Properties

Label 4034.2.a.b.1.15
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $1$
Dimension $35$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(1\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.841269 q^{3} +1.00000 q^{4} -1.88225 q^{5} +0.841269 q^{6} -4.21612 q^{7} -1.00000 q^{8} -2.29227 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.841269 q^{3} +1.00000 q^{4} -1.88225 q^{5} +0.841269 q^{6} -4.21612 q^{7} -1.00000 q^{8} -2.29227 q^{9} +1.88225 q^{10} -4.82481 q^{11} -0.841269 q^{12} +5.72931 q^{13} +4.21612 q^{14} +1.58348 q^{15} +1.00000 q^{16} -1.08937 q^{17} +2.29227 q^{18} +3.42362 q^{19} -1.88225 q^{20} +3.54690 q^{21} +4.82481 q^{22} +3.34454 q^{23} +0.841269 q^{24} -1.45713 q^{25} -5.72931 q^{26} +4.45222 q^{27} -4.21612 q^{28} +6.98169 q^{29} -1.58348 q^{30} -1.44739 q^{31} -1.00000 q^{32} +4.05897 q^{33} +1.08937 q^{34} +7.93580 q^{35} -2.29227 q^{36} +2.43857 q^{37} -3.42362 q^{38} -4.81989 q^{39} +1.88225 q^{40} +10.5413 q^{41} -3.54690 q^{42} -4.80820 q^{43} -4.82481 q^{44} +4.31462 q^{45} -3.34454 q^{46} +9.61304 q^{47} -0.841269 q^{48} +10.7757 q^{49} +1.45713 q^{50} +0.916455 q^{51} +5.72931 q^{52} -0.675316 q^{53} -4.45222 q^{54} +9.08151 q^{55} +4.21612 q^{56} -2.88019 q^{57} -6.98169 q^{58} -7.24193 q^{59} +1.58348 q^{60} -3.66784 q^{61} +1.44739 q^{62} +9.66448 q^{63} +1.00000 q^{64} -10.7840 q^{65} -4.05897 q^{66} -6.78487 q^{67} -1.08937 q^{68} -2.81366 q^{69} -7.93580 q^{70} +8.42340 q^{71} +2.29227 q^{72} -9.24909 q^{73} -2.43857 q^{74} +1.22584 q^{75} +3.42362 q^{76} +20.3420 q^{77} +4.81989 q^{78} -13.6584 q^{79} -1.88225 q^{80} +3.13128 q^{81} -10.5413 q^{82} +12.3940 q^{83} +3.54690 q^{84} +2.05047 q^{85} +4.80820 q^{86} -5.87348 q^{87} +4.82481 q^{88} +4.99591 q^{89} -4.31462 q^{90} -24.1555 q^{91} +3.34454 q^{92} +1.21765 q^{93} -9.61304 q^{94} -6.44412 q^{95} +0.841269 q^{96} -8.10568 q^{97} -10.7757 q^{98} +11.0598 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.841269 −0.485707 −0.242854 0.970063i \(-0.578083\pi\)
−0.242854 + 0.970063i \(0.578083\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.88225 −0.841768 −0.420884 0.907114i \(-0.638280\pi\)
−0.420884 + 0.907114i \(0.638280\pi\)
\(6\) 0.841269 0.343447
\(7\) −4.21612 −1.59355 −0.796773 0.604279i \(-0.793461\pi\)
−0.796773 + 0.604279i \(0.793461\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.29227 −0.764089
\(10\) 1.88225 0.595220
\(11\) −4.82481 −1.45474 −0.727368 0.686248i \(-0.759257\pi\)
−0.727368 + 0.686248i \(0.759257\pi\)
\(12\) −0.841269 −0.242854
\(13\) 5.72931 1.58902 0.794512 0.607248i \(-0.207727\pi\)
0.794512 + 0.607248i \(0.207727\pi\)
\(14\) 4.21612 1.12681
\(15\) 1.58348 0.408853
\(16\) 1.00000 0.250000
\(17\) −1.08937 −0.264211 −0.132106 0.991236i \(-0.542174\pi\)
−0.132106 + 0.991236i \(0.542174\pi\)
\(18\) 2.29227 0.540292
\(19\) 3.42362 0.785433 0.392716 0.919660i \(-0.371535\pi\)
0.392716 + 0.919660i \(0.371535\pi\)
\(20\) −1.88225 −0.420884
\(21\) 3.54690 0.773996
\(22\) 4.82481 1.02865
\(23\) 3.34454 0.697386 0.348693 0.937237i \(-0.386626\pi\)
0.348693 + 0.937237i \(0.386626\pi\)
\(24\) 0.841269 0.171723
\(25\) −1.45713 −0.291426
\(26\) −5.72931 −1.12361
\(27\) 4.45222 0.856830
\(28\) −4.21612 −0.796773
\(29\) 6.98169 1.29647 0.648234 0.761441i \(-0.275508\pi\)
0.648234 + 0.761441i \(0.275508\pi\)
\(30\) −1.58348 −0.289103
\(31\) −1.44739 −0.259960 −0.129980 0.991517i \(-0.541491\pi\)
−0.129980 + 0.991517i \(0.541491\pi\)
\(32\) −1.00000 −0.176777
\(33\) 4.05897 0.706576
\(34\) 1.08937 0.186826
\(35\) 7.93580 1.34140
\(36\) −2.29227 −0.382044
\(37\) 2.43857 0.400899 0.200450 0.979704i \(-0.435760\pi\)
0.200450 + 0.979704i \(0.435760\pi\)
\(38\) −3.42362 −0.555385
\(39\) −4.81989 −0.771800
\(40\) 1.88225 0.297610
\(41\) 10.5413 1.64627 0.823135 0.567846i \(-0.192223\pi\)
0.823135 + 0.567846i \(0.192223\pi\)
\(42\) −3.54690 −0.547298
\(43\) −4.80820 −0.733243 −0.366622 0.930370i \(-0.619486\pi\)
−0.366622 + 0.930370i \(0.619486\pi\)
\(44\) −4.82481 −0.727368
\(45\) 4.31462 0.643186
\(46\) −3.34454 −0.493126
\(47\) 9.61304 1.40221 0.701103 0.713060i \(-0.252691\pi\)
0.701103 + 0.713060i \(0.252691\pi\)
\(48\) −0.841269 −0.121427
\(49\) 10.7757 1.53939
\(50\) 1.45713 0.206069
\(51\) 0.916455 0.128329
\(52\) 5.72931 0.794512
\(53\) −0.675316 −0.0927617 −0.0463809 0.998924i \(-0.514769\pi\)
−0.0463809 + 0.998924i \(0.514769\pi\)
\(54\) −4.45222 −0.605871
\(55\) 9.08151 1.22455
\(56\) 4.21612 0.563403
\(57\) −2.88019 −0.381490
\(58\) −6.98169 −0.916741
\(59\) −7.24193 −0.942819 −0.471410 0.881914i \(-0.656255\pi\)
−0.471410 + 0.881914i \(0.656255\pi\)
\(60\) 1.58348 0.204426
\(61\) −3.66784 −0.469619 −0.234810 0.972041i \(-0.575447\pi\)
−0.234810 + 0.972041i \(0.575447\pi\)
\(62\) 1.44739 0.183819
\(63\) 9.66448 1.21761
\(64\) 1.00000 0.125000
\(65\) −10.7840 −1.33759
\(66\) −4.05897 −0.499624
\(67\) −6.78487 −0.828903 −0.414452 0.910071i \(-0.636027\pi\)
−0.414452 + 0.910071i \(0.636027\pi\)
\(68\) −1.08937 −0.132106
\(69\) −2.81366 −0.338725
\(70\) −7.93580 −0.948510
\(71\) 8.42340 0.999673 0.499837 0.866120i \(-0.333393\pi\)
0.499837 + 0.866120i \(0.333393\pi\)
\(72\) 2.29227 0.270146
\(73\) −9.24909 −1.08252 −0.541262 0.840854i \(-0.682053\pi\)
−0.541262 + 0.840854i \(0.682053\pi\)
\(74\) −2.43857 −0.283479
\(75\) 1.22584 0.141548
\(76\) 3.42362 0.392716
\(77\) 20.3420 2.31819
\(78\) 4.81989 0.545745
\(79\) −13.6584 −1.53669 −0.768344 0.640037i \(-0.778919\pi\)
−0.768344 + 0.640037i \(0.778919\pi\)
\(80\) −1.88225 −0.210442
\(81\) 3.13128 0.347920
\(82\) −10.5413 −1.16409
\(83\) 12.3940 1.36042 0.680210 0.733017i \(-0.261889\pi\)
0.680210 + 0.733017i \(0.261889\pi\)
\(84\) 3.54690 0.386998
\(85\) 2.05047 0.222405
\(86\) 4.80820 0.518481
\(87\) −5.87348 −0.629704
\(88\) 4.82481 0.514327
\(89\) 4.99591 0.529565 0.264783 0.964308i \(-0.414700\pi\)
0.264783 + 0.964308i \(0.414700\pi\)
\(90\) −4.31462 −0.454801
\(91\) −24.1555 −2.53218
\(92\) 3.34454 0.348693
\(93\) 1.21765 0.126264
\(94\) −9.61304 −0.991509
\(95\) −6.44412 −0.661153
\(96\) 0.841269 0.0858617
\(97\) −8.10568 −0.823007 −0.411503 0.911408i \(-0.634996\pi\)
−0.411503 + 0.911408i \(0.634996\pi\)
\(98\) −10.7757 −1.08851
\(99\) 11.0598 1.11155
\(100\) −1.45713 −0.145713
\(101\) 16.1791 1.60988 0.804940 0.593356i \(-0.202197\pi\)
0.804940 + 0.593356i \(0.202197\pi\)
\(102\) −0.916455 −0.0907425
\(103\) 0.329723 0.0324886 0.0162443 0.999868i \(-0.494829\pi\)
0.0162443 + 0.999868i \(0.494829\pi\)
\(104\) −5.72931 −0.561805
\(105\) −6.67615 −0.651526
\(106\) 0.675316 0.0655924
\(107\) −15.4568 −1.49426 −0.747130 0.664678i \(-0.768569\pi\)
−0.747130 + 0.664678i \(0.768569\pi\)
\(108\) 4.45222 0.428415
\(109\) −18.6885 −1.79003 −0.895015 0.446037i \(-0.852835\pi\)
−0.895015 + 0.446037i \(0.852835\pi\)
\(110\) −9.08151 −0.865888
\(111\) −2.05150 −0.194720
\(112\) −4.21612 −0.398386
\(113\) −12.7969 −1.20383 −0.601915 0.798560i \(-0.705595\pi\)
−0.601915 + 0.798560i \(0.705595\pi\)
\(114\) 2.88019 0.269754
\(115\) −6.29527 −0.587037
\(116\) 6.98169 0.648234
\(117\) −13.1331 −1.21416
\(118\) 7.24193 0.666674
\(119\) 4.59292 0.421033
\(120\) −1.58348 −0.144551
\(121\) 12.2788 1.11626
\(122\) 3.66784 0.332071
\(123\) −8.86804 −0.799605
\(124\) −1.44739 −0.129980
\(125\) 12.1539 1.08708
\(126\) −9.66448 −0.860980
\(127\) 3.48412 0.309166 0.154583 0.987980i \(-0.450597\pi\)
0.154583 + 0.987980i \(0.450597\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.04499 0.356141
\(130\) 10.7840 0.945819
\(131\) −12.8713 −1.12457 −0.562287 0.826942i \(-0.690078\pi\)
−0.562287 + 0.826942i \(0.690078\pi\)
\(132\) 4.05897 0.353288
\(133\) −14.4344 −1.25162
\(134\) 6.78487 0.586123
\(135\) −8.38020 −0.721253
\(136\) 1.08937 0.0934128
\(137\) −2.81809 −0.240766 −0.120383 0.992728i \(-0.538412\pi\)
−0.120383 + 0.992728i \(0.538412\pi\)
\(138\) 2.81366 0.239515
\(139\) −11.5121 −0.976443 −0.488221 0.872720i \(-0.662354\pi\)
−0.488221 + 0.872720i \(0.662354\pi\)
\(140\) 7.93580 0.670698
\(141\) −8.08716 −0.681061
\(142\) −8.42340 −0.706876
\(143\) −27.6428 −2.31161
\(144\) −2.29227 −0.191022
\(145\) −13.1413 −1.09133
\(146\) 9.24909 0.765460
\(147\) −9.06527 −0.747691
\(148\) 2.43857 0.200450
\(149\) 1.59309 0.130511 0.0652555 0.997869i \(-0.479214\pi\)
0.0652555 + 0.997869i \(0.479214\pi\)
\(150\) −1.22584 −0.100089
\(151\) 3.71839 0.302598 0.151299 0.988488i \(-0.451654\pi\)
0.151299 + 0.988488i \(0.451654\pi\)
\(152\) −3.42362 −0.277692
\(153\) 2.49713 0.201881
\(154\) −20.3420 −1.63921
\(155\) 2.72436 0.218826
\(156\) −4.81989 −0.385900
\(157\) 7.02202 0.560418 0.280209 0.959939i \(-0.409596\pi\)
0.280209 + 0.959939i \(0.409596\pi\)
\(158\) 13.6584 1.08660
\(159\) 0.568122 0.0450550
\(160\) 1.88225 0.148805
\(161\) −14.1010 −1.11132
\(162\) −3.13128 −0.246016
\(163\) −4.57079 −0.358012 −0.179006 0.983848i \(-0.557288\pi\)
−0.179006 + 0.983848i \(0.557288\pi\)
\(164\) 10.5413 0.823135
\(165\) −7.64000 −0.594773
\(166\) −12.3940 −0.961962
\(167\) −3.09616 −0.239588 −0.119794 0.992799i \(-0.538223\pi\)
−0.119794 + 0.992799i \(0.538223\pi\)
\(168\) −3.54690 −0.273649
\(169\) 19.8250 1.52500
\(170\) −2.05047 −0.157264
\(171\) −7.84785 −0.600140
\(172\) −4.80820 −0.366622
\(173\) 16.7004 1.26971 0.634854 0.772632i \(-0.281060\pi\)
0.634854 + 0.772632i \(0.281060\pi\)
\(174\) 5.87348 0.445268
\(175\) 6.14344 0.464401
\(176\) −4.82481 −0.363684
\(177\) 6.09242 0.457934
\(178\) −4.99591 −0.374459
\(179\) −5.79649 −0.433250 −0.216625 0.976255i \(-0.569505\pi\)
−0.216625 + 0.976255i \(0.569505\pi\)
\(180\) 4.31462 0.321593
\(181\) −1.60336 −0.119177 −0.0595883 0.998223i \(-0.518979\pi\)
−0.0595883 + 0.998223i \(0.518979\pi\)
\(182\) 24.1555 1.79052
\(183\) 3.08564 0.228097
\(184\) −3.34454 −0.246563
\(185\) −4.59001 −0.337464
\(186\) −1.21765 −0.0892823
\(187\) 5.25601 0.384358
\(188\) 9.61304 0.701103
\(189\) −18.7711 −1.36540
\(190\) 6.44412 0.467505
\(191\) 16.5291 1.19600 0.598002 0.801494i \(-0.295961\pi\)
0.598002 + 0.801494i \(0.295961\pi\)
\(192\) −0.841269 −0.0607134
\(193\) 16.4414 1.18348 0.591739 0.806130i \(-0.298442\pi\)
0.591739 + 0.806130i \(0.298442\pi\)
\(194\) 8.10568 0.581954
\(195\) 9.07225 0.649677
\(196\) 10.7757 0.769693
\(197\) 22.3038 1.58908 0.794538 0.607214i \(-0.207713\pi\)
0.794538 + 0.607214i \(0.207713\pi\)
\(198\) −11.0598 −0.785982
\(199\) 15.8172 1.12125 0.560627 0.828069i \(-0.310560\pi\)
0.560627 + 0.828069i \(0.310560\pi\)
\(200\) 1.45713 0.103035
\(201\) 5.70790 0.402604
\(202\) −16.1791 −1.13836
\(203\) −29.4357 −2.06598
\(204\) 0.916455 0.0641647
\(205\) −19.8413 −1.38578
\(206\) −0.329723 −0.0229729
\(207\) −7.66658 −0.532864
\(208\) 5.72931 0.397256
\(209\) −16.5183 −1.14260
\(210\) 6.67615 0.460698
\(211\) −10.4508 −0.719463 −0.359732 0.933056i \(-0.617132\pi\)
−0.359732 + 0.933056i \(0.617132\pi\)
\(212\) −0.675316 −0.0463809
\(213\) −7.08635 −0.485548
\(214\) 15.4568 1.05660
\(215\) 9.05023 0.617221
\(216\) −4.45222 −0.302935
\(217\) 6.10239 0.414258
\(218\) 18.6885 1.26574
\(219\) 7.78098 0.525790
\(220\) 9.08151 0.612275
\(221\) −6.24134 −0.419838
\(222\) 2.05150 0.137688
\(223\) −4.03071 −0.269916 −0.134958 0.990851i \(-0.543090\pi\)
−0.134958 + 0.990851i \(0.543090\pi\)
\(224\) 4.21612 0.281702
\(225\) 3.34013 0.222675
\(226\) 12.7969 0.851236
\(227\) 25.1961 1.67232 0.836161 0.548484i \(-0.184795\pi\)
0.836161 + 0.548484i \(0.184795\pi\)
\(228\) −2.88019 −0.190745
\(229\) −22.4179 −1.48142 −0.740708 0.671827i \(-0.765510\pi\)
−0.740708 + 0.671827i \(0.765510\pi\)
\(230\) 6.29527 0.415098
\(231\) −17.1131 −1.12596
\(232\) −6.98169 −0.458371
\(233\) −11.6626 −0.764041 −0.382020 0.924154i \(-0.624772\pi\)
−0.382020 + 0.924154i \(0.624772\pi\)
\(234\) 13.1331 0.858537
\(235\) −18.0942 −1.18033
\(236\) −7.24193 −0.471410
\(237\) 11.4904 0.746381
\(238\) −4.59292 −0.297715
\(239\) −24.8251 −1.60580 −0.802902 0.596111i \(-0.796712\pi\)
−0.802902 + 0.596111i \(0.796712\pi\)
\(240\) 1.58348 0.102213
\(241\) 12.5505 0.808447 0.404223 0.914660i \(-0.367542\pi\)
0.404223 + 0.914660i \(0.367542\pi\)
\(242\) −12.2788 −0.789312
\(243\) −15.9909 −1.02582
\(244\) −3.66784 −0.234810
\(245\) −20.2826 −1.29581
\(246\) 8.86804 0.565406
\(247\) 19.6150 1.24807
\(248\) 1.44739 0.0919096
\(249\) −10.4267 −0.660766
\(250\) −12.1539 −0.768683
\(251\) 16.4964 1.04124 0.520620 0.853788i \(-0.325701\pi\)
0.520620 + 0.853788i \(0.325701\pi\)
\(252\) 9.66448 0.608805
\(253\) −16.1368 −1.01451
\(254\) −3.48412 −0.218613
\(255\) −1.72500 −0.108024
\(256\) 1.00000 0.0625000
\(257\) 13.7888 0.860121 0.430060 0.902800i \(-0.358492\pi\)
0.430060 + 0.902800i \(0.358492\pi\)
\(258\) −4.04499 −0.251830
\(259\) −10.2813 −0.638851
\(260\) −10.7840 −0.668795
\(261\) −16.0039 −0.990616
\(262\) 12.8713 0.795193
\(263\) −4.32499 −0.266691 −0.133345 0.991070i \(-0.542572\pi\)
−0.133345 + 0.991070i \(0.542572\pi\)
\(264\) −4.05897 −0.249812
\(265\) 1.27111 0.0780839
\(266\) 14.4344 0.885031
\(267\) −4.20291 −0.257214
\(268\) −6.78487 −0.414452
\(269\) −11.0027 −0.670844 −0.335422 0.942068i \(-0.608879\pi\)
−0.335422 + 0.942068i \(0.608879\pi\)
\(270\) 8.38020 0.510003
\(271\) 2.35759 0.143213 0.0716066 0.997433i \(-0.477187\pi\)
0.0716066 + 0.997433i \(0.477187\pi\)
\(272\) −1.08937 −0.0660528
\(273\) 20.3213 1.22990
\(274\) 2.81809 0.170247
\(275\) 7.03038 0.423948
\(276\) −2.81366 −0.169363
\(277\) 21.4480 1.28868 0.644342 0.764738i \(-0.277131\pi\)
0.644342 + 0.764738i \(0.277131\pi\)
\(278\) 11.5121 0.690449
\(279\) 3.31781 0.198632
\(280\) −7.93580 −0.474255
\(281\) 25.9927 1.55059 0.775297 0.631597i \(-0.217600\pi\)
0.775297 + 0.631597i \(0.217600\pi\)
\(282\) 8.08716 0.481583
\(283\) 5.87483 0.349222 0.174611 0.984637i \(-0.444133\pi\)
0.174611 + 0.984637i \(0.444133\pi\)
\(284\) 8.42340 0.499837
\(285\) 5.42124 0.321127
\(286\) 27.6428 1.63456
\(287\) −44.4433 −2.62340
\(288\) 2.29227 0.135073
\(289\) −15.8133 −0.930192
\(290\) 13.1413 0.771684
\(291\) 6.81906 0.399740
\(292\) −9.24909 −0.541262
\(293\) 13.6295 0.796245 0.398122 0.917332i \(-0.369662\pi\)
0.398122 + 0.917332i \(0.369662\pi\)
\(294\) 9.06527 0.528697
\(295\) 13.6311 0.793635
\(296\) −2.43857 −0.141739
\(297\) −21.4811 −1.24646
\(298\) −1.59309 −0.0922852
\(299\) 19.1619 1.10816
\(300\) 1.22584 0.0707739
\(301\) 20.2720 1.16846
\(302\) −3.71839 −0.213969
\(303\) −13.6110 −0.781930
\(304\) 3.42362 0.196358
\(305\) 6.90380 0.395311
\(306\) −2.49713 −0.142751
\(307\) 13.4101 0.765354 0.382677 0.923882i \(-0.375002\pi\)
0.382677 + 0.923882i \(0.375002\pi\)
\(308\) 20.3420 1.15909
\(309\) −0.277386 −0.0157799
\(310\) −2.72436 −0.154733
\(311\) −21.1385 −1.19866 −0.599328 0.800504i \(-0.704565\pi\)
−0.599328 + 0.800504i \(0.704565\pi\)
\(312\) 4.81989 0.272873
\(313\) 2.40819 0.136119 0.0680594 0.997681i \(-0.478319\pi\)
0.0680594 + 0.997681i \(0.478319\pi\)
\(314\) −7.02202 −0.396275
\(315\) −18.1910 −1.02495
\(316\) −13.6584 −0.768344
\(317\) −21.6410 −1.21548 −0.607739 0.794137i \(-0.707923\pi\)
−0.607739 + 0.794137i \(0.707923\pi\)
\(318\) −0.568122 −0.0318587
\(319\) −33.6854 −1.88602
\(320\) −1.88225 −0.105221
\(321\) 13.0033 0.725773
\(322\) 14.1010 0.785819
\(323\) −3.72960 −0.207520
\(324\) 3.13128 0.173960
\(325\) −8.34835 −0.463083
\(326\) 4.57079 0.253153
\(327\) 15.7220 0.869430
\(328\) −10.5413 −0.582044
\(329\) −40.5298 −2.23448
\(330\) 7.64000 0.420568
\(331\) 0.855744 0.0470360 0.0235180 0.999723i \(-0.492513\pi\)
0.0235180 + 0.999723i \(0.492513\pi\)
\(332\) 12.3940 0.680210
\(333\) −5.58986 −0.306322
\(334\) 3.09616 0.169414
\(335\) 12.7708 0.697745
\(336\) 3.54690 0.193499
\(337\) −34.5078 −1.87976 −0.939881 0.341502i \(-0.889064\pi\)
−0.939881 + 0.341502i \(0.889064\pi\)
\(338\) −19.8250 −1.07834
\(339\) 10.7656 0.584709
\(340\) 2.05047 0.111202
\(341\) 6.98341 0.378173
\(342\) 7.84785 0.424363
\(343\) −15.9188 −0.859536
\(344\) 4.80820 0.259241
\(345\) 5.29602 0.285128
\(346\) −16.7004 −0.897820
\(347\) −22.2428 −1.19405 −0.597027 0.802221i \(-0.703651\pi\)
−0.597027 + 0.802221i \(0.703651\pi\)
\(348\) −5.87348 −0.314852
\(349\) 32.4327 1.73608 0.868042 0.496490i \(-0.165378\pi\)
0.868042 + 0.496490i \(0.165378\pi\)
\(350\) −6.14344 −0.328381
\(351\) 25.5081 1.36152
\(352\) 4.82481 0.257163
\(353\) 32.9861 1.75567 0.877837 0.478960i \(-0.158986\pi\)
0.877837 + 0.478960i \(0.158986\pi\)
\(354\) −6.09242 −0.323808
\(355\) −15.8549 −0.841493
\(356\) 4.99591 0.264783
\(357\) −3.86389 −0.204499
\(358\) 5.79649 0.306354
\(359\) −13.4018 −0.707320 −0.353660 0.935374i \(-0.615063\pi\)
−0.353660 + 0.935374i \(0.615063\pi\)
\(360\) −4.31462 −0.227400
\(361\) −7.27881 −0.383095
\(362\) 1.60336 0.0842705
\(363\) −10.3298 −0.542173
\(364\) −24.1555 −1.26609
\(365\) 17.4091 0.911235
\(366\) −3.08564 −0.161289
\(367\) 19.7119 1.02895 0.514477 0.857504i \(-0.327986\pi\)
0.514477 + 0.857504i \(0.327986\pi\)
\(368\) 3.34454 0.174346
\(369\) −24.1634 −1.25790
\(370\) 4.59001 0.238623
\(371\) 2.84721 0.147820
\(372\) 1.21765 0.0631322
\(373\) −22.9719 −1.18944 −0.594719 0.803933i \(-0.702737\pi\)
−0.594719 + 0.803933i \(0.702737\pi\)
\(374\) −5.25601 −0.271782
\(375\) −10.2247 −0.528003
\(376\) −9.61304 −0.495755
\(377\) 40.0003 2.06012
\(378\) 18.7711 0.965482
\(379\) −32.5199 −1.67044 −0.835218 0.549919i \(-0.814658\pi\)
−0.835218 + 0.549919i \(0.814658\pi\)
\(380\) −6.44412 −0.330576
\(381\) −2.93108 −0.150164
\(382\) −16.5291 −0.845703
\(383\) −29.4514 −1.50490 −0.752448 0.658651i \(-0.771127\pi\)
−0.752448 + 0.658651i \(0.771127\pi\)
\(384\) 0.841269 0.0429309
\(385\) −38.2888 −1.95138
\(386\) −16.4414 −0.836845
\(387\) 11.0217 0.560263
\(388\) −8.10568 −0.411503
\(389\) −33.4454 −1.69575 −0.847874 0.530198i \(-0.822118\pi\)
−0.847874 + 0.530198i \(0.822118\pi\)
\(390\) −9.07225 −0.459391
\(391\) −3.64345 −0.184257
\(392\) −10.7757 −0.544255
\(393\) 10.8283 0.546213
\(394\) −22.3038 −1.12365
\(395\) 25.7085 1.29354
\(396\) 11.0598 0.555773
\(397\) −2.19143 −0.109985 −0.0549923 0.998487i \(-0.517513\pi\)
−0.0549923 + 0.998487i \(0.517513\pi\)
\(398\) −15.8172 −0.792846
\(399\) 12.1432 0.607922
\(400\) −1.45713 −0.0728565
\(401\) 19.6058 0.979068 0.489534 0.871984i \(-0.337167\pi\)
0.489534 + 0.871984i \(0.337167\pi\)
\(402\) −5.70790 −0.284684
\(403\) −8.29257 −0.413082
\(404\) 16.1791 0.804940
\(405\) −5.89385 −0.292868
\(406\) 29.4357 1.46087
\(407\) −11.7657 −0.583202
\(408\) −0.916455 −0.0453713
\(409\) −6.19236 −0.306192 −0.153096 0.988211i \(-0.548924\pi\)
−0.153096 + 0.988211i \(0.548924\pi\)
\(410\) 19.8413 0.979892
\(411\) 2.37078 0.116942
\(412\) 0.329723 0.0162443
\(413\) 30.5329 1.50242
\(414\) 7.66658 0.376792
\(415\) −23.3287 −1.14516
\(416\) −5.72931 −0.280902
\(417\) 9.68477 0.474265
\(418\) 16.5183 0.807938
\(419\) −21.1687 −1.03416 −0.517079 0.855938i \(-0.672981\pi\)
−0.517079 + 0.855938i \(0.672981\pi\)
\(420\) −6.67615 −0.325763
\(421\) −12.1390 −0.591617 −0.295809 0.955247i \(-0.595589\pi\)
−0.295809 + 0.955247i \(0.595589\pi\)
\(422\) 10.4508 0.508737
\(423\) −22.0356 −1.07141
\(424\) 0.675316 0.0327962
\(425\) 1.58736 0.0769980
\(426\) 7.08635 0.343335
\(427\) 15.4641 0.748359
\(428\) −15.4568 −0.747130
\(429\) 23.2551 1.12277
\(430\) −9.05023 −0.436441
\(431\) −9.81860 −0.472945 −0.236473 0.971638i \(-0.575991\pi\)
−0.236473 + 0.971638i \(0.575991\pi\)
\(432\) 4.45222 0.214208
\(433\) 11.0706 0.532019 0.266009 0.963970i \(-0.414295\pi\)
0.266009 + 0.963970i \(0.414295\pi\)
\(434\) −6.10239 −0.292924
\(435\) 11.0554 0.530065
\(436\) −18.6885 −0.895015
\(437\) 11.4505 0.547750
\(438\) −7.78098 −0.371790
\(439\) 26.2880 1.25466 0.627330 0.778754i \(-0.284148\pi\)
0.627330 + 0.778754i \(0.284148\pi\)
\(440\) −9.08151 −0.432944
\(441\) −24.7008 −1.17623
\(442\) 6.24134 0.296870
\(443\) 5.19550 0.246846 0.123423 0.992354i \(-0.460613\pi\)
0.123423 + 0.992354i \(0.460613\pi\)
\(444\) −2.05150 −0.0973598
\(445\) −9.40356 −0.445771
\(446\) 4.03071 0.190859
\(447\) −1.34022 −0.0633901
\(448\) −4.21612 −0.199193
\(449\) −37.2659 −1.75869 −0.879343 0.476188i \(-0.842018\pi\)
−0.879343 + 0.476188i \(0.842018\pi\)
\(450\) −3.34013 −0.157455
\(451\) −50.8596 −2.39489
\(452\) −12.7969 −0.601915
\(453\) −3.12817 −0.146974
\(454\) −25.1961 −1.18251
\(455\) 45.4667 2.13151
\(456\) 2.88019 0.134877
\(457\) 2.71322 0.126919 0.0634596 0.997984i \(-0.479787\pi\)
0.0634596 + 0.997984i \(0.479787\pi\)
\(458\) 22.4179 1.04752
\(459\) −4.85012 −0.226384
\(460\) −6.29527 −0.293519
\(461\) −19.6834 −0.916750 −0.458375 0.888759i \(-0.651568\pi\)
−0.458375 + 0.888759i \(0.651568\pi\)
\(462\) 17.1131 0.796174
\(463\) 22.2994 1.03634 0.518170 0.855278i \(-0.326614\pi\)
0.518170 + 0.855278i \(0.326614\pi\)
\(464\) 6.98169 0.324117
\(465\) −2.29192 −0.106285
\(466\) 11.6626 0.540258
\(467\) −0.279514 −0.0129343 −0.00646717 0.999979i \(-0.502059\pi\)
−0.00646717 + 0.999979i \(0.502059\pi\)
\(468\) −13.1331 −0.607078
\(469\) 28.6058 1.32089
\(470\) 18.0942 0.834621
\(471\) −5.90741 −0.272199
\(472\) 7.24193 0.333337
\(473\) 23.1986 1.06667
\(474\) −11.4904 −0.527771
\(475\) −4.98866 −0.228896
\(476\) 4.59292 0.210516
\(477\) 1.54800 0.0708782
\(478\) 24.8251 1.13548
\(479\) −38.7175 −1.76905 −0.884524 0.466494i \(-0.845517\pi\)
−0.884524 + 0.466494i \(0.845517\pi\)
\(480\) −1.58348 −0.0722757
\(481\) 13.9713 0.637038
\(482\) −12.5505 −0.571658
\(483\) 11.8628 0.539774
\(484\) 12.2788 0.558128
\(485\) 15.2569 0.692781
\(486\) 15.9909 0.725363
\(487\) 24.8964 1.12816 0.564082 0.825718i \(-0.309230\pi\)
0.564082 + 0.825718i \(0.309230\pi\)
\(488\) 3.66784 0.166035
\(489\) 3.84527 0.173889
\(490\) 20.2826 0.916273
\(491\) −23.7423 −1.07147 −0.535737 0.844385i \(-0.679966\pi\)
−0.535737 + 0.844385i \(0.679966\pi\)
\(492\) −8.86804 −0.399802
\(493\) −7.60565 −0.342541
\(494\) −19.6150 −0.882520
\(495\) −20.8172 −0.935665
\(496\) −1.44739 −0.0649899
\(497\) −35.5141 −1.59302
\(498\) 10.4267 0.467232
\(499\) −1.12134 −0.0501983 −0.0250991 0.999685i \(-0.507990\pi\)
−0.0250991 + 0.999685i \(0.507990\pi\)
\(500\) 12.1539 0.543541
\(501\) 2.60471 0.116370
\(502\) −16.4964 −0.736268
\(503\) 1.55759 0.0694496 0.0347248 0.999397i \(-0.488945\pi\)
0.0347248 + 0.999397i \(0.488945\pi\)
\(504\) −9.66448 −0.430490
\(505\) −30.4531 −1.35515
\(506\) 16.1368 0.717368
\(507\) −16.6781 −0.740702
\(508\) 3.48412 0.154583
\(509\) −8.05217 −0.356906 −0.178453 0.983948i \(-0.557109\pi\)
−0.178453 + 0.983948i \(0.557109\pi\)
\(510\) 1.72500 0.0763842
\(511\) 38.9953 1.72505
\(512\) −1.00000 −0.0441942
\(513\) 15.2427 0.672983
\(514\) −13.7888 −0.608197
\(515\) −0.620621 −0.0273478
\(516\) 4.04499 0.178071
\(517\) −46.3811 −2.03984
\(518\) 10.2813 0.451736
\(519\) −14.0495 −0.616707
\(520\) 10.7840 0.472910
\(521\) 23.6403 1.03570 0.517851 0.855471i \(-0.326732\pi\)
0.517851 + 0.855471i \(0.326732\pi\)
\(522\) 16.0039 0.700471
\(523\) −19.8303 −0.867118 −0.433559 0.901125i \(-0.642742\pi\)
−0.433559 + 0.901125i \(0.642742\pi\)
\(524\) −12.8713 −0.562287
\(525\) −5.16829 −0.225563
\(526\) 4.32499 0.188579
\(527\) 1.57675 0.0686843
\(528\) 4.05897 0.176644
\(529\) −11.8140 −0.513653
\(530\) −1.27111 −0.0552136
\(531\) 16.6004 0.720397
\(532\) −14.4344 −0.625811
\(533\) 60.3942 2.61596
\(534\) 4.20291 0.181878
\(535\) 29.0935 1.25782
\(536\) 6.78487 0.293062
\(537\) 4.87641 0.210433
\(538\) 11.0027 0.474358
\(539\) −51.9907 −2.23940
\(540\) −8.38020 −0.360626
\(541\) 12.1772 0.523540 0.261770 0.965130i \(-0.415694\pi\)
0.261770 + 0.965130i \(0.415694\pi\)
\(542\) −2.35759 −0.101267
\(543\) 1.34885 0.0578849
\(544\) 1.08937 0.0467064
\(545\) 35.1764 1.50679
\(546\) −20.3213 −0.869670
\(547\) −37.2881 −1.59433 −0.797163 0.603764i \(-0.793667\pi\)
−0.797163 + 0.603764i \(0.793667\pi\)
\(548\) −2.81809 −0.120383
\(549\) 8.40767 0.358831
\(550\) −7.03038 −0.299776
\(551\) 23.9027 1.01829
\(552\) 2.81366 0.119757
\(553\) 57.5855 2.44878
\(554\) −21.4480 −0.911237
\(555\) 3.86144 0.163909
\(556\) −11.5121 −0.488221
\(557\) −44.7533 −1.89626 −0.948129 0.317885i \(-0.897027\pi\)
−0.948129 + 0.317885i \(0.897027\pi\)
\(558\) −3.31781 −0.140454
\(559\) −27.5476 −1.16514
\(560\) 7.93580 0.335349
\(561\) −4.42172 −0.186685
\(562\) −25.9927 −1.09644
\(563\) 4.21839 0.177784 0.0888919 0.996041i \(-0.471667\pi\)
0.0888919 + 0.996041i \(0.471667\pi\)
\(564\) −8.08716 −0.340531
\(565\) 24.0870 1.01335
\(566\) −5.87483 −0.246938
\(567\) −13.2019 −0.554426
\(568\) −8.42340 −0.353438
\(569\) −18.3444 −0.769035 −0.384518 0.923118i \(-0.625632\pi\)
−0.384518 + 0.923118i \(0.625632\pi\)
\(570\) −5.42124 −0.227071
\(571\) 2.17978 0.0912208 0.0456104 0.998959i \(-0.485477\pi\)
0.0456104 + 0.998959i \(0.485477\pi\)
\(572\) −27.6428 −1.15581
\(573\) −13.9054 −0.580908
\(574\) 44.4433 1.85503
\(575\) −4.87344 −0.203236
\(576\) −2.29227 −0.0955111
\(577\) −17.0901 −0.711472 −0.355736 0.934587i \(-0.615770\pi\)
−0.355736 + 0.934587i \(0.615770\pi\)
\(578\) 15.8133 0.657745
\(579\) −13.8316 −0.574823
\(580\) −13.1413 −0.545663
\(581\) −52.2547 −2.16789
\(582\) −6.81906 −0.282659
\(583\) 3.25827 0.134944
\(584\) 9.24909 0.382730
\(585\) 24.7198 1.02204
\(586\) −13.6295 −0.563030
\(587\) 26.5055 1.09400 0.547000 0.837133i \(-0.315770\pi\)
0.547000 + 0.837133i \(0.315770\pi\)
\(588\) −9.06527 −0.373845
\(589\) −4.95533 −0.204181
\(590\) −13.6311 −0.561185
\(591\) −18.7635 −0.771826
\(592\) 2.43857 0.100225
\(593\) −12.7116 −0.522002 −0.261001 0.965339i \(-0.584053\pi\)
−0.261001 + 0.965339i \(0.584053\pi\)
\(594\) 21.4811 0.881382
\(595\) −8.64504 −0.354412
\(596\) 1.59309 0.0652555
\(597\) −13.3065 −0.544601
\(598\) −19.1619 −0.783589
\(599\) −6.48987 −0.265169 −0.132584 0.991172i \(-0.542328\pi\)
−0.132584 + 0.991172i \(0.542328\pi\)
\(600\) −1.22584 −0.0500447
\(601\) −6.21476 −0.253505 −0.126753 0.991934i \(-0.540455\pi\)
−0.126753 + 0.991934i \(0.540455\pi\)
\(602\) −20.2720 −0.826223
\(603\) 15.5527 0.633356
\(604\) 3.71839 0.151299
\(605\) −23.1118 −0.939629
\(606\) 13.6110 0.552908
\(607\) 16.5887 0.673314 0.336657 0.941627i \(-0.390704\pi\)
0.336657 + 0.941627i \(0.390704\pi\)
\(608\) −3.42362 −0.138846
\(609\) 24.7633 1.00346
\(610\) −6.90380 −0.279527
\(611\) 55.0761 2.22814
\(612\) 2.49713 0.100940
\(613\) 42.5422 1.71826 0.859132 0.511754i \(-0.171004\pi\)
0.859132 + 0.511754i \(0.171004\pi\)
\(614\) −13.4101 −0.541187
\(615\) 16.6919 0.673082
\(616\) −20.3420 −0.819603
\(617\) 36.7530 1.47962 0.739810 0.672815i \(-0.234915\pi\)
0.739810 + 0.672815i \(0.234915\pi\)
\(618\) 0.277386 0.0111581
\(619\) 12.9809 0.521746 0.260873 0.965373i \(-0.415990\pi\)
0.260873 + 0.965373i \(0.415990\pi\)
\(620\) 2.72436 0.109413
\(621\) 14.8907 0.597541
\(622\) 21.1385 0.847578
\(623\) −21.0634 −0.843886
\(624\) −4.81989 −0.192950
\(625\) −15.5911 −0.623645
\(626\) −2.40819 −0.0962505
\(627\) 13.8964 0.554968
\(628\) 7.02202 0.280209
\(629\) −2.65651 −0.105922
\(630\) 18.1910 0.724746
\(631\) 10.4456 0.415832 0.207916 0.978147i \(-0.433332\pi\)
0.207916 + 0.978147i \(0.433332\pi\)
\(632\) 13.6584 0.543302
\(633\) 8.79194 0.349448
\(634\) 21.6410 0.859472
\(635\) −6.55799 −0.260246
\(636\) 0.568122 0.0225275
\(637\) 61.7373 2.44612
\(638\) 33.6854 1.33362
\(639\) −19.3087 −0.763839
\(640\) 1.88225 0.0744025
\(641\) −7.70732 −0.304421 −0.152210 0.988348i \(-0.548639\pi\)
−0.152210 + 0.988348i \(0.548639\pi\)
\(642\) −13.0033 −0.513199
\(643\) −0.243674 −0.00960956 −0.00480478 0.999988i \(-0.501529\pi\)
−0.00480478 + 0.999988i \(0.501529\pi\)
\(644\) −14.1010 −0.555658
\(645\) −7.61369 −0.299789
\(646\) 3.72960 0.146739
\(647\) −22.3444 −0.878450 −0.439225 0.898377i \(-0.644747\pi\)
−0.439225 + 0.898377i \(0.644747\pi\)
\(648\) −3.13128 −0.123008
\(649\) 34.9410 1.37155
\(650\) 8.34835 0.327449
\(651\) −5.13376 −0.201208
\(652\) −4.57079 −0.179006
\(653\) −3.83956 −0.150254 −0.0751268 0.997174i \(-0.523936\pi\)
−0.0751268 + 0.997174i \(0.523936\pi\)
\(654\) −15.7220 −0.614780
\(655\) 24.2271 0.946630
\(656\) 10.5413 0.411567
\(657\) 21.2014 0.827144
\(658\) 40.5298 1.58001
\(659\) 6.40909 0.249663 0.124831 0.992178i \(-0.460161\pi\)
0.124831 + 0.992178i \(0.460161\pi\)
\(660\) −7.64000 −0.297386
\(661\) −10.4490 −0.406418 −0.203209 0.979135i \(-0.565137\pi\)
−0.203209 + 0.979135i \(0.565137\pi\)
\(662\) −0.855744 −0.0332594
\(663\) 5.25065 0.203918
\(664\) −12.3940 −0.480981
\(665\) 27.1692 1.05358
\(666\) 5.58986 0.216603
\(667\) 23.3506 0.904138
\(668\) −3.09616 −0.119794
\(669\) 3.39091 0.131100
\(670\) −12.7708 −0.493380
\(671\) 17.6967 0.683172
\(672\) −3.54690 −0.136825
\(673\) −38.6084 −1.48824 −0.744122 0.668044i \(-0.767132\pi\)
−0.744122 + 0.668044i \(0.767132\pi\)
\(674\) 34.5078 1.32919
\(675\) −6.48747 −0.249703
\(676\) 19.8250 0.762499
\(677\) 5.45005 0.209463 0.104731 0.994501i \(-0.466602\pi\)
0.104731 + 0.994501i \(0.466602\pi\)
\(678\) −10.7656 −0.413452
\(679\) 34.1745 1.31150
\(680\) −2.05047 −0.0786319
\(681\) −21.1967 −0.812259
\(682\) −6.98341 −0.267408
\(683\) −1.23732 −0.0473446 −0.0236723 0.999720i \(-0.507536\pi\)
−0.0236723 + 0.999720i \(0.507536\pi\)
\(684\) −7.84785 −0.300070
\(685\) 5.30436 0.202669
\(686\) 15.9188 0.607784
\(687\) 18.8595 0.719534
\(688\) −4.80820 −0.183311
\(689\) −3.86909 −0.147401
\(690\) −5.29602 −0.201616
\(691\) 23.4044 0.890347 0.445174 0.895444i \(-0.353142\pi\)
0.445174 + 0.895444i \(0.353142\pi\)
\(692\) 16.7004 0.634854
\(693\) −46.6293 −1.77130
\(694\) 22.2428 0.844324
\(695\) 21.6686 0.821939
\(696\) 5.87348 0.222634
\(697\) −11.4833 −0.434963
\(698\) −32.4327 −1.22760
\(699\) 9.81137 0.371100
\(700\) 6.14344 0.232200
\(701\) −39.0654 −1.47548 −0.737739 0.675086i \(-0.764107\pi\)
−0.737739 + 0.675086i \(0.764107\pi\)
\(702\) −25.5081 −0.962743
\(703\) 8.34876 0.314879
\(704\) −4.82481 −0.181842
\(705\) 15.2221 0.573296
\(706\) −32.9861 −1.24145
\(707\) −68.2131 −2.56542
\(708\) 6.09242 0.228967
\(709\) −20.9689 −0.787504 −0.393752 0.919217i \(-0.628823\pi\)
−0.393752 + 0.919217i \(0.628823\pi\)
\(710\) 15.8549 0.595026
\(711\) 31.3087 1.17417
\(712\) −4.99591 −0.187230
\(713\) −4.84088 −0.181292
\(714\) 3.86389 0.144602
\(715\) 52.0308 1.94584
\(716\) −5.79649 −0.216625
\(717\) 20.8846 0.779951
\(718\) 13.4018 0.500151
\(719\) 7.68056 0.286436 0.143218 0.989691i \(-0.454255\pi\)
0.143218 + 0.989691i \(0.454255\pi\)
\(720\) 4.31462 0.160796
\(721\) −1.39015 −0.0517720
\(722\) 7.27881 0.270889
\(723\) −10.5583 −0.392668
\(724\) −1.60336 −0.0595883
\(725\) −10.1732 −0.377824
\(726\) 10.3298 0.383375
\(727\) 22.8897 0.848932 0.424466 0.905444i \(-0.360462\pi\)
0.424466 + 0.905444i \(0.360462\pi\)
\(728\) 24.1555 0.895261
\(729\) 4.05883 0.150327
\(730\) −17.4091 −0.644340
\(731\) 5.23791 0.193731
\(732\) 3.08564 0.114049
\(733\) −9.73597 −0.359606 −0.179803 0.983703i \(-0.557546\pi\)
−0.179803 + 0.983703i \(0.557546\pi\)
\(734\) −19.7119 −0.727580
\(735\) 17.0631 0.629382
\(736\) −3.34454 −0.123282
\(737\) 32.7357 1.20584
\(738\) 24.1634 0.889466
\(739\) −7.70807 −0.283546 −0.141773 0.989899i \(-0.545280\pi\)
−0.141773 + 0.989899i \(0.545280\pi\)
\(740\) −4.59001 −0.168732
\(741\) −16.5015 −0.606197
\(742\) −2.84721 −0.104525
\(743\) −52.5541 −1.92802 −0.964011 0.265862i \(-0.914344\pi\)
−0.964011 + 0.265862i \(0.914344\pi\)
\(744\) −1.21765 −0.0446412
\(745\) −2.99860 −0.109860
\(746\) 22.9719 0.841060
\(747\) −28.4104 −1.03948
\(748\) 5.25601 0.192179
\(749\) 65.1676 2.38117
\(750\) 10.2247 0.373355
\(751\) 48.8917 1.78408 0.892042 0.451952i \(-0.149272\pi\)
0.892042 + 0.451952i \(0.149272\pi\)
\(752\) 9.61304 0.350551
\(753\) −13.8779 −0.505738
\(754\) −40.0003 −1.45672
\(755\) −6.99895 −0.254718
\(756\) −18.7711 −0.682699
\(757\) 15.4485 0.561486 0.280743 0.959783i \(-0.409419\pi\)
0.280743 + 0.959783i \(0.409419\pi\)
\(758\) 32.5199 1.18118
\(759\) 13.5754 0.492756
\(760\) 6.44412 0.233753
\(761\) −41.9102 −1.51924 −0.759622 0.650365i \(-0.774616\pi\)
−0.759622 + 0.650365i \(0.774616\pi\)
\(762\) 2.93108 0.106182
\(763\) 78.7929 2.85249
\(764\) 16.5291 0.598002
\(765\) −4.70022 −0.169937
\(766\) 29.4514 1.06412
\(767\) −41.4913 −1.49816
\(768\) −0.841269 −0.0303567
\(769\) 7.30644 0.263477 0.131738 0.991285i \(-0.457944\pi\)
0.131738 + 0.991285i \(0.457944\pi\)
\(770\) 38.2888 1.37983
\(771\) −11.6001 −0.417767
\(772\) 16.4414 0.591739
\(773\) 2.27618 0.0818683 0.0409342 0.999162i \(-0.486967\pi\)
0.0409342 + 0.999162i \(0.486967\pi\)
\(774\) −11.0217 −0.396166
\(775\) 2.10904 0.0757590
\(776\) 8.10568 0.290977
\(777\) 8.64937 0.310294
\(778\) 33.4454 1.19907
\(779\) 36.0893 1.29303
\(780\) 9.07225 0.324839
\(781\) −40.6413 −1.45426
\(782\) 3.64345 0.130290
\(783\) 31.0840 1.11085
\(784\) 10.7757 0.384846
\(785\) −13.2172 −0.471742
\(786\) −10.8283 −0.386231
\(787\) −15.8048 −0.563379 −0.281689 0.959506i \(-0.590895\pi\)
−0.281689 + 0.959506i \(0.590895\pi\)
\(788\) 22.3038 0.794538
\(789\) 3.63848 0.129533
\(790\) −25.7085 −0.914668
\(791\) 53.9533 1.91836
\(792\) −11.0598 −0.392991
\(793\) −21.0142 −0.746236
\(794\) 2.19143 0.0777708
\(795\) −1.06935 −0.0379259
\(796\) 15.8172 0.560627
\(797\) 39.0142 1.38196 0.690978 0.722876i \(-0.257180\pi\)
0.690978 + 0.722876i \(0.257180\pi\)
\(798\) −12.1432 −0.429866
\(799\) −10.4722 −0.370479
\(800\) 1.45713 0.0515173
\(801\) −11.4520 −0.404635
\(802\) −19.6058 −0.692306
\(803\) 44.6251 1.57479
\(804\) 5.70790 0.201302
\(805\) 26.5417 0.935470
\(806\) 8.29257 0.292093
\(807\) 9.25620 0.325834
\(808\) −16.1791 −0.569179
\(809\) −20.4669 −0.719579 −0.359789 0.933034i \(-0.617151\pi\)
−0.359789 + 0.933034i \(0.617151\pi\)
\(810\) 5.89385 0.207089
\(811\) −41.3406 −1.45167 −0.725833 0.687871i \(-0.758545\pi\)
−0.725833 + 0.687871i \(0.758545\pi\)
\(812\) −29.4357 −1.03299
\(813\) −1.98336 −0.0695596
\(814\) 11.7657 0.412386
\(815\) 8.60338 0.301363
\(816\) 0.916455 0.0320823
\(817\) −16.4615 −0.575913
\(818\) 6.19236 0.216511
\(819\) 55.3708 1.93481
\(820\) −19.8413 −0.692889
\(821\) −11.7942 −0.411621 −0.205811 0.978592i \(-0.565983\pi\)
−0.205811 + 0.978592i \(0.565983\pi\)
\(822\) −2.37078 −0.0826903
\(823\) −30.0981 −1.04915 −0.524577 0.851363i \(-0.675777\pi\)
−0.524577 + 0.851363i \(0.675777\pi\)
\(824\) −0.329723 −0.0114864
\(825\) −5.91444 −0.205915
\(826\) −30.5329 −1.06237
\(827\) 17.0117 0.591556 0.295778 0.955257i \(-0.404421\pi\)
0.295778 + 0.955257i \(0.404421\pi\)
\(828\) −7.66658 −0.266432
\(829\) −22.7288 −0.789404 −0.394702 0.918809i \(-0.629152\pi\)
−0.394702 + 0.918809i \(0.629152\pi\)
\(830\) 23.3287 0.809749
\(831\) −18.0435 −0.625923
\(832\) 5.72931 0.198628
\(833\) −11.7387 −0.406723
\(834\) −9.68477 −0.335356
\(835\) 5.82775 0.201678
\(836\) −16.5183 −0.571299
\(837\) −6.44412 −0.222741
\(838\) 21.1687 0.731260
\(839\) 28.2670 0.975886 0.487943 0.872875i \(-0.337747\pi\)
0.487943 + 0.872875i \(0.337747\pi\)
\(840\) 6.67615 0.230349
\(841\) 19.7440 0.680829
\(842\) 12.1390 0.418337
\(843\) −21.8669 −0.753135
\(844\) −10.4508 −0.359732
\(845\) −37.3156 −1.28369
\(846\) 22.0356 0.757601
\(847\) −51.7690 −1.77880
\(848\) −0.675316 −0.0231904
\(849\) −4.94232 −0.169620
\(850\) −1.58736 −0.0544458
\(851\) 8.15592 0.279581
\(852\) −7.08635 −0.242774
\(853\) 2.85678 0.0978143 0.0489071 0.998803i \(-0.484426\pi\)
0.0489071 + 0.998803i \(0.484426\pi\)
\(854\) −15.4641 −0.529170
\(855\) 14.7716 0.505179
\(856\) 15.4568 0.528301
\(857\) 25.4106 0.868009 0.434004 0.900911i \(-0.357100\pi\)
0.434004 + 0.900911i \(0.357100\pi\)
\(858\) −23.2551 −0.793915
\(859\) −2.02573 −0.0691171 −0.0345585 0.999403i \(-0.511003\pi\)
−0.0345585 + 0.999403i \(0.511003\pi\)
\(860\) 9.05023 0.308610
\(861\) 37.3888 1.27421
\(862\) 9.81860 0.334423
\(863\) −29.6812 −1.01036 −0.505179 0.863014i \(-0.668574\pi\)
−0.505179 + 0.863014i \(0.668574\pi\)
\(864\) −4.45222 −0.151468
\(865\) −31.4344 −1.06880
\(866\) −11.0706 −0.376194
\(867\) 13.3032 0.451801
\(868\) 6.10239 0.207129
\(869\) 65.8992 2.23548
\(870\) −11.0554 −0.374812
\(871\) −38.8726 −1.31715
\(872\) 18.6885 0.632871
\(873\) 18.5804 0.628850
\(874\) −11.4505 −0.387318
\(875\) −51.2425 −1.73231
\(876\) 7.78098 0.262895
\(877\) −47.3190 −1.59785 −0.798924 0.601432i \(-0.794597\pi\)
−0.798924 + 0.601432i \(0.794597\pi\)
\(878\) −26.2880 −0.887178
\(879\) −11.4661 −0.386742
\(880\) 9.08151 0.306138
\(881\) 10.5126 0.354178 0.177089 0.984195i \(-0.443332\pi\)
0.177089 + 0.984195i \(0.443332\pi\)
\(882\) 24.7008 0.831718
\(883\) −18.7643 −0.631469 −0.315735 0.948848i \(-0.602251\pi\)
−0.315735 + 0.948848i \(0.602251\pi\)
\(884\) −6.24134 −0.209919
\(885\) −11.4675 −0.385474
\(886\) −5.19550 −0.174546
\(887\) −6.22353 −0.208966 −0.104483 0.994527i \(-0.533319\pi\)
−0.104483 + 0.994527i \(0.533319\pi\)
\(888\) 2.05150 0.0688438
\(889\) −14.6895 −0.492669
\(890\) 9.40356 0.315208
\(891\) −15.1078 −0.506131
\(892\) −4.03071 −0.134958
\(893\) 32.9114 1.10134
\(894\) 1.34022 0.0448236
\(895\) 10.9105 0.364696
\(896\) 4.21612 0.140851
\(897\) −16.1203 −0.538243
\(898\) 37.2659 1.24358
\(899\) −10.1053 −0.337029
\(900\) 3.34013 0.111338
\(901\) 0.735669 0.0245087
\(902\) 50.8596 1.69344
\(903\) −17.0542 −0.567527
\(904\) 12.7969 0.425618
\(905\) 3.01792 0.100319
\(906\) 3.12817 0.103926
\(907\) −27.4858 −0.912651 −0.456326 0.889813i \(-0.650835\pi\)
−0.456326 + 0.889813i \(0.650835\pi\)
\(908\) 25.1961 0.836161
\(909\) −37.0868 −1.23009
\(910\) −45.4667 −1.50721
\(911\) 28.3475 0.939196 0.469598 0.882880i \(-0.344399\pi\)
0.469598 + 0.882880i \(0.344399\pi\)
\(912\) −2.88019 −0.0953726
\(913\) −59.7988 −1.97905
\(914\) −2.71322 −0.0897454
\(915\) −5.80796 −0.192005
\(916\) −22.4179 −0.740708
\(917\) 54.2671 1.79206
\(918\) 4.85012 0.160078
\(919\) 22.8047 0.752259 0.376129 0.926567i \(-0.377255\pi\)
0.376129 + 0.926567i \(0.377255\pi\)
\(920\) 6.29527 0.207549
\(921\) −11.2815 −0.371738
\(922\) 19.6834 0.648240
\(923\) 48.2602 1.58850
\(924\) −17.1131 −0.562980
\(925\) −3.55332 −0.116832
\(926\) −22.2994 −0.732803
\(927\) −0.755812 −0.0248241
\(928\) −6.98169 −0.229185
\(929\) −47.7286 −1.56592 −0.782962 0.622070i \(-0.786292\pi\)
−0.782962 + 0.622070i \(0.786292\pi\)
\(930\) 2.29192 0.0751551
\(931\) 36.8919 1.20908
\(932\) −11.6626 −0.382020
\(933\) 17.7832 0.582196
\(934\) 0.279514 0.00914597
\(935\) −9.89313 −0.323540
\(936\) 13.1331 0.429269
\(937\) 3.29283 0.107572 0.0537860 0.998552i \(-0.482871\pi\)
0.0537860 + 0.998552i \(0.482871\pi\)
\(938\) −28.6058 −0.934014
\(939\) −2.02593 −0.0661138
\(940\) −18.0942 −0.590166
\(941\) 0.973513 0.0317356 0.0158678 0.999874i \(-0.494949\pi\)
0.0158678 + 0.999874i \(0.494949\pi\)
\(942\) 5.90741 0.192474
\(943\) 35.2557 1.14808
\(944\) −7.24193 −0.235705
\(945\) 35.3320 1.14935
\(946\) −23.1986 −0.754253
\(947\) 45.0759 1.46477 0.732385 0.680891i \(-0.238407\pi\)
0.732385 + 0.680891i \(0.238407\pi\)
\(948\) 11.4904 0.373190
\(949\) −52.9909 −1.72016
\(950\) 4.98866 0.161854
\(951\) 18.2059 0.590366
\(952\) −4.59292 −0.148857
\(953\) 49.3118 1.59737 0.798684 0.601751i \(-0.205530\pi\)
0.798684 + 0.601751i \(0.205530\pi\)
\(954\) −1.54800 −0.0501184
\(955\) −31.1119 −1.00676
\(956\) −24.8251 −0.802902
\(957\) 28.3385 0.916052
\(958\) 38.7175 1.25091
\(959\) 11.8814 0.383671
\(960\) 1.58348 0.0511066
\(961\) −28.9050 −0.932421
\(962\) −13.9713 −0.450454
\(963\) 35.4310 1.14175
\(964\) 12.5505 0.404223
\(965\) −30.9468 −0.996213
\(966\) −11.8628 −0.381678
\(967\) −37.9805 −1.22137 −0.610685 0.791874i \(-0.709106\pi\)
−0.610685 + 0.791874i \(0.709106\pi\)
\(968\) −12.2788 −0.394656
\(969\) 3.13759 0.100794
\(970\) −15.2569 −0.489870
\(971\) 14.0225 0.450005 0.225002 0.974358i \(-0.427761\pi\)
0.225002 + 0.974358i \(0.427761\pi\)
\(972\) −15.9909 −0.512909
\(973\) 48.5364 1.55601
\(974\) −24.8964 −0.797733
\(975\) 7.02321 0.224923
\(976\) −3.66784 −0.117405
\(977\) 22.9616 0.734607 0.367304 0.930101i \(-0.380281\pi\)
0.367304 + 0.930101i \(0.380281\pi\)
\(978\) −3.84527 −0.122958
\(979\) −24.1043 −0.770378
\(980\) −20.2826 −0.647903
\(981\) 42.8389 1.36774
\(982\) 23.7423 0.757646
\(983\) 12.3091 0.392599 0.196299 0.980544i \(-0.437108\pi\)
0.196299 + 0.980544i \(0.437108\pi\)
\(984\) 8.86804 0.282703
\(985\) −41.9813 −1.33763
\(986\) 7.60565 0.242213
\(987\) 34.0965 1.08530
\(988\) 19.6150 0.624036
\(989\) −16.0812 −0.511353
\(990\) 20.8172 0.661615
\(991\) −28.1922 −0.895554 −0.447777 0.894145i \(-0.647784\pi\)
−0.447777 + 0.894145i \(0.647784\pi\)
\(992\) 1.44739 0.0459548
\(993\) −0.719911 −0.0228457
\(994\) 35.5141 1.12644
\(995\) −29.7720 −0.943835
\(996\) −10.4267 −0.330383
\(997\) 30.1377 0.954470 0.477235 0.878776i \(-0.341639\pi\)
0.477235 + 0.878776i \(0.341639\pi\)
\(998\) 1.12134 0.0354955
\(999\) 10.8571 0.343503
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 4034.2.a.b.1.15 35
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.b.1.15 35 1.1 even 1 trivial