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Properties

Label 2310.2.a.d.1.1
Level $2310$
Weight $2$
Character 2310.1
Self dual yes
Analytic conductor $18.445$
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] = [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: \(1\)
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 \(\chi\) \(=\) 2310.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -2.00000 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.00000 q^{17} -1.00000 q^{18} -4.00000 q^{19} +1.00000 q^{20} -1.00000 q^{21} +1.00000 q^{22} +4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} -10.0000 q^{29} +1.00000 q^{30} -4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -2.00000 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.0000 q^{37} +4.00000 q^{38} +2.00000 q^{39} -1.00000 q^{40} +6.00000 q^{41} +1.00000 q^{42} +4.00000 q^{43} -1.00000 q^{44} +1.00000 q^{45} -4.00000 q^{46} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -2.00000 q^{51} -2.00000 q^{52} -2.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} -1.00000 q^{56} +4.00000 q^{57} +10.0000 q^{58} -1.00000 q^{60} -14.0000 q^{61} +4.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{65} -1.00000 q^{66} +2.00000 q^{68} -4.00000 q^{69} -1.00000 q^{70} -1.00000 q^{72} +2.00000 q^{73} +10.0000 q^{74} -1.00000 q^{75} -4.00000 q^{76} -1.00000 q^{77} -2.00000 q^{78} -8.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -6.00000 q^{82} +4.00000 q^{83} -1.00000 q^{84} +2.00000 q^{85} -4.00000 q^{86} +10.0000 q^{87} +1.00000 q^{88} +18.0000 q^{89} -1.00000 q^{90} -2.00000 q^{91} +4.00000 q^{92} +4.00000 q^{93} -4.00000 q^{95} +1.00000 q^{96} +2.00000 q^{97} -1.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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 \(-0.589456\pi\)
−0.277350 + 0.960769i \(0.589456\pi\)
\(14\) −1.00000 −0.267261
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 2.00000 0.485071 0.242536 − 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.00000 −0.917663 −0.458831 − 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 1.00000 0.223607
\(21\) −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
\(29\) −10.0000 −1.85695 −0.928477 − 0.371391i \(-0.878881\pi\)
−0.928477 + 0.371391i \(0.878881\pi\)
\(30\) 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
\(34\) −2.00000 −0.342997
\(35\) 1.00000 0.169031
\(36\) 1.00000 0.166667
\(37\) −10.0000 −1.64399 −0.821995 − 0.569495i \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 4.00000 0.648886
\(39\) 2.00000 0.320256
\(40\) −1.00000 −0.158114
\(41\) 6.00000 0.937043 0.468521 − 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 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
\(58\) 10.0000 1.31306
\(59\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) −1.00000 −0.129099
\(61\) −14.0000 −1.79252 −0.896258 − 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 4.00000 0.508001
\(63\) 1.00000 0.125988
\(64\) 1.00000 0.125000
\(65\) −2.00000 −0.248069
\(66\) −1.00000 −0.123091
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 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 \(0.462659\pi\)
\(74\) 10.0000 1.16248
\(75\) −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
\(82\) −6.00000 −0.662589
\(83\) 4.00000 0.439057 0.219529 − 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) −1.00000 −0.109109
\(85\) 2.00000 0.216930
\(86\) −4.00000 −0.431331
\(87\) 10.0000 1.07211
\(88\) 1.00000 0.106600
\(89\) 18.0000 1.90800 0.953998 − 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.00000 −0.209657
\(92\) 4.00000 0.417029
\(93\) 4.00000 0.414781
\(94\) 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
\(101\) −14.0000 −1.39305 −0.696526 − 0.717532i \(-0.745272\pi\)
−0.696526 + 0.717532i \(0.745272\pi\)
\(102\) 2.00000 0.198030
\(103\) 8.00000 0.788263 0.394132 − 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 2.00000 0.196116
\(105\) −1.00000 −0.0975900
\(106\) 2.00000 0.194257
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −18.0000 −1.72409 −0.862044 − 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 1.00000 0.0953463
\(111\) 10.0000 0.949158
\(112\) 1.00000 0.0944911
\(113\) 2.00000 0.188144 0.0940721 − 0.995565i \(-0.470012\pi\)
0.0940721 + 0.995565i \(0.470012\pi\)
\(114\) −4.00000 −0.374634
\(115\) 4.00000 0.373002
\(116\) −10.0000 −0.928477
\(117\) −2.00000 −0.184900
\(118\) 0 0
\(119\) 2.00000 0.183340
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) 14.0000 1.26750
\(123\) −6.00000 −0.541002
\(124\) −4.00000 −0.359211
\(125\) 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
\(134\) 0 0
\(135\) −1.00000 −0.0860663
\(136\) −2.00000 −0.171499
\(137\) −22.0000 −1.87959 −0.939793 − 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 4.00000 0.340503
\(139\) −20.0000 −1.69638 −0.848189 − 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 1.00000 0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 1.00000 0.0833333
\(145\) −10.0000 −0.830455
\(146\) −2.00000 −0.165521
\(147\) −1.00000 −0.0824786
\(148\) −10.0000 −0.821995
\(149\) −18.0000 −1.47462 −0.737309 − 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 1.00000 0.0816497
\(151\) −8.00000 −0.651031 −0.325515 − 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 4.00000 0.324443
\(153\) 2.00000 0.161690
\(154\) 1.00000 0.0805823
\(155\) −4.00000 −0.321288
\(156\) 2.00000 0.160128
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 8.00000 0.636446
\(159\) 2.00000 0.158610
\(160\) −1.00000 −0.0790569
\(161\) 4.00000 0.315244
\(162\) −1.00000 −0.0785674
\(163\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 6.00000 0.468521
\(165\) 1.00000 0.0778499
\(166\) −4.00000 −0.310460
\(167\) −16.0000 −1.23812 −0.619059 − 0.785345i \(-0.712486\pi\)
−0.619059 + 0.785345i \(0.712486\pi\)
\(168\) 1.00000 0.0771517
\(169\) −9.00000 −0.692308
\(170\) −2.00000 −0.153393
\(171\) −4.00000 −0.305888
\(172\) 4.00000 0.304997
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) −10.0000 −0.758098
\(175\) 1.00000 0.0755929
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −18.0000 −1.34916
\(179\) −12.0000 −0.896922 −0.448461 − 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 1.00000 0.0745356
\(181\) −10.0000 −0.743294 −0.371647 − 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 2.00000 0.148250
\(183\) 14.0000 1.03491
\(184\) −4.00000 −0.294884
\(185\) −10.0000 −0.735215
\(186\) −4.00000 −0.293294
\(187\) −2.00000 −0.146254
\(188\) 0 0
\(189\) −1.00000 −0.0727393
\(190\) 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
\(193\) −26.0000 −1.87152 −0.935760 − 0.352636i \(-0.885285\pi\)
−0.935760 + 0.352636i \(0.885285\pi\)
\(194\) −2.00000 −0.143592
\(195\) 2.00000 0.143223
\(196\) 1.00000 0.0714286
\(197\) 10.0000 0.712470 0.356235 − 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 1.00000 0.0710669
\(199\) −20.0000 −1.41776 −0.708881 − 0.705328i \(-0.750800\pi\)
−0.708881 + 0.705328i \(0.750800\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) 14.0000 0.985037
\(203\) −10.0000 −0.701862
\(204\) −2.00000 −0.140028
\(205\) 6.00000 0.419058
\(206\) −8.00000 −0.557386
\(207\) 4.00000 0.278019
\(208\) −2.00000 −0.138675
\(209\) 4.00000 0.276686
\(210\) 1.00000 0.0690066
\(211\) 20.0000 1.37686 0.688428 − 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −2.00000 −0.137361
\(213\) 0 0
\(214\) −12.0000 −0.820303
\(215\) 4.00000 0.272798
\(216\) 1.00000 0.0680414
\(217\) −4.00000 −0.271538
\(218\) 18.0000 1.21911
\(219\) −2.00000 −0.135147
\(220\) −1.00000 −0.0674200
\(221\) −4.00000 −0.269069
\(222\) −10.0000 −0.671156
\(223\) −8.00000 −0.535720 −0.267860 − 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 1.00000 0.0666667
\(226\) −2.00000 −0.133038
\(227\) 12.0000 0.796468 0.398234 − 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) 4.00000 0.264906
\(229\) 6.00000 0.396491 0.198246 − 0.980152i \(-0.436476\pi\)
0.198246 + 0.980152i \(0.436476\pi\)
\(230\) −4.00000 −0.263752
\(231\) 1.00000 0.0657952
\(232\) 10.0000 0.656532
\(233\) 6.00000 0.393073 0.196537 − 0.980497i \(-0.437031\pi\)
0.196537 + 0.980497i \(0.437031\pi\)
\(234\) 2.00000 0.130744
\(235\) 0 0
\(236\) 0 0
\(237\) 8.00000 0.519656
\(238\) −2.00000 −0.129641
\(239\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) −1.00000 −0.0645497
\(241\) 22.0000 1.41714 0.708572 − 0.705638i \(-0.249340\pi\)
0.708572 + 0.705638i \(0.249340\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) −14.0000 −0.896258
\(245\) 1.00000 0.0638877
\(246\) 6.00000 0.382546
\(247\) 8.00000 0.509028
\(248\) 4.00000 0.254000
\(249\) −4.00000 −0.253490
\(250\) −1.00000 −0.0632456
\(251\) −16.0000 −1.00991 −0.504956 − 0.863145i \(-0.668491\pi\)
−0.504956 + 0.863145i \(0.668491\pi\)
\(252\) 1.00000 0.0629941
\(253\) −4.00000 −0.251478
\(254\) −8.00000 −0.501965
\(255\) −2.00000 −0.125245
\(256\) 1.00000 0.0625000
\(257\) −30.0000 −1.87135 −0.935674 − 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) 4.00000 0.249029
\(259\) −10.0000 −0.621370
\(260\) −2.00000 −0.124035
\(261\) −10.0000 −0.618984
\(262\) −4.00000 −0.247121
\(263\) −24.0000 −1.47990 −0.739952 − 0.672660i \(-0.765152\pi\)
−0.739952 + 0.672660i \(0.765152\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −2.00000 −0.122859
\(266\) 4.00000 0.245256
\(267\) −18.0000 −1.10158
\(268\) 0 0
\(269\) 6.00000 0.365826 0.182913 − 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 1.00000 0.0608581
\(271\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 2.00000 0.121268
\(273\) 2.00000 0.121046
\(274\) 22.0000 1.32907
\(275\) −1.00000 −0.0603023
\(276\) −4.00000 −0.240772
\(277\) −22.0000 −1.32185 −0.660926 − 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 20.0000 1.19952
\(279\) −4.00000 −0.239474
\(280\) −1.00000 −0.0597614
\(281\) 10.0000 0.596550 0.298275 − 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 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
\(286\) −2.00000 −0.118262
\(287\) 6.00000 0.354169
\(288\) −1.00000 −0.0589256
\(289\) −13.0000 −0.764706
\(290\) 10.0000 0.587220
\(291\) −2.00000 −0.117242
\(292\) 2.00000 0.117041
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 1.00000 0.0583212
\(295\) 0 0
\(296\) 10.0000 0.581238
\(297\) 1.00000 0.0580259
\(298\) 18.0000 1.04271
\(299\) −8.00000 −0.462652
\(300\) −1.00000 −0.0577350
\(301\) 4.00000 0.230556
\(302\) 8.00000 0.460348
\(303\) 14.0000 0.804279
\(304\) −4.00000 −0.229416
\(305\) −14.0000 −0.801638
\(306\) −2.00000 −0.114332
\(307\) −28.0000 −1.59804 −0.799022 − 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −1.00000 −0.0569803
\(309\) −8.00000 −0.455104
\(310\) 4.00000 0.227185
\(311\) 28.0000 1.58773 0.793867 − 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) −2.00000 −0.113228
\(313\) 10.0000 0.565233 0.282617 − 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 2.00000 0.112867
\(315\) 1.00000 0.0563436
\(316\) −8.00000 −0.450035
\(317\) 14.0000 0.786318 0.393159 − 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(318\) −2.00000 −0.112154
\(319\) 10.0000 0.559893
\(320\) 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
\(326\) 0 0
\(327\) 18.0000 0.995402
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 4.00000 0.219860 0.109930 − 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 4.00000 0.219529
\(333\) −10.0000 −0.547997
\(334\) 16.0000 0.875481
\(335\) 0 0
\(336\) −1.00000 −0.0545545
\(337\) −18.0000 −0.980522 −0.490261 − 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 9.00000 0.489535
\(339\) −2.00000 −0.108625
\(340\) 2.00000 0.108465
\(341\) 4.00000 0.216612
\(342\) 4.00000 0.216295
\(343\) 1.00000 0.0539949
\(344\) −4.00000 −0.215666
\(345\) −4.00000 −0.215353
\(346\) −6.00000 −0.322562
\(347\) 36.0000 1.93258 0.966291 − 0.257454i \(-0.0828835\pi\)
0.966291 + 0.257454i \(0.0828835\pi\)
\(348\) 10.0000 0.536056
\(349\) 18.0000 0.963518 0.481759 − 0.876304i \(-0.339998\pi\)
0.481759 + 0.876304i \(0.339998\pi\)
\(350\) −1.00000 −0.0534522
\(351\) 2.00000 0.106752
\(352\) 1.00000 0.0533002
\(353\) 18.0000 0.958043 0.479022 − 0.877803i \(-0.340992\pi\)
0.479022 + 0.877803i \(0.340992\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 18.0000 0.953998
\(357\) −2.00000 −0.105851
\(358\) 12.0000 0.634220
\(359\) 16.0000 0.844448 0.422224 − 0.906492i \(-0.361250\pi\)
0.422224 + 0.906492i \(0.361250\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 10.0000 0.525588
\(363\) −1.00000 −0.0524864
\(364\) −2.00000 −0.104828
\(365\) 2.00000 0.104685
\(366\) −14.0000 −0.731792
\(367\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(368\) 4.00000 0.208514
\(369\) 6.00000 0.312348
\(370\) 10.0000 0.519875
\(371\) −2.00000 −0.103835
\(372\) 4.00000 0.207390
\(373\) −14.0000 −0.724893 −0.362446 − 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 2.00000 0.103418
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) 20.0000 1.03005
\(378\) 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
\(382\) −8.00000 −0.409316
\(383\) 24.0000 1.22634 0.613171 − 0.789950i \(-0.289894\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(384\) 1.00000 0.0510310
\(385\) −1.00000 −0.0509647
\(386\) 26.0000 1.32337
\(387\) 4.00000 0.203331
\(388\) 2.00000 0.101535
\(389\) −26.0000 −1.31825 −0.659126 − 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) −2.00000 −0.101274
\(391\) 8.00000 0.404577
\(392\) −1.00000 −0.0505076
\(393\) −4.00000 −0.201773
\(394\) −10.0000 −0.503793
\(395\) −8.00000 −0.402524
\(396\) −1.00000 −0.0502519
\(397\) 30.0000 1.50566 0.752828 − 0.658217i \(-0.228689\pi\)
0.752828 + 0.658217i \(0.228689\pi\)
\(398\) 20.0000 1.00251
\(399\) 4.00000 0.200250
\(400\) 1.00000 0.0500000
\(401\) 2.00000 0.0998752 0.0499376 − 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) −14.0000 −0.696526
\(405\) 1.00000 0.0496904
\(406\) 10.0000 0.496292
\(407\) 10.0000 0.495682
\(408\) 2.00000 0.0990148
\(409\) −34.0000 −1.68119 −0.840596 − 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(410\) −6.00000 −0.296319
\(411\) 22.0000 1.08518
\(412\) 8.00000 0.394132
\(413\) 0 0
\(414\) −4.00000 −0.196589
\(415\) 4.00000 0.196352
\(416\) 2.00000 0.0980581
\(417\) 20.0000 0.979404
\(418\) −4.00000 −0.195646
\(419\) 32.0000 1.56330 0.781651 − 0.623716i \(-0.214378\pi\)
0.781651 + 0.623716i \(0.214378\pi\)
\(420\) −1.00000 −0.0487950
\(421\) 6.00000 0.292422 0.146211 − 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) 2.00000 0.0971286
\(425\) 2.00000 0.0970143
\(426\) 0 0
\(427\) −14.0000 −0.677507
\(428\) 12.0000 0.580042
\(429\) −2.00000 −0.0965609
\(430\) −4.00000 −0.192897
\(431\) −40.0000 −1.92673 −0.963366 − 0.268190i \(-0.913575\pi\)
−0.963366 + 0.268190i \(0.913575\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 18.0000 0.865025 0.432512 − 0.901628i \(-0.357627\pi\)
0.432512 + 0.901628i \(0.357627\pi\)
\(434\) 4.00000 0.192006
\(435\) 10.0000 0.479463
\(436\) −18.0000 −0.862044
\(437\) −16.0000 −0.765384
\(438\) 2.00000 0.0955637
\(439\) −24.0000 −1.14546 −0.572729 − 0.819745i \(-0.694115\pi\)
−0.572729 + 0.819745i \(0.694115\pi\)
\(440\) 1.00000 0.0476731
\(441\) 1.00000 0.0476190
\(442\) 4.00000 0.190261
\(443\) −8.00000 −0.380091 −0.190046 − 0.981775i \(-0.560864\pi\)
−0.190046 + 0.981775i \(0.560864\pi\)
\(444\) 10.0000 0.474579
\(445\) 18.0000 0.853282
\(446\) 8.00000 0.378811
\(447\) 18.0000 0.851371
\(448\) 1.00000 0.0472456
\(449\) −14.0000 −0.660701 −0.330350 − 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −6.00000 −0.282529
\(452\) 2.00000 0.0940721
\(453\) 8.00000 0.375873
\(454\) −12.0000 −0.563188
\(455\) −2.00000 −0.0937614
\(456\) −4.00000 −0.187317
\(457\) 22.0000 1.02912 0.514558 − 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −6.00000 −0.280362
\(459\) −2.00000 −0.0933520
\(460\) 4.00000 0.186501
\(461\) 18.0000 0.838344 0.419172 − 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) −1.00000 −0.0465242
\(463\) 20.0000 0.929479 0.464739 − 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −10.0000 −0.464238
\(465\) 4.00000 0.185496
\(466\) −6.00000 −0.277945
\(467\) 20.0000 0.925490 0.462745 − 0.886492i \(-0.346865\pi\)
0.462745 + 0.886492i \(0.346865\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 0 0
\(470\) 0 0
\(471\) 2.00000 0.0921551
\(472\) 0 0
\(473\) −4.00000 −0.183920
\(474\) −8.00000 −0.367452
\(475\) −4.00000 −0.183533
\(476\) 2.00000 0.0916698
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(480\) 1.00000 0.0456435
\(481\) 20.0000 0.911922
\(482\) −22.0000 −1.00207
\(483\) −4.00000 −0.182006
\(484\) 1.00000 0.0454545
\(485\) 2.00000 0.0908153
\(486\) 1.00000 0.0453609
\(487\) 4.00000 0.181257 0.0906287 − 0.995885i \(-0.471112\pi\)
0.0906287 + 0.995885i \(0.471112\pi\)
\(488\) 14.0000 0.633750
\(489\) 0 0
\(490\) −1.00000 −0.0451754
\(491\) 12.0000 0.541552 0.270776 − 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) −6.00000 −0.270501
\(493\) −20.0000 −0.900755
\(494\) −8.00000 −0.359937
\(495\) −1.00000 −0.0449467
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) 4.00000 0.179244
\(499\) 4.00000 0.179065 0.0895323 − 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 1.00000 0.0447214
\(501\) 16.0000 0.714827
\(502\) 16.0000 0.714115
\(503\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) −1.00000 −0.0445435
\(505\) −14.0000 −0.622992
\(506\) 4.00000 0.177822
\(507\) 9.00000 0.399704
\(508\) 8.00000 0.354943
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 2.00000 0.0885615
\(511\) 2.00000 0.0884748
\(512\) −1.00000 −0.0441942
\(513\) 4.00000 0.176604
\(514\) 30.0000 1.32324
\(515\) 8.00000 0.352522
\(516\) −4.00000 −0.176090
\(517\) 0 0
\(518\) 10.0000 0.439375
\(519\) −6.00000 −0.263371
\(520\) 2.00000 0.0877058
\(521\) 10.0000 0.438108 0.219054 − 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 10.0000 0.437688
\(523\) 28.0000 1.22435 0.612177 − 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 4.00000 0.174741
\(525\) −1.00000 −0.0436436
\(526\) 24.0000 1.04645
\(527\) −8.00000 −0.348485
\(528\) 1.00000 0.0435194
\(529\) −7.00000 −0.304348
\(530\) 2.00000 0.0868744
\(531\) 0 0
\(532\) −4.00000 −0.173422
\(533\) −12.0000 −0.519778
\(534\) 18.0000 0.778936
\(535\) 12.0000 0.518805
\(536\) 0 0
\(537\) 12.0000 0.517838
\(538\) −6.00000 −0.258678
\(539\) −1.00000 −0.0430730
\(540\) −1.00000 −0.0430331
\(541\) 38.0000 1.63375 0.816874 − 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 0 0
\(543\) 10.0000 0.429141
\(544\) −2.00000 −0.0857493
\(545\) −18.0000 −0.771035
\(546\) −2.00000 −0.0855921
\(547\) 36.0000 1.53925 0.769624 − 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) −22.0000 −0.939793
\(549\) −14.0000 −0.597505
\(550\) 1.00000 0.0426401
\(551\) 40.0000 1.70406
\(552\) 4.00000 0.170251
\(553\) −8.00000 −0.340195
\(554\) 22.0000 0.934690
\(555\) 10.0000 0.424476
\(556\) −20.0000 −0.848189
\(557\) −30.0000 −1.27114 −0.635570 − 0.772043i \(-0.719235\pi\)
−0.635570 + 0.772043i \(0.719235\pi\)
\(558\) 4.00000 0.169334
\(559\) −8.00000 −0.338364
\(560\) 1.00000 0.0422577
\(561\) 2.00000 0.0844401
\(562\) −10.0000 −0.421825
\(563\) −20.0000 −0.842900 −0.421450 − 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 0 0
\(565\) 2.00000 0.0841406
\(566\) −4.00000 −0.168133
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −30.0000 −1.25767 −0.628833 − 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −4.00000 −0.167542
\(571\) −12.0000 −0.502184 −0.251092 − 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 2.00000 0.0836242
\(573\) −8.00000 −0.334205
\(574\) −6.00000 −0.250435
\(575\) 4.00000 0.166812
\(576\) 1.00000 0.0416667
\(577\) −14.0000 −0.582828 −0.291414 − 0.956597i \(-0.594126\pi\)
−0.291414 + 0.956597i \(0.594126\pi\)
\(578\) 13.0000 0.540729
\(579\) 26.0000 1.08052
\(580\) −10.0000 −0.415227
\(581\) 4.00000 0.165948
\(582\) 2.00000 0.0829027
\(583\) 2.00000 0.0828315
\(584\) −2.00000 −0.0827606
\(585\) −2.00000 −0.0826898
\(586\) 18.0000 0.743573
\(587\) 12.0000 0.495293 0.247647 − 0.968850i \(-0.420343\pi\)
0.247647 + 0.968850i \(0.420343\pi\)
\(588\) −1.00000 −0.0412393
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −10.0000 −0.411345
\(592\) −10.0000 −0.410997
\(593\) −6.00000 −0.246390 −0.123195 − 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 2.00000 0.0819920
\(596\) −18.0000 −0.737309
\(597\) 20.0000 0.818546
\(598\) 8.00000 0.327144
\(599\) 16.0000 0.653742 0.326871 − 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 1.00000 0.0408248
\(601\) −2.00000 −0.0815817 −0.0407909 − 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) −4.00000 −0.163028
\(603\) 0 0
\(604\) −8.00000 −0.325515
\(605\) 1.00000 0.0406558
\(606\) −14.0000 −0.568711
\(607\) 24.0000 0.974130 0.487065 − 0.873366i \(-0.338067\pi\)
0.487065 + 0.873366i \(0.338067\pi\)
\(608\) 4.00000 0.162221
\(609\) 10.0000 0.405220
\(610\) 14.0000 0.566843
\(611\) 0 0
\(612\) 2.00000 0.0808452
\(613\) 10.0000 0.403896 0.201948 − 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) 28.0000 1.12999
\(615\) −6.00000 −0.241943
\(616\) 1.00000 0.0402911
\(617\) 26.0000 1.04672 0.523360 − 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 8.00000 0.321807
\(619\) 24.0000 0.964641 0.482321 − 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) −4.00000 −0.160644
\(621\) −4.00000 −0.160514
\(622\) −28.0000 −1.12270
\(623\) 18.0000 0.721155
\(624\) 2.00000 0.0800641
\(625\) 1.00000 0.0400000
\(626\) −10.0000 −0.399680
\(627\) −4.00000 −0.159745
\(628\) −2.00000 −0.0798087
\(629\) −20.0000 −0.797452
\(630\) −1.00000 −0.0398410
\(631\) 40.0000 1.59237 0.796187 − 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 8.00000 0.318223
\(633\) −20.0000 −0.794929
\(634\) −14.0000 −0.556011
\(635\) 8.00000 0.317470
\(636\) 2.00000 0.0793052
\(637\) −2.00000 −0.0792429
\(638\) −10.0000 −0.395904
\(639\) 0 0
\(640\) −1.00000 −0.0395285
\(641\) −14.0000 −0.552967 −0.276483 − 0.961019i \(-0.589169\pi\)
−0.276483 + 0.961019i \(0.589169\pi\)
\(642\) 12.0000 0.473602
\(643\) 36.0000 1.41970 0.709851 − 0.704352i \(-0.248762\pi\)
0.709851 + 0.704352i \(0.248762\pi\)
\(644\) 4.00000 0.157622
\(645\) −4.00000 −0.157500
\(646\) 8.00000 0.314756
\(647\) −24.0000 −0.943537 −0.471769 − 0.881722i \(-0.656384\pi\)
−0.471769 + 0.881722i \(0.656384\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0 0
\(650\) 2.00000 0.0784465
\(651\) 4.00000 0.156772
\(652\) 0 0
\(653\) 38.0000 1.48705 0.743527 − 0.668705i \(-0.233151\pi\)
0.743527 + 0.668705i \(0.233151\pi\)
\(654\) −18.0000 −0.703856
\(655\) 4.00000 0.156293
\(656\) 6.00000 0.234261
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −4.00000 −0.155818 −0.0779089 − 0.996960i \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 1.00000 0.0389249
\(661\) 30.0000 1.16686 0.583432 − 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) −4.00000 −0.155464
\(663\) 4.00000 0.155347
\(664\) −4.00000 −0.155230
\(665\) −4.00000 −0.155113
\(666\) 10.0000 0.387492
\(667\) −40.0000 −1.54881
\(668\) −16.0000 −0.619059
\(669\) 8.00000 0.309298
\(670\) 0 0
\(671\) 14.0000 0.540464
\(672\) 1.00000 0.0385758
\(673\) −34.0000 −1.31060 −0.655302 − 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 18.0000 0.693334
\(675\) −1.00000 −0.0384900
\(676\) −9.00000 −0.346154
\(677\) 6.00000 0.230599 0.115299 − 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 2.00000 0.0768095
\(679\) 2.00000 0.0767530
\(680\) −2.00000 −0.0766965
\(681\) −12.0000 −0.459841
\(682\) −4.00000 −0.153168
\(683\) 16.0000 0.612223 0.306111 − 0.951996i \(-0.400972\pi\)
0.306111 + 0.951996i \(0.400972\pi\)
\(684\) −4.00000 −0.152944
\(685\) −22.0000 −0.840577
\(686\) −1.00000 −0.0381802
\(687\) −6.00000 −0.228914
\(688\) 4.00000 0.152499
\(689\) 4.00000 0.152388
\(690\) 4.00000 0.152277
\(691\) 8.00000 0.304334 0.152167 − 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 6.00000 0.228086
\(693\) −1.00000 −0.0379869
\(694\) −36.0000 −1.36654
\(695\) −20.0000 −0.758643
\(696\) −10.0000 −0.379049
\(697\) 12.0000 0.454532
\(698\) −18.0000 −0.681310
\(699\) −6.00000 −0.226941
\(700\) 1.00000 0.0377964
\(701\) −26.0000 −0.982006 −0.491003 − 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) −2.00000 −0.0754851
\(703\) 40.0000 1.50863
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) −14.0000 −0.526524
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) −8.00000 −0.300023
\(712\) −18.0000 −0.674579
\(713\) −16.0000 −0.599205
\(714\) 2.00000 0.0748481
\(715\) 2.00000 0.0747958
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) −16.0000 −0.597115
\(719\) 28.0000 1.04422 0.522112 − 0.852877i \(-0.325144\pi\)
0.522112 + 0.852877i \(0.325144\pi\)
\(720\) 1.00000 0.0372678
\(721\) 8.00000 0.297936
\(722\) 3.00000 0.111648
\(723\) −22.0000 −0.818189
\(724\) −10.0000 −0.371647
\(725\) −10.0000 −0.371391
\(726\) 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
\(732\) 14.0000 0.517455
\(733\) −18.0000 −0.664845 −0.332423 − 0.943131i \(-0.607866\pi\)
−0.332423 + 0.943131i \(0.607866\pi\)
\(734\) 0 0
\(735\) −1.00000 −0.0368856
\(736\) −4.00000 −0.147442
\(737\) 0 0
\(738\) −6.00000 −0.220863
\(739\) −44.0000 −1.61857 −0.809283 − 0.587419i \(-0.800144\pi\)
−0.809283 + 0.587419i \(0.800144\pi\)
\(740\) −10.0000 −0.367607
\(741\) −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 \(0.645106\pi\)
\(744\) −4.00000 −0.146647
\(745\) −18.0000 −0.659469
\(746\) 14.0000 0.512576
\(747\) 4.00000 0.146352
\(748\) −2.00000 −0.0731272
\(749\) 12.0000 0.438470
\(750\) 1.00000 0.0365148
\(751\) −8.00000 −0.291924 −0.145962 − 0.989290i \(-0.546628\pi\)
−0.145962 + 0.989290i \(0.546628\pi\)
\(752\) 0 0
\(753\) 16.0000 0.583072
\(754\) −20.0000 −0.728357
\(755\) −8.00000 −0.291150
\(756\) −1.00000 −0.0363696
\(757\) −2.00000 −0.0726912 −0.0363456 − 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 20.0000 0.726433
\(759\) 4.00000 0.145191
\(760\) 4.00000 0.145095
\(761\) 6.00000 0.217500 0.108750 − 0.994069i \(-0.465315\pi\)
0.108750 + 0.994069i \(0.465315\pi\)
\(762\) 8.00000 0.289809
\(763\) −18.0000 −0.651644
\(764\) 8.00000 0.289430
\(765\) 2.00000 0.0723102
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) −1.00000 −0.0360844
\(769\) 30.0000 1.08183 0.540914 − 0.841078i \(-0.318079\pi\)
0.540914 + 0.841078i \(0.318079\pi\)
\(770\) 1.00000 0.0360375
\(771\) 30.0000 1.08042
\(772\) −26.0000 −0.935760
\(773\) 6.00000 0.215805 0.107903 − 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) −4.00000 −0.143777
\(775\) −4.00000 −0.143684
\(776\) −2.00000 −0.0717958
\(777\) 10.0000 0.358748
\(778\) 26.0000 0.932145
\(779\) −24.0000 −0.859889
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) −8.00000 −0.286079
\(783\) 10.0000 0.357371
\(784\) 1.00000 0.0357143
\(785\) −2.00000 −0.0713831
\(786\) 4.00000 0.142675
\(787\) 44.0000 1.56843 0.784215 − 0.620489i \(-0.213066\pi\)
0.784215 + 0.620489i \(0.213066\pi\)
\(788\) 10.0000 0.356235
\(789\) 24.0000 0.854423
\(790\) 8.00000 0.284627
\(791\) 2.00000 0.0711118
\(792\) 1.00000 0.0355335
\(793\) 28.0000 0.994309
\(794\) −30.0000 −1.06466
\(795\) 2.00000 0.0709327
\(796\) −20.0000 −0.708881
\(797\) −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
\(801\) 18.0000 0.635999
\(802\) −2.00000 −0.0706225
\(803\) −2.00000 −0.0705785
\(804\) 0 0
\(805\) 4.00000 0.140981
\(806\) −8.00000 −0.281788
\(807\) −6.00000 −0.211210
\(808\) 14.0000 0.492518
\(809\) −30.0000 −1.05474 −0.527372 − 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 44.0000 1.54505 0.772524 − 0.634985i \(-0.218994\pi\)
0.772524 + 0.634985i \(0.218994\pi\)
\(812\) −10.0000 −0.350931
\(813\) 0 0
\(814\) −10.0000 −0.350500
\(815\) 0 0
\(816\) −2.00000 −0.0700140
\(817\) −16.0000 −0.559769
\(818\) 34.0000 1.18878
\(819\) −2.00000 −0.0698857
\(820\) 6.00000 0.209529
\(821\) 22.0000 0.767805 0.383903 − 0.923374i \(-0.374580\pi\)
0.383903 + 0.923374i \(0.374580\pi\)
\(822\) −22.0000 −0.767338
\(823\) −4.00000 −0.139431 −0.0697156 − 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) −8.00000 −0.278693
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) −28.0000 −0.973655 −0.486828 − 0.873498i \(-0.661846\pi\)
−0.486828 + 0.873498i \(0.661846\pi\)
\(828\) 4.00000 0.139010
\(829\) 6.00000 0.208389 0.104194 − 0.994557i \(-0.466774\pi\)
0.104194 + 0.994557i \(0.466774\pi\)
\(830\) −4.00000 −0.138842
\(831\) 22.0000 0.763172
\(832\) −2.00000 −0.0693375
\(833\) 2.00000 0.0692959
\(834\) −20.0000 −0.692543
\(835\) −16.0000 −0.553703
\(836\) 4.00000 0.138343
\(837\) 4.00000 0.138260
\(838\) −32.0000 −1.10542
\(839\) −4.00000 −0.138095 −0.0690477 − 0.997613i \(-0.521996\pi\)
−0.0690477 + 0.997613i \(0.521996\pi\)
\(840\) 1.00000 0.0345033
\(841\) 71.0000 2.44828
\(842\) −6.00000 −0.206774
\(843\) −10.0000 −0.344418
\(844\) 20.0000 0.688428
\(845\) −9.00000 −0.309609
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) −2.00000 −0.0686803
\(849\) −4.00000 −0.137280
\(850\) −2.00000 −0.0685994
\(851\) −40.0000 −1.37118
\(852\) 0 0
\(853\) 14.0000 0.479351 0.239675 − 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) 14.0000 0.479070
\(855\) −4.00000 −0.136797
\(856\) −12.0000 −0.410152
\(857\) −30.0000 −1.02478 −0.512390 − 0.858753i \(-0.671240\pi\)
−0.512390 + 0.858753i \(0.671240\pi\)
\(858\) 2.00000 0.0682789
\(859\) 24.0000 0.818869 0.409435 − 0.912339i \(-0.365726\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(860\) 4.00000 0.136399
\(861\) −6.00000 −0.204479
\(862\) 40.0000 1.36241
\(863\) −36.0000 −1.22545 −0.612727 − 0.790295i \(-0.709928\pi\)
−0.612727 + 0.790295i \(0.709928\pi\)
\(864\) 1.00000 0.0340207
\(865\) 6.00000 0.204006
\(866\) −18.0000 −0.611665
\(867\) 13.0000 0.441503
\(868\) −4.00000 −0.135769
\(869\) 8.00000 0.271381
\(870\) −10.0000 −0.339032
\(871\) 0 0
\(872\) 18.0000 0.609557
\(873\) 2.00000 0.0676897
\(874\) 16.0000 0.541208
\(875\) 1.00000 0.0338062
\(876\) −2.00000 −0.0675737
\(877\) 2.00000 0.0675352 0.0337676 − 0.999430i \(-0.489249\pi\)
0.0337676 + 0.999430i \(0.489249\pi\)
\(878\) 24.0000 0.809961
\(879\) 18.0000 0.607125
\(880\) −1.00000 −0.0337100
\(881\) 2.00000 0.0673817 0.0336909 − 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) −1.00000 −0.0336718
\(883\) −40.0000 −1.34611 −0.673054 − 0.739594i \(-0.735018\pi\)
−0.673054 + 0.739594i \(0.735018\pi\)
\(884\) −4.00000 −0.134535
\(885\) 0 0
\(886\) 8.00000 0.268765
\(887\) −24.0000 −0.805841 −0.402921 − 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) −10.0000 −0.335578
\(889\) 8.00000 0.268311
\(890\) −18.0000 −0.603361
\(891\) −1.00000 −0.0335013
\(892\) −8.00000 −0.267860
\(893\) 0 0
\(894\) −18.0000 −0.602010
\(895\) −12.0000 −0.401116
\(896\) −1.00000 −0.0334077
\(897\) 8.00000 0.267112
\(898\) 14.0000 0.467186
\(899\) 40.0000 1.33407
\(900\) 1.00000 0.0333333
\(901\) −4.00000 −0.133259
\(902\) 6.00000 0.199778
\(903\) −4.00000 −0.133112
\(904\) −2.00000 −0.0665190
\(905\) −10.0000 −0.332411
\(906\) −8.00000 −0.265782
\(907\) 40.0000 1.32818 0.664089 − 0.747653i \(-0.268820\pi\)
0.664089 + 0.747653i \(0.268820\pi\)
\(908\) 12.0000 0.398234
\(909\) −14.0000 −0.464351
\(910\) 2.00000 0.0662994
\(911\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 4.00000 0.132453
\(913\) −4.00000 −0.132381
\(914\) −22.0000 −0.727695
\(915\) 14.0000 0.462826
\(916\) 6.00000 0.198246
\(917\) 4.00000 0.132092
\(918\) 2.00000 0.0660098
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) −4.00000 −0.131876
\(921\) 28.0000 0.922631
\(922\) −18.0000 −0.592798
\(923\) 0 0
\(924\) 1.00000 0.0328976
\(925\) −10.0000 −0.328798
\(926\) −20.0000 −0.657241
\(927\) 8.00000 0.262754
\(928\) 10.0000 0.328266
\(929\) 18.0000 0.590561 0.295280 − 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) −4.00000 −0.131165
\(931\) −4.00000 −0.131095
\(932\) 6.00000 0.196537
\(933\) −28.0000 −0.916679
\(934\) −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 \(0.447772\pi\)
\(938\) 0 0
\(939\) −10.0000 −0.326338
\(940\) 0 0
\(941\) 18.0000 0.586783 0.293392 − 0.955992i \(-0.405216\pi\)
0.293392 + 0.955992i \(0.405216\pi\)
\(942\) −2.00000 −0.0651635
\(943\) 24.0000 0.781548
\(944\) 0 0
\(945\) −1.00000 −0.0325300
\(946\) 4.00000 0.130051
\(947\) −32.0000 −1.03986 −0.519930 − 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(948\) 8.00000 0.259828
\(949\) −4.00000 −0.129845
\(950\) 4.00000 0.129777
\(951\) −14.0000 −0.453981
\(952\) −2.00000 −0.0648204
\(953\) −2.00000 −0.0647864 −0.0323932 − 0.999475i \(-0.510313\pi\)
−0.0323932 + 0.999475i \(0.510313\pi\)
\(954\) 2.00000 0.0647524
\(955\) 8.00000 0.258874
\(956\) 0 0
\(957\) −10.0000 −0.323254
\(958\) 0 0
\(959\) −22.0000 −0.710417
\(960\) −1.00000 −0.0322749
\(961\) −15.0000 −0.483871
\(962\) −20.0000 −0.644826
\(963\) 12.0000 0.386695
\(964\) 22.0000 0.708572
\(965\) −26.0000 −0.836970
\(966\) 4.00000 0.128698
\(967\) 24.0000 0.771788 0.385894 − 0.922543i \(-0.373893\pi\)
0.385894 + 0.922543i \(0.373893\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 8.00000 0.256997
\(970\) −2.00000 −0.0642161
\(971\) −40.0000 −1.28366 −0.641831 − 0.766846i \(-0.721825\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −20.0000 −0.641171
\(974\) −4.00000 −0.128168
\(975\) 2.00000 0.0640513
\(976\) −14.0000 −0.448129
\(977\) −46.0000 −1.47167 −0.735835 − 0.677161i \(-0.763210\pi\)
−0.735835 + 0.677161i \(0.763210\pi\)
\(978\) 0 0
\(979\) −18.0000 −0.575282
\(980\) 1.00000 0.0319438
\(981\) −18.0000 −0.574696
\(982\) −12.0000 −0.382935
\(983\) −56.0000 −1.78612 −0.893061 − 0.449935i \(-0.851447\pi\)
−0.893061 + 0.449935i \(0.851447\pi\)
\(984\) 6.00000 0.191273
\(985\) 10.0000 0.318626
\(986\) 20.0000 0.636930
\(987\) 0 0
\(988\) 8.00000 0.254514
\(989\) 16.0000 0.508770
\(990\) 1.00000 0.0317821
\(991\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 4.00000 0.127000
\(993\) −4.00000 −0.126936
\(994\) 0 0
\(995\) −20.0000 −0.634043
\(996\) −4.00000 −0.126745
\(997\) −34.0000 −1.07679 −0.538395 − 0.842692i \(-0.680969\pi\)
−0.538395 + 0.842692i \(0.680969\pi\)
\(998\) −4.00000 −0.126618
\(999\) 10.0000 0.316386
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.d.1.1 ✓ 1
3.2 odd 2 6930.2.a.y.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2310.2.a.d.1.1 ✓ 1 1.1 even 1 trivial
6930.2.a.y.1.1 1 3.2 odd 2