Properties

Label 4027.2.a.b.1.17
Level $4027$
Weight $2$
Character 4027.1
Self dual yes
Analytic conductor $32.156$
Analytic rank $1$
Dimension $159$
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] = [4027,2,Mod(1,4027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4027, 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("4027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4027 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4027.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: \(32.1557568940\)
Analytic rank: \(1\)
Dimension: \(159\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) \(=\) 4027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.46215 q^{2} -2.74752 q^{3} +4.06218 q^{4} +4.08202 q^{5} +6.76481 q^{6} -0.414263 q^{7} -5.07738 q^{8} +4.54887 q^{9} +O(q^{10})\) \(q-2.46215 q^{2} -2.74752 q^{3} +4.06218 q^{4} +4.08202 q^{5} +6.76481 q^{6} -0.414263 q^{7} -5.07738 q^{8} +4.54887 q^{9} -10.0505 q^{10} -1.04639 q^{11} -11.1609 q^{12} -3.10620 q^{13} +1.01998 q^{14} -11.2154 q^{15} +4.37692 q^{16} -5.65244 q^{17} -11.2000 q^{18} +7.50064 q^{19} +16.5819 q^{20} +1.13820 q^{21} +2.57638 q^{22} -2.17262 q^{23} +13.9502 q^{24} +11.6629 q^{25} +7.64792 q^{26} -4.25556 q^{27} -1.68281 q^{28} -2.51610 q^{29} +27.6141 q^{30} +5.60122 q^{31} -0.621864 q^{32} +2.87499 q^{33} +13.9171 q^{34} -1.69103 q^{35} +18.4783 q^{36} -1.62812 q^{37} -18.4677 q^{38} +8.53435 q^{39} -20.7260 q^{40} +3.34375 q^{41} -2.80241 q^{42} -7.04304 q^{43} -4.25064 q^{44} +18.5686 q^{45} +5.34932 q^{46} +1.11167 q^{47} -12.0257 q^{48} -6.82839 q^{49} -28.7157 q^{50} +15.5302 q^{51} -12.6179 q^{52} -4.59677 q^{53} +10.4778 q^{54} -4.27140 q^{55} +2.10337 q^{56} -20.6082 q^{57} +6.19502 q^{58} +0.852632 q^{59} -45.5591 q^{60} -10.6152 q^{61} -13.7910 q^{62} -1.88443 q^{63} -7.22272 q^{64} -12.6796 q^{65} -7.07866 q^{66} +1.13238 q^{67} -22.9612 q^{68} +5.96933 q^{69} +4.16357 q^{70} +5.98152 q^{71} -23.0964 q^{72} +1.54575 q^{73} +4.00867 q^{74} -32.0440 q^{75} +30.4689 q^{76} +0.433483 q^{77} -21.0128 q^{78} +5.91311 q^{79} +17.8667 q^{80} -1.95437 q^{81} -8.23282 q^{82} +6.56935 q^{83} +4.62356 q^{84} -23.0734 q^{85} +17.3410 q^{86} +6.91305 q^{87} +5.31295 q^{88} +3.12143 q^{89} -45.7186 q^{90} +1.28678 q^{91} -8.82558 q^{92} -15.3895 q^{93} -2.73711 q^{94} +30.6178 q^{95} +1.70859 q^{96} -5.70638 q^{97} +16.8125 q^{98} -4.75992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 159 q - 22 q^{2} - 19 q^{3} + 148 q^{4} - 70 q^{5} - 23 q^{6} - 19 q^{7} - 66 q^{8} + 126 q^{9} - 23 q^{10} - 33 q^{11} - 57 q^{12} - 90 q^{13} - 28 q^{14} - 22 q^{15} + 130 q^{16} - 145 q^{17} - 50 q^{18} - 28 q^{19} - 121 q^{20} - 69 q^{21} - 26 q^{22} - 79 q^{23} - 62 q^{24} + 123 q^{25} - 40 q^{26} - 70 q^{27} - 43 q^{28} - 109 q^{29} - 43 q^{30} - 21 q^{31} - 139 q^{32} - 83 q^{33} - 93 q^{35} + 75 q^{36} - 65 q^{37} - 122 q^{38} - 18 q^{39} - 43 q^{40} - 71 q^{41} - 88 q^{42} - 72 q^{43} - 79 q^{44} - 181 q^{45} - 11 q^{46} - 114 q^{47} - 118 q^{48} + 118 q^{49} - 77 q^{50} - 29 q^{51} - 169 q^{52} - 220 q^{53} - 80 q^{54} - 37 q^{55} - 72 q^{56} - 90 q^{57} - 8 q^{58} - 60 q^{59} - 42 q^{60} - 108 q^{61} - 152 q^{62} - 65 q^{63} + 114 q^{64} - 81 q^{65} - 40 q^{66} - 50 q^{67} - 319 q^{68} - 103 q^{69} + 4 q^{70} - 7 q^{71} - 129 q^{72} - 94 q^{73} - 79 q^{74} - 59 q^{75} - 46 q^{76} - 329 q^{77} + 8 q^{78} - 18 q^{79} - 190 q^{80} + 59 q^{81} - 56 q^{82} - 201 q^{83} - 71 q^{84} - 26 q^{85} - 52 q^{86} - 126 q^{87} - 66 q^{88} - 114 q^{89} - 33 q^{90} - 30 q^{91} - 204 q^{92} - 125 q^{93} + 9 q^{94} - 84 q^{95} - 88 q^{96} - 56 q^{97} - 110 q^{98} - 46 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46215 −1.74100 −0.870501 0.492167i \(-0.836205\pi\)
−0.870501 + 0.492167i \(0.836205\pi\)
\(3\) −2.74752 −1.58628 −0.793141 0.609038i \(-0.791556\pi\)
−0.793141 + 0.609038i \(0.791556\pi\)
\(4\) 4.06218 2.03109
\(5\) 4.08202 1.82553 0.912767 0.408480i \(-0.133941\pi\)
0.912767 + 0.408480i \(0.133941\pi\)
\(6\) 6.76481 2.76172
\(7\) −0.414263 −0.156577 −0.0782884 0.996931i \(-0.524946\pi\)
−0.0782884 + 0.996931i \(0.524946\pi\)
\(8\) −5.07738 −1.79513
\(9\) 4.54887 1.51629
\(10\) −10.0505 −3.17826
\(11\) −1.04639 −0.315500 −0.157750 0.987479i \(-0.550424\pi\)
−0.157750 + 0.987479i \(0.550424\pi\)
\(12\) −11.1609 −3.22188
\(13\) −3.10620 −0.861505 −0.430752 0.902470i \(-0.641752\pi\)
−0.430752 + 0.902470i \(0.641752\pi\)
\(14\) 1.01998 0.272601
\(15\) −11.2154 −2.89581
\(16\) 4.37692 1.09423
\(17\) −5.65244 −1.37092 −0.685459 0.728112i \(-0.740398\pi\)
−0.685459 + 0.728112i \(0.740398\pi\)
\(18\) −11.2000 −2.63987
\(19\) 7.50064 1.72076 0.860382 0.509649i \(-0.170225\pi\)
0.860382 + 0.509649i \(0.170225\pi\)
\(20\) 16.5819 3.70782
\(21\) 1.13820 0.248375
\(22\) 2.57638 0.549286
\(23\) −2.17262 −0.453023 −0.226512 0.974008i \(-0.572732\pi\)
−0.226512 + 0.974008i \(0.572732\pi\)
\(24\) 13.9502 2.84758
\(25\) 11.6629 2.33258
\(26\) 7.64792 1.49988
\(27\) −4.25556 −0.818984
\(28\) −1.68281 −0.318021
\(29\) −2.51610 −0.467229 −0.233614 0.972329i \(-0.575055\pi\)
−0.233614 + 0.972329i \(0.575055\pi\)
\(30\) 27.6141 5.04162
\(31\) 5.60122 1.00601 0.503004 0.864284i \(-0.332228\pi\)
0.503004 + 0.864284i \(0.332228\pi\)
\(32\) −0.621864 −0.109931
\(33\) 2.87499 0.500472
\(34\) 13.9171 2.38677
\(35\) −1.69103 −0.285836
\(36\) 18.4783 3.07972
\(37\) −1.62812 −0.267661 −0.133831 0.991004i \(-0.542728\pi\)
−0.133831 + 0.991004i \(0.542728\pi\)
\(38\) −18.4677 −2.99586
\(39\) 8.53435 1.36659
\(40\) −20.7260 −3.27706
\(41\) 3.34375 0.522206 0.261103 0.965311i \(-0.415914\pi\)
0.261103 + 0.965311i \(0.415914\pi\)
\(42\) −2.80241 −0.432422
\(43\) −7.04304 −1.07405 −0.537027 0.843565i \(-0.680453\pi\)
−0.537027 + 0.843565i \(0.680453\pi\)
\(44\) −4.25064 −0.640808
\(45\) 18.5686 2.76804
\(46\) 5.34932 0.788715
\(47\) 1.11167 0.162154 0.0810772 0.996708i \(-0.474164\pi\)
0.0810772 + 0.996708i \(0.474164\pi\)
\(48\) −12.0257 −1.73576
\(49\) −6.82839 −0.975484
\(50\) −28.7157 −4.06102
\(51\) 15.5302 2.17466
\(52\) −12.6179 −1.74979
\(53\) −4.59677 −0.631415 −0.315708 0.948857i \(-0.602242\pi\)
−0.315708 + 0.948857i \(0.602242\pi\)
\(54\) 10.4778 1.42585
\(55\) −4.27140 −0.575956
\(56\) 2.10337 0.281075
\(57\) −20.6082 −2.72962
\(58\) 6.19502 0.813446
\(59\) 0.852632 0.111003 0.0555016 0.998459i \(-0.482324\pi\)
0.0555016 + 0.998459i \(0.482324\pi\)
\(60\) −45.5591 −5.88165
\(61\) −10.6152 −1.35913 −0.679567 0.733613i \(-0.737833\pi\)
−0.679567 + 0.733613i \(0.737833\pi\)
\(62\) −13.7910 −1.75146
\(63\) −1.88443 −0.237416
\(64\) −7.22272 −0.902840
\(65\) −12.6796 −1.57271
\(66\) −7.07866 −0.871322
\(67\) 1.13238 0.138342 0.0691709 0.997605i \(-0.477965\pi\)
0.0691709 + 0.997605i \(0.477965\pi\)
\(68\) −22.9612 −2.78445
\(69\) 5.96933 0.718623
\(70\) 4.16357 0.497642
\(71\) 5.98152 0.709876 0.354938 0.934890i \(-0.384502\pi\)
0.354938 + 0.934890i \(0.384502\pi\)
\(72\) −23.0964 −2.72193
\(73\) 1.54575 0.180917 0.0904583 0.995900i \(-0.471167\pi\)
0.0904583 + 0.995900i \(0.471167\pi\)
\(74\) 4.00867 0.465999
\(75\) −32.0440 −3.70012
\(76\) 30.4689 3.49503
\(77\) 0.433483 0.0494000
\(78\) −21.0128 −2.37923
\(79\) 5.91311 0.665277 0.332639 0.943054i \(-0.392061\pi\)
0.332639 + 0.943054i \(0.392061\pi\)
\(80\) 17.8667 1.99756
\(81\) −1.95437 −0.217152
\(82\) −8.23282 −0.909162
\(83\) 6.56935 0.721079 0.360540 0.932744i \(-0.382593\pi\)
0.360540 + 0.932744i \(0.382593\pi\)
\(84\) 4.62356 0.504472
\(85\) −23.0734 −2.50266
\(86\) 17.3410 1.86993
\(87\) 6.91305 0.741157
\(88\) 5.31295 0.566362
\(89\) 3.12143 0.330871 0.165436 0.986221i \(-0.447097\pi\)
0.165436 + 0.986221i \(0.447097\pi\)
\(90\) −45.7186 −4.81917
\(91\) 1.28678 0.134892
\(92\) −8.82558 −0.920130
\(93\) −15.3895 −1.59581
\(94\) −2.73711 −0.282311
\(95\) 30.6178 3.14132
\(96\) 1.70859 0.174382
\(97\) −5.70638 −0.579395 −0.289697 0.957118i \(-0.593555\pi\)
−0.289697 + 0.957118i \(0.593555\pi\)
\(98\) 16.8125 1.69832
\(99\) −4.75992 −0.478390
\(100\) 47.3767 4.73767
\(101\) −10.2572 −1.02063 −0.510313 0.859989i \(-0.670470\pi\)
−0.510313 + 0.859989i \(0.670470\pi\)
\(102\) −38.2376 −3.78609
\(103\) 10.4726 1.03190 0.515950 0.856619i \(-0.327439\pi\)
0.515950 + 0.856619i \(0.327439\pi\)
\(104\) 15.7714 1.54651
\(105\) 4.64615 0.453417
\(106\) 11.3179 1.09930
\(107\) −12.8990 −1.24699 −0.623496 0.781827i \(-0.714288\pi\)
−0.623496 + 0.781827i \(0.714288\pi\)
\(108\) −17.2869 −1.66343
\(109\) −3.53272 −0.338373 −0.169187 0.985584i \(-0.554114\pi\)
−0.169187 + 0.985584i \(0.554114\pi\)
\(110\) 10.5168 1.00274
\(111\) 4.47329 0.424586
\(112\) −1.81320 −0.171331
\(113\) −4.41603 −0.415426 −0.207713 0.978190i \(-0.566602\pi\)
−0.207713 + 0.978190i \(0.566602\pi\)
\(114\) 50.7404 4.75227
\(115\) −8.86869 −0.827010
\(116\) −10.2209 −0.948983
\(117\) −14.1297 −1.30629
\(118\) −2.09931 −0.193257
\(119\) 2.34160 0.214654
\(120\) 56.9451 5.19835
\(121\) −9.90506 −0.900460
\(122\) 26.1362 2.36626
\(123\) −9.18703 −0.828367
\(124\) 22.7531 2.04329
\(125\) 27.1980 2.43266
\(126\) 4.63975 0.413342
\(127\) 10.7995 0.958301 0.479151 0.877733i \(-0.340945\pi\)
0.479151 + 0.877733i \(0.340945\pi\)
\(128\) 19.0271 1.68178
\(129\) 19.3509 1.70375
\(130\) 31.2190 2.73808
\(131\) −16.9102 −1.47745 −0.738725 0.674007i \(-0.764572\pi\)
−0.738725 + 0.674007i \(0.764572\pi\)
\(132\) 11.6787 1.01650
\(133\) −3.10724 −0.269432
\(134\) −2.78808 −0.240853
\(135\) −17.3713 −1.49508
\(136\) 28.6996 2.46097
\(137\) 16.4916 1.40897 0.704486 0.709718i \(-0.251177\pi\)
0.704486 + 0.709718i \(0.251177\pi\)
\(138\) −14.6974 −1.25112
\(139\) −5.95907 −0.505442 −0.252721 0.967539i \(-0.581325\pi\)
−0.252721 + 0.967539i \(0.581325\pi\)
\(140\) −6.86927 −0.580559
\(141\) −3.05435 −0.257223
\(142\) −14.7274 −1.23589
\(143\) 3.25031 0.271805
\(144\) 19.9101 1.65917
\(145\) −10.2708 −0.852942
\(146\) −3.80587 −0.314976
\(147\) 18.7611 1.54739
\(148\) −6.61371 −0.543644
\(149\) −19.1429 −1.56825 −0.784123 0.620605i \(-0.786887\pi\)
−0.784123 + 0.620605i \(0.786887\pi\)
\(150\) 78.8971 6.44192
\(151\) −0.170292 −0.0138582 −0.00692910 0.999976i \(-0.502206\pi\)
−0.00692910 + 0.999976i \(0.502206\pi\)
\(152\) −38.0836 −3.08899
\(153\) −25.7122 −2.07871
\(154\) −1.06730 −0.0860055
\(155\) 22.8643 1.83650
\(156\) 34.6680 2.77566
\(157\) 19.3005 1.54035 0.770175 0.637833i \(-0.220169\pi\)
0.770175 + 0.637833i \(0.220169\pi\)
\(158\) −14.5590 −1.15825
\(159\) 12.6297 1.00160
\(160\) −2.53846 −0.200683
\(161\) 0.900039 0.0709330
\(162\) 4.81194 0.378062
\(163\) −4.25484 −0.333265 −0.166632 0.986019i \(-0.553289\pi\)
−0.166632 + 0.986019i \(0.553289\pi\)
\(164\) 13.5829 1.06065
\(165\) 11.7358 0.913629
\(166\) −16.1747 −1.25540
\(167\) −3.70448 −0.286661 −0.143330 0.989675i \(-0.545781\pi\)
−0.143330 + 0.989675i \(0.545781\pi\)
\(168\) −5.77907 −0.445865
\(169\) −3.35153 −0.257810
\(170\) 56.8100 4.35713
\(171\) 34.1195 2.60918
\(172\) −28.6101 −2.18150
\(173\) −12.8959 −0.980460 −0.490230 0.871593i \(-0.663087\pi\)
−0.490230 + 0.871593i \(0.663087\pi\)
\(174\) −17.0210 −1.29036
\(175\) −4.83151 −0.365227
\(176\) −4.57999 −0.345230
\(177\) −2.34262 −0.176082
\(178\) −7.68543 −0.576047
\(179\) −1.03104 −0.0770638 −0.0385319 0.999257i \(-0.512268\pi\)
−0.0385319 + 0.999257i \(0.512268\pi\)
\(180\) 75.4289 5.62214
\(181\) 8.70696 0.647183 0.323591 0.946197i \(-0.395110\pi\)
0.323591 + 0.946197i \(0.395110\pi\)
\(182\) −3.16826 −0.234847
\(183\) 29.1654 2.15597
\(184\) 11.0312 0.813234
\(185\) −6.64602 −0.488625
\(186\) 37.8912 2.77832
\(187\) 5.91468 0.432524
\(188\) 4.51582 0.329350
\(189\) 1.76292 0.128234
\(190\) −75.3855 −5.46904
\(191\) 3.88309 0.280971 0.140485 0.990083i \(-0.455134\pi\)
0.140485 + 0.990083i \(0.455134\pi\)
\(192\) 19.8446 1.43216
\(193\) −19.4858 −1.40262 −0.701311 0.712855i \(-0.747402\pi\)
−0.701311 + 0.712855i \(0.747402\pi\)
\(194\) 14.0499 1.00873
\(195\) 34.8374 2.49476
\(196\) −27.7381 −1.98129
\(197\) 0.0769289 0.00548096 0.00274048 0.999996i \(-0.499128\pi\)
0.00274048 + 0.999996i \(0.499128\pi\)
\(198\) 11.7196 0.832877
\(199\) 19.3072 1.36865 0.684326 0.729176i \(-0.260096\pi\)
0.684326 + 0.729176i \(0.260096\pi\)
\(200\) −59.2169 −4.18727
\(201\) −3.11123 −0.219449
\(202\) 25.2546 1.77691
\(203\) 1.04233 0.0731572
\(204\) 63.0864 4.41693
\(205\) 13.6493 0.953306
\(206\) −25.7852 −1.79654
\(207\) −9.88299 −0.686915
\(208\) −13.5956 −0.942685
\(209\) −7.84863 −0.542901
\(210\) −11.4395 −0.789400
\(211\) 22.1983 1.52819 0.764095 0.645103i \(-0.223186\pi\)
0.764095 + 0.645103i \(0.223186\pi\)
\(212\) −18.6729 −1.28246
\(213\) −16.4344 −1.12606
\(214\) 31.7592 2.17101
\(215\) −28.7498 −1.96072
\(216\) 21.6071 1.47018
\(217\) −2.32038 −0.157518
\(218\) 8.69808 0.589108
\(219\) −4.24699 −0.286985
\(220\) −17.3512 −1.16982
\(221\) 17.5576 1.18105
\(222\) −11.0139 −0.739206
\(223\) −5.30991 −0.355578 −0.177789 0.984069i \(-0.556894\pi\)
−0.177789 + 0.984069i \(0.556894\pi\)
\(224\) 0.257616 0.0172127
\(225\) 53.0530 3.53686
\(226\) 10.8729 0.723257
\(227\) −9.16017 −0.607982 −0.303991 0.952675i \(-0.598319\pi\)
−0.303991 + 0.952675i \(0.598319\pi\)
\(228\) −83.7140 −5.54410
\(229\) −19.3584 −1.27924 −0.639619 0.768692i \(-0.720908\pi\)
−0.639619 + 0.768692i \(0.720908\pi\)
\(230\) 21.8360 1.43983
\(231\) −1.19100 −0.0783623
\(232\) 12.7752 0.838735
\(233\) −11.5662 −0.757727 −0.378863 0.925453i \(-0.623685\pi\)
−0.378863 + 0.925453i \(0.623685\pi\)
\(234\) 34.7894 2.27426
\(235\) 4.53788 0.296019
\(236\) 3.46354 0.225457
\(237\) −16.2464 −1.05532
\(238\) −5.76536 −0.373713
\(239\) −14.6432 −0.947193 −0.473596 0.880742i \(-0.657044\pi\)
−0.473596 + 0.880742i \(0.657044\pi\)
\(240\) −49.0891 −3.16869
\(241\) −9.75696 −0.628501 −0.314251 0.949340i \(-0.601753\pi\)
−0.314251 + 0.949340i \(0.601753\pi\)
\(242\) 24.3877 1.56770
\(243\) 18.1364 1.16345
\(244\) −43.1207 −2.76052
\(245\) −27.8736 −1.78078
\(246\) 22.6198 1.44219
\(247\) −23.2985 −1.48245
\(248\) −28.4395 −1.80591
\(249\) −18.0494 −1.14384
\(250\) −66.9655 −4.23527
\(251\) 2.86719 0.180975 0.0904876 0.995898i \(-0.471157\pi\)
0.0904876 + 0.995898i \(0.471157\pi\)
\(252\) −7.65490 −0.482213
\(253\) 2.27342 0.142929
\(254\) −26.5900 −1.66840
\(255\) 63.3945 3.96992
\(256\) −32.4022 −2.02514
\(257\) −19.6600 −1.22636 −0.613180 0.789943i \(-0.710110\pi\)
−0.613180 + 0.789943i \(0.710110\pi\)
\(258\) −47.6448 −2.96624
\(259\) 0.674471 0.0419096
\(260\) −51.5066 −3.19430
\(261\) −11.4454 −0.708455
\(262\) 41.6354 2.57224
\(263\) −7.74810 −0.477768 −0.238884 0.971048i \(-0.576782\pi\)
−0.238884 + 0.971048i \(0.576782\pi\)
\(264\) −14.5974 −0.898410
\(265\) −18.7641 −1.15267
\(266\) 7.65049 0.469082
\(267\) −8.57620 −0.524855
\(268\) 4.59991 0.280984
\(269\) 18.9295 1.15415 0.577076 0.816690i \(-0.304194\pi\)
0.577076 + 0.816690i \(0.304194\pi\)
\(270\) 42.7707 2.60294
\(271\) 25.2172 1.53184 0.765918 0.642938i \(-0.222285\pi\)
0.765918 + 0.642938i \(0.222285\pi\)
\(272\) −24.7403 −1.50010
\(273\) −3.53547 −0.213976
\(274\) −40.6048 −2.45302
\(275\) −12.2040 −0.735927
\(276\) 24.2485 1.45959
\(277\) 13.3008 0.799168 0.399584 0.916697i \(-0.369155\pi\)
0.399584 + 0.916697i \(0.369155\pi\)
\(278\) 14.6721 0.879975
\(279\) 25.4792 1.52540
\(280\) 8.58602 0.513113
\(281\) −17.5257 −1.04550 −0.522748 0.852487i \(-0.675093\pi\)
−0.522748 + 0.852487i \(0.675093\pi\)
\(282\) 7.52027 0.447825
\(283\) 10.5670 0.628142 0.314071 0.949400i \(-0.398307\pi\)
0.314071 + 0.949400i \(0.398307\pi\)
\(284\) 24.2980 1.44182
\(285\) −84.1229 −4.98301
\(286\) −8.00275 −0.473212
\(287\) −1.38519 −0.0817654
\(288\) −2.82878 −0.166688
\(289\) 14.9500 0.879414
\(290\) 25.2882 1.48497
\(291\) 15.6784 0.919083
\(292\) 6.27912 0.367457
\(293\) 32.6743 1.90885 0.954425 0.298451i \(-0.0964699\pi\)
0.954425 + 0.298451i \(0.0964699\pi\)
\(294\) −46.1927 −2.69401
\(295\) 3.48046 0.202640
\(296\) 8.26659 0.480486
\(297\) 4.45300 0.258389
\(298\) 47.1326 2.73032
\(299\) 6.74860 0.390282
\(300\) −130.168 −7.51528
\(301\) 2.91768 0.168172
\(302\) 0.419285 0.0241271
\(303\) 28.1818 1.61900
\(304\) 32.8297 1.88291
\(305\) −43.3314 −2.48115
\(306\) 63.3073 3.61904
\(307\) 16.8437 0.961322 0.480661 0.876907i \(-0.340397\pi\)
0.480661 + 0.876907i \(0.340397\pi\)
\(308\) 1.76088 0.100336
\(309\) −28.7738 −1.63689
\(310\) −56.2953 −3.19736
\(311\) 0.679529 0.0385326 0.0192663 0.999814i \(-0.493867\pi\)
0.0192663 + 0.999814i \(0.493867\pi\)
\(312\) −43.3322 −2.45320
\(313\) −17.5163 −0.990082 −0.495041 0.868870i \(-0.664847\pi\)
−0.495041 + 0.868870i \(0.664847\pi\)
\(314\) −47.5208 −2.68175
\(315\) −7.69229 −0.433411
\(316\) 24.0201 1.35124
\(317\) 32.4145 1.82058 0.910290 0.413971i \(-0.135858\pi\)
0.910290 + 0.413971i \(0.135858\pi\)
\(318\) −31.0963 −1.74379
\(319\) 2.63284 0.147411
\(320\) −29.4833 −1.64817
\(321\) 35.4402 1.97808
\(322\) −2.21603 −0.123494
\(323\) −42.3969 −2.35903
\(324\) −7.93899 −0.441055
\(325\) −36.2272 −2.00953
\(326\) 10.4761 0.580215
\(327\) 9.70622 0.536755
\(328\) −16.9775 −0.937426
\(329\) −0.460526 −0.0253896
\(330\) −28.8952 −1.59063
\(331\) −16.4167 −0.902345 −0.451173 0.892437i \(-0.648994\pi\)
−0.451173 + 0.892437i \(0.648994\pi\)
\(332\) 26.6858 1.46458
\(333\) −7.40611 −0.405852
\(334\) 9.12097 0.499077
\(335\) 4.62238 0.252548
\(336\) 4.98180 0.271780
\(337\) 6.69723 0.364821 0.182411 0.983222i \(-0.441610\pi\)
0.182411 + 0.983222i \(0.441610\pi\)
\(338\) 8.25196 0.448847
\(339\) 12.1331 0.658982
\(340\) −93.7280 −5.08312
\(341\) −5.86109 −0.317396
\(342\) −84.0072 −4.54259
\(343\) 5.72860 0.309315
\(344\) 35.7602 1.92806
\(345\) 24.3669 1.31187
\(346\) 31.7517 1.70698
\(347\) −23.6723 −1.27080 −0.635398 0.772185i \(-0.719164\pi\)
−0.635398 + 0.772185i \(0.719164\pi\)
\(348\) 28.0820 1.50535
\(349\) 25.2186 1.34992 0.674961 0.737853i \(-0.264160\pi\)
0.674961 + 0.737853i \(0.264160\pi\)
\(350\) 11.8959 0.635862
\(351\) 13.2186 0.705558
\(352\) 0.650715 0.0346833
\(353\) −32.4088 −1.72495 −0.862473 0.506102i \(-0.831086\pi\)
−0.862473 + 0.506102i \(0.831086\pi\)
\(354\) 5.76789 0.306560
\(355\) 24.4167 1.29590
\(356\) 12.6798 0.672029
\(357\) −6.43359 −0.340502
\(358\) 2.53858 0.134168
\(359\) −11.2918 −0.595960 −0.297980 0.954572i \(-0.596313\pi\)
−0.297980 + 0.954572i \(0.596313\pi\)
\(360\) −94.2799 −4.96898
\(361\) 37.2596 1.96103
\(362\) −21.4378 −1.12675
\(363\) 27.2144 1.42838
\(364\) 5.22715 0.273977
\(365\) 6.30979 0.330269
\(366\) −71.8097 −3.75355
\(367\) −26.8877 −1.40353 −0.701763 0.712410i \(-0.747604\pi\)
−0.701763 + 0.712410i \(0.747604\pi\)
\(368\) −9.50940 −0.495712
\(369\) 15.2103 0.791817
\(370\) 16.3635 0.850697
\(371\) 1.90427 0.0988650
\(372\) −62.5148 −3.24124
\(373\) 32.3716 1.67614 0.838069 0.545565i \(-0.183685\pi\)
0.838069 + 0.545565i \(0.183685\pi\)
\(374\) −14.5628 −0.753025
\(375\) −74.7271 −3.85889
\(376\) −5.64440 −0.291088
\(377\) 7.81552 0.402520
\(378\) −4.34058 −0.223255
\(379\) −11.6248 −0.597127 −0.298563 0.954390i \(-0.596507\pi\)
−0.298563 + 0.954390i \(0.596507\pi\)
\(380\) 124.375 6.38029
\(381\) −29.6719 −1.52014
\(382\) −9.56075 −0.489170
\(383\) −38.4740 −1.96593 −0.982965 0.183792i \(-0.941163\pi\)
−0.982965 + 0.183792i \(0.941163\pi\)
\(384\) −52.2775 −2.66777
\(385\) 1.76949 0.0901814
\(386\) 47.9771 2.44197
\(387\) −32.0379 −1.62858
\(388\) −23.1803 −1.17680
\(389\) −16.2556 −0.824192 −0.412096 0.911140i \(-0.635203\pi\)
−0.412096 + 0.911140i \(0.635203\pi\)
\(390\) −85.7748 −4.34338
\(391\) 12.2806 0.621057
\(392\) 34.6703 1.75112
\(393\) 46.4611 2.34365
\(394\) −0.189410 −0.00954235
\(395\) 24.1374 1.21449
\(396\) −19.3356 −0.971652
\(397\) 13.3222 0.668623 0.334312 0.942463i \(-0.391496\pi\)
0.334312 + 0.942463i \(0.391496\pi\)
\(398\) −47.5372 −2.38283
\(399\) 8.53721 0.427395
\(400\) 51.0475 2.55238
\(401\) 6.37051 0.318128 0.159064 0.987268i \(-0.449152\pi\)
0.159064 + 0.987268i \(0.449152\pi\)
\(402\) 7.66031 0.382061
\(403\) −17.3985 −0.866681
\(404\) −41.6664 −2.07298
\(405\) −7.97777 −0.396418
\(406\) −2.56637 −0.127367
\(407\) 1.70366 0.0844471
\(408\) −78.8527 −3.90379
\(409\) −16.4826 −0.815012 −0.407506 0.913203i \(-0.633601\pi\)
−0.407506 + 0.913203i \(0.633601\pi\)
\(410\) −33.6065 −1.65971
\(411\) −45.3110 −2.23503
\(412\) 42.5417 2.09588
\(413\) −0.353214 −0.0173805
\(414\) 24.3334 1.19592
\(415\) 26.8162 1.31636
\(416\) 1.93163 0.0947062
\(417\) 16.3727 0.801773
\(418\) 19.3245 0.945192
\(419\) −30.1997 −1.47535 −0.737676 0.675155i \(-0.764077\pi\)
−0.737676 + 0.675155i \(0.764077\pi\)
\(420\) 18.8735 0.920930
\(421\) −23.4162 −1.14124 −0.570619 0.821215i \(-0.693297\pi\)
−0.570619 + 0.821215i \(0.693297\pi\)
\(422\) −54.6554 −2.66058
\(423\) 5.05687 0.245873
\(424\) 23.3396 1.13347
\(425\) −65.9237 −3.19777
\(426\) 40.4638 1.96048
\(427\) 4.39748 0.212809
\(428\) −52.3979 −2.53275
\(429\) −8.93030 −0.431159
\(430\) 70.7864 3.41362
\(431\) −18.2209 −0.877671 −0.438836 0.898567i \(-0.644609\pi\)
−0.438836 + 0.898567i \(0.644609\pi\)
\(432\) −18.6263 −0.896157
\(433\) 38.5721 1.85366 0.926829 0.375483i \(-0.122523\pi\)
0.926829 + 0.375483i \(0.122523\pi\)
\(434\) 5.71312 0.274239
\(435\) 28.2192 1.35301
\(436\) −14.3505 −0.687265
\(437\) −16.2961 −0.779547
\(438\) 10.4567 0.499641
\(439\) 25.5223 1.21811 0.609057 0.793126i \(-0.291548\pi\)
0.609057 + 0.793126i \(0.291548\pi\)
\(440\) 21.6876 1.03391
\(441\) −31.0615 −1.47912
\(442\) −43.2294 −2.05621
\(443\) 22.2503 1.05715 0.528573 0.848888i \(-0.322727\pi\)
0.528573 + 0.848888i \(0.322727\pi\)
\(444\) 18.1713 0.862372
\(445\) 12.7417 0.604017
\(446\) 13.0738 0.619061
\(447\) 52.5955 2.48768
\(448\) 2.99211 0.141364
\(449\) 4.93577 0.232933 0.116467 0.993195i \(-0.462843\pi\)
0.116467 + 0.993195i \(0.462843\pi\)
\(450\) −130.624 −6.15769
\(451\) −3.49888 −0.164756
\(452\) −17.9387 −0.843766
\(453\) 0.467882 0.0219830
\(454\) 22.5537 1.05850
\(455\) 5.25268 0.246249
\(456\) 104.636 4.90001
\(457\) −21.9920 −1.02874 −0.514371 0.857568i \(-0.671975\pi\)
−0.514371 + 0.857568i \(0.671975\pi\)
\(458\) 47.6632 2.22716
\(459\) 24.0543 1.12276
\(460\) −36.0262 −1.67973
\(461\) −9.56974 −0.445707 −0.222854 0.974852i \(-0.571537\pi\)
−0.222854 + 0.974852i \(0.571537\pi\)
\(462\) 2.93243 0.136429
\(463\) −30.3970 −1.41267 −0.706334 0.707879i \(-0.749652\pi\)
−0.706334 + 0.707879i \(0.749652\pi\)
\(464\) −11.0128 −0.511256
\(465\) −62.8201 −2.91321
\(466\) 28.4777 1.31920
\(467\) −17.8963 −0.828143 −0.414072 0.910244i \(-0.635894\pi\)
−0.414072 + 0.910244i \(0.635894\pi\)
\(468\) −57.3974 −2.65319
\(469\) −0.469102 −0.0216611
\(470\) −11.1729 −0.515369
\(471\) −53.0286 −2.44343
\(472\) −4.32914 −0.199265
\(473\) 7.36980 0.338864
\(474\) 40.0011 1.83731
\(475\) 87.4791 4.01382
\(476\) 9.51198 0.435981
\(477\) −20.9101 −0.957409
\(478\) 36.0538 1.64906
\(479\) 3.77902 0.172668 0.0863338 0.996266i \(-0.472485\pi\)
0.0863338 + 0.996266i \(0.472485\pi\)
\(480\) 6.97448 0.318340
\(481\) 5.05726 0.230591
\(482\) 24.0231 1.09422
\(483\) −2.47288 −0.112520
\(484\) −40.2361 −1.82891
\(485\) −23.2935 −1.05770
\(486\) −44.6544 −2.02557
\(487\) −31.9090 −1.44594 −0.722969 0.690881i \(-0.757223\pi\)
−0.722969 + 0.690881i \(0.757223\pi\)
\(488\) 53.8974 2.43982
\(489\) 11.6903 0.528652
\(490\) 68.6290 3.10034
\(491\) −29.7666 −1.34335 −0.671673 0.740848i \(-0.734424\pi\)
−0.671673 + 0.740848i \(0.734424\pi\)
\(492\) −37.3193 −1.68249
\(493\) 14.2221 0.640532
\(494\) 57.3643 2.58094
\(495\) −19.4301 −0.873317
\(496\) 24.5161 1.10081
\(497\) −2.47792 −0.111150
\(498\) 44.4404 1.99142
\(499\) −30.5295 −1.36669 −0.683344 0.730097i \(-0.739475\pi\)
−0.683344 + 0.730097i \(0.739475\pi\)
\(500\) 110.483 4.94095
\(501\) 10.1781 0.454725
\(502\) −7.05944 −0.315078
\(503\) −0.566391 −0.0252541 −0.0126271 0.999920i \(-0.504019\pi\)
−0.0126271 + 0.999920i \(0.504019\pi\)
\(504\) 9.56799 0.426192
\(505\) −41.8699 −1.86319
\(506\) −5.59750 −0.248839
\(507\) 9.20839 0.408959
\(508\) 43.8695 1.94639
\(509\) −39.8513 −1.76638 −0.883188 0.469019i \(-0.844608\pi\)
−0.883188 + 0.469019i \(0.844608\pi\)
\(510\) −156.087 −6.91164
\(511\) −0.640348 −0.0283273
\(512\) 41.7248 1.84399
\(513\) −31.9195 −1.40928
\(514\) 48.4059 2.13509
\(515\) 42.7495 1.88377
\(516\) 78.6068 3.46047
\(517\) −1.16325 −0.0511597
\(518\) −1.66065 −0.0729646
\(519\) 35.4319 1.55529
\(520\) 64.3790 2.82321
\(521\) 44.0163 1.92839 0.964194 0.265197i \(-0.0854370\pi\)
0.964194 + 0.265197i \(0.0854370\pi\)
\(522\) 28.1804 1.23342
\(523\) −44.3577 −1.93963 −0.969813 0.243848i \(-0.921590\pi\)
−0.969813 + 0.243848i \(0.921590\pi\)
\(524\) −68.6922 −3.00083
\(525\) 13.2747 0.579354
\(526\) 19.0770 0.831796
\(527\) −31.6605 −1.37915
\(528\) 12.5836 0.547631
\(529\) −18.2797 −0.794770
\(530\) 46.2000 2.00680
\(531\) 3.87851 0.168313
\(532\) −12.6222 −0.547240
\(533\) −10.3864 −0.449883
\(534\) 21.1159 0.913774
\(535\) −52.6539 −2.27643
\(536\) −5.74951 −0.248341
\(537\) 2.83282 0.122245
\(538\) −46.6073 −2.00938
\(539\) 7.14519 0.307765
\(540\) −70.5653 −3.03665
\(541\) 34.2022 1.47047 0.735234 0.677813i \(-0.237072\pi\)
0.735234 + 0.677813i \(0.237072\pi\)
\(542\) −62.0885 −2.66693
\(543\) −23.9225 −1.02661
\(544\) 3.51505 0.150706
\(545\) −14.4206 −0.617712
\(546\) 8.70485 0.372533
\(547\) 27.6289 1.18133 0.590663 0.806919i \(-0.298866\pi\)
0.590663 + 0.806919i \(0.298866\pi\)
\(548\) 66.9918 2.86175
\(549\) −48.2871 −2.06084
\(550\) 30.0480 1.28125
\(551\) −18.8724 −0.803991
\(552\) −30.3086 −1.29002
\(553\) −2.44959 −0.104167
\(554\) −32.7486 −1.39135
\(555\) 18.2601 0.775097
\(556\) −24.2068 −1.02660
\(557\) −2.24768 −0.0952371 −0.0476185 0.998866i \(-0.515163\pi\)
−0.0476185 + 0.998866i \(0.515163\pi\)
\(558\) −62.7337 −2.65573
\(559\) 21.8771 0.925303
\(560\) −7.40151 −0.312771
\(561\) −16.2507 −0.686105
\(562\) 43.1509 1.82021
\(563\) 0.661773 0.0278904 0.0139452 0.999903i \(-0.495561\pi\)
0.0139452 + 0.999903i \(0.495561\pi\)
\(564\) −12.4073 −0.522442
\(565\) −18.0263 −0.758374
\(566\) −26.0175 −1.09360
\(567\) 0.809623 0.0340010
\(568\) −30.3705 −1.27432
\(569\) −21.0741 −0.883473 −0.441736 0.897145i \(-0.645637\pi\)
−0.441736 + 0.897145i \(0.645637\pi\)
\(570\) 207.123 8.67544
\(571\) −36.2154 −1.51557 −0.757784 0.652505i \(-0.773718\pi\)
−0.757784 + 0.652505i \(0.773718\pi\)
\(572\) 13.2033 0.552059
\(573\) −10.6689 −0.445699
\(574\) 3.41055 0.142354
\(575\) −25.3391 −1.05671
\(576\) −32.8552 −1.36897
\(577\) 42.0271 1.74961 0.874805 0.484476i \(-0.160990\pi\)
0.874805 + 0.484476i \(0.160990\pi\)
\(578\) −36.8092 −1.53106
\(579\) 53.5378 2.22495
\(580\) −41.7217 −1.73240
\(581\) −2.72144 −0.112904
\(582\) −38.6025 −1.60013
\(583\) 4.81004 0.199211
\(584\) −7.84837 −0.324768
\(585\) −57.6777 −2.38468
\(586\) −80.4489 −3.32331
\(587\) 43.0236 1.77578 0.887888 0.460060i \(-0.152172\pi\)
0.887888 + 0.460060i \(0.152172\pi\)
\(588\) 76.2110 3.14289
\(589\) 42.0127 1.73111
\(590\) −8.56941 −0.352797
\(591\) −0.211364 −0.00869434
\(592\) −7.12615 −0.292883
\(593\) −3.73015 −0.153179 −0.0765894 0.997063i \(-0.524403\pi\)
−0.0765894 + 0.997063i \(0.524403\pi\)
\(594\) −10.9639 −0.449856
\(595\) 9.55845 0.391858
\(596\) −77.7618 −3.18525
\(597\) −53.0470 −2.17107
\(598\) −16.6161 −0.679481
\(599\) −17.4284 −0.712107 −0.356053 0.934466i \(-0.615878\pi\)
−0.356053 + 0.934466i \(0.615878\pi\)
\(600\) 162.700 6.64219
\(601\) −38.1729 −1.55711 −0.778553 0.627579i \(-0.784046\pi\)
−0.778553 + 0.627579i \(0.784046\pi\)
\(602\) −7.18375 −0.292788
\(603\) 5.15104 0.209767
\(604\) −0.691757 −0.0281472
\(605\) −40.4326 −1.64382
\(606\) −69.3877 −2.81868
\(607\) −12.3748 −0.502279 −0.251139 0.967951i \(-0.580805\pi\)
−0.251139 + 0.967951i \(0.580805\pi\)
\(608\) −4.66438 −0.189166
\(609\) −2.86382 −0.116048
\(610\) 106.688 4.31968
\(611\) −3.45308 −0.139697
\(612\) −104.448 −4.22204
\(613\) 7.24873 0.292773 0.146387 0.989227i \(-0.453236\pi\)
0.146387 + 0.989227i \(0.453236\pi\)
\(614\) −41.4717 −1.67366
\(615\) −37.5016 −1.51221
\(616\) −2.20096 −0.0886792
\(617\) 11.1223 0.447766 0.223883 0.974616i \(-0.428127\pi\)
0.223883 + 0.974616i \(0.428127\pi\)
\(618\) 70.8454 2.84982
\(619\) −2.22920 −0.0895991 −0.0447996 0.998996i \(-0.514265\pi\)
−0.0447996 + 0.998996i \(0.514265\pi\)
\(620\) 92.8788 3.73010
\(621\) 9.24574 0.371019
\(622\) −1.67310 −0.0670853
\(623\) −1.29310 −0.0518068
\(624\) 37.3542 1.49536
\(625\) 52.7084 2.10834
\(626\) 43.1278 1.72373
\(627\) 21.5643 0.861194
\(628\) 78.4021 3.12859
\(629\) 9.20284 0.366941
\(630\) 18.9396 0.754570
\(631\) −3.10565 −0.123634 −0.0618171 0.998087i \(-0.519690\pi\)
−0.0618171 + 0.998087i \(0.519690\pi\)
\(632\) −30.0231 −1.19426
\(633\) −60.9902 −2.42414
\(634\) −79.8094 −3.16963
\(635\) 44.0838 1.74941
\(636\) 51.3042 2.03434
\(637\) 21.2103 0.840384
\(638\) −6.48244 −0.256642
\(639\) 27.2092 1.07638
\(640\) 77.6692 3.07014
\(641\) 43.7340 1.72739 0.863694 0.504017i \(-0.168145\pi\)
0.863694 + 0.504017i \(0.168145\pi\)
\(642\) −87.2591 −3.44384
\(643\) −3.45930 −0.136421 −0.0682107 0.997671i \(-0.521729\pi\)
−0.0682107 + 0.997671i \(0.521729\pi\)
\(644\) 3.65612 0.144071
\(645\) 78.9908 3.11026
\(646\) 104.387 4.10707
\(647\) 14.7310 0.579137 0.289568 0.957157i \(-0.406488\pi\)
0.289568 + 0.957157i \(0.406488\pi\)
\(648\) 9.92308 0.389815
\(649\) −0.892189 −0.0350215
\(650\) 89.1968 3.49859
\(651\) 6.37530 0.249868
\(652\) −17.2839 −0.676890
\(653\) −41.7818 −1.63505 −0.817524 0.575894i \(-0.804654\pi\)
−0.817524 + 0.575894i \(0.804654\pi\)
\(654\) −23.8982 −0.934492
\(655\) −69.0277 −2.69714
\(656\) 14.6353 0.571414
\(657\) 7.03143 0.274322
\(658\) 1.13388 0.0442034
\(659\) 0.714733 0.0278420 0.0139210 0.999903i \(-0.495569\pi\)
0.0139210 + 0.999903i \(0.495569\pi\)
\(660\) 47.6728 1.85566
\(661\) 5.10562 0.198586 0.0992928 0.995058i \(-0.468342\pi\)
0.0992928 + 0.995058i \(0.468342\pi\)
\(662\) 40.4204 1.57098
\(663\) −48.2399 −1.87348
\(664\) −33.3551 −1.29443
\(665\) −12.6838 −0.491857
\(666\) 18.2350 0.706590
\(667\) 5.46655 0.211666
\(668\) −15.0482 −0.582234
\(669\) 14.5891 0.564046
\(670\) −11.3810 −0.439686
\(671\) 11.1077 0.428807
\(672\) −0.707805 −0.0273042
\(673\) 46.4770 1.79156 0.895778 0.444502i \(-0.146619\pi\)
0.895778 + 0.444502i \(0.146619\pi\)
\(674\) −16.4896 −0.635155
\(675\) −49.6321 −1.91034
\(676\) −13.6145 −0.523634
\(677\) −35.0344 −1.34648 −0.673240 0.739424i \(-0.735098\pi\)
−0.673240 + 0.739424i \(0.735098\pi\)
\(678\) −29.8736 −1.14729
\(679\) 2.36394 0.0907198
\(680\) 117.152 4.49258
\(681\) 25.1678 0.964431
\(682\) 14.4309 0.552587
\(683\) −18.3464 −0.702007 −0.351004 0.936374i \(-0.614160\pi\)
−0.351004 + 0.936374i \(0.614160\pi\)
\(684\) 138.599 5.29948
\(685\) 67.3190 2.57213
\(686\) −14.1047 −0.538518
\(687\) 53.1876 2.02923
\(688\) −30.8268 −1.17526
\(689\) 14.2785 0.543967
\(690\) −59.9950 −2.28397
\(691\) 0.690266 0.0262590 0.0131295 0.999914i \(-0.495821\pi\)
0.0131295 + 0.999914i \(0.495821\pi\)
\(692\) −52.3856 −1.99140
\(693\) 1.97186 0.0749048
\(694\) 58.2848 2.21246
\(695\) −24.3250 −0.922701
\(696\) −35.1002 −1.33047
\(697\) −18.9003 −0.715902
\(698\) −62.0920 −2.35022
\(699\) 31.7784 1.20197
\(700\) −19.6264 −0.741809
\(701\) −1.31304 −0.0495927 −0.0247964 0.999693i \(-0.507894\pi\)
−0.0247964 + 0.999693i \(0.507894\pi\)
\(702\) −32.5462 −1.22838
\(703\) −12.2119 −0.460582
\(704\) 7.55782 0.284846
\(705\) −12.4679 −0.469569
\(706\) 79.7953 3.00314
\(707\) 4.24917 0.159806
\(708\) −9.51615 −0.357639
\(709\) 31.1210 1.16877 0.584386 0.811476i \(-0.301335\pi\)
0.584386 + 0.811476i \(0.301335\pi\)
\(710\) −60.1175 −2.25617
\(711\) 26.8980 1.00875
\(712\) −15.8487 −0.593956
\(713\) −12.1693 −0.455746
\(714\) 15.8405 0.592814
\(715\) 13.2678 0.496189
\(716\) −4.18828 −0.156523
\(717\) 40.2326 1.50251
\(718\) 27.8022 1.03757
\(719\) 3.41929 0.127518 0.0637590 0.997965i \(-0.479691\pi\)
0.0637590 + 0.997965i \(0.479691\pi\)
\(720\) 81.2733 3.02888
\(721\) −4.33843 −0.161572
\(722\) −91.7387 −3.41416
\(723\) 26.8075 0.996980
\(724\) 35.3692 1.31449
\(725\) −29.3450 −1.08985
\(726\) −67.0058 −2.48682
\(727\) −0.759734 −0.0281770 −0.0140885 0.999901i \(-0.504485\pi\)
−0.0140885 + 0.999901i \(0.504485\pi\)
\(728\) −6.53350 −0.242148
\(729\) −43.9669 −1.62840
\(730\) −15.5356 −0.575000
\(731\) 39.8104 1.47244
\(732\) 118.475 4.37897
\(733\) −16.9363 −0.625556 −0.312778 0.949826i \(-0.601260\pi\)
−0.312778 + 0.949826i \(0.601260\pi\)
\(734\) 66.2015 2.44354
\(735\) 76.5833 2.82482
\(736\) 1.35108 0.0498014
\(737\) −1.18491 −0.0436468
\(738\) −37.4500 −1.37856
\(739\) 23.8625 0.877797 0.438898 0.898537i \(-0.355369\pi\)
0.438898 + 0.898537i \(0.355369\pi\)
\(740\) −26.9973 −0.992440
\(741\) 64.0131 2.35158
\(742\) −4.68861 −0.172124
\(743\) −23.6771 −0.868630 −0.434315 0.900761i \(-0.643009\pi\)
−0.434315 + 0.900761i \(0.643009\pi\)
\(744\) 78.1383 2.86469
\(745\) −78.1416 −2.86289
\(746\) −79.7037 −2.91816
\(747\) 29.8831 1.09337
\(748\) 24.0265 0.878495
\(749\) 5.34358 0.195250
\(750\) 183.989 6.71834
\(751\) −13.2391 −0.483100 −0.241550 0.970388i \(-0.577656\pi\)
−0.241550 + 0.970388i \(0.577656\pi\)
\(752\) 4.86571 0.177434
\(753\) −7.87766 −0.287078
\(754\) −19.2430 −0.700788
\(755\) −0.695136 −0.0252986
\(756\) 7.16131 0.260454
\(757\) −20.1788 −0.733409 −0.366705 0.930337i \(-0.619514\pi\)
−0.366705 + 0.930337i \(0.619514\pi\)
\(758\) 28.6220 1.03960
\(759\) −6.24628 −0.226725
\(760\) −155.458 −5.63906
\(761\) −4.58470 −0.166195 −0.0830975 0.996541i \(-0.526481\pi\)
−0.0830975 + 0.996541i \(0.526481\pi\)
\(762\) 73.0566 2.64656
\(763\) 1.46348 0.0529814
\(764\) 15.7738 0.570676
\(765\) −104.958 −3.79476
\(766\) 94.7287 3.42269
\(767\) −2.64844 −0.0956297
\(768\) 89.0258 3.21244
\(769\) −38.0361 −1.37162 −0.685809 0.727781i \(-0.740552\pi\)
−0.685809 + 0.727781i \(0.740552\pi\)
\(770\) −4.35674 −0.157006
\(771\) 54.0164 1.94535
\(772\) −79.1549 −2.84885
\(773\) −42.0761 −1.51337 −0.756686 0.653778i \(-0.773183\pi\)
−0.756686 + 0.653778i \(0.773183\pi\)
\(774\) 78.8821 2.83536
\(775\) 65.3264 2.34659
\(776\) 28.9735 1.04009
\(777\) −1.85312 −0.0664804
\(778\) 40.0237 1.43492
\(779\) 25.0803 0.898594
\(780\) 141.516 5.06707
\(781\) −6.25903 −0.223966
\(782\) −30.2367 −1.08126
\(783\) 10.7074 0.382653
\(784\) −29.8873 −1.06740
\(785\) 78.7851 2.81196
\(786\) −114.394 −4.08031
\(787\) 17.7659 0.633287 0.316643 0.948545i \(-0.397444\pi\)
0.316643 + 0.948545i \(0.397444\pi\)
\(788\) 0.312499 0.0111323
\(789\) 21.2881 0.757876
\(790\) −59.4300 −2.11442
\(791\) 1.82940 0.0650460
\(792\) 24.1679 0.858770
\(793\) 32.9729 1.17090
\(794\) −32.8013 −1.16407
\(795\) 51.5548 1.82846
\(796\) 78.4293 2.77985
\(797\) −3.51128 −0.124376 −0.0621880 0.998064i \(-0.519808\pi\)
−0.0621880 + 0.998064i \(0.519808\pi\)
\(798\) −21.0199 −0.744096
\(799\) −6.28367 −0.222300
\(800\) −7.25273 −0.256423
\(801\) 14.1990 0.501697
\(802\) −15.6851 −0.553861
\(803\) −1.61747 −0.0570791
\(804\) −12.6384 −0.445721
\(805\) 3.67398 0.129491
\(806\) 42.8377 1.50889
\(807\) −52.0092 −1.83081
\(808\) 52.0795 1.83215
\(809\) 30.4006 1.06883 0.534414 0.845223i \(-0.320532\pi\)
0.534414 + 0.845223i \(0.320532\pi\)
\(810\) 19.6425 0.690165
\(811\) 39.4705 1.38600 0.692999 0.720938i \(-0.256289\pi\)
0.692999 + 0.720938i \(0.256289\pi\)
\(812\) 4.23413 0.148589
\(813\) −69.2848 −2.42992
\(814\) −4.19465 −0.147023
\(815\) −17.3683 −0.608386
\(816\) 67.9744 2.37958
\(817\) −52.8273 −1.84819
\(818\) 40.5826 1.41894
\(819\) 5.85342 0.204535
\(820\) 55.4457 1.93625
\(821\) 0.201687 0.00703892 0.00351946 0.999994i \(-0.498880\pi\)
0.00351946 + 0.999994i \(0.498880\pi\)
\(822\) 111.562 3.89119
\(823\) 21.2581 0.741010 0.370505 0.928830i \(-0.379185\pi\)
0.370505 + 0.928830i \(0.379185\pi\)
\(824\) −53.1736 −1.85239
\(825\) 33.5307 1.16739
\(826\) 0.869666 0.0302595
\(827\) −33.8665 −1.17765 −0.588826 0.808260i \(-0.700410\pi\)
−0.588826 + 0.808260i \(0.700410\pi\)
\(828\) −40.1464 −1.39519
\(829\) 23.9518 0.831880 0.415940 0.909392i \(-0.363453\pi\)
0.415940 + 0.909392i \(0.363453\pi\)
\(830\) −66.0255 −2.29178
\(831\) −36.5443 −1.26771
\(832\) 22.4352 0.777801
\(833\) 38.5970 1.33731
\(834\) −40.3119 −1.39589
\(835\) −15.1217 −0.523309
\(836\) −31.8825 −1.10268
\(837\) −23.8364 −0.823905
\(838\) 74.3562 2.56859
\(839\) −35.4557 −1.22407 −0.612033 0.790832i \(-0.709648\pi\)
−0.612033 + 0.790832i \(0.709648\pi\)
\(840\) −23.5903 −0.813941
\(841\) −22.6692 −0.781697
\(842\) 57.6542 1.98690
\(843\) 48.1522 1.65845
\(844\) 90.1732 3.10389
\(845\) −13.6810 −0.470641
\(846\) −12.4508 −0.428066
\(847\) 4.10330 0.140991
\(848\) −20.1197 −0.690914
\(849\) −29.0330 −0.996410
\(850\) 162.314 5.56732
\(851\) 3.53729 0.121257
\(852\) −66.7592 −2.28713
\(853\) −49.0210 −1.67845 −0.839224 0.543785i \(-0.816991\pi\)
−0.839224 + 0.543785i \(0.816991\pi\)
\(854\) −10.8273 −0.370501
\(855\) 139.276 4.76315
\(856\) 65.4931 2.23851
\(857\) −17.9429 −0.612918 −0.306459 0.951884i \(-0.599144\pi\)
−0.306459 + 0.951884i \(0.599144\pi\)
\(858\) 21.9877 0.750648
\(859\) 21.4311 0.731220 0.365610 0.930768i \(-0.380860\pi\)
0.365610 + 0.930768i \(0.380860\pi\)
\(860\) −116.787 −3.98240
\(861\) 3.80585 0.129703
\(862\) 44.8626 1.52803
\(863\) −19.3374 −0.658254 −0.329127 0.944286i \(-0.606754\pi\)
−0.329127 + 0.944286i \(0.606754\pi\)
\(864\) 2.64638 0.0900318
\(865\) −52.6415 −1.78986
\(866\) −94.9703 −3.22722
\(867\) −41.0755 −1.39500
\(868\) −9.42580 −0.319932
\(869\) −6.18745 −0.209895
\(870\) −69.4799 −2.35559
\(871\) −3.51739 −0.119182
\(872\) 17.9370 0.607422
\(873\) −25.9576 −0.878531
\(874\) 40.1233 1.35719
\(875\) −11.2671 −0.380899
\(876\) −17.2520 −0.582891
\(877\) −35.8836 −1.21170 −0.605852 0.795578i \(-0.707168\pi\)
−0.605852 + 0.795578i \(0.707168\pi\)
\(878\) −62.8398 −2.12074
\(879\) −89.7732 −3.02797
\(880\) −18.6956 −0.630228
\(881\) −41.1089 −1.38499 −0.692497 0.721420i \(-0.743490\pi\)
−0.692497 + 0.721420i \(0.743490\pi\)
\(882\) 76.4779 2.57515
\(883\) −14.2129 −0.478302 −0.239151 0.970982i \(-0.576869\pi\)
−0.239151 + 0.970982i \(0.576869\pi\)
\(884\) 71.3220 2.39882
\(885\) −9.56263 −0.321444
\(886\) −54.7837 −1.84049
\(887\) −23.2870 −0.781901 −0.390950 0.920412i \(-0.627854\pi\)
−0.390950 + 0.920412i \(0.627854\pi\)
\(888\) −22.7126 −0.762186
\(889\) −4.47384 −0.150048
\(890\) −31.3721 −1.05159
\(891\) 2.04504 0.0685114
\(892\) −21.5698 −0.722209
\(893\) 8.33827 0.279030
\(894\) −129.498 −4.33106
\(895\) −4.20874 −0.140683
\(896\) −7.88225 −0.263327
\(897\) −18.5419 −0.619097
\(898\) −12.1526 −0.405537
\(899\) −14.0933 −0.470036
\(900\) 215.511 7.18368
\(901\) 25.9830 0.865618
\(902\) 8.61477 0.286841
\(903\) −8.01638 −0.266768
\(904\) 22.4219 0.745741
\(905\) 35.5420 1.18145
\(906\) −1.15199 −0.0382725
\(907\) 43.6080 1.44798 0.723989 0.689811i \(-0.242306\pi\)
0.723989 + 0.689811i \(0.242306\pi\)
\(908\) −37.2102 −1.23486
\(909\) −46.6585 −1.54757
\(910\) −12.9329 −0.428721
\(911\) −18.8017 −0.622927 −0.311463 0.950258i \(-0.600819\pi\)
−0.311463 + 0.950258i \(0.600819\pi\)
\(912\) −90.2003 −2.98683
\(913\) −6.87413 −0.227500
\(914\) 54.1476 1.79104
\(915\) 119.054 3.93580
\(916\) −78.6372 −2.59825
\(917\) 7.00528 0.231335
\(918\) −59.2253 −1.95473
\(919\) 5.99902 0.197889 0.0989447 0.995093i \(-0.468453\pi\)
0.0989447 + 0.995093i \(0.468453\pi\)
\(920\) 45.0298 1.48459
\(921\) −46.2785 −1.52493
\(922\) 23.5621 0.775977
\(923\) −18.5798 −0.611561
\(924\) −4.83807 −0.159161
\(925\) −18.9886 −0.624340
\(926\) 74.8419 2.45946
\(927\) 47.6387 1.56466
\(928\) 1.56468 0.0513630
\(929\) 6.97085 0.228706 0.114353 0.993440i \(-0.463520\pi\)
0.114353 + 0.993440i \(0.463520\pi\)
\(930\) 154.673 5.07191
\(931\) −51.2173 −1.67858
\(932\) −46.9839 −1.53901
\(933\) −1.86702 −0.0611235
\(934\) 44.0634 1.44180
\(935\) 24.1438 0.789588
\(936\) 71.7419 2.34496
\(937\) 9.07755 0.296550 0.148275 0.988946i \(-0.452628\pi\)
0.148275 + 0.988946i \(0.452628\pi\)
\(938\) 1.15500 0.0377121
\(939\) 48.1265 1.57055
\(940\) 18.4337 0.601240
\(941\) −5.55903 −0.181219 −0.0906096 0.995886i \(-0.528882\pi\)
−0.0906096 + 0.995886i \(0.528882\pi\)
\(942\) 130.564 4.25401
\(943\) −7.26472 −0.236572
\(944\) 3.73190 0.121463
\(945\) 7.19629 0.234095
\(946\) −18.1456 −0.589963
\(947\) −47.2154 −1.53430 −0.767148 0.641470i \(-0.778325\pi\)
−0.767148 + 0.641470i \(0.778325\pi\)
\(948\) −65.9957 −2.14344
\(949\) −4.80141 −0.155860
\(950\) −215.386 −6.98806
\(951\) −89.0596 −2.88795
\(952\) −11.8892 −0.385331
\(953\) 11.4953 0.372370 0.186185 0.982515i \(-0.440388\pi\)
0.186185 + 0.982515i \(0.440388\pi\)
\(954\) 51.4839 1.66685
\(955\) 15.8509 0.512922
\(956\) −59.4834 −1.92383
\(957\) −7.23378 −0.233835
\(958\) −9.30450 −0.300615
\(959\) −6.83187 −0.220613
\(960\) 81.0060 2.61446
\(961\) 0.373677 0.0120541
\(962\) −12.4517 −0.401460
\(963\) −58.6758 −1.89080
\(964\) −39.6345 −1.27654
\(965\) −79.5416 −2.56053
\(966\) 6.08859 0.195897
\(967\) 28.6038 0.919837 0.459919 0.887961i \(-0.347879\pi\)
0.459919 + 0.887961i \(0.347879\pi\)
\(968\) 50.2918 1.61644
\(969\) 116.486 3.74208
\(970\) 57.3521 1.84147
\(971\) −51.2873 −1.64589 −0.822943 0.568123i \(-0.807670\pi\)
−0.822943 + 0.568123i \(0.807670\pi\)
\(972\) 73.6731 2.36307
\(973\) 2.46862 0.0791405
\(974\) 78.5648 2.51738
\(975\) 99.5351 3.18767
\(976\) −46.4618 −1.48721
\(977\) 0.318090 0.0101766 0.00508830 0.999987i \(-0.498380\pi\)
0.00508830 + 0.999987i \(0.498380\pi\)
\(978\) −28.7832 −0.920384
\(979\) −3.26625 −0.104390
\(980\) −113.227 −3.61692
\(981\) −16.0699 −0.513072
\(982\) 73.2897 2.33877
\(983\) −17.8105 −0.568068 −0.284034 0.958814i \(-0.591673\pi\)
−0.284034 + 0.958814i \(0.591673\pi\)
\(984\) 46.6461 1.48702
\(985\) 0.314025 0.0100057
\(986\) −35.0170 −1.11517
\(987\) 1.26531 0.0402751
\(988\) −94.6425 −3.01098
\(989\) 15.3019 0.486572
\(990\) 47.8397 1.52045
\(991\) 40.0345 1.27174 0.635869 0.771797i \(-0.280642\pi\)
0.635869 + 0.771797i \(0.280642\pi\)
\(992\) −3.48320 −0.110592
\(993\) 45.1053 1.43137
\(994\) 6.10102 0.193513
\(995\) 78.8124 2.49852
\(996\) −73.3199 −2.32323
\(997\) −31.6276 −1.00166 −0.500829 0.865547i \(-0.666971\pi\)
−0.500829 + 0.865547i \(0.666971\pi\)
\(998\) 75.1682 2.37941
\(999\) 6.92857 0.219210
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 4027.2.a.b.1.17 159
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4027.2.a.b.1.17 159 1.1 even 1 trivial