Properties

Label 1450.2.a.l.1.1
Level $1450$
Weight $2$
Character 1450.1
Self dual yes
Analytic conductor $11.578$
Analytic rank $1$
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] = [1450,2,Mod(1,1450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1450, 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("1450.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1450.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: \(11.5783082931\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 290)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 1450.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} +3.85410 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.61803 q^{3} +1.00000 q^{4} -2.61803 q^{6} -0.381966 q^{7} +1.00000 q^{8} +3.85410 q^{9} +2.00000 q^{11} -2.61803 q^{12} -2.61803 q^{13} -0.381966 q^{14} +1.00000 q^{16} -5.61803 q^{17} +3.85410 q^{18} -2.00000 q^{19} +1.00000 q^{21} +2.00000 q^{22} +1.85410 q^{23} -2.61803 q^{24} -2.61803 q^{26} -2.23607 q^{27} -0.381966 q^{28} -1.00000 q^{29} +2.85410 q^{31} +1.00000 q^{32} -5.23607 q^{33} -5.61803 q^{34} +3.85410 q^{36} +8.94427 q^{37} -2.00000 q^{38} +6.85410 q^{39} -5.70820 q^{41} +1.00000 q^{42} -5.61803 q^{43} +2.00000 q^{44} +1.85410 q^{46} -10.4721 q^{47} -2.61803 q^{48} -6.85410 q^{49} +14.7082 q^{51} -2.61803 q^{52} -11.6180 q^{53} -2.23607 q^{54} -0.381966 q^{56} +5.23607 q^{57} -1.00000 q^{58} -3.85410 q^{59} -4.14590 q^{61} +2.85410 q^{62} -1.47214 q^{63} +1.00000 q^{64} -5.23607 q^{66} -8.94427 q^{67} -5.61803 q^{68} -4.85410 q^{69} +7.70820 q^{71} +3.85410 q^{72} -14.5623 q^{73} +8.94427 q^{74} -2.00000 q^{76} -0.763932 q^{77} +6.85410 q^{78} -13.5623 q^{79} -5.70820 q^{81} -5.70820 q^{82} +2.94427 q^{83} +1.00000 q^{84} -5.61803 q^{86} +2.61803 q^{87} +2.00000 q^{88} +2.00000 q^{89} +1.00000 q^{91} +1.85410 q^{92} -7.47214 q^{93} -10.4721 q^{94} -2.61803 q^{96} -13.8541 q^{97} -6.85410 q^{98} +7.70820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 3 q^{3} + 2 q^{4} - 3 q^{6} - 3 q^{7} + 2 q^{8} + q^{9} + 4 q^{11} - 3 q^{12} - 3 q^{13} - 3 q^{14} + 2 q^{16} - 9 q^{17} + q^{18} - 4 q^{19} + 2 q^{21} + 4 q^{22} - 3 q^{23} - 3 q^{24} - 3 q^{26} - 3 q^{28} - 2 q^{29} - q^{31} + 2 q^{32} - 6 q^{33} - 9 q^{34} + q^{36} - 4 q^{38} + 7 q^{39} + 2 q^{41} + 2 q^{42} - 9 q^{43} + 4 q^{44} - 3 q^{46} - 12 q^{47} - 3 q^{48} - 7 q^{49} + 16 q^{51} - 3 q^{52} - 21 q^{53} - 3 q^{56} + 6 q^{57} - 2 q^{58} - q^{59} - 15 q^{61} - q^{62} + 6 q^{63} + 2 q^{64} - 6 q^{66} - 9 q^{68} - 3 q^{69} + 2 q^{71} + q^{72} - 9 q^{73} - 4 q^{76} - 6 q^{77} + 7 q^{78} - 7 q^{79} + 2 q^{81} + 2 q^{82} - 12 q^{83} + 2 q^{84} - 9 q^{86} + 3 q^{87} + 4 q^{88} + 4 q^{89} + 2 q^{91} - 3 q^{92} - 6 q^{93} - 12 q^{94} - 3 q^{96} - 21 q^{97} - 7 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.61803 −1.51152 −0.755761 0.654847i \(-0.772733\pi\)
−0.755761 + 0.654847i \(0.772733\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −2.61803 −1.06881
\(7\) −0.381966 −0.144370 −0.0721848 0.997391i \(-0.522997\pi\)
−0.0721848 + 0.997391i \(0.522997\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.85410 1.28470
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −2.61803 −0.755761
\(13\) −2.61803 −0.726112 −0.363056 0.931767i \(-0.618267\pi\)
−0.363056 + 0.931767i \(0.618267\pi\)
\(14\) −0.381966 −0.102085
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −5.61803 −1.36257 −0.681287 0.732017i \(-0.738579\pi\)
−0.681287 + 0.732017i \(0.738579\pi\)
\(18\) 3.85410 0.908421
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 2.00000 0.426401
\(23\) 1.85410 0.386607 0.193303 0.981139i \(-0.438080\pi\)
0.193303 + 0.981139i \(0.438080\pi\)
\(24\) −2.61803 −0.534404
\(25\) 0 0
\(26\) −2.61803 −0.513439
\(27\) −2.23607 −0.430331
\(28\) −0.381966 −0.0721848
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 2.85410 0.512612 0.256306 0.966596i \(-0.417495\pi\)
0.256306 + 0.966596i \(0.417495\pi\)
\(32\) 1.00000 0.176777
\(33\) −5.23607 −0.911482
\(34\) −5.61803 −0.963485
\(35\) 0 0
\(36\) 3.85410 0.642350
\(37\) 8.94427 1.47043 0.735215 0.677834i \(-0.237081\pi\)
0.735215 + 0.677834i \(0.237081\pi\)
\(38\) −2.00000 −0.324443
\(39\) 6.85410 1.09753
\(40\) 0 0
\(41\) −5.70820 −0.891472 −0.445736 0.895165i \(-0.647058\pi\)
−0.445736 + 0.895165i \(0.647058\pi\)
\(42\) 1.00000 0.154303
\(43\) −5.61803 −0.856742 −0.428371 0.903603i \(-0.640912\pi\)
−0.428371 + 0.903603i \(0.640912\pi\)
\(44\) 2.00000 0.301511
\(45\) 0 0
\(46\) 1.85410 0.273372
\(47\) −10.4721 −1.52752 −0.763759 0.645501i \(-0.776648\pi\)
−0.763759 + 0.645501i \(0.776648\pi\)
\(48\) −2.61803 −0.377881
\(49\) −6.85410 −0.979157
\(50\) 0 0
\(51\) 14.7082 2.05956
\(52\) −2.61803 −0.363056
\(53\) −11.6180 −1.59586 −0.797930 0.602750i \(-0.794071\pi\)
−0.797930 + 0.602750i \(0.794071\pi\)
\(54\) −2.23607 −0.304290
\(55\) 0 0
\(56\) −0.381966 −0.0510424
\(57\) 5.23607 0.693534
\(58\) −1.00000 −0.131306
\(59\) −3.85410 −0.501761 −0.250881 0.968018i \(-0.580720\pi\)
−0.250881 + 0.968018i \(0.580720\pi\)
\(60\) 0 0
\(61\) −4.14590 −0.530828 −0.265414 0.964135i \(-0.585509\pi\)
−0.265414 + 0.964135i \(0.585509\pi\)
\(62\) 2.85410 0.362471
\(63\) −1.47214 −0.185472
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −5.23607 −0.644515
\(67\) −8.94427 −1.09272 −0.546358 0.837552i \(-0.683986\pi\)
−0.546358 + 0.837552i \(0.683986\pi\)
\(68\) −5.61803 −0.681287
\(69\) −4.85410 −0.584365
\(70\) 0 0
\(71\) 7.70820 0.914796 0.457398 0.889262i \(-0.348782\pi\)
0.457398 + 0.889262i \(0.348782\pi\)
\(72\) 3.85410 0.454210
\(73\) −14.5623 −1.70439 −0.852194 0.523225i \(-0.824729\pi\)
−0.852194 + 0.523225i \(0.824729\pi\)
\(74\) 8.94427 1.03975
\(75\) 0 0
\(76\) −2.00000 −0.229416
\(77\) −0.763932 −0.0870581
\(78\) 6.85410 0.776074
\(79\) −13.5623 −1.52588 −0.762939 0.646470i \(-0.776245\pi\)
−0.762939 + 0.646470i \(0.776245\pi\)
\(80\) 0 0
\(81\) −5.70820 −0.634245
\(82\) −5.70820 −0.630366
\(83\) 2.94427 0.323176 0.161588 0.986858i \(-0.448338\pi\)
0.161588 + 0.986858i \(0.448338\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) −5.61803 −0.605808
\(87\) 2.61803 0.280683
\(88\) 2.00000 0.213201
\(89\) 2.00000 0.212000 0.106000 0.994366i \(-0.466196\pi\)
0.106000 + 0.994366i \(0.466196\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 1.85410 0.193303
\(93\) −7.47214 −0.774824
\(94\) −10.4721 −1.08012
\(95\) 0 0
\(96\) −2.61803 −0.267202
\(97\) −13.8541 −1.40667 −0.703335 0.710858i \(-0.748307\pi\)
−0.703335 + 0.710858i \(0.748307\pi\)
\(98\) −6.85410 −0.692369
\(99\) 7.70820 0.774704
\(100\) 0 0
\(101\) 4.14590 0.412532 0.206266 0.978496i \(-0.433869\pi\)
0.206266 + 0.978496i \(0.433869\pi\)
\(102\) 14.7082 1.45633
\(103\) 19.4164 1.91316 0.956578 0.291477i \(-0.0941468\pi\)
0.956578 + 0.291477i \(0.0941468\pi\)
\(104\) −2.61803 −0.256719
\(105\) 0 0
\(106\) −11.6180 −1.12844
\(107\) −8.18034 −0.790823 −0.395412 0.918504i \(-0.629398\pi\)
−0.395412 + 0.918504i \(0.629398\pi\)
\(108\) −2.23607 −0.215166
\(109\) −7.41641 −0.710363 −0.355182 0.934797i \(-0.615581\pi\)
−0.355182 + 0.934797i \(0.615581\pi\)
\(110\) 0 0
\(111\) −23.4164 −2.22259
\(112\) −0.381966 −0.0360924
\(113\) 7.09017 0.666987 0.333494 0.942752i \(-0.391772\pi\)
0.333494 + 0.942752i \(0.391772\pi\)
\(114\) 5.23607 0.490403
\(115\) 0 0
\(116\) −1.00000 −0.0928477
\(117\) −10.0902 −0.932837
\(118\) −3.85410 −0.354799
\(119\) 2.14590 0.196714
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −4.14590 −0.375352
\(123\) 14.9443 1.34748
\(124\) 2.85410 0.256306
\(125\) 0 0
\(126\) −1.47214 −0.131148
\(127\) 21.7082 1.92629 0.963146 0.268980i \(-0.0866865\pi\)
0.963146 + 0.268980i \(0.0866865\pi\)
\(128\) 1.00000 0.0883883
\(129\) 14.7082 1.29499
\(130\) 0 0
\(131\) −5.41641 −0.473234 −0.236617 0.971603i \(-0.576039\pi\)
−0.236617 + 0.971603i \(0.576039\pi\)
\(132\) −5.23607 −0.455741
\(133\) 0.763932 0.0662413
\(134\) −8.94427 −0.772667
\(135\) 0 0
\(136\) −5.61803 −0.481742
\(137\) −1.85410 −0.158407 −0.0792033 0.996858i \(-0.525238\pi\)
−0.0792033 + 0.996858i \(0.525238\pi\)
\(138\) −4.85410 −0.413209
\(139\) 14.5623 1.23516 0.617579 0.786509i \(-0.288113\pi\)
0.617579 + 0.786509i \(0.288113\pi\)
\(140\) 0 0
\(141\) 27.4164 2.30888
\(142\) 7.70820 0.646858
\(143\) −5.23607 −0.437862
\(144\) 3.85410 0.321175
\(145\) 0 0
\(146\) −14.5623 −1.20519
\(147\) 17.9443 1.48002
\(148\) 8.94427 0.735215
\(149\) 5.41641 0.443729 0.221865 0.975077i \(-0.428786\pi\)
0.221865 + 0.975077i \(0.428786\pi\)
\(150\) 0 0
\(151\) 17.7082 1.44107 0.720537 0.693417i \(-0.243896\pi\)
0.720537 + 0.693417i \(0.243896\pi\)
\(152\) −2.00000 −0.162221
\(153\) −21.6525 −1.75050
\(154\) −0.763932 −0.0615594
\(155\) 0 0
\(156\) 6.85410 0.548767
\(157\) 3.70820 0.295947 0.147973 0.988991i \(-0.452725\pi\)
0.147973 + 0.988991i \(0.452725\pi\)
\(158\) −13.5623 −1.07896
\(159\) 30.4164 2.41218
\(160\) 0 0
\(161\) −0.708204 −0.0558143
\(162\) −5.70820 −0.448479
\(163\) 19.4164 1.52081 0.760405 0.649449i \(-0.225000\pi\)
0.760405 + 0.649449i \(0.225000\pi\)
\(164\) −5.70820 −0.445736
\(165\) 0 0
\(166\) 2.94427 0.228520
\(167\) −0.381966 −0.0295574 −0.0147787 0.999891i \(-0.504704\pi\)
−0.0147787 + 0.999891i \(0.504704\pi\)
\(168\) 1.00000 0.0771517
\(169\) −6.14590 −0.472761
\(170\) 0 0
\(171\) −7.70820 −0.589461
\(172\) −5.61803 −0.428371
\(173\) 20.5066 1.55909 0.779543 0.626349i \(-0.215451\pi\)
0.779543 + 0.626349i \(0.215451\pi\)
\(174\) 2.61803 0.198473
\(175\) 0 0
\(176\) 2.00000 0.150756
\(177\) 10.0902 0.758424
\(178\) 2.00000 0.149906
\(179\) 15.8541 1.18499 0.592496 0.805574i \(-0.298143\pi\)
0.592496 + 0.805574i \(0.298143\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 1.00000 0.0741249
\(183\) 10.8541 0.802358
\(184\) 1.85410 0.136686
\(185\) 0 0
\(186\) −7.47214 −0.547884
\(187\) −11.2361 −0.821663
\(188\) −10.4721 −0.763759
\(189\) 0.854102 0.0621268
\(190\) 0 0
\(191\) −10.2705 −0.743148 −0.371574 0.928403i \(-0.621182\pi\)
−0.371574 + 0.928403i \(0.621182\pi\)
\(192\) −2.61803 −0.188940
\(193\) −17.5623 −1.26416 −0.632081 0.774902i \(-0.717799\pi\)
−0.632081 + 0.774902i \(0.717799\pi\)
\(194\) −13.8541 −0.994667
\(195\) 0 0
\(196\) −6.85410 −0.489579
\(197\) −11.6180 −0.827751 −0.413875 0.910334i \(-0.635825\pi\)
−0.413875 + 0.910334i \(0.635825\pi\)
\(198\) 7.70820 0.547798
\(199\) −21.1246 −1.49748 −0.748742 0.662862i \(-0.769342\pi\)
−0.748742 + 0.662862i \(0.769342\pi\)
\(200\) 0 0
\(201\) 23.4164 1.65167
\(202\) 4.14590 0.291704
\(203\) 0.381966 0.0268088
\(204\) 14.7082 1.02978
\(205\) 0 0
\(206\) 19.4164 1.35281
\(207\) 7.14590 0.496674
\(208\) −2.61803 −0.181528
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) 15.4164 1.06131 0.530655 0.847588i \(-0.321946\pi\)
0.530655 + 0.847588i \(0.321946\pi\)
\(212\) −11.6180 −0.797930
\(213\) −20.1803 −1.38273
\(214\) −8.18034 −0.559197
\(215\) 0 0
\(216\) −2.23607 −0.152145
\(217\) −1.09017 −0.0740056
\(218\) −7.41641 −0.502303
\(219\) 38.1246 2.57622
\(220\) 0 0
\(221\) 14.7082 0.989381
\(222\) −23.4164 −1.57161
\(223\) 6.43769 0.431100 0.215550 0.976493i \(-0.430846\pi\)
0.215550 + 0.976493i \(0.430846\pi\)
\(224\) −0.381966 −0.0255212
\(225\) 0 0
\(226\) 7.09017 0.471631
\(227\) −7.52786 −0.499642 −0.249821 0.968292i \(-0.580372\pi\)
−0.249821 + 0.968292i \(0.580372\pi\)
\(228\) 5.23607 0.346767
\(229\) −14.8541 −0.981587 −0.490793 0.871276i \(-0.663293\pi\)
−0.490793 + 0.871276i \(0.663293\pi\)
\(230\) 0 0
\(231\) 2.00000 0.131590
\(232\) −1.00000 −0.0656532
\(233\) 6.76393 0.443120 0.221560 0.975147i \(-0.428885\pi\)
0.221560 + 0.975147i \(0.428885\pi\)
\(234\) −10.0902 −0.659615
\(235\) 0 0
\(236\) −3.85410 −0.250881
\(237\) 35.5066 2.30640
\(238\) 2.14590 0.139098
\(239\) −7.70820 −0.498602 −0.249301 0.968426i \(-0.580201\pi\)
−0.249301 + 0.968426i \(0.580201\pi\)
\(240\) 0 0
\(241\) −2.14590 −0.138229 −0.0691147 0.997609i \(-0.522017\pi\)
−0.0691147 + 0.997609i \(0.522017\pi\)
\(242\) −7.00000 −0.449977
\(243\) 21.6525 1.38901
\(244\) −4.14590 −0.265414
\(245\) 0 0
\(246\) 14.9443 0.952812
\(247\) 5.23607 0.333163
\(248\) 2.85410 0.181236
\(249\) −7.70820 −0.488488
\(250\) 0 0
\(251\) 11.1246 0.702179 0.351090 0.936342i \(-0.385811\pi\)
0.351090 + 0.936342i \(0.385811\pi\)
\(252\) −1.47214 −0.0927358
\(253\) 3.70820 0.233133
\(254\) 21.7082 1.36209
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −15.7082 −0.979851 −0.489925 0.871764i \(-0.662976\pi\)
−0.489925 + 0.871764i \(0.662976\pi\)
\(258\) 14.7082 0.915693
\(259\) −3.41641 −0.212285
\(260\) 0 0
\(261\) −3.85410 −0.238563
\(262\) −5.41641 −0.334627
\(263\) −27.5967 −1.70169 −0.850844 0.525418i \(-0.823909\pi\)
−0.850844 + 0.525418i \(0.823909\pi\)
\(264\) −5.23607 −0.322258
\(265\) 0 0
\(266\) 0.763932 0.0468397
\(267\) −5.23607 −0.320442
\(268\) −8.94427 −0.546358
\(269\) −30.2705 −1.84563 −0.922813 0.385249i \(-0.874116\pi\)
−0.922813 + 0.385249i \(0.874116\pi\)
\(270\) 0 0
\(271\) −3.41641 −0.207532 −0.103766 0.994602i \(-0.533089\pi\)
−0.103766 + 0.994602i \(0.533089\pi\)
\(272\) −5.61803 −0.340643
\(273\) −2.61803 −0.158451
\(274\) −1.85410 −0.112010
\(275\) 0 0
\(276\) −4.85410 −0.292183
\(277\) 30.0000 1.80253 0.901263 0.433273i \(-0.142641\pi\)
0.901263 + 0.433273i \(0.142641\pi\)
\(278\) 14.5623 0.873389
\(279\) 11.0000 0.658553
\(280\) 0 0
\(281\) 2.56231 0.152854 0.0764272 0.997075i \(-0.475649\pi\)
0.0764272 + 0.997075i \(0.475649\pi\)
\(282\) 27.4164 1.63262
\(283\) 11.2361 0.667915 0.333957 0.942588i \(-0.391616\pi\)
0.333957 + 0.942588i \(0.391616\pi\)
\(284\) 7.70820 0.457398
\(285\) 0 0
\(286\) −5.23607 −0.309615
\(287\) 2.18034 0.128701
\(288\) 3.85410 0.227105
\(289\) 14.5623 0.856606
\(290\) 0 0
\(291\) 36.2705 2.12621
\(292\) −14.5623 −0.852194
\(293\) −7.41641 −0.433271 −0.216636 0.976253i \(-0.569508\pi\)
−0.216636 + 0.976253i \(0.569508\pi\)
\(294\) 17.9443 1.04653
\(295\) 0 0
\(296\) 8.94427 0.519875
\(297\) −4.47214 −0.259500
\(298\) 5.41641 0.313764
\(299\) −4.85410 −0.280720
\(300\) 0 0
\(301\) 2.14590 0.123688
\(302\) 17.7082 1.01899
\(303\) −10.8541 −0.623552
\(304\) −2.00000 −0.114708
\(305\) 0 0
\(306\) −21.6525 −1.23779
\(307\) 24.0000 1.36975 0.684876 0.728659i \(-0.259856\pi\)
0.684876 + 0.728659i \(0.259856\pi\)
\(308\) −0.763932 −0.0435291
\(309\) −50.8328 −2.89178
\(310\) 0 0
\(311\) −14.4377 −0.818687 −0.409343 0.912380i \(-0.634242\pi\)
−0.409343 + 0.912380i \(0.634242\pi\)
\(312\) 6.85410 0.388037
\(313\) 17.2361 0.974240 0.487120 0.873335i \(-0.338047\pi\)
0.487120 + 0.873335i \(0.338047\pi\)
\(314\) 3.70820 0.209266
\(315\) 0 0
\(316\) −13.5623 −0.762939
\(317\) −2.18034 −0.122460 −0.0612300 0.998124i \(-0.519502\pi\)
−0.0612300 + 0.998124i \(0.519502\pi\)
\(318\) 30.4164 1.70567
\(319\) −2.00000 −0.111979
\(320\) 0 0
\(321\) 21.4164 1.19535
\(322\) −0.708204 −0.0394667
\(323\) 11.2361 0.625192
\(324\) −5.70820 −0.317122
\(325\) 0 0
\(326\) 19.4164 1.07538
\(327\) 19.4164 1.07373
\(328\) −5.70820 −0.315183
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −13.1246 −0.721394 −0.360697 0.932683i \(-0.617461\pi\)
−0.360697 + 0.932683i \(0.617461\pi\)
\(332\) 2.94427 0.161588
\(333\) 34.4721 1.88906
\(334\) −0.381966 −0.0209003
\(335\) 0 0
\(336\) 1.00000 0.0545545
\(337\) −6.38197 −0.347648 −0.173824 0.984777i \(-0.555612\pi\)
−0.173824 + 0.984777i \(0.555612\pi\)
\(338\) −6.14590 −0.334293
\(339\) −18.5623 −1.00817
\(340\) 0 0
\(341\) 5.70820 0.309117
\(342\) −7.70820 −0.416812
\(343\) 5.29180 0.285730
\(344\) −5.61803 −0.302904
\(345\) 0 0
\(346\) 20.5066 1.10244
\(347\) 6.00000 0.322097 0.161048 0.986947i \(-0.448512\pi\)
0.161048 + 0.986947i \(0.448512\pi\)
\(348\) 2.61803 0.140341
\(349\) 28.8328 1.54339 0.771693 0.635996i \(-0.219410\pi\)
0.771693 + 0.635996i \(0.219410\pi\)
\(350\) 0 0
\(351\) 5.85410 0.312469
\(352\) 2.00000 0.106600
\(353\) 20.9443 1.11475 0.557376 0.830260i \(-0.311808\pi\)
0.557376 + 0.830260i \(0.311808\pi\)
\(354\) 10.0902 0.536286
\(355\) 0 0
\(356\) 2.00000 0.106000
\(357\) −5.61803 −0.297338
\(358\) 15.8541 0.837915
\(359\) −33.2705 −1.75595 −0.877975 0.478706i \(-0.841106\pi\)
−0.877975 + 0.478706i \(0.841106\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −10.0000 −0.525588
\(363\) 18.3262 0.961878
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) 10.8541 0.567353
\(367\) 5.12461 0.267503 0.133751 0.991015i \(-0.457298\pi\)
0.133751 + 0.991015i \(0.457298\pi\)
\(368\) 1.85410 0.0966517
\(369\) −22.0000 −1.14527
\(370\) 0 0
\(371\) 4.43769 0.230394
\(372\) −7.47214 −0.387412
\(373\) 18.2705 0.946011 0.473006 0.881059i \(-0.343169\pi\)
0.473006 + 0.881059i \(0.343169\pi\)
\(374\) −11.2361 −0.581003
\(375\) 0 0
\(376\) −10.4721 −0.540059
\(377\) 2.61803 0.134836
\(378\) 0.854102 0.0439303
\(379\) 26.0000 1.33553 0.667765 0.744372i \(-0.267251\pi\)
0.667765 + 0.744372i \(0.267251\pi\)
\(380\) 0 0
\(381\) −56.8328 −2.91163
\(382\) −10.2705 −0.525485
\(383\) 1.14590 0.0585527 0.0292763 0.999571i \(-0.490680\pi\)
0.0292763 + 0.999571i \(0.490680\pi\)
\(384\) −2.61803 −0.133601
\(385\) 0 0
\(386\) −17.5623 −0.893898
\(387\) −21.6525 −1.10066
\(388\) −13.8541 −0.703335
\(389\) 32.8328 1.66469 0.832345 0.554258i \(-0.186998\pi\)
0.832345 + 0.554258i \(0.186998\pi\)
\(390\) 0 0
\(391\) −10.4164 −0.526780
\(392\) −6.85410 −0.346184
\(393\) 14.1803 0.715304
\(394\) −11.6180 −0.585308
\(395\) 0 0
\(396\) 7.70820 0.387352
\(397\) 31.0344 1.55757 0.778787 0.627288i \(-0.215835\pi\)
0.778787 + 0.627288i \(0.215835\pi\)
\(398\) −21.1246 −1.05888
\(399\) −2.00000 −0.100125
\(400\) 0 0
\(401\) −24.9787 −1.24738 −0.623689 0.781673i \(-0.714367\pi\)
−0.623689 + 0.781673i \(0.714367\pi\)
\(402\) 23.4164 1.16790
\(403\) −7.47214 −0.372214
\(404\) 4.14590 0.206266
\(405\) 0 0
\(406\) 0.381966 0.0189567
\(407\) 17.8885 0.886702
\(408\) 14.7082 0.728165
\(409\) 33.1246 1.63791 0.818953 0.573860i \(-0.194555\pi\)
0.818953 + 0.573860i \(0.194555\pi\)
\(410\) 0 0
\(411\) 4.85410 0.239435
\(412\) 19.4164 0.956578
\(413\) 1.47214 0.0724391
\(414\) 7.14590 0.351202
\(415\) 0 0
\(416\) −2.61803 −0.128360
\(417\) −38.1246 −1.86697
\(418\) −4.00000 −0.195646
\(419\) −15.1459 −0.739926 −0.369963 0.929047i \(-0.620630\pi\)
−0.369963 + 0.929047i \(0.620630\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 15.4164 0.750459
\(423\) −40.3607 −1.96240
\(424\) −11.6180 −0.564222
\(425\) 0 0
\(426\) −20.1803 −0.977741
\(427\) 1.58359 0.0766354
\(428\) −8.18034 −0.395412
\(429\) 13.7082 0.661838
\(430\) 0 0
\(431\) −6.58359 −0.317120 −0.158560 0.987349i \(-0.550685\pi\)
−0.158560 + 0.987349i \(0.550685\pi\)
\(432\) −2.23607 −0.107583
\(433\) 7.52786 0.361766 0.180883 0.983505i \(-0.442104\pi\)
0.180883 + 0.983505i \(0.442104\pi\)
\(434\) −1.09017 −0.0523298
\(435\) 0 0
\(436\) −7.41641 −0.355182
\(437\) −3.70820 −0.177387
\(438\) 38.1246 1.82166
\(439\) 3.12461 0.149130 0.0745648 0.997216i \(-0.476243\pi\)
0.0745648 + 0.997216i \(0.476243\pi\)
\(440\) 0 0
\(441\) −26.4164 −1.25792
\(442\) 14.7082 0.699598
\(443\) 13.0902 0.621933 0.310966 0.950421i \(-0.399347\pi\)
0.310966 + 0.950421i \(0.399347\pi\)
\(444\) −23.4164 −1.11129
\(445\) 0 0
\(446\) 6.43769 0.304834
\(447\) −14.1803 −0.670707
\(448\) −0.381966 −0.0180462
\(449\) −31.4164 −1.48263 −0.741316 0.671156i \(-0.765798\pi\)
−0.741316 + 0.671156i \(0.765798\pi\)
\(450\) 0 0
\(451\) −11.4164 −0.537578
\(452\) 7.09017 0.333494
\(453\) −46.3607 −2.17821
\(454\) −7.52786 −0.353300
\(455\) 0 0
\(456\) 5.23607 0.245201
\(457\) 27.7082 1.29614 0.648068 0.761583i \(-0.275577\pi\)
0.648068 + 0.761583i \(0.275577\pi\)
\(458\) −14.8541 −0.694087
\(459\) 12.5623 0.586358
\(460\) 0 0
\(461\) −30.8541 −1.43702 −0.718509 0.695517i \(-0.755175\pi\)
−0.718509 + 0.695517i \(0.755175\pi\)
\(462\) 2.00000 0.0930484
\(463\) −17.8885 −0.831351 −0.415676 0.909513i \(-0.636455\pi\)
−0.415676 + 0.909513i \(0.636455\pi\)
\(464\) −1.00000 −0.0464238
\(465\) 0 0
\(466\) 6.76393 0.313333
\(467\) −10.2016 −0.472075 −0.236037 0.971744i \(-0.575849\pi\)
−0.236037 + 0.971744i \(0.575849\pi\)
\(468\) −10.0902 −0.466418
\(469\) 3.41641 0.157755
\(470\) 0 0
\(471\) −9.70820 −0.447330
\(472\) −3.85410 −0.177399
\(473\) −11.2361 −0.516635
\(474\) 35.5066 1.63087
\(475\) 0 0
\(476\) 2.14590 0.0983571
\(477\) −44.7771 −2.05020
\(478\) −7.70820 −0.352565
\(479\) 27.9787 1.27838 0.639190 0.769049i \(-0.279270\pi\)
0.639190 + 0.769049i \(0.279270\pi\)
\(480\) 0 0
\(481\) −23.4164 −1.06770
\(482\) −2.14590 −0.0977430
\(483\) 1.85410 0.0843646
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) 21.6525 0.982176
\(487\) −18.4377 −0.835492 −0.417746 0.908564i \(-0.637180\pi\)
−0.417746 + 0.908564i \(0.637180\pi\)
\(488\) −4.14590 −0.187676
\(489\) −50.8328 −2.29874
\(490\) 0 0
\(491\) −19.7082 −0.889419 −0.444709 0.895675i \(-0.646693\pi\)
−0.444709 + 0.895675i \(0.646693\pi\)
\(492\) 14.9443 0.673740
\(493\) 5.61803 0.253024
\(494\) 5.23607 0.235582
\(495\) 0 0
\(496\) 2.85410 0.128153
\(497\) −2.94427 −0.132069
\(498\) −7.70820 −0.345413
\(499\) 8.43769 0.377723 0.188862 0.982004i \(-0.439520\pi\)
0.188862 + 0.982004i \(0.439520\pi\)
\(500\) 0 0
\(501\) 1.00000 0.0446767
\(502\) 11.1246 0.496516
\(503\) −15.0557 −0.671302 −0.335651 0.941986i \(-0.608956\pi\)
−0.335651 + 0.941986i \(0.608956\pi\)
\(504\) −1.47214 −0.0655741
\(505\) 0 0
\(506\) 3.70820 0.164850
\(507\) 16.0902 0.714590
\(508\) 21.7082 0.963146
\(509\) 19.1246 0.847684 0.423842 0.905736i \(-0.360681\pi\)
0.423842 + 0.905736i \(0.360681\pi\)
\(510\) 0 0
\(511\) 5.56231 0.246062
\(512\) 1.00000 0.0441942
\(513\) 4.47214 0.197450
\(514\) −15.7082 −0.692859
\(515\) 0 0
\(516\) 14.7082 0.647493
\(517\) −20.9443 −0.921128
\(518\) −3.41641 −0.150108
\(519\) −53.6869 −2.35659
\(520\) 0 0
\(521\) 37.3951 1.63831 0.819155 0.573572i \(-0.194443\pi\)
0.819155 + 0.573572i \(0.194443\pi\)
\(522\) −3.85410 −0.168689
\(523\) −29.1246 −1.27353 −0.636765 0.771058i \(-0.719728\pi\)
−0.636765 + 0.771058i \(0.719728\pi\)
\(524\) −5.41641 −0.236617
\(525\) 0 0
\(526\) −27.5967 −1.20328
\(527\) −16.0344 −0.698471
\(528\) −5.23607 −0.227871
\(529\) −19.5623 −0.850535
\(530\) 0 0
\(531\) −14.8541 −0.644613
\(532\) 0.763932 0.0331207
\(533\) 14.9443 0.647308
\(534\) −5.23607 −0.226587
\(535\) 0 0
\(536\) −8.94427 −0.386334
\(537\) −41.5066 −1.79114
\(538\) −30.2705 −1.30505
\(539\) −13.7082 −0.590454
\(540\) 0 0
\(541\) −7.43769 −0.319771 −0.159886 0.987136i \(-0.551113\pi\)
−0.159886 + 0.987136i \(0.551113\pi\)
\(542\) −3.41641 −0.146747
\(543\) 26.1803 1.12351
\(544\) −5.61803 −0.240871
\(545\) 0 0
\(546\) −2.61803 −0.112042
\(547\) −38.8328 −1.66037 −0.830186 0.557487i \(-0.811766\pi\)
−0.830186 + 0.557487i \(0.811766\pi\)
\(548\) −1.85410 −0.0792033
\(549\) −15.9787 −0.681955
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) −4.85410 −0.206604
\(553\) 5.18034 0.220290
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) 14.5623 0.617579
\(557\) −16.7984 −0.711770 −0.355885 0.934530i \(-0.615821\pi\)
−0.355885 + 0.934530i \(0.615821\pi\)
\(558\) 11.0000 0.465667
\(559\) 14.7082 0.622091
\(560\) 0 0
\(561\) 29.4164 1.24196
\(562\) 2.56231 0.108084
\(563\) −17.6738 −0.744860 −0.372430 0.928060i \(-0.621475\pi\)
−0.372430 + 0.928060i \(0.621475\pi\)
\(564\) 27.4164 1.15444
\(565\) 0 0
\(566\) 11.2361 0.472287
\(567\) 2.18034 0.0915657
\(568\) 7.70820 0.323429
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) 0 0
\(571\) −0.145898 −0.00610564 −0.00305282 0.999995i \(-0.500972\pi\)
−0.00305282 + 0.999995i \(0.500972\pi\)
\(572\) −5.23607 −0.218931
\(573\) 26.8885 1.12329
\(574\) 2.18034 0.0910056
\(575\) 0 0
\(576\) 3.85410 0.160588
\(577\) −1.03444 −0.0430644 −0.0215322 0.999768i \(-0.506854\pi\)
−0.0215322 + 0.999768i \(0.506854\pi\)
\(578\) 14.5623 0.605712
\(579\) 45.9787 1.91081
\(580\) 0 0
\(581\) −1.12461 −0.0466568
\(582\) 36.2705 1.50346
\(583\) −23.2361 −0.962340
\(584\) −14.5623 −0.602593
\(585\) 0 0
\(586\) −7.41641 −0.306369
\(587\) 18.6525 0.769870 0.384935 0.922944i \(-0.374224\pi\)
0.384935 + 0.922944i \(0.374224\pi\)
\(588\) 17.9443 0.740009
\(589\) −5.70820 −0.235202
\(590\) 0 0
\(591\) 30.4164 1.25116
\(592\) 8.94427 0.367607
\(593\) 19.3050 0.792759 0.396380 0.918087i \(-0.370266\pi\)
0.396380 + 0.918087i \(0.370266\pi\)
\(594\) −4.47214 −0.183494
\(595\) 0 0
\(596\) 5.41641 0.221865
\(597\) 55.3050 2.26348
\(598\) −4.85410 −0.198499
\(599\) 3.43769 0.140460 0.0702302 0.997531i \(-0.477627\pi\)
0.0702302 + 0.997531i \(0.477627\pi\)
\(600\) 0 0
\(601\) −7.70820 −0.314424 −0.157212 0.987565i \(-0.550251\pi\)
−0.157212 + 0.987565i \(0.550251\pi\)
\(602\) 2.14590 0.0874603
\(603\) −34.4721 −1.40381
\(604\) 17.7082 0.720537
\(605\) 0 0
\(606\) −10.8541 −0.440918
\(607\) −5.23607 −0.212525 −0.106263 0.994338i \(-0.533888\pi\)
−0.106263 + 0.994338i \(0.533888\pi\)
\(608\) −2.00000 −0.0811107
\(609\) −1.00000 −0.0405220
\(610\) 0 0
\(611\) 27.4164 1.10915
\(612\) −21.6525 −0.875249
\(613\) 28.7426 1.16090 0.580452 0.814294i \(-0.302876\pi\)
0.580452 + 0.814294i \(0.302876\pi\)
\(614\) 24.0000 0.968561
\(615\) 0 0
\(616\) −0.763932 −0.0307797
\(617\) −30.3820 −1.22313 −0.611566 0.791193i \(-0.709460\pi\)
−0.611566 + 0.791193i \(0.709460\pi\)
\(618\) −50.8328 −2.04480
\(619\) 19.4164 0.780411 0.390206 0.920728i \(-0.372404\pi\)
0.390206 + 0.920728i \(0.372404\pi\)
\(620\) 0 0
\(621\) −4.14590 −0.166369
\(622\) −14.4377 −0.578899
\(623\) −0.763932 −0.0306063
\(624\) 6.85410 0.274384
\(625\) 0 0
\(626\) 17.2361 0.688892
\(627\) 10.4721 0.418217
\(628\) 3.70820 0.147973
\(629\) −50.2492 −2.00357
\(630\) 0 0
\(631\) 18.8328 0.749723 0.374861 0.927081i \(-0.377690\pi\)
0.374861 + 0.927081i \(0.377690\pi\)
\(632\) −13.5623 −0.539480
\(633\) −40.3607 −1.60419
\(634\) −2.18034 −0.0865924
\(635\) 0 0
\(636\) 30.4164 1.20609
\(637\) 17.9443 0.710978
\(638\) −2.00000 −0.0791808
\(639\) 29.7082 1.17524
\(640\) 0 0
\(641\) 13.7082 0.541442 0.270721 0.962658i \(-0.412738\pi\)
0.270721 + 0.962658i \(0.412738\pi\)
\(642\) 21.4164 0.845238
\(643\) 43.4164 1.71218 0.856088 0.516830i \(-0.172888\pi\)
0.856088 + 0.516830i \(0.172888\pi\)
\(644\) −0.708204 −0.0279071
\(645\) 0 0
\(646\) 11.2361 0.442077
\(647\) −22.4721 −0.883471 −0.441735 0.897145i \(-0.645637\pi\)
−0.441735 + 0.897145i \(0.645637\pi\)
\(648\) −5.70820 −0.224239
\(649\) −7.70820 −0.302573
\(650\) 0 0
\(651\) 2.85410 0.111861
\(652\) 19.4164 0.760405
\(653\) 25.3050 0.990259 0.495130 0.868819i \(-0.335121\pi\)
0.495130 + 0.868819i \(0.335121\pi\)
\(654\) 19.4164 0.759242
\(655\) 0 0
\(656\) −5.70820 −0.222868
\(657\) −56.1246 −2.18963
\(658\) 4.00000 0.155936
\(659\) −26.5410 −1.03389 −0.516946 0.856018i \(-0.672931\pi\)
−0.516946 + 0.856018i \(0.672931\pi\)
\(660\) 0 0
\(661\) −24.8328 −0.965885 −0.482942 0.875652i \(-0.660432\pi\)
−0.482942 + 0.875652i \(0.660432\pi\)
\(662\) −13.1246 −0.510103
\(663\) −38.5066 −1.49547
\(664\) 2.94427 0.114260
\(665\) 0 0
\(666\) 34.4721 1.33577
\(667\) −1.85410 −0.0717911
\(668\) −0.381966 −0.0147787
\(669\) −16.8541 −0.651617
\(670\) 0 0
\(671\) −8.29180 −0.320101
\(672\) 1.00000 0.0385758
\(673\) −9.05573 −0.349073 −0.174536 0.984651i \(-0.555843\pi\)
−0.174536 + 0.984651i \(0.555843\pi\)
\(674\) −6.38197 −0.245824
\(675\) 0 0
\(676\) −6.14590 −0.236381
\(677\) −15.0557 −0.578639 −0.289319 0.957233i \(-0.593429\pi\)
−0.289319 + 0.957233i \(0.593429\pi\)
\(678\) −18.5623 −0.712881
\(679\) 5.29180 0.203080
\(680\) 0 0
\(681\) 19.7082 0.755220
\(682\) 5.70820 0.218578
\(683\) −47.7771 −1.82814 −0.914070 0.405557i \(-0.867078\pi\)
−0.914070 + 0.405557i \(0.867078\pi\)
\(684\) −7.70820 −0.294731
\(685\) 0 0
\(686\) 5.29180 0.202042
\(687\) 38.8885 1.48369
\(688\) −5.61803 −0.214186
\(689\) 30.4164 1.15877
\(690\) 0 0
\(691\) 6.56231 0.249642 0.124821 0.992179i \(-0.460164\pi\)
0.124821 + 0.992179i \(0.460164\pi\)
\(692\) 20.5066 0.779543
\(693\) −2.94427 −0.111844
\(694\) 6.00000 0.227757
\(695\) 0 0
\(696\) 2.61803 0.0992363
\(697\) 32.0689 1.21470
\(698\) 28.8328 1.09134
\(699\) −17.7082 −0.669786
\(700\) 0 0
\(701\) 31.1246 1.17556 0.587780 0.809021i \(-0.300002\pi\)
0.587780 + 0.809021i \(0.300002\pi\)
\(702\) 5.85410 0.220949
\(703\) −17.8885 −0.674679
\(704\) 2.00000 0.0753778
\(705\) 0 0
\(706\) 20.9443 0.788248
\(707\) −1.58359 −0.0595571
\(708\) 10.0902 0.379212
\(709\) 25.7082 0.965492 0.482746 0.875760i \(-0.339639\pi\)
0.482746 + 0.875760i \(0.339639\pi\)
\(710\) 0 0
\(711\) −52.2705 −1.96030
\(712\) 2.00000 0.0749532
\(713\) 5.29180 0.198179
\(714\) −5.61803 −0.210250
\(715\) 0 0
\(716\) 15.8541 0.592496
\(717\) 20.1803 0.753649
\(718\) −33.2705 −1.24164
\(719\) 21.7082 0.809579 0.404790 0.914410i \(-0.367345\pi\)
0.404790 + 0.914410i \(0.367345\pi\)
\(720\) 0 0
\(721\) −7.41641 −0.276201
\(722\) −15.0000 −0.558242
\(723\) 5.61803 0.208937
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) 18.3262 0.680150
\(727\) 15.0557 0.558386 0.279193 0.960235i \(-0.409933\pi\)
0.279193 + 0.960235i \(0.409933\pi\)
\(728\) 1.00000 0.0370625
\(729\) −39.5623 −1.46527
\(730\) 0 0
\(731\) 31.5623 1.16737
\(732\) 10.8541 0.401179
\(733\) −12.0000 −0.443230 −0.221615 0.975134i \(-0.571133\pi\)
−0.221615 + 0.975134i \(0.571133\pi\)
\(734\) 5.12461 0.189153
\(735\) 0 0
\(736\) 1.85410 0.0683431
\(737\) −17.8885 −0.658933
\(738\) −22.0000 −0.809831
\(739\) 41.7082 1.53426 0.767131 0.641491i \(-0.221684\pi\)
0.767131 + 0.641491i \(0.221684\pi\)
\(740\) 0 0
\(741\) −13.7082 −0.503583
\(742\) 4.43769 0.162913
\(743\) −1.41641 −0.0519630 −0.0259815 0.999662i \(-0.508271\pi\)
−0.0259815 + 0.999662i \(0.508271\pi\)
\(744\) −7.47214 −0.273942
\(745\) 0 0
\(746\) 18.2705 0.668931
\(747\) 11.3475 0.415184
\(748\) −11.2361 −0.410831
\(749\) 3.12461 0.114171
\(750\) 0 0
\(751\) −4.00000 −0.145962 −0.0729810 0.997333i \(-0.523251\pi\)
−0.0729810 + 0.997333i \(0.523251\pi\)
\(752\) −10.4721 −0.381880
\(753\) −29.1246 −1.06136
\(754\) 2.61803 0.0953432
\(755\) 0 0
\(756\) 0.854102 0.0310634
\(757\) 26.0689 0.947490 0.473745 0.880662i \(-0.342902\pi\)
0.473745 + 0.880662i \(0.342902\pi\)
\(758\) 26.0000 0.944363
\(759\) −9.70820 −0.352385
\(760\) 0 0
\(761\) −3.14590 −0.114039 −0.0570194 0.998373i \(-0.518160\pi\)
−0.0570194 + 0.998373i \(0.518160\pi\)
\(762\) −56.8328 −2.05884
\(763\) 2.83282 0.102555
\(764\) −10.2705 −0.371574
\(765\) 0 0
\(766\) 1.14590 0.0414030
\(767\) 10.0902 0.364335
\(768\) −2.61803 −0.0944702
\(769\) −45.4164 −1.63776 −0.818879 0.573967i \(-0.805404\pi\)
−0.818879 + 0.573967i \(0.805404\pi\)
\(770\) 0 0
\(771\) 41.1246 1.48107
\(772\) −17.5623 −0.632081
\(773\) −11.2361 −0.404133 −0.202067 0.979372i \(-0.564766\pi\)
−0.202067 + 0.979372i \(0.564766\pi\)
\(774\) −21.6525 −0.778282
\(775\) 0 0
\(776\) −13.8541 −0.497333
\(777\) 8.94427 0.320874
\(778\) 32.8328 1.17711
\(779\) 11.4164 0.409035
\(780\) 0 0
\(781\) 15.4164 0.551642
\(782\) −10.4164 −0.372490
\(783\) 2.23607 0.0799106
\(784\) −6.85410 −0.244789
\(785\) 0 0
\(786\) 14.1803 0.505796
\(787\) −29.7771 −1.06144 −0.530719 0.847548i \(-0.678078\pi\)
−0.530719 + 0.847548i \(0.678078\pi\)
\(788\) −11.6180 −0.413875
\(789\) 72.2492 2.57214
\(790\) 0 0
\(791\) −2.70820 −0.0962926
\(792\) 7.70820 0.273899
\(793\) 10.8541 0.385440
\(794\) 31.0344 1.10137
\(795\) 0 0
\(796\) −21.1246 −0.748742
\(797\) 30.7639 1.08971 0.544857 0.838529i \(-0.316584\pi\)
0.544857 + 0.838529i \(0.316584\pi\)
\(798\) −2.00000 −0.0707992
\(799\) 58.8328 2.08136
\(800\) 0 0
\(801\) 7.70820 0.272356
\(802\) −24.9787 −0.882029
\(803\) −29.1246 −1.02779
\(804\) 23.4164 0.825833
\(805\) 0 0
\(806\) −7.47214 −0.263195
\(807\) 79.2492 2.78970
\(808\) 4.14590 0.145852
\(809\) −12.5836 −0.442416 −0.221208 0.975227i \(-0.571000\pi\)
−0.221208 + 0.975227i \(0.571000\pi\)
\(810\) 0 0
\(811\) −25.3951 −0.891743 −0.445872 0.895097i \(-0.647106\pi\)
−0.445872 + 0.895097i \(0.647106\pi\)
\(812\) 0.381966 0.0134044
\(813\) 8.94427 0.313689
\(814\) 17.8885 0.626993
\(815\) 0 0
\(816\) 14.7082 0.514890
\(817\) 11.2361 0.393100
\(818\) 33.1246 1.15817
\(819\) 3.85410 0.134673
\(820\) 0 0
\(821\) −8.00000 −0.279202 −0.139601 0.990208i \(-0.544582\pi\)
−0.139601 + 0.990208i \(0.544582\pi\)
\(822\) 4.85410 0.169306
\(823\) −0.763932 −0.0266290 −0.0133145 0.999911i \(-0.504238\pi\)
−0.0133145 + 0.999911i \(0.504238\pi\)
\(824\) 19.4164 0.676403
\(825\) 0 0
\(826\) 1.47214 0.0512222
\(827\) −49.7984 −1.73166 −0.865830 0.500339i \(-0.833209\pi\)
−0.865830 + 0.500339i \(0.833209\pi\)
\(828\) 7.14590 0.248337
\(829\) −34.2705 −1.19026 −0.595132 0.803628i \(-0.702900\pi\)
−0.595132 + 0.803628i \(0.702900\pi\)
\(830\) 0 0
\(831\) −78.5410 −2.72456
\(832\) −2.61803 −0.0907640
\(833\) 38.5066 1.33417
\(834\) −38.1246 −1.32015
\(835\) 0 0
\(836\) −4.00000 −0.138343
\(837\) −6.38197 −0.220593
\(838\) −15.1459 −0.523206
\(839\) 14.8328 0.512086 0.256043 0.966665i \(-0.417581\pi\)
0.256043 + 0.966665i \(0.417581\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −10.0000 −0.344623
\(843\) −6.70820 −0.231043
\(844\) 15.4164 0.530655
\(845\) 0 0
\(846\) −40.3607 −1.38763
\(847\) 2.67376 0.0918716
\(848\) −11.6180 −0.398965
\(849\) −29.4164 −1.00957
\(850\) 0 0
\(851\) 16.5836 0.568478
\(852\) −20.1803 −0.691367
\(853\) −44.8328 −1.53505 −0.767523 0.641021i \(-0.778511\pi\)
−0.767523 + 0.641021i \(0.778511\pi\)
\(854\) 1.58359 0.0541894
\(855\) 0 0
\(856\) −8.18034 −0.279598
\(857\) −44.1803 −1.50917 −0.754586 0.656201i \(-0.772162\pi\)
−0.754586 + 0.656201i \(0.772162\pi\)
\(858\) 13.7082 0.467990
\(859\) 14.2918 0.487630 0.243815 0.969822i \(-0.421601\pi\)
0.243815 + 0.969822i \(0.421601\pi\)
\(860\) 0 0
\(861\) −5.70820 −0.194535
\(862\) −6.58359 −0.224238
\(863\) 33.9230 1.15475 0.577376 0.816478i \(-0.304077\pi\)
0.577376 + 0.816478i \(0.304077\pi\)
\(864\) −2.23607 −0.0760726
\(865\) 0 0
\(866\) 7.52786 0.255807
\(867\) −38.1246 −1.29478
\(868\) −1.09017 −0.0370028
\(869\) −27.1246 −0.920139
\(870\) 0 0
\(871\) 23.4164 0.793435
\(872\) −7.41641 −0.251151
\(873\) −53.3951 −1.80715
\(874\) −3.70820 −0.125432
\(875\) 0 0
\(876\) 38.1246 1.28811
\(877\) 8.72949 0.294774 0.147387 0.989079i \(-0.452914\pi\)
0.147387 + 0.989079i \(0.452914\pi\)
\(878\) 3.12461 0.105451
\(879\) 19.4164 0.654899
\(880\) 0 0
\(881\) −41.4164 −1.39535 −0.697677 0.716412i \(-0.745783\pi\)
−0.697677 + 0.716412i \(0.745783\pi\)
\(882\) −26.4164 −0.889487
\(883\) 20.2918 0.682873 0.341437 0.939905i \(-0.389087\pi\)
0.341437 + 0.939905i \(0.389087\pi\)
\(884\) 14.7082 0.494690
\(885\) 0 0
\(886\) 13.0902 0.439773
\(887\) −24.0000 −0.805841 −0.402921 0.915235i \(-0.632005\pi\)
−0.402921 + 0.915235i \(0.632005\pi\)
\(888\) −23.4164 −0.785803
\(889\) −8.29180 −0.278098
\(890\) 0 0
\(891\) −11.4164 −0.382464
\(892\) 6.43769 0.215550
\(893\) 20.9443 0.700873
\(894\) −14.1803 −0.474262
\(895\) 0 0
\(896\) −0.381966 −0.0127606
\(897\) 12.7082 0.424315
\(898\) −31.4164 −1.04838
\(899\) −2.85410 −0.0951896
\(900\) 0 0
\(901\) 65.2705 2.17448
\(902\) −11.4164 −0.380125
\(903\) −5.61803 −0.186956
\(904\) 7.09017 0.235816
\(905\) 0 0
\(906\) −46.3607 −1.54023
\(907\) −34.7426 −1.15361 −0.576805 0.816882i \(-0.695701\pi\)
−0.576805 + 0.816882i \(0.695701\pi\)
\(908\) −7.52786 −0.249821
\(909\) 15.9787 0.529980
\(910\) 0 0
\(911\) 6.14590 0.203623 0.101811 0.994804i \(-0.467536\pi\)
0.101811 + 0.994804i \(0.467536\pi\)
\(912\) 5.23607 0.173384
\(913\) 5.88854 0.194882
\(914\) 27.7082 0.916506
\(915\) 0 0
\(916\) −14.8541 −0.490793
\(917\) 2.06888 0.0683206
\(918\) 12.5623 0.414618
\(919\) 14.5410 0.479664 0.239832 0.970814i \(-0.422908\pi\)
0.239832 + 0.970814i \(0.422908\pi\)
\(920\) 0 0
\(921\) −62.8328 −2.07041
\(922\) −30.8541 −1.01613
\(923\) −20.1803 −0.664244
\(924\) 2.00000 0.0657952
\(925\) 0 0
\(926\) −17.8885 −0.587854
\(927\) 74.8328 2.45783
\(928\) −1.00000 −0.0328266
\(929\) 40.8541 1.34038 0.670190 0.742190i \(-0.266213\pi\)
0.670190 + 0.742190i \(0.266213\pi\)
\(930\) 0 0
\(931\) 13.7082 0.449268
\(932\) 6.76393 0.221560
\(933\) 37.7984 1.23746
\(934\) −10.2016 −0.333807
\(935\) 0 0
\(936\) −10.0902 −0.329808
\(937\) 14.0689 0.459610 0.229805 0.973237i \(-0.426191\pi\)
0.229805 + 0.973237i \(0.426191\pi\)
\(938\) 3.41641 0.111550
\(939\) −45.1246 −1.47259
\(940\) 0 0
\(941\) −8.29180 −0.270305 −0.135152 0.990825i \(-0.543152\pi\)
−0.135152 + 0.990825i \(0.543152\pi\)
\(942\) −9.70820 −0.316310
\(943\) −10.5836 −0.344649
\(944\) −3.85410 −0.125440
\(945\) 0 0
\(946\) −11.2361 −0.365316
\(947\) 9.15905 0.297629 0.148815 0.988865i \(-0.452454\pi\)
0.148815 + 0.988865i \(0.452454\pi\)
\(948\) 35.5066 1.15320
\(949\) 38.1246 1.23758
\(950\) 0 0
\(951\) 5.70820 0.185101
\(952\) 2.14590 0.0695490
\(953\) −50.8328 −1.64664 −0.823318 0.567580i \(-0.807880\pi\)
−0.823318 + 0.567580i \(0.807880\pi\)
\(954\) −44.7771 −1.44971
\(955\) 0 0
\(956\) −7.70820 −0.249301
\(957\) 5.23607 0.169258
\(958\) 27.9787 0.903951
\(959\) 0.708204 0.0228691
\(960\) 0 0
\(961\) −22.8541 −0.737229
\(962\) −23.4164 −0.754975
\(963\) −31.5279 −1.01597
\(964\) −2.14590 −0.0691147
\(965\) 0 0
\(966\) 1.85410 0.0596548
\(967\) −20.2918 −0.652540 −0.326270 0.945277i \(-0.605792\pi\)
−0.326270 + 0.945277i \(0.605792\pi\)
\(968\) −7.00000 −0.224989
\(969\) −29.4164 −0.944991
\(970\) 0 0
\(971\) −11.7082 −0.375734 −0.187867 0.982194i \(-0.560157\pi\)
−0.187867 + 0.982194i \(0.560157\pi\)
\(972\) 21.6525 0.694503
\(973\) −5.56231 −0.178319
\(974\) −18.4377 −0.590782
\(975\) 0 0
\(976\) −4.14590 −0.132707
\(977\) 50.9443 1.62985 0.814926 0.579565i \(-0.196778\pi\)
0.814926 + 0.579565i \(0.196778\pi\)
\(978\) −50.8328 −1.62545
\(979\) 4.00000 0.127841
\(980\) 0 0
\(981\) −28.5836 −0.912604
\(982\) −19.7082 −0.628914
\(983\) −45.5967 −1.45431 −0.727155 0.686473i \(-0.759158\pi\)
−0.727155 + 0.686473i \(0.759158\pi\)
\(984\) 14.9443 0.476406
\(985\) 0 0
\(986\) 5.61803 0.178915
\(987\) −10.4721 −0.333332
\(988\) 5.23607 0.166582
\(989\) −10.4164 −0.331223
\(990\) 0 0
\(991\) −14.5836 −0.463263 −0.231632 0.972804i \(-0.574406\pi\)
−0.231632 + 0.972804i \(0.574406\pi\)
\(992\) 2.85410 0.0906178
\(993\) 34.3607 1.09040
\(994\) −2.94427 −0.0933866
\(995\) 0 0
\(996\) −7.70820 −0.244244
\(997\) 23.1246 0.732364 0.366182 0.930543i \(-0.380665\pi\)
0.366182 + 0.930543i \(0.380665\pi\)
\(998\) 8.43769 0.267091
\(999\) −20.0000 −0.632772
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 1450.2.a.l.1.1 2
5.2 odd 4 290.2.b.a.59.4 yes 4
5.3 odd 4 290.2.b.a.59.1 4
5.4 even 2 1450.2.a.k.1.2 2
15.2 even 4 2610.2.e.e.2089.1 4
15.8 even 4 2610.2.e.e.2089.4 4
20.3 even 4 2320.2.d.d.929.4 4
20.7 even 4 2320.2.d.d.929.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
290.2.b.a.59.1 4 5.3 odd 4
290.2.b.a.59.4 yes 4 5.2 odd 4
1450.2.a.k.1.2 2 5.4 even 2
1450.2.a.l.1.1 2 1.1 even 1 trivial
2320.2.d.d.929.1 4 20.7 even 4
2320.2.d.d.929.4 4 20.3 even 4
2610.2.e.e.2089.1 4 15.2 even 4
2610.2.e.e.2089.4 4 15.8 even 4