Properties

Label 3549.2.a.j.1.1
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3549,2,Mod(1,3549)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3549.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.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: \(28.3389076774\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.80194\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.00000 q^{5} -1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.80194 q^{2} +1.00000 q^{3} +1.24698 q^{4} +1.00000 q^{5} -1.80194 q^{6} -1.00000 q^{7} +1.35690 q^{8} +1.00000 q^{9} -1.80194 q^{10} +1.80194 q^{11} +1.24698 q^{12} +1.80194 q^{14} +1.00000 q^{15} -4.93900 q^{16} -2.44504 q^{17} -1.80194 q^{18} +5.74094 q^{19} +1.24698 q^{20} -1.00000 q^{21} -3.24698 q^{22} -7.04892 q^{23} +1.35690 q^{24} -4.00000 q^{25} +1.00000 q^{27} -1.24698 q^{28} -3.15883 q^{29} -1.80194 q^{30} -0.445042 q^{31} +6.18598 q^{32} +1.80194 q^{33} +4.40581 q^{34} -1.00000 q^{35} +1.24698 q^{36} -3.98792 q^{37} -10.3448 q^{38} +1.35690 q^{40} -10.3448 q^{41} +1.80194 q^{42} -8.00000 q^{43} +2.24698 q^{44} +1.00000 q^{45} +12.7017 q^{46} +5.14675 q^{47} -4.93900 q^{48} +1.00000 q^{49} +7.20775 q^{50} -2.44504 q^{51} +8.92154 q^{53} -1.80194 q^{54} +1.80194 q^{55} -1.35690 q^{56} +5.74094 q^{57} +5.69202 q^{58} -9.71379 q^{59} +1.24698 q^{60} -9.93900 q^{61} +0.801938 q^{62} -1.00000 q^{63} -1.26875 q^{64} -3.24698 q^{66} -4.33513 q^{67} -3.04892 q^{68} -7.04892 q^{69} +1.80194 q^{70} -2.40581 q^{71} +1.35690 q^{72} +0.664874 q^{73} +7.18598 q^{74} -4.00000 q^{75} +7.15883 q^{76} -1.80194 q^{77} +4.11960 q^{79} -4.93900 q^{80} +1.00000 q^{81} +18.6407 q^{82} +11.0586 q^{83} -1.24698 q^{84} -2.44504 q^{85} +14.4155 q^{86} -3.15883 q^{87} +2.44504 q^{88} +2.72587 q^{89} -1.80194 q^{90} -8.78986 q^{92} -0.445042 q^{93} -9.27413 q^{94} +5.74094 q^{95} +6.18598 q^{96} -5.39373 q^{97} -1.80194 q^{98} +1.80194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - q^{2} + 3 q^{3} - q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - q^{2} + 3 q^{3} - q^{4} + 3 q^{5} - q^{6} - 3 q^{7} + 3 q^{9} - q^{10} + q^{11} - q^{12} + q^{14} + 3 q^{15} - 5 q^{16} - 7 q^{17} - q^{18} + 3 q^{19} - q^{20} - 3 q^{21} - 5 q^{22} - 12 q^{23} - 12 q^{25} + 3 q^{27} + q^{28} - q^{29} - q^{30} - q^{31} + 4 q^{32} + q^{33} - 3 q^{35} - q^{36} + 7 q^{37} - 8 q^{38} - 8 q^{41} + q^{42} - 24 q^{43} + 2 q^{44} + 3 q^{45} + 11 q^{46} - 12 q^{47} - 5 q^{48} + 3 q^{49} + 4 q^{50} - 7 q^{51} + q^{53} - q^{54} + q^{55} + 3 q^{57} + 12 q^{58} - 21 q^{59} - q^{60} - 20 q^{61} - 2 q^{62} - 3 q^{63} + 4 q^{64} - 5 q^{66} - 12 q^{67} - 12 q^{69} + q^{70} + 6 q^{71} + 3 q^{73} + 7 q^{74} - 12 q^{75} + 13 q^{76} - q^{77} - 9 q^{79} - 5 q^{80} + 3 q^{81} + 19 q^{82} + 2 q^{83} + q^{84} - 7 q^{85} + 8 q^{86} - q^{87} + 7 q^{88} + 19 q^{89} - q^{90} - 3 q^{92} - q^{93} - 17 q^{94} + 3 q^{95} + 4 q^{96} + 16 q^{97} - q^{98} + q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80194 −1.27416 −0.637081 0.770797i \(-0.719858\pi\)
−0.637081 + 0.770797i \(0.719858\pi\)
\(3\) 1.00000 0.577350
\(4\) 1.24698 0.623490
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −1.80194 −0.735638
\(7\) −1.00000 −0.377964
\(8\) 1.35690 0.479735
\(9\) 1.00000 0.333333
\(10\) −1.80194 −0.569823
\(11\) 1.80194 0.543305 0.271652 0.962395i \(-0.412430\pi\)
0.271652 + 0.962395i \(0.412430\pi\)
\(12\) 1.24698 0.359972
\(13\) 0 0
\(14\) 1.80194 0.481588
\(15\) 1.00000 0.258199
\(16\) −4.93900 −1.23475
\(17\) −2.44504 −0.593010 −0.296505 0.955031i \(-0.595821\pi\)
−0.296505 + 0.955031i \(0.595821\pi\)
\(18\) −1.80194 −0.424721
\(19\) 5.74094 1.31706 0.658531 0.752554i \(-0.271178\pi\)
0.658531 + 0.752554i \(0.271178\pi\)
\(20\) 1.24698 0.278833
\(21\) −1.00000 −0.218218
\(22\) −3.24698 −0.692258
\(23\) −7.04892 −1.46980 −0.734900 0.678175i \(-0.762771\pi\)
−0.734900 + 0.678175i \(0.762771\pi\)
\(24\) 1.35690 0.276975
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −1.24698 −0.235657
\(29\) −3.15883 −0.586581 −0.293290 0.956023i \(-0.594750\pi\)
−0.293290 + 0.956023i \(0.594750\pi\)
\(30\) −1.80194 −0.328987
\(31\) −0.445042 −0.0799319 −0.0399659 0.999201i \(-0.512725\pi\)
−0.0399659 + 0.999201i \(0.512725\pi\)
\(32\) 6.18598 1.09354
\(33\) 1.80194 0.313677
\(34\) 4.40581 0.755591
\(35\) −1.00000 −0.169031
\(36\) 1.24698 0.207830
\(37\) −3.98792 −0.655610 −0.327805 0.944745i \(-0.606309\pi\)
−0.327805 + 0.944745i \(0.606309\pi\)
\(38\) −10.3448 −1.67815
\(39\) 0 0
\(40\) 1.35690 0.214544
\(41\) −10.3448 −1.61559 −0.807794 0.589465i \(-0.799339\pi\)
−0.807794 + 0.589465i \(0.799339\pi\)
\(42\) 1.80194 0.278045
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 2.24698 0.338745
\(45\) 1.00000 0.149071
\(46\) 12.7017 1.87276
\(47\) 5.14675 0.750731 0.375365 0.926877i \(-0.377517\pi\)
0.375365 + 0.926877i \(0.377517\pi\)
\(48\) −4.93900 −0.712883
\(49\) 1.00000 0.142857
\(50\) 7.20775 1.01933
\(51\) −2.44504 −0.342374
\(52\) 0 0
\(53\) 8.92154 1.22547 0.612734 0.790289i \(-0.290070\pi\)
0.612734 + 0.790289i \(0.290070\pi\)
\(54\) −1.80194 −0.245213
\(55\) 1.80194 0.242973
\(56\) −1.35690 −0.181323
\(57\) 5.74094 0.760406
\(58\) 5.69202 0.747399
\(59\) −9.71379 −1.26463 −0.632314 0.774712i \(-0.717895\pi\)
−0.632314 + 0.774712i \(0.717895\pi\)
\(60\) 1.24698 0.160984
\(61\) −9.93900 −1.27256 −0.636279 0.771459i \(-0.719527\pi\)
−0.636279 + 0.771459i \(0.719527\pi\)
\(62\) 0.801938 0.101846
\(63\) −1.00000 −0.125988
\(64\) −1.26875 −0.158594
\(65\) 0 0
\(66\) −3.24698 −0.399676
\(67\) −4.33513 −0.529620 −0.264810 0.964301i \(-0.585309\pi\)
−0.264810 + 0.964301i \(0.585309\pi\)
\(68\) −3.04892 −0.369736
\(69\) −7.04892 −0.848590
\(70\) 1.80194 0.215373
\(71\) −2.40581 −0.285517 −0.142759 0.989758i \(-0.545597\pi\)
−0.142759 + 0.989758i \(0.545597\pi\)
\(72\) 1.35690 0.159912
\(73\) 0.664874 0.0778177 0.0389088 0.999243i \(-0.487612\pi\)
0.0389088 + 0.999243i \(0.487612\pi\)
\(74\) 7.18598 0.835353
\(75\) −4.00000 −0.461880
\(76\) 7.15883 0.821175
\(77\) −1.80194 −0.205350
\(78\) 0 0
\(79\) 4.11960 0.463492 0.231746 0.972776i \(-0.425556\pi\)
0.231746 + 0.972776i \(0.425556\pi\)
\(80\) −4.93900 −0.552197
\(81\) 1.00000 0.111111
\(82\) 18.6407 2.05852
\(83\) 11.0586 1.21384 0.606920 0.794763i \(-0.292405\pi\)
0.606920 + 0.794763i \(0.292405\pi\)
\(84\) −1.24698 −0.136057
\(85\) −2.44504 −0.265202
\(86\) 14.4155 1.55446
\(87\) −3.15883 −0.338663
\(88\) 2.44504 0.260642
\(89\) 2.72587 0.288942 0.144471 0.989509i \(-0.453852\pi\)
0.144471 + 0.989509i \(0.453852\pi\)
\(90\) −1.80194 −0.189941
\(91\) 0 0
\(92\) −8.78986 −0.916406
\(93\) −0.445042 −0.0461487
\(94\) −9.27413 −0.956553
\(95\) 5.74094 0.589008
\(96\) 6.18598 0.631354
\(97\) −5.39373 −0.547650 −0.273825 0.961779i \(-0.588289\pi\)
−0.273825 + 0.961779i \(0.588289\pi\)
\(98\) −1.80194 −0.182023
\(99\) 1.80194 0.181102
\(100\) −4.98792 −0.498792
\(101\) −0.835790 −0.0831642 −0.0415821 0.999135i \(-0.513240\pi\)
−0.0415821 + 0.999135i \(0.513240\pi\)
\(102\) 4.40581 0.436241
\(103\) −16.6136 −1.63698 −0.818492 0.574519i \(-0.805189\pi\)
−0.818492 + 0.574519i \(0.805189\pi\)
\(104\) 0 0
\(105\) −1.00000 −0.0975900
\(106\) −16.0761 −1.56145
\(107\) 13.0640 1.26294 0.631471 0.775399i \(-0.282451\pi\)
0.631471 + 0.775399i \(0.282451\pi\)
\(108\) 1.24698 0.119991
\(109\) −1.91185 −0.183122 −0.0915612 0.995799i \(-0.529186\pi\)
−0.0915612 + 0.995799i \(0.529186\pi\)
\(110\) −3.24698 −0.309587
\(111\) −3.98792 −0.378516
\(112\) 4.93900 0.466692
\(113\) 7.05429 0.663612 0.331806 0.943348i \(-0.392342\pi\)
0.331806 + 0.943348i \(0.392342\pi\)
\(114\) −10.3448 −0.968881
\(115\) −7.04892 −0.657315
\(116\) −3.93900 −0.365727
\(117\) 0 0
\(118\) 17.5036 1.61134
\(119\) 2.44504 0.224137
\(120\) 1.35690 0.123867
\(121\) −7.75302 −0.704820
\(122\) 17.9095 1.62145
\(123\) −10.3448 −0.932760
\(124\) −0.554958 −0.0498367
\(125\) −9.00000 −0.804984
\(126\) 1.80194 0.160529
\(127\) −7.69633 −0.682939 −0.341470 0.939893i \(-0.610925\pi\)
−0.341470 + 0.939893i \(0.610925\pi\)
\(128\) −10.0858 −0.891463
\(129\) −8.00000 −0.704361
\(130\) 0 0
\(131\) −8.18598 −0.715212 −0.357606 0.933872i \(-0.616407\pi\)
−0.357606 + 0.933872i \(0.616407\pi\)
\(132\) 2.24698 0.195574
\(133\) −5.74094 −0.497803
\(134\) 7.81163 0.674822
\(135\) 1.00000 0.0860663
\(136\) −3.31767 −0.284488
\(137\) 8.79523 0.751427 0.375714 0.926736i \(-0.377398\pi\)
0.375714 + 0.926736i \(0.377398\pi\)
\(138\) 12.7017 1.08124
\(139\) −19.4330 −1.64828 −0.824141 0.566385i \(-0.808342\pi\)
−0.824141 + 0.566385i \(0.808342\pi\)
\(140\) −1.24698 −0.105389
\(141\) 5.14675 0.433435
\(142\) 4.33513 0.363796
\(143\) 0 0
\(144\) −4.93900 −0.411583
\(145\) −3.15883 −0.262327
\(146\) −1.19806 −0.0991523
\(147\) 1.00000 0.0824786
\(148\) −4.97285 −0.408766
\(149\) −10.5090 −0.860933 −0.430466 0.902607i \(-0.641651\pi\)
−0.430466 + 0.902607i \(0.641651\pi\)
\(150\) 7.20775 0.588510
\(151\) 20.9758 1.70699 0.853495 0.521102i \(-0.174479\pi\)
0.853495 + 0.521102i \(0.174479\pi\)
\(152\) 7.78986 0.631841
\(153\) −2.44504 −0.197670
\(154\) 3.24698 0.261649
\(155\) −0.445042 −0.0357466
\(156\) 0 0
\(157\) 0.838773 0.0669414 0.0334707 0.999440i \(-0.489344\pi\)
0.0334707 + 0.999440i \(0.489344\pi\)
\(158\) −7.42327 −0.590564
\(159\) 8.92154 0.707524
\(160\) 6.18598 0.489045
\(161\) 7.04892 0.555533
\(162\) −1.80194 −0.141574
\(163\) 12.7409 0.997947 0.498974 0.866617i \(-0.333710\pi\)
0.498974 + 0.866617i \(0.333710\pi\)
\(164\) −12.8998 −1.00730
\(165\) 1.80194 0.140281
\(166\) −19.9269 −1.54663
\(167\) 13.5646 1.04966 0.524832 0.851206i \(-0.324128\pi\)
0.524832 + 0.851206i \(0.324128\pi\)
\(168\) −1.35690 −0.104687
\(169\) 0 0
\(170\) 4.40581 0.337910
\(171\) 5.74094 0.439021
\(172\) −9.97584 −0.760650
\(173\) 7.75733 0.589779 0.294890 0.955531i \(-0.404717\pi\)
0.294890 + 0.955531i \(0.404717\pi\)
\(174\) 5.69202 0.431511
\(175\) 4.00000 0.302372
\(176\) −8.89977 −0.670846
\(177\) −9.71379 −0.730133
\(178\) −4.91185 −0.368159
\(179\) 2.16852 0.162083 0.0810415 0.996711i \(-0.474175\pi\)
0.0810415 + 0.996711i \(0.474175\pi\)
\(180\) 1.24698 0.0929444
\(181\) −2.52781 −0.187891 −0.0939454 0.995577i \(-0.529948\pi\)
−0.0939454 + 0.995577i \(0.529948\pi\)
\(182\) 0 0
\(183\) −9.93900 −0.734712
\(184\) −9.56465 −0.705115
\(185\) −3.98792 −0.293198
\(186\) 0.801938 0.0588009
\(187\) −4.40581 −0.322185
\(188\) 6.41789 0.468073
\(189\) −1.00000 −0.0727393
\(190\) −10.3448 −0.750492
\(191\) 20.2107 1.46240 0.731199 0.682165i \(-0.238961\pi\)
0.731199 + 0.682165i \(0.238961\pi\)
\(192\) −1.26875 −0.0915641
\(193\) −24.3424 −1.75221 −0.876103 0.482124i \(-0.839865\pi\)
−0.876103 + 0.482124i \(0.839865\pi\)
\(194\) 9.71917 0.697796
\(195\) 0 0
\(196\) 1.24698 0.0890700
\(197\) −1.36898 −0.0975356 −0.0487678 0.998810i \(-0.515529\pi\)
−0.0487678 + 0.998810i \(0.515529\pi\)
\(198\) −3.24698 −0.230753
\(199\) −4.01746 −0.284790 −0.142395 0.989810i \(-0.545480\pi\)
−0.142395 + 0.989810i \(0.545480\pi\)
\(200\) −5.42758 −0.383788
\(201\) −4.33513 −0.305776
\(202\) 1.50604 0.105965
\(203\) 3.15883 0.221707
\(204\) −3.04892 −0.213467
\(205\) −10.3448 −0.722513
\(206\) 29.9366 2.08578
\(207\) −7.04892 −0.489934
\(208\) 0 0
\(209\) 10.3448 0.715566
\(210\) 1.80194 0.124346
\(211\) −24.6504 −1.69700 −0.848502 0.529193i \(-0.822495\pi\)
−0.848502 + 0.529193i \(0.822495\pi\)
\(212\) 11.1250 0.764067
\(213\) −2.40581 −0.164844
\(214\) −23.5405 −1.60919
\(215\) −8.00000 −0.545595
\(216\) 1.35690 0.0923251
\(217\) 0.445042 0.0302114
\(218\) 3.44504 0.233328
\(219\) 0.664874 0.0449280
\(220\) 2.24698 0.151491
\(221\) 0 0
\(222\) 7.18598 0.482291
\(223\) −9.41013 −0.630149 −0.315074 0.949067i \(-0.602029\pi\)
−0.315074 + 0.949067i \(0.602029\pi\)
\(224\) −6.18598 −0.413318
\(225\) −4.00000 −0.266667
\(226\) −12.7114 −0.845550
\(227\) 5.33513 0.354105 0.177052 0.984201i \(-0.443344\pi\)
0.177052 + 0.984201i \(0.443344\pi\)
\(228\) 7.15883 0.474105
\(229\) 9.13036 0.603351 0.301676 0.953411i \(-0.402454\pi\)
0.301676 + 0.953411i \(0.402454\pi\)
\(230\) 12.7017 0.837526
\(231\) −1.80194 −0.118559
\(232\) −4.28621 −0.281403
\(233\) −26.7265 −1.75091 −0.875454 0.483301i \(-0.839438\pi\)
−0.875454 + 0.483301i \(0.839438\pi\)
\(234\) 0 0
\(235\) 5.14675 0.335737
\(236\) −12.1129 −0.788483
\(237\) 4.11960 0.267597
\(238\) −4.40581 −0.285586
\(239\) −8.13169 −0.525995 −0.262998 0.964797i \(-0.584711\pi\)
−0.262998 + 0.964797i \(0.584711\pi\)
\(240\) −4.93900 −0.318811
\(241\) 7.64848 0.492682 0.246341 0.969183i \(-0.420772\pi\)
0.246341 + 0.969183i \(0.420772\pi\)
\(242\) 13.9705 0.898055
\(243\) 1.00000 0.0641500
\(244\) −12.3937 −0.793427
\(245\) 1.00000 0.0638877
\(246\) 18.6407 1.18849
\(247\) 0 0
\(248\) −0.603875 −0.0383461
\(249\) 11.0586 0.700811
\(250\) 16.2174 1.02568
\(251\) −8.24459 −0.520394 −0.260197 0.965556i \(-0.583787\pi\)
−0.260197 + 0.965556i \(0.583787\pi\)
\(252\) −1.24698 −0.0785523
\(253\) −12.7017 −0.798550
\(254\) 13.8683 0.870175
\(255\) −2.44504 −0.153114
\(256\) 20.7114 1.29446
\(257\) 24.6329 1.53656 0.768280 0.640114i \(-0.221113\pi\)
0.768280 + 0.640114i \(0.221113\pi\)
\(258\) 14.4155 0.897470
\(259\) 3.98792 0.247797
\(260\) 0 0
\(261\) −3.15883 −0.195527
\(262\) 14.7506 0.911297
\(263\) 17.1588 1.05806 0.529030 0.848603i \(-0.322556\pi\)
0.529030 + 0.848603i \(0.322556\pi\)
\(264\) 2.44504 0.150482
\(265\) 8.92154 0.548046
\(266\) 10.3448 0.634281
\(267\) 2.72587 0.166821
\(268\) −5.40581 −0.330213
\(269\) −7.08708 −0.432107 −0.216053 0.976382i \(-0.569319\pi\)
−0.216053 + 0.976382i \(0.569319\pi\)
\(270\) −1.80194 −0.109662
\(271\) −24.5483 −1.49120 −0.745600 0.666394i \(-0.767837\pi\)
−0.745600 + 0.666394i \(0.767837\pi\)
\(272\) 12.0761 0.732219
\(273\) 0 0
\(274\) −15.8485 −0.957441
\(275\) −7.20775 −0.434644
\(276\) −8.78986 −0.529087
\(277\) 33.0810 1.98764 0.993821 0.110992i \(-0.0354027\pi\)
0.993821 + 0.110992i \(0.0354027\pi\)
\(278\) 35.0170 2.10018
\(279\) −0.445042 −0.0266440
\(280\) −1.35690 −0.0810900
\(281\) −26.3163 −1.56990 −0.784951 0.619558i \(-0.787312\pi\)
−0.784951 + 0.619558i \(0.787312\pi\)
\(282\) −9.27413 −0.552266
\(283\) 31.7778 1.88899 0.944496 0.328522i \(-0.106551\pi\)
0.944496 + 0.328522i \(0.106551\pi\)
\(284\) −3.00000 −0.178017
\(285\) 5.74094 0.340064
\(286\) 0 0
\(287\) 10.3448 0.610635
\(288\) 6.18598 0.364512
\(289\) −11.0218 −0.648339
\(290\) 5.69202 0.334247
\(291\) −5.39373 −0.316186
\(292\) 0.829085 0.0485185
\(293\) 12.8616 0.751383 0.375692 0.926745i \(-0.377405\pi\)
0.375692 + 0.926745i \(0.377405\pi\)
\(294\) −1.80194 −0.105091
\(295\) −9.71379 −0.565559
\(296\) −5.41119 −0.314519
\(297\) 1.80194 0.104559
\(298\) 18.9366 1.09697
\(299\) 0 0
\(300\) −4.98792 −0.287978
\(301\) 8.00000 0.461112
\(302\) −37.7972 −2.17498
\(303\) −0.835790 −0.0480149
\(304\) −28.3545 −1.62624
\(305\) −9.93900 −0.569106
\(306\) 4.40581 0.251864
\(307\) −29.5937 −1.68900 −0.844501 0.535554i \(-0.820103\pi\)
−0.844501 + 0.535554i \(0.820103\pi\)
\(308\) −2.24698 −0.128034
\(309\) −16.6136 −0.945113
\(310\) 0.801938 0.0455470
\(311\) −8.55794 −0.485276 −0.242638 0.970117i \(-0.578013\pi\)
−0.242638 + 0.970117i \(0.578013\pi\)
\(312\) 0 0
\(313\) −16.3569 −0.924546 −0.462273 0.886738i \(-0.652966\pi\)
−0.462273 + 0.886738i \(0.652966\pi\)
\(314\) −1.51142 −0.0852942
\(315\) −1.00000 −0.0563436
\(316\) 5.13706 0.288982
\(317\) 28.3545 1.59255 0.796274 0.604936i \(-0.206801\pi\)
0.796274 + 0.604936i \(0.206801\pi\)
\(318\) −16.0761 −0.901501
\(319\) −5.69202 −0.318692
\(320\) −1.26875 −0.0709253
\(321\) 13.0640 0.729160
\(322\) −12.7017 −0.707839
\(323\) −14.0368 −0.781030
\(324\) 1.24698 0.0692766
\(325\) 0 0
\(326\) −22.9584 −1.27155
\(327\) −1.91185 −0.105726
\(328\) −14.0368 −0.775055
\(329\) −5.14675 −0.283750
\(330\) −3.24698 −0.178740
\(331\) −11.3894 −0.626019 −0.313010 0.949750i \(-0.601337\pi\)
−0.313010 + 0.949750i \(0.601337\pi\)
\(332\) 13.7899 0.756817
\(333\) −3.98792 −0.218537
\(334\) −24.4426 −1.33744
\(335\) −4.33513 −0.236853
\(336\) 4.93900 0.269445
\(337\) −7.64609 −0.416509 −0.208254 0.978075i \(-0.566778\pi\)
−0.208254 + 0.978075i \(0.566778\pi\)
\(338\) 0 0
\(339\) 7.05429 0.383137
\(340\) −3.04892 −0.165351
\(341\) −0.801938 −0.0434274
\(342\) −10.3448 −0.559383
\(343\) −1.00000 −0.0539949
\(344\) −10.8552 −0.585271
\(345\) −7.04892 −0.379501
\(346\) −13.9782 −0.751474
\(347\) 14.4668 0.776619 0.388310 0.921529i \(-0.373059\pi\)
0.388310 + 0.921529i \(0.373059\pi\)
\(348\) −3.93900 −0.211153
\(349\) −17.0519 −0.912767 −0.456384 0.889783i \(-0.650856\pi\)
−0.456384 + 0.889783i \(0.650856\pi\)
\(350\) −7.20775 −0.385270
\(351\) 0 0
\(352\) 11.1468 0.594124
\(353\) 21.0151 1.11852 0.559260 0.828993i \(-0.311086\pi\)
0.559260 + 0.828993i \(0.311086\pi\)
\(354\) 17.5036 0.930308
\(355\) −2.40581 −0.127687
\(356\) 3.39911 0.180152
\(357\) 2.44504 0.129405
\(358\) −3.90754 −0.206520
\(359\) −16.3424 −0.862520 −0.431260 0.902228i \(-0.641931\pi\)
−0.431260 + 0.902228i \(0.641931\pi\)
\(360\) 1.35690 0.0715147
\(361\) 13.9584 0.734651
\(362\) 4.55496 0.239403
\(363\) −7.75302 −0.406928
\(364\) 0 0
\(365\) 0.664874 0.0348011
\(366\) 17.9095 0.936143
\(367\) −34.4209 −1.79676 −0.898378 0.439224i \(-0.855253\pi\)
−0.898378 + 0.439224i \(0.855253\pi\)
\(368\) 34.8146 1.81484
\(369\) −10.3448 −0.538530
\(370\) 7.18598 0.373581
\(371\) −8.92154 −0.463183
\(372\) −0.554958 −0.0287732
\(373\) 1.35391 0.0701029 0.0350515 0.999386i \(-0.488840\pi\)
0.0350515 + 0.999386i \(0.488840\pi\)
\(374\) 7.93900 0.410516
\(375\) −9.00000 −0.464758
\(376\) 6.98361 0.360152
\(377\) 0 0
\(378\) 1.80194 0.0926817
\(379\) 30.7590 1.57998 0.789992 0.613118i \(-0.210085\pi\)
0.789992 + 0.613118i \(0.210085\pi\)
\(380\) 7.15883 0.367240
\(381\) −7.69633 −0.394295
\(382\) −36.4185 −1.86333
\(383\) −31.6582 −1.61766 −0.808828 0.588045i \(-0.799898\pi\)
−0.808828 + 0.588045i \(0.799898\pi\)
\(384\) −10.0858 −0.514686
\(385\) −1.80194 −0.0918353
\(386\) 43.8635 2.23259
\(387\) −8.00000 −0.406663
\(388\) −6.72587 −0.341454
\(389\) −19.0495 −0.965848 −0.482924 0.875662i \(-0.660425\pi\)
−0.482924 + 0.875662i \(0.660425\pi\)
\(390\) 0 0
\(391\) 17.2349 0.871606
\(392\) 1.35690 0.0685336
\(393\) −8.18598 −0.412928
\(394\) 2.46681 0.124276
\(395\) 4.11960 0.207280
\(396\) 2.24698 0.112915
\(397\) 6.37435 0.319920 0.159960 0.987124i \(-0.448864\pi\)
0.159960 + 0.987124i \(0.448864\pi\)
\(398\) 7.23921 0.362869
\(399\) −5.74094 −0.287406
\(400\) 19.7560 0.987800
\(401\) −20.7754 −1.03747 −0.518737 0.854934i \(-0.673597\pi\)
−0.518737 + 0.854934i \(0.673597\pi\)
\(402\) 7.81163 0.389609
\(403\) 0 0
\(404\) −1.04221 −0.0518520
\(405\) 1.00000 0.0496904
\(406\) −5.69202 −0.282490
\(407\) −7.18598 −0.356196
\(408\) −3.31767 −0.164249
\(409\) 5.48725 0.271327 0.135664 0.990755i \(-0.456683\pi\)
0.135664 + 0.990755i \(0.456683\pi\)
\(410\) 18.6407 0.920599
\(411\) 8.79523 0.433837
\(412\) −20.7168 −1.02064
\(413\) 9.71379 0.477984
\(414\) 12.7017 0.624255
\(415\) 11.0586 0.542846
\(416\) 0 0
\(417\) −19.4330 −0.951636
\(418\) −18.6407 −0.911747
\(419\) −14.7259 −0.719406 −0.359703 0.933067i \(-0.617122\pi\)
−0.359703 + 0.933067i \(0.617122\pi\)
\(420\) −1.24698 −0.0608464
\(421\) 1.64071 0.0799634 0.0399817 0.999200i \(-0.487270\pi\)
0.0399817 + 0.999200i \(0.487270\pi\)
\(422\) 44.4185 2.16226
\(423\) 5.14675 0.250244
\(424\) 12.1056 0.587900
\(425\) 9.78017 0.474408
\(426\) 4.33513 0.210038
\(427\) 9.93900 0.480982
\(428\) 16.2905 0.787432
\(429\) 0 0
\(430\) 14.4155 0.695177
\(431\) 6.94331 0.334448 0.167224 0.985919i \(-0.446520\pi\)
0.167224 + 0.985919i \(0.446520\pi\)
\(432\) −4.93900 −0.237628
\(433\) −36.1909 −1.73922 −0.869611 0.493737i \(-0.835631\pi\)
−0.869611 + 0.493737i \(0.835631\pi\)
\(434\) −0.801938 −0.0384942
\(435\) −3.15883 −0.151454
\(436\) −2.38404 −0.114175
\(437\) −40.4674 −1.93582
\(438\) −1.19806 −0.0572456
\(439\) 8.76032 0.418107 0.209054 0.977904i \(-0.432962\pi\)
0.209054 + 0.977904i \(0.432962\pi\)
\(440\) 2.44504 0.116563
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −18.4577 −0.876952 −0.438476 0.898743i \(-0.644482\pi\)
−0.438476 + 0.898743i \(0.644482\pi\)
\(444\) −4.97285 −0.236001
\(445\) 2.72587 0.129219
\(446\) 16.9565 0.802912
\(447\) −10.5090 −0.497060
\(448\) 1.26875 0.0599428
\(449\) −34.7952 −1.64209 −0.821044 0.570865i \(-0.806608\pi\)
−0.821044 + 0.570865i \(0.806608\pi\)
\(450\) 7.20775 0.339777
\(451\) −18.6407 −0.877757
\(452\) 8.79656 0.413755
\(453\) 20.9758 0.985531
\(454\) −9.61356 −0.451187
\(455\) 0 0
\(456\) 7.78986 0.364793
\(457\) −23.2664 −1.08835 −0.544177 0.838970i \(-0.683158\pi\)
−0.544177 + 0.838970i \(0.683158\pi\)
\(458\) −16.4523 −0.768767
\(459\) −2.44504 −0.114125
\(460\) −8.78986 −0.409829
\(461\) 32.8702 1.53092 0.765460 0.643484i \(-0.222512\pi\)
0.765460 + 0.643484i \(0.222512\pi\)
\(462\) 3.24698 0.151063
\(463\) −22.6015 −1.05038 −0.525190 0.850985i \(-0.676006\pi\)
−0.525190 + 0.850985i \(0.676006\pi\)
\(464\) 15.6015 0.724281
\(465\) −0.445042 −0.0206383
\(466\) 48.1594 2.23094
\(467\) −12.4886 −0.577903 −0.288951 0.957344i \(-0.593307\pi\)
−0.288951 + 0.957344i \(0.593307\pi\)
\(468\) 0 0
\(469\) 4.33513 0.200178
\(470\) −9.27413 −0.427784
\(471\) 0.838773 0.0386486
\(472\) −13.1806 −0.606686
\(473\) −14.4155 −0.662825
\(474\) −7.42327 −0.340962
\(475\) −22.9638 −1.05365
\(476\) 3.04892 0.139747
\(477\) 8.92154 0.408489
\(478\) 14.6528 0.670203
\(479\) 13.5536 0.619281 0.309641 0.950854i \(-0.399791\pi\)
0.309641 + 0.950854i \(0.399791\pi\)
\(480\) 6.18598 0.282350
\(481\) 0 0
\(482\) −13.7821 −0.627757
\(483\) 7.04892 0.320737
\(484\) −9.66786 −0.439448
\(485\) −5.39373 −0.244917
\(486\) −1.80194 −0.0817376
\(487\) −14.9414 −0.677059 −0.338530 0.940956i \(-0.609930\pi\)
−0.338530 + 0.940956i \(0.609930\pi\)
\(488\) −13.4862 −0.610491
\(489\) 12.7409 0.576165
\(490\) −1.80194 −0.0814032
\(491\) 27.4862 1.24043 0.620217 0.784430i \(-0.287044\pi\)
0.620217 + 0.784430i \(0.287044\pi\)
\(492\) −12.8998 −0.581567
\(493\) 7.72348 0.347848
\(494\) 0 0
\(495\) 1.80194 0.0809911
\(496\) 2.19806 0.0986959
\(497\) 2.40581 0.107915
\(498\) −19.9269 −0.892947
\(499\) −17.8756 −0.800222 −0.400111 0.916467i \(-0.631028\pi\)
−0.400111 + 0.916467i \(0.631028\pi\)
\(500\) −11.2228 −0.501900
\(501\) 13.5646 0.606024
\(502\) 14.8562 0.663066
\(503\) −37.6510 −1.67877 −0.839387 0.543534i \(-0.817086\pi\)
−0.839387 + 0.543534i \(0.817086\pi\)
\(504\) −1.35690 −0.0604409
\(505\) −0.835790 −0.0371921
\(506\) 22.8877 1.01748
\(507\) 0 0
\(508\) −9.59717 −0.425806
\(509\) −0.552565 −0.0244920 −0.0122460 0.999925i \(-0.503898\pi\)
−0.0122460 + 0.999925i \(0.503898\pi\)
\(510\) 4.40581 0.195093
\(511\) −0.664874 −0.0294123
\(512\) −17.1491 −0.757892
\(513\) 5.74094 0.253469
\(514\) −44.3870 −1.95783
\(515\) −16.6136 −0.732081
\(516\) −9.97584 −0.439162
\(517\) 9.27413 0.407876
\(518\) −7.18598 −0.315734
\(519\) 7.75733 0.340509
\(520\) 0 0
\(521\) −26.0127 −1.13964 −0.569818 0.821771i \(-0.692986\pi\)
−0.569818 + 0.821771i \(0.692986\pi\)
\(522\) 5.69202 0.249133
\(523\) 41.0428 1.79468 0.897338 0.441343i \(-0.145498\pi\)
0.897338 + 0.441343i \(0.145498\pi\)
\(524\) −10.2078 −0.445928
\(525\) 4.00000 0.174574
\(526\) −30.9191 −1.34814
\(527\) 1.08815 0.0474004
\(528\) −8.89977 −0.387313
\(529\) 26.6872 1.16031
\(530\) −16.0761 −0.698300
\(531\) −9.71379 −0.421543
\(532\) −7.15883 −0.310375
\(533\) 0 0
\(534\) −4.91185 −0.212557
\(535\) 13.0640 0.564805
\(536\) −5.88231 −0.254077
\(537\) 2.16852 0.0935786
\(538\) 12.7705 0.550574
\(539\) 1.80194 0.0776150
\(540\) 1.24698 0.0536615
\(541\) 33.2664 1.43023 0.715116 0.699006i \(-0.246374\pi\)
0.715116 + 0.699006i \(0.246374\pi\)
\(542\) 44.2344 1.90003
\(543\) −2.52781 −0.108479
\(544\) −15.1250 −0.648478
\(545\) −1.91185 −0.0818948
\(546\) 0 0
\(547\) −39.4808 −1.68808 −0.844039 0.536282i \(-0.819828\pi\)
−0.844039 + 0.536282i \(0.819828\pi\)
\(548\) 10.9675 0.468507
\(549\) −9.93900 −0.424186
\(550\) 12.9879 0.553807
\(551\) −18.1347 −0.772563
\(552\) −9.56465 −0.407098
\(553\) −4.11960 −0.175183
\(554\) −59.6098 −2.53258
\(555\) −3.98792 −0.169278
\(556\) −24.2325 −1.02769
\(557\) −33.4446 −1.41709 −0.708546 0.705665i \(-0.750648\pi\)
−0.708546 + 0.705665i \(0.750648\pi\)
\(558\) 0.801938 0.0339487
\(559\) 0 0
\(560\) 4.93900 0.208711
\(561\) −4.40581 −0.186014
\(562\) 47.4204 2.00031
\(563\) −32.4674 −1.36834 −0.684169 0.729324i \(-0.739835\pi\)
−0.684169 + 0.729324i \(0.739835\pi\)
\(564\) 6.41789 0.270242
\(565\) 7.05429 0.296776
\(566\) −57.2616 −2.40688
\(567\) −1.00000 −0.0419961
\(568\) −3.26444 −0.136973
\(569\) 17.7506 0.744145 0.372073 0.928204i \(-0.378647\pi\)
0.372073 + 0.928204i \(0.378647\pi\)
\(570\) −10.3448 −0.433297
\(571\) 33.1336 1.38660 0.693299 0.720650i \(-0.256156\pi\)
0.693299 + 0.720650i \(0.256156\pi\)
\(572\) 0 0
\(573\) 20.2107 0.844316
\(574\) −18.6407 −0.778048
\(575\) 28.1957 1.17584
\(576\) −1.26875 −0.0528646
\(577\) 9.76702 0.406606 0.203303 0.979116i \(-0.434832\pi\)
0.203303 + 0.979116i \(0.434832\pi\)
\(578\) 19.8605 0.826090
\(579\) −24.3424 −1.01164
\(580\) −3.93900 −0.163558
\(581\) −11.0586 −0.458788
\(582\) 9.71917 0.402872
\(583\) 16.0761 0.665803
\(584\) 0.902165 0.0373319
\(585\) 0 0
\(586\) −23.1758 −0.957384
\(587\) −7.43488 −0.306870 −0.153435 0.988159i \(-0.549034\pi\)
−0.153435 + 0.988159i \(0.549034\pi\)
\(588\) 1.24698 0.0514246
\(589\) −2.55496 −0.105275
\(590\) 17.5036 0.720614
\(591\) −1.36898 −0.0563122
\(592\) 19.6963 0.809514
\(593\) 42.9366 1.76320 0.881598 0.472002i \(-0.156468\pi\)
0.881598 + 0.472002i \(0.156468\pi\)
\(594\) −3.24698 −0.133225
\(595\) 2.44504 0.100237
\(596\) −13.1045 −0.536783
\(597\) −4.01746 −0.164424
\(598\) 0 0
\(599\) −21.0151 −0.858652 −0.429326 0.903150i \(-0.641249\pi\)
−0.429326 + 0.903150i \(0.641249\pi\)
\(600\) −5.42758 −0.221580
\(601\) −3.18837 −0.130056 −0.0650282 0.997883i \(-0.520714\pi\)
−0.0650282 + 0.997883i \(0.520714\pi\)
\(602\) −14.4155 −0.587532
\(603\) −4.33513 −0.176540
\(604\) 26.1564 1.06429
\(605\) −7.75302 −0.315205
\(606\) 1.50604 0.0611787
\(607\) −36.6491 −1.48754 −0.743770 0.668436i \(-0.766964\pi\)
−0.743770 + 0.668436i \(0.766964\pi\)
\(608\) 35.5133 1.44026
\(609\) 3.15883 0.128002
\(610\) 17.9095 0.725133
\(611\) 0 0
\(612\) −3.04892 −0.123245
\(613\) 13.9433 0.563165 0.281583 0.959537i \(-0.409141\pi\)
0.281583 + 0.959537i \(0.409141\pi\)
\(614\) 53.3260 2.15206
\(615\) −10.3448 −0.417143
\(616\) −2.44504 −0.0985135
\(617\) −14.3026 −0.575801 −0.287901 0.957660i \(-0.592957\pi\)
−0.287901 + 0.957660i \(0.592957\pi\)
\(618\) 29.9366 1.20423
\(619\) 10.5690 0.424802 0.212401 0.977183i \(-0.431872\pi\)
0.212401 + 0.977183i \(0.431872\pi\)
\(620\) −0.554958 −0.0222877
\(621\) −7.04892 −0.282863
\(622\) 15.4209 0.618321
\(623\) −2.72587 −0.109210
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 29.4741 1.17802
\(627\) 10.3448 0.413132
\(628\) 1.04593 0.0417373
\(629\) 9.75063 0.388783
\(630\) 1.80194 0.0717909
\(631\) 26.6614 1.06137 0.530687 0.847568i \(-0.321934\pi\)
0.530687 + 0.847568i \(0.321934\pi\)
\(632\) 5.58987 0.222353
\(633\) −24.6504 −0.979765
\(634\) −51.0930 −2.02916
\(635\) −7.69633 −0.305420
\(636\) 11.1250 0.441134
\(637\) 0 0
\(638\) 10.2567 0.406065
\(639\) −2.40581 −0.0951725
\(640\) −10.0858 −0.398674
\(641\) 35.0291 1.38356 0.691782 0.722106i \(-0.256826\pi\)
0.691782 + 0.722106i \(0.256826\pi\)
\(642\) −23.5405 −0.929069
\(643\) −3.53558 −0.139430 −0.0697148 0.997567i \(-0.522209\pi\)
−0.0697148 + 0.997567i \(0.522209\pi\)
\(644\) 8.78986 0.346369
\(645\) −8.00000 −0.315000
\(646\) 25.2935 0.995160
\(647\) 8.69309 0.341760 0.170880 0.985292i \(-0.445339\pi\)
0.170880 + 0.985292i \(0.445339\pi\)
\(648\) 1.35690 0.0533039
\(649\) −17.5036 −0.687078
\(650\) 0 0
\(651\) 0.445042 0.0174426
\(652\) 15.8877 0.622210
\(653\) −4.93123 −0.192974 −0.0964870 0.995334i \(-0.530761\pi\)
−0.0964870 + 0.995334i \(0.530761\pi\)
\(654\) 3.44504 0.134712
\(655\) −8.18598 −0.319853
\(656\) 51.0930 1.99485
\(657\) 0.664874 0.0259392
\(658\) 9.27413 0.361543
\(659\) −25.6571 −0.999459 −0.499729 0.866182i \(-0.666567\pi\)
−0.499729 + 0.866182i \(0.666567\pi\)
\(660\) 2.24698 0.0874636
\(661\) 4.18359 0.162723 0.0813614 0.996685i \(-0.474073\pi\)
0.0813614 + 0.996685i \(0.474073\pi\)
\(662\) 20.5230 0.797650
\(663\) 0 0
\(664\) 15.0054 0.582322
\(665\) −5.74094 −0.222624
\(666\) 7.18598 0.278451
\(667\) 22.2664 0.862157
\(668\) 16.9148 0.654455
\(669\) −9.41013 −0.363816
\(670\) 7.81163 0.301789
\(671\) −17.9095 −0.691387
\(672\) −6.18598 −0.238629
\(673\) 15.2946 0.589562 0.294781 0.955565i \(-0.404753\pi\)
0.294781 + 0.955565i \(0.404753\pi\)
\(674\) 13.7778 0.530700
\(675\) −4.00000 −0.153960
\(676\) 0 0
\(677\) 28.4547 1.09360 0.546802 0.837262i \(-0.315845\pi\)
0.546802 + 0.837262i \(0.315845\pi\)
\(678\) −12.7114 −0.488178
\(679\) 5.39373 0.206992
\(680\) −3.31767 −0.127227
\(681\) 5.33513 0.204442
\(682\) 1.44504 0.0553335
\(683\) 50.4844 1.93173 0.965866 0.259043i \(-0.0834072\pi\)
0.965866 + 0.259043i \(0.0834072\pi\)
\(684\) 7.15883 0.273725
\(685\) 8.79523 0.336049
\(686\) 1.80194 0.0687983
\(687\) 9.13036 0.348345
\(688\) 39.5120 1.50638
\(689\) 0 0
\(690\) 12.7017 0.483546
\(691\) 39.9845 1.52108 0.760540 0.649291i \(-0.224934\pi\)
0.760540 + 0.649291i \(0.224934\pi\)
\(692\) 9.67324 0.367721
\(693\) −1.80194 −0.0684500
\(694\) −26.0683 −0.989539
\(695\) −19.4330 −0.737134
\(696\) −4.28621 −0.162468
\(697\) 25.2935 0.958060
\(698\) 30.7265 1.16301
\(699\) −26.7265 −1.01089
\(700\) 4.98792 0.188526
\(701\) −7.83984 −0.296107 −0.148053 0.988979i \(-0.547301\pi\)
−0.148053 + 0.988979i \(0.547301\pi\)
\(702\) 0 0
\(703\) −22.8944 −0.863478
\(704\) −2.28621 −0.0861647
\(705\) 5.14675 0.193838
\(706\) −37.8678 −1.42517
\(707\) 0.835790 0.0314331
\(708\) −12.1129 −0.455231
\(709\) 30.4631 1.14407 0.572033 0.820231i \(-0.306155\pi\)
0.572033 + 0.820231i \(0.306155\pi\)
\(710\) 4.33513 0.162694
\(711\) 4.11960 0.154497
\(712\) 3.69873 0.138616
\(713\) 3.13706 0.117484
\(714\) −4.40581 −0.164883
\(715\) 0 0
\(716\) 2.70410 0.101057
\(717\) −8.13169 −0.303683
\(718\) 29.4480 1.09899
\(719\) −7.19673 −0.268393 −0.134196 0.990955i \(-0.542845\pi\)
−0.134196 + 0.990955i \(0.542845\pi\)
\(720\) −4.93900 −0.184066
\(721\) 16.6136 0.618721
\(722\) −25.1521 −0.936065
\(723\) 7.64848 0.284450
\(724\) −3.15213 −0.117148
\(725\) 12.6353 0.469265
\(726\) 13.9705 0.518492
\(727\) −10.8304 −0.401678 −0.200839 0.979624i \(-0.564367\pi\)
−0.200839 + 0.979624i \(0.564367\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.19806 −0.0443423
\(731\) 19.5603 0.723465
\(732\) −12.3937 −0.458086
\(733\) 37.3569 1.37981 0.689904 0.723901i \(-0.257653\pi\)
0.689904 + 0.723901i \(0.257653\pi\)
\(734\) 62.0243 2.28936
\(735\) 1.00000 0.0368856
\(736\) −43.6045 −1.60728
\(737\) −7.81163 −0.287745
\(738\) 18.6407 0.686174
\(739\) −22.5515 −0.829570 −0.414785 0.909919i \(-0.636143\pi\)
−0.414785 + 0.909919i \(0.636143\pi\)
\(740\) −4.97285 −0.182806
\(741\) 0 0
\(742\) 16.0761 0.590171
\(743\) 12.6568 0.464334 0.232167 0.972676i \(-0.425418\pi\)
0.232167 + 0.972676i \(0.425418\pi\)
\(744\) −0.603875 −0.0221391
\(745\) −10.5090 −0.385021
\(746\) −2.43967 −0.0893225
\(747\) 11.0586 0.404613
\(748\) −5.49396 −0.200879
\(749\) −13.0640 −0.477348
\(750\) 16.2174 0.592177
\(751\) −2.04892 −0.0747661 −0.0373830 0.999301i \(-0.511902\pi\)
−0.0373830 + 0.999301i \(0.511902\pi\)
\(752\) −25.4198 −0.926965
\(753\) −8.24459 −0.300449
\(754\) 0 0
\(755\) 20.9758 0.763389
\(756\) −1.24698 −0.0453522
\(757\) −9.19460 −0.334184 −0.167092 0.985941i \(-0.553438\pi\)
−0.167092 + 0.985941i \(0.553438\pi\)
\(758\) −55.4258 −2.01316
\(759\) −12.7017 −0.461043
\(760\) 7.78986 0.282568
\(761\) 19.7095 0.714468 0.357234 0.934015i \(-0.383720\pi\)
0.357234 + 0.934015i \(0.383720\pi\)
\(762\) 13.8683 0.502396
\(763\) 1.91185 0.0692138
\(764\) 25.2024 0.911790
\(765\) −2.44504 −0.0884007
\(766\) 57.0461 2.06116
\(767\) 0 0
\(768\) 20.7114 0.747358
\(769\) −2.24996 −0.0811358 −0.0405679 0.999177i \(-0.512917\pi\)
−0.0405679 + 0.999177i \(0.512917\pi\)
\(770\) 3.24698 0.117013
\(771\) 24.6329 0.887134
\(772\) −30.3545 −1.09248
\(773\) 41.3080 1.48574 0.742872 0.669433i \(-0.233463\pi\)
0.742872 + 0.669433i \(0.233463\pi\)
\(774\) 14.4155 0.518155
\(775\) 1.78017 0.0639455
\(776\) −7.31873 −0.262727
\(777\) 3.98792 0.143066
\(778\) 34.3260 1.23065
\(779\) −59.3889 −2.12783
\(780\) 0 0
\(781\) −4.33513 −0.155123
\(782\) −31.0562 −1.11057
\(783\) −3.15883 −0.112888
\(784\) −4.93900 −0.176393
\(785\) 0.838773 0.0299371
\(786\) 14.7506 0.526137
\(787\) −38.1702 −1.36062 −0.680310 0.732925i \(-0.738155\pi\)
−0.680310 + 0.732925i \(0.738155\pi\)
\(788\) −1.70709 −0.0608125
\(789\) 17.1588 0.610871
\(790\) −7.42327 −0.264108
\(791\) −7.05429 −0.250822
\(792\) 2.44504 0.0868808
\(793\) 0 0
\(794\) −11.4862 −0.407630
\(795\) 8.92154 0.316415
\(796\) −5.00969 −0.177564
\(797\) 49.7265 1.76140 0.880701 0.473673i \(-0.157072\pi\)
0.880701 + 0.473673i \(0.157072\pi\)
\(798\) 10.3448 0.366202
\(799\) −12.5840 −0.445191
\(800\) −24.7439 −0.874830
\(801\) 2.72587 0.0963140
\(802\) 37.4359 1.32191
\(803\) 1.19806 0.0422787
\(804\) −5.40581 −0.190648
\(805\) 7.04892 0.248442
\(806\) 0 0
\(807\) −7.08708 −0.249477
\(808\) −1.13408 −0.0398968
\(809\) 50.9111 1.78994 0.894970 0.446127i \(-0.147197\pi\)
0.894970 + 0.446127i \(0.147197\pi\)
\(810\) −1.80194 −0.0633136
\(811\) 35.8106 1.25748 0.628739 0.777616i \(-0.283571\pi\)
0.628739 + 0.777616i \(0.283571\pi\)
\(812\) 3.93900 0.138232
\(813\) −24.5483 −0.860945
\(814\) 12.9487 0.453851
\(815\) 12.7409 0.446296
\(816\) 12.0761 0.422747
\(817\) −45.9275 −1.60680
\(818\) −9.88769 −0.345715
\(819\) 0 0
\(820\) −12.8998 −0.450480
\(821\) −16.2457 −0.566977 −0.283489 0.958976i \(-0.591492\pi\)
−0.283489 + 0.958976i \(0.591492\pi\)
\(822\) −15.8485 −0.552779
\(823\) −39.5120 −1.37730 −0.688651 0.725093i \(-0.741797\pi\)
−0.688651 + 0.725093i \(0.741797\pi\)
\(824\) −22.5429 −0.785318
\(825\) −7.20775 −0.250942
\(826\) −17.5036 −0.609030
\(827\) 22.8377 0.794145 0.397072 0.917787i \(-0.370026\pi\)
0.397072 + 0.917787i \(0.370026\pi\)
\(828\) −8.78986 −0.305469
\(829\) −24.1823 −0.839885 −0.419942 0.907551i \(-0.637950\pi\)
−0.419942 + 0.907551i \(0.637950\pi\)
\(830\) −19.9269 −0.691673
\(831\) 33.0810 1.14757
\(832\) 0 0
\(833\) −2.44504 −0.0847157
\(834\) 35.0170 1.21254
\(835\) 13.5646 0.469424
\(836\) 12.8998 0.446148
\(837\) −0.445042 −0.0153829
\(838\) 26.5351 0.916640
\(839\) 5.10082 0.176100 0.0880499 0.996116i \(-0.471937\pi\)
0.0880499 + 0.996116i \(0.471937\pi\)
\(840\) −1.35690 −0.0468174
\(841\) −19.0218 −0.655923
\(842\) −2.95646 −0.101886
\(843\) −26.3163 −0.906383
\(844\) −30.7385 −1.05806
\(845\) 0 0
\(846\) −9.27413 −0.318851
\(847\) 7.75302 0.266397
\(848\) −44.0635 −1.51315
\(849\) 31.7778 1.09061
\(850\) −17.6233 −0.604473
\(851\) 28.1105 0.963616
\(852\) −3.00000 −0.102778
\(853\) 43.0170 1.47287 0.736437 0.676506i \(-0.236507\pi\)
0.736437 + 0.676506i \(0.236507\pi\)
\(854\) −17.9095 −0.612849
\(855\) 5.74094 0.196336
\(856\) 17.7265 0.605878
\(857\) −0.479485 −0.0163789 −0.00818944 0.999966i \(-0.502607\pi\)
−0.00818944 + 0.999966i \(0.502607\pi\)
\(858\) 0 0
\(859\) −23.9627 −0.817596 −0.408798 0.912625i \(-0.634052\pi\)
−0.408798 + 0.912625i \(0.634052\pi\)
\(860\) −9.97584 −0.340173
\(861\) 10.3448 0.352550
\(862\) −12.5114 −0.426141
\(863\) −6.91590 −0.235420 −0.117710 0.993048i \(-0.537555\pi\)
−0.117710 + 0.993048i \(0.537555\pi\)
\(864\) 6.18598 0.210451
\(865\) 7.75733 0.263757
\(866\) 65.2137 2.21605
\(867\) −11.0218 −0.374319
\(868\) 0.554958 0.0188365
\(869\) 7.42327 0.251817
\(870\) 5.69202 0.192978
\(871\) 0 0
\(872\) −2.59419 −0.0878502
\(873\) −5.39373 −0.182550
\(874\) 72.9197 2.46655
\(875\) 9.00000 0.304256
\(876\) 0.829085 0.0280122
\(877\) 32.5153 1.09796 0.548981 0.835835i \(-0.315016\pi\)
0.548981 + 0.835835i \(0.315016\pi\)
\(878\) −15.7855 −0.532736
\(879\) 12.8616 0.433811
\(880\) −8.89977 −0.300011
\(881\) −49.0350 −1.65203 −0.826016 0.563646i \(-0.809398\pi\)
−0.826016 + 0.563646i \(0.809398\pi\)
\(882\) −1.80194 −0.0606744
\(883\) 22.5190 0.757824 0.378912 0.925433i \(-0.376298\pi\)
0.378912 + 0.925433i \(0.376298\pi\)
\(884\) 0 0
\(885\) −9.71379 −0.326526
\(886\) 33.2597 1.11738
\(887\) 55.5889 1.86649 0.933247 0.359236i \(-0.116963\pi\)
0.933247 + 0.359236i \(0.116963\pi\)
\(888\) −5.41119 −0.181588
\(889\) 7.69633 0.258127
\(890\) −4.91185 −0.164646
\(891\) 1.80194 0.0603672
\(892\) −11.7342 −0.392891
\(893\) 29.5472 0.988759
\(894\) 18.9366 0.633335
\(895\) 2.16852 0.0724857
\(896\) 10.0858 0.336941
\(897\) 0 0
\(898\) 62.6988 2.09229
\(899\) 1.40581 0.0468865
\(900\) −4.98792 −0.166264
\(901\) −21.8135 −0.726715
\(902\) 33.5894 1.11840
\(903\) 8.00000 0.266223
\(904\) 9.57194 0.318358
\(905\) −2.52781 −0.0840273
\(906\) −37.7972 −1.25573
\(907\) −0.801938 −0.0266279 −0.0133140 0.999911i \(-0.504238\pi\)
−0.0133140 + 0.999911i \(0.504238\pi\)
\(908\) 6.65279 0.220781
\(909\) −0.835790 −0.0277214
\(910\) 0 0
\(911\) 11.2131 0.371507 0.185754 0.982596i \(-0.440527\pi\)
0.185754 + 0.982596i \(0.440527\pi\)
\(912\) −28.3545 −0.938911
\(913\) 19.9269 0.659485
\(914\) 41.9245 1.38674
\(915\) −9.93900 −0.328573
\(916\) 11.3854 0.376183
\(917\) 8.18598 0.270325
\(918\) 4.40581 0.145414
\(919\) −15.1226 −0.498848 −0.249424 0.968394i \(-0.580241\pi\)
−0.249424 + 0.968394i \(0.580241\pi\)
\(920\) −9.56465 −0.315337
\(921\) −29.5937 −0.975146
\(922\) −59.2301 −1.95064
\(923\) 0 0
\(924\) −2.24698 −0.0739202
\(925\) 15.9517 0.524488
\(926\) 40.7265 1.33835
\(927\) −16.6136 −0.545661
\(928\) −19.5405 −0.641448
\(929\) 17.7573 0.582599 0.291300 0.956632i \(-0.405912\pi\)
0.291300 + 0.956632i \(0.405912\pi\)
\(930\) 0.801938 0.0262966
\(931\) 5.74094 0.188152
\(932\) −33.3274 −1.09167
\(933\) −8.55794 −0.280174
\(934\) 22.5036 0.736342
\(935\) −4.40581 −0.144085
\(936\) 0 0
\(937\) −46.0170 −1.50331 −0.751655 0.659557i \(-0.770744\pi\)
−0.751655 + 0.659557i \(0.770744\pi\)
\(938\) −7.81163 −0.255059
\(939\) −16.3569 −0.533787
\(940\) 6.41789 0.209329
\(941\) −13.9685 −0.455361 −0.227681 0.973736i \(-0.573114\pi\)
−0.227681 + 0.973736i \(0.573114\pi\)
\(942\) −1.51142 −0.0492446
\(943\) 72.9197 2.37459
\(944\) 47.9764 1.56150
\(945\) −1.00000 −0.0325300
\(946\) 25.9758 0.844547
\(947\) −0.994623 −0.0323209 −0.0161605 0.999869i \(-0.505144\pi\)
−0.0161605 + 0.999869i \(0.505144\pi\)
\(948\) 5.13706 0.166844
\(949\) 0 0
\(950\) 41.3793 1.34252
\(951\) 28.3545 0.919458
\(952\) 3.31767 0.107526
\(953\) 23.5937 0.764275 0.382138 0.924105i \(-0.375188\pi\)
0.382138 + 0.924105i \(0.375188\pi\)
\(954\) −16.0761 −0.520482
\(955\) 20.2107 0.654004
\(956\) −10.1400 −0.327953
\(957\) −5.69202 −0.183997
\(958\) −24.4228 −0.789065
\(959\) −8.79523 −0.284013
\(960\) −1.26875 −0.0409487
\(961\) −30.8019 −0.993611
\(962\) 0 0
\(963\) 13.0640 0.420981
\(964\) 9.53750 0.307182
\(965\) −24.3424 −0.783610
\(966\) −12.7017 −0.408671
\(967\) 50.4228 1.62149 0.810744 0.585401i \(-0.199063\pi\)
0.810744 + 0.585401i \(0.199063\pi\)
\(968\) −10.5200 −0.338127
\(969\) −14.0368 −0.450928
\(970\) 9.71917 0.312064
\(971\) 1.06770 0.0342642 0.0171321 0.999853i \(-0.494546\pi\)
0.0171321 + 0.999853i \(0.494546\pi\)
\(972\) 1.24698 0.0399969
\(973\) 19.4330 0.622992
\(974\) 26.9235 0.862683
\(975\) 0 0
\(976\) 49.0887 1.57129
\(977\) 4.03444 0.129073 0.0645366 0.997915i \(-0.479443\pi\)
0.0645366 + 0.997915i \(0.479443\pi\)
\(978\) −22.9584 −0.734128
\(979\) 4.91185 0.156984
\(980\) 1.24698 0.0398333
\(981\) −1.91185 −0.0610408
\(982\) −49.5284 −1.58051
\(983\) −33.6534 −1.07338 −0.536688 0.843781i \(-0.680325\pi\)
−0.536688 + 0.843781i \(0.680325\pi\)
\(984\) −14.0368 −0.447478
\(985\) −1.36898 −0.0436192
\(986\) −13.9172 −0.443215
\(987\) −5.14675 −0.163823
\(988\) 0 0
\(989\) 56.3913 1.79314
\(990\) −3.24698 −0.103196
\(991\) 33.3739 1.06016 0.530078 0.847949i \(-0.322163\pi\)
0.530078 + 0.847949i \(0.322163\pi\)
\(992\) −2.75302 −0.0874085
\(993\) −11.3894 −0.361432
\(994\) −4.33513 −0.137502
\(995\) −4.01746 −0.127362
\(996\) 13.7899 0.436948
\(997\) 54.4172 1.72341 0.861704 0.507411i \(-0.169397\pi\)
0.861704 + 0.507411i \(0.169397\pi\)
\(998\) 32.2107 1.01961
\(999\) −3.98792 −0.126172
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 3549.2.a.j.1.1 3
13.12 even 2 3549.2.a.p.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.j.1.1 3 1.1 even 1 trivial
3549.2.a.p.1.3 yes 3 13.12 even 2