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Properties

Label 6630.2.a.v.1.1
Level $6630$
Weight $2$
Character 6630.1
Self dual yes
Analytic conductor $52.941$
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] = [6630,2,Mod(1,6630)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6630, 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("6630.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6630 = 2 \cdot 3 \cdot 5 \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6630.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: \(52.9408165401\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 6630.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -4.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +1.00000 q^{13} -4.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} -4.00000 q^{21} +1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.00000 q^{27} -4.00000 q^{28} +6.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} +1.00000 q^{34} +4.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.00000 q^{38} +1.00000 q^{39} -1.00000 q^{40} +6.00000 q^{41} -4.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} +1.00000 q^{48} +9.00000 q^{49} +1.00000 q^{50} +1.00000 q^{51} +1.00000 q^{52} +6.00000 q^{53} +1.00000 q^{54} -4.00000 q^{56} -4.00000 q^{57} +6.00000 q^{58} -12.0000 q^{59} -1.00000 q^{60} -10.0000 q^{61} -4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} -1.00000 q^{65} -4.00000 q^{67} +1.00000 q^{68} +4.00000 q^{70} -12.0000 q^{71} +1.00000 q^{72} -10.0000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +1.00000 q^{78} -16.0000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +6.00000 q^{82} -12.0000 q^{83} -4.00000 q^{84} -1.00000 q^{85} -4.00000 q^{86} +6.00000 q^{87} -6.00000 q^{89} -1.00000 q^{90} -4.00000 q^{91} -4.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} -10.0000 q^{97} +9.00000 q^{98} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 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
\(10\) −1.00000 −0.316228
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) −4.00000 −1.06904
\(15\) −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 \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 −0.223607
\(21\) −4.00000 −0.872872
\(22\) 0 0
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 1.00000 0.192450
\(28\) −4.00000 −0.755929
\(29\) 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 \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 1.00000 0.171499
\(35\) 4.00000 0.676123
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.00000 −0.648886
\(39\) 1.00000 0.160128
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) −4.00000 −0.617213
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) 9.00000 1.28571
\(50\) 1.00000 0.141421
\(51\) 1.00000 0.140028
\(52\) 1.00000 0.138675
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 1.00000 0.136083
\(55\) 0 0
\(56\) −4.00000 −0.534522
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) −12.0000 −1.56227 −0.781133 − 0.624364i \(-0.785358\pi\)
−0.781133 + 0.624364i \(0.785358\pi\)
\(60\) −1.00000 −0.129099
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) −4.00000 −0.508001
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 − 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 4.00000 0.478091
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.00000 0.117851
\(73\) −10.0000 −1.17041 −0.585206 − 0.810885i \(-0.698986\pi\)
−0.585206 + 0.810885i \(0.698986\pi\)
\(74\) 2.00000 0.232495
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) 0 0
\(78\) 1.00000 0.113228
\(79\) −16.0000 −1.80014 −0.900070 − 0.435745i \(-0.856485\pi\)
−0.900070 + 0.435745i \(0.856485\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 6.00000 0.662589
\(83\) −12.0000 −1.31717 −0.658586 − 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) −4.00000 −0.436436
\(85\) −1.00000 −0.108465
\(86\) −4.00000 −0.431331
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) −1.00000 −0.105409
\(91\) −4.00000 −0.419314
\(92\) 0 0
\(93\) −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 \(0.669494\pi\)
\(98\) 9.00000 0.909137
\(99\) 0 0
\(100\) 1.00000 0.100000
\(101\) 6.00000 0.597022 0.298511 − 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 1.00000 0.0990148
\(103\) −16.0000 −1.57653 −0.788263 − 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 1.00000 0.0980581
\(105\) 4.00000 0.390360
\(106\) 6.00000 0.582772
\(107\) −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 \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) −4.00000 −0.377964
\(113\) −6.00000 −0.564433 −0.282216 − 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 1.00000 0.0924500
\(118\) −12.0000 −1.10469
\(119\) −4.00000 −0.366679
\(120\) −1.00000 −0.0912871
\(121\) −11.0000 −1.00000
\(122\) −10.0000 −0.905357
\(123\) 6.00000 0.541002
\(124\) −4.00000 −0.359211
\(125\) −1.00000 −0.0894427
\(126\) −4.00000 −0.356348
\(127\) 8.00000 0.709885 0.354943 − 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 1.00000 0.0883883
\(129\) −4.00000 −0.352180
\(130\) −1.00000 −0.0877058
\(131\) −12.0000 −1.04844 −0.524222 − 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 0 0
\(133\) 16.0000 1.38738
\(134\) −4.00000 −0.345547
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) 18.0000 1.53784 0.768922 − 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 − 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 4.00000 0.338062
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) −6.00000 −0.498273
\(146\) −10.0000 −0.827606
\(147\) 9.00000 0.742307
\(148\) 2.00000 0.164399
\(149\) −18.0000 −1.47462 −0.737309 − 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 1.00000 0.0816497
\(151\) 8.00000 0.651031 0.325515 − 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) −4.00000 −0.324443
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 1.00000 0.0800641
\(157\) 14.0000 1.11732 0.558661 − 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −16.0000 −1.27289
\(159\) 6.00000 0.475831
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) −16.0000 −1.25322 −0.626608 − 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 6.00000 0.468521
\(165\) 0 0
\(166\) −12.0000 −0.931381
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −4.00000 −0.308607
\(169\) 1.00000 0.0769231
\(170\) −1.00000 −0.0766965
\(171\) −4.00000 −0.305888
\(172\) −4.00000 −0.304997
\(173\) −18.0000 −1.36851 −0.684257 − 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 6.00000 0.454859
\(175\) −4.00000 −0.302372
\(176\) 0 0
\(177\) −12.0000 −0.901975
\(178\) −6.00000 −0.449719
\(179\) 12.0000 0.896922 0.448461 − 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) −4.00000 −0.296500
\(183\) −10.0000 −0.739221
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) 0 0
\(189\) −4.00000 −0.290957
\(190\) 4.00000 0.290191
\(191\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) 14.0000 1.00774 0.503871 − 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) −10.0000 −0.717958
\(195\) −1.00000 −0.0716115
\(196\) 9.00000 0.642857
\(197\) −6.00000 −0.427482 −0.213741 − 0.976890i \(-0.568565\pi\)
−0.213741 + 0.976890i \(0.568565\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 − 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 1.00000 0.0707107
\(201\) −4.00000 −0.282138
\(202\) 6.00000 0.422159
\(203\) −24.0000 −1.68447
\(204\) 1.00000 0.0700140
\(205\) −6.00000 −0.419058
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) 4.00000 0.276026
\(211\) −4.00000 −0.275371 −0.137686 − 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 6.00000 0.412082
\(213\) −12.0000 −0.822226
\(214\) −12.0000 −0.820303
\(215\) 4.00000 0.272798
\(216\) 1.00000 0.0680414
\(217\) 16.0000 1.08615
\(218\) 2.00000 0.135457
\(219\) −10.0000 −0.675737
\(220\) 0 0
\(221\) 1.00000 0.0672673
\(222\) 2.00000 0.134231
\(223\) −16.0000 −1.07144 −0.535720 − 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −4.00000 −0.267261
\(225\) 1.00000 0.0666667
\(226\) −6.00000 −0.399114
\(227\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(228\) −4.00000 −0.264906
\(229\) −10.0000 −0.660819 −0.330409 − 0.943838i \(-0.607187\pi\)
−0.330409 + 0.943838i \(0.607187\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 18.0000 1.17922 0.589610 − 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 1.00000 0.0653720
\(235\) 0 0
\(236\) −12.0000 −0.781133
\(237\) −16.0000 −1.03931
\(238\) −4.00000 −0.259281
\(239\) 24.0000 1.55243 0.776215 − 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −10.0000 −0.644157 −0.322078 − 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −11.0000 −0.707107
\(243\) 1.00000 0.0641500
\(244\) −10.0000 −0.640184
\(245\) −9.00000 −0.574989
\(246\) 6.00000 0.382546
\(247\) −4.00000 −0.254514
\(248\) −4.00000 −0.254000
\(249\) −12.0000 −0.760469
\(250\) −1.00000 −0.0632456
\(251\) −12.0000 −0.757433 −0.378717 − 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) −4.00000 −0.251976
\(253\) 0 0
\(254\) 8.00000 0.501965
\(255\) −1.00000 −0.0626224
\(256\) 1.00000 0.0625000
\(257\) 18.0000 1.12281 0.561405 − 0.827541i \(-0.310261\pi\)
0.561405 + 0.827541i \(0.310261\pi\)
\(258\) −4.00000 −0.249029
\(259\) −8.00000 −0.497096
\(260\) −1.00000 −0.0620174
\(261\) 6.00000 0.371391
\(262\) −12.0000 −0.741362
\(263\) 24.0000 1.47990 0.739952 − 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 16.0000 0.981023
\(267\) −6.00000 −0.367194
\(268\) −4.00000 −0.244339
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −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
\(273\) −4.00000 −0.242091
\(274\) 18.0000 1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 − 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 20.0000 1.19952
\(279\) −4.00000 −0.239474
\(280\) 4.00000 0.239046
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 − 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) −12.0000 −0.712069
\(285\) 4.00000 0.236940
\(286\) 0 0
\(287\) −24.0000 −1.41668
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) −6.00000 −0.352332
\(291\) −10.0000 −0.586210
\(292\) −10.0000 −0.585206
\(293\) 6.00000 0.350524 0.175262 − 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 9.00000 0.524891
\(295\) 12.0000 0.698667
\(296\) 2.00000 0.116248
\(297\) 0 0
\(298\) −18.0000 −1.04271
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 16.0000 0.922225
\(302\) 8.00000 0.460348
\(303\) 6.00000 0.344691
\(304\) −4.00000 −0.229416
\(305\) 10.0000 0.572598
\(306\) 1.00000 0.0571662
\(307\) 20.0000 1.14146 0.570730 − 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −16.0000 −0.910208
\(310\) 4.00000 0.227185
\(311\) −24.0000 −1.36092 −0.680458 − 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) 1.00000 0.0566139
\(313\) −22.0000 −1.24351 −0.621757 − 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 14.0000 0.790066
\(315\) 4.00000 0.225374
\(316\) −16.0000 −0.900070
\(317\) 18.0000 1.01098 0.505490 − 0.862832i \(-0.331312\pi\)
0.505490 + 0.862832i \(0.331312\pi\)
\(318\) 6.00000 0.336463
\(319\) 0 0
\(320\) −1.00000 −0.0559017
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) 1.00000 0.0555556
\(325\) 1.00000 0.0554700
\(326\) −16.0000 −0.886158
\(327\) 2.00000 0.110600
\(328\) 6.00000 0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 −0.219860 −0.109930 − 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) −12.0000 −0.658586
\(333\) 2.00000 0.109599
\(334\) 12.0000 0.656611
\(335\) 4.00000 0.218543
\(336\) −4.00000 −0.218218
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 1.00000 0.0543928
\(339\) −6.00000 −0.325875
\(340\) −1.00000 −0.0542326
\(341\) 0 0
\(342\) −4.00000 −0.216295
\(343\) −8.00000 −0.431959
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) −12.0000 −0.644194 −0.322097 − 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 6.00000 0.321634
\(349\) −10.0000 −0.535288 −0.267644 − 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −4.00000 −0.213809
\(351\) 1.00000 0.0533761
\(352\) 0 0
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) −12.0000 −0.637793
\(355\) 12.0000 0.636894
\(356\) −6.00000 −0.317999
\(357\) −4.00000 −0.211702
\(358\) 12.0000 0.634220
\(359\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 14.0000 0.735824
\(363\) −11.0000 −0.577350
\(364\) −4.00000 −0.209657
\(365\) 10.0000 0.523424
\(366\) −10.0000 −0.522708
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) −2.00000 −0.103975
\(371\) −24.0000 −1.24602
\(372\) −4.00000 −0.207390
\(373\) −10.0000 −0.517780 −0.258890 − 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) −4.00000 −0.205738
\(379\) 8.00000 0.410932 0.205466 − 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 4.00000 0.205196
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) −24.0000 −1.22634 −0.613171 − 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) −4.00000 −0.203331
\(388\) −10.0000 −0.507673
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) −1.00000 −0.0506370
\(391\) 0 0
\(392\) 9.00000 0.454569
\(393\) −12.0000 −0.605320
\(394\) −6.00000 −0.302276
\(395\) 16.0000 0.805047
\(396\) 0 0
\(397\) 26.0000 1.30490 0.652451 − 0.757831i \(-0.273741\pi\)
0.652451 + 0.757831i \(0.273741\pi\)
\(398\) 8.00000 0.401004
\(399\) 16.0000 0.801002
\(400\) 1.00000 0.0500000
\(401\) 6.00000 0.299626 0.149813 − 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −4.00000 −0.199502
\(403\) −4.00000 −0.199254
\(404\) 6.00000 0.298511
\(405\) −1.00000 −0.0496904
\(406\) −24.0000 −1.19110
\(407\) 0 0
\(408\) 1.00000 0.0495074
\(409\) −22.0000 −1.08783 −0.543915 − 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) −6.00000 −0.296319
\(411\) 18.0000 0.887875
\(412\) −16.0000 −0.788263
\(413\) 48.0000 2.36193
\(414\) 0 0
\(415\) 12.0000 0.589057
\(416\) 1.00000 0.0490290
\(417\) 20.0000 0.979404
\(418\) 0 0
\(419\) −36.0000 −1.75872 −0.879358 − 0.476162i \(-0.842028\pi\)
−0.879358 + 0.476162i \(0.842028\pi\)
\(420\) 4.00000 0.195180
\(421\) 14.0000 0.682318 0.341159 − 0.940006i \(-0.389181\pi\)
0.341159 + 0.940006i \(0.389181\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 1.00000 0.0485071
\(426\) −12.0000 −0.581402
\(427\) 40.0000 1.93574
\(428\) −12.0000 −0.580042
\(429\) 0 0
\(430\) 4.00000 0.192897
\(431\) −36.0000 −1.73406 −0.867029 − 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) 1.00000 0.0481125
\(433\) 2.00000 0.0961139 0.0480569 − 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 16.0000 0.768025
\(435\) −6.00000 −0.287678
\(436\) 2.00000 0.0957826
\(437\) 0 0
\(438\) −10.0000 −0.477818
\(439\) 32.0000 1.52728 0.763638 − 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) 9.00000 0.428571
\(442\) 1.00000 0.0475651
\(443\) 36.0000 1.71041 0.855206 − 0.518289i \(-0.173431\pi\)
0.855206 + 0.518289i \(0.173431\pi\)
\(444\) 2.00000 0.0949158
\(445\) 6.00000 0.284427
\(446\) −16.0000 −0.757622
\(447\) −18.0000 −0.851371
\(448\) −4.00000 −0.188982
\(449\) −42.0000 −1.98210 −0.991051 − 0.133482i \(-0.957384\pi\)
−0.991051 + 0.133482i \(0.957384\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) −6.00000 −0.282216
\(453\) 8.00000 0.375873
\(454\) 0 0
\(455\) 4.00000 0.187523
\(456\) −4.00000 −0.187317
\(457\) 2.00000 0.0935561 0.0467780 − 0.998905i \(-0.485105\pi\)
0.0467780 + 0.998905i \(0.485105\pi\)
\(458\) −10.0000 −0.467269
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 − 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 − 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 6.00000 0.278543
\(465\) 4.00000 0.185496
\(466\) 18.0000 0.833834
\(467\) 12.0000 0.555294 0.277647 − 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 1.00000 0.0462250
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 14.0000 0.645086
\(472\) −12.0000 −0.552345
\(473\) 0 0
\(474\) −16.0000 −0.734904
\(475\) −4.00000 −0.183533
\(476\) −4.00000 −0.183340
\(477\) 6.00000 0.274721
\(478\) 24.0000 1.09773
\(479\) −36.0000 −1.64488 −0.822441 − 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 2.00000 0.0911922
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 10.0000 0.454077
\(486\) 1.00000 0.0453609
\(487\) 20.0000 0.906287 0.453143 − 0.891438i \(-0.350303\pi\)
0.453143 + 0.891438i \(0.350303\pi\)
\(488\) −10.0000 −0.452679
\(489\) −16.0000 −0.723545
\(490\) −9.00000 −0.406579
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 6.00000 0.270501
\(493\) 6.00000 0.270226
\(494\) −4.00000 −0.179969
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 48.0000 2.15309
\(498\) −12.0000 −0.537733
\(499\) 8.00000 0.358129 0.179065 − 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 12.0000 0.536120
\(502\) −12.0000 −0.535586
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −4.00000 −0.178174
\(505\) −6.00000 −0.266996
\(506\) 0 0
\(507\) 1.00000 0.0444116
\(508\) 8.00000 0.354943
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 40.0000 1.76950
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) 18.0000 0.793946
\(515\) 16.0000 0.705044
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) −8.00000 −0.351500
\(519\) −18.0000 −0.790112
\(520\) −1.00000 −0.0438529
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 6.00000 0.262613
\(523\) −4.00000 −0.174908 −0.0874539 − 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −12.0000 −0.524222
\(525\) −4.00000 −0.174574
\(526\) 24.0000 1.04645
\(527\) −4.00000 −0.174243
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) −6.00000 −0.260623
\(531\) −12.0000 −0.520756
\(532\) 16.0000 0.693688
\(533\) 6.00000 0.259889
\(534\) −6.00000 −0.259645
\(535\) 12.0000 0.518805
\(536\) −4.00000 −0.172774
\(537\) 12.0000 0.517838
\(538\) 6.00000 0.258678
\(539\) 0 0
\(540\) −1.00000 −0.0430331
\(541\) 2.00000 0.0859867 0.0429934 − 0.999075i \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 8.00000 0.343629
\(543\) 14.0000 0.600798
\(544\) 1.00000 0.0428746
\(545\) −2.00000 −0.0856706
\(546\) −4.00000 −0.171184
\(547\) −28.0000 −1.19719 −0.598597 − 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 18.0000 0.768922
\(549\) −10.0000 −0.426790
\(550\) 0 0
\(551\) −24.0000 −1.02243
\(552\) 0 0
\(553\) 64.0000 2.72156
\(554\) 14.0000 0.594803
\(555\) −2.00000 −0.0848953
\(556\) 20.0000 0.848189
\(557\) 6.00000 0.254228 0.127114 − 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) −4.00000 −0.169334
\(559\) −4.00000 −0.169182
\(560\) 4.00000 0.169031
\(561\) 0 0
\(562\) −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
\(565\) 6.00000 0.252422
\(566\) −4.00000 −0.168133
\(567\) −4.00000 −0.167984
\(568\) −12.0000 −0.503509
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 4.00000 0.167542
\(571\) 20.0000 0.836974 0.418487 − 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −24.0000 −1.00174
\(575\) 0 0
\(576\) 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
\(579\) 14.0000 0.581820
\(580\) −6.00000 −0.249136
\(581\) 48.0000 1.99138
\(582\) −10.0000 −0.414513
\(583\) 0 0
\(584\) −10.0000 −0.413803
\(585\) −1.00000 −0.0413449
\(586\) 6.00000 0.247858
\(587\) −12.0000 −0.495293 −0.247647 − 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 9.00000 0.371154
\(589\) 16.0000 0.659269
\(590\) 12.0000 0.494032
\(591\) −6.00000 −0.246807
\(592\) 2.00000 0.0821995
\(593\) −6.00000 −0.246390 −0.123195 − 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 0 0
\(595\) 4.00000 0.163984
\(596\) −18.0000 −0.737309
\(597\) 8.00000 0.327418
\(598\) 0 0
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 1.00000 0.0408248
\(601\) 2.00000 0.0815817 0.0407909 − 0.999168i \(-0.487012\pi\)
0.0407909 + 0.999168i \(0.487012\pi\)
\(602\) 16.0000 0.652111
\(603\) −4.00000 −0.162893
\(604\) 8.00000 0.325515
\(605\) 11.0000 0.447214
\(606\) 6.00000 0.243733
\(607\) 32.0000 1.29884 0.649420 − 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) −4.00000 −0.162221
\(609\) −24.0000 −0.972529
\(610\) 10.0000 0.404888
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) −34.0000 −1.37325 −0.686624 − 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 20.0000 0.807134
\(615\) −6.00000 −0.241943
\(616\) 0 0
\(617\) −42.0000 −1.69086 −0.845428 − 0.534089i \(-0.820655\pi\)
−0.845428 + 0.534089i \(0.820655\pi\)
\(618\) −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
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 24.0000 0.961540
\(624\) 1.00000 0.0400320
\(625\) 1.00000 0.0400000
\(626\) −22.0000 −0.879297
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) 2.00000 0.0797452
\(630\) 4.00000 0.159364
\(631\) 32.0000 1.27390 0.636950 − 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) −16.0000 −0.636446
\(633\) −4.00000 −0.158986
\(634\) 18.0000 0.714871
\(635\) −8.00000 −0.317470
\(636\) 6.00000 0.237915
\(637\) 9.00000 0.356593
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) −1.00000 −0.0395285
\(641\) −6.00000 −0.236986 −0.118493 − 0.992955i \(-0.537806\pi\)
−0.118493 + 0.992955i \(0.537806\pi\)
\(642\) −12.0000 −0.473602
\(643\) 8.00000 0.315489 0.157745 − 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) −4.00000 −0.157378
\(647\) 24.0000 0.943537 0.471769 − 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 1.00000 0.0392232
\(651\) 16.0000 0.627089
\(652\) −16.0000 −0.626608
\(653\) −18.0000 −0.704394 −0.352197 − 0.935926i \(-0.614565\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(654\) 2.00000 0.0782062
\(655\) 12.0000 0.468879
\(656\) 6.00000 0.234261
\(657\) −10.0000 −0.390137
\(658\) 0 0
\(659\) −12.0000 −0.467454 −0.233727 − 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 − 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) −4.00000 −0.155464
\(663\) 1.00000 0.0388368
\(664\) −12.0000 −0.465690
\(665\) −16.0000 −0.620453
\(666\) 2.00000 0.0774984
\(667\) 0 0
\(668\) 12.0000 0.464294
\(669\) −16.0000 −0.618596
\(670\) 4.00000 0.154533
\(671\) 0 0
\(672\) −4.00000 −0.154303
\(673\) −22.0000 −0.848038 −0.424019 − 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) −22.0000 −0.847408
\(675\) 1.00000 0.0384900
\(676\) 1.00000 0.0384615
\(677\) −18.0000 −0.691796 −0.345898 − 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −6.00000 −0.230429
\(679\) 40.0000 1.53506
\(680\) −1.00000 −0.0383482
\(681\) 0 0
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 − 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) −4.00000 −0.152944
\(685\) −18.0000 −0.687745
\(686\) −8.00000 −0.305441
\(687\) −10.0000 −0.381524
\(688\) −4.00000 −0.152499
\(689\) 6.00000 0.228582
\(690\) 0 0
\(691\) −16.0000 −0.608669 −0.304334 − 0.952565i \(-0.598434\pi\)
−0.304334 + 0.952565i \(0.598434\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −20.0000 −0.758643
\(696\) 6.00000 0.227429
\(697\) 6.00000 0.227266
\(698\) −10.0000 −0.378506
\(699\) 18.0000 0.680823
\(700\) −4.00000 −0.151186
\(701\) 30.0000 1.13308 0.566542 − 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 1.00000 0.0377426
\(703\) −8.00000 −0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) −24.0000 −0.902613
\(708\) −12.0000 −0.450988
\(709\) 50.0000 1.87779 0.938895 − 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) 12.0000 0.450352
\(711\) −16.0000 −0.600047
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) −4.00000 −0.149696
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 24.0000 0.896296
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 − 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 64.0000 2.38348
\(722\) −3.00000 −0.111648
\(723\) −10.0000 −0.371904
\(724\) 14.0000 0.520306
\(725\) 6.00000 0.222834
\(726\) −11.0000 −0.408248
\(727\) −40.0000 −1.48352 −0.741759 − 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) −4.00000 −0.148250
\(729\) 1.00000 0.0370370
\(730\) 10.0000 0.370117
\(731\) −4.00000 −0.147945
\(732\) −10.0000 −0.369611
\(733\) 14.0000 0.517102 0.258551 − 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) 8.00000 0.295285
\(735\) −9.00000 −0.331970
\(736\) 0 0
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) 20.0000 0.735712 0.367856 − 0.929883i \(-0.380092\pi\)
0.367856 + 0.929883i \(0.380092\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −4.00000 −0.146944
\(742\) −24.0000 −0.881068
\(743\) 36.0000 1.32071 0.660356 − 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) −4.00000 −0.146647
\(745\) 18.0000 0.659469
\(746\) −10.0000 −0.366126
\(747\) −12.0000 −0.439057
\(748\) 0 0
\(749\) 48.0000 1.75388
\(750\) −1.00000 −0.0365148
\(751\) 32.0000 1.16770 0.583848 − 0.811863i \(-0.301546\pi\)
0.583848 + 0.811863i \(0.301546\pi\)
\(752\) 0 0
\(753\) −12.0000 −0.437304
\(754\) 6.00000 0.218507
\(755\) −8.00000 −0.291150
\(756\) −4.00000 −0.145479
\(757\) −10.0000 −0.363456 −0.181728 − 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 8.00000 0.290573
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) 42.0000 1.52250 0.761249 − 0.648459i \(-0.224586\pi\)
0.761249 + 0.648459i \(0.224586\pi\)
\(762\) 8.00000 0.289809
\(763\) −8.00000 −0.289619
\(764\) 0 0
\(765\) −1.00000 −0.0361551
\(766\) −24.0000 −0.867155
\(767\) −12.0000 −0.433295
\(768\) 1.00000 0.0360844
\(769\) 26.0000 0.937584 0.468792 − 0.883309i \(-0.344689\pi\)
0.468792 + 0.883309i \(0.344689\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 14.0000 0.503871
\(773\) −42.0000 −1.51064 −0.755318 − 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) −4.00000 −0.143777
\(775\) −4.00000 −0.143684
\(776\) −10.0000 −0.358979
\(777\) −8.00000 −0.286998
\(778\) 6.00000 0.215110
\(779\) −24.0000 −0.859889
\(780\) −1.00000 −0.0358057
\(781\) 0 0
\(782\) 0 0
\(783\) 6.00000 0.214423
\(784\) 9.00000 0.321429
\(785\) −14.0000 −0.499681
\(786\) −12.0000 −0.428026
\(787\) 32.0000 1.14068 0.570338 − 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) −6.00000 −0.213741
\(789\) 24.0000 0.854423
\(790\) 16.0000 0.569254
\(791\) 24.0000 0.853342
\(792\) 0 0
\(793\) −10.0000 −0.355110
\(794\) 26.0000 0.922705
\(795\) −6.00000 −0.212798
\(796\) 8.00000 0.283552
\(797\) −18.0000 −0.637593 −0.318796 − 0.947823i \(-0.603279\pi\)
−0.318796 + 0.947823i \(0.603279\pi\)
\(798\) 16.0000 0.566394
\(799\) 0 0
\(800\) 1.00000 0.0353553
\(801\) −6.00000 −0.212000
\(802\) 6.00000 0.211867
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) −4.00000 −0.140894
\(807\) 6.00000 0.211210
\(808\) 6.00000 0.211079
\(809\) −6.00000 −0.210949 −0.105474 − 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −16.0000 −0.561836 −0.280918 − 0.959732i \(-0.590639\pi\)
−0.280918 + 0.959732i \(0.590639\pi\)
\(812\) −24.0000 −0.842235
\(813\) 8.00000 0.280572
\(814\) 0 0
\(815\) 16.0000 0.560456
\(816\) 1.00000 0.0350070
\(817\) 16.0000 0.559769
\(818\) −22.0000 −0.769212
\(819\) −4.00000 −0.139771
\(820\) −6.00000 −0.209529
\(821\) −30.0000 −1.04701 −0.523504 − 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 18.0000 0.627822
\(823\) −40.0000 −1.39431 −0.697156 − 0.716919i \(-0.745552\pi\)
−0.697156 + 0.716919i \(0.745552\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) 48.0000 1.67013
\(827\) 24.0000 0.834562 0.417281 − 0.908778i \(-0.362983\pi\)
0.417281 + 0.908778i \(0.362983\pi\)
\(828\) 0 0
\(829\) −34.0000 −1.18087 −0.590434 − 0.807086i \(-0.701044\pi\)
−0.590434 + 0.807086i \(0.701044\pi\)
\(830\) 12.0000 0.416526
\(831\) 14.0000 0.485655
\(832\) 1.00000 0.0346688
\(833\) 9.00000 0.311832
\(834\) 20.0000 0.692543
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) −4.00000 −0.138260
\(838\) −36.0000 −1.24360
\(839\) 36.0000 1.24286 0.621429 − 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 4.00000 0.138013
\(841\) 7.00000 0.241379
\(842\) 14.0000 0.482472
\(843\) −6.00000 −0.206651
\(844\) −4.00000 −0.137686
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 44.0000 1.51186
\(848\) 6.00000 0.206041
\(849\) −4.00000 −0.137280
\(850\) 1.00000 0.0342997
\(851\) 0 0
\(852\) −12.0000 −0.411113
\(853\) −46.0000 −1.57501 −0.787505 − 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) 40.0000 1.36877
\(855\) 4.00000 0.136797
\(856\) −12.0000 −0.410152
\(857\) 18.0000 0.614868 0.307434 − 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −28.0000 −0.955348 −0.477674 − 0.878537i \(-0.658520\pi\)
−0.477674 + 0.878537i \(0.658520\pi\)
\(860\) 4.00000 0.136399
\(861\) −24.0000 −0.817918
\(862\) −36.0000 −1.22616
\(863\) 24.0000 0.816970 0.408485 − 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 1.00000 0.0340207
\(865\) 18.0000 0.612018
\(866\) 2.00000 0.0679628
\(867\) 1.00000 0.0339618
\(868\) 16.0000 0.543075
\(869\) 0 0
\(870\) −6.00000 −0.203419
\(871\) −4.00000 −0.135535
\(872\) 2.00000 0.0677285
\(873\) −10.0000 −0.338449
\(874\) 0 0
\(875\) 4.00000 0.135225
\(876\) −10.0000 −0.337869
\(877\) −22.0000 −0.742887 −0.371444 − 0.928456i \(-0.621137\pi\)
−0.371444 + 0.928456i \(0.621137\pi\)
\(878\) 32.0000 1.07995
\(879\) 6.00000 0.202375
\(880\) 0 0
\(881\) −30.0000 −1.01073 −0.505363 − 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) 9.00000 0.303046
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 1.00000 0.0336336
\(885\) 12.0000 0.403376
\(886\) 36.0000 1.20944
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 2.00000 0.0671156
\(889\) −32.0000 −1.07325
\(890\) 6.00000 0.201120
\(891\) 0 0
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) −18.0000 −0.602010
\(895\) −12.0000 −0.401116
\(896\) −4.00000 −0.133631
\(897\) 0 0
\(898\) −42.0000 −1.40156
\(899\) −24.0000 −0.800445
\(900\) 1.00000 0.0333333
\(901\) 6.00000 0.199889
\(902\) 0 0
\(903\) 16.0000 0.532447
\(904\) −6.00000 −0.199557
\(905\) −14.0000 −0.465376
\(906\) 8.00000 0.265782
\(907\) 44.0000 1.46100 0.730498 − 0.682915i \(-0.239288\pi\)
0.730498 + 0.682915i \(0.239288\pi\)
\(908\) 0 0
\(909\) 6.00000 0.199007
\(910\) 4.00000 0.132599
\(911\) −24.0000 −0.795155 −0.397578 − 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) −4.00000 −0.132453
\(913\) 0 0
\(914\) 2.00000 0.0661541
\(915\) 10.0000 0.330590
\(916\) −10.0000 −0.330409
\(917\) 48.0000 1.58510
\(918\) 1.00000 0.0330049
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 20.0000 0.659022
\(922\) −18.0000 −0.592798
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) 2.00000 0.0657596
\(926\) 32.0000 1.05159
\(927\) −16.0000 −0.525509
\(928\) 6.00000 0.196960
\(929\) −42.0000 −1.37798 −0.688988 − 0.724773i \(-0.741945\pi\)
−0.688988 + 0.724773i \(0.741945\pi\)
\(930\) 4.00000 0.131165
\(931\) −36.0000 −1.17985
\(932\) 18.0000 0.589610
\(933\) −24.0000 −0.785725
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) 1.00000 0.0326860
\(937\) 26.0000 0.849383 0.424691 − 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 16.0000 0.522419
\(939\) −22.0000 −0.717943
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 − 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 14.0000 0.456145
\(943\) 0 0
\(944\) −12.0000 −0.390567
\(945\) 4.00000 0.130120
\(946\) 0 0
\(947\) −24.0000 −0.779895 −0.389948 − 0.920837i \(-0.627507\pi\)
−0.389948 + 0.920837i \(0.627507\pi\)
\(948\) −16.0000 −0.519656
\(949\) −10.0000 −0.324614
\(950\) −4.00000 −0.129777
\(951\) 18.0000 0.583690
\(952\) −4.00000 −0.129641
\(953\) 42.0000 1.36051 0.680257 − 0.732974i \(-0.261868\pi\)
0.680257 + 0.732974i \(0.261868\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −36.0000 −1.16311
\(959\) −72.0000 −2.32500
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) 2.00000 0.0644826
\(963\) −12.0000 −0.386695
\(964\) −10.0000 −0.322078
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) 32.0000 1.02905 0.514525 − 0.857475i \(-0.327968\pi\)
0.514525 + 0.857475i \(0.327968\pi\)
\(968\) −11.0000 −0.353553
\(969\) −4.00000 −0.128499
\(970\) 10.0000 0.321081
\(971\) −12.0000 −0.385098 −0.192549 − 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) 1.00000 0.0320750
\(973\) −80.0000 −2.56468
\(974\) 20.0000 0.640841
\(975\) 1.00000 0.0320256
\(976\) −10.0000 −0.320092
\(977\) −6.00000 −0.191957 −0.0959785 − 0.995383i \(-0.530598\pi\)
−0.0959785 + 0.995383i \(0.530598\pi\)
\(978\) −16.0000 −0.511624
\(979\) 0 0
\(980\) −9.00000 −0.287494
\(981\) 2.00000 0.0638551
\(982\) 12.0000 0.382935
\(983\) −12.0000 −0.382741 −0.191370 − 0.981518i \(-0.561293\pi\)
−0.191370 + 0.981518i \(0.561293\pi\)
\(984\) 6.00000 0.191273
\(985\) 6.00000 0.191176
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) −4.00000 −0.127257
\(989\) 0 0
\(990\) 0 0
\(991\) 32.0000 1.01651 0.508257 − 0.861206i \(-0.330290\pi\)
0.508257 + 0.861206i \(0.330290\pi\)
\(992\) −4.00000 −0.127000
\(993\) −4.00000 −0.126936
\(994\) 48.0000 1.52247
\(995\) −8.00000 −0.253617
\(996\) −12.0000 −0.380235
\(997\) 38.0000 1.20347 0.601736 − 0.798695i \(-0.294476\pi\)
0.601736 + 0.798695i \(0.294476\pi\)
\(998\) 8.00000 0.253236
\(999\) 2.00000 0.0632772
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 6630.2.a.v.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6630.2.a.v.1.1 ✓ 1 1.1 even 1 trivial