Properties

Label 201.2.a.e.1.5
Level $201$
Weight $2$
Character 201.1
Self dual yes
Analytic conductor $1.605$
Analytic rank $0$
Dimension $5$
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] = [201,2,Mod(1,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 201.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: \(1.60499308063\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.1025428.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 8x^{3} + 13x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-2.33760\) of defining polynomial
Character \(\chi\) \(=\) 201.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.33760 q^{2} +1.00000 q^{3} +3.46438 q^{4} -1.73837 q^{5} +2.33760 q^{6} -3.14916 q^{7} +3.42315 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.33760 q^{2} +1.00000 q^{3} +3.46438 q^{4} -1.73837 q^{5} +2.33760 q^{6} -3.14916 q^{7} +3.42315 q^{8} +1.00000 q^{9} -4.06362 q^{10} +1.08555 q^{11} +3.46438 q^{12} +3.08555 q^{13} -7.36149 q^{14} -1.73837 q^{15} +1.07319 q^{16} -7.83394 q^{17} +2.33760 q^{18} +0.987645 q^{19} -6.02238 q^{20} -3.14916 q^{21} +2.53758 q^{22} +1.81156 q^{23} +3.42315 q^{24} -1.97807 q^{25} +7.21278 q^{26} +1.00000 q^{27} -10.9099 q^{28} +8.47870 q^{29} -4.06362 q^{30} +2.86515 q^{31} -4.33760 q^{32} +1.08555 q^{33} -18.3126 q^{34} +5.47441 q^{35} +3.46438 q^{36} +9.75118 q^{37} +2.30872 q^{38} +3.08555 q^{39} -5.95070 q^{40} -6.02238 q^{41} -7.36149 q^{42} +3.81005 q^{43} +3.76075 q^{44} -1.73837 q^{45} +4.23471 q^{46} -0.987645 q^{47} +1.07319 q^{48} +2.91723 q^{49} -4.62394 q^{50} -7.83394 q^{51} +10.6895 q^{52} -11.8991 q^{53} +2.33760 q^{54} -1.88708 q^{55} -10.7801 q^{56} +0.987645 q^{57} +19.8198 q^{58} +4.34914 q^{59} -6.02238 q^{60} +6.70867 q^{61} +6.69759 q^{62} -3.14916 q^{63} -12.2860 q^{64} -5.36382 q^{65} +2.53758 q^{66} -1.00000 q^{67} -27.1398 q^{68} +1.81156 q^{69} +12.7970 q^{70} +1.02163 q^{71} +3.42315 q^{72} +4.74810 q^{73} +22.7944 q^{74} -1.97807 q^{75} +3.42158 q^{76} -3.41856 q^{77} +7.21278 q^{78} +15.0968 q^{79} -1.86560 q^{80} +1.00000 q^{81} -14.0779 q^{82} -16.5551 q^{83} -10.9099 q^{84} +13.6183 q^{85} +8.90639 q^{86} +8.47870 q^{87} +3.71599 q^{88} +2.38191 q^{89} -4.06362 q^{90} -9.71689 q^{91} +6.27595 q^{92} +2.86515 q^{93} -2.30872 q^{94} -1.71689 q^{95} -4.33760 q^{96} -6.12150 q^{97} +6.81933 q^{98} +1.08555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q + 5 q^{3} + 6 q^{4} - 3 q^{5} + 7 q^{7} + 5 q^{9} - 3 q^{10} + 6 q^{12} + 10 q^{13} - 9 q^{14} - 3 q^{15} - 5 q^{17} + 5 q^{19} - 7 q^{20} + 7 q^{21} - 4 q^{22} - 2 q^{23} + 2 q^{25} - 4 q^{26} + 5 q^{27} - 3 q^{28} + 3 q^{29} - 3 q^{30} + 9 q^{31} - 10 q^{32} - 18 q^{34} - 7 q^{35} + 6 q^{36} + 8 q^{37} - 6 q^{38} + 10 q^{39} - 19 q^{40} - 7 q^{41} - 9 q^{42} + q^{43} - 10 q^{44} - 3 q^{45} - 7 q^{46} - 5 q^{47} + 8 q^{49} - 17 q^{50} - 5 q^{51} + 2 q^{52} - 15 q^{53} - 16 q^{55} - 19 q^{56} + 5 q^{57} - 4 q^{58} - 6 q^{59} - 7 q^{60} + 6 q^{61} - 13 q^{62} + 7 q^{63} - 16 q^{64} - 22 q^{65} - 4 q^{66} - 5 q^{67} - 4 q^{68} - 2 q^{69} + 19 q^{70} + 22 q^{71} + 51 q^{74} + 2 q^{75} + 24 q^{76} - 10 q^{77} - 4 q^{78} + 28 q^{79} + 31 q^{80} + 5 q^{81} - 25 q^{82} + 9 q^{83} - 3 q^{84} - 6 q^{85} + 45 q^{86} + 3 q^{87} + 36 q^{88} - 11 q^{89} - 3 q^{90} + 4 q^{91} + 9 q^{92} + 9 q^{93} + 6 q^{94} + 44 q^{95} - 10 q^{96} - 14 q^{97} + 33 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.33760 1.65293 0.826467 0.562985i \(-0.190347\pi\)
0.826467 + 0.562985i \(0.190347\pi\)
\(3\) 1.00000 0.577350
\(4\) 3.46438 1.73219
\(5\) −1.73837 −0.777423 −0.388711 0.921360i \(-0.627080\pi\)
−0.388711 + 0.921360i \(0.627080\pi\)
\(6\) 2.33760 0.954322
\(7\) −3.14916 −1.19027 −0.595136 0.803625i \(-0.702902\pi\)
−0.595136 + 0.803625i \(0.702902\pi\)
\(8\) 3.42315 1.21027
\(9\) 1.00000 0.333333
\(10\) −4.06362 −1.28503
\(11\) 1.08555 0.327305 0.163652 0.986518i \(-0.447672\pi\)
0.163652 + 0.986518i \(0.447672\pi\)
\(12\) 3.46438 1.00008
\(13\) 3.08555 0.855777 0.427888 0.903832i \(-0.359258\pi\)
0.427888 + 0.903832i \(0.359258\pi\)
\(14\) −7.36149 −1.96744
\(15\) −1.73837 −0.448845
\(16\) 1.07319 0.268298
\(17\) −7.83394 −1.90001 −0.950005 0.312234i \(-0.898923\pi\)
−0.950005 + 0.312234i \(0.898923\pi\)
\(18\) 2.33760 0.550978
\(19\) 0.987645 0.226581 0.113291 0.993562i \(-0.463861\pi\)
0.113291 + 0.993562i \(0.463861\pi\)
\(20\) −6.02238 −1.34665
\(21\) −3.14916 −0.687204
\(22\) 2.53758 0.541013
\(23\) 1.81156 0.377737 0.188868 0.982002i \(-0.439518\pi\)
0.188868 + 0.982002i \(0.439518\pi\)
\(24\) 3.42315 0.698747
\(25\) −1.97807 −0.395614
\(26\) 7.21278 1.41454
\(27\) 1.00000 0.192450
\(28\) −10.9099 −2.06178
\(29\) 8.47870 1.57446 0.787228 0.616663i \(-0.211516\pi\)
0.787228 + 0.616663i \(0.211516\pi\)
\(30\) −4.06362 −0.741912
\(31\) 2.86515 0.514597 0.257298 0.966332i \(-0.417168\pi\)
0.257298 + 0.966332i \(0.417168\pi\)
\(32\) −4.33760 −0.766787
\(33\) 1.08555 0.188969
\(34\) −18.3126 −3.14059
\(35\) 5.47441 0.925344
\(36\) 3.46438 0.577397
\(37\) 9.75118 1.60308 0.801542 0.597939i \(-0.204013\pi\)
0.801542 + 0.597939i \(0.204013\pi\)
\(38\) 2.30872 0.374524
\(39\) 3.08555 0.494083
\(40\) −5.95070 −0.940888
\(41\) −6.02238 −0.940538 −0.470269 0.882523i \(-0.655843\pi\)
−0.470269 + 0.882523i \(0.655843\pi\)
\(42\) −7.36149 −1.13590
\(43\) 3.81005 0.581028 0.290514 0.956871i \(-0.406174\pi\)
0.290514 + 0.956871i \(0.406174\pi\)
\(44\) 3.76075 0.566955
\(45\) −1.73837 −0.259141
\(46\) 4.23471 0.624374
\(47\) −0.987645 −0.144063 −0.0720314 0.997402i \(-0.522948\pi\)
−0.0720314 + 0.997402i \(0.522948\pi\)
\(48\) 1.07319 0.154902
\(49\) 2.91723 0.416748
\(50\) −4.62394 −0.653924
\(51\) −7.83394 −1.09697
\(52\) 10.6895 1.48237
\(53\) −11.8991 −1.63446 −0.817231 0.576310i \(-0.804492\pi\)
−0.817231 + 0.576310i \(0.804492\pi\)
\(54\) 2.33760 0.318107
\(55\) −1.88708 −0.254454
\(56\) −10.7801 −1.44055
\(57\) 0.987645 0.130817
\(58\) 19.8198 2.60247
\(59\) 4.34914 0.566210 0.283105 0.959089i \(-0.408636\pi\)
0.283105 + 0.959089i \(0.408636\pi\)
\(60\) −6.02238 −0.777486
\(61\) 6.70867 0.858957 0.429479 0.903077i \(-0.358697\pi\)
0.429479 + 0.903077i \(0.358697\pi\)
\(62\) 6.69759 0.850594
\(63\) −3.14916 −0.396757
\(64\) −12.2860 −1.53575
\(65\) −5.36382 −0.665300
\(66\) 2.53758 0.312354
\(67\) −1.00000 −0.122169
\(68\) −27.1398 −3.29118
\(69\) 1.81156 0.218086
\(70\) 12.7970 1.52953
\(71\) 1.02163 0.121246 0.0606228 0.998161i \(-0.480691\pi\)
0.0606228 + 0.998161i \(0.480691\pi\)
\(72\) 3.42315 0.403422
\(73\) 4.74810 0.555723 0.277862 0.960621i \(-0.410374\pi\)
0.277862 + 0.960621i \(0.410374\pi\)
\(74\) 22.7944 2.64979
\(75\) −1.97807 −0.228408
\(76\) 3.42158 0.392482
\(77\) −3.41856 −0.389582
\(78\) 7.21278 0.816687
\(79\) 15.0968 1.69853 0.849264 0.527969i \(-0.177046\pi\)
0.849264 + 0.527969i \(0.177046\pi\)
\(80\) −1.86560 −0.208581
\(81\) 1.00000 0.111111
\(82\) −14.0779 −1.55465
\(83\) −16.5551 −1.81716 −0.908581 0.417710i \(-0.862833\pi\)
−0.908581 + 0.417710i \(0.862833\pi\)
\(84\) −10.9099 −1.19037
\(85\) 13.6183 1.47711
\(86\) 8.90639 0.960400
\(87\) 8.47870 0.909012
\(88\) 3.71599 0.396126
\(89\) 2.38191 0.252482 0.126241 0.992000i \(-0.459709\pi\)
0.126241 + 0.992000i \(0.459709\pi\)
\(90\) −4.06362 −0.428343
\(91\) −9.71689 −1.01861
\(92\) 6.27595 0.654313
\(93\) 2.86515 0.297102
\(94\) −2.30872 −0.238126
\(95\) −1.71689 −0.176149
\(96\) −4.33760 −0.442705
\(97\) −6.12150 −0.621544 −0.310772 0.950485i \(-0.600588\pi\)
−0.310772 + 0.950485i \(0.600588\pi\)
\(98\) 6.81933 0.688857
\(99\) 1.08555 0.109102
\(100\) −6.85280 −0.685280
\(101\) −7.86793 −0.782889 −0.391444 0.920202i \(-0.628024\pi\)
−0.391444 + 0.920202i \(0.628024\pi\)
\(102\) −18.3126 −1.81322
\(103\) −7.66215 −0.754974 −0.377487 0.926015i \(-0.623212\pi\)
−0.377487 + 0.926015i \(0.623212\pi\)
\(104\) 10.5623 1.03572
\(105\) 5.47441 0.534248
\(106\) −27.8153 −2.70166
\(107\) 8.86688 0.857193 0.428597 0.903496i \(-0.359008\pi\)
0.428597 + 0.903496i \(0.359008\pi\)
\(108\) 3.46438 0.333361
\(109\) 6.34792 0.608021 0.304010 0.952669i \(-0.401674\pi\)
0.304010 + 0.952669i \(0.401674\pi\)
\(110\) −4.41125 −0.420596
\(111\) 9.75118 0.925541
\(112\) −3.37966 −0.319348
\(113\) −17.4472 −1.64129 −0.820647 0.571435i \(-0.806387\pi\)
−0.820647 + 0.571435i \(0.806387\pi\)
\(114\) 2.30872 0.216232
\(115\) −3.14916 −0.293661
\(116\) 29.3735 2.72726
\(117\) 3.08555 0.285259
\(118\) 10.1666 0.935907
\(119\) 24.6704 2.26153
\(120\) −5.95070 −0.543222
\(121\) −9.82159 −0.892872
\(122\) 15.6822 1.41980
\(123\) −6.02238 −0.543020
\(124\) 9.92599 0.891380
\(125\) 12.1305 1.08498
\(126\) −7.36149 −0.655814
\(127\) 14.7466 1.30855 0.654274 0.756258i \(-0.272974\pi\)
0.654274 + 0.756258i \(0.272974\pi\)
\(128\) −20.0445 −1.77170
\(129\) 3.81005 0.335456
\(130\) −12.5385 −1.09970
\(131\) 2.15445 0.188235 0.0941176 0.995561i \(-0.469997\pi\)
0.0941176 + 0.995561i \(0.469997\pi\)
\(132\) 3.76075 0.327331
\(133\) −3.11026 −0.269693
\(134\) −2.33760 −0.201938
\(135\) −1.73837 −0.149615
\(136\) −26.8168 −2.29952
\(137\) 6.51036 0.556218 0.278109 0.960550i \(-0.410292\pi\)
0.278109 + 0.960550i \(0.410292\pi\)
\(138\) 4.23471 0.360483
\(139\) −15.5547 −1.31933 −0.659665 0.751560i \(-0.729302\pi\)
−0.659665 + 0.751560i \(0.729302\pi\)
\(140\) 18.9655 1.60287
\(141\) −0.987645 −0.0831747
\(142\) 2.38817 0.200411
\(143\) 3.34951 0.280100
\(144\) 1.07319 0.0894327
\(145\) −14.7391 −1.22402
\(146\) 11.0992 0.918574
\(147\) 2.91723 0.240609
\(148\) 33.7818 2.77685
\(149\) −14.0932 −1.15456 −0.577282 0.816545i \(-0.695887\pi\)
−0.577282 + 0.816545i \(0.695887\pi\)
\(150\) −4.62394 −0.377543
\(151\) 15.5834 1.26816 0.634079 0.773268i \(-0.281379\pi\)
0.634079 + 0.773268i \(0.281379\pi\)
\(152\) 3.38086 0.274224
\(153\) −7.83394 −0.633337
\(154\) −7.99124 −0.643953
\(155\) −4.98069 −0.400059
\(156\) 10.6895 0.855847
\(157\) −18.1021 −1.44471 −0.722353 0.691524i \(-0.756939\pi\)
−0.722353 + 0.691524i \(0.756939\pi\)
\(158\) 35.2904 2.80756
\(159\) −11.8991 −0.943658
\(160\) 7.54036 0.596118
\(161\) −5.70490 −0.449609
\(162\) 2.33760 0.183659
\(163\) 19.3058 1.51215 0.756075 0.654484i \(-0.227114\pi\)
0.756075 + 0.654484i \(0.227114\pi\)
\(164\) −20.8638 −1.62919
\(165\) −1.88708 −0.146909
\(166\) −38.6993 −3.00365
\(167\) 14.5408 1.12520 0.562601 0.826729i \(-0.309801\pi\)
0.562601 + 0.826729i \(0.309801\pi\)
\(168\) −10.7801 −0.831699
\(169\) −3.47940 −0.267646
\(170\) 31.8341 2.44157
\(171\) 0.987645 0.0755271
\(172\) 13.1995 1.00645
\(173\) 13.1049 0.996347 0.498174 0.867077i \(-0.334004\pi\)
0.498174 + 0.867077i \(0.334004\pi\)
\(174\) 19.8198 1.50254
\(175\) 6.22927 0.470888
\(176\) 1.16500 0.0878152
\(177\) 4.34914 0.326901
\(178\) 5.56797 0.417337
\(179\) 22.6457 1.69262 0.846308 0.532694i \(-0.178820\pi\)
0.846308 + 0.532694i \(0.178820\pi\)
\(180\) −6.02238 −0.448882
\(181\) −23.3799 −1.73781 −0.868906 0.494978i \(-0.835176\pi\)
−0.868906 + 0.494978i \(0.835176\pi\)
\(182\) −22.7142 −1.68369
\(183\) 6.70867 0.495919
\(184\) 6.20125 0.457162
\(185\) −16.9512 −1.24627
\(186\) 6.69759 0.491091
\(187\) −8.50411 −0.621882
\(188\) −3.42158 −0.249545
\(189\) −3.14916 −0.229068
\(190\) −4.01341 −0.291163
\(191\) −27.2366 −1.97077 −0.985385 0.170343i \(-0.945513\pi\)
−0.985385 + 0.170343i \(0.945513\pi\)
\(192\) −12.2860 −0.886664
\(193\) −19.9913 −1.43901 −0.719504 0.694489i \(-0.755631\pi\)
−0.719504 + 0.694489i \(0.755631\pi\)
\(194\) −14.3096 −1.02737
\(195\) −5.36382 −0.384111
\(196\) 10.1064 0.721887
\(197\) −12.5542 −0.894451 −0.447226 0.894421i \(-0.647588\pi\)
−0.447226 + 0.894421i \(0.647588\pi\)
\(198\) 2.53758 0.180338
\(199\) 5.17305 0.366708 0.183354 0.983047i \(-0.441305\pi\)
0.183354 + 0.983047i \(0.441305\pi\)
\(200\) −6.77123 −0.478798
\(201\) −1.00000 −0.0705346
\(202\) −18.3921 −1.29406
\(203\) −26.7008 −1.87403
\(204\) −27.1398 −1.90017
\(205\) 10.4691 0.731195
\(206\) −17.9111 −1.24792
\(207\) 1.81156 0.125912
\(208\) 3.31138 0.229603
\(209\) 1.07213 0.0741611
\(210\) 12.7970 0.883077
\(211\) −17.3952 −1.19753 −0.598767 0.800924i \(-0.704342\pi\)
−0.598767 + 0.800924i \(0.704342\pi\)
\(212\) −41.2230 −2.83120
\(213\) 1.02163 0.0700012
\(214\) 20.7272 1.41688
\(215\) −6.62328 −0.451704
\(216\) 3.42315 0.232916
\(217\) −9.02283 −0.612510
\(218\) 14.8389 1.00502
\(219\) 4.74810 0.320847
\(220\) −6.53758 −0.440763
\(221\) −24.1720 −1.62598
\(222\) 22.7944 1.52986
\(223\) −9.07143 −0.607468 −0.303734 0.952757i \(-0.598233\pi\)
−0.303734 + 0.952757i \(0.598233\pi\)
\(224\) 13.6598 0.912685
\(225\) −1.97807 −0.131871
\(226\) −40.7846 −2.71295
\(227\) −8.49716 −0.563976 −0.281988 0.959418i \(-0.590994\pi\)
−0.281988 + 0.959418i \(0.590994\pi\)
\(228\) 3.42158 0.226600
\(229\) −15.7368 −1.03991 −0.519957 0.854192i \(-0.674052\pi\)
−0.519957 + 0.854192i \(0.674052\pi\)
\(230\) −7.36149 −0.485402
\(231\) −3.41856 −0.224925
\(232\) 29.0239 1.90551
\(233\) 14.3350 0.939119 0.469559 0.882901i \(-0.344413\pi\)
0.469559 + 0.882901i \(0.344413\pi\)
\(234\) 7.21278 0.471514
\(235\) 1.71689 0.111998
\(236\) 15.0671 0.980784
\(237\) 15.0968 0.980645
\(238\) 57.6695 3.73816
\(239\) 5.30565 0.343194 0.171597 0.985167i \(-0.445107\pi\)
0.171597 + 0.985167i \(0.445107\pi\)
\(240\) −1.86560 −0.120424
\(241\) 19.2318 1.23883 0.619416 0.785063i \(-0.287370\pi\)
0.619416 + 0.785063i \(0.287370\pi\)
\(242\) −22.9590 −1.47586
\(243\) 1.00000 0.0641500
\(244\) 23.2414 1.48788
\(245\) −5.07123 −0.323989
\(246\) −14.0779 −0.897576
\(247\) 3.04743 0.193903
\(248\) 9.80784 0.622799
\(249\) −16.5551 −1.04914
\(250\) 28.3562 1.79340
\(251\) 26.6500 1.68213 0.841066 0.540932i \(-0.181928\pi\)
0.841066 + 0.540932i \(0.181928\pi\)
\(252\) −10.9099 −0.687260
\(253\) 1.96653 0.123635
\(254\) 34.4716 2.16294
\(255\) 13.6183 0.852810
\(256\) −22.2842 −1.39276
\(257\) −3.35636 −0.209364 −0.104682 0.994506i \(-0.533382\pi\)
−0.104682 + 0.994506i \(0.533382\pi\)
\(258\) 8.90639 0.554487
\(259\) −30.7081 −1.90811
\(260\) −18.5823 −1.15243
\(261\) 8.47870 0.524818
\(262\) 5.03625 0.311140
\(263\) 13.4905 0.831862 0.415931 0.909396i \(-0.363456\pi\)
0.415931 + 0.909396i \(0.363456\pi\)
\(264\) 3.71599 0.228703
\(265\) 20.6850 1.27067
\(266\) −7.27054 −0.445786
\(267\) 2.38191 0.145771
\(268\) −3.46438 −0.211621
\(269\) 0.978366 0.0596520 0.0298260 0.999555i \(-0.490505\pi\)
0.0298260 + 0.999555i \(0.490505\pi\)
\(270\) −4.06362 −0.247304
\(271\) −2.39995 −0.145786 −0.0728932 0.997340i \(-0.523223\pi\)
−0.0728932 + 0.997340i \(0.523223\pi\)
\(272\) −8.40732 −0.509769
\(273\) −9.71689 −0.588093
\(274\) 15.2186 0.919391
\(275\) −2.14729 −0.129486
\(276\) 6.27595 0.377768
\(277\) −15.4674 −0.929344 −0.464672 0.885483i \(-0.653828\pi\)
−0.464672 + 0.885483i \(0.653828\pi\)
\(278\) −36.3606 −2.18077
\(279\) 2.86515 0.171532
\(280\) 18.7397 1.11991
\(281\) −6.69254 −0.399243 −0.199622 0.979873i \(-0.563971\pi\)
−0.199622 + 0.979873i \(0.563971\pi\)
\(282\) −2.30872 −0.137482
\(283\) 20.1770 1.19940 0.599700 0.800225i \(-0.295287\pi\)
0.599700 + 0.800225i \(0.295287\pi\)
\(284\) 3.53933 0.210021
\(285\) −1.71689 −0.101700
\(286\) 7.82981 0.462986
\(287\) 18.9655 1.11950
\(288\) −4.33760 −0.255596
\(289\) 44.3707 2.61004
\(290\) −34.4542 −2.02322
\(291\) −6.12150 −0.358849
\(292\) 16.4492 0.962620
\(293\) 22.3656 1.30661 0.653305 0.757095i \(-0.273382\pi\)
0.653305 + 0.757095i \(0.273382\pi\)
\(294\) 6.81933 0.397712
\(295\) −7.56041 −0.440184
\(296\) 33.3797 1.94016
\(297\) 1.08555 0.0629898
\(298\) −32.9444 −1.90842
\(299\) 5.58966 0.323258
\(300\) −6.85280 −0.395646
\(301\) −11.9985 −0.691581
\(302\) 36.4278 2.09618
\(303\) −7.86793 −0.452001
\(304\) 1.05993 0.0607913
\(305\) −11.6621 −0.667773
\(306\) −18.3126 −1.04686
\(307\) −12.8565 −0.733758 −0.366879 0.930269i \(-0.619574\pi\)
−0.366879 + 0.930269i \(0.619574\pi\)
\(308\) −11.8432 −0.674830
\(309\) −7.66215 −0.435884
\(310\) −11.6429 −0.661271
\(311\) −2.33735 −0.132539 −0.0662696 0.997802i \(-0.521110\pi\)
−0.0662696 + 0.997802i \(0.521110\pi\)
\(312\) 10.5623 0.597972
\(313\) 3.73768 0.211266 0.105633 0.994405i \(-0.466313\pi\)
0.105633 + 0.994405i \(0.466313\pi\)
\(314\) −42.3156 −2.38800
\(315\) 5.47441 0.308448
\(316\) 52.3013 2.94218
\(317\) −5.08947 −0.285853 −0.142927 0.989733i \(-0.545651\pi\)
−0.142927 + 0.989733i \(0.545651\pi\)
\(318\) −27.8153 −1.55980
\(319\) 9.20403 0.515327
\(320\) 21.3576 1.19392
\(321\) 8.86688 0.494901
\(322\) −13.3358 −0.743175
\(323\) −7.73716 −0.430507
\(324\) 3.46438 0.192466
\(325\) −6.10343 −0.338557
\(326\) 45.1294 2.49949
\(327\) 6.34792 0.351041
\(328\) −20.6155 −1.13830
\(329\) 3.11026 0.171474
\(330\) −4.41125 −0.242831
\(331\) 22.6794 1.24657 0.623287 0.781993i \(-0.285797\pi\)
0.623287 + 0.781993i \(0.285797\pi\)
\(332\) −57.3533 −3.14767
\(333\) 9.75118 0.534361
\(334\) 33.9906 1.85988
\(335\) 1.73837 0.0949773
\(336\) −3.37966 −0.184375
\(337\) −17.5952 −0.958473 −0.479236 0.877686i \(-0.659086\pi\)
−0.479236 + 0.877686i \(0.659086\pi\)
\(338\) −8.13346 −0.442402
\(339\) −17.4472 −0.947602
\(340\) 47.1790 2.55864
\(341\) 3.11026 0.168430
\(342\) 2.30872 0.124841
\(343\) 12.8573 0.694229
\(344\) 13.0424 0.703198
\(345\) −3.14916 −0.169545
\(346\) 30.6340 1.64690
\(347\) 5.81035 0.311916 0.155958 0.987764i \(-0.450154\pi\)
0.155958 + 0.987764i \(0.450154\pi\)
\(348\) 29.3735 1.57458
\(349\) 21.4083 1.14596 0.572980 0.819570i \(-0.305787\pi\)
0.572980 + 0.819570i \(0.305787\pi\)
\(350\) 14.5616 0.778348
\(351\) 3.08555 0.164694
\(352\) −4.70867 −0.250973
\(353\) −0.696269 −0.0370586 −0.0185293 0.999828i \(-0.505898\pi\)
−0.0185293 + 0.999828i \(0.505898\pi\)
\(354\) 10.1666 0.540346
\(355\) −1.77598 −0.0942591
\(356\) 8.25186 0.437348
\(357\) 24.6704 1.30569
\(358\) 52.9366 2.79778
\(359\) 14.1437 0.746475 0.373237 0.927736i \(-0.378248\pi\)
0.373237 + 0.927736i \(0.378248\pi\)
\(360\) −5.95070 −0.313629
\(361\) −18.0246 −0.948661
\(362\) −54.6528 −2.87249
\(363\) −9.82159 −0.515500
\(364\) −33.6631 −1.76442
\(365\) −8.25396 −0.432032
\(366\) 15.6822 0.819722
\(367\) −8.41862 −0.439448 −0.219724 0.975562i \(-0.570516\pi\)
−0.219724 + 0.975562i \(0.570516\pi\)
\(368\) 1.94415 0.101346
\(369\) −6.02238 −0.313513
\(370\) −39.6251 −2.06001
\(371\) 37.4721 1.94546
\(372\) 9.92599 0.514639
\(373\) 2.44594 0.126646 0.0633229 0.997993i \(-0.479830\pi\)
0.0633229 + 0.997993i \(0.479830\pi\)
\(374\) −19.8792 −1.02793
\(375\) 12.1305 0.626415
\(376\) −3.38086 −0.174354
\(377\) 26.1614 1.34738
\(378\) −7.36149 −0.378634
\(379\) −29.8978 −1.53574 −0.767872 0.640603i \(-0.778685\pi\)
−0.767872 + 0.640603i \(0.778685\pi\)
\(380\) −5.94798 −0.305125
\(381\) 14.7466 0.755490
\(382\) −63.6683 −3.25755
\(383\) −17.8360 −0.911375 −0.455688 0.890140i \(-0.650607\pi\)
−0.455688 + 0.890140i \(0.650607\pi\)
\(384\) −20.0445 −1.02289
\(385\) 5.94273 0.302870
\(386\) −46.7318 −2.37858
\(387\) 3.81005 0.193676
\(388\) −21.2072 −1.07663
\(389\) −5.78292 −0.293206 −0.146603 0.989195i \(-0.546834\pi\)
−0.146603 + 0.989195i \(0.546834\pi\)
\(390\) −12.5385 −0.634911
\(391\) −14.1917 −0.717704
\(392\) 9.98613 0.504375
\(393\) 2.15445 0.108678
\(394\) −29.3468 −1.47847
\(395\) −26.2439 −1.32047
\(396\) 3.76075 0.188985
\(397\) 20.7917 1.04350 0.521752 0.853097i \(-0.325279\pi\)
0.521752 + 0.853097i \(0.325279\pi\)
\(398\) 12.0925 0.606144
\(399\) −3.11026 −0.155708
\(400\) −2.12285 −0.106142
\(401\) 15.4905 0.773561 0.386780 0.922172i \(-0.373587\pi\)
0.386780 + 0.922172i \(0.373587\pi\)
\(402\) −2.33760 −0.116589
\(403\) 8.84056 0.440380
\(404\) −27.2575 −1.35611
\(405\) −1.73837 −0.0863803
\(406\) −62.4159 −3.09765
\(407\) 10.5854 0.524697
\(408\) −26.8168 −1.32763
\(409\) 23.1838 1.14637 0.573183 0.819427i \(-0.305708\pi\)
0.573183 + 0.819427i \(0.305708\pi\)
\(410\) 24.4727 1.20862
\(411\) 6.51036 0.321132
\(412\) −26.5446 −1.30776
\(413\) −13.6961 −0.673943
\(414\) 4.23471 0.208125
\(415\) 28.7789 1.41270
\(416\) −13.3839 −0.656198
\(417\) −15.5547 −0.761716
\(418\) 2.50623 0.122583
\(419\) 3.70438 0.180971 0.0904854 0.995898i \(-0.471158\pi\)
0.0904854 + 0.995898i \(0.471158\pi\)
\(420\) 18.9655 0.925420
\(421\) 5.02231 0.244772 0.122386 0.992483i \(-0.460945\pi\)
0.122386 + 0.992483i \(0.460945\pi\)
\(422\) −40.6630 −1.97944
\(423\) −0.987645 −0.0480209
\(424\) −40.7323 −1.97813
\(425\) 15.4961 0.751671
\(426\) 2.38817 0.115707
\(427\) −21.1267 −1.02239
\(428\) 30.7183 1.48482
\(429\) 3.34951 0.161716
\(430\) −15.4826 −0.746637
\(431\) 4.57015 0.220136 0.110068 0.993924i \(-0.464893\pi\)
0.110068 + 0.993924i \(0.464893\pi\)
\(432\) 1.07319 0.0516340
\(433\) 0.218875 0.0105184 0.00525922 0.999986i \(-0.498326\pi\)
0.00525922 + 0.999986i \(0.498326\pi\)
\(434\) −21.0918 −1.01244
\(435\) −14.7391 −0.706687
\(436\) 21.9917 1.05321
\(437\) 1.78918 0.0855881
\(438\) 11.0992 0.530339
\(439\) 4.34453 0.207353 0.103676 0.994611i \(-0.466939\pi\)
0.103676 + 0.994611i \(0.466939\pi\)
\(440\) −6.45976 −0.307957
\(441\) 2.91723 0.138916
\(442\) −56.5045 −2.68765
\(443\) 20.5054 0.974242 0.487121 0.873334i \(-0.338047\pi\)
0.487121 + 0.873334i \(0.338047\pi\)
\(444\) 33.7818 1.60321
\(445\) −4.14065 −0.196285
\(446\) −21.2054 −1.00411
\(447\) −14.0932 −0.666588
\(448\) 38.6905 1.82796
\(449\) 12.8291 0.605440 0.302720 0.953079i \(-0.402105\pi\)
0.302720 + 0.953079i \(0.402105\pi\)
\(450\) −4.62394 −0.217975
\(451\) −6.53758 −0.307842
\(452\) −60.4438 −2.84304
\(453\) 15.5834 0.732172
\(454\) −19.8630 −0.932216
\(455\) 16.8916 0.791888
\(456\) 3.38086 0.158323
\(457\) 28.9481 1.35414 0.677068 0.735920i \(-0.263250\pi\)
0.677068 + 0.735920i \(0.263250\pi\)
\(458\) −36.7863 −1.71891
\(459\) −7.83394 −0.365657
\(460\) −10.9099 −0.508677
\(461\) 6.81172 0.317253 0.158627 0.987339i \(-0.449293\pi\)
0.158627 + 0.987339i \(0.449293\pi\)
\(462\) −7.99124 −0.371786
\(463\) −20.2404 −0.940653 −0.470327 0.882492i \(-0.655864\pi\)
−0.470327 + 0.882492i \(0.655864\pi\)
\(464\) 9.09927 0.422423
\(465\) −4.98069 −0.230974
\(466\) 33.5096 1.55230
\(467\) −13.1287 −0.607522 −0.303761 0.952748i \(-0.598243\pi\)
−0.303761 + 0.952748i \(0.598243\pi\)
\(468\) 10.6895 0.494123
\(469\) 3.14916 0.145415
\(470\) 4.01341 0.185125
\(471\) −18.1021 −0.834102
\(472\) 14.8877 0.685264
\(473\) 4.13599 0.190173
\(474\) 35.2904 1.62094
\(475\) −1.95363 −0.0896388
\(476\) 85.4677 3.91740
\(477\) −11.8991 −0.544821
\(478\) 12.4025 0.567277
\(479\) 5.64065 0.257728 0.128864 0.991662i \(-0.458867\pi\)
0.128864 + 0.991662i \(0.458867\pi\)
\(480\) 7.54036 0.344169
\(481\) 30.0877 1.37188
\(482\) 44.9564 2.04771
\(483\) −5.70490 −0.259582
\(484\) −34.0258 −1.54663
\(485\) 10.6414 0.483202
\(486\) 2.33760 0.106036
\(487\) −22.3820 −1.01423 −0.507113 0.861880i \(-0.669287\pi\)
−0.507113 + 0.861880i \(0.669287\pi\)
\(488\) 22.9648 1.03957
\(489\) 19.3058 0.873041
\(490\) −11.8545 −0.535533
\(491\) 7.82286 0.353041 0.176520 0.984297i \(-0.443516\pi\)
0.176520 + 0.984297i \(0.443516\pi\)
\(492\) −20.8638 −0.940615
\(493\) −66.4217 −2.99148
\(494\) 7.12367 0.320509
\(495\) −1.88708 −0.0848180
\(496\) 3.07486 0.138065
\(497\) −3.21729 −0.144315
\(498\) −38.6993 −1.73416
\(499\) 34.1870 1.53042 0.765211 0.643779i \(-0.222635\pi\)
0.765211 + 0.643779i \(0.222635\pi\)
\(500\) 42.0246 1.87940
\(501\) 14.5408 0.649635
\(502\) 62.2971 2.78046
\(503\) −25.3215 −1.12903 −0.564514 0.825424i \(-0.690936\pi\)
−0.564514 + 0.825424i \(0.690936\pi\)
\(504\) −10.7801 −0.480182
\(505\) 13.6774 0.608635
\(506\) 4.59698 0.204361
\(507\) −3.47940 −0.154526
\(508\) 51.0878 2.26666
\(509\) 20.7214 0.918460 0.459230 0.888317i \(-0.348125\pi\)
0.459230 + 0.888317i \(0.348125\pi\)
\(510\) 31.8341 1.40964
\(511\) −14.9525 −0.661462
\(512\) −12.0025 −0.530439
\(513\) 0.987645 0.0436056
\(514\) −7.84583 −0.346065
\(515\) 13.3196 0.586934
\(516\) 13.1995 0.581075
\(517\) −1.07213 −0.0471524
\(518\) −71.7832 −3.15397
\(519\) 13.1049 0.575241
\(520\) −18.3612 −0.805190
\(521\) −6.52760 −0.285979 −0.142990 0.989724i \(-0.545672\pi\)
−0.142990 + 0.989724i \(0.545672\pi\)
\(522\) 19.8198 0.867490
\(523\) 28.4978 1.24612 0.623062 0.782173i \(-0.285888\pi\)
0.623062 + 0.782173i \(0.285888\pi\)
\(524\) 7.46384 0.326059
\(525\) 6.22927 0.271868
\(526\) 31.5355 1.37501
\(527\) −22.4454 −0.977739
\(528\) 1.16500 0.0507001
\(529\) −19.7182 −0.857315
\(530\) 48.3533 2.10033
\(531\) 4.34914 0.188737
\(532\) −10.7751 −0.467161
\(533\) −18.5823 −0.804890
\(534\) 5.56797 0.240949
\(535\) −15.4139 −0.666401
\(536\) −3.42315 −0.147858
\(537\) 22.6457 0.977232
\(538\) 2.28703 0.0986009
\(539\) 3.16679 0.136403
\(540\) −6.02238 −0.259162
\(541\) −10.8749 −0.467550 −0.233775 0.972291i \(-0.575108\pi\)
−0.233775 + 0.972291i \(0.575108\pi\)
\(542\) −5.61012 −0.240975
\(543\) −23.3799 −1.00333
\(544\) 33.9805 1.45690
\(545\) −11.0350 −0.472689
\(546\) −22.7142 −0.972079
\(547\) −23.1923 −0.991631 −0.495815 0.868428i \(-0.665131\pi\)
−0.495815 + 0.868428i \(0.665131\pi\)
\(548\) 22.5544 0.963476
\(549\) 6.70867 0.286319
\(550\) −5.01951 −0.214032
\(551\) 8.37395 0.356742
\(552\) 6.20125 0.263943
\(553\) −47.5424 −2.02171
\(554\) −36.1566 −1.53614
\(555\) −16.9512 −0.719536
\(556\) −53.8874 −2.28533
\(557\) 17.9172 0.759176 0.379588 0.925156i \(-0.376066\pi\)
0.379588 + 0.925156i \(0.376066\pi\)
\(558\) 6.69759 0.283531
\(559\) 11.7561 0.497230
\(560\) 5.87509 0.248268
\(561\) −8.50411 −0.359044
\(562\) −15.6445 −0.659923
\(563\) −7.97511 −0.336111 −0.168055 0.985778i \(-0.553749\pi\)
−0.168055 + 0.985778i \(0.553749\pi\)
\(564\) −3.42158 −0.144075
\(565\) 30.3297 1.27598
\(566\) 47.1659 1.98253
\(567\) −3.14916 −0.132252
\(568\) 3.49721 0.146740
\(569\) 33.1240 1.38863 0.694316 0.719670i \(-0.255707\pi\)
0.694316 + 0.719670i \(0.255707\pi\)
\(570\) −4.01341 −0.168103
\(571\) −5.25178 −0.219780 −0.109890 0.993944i \(-0.535050\pi\)
−0.109890 + 0.993944i \(0.535050\pi\)
\(572\) 11.6040 0.485187
\(573\) −27.2366 −1.13782
\(574\) 44.3337 1.85045
\(575\) −3.58340 −0.149438
\(576\) −12.2860 −0.511916
\(577\) −11.3645 −0.473112 −0.236556 0.971618i \(-0.576019\pi\)
−0.236556 + 0.971618i \(0.576019\pi\)
\(578\) 103.721 4.31422
\(579\) −19.9913 −0.830811
\(580\) −51.0620 −2.12023
\(581\) 52.1348 2.16292
\(582\) −14.3096 −0.593153
\(583\) −12.9170 −0.534967
\(584\) 16.2535 0.672573
\(585\) −5.36382 −0.221767
\(586\) 52.2818 2.15974
\(587\) 5.66033 0.233627 0.116813 0.993154i \(-0.462732\pi\)
0.116813 + 0.993154i \(0.462732\pi\)
\(588\) 10.1064 0.416782
\(589\) 2.82975 0.116598
\(590\) −17.6732 −0.727595
\(591\) −12.5542 −0.516412
\(592\) 10.4649 0.430104
\(593\) −13.4864 −0.553822 −0.276911 0.960896i \(-0.589311\pi\)
−0.276911 + 0.960896i \(0.589311\pi\)
\(594\) 2.53758 0.104118
\(595\) −42.8862 −1.75816
\(596\) −48.8244 −1.99993
\(597\) 5.17305 0.211719
\(598\) 13.0664 0.534325
\(599\) −0.375966 −0.0153616 −0.00768078 0.999971i \(-0.502445\pi\)
−0.00768078 + 0.999971i \(0.502445\pi\)
\(600\) −6.77123 −0.276434
\(601\) 0.287554 0.0117296 0.00586478 0.999983i \(-0.498133\pi\)
0.00586478 + 0.999983i \(0.498133\pi\)
\(602\) −28.0477 −1.14314
\(603\) −1.00000 −0.0407231
\(604\) 53.9869 2.19670
\(605\) 17.0736 0.694139
\(606\) −18.3921 −0.747128
\(607\) 8.89680 0.361110 0.180555 0.983565i \(-0.442211\pi\)
0.180555 + 0.983565i \(0.442211\pi\)
\(608\) −4.28401 −0.173740
\(609\) −26.7008 −1.08197
\(610\) −27.2615 −1.10378
\(611\) −3.04743 −0.123286
\(612\) −27.1398 −1.09706
\(613\) 19.1981 0.775402 0.387701 0.921785i \(-0.373269\pi\)
0.387701 + 0.921785i \(0.373269\pi\)
\(614\) −30.0533 −1.21285
\(615\) 10.4691 0.422156
\(616\) −11.7023 −0.471497
\(617\) −4.26972 −0.171893 −0.0859463 0.996300i \(-0.527391\pi\)
−0.0859463 + 0.996300i \(0.527391\pi\)
\(618\) −17.9111 −0.720488
\(619\) 14.4053 0.578999 0.289500 0.957178i \(-0.406511\pi\)
0.289500 + 0.957178i \(0.406511\pi\)
\(620\) −17.2550 −0.692979
\(621\) 1.81156 0.0726955
\(622\) −5.46380 −0.219079
\(623\) −7.50104 −0.300523
\(624\) 3.31138 0.132561
\(625\) −11.1969 −0.447875
\(626\) 8.73721 0.349209
\(627\) 1.07213 0.0428169
\(628\) −62.7127 −2.50251
\(629\) −76.3902 −3.04588
\(630\) 12.7970 0.509845
\(631\) 21.3988 0.851872 0.425936 0.904753i \(-0.359945\pi\)
0.425936 + 0.904753i \(0.359945\pi\)
\(632\) 51.6787 2.05567
\(633\) −17.3952 −0.691396
\(634\) −11.8972 −0.472496
\(635\) −25.6350 −1.01729
\(636\) −41.2230 −1.63460
\(637\) 9.00126 0.356643
\(638\) 21.5154 0.851801
\(639\) 1.02163 0.0404152
\(640\) 34.8448 1.37736
\(641\) 3.40675 0.134559 0.0672793 0.997734i \(-0.478568\pi\)
0.0672793 + 0.997734i \(0.478568\pi\)
\(642\) 20.7272 0.818038
\(643\) 33.5267 1.32217 0.661083 0.750313i \(-0.270097\pi\)
0.661083 + 0.750313i \(0.270097\pi\)
\(644\) −19.7640 −0.778810
\(645\) −6.62328 −0.260791
\(646\) −18.0864 −0.711600
\(647\) 5.05600 0.198772 0.0993860 0.995049i \(-0.468312\pi\)
0.0993860 + 0.995049i \(0.468312\pi\)
\(648\) 3.42315 0.134474
\(649\) 4.72119 0.185323
\(650\) −14.2674 −0.559613
\(651\) −9.02283 −0.353633
\(652\) 66.8829 2.61934
\(653\) −37.7646 −1.47784 −0.738921 0.673792i \(-0.764664\pi\)
−0.738921 + 0.673792i \(0.764664\pi\)
\(654\) 14.8389 0.580248
\(655\) −3.74523 −0.146338
\(656\) −6.46317 −0.252344
\(657\) 4.74810 0.185241
\(658\) 7.27054 0.283435
\(659\) −7.86631 −0.306428 −0.153214 0.988193i \(-0.548962\pi\)
−0.153214 + 0.988193i \(0.548962\pi\)
\(660\) −6.53758 −0.254475
\(661\) 43.1580 1.67865 0.839326 0.543628i \(-0.182950\pi\)
0.839326 + 0.543628i \(0.182950\pi\)
\(662\) 53.0155 2.06050
\(663\) −24.1720 −0.938763
\(664\) −56.6707 −2.19925
\(665\) 5.40678 0.209666
\(666\) 22.7944 0.883264
\(667\) 15.3597 0.594730
\(668\) 50.3750 1.94907
\(669\) −9.07143 −0.350722
\(670\) 4.06362 0.156991
\(671\) 7.28257 0.281141
\(672\) 13.6598 0.526939
\(673\) −23.1525 −0.892462 −0.446231 0.894918i \(-0.647234\pi\)
−0.446231 + 0.894918i \(0.647234\pi\)
\(674\) −41.1306 −1.58429
\(675\) −1.97807 −0.0761360
\(676\) −12.0540 −0.463615
\(677\) −19.6663 −0.755837 −0.377918 0.925839i \(-0.623360\pi\)
−0.377918 + 0.925839i \(0.623360\pi\)
\(678\) −40.7846 −1.56632
\(679\) 19.2776 0.739806
\(680\) 46.6174 1.78770
\(681\) −8.49716 −0.325612
\(682\) 7.27054 0.278403
\(683\) −42.8560 −1.63984 −0.819919 0.572480i \(-0.805981\pi\)
−0.819919 + 0.572480i \(0.805981\pi\)
\(684\) 3.42158 0.130827
\(685\) −11.3174 −0.432416
\(686\) 30.0553 1.14752
\(687\) −15.7368 −0.600395
\(688\) 4.08892 0.155889
\(689\) −36.7151 −1.39874
\(690\) −7.36149 −0.280247
\(691\) −51.2504 −1.94966 −0.974828 0.222958i \(-0.928429\pi\)
−0.974828 + 0.222958i \(0.928429\pi\)
\(692\) 45.4004 1.72586
\(693\) −3.41856 −0.129861
\(694\) 13.5823 0.515576
\(695\) 27.0398 1.02568
\(696\) 29.0239 1.10015
\(697\) 47.1790 1.78703
\(698\) 50.0441 1.89420
\(699\) 14.3350 0.542200
\(700\) 21.5806 0.815669
\(701\) −48.4487 −1.82988 −0.914941 0.403589i \(-0.867763\pi\)
−0.914941 + 0.403589i \(0.867763\pi\)
\(702\) 7.21278 0.272229
\(703\) 9.63070 0.363229
\(704\) −13.3370 −0.502657
\(705\) 1.71689 0.0646619
\(706\) −1.62760 −0.0612555
\(707\) 24.7774 0.931850
\(708\) 15.0671 0.566256
\(709\) 37.1475 1.39510 0.697551 0.716535i \(-0.254273\pi\)
0.697551 + 0.716535i \(0.254273\pi\)
\(710\) −4.15153 −0.155804
\(711\) 15.0968 0.566176
\(712\) 8.15364 0.305571
\(713\) 5.19040 0.194382
\(714\) 57.6695 2.15823
\(715\) −5.82268 −0.217756
\(716\) 78.4533 2.93194
\(717\) 5.30565 0.198143
\(718\) 33.0623 1.23387
\(719\) 33.6911 1.25646 0.628232 0.778026i \(-0.283779\pi\)
0.628232 + 0.778026i \(0.283779\pi\)
\(720\) −1.86560 −0.0695270
\(721\) 24.1294 0.898624
\(722\) −42.1342 −1.56807
\(723\) 19.2318 0.715240
\(724\) −80.9968 −3.01022
\(725\) −16.7715 −0.622877
\(726\) −22.9590 −0.852087
\(727\) 21.6307 0.802237 0.401119 0.916026i \(-0.368622\pi\)
0.401119 + 0.916026i \(0.368622\pi\)
\(728\) −33.2624 −1.23279
\(729\) 1.00000 0.0370370
\(730\) −19.2945 −0.714120
\(731\) −29.8477 −1.10396
\(732\) 23.2414 0.859027
\(733\) 8.90406 0.328879 0.164439 0.986387i \(-0.447418\pi\)
0.164439 + 0.986387i \(0.447418\pi\)
\(734\) −19.6794 −0.726380
\(735\) −5.07123 −0.187055
\(736\) −7.85783 −0.289644
\(737\) −1.08555 −0.0399866
\(738\) −14.0779 −0.518216
\(739\) 5.22982 0.192382 0.0961910 0.995363i \(-0.469334\pi\)
0.0961910 + 0.995363i \(0.469334\pi\)
\(740\) −58.7253 −2.15879
\(741\) 3.04743 0.111950
\(742\) 87.5949 3.21571
\(743\) −5.50983 −0.202136 −0.101068 0.994880i \(-0.532226\pi\)
−0.101068 + 0.994880i \(0.532226\pi\)
\(744\) 9.80784 0.359573
\(745\) 24.4993 0.897584
\(746\) 5.71763 0.209337
\(747\) −16.5551 −0.605720
\(748\) −29.4615 −1.07722
\(749\) −27.9232 −1.02029
\(750\) 28.3562 1.03542
\(751\) 4.09731 0.149513 0.0747565 0.997202i \(-0.476182\pi\)
0.0747565 + 0.997202i \(0.476182\pi\)
\(752\) −1.05993 −0.0386518
\(753\) 26.6500 0.971180
\(754\) 61.1550 2.22713
\(755\) −27.0897 −0.985895
\(756\) −10.9099 −0.396790
\(757\) −5.73586 −0.208474 −0.104237 0.994553i \(-0.533240\pi\)
−0.104237 + 0.994553i \(0.533240\pi\)
\(758\) −69.8891 −2.53849
\(759\) 1.96653 0.0713807
\(760\) −5.87718 −0.213188
\(761\) 29.3667 1.06454 0.532272 0.846574i \(-0.321338\pi\)
0.532272 + 0.846574i \(0.321338\pi\)
\(762\) 34.4716 1.24878
\(763\) −19.9907 −0.723710
\(764\) −94.3580 −3.41375
\(765\) 13.6183 0.492370
\(766\) −41.6934 −1.50644
\(767\) 13.4195 0.484549
\(768\) −22.2842 −0.804110
\(769\) −11.4403 −0.412546 −0.206273 0.978494i \(-0.566134\pi\)
−0.206273 + 0.978494i \(0.566134\pi\)
\(770\) 13.8917 0.500623
\(771\) −3.35636 −0.120876
\(772\) −69.2577 −2.49264
\(773\) 29.1548 1.04863 0.524313 0.851526i \(-0.324322\pi\)
0.524313 + 0.851526i \(0.324322\pi\)
\(774\) 8.90639 0.320133
\(775\) −5.66747 −0.203582
\(776\) −20.9548 −0.752233
\(777\) −30.7081 −1.10165
\(778\) −13.5182 −0.484650
\(779\) −5.94798 −0.213108
\(780\) −18.5823 −0.665354
\(781\) 1.10903 0.0396843
\(782\) −33.1745 −1.18632
\(783\) 8.47870 0.303004
\(784\) 3.13075 0.111813
\(785\) 31.4682 1.12315
\(786\) 5.03625 0.179637
\(787\) −26.9321 −0.960025 −0.480013 0.877262i \(-0.659368\pi\)
−0.480013 + 0.877262i \(0.659368\pi\)
\(788\) −43.4926 −1.54936
\(789\) 13.4905 0.480276
\(790\) −61.3478 −2.18266
\(791\) 54.9441 1.95359
\(792\) 3.71599 0.132042
\(793\) 20.6999 0.735076
\(794\) 48.6026 1.72484
\(795\) 20.6850 0.733621
\(796\) 17.9215 0.635209
\(797\) −25.5458 −0.904879 −0.452439 0.891795i \(-0.649446\pi\)
−0.452439 + 0.891795i \(0.649446\pi\)
\(798\) −7.27054 −0.257374
\(799\) 7.73716 0.273721
\(800\) 8.58008 0.303352
\(801\) 2.38191 0.0841608
\(802\) 36.2107 1.27865
\(803\) 5.15429 0.181891
\(804\) −3.46438 −0.122179
\(805\) 9.91723 0.349537
\(806\) 20.6657 0.727919
\(807\) 0.978366 0.0344401
\(808\) −26.9331 −0.947503
\(809\) −25.5600 −0.898642 −0.449321 0.893370i \(-0.648334\pi\)
−0.449321 + 0.893370i \(0.648334\pi\)
\(810\) −4.06362 −0.142781
\(811\) −21.5151 −0.755499 −0.377750 0.925908i \(-0.623302\pi\)
−0.377750 + 0.925908i \(0.623302\pi\)
\(812\) −92.5019 −3.24618
\(813\) −2.39995 −0.0841699
\(814\) 24.7444 0.867289
\(815\) −33.5607 −1.17558
\(816\) −8.40732 −0.294315
\(817\) 3.76298 0.131650
\(818\) 54.1946 1.89487
\(819\) −9.71689 −0.339536
\(820\) 36.2691 1.26657
\(821\) −26.7518 −0.933646 −0.466823 0.884351i \(-0.654601\pi\)
−0.466823 + 0.884351i \(0.654601\pi\)
\(822\) 15.2186 0.530811
\(823\) −47.0767 −1.64099 −0.820495 0.571654i \(-0.806302\pi\)
−0.820495 + 0.571654i \(0.806302\pi\)
\(824\) −26.2287 −0.913719
\(825\) −2.14729 −0.0747590
\(826\) −32.0161 −1.11398
\(827\) −6.63909 −0.230864 −0.115432 0.993315i \(-0.536825\pi\)
−0.115432 + 0.993315i \(0.536825\pi\)
\(828\) 6.27595 0.218104
\(829\) −54.1098 −1.87931 −0.939655 0.342123i \(-0.888854\pi\)
−0.939655 + 0.342123i \(0.888854\pi\)
\(830\) 67.2737 2.33510
\(831\) −15.4674 −0.536557
\(832\) −37.9089 −1.31426
\(833\) −22.8534 −0.791825
\(834\) −36.3606 −1.25907
\(835\) −25.2773 −0.874757
\(836\) 3.71429 0.128461
\(837\) 2.86515 0.0990341
\(838\) 8.65937 0.299133
\(839\) 57.3714 1.98068 0.990340 0.138659i \(-0.0442791\pi\)
0.990340 + 0.138659i \(0.0442791\pi\)
\(840\) 18.7397 0.646582
\(841\) 42.8884 1.47891
\(842\) 11.7402 0.404593
\(843\) −6.69254 −0.230503
\(844\) −60.2636 −2.07436
\(845\) 6.04849 0.208074
\(846\) −2.30872 −0.0793755
\(847\) 30.9298 1.06276
\(848\) −12.7700 −0.438523
\(849\) 20.1770 0.692474
\(850\) 36.2237 1.24246
\(851\) 17.6649 0.605544
\(852\) 3.53933 0.121256
\(853\) 19.5977 0.671013 0.335506 0.942038i \(-0.391093\pi\)
0.335506 + 0.942038i \(0.391093\pi\)
\(854\) −49.3858 −1.68995
\(855\) −1.71689 −0.0587165
\(856\) 30.3526 1.03743
\(857\) 41.6015 1.42108 0.710540 0.703657i \(-0.248451\pi\)
0.710540 + 0.703657i \(0.248451\pi\)
\(858\) 7.82981 0.267305
\(859\) −2.98279 −0.101771 −0.0508857 0.998704i \(-0.516204\pi\)
−0.0508857 + 0.998704i \(0.516204\pi\)
\(860\) −22.9456 −0.782438
\(861\) 18.9655 0.646341
\(862\) 10.6832 0.363871
\(863\) −15.0457 −0.512162 −0.256081 0.966655i \(-0.582431\pi\)
−0.256081 + 0.966655i \(0.582431\pi\)
\(864\) −4.33760 −0.147568
\(865\) −22.7812 −0.774583
\(866\) 0.511642 0.0173863
\(867\) 44.3707 1.50691
\(868\) −31.2586 −1.06098
\(869\) 16.3883 0.555936
\(870\) −34.4542 −1.16811
\(871\) −3.08555 −0.104550
\(872\) 21.7299 0.735867
\(873\) −6.12150 −0.207181
\(874\) 4.18239 0.141471
\(875\) −38.2008 −1.29142
\(876\) 16.4492 0.555769
\(877\) −10.5987 −0.357894 −0.178947 0.983859i \(-0.557269\pi\)
−0.178947 + 0.983859i \(0.557269\pi\)
\(878\) 10.1558 0.342741
\(879\) 22.3656 0.754372
\(880\) −2.02520 −0.0682695
\(881\) 23.5147 0.792229 0.396114 0.918201i \(-0.370358\pi\)
0.396114 + 0.918201i \(0.370358\pi\)
\(882\) 6.81933 0.229619
\(883\) −49.9816 −1.68201 −0.841007 0.541025i \(-0.818036\pi\)
−0.841007 + 0.541025i \(0.818036\pi\)
\(884\) −83.7411 −2.81652
\(885\) −7.56041 −0.254140
\(886\) 47.9335 1.61036
\(887\) −19.0088 −0.638253 −0.319127 0.947712i \(-0.603390\pi\)
−0.319127 + 0.947712i \(0.603390\pi\)
\(888\) 33.3797 1.12015
\(889\) −46.4394 −1.55753
\(890\) −9.67918 −0.324447
\(891\) 1.08555 0.0363672
\(892\) −31.4269 −1.05225
\(893\) −0.975443 −0.0326420
\(894\) −32.9444 −1.10183
\(895\) −39.3665 −1.31588
\(896\) 63.1235 2.10881
\(897\) 5.58966 0.186633
\(898\) 29.9892 1.00075
\(899\) 24.2928 0.810209
\(900\) −6.85280 −0.228427
\(901\) 93.2166 3.10550
\(902\) −15.2823 −0.508843
\(903\) −11.9985 −0.399284
\(904\) −59.7244 −1.98640
\(905\) 40.6428 1.35101
\(906\) 36.4278 1.21023
\(907\) −45.3796 −1.50680 −0.753402 0.657560i \(-0.771588\pi\)
−0.753402 + 0.657560i \(0.771588\pi\)
\(908\) −29.4374 −0.976915
\(909\) −7.86793 −0.260963
\(910\) 39.4857 1.30894
\(911\) 50.7167 1.68032 0.840160 0.542339i \(-0.182461\pi\)
0.840160 + 0.542339i \(0.182461\pi\)
\(912\) 1.05993 0.0350979
\(913\) −17.9714 −0.594765
\(914\) 67.6692 2.23830
\(915\) −11.6621 −0.385539
\(916\) −54.5182 −1.80133
\(917\) −6.78471 −0.224051
\(918\) −18.3126 −0.604407
\(919\) 28.1853 0.929747 0.464873 0.885377i \(-0.346100\pi\)
0.464873 + 0.885377i \(0.346100\pi\)
\(920\) −10.7801 −0.355408
\(921\) −12.8565 −0.423635
\(922\) 15.9231 0.524399
\(923\) 3.15230 0.103759
\(924\) −11.8432 −0.389613
\(925\) −19.2885 −0.634202
\(926\) −47.3141 −1.55484
\(927\) −7.66215 −0.251658
\(928\) −36.7772 −1.20727
\(929\) −16.2587 −0.533431 −0.266716 0.963775i \(-0.585938\pi\)
−0.266716 + 0.963775i \(0.585938\pi\)
\(930\) −11.6429 −0.381785
\(931\) 2.88119 0.0944272
\(932\) 49.6620 1.62673
\(933\) −2.33735 −0.0765215
\(934\) −30.6896 −1.00419
\(935\) 14.7833 0.483465
\(936\) 10.5623 0.345239
\(937\) −13.6287 −0.445229 −0.222615 0.974906i \(-0.571459\pi\)
−0.222615 + 0.974906i \(0.571459\pi\)
\(938\) 7.36149 0.240361
\(939\) 3.73768 0.121975
\(940\) 5.94798 0.194002
\(941\) 53.9031 1.75719 0.878596 0.477566i \(-0.158481\pi\)
0.878596 + 0.477566i \(0.158481\pi\)
\(942\) −42.3156 −1.37872
\(943\) −10.9099 −0.355276
\(944\) 4.66746 0.151913
\(945\) 5.47441 0.178083
\(946\) 9.66830 0.314344
\(947\) −12.4115 −0.403321 −0.201661 0.979455i \(-0.564634\pi\)
−0.201661 + 0.979455i \(0.564634\pi\)
\(948\) 52.3013 1.69867
\(949\) 14.6505 0.475575
\(950\) −4.56681 −0.148167
\(951\) −5.08947 −0.165037
\(952\) 84.4504 2.73705
\(953\) 2.05797 0.0666640 0.0333320 0.999444i \(-0.489388\pi\)
0.0333320 + 0.999444i \(0.489388\pi\)
\(954\) −27.8153 −0.900553
\(955\) 47.3472 1.53212
\(956\) 18.3808 0.594478
\(957\) 9.20403 0.297524
\(958\) 13.1856 0.426007
\(959\) −20.5022 −0.662050
\(960\) 21.3576 0.689312
\(961\) −22.7909 −0.735190
\(962\) 70.3331 2.26763
\(963\) 8.86688 0.285731
\(964\) 66.6265 2.14589
\(965\) 34.7523 1.11872
\(966\) −13.3358 −0.429072
\(967\) −3.78938 −0.121858 −0.0609292 0.998142i \(-0.519406\pi\)
−0.0609292 + 0.998142i \(0.519406\pi\)
\(968\) −33.6208 −1.08061
\(969\) −7.73716 −0.248553
\(970\) 24.8754 0.798702
\(971\) −48.7908 −1.56577 −0.782886 0.622165i \(-0.786253\pi\)
−0.782886 + 0.622165i \(0.786253\pi\)
\(972\) 3.46438 0.111120
\(973\) 48.9842 1.57036
\(974\) −52.3202 −1.67645
\(975\) −6.10343 −0.195466
\(976\) 7.19969 0.230456
\(977\) −6.74735 −0.215867 −0.107933 0.994158i \(-0.534423\pi\)
−0.107933 + 0.994158i \(0.534423\pi\)
\(978\) 45.1294 1.44308
\(979\) 2.58568 0.0826386
\(980\) −17.5687 −0.561211
\(981\) 6.34792 0.202674
\(982\) 18.2867 0.583553
\(983\) −8.27198 −0.263835 −0.131918 0.991261i \(-0.542113\pi\)
−0.131918 + 0.991261i \(0.542113\pi\)
\(984\) −20.6155 −0.657198
\(985\) 21.8239 0.695367
\(986\) −155.267 −4.94472
\(987\) 3.11026 0.0990006
\(988\) 10.5575 0.335877
\(989\) 6.90214 0.219475
\(990\) −4.41125 −0.140199
\(991\) −33.9736 −1.07921 −0.539604 0.841919i \(-0.681426\pi\)
−0.539604 + 0.841919i \(0.681426\pi\)
\(992\) −12.4279 −0.394586
\(993\) 22.6794 0.719710
\(994\) −7.52075 −0.238544
\(995\) −8.99268 −0.285087
\(996\) −57.3533 −1.81731
\(997\) 24.0155 0.760579 0.380290 0.924868i \(-0.375824\pi\)
0.380290 + 0.924868i \(0.375824\pi\)
\(998\) 79.9157 2.52969
\(999\) 9.75118 0.308514
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 201.2.a.e.1.5 5
3.2 odd 2 603.2.a.k.1.1 5
4.3 odd 2 3216.2.a.y.1.2 5
5.4 even 2 5025.2.a.x.1.1 5
7.6 odd 2 9849.2.a.bb.1.5 5
12.11 even 2 9648.2.a.cd.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.2.a.e.1.5 5 1.1 even 1 trivial
603.2.a.k.1.1 5 3.2 odd 2
3216.2.a.y.1.2 5 4.3 odd 2
5025.2.a.x.1.1 5 5.4 even 2
9648.2.a.cd.1.4 5 12.11 even 2
9849.2.a.bb.1.5 5 7.6 odd 2