Properties

Label 6019.2.a.d.1.15
Level $6019$
Weight $2$
Character 6019.1
Self dual yes
Analytic conductor $48.062$
Analytic rank $0$
Dimension $123$
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] = [6019,2,Mod(1,6019)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6019, 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("6019.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6019 = 13 \cdot 463 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6019.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: \(48.0619569766\)
Analytic rank: \(0\)
Dimension: \(123\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 6019.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.22237 q^{2} +3.41646 q^{3} +2.93895 q^{4} +1.79804 q^{5} -7.59266 q^{6} +3.28634 q^{7} -2.08670 q^{8} +8.67221 q^{9} +O(q^{10})\) \(q-2.22237 q^{2} +3.41646 q^{3} +2.93895 q^{4} +1.79804 q^{5} -7.59266 q^{6} +3.28634 q^{7} -2.08670 q^{8} +8.67221 q^{9} -3.99592 q^{10} -4.05989 q^{11} +10.0408 q^{12} -1.00000 q^{13} -7.30349 q^{14} +6.14293 q^{15} -1.24047 q^{16} -4.46412 q^{17} -19.2729 q^{18} +0.417933 q^{19} +5.28435 q^{20} +11.2277 q^{21} +9.02260 q^{22} +4.47938 q^{23} -7.12912 q^{24} -1.76705 q^{25} +2.22237 q^{26} +19.3789 q^{27} +9.65840 q^{28} +5.39566 q^{29} -13.6519 q^{30} +3.46752 q^{31} +6.93020 q^{32} -13.8705 q^{33} +9.92095 q^{34} +5.90898 q^{35} +25.4872 q^{36} +1.78289 q^{37} -0.928805 q^{38} -3.41646 q^{39} -3.75197 q^{40} +1.09922 q^{41} -24.9521 q^{42} -7.80801 q^{43} -11.9318 q^{44} +15.5930 q^{45} -9.95485 q^{46} +11.2703 q^{47} -4.23804 q^{48} +3.80005 q^{49} +3.92705 q^{50} -15.2515 q^{51} -2.93895 q^{52} -13.1278 q^{53} -43.0672 q^{54} -7.29985 q^{55} -6.85761 q^{56} +1.42785 q^{57} -11.9912 q^{58} +11.8757 q^{59} +18.0538 q^{60} -4.80558 q^{61} -7.70613 q^{62} +28.4999 q^{63} -12.9205 q^{64} -1.79804 q^{65} +30.8254 q^{66} -6.97405 q^{67} -13.1198 q^{68} +15.3036 q^{69} -13.1320 q^{70} -5.74506 q^{71} -18.0963 q^{72} -4.06268 q^{73} -3.96226 q^{74} -6.03707 q^{75} +1.22829 q^{76} -13.3422 q^{77} +7.59266 q^{78} +14.0395 q^{79} -2.23042 q^{80} +40.1906 q^{81} -2.44289 q^{82} +10.5828 q^{83} +32.9976 q^{84} -8.02667 q^{85} +17.3523 q^{86} +18.4341 q^{87} +8.47177 q^{88} +9.73193 q^{89} -34.6535 q^{90} -3.28634 q^{91} +13.1647 q^{92} +11.8466 q^{93} -25.0468 q^{94} +0.751461 q^{95} +23.6768 q^{96} +19.3207 q^{97} -8.44515 q^{98} -35.2082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22237 −1.57146 −0.785728 0.618572i \(-0.787712\pi\)
−0.785728 + 0.618572i \(0.787712\pi\)
\(3\) 3.41646 1.97250 0.986248 0.165274i \(-0.0528509\pi\)
0.986248 + 0.165274i \(0.0528509\pi\)
\(4\) 2.93895 1.46947
\(5\) 1.79804 0.804108 0.402054 0.915616i \(-0.368296\pi\)
0.402054 + 0.915616i \(0.368296\pi\)
\(6\) −7.59266 −3.09969
\(7\) 3.28634 1.24212 0.621061 0.783763i \(-0.286702\pi\)
0.621061 + 0.783763i \(0.286702\pi\)
\(8\) −2.08670 −0.737759
\(9\) 8.67221 2.89074
\(10\) −3.99592 −1.26362
\(11\) −4.05989 −1.22410 −0.612052 0.790818i \(-0.709656\pi\)
−0.612052 + 0.790818i \(0.709656\pi\)
\(12\) 10.0408 2.89853
\(13\) −1.00000 −0.277350
\(14\) −7.30349 −1.95194
\(15\) 6.14293 1.58610
\(16\) −1.24047 −0.310119
\(17\) −4.46412 −1.08271 −0.541354 0.840794i \(-0.682088\pi\)
−0.541354 + 0.840794i \(0.682088\pi\)
\(18\) −19.2729 −4.54267
\(19\) 0.417933 0.0958805 0.0479402 0.998850i \(-0.484734\pi\)
0.0479402 + 0.998850i \(0.484734\pi\)
\(20\) 5.28435 1.18162
\(21\) 11.2277 2.45008
\(22\) 9.02260 1.92362
\(23\) 4.47938 0.934014 0.467007 0.884254i \(-0.345332\pi\)
0.467007 + 0.884254i \(0.345332\pi\)
\(24\) −7.12912 −1.45523
\(25\) −1.76705 −0.353411
\(26\) 2.22237 0.435844
\(27\) 19.3789 3.72947
\(28\) 9.65840 1.82527
\(29\) 5.39566 1.00195 0.500975 0.865462i \(-0.332975\pi\)
0.500975 + 0.865462i \(0.332975\pi\)
\(30\) −13.6519 −2.49249
\(31\) 3.46752 0.622785 0.311392 0.950281i \(-0.399205\pi\)
0.311392 + 0.950281i \(0.399205\pi\)
\(32\) 6.93020 1.22510
\(33\) −13.8705 −2.41454
\(34\) 9.92095 1.70143
\(35\) 5.90898 0.998799
\(36\) 25.4872 4.24787
\(37\) 1.78289 0.293106 0.146553 0.989203i \(-0.453182\pi\)
0.146553 + 0.989203i \(0.453182\pi\)
\(38\) −0.928805 −0.150672
\(39\) −3.41646 −0.547072
\(40\) −3.75197 −0.593238
\(41\) 1.09922 0.171670 0.0858351 0.996309i \(-0.472644\pi\)
0.0858351 + 0.996309i \(0.472644\pi\)
\(42\) −24.9521 −3.85019
\(43\) −7.80801 −1.19071 −0.595355 0.803463i \(-0.702989\pi\)
−0.595355 + 0.803463i \(0.702989\pi\)
\(44\) −11.9318 −1.79879
\(45\) 15.5930 2.32447
\(46\) −9.95485 −1.46776
\(47\) 11.2703 1.64394 0.821969 0.569532i \(-0.192876\pi\)
0.821969 + 0.569532i \(0.192876\pi\)
\(48\) −4.23804 −0.611708
\(49\) 3.80005 0.542865
\(50\) 3.92705 0.555369
\(51\) −15.2515 −2.13564
\(52\) −2.93895 −0.407559
\(53\) −13.1278 −1.80324 −0.901618 0.432532i \(-0.857620\pi\)
−0.901618 + 0.432532i \(0.857620\pi\)
\(54\) −43.0672 −5.86070
\(55\) −7.29985 −0.984311
\(56\) −6.85761 −0.916386
\(57\) 1.42785 0.189124
\(58\) −11.9912 −1.57452
\(59\) 11.8757 1.54608 0.773041 0.634357i \(-0.218735\pi\)
0.773041 + 0.634357i \(0.218735\pi\)
\(60\) 18.0538 2.33073
\(61\) −4.80558 −0.615292 −0.307646 0.951501i \(-0.599541\pi\)
−0.307646 + 0.951501i \(0.599541\pi\)
\(62\) −7.70613 −0.978679
\(63\) 28.4999 3.59065
\(64\) −12.9205 −1.61507
\(65\) −1.79804 −0.223019
\(66\) 30.8254 3.79434
\(67\) −6.97405 −0.852016 −0.426008 0.904719i \(-0.640080\pi\)
−0.426008 + 0.904719i \(0.640080\pi\)
\(68\) −13.1198 −1.59101
\(69\) 15.3036 1.84234
\(70\) −13.1320 −1.56957
\(71\) −5.74506 −0.681813 −0.340907 0.940097i \(-0.610734\pi\)
−0.340907 + 0.940097i \(0.610734\pi\)
\(72\) −18.0963 −2.13267
\(73\) −4.06268 −0.475500 −0.237750 0.971326i \(-0.576410\pi\)
−0.237750 + 0.971326i \(0.576410\pi\)
\(74\) −3.96226 −0.460603
\(75\) −6.03707 −0.697101
\(76\) 1.22829 0.140894
\(77\) −13.3422 −1.52048
\(78\) 7.59266 0.859699
\(79\) 14.0395 1.57956 0.789782 0.613388i \(-0.210194\pi\)
0.789782 + 0.613388i \(0.210194\pi\)
\(80\) −2.23042 −0.249369
\(81\) 40.1906 4.46563
\(82\) −2.44289 −0.269772
\(83\) 10.5828 1.16161 0.580804 0.814043i \(-0.302738\pi\)
0.580804 + 0.814043i \(0.302738\pi\)
\(84\) 32.9976 3.60033
\(85\) −8.02667 −0.870615
\(86\) 17.3523 1.87115
\(87\) 18.4341 1.97634
\(88\) 8.47177 0.903093
\(89\) 9.73193 1.03158 0.515791 0.856714i \(-0.327498\pi\)
0.515791 + 0.856714i \(0.327498\pi\)
\(90\) −34.6535 −3.65280
\(91\) −3.28634 −0.344502
\(92\) 13.1647 1.37251
\(93\) 11.8466 1.22844
\(94\) −25.0468 −2.58338
\(95\) 0.751461 0.0770983
\(96\) 23.6768 2.41650
\(97\) 19.3207 1.96172 0.980858 0.194722i \(-0.0623805\pi\)
0.980858 + 0.194722i \(0.0623805\pi\)
\(98\) −8.44515 −0.853089
\(99\) −35.2082 −3.53856
\(100\) −5.19328 −0.519328
\(101\) −2.68935 −0.267601 −0.133800 0.991008i \(-0.542718\pi\)
−0.133800 + 0.991008i \(0.542718\pi\)
\(102\) 33.8946 3.35606
\(103\) 7.46169 0.735222 0.367611 0.929980i \(-0.380176\pi\)
0.367611 + 0.929980i \(0.380176\pi\)
\(104\) 2.08670 0.204618
\(105\) 20.1878 1.97013
\(106\) 29.1748 2.83371
\(107\) 20.0130 1.93473 0.967363 0.253393i \(-0.0815467\pi\)
0.967363 + 0.253393i \(0.0815467\pi\)
\(108\) 56.9536 5.48036
\(109\) −11.9153 −1.14128 −0.570638 0.821201i \(-0.693304\pi\)
−0.570638 + 0.821201i \(0.693304\pi\)
\(110\) 16.2230 1.54680
\(111\) 6.09119 0.578150
\(112\) −4.07663 −0.385205
\(113\) −8.41299 −0.791427 −0.395714 0.918374i \(-0.629503\pi\)
−0.395714 + 0.918374i \(0.629503\pi\)
\(114\) −3.17323 −0.297200
\(115\) 8.05409 0.751048
\(116\) 15.8576 1.47234
\(117\) −8.67221 −0.801746
\(118\) −26.3922 −2.42960
\(119\) −14.6706 −1.34486
\(120\) −12.8184 −1.17016
\(121\) 5.48272 0.498429
\(122\) 10.6798 0.966904
\(123\) 3.75546 0.338618
\(124\) 10.1909 0.915167
\(125\) −12.1674 −1.08829
\(126\) −63.3374 −5.64254
\(127\) 1.14769 0.101841 0.0509204 0.998703i \(-0.483785\pi\)
0.0509204 + 0.998703i \(0.483785\pi\)
\(128\) 14.8539 1.31291
\(129\) −26.6758 −2.34867
\(130\) 3.99592 0.350465
\(131\) 14.9017 1.30197 0.650986 0.759090i \(-0.274356\pi\)
0.650986 + 0.759090i \(0.274356\pi\)
\(132\) −40.7646 −3.54810
\(133\) 1.37347 0.119095
\(134\) 15.4989 1.33891
\(135\) 34.8440 2.99890
\(136\) 9.31528 0.798778
\(137\) 13.2206 1.12951 0.564757 0.825257i \(-0.308970\pi\)
0.564757 + 0.825257i \(0.308970\pi\)
\(138\) −34.0104 −2.89515
\(139\) −16.6683 −1.41379 −0.706895 0.707318i \(-0.749905\pi\)
−0.706895 + 0.707318i \(0.749905\pi\)
\(140\) 17.3662 1.46771
\(141\) 38.5045 3.24266
\(142\) 12.7677 1.07144
\(143\) 4.05989 0.339505
\(144\) −10.7577 −0.896472
\(145\) 9.70162 0.805675
\(146\) 9.02879 0.747228
\(147\) 12.9827 1.07080
\(148\) 5.23983 0.430712
\(149\) 21.1768 1.73487 0.867436 0.497549i \(-0.165766\pi\)
0.867436 + 0.497549i \(0.165766\pi\)
\(150\) 13.4166 1.09546
\(151\) 1.85169 0.150689 0.0753443 0.997158i \(-0.475994\pi\)
0.0753443 + 0.997158i \(0.475994\pi\)
\(152\) −0.872101 −0.0707367
\(153\) −38.7138 −3.12983
\(154\) 29.6514 2.38938
\(155\) 6.23474 0.500786
\(156\) −10.0408 −0.803908
\(157\) −22.8449 −1.82322 −0.911610 0.411056i \(-0.865160\pi\)
−0.911610 + 0.411056i \(0.865160\pi\)
\(158\) −31.2010 −2.48221
\(159\) −44.8505 −3.55688
\(160\) 12.4608 0.985110
\(161\) 14.7208 1.16016
\(162\) −89.3187 −7.01754
\(163\) 6.70912 0.525499 0.262749 0.964864i \(-0.415371\pi\)
0.262749 + 0.964864i \(0.415371\pi\)
\(164\) 3.23057 0.252265
\(165\) −24.9397 −1.94155
\(166\) −23.5189 −1.82542
\(167\) −6.30922 −0.488222 −0.244111 0.969747i \(-0.578496\pi\)
−0.244111 + 0.969747i \(0.578496\pi\)
\(168\) −23.4287 −1.80757
\(169\) 1.00000 0.0769231
\(170\) 17.8383 1.36813
\(171\) 3.62441 0.277165
\(172\) −22.9473 −1.74972
\(173\) −16.0129 −1.21744 −0.608719 0.793386i \(-0.708316\pi\)
−0.608719 + 0.793386i \(0.708316\pi\)
\(174\) −40.9674 −3.10573
\(175\) −5.80714 −0.438979
\(176\) 5.03619 0.379617
\(177\) 40.5728 3.04964
\(178\) −21.6280 −1.62109
\(179\) 20.2620 1.51445 0.757225 0.653154i \(-0.226555\pi\)
0.757225 + 0.653154i \(0.226555\pi\)
\(180\) 45.8270 3.41574
\(181\) −9.23200 −0.686209 −0.343105 0.939297i \(-0.611479\pi\)
−0.343105 + 0.939297i \(0.611479\pi\)
\(182\) 7.30349 0.541370
\(183\) −16.4181 −1.21366
\(184\) −9.34710 −0.689077
\(185\) 3.20571 0.235689
\(186\) −26.3277 −1.93044
\(187\) 18.1239 1.32535
\(188\) 33.1228 2.41573
\(189\) 63.6857 4.63246
\(190\) −1.67003 −0.121157
\(191\) 18.8404 1.36324 0.681622 0.731705i \(-0.261275\pi\)
0.681622 + 0.731705i \(0.261275\pi\)
\(192\) −44.1425 −3.18571
\(193\) −12.7373 −0.916849 −0.458425 0.888733i \(-0.651586\pi\)
−0.458425 + 0.888733i \(0.651586\pi\)
\(194\) −42.9378 −3.08275
\(195\) −6.14293 −0.439905
\(196\) 11.1682 0.797726
\(197\) −3.36172 −0.239513 −0.119756 0.992803i \(-0.538211\pi\)
−0.119756 + 0.992803i \(0.538211\pi\)
\(198\) 78.2459 5.56070
\(199\) 24.0099 1.70202 0.851010 0.525150i \(-0.175991\pi\)
0.851010 + 0.525150i \(0.175991\pi\)
\(200\) 3.68730 0.260732
\(201\) −23.8266 −1.68060
\(202\) 5.97675 0.420523
\(203\) 17.7320 1.24454
\(204\) −44.8234 −3.13827
\(205\) 1.97645 0.138041
\(206\) −16.5827 −1.15537
\(207\) 38.8461 2.69999
\(208\) 1.24047 0.0860115
\(209\) −1.69676 −0.117368
\(210\) −44.8648 −3.09597
\(211\) −4.72483 −0.325271 −0.162635 0.986686i \(-0.551999\pi\)
−0.162635 + 0.986686i \(0.551999\pi\)
\(212\) −38.5818 −2.64981
\(213\) −19.6278 −1.34487
\(214\) −44.4763 −3.04034
\(215\) −14.0391 −0.957459
\(216\) −40.4379 −2.75145
\(217\) 11.3955 0.773574
\(218\) 26.4802 1.79347
\(219\) −13.8800 −0.937922
\(220\) −21.4539 −1.44642
\(221\) 4.46412 0.300289
\(222\) −13.5369 −0.908537
\(223\) −13.9942 −0.937124 −0.468562 0.883431i \(-0.655228\pi\)
−0.468562 + 0.883431i \(0.655228\pi\)
\(224\) 22.7750 1.52172
\(225\) −15.3243 −1.02162
\(226\) 18.6968 1.24369
\(227\) 15.6265 1.03717 0.518584 0.855027i \(-0.326459\pi\)
0.518584 + 0.855027i \(0.326459\pi\)
\(228\) 4.19639 0.277913
\(229\) 11.1960 0.739855 0.369927 0.929061i \(-0.379383\pi\)
0.369927 + 0.929061i \(0.379383\pi\)
\(230\) −17.8992 −1.18024
\(231\) −45.5831 −2.99915
\(232\) −11.2591 −0.739197
\(233\) −20.0152 −1.31124 −0.655619 0.755092i \(-0.727592\pi\)
−0.655619 + 0.755092i \(0.727592\pi\)
\(234\) 19.2729 1.25991
\(235\) 20.2644 1.32190
\(236\) 34.9020 2.27193
\(237\) 47.9653 3.11568
\(238\) 32.6037 2.11338
\(239\) −26.4183 −1.70886 −0.854430 0.519566i \(-0.826094\pi\)
−0.854430 + 0.519566i \(0.826094\pi\)
\(240\) −7.62016 −0.491879
\(241\) −25.0808 −1.61560 −0.807798 0.589459i \(-0.799341\pi\)
−0.807798 + 0.589459i \(0.799341\pi\)
\(242\) −12.1847 −0.783260
\(243\) 79.1731 5.07896
\(244\) −14.1234 −0.904156
\(245\) 6.83265 0.436522
\(246\) −8.34604 −0.532124
\(247\) −0.417933 −0.0265925
\(248\) −7.23566 −0.459465
\(249\) 36.1556 2.29127
\(250\) 27.0406 1.71020
\(251\) −2.58320 −0.163050 −0.0815252 0.996671i \(-0.525979\pi\)
−0.0815252 + 0.996671i \(0.525979\pi\)
\(252\) 83.7597 5.27636
\(253\) −18.1858 −1.14333
\(254\) −2.55059 −0.160038
\(255\) −27.4228 −1.71728
\(256\) −7.16984 −0.448115
\(257\) −10.8616 −0.677525 −0.338763 0.940872i \(-0.610008\pi\)
−0.338763 + 0.940872i \(0.610008\pi\)
\(258\) 59.2835 3.69083
\(259\) 5.85920 0.364073
\(260\) −5.28435 −0.327721
\(261\) 46.7923 2.89637
\(262\) −33.1173 −2.04599
\(263\) −23.2838 −1.43574 −0.717869 0.696178i \(-0.754882\pi\)
−0.717869 + 0.696178i \(0.754882\pi\)
\(264\) 28.9435 1.78135
\(265\) −23.6042 −1.45000
\(266\) −3.05237 −0.187153
\(267\) 33.2488 2.03479
\(268\) −20.4964 −1.25202
\(269\) −10.2088 −0.622439 −0.311219 0.950338i \(-0.600737\pi\)
−0.311219 + 0.950338i \(0.600737\pi\)
\(270\) −77.4365 −4.71264
\(271\) 5.61223 0.340918 0.170459 0.985365i \(-0.445475\pi\)
0.170459 + 0.985365i \(0.445475\pi\)
\(272\) 5.53763 0.335768
\(273\) −11.2277 −0.679529
\(274\) −29.3812 −1.77498
\(275\) 7.17404 0.432611
\(276\) 44.9766 2.70727
\(277\) −2.07933 −0.124935 −0.0624673 0.998047i \(-0.519897\pi\)
−0.0624673 + 0.998047i \(0.519897\pi\)
\(278\) 37.0433 2.22171
\(279\) 30.0711 1.80031
\(280\) −12.3302 −0.736873
\(281\) 9.70074 0.578698 0.289349 0.957224i \(-0.406561\pi\)
0.289349 + 0.957224i \(0.406561\pi\)
\(282\) −85.5713 −5.09570
\(283\) −16.4112 −0.975544 −0.487772 0.872971i \(-0.662190\pi\)
−0.487772 + 0.872971i \(0.662190\pi\)
\(284\) −16.8844 −1.00191
\(285\) 2.56734 0.152076
\(286\) −9.02260 −0.533518
\(287\) 3.61243 0.213235
\(288\) 60.1001 3.54143
\(289\) 2.92840 0.172259
\(290\) −21.5606 −1.26608
\(291\) 66.0083 3.86948
\(292\) −11.9400 −0.698736
\(293\) 4.79139 0.279916 0.139958 0.990157i \(-0.455303\pi\)
0.139958 + 0.990157i \(0.455303\pi\)
\(294\) −28.8525 −1.68271
\(295\) 21.3529 1.24322
\(296\) −3.72036 −0.216242
\(297\) −78.6762 −4.56526
\(298\) −47.0628 −2.72628
\(299\) −4.47938 −0.259049
\(300\) −17.7426 −1.02437
\(301\) −25.6598 −1.47901
\(302\) −4.11515 −0.236801
\(303\) −9.18807 −0.527841
\(304\) −0.518436 −0.0297343
\(305\) −8.64063 −0.494761
\(306\) 86.0366 4.91839
\(307\) 23.7475 1.35534 0.677671 0.735365i \(-0.262989\pi\)
0.677671 + 0.735365i \(0.262989\pi\)
\(308\) −39.2120 −2.23431
\(309\) 25.4926 1.45022
\(310\) −13.8559 −0.786964
\(311\) −30.2359 −1.71452 −0.857261 0.514882i \(-0.827836\pi\)
−0.857261 + 0.514882i \(0.827836\pi\)
\(312\) 7.12912 0.403607
\(313\) 16.9689 0.959137 0.479569 0.877504i \(-0.340793\pi\)
0.479569 + 0.877504i \(0.340793\pi\)
\(314\) 50.7699 2.86511
\(315\) 51.2439 2.88727
\(316\) 41.2613 2.32113
\(317\) 14.4572 0.811997 0.405999 0.913874i \(-0.366924\pi\)
0.405999 + 0.913874i \(0.366924\pi\)
\(318\) 99.6746 5.58948
\(319\) −21.9058 −1.22649
\(320\) −23.2316 −1.29869
\(321\) 68.3735 3.81624
\(322\) −32.7151 −1.82314
\(323\) −1.86571 −0.103811
\(324\) 118.118 6.56213
\(325\) 1.76705 0.0980185
\(326\) −14.9102 −0.825798
\(327\) −40.7081 −2.25116
\(328\) −2.29375 −0.126651
\(329\) 37.0380 2.04197
\(330\) 55.4252 3.05106
\(331\) −14.8197 −0.814567 −0.407283 0.913302i \(-0.633524\pi\)
−0.407283 + 0.913302i \(0.633524\pi\)
\(332\) 31.1022 1.70695
\(333\) 15.4616 0.847292
\(334\) 14.0215 0.767220
\(335\) −12.5396 −0.685112
\(336\) −13.9276 −0.759815
\(337\) −22.6703 −1.23493 −0.617464 0.786599i \(-0.711840\pi\)
−0.617464 + 0.786599i \(0.711840\pi\)
\(338\) −2.22237 −0.120881
\(339\) −28.7427 −1.56109
\(340\) −23.5900 −1.27935
\(341\) −14.0778 −0.762353
\(342\) −8.05479 −0.435553
\(343\) −10.5161 −0.567817
\(344\) 16.2929 0.878457
\(345\) 27.5165 1.48144
\(346\) 35.5867 1.91315
\(347\) 13.5698 0.728463 0.364232 0.931308i \(-0.381332\pi\)
0.364232 + 0.931308i \(0.381332\pi\)
\(348\) 54.1768 2.90418
\(349\) −30.2693 −1.62028 −0.810140 0.586236i \(-0.800609\pi\)
−0.810140 + 0.586236i \(0.800609\pi\)
\(350\) 12.9056 0.689836
\(351\) −19.3789 −1.03437
\(352\) −28.1358 −1.49965
\(353\) −20.6705 −1.10018 −0.550090 0.835105i \(-0.685407\pi\)
−0.550090 + 0.835105i \(0.685407\pi\)
\(354\) −90.1679 −4.79237
\(355\) −10.3298 −0.548251
\(356\) 28.6016 1.51588
\(357\) −50.1217 −2.65272
\(358\) −45.0297 −2.37989
\(359\) −17.2013 −0.907850 −0.453925 0.891040i \(-0.649977\pi\)
−0.453925 + 0.891040i \(0.649977\pi\)
\(360\) −32.5378 −1.71490
\(361\) −18.8253 −0.990807
\(362\) 20.5170 1.07835
\(363\) 18.7315 0.983149
\(364\) −9.65840 −0.506238
\(365\) −7.30485 −0.382353
\(366\) 36.4871 1.90721
\(367\) −7.83476 −0.408971 −0.204485 0.978870i \(-0.565552\pi\)
−0.204485 + 0.978870i \(0.565552\pi\)
\(368\) −5.55655 −0.289655
\(369\) 9.53271 0.496253
\(370\) −7.12430 −0.370375
\(371\) −43.1423 −2.23984
\(372\) 34.8167 1.80516
\(373\) 21.2783 1.10175 0.550876 0.834587i \(-0.314294\pi\)
0.550876 + 0.834587i \(0.314294\pi\)
\(374\) −40.2780 −2.08273
\(375\) −41.5696 −2.14664
\(376\) −23.5177 −1.21283
\(377\) −5.39566 −0.277891
\(378\) −141.534 −7.27970
\(379\) 15.5519 0.798847 0.399423 0.916767i \(-0.369210\pi\)
0.399423 + 0.916767i \(0.369210\pi\)
\(380\) 2.20851 0.113294
\(381\) 3.92103 0.200881
\(382\) −41.8704 −2.14228
\(383\) 9.84593 0.503103 0.251552 0.967844i \(-0.419059\pi\)
0.251552 + 0.967844i \(0.419059\pi\)
\(384\) 50.7478 2.58971
\(385\) −23.9898 −1.22263
\(386\) 28.3070 1.44079
\(387\) −67.7127 −3.44203
\(388\) 56.7825 2.88269
\(389\) −15.4843 −0.785085 −0.392542 0.919734i \(-0.628404\pi\)
−0.392542 + 0.919734i \(0.628404\pi\)
\(390\) 13.6519 0.691291
\(391\) −19.9965 −1.01127
\(392\) −7.92956 −0.400504
\(393\) 50.9113 2.56813
\(394\) 7.47101 0.376384
\(395\) 25.2435 1.27014
\(396\) −103.475 −5.19983
\(397\) 10.2481 0.514336 0.257168 0.966367i \(-0.417211\pi\)
0.257168 + 0.966367i \(0.417211\pi\)
\(398\) −53.3591 −2.67465
\(399\) 4.69242 0.234915
\(400\) 2.19198 0.109599
\(401\) −17.6518 −0.881488 −0.440744 0.897633i \(-0.645285\pi\)
−0.440744 + 0.897633i \(0.645285\pi\)
\(402\) 52.9516 2.64098
\(403\) −3.46752 −0.172729
\(404\) −7.90387 −0.393232
\(405\) 72.2644 3.59085
\(406\) −39.4072 −1.95574
\(407\) −7.23835 −0.358792
\(408\) 31.8253 1.57559
\(409\) −11.8531 −0.586099 −0.293050 0.956097i \(-0.594670\pi\)
−0.293050 + 0.956097i \(0.594670\pi\)
\(410\) −4.39241 −0.216926
\(411\) 45.1678 2.22796
\(412\) 21.9295 1.08039
\(413\) 39.0275 1.92042
\(414\) −86.3306 −4.24292
\(415\) 19.0282 0.934059
\(416\) −6.93020 −0.339781
\(417\) −56.9468 −2.78870
\(418\) 3.77085 0.184438
\(419\) 1.88470 0.0920738 0.0460369 0.998940i \(-0.485341\pi\)
0.0460369 + 0.998940i \(0.485341\pi\)
\(420\) 59.3309 2.89505
\(421\) −12.8246 −0.625035 −0.312518 0.949912i \(-0.601172\pi\)
−0.312518 + 0.949912i \(0.601172\pi\)
\(422\) 10.5003 0.511148
\(423\) 97.7382 4.75219
\(424\) 27.3937 1.33035
\(425\) 7.88834 0.382641
\(426\) 43.6203 2.11341
\(427\) −15.7928 −0.764267
\(428\) 58.8171 2.84303
\(429\) 13.8705 0.669672
\(430\) 31.2002 1.50461
\(431\) −7.16635 −0.345191 −0.172596 0.984993i \(-0.555215\pi\)
−0.172596 + 0.984993i \(0.555215\pi\)
\(432\) −24.0390 −1.15658
\(433\) −2.01706 −0.0969337 −0.0484668 0.998825i \(-0.515434\pi\)
−0.0484668 + 0.998825i \(0.515434\pi\)
\(434\) −25.3250 −1.21564
\(435\) 33.1452 1.58919
\(436\) −35.0184 −1.67708
\(437\) 1.87208 0.0895538
\(438\) 30.8465 1.47390
\(439\) −3.68912 −0.176072 −0.0880360 0.996117i \(-0.528059\pi\)
−0.0880360 + 0.996117i \(0.528059\pi\)
\(440\) 15.2326 0.726184
\(441\) 32.9549 1.56928
\(442\) −9.92095 −0.471892
\(443\) −8.36432 −0.397401 −0.198700 0.980060i \(-0.563672\pi\)
−0.198700 + 0.980060i \(0.563672\pi\)
\(444\) 17.9017 0.849577
\(445\) 17.4984 0.829504
\(446\) 31.1004 1.47265
\(447\) 72.3498 3.42203
\(448\) −42.4613 −2.00611
\(449\) 2.94379 0.138926 0.0694629 0.997585i \(-0.477871\pi\)
0.0694629 + 0.997585i \(0.477871\pi\)
\(450\) 34.0562 1.60543
\(451\) −4.46273 −0.210142
\(452\) −24.7253 −1.16298
\(453\) 6.32624 0.297233
\(454\) −34.7280 −1.62986
\(455\) −5.90898 −0.277017
\(456\) −2.97950 −0.139528
\(457\) 12.7984 0.598686 0.299343 0.954146i \(-0.403233\pi\)
0.299343 + 0.954146i \(0.403233\pi\)
\(458\) −24.8818 −1.16265
\(459\) −86.5098 −4.03793
\(460\) 23.6706 1.10365
\(461\) 8.19307 0.381589 0.190795 0.981630i \(-0.438894\pi\)
0.190795 + 0.981630i \(0.438894\pi\)
\(462\) 101.303 4.71303
\(463\) 1.00000 0.0464739
\(464\) −6.69319 −0.310723
\(465\) 21.3007 0.987798
\(466\) 44.4812 2.06055
\(467\) −18.2894 −0.846332 −0.423166 0.906052i \(-0.639081\pi\)
−0.423166 + 0.906052i \(0.639081\pi\)
\(468\) −25.4872 −1.17815
\(469\) −22.9191 −1.05831
\(470\) −45.0351 −2.07731
\(471\) −78.0487 −3.59629
\(472\) −24.7809 −1.14064
\(473\) 31.6997 1.45755
\(474\) −106.597 −4.89616
\(475\) −0.738510 −0.0338852
\(476\) −43.1163 −1.97623
\(477\) −113.847 −5.21268
\(478\) 58.7115 2.68540
\(479\) −30.1722 −1.37860 −0.689301 0.724475i \(-0.742082\pi\)
−0.689301 + 0.724475i \(0.742082\pi\)
\(480\) 42.5717 1.94313
\(481\) −1.78289 −0.0812929
\(482\) 55.7389 2.53884
\(483\) 50.2929 2.28841
\(484\) 16.1134 0.732429
\(485\) 34.7393 1.57743
\(486\) −175.952 −7.98136
\(487\) 10.0469 0.455269 0.227635 0.973747i \(-0.426901\pi\)
0.227635 + 0.973747i \(0.426901\pi\)
\(488\) 10.0278 0.453937
\(489\) 22.9214 1.03654
\(490\) −15.1847 −0.685975
\(491\) −24.0537 −1.08553 −0.542765 0.839885i \(-0.682622\pi\)
−0.542765 + 0.839885i \(0.682622\pi\)
\(492\) 11.0371 0.497591
\(493\) −24.0869 −1.08482
\(494\) 0.928805 0.0417889
\(495\) −63.3058 −2.84539
\(496\) −4.30137 −0.193137
\(497\) −18.8802 −0.846894
\(498\) −80.3513 −3.60063
\(499\) 29.4803 1.31972 0.659860 0.751389i \(-0.270616\pi\)
0.659860 + 0.751389i \(0.270616\pi\)
\(500\) −35.7595 −1.59921
\(501\) −21.5552 −0.963017
\(502\) 5.74085 0.256226
\(503\) 22.7117 1.01266 0.506332 0.862339i \(-0.331001\pi\)
0.506332 + 0.862339i \(0.331001\pi\)
\(504\) −59.4706 −2.64903
\(505\) −4.83556 −0.215180
\(506\) 40.4156 1.79669
\(507\) 3.41646 0.151730
\(508\) 3.37300 0.149653
\(509\) −17.5167 −0.776412 −0.388206 0.921573i \(-0.626905\pi\)
−0.388206 + 0.921573i \(0.626905\pi\)
\(510\) 60.9438 2.69864
\(511\) −13.3513 −0.590629
\(512\) −13.7737 −0.608718
\(513\) 8.09909 0.357584
\(514\) 24.1384 1.06470
\(515\) 13.4164 0.591198
\(516\) −78.3987 −3.45131
\(517\) −45.7561 −2.01235
\(518\) −13.0213 −0.572125
\(519\) −54.7075 −2.40139
\(520\) 3.75197 0.164535
\(521\) −4.02031 −0.176133 −0.0880665 0.996115i \(-0.528069\pi\)
−0.0880665 + 0.996115i \(0.528069\pi\)
\(522\) −103.990 −4.55152
\(523\) −17.8356 −0.779898 −0.389949 0.920837i \(-0.627507\pi\)
−0.389949 + 0.920837i \(0.627507\pi\)
\(524\) 43.7955 1.91321
\(525\) −19.8399 −0.865884
\(526\) 51.7453 2.25620
\(527\) −15.4794 −0.674295
\(528\) 17.2060 0.748794
\(529\) −2.93520 −0.127617
\(530\) 52.4575 2.27861
\(531\) 102.988 4.46932
\(532\) 4.03657 0.175007
\(533\) −1.09922 −0.0476127
\(534\) −73.8912 −3.19759
\(535\) 35.9841 1.55573
\(536\) 14.5527 0.628582
\(537\) 69.2242 2.98724
\(538\) 22.6877 0.978135
\(539\) −15.4278 −0.664523
\(540\) 102.405 4.40680
\(541\) −22.9843 −0.988171 −0.494086 0.869413i \(-0.664497\pi\)
−0.494086 + 0.869413i \(0.664497\pi\)
\(542\) −12.4725 −0.535738
\(543\) −31.5408 −1.35354
\(544\) −30.9372 −1.32642
\(545\) −21.4241 −0.917710
\(546\) 24.9521 1.06785
\(547\) 2.29716 0.0982195 0.0491097 0.998793i \(-0.484362\pi\)
0.0491097 + 0.998793i \(0.484362\pi\)
\(548\) 38.8548 1.65979
\(549\) −41.6750 −1.77865
\(550\) −15.9434 −0.679829
\(551\) 2.25503 0.0960674
\(552\) −31.9340 −1.35920
\(553\) 46.1385 1.96201
\(554\) 4.62104 0.196329
\(555\) 10.9522 0.464895
\(556\) −48.9874 −2.07753
\(557\) −13.9334 −0.590376 −0.295188 0.955439i \(-0.595382\pi\)
−0.295188 + 0.955439i \(0.595382\pi\)
\(558\) −66.8292 −2.82910
\(559\) 7.80801 0.330244
\(560\) −7.32994 −0.309746
\(561\) 61.9195 2.61424
\(562\) −21.5587 −0.909398
\(563\) −18.4209 −0.776346 −0.388173 0.921586i \(-0.626894\pi\)
−0.388173 + 0.921586i \(0.626894\pi\)
\(564\) 113.163 4.76501
\(565\) −15.1269 −0.636393
\(566\) 36.4718 1.53302
\(567\) 132.080 5.54685
\(568\) 11.9882 0.503014
\(569\) −36.3145 −1.52238 −0.761191 0.648527i \(-0.775385\pi\)
−0.761191 + 0.648527i \(0.775385\pi\)
\(570\) −5.70559 −0.238981
\(571\) −26.2098 −1.09684 −0.548422 0.836202i \(-0.684771\pi\)
−0.548422 + 0.836202i \(0.684771\pi\)
\(572\) 11.9318 0.498894
\(573\) 64.3675 2.68899
\(574\) −8.02818 −0.335090
\(575\) −7.91529 −0.330091
\(576\) −112.050 −4.66874
\(577\) −29.9862 −1.24834 −0.624170 0.781288i \(-0.714563\pi\)
−0.624170 + 0.781288i \(0.714563\pi\)
\(578\) −6.50799 −0.270697
\(579\) −43.5164 −1.80848
\(580\) 28.5126 1.18392
\(581\) 34.7786 1.44286
\(582\) −146.695 −6.08071
\(583\) 53.2973 2.20735
\(584\) 8.47757 0.350805
\(585\) −15.5930 −0.644691
\(586\) −10.6483 −0.439876
\(587\) 7.57230 0.312542 0.156271 0.987714i \(-0.450053\pi\)
0.156271 + 0.987714i \(0.450053\pi\)
\(588\) 38.1556 1.57351
\(589\) 1.44919 0.0597129
\(590\) −47.4542 −1.95366
\(591\) −11.4852 −0.472438
\(592\) −2.21163 −0.0908976
\(593\) 9.54738 0.392064 0.196032 0.980598i \(-0.437194\pi\)
0.196032 + 0.980598i \(0.437194\pi\)
\(594\) 174.848 7.17410
\(595\) −26.3784 −1.08141
\(596\) 62.2376 2.54935
\(597\) 82.0290 3.35723
\(598\) 9.95485 0.407084
\(599\) −33.5561 −1.37107 −0.685534 0.728041i \(-0.740431\pi\)
−0.685534 + 0.728041i \(0.740431\pi\)
\(600\) 12.5975 0.514292
\(601\) 33.5669 1.36922 0.684611 0.728908i \(-0.259972\pi\)
0.684611 + 0.728908i \(0.259972\pi\)
\(602\) 57.0257 2.32419
\(603\) −60.4804 −2.46295
\(604\) 5.44203 0.221433
\(605\) 9.85815 0.400791
\(606\) 20.4193 0.829479
\(607\) −24.7411 −1.00421 −0.502105 0.864807i \(-0.667441\pi\)
−0.502105 + 0.864807i \(0.667441\pi\)
\(608\) 2.89636 0.117463
\(609\) 60.5807 2.45485
\(610\) 19.2027 0.777495
\(611\) −11.2703 −0.455946
\(612\) −113.778 −4.59920
\(613\) 5.90221 0.238388 0.119194 0.992871i \(-0.461969\pi\)
0.119194 + 0.992871i \(0.461969\pi\)
\(614\) −52.7759 −2.12986
\(615\) 6.75247 0.272286
\(616\) 27.8411 1.12175
\(617\) −31.0882 −1.25156 −0.625781 0.779998i \(-0.715220\pi\)
−0.625781 + 0.779998i \(0.715220\pi\)
\(618\) −56.6541 −2.27896
\(619\) 2.23055 0.0896534 0.0448267 0.998995i \(-0.485726\pi\)
0.0448267 + 0.998995i \(0.485726\pi\)
\(620\) 18.3236 0.735893
\(621\) 86.8054 3.48338
\(622\) 67.1956 2.69430
\(623\) 31.9825 1.28135
\(624\) 4.23804 0.169657
\(625\) −13.0423 −0.521690
\(626\) −37.7112 −1.50724
\(627\) −5.79693 −0.231507
\(628\) −67.1399 −2.67918
\(629\) −7.95906 −0.317348
\(630\) −113.883 −4.53721
\(631\) −24.0250 −0.956420 −0.478210 0.878245i \(-0.658714\pi\)
−0.478210 + 0.878245i \(0.658714\pi\)
\(632\) −29.2961 −1.16534
\(633\) −16.1422 −0.641595
\(634\) −32.1293 −1.27602
\(635\) 2.06359 0.0818910
\(636\) −131.813 −5.22674
\(637\) −3.80005 −0.150564
\(638\) 48.6829 1.92738
\(639\) −49.8224 −1.97094
\(640\) 26.7079 1.05572
\(641\) 14.2998 0.564810 0.282405 0.959295i \(-0.408868\pi\)
0.282405 + 0.959295i \(0.408868\pi\)
\(642\) −151.952 −5.99705
\(643\) 14.7046 0.579892 0.289946 0.957043i \(-0.406363\pi\)
0.289946 + 0.957043i \(0.406363\pi\)
\(644\) 43.2636 1.70482
\(645\) −47.9641 −1.88858
\(646\) 4.14630 0.163134
\(647\) −37.0064 −1.45487 −0.727436 0.686175i \(-0.759288\pi\)
−0.727436 + 0.686175i \(0.759288\pi\)
\(648\) −83.8657 −3.29456
\(649\) −48.2140 −1.89256
\(650\) −3.92705 −0.154032
\(651\) 38.9322 1.52587
\(652\) 19.7178 0.772207
\(653\) 39.9763 1.56439 0.782196 0.623032i \(-0.214099\pi\)
0.782196 + 0.623032i \(0.214099\pi\)
\(654\) 90.4686 3.53760
\(655\) 26.7939 1.04693
\(656\) −1.36356 −0.0532381
\(657\) −35.2324 −1.37455
\(658\) −82.3123 −3.20887
\(659\) −0.892490 −0.0347665 −0.0173832 0.999849i \(-0.505534\pi\)
−0.0173832 + 0.999849i \(0.505534\pi\)
\(660\) −73.2964 −2.85306
\(661\) 12.9330 0.503036 0.251518 0.967853i \(-0.419070\pi\)
0.251518 + 0.967853i \(0.419070\pi\)
\(662\) 32.9350 1.28006
\(663\) 15.2515 0.592319
\(664\) −22.0830 −0.856987
\(665\) 2.46956 0.0957654
\(666\) −34.3615 −1.33148
\(667\) 24.1692 0.935835
\(668\) −18.5425 −0.717431
\(669\) −47.8108 −1.84847
\(670\) 27.8677 1.07662
\(671\) 19.5101 0.753181
\(672\) 77.8099 3.00158
\(673\) −7.92814 −0.305607 −0.152804 0.988257i \(-0.548830\pi\)
−0.152804 + 0.988257i \(0.548830\pi\)
\(674\) 50.3819 1.94064
\(675\) −34.2435 −1.31803
\(676\) 2.93895 0.113037
\(677\) −10.6291 −0.408511 −0.204256 0.978918i \(-0.565477\pi\)
−0.204256 + 0.978918i \(0.565477\pi\)
\(678\) 63.8770 2.45318
\(679\) 63.4944 2.43669
\(680\) 16.7492 0.642304
\(681\) 53.3874 2.04581
\(682\) 31.2860 1.19800
\(683\) −33.7028 −1.28960 −0.644802 0.764350i \(-0.723060\pi\)
−0.644802 + 0.764350i \(0.723060\pi\)
\(684\) 10.6520 0.407288
\(685\) 23.7712 0.908252
\(686\) 23.3708 0.892300
\(687\) 38.2508 1.45936
\(688\) 9.68564 0.369261
\(689\) 13.1278 0.500128
\(690\) −61.1520 −2.32802
\(691\) −10.4729 −0.398408 −0.199204 0.979958i \(-0.563836\pi\)
−0.199204 + 0.979958i \(0.563836\pi\)
\(692\) −47.0611 −1.78900
\(693\) −115.706 −4.39532
\(694\) −30.1571 −1.14475
\(695\) −29.9703 −1.13684
\(696\) −38.4663 −1.45806
\(697\) −4.90708 −0.185869
\(698\) 67.2698 2.54620
\(699\) −68.3811 −2.58641
\(700\) −17.0669 −0.645068
\(701\) 12.3305 0.465717 0.232859 0.972511i \(-0.425192\pi\)
0.232859 + 0.972511i \(0.425192\pi\)
\(702\) 43.0672 1.62547
\(703\) 0.745131 0.0281031
\(704\) 52.4560 1.97701
\(705\) 69.2326 2.60745
\(706\) 45.9376 1.72889
\(707\) −8.83814 −0.332392
\(708\) 119.241 4.48137
\(709\) −2.70298 −0.101512 −0.0507562 0.998711i \(-0.516163\pi\)
−0.0507562 + 0.998711i \(0.516163\pi\)
\(710\) 22.9568 0.861553
\(711\) 121.753 4.56610
\(712\) −20.3076 −0.761059
\(713\) 15.5323 0.581690
\(714\) 111.389 4.16864
\(715\) 7.29985 0.272999
\(716\) 59.5489 2.22545
\(717\) −90.2573 −3.37072
\(718\) 38.2277 1.42665
\(719\) 14.3855 0.536487 0.268244 0.963351i \(-0.413557\pi\)
0.268244 + 0.963351i \(0.413557\pi\)
\(720\) −19.3427 −0.720860
\(721\) 24.5217 0.913235
\(722\) 41.8369 1.55701
\(723\) −85.6876 −3.18676
\(724\) −27.1324 −1.00837
\(725\) −9.53442 −0.354100
\(726\) −41.6284 −1.54498
\(727\) −29.3651 −1.08909 −0.544545 0.838732i \(-0.683298\pi\)
−0.544545 + 0.838732i \(0.683298\pi\)
\(728\) 6.85761 0.254160
\(729\) 149.920 5.55259
\(730\) 16.2341 0.600852
\(731\) 34.8559 1.28919
\(732\) −48.2519 −1.78344
\(733\) −25.8494 −0.954769 −0.477385 0.878694i \(-0.658415\pi\)
−0.477385 + 0.878694i \(0.658415\pi\)
\(734\) 17.4118 0.642680
\(735\) 23.3435 0.861038
\(736\) 31.0429 1.14426
\(737\) 28.3139 1.04296
\(738\) −21.1853 −0.779840
\(739\) 46.7138 1.71839 0.859197 0.511645i \(-0.170964\pi\)
0.859197 + 0.511645i \(0.170964\pi\)
\(740\) 9.42143 0.346339
\(741\) −1.42785 −0.0524535
\(742\) 95.8784 3.51981
\(743\) 31.3998 1.15195 0.575974 0.817468i \(-0.304623\pi\)
0.575974 + 0.817468i \(0.304623\pi\)
\(744\) −24.7204 −0.906293
\(745\) 38.0768 1.39502
\(746\) −47.2885 −1.73135
\(747\) 91.7759 3.35791
\(748\) 53.2651 1.94756
\(749\) 65.7695 2.40316
\(750\) 92.3832 3.37336
\(751\) 29.1819 1.06486 0.532431 0.846473i \(-0.321278\pi\)
0.532431 + 0.846473i \(0.321278\pi\)
\(752\) −13.9805 −0.509816
\(753\) −8.82542 −0.321616
\(754\) 11.9912 0.436693
\(755\) 3.32942 0.121170
\(756\) 187.169 6.80728
\(757\) 38.0007 1.38116 0.690579 0.723257i \(-0.257356\pi\)
0.690579 + 0.723257i \(0.257356\pi\)
\(758\) −34.5621 −1.25535
\(759\) −62.1310 −2.25521
\(760\) −1.56807 −0.0568799
\(761\) 8.59225 0.311469 0.155734 0.987799i \(-0.450226\pi\)
0.155734 + 0.987799i \(0.450226\pi\)
\(762\) −8.71401 −0.315675
\(763\) −39.1577 −1.41760
\(764\) 55.3710 2.00325
\(765\) −69.6090 −2.51672
\(766\) −21.8813 −0.790605
\(767\) −11.8757 −0.428806
\(768\) −24.4955 −0.883904
\(769\) 3.38494 0.122064 0.0610321 0.998136i \(-0.480561\pi\)
0.0610321 + 0.998136i \(0.480561\pi\)
\(770\) 53.3143 1.92132
\(771\) −37.1081 −1.33642
\(772\) −37.4342 −1.34729
\(773\) 10.8238 0.389303 0.194652 0.980872i \(-0.437642\pi\)
0.194652 + 0.980872i \(0.437642\pi\)
\(774\) 150.483 5.40900
\(775\) −6.12729 −0.220099
\(776\) −40.3164 −1.44727
\(777\) 20.0177 0.718132
\(778\) 34.4119 1.23373
\(779\) 0.459403 0.0164598
\(780\) −18.0538 −0.646429
\(781\) 23.3243 0.834610
\(782\) 44.4397 1.58916
\(783\) 104.562 3.73674
\(784\) −4.71387 −0.168353
\(785\) −41.0760 −1.46607
\(786\) −113.144 −4.03571
\(787\) 30.0825 1.07232 0.536162 0.844115i \(-0.319874\pi\)
0.536162 + 0.844115i \(0.319874\pi\)
\(788\) −9.87993 −0.351958
\(789\) −79.5481 −2.83199
\(790\) −56.1006 −1.99597
\(791\) −27.6480 −0.983049
\(792\) 73.4690 2.61061
\(793\) 4.80558 0.170651
\(794\) −22.7751 −0.808257
\(795\) −80.6430 −2.86011
\(796\) 70.5640 2.50107
\(797\) 30.1788 1.06899 0.534494 0.845172i \(-0.320502\pi\)
0.534494 + 0.845172i \(0.320502\pi\)
\(798\) −10.4283 −0.369158
\(799\) −50.3119 −1.77991
\(800\) −12.2460 −0.432962
\(801\) 84.3974 2.98203
\(802\) 39.2289 1.38522
\(803\) 16.4940 0.582061
\(804\) −70.0251 −2.46959
\(805\) 26.4685 0.932893
\(806\) 7.70613 0.271437
\(807\) −34.8778 −1.22776
\(808\) 5.61187 0.197425
\(809\) 14.0526 0.494063 0.247031 0.969008i \(-0.420545\pi\)
0.247031 + 0.969008i \(0.420545\pi\)
\(810\) −160.599 −5.64286
\(811\) −25.4786 −0.894676 −0.447338 0.894365i \(-0.647628\pi\)
−0.447338 + 0.894365i \(0.647628\pi\)
\(812\) 52.1135 1.82882
\(813\) 19.1740 0.672460
\(814\) 16.0863 0.563826
\(815\) 12.0633 0.422558
\(816\) 18.9191 0.662301
\(817\) −3.26323 −0.114166
\(818\) 26.3421 0.921029
\(819\) −28.4999 −0.995866
\(820\) 5.80869 0.202848
\(821\) 22.2392 0.776154 0.388077 0.921627i \(-0.373139\pi\)
0.388077 + 0.921627i \(0.373139\pi\)
\(822\) −100.380 −3.50115
\(823\) 16.7355 0.583363 0.291681 0.956516i \(-0.405785\pi\)
0.291681 + 0.956516i \(0.405785\pi\)
\(824\) −15.5703 −0.542417
\(825\) 24.5098 0.853323
\(826\) −86.7338 −3.01786
\(827\) 21.2077 0.737465 0.368732 0.929536i \(-0.379792\pi\)
0.368732 + 0.929536i \(0.379792\pi\)
\(828\) 114.167 3.96757
\(829\) 43.3397 1.50525 0.752624 0.658450i \(-0.228788\pi\)
0.752624 + 0.658450i \(0.228788\pi\)
\(830\) −42.2878 −1.46783
\(831\) −7.10394 −0.246433
\(832\) 12.9205 0.447939
\(833\) −16.9639 −0.587765
\(834\) 126.557 4.38231
\(835\) −11.3442 −0.392584
\(836\) −4.98670 −0.172469
\(837\) 67.1967 2.32266
\(838\) −4.18852 −0.144690
\(839\) 41.7931 1.44286 0.721429 0.692488i \(-0.243486\pi\)
0.721429 + 0.692488i \(0.243486\pi\)
\(840\) −42.1258 −1.45348
\(841\) 0.113183 0.00390287
\(842\) 28.5012 0.982215
\(843\) 33.1422 1.14148
\(844\) −13.8860 −0.477977
\(845\) 1.79804 0.0618544
\(846\) −217.211 −7.46787
\(847\) 18.0181 0.619109
\(848\) 16.2847 0.559217
\(849\) −56.0682 −1.92426
\(850\) −17.5309 −0.601303
\(851\) 7.98625 0.273765
\(852\) −57.6850 −1.97626
\(853\) −18.3044 −0.626732 −0.313366 0.949632i \(-0.601457\pi\)
−0.313366 + 0.949632i \(0.601457\pi\)
\(854\) 35.0975 1.20101
\(855\) 6.51683 0.222871
\(856\) −41.7610 −1.42736
\(857\) 43.0938 1.47206 0.736028 0.676951i \(-0.236699\pi\)
0.736028 + 0.676951i \(0.236699\pi\)
\(858\) −30.8254 −1.05236
\(859\) −37.6722 −1.28536 −0.642679 0.766136i \(-0.722177\pi\)
−0.642679 + 0.766136i \(0.722177\pi\)
\(860\) −41.2602 −1.40696
\(861\) 12.3417 0.420605
\(862\) 15.9263 0.542453
\(863\) 4.48735 0.152751 0.0763757 0.997079i \(-0.475665\pi\)
0.0763757 + 0.997079i \(0.475665\pi\)
\(864\) 134.300 4.56896
\(865\) −28.7918 −0.978952
\(866\) 4.48266 0.152327
\(867\) 10.0048 0.339779
\(868\) 33.4907 1.13675
\(869\) −56.9987 −1.93355
\(870\) −73.6611 −2.49734
\(871\) 6.97405 0.236307
\(872\) 24.8636 0.841987
\(873\) 167.553 5.67081
\(874\) −4.16046 −0.140730
\(875\) −39.9864 −1.35179
\(876\) −40.7925 −1.37825
\(877\) −18.8002 −0.634836 −0.317418 0.948286i \(-0.602816\pi\)
−0.317418 + 0.948286i \(0.602816\pi\)
\(878\) 8.19861 0.276690
\(879\) 16.3696 0.552133
\(880\) 9.05528 0.305253
\(881\) −53.2861 −1.79525 −0.897627 0.440755i \(-0.854711\pi\)
−0.897627 + 0.440755i \(0.854711\pi\)
\(882\) −73.2381 −2.46606
\(883\) −2.76365 −0.0930044 −0.0465022 0.998918i \(-0.514807\pi\)
−0.0465022 + 0.998918i \(0.514807\pi\)
\(884\) 13.1198 0.441268
\(885\) 72.9515 2.45224
\(886\) 18.5886 0.624498
\(887\) 20.7524 0.696796 0.348398 0.937347i \(-0.386726\pi\)
0.348398 + 0.937347i \(0.386726\pi\)
\(888\) −12.7105 −0.426535
\(889\) 3.77170 0.126499
\(890\) −38.8880 −1.30353
\(891\) −163.170 −5.46639
\(892\) −41.1284 −1.37708
\(893\) 4.71022 0.157622
\(894\) −160.788 −5.37757
\(895\) 36.4318 1.21778
\(896\) 48.8150 1.63079
\(897\) −15.3036 −0.510973
\(898\) −6.54219 −0.218316
\(899\) 18.7096 0.623999
\(900\) −45.0372 −1.50124
\(901\) 58.6039 1.95238
\(902\) 9.91787 0.330229
\(903\) −87.6657 −2.91733
\(904\) 17.5554 0.583883
\(905\) −16.5995 −0.551786
\(906\) −14.0593 −0.467088
\(907\) 7.76420 0.257806 0.128903 0.991657i \(-0.458854\pi\)
0.128903 + 0.991657i \(0.458854\pi\)
\(908\) 45.9255 1.52409
\(909\) −23.3226 −0.773563
\(910\) 13.1320 0.435320
\(911\) −57.5721 −1.90745 −0.953725 0.300680i \(-0.902786\pi\)
−0.953725 + 0.300680i \(0.902786\pi\)
\(912\) −1.77122 −0.0586508
\(913\) −42.9649 −1.42193
\(914\) −28.4429 −0.940808
\(915\) −29.5204 −0.975914
\(916\) 32.9046 1.08720
\(917\) 48.9723 1.61721
\(918\) 192.257 6.34543
\(919\) −19.9024 −0.656521 −0.328261 0.944587i \(-0.606462\pi\)
−0.328261 + 0.944587i \(0.606462\pi\)
\(920\) −16.8065 −0.554093
\(921\) 81.1325 2.67341
\(922\) −18.2081 −0.599651
\(923\) 5.74506 0.189101
\(924\) −133.966 −4.40717
\(925\) −3.15047 −0.103587
\(926\) −2.22237 −0.0730318
\(927\) 64.7094 2.12534
\(928\) 37.3930 1.22749
\(929\) 2.30016 0.0754659 0.0377329 0.999288i \(-0.487986\pi\)
0.0377329 + 0.999288i \(0.487986\pi\)
\(930\) −47.3382 −1.55228
\(931\) 1.58817 0.0520502
\(932\) −58.8236 −1.92683
\(933\) −103.300 −3.38189
\(934\) 40.6459 1.32997
\(935\) 32.5874 1.06572
\(936\) 18.0963 0.591496
\(937\) −17.7147 −0.578714 −0.289357 0.957221i \(-0.593441\pi\)
−0.289357 + 0.957221i \(0.593441\pi\)
\(938\) 50.9349 1.66308
\(939\) 57.9735 1.89189
\(940\) 59.5560 1.94250
\(941\) 0.846668 0.0276006 0.0138003 0.999905i \(-0.495607\pi\)
0.0138003 + 0.999905i \(0.495607\pi\)
\(942\) 173.453 5.65142
\(943\) 4.92384 0.160342
\(944\) −14.7315 −0.479469
\(945\) 114.509 3.72499
\(946\) −70.4485 −2.29048
\(947\) 27.2245 0.884679 0.442339 0.896848i \(-0.354149\pi\)
0.442339 + 0.896848i \(0.354149\pi\)
\(948\) 140.968 4.57842
\(949\) 4.06268 0.131880
\(950\) 1.64125 0.0532491
\(951\) 49.3925 1.60166
\(952\) 30.6132 0.992179
\(953\) 11.9329 0.386545 0.193273 0.981145i \(-0.438090\pi\)
0.193273 + 0.981145i \(0.438090\pi\)
\(954\) 253.010 8.19151
\(955\) 33.8758 1.09619
\(956\) −77.6422 −2.51113
\(957\) −74.8404 −2.41925
\(958\) 67.0539 2.16641
\(959\) 43.4475 1.40299
\(960\) −79.3700 −2.56166
\(961\) −18.9763 −0.612139
\(962\) 3.96226 0.127748
\(963\) 173.557 5.59279
\(964\) −73.7112 −2.37408
\(965\) −22.9021 −0.737246
\(966\) −111.770 −3.59613
\(967\) −50.6049 −1.62734 −0.813671 0.581325i \(-0.802534\pi\)
−0.813671 + 0.581325i \(0.802534\pi\)
\(968\) −11.4408 −0.367721
\(969\) −6.37411 −0.204766
\(970\) −77.2038 −2.47887
\(971\) 1.98036 0.0635528 0.0317764 0.999495i \(-0.489884\pi\)
0.0317764 + 0.999495i \(0.489884\pi\)
\(972\) 232.686 7.46340
\(973\) −54.7779 −1.75610
\(974\) −22.3280 −0.715435
\(975\) 6.03707 0.193341
\(976\) 5.96120 0.190813
\(977\) −37.7398 −1.20740 −0.603702 0.797210i \(-0.706308\pi\)
−0.603702 + 0.797210i \(0.706308\pi\)
\(978\) −50.9400 −1.62888
\(979\) −39.5106 −1.26276
\(980\) 20.0808 0.641458
\(981\) −103.332 −3.29913
\(982\) 53.4564 1.70586
\(983\) 11.7034 0.373280 0.186640 0.982428i \(-0.440240\pi\)
0.186640 + 0.982428i \(0.440240\pi\)
\(984\) −7.83651 −0.249819
\(985\) −6.04451 −0.192594
\(986\) 53.5301 1.70475
\(987\) 126.539 4.02778
\(988\) −1.22829 −0.0390770
\(989\) −34.9750 −1.11214
\(990\) 140.689 4.47140
\(991\) 20.3129 0.645262 0.322631 0.946525i \(-0.395433\pi\)
0.322631 + 0.946525i \(0.395433\pi\)
\(992\) 24.0306 0.762972
\(993\) −50.6311 −1.60673
\(994\) 41.9590 1.33086
\(995\) 43.1708 1.36861
\(996\) 106.259 3.36696
\(997\) −30.5373 −0.967125 −0.483563 0.875310i \(-0.660658\pi\)
−0.483563 + 0.875310i \(0.660658\pi\)
\(998\) −65.5163 −2.07388
\(999\) 34.5505 1.09313
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 6019.2.a.d.1.15 123
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6019.2.a.d.1.15 123 1.1 even 1 trivial