Properties

Label 1134.2.a.l.1.1
Level $1134$
Weight $2$
Character 1134.1
Self dual yes
Analytic conductor $9.055$
Analytic rank $0$
Dimension $2$
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] = [1134,2,Mod(1,1134)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1134, 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("1134.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.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: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{12})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.73205\) of defining polynomial
Character \(\chi\) \(=\) 1134.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} +0.267949 q^{5} -1.00000 q^{7} -1.00000 q^{8} -0.267949 q^{10} +6.19615 q^{11} -6.46410 q^{13} +1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} +0.732051 q^{19} +0.267949 q^{20} -6.19615 q^{22} -4.19615 q^{23} -4.92820 q^{25} +6.46410 q^{26} -1.00000 q^{28} +1.53590 q^{29} +8.19615 q^{31} -1.00000 q^{32} -7.00000 q^{34} -0.267949 q^{35} +10.6603 q^{37} -0.732051 q^{38} -0.267949 q^{40} +2.53590 q^{41} -1.46410 q^{43} +6.19615 q^{44} +4.19615 q^{46} +4.73205 q^{47} +1.00000 q^{49} +4.92820 q^{50} -6.46410 q^{52} -9.46410 q^{53} +1.66025 q^{55} +1.00000 q^{56} -1.53590 q^{58} +4.19615 q^{59} +3.92820 q^{61} -8.19615 q^{62} +1.00000 q^{64} -1.73205 q^{65} -6.73205 q^{67} +7.00000 q^{68} +0.267949 q^{70} +6.53590 q^{71} +8.26795 q^{73} -10.6603 q^{74} +0.732051 q^{76} -6.19615 q^{77} -9.12436 q^{79} +0.267949 q^{80} -2.53590 q^{82} +16.5885 q^{83} +1.87564 q^{85} +1.46410 q^{86} -6.19615 q^{88} +9.92820 q^{89} +6.46410 q^{91} -4.19615 q^{92} -4.73205 q^{94} +0.196152 q^{95} +10.9282 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} + 2 q^{4} + 4 q^{5} - 2 q^{7} - 2 q^{8} - 4 q^{10} + 2 q^{11} - 6 q^{13} + 2 q^{14} + 2 q^{16} + 14 q^{17} - 2 q^{19} + 4 q^{20} - 2 q^{22} + 2 q^{23} + 4 q^{25} + 6 q^{26} - 2 q^{28} + 10 q^{29} + 6 q^{31} - 2 q^{32} - 14 q^{34} - 4 q^{35} + 4 q^{37} + 2 q^{38} - 4 q^{40} + 12 q^{41} + 4 q^{43} + 2 q^{44} - 2 q^{46} + 6 q^{47} + 2 q^{49} - 4 q^{50} - 6 q^{52} - 12 q^{53} - 14 q^{55} + 2 q^{56} - 10 q^{58} - 2 q^{59} - 6 q^{61} - 6 q^{62} + 2 q^{64} - 10 q^{67} + 14 q^{68} + 4 q^{70} + 20 q^{71} + 20 q^{73} - 4 q^{74} - 2 q^{76} - 2 q^{77} + 6 q^{79} + 4 q^{80} - 12 q^{82} + 2 q^{83} + 28 q^{85} - 4 q^{86} - 2 q^{88} + 6 q^{89} + 6 q^{91} + 2 q^{92} - 6 q^{94} - 10 q^{95} + 8 q^{97} - 2 q^{98}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0.267949 0.119831 0.0599153 0.998203i \(-0.480917\pi\)
0.0599153 + 0.998203i \(0.480917\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −0.267949 −0.0847330
\(11\) 6.19615 1.86821 0.934105 0.356998i \(-0.116200\pi\)
0.934105 + 0.356998i \(0.116200\pi\)
\(12\) 0 0
\(13\) −6.46410 −1.79282 −0.896410 0.443227i \(-0.853834\pi\)
−0.896410 + 0.443227i \(0.853834\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 0.732051 0.167944 0.0839720 0.996468i \(-0.473239\pi\)
0.0839720 + 0.996468i \(0.473239\pi\)
\(20\) 0.267949 0.0599153
\(21\) 0 0
\(22\) −6.19615 −1.32102
\(23\) −4.19615 −0.874958 −0.437479 0.899229i \(-0.644129\pi\)
−0.437479 + 0.899229i \(0.644129\pi\)
\(24\) 0 0
\(25\) −4.92820 −0.985641
\(26\) 6.46410 1.26771
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 1.53590 0.285209 0.142605 0.989780i \(-0.454452\pi\)
0.142605 + 0.989780i \(0.454452\pi\)
\(30\) 0 0
\(31\) 8.19615 1.47207 0.736036 0.676942i \(-0.236695\pi\)
0.736036 + 0.676942i \(0.236695\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −7.00000 −1.20049
\(35\) −0.267949 −0.0452917
\(36\) 0 0
\(37\) 10.6603 1.75253 0.876267 0.481825i \(-0.160026\pi\)
0.876267 + 0.481825i \(0.160026\pi\)
\(38\) −0.732051 −0.118754
\(39\) 0 0
\(40\) −0.267949 −0.0423665
\(41\) 2.53590 0.396041 0.198020 0.980198i \(-0.436549\pi\)
0.198020 + 0.980198i \(0.436549\pi\)
\(42\) 0 0
\(43\) −1.46410 −0.223273 −0.111637 0.993749i \(-0.535609\pi\)
−0.111637 + 0.993749i \(0.535609\pi\)
\(44\) 6.19615 0.934105
\(45\) 0 0
\(46\) 4.19615 0.618689
\(47\) 4.73205 0.690241 0.345120 0.938558i \(-0.387838\pi\)
0.345120 + 0.938558i \(0.387838\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 4.92820 0.696953
\(51\) 0 0
\(52\) −6.46410 −0.896410
\(53\) −9.46410 −1.29999 −0.649997 0.759937i \(-0.725230\pi\)
−0.649997 + 0.759937i \(0.725230\pi\)
\(54\) 0 0
\(55\) 1.66025 0.223869
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −1.53590 −0.201673
\(59\) 4.19615 0.546293 0.273146 0.961973i \(-0.411936\pi\)
0.273146 + 0.961973i \(0.411936\pi\)
\(60\) 0 0
\(61\) 3.92820 0.502955 0.251477 0.967863i \(-0.419084\pi\)
0.251477 + 0.967863i \(0.419084\pi\)
\(62\) −8.19615 −1.04091
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.73205 −0.214834
\(66\) 0 0
\(67\) −6.73205 −0.822451 −0.411225 0.911534i \(-0.634899\pi\)
−0.411225 + 0.911534i \(0.634899\pi\)
\(68\) 7.00000 0.848875
\(69\) 0 0
\(70\) 0.267949 0.0320261
\(71\) 6.53590 0.775668 0.387834 0.921729i \(-0.373223\pi\)
0.387834 + 0.921729i \(0.373223\pi\)
\(72\) 0 0
\(73\) 8.26795 0.967690 0.483845 0.875154i \(-0.339240\pi\)
0.483845 + 0.875154i \(0.339240\pi\)
\(74\) −10.6603 −1.23923
\(75\) 0 0
\(76\) 0.732051 0.0839720
\(77\) −6.19615 −0.706117
\(78\) 0 0
\(79\) −9.12436 −1.02657 −0.513285 0.858218i \(-0.671572\pi\)
−0.513285 + 0.858218i \(0.671572\pi\)
\(80\) 0.267949 0.0299576
\(81\) 0 0
\(82\) −2.53590 −0.280043
\(83\) 16.5885 1.82082 0.910410 0.413707i \(-0.135766\pi\)
0.910410 + 0.413707i \(0.135766\pi\)
\(84\) 0 0
\(85\) 1.87564 0.203442
\(86\) 1.46410 0.157878
\(87\) 0 0
\(88\) −6.19615 −0.660512
\(89\) 9.92820 1.05239 0.526194 0.850365i \(-0.323619\pi\)
0.526194 + 0.850365i \(0.323619\pi\)
\(90\) 0 0
\(91\) 6.46410 0.677622
\(92\) −4.19615 −0.437479
\(93\) 0 0
\(94\) −4.73205 −0.488074
\(95\) 0.196152 0.0201248
\(96\) 0 0
\(97\) 10.9282 1.10959 0.554795 0.831987i \(-0.312797\pi\)
0.554795 + 0.831987i \(0.312797\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) −4.92820 −0.492820
\(101\) 8.92820 0.888389 0.444195 0.895930i \(-0.353490\pi\)
0.444195 + 0.895930i \(0.353490\pi\)
\(102\) 0 0
\(103\) −8.39230 −0.826918 −0.413459 0.910523i \(-0.635680\pi\)
−0.413459 + 0.910523i \(0.635680\pi\)
\(104\) 6.46410 0.633857
\(105\) 0 0
\(106\) 9.46410 0.919235
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) 3.19615 0.306136 0.153068 0.988216i \(-0.451085\pi\)
0.153068 + 0.988216i \(0.451085\pi\)
\(110\) −1.66025 −0.158299
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −5.73205 −0.539226 −0.269613 0.962969i \(-0.586896\pi\)
−0.269613 + 0.962969i \(0.586896\pi\)
\(114\) 0 0
\(115\) −1.12436 −0.104847
\(116\) 1.53590 0.142605
\(117\) 0 0
\(118\) −4.19615 −0.386287
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) 27.3923 2.49021
\(122\) −3.92820 −0.355643
\(123\) 0 0
\(124\) 8.19615 0.736036
\(125\) −2.66025 −0.237940
\(126\) 0 0
\(127\) 12.0000 1.06483 0.532414 0.846484i \(-0.321285\pi\)
0.532414 + 0.846484i \(0.321285\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 1.73205 0.151911
\(131\) 10.5359 0.920526 0.460263 0.887783i \(-0.347755\pi\)
0.460263 + 0.887783i \(0.347755\pi\)
\(132\) 0 0
\(133\) −0.732051 −0.0634769
\(134\) 6.73205 0.581561
\(135\) 0 0
\(136\) −7.00000 −0.600245
\(137\) −8.26795 −0.706379 −0.353189 0.935552i \(-0.614903\pi\)
−0.353189 + 0.935552i \(0.614903\pi\)
\(138\) 0 0
\(139\) −3.26795 −0.277184 −0.138592 0.990350i \(-0.544258\pi\)
−0.138592 + 0.990350i \(0.544258\pi\)
\(140\) −0.267949 −0.0226458
\(141\) 0 0
\(142\) −6.53590 −0.548480
\(143\) −40.0526 −3.34936
\(144\) 0 0
\(145\) 0.411543 0.0341768
\(146\) −8.26795 −0.684260
\(147\) 0 0
\(148\) 10.6603 0.876267
\(149\) 9.00000 0.737309 0.368654 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(150\) 0 0
\(151\) −5.80385 −0.472310 −0.236155 0.971715i \(-0.575887\pi\)
−0.236155 + 0.971715i \(0.575887\pi\)
\(152\) −0.732051 −0.0593772
\(153\) 0 0
\(154\) 6.19615 0.499300
\(155\) 2.19615 0.176399
\(156\) 0 0
\(157\) −1.00000 −0.0798087 −0.0399043 0.999204i \(-0.512705\pi\)
−0.0399043 + 0.999204i \(0.512705\pi\)
\(158\) 9.12436 0.725895
\(159\) 0 0
\(160\) −0.267949 −0.0211832
\(161\) 4.19615 0.330703
\(162\) 0 0
\(163\) −13.4641 −1.05459 −0.527295 0.849682i \(-0.676794\pi\)
−0.527295 + 0.849682i \(0.676794\pi\)
\(164\) 2.53590 0.198020
\(165\) 0 0
\(166\) −16.5885 −1.28751
\(167\) −1.80385 −0.139586 −0.0697930 0.997561i \(-0.522234\pi\)
−0.0697930 + 0.997561i \(0.522234\pi\)
\(168\) 0 0
\(169\) 28.7846 2.21420
\(170\) −1.87564 −0.143855
\(171\) 0 0
\(172\) −1.46410 −0.111637
\(173\) 6.26795 0.476543 0.238272 0.971199i \(-0.423419\pi\)
0.238272 + 0.971199i \(0.423419\pi\)
\(174\) 0 0
\(175\) 4.92820 0.372537
\(176\) 6.19615 0.467053
\(177\) 0 0
\(178\) −9.92820 −0.744150
\(179\) −2.19615 −0.164148 −0.0820741 0.996626i \(-0.526154\pi\)
−0.0820741 + 0.996626i \(0.526154\pi\)
\(180\) 0 0
\(181\) −16.3923 −1.21843 −0.609215 0.793005i \(-0.708515\pi\)
−0.609215 + 0.793005i \(0.708515\pi\)
\(182\) −6.46410 −0.479151
\(183\) 0 0
\(184\) 4.19615 0.309344
\(185\) 2.85641 0.210007
\(186\) 0 0
\(187\) 43.3731 3.17175
\(188\) 4.73205 0.345120
\(189\) 0 0
\(190\) −0.196152 −0.0142304
\(191\) −5.66025 −0.409562 −0.204781 0.978808i \(-0.565648\pi\)
−0.204781 + 0.978808i \(0.565648\pi\)
\(192\) 0 0
\(193\) 18.8564 1.35731 0.678657 0.734455i \(-0.262562\pi\)
0.678657 + 0.734455i \(0.262562\pi\)
\(194\) −10.9282 −0.784599
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 15.7846 1.12461 0.562303 0.826931i \(-0.309915\pi\)
0.562303 + 0.826931i \(0.309915\pi\)
\(198\) 0 0
\(199\) −19.1244 −1.35569 −0.677845 0.735205i \(-0.737086\pi\)
−0.677845 + 0.735205i \(0.737086\pi\)
\(200\) 4.92820 0.348477
\(201\) 0 0
\(202\) −8.92820 −0.628186
\(203\) −1.53590 −0.107799
\(204\) 0 0
\(205\) 0.679492 0.0474578
\(206\) 8.39230 0.584720
\(207\) 0 0
\(208\) −6.46410 −0.448205
\(209\) 4.53590 0.313755
\(210\) 0 0
\(211\) −17.2679 −1.18877 −0.594387 0.804179i \(-0.702605\pi\)
−0.594387 + 0.804179i \(0.702605\pi\)
\(212\) −9.46410 −0.649997
\(213\) 0 0
\(214\) 0 0
\(215\) −0.392305 −0.0267550
\(216\) 0 0
\(217\) −8.19615 −0.556391
\(218\) −3.19615 −0.216471
\(219\) 0 0
\(220\) 1.66025 0.111934
\(221\) −45.2487 −3.04376
\(222\) 0 0
\(223\) −25.4641 −1.70520 −0.852601 0.522562i \(-0.824976\pi\)
−0.852601 + 0.522562i \(0.824976\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 5.73205 0.381290
\(227\) −18.9282 −1.25631 −0.628154 0.778089i \(-0.716189\pi\)
−0.628154 + 0.778089i \(0.716189\pi\)
\(228\) 0 0
\(229\) −2.46410 −0.162832 −0.0814162 0.996680i \(-0.525944\pi\)
−0.0814162 + 0.996680i \(0.525944\pi\)
\(230\) 1.12436 0.0741378
\(231\) 0 0
\(232\) −1.53590 −0.100837
\(233\) −2.80385 −0.183686 −0.0918431 0.995773i \(-0.529276\pi\)
−0.0918431 + 0.995773i \(0.529276\pi\)
\(234\) 0 0
\(235\) 1.26795 0.0827119
\(236\) 4.19615 0.273146
\(237\) 0 0
\(238\) 7.00000 0.453743
\(239\) −10.0526 −0.650246 −0.325123 0.945672i \(-0.605406\pi\)
−0.325123 + 0.945672i \(0.605406\pi\)
\(240\) 0 0
\(241\) −14.2679 −0.919079 −0.459540 0.888157i \(-0.651986\pi\)
−0.459540 + 0.888157i \(0.651986\pi\)
\(242\) −27.3923 −1.76084
\(243\) 0 0
\(244\) 3.92820 0.251477
\(245\) 0.267949 0.0171186
\(246\) 0 0
\(247\) −4.73205 −0.301093
\(248\) −8.19615 −0.520456
\(249\) 0 0
\(250\) 2.66025 0.168249
\(251\) −22.0526 −1.39195 −0.695973 0.718068i \(-0.745027\pi\)
−0.695973 + 0.718068i \(0.745027\pi\)
\(252\) 0 0
\(253\) −26.0000 −1.63461
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.46410 0.403220 0.201610 0.979466i \(-0.435383\pi\)
0.201610 + 0.979466i \(0.435383\pi\)
\(258\) 0 0
\(259\) −10.6603 −0.662396
\(260\) −1.73205 −0.107417
\(261\) 0 0
\(262\) −10.5359 −0.650910
\(263\) −6.33975 −0.390925 −0.195463 0.980711i \(-0.562621\pi\)
−0.195463 + 0.980711i \(0.562621\pi\)
\(264\) 0 0
\(265\) −2.53590 −0.155779
\(266\) 0.732051 0.0448849
\(267\) 0 0
\(268\) −6.73205 −0.411225
\(269\) 5.58846 0.340734 0.170367 0.985381i \(-0.445505\pi\)
0.170367 + 0.985381i \(0.445505\pi\)
\(270\) 0 0
\(271\) −19.5167 −1.18555 −0.592776 0.805367i \(-0.701968\pi\)
−0.592776 + 0.805367i \(0.701968\pi\)
\(272\) 7.00000 0.424437
\(273\) 0 0
\(274\) 8.26795 0.499485
\(275\) −30.5359 −1.84138
\(276\) 0 0
\(277\) −18.7846 −1.12866 −0.564329 0.825550i \(-0.690865\pi\)
−0.564329 + 0.825550i \(0.690865\pi\)
\(278\) 3.26795 0.195999
\(279\) 0 0
\(280\) 0.267949 0.0160130
\(281\) −13.1962 −0.787216 −0.393608 0.919278i \(-0.628773\pi\)
−0.393608 + 0.919278i \(0.628773\pi\)
\(282\) 0 0
\(283\) 15.3205 0.910710 0.455355 0.890310i \(-0.349512\pi\)
0.455355 + 0.890310i \(0.349512\pi\)
\(284\) 6.53590 0.387834
\(285\) 0 0
\(286\) 40.0526 2.36836
\(287\) −2.53590 −0.149689
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) −0.411543 −0.0241666
\(291\) 0 0
\(292\) 8.26795 0.483845
\(293\) 3.33975 0.195110 0.0975550 0.995230i \(-0.468898\pi\)
0.0975550 + 0.995230i \(0.468898\pi\)
\(294\) 0 0
\(295\) 1.12436 0.0654625
\(296\) −10.6603 −0.619615
\(297\) 0 0
\(298\) −9.00000 −0.521356
\(299\) 27.1244 1.56864
\(300\) 0 0
\(301\) 1.46410 0.0843894
\(302\) 5.80385 0.333974
\(303\) 0 0
\(304\) 0.732051 0.0419860
\(305\) 1.05256 0.0602693
\(306\) 0 0
\(307\) −21.8564 −1.24741 −0.623706 0.781659i \(-0.714374\pi\)
−0.623706 + 0.781659i \(0.714374\pi\)
\(308\) −6.19615 −0.353059
\(309\) 0 0
\(310\) −2.19615 −0.124733
\(311\) 10.1962 0.578171 0.289085 0.957303i \(-0.406649\pi\)
0.289085 + 0.957303i \(0.406649\pi\)
\(312\) 0 0
\(313\) 25.5885 1.44635 0.723173 0.690667i \(-0.242683\pi\)
0.723173 + 0.690667i \(0.242683\pi\)
\(314\) 1.00000 0.0564333
\(315\) 0 0
\(316\) −9.12436 −0.513285
\(317\) −31.3923 −1.76317 −0.881584 0.472028i \(-0.843522\pi\)
−0.881584 + 0.472028i \(0.843522\pi\)
\(318\) 0 0
\(319\) 9.51666 0.532831
\(320\) 0.267949 0.0149788
\(321\) 0 0
\(322\) −4.19615 −0.233842
\(323\) 5.12436 0.285127
\(324\) 0 0
\(325\) 31.8564 1.76708
\(326\) 13.4641 0.745708
\(327\) 0 0
\(328\) −2.53590 −0.140022
\(329\) −4.73205 −0.260886
\(330\) 0 0
\(331\) 12.3923 0.681143 0.340571 0.940219i \(-0.389380\pi\)
0.340571 + 0.940219i \(0.389380\pi\)
\(332\) 16.5885 0.910410
\(333\) 0 0
\(334\) 1.80385 0.0987021
\(335\) −1.80385 −0.0985547
\(336\) 0 0
\(337\) −16.3923 −0.892946 −0.446473 0.894797i \(-0.647320\pi\)
−0.446473 + 0.894797i \(0.647320\pi\)
\(338\) −28.7846 −1.56568
\(339\) 0 0
\(340\) 1.87564 0.101721
\(341\) 50.7846 2.75014
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 1.46410 0.0789391
\(345\) 0 0
\(346\) −6.26795 −0.336967
\(347\) 21.4641 1.15225 0.576127 0.817360i \(-0.304563\pi\)
0.576127 + 0.817360i \(0.304563\pi\)
\(348\) 0 0
\(349\) 1.46410 0.0783716 0.0391858 0.999232i \(-0.487524\pi\)
0.0391858 + 0.999232i \(0.487524\pi\)
\(350\) −4.92820 −0.263424
\(351\) 0 0
\(352\) −6.19615 −0.330256
\(353\) −18.0000 −0.958043 −0.479022 0.877803i \(-0.659008\pi\)
−0.479022 + 0.877803i \(0.659008\pi\)
\(354\) 0 0
\(355\) 1.75129 0.0929488
\(356\) 9.92820 0.526194
\(357\) 0 0
\(358\) 2.19615 0.116070
\(359\) −10.9282 −0.576769 −0.288384 0.957515i \(-0.593118\pi\)
−0.288384 + 0.957515i \(0.593118\pi\)
\(360\) 0 0
\(361\) −18.4641 −0.971795
\(362\) 16.3923 0.861560
\(363\) 0 0
\(364\) 6.46410 0.338811
\(365\) 2.21539 0.115959
\(366\) 0 0
\(367\) 11.1244 0.580687 0.290343 0.956923i \(-0.406230\pi\)
0.290343 + 0.956923i \(0.406230\pi\)
\(368\) −4.19615 −0.218740
\(369\) 0 0
\(370\) −2.85641 −0.148498
\(371\) 9.46410 0.491352
\(372\) 0 0
\(373\) −6.14359 −0.318103 −0.159052 0.987270i \(-0.550844\pi\)
−0.159052 + 0.987270i \(0.550844\pi\)
\(374\) −43.3731 −2.24277
\(375\) 0 0
\(376\) −4.73205 −0.244037
\(377\) −9.92820 −0.511328
\(378\) 0 0
\(379\) −27.5167 −1.41344 −0.706718 0.707495i \(-0.749825\pi\)
−0.706718 + 0.707495i \(0.749825\pi\)
\(380\) 0.196152 0.0100624
\(381\) 0 0
\(382\) 5.66025 0.289604
\(383\) 19.7128 1.00728 0.503639 0.863914i \(-0.331994\pi\)
0.503639 + 0.863914i \(0.331994\pi\)
\(384\) 0 0
\(385\) −1.66025 −0.0846144
\(386\) −18.8564 −0.959766
\(387\) 0 0
\(388\) 10.9282 0.554795
\(389\) −13.4641 −0.682657 −0.341329 0.939944i \(-0.610877\pi\)
−0.341329 + 0.939944i \(0.610877\pi\)
\(390\) 0 0
\(391\) −29.3731 −1.48546
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) −15.7846 −0.795217
\(395\) −2.44486 −0.123014
\(396\) 0 0
\(397\) −21.0000 −1.05396 −0.526980 0.849878i \(-0.676676\pi\)
−0.526980 + 0.849878i \(0.676676\pi\)
\(398\) 19.1244 0.958617
\(399\) 0 0
\(400\) −4.92820 −0.246410
\(401\) 10.5167 0.525177 0.262588 0.964908i \(-0.415424\pi\)
0.262588 + 0.964908i \(0.415424\pi\)
\(402\) 0 0
\(403\) −52.9808 −2.63916
\(404\) 8.92820 0.444195
\(405\) 0 0
\(406\) 1.53590 0.0762254
\(407\) 66.0526 3.27410
\(408\) 0 0
\(409\) 17.3397 0.857395 0.428698 0.903448i \(-0.358973\pi\)
0.428698 + 0.903448i \(0.358973\pi\)
\(410\) −0.679492 −0.0335577
\(411\) 0 0
\(412\) −8.39230 −0.413459
\(413\) −4.19615 −0.206479
\(414\) 0 0
\(415\) 4.44486 0.218190
\(416\) 6.46410 0.316929
\(417\) 0 0
\(418\) −4.53590 −0.221858
\(419\) −9.46410 −0.462352 −0.231176 0.972912i \(-0.574257\pi\)
−0.231176 + 0.972912i \(0.574257\pi\)
\(420\) 0 0
\(421\) 0.124356 0.00606072 0.00303036 0.999995i \(-0.499035\pi\)
0.00303036 + 0.999995i \(0.499035\pi\)
\(422\) 17.2679 0.840591
\(423\) 0 0
\(424\) 9.46410 0.459617
\(425\) −34.4974 −1.67337
\(426\) 0 0
\(427\) −3.92820 −0.190099
\(428\) 0 0
\(429\) 0 0
\(430\) 0.392305 0.0189186
\(431\) −14.5359 −0.700170 −0.350085 0.936718i \(-0.613847\pi\)
−0.350085 + 0.936718i \(0.613847\pi\)
\(432\) 0 0
\(433\) 15.7321 0.756034 0.378017 0.925799i \(-0.376606\pi\)
0.378017 + 0.925799i \(0.376606\pi\)
\(434\) 8.19615 0.393428
\(435\) 0 0
\(436\) 3.19615 0.153068
\(437\) −3.07180 −0.146944
\(438\) 0 0
\(439\) 23.3205 1.11303 0.556514 0.830839i \(-0.312139\pi\)
0.556514 + 0.830839i \(0.312139\pi\)
\(440\) −1.66025 −0.0791495
\(441\) 0 0
\(442\) 45.2487 2.15226
\(443\) −15.2679 −0.725402 −0.362701 0.931906i \(-0.618145\pi\)
−0.362701 + 0.931906i \(0.618145\pi\)
\(444\) 0 0
\(445\) 2.66025 0.126108
\(446\) 25.4641 1.20576
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) 15.8564 0.748310 0.374155 0.927366i \(-0.377933\pi\)
0.374155 + 0.927366i \(0.377933\pi\)
\(450\) 0 0
\(451\) 15.7128 0.739887
\(452\) −5.73205 −0.269613
\(453\) 0 0
\(454\) 18.9282 0.888345
\(455\) 1.73205 0.0811998
\(456\) 0 0
\(457\) −6.85641 −0.320729 −0.160365 0.987058i \(-0.551267\pi\)
−0.160365 + 0.987058i \(0.551267\pi\)
\(458\) 2.46410 0.115140
\(459\) 0 0
\(460\) −1.12436 −0.0524234
\(461\) −6.78461 −0.315991 −0.157995 0.987440i \(-0.550503\pi\)
−0.157995 + 0.987440i \(0.550503\pi\)
\(462\) 0 0
\(463\) −1.41154 −0.0656000 −0.0328000 0.999462i \(-0.510442\pi\)
−0.0328000 + 0.999462i \(0.510442\pi\)
\(464\) 1.53590 0.0713023
\(465\) 0 0
\(466\) 2.80385 0.129886
\(467\) −16.5885 −0.767622 −0.383811 0.923412i \(-0.625389\pi\)
−0.383811 + 0.923412i \(0.625389\pi\)
\(468\) 0 0
\(469\) 6.73205 0.310857
\(470\) −1.26795 −0.0584861
\(471\) 0 0
\(472\) −4.19615 −0.193144
\(473\) −9.07180 −0.417122
\(474\) 0 0
\(475\) −3.60770 −0.165532
\(476\) −7.00000 −0.320844
\(477\) 0 0
\(478\) 10.0526 0.459793
\(479\) −21.5167 −0.983121 −0.491561 0.870843i \(-0.663573\pi\)
−0.491561 + 0.870843i \(0.663573\pi\)
\(480\) 0 0
\(481\) −68.9090 −3.14198
\(482\) 14.2679 0.649887
\(483\) 0 0
\(484\) 27.3923 1.24510
\(485\) 2.92820 0.132963
\(486\) 0 0
\(487\) 2.58846 0.117294 0.0586471 0.998279i \(-0.481321\pi\)
0.0586471 + 0.998279i \(0.481321\pi\)
\(488\) −3.92820 −0.177821
\(489\) 0 0
\(490\) −0.267949 −0.0121047
\(491\) 26.5359 1.19755 0.598774 0.800918i \(-0.295655\pi\)
0.598774 + 0.800918i \(0.295655\pi\)
\(492\) 0 0
\(493\) 10.7513 0.484214
\(494\) 4.73205 0.212905
\(495\) 0 0
\(496\) 8.19615 0.368018
\(497\) −6.53590 −0.293175
\(498\) 0 0
\(499\) 19.8038 0.886542 0.443271 0.896388i \(-0.353818\pi\)
0.443271 + 0.896388i \(0.353818\pi\)
\(500\) −2.66025 −0.118970
\(501\) 0 0
\(502\) 22.0526 0.984254
\(503\) 40.0526 1.78586 0.892928 0.450200i \(-0.148647\pi\)
0.892928 + 0.450200i \(0.148647\pi\)
\(504\) 0 0
\(505\) 2.39230 0.106456
\(506\) 26.0000 1.15584
\(507\) 0 0
\(508\) 12.0000 0.532414
\(509\) 31.8564 1.41201 0.706005 0.708207i \(-0.250496\pi\)
0.706005 + 0.708207i \(0.250496\pi\)
\(510\) 0 0
\(511\) −8.26795 −0.365753
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.46410 −0.285119
\(515\) −2.24871 −0.0990901
\(516\) 0 0
\(517\) 29.3205 1.28951
\(518\) 10.6603 0.468385
\(519\) 0 0
\(520\) 1.73205 0.0759555
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 0 0
\(523\) 33.1769 1.45073 0.725363 0.688367i \(-0.241672\pi\)
0.725363 + 0.688367i \(0.241672\pi\)
\(524\) 10.5359 0.460263
\(525\) 0 0
\(526\) 6.33975 0.276426
\(527\) 57.3731 2.49921
\(528\) 0 0
\(529\) −5.39230 −0.234448
\(530\) 2.53590 0.110152
\(531\) 0 0
\(532\) −0.732051 −0.0317384
\(533\) −16.3923 −0.710030
\(534\) 0 0
\(535\) 0 0
\(536\) 6.73205 0.290780
\(537\) 0 0
\(538\) −5.58846 −0.240936
\(539\) 6.19615 0.266887
\(540\) 0 0
\(541\) 3.33975 0.143587 0.0717934 0.997420i \(-0.477128\pi\)
0.0717934 + 0.997420i \(0.477128\pi\)
\(542\) 19.5167 0.838312
\(543\) 0 0
\(544\) −7.00000 −0.300123
\(545\) 0.856406 0.0366844
\(546\) 0 0
\(547\) −22.7321 −0.971952 −0.485976 0.873972i \(-0.661536\pi\)
−0.485976 + 0.873972i \(0.661536\pi\)
\(548\) −8.26795 −0.353189
\(549\) 0 0
\(550\) 30.5359 1.30206
\(551\) 1.12436 0.0478992
\(552\) 0 0
\(553\) 9.12436 0.388007
\(554\) 18.7846 0.798082
\(555\) 0 0
\(556\) −3.26795 −0.138592
\(557\) 23.9282 1.01387 0.506935 0.861984i \(-0.330778\pi\)
0.506935 + 0.861984i \(0.330778\pi\)
\(558\) 0 0
\(559\) 9.46410 0.400289
\(560\) −0.267949 −0.0113229
\(561\) 0 0
\(562\) 13.1962 0.556646
\(563\) 19.7128 0.830796 0.415398 0.909640i \(-0.363642\pi\)
0.415398 + 0.909640i \(0.363642\pi\)
\(564\) 0 0
\(565\) −1.53590 −0.0646157
\(566\) −15.3205 −0.643969
\(567\) 0 0
\(568\) −6.53590 −0.274240
\(569\) 23.1962 0.972433 0.486217 0.873838i \(-0.338377\pi\)
0.486217 + 0.873838i \(0.338377\pi\)
\(570\) 0 0
\(571\) −22.7321 −0.951307 −0.475653 0.879633i \(-0.657788\pi\)
−0.475653 + 0.879633i \(0.657788\pi\)
\(572\) −40.0526 −1.67468
\(573\) 0 0
\(574\) 2.53590 0.105846
\(575\) 20.6795 0.862394
\(576\) 0 0
\(577\) 24.6603 1.02662 0.513310 0.858203i \(-0.328419\pi\)
0.513310 + 0.858203i \(0.328419\pi\)
\(578\) −32.0000 −1.33102
\(579\) 0 0
\(580\) 0.411543 0.0170884
\(581\) −16.5885 −0.688205
\(582\) 0 0
\(583\) −58.6410 −2.42866
\(584\) −8.26795 −0.342130
\(585\) 0 0
\(586\) −3.33975 −0.137964
\(587\) 14.7321 0.608057 0.304028 0.952663i \(-0.401668\pi\)
0.304028 + 0.952663i \(0.401668\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) −1.12436 −0.0462890
\(591\) 0 0
\(592\) 10.6603 0.438134
\(593\) −22.1769 −0.910697 −0.455348 0.890313i \(-0.650485\pi\)
−0.455348 + 0.890313i \(0.650485\pi\)
\(594\) 0 0
\(595\) −1.87564 −0.0768939
\(596\) 9.00000 0.368654
\(597\) 0 0
\(598\) −27.1244 −1.10920
\(599\) −15.1244 −0.617964 −0.308982 0.951068i \(-0.599988\pi\)
−0.308982 + 0.951068i \(0.599988\pi\)
\(600\) 0 0
\(601\) 19.1962 0.783027 0.391514 0.920172i \(-0.371952\pi\)
0.391514 + 0.920172i \(0.371952\pi\)
\(602\) −1.46410 −0.0596723
\(603\) 0 0
\(604\) −5.80385 −0.236155
\(605\) 7.33975 0.298403
\(606\) 0 0
\(607\) −24.5885 −0.998015 −0.499007 0.866598i \(-0.666302\pi\)
−0.499007 + 0.866598i \(0.666302\pi\)
\(608\) −0.732051 −0.0296886
\(609\) 0 0
\(610\) −1.05256 −0.0426169
\(611\) −30.5885 −1.23748
\(612\) 0 0
\(613\) 26.7846 1.08182 0.540910 0.841080i \(-0.318080\pi\)
0.540910 + 0.841080i \(0.318080\pi\)
\(614\) 21.8564 0.882053
\(615\) 0 0
\(616\) 6.19615 0.249650
\(617\) 11.9808 0.482327 0.241164 0.970484i \(-0.422471\pi\)
0.241164 + 0.970484i \(0.422471\pi\)
\(618\) 0 0
\(619\) −23.7128 −0.953098 −0.476549 0.879148i \(-0.658113\pi\)
−0.476549 + 0.879148i \(0.658113\pi\)
\(620\) 2.19615 0.0881996
\(621\) 0 0
\(622\) −10.1962 −0.408828
\(623\) −9.92820 −0.397765
\(624\) 0 0
\(625\) 23.9282 0.957128
\(626\) −25.5885 −1.02272
\(627\) 0 0
\(628\) −1.00000 −0.0399043
\(629\) 74.6218 2.97537
\(630\) 0 0
\(631\) −3.66025 −0.145712 −0.0728562 0.997342i \(-0.523211\pi\)
−0.0728562 + 0.997342i \(0.523211\pi\)
\(632\) 9.12436 0.362947
\(633\) 0 0
\(634\) 31.3923 1.24675
\(635\) 3.21539 0.127599
\(636\) 0 0
\(637\) −6.46410 −0.256117
\(638\) −9.51666 −0.376768
\(639\) 0 0
\(640\) −0.267949 −0.0105916
\(641\) 39.4449 1.55798 0.778989 0.627037i \(-0.215733\pi\)
0.778989 + 0.627037i \(0.215733\pi\)
\(642\) 0 0
\(643\) −9.41154 −0.371155 −0.185578 0.982630i \(-0.559416\pi\)
−0.185578 + 0.982630i \(0.559416\pi\)
\(644\) 4.19615 0.165352
\(645\) 0 0
\(646\) −5.12436 −0.201615
\(647\) −4.39230 −0.172679 −0.0863397 0.996266i \(-0.527517\pi\)
−0.0863397 + 0.996266i \(0.527517\pi\)
\(648\) 0 0
\(649\) 26.0000 1.02059
\(650\) −31.8564 −1.24951
\(651\) 0 0
\(652\) −13.4641 −0.527295
\(653\) −30.2487 −1.18372 −0.591862 0.806039i \(-0.701607\pi\)
−0.591862 + 0.806039i \(0.701607\pi\)
\(654\) 0 0
\(655\) 2.82309 0.110307
\(656\) 2.53590 0.0990102
\(657\) 0 0
\(658\) 4.73205 0.184475
\(659\) −36.3923 −1.41764 −0.708821 0.705388i \(-0.750773\pi\)
−0.708821 + 0.705388i \(0.750773\pi\)
\(660\) 0 0
\(661\) −12.8564 −0.500056 −0.250028 0.968239i \(-0.580440\pi\)
−0.250028 + 0.968239i \(0.580440\pi\)
\(662\) −12.3923 −0.481641
\(663\) 0 0
\(664\) −16.5885 −0.643757
\(665\) −0.196152 −0.00760646
\(666\) 0 0
\(667\) −6.44486 −0.249546
\(668\) −1.80385 −0.0697930
\(669\) 0 0
\(670\) 1.80385 0.0696887
\(671\) 24.3397 0.939625
\(672\) 0 0
\(673\) −18.3205 −0.706204 −0.353102 0.935585i \(-0.614873\pi\)
−0.353102 + 0.935585i \(0.614873\pi\)
\(674\) 16.3923 0.631408
\(675\) 0 0
\(676\) 28.7846 1.10710
\(677\) 36.0000 1.38359 0.691796 0.722093i \(-0.256820\pi\)
0.691796 + 0.722093i \(0.256820\pi\)
\(678\) 0 0
\(679\) −10.9282 −0.419386
\(680\) −1.87564 −0.0719277
\(681\) 0 0
\(682\) −50.7846 −1.94464
\(683\) −1.85641 −0.0710334 −0.0355167 0.999369i \(-0.511308\pi\)
−0.0355167 + 0.999369i \(0.511308\pi\)
\(684\) 0 0
\(685\) −2.21539 −0.0846457
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −1.46410 −0.0558184
\(689\) 61.1769 2.33065
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 6.26795 0.238272
\(693\) 0 0
\(694\) −21.4641 −0.814766
\(695\) −0.875644 −0.0332151
\(696\) 0 0
\(697\) 17.7513 0.672378
\(698\) −1.46410 −0.0554171
\(699\) 0 0
\(700\) 4.92820 0.186269
\(701\) 27.3923 1.03459 0.517297 0.855806i \(-0.326938\pi\)
0.517297 + 0.855806i \(0.326938\pi\)
\(702\) 0 0
\(703\) 7.80385 0.294328
\(704\) 6.19615 0.233526
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) −8.92820 −0.335780
\(708\) 0 0
\(709\) −3.87564 −0.145553 −0.0727764 0.997348i \(-0.523186\pi\)
−0.0727764 + 0.997348i \(0.523186\pi\)
\(710\) −1.75129 −0.0657247
\(711\) 0 0
\(712\) −9.92820 −0.372075
\(713\) −34.3923 −1.28800
\(714\) 0 0
\(715\) −10.7321 −0.401356
\(716\) −2.19615 −0.0820741
\(717\) 0 0
\(718\) 10.9282 0.407837
\(719\) −9.46410 −0.352951 −0.176476 0.984305i \(-0.556470\pi\)
−0.176476 + 0.984305i \(0.556470\pi\)
\(720\) 0 0
\(721\) 8.39230 0.312546
\(722\) 18.4641 0.687163
\(723\) 0 0
\(724\) −16.3923 −0.609215
\(725\) −7.56922 −0.281114
\(726\) 0 0
\(727\) 51.3205 1.90337 0.951686 0.307072i \(-0.0993494\pi\)
0.951686 + 0.307072i \(0.0993494\pi\)
\(728\) −6.46410 −0.239576
\(729\) 0 0
\(730\) −2.21539 −0.0819953
\(731\) −10.2487 −0.379062
\(732\) 0 0
\(733\) 47.3205 1.74782 0.873911 0.486085i \(-0.161576\pi\)
0.873911 + 0.486085i \(0.161576\pi\)
\(734\) −11.1244 −0.410607
\(735\) 0 0
\(736\) 4.19615 0.154672
\(737\) −41.7128 −1.53651
\(738\) 0 0
\(739\) −13.2679 −0.488069 −0.244035 0.969767i \(-0.578471\pi\)
−0.244035 + 0.969767i \(0.578471\pi\)
\(740\) 2.85641 0.105004
\(741\) 0 0
\(742\) −9.46410 −0.347438
\(743\) −40.3923 −1.48185 −0.740925 0.671588i \(-0.765613\pi\)
−0.740925 + 0.671588i \(0.765613\pi\)
\(744\) 0 0
\(745\) 2.41154 0.0883521
\(746\) 6.14359 0.224933
\(747\) 0 0
\(748\) 43.3731 1.58588
\(749\) 0 0
\(750\) 0 0
\(751\) −22.1436 −0.808031 −0.404016 0.914752i \(-0.632386\pi\)
−0.404016 + 0.914752i \(0.632386\pi\)
\(752\) 4.73205 0.172560
\(753\) 0 0
\(754\) 9.92820 0.361564
\(755\) −1.55514 −0.0565972
\(756\) 0 0
\(757\) 20.7846 0.755429 0.377715 0.925922i \(-0.376710\pi\)
0.377715 + 0.925922i \(0.376710\pi\)
\(758\) 27.5167 0.999450
\(759\) 0 0
\(760\) −0.196152 −0.00711520
\(761\) 37.0000 1.34125 0.670624 0.741797i \(-0.266026\pi\)
0.670624 + 0.741797i \(0.266026\pi\)
\(762\) 0 0
\(763\) −3.19615 −0.115708
\(764\) −5.66025 −0.204781
\(765\) 0 0
\(766\) −19.7128 −0.712253
\(767\) −27.1244 −0.979404
\(768\) 0 0
\(769\) −4.41154 −0.159084 −0.0795421 0.996832i \(-0.525346\pi\)
−0.0795421 + 0.996832i \(0.525346\pi\)
\(770\) 1.66025 0.0598314
\(771\) 0 0
\(772\) 18.8564 0.678657
\(773\) −4.12436 −0.148343 −0.0741714 0.997246i \(-0.523631\pi\)
−0.0741714 + 0.997246i \(0.523631\pi\)
\(774\) 0 0
\(775\) −40.3923 −1.45093
\(776\) −10.9282 −0.392300
\(777\) 0 0
\(778\) 13.4641 0.482711
\(779\) 1.85641 0.0665127
\(780\) 0 0
\(781\) 40.4974 1.44911
\(782\) 29.3731 1.05038
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) −0.267949 −0.00956352
\(786\) 0 0
\(787\) −28.3923 −1.01208 −0.506038 0.862511i \(-0.668891\pi\)
−0.506038 + 0.862511i \(0.668891\pi\)
\(788\) 15.7846 0.562303
\(789\) 0 0
\(790\) 2.44486 0.0869843
\(791\) 5.73205 0.203808
\(792\) 0 0
\(793\) −25.3923 −0.901707
\(794\) 21.0000 0.745262
\(795\) 0 0
\(796\) −19.1244 −0.677845
\(797\) −29.4449 −1.04299 −0.521495 0.853254i \(-0.674626\pi\)
−0.521495 + 0.853254i \(0.674626\pi\)
\(798\) 0 0
\(799\) 33.1244 1.17186
\(800\) 4.92820 0.174238
\(801\) 0 0
\(802\) −10.5167 −0.371356
\(803\) 51.2295 1.80785
\(804\) 0 0
\(805\) 1.12436 0.0396283
\(806\) 52.9808 1.86617
\(807\) 0 0
\(808\) −8.92820 −0.314093
\(809\) 32.1244 1.12943 0.564716 0.825285i \(-0.308986\pi\)
0.564716 + 0.825285i \(0.308986\pi\)
\(810\) 0 0
\(811\) 18.1962 0.638953 0.319477 0.947594i \(-0.396493\pi\)
0.319477 + 0.947594i \(0.396493\pi\)
\(812\) −1.53590 −0.0538995
\(813\) 0 0
\(814\) −66.0526 −2.31514
\(815\) −3.60770 −0.126372
\(816\) 0 0
\(817\) −1.07180 −0.0374974
\(818\) −17.3397 −0.606270
\(819\) 0 0
\(820\) 0.679492 0.0237289
\(821\) 25.9282 0.904901 0.452450 0.891790i \(-0.350550\pi\)
0.452450 + 0.891790i \(0.350550\pi\)
\(822\) 0 0
\(823\) 0.784610 0.0273498 0.0136749 0.999906i \(-0.495647\pi\)
0.0136749 + 0.999906i \(0.495647\pi\)
\(824\) 8.39230 0.292360
\(825\) 0 0
\(826\) 4.19615 0.146003
\(827\) −23.3205 −0.810934 −0.405467 0.914110i \(-0.632891\pi\)
−0.405467 + 0.914110i \(0.632891\pi\)
\(828\) 0 0
\(829\) −14.0000 −0.486240 −0.243120 0.969996i \(-0.578171\pi\)
−0.243120 + 0.969996i \(0.578171\pi\)
\(830\) −4.44486 −0.154283
\(831\) 0 0
\(832\) −6.46410 −0.224102
\(833\) 7.00000 0.242536
\(834\) 0 0
\(835\) −0.483340 −0.0167267
\(836\) 4.53590 0.156877
\(837\) 0 0
\(838\) 9.46410 0.326932
\(839\) 1.46410 0.0505464 0.0252732 0.999681i \(-0.491954\pi\)
0.0252732 + 0.999681i \(0.491954\pi\)
\(840\) 0 0
\(841\) −26.6410 −0.918656
\(842\) −0.124356 −0.00428558
\(843\) 0 0
\(844\) −17.2679 −0.594387
\(845\) 7.71281 0.265329
\(846\) 0 0
\(847\) −27.3923 −0.941211
\(848\) −9.46410 −0.324999
\(849\) 0 0
\(850\) 34.4974 1.18325
\(851\) −44.7321 −1.53339
\(852\) 0 0
\(853\) −49.7128 −1.70213 −0.851067 0.525057i \(-0.824044\pi\)
−0.851067 + 0.525057i \(0.824044\pi\)
\(854\) 3.92820 0.134420
\(855\) 0 0
\(856\) 0 0
\(857\) −16.8564 −0.575804 −0.287902 0.957660i \(-0.592958\pi\)
−0.287902 + 0.957660i \(0.592958\pi\)
\(858\) 0 0
\(859\) 24.3923 0.832255 0.416127 0.909306i \(-0.363387\pi\)
0.416127 + 0.909306i \(0.363387\pi\)
\(860\) −0.392305 −0.0133775
\(861\) 0 0
\(862\) 14.5359 0.495095
\(863\) −7.12436 −0.242516 −0.121258 0.992621i \(-0.538693\pi\)
−0.121258 + 0.992621i \(0.538693\pi\)
\(864\) 0 0
\(865\) 1.67949 0.0571044
\(866\) −15.7321 −0.534597
\(867\) 0 0
\(868\) −8.19615 −0.278196
\(869\) −56.5359 −1.91785
\(870\) 0 0
\(871\) 43.5167 1.47451
\(872\) −3.19615 −0.108235
\(873\) 0 0
\(874\) 3.07180 0.103905
\(875\) 2.66025 0.0899330
\(876\) 0 0
\(877\) −36.5167 −1.23308 −0.616540 0.787324i \(-0.711466\pi\)
−0.616540 + 0.787324i \(0.711466\pi\)
\(878\) −23.3205 −0.787029
\(879\) 0 0
\(880\) 1.66025 0.0559672
\(881\) 30.2487 1.01910 0.509552 0.860440i \(-0.329811\pi\)
0.509552 + 0.860440i \(0.329811\pi\)
\(882\) 0 0
\(883\) −9.66025 −0.325093 −0.162547 0.986701i \(-0.551971\pi\)
−0.162547 + 0.986701i \(0.551971\pi\)
\(884\) −45.2487 −1.52188
\(885\) 0 0
\(886\) 15.2679 0.512937
\(887\) −56.4449 −1.89523 −0.947617 0.319410i \(-0.896515\pi\)
−0.947617 + 0.319410i \(0.896515\pi\)
\(888\) 0 0
\(889\) −12.0000 −0.402467
\(890\) −2.66025 −0.0891719
\(891\) 0 0
\(892\) −25.4641 −0.852601
\(893\) 3.46410 0.115922
\(894\) 0 0
\(895\) −0.588457 −0.0196700
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) −15.8564 −0.529135
\(899\) 12.5885 0.419849
\(900\) 0 0
\(901\) −66.2487 −2.20706
\(902\) −15.7128 −0.523179
\(903\) 0 0
\(904\) 5.73205 0.190645
\(905\) −4.39230 −0.146005
\(906\) 0 0
\(907\) −36.0000 −1.19536 −0.597680 0.801735i \(-0.703911\pi\)
−0.597680 + 0.801735i \(0.703911\pi\)
\(908\) −18.9282 −0.628154
\(909\) 0 0
\(910\) −1.73205 −0.0574169
\(911\) 42.2487 1.39976 0.699881 0.714259i \(-0.253236\pi\)
0.699881 + 0.714259i \(0.253236\pi\)
\(912\) 0 0
\(913\) 102.785 3.40167
\(914\) 6.85641 0.226790
\(915\) 0 0
\(916\) −2.46410 −0.0814162
\(917\) −10.5359 −0.347926
\(918\) 0 0
\(919\) 26.9808 0.890013 0.445007 0.895527i \(-0.353201\pi\)
0.445007 + 0.895527i \(0.353201\pi\)
\(920\) 1.12436 0.0370689
\(921\) 0 0
\(922\) 6.78461 0.223439
\(923\) −42.2487 −1.39063
\(924\) 0 0
\(925\) −52.5359 −1.72737
\(926\) 1.41154 0.0463862
\(927\) 0 0
\(928\) −1.53590 −0.0504183
\(929\) −51.4974 −1.68958 −0.844788 0.535101i \(-0.820273\pi\)
−0.844788 + 0.535101i \(0.820273\pi\)
\(930\) 0 0
\(931\) 0.732051 0.0239920
\(932\) −2.80385 −0.0918431
\(933\) 0 0
\(934\) 16.5885 0.542791
\(935\) 11.6218 0.380073
\(936\) 0 0
\(937\) −25.8372 −0.844064 −0.422032 0.906581i \(-0.638683\pi\)
−0.422032 + 0.906581i \(0.638683\pi\)
\(938\) −6.73205 −0.219809
\(939\) 0 0
\(940\) 1.26795 0.0413559
\(941\) −34.1244 −1.11242 −0.556211 0.831041i \(-0.687745\pi\)
−0.556211 + 0.831041i \(0.687745\pi\)
\(942\) 0 0
\(943\) −10.6410 −0.346519
\(944\) 4.19615 0.136573
\(945\) 0 0
\(946\) 9.07180 0.294950
\(947\) −46.2487 −1.50288 −0.751441 0.659801i \(-0.770641\pi\)
−0.751441 + 0.659801i \(0.770641\pi\)
\(948\) 0 0
\(949\) −53.4449 −1.73489
\(950\) 3.60770 0.117049
\(951\) 0 0
\(952\) 7.00000 0.226871
\(953\) −41.5885 −1.34718 −0.673591 0.739104i \(-0.735249\pi\)
−0.673591 + 0.739104i \(0.735249\pi\)
\(954\) 0 0
\(955\) −1.51666 −0.0490780
\(956\) −10.0526 −0.325123
\(957\) 0 0
\(958\) 21.5167 0.695172
\(959\) 8.26795 0.266986
\(960\) 0 0
\(961\) 36.1769 1.16700
\(962\) 68.9090 2.22171
\(963\) 0 0
\(964\) −14.2679 −0.459540
\(965\) 5.05256 0.162648
\(966\) 0 0
\(967\) −3.66025 −0.117706 −0.0588529 0.998267i \(-0.518744\pi\)
−0.0588529 + 0.998267i \(0.518744\pi\)
\(968\) −27.3923 −0.880422
\(969\) 0 0
\(970\) −2.92820 −0.0940189
\(971\) 8.87564 0.284833 0.142416 0.989807i \(-0.454513\pi\)
0.142416 + 0.989807i \(0.454513\pi\)
\(972\) 0 0
\(973\) 3.26795 0.104766
\(974\) −2.58846 −0.0829395
\(975\) 0 0
\(976\) 3.92820 0.125739
\(977\) 57.7128 1.84640 0.923198 0.384324i \(-0.125565\pi\)
0.923198 + 0.384324i \(0.125565\pi\)
\(978\) 0 0
\(979\) 61.5167 1.96608
\(980\) 0.267949 0.00855932
\(981\) 0 0
\(982\) −26.5359 −0.846795
\(983\) 58.6410 1.87036 0.935179 0.354176i \(-0.115238\pi\)
0.935179 + 0.354176i \(0.115238\pi\)
\(984\) 0 0
\(985\) 4.22947 0.134762
\(986\) −10.7513 −0.342391
\(987\) 0 0
\(988\) −4.73205 −0.150547
\(989\) 6.14359 0.195355
\(990\) 0 0
\(991\) −27.6603 −0.878657 −0.439328 0.898327i \(-0.644784\pi\)
−0.439328 + 0.898327i \(0.644784\pi\)
\(992\) −8.19615 −0.260228
\(993\) 0 0
\(994\) 6.53590 0.207306
\(995\) −5.12436 −0.162453
\(996\) 0 0
\(997\) 41.2487 1.30636 0.653180 0.757203i \(-0.273435\pi\)
0.653180 + 0.757203i \(0.273435\pi\)
\(998\) −19.8038 −0.626880
\(999\) 0 0
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 1134.2.a.l.1.1 2
3.2 odd 2 1134.2.a.m.1.2 yes 2
4.3 odd 2 9072.2.a.bp.1.1 2
7.6 odd 2 7938.2.a.bg.1.2 2
9.2 odd 6 1134.2.f.r.757.1 4
9.4 even 3 1134.2.f.s.379.2 4
9.5 odd 6 1134.2.f.r.379.1 4
9.7 even 3 1134.2.f.s.757.2 4
12.11 even 2 9072.2.a.y.1.2 2
21.20 even 2 7938.2.a.bt.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1134.2.a.l.1.1 2 1.1 even 1 trivial
1134.2.a.m.1.2 yes 2 3.2 odd 2
1134.2.f.r.379.1 4 9.5 odd 6
1134.2.f.r.757.1 4 9.2 odd 6
1134.2.f.s.379.2 4 9.4 even 3
1134.2.f.s.757.2 4 9.7 even 3
7938.2.a.bg.1.2 2 7.6 odd 2
7938.2.a.bt.1.1 2 21.20 even 2
9072.2.a.y.1.2 2 12.11 even 2
9072.2.a.bp.1.1 2 4.3 odd 2