↑

Properties

Label 2310.2.a.v.1.1
Level $2310$
Weight $2$
Character 2310.1
Self dual yes
Analytic conductor $18.445$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2310,2,Mod(1,2310)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2310, 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("2310.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.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: \(18.4454428669\)
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 \(\chi\) \(=\) 2310.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.00000 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} -1.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +6.00000 q^{29} +1.00000 q^{30} +1.00000 q^{32} -1.00000 q^{33} -2.00000 q^{34} -1.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} +4.00000 q^{38} +2.00000 q^{39} +1.00000 q^{40} +10.0000 q^{41} -1.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +4.00000 q^{46} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -2.00000 q^{51} +2.00000 q^{52} -2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -1.00000 q^{56} +4.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} +1.00000 q^{60} -10.0000 q^{61} -1.00000 q^{63} +1.00000 q^{64} +2.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} -2.00000 q^{68} +4.00000 q^{69} -1.00000 q^{70} +1.00000 q^{72} +2.00000 q^{73} -6.00000 q^{74} +1.00000 q^{75} +4.00000 q^{76} +1.00000 q^{77} +2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0000 q^{82} -4.00000 q^{83} -1.00000 q^{84} -2.00000 q^{85} +4.00000 q^{86} +6.00000 q^{87} -1.00000 q^{88} -2.00000 q^{89} +1.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} +4.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} +1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
\(7\) −1.00000 −0.377964
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) −1.00000 −0.301511
\(12\) 1.00000 0.288675
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) −1.00000 −0.267261
\(15\) 1.00000 0.258199
\(16\) 1.00000 0.250000
\(17\) −2.00000 −0.485071 −0.242536 − 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 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
\(21\) −1.00000 −0.218218
\(22\) −1.00000 −0.213201
\(23\) 4.00000 0.834058 0.417029 − 0.908893i \(-0.363071\pi\)
0.417029 + 0.908893i \(0.363071\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 2.00000 0.392232
\(27\) 1.00000 0.192450
\(28\) −1.00000 −0.188982
\(29\) 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
\(34\) −2.00000 −0.342997
\(35\) −1.00000 −0.169031
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 − 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) 4.00000 0.648886
\(39\) 2.00000 0.320256
\(40\) 1.00000 0.158114
\(41\) 10.0000 1.56174 0.780869 − 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) −1.00000 −0.154303
\(43\) 4.00000 0.609994 0.304997 − 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) 4.00000 0.589768
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) 1.00000 0.141421
\(51\) −2.00000 −0.280056
\(52\) 2.00000 0.277350
\(53\) −2.00000 −0.274721 −0.137361 − 0.990521i \(-0.543862\pi\)
−0.137361 + 0.990521i \(0.543862\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) −1.00000 −0.133631
\(57\) 4.00000 0.529813
\(58\) 6.00000 0.787839
\(59\) 4.00000 0.520756 0.260378 − 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 1.00000 0.129099
\(61\) −10.0000 −1.28037 −0.640184 − 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 1.00000 0.125000
\(65\) 2.00000 0.248069
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 − 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −2.00000 −0.242536
\(69\) 4.00000 0.481543
\(70\) −1.00000 −0.119523
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 1.00000 0.117851
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −6.00000 −0.697486
\(75\) 1.00000 0.115470
\(76\) 4.00000 0.458831
\(77\) 1.00000 0.113961
\(78\) 2.00000 0.226455
\(79\) −8.00000 −0.900070 −0.450035 − 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) 10.0000 1.10432
\(83\) −4.00000 −0.439057 −0.219529 − 0.975606i \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) −1.00000 −0.109109
\(85\) −2.00000 −0.216930
\(86\) 4.00000 0.431331
\(87\) 6.00000 0.643268
\(88\) −1.00000 −0.106600
\(89\) −2.00000 −0.212000 −0.106000 − 0.994366i \(-0.533804\pi\)
−0.106000 + 0.994366i \(0.533804\pi\)
\(90\) 1.00000 0.105409
\(91\) −2.00000 −0.209657
\(92\) 4.00000 0.417029
\(93\) 0 0
\(94\) 0 0
\(95\) 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 \(0.467625\pi\)
\(98\) 1.00000 0.101015
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) −10.0000 −0.995037 −0.497519 − 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) −2.00000 −0.198030
\(103\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 2.00000 0.196116
\(105\) −1.00000 −0.0975900
\(106\) −2.00000 −0.194257
\(107\) −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 \(0.469465\pi\)
\(110\) −1.00000 −0.0953463
\(111\) −6.00000 −0.569495
\(112\) −1.00000 −0.0944911
\(113\) −18.0000 −1.69330 −0.846649 − 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 4.00000 0.374634
\(115\) 4.00000 0.373002
\(116\) 6.00000 0.557086
\(117\) 2.00000 0.184900
\(118\) 4.00000 0.368230
\(119\) 2.00000 0.183340
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) −10.0000 −0.905357
\(123\) 10.0000 0.901670
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) −1.00000 −0.0890871
\(127\) 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
\(130\) 2.00000 0.175412
\(131\) 4.00000 0.349482 0.174741 − 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) −1.00000 −0.0870388
\(133\) −4.00000 −0.346844
\(134\) 8.00000 0.691095
\(135\) 1.00000 0.0860663
\(136\) −2.00000 −0.171499
\(137\) −10.0000 −0.854358 −0.427179 − 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) 4.00000 0.340503
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) −2.00000 −0.167248
\(144\) 1.00000 0.0833333
\(145\) 6.00000 0.498273
\(146\) 2.00000 0.165521
\(147\) 1.00000 0.0824786
\(148\) −6.00000 −0.493197
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 1.00000 0.0816497
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 4.00000 0.324443
\(153\) −2.00000 −0.161690
\(154\) 1.00000 0.0805823
\(155\) 0 0
\(156\) 2.00000 0.160128
\(157\) −18.0000 −1.43656 −0.718278 − 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −8.00000 −0.636446
\(159\) −2.00000 −0.158610
\(160\) 1.00000 0.0790569
\(161\) −4.00000 −0.315244
\(162\) 1.00000 0.0785674
\(163\) −8.00000 −0.626608 −0.313304 − 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) 10.0000 0.780869
\(165\) −1.00000 −0.0778499
\(166\) −4.00000 −0.310460
\(167\) 12.0000 0.928588 0.464294 − 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −9.00000 −0.692308
\(170\) −2.00000 −0.153393
\(171\) 4.00000 0.305888
\(172\) 4.00000 0.304997
\(173\) 14.0000 1.06440 0.532200 − 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 6.00000 0.454859
\(175\) −1.00000 −0.0755929
\(176\) −1.00000 −0.0753778
\(177\) 4.00000 0.300658
\(178\) −2.00000 −0.149906
\(179\) 4.00000 0.298974 0.149487 − 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 1.00000 0.0745356
\(181\) −14.0000 −1.04061 −0.520306 − 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −2.00000 −0.148250
\(183\) −10.0000 −0.739221
\(184\) 4.00000 0.294884
\(185\) −6.00000 −0.441129
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 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 \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 2.00000 0.143592
\(195\) 2.00000 0.143223
\(196\) 1.00000 0.0714286
\(197\) 6.00000 0.427482 0.213741 − 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) −1.00000 −0.0710669
\(199\) −8.00000 −0.567105 −0.283552 − 0.958957i \(-0.591513\pi\)
−0.283552 + 0.958957i \(0.591513\pi\)
\(200\) 1.00000 0.0707107
\(201\) 8.00000 0.564276
\(202\) −10.0000 −0.703598
\(203\) −6.00000 −0.421117
\(204\) −2.00000 −0.140028
\(205\) 10.0000 0.698430
\(206\) 0 0
\(207\) 4.00000 0.278019
\(208\) 2.00000 0.138675
\(209\) −4.00000 −0.276686
\(210\) −1.00000 −0.0690066
\(211\) −16.0000 −1.10149 −0.550743 − 0.834675i \(-0.685655\pi\)
−0.550743 + 0.834675i \(0.685655\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 4.00000 0.272798
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 2.00000 0.135457
\(219\) 2.00000 0.135147
\(220\) −1.00000 −0.0674200
\(221\) −4.00000 −0.269069
\(222\) −6.00000 −0.402694
\(223\) −16.0000 −1.07144 −0.535720 − 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −18.0000 −1.19734
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 4.00000 0.264906
\(229\) 10.0000 0.660819 0.330409 − 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 4.00000 0.263752
\(231\) 1.00000 0.0657952
\(232\) 6.00000 0.393919
\(233\) −22.0000 −1.44127 −0.720634 − 0.693316i \(-0.756149\pi\)
−0.720634 + 0.693316i \(0.756149\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 4.00000 0.260378
\(237\) −8.00000 −0.519656
\(238\) 2.00000 0.129641
\(239\) 4.00000 0.258738 0.129369 − 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 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
\(244\) −10.0000 −0.640184
\(245\) 1.00000 0.0638877
\(246\) 10.0000 0.637577
\(247\) 8.00000 0.509028
\(248\) 0 0
\(249\) −4.00000 −0.253490
\(250\) 1.00000 0.0632456
\(251\) 20.0000 1.26239 0.631194 − 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −4.00000 −0.251478
\(254\) 8.00000 0.501965
\(255\) −2.00000 −0.125245
\(256\) 1.00000 0.0625000
\(257\) 2.00000 0.124757 0.0623783 − 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 4.00000 0.249029
\(259\) 6.00000 0.372822
\(260\) 2.00000 0.124035
\(261\) 6.00000 0.371391
\(262\) 4.00000 0.247121
\(263\) 16.0000 0.986602 0.493301 − 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −2.00000 −0.122859
\(266\) −4.00000 −0.245256
\(267\) −2.00000 −0.122398
\(268\) 8.00000 0.488678
\(269\) −10.0000 −0.609711 −0.304855 − 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 1.00000 0.0608581
\(271\) −8.00000 −0.485965 −0.242983 − 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) −2.00000 −0.121268
\(273\) −2.00000 −0.121046
\(274\) −10.0000 −0.604122
\(275\) −1.00000 −0.0603023
\(276\) 4.00000 0.240772
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 4.00000 0.239904
\(279\) 0 0
\(280\) −1.00000 −0.0597614
\(281\) 6.00000 0.357930 0.178965 − 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −16.0000 −0.951101 −0.475551 − 0.879688i \(-0.657751\pi\)
−0.475551 + 0.879688i \(0.657751\pi\)
\(284\) 0 0
\(285\) 4.00000 0.236940
\(286\) −2.00000 −0.118262
\(287\) −10.0000 −0.590281
\(288\) 1.00000 0.0589256
\(289\) −13.0000 −0.764706
\(290\) 6.00000 0.352332
\(291\) 2.00000 0.117242
\(292\) 2.00000 0.117041
\(293\) 14.0000 0.817889 0.408944 − 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 1.00000 0.0583212
\(295\) 4.00000 0.232889
\(296\) −6.00000 −0.348743
\(297\) −1.00000 −0.0580259
\(298\) 6.00000 0.347571
\(299\) 8.00000 0.462652
\(300\) 1.00000 0.0577350
\(301\) −4.00000 −0.230556
\(302\) 0 0
\(303\) −10.0000 −0.574485
\(304\) 4.00000 0.229416
\(305\) −10.0000 −0.572598
\(306\) −2.00000 −0.114332
\(307\) 8.00000 0.456584 0.228292 − 0.973593i \(-0.426686\pi\)
0.228292 + 0.973593i \(0.426686\pi\)
\(308\) 1.00000 0.0569803
\(309\) 0 0
\(310\) 0 0
\(311\) 20.0000 1.13410 0.567048 − 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 2.00000 0.113228
\(313\) −6.00000 −0.339140 −0.169570 − 0.985518i \(-0.554238\pi\)
−0.169570 + 0.985518i \(0.554238\pi\)
\(314\) −18.0000 −1.01580
\(315\) −1.00000 −0.0563436
\(316\) −8.00000 −0.450035
\(317\) −10.0000 −0.561656 −0.280828 − 0.959758i \(-0.590609\pi\)
−0.280828 + 0.959758i \(0.590609\pi\)
\(318\) −2.00000 −0.112154
\(319\) −6.00000 −0.335936
\(320\) 1.00000 0.0559017
\(321\) −12.0000 −0.669775
\(322\) −4.00000 −0.222911
\(323\) −8.00000 −0.445132
\(324\) 1.00000 0.0555556
\(325\) 2.00000 0.110940
\(326\) −8.00000 −0.443079
\(327\) 2.00000 0.110600
\(328\) 10.0000 0.552158
\(329\) 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
\(333\) −6.00000 −0.328798
\(334\) 12.0000 0.656611
\(335\) 8.00000 0.437087
\(336\) −1.00000 −0.0545545
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) −9.00000 −0.489535
\(339\) −18.0000 −0.977626
\(340\) −2.00000 −0.108465
\(341\) 0 0
\(342\) 4.00000 0.216295
\(343\) −1.00000 −0.0539949
\(344\) 4.00000 0.215666
\(345\) 4.00000 0.215353
\(346\) 14.0000 0.752645
\(347\) 4.00000 0.214731 0.107366 − 0.994220i \(-0.465758\pi\)
0.107366 + 0.994220i \(0.465758\pi\)
\(348\) 6.00000 0.321634
\(349\) 22.0000 1.17763 0.588817 − 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 2.00000 0.106752
\(352\) −1.00000 −0.0533002
\(353\) −14.0000 −0.745145 −0.372572 − 0.928003i \(-0.621524\pi\)
−0.372572 + 0.928003i \(0.621524\pi\)
\(354\) 4.00000 0.212598
\(355\) 0 0
\(356\) −2.00000 −0.106000
\(357\) 2.00000 0.105851
\(358\) 4.00000 0.211407
\(359\) 4.00000 0.211112 0.105556 − 0.994413i \(-0.466338\pi\)
0.105556 + 0.994413i \(0.466338\pi\)
\(360\) 1.00000 0.0527046
\(361\) −3.00000 −0.157895
\(362\) −14.0000 −0.735824
\(363\) 1.00000 0.0524864
\(364\) −2.00000 −0.104828
\(365\) 2.00000 0.104685
\(366\) −10.0000 −0.522708
\(367\) −8.00000 −0.417597 −0.208798 − 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 4.00000 0.208514
\(369\) 10.0000 0.520579
\(370\) −6.00000 −0.311925
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) −26.0000 −1.34623 −0.673114 − 0.739538i \(-0.735044\pi\)
−0.673114 + 0.739538i \(0.735044\pi\)
\(374\) 2.00000 0.103418
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) −1.00000 −0.0514344
\(379\) −20.0000 −1.02733 −0.513665 − 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) 4.00000 0.205196
\(381\) 8.00000 0.409852
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.00000 0.0509647
\(386\) −14.0000 −0.712581
\(387\) 4.00000 0.203331
\(388\) 2.00000 0.101535
\(389\) 6.00000 0.304212 0.152106 − 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 2.00000 0.101274
\(391\) −8.00000 −0.404577
\(392\) 1.00000 0.0505076
\(393\) 4.00000 0.201773
\(394\) 6.00000 0.302276
\(395\) −8.00000 −0.402524
\(396\) −1.00000 −0.0502519
\(397\) 22.0000 1.10415 0.552074 − 0.833795i \(-0.313837\pi\)
0.552074 + 0.833795i \(0.313837\pi\)
\(398\) −8.00000 −0.401004
\(399\) −4.00000 −0.200250
\(400\) 1.00000 0.0500000
\(401\) −14.0000 −0.699127 −0.349563 − 0.936913i \(-0.613670\pi\)
−0.349563 + 0.936913i \(0.613670\pi\)
\(402\) 8.00000 0.399004
\(403\) 0 0
\(404\) −10.0000 −0.497519
\(405\) 1.00000 0.0496904
\(406\) −6.00000 −0.297775
\(407\) 6.00000 0.297409
\(408\) −2.00000 −0.0990148
\(409\) 26.0000 1.28562 0.642809 − 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 10.0000 0.493865
\(411\) −10.0000 −0.493264
\(412\) 0 0
\(413\) −4.00000 −0.196827
\(414\) 4.00000 0.196589
\(415\) −4.00000 −0.196352
\(416\) 2.00000 0.0980581
\(417\) 4.00000 0.195881
\(418\) −4.00000 −0.195646
\(419\) 36.0000 1.75872 0.879358 − 0.476162i \(-0.157972\pi\)
0.879358 + 0.476162i \(0.157972\pi\)
\(420\) −1.00000 −0.0487950
\(421\) −26.0000 −1.26716 −0.633581 − 0.773676i \(-0.718416\pi\)
−0.633581 + 0.773676i \(0.718416\pi\)
\(422\) −16.0000 −0.778868
\(423\) 0 0
\(424\) −2.00000 −0.0971286
\(425\) −2.00000 −0.0970143
\(426\) 0 0
\(427\) 10.0000 0.483934
\(428\) −12.0000 −0.580042
\(429\) −2.00000 −0.0965609
\(430\) 4.00000 0.192897
\(431\) −12.0000 −0.578020 −0.289010 − 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 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
\(436\) 2.00000 0.0957826
\(437\) 16.0000 0.765384
\(438\) 2.00000 0.0955637
\(439\) 24.0000 1.14546 0.572729 − 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 1.00000 0.0476190
\(442\) −4.00000 −0.190261
\(443\) 12.0000 0.570137 0.285069 − 0.958507i \(-0.407984\pi\)
0.285069 + 0.958507i \(0.407984\pi\)
\(444\) −6.00000 −0.284747
\(445\) −2.00000 −0.0948091
\(446\) −16.0000 −0.757622
\(447\) 6.00000 0.283790
\(448\) −1.00000 −0.0472456
\(449\) 18.0000 0.849473 0.424736 − 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) 1.00000 0.0471405
\(451\) −10.0000 −0.470882
\(452\) −18.0000 −0.846649
\(453\) 0 0
\(454\) 12.0000 0.563188
\(455\) −2.00000 −0.0937614
\(456\) 4.00000 0.187317
\(457\) −6.00000 −0.280668 −0.140334 − 0.990104i \(-0.544818\pi\)
−0.140334 + 0.990104i \(0.544818\pi\)
\(458\) 10.0000 0.467269
\(459\) −2.00000 −0.0933520
\(460\) 4.00000 0.186501
\(461\) 14.0000 0.652045 0.326023 − 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) 1.00000 0.0465242
\(463\) −40.0000 −1.85896 −0.929479 − 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −22.0000 −1.01913
\(467\) −20.0000 −0.925490 −0.462745 − 0.886492i \(-0.653135\pi\)
−0.462745 + 0.886492i \(0.653135\pi\)
\(468\) 2.00000 0.0924500
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) −18.0000 −0.829396
\(472\) 4.00000 0.184115
\(473\) −4.00000 −0.183920
\(474\) −8.00000 −0.367452
\(475\) 4.00000 0.183533
\(476\) 2.00000 0.0916698
\(477\) −2.00000 −0.0915737
\(478\) 4.00000 0.182956
\(479\) −32.0000 −1.46212 −0.731059 − 0.682315i \(-0.760973\pi\)
−0.731059 + 0.682315i \(0.760973\pi\)
\(480\) 1.00000 0.0456435
\(481\) −12.0000 −0.547153
\(482\) 2.00000 0.0910975
\(483\) −4.00000 −0.182006
\(484\) 1.00000 0.0454545
\(485\) 2.00000 0.0908153
\(486\) 1.00000 0.0453609
\(487\) −16.0000 −0.725029 −0.362515 − 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) −10.0000 −0.452679
\(489\) −8.00000 −0.361773
\(490\) 1.00000 0.0451754
\(491\) 20.0000 0.902587 0.451294 − 0.892375i \(-0.350963\pi\)
0.451294 + 0.892375i \(0.350963\pi\)
\(492\) 10.0000 0.450835
\(493\) −12.0000 −0.540453
\(494\) 8.00000 0.359937
\(495\) −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
\(501\) 12.0000 0.536120
\(502\) 20.0000 0.892644
\(503\) −36.0000 −1.60516 −0.802580 − 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −10.0000 −0.444994
\(506\) −4.00000 −0.177822
\(507\) −9.00000 −0.399704
\(508\) 8.00000 0.354943
\(509\) −10.0000 −0.443242 −0.221621 − 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) −2.00000 −0.0885615
\(511\) −2.00000 −0.0884748
\(512\) 1.00000 0.0441942
\(513\) 4.00000 0.176604
\(514\) 2.00000 0.0882162
\(515\) 0 0
\(516\) 4.00000 0.176090
\(517\) 0 0
\(518\) 6.00000 0.263625
\(519\) 14.0000 0.614532
\(520\) 2.00000 0.0877058
\(521\) −18.0000 −0.788594 −0.394297 − 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 6.00000 0.262613
\(523\) 24.0000 1.04945 0.524723 − 0.851273i \(-0.324169\pi\)
0.524723 + 0.851273i \(0.324169\pi\)
\(524\) 4.00000 0.174741
\(525\) −1.00000 −0.0436436
\(526\) 16.0000 0.697633
\(527\) 0 0
\(528\) −1.00000 −0.0435194
\(529\) −7.00000 −0.304348
\(530\) −2.00000 −0.0868744
\(531\) 4.00000 0.173585
\(532\) −4.00000 −0.173422
\(533\) 20.0000 0.866296
\(534\) −2.00000 −0.0865485
\(535\) −12.0000 −0.518805
\(536\) 8.00000 0.345547
\(537\) 4.00000 0.172613
\(538\) −10.0000 −0.431131
\(539\) −1.00000 −0.0430730
\(540\) 1.00000 0.0430331
\(541\) −22.0000 −0.945854 −0.472927 − 0.881102i \(-0.656803\pi\)
−0.472927 + 0.881102i \(0.656803\pi\)
\(542\) −8.00000 −0.343629
\(543\) −14.0000 −0.600798
\(544\) −2.00000 −0.0857493
\(545\) 2.00000 0.0856706
\(546\) −2.00000 −0.0855921
\(547\) 20.0000 0.855138 0.427569 − 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) −10.0000 −0.427179
\(549\) −10.0000 −0.426790
\(550\) −1.00000 −0.0426401
\(551\) 24.0000 1.02243
\(552\) 4.00000 0.170251
\(553\) 8.00000 0.340195
\(554\) −2.00000 −0.0849719
\(555\) −6.00000 −0.254686
\(556\) 4.00000 0.169638
\(557\) −18.0000 −0.762684 −0.381342 − 0.924434i \(-0.624538\pi\)
−0.381342 + 0.924434i \(0.624538\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) −1.00000 −0.0422577
\(561\) 2.00000 0.0844401
\(562\) 6.00000 0.253095
\(563\) −12.0000 −0.505740 −0.252870 − 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −18.0000 −0.757266
\(566\) −16.0000 −0.672530
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) 14.0000 0.586911 0.293455 − 0.955973i \(-0.405195\pi\)
0.293455 + 0.955973i \(0.405195\pi\)
\(570\) 4.00000 0.167542
\(571\) 16.0000 0.669579 0.334790 − 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) −2.00000 −0.0836242
\(573\) 0 0
\(574\) −10.0000 −0.417392
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) 18.0000 0.749350 0.374675 − 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) −13.0000 −0.540729
\(579\) −14.0000 −0.581820
\(580\) 6.00000 0.249136
\(581\) 4.00000 0.165948
\(582\) 2.00000 0.0829027
\(583\) 2.00000 0.0828315
\(584\) 2.00000 0.0827606
\(585\) 2.00000 0.0826898
\(586\) 14.0000 0.578335
\(587\) −28.0000 −1.15568 −0.577842 − 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 1.00000 0.0412393
\(589\) 0 0
\(590\) 4.00000 0.164677
\(591\) 6.00000 0.246807
\(592\) −6.00000 −0.246598
\(593\) 22.0000 0.903432 0.451716 − 0.892162i \(-0.350812\pi\)
0.451716 + 0.892162i \(0.350812\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 2.00000 0.0819920
\(596\) 6.00000 0.245770
\(597\) −8.00000 −0.327418
\(598\) 8.00000 0.327144
\(599\) 8.00000 0.326871 0.163436 − 0.986554i \(-0.447742\pi\)
0.163436 + 0.986554i \(0.447742\pi\)
\(600\) 1.00000 0.0408248
\(601\) 26.0000 1.06056 0.530281 − 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) −4.00000 −0.163028
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) 1.00000 0.0406558
\(606\) −10.0000 −0.406222
\(607\) 16.0000 0.649420 0.324710 − 0.945814i \(-0.394733\pi\)
0.324710 + 0.945814i \(0.394733\pi\)
\(608\) 4.00000 0.162221
\(609\) −6.00000 −0.243132
\(610\) −10.0000 −0.404888
\(611\) 0 0
\(612\) −2.00000 −0.0808452
\(613\) −2.00000 −0.0807792 −0.0403896 − 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 8.00000 0.322854
\(615\) 10.0000 0.403239
\(616\) 1.00000 0.0402911
\(617\) 38.0000 1.52982 0.764911 − 0.644136i \(-0.222783\pi\)
0.764911 + 0.644136i \(0.222783\pi\)
\(618\) 0 0
\(619\) −32.0000 −1.28619 −0.643094 − 0.765787i \(-0.722350\pi\)
−0.643094 + 0.765787i \(0.722350\pi\)
\(620\) 0 0
\(621\) 4.00000 0.160514
\(622\) 20.0000 0.801927
\(623\) 2.00000 0.0801283
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) −6.00000 −0.239808
\(627\) −4.00000 −0.159745
\(628\) −18.0000 −0.718278
\(629\) 12.0000 0.478471
\(630\) −1.00000 −0.0398410
\(631\) −32.0000 −1.27390 −0.636950 − 0.770905i \(-0.719804\pi\)
−0.636950 + 0.770905i \(0.719804\pi\)
\(632\) −8.00000 −0.318223
\(633\) −16.0000 −0.635943
\(634\) −10.0000 −0.397151
\(635\) 8.00000 0.317470
\(636\) −2.00000 −0.0793052
\(637\) 2.00000 0.0792429
\(638\) −6.00000 −0.237542
\(639\) 0 0
\(640\) 1.00000 0.0395285
\(641\) 2.00000 0.0789953 0.0394976 − 0.999220i \(-0.487424\pi\)
0.0394976 + 0.999220i \(0.487424\pi\)
\(642\) −12.0000 −0.473602
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) −4.00000 −0.157622
\(645\) 4.00000 0.157500
\(646\) −8.00000 −0.314756
\(647\) 24.0000 0.943537 0.471769 − 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) 1.00000 0.0392837
\(649\) −4.00000 −0.157014
\(650\) 2.00000 0.0784465
\(651\) 0 0
\(652\) −8.00000 −0.313304
\(653\) −34.0000 −1.33052 −0.665261 − 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) 2.00000 0.0782062
\(655\) 4.00000 0.156293
\(656\) 10.0000 0.390434
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 44.0000 1.71400 0.856998 − 0.515319i \(-0.172327\pi\)
0.856998 + 0.515319i \(0.172327\pi\)
\(660\) −1.00000 −0.0389249
\(661\) −46.0000 −1.78919 −0.894596 − 0.446875i \(-0.852537\pi\)
−0.894596 + 0.446875i \(0.852537\pi\)
\(662\) −20.0000 −0.777322
\(663\) −4.00000 −0.155347
\(664\) −4.00000 −0.155230
\(665\) −4.00000 −0.155113
\(666\) −6.00000 −0.232495
\(667\) 24.0000 0.929284
\(668\) 12.0000 0.464294
\(669\) −16.0000 −0.618596
\(670\) 8.00000 0.309067
\(671\) 10.0000 0.386046
\(672\) −1.00000 −0.0385758
\(673\) −46.0000 −1.77317 −0.886585 − 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 2.00000 0.0770371
\(675\) 1.00000 0.0384900
\(676\) −9.00000 −0.346154
\(677\) −26.0000 −0.999261 −0.499631 − 0.866239i \(-0.666531\pi\)
−0.499631 + 0.866239i \(0.666531\pi\)
\(678\) −18.0000 −0.691286
\(679\) −2.00000 −0.0767530
\(680\) −2.00000 −0.0766965
\(681\) 12.0000 0.459841
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 − 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 4.00000 0.152944
\(685\) −10.0000 −0.382080
\(686\) −1.00000 −0.0381802
\(687\) 10.0000 0.381524
\(688\) 4.00000 0.152499
\(689\) −4.00000 −0.152388
\(690\) 4.00000 0.152277
\(691\) 40.0000 1.52167 0.760836 − 0.648944i \(-0.224789\pi\)
0.760836 + 0.648944i \(0.224789\pi\)
\(692\) 14.0000 0.532200
\(693\) 1.00000 0.0379869
\(694\) 4.00000 0.151838
\(695\) 4.00000 0.151729
\(696\) 6.00000 0.227429
\(697\) −20.0000 −0.757554
\(698\) 22.0000 0.832712
\(699\) −22.0000 −0.832116
\(700\) −1.00000 −0.0377964
\(701\) −10.0000 −0.377695 −0.188847 − 0.982006i \(-0.560475\pi\)
−0.188847 + 0.982006i \(0.560475\pi\)
\(702\) 2.00000 0.0754851
\(703\) −24.0000 −0.905177
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −14.0000 −0.526897
\(707\) 10.0000 0.376089
\(708\) 4.00000 0.150329
\(709\) 22.0000 0.826227 0.413114 − 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) −2.00000 −0.0749532
\(713\) 0 0
\(714\) 2.00000 0.0748481
\(715\) −2.00000 −0.0747958
\(716\) 4.00000 0.149487
\(717\) 4.00000 0.149383
\(718\) 4.00000 0.149279
\(719\) 36.0000 1.34257 0.671287 − 0.741198i \(-0.265742\pi\)
0.671287 + 0.741198i \(0.265742\pi\)
\(720\) 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
\(727\) −8.00000 −0.296704 −0.148352 − 0.988935i \(-0.547397\pi\)
−0.148352 + 0.988935i \(0.547397\pi\)
\(728\) −2.00000 −0.0741249
\(729\) 1.00000 0.0370370
\(730\) 2.00000 0.0740233
\(731\) −8.00000 −0.295891
\(732\) −10.0000 −0.369611
\(733\) 2.00000 0.0738717 0.0369358 − 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) −8.00000 −0.295285
\(735\) 1.00000 0.0368856
\(736\) 4.00000 0.147442
\(737\) −8.00000 −0.294684
\(738\) 10.0000 0.368105
\(739\) 24.0000 0.882854 0.441427 − 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) −6.00000 −0.220564
\(741\) 8.00000 0.293887
\(742\) 2.00000 0.0734223
\(743\) −24.0000 −0.880475 −0.440237 − 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 0 0
\(745\) 6.00000 0.219823
\(746\) −26.0000 −0.951928
\(747\) −4.00000 −0.146352
\(748\) 2.00000 0.0731272
\(749\) 12.0000 0.438470
\(750\) 1.00000 0.0365148
\(751\) −40.0000 −1.45962 −0.729810 − 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 0 0
\(753\) 20.0000 0.728841
\(754\) 12.0000 0.437014
\(755\) 0 0
\(756\) −1.00000 −0.0363696
\(757\) 10.0000 0.363456 0.181728 − 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) −20.0000 −0.726433
\(759\) −4.00000 −0.145191
\(760\) 4.00000 0.145095
\(761\) 26.0000 0.942499 0.471250 − 0.882000i \(-0.343803\pi\)
0.471250 + 0.882000i \(0.343803\pi\)
\(762\) 8.00000 0.289809
\(763\) −2.00000 −0.0724049
\(764\) 0 0
\(765\) −2.00000 −0.0723102
\(766\) 0 0
\(767\) 8.00000 0.288863
\(768\) 1.00000 0.0360844
\(769\) 50.0000 1.80305 0.901523 − 0.432731i \(-0.142450\pi\)
0.901523 + 0.432731i \(0.142450\pi\)
\(770\) 1.00000 0.0360375
\(771\) 2.00000 0.0720282
\(772\) −14.0000 −0.503871
\(773\) −10.0000 −0.359675 −0.179838 − 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) 4.00000 0.143777
\(775\) 0 0
\(776\) 2.00000 0.0717958
\(777\) 6.00000 0.215249
\(778\) 6.00000 0.215110
\(779\) 40.0000 1.43315
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 6.00000 0.214423
\(784\) 1.00000 0.0357143
\(785\) −18.0000 −0.642448
\(786\) 4.00000 0.142675
\(787\) −24.0000 −0.855508 −0.427754 − 0.903895i \(-0.640695\pi\)
−0.427754 + 0.903895i \(0.640695\pi\)
\(788\) 6.00000 0.213741
\(789\) 16.0000 0.569615
\(790\) −8.00000 −0.284627
\(791\) 18.0000 0.640006
\(792\) −1.00000 −0.0355335
\(793\) −20.0000 −0.710221
\(794\) 22.0000 0.780751
\(795\) −2.00000 −0.0709327
\(796\) −8.00000 −0.283552
\(797\) −2.00000 −0.0708436 −0.0354218 − 0.999372i \(-0.511277\pi\)
−0.0354218 + 0.999372i \(0.511277\pi\)
\(798\) −4.00000 −0.141598
\(799\) 0 0
\(800\) 1.00000 0.0353553
\(801\) −2.00000 −0.0706665
\(802\) −14.0000 −0.494357
\(803\) −2.00000 −0.0705785
\(804\) 8.00000 0.282138
\(805\) −4.00000 −0.140981
\(806\) 0 0
\(807\) −10.0000 −0.352017
\(808\) −10.0000 −0.351799
\(809\) −18.0000 −0.632846 −0.316423 − 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 1.00000 0.0351364
\(811\) 44.0000 1.54505 0.772524 − 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) −6.00000 −0.210559
\(813\) −8.00000 −0.280572
\(814\) 6.00000 0.210300
\(815\) −8.00000 −0.280228
\(816\) −2.00000 −0.0700140
\(817\) 16.0000 0.559769
\(818\) 26.0000 0.909069
\(819\) −2.00000 −0.0698857
\(820\) 10.0000 0.349215
\(821\) −18.0000 −0.628204 −0.314102 − 0.949389i \(-0.601703\pi\)
−0.314102 + 0.949389i \(0.601703\pi\)
\(822\) −10.0000 −0.348790
\(823\) 8.00000 0.278862 0.139431 − 0.990232i \(-0.455473\pi\)
0.139431 + 0.990232i \(0.455473\pi\)
\(824\) 0 0
\(825\) −1.00000 −0.0348155
\(826\) −4.00000 −0.139178
\(827\) 20.0000 0.695468 0.347734 − 0.937593i \(-0.386951\pi\)
0.347734 + 0.937593i \(0.386951\pi\)
\(828\) 4.00000 0.139010
\(829\) −6.00000 −0.208389 −0.104194 − 0.994557i \(-0.533226\pi\)
−0.104194 + 0.994557i \(0.533226\pi\)
\(830\) −4.00000 −0.138842
\(831\) −2.00000 −0.0693792
\(832\) 2.00000 0.0693375
\(833\) −2.00000 −0.0692959
\(834\) 4.00000 0.138509
\(835\) 12.0000 0.415277
\(836\) −4.00000 −0.138343
\(837\) 0 0
\(838\) 36.0000 1.24360
\(839\) 36.0000 1.24286 0.621429 − 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) −1.00000 −0.0345033
\(841\) 7.00000 0.241379
\(842\) −26.0000 −0.896019
\(843\) 6.00000 0.206651
\(844\) −16.0000 −0.550743
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) −1.00000 −0.0343604
\(848\) −2.00000 −0.0686803
\(849\) −16.0000 −0.549119
\(850\) −2.00000 −0.0685994
\(851\) −24.0000 −0.822709
\(852\) 0 0
\(853\) −38.0000 −1.30110 −0.650548 − 0.759465i \(-0.725461\pi\)
−0.650548 + 0.759465i \(0.725461\pi\)
\(854\) 10.0000 0.342193
\(855\) 4.00000 0.136797
\(856\) −12.0000 −0.410152
\(857\) −18.0000 −0.614868 −0.307434 − 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) −2.00000 −0.0682789
\(859\) 40.0000 1.36478 0.682391 − 0.730987i \(-0.260940\pi\)
0.682391 + 0.730987i \(0.260940\pi\)
\(860\) 4.00000 0.136399
\(861\) −10.0000 −0.340799
\(862\) −12.0000 −0.408722
\(863\) −36.0000 −1.22545 −0.612727 − 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 1.00000 0.0340207
\(865\) 14.0000 0.476014
\(866\) −14.0000 −0.475739
\(867\) −13.0000 −0.441503
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 6.00000 0.203419
\(871\) 16.0000 0.542139
\(872\) 2.00000 0.0677285
\(873\) 2.00000 0.0676897
\(874\) 16.0000 0.541208
\(875\) −1.00000 −0.0338062
\(876\) 2.00000 0.0675737
\(877\) −58.0000 −1.95852 −0.979260 − 0.202606i \(-0.935059\pi\)
−0.979260 + 0.202606i \(0.935059\pi\)
\(878\) 24.0000 0.809961
\(879\) 14.0000 0.472208
\(880\) −1.00000 −0.0337100
\(881\) 54.0000 1.81931 0.909653 − 0.415369i \(-0.136347\pi\)
0.909653 + 0.415369i \(0.136347\pi\)
\(882\) 1.00000 0.0336718
\(883\) −8.00000 −0.269221 −0.134611 − 0.990899i \(-0.542978\pi\)
−0.134611 + 0.990899i \(0.542978\pi\)
\(884\) −4.00000 −0.134535
\(885\) 4.00000 0.134459
\(886\) 12.0000 0.403148
\(887\) −12.0000 −0.402921 −0.201460 − 0.979497i \(-0.564569\pi\)
−0.201460 + 0.979497i \(0.564569\pi\)
\(888\) −6.00000 −0.201347
\(889\) −8.00000 −0.268311
\(890\) −2.00000 −0.0670402
\(891\) −1.00000 −0.0335013
\(892\) −16.0000 −0.535720
\(893\) 0 0
\(894\) 6.00000 0.200670
\(895\) 4.00000 0.133705
\(896\) −1.00000 −0.0334077
\(897\) 8.00000 0.267112
\(898\) 18.0000 0.600668
\(899\) 0 0
\(900\) 1.00000 0.0333333
\(901\) 4.00000 0.133259
\(902\) −10.0000 −0.332964
\(903\) −4.00000 −0.133112
\(904\) −18.0000 −0.598671
\(905\) −14.0000 −0.465376
\(906\) 0 0
\(907\) 40.0000 1.32818 0.664089 − 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(908\) 12.0000 0.398234
\(909\) −10.0000 −0.331679
\(910\) −2.00000 −0.0662994
\(911\) 56.0000 1.85536 0.927681 − 0.373373i \(-0.121799\pi\)
0.927681 + 0.373373i \(0.121799\pi\)
\(912\) 4.00000 0.132453
\(913\) 4.00000 0.132381
\(914\) −6.00000 −0.198462
\(915\) −10.0000 −0.330590
\(916\) 10.0000 0.330409
\(917\) −4.00000 −0.132092
\(918\) −2.00000 −0.0660098
\(919\) −8.00000 −0.263896 −0.131948 − 0.991257i \(-0.542123\pi\)
−0.131948 + 0.991257i \(0.542123\pi\)
\(920\) 4.00000 0.131876
\(921\) 8.00000 0.263609
\(922\) 14.0000 0.461065
\(923\) 0 0
\(924\) 1.00000 0.0328976
\(925\) −6.00000 −0.197279
\(926\) −40.0000 −1.31448
\(927\) 0 0
\(928\) 6.00000 0.196960
\(929\) 14.0000 0.459325 0.229663 − 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) 4.00000 0.131095
\(932\) −22.0000 −0.720634
\(933\) 20.0000 0.654771
\(934\) −20.0000 −0.654420
\(935\) 2.00000 0.0654070
\(936\) 2.00000 0.0653720
\(937\) 10.0000 0.326686 0.163343 − 0.986569i \(-0.447772\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(938\) −8.00000 −0.261209
\(939\) −6.00000 −0.195803
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 − 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −18.0000 −0.586472
\(943\) 40.0000 1.30258
\(944\) 4.00000 0.130189
\(945\) −1.00000 −0.0325300
\(946\) −4.00000 −0.130051
\(947\) 44.0000 1.42981 0.714904 − 0.699223i \(-0.246470\pi\)
0.714904 + 0.699223i \(0.246470\pi\)
\(948\) −8.00000 −0.259828
\(949\) 4.00000 0.129845
\(950\) 4.00000 0.129777
\(951\) −10.0000 −0.324272
\(952\) 2.00000 0.0648204
\(953\) 34.0000 1.10137 0.550684 − 0.834714i \(-0.314367\pi\)
0.550684 + 0.834714i \(0.314367\pi\)
\(954\) −2.00000 −0.0647524
\(955\) 0 0
\(956\) 4.00000 0.129369
\(957\) −6.00000 −0.193952
\(958\) −32.0000 −1.03387
\(959\) 10.0000 0.322917
\(960\) 1.00000 0.0322749
\(961\) −31.0000 −1.00000
\(962\) −12.0000 −0.386896
\(963\) −12.0000 −0.386695
\(964\) 2.00000 0.0644157
\(965\) −14.0000 −0.450676
\(966\) −4.00000 −0.128698
\(967\) 16.0000 0.514525 0.257263 − 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 1.00000 0.0321412
\(969\) −8.00000 −0.256997
\(970\) 2.00000 0.0642161
\(971\) 12.0000 0.385098 0.192549 − 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 1.00000 0.0320750
\(973\) −4.00000 −0.128234
\(974\) −16.0000 −0.512673
\(975\) 2.00000 0.0640513
\(976\) −10.0000 −0.320092
\(977\) −42.0000 −1.34370 −0.671850 − 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) −8.00000 −0.255812
\(979\) 2.00000 0.0639203
\(980\) 1.00000 0.0319438
\(981\) 2.00000 0.0638551
\(982\) 20.0000 0.638226
\(983\) 24.0000 0.765481 0.382741 − 0.923856i \(-0.374980\pi\)
0.382741 + 0.923856i \(0.374980\pi\)
\(984\) 10.0000 0.318788
\(985\) 6.00000 0.191176
\(986\) −12.0000 −0.382158
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) 16.0000 0.508770
\(990\) −1.00000 −0.0317821
\(991\) 8.00000 0.254128 0.127064 − 0.991894i \(-0.459445\pi\)
0.127064 + 0.991894i \(0.459445\pi\)
\(992\) 0 0
\(993\) −20.0000 −0.634681
\(994\) 0 0
\(995\) −8.00000 −0.253617
\(996\) −4.00000 −0.126745
\(997\) −14.0000 −0.443384 −0.221692 − 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) −20.0000 −0.633089
\(999\) −6.00000 −0.189832
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2310.2.a.v.1.1 ✓ 1
3.2 odd 2 6930.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2310.2.a.v.1.1 ✓ 1 1.1 even 1 trivial
6930.2.a.b.1.1 1 3.2 odd 2