Properties

Label 8023.2.a.d.1.8
Level $8023$
Weight $2$
Character 8023.1
Self dual yes
Analytic conductor $64.064$
Analytic rank $0$
Dimension $165$
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] = [8023,2,Mod(1,8023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8023, 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("8023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8023 = 71 \cdot 113 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8023.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: \(64.0639775417\)
Analytic rank: \(0\)
Dimension: \(165\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Character \(\chi\) \(=\) 8023.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.52899 q^{2} +1.55552 q^{3} +4.39577 q^{4} -1.46602 q^{5} -3.93388 q^{6} +0.126533 q^{7} -6.05887 q^{8} -0.580366 q^{9} +O(q^{10})\) \(q-2.52899 q^{2} +1.55552 q^{3} +4.39577 q^{4} -1.46602 q^{5} -3.93388 q^{6} +0.126533 q^{7} -6.05887 q^{8} -0.580366 q^{9} +3.70754 q^{10} -4.01915 q^{11} +6.83770 q^{12} -5.72744 q^{13} -0.320001 q^{14} -2.28042 q^{15} +6.53125 q^{16} -2.33060 q^{17} +1.46774 q^{18} -5.14352 q^{19} -6.44428 q^{20} +0.196825 q^{21} +10.1644 q^{22} -2.19537 q^{23} -9.42467 q^{24} -2.85079 q^{25} +14.4846 q^{26} -5.56932 q^{27} +0.556211 q^{28} +5.20671 q^{29} +5.76715 q^{30} +8.59587 q^{31} -4.39971 q^{32} -6.25185 q^{33} +5.89405 q^{34} -0.185500 q^{35} -2.55115 q^{36} -8.51681 q^{37} +13.0079 q^{38} -8.90914 q^{39} +8.88242 q^{40} +4.39062 q^{41} -0.497767 q^{42} -4.38155 q^{43} -17.6672 q^{44} +0.850827 q^{45} +5.55207 q^{46} +6.14196 q^{47} +10.1595 q^{48} -6.98399 q^{49} +7.20960 q^{50} -3.62528 q^{51} -25.1765 q^{52} +8.38992 q^{53} +14.0847 q^{54} +5.89215 q^{55} -0.766649 q^{56} -8.00083 q^{57} -13.1677 q^{58} -14.9961 q^{59} -10.0242 q^{60} -7.23445 q^{61} -21.7388 q^{62} -0.0734356 q^{63} -1.93570 q^{64} +8.39654 q^{65} +15.8108 q^{66} -8.80712 q^{67} -10.2448 q^{68} -3.41494 q^{69} +0.469127 q^{70} +1.00000 q^{71} +3.51636 q^{72} +11.1257 q^{73} +21.5389 q^{74} -4.43445 q^{75} -22.6097 q^{76} -0.508556 q^{77} +22.5311 q^{78} -4.90725 q^{79} -9.57494 q^{80} -6.92208 q^{81} -11.1038 q^{82} +1.13933 q^{83} +0.865196 q^{84} +3.41670 q^{85} +11.0809 q^{86} +8.09913 q^{87} +24.3515 q^{88} -15.1049 q^{89} -2.15173 q^{90} -0.724712 q^{91} -9.65036 q^{92} +13.3710 q^{93} -15.5329 q^{94} +7.54049 q^{95} -6.84382 q^{96} -6.13881 q^{97} +17.6624 q^{98} +2.33258 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52899 −1.78826 −0.894132 0.447804i \(-0.852206\pi\)
−0.894132 + 0.447804i \(0.852206\pi\)
\(3\) 1.55552 0.898078 0.449039 0.893512i \(-0.351766\pi\)
0.449039 + 0.893512i \(0.351766\pi\)
\(4\) 4.39577 2.19788
\(5\) −1.46602 −0.655624 −0.327812 0.944743i \(-0.606311\pi\)
−0.327812 + 0.944743i \(0.606311\pi\)
\(6\) −3.93388 −1.60600
\(7\) 0.126533 0.0478251 0.0239125 0.999714i \(-0.492388\pi\)
0.0239125 + 0.999714i \(0.492388\pi\)
\(8\) −6.05887 −2.14213
\(9\) −0.580366 −0.193455
\(10\) 3.70754 1.17243
\(11\) −4.01915 −1.21182 −0.605909 0.795534i \(-0.707191\pi\)
−0.605909 + 0.795534i \(0.707191\pi\)
\(12\) 6.83770 1.97387
\(13\) −5.72744 −1.58851 −0.794253 0.607587i \(-0.792138\pi\)
−0.794253 + 0.607587i \(0.792138\pi\)
\(14\) −0.320001 −0.0855238
\(15\) −2.28042 −0.588801
\(16\) 6.53125 1.63281
\(17\) −2.33060 −0.565253 −0.282626 0.959230i \(-0.591206\pi\)
−0.282626 + 0.959230i \(0.591206\pi\)
\(18\) 1.46774 0.345949
\(19\) −5.14352 −1.18000 −0.590002 0.807402i \(-0.700873\pi\)
−0.590002 + 0.807402i \(0.700873\pi\)
\(20\) −6.44428 −1.44099
\(21\) 0.196825 0.0429507
\(22\) 10.1644 2.16705
\(23\) −2.19537 −0.457767 −0.228884 0.973454i \(-0.573508\pi\)
−0.228884 + 0.973454i \(0.573508\pi\)
\(24\) −9.42467 −1.92380
\(25\) −2.85079 −0.570158
\(26\) 14.4846 2.84067
\(27\) −5.56932 −1.07182
\(28\) 0.556211 0.105114
\(29\) 5.20671 0.966862 0.483431 0.875382i \(-0.339390\pi\)
0.483431 + 0.875382i \(0.339390\pi\)
\(30\) 5.76715 1.05293
\(31\) 8.59587 1.54386 0.771932 0.635705i \(-0.219291\pi\)
0.771932 + 0.635705i \(0.219291\pi\)
\(32\) −4.39971 −0.777766
\(33\) −6.25185 −1.08831
\(34\) 5.89405 1.01082
\(35\) −0.185500 −0.0313553
\(36\) −2.55115 −0.425192
\(37\) −8.51681 −1.40016 −0.700078 0.714067i \(-0.746851\pi\)
−0.700078 + 0.714067i \(0.746851\pi\)
\(38\) 13.0079 2.11016
\(39\) −8.90914 −1.42660
\(40\) 8.88242 1.40443
\(41\) 4.39062 0.685699 0.342850 0.939390i \(-0.388608\pi\)
0.342850 + 0.939390i \(0.388608\pi\)
\(42\) −0.497767 −0.0768071
\(43\) −4.38155 −0.668181 −0.334090 0.942541i \(-0.608429\pi\)
−0.334090 + 0.942541i \(0.608429\pi\)
\(44\) −17.6672 −2.66344
\(45\) 0.850827 0.126834
\(46\) 5.55207 0.818608
\(47\) 6.14196 0.895896 0.447948 0.894060i \(-0.352155\pi\)
0.447948 + 0.894060i \(0.352155\pi\)
\(48\) 10.1595 1.46639
\(49\) −6.98399 −0.997713
\(50\) 7.20960 1.01959
\(51\) −3.62528 −0.507641
\(52\) −25.1765 −3.49135
\(53\) 8.38992 1.15244 0.576222 0.817293i \(-0.304526\pi\)
0.576222 + 0.817293i \(0.304526\pi\)
\(54\) 14.0847 1.91669
\(55\) 5.89215 0.794497
\(56\) −0.766649 −0.102448
\(57\) −8.00083 −1.05974
\(58\) −13.1677 −1.72900
\(59\) −14.9961 −1.95232 −0.976162 0.217041i \(-0.930359\pi\)
−0.976162 + 0.217041i \(0.930359\pi\)
\(60\) −10.0242 −1.29412
\(61\) −7.23445 −0.926277 −0.463138 0.886286i \(-0.653277\pi\)
−0.463138 + 0.886286i \(0.653277\pi\)
\(62\) −21.7388 −2.76083
\(63\) −0.0734356 −0.00925202
\(64\) −1.93570 −0.241963
\(65\) 8.39654 1.04146
\(66\) 15.8108 1.94618
\(67\) −8.80712 −1.07596 −0.537981 0.842957i \(-0.680813\pi\)
−0.537981 + 0.842957i \(0.680813\pi\)
\(68\) −10.2448 −1.24236
\(69\) −3.41494 −0.411111
\(70\) 0.469127 0.0560715
\(71\) 1.00000 0.118678
\(72\) 3.51636 0.414407
\(73\) 11.1257 1.30217 0.651083 0.759006i \(-0.274315\pi\)
0.651083 + 0.759006i \(0.274315\pi\)
\(74\) 21.5389 2.50385
\(75\) −4.43445 −0.512046
\(76\) −22.6097 −2.59351
\(77\) −0.508556 −0.0579553
\(78\) 22.5311 2.55114
\(79\) −4.90725 −0.552109 −0.276054 0.961142i \(-0.589027\pi\)
−0.276054 + 0.961142i \(0.589027\pi\)
\(80\) −9.57494 −1.07051
\(81\) −6.92208 −0.769120
\(82\) −11.1038 −1.22621
\(83\) 1.13933 0.125057 0.0625287 0.998043i \(-0.480083\pi\)
0.0625287 + 0.998043i \(0.480083\pi\)
\(84\) 0.865196 0.0944006
\(85\) 3.41670 0.370593
\(86\) 11.0809 1.19488
\(87\) 8.09913 0.868318
\(88\) 24.3515 2.59588
\(89\) −15.1049 −1.60112 −0.800558 0.599255i \(-0.795464\pi\)
−0.800558 + 0.599255i \(0.795464\pi\)
\(90\) −2.15173 −0.226812
\(91\) −0.724712 −0.0759705
\(92\) −9.65036 −1.00612
\(93\) 13.3710 1.38651
\(94\) −15.5329 −1.60210
\(95\) 7.54049 0.773638
\(96\) −6.84382 −0.698495
\(97\) −6.13881 −0.623302 −0.311651 0.950197i \(-0.600882\pi\)
−0.311651 + 0.950197i \(0.600882\pi\)
\(98\) 17.6624 1.78417
\(99\) 2.33258 0.234433
\(100\) −12.5314 −1.25314
\(101\) 0.0789165 0.00785249 0.00392624 0.999992i \(-0.498750\pi\)
0.00392624 + 0.999992i \(0.498750\pi\)
\(102\) 9.16829 0.907796
\(103\) 7.10686 0.700260 0.350130 0.936701i \(-0.386137\pi\)
0.350130 + 0.936701i \(0.386137\pi\)
\(104\) 34.7018 3.40279
\(105\) −0.288549 −0.0281595
\(106\) −21.2180 −2.06087
\(107\) −10.0930 −0.975730 −0.487865 0.872919i \(-0.662224\pi\)
−0.487865 + 0.872919i \(0.662224\pi\)
\(108\) −24.4815 −2.35573
\(109\) 4.69787 0.449974 0.224987 0.974362i \(-0.427766\pi\)
0.224987 + 0.974362i \(0.427766\pi\)
\(110\) −14.9012 −1.42077
\(111\) −13.2480 −1.25745
\(112\) 0.826421 0.0780894
\(113\) −1.00000 −0.0940721
\(114\) 20.2340 1.89509
\(115\) 3.21846 0.300123
\(116\) 22.8875 2.12505
\(117\) 3.32401 0.307305
\(118\) 37.9249 3.49127
\(119\) −0.294898 −0.0270333
\(120\) 13.8168 1.26129
\(121\) 5.15354 0.468504
\(122\) 18.2958 1.65643
\(123\) 6.82968 0.615812
\(124\) 37.7855 3.39323
\(125\) 11.5094 1.02943
\(126\) 0.185718 0.0165450
\(127\) −7.71496 −0.684592 −0.342296 0.939592i \(-0.611205\pi\)
−0.342296 + 0.939592i \(0.611205\pi\)
\(128\) 13.6948 1.21046
\(129\) −6.81558 −0.600079
\(130\) −21.2347 −1.86241
\(131\) −19.8278 −1.73236 −0.866180 0.499732i \(-0.833432\pi\)
−0.866180 + 0.499732i \(0.833432\pi\)
\(132\) −27.4817 −2.39198
\(133\) −0.650826 −0.0564338
\(134\) 22.2731 1.92410
\(135\) 8.16473 0.702708
\(136\) 14.1208 1.21085
\(137\) −7.06541 −0.603638 −0.301819 0.953365i \(-0.597594\pi\)
−0.301819 + 0.953365i \(0.597594\pi\)
\(138\) 8.63634 0.735174
\(139\) −21.3743 −1.81294 −0.906471 0.422269i \(-0.861234\pi\)
−0.906471 + 0.422269i \(0.861234\pi\)
\(140\) −0.815416 −0.0689153
\(141\) 9.55392 0.804585
\(142\) −2.52899 −0.212228
\(143\) 23.0194 1.92498
\(144\) −3.79051 −0.315876
\(145\) −7.63314 −0.633898
\(146\) −28.1368 −2.32862
\(147\) −10.8637 −0.896024
\(148\) −37.4379 −3.07738
\(149\) 0.898542 0.0736114 0.0368057 0.999322i \(-0.488282\pi\)
0.0368057 + 0.999322i \(0.488282\pi\)
\(150\) 11.2147 0.915673
\(151\) −1.43144 −0.116489 −0.0582443 0.998302i \(-0.518550\pi\)
−0.0582443 + 0.998302i \(0.518550\pi\)
\(152\) 31.1639 2.52772
\(153\) 1.35260 0.109351
\(154\) 1.28613 0.103639
\(155\) −12.6017 −1.01219
\(156\) −39.1625 −3.13551
\(157\) 14.0110 1.11820 0.559100 0.829100i \(-0.311147\pi\)
0.559100 + 0.829100i \(0.311147\pi\)
\(158\) 12.4104 0.987315
\(159\) 13.0507 1.03499
\(160\) 6.45006 0.509922
\(161\) −0.277788 −0.0218928
\(162\) 17.5058 1.37539
\(163\) −4.43070 −0.347040 −0.173520 0.984830i \(-0.555514\pi\)
−0.173520 + 0.984830i \(0.555514\pi\)
\(164\) 19.3001 1.50709
\(165\) 9.16533 0.713520
\(166\) −2.88134 −0.223636
\(167\) 11.0476 0.854890 0.427445 0.904041i \(-0.359414\pi\)
0.427445 + 0.904041i \(0.359414\pi\)
\(168\) −1.19254 −0.0920061
\(169\) 19.8036 1.52335
\(170\) −8.64079 −0.662718
\(171\) 2.98512 0.228278
\(172\) −19.2603 −1.46858
\(173\) −7.55934 −0.574726 −0.287363 0.957822i \(-0.592779\pi\)
−0.287363 + 0.957822i \(0.592779\pi\)
\(174\) −20.4826 −1.55278
\(175\) −0.360720 −0.0272678
\(176\) −26.2501 −1.97867
\(177\) −23.3267 −1.75334
\(178\) 38.2001 2.86322
\(179\) 25.9799 1.94183 0.970915 0.239423i \(-0.0769583\pi\)
0.970915 + 0.239423i \(0.0769583\pi\)
\(180\) 3.74004 0.278766
\(181\) −9.53223 −0.708525 −0.354263 0.935146i \(-0.615268\pi\)
−0.354263 + 0.935146i \(0.615268\pi\)
\(182\) 1.83279 0.135855
\(183\) −11.2533 −0.831869
\(184\) 13.3015 0.980598
\(185\) 12.4858 0.917975
\(186\) −33.8151 −2.47945
\(187\) 9.36701 0.684984
\(188\) 26.9986 1.96908
\(189\) −0.704705 −0.0512597
\(190\) −19.0698 −1.38347
\(191\) 13.0590 0.944916 0.472458 0.881353i \(-0.343367\pi\)
0.472458 + 0.881353i \(0.343367\pi\)
\(192\) −3.01102 −0.217302
\(193\) −8.36874 −0.602395 −0.301197 0.953562i \(-0.597386\pi\)
−0.301197 + 0.953562i \(0.597386\pi\)
\(194\) 15.5250 1.11463
\(195\) 13.0610 0.935315
\(196\) −30.7000 −2.19286
\(197\) 7.30532 0.520482 0.260241 0.965544i \(-0.416198\pi\)
0.260241 + 0.965544i \(0.416198\pi\)
\(198\) −5.89905 −0.419227
\(199\) −20.9848 −1.48757 −0.743787 0.668417i \(-0.766972\pi\)
−0.743787 + 0.668417i \(0.766972\pi\)
\(200\) 17.2725 1.22135
\(201\) −13.6996 −0.966298
\(202\) −0.199579 −0.0140423
\(203\) 0.658822 0.0462403
\(204\) −15.9359 −1.11574
\(205\) −6.43673 −0.449561
\(206\) −17.9731 −1.25225
\(207\) 1.27412 0.0885575
\(208\) −37.4074 −2.59373
\(209\) 20.6725 1.42995
\(210\) 0.729736 0.0503566
\(211\) 25.0490 1.72444 0.862222 0.506530i \(-0.169072\pi\)
0.862222 + 0.506530i \(0.169072\pi\)
\(212\) 36.8802 2.53294
\(213\) 1.55552 0.106582
\(214\) 25.5251 1.74486
\(215\) 6.42344 0.438075
\(216\) 33.7438 2.29597
\(217\) 1.08766 0.0738354
\(218\) −11.8808 −0.804672
\(219\) 17.3062 1.16945
\(220\) 25.9005 1.74621
\(221\) 13.3484 0.897908
\(222\) 33.5041 2.24865
\(223\) 0.793743 0.0531530 0.0265765 0.999647i \(-0.491539\pi\)
0.0265765 + 0.999647i \(0.491539\pi\)
\(224\) −0.556710 −0.0371967
\(225\) 1.65450 0.110300
\(226\) 2.52899 0.168226
\(227\) −3.86706 −0.256666 −0.128333 0.991731i \(-0.540963\pi\)
−0.128333 + 0.991731i \(0.540963\pi\)
\(228\) −35.1698 −2.32918
\(229\) −13.0632 −0.863241 −0.431620 0.902055i \(-0.642058\pi\)
−0.431620 + 0.902055i \(0.642058\pi\)
\(230\) −8.13944 −0.536699
\(231\) −0.791068 −0.0520484
\(232\) −31.5468 −2.07115
\(233\) 10.7712 0.705643 0.352821 0.935691i \(-0.385222\pi\)
0.352821 + 0.935691i \(0.385222\pi\)
\(234\) −8.40638 −0.549542
\(235\) −9.00423 −0.587371
\(236\) −65.9194 −4.29098
\(237\) −7.63331 −0.495837
\(238\) 0.745793 0.0483426
\(239\) 24.3711 1.57644 0.788218 0.615397i \(-0.211004\pi\)
0.788218 + 0.615397i \(0.211004\pi\)
\(240\) −14.8940 −0.961403
\(241\) 0.551876 0.0355494 0.0177747 0.999842i \(-0.494342\pi\)
0.0177747 + 0.999842i \(0.494342\pi\)
\(242\) −13.0332 −0.837808
\(243\) 5.94055 0.381086
\(244\) −31.8010 −2.03585
\(245\) 10.2387 0.654124
\(246\) −17.2722 −1.10123
\(247\) 29.4592 1.87444
\(248\) −52.0812 −3.30716
\(249\) 1.77224 0.112311
\(250\) −29.1071 −1.84090
\(251\) 20.9235 1.32068 0.660341 0.750966i \(-0.270412\pi\)
0.660341 + 0.750966i \(0.270412\pi\)
\(252\) −0.322806 −0.0203349
\(253\) 8.82353 0.554731
\(254\) 19.5110 1.22423
\(255\) 5.31474 0.332822
\(256\) −30.7625 −1.92266
\(257\) 16.9880 1.05968 0.529841 0.848097i \(-0.322251\pi\)
0.529841 + 0.848097i \(0.322251\pi\)
\(258\) 17.2365 1.07310
\(259\) −1.07766 −0.0669626
\(260\) 36.9093 2.28901
\(261\) −3.02180 −0.187045
\(262\) 50.1442 3.09792
\(263\) −27.7246 −1.70957 −0.854785 0.518982i \(-0.826311\pi\)
−0.854785 + 0.518982i \(0.826311\pi\)
\(264\) 37.8791 2.33130
\(265\) −12.2998 −0.755570
\(266\) 1.64593 0.100918
\(267\) −23.4959 −1.43793
\(268\) −38.7141 −2.36484
\(269\) −19.1130 −1.16534 −0.582670 0.812709i \(-0.697992\pi\)
−0.582670 + 0.812709i \(0.697992\pi\)
\(270\) −20.6485 −1.25663
\(271\) 3.93835 0.239238 0.119619 0.992820i \(-0.461833\pi\)
0.119619 + 0.992820i \(0.461833\pi\)
\(272\) −15.2217 −0.922952
\(273\) −1.12730 −0.0682274
\(274\) 17.8683 1.07946
\(275\) 11.4577 0.690927
\(276\) −15.0113 −0.903574
\(277\) 6.43083 0.386391 0.193195 0.981160i \(-0.438115\pi\)
0.193195 + 0.981160i \(0.438115\pi\)
\(278\) 54.0552 3.24202
\(279\) −4.98875 −0.298669
\(280\) 1.12392 0.0671671
\(281\) 28.7027 1.71226 0.856129 0.516762i \(-0.172863\pi\)
0.856129 + 0.516762i \(0.172863\pi\)
\(282\) −24.1617 −1.43881
\(283\) 0.593602 0.0352860 0.0176430 0.999844i \(-0.494384\pi\)
0.0176430 + 0.999844i \(0.494384\pi\)
\(284\) 4.39577 0.260841
\(285\) 11.7294 0.694788
\(286\) −58.2158 −3.44237
\(287\) 0.555559 0.0327936
\(288\) 2.55344 0.150463
\(289\) −11.5683 −0.680489
\(290\) 19.3041 1.13358
\(291\) −9.54903 −0.559774
\(292\) 48.9061 2.86201
\(293\) 20.9179 1.22204 0.611020 0.791616i \(-0.290760\pi\)
0.611020 + 0.791616i \(0.290760\pi\)
\(294\) 27.4742 1.60233
\(295\) 21.9846 1.27999
\(296\) 51.6022 2.99932
\(297\) 22.3839 1.29885
\(298\) −2.27240 −0.131637
\(299\) 12.5739 0.727166
\(300\) −19.4928 −1.12542
\(301\) −0.554412 −0.0319558
\(302\) 3.62008 0.208312
\(303\) 0.122756 0.00705215
\(304\) −33.5936 −1.92672
\(305\) 10.6058 0.607289
\(306\) −3.42070 −0.195549
\(307\) 19.8380 1.13221 0.566107 0.824332i \(-0.308449\pi\)
0.566107 + 0.824332i \(0.308449\pi\)
\(308\) −2.23549 −0.127379
\(309\) 11.0548 0.628888
\(310\) 31.8695 1.81007
\(311\) 35.0957 1.99010 0.995048 0.0993923i \(-0.0316899\pi\)
0.995048 + 0.0993923i \(0.0316899\pi\)
\(312\) 53.9793 3.05597
\(313\) −6.78306 −0.383401 −0.191701 0.981453i \(-0.561400\pi\)
−0.191701 + 0.981453i \(0.561400\pi\)
\(314\) −35.4336 −1.99964
\(315\) 0.107658 0.00606584
\(316\) −21.5711 −1.21347
\(317\) −11.7428 −0.659544 −0.329772 0.944061i \(-0.606972\pi\)
−0.329772 + 0.944061i \(0.606972\pi\)
\(318\) −33.0050 −1.85083
\(319\) −20.9265 −1.17166
\(320\) 2.83778 0.158637
\(321\) −15.6999 −0.876282
\(322\) 0.702522 0.0391500
\(323\) 11.9875 0.667000
\(324\) −30.4279 −1.69044
\(325\) 16.3277 0.905699
\(326\) 11.2052 0.620598
\(327\) 7.30761 0.404112
\(328\) −26.6022 −1.46886
\(329\) 0.777162 0.0428463
\(330\) −23.1790 −1.27596
\(331\) −25.7407 −1.41483 −0.707417 0.706796i \(-0.750140\pi\)
−0.707417 + 0.706796i \(0.750140\pi\)
\(332\) 5.00822 0.274862
\(333\) 4.94287 0.270867
\(334\) −27.9393 −1.52877
\(335\) 12.9114 0.705426
\(336\) 1.28551 0.0701304
\(337\) 12.9394 0.704857 0.352428 0.935839i \(-0.385356\pi\)
0.352428 + 0.935839i \(0.385356\pi\)
\(338\) −50.0830 −2.72416
\(339\) −1.55552 −0.0844841
\(340\) 15.0190 0.814521
\(341\) −34.5481 −1.87088
\(342\) −7.54933 −0.408221
\(343\) −1.76944 −0.0955408
\(344\) 26.5473 1.43133
\(345\) 5.00637 0.269534
\(346\) 19.1175 1.02776
\(347\) −2.10574 −0.113042 −0.0565209 0.998401i \(-0.518001\pi\)
−0.0565209 + 0.998401i \(0.518001\pi\)
\(348\) 35.6019 1.90846
\(349\) 16.0672 0.860056 0.430028 0.902815i \(-0.358504\pi\)
0.430028 + 0.902815i \(0.358504\pi\)
\(350\) 0.912255 0.0487621
\(351\) 31.8980 1.70259
\(352\) 17.6831 0.942511
\(353\) 31.3616 1.66921 0.834604 0.550850i \(-0.185696\pi\)
0.834604 + 0.550850i \(0.185696\pi\)
\(354\) 58.9928 3.13543
\(355\) −1.46602 −0.0778082
\(356\) −66.3977 −3.51907
\(357\) −0.458719 −0.0242780
\(358\) −65.7029 −3.47250
\(359\) −9.84325 −0.519507 −0.259753 0.965675i \(-0.583641\pi\)
−0.259753 + 0.965675i \(0.583641\pi\)
\(360\) −5.15505 −0.271695
\(361\) 7.45576 0.392408
\(362\) 24.1069 1.26703
\(363\) 8.01642 0.420753
\(364\) −3.18567 −0.166974
\(365\) −16.3105 −0.853731
\(366\) 28.4595 1.48760
\(367\) 10.5454 0.550466 0.275233 0.961378i \(-0.411245\pi\)
0.275233 + 0.961378i \(0.411245\pi\)
\(368\) −14.3385 −0.747448
\(369\) −2.54816 −0.132652
\(370\) −31.5764 −1.64158
\(371\) 1.06160 0.0551158
\(372\) 58.7759 3.04739
\(373\) 5.72131 0.296238 0.148119 0.988970i \(-0.452678\pi\)
0.148119 + 0.988970i \(0.452678\pi\)
\(374\) −23.6890 −1.22493
\(375\) 17.9031 0.924511
\(376\) −37.2133 −1.91913
\(377\) −29.8211 −1.53587
\(378\) 1.78219 0.0916659
\(379\) −13.7764 −0.707647 −0.353823 0.935312i \(-0.615119\pi\)
−0.353823 + 0.935312i \(0.615119\pi\)
\(380\) 33.1463 1.70037
\(381\) −12.0008 −0.614817
\(382\) −33.0260 −1.68976
\(383\) 30.7625 1.57189 0.785944 0.618297i \(-0.212177\pi\)
0.785944 + 0.618297i \(0.212177\pi\)
\(384\) 21.3025 1.08709
\(385\) 0.745553 0.0379969
\(386\) 21.1644 1.07724
\(387\) 2.54290 0.129263
\(388\) −26.9848 −1.36995
\(389\) −0.515274 −0.0261254 −0.0130627 0.999915i \(-0.504158\pi\)
−0.0130627 + 0.999915i \(0.504158\pi\)
\(390\) −33.0310 −1.67259
\(391\) 5.11653 0.258754
\(392\) 42.3151 2.13723
\(393\) −30.8424 −1.55580
\(394\) −18.4750 −0.930760
\(395\) 7.19412 0.361975
\(396\) 10.2535 0.515256
\(397\) −7.32240 −0.367501 −0.183750 0.982973i \(-0.558824\pi\)
−0.183750 + 0.982973i \(0.558824\pi\)
\(398\) 53.0703 2.66017
\(399\) −1.01237 −0.0506820
\(400\) −18.6192 −0.930961
\(401\) −38.4911 −1.92215 −0.961076 0.276284i \(-0.910897\pi\)
−0.961076 + 0.276284i \(0.910897\pi\)
\(402\) 34.6462 1.72799
\(403\) −49.2323 −2.45244
\(404\) 0.346899 0.0172589
\(405\) 10.1479 0.504253
\(406\) −1.66615 −0.0826898
\(407\) 34.2303 1.69673
\(408\) 21.9651 1.08744
\(409\) 18.5224 0.915874 0.457937 0.888985i \(-0.348589\pi\)
0.457937 + 0.888985i \(0.348589\pi\)
\(410\) 16.2784 0.803933
\(411\) −10.9904 −0.542115
\(412\) 31.2401 1.53909
\(413\) −1.89750 −0.0933701
\(414\) −3.22223 −0.158364
\(415\) −1.67028 −0.0819906
\(416\) 25.1991 1.23549
\(417\) −33.2480 −1.62816
\(418\) −52.2806 −2.55713
\(419\) −19.4289 −0.949163 −0.474582 0.880211i \(-0.657401\pi\)
−0.474582 + 0.880211i \(0.657401\pi\)
\(420\) −1.26839 −0.0618913
\(421\) 25.6738 1.25127 0.625633 0.780118i \(-0.284841\pi\)
0.625633 + 0.780118i \(0.284841\pi\)
\(422\) −63.3486 −3.08376
\(423\) −3.56458 −0.173316
\(424\) −50.8334 −2.46869
\(425\) 6.64404 0.322283
\(426\) −3.93388 −0.190597
\(427\) −0.915399 −0.0442993
\(428\) −44.3666 −2.14454
\(429\) 35.8071 1.72878
\(430\) −16.2448 −0.783393
\(431\) −37.9485 −1.82791 −0.913957 0.405812i \(-0.866989\pi\)
−0.913957 + 0.405812i \(0.866989\pi\)
\(432\) −36.3746 −1.75008
\(433\) −0.953598 −0.0458270 −0.0229135 0.999737i \(-0.507294\pi\)
−0.0229135 + 0.999737i \(0.507294\pi\)
\(434\) −2.75069 −0.132037
\(435\) −11.8735 −0.569290
\(436\) 20.6507 0.988991
\(437\) 11.2919 0.540167
\(438\) −43.7673 −2.09128
\(439\) −15.7958 −0.753891 −0.376946 0.926235i \(-0.623026\pi\)
−0.376946 + 0.926235i \(0.623026\pi\)
\(440\) −35.6997 −1.70192
\(441\) 4.05327 0.193013
\(442\) −33.7578 −1.60570
\(443\) −21.0372 −0.999506 −0.499753 0.866168i \(-0.666576\pi\)
−0.499753 + 0.866168i \(0.666576\pi\)
\(444\) −58.2354 −2.76373
\(445\) 22.1441 1.04973
\(446\) −2.00737 −0.0950515
\(447\) 1.39770 0.0661088
\(448\) −0.244931 −0.0115719
\(449\) −1.23116 −0.0581020 −0.0290510 0.999578i \(-0.509249\pi\)
−0.0290510 + 0.999578i \(0.509249\pi\)
\(450\) −4.18421 −0.197245
\(451\) −17.6465 −0.830943
\(452\) −4.39577 −0.206760
\(453\) −2.22662 −0.104616
\(454\) 9.77974 0.458986
\(455\) 1.06244 0.0498080
\(456\) 48.4760 2.27009
\(457\) −33.7008 −1.57646 −0.788229 0.615383i \(-0.789002\pi\)
−0.788229 + 0.615383i \(0.789002\pi\)
\(458\) 33.0367 1.54370
\(459\) 12.9798 0.605847
\(460\) 14.1476 0.659636
\(461\) 35.6808 1.66182 0.830911 0.556405i \(-0.187820\pi\)
0.830911 + 0.556405i \(0.187820\pi\)
\(462\) 2.00060 0.0930763
\(463\) 23.4896 1.09166 0.545828 0.837897i \(-0.316215\pi\)
0.545828 + 0.837897i \(0.316215\pi\)
\(464\) 34.0063 1.57870
\(465\) −19.6022 −0.909029
\(466\) −27.2401 −1.26187
\(467\) 10.7281 0.496439 0.248220 0.968704i \(-0.420155\pi\)
0.248220 + 0.968704i \(0.420155\pi\)
\(468\) 14.6116 0.675421
\(469\) −1.11439 −0.0514579
\(470\) 22.7716 1.05037
\(471\) 21.7944 1.00423
\(472\) 90.8593 4.18214
\(473\) 17.6101 0.809713
\(474\) 19.3045 0.886687
\(475\) 14.6631 0.672788
\(476\) −1.29630 −0.0594160
\(477\) −4.86922 −0.222946
\(478\) −61.6342 −2.81908
\(479\) 21.4770 0.981307 0.490654 0.871355i \(-0.336758\pi\)
0.490654 + 0.871355i \(0.336758\pi\)
\(480\) 10.0332 0.457950
\(481\) 48.7796 2.22416
\(482\) −1.39569 −0.0635717
\(483\) −0.432104 −0.0196614
\(484\) 22.6538 1.02972
\(485\) 8.99961 0.408651
\(486\) −15.0236 −0.681483
\(487\) 38.0452 1.72399 0.861997 0.506913i \(-0.169214\pi\)
0.861997 + 0.506913i \(0.169214\pi\)
\(488\) 43.8326 1.98421
\(489\) −6.89204 −0.311669
\(490\) −25.8934 −1.16975
\(491\) 6.73665 0.304021 0.152010 0.988379i \(-0.451425\pi\)
0.152010 + 0.988379i \(0.451425\pi\)
\(492\) 30.0217 1.35348
\(493\) −12.1347 −0.546521
\(494\) −74.5019 −3.35200
\(495\) −3.41960 −0.153700
\(496\) 56.1418 2.52084
\(497\) 0.126533 0.00567579
\(498\) −4.48198 −0.200842
\(499\) 9.47595 0.424202 0.212101 0.977248i \(-0.431969\pi\)
0.212101 + 0.977248i \(0.431969\pi\)
\(500\) 50.5927 2.26257
\(501\) 17.1847 0.767758
\(502\) −52.9153 −2.36173
\(503\) −6.68842 −0.298222 −0.149111 0.988820i \(-0.547641\pi\)
−0.149111 + 0.988820i \(0.547641\pi\)
\(504\) 0.444937 0.0198190
\(505\) −0.115693 −0.00514828
\(506\) −22.3146 −0.992004
\(507\) 30.8048 1.36809
\(508\) −33.9132 −1.50465
\(509\) −27.2002 −1.20563 −0.602815 0.797881i \(-0.705954\pi\)
−0.602815 + 0.797881i \(0.705954\pi\)
\(510\) −13.4409 −0.595173
\(511\) 1.40777 0.0622763
\(512\) 50.4084 2.22776
\(513\) 28.6459 1.26475
\(514\) −42.9624 −1.89499
\(515\) −10.4188 −0.459107
\(516\) −29.9597 −1.31890
\(517\) −24.6854 −1.08566
\(518\) 2.72539 0.119747
\(519\) −11.7587 −0.516149
\(520\) −50.8735 −2.23095
\(521\) 7.36141 0.322509 0.161255 0.986913i \(-0.448446\pi\)
0.161255 + 0.986913i \(0.448446\pi\)
\(522\) 7.64208 0.334485
\(523\) −30.0860 −1.31557 −0.657784 0.753206i \(-0.728506\pi\)
−0.657784 + 0.753206i \(0.728506\pi\)
\(524\) −87.1583 −3.80753
\(525\) −0.561106 −0.0244887
\(526\) 70.1151 3.05716
\(527\) −20.0335 −0.872673
\(528\) −40.8324 −1.77700
\(529\) −18.1803 −0.790449
\(530\) 31.1060 1.35116
\(531\) 8.70322 0.377687
\(532\) −2.86088 −0.124035
\(533\) −25.1470 −1.08924
\(534\) 59.4209 2.57139
\(535\) 14.7966 0.639712
\(536\) 53.3612 2.30485
\(537\) 40.4122 1.74392
\(538\) 48.3365 2.08393
\(539\) 28.0697 1.20905
\(540\) 35.8903 1.54447
\(541\) −14.4789 −0.622498 −0.311249 0.950328i \(-0.600747\pi\)
−0.311249 + 0.950328i \(0.600747\pi\)
\(542\) −9.96003 −0.427820
\(543\) −14.8276 −0.636311
\(544\) 10.2539 0.439634
\(545\) −6.88716 −0.295014
\(546\) 2.85093 0.122009
\(547\) 23.8536 1.01991 0.509954 0.860202i \(-0.329663\pi\)
0.509954 + 0.860202i \(0.329663\pi\)
\(548\) −31.0579 −1.32673
\(549\) 4.19863 0.179193
\(550\) −28.9765 −1.23556
\(551\) −26.7808 −1.14090
\(552\) 20.6907 0.880654
\(553\) −0.620930 −0.0264046
\(554\) −16.2635 −0.690969
\(555\) 19.4219 0.824413
\(556\) −93.9563 −3.98464
\(557\) 13.7010 0.580528 0.290264 0.956947i \(-0.406257\pi\)
0.290264 + 0.956947i \(0.406257\pi\)
\(558\) 12.6165 0.534098
\(559\) 25.0951 1.06141
\(560\) −1.21155 −0.0511973
\(561\) 14.5705 0.615169
\(562\) −72.5887 −3.06197
\(563\) −39.4919 −1.66439 −0.832193 0.554487i \(-0.812915\pi\)
−0.832193 + 0.554487i \(0.812915\pi\)
\(564\) 41.9968 1.76839
\(565\) 1.46602 0.0616759
\(566\) −1.50121 −0.0631006
\(567\) −0.875873 −0.0367832
\(568\) −6.05887 −0.254224
\(569\) −16.0762 −0.673950 −0.336975 0.941514i \(-0.609404\pi\)
−0.336975 + 0.941514i \(0.609404\pi\)
\(570\) −29.6634 −1.24246
\(571\) −26.2582 −1.09887 −0.549437 0.835535i \(-0.685158\pi\)
−0.549437 + 0.835535i \(0.685158\pi\)
\(572\) 101.188 4.23089
\(573\) 20.3135 0.848609
\(574\) −1.40500 −0.0586437
\(575\) 6.25855 0.260999
\(576\) 1.12342 0.0468090
\(577\) 32.8109 1.36594 0.682968 0.730449i \(-0.260689\pi\)
0.682968 + 0.730449i \(0.260689\pi\)
\(578\) 29.2561 1.21689
\(579\) −13.0177 −0.540998
\(580\) −33.5535 −1.39323
\(581\) 0.144163 0.00598088
\(582\) 24.1494 1.00102
\(583\) −33.7203 −1.39655
\(584\) −67.4093 −2.78942
\(585\) −4.87306 −0.201476
\(586\) −52.9012 −2.18533
\(587\) −26.6680 −1.10071 −0.550354 0.834932i \(-0.685507\pi\)
−0.550354 + 0.834932i \(0.685507\pi\)
\(588\) −47.7544 −1.96936
\(589\) −44.2130 −1.82176
\(590\) −55.5986 −2.28896
\(591\) 11.3636 0.467434
\(592\) −55.6254 −2.28619
\(593\) −21.1873 −0.870060 −0.435030 0.900416i \(-0.643262\pi\)
−0.435030 + 0.900416i \(0.643262\pi\)
\(594\) −56.6086 −2.32268
\(595\) 0.432326 0.0177236
\(596\) 3.94978 0.161789
\(597\) −32.6422 −1.33596
\(598\) −31.7992 −1.30036
\(599\) 22.5444 0.921141 0.460571 0.887623i \(-0.347645\pi\)
0.460571 + 0.887623i \(0.347645\pi\)
\(600\) 26.8677 1.09687
\(601\) 0.870084 0.0354915 0.0177457 0.999843i \(-0.494351\pi\)
0.0177457 + 0.999843i \(0.494351\pi\)
\(602\) 1.40210 0.0571454
\(603\) 5.11135 0.208150
\(604\) −6.29226 −0.256028
\(605\) −7.55519 −0.307162
\(606\) −0.310448 −0.0126111
\(607\) −11.2962 −0.458500 −0.229250 0.973368i \(-0.573627\pi\)
−0.229250 + 0.973368i \(0.573627\pi\)
\(608\) 22.6300 0.917766
\(609\) 1.02481 0.0415274
\(610\) −26.8220 −1.08599
\(611\) −35.1777 −1.42314
\(612\) 5.94571 0.240341
\(613\) 43.7112 1.76548 0.882739 0.469864i \(-0.155697\pi\)
0.882739 + 0.469864i \(0.155697\pi\)
\(614\) −50.1700 −2.02470
\(615\) −10.0124 −0.403741
\(616\) 3.08127 0.124148
\(617\) −41.3104 −1.66310 −0.831548 0.555454i \(-0.812545\pi\)
−0.831548 + 0.555454i \(0.812545\pi\)
\(618\) −27.9575 −1.12462
\(619\) −30.6617 −1.23240 −0.616198 0.787591i \(-0.711328\pi\)
−0.616198 + 0.787591i \(0.711328\pi\)
\(620\) −55.3942 −2.22468
\(621\) 12.2267 0.490642
\(622\) −88.7566 −3.55882
\(623\) −1.91127 −0.0765736
\(624\) −58.1878 −2.32938
\(625\) −2.61907 −0.104763
\(626\) 17.1543 0.685622
\(627\) 32.1565 1.28421
\(628\) 61.5892 2.45768
\(629\) 19.8493 0.791442
\(630\) −0.272266 −0.0108473
\(631\) 3.94393 0.157005 0.0785026 0.996914i \(-0.474986\pi\)
0.0785026 + 0.996914i \(0.474986\pi\)
\(632\) 29.7324 1.18269
\(633\) 38.9642 1.54869
\(634\) 29.6975 1.17944
\(635\) 11.3103 0.448835
\(636\) 57.3677 2.27478
\(637\) 40.0004 1.58487
\(638\) 52.9229 2.09524
\(639\) −0.580366 −0.0229589
\(640\) −20.0768 −0.793606
\(641\) −33.6306 −1.32833 −0.664164 0.747587i \(-0.731213\pi\)
−0.664164 + 0.747587i \(0.731213\pi\)
\(642\) 39.7048 1.56702
\(643\) 1.95780 0.0772079 0.0386040 0.999255i \(-0.487709\pi\)
0.0386040 + 0.999255i \(0.487709\pi\)
\(644\) −1.22109 −0.0481178
\(645\) 9.99177 0.393426
\(646\) −30.3161 −1.19277
\(647\) −31.5865 −1.24179 −0.620896 0.783893i \(-0.713231\pi\)
−0.620896 + 0.783893i \(0.713231\pi\)
\(648\) 41.9400 1.64756
\(649\) 60.2715 2.36586
\(650\) −41.2926 −1.61963
\(651\) 1.69188 0.0663100
\(652\) −19.4764 −0.762753
\(653\) −40.4811 −1.58415 −0.792074 0.610425i \(-0.790999\pi\)
−0.792074 + 0.610425i \(0.790999\pi\)
\(654\) −18.4809 −0.722659
\(655\) 29.0679 1.13578
\(656\) 28.6762 1.11962
\(657\) −6.45699 −0.251911
\(658\) −1.96543 −0.0766205
\(659\) 37.1392 1.44674 0.723369 0.690462i \(-0.242593\pi\)
0.723369 + 0.690462i \(0.242593\pi\)
\(660\) 40.2887 1.56824
\(661\) −20.1610 −0.784172 −0.392086 0.919929i \(-0.628246\pi\)
−0.392086 + 0.919929i \(0.628246\pi\)
\(662\) 65.0978 2.53010
\(663\) 20.7636 0.806392
\(664\) −6.90304 −0.267890
\(665\) 0.954123 0.0369993
\(666\) −12.5004 −0.484382
\(667\) −11.4307 −0.442598
\(668\) 48.5627 1.87895
\(669\) 1.23468 0.0477356
\(670\) −32.6528 −1.26149
\(671\) 29.0763 1.12248
\(672\) −0.865971 −0.0334056
\(673\) −31.1525 −1.20084 −0.600420 0.799685i \(-0.705000\pi\)
−0.600420 + 0.799685i \(0.705000\pi\)
\(674\) −32.7237 −1.26047
\(675\) 15.8770 0.611104
\(676\) 87.0521 3.34816
\(677\) 9.87390 0.379485 0.189742 0.981834i \(-0.439235\pi\)
0.189742 + 0.981834i \(0.439235\pi\)
\(678\) 3.93388 0.151080
\(679\) −0.776764 −0.0298095
\(680\) −20.7013 −0.793860
\(681\) −6.01528 −0.230506
\(682\) 87.3716 3.34563
\(683\) −33.2088 −1.27070 −0.635350 0.772224i \(-0.719144\pi\)
−0.635350 + 0.772224i \(0.719144\pi\)
\(684\) 13.1219 0.501729
\(685\) 10.3580 0.395760
\(686\) 4.47489 0.170852
\(687\) −20.3200 −0.775258
\(688\) −28.6170 −1.09101
\(689\) −48.0528 −1.83067
\(690\) −12.6610 −0.481998
\(691\) −0.384714 −0.0146352 −0.00731761 0.999973i \(-0.502329\pi\)
−0.00731761 + 0.999973i \(0.502329\pi\)
\(692\) −33.2291 −1.26318
\(693\) 0.295148 0.0112118
\(694\) 5.32538 0.202148
\(695\) 31.3351 1.18861
\(696\) −49.0716 −1.86005
\(697\) −10.2328 −0.387594
\(698\) −40.6337 −1.53801
\(699\) 16.7547 0.633723
\(700\) −1.58564 −0.0599316
\(701\) 25.6388 0.968363 0.484181 0.874968i \(-0.339117\pi\)
0.484181 + 0.874968i \(0.339117\pi\)
\(702\) −80.6695 −3.04467
\(703\) 43.8064 1.65219
\(704\) 7.77988 0.293215
\(705\) −14.0062 −0.527505
\(706\) −79.3130 −2.98498
\(707\) 0.00998557 0.000375546 0
\(708\) −102.539 −3.85364
\(709\) 10.0531 0.377552 0.188776 0.982020i \(-0.439548\pi\)
0.188776 + 0.982020i \(0.439548\pi\)
\(710\) 3.70754 0.139142
\(711\) 2.84800 0.106808
\(712\) 91.5186 3.42981
\(713\) −18.8711 −0.706730
\(714\) 1.16009 0.0434154
\(715\) −33.7469 −1.26206
\(716\) 114.202 4.26792
\(717\) 37.9097 1.41576
\(718\) 24.8934 0.929015
\(719\) −21.9236 −0.817611 −0.408806 0.912621i \(-0.634055\pi\)
−0.408806 + 0.912621i \(0.634055\pi\)
\(720\) 5.55697 0.207096
\(721\) 0.899254 0.0334900
\(722\) −18.8555 −0.701729
\(723\) 0.858452 0.0319262
\(724\) −41.9015 −1.55726
\(725\) −14.8432 −0.551264
\(726\) −20.2734 −0.752417
\(727\) −19.4429 −0.721097 −0.360548 0.932740i \(-0.617410\pi\)
−0.360548 + 0.932740i \(0.617410\pi\)
\(728\) 4.39094 0.162739
\(729\) 30.0069 1.11137
\(730\) 41.2491 1.52670
\(731\) 10.2116 0.377691
\(732\) −49.4670 −1.82835
\(733\) 23.0709 0.852144 0.426072 0.904689i \(-0.359897\pi\)
0.426072 + 0.904689i \(0.359897\pi\)
\(734\) −26.6692 −0.984378
\(735\) 15.9264 0.587455
\(736\) 9.65900 0.356036
\(737\) 35.3971 1.30387
\(738\) 6.44427 0.237217
\(739\) −14.3648 −0.528419 −0.264209 0.964465i \(-0.585111\pi\)
−0.264209 + 0.964465i \(0.585111\pi\)
\(740\) 54.8847 2.01760
\(741\) 45.8243 1.68340
\(742\) −2.68478 −0.0985615
\(743\) 5.22735 0.191773 0.0958865 0.995392i \(-0.469431\pi\)
0.0958865 + 0.995392i \(0.469431\pi\)
\(744\) −81.0133 −2.97009
\(745\) −1.31728 −0.0482614
\(746\) −14.4691 −0.529751
\(747\) −0.661227 −0.0241930
\(748\) 41.1752 1.50552
\(749\) −1.27710 −0.0466644
\(750\) −45.2766 −1.65327
\(751\) 27.8328 1.01563 0.507816 0.861465i \(-0.330453\pi\)
0.507816 + 0.861465i \(0.330453\pi\)
\(752\) 40.1147 1.46283
\(753\) 32.5469 1.18608
\(754\) 75.4172 2.74653
\(755\) 2.09851 0.0763726
\(756\) −3.09772 −0.112663
\(757\) −45.9267 −1.66923 −0.834617 0.550831i \(-0.814311\pi\)
−0.834617 + 0.550831i \(0.814311\pi\)
\(758\) 34.8403 1.26546
\(759\) 13.7252 0.498192
\(760\) −45.6868 −1.65724
\(761\) 6.73146 0.244015 0.122008 0.992529i \(-0.461067\pi\)
0.122008 + 0.992529i \(0.461067\pi\)
\(762\) 30.3497 1.09945
\(763\) 0.594437 0.0215201
\(764\) 57.4044 2.07682
\(765\) −1.98294 −0.0716932
\(766\) −77.7978 −2.81095
\(767\) 85.8893 3.10128
\(768\) −47.8516 −1.72670
\(769\) 1.11139 0.0400779 0.0200389 0.999799i \(-0.493621\pi\)
0.0200389 + 0.999799i \(0.493621\pi\)
\(770\) −1.88549 −0.0679484
\(771\) 26.4251 0.951678
\(772\) −36.7870 −1.32399
\(773\) −9.34034 −0.335949 −0.167974 0.985791i \(-0.553723\pi\)
−0.167974 + 0.985791i \(0.553723\pi\)
\(774\) −6.43097 −0.231156
\(775\) −24.5050 −0.880246
\(776\) 37.1942 1.33520
\(777\) −1.67632 −0.0601376
\(778\) 1.30312 0.0467192
\(779\) −22.5832 −0.809128
\(780\) 57.4130 2.05571
\(781\) −4.01915 −0.143816
\(782\) −12.9396 −0.462721
\(783\) −28.9978 −1.03630
\(784\) −45.6142 −1.62908
\(785\) −20.5404 −0.733119
\(786\) 78.0001 2.78217
\(787\) −22.3063 −0.795134 −0.397567 0.917573i \(-0.630145\pi\)
−0.397567 + 0.917573i \(0.630145\pi\)
\(788\) 32.1125 1.14396
\(789\) −43.1261 −1.53533
\(790\) −18.1938 −0.647307
\(791\) −0.126533 −0.00449901
\(792\) −14.1328 −0.502186
\(793\) 41.4349 1.47140
\(794\) 18.5182 0.657188
\(795\) −19.1325 −0.678561
\(796\) −92.2444 −3.26951
\(797\) 4.91016 0.173927 0.0869634 0.996212i \(-0.472284\pi\)
0.0869634 + 0.996212i \(0.472284\pi\)
\(798\) 2.56027 0.0906327
\(799\) −14.3144 −0.506408
\(800\) 12.5426 0.443449
\(801\) 8.76637 0.309744
\(802\) 97.3434 3.43731
\(803\) −44.7159 −1.57799
\(804\) −60.2204 −2.12381
\(805\) 0.407242 0.0143534
\(806\) 124.508 4.38560
\(807\) −29.7306 −1.04657
\(808\) −0.478145 −0.0168211
\(809\) 23.7397 0.834644 0.417322 0.908759i \(-0.362969\pi\)
0.417322 + 0.908759i \(0.362969\pi\)
\(810\) −25.6639 −0.901737
\(811\) 49.6713 1.74420 0.872098 0.489331i \(-0.162759\pi\)
0.872098 + 0.489331i \(0.162759\pi\)
\(812\) 2.89603 0.101631
\(813\) 6.12617 0.214854
\(814\) −86.5680 −3.03421
\(815\) 6.49550 0.227527
\(816\) −23.6776 −0.828883
\(817\) 22.5366 0.788455
\(818\) −46.8429 −1.63782
\(819\) 0.420598 0.0146969
\(820\) −28.2944 −0.988083
\(821\) −52.7231 −1.84005 −0.920025 0.391861i \(-0.871832\pi\)
−0.920025 + 0.391861i \(0.871832\pi\)
\(822\) 27.7945 0.969444
\(823\) 13.7554 0.479484 0.239742 0.970837i \(-0.422937\pi\)
0.239742 + 0.970837i \(0.422937\pi\)
\(824\) −43.0595 −1.50005
\(825\) 17.8227 0.620507
\(826\) 4.79876 0.166970
\(827\) 37.9574 1.31991 0.659954 0.751306i \(-0.270576\pi\)
0.659954 + 0.751306i \(0.270576\pi\)
\(828\) 5.60074 0.194639
\(829\) 7.87068 0.273360 0.136680 0.990615i \(-0.456357\pi\)
0.136680 + 0.990615i \(0.456357\pi\)
\(830\) 4.22410 0.146621
\(831\) 10.0033 0.347009
\(832\) 11.0866 0.384360
\(833\) 16.2769 0.563960
\(834\) 84.0838 2.91158
\(835\) −16.1960 −0.560486
\(836\) 90.8718 3.14287
\(837\) −47.8732 −1.65474
\(838\) 49.1354 1.69735
\(839\) 11.2368 0.387936 0.193968 0.981008i \(-0.437864\pi\)
0.193968 + 0.981008i \(0.437864\pi\)
\(840\) 1.74828 0.0603214
\(841\) −1.89016 −0.0651779
\(842\) −64.9288 −2.23759
\(843\) 44.6475 1.53774
\(844\) 110.110 3.79013
\(845\) −29.0325 −0.998747
\(846\) 9.01478 0.309934
\(847\) 0.652094 0.0224062
\(848\) 54.7967 1.88173
\(849\) 0.923358 0.0316896
\(850\) −16.8027 −0.576327
\(851\) 18.6976 0.640945
\(852\) 6.83770 0.234256
\(853\) 4.26322 0.145970 0.0729850 0.997333i \(-0.476747\pi\)
0.0729850 + 0.997333i \(0.476747\pi\)
\(854\) 2.31503 0.0792188
\(855\) −4.37624 −0.149664
\(856\) 61.1523 2.09014
\(857\) 18.9123 0.646032 0.323016 0.946394i \(-0.395303\pi\)
0.323016 + 0.946394i \(0.395303\pi\)
\(858\) −90.5557 −3.09152
\(859\) −46.6730 −1.59246 −0.796230 0.604993i \(-0.793176\pi\)
−0.796230 + 0.604993i \(0.793176\pi\)
\(860\) 28.2360 0.962838
\(861\) 0.864182 0.0294513
\(862\) 95.9711 3.26879
\(863\) −35.5891 −1.21147 −0.605733 0.795668i \(-0.707120\pi\)
−0.605733 + 0.795668i \(0.707120\pi\)
\(864\) 24.5034 0.833622
\(865\) 11.0821 0.376804
\(866\) 2.41164 0.0819507
\(867\) −17.9947 −0.611133
\(868\) 4.78112 0.162282
\(869\) 19.7230 0.669055
\(870\) 30.0279 1.01804
\(871\) 50.4423 1.70917
\(872\) −28.4638 −0.963904
\(873\) 3.56276 0.120581
\(874\) −28.5572 −0.965960
\(875\) 1.45632 0.0492327
\(876\) 76.0743 2.57031
\(877\) 7.85452 0.265228 0.132614 0.991168i \(-0.457663\pi\)
0.132614 + 0.991168i \(0.457663\pi\)
\(878\) 39.9473 1.34816
\(879\) 32.5382 1.09749
\(880\) 38.4831 1.29726
\(881\) −26.9723 −0.908718 −0.454359 0.890819i \(-0.650132\pi\)
−0.454359 + 0.890819i \(0.650132\pi\)
\(882\) −10.2507 −0.345158
\(883\) 25.7185 0.865497 0.432749 0.901515i \(-0.357544\pi\)
0.432749 + 0.901515i \(0.357544\pi\)
\(884\) 58.6763 1.97350
\(885\) 34.1974 1.14953
\(886\) 53.2027 1.78738
\(887\) −23.8388 −0.800429 −0.400215 0.916421i \(-0.631064\pi\)
−0.400215 + 0.916421i \(0.631064\pi\)
\(888\) 80.2682 2.69362
\(889\) −0.976199 −0.0327407
\(890\) −56.0021 −1.87719
\(891\) 27.8208 0.932033
\(892\) 3.48911 0.116824
\(893\) −31.5913 −1.05716
\(894\) −3.53476 −0.118220
\(895\) −38.0871 −1.27311
\(896\) 1.73285 0.0578903
\(897\) 19.5589 0.653052
\(898\) 3.11358 0.103902
\(899\) 44.7562 1.49270
\(900\) 7.27280 0.242427
\(901\) −19.5535 −0.651422
\(902\) 44.6279 1.48594
\(903\) −0.862398 −0.0286988
\(904\) 6.05887 0.201515
\(905\) 13.9744 0.464526
\(906\) 5.63110 0.187081
\(907\) 7.80841 0.259274 0.129637 0.991562i \(-0.458619\pi\)
0.129637 + 0.991562i \(0.458619\pi\)
\(908\) −16.9987 −0.564122
\(909\) −0.0458004 −0.00151910
\(910\) −2.68690 −0.0890699
\(911\) 53.8829 1.78522 0.892610 0.450830i \(-0.148872\pi\)
0.892610 + 0.450830i \(0.148872\pi\)
\(912\) −52.2554 −1.73035
\(913\) −4.57912 −0.151547
\(914\) 85.2289 2.81912
\(915\) 16.4976 0.545393
\(916\) −57.4228 −1.89730
\(917\) −2.50887 −0.0828503
\(918\) −32.8258 −1.08341
\(919\) 43.5175 1.43551 0.717755 0.696295i \(-0.245170\pi\)
0.717755 + 0.696295i \(0.245170\pi\)
\(920\) −19.5002 −0.642903
\(921\) 30.8583 1.01682
\(922\) −90.2363 −2.97177
\(923\) −5.72744 −0.188521
\(924\) −3.47735 −0.114396
\(925\) 24.2796 0.798309
\(926\) −59.4050 −1.95217
\(927\) −4.12458 −0.135469
\(928\) −22.9080 −0.751992
\(929\) 27.1004 0.889135 0.444568 0.895745i \(-0.353357\pi\)
0.444568 + 0.895745i \(0.353357\pi\)
\(930\) 49.5736 1.62558
\(931\) 35.9223 1.17730
\(932\) 47.3476 1.55092
\(933\) 54.5920 1.78726
\(934\) −27.1313 −0.887764
\(935\) −13.7322 −0.449092
\(936\) −20.1397 −0.658288
\(937\) 42.3293 1.38284 0.691419 0.722454i \(-0.256986\pi\)
0.691419 + 0.722454i \(0.256986\pi\)
\(938\) 2.81829 0.0920203
\(939\) −10.5512 −0.344324
\(940\) −39.5805 −1.29097
\(941\) −24.2063 −0.789101 −0.394551 0.918874i \(-0.629100\pi\)
−0.394551 + 0.918874i \(0.629100\pi\)
\(942\) −55.1176 −1.79583
\(943\) −9.63905 −0.313891
\(944\) −97.9432 −3.18778
\(945\) 1.03311 0.0336071
\(946\) −44.5357 −1.44798
\(947\) 45.6920 1.48479 0.742394 0.669963i \(-0.233690\pi\)
0.742394 + 0.669963i \(0.233690\pi\)
\(948\) −33.5543 −1.08979
\(949\) −63.7219 −2.06850
\(950\) −37.0827 −1.20312
\(951\) −18.2662 −0.592322
\(952\) 1.78675 0.0579089
\(953\) 19.4220 0.629139 0.314570 0.949234i \(-0.398140\pi\)
0.314570 + 0.949234i \(0.398140\pi\)
\(954\) 12.3142 0.398687
\(955\) −19.1447 −0.619510
\(956\) 107.130 3.46482
\(957\) −32.5516 −1.05224
\(958\) −54.3149 −1.75484
\(959\) −0.894009 −0.0288691
\(960\) 4.41422 0.142468
\(961\) 42.8890 1.38351
\(962\) −123.363 −3.97738
\(963\) 5.85765 0.188760
\(964\) 2.42592 0.0781336
\(965\) 12.2687 0.394944
\(966\) 1.09278 0.0351598
\(967\) 4.88290 0.157023 0.0785117 0.996913i \(-0.474983\pi\)
0.0785117 + 0.996913i \(0.474983\pi\)
\(968\) −31.2246 −1.00360
\(969\) 18.6467 0.599019
\(970\) −22.7599 −0.730776
\(971\) −25.5279 −0.819229 −0.409614 0.912259i \(-0.634337\pi\)
−0.409614 + 0.912259i \(0.634337\pi\)
\(972\) 26.1133 0.837584
\(973\) −2.70456 −0.0867041
\(974\) −96.2159 −3.08296
\(975\) 25.3981 0.813389
\(976\) −47.2500 −1.51244
\(977\) 42.9087 1.37277 0.686386 0.727238i \(-0.259196\pi\)
0.686386 + 0.727238i \(0.259196\pi\)
\(978\) 17.4299 0.557346
\(979\) 60.7088 1.94026
\(980\) 45.0068 1.43769
\(981\) −2.72648 −0.0870499
\(982\) −17.0369 −0.543669
\(983\) 46.7178 1.49007 0.745034 0.667027i \(-0.232433\pi\)
0.745034 + 0.667027i \(0.232433\pi\)
\(984\) −41.3801 −1.31915
\(985\) −10.7097 −0.341241
\(986\) 30.6886 0.977324
\(987\) 1.20889 0.0384794
\(988\) 129.496 4.11981
\(989\) 9.61915 0.305871
\(990\) 8.64812 0.274855
\(991\) −0.594536 −0.0188861 −0.00944303 0.999955i \(-0.503006\pi\)
−0.00944303 + 0.999955i \(0.503006\pi\)
\(992\) −37.8193 −1.20076
\(993\) −40.0400 −1.27063
\(994\) −0.320001 −0.0101498
\(995\) 30.7641 0.975288
\(996\) 7.79038 0.246848
\(997\) −2.29730 −0.0727562 −0.0363781 0.999338i \(-0.511582\pi\)
−0.0363781 + 0.999338i \(0.511582\pi\)
\(998\) −23.9646 −0.758585
\(999\) 47.4329 1.50071
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 8023.2.a.d.1.8 165
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8023.2.a.d.1.8 165 1.1 even 1 trivial