Properties

Label 5225.2.a.p.1.7
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $1$
Dimension $9$
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] = [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: \(1\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 3x^{8} - 9x^{7} + 29x^{6} + 23x^{5} - 84x^{4} - 23x^{3} + 89x^{2} + 8x - 27 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-1.24377\) 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)
 
\(f(q)\) \(=\) \(q+1.24377 q^{2} -3.09454 q^{3} -0.453038 q^{4} -3.84889 q^{6} -3.83759 q^{7} -3.05101 q^{8} +6.57616 q^{9} +O(q^{10})\) \(q+1.24377 q^{2} -3.09454 q^{3} -0.453038 q^{4} -3.84889 q^{6} -3.83759 q^{7} -3.05101 q^{8} +6.57616 q^{9} +1.00000 q^{11} +1.40194 q^{12} +2.44695 q^{13} -4.77307 q^{14} -2.88868 q^{16} -4.44695 q^{17} +8.17922 q^{18} +1.00000 q^{19} +11.8755 q^{21} +1.24377 q^{22} +5.34873 q^{23} +9.44147 q^{24} +3.04344 q^{26} -11.0665 q^{27} +1.73857 q^{28} -9.42505 q^{29} -2.25347 q^{31} +2.50917 q^{32} -3.09454 q^{33} -5.53098 q^{34} -2.97925 q^{36} +9.50113 q^{37} +1.24377 q^{38} -7.57217 q^{39} +6.98607 q^{41} +14.7704 q^{42} -3.25340 q^{43} -0.453038 q^{44} +6.65259 q^{46} +4.99452 q^{47} +8.93913 q^{48} +7.72706 q^{49} +13.7612 q^{51} -1.10856 q^{52} +6.72067 q^{53} -13.7642 q^{54} +11.7085 q^{56} -3.09454 q^{57} -11.7226 q^{58} +3.81487 q^{59} +7.33227 q^{61} -2.80280 q^{62} -25.2366 q^{63} +8.89820 q^{64} -3.84889 q^{66} +8.95031 q^{67} +2.01463 q^{68} -16.5518 q^{69} +4.94182 q^{71} -20.0639 q^{72} +3.88580 q^{73} +11.8172 q^{74} -0.453038 q^{76} -3.83759 q^{77} -9.41804 q^{78} -13.5466 q^{79} +14.5174 q^{81} +8.68906 q^{82} -8.59991 q^{83} -5.38007 q^{84} -4.04648 q^{86} +29.1661 q^{87} -3.05101 q^{88} -3.34023 q^{89} -9.39038 q^{91} -2.42317 q^{92} +6.97346 q^{93} +6.21203 q^{94} -7.76472 q^{96} +8.42974 q^{97} +9.61068 q^{98} +6.57616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - 3 q^{2} - 3 q^{3} + 9 q^{4} - 13 q^{7} - 9 q^{8} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - 3 q^{2} - 3 q^{3} + 9 q^{4} - 13 q^{7} - 9 q^{8} + 12 q^{9} + 9 q^{11} + 5 q^{12} - 5 q^{13} - 2 q^{14} + q^{16} - 13 q^{17} - q^{18} + 9 q^{19} + q^{21} - 3 q^{22} - 8 q^{23} - 7 q^{24} + 8 q^{26} - 6 q^{27} - 10 q^{28} - 3 q^{29} - 9 q^{31} - 6 q^{32} - 3 q^{33} - 2 q^{34} - 15 q^{36} + 7 q^{37} - 3 q^{38} - 2 q^{39} + 9 q^{41} + 9 q^{42} - 23 q^{43} + 9 q^{44} - 32 q^{46} - 20 q^{47} + 18 q^{48} - 4 q^{49} + 8 q^{51} - 9 q^{52} + 5 q^{53} + 9 q^{54} + 4 q^{56} - 3 q^{57} - 3 q^{58} + 19 q^{59} + q^{61} - 18 q^{62} - 24 q^{63} + 23 q^{64} + 10 q^{67} - 9 q^{68} - 28 q^{69} - 24 q^{72} - 12 q^{73} + 5 q^{74} + 9 q^{76} - 13 q^{77} - 19 q^{78} - 21 q^{79} - 3 q^{81} + 14 q^{82} - 47 q^{83} - 11 q^{84} + 12 q^{86} + 2 q^{87} - 9 q^{88} - 2 q^{89} + 2 q^{91} + 19 q^{92} + 2 q^{93} + 26 q^{94} - 55 q^{96} + 32 q^{97} + 12 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.24377 0.879478 0.439739 0.898126i \(-0.355071\pi\)
0.439739 + 0.898126i \(0.355071\pi\)
\(3\) −3.09454 −1.78663 −0.893316 0.449430i \(-0.851627\pi\)
−0.893316 + 0.449430i \(0.851627\pi\)
\(4\) −0.453038 −0.226519
\(5\) 0 0
\(6\) −3.84889 −1.57130
\(7\) −3.83759 −1.45047 −0.725235 0.688501i \(-0.758269\pi\)
−0.725235 + 0.688501i \(0.758269\pi\)
\(8\) −3.05101 −1.07870
\(9\) 6.57616 2.19205
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) 1.40194 0.404706
\(13\) 2.44695 0.678661 0.339331 0.940667i \(-0.389799\pi\)
0.339331 + 0.940667i \(0.389799\pi\)
\(14\) −4.77307 −1.27566
\(15\) 0 0
\(16\) −2.88868 −0.722170
\(17\) −4.44695 −1.07854 −0.539272 0.842132i \(-0.681300\pi\)
−0.539272 + 0.842132i \(0.681300\pi\)
\(18\) 8.17922 1.92786
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 11.8755 2.59146
\(22\) 1.24377 0.265173
\(23\) 5.34873 1.11529 0.557644 0.830081i \(-0.311706\pi\)
0.557644 + 0.830081i \(0.311706\pi\)
\(24\) 9.44147 1.92723
\(25\) 0 0
\(26\) 3.04344 0.596868
\(27\) −11.0665 −2.12976
\(28\) 1.73857 0.328559
\(29\) −9.42505 −1.75019 −0.875094 0.483954i \(-0.839200\pi\)
−0.875094 + 0.483954i \(0.839200\pi\)
\(30\) 0 0
\(31\) −2.25347 −0.404736 −0.202368 0.979310i \(-0.564864\pi\)
−0.202368 + 0.979310i \(0.564864\pi\)
\(32\) 2.50917 0.443563
\(33\) −3.09454 −0.538690
\(34\) −5.53098 −0.948555
\(35\) 0 0
\(36\) −2.97925 −0.496541
\(37\) 9.50113 1.56198 0.780988 0.624546i \(-0.214716\pi\)
0.780988 + 0.624546i \(0.214716\pi\)
\(38\) 1.24377 0.201766
\(39\) −7.57217 −1.21252
\(40\) 0 0
\(41\) 6.98607 1.09104 0.545521 0.838097i \(-0.316332\pi\)
0.545521 + 0.838097i \(0.316332\pi\)
\(42\) 14.7704 2.27913
\(43\) −3.25340 −0.496138 −0.248069 0.968742i \(-0.579796\pi\)
−0.248069 + 0.968742i \(0.579796\pi\)
\(44\) −0.453038 −0.0682980
\(45\) 0 0
\(46\) 6.65259 0.980870
\(47\) 4.99452 0.728526 0.364263 0.931296i \(-0.381321\pi\)
0.364263 + 0.931296i \(0.381321\pi\)
\(48\) 8.93913 1.29025
\(49\) 7.72706 1.10387
\(50\) 0 0
\(51\) 13.7612 1.92696
\(52\) −1.10856 −0.153730
\(53\) 6.72067 0.923154 0.461577 0.887100i \(-0.347284\pi\)
0.461577 + 0.887100i \(0.347284\pi\)
\(54\) −13.7642 −1.87307
\(55\) 0 0
\(56\) 11.7085 1.56462
\(57\) −3.09454 −0.409881
\(58\) −11.7226 −1.53925
\(59\) 3.81487 0.496654 0.248327 0.968676i \(-0.420119\pi\)
0.248327 + 0.968676i \(0.420119\pi\)
\(60\) 0 0
\(61\) 7.33227 0.938801 0.469400 0.882985i \(-0.344470\pi\)
0.469400 + 0.882985i \(0.344470\pi\)
\(62\) −2.80280 −0.355956
\(63\) −25.2366 −3.17951
\(64\) 8.89820 1.11227
\(65\) 0 0
\(66\) −3.84889 −0.473766
\(67\) 8.95031 1.09345 0.546727 0.837311i \(-0.315873\pi\)
0.546727 + 0.837311i \(0.315873\pi\)
\(68\) 2.01463 0.244310
\(69\) −16.5518 −1.99261
\(70\) 0 0
\(71\) 4.94182 0.586486 0.293243 0.956038i \(-0.405266\pi\)
0.293243 + 0.956038i \(0.405266\pi\)
\(72\) −20.0639 −2.36456
\(73\) 3.88580 0.454799 0.227400 0.973802i \(-0.426978\pi\)
0.227400 + 0.973802i \(0.426978\pi\)
\(74\) 11.8172 1.37372
\(75\) 0 0
\(76\) −0.453038 −0.0519670
\(77\) −3.83759 −0.437333
\(78\) −9.41804 −1.06638
\(79\) −13.5466 −1.52411 −0.762053 0.647514i \(-0.775809\pi\)
−0.762053 + 0.647514i \(0.775809\pi\)
\(80\) 0 0
\(81\) 14.5174 1.61304
\(82\) 8.68906 0.959546
\(83\) −8.59991 −0.943963 −0.471982 0.881608i \(-0.656461\pi\)
−0.471982 + 0.881608i \(0.656461\pi\)
\(84\) −5.38007 −0.587014
\(85\) 0 0
\(86\) −4.04648 −0.436343
\(87\) 29.1661 3.12694
\(88\) −3.05101 −0.325239
\(89\) −3.34023 −0.354063 −0.177032 0.984205i \(-0.556649\pi\)
−0.177032 + 0.984205i \(0.556649\pi\)
\(90\) 0 0
\(91\) −9.39038 −0.984379
\(92\) −2.42317 −0.252633
\(93\) 6.97346 0.723114
\(94\) 6.21203 0.640722
\(95\) 0 0
\(96\) −7.76472 −0.792484
\(97\) 8.42974 0.855911 0.427955 0.903800i \(-0.359234\pi\)
0.427955 + 0.903800i \(0.359234\pi\)
\(98\) 9.61068 0.970826
\(99\) 6.57616 0.660929
\(100\) 0 0
\(101\) 14.9671 1.48928 0.744639 0.667467i \(-0.232621\pi\)
0.744639 + 0.667467i \(0.232621\pi\)
\(102\) 17.1158 1.69472
\(103\) −0.113124 −0.0111464 −0.00557320 0.999984i \(-0.501774\pi\)
−0.00557320 + 0.999984i \(0.501774\pi\)
\(104\) −7.46567 −0.732069
\(105\) 0 0
\(106\) 8.35896 0.811894
\(107\) −16.5759 −1.60246 −0.801229 0.598358i \(-0.795820\pi\)
−0.801229 + 0.598358i \(0.795820\pi\)
\(108\) 5.01356 0.482430
\(109\) −7.56098 −0.724211 −0.362105 0.932137i \(-0.617942\pi\)
−0.362105 + 0.932137i \(0.617942\pi\)
\(110\) 0 0
\(111\) −29.4016 −2.79068
\(112\) 11.0856 1.04749
\(113\) −3.29190 −0.309676 −0.154838 0.987940i \(-0.549486\pi\)
−0.154838 + 0.987940i \(0.549486\pi\)
\(114\) −3.84889 −0.360482
\(115\) 0 0
\(116\) 4.26990 0.396450
\(117\) 16.0915 1.48766
\(118\) 4.74482 0.436796
\(119\) 17.0655 1.56440
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 9.11965 0.825655
\(123\) −21.6187 −1.94929
\(124\) 1.02091 0.0916803
\(125\) 0 0
\(126\) −31.3885 −2.79631
\(127\) −21.6432 −1.92053 −0.960264 0.279094i \(-0.909966\pi\)
−0.960264 + 0.279094i \(0.909966\pi\)
\(128\) 6.04896 0.534658
\(129\) 10.0678 0.886416
\(130\) 0 0
\(131\) −17.0780 −1.49211 −0.746057 0.665882i \(-0.768055\pi\)
−0.746057 + 0.665882i \(0.768055\pi\)
\(132\) 1.40194 0.122023
\(133\) −3.83759 −0.332761
\(134\) 11.1321 0.961669
\(135\) 0 0
\(136\) 13.5677 1.16342
\(137\) −14.0843 −1.20330 −0.601650 0.798760i \(-0.705490\pi\)
−0.601650 + 0.798760i \(0.705490\pi\)
\(138\) −20.5867 −1.75245
\(139\) −14.6799 −1.24513 −0.622567 0.782567i \(-0.713910\pi\)
−0.622567 + 0.782567i \(0.713910\pi\)
\(140\) 0 0
\(141\) −15.4557 −1.30161
\(142\) 6.14648 0.515801
\(143\) 2.44695 0.204624
\(144\) −18.9964 −1.58304
\(145\) 0 0
\(146\) 4.83305 0.399986
\(147\) −23.9117 −1.97220
\(148\) −4.30437 −0.353817
\(149\) 11.0069 0.901718 0.450859 0.892595i \(-0.351118\pi\)
0.450859 + 0.892595i \(0.351118\pi\)
\(150\) 0 0
\(151\) −4.88477 −0.397517 −0.198758 0.980049i \(-0.563691\pi\)
−0.198758 + 0.980049i \(0.563691\pi\)
\(152\) −3.05101 −0.247470
\(153\) −29.2438 −2.36422
\(154\) −4.77307 −0.384625
\(155\) 0 0
\(156\) 3.43048 0.274658
\(157\) −3.30059 −0.263416 −0.131708 0.991289i \(-0.542046\pi\)
−0.131708 + 0.991289i \(0.542046\pi\)
\(158\) −16.8488 −1.34042
\(159\) −20.7973 −1.64934
\(160\) 0 0
\(161\) −20.5262 −1.61769
\(162\) 18.0562 1.41863
\(163\) −5.58288 −0.437285 −0.218642 0.975805i \(-0.570163\pi\)
−0.218642 + 0.975805i \(0.570163\pi\)
\(164\) −3.16495 −0.247141
\(165\) 0 0
\(166\) −10.6963 −0.830195
\(167\) 21.7614 1.68395 0.841973 0.539520i \(-0.181394\pi\)
0.841973 + 0.539520i \(0.181394\pi\)
\(168\) −36.2325 −2.79539
\(169\) −7.01244 −0.539419
\(170\) 0 0
\(171\) 6.57616 0.502891
\(172\) 1.47391 0.112385
\(173\) −19.7081 −1.49838 −0.749188 0.662357i \(-0.769556\pi\)
−0.749188 + 0.662357i \(0.769556\pi\)
\(174\) 36.2760 2.75007
\(175\) 0 0
\(176\) −2.88868 −0.217743
\(177\) −11.8053 −0.887337
\(178\) −4.15447 −0.311391
\(179\) −23.0630 −1.72381 −0.861905 0.507070i \(-0.830728\pi\)
−0.861905 + 0.507070i \(0.830728\pi\)
\(180\) 0 0
\(181\) 7.03753 0.523096 0.261548 0.965190i \(-0.415767\pi\)
0.261548 + 0.965190i \(0.415767\pi\)
\(182\) −11.6795 −0.865739
\(183\) −22.6900 −1.67729
\(184\) −16.3190 −1.20306
\(185\) 0 0
\(186\) 8.67337 0.635963
\(187\) −4.44695 −0.325193
\(188\) −2.26271 −0.165025
\(189\) 42.4688 3.08915
\(190\) 0 0
\(191\) 13.6102 0.984798 0.492399 0.870370i \(-0.336120\pi\)
0.492399 + 0.870370i \(0.336120\pi\)
\(192\) −27.5358 −1.98722
\(193\) −0.756294 −0.0544392 −0.0272196 0.999629i \(-0.508665\pi\)
−0.0272196 + 0.999629i \(0.508665\pi\)
\(194\) 10.4847 0.752755
\(195\) 0 0
\(196\) −3.50065 −0.250046
\(197\) −3.15982 −0.225128 −0.112564 0.993644i \(-0.535906\pi\)
−0.112564 + 0.993644i \(0.535906\pi\)
\(198\) 8.17922 0.581272
\(199\) −12.5193 −0.887471 −0.443736 0.896158i \(-0.646347\pi\)
−0.443736 + 0.896158i \(0.646347\pi\)
\(200\) 0 0
\(201\) −27.6971 −1.95360
\(202\) 18.6156 1.30979
\(203\) 36.1694 2.53860
\(204\) −6.23436 −0.436493
\(205\) 0 0
\(206\) −0.140700 −0.00980301
\(207\) 35.1741 2.44477
\(208\) −7.06846 −0.490109
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 14.8799 1.02437 0.512186 0.858875i \(-0.328836\pi\)
0.512186 + 0.858875i \(0.328836\pi\)
\(212\) −3.04471 −0.209112
\(213\) −15.2926 −1.04783
\(214\) −20.6167 −1.40933
\(215\) 0 0
\(216\) 33.7642 2.29736
\(217\) 8.64790 0.587058
\(218\) −9.40412 −0.636927
\(219\) −12.0248 −0.812558
\(220\) 0 0
\(221\) −10.8815 −0.731966
\(222\) −36.5688 −2.45434
\(223\) 6.74009 0.451350 0.225675 0.974203i \(-0.427541\pi\)
0.225675 + 0.974203i \(0.427541\pi\)
\(224\) −9.62916 −0.643375
\(225\) 0 0
\(226\) −4.09437 −0.272353
\(227\) −9.13145 −0.606075 −0.303038 0.952979i \(-0.598001\pi\)
−0.303038 + 0.952979i \(0.598001\pi\)
\(228\) 1.40194 0.0928458
\(229\) −20.5688 −1.35922 −0.679612 0.733572i \(-0.737852\pi\)
−0.679612 + 0.733572i \(0.737852\pi\)
\(230\) 0 0
\(231\) 11.8755 0.781354
\(232\) 28.7559 1.88792
\(233\) −6.63624 −0.434754 −0.217377 0.976088i \(-0.569750\pi\)
−0.217377 + 0.976088i \(0.569750\pi\)
\(234\) 20.0141 1.30837
\(235\) 0 0
\(236\) −1.72828 −0.112501
\(237\) 41.9203 2.72302
\(238\) 21.2256 1.37585
\(239\) 13.8790 0.897758 0.448879 0.893593i \(-0.351823\pi\)
0.448879 + 0.893593i \(0.351823\pi\)
\(240\) 0 0
\(241\) 12.3764 0.797232 0.398616 0.917118i \(-0.369491\pi\)
0.398616 + 0.917118i \(0.369491\pi\)
\(242\) 1.24377 0.0799525
\(243\) −11.7249 −0.752150
\(244\) −3.32179 −0.212656
\(245\) 0 0
\(246\) −26.8886 −1.71436
\(247\) 2.44695 0.155696
\(248\) 6.87538 0.436587
\(249\) 26.6127 1.68651
\(250\) 0 0
\(251\) 26.9081 1.69842 0.849212 0.528051i \(-0.177077\pi\)
0.849212 + 0.528051i \(0.177077\pi\)
\(252\) 11.4331 0.720218
\(253\) 5.34873 0.336272
\(254\) −26.9192 −1.68906
\(255\) 0 0
\(256\) −10.2729 −0.642055
\(257\) 23.3930 1.45921 0.729607 0.683867i \(-0.239703\pi\)
0.729607 + 0.683867i \(0.239703\pi\)
\(258\) 12.5220 0.779584
\(259\) −36.4614 −2.26560
\(260\) 0 0
\(261\) −61.9806 −3.83650
\(262\) −21.2411 −1.31228
\(263\) 27.2224 1.67860 0.839302 0.543665i \(-0.182964\pi\)
0.839302 + 0.543665i \(0.182964\pi\)
\(264\) 9.44147 0.581082
\(265\) 0 0
\(266\) −4.77307 −0.292656
\(267\) 10.3364 0.632580
\(268\) −4.05483 −0.247688
\(269\) 14.5520 0.887249 0.443624 0.896213i \(-0.353692\pi\)
0.443624 + 0.896213i \(0.353692\pi\)
\(270\) 0 0
\(271\) −31.7669 −1.92970 −0.964851 0.262798i \(-0.915355\pi\)
−0.964851 + 0.262798i \(0.915355\pi\)
\(272\) 12.8458 0.778892
\(273\) 29.0589 1.75872
\(274\) −17.5176 −1.05828
\(275\) 0 0
\(276\) 7.49860 0.451363
\(277\) 13.9031 0.835358 0.417679 0.908595i \(-0.362844\pi\)
0.417679 + 0.908595i \(0.362844\pi\)
\(278\) −18.2584 −1.09507
\(279\) −14.8192 −0.887202
\(280\) 0 0
\(281\) −9.22180 −0.550126 −0.275063 0.961426i \(-0.588699\pi\)
−0.275063 + 0.961426i \(0.588699\pi\)
\(282\) −19.2234 −1.14473
\(283\) 15.2824 0.908444 0.454222 0.890888i \(-0.349917\pi\)
0.454222 + 0.890888i \(0.349917\pi\)
\(284\) −2.23883 −0.132850
\(285\) 0 0
\(286\) 3.04344 0.179962
\(287\) −26.8096 −1.58252
\(288\) 16.5007 0.972313
\(289\) 2.77535 0.163256
\(290\) 0 0
\(291\) −26.0861 −1.52920
\(292\) −1.76042 −0.103021
\(293\) −1.81359 −0.105951 −0.0529756 0.998596i \(-0.516871\pi\)
−0.0529756 + 0.998596i \(0.516871\pi\)
\(294\) −29.7406 −1.73451
\(295\) 0 0
\(296\) −28.9881 −1.68490
\(297\) −11.0665 −0.642146
\(298\) 13.6900 0.793041
\(299\) 13.0881 0.756902
\(300\) 0 0
\(301\) 12.4852 0.719634
\(302\) −6.07552 −0.349607
\(303\) −46.3161 −2.66079
\(304\) −2.88868 −0.165677
\(305\) 0 0
\(306\) −36.3726 −2.07928
\(307\) −17.7976 −1.01576 −0.507880 0.861428i \(-0.669571\pi\)
−0.507880 + 0.861428i \(0.669571\pi\)
\(308\) 1.73857 0.0990642
\(309\) 0.350065 0.0199145
\(310\) 0 0
\(311\) −17.2822 −0.979982 −0.489991 0.871727i \(-0.663000\pi\)
−0.489991 + 0.871727i \(0.663000\pi\)
\(312\) 23.1028 1.30794
\(313\) 29.6212 1.67429 0.837145 0.546981i \(-0.184223\pi\)
0.837145 + 0.546981i \(0.184223\pi\)
\(314\) −4.10518 −0.231669
\(315\) 0 0
\(316\) 6.13710 0.345239
\(317\) −31.6170 −1.77579 −0.887893 0.460049i \(-0.847832\pi\)
−0.887893 + 0.460049i \(0.847832\pi\)
\(318\) −25.8671 −1.45056
\(319\) −9.42505 −0.527701
\(320\) 0 0
\(321\) 51.2949 2.86300
\(322\) −25.5299 −1.42272
\(323\) −4.44695 −0.247435
\(324\) −6.57691 −0.365384
\(325\) 0 0
\(326\) −6.94381 −0.384582
\(327\) 23.3977 1.29390
\(328\) −21.3146 −1.17690
\(329\) −19.1669 −1.05671
\(330\) 0 0
\(331\) −2.20361 −0.121121 −0.0605607 0.998165i \(-0.519289\pi\)
−0.0605607 + 0.998165i \(0.519289\pi\)
\(332\) 3.89608 0.213825
\(333\) 62.4809 3.42393
\(334\) 27.0661 1.48099
\(335\) 0 0
\(336\) −34.3047 −1.87147
\(337\) −9.15267 −0.498577 −0.249289 0.968429i \(-0.580197\pi\)
−0.249289 + 0.968429i \(0.580197\pi\)
\(338\) −8.72186 −0.474407
\(339\) 10.1869 0.553277
\(340\) 0 0
\(341\) −2.25347 −0.122032
\(342\) 8.17922 0.442282
\(343\) −2.79017 −0.150655
\(344\) 9.92616 0.535183
\(345\) 0 0
\(346\) −24.5123 −1.31779
\(347\) −10.9854 −0.589726 −0.294863 0.955540i \(-0.595274\pi\)
−0.294863 + 0.955540i \(0.595274\pi\)
\(348\) −13.2134 −0.708310
\(349\) −18.1845 −0.973396 −0.486698 0.873570i \(-0.661799\pi\)
−0.486698 + 0.873570i \(0.661799\pi\)
\(350\) 0 0
\(351\) −27.0793 −1.44538
\(352\) 2.50917 0.133739
\(353\) 0.0447307 0.00238077 0.00119039 0.999999i \(-0.499621\pi\)
0.00119039 + 0.999999i \(0.499621\pi\)
\(354\) −14.6830 −0.780393
\(355\) 0 0
\(356\) 1.51325 0.0802019
\(357\) −52.8100 −2.79500
\(358\) −28.6851 −1.51605
\(359\) −16.6983 −0.881303 −0.440652 0.897678i \(-0.645253\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 8.75307 0.460051
\(363\) −3.09454 −0.162421
\(364\) 4.25419 0.222980
\(365\) 0 0
\(366\) −28.2211 −1.47514
\(367\) −6.08480 −0.317624 −0.158812 0.987309i \(-0.550766\pi\)
−0.158812 + 0.987309i \(0.550766\pi\)
\(368\) −15.4508 −0.805427
\(369\) 45.9415 2.39162
\(370\) 0 0
\(371\) −25.7911 −1.33901
\(372\) −3.15924 −0.163799
\(373\) −6.64786 −0.344213 −0.172107 0.985078i \(-0.555057\pi\)
−0.172107 + 0.985078i \(0.555057\pi\)
\(374\) −5.53098 −0.286000
\(375\) 0 0
\(376\) −15.2384 −0.785858
\(377\) −23.0626 −1.18778
\(378\) 52.8214 2.71684
\(379\) 16.3481 0.839745 0.419873 0.907583i \(-0.362075\pi\)
0.419873 + 0.907583i \(0.362075\pi\)
\(380\) 0 0
\(381\) 66.9758 3.43128
\(382\) 16.9279 0.866108
\(383\) 3.93415 0.201026 0.100513 0.994936i \(-0.467952\pi\)
0.100513 + 0.994936i \(0.467952\pi\)
\(384\) −18.7187 −0.955236
\(385\) 0 0
\(386\) −0.940655 −0.0478781
\(387\) −21.3948 −1.08756
\(388\) −3.81899 −0.193880
\(389\) 38.6765 1.96098 0.980489 0.196572i \(-0.0629811\pi\)
0.980489 + 0.196572i \(0.0629811\pi\)
\(390\) 0 0
\(391\) −23.7855 −1.20289
\(392\) −23.5754 −1.19074
\(393\) 52.8486 2.66586
\(394\) −3.93009 −0.197995
\(395\) 0 0
\(396\) −2.97925 −0.149713
\(397\) −8.45961 −0.424576 −0.212288 0.977207i \(-0.568091\pi\)
−0.212288 + 0.977207i \(0.568091\pi\)
\(398\) −15.5712 −0.780511
\(399\) 11.8755 0.594521
\(400\) 0 0
\(401\) −28.4450 −1.42047 −0.710237 0.703963i \(-0.751412\pi\)
−0.710237 + 0.703963i \(0.751412\pi\)
\(402\) −34.4488 −1.71815
\(403\) −5.51414 −0.274679
\(404\) −6.78064 −0.337350
\(405\) 0 0
\(406\) 44.9864 2.23264
\(407\) 9.50113 0.470954
\(408\) −41.9857 −2.07860
\(409\) −24.9510 −1.23375 −0.616873 0.787063i \(-0.711601\pi\)
−0.616873 + 0.787063i \(0.711601\pi\)
\(410\) 0 0
\(411\) 43.5843 2.14985
\(412\) 0.0512492 0.00252487
\(413\) −14.6399 −0.720382
\(414\) 43.7484 2.15012
\(415\) 0 0
\(416\) 6.13982 0.301029
\(417\) 45.4275 2.22459
\(418\) 1.24377 0.0608348
\(419\) −11.7203 −0.572575 −0.286287 0.958144i \(-0.592421\pi\)
−0.286287 + 0.958144i \(0.592421\pi\)
\(420\) 0 0
\(421\) 18.5710 0.905095 0.452547 0.891740i \(-0.350515\pi\)
0.452547 + 0.891740i \(0.350515\pi\)
\(422\) 18.5071 0.900913
\(423\) 32.8448 1.59697
\(424\) −20.5048 −0.995803
\(425\) 0 0
\(426\) −19.0205 −0.921547
\(427\) −28.1382 −1.36170
\(428\) 7.50953 0.362987
\(429\) −7.57217 −0.365588
\(430\) 0 0
\(431\) −13.5731 −0.653792 −0.326896 0.945060i \(-0.606003\pi\)
−0.326896 + 0.945060i \(0.606003\pi\)
\(432\) 31.9677 1.53805
\(433\) 33.2974 1.60017 0.800086 0.599885i \(-0.204787\pi\)
0.800086 + 0.599885i \(0.204787\pi\)
\(434\) 10.7560 0.516304
\(435\) 0 0
\(436\) 3.42541 0.164047
\(437\) 5.34873 0.255864
\(438\) −14.9560 −0.714627
\(439\) 18.5043 0.883163 0.441581 0.897221i \(-0.354418\pi\)
0.441581 + 0.897221i \(0.354418\pi\)
\(440\) 0 0
\(441\) 50.8144 2.41973
\(442\) −13.5340 −0.643748
\(443\) 26.8846 1.27733 0.638664 0.769486i \(-0.279488\pi\)
0.638664 + 0.769486i \(0.279488\pi\)
\(444\) 13.3200 0.632141
\(445\) 0 0
\(446\) 8.38312 0.396952
\(447\) −34.0612 −1.61104
\(448\) −34.1476 −1.61332
\(449\) 9.74064 0.459689 0.229845 0.973227i \(-0.426178\pi\)
0.229845 + 0.973227i \(0.426178\pi\)
\(450\) 0 0
\(451\) 6.98607 0.328961
\(452\) 1.49136 0.0701475
\(453\) 15.1161 0.710216
\(454\) −11.3574 −0.533030
\(455\) 0 0
\(456\) 9.44147 0.442137
\(457\) 6.33245 0.296219 0.148110 0.988971i \(-0.452681\pi\)
0.148110 + 0.988971i \(0.452681\pi\)
\(458\) −25.5828 −1.19541
\(459\) 49.2124 2.29704
\(460\) 0 0
\(461\) 17.9981 0.838253 0.419127 0.907928i \(-0.362336\pi\)
0.419127 + 0.907928i \(0.362336\pi\)
\(462\) 14.7704 0.687183
\(463\) −23.2596 −1.08097 −0.540483 0.841355i \(-0.681758\pi\)
−0.540483 + 0.841355i \(0.681758\pi\)
\(464\) 27.2260 1.26393
\(465\) 0 0
\(466\) −8.25395 −0.382357
\(467\) −27.9976 −1.29557 −0.647787 0.761822i \(-0.724305\pi\)
−0.647787 + 0.761822i \(0.724305\pi\)
\(468\) −7.29006 −0.336983
\(469\) −34.3476 −1.58602
\(470\) 0 0
\(471\) 10.2138 0.470627
\(472\) −11.6392 −0.535738
\(473\) −3.25340 −0.149591
\(474\) 52.1392 2.39483
\(475\) 0 0
\(476\) −7.73133 −0.354365
\(477\) 44.1961 2.02360
\(478\) 17.2623 0.789558
\(479\) 18.8574 0.861615 0.430808 0.902444i \(-0.358229\pi\)
0.430808 + 0.902444i \(0.358229\pi\)
\(480\) 0 0
\(481\) 23.2488 1.06005
\(482\) 15.3934 0.701148
\(483\) 63.5191 2.89022
\(484\) −0.453038 −0.0205926
\(485\) 0 0
\(486\) −14.5830 −0.661499
\(487\) 17.3588 0.786601 0.393301 0.919410i \(-0.371333\pi\)
0.393301 + 0.919410i \(0.371333\pi\)
\(488\) −22.3709 −1.01268
\(489\) 17.2764 0.781267
\(490\) 0 0
\(491\) −31.7460 −1.43268 −0.716338 0.697754i \(-0.754183\pi\)
−0.716338 + 0.697754i \(0.754183\pi\)
\(492\) 9.79406 0.441550
\(493\) 41.9127 1.88765
\(494\) 3.04344 0.136931
\(495\) 0 0
\(496\) 6.50957 0.292288
\(497\) −18.9646 −0.850680
\(498\) 33.1001 1.48325
\(499\) −4.37020 −0.195637 −0.0978185 0.995204i \(-0.531186\pi\)
−0.0978185 + 0.995204i \(0.531186\pi\)
\(500\) 0 0
\(501\) −67.3414 −3.00859
\(502\) 33.4675 1.49373
\(503\) −37.9393 −1.69163 −0.845816 0.533475i \(-0.820886\pi\)
−0.845816 + 0.533475i \(0.820886\pi\)
\(504\) 76.9971 3.42972
\(505\) 0 0
\(506\) 6.65259 0.295744
\(507\) 21.7003 0.963742
\(508\) 9.80520 0.435036
\(509\) 42.2367 1.87211 0.936055 0.351853i \(-0.114448\pi\)
0.936055 + 0.351853i \(0.114448\pi\)
\(510\) 0 0
\(511\) −14.9121 −0.659673
\(512\) −24.8750 −1.09933
\(513\) −11.0665 −0.488600
\(514\) 29.0955 1.28335
\(515\) 0 0
\(516\) −4.56107 −0.200790
\(517\) 4.99452 0.219659
\(518\) −45.3496 −1.99255
\(519\) 60.9873 2.67705
\(520\) 0 0
\(521\) −23.2491 −1.01856 −0.509280 0.860601i \(-0.670088\pi\)
−0.509280 + 0.860601i \(0.670088\pi\)
\(522\) −77.0895 −3.37412
\(523\) 1.46476 0.0640496 0.0320248 0.999487i \(-0.489804\pi\)
0.0320248 + 0.999487i \(0.489804\pi\)
\(524\) 7.73699 0.337992
\(525\) 0 0
\(526\) 33.8584 1.47630
\(527\) 10.0211 0.436525
\(528\) 8.93913 0.389026
\(529\) 5.60890 0.243865
\(530\) 0 0
\(531\) 25.0872 1.08869
\(532\) 1.73857 0.0753766
\(533\) 17.0946 0.740447
\(534\) 12.8562 0.556340
\(535\) 0 0
\(536\) −27.3075 −1.17951
\(537\) 71.3693 3.07981
\(538\) 18.0993 0.780316
\(539\) 7.72706 0.332828
\(540\) 0 0
\(541\) −21.5910 −0.928268 −0.464134 0.885765i \(-0.653634\pi\)
−0.464134 + 0.885765i \(0.653634\pi\)
\(542\) −39.5107 −1.69713
\(543\) −21.7779 −0.934579
\(544\) −11.1582 −0.478402
\(545\) 0 0
\(546\) 36.1425 1.54676
\(547\) −33.5992 −1.43660 −0.718300 0.695734i \(-0.755079\pi\)
−0.718300 + 0.695734i \(0.755079\pi\)
\(548\) 6.38070 0.272570
\(549\) 48.2181 2.05790
\(550\) 0 0
\(551\) −9.42505 −0.401520
\(552\) 50.4999 2.14942
\(553\) 51.9861 2.21067
\(554\) 17.2923 0.734678
\(555\) 0 0
\(556\) 6.65055 0.282046
\(557\) −37.7230 −1.59838 −0.799188 0.601082i \(-0.794737\pi\)
−0.799188 + 0.601082i \(0.794737\pi\)
\(558\) −18.4317 −0.780275
\(559\) −7.96090 −0.336710
\(560\) 0 0
\(561\) 13.7612 0.581000
\(562\) −11.4698 −0.483824
\(563\) −0.353129 −0.0148826 −0.00744131 0.999972i \(-0.502369\pi\)
−0.00744131 + 0.999972i \(0.502369\pi\)
\(564\) 7.00203 0.294839
\(565\) 0 0
\(566\) 19.0078 0.798957
\(567\) −55.7116 −2.33967
\(568\) −15.0775 −0.632640
\(569\) −6.10053 −0.255747 −0.127874 0.991790i \(-0.540815\pi\)
−0.127874 + 0.991790i \(0.540815\pi\)
\(570\) 0 0
\(571\) 10.7153 0.448420 0.224210 0.974541i \(-0.428020\pi\)
0.224210 + 0.974541i \(0.428020\pi\)
\(572\) −1.10856 −0.0463512
\(573\) −42.1172 −1.75947
\(574\) −33.3450 −1.39179
\(575\) 0 0
\(576\) 58.5159 2.43816
\(577\) 22.8110 0.949636 0.474818 0.880084i \(-0.342514\pi\)
0.474818 + 0.880084i \(0.342514\pi\)
\(578\) 3.45190 0.143580
\(579\) 2.34038 0.0972628
\(580\) 0 0
\(581\) 33.0029 1.36919
\(582\) −32.4452 −1.34489
\(583\) 6.72067 0.278342
\(584\) −11.8556 −0.490590
\(585\) 0 0
\(586\) −2.25569 −0.0931817
\(587\) −11.2009 −0.462311 −0.231156 0.972917i \(-0.574251\pi\)
−0.231156 + 0.972917i \(0.574251\pi\)
\(588\) 10.8329 0.446741
\(589\) −2.25347 −0.0928528
\(590\) 0 0
\(591\) 9.77819 0.402221
\(592\) −27.4458 −1.12801
\(593\) −21.1463 −0.868376 −0.434188 0.900822i \(-0.642965\pi\)
−0.434188 + 0.900822i \(0.642965\pi\)
\(594\) −13.7642 −0.564753
\(595\) 0 0
\(596\) −4.98653 −0.204256
\(597\) 38.7415 1.58558
\(598\) 16.2785 0.665679
\(599\) 5.65347 0.230995 0.115497 0.993308i \(-0.463154\pi\)
0.115497 + 0.993308i \(0.463154\pi\)
\(600\) 0 0
\(601\) −10.2942 −0.419911 −0.209955 0.977711i \(-0.567332\pi\)
−0.209955 + 0.977711i \(0.567332\pi\)
\(602\) 15.5287 0.632902
\(603\) 58.8586 2.39691
\(604\) 2.21298 0.0900450
\(605\) 0 0
\(606\) −57.6066 −2.34011
\(607\) 7.90688 0.320930 0.160465 0.987041i \(-0.448701\pi\)
0.160465 + 0.987041i \(0.448701\pi\)
\(608\) 2.50917 0.101760
\(609\) −111.928 −4.53553
\(610\) 0 0
\(611\) 12.2213 0.494423
\(612\) 13.2486 0.535541
\(613\) −19.1079 −0.771761 −0.385880 0.922549i \(-0.626102\pi\)
−0.385880 + 0.922549i \(0.626102\pi\)
\(614\) −22.1361 −0.893339
\(615\) 0 0
\(616\) 11.7085 0.471750
\(617\) −9.68005 −0.389704 −0.194852 0.980833i \(-0.562423\pi\)
−0.194852 + 0.980833i \(0.562423\pi\)
\(618\) 0.435400 0.0175144
\(619\) 46.7198 1.87783 0.938913 0.344155i \(-0.111835\pi\)
0.938913 + 0.344155i \(0.111835\pi\)
\(620\) 0 0
\(621\) −59.1919 −2.37529
\(622\) −21.4950 −0.861873
\(623\) 12.8184 0.513558
\(624\) 21.8736 0.875645
\(625\) 0 0
\(626\) 36.8420 1.47250
\(627\) −3.09454 −0.123584
\(628\) 1.49529 0.0596687
\(629\) −42.2511 −1.68466
\(630\) 0 0
\(631\) 21.8178 0.868551 0.434276 0.900780i \(-0.357004\pi\)
0.434276 + 0.900780i \(0.357004\pi\)
\(632\) 41.3307 1.64405
\(633\) −46.0463 −1.83018
\(634\) −39.3242 −1.56177
\(635\) 0 0
\(636\) 9.42198 0.373606
\(637\) 18.9077 0.749151
\(638\) −11.7226 −0.464102
\(639\) 32.4982 1.28561
\(640\) 0 0
\(641\) 23.1143 0.912960 0.456480 0.889734i \(-0.349110\pi\)
0.456480 + 0.889734i \(0.349110\pi\)
\(642\) 63.7990 2.51795
\(643\) −25.6612 −1.01198 −0.505989 0.862540i \(-0.668872\pi\)
−0.505989 + 0.862540i \(0.668872\pi\)
\(644\) 9.29914 0.366438
\(645\) 0 0
\(646\) −5.53098 −0.217613
\(647\) −21.4078 −0.841628 −0.420814 0.907147i \(-0.638255\pi\)
−0.420814 + 0.907147i \(0.638255\pi\)
\(648\) −44.2927 −1.73998
\(649\) 3.81487 0.149747
\(650\) 0 0
\(651\) −26.7612 −1.04886
\(652\) 2.52925 0.0990532
\(653\) −32.4660 −1.27049 −0.635246 0.772310i \(-0.719101\pi\)
−0.635246 + 0.772310i \(0.719101\pi\)
\(654\) 29.1014 1.13795
\(655\) 0 0
\(656\) −20.1805 −0.787918
\(657\) 25.5537 0.996943
\(658\) −23.8392 −0.929349
\(659\) −17.6170 −0.686259 −0.343130 0.939288i \(-0.611487\pi\)
−0.343130 + 0.939288i \(0.611487\pi\)
\(660\) 0 0
\(661\) 47.7091 1.85567 0.927834 0.372993i \(-0.121669\pi\)
0.927834 + 0.372993i \(0.121669\pi\)
\(662\) −2.74078 −0.106524
\(663\) 33.6731 1.30775
\(664\) 26.2384 1.01825
\(665\) 0 0
\(666\) 77.7119 3.01127
\(667\) −50.4120 −1.95196
\(668\) −9.85872 −0.381445
\(669\) −20.8575 −0.806396
\(670\) 0 0
\(671\) 7.33227 0.283059
\(672\) 29.7978 1.14947
\(673\) −43.3750 −1.67199 −0.835993 0.548741i \(-0.815107\pi\)
−0.835993 + 0.548741i \(0.815107\pi\)
\(674\) −11.3838 −0.438488
\(675\) 0 0
\(676\) 3.17690 0.122188
\(677\) 32.9976 1.26820 0.634100 0.773251i \(-0.281371\pi\)
0.634100 + 0.773251i \(0.281371\pi\)
\(678\) 12.6702 0.486595
\(679\) −32.3499 −1.24147
\(680\) 0 0
\(681\) 28.2576 1.08283
\(682\) −2.80280 −0.107325
\(683\) −11.0439 −0.422585 −0.211292 0.977423i \(-0.567767\pi\)
−0.211292 + 0.977423i \(0.567767\pi\)
\(684\) −2.97925 −0.113914
\(685\) 0 0
\(686\) −3.47032 −0.132498
\(687\) 63.6509 2.42843
\(688\) 9.39803 0.358297
\(689\) 16.4451 0.626509
\(690\) 0 0
\(691\) −10.1642 −0.386665 −0.193332 0.981133i \(-0.561930\pi\)
−0.193332 + 0.981133i \(0.561930\pi\)
\(692\) 8.92849 0.339410
\(693\) −25.2366 −0.958658
\(694\) −13.6633 −0.518651
\(695\) 0 0
\(696\) −88.9863 −3.37302
\(697\) −31.0667 −1.17674
\(698\) −22.6174 −0.856080
\(699\) 20.5361 0.776746
\(700\) 0 0
\(701\) 18.7655 0.708762 0.354381 0.935101i \(-0.384692\pi\)
0.354381 + 0.935101i \(0.384692\pi\)
\(702\) −33.6804 −1.27118
\(703\) 9.50113 0.358342
\(704\) 8.89820 0.335363
\(705\) 0 0
\(706\) 0.0556347 0.00209384
\(707\) −57.4374 −2.16016
\(708\) 5.34822 0.200998
\(709\) −0.593064 −0.0222730 −0.0111365 0.999938i \(-0.503545\pi\)
−0.0111365 + 0.999938i \(0.503545\pi\)
\(710\) 0 0
\(711\) −89.0843 −3.34092
\(712\) 10.1911 0.381927
\(713\) −12.0532 −0.451397
\(714\) −65.6834 −2.45814
\(715\) 0 0
\(716\) 10.4484 0.390475
\(717\) −42.9491 −1.60396
\(718\) −20.7688 −0.775087
\(719\) −39.7948 −1.48410 −0.742049 0.670346i \(-0.766146\pi\)
−0.742049 + 0.670346i \(0.766146\pi\)
\(720\) 0 0
\(721\) 0.434121 0.0161675
\(722\) 1.24377 0.0462883
\(723\) −38.2991 −1.42436
\(724\) −3.18827 −0.118491
\(725\) 0 0
\(726\) −3.84889 −0.142846
\(727\) −10.2940 −0.381782 −0.190891 0.981611i \(-0.561138\pi\)
−0.190891 + 0.981611i \(0.561138\pi\)
\(728\) 28.6502 1.06185
\(729\) −7.26907 −0.269225
\(730\) 0 0
\(731\) 14.4677 0.535107
\(732\) 10.2794 0.379938
\(733\) −11.7380 −0.433551 −0.216776 0.976221i \(-0.569554\pi\)
−0.216776 + 0.976221i \(0.569554\pi\)
\(734\) −7.56809 −0.279343
\(735\) 0 0
\(736\) 13.4209 0.494700
\(737\) 8.95031 0.329689
\(738\) 57.1406 2.10338
\(739\) 24.1090 0.886865 0.443433 0.896308i \(-0.353761\pi\)
0.443433 + 0.896308i \(0.353761\pi\)
\(740\) 0 0
\(741\) −7.57217 −0.278171
\(742\) −32.0782 −1.17763
\(743\) 9.25055 0.339370 0.169685 0.985498i \(-0.445725\pi\)
0.169685 + 0.985498i \(0.445725\pi\)
\(744\) −21.2761 −0.780020
\(745\) 0 0
\(746\) −8.26841 −0.302728
\(747\) −56.5544 −2.06922
\(748\) 2.01463 0.0736623
\(749\) 63.6116 2.32432
\(750\) 0 0
\(751\) −34.6758 −1.26534 −0.632669 0.774422i \(-0.718041\pi\)
−0.632669 + 0.774422i \(0.718041\pi\)
\(752\) −14.4276 −0.526120
\(753\) −83.2681 −3.03446
\(754\) −28.6846 −1.04463
\(755\) 0 0
\(756\) −19.2400 −0.699751
\(757\) 23.2943 0.846647 0.423323 0.905979i \(-0.360863\pi\)
0.423323 + 0.905979i \(0.360863\pi\)
\(758\) 20.3333 0.738537
\(759\) −16.5518 −0.600794
\(760\) 0 0
\(761\) −1.10679 −0.0401210 −0.0200605 0.999799i \(-0.506386\pi\)
−0.0200605 + 0.999799i \(0.506386\pi\)
\(762\) 83.3025 3.01773
\(763\) 29.0159 1.05045
\(764\) −6.16592 −0.223075
\(765\) 0 0
\(766\) 4.89317 0.176798
\(767\) 9.33479 0.337060
\(768\) 31.7898 1.14712
\(769\) 3.11121 0.112193 0.0560965 0.998425i \(-0.482135\pi\)
0.0560965 + 0.998425i \(0.482135\pi\)
\(770\) 0 0
\(771\) −72.3904 −2.60708
\(772\) 0.342630 0.0123315
\(773\) 11.7199 0.421536 0.210768 0.977536i \(-0.432404\pi\)
0.210768 + 0.977536i \(0.432404\pi\)
\(774\) −26.6103 −0.956486
\(775\) 0 0
\(776\) −25.7193 −0.923268
\(777\) 112.831 4.04780
\(778\) 48.1047 1.72464
\(779\) 6.98607 0.250302
\(780\) 0 0
\(781\) 4.94182 0.176832
\(782\) −29.5837 −1.05791
\(783\) 104.303 3.72747
\(784\) −22.3210 −0.797180
\(785\) 0 0
\(786\) 65.7315 2.34456
\(787\) 41.2119 1.46904 0.734522 0.678584i \(-0.237406\pi\)
0.734522 + 0.678584i \(0.237406\pi\)
\(788\) 1.43152 0.0509957
\(789\) −84.2407 −2.99905
\(790\) 0 0
\(791\) 12.6330 0.449176
\(792\) −20.0639 −0.712941
\(793\) 17.9417 0.637128
\(794\) −10.5218 −0.373405
\(795\) 0 0
\(796\) 5.67172 0.201029
\(797\) 25.6880 0.909915 0.454958 0.890513i \(-0.349654\pi\)
0.454958 + 0.890513i \(0.349654\pi\)
\(798\) 14.7704 0.522868
\(799\) −22.2104 −0.785747
\(800\) 0 0
\(801\) −21.9658 −0.776125
\(802\) −35.3790 −1.24927
\(803\) 3.88580 0.137127
\(804\) 12.5478 0.442527
\(805\) 0 0
\(806\) −6.85831 −0.241574
\(807\) −45.0316 −1.58519
\(808\) −45.6647 −1.60648
\(809\) −16.4577 −0.578623 −0.289311 0.957235i \(-0.593426\pi\)
−0.289311 + 0.957235i \(0.593426\pi\)
\(810\) 0 0
\(811\) −4.99059 −0.175243 −0.0876217 0.996154i \(-0.527927\pi\)
−0.0876217 + 0.996154i \(0.527927\pi\)
\(812\) −16.3861 −0.575040
\(813\) 98.3038 3.44767
\(814\) 11.8172 0.414193
\(815\) 0 0
\(816\) −39.7519 −1.39159
\(817\) −3.25340 −0.113822
\(818\) −31.0333 −1.08505
\(819\) −61.7526 −2.15781
\(820\) 0 0
\(821\) −33.8114 −1.18003 −0.590013 0.807393i \(-0.700878\pi\)
−0.590013 + 0.807393i \(0.700878\pi\)
\(822\) 54.2088 1.89075
\(823\) −50.7096 −1.76762 −0.883812 0.467842i \(-0.845032\pi\)
−0.883812 + 0.467842i \(0.845032\pi\)
\(824\) 0.345141 0.0120236
\(825\) 0 0
\(826\) −18.2086 −0.633560
\(827\) −10.5942 −0.368396 −0.184198 0.982889i \(-0.558969\pi\)
−0.184198 + 0.982889i \(0.558969\pi\)
\(828\) −15.9352 −0.553786
\(829\) −43.2271 −1.50134 −0.750670 0.660677i \(-0.770269\pi\)
−0.750670 + 0.660677i \(0.770269\pi\)
\(830\) 0 0
\(831\) −43.0237 −1.49248
\(832\) 21.7734 0.754858
\(833\) −34.3619 −1.19057
\(834\) 56.5014 1.95648
\(835\) 0 0
\(836\) −0.453038 −0.0156686
\(837\) 24.9382 0.861989
\(838\) −14.5774 −0.503567
\(839\) −34.4342 −1.18880 −0.594401 0.804169i \(-0.702611\pi\)
−0.594401 + 0.804169i \(0.702611\pi\)
\(840\) 0 0
\(841\) 59.8315 2.06315
\(842\) 23.0980 0.796011
\(843\) 28.5372 0.982873
\(844\) −6.74114 −0.232040
\(845\) 0 0
\(846\) 40.8513 1.40450
\(847\) −3.83759 −0.131861
\(848\) −19.4139 −0.666675
\(849\) −47.2919 −1.62306
\(850\) 0 0
\(851\) 50.8190 1.74205
\(852\) 6.92814 0.237354
\(853\) 0.0569549 0.00195010 0.000975050 1.00000i \(-0.499690\pi\)
0.000975050 1.00000i \(0.499690\pi\)
\(854\) −34.9974 −1.19759
\(855\) 0 0
\(856\) 50.5734 1.72856
\(857\) −7.28367 −0.248805 −0.124403 0.992232i \(-0.539701\pi\)
−0.124403 + 0.992232i \(0.539701\pi\)
\(858\) −9.41804 −0.321526
\(859\) 1.89445 0.0646379 0.0323189 0.999478i \(-0.489711\pi\)
0.0323189 + 0.999478i \(0.489711\pi\)
\(860\) 0 0
\(861\) 82.9634 2.82739
\(862\) −16.8818 −0.574996
\(863\) 1.45592 0.0495602 0.0247801 0.999693i \(-0.492111\pi\)
0.0247801 + 0.999693i \(0.492111\pi\)
\(864\) −27.7679 −0.944682
\(865\) 0 0
\(866\) 41.4143 1.40732
\(867\) −8.58843 −0.291678
\(868\) −3.91782 −0.132980
\(869\) −13.5466 −0.459535
\(870\) 0 0
\(871\) 21.9010 0.742085
\(872\) 23.0687 0.781203
\(873\) 55.4353 1.87620
\(874\) 6.65259 0.225027
\(875\) 0 0
\(876\) 5.44767 0.184060
\(877\) −9.00209 −0.303979 −0.151990 0.988382i \(-0.548568\pi\)
−0.151990 + 0.988382i \(0.548568\pi\)
\(878\) 23.0151 0.776722
\(879\) 5.61222 0.189296
\(880\) 0 0
\(881\) −49.4226 −1.66509 −0.832545 0.553957i \(-0.813117\pi\)
−0.832545 + 0.553957i \(0.813117\pi\)
\(882\) 63.2014 2.12810
\(883\) 11.5155 0.387529 0.193764 0.981048i \(-0.437930\pi\)
0.193764 + 0.981048i \(0.437930\pi\)
\(884\) 4.92971 0.165804
\(885\) 0 0
\(886\) 33.4383 1.12338
\(887\) 5.16282 0.173350 0.0866752 0.996237i \(-0.472376\pi\)
0.0866752 + 0.996237i \(0.472376\pi\)
\(888\) 89.7047 3.01029
\(889\) 83.0578 2.78567
\(890\) 0 0
\(891\) 14.5174 0.486350
\(892\) −3.05351 −0.102239
\(893\) 4.99452 0.167135
\(894\) −42.3642 −1.41687
\(895\) 0 0
\(896\) −23.2134 −0.775505
\(897\) −40.5015 −1.35231
\(898\) 12.1151 0.404286
\(899\) 21.2391 0.708363
\(900\) 0 0
\(901\) −29.8865 −0.995662
\(902\) 8.68906 0.289314
\(903\) −38.6359 −1.28572
\(904\) 10.0436 0.334046
\(905\) 0 0
\(906\) 18.8009 0.624619
\(907\) −36.5420 −1.21336 −0.606679 0.794947i \(-0.707499\pi\)
−0.606679 + 0.794947i \(0.707499\pi\)
\(908\) 4.13689 0.137287
\(909\) 98.4258 3.26458
\(910\) 0 0
\(911\) 9.84473 0.326171 0.163085 0.986612i \(-0.447855\pi\)
0.163085 + 0.986612i \(0.447855\pi\)
\(912\) 8.93913 0.296004
\(913\) −8.59991 −0.284616
\(914\) 7.87610 0.260518
\(915\) 0 0
\(916\) 9.31843 0.307890
\(917\) 65.5384 2.16427
\(918\) 61.2088 2.02019
\(919\) 8.16405 0.269307 0.134654 0.990893i \(-0.457008\pi\)
0.134654 + 0.990893i \(0.457008\pi\)
\(920\) 0 0
\(921\) 55.0752 1.81479
\(922\) 22.3854 0.737225
\(923\) 12.0924 0.398025
\(924\) −5.38007 −0.176991
\(925\) 0 0
\(926\) −28.9296 −0.950685
\(927\) −0.743918 −0.0244335
\(928\) −23.6491 −0.776318
\(929\) 33.3986 1.09577 0.547887 0.836552i \(-0.315432\pi\)
0.547887 + 0.836552i \(0.315432\pi\)
\(930\) 0 0
\(931\) 7.72706 0.253244
\(932\) 3.00646 0.0984800
\(933\) 53.4803 1.75087
\(934\) −34.8225 −1.13943
\(935\) 0 0
\(936\) −49.0954 −1.60473
\(937\) 8.19016 0.267561 0.133780 0.991011i \(-0.457288\pi\)
0.133780 + 0.991011i \(0.457288\pi\)
\(938\) −42.7205 −1.39487
\(939\) −91.6639 −2.99134
\(940\) 0 0
\(941\) −15.7134 −0.512243 −0.256122 0.966645i \(-0.582445\pi\)
−0.256122 + 0.966645i \(0.582445\pi\)
\(942\) 12.7036 0.413906
\(943\) 37.3666 1.21682
\(944\) −11.0199 −0.358669
\(945\) 0 0
\(946\) −4.04648 −0.131562
\(947\) −51.1369 −1.66172 −0.830862 0.556478i \(-0.812152\pi\)
−0.830862 + 0.556478i \(0.812152\pi\)
\(948\) −18.9915 −0.616814
\(949\) 9.50837 0.308655
\(950\) 0 0
\(951\) 97.8399 3.17268
\(952\) −52.0672 −1.68751
\(953\) 40.0172 1.29628 0.648142 0.761520i \(-0.275546\pi\)
0.648142 + 0.761520i \(0.275546\pi\)
\(954\) 54.9698 1.77971
\(955\) 0 0
\(956\) −6.28771 −0.203359
\(957\) 29.1661 0.942808
\(958\) 23.4542 0.757772
\(959\) 54.0495 1.74535
\(960\) 0 0
\(961\) −25.9219 −0.836189
\(962\) 28.9161 0.932293
\(963\) −109.006 −3.51267
\(964\) −5.60696 −0.180588
\(965\) 0 0
\(966\) 79.0031 2.54188
\(967\) 32.3043 1.03884 0.519418 0.854520i \(-0.326149\pi\)
0.519418 + 0.854520i \(0.326149\pi\)
\(968\) −3.05101 −0.0980633
\(969\) 13.7612 0.442075
\(970\) 0 0
\(971\) −15.9162 −0.510775 −0.255387 0.966839i \(-0.582203\pi\)
−0.255387 + 0.966839i \(0.582203\pi\)
\(972\) 5.31180 0.170376
\(973\) 56.3354 1.80603
\(974\) 21.5903 0.691798
\(975\) 0 0
\(976\) −21.1806 −0.677974
\(977\) −16.2932 −0.521264 −0.260632 0.965438i \(-0.583931\pi\)
−0.260632 + 0.965438i \(0.583931\pi\)
\(978\) 21.4879 0.687107
\(979\) −3.34023 −0.106754
\(980\) 0 0
\(981\) −49.7222 −1.58751
\(982\) −39.4847 −1.26001
\(983\) −12.4417 −0.396830 −0.198415 0.980118i \(-0.563579\pi\)
−0.198415 + 0.980118i \(0.563579\pi\)
\(984\) 65.9588 2.10269
\(985\) 0 0
\(986\) 52.1297 1.66015
\(987\) 59.3127 1.88794
\(988\) −1.10856 −0.0352680
\(989\) −17.4015 −0.553337
\(990\) 0 0
\(991\) 15.7073 0.498960 0.249480 0.968380i \(-0.419740\pi\)
0.249480 + 0.968380i \(0.419740\pi\)
\(992\) −5.65435 −0.179526
\(993\) 6.81915 0.216399
\(994\) −23.5876 −0.748155
\(995\) 0 0
\(996\) −12.0566 −0.382027
\(997\) 46.9517 1.48698 0.743488 0.668749i \(-0.233170\pi\)
0.743488 + 0.668749i \(0.233170\pi\)
\(998\) −5.43552 −0.172058
\(999\) −105.145 −3.32663
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.p.1.7 9
5.4 even 2 1045.2.a.k.1.3 9
15.14 odd 2 9405.2.a.bh.1.7 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.k.1.3 9 5.4 even 2
5225.2.a.p.1.7 9 1.1 even 1 trivial
9405.2.a.bh.1.7 9 15.14 odd 2