Properties

Label 8005.2.a.e.1.8
Level $8005$
Weight $2$
Character 8005.1
Self dual yes
Analytic conductor $63.920$
Analytic rank $1$
Dimension $126$
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] = [8005,2,Mod(1,8005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8005, 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("8005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8005 = 5 \cdot 1601 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8005.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: \(63.9202468180\)
Analytic rank: \(1\)
Dimension: \(126\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.60227 q^{2} -2.65544 q^{3} +4.77178 q^{4} +1.00000 q^{5} +6.91016 q^{6} +2.75161 q^{7} -7.21291 q^{8} +4.05137 q^{9} +O(q^{10})\) \(q-2.60227 q^{2} -2.65544 q^{3} +4.77178 q^{4} +1.00000 q^{5} +6.91016 q^{6} +2.75161 q^{7} -7.21291 q^{8} +4.05137 q^{9} -2.60227 q^{10} -0.255242 q^{11} -12.6712 q^{12} +2.04832 q^{13} -7.16043 q^{14} -2.65544 q^{15} +9.22635 q^{16} -7.65192 q^{17} -10.5427 q^{18} -3.20945 q^{19} +4.77178 q^{20} -7.30675 q^{21} +0.664208 q^{22} -1.51464 q^{23} +19.1535 q^{24} +1.00000 q^{25} -5.33028 q^{26} -2.79186 q^{27} +13.1301 q^{28} -7.77707 q^{29} +6.91016 q^{30} +9.40876 q^{31} -9.58357 q^{32} +0.677781 q^{33} +19.9123 q^{34} +2.75161 q^{35} +19.3323 q^{36} -10.9863 q^{37} +8.35185 q^{38} -5.43920 q^{39} -7.21291 q^{40} +12.1796 q^{41} +19.0141 q^{42} +1.81152 q^{43} -1.21796 q^{44} +4.05137 q^{45} +3.94149 q^{46} +5.19390 q^{47} -24.5000 q^{48} +0.571374 q^{49} -2.60227 q^{50} +20.3192 q^{51} +9.77415 q^{52} -8.31779 q^{53} +7.26516 q^{54} -0.255242 q^{55} -19.8471 q^{56} +8.52252 q^{57} +20.2380 q^{58} +6.33586 q^{59} -12.6712 q^{60} +10.4139 q^{61} -24.4841 q^{62} +11.1478 q^{63} +6.48630 q^{64} +2.04832 q^{65} -1.76377 q^{66} -0.920885 q^{67} -36.5133 q^{68} +4.02204 q^{69} -7.16043 q^{70} -5.84286 q^{71} -29.2222 q^{72} +13.3537 q^{73} +28.5892 q^{74} -2.65544 q^{75} -15.3148 q^{76} -0.702328 q^{77} +14.1542 q^{78} +0.662656 q^{79} +9.22635 q^{80} -4.74049 q^{81} -31.6947 q^{82} -5.01500 q^{83} -34.8662 q^{84} -7.65192 q^{85} -4.71405 q^{86} +20.6516 q^{87} +1.84104 q^{88} +8.04409 q^{89} -10.5427 q^{90} +5.63619 q^{91} -7.22753 q^{92} -24.9844 q^{93} -13.5159 q^{94} -3.20945 q^{95} +25.4486 q^{96} -3.17274 q^{97} -1.48687 q^{98} -1.03408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 15 q^{2} - 46 q^{3} + 119 q^{4} + 126 q^{5} - 10 q^{6} - 60 q^{7} - 57 q^{8} + 112 q^{9} - 15 q^{10} - 35 q^{11} - 86 q^{12} - 36 q^{13} - 31 q^{14} - 46 q^{15} + 101 q^{16} - 62 q^{17} - 45 q^{18} - 29 q^{19} + 119 q^{20} - 16 q^{21} - 67 q^{22} - 107 q^{23} - 9 q^{24} + 126 q^{25} - 53 q^{26} - 181 q^{27} - 100 q^{28} - 39 q^{29} - 10 q^{30} - 29 q^{31} - 99 q^{32} - 72 q^{33} - 18 q^{34} - 60 q^{35} + 93 q^{36} - 72 q^{37} - 93 q^{38} - 8 q^{39} - 57 q^{40} - 28 q^{41} - 22 q^{42} - 103 q^{43} - 47 q^{44} + 112 q^{45} + q^{46} - 130 q^{47} - 134 q^{48} + 116 q^{49} - 15 q^{50} - 46 q^{51} - 117 q^{52} - 103 q^{53} + 11 q^{54} - 35 q^{55} - 84 q^{56} - 70 q^{57} - 77 q^{58} - 219 q^{59} - 86 q^{60} - 4 q^{61} - 77 q^{62} - 145 q^{63} + 51 q^{64} - 36 q^{65} + 16 q^{66} - 150 q^{67} - 130 q^{68} - 21 q^{69} - 31 q^{70} - 92 q^{71} - 115 q^{72} - 79 q^{73} - 57 q^{74} - 46 q^{75} - 38 q^{76} - 75 q^{77} - 23 q^{78} - 20 q^{79} + 101 q^{80} + 142 q^{81} - 63 q^{82} - 243 q^{83} - 2 q^{84} - 62 q^{85} - 14 q^{86} - 107 q^{87} - 121 q^{88} - 84 q^{89} - 45 q^{90} - 82 q^{91} - 228 q^{92} - 149 q^{93} - 29 q^{95} + 38 q^{96} - 85 q^{97} - 48 q^{98} - 33 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.60227 −1.84008 −0.920040 0.391825i \(-0.871844\pi\)
−0.920040 + 0.391825i \(0.871844\pi\)
\(3\) −2.65544 −1.53312 −0.766560 0.642173i \(-0.778033\pi\)
−0.766560 + 0.642173i \(0.778033\pi\)
\(4\) 4.77178 2.38589
\(5\) 1.00000 0.447214
\(6\) 6.91016 2.82106
\(7\) 2.75161 1.04001 0.520006 0.854163i \(-0.325930\pi\)
0.520006 + 0.854163i \(0.325930\pi\)
\(8\) −7.21291 −2.55015
\(9\) 4.05137 1.35046
\(10\) −2.60227 −0.822908
\(11\) −0.255242 −0.0769584 −0.0384792 0.999259i \(-0.512251\pi\)
−0.0384792 + 0.999259i \(0.512251\pi\)
\(12\) −12.6712 −3.65786
\(13\) 2.04832 0.568102 0.284051 0.958809i \(-0.408321\pi\)
0.284051 + 0.958809i \(0.408321\pi\)
\(14\) −7.16043 −1.91370
\(15\) −2.65544 −0.685632
\(16\) 9.22635 2.30659
\(17\) −7.65192 −1.85586 −0.927931 0.372752i \(-0.878414\pi\)
−0.927931 + 0.372752i \(0.878414\pi\)
\(18\) −10.5427 −2.48495
\(19\) −3.20945 −0.736299 −0.368150 0.929767i \(-0.620009\pi\)
−0.368150 + 0.929767i \(0.620009\pi\)
\(20\) 4.77178 1.06700
\(21\) −7.30675 −1.59446
\(22\) 0.664208 0.141610
\(23\) −1.51464 −0.315824 −0.157912 0.987453i \(-0.550476\pi\)
−0.157912 + 0.987453i \(0.550476\pi\)
\(24\) 19.1535 3.90969
\(25\) 1.00000 0.200000
\(26\) −5.33028 −1.04535
\(27\) −2.79186 −0.537294
\(28\) 13.1301 2.48136
\(29\) −7.77707 −1.44417 −0.722083 0.691806i \(-0.756815\pi\)
−0.722083 + 0.691806i \(0.756815\pi\)
\(30\) 6.91016 1.26162
\(31\) 9.40876 1.68986 0.844932 0.534874i \(-0.179641\pi\)
0.844932 + 0.534874i \(0.179641\pi\)
\(32\) −9.58357 −1.69415
\(33\) 0.677781 0.117987
\(34\) 19.9123 3.41493
\(35\) 2.75161 0.465107
\(36\) 19.3323 3.22205
\(37\) −10.9863 −1.80613 −0.903066 0.429502i \(-0.858689\pi\)
−0.903066 + 0.429502i \(0.858689\pi\)
\(38\) 8.35185 1.35485
\(39\) −5.43920 −0.870969
\(40\) −7.21291 −1.14046
\(41\) 12.1796 1.90214 0.951071 0.308974i \(-0.0999855\pi\)
0.951071 + 0.308974i \(0.0999855\pi\)
\(42\) 19.0141 2.93394
\(43\) 1.81152 0.276254 0.138127 0.990415i \(-0.455892\pi\)
0.138127 + 0.990415i \(0.455892\pi\)
\(44\) −1.21796 −0.183614
\(45\) 4.05137 0.603943
\(46\) 3.94149 0.581142
\(47\) 5.19390 0.757608 0.378804 0.925477i \(-0.376335\pi\)
0.378804 + 0.925477i \(0.376335\pi\)
\(48\) −24.5000 −3.53628
\(49\) 0.571374 0.0816249
\(50\) −2.60227 −0.368016
\(51\) 20.3192 2.84526
\(52\) 9.77415 1.35543
\(53\) −8.31779 −1.14254 −0.571268 0.820764i \(-0.693548\pi\)
−0.571268 + 0.820764i \(0.693548\pi\)
\(54\) 7.26516 0.988663
\(55\) −0.255242 −0.0344169
\(56\) −19.8471 −2.65219
\(57\) 8.52252 1.12883
\(58\) 20.2380 2.65738
\(59\) 6.33586 0.824859 0.412430 0.910990i \(-0.364680\pi\)
0.412430 + 0.910990i \(0.364680\pi\)
\(60\) −12.6712 −1.63584
\(61\) 10.4139 1.33336 0.666681 0.745343i \(-0.267714\pi\)
0.666681 + 0.745343i \(0.267714\pi\)
\(62\) −24.4841 −3.10948
\(63\) 11.1478 1.40449
\(64\) 6.48630 0.810788
\(65\) 2.04832 0.254063
\(66\) −1.76377 −0.217105
\(67\) −0.920885 −0.112504 −0.0562520 0.998417i \(-0.517915\pi\)
−0.0562520 + 0.998417i \(0.517915\pi\)
\(68\) −36.5133 −4.42789
\(69\) 4.02204 0.484197
\(70\) −7.16043 −0.855835
\(71\) −5.84286 −0.693420 −0.346710 0.937972i \(-0.612701\pi\)
−0.346710 + 0.937972i \(0.612701\pi\)
\(72\) −29.2222 −3.44387
\(73\) 13.3537 1.56294 0.781469 0.623944i \(-0.214471\pi\)
0.781469 + 0.623944i \(0.214471\pi\)
\(74\) 28.5892 3.32343
\(75\) −2.65544 −0.306624
\(76\) −15.3148 −1.75673
\(77\) −0.702328 −0.0800377
\(78\) 14.1542 1.60265
\(79\) 0.662656 0.0745546 0.0372773 0.999305i \(-0.488132\pi\)
0.0372773 + 0.999305i \(0.488132\pi\)
\(80\) 9.22635 1.03154
\(81\) −4.74049 −0.526722
\(82\) −31.6947 −3.50009
\(83\) −5.01500 −0.550468 −0.275234 0.961377i \(-0.588755\pi\)
−0.275234 + 0.961377i \(0.588755\pi\)
\(84\) −34.8662 −3.80422
\(85\) −7.65192 −0.829967
\(86\) −4.71405 −0.508329
\(87\) 20.6516 2.21408
\(88\) 1.84104 0.196256
\(89\) 8.04409 0.852672 0.426336 0.904565i \(-0.359804\pi\)
0.426336 + 0.904565i \(0.359804\pi\)
\(90\) −10.5427 −1.11130
\(91\) 5.63619 0.590833
\(92\) −7.22753 −0.753523
\(93\) −24.9844 −2.59076
\(94\) −13.5159 −1.39406
\(95\) −3.20945 −0.329283
\(96\) 25.4486 2.59734
\(97\) −3.17274 −0.322143 −0.161072 0.986943i \(-0.551495\pi\)
−0.161072 + 0.986943i \(0.551495\pi\)
\(98\) −1.48687 −0.150196
\(99\) −1.03408 −0.103929
\(100\) 4.77178 0.477178
\(101\) 8.90088 0.885670 0.442835 0.896603i \(-0.353973\pi\)
0.442835 + 0.896603i \(0.353973\pi\)
\(102\) −52.8760 −5.23550
\(103\) 4.31504 0.425174 0.212587 0.977142i \(-0.431811\pi\)
0.212587 + 0.977142i \(0.431811\pi\)
\(104\) −14.7744 −1.44875
\(105\) −7.30675 −0.713066
\(106\) 21.6451 2.10236
\(107\) −16.3847 −1.58396 −0.791982 0.610544i \(-0.790951\pi\)
−0.791982 + 0.610544i \(0.790951\pi\)
\(108\) −13.3222 −1.28193
\(109\) −3.94538 −0.377899 −0.188950 0.981987i \(-0.560508\pi\)
−0.188950 + 0.981987i \(0.560508\pi\)
\(110\) 0.664208 0.0633297
\(111\) 29.1734 2.76902
\(112\) 25.3873 2.39888
\(113\) 2.76272 0.259895 0.129948 0.991521i \(-0.458519\pi\)
0.129948 + 0.991521i \(0.458519\pi\)
\(114\) −22.1778 −2.07715
\(115\) −1.51464 −0.141241
\(116\) −37.1105 −3.44562
\(117\) 8.29852 0.767198
\(118\) −16.4876 −1.51781
\(119\) −21.0551 −1.93012
\(120\) 19.1535 1.74847
\(121\) −10.9349 −0.994077
\(122\) −27.0997 −2.45349
\(123\) −32.3423 −2.91621
\(124\) 44.8966 4.03183
\(125\) 1.00000 0.0894427
\(126\) −29.0096 −2.58438
\(127\) 10.1331 0.899164 0.449582 0.893239i \(-0.351573\pi\)
0.449582 + 0.893239i \(0.351573\pi\)
\(128\) 2.28807 0.202238
\(129\) −4.81038 −0.423531
\(130\) −5.33028 −0.467496
\(131\) 0.749989 0.0655268 0.0327634 0.999463i \(-0.489569\pi\)
0.0327634 + 0.999463i \(0.489569\pi\)
\(132\) 3.23422 0.281503
\(133\) −8.83117 −0.765760
\(134\) 2.39639 0.207016
\(135\) −2.79186 −0.240285
\(136\) 55.1926 4.73273
\(137\) −0.947492 −0.0809497 −0.0404748 0.999181i \(-0.512887\pi\)
−0.0404748 + 0.999181i \(0.512887\pi\)
\(138\) −10.4664 −0.890960
\(139\) 1.53935 0.130566 0.0652829 0.997867i \(-0.479205\pi\)
0.0652829 + 0.997867i \(0.479205\pi\)
\(140\) 13.1301 1.10970
\(141\) −13.7921 −1.16150
\(142\) 15.2047 1.27595
\(143\) −0.522818 −0.0437202
\(144\) 37.3794 3.11495
\(145\) −7.77707 −0.645851
\(146\) −34.7500 −2.87593
\(147\) −1.51725 −0.125141
\(148\) −52.4241 −4.30923
\(149\) −16.2503 −1.33128 −0.665639 0.746274i \(-0.731841\pi\)
−0.665639 + 0.746274i \(0.731841\pi\)
\(150\) 6.91016 0.564213
\(151\) 4.29802 0.349768 0.174884 0.984589i \(-0.444045\pi\)
0.174884 + 0.984589i \(0.444045\pi\)
\(152\) 23.1495 1.87767
\(153\) −31.0008 −2.50626
\(154\) 1.82764 0.147276
\(155\) 9.40876 0.755730
\(156\) −25.9547 −2.07804
\(157\) −10.2831 −0.820683 −0.410342 0.911932i \(-0.634591\pi\)
−0.410342 + 0.911932i \(0.634591\pi\)
\(158\) −1.72441 −0.137186
\(159\) 22.0874 1.75164
\(160\) −9.58357 −0.757648
\(161\) −4.16770 −0.328461
\(162\) 12.3360 0.969209
\(163\) 8.35764 0.654621 0.327310 0.944917i \(-0.393858\pi\)
0.327310 + 0.944917i \(0.393858\pi\)
\(164\) 58.1186 4.53830
\(165\) 0.677781 0.0527652
\(166\) 13.0504 1.01290
\(167\) −20.9145 −1.61841 −0.809206 0.587525i \(-0.800102\pi\)
−0.809206 + 0.587525i \(0.800102\pi\)
\(168\) 52.7030 4.06612
\(169\) −8.80438 −0.677260
\(170\) 19.9123 1.52720
\(171\) −13.0027 −0.994341
\(172\) 8.64417 0.659112
\(173\) 0.973306 0.0739991 0.0369995 0.999315i \(-0.488220\pi\)
0.0369995 + 0.999315i \(0.488220\pi\)
\(174\) −53.7408 −4.07408
\(175\) 2.75161 0.208002
\(176\) −2.35495 −0.177511
\(177\) −16.8245 −1.26461
\(178\) −20.9329 −1.56898
\(179\) 13.5387 1.01193 0.505965 0.862554i \(-0.331136\pi\)
0.505965 + 0.862554i \(0.331136\pi\)
\(180\) 19.3323 1.44094
\(181\) 5.29939 0.393901 0.196950 0.980413i \(-0.436896\pi\)
0.196950 + 0.980413i \(0.436896\pi\)
\(182\) −14.6669 −1.08718
\(183\) −27.6535 −2.04421
\(184\) 10.9250 0.805399
\(185\) −10.9863 −0.807727
\(186\) 65.0161 4.76721
\(187\) 1.95309 0.142824
\(188\) 24.7842 1.80757
\(189\) −7.68212 −0.558792
\(190\) 8.35185 0.605907
\(191\) −9.65146 −0.698355 −0.349177 0.937057i \(-0.613539\pi\)
−0.349177 + 0.937057i \(0.613539\pi\)
\(192\) −17.2240 −1.24304
\(193\) 16.5722 1.19289 0.596445 0.802654i \(-0.296579\pi\)
0.596445 + 0.802654i \(0.296579\pi\)
\(194\) 8.25632 0.592769
\(195\) −5.43920 −0.389509
\(196\) 2.72647 0.194748
\(197\) −3.54848 −0.252819 −0.126409 0.991978i \(-0.540345\pi\)
−0.126409 + 0.991978i \(0.540345\pi\)
\(198\) 2.69095 0.191238
\(199\) 9.54313 0.676495 0.338247 0.941057i \(-0.390166\pi\)
0.338247 + 0.941057i \(0.390166\pi\)
\(200\) −7.21291 −0.510030
\(201\) 2.44536 0.172482
\(202\) −23.1624 −1.62970
\(203\) −21.3995 −1.50195
\(204\) 96.9589 6.78848
\(205\) 12.1796 0.850663
\(206\) −11.2289 −0.782354
\(207\) −6.13637 −0.426507
\(208\) 18.8985 1.31038
\(209\) 0.819188 0.0566644
\(210\) 19.0141 1.31210
\(211\) −16.4839 −1.13480 −0.567401 0.823442i \(-0.692051\pi\)
−0.567401 + 0.823442i \(0.692051\pi\)
\(212\) −39.6907 −2.72597
\(213\) 15.5154 1.06310
\(214\) 42.6372 2.91462
\(215\) 1.81152 0.123545
\(216\) 20.1375 1.37018
\(217\) 25.8893 1.75748
\(218\) 10.2669 0.695365
\(219\) −35.4601 −2.39617
\(220\) −1.21796 −0.0821149
\(221\) −15.6736 −1.05432
\(222\) −75.9169 −5.09521
\(223\) −17.3492 −1.16179 −0.580894 0.813979i \(-0.697297\pi\)
−0.580894 + 0.813979i \(0.697297\pi\)
\(224\) −26.3703 −1.76194
\(225\) 4.05137 0.270092
\(226\) −7.18934 −0.478227
\(227\) −11.4398 −0.759286 −0.379643 0.925133i \(-0.623953\pi\)
−0.379643 + 0.925133i \(0.623953\pi\)
\(228\) 40.6676 2.69328
\(229\) 27.3345 1.80631 0.903157 0.429309i \(-0.141243\pi\)
0.903157 + 0.429309i \(0.141243\pi\)
\(230\) 3.94149 0.259894
\(231\) 1.86499 0.122707
\(232\) 56.0954 3.68284
\(233\) 15.3749 1.00724 0.503621 0.863925i \(-0.332001\pi\)
0.503621 + 0.863925i \(0.332001\pi\)
\(234\) −21.5949 −1.41171
\(235\) 5.19390 0.338813
\(236\) 30.2334 1.96802
\(237\) −1.75964 −0.114301
\(238\) 54.7910 3.55157
\(239\) −8.38075 −0.542106 −0.271053 0.962564i \(-0.587372\pi\)
−0.271053 + 0.962564i \(0.587372\pi\)
\(240\) −24.5000 −1.58147
\(241\) 12.6311 0.813643 0.406822 0.913508i \(-0.366637\pi\)
0.406822 + 0.913508i \(0.366637\pi\)
\(242\) 28.4554 1.82918
\(243\) 20.9637 1.34482
\(244\) 49.6929 3.18126
\(245\) 0.571374 0.0365037
\(246\) 84.1634 5.36606
\(247\) −6.57399 −0.418293
\(248\) −67.8646 −4.30941
\(249\) 13.3170 0.843933
\(250\) −2.60227 −0.164582
\(251\) −10.3834 −0.655394 −0.327697 0.944783i \(-0.606272\pi\)
−0.327697 + 0.944783i \(0.606272\pi\)
\(252\) 53.1949 3.35097
\(253\) 0.386600 0.0243053
\(254\) −26.3689 −1.65453
\(255\) 20.3192 1.27244
\(256\) −18.9268 −1.18292
\(257\) −9.71540 −0.606030 −0.303015 0.952986i \(-0.597993\pi\)
−0.303015 + 0.952986i \(0.597993\pi\)
\(258\) 12.5179 0.779330
\(259\) −30.2300 −1.87840
\(260\) 9.77415 0.606167
\(261\) −31.5078 −1.95029
\(262\) −1.95167 −0.120575
\(263\) 14.4204 0.889202 0.444601 0.895729i \(-0.353345\pi\)
0.444601 + 0.895729i \(0.353345\pi\)
\(264\) −4.88878 −0.300883
\(265\) −8.31779 −0.510958
\(266\) 22.9811 1.40906
\(267\) −21.3606 −1.30725
\(268\) −4.39426 −0.268422
\(269\) −10.0265 −0.611324 −0.305662 0.952140i \(-0.598878\pi\)
−0.305662 + 0.952140i \(0.598878\pi\)
\(270\) 7.26516 0.442144
\(271\) −22.7416 −1.38145 −0.690727 0.723116i \(-0.742709\pi\)
−0.690727 + 0.723116i \(0.742709\pi\)
\(272\) −70.5992 −4.28071
\(273\) −14.9666 −0.905818
\(274\) 2.46562 0.148954
\(275\) −0.255242 −0.0153917
\(276\) 19.1923 1.15524
\(277\) −15.9153 −0.956256 −0.478128 0.878290i \(-0.658685\pi\)
−0.478128 + 0.878290i \(0.658685\pi\)
\(278\) −4.00579 −0.240251
\(279\) 38.1184 2.28209
\(280\) −19.8471 −1.18609
\(281\) 22.4614 1.33994 0.669969 0.742389i \(-0.266308\pi\)
0.669969 + 0.742389i \(0.266308\pi\)
\(282\) 35.8907 2.13726
\(283\) −14.0120 −0.832924 −0.416462 0.909153i \(-0.636730\pi\)
−0.416462 + 0.909153i \(0.636730\pi\)
\(284\) −27.8809 −1.65443
\(285\) 8.52252 0.504830
\(286\) 1.36051 0.0804487
\(287\) 33.5137 1.97825
\(288\) −38.8266 −2.28788
\(289\) 41.5518 2.44422
\(290\) 20.2380 1.18842
\(291\) 8.42504 0.493885
\(292\) 63.7212 3.72900
\(293\) 6.43164 0.375741 0.187870 0.982194i \(-0.439842\pi\)
0.187870 + 0.982194i \(0.439842\pi\)
\(294\) 3.94829 0.230269
\(295\) 6.33586 0.368888
\(296\) 79.2430 4.60591
\(297\) 0.712601 0.0413493
\(298\) 42.2876 2.44966
\(299\) −3.10247 −0.179420
\(300\) −12.6712 −0.731572
\(301\) 4.98460 0.287307
\(302\) −11.1846 −0.643600
\(303\) −23.6358 −1.35784
\(304\) −29.6115 −1.69834
\(305\) 10.4139 0.596298
\(306\) 80.6722 4.61172
\(307\) −12.7754 −0.729132 −0.364566 0.931178i \(-0.618783\pi\)
−0.364566 + 0.931178i \(0.618783\pi\)
\(308\) −3.35136 −0.190961
\(309\) −11.4584 −0.651843
\(310\) −24.4841 −1.39060
\(311\) 18.2371 1.03413 0.517066 0.855945i \(-0.327024\pi\)
0.517066 + 0.855945i \(0.327024\pi\)
\(312\) 39.2325 2.22110
\(313\) 20.9210 1.18252 0.591261 0.806480i \(-0.298630\pi\)
0.591261 + 0.806480i \(0.298630\pi\)
\(314\) 26.7594 1.51012
\(315\) 11.1478 0.628108
\(316\) 3.16205 0.177879
\(317\) −3.75276 −0.210776 −0.105388 0.994431i \(-0.533608\pi\)
−0.105388 + 0.994431i \(0.533608\pi\)
\(318\) −57.4773 −3.22317
\(319\) 1.98504 0.111141
\(320\) 6.48630 0.362595
\(321\) 43.5085 2.42841
\(322\) 10.8455 0.604394
\(323\) 24.5585 1.36647
\(324\) −22.6206 −1.25670
\(325\) 2.04832 0.113620
\(326\) −21.7488 −1.20455
\(327\) 10.4767 0.579365
\(328\) −87.8507 −4.85075
\(329\) 14.2916 0.787922
\(330\) −1.76377 −0.0970921
\(331\) −21.8059 −1.19856 −0.599279 0.800540i \(-0.704546\pi\)
−0.599279 + 0.800540i \(0.704546\pi\)
\(332\) −23.9305 −1.31336
\(333\) −44.5095 −2.43910
\(334\) 54.4250 2.97801
\(335\) −0.920885 −0.0503133
\(336\) −67.4146 −3.67777
\(337\) −8.72009 −0.475014 −0.237507 0.971386i \(-0.576330\pi\)
−0.237507 + 0.971386i \(0.576330\pi\)
\(338\) 22.9113 1.24621
\(339\) −7.33625 −0.398450
\(340\) −36.5133 −1.98021
\(341\) −2.40151 −0.130049
\(342\) 33.8365 1.82967
\(343\) −17.6891 −0.955121
\(344\) −13.0663 −0.704489
\(345\) 4.02204 0.216539
\(346\) −2.53280 −0.136164
\(347\) −17.1834 −0.922452 −0.461226 0.887283i \(-0.652590\pi\)
−0.461226 + 0.887283i \(0.652590\pi\)
\(348\) 98.5448 5.28256
\(349\) 12.0183 0.643324 0.321662 0.946855i \(-0.395759\pi\)
0.321662 + 0.946855i \(0.395759\pi\)
\(350\) −7.16043 −0.382741
\(351\) −5.71863 −0.305238
\(352\) 2.44613 0.130379
\(353\) 8.78586 0.467624 0.233812 0.972282i \(-0.424880\pi\)
0.233812 + 0.972282i \(0.424880\pi\)
\(354\) 43.7819 2.32698
\(355\) −5.84286 −0.310107
\(356\) 38.3846 2.03438
\(357\) 55.9106 2.95910
\(358\) −35.2313 −1.86203
\(359\) −1.78811 −0.0943729 −0.0471865 0.998886i \(-0.515025\pi\)
−0.0471865 + 0.998886i \(0.515025\pi\)
\(360\) −29.2222 −1.54015
\(361\) −8.69941 −0.457864
\(362\) −13.7904 −0.724809
\(363\) 29.0369 1.52404
\(364\) 26.8947 1.40966
\(365\) 13.3537 0.698967
\(366\) 71.9617 3.76150
\(367\) 6.46016 0.337218 0.168609 0.985683i \(-0.446073\pi\)
0.168609 + 0.985683i \(0.446073\pi\)
\(368\) −13.9746 −0.728476
\(369\) 49.3443 2.56876
\(370\) 28.5892 1.48628
\(371\) −22.8873 −1.18825
\(372\) −119.220 −6.18128
\(373\) −7.28401 −0.377152 −0.188576 0.982059i \(-0.560387\pi\)
−0.188576 + 0.982059i \(0.560387\pi\)
\(374\) −5.08246 −0.262808
\(375\) −2.65544 −0.137126
\(376\) −37.4632 −1.93202
\(377\) −15.9299 −0.820434
\(378\) 19.9909 1.02822
\(379\) −20.3956 −1.04765 −0.523826 0.851825i \(-0.675496\pi\)
−0.523826 + 0.851825i \(0.675496\pi\)
\(380\) −15.3148 −0.785633
\(381\) −26.9078 −1.37853
\(382\) 25.1156 1.28503
\(383\) 19.8690 1.01526 0.507630 0.861575i \(-0.330522\pi\)
0.507630 + 0.861575i \(0.330522\pi\)
\(384\) −6.07583 −0.310056
\(385\) −0.702328 −0.0357939
\(386\) −43.1251 −2.19501
\(387\) 7.33914 0.373069
\(388\) −15.1396 −0.768599
\(389\) 28.5665 1.44838 0.724189 0.689602i \(-0.242214\pi\)
0.724189 + 0.689602i \(0.242214\pi\)
\(390\) 14.1542 0.716728
\(391\) 11.5899 0.586126
\(392\) −4.12127 −0.208156
\(393\) −1.99155 −0.100460
\(394\) 9.23408 0.465206
\(395\) 0.662656 0.0333418
\(396\) −4.93441 −0.247964
\(397\) 25.9083 1.30030 0.650150 0.759806i \(-0.274706\pi\)
0.650150 + 0.759806i \(0.274706\pi\)
\(398\) −24.8338 −1.24480
\(399\) 23.4507 1.17400
\(400\) 9.22635 0.461317
\(401\) −27.5549 −1.37603 −0.688013 0.725698i \(-0.741517\pi\)
−0.688013 + 0.725698i \(0.741517\pi\)
\(402\) −6.36347 −0.317381
\(403\) 19.2722 0.960015
\(404\) 42.4731 2.11311
\(405\) −4.74049 −0.235557
\(406\) 55.6871 2.76371
\(407\) 2.80416 0.138997
\(408\) −146.561 −7.25584
\(409\) −11.6625 −0.576671 −0.288336 0.957529i \(-0.593102\pi\)
−0.288336 + 0.957529i \(0.593102\pi\)
\(410\) −31.6947 −1.56529
\(411\) 2.51601 0.124106
\(412\) 20.5905 1.01442
\(413\) 17.4338 0.857863
\(414\) 15.9685 0.784807
\(415\) −5.01500 −0.246177
\(416\) −19.6302 −0.962452
\(417\) −4.08765 −0.200173
\(418\) −2.13174 −0.104267
\(419\) 8.70010 0.425028 0.212514 0.977158i \(-0.431835\pi\)
0.212514 + 0.977158i \(0.431835\pi\)
\(420\) −34.8662 −1.70130
\(421\) −30.6168 −1.49217 −0.746086 0.665849i \(-0.768069\pi\)
−0.746086 + 0.665849i \(0.768069\pi\)
\(422\) 42.8956 2.08813
\(423\) 21.0424 1.02312
\(424\) 59.9955 2.91364
\(425\) −7.65192 −0.371172
\(426\) −40.3752 −1.95618
\(427\) 28.6550 1.38671
\(428\) −78.1840 −3.77917
\(429\) 1.38831 0.0670284
\(430\) −4.71405 −0.227332
\(431\) −39.6091 −1.90790 −0.953952 0.299961i \(-0.903026\pi\)
−0.953952 + 0.299961i \(0.903026\pi\)
\(432\) −25.7587 −1.23932
\(433\) −31.3493 −1.50655 −0.753276 0.657704i \(-0.771528\pi\)
−0.753276 + 0.657704i \(0.771528\pi\)
\(434\) −67.3708 −3.23390
\(435\) 20.6516 0.990167
\(436\) −18.8265 −0.901627
\(437\) 4.86117 0.232541
\(438\) 92.2766 4.40914
\(439\) 13.5850 0.648376 0.324188 0.945993i \(-0.394909\pi\)
0.324188 + 0.945993i \(0.394909\pi\)
\(440\) 1.84104 0.0877681
\(441\) 2.31485 0.110231
\(442\) 40.7868 1.94003
\(443\) 1.66550 0.0791302 0.0395651 0.999217i \(-0.487403\pi\)
0.0395651 + 0.999217i \(0.487403\pi\)
\(444\) 139.209 6.60657
\(445\) 8.04409 0.381326
\(446\) 45.1472 2.13778
\(447\) 43.1518 2.04101
\(448\) 17.8478 0.843229
\(449\) 5.36062 0.252983 0.126492 0.991968i \(-0.459628\pi\)
0.126492 + 0.991968i \(0.459628\pi\)
\(450\) −10.5427 −0.496990
\(451\) −3.10876 −0.146386
\(452\) 13.1831 0.620081
\(453\) −11.4131 −0.536236
\(454\) 29.7694 1.39715
\(455\) 5.63619 0.264229
\(456\) −61.4722 −2.87870
\(457\) 15.7380 0.736192 0.368096 0.929788i \(-0.380010\pi\)
0.368096 + 0.929788i \(0.380010\pi\)
\(458\) −71.1316 −3.32376
\(459\) 21.3631 0.997144
\(460\) −7.22753 −0.336986
\(461\) −5.74844 −0.267732 −0.133866 0.990999i \(-0.542739\pi\)
−0.133866 + 0.990999i \(0.542739\pi\)
\(462\) −4.85320 −0.225791
\(463\) −35.5404 −1.65170 −0.825851 0.563889i \(-0.809305\pi\)
−0.825851 + 0.563889i \(0.809305\pi\)
\(464\) −71.7540 −3.33109
\(465\) −24.9844 −1.15863
\(466\) −40.0095 −1.85341
\(467\) 26.4982 1.22619 0.613096 0.790009i \(-0.289924\pi\)
0.613096 + 0.790009i \(0.289924\pi\)
\(468\) 39.5987 1.83045
\(469\) −2.53392 −0.117006
\(470\) −13.5159 −0.623442
\(471\) 27.3063 1.25821
\(472\) −45.7000 −2.10351
\(473\) −0.462376 −0.0212601
\(474\) 4.57906 0.210323
\(475\) −3.20945 −0.147260
\(476\) −100.470 −4.60505
\(477\) −33.6985 −1.54295
\(478\) 21.8089 0.997518
\(479\) 22.8888 1.04582 0.522908 0.852389i \(-0.324847\pi\)
0.522908 + 0.852389i \(0.324847\pi\)
\(480\) 25.4486 1.16157
\(481\) −22.5034 −1.02607
\(482\) −32.8696 −1.49717
\(483\) 11.0671 0.503570
\(484\) −52.1787 −2.37176
\(485\) −3.17274 −0.144067
\(486\) −54.5531 −2.47458
\(487\) −37.7392 −1.71013 −0.855063 0.518524i \(-0.826482\pi\)
−0.855063 + 0.518524i \(0.826482\pi\)
\(488\) −75.1146 −3.40028
\(489\) −22.1932 −1.00361
\(490\) −1.48687 −0.0671698
\(491\) 31.7506 1.43288 0.716442 0.697646i \(-0.245769\pi\)
0.716442 + 0.697646i \(0.245769\pi\)
\(492\) −154.331 −6.95776
\(493\) 59.5095 2.68017
\(494\) 17.1073 0.769692
\(495\) −1.03408 −0.0464785
\(496\) 86.8085 3.89782
\(497\) −16.0773 −0.721166
\(498\) −34.6545 −1.55290
\(499\) 21.8588 0.978536 0.489268 0.872134i \(-0.337264\pi\)
0.489268 + 0.872134i \(0.337264\pi\)
\(500\) 4.77178 0.213401
\(501\) 55.5372 2.48122
\(502\) 27.0203 1.20598
\(503\) −9.43807 −0.420823 −0.210411 0.977613i \(-0.567480\pi\)
−0.210411 + 0.977613i \(0.567480\pi\)
\(504\) −80.4082 −3.58167
\(505\) 8.90088 0.396084
\(506\) −1.00604 −0.0447237
\(507\) 23.3795 1.03832
\(508\) 48.3528 2.14531
\(509\) 21.3682 0.947131 0.473565 0.880759i \(-0.342967\pi\)
0.473565 + 0.880759i \(0.342967\pi\)
\(510\) −52.8760 −2.34139
\(511\) 36.7443 1.62547
\(512\) 44.6763 1.97443
\(513\) 8.96035 0.395609
\(514\) 25.2821 1.11514
\(515\) 4.31504 0.190144
\(516\) −22.9541 −1.01050
\(517\) −1.32570 −0.0583043
\(518\) 78.6664 3.45640
\(519\) −2.58456 −0.113450
\(520\) −14.7744 −0.647899
\(521\) −18.5818 −0.814083 −0.407041 0.913410i \(-0.633440\pi\)
−0.407041 + 0.913410i \(0.633440\pi\)
\(522\) 81.9917 3.58868
\(523\) −26.9576 −1.17877 −0.589386 0.807852i \(-0.700630\pi\)
−0.589386 + 0.807852i \(0.700630\pi\)
\(524\) 3.57878 0.156340
\(525\) −7.30675 −0.318893
\(526\) −37.5258 −1.63620
\(527\) −71.9951 −3.13615
\(528\) 6.25344 0.272146
\(529\) −20.7059 −0.900255
\(530\) 21.6451 0.940202
\(531\) 25.6689 1.11394
\(532\) −42.1404 −1.82702
\(533\) 24.9478 1.08061
\(534\) 55.5860 2.40544
\(535\) −16.3847 −0.708371
\(536\) 6.64227 0.286902
\(537\) −35.9513 −1.55141
\(538\) 26.0915 1.12489
\(539\) −0.145839 −0.00628172
\(540\) −13.3222 −0.573294
\(541\) 9.03487 0.388440 0.194220 0.980958i \(-0.437783\pi\)
0.194220 + 0.980958i \(0.437783\pi\)
\(542\) 59.1797 2.54198
\(543\) −14.0722 −0.603897
\(544\) 73.3327 3.14411
\(545\) −3.94538 −0.169002
\(546\) 38.9470 1.66678
\(547\) 34.3299 1.46784 0.733920 0.679236i \(-0.237689\pi\)
0.733920 + 0.679236i \(0.237689\pi\)
\(548\) −4.52123 −0.193137
\(549\) 42.1906 1.80065
\(550\) 0.664208 0.0283219
\(551\) 24.9601 1.06334
\(552\) −29.0106 −1.23477
\(553\) 1.82337 0.0775377
\(554\) 41.4158 1.75959
\(555\) 29.1734 1.23834
\(556\) 7.34543 0.311516
\(557\) 17.9907 0.762290 0.381145 0.924515i \(-0.375530\pi\)
0.381145 + 0.924515i \(0.375530\pi\)
\(558\) −99.1942 −4.19923
\(559\) 3.71057 0.156941
\(560\) 25.3873 1.07281
\(561\) −5.18632 −0.218967
\(562\) −58.4506 −2.46559
\(563\) −25.7960 −1.08717 −0.543587 0.839353i \(-0.682934\pi\)
−0.543587 + 0.839353i \(0.682934\pi\)
\(564\) −65.8129 −2.77122
\(565\) 2.76272 0.116229
\(566\) 36.4628 1.53265
\(567\) −13.0440 −0.547797
\(568\) 42.1441 1.76833
\(569\) −20.9667 −0.878971 −0.439486 0.898250i \(-0.644839\pi\)
−0.439486 + 0.898250i \(0.644839\pi\)
\(570\) −22.1778 −0.928928
\(571\) −16.9091 −0.707624 −0.353812 0.935317i \(-0.615115\pi\)
−0.353812 + 0.935317i \(0.615115\pi\)
\(572\) −2.49477 −0.104312
\(573\) 25.6289 1.07066
\(574\) −87.2115 −3.64014
\(575\) −1.51464 −0.0631649
\(576\) 26.2784 1.09494
\(577\) 30.8871 1.28585 0.642924 0.765930i \(-0.277721\pi\)
0.642924 + 0.765930i \(0.277721\pi\)
\(578\) −108.129 −4.49757
\(579\) −44.0064 −1.82884
\(580\) −37.1105 −1.54093
\(581\) −13.7993 −0.572493
\(582\) −21.9242 −0.908787
\(583\) 2.12305 0.0879277
\(584\) −96.3194 −3.98573
\(585\) 8.29852 0.343101
\(586\) −16.7368 −0.691392
\(587\) −42.3565 −1.74824 −0.874119 0.485711i \(-0.838561\pi\)
−0.874119 + 0.485711i \(0.838561\pi\)
\(588\) −7.23999 −0.298572
\(589\) −30.1970 −1.24425
\(590\) −16.4876 −0.678783
\(591\) 9.42278 0.387601
\(592\) −101.363 −4.16600
\(593\) 29.4538 1.20952 0.604760 0.796408i \(-0.293269\pi\)
0.604760 + 0.796408i \(0.293269\pi\)
\(594\) −1.85438 −0.0760860
\(595\) −21.0551 −0.863175
\(596\) −77.5430 −3.17628
\(597\) −25.3412 −1.03715
\(598\) 8.07345 0.330148
\(599\) 22.9344 0.937073 0.468537 0.883444i \(-0.344781\pi\)
0.468537 + 0.883444i \(0.344781\pi\)
\(600\) 19.1535 0.781937
\(601\) −11.7080 −0.477579 −0.238789 0.971071i \(-0.576751\pi\)
−0.238789 + 0.971071i \(0.576751\pi\)
\(602\) −12.9712 −0.528668
\(603\) −3.73085 −0.151932
\(604\) 20.5092 0.834508
\(605\) −10.9349 −0.444565
\(606\) 61.5065 2.49853
\(607\) 26.3800 1.07073 0.535366 0.844620i \(-0.320174\pi\)
0.535366 + 0.844620i \(0.320174\pi\)
\(608\) 30.7580 1.24740
\(609\) 56.8251 2.30267
\(610\) −27.0997 −1.09724
\(611\) 10.6388 0.430399
\(612\) −147.929 −5.97967
\(613\) 38.1142 1.53942 0.769709 0.638395i \(-0.220401\pi\)
0.769709 + 0.638395i \(0.220401\pi\)
\(614\) 33.2450 1.34166
\(615\) −32.3423 −1.30417
\(616\) 5.06583 0.204108
\(617\) 6.51019 0.262090 0.131045 0.991376i \(-0.458167\pi\)
0.131045 + 0.991376i \(0.458167\pi\)
\(618\) 29.8177 1.19944
\(619\) −43.3005 −1.74039 −0.870197 0.492703i \(-0.836009\pi\)
−0.870197 + 0.492703i \(0.836009\pi\)
\(620\) 44.8966 1.80309
\(621\) 4.22867 0.169690
\(622\) −47.4579 −1.90289
\(623\) 22.1342 0.886789
\(624\) −50.1840 −2.00897
\(625\) 1.00000 0.0400000
\(626\) −54.4419 −2.17594
\(627\) −2.17531 −0.0868734
\(628\) −49.0689 −1.95806
\(629\) 84.0660 3.35193
\(630\) −29.0096 −1.15577
\(631\) −32.2621 −1.28433 −0.642166 0.766565i \(-0.721964\pi\)
−0.642166 + 0.766565i \(0.721964\pi\)
\(632\) −4.77968 −0.190125
\(633\) 43.7722 1.73979
\(634\) 9.76567 0.387844
\(635\) 10.1331 0.402118
\(636\) 105.396 4.17923
\(637\) 1.17036 0.0463713
\(638\) −5.16559 −0.204508
\(639\) −23.6716 −0.936435
\(640\) 2.28807 0.0904437
\(641\) −25.5128 −1.00769 −0.503847 0.863793i \(-0.668082\pi\)
−0.503847 + 0.863793i \(0.668082\pi\)
\(642\) −113.221 −4.46846
\(643\) 9.84898 0.388406 0.194203 0.980961i \(-0.437788\pi\)
0.194203 + 0.980961i \(0.437788\pi\)
\(644\) −19.8874 −0.783672
\(645\) −4.81038 −0.189409
\(646\) −63.9076 −2.51441
\(647\) 6.48902 0.255110 0.127555 0.991832i \(-0.459287\pi\)
0.127555 + 0.991832i \(0.459287\pi\)
\(648\) 34.1928 1.34322
\(649\) −1.61718 −0.0634798
\(650\) −5.33028 −0.209071
\(651\) −68.7475 −2.69443
\(652\) 39.8809 1.56185
\(653\) −38.9254 −1.52327 −0.761634 0.648008i \(-0.775603\pi\)
−0.761634 + 0.648008i \(0.775603\pi\)
\(654\) −27.2633 −1.06608
\(655\) 0.749989 0.0293045
\(656\) 112.374 4.38745
\(657\) 54.1010 2.11068
\(658\) −37.1905 −1.44984
\(659\) −35.0037 −1.36355 −0.681775 0.731562i \(-0.738792\pi\)
−0.681775 + 0.731562i \(0.738792\pi\)
\(660\) 3.23422 0.125892
\(661\) −13.6897 −0.532469 −0.266235 0.963908i \(-0.585780\pi\)
−0.266235 + 0.963908i \(0.585780\pi\)
\(662\) 56.7446 2.20544
\(663\) 41.6203 1.61640
\(664\) 36.1728 1.40378
\(665\) −8.83117 −0.342458
\(666\) 115.825 4.48815
\(667\) 11.7795 0.456103
\(668\) −99.7994 −3.86135
\(669\) 46.0698 1.78116
\(670\) 2.39639 0.0925805
\(671\) −2.65807 −0.102614
\(672\) 70.0248 2.70126
\(673\) 29.4839 1.13652 0.568261 0.822848i \(-0.307616\pi\)
0.568261 + 0.822848i \(0.307616\pi\)
\(674\) 22.6920 0.874063
\(675\) −2.79186 −0.107459
\(676\) −42.0126 −1.61587
\(677\) −0.0362667 −0.00139384 −0.000696921 1.00000i \(-0.500222\pi\)
−0.000696921 1.00000i \(0.500222\pi\)
\(678\) 19.0909 0.733180
\(679\) −8.73016 −0.335033
\(680\) 55.1926 2.11654
\(681\) 30.3777 1.16408
\(682\) 6.24938 0.239301
\(683\) −39.8114 −1.52334 −0.761670 0.647965i \(-0.775620\pi\)
−0.761670 + 0.647965i \(0.775620\pi\)
\(684\) −62.0460 −2.37239
\(685\) −0.947492 −0.0362018
\(686\) 46.0317 1.75750
\(687\) −72.5852 −2.76930
\(688\) 16.7137 0.637204
\(689\) −17.0375 −0.649077
\(690\) −10.4664 −0.398450
\(691\) 23.4142 0.890718 0.445359 0.895352i \(-0.353076\pi\)
0.445359 + 0.895352i \(0.353076\pi\)
\(692\) 4.64441 0.176554
\(693\) −2.84539 −0.108087
\(694\) 44.7157 1.69738
\(695\) 1.53935 0.0583908
\(696\) −148.958 −5.64624
\(697\) −93.1976 −3.53011
\(698\) −31.2748 −1.18377
\(699\) −40.8271 −1.54422
\(700\) 13.1301 0.496271
\(701\) 4.48116 0.169251 0.0846255 0.996413i \(-0.473031\pi\)
0.0846255 + 0.996413i \(0.473031\pi\)
\(702\) 14.8814 0.561662
\(703\) 35.2599 1.32985
\(704\) −1.65558 −0.0623970
\(705\) −13.7921 −0.519441
\(706\) −22.8631 −0.860466
\(707\) 24.4918 0.921108
\(708\) −80.2829 −3.01722
\(709\) −24.2229 −0.909712 −0.454856 0.890565i \(-0.650309\pi\)
−0.454856 + 0.890565i \(0.650309\pi\)
\(710\) 15.2047 0.570622
\(711\) 2.68467 0.100683
\(712\) −58.0213 −2.17444
\(713\) −14.2509 −0.533700
\(714\) −145.494 −5.44499
\(715\) −0.522818 −0.0195523
\(716\) 64.6038 2.41436
\(717\) 22.2546 0.831113
\(718\) 4.65314 0.173654
\(719\) −27.3429 −1.01972 −0.509859 0.860258i \(-0.670302\pi\)
−0.509859 + 0.860258i \(0.670302\pi\)
\(720\) 37.3794 1.39305
\(721\) 11.8733 0.442186
\(722\) 22.6382 0.842506
\(723\) −33.5413 −1.24741
\(724\) 25.2876 0.939805
\(725\) −7.77707 −0.288833
\(726\) −75.5616 −2.80435
\(727\) −21.7008 −0.804839 −0.402420 0.915455i \(-0.631831\pi\)
−0.402420 + 0.915455i \(0.631831\pi\)
\(728\) −40.6533 −1.50671
\(729\) −41.4464 −1.53505
\(730\) −34.7500 −1.28615
\(731\) −13.8616 −0.512689
\(732\) −131.957 −4.87725
\(733\) 34.5377 1.27568 0.637840 0.770169i \(-0.279828\pi\)
0.637840 + 0.770169i \(0.279828\pi\)
\(734\) −16.8111 −0.620507
\(735\) −1.51725 −0.0559646
\(736\) 14.5157 0.535055
\(737\) 0.235049 0.00865813
\(738\) −128.407 −4.72672
\(739\) 5.65559 0.208044 0.104022 0.994575i \(-0.466829\pi\)
0.104022 + 0.994575i \(0.466829\pi\)
\(740\) −52.4241 −1.92715
\(741\) 17.4569 0.641294
\(742\) 59.5589 2.18648
\(743\) −12.1078 −0.444193 −0.222096 0.975025i \(-0.571290\pi\)
−0.222096 + 0.975025i \(0.571290\pi\)
\(744\) 180.211 6.60684
\(745\) −16.2503 −0.595365
\(746\) 18.9549 0.693989
\(747\) −20.3176 −0.743384
\(748\) 9.31973 0.340763
\(749\) −45.0842 −1.64734
\(750\) 6.91016 0.252324
\(751\) 8.66996 0.316371 0.158186 0.987409i \(-0.449436\pi\)
0.158186 + 0.987409i \(0.449436\pi\)
\(752\) 47.9207 1.74749
\(753\) 27.5725 1.00480
\(754\) 41.4539 1.50966
\(755\) 4.29802 0.156421
\(756\) −36.6574 −1.33322
\(757\) 9.77857 0.355408 0.177704 0.984084i \(-0.443133\pi\)
0.177704 + 0.984084i \(0.443133\pi\)
\(758\) 53.0748 1.92776
\(759\) −1.02659 −0.0372630
\(760\) 23.1495 0.839721
\(761\) 9.95003 0.360688 0.180344 0.983604i \(-0.442279\pi\)
0.180344 + 0.983604i \(0.442279\pi\)
\(762\) 70.0211 2.53660
\(763\) −10.8562 −0.393020
\(764\) −46.0547 −1.66620
\(765\) −31.0008 −1.12084
\(766\) −51.7045 −1.86816
\(767\) 12.9779 0.468604
\(768\) 50.2589 1.81356
\(769\) −48.2482 −1.73988 −0.869938 0.493161i \(-0.835841\pi\)
−0.869938 + 0.493161i \(0.835841\pi\)
\(770\) 1.82764 0.0658637
\(771\) 25.7987 0.929117
\(772\) 79.0787 2.84611
\(773\) −44.4332 −1.59815 −0.799076 0.601230i \(-0.794678\pi\)
−0.799076 + 0.601230i \(0.794678\pi\)
\(774\) −19.0984 −0.686477
\(775\) 9.40876 0.337973
\(776\) 22.8847 0.821514
\(777\) 80.2739 2.87981
\(778\) −74.3375 −2.66513
\(779\) −39.0900 −1.40054
\(780\) −25.9547 −0.929327
\(781\) 1.49135 0.0533645
\(782\) −30.1600 −1.07852
\(783\) 21.7125 0.775942
\(784\) 5.27170 0.188275
\(785\) −10.2831 −0.367021
\(786\) 5.18255 0.184855
\(787\) −48.6166 −1.73299 −0.866497 0.499183i \(-0.833634\pi\)
−0.866497 + 0.499183i \(0.833634\pi\)
\(788\) −16.9326 −0.603198
\(789\) −38.2926 −1.36325
\(790\) −1.72441 −0.0613516
\(791\) 7.60194 0.270294
\(792\) 7.45874 0.265035
\(793\) 21.3310 0.757486
\(794\) −67.4203 −2.39266
\(795\) 22.0874 0.783359
\(796\) 45.5378 1.61404
\(797\) −53.0582 −1.87942 −0.939709 0.341975i \(-0.888904\pi\)
−0.939709 + 0.341975i \(0.888904\pi\)
\(798\) −61.0249 −2.16026
\(799\) −39.7433 −1.40602
\(800\) −9.58357 −0.338831
\(801\) 32.5896 1.15150
\(802\) 71.7052 2.53200
\(803\) −3.40844 −0.120281
\(804\) 11.6687 0.411524
\(805\) −4.16770 −0.146892
\(806\) −50.1513 −1.76650
\(807\) 26.6247 0.937234
\(808\) −64.2013 −2.25859
\(809\) −16.0781 −0.565278 −0.282639 0.959226i \(-0.591210\pi\)
−0.282639 + 0.959226i \(0.591210\pi\)
\(810\) 12.3360 0.433444
\(811\) −34.8349 −1.22322 −0.611609 0.791160i \(-0.709478\pi\)
−0.611609 + 0.791160i \(0.709478\pi\)
\(812\) −102.114 −3.58349
\(813\) 60.3890 2.11793
\(814\) −7.29717 −0.255766
\(815\) 8.35764 0.292755
\(816\) 187.472 6.56284
\(817\) −5.81398 −0.203406
\(818\) 30.3488 1.06112
\(819\) 22.8343 0.797895
\(820\) 58.1186 2.02959
\(821\) −33.0689 −1.15411 −0.577056 0.816705i \(-0.695798\pi\)
−0.577056 + 0.816705i \(0.695798\pi\)
\(822\) −6.54732 −0.228364
\(823\) 53.3234 1.85874 0.929368 0.369154i \(-0.120353\pi\)
0.929368 + 0.369154i \(0.120353\pi\)
\(824\) −31.1240 −1.08426
\(825\) 0.677781 0.0235973
\(826\) −45.3675 −1.57854
\(827\) −4.73099 −0.164512 −0.0822562 0.996611i \(-0.526213\pi\)
−0.0822562 + 0.996611i \(0.526213\pi\)
\(828\) −29.2814 −1.01760
\(829\) 18.2801 0.634894 0.317447 0.948276i \(-0.397174\pi\)
0.317447 + 0.948276i \(0.397174\pi\)
\(830\) 13.0504 0.452985
\(831\) 42.2621 1.46606
\(832\) 13.2860 0.460610
\(833\) −4.37211 −0.151484
\(834\) 10.6371 0.368334
\(835\) −20.9145 −0.723776
\(836\) 3.90899 0.135195
\(837\) −26.2680 −0.907954
\(838\) −22.6400 −0.782085
\(839\) −14.9349 −0.515609 −0.257805 0.966197i \(-0.582999\pi\)
−0.257805 + 0.966197i \(0.582999\pi\)
\(840\) 52.7030 1.81842
\(841\) 31.4828 1.08562
\(842\) 79.6731 2.74572
\(843\) −59.6451 −2.05428
\(844\) −78.6578 −2.70751
\(845\) −8.80438 −0.302880
\(846\) −54.7580 −1.88262
\(847\) −30.0885 −1.03385
\(848\) −76.7428 −2.63536
\(849\) 37.2079 1.27697
\(850\) 19.9123 0.682987
\(851\) 16.6402 0.570420
\(852\) 74.0361 2.53643
\(853\) 10.8532 0.371607 0.185804 0.982587i \(-0.440511\pi\)
0.185804 + 0.982587i \(0.440511\pi\)
\(854\) −74.5679 −2.55166
\(855\) −13.0027 −0.444683
\(856\) 118.181 4.03935
\(857\) 17.9480 0.613091 0.306545 0.951856i \(-0.400827\pi\)
0.306545 + 0.951856i \(0.400827\pi\)
\(858\) −3.61276 −0.123338
\(859\) −41.9916 −1.43273 −0.716367 0.697723i \(-0.754196\pi\)
−0.716367 + 0.697723i \(0.754196\pi\)
\(860\) 8.64417 0.294764
\(861\) −88.9936 −3.03289
\(862\) 103.073 3.51069
\(863\) −22.9489 −0.781189 −0.390594 0.920563i \(-0.627730\pi\)
−0.390594 + 0.920563i \(0.627730\pi\)
\(864\) 26.7560 0.910258
\(865\) 0.973306 0.0330934
\(866\) 81.5793 2.77218
\(867\) −110.338 −3.74729
\(868\) 123.538 4.19315
\(869\) −0.169138 −0.00573761
\(870\) −53.7408 −1.82199
\(871\) −1.88627 −0.0639138
\(872\) 28.4577 0.963700
\(873\) −12.8540 −0.435041
\(874\) −12.6500 −0.427894
\(875\) 2.75161 0.0930215
\(876\) −169.208 −5.71700
\(877\) 24.3636 0.822700 0.411350 0.911477i \(-0.365057\pi\)
0.411350 + 0.911477i \(0.365057\pi\)
\(878\) −35.3517 −1.19306
\(879\) −17.0789 −0.576055
\(880\) −2.35495 −0.0793855
\(881\) −28.2722 −0.952514 −0.476257 0.879306i \(-0.658007\pi\)
−0.476257 + 0.879306i \(0.658007\pi\)
\(882\) −6.02385 −0.202834
\(883\) 51.2260 1.72389 0.861947 0.506999i \(-0.169245\pi\)
0.861947 + 0.506999i \(0.169245\pi\)
\(884\) −74.7909 −2.51549
\(885\) −16.8245 −0.565550
\(886\) −4.33407 −0.145606
\(887\) 25.7314 0.863977 0.431989 0.901879i \(-0.357812\pi\)
0.431989 + 0.901879i \(0.357812\pi\)
\(888\) −210.425 −7.06141
\(889\) 27.8823 0.935141
\(890\) −20.9329 −0.701671
\(891\) 1.20997 0.0405357
\(892\) −82.7865 −2.77190
\(893\) −16.6696 −0.557826
\(894\) −112.292 −3.75562
\(895\) 13.5387 0.452549
\(896\) 6.29587 0.210330
\(897\) 8.23843 0.275073
\(898\) −13.9498 −0.465509
\(899\) −73.1726 −2.44044
\(900\) 19.3323 0.644409
\(901\) 63.6470 2.12039
\(902\) 8.08982 0.269361
\(903\) −13.2363 −0.440477
\(904\) −19.9273 −0.662771
\(905\) 5.29939 0.176158
\(906\) 29.7000 0.986717
\(907\) −18.8636 −0.626356 −0.313178 0.949695i \(-0.601394\pi\)
−0.313178 + 0.949695i \(0.601394\pi\)
\(908\) −54.5883 −1.81157
\(909\) 36.0608 1.19606
\(910\) −14.6669 −0.486202
\(911\) −7.87007 −0.260747 −0.130373 0.991465i \(-0.541618\pi\)
−0.130373 + 0.991465i \(0.541618\pi\)
\(912\) 78.6317 2.60376
\(913\) 1.28004 0.0423631
\(914\) −40.9544 −1.35465
\(915\) −27.6535 −0.914197
\(916\) 130.434 4.30967
\(917\) 2.06368 0.0681487
\(918\) −55.5924 −1.83482
\(919\) 24.8253 0.818910 0.409455 0.912330i \(-0.365719\pi\)
0.409455 + 0.912330i \(0.365719\pi\)
\(920\) 10.9250 0.360186
\(921\) 33.9244 1.11785
\(922\) 14.9590 0.492648
\(923\) −11.9681 −0.393934
\(924\) 8.89933 0.292767
\(925\) −10.9863 −0.361226
\(926\) 92.4855 3.03926
\(927\) 17.4819 0.574179
\(928\) 74.5321 2.44664
\(929\) −14.3792 −0.471767 −0.235884 0.971781i \(-0.575798\pi\)
−0.235884 + 0.971781i \(0.575798\pi\)
\(930\) 65.0161 2.13196
\(931\) −1.83380 −0.0601003
\(932\) 73.3656 2.40317
\(933\) −48.4277 −1.58545
\(934\) −68.9554 −2.25629
\(935\) 1.95309 0.0638729
\(936\) −59.8565 −1.95647
\(937\) −24.8632 −0.812244 −0.406122 0.913819i \(-0.633119\pi\)
−0.406122 + 0.913819i \(0.633119\pi\)
\(938\) 6.59393 0.215299
\(939\) −55.5544 −1.81295
\(940\) 24.7842 0.808371
\(941\) −53.0030 −1.72785 −0.863923 0.503623i \(-0.832000\pi\)
−0.863923 + 0.503623i \(0.832000\pi\)
\(942\) −71.0581 −2.31520
\(943\) −18.4478 −0.600742
\(944\) 58.4569 1.90261
\(945\) −7.68212 −0.249899
\(946\) 1.20322 0.0391202
\(947\) −21.2878 −0.691761 −0.345880 0.938279i \(-0.612420\pi\)
−0.345880 + 0.938279i \(0.612420\pi\)
\(948\) −8.39664 −0.272710
\(949\) 27.3528 0.887908
\(950\) 8.35185 0.270970
\(951\) 9.96523 0.323145
\(952\) 151.869 4.92209
\(953\) 59.4457 1.92563 0.962817 0.270154i \(-0.0870745\pi\)
0.962817 + 0.270154i \(0.0870745\pi\)
\(954\) 87.6923 2.83914
\(955\) −9.65146 −0.312314
\(956\) −39.9911 −1.29341
\(957\) −5.27115 −0.170392
\(958\) −59.5627 −1.92438
\(959\) −2.60713 −0.0841886
\(960\) −17.2240 −0.555902
\(961\) 57.5249 1.85564
\(962\) 58.5598 1.88805
\(963\) −66.3804 −2.13908
\(964\) 60.2730 1.94126
\(965\) 16.5722 0.533476
\(966\) −28.7995 −0.926609
\(967\) −4.61942 −0.148551 −0.0742753 0.997238i \(-0.523664\pi\)
−0.0742753 + 0.997238i \(0.523664\pi\)
\(968\) 78.8721 2.53505
\(969\) −65.2136 −2.09496
\(970\) 8.25632 0.265095
\(971\) −1.58904 −0.0509947 −0.0254974 0.999675i \(-0.508117\pi\)
−0.0254974 + 0.999675i \(0.508117\pi\)
\(972\) 100.034 3.20860
\(973\) 4.23569 0.135790
\(974\) 98.2074 3.14677
\(975\) −5.43920 −0.174194
\(976\) 96.0823 3.07552
\(977\) −9.58052 −0.306508 −0.153254 0.988187i \(-0.548975\pi\)
−0.153254 + 0.988187i \(0.548975\pi\)
\(978\) 57.7527 1.84673
\(979\) −2.05319 −0.0656203
\(980\) 2.72647 0.0870940
\(981\) −15.9842 −0.510337
\(982\) −82.6235 −2.63662
\(983\) 6.52689 0.208176 0.104088 0.994568i \(-0.466808\pi\)
0.104088 + 0.994568i \(0.466808\pi\)
\(984\) 233.283 7.43678
\(985\) −3.54848 −0.113064
\(986\) −154.859 −4.93173
\(987\) −37.9505 −1.20798
\(988\) −31.3697 −0.998002
\(989\) −2.74380 −0.0872477
\(990\) 2.69095 0.0855241
\(991\) −0.309693 −0.00983771 −0.00491885 0.999988i \(-0.501566\pi\)
−0.00491885 + 0.999988i \(0.501566\pi\)
\(992\) −90.1696 −2.86289
\(993\) 57.9042 1.83753
\(994\) 41.8374 1.32700
\(995\) 9.54313 0.302538
\(996\) 63.5460 2.01353
\(997\) 36.7274 1.16317 0.581584 0.813487i \(-0.302433\pi\)
0.581584 + 0.813487i \(0.302433\pi\)
\(998\) −56.8825 −1.80058
\(999\) 30.6721 0.970424
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 8005.2.a.e.1.8 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8005.2.a.e.1.8 126 1.1 even 1 trivial