759
\(395\) 0 0
\(396\) 2.00000 0.100504
\(397\) 21.0000 1.05396 0.526980 − 0.849878i \(-0.323324\pi\)
0.526980 + 0.849878i \(0.323324\pi\)
\(398\) 10.0000 0.501255
\(399\) 32.0000 1.60200
\(400\) 0 0
\(401\) 3.00000 0.149813 0.0749064 − 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) −10.0000 −0.498755
\(403\) 4.00000 0.199254
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) 16.0000 0.794067
\(407\) −6.00000 −0.297409
\(408\) −1.00000 −0.0495074
\(409\) 19.0000 0.939490 0.469745 − 0.882802i \(-0.344346\pi\)
0.469745 + 0.882802i \(0.344346\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) −3.00000 −0.147799
\(413\) −60.0000 −2.95241
\(414\) −1.00000 −0.0491473
\(415\) 0 0
\(416\) −2.00000 −0.0980581
\(417\) −1.00000 −0.0489702
\(418\) 16.0000 0.782586
\(419\) 24.0000 1.17248 0.586238 − 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) −24.0000 −1.16969 −0.584844 − 0.811146i \(-0.698844\pi\)
−0.584844 + 0.811146i \(0.698844\pi\)
\(422\) 4.00000 0.194717
\(423\) −4.00000 −0.194487
\(424\) 13.0000 0.631336
\(425\) 0 0
\(426\) 1.00000 0.0484502
\(427\) −20.0000 −0.967868
\(428\) −12.0000 −0.580042
\(429\) 4.00000 0.193122
\(430\) 0 0
\(431\) −28.0000 −1.34871 −0.674356 − 0.738406i \(-0.735579\pi\)
−0.674356 + 0.738406i \(0.735579\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −14.0000 −0.672797 −0.336399 − 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 8.00000 0.384012
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −8.00000 −0.382692
\(438\) −16.0000 −0.764510
\(439\) −12.0000 −0.572729 −0.286364 − 0.958121i \(-0.592447\pi\)
−0.286364 + 0.958121i \(0.592447\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) −2.00000 −0.0951303
\(443\) 39.0000 1.85295 0.926473 − 0.376361i \(-0.122825\pi\)
0.926473 + 0.376361i \(0.122825\pi\)
\(444\) 3.00000 0.142374
\(445\) 0 0
\(446\) −17.0000 −0.804973
\(447\) −1.00000 −0.0472984
\(448\) −4.00000 −0.188982
\(449\) −42.0000 −1.98210 −0.991051 − 0.133482i \(-0.957384\pi\)
−0.991051 + 0.133482i \(0.957384\pi\)
\(450\) 0 0
\(451\) −2.00000 −0.0941763
\(452\) 15.0000 0.705541
\(453\) −1.00000 −0.0469841
\(454\) 22.0000 1.03251
\(455\) 0 0
\(456\) −8.00000 −0.374634
\(457\) 31.0000 1.45012 0.725059 − 0.688686i \(-0.241812\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) −18.0000 −0.841085
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −1.00000 −0.0465746 −0.0232873 − 0.999729i \(-0.507413\pi\)
−0.0232873 + 0.999729i \(0.507413\pi\)
\(462\) 8.00000 0.372194
\(463\) −35.0000 −1.62659 −0.813294 − 0.581853i \(-0.802328\pi\)
−0.813294 + 0.581853i \(0.802328\pi\)
\(464\) −4.00000 −0.185695
\(465\) 0 0
\(466\) −3.00000 −0.138972
\(467\) −3.00000 −0.138823 −0.0694117 − 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) −2.00000 −0.0924500
\(469\) −40.0000 −1.84703
\(470\) 0 0
\(471\) −14.0000 −0.645086
\(472\) 15.0000 0.690431
\(473\) 12.0000 0.551761
\(474\) −12.0000 −0.551178
\(475\) 0 0
\(476\) −4.00000 −0.183340
\(477\) 13.0000 0.595229
\(478\) 6.00000 0.274434
\(479\) −16.0000 −0.731059 −0.365529 − 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) −14.0000 −0.637683
\(483\) −4.00000 −0.182006
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) 2.00000 0.0906287 0.0453143 − 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 5.00000 0.226339
\(489\) −7.00000 −0.316551
\(490\) 0 0
\(491\) 39.0000 1.76005 0.880023 − 0.474932i \(-0.157527\pi\)
0.880023 + 0.474932i \(0.157527\pi\)
\(492\) 1.00000 0.0450835
\(493\) −4.00000 −0.180151
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) −2.00000 −0.0898027
\(497\) 4.00000 0.179425
\(498\) −11.0000 −0.492922
\(499\) −41.0000 −1.83541 −0.917706 − 0.397260i \(-0.869961\pi\)
−0.917706 + 0.397260i \(0.869961\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) −4.00000 −0.178529
\(503\) 41.0000 1.82810 0.914050 − 0.405602i \(-0.132938\pi\)
0.914050 + 0.405602i \(0.132938\pi\)
\(504\) −4.00000 −0.178174
\(505\) 0 0
\(506\) −2.00000 −0.0889108
\(507\) 9.00000 0.399704
\(508\) −16.0000 −0.709885
\(509\) 2.00000 0.0886484 0.0443242 − 0.999017i \(-0.485887\pi\)
0.0443242 + 0.999017i \(0.485887\pi\)
\(510\) 0 0
\(511\) −64.0000 −2.83119
\(512\) 1.00000 0.0441942
\(513\) −8.00000 −0.353209
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) −6.00000 −0.264135
\(517\) −8.00000 −0.351840
\(518\) 12.0000 0.527250
\(519\) 8.00000 0.351161
\(520\) 0 0
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) −4.00000 −0.175075
\(523\) 34.0000 1.48672 0.743358 − 0.668894i \(-0.233232\pi\)
0.743358 + 0.668894i \(0.233232\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) −4.00000 −0.174408
\(527\) −2.00000 −0.0871214
\(528\) −2.00000 −0.0870388
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 15.0000 0.650945
\(532\) −32.0000 −1.38738
\(533\) 2.00000 0.0866296
\(534\) 2.00000 0.0865485
\(535\) 0 0
\(536\) 10.0000 0.431934
\(537\) −9.00000 −0.388379
\(538\) −6.00000 −0.258678
\(539\) 18.0000 0.775315
\(540\) 0 0
\(541\) 15.0000 0.644900 0.322450 − 0.946586i \(-0.395494\pi\)
0.322450 + 0.946586i \(0.395494\pi\)
\(542\) −21.0000 −0.902027
\(543\) −11.0000 −0.472055
\(544\) 1.00000 0.0428746
\(545\) 0 0
\(546\) −8.00000 −0.342368
\(547\) −13.0000 −0.555840 −0.277920 − 0.960604i \(-0.589645\pi\)
−0.277920 + 0.960604i \(0.589645\pi\)
\(548\) −12.0000 −0.512615
\(549\) 5.00000 0.213395
\(550\) 0 0
\(551\) −32.0000 −1.36325
\(552\) 1.00000 0.0425628
\(553\) −48.0000 −2.04117
\(554\) −31.0000 −1.31706
\(555\) 0 0
\(556\) 1.00000 0.0424094
\(557\) 31.0000 1.31351 0.656756 − 0.754103i \(-0.271928\pi\)
0.656756 + 0.754103i \(0.271928\pi\)
\(558\) −2.00000 −0.0846668
\(559\) −12.0000 −0.507546
\(560\) 0 0
\(561\) −2.00000 −0.0844401
\(562\) −2.00000 −0.0843649
\(563\) −15.0000 −0.632175 −0.316087 − 0.948730i \(-0.602369\pi\)
−0.316087 + 0.948730i \(0.602369\pi\)
\(564\) 4.00000 0.168430
\(565\) 0 0
\(566\) 7.00000 0.294232
\(567\) −4.00000 −0.167984
\(568\) −1.00000 −0.0419591
\(569\) 6.00000 0.251533 0.125767 − 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −41.0000 −1.71580 −0.857898 − 0.513820i \(-0.828230\pi\)
−0.857898 + 0.513820i \(0.828230\pi\)
\(572\) −4.00000 −0.167248
\(573\) −10.0000 −0.417756
\(574\) 4.00000 0.166957
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 33.0000 1.37381 0.686904 − 0.726748i \(-0.258969\pi\)
0.686904 + 0.726748i \(0.258969\pi\)
\(578\) 1.00000 0.0415945
\(579\) 24.0000 0.997406
\(580\) 0 0
\(581\) −44.0000 −1.82543
\(582\) 0 0
\(583\) 26.0000 1.07681
\(584\) 16.0000 0.662085
\(585\) 0 0
\(586\) 31.0000 1.28060
\(587\) −25.0000 −1.03186 −0.515930 − 0.856631i \(-0.672554\pi\)
−0.515930 + 0.856631i \(0.672554\pi\)
\(588\) −9.00000 −0.371154
\(589\) −16.0000 −0.659269
\(590\) 0 0
\(591\) 2.00000 0.0822690
\(592\) −3.00000 −0.123299
\(593\) 12.0000 0.492781 0.246390 − 0.969171i \(-0.420755\pi\)
0.246390 + 0.969171i \(0.420755\pi\)
\(594\) −2.00000 −0.0820610
\(595\) 0 0
\(596\) 1.00000 0.0409616
\(597\) −10.0000 −0.409273
\(598\) 2.00000 0.0817861
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 6.00000 0.244745 0.122373 − 0.992484i \(-0.460950\pi\)
0.122373 + 0.992484i \(0.460950\pi\)
\(602\) −24.0000 −0.978167
\(603\) 10.0000 0.407231
\(604\) 1.00000 0.0406894
\(605\) 0 0
\(606\) 10.0000 0.406222
\(607\) 34.0000 1.38002 0.690009 − 0.723801i \(-0.257607\pi\)
0.690009 + 0.723801i \(0.257607\pi\)
\(608\) 8.00000 0.324443
\(609\) −16.0000 −0.648353
\(610\) 0 0
\(611\) 8.00000 0.323645
\(612\) 1.00000 0.0404226
\(613\) −26.0000 −1.05013 −0.525065 − 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) −22.0000 −0.887848
\(615\) 0 0
\(616\) −8.00000 −0.322329
\(617\) −6.00000 −0.241551 −0.120775 − 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 3.00000 0.120678
\(619\) 20.0000 0.803868 0.401934 − 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 5.00000 0.200482
\(623\) 8.00000 0.320513
\(624\) 2.00000 0.0800641
\(625\) 0 0
\(626\) −20.0000 −0.799361
\(627\) −16.0000 −0.638978
\(628\) 14.0000 0.558661
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) −7.00000 −0.278666 −0.139333 − 0.990246i \(-0.544496\pi\)
−0.139333 + 0.990246i \(0.544496\pi\)
\(632\) 12.0000 0.477334
\(633\) −4.00000 −0.158986
\(634\) −26.0000 −1.03259
\(635\) 0 0
\(636\) −13.0000 −0.515484
\(637\) −18.0000 −0.713186
\(638\) −8.00000 −0.316723
\(639\) −1.00000 −0.0395594
\(640\) 0 0
\(641\) −30.0000 −1.18493 −0.592464 − 0.805597i \(-0.701845\pi\)
−0.592464 + 0.805597i \(0.701845\pi\)
\(642\) 12.0000 0.473602
\(643\) −29.0000 −1.14365 −0.571824 − 0.820376i \(-0.693764\pi\)
−0.571824 + 0.820376i \(0.693764\pi\)
\(644\) 4.00000 0.157622
\(645\) 0 0
\(646\) 8.00000 0.314756
\(647\) 38.0000 1.49393 0.746967 − 0.664861i \(-0.231509\pi\)
0.746967 + 0.664861i \(0.231509\pi\)
\(648\) 1.00000 0.0392837
\(649\) 30.0000 1.17760
\(650\) 0 0
\(651\) −8.00000 −0.313545
\(652\) 7.00000 0.274141
\(653\) 12.0000 0.469596 0.234798 − 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) −1.00000 −0.0390434
\(657\) 16.0000 0.624219
\(658\) 16.0000 0.623745
\(659\) −40.0000 −1.55818 −0.779089 − 0.626913i \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) 50.0000 1.94477 0.972387 − 0.233373i \(-0.0749763\pi\)
0.972387 + 0.233373i \(0.0749763\pi\)
\(662\) 10.0000 0.388661
\(663\) 2.00000 0.0776736
\(664\) 11.0000 0.426883
\(665\) 0 0
\(666\) −3.00000 −0.116248
\(667\) 4.00000 0.154881
\(668\) 24.0000 0.928588
\(669\) 17.0000 0.657258
\(670\) 0 0
\(671\) 10.0000 0.386046
\(672\) 4.00000 0.154303
\(673\) 28.0000 1.07932 0.539660 − 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 26.0000 1.00148
\(675\) 0 0
\(676\) −9.00000 −0.346154
\(677\) 12.0000 0.461197 0.230599 − 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −15.0000 −0.576072
\(679\) 0 0
\(680\) 0 0
\(681\) −22.0000 −0.843042
\(682\) −4.00000 −0.153168
\(683\) 6.00000 0.229584 0.114792 − 0.993390i \(-0.463380\pi\)
0.114792 + 0.993390i \(0.463380\pi\)
\(684\) 8.00000 0.305888
\(685\) 0 0
\(686\) −8.00000 −0.305441
\(687\) 18.0000 0.686743
\(688\) 6.00000 0.228748
\(689\) −26.0000 −0.990521
\(690\) 0 0
\(691\) −41.0000 −1.55971 −0.779857 − 0.625958i \(-0.784708\pi\)
−0.779857 + 0.625958i \(0.784708\pi\)
\(692\) −8.00000 −0.304114
\(693\) −8.00000 −0.303895
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) 4.00000 0.151620
\(697\) −1.00000 −0.0378777
\(698\) −14.0000 −0.529908
\(699\) 3.00000 0.113470
\(700\) 0 0
\(701\) −3.00000 −0.113308 −0.0566542 − 0.998394i \(-0.518043\pi\)
−0.0566542 + 0.998394i \(0.518043\pi\)
\(702\) 2.00000 0.0754851
\(703\) −24.0000 −0.905177
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) −16.0000 −0.602168
\(707\) 40.0000 1.50435
\(708\) −15.0000 −0.563735
\(709\) 46.0000 1.72757 0.863783 − 0.503864i \(-0.168089\pi\)
0.863783 + 0.503864i \(0.168089\pi\)
\(710\) 0 0
\(711\) 12.0000 0.450035
\(712\) −2.00000 −0.0749532
\(713\) 2.00000 0.0749006
\(714\) 4.00000 0.149696
\(715\) 0 0
\(716\) 9.00000 0.336346
\(717\) −6.00000 −0.224074
\(718\) 36.0000 1.34351
\(719\) −8.00000 −0.298350 −0.149175 − 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 45.0000 1.67473
\(723\) 14.0000 0.520666
\(724\) 11.0000 0.408812
\(725\) 0 0
\(726\) 7.00000 0.259794
\(727\) 44.0000 1.63187 0.815935 − 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 8.00000 0.296500
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 6.00000 0.221918
\(732\) −5.00000 −0.184805
\(733\) −30.0000 −1.10808 −0.554038 − 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) −2.00000 −0.0738213
\(735\) 0 0
\(736\) −1.00000 −0.0368605
\(737\) 20.0000 0.736709
\(738\) −1.00000 −0.0368105
\(739\) −12.0000 −0.441427 −0.220714 − 0.975339i \(-0.570839\pi\)
−0.220714 + 0.975339i \(0.570839\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) −52.0000 −1.90898
\(743\) −17.0000 −0.623670 −0.311835 − 0.950136i \(-0.600944\pi\)
−0.311835 + 0.950136i \(0.600944\pi\)
\(744\) 2.00000 0.0733236
\(745\) 0 0
\(746\) −4.00000 −0.146450
\(747\) 11.0000 0.402469
\(748\) 2.00000 0.0731272
\(749\) 48.0000 1.75388
\(750\) 0 0
\(751\) −48.0000 −1.75154 −0.875772 − 0.482724i \(-0.839647\pi\)
−0.875772 + 0.482724i \(0.839647\pi\)
\(752\) −4.00000 −0.145865
\(753\) 4.00000 0.145768
\(754\) 8.00000 0.291343
\(755\) 0 0
\(756\) 4.00000 0.145479
\(757\) −28.0000 −1.01768 −0.508839 − 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) −1.00000 −0.0363216
\(759\) 2.00000 0.0725954
\(760\) 0 0
\(761\) 36.0000 1.30500 0.652499 − 0.757789i \(-0.273720\pi\)
0.652499 + 0.757789i \(0.273720\pi\)
\(762\) 16.0000 0.579619
\(763\) 8.00000 0.289619
\(764\) 10.0000 0.361787
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) −30.0000 −1.08324
\(768\) −1.00000 −0.0360844
\(769\) −37.0000 −1.33425 −0.667127 − 0.744944i \(-0.732476\pi\)
−0.667127 + 0.744944i \(0.732476\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) −24.0000 −0.863779
\(773\) 15.0000 0.539513 0.269756 − 0.962929i \(-0.413057\pi\)
0.269756 + 0.962929i \(0.413057\pi\)
\(774\) 6.00000 0.215666
\(775\) 0 0
\(776\) 0 0
\(777\) −12.0000 −0.430498
\(778\) 9.00000 0.322666
\(779\) −8.00000 −0.286630
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) −1.00000 −0.0357599
\(783\) 4.00000 0.142948
\(784\) 9.00000 0.321429
\(785\) 0 0
\(786\) −8.00000 −0.285351
\(787\) −3.00000 −0.106938 −0.0534692 − 0.998569i \(-0.517028\pi\)
−0.0534692 + 0.998569i \(0.517028\pi\)
\(788\) −2.00000 −0.0712470
\(789\) 4.00000 0.142404
\(790\) 0 0
\(791\) −60.0000 −2.13335
\(792\) 2.00000 0.0710669
\(793\) −10.0000 −0.355110
\(794\) 21.0000 0.745262
\(795\) 0 0
\(796\) 10.0000 0.354441
\(797\) 31.0000 1.09808 0.549038 − 0.835797i \(-0.314994\pi\)
0.549038 + 0.835797i \(0.314994\pi\)
\(798\) 32.0000 1.13279
\(799\) −4.00000 −0.141510
\(800\) 0 0
\(801\) −2.00000 −0.0706665
\(802\) 3.00000 0.105934
\(803\) 32.0000 1.12926
\(804\) −10.0000 −0.352673
\(805\) 0 0
\(806\) 4.00000 0.140894
\(807\) 6.00000 0.211210
\(808\) −10.0000 −0.351799
\(809\) −18.0000 −0.632846 −0.316423 − 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) −28.0000 −0.983213 −0.491606 − 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 16.0000 0.561490
\(813\) 21.0000 0.736502
\(814\) −6.00000 −0.210300
\(815\) 0 0
\(816\) −1.00000 −0.0350070
\(817\) 48.0000 1.67931
\(818\) 19.0000 0.664319
\(819\) 8.00000 0.279543
\(820\) 0 0
\(821\) 12.0000 0.418803 0.209401 − 0.977830i \(-0.432848\pi\)
0.209401 + 0.977830i \(0.432848\pi\)
\(822\) 12.0000 0.418548
\(823\) 32.0000 1.11545 0.557725 − 0.830026i \(-0.311674\pi\)
0.557725 + 0.830026i \(0.311674\pi\)
\(824\) −3.00000 −0.104510
\(825\) 0 0
\(826\) −60.0000 −2.08767
\(827\) 38.0000 1.32139 0.660695 − 0.750655i \(-0.270262\pi\)
0.660695 + 0.750655i \(0.270262\pi\)
\(828\) −1.00000 −0.0347524
\(829\) −16.0000 −0.555703 −0.277851 − 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) 31.0000 1.07538
\(832\) −2.00000 −0.0693375
\(833\) 9.00000 0.311832
\(834\) −1.00000 −0.0346272
\(835\) 0 0
\(836\) 16.0000 0.553372
\(837\) 2.00000 0.0691301
\(838\) 24.0000 0.829066
\(839\) 27.0000 0.932144 0.466072 − 0.884747i \(-0.345669\pi\)
0.466072 + 0.884747i \(0.345669\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) −24.0000 −0.827095
\(843\) 2.00000 0.0688837
\(844\) 4.00000 0.137686
\(845\) 0 0
\(846\) −4.00000 −0.137523
\(847\) 28.0000 0.962091
\(848\) 13.0000 0.446422
\(849\) −7.00000 −0.240239
\(850\) 0 0
\(851\) 3.00000 0.102839
\(852\) 1.00000 0.0342594
\(853\) 26.0000 0.890223 0.445112 − 0.895475i \(-0.353164\pi\)
0.445112 + 0.895475i \(0.353164\pi\)
\(854\) −20.0000 −0.684386
\(855\) 0 0
\(856\) −12.0000 −0.410152
\(857\) −7.00000 −0.239115 −0.119558 − 0.992827i \(-0.538148\pi\)
−0.119558 + 0.992827i \(0.538148\pi\)
\(858\) 4.00000 0.136558
\(859\) −44.0000 −1.50126 −0.750630 − 0.660722i \(-0.770250\pi\)
−0.750630 + 0.660722i \(0.770250\pi\)
\(860\) 0 0
\(861\) −4.00000 −0.136320
\(862\) −28.0000 −0.953684
\(863\) −40.0000 −1.36162 −0.680808 − 0.732462i \(-0.738371\pi\)
−0.680808 + 0.732462i \(0.738371\pi\)
\(864\) −1.00000 −0.0340207
\(865\) 0 0
\(866\) −14.0000 −0.475739
\(867\) −1.00000 −0.0339618
\(868\) 8.00000 0.271538
\(869\) 24.0000 0.814144
\(870\) 0 0
\(871\) −20.0000 −0.677674
\(872\) −2.00000 −0.0677285
\(873\) 0 0
\(874\) −8.00000 −0.270604
\(875\) 0 0
\(876\) −16.0000 −0.540590
\(877\) 14.0000 0.472746 0.236373 − 0.971662i \(-0.424041\pi\)
0.236373 + 0.971662i \(0.424041\pi\)
\(878\) −12.0000 −0.404980
\(879\) −31.0000 −1.04560
\(880\) 0 0
\(881\) 33.0000 1.11180 0.555899 − 0.831250i \(-0.312374\pi\)
0.555899 + 0.831250i \(0.312374\pi\)
\(882\) 9.00000 0.303046
\(883\) 50.0000 1.68263 0.841317 − 0.540542i \(-0.181781\pi\)
0.841317 + 0.540542i \(0.181781\pi\)
\(884\) −2.00000 −0.0672673
\(885\) 0 0
\(886\) 39.0000 1.31023
\(887\) −15.0000 −0.503651 −0.251825 − 0.967773i \(-0.581031\pi\)
−0.251825 + 0.967773i \(0.581031\pi\)
\(888\) 3.00000 0.100673
\(889\) 64.0000 2.14649
\(890\) 0 0
\(891\) 2.00000 0.0670025
\(892\) −17.0000 −0.569202
\(893\) −32.0000 −1.07084
\(894\) −1.00000 −0.0334450
\(895\) 0 0
\(896\) −4.00000 −0.133631
\(897\) −2.00000 −0.0667781
\(898\) −42.0000 −1.40156
\(899\) 8.00000 0.266815
\(900\) 0 0
\(901\) 13.0000 0.433093
\(902\) −2.00000 −0.0665927
\(903\) 24.0000 0.798670
\(904\) 15.0000 0.498893
\(905\) 0 0
\(906\) −1.00000 −0.0332228
\(907\) −23.0000 −0.763702 −0.381851 − 0.924224i \(-0.624713\pi\)
−0.381851 + 0.924224i \(0.624713\pi\)
\(908\) 22.0000 0.730096
\(909\) −10.0000 −0.331679
\(910\) 0 0
\(911\) 56.0000 1.85536 0.927681 − 0.373373i \(-0.121799\pi\)
0.927681 + 0.373373i \(0.121799\pi\)
\(912\) −8.00000 −0.264906
\(913\) 22.0000 0.728094
\(914\) 31.0000 1.02539
\(915\) 0 0
\(916\) −18.0000 −0.594737
\(917\) −32.0000 −1.05673
\(918\) −1.00000 −0.0330049
\(919\) −47.0000 −1.55039 −0.775193 − 0.631724i \(-0.782348\pi\)
−0.775193 + 0.631724i \(0.782348\pi\)
\(920\) 0 0
\(921\) 22.0000 0.724925
\(922\) −1.00000 −0.0329332
\(923\) 2.00000 0.0658308
\(924\) 8.00000 0.263181
\(925\) 0 0
\(926\) −35.0000 −1.15017
\(927\) −3.00000 −0.0985329
\(928\) −4.00000 −0.131306
\(929\) −15.0000 −0.492134 −0.246067 − 0.969253i \(-0.579138\pi\)
−0.246067 + 0.969253i \(0.579138\pi\)
\(930\) 0 0
\(931\) 72.0000 2.35970
\(932\) −3.00000 −0.0982683
\(933\) −5.00000 −0.163693
\(934\) −3.00000 −0.0981630
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) 17.0000 0.555366 0.277683 − 0.960673i \(-0.410434\pi\)
0.277683 + 0.960673i \(0.410434\pi\)
\(938\) −40.0000 −1.30605
\(939\) 20.0000 0.652675
\(940\) 0 0
\(941\) 22.0000 0.717180 0.358590 − 0.933495i \(-0.383258\pi\)
0.358590 + 0.933495i \(0.383258\pi\)
\(942\) −14.0000 −0.456145
\(943\) 1.00000 0.0325645
\(944\) 15.0000 0.488208
\(945\) 0 0
\(946\) 12.0000 0.390154
\(947\) −16.0000 −0.519930 −0.259965 − 0.965618i \(-0.583711\pi\)
−0.259965 + 0.965618i \(0.583711\pi\)
\(948\) −12.0000 −0.389742
\(949\) −32.0000 −1.03876
\(950\) 0 0
\(951\) 26.0000 0.843108
\(952\) −4.00000 −0.129641
\(953\) −42.0000 −1.36051 −0.680257 − 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 13.0000 0.420891
\(955\) 0 0
\(956\) 6.00000 0.194054
\(957\) 8.00000 0.258603
\(958\) −16.0000 −0.516937
\(959\) 48.0000 1.55000
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 6.00000 0.193448
\(963\) −12.0000 −0.386695
\(964\) −14.0000 −0.450910
\(965\) 0 0
\(966\) −4.00000 −0.128698
\(967\) −1.00000 −0.0321578 −0.0160789 − 0.999871i \(-0.505118\pi\)
−0.0160789 + 0.999871i \(0.505118\pi\)
\(968\) −7.00000 −0.224989
\(969\) −8.00000 −0.256997
\(970\) 0 0
\(971\) 25.0000 0.802288 0.401144 − 0.916015i \(-0.368613\pi\)
0.401144 + 0.916015i \(0.368613\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −4.00000 −0.128234
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) 5.00000 0.160046
\(977\) 18.0000 0.575871 0.287936 − 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −7.00000 −0.223835
\(979\) −4.00000 −0.127841
\(980\) 0 0
\(981\) −2.00000 −0.0638551
\(982\) 39.0000 1.24454
\(983\) 8.00000 0.255160 0.127580 − 0.991828i \(-0.459279\pi\)
0.127580 + 0.991828i \(0.459279\pi\)
\(984\) 1.00000 0.0318788
\(985\) 0 0
\(986\) −4.00000 −0.127386
\(987\) −16.0000 −0.509286
\(988\) −16.0000 −0.509028
\(989\) −6.00000 −0.190789
\(990\) 0 0
\(991\) −4.00000 −0.127064 −0.0635321 − 0.997980i \(-0.520237\pi\)
−0.0635321 + 0.997980i \(0.520237\pi\)
\(992\) −2.00000 −0.0635001
\(993\) −10.0000 −0.317340
\(994\) 4.00000 0.126872
\(995\) 0 0
\(996\) −11.0000 −0.348548
\(997\) −50.0000 −1.58352 −0.791758 − 0.610835i \(-0.790834\pi\)
−0.791758 + 0.610835i \(0.790834\pi\)
\(998\) −41.0000 −1.29783
\(999\) 3.00000 0.0949158
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 2550.2.a.t.1.1 yes 1
3.2 odd 2 7650.2.a.c.1.1 1
5.2 odd 4 2550.2.d.h.2449.2 2
5.3 odd 4 2550.2.d.h.2449.1 2
5.4 even 2 2550.2.a.q.1.1 ✓ 1
15.14 odd 2 7650.2.a.cj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2550.2.a.q.1.1 ✓ 1 5.4 even 2
2550.2.a.t.1.1 yes 1 1.1 even 1 trivial
2550.2.d.h.2449.1 2 5.3 odd 4
2550.2.d.h.2449.2 2 5.2 odd 4
7650.2.a.c.1.1 1 3.2 odd 2
7650.2.a.cj.1.1 1 15.14 odd 2