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Properties

Label 5610.2.a.bc.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)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} +6.00000 q^{13} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{22} -1.00000 q^{24} +1.00000 q^{25} +6.00000 q^{26} -1.00000 q^{27} +6.00000 q^{29} -1.00000 q^{30} +1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000 q^{36} -2.00000 q^{37} +4.00000 q^{38} -6.00000 q^{39} +1.00000 q^{40} -6.00000 q^{41} -4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -8.00000 q^{47} -1.00000 q^{48} -7.00000 q^{49} +1.00000 q^{50} -1.00000 q^{51} +6.00000 q^{52} +14.0000 q^{53} -1.00000 q^{54} -1.00000 q^{55} -4.00000 q^{57} +6.00000 q^{58} +12.0000 q^{59} -1.00000 q^{60} -2.00000 q^{61} +1.00000 q^{64} +6.00000 q^{65} +1.00000 q^{66} +4.00000 q^{67} +1.00000 q^{68} +1.00000 q^{72} -6.00000 q^{73} -2.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} -6.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} +1.00000 q^{85} -4.00000 q^{86} -6.00000 q^{87} -1.00000 q^{88} -6.00000 q^{89} +1.00000 q^{90} -8.00000 q^{94} +4.00000 q^{95} -1.00000 q^{96} +2.00000 q^{97} -7.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
\(13\) 6.00000 1.66410 0.832050 − 0.554700i \(-0.187167\pi\)
0.832050 + 0.554700i \(0.187167\pi\)
\(14\) 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
\(23\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 6.00000 1.17670
\(27\) −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
\(31\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 4.00000 0.648886
\(39\) −6.00000 −0.960769
\(40\) 1.00000 0.158114
\(41\) −6.00000 −0.937043 −0.468521 − 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 − 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 − 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) −1.00000 −0.144338
\(49\) −7.00000 −1.00000
\(50\) 1.00000 0.141421
\(51\) −1.00000 −0.140028
\(52\) 6.00000 0.832050
\(53\) 14.0000 1.92305 0.961524 − 0.274721i \(-0.0885855\pi\)
0.961524 + 0.274721i \(0.0885855\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) 6.00000 0.787839
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) −1.00000 −0.129099
\(61\) −2.00000 −0.256074 −0.128037 − 0.991769i \(-0.540868\pi\)
−0.128037 + 0.991769i \(0.540868\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.00000 0.744208
\(66\) 1.00000 0.123091
\(67\) 4.00000 0.488678 0.244339 − 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) 1.00000 0.121268
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) −6.00000 −0.702247 −0.351123 − 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) −1.00000 −0.115470
\(76\) 4.00000 0.458831
\(77\) 0 0
\(78\) −6.00000 −0.679366
\(79\) −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
\(82\) −6.00000 −0.662589
\(83\) 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
\(86\) −4.00000 −0.431331
\(87\) −6.00000 −0.643268
\(88\) −1.00000 −0.106600
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −8.00000 −0.825137
\(95\) 4.00000 0.410391
\(96\) −1.00000 −0.102062
\(97\) 2.00000 0.203069 0.101535 − 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −7.00000 −0.707107
\(99\) −1.00000 −0.100504
\(100\) 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
\(103\) −8.00000 −0.788263 −0.394132 − 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) 14.0000 1.35980
\(107\) 4.00000 0.386695 0.193347 − 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 14.0000 1.34096 0.670478 − 0.741929i \(-0.266089\pi\)
0.670478 + 0.741929i \(0.266089\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) 2.00000 0.188144 0.0940721 − 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −4.00000 −0.374634
\(115\) 0 0
\(116\) 6.00000 0.557086
\(117\) 6.00000 0.554700
\(118\) 12.0000 1.10469
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −2.00000 −0.181071
\(123\) 6.00000 0.541002
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 − 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 4.00000 0.352180
\(130\) 6.00000 0.526235
\(131\) 12.0000 1.04844 0.524222 − 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) 10.0000 0.854358 0.427179 − 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) −6.00000 −0.501745
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) −6.00000 −0.496564
\(147\) 7.00000 0.577350
\(148\) −2.00000 −0.164399
\(149\) 22.0000 1.80231 0.901155 − 0.433497i \(-0.142720\pi\)
0.901155 + 0.433497i \(0.142720\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 4.00000 0.324443
\(153\) 1.00000 0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) 14.0000 1.11732 0.558661 − 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) −8.00000 −0.636446
\(159\) −14.0000 −1.11027
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 1.00000 0.0785674
\(163\) 12.0000 0.939913 0.469956 − 0.882690i \(-0.344270\pi\)
0.469956 + 0.882690i \(0.344270\pi\)
\(164\) −6.00000 −0.468521
\(165\) 1.00000 0.0778499
\(166\) 4.00000 0.310460
\(167\) 8.00000 0.619059 0.309529 − 0.950890i \(-0.399829\pi\)
0.309529 + 0.950890i \(0.399829\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 1.00000 0.0766965
\(171\) 4.00000 0.305888
\(172\) −4.00000 −0.304997
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −6.00000 −0.454859
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) −12.0000 −0.901975
\(178\) −6.00000 −0.449719
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 0.0745356
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 2.00000 0.147844
\(184\) 0 0
\(185\) −2.00000 −0.147043
\(186\) 0 0
\(187\) −1.00000 −0.0731272
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) 4.00000 0.290191
\(191\) 8.00000 0.578860 0.289430 − 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −14.0000 −1.00774 −0.503871 − 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 2.00000 0.143592
\(195\) −6.00000 −0.429669
\(196\) −7.00000 −0.500000
\(197\) −18.0000 −1.28245 −0.641223 − 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) −1.00000 −0.0710669
\(199\) −24.0000 −1.70131 −0.850657 − 0.525720i \(-0.823796\pi\)
−0.850657 + 0.525720i \(0.823796\pi\)
\(200\) 1.00000 0.0707107
\(201\) −4.00000 −0.282138
\(202\) 6.00000 0.422159
\(203\) 0 0
\(204\) −1.00000 −0.0700140
\(205\) −6.00000 −0.419058
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 6.00000 0.416025
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −20.0000 −1.37686 −0.688428 − 0.725304i \(-0.741699\pi\)
−0.688428 + 0.725304i \(0.741699\pi\)
\(212\) 14.0000 0.961524
\(213\) 0 0
\(214\) 4.00000 0.273434
\(215\) −4.00000 −0.272798
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 14.0000 0.948200
\(219\) 6.00000 0.405442
\(220\) −1.00000 −0.0674200
\(221\) 6.00000 0.403604
\(222\) 2.00000 0.134231
\(223\) 16.0000 1.07144 0.535720 − 0.844396i \(-0.320040\pi\)
0.535720 + 0.844396i \(0.320040\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 2.00000 0.133038
\(227\) −4.00000 −0.265489 −0.132745 − 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) −4.00000 −0.264906
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) −6.00000 −0.393073 −0.196537 − 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 6.00000 0.392232
\(235\) −8.00000 −0.521862
\(236\) 12.0000 0.781133
\(237\) 8.00000 0.519656
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 − 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 2.00000 0.128831 0.0644157 − 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 1.00000 0.0642824
\(243\) −1.00000 −0.0641500
\(244\) −2.00000 −0.128037
\(245\) −7.00000 −0.447214
\(246\) 6.00000 0.382546
\(247\) 24.0000 1.52708
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 1.00000 0.0632456
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 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
\(259\) 0 0
\(260\) 6.00000 0.372104
\(261\) 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 \(0.234848\pi\)
\(264\) 1.00000 0.0615457
\(265\) 14.0000 0.860013
\(266\) 0 0
\(267\) 6.00000 0.367194
\(268\) 4.00000 0.244339
\(269\) −18.0000 −1.09748 −0.548740 − 0.835993i \(-0.684892\pi\)
−0.548740 + 0.835993i \(0.684892\pi\)
\(270\) −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
\(276\) 0 0
\(277\) −26.0000 −1.56219 −0.781094 − 0.624413i \(-0.785338\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) 0 0
\(281\) 26.0000 1.55103 0.775515 − 0.631329i \(-0.217490\pi\)
0.775515 + 0.631329i \(0.217490\pi\)
\(282\) 8.00000 0.476393
\(283\) 4.00000 0.237775 0.118888 − 0.992908i \(-0.462067\pi\)
0.118888 + 0.992908i \(0.462067\pi\)
\(284\) 0 0
\(285\) −4.00000 −0.236940
\(286\) −6.00000 −0.354787
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) 6.00000 0.352332
\(291\) −2.00000 −0.117242
\(292\) −6.00000 −0.351123
\(293\) −26.0000 −1.51894 −0.759468 − 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 7.00000 0.408248
\(295\) 12.0000 0.698667
\(296\) −2.00000 −0.116248
\(297\) 1.00000 0.0580259
\(298\) 22.0000 1.27443
\(299\) 0 0
\(300\) −1.00000 −0.0577350
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) −6.00000 −0.344691
\(304\) 4.00000 0.229416
\(305\) −2.00000 −0.114520
\(306\) 1.00000 0.0571662
\(307\) 4.00000 0.228292 0.114146 − 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −6.00000 −0.339683
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −2.00000 −0.112331 −0.0561656 − 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) −14.0000 −0.785081
\(319\) −6.00000 −0.335936
\(320\) 1.00000 0.0559017
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) 6.00000 0.332820
\(326\) 12.0000 0.664619
\(327\) −14.0000 −0.774202
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) −20.0000 −1.09930 −0.549650 − 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 4.00000 0.219529
\(333\) −2.00000 −0.109599
\(334\) 8.00000 0.437741
\(335\) 4.00000 0.218543
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 − 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 23.0000 1.25104
\(339\) −2.00000 −0.108625
\(340\) 1.00000 0.0542326
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) 0 0
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −28.0000 −1.50312 −0.751559 − 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) −6.00000 −0.321634
\(349\) 6.00000 0.321173 0.160586 − 0.987022i \(-0.448662\pi\)
0.160586 + 0.987022i \(0.448662\pi\)
\(350\) 0 0
\(351\) −6.00000 −0.320256
\(352\) −1.00000 −0.0533002
\(353\) −14.0000 −0.745145 −0.372572 − 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) −12.0000 −0.637793
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) −24.0000 −1.26667 −0.633336 − 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 1.00000 0.0527046
\(361\) −3.00000 −0.157895
\(362\) 14.0000 0.735824
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −6.00000 −0.314054
\(366\) 2.00000 0.104542
\(367\) 32.0000 1.67039 0.835193 − 0.549957i \(-0.185356\pi\)
0.835193 + 0.549957i \(0.185356\pi\)
\(368\) 0 0
\(369\) −6.00000 −0.312348
\(370\) −2.00000 −0.103975
\(371\) 0 0
\(372\) 0 0
\(373\) −18.0000 −0.932005 −0.466002 − 0.884783i \(-0.654306\pi\)
−0.466002 + 0.884783i \(0.654306\pi\)
\(374\) −1.00000 −0.0517088
\(375\) −1.00000 −0.0516398
\(376\) −8.00000 −0.412568
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) 20.0000 1.02733 0.513665 − 0.857991i \(-0.328287\pi\)
0.513665 + 0.857991i \(0.328287\pi\)
\(380\) 4.00000 0.205196
\(381\) 8.00000 0.409852
\(382\) 8.00000 0.409316
\(383\) −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
\(388\) 2.00000 0.101535
\(389\) −2.00000 −0.101404 −0.0507020 − 0.998714i \(-0.516146\pi\)
−0.0507020 + 0.998714i \(0.516146\pi\)
\(390\) −6.00000 −0.303822
\(391\) 0 0
\(392\) −7.00000 −0.353553
\(393\) −12.0000 −0.605320
\(394\) −18.0000 −0.906827
\(395\) −8.00000 −0.402524
\(396\) −1.00000 −0.0502519
\(397\) −10.0000 −0.501886 −0.250943 − 0.968002i \(-0.580741\pi\)
−0.250943 + 0.968002i \(0.580741\pi\)
\(398\) −24.0000 −1.20301
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 34.0000 1.69788 0.848939 − 0.528490i \(-0.177242\pi\)
0.848939 + 0.528490i \(0.177242\pi\)
\(402\) −4.00000 −0.199502
\(403\) 0 0
\(404\) 6.00000 0.298511
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) −1.00000 −0.0495074
\(409\) 10.0000 0.494468 0.247234 − 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −6.00000 −0.296319
\(411\) −10.0000 −0.493264
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) 0 0
\(415\) 4.00000 0.196352
\(416\) 6.00000 0.294174
\(417\) −4.00000 −0.195881
\(418\) −4.00000 −0.195646
\(419\) 12.0000 0.586238 0.293119 − 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 − 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −20.0000 −0.973585
\(423\) −8.00000 −0.388973
\(424\) 14.0000 0.679900
\(425\) 1.00000 0.0485071
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) 6.00000 0.289683
\(430\) −4.00000 −0.192897
\(431\) 16.0000 0.770693 0.385346 − 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −14.0000 −0.672797 −0.336399 − 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) −6.00000 −0.287678
\(436\) 14.0000 0.670478
\(437\) 0 0
\(438\) 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
\(442\) 6.00000 0.285391
\(443\) −20.0000 −0.950229 −0.475114 − 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 2.00000 0.0949158
\(445\) −6.00000 −0.284427
\(446\) 16.0000 0.757622
\(447\) −22.0000 −1.04056
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 1.00000 0.0471405
\(451\) 6.00000 0.282529
\(452\) 2.00000 0.0940721
\(453\) 16.0000 0.751746
\(454\) −4.00000 −0.187729
\(455\) 0 0
\(456\) −4.00000 −0.187317
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) 22.0000 1.02799
\(459\) −1.00000 −0.0466760
\(460\) 0 0
\(461\) −2.00000 −0.0931493 −0.0465746 − 0.998915i \(-0.514831\pi\)
−0.0465746 + 0.998915i \(0.514831\pi\)
\(462\) 0 0
\(463\) −32.0000 −1.48717 −0.743583 − 0.668644i \(-0.766875\pi\)
−0.743583 + 0.668644i \(0.766875\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) 36.0000 1.66588 0.832941 − 0.553362i \(-0.186655\pi\)
0.832941 + 0.553362i \(0.186655\pi\)
\(468\) 6.00000 0.277350
\(469\) 0 0
\(470\) −8.00000 −0.369012
\(471\) −14.0000 −0.645086
\(472\) 12.0000 0.552345
\(473\) 4.00000 0.183920
\(474\) 8.00000 0.367452
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) 14.0000 0.641016
\(478\) −16.0000 −0.731823
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −12.0000 −0.547153
\(482\) 2.00000 0.0910975
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 2.00000 0.0908153
\(486\) −1.00000 −0.0453609
\(487\) −24.0000 −1.08754 −0.543772 − 0.839233i \(-0.683004\pi\)
−0.543772 + 0.839233i \(0.683004\pi\)
\(488\) −2.00000 −0.0905357
\(489\) −12.0000 −0.542659
\(490\) −7.00000 −0.316228
\(491\) 44.0000 1.98569 0.992846 − 0.119401i \(-0.0380974\pi\)
0.992846 + 0.119401i \(0.0380974\pi\)
\(492\) 6.00000 0.270501
\(493\) 6.00000 0.270226
\(494\) 24.0000 1.07981
\(495\) −1.00000 −0.0449467
\(496\) 0 0
\(497\) 0 0
\(498\) −4.00000 −0.179244
\(499\) −20.0000 −0.895323 −0.447661 − 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 1.00000 0.0447214
\(501\) −8.00000 −0.357414
\(502\) 12.0000 0.535586
\(503\) −24.0000 −1.07011 −0.535054 − 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −23.0000 −1.02147
\(508\) −8.00000 −0.354943
\(509\) 22.0000 0.975133 0.487566 − 0.873086i \(-0.337885\pi\)
0.487566 + 0.873086i \(0.337885\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) 18.0000 0.793946
\(515\) −8.00000 −0.352522
\(516\) 4.00000 0.176090
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) −6.00000 −0.263371
\(520\) 6.00000 0.263117
\(521\) −6.00000 −0.262865 −0.131432 − 0.991325i \(-0.541958\pi\)
−0.131432 + 0.991325i \(0.541958\pi\)
\(522\) 6.00000 0.262613
\(523\) −36.0000 −1.57417 −0.787085 − 0.616844i \(-0.788411\pi\)
−0.787085 + 0.616844i \(0.788411\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 1.00000 0.0435194
\(529\) −23.0000 −1.00000
\(530\) 14.0000 0.608121
\(531\) 12.0000 0.520756
\(532\) 0 0
\(533\) −36.0000 −1.55933
\(534\) 6.00000 0.259645
\(535\) 4.00000 0.172935
\(536\) 4.00000 0.172774
\(537\) 12.0000 0.517838
\(538\) −18.0000 −0.776035
\(539\) 7.00000 0.301511
\(540\) −1.00000 −0.0430331
\(541\) −18.0000 −0.773880 −0.386940 − 0.922105i \(-0.626468\pi\)
−0.386940 + 0.922105i \(0.626468\pi\)
\(542\) 8.00000 0.343629
\(543\) −14.0000 −0.600798
\(544\) 1.00000 0.0428746
\(545\) 14.0000 0.599694
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 − 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 10.0000 0.427179
\(549\) −2.00000 −0.0853579
\(550\) −1.00000 −0.0426401
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) 0 0
\(554\) −26.0000 −1.10463
\(555\) 2.00000 0.0848953
\(556\) 4.00000 0.169638
\(557\) 30.0000 1.27114 0.635570 − 0.772043i \(-0.280765\pi\)
0.635570 + 0.772043i \(0.280765\pi\)
\(558\) 0 0
\(559\) −24.0000 −1.01509
\(560\) 0 0
\(561\) 1.00000 0.0422200
\(562\) 26.0000 1.09674
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 8.00000 0.336861
\(565\) 2.00000 0.0841406
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) 0 0
\(569\) 26.0000 1.08998 0.544988 − 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(570\) −4.00000 −0.167542
\(571\) 20.0000 0.836974 0.418487 − 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) −6.00000 −0.250873
\(573\) −8.00000 −0.334205
\(574\) 0 0
\(575\) 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
\(581\) 0 0
\(582\) −2.00000 −0.0829027
\(583\) −14.0000 −0.579821
\(584\) −6.00000 −0.248282
\(585\) 6.00000 0.248069
\(586\) −26.0000 −1.07405
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) 7.00000 0.288675
\(589\) 0 0
\(590\) 12.0000 0.494032
\(591\) 18.0000 0.740421
\(592\) −2.00000 −0.0821995
\(593\) −46.0000 −1.88899 −0.944497 − 0.328521i \(-0.893450\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) 1.00000 0.0410305
\(595\) 0 0
\(596\) 22.0000 0.901155
\(597\) 24.0000 0.982255
\(598\) 0 0
\(599\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −22.0000 −0.897399 −0.448699 − 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 0 0
\(603\) 4.00000 0.162893
\(604\) −16.0000 −0.651031
\(605\) 1.00000 0.0406558
\(606\) −6.00000 −0.243733
\(607\) −24.0000 −0.974130 −0.487065 − 0.873366i \(-0.661933\pi\)
−0.487065 + 0.873366i \(0.661933\pi\)
\(608\) 4.00000 0.162221
\(609\) 0 0
\(610\) −2.00000 −0.0809776
\(611\) −48.0000 −1.94187
\(612\) 1.00000 0.0404226
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 4.00000 0.161427
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) −38.0000 −1.52982 −0.764911 − 0.644136i \(-0.777217\pi\)
−0.764911 + 0.644136i \(0.777217\pi\)
\(618\) 8.00000 0.321807
\(619\) −28.0000 −1.12542 −0.562708 − 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) −6.00000 −0.240192
\(625\) 1.00000 0.0400000
\(626\) −6.00000 −0.239808
\(627\) 4.00000 0.159745
\(628\) 14.0000 0.558661
\(629\) −2.00000 −0.0797452
\(630\) 0 0
\(631\) −8.00000 −0.318475 −0.159237 − 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) −8.00000 −0.318223
\(633\) 20.0000 0.794929
\(634\) −2.00000 −0.0794301
\(635\) −8.00000 −0.317470
\(636\) −14.0000 −0.555136
\(637\) −42.0000 −1.66410
\(638\) −6.00000 −0.237542
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 18.0000 0.710957 0.355479 − 0.934684i \(-0.384318\pi\)
0.355479 + 0.934684i \(0.384318\pi\)
\(642\) −4.00000 −0.157867
\(643\) −20.0000 −0.788723 −0.394362 − 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) 4.00000 0.157378
\(647\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000 0.0392837
\(649\) −12.0000 −0.471041
\(650\) 6.00000 0.235339
\(651\) 0 0
\(652\) 12.0000 0.469956
\(653\) 30.0000 1.17399 0.586995 − 0.809590i \(-0.300311\pi\)
0.586995 + 0.809590i \(0.300311\pi\)
\(654\) −14.0000 −0.547443
\(655\) 12.0000 0.468879
\(656\) −6.00000 −0.234261
\(657\) −6.00000 −0.234082
\(658\) 0 0
\(659\) −44.0000 −1.71400 −0.856998 − 0.515319i \(-0.827673\pi\)
−0.856998 + 0.515319i \(0.827673\pi\)
\(660\) 1.00000 0.0389249
\(661\) 22.0000 0.855701 0.427850 − 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) −20.0000 −0.777322
\(663\) −6.00000 −0.233021
\(664\) 4.00000 0.155230
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 8.00000 0.309529
\(669\) −16.0000 −0.618596
\(670\) 4.00000 0.154533
\(671\) 2.00000 0.0772091
\(672\) 0 0
\(673\) −46.0000 −1.77317 −0.886585 − 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 34.0000 1.30963
\(675\) −1.00000 −0.0384900
\(676\) 23.0000 0.884615
\(677\) −18.0000 −0.691796 −0.345898 − 0.938272i \(-0.612426\pi\)
−0.345898 + 0.938272i \(0.612426\pi\)
\(678\) −2.00000 −0.0768095
\(679\) 0 0
\(680\) 1.00000 0.0383482
\(681\) 4.00000 0.153280
\(682\) 0 0
\(683\) −12.0000 −0.459167 −0.229584 − 0.973289i \(-0.573736\pi\)
−0.229584 + 0.973289i \(0.573736\pi\)
\(684\) 4.00000 0.152944
\(685\) 10.0000 0.382080
\(686\) 0 0
\(687\) −22.0000 −0.839352
\(688\) −4.00000 −0.152499
\(689\) 84.0000 3.20015
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 − 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −28.0000 −1.06287
\(695\) 4.00000 0.151729
\(696\) −6.00000 −0.227429
\(697\) −6.00000 −0.227266
\(698\) 6.00000 0.227103
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 46.0000 1.73740 0.868698 − 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(702\) −6.00000 −0.226455
\(703\) −8.00000 −0.301726
\(704\) −1.00000 −0.0376889
\(705\) 8.00000 0.301297
\(706\) −14.0000 −0.526897
\(707\) 0 0
\(708\) −12.0000 −0.450988
\(709\) −18.0000 −0.676004 −0.338002 − 0.941145i \(-0.609751\pi\)
−0.338002 + 0.941145i \(0.609751\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) −6.00000 −0.224860
\(713\) 0 0
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) −12.0000 −0.448461
\(717\) 16.0000 0.597531
\(718\) −24.0000 −0.895672
\(719\) 40.0000 1.49175 0.745874 − 0.666087i \(-0.232032\pi\)
0.745874 + 0.666087i \(0.232032\pi\)
\(720\) 1.00000 0.0372678
\(721\) 0 0
\(722\) −3.00000 −0.111648
\(723\) −2.00000 −0.0743808
\(724\) 14.0000 0.520306
\(725\) 6.00000 0.222834
\(726\) −1.00000 −0.0371135
\(727\) −40.0000 −1.48352 −0.741759 − 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −6.00000 −0.222070
\(731\) −4.00000 −0.147945
\(732\) 2.00000 0.0739221
\(733\) −10.0000 −0.369358 −0.184679 − 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) 32.0000 1.18114
\(735\) 7.00000 0.258199
\(736\) 0 0
\(737\) −4.00000 −0.147342
\(738\) −6.00000 −0.220863
\(739\) 36.0000 1.32428 0.662141 − 0.749380i \(-0.269648\pi\)
0.662141 + 0.749380i \(0.269648\pi\)
\(740\) −2.00000 −0.0735215
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 22.0000 0.806018
\(746\) −18.0000 −0.659027
\(747\) 4.00000 0.146352
\(748\) −1.00000 −0.0365636
\(749\) 0 0
\(750\) −1.00000 −0.0365148
\(751\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) −8.00000 −0.291730
\(753\) −12.0000 −0.437304
\(754\) 36.0000 1.31104
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) −10.0000 −0.363456 −0.181728 − 0.983349i \(-0.558169\pi\)
−0.181728 + 0.983349i \(0.558169\pi\)
\(758\) 20.0000 0.726433
\(759\) 0 0
\(760\) 4.00000 0.145095
\(761\) −38.0000 −1.37750 −0.688749 − 0.724999i \(-0.741840\pi\)
−0.688749 + 0.724999i \(0.741840\pi\)
\(762\) 8.00000 0.289809
\(763\) 0 0
\(764\) 8.00000 0.289430
\(765\) 1.00000 0.0361551
\(766\) −24.0000 −0.867155
\(767\) 72.0000 2.59977
\(768\) −1.00000 −0.0360844
\(769\) −14.0000 −0.504853 −0.252426 − 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) −14.0000 −0.503871
\(773\) 14.0000 0.503545 0.251773 − 0.967786i \(-0.418987\pi\)
0.251773 + 0.967786i \(0.418987\pi\)
\(774\) −4.00000 −0.143777
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) 0 0
\(778\) −2.00000 −0.0717035
\(779\) −24.0000 −0.859889
\(780\) −6.00000 −0.214834
\(781\) 0 0
\(782\) 0 0
\(783\) −6.00000 −0.214423
\(784\) −7.00000 −0.250000
\(785\) 14.0000 0.499681
\(786\) −12.0000 −0.428026
\(787\) 44.0000 1.56843 0.784215 − 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) −18.0000 −0.641223
\(789\) −24.0000 −0.854423
\(790\) −8.00000 −0.284627
\(791\) 0 0
\(792\) −1.00000 −0.0355335
\(793\) −12.0000 −0.426132
\(794\) −10.0000 −0.354887
\(795\) −14.0000 −0.496529
\(796\) −24.0000 −0.850657
\(797\) −42.0000 −1.48772 −0.743858 − 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 1.00000 0.0353553
\(801\) −6.00000 −0.212000
\(802\) 34.0000 1.20058
\(803\) 6.00000 0.211735
\(804\) −4.00000 −0.141069
\(805\) 0 0
\(806\) 0 0
\(807\) 18.0000 0.633630
\(808\) 6.00000 0.211079
\(809\) 26.0000 0.914111 0.457056 − 0.889438i \(-0.348904\pi\)
0.457056 + 0.889438i \(0.348904\pi\)
\(810\) 1.00000 0.0351364
\(811\) −28.0000 −0.983213 −0.491606 − 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 0 0
\(813\) −8.00000 −0.280572
\(814\) 2.00000 0.0701000
\(815\) 12.0000 0.420342
\(816\) −1.00000 −0.0350070
\(817\) −16.0000 −0.559769
\(818\) 10.0000 0.349642
\(819\) 0 0
\(820\) −6.00000 −0.209529
\(821\) −18.0000 −0.628204 −0.314102 − 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) −10.0000 −0.348790
\(823\) 40.0000 1.39431 0.697156 − 0.716919i \(-0.254448\pi\)
0.697156 + 0.716919i \(0.254448\pi\)
\(824\) −8.00000 −0.278693
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) −12.0000 −0.417281 −0.208640 − 0.977992i \(-0.566904\pi\)
−0.208640 + 0.977992i \(0.566904\pi\)
\(828\) 0 0
\(829\) −2.00000 −0.0694629 −0.0347314 − 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 4.00000 0.138842
\(831\) 26.0000 0.901930
\(832\) 6.00000 0.208013
\(833\) −7.00000 −0.242536
\(834\) −4.00000 −0.138509
\(835\) 8.00000 0.276851
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) 12.0000 0.414533
\(839\) −32.0000 −1.10476 −0.552381 − 0.833592i \(-0.686281\pi\)
−0.552381 + 0.833592i \(0.686281\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −10.0000 −0.344623
\(843\) −26.0000 −0.895488
\(844\) −20.0000 −0.688428
\(845\) 23.0000 0.791224
\(846\) −8.00000 −0.275046
\(847\) 0 0
\(848\) 14.0000 0.480762
\(849\) −4.00000 −0.137280
\(850\) 1.00000 0.0342997
\(851\) 0 0
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 − 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 0 0
\(855\) 4.00000 0.136797
\(856\) 4.00000 0.136717
\(857\) 26.0000 0.888143 0.444072 − 0.895991i \(-0.353534\pi\)
0.444072 + 0.895991i \(0.353534\pi\)
\(858\) 6.00000 0.204837
\(859\) −4.00000 −0.136478 −0.0682391 − 0.997669i \(-0.521738\pi\)
−0.0682391 + 0.997669i \(0.521738\pi\)
\(860\) −4.00000 −0.136399
\(861\) 0 0
\(862\) 16.0000 0.544962
\(863\) −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
\(866\) −14.0000 −0.475739
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) −6.00000 −0.203419
\(871\) 24.0000 0.813209
\(872\) 14.0000 0.474100
\(873\) 2.00000 0.0676897
\(874\) 0 0
\(875\) 0 0
\(876\) 6.00000 0.202721
\(877\) 46.0000 1.55331 0.776655 − 0.629926i \(-0.216915\pi\)
0.776655 + 0.629926i \(0.216915\pi\)
\(878\) 32.0000 1.07995
\(879\) 26.0000 0.876958
\(880\) −1.00000 −0.0337100
\(881\) −30.0000 −1.01073 −0.505363 − 0.862907i \(-0.668641\pi\)
−0.505363 + 0.862907i \(0.668641\pi\)
\(882\) −7.00000 −0.235702
\(883\) −12.0000 −0.403832 −0.201916 − 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 6.00000 0.201802
\(885\) −12.0000 −0.403376
\(886\) −20.0000 −0.671913
\(887\) −56.0000 −1.88030 −0.940148 − 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 2.00000 0.0671156
\(889\) 0 0
\(890\) −6.00000 −0.201120
\(891\) −1.00000 −0.0335013
\(892\) 16.0000 0.535720
\(893\) −32.0000 −1.07084
\(894\) −22.0000 −0.735790
\(895\) −12.0000 −0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 18.0000 0.600668
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 14.0000 0.466408
\(902\) 6.00000 0.199778
\(903\) 0 0
\(904\) 2.00000 0.0665190
\(905\) 14.0000 0.465376
\(906\) 16.0000 0.531564
\(907\) −44.0000 −1.46100 −0.730498 − 0.682915i \(-0.760712\pi\)
−0.730498 + 0.682915i \(0.760712\pi\)
\(908\) −4.00000 −0.132745
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) −8.00000 −0.265052 −0.132526 − 0.991180i \(-0.542309\pi\)
−0.132526 + 0.991180i \(0.542309\pi\)
\(912\) −4.00000 −0.132453
\(913\) −4.00000 −0.132381
\(914\) 10.0000 0.330771
\(915\) 2.00000 0.0661180
\(916\) 22.0000 0.726900
\(917\) 0 0
\(918\) −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
\(921\) −4.00000 −0.131804
\(922\) −2.00000 −0.0658665
\(923\) 0 0
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) −32.0000 −1.05159
\(927\) −8.00000 −0.262754
\(928\) 6.00000 0.196960
\(929\) −14.0000 −0.459325 −0.229663 − 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 0 0
\(931\) −28.0000 −0.917663
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) 36.0000 1.17796
\(935\) −1.00000 −0.0327035
\(936\) 6.00000 0.196116
\(937\) 58.0000 1.89478 0.947389 − 0.320085i \(-0.103712\pi\)
0.947389 + 0.320085i \(0.103712\pi\)
\(938\) 0 0
\(939\) 6.00000 0.195803
\(940\) −8.00000 −0.260931
\(941\) 6.00000 0.195594 0.0977972 − 0.995206i \(-0.468820\pi\)
0.0977972 + 0.995206i \(0.468820\pi\)
\(942\) −14.0000 −0.456145
\(943\) 0 0
\(944\) 12.0000 0.390567
\(945\) 0 0
\(946\) 4.00000 0.130051
\(947\) −36.0000 −1.16984 −0.584921 − 0.811090i \(-0.698875\pi\)
−0.584921 + 0.811090i \(0.698875\pi\)
\(948\) 8.00000 0.259828
\(949\) −36.0000 −1.16861
\(950\) 4.00000 0.129777
\(951\) 2.00000 0.0648544
\(952\) 0 0
\(953\) −6.00000 −0.194359 −0.0971795 − 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 14.0000 0.453267
\(955\) 8.00000 0.258874
\(956\) −16.0000 −0.517477
\(957\) 6.00000 0.193952
\(958\) 0 0
\(959\) 0 0
\(960\) −1.00000 −0.0322749
\(961\) −31.0000 −1.00000
\(962\) −12.0000 −0.386896
\(963\) 4.00000 0.128898
\(964\) 2.00000 0.0644157
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 − 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 1.00000 0.0321412
\(969\) −4.00000 −0.128499
\(970\) 2.00000 0.0642161
\(971\) 28.0000 0.898563 0.449281 − 0.893390i \(-0.351680\pi\)
0.449281 + 0.893390i \(0.351680\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 0 0
\(974\) −24.0000 −0.769010
\(975\) −6.00000 −0.192154
\(976\) −2.00000 −0.0640184
\(977\) 18.0000 0.575871 0.287936 − 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) −12.0000 −0.383718
\(979\) 6.00000 0.191761
\(980\) −7.00000 −0.223607
\(981\) 14.0000 0.446986
\(982\) 44.0000 1.40410
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 6.00000 0.191273
\(985\) −18.0000 −0.573528
\(986\) 6.00000 0.191079
\(987\) 0 0
\(988\) 24.0000 0.763542
\(989\) 0 0
\(990\) −1.00000 −0.0317821
\(991\) −16.0000 −0.508257 −0.254128 − 0.967170i \(-0.581789\pi\)
−0.254128 + 0.967170i \(0.581789\pi\)
\(992\) 0 0
\(993\) 20.0000 0.634681
\(994\) 0 0
\(995\) −24.0000 −0.760851
\(996\) −4.00000 −0.126745
\(997\) −42.0000 −1.33015 −0.665077 − 0.746775i \(-0.731601\pi\)
−0.665077 + 0.746775i \(0.731601\pi\)
\(998\) −20.0000 −0.633089
\(999\) 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 5610.2.a.bc.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.bc.1.1 ✓ 1 1.1 even 1 trivial