Properties

Label 4334.2.a.h.1.18
Level $4334$
Weight $2$
Character 4334.1
Self dual yes
Analytic conductor $34.607$
Analytic rank $0$
Dimension $27$
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] = [4334,2,Mod(1,4334)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4334, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4334.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4334 = 2 \cdot 11 \cdot 197 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4334.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: \(34.6071642360\)
Analytic rank: \(0\)
Dimension: \(27\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4334.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.14059 q^{3} +1.00000 q^{4} -0.375030 q^{5} -1.14059 q^{6} +0.176944 q^{7} -1.00000 q^{8} -1.69906 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.14059 q^{3} +1.00000 q^{4} -0.375030 q^{5} -1.14059 q^{6} +0.176944 q^{7} -1.00000 q^{8} -1.69906 q^{9} +0.375030 q^{10} +1.00000 q^{11} +1.14059 q^{12} +5.77706 q^{13} -0.176944 q^{14} -0.427755 q^{15} +1.00000 q^{16} -1.61006 q^{17} +1.69906 q^{18} +5.31123 q^{19} -0.375030 q^{20} +0.201821 q^{21} -1.00000 q^{22} +6.15672 q^{23} -1.14059 q^{24} -4.85935 q^{25} -5.77706 q^{26} -5.35969 q^{27} +0.176944 q^{28} +3.06238 q^{29} +0.427755 q^{30} +8.87367 q^{31} -1.00000 q^{32} +1.14059 q^{33} +1.61006 q^{34} -0.0663595 q^{35} -1.69906 q^{36} -3.49928 q^{37} -5.31123 q^{38} +6.58924 q^{39} +0.375030 q^{40} -11.5908 q^{41} -0.201821 q^{42} +8.97270 q^{43} +1.00000 q^{44} +0.637199 q^{45} -6.15672 q^{46} +7.36380 q^{47} +1.14059 q^{48} -6.96869 q^{49} +4.85935 q^{50} -1.83641 q^{51} +5.77706 q^{52} -11.0118 q^{53} +5.35969 q^{54} -0.375030 q^{55} -0.176944 q^{56} +6.05792 q^{57} -3.06238 q^{58} -10.0186 q^{59} -0.427755 q^{60} +1.83225 q^{61} -8.87367 q^{62} -0.300639 q^{63} +1.00000 q^{64} -2.16657 q^{65} -1.14059 q^{66} +1.50796 q^{67} -1.61006 q^{68} +7.02228 q^{69} +0.0663595 q^{70} +8.55660 q^{71} +1.69906 q^{72} -6.63706 q^{73} +3.49928 q^{74} -5.54252 q^{75} +5.31123 q^{76} +0.176944 q^{77} -6.58924 q^{78} +2.84138 q^{79} -0.375030 q^{80} -1.01601 q^{81} +11.5908 q^{82} +7.86977 q^{83} +0.201821 q^{84} +0.603820 q^{85} -8.97270 q^{86} +3.49292 q^{87} -1.00000 q^{88} +0.885668 q^{89} -0.637199 q^{90} +1.02222 q^{91} +6.15672 q^{92} +10.1212 q^{93} -7.36380 q^{94} -1.99187 q^{95} -1.14059 q^{96} +7.17673 q^{97} +6.96869 q^{98} -1.69906 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 27 q - 27 q^{2} + 27 q^{4} + 9 q^{5} + q^{7} - 27 q^{8} + 43 q^{9} - 9 q^{10} + 27 q^{11} + 4 q^{13} - q^{14} + 8 q^{15} + 27 q^{16} + 3 q^{17} - 43 q^{18} + 30 q^{19} + 9 q^{20} + 11 q^{21} - 27 q^{22} + 13 q^{23} + 50 q^{25} - 4 q^{26} - 3 q^{27} + q^{28} + 5 q^{29} - 8 q^{30} + 40 q^{31} - 27 q^{32} - 3 q^{34} - 16 q^{35} + 43 q^{36} + 21 q^{37} - 30 q^{38} + 5 q^{39} - 9 q^{40} + 13 q^{41} - 11 q^{42} + 10 q^{43} + 27 q^{44} + 48 q^{45} - 13 q^{46} + 78 q^{49} - 50 q^{50} + 8 q^{51} + 4 q^{52} + 8 q^{53} + 3 q^{54} + 9 q^{55} - q^{56} - 16 q^{57} - 5 q^{58} + 24 q^{59} + 8 q^{60} + 28 q^{61} - 40 q^{62} - 18 q^{63} + 27 q^{64} - q^{65} + 24 q^{67} + 3 q^{68} - 3 q^{69} + 16 q^{70} - 3 q^{71} - 43 q^{72} + 9 q^{73} - 21 q^{74} + 26 q^{75} + 30 q^{76} + q^{77} - 5 q^{78} + 12 q^{79} + 9 q^{80} + 99 q^{81} - 13 q^{82} - 11 q^{83} + 11 q^{84} + 15 q^{85} - 10 q^{86} - 34 q^{87} - 27 q^{88} + 69 q^{89} - 48 q^{90} + q^{91} + 13 q^{92} - 24 q^{93} - 31 q^{95} + 41 q^{97} - 78 q^{98} + 43 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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
\(3\) 1.14059 0.658518 0.329259 0.944240i \(-0.393201\pi\)
0.329259 + 0.944240i \(0.393201\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.375030 −0.167719 −0.0838594 0.996478i \(-0.526725\pi\)
−0.0838594 + 0.996478i \(0.526725\pi\)
\(6\) −1.14059 −0.465643
\(7\) 0.176944 0.0668787 0.0334394 0.999441i \(-0.489354\pi\)
0.0334394 + 0.999441i \(0.489354\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.69906 −0.566353
\(10\) 0.375030 0.118595
\(11\) 1.00000 0.301511
\(12\) 1.14059 0.329259
\(13\) 5.77706 1.60227 0.801134 0.598485i \(-0.204230\pi\)
0.801134 + 0.598485i \(0.204230\pi\)
\(14\) −0.176944 −0.0472904
\(15\) −0.427755 −0.110446
\(16\) 1.00000 0.250000
\(17\) −1.61006 −0.390496 −0.195248 0.980754i \(-0.562551\pi\)
−0.195248 + 0.980754i \(0.562551\pi\)
\(18\) 1.69906 0.400472
\(19\) 5.31123 1.21848 0.609239 0.792986i \(-0.291475\pi\)
0.609239 + 0.792986i \(0.291475\pi\)
\(20\) −0.375030 −0.0838594
\(21\) 0.201821 0.0440409
\(22\) −1.00000 −0.213201
\(23\) 6.15672 1.28377 0.641883 0.766803i \(-0.278154\pi\)
0.641883 + 0.766803i \(0.278154\pi\)
\(24\) −1.14059 −0.232821
\(25\) −4.85935 −0.971870
\(26\) −5.77706 −1.13297
\(27\) −5.35969 −1.03147
\(28\) 0.176944 0.0334394
\(29\) 3.06238 0.568670 0.284335 0.958725i \(-0.408227\pi\)
0.284335 + 0.958725i \(0.408227\pi\)
\(30\) 0.427755 0.0780970
\(31\) 8.87367 1.59376 0.796879 0.604139i \(-0.206483\pi\)
0.796879 + 0.604139i \(0.206483\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.14059 0.198551
\(34\) 1.61006 0.276122
\(35\) −0.0663595 −0.0112168
\(36\) −1.69906 −0.283177
\(37\) −3.49928 −0.575279 −0.287639 0.957739i \(-0.592870\pi\)
−0.287639 + 0.957739i \(0.592870\pi\)
\(38\) −5.31123 −0.861595
\(39\) 6.58924 1.05512
\(40\) 0.375030 0.0592975
\(41\) −11.5908 −1.81018 −0.905088 0.425223i \(-0.860196\pi\)
−0.905088 + 0.425223i \(0.860196\pi\)
\(42\) −0.201821 −0.0311416
\(43\) 8.97270 1.36832 0.684162 0.729330i \(-0.260168\pi\)
0.684162 + 0.729330i \(0.260168\pi\)
\(44\) 1.00000 0.150756
\(45\) 0.637199 0.0949881
\(46\) −6.15672 −0.907759
\(47\) 7.36380 1.07412 0.537061 0.843544i \(-0.319535\pi\)
0.537061 + 0.843544i \(0.319535\pi\)
\(48\) 1.14059 0.164630
\(49\) −6.96869 −0.995527
\(50\) 4.85935 0.687216
\(51\) −1.83641 −0.257149
\(52\) 5.77706 0.801134
\(53\) −11.0118 −1.51259 −0.756293 0.654233i \(-0.772992\pi\)
−0.756293 + 0.654233i \(0.772992\pi\)
\(54\) 5.35969 0.729361
\(55\) −0.375030 −0.0505691
\(56\) −0.176944 −0.0236452
\(57\) 6.05792 0.802391
\(58\) −3.06238 −0.402111
\(59\) −10.0186 −1.30431 −0.652155 0.758086i \(-0.726135\pi\)
−0.652155 + 0.758086i \(0.726135\pi\)
\(60\) −0.427755 −0.0552229
\(61\) 1.83225 0.234595 0.117298 0.993097i \(-0.462577\pi\)
0.117298 + 0.993097i \(0.462577\pi\)
\(62\) −8.87367 −1.12696
\(63\) −0.300639 −0.0378770
\(64\) 1.00000 0.125000
\(65\) −2.16657 −0.268730
\(66\) −1.14059 −0.140397
\(67\) 1.50796 0.184226 0.0921132 0.995749i \(-0.470638\pi\)
0.0921132 + 0.995749i \(0.470638\pi\)
\(68\) −1.61006 −0.195248
\(69\) 7.02228 0.845383
\(70\) 0.0663595 0.00793148
\(71\) 8.55660 1.01548 0.507741 0.861510i \(-0.330481\pi\)
0.507741 + 0.861510i \(0.330481\pi\)
\(72\) 1.69906 0.200236
\(73\) −6.63706 −0.776809 −0.388404 0.921489i \(-0.626974\pi\)
−0.388404 + 0.921489i \(0.626974\pi\)
\(74\) 3.49928 0.406784
\(75\) −5.54252 −0.639995
\(76\) 5.31123 0.609239
\(77\) 0.176944 0.0201647
\(78\) −6.58924 −0.746085
\(79\) 2.84138 0.319680 0.159840 0.987143i \(-0.448902\pi\)
0.159840 + 0.987143i \(0.448902\pi\)
\(80\) −0.375030 −0.0419297
\(81\) −1.01601 −0.112890
\(82\) 11.5908 1.27999
\(83\) 7.86977 0.863819 0.431910 0.901917i \(-0.357840\pi\)
0.431910 + 0.901917i \(0.357840\pi\)
\(84\) 0.201821 0.0220204
\(85\) 0.603820 0.0654935
\(86\) −8.97270 −0.967551
\(87\) 3.49292 0.374480
\(88\) −1.00000 −0.106600
\(89\) 0.885668 0.0938807 0.0469403 0.998898i \(-0.485053\pi\)
0.0469403 + 0.998898i \(0.485053\pi\)
\(90\) −0.637199 −0.0671667
\(91\) 1.02222 0.107158
\(92\) 6.15672 0.641883
\(93\) 10.1212 1.04952
\(94\) −7.36380 −0.759518
\(95\) −1.99187 −0.204362
\(96\) −1.14059 −0.116411
\(97\) 7.17673 0.728686 0.364343 0.931265i \(-0.381294\pi\)
0.364343 + 0.931265i \(0.381294\pi\)
\(98\) 6.96869 0.703944
\(99\) −1.69906 −0.170762
\(100\) −4.85935 −0.485935
\(101\) −14.6793 −1.46064 −0.730322 0.683103i \(-0.760630\pi\)
−0.730322 + 0.683103i \(0.760630\pi\)
\(102\) 1.83641 0.181832
\(103\) 5.93610 0.584901 0.292450 0.956281i \(-0.405529\pi\)
0.292450 + 0.956281i \(0.405529\pi\)
\(104\) −5.77706 −0.566487
\(105\) −0.0756889 −0.00738648
\(106\) 11.0118 1.06956
\(107\) −11.0816 −1.07130 −0.535649 0.844441i \(-0.679933\pi\)
−0.535649 + 0.844441i \(0.679933\pi\)
\(108\) −5.35969 −0.515736
\(109\) 4.02602 0.385623 0.192811 0.981236i \(-0.438239\pi\)
0.192811 + 0.981236i \(0.438239\pi\)
\(110\) 0.375030 0.0357578
\(111\) −3.99124 −0.378832
\(112\) 0.176944 0.0167197
\(113\) 20.8267 1.95921 0.979606 0.200928i \(-0.0643958\pi\)
0.979606 + 0.200928i \(0.0643958\pi\)
\(114\) −6.05792 −0.567376
\(115\) −2.30896 −0.215311
\(116\) 3.06238 0.284335
\(117\) −9.81558 −0.907450
\(118\) 10.0186 0.922286
\(119\) −0.284890 −0.0261159
\(120\) 0.427755 0.0390485
\(121\) 1.00000 0.0909091
\(122\) −1.83225 −0.165884
\(123\) −13.2203 −1.19203
\(124\) 8.87367 0.796879
\(125\) 3.69756 0.330720
\(126\) 0.300639 0.0267831
\(127\) 5.71335 0.506978 0.253489 0.967338i \(-0.418422\pi\)
0.253489 + 0.967338i \(0.418422\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.2342 0.901067
\(130\) 2.16657 0.190021
\(131\) 12.9789 1.13397 0.566986 0.823727i \(-0.308109\pi\)
0.566986 + 0.823727i \(0.308109\pi\)
\(132\) 1.14059 0.0992754
\(133\) 0.939792 0.0814903
\(134\) −1.50796 −0.130268
\(135\) 2.01005 0.172997
\(136\) 1.61006 0.138061
\(137\) −3.53736 −0.302217 −0.151109 0.988517i \(-0.548284\pi\)
−0.151109 + 0.988517i \(0.548284\pi\)
\(138\) −7.02228 −0.597776
\(139\) 10.0260 0.850391 0.425195 0.905102i \(-0.360205\pi\)
0.425195 + 0.905102i \(0.360205\pi\)
\(140\) −0.0663595 −0.00560841
\(141\) 8.39906 0.707329
\(142\) −8.55660 −0.718054
\(143\) 5.77706 0.483102
\(144\) −1.69906 −0.141588
\(145\) −1.14849 −0.0953767
\(146\) 6.63706 0.549287
\(147\) −7.94840 −0.655573
\(148\) −3.49928 −0.287639
\(149\) 24.1445 1.97799 0.988996 0.147939i \(-0.0472640\pi\)
0.988996 + 0.147939i \(0.0472640\pi\)
\(150\) 5.54252 0.452545
\(151\) −0.198077 −0.0161193 −0.00805965 0.999968i \(-0.502565\pi\)
−0.00805965 + 0.999968i \(0.502565\pi\)
\(152\) −5.31123 −0.430797
\(153\) 2.73558 0.221159
\(154\) −0.176944 −0.0142586
\(155\) −3.32790 −0.267303
\(156\) 6.58924 0.527562
\(157\) 20.2212 1.61383 0.806913 0.590670i \(-0.201137\pi\)
0.806913 + 0.590670i \(0.201137\pi\)
\(158\) −2.84138 −0.226048
\(159\) −12.5599 −0.996066
\(160\) 0.375030 0.0296488
\(161\) 1.08940 0.0858566
\(162\) 1.01601 0.0798255
\(163\) 11.7335 0.919039 0.459519 0.888168i \(-0.348022\pi\)
0.459519 + 0.888168i \(0.348022\pi\)
\(164\) −11.5908 −0.905088
\(165\) −0.427755 −0.0333007
\(166\) −7.86977 −0.610813
\(167\) 19.8909 1.53920 0.769602 0.638524i \(-0.220455\pi\)
0.769602 + 0.638524i \(0.220455\pi\)
\(168\) −0.201821 −0.0155708
\(169\) 20.3744 1.56726
\(170\) −0.603820 −0.0463109
\(171\) −9.02409 −0.690090
\(172\) 8.97270 0.684162
\(173\) 20.3715 1.54882 0.774408 0.632687i \(-0.218048\pi\)
0.774408 + 0.632687i \(0.218048\pi\)
\(174\) −3.49292 −0.264797
\(175\) −0.859835 −0.0649974
\(176\) 1.00000 0.0753778
\(177\) −11.4271 −0.858912
\(178\) −0.885668 −0.0663836
\(179\) 11.3922 0.851491 0.425745 0.904843i \(-0.360012\pi\)
0.425745 + 0.904843i \(0.360012\pi\)
\(180\) 0.637199 0.0474940
\(181\) −8.49660 −0.631547 −0.315774 0.948835i \(-0.602264\pi\)
−0.315774 + 0.948835i \(0.602264\pi\)
\(182\) −1.02222 −0.0757719
\(183\) 2.08984 0.154485
\(184\) −6.15672 −0.453880
\(185\) 1.31234 0.0964850
\(186\) −10.1212 −0.742122
\(187\) −1.61006 −0.117739
\(188\) 7.36380 0.537061
\(189\) −0.948367 −0.0689836
\(190\) 1.99187 0.144506
\(191\) −4.10814 −0.297255 −0.148627 0.988893i \(-0.547486\pi\)
−0.148627 + 0.988893i \(0.547486\pi\)
\(192\) 1.14059 0.0823148
\(193\) −19.8031 −1.42546 −0.712731 0.701438i \(-0.752542\pi\)
−0.712731 + 0.701438i \(0.752542\pi\)
\(194\) −7.17673 −0.515259
\(195\) −2.47117 −0.176964
\(196\) −6.96869 −0.497764
\(197\) −1.00000 −0.0712470
\(198\) 1.69906 0.120747
\(199\) 17.2853 1.22532 0.612661 0.790346i \(-0.290099\pi\)
0.612661 + 0.790346i \(0.290099\pi\)
\(200\) 4.85935 0.343608
\(201\) 1.71996 0.121316
\(202\) 14.6793 1.03283
\(203\) 0.541872 0.0380319
\(204\) −1.83641 −0.128574
\(205\) 4.34690 0.303601
\(206\) −5.93610 −0.413587
\(207\) −10.4606 −0.727065
\(208\) 5.77706 0.400567
\(209\) 5.31123 0.367385
\(210\) 0.0756889 0.00522303
\(211\) −6.16750 −0.424588 −0.212294 0.977206i \(-0.568093\pi\)
−0.212294 + 0.977206i \(0.568093\pi\)
\(212\) −11.0118 −0.756293
\(213\) 9.75955 0.668713
\(214\) 11.0816 0.757522
\(215\) −3.36504 −0.229494
\(216\) 5.35969 0.364681
\(217\) 1.57015 0.106588
\(218\) −4.02602 −0.272677
\(219\) −7.57014 −0.511543
\(220\) −0.375030 −0.0252845
\(221\) −9.30139 −0.625679
\(222\) 3.99124 0.267874
\(223\) −21.1361 −1.41538 −0.707688 0.706525i \(-0.750262\pi\)
−0.707688 + 0.706525i \(0.750262\pi\)
\(224\) −0.176944 −0.0118226
\(225\) 8.25633 0.550422
\(226\) −20.8267 −1.38537
\(227\) −16.8202 −1.11640 −0.558199 0.829707i \(-0.688507\pi\)
−0.558199 + 0.829707i \(0.688507\pi\)
\(228\) 6.05792 0.401195
\(229\) 20.4813 1.35344 0.676720 0.736241i \(-0.263401\pi\)
0.676720 + 0.736241i \(0.263401\pi\)
\(230\) 2.30896 0.152248
\(231\) 0.201821 0.0132788
\(232\) −3.06238 −0.201055
\(233\) −26.4406 −1.73218 −0.866091 0.499886i \(-0.833375\pi\)
−0.866091 + 0.499886i \(0.833375\pi\)
\(234\) 9.81558 0.641664
\(235\) −2.76165 −0.180150
\(236\) −10.0186 −0.652155
\(237\) 3.24084 0.210515
\(238\) 0.284890 0.0184667
\(239\) −22.1273 −1.43130 −0.715648 0.698461i \(-0.753869\pi\)
−0.715648 + 0.698461i \(0.753869\pi\)
\(240\) −0.427755 −0.0276115
\(241\) 12.7215 0.819463 0.409731 0.912206i \(-0.365622\pi\)
0.409731 + 0.912206i \(0.365622\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 14.9202 0.957132
\(244\) 1.83225 0.117298
\(245\) 2.61347 0.166969
\(246\) 13.2203 0.842896
\(247\) 30.6833 1.95233
\(248\) −8.87367 −0.563478
\(249\) 8.97616 0.568841
\(250\) −3.69756 −0.233854
\(251\) −1.39768 −0.0882206 −0.0441103 0.999027i \(-0.514045\pi\)
−0.0441103 + 0.999027i \(0.514045\pi\)
\(252\) −0.300639 −0.0189385
\(253\) 6.15672 0.387070
\(254\) −5.71335 −0.358487
\(255\) 0.688709 0.0431287
\(256\) 1.00000 0.0625000
\(257\) −22.1133 −1.37939 −0.689695 0.724100i \(-0.742255\pi\)
−0.689695 + 0.724100i \(0.742255\pi\)
\(258\) −10.2342 −0.637150
\(259\) −0.619179 −0.0384739
\(260\) −2.16657 −0.134365
\(261\) −5.20317 −0.322068
\(262\) −12.9789 −0.801840
\(263\) 3.97155 0.244896 0.122448 0.992475i \(-0.460925\pi\)
0.122448 + 0.992475i \(0.460925\pi\)
\(264\) −1.14059 −0.0701983
\(265\) 4.12976 0.253689
\(266\) −0.939792 −0.0576223
\(267\) 1.01018 0.0618221
\(268\) 1.50796 0.0921132
\(269\) 25.6677 1.56499 0.782495 0.622657i \(-0.213947\pi\)
0.782495 + 0.622657i \(0.213947\pi\)
\(270\) −2.01005 −0.122328
\(271\) −0.364186 −0.0221227 −0.0110614 0.999939i \(-0.503521\pi\)
−0.0110614 + 0.999939i \(0.503521\pi\)
\(272\) −1.61006 −0.0976240
\(273\) 1.16593 0.0705653
\(274\) 3.53736 0.213700
\(275\) −4.85935 −0.293030
\(276\) 7.02228 0.422691
\(277\) 18.9045 1.13586 0.567931 0.823076i \(-0.307744\pi\)
0.567931 + 0.823076i \(0.307744\pi\)
\(278\) −10.0260 −0.601317
\(279\) −15.0769 −0.902630
\(280\) 0.0663595 0.00396574
\(281\) −27.4959 −1.64027 −0.820135 0.572170i \(-0.806102\pi\)
−0.820135 + 0.572170i \(0.806102\pi\)
\(282\) −8.39906 −0.500157
\(283\) 6.24017 0.370939 0.185470 0.982650i \(-0.440619\pi\)
0.185470 + 0.982650i \(0.440619\pi\)
\(284\) 8.55660 0.507741
\(285\) −2.27190 −0.134576
\(286\) −5.77706 −0.341605
\(287\) −2.05093 −0.121062
\(288\) 1.69906 0.100118
\(289\) −14.4077 −0.847513
\(290\) 1.14849 0.0674415
\(291\) 8.18568 0.479853
\(292\) −6.63706 −0.388404
\(293\) −16.9894 −0.992533 −0.496267 0.868170i \(-0.665296\pi\)
−0.496267 + 0.868170i \(0.665296\pi\)
\(294\) 7.94840 0.463560
\(295\) 3.75728 0.218757
\(296\) 3.49928 0.203392
\(297\) −5.35969 −0.311001
\(298\) −24.1445 −1.39865
\(299\) 35.5678 2.05694
\(300\) −5.54252 −0.319997
\(301\) 1.58767 0.0915118
\(302\) 0.198077 0.0113981
\(303\) −16.7430 −0.961861
\(304\) 5.31123 0.304620
\(305\) −0.687148 −0.0393460
\(306\) −2.73558 −0.156383
\(307\) −30.2004 −1.72363 −0.861813 0.507226i \(-0.830671\pi\)
−0.861813 + 0.507226i \(0.830671\pi\)
\(308\) 0.176944 0.0100823
\(309\) 6.77064 0.385168
\(310\) 3.32790 0.189012
\(311\) 25.5594 1.44934 0.724670 0.689096i \(-0.241992\pi\)
0.724670 + 0.689096i \(0.241992\pi\)
\(312\) −6.58924 −0.373042
\(313\) 26.4591 1.49556 0.747779 0.663948i \(-0.231120\pi\)
0.747779 + 0.663948i \(0.231120\pi\)
\(314\) −20.2212 −1.14115
\(315\) 0.112749 0.00635268
\(316\) 2.84138 0.159840
\(317\) 26.8098 1.50579 0.752894 0.658142i \(-0.228657\pi\)
0.752894 + 0.658142i \(0.228657\pi\)
\(318\) 12.5599 0.704325
\(319\) 3.06238 0.171461
\(320\) −0.375030 −0.0209648
\(321\) −12.6395 −0.705469
\(322\) −1.08940 −0.0607097
\(323\) −8.55137 −0.475811
\(324\) −1.01601 −0.0564451
\(325\) −28.0728 −1.55720
\(326\) −11.7335 −0.649859
\(327\) 4.59203 0.253940
\(328\) 11.5908 0.639994
\(329\) 1.30298 0.0718358
\(330\) 0.427755 0.0235471
\(331\) −2.24781 −0.123551 −0.0617753 0.998090i \(-0.519676\pi\)
−0.0617753 + 0.998090i \(0.519676\pi\)
\(332\) 7.86977 0.431910
\(333\) 5.94550 0.325811
\(334\) −19.8909 −1.08838
\(335\) −0.565530 −0.0308982
\(336\) 0.201821 0.0110102
\(337\) −20.0951 −1.09465 −0.547325 0.836920i \(-0.684354\pi\)
−0.547325 + 0.836920i \(0.684354\pi\)
\(338\) −20.3744 −1.10822
\(339\) 23.7547 1.29018
\(340\) 0.603820 0.0327467
\(341\) 8.87367 0.480536
\(342\) 9.02409 0.487967
\(343\) −2.47168 −0.133458
\(344\) −8.97270 −0.483776
\(345\) −2.63357 −0.141787
\(346\) −20.3715 −1.09518
\(347\) 7.48401 0.401763 0.200881 0.979616i \(-0.435619\pi\)
0.200881 + 0.979616i \(0.435619\pi\)
\(348\) 3.49292 0.187240
\(349\) −3.60092 −0.192753 −0.0963764 0.995345i \(-0.530725\pi\)
−0.0963764 + 0.995345i \(0.530725\pi\)
\(350\) 0.859835 0.0459601
\(351\) −30.9633 −1.65270
\(352\) −1.00000 −0.0533002
\(353\) −19.9929 −1.06411 −0.532057 0.846709i \(-0.678581\pi\)
−0.532057 + 0.846709i \(0.678581\pi\)
\(354\) 11.4271 0.607342
\(355\) −3.20899 −0.170315
\(356\) 0.885668 0.0469403
\(357\) −0.324942 −0.0171978
\(358\) −11.3922 −0.602095
\(359\) 17.4829 0.922713 0.461357 0.887215i \(-0.347363\pi\)
0.461357 + 0.887215i \(0.347363\pi\)
\(360\) −0.637199 −0.0335834
\(361\) 9.20912 0.484690
\(362\) 8.49660 0.446571
\(363\) 1.14059 0.0598653
\(364\) 1.02222 0.0535788
\(365\) 2.48910 0.130285
\(366\) −2.08984 −0.109238
\(367\) 29.5756 1.54383 0.771917 0.635724i \(-0.219298\pi\)
0.771917 + 0.635724i \(0.219298\pi\)
\(368\) 6.15672 0.320941
\(369\) 19.6934 1.02520
\(370\) −1.31234 −0.0682252
\(371\) −1.94848 −0.101160
\(372\) 10.1212 0.524759
\(373\) 23.6488 1.22449 0.612244 0.790669i \(-0.290267\pi\)
0.612244 + 0.790669i \(0.290267\pi\)
\(374\) 1.61006 0.0832540
\(375\) 4.21739 0.217785
\(376\) −7.36380 −0.379759
\(377\) 17.6916 0.911163
\(378\) 0.948367 0.0487787
\(379\) 22.9373 1.17821 0.589105 0.808057i \(-0.299481\pi\)
0.589105 + 0.808057i \(0.299481\pi\)
\(380\) −1.99187 −0.102181
\(381\) 6.51658 0.333854
\(382\) 4.10814 0.210191
\(383\) −18.5190 −0.946277 −0.473139 0.880988i \(-0.656879\pi\)
−0.473139 + 0.880988i \(0.656879\pi\)
\(384\) −1.14059 −0.0582054
\(385\) −0.0663595 −0.00338200
\(386\) 19.8031 1.00795
\(387\) −15.2452 −0.774955
\(388\) 7.17673 0.364343
\(389\) −18.5454 −0.940288 −0.470144 0.882590i \(-0.655798\pi\)
−0.470144 + 0.882590i \(0.655798\pi\)
\(390\) 2.47117 0.125132
\(391\) −9.91266 −0.501305
\(392\) 6.96869 0.351972
\(393\) 14.8036 0.746742
\(394\) 1.00000 0.0503793
\(395\) −1.06560 −0.0536163
\(396\) −1.69906 −0.0853810
\(397\) 2.64088 0.132542 0.0662711 0.997802i \(-0.478890\pi\)
0.0662711 + 0.997802i \(0.478890\pi\)
\(398\) −17.2853 −0.866434
\(399\) 1.07191 0.0536629
\(400\) −4.85935 −0.242968
\(401\) −24.6618 −1.23155 −0.615777 0.787921i \(-0.711158\pi\)
−0.615777 + 0.787921i \(0.711158\pi\)
\(402\) −1.71996 −0.0857837
\(403\) 51.2637 2.55363
\(404\) −14.6793 −0.730322
\(405\) 0.381036 0.0189338
\(406\) −0.541872 −0.0268926
\(407\) −3.49928 −0.173453
\(408\) 1.83641 0.0909158
\(409\) −3.50713 −0.173416 −0.0867082 0.996234i \(-0.527635\pi\)
−0.0867082 + 0.996234i \(0.527635\pi\)
\(410\) −4.34690 −0.214678
\(411\) −4.03467 −0.199016
\(412\) 5.93610 0.292450
\(413\) −1.77273 −0.0872305
\(414\) 10.4606 0.514112
\(415\) −2.95140 −0.144879
\(416\) −5.77706 −0.283244
\(417\) 11.4355 0.559998
\(418\) −5.31123 −0.259781
\(419\) −4.67818 −0.228544 −0.114272 0.993449i \(-0.536454\pi\)
−0.114272 + 0.993449i \(0.536454\pi\)
\(420\) −0.0756889 −0.00369324
\(421\) −26.2204 −1.27791 −0.638953 0.769246i \(-0.720632\pi\)
−0.638953 + 0.769246i \(0.720632\pi\)
\(422\) 6.16750 0.300229
\(423\) −12.5115 −0.608332
\(424\) 11.0118 0.534780
\(425\) 7.82383 0.379511
\(426\) −9.75955 −0.472852
\(427\) 0.324206 0.0156894
\(428\) −11.0816 −0.535649
\(429\) 6.58924 0.318132
\(430\) 3.36504 0.162276
\(431\) −4.21940 −0.203241 −0.101621 0.994823i \(-0.532403\pi\)
−0.101621 + 0.994823i \(0.532403\pi\)
\(432\) −5.35969 −0.257868
\(433\) −26.6218 −1.27936 −0.639681 0.768640i \(-0.720934\pi\)
−0.639681 + 0.768640i \(0.720934\pi\)
\(434\) −1.57015 −0.0753694
\(435\) −1.30995 −0.0628073
\(436\) 4.02602 0.192811
\(437\) 32.6997 1.56424
\(438\) 7.57014 0.361715
\(439\) 0.548668 0.0261865 0.0130932 0.999914i \(-0.495832\pi\)
0.0130932 + 0.999914i \(0.495832\pi\)
\(440\) 0.375030 0.0178789
\(441\) 11.8402 0.563820
\(442\) 9.30139 0.442422
\(443\) 33.8396 1.60777 0.803883 0.594788i \(-0.202764\pi\)
0.803883 + 0.594788i \(0.202764\pi\)
\(444\) −3.99124 −0.189416
\(445\) −0.332153 −0.0157455
\(446\) 21.1361 1.00082
\(447\) 27.5389 1.30254
\(448\) 0.176944 0.00835984
\(449\) 0.977296 0.0461215 0.0230607 0.999734i \(-0.492659\pi\)
0.0230607 + 0.999734i \(0.492659\pi\)
\(450\) −8.25633 −0.389207
\(451\) −11.5908 −0.545789
\(452\) 20.8267 0.979606
\(453\) −0.225925 −0.0106149
\(454\) 16.8202 0.789412
\(455\) −0.383363 −0.0179723
\(456\) −6.05792 −0.283688
\(457\) −0.113660 −0.00531680 −0.00265840 0.999996i \(-0.500846\pi\)
−0.00265840 + 0.999996i \(0.500846\pi\)
\(458\) −20.4813 −0.957026
\(459\) 8.62940 0.402786
\(460\) −2.30896 −0.107656
\(461\) 3.00340 0.139882 0.0699412 0.997551i \(-0.477719\pi\)
0.0699412 + 0.997551i \(0.477719\pi\)
\(462\) −0.201821 −0.00938954
\(463\) 14.9797 0.696166 0.348083 0.937464i \(-0.386833\pi\)
0.348083 + 0.937464i \(0.386833\pi\)
\(464\) 3.06238 0.142168
\(465\) −3.79576 −0.176024
\(466\) 26.4406 1.22484
\(467\) −26.3116 −1.21756 −0.608778 0.793341i \(-0.708340\pi\)
−0.608778 + 0.793341i \(0.708340\pi\)
\(468\) −9.81558 −0.453725
\(469\) 0.266825 0.0123208
\(470\) 2.76165 0.127385
\(471\) 23.0640 1.06273
\(472\) 10.0186 0.461143
\(473\) 8.97270 0.412565
\(474\) −3.24084 −0.148857
\(475\) −25.8091 −1.18420
\(476\) −0.284890 −0.0130579
\(477\) 18.7097 0.856659
\(478\) 22.1273 1.01208
\(479\) −25.7015 −1.17433 −0.587165 0.809467i \(-0.699756\pi\)
−0.587165 + 0.809467i \(0.699756\pi\)
\(480\) 0.427755 0.0195243
\(481\) −20.2156 −0.921751
\(482\) −12.7215 −0.579448
\(483\) 1.24255 0.0565381
\(484\) 1.00000 0.0454545
\(485\) −2.69149 −0.122214
\(486\) −14.9202 −0.676795
\(487\) 15.4358 0.699464 0.349732 0.936850i \(-0.386273\pi\)
0.349732 + 0.936850i \(0.386273\pi\)
\(488\) −1.83225 −0.0829419
\(489\) 13.3831 0.605204
\(490\) −2.61347 −0.118065
\(491\) 13.1337 0.592717 0.296359 0.955077i \(-0.404228\pi\)
0.296359 + 0.955077i \(0.404228\pi\)
\(492\) −13.2203 −0.596017
\(493\) −4.93061 −0.222063
\(494\) −30.6833 −1.38051
\(495\) 0.637199 0.0286400
\(496\) 8.87367 0.398439
\(497\) 1.51404 0.0679141
\(498\) −8.97616 −0.402231
\(499\) 1.38739 0.0621080 0.0310540 0.999518i \(-0.490114\pi\)
0.0310540 + 0.999518i \(0.490114\pi\)
\(500\) 3.69756 0.165360
\(501\) 22.6873 1.01359
\(502\) 1.39768 0.0623814
\(503\) −31.6192 −1.40983 −0.704915 0.709292i \(-0.749015\pi\)
−0.704915 + 0.709292i \(0.749015\pi\)
\(504\) 0.300639 0.0133915
\(505\) 5.50518 0.244977
\(506\) −6.15672 −0.273700
\(507\) 23.2388 1.03207
\(508\) 5.71335 0.253489
\(509\) −14.2574 −0.631948 −0.315974 0.948768i \(-0.602331\pi\)
−0.315974 + 0.948768i \(0.602331\pi\)
\(510\) −0.688709 −0.0304966
\(511\) −1.17439 −0.0519520
\(512\) −1.00000 −0.0441942
\(513\) −28.4665 −1.25683
\(514\) 22.1133 0.975376
\(515\) −2.22622 −0.0980988
\(516\) 10.2342 0.450533
\(517\) 7.36380 0.323860
\(518\) 0.619179 0.0272052
\(519\) 23.2355 1.01992
\(520\) 2.16657 0.0950106
\(521\) −28.0934 −1.23079 −0.615397 0.788217i \(-0.711004\pi\)
−0.615397 + 0.788217i \(0.711004\pi\)
\(522\) 5.20317 0.227737
\(523\) −13.8013 −0.603487 −0.301743 0.953389i \(-0.597569\pi\)
−0.301743 + 0.953389i \(0.597569\pi\)
\(524\) 12.9789 0.566986
\(525\) −0.980717 −0.0428020
\(526\) −3.97155 −0.173168
\(527\) −14.2871 −0.622356
\(528\) 1.14059 0.0496377
\(529\) 14.9052 0.648053
\(530\) −4.12976 −0.179385
\(531\) 17.0222 0.738700
\(532\) 0.939792 0.0407451
\(533\) −66.9607 −2.90039
\(534\) −1.01018 −0.0437149
\(535\) 4.15593 0.179677
\(536\) −1.50796 −0.0651338
\(537\) 12.9938 0.560722
\(538\) −25.6677 −1.10662
\(539\) −6.96869 −0.300163
\(540\) 2.01005 0.0864986
\(541\) −1.42879 −0.0614286 −0.0307143 0.999528i \(-0.509778\pi\)
−0.0307143 + 0.999528i \(0.509778\pi\)
\(542\) 0.364186 0.0156431
\(543\) −9.69112 −0.415886
\(544\) 1.61006 0.0690306
\(545\) −1.50988 −0.0646762
\(546\) −1.16593 −0.0498972
\(547\) 3.66640 0.156764 0.0783820 0.996923i \(-0.475025\pi\)
0.0783820 + 0.996923i \(0.475025\pi\)
\(548\) −3.53736 −0.151109
\(549\) −3.11310 −0.132864
\(550\) 4.85935 0.207203
\(551\) 16.2650 0.692913
\(552\) −7.02228 −0.298888
\(553\) 0.502766 0.0213798
\(554\) −18.9045 −0.803175
\(555\) 1.49684 0.0635372
\(556\) 10.0260 0.425195
\(557\) −33.5713 −1.42246 −0.711231 0.702958i \(-0.751862\pi\)
−0.711231 + 0.702958i \(0.751862\pi\)
\(558\) 15.0769 0.638256
\(559\) 51.8358 2.19242
\(560\) −0.0663595 −0.00280420
\(561\) −1.83641 −0.0775333
\(562\) 27.4959 1.15985
\(563\) 45.5619 1.92021 0.960103 0.279646i \(-0.0902172\pi\)
0.960103 + 0.279646i \(0.0902172\pi\)
\(564\) 8.39906 0.353664
\(565\) −7.81065 −0.328597
\(566\) −6.24017 −0.262294
\(567\) −0.179778 −0.00754996
\(568\) −8.55660 −0.359027
\(569\) 24.0234 1.00711 0.503556 0.863962i \(-0.332025\pi\)
0.503556 + 0.863962i \(0.332025\pi\)
\(570\) 2.27190 0.0951596
\(571\) −37.8054 −1.58211 −0.791054 0.611747i \(-0.790467\pi\)
−0.791054 + 0.611747i \(0.790467\pi\)
\(572\) 5.77706 0.241551
\(573\) −4.68570 −0.195748
\(574\) 2.05093 0.0856040
\(575\) −29.9177 −1.24765
\(576\) −1.69906 −0.0707942
\(577\) −39.3180 −1.63683 −0.818414 0.574629i \(-0.805147\pi\)
−0.818414 + 0.574629i \(0.805147\pi\)
\(578\) 14.4077 0.599282
\(579\) −22.5872 −0.938693
\(580\) −1.14849 −0.0476883
\(581\) 1.39251 0.0577711
\(582\) −8.18568 −0.339307
\(583\) −11.0118 −0.456062
\(584\) 6.63706 0.274643
\(585\) 3.68114 0.152196
\(586\) 16.9894 0.701827
\(587\) 31.7779 1.31162 0.655808 0.754928i \(-0.272328\pi\)
0.655808 + 0.754928i \(0.272328\pi\)
\(588\) −7.94840 −0.327787
\(589\) 47.1301 1.94196
\(590\) −3.75728 −0.154685
\(591\) −1.14059 −0.0469175
\(592\) −3.49928 −0.143820
\(593\) 48.3451 1.98530 0.992648 0.121038i \(-0.0386223\pi\)
0.992648 + 0.121038i \(0.0386223\pi\)
\(594\) 5.35969 0.219911
\(595\) 0.106843 0.00438012
\(596\) 24.1445 0.988996
\(597\) 19.7154 0.806897
\(598\) −35.5678 −1.45447
\(599\) −32.3091 −1.32011 −0.660057 0.751215i \(-0.729468\pi\)
−0.660057 + 0.751215i \(0.729468\pi\)
\(600\) 5.54252 0.226272
\(601\) −4.59377 −0.187384 −0.0936919 0.995601i \(-0.529867\pi\)
−0.0936919 + 0.995601i \(0.529867\pi\)
\(602\) −1.58767 −0.0647086
\(603\) −2.56211 −0.104337
\(604\) −0.198077 −0.00805965
\(605\) −0.375030 −0.0152472
\(606\) 16.7430 0.680138
\(607\) −20.1052 −0.816043 −0.408021 0.912972i \(-0.633781\pi\)
−0.408021 + 0.912972i \(0.633781\pi\)
\(608\) −5.31123 −0.215399
\(609\) 0.618052 0.0250447
\(610\) 0.687148 0.0278218
\(611\) 42.5411 1.72103
\(612\) 2.73558 0.110579
\(613\) 5.58115 0.225421 0.112710 0.993628i \(-0.464047\pi\)
0.112710 + 0.993628i \(0.464047\pi\)
\(614\) 30.2004 1.21879
\(615\) 4.95802 0.199927
\(616\) −0.176944 −0.00712929
\(617\) 13.6960 0.551378 0.275689 0.961247i \(-0.411094\pi\)
0.275689 + 0.961247i \(0.411094\pi\)
\(618\) −6.77064 −0.272355
\(619\) 20.9151 0.840650 0.420325 0.907374i \(-0.361916\pi\)
0.420325 + 0.907374i \(0.361916\pi\)
\(620\) −3.32790 −0.133652
\(621\) −32.9981 −1.32417
\(622\) −25.5594 −1.02484
\(623\) 0.156714 0.00627862
\(624\) 6.58924 0.263781
\(625\) 22.9101 0.916403
\(626\) −26.4591 −1.05752
\(627\) 6.05792 0.241930
\(628\) 20.2212 0.806913
\(629\) 5.63404 0.224644
\(630\) −0.112749 −0.00449202
\(631\) −9.86703 −0.392800 −0.196400 0.980524i \(-0.562925\pi\)
−0.196400 + 0.980524i \(0.562925\pi\)
\(632\) −2.84138 −0.113024
\(633\) −7.03457 −0.279599
\(634\) −26.8098 −1.06475
\(635\) −2.14268 −0.0850297
\(636\) −12.5599 −0.498033
\(637\) −40.2586 −1.59510
\(638\) −3.06238 −0.121241
\(639\) −14.5382 −0.575122
\(640\) 0.375030 0.0148244
\(641\) 44.8732 1.77239 0.886193 0.463317i \(-0.153341\pi\)
0.886193 + 0.463317i \(0.153341\pi\)
\(642\) 12.6395 0.498842
\(643\) 29.4827 1.16268 0.581342 0.813660i \(-0.302528\pi\)
0.581342 + 0.813660i \(0.302528\pi\)
\(644\) 1.08940 0.0429283
\(645\) −3.83812 −0.151126
\(646\) 8.55137 0.336449
\(647\) 14.0866 0.553800 0.276900 0.960899i \(-0.410693\pi\)
0.276900 + 0.960899i \(0.410693\pi\)
\(648\) 1.01601 0.0399127
\(649\) −10.0186 −0.393264
\(650\) 28.0728 1.10110
\(651\) 1.79089 0.0701905
\(652\) 11.7335 0.459519
\(653\) 17.9797 0.703601 0.351801 0.936075i \(-0.385570\pi\)
0.351801 + 0.936075i \(0.385570\pi\)
\(654\) −4.59203 −0.179563
\(655\) −4.86749 −0.190188
\(656\) −11.5908 −0.452544
\(657\) 11.2768 0.439948
\(658\) −1.30298 −0.0507956
\(659\) −33.0433 −1.28719 −0.643593 0.765368i \(-0.722557\pi\)
−0.643593 + 0.765368i \(0.722557\pi\)
\(660\) −0.427755 −0.0166503
\(661\) 33.7044 1.31095 0.655474 0.755218i \(-0.272469\pi\)
0.655474 + 0.755218i \(0.272469\pi\)
\(662\) 2.24781 0.0873635
\(663\) −10.6090 −0.412021
\(664\) −7.86977 −0.305406
\(665\) −0.352451 −0.0136674
\(666\) −5.94550 −0.230383
\(667\) 18.8542 0.730039
\(668\) 19.8909 0.769602
\(669\) −24.1075 −0.932052
\(670\) 0.565530 0.0218483
\(671\) 1.83225 0.0707331
\(672\) −0.201821 −0.00778540
\(673\) −3.52827 −0.136005 −0.0680023 0.997685i \(-0.521663\pi\)
−0.0680023 + 0.997685i \(0.521663\pi\)
\(674\) 20.0951 0.774034
\(675\) 26.0446 1.00246
\(676\) 20.3744 0.783632
\(677\) 31.2837 1.20233 0.601166 0.799124i \(-0.294703\pi\)
0.601166 + 0.799124i \(0.294703\pi\)
\(678\) −23.7547 −0.912293
\(679\) 1.26988 0.0487336
\(680\) −0.603820 −0.0231554
\(681\) −19.1849 −0.735168
\(682\) −8.87367 −0.339790
\(683\) 12.2691 0.469464 0.234732 0.972060i \(-0.424579\pi\)
0.234732 + 0.972060i \(0.424579\pi\)
\(684\) −9.02409 −0.345045
\(685\) 1.32662 0.0506875
\(686\) 2.47168 0.0943693
\(687\) 23.3607 0.891265
\(688\) 8.97270 0.342081
\(689\) −63.6158 −2.42357
\(690\) 2.63357 0.100258
\(691\) 30.1833 1.14823 0.574113 0.818776i \(-0.305347\pi\)
0.574113 + 0.818776i \(0.305347\pi\)
\(692\) 20.3715 0.774408
\(693\) −0.300639 −0.0114203
\(694\) −7.48401 −0.284089
\(695\) −3.76004 −0.142626
\(696\) −3.49292 −0.132399
\(697\) 18.6618 0.706867
\(698\) 3.60092 0.136297
\(699\) −30.1578 −1.14067
\(700\) −0.859835 −0.0324987
\(701\) 5.77248 0.218024 0.109012 0.994040i \(-0.465231\pi\)
0.109012 + 0.994040i \(0.465231\pi\)
\(702\) 30.9633 1.16863
\(703\) −18.5855 −0.700965
\(704\) 1.00000 0.0376889
\(705\) −3.14990 −0.118632
\(706\) 19.9929 0.752442
\(707\) −2.59742 −0.0976860
\(708\) −11.4271 −0.429456
\(709\) 31.3260 1.17647 0.588237 0.808689i \(-0.299822\pi\)
0.588237 + 0.808689i \(0.299822\pi\)
\(710\) 3.20899 0.120431
\(711\) −4.82767 −0.181052
\(712\) −0.885668 −0.0331918
\(713\) 54.6327 2.04601
\(714\) 0.324942 0.0121607
\(715\) −2.16657 −0.0810253
\(716\) 11.3922 0.425745
\(717\) −25.2381 −0.942535
\(718\) −17.4829 −0.652457
\(719\) −24.2491 −0.904339 −0.452170 0.891932i \(-0.649350\pi\)
−0.452170 + 0.891932i \(0.649350\pi\)
\(720\) 0.637199 0.0237470
\(721\) 1.05036 0.0391174
\(722\) −9.20912 −0.342728
\(723\) 14.5100 0.539631
\(724\) −8.49660 −0.315774
\(725\) −14.8812 −0.552674
\(726\) −1.14059 −0.0423312
\(727\) −21.0147 −0.779393 −0.389697 0.920943i \(-0.627420\pi\)
−0.389697 + 0.920943i \(0.627420\pi\)
\(728\) −1.02222 −0.0378860
\(729\) 20.0658 0.743180
\(730\) −2.48910 −0.0921257
\(731\) −14.4465 −0.534325
\(732\) 2.08984 0.0772426
\(733\) −23.0662 −0.851970 −0.425985 0.904730i \(-0.640072\pi\)
−0.425985 + 0.904730i \(0.640072\pi\)
\(734\) −29.5756 −1.09165
\(735\) 2.98089 0.109952
\(736\) −6.15672 −0.226940
\(737\) 1.50796 0.0555463
\(738\) −19.6934 −0.724926
\(739\) 1.69074 0.0621950 0.0310975 0.999516i \(-0.490100\pi\)
0.0310975 + 0.999516i \(0.490100\pi\)
\(740\) 1.31234 0.0482425
\(741\) 34.9970 1.28565
\(742\) 1.94848 0.0715308
\(743\) −23.1676 −0.849937 −0.424969 0.905208i \(-0.639715\pi\)
−0.424969 + 0.905208i \(0.639715\pi\)
\(744\) −10.1212 −0.371061
\(745\) −9.05492 −0.331746
\(746\) −23.6488 −0.865843
\(747\) −13.3712 −0.489227
\(748\) −1.61006 −0.0588695
\(749\) −1.96083 −0.0716470
\(750\) −4.21739 −0.153997
\(751\) 12.5875 0.459323 0.229661 0.973271i \(-0.426238\pi\)
0.229661 + 0.973271i \(0.426238\pi\)
\(752\) 7.36380 0.268530
\(753\) −1.59417 −0.0580949
\(754\) −17.6916 −0.644289
\(755\) 0.0742850 0.00270351
\(756\) −0.948367 −0.0344918
\(757\) −25.9849 −0.944439 −0.472220 0.881481i \(-0.656547\pi\)
−0.472220 + 0.881481i \(0.656547\pi\)
\(758\) −22.9373 −0.833120
\(759\) 7.02228 0.254893
\(760\) 1.99187 0.0722528
\(761\) −39.9523 −1.44827 −0.724135 0.689658i \(-0.757761\pi\)
−0.724135 + 0.689658i \(0.757761\pi\)
\(762\) −6.51658 −0.236071
\(763\) 0.712382 0.0257900
\(764\) −4.10814 −0.148627
\(765\) −1.02593 −0.0370925
\(766\) 18.5190 0.669119
\(767\) −57.8780 −2.08985
\(768\) 1.14059 0.0411574
\(769\) 15.2858 0.551220 0.275610 0.961270i \(-0.411120\pi\)
0.275610 + 0.961270i \(0.411120\pi\)
\(770\) 0.0663595 0.00239143
\(771\) −25.2221 −0.908354
\(772\) −19.8031 −0.712731
\(773\) 41.8515 1.50529 0.752647 0.658424i \(-0.228777\pi\)
0.752647 + 0.658424i \(0.228777\pi\)
\(774\) 15.2452 0.547976
\(775\) −43.1203 −1.54893
\(776\) −7.17673 −0.257629
\(777\) −0.706228 −0.0253358
\(778\) 18.5454 0.664884
\(779\) −61.5613 −2.20566
\(780\) −2.47117 −0.0884820
\(781\) 8.55660 0.306179
\(782\) 9.91266 0.354476
\(783\) −16.4134 −0.586568
\(784\) −6.96869 −0.248882
\(785\) −7.58356 −0.270669
\(786\) −14.8036 −0.528026
\(787\) −2.30597 −0.0821991 −0.0410995 0.999155i \(-0.513086\pi\)
−0.0410995 + 0.999155i \(0.513086\pi\)
\(788\) −1.00000 −0.0356235
\(789\) 4.52990 0.161269
\(790\) 1.06560 0.0379124
\(791\) 3.68517 0.131030
\(792\) 1.69906 0.0603735
\(793\) 10.5850 0.375884
\(794\) −2.64088 −0.0937214
\(795\) 4.71035 0.167059
\(796\) 17.2853 0.612661
\(797\) −25.3488 −0.897902 −0.448951 0.893556i \(-0.648202\pi\)
−0.448951 + 0.893556i \(0.648202\pi\)
\(798\) −1.07191 −0.0379454
\(799\) −11.8561 −0.419440
\(800\) 4.85935 0.171804
\(801\) −1.50480 −0.0531696
\(802\) 24.6618 0.870840
\(803\) −6.63706 −0.234217
\(804\) 1.71996 0.0606582
\(805\) −0.408557 −0.0143998
\(806\) −51.2637 −1.80569
\(807\) 29.2763 1.03057
\(808\) 14.6793 0.516416
\(809\) 6.17589 0.217133 0.108566 0.994089i \(-0.465374\pi\)
0.108566 + 0.994089i \(0.465374\pi\)
\(810\) −0.381036 −0.0133882
\(811\) −43.7164 −1.53509 −0.767545 0.640995i \(-0.778522\pi\)
−0.767545 + 0.640995i \(0.778522\pi\)
\(812\) 0.541872 0.0190160
\(813\) −0.415386 −0.0145682
\(814\) 3.49928 0.122650
\(815\) −4.40042 −0.154140
\(816\) −1.83641 −0.0642872
\(817\) 47.6560 1.66727
\(818\) 3.50713 0.122624
\(819\) −1.73681 −0.0606891
\(820\) 4.34690 0.151800
\(821\) −16.7716 −0.585332 −0.292666 0.956215i \(-0.594542\pi\)
−0.292666 + 0.956215i \(0.594542\pi\)
\(822\) 4.03467 0.140725
\(823\) 19.9978 0.697080 0.348540 0.937294i \(-0.386678\pi\)
0.348540 + 0.937294i \(0.386678\pi\)
\(824\) −5.93610 −0.206794
\(825\) −5.54252 −0.192966
\(826\) 1.77273 0.0616813
\(827\) 3.08574 0.107302 0.0536508 0.998560i \(-0.482914\pi\)
0.0536508 + 0.998560i \(0.482914\pi\)
\(828\) −10.4606 −0.363532
\(829\) −41.5406 −1.44276 −0.721382 0.692537i \(-0.756493\pi\)
−0.721382 + 0.692537i \(0.756493\pi\)
\(830\) 2.95140 0.102445
\(831\) 21.5622 0.747986
\(832\) 5.77706 0.200284
\(833\) 11.2200 0.388749
\(834\) −11.4355 −0.395978
\(835\) −7.45969 −0.258153
\(836\) 5.31123 0.183693
\(837\) −47.5601 −1.64392
\(838\) 4.67818 0.161605
\(839\) −10.8880 −0.375895 −0.187948 0.982179i \(-0.560184\pi\)
−0.187948 + 0.982179i \(0.560184\pi\)
\(840\) 0.0756889 0.00261151
\(841\) −19.6218 −0.676614
\(842\) 26.2204 0.903615
\(843\) −31.3615 −1.08015
\(844\) −6.16750 −0.212294
\(845\) −7.64104 −0.262860
\(846\) 12.5115 0.430156
\(847\) 0.176944 0.00607988
\(848\) −11.0118 −0.378147
\(849\) 7.11746 0.244270
\(850\) −7.82383 −0.268355
\(851\) −21.5441 −0.738523
\(852\) 9.75955 0.334357
\(853\) −38.0063 −1.30131 −0.650655 0.759373i \(-0.725506\pi\)
−0.650655 + 0.759373i \(0.725506\pi\)
\(854\) −0.324206 −0.0110941
\(855\) 3.38431 0.115741
\(856\) 11.0816 0.378761
\(857\) −29.0051 −0.990796 −0.495398 0.868666i \(-0.664978\pi\)
−0.495398 + 0.868666i \(0.664978\pi\)
\(858\) −6.58924 −0.224953
\(859\) −26.7452 −0.912535 −0.456267 0.889843i \(-0.650814\pi\)
−0.456267 + 0.889843i \(0.650814\pi\)
\(860\) −3.36504 −0.114747
\(861\) −2.33926 −0.0797217
\(862\) 4.21940 0.143713
\(863\) −7.92679 −0.269831 −0.134916 0.990857i \(-0.543076\pi\)
−0.134916 + 0.990857i \(0.543076\pi\)
\(864\) 5.35969 0.182340
\(865\) −7.63993 −0.259765
\(866\) 26.6218 0.904646
\(867\) −16.4333 −0.558103
\(868\) 1.57015 0.0532942
\(869\) 2.84138 0.0963871
\(870\) 1.30995 0.0444115
\(871\) 8.71156 0.295180
\(872\) −4.02602 −0.136338
\(873\) −12.1937 −0.412694
\(874\) −32.6997 −1.10609
\(875\) 0.654262 0.0221181
\(876\) −7.57014 −0.255771
\(877\) −35.7593 −1.20751 −0.603753 0.797172i \(-0.706329\pi\)
−0.603753 + 0.797172i \(0.706329\pi\)
\(878\) −0.548668 −0.0185167
\(879\) −19.3779 −0.653601
\(880\) −0.375030 −0.0126423
\(881\) −6.35043 −0.213951 −0.106976 0.994262i \(-0.534117\pi\)
−0.106976 + 0.994262i \(0.534117\pi\)
\(882\) −11.8402 −0.398681
\(883\) 19.9632 0.671816 0.335908 0.941895i \(-0.390957\pi\)
0.335908 + 0.941895i \(0.390957\pi\)
\(884\) −9.30139 −0.312840
\(885\) 4.28550 0.144056
\(886\) −33.8396 −1.13686
\(887\) −9.65391 −0.324147 −0.162073 0.986779i \(-0.551818\pi\)
−0.162073 + 0.986779i \(0.551818\pi\)
\(888\) 3.99124 0.133937
\(889\) 1.01095 0.0339060
\(890\) 0.332153 0.0111338
\(891\) −1.01601 −0.0340377
\(892\) −21.1361 −0.707688
\(893\) 39.1108 1.30879
\(894\) −27.5389 −0.921038
\(895\) −4.27241 −0.142811
\(896\) −0.176944 −0.00591130
\(897\) 40.5681 1.35453
\(898\) −0.977296 −0.0326128
\(899\) 27.1746 0.906323
\(900\) 8.25633 0.275211
\(901\) 17.7296 0.590659
\(902\) 11.5908 0.385931
\(903\) 1.81088 0.0602622
\(904\) −20.8267 −0.692686
\(905\) 3.18648 0.105922
\(906\) 0.225925 0.00750584
\(907\) −7.13100 −0.236781 −0.118390 0.992967i \(-0.537773\pi\)
−0.118390 + 0.992967i \(0.537773\pi\)
\(908\) −16.8202 −0.558199
\(909\) 24.9410 0.827241
\(910\) 0.383363 0.0127084
\(911\) −0.408592 −0.0135373 −0.00676863 0.999977i \(-0.502155\pi\)
−0.00676863 + 0.999977i \(0.502155\pi\)
\(912\) 6.05792 0.200598
\(913\) 7.86977 0.260451
\(914\) 0.113660 0.00375954
\(915\) −0.783753 −0.0259101
\(916\) 20.4813 0.676720
\(917\) 2.29655 0.0758386
\(918\) −8.62940 −0.284813
\(919\) 27.7150 0.914232 0.457116 0.889407i \(-0.348882\pi\)
0.457116 + 0.889407i \(0.348882\pi\)
\(920\) 2.30896 0.0761241
\(921\) −34.4462 −1.13504
\(922\) −3.00340 −0.0989118
\(923\) 49.4320 1.62707
\(924\) 0.201821 0.00663941
\(925\) 17.0043 0.559097
\(926\) −14.9797 −0.492264
\(927\) −10.0858 −0.331261
\(928\) −3.06238 −0.100528
\(929\) −49.5070 −1.62427 −0.812136 0.583468i \(-0.801695\pi\)
−0.812136 + 0.583468i \(0.801695\pi\)
\(930\) 3.79576 0.124468
\(931\) −37.0123 −1.21303
\(932\) −26.4406 −0.866091
\(933\) 29.1527 0.954417
\(934\) 26.3116 0.860942
\(935\) 0.603820 0.0197470
\(936\) 9.81558 0.320832
\(937\) −14.9508 −0.488421 −0.244211 0.969722i \(-0.578529\pi\)
−0.244211 + 0.969722i \(0.578529\pi\)
\(938\) −0.266825 −0.00871213
\(939\) 30.1789 0.984852
\(940\) −2.76165 −0.0900751
\(941\) 31.4853 1.02639 0.513196 0.858271i \(-0.328461\pi\)
0.513196 + 0.858271i \(0.328461\pi\)
\(942\) −23.0640 −0.751467
\(943\) −71.3612 −2.32384
\(944\) −10.0186 −0.326077
\(945\) 0.355667 0.0115698
\(946\) −8.97270 −0.291728
\(947\) 11.7996 0.383436 0.191718 0.981450i \(-0.438594\pi\)
0.191718 + 0.981450i \(0.438594\pi\)
\(948\) 3.24084 0.105258
\(949\) −38.3427 −1.24466
\(950\) 25.8091 0.837358
\(951\) 30.5789 0.991589
\(952\) 0.284890 0.00923335
\(953\) −22.0070 −0.712877 −0.356439 0.934319i \(-0.616009\pi\)
−0.356439 + 0.934319i \(0.616009\pi\)
\(954\) −18.7097 −0.605749
\(955\) 1.54068 0.0498552
\(956\) −22.1273 −0.715648
\(957\) 3.49292 0.112910
\(958\) 25.7015 0.830377
\(959\) −0.625916 −0.0202119
\(960\) −0.427755 −0.0138057
\(961\) 47.7420 1.54006
\(962\) 20.2156 0.651777
\(963\) 18.8283 0.606733
\(964\) 12.7215 0.409731
\(965\) 7.42678 0.239077
\(966\) −1.24255 −0.0399785
\(967\) −26.5423 −0.853542 −0.426771 0.904360i \(-0.640349\pi\)
−0.426771 + 0.904360i \(0.640349\pi\)
\(968\) −1.00000 −0.0321412
\(969\) −9.75358 −0.313330
\(970\) 2.69149 0.0864186
\(971\) 37.2714 1.19609 0.598047 0.801461i \(-0.295943\pi\)
0.598047 + 0.801461i \(0.295943\pi\)
\(972\) 14.9202 0.478566
\(973\) 1.77404 0.0568730
\(974\) −15.4358 −0.494595
\(975\) −32.0195 −1.02544
\(976\) 1.83225 0.0586488
\(977\) −14.6805 −0.469672 −0.234836 0.972035i \(-0.575455\pi\)
−0.234836 + 0.972035i \(0.575455\pi\)
\(978\) −13.3831 −0.427944
\(979\) 0.885668 0.0283061
\(980\) 2.61347 0.0834843
\(981\) −6.84045 −0.218399
\(982\) −13.1337 −0.419115
\(983\) 1.57010 0.0500785 0.0250393 0.999686i \(-0.492029\pi\)
0.0250393 + 0.999686i \(0.492029\pi\)
\(984\) 13.2203 0.421448
\(985\) 0.375030 0.0119495
\(986\) 4.93061 0.157023
\(987\) 1.48617 0.0473052
\(988\) 30.6833 0.976165
\(989\) 55.2424 1.75661
\(990\) −0.637199 −0.0202515
\(991\) 24.8193 0.788411 0.394205 0.919022i \(-0.371020\pi\)
0.394205 + 0.919022i \(0.371020\pi\)
\(992\) −8.87367 −0.281739
\(993\) −2.56382 −0.0813604
\(994\) −1.51404 −0.0480225
\(995\) −6.48251 −0.205509
\(996\) 8.97616 0.284421
\(997\) −33.5113 −1.06131 −0.530657 0.847587i \(-0.678055\pi\)
−0.530657 + 0.847587i \(0.678055\pi\)
\(998\) −1.38739 −0.0439170
\(999\) 18.7551 0.593384
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 4334.2.a.h.1.18 27
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4334.2.a.h.1.18 27 1.1 even 1 trivial