Properties

Label 6038.2.a.d.1.10
Level $6038$
Weight $2$
Character 6038.1
Self dual yes
Analytic conductor $48.214$
Analytic rank $0$
Dimension $69$
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] = [6038,2,Mod(1,6038)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6038, 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("6038.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6038 = 2 \cdot 3019 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6038.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: \(48.2136727404\)
Analytic rank: \(0\)
Dimension: \(69\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6038.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -2.29973 q^{3} +1.00000 q^{4} +4.30527 q^{5} +2.29973 q^{6} -2.14109 q^{7} -1.00000 q^{8} +2.28878 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -2.29973 q^{3} +1.00000 q^{4} +4.30527 q^{5} +2.29973 q^{6} -2.14109 q^{7} -1.00000 q^{8} +2.28878 q^{9} -4.30527 q^{10} +3.89862 q^{11} -2.29973 q^{12} +5.85266 q^{13} +2.14109 q^{14} -9.90096 q^{15} +1.00000 q^{16} -7.43093 q^{17} -2.28878 q^{18} -4.19092 q^{19} +4.30527 q^{20} +4.92393 q^{21} -3.89862 q^{22} -2.89167 q^{23} +2.29973 q^{24} +13.5353 q^{25} -5.85266 q^{26} +1.63563 q^{27} -2.14109 q^{28} +0.280020 q^{29} +9.90096 q^{30} -1.81691 q^{31} -1.00000 q^{32} -8.96579 q^{33} +7.43093 q^{34} -9.21795 q^{35} +2.28878 q^{36} +4.64283 q^{37} +4.19092 q^{38} -13.4596 q^{39} -4.30527 q^{40} -5.26094 q^{41} -4.92393 q^{42} +7.25858 q^{43} +3.89862 q^{44} +9.85378 q^{45} +2.89167 q^{46} -8.27119 q^{47} -2.29973 q^{48} -2.41575 q^{49} -13.5353 q^{50} +17.0892 q^{51} +5.85266 q^{52} +8.63037 q^{53} -1.63563 q^{54} +16.7846 q^{55} +2.14109 q^{56} +9.63799 q^{57} -0.280020 q^{58} +1.39283 q^{59} -9.90096 q^{60} -4.72509 q^{61} +1.81691 q^{62} -4.90047 q^{63} +1.00000 q^{64} +25.1973 q^{65} +8.96579 q^{66} +11.6766 q^{67} -7.43093 q^{68} +6.65007 q^{69} +9.21795 q^{70} -3.22774 q^{71} -2.28878 q^{72} +14.8491 q^{73} -4.64283 q^{74} -31.1276 q^{75} -4.19092 q^{76} -8.34729 q^{77} +13.4596 q^{78} +4.69214 q^{79} +4.30527 q^{80} -10.6278 q^{81} +5.26094 q^{82} -2.93193 q^{83} +4.92393 q^{84} -31.9921 q^{85} -7.25858 q^{86} -0.643970 q^{87} -3.89862 q^{88} +7.89771 q^{89} -9.85378 q^{90} -12.5311 q^{91} -2.89167 q^{92} +4.17840 q^{93} +8.27119 q^{94} -18.0430 q^{95} +2.29973 q^{96} +15.0883 q^{97} +2.41575 q^{98} +8.92307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 69 q - 69 q^{2} + 8 q^{3} + 69 q^{4} + 18 q^{5} - 8 q^{6} + 32 q^{7} - 69 q^{8} + 79 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 69 q - 69 q^{2} + 8 q^{3} + 69 q^{4} + 18 q^{5} - 8 q^{6} + 32 q^{7} - 69 q^{8} + 79 q^{9} - 18 q^{10} - 4 q^{11} + 8 q^{12} + 40 q^{13} - 32 q^{14} + 6 q^{15} + 69 q^{16} + 6 q^{17} - 79 q^{18} + 13 q^{19} + 18 q^{20} + 23 q^{21} + 4 q^{22} + 11 q^{23} - 8 q^{24} + 111 q^{25} - 40 q^{26} + 32 q^{27} + 32 q^{28} + 23 q^{29} - 6 q^{30} + 30 q^{31} - 69 q^{32} + 37 q^{33} - 6 q^{34} - 12 q^{35} + 79 q^{36} + 81 q^{37} - 13 q^{38} - 8 q^{39} - 18 q^{40} - 13 q^{41} - 23 q^{42} + 42 q^{43} - 4 q^{44} + 89 q^{45} - 11 q^{46} + 35 q^{47} + 8 q^{48} + 115 q^{49} - 111 q^{50} - 21 q^{51} + 40 q^{52} + 41 q^{53} - 32 q^{54} + 28 q^{55} - 32 q^{56} + 39 q^{57} - 23 q^{58} - 24 q^{59} + 6 q^{60} + 69 q^{61} - 30 q^{62} + 79 q^{63} + 69 q^{64} + 15 q^{65} - 37 q^{66} + 87 q^{67} + 6 q^{68} + 51 q^{69} + 12 q^{70} - 22 q^{71} - 79 q^{72} + 104 q^{73} - 81 q^{74} + 39 q^{75} + 13 q^{76} + 47 q^{77} + 8 q^{78} + 16 q^{79} + 18 q^{80} + 105 q^{81} + 13 q^{82} + 30 q^{83} + 23 q^{84} + 74 q^{85} - 42 q^{86} + 47 q^{87} + 4 q^{88} - 4 q^{89} - 89 q^{90} + 70 q^{91} + 11 q^{92} + 104 q^{93} - 35 q^{94} - 36 q^{95} - 8 q^{96} + 158 q^{97} - 115 q^{98} + 34 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −2.29973 −1.32775 −0.663876 0.747843i \(-0.731090\pi\)
−0.663876 + 0.747843i \(0.731090\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.30527 1.92537 0.962687 0.270619i \(-0.0872283\pi\)
0.962687 + 0.270619i \(0.0872283\pi\)
\(6\) 2.29973 0.938862
\(7\) −2.14109 −0.809255 −0.404627 0.914482i \(-0.632599\pi\)
−0.404627 + 0.914482i \(0.632599\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.28878 0.762925
\(10\) −4.30527 −1.36144
\(11\) 3.89862 1.17548 0.587740 0.809050i \(-0.300018\pi\)
0.587740 + 0.809050i \(0.300018\pi\)
\(12\) −2.29973 −0.663876
\(13\) 5.85266 1.62324 0.811618 0.584189i \(-0.198587\pi\)
0.811618 + 0.584189i \(0.198587\pi\)
\(14\) 2.14109 0.572229
\(15\) −9.90096 −2.55642
\(16\) 1.00000 0.250000
\(17\) −7.43093 −1.80226 −0.901132 0.433544i \(-0.857263\pi\)
−0.901132 + 0.433544i \(0.857263\pi\)
\(18\) −2.28878 −0.539469
\(19\) −4.19092 −0.961462 −0.480731 0.876868i \(-0.659629\pi\)
−0.480731 + 0.876868i \(0.659629\pi\)
\(20\) 4.30527 0.962687
\(21\) 4.92393 1.07449
\(22\) −3.89862 −0.831189
\(23\) −2.89167 −0.602955 −0.301477 0.953473i \(-0.597480\pi\)
−0.301477 + 0.953473i \(0.597480\pi\)
\(24\) 2.29973 0.469431
\(25\) 13.5353 2.70706
\(26\) −5.85266 −1.14780
\(27\) 1.63563 0.314777
\(28\) −2.14109 −0.404627
\(29\) 0.280020 0.0519983 0.0259992 0.999662i \(-0.491723\pi\)
0.0259992 + 0.999662i \(0.491723\pi\)
\(30\) 9.90096 1.80766
\(31\) −1.81691 −0.326326 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(32\) −1.00000 −0.176777
\(33\) −8.96579 −1.56074
\(34\) 7.43093 1.27439
\(35\) −9.21795 −1.55812
\(36\) 2.28878 0.381463
\(37\) 4.64283 0.763276 0.381638 0.924312i \(-0.375360\pi\)
0.381638 + 0.924312i \(0.375360\pi\)
\(38\) 4.19092 0.679857
\(39\) −13.4596 −2.15525
\(40\) −4.30527 −0.680722
\(41\) −5.26094 −0.821621 −0.410811 0.911721i \(-0.634754\pi\)
−0.410811 + 0.911721i \(0.634754\pi\)
\(42\) −4.92393 −0.759779
\(43\) 7.25858 1.10692 0.553461 0.832875i \(-0.313307\pi\)
0.553461 + 0.832875i \(0.313307\pi\)
\(44\) 3.89862 0.587740
\(45\) 9.85378 1.46892
\(46\) 2.89167 0.426353
\(47\) −8.27119 −1.20648 −0.603238 0.797561i \(-0.706123\pi\)
−0.603238 + 0.797561i \(0.706123\pi\)
\(48\) −2.29973 −0.331938
\(49\) −2.41575 −0.345107
\(50\) −13.5353 −1.91418
\(51\) 17.0892 2.39296
\(52\) 5.85266 0.811618
\(53\) 8.63037 1.18547 0.592736 0.805397i \(-0.298048\pi\)
0.592736 + 0.805397i \(0.298048\pi\)
\(54\) −1.63563 −0.222581
\(55\) 16.7846 2.26324
\(56\) 2.14109 0.286115
\(57\) 9.63799 1.27658
\(58\) −0.280020 −0.0367684
\(59\) 1.39283 0.181330 0.0906652 0.995881i \(-0.471101\pi\)
0.0906652 + 0.995881i \(0.471101\pi\)
\(60\) −9.90096 −1.27821
\(61\) −4.72509 −0.604986 −0.302493 0.953152i \(-0.597819\pi\)
−0.302493 + 0.953152i \(0.597819\pi\)
\(62\) 1.81691 0.230747
\(63\) −4.90047 −0.617401
\(64\) 1.00000 0.125000
\(65\) 25.1973 3.12533
\(66\) 8.96579 1.10361
\(67\) 11.6766 1.42653 0.713264 0.700895i \(-0.247216\pi\)
0.713264 + 0.700895i \(0.247216\pi\)
\(68\) −7.43093 −0.901132
\(69\) 6.65007 0.800574
\(70\) 9.21795 1.10176
\(71\) −3.22774 −0.383062 −0.191531 0.981487i \(-0.561345\pi\)
−0.191531 + 0.981487i \(0.561345\pi\)
\(72\) −2.28878 −0.269735
\(73\) 14.8491 1.73795 0.868976 0.494854i \(-0.164778\pi\)
0.868976 + 0.494854i \(0.164778\pi\)
\(74\) −4.64283 −0.539718
\(75\) −31.1276 −3.59431
\(76\) −4.19092 −0.480731
\(77\) −8.34729 −0.951262
\(78\) 13.4596 1.52400
\(79\) 4.69214 0.527907 0.263953 0.964535i \(-0.414973\pi\)
0.263953 + 0.964535i \(0.414973\pi\)
\(80\) 4.30527 0.481343
\(81\) −10.6278 −1.18087
\(82\) 5.26094 0.580974
\(83\) −2.93193 −0.321821 −0.160910 0.986969i \(-0.551443\pi\)
−0.160910 + 0.986969i \(0.551443\pi\)
\(84\) 4.92393 0.537245
\(85\) −31.9921 −3.47003
\(86\) −7.25858 −0.782713
\(87\) −0.643970 −0.0690409
\(88\) −3.89862 −0.415595
\(89\) 7.89771 0.837155 0.418578 0.908181i \(-0.362529\pi\)
0.418578 + 0.908181i \(0.362529\pi\)
\(90\) −9.85378 −1.03868
\(91\) −12.5311 −1.31361
\(92\) −2.89167 −0.301477
\(93\) 4.17840 0.433280
\(94\) 8.27119 0.853108
\(95\) −18.0430 −1.85117
\(96\) 2.29973 0.234716
\(97\) 15.0883 1.53199 0.765994 0.642847i \(-0.222247\pi\)
0.765994 + 0.642847i \(0.222247\pi\)
\(98\) 2.41575 0.244027
\(99\) 8.92307 0.896802
\(100\) 13.5353 1.35353
\(101\) 17.0591 1.69744 0.848722 0.528839i \(-0.177372\pi\)
0.848722 + 0.528839i \(0.177372\pi\)
\(102\) −17.0892 −1.69208
\(103\) 5.57578 0.549398 0.274699 0.961530i \(-0.411422\pi\)
0.274699 + 0.961530i \(0.411422\pi\)
\(104\) −5.85266 −0.573901
\(105\) 21.1988 2.06879
\(106\) −8.63037 −0.838256
\(107\) −2.17223 −0.209997 −0.104999 0.994472i \(-0.533484\pi\)
−0.104999 + 0.994472i \(0.533484\pi\)
\(108\) 1.63563 0.157388
\(109\) −10.9597 −1.04975 −0.524874 0.851180i \(-0.675888\pi\)
−0.524874 + 0.851180i \(0.675888\pi\)
\(110\) −16.7846 −1.60035
\(111\) −10.6773 −1.01344
\(112\) −2.14109 −0.202314
\(113\) −10.4854 −0.986381 −0.493191 0.869921i \(-0.664169\pi\)
−0.493191 + 0.869921i \(0.664169\pi\)
\(114\) −9.63799 −0.902681
\(115\) −12.4494 −1.16091
\(116\) 0.280020 0.0259992
\(117\) 13.3954 1.23841
\(118\) −1.39283 −0.128220
\(119\) 15.9103 1.45849
\(120\) 9.90096 0.903830
\(121\) 4.19926 0.381751
\(122\) 4.72509 0.427790
\(123\) 12.0988 1.09091
\(124\) −1.81691 −0.163163
\(125\) 36.7468 3.28673
\(126\) 4.90047 0.436568
\(127\) 17.4195 1.54573 0.772864 0.634572i \(-0.218823\pi\)
0.772864 + 0.634572i \(0.218823\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −16.6928 −1.46972
\(130\) −25.1973 −2.20995
\(131\) −22.0261 −1.92443 −0.962216 0.272288i \(-0.912220\pi\)
−0.962216 + 0.272288i \(0.912220\pi\)
\(132\) −8.96579 −0.780372
\(133\) 8.97312 0.778068
\(134\) −11.6766 −1.00871
\(135\) 7.04181 0.606063
\(136\) 7.43093 0.637197
\(137\) 6.39282 0.546175 0.273088 0.961989i \(-0.411955\pi\)
0.273088 + 0.961989i \(0.411955\pi\)
\(138\) −6.65007 −0.566092
\(139\) −7.88978 −0.669203 −0.334601 0.942360i \(-0.608602\pi\)
−0.334601 + 0.942360i \(0.608602\pi\)
\(140\) −9.21795 −0.779059
\(141\) 19.0215 1.60190
\(142\) 3.22774 0.270866
\(143\) 22.8173 1.90808
\(144\) 2.28878 0.190731
\(145\) 1.20556 0.100116
\(146\) −14.8491 −1.22892
\(147\) 5.55558 0.458216
\(148\) 4.64283 0.381638
\(149\) 2.83546 0.232290 0.116145 0.993232i \(-0.462946\pi\)
0.116145 + 0.993232i \(0.462946\pi\)
\(150\) 31.1276 2.54156
\(151\) −8.12924 −0.661548 −0.330774 0.943710i \(-0.607310\pi\)
−0.330774 + 0.943710i \(0.607310\pi\)
\(152\) 4.19092 0.339928
\(153\) −17.0077 −1.37499
\(154\) 8.34729 0.672644
\(155\) −7.82226 −0.628299
\(156\) −13.4596 −1.07763
\(157\) −8.03302 −0.641105 −0.320552 0.947231i \(-0.603869\pi\)
−0.320552 + 0.947231i \(0.603869\pi\)
\(158\) −4.69214 −0.373287
\(159\) −19.8476 −1.57401
\(160\) −4.30527 −0.340361
\(161\) 6.19131 0.487944
\(162\) 10.6278 0.835001
\(163\) 3.51694 0.275468 0.137734 0.990469i \(-0.456018\pi\)
0.137734 + 0.990469i \(0.456018\pi\)
\(164\) −5.26094 −0.410811
\(165\) −38.6001 −3.00502
\(166\) 2.93193 0.227562
\(167\) 23.0013 1.77989 0.889947 0.456065i \(-0.150742\pi\)
0.889947 + 0.456065i \(0.150742\pi\)
\(168\) −4.92393 −0.379889
\(169\) 21.2536 1.63490
\(170\) 31.9921 2.45368
\(171\) −9.59207 −0.733524
\(172\) 7.25858 0.553461
\(173\) 20.5463 1.56211 0.781053 0.624465i \(-0.214683\pi\)
0.781053 + 0.624465i \(0.214683\pi\)
\(174\) 0.643970 0.0488193
\(175\) −28.9803 −2.19070
\(176\) 3.89862 0.293870
\(177\) −3.20313 −0.240762
\(178\) −7.89771 −0.591958
\(179\) 23.6137 1.76497 0.882487 0.470337i \(-0.155868\pi\)
0.882487 + 0.470337i \(0.155868\pi\)
\(180\) 9.85378 0.734458
\(181\) 6.20711 0.461371 0.230686 0.973028i \(-0.425903\pi\)
0.230686 + 0.973028i \(0.425903\pi\)
\(182\) 12.5311 0.928863
\(183\) 10.8665 0.803271
\(184\) 2.89167 0.213177
\(185\) 19.9886 1.46959
\(186\) −4.17840 −0.306375
\(187\) −28.9704 −2.11852
\(188\) −8.27119 −0.603238
\(189\) −3.50202 −0.254735
\(190\) 18.0430 1.30898
\(191\) 1.54240 0.111604 0.0558022 0.998442i \(-0.482228\pi\)
0.0558022 + 0.998442i \(0.482228\pi\)
\(192\) −2.29973 −0.165969
\(193\) −16.0416 −1.15470 −0.577349 0.816497i \(-0.695913\pi\)
−0.577349 + 0.816497i \(0.695913\pi\)
\(194\) −15.0883 −1.08328
\(195\) −57.9470 −4.14967
\(196\) −2.41575 −0.172553
\(197\) −1.14901 −0.0818638 −0.0409319 0.999162i \(-0.513033\pi\)
−0.0409319 + 0.999162i \(0.513033\pi\)
\(198\) −8.92307 −0.634135
\(199\) −12.0770 −0.856117 −0.428058 0.903751i \(-0.640802\pi\)
−0.428058 + 0.903751i \(0.640802\pi\)
\(200\) −13.5353 −0.957091
\(201\) −26.8532 −1.89408
\(202\) −17.0591 −1.20027
\(203\) −0.599546 −0.0420799
\(204\) 17.0892 1.19648
\(205\) −22.6498 −1.58193
\(206\) −5.57578 −0.388483
\(207\) −6.61838 −0.460009
\(208\) 5.85266 0.405809
\(209\) −16.3388 −1.13018
\(210\) −21.1988 −1.46286
\(211\) −25.8902 −1.78236 −0.891178 0.453653i \(-0.850120\pi\)
−0.891178 + 0.453653i \(0.850120\pi\)
\(212\) 8.63037 0.592736
\(213\) 7.42294 0.508611
\(214\) 2.17223 0.148490
\(215\) 31.2501 2.13124
\(216\) −1.63563 −0.111290
\(217\) 3.89015 0.264081
\(218\) 10.9597 0.742284
\(219\) −34.1489 −2.30757
\(220\) 16.7846 1.13162
\(221\) −43.4907 −2.92550
\(222\) 10.6773 0.716612
\(223\) −10.6083 −0.710381 −0.355191 0.934794i \(-0.615584\pi\)
−0.355191 + 0.934794i \(0.615584\pi\)
\(224\) 2.14109 0.143057
\(225\) 30.9793 2.06529
\(226\) 10.4854 0.697477
\(227\) −18.8647 −1.25209 −0.626046 0.779786i \(-0.715328\pi\)
−0.626046 + 0.779786i \(0.715328\pi\)
\(228\) 9.63799 0.638292
\(229\) 16.8459 1.11321 0.556605 0.830777i \(-0.312104\pi\)
0.556605 + 0.830777i \(0.312104\pi\)
\(230\) 12.4494 0.820889
\(231\) 19.1965 1.26304
\(232\) −0.280020 −0.0183842
\(233\) −3.84736 −0.252049 −0.126024 0.992027i \(-0.540222\pi\)
−0.126024 + 0.992027i \(0.540222\pi\)
\(234\) −13.3954 −0.875686
\(235\) −35.6097 −2.32292
\(236\) 1.39283 0.0906652
\(237\) −10.7907 −0.700929
\(238\) −15.9103 −1.03131
\(239\) −17.4034 −1.12573 −0.562867 0.826548i \(-0.690302\pi\)
−0.562867 + 0.826548i \(0.690302\pi\)
\(240\) −9.90096 −0.639104
\(241\) 16.4594 1.06024 0.530122 0.847921i \(-0.322146\pi\)
0.530122 + 0.847921i \(0.322146\pi\)
\(242\) −4.19926 −0.269939
\(243\) 19.5343 1.25313
\(244\) −4.72509 −0.302493
\(245\) −10.4004 −0.664459
\(246\) −12.0988 −0.771389
\(247\) −24.5280 −1.56068
\(248\) 1.81691 0.115374
\(249\) 6.74265 0.427298
\(250\) −36.7468 −2.32407
\(251\) −18.7120 −1.18109 −0.590544 0.807005i \(-0.701087\pi\)
−0.590544 + 0.807005i \(0.701087\pi\)
\(252\) −4.90047 −0.308700
\(253\) −11.2735 −0.708761
\(254\) −17.4195 −1.09299
\(255\) 73.5733 4.60734
\(256\) 1.00000 0.0625000
\(257\) 15.0436 0.938395 0.469198 0.883093i \(-0.344543\pi\)
0.469198 + 0.883093i \(0.344543\pi\)
\(258\) 16.6928 1.03925
\(259\) −9.94070 −0.617685
\(260\) 25.1973 1.56267
\(261\) 0.640902 0.0396708
\(262\) 22.0261 1.36078
\(263\) −3.06598 −0.189056 −0.0945282 0.995522i \(-0.530134\pi\)
−0.0945282 + 0.995522i \(0.530134\pi\)
\(264\) 8.96579 0.551807
\(265\) 37.1560 2.28248
\(266\) −8.97312 −0.550177
\(267\) −18.1626 −1.11153
\(268\) 11.6766 0.713264
\(269\) 6.91528 0.421632 0.210816 0.977526i \(-0.432388\pi\)
0.210816 + 0.977526i \(0.432388\pi\)
\(270\) −7.04181 −0.428551
\(271\) −15.9621 −0.969626 −0.484813 0.874618i \(-0.661112\pi\)
−0.484813 + 0.874618i \(0.661112\pi\)
\(272\) −7.43093 −0.450566
\(273\) 28.8181 1.74415
\(274\) −6.39282 −0.386204
\(275\) 52.7691 3.18209
\(276\) 6.65007 0.400287
\(277\) −3.73209 −0.224240 −0.112120 0.993695i \(-0.535764\pi\)
−0.112120 + 0.993695i \(0.535764\pi\)
\(278\) 7.88978 0.473198
\(279\) −4.15849 −0.248962
\(280\) 9.21795 0.550878
\(281\) −3.92086 −0.233899 −0.116950 0.993138i \(-0.537312\pi\)
−0.116950 + 0.993138i \(0.537312\pi\)
\(282\) −19.0215 −1.13272
\(283\) 21.4635 1.27587 0.637935 0.770090i \(-0.279789\pi\)
0.637935 + 0.770090i \(0.279789\pi\)
\(284\) −3.22774 −0.191531
\(285\) 41.4941 2.45790
\(286\) −22.8173 −1.34922
\(287\) 11.2641 0.664901
\(288\) −2.28878 −0.134867
\(289\) 38.2187 2.24816
\(290\) −1.20556 −0.0707928
\(291\) −34.6992 −2.03410
\(292\) 14.8491 0.868976
\(293\) −15.5987 −0.911284 −0.455642 0.890163i \(-0.650590\pi\)
−0.455642 + 0.890163i \(0.650590\pi\)
\(294\) −5.55558 −0.324008
\(295\) 5.99648 0.349129
\(296\) −4.64283 −0.269859
\(297\) 6.37670 0.370013
\(298\) −2.83546 −0.164254
\(299\) −16.9240 −0.978738
\(300\) −31.1276 −1.79715
\(301\) −15.5412 −0.895782
\(302\) 8.12924 0.467785
\(303\) −39.2314 −2.25379
\(304\) −4.19092 −0.240366
\(305\) −20.3428 −1.16482
\(306\) 17.0077 0.972267
\(307\) 1.62354 0.0926606 0.0463303 0.998926i \(-0.485247\pi\)
0.0463303 + 0.998926i \(0.485247\pi\)
\(308\) −8.34729 −0.475631
\(309\) −12.8228 −0.729464
\(310\) 7.82226 0.444275
\(311\) 10.5682 0.599267 0.299634 0.954054i \(-0.403136\pi\)
0.299634 + 0.954054i \(0.403136\pi\)
\(312\) 13.4596 0.761998
\(313\) 26.4726 1.49632 0.748159 0.663520i \(-0.230938\pi\)
0.748159 + 0.663520i \(0.230938\pi\)
\(314\) 8.03302 0.453330
\(315\) −21.0978 −1.18873
\(316\) 4.69214 0.263953
\(317\) −2.80286 −0.157424 −0.0787122 0.996897i \(-0.525081\pi\)
−0.0787122 + 0.996897i \(0.525081\pi\)
\(318\) 19.8476 1.11300
\(319\) 1.09169 0.0611229
\(320\) 4.30527 0.240672
\(321\) 4.99555 0.278824
\(322\) −6.19131 −0.345028
\(323\) 31.1424 1.73281
\(324\) −10.6278 −0.590435
\(325\) 79.2176 4.39420
\(326\) −3.51694 −0.194785
\(327\) 25.2044 1.39381
\(328\) 5.26094 0.290487
\(329\) 17.7093 0.976347
\(330\) 38.6001 2.12487
\(331\) −1.78735 −0.0982418 −0.0491209 0.998793i \(-0.515642\pi\)
−0.0491209 + 0.998793i \(0.515642\pi\)
\(332\) −2.93193 −0.160910
\(333\) 10.6264 0.582323
\(334\) −23.0013 −1.25857
\(335\) 50.2710 2.74660
\(336\) 4.92393 0.268622
\(337\) −22.8434 −1.24436 −0.622181 0.782874i \(-0.713753\pi\)
−0.622181 + 0.782874i \(0.713753\pi\)
\(338\) −21.2536 −1.15605
\(339\) 24.1136 1.30967
\(340\) −31.9921 −1.73502
\(341\) −7.08343 −0.383589
\(342\) 9.59207 0.518680
\(343\) 20.1599 1.08853
\(344\) −7.25858 −0.391356
\(345\) 28.6303 1.54140
\(346\) −20.5463 −1.10458
\(347\) 1.28394 0.0689254 0.0344627 0.999406i \(-0.489028\pi\)
0.0344627 + 0.999406i \(0.489028\pi\)
\(348\) −0.643970 −0.0345204
\(349\) 8.58415 0.459499 0.229749 0.973250i \(-0.426209\pi\)
0.229749 + 0.973250i \(0.426209\pi\)
\(350\) 28.9803 1.54906
\(351\) 9.57277 0.510957
\(352\) −3.89862 −0.207797
\(353\) 10.3829 0.552628 0.276314 0.961067i \(-0.410887\pi\)
0.276314 + 0.961067i \(0.410887\pi\)
\(354\) 3.20313 0.170244
\(355\) −13.8963 −0.737537
\(356\) 7.89771 0.418578
\(357\) −36.5894 −1.93651
\(358\) −23.6137 −1.24803
\(359\) −22.8669 −1.20687 −0.603435 0.797412i \(-0.706202\pi\)
−0.603435 + 0.797412i \(0.706202\pi\)
\(360\) −9.85378 −0.519340
\(361\) −1.43621 −0.0755902
\(362\) −6.20711 −0.326239
\(363\) −9.65718 −0.506871
\(364\) −12.5311 −0.656806
\(365\) 63.9292 3.34621
\(366\) −10.8665 −0.567999
\(367\) 23.2295 1.21257 0.606284 0.795248i \(-0.292659\pi\)
0.606284 + 0.795248i \(0.292659\pi\)
\(368\) −2.89167 −0.150739
\(369\) −12.0411 −0.626836
\(370\) −19.9886 −1.03916
\(371\) −18.4784 −0.959349
\(372\) 4.17840 0.216640
\(373\) −2.21307 −0.114588 −0.0572942 0.998357i \(-0.518247\pi\)
−0.0572942 + 0.998357i \(0.518247\pi\)
\(374\) 28.9704 1.49802
\(375\) −84.5078 −4.36396
\(376\) 8.27119 0.426554
\(377\) 1.63886 0.0844055
\(378\) 3.50202 0.180125
\(379\) 29.8174 1.53162 0.765810 0.643067i \(-0.222339\pi\)
0.765810 + 0.643067i \(0.222339\pi\)
\(380\) −18.0430 −0.925587
\(381\) −40.0601 −2.05234
\(382\) −1.54240 −0.0789162
\(383\) 0.812538 0.0415187 0.0207594 0.999785i \(-0.493392\pi\)
0.0207594 + 0.999785i \(0.493392\pi\)
\(384\) 2.29973 0.117358
\(385\) −35.9373 −1.83153
\(386\) 16.0416 0.816495
\(387\) 16.6133 0.844499
\(388\) 15.0883 0.765994
\(389\) 34.6668 1.75768 0.878839 0.477119i \(-0.158319\pi\)
0.878839 + 0.477119i \(0.158319\pi\)
\(390\) 57.9470 2.93426
\(391\) 21.4878 1.08668
\(392\) 2.41575 0.122014
\(393\) 50.6542 2.55517
\(394\) 1.14901 0.0578864
\(395\) 20.2009 1.01642
\(396\) 8.92307 0.448401
\(397\) −2.02605 −0.101684 −0.0508422 0.998707i \(-0.516191\pi\)
−0.0508422 + 0.998707i \(0.516191\pi\)
\(398\) 12.0770 0.605366
\(399\) −20.6358 −1.03308
\(400\) 13.5353 0.676765
\(401\) −25.3333 −1.26508 −0.632541 0.774527i \(-0.717988\pi\)
−0.632541 + 0.774527i \(0.717988\pi\)
\(402\) 26.8532 1.33931
\(403\) −10.6337 −0.529704
\(404\) 17.0591 0.848722
\(405\) −45.7556 −2.27362
\(406\) 0.599546 0.0297550
\(407\) 18.1006 0.897215
\(408\) −17.0892 −0.846039
\(409\) −4.66049 −0.230447 −0.115223 0.993340i \(-0.536758\pi\)
−0.115223 + 0.993340i \(0.536758\pi\)
\(410\) 22.6498 1.11859
\(411\) −14.7018 −0.725185
\(412\) 5.57578 0.274699
\(413\) −2.98216 −0.146742
\(414\) 6.61838 0.325276
\(415\) −12.6227 −0.619625
\(416\) −5.85266 −0.286950
\(417\) 18.1444 0.888535
\(418\) 16.3388 0.799157
\(419\) 28.2376 1.37950 0.689748 0.724050i \(-0.257721\pi\)
0.689748 + 0.724050i \(0.257721\pi\)
\(420\) 21.1988 1.03440
\(421\) −26.7983 −1.30607 −0.653034 0.757328i \(-0.726504\pi\)
−0.653034 + 0.757328i \(0.726504\pi\)
\(422\) 25.8902 1.26032
\(423\) −18.9309 −0.920451
\(424\) −8.63037 −0.419128
\(425\) −100.580 −4.87884
\(426\) −7.42294 −0.359643
\(427\) 10.1168 0.489588
\(428\) −2.17223 −0.104999
\(429\) −52.4738 −2.53346
\(430\) −31.2501 −1.50701
\(431\) 7.29725 0.351496 0.175748 0.984435i \(-0.443766\pi\)
0.175748 + 0.984435i \(0.443766\pi\)
\(432\) 1.63563 0.0786942
\(433\) −4.31925 −0.207570 −0.103785 0.994600i \(-0.533095\pi\)
−0.103785 + 0.994600i \(0.533095\pi\)
\(434\) −3.89015 −0.186733
\(435\) −2.77246 −0.132929
\(436\) −10.9597 −0.524874
\(437\) 12.1187 0.579718
\(438\) 34.1489 1.63170
\(439\) 41.0464 1.95904 0.979519 0.201351i \(-0.0645333\pi\)
0.979519 + 0.201351i \(0.0645333\pi\)
\(440\) −16.7846 −0.800175
\(441\) −5.52910 −0.263291
\(442\) 43.4907 2.06864
\(443\) 5.76790 0.274041 0.137021 0.990568i \(-0.456247\pi\)
0.137021 + 0.990568i \(0.456247\pi\)
\(444\) −10.6773 −0.506721
\(445\) 34.0017 1.61184
\(446\) 10.6083 0.502315
\(447\) −6.52080 −0.308423
\(448\) −2.14109 −0.101157
\(449\) −15.6905 −0.740478 −0.370239 0.928936i \(-0.620724\pi\)
−0.370239 + 0.928936i \(0.620724\pi\)
\(450\) −30.9793 −1.46038
\(451\) −20.5104 −0.965799
\(452\) −10.4854 −0.493191
\(453\) 18.6951 0.878371
\(454\) 18.8647 0.885362
\(455\) −53.9495 −2.52919
\(456\) −9.63799 −0.451340
\(457\) 23.2567 1.08790 0.543952 0.839116i \(-0.316927\pi\)
0.543952 + 0.839116i \(0.316927\pi\)
\(458\) −16.8459 −0.787158
\(459\) −12.1542 −0.567311
\(460\) −12.4494 −0.580456
\(461\) 34.5518 1.60924 0.804619 0.593791i \(-0.202369\pi\)
0.804619 + 0.593791i \(0.202369\pi\)
\(462\) −19.1965 −0.893104
\(463\) −2.86618 −0.133202 −0.0666012 0.997780i \(-0.521216\pi\)
−0.0666012 + 0.997780i \(0.521216\pi\)
\(464\) 0.280020 0.0129996
\(465\) 17.9891 0.834225
\(466\) 3.84736 0.178225
\(467\) −12.4586 −0.576513 −0.288257 0.957553i \(-0.593076\pi\)
−0.288257 + 0.957553i \(0.593076\pi\)
\(468\) 13.3954 0.619204
\(469\) −25.0007 −1.15442
\(470\) 35.6097 1.64255
\(471\) 18.4738 0.851228
\(472\) −1.39283 −0.0641100
\(473\) 28.2985 1.30116
\(474\) 10.7907 0.495632
\(475\) −56.7254 −2.60274
\(476\) 15.9103 0.729246
\(477\) 19.7530 0.904427
\(478\) 17.4034 0.796014
\(479\) 6.58838 0.301031 0.150515 0.988608i \(-0.451907\pi\)
0.150515 + 0.988608i \(0.451907\pi\)
\(480\) 9.90096 0.451915
\(481\) 27.1729 1.23898
\(482\) −16.4594 −0.749706
\(483\) −14.2384 −0.647868
\(484\) 4.19926 0.190876
\(485\) 64.9593 2.94965
\(486\) −19.5343 −0.886094
\(487\) 36.8423 1.66948 0.834742 0.550641i \(-0.185617\pi\)
0.834742 + 0.550641i \(0.185617\pi\)
\(488\) 4.72509 0.213895
\(489\) −8.08802 −0.365753
\(490\) 10.4004 0.469844
\(491\) 27.2499 1.22977 0.614884 0.788617i \(-0.289203\pi\)
0.614884 + 0.788617i \(0.289203\pi\)
\(492\) 12.0988 0.545455
\(493\) −2.08080 −0.0937147
\(494\) 24.5280 1.10357
\(495\) 38.4162 1.72668
\(496\) −1.81691 −0.0815815
\(497\) 6.91087 0.309995
\(498\) −6.74265 −0.302146
\(499\) 11.0765 0.495853 0.247927 0.968779i \(-0.420251\pi\)
0.247927 + 0.968779i \(0.420251\pi\)
\(500\) 36.7468 1.64337
\(501\) −52.8968 −2.36326
\(502\) 18.7120 0.835155
\(503\) 39.9675 1.78206 0.891032 0.453940i \(-0.149982\pi\)
0.891032 + 0.453940i \(0.149982\pi\)
\(504\) 4.90047 0.218284
\(505\) 73.4440 3.26821
\(506\) 11.2735 0.501169
\(507\) −48.8777 −2.17073
\(508\) 17.4195 0.772864
\(509\) −12.0712 −0.535046 −0.267523 0.963551i \(-0.586205\pi\)
−0.267523 + 0.963551i \(0.586205\pi\)
\(510\) −73.5733 −3.25788
\(511\) −31.7932 −1.40645
\(512\) −1.00000 −0.0441942
\(513\) −6.85478 −0.302646
\(514\) −15.0436 −0.663546
\(515\) 24.0052 1.05780
\(516\) −16.6928 −0.734859
\(517\) −32.2462 −1.41819
\(518\) 9.94070 0.436769
\(519\) −47.2510 −2.07409
\(520\) −25.1973 −1.10497
\(521\) 19.7906 0.867042 0.433521 0.901143i \(-0.357271\pi\)
0.433521 + 0.901143i \(0.357271\pi\)
\(522\) −0.640902 −0.0280515
\(523\) −21.9793 −0.961088 −0.480544 0.876971i \(-0.659561\pi\)
−0.480544 + 0.876971i \(0.659561\pi\)
\(524\) −22.0261 −0.962216
\(525\) 66.6469 2.90871
\(526\) 3.06598 0.133683
\(527\) 13.5013 0.588126
\(528\) −8.96579 −0.390186
\(529\) −14.6382 −0.636446
\(530\) −37.1560 −1.61396
\(531\) 3.18786 0.138342
\(532\) 8.97312 0.389034
\(533\) −30.7905 −1.33369
\(534\) 18.1626 0.785974
\(535\) −9.35202 −0.404323
\(536\) −11.6766 −0.504354
\(537\) −54.3053 −2.34345
\(538\) −6.91528 −0.298139
\(539\) −9.41809 −0.405666
\(540\) 7.04181 0.303031
\(541\) 2.16876 0.0932421 0.0466210 0.998913i \(-0.485155\pi\)
0.0466210 + 0.998913i \(0.485155\pi\)
\(542\) 15.9621 0.685629
\(543\) −14.2747 −0.612586
\(544\) 7.43093 0.318598
\(545\) −47.1844 −2.02116
\(546\) −28.8181 −1.23330
\(547\) −3.51556 −0.150314 −0.0751572 0.997172i \(-0.523946\pi\)
−0.0751572 + 0.997172i \(0.523946\pi\)
\(548\) 6.39282 0.273088
\(549\) −10.8147 −0.461559
\(550\) −52.7691 −2.25008
\(551\) −1.17354 −0.0499944
\(552\) −6.65007 −0.283046
\(553\) −10.0463 −0.427211
\(554\) 3.73209 0.158561
\(555\) −45.9685 −1.95125
\(556\) −7.88978 −0.334601
\(557\) −25.1086 −1.06389 −0.531943 0.846780i \(-0.678538\pi\)
−0.531943 + 0.846780i \(0.678538\pi\)
\(558\) 4.15849 0.176043
\(559\) 42.4820 1.79680
\(560\) −9.21795 −0.389529
\(561\) 66.6242 2.81287
\(562\) 3.92086 0.165392
\(563\) −13.6667 −0.575984 −0.287992 0.957633i \(-0.592988\pi\)
−0.287992 + 0.957633i \(0.592988\pi\)
\(564\) 19.0215 0.800951
\(565\) −45.1423 −1.89915
\(566\) −21.4635 −0.902177
\(567\) 22.7551 0.955625
\(568\) 3.22774 0.135433
\(569\) 28.6430 1.20078 0.600389 0.799708i \(-0.295012\pi\)
0.600389 + 0.799708i \(0.295012\pi\)
\(570\) −41.4941 −1.73800
\(571\) 16.8022 0.703151 0.351576 0.936160i \(-0.385646\pi\)
0.351576 + 0.936160i \(0.385646\pi\)
\(572\) 22.8173 0.954040
\(573\) −3.54712 −0.148183
\(574\) −11.2641 −0.470156
\(575\) −39.1396 −1.63224
\(576\) 2.28878 0.0953656
\(577\) −41.7611 −1.73854 −0.869269 0.494340i \(-0.835410\pi\)
−0.869269 + 0.494340i \(0.835410\pi\)
\(578\) −38.2187 −1.58969
\(579\) 36.8914 1.53315
\(580\) 1.20556 0.0500581
\(581\) 6.27751 0.260435
\(582\) 34.6992 1.43833
\(583\) 33.6466 1.39350
\(584\) −14.8491 −0.614459
\(585\) 57.6709 2.38440
\(586\) 15.5987 0.644375
\(587\) 43.3782 1.79041 0.895204 0.445656i \(-0.147030\pi\)
0.895204 + 0.445656i \(0.147030\pi\)
\(588\) 5.55558 0.229108
\(589\) 7.61450 0.313750
\(590\) −5.99648 −0.246871
\(591\) 2.64242 0.108695
\(592\) 4.64283 0.190819
\(593\) 34.7457 1.42683 0.713417 0.700740i \(-0.247147\pi\)
0.713417 + 0.700740i \(0.247147\pi\)
\(594\) −6.37670 −0.261639
\(595\) 68.4979 2.80814
\(596\) 2.83546 0.116145
\(597\) 27.7739 1.13671
\(598\) 16.9240 0.692072
\(599\) −26.0543 −1.06455 −0.532274 0.846572i \(-0.678662\pi\)
−0.532274 + 0.846572i \(0.678662\pi\)
\(600\) 31.1276 1.27078
\(601\) 35.6867 1.45569 0.727846 0.685741i \(-0.240522\pi\)
0.727846 + 0.685741i \(0.240522\pi\)
\(602\) 15.5412 0.633414
\(603\) 26.7252 1.08833
\(604\) −8.12924 −0.330774
\(605\) 18.0789 0.735013
\(606\) 39.2314 1.59367
\(607\) 13.7086 0.556415 0.278208 0.960521i \(-0.410260\pi\)
0.278208 + 0.960521i \(0.410260\pi\)
\(608\) 4.19092 0.169964
\(609\) 1.37880 0.0558716
\(610\) 20.3428 0.823655
\(611\) −48.4085 −1.95840
\(612\) −17.0077 −0.687496
\(613\) 25.5036 1.03008 0.515041 0.857165i \(-0.327777\pi\)
0.515041 + 0.857165i \(0.327777\pi\)
\(614\) −1.62354 −0.0655209
\(615\) 52.0884 2.10041
\(616\) 8.34729 0.336322
\(617\) −13.5322 −0.544788 −0.272394 0.962186i \(-0.587815\pi\)
−0.272394 + 0.962186i \(0.587815\pi\)
\(618\) 12.8228 0.515809
\(619\) 41.7586 1.67842 0.839210 0.543807i \(-0.183018\pi\)
0.839210 + 0.543807i \(0.183018\pi\)
\(620\) −7.82226 −0.314150
\(621\) −4.72969 −0.189796
\(622\) −10.5682 −0.423746
\(623\) −16.9097 −0.677472
\(624\) −13.4596 −0.538814
\(625\) 90.5280 3.62112
\(626\) −26.4726 −1.05806
\(627\) 37.5749 1.50060
\(628\) −8.03302 −0.320552
\(629\) −34.5005 −1.37563
\(630\) 21.0978 0.840557
\(631\) 35.8980 1.42908 0.714539 0.699596i \(-0.246637\pi\)
0.714539 + 0.699596i \(0.246637\pi\)
\(632\) −4.69214 −0.186643
\(633\) 59.5406 2.36653
\(634\) 2.80286 0.111316
\(635\) 74.9954 2.97610
\(636\) −19.8476 −0.787007
\(637\) −14.1386 −0.560190
\(638\) −1.09169 −0.0432204
\(639\) −7.38757 −0.292248
\(640\) −4.30527 −0.170181
\(641\) −11.1701 −0.441193 −0.220597 0.975365i \(-0.570800\pi\)
−0.220597 + 0.975365i \(0.570800\pi\)
\(642\) −4.99555 −0.197158
\(643\) 38.1131 1.50304 0.751518 0.659713i \(-0.229322\pi\)
0.751518 + 0.659713i \(0.229322\pi\)
\(644\) 6.19131 0.243972
\(645\) −71.8669 −2.82976
\(646\) −31.1424 −1.22528
\(647\) 31.6345 1.24368 0.621841 0.783143i \(-0.286385\pi\)
0.621841 + 0.783143i \(0.286385\pi\)
\(648\) 10.6278 0.417501
\(649\) 5.43010 0.213150
\(650\) −79.2176 −3.10717
\(651\) −8.94632 −0.350634
\(652\) 3.51694 0.137734
\(653\) −46.7416 −1.82914 −0.914570 0.404427i \(-0.867471\pi\)
−0.914570 + 0.404427i \(0.867471\pi\)
\(654\) −25.2044 −0.985569
\(655\) −94.8283 −3.70525
\(656\) −5.26094 −0.205405
\(657\) 33.9862 1.32593
\(658\) −17.7093 −0.690382
\(659\) −5.72371 −0.222964 −0.111482 0.993766i \(-0.535560\pi\)
−0.111482 + 0.993766i \(0.535560\pi\)
\(660\) −38.6001 −1.50251
\(661\) 6.55187 0.254838 0.127419 0.991849i \(-0.459331\pi\)
0.127419 + 0.991849i \(0.459331\pi\)
\(662\) 1.78735 0.0694674
\(663\) 100.017 3.88434
\(664\) 2.93193 0.113781
\(665\) 38.6316 1.49807
\(666\) −10.6264 −0.411764
\(667\) −0.809724 −0.0313526
\(668\) 23.0013 0.889947
\(669\) 24.3962 0.943210
\(670\) −50.2710 −1.94214
\(671\) −18.4213 −0.711148
\(672\) −4.92393 −0.189945
\(673\) −6.88356 −0.265342 −0.132671 0.991160i \(-0.542355\pi\)
−0.132671 + 0.991160i \(0.542355\pi\)
\(674\) 22.8434 0.879896
\(675\) 22.1387 0.852120
\(676\) 21.2536 0.817448
\(677\) 22.0692 0.848189 0.424094 0.905618i \(-0.360593\pi\)
0.424094 + 0.905618i \(0.360593\pi\)
\(678\) −24.1136 −0.926076
\(679\) −32.3054 −1.23977
\(680\) 31.9921 1.22684
\(681\) 43.3837 1.66247
\(682\) 7.08343 0.271239
\(683\) −7.77409 −0.297467 −0.148734 0.988877i \(-0.547520\pi\)
−0.148734 + 0.988877i \(0.547520\pi\)
\(684\) −9.59207 −0.366762
\(685\) 27.5228 1.05159
\(686\) −20.1599 −0.769710
\(687\) −38.7411 −1.47807
\(688\) 7.25858 0.276731
\(689\) 50.5106 1.92430
\(690\) −28.6303 −1.08994
\(691\) 17.8552 0.679243 0.339622 0.940562i \(-0.389701\pi\)
0.339622 + 0.940562i \(0.389701\pi\)
\(692\) 20.5463 0.781053
\(693\) −19.1051 −0.725742
\(694\) −1.28394 −0.0487376
\(695\) −33.9676 −1.28846
\(696\) 0.643970 0.0244096
\(697\) 39.0937 1.48078
\(698\) −8.58415 −0.324915
\(699\) 8.84790 0.334658
\(700\) −28.9803 −1.09535
\(701\) −10.1830 −0.384607 −0.192304 0.981335i \(-0.561596\pi\)
−0.192304 + 0.981335i \(0.561596\pi\)
\(702\) −9.57277 −0.361301
\(703\) −19.4577 −0.733862
\(704\) 3.89862 0.146935
\(705\) 81.8927 3.08426
\(706\) −10.3829 −0.390767
\(707\) −36.5250 −1.37367
\(708\) −3.20313 −0.120381
\(709\) −4.60367 −0.172894 −0.0864471 0.996256i \(-0.527551\pi\)
−0.0864471 + 0.996256i \(0.527551\pi\)
\(710\) 13.8963 0.521518
\(711\) 10.7393 0.402753
\(712\) −7.89771 −0.295979
\(713\) 5.25389 0.196760
\(714\) 36.5894 1.36932
\(715\) 98.2346 3.67377
\(716\) 23.6137 0.882487
\(717\) 40.0232 1.49469
\(718\) 22.8669 0.853386
\(719\) −34.6283 −1.29142 −0.645708 0.763584i \(-0.723438\pi\)
−0.645708 + 0.763584i \(0.723438\pi\)
\(720\) 9.85378 0.367229
\(721\) −11.9382 −0.444603
\(722\) 1.43621 0.0534503
\(723\) −37.8523 −1.40774
\(724\) 6.20711 0.230686
\(725\) 3.79015 0.140763
\(726\) 9.65718 0.358412
\(727\) −21.4295 −0.794775 −0.397388 0.917651i \(-0.630083\pi\)
−0.397388 + 0.917651i \(0.630083\pi\)
\(728\) 12.5311 0.464432
\(729\) −13.0402 −0.482970
\(730\) −63.9292 −2.36613
\(731\) −53.9380 −1.99497
\(732\) 10.8665 0.401636
\(733\) 40.3462 1.49022 0.745111 0.666940i \(-0.232396\pi\)
0.745111 + 0.666940i \(0.232396\pi\)
\(734\) −23.2295 −0.857415
\(735\) 23.9182 0.882237
\(736\) 2.89167 0.106588
\(737\) 45.5228 1.67685
\(738\) 12.0411 0.443240
\(739\) −24.4528 −0.899509 −0.449755 0.893152i \(-0.648489\pi\)
−0.449755 + 0.893152i \(0.648489\pi\)
\(740\) 19.9886 0.734796
\(741\) 56.4079 2.07220
\(742\) 18.4784 0.678362
\(743\) −10.8968 −0.399767 −0.199883 0.979820i \(-0.564056\pi\)
−0.199883 + 0.979820i \(0.564056\pi\)
\(744\) −4.17840 −0.153188
\(745\) 12.2074 0.447245
\(746\) 2.21307 0.0810262
\(747\) −6.71052 −0.245525
\(748\) −28.9704 −1.05926
\(749\) 4.65093 0.169941
\(750\) 84.5078 3.08579
\(751\) 8.10066 0.295597 0.147799 0.989017i \(-0.452781\pi\)
0.147799 + 0.989017i \(0.452781\pi\)
\(752\) −8.27119 −0.301619
\(753\) 43.0325 1.56819
\(754\) −1.63886 −0.0596837
\(755\) −34.9985 −1.27373
\(756\) −3.50202 −0.127367
\(757\) −41.3597 −1.50325 −0.751623 0.659593i \(-0.770729\pi\)
−0.751623 + 0.659593i \(0.770729\pi\)
\(758\) −29.8174 −1.08302
\(759\) 25.9261 0.941058
\(760\) 18.0430 0.654489
\(761\) 20.8524 0.755897 0.377949 0.925827i \(-0.376630\pi\)
0.377949 + 0.925827i \(0.376630\pi\)
\(762\) 40.0601 1.45123
\(763\) 23.4657 0.849514
\(764\) 1.54240 0.0558022
\(765\) −73.2228 −2.64737
\(766\) −0.812538 −0.0293582
\(767\) 8.15173 0.294342
\(768\) −2.29973 −0.0829845
\(769\) 22.8569 0.824240 0.412120 0.911130i \(-0.364788\pi\)
0.412120 + 0.911130i \(0.364788\pi\)
\(770\) 35.9373 1.29509
\(771\) −34.5963 −1.24596
\(772\) −16.0416 −0.577349
\(773\) 7.34957 0.264346 0.132173 0.991227i \(-0.457805\pi\)
0.132173 + 0.991227i \(0.457805\pi\)
\(774\) −16.6133 −0.597151
\(775\) −24.5924 −0.883384
\(776\) −15.0883 −0.541640
\(777\) 22.8610 0.820132
\(778\) −34.6668 −1.24287
\(779\) 22.0482 0.789958
\(780\) −57.9470 −2.07483
\(781\) −12.5837 −0.450281
\(782\) −21.4878 −0.768402
\(783\) 0.458008 0.0163679
\(784\) −2.41575 −0.0862767
\(785\) −34.5843 −1.23437
\(786\) −50.6542 −1.80678
\(787\) 23.6963 0.844682 0.422341 0.906437i \(-0.361208\pi\)
0.422341 + 0.906437i \(0.361208\pi\)
\(788\) −1.14901 −0.0409319
\(789\) 7.05094 0.251020
\(790\) −20.2009 −0.718716
\(791\) 22.4501 0.798234
\(792\) −8.92307 −0.317068
\(793\) −27.6544 −0.982035
\(794\) 2.02605 0.0719018
\(795\) −85.4490 −3.03056
\(796\) −12.0770 −0.428058
\(797\) −43.4409 −1.53876 −0.769378 0.638793i \(-0.779434\pi\)
−0.769378 + 0.638793i \(0.779434\pi\)
\(798\) 20.6358 0.730499
\(799\) 61.4626 2.17439
\(800\) −13.5353 −0.478545
\(801\) 18.0761 0.638687
\(802\) 25.3333 0.894549
\(803\) 57.8909 2.04293
\(804\) −26.8532 −0.947038
\(805\) 26.6553 0.939474
\(806\) 10.6337 0.374557
\(807\) −15.9033 −0.559823
\(808\) −17.0591 −0.600137
\(809\) 20.5117 0.721151 0.360576 0.932730i \(-0.382580\pi\)
0.360576 + 0.932730i \(0.382580\pi\)
\(810\) 45.7556 1.60769
\(811\) −30.4952 −1.07083 −0.535415 0.844589i \(-0.679845\pi\)
−0.535415 + 0.844589i \(0.679845\pi\)
\(812\) −0.599546 −0.0210399
\(813\) 36.7085 1.28742
\(814\) −18.1006 −0.634427
\(815\) 15.1414 0.530379
\(816\) 17.0892 0.598240
\(817\) −30.4201 −1.06426
\(818\) 4.66049 0.162950
\(819\) −28.6808 −1.00219
\(820\) −22.6498 −0.790964
\(821\) −15.3526 −0.535808 −0.267904 0.963446i \(-0.586331\pi\)
−0.267904 + 0.963446i \(0.586331\pi\)
\(822\) 14.7018 0.512783
\(823\) 40.2115 1.40168 0.700842 0.713316i \(-0.252808\pi\)
0.700842 + 0.713316i \(0.252808\pi\)
\(824\) −5.57578 −0.194241
\(825\) −121.355 −4.22503
\(826\) 2.98216 0.103763
\(827\) −35.1509 −1.22232 −0.611159 0.791508i \(-0.709296\pi\)
−0.611159 + 0.791508i \(0.709296\pi\)
\(828\) −6.61838 −0.230005
\(829\) −4.26109 −0.147994 −0.0739969 0.997258i \(-0.523575\pi\)
−0.0739969 + 0.997258i \(0.523575\pi\)
\(830\) 12.6227 0.438141
\(831\) 8.58282 0.297735
\(832\) 5.85266 0.202904
\(833\) 17.9513 0.621974
\(834\) −18.1444 −0.628289
\(835\) 99.0266 3.42696
\(836\) −16.3388 −0.565089
\(837\) −2.97178 −0.102720
\(838\) −28.2376 −0.975451
\(839\) 44.6142 1.54025 0.770126 0.637892i \(-0.220193\pi\)
0.770126 + 0.637892i \(0.220193\pi\)
\(840\) −21.1988 −0.731429
\(841\) −28.9216 −0.997296
\(842\) 26.7983 0.923530
\(843\) 9.01694 0.310560
\(844\) −25.8902 −0.891178
\(845\) 91.5025 3.14778
\(846\) 18.9309 0.650857
\(847\) −8.99098 −0.308934
\(848\) 8.63037 0.296368
\(849\) −49.3603 −1.69404
\(850\) 100.580 3.44986
\(851\) −13.4255 −0.460221
\(852\) 7.42294 0.254306
\(853\) −8.26990 −0.283156 −0.141578 0.989927i \(-0.545218\pi\)
−0.141578 + 0.989927i \(0.545218\pi\)
\(854\) −10.1168 −0.346191
\(855\) −41.2964 −1.41231
\(856\) 2.17223 0.0742452
\(857\) −37.8927 −1.29439 −0.647195 0.762324i \(-0.724058\pi\)
−0.647195 + 0.762324i \(0.724058\pi\)
\(858\) 52.4738 1.79142
\(859\) 3.31060 0.112956 0.0564780 0.998404i \(-0.482013\pi\)
0.0564780 + 0.998404i \(0.482013\pi\)
\(860\) 31.2501 1.06562
\(861\) −25.9045 −0.882824
\(862\) −7.29725 −0.248545
\(863\) −13.3775 −0.455376 −0.227688 0.973734i \(-0.573117\pi\)
−0.227688 + 0.973734i \(0.573117\pi\)
\(864\) −1.63563 −0.0556452
\(865\) 88.4572 3.00764
\(866\) 4.31925 0.146774
\(867\) −87.8928 −2.98500
\(868\) 3.89015 0.132040
\(869\) 18.2929 0.620544
\(870\) 2.77246 0.0939953
\(871\) 68.3394 2.31559
\(872\) 10.9597 0.371142
\(873\) 34.5338 1.16879
\(874\) −12.1187 −0.409923
\(875\) −78.6780 −2.65980
\(876\) −34.1489 −1.15378
\(877\) −51.1512 −1.72725 −0.863627 0.504131i \(-0.831813\pi\)
−0.863627 + 0.504131i \(0.831813\pi\)
\(878\) −41.0464 −1.38525
\(879\) 35.8728 1.20996
\(880\) 16.7846 0.565809
\(881\) 14.7329 0.496364 0.248182 0.968713i \(-0.420167\pi\)
0.248182 + 0.968713i \(0.420167\pi\)
\(882\) 5.52910 0.186175
\(883\) −2.22046 −0.0747244 −0.0373622 0.999302i \(-0.511896\pi\)
−0.0373622 + 0.999302i \(0.511896\pi\)
\(884\) −43.4907 −1.46275
\(885\) −13.7903 −0.463556
\(886\) −5.76790 −0.193776
\(887\) −5.41606 −0.181853 −0.0909267 0.995858i \(-0.528983\pi\)
−0.0909267 + 0.995858i \(0.528983\pi\)
\(888\) 10.6773 0.358306
\(889\) −37.2966 −1.25089
\(890\) −34.0017 −1.13974
\(891\) −41.4339 −1.38809
\(892\) −10.6083 −0.355191
\(893\) 34.6639 1.15998
\(894\) 6.52080 0.218088
\(895\) 101.663 3.39823
\(896\) 2.14109 0.0715287
\(897\) 38.9206 1.29952
\(898\) 15.6905 0.523597
\(899\) −0.508769 −0.0169684
\(900\) 30.9793 1.03264
\(901\) −64.1317 −2.13654
\(902\) 20.5104 0.682923
\(903\) 35.7407 1.18938
\(904\) 10.4854 0.348738
\(905\) 26.7233 0.888312
\(906\) −18.6951 −0.621102
\(907\) −34.6455 −1.15039 −0.575193 0.818018i \(-0.695073\pi\)
−0.575193 + 0.818018i \(0.695073\pi\)
\(908\) −18.8647 −0.626046
\(909\) 39.0445 1.29502
\(910\) 53.9495 1.78841
\(911\) −5.96343 −0.197577 −0.0987886 0.995108i \(-0.531497\pi\)
−0.0987886 + 0.995108i \(0.531497\pi\)
\(912\) 9.63799 0.319146
\(913\) −11.4305 −0.378294
\(914\) −23.2567 −0.769265
\(915\) 46.7830 1.54660
\(916\) 16.8459 0.556605
\(917\) 47.1598 1.55736
\(918\) 12.1542 0.401149
\(919\) −22.9004 −0.755413 −0.377707 0.925925i \(-0.623287\pi\)
−0.377707 + 0.925925i \(0.623287\pi\)
\(920\) 12.4494 0.410445
\(921\) −3.73372 −0.123030
\(922\) −34.5518 −1.13790
\(923\) −18.8909 −0.621800
\(924\) 19.1965 0.631520
\(925\) 62.8421 2.06624
\(926\) 2.86618 0.0941884
\(927\) 12.7617 0.419149
\(928\) −0.280020 −0.00919209
\(929\) −25.5399 −0.837937 −0.418968 0.908001i \(-0.637608\pi\)
−0.418968 + 0.908001i \(0.637608\pi\)
\(930\) −17.9891 −0.589886
\(931\) 10.1242 0.331807
\(932\) −3.84736 −0.126024
\(933\) −24.3040 −0.795678
\(934\) 12.4586 0.407657
\(935\) −124.725 −4.07895
\(936\) −13.3954 −0.437843
\(937\) −11.0308 −0.360360 −0.180180 0.983634i \(-0.557668\pi\)
−0.180180 + 0.983634i \(0.557668\pi\)
\(938\) 25.0007 0.816301
\(939\) −60.8798 −1.98674
\(940\) −35.6097 −1.16146
\(941\) 32.9011 1.07255 0.536273 0.844044i \(-0.319832\pi\)
0.536273 + 0.844044i \(0.319832\pi\)
\(942\) −18.4738 −0.601909
\(943\) 15.2129 0.495401
\(944\) 1.39283 0.0453326
\(945\) −15.0771 −0.490459
\(946\) −28.2985 −0.920062
\(947\) −32.2923 −1.04936 −0.524680 0.851300i \(-0.675815\pi\)
−0.524680 + 0.851300i \(0.675815\pi\)
\(948\) −10.7907 −0.350465
\(949\) 86.9066 2.82111
\(950\) 56.7254 1.84041
\(951\) 6.44583 0.209020
\(952\) −15.9103 −0.515655
\(953\) −7.13993 −0.231285 −0.115643 0.993291i \(-0.536893\pi\)
−0.115643 + 0.993291i \(0.536893\pi\)
\(954\) −19.7530 −0.639526
\(955\) 6.64045 0.214880
\(956\) −17.4034 −0.562867
\(957\) −2.51060 −0.0811561
\(958\) −6.58838 −0.212861
\(959\) −13.6876 −0.441995
\(960\) −9.90096 −0.319552
\(961\) −27.6989 −0.893511
\(962\) −27.1729 −0.876090
\(963\) −4.97174 −0.160212
\(964\) 16.4594 0.530122
\(965\) −69.0633 −2.22322
\(966\) 14.2384 0.458112
\(967\) 46.4553 1.49390 0.746952 0.664878i \(-0.231517\pi\)
0.746952 + 0.664878i \(0.231517\pi\)
\(968\) −4.19926 −0.134969
\(969\) −71.6192 −2.30074
\(970\) −64.9593 −2.08572
\(971\) −37.4217 −1.20092 −0.600459 0.799656i \(-0.705015\pi\)
−0.600459 + 0.799656i \(0.705015\pi\)
\(972\) 19.5343 0.626563
\(973\) 16.8927 0.541555
\(974\) −36.8423 −1.18050
\(975\) −182.179 −5.83441
\(976\) −4.72509 −0.151246
\(977\) 51.9228 1.66116 0.830579 0.556902i \(-0.188010\pi\)
0.830579 + 0.556902i \(0.188010\pi\)
\(978\) 8.08802 0.258627
\(979\) 30.7902 0.984059
\(980\) −10.4004 −0.332230
\(981\) −25.0843 −0.800879
\(982\) −27.2499 −0.869578
\(983\) −37.2095 −1.18680 −0.593399 0.804908i \(-0.702214\pi\)
−0.593399 + 0.804908i \(0.702214\pi\)
\(984\) −12.0988 −0.385695
\(985\) −4.94681 −0.157618
\(986\) 2.08080 0.0662663
\(987\) −40.7267 −1.29635
\(988\) −24.5280 −0.780340
\(989\) −20.9894 −0.667424
\(990\) −38.4162 −1.22095
\(991\) −33.3346 −1.05891 −0.529454 0.848339i \(-0.677603\pi\)
−0.529454 + 0.848339i \(0.677603\pi\)
\(992\) 1.81691 0.0576868
\(993\) 4.11044 0.130441
\(994\) −6.91087 −0.219199
\(995\) −51.9947 −1.64834
\(996\) 6.74265 0.213649
\(997\) 41.8887 1.32663 0.663315 0.748340i \(-0.269149\pi\)
0.663315 + 0.748340i \(0.269149\pi\)
\(998\) −11.0765 −0.350621
\(999\) 7.59394 0.240262
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 6038.2.a.d.1.10 69
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6038.2.a.d.1.10 69 1.1 even 1 trivial