Properties

Label 4001.2.a.a.1.5
Level $4001$
Weight $2$
Character 4001.1
Self dual yes
Analytic conductor $31.948$
Analytic rank $1$
Dimension $149$
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] = [4001,2,Mod(1,4001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4001, 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("4001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4001 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4001.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: \(31.9481458487\)
Analytic rank: \(1\)
Dimension: \(149\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 4001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62536 q^{2} +1.08746 q^{3} +4.89252 q^{4} +0.733437 q^{5} -2.85498 q^{6} -4.12609 q^{7} -7.59390 q^{8} -1.81743 q^{9} +O(q^{10})\) \(q-2.62536 q^{2} +1.08746 q^{3} +4.89252 q^{4} +0.733437 q^{5} -2.85498 q^{6} -4.12609 q^{7} -7.59390 q^{8} -1.81743 q^{9} -1.92554 q^{10} -1.44851 q^{11} +5.32042 q^{12} +4.28374 q^{13} +10.8325 q^{14} +0.797584 q^{15} +10.1517 q^{16} +1.99209 q^{17} +4.77140 q^{18} +0.597631 q^{19} +3.58835 q^{20} -4.48697 q^{21} +3.80286 q^{22} +1.41089 q^{23} -8.25807 q^{24} -4.46207 q^{25} -11.2464 q^{26} -5.23877 q^{27} -20.1870 q^{28} +4.25595 q^{29} -2.09395 q^{30} -0.639790 q^{31} -11.4641 q^{32} -1.57520 q^{33} -5.22995 q^{34} -3.02623 q^{35} -8.89180 q^{36} +10.0922 q^{37} -1.56900 q^{38} +4.65840 q^{39} -5.56965 q^{40} -1.23998 q^{41} +11.7799 q^{42} -10.4464 q^{43} -7.08686 q^{44} -1.33297 q^{45} -3.70409 q^{46} +6.42172 q^{47} +11.0396 q^{48} +10.0247 q^{49} +11.7145 q^{50} +2.16632 q^{51} +20.9583 q^{52} +6.12751 q^{53} +13.7536 q^{54} -1.06239 q^{55} +31.3332 q^{56} +0.649900 q^{57} -11.1734 q^{58} -13.2345 q^{59} +3.90219 q^{60} +10.1737 q^{61} +1.67968 q^{62} +7.49888 q^{63} +9.79389 q^{64} +3.14185 q^{65} +4.13546 q^{66} -14.3855 q^{67} +9.74633 q^{68} +1.53428 q^{69} +7.94494 q^{70} +11.0048 q^{71} +13.8014 q^{72} +13.2009 q^{73} -26.4958 q^{74} -4.85233 q^{75} +2.92392 q^{76} +5.97669 q^{77} -12.2300 q^{78} -14.1339 q^{79} +7.44563 q^{80} -0.244671 q^{81} +3.25538 q^{82} +1.26751 q^{83} -21.9526 q^{84} +1.46107 q^{85} +27.4255 q^{86} +4.62819 q^{87} +10.9998 q^{88} -2.34175 q^{89} +3.49952 q^{90} -17.6751 q^{91} +6.90279 q^{92} -0.695747 q^{93} -16.8593 q^{94} +0.438324 q^{95} -12.4667 q^{96} -6.34090 q^{97} -26.3183 q^{98} +2.63256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 149 q - 6 q^{2} - 28 q^{3} + 116 q^{4} - 19 q^{5} - 31 q^{6} - 47 q^{7} - 15 q^{8} + 115 q^{9} - 48 q^{10} - 31 q^{11} - 61 q^{12} - 54 q^{13} - 44 q^{14} - 65 q^{15} + 58 q^{16} - 26 q^{17} - 23 q^{18} - 86 q^{19} - 52 q^{20} - 30 q^{21} - 56 q^{22} - 63 q^{23} - 90 q^{24} + 92 q^{25} - 38 q^{26} - 103 q^{27} - 77 q^{28} - 51 q^{29} - 22 q^{30} - 256 q^{31} - 21 q^{32} - 36 q^{33} - 124 q^{34} - 50 q^{35} + 45 q^{36} - 42 q^{37} - 14 q^{38} - 119 q^{39} - 131 q^{40} - 55 q^{41} - 5 q^{42} - 55 q^{43} - 54 q^{44} - 68 q^{45} - 59 q^{46} - 82 q^{47} - 89 q^{48} + 30 q^{49} + 13 q^{50} - 83 q^{51} - 126 q^{52} - 23 q^{53} - 83 q^{54} - 244 q^{55} - 94 q^{56} - 14 q^{57} - 60 q^{58} - 93 q^{59} - 70 q^{60} - 139 q^{61} - 10 q^{62} - 120 q^{63} - 45 q^{64} - 37 q^{65} - 28 q^{66} - 110 q^{67} - 27 q^{68} - 79 q^{69} - 78 q^{70} - 123 q^{71} - 74 q^{73} - 25 q^{74} - 146 q^{75} - 192 q^{76} - q^{77} + 26 q^{78} - 273 q^{79} - 51 q^{80} + 41 q^{81} - 120 q^{82} - 27 q^{83} - 14 q^{84} - 71 q^{85} + 3 q^{86} - 98 q^{87} - 143 q^{88} - 70 q^{89} - 24 q^{90} - 256 q^{91} - 47 q^{92} + 16 q^{93} - 151 q^{94} - 83 q^{95} - 137 q^{96} - 108 q^{97} + 17 q^{98} - 131 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62536 −1.85641 −0.928205 0.372069i \(-0.878649\pi\)
−0.928205 + 0.372069i \(0.878649\pi\)
\(3\) 1.08746 0.627846 0.313923 0.949448i \(-0.398357\pi\)
0.313923 + 0.949448i \(0.398357\pi\)
\(4\) 4.89252 2.44626
\(5\) 0.733437 0.328003 0.164001 0.986460i \(-0.447560\pi\)
0.164001 + 0.986460i \(0.447560\pi\)
\(6\) −2.85498 −1.16554
\(7\) −4.12609 −1.55952 −0.779759 0.626080i \(-0.784658\pi\)
−0.779759 + 0.626080i \(0.784658\pi\)
\(8\) −7.59390 −2.68485
\(9\) −1.81743 −0.605809
\(10\) −1.92554 −0.608908
\(11\) −1.44851 −0.436742 −0.218371 0.975866i \(-0.570074\pi\)
−0.218371 + 0.975866i \(0.570074\pi\)
\(12\) 5.32042 1.53587
\(13\) 4.28374 1.18810 0.594048 0.804429i \(-0.297529\pi\)
0.594048 + 0.804429i \(0.297529\pi\)
\(14\) 10.8325 2.89510
\(15\) 0.797584 0.205935
\(16\) 10.1517 2.53792
\(17\) 1.99209 0.483152 0.241576 0.970382i \(-0.422336\pi\)
0.241576 + 0.970382i \(0.422336\pi\)
\(18\) 4.77140 1.12463
\(19\) 0.597631 0.137106 0.0685530 0.997647i \(-0.478162\pi\)
0.0685530 + 0.997647i \(0.478162\pi\)
\(20\) 3.58835 0.802380
\(21\) −4.48697 −0.979137
\(22\) 3.80286 0.810772
\(23\) 1.41089 0.294190 0.147095 0.989122i \(-0.453008\pi\)
0.147095 + 0.989122i \(0.453008\pi\)
\(24\) −8.25807 −1.68567
\(25\) −4.46207 −0.892414
\(26\) −11.2464 −2.20559
\(27\) −5.23877 −1.00820
\(28\) −20.1870 −3.81498
\(29\) 4.25595 0.790311 0.395155 0.918614i \(-0.370691\pi\)
0.395155 + 0.918614i \(0.370691\pi\)
\(30\) −2.09395 −0.382300
\(31\) −0.639790 −0.114910 −0.0574548 0.998348i \(-0.518299\pi\)
−0.0574548 + 0.998348i \(0.518299\pi\)
\(32\) −11.4641 −2.02658
\(33\) −1.57520 −0.274207
\(34\) −5.22995 −0.896929
\(35\) −3.02623 −0.511526
\(36\) −8.89180 −1.48197
\(37\) 10.0922 1.65915 0.829577 0.558392i \(-0.188581\pi\)
0.829577 + 0.558392i \(0.188581\pi\)
\(38\) −1.56900 −0.254525
\(39\) 4.65840 0.745942
\(40\) −5.56965 −0.880638
\(41\) −1.23998 −0.193652 −0.0968259 0.995301i \(-0.530869\pi\)
−0.0968259 + 0.995301i \(0.530869\pi\)
\(42\) 11.7799 1.81768
\(43\) −10.4464 −1.59306 −0.796530 0.604600i \(-0.793333\pi\)
−0.796530 + 0.604600i \(0.793333\pi\)
\(44\) −7.08686 −1.06838
\(45\) −1.33297 −0.198707
\(46\) −3.70409 −0.546138
\(47\) 6.42172 0.936704 0.468352 0.883542i \(-0.344848\pi\)
0.468352 + 0.883542i \(0.344848\pi\)
\(48\) 11.0396 1.59343
\(49\) 10.0247 1.43209
\(50\) 11.7145 1.65669
\(51\) 2.16632 0.303345
\(52\) 20.9583 2.90639
\(53\) 6.12751 0.841678 0.420839 0.907135i \(-0.361736\pi\)
0.420839 + 0.907135i \(0.361736\pi\)
\(54\) 13.7536 1.87163
\(55\) −1.06239 −0.143253
\(56\) 31.3332 4.18707
\(57\) 0.649900 0.0860814
\(58\) −11.1734 −1.46714
\(59\) −13.2345 −1.72298 −0.861492 0.507771i \(-0.830470\pi\)
−0.861492 + 0.507771i \(0.830470\pi\)
\(60\) 3.90219 0.503771
\(61\) 10.1737 1.30261 0.651303 0.758818i \(-0.274223\pi\)
0.651303 + 0.758818i \(0.274223\pi\)
\(62\) 1.67968 0.213320
\(63\) 7.49888 0.944770
\(64\) 9.79389 1.22424
\(65\) 3.14185 0.389699
\(66\) 4.13546 0.509040
\(67\) −14.3855 −1.75747 −0.878734 0.477312i \(-0.841611\pi\)
−0.878734 + 0.477312i \(0.841611\pi\)
\(68\) 9.74633 1.18192
\(69\) 1.53428 0.184706
\(70\) 7.94494 0.949602
\(71\) 11.0048 1.30603 0.653015 0.757345i \(-0.273504\pi\)
0.653015 + 0.757345i \(0.273504\pi\)
\(72\) 13.8014 1.62651
\(73\) 13.2009 1.54505 0.772523 0.634987i \(-0.218995\pi\)
0.772523 + 0.634987i \(0.218995\pi\)
\(74\) −26.4958 −3.08007
\(75\) −4.85233 −0.560299
\(76\) 2.92392 0.335397
\(77\) 5.97669 0.681107
\(78\) −12.2300 −1.38477
\(79\) −14.1339 −1.59019 −0.795093 0.606488i \(-0.792578\pi\)
−0.795093 + 0.606488i \(0.792578\pi\)
\(80\) 7.44563 0.832446
\(81\) −0.244671 −0.0271856
\(82\) 3.25538 0.359497
\(83\) 1.26751 0.139128 0.0695639 0.997577i \(-0.477839\pi\)
0.0695639 + 0.997577i \(0.477839\pi\)
\(84\) −21.9526 −2.39522
\(85\) 1.46107 0.158475
\(86\) 27.4255 2.95737
\(87\) 4.62819 0.496194
\(88\) 10.9998 1.17259
\(89\) −2.34175 −0.248225 −0.124113 0.992268i \(-0.539608\pi\)
−0.124113 + 0.992268i \(0.539608\pi\)
\(90\) 3.49952 0.368882
\(91\) −17.6751 −1.85286
\(92\) 6.90279 0.719665
\(93\) −0.695747 −0.0721456
\(94\) −16.8593 −1.73891
\(95\) 0.438324 0.0449711
\(96\) −12.4667 −1.27238
\(97\) −6.34090 −0.643820 −0.321910 0.946770i \(-0.604325\pi\)
−0.321910 + 0.946770i \(0.604325\pi\)
\(98\) −26.3183 −2.65855
\(99\) 2.63256 0.264582
\(100\) −21.8308 −2.18308
\(101\) 14.9900 1.49156 0.745781 0.666192i \(-0.232077\pi\)
0.745781 + 0.666192i \(0.232077\pi\)
\(102\) −5.68737 −0.563133
\(103\) −9.59391 −0.945316 −0.472658 0.881246i \(-0.656705\pi\)
−0.472658 + 0.881246i \(0.656705\pi\)
\(104\) −32.5303 −3.18986
\(105\) −3.29091 −0.321160
\(106\) −16.0869 −1.56250
\(107\) 2.66701 0.257830 0.128915 0.991656i \(-0.458851\pi\)
0.128915 + 0.991656i \(0.458851\pi\)
\(108\) −25.6308 −2.46632
\(109\) 2.89810 0.277588 0.138794 0.990321i \(-0.455677\pi\)
0.138794 + 0.990321i \(0.455677\pi\)
\(110\) 2.78916 0.265936
\(111\) 10.9749 1.04169
\(112\) −41.8869 −3.95794
\(113\) −20.1989 −1.90015 −0.950077 0.312017i \(-0.898995\pi\)
−0.950077 + 0.312017i \(0.898995\pi\)
\(114\) −1.70622 −0.159802
\(115\) 1.03480 0.0964952
\(116\) 20.8223 1.93331
\(117\) −7.78539 −0.719760
\(118\) 34.7453 3.19857
\(119\) −8.21954 −0.753484
\(120\) −6.05677 −0.552905
\(121\) −8.90182 −0.809256
\(122\) −26.7096 −2.41817
\(123\) −1.34843 −0.121583
\(124\) −3.13018 −0.281099
\(125\) −6.93983 −0.620717
\(126\) −19.6873 −1.75388
\(127\) −12.6383 −1.12147 −0.560734 0.827996i \(-0.689481\pi\)
−0.560734 + 0.827996i \(0.689481\pi\)
\(128\) −2.78438 −0.246106
\(129\) −11.3600 −1.00020
\(130\) −8.24850 −0.723441
\(131\) −11.3099 −0.988149 −0.494075 0.869419i \(-0.664493\pi\)
−0.494075 + 0.869419i \(0.664493\pi\)
\(132\) −7.70668 −0.670781
\(133\) −2.46588 −0.213819
\(134\) 37.7671 3.26258
\(135\) −3.84230 −0.330693
\(136\) −15.1277 −1.29719
\(137\) −11.1111 −0.949282 −0.474641 0.880179i \(-0.657422\pi\)
−0.474641 + 0.880179i \(0.657422\pi\)
\(138\) −4.02805 −0.342890
\(139\) −11.2859 −0.957259 −0.478630 0.878017i \(-0.658866\pi\)
−0.478630 + 0.878017i \(0.658866\pi\)
\(140\) −14.8059 −1.25133
\(141\) 6.98337 0.588106
\(142\) −28.8916 −2.42453
\(143\) −6.20504 −0.518892
\(144\) −18.4500 −1.53750
\(145\) 3.12147 0.259224
\(146\) −34.6570 −2.86824
\(147\) 10.9014 0.899134
\(148\) 49.3765 4.05872
\(149\) −12.4674 −1.02137 −0.510686 0.859767i \(-0.670609\pi\)
−0.510686 + 0.859767i \(0.670609\pi\)
\(150\) 12.7391 1.04014
\(151\) 2.73646 0.222690 0.111345 0.993782i \(-0.464484\pi\)
0.111345 + 0.993782i \(0.464484\pi\)
\(152\) −4.53835 −0.368109
\(153\) −3.62048 −0.292698
\(154\) −15.6910 −1.26441
\(155\) −0.469245 −0.0376907
\(156\) 22.7913 1.82477
\(157\) −23.7635 −1.89654 −0.948269 0.317469i \(-0.897167\pi\)
−0.948269 + 0.317469i \(0.897167\pi\)
\(158\) 37.1065 2.95204
\(159\) 6.66343 0.528444
\(160\) −8.40816 −0.664723
\(161\) −5.82145 −0.458795
\(162\) 0.642349 0.0504677
\(163\) 18.4864 1.44796 0.723982 0.689819i \(-0.242310\pi\)
0.723982 + 0.689819i \(0.242310\pi\)
\(164\) −6.06660 −0.473722
\(165\) −1.15531 −0.0899406
\(166\) −3.32768 −0.258278
\(167\) 19.8629 1.53704 0.768520 0.639826i \(-0.220994\pi\)
0.768520 + 0.639826i \(0.220994\pi\)
\(168\) 34.0736 2.62883
\(169\) 5.35045 0.411573
\(170\) −3.83584 −0.294195
\(171\) −1.08615 −0.0830601
\(172\) −51.1091 −3.89704
\(173\) 14.5017 1.10254 0.551271 0.834326i \(-0.314143\pi\)
0.551271 + 0.834326i \(0.314143\pi\)
\(174\) −12.1507 −0.921139
\(175\) 18.4109 1.39174
\(176\) −14.7048 −1.10842
\(177\) −14.3920 −1.08177
\(178\) 6.14794 0.460808
\(179\) 0.933072 0.0697411 0.0348706 0.999392i \(-0.488898\pi\)
0.0348706 + 0.999392i \(0.488898\pi\)
\(180\) −6.52157 −0.486089
\(181\) 15.3228 1.13894 0.569468 0.822014i \(-0.307149\pi\)
0.569468 + 0.822014i \(0.307149\pi\)
\(182\) 46.4036 3.43966
\(183\) 11.0635 0.817836
\(184\) −10.7141 −0.789856
\(185\) 7.40202 0.544207
\(186\) 1.82659 0.133932
\(187\) −2.88556 −0.211013
\(188\) 31.4184 2.29142
\(189\) 21.6156 1.57231
\(190\) −1.15076 −0.0834849
\(191\) −18.7002 −1.35310 −0.676549 0.736398i \(-0.736525\pi\)
−0.676549 + 0.736398i \(0.736525\pi\)
\(192\) 10.6505 0.768632
\(193\) −1.22566 −0.0882250 −0.0441125 0.999027i \(-0.514046\pi\)
−0.0441125 + 0.999027i \(0.514046\pi\)
\(194\) 16.6471 1.19519
\(195\) 3.41664 0.244671
\(196\) 49.0458 3.50327
\(197\) 11.8434 0.843807 0.421904 0.906641i \(-0.361362\pi\)
0.421904 + 0.906641i \(0.361362\pi\)
\(198\) −6.91142 −0.491173
\(199\) −14.7180 −1.04333 −0.521665 0.853150i \(-0.674689\pi\)
−0.521665 + 0.853150i \(0.674689\pi\)
\(200\) 33.8845 2.39600
\(201\) −15.6437 −1.10342
\(202\) −39.3542 −2.76895
\(203\) −17.5605 −1.23250
\(204\) 10.5988 0.742061
\(205\) −0.909444 −0.0635183
\(206\) 25.1875 1.75489
\(207\) −2.56418 −0.178223
\(208\) 43.4872 3.01530
\(209\) −0.865674 −0.0598799
\(210\) 8.63982 0.596204
\(211\) −28.1994 −1.94132 −0.970662 0.240447i \(-0.922706\pi\)
−0.970662 + 0.240447i \(0.922706\pi\)
\(212\) 29.9789 2.05896
\(213\) 11.9673 0.819985
\(214\) −7.00187 −0.478638
\(215\) −7.66176 −0.522528
\(216\) 39.7827 2.70687
\(217\) 2.63983 0.179204
\(218\) −7.60857 −0.515317
\(219\) 14.3554 0.970050
\(220\) −5.19776 −0.350433
\(221\) 8.53359 0.574031
\(222\) −28.8131 −1.93381
\(223\) −0.455850 −0.0305260 −0.0152630 0.999884i \(-0.504859\pi\)
−0.0152630 + 0.999884i \(0.504859\pi\)
\(224\) 47.3018 3.16048
\(225\) 8.10949 0.540633
\(226\) 53.0294 3.52746
\(227\) 14.7658 0.980040 0.490020 0.871711i \(-0.336989\pi\)
0.490020 + 0.871711i \(0.336989\pi\)
\(228\) 3.17965 0.210577
\(229\) 10.8749 0.718631 0.359316 0.933216i \(-0.383010\pi\)
0.359316 + 0.933216i \(0.383010\pi\)
\(230\) −2.71671 −0.179135
\(231\) 6.49941 0.427630
\(232\) −32.3193 −2.12187
\(233\) −24.1947 −1.58505 −0.792524 0.609841i \(-0.791233\pi\)
−0.792524 + 0.609841i \(0.791233\pi\)
\(234\) 20.4395 1.33617
\(235\) 4.70992 0.307241
\(236\) −64.7500 −4.21487
\(237\) −15.3700 −0.998392
\(238\) 21.5793 1.39878
\(239\) −18.7835 −1.21500 −0.607502 0.794318i \(-0.707828\pi\)
−0.607502 + 0.794318i \(0.707828\pi\)
\(240\) 8.09683 0.522648
\(241\) −24.7403 −1.59366 −0.796831 0.604203i \(-0.793492\pi\)
−0.796831 + 0.604203i \(0.793492\pi\)
\(242\) 23.3705 1.50231
\(243\) 15.4502 0.991133
\(244\) 49.7749 3.18651
\(245\) 7.35245 0.469731
\(246\) 3.54010 0.225709
\(247\) 2.56010 0.162895
\(248\) 4.85850 0.308515
\(249\) 1.37837 0.0873508
\(250\) 18.2196 1.15231
\(251\) −6.55742 −0.413901 −0.206950 0.978351i \(-0.566354\pi\)
−0.206950 + 0.978351i \(0.566354\pi\)
\(252\) 36.6884 2.31115
\(253\) −2.04368 −0.128485
\(254\) 33.1801 2.08190
\(255\) 1.58886 0.0994981
\(256\) −12.2778 −0.767362
\(257\) −12.5523 −0.782988 −0.391494 0.920181i \(-0.628042\pi\)
−0.391494 + 0.920181i \(0.628042\pi\)
\(258\) 29.8242 1.85677
\(259\) −41.6415 −2.58748
\(260\) 15.3716 0.953305
\(261\) −7.73489 −0.478778
\(262\) 29.6925 1.83441
\(263\) 21.0005 1.29494 0.647472 0.762089i \(-0.275826\pi\)
0.647472 + 0.762089i \(0.275826\pi\)
\(264\) 11.9619 0.736204
\(265\) 4.49414 0.276073
\(266\) 6.47383 0.396936
\(267\) −2.54656 −0.155847
\(268\) −70.3813 −4.29922
\(269\) −18.9122 −1.15310 −0.576550 0.817062i \(-0.695601\pi\)
−0.576550 + 0.817062i \(0.695601\pi\)
\(270\) 10.0874 0.613901
\(271\) −13.2394 −0.804239 −0.402120 0.915587i \(-0.631726\pi\)
−0.402120 + 0.915587i \(0.631726\pi\)
\(272\) 20.2231 1.22620
\(273\) −19.2210 −1.16331
\(274\) 29.1706 1.76226
\(275\) 6.46335 0.389755
\(276\) 7.50651 0.451839
\(277\) −28.4071 −1.70682 −0.853409 0.521242i \(-0.825469\pi\)
−0.853409 + 0.521242i \(0.825469\pi\)
\(278\) 29.6296 1.77707
\(279\) 1.16277 0.0696134
\(280\) 22.9809 1.37337
\(281\) 4.02100 0.239873 0.119936 0.992782i \(-0.461731\pi\)
0.119936 + 0.992782i \(0.461731\pi\)
\(282\) −18.3339 −1.09177
\(283\) 32.1318 1.91004 0.955018 0.296547i \(-0.0958351\pi\)
0.955018 + 0.296547i \(0.0958351\pi\)
\(284\) 53.8412 3.19489
\(285\) 0.476661 0.0282350
\(286\) 16.2905 0.963276
\(287\) 5.11626 0.302003
\(288\) 20.8351 1.22772
\(289\) −13.0316 −0.766564
\(290\) −8.19499 −0.481226
\(291\) −6.89548 −0.404220
\(292\) 64.5855 3.77958
\(293\) −15.7469 −0.919944 −0.459972 0.887934i \(-0.652140\pi\)
−0.459972 + 0.887934i \(0.652140\pi\)
\(294\) −28.6202 −1.66916
\(295\) −9.70666 −0.565144
\(296\) −76.6395 −4.45458
\(297\) 7.58840 0.440324
\(298\) 32.7315 1.89609
\(299\) 6.04387 0.349526
\(300\) −23.7401 −1.37064
\(301\) 43.1028 2.48440
\(302\) −7.18419 −0.413403
\(303\) 16.3010 0.936471
\(304\) 6.06697 0.347964
\(305\) 7.46175 0.427259
\(306\) 9.50506 0.543368
\(307\) 14.1736 0.808928 0.404464 0.914554i \(-0.367458\pi\)
0.404464 + 0.914554i \(0.367458\pi\)
\(308\) 29.2410 1.66616
\(309\) −10.4330 −0.593513
\(310\) 1.23194 0.0699694
\(311\) 6.64208 0.376638 0.188319 0.982108i \(-0.439696\pi\)
0.188319 + 0.982108i \(0.439696\pi\)
\(312\) −35.3755 −2.00274
\(313\) −19.0713 −1.07797 −0.538987 0.842314i \(-0.681193\pi\)
−0.538987 + 0.842314i \(0.681193\pi\)
\(314\) 62.3879 3.52075
\(315\) 5.49995 0.309887
\(316\) −69.1502 −3.89001
\(317\) 8.46312 0.475336 0.237668 0.971346i \(-0.423617\pi\)
0.237668 + 0.971346i \(0.423617\pi\)
\(318\) −17.4939 −0.981009
\(319\) −6.16479 −0.345162
\(320\) 7.18320 0.401553
\(321\) 2.90027 0.161877
\(322\) 15.2834 0.851711
\(323\) 1.19053 0.0662430
\(324\) −1.19706 −0.0665031
\(325\) −19.1144 −1.06027
\(326\) −48.5334 −2.68801
\(327\) 3.15158 0.174283
\(328\) 9.41626 0.519926
\(329\) −26.4966 −1.46081
\(330\) 3.03310 0.166967
\(331\) −1.71062 −0.0940244 −0.0470122 0.998894i \(-0.514970\pi\)
−0.0470122 + 0.998894i \(0.514970\pi\)
\(332\) 6.20133 0.340342
\(333\) −18.3419 −1.00513
\(334\) −52.1474 −2.85338
\(335\) −10.5508 −0.576454
\(336\) −45.5503 −2.48497
\(337\) 12.1880 0.663924 0.331962 0.943293i \(-0.392289\pi\)
0.331962 + 0.943293i \(0.392289\pi\)
\(338\) −14.0469 −0.764048
\(339\) −21.9655 −1.19300
\(340\) 7.14831 0.387672
\(341\) 0.926742 0.0501859
\(342\) 2.85154 0.154194
\(343\) −12.4800 −0.673858
\(344\) 79.3288 4.27712
\(345\) 1.12530 0.0605841
\(346\) −38.0721 −2.04677
\(347\) −15.8787 −0.852415 −0.426208 0.904625i \(-0.640151\pi\)
−0.426208 + 0.904625i \(0.640151\pi\)
\(348\) 22.6435 1.21382
\(349\) −18.0671 −0.967110 −0.483555 0.875314i \(-0.660655\pi\)
−0.483555 + 0.875314i \(0.660655\pi\)
\(350\) −48.3353 −2.58363
\(351\) −22.4415 −1.19784
\(352\) 16.6058 0.885092
\(353\) 19.2972 1.02709 0.513543 0.858064i \(-0.328333\pi\)
0.513543 + 0.858064i \(0.328333\pi\)
\(354\) 37.7842 2.00821
\(355\) 8.07132 0.428381
\(356\) −11.4571 −0.607223
\(357\) −8.93843 −0.473072
\(358\) −2.44965 −0.129468
\(359\) 8.53872 0.450656 0.225328 0.974283i \(-0.427655\pi\)
0.225328 + 0.974283i \(0.427655\pi\)
\(360\) 10.1224 0.533499
\(361\) −18.6428 −0.981202
\(362\) −40.2279 −2.11433
\(363\) −9.68038 −0.508088
\(364\) −86.4759 −4.53257
\(365\) 9.68200 0.506779
\(366\) −29.0456 −1.51824
\(367\) −15.1636 −0.791533 −0.395766 0.918351i \(-0.629521\pi\)
−0.395766 + 0.918351i \(0.629521\pi\)
\(368\) 14.3229 0.746632
\(369\) 2.25357 0.117316
\(370\) −19.4330 −1.01027
\(371\) −25.2827 −1.31261
\(372\) −3.40395 −0.176487
\(373\) 2.17168 0.112445 0.0562225 0.998418i \(-0.482094\pi\)
0.0562225 + 0.998418i \(0.482094\pi\)
\(374\) 7.57563 0.391726
\(375\) −7.54680 −0.389715
\(376\) −48.7659 −2.51491
\(377\) 18.2314 0.938965
\(378\) −56.7489 −2.91885
\(379\) −21.5504 −1.10697 −0.553485 0.832859i \(-0.686702\pi\)
−0.553485 + 0.832859i \(0.686702\pi\)
\(380\) 2.14451 0.110011
\(381\) −13.7437 −0.704109
\(382\) 49.0947 2.51191
\(383\) 11.5508 0.590216 0.295108 0.955464i \(-0.404644\pi\)
0.295108 + 0.955464i \(0.404644\pi\)
\(384\) −3.02790 −0.154517
\(385\) 4.38352 0.223405
\(386\) 3.21780 0.163782
\(387\) 18.9856 0.965090
\(388\) −31.0229 −1.57495
\(389\) 13.1413 0.666289 0.333144 0.942876i \(-0.391890\pi\)
0.333144 + 0.942876i \(0.391890\pi\)
\(390\) −8.96992 −0.454210
\(391\) 2.81061 0.142139
\(392\) −76.1263 −3.84496
\(393\) −12.2991 −0.620406
\(394\) −31.0932 −1.56645
\(395\) −10.3663 −0.521585
\(396\) 12.8799 0.647237
\(397\) 3.76584 0.189002 0.0945011 0.995525i \(-0.469874\pi\)
0.0945011 + 0.995525i \(0.469874\pi\)
\(398\) 38.6400 1.93685
\(399\) −2.68155 −0.134245
\(400\) −45.2976 −2.26488
\(401\) 21.6231 1.07980 0.539902 0.841728i \(-0.318461\pi\)
0.539902 + 0.841728i \(0.318461\pi\)
\(402\) 41.0703 2.04840
\(403\) −2.74070 −0.136524
\(404\) 73.3389 3.64874
\(405\) −0.179450 −0.00891696
\(406\) 46.1026 2.28803
\(407\) −14.6187 −0.724622
\(408\) −16.4508 −0.814436
\(409\) 5.32155 0.263134 0.131567 0.991307i \(-0.457999\pi\)
0.131567 + 0.991307i \(0.457999\pi\)
\(410\) 2.38762 0.117916
\(411\) −12.0829 −0.596003
\(412\) −46.9384 −2.31249
\(413\) 54.6068 2.68702
\(414\) 6.73191 0.330855
\(415\) 0.929641 0.0456343
\(416\) −49.1091 −2.40777
\(417\) −12.2730 −0.601011
\(418\) 2.27271 0.111162
\(419\) 31.1047 1.51957 0.759783 0.650177i \(-0.225305\pi\)
0.759783 + 0.650177i \(0.225305\pi\)
\(420\) −16.1008 −0.785640
\(421\) −0.523219 −0.0255001 −0.0127501 0.999919i \(-0.504059\pi\)
−0.0127501 + 0.999919i \(0.504059\pi\)
\(422\) 74.0335 3.60389
\(423\) −11.6710 −0.567464
\(424\) −46.5317 −2.25978
\(425\) −8.88884 −0.431172
\(426\) −31.4185 −1.52223
\(427\) −41.9776 −2.03144
\(428\) 13.0484 0.630718
\(429\) −6.74774 −0.325784
\(430\) 20.1149 0.970026
\(431\) 25.3742 1.22223 0.611116 0.791541i \(-0.290721\pi\)
0.611116 + 0.791541i \(0.290721\pi\)
\(432\) −53.1824 −2.55874
\(433\) 31.0150 1.49049 0.745243 0.666793i \(-0.232334\pi\)
0.745243 + 0.666793i \(0.232334\pi\)
\(434\) −6.93052 −0.332675
\(435\) 3.39448 0.162753
\(436\) 14.1790 0.679052
\(437\) 0.843189 0.0403352
\(438\) −37.6882 −1.80081
\(439\) −29.1319 −1.39039 −0.695195 0.718821i \(-0.744682\pi\)
−0.695195 + 0.718821i \(0.744682\pi\)
\(440\) 8.06768 0.384612
\(441\) −18.2191 −0.867576
\(442\) −22.4038 −1.06564
\(443\) −6.88182 −0.326965 −0.163483 0.986546i \(-0.552273\pi\)
−0.163483 + 0.986546i \(0.552273\pi\)
\(444\) 53.6950 2.54825
\(445\) −1.71753 −0.0814186
\(446\) 1.19677 0.0566687
\(447\) −13.5579 −0.641265
\(448\) −40.4105 −1.90922
\(449\) −29.6542 −1.39947 −0.699735 0.714402i \(-0.746699\pi\)
−0.699735 + 0.714402i \(0.746699\pi\)
\(450\) −21.2903 −1.00364
\(451\) 1.79612 0.0845758
\(452\) −98.8235 −4.64827
\(453\) 2.97579 0.139815
\(454\) −38.7655 −1.81936
\(455\) −12.9636 −0.607742
\(456\) −4.93528 −0.231116
\(457\) 14.7253 0.688820 0.344410 0.938819i \(-0.388079\pi\)
0.344410 + 0.938819i \(0.388079\pi\)
\(458\) −28.5504 −1.33407
\(459\) −10.4361 −0.487115
\(460\) 5.06276 0.236052
\(461\) −14.6573 −0.682658 −0.341329 0.939944i \(-0.610877\pi\)
−0.341329 + 0.939944i \(0.610877\pi\)
\(462\) −17.0633 −0.793857
\(463\) −27.9279 −1.29792 −0.648960 0.760822i \(-0.724796\pi\)
−0.648960 + 0.760822i \(0.724796\pi\)
\(464\) 43.2052 2.00575
\(465\) −0.510286 −0.0236640
\(466\) 63.5198 2.94250
\(467\) −37.5168 −1.73607 −0.868035 0.496504i \(-0.834617\pi\)
−0.868035 + 0.496504i \(0.834617\pi\)
\(468\) −38.0902 −1.76072
\(469\) 59.3559 2.74080
\(470\) −12.3652 −0.570366
\(471\) −25.8419 −1.19073
\(472\) 100.501 4.62595
\(473\) 15.1317 0.695756
\(474\) 40.3519 1.85342
\(475\) −2.66667 −0.122355
\(476\) −40.2143 −1.84322
\(477\) −11.1363 −0.509896
\(478\) 49.3135 2.25555
\(479\) 15.1993 0.694475 0.347238 0.937777i \(-0.387120\pi\)
0.347238 + 0.937777i \(0.387120\pi\)
\(480\) −9.14355 −0.417344
\(481\) 43.2326 1.97124
\(482\) 64.9521 2.95849
\(483\) −6.33060 −0.288052
\(484\) −43.5523 −1.97965
\(485\) −4.65064 −0.211175
\(486\) −40.5624 −1.83995
\(487\) −21.9599 −0.995099 −0.497550 0.867435i \(-0.665767\pi\)
−0.497550 + 0.867435i \(0.665767\pi\)
\(488\) −77.2579 −3.49730
\(489\) 20.1032 0.909098
\(490\) −19.3028 −0.872013
\(491\) 10.9171 0.492680 0.246340 0.969183i \(-0.420772\pi\)
0.246340 + 0.969183i \(0.420772\pi\)
\(492\) −6.59720 −0.297425
\(493\) 8.47823 0.381840
\(494\) −6.72118 −0.302400
\(495\) 1.93082 0.0867838
\(496\) −6.49495 −0.291632
\(497\) −45.4068 −2.03678
\(498\) −3.61872 −0.162159
\(499\) −32.0158 −1.43322 −0.716612 0.697472i \(-0.754308\pi\)
−0.716612 + 0.697472i \(0.754308\pi\)
\(500\) −33.9532 −1.51843
\(501\) 21.6002 0.965024
\(502\) 17.2156 0.768370
\(503\) 29.5367 1.31698 0.658488 0.752591i \(-0.271196\pi\)
0.658488 + 0.752591i \(0.271196\pi\)
\(504\) −56.9458 −2.53657
\(505\) 10.9942 0.489236
\(506\) 5.36540 0.238521
\(507\) 5.81840 0.258404
\(508\) −61.8331 −2.74340
\(509\) −32.0629 −1.42116 −0.710581 0.703615i \(-0.751568\pi\)
−0.710581 + 0.703615i \(0.751568\pi\)
\(510\) −4.17132 −0.184709
\(511\) −54.4680 −2.40952
\(512\) 37.8024 1.67064
\(513\) −3.13085 −0.138230
\(514\) 32.9542 1.45355
\(515\) −7.03652 −0.310066
\(516\) −55.5792 −2.44674
\(517\) −9.30192 −0.409098
\(518\) 109.324 4.80342
\(519\) 15.7700 0.692227
\(520\) −23.8589 −1.04628
\(521\) 32.3202 1.41598 0.707988 0.706225i \(-0.249603\pi\)
0.707988 + 0.706225i \(0.249603\pi\)
\(522\) 20.3069 0.888808
\(523\) −18.8329 −0.823504 −0.411752 0.911296i \(-0.635083\pi\)
−0.411752 + 0.911296i \(0.635083\pi\)
\(524\) −55.3338 −2.41727
\(525\) 20.0212 0.873795
\(526\) −55.1338 −2.40395
\(527\) −1.27452 −0.0555189
\(528\) −15.9909 −0.695916
\(529\) −21.0094 −0.913452
\(530\) −11.7987 −0.512504
\(531\) 24.0527 1.04380
\(532\) −12.0644 −0.523057
\(533\) −5.31174 −0.230077
\(534\) 6.68565 0.289316
\(535\) 1.95608 0.0845689
\(536\) 109.242 4.71854
\(537\) 1.01468 0.0437867
\(538\) 49.6515 2.14063
\(539\) −14.5208 −0.625455
\(540\) −18.7985 −0.808960
\(541\) 19.3724 0.832883 0.416442 0.909162i \(-0.363277\pi\)
0.416442 + 0.909162i \(0.363277\pi\)
\(542\) 34.7583 1.49300
\(543\) 16.6630 0.715076
\(544\) −22.8374 −0.979146
\(545\) 2.12558 0.0910497
\(546\) 50.4621 2.15958
\(547\) 28.3258 1.21112 0.605561 0.795799i \(-0.292949\pi\)
0.605561 + 0.795799i \(0.292949\pi\)
\(548\) −54.3611 −2.32219
\(549\) −18.4899 −0.789131
\(550\) −16.9686 −0.723545
\(551\) 2.54349 0.108356
\(552\) −11.6512 −0.495908
\(553\) 58.3177 2.47992
\(554\) 74.5789 3.16855
\(555\) 8.04941 0.341678
\(556\) −55.2166 −2.34170
\(557\) −3.53402 −0.149741 −0.0748706 0.997193i \(-0.523854\pi\)
−0.0748706 + 0.997193i \(0.523854\pi\)
\(558\) −3.05270 −0.129231
\(559\) −44.7496 −1.89271
\(560\) −30.7214 −1.29821
\(561\) −3.13793 −0.132484
\(562\) −10.5566 −0.445302
\(563\) 6.88783 0.290287 0.145144 0.989411i \(-0.453636\pi\)
0.145144 + 0.989411i \(0.453636\pi\)
\(564\) 34.1663 1.43866
\(565\) −14.8146 −0.623256
\(566\) −84.3575 −3.54581
\(567\) 1.00953 0.0423965
\(568\) −83.5694 −3.50649
\(569\) −38.2911 −1.60525 −0.802623 0.596486i \(-0.796563\pi\)
−0.802623 + 0.596486i \(0.796563\pi\)
\(570\) −1.25141 −0.0524157
\(571\) −21.1785 −0.886294 −0.443147 0.896449i \(-0.646138\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(572\) −30.3583 −1.26934
\(573\) −20.3357 −0.849537
\(574\) −13.4320 −0.560642
\(575\) −6.29547 −0.262539
\(576\) −17.7997 −0.741654
\(577\) −27.9086 −1.16185 −0.580925 0.813957i \(-0.697309\pi\)
−0.580925 + 0.813957i \(0.697309\pi\)
\(578\) 34.2126 1.42306
\(579\) −1.33286 −0.0553917
\(580\) 15.2719 0.634130
\(581\) −5.22988 −0.216972
\(582\) 18.1031 0.750398
\(583\) −8.87575 −0.367596
\(584\) −100.246 −4.14821
\(585\) −5.71009 −0.236083
\(586\) 41.3413 1.70779
\(587\) −7.26336 −0.299791 −0.149895 0.988702i \(-0.547894\pi\)
−0.149895 + 0.988702i \(0.547894\pi\)
\(588\) 53.3354 2.19952
\(589\) −0.382358 −0.0157548
\(590\) 25.4835 1.04914
\(591\) 12.8792 0.529781
\(592\) 102.453 4.21081
\(593\) 19.0796 0.783507 0.391754 0.920070i \(-0.371869\pi\)
0.391754 + 0.920070i \(0.371869\pi\)
\(594\) −19.9223 −0.817421
\(595\) −6.02851 −0.247145
\(596\) −60.9972 −2.49854
\(597\) −16.0052 −0.655051
\(598\) −15.8673 −0.648864
\(599\) 30.4303 1.24335 0.621674 0.783276i \(-0.286453\pi\)
0.621674 + 0.783276i \(0.286453\pi\)
\(600\) 36.8481 1.50432
\(601\) −35.0202 −1.42850 −0.714252 0.699888i \(-0.753233\pi\)
−0.714252 + 0.699888i \(0.753233\pi\)
\(602\) −113.160 −4.61207
\(603\) 26.1446 1.06469
\(604\) 13.3882 0.544757
\(605\) −6.52892 −0.265438
\(606\) −42.7961 −1.73847
\(607\) 19.6820 0.798869 0.399434 0.916762i \(-0.369207\pi\)
0.399434 + 0.916762i \(0.369207\pi\)
\(608\) −6.85127 −0.277856
\(609\) −19.0963 −0.773822
\(610\) −19.5898 −0.793167
\(611\) 27.5090 1.11289
\(612\) −17.7132 −0.716016
\(613\) 33.9941 1.37301 0.686505 0.727125i \(-0.259144\pi\)
0.686505 + 0.727125i \(0.259144\pi\)
\(614\) −37.2107 −1.50170
\(615\) −0.988985 −0.0398797
\(616\) −45.3864 −1.82867
\(617\) 35.3575 1.42344 0.711720 0.702463i \(-0.247916\pi\)
0.711720 + 0.702463i \(0.247916\pi\)
\(618\) 27.3904 1.10180
\(619\) −42.6361 −1.71369 −0.856846 0.515573i \(-0.827579\pi\)
−0.856846 + 0.515573i \(0.827579\pi\)
\(620\) −2.29579 −0.0922012
\(621\) −7.39130 −0.296603
\(622\) −17.4378 −0.699194
\(623\) 9.66229 0.387112
\(624\) 47.2907 1.89314
\(625\) 17.2204 0.688817
\(626\) 50.0691 2.00116
\(627\) −0.941387 −0.0375954
\(628\) −116.264 −4.63942
\(629\) 20.1046 0.801624
\(630\) −14.4394 −0.575278
\(631\) 26.4466 1.05282 0.526412 0.850230i \(-0.323537\pi\)
0.526412 + 0.850230i \(0.323537\pi\)
\(632\) 107.331 4.26941
\(633\) −30.6657 −1.21885
\(634\) −22.2187 −0.882419
\(635\) −9.26939 −0.367845
\(636\) 32.6009 1.29271
\(637\) 42.9430 1.70147
\(638\) 16.1848 0.640762
\(639\) −20.0004 −0.791205
\(640\) −2.04216 −0.0807236
\(641\) −9.25871 −0.365697 −0.182848 0.983141i \(-0.558532\pi\)
−0.182848 + 0.983141i \(0.558532\pi\)
\(642\) −7.61426 −0.300511
\(643\) 16.0559 0.633181 0.316591 0.948562i \(-0.397462\pi\)
0.316591 + 0.948562i \(0.397462\pi\)
\(644\) −28.4815 −1.12233
\(645\) −8.33187 −0.328067
\(646\) −3.12558 −0.122974
\(647\) −8.96477 −0.352442 −0.176221 0.984351i \(-0.556387\pi\)
−0.176221 + 0.984351i \(0.556387\pi\)
\(648\) 1.85801 0.0729893
\(649\) 19.1703 0.752500
\(650\) 50.1821 1.96830
\(651\) 2.87072 0.112512
\(652\) 90.4448 3.54209
\(653\) −27.5018 −1.07623 −0.538115 0.842872i \(-0.680863\pi\)
−0.538115 + 0.842872i \(0.680863\pi\)
\(654\) −8.27402 −0.323540
\(655\) −8.29509 −0.324116
\(656\) −12.5879 −0.491473
\(657\) −23.9916 −0.936003
\(658\) 69.5632 2.71185
\(659\) −11.5297 −0.449135 −0.224567 0.974459i \(-0.572097\pi\)
−0.224567 + 0.974459i \(0.572097\pi\)
\(660\) −5.65236 −0.220018
\(661\) −27.2742 −1.06084 −0.530422 0.847734i \(-0.677966\pi\)
−0.530422 + 0.847734i \(0.677966\pi\)
\(662\) 4.49101 0.174548
\(663\) 9.27995 0.360403
\(664\) −9.62538 −0.373537
\(665\) −1.80857 −0.0701333
\(666\) 48.1542 1.86594
\(667\) 6.00467 0.232502
\(668\) 97.1797 3.76000
\(669\) −0.495719 −0.0191656
\(670\) 27.6998 1.07014
\(671\) −14.7367 −0.568903
\(672\) 51.4388 1.98430
\(673\) 29.2840 1.12881 0.564407 0.825497i \(-0.309105\pi\)
0.564407 + 0.825497i \(0.309105\pi\)
\(674\) −31.9979 −1.23251
\(675\) 23.3757 0.899733
\(676\) 26.1772 1.00681
\(677\) 7.58709 0.291595 0.145798 0.989314i \(-0.453425\pi\)
0.145798 + 0.989314i \(0.453425\pi\)
\(678\) 57.6674 2.21470
\(679\) 26.1631 1.00405
\(680\) −11.0952 −0.425482
\(681\) 16.0572 0.615314
\(682\) −2.43303 −0.0931656
\(683\) 29.2676 1.11989 0.559947 0.828529i \(-0.310822\pi\)
0.559947 + 0.828529i \(0.310822\pi\)
\(684\) −5.31401 −0.203186
\(685\) −8.14926 −0.311367
\(686\) 32.7645 1.25096
\(687\) 11.8260 0.451190
\(688\) −106.049 −4.04306
\(689\) 26.2487 0.999995
\(690\) −2.95432 −0.112469
\(691\) −23.1378 −0.880205 −0.440103 0.897948i \(-0.645058\pi\)
−0.440103 + 0.897948i \(0.645058\pi\)
\(692\) 70.9497 2.69710
\(693\) −10.8622 −0.412621
\(694\) 41.6874 1.58243
\(695\) −8.27751 −0.313984
\(696\) −35.1460 −1.33221
\(697\) −2.47014 −0.0935633
\(698\) 47.4327 1.79535
\(699\) −26.3108 −0.995165
\(700\) 90.0758 3.40454
\(701\) −9.53588 −0.360165 −0.180083 0.983652i \(-0.557636\pi\)
−0.180083 + 0.983652i \(0.557636\pi\)
\(702\) 58.9171 2.22368
\(703\) 6.03144 0.227480
\(704\) −14.1865 −0.534675
\(705\) 5.12186 0.192900
\(706\) −50.6621 −1.90669
\(707\) −61.8502 −2.32612
\(708\) −70.4131 −2.64629
\(709\) −26.2648 −0.986395 −0.493198 0.869917i \(-0.664172\pi\)
−0.493198 + 0.869917i \(0.664172\pi\)
\(710\) −21.1901 −0.795251
\(711\) 25.6873 0.963349
\(712\) 17.7830 0.666448
\(713\) −0.902671 −0.0338053
\(714\) 23.4666 0.878216
\(715\) −4.55100 −0.170198
\(716\) 4.56507 0.170605
\(717\) −20.4263 −0.762836
\(718\) −22.4172 −0.836603
\(719\) 4.08826 0.152466 0.0762331 0.997090i \(-0.475711\pi\)
0.0762331 + 0.997090i \(0.475711\pi\)
\(720\) −13.5319 −0.504304
\(721\) 39.5854 1.47424
\(722\) 48.9442 1.82151
\(723\) −26.9041 −1.00057
\(724\) 74.9671 2.78613
\(725\) −18.9904 −0.705285
\(726\) 25.4145 0.943221
\(727\) 28.2309 1.04703 0.523514 0.852017i \(-0.324621\pi\)
0.523514 + 0.852017i \(0.324621\pi\)
\(728\) 134.223 4.97464
\(729\) 17.5355 0.649464
\(730\) −25.4187 −0.940790
\(731\) −20.8101 −0.769690
\(732\) 54.1283 2.00064
\(733\) −46.2094 −1.70678 −0.853392 0.521270i \(-0.825458\pi\)
−0.853392 + 0.521270i \(0.825458\pi\)
\(734\) 39.8099 1.46941
\(735\) 7.99550 0.294919
\(736\) −16.1745 −0.596199
\(737\) 20.8375 0.767560
\(738\) −5.91643 −0.217787
\(739\) 10.8698 0.399853 0.199926 0.979811i \(-0.435930\pi\)
0.199926 + 0.979811i \(0.435930\pi\)
\(740\) 36.2145 1.33127
\(741\) 2.78401 0.102273
\(742\) 66.3761 2.43675
\(743\) −34.5313 −1.26683 −0.633416 0.773812i \(-0.718348\pi\)
−0.633416 + 0.773812i \(0.718348\pi\)
\(744\) 5.28343 0.193700
\(745\) −9.14408 −0.335013
\(746\) −5.70143 −0.208744
\(747\) −2.30362 −0.0842849
\(748\) −14.1176 −0.516192
\(749\) −11.0043 −0.402090
\(750\) 19.8131 0.723471
\(751\) 34.4642 1.25762 0.628809 0.777560i \(-0.283543\pi\)
0.628809 + 0.777560i \(0.283543\pi\)
\(752\) 65.1913 2.37728
\(753\) −7.13094 −0.259866
\(754\) −47.8640 −1.74311
\(755\) 2.00702 0.0730429
\(756\) 105.755 3.84627
\(757\) −22.1515 −0.805109 −0.402554 0.915396i \(-0.631878\pi\)
−0.402554 + 0.915396i \(0.631878\pi\)
\(758\) 56.5775 2.05499
\(759\) −2.22242 −0.0806689
\(760\) −3.32859 −0.120741
\(761\) −16.7417 −0.606885 −0.303443 0.952850i \(-0.598136\pi\)
−0.303443 + 0.952850i \(0.598136\pi\)
\(762\) 36.0821 1.30712
\(763\) −11.9579 −0.432903
\(764\) −91.4910 −3.31003
\(765\) −2.65539 −0.0960058
\(766\) −30.3249 −1.09568
\(767\) −56.6932 −2.04707
\(768\) −13.3516 −0.481785
\(769\) 22.0382 0.794719 0.397359 0.917663i \(-0.369927\pi\)
0.397359 + 0.917663i \(0.369927\pi\)
\(770\) −11.5083 −0.414731
\(771\) −13.6501 −0.491596
\(772\) −5.99656 −0.215821
\(773\) −20.7072 −0.744785 −0.372393 0.928075i \(-0.621463\pi\)
−0.372393 + 0.928075i \(0.621463\pi\)
\(774\) −49.8439 −1.79160
\(775\) 2.85479 0.102547
\(776\) 48.1521 1.72856
\(777\) −45.2836 −1.62454
\(778\) −34.5006 −1.23691
\(779\) −0.741048 −0.0265508
\(780\) 16.7160 0.598528
\(781\) −15.9406 −0.570398
\(782\) −7.37886 −0.263868
\(783\) −22.2960 −0.796792
\(784\) 101.767 3.63454
\(785\) −17.4291 −0.622070
\(786\) 32.2895 1.15173
\(787\) 14.7571 0.526035 0.263018 0.964791i \(-0.415282\pi\)
0.263018 + 0.964791i \(0.415282\pi\)
\(788\) 57.9440 2.06417
\(789\) 22.8372 0.813026
\(790\) 27.2153 0.968276
\(791\) 83.3426 2.96332
\(792\) −19.9914 −0.710364
\(793\) 43.5814 1.54762
\(794\) −9.88669 −0.350865
\(795\) 4.88720 0.173331
\(796\) −72.0080 −2.55226
\(797\) −17.2782 −0.612026 −0.306013 0.952027i \(-0.598995\pi\)
−0.306013 + 0.952027i \(0.598995\pi\)
\(798\) 7.04004 0.249215
\(799\) 12.7926 0.452570
\(800\) 51.1534 1.80855
\(801\) 4.25597 0.150377
\(802\) −56.7684 −2.00456
\(803\) −19.1216 −0.674786
\(804\) −76.5369 −2.69925
\(805\) −4.26966 −0.150486
\(806\) 7.19531 0.253444
\(807\) −20.5663 −0.723969
\(808\) −113.833 −4.00462
\(809\) −30.5611 −1.07447 −0.537235 0.843432i \(-0.680531\pi\)
−0.537235 + 0.843432i \(0.680531\pi\)
\(810\) 0.471122 0.0165535
\(811\) 1.40629 0.0493815 0.0246908 0.999695i \(-0.492140\pi\)
0.0246908 + 0.999695i \(0.492140\pi\)
\(812\) −85.9149 −3.01502
\(813\) −14.3974 −0.504938
\(814\) 38.3794 1.34520
\(815\) 13.5586 0.474936
\(816\) 21.9918 0.769867
\(817\) −6.24308 −0.218418
\(818\) −13.9710 −0.488485
\(819\) 32.1233 1.12248
\(820\) −4.44947 −0.155382
\(821\) −2.56990 −0.0896902 −0.0448451 0.998994i \(-0.514279\pi\)
−0.0448451 + 0.998994i \(0.514279\pi\)
\(822\) 31.7218 1.10643
\(823\) 11.2393 0.391778 0.195889 0.980626i \(-0.437241\pi\)
0.195889 + 0.980626i \(0.437241\pi\)
\(824\) 72.8552 2.53803
\(825\) 7.02864 0.244706
\(826\) −143.362 −4.98822
\(827\) −25.9668 −0.902953 −0.451477 0.892283i \(-0.649103\pi\)
−0.451477 + 0.892283i \(0.649103\pi\)
\(828\) −12.5453 −0.435980
\(829\) 22.5883 0.784524 0.392262 0.919853i \(-0.371693\pi\)
0.392262 + 0.919853i \(0.371693\pi\)
\(830\) −2.44064 −0.0847160
\(831\) −30.8916 −1.07162
\(832\) 41.9545 1.45451
\(833\) 19.9700 0.691919
\(834\) 32.2211 1.11572
\(835\) 14.5682 0.504153
\(836\) −4.23533 −0.146482
\(837\) 3.35171 0.115852
\(838\) −81.6611 −2.82094
\(839\) 13.7761 0.475602 0.237801 0.971314i \(-0.423573\pi\)
0.237801 + 0.971314i \(0.423573\pi\)
\(840\) 24.9908 0.862265
\(841\) −10.8869 −0.375409
\(842\) 1.37364 0.0473387
\(843\) 4.37268 0.150603
\(844\) −137.966 −4.74898
\(845\) 3.92421 0.134997
\(846\) 30.6406 1.05345
\(847\) 36.7298 1.26205
\(848\) 62.2046 2.13611
\(849\) 34.9421 1.19921
\(850\) 23.3364 0.800432
\(851\) 14.2390 0.488107
\(852\) 58.5502 2.00590
\(853\) −1.35058 −0.0462429 −0.0231215 0.999733i \(-0.507360\pi\)
−0.0231215 + 0.999733i \(0.507360\pi\)
\(854\) 110.206 3.77118
\(855\) −0.796623 −0.0272439
\(856\) −20.2530 −0.692234
\(857\) 37.1394 1.26866 0.634329 0.773063i \(-0.281277\pi\)
0.634329 + 0.773063i \(0.281277\pi\)
\(858\) 17.7153 0.604789
\(859\) −43.1363 −1.47179 −0.735896 0.677095i \(-0.763239\pi\)
−0.735896 + 0.677095i \(0.763239\pi\)
\(860\) −37.4853 −1.27824
\(861\) 5.56373 0.189611
\(862\) −66.6164 −2.26897
\(863\) −1.23618 −0.0420802 −0.0210401 0.999779i \(-0.506698\pi\)
−0.0210401 + 0.999779i \(0.506698\pi\)
\(864\) 60.0575 2.04320
\(865\) 10.6361 0.361637
\(866\) −81.4256 −2.76695
\(867\) −14.1713 −0.481284
\(868\) 12.9154 0.438378
\(869\) 20.4731 0.694501
\(870\) −8.91174 −0.302136
\(871\) −61.6237 −2.08804
\(872\) −22.0079 −0.745282
\(873\) 11.5241 0.390032
\(874\) −2.21368 −0.0748787
\(875\) 28.6344 0.968019
\(876\) 70.2342 2.37299
\(877\) −11.8821 −0.401229 −0.200614 0.979670i \(-0.564294\pi\)
−0.200614 + 0.979670i \(0.564294\pi\)
\(878\) 76.4818 2.58114
\(879\) −17.1241 −0.577583
\(880\) −10.7851 −0.363564
\(881\) 12.8350 0.432422 0.216211 0.976347i \(-0.430630\pi\)
0.216211 + 0.976347i \(0.430630\pi\)
\(882\) 47.8317 1.61058
\(883\) 8.18532 0.275458 0.137729 0.990470i \(-0.456020\pi\)
0.137729 + 0.990470i \(0.456020\pi\)
\(884\) 41.7507 1.40423
\(885\) −10.5556 −0.354823
\(886\) 18.0673 0.606981
\(887\) −7.41031 −0.248814 −0.124407 0.992231i \(-0.539703\pi\)
−0.124407 + 0.992231i \(0.539703\pi\)
\(888\) −83.3425 −2.79679
\(889\) 52.1468 1.74895
\(890\) 4.50913 0.151146
\(891\) 0.354408 0.0118731
\(892\) −2.23025 −0.0746744
\(893\) 3.83782 0.128428
\(894\) 35.5943 1.19045
\(895\) 0.684350 0.0228753
\(896\) 11.4886 0.383807
\(897\) 6.57248 0.219449
\(898\) 77.8531 2.59799
\(899\) −2.72292 −0.0908144
\(900\) 39.6758 1.32253
\(901\) 12.2065 0.406659
\(902\) −4.71545 −0.157007
\(903\) 46.8726 1.55982
\(904\) 153.389 5.10163
\(905\) 11.2383 0.373574
\(906\) −7.81252 −0.259554
\(907\) 46.4019 1.54075 0.770375 0.637592i \(-0.220069\pi\)
0.770375 + 0.637592i \(0.220069\pi\)
\(908\) 72.2419 2.39743
\(909\) −27.2433 −0.903602
\(910\) 34.0341 1.12822
\(911\) −57.6163 −1.90891 −0.954457 0.298350i \(-0.903564\pi\)
−0.954457 + 0.298350i \(0.903564\pi\)
\(912\) 6.59759 0.218468
\(913\) −1.83601 −0.0607629
\(914\) −38.6592 −1.27873
\(915\) 8.11436 0.268253
\(916\) 53.2055 1.75796
\(917\) 46.6657 1.54104
\(918\) 27.3985 0.904285
\(919\) 31.7158 1.04621 0.523104 0.852269i \(-0.324774\pi\)
0.523104 + 0.852269i \(0.324774\pi\)
\(920\) −7.85814 −0.259075
\(921\) 15.4132 0.507882
\(922\) 38.4807 1.26729
\(923\) 47.1417 1.55169
\(924\) 31.7985 1.04609
\(925\) −45.0323 −1.48065
\(926\) 73.3209 2.40947
\(927\) 17.4362 0.572681
\(928\) −48.7905 −1.60163
\(929\) −7.50547 −0.246246 −0.123123 0.992391i \(-0.539291\pi\)
−0.123123 + 0.992391i \(0.539291\pi\)
\(930\) 1.33969 0.0439300
\(931\) 5.99104 0.196349
\(932\) −118.373 −3.87744
\(933\) 7.22300 0.236470
\(934\) 98.4950 3.22286
\(935\) −2.11637 −0.0692128
\(936\) 59.1215 1.93245
\(937\) 28.8016 0.940906 0.470453 0.882425i \(-0.344091\pi\)
0.470453 + 0.882425i \(0.344091\pi\)
\(938\) −155.831 −5.08805
\(939\) −20.7393 −0.676802
\(940\) 23.0434 0.751592
\(941\) 5.22681 0.170389 0.0851945 0.996364i \(-0.472849\pi\)
0.0851945 + 0.996364i \(0.472849\pi\)
\(942\) 67.8444 2.21049
\(943\) −1.74946 −0.0569704
\(944\) −134.353 −4.37280
\(945\) 15.8537 0.515721
\(946\) −39.7261 −1.29161
\(947\) 1.56923 0.0509931 0.0254966 0.999675i \(-0.491883\pi\)
0.0254966 + 0.999675i \(0.491883\pi\)
\(948\) −75.1982 −2.44232
\(949\) 56.5491 1.83566
\(950\) 7.00097 0.227142
\(951\) 9.20331 0.298438
\(952\) 62.4184 2.02299
\(953\) −45.1574 −1.46279 −0.731396 0.681953i \(-0.761131\pi\)
−0.731396 + 0.681953i \(0.761131\pi\)
\(954\) 29.2368 0.946577
\(955\) −13.7154 −0.443820
\(956\) −91.8987 −2.97222
\(957\) −6.70397 −0.216709
\(958\) −39.9037 −1.28923
\(959\) 45.8453 1.48042
\(960\) 7.81145 0.252113
\(961\) −30.5907 −0.986796
\(962\) −113.501 −3.65942
\(963\) −4.84710 −0.156196
\(964\) −121.042 −3.89851
\(965\) −0.898944 −0.0289380
\(966\) 16.6201 0.534743
\(967\) −22.7568 −0.731809 −0.365905 0.930652i \(-0.619240\pi\)
−0.365905 + 0.930652i \(0.619240\pi\)
\(968\) 67.5996 2.17273
\(969\) 1.29466 0.0415904
\(970\) 12.2096 0.392027
\(971\) −48.2255 −1.54763 −0.773814 0.633412i \(-0.781654\pi\)
−0.773814 + 0.633412i \(0.781654\pi\)
\(972\) 75.5905 2.42457
\(973\) 46.5668 1.49286
\(974\) 57.6527 1.84731
\(975\) −20.7861 −0.665689
\(976\) 103.280 3.30592
\(977\) 1.41093 0.0451395 0.0225698 0.999745i \(-0.492815\pi\)
0.0225698 + 0.999745i \(0.492815\pi\)
\(978\) −52.7781 −1.68766
\(979\) 3.39205 0.108410
\(980\) 35.9720 1.14908
\(981\) −5.26710 −0.168165
\(982\) −28.6612 −0.914617
\(983\) −18.3208 −0.584344 −0.292172 0.956366i \(-0.594378\pi\)
−0.292172 + 0.956366i \(0.594378\pi\)
\(984\) 10.2398 0.326433
\(985\) 8.68638 0.276771
\(986\) −22.2584 −0.708853
\(987\) −28.8140 −0.917161
\(988\) 12.5253 0.398484
\(989\) −14.7387 −0.468662
\(990\) −5.06909 −0.161106
\(991\) 3.18882 0.101296 0.0506481 0.998717i \(-0.483871\pi\)
0.0506481 + 0.998717i \(0.483871\pi\)
\(992\) 7.33459 0.232873
\(993\) −1.86024 −0.0590329
\(994\) 119.209 3.78109
\(995\) −10.7947 −0.342215
\(996\) 6.74371 0.213683
\(997\) 24.4181 0.773328 0.386664 0.922221i \(-0.373627\pi\)
0.386664 + 0.922221i \(0.373627\pi\)
\(998\) 84.0530 2.66065
\(999\) −52.8709 −1.67276
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 4001.2.a.a.1.5 149
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4001.2.a.a.1.5 149 1.1 even 1 trivial