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Properties

Label 4730.2.a.h.1.1
Level $4730$
Weight $2$
Character 4730.1
Self dual yes
Analytic conductor $37.769$
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] = [4730,2,Mod(1,4730)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4730, 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("4730.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4730.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: \(37.7692401561\)
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 \(\chi\) \(=\) 4730.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +2.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +2.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{18} +2.00000 q^{19} -1.00000 q^{20} +2.00000 q^{21} -1.00000 q^{22} -6.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} -5.00000 q^{27} +2.00000 q^{28} -9.00000 q^{29} -1.00000 q^{30} -4.00000 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.00000 q^{35} -2.00000 q^{36} -4.00000 q^{37} +2.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +2.00000 q^{42} +1.00000 q^{43} -1.00000 q^{44} +2.00000 q^{45} -6.00000 q^{46} -6.00000 q^{47} +1.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -4.00000 q^{52} +3.00000 q^{53} -5.00000 q^{54} +1.00000 q^{55} +2.00000 q^{56} +2.00000 q^{57} -9.00000 q^{58} -1.00000 q^{60} -1.00000 q^{61} -4.00000 q^{62} -4.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} -1.00000 q^{66} +2.00000 q^{67} -6.00000 q^{69} -2.00000 q^{70} +12.0000 q^{71} -2.00000 q^{72} +11.0000 q^{73} -4.00000 q^{74} +1.00000 q^{75} +2.00000 q^{76} -2.00000 q^{77} -4.00000 q^{78} -7.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +15.0000 q^{83} +2.00000 q^{84} +1.00000 q^{86} -9.00000 q^{87} -1.00000 q^{88} +2.00000 q^{90} -8.00000 q^{91} -6.00000 q^{92} -4.00000 q^{93} -6.00000 q^{94} -2.00000 q^{95} +1.00000 q^{96} -13.0000 q^{97} -3.00000 q^{98} +2.00000 q^{99} +O(q^{100})\)

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 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 2.00000 0.755929 0.377964 − 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) −1.00000 −0.316228
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 − 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 2.00000 0.534522
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −2.00000 −0.471405
\(19\) 2.00000 0.458831 0.229416 − 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.00000 0.436436
\(22\) −1.00000 −0.213201
\(23\) −6.00000 −1.25109 −0.625543 − 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −4.00000 −0.784465
\(27\) −5.00000 −0.962250
\(28\) 2.00000 0.377964
\(29\) −9.00000 −1.67126 −0.835629 − 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) −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
\(33\) −1.00000 −0.174078
\(34\) 0 0
\(35\) −2.00000 −0.338062
\(36\) −2.00000 −0.333333
\(37\) −4.00000 −0.657596 −0.328798 − 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 2.00000 0.324443
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 2.00000 0.308607
\(43\) 1.00000 0.152499
\(44\) −1.00000 −0.150756
\(45\) 2.00000 0.298142
\(46\) −6.00000 −0.884652
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 1.00000 0.144338
\(49\) −3.00000 −0.428571
\(50\) 1.00000 0.141421
\(51\) 0 0
\(52\) −4.00000 −0.554700
\(53\) 3.00000 0.412082 0.206041 − 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) −5.00000 −0.680414
\(55\) 1.00000 0.134840
\(56\) 2.00000 0.267261
\(57\) 2.00000 0.264906
\(58\) −9.00000 −1.18176
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) −1.00000 −0.128037 −0.0640184 − 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) −4.00000 −0.508001
\(63\) −4.00000 −0.503953
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) −1.00000 −0.123091
\(67\) 2.00000 0.244339 0.122169 − 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) −2.00000 −0.239046
\(71\) 12.0000 1.42414 0.712069 − 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −2.00000 −0.235702
\(73\) 11.0000 1.28745 0.643726 − 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) −4.00000 −0.464991
\(75\) 1.00000 0.115470
\(76\) 2.00000 0.229416
\(77\) −2.00000 −0.227921
\(78\) −4.00000 −0.452911
\(79\) −7.00000 −0.787562 −0.393781 − 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 15.0000 1.64646 0.823232 − 0.567705i \(-0.192169\pi\)
0.823232 + 0.567705i \(0.192169\pi\)
\(84\) 2.00000 0.218218
\(85\) 0 0
\(86\) 1.00000 0.107833
\(87\) −9.00000 −0.964901
\(88\) −1.00000 −0.106600
\(89\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 2.00000 0.210819
\(91\) −8.00000 −0.838628
\(92\) −6.00000 −0.625543
\(93\) −4.00000 −0.414781
\(94\) −6.00000 −0.618853
\(95\) −2.00000 −0.205196
\(96\) 1.00000 0.102062
\(97\) −13.0000 −1.31995 −0.659975 − 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) −3.00000 −0.303046
\(99\) 2.00000 0.201008
\(100\) 1.00000 0.100000
\(101\) 6.00000 0.597022 0.298511 − 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 − 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −4.00000 −0.392232
\(105\) −2.00000 −0.195180
\(106\) 3.00000 0.291386
\(107\) 3.00000 0.290021 0.145010 − 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) −5.00000 −0.481125
\(109\) −16.0000 −1.53252 −0.766261 − 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 1.00000 0.0953463
\(111\) −4.00000 −0.379663
\(112\) 2.00000 0.188982
\(113\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 2.00000 0.187317
\(115\) 6.00000 0.559503
\(116\) −9.00000 −0.835629
\(117\) 8.00000 0.739600
\(118\) 0 0
\(119\) 0 0
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) −1.00000 −0.0894427
\(126\) −4.00000 −0.356348
\(127\) −7.00000 −0.621150 −0.310575 − 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.00000 0.0880451
\(130\) 4.00000 0.350823
\(131\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −1.00000 −0.0870388
\(133\) 4.00000 0.346844
\(134\) 2.00000 0.172774
\(135\) 5.00000 0.430331
\(136\) 0 0
\(137\) 12.0000 1.02523 0.512615 − 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) −6.00000 −0.510754
\(139\) −13.0000 −1.10265 −0.551323 − 0.834292i \(-0.685877\pi\)
−0.551323 + 0.834292i \(0.685877\pi\)
\(140\) −2.00000 −0.169031
\(141\) −6.00000 −0.505291
\(142\) 12.0000 1.00702
\(143\) 4.00000 0.334497
\(144\) −2.00000 −0.166667
\(145\) 9.00000 0.747409
\(146\) 11.0000 0.910366
\(147\) −3.00000 −0.247436
\(148\) −4.00000 −0.328798
\(149\) 15.0000 1.22885 0.614424 − 0.788976i \(-0.289388\pi\)
0.614424 + 0.788976i \(0.289388\pi\)
\(150\) 1.00000 0.0816497
\(151\) −22.0000 −1.79033 −0.895167 − 0.445730i \(-0.852944\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) −2.00000 −0.161165
\(155\) 4.00000 0.321288
\(156\) −4.00000 −0.320256
\(157\) −22.0000 −1.75579 −0.877896 − 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) −7.00000 −0.556890
\(159\) 3.00000 0.237915
\(160\) −1.00000 −0.0790569
\(161\) −12.0000 −0.945732
\(162\) 1.00000 0.0785674
\(163\) −13.0000 −1.01824 −0.509119 − 0.860696i \(-0.670029\pi\)
−0.509119 + 0.860696i \(0.670029\pi\)
\(164\) 0 0
\(165\) 1.00000 0.0778499
\(166\) 15.0000 1.16423
\(167\) 3.00000 0.232147 0.116073 − 0.993241i \(-0.462969\pi\)
0.116073 + 0.993241i \(0.462969\pi\)
\(168\) 2.00000 0.154303
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 1.00000 0.0762493
\(173\) −24.0000 −1.82469 −0.912343 − 0.409426i \(-0.865729\pi\)
−0.912343 + 0.409426i \(0.865729\pi\)
\(174\) −9.00000 −0.682288
\(175\) 2.00000 0.151186
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) 0 0
\(179\) −15.0000 −1.12115 −0.560576 − 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 2.00000 0.149071
\(181\) 23.0000 1.70958 0.854788 − 0.518977i \(-0.173687\pi\)
0.854788 + 0.518977i \(0.173687\pi\)
\(182\) −8.00000 −0.592999
\(183\) −1.00000 −0.0739221
\(184\) −6.00000 −0.442326
\(185\) 4.00000 0.294086
\(186\) −4.00000 −0.293294
\(187\) 0 0
\(188\) −6.00000 −0.437595
\(189\) −10.0000 −0.727393
\(190\) −2.00000 −0.145095
\(191\) 9.00000 0.651217 0.325609 − 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) 1.00000 0.0721688
\(193\) 20.0000 1.43963 0.719816 − 0.694165i \(-0.244226\pi\)
0.719816 + 0.694165i \(0.244226\pi\)
\(194\) −13.0000 −0.933346
\(195\) 4.00000 0.286446
\(196\) −3.00000 −0.214286
\(197\) 12.0000 0.854965 0.427482 − 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 2.00000 0.142134
\(199\) −4.00000 −0.283552 −0.141776 − 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.00000 0.141069
\(202\) 6.00000 0.422159
\(203\) −18.0000 −1.26335
\(204\) 0 0
\(205\) 0 0
\(206\) −10.0000 −0.696733
\(207\) 12.0000 0.834058
\(208\) −4.00000 −0.277350
\(209\) −2.00000 −0.138343
\(210\) −2.00000 −0.138013
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) 3.00000 0.206041
\(213\) 12.0000 0.822226
\(214\) 3.00000 0.205076
\(215\) −1.00000 −0.0681994
\(216\) −5.00000 −0.340207
\(217\) −8.00000 −0.543075
\(218\) −16.0000 −1.08366
\(219\) 11.0000 0.743311
\(220\) 1.00000 0.0674200
\(221\) 0 0
\(222\) −4.00000 −0.268462
\(223\) −19.0000 −1.27233 −0.636167 − 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 2.00000 0.133631
\(225\) −2.00000 −0.133333
\(226\) 0 0
\(227\) 6.00000 0.398234 0.199117 − 0.979976i \(-0.436193\pi\)
0.199117 + 0.979976i \(0.436193\pi\)
\(228\) 2.00000 0.132453
\(229\) 23.0000 1.51988 0.759941 − 0.649992i \(-0.225228\pi\)
0.759941 + 0.649992i \(0.225228\pi\)
\(230\) 6.00000 0.395628
\(231\) −2.00000 −0.131590
\(232\) −9.00000 −0.590879
\(233\) 27.0000 1.76883 0.884414 − 0.466702i \(-0.154558\pi\)
0.884414 + 0.466702i \(0.154558\pi\)
\(234\) 8.00000 0.522976
\(235\) 6.00000 0.391397
\(236\) 0 0
\(237\) −7.00000 −0.454699
\(238\) 0 0
\(239\) 21.0000 1.35838 0.679189 − 0.733964i \(-0.262332\pi\)
0.679189 + 0.733964i \(0.262332\pi\)
\(240\) −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
\(243\) 16.0000 1.02640
\(244\) −1.00000 −0.0640184
\(245\) 3.00000 0.191663
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) −4.00000 −0.254000
\(249\) 15.0000 0.950586
\(250\) −1.00000 −0.0632456
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) −4.00000 −0.251976
\(253\) 6.00000 0.377217
\(254\) −7.00000 −0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 1.00000 0.0622573
\(259\) −8.00000 −0.497096
\(260\) 4.00000 0.248069
\(261\) 18.0000 1.11417
\(262\) 0 0
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −3.00000 −0.184289
\(266\) 4.00000 0.245256
\(267\) 0 0
\(268\) 2.00000 0.122169
\(269\) −15.0000 −0.914566 −0.457283 − 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(270\) 5.00000 0.304290
\(271\) −4.00000 −0.242983 −0.121491 − 0.992592i \(-0.538768\pi\)
−0.121491 + 0.992592i \(0.538768\pi\)
\(272\) 0 0
\(273\) −8.00000 −0.484182
\(274\) 12.0000 0.724947
\(275\) −1.00000 −0.0603023
\(276\) −6.00000 −0.361158
\(277\) −10.0000 −0.600842 −0.300421 − 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −13.0000 −0.779688
\(279\) 8.00000 0.478947
\(280\) −2.00000 −0.119523
\(281\) 24.0000 1.43172 0.715860 − 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) −6.00000 −0.357295
\(283\) −13.0000 −0.772770 −0.386385 − 0.922338i \(-0.626276\pi\)
−0.386385 + 0.922338i \(0.626276\pi\)
\(284\) 12.0000 0.712069
\(285\) −2.00000 −0.118470
\(286\) 4.00000 0.236525
\(287\) 0 0
\(288\) −2.00000 −0.117851
\(289\) −17.0000 −1.00000
\(290\) 9.00000 0.528498
\(291\) −13.0000 −0.762073
\(292\) 11.0000 0.643726
\(293\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) −3.00000 −0.174964
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 5.00000 0.290129
\(298\) 15.0000 0.868927
\(299\) 24.0000 1.38796
\(300\) 1.00000 0.0577350
\(301\) 2.00000 0.115278
\(302\) −22.0000 −1.26596
\(303\) 6.00000 0.344691
\(304\) 2.00000 0.114708
\(305\) 1.00000 0.0572598
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 − 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) −2.00000 −0.113961
\(309\) −10.0000 −0.568880
\(310\) 4.00000 0.227185
\(311\) −18.0000 −1.02069 −0.510343 − 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) −4.00000 −0.226455
\(313\) −4.00000 −0.226093 −0.113047 − 0.993590i \(-0.536061\pi\)
−0.113047 + 0.993590i \(0.536061\pi\)
\(314\) −22.0000 −1.24153
\(315\) 4.00000 0.225374
\(316\) −7.00000 −0.393781
\(317\) 15.0000 0.842484 0.421242 − 0.906948i \(-0.361594\pi\)
0.421242 + 0.906948i \(0.361594\pi\)
\(318\) 3.00000 0.168232
\(319\) 9.00000 0.503903
\(320\) −1.00000 −0.0559017
\(321\) 3.00000 0.167444
\(322\) −12.0000 −0.668734
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) −13.0000 −0.720003
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) −12.0000 −0.661581
\(330\) 1.00000 0.0550482
\(331\) 20.0000 1.09930 0.549650 − 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) 15.0000 0.823232
\(333\) 8.00000 0.438397
\(334\) 3.00000 0.164153
\(335\) −2.00000 −0.109272
\(336\) 2.00000 0.109109
\(337\) −22.0000 −1.19842 −0.599208 − 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) 3.00000 0.163178
\(339\) 0 0
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) −4.00000 −0.216295
\(343\) −20.0000 −1.07990
\(344\) 1.00000 0.0539164
\(345\) 6.00000 0.323029
\(346\) −24.0000 −1.29025
\(347\) −36.0000 −1.93258 −0.966291 − 0.257454i \(-0.917117\pi\)
−0.966291 + 0.257454i \(0.917117\pi\)
\(348\) −9.00000 −0.482451
\(349\) 26.0000 1.39175 0.695874 − 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 2.00000 0.106904
\(351\) 20.0000 1.06752
\(352\) −1.00000 −0.0533002
\(353\) −9.00000 −0.479022 −0.239511 − 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 0 0
\(355\) −12.0000 −0.636894
\(356\) 0 0
\(357\) 0 0
\(358\) −15.0000 −0.792775
\(359\) 3.00000 0.158334 0.0791670 − 0.996861i \(-0.474774\pi\)
0.0791670 + 0.996861i \(0.474774\pi\)
\(360\) 2.00000 0.105409
\(361\) −15.0000 −0.789474
\(362\) 23.0000 1.20885
\(363\) 1.00000 0.0524864
\(364\) −8.00000 −0.419314
\(365\) −11.0000 −0.575766
\(366\) −1.00000 −0.0522708
\(367\) 26.0000 1.35719 0.678594 − 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 4.00000 0.207950
\(371\) 6.00000 0.311504
\(372\) −4.00000 −0.207390
\(373\) −13.0000 −0.673114 −0.336557 − 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) 0 0
\(375\) −1.00000 −0.0516398
\(376\) −6.00000 −0.309426
\(377\) 36.0000 1.85409
\(378\) −10.0000 −0.514344
\(379\) 2.00000 0.102733 0.0513665 − 0.998680i \(-0.483642\pi\)
0.0513665 + 0.998680i \(0.483642\pi\)
\(380\) −2.00000 −0.102598
\(381\) −7.00000 −0.358621
\(382\) 9.00000 0.460480
\(383\) −33.0000 −1.68622 −0.843111 − 0.537740i \(-0.819278\pi\)
−0.843111 + 0.537740i \(0.819278\pi\)
\(384\) 1.00000 0.0510310
\(385\) 2.00000 0.101929
\(386\) 20.0000 1.01797
\(387\) −2.00000 −0.101666
\(388\) −13.0000 −0.659975
\(389\) −6.00000 −0.304212 −0.152106 − 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 4.00000 0.202548
\(391\) 0 0
\(392\) −3.00000 −0.151523
\(393\) 0 0
\(394\) 12.0000 0.604551
\(395\) 7.00000 0.352208
\(396\) 2.00000 0.100504
\(397\) 29.0000 1.45547 0.727734 − 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) −4.00000 −0.200502
\(399\) 4.00000 0.200250
\(400\) 1.00000 0.0500000
\(401\) 3.00000 0.149813 0.0749064 − 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 2.00000 0.0997509
\(403\) 16.0000 0.797017
\(404\) 6.00000 0.298511
\(405\) −1.00000 −0.0496904
\(406\) −18.0000 −0.893325
\(407\) 4.00000 0.198273
\(408\) 0 0
\(409\) −13.0000 −0.642809 −0.321404 − 0.946942i \(-0.604155\pi\)
−0.321404 + 0.946942i \(0.604155\pi\)
\(410\) 0 0
\(411\) 12.0000 0.591916
\(412\) −10.0000 −0.492665
\(413\) 0 0
\(414\) 12.0000 0.589768
\(415\) −15.0000 −0.736321
\(416\) −4.00000 −0.196116
\(417\) −13.0000 −0.636613
\(418\) −2.00000 −0.0978232
\(419\) −15.0000 −0.732798 −0.366399 − 0.930458i \(-0.619409\pi\)
−0.366399 + 0.930458i \(0.619409\pi\)
\(420\) −2.00000 −0.0975900
\(421\) 8.00000 0.389896 0.194948 − 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 20.0000 0.973585
\(423\) 12.0000 0.583460
\(424\) 3.00000 0.145693
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) −2.00000 −0.0967868
\(428\) 3.00000 0.145010
\(429\) 4.00000 0.193122
\(430\) −1.00000 −0.0482243
\(431\) −36.0000 −1.73406 −0.867029 − 0.498257i \(-0.833974\pi\)
−0.867029 + 0.498257i \(0.833974\pi\)
\(432\) −5.00000 −0.240563
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) −8.00000 −0.384012
\(435\) 9.00000 0.431517
\(436\) −16.0000 −0.766261
\(437\) −12.0000 −0.574038
\(438\) 11.0000 0.525600
\(439\) 8.00000 0.381819 0.190910 − 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 1.00000 0.0476731
\(441\) 6.00000 0.285714
\(442\) 0 0
\(443\) 18.0000 0.855206 0.427603 − 0.903967i \(-0.359358\pi\)
0.427603 + 0.903967i \(0.359358\pi\)
\(444\) −4.00000 −0.189832
\(445\) 0 0
\(446\) −19.0000 −0.899676
\(447\) 15.0000 0.709476
\(448\) 2.00000 0.0944911
\(449\) −30.0000 −1.41579 −0.707894 − 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) −2.00000 −0.0942809
\(451\) 0 0
\(452\) 0 0
\(453\) −22.0000 −1.03365
\(454\) 6.00000 0.281594
\(455\) 8.00000 0.375046
\(456\) 2.00000 0.0936586
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 23.0000 1.07472
\(459\) 0 0
\(460\) 6.00000 0.279751
\(461\) −12.0000 −0.558896 −0.279448 − 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) −2.00000 −0.0930484
\(463\) 8.00000 0.371792 0.185896 − 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −9.00000 −0.417815
\(465\) 4.00000 0.185496
\(466\) 27.0000 1.25075
\(467\) −12.0000 −0.555294 −0.277647 − 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 8.00000 0.369800
\(469\) 4.00000 0.184703
\(470\) 6.00000 0.276759
\(471\) −22.0000 −1.01371
\(472\) 0 0
\(473\) −1.00000 −0.0459800
\(474\) −7.00000 −0.321521
\(475\) 2.00000 0.0917663
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 21.0000 0.960518
\(479\) 21.0000 0.959514 0.479757 − 0.877401i \(-0.340725\pi\)
0.479757 + 0.877401i \(0.340725\pi\)
\(480\) −1.00000 −0.0456435
\(481\) 16.0000 0.729537
\(482\) 2.00000 0.0910975
\(483\) −12.0000 −0.546019
\(484\) 1.00000 0.0454545
\(485\) 13.0000 0.590300
\(486\) 16.0000 0.725775
\(487\) 14.0000 0.634401 0.317200 − 0.948359i \(-0.397257\pi\)
0.317200 + 0.948359i \(0.397257\pi\)
\(488\) −1.00000 −0.0452679
\(489\) −13.0000 −0.587880
\(490\) 3.00000 0.135526
\(491\) −30.0000 −1.35388 −0.676941 − 0.736038i \(-0.736695\pi\)
−0.676941 + 0.736038i \(0.736695\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −8.00000 −0.359937
\(495\) −2.00000 −0.0898933
\(496\) −4.00000 −0.179605
\(497\) 24.0000 1.07655
\(498\) 15.0000 0.672166
\(499\) 5.00000 0.223831 0.111915 − 0.993718i \(-0.464301\pi\)
0.111915 + 0.993718i \(0.464301\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 3.00000 0.134030
\(502\) −6.00000 −0.267793
\(503\) 12.0000 0.535054 0.267527 − 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −4.00000 −0.178174
\(505\) −6.00000 −0.266996
\(506\) 6.00000 0.266733
\(507\) 3.00000 0.133235
\(508\) −7.00000 −0.310575
\(509\) 30.0000 1.32973 0.664863 − 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 0 0
\(511\) 22.0000 0.973223
\(512\) 1.00000 0.0441942
\(513\) −10.0000 −0.441511
\(514\) 6.00000 0.264649
\(515\) 10.0000 0.440653
\(516\) 1.00000 0.0440225
\(517\) 6.00000 0.263880
\(518\) −8.00000 −0.351500
\(519\) −24.0000 −1.05348
\(520\) 4.00000 0.175412
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 18.0000 0.787839
\(523\) 8.00000 0.349816 0.174908 − 0.984585i \(-0.444037\pi\)
0.174908 + 0.984585i \(0.444037\pi\)
\(524\) 0 0
\(525\) 2.00000 0.0872872
\(526\) −24.0000 −1.04645
\(527\) 0 0
\(528\) −1.00000 −0.0435194
\(529\) 13.0000 0.565217
\(530\) −3.00000 −0.130312
\(531\) 0 0
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) 0 0
\(535\) −3.00000 −0.129701
\(536\) 2.00000 0.0863868
\(537\) −15.0000 −0.647298
\(538\) −15.0000 −0.646696
\(539\) 3.00000 0.129219
\(540\) 5.00000 0.215166
\(541\) 14.0000 0.601907 0.300954 − 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) −4.00000 −0.171815
\(543\) 23.0000 0.987024
\(544\) 0 0
\(545\) 16.0000 0.685365
\(546\) −8.00000 −0.342368
\(547\) 17.0000 0.726868 0.363434 − 0.931620i \(-0.381604\pi\)
0.363434 + 0.931620i \(0.381604\pi\)
\(548\) 12.0000 0.512615
\(549\) 2.00000 0.0853579
\(550\) −1.00000 −0.0426401
\(551\) −18.0000 −0.766826
\(552\) −6.00000 −0.255377
\(553\) −14.0000 −0.595341
\(554\) −10.0000 −0.424859
\(555\) 4.00000 0.169791
\(556\) −13.0000 −0.551323
\(557\) −6.00000 −0.254228 −0.127114 − 0.991888i \(-0.540571\pi\)
−0.127114 + 0.991888i \(0.540571\pi\)
\(558\) 8.00000 0.338667
\(559\) −4.00000 −0.169182
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 24.0000 1.01238
\(563\) 12.0000 0.505740 0.252870 − 0.967500i \(-0.418626\pi\)
0.252870 + 0.967500i \(0.418626\pi\)
\(564\) −6.00000 −0.252646
\(565\) 0 0
\(566\) −13.0000 −0.546431
\(567\) 2.00000 0.0839921
\(568\) 12.0000 0.503509
\(569\) −6.00000 −0.251533 −0.125767 − 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) −2.00000 −0.0837708
\(571\) 14.0000 0.585882 0.292941 − 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) 4.00000 0.167248
\(573\) 9.00000 0.375980
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) −2.00000 −0.0833333
\(577\) −4.00000 −0.166522 −0.0832611 − 0.996528i \(-0.526534\pi\)
−0.0832611 + 0.996528i \(0.526534\pi\)
\(578\) −17.0000 −0.707107
\(579\) 20.0000 0.831172
\(580\) 9.00000 0.373705
\(581\) 30.0000 1.24461
\(582\) −13.0000 −0.538867
\(583\) −3.00000 −0.124247
\(584\) 11.0000 0.455183
\(585\) −8.00000 −0.330759
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 − 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) −3.00000 −0.123718
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) 12.0000 0.493614
\(592\) −4.00000 −0.164399
\(593\) 21.0000 0.862367 0.431183 − 0.902264i \(-0.358096\pi\)
0.431183 + 0.902264i \(0.358096\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) 15.0000 0.614424
\(597\) −4.00000 −0.163709
\(598\) 24.0000 0.981433
\(599\) −36.0000 −1.47092 −0.735460 − 0.677568i \(-0.763034\pi\)
−0.735460 + 0.677568i \(0.763034\pi\)
\(600\) 1.00000 0.0408248
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 2.00000 0.0815139
\(603\) −4.00000 −0.162893
\(604\) −22.0000 −0.895167
\(605\) −1.00000 −0.0406558
\(606\) 6.00000 0.243733
\(607\) 14.0000 0.568242 0.284121 − 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 2.00000 0.0811107
\(609\) −18.0000 −0.729397
\(610\) 1.00000 0.0404888
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) −34.0000 −1.37325 −0.686624 − 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 11.0000 0.443924
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) −18.0000 −0.724653 −0.362326 − 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) −10.0000 −0.402259
\(619\) −28.0000 −1.12542 −0.562708 − 0.826656i \(-0.690240\pi\)
−0.562708 + 0.826656i \(0.690240\pi\)
\(620\) 4.00000 0.160644
\(621\) 30.0000 1.20386
\(622\) −18.0000 −0.721734
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) −4.00000 −0.159872
\(627\) −2.00000 −0.0798723
\(628\) −22.0000 −0.877896
\(629\) 0 0
\(630\) 4.00000 0.159364
\(631\) 23.0000 0.915616 0.457808 − 0.889051i \(-0.348635\pi\)
0.457808 + 0.889051i \(0.348635\pi\)
\(632\) −7.00000 −0.278445
\(633\) 20.0000 0.794929
\(634\) 15.0000 0.595726
\(635\) 7.00000 0.277787
\(636\) 3.00000 0.118958
\(637\) 12.0000 0.475457
\(638\) 9.00000 0.356313
\(639\) −24.0000 −0.949425
\(640\) −1.00000 −0.0395285
\(641\) 42.0000 1.65890 0.829450 − 0.558581i \(-0.188654\pi\)
0.829450 + 0.558581i \(0.188654\pi\)
\(642\) 3.00000 0.118401
\(643\) −22.0000 −0.867595 −0.433798 − 0.901010i \(-0.642827\pi\)
−0.433798 + 0.901010i \(0.642827\pi\)
\(644\) −12.0000 −0.472866
\(645\) −1.00000 −0.0393750
\(646\) 0 0
\(647\) 33.0000 1.29736 0.648682 − 0.761060i \(-0.275321\pi\)
0.648682 + 0.761060i \(0.275321\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) −8.00000 −0.313545
\(652\) −13.0000 −0.509119
\(653\) 42.0000 1.64359 0.821794 − 0.569785i \(-0.192974\pi\)
0.821794 + 0.569785i \(0.192974\pi\)
\(654\) −16.0000 −0.625650
\(655\) 0 0
\(656\) 0 0
\(657\) −22.0000 −0.858302
\(658\) −12.0000 −0.467809
\(659\) −33.0000 −1.28550 −0.642749 − 0.766077i \(-0.722206\pi\)
−0.642749 + 0.766077i \(0.722206\pi\)
\(660\) 1.00000 0.0389249
\(661\) −25.0000 −0.972387 −0.486194 − 0.873851i \(-0.661615\pi\)
−0.486194 + 0.873851i \(0.661615\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) 15.0000 0.582113
\(665\) −4.00000 −0.155113
\(666\) 8.00000 0.309994
\(667\) 54.0000 2.09089
\(668\) 3.00000 0.116073
\(669\) −19.0000 −0.734582
\(670\) −2.00000 −0.0772667
\(671\) 1.00000 0.0386046
\(672\) 2.00000 0.0771517
\(673\) 41.0000 1.58043 0.790217 − 0.612827i \(-0.209968\pi\)
0.790217 + 0.612827i \(0.209968\pi\)
\(674\) −22.0000 −0.847408
\(675\) −5.00000 −0.192450
\(676\) 3.00000 0.115385
\(677\) 45.0000 1.72949 0.864745 − 0.502211i \(-0.167480\pi\)
0.864745 + 0.502211i \(0.167480\pi\)
\(678\) 0 0
\(679\) −26.0000 −0.997788
\(680\) 0 0
\(681\) 6.00000 0.229920
\(682\) 4.00000 0.153168
\(683\) 48.0000 1.83667 0.918334 − 0.395805i \(-0.129534\pi\)
0.918334 + 0.395805i \(0.129534\pi\)
\(684\) −4.00000 −0.152944
\(685\) −12.0000 −0.458496
\(686\) −20.0000 −0.763604
\(687\) 23.0000 0.877505
\(688\) 1.00000 0.0381246
\(689\) −12.0000 −0.457164
\(690\) 6.00000 0.228416
\(691\) −37.0000 −1.40755 −0.703773 − 0.710425i \(-0.748503\pi\)
−0.703773 + 0.710425i \(0.748503\pi\)
\(692\) −24.0000 −0.912343
\(693\) 4.00000 0.151947
\(694\) −36.0000 −1.36654
\(695\) 13.0000 0.493118
\(696\) −9.00000 −0.341144
\(697\) 0 0
\(698\) 26.0000 0.984115
\(699\) 27.0000 1.02123
\(700\) 2.00000 0.0755929
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 20.0000 0.754851
\(703\) −8.00000 −0.301726
\(704\) −1.00000 −0.0376889
\(705\) 6.00000 0.225973
\(706\) −9.00000 −0.338719
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) −7.00000 −0.262891 −0.131445 − 0.991323i \(-0.541962\pi\)
−0.131445 + 0.991323i \(0.541962\pi\)
\(710\) −12.0000 −0.450352
\(711\) 14.0000 0.525041
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) −4.00000 −0.149592
\(716\) −15.0000 −0.560576
\(717\) 21.0000 0.784259
\(718\) 3.00000 0.111959
\(719\) 42.0000 1.56634 0.783168 − 0.621810i \(-0.213603\pi\)
0.783168 + 0.621810i \(0.213603\pi\)
\(720\) 2.00000 0.0745356
\(721\) −20.0000 −0.744839
\(722\) −15.0000 −0.558242
\(723\) 2.00000 0.0743808
\(724\) 23.0000 0.854788
\(725\) −9.00000 −0.334252
\(726\) 1.00000 0.0371135
\(727\) −1.00000 −0.0370879 −0.0185440 − 0.999828i \(-0.505903\pi\)
−0.0185440 + 0.999828i \(0.505903\pi\)
\(728\) −8.00000 −0.296500
\(729\) 13.0000 0.481481
\(730\) −11.0000 −0.407128
\(731\) 0 0
\(732\) −1.00000 −0.0369611
\(733\) −13.0000 −0.480166 −0.240083 − 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(734\) 26.0000 0.959678
\(735\) 3.00000 0.110657
\(736\) −6.00000 −0.221163
\(737\) −2.00000 −0.0736709
\(738\) 0 0
\(739\) −16.0000 −0.588570 −0.294285 − 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 4.00000 0.147043
\(741\) −8.00000 −0.293887
\(742\) 6.00000 0.220267
\(743\) 30.0000 1.10059 0.550297 − 0.834969i \(-0.314515\pi\)
0.550297 + 0.834969i \(0.314515\pi\)
\(744\) −4.00000 −0.146647
\(745\) −15.0000 −0.549557
\(746\) −13.0000 −0.475964
\(747\) −30.0000 −1.09764
\(748\) 0 0
\(749\) 6.00000 0.219235
\(750\) −1.00000 −0.0365148
\(751\) 23.0000 0.839282 0.419641 − 0.907690i \(-0.362156\pi\)
0.419641 + 0.907690i \(0.362156\pi\)
\(752\) −6.00000 −0.218797
\(753\) −6.00000 −0.218652
\(754\) 36.0000 1.31104
\(755\) 22.0000 0.800662
\(756\) −10.0000 −0.363696
\(757\) −46.0000 −1.67190 −0.835949 − 0.548807i \(-0.815082\pi\)
−0.835949 + 0.548807i \(0.815082\pi\)
\(758\) 2.00000 0.0726433
\(759\) 6.00000 0.217786
\(760\) −2.00000 −0.0725476
\(761\) −21.0000 −0.761249 −0.380625 − 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) −7.00000 −0.253583
\(763\) −32.0000 −1.15848
\(764\) 9.00000 0.325609
\(765\) 0 0
\(766\) −33.0000 −1.19234
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) 2.00000 0.0721218 0.0360609 − 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 2.00000 0.0720750
\(771\) 6.00000 0.216085
\(772\) 20.0000 0.719816
\(773\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(774\) −2.00000 −0.0718885
\(775\) −4.00000 −0.143684
\(776\) −13.0000 −0.466673
\(777\) −8.00000 −0.286998
\(778\) −6.00000 −0.215110
\(779\) 0 0
\(780\) 4.00000 0.143223
\(781\) −12.0000 −0.429394
\(782\) 0 0
\(783\) 45.0000 1.60817
\(784\) −3.00000 −0.107143
\(785\) 22.0000 0.785214
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 − 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 12.0000 0.427482
\(789\) −24.0000 −0.854423
\(790\) 7.00000 0.249049
\(791\) 0 0
\(792\) 2.00000 0.0710669
\(793\) 4.00000 0.142044
\(794\) 29.0000 1.02917
\(795\) −3.00000 −0.106399
\(796\) −4.00000 −0.141776
\(797\) −30.0000 −1.06265 −0.531327 − 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 4.00000 0.141598
\(799\) 0 0
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) 3.00000 0.105934
\(803\) −11.0000 −0.388182
\(804\) 2.00000 0.0705346
\(805\) 12.0000 0.422944
\(806\) 16.0000 0.563576
\(807\) −15.0000 −0.528025
\(808\) 6.00000 0.211079
\(809\) −36.0000 −1.26569 −0.632846 − 0.774277i \(-0.718114\pi\)
−0.632846 + 0.774277i \(0.718114\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 38.0000 1.33436 0.667180 − 0.744896i \(-0.267501\pi\)
0.667180 + 0.744896i \(0.267501\pi\)
\(812\) −18.0000 −0.631676
\(813\) −4.00000 −0.140286
\(814\) 4.00000 0.140200
\(815\) 13.0000 0.455370
\(816\) 0 0
\(817\) 2.00000 0.0699711
\(818\) −13.0000 −0.454534
\(819\) 16.0000 0.559085
\(820\) 0 0
\(821\) −24.0000 −0.837606 −0.418803 − 0.908077i \(-0.637550\pi\)
−0.418803 + 0.908077i \(0.637550\pi\)
\(822\) 12.0000 0.418548
\(823\) 2.00000 0.0697156 0.0348578 − 0.999392i \(-0.488902\pi\)
0.0348578 + 0.999392i \(0.488902\pi\)
\(824\) −10.0000 −0.348367
\(825\) −1.00000 −0.0348155
\(826\) 0 0
\(827\) 45.0000 1.56480 0.782402 − 0.622774i \(-0.213994\pi\)
0.782402 + 0.622774i \(0.213994\pi\)
\(828\) 12.0000 0.417029
\(829\) 20.0000 0.694629 0.347314 − 0.937749i \(-0.387094\pi\)
0.347314 + 0.937749i \(0.387094\pi\)
\(830\) −15.0000 −0.520658
\(831\) −10.0000 −0.346896
\(832\) −4.00000 −0.138675
\(833\) 0 0
\(834\) −13.0000 −0.450153
\(835\) −3.00000 −0.103819
\(836\) −2.00000 −0.0691714
\(837\) 20.0000 0.691301
\(838\) −15.0000 −0.518166
\(839\) −21.0000 −0.725001 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) −2.00000 −0.0690066
\(841\) 52.0000 1.79310
\(842\) 8.00000 0.275698
\(843\) 24.0000 0.826604
\(844\) 20.0000 0.688428
\(845\) −3.00000 −0.103203
\(846\) 12.0000 0.412568
\(847\) 2.00000 0.0687208
\(848\) 3.00000 0.103020
\(849\) −13.0000 −0.446159
\(850\) 0 0
\(851\) 24.0000 0.822709
\(852\) 12.0000 0.411113
\(853\) −46.0000 −1.57501 −0.787505 − 0.616308i \(-0.788628\pi\)
−0.787505 + 0.616308i \(0.788628\pi\)
\(854\) −2.00000 −0.0684386
\(855\) 4.00000 0.136797
\(856\) 3.00000 0.102538
\(857\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(858\) 4.00000 0.136558
\(859\) −40.0000 −1.36478 −0.682391 − 0.730987i \(-0.739060\pi\)
−0.682391 + 0.730987i \(0.739060\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 0 0
\(862\) −36.0000 −1.22616
\(863\) −39.0000 −1.32758 −0.663788 − 0.747921i \(-0.731052\pi\)
−0.663788 + 0.747921i \(0.731052\pi\)
\(864\) −5.00000 −0.170103
\(865\) 24.0000 0.816024
\(866\) −16.0000 −0.543702
\(867\) −17.0000 −0.577350
\(868\) −8.00000 −0.271538
\(869\) 7.00000 0.237459
\(870\) 9.00000 0.305129
\(871\) −8.00000 −0.271070
\(872\) −16.0000 −0.541828
\(873\) 26.0000 0.879967
\(874\) −12.0000 −0.405906
\(875\) −2.00000 −0.0676123
\(876\) 11.0000 0.371656
\(877\) 20.0000 0.675352 0.337676 − 0.941262i \(-0.390359\pi\)
0.337676 + 0.941262i \(0.390359\pi\)
\(878\) 8.00000 0.269987
\(879\) 0 0
\(880\) 1.00000 0.0337100
\(881\) 3.00000 0.101073 0.0505363 − 0.998722i \(-0.483907\pi\)
0.0505363 + 0.998722i \(0.483907\pi\)
\(882\) 6.00000 0.202031
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 18.0000 0.604722
\(887\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) −4.00000 −0.134231
\(889\) −14.0000 −0.469545
\(890\) 0 0
\(891\) −1.00000 −0.0335013
\(892\) −19.0000 −0.636167
\(893\) −12.0000 −0.401565
\(894\) 15.0000 0.501675
\(895\) 15.0000 0.501395
\(896\) 2.00000 0.0668153
\(897\) 24.0000 0.801337
\(898\) −30.0000 −1.00111
\(899\) 36.0000 1.20067
\(900\) −2.00000 −0.0666667
\(901\) 0 0
\(902\) 0 0
\(903\) 2.00000 0.0665558
\(904\) 0 0
\(905\) −23.0000 −0.764546
\(906\) −22.0000 −0.730901
\(907\) −10.0000 −0.332045 −0.166022 − 0.986122i \(-0.553092\pi\)
−0.166022 + 0.986122i \(0.553092\pi\)
\(908\) 6.00000 0.199117
\(909\) −12.0000 −0.398015
\(910\) 8.00000 0.265197
\(911\) −45.0000 −1.49092 −0.745458 − 0.666552i \(-0.767769\pi\)
−0.745458 + 0.666552i \(0.767769\pi\)
\(912\) 2.00000 0.0662266
\(913\) −15.0000 −0.496428
\(914\) −10.0000 −0.330771
\(915\) 1.00000 0.0330590
\(916\) 23.0000 0.759941
\(917\) 0 0
\(918\) 0 0
\(919\) −25.0000 −0.824674 −0.412337 − 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 6.00000 0.197814
\(921\) 11.0000 0.362462
\(922\) −12.0000 −0.395199
\(923\) −48.0000 −1.57994
\(924\) −2.00000 −0.0657952
\(925\) −4.00000 −0.131519
\(926\) 8.00000 0.262896
\(927\) 20.0000 0.656886
\(928\) −9.00000 −0.295439
\(929\) 36.0000 1.18112 0.590561 − 0.806993i \(-0.298907\pi\)
0.590561 + 0.806993i \(0.298907\pi\)
\(930\) 4.00000 0.131165
\(931\) −6.00000 −0.196642
\(932\) 27.0000 0.884414
\(933\) −18.0000 −0.589294
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) 8.00000 0.261488
\(937\) −55.0000 −1.79677 −0.898386 − 0.439207i \(-0.855259\pi\)
−0.898386 + 0.439207i \(0.855259\pi\)
\(938\) 4.00000 0.130605
\(939\) −4.00000 −0.130535
\(940\) 6.00000 0.195698
\(941\) 48.0000 1.56476 0.782378 − 0.622804i \(-0.214007\pi\)
0.782378 + 0.622804i \(0.214007\pi\)
\(942\) −22.0000 −0.716799
\(943\) 0 0
\(944\) 0 0
\(945\) 10.0000 0.325300
\(946\) −1.00000 −0.0325128
\(947\) 30.0000 0.974869 0.487435 − 0.873160i \(-0.337933\pi\)
0.487435 + 0.873160i \(0.337933\pi\)
\(948\) −7.00000 −0.227349
\(949\) −44.0000 −1.42830
\(950\) 2.00000 0.0648886
\(951\) 15.0000 0.486408
\(952\) 0 0
\(953\) −57.0000 −1.84641 −0.923206 − 0.384307i \(-0.874441\pi\)
−0.923206 + 0.384307i \(0.874441\pi\)
\(954\) −6.00000 −0.194257
\(955\) −9.00000 −0.291233
\(956\) 21.0000 0.679189
\(957\) 9.00000 0.290929
\(958\) 21.0000 0.678479
\(959\) 24.0000 0.775000
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) 16.0000 0.515861
\(963\) −6.00000 −0.193347
\(964\) 2.00000 0.0644157
\(965\) −20.0000 −0.643823
\(966\) −12.0000 −0.386094
\(967\) 47.0000 1.51142 0.755709 − 0.654907i \(-0.227292\pi\)
0.755709 + 0.654907i \(0.227292\pi\)
\(968\) 1.00000 0.0321412
\(969\) 0 0
\(970\) 13.0000 0.417405
\(971\) 12.0000 0.385098 0.192549 − 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 16.0000 0.513200
\(973\) −26.0000 −0.833522
\(974\) 14.0000 0.448589
\(975\) −4.00000 −0.128103
\(976\) −1.00000 −0.0320092
\(977\) 3.00000 0.0959785 0.0479893 − 0.998848i \(-0.484719\pi\)
0.0479893 + 0.998848i \(0.484719\pi\)
\(978\) −13.0000 −0.415694
\(979\) 0 0
\(980\) 3.00000 0.0958315
\(981\) 32.0000 1.02168
\(982\) −30.0000 −0.957338
\(983\) −48.0000 −1.53096 −0.765481 − 0.643458i \(-0.777499\pi\)
−0.765481 + 0.643458i \(0.777499\pi\)
\(984\) 0 0
\(985\) −12.0000 −0.382352
\(986\) 0 0
\(987\) −12.0000 −0.381964
\(988\) −8.00000 −0.254514
\(989\) −6.00000 −0.190789
\(990\) −2.00000 −0.0635642
\(991\) −1.00000 −0.0317660 −0.0158830 − 0.999874i \(-0.505056\pi\)
−0.0158830 + 0.999874i \(0.505056\pi\)
\(992\) −4.00000 −0.127000
\(993\) 20.0000 0.634681
\(994\) 24.0000 0.761234
\(995\) 4.00000 0.126809
\(996\) 15.0000 0.475293
\(997\) −10.0000 −0.316703 −0.158352 − 0.987383i \(-0.550618\pi\)
−0.158352 + 0.987383i \(0.550618\pi\)
\(998\) 5.00000 0.158272
\(999\) 20.0000 0.632772
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 4730.2.a.h.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4730.2.a.h.1.1 ✓ 1 1.1 even 1 trivial