Properties

Label 1183.2.a.j.1.1
Level $1183$
Weight $2$
Character 1183.1
Self dual yes
Analytic conductor $9.446$
Analytic rank $0$
Dimension $3$
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] = [1183,2,Mod(1,1183)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1183, 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("1183.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.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: \(9.44630255912\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.17009\) of defining polynomial
Character \(\chi\) \(=\) 1183.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.17009 q^{2} +0.539189 q^{3} -0.630898 q^{4} +0.460811 q^{5} -0.630898 q^{6} -1.00000 q^{7} +3.07838 q^{8} -2.70928 q^{9} +O(q^{10})\) \(q-1.17009 q^{2} +0.539189 q^{3} -0.630898 q^{4} +0.460811 q^{5} -0.630898 q^{6} -1.00000 q^{7} +3.07838 q^{8} -2.70928 q^{9} -0.539189 q^{10} +0.829914 q^{11} -0.340173 q^{12} +1.17009 q^{14} +0.248464 q^{15} -2.34017 q^{16} -2.87936 q^{17} +3.17009 q^{18} +4.32684 q^{19} -0.290725 q^{20} -0.539189 q^{21} -0.971071 q^{22} +5.04945 q^{23} +1.65983 q^{24} -4.78765 q^{25} -3.07838 q^{27} +0.630898 q^{28} +0.261795 q^{29} -0.290725 q^{30} +6.80098 q^{31} -3.41855 q^{32} +0.447480 q^{33} +3.36910 q^{34} -0.460811 q^{35} +1.70928 q^{36} +9.51026 q^{37} -5.06278 q^{38} +1.41855 q^{40} -6.68035 q^{41} +0.630898 q^{42} -0.418551 q^{43} -0.523590 q^{44} -1.24846 q^{45} -5.90829 q^{46} +9.24846 q^{47} -1.26180 q^{48} +1.00000 q^{49} +5.60197 q^{50} -1.55252 q^{51} +1.63090 q^{53} +3.60197 q^{54} +0.382433 q^{55} -3.07838 q^{56} +2.33299 q^{57} -0.306323 q^{58} -2.78765 q^{59} -0.156755 q^{60} +7.26180 q^{61} -7.95774 q^{62} +2.70928 q^{63} +8.68035 q^{64} -0.523590 q^{66} -5.07838 q^{67} +1.81658 q^{68} +2.72261 q^{69} +0.539189 q^{70} +12.7721 q^{71} -8.34017 q^{72} +0.353504 q^{73} -11.1278 q^{74} -2.58145 q^{75} -2.72979 q^{76} -0.829914 q^{77} +2.81658 q^{79} -1.07838 q^{80} +6.46800 q^{81} +7.81658 q^{82} +10.3763 q^{83} +0.340173 q^{84} -1.32684 q^{85} +0.489741 q^{86} +0.141157 q^{87} +2.55479 q^{88} +5.43188 q^{89} +1.46081 q^{90} -3.18568 q^{92} +3.66701 q^{93} -10.8215 q^{94} +1.99386 q^{95} -1.84324 q^{96} -12.6092 q^{97} -1.17009 q^{98} -2.24846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{2} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 3 q^{7} + 6 q^{8} - q^{9} + 8 q^{11} + 10 q^{12} - 2 q^{14} - 8 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} - 8 q^{20} + 12 q^{22} - 3 q^{23} + 16 q^{24} - 4 q^{25} - 6 q^{27} - 2 q^{28} - 7 q^{29} - 8 q^{30} + 11 q^{31} + 4 q^{32} + 2 q^{33} + 14 q^{34} - 3 q^{35} - 2 q^{36} + 12 q^{37} + 2 q^{38} - 10 q^{40} + 2 q^{41} - 2 q^{42} + 13 q^{43} + 14 q^{44} + 5 q^{45} - 20 q^{46} + 19 q^{47} + 4 q^{48} + 3 q^{49} - 2 q^{50} - 4 q^{51} + q^{53} - 8 q^{54} + 6 q^{55} - 6 q^{56} + 30 q^{57} - 22 q^{58} + 2 q^{59} + 6 q^{60} + 14 q^{61} - 8 q^{62} + q^{63} + 4 q^{64} + 14 q^{66} - 12 q^{67} + 10 q^{68} + 2 q^{69} + 14 q^{71} - 14 q^{72} - 9 q^{73} - 12 q^{74} - 22 q^{75} + 32 q^{76} - 8 q^{77} + 13 q^{79} - 13 q^{81} + 28 q^{82} + q^{83} - 10 q^{84} + 8 q^{85} + 18 q^{86} - 20 q^{87} + 20 q^{88} + 3 q^{89} + 6 q^{90} - 18 q^{92} - 12 q^{93} + 10 q^{94} - 29 q^{95} - 12 q^{96} + 15 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17009 −0.827376 −0.413688 0.910419i \(-0.635760\pi\)
−0.413688 + 0.910419i \(0.635760\pi\)
\(3\) 0.539189 0.311301 0.155650 0.987812i \(-0.450253\pi\)
0.155650 + 0.987812i \(0.450253\pi\)
\(4\) −0.630898 −0.315449
\(5\) 0.460811 0.206081 0.103041 0.994677i \(-0.467143\pi\)
0.103041 + 0.994677i \(0.467143\pi\)
\(6\) −0.630898 −0.257563
\(7\) −1.00000 −0.377964
\(8\) 3.07838 1.08837
\(9\) −2.70928 −0.903092
\(10\) −0.539189 −0.170506
\(11\) 0.829914 0.250228 0.125114 0.992142i \(-0.460070\pi\)
0.125114 + 0.992142i \(0.460070\pi\)
\(12\) −0.340173 −0.0981995
\(13\) 0 0
\(14\) 1.17009 0.312719
\(15\) 0.248464 0.0641532
\(16\) −2.34017 −0.585043
\(17\) −2.87936 −0.698348 −0.349174 0.937058i \(-0.613538\pi\)
−0.349174 + 0.937058i \(0.613538\pi\)
\(18\) 3.17009 0.747197
\(19\) 4.32684 0.992646 0.496323 0.868138i \(-0.334683\pi\)
0.496323 + 0.868138i \(0.334683\pi\)
\(20\) −0.290725 −0.0650080
\(21\) −0.539189 −0.117661
\(22\) −0.971071 −0.207033
\(23\) 5.04945 1.05288 0.526441 0.850211i \(-0.323526\pi\)
0.526441 + 0.850211i \(0.323526\pi\)
\(24\) 1.65983 0.338811
\(25\) −4.78765 −0.957531
\(26\) 0 0
\(27\) −3.07838 −0.592434
\(28\) 0.630898 0.119228
\(29\) 0.261795 0.0486142 0.0243071 0.999705i \(-0.492262\pi\)
0.0243071 + 0.999705i \(0.492262\pi\)
\(30\) −0.290725 −0.0530788
\(31\) 6.80098 1.22149 0.610746 0.791826i \(-0.290869\pi\)
0.610746 + 0.791826i \(0.290869\pi\)
\(32\) −3.41855 −0.604320
\(33\) 0.447480 0.0778963
\(34\) 3.36910 0.577796
\(35\) −0.460811 −0.0778913
\(36\) 1.70928 0.284879
\(37\) 9.51026 1.56348 0.781739 0.623606i \(-0.214333\pi\)
0.781739 + 0.623606i \(0.214333\pi\)
\(38\) −5.06278 −0.821291
\(39\) 0 0
\(40\) 1.41855 0.224293
\(41\) −6.68035 −1.04329 −0.521647 0.853161i \(-0.674682\pi\)
−0.521647 + 0.853161i \(0.674682\pi\)
\(42\) 0.630898 0.0973496
\(43\) −0.418551 −0.0638284 −0.0319142 0.999491i \(-0.510160\pi\)
−0.0319142 + 0.999491i \(0.510160\pi\)
\(44\) −0.523590 −0.0789342
\(45\) −1.24846 −0.186110
\(46\) −5.90829 −0.871130
\(47\) 9.24846 1.34903 0.674514 0.738262i \(-0.264353\pi\)
0.674514 + 0.738262i \(0.264353\pi\)
\(48\) −1.26180 −0.182124
\(49\) 1.00000 0.142857
\(50\) 5.60197 0.792238
\(51\) −1.55252 −0.217396
\(52\) 0 0
\(53\) 1.63090 0.224021 0.112011 0.993707i \(-0.464271\pi\)
0.112011 + 0.993707i \(0.464271\pi\)
\(54\) 3.60197 0.490166
\(55\) 0.382433 0.0515673
\(56\) −3.07838 −0.411366
\(57\) 2.33299 0.309011
\(58\) −0.306323 −0.0402222
\(59\) −2.78765 −0.362922 −0.181461 0.983398i \(-0.558083\pi\)
−0.181461 + 0.983398i \(0.558083\pi\)
\(60\) −0.156755 −0.0202370
\(61\) 7.26180 0.929778 0.464889 0.885369i \(-0.346094\pi\)
0.464889 + 0.885369i \(0.346094\pi\)
\(62\) −7.95774 −1.01063
\(63\) 2.70928 0.341337
\(64\) 8.68035 1.08504
\(65\) 0 0
\(66\) −0.523590 −0.0644495
\(67\) −5.07838 −0.620423 −0.310211 0.950668i \(-0.600400\pi\)
−0.310211 + 0.950668i \(0.600400\pi\)
\(68\) 1.81658 0.220293
\(69\) 2.72261 0.327763
\(70\) 0.539189 0.0644454
\(71\) 12.7721 1.51576 0.757882 0.652392i \(-0.226234\pi\)
0.757882 + 0.652392i \(0.226234\pi\)
\(72\) −8.34017 −0.982899
\(73\) 0.353504 0.0413745 0.0206873 0.999786i \(-0.493415\pi\)
0.0206873 + 0.999786i \(0.493415\pi\)
\(74\) −11.1278 −1.29358
\(75\) −2.58145 −0.298080
\(76\) −2.72979 −0.313129
\(77\) −0.829914 −0.0945774
\(78\) 0 0
\(79\) 2.81658 0.316890 0.158445 0.987368i \(-0.449352\pi\)
0.158445 + 0.987368i \(0.449352\pi\)
\(80\) −1.07838 −0.120566
\(81\) 6.46800 0.718667
\(82\) 7.81658 0.863197
\(83\) 10.3763 1.13895 0.569473 0.822010i \(-0.307147\pi\)
0.569473 + 0.822010i \(0.307147\pi\)
\(84\) 0.340173 0.0371159
\(85\) −1.32684 −0.143916
\(86\) 0.489741 0.0528101
\(87\) 0.141157 0.0151336
\(88\) 2.55479 0.272341
\(89\) 5.43188 0.575778 0.287889 0.957664i \(-0.407047\pi\)
0.287889 + 0.957664i \(0.407047\pi\)
\(90\) 1.46081 0.153983
\(91\) 0 0
\(92\) −3.18568 −0.332131
\(93\) 3.66701 0.380252
\(94\) −10.8215 −1.11615
\(95\) 1.99386 0.204565
\(96\) −1.84324 −0.188125
\(97\) −12.6092 −1.28027 −0.640133 0.768264i \(-0.721121\pi\)
−0.640133 + 0.768264i \(0.721121\pi\)
\(98\) −1.17009 −0.118197
\(99\) −2.24846 −0.225979
\(100\) 3.02052 0.302052
\(101\) 3.64423 0.362614 0.181307 0.983427i \(-0.441967\pi\)
0.181307 + 0.983427i \(0.441967\pi\)
\(102\) 1.81658 0.179868
\(103\) 17.9421 1.76789 0.883946 0.467589i \(-0.154877\pi\)
0.883946 + 0.467589i \(0.154877\pi\)
\(104\) 0 0
\(105\) −0.248464 −0.0242476
\(106\) −1.90829 −0.185350
\(107\) 2.94441 0.284647 0.142323 0.989820i \(-0.454543\pi\)
0.142323 + 0.989820i \(0.454543\pi\)
\(108\) 1.94214 0.186883
\(109\) 8.43188 0.807628 0.403814 0.914841i \(-0.367684\pi\)
0.403814 + 0.914841i \(0.367684\pi\)
\(110\) −0.447480 −0.0426656
\(111\) 5.12783 0.486712
\(112\) 2.34017 0.221126
\(113\) 12.8082 1.20489 0.602446 0.798160i \(-0.294193\pi\)
0.602446 + 0.798160i \(0.294193\pi\)
\(114\) −2.72979 −0.255669
\(115\) 2.32684 0.216979
\(116\) −0.165166 −0.0153353
\(117\) 0 0
\(118\) 3.26180 0.300273
\(119\) 2.87936 0.263951
\(120\) 0.764867 0.0698225
\(121\) −10.3112 −0.937386
\(122\) −8.49693 −0.769276
\(123\) −3.60197 −0.324779
\(124\) −4.29072 −0.385318
\(125\) −4.51026 −0.403410
\(126\) −3.17009 −0.282414
\(127\) −13.4680 −1.19509 −0.597546 0.801835i \(-0.703857\pi\)
−0.597546 + 0.801835i \(0.703857\pi\)
\(128\) −3.31965 −0.293419
\(129\) −0.225678 −0.0198698
\(130\) 0 0
\(131\) −14.4391 −1.26155 −0.630774 0.775967i \(-0.717262\pi\)
−0.630774 + 0.775967i \(0.717262\pi\)
\(132\) −0.282314 −0.0245723
\(133\) −4.32684 −0.375185
\(134\) 5.94214 0.513323
\(135\) −1.41855 −0.122089
\(136\) −8.86376 −0.760061
\(137\) 16.4319 1.40387 0.701935 0.712241i \(-0.252320\pi\)
0.701935 + 0.712241i \(0.252320\pi\)
\(138\) −3.18568 −0.271184
\(139\) 13.2195 1.12127 0.560633 0.828064i \(-0.310558\pi\)
0.560633 + 0.828064i \(0.310558\pi\)
\(140\) 0.290725 0.0245707
\(141\) 4.98667 0.419953
\(142\) −14.9444 −1.25411
\(143\) 0 0
\(144\) 6.34017 0.528348
\(145\) 0.120638 0.0100185
\(146\) −0.413630 −0.0342323
\(147\) 0.539189 0.0444715
\(148\) −6.00000 −0.493197
\(149\) 20.5041 1.67976 0.839881 0.542770i \(-0.182624\pi\)
0.839881 + 0.542770i \(0.182624\pi\)
\(150\) 3.02052 0.246624
\(151\) −1.59478 −0.129781 −0.0648907 0.997892i \(-0.520670\pi\)
−0.0648907 + 0.997892i \(0.520670\pi\)
\(152\) 13.3197 1.08037
\(153\) 7.80098 0.630672
\(154\) 0.971071 0.0782511
\(155\) 3.13397 0.251726
\(156\) 0 0
\(157\) −8.29791 −0.662246 −0.331123 0.943588i \(-0.607427\pi\)
−0.331123 + 0.943588i \(0.607427\pi\)
\(158\) −3.29565 −0.262187
\(159\) 0.879362 0.0697379
\(160\) −1.57531 −0.124539
\(161\) −5.04945 −0.397952
\(162\) −7.56812 −0.594608
\(163\) 0.398032 0.0311763 0.0155881 0.999878i \(-0.495038\pi\)
0.0155881 + 0.999878i \(0.495038\pi\)
\(164\) 4.21461 0.329106
\(165\) 0.206204 0.0160529
\(166\) −12.1412 −0.942337
\(167\) −23.8710 −1.84719 −0.923595 0.383370i \(-0.874763\pi\)
−0.923595 + 0.383370i \(0.874763\pi\)
\(168\) −1.65983 −0.128058
\(169\) 0 0
\(170\) 1.55252 0.119073
\(171\) −11.7226 −0.896450
\(172\) 0.264063 0.0201346
\(173\) 25.8999 1.96913 0.984566 0.175015i \(-0.0559975\pi\)
0.984566 + 0.175015i \(0.0559975\pi\)
\(174\) −0.165166 −0.0125212
\(175\) 4.78765 0.361913
\(176\) −1.94214 −0.146394
\(177\) −1.50307 −0.112978
\(178\) −6.35577 −0.476385
\(179\) 20.6742 1.54526 0.772631 0.634855i \(-0.218940\pi\)
0.772631 + 0.634855i \(0.218940\pi\)
\(180\) 0.787653 0.0587082
\(181\) 15.7165 1.16820 0.584098 0.811683i \(-0.301448\pi\)
0.584098 + 0.811683i \(0.301448\pi\)
\(182\) 0 0
\(183\) 3.91548 0.289441
\(184\) 15.5441 1.14593
\(185\) 4.38243 0.322203
\(186\) −4.29072 −0.314611
\(187\) −2.38962 −0.174746
\(188\) −5.83483 −0.425549
\(189\) 3.07838 0.223919
\(190\) −2.33299 −0.169253
\(191\) −16.7877 −1.21471 −0.607356 0.794430i \(-0.707770\pi\)
−0.607356 + 0.794430i \(0.707770\pi\)
\(192\) 4.68035 0.337775
\(193\) −20.0144 −1.44067 −0.720333 0.693628i \(-0.756011\pi\)
−0.720333 + 0.693628i \(0.756011\pi\)
\(194\) 14.7538 1.05926
\(195\) 0 0
\(196\) −0.630898 −0.0450641
\(197\) 17.5174 1.24807 0.624033 0.781398i \(-0.285493\pi\)
0.624033 + 0.781398i \(0.285493\pi\)
\(198\) 2.63090 0.186970
\(199\) −16.2979 −1.15533 −0.577664 0.816275i \(-0.696036\pi\)
−0.577664 + 0.816275i \(0.696036\pi\)
\(200\) −14.7382 −1.04215
\(201\) −2.73820 −0.193138
\(202\) −4.26406 −0.300018
\(203\) −0.261795 −0.0183744
\(204\) 0.979481 0.0685774
\(205\) −3.07838 −0.215003
\(206\) −20.9939 −1.46271
\(207\) −13.6803 −0.950850
\(208\) 0 0
\(209\) 3.59090 0.248388
\(210\) 0.290725 0.0200619
\(211\) 2.70928 0.186514 0.0932571 0.995642i \(-0.470272\pi\)
0.0932571 + 0.995642i \(0.470272\pi\)
\(212\) −1.02893 −0.0706672
\(213\) 6.88655 0.471859
\(214\) −3.44521 −0.235510
\(215\) −0.192873 −0.0131538
\(216\) −9.47641 −0.644788
\(217\) −6.80098 −0.461681
\(218\) −9.86603 −0.668212
\(219\) 0.190605 0.0128799
\(220\) −0.241276 −0.0162668
\(221\) 0 0
\(222\) −6.00000 −0.402694
\(223\) −19.7948 −1.32556 −0.662780 0.748814i \(-0.730624\pi\)
−0.662780 + 0.748814i \(0.730624\pi\)
\(224\) 3.41855 0.228412
\(225\) 12.9711 0.864738
\(226\) −14.9867 −0.996898
\(227\) 13.2618 0.880216 0.440108 0.897945i \(-0.354940\pi\)
0.440108 + 0.897945i \(0.354940\pi\)
\(228\) −1.47187 −0.0974773
\(229\) −27.8082 −1.83762 −0.918808 0.394705i \(-0.870847\pi\)
−0.918808 + 0.394705i \(0.870847\pi\)
\(230\) −2.72261 −0.179523
\(231\) −0.447480 −0.0294420
\(232\) 0.805905 0.0529102
\(233\) −13.3668 −0.875690 −0.437845 0.899050i \(-0.644258\pi\)
−0.437845 + 0.899050i \(0.644258\pi\)
\(234\) 0 0
\(235\) 4.26180 0.278009
\(236\) 1.75872 0.114483
\(237\) 1.51867 0.0986482
\(238\) −3.36910 −0.218386
\(239\) −8.70701 −0.563210 −0.281605 0.959530i \(-0.590867\pi\)
−0.281605 + 0.959530i \(0.590867\pi\)
\(240\) −0.581449 −0.0375324
\(241\) 16.9311 1.09063 0.545313 0.838232i \(-0.316411\pi\)
0.545313 + 0.838232i \(0.316411\pi\)
\(242\) 12.0650 0.775571
\(243\) 12.7226 0.816156
\(244\) −4.58145 −0.293297
\(245\) 0.460811 0.0294401
\(246\) 4.21461 0.268714
\(247\) 0 0
\(248\) 20.9360 1.32944
\(249\) 5.59478 0.354555
\(250\) 5.27739 0.333772
\(251\) −8.82150 −0.556808 −0.278404 0.960464i \(-0.589805\pi\)
−0.278404 + 0.960464i \(0.589805\pi\)
\(252\) −1.70928 −0.107674
\(253\) 4.19061 0.263461
\(254\) 15.7587 0.988790
\(255\) −0.715418 −0.0448012
\(256\) −13.4764 −0.842276
\(257\) −13.6442 −0.851104 −0.425552 0.904934i \(-0.639920\pi\)
−0.425552 + 0.904934i \(0.639920\pi\)
\(258\) 0.264063 0.0164398
\(259\) −9.51026 −0.590939
\(260\) 0 0
\(261\) −0.709275 −0.0439030
\(262\) 16.8950 1.04377
\(263\) −12.1773 −0.750883 −0.375441 0.926846i \(-0.622509\pi\)
−0.375441 + 0.926846i \(0.622509\pi\)
\(264\) 1.37751 0.0847801
\(265\) 0.751536 0.0461665
\(266\) 5.06278 0.310419
\(267\) 2.92881 0.179240
\(268\) 3.20394 0.195712
\(269\) −11.0472 −0.673559 −0.336779 0.941584i \(-0.609338\pi\)
−0.336779 + 0.941584i \(0.609338\pi\)
\(270\) 1.65983 0.101014
\(271\) 10.9360 0.664315 0.332157 0.943224i \(-0.392224\pi\)
0.332157 + 0.943224i \(0.392224\pi\)
\(272\) 6.73820 0.408564
\(273\) 0 0
\(274\) −19.2267 −1.16153
\(275\) −3.97334 −0.239601
\(276\) −1.71769 −0.103393
\(277\) −26.1194 −1.56936 −0.784682 0.619899i \(-0.787174\pi\)
−0.784682 + 0.619899i \(0.787174\pi\)
\(278\) −15.4680 −0.927709
\(279\) −18.4257 −1.10312
\(280\) −1.41855 −0.0847746
\(281\) −4.80325 −0.286538 −0.143269 0.989684i \(-0.545761\pi\)
−0.143269 + 0.989684i \(0.545761\pi\)
\(282\) −5.83483 −0.347459
\(283\) 0.979481 0.0582241 0.0291121 0.999576i \(-0.490732\pi\)
0.0291121 + 0.999576i \(0.490732\pi\)
\(284\) −8.05786 −0.478146
\(285\) 1.07507 0.0636814
\(286\) 0 0
\(287\) 6.68035 0.394328
\(288\) 9.26180 0.545757
\(289\) −8.70928 −0.512310
\(290\) −0.141157 −0.00828903
\(291\) −6.79872 −0.398548
\(292\) −0.223025 −0.0130515
\(293\) 24.3268 1.42119 0.710595 0.703602i \(-0.248426\pi\)
0.710595 + 0.703602i \(0.248426\pi\)
\(294\) −0.630898 −0.0367947
\(295\) −1.28458 −0.0747912
\(296\) 29.2762 1.70164
\(297\) −2.55479 −0.148244
\(298\) −23.9916 −1.38980
\(299\) 0 0
\(300\) 1.62863 0.0940290
\(301\) 0.418551 0.0241249
\(302\) 1.86603 0.107378
\(303\) 1.96493 0.112882
\(304\) −10.1256 −0.580741
\(305\) 3.34632 0.191609
\(306\) −9.12783 −0.521803
\(307\) −6.21953 −0.354968 −0.177484 0.984124i \(-0.556796\pi\)
−0.177484 + 0.984124i \(0.556796\pi\)
\(308\) 0.523590 0.0298343
\(309\) 9.67420 0.550346
\(310\) −3.66701 −0.208272
\(311\) −25.1084 −1.42376 −0.711882 0.702299i \(-0.752157\pi\)
−0.711882 + 0.702299i \(0.752157\pi\)
\(312\) 0 0
\(313\) 2.24005 0.126615 0.0633077 0.997994i \(-0.479835\pi\)
0.0633077 + 0.997994i \(0.479835\pi\)
\(314\) 9.70928 0.547926
\(315\) 1.24846 0.0703430
\(316\) −1.77698 −0.0999627
\(317\) −2.89496 −0.162597 −0.0812986 0.996690i \(-0.525907\pi\)
−0.0812986 + 0.996690i \(0.525907\pi\)
\(318\) −1.02893 −0.0576995
\(319\) 0.217267 0.0121646
\(320\) 4.00000 0.223607
\(321\) 1.58759 0.0886108
\(322\) 5.90829 0.329256
\(323\) −12.4585 −0.693212
\(324\) −4.08065 −0.226703
\(325\) 0 0
\(326\) −0.465732 −0.0257945
\(327\) 4.54638 0.251415
\(328\) −20.5646 −1.13549
\(329\) −9.24846 −0.509884
\(330\) −0.241276 −0.0132818
\(331\) −4.25565 −0.233912 −0.116956 0.993137i \(-0.537314\pi\)
−0.116956 + 0.993137i \(0.537314\pi\)
\(332\) −6.54638 −0.359279
\(333\) −25.7659 −1.41196
\(334\) 27.9311 1.52832
\(335\) −2.34017 −0.127857
\(336\) 1.26180 0.0688366
\(337\) 15.5464 0.846865 0.423433 0.905928i \(-0.360825\pi\)
0.423433 + 0.905928i \(0.360825\pi\)
\(338\) 0 0
\(339\) 6.90602 0.375084
\(340\) 0.837101 0.0453982
\(341\) 5.64423 0.305652
\(342\) 13.7165 0.741701
\(343\) −1.00000 −0.0539949
\(344\) −1.28846 −0.0694690
\(345\) 1.25461 0.0675458
\(346\) −30.3051 −1.62921
\(347\) −20.3812 −1.09412 −0.547060 0.837093i \(-0.684253\pi\)
−0.547060 + 0.837093i \(0.684253\pi\)
\(348\) −0.0890557 −0.00477388
\(349\) −7.16394 −0.383477 −0.191739 0.981446i \(-0.561413\pi\)
−0.191739 + 0.981446i \(0.561413\pi\)
\(350\) −5.60197 −0.299438
\(351\) 0 0
\(352\) −2.83710 −0.151218
\(353\) −5.38348 −0.286534 −0.143267 0.989684i \(-0.545761\pi\)
−0.143267 + 0.989684i \(0.545761\pi\)
\(354\) 1.75872 0.0934751
\(355\) 5.88550 0.312370
\(356\) −3.42696 −0.181629
\(357\) 1.55252 0.0821681
\(358\) −24.1906 −1.27851
\(359\) 15.6937 0.828281 0.414140 0.910213i \(-0.364082\pi\)
0.414140 + 0.910213i \(0.364082\pi\)
\(360\) −3.84324 −0.202557
\(361\) −0.278438 −0.0146547
\(362\) −18.3896 −0.966537
\(363\) −5.55971 −0.291809
\(364\) 0 0
\(365\) 0.162899 0.00852650
\(366\) −4.58145 −0.239476
\(367\) 0.324575 0.0169427 0.00847133 0.999964i \(-0.497303\pi\)
0.00847133 + 0.999964i \(0.497303\pi\)
\(368\) −11.8166 −0.615982
\(369\) 18.0989 0.942191
\(370\) −5.12783 −0.266583
\(371\) −1.63090 −0.0846720
\(372\) −2.31351 −0.119950
\(373\) −25.3112 −1.31057 −0.655283 0.755383i \(-0.727451\pi\)
−0.655283 + 0.755383i \(0.727451\pi\)
\(374\) 2.79606 0.144581
\(375\) −2.43188 −0.125582
\(376\) 28.4703 1.46824
\(377\) 0 0
\(378\) −3.60197 −0.185265
\(379\) −16.7187 −0.858784 −0.429392 0.903118i \(-0.641272\pi\)
−0.429392 + 0.903118i \(0.641272\pi\)
\(380\) −1.25792 −0.0645299
\(381\) −7.26180 −0.372033
\(382\) 19.6430 1.00502
\(383\) 13.1629 0.672593 0.336296 0.941756i \(-0.390826\pi\)
0.336296 + 0.941756i \(0.390826\pi\)
\(384\) −1.78992 −0.0913415
\(385\) −0.382433 −0.0194906
\(386\) 23.4186 1.19197
\(387\) 1.13397 0.0576429
\(388\) 7.95509 0.403858
\(389\) −10.0761 −0.510879 −0.255440 0.966825i \(-0.582220\pi\)
−0.255440 + 0.966825i \(0.582220\pi\)
\(390\) 0 0
\(391\) −14.5392 −0.735278
\(392\) 3.07838 0.155482
\(393\) −7.78539 −0.392721
\(394\) −20.4969 −1.03262
\(395\) 1.29791 0.0653051
\(396\) 1.41855 0.0712849
\(397\) 8.07119 0.405081 0.202541 0.979274i \(-0.435080\pi\)
0.202541 + 0.979274i \(0.435080\pi\)
\(398\) 19.0700 0.955891
\(399\) −2.33299 −0.116795
\(400\) 11.2039 0.560197
\(401\) 12.8371 0.641054 0.320527 0.947239i \(-0.396140\pi\)
0.320527 + 0.947239i \(0.396140\pi\)
\(402\) 3.20394 0.159798
\(403\) 0 0
\(404\) −2.29914 −0.114386
\(405\) 2.98053 0.148104
\(406\) 0.306323 0.0152026
\(407\) 7.89269 0.391226
\(408\) −4.77924 −0.236608
\(409\) −18.7515 −0.927204 −0.463602 0.886044i \(-0.653443\pi\)
−0.463602 + 0.886044i \(0.653443\pi\)
\(410\) 3.60197 0.177889
\(411\) 8.85989 0.437026
\(412\) −11.3197 −0.557679
\(413\) 2.78765 0.137171
\(414\) 16.0072 0.786710
\(415\) 4.78151 0.234715
\(416\) 0 0
\(417\) 7.12783 0.349051
\(418\) −4.20167 −0.205510
\(419\) 23.6319 1.15450 0.577248 0.816569i \(-0.304127\pi\)
0.577248 + 0.816569i \(0.304127\pi\)
\(420\) 0.156755 0.00764888
\(421\) −19.4524 −0.948052 −0.474026 0.880511i \(-0.657200\pi\)
−0.474026 + 0.880511i \(0.657200\pi\)
\(422\) −3.17009 −0.154317
\(423\) −25.0566 −1.21830
\(424\) 5.02052 0.243818
\(425\) 13.7854 0.668689
\(426\) −8.05786 −0.390405
\(427\) −7.26180 −0.351423
\(428\) −1.85762 −0.0897915
\(429\) 0 0
\(430\) 0.225678 0.0108832
\(431\) −18.0989 −0.871793 −0.435897 0.899997i \(-0.643569\pi\)
−0.435897 + 0.899997i \(0.643569\pi\)
\(432\) 7.20394 0.346600
\(433\) 20.5380 0.986992 0.493496 0.869748i \(-0.335719\pi\)
0.493496 + 0.869748i \(0.335719\pi\)
\(434\) 7.95774 0.381984
\(435\) 0.0650468 0.00311875
\(436\) −5.31965 −0.254765
\(437\) 21.8482 1.04514
\(438\) −0.223025 −0.0106565
\(439\) −26.9627 −1.28686 −0.643429 0.765506i \(-0.722489\pi\)
−0.643429 + 0.765506i \(0.722489\pi\)
\(440\) 1.17727 0.0561244
\(441\) −2.70928 −0.129013
\(442\) 0 0
\(443\) 26.4101 1.25478 0.627392 0.778704i \(-0.284122\pi\)
0.627392 + 0.778704i \(0.284122\pi\)
\(444\) −3.23513 −0.153533
\(445\) 2.50307 0.118657
\(446\) 23.1617 1.09674
\(447\) 11.0556 0.522912
\(448\) −8.68035 −0.410108
\(449\) 31.4329 1.48341 0.741706 0.670725i \(-0.234017\pi\)
0.741706 + 0.670725i \(0.234017\pi\)
\(450\) −15.1773 −0.715464
\(451\) −5.54411 −0.261062
\(452\) −8.08065 −0.380082
\(453\) −0.859888 −0.0404011
\(454\) −15.5174 −0.728270
\(455\) 0 0
\(456\) 7.18181 0.336319
\(457\) 18.0650 0.845047 0.422524 0.906352i \(-0.361144\pi\)
0.422524 + 0.906352i \(0.361144\pi\)
\(458\) 32.5380 1.52040
\(459\) 8.86376 0.413725
\(460\) −1.46800 −0.0684458
\(461\) 23.0784 1.07487 0.537434 0.843306i \(-0.319394\pi\)
0.537434 + 0.843306i \(0.319394\pi\)
\(462\) 0.523590 0.0243596
\(463\) 4.54760 0.211345 0.105672 0.994401i \(-0.466301\pi\)
0.105672 + 0.994401i \(0.466301\pi\)
\(464\) −0.612646 −0.0284414
\(465\) 1.68980 0.0783627
\(466\) 15.6404 0.724525
\(467\) 37.8154 1.74989 0.874943 0.484226i \(-0.160899\pi\)
0.874943 + 0.484226i \(0.160899\pi\)
\(468\) 0 0
\(469\) 5.07838 0.234498
\(470\) −4.98667 −0.230018
\(471\) −4.47414 −0.206158
\(472\) −8.58145 −0.394993
\(473\) −0.347361 −0.0159717
\(474\) −1.77698 −0.0816192
\(475\) −20.7154 −0.950489
\(476\) −1.81658 −0.0832629
\(477\) −4.41855 −0.202312
\(478\) 10.1880 0.465986
\(479\) 9.24005 0.422189 0.211094 0.977466i \(-0.432297\pi\)
0.211094 + 0.977466i \(0.432297\pi\)
\(480\) −0.849388 −0.0387691
\(481\) 0 0
\(482\) −19.8108 −0.902358
\(483\) −2.72261 −0.123883
\(484\) 6.50534 0.295697
\(485\) −5.81044 −0.263838
\(486\) −14.8865 −0.675268
\(487\) −13.6598 −0.618986 −0.309493 0.950902i \(-0.600159\pi\)
−0.309493 + 0.950902i \(0.600159\pi\)
\(488\) 22.3545 1.01194
\(489\) 0.214614 0.00970519
\(490\) −0.539189 −0.0243581
\(491\) −29.6514 −1.33815 −0.669075 0.743195i \(-0.733309\pi\)
−0.669075 + 0.743195i \(0.733309\pi\)
\(492\) 2.27247 0.102451
\(493\) −0.753803 −0.0339496
\(494\) 0 0
\(495\) −1.03612 −0.0465700
\(496\) −15.9155 −0.714626
\(497\) −12.7721 −0.572905
\(498\) −6.54638 −0.293350
\(499\) 35.5246 1.59030 0.795151 0.606412i \(-0.207392\pi\)
0.795151 + 0.606412i \(0.207392\pi\)
\(500\) 2.84551 0.127255
\(501\) −12.8710 −0.575032
\(502\) 10.3219 0.460690
\(503\) 34.4124 1.53437 0.767187 0.641424i \(-0.221656\pi\)
0.767187 + 0.641424i \(0.221656\pi\)
\(504\) 8.34017 0.371501
\(505\) 1.67930 0.0747279
\(506\) −4.90337 −0.217981
\(507\) 0 0
\(508\) 8.49693 0.376990
\(509\) 11.1184 0.492813 0.246407 0.969167i \(-0.420750\pi\)
0.246407 + 0.969167i \(0.420750\pi\)
\(510\) 0.837101 0.0370675
\(511\) −0.353504 −0.0156381
\(512\) 22.4079 0.990297
\(513\) −13.3197 −0.588077
\(514\) 15.9649 0.704183
\(515\) 8.26794 0.364329
\(516\) 0.142380 0.00626791
\(517\) 7.67543 0.337565
\(518\) 11.1278 0.488929
\(519\) 13.9649 0.612992
\(520\) 0 0
\(521\) −17.8888 −0.783723 −0.391862 0.920024i \(-0.628169\pi\)
−0.391862 + 0.920024i \(0.628169\pi\)
\(522\) 0.829914 0.0363243
\(523\) −23.9877 −1.04891 −0.524455 0.851438i \(-0.675731\pi\)
−0.524455 + 0.851438i \(0.675731\pi\)
\(524\) 9.10957 0.397954
\(525\) 2.58145 0.112664
\(526\) 14.2485 0.621263
\(527\) −19.5825 −0.853027
\(528\) −1.04718 −0.0455727
\(529\) 2.49693 0.108562
\(530\) −0.879362 −0.0381970
\(531\) 7.55252 0.327751
\(532\) 2.72979 0.118352
\(533\) 0 0
\(534\) −3.42696 −0.148299
\(535\) 1.35682 0.0586603
\(536\) −15.6332 −0.675250
\(537\) 11.1473 0.481042
\(538\) 12.9262 0.557286
\(539\) 0.829914 0.0357469
\(540\) 0.894960 0.0385130
\(541\) −19.4114 −0.834560 −0.417280 0.908778i \(-0.637017\pi\)
−0.417280 + 0.908778i \(0.637017\pi\)
\(542\) −12.7961 −0.549638
\(543\) 8.47414 0.363660
\(544\) 9.84324 0.422026
\(545\) 3.88550 0.166437
\(546\) 0 0
\(547\) −1.81432 −0.0775745 −0.0387873 0.999247i \(-0.512349\pi\)
−0.0387873 + 0.999247i \(0.512349\pi\)
\(548\) −10.3668 −0.442849
\(549\) −19.6742 −0.839675
\(550\) 4.64915 0.198240
\(551\) 1.13275 0.0482566
\(552\) 8.38121 0.356728
\(553\) −2.81658 −0.119773
\(554\) 30.5620 1.29845
\(555\) 2.36296 0.100302
\(556\) −8.34017 −0.353702
\(557\) 23.4186 0.992276 0.496138 0.868244i \(-0.334751\pi\)
0.496138 + 0.868244i \(0.334751\pi\)
\(558\) 21.5597 0.912695
\(559\) 0 0
\(560\) 1.07838 0.0455698
\(561\) −1.28846 −0.0543987
\(562\) 5.62022 0.237075
\(563\) 26.6947 1.12505 0.562524 0.826781i \(-0.309830\pi\)
0.562524 + 0.826781i \(0.309830\pi\)
\(564\) −3.14608 −0.132474
\(565\) 5.90215 0.248305
\(566\) −1.14608 −0.0481732
\(567\) −6.46800 −0.271630
\(568\) 39.3172 1.64971
\(569\) −26.5897 −1.11470 −0.557349 0.830279i \(-0.688181\pi\)
−0.557349 + 0.830279i \(0.688181\pi\)
\(570\) −1.25792 −0.0526885
\(571\) −3.43310 −0.143671 −0.0718355 0.997416i \(-0.522886\pi\)
−0.0718355 + 0.997416i \(0.522886\pi\)
\(572\) 0 0
\(573\) −9.05172 −0.378141
\(574\) −7.81658 −0.326258
\(575\) −24.1750 −1.00817
\(576\) −23.5174 −0.979894
\(577\) 30.4657 1.26831 0.634153 0.773208i \(-0.281349\pi\)
0.634153 + 0.773208i \(0.281349\pi\)
\(578\) 10.1906 0.423873
\(579\) −10.7915 −0.448481
\(580\) −0.0761103 −0.00316031
\(581\) −10.3763 −0.430481
\(582\) 7.95509 0.329749
\(583\) 1.35350 0.0560564
\(584\) 1.08822 0.0450308
\(585\) 0 0
\(586\) −28.4645 −1.17586
\(587\) 26.2606 1.08389 0.541945 0.840414i \(-0.317688\pi\)
0.541945 + 0.840414i \(0.317688\pi\)
\(588\) −0.340173 −0.0140285
\(589\) 29.4268 1.21251
\(590\) 1.50307 0.0618805
\(591\) 9.44521 0.388524
\(592\) −22.2557 −0.914702
\(593\) 40.8420 1.67718 0.838590 0.544762i \(-0.183380\pi\)
0.838590 + 0.544762i \(0.183380\pi\)
\(594\) 2.98932 0.122653
\(595\) 1.32684 0.0543952
\(596\) −12.9360 −0.529879
\(597\) −8.78765 −0.359655
\(598\) 0 0
\(599\) −27.3545 −1.11768 −0.558838 0.829277i \(-0.688753\pi\)
−0.558838 + 0.829277i \(0.688753\pi\)
\(600\) −7.94668 −0.324422
\(601\) 25.4908 1.03979 0.519895 0.854230i \(-0.325971\pi\)
0.519895 + 0.854230i \(0.325971\pi\)
\(602\) −0.489741 −0.0199603
\(603\) 13.7587 0.560299
\(604\) 1.00614 0.0409394
\(605\) −4.75154 −0.193177
\(606\) −2.29914 −0.0933960
\(607\) 19.9311 0.808977 0.404489 0.914543i \(-0.367449\pi\)
0.404489 + 0.914543i \(0.367449\pi\)
\(608\) −14.7915 −0.599876
\(609\) −0.141157 −0.00571997
\(610\) −3.91548 −0.158533
\(611\) 0 0
\(612\) −4.92162 −0.198945
\(613\) 22.7214 0.917708 0.458854 0.888512i \(-0.348260\pi\)
0.458854 + 0.888512i \(0.348260\pi\)
\(614\) 7.27739 0.293692
\(615\) −1.65983 −0.0669307
\(616\) −2.55479 −0.102935
\(617\) −14.3545 −0.577892 −0.288946 0.957345i \(-0.593305\pi\)
−0.288946 + 0.957345i \(0.593305\pi\)
\(618\) −11.3197 −0.455343
\(619\) 27.9832 1.12474 0.562369 0.826886i \(-0.309890\pi\)
0.562369 + 0.826886i \(0.309890\pi\)
\(620\) −1.97721 −0.0794068
\(621\) −15.5441 −0.623764
\(622\) 29.3789 1.17799
\(623\) −5.43188 −0.217624
\(624\) 0 0
\(625\) 21.8599 0.874396
\(626\) −2.62106 −0.104758
\(627\) 1.93618 0.0773234
\(628\) 5.23513 0.208905
\(629\) −27.3835 −1.09185
\(630\) −1.46081 −0.0582001
\(631\) −21.4186 −0.852659 −0.426330 0.904568i \(-0.640194\pi\)
−0.426330 + 0.904568i \(0.640194\pi\)
\(632\) 8.67050 0.344894
\(633\) 1.46081 0.0580620
\(634\) 3.38735 0.134529
\(635\) −6.20620 −0.246286
\(636\) −0.554787 −0.0219987
\(637\) 0 0
\(638\) −0.254222 −0.0100647
\(639\) −34.6030 −1.36887
\(640\) −1.52973 −0.0604680
\(641\) −37.9360 −1.49838 −0.749191 0.662354i \(-0.769557\pi\)
−0.749191 + 0.662354i \(0.769557\pi\)
\(642\) −1.85762 −0.0733144
\(643\) 36.2122 1.42807 0.714034 0.700111i \(-0.246866\pi\)
0.714034 + 0.700111i \(0.246866\pi\)
\(644\) 3.18568 0.125534
\(645\) −0.103995 −0.00409479
\(646\) 14.5776 0.573547
\(647\) 42.7948 1.68244 0.841219 0.540694i \(-0.181838\pi\)
0.841219 + 0.540694i \(0.181838\pi\)
\(648\) 19.9109 0.782176
\(649\) −2.31351 −0.0908132
\(650\) 0 0
\(651\) −3.66701 −0.143722
\(652\) −0.251117 −0.00983451
\(653\) 5.54864 0.217135 0.108568 0.994089i \(-0.465374\pi\)
0.108568 + 0.994089i \(0.465374\pi\)
\(654\) −5.31965 −0.208015
\(655\) −6.65368 −0.259981
\(656\) 15.6332 0.610373
\(657\) −0.957740 −0.0373650
\(658\) 10.8215 0.421866
\(659\) −23.1529 −0.901908 −0.450954 0.892547i \(-0.648916\pi\)
−0.450954 + 0.892547i \(0.648916\pi\)
\(660\) −0.130094 −0.00506388
\(661\) 47.2544 1.83798 0.918992 0.394276i \(-0.129005\pi\)
0.918992 + 0.394276i \(0.129005\pi\)
\(662\) 4.97948 0.193533
\(663\) 0 0
\(664\) 31.9421 1.23960
\(665\) −1.99386 −0.0773185
\(666\) 30.1483 1.16822
\(667\) 1.32192 0.0511850
\(668\) 15.0601 0.582694
\(669\) −10.6732 −0.412648
\(670\) 2.73820 0.105786
\(671\) 6.02666 0.232657
\(672\) 1.84324 0.0711047
\(673\) −3.42082 −0.131863 −0.0659314 0.997824i \(-0.521002\pi\)
−0.0659314 + 0.997824i \(0.521002\pi\)
\(674\) −18.1906 −0.700676
\(675\) 14.7382 0.567274
\(676\) 0 0
\(677\) 10.6959 0.411079 0.205539 0.978649i \(-0.434105\pi\)
0.205539 + 0.978649i \(0.434105\pi\)
\(678\) −8.08065 −0.310335
\(679\) 12.6092 0.483895
\(680\) −4.08452 −0.156634
\(681\) 7.15061 0.274012
\(682\) −6.60424 −0.252889
\(683\) 6.59583 0.252382 0.126191 0.992006i \(-0.459725\pi\)
0.126191 + 0.992006i \(0.459725\pi\)
\(684\) 7.39576 0.282784
\(685\) 7.57199 0.289311
\(686\) 1.17009 0.0446741
\(687\) −14.9939 −0.572051
\(688\) 0.979481 0.0373424
\(689\) 0 0
\(690\) −1.46800 −0.0558858
\(691\) −49.4729 −1.88204 −0.941019 0.338353i \(-0.890130\pi\)
−0.941019 + 0.338353i \(0.890130\pi\)
\(692\) −16.3402 −0.621160
\(693\) 2.24846 0.0854121
\(694\) 23.8478 0.905249
\(695\) 6.09171 0.231072
\(696\) 0.434535 0.0164710
\(697\) 19.2351 0.728583
\(698\) 8.38243 0.317280
\(699\) −7.20725 −0.272603
\(700\) −3.02052 −0.114165
\(701\) 20.8166 0.786231 0.393116 0.919489i \(-0.371397\pi\)
0.393116 + 0.919489i \(0.371397\pi\)
\(702\) 0 0
\(703\) 41.1494 1.55198
\(704\) 7.20394 0.271509
\(705\) 2.29791 0.0865444
\(706\) 6.29914 0.237071
\(707\) −3.64423 −0.137055
\(708\) 0.948284 0.0356387
\(709\) 5.95386 0.223602 0.111801 0.993731i \(-0.464338\pi\)
0.111801 + 0.993731i \(0.464338\pi\)
\(710\) −6.88655 −0.258448
\(711\) −7.63090 −0.286181
\(712\) 16.7214 0.626660
\(713\) 34.3412 1.28609
\(714\) −1.81658 −0.0679839
\(715\) 0 0
\(716\) −13.0433 −0.487451
\(717\) −4.69472 −0.175328
\(718\) −18.3630 −0.685300
\(719\) −1.68980 −0.0630190 −0.0315095 0.999503i \(-0.510031\pi\)
−0.0315095 + 0.999503i \(0.510031\pi\)
\(720\) 2.92162 0.108882
\(721\) −17.9421 −0.668200
\(722\) 0.325797 0.0121249
\(723\) 9.12905 0.339513
\(724\) −9.91548 −0.368506
\(725\) −1.25338 −0.0465495
\(726\) 6.50534 0.241436
\(727\) 14.0722 0.521910 0.260955 0.965351i \(-0.415963\pi\)
0.260955 + 0.965351i \(0.415963\pi\)
\(728\) 0 0
\(729\) −12.5441 −0.464597
\(730\) −0.190605 −0.00705462
\(731\) 1.20516 0.0445744
\(732\) −2.47027 −0.0913037
\(733\) −10.9311 −0.403749 −0.201874 0.979411i \(-0.564703\pi\)
−0.201874 + 0.979411i \(0.564703\pi\)
\(734\) −0.379780 −0.0140179
\(735\) 0.248464 0.00916474
\(736\) −17.2618 −0.636278
\(737\) −4.21461 −0.155247
\(738\) −21.1773 −0.779546
\(739\) −3.17009 −0.116614 −0.0583068 0.998299i \(-0.518570\pi\)
−0.0583068 + 0.998299i \(0.518570\pi\)
\(740\) −2.76487 −0.101639
\(741\) 0 0
\(742\) 1.90829 0.0700556
\(743\) 9.73206 0.357035 0.178517 0.983937i \(-0.442870\pi\)
0.178517 + 0.983937i \(0.442870\pi\)
\(744\) 11.2885 0.413855
\(745\) 9.44852 0.346167
\(746\) 29.6163 1.08433
\(747\) −28.1122 −1.02857
\(748\) 1.50761 0.0551235
\(749\) −2.94441 −0.107586
\(750\) 2.84551 0.103903
\(751\) 7.77924 0.283869 0.141934 0.989876i \(-0.454668\pi\)
0.141934 + 0.989876i \(0.454668\pi\)
\(752\) −21.6430 −0.789239
\(753\) −4.75646 −0.173335
\(754\) 0 0
\(755\) −0.734892 −0.0267455
\(756\) −1.94214 −0.0706350
\(757\) 10.8576 0.394627 0.197313 0.980340i \(-0.436778\pi\)
0.197313 + 0.980340i \(0.436778\pi\)
\(758\) 19.5624 0.710537
\(759\) 2.25953 0.0820157
\(760\) 6.13784 0.222643
\(761\) 1.82150 0.0660294 0.0330147 0.999455i \(-0.489489\pi\)
0.0330147 + 0.999455i \(0.489489\pi\)
\(762\) 8.49693 0.307811
\(763\) −8.43188 −0.305255
\(764\) 10.5913 0.383179
\(765\) 3.59478 0.129970
\(766\) −15.4017 −0.556487
\(767\) 0 0
\(768\) −7.26633 −0.262201
\(769\) 39.7948 1.43504 0.717519 0.696539i \(-0.245277\pi\)
0.717519 + 0.696539i \(0.245277\pi\)
\(770\) 0.447480 0.0161261
\(771\) −7.35682 −0.264949
\(772\) 12.6270 0.454456
\(773\) 18.3135 0.658691 0.329346 0.944209i \(-0.393172\pi\)
0.329346 + 0.944209i \(0.393172\pi\)
\(774\) −1.32684 −0.0476924
\(775\) −32.5608 −1.16962
\(776\) −38.8157 −1.39340
\(777\) −5.12783 −0.183960
\(778\) 11.7899 0.422689
\(779\) −28.9048 −1.03562
\(780\) 0 0
\(781\) 10.5997 0.379287
\(782\) 17.0121 0.608352
\(783\) −0.805905 −0.0288007
\(784\) −2.34017 −0.0835776
\(785\) −3.82377 −0.136476
\(786\) 9.10957 0.324928
\(787\) −26.2606 −0.936088 −0.468044 0.883705i \(-0.655041\pi\)
−0.468044 + 0.883705i \(0.655041\pi\)
\(788\) −11.0517 −0.393701
\(789\) −6.56585 −0.233750
\(790\) −1.51867 −0.0540319
\(791\) −12.8082 −0.455406
\(792\) −6.92162 −0.245949
\(793\) 0 0
\(794\) −9.44399 −0.335155
\(795\) 0.405220 0.0143717
\(796\) 10.2823 0.364447
\(797\) −44.0677 −1.56096 −0.780479 0.625182i \(-0.785025\pi\)
−0.780479 + 0.625182i \(0.785025\pi\)
\(798\) 2.72979 0.0966337
\(799\) −26.6297 −0.942090
\(800\) 16.3668 0.578655
\(801\) −14.7165 −0.519981
\(802\) −15.0205 −0.530393
\(803\) 0.293378 0.0103531
\(804\) 1.72753 0.0609252
\(805\) −2.32684 −0.0820104
\(806\) 0 0
\(807\) −5.95652 −0.209679
\(808\) 11.2183 0.394659
\(809\) −8.07838 −0.284021 −0.142010 0.989865i \(-0.545357\pi\)
−0.142010 + 0.989865i \(0.545357\pi\)
\(810\) −3.48747 −0.122537
\(811\) −38.0098 −1.33471 −0.667353 0.744742i \(-0.732573\pi\)
−0.667353 + 0.744742i \(0.732573\pi\)
\(812\) 0.165166 0.00579619
\(813\) 5.89657 0.206802
\(814\) −9.23513 −0.323691
\(815\) 0.183417 0.00642483
\(816\) 3.63317 0.127186
\(817\) −1.81100 −0.0633590
\(818\) 21.9409 0.767146
\(819\) 0 0
\(820\) 1.94214 0.0678225
\(821\) −13.7542 −0.480025 −0.240012 0.970770i \(-0.577151\pi\)
−0.240012 + 0.970770i \(0.577151\pi\)
\(822\) −10.3668 −0.361585
\(823\) 9.91935 0.345767 0.172883 0.984942i \(-0.444692\pi\)
0.172883 + 0.984942i \(0.444692\pi\)
\(824\) 55.2327 1.92412
\(825\) −2.14238 −0.0745881
\(826\) −3.26180 −0.113492
\(827\) 3.77101 0.131131 0.0655654 0.997848i \(-0.479115\pi\)
0.0655654 + 0.997848i \(0.479115\pi\)
\(828\) 8.63090 0.299944
\(829\) −11.5187 −0.400060 −0.200030 0.979790i \(-0.564104\pi\)
−0.200030 + 0.979790i \(0.564104\pi\)
\(830\) −5.59478 −0.194198
\(831\) −14.0833 −0.488544
\(832\) 0 0
\(833\) −2.87936 −0.0997640
\(834\) −8.34017 −0.288797
\(835\) −11.0000 −0.380671
\(836\) −2.26549 −0.0783537
\(837\) −20.9360 −0.723654
\(838\) −27.6514 −0.955202
\(839\) −43.6475 −1.50688 −0.753440 0.657516i \(-0.771607\pi\)
−0.753440 + 0.657516i \(0.771607\pi\)
\(840\) −0.764867 −0.0263904
\(841\) −28.9315 −0.997637
\(842\) 22.7610 0.784396
\(843\) −2.58986 −0.0891995
\(844\) −1.70928 −0.0588357
\(845\) 0 0
\(846\) 29.3184 1.00799
\(847\) 10.3112 0.354299
\(848\) −3.81658 −0.131062
\(849\) 0.528125 0.0181252
\(850\) −16.1301 −0.553258
\(851\) 48.0216 1.64616
\(852\) −4.34471 −0.148847
\(853\) −10.0940 −0.345611 −0.172806 0.984956i \(-0.555283\pi\)
−0.172806 + 0.984956i \(0.555283\pi\)
\(854\) 8.49693 0.290759
\(855\) −5.40191 −0.184741
\(856\) 9.06400 0.309801
\(857\) −24.0267 −0.820735 −0.410368 0.911920i \(-0.634600\pi\)
−0.410368 + 0.911920i \(0.634600\pi\)
\(858\) 0 0
\(859\) −1.65983 −0.0566326 −0.0283163 0.999599i \(-0.509015\pi\)
−0.0283163 + 0.999599i \(0.509015\pi\)
\(860\) 0.121683 0.00414936
\(861\) 3.60197 0.122755
\(862\) 21.1773 0.721301
\(863\) −28.6270 −0.974475 −0.487238 0.873269i \(-0.661995\pi\)
−0.487238 + 0.873269i \(0.661995\pi\)
\(864\) 10.5236 0.358020
\(865\) 11.9350 0.405801
\(866\) −24.0312 −0.816613
\(867\) −4.69594 −0.159483
\(868\) 4.29072 0.145637
\(869\) 2.33752 0.0792949
\(870\) −0.0761103 −0.00258038
\(871\) 0 0
\(872\) 25.9565 0.878999
\(873\) 34.1617 1.15620
\(874\) −25.5642 −0.864723
\(875\) 4.51026 0.152475
\(876\) −0.120252 −0.00406296
\(877\) −40.8587 −1.37970 −0.689850 0.723953i \(-0.742323\pi\)
−0.689850 + 0.723953i \(0.742323\pi\)
\(878\) 31.5486 1.06472
\(879\) 13.1168 0.442417
\(880\) −0.894960 −0.0301691
\(881\) 48.5835 1.63682 0.818411 0.574634i \(-0.194856\pi\)
0.818411 + 0.574634i \(0.194856\pi\)
\(882\) 3.17009 0.106742
\(883\) −49.2456 −1.65725 −0.828624 0.559806i \(-0.810876\pi\)
−0.828624 + 0.559806i \(0.810876\pi\)
\(884\) 0 0
\(885\) −0.692632 −0.0232826
\(886\) −30.9021 −1.03818
\(887\) −13.1773 −0.442450 −0.221225 0.975223i \(-0.571005\pi\)
−0.221225 + 0.975223i \(0.571005\pi\)
\(888\) 15.7854 0.529723
\(889\) 13.4680 0.451702
\(890\) −2.92881 −0.0981739
\(891\) 5.36788 0.179831
\(892\) 12.4885 0.418147
\(893\) 40.0166 1.33911
\(894\) −12.9360 −0.432644
\(895\) 9.52690 0.318449
\(896\) 3.31965 0.110902
\(897\) 0 0
\(898\) −36.7792 −1.22734
\(899\) 1.78047 0.0593818
\(900\) −8.18342 −0.272781
\(901\) −4.69594 −0.156445
\(902\) 6.48709 0.215996
\(903\) 0.225678 0.00751009
\(904\) 39.4284 1.31137
\(905\) 7.24232 0.240743
\(906\) 1.00614 0.0334269
\(907\) 15.3051 0.508198 0.254099 0.967178i \(-0.418221\pi\)
0.254099 + 0.967178i \(0.418221\pi\)
\(908\) −8.36683 −0.277663
\(909\) −9.87322 −0.327474
\(910\) 0 0
\(911\) −5.07223 −0.168051 −0.0840253 0.996464i \(-0.526778\pi\)
−0.0840253 + 0.996464i \(0.526778\pi\)
\(912\) −5.45959 −0.180785
\(913\) 8.61142 0.284997
\(914\) −21.1377 −0.699172
\(915\) 1.80430 0.0596482
\(916\) 17.5441 0.579674
\(917\) 14.4391 0.476820
\(918\) −10.3714 −0.342306
\(919\) −46.3689 −1.52957 −0.764785 0.644286i \(-0.777155\pi\)
−0.764785 + 0.644286i \(0.777155\pi\)
\(920\) 7.16290 0.236154
\(921\) −3.35350 −0.110502
\(922\) −27.0037 −0.889319
\(923\) 0 0
\(924\) 0.282314 0.00928745
\(925\) −45.5318 −1.49708
\(926\) −5.32108 −0.174862
\(927\) −48.6102 −1.59657
\(928\) −0.894960 −0.0293785
\(929\) −23.4547 −0.769523 −0.384761 0.923016i \(-0.625716\pi\)
−0.384761 + 0.923016i \(0.625716\pi\)
\(930\) −1.97721 −0.0648354
\(931\) 4.32684 0.141807
\(932\) 8.43310 0.276236
\(933\) −13.5381 −0.443219
\(934\) −44.2472 −1.44781
\(935\) −1.10116 −0.0360119
\(936\) 0 0
\(937\) −18.0156 −0.588544 −0.294272 0.955722i \(-0.595077\pi\)
−0.294272 + 0.955722i \(0.595077\pi\)
\(938\) −5.94214 −0.194018
\(939\) 1.20781 0.0394155
\(940\) −2.68876 −0.0876976
\(941\) −31.7805 −1.03601 −0.518007 0.855377i \(-0.673326\pi\)
−0.518007 + 0.855377i \(0.673326\pi\)
\(942\) 5.23513 0.170570
\(943\) −33.7321 −1.09847
\(944\) 6.52359 0.212325
\(945\) 1.41855 0.0461455
\(946\) 0.406442 0.0132146
\(947\) −46.3812 −1.50719 −0.753593 0.657341i \(-0.771681\pi\)
−0.753593 + 0.657341i \(0.771681\pi\)
\(948\) −0.958125 −0.0311185
\(949\) 0 0
\(950\) 24.2388 0.786412
\(951\) −1.56093 −0.0506166
\(952\) 8.86376 0.287276
\(953\) −27.2511 −0.882750 −0.441375 0.897323i \(-0.645509\pi\)
−0.441375 + 0.897323i \(0.645509\pi\)
\(954\) 5.17009 0.167388
\(955\) −7.73594 −0.250329
\(956\) 5.49323 0.177664
\(957\) 0.117148 0.00378686
\(958\) −10.8117 −0.349309
\(959\) −16.4319 −0.530613
\(960\) 2.15676 0.0696090
\(961\) 15.2534 0.492045
\(962\) 0 0
\(963\) −7.97721 −0.257062
\(964\) −10.6818 −0.344037
\(965\) −9.22285 −0.296894
\(966\) 3.18568 0.102498
\(967\) −9.77045 −0.314196 −0.157098 0.987583i \(-0.550214\pi\)
−0.157098 + 0.987583i \(0.550214\pi\)
\(968\) −31.7419 −1.02022
\(969\) −6.71751 −0.215797
\(970\) 6.79872 0.218294
\(971\) −13.9856 −0.448820 −0.224410 0.974495i \(-0.572045\pi\)
−0.224410 + 0.974495i \(0.572045\pi\)
\(972\) −8.02666 −0.257455
\(973\) −13.2195 −0.423799
\(974\) 15.9832 0.512134
\(975\) 0 0
\(976\) −16.9939 −0.543960
\(977\) 54.7454 1.75146 0.875730 0.482801i \(-0.160381\pi\)
0.875730 + 0.482801i \(0.160381\pi\)
\(978\) −0.251117 −0.00802985
\(979\) 4.50799 0.144076
\(980\) −0.290725 −0.00928686
\(981\) −22.8443 −0.729362
\(982\) 34.6947 1.10715
\(983\) −0.0399930 −0.00127558 −0.000637789 1.00000i \(-0.500203\pi\)
−0.000637789 1.00000i \(0.500203\pi\)
\(984\) −11.0882 −0.353480
\(985\) 8.07223 0.257203
\(986\) 0.882015 0.0280891
\(987\) −4.98667 −0.158727
\(988\) 0 0
\(989\) −2.11345 −0.0672038
\(990\) 1.21235 0.0385309
\(991\) 53.9481 1.71372 0.856859 0.515551i \(-0.172413\pi\)
0.856859 + 0.515551i \(0.172413\pi\)
\(992\) −23.2495 −0.738173
\(993\) −2.29460 −0.0728169
\(994\) 14.9444 0.474008
\(995\) −7.51026 −0.238091
\(996\) −3.52973 −0.111844
\(997\) 42.0554 1.33191 0.665954 0.745993i \(-0.268025\pi\)
0.665954 + 0.745993i \(0.268025\pi\)
\(998\) −41.5669 −1.31578
\(999\) −29.2762 −0.926257
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 1183.2.a.j.1.1 3
7.6 odd 2 8281.2.a.bi.1.1 3
13.5 odd 4 91.2.c.a.64.5 yes 6
13.8 odd 4 91.2.c.a.64.2 6
13.12 even 2 1183.2.a.h.1.3 3
39.5 even 4 819.2.c.b.64.2 6
39.8 even 4 819.2.c.b.64.5 6
52.31 even 4 1456.2.k.c.337.3 6
52.47 even 4 1456.2.k.c.337.4 6
91.5 even 12 637.2.r.d.116.5 12
91.18 odd 12 637.2.r.e.324.2 12
91.31 even 12 637.2.r.d.324.2 12
91.34 even 4 637.2.c.d.246.2 6
91.44 odd 12 637.2.r.e.116.5 12
91.47 even 12 637.2.r.d.116.2 12
91.60 odd 12 637.2.r.e.324.5 12
91.73 even 12 637.2.r.d.324.5 12
91.83 even 4 637.2.c.d.246.5 6
91.86 odd 12 637.2.r.e.116.2 12
91.90 odd 2 8281.2.a.be.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.c.a.64.2 6 13.8 odd 4
91.2.c.a.64.5 yes 6 13.5 odd 4
637.2.c.d.246.2 6 91.34 even 4
637.2.c.d.246.5 6 91.83 even 4
637.2.r.d.116.2 12 91.47 even 12
637.2.r.d.116.5 12 91.5 even 12
637.2.r.d.324.2 12 91.31 even 12
637.2.r.d.324.5 12 91.73 even 12
637.2.r.e.116.2 12 91.86 odd 12
637.2.r.e.116.5 12 91.44 odd 12
637.2.r.e.324.2 12 91.18 odd 12
637.2.r.e.324.5 12 91.60 odd 12
819.2.c.b.64.2 6 39.5 even 4
819.2.c.b.64.5 6 39.8 even 4
1183.2.a.h.1.3 3 13.12 even 2
1183.2.a.j.1.1 3 1.1 even 1 trivial
1456.2.k.c.337.3 6 52.31 even 4
1456.2.k.c.337.4 6 52.47 even 4
8281.2.a.be.1.3 3 91.90 odd 2
8281.2.a.bi.1.1 3 7.6 odd 2