Properties

Label 6023.2.a.a.1.5
Level $6023$
Weight $2$
Character 6023.1
Self dual yes
Analytic conductor $48.094$
Analytic rank $1$
Dimension $98$
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] = [6023,2,Mod(1,6023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6023, 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("6023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6023 = 19 \cdot 317 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6023.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: \(48.0938971374\)
Analytic rank: \(1\)
Dimension: \(98\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6023.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.52650 q^{2} +1.56416 q^{3} +4.38319 q^{4} +1.08994 q^{5} -3.95184 q^{6} +4.94624 q^{7} -6.02111 q^{8} -0.553409 q^{9} +O(q^{10})\) \(q-2.52650 q^{2} +1.56416 q^{3} +4.38319 q^{4} +1.08994 q^{5} -3.95184 q^{6} +4.94624 q^{7} -6.02111 q^{8} -0.553409 q^{9} -2.75372 q^{10} +1.08607 q^{11} +6.85600 q^{12} -7.15585 q^{13} -12.4967 q^{14} +1.70483 q^{15} +6.44594 q^{16} -0.679762 q^{17} +1.39818 q^{18} +1.00000 q^{19} +4.77739 q^{20} +7.73670 q^{21} -2.74394 q^{22} +0.230492 q^{23} -9.41797 q^{24} -3.81204 q^{25} +18.0792 q^{26} -5.55809 q^{27} +21.6803 q^{28} -3.96002 q^{29} -4.30726 q^{30} -3.60722 q^{31} -4.24343 q^{32} +1.69878 q^{33} +1.71742 q^{34} +5.39109 q^{35} -2.42569 q^{36} -11.1155 q^{37} -2.52650 q^{38} -11.1929 q^{39} -6.56263 q^{40} -0.857779 q^{41} -19.5468 q^{42} -4.76742 q^{43} +4.76043 q^{44} -0.603180 q^{45} -0.582338 q^{46} -4.63322 q^{47} +10.0825 q^{48} +17.4653 q^{49} +9.63110 q^{50} -1.06326 q^{51} -31.3654 q^{52} -1.85027 q^{53} +14.0425 q^{54} +1.18374 q^{55} -29.7818 q^{56} +1.56416 q^{57} +10.0050 q^{58} +13.1898 q^{59} +7.47260 q^{60} +8.77867 q^{61} +9.11362 q^{62} -2.73729 q^{63} -2.17087 q^{64} -7.79942 q^{65} -4.29196 q^{66} +14.4757 q^{67} -2.97952 q^{68} +0.360526 q^{69} -13.6206 q^{70} +10.2052 q^{71} +3.33213 q^{72} -7.59914 q^{73} +28.0832 q^{74} -5.96263 q^{75} +4.38319 q^{76} +5.37195 q^{77} +28.2788 q^{78} -11.4880 q^{79} +7.02567 q^{80} -7.03351 q^{81} +2.16717 q^{82} -11.0248 q^{83} +33.9114 q^{84} -0.740898 q^{85} +12.0449 q^{86} -6.19410 q^{87} -6.53932 q^{88} -5.17570 q^{89} +1.52393 q^{90} -35.3945 q^{91} +1.01029 q^{92} -5.64226 q^{93} +11.7058 q^{94} +1.08994 q^{95} -6.63740 q^{96} -6.09815 q^{97} -44.1260 q^{98} -0.601038 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 98 q - 8 q^{2} - 25 q^{3} + 82 q^{4} - 10 q^{5} - 4 q^{6} - 18 q^{7} - 18 q^{8} + 61 q^{9} - 24 q^{10} - 12 q^{11} - 51 q^{12} - 58 q^{13} - 15 q^{14} - 18 q^{15} + 58 q^{16} - 25 q^{17} - 40 q^{18} + 98 q^{19} - 12 q^{20} - 24 q^{21} - 59 q^{22} - 38 q^{23} - 9 q^{24} - 12 q^{25} - 3 q^{26} - 85 q^{27} - 33 q^{28} - 24 q^{29} - 22 q^{30} - 56 q^{31} - 29 q^{32} - 51 q^{33} - 38 q^{34} - 10 q^{35} + 50 q^{36} - 124 q^{37} - 8 q^{38} - 4 q^{39} - 80 q^{40} - 28 q^{41} - 37 q^{42} - 63 q^{43} - 7 q^{44} - 32 q^{45} - 47 q^{46} - 10 q^{47} - 88 q^{48} + 6 q^{49} - 17 q^{50} - 22 q^{51} - 119 q^{52} - 65 q^{53} + 24 q^{54} - 30 q^{55} - 39 q^{56} - 25 q^{57} - 91 q^{58} - 26 q^{59} - 60 q^{60} - 60 q^{61} + 6 q^{62} - 26 q^{63} + 50 q^{64} - 40 q^{65} + 57 q^{66} - 108 q^{67} - 41 q^{68} - 15 q^{69} - 36 q^{70} - 19 q^{71} - 47 q^{72} - 136 q^{73} + 22 q^{74} - 48 q^{75} + 82 q^{76} - 35 q^{77} - 56 q^{78} - 98 q^{79} - 42 q^{80} + 6 q^{81} - 37 q^{82} - 31 q^{83} - 24 q^{84} - 71 q^{85} - 24 q^{86} + 7 q^{87} - 166 q^{88} - 38 q^{89} + 26 q^{90} - 100 q^{91} - 59 q^{92} - 21 q^{93} - 48 q^{94} - 10 q^{95} - 16 q^{96} - 190 q^{97} - 80 q^{98} - 17 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52650 −1.78650 −0.893251 0.449557i \(-0.851582\pi\)
−0.893251 + 0.449557i \(0.851582\pi\)
\(3\) 1.56416 0.903067 0.451534 0.892254i \(-0.350877\pi\)
0.451534 + 0.892254i \(0.350877\pi\)
\(4\) 4.38319 2.19159
\(5\) 1.08994 0.487434 0.243717 0.969846i \(-0.421633\pi\)
0.243717 + 0.969846i \(0.421633\pi\)
\(6\) −3.95184 −1.61333
\(7\) 4.94624 1.86950 0.934751 0.355302i \(-0.115622\pi\)
0.934751 + 0.355302i \(0.115622\pi\)
\(8\) −6.02111 −2.12878
\(9\) −0.553409 −0.184470
\(10\) −2.75372 −0.870803
\(11\) 1.08607 0.327461 0.163731 0.986505i \(-0.447647\pi\)
0.163731 + 0.986505i \(0.447647\pi\)
\(12\) 6.85600 1.97916
\(13\) −7.15585 −1.98468 −0.992338 0.123555i \(-0.960571\pi\)
−0.992338 + 0.123555i \(0.960571\pi\)
\(14\) −12.4967 −3.33987
\(15\) 1.70483 0.440186
\(16\) 6.44594 1.61149
\(17\) −0.679762 −0.164867 −0.0824333 0.996597i \(-0.526269\pi\)
−0.0824333 + 0.996597i \(0.526269\pi\)
\(18\) 1.39818 0.329555
\(19\) 1.00000 0.229416
\(20\) 4.77739 1.06826
\(21\) 7.73670 1.68829
\(22\) −2.74394 −0.585011
\(23\) 0.230492 0.0480609 0.0240305 0.999711i \(-0.492350\pi\)
0.0240305 + 0.999711i \(0.492350\pi\)
\(24\) −9.41797 −1.92243
\(25\) −3.81204 −0.762408
\(26\) 18.0792 3.54563
\(27\) −5.55809 −1.06966
\(28\) 21.6803 4.09719
\(29\) −3.96002 −0.735357 −0.367679 0.929953i \(-0.619847\pi\)
−0.367679 + 0.929953i \(0.619847\pi\)
\(30\) −4.30726 −0.786394
\(31\) −3.60722 −0.647875 −0.323938 0.946078i \(-0.605007\pi\)
−0.323938 + 0.946078i \(0.605007\pi\)
\(32\) −4.24343 −0.750140
\(33\) 1.69878 0.295720
\(34\) 1.71742 0.294535
\(35\) 5.39109 0.911260
\(36\) −2.42569 −0.404282
\(37\) −11.1155 −1.82737 −0.913687 0.406419i \(-0.866777\pi\)
−0.913687 + 0.406419i \(0.866777\pi\)
\(38\) −2.52650 −0.409852
\(39\) −11.1929 −1.79230
\(40\) −6.56263 −1.03764
\(41\) −0.857779 −0.133963 −0.0669813 0.997754i \(-0.521337\pi\)
−0.0669813 + 0.997754i \(0.521337\pi\)
\(42\) −19.5468 −3.01613
\(43\) −4.76742 −0.727025 −0.363512 0.931589i \(-0.618423\pi\)
−0.363512 + 0.931589i \(0.618423\pi\)
\(44\) 4.76043 0.717662
\(45\) −0.603180 −0.0899168
\(46\) −0.582338 −0.0858610
\(47\) −4.63322 −0.675825 −0.337912 0.941178i \(-0.609721\pi\)
−0.337912 + 0.941178i \(0.609721\pi\)
\(48\) 10.0825 1.45528
\(49\) 17.4653 2.49504
\(50\) 9.63110 1.36204
\(51\) −1.06326 −0.148886
\(52\) −31.3654 −4.34960
\(53\) −1.85027 −0.254154 −0.127077 0.991893i \(-0.540560\pi\)
−0.127077 + 0.991893i \(0.540560\pi\)
\(54\) 14.0425 1.91094
\(55\) 1.18374 0.159616
\(56\) −29.7818 −3.97977
\(57\) 1.56416 0.207178
\(58\) 10.0050 1.31372
\(59\) 13.1898 1.71716 0.858580 0.512680i \(-0.171347\pi\)
0.858580 + 0.512680i \(0.171347\pi\)
\(60\) 7.47260 0.964708
\(61\) 8.77867 1.12399 0.561997 0.827139i \(-0.310033\pi\)
0.561997 + 0.827139i \(0.310033\pi\)
\(62\) 9.11362 1.15743
\(63\) −2.73729 −0.344866
\(64\) −2.17087 −0.271359
\(65\) −7.79942 −0.967399
\(66\) −4.29196 −0.528304
\(67\) 14.4757 1.76849 0.884247 0.467020i \(-0.154672\pi\)
0.884247 + 0.467020i \(0.154672\pi\)
\(68\) −2.97952 −0.361320
\(69\) 0.360526 0.0434023
\(70\) −13.6206 −1.62797
\(71\) 10.2052 1.21113 0.605565 0.795796i \(-0.292947\pi\)
0.605565 + 0.795796i \(0.292947\pi\)
\(72\) 3.33213 0.392696
\(73\) −7.59914 −0.889412 −0.444706 0.895677i \(-0.646692\pi\)
−0.444706 + 0.895677i \(0.646692\pi\)
\(74\) 28.0832 3.26461
\(75\) −5.96263 −0.688505
\(76\) 4.38319 0.502786
\(77\) 5.37195 0.612190
\(78\) 28.2788 3.20194
\(79\) −11.4880 −1.29250 −0.646250 0.763125i \(-0.723664\pi\)
−0.646250 + 0.763125i \(0.723664\pi\)
\(80\) 7.02567 0.785493
\(81\) −7.03351 −0.781501
\(82\) 2.16717 0.239324
\(83\) −11.0248 −1.21012 −0.605062 0.796178i \(-0.706852\pi\)
−0.605062 + 0.796178i \(0.706852\pi\)
\(84\) 33.9114 3.70004
\(85\) −0.740898 −0.0803616
\(86\) 12.0449 1.29883
\(87\) −6.19410 −0.664077
\(88\) −6.53932 −0.697094
\(89\) −5.17570 −0.548623 −0.274311 0.961641i \(-0.588450\pi\)
−0.274311 + 0.961641i \(0.588450\pi\)
\(90\) 1.52393 0.160637
\(91\) −35.3945 −3.71036
\(92\) 1.01029 0.105330
\(93\) −5.64226 −0.585075
\(94\) 11.7058 1.20736
\(95\) 1.08994 0.111825
\(96\) −6.63740 −0.677426
\(97\) −6.09815 −0.619173 −0.309586 0.950871i \(-0.600191\pi\)
−0.309586 + 0.950871i \(0.600191\pi\)
\(98\) −44.1260 −4.45740
\(99\) −0.601038 −0.0604066
\(100\) −16.7089 −1.67089
\(101\) 8.32395 0.828264 0.414132 0.910217i \(-0.364085\pi\)
0.414132 + 0.910217i \(0.364085\pi\)
\(102\) 2.68631 0.265985
\(103\) −2.78965 −0.274872 −0.137436 0.990511i \(-0.543886\pi\)
−0.137436 + 0.990511i \(0.543886\pi\)
\(104\) 43.0861 4.22494
\(105\) 8.43251 0.822929
\(106\) 4.67470 0.454047
\(107\) −6.32819 −0.611769 −0.305884 0.952069i \(-0.598952\pi\)
−0.305884 + 0.952069i \(0.598952\pi\)
\(108\) −24.3622 −2.34425
\(109\) −9.97996 −0.955907 −0.477954 0.878385i \(-0.658621\pi\)
−0.477954 + 0.878385i \(0.658621\pi\)
\(110\) −2.99072 −0.285154
\(111\) −17.3864 −1.65024
\(112\) 31.8832 3.01268
\(113\) −10.3965 −0.978021 −0.489011 0.872278i \(-0.662642\pi\)
−0.489011 + 0.872278i \(0.662642\pi\)
\(114\) −3.95184 −0.370124
\(115\) 0.251222 0.0234266
\(116\) −17.3575 −1.61160
\(117\) 3.96011 0.366112
\(118\) −33.3239 −3.06771
\(119\) −3.36227 −0.308218
\(120\) −10.2650 −0.937061
\(121\) −9.82046 −0.892769
\(122\) −22.1793 −2.00802
\(123\) −1.34170 −0.120977
\(124\) −15.8111 −1.41988
\(125\) −9.60456 −0.859058
\(126\) 6.91576 0.616105
\(127\) 12.1778 1.08060 0.540301 0.841472i \(-0.318310\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(128\) 13.9716 1.23492
\(129\) −7.45700 −0.656552
\(130\) 19.7052 1.72826
\(131\) 10.9871 0.959952 0.479976 0.877282i \(-0.340645\pi\)
0.479976 + 0.877282i \(0.340645\pi\)
\(132\) 7.44607 0.648097
\(133\) 4.94624 0.428893
\(134\) −36.5729 −3.15942
\(135\) −6.05797 −0.521387
\(136\) 4.09292 0.350965
\(137\) −14.4313 −1.23295 −0.616476 0.787374i \(-0.711440\pi\)
−0.616476 + 0.787374i \(0.711440\pi\)
\(138\) −0.910868 −0.0775383
\(139\) 2.31242 0.196137 0.0980685 0.995180i \(-0.468734\pi\)
0.0980685 + 0.995180i \(0.468734\pi\)
\(140\) 23.6301 1.99711
\(141\) −7.24709 −0.610315
\(142\) −25.7833 −2.16369
\(143\) −7.77173 −0.649905
\(144\) −3.56724 −0.297270
\(145\) −4.31617 −0.358438
\(146\) 19.1992 1.58894
\(147\) 27.3185 2.25319
\(148\) −48.7212 −4.00486
\(149\) −8.39291 −0.687574 −0.343787 0.939048i \(-0.611710\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(150\) 15.0646 1.23002
\(151\) −19.5139 −1.58802 −0.794008 0.607907i \(-0.792009\pi\)
−0.794008 + 0.607907i \(0.792009\pi\)
\(152\) −6.02111 −0.488376
\(153\) 0.376186 0.0304129
\(154\) −13.5722 −1.09368
\(155\) −3.93164 −0.315797
\(156\) −49.0605 −3.92798
\(157\) −1.52650 −0.121828 −0.0609138 0.998143i \(-0.519401\pi\)
−0.0609138 + 0.998143i \(0.519401\pi\)
\(158\) 29.0244 2.30906
\(159\) −2.89412 −0.229518
\(160\) −4.62507 −0.365644
\(161\) 1.14007 0.0898501
\(162\) 17.7701 1.39615
\(163\) −0.774360 −0.0606526 −0.0303263 0.999540i \(-0.509655\pi\)
−0.0303263 + 0.999540i \(0.509655\pi\)
\(164\) −3.75980 −0.293591
\(165\) 1.85156 0.144144
\(166\) 27.8540 2.16189
\(167\) 14.8449 1.14873 0.574365 0.818599i \(-0.305249\pi\)
0.574365 + 0.818599i \(0.305249\pi\)
\(168\) −46.5835 −3.59400
\(169\) 38.2062 2.93894
\(170\) 1.87188 0.143566
\(171\) −0.553409 −0.0423202
\(172\) −20.8965 −1.59334
\(173\) 3.38019 0.256991 0.128495 0.991710i \(-0.458985\pi\)
0.128495 + 0.991710i \(0.458985\pi\)
\(174\) 15.6494 1.18638
\(175\) −18.8553 −1.42532
\(176\) 7.00072 0.527699
\(177\) 20.6309 1.55071
\(178\) 13.0764 0.980116
\(179\) −17.4992 −1.30795 −0.653977 0.756514i \(-0.726901\pi\)
−0.653977 + 0.756514i \(0.726901\pi\)
\(180\) −2.64385 −0.197061
\(181\) −20.1776 −1.49979 −0.749894 0.661558i \(-0.769896\pi\)
−0.749894 + 0.661558i \(0.769896\pi\)
\(182\) 89.4242 6.62856
\(183\) 13.7312 1.01504
\(184\) −1.38782 −0.102311
\(185\) −12.1152 −0.890725
\(186\) 14.2552 1.04524
\(187\) −0.738267 −0.0539874
\(188\) −20.3083 −1.48113
\(189\) −27.4917 −1.99972
\(190\) −2.75372 −0.199776
\(191\) 15.8641 1.14788 0.573942 0.818896i \(-0.305413\pi\)
0.573942 + 0.818896i \(0.305413\pi\)
\(192\) −3.39559 −0.245055
\(193\) −19.3179 −1.39053 −0.695266 0.718752i \(-0.744713\pi\)
−0.695266 + 0.718752i \(0.744713\pi\)
\(194\) 15.4069 1.10615
\(195\) −12.1995 −0.873626
\(196\) 76.5536 5.46811
\(197\) 20.9441 1.49221 0.746103 0.665831i \(-0.231923\pi\)
0.746103 + 0.665831i \(0.231923\pi\)
\(198\) 1.51852 0.107917
\(199\) −8.92410 −0.632613 −0.316306 0.948657i \(-0.602443\pi\)
−0.316306 + 0.948657i \(0.602443\pi\)
\(200\) 22.9527 1.62300
\(201\) 22.6424 1.59707
\(202\) −21.0304 −1.47970
\(203\) −19.5872 −1.37475
\(204\) −4.66045 −0.326297
\(205\) −0.934924 −0.0652979
\(206\) 7.04803 0.491060
\(207\) −0.127556 −0.00886578
\(208\) −46.1262 −3.19828
\(209\) 1.08607 0.0751248
\(210\) −21.3047 −1.47017
\(211\) 2.97263 0.204644 0.102322 0.994751i \(-0.467373\pi\)
0.102322 + 0.994751i \(0.467373\pi\)
\(212\) −8.11008 −0.557003
\(213\) 15.9625 1.09373
\(214\) 15.9881 1.09293
\(215\) −5.19619 −0.354377
\(216\) 33.4659 2.27707
\(217\) −17.8422 −1.21121
\(218\) 25.2143 1.70773
\(219\) −11.8863 −0.803199
\(220\) 5.18857 0.349813
\(221\) 4.86428 0.327207
\(222\) 43.9266 2.94816
\(223\) −28.2585 −1.89233 −0.946165 0.323685i \(-0.895078\pi\)
−0.946165 + 0.323685i \(0.895078\pi\)
\(224\) −20.9890 −1.40239
\(225\) 2.10961 0.140641
\(226\) 26.2667 1.74724
\(227\) −25.2225 −1.67408 −0.837039 0.547143i \(-0.815715\pi\)
−0.837039 + 0.547143i \(0.815715\pi\)
\(228\) 6.85600 0.454049
\(229\) −14.1035 −0.931984 −0.465992 0.884789i \(-0.654303\pi\)
−0.465992 + 0.884789i \(0.654303\pi\)
\(230\) −0.634711 −0.0418516
\(231\) 8.40257 0.552849
\(232\) 23.8437 1.56542
\(233\) 14.7493 0.966257 0.483128 0.875550i \(-0.339500\pi\)
0.483128 + 0.875550i \(0.339500\pi\)
\(234\) −10.0052 −0.654060
\(235\) −5.04992 −0.329420
\(236\) 57.8131 3.76332
\(237\) −17.9690 −1.16722
\(238\) 8.49476 0.550633
\(239\) −17.7477 −1.14800 −0.574002 0.818854i \(-0.694610\pi\)
−0.574002 + 0.818854i \(0.694610\pi\)
\(240\) 10.9893 0.709353
\(241\) 6.15271 0.396331 0.198165 0.980169i \(-0.436502\pi\)
0.198165 + 0.980169i \(0.436502\pi\)
\(242\) 24.8114 1.59493
\(243\) 5.67275 0.363907
\(244\) 38.4785 2.46334
\(245\) 19.0361 1.21617
\(246\) 3.38980 0.216126
\(247\) −7.15585 −0.455316
\(248\) 21.7195 1.37919
\(249\) −17.2445 −1.09282
\(250\) 24.2659 1.53471
\(251\) −15.0438 −0.949556 −0.474778 0.880106i \(-0.657472\pi\)
−0.474778 + 0.880106i \(0.657472\pi\)
\(252\) −11.9981 −0.755806
\(253\) 0.250330 0.0157381
\(254\) −30.7671 −1.93050
\(255\) −1.15888 −0.0725720
\(256\) −30.9573 −1.93483
\(257\) 17.8353 1.11253 0.556267 0.831003i \(-0.312233\pi\)
0.556267 + 0.831003i \(0.312233\pi\)
\(258\) 18.8401 1.17293
\(259\) −54.9798 −3.41628
\(260\) −34.1863 −2.12014
\(261\) 2.19151 0.135651
\(262\) −27.7590 −1.71496
\(263\) 19.8621 1.22475 0.612374 0.790568i \(-0.290215\pi\)
0.612374 + 0.790568i \(0.290215\pi\)
\(264\) −10.2285 −0.629523
\(265\) −2.01668 −0.123884
\(266\) −12.4967 −0.766219
\(267\) −8.09561 −0.495443
\(268\) 63.4499 3.87582
\(269\) 14.7102 0.896899 0.448450 0.893808i \(-0.351976\pi\)
0.448450 + 0.893808i \(0.351976\pi\)
\(270\) 15.3054 0.931459
\(271\) 19.6873 1.19592 0.597959 0.801527i \(-0.295978\pi\)
0.597959 + 0.801527i \(0.295978\pi\)
\(272\) −4.38171 −0.265680
\(273\) −55.3627 −3.35070
\(274\) 36.4607 2.20267
\(275\) −4.14013 −0.249659
\(276\) 1.58025 0.0951201
\(277\) −11.8717 −0.713302 −0.356651 0.934238i \(-0.616082\pi\)
−0.356651 + 0.934238i \(0.616082\pi\)
\(278\) −5.84233 −0.350399
\(279\) 1.99627 0.119513
\(280\) −32.4603 −1.93988
\(281\) 29.0110 1.73065 0.865327 0.501209i \(-0.167111\pi\)
0.865327 + 0.501209i \(0.167111\pi\)
\(282\) 18.3097 1.09033
\(283\) 8.21889 0.488562 0.244281 0.969704i \(-0.421448\pi\)
0.244281 + 0.969704i \(0.421448\pi\)
\(284\) 44.7311 2.65430
\(285\) 1.70483 0.100986
\(286\) 19.6352 1.16106
\(287\) −4.24278 −0.250443
\(288\) 2.34835 0.138378
\(289\) −16.5379 −0.972819
\(290\) 10.9048 0.640351
\(291\) −9.53847 −0.559155
\(292\) −33.3084 −1.94923
\(293\) 11.3717 0.664344 0.332172 0.943219i \(-0.392218\pi\)
0.332172 + 0.943219i \(0.392218\pi\)
\(294\) −69.0200 −4.02533
\(295\) 14.3760 0.837003
\(296\) 66.9275 3.89008
\(297\) −6.03646 −0.350271
\(298\) 21.2047 1.22835
\(299\) −1.64937 −0.0953854
\(300\) −26.1353 −1.50892
\(301\) −23.5808 −1.35918
\(302\) 49.3017 2.83700
\(303\) 13.0200 0.747978
\(304\) 6.44594 0.369700
\(305\) 9.56819 0.547873
\(306\) −0.950433 −0.0543326
\(307\) 20.2354 1.15490 0.577448 0.816427i \(-0.304048\pi\)
0.577448 + 0.816427i \(0.304048\pi\)
\(308\) 23.5462 1.34167
\(309\) −4.36345 −0.248228
\(310\) 9.93327 0.564172
\(311\) 28.2180 1.60010 0.800049 0.599935i \(-0.204807\pi\)
0.800049 + 0.599935i \(0.204807\pi\)
\(312\) 67.3936 3.81541
\(313\) −12.7460 −0.720448 −0.360224 0.932866i \(-0.617300\pi\)
−0.360224 + 0.932866i \(0.617300\pi\)
\(314\) 3.85669 0.217645
\(315\) −2.98347 −0.168100
\(316\) −50.3540 −2.83263
\(317\) 1.00000 0.0561656
\(318\) 7.31198 0.410035
\(319\) −4.30084 −0.240801
\(320\) −2.36611 −0.132270
\(321\) −9.89829 −0.552468
\(322\) −2.88038 −0.160517
\(323\) −0.679762 −0.0378230
\(324\) −30.8292 −1.71273
\(325\) 27.2784 1.51313
\(326\) 1.95642 0.108356
\(327\) −15.6102 −0.863248
\(328\) 5.16478 0.285177
\(329\) −22.9170 −1.26346
\(330\) −4.67797 −0.257514
\(331\) −22.1309 −1.21642 −0.608211 0.793775i \(-0.708113\pi\)
−0.608211 + 0.793775i \(0.708113\pi\)
\(332\) −48.3236 −2.65210
\(333\) 6.15140 0.337095
\(334\) −37.5055 −2.05221
\(335\) 15.7776 0.862025
\(336\) 49.8703 2.72065
\(337\) −0.334438 −0.0182180 −0.00910900 0.999959i \(-0.502900\pi\)
−0.00910900 + 0.999959i \(0.502900\pi\)
\(338\) −96.5278 −5.25042
\(339\) −16.2618 −0.883219
\(340\) −3.24749 −0.176120
\(341\) −3.91768 −0.212154
\(342\) 1.39818 0.0756052
\(343\) 51.7638 2.79498
\(344\) 28.7052 1.54768
\(345\) 0.392951 0.0211558
\(346\) −8.54003 −0.459115
\(347\) −19.4158 −1.04230 −0.521148 0.853466i \(-0.674496\pi\)
−0.521148 + 0.853466i \(0.674496\pi\)
\(348\) −27.1499 −1.45539
\(349\) 23.5709 1.26172 0.630860 0.775896i \(-0.282702\pi\)
0.630860 + 0.775896i \(0.282702\pi\)
\(350\) 47.6377 2.54634
\(351\) 39.7729 2.12292
\(352\) −4.60865 −0.245642
\(353\) −20.0642 −1.06791 −0.533954 0.845514i \(-0.679294\pi\)
−0.533954 + 0.845514i \(0.679294\pi\)
\(354\) −52.1238 −2.77035
\(355\) 11.1230 0.590346
\(356\) −22.6860 −1.20236
\(357\) −5.25912 −0.278342
\(358\) 44.2118 2.33667
\(359\) −9.74718 −0.514437 −0.257218 0.966353i \(-0.582806\pi\)
−0.257218 + 0.966353i \(0.582806\pi\)
\(360\) 3.63181 0.191413
\(361\) 1.00000 0.0526316
\(362\) 50.9786 2.67938
\(363\) −15.3608 −0.806230
\(364\) −155.141 −8.13159
\(365\) −8.28258 −0.433530
\(366\) −34.6919 −1.81338
\(367\) −18.9550 −0.989442 −0.494721 0.869052i \(-0.664730\pi\)
−0.494721 + 0.869052i \(0.664730\pi\)
\(368\) 1.48574 0.0774495
\(369\) 0.474702 0.0247120
\(370\) 30.6089 1.59128
\(371\) −9.15189 −0.475142
\(372\) −24.7311 −1.28225
\(373\) 20.2175 1.04682 0.523411 0.852080i \(-0.324659\pi\)
0.523411 + 0.852080i \(0.324659\pi\)
\(374\) 1.86523 0.0964487
\(375\) −15.0231 −0.775787
\(376\) 27.8971 1.43868
\(377\) 28.3373 1.45945
\(378\) 69.4576 3.57251
\(379\) −16.9758 −0.871986 −0.435993 0.899950i \(-0.643603\pi\)
−0.435993 + 0.899950i \(0.643603\pi\)
\(380\) 4.77739 0.245075
\(381\) 19.0479 0.975856
\(382\) −40.0806 −2.05070
\(383\) −23.9921 −1.22594 −0.612970 0.790106i \(-0.710025\pi\)
−0.612970 + 0.790106i \(0.710025\pi\)
\(384\) 21.8537 1.11522
\(385\) 5.85508 0.298402
\(386\) 48.8066 2.48419
\(387\) 2.63833 0.134114
\(388\) −26.7293 −1.35697
\(389\) 22.3846 1.13494 0.567471 0.823393i \(-0.307922\pi\)
0.567471 + 0.823393i \(0.307922\pi\)
\(390\) 30.8221 1.56074
\(391\) −0.156680 −0.00792364
\(392\) −105.160 −5.31140
\(393\) 17.1856 0.866901
\(394\) −52.9152 −2.66583
\(395\) −12.5212 −0.630009
\(396\) −2.63446 −0.132387
\(397\) 27.7445 1.39246 0.696229 0.717820i \(-0.254860\pi\)
0.696229 + 0.717820i \(0.254860\pi\)
\(398\) 22.5467 1.13016
\(399\) 7.73670 0.387320
\(400\) −24.5722 −1.22861
\(401\) 35.3887 1.76723 0.883615 0.468215i \(-0.155103\pi\)
0.883615 + 0.468215i \(0.155103\pi\)
\(402\) −57.2058 −2.85317
\(403\) 25.8127 1.28582
\(404\) 36.4854 1.81522
\(405\) −7.66608 −0.380931
\(406\) 49.4870 2.45600
\(407\) −12.0722 −0.598394
\(408\) 6.40198 0.316945
\(409\) −25.7216 −1.27185 −0.635925 0.771750i \(-0.719381\pi\)
−0.635925 + 0.771750i \(0.719381\pi\)
\(410\) 2.36208 0.116655
\(411\) −22.5729 −1.11344
\(412\) −12.2275 −0.602407
\(413\) 65.2397 3.21024
\(414\) 0.322271 0.0158387
\(415\) −12.0163 −0.589856
\(416\) 30.3653 1.48878
\(417\) 3.61699 0.177125
\(418\) −2.74394 −0.134211
\(419\) 22.9381 1.12060 0.560299 0.828290i \(-0.310686\pi\)
0.560299 + 0.828290i \(0.310686\pi\)
\(420\) 36.9613 1.80353
\(421\) 28.5656 1.39220 0.696100 0.717945i \(-0.254917\pi\)
0.696100 + 0.717945i \(0.254917\pi\)
\(422\) −7.51034 −0.365598
\(423\) 2.56406 0.124669
\(424\) 11.1407 0.541039
\(425\) 2.59128 0.125696
\(426\) −40.3291 −1.95395
\(427\) 43.4214 2.10131
\(428\) −27.7376 −1.34075
\(429\) −12.1562 −0.586908
\(430\) 13.1281 0.633095
\(431\) −30.5462 −1.47136 −0.735680 0.677329i \(-0.763137\pi\)
−0.735680 + 0.677329i \(0.763137\pi\)
\(432\) −35.8271 −1.72373
\(433\) 18.6217 0.894903 0.447452 0.894308i \(-0.352332\pi\)
0.447452 + 0.894308i \(0.352332\pi\)
\(434\) 45.0782 2.16382
\(435\) −6.75117 −0.323694
\(436\) −43.7440 −2.09496
\(437\) 0.230492 0.0110259
\(438\) 30.0306 1.43492
\(439\) 7.49912 0.357913 0.178957 0.983857i \(-0.442728\pi\)
0.178957 + 0.983857i \(0.442728\pi\)
\(440\) −7.12745 −0.339788
\(441\) −9.66544 −0.460259
\(442\) −12.2896 −0.584556
\(443\) 3.57056 0.169643 0.0848213 0.996396i \(-0.472968\pi\)
0.0848213 + 0.996396i \(0.472968\pi\)
\(444\) −76.2077 −3.61666
\(445\) −5.64118 −0.267418
\(446\) 71.3950 3.38065
\(447\) −13.1278 −0.620926
\(448\) −10.7376 −0.507306
\(449\) 15.5917 0.735820 0.367910 0.929861i \(-0.380073\pi\)
0.367910 + 0.929861i \(0.380073\pi\)
\(450\) −5.32993 −0.251256
\(451\) −0.931605 −0.0438676
\(452\) −45.5698 −2.14342
\(453\) −30.5228 −1.43409
\(454\) 63.7246 2.99074
\(455\) −38.5778 −1.80856
\(456\) −9.41797 −0.441037
\(457\) −6.59009 −0.308271 −0.154136 0.988050i \(-0.549259\pi\)
−0.154136 + 0.988050i \(0.549259\pi\)
\(458\) 35.6324 1.66499
\(459\) 3.77818 0.176350
\(460\) 1.10115 0.0513415
\(461\) −1.33639 −0.0622418 −0.0311209 0.999516i \(-0.509908\pi\)
−0.0311209 + 0.999516i \(0.509908\pi\)
\(462\) −21.2291 −0.987666
\(463\) 17.4498 0.810962 0.405481 0.914103i \(-0.367104\pi\)
0.405481 + 0.914103i \(0.367104\pi\)
\(464\) −25.5260 −1.18502
\(465\) −6.14970 −0.285186
\(466\) −37.2640 −1.72622
\(467\) −28.5225 −1.31986 −0.659932 0.751325i \(-0.729415\pi\)
−0.659932 + 0.751325i \(0.729415\pi\)
\(468\) 17.3579 0.802369
\(469\) 71.6005 3.30620
\(470\) 12.7586 0.588510
\(471\) −2.38768 −0.110019
\(472\) −79.4170 −3.65546
\(473\) −5.17774 −0.238073
\(474\) 45.3987 2.08523
\(475\) −3.81204 −0.174908
\(476\) −14.7374 −0.675489
\(477\) 1.02396 0.0468837
\(478\) 44.8395 2.05091
\(479\) 15.5893 0.712291 0.356146 0.934430i \(-0.384091\pi\)
0.356146 + 0.934430i \(0.384091\pi\)
\(480\) −7.23434 −0.330201
\(481\) 79.5407 3.62674
\(482\) −15.5448 −0.708046
\(483\) 1.78325 0.0811407
\(484\) −43.0449 −1.95659
\(485\) −6.64659 −0.301806
\(486\) −14.3322 −0.650121
\(487\) 16.8684 0.764381 0.382190 0.924084i \(-0.375170\pi\)
0.382190 + 0.924084i \(0.375170\pi\)
\(488\) −52.8573 −2.39274
\(489\) −1.21122 −0.0547734
\(490\) −48.0945 −2.17269
\(491\) 32.8365 1.48189 0.740945 0.671566i \(-0.234378\pi\)
0.740945 + 0.671566i \(0.234378\pi\)
\(492\) −5.88093 −0.265133
\(493\) 2.69187 0.121236
\(494\) 18.0792 0.813423
\(495\) −0.655094 −0.0294443
\(496\) −23.2519 −1.04404
\(497\) 50.4771 2.26421
\(498\) 43.5681 1.95233
\(499\) −28.1262 −1.25910 −0.629552 0.776958i \(-0.716761\pi\)
−0.629552 + 0.776958i \(0.716761\pi\)
\(500\) −42.0986 −1.88271
\(501\) 23.2197 1.03738
\(502\) 38.0081 1.69638
\(503\) −26.8851 −1.19875 −0.599374 0.800469i \(-0.704584\pi\)
−0.599374 + 0.800469i \(0.704584\pi\)
\(504\) 16.4815 0.734146
\(505\) 9.07258 0.403724
\(506\) −0.632457 −0.0281162
\(507\) 59.7605 2.65406
\(508\) 53.3774 2.36824
\(509\) −34.1150 −1.51212 −0.756060 0.654502i \(-0.772878\pi\)
−0.756060 + 0.654502i \(0.772878\pi\)
\(510\) 2.92791 0.129650
\(511\) −37.5872 −1.66276
\(512\) 50.2705 2.22166
\(513\) −5.55809 −0.245396
\(514\) −45.0608 −1.98755
\(515\) −3.04054 −0.133982
\(516\) −32.6854 −1.43890
\(517\) −5.03199 −0.221306
\(518\) 138.906 6.10320
\(519\) 5.28715 0.232080
\(520\) 46.9612 2.05938
\(521\) 5.07349 0.222274 0.111137 0.993805i \(-0.464551\pi\)
0.111137 + 0.993805i \(0.464551\pi\)
\(522\) −5.53684 −0.242341
\(523\) 3.54269 0.154911 0.0774555 0.996996i \(-0.475320\pi\)
0.0774555 + 0.996996i \(0.475320\pi\)
\(524\) 48.1587 2.10382
\(525\) −29.4926 −1.28716
\(526\) −50.1814 −2.18802
\(527\) 2.45205 0.106813
\(528\) 10.9502 0.476548
\(529\) −22.9469 −0.997690
\(530\) 5.09513 0.221318
\(531\) −7.29932 −0.316764
\(532\) 21.6803 0.939960
\(533\) 6.13813 0.265872
\(534\) 20.4535 0.885111
\(535\) −6.89732 −0.298197
\(536\) −87.1600 −3.76474
\(537\) −27.3716 −1.18117
\(538\) −37.1654 −1.60231
\(539\) 18.9685 0.817030
\(540\) −26.5532 −1.14267
\(541\) −20.8311 −0.895599 −0.447800 0.894134i \(-0.647792\pi\)
−0.447800 + 0.894134i \(0.647792\pi\)
\(542\) −49.7399 −2.13651
\(543\) −31.5609 −1.35441
\(544\) 2.88452 0.123673
\(545\) −10.8775 −0.465942
\(546\) 139.874 5.98604
\(547\) −30.5107 −1.30454 −0.652272 0.757985i \(-0.726184\pi\)
−0.652272 + 0.757985i \(0.726184\pi\)
\(548\) −63.2552 −2.70213
\(549\) −4.85819 −0.207343
\(550\) 10.4600 0.446017
\(551\) −3.96002 −0.168702
\(552\) −2.17077 −0.0923940
\(553\) −56.8224 −2.41633
\(554\) 29.9939 1.27432
\(555\) −18.9500 −0.804384
\(556\) 10.1358 0.429853
\(557\) −30.2259 −1.28071 −0.640357 0.768078i \(-0.721213\pi\)
−0.640357 + 0.768078i \(0.721213\pi\)
\(558\) −5.04356 −0.213511
\(559\) 34.1149 1.44291
\(560\) 34.7506 1.46848
\(561\) −1.15477 −0.0487543
\(562\) −73.2963 −3.09182
\(563\) −20.3338 −0.856966 −0.428483 0.903550i \(-0.640952\pi\)
−0.428483 + 0.903550i \(0.640952\pi\)
\(564\) −31.7653 −1.33756
\(565\) −11.3315 −0.476721
\(566\) −20.7650 −0.872818
\(567\) −34.7894 −1.46102
\(568\) −61.4463 −2.57823
\(569\) 1.56010 0.0654027 0.0327014 0.999465i \(-0.489589\pi\)
0.0327014 + 0.999465i \(0.489589\pi\)
\(570\) −4.30726 −0.180411
\(571\) 1.29713 0.0542831 0.0271416 0.999632i \(-0.491360\pi\)
0.0271416 + 0.999632i \(0.491360\pi\)
\(572\) −34.0649 −1.42433
\(573\) 24.8139 1.03662
\(574\) 10.7194 0.447418
\(575\) −0.878645 −0.0366420
\(576\) 1.20138 0.0500574
\(577\) 30.6272 1.27503 0.637513 0.770440i \(-0.279963\pi\)
0.637513 + 0.770440i \(0.279963\pi\)
\(578\) 41.7830 1.73794
\(579\) −30.2162 −1.25574
\(580\) −18.9186 −0.785551
\(581\) −54.5311 −2.26233
\(582\) 24.0989 0.998932
\(583\) −2.00952 −0.0832257
\(584\) 45.7552 1.89337
\(585\) 4.31627 0.178456
\(586\) −28.7307 −1.18685
\(587\) 13.3473 0.550903 0.275452 0.961315i \(-0.411173\pi\)
0.275452 + 0.961315i \(0.411173\pi\)
\(588\) 119.742 4.93807
\(589\) −3.60722 −0.148633
\(590\) −36.3209 −1.49531
\(591\) 32.7599 1.34756
\(592\) −71.6497 −2.94479
\(593\) −31.1248 −1.27814 −0.639071 0.769148i \(-0.720681\pi\)
−0.639071 + 0.769148i \(0.720681\pi\)
\(594\) 15.2511 0.625760
\(595\) −3.66466 −0.150236
\(596\) −36.7877 −1.50688
\(597\) −13.9587 −0.571292
\(598\) 4.16712 0.170406
\(599\) −18.5336 −0.757264 −0.378632 0.925547i \(-0.623605\pi\)
−0.378632 + 0.925547i \(0.623605\pi\)
\(600\) 35.9017 1.46568
\(601\) 1.96473 0.0801428 0.0400714 0.999197i \(-0.487241\pi\)
0.0400714 + 0.999197i \(0.487241\pi\)
\(602\) 59.5768 2.42817
\(603\) −8.01100 −0.326233
\(604\) −85.5329 −3.48029
\(605\) −10.7037 −0.435166
\(606\) −32.8949 −1.33627
\(607\) −2.33732 −0.0948689 −0.0474345 0.998874i \(-0.515105\pi\)
−0.0474345 + 0.998874i \(0.515105\pi\)
\(608\) −4.24343 −0.172094
\(609\) −30.6375 −1.24149
\(610\) −24.1740 −0.978777
\(611\) 33.1546 1.34129
\(612\) 1.64889 0.0666526
\(613\) 39.2279 1.58440 0.792201 0.610261i \(-0.208935\pi\)
0.792201 + 0.610261i \(0.208935\pi\)
\(614\) −51.1247 −2.06323
\(615\) −1.46237 −0.0589684
\(616\) −32.3451 −1.30322
\(617\) 33.8445 1.36253 0.681263 0.732038i \(-0.261431\pi\)
0.681263 + 0.732038i \(0.261431\pi\)
\(618\) 11.0242 0.443460
\(619\) −6.80103 −0.273356 −0.136678 0.990615i \(-0.543643\pi\)
−0.136678 + 0.990615i \(0.543643\pi\)
\(620\) −17.2331 −0.692098
\(621\) −1.28110 −0.0514087
\(622\) −71.2928 −2.85858
\(623\) −25.6002 −1.02565
\(624\) −72.1487 −2.88826
\(625\) 8.59183 0.343673
\(626\) 32.2028 1.28708
\(627\) 1.69878 0.0678427
\(628\) −6.69091 −0.266997
\(629\) 7.55588 0.301273
\(630\) 7.53774 0.300311
\(631\) −28.3081 −1.12693 −0.563463 0.826141i \(-0.690531\pi\)
−0.563463 + 0.826141i \(0.690531\pi\)
\(632\) 69.1705 2.75145
\(633\) 4.64966 0.184808
\(634\) −2.52650 −0.100340
\(635\) 13.2730 0.526722
\(636\) −12.6855 −0.503011
\(637\) −124.979 −4.95185
\(638\) 10.8661 0.430192
\(639\) −5.64762 −0.223416
\(640\) 15.2281 0.601944
\(641\) 46.3460 1.83056 0.915278 0.402822i \(-0.131971\pi\)
0.915278 + 0.402822i \(0.131971\pi\)
\(642\) 25.0080 0.986986
\(643\) −23.8157 −0.939199 −0.469600 0.882879i \(-0.655602\pi\)
−0.469600 + 0.882879i \(0.655602\pi\)
\(644\) 4.99714 0.196915
\(645\) −8.12766 −0.320026
\(646\) 1.71742 0.0675709
\(647\) −4.30112 −0.169094 −0.0845472 0.996419i \(-0.526944\pi\)
−0.0845472 + 0.996419i \(0.526944\pi\)
\(648\) 42.3495 1.66365
\(649\) 14.3250 0.562304
\(650\) −68.9187 −2.70321
\(651\) −27.9080 −1.09380
\(652\) −3.39416 −0.132926
\(653\) −1.74204 −0.0681714 −0.0340857 0.999419i \(-0.510852\pi\)
−0.0340857 + 0.999419i \(0.510852\pi\)
\(654\) 39.4392 1.54220
\(655\) 11.9753 0.467913
\(656\) −5.52919 −0.215879
\(657\) 4.20543 0.164069
\(658\) 57.8998 2.25717
\(659\) −1.76466 −0.0687413 −0.0343706 0.999409i \(-0.510943\pi\)
−0.0343706 + 0.999409i \(0.510943\pi\)
\(660\) 8.11574 0.315905
\(661\) −22.2928 −0.867088 −0.433544 0.901132i \(-0.642737\pi\)
−0.433544 + 0.901132i \(0.642737\pi\)
\(662\) 55.9135 2.17314
\(663\) 7.60850 0.295490
\(664\) 66.3813 2.57609
\(665\) 5.39109 0.209057
\(666\) −15.5415 −0.602221
\(667\) −0.912753 −0.0353420
\(668\) 65.0678 2.51755
\(669\) −44.2008 −1.70890
\(670\) −39.8622 −1.54001
\(671\) 9.53422 0.368064
\(672\) −32.8302 −1.26645
\(673\) −4.85367 −0.187095 −0.0935476 0.995615i \(-0.529821\pi\)
−0.0935476 + 0.995615i \(0.529821\pi\)
\(674\) 0.844956 0.0325465
\(675\) 21.1877 0.815514
\(676\) 167.465 6.44095
\(677\) 3.03074 0.116481 0.0582404 0.998303i \(-0.481451\pi\)
0.0582404 + 0.998303i \(0.481451\pi\)
\(678\) 41.0853 1.57787
\(679\) −30.1629 −1.15755
\(680\) 4.46102 0.171072
\(681\) −39.4520 −1.51180
\(682\) 9.89800 0.379014
\(683\) −1.60987 −0.0615999 −0.0308000 0.999526i \(-0.509805\pi\)
−0.0308000 + 0.999526i \(0.509805\pi\)
\(684\) −2.42569 −0.0927487
\(685\) −15.7292 −0.600983
\(686\) −130.781 −4.99325
\(687\) −22.0601 −0.841645
\(688\) −30.7305 −1.17159
\(689\) 13.2403 0.504414
\(690\) −0.992789 −0.0377948
\(691\) −48.1106 −1.83022 −0.915108 0.403210i \(-0.867894\pi\)
−0.915108 + 0.403210i \(0.867894\pi\)
\(692\) 14.8160 0.563219
\(693\) −2.97288 −0.112930
\(694\) 49.0540 1.86207
\(695\) 2.52039 0.0956040
\(696\) 37.2953 1.41368
\(697\) 0.583086 0.0220859
\(698\) −59.5518 −2.25407
\(699\) 23.0702 0.872595
\(700\) −82.6461 −3.12373
\(701\) −12.5629 −0.474495 −0.237247 0.971449i \(-0.576245\pi\)
−0.237247 + 0.971449i \(0.576245\pi\)
\(702\) −100.486 −3.79260
\(703\) −11.1155 −0.419228
\(704\) −2.35771 −0.0888595
\(705\) −7.89887 −0.297489
\(706\) 50.6921 1.90782
\(707\) 41.1723 1.54844
\(708\) 90.4289 3.39853
\(709\) 14.9568 0.561713 0.280857 0.959750i \(-0.409381\pi\)
0.280857 + 0.959750i \(0.409381\pi\)
\(710\) −28.1021 −1.05465
\(711\) 6.35756 0.238427
\(712\) 31.1634 1.16790
\(713\) −0.831435 −0.0311375
\(714\) 13.2871 0.497259
\(715\) −8.47069 −0.316786
\(716\) −76.7024 −2.86650
\(717\) −27.7602 −1.03672
\(718\) 24.6262 0.919042
\(719\) −29.6085 −1.10421 −0.552105 0.833775i \(-0.686175\pi\)
−0.552105 + 0.833775i \(0.686175\pi\)
\(720\) −3.88806 −0.144900
\(721\) −13.7983 −0.513874
\(722\) −2.52650 −0.0940265
\(723\) 9.62381 0.357913
\(724\) −88.4421 −3.28692
\(725\) 15.0957 0.560642
\(726\) 38.8089 1.44033
\(727\) 48.2384 1.78906 0.894531 0.447005i \(-0.147509\pi\)
0.894531 + 0.447005i \(0.147509\pi\)
\(728\) 213.114 7.89855
\(729\) 29.9736 1.11013
\(730\) 20.9259 0.774503
\(731\) 3.24071 0.119862
\(732\) 60.1865 2.22456
\(733\) −40.9201 −1.51142 −0.755709 0.654908i \(-0.772707\pi\)
−0.755709 + 0.654908i \(0.772707\pi\)
\(734\) 47.8897 1.76764
\(735\) 29.7754 1.09828
\(736\) −0.978077 −0.0360524
\(737\) 15.7216 0.579113
\(738\) −1.19933 −0.0441481
\(739\) 24.2818 0.893221 0.446611 0.894728i \(-0.352631\pi\)
0.446611 + 0.894728i \(0.352631\pi\)
\(740\) −53.1030 −1.95211
\(741\) −11.1929 −0.411181
\(742\) 23.1222 0.848843
\(743\) 48.3605 1.77417 0.887087 0.461602i \(-0.152725\pi\)
0.887087 + 0.461602i \(0.152725\pi\)
\(744\) 33.9727 1.24550
\(745\) −9.14774 −0.335147
\(746\) −51.0794 −1.87015
\(747\) 6.10120 0.223231
\(748\) −3.23596 −0.118318
\(749\) −31.3007 −1.14370
\(750\) 37.9557 1.38595
\(751\) 2.37184 0.0865497 0.0432749 0.999063i \(-0.486221\pi\)
0.0432749 + 0.999063i \(0.486221\pi\)
\(752\) −29.8655 −1.08908
\(753\) −23.5309 −0.857513
\(754\) −71.5941 −2.60730
\(755\) −21.2689 −0.774054
\(756\) −120.501 −4.38258
\(757\) 36.2025 1.31580 0.657902 0.753104i \(-0.271444\pi\)
0.657902 + 0.753104i \(0.271444\pi\)
\(758\) 42.8892 1.55781
\(759\) 0.391556 0.0142126
\(760\) −6.56263 −0.238051
\(761\) 6.61942 0.239954 0.119977 0.992777i \(-0.461718\pi\)
0.119977 + 0.992777i \(0.461718\pi\)
\(762\) −48.1246 −1.74337
\(763\) −49.3633 −1.78707
\(764\) 69.5352 2.51570
\(765\) 0.410019 0.0148243
\(766\) 60.6160 2.19014
\(767\) −94.3839 −3.40801
\(768\) −48.4222 −1.74729
\(769\) −31.7930 −1.14649 −0.573243 0.819385i \(-0.694315\pi\)
−0.573243 + 0.819385i \(0.694315\pi\)
\(770\) −14.7928 −0.533097
\(771\) 27.8972 1.00469
\(772\) −84.6739 −3.04748
\(773\) 42.4789 1.52786 0.763929 0.645300i \(-0.223268\pi\)
0.763929 + 0.645300i \(0.223268\pi\)
\(774\) −6.66574 −0.239595
\(775\) 13.7509 0.493945
\(776\) 36.7176 1.31808
\(777\) −85.9972 −3.08513
\(778\) −56.5545 −2.02758
\(779\) −0.857779 −0.0307331
\(780\) −53.4728 −1.91463
\(781\) 11.0835 0.396598
\(782\) 0.395851 0.0141556
\(783\) 22.0102 0.786579
\(784\) 112.580 4.02072
\(785\) −1.66378 −0.0593830
\(786\) −43.4195 −1.54872
\(787\) −19.1658 −0.683186 −0.341593 0.939848i \(-0.610966\pi\)
−0.341593 + 0.939848i \(0.610966\pi\)
\(788\) 91.8018 3.27031
\(789\) 31.0674 1.10603
\(790\) 31.6347 1.12551
\(791\) −51.4236 −1.82841
\(792\) 3.61892 0.128593
\(793\) −62.8188 −2.23076
\(794\) −70.0964 −2.48763
\(795\) −3.15440 −0.111875
\(796\) −39.1160 −1.38643
\(797\) −0.226571 −0.00802554 −0.00401277 0.999992i \(-0.501277\pi\)
−0.00401277 + 0.999992i \(0.501277\pi\)
\(798\) −19.5468 −0.691948
\(799\) 3.14949 0.111421
\(800\) 16.1761 0.571912
\(801\) 2.86428 0.101204
\(802\) −89.4095 −3.15716
\(803\) −8.25317 −0.291248
\(804\) 99.2456 3.50012
\(805\) 1.24260 0.0437960
\(806\) −65.2157 −2.29713
\(807\) 23.0091 0.809960
\(808\) −50.1194 −1.76319
\(809\) 21.5192 0.756574 0.378287 0.925688i \(-0.376513\pi\)
0.378287 + 0.925688i \(0.376513\pi\)
\(810\) 19.3683 0.680534
\(811\) 28.8811 1.01415 0.507077 0.861901i \(-0.330726\pi\)
0.507077 + 0.861901i \(0.330726\pi\)
\(812\) −85.8543 −3.01290
\(813\) 30.7941 1.07999
\(814\) 30.5003 1.06903
\(815\) −0.844004 −0.0295642
\(816\) −6.85368 −0.239927
\(817\) −4.76742 −0.166791
\(818\) 64.9855 2.27217
\(819\) 19.5876 0.684448
\(820\) −4.09795 −0.143106
\(821\) 26.8015 0.935380 0.467690 0.883893i \(-0.345086\pi\)
0.467690 + 0.883893i \(0.345086\pi\)
\(822\) 57.0303 1.98916
\(823\) 21.0600 0.734106 0.367053 0.930200i \(-0.380367\pi\)
0.367053 + 0.930200i \(0.380367\pi\)
\(824\) 16.7968 0.585143
\(825\) −6.47582 −0.225459
\(826\) −164.828 −5.73510
\(827\) 24.9182 0.866489 0.433245 0.901276i \(-0.357369\pi\)
0.433245 + 0.901276i \(0.357369\pi\)
\(828\) −0.559103 −0.0194302
\(829\) 23.7210 0.823864 0.411932 0.911215i \(-0.364854\pi\)
0.411932 + 0.911215i \(0.364854\pi\)
\(830\) 30.3591 1.05378
\(831\) −18.5692 −0.644160
\(832\) 15.5344 0.538559
\(833\) −11.8722 −0.411349
\(834\) −9.13832 −0.316434
\(835\) 16.1800 0.559930
\(836\) 4.76043 0.164643
\(837\) 20.0493 0.693004
\(838\) −57.9530 −2.00195
\(839\) −3.94848 −0.136317 −0.0681584 0.997675i \(-0.521712\pi\)
−0.0681584 + 0.997675i \(0.521712\pi\)
\(840\) −50.7731 −1.75184
\(841\) −13.3182 −0.459250
\(842\) −72.1708 −2.48717
\(843\) 45.3778 1.56290
\(844\) 13.0296 0.448497
\(845\) 41.6423 1.43254
\(846\) −6.47810 −0.222722
\(847\) −48.5743 −1.66903
\(848\) −11.9267 −0.409566
\(849\) 12.8556 0.441205
\(850\) −6.54686 −0.224555
\(851\) −2.56203 −0.0878253
\(852\) 69.9665 2.39701
\(853\) 17.6713 0.605053 0.302527 0.953141i \(-0.402170\pi\)
0.302527 + 0.953141i \(0.402170\pi\)
\(854\) −109.704 −3.75399
\(855\) −0.603180 −0.0206283
\(856\) 38.1027 1.30232
\(857\) −18.0772 −0.617507 −0.308754 0.951142i \(-0.599912\pi\)
−0.308754 + 0.951142i \(0.599912\pi\)
\(858\) 30.7126 1.04851
\(859\) 7.23881 0.246985 0.123493 0.992345i \(-0.460590\pi\)
0.123493 + 0.992345i \(0.460590\pi\)
\(860\) −22.7758 −0.776650
\(861\) −6.63638 −0.226167
\(862\) 77.1749 2.62859
\(863\) −31.2903 −1.06514 −0.532568 0.846387i \(-0.678773\pi\)
−0.532568 + 0.846387i \(0.678773\pi\)
\(864\) 23.5854 0.802391
\(865\) 3.68419 0.125266
\(866\) −47.0477 −1.59875
\(867\) −25.8679 −0.878521
\(868\) −78.2055 −2.65447
\(869\) −12.4767 −0.423244
\(870\) 17.0568 0.578280
\(871\) −103.586 −3.50989
\(872\) 60.0904 2.03492
\(873\) 3.37477 0.114219
\(874\) −0.582338 −0.0196979
\(875\) −47.5065 −1.60601
\(876\) −52.0997 −1.76028
\(877\) 38.9893 1.31658 0.658288 0.752766i \(-0.271281\pi\)
0.658288 + 0.752766i \(0.271281\pi\)
\(878\) −18.9465 −0.639413
\(879\) 17.7872 0.599948
\(880\) 7.63034 0.257219
\(881\) 16.8434 0.567468 0.283734 0.958903i \(-0.408427\pi\)
0.283734 + 0.958903i \(0.408427\pi\)
\(882\) 24.4197 0.822254
\(883\) 51.2388 1.72432 0.862161 0.506634i \(-0.169111\pi\)
0.862161 + 0.506634i \(0.169111\pi\)
\(884\) 21.3210 0.717104
\(885\) 22.4863 0.755870
\(886\) −9.02101 −0.303067
\(887\) −50.0077 −1.67909 −0.839547 0.543287i \(-0.817180\pi\)
−0.839547 + 0.543287i \(0.817180\pi\)
\(888\) 104.685 3.51301
\(889\) 60.2341 2.02019
\(890\) 14.2524 0.477742
\(891\) −7.63886 −0.255912
\(892\) −123.862 −4.14722
\(893\) −4.63322 −0.155045
\(894\) 33.1675 1.10929
\(895\) −19.0731 −0.637542
\(896\) 69.1067 2.30869
\(897\) −2.57987 −0.0861394
\(898\) −39.3925 −1.31454
\(899\) 14.2847 0.476420
\(900\) 9.24683 0.308228
\(901\) 1.25774 0.0419015
\(902\) 2.35370 0.0783695
\(903\) −36.8841 −1.22743
\(904\) 62.5985 2.08200
\(905\) −21.9923 −0.731048
\(906\) 77.1157 2.56200
\(907\) 8.58049 0.284910 0.142455 0.989801i \(-0.454500\pi\)
0.142455 + 0.989801i \(0.454500\pi\)
\(908\) −110.555 −3.66890
\(909\) −4.60655 −0.152789
\(910\) 97.4667 3.23099
\(911\) 13.8391 0.458509 0.229254 0.973367i \(-0.426371\pi\)
0.229254 + 0.973367i \(0.426371\pi\)
\(912\) 10.0825 0.333864
\(913\) −11.9736 −0.396269
\(914\) 16.6498 0.550728
\(915\) 14.9662 0.494766
\(916\) −61.8182 −2.04253
\(917\) 54.3451 1.79463
\(918\) −9.54556 −0.315051
\(919\) 29.9296 0.987285 0.493642 0.869665i \(-0.335665\pi\)
0.493642 + 0.869665i \(0.335665\pi\)
\(920\) −1.51263 −0.0498701
\(921\) 31.6514 1.04295
\(922\) 3.37638 0.111195
\(923\) −73.0265 −2.40370
\(924\) 36.8300 1.21162
\(925\) 42.3726 1.39320
\(926\) −44.0869 −1.44879
\(927\) 1.54381 0.0507055
\(928\) 16.8041 0.551620
\(929\) 16.1468 0.529760 0.264880 0.964281i \(-0.414668\pi\)
0.264880 + 0.964281i \(0.414668\pi\)
\(930\) 15.5372 0.509485
\(931\) 17.4653 0.572402
\(932\) 64.6488 2.11764
\(933\) 44.1375 1.44500
\(934\) 72.0620 2.35794
\(935\) −0.804664 −0.0263153
\(936\) −23.8442 −0.779373
\(937\) −32.5614 −1.06373 −0.531867 0.846828i \(-0.678510\pi\)
−0.531867 + 0.846828i \(0.678510\pi\)
\(938\) −180.898 −5.90654
\(939\) −19.9368 −0.650613
\(940\) −22.1347 −0.721955
\(941\) 30.4932 0.994049 0.497024 0.867737i \(-0.334426\pi\)
0.497024 + 0.867737i \(0.334426\pi\)
\(942\) 6.03247 0.196548
\(943\) −0.197711 −0.00643836
\(944\) 85.0204 2.76718
\(945\) −29.9642 −0.974734
\(946\) 13.0815 0.425317
\(947\) −4.38751 −0.142575 −0.0712874 0.997456i \(-0.522711\pi\)
−0.0712874 + 0.997456i \(0.522711\pi\)
\(948\) −78.7617 −2.55806
\(949\) 54.3783 1.76519
\(950\) 9.63110 0.312474
\(951\) 1.56416 0.0507213
\(952\) 20.2446 0.656130
\(953\) −55.9899 −1.81369 −0.906846 0.421462i \(-0.861517\pi\)
−0.906846 + 0.421462i \(0.861517\pi\)
\(954\) −2.58702 −0.0837579
\(955\) 17.2908 0.559518
\(956\) −77.7914 −2.51596
\(957\) −6.72720 −0.217460
\(958\) −39.3862 −1.27251
\(959\) −71.3808 −2.30501
\(960\) −3.70097 −0.119448
\(961\) −17.9880 −0.580257
\(962\) −200.959 −6.47919
\(963\) 3.50207 0.112853
\(964\) 26.9685 0.868596
\(965\) −21.0553 −0.677793
\(966\) −4.50537 −0.144958
\(967\) −40.7878 −1.31165 −0.655824 0.754913i \(-0.727679\pi\)
−0.655824 + 0.754913i \(0.727679\pi\)
\(968\) 59.1301 1.90051
\(969\) −1.06326 −0.0341567
\(970\) 16.7926 0.539178
\(971\) −49.7805 −1.59753 −0.798766 0.601642i \(-0.794513\pi\)
−0.798766 + 0.601642i \(0.794513\pi\)
\(972\) 24.8647 0.797536
\(973\) 11.4378 0.366679
\(974\) −42.6180 −1.36557
\(975\) 42.6677 1.36646
\(976\) 56.5868 1.81130
\(977\) −17.1616 −0.549047 −0.274524 0.961580i \(-0.588520\pi\)
−0.274524 + 0.961580i \(0.588520\pi\)
\(978\) 3.06015 0.0978528
\(979\) −5.62115 −0.179653
\(980\) 83.4385 2.66535
\(981\) 5.52300 0.176336
\(982\) −82.9613 −2.64740
\(983\) −18.4797 −0.589412 −0.294706 0.955588i \(-0.595222\pi\)
−0.294706 + 0.955588i \(0.595222\pi\)
\(984\) 8.07853 0.257534
\(985\) 22.8277 0.727352
\(986\) −6.80100 −0.216588
\(987\) −35.8458 −1.14099
\(988\) −31.3654 −0.997867
\(989\) −1.09885 −0.0349415
\(990\) 1.65509 0.0526023
\(991\) −28.4916 −0.905065 −0.452533 0.891748i \(-0.649479\pi\)
−0.452533 + 0.891748i \(0.649479\pi\)
\(992\) 15.3070 0.485997
\(993\) −34.6162 −1.09851
\(994\) −127.530 −4.04502
\(995\) −9.72670 −0.308357
\(996\) −75.5857 −2.39502
\(997\) −31.4158 −0.994948 −0.497474 0.867479i \(-0.665739\pi\)
−0.497474 + 0.867479i \(0.665739\pi\)
\(998\) 71.0609 2.24939
\(999\) 61.7809 1.95466
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 6023.2.a.a.1.5 98
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6023.2.a.a.1.5 98 1.1 even 1 trivial