Properties

Label 5225.2.a.m.1.3
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $7$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(0.745312\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.745312 q^{2} +2.05058 q^{3} -1.44451 q^{4} -1.52832 q^{6} +3.86782 q^{7} +2.56724 q^{8} +1.20489 q^{9} +O(q^{10})\) \(q-0.745312 q^{2} +2.05058 q^{3} -1.44451 q^{4} -1.52832 q^{6} +3.86782 q^{7} +2.56724 q^{8} +1.20489 q^{9} +1.00000 q^{11} -2.96208 q^{12} +2.04430 q^{13} -2.88274 q^{14} +0.975626 q^{16} +3.70255 q^{17} -0.898017 q^{18} -1.00000 q^{19} +7.93129 q^{21} -0.745312 q^{22} -2.09412 q^{23} +5.26433 q^{24} -1.52364 q^{26} -3.68103 q^{27} -5.58711 q^{28} -1.56558 q^{29} +5.38850 q^{31} -5.86162 q^{32} +2.05058 q^{33} -2.75956 q^{34} -1.74047 q^{36} +7.65441 q^{37} +0.745312 q^{38} +4.19200 q^{39} +2.55527 q^{41} -5.91129 q^{42} -1.43588 q^{43} -1.44451 q^{44} +1.56077 q^{46} +5.29091 q^{47} +2.00060 q^{48} +7.96005 q^{49} +7.59239 q^{51} -2.95301 q^{52} -2.10441 q^{53} +2.74352 q^{54} +9.92961 q^{56} -2.05058 q^{57} +1.16685 q^{58} +0.643913 q^{59} +14.3858 q^{61} -4.01612 q^{62} +4.66029 q^{63} +2.41748 q^{64} -1.52832 q^{66} +7.38466 q^{67} -5.34837 q^{68} -4.29417 q^{69} -3.12919 q^{71} +3.09323 q^{72} -6.41053 q^{73} -5.70492 q^{74} +1.44451 q^{76} +3.86782 q^{77} -3.12435 q^{78} -3.06249 q^{79} -11.1629 q^{81} -1.90448 q^{82} -6.28445 q^{83} -11.4568 q^{84} +1.07018 q^{86} -3.21035 q^{87} +2.56724 q^{88} -1.85225 q^{89} +7.90699 q^{91} +3.02498 q^{92} +11.0496 q^{93} -3.94338 q^{94} -12.0197 q^{96} -6.58248 q^{97} -5.93273 q^{98} +1.20489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9} + 7 q^{11} - 13 q^{12} - q^{13} + 12 q^{14} + 3 q^{16} - q^{17} - 7 q^{18} - 7 q^{19} + 5 q^{21} - q^{22} + 8 q^{23} + 25 q^{24} - 12 q^{27} - 4 q^{28} + 11 q^{29} + 7 q^{31} - 12 q^{32} - 3 q^{33} - 14 q^{34} + 7 q^{36} + 17 q^{37} + q^{38} + 30 q^{39} + 17 q^{41} - 33 q^{42} + 3 q^{43} + 7 q^{44} + 18 q^{46} - 14 q^{47} + 12 q^{48} + 6 q^{49} + 8 q^{51} + 17 q^{52} - 7 q^{53} - 27 q^{54} + 36 q^{56} + 3 q^{57} + 15 q^{58} + 35 q^{59} + 17 q^{61} - 46 q^{62} + 22 q^{63} + 5 q^{64} + 8 q^{66} - 4 q^{67} + 35 q^{68} - 4 q^{69} + 10 q^{71} - 12 q^{72} - 22 q^{73} - 11 q^{74} - 7 q^{76} + q^{77} + 41 q^{78} + 11 q^{79} - 21 q^{81} + 14 q^{82} - 39 q^{83} + 21 q^{84} - 24 q^{86} + 2 q^{87} - 3 q^{88} + 18 q^{89} - 22 q^{91} + 51 q^{92} - 10 q^{93} + 14 q^{94} - 11 q^{96} + 4 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.745312 −0.527015 −0.263508 0.964657i \(-0.584879\pi\)
−0.263508 + 0.964657i \(0.584879\pi\)
\(3\) 2.05058 1.18390 0.591952 0.805973i \(-0.298357\pi\)
0.591952 + 0.805973i \(0.298357\pi\)
\(4\) −1.44451 −0.722255
\(5\) 0 0
\(6\) −1.52832 −0.623936
\(7\) 3.86782 1.46190 0.730950 0.682431i \(-0.239077\pi\)
0.730950 + 0.682431i \(0.239077\pi\)
\(8\) 2.56724 0.907655
\(9\) 1.20489 0.401629
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −2.96208 −0.855080
\(13\) 2.04430 0.566987 0.283493 0.958974i \(-0.408507\pi\)
0.283493 + 0.958974i \(0.408507\pi\)
\(14\) −2.88274 −0.770444
\(15\) 0 0
\(16\) 0.975626 0.243907
\(17\) 3.70255 0.898001 0.449001 0.893531i \(-0.351780\pi\)
0.449001 + 0.893531i \(0.351780\pi\)
\(18\) −0.898017 −0.211665
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 7.93129 1.73075
\(22\) −0.745312 −0.158901
\(23\) −2.09412 −0.436654 −0.218327 0.975876i \(-0.570060\pi\)
−0.218327 + 0.975876i \(0.570060\pi\)
\(24\) 5.26433 1.07458
\(25\) 0 0
\(26\) −1.52364 −0.298811
\(27\) −3.68103 −0.708414
\(28\) −5.58711 −1.05586
\(29\) −1.56558 −0.290721 −0.145361 0.989379i \(-0.546434\pi\)
−0.145361 + 0.989379i \(0.546434\pi\)
\(30\) 0 0
\(31\) 5.38850 0.967804 0.483902 0.875122i \(-0.339219\pi\)
0.483902 + 0.875122i \(0.339219\pi\)
\(32\) −5.86162 −1.03620
\(33\) 2.05058 0.356960
\(34\) −2.75956 −0.473261
\(35\) 0 0
\(36\) −1.74047 −0.290078
\(37\) 7.65441 1.25838 0.629188 0.777253i \(-0.283387\pi\)
0.629188 + 0.777253i \(0.283387\pi\)
\(38\) 0.745312 0.120906
\(39\) 4.19200 0.671258
\(40\) 0 0
\(41\) 2.55527 0.399067 0.199533 0.979891i \(-0.436057\pi\)
0.199533 + 0.979891i \(0.436057\pi\)
\(42\) −5.91129 −0.912131
\(43\) −1.43588 −0.218969 −0.109485 0.993988i \(-0.534920\pi\)
−0.109485 + 0.993988i \(0.534920\pi\)
\(44\) −1.44451 −0.217768
\(45\) 0 0
\(46\) 1.56077 0.230124
\(47\) 5.29091 0.771758 0.385879 0.922549i \(-0.373898\pi\)
0.385879 + 0.922549i \(0.373898\pi\)
\(48\) 2.00060 0.288762
\(49\) 7.96005 1.13715
\(50\) 0 0
\(51\) 7.59239 1.06315
\(52\) −2.95301 −0.409509
\(53\) −2.10441 −0.289063 −0.144531 0.989500i \(-0.546167\pi\)
−0.144531 + 0.989500i \(0.546167\pi\)
\(54\) 2.74352 0.373345
\(55\) 0 0
\(56\) 9.92961 1.32690
\(57\) −2.05058 −0.271606
\(58\) 1.16685 0.153214
\(59\) 0.643913 0.0838303 0.0419152 0.999121i \(-0.486654\pi\)
0.0419152 + 0.999121i \(0.486654\pi\)
\(60\) 0 0
\(61\) 14.3858 1.84191 0.920957 0.389664i \(-0.127409\pi\)
0.920957 + 0.389664i \(0.127409\pi\)
\(62\) −4.01612 −0.510047
\(63\) 4.66029 0.587141
\(64\) 2.41748 0.302186
\(65\) 0 0
\(66\) −1.52832 −0.188124
\(67\) 7.38466 0.902179 0.451090 0.892479i \(-0.351035\pi\)
0.451090 + 0.892479i \(0.351035\pi\)
\(68\) −5.34837 −0.648586
\(69\) −4.29417 −0.516957
\(70\) 0 0
\(71\) −3.12919 −0.371366 −0.185683 0.982610i \(-0.559450\pi\)
−0.185683 + 0.982610i \(0.559450\pi\)
\(72\) 3.09323 0.364540
\(73\) −6.41053 −0.750296 −0.375148 0.926965i \(-0.622408\pi\)
−0.375148 + 0.926965i \(0.622408\pi\)
\(74\) −5.70492 −0.663184
\(75\) 0 0
\(76\) 1.44451 0.165697
\(77\) 3.86782 0.440779
\(78\) −3.12435 −0.353763
\(79\) −3.06249 −0.344557 −0.172278 0.985048i \(-0.555113\pi\)
−0.172278 + 0.985048i \(0.555113\pi\)
\(80\) 0 0
\(81\) −11.1629 −1.24032
\(82\) −1.90448 −0.210314
\(83\) −6.28445 −0.689808 −0.344904 0.938638i \(-0.612089\pi\)
−0.344904 + 0.938638i \(0.612089\pi\)
\(84\) −11.4568 −1.25004
\(85\) 0 0
\(86\) 1.07018 0.115400
\(87\) −3.21035 −0.344186
\(88\) 2.56724 0.273668
\(89\) −1.85225 −0.196338 −0.0981691 0.995170i \(-0.531299\pi\)
−0.0981691 + 0.995170i \(0.531299\pi\)
\(90\) 0 0
\(91\) 7.90699 0.828878
\(92\) 3.02498 0.315376
\(93\) 11.0496 1.14579
\(94\) −3.94338 −0.406729
\(95\) 0 0
\(96\) −12.0197 −1.22676
\(97\) −6.58248 −0.668349 −0.334175 0.942511i \(-0.608458\pi\)
−0.334175 + 0.942511i \(0.608458\pi\)
\(98\) −5.93273 −0.599296
\(99\) 1.20489 0.121096
\(100\) 0 0
\(101\) −13.7356 −1.36674 −0.683372 0.730070i \(-0.739487\pi\)
−0.683372 + 0.730070i \(0.739487\pi\)
\(102\) −5.65870 −0.560295
\(103\) 6.59626 0.649949 0.324975 0.945723i \(-0.394644\pi\)
0.324975 + 0.945723i \(0.394644\pi\)
\(104\) 5.24820 0.514628
\(105\) 0 0
\(106\) 1.56844 0.152341
\(107\) −7.49964 −0.725018 −0.362509 0.931980i \(-0.618080\pi\)
−0.362509 + 0.931980i \(0.618080\pi\)
\(108\) 5.31728 0.511655
\(109\) −12.0403 −1.15325 −0.576624 0.817010i \(-0.695630\pi\)
−0.576624 + 0.817010i \(0.695630\pi\)
\(110\) 0 0
\(111\) 15.6960 1.48980
\(112\) 3.77355 0.356567
\(113\) 11.8491 1.11467 0.557333 0.830289i \(-0.311825\pi\)
0.557333 + 0.830289i \(0.311825\pi\)
\(114\) 1.52832 0.143141
\(115\) 0 0
\(116\) 2.26150 0.209975
\(117\) 2.46315 0.227718
\(118\) −0.479916 −0.0441799
\(119\) 14.3208 1.31279
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −10.7219 −0.970717
\(123\) 5.23980 0.472457
\(124\) −7.78374 −0.699001
\(125\) 0 0
\(126\) −3.47337 −0.309432
\(127\) −12.8805 −1.14296 −0.571479 0.820617i \(-0.693630\pi\)
−0.571479 + 0.820617i \(0.693630\pi\)
\(128\) 9.92145 0.876941
\(129\) −2.94439 −0.259239
\(130\) 0 0
\(131\) 14.3038 1.24973 0.624865 0.780733i \(-0.285154\pi\)
0.624865 + 0.780733i \(0.285154\pi\)
\(132\) −2.96208 −0.257816
\(133\) −3.86782 −0.335383
\(134\) −5.50388 −0.475462
\(135\) 0 0
\(136\) 9.50533 0.815075
\(137\) 15.1224 1.29200 0.645998 0.763339i \(-0.276442\pi\)
0.645998 + 0.763339i \(0.276442\pi\)
\(138\) 3.20050 0.272444
\(139\) 9.76738 0.828458 0.414229 0.910173i \(-0.364051\pi\)
0.414229 + 0.910173i \(0.364051\pi\)
\(140\) 0 0
\(141\) 10.8494 0.913688
\(142\) 2.33222 0.195716
\(143\) 2.04430 0.170953
\(144\) 1.17552 0.0979599
\(145\) 0 0
\(146\) 4.77785 0.395418
\(147\) 16.3227 1.34628
\(148\) −11.0569 −0.908869
\(149\) −14.1604 −1.16007 −0.580034 0.814592i \(-0.696961\pi\)
−0.580034 + 0.814592i \(0.696961\pi\)
\(150\) 0 0
\(151\) 18.0003 1.46484 0.732420 0.680853i \(-0.238391\pi\)
0.732420 + 0.680853i \(0.238391\pi\)
\(152\) −2.56724 −0.208230
\(153\) 4.46116 0.360663
\(154\) −2.88274 −0.232298
\(155\) 0 0
\(156\) −6.05539 −0.484819
\(157\) −2.90903 −0.232166 −0.116083 0.993240i \(-0.537034\pi\)
−0.116083 + 0.993240i \(0.537034\pi\)
\(158\) 2.28251 0.181587
\(159\) −4.31526 −0.342223
\(160\) 0 0
\(161\) −8.09969 −0.638345
\(162\) 8.31985 0.653669
\(163\) −9.73587 −0.762572 −0.381286 0.924457i \(-0.624519\pi\)
−0.381286 + 0.924457i \(0.624519\pi\)
\(164\) −3.69112 −0.288228
\(165\) 0 0
\(166\) 4.68388 0.363539
\(167\) −22.9362 −1.77486 −0.887430 0.460943i \(-0.847511\pi\)
−0.887430 + 0.460943i \(0.847511\pi\)
\(168\) 20.3615 1.57092
\(169\) −8.82084 −0.678526
\(170\) 0 0
\(171\) −1.20489 −0.0921399
\(172\) 2.07414 0.158152
\(173\) 5.44966 0.414330 0.207165 0.978306i \(-0.433576\pi\)
0.207165 + 0.978306i \(0.433576\pi\)
\(174\) 2.39271 0.181391
\(175\) 0 0
\(176\) 0.975626 0.0735406
\(177\) 1.32040 0.0992471
\(178\) 1.38051 0.103473
\(179\) 17.7565 1.32718 0.663590 0.748096i \(-0.269032\pi\)
0.663590 + 0.748096i \(0.269032\pi\)
\(180\) 0 0
\(181\) −22.0588 −1.63962 −0.819810 0.572636i \(-0.805921\pi\)
−0.819810 + 0.572636i \(0.805921\pi\)
\(182\) −5.89318 −0.436831
\(183\) 29.4993 2.18065
\(184\) −5.37610 −0.396331
\(185\) 0 0
\(186\) −8.23538 −0.603847
\(187\) 3.70255 0.270758
\(188\) −7.64277 −0.557406
\(189\) −14.2376 −1.03563
\(190\) 0 0
\(191\) 12.6095 0.912390 0.456195 0.889880i \(-0.349212\pi\)
0.456195 + 0.889880i \(0.349212\pi\)
\(192\) 4.95725 0.357759
\(193\) 8.37178 0.602614 0.301307 0.953527i \(-0.402577\pi\)
0.301307 + 0.953527i \(0.402577\pi\)
\(194\) 4.90600 0.352230
\(195\) 0 0
\(196\) −11.4984 −0.821312
\(197\) −9.63861 −0.686722 −0.343361 0.939203i \(-0.611565\pi\)
−0.343361 + 0.939203i \(0.611565\pi\)
\(198\) −0.898017 −0.0638193
\(199\) −17.1167 −1.21337 −0.606684 0.794943i \(-0.707501\pi\)
−0.606684 + 0.794943i \(0.707501\pi\)
\(200\) 0 0
\(201\) 15.1428 1.06809
\(202\) 10.2373 0.720295
\(203\) −6.05539 −0.425005
\(204\) −10.9673 −0.767863
\(205\) 0 0
\(206\) −4.91628 −0.342533
\(207\) −2.52318 −0.175373
\(208\) 1.99447 0.138292
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −0.310300 −0.0213619 −0.0106810 0.999943i \(-0.503400\pi\)
−0.0106810 + 0.999943i \(0.503400\pi\)
\(212\) 3.03984 0.208777
\(213\) −6.41666 −0.439662
\(214\) 5.58958 0.382096
\(215\) 0 0
\(216\) −9.45007 −0.642996
\(217\) 20.8418 1.41483
\(218\) 8.97375 0.607779
\(219\) −13.1453 −0.888279
\(220\) 0 0
\(221\) 7.56913 0.509155
\(222\) −11.6984 −0.785146
\(223\) 3.81396 0.255402 0.127701 0.991813i \(-0.459240\pi\)
0.127701 + 0.991813i \(0.459240\pi\)
\(224\) −22.6717 −1.51482
\(225\) 0 0
\(226\) −8.83126 −0.587447
\(227\) 17.7004 1.17482 0.587410 0.809290i \(-0.300148\pi\)
0.587410 + 0.809290i \(0.300148\pi\)
\(228\) 2.96208 0.196169
\(229\) 27.1634 1.79501 0.897505 0.441004i \(-0.145378\pi\)
0.897505 + 0.441004i \(0.145378\pi\)
\(230\) 0 0
\(231\) 7.93129 0.521840
\(232\) −4.01921 −0.263874
\(233\) −0.550837 −0.0360865 −0.0180433 0.999837i \(-0.505744\pi\)
−0.0180433 + 0.999837i \(0.505744\pi\)
\(234\) −1.83581 −0.120011
\(235\) 0 0
\(236\) −0.930138 −0.0605469
\(237\) −6.27988 −0.407922
\(238\) −10.6735 −0.691859
\(239\) −5.37952 −0.347972 −0.173986 0.984748i \(-0.555665\pi\)
−0.173986 + 0.984748i \(0.555665\pi\)
\(240\) 0 0
\(241\) 22.5371 1.45174 0.725872 0.687830i \(-0.241437\pi\)
0.725872 + 0.687830i \(0.241437\pi\)
\(242\) −0.745312 −0.0479105
\(243\) −11.8474 −0.760009
\(244\) −20.7804 −1.33033
\(245\) 0 0
\(246\) −3.90529 −0.248992
\(247\) −2.04430 −0.130076
\(248\) 13.8336 0.878432
\(249\) −12.8868 −0.816666
\(250\) 0 0
\(251\) 7.58349 0.478665 0.239333 0.970938i \(-0.423071\pi\)
0.239333 + 0.970938i \(0.423071\pi\)
\(252\) −6.73183 −0.424065
\(253\) −2.09412 −0.131656
\(254\) 9.59998 0.602356
\(255\) 0 0
\(256\) −12.2296 −0.764347
\(257\) −13.6317 −0.850320 −0.425160 0.905118i \(-0.639782\pi\)
−0.425160 + 0.905118i \(0.639782\pi\)
\(258\) 2.19449 0.136623
\(259\) 29.6059 1.83962
\(260\) 0 0
\(261\) −1.88635 −0.116762
\(262\) −10.6608 −0.658627
\(263\) 4.03027 0.248517 0.124259 0.992250i \(-0.460345\pi\)
0.124259 + 0.992250i \(0.460345\pi\)
\(264\) 5.26433 0.323997
\(265\) 0 0
\(266\) 2.88274 0.176752
\(267\) −3.79819 −0.232446
\(268\) −10.6672 −0.651603
\(269\) 26.6319 1.62378 0.811889 0.583812i \(-0.198439\pi\)
0.811889 + 0.583812i \(0.198439\pi\)
\(270\) 0 0
\(271\) 22.3349 1.35675 0.678375 0.734716i \(-0.262685\pi\)
0.678375 + 0.734716i \(0.262685\pi\)
\(272\) 3.61231 0.219028
\(273\) 16.2139 0.981311
\(274\) −11.2709 −0.680901
\(275\) 0 0
\(276\) 6.20296 0.373374
\(277\) 22.6811 1.36277 0.681387 0.731923i \(-0.261377\pi\)
0.681387 + 0.731923i \(0.261377\pi\)
\(278\) −7.27975 −0.436610
\(279\) 6.49253 0.388698
\(280\) 0 0
\(281\) 22.0886 1.31770 0.658848 0.752276i \(-0.271044\pi\)
0.658848 + 0.752276i \(0.271044\pi\)
\(282\) −8.08622 −0.481528
\(283\) 17.4483 1.03719 0.518597 0.855019i \(-0.326454\pi\)
0.518597 + 0.855019i \(0.326454\pi\)
\(284\) 4.52014 0.268221
\(285\) 0 0
\(286\) −1.52364 −0.0900948
\(287\) 9.88335 0.583396
\(288\) −7.06258 −0.416167
\(289\) −3.29109 −0.193594
\(290\) 0 0
\(291\) −13.4979 −0.791261
\(292\) 9.26007 0.541905
\(293\) −17.0451 −0.995785 −0.497892 0.867239i \(-0.665893\pi\)
−0.497892 + 0.867239i \(0.665893\pi\)
\(294\) −12.1655 −0.709509
\(295\) 0 0
\(296\) 19.6507 1.14217
\(297\) −3.68103 −0.213595
\(298\) 10.5539 0.611374
\(299\) −4.28101 −0.247577
\(300\) 0 0
\(301\) −5.55372 −0.320111
\(302\) −13.4158 −0.771993
\(303\) −28.1660 −1.61809
\(304\) −0.975626 −0.0559560
\(305\) 0 0
\(306\) −3.32495 −0.190075
\(307\) 9.52713 0.543742 0.271871 0.962334i \(-0.412358\pi\)
0.271871 + 0.962334i \(0.412358\pi\)
\(308\) −5.58711 −0.318355
\(309\) 13.5262 0.769477
\(310\) 0 0
\(311\) −25.1706 −1.42730 −0.713648 0.700505i \(-0.752958\pi\)
−0.713648 + 0.700505i \(0.752958\pi\)
\(312\) 10.7619 0.609270
\(313\) 8.19113 0.462990 0.231495 0.972836i \(-0.425638\pi\)
0.231495 + 0.972836i \(0.425638\pi\)
\(314\) 2.16813 0.122355
\(315\) 0 0
\(316\) 4.42379 0.248858
\(317\) −20.9949 −1.17919 −0.589596 0.807699i \(-0.700713\pi\)
−0.589596 + 0.807699i \(0.700713\pi\)
\(318\) 3.21622 0.180357
\(319\) −1.56558 −0.0876557
\(320\) 0 0
\(321\) −15.3786 −0.858351
\(322\) 6.03680 0.336418
\(323\) −3.70255 −0.206016
\(324\) 16.1249 0.895829
\(325\) 0 0
\(326\) 7.25627 0.401887
\(327\) −24.6895 −1.36533
\(328\) 6.55999 0.362215
\(329\) 20.4643 1.12823
\(330\) 0 0
\(331\) 3.28061 0.180319 0.0901594 0.995927i \(-0.471262\pi\)
0.0901594 + 0.995927i \(0.471262\pi\)
\(332\) 9.07795 0.498217
\(333\) 9.22269 0.505400
\(334\) 17.0947 0.935378
\(335\) 0 0
\(336\) 7.73797 0.422141
\(337\) 18.4493 1.00500 0.502499 0.864578i \(-0.332414\pi\)
0.502499 + 0.864578i \(0.332414\pi\)
\(338\) 6.57428 0.357594
\(339\) 24.2975 1.31966
\(340\) 0 0
\(341\) 5.38850 0.291804
\(342\) 0.898017 0.0485592
\(343\) 3.71331 0.200500
\(344\) −3.68624 −0.198749
\(345\) 0 0
\(346\) −4.06170 −0.218358
\(347\) −29.8792 −1.60400 −0.801999 0.597325i \(-0.796230\pi\)
−0.801999 + 0.597325i \(0.796230\pi\)
\(348\) 4.63738 0.248590
\(349\) 27.5340 1.47386 0.736932 0.675967i \(-0.236274\pi\)
0.736932 + 0.675967i \(0.236274\pi\)
\(350\) 0 0
\(351\) −7.52512 −0.401661
\(352\) −5.86162 −0.312425
\(353\) −3.83620 −0.204180 −0.102090 0.994775i \(-0.532553\pi\)
−0.102090 + 0.994775i \(0.532553\pi\)
\(354\) −0.984108 −0.0523047
\(355\) 0 0
\(356\) 2.67559 0.141806
\(357\) 29.3660 1.55421
\(358\) −13.2341 −0.699445
\(359\) 32.7643 1.72923 0.864617 0.502432i \(-0.167561\pi\)
0.864617 + 0.502432i \(0.167561\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 16.4407 0.864105
\(363\) 2.05058 0.107628
\(364\) −11.4217 −0.598661
\(365\) 0 0
\(366\) −21.9862 −1.14924
\(367\) −21.0340 −1.09797 −0.548983 0.835833i \(-0.684985\pi\)
−0.548983 + 0.835833i \(0.684985\pi\)
\(368\) −2.04308 −0.106503
\(369\) 3.07881 0.160277
\(370\) 0 0
\(371\) −8.13948 −0.422581
\(372\) −15.9612 −0.827550
\(373\) −2.07953 −0.107674 −0.0538371 0.998550i \(-0.517145\pi\)
−0.0538371 + 0.998550i \(0.517145\pi\)
\(374\) −2.75956 −0.142693
\(375\) 0 0
\(376\) 13.5830 0.700490
\(377\) −3.20052 −0.164835
\(378\) 10.6114 0.545793
\(379\) 30.7796 1.58104 0.790520 0.612436i \(-0.209810\pi\)
0.790520 + 0.612436i \(0.209810\pi\)
\(380\) 0 0
\(381\) −26.4125 −1.35315
\(382\) −9.39800 −0.480843
\(383\) 0.0147152 0.000751912 0 0.000375956 1.00000i \(-0.499880\pi\)
0.000375956 1.00000i \(0.499880\pi\)
\(384\) 20.3448 1.03821
\(385\) 0 0
\(386\) −6.23959 −0.317587
\(387\) −1.73007 −0.0879444
\(388\) 9.50845 0.482718
\(389\) −22.9201 −1.16209 −0.581047 0.813870i \(-0.697357\pi\)
−0.581047 + 0.813870i \(0.697357\pi\)
\(390\) 0 0
\(391\) −7.75359 −0.392116
\(392\) 20.4353 1.03214
\(393\) 29.3311 1.47956
\(394\) 7.18377 0.361913
\(395\) 0 0
\(396\) −1.74047 −0.0874619
\(397\) 17.6494 0.885800 0.442900 0.896571i \(-0.353950\pi\)
0.442900 + 0.896571i \(0.353950\pi\)
\(398\) 12.7573 0.639463
\(399\) −7.93129 −0.397061
\(400\) 0 0
\(401\) −18.7621 −0.936934 −0.468467 0.883481i \(-0.655193\pi\)
−0.468467 + 0.883481i \(0.655193\pi\)
\(402\) −11.2861 −0.562902
\(403\) 11.0157 0.548732
\(404\) 19.8412 0.987137
\(405\) 0 0
\(406\) 4.51316 0.223984
\(407\) 7.65441 0.379415
\(408\) 19.4915 0.964971
\(409\) −15.7447 −0.778524 −0.389262 0.921127i \(-0.627270\pi\)
−0.389262 + 0.921127i \(0.627270\pi\)
\(410\) 0 0
\(411\) 31.0097 1.52960
\(412\) −9.52837 −0.469429
\(413\) 2.49054 0.122552
\(414\) 1.88055 0.0924242
\(415\) 0 0
\(416\) −11.9829 −0.587510
\(417\) 20.0288 0.980815
\(418\) 0.745312 0.0364544
\(419\) 25.7072 1.25588 0.627938 0.778263i \(-0.283899\pi\)
0.627938 + 0.778263i \(0.283899\pi\)
\(420\) 0 0
\(421\) −17.2694 −0.841657 −0.420828 0.907140i \(-0.638261\pi\)
−0.420828 + 0.907140i \(0.638261\pi\)
\(422\) 0.231271 0.0112581
\(423\) 6.37494 0.309960
\(424\) −5.40252 −0.262369
\(425\) 0 0
\(426\) 4.78241 0.231709
\(427\) 55.6418 2.69269
\(428\) 10.8333 0.523647
\(429\) 4.19200 0.202392
\(430\) 0 0
\(431\) −2.81774 −0.135726 −0.0678628 0.997695i \(-0.521618\pi\)
−0.0678628 + 0.997695i \(0.521618\pi\)
\(432\) −3.59131 −0.172787
\(433\) −8.85731 −0.425655 −0.212828 0.977090i \(-0.568267\pi\)
−0.212828 + 0.977090i \(0.568267\pi\)
\(434\) −15.5336 −0.745638
\(435\) 0 0
\(436\) 17.3923 0.832939
\(437\) 2.09412 0.100175
\(438\) 9.79737 0.468137
\(439\) −9.71132 −0.463496 −0.231748 0.972776i \(-0.574444\pi\)
−0.231748 + 0.972776i \(0.574444\pi\)
\(440\) 0 0
\(441\) 9.59096 0.456712
\(442\) −5.64137 −0.268332
\(443\) −28.3968 −1.34917 −0.674586 0.738196i \(-0.735678\pi\)
−0.674586 + 0.738196i \(0.735678\pi\)
\(444\) −22.6730 −1.07601
\(445\) 0 0
\(446\) −2.84259 −0.134601
\(447\) −29.0371 −1.37341
\(448\) 9.35040 0.441765
\(449\) 34.9628 1.65000 0.824998 0.565136i \(-0.191176\pi\)
0.824998 + 0.565136i \(0.191176\pi\)
\(450\) 0 0
\(451\) 2.55527 0.120323
\(452\) −17.1161 −0.805073
\(453\) 36.9110 1.73423
\(454\) −13.1924 −0.619148
\(455\) 0 0
\(456\) −5.26433 −0.246525
\(457\) −38.6808 −1.80941 −0.904705 0.426039i \(-0.859909\pi\)
−0.904705 + 0.426039i \(0.859909\pi\)
\(458\) −20.2452 −0.945998
\(459\) −13.6292 −0.636157
\(460\) 0 0
\(461\) −19.6046 −0.913078 −0.456539 0.889703i \(-0.650911\pi\)
−0.456539 + 0.889703i \(0.650911\pi\)
\(462\) −5.91129 −0.275018
\(463\) 3.18393 0.147970 0.0739850 0.997259i \(-0.476428\pi\)
0.0739850 + 0.997259i \(0.476428\pi\)
\(464\) −1.52742 −0.0709088
\(465\) 0 0
\(466\) 0.410545 0.0190182
\(467\) −28.7840 −1.33197 −0.665983 0.745967i \(-0.731988\pi\)
−0.665983 + 0.745967i \(0.731988\pi\)
\(468\) −3.55804 −0.164470
\(469\) 28.5625 1.31890
\(470\) 0 0
\(471\) −5.96520 −0.274862
\(472\) 1.65308 0.0760890
\(473\) −1.43588 −0.0660217
\(474\) 4.68047 0.214981
\(475\) 0 0
\(476\) −20.6866 −0.948167
\(477\) −2.53557 −0.116096
\(478\) 4.00942 0.183387
\(479\) 9.57656 0.437564 0.218782 0.975774i \(-0.429792\pi\)
0.218782 + 0.975774i \(0.429792\pi\)
\(480\) 0 0
\(481\) 15.6479 0.713483
\(482\) −16.7972 −0.765091
\(483\) −16.6091 −0.755739
\(484\) −1.44451 −0.0656595
\(485\) 0 0
\(486\) 8.82999 0.400537
\(487\) 32.8807 1.48997 0.744984 0.667083i \(-0.232457\pi\)
0.744984 + 0.667083i \(0.232457\pi\)
\(488\) 36.9318 1.67182
\(489\) −19.9642 −0.902812
\(490\) 0 0
\(491\) 4.43763 0.200267 0.100134 0.994974i \(-0.468073\pi\)
0.100134 + 0.994974i \(0.468073\pi\)
\(492\) −7.56894 −0.341234
\(493\) −5.79665 −0.261068
\(494\) 1.52364 0.0685519
\(495\) 0 0
\(496\) 5.25716 0.236054
\(497\) −12.1031 −0.542900
\(498\) 9.60468 0.430396
\(499\) −18.3904 −0.823266 −0.411633 0.911350i \(-0.635041\pi\)
−0.411633 + 0.911350i \(0.635041\pi\)
\(500\) 0 0
\(501\) −47.0326 −2.10126
\(502\) −5.65207 −0.252264
\(503\) 35.0565 1.56309 0.781545 0.623849i \(-0.214432\pi\)
0.781545 + 0.623849i \(0.214432\pi\)
\(504\) 11.9641 0.532921
\(505\) 0 0
\(506\) 1.56077 0.0693849
\(507\) −18.0879 −0.803310
\(508\) 18.6060 0.825507
\(509\) 29.8890 1.32481 0.662403 0.749147i \(-0.269537\pi\)
0.662403 + 0.749147i \(0.269537\pi\)
\(510\) 0 0
\(511\) −24.7948 −1.09686
\(512\) −10.7281 −0.474118
\(513\) 3.68103 0.162521
\(514\) 10.1598 0.448132
\(515\) 0 0
\(516\) 4.25319 0.187236
\(517\) 5.29091 0.232694
\(518\) −22.0656 −0.969508
\(519\) 11.1750 0.490527
\(520\) 0 0
\(521\) 3.35923 0.147170 0.0735852 0.997289i \(-0.476556\pi\)
0.0735852 + 0.997289i \(0.476556\pi\)
\(522\) 1.40592 0.0615353
\(523\) −41.7591 −1.82600 −0.913000 0.407961i \(-0.866240\pi\)
−0.913000 + 0.407961i \(0.866240\pi\)
\(524\) −20.6620 −0.902623
\(525\) 0 0
\(526\) −3.00381 −0.130972
\(527\) 19.9512 0.869089
\(528\) 2.00060 0.0870650
\(529\) −18.6147 −0.809333
\(530\) 0 0
\(531\) 0.775842 0.0336687
\(532\) 5.58711 0.242232
\(533\) 5.22375 0.226266
\(534\) 2.83084 0.122502
\(535\) 0 0
\(536\) 18.9582 0.818867
\(537\) 36.4111 1.57125
\(538\) −19.8491 −0.855756
\(539\) 7.96005 0.342864
\(540\) 0 0
\(541\) −10.2418 −0.440331 −0.220165 0.975463i \(-0.570660\pi\)
−0.220165 + 0.975463i \(0.570660\pi\)
\(542\) −16.6465 −0.715028
\(543\) −45.2334 −1.94115
\(544\) −21.7030 −0.930507
\(545\) 0 0
\(546\) −12.0844 −0.517166
\(547\) 12.8348 0.548779 0.274389 0.961619i \(-0.411524\pi\)
0.274389 + 0.961619i \(0.411524\pi\)
\(548\) −21.8445 −0.933150
\(549\) 17.3333 0.739766
\(550\) 0 0
\(551\) 1.56558 0.0666960
\(552\) −11.0241 −0.469218
\(553\) −11.8452 −0.503707
\(554\) −16.9045 −0.718203
\(555\) 0 0
\(556\) −14.1091 −0.598358
\(557\) −28.3802 −1.20251 −0.601254 0.799058i \(-0.705332\pi\)
−0.601254 + 0.799058i \(0.705332\pi\)
\(558\) −4.83896 −0.204850
\(559\) −2.93536 −0.124153
\(560\) 0 0
\(561\) 7.59239 0.320551
\(562\) −16.4629 −0.694446
\(563\) −18.5823 −0.783149 −0.391575 0.920146i \(-0.628070\pi\)
−0.391575 + 0.920146i \(0.628070\pi\)
\(564\) −15.6721 −0.659915
\(565\) 0 0
\(566\) −13.0044 −0.546618
\(567\) −43.1761 −1.81323
\(568\) −8.03336 −0.337072
\(569\) 5.80939 0.243542 0.121771 0.992558i \(-0.461143\pi\)
0.121771 + 0.992558i \(0.461143\pi\)
\(570\) 0 0
\(571\) −25.5528 −1.06935 −0.534675 0.845058i \(-0.679566\pi\)
−0.534675 + 0.845058i \(0.679566\pi\)
\(572\) −2.95301 −0.123472
\(573\) 25.8568 1.08018
\(574\) −7.36618 −0.307459
\(575\) 0 0
\(576\) 2.91279 0.121366
\(577\) 1.44616 0.0602043 0.0301021 0.999547i \(-0.490417\pi\)
0.0301021 + 0.999547i \(0.490417\pi\)
\(578\) 2.45289 0.102027
\(579\) 17.1670 0.713437
\(580\) 0 0
\(581\) −24.3071 −1.00843
\(582\) 10.0602 0.417007
\(583\) −2.10441 −0.0871557
\(584\) −16.4573 −0.681010
\(585\) 0 0
\(586\) 12.7039 0.524794
\(587\) 5.15981 0.212968 0.106484 0.994314i \(-0.466041\pi\)
0.106484 + 0.994314i \(0.466041\pi\)
\(588\) −23.5784 −0.972355
\(589\) −5.38850 −0.222029
\(590\) 0 0
\(591\) −19.7648 −0.813013
\(592\) 7.46784 0.306926
\(593\) −3.99385 −0.164008 −0.0820038 0.996632i \(-0.526132\pi\)
−0.0820038 + 0.996632i \(0.526132\pi\)
\(594\) 2.74352 0.112568
\(595\) 0 0
\(596\) 20.4549 0.837864
\(597\) −35.0991 −1.43651
\(598\) 3.19069 0.130477
\(599\) −20.1155 −0.821899 −0.410949 0.911658i \(-0.634803\pi\)
−0.410949 + 0.911658i \(0.634803\pi\)
\(600\) 0 0
\(601\) 34.2267 1.39614 0.698069 0.716031i \(-0.254043\pi\)
0.698069 + 0.716031i \(0.254043\pi\)
\(602\) 4.13926 0.168704
\(603\) 8.89767 0.362341
\(604\) −26.0015 −1.05799
\(605\) 0 0
\(606\) 20.9925 0.852760
\(607\) −10.0999 −0.409943 −0.204971 0.978768i \(-0.565710\pi\)
−0.204971 + 0.978768i \(0.565710\pi\)
\(608\) 5.86162 0.237720
\(609\) −12.4171 −0.503165
\(610\) 0 0
\(611\) 10.8162 0.437577
\(612\) −6.44418 −0.260491
\(613\) −0.860528 −0.0347564 −0.0173782 0.999849i \(-0.505532\pi\)
−0.0173782 + 0.999849i \(0.505532\pi\)
\(614\) −7.10069 −0.286561
\(615\) 0 0
\(616\) 9.92961 0.400075
\(617\) 40.8378 1.64407 0.822033 0.569439i \(-0.192840\pi\)
0.822033 + 0.569439i \(0.192840\pi\)
\(618\) −10.0812 −0.405527
\(619\) −12.7328 −0.511774 −0.255887 0.966707i \(-0.582367\pi\)
−0.255887 + 0.966707i \(0.582367\pi\)
\(620\) 0 0
\(621\) 7.70852 0.309332
\(622\) 18.7600 0.752207
\(623\) −7.16418 −0.287027
\(624\) 4.08983 0.163724
\(625\) 0 0
\(626\) −6.10495 −0.244003
\(627\) −2.05058 −0.0818924
\(628\) 4.20212 0.167683
\(629\) 28.3409 1.13002
\(630\) 0 0
\(631\) −27.2662 −1.08545 −0.542725 0.839911i \(-0.682607\pi\)
−0.542725 + 0.839911i \(0.682607\pi\)
\(632\) −7.86213 −0.312739
\(633\) −0.636296 −0.0252905
\(634\) 15.6478 0.621452
\(635\) 0 0
\(636\) 6.23344 0.247172
\(637\) 16.2727 0.644749
\(638\) 1.16685 0.0461959
\(639\) −3.77031 −0.149151
\(640\) 0 0
\(641\) −16.6825 −0.658920 −0.329460 0.944170i \(-0.606867\pi\)
−0.329460 + 0.944170i \(0.606867\pi\)
\(642\) 11.4619 0.452364
\(643\) 19.6733 0.775839 0.387919 0.921693i \(-0.373194\pi\)
0.387919 + 0.921693i \(0.373194\pi\)
\(644\) 11.7001 0.461048
\(645\) 0 0
\(646\) 2.75956 0.108573
\(647\) −28.9630 −1.13865 −0.569326 0.822112i \(-0.692796\pi\)
−0.569326 + 0.822112i \(0.692796\pi\)
\(648\) −28.6578 −1.12579
\(649\) 0.643913 0.0252758
\(650\) 0 0
\(651\) 42.7378 1.67502
\(652\) 14.0636 0.550771
\(653\) 2.45120 0.0959230 0.0479615 0.998849i \(-0.484728\pi\)
0.0479615 + 0.998849i \(0.484728\pi\)
\(654\) 18.4014 0.719552
\(655\) 0 0
\(656\) 2.49299 0.0973350
\(657\) −7.72396 −0.301340
\(658\) −15.2523 −0.594596
\(659\) 4.60105 0.179231 0.0896157 0.995976i \(-0.471436\pi\)
0.0896157 + 0.995976i \(0.471436\pi\)
\(660\) 0 0
\(661\) 1.55553 0.0605029 0.0302515 0.999542i \(-0.490369\pi\)
0.0302515 + 0.999542i \(0.490369\pi\)
\(662\) −2.44508 −0.0950308
\(663\) 15.5211 0.602790
\(664\) −16.1337 −0.626108
\(665\) 0 0
\(666\) −6.87378 −0.266354
\(667\) 3.27851 0.126945
\(668\) 33.1316 1.28190
\(669\) 7.82084 0.302371
\(670\) 0 0
\(671\) 14.3858 0.555358
\(672\) −46.4902 −1.79340
\(673\) −40.7350 −1.57022 −0.785110 0.619356i \(-0.787394\pi\)
−0.785110 + 0.619356i \(0.787394\pi\)
\(674\) −13.7505 −0.529650
\(675\) 0 0
\(676\) 12.7418 0.490069
\(677\) −11.5539 −0.444051 −0.222025 0.975041i \(-0.571267\pi\)
−0.222025 + 0.975041i \(0.571267\pi\)
\(678\) −18.1092 −0.695480
\(679\) −25.4599 −0.977059
\(680\) 0 0
\(681\) 36.2962 1.39087
\(682\) −4.01612 −0.153785
\(683\) −18.1027 −0.692679 −0.346339 0.938109i \(-0.612575\pi\)
−0.346339 + 0.938109i \(0.612575\pi\)
\(684\) 1.74047 0.0665485
\(685\) 0 0
\(686\) −2.76758 −0.105667
\(687\) 55.7008 2.12512
\(688\) −1.40088 −0.0534081
\(689\) −4.30204 −0.163895
\(690\) 0 0
\(691\) −6.04864 −0.230101 −0.115051 0.993360i \(-0.536703\pi\)
−0.115051 + 0.993360i \(0.536703\pi\)
\(692\) −7.87208 −0.299252
\(693\) 4.66029 0.177030
\(694\) 22.2693 0.845332
\(695\) 0 0
\(696\) −8.24173 −0.312402
\(697\) 9.46104 0.358363
\(698\) −20.5215 −0.776749
\(699\) −1.12954 −0.0427230
\(700\) 0 0
\(701\) 31.8527 1.20306 0.601530 0.798850i \(-0.294558\pi\)
0.601530 + 0.798850i \(0.294558\pi\)
\(702\) 5.60857 0.211682
\(703\) −7.65441 −0.288691
\(704\) 2.41748 0.0911124
\(705\) 0 0
\(706\) 2.85917 0.107606
\(707\) −53.1269 −1.99804
\(708\) −1.90733 −0.0716817
\(709\) −38.1780 −1.43381 −0.716903 0.697173i \(-0.754441\pi\)
−0.716903 + 0.697173i \(0.754441\pi\)
\(710\) 0 0
\(711\) −3.68995 −0.138384
\(712\) −4.75516 −0.178207
\(713\) −11.2842 −0.422596
\(714\) −21.8869 −0.819095
\(715\) 0 0
\(716\) −25.6494 −0.958563
\(717\) −11.0311 −0.411965
\(718\) −24.4196 −0.911333
\(719\) −28.3038 −1.05555 −0.527777 0.849383i \(-0.676974\pi\)
−0.527777 + 0.849383i \(0.676974\pi\)
\(720\) 0 0
\(721\) 25.5132 0.950160
\(722\) −0.745312 −0.0277377
\(723\) 46.2142 1.71872
\(724\) 31.8642 1.18422
\(725\) 0 0
\(726\) −1.52832 −0.0567214
\(727\) 31.1881 1.15670 0.578352 0.815787i \(-0.303696\pi\)
0.578352 + 0.815787i \(0.303696\pi\)
\(728\) 20.2991 0.752335
\(729\) 9.19472 0.340545
\(730\) 0 0
\(731\) −5.31642 −0.196635
\(732\) −42.6120 −1.57498
\(733\) −4.62188 −0.170713 −0.0853565 0.996350i \(-0.527203\pi\)
−0.0853565 + 0.996350i \(0.527203\pi\)
\(734\) 15.6769 0.578645
\(735\) 0 0
\(736\) 12.2749 0.452460
\(737\) 7.38466 0.272017
\(738\) −2.29468 −0.0844683
\(739\) −5.87519 −0.216122 −0.108061 0.994144i \(-0.534464\pi\)
−0.108061 + 0.994144i \(0.534464\pi\)
\(740\) 0 0
\(741\) −4.19200 −0.153997
\(742\) 6.06646 0.222707
\(743\) 19.5669 0.717839 0.358919 0.933369i \(-0.383145\pi\)
0.358919 + 0.933369i \(0.383145\pi\)
\(744\) 28.3668 1.03998
\(745\) 0 0
\(746\) 1.54990 0.0567460
\(747\) −7.57205 −0.277047
\(748\) −5.34837 −0.195556
\(749\) −29.0073 −1.05990
\(750\) 0 0
\(751\) −17.1912 −0.627314 −0.313657 0.949536i \(-0.601554\pi\)
−0.313657 + 0.949536i \(0.601554\pi\)
\(752\) 5.16195 0.188237
\(753\) 15.5506 0.566694
\(754\) 2.38538 0.0868706
\(755\) 0 0
\(756\) 20.5663 0.747989
\(757\) 54.9157 1.99595 0.997973 0.0636322i \(-0.0202685\pi\)
0.997973 + 0.0636322i \(0.0202685\pi\)
\(758\) −22.9404 −0.833233
\(759\) −4.29417 −0.155868
\(760\) 0 0
\(761\) −2.42585 −0.0879372 −0.0439686 0.999033i \(-0.514000\pi\)
−0.0439686 + 0.999033i \(0.514000\pi\)
\(762\) 19.6855 0.713132
\(763\) −46.5696 −1.68593
\(764\) −18.2145 −0.658978
\(765\) 0 0
\(766\) −0.0109674 −0.000396269 0
\(767\) 1.31635 0.0475307
\(768\) −25.0777 −0.904913
\(769\) −4.51504 −0.162816 −0.0814082 0.996681i \(-0.525942\pi\)
−0.0814082 + 0.996681i \(0.525942\pi\)
\(770\) 0 0
\(771\) −27.9528 −1.00670
\(772\) −12.0931 −0.435241
\(773\) 4.60263 0.165545 0.0827726 0.996568i \(-0.473622\pi\)
0.0827726 + 0.996568i \(0.473622\pi\)
\(774\) 1.28944 0.0463480
\(775\) 0 0
\(776\) −16.8988 −0.606630
\(777\) 60.7093 2.17793
\(778\) 17.0826 0.612441
\(779\) −2.55527 −0.0915522
\(780\) 0 0
\(781\) −3.12919 −0.111971
\(782\) 5.77885 0.206651
\(783\) 5.76295 0.205951
\(784\) 7.76604 0.277358
\(785\) 0 0
\(786\) −21.8608 −0.779751
\(787\) −0.615078 −0.0219252 −0.0109626 0.999940i \(-0.503490\pi\)
−0.0109626 + 0.999940i \(0.503490\pi\)
\(788\) 13.9231 0.495988
\(789\) 8.26440 0.294220
\(790\) 0 0
\(791\) 45.8301 1.62953
\(792\) 3.09323 0.109913
\(793\) 29.4089 1.04434
\(794\) −13.1544 −0.466831
\(795\) 0 0
\(796\) 24.7252 0.876360
\(797\) −54.0423 −1.91428 −0.957139 0.289630i \(-0.906468\pi\)
−0.957139 + 0.289630i \(0.906468\pi\)
\(798\) 5.91129 0.209257
\(799\) 19.5899 0.693040
\(800\) 0 0
\(801\) −2.23175 −0.0788550
\(802\) 13.9836 0.493778
\(803\) −6.41053 −0.226223
\(804\) −21.8740 −0.771436
\(805\) 0 0
\(806\) −8.21015 −0.289190
\(807\) 54.6110 1.92240
\(808\) −35.2625 −1.24053
\(809\) −14.6049 −0.513480 −0.256740 0.966481i \(-0.582648\pi\)
−0.256740 + 0.966481i \(0.582648\pi\)
\(810\) 0 0
\(811\) 18.1014 0.635626 0.317813 0.948153i \(-0.397052\pi\)
0.317813 + 0.948153i \(0.397052\pi\)
\(812\) 8.74707 0.306962
\(813\) 45.7996 1.60626
\(814\) −5.70492 −0.199958
\(815\) 0 0
\(816\) 7.40733 0.259309
\(817\) 1.43588 0.0502350
\(818\) 11.7347 0.410294
\(819\) 9.52702 0.332901
\(820\) 0 0
\(821\) 17.5804 0.613562 0.306781 0.951780i \(-0.400748\pi\)
0.306781 + 0.951780i \(0.400748\pi\)
\(822\) −23.1120 −0.806122
\(823\) 42.5561 1.48341 0.741706 0.670725i \(-0.234017\pi\)
0.741706 + 0.670725i \(0.234017\pi\)
\(824\) 16.9342 0.589930
\(825\) 0 0
\(826\) −1.85623 −0.0645866
\(827\) −48.0006 −1.66914 −0.834572 0.550899i \(-0.814285\pi\)
−0.834572 + 0.550899i \(0.814285\pi\)
\(828\) 3.64475 0.126664
\(829\) 34.1185 1.18498 0.592492 0.805576i \(-0.298144\pi\)
0.592492 + 0.805576i \(0.298144\pi\)
\(830\) 0 0
\(831\) 46.5094 1.61339
\(832\) 4.94206 0.171335
\(833\) 29.4725 1.02116
\(834\) −14.9277 −0.516905
\(835\) 0 0
\(836\) 1.44451 0.0499594
\(837\) −19.8352 −0.685606
\(838\) −19.1599 −0.661866
\(839\) −13.4842 −0.465528 −0.232764 0.972533i \(-0.574777\pi\)
−0.232764 + 0.972533i \(0.574777\pi\)
\(840\) 0 0
\(841\) −26.5490 −0.915481
\(842\) 12.8711 0.443566
\(843\) 45.2945 1.56003
\(844\) 0.448231 0.0154288
\(845\) 0 0
\(846\) −4.75132 −0.163354
\(847\) 3.86782 0.132900
\(848\) −2.05312 −0.0705043
\(849\) 35.7792 1.22794
\(850\) 0 0
\(851\) −16.0293 −0.549476
\(852\) 9.26892 0.317548
\(853\) −7.34151 −0.251369 −0.125684 0.992070i \(-0.540113\pi\)
−0.125684 + 0.992070i \(0.540113\pi\)
\(854\) −41.4705 −1.41909
\(855\) 0 0
\(856\) −19.2533 −0.658066
\(857\) 25.9177 0.885331 0.442666 0.896687i \(-0.354033\pi\)
0.442666 + 0.896687i \(0.354033\pi\)
\(858\) −3.12435 −0.106664
\(859\) −12.6379 −0.431200 −0.215600 0.976482i \(-0.569171\pi\)
−0.215600 + 0.976482i \(0.569171\pi\)
\(860\) 0 0
\(861\) 20.2666 0.690684
\(862\) 2.10009 0.0715295
\(863\) −37.4073 −1.27336 −0.636679 0.771129i \(-0.719693\pi\)
−0.636679 + 0.771129i \(0.719693\pi\)
\(864\) 21.5768 0.734057
\(865\) 0 0
\(866\) 6.60146 0.224327
\(867\) −6.74866 −0.229196
\(868\) −30.1061 −1.02187
\(869\) −3.06249 −0.103888
\(870\) 0 0
\(871\) 15.0964 0.511524
\(872\) −30.9102 −1.04675
\(873\) −7.93113 −0.268428
\(874\) −1.56077 −0.0527940
\(875\) 0 0
\(876\) 18.9885 0.641563
\(877\) 49.5616 1.67358 0.836788 0.547527i \(-0.184431\pi\)
0.836788 + 0.547527i \(0.184431\pi\)
\(878\) 7.23796 0.244269
\(879\) −34.9523 −1.17891
\(880\) 0 0
\(881\) −19.9617 −0.672527 −0.336263 0.941768i \(-0.609163\pi\)
−0.336263 + 0.941768i \(0.609163\pi\)
\(882\) −7.14826 −0.240694
\(883\) −26.4622 −0.890524 −0.445262 0.895400i \(-0.646889\pi\)
−0.445262 + 0.895400i \(0.646889\pi\)
\(884\) −10.9337 −0.367739
\(885\) 0 0
\(886\) 21.1645 0.711035
\(887\) 0.489272 0.0164281 0.00821407 0.999966i \(-0.497385\pi\)
0.00821407 + 0.999966i \(0.497385\pi\)
\(888\) 40.2953 1.35222
\(889\) −49.8194 −1.67089
\(890\) 0 0
\(891\) −11.1629 −0.373971
\(892\) −5.50930 −0.184465
\(893\) −5.29091 −0.177053
\(894\) 21.6417 0.723808
\(895\) 0 0
\(896\) 38.3744 1.28200
\(897\) −8.77856 −0.293108
\(898\) −26.0582 −0.869574
\(899\) −8.43614 −0.281361
\(900\) 0 0
\(901\) −7.79169 −0.259579
\(902\) −1.90448 −0.0634122
\(903\) −11.3884 −0.378981
\(904\) 30.4194 1.01173
\(905\) 0 0
\(906\) −27.5102 −0.913966
\(907\) −48.9032 −1.62381 −0.811903 0.583793i \(-0.801568\pi\)
−0.811903 + 0.583793i \(0.801568\pi\)
\(908\) −25.5685 −0.848519
\(909\) −16.5498 −0.548924
\(910\) 0 0
\(911\) −7.54945 −0.250125 −0.125062 0.992149i \(-0.539913\pi\)
−0.125062 + 0.992149i \(0.539913\pi\)
\(912\) −2.00060 −0.0662465
\(913\) −6.28445 −0.207985
\(914\) 28.8292 0.953587
\(915\) 0 0
\(916\) −39.2378 −1.29645
\(917\) 55.3246 1.82698
\(918\) 10.1580 0.335264
\(919\) −31.0368 −1.02381 −0.511905 0.859042i \(-0.671060\pi\)
−0.511905 + 0.859042i \(0.671060\pi\)
\(920\) 0 0
\(921\) 19.5362 0.643738
\(922\) 14.6116 0.481206
\(923\) −6.39700 −0.210560
\(924\) −11.4568 −0.376902
\(925\) 0 0
\(926\) −2.37303 −0.0779825
\(927\) 7.94775 0.261038
\(928\) 9.17683 0.301244
\(929\) 3.46660 0.113735 0.0568677 0.998382i \(-0.481889\pi\)
0.0568677 + 0.998382i \(0.481889\pi\)
\(930\) 0 0
\(931\) −7.96005 −0.260880
\(932\) 0.795689 0.0260637
\(933\) −51.6144 −1.68978
\(934\) 21.4531 0.701966
\(935\) 0 0
\(936\) 6.32348 0.206689
\(937\) 26.4876 0.865313 0.432657 0.901559i \(-0.357576\pi\)
0.432657 + 0.901559i \(0.357576\pi\)
\(938\) −21.2880 −0.695078
\(939\) 16.7966 0.548136
\(940\) 0 0
\(941\) −48.9435 −1.59551 −0.797756 0.602981i \(-0.793980\pi\)
−0.797756 + 0.602981i \(0.793980\pi\)
\(942\) 4.44594 0.144856
\(943\) −5.35105 −0.174254
\(944\) 0.628218 0.0204468
\(945\) 0 0
\(946\) 1.07018 0.0347945
\(947\) −14.6896 −0.477346 −0.238673 0.971100i \(-0.576712\pi\)
−0.238673 + 0.971100i \(0.576712\pi\)
\(948\) 9.07135 0.294624
\(949\) −13.1050 −0.425408
\(950\) 0 0
\(951\) −43.0518 −1.39605
\(952\) 36.7649 1.19156
\(953\) −13.8224 −0.447752 −0.223876 0.974618i \(-0.571871\pi\)
−0.223876 + 0.974618i \(0.571871\pi\)
\(954\) 1.88979 0.0611844
\(955\) 0 0
\(956\) 7.77076 0.251324
\(957\) −3.21035 −0.103776
\(958\) −7.13753 −0.230603
\(959\) 58.4908 1.88877
\(960\) 0 0
\(961\) −1.96404 −0.0633561
\(962\) −11.6626 −0.376017
\(963\) −9.03621 −0.291188
\(964\) −32.5551 −1.04853
\(965\) 0 0
\(966\) 12.3789 0.398286
\(967\) 48.0516 1.54523 0.772617 0.634872i \(-0.218947\pi\)
0.772617 + 0.634872i \(0.218947\pi\)
\(968\) 2.56724 0.0825141
\(969\) −7.59239 −0.243903
\(970\) 0 0
\(971\) −14.9180 −0.478740 −0.239370 0.970928i \(-0.576941\pi\)
−0.239370 + 0.970928i \(0.576941\pi\)
\(972\) 17.1136 0.548920
\(973\) 37.7785 1.21112
\(974\) −24.5064 −0.785236
\(975\) 0 0
\(976\) 14.0352 0.449255
\(977\) 13.7541 0.440032 0.220016 0.975496i \(-0.429389\pi\)
0.220016 + 0.975496i \(0.429389\pi\)
\(978\) 14.8796 0.475796
\(979\) −1.85225 −0.0591982
\(980\) 0 0
\(981\) −14.5071 −0.463177
\(982\) −3.30742 −0.105544
\(983\) −34.7768 −1.10921 −0.554604 0.832115i \(-0.687130\pi\)
−0.554604 + 0.832115i \(0.687130\pi\)
\(984\) 13.4518 0.428828
\(985\) 0 0
\(986\) 4.32031 0.137587
\(987\) 41.9637 1.33572
\(988\) 2.95301 0.0939478
\(989\) 3.00690 0.0956139
\(990\) 0 0
\(991\) −58.8419 −1.86917 −0.934587 0.355734i \(-0.884231\pi\)
−0.934587 + 0.355734i \(0.884231\pi\)
\(992\) −31.5853 −1.00284
\(993\) 6.72717 0.213480
\(994\) 9.02062 0.286117
\(995\) 0 0
\(996\) 18.6151 0.589841
\(997\) −9.48200 −0.300298 −0.150149 0.988663i \(-0.547975\pi\)
−0.150149 + 0.988663i \(0.547975\pi\)
\(998\) 13.7066 0.433874
\(999\) −28.1761 −0.891452
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 5225.2.a.m.1.3 7
5.4 even 2 1045.2.a.h.1.5 7
15.14 odd 2 9405.2.a.bd.1.3 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.h.1.5 7 5.4 even 2
5225.2.a.m.1.3 7 1.1 even 1 trivial
9405.2.a.bd.1.3 7 15.14 odd 2