Properties

Label 8003.2.a.d.1.9
Level $8003$
Weight $2$
Character 8003.1
Self dual yes
Analytic conductor $63.904$
Analytic rank $0$
Dimension $179$
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] = [8003,2,Mod(1,8003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8003, 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("8003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.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: \(63.9042767376\)
Analytic rank: \(0\)
Dimension: \(179\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Character \(\chi\) \(=\) 8003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62553 q^{2} -3.09813 q^{3} +4.89340 q^{4} -2.94807 q^{5} +8.13422 q^{6} +1.83284 q^{7} -7.59671 q^{8} +6.59839 q^{9} +O(q^{10})\) \(q-2.62553 q^{2} -3.09813 q^{3} +4.89340 q^{4} -2.94807 q^{5} +8.13422 q^{6} +1.83284 q^{7} -7.59671 q^{8} +6.59839 q^{9} +7.74024 q^{10} -3.15693 q^{11} -15.1604 q^{12} +4.64425 q^{13} -4.81218 q^{14} +9.13349 q^{15} +10.1586 q^{16} +0.513047 q^{17} -17.3243 q^{18} -2.75003 q^{19} -14.4261 q^{20} -5.67838 q^{21} +8.28860 q^{22} -4.64078 q^{23} +23.5356 q^{24} +3.69110 q^{25} -12.1936 q^{26} -11.1483 q^{27} +8.96884 q^{28} +0.719407 q^{29} -23.9802 q^{30} -3.37968 q^{31} -11.4782 q^{32} +9.78056 q^{33} -1.34702 q^{34} -5.40335 q^{35} +32.2886 q^{36} -9.47375 q^{37} +7.22027 q^{38} -14.3885 q^{39} +22.3956 q^{40} -1.25001 q^{41} +14.9088 q^{42} +9.40106 q^{43} -15.4481 q^{44} -19.4525 q^{45} +12.1845 q^{46} -4.35788 q^{47} -31.4725 q^{48} -3.64069 q^{49} -9.69110 q^{50} -1.58949 q^{51} +22.7262 q^{52} +1.00000 q^{53} +29.2701 q^{54} +9.30683 q^{55} -13.9236 q^{56} +8.51993 q^{57} -1.88882 q^{58} +7.84428 q^{59} +44.6938 q^{60} +0.0682438 q^{61} +8.87345 q^{62} +12.0938 q^{63} +9.81921 q^{64} -13.6916 q^{65} -25.6791 q^{66} +15.2544 q^{67} +2.51055 q^{68} +14.3777 q^{69} +14.1866 q^{70} -3.31681 q^{71} -50.1260 q^{72} -3.94635 q^{73} +24.8736 q^{74} -11.4355 q^{75} -13.4570 q^{76} -5.78615 q^{77} +37.7773 q^{78} -9.41853 q^{79} -29.9482 q^{80} +14.7436 q^{81} +3.28194 q^{82} +6.55129 q^{83} -27.7866 q^{84} -1.51250 q^{85} -24.6827 q^{86} -2.22881 q^{87} +23.9822 q^{88} -5.36837 q^{89} +51.0731 q^{90} +8.51218 q^{91} -22.7092 q^{92} +10.4707 q^{93} +11.4417 q^{94} +8.10727 q^{95} +35.5609 q^{96} +5.60546 q^{97} +9.55872 q^{98} -20.8306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 179 q + 8 q^{2} + 15 q^{3} + 202 q^{4} + 27 q^{5} + 18 q^{6} + 23 q^{7} + 21 q^{8} + 214 q^{9} + 28 q^{10} + 21 q^{11} + 46 q^{12} + 113 q^{13} - 2 q^{14} + 30 q^{15} + 240 q^{16} + 48 q^{17} + 40 q^{18} + 35 q^{19} + 24 q^{20} + 56 q^{21} + 22 q^{22} + 16 q^{23} + 54 q^{24} + 266 q^{25} + 60 q^{27} + 64 q^{28} + 34 q^{29} - 19 q^{30} + 60 q^{31} + 15 q^{32} + 65 q^{33} + 31 q^{34} - 20 q^{35} + 282 q^{36} + 169 q^{37} + 52 q^{38} + 20 q^{39} + 74 q^{40} + 20 q^{41} + 34 q^{42} + 43 q^{43} + 56 q^{44} + 139 q^{45} + 13 q^{46} + 73 q^{47} + 88 q^{48} + 292 q^{49} + 12 q^{50} + 8 q^{51} + 225 q^{52} + 179 q^{53} - 16 q^{54} + 72 q^{55} - 17 q^{56} + 62 q^{57} + 125 q^{58} + 68 q^{59} + 116 q^{60} + 96 q^{61} + 71 q^{62} + 52 q^{63} + 309 q^{64} - 5 q^{65} + 90 q^{67} + 122 q^{68} + 111 q^{69} + 72 q^{70} + 26 q^{71} + 65 q^{72} + 139 q^{73} - 82 q^{74} + 55 q^{75} + 146 q^{76} + 76 q^{77} - 9 q^{78} + 29 q^{79} + 68 q^{80} + 231 q^{81} + 84 q^{82} + 8 q^{83} - 24 q^{84} + 115 q^{85} - 20 q^{86} + 47 q^{87} + 143 q^{88} + 150 q^{89} + 34 q^{90} + 113 q^{91} - 31 q^{92} + 195 q^{93} + 131 q^{94} + 55 q^{95} + 90 q^{96} + 235 q^{97} + 84 q^{98} + 7 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62553 −1.85653 −0.928265 0.371921i \(-0.878699\pi\)
−0.928265 + 0.371921i \(0.878699\pi\)
\(3\) −3.09813 −1.78870 −0.894352 0.447363i \(-0.852363\pi\)
−0.894352 + 0.447363i \(0.852363\pi\)
\(4\) 4.89340 2.44670
\(5\) −2.94807 −1.31842 −0.659208 0.751961i \(-0.729108\pi\)
−0.659208 + 0.751961i \(0.729108\pi\)
\(6\) 8.13422 3.32078
\(7\) 1.83284 0.692750 0.346375 0.938096i \(-0.387413\pi\)
0.346375 + 0.938096i \(0.387413\pi\)
\(8\) −7.59671 −2.68584
\(9\) 6.59839 2.19946
\(10\) 7.74024 2.44768
\(11\) −3.15693 −0.951849 −0.475925 0.879486i \(-0.657886\pi\)
−0.475925 + 0.879486i \(0.657886\pi\)
\(12\) −15.1604 −4.37642
\(13\) 4.64425 1.28808 0.644041 0.764991i \(-0.277257\pi\)
0.644041 + 0.764991i \(0.277257\pi\)
\(14\) −4.81218 −1.28611
\(15\) 9.13349 2.35826
\(16\) 10.1586 2.53964
\(17\) 0.513047 0.124432 0.0622161 0.998063i \(-0.480183\pi\)
0.0622161 + 0.998063i \(0.480183\pi\)
\(18\) −17.3243 −4.08337
\(19\) −2.75003 −0.630899 −0.315450 0.948942i \(-0.602155\pi\)
−0.315450 + 0.948942i \(0.602155\pi\)
\(20\) −14.4261 −3.22577
\(21\) −5.67838 −1.23912
\(22\) 8.28860 1.76714
\(23\) −4.64078 −0.967670 −0.483835 0.875159i \(-0.660757\pi\)
−0.483835 + 0.875159i \(0.660757\pi\)
\(24\) 23.5356 4.80418
\(25\) 3.69110 0.738221
\(26\) −12.1936 −2.39136
\(27\) −11.1483 −2.14549
\(28\) 8.96884 1.69495
\(29\) 0.719407 0.133590 0.0667952 0.997767i \(-0.478723\pi\)
0.0667952 + 0.997767i \(0.478723\pi\)
\(30\) −23.9802 −4.37817
\(31\) −3.37968 −0.607008 −0.303504 0.952830i \(-0.598157\pi\)
−0.303504 + 0.952830i \(0.598157\pi\)
\(32\) −11.4782 −2.02908
\(33\) 9.78056 1.70258
\(34\) −1.34702 −0.231012
\(35\) −5.40335 −0.913332
\(36\) 32.2886 5.38143
\(37\) −9.47375 −1.55747 −0.778737 0.627350i \(-0.784140\pi\)
−0.778737 + 0.627350i \(0.784140\pi\)
\(38\) 7.22027 1.17128
\(39\) −14.3885 −2.30400
\(40\) 22.3956 3.54106
\(41\) −1.25001 −0.195219 −0.0976094 0.995225i \(-0.531120\pi\)
−0.0976094 + 0.995225i \(0.531120\pi\)
\(42\) 14.9088 2.30047
\(43\) 9.40106 1.43365 0.716824 0.697254i \(-0.245595\pi\)
0.716824 + 0.697254i \(0.245595\pi\)
\(44\) −15.4481 −2.32889
\(45\) −19.4525 −2.89981
\(46\) 12.1845 1.79651
\(47\) −4.35788 −0.635662 −0.317831 0.948147i \(-0.602954\pi\)
−0.317831 + 0.948147i \(0.602954\pi\)
\(48\) −31.4725 −4.54267
\(49\) −3.64069 −0.520098
\(50\) −9.69110 −1.37053
\(51\) −1.58949 −0.222572
\(52\) 22.7262 3.15155
\(53\) 1.00000 0.137361
\(54\) 29.2701 3.98316
\(55\) 9.30683 1.25493
\(56\) −13.9236 −1.86062
\(57\) 8.51993 1.12849
\(58\) −1.88882 −0.248015
\(59\) 7.84428 1.02124 0.510619 0.859807i \(-0.329416\pi\)
0.510619 + 0.859807i \(0.329416\pi\)
\(60\) 44.6938 5.76995
\(61\) 0.0682438 0.00873772 0.00436886 0.999990i \(-0.498609\pi\)
0.00436886 + 0.999990i \(0.498609\pi\)
\(62\) 8.87345 1.12693
\(63\) 12.0938 1.52368
\(64\) 9.81921 1.22740
\(65\) −13.6916 −1.69823
\(66\) −25.6791 −3.16088
\(67\) 15.2544 1.86362 0.931811 0.362943i \(-0.118228\pi\)
0.931811 + 0.362943i \(0.118228\pi\)
\(68\) 2.51055 0.304448
\(69\) 14.3777 1.73088
\(70\) 14.1866 1.69563
\(71\) −3.31681 −0.393632 −0.196816 0.980440i \(-0.563060\pi\)
−0.196816 + 0.980440i \(0.563060\pi\)
\(72\) −50.1260 −5.90741
\(73\) −3.94635 −0.461885 −0.230943 0.972967i \(-0.574181\pi\)
−0.230943 + 0.972967i \(0.574181\pi\)
\(74\) 24.8736 2.89150
\(75\) −11.4355 −1.32046
\(76\) −13.4570 −1.54362
\(77\) −5.78615 −0.659393
\(78\) 37.7773 4.27744
\(79\) −9.41853 −1.05967 −0.529834 0.848101i \(-0.677746\pi\)
−0.529834 + 0.848101i \(0.677746\pi\)
\(80\) −29.9482 −3.34831
\(81\) 14.7436 1.63818
\(82\) 3.28194 0.362429
\(83\) 6.55129 0.719097 0.359549 0.933126i \(-0.382931\pi\)
0.359549 + 0.933126i \(0.382931\pi\)
\(84\) −27.7866 −3.03177
\(85\) −1.51250 −0.164053
\(86\) −24.6827 −2.66161
\(87\) −2.22881 −0.238954
\(88\) 23.9822 2.55652
\(89\) −5.36837 −0.569047 −0.284523 0.958669i \(-0.591835\pi\)
−0.284523 + 0.958669i \(0.591835\pi\)
\(90\) 51.0731 5.38358
\(91\) 8.51218 0.892319
\(92\) −22.7092 −2.36760
\(93\) 10.4707 1.08576
\(94\) 11.4417 1.18012
\(95\) 8.10727 0.831788
\(96\) 35.5609 3.62942
\(97\) 5.60546 0.569148 0.284574 0.958654i \(-0.408148\pi\)
0.284574 + 0.958654i \(0.408148\pi\)
\(98\) 9.55872 0.965577
\(99\) −20.8306 −2.09356
\(100\) 18.0621 1.80621
\(101\) 3.52757 0.351007 0.175503 0.984479i \(-0.443845\pi\)
0.175503 + 0.984479i \(0.443845\pi\)
\(102\) 4.17324 0.413212
\(103\) 2.93263 0.288961 0.144481 0.989508i \(-0.453849\pi\)
0.144481 + 0.989508i \(0.453849\pi\)
\(104\) −35.2810 −3.45958
\(105\) 16.7403 1.63368
\(106\) −2.62553 −0.255014
\(107\) −4.68067 −0.452498 −0.226249 0.974070i \(-0.572646\pi\)
−0.226249 + 0.974070i \(0.572646\pi\)
\(108\) −54.5530 −5.24936
\(109\) 5.07450 0.486049 0.243025 0.970020i \(-0.421860\pi\)
0.243025 + 0.970020i \(0.421860\pi\)
\(110\) −24.4354 −2.32982
\(111\) 29.3509 2.78586
\(112\) 18.6191 1.75934
\(113\) −7.44673 −0.700529 −0.350265 0.936651i \(-0.613908\pi\)
−0.350265 + 0.936651i \(0.613908\pi\)
\(114\) −22.3693 −2.09508
\(115\) 13.6813 1.27579
\(116\) 3.52034 0.326856
\(117\) 30.6446 2.83309
\(118\) −20.5954 −1.89596
\(119\) 0.940335 0.0862004
\(120\) −69.3844 −6.33390
\(121\) −1.03382 −0.0939834
\(122\) −0.179176 −0.0162218
\(123\) 3.87269 0.349189
\(124\) −16.5381 −1.48517
\(125\) 3.85871 0.345134
\(126\) −31.7527 −2.82875
\(127\) −2.74007 −0.243142 −0.121571 0.992583i \(-0.538793\pi\)
−0.121571 + 0.992583i \(0.538793\pi\)
\(128\) −2.82421 −0.249628
\(129\) −29.1257 −2.56437
\(130\) 35.9476 3.15281
\(131\) −12.7274 −1.11200 −0.556000 0.831183i \(-0.687664\pi\)
−0.556000 + 0.831183i \(0.687664\pi\)
\(132\) 47.8602 4.16569
\(133\) −5.04037 −0.437055
\(134\) −40.0509 −3.45987
\(135\) 32.8659 2.82864
\(136\) −3.89747 −0.334205
\(137\) 13.8335 1.18187 0.590937 0.806718i \(-0.298758\pi\)
0.590937 + 0.806718i \(0.298758\pi\)
\(138\) −37.7492 −3.21342
\(139\) −20.7006 −1.75580 −0.877900 0.478844i \(-0.841056\pi\)
−0.877900 + 0.478844i \(0.841056\pi\)
\(140\) −26.4407 −2.23465
\(141\) 13.5013 1.13701
\(142\) 8.70837 0.730790
\(143\) −14.6615 −1.22606
\(144\) 67.0302 5.58585
\(145\) −2.12086 −0.176128
\(146\) 10.3612 0.857503
\(147\) 11.2793 0.930302
\(148\) −46.3589 −3.81067
\(149\) 22.1370 1.81354 0.906768 0.421631i \(-0.138542\pi\)
0.906768 + 0.421631i \(0.138542\pi\)
\(150\) 30.0243 2.45147
\(151\) −1.00000 −0.0813788
\(152\) 20.8911 1.69450
\(153\) 3.38529 0.273684
\(154\) 15.1917 1.22418
\(155\) 9.96352 0.800290
\(156\) −70.4085 −5.63719
\(157\) 9.03696 0.721228 0.360614 0.932715i \(-0.382567\pi\)
0.360614 + 0.932715i \(0.382567\pi\)
\(158\) 24.7286 1.96730
\(159\) −3.09813 −0.245697
\(160\) 33.8385 2.67517
\(161\) −8.50583 −0.670353
\(162\) −38.7097 −3.04132
\(163\) 11.2227 0.879033 0.439517 0.898234i \(-0.355150\pi\)
0.439517 + 0.898234i \(0.355150\pi\)
\(164\) −6.11680 −0.477642
\(165\) −28.8337 −2.24470
\(166\) −17.2006 −1.33503
\(167\) −15.1449 −1.17195 −0.585974 0.810330i \(-0.699288\pi\)
−0.585974 + 0.810330i \(0.699288\pi\)
\(168\) 43.1370 3.32809
\(169\) 8.56903 0.659156
\(170\) 3.97111 0.304570
\(171\) −18.1458 −1.38764
\(172\) 46.0031 3.50771
\(173\) 22.1503 1.68405 0.842026 0.539437i \(-0.181363\pi\)
0.842026 + 0.539437i \(0.181363\pi\)
\(174\) 5.85181 0.443625
\(175\) 6.76521 0.511402
\(176\) −32.0699 −2.41736
\(177\) −24.3026 −1.82669
\(178\) 14.0948 1.05645
\(179\) −6.56444 −0.490649 −0.245325 0.969441i \(-0.578895\pi\)
−0.245325 + 0.969441i \(0.578895\pi\)
\(180\) −95.1889 −7.09496
\(181\) 7.75561 0.576470 0.288235 0.957560i \(-0.406932\pi\)
0.288235 + 0.957560i \(0.406932\pi\)
\(182\) −22.3490 −1.65662
\(183\) −0.211428 −0.0156292
\(184\) 35.2547 2.59901
\(185\) 27.9293 2.05340
\(186\) −27.4911 −2.01574
\(187\) −1.61965 −0.118441
\(188\) −21.3248 −1.55527
\(189\) −20.4330 −1.48628
\(190\) −21.2859 −1.54424
\(191\) −6.13645 −0.444018 −0.222009 0.975045i \(-0.571261\pi\)
−0.222009 + 0.975045i \(0.571261\pi\)
\(192\) −30.4212 −2.19546
\(193\) 18.6602 1.34319 0.671595 0.740919i \(-0.265610\pi\)
0.671595 + 0.740919i \(0.265610\pi\)
\(194\) −14.7173 −1.05664
\(195\) 42.4182 3.03763
\(196\) −17.8153 −1.27252
\(197\) −18.2172 −1.29792 −0.648962 0.760821i \(-0.724796\pi\)
−0.648962 + 0.760821i \(0.724796\pi\)
\(198\) 54.6914 3.88675
\(199\) 3.98154 0.282244 0.141122 0.989992i \(-0.454929\pi\)
0.141122 + 0.989992i \(0.454929\pi\)
\(200\) −28.0402 −1.98274
\(201\) −47.2601 −3.33347
\(202\) −9.26174 −0.651654
\(203\) 1.31856 0.0925447
\(204\) −7.77799 −0.544568
\(205\) 3.68512 0.257380
\(206\) −7.69972 −0.536465
\(207\) −30.6217 −2.12836
\(208\) 47.1789 3.27127
\(209\) 8.68163 0.600521
\(210\) −43.9520 −3.03298
\(211\) −20.7038 −1.42531 −0.712655 0.701514i \(-0.752508\pi\)
−0.712655 + 0.701514i \(0.752508\pi\)
\(212\) 4.89340 0.336080
\(213\) 10.2759 0.704092
\(214\) 12.2892 0.840075
\(215\) −27.7150 −1.89014
\(216\) 84.6902 5.76244
\(217\) −6.19442 −0.420505
\(218\) −13.3233 −0.902365
\(219\) 12.2263 0.826176
\(220\) 45.5421 3.07045
\(221\) 2.38272 0.160279
\(222\) −77.0616 −5.17203
\(223\) −23.1997 −1.55357 −0.776785 0.629766i \(-0.783151\pi\)
−0.776785 + 0.629766i \(0.783151\pi\)
\(224\) −21.0377 −1.40564
\(225\) 24.3553 1.62369
\(226\) 19.5516 1.30055
\(227\) −8.38633 −0.556620 −0.278310 0.960491i \(-0.589774\pi\)
−0.278310 + 0.960491i \(0.589774\pi\)
\(228\) 41.6914 2.76108
\(229\) −12.3383 −0.815336 −0.407668 0.913130i \(-0.633658\pi\)
−0.407668 + 0.913130i \(0.633658\pi\)
\(230\) −35.9208 −2.36854
\(231\) 17.9262 1.17946
\(232\) −5.46512 −0.358803
\(233\) −10.7202 −0.702306 −0.351153 0.936318i \(-0.614210\pi\)
−0.351153 + 0.936318i \(0.614210\pi\)
\(234\) −80.4582 −5.25971
\(235\) 12.8473 0.838066
\(236\) 38.3852 2.49866
\(237\) 29.1798 1.89543
\(238\) −2.46888 −0.160034
\(239\) −18.9842 −1.22798 −0.613992 0.789312i \(-0.710437\pi\)
−0.613992 + 0.789312i \(0.710437\pi\)
\(240\) 92.7832 5.98913
\(241\) 1.98619 0.127942 0.0639710 0.997952i \(-0.479623\pi\)
0.0639710 + 0.997952i \(0.479623\pi\)
\(242\) 2.71432 0.174483
\(243\) −12.2327 −0.784728
\(244\) 0.333944 0.0213786
\(245\) 10.7330 0.685705
\(246\) −10.1679 −0.648279
\(247\) −12.7718 −0.812650
\(248\) 25.6744 1.63033
\(249\) −20.2967 −1.28625
\(250\) −10.1312 −0.640751
\(251\) −0.665703 −0.0420188 −0.0210094 0.999779i \(-0.506688\pi\)
−0.0210094 + 0.999779i \(0.506688\pi\)
\(252\) 59.1799 3.72798
\(253\) 14.6506 0.921076
\(254\) 7.19413 0.451400
\(255\) 4.68591 0.293443
\(256\) −12.2234 −0.763960
\(257\) −16.0784 −1.00294 −0.501471 0.865174i \(-0.667208\pi\)
−0.501471 + 0.865174i \(0.667208\pi\)
\(258\) 76.4703 4.76083
\(259\) −17.3639 −1.07894
\(260\) −66.9983 −4.15506
\(261\) 4.74693 0.293827
\(262\) 33.4162 2.06446
\(263\) −10.1686 −0.627021 −0.313510 0.949585i \(-0.601505\pi\)
−0.313510 + 0.949585i \(0.601505\pi\)
\(264\) −74.3000 −4.57285
\(265\) −2.94807 −0.181098
\(266\) 13.2336 0.811406
\(267\) 16.6319 1.01786
\(268\) 74.6459 4.55973
\(269\) −18.5411 −1.13047 −0.565234 0.824931i \(-0.691214\pi\)
−0.565234 + 0.824931i \(0.691214\pi\)
\(270\) −86.2903 −5.25146
\(271\) 10.6290 0.645664 0.322832 0.946456i \(-0.395365\pi\)
0.322832 + 0.946456i \(0.395365\pi\)
\(272\) 5.21183 0.316013
\(273\) −26.3718 −1.59609
\(274\) −36.3202 −2.19418
\(275\) −11.6525 −0.702675
\(276\) 70.3560 4.23493
\(277\) −9.83047 −0.590656 −0.295328 0.955396i \(-0.595429\pi\)
−0.295328 + 0.955396i \(0.595429\pi\)
\(278\) 54.3500 3.25969
\(279\) −22.3004 −1.33509
\(280\) 41.0476 2.45307
\(281\) 22.8333 1.36212 0.681062 0.732226i \(-0.261519\pi\)
0.681062 + 0.732226i \(0.261519\pi\)
\(282\) −35.4479 −2.11089
\(283\) 31.8872 1.89549 0.947747 0.319022i \(-0.103354\pi\)
0.947747 + 0.319022i \(0.103354\pi\)
\(284\) −16.2305 −0.963101
\(285\) −25.1173 −1.48782
\(286\) 38.4943 2.27622
\(287\) −2.29107 −0.135238
\(288\) −75.7377 −4.46289
\(289\) −16.7368 −0.984517
\(290\) 5.56838 0.326986
\(291\) −17.3664 −1.01804
\(292\) −19.3111 −1.13009
\(293\) −3.78095 −0.220885 −0.110443 0.993882i \(-0.535227\pi\)
−0.110443 + 0.993882i \(0.535227\pi\)
\(294\) −29.6141 −1.72713
\(295\) −23.1255 −1.34642
\(296\) 71.9693 4.18313
\(297\) 35.1943 2.04218
\(298\) −58.1214 −3.36688
\(299\) −21.5529 −1.24644
\(300\) −55.9585 −3.23077
\(301\) 17.2307 0.993159
\(302\) 2.62553 0.151082
\(303\) −10.9289 −0.627847
\(304\) −27.9363 −1.60226
\(305\) −0.201187 −0.0115200
\(306\) −8.88817 −0.508103
\(307\) −33.5690 −1.91588 −0.957942 0.286961i \(-0.907355\pi\)
−0.957942 + 0.286961i \(0.907355\pi\)
\(308\) −28.3140 −1.61334
\(309\) −9.08567 −0.516866
\(310\) −26.1595 −1.48576
\(311\) 0.989914 0.0561328 0.0280664 0.999606i \(-0.491065\pi\)
0.0280664 + 0.999606i \(0.491065\pi\)
\(312\) 109.305 6.18817
\(313\) −9.05645 −0.511901 −0.255950 0.966690i \(-0.582388\pi\)
−0.255950 + 0.966690i \(0.582388\pi\)
\(314\) −23.7268 −1.33898
\(315\) −35.6534 −2.00884
\(316\) −46.0887 −2.59269
\(317\) −10.0173 −0.562626 −0.281313 0.959616i \(-0.590770\pi\)
−0.281313 + 0.959616i \(0.590770\pi\)
\(318\) 8.13422 0.456144
\(319\) −2.27111 −0.127158
\(320\) −28.9477 −1.61823
\(321\) 14.5013 0.809385
\(322\) 22.3323 1.24453
\(323\) −1.41089 −0.0785042
\(324\) 72.1463 4.00813
\(325\) 17.1424 0.950889
\(326\) −29.4656 −1.63195
\(327\) −15.7215 −0.869398
\(328\) 9.49596 0.524327
\(329\) −7.98731 −0.440354
\(330\) 75.7038 4.16736
\(331\) −18.0341 −0.991243 −0.495622 0.868539i \(-0.665060\pi\)
−0.495622 + 0.868539i \(0.665060\pi\)
\(332\) 32.0581 1.75942
\(333\) −62.5115 −3.42561
\(334\) 39.7634 2.17576
\(335\) −44.9710 −2.45703
\(336\) −57.6842 −3.14693
\(337\) 20.7190 1.12864 0.564318 0.825558i \(-0.309139\pi\)
0.564318 + 0.825558i \(0.309139\pi\)
\(338\) −22.4982 −1.22374
\(339\) 23.0709 1.25304
\(340\) −7.40126 −0.401390
\(341\) 10.6694 0.577780
\(342\) 47.6422 2.57620
\(343\) −19.5027 −1.05305
\(344\) −71.4171 −3.85055
\(345\) −42.3865 −2.28201
\(346\) −58.1561 −3.12649
\(347\) 11.0897 0.595325 0.297662 0.954671i \(-0.403793\pi\)
0.297662 + 0.954671i \(0.403793\pi\)
\(348\) −10.9065 −0.584648
\(349\) 7.67207 0.410676 0.205338 0.978691i \(-0.434171\pi\)
0.205338 + 0.978691i \(0.434171\pi\)
\(350\) −17.7623 −0.949433
\(351\) −51.7753 −2.76356
\(352\) 36.2358 1.93138
\(353\) 15.7014 0.835699 0.417850 0.908516i \(-0.362784\pi\)
0.417850 + 0.908516i \(0.362784\pi\)
\(354\) 63.8071 3.39131
\(355\) 9.77817 0.518971
\(356\) −26.2696 −1.39229
\(357\) −2.91328 −0.154187
\(358\) 17.2351 0.910904
\(359\) 11.6954 0.617262 0.308631 0.951182i \(-0.400129\pi\)
0.308631 + 0.951182i \(0.400129\pi\)
\(360\) 147.775 7.78843
\(361\) −11.4374 −0.601966
\(362\) −20.3626 −1.07023
\(363\) 3.20290 0.168109
\(364\) 41.6535 2.18324
\(365\) 11.6341 0.608957
\(366\) 0.555110 0.0290161
\(367\) 17.7022 0.924049 0.462024 0.886867i \(-0.347123\pi\)
0.462024 + 0.886867i \(0.347123\pi\)
\(368\) −47.1437 −2.45754
\(369\) −8.24806 −0.429377
\(370\) −73.3291 −3.81220
\(371\) 1.83284 0.0951565
\(372\) 51.2372 2.65653
\(373\) −22.6795 −1.17430 −0.587149 0.809479i \(-0.699750\pi\)
−0.587149 + 0.809479i \(0.699750\pi\)
\(374\) 4.25244 0.219889
\(375\) −11.9548 −0.617343
\(376\) 33.1055 1.70729
\(377\) 3.34110 0.172075
\(378\) 53.6475 2.75933
\(379\) −5.96614 −0.306460 −0.153230 0.988191i \(-0.548968\pi\)
−0.153230 + 0.988191i \(0.548968\pi\)
\(380\) 39.6721 2.03514
\(381\) 8.48908 0.434909
\(382\) 16.1114 0.824332
\(383\) 16.0768 0.821485 0.410742 0.911751i \(-0.365270\pi\)
0.410742 + 0.911751i \(0.365270\pi\)
\(384\) 8.74977 0.446510
\(385\) 17.0580 0.869354
\(386\) −48.9928 −2.49367
\(387\) 62.0319 3.15326
\(388\) 27.4298 1.39254
\(389\) −10.0844 −0.511299 −0.255650 0.966769i \(-0.582289\pi\)
−0.255650 + 0.966769i \(0.582289\pi\)
\(390\) −111.370 −5.63945
\(391\) −2.38094 −0.120409
\(392\) 27.6572 1.39690
\(393\) 39.4311 1.98904
\(394\) 47.8298 2.40963
\(395\) 27.7665 1.39708
\(396\) −101.933 −5.12231
\(397\) 3.38989 0.170134 0.0850669 0.996375i \(-0.472890\pi\)
0.0850669 + 0.996375i \(0.472890\pi\)
\(398\) −10.4536 −0.523994
\(399\) 15.6157 0.781763
\(400\) 37.4963 1.87482
\(401\) 1.84242 0.0920059 0.0460029 0.998941i \(-0.485352\pi\)
0.0460029 + 0.998941i \(0.485352\pi\)
\(402\) 124.083 6.18869
\(403\) −15.6961 −0.781877
\(404\) 17.2618 0.858808
\(405\) −43.4651 −2.15980
\(406\) −3.46192 −0.171812
\(407\) 29.9079 1.48248
\(408\) 12.0749 0.597794
\(409\) −14.1788 −0.701098 −0.350549 0.936544i \(-0.614005\pi\)
−0.350549 + 0.936544i \(0.614005\pi\)
\(410\) −9.67538 −0.477833
\(411\) −42.8579 −2.11402
\(412\) 14.3506 0.707001
\(413\) 14.3773 0.707462
\(414\) 80.3982 3.95135
\(415\) −19.3136 −0.948070
\(416\) −53.3076 −2.61362
\(417\) 64.1330 3.14061
\(418\) −22.7939 −1.11488
\(419\) −1.73139 −0.0845839 −0.0422919 0.999105i \(-0.513466\pi\)
−0.0422919 + 0.999105i \(0.513466\pi\)
\(420\) 81.9168 3.99713
\(421\) −18.7536 −0.913994 −0.456997 0.889468i \(-0.651075\pi\)
−0.456997 + 0.889468i \(0.651075\pi\)
\(422\) 54.3585 2.64613
\(423\) −28.7550 −1.39811
\(424\) −7.59671 −0.368929
\(425\) 1.89371 0.0918584
\(426\) −26.9796 −1.30717
\(427\) 0.125080 0.00605306
\(428\) −22.9044 −1.10713
\(429\) 45.4233 2.19306
\(430\) 72.7664 3.50911
\(431\) 30.9135 1.48905 0.744526 0.667593i \(-0.232676\pi\)
0.744526 + 0.667593i \(0.232676\pi\)
\(432\) −113.251 −5.44877
\(433\) 8.05092 0.386903 0.193451 0.981110i \(-0.438032\pi\)
0.193451 + 0.981110i \(0.438032\pi\)
\(434\) 16.2636 0.780679
\(435\) 6.57069 0.315041
\(436\) 24.8316 1.18922
\(437\) 12.7623 0.610503
\(438\) −32.1005 −1.53382
\(439\) 5.99928 0.286330 0.143165 0.989699i \(-0.454272\pi\)
0.143165 + 0.989699i \(0.454272\pi\)
\(440\) −70.7013 −3.37055
\(441\) −24.0227 −1.14394
\(442\) −6.25589 −0.297563
\(443\) −12.5365 −0.595627 −0.297814 0.954624i \(-0.596257\pi\)
−0.297814 + 0.954624i \(0.596257\pi\)
\(444\) 143.626 6.81617
\(445\) 15.8263 0.750240
\(446\) 60.9116 2.88425
\(447\) −68.5833 −3.24388
\(448\) 17.9971 0.850282
\(449\) −13.3728 −0.631103 −0.315552 0.948908i \(-0.602190\pi\)
−0.315552 + 0.948908i \(0.602190\pi\)
\(450\) −63.9457 −3.01443
\(451\) 3.94619 0.185819
\(452\) −36.4398 −1.71399
\(453\) 3.09813 0.145563
\(454\) 22.0186 1.03338
\(455\) −25.0945 −1.17645
\(456\) −64.7234 −3.03095
\(457\) −23.3645 −1.09294 −0.546472 0.837477i \(-0.684030\pi\)
−0.546472 + 0.837477i \(0.684030\pi\)
\(458\) 32.3945 1.51370
\(459\) −5.71959 −0.266968
\(460\) 66.9483 3.12148
\(461\) 13.7177 0.638896 0.319448 0.947604i \(-0.396502\pi\)
0.319448 + 0.947604i \(0.396502\pi\)
\(462\) −47.0658 −2.18970
\(463\) 6.18162 0.287284 0.143642 0.989630i \(-0.454119\pi\)
0.143642 + 0.989630i \(0.454119\pi\)
\(464\) 7.30814 0.339272
\(465\) −30.8683 −1.43148
\(466\) 28.1463 1.30385
\(467\) 0.687062 0.0317935 0.0158967 0.999874i \(-0.494940\pi\)
0.0158967 + 0.999874i \(0.494940\pi\)
\(468\) 149.956 6.93172
\(469\) 27.9589 1.29102
\(470\) −33.7310 −1.55589
\(471\) −27.9977 −1.29006
\(472\) −59.5907 −2.74288
\(473\) −29.6784 −1.36462
\(474\) −76.6124 −3.51893
\(475\) −10.1506 −0.465743
\(476\) 4.60144 0.210906
\(477\) 6.59839 0.302120
\(478\) 49.8435 2.27979
\(479\) −28.4118 −1.29817 −0.649085 0.760716i \(-0.724848\pi\)
−0.649085 + 0.760716i \(0.724848\pi\)
\(480\) −104.836 −4.78509
\(481\) −43.9984 −2.00616
\(482\) −5.21481 −0.237528
\(483\) 26.3521 1.19906
\(484\) −5.05888 −0.229949
\(485\) −16.5253 −0.750374
\(486\) 32.1173 1.45687
\(487\) 4.07601 0.184702 0.0923509 0.995727i \(-0.470562\pi\)
0.0923509 + 0.995727i \(0.470562\pi\)
\(488\) −0.518428 −0.0234681
\(489\) −34.7695 −1.57233
\(490\) −28.1798 −1.27303
\(491\) −38.2986 −1.72839 −0.864196 0.503156i \(-0.832172\pi\)
−0.864196 + 0.503156i \(0.832172\pi\)
\(492\) 18.9506 0.854360
\(493\) 0.369089 0.0166230
\(494\) 33.5327 1.50871
\(495\) 61.4101 2.76018
\(496\) −34.3327 −1.54158
\(497\) −6.07918 −0.272689
\(498\) 53.2896 2.38797
\(499\) −31.0255 −1.38889 −0.694447 0.719544i \(-0.744351\pi\)
−0.694447 + 0.719544i \(0.744351\pi\)
\(500\) 18.8822 0.844439
\(501\) 46.9209 2.09627
\(502\) 1.74782 0.0780091
\(503\) −31.5136 −1.40512 −0.702561 0.711623i \(-0.747960\pi\)
−0.702561 + 0.711623i \(0.747960\pi\)
\(504\) −91.8732 −4.09236
\(505\) −10.3995 −0.462773
\(506\) −38.4656 −1.71000
\(507\) −26.5479 −1.17904
\(508\) −13.4083 −0.594895
\(509\) −22.8584 −1.01318 −0.506590 0.862187i \(-0.669094\pi\)
−0.506590 + 0.862187i \(0.669094\pi\)
\(510\) −12.3030 −0.544786
\(511\) −7.23304 −0.319971
\(512\) 37.7412 1.66794
\(513\) 30.6581 1.35359
\(514\) 42.2143 1.86199
\(515\) −8.64561 −0.380971
\(516\) −142.524 −6.27425
\(517\) 13.7575 0.605054
\(518\) 45.5894 2.00308
\(519\) −68.6243 −3.01227
\(520\) 104.011 4.56117
\(521\) −24.4911 −1.07297 −0.536486 0.843909i \(-0.680249\pi\)
−0.536486 + 0.843909i \(0.680249\pi\)
\(522\) −12.4632 −0.545499
\(523\) 41.7013 1.82347 0.911735 0.410779i \(-0.134743\pi\)
0.911735 + 0.410779i \(0.134743\pi\)
\(524\) −62.2803 −2.72073
\(525\) −20.9595 −0.914747
\(526\) 26.6979 1.16408
\(527\) −1.73393 −0.0755314
\(528\) 99.3565 4.32394
\(529\) −1.46314 −0.0636146
\(530\) 7.74024 0.336214
\(531\) 51.7596 2.24618
\(532\) −24.6645 −1.06934
\(533\) −5.80536 −0.251458
\(534\) −43.6675 −1.88968
\(535\) 13.7989 0.596580
\(536\) −115.883 −5.00540
\(537\) 20.3375 0.877626
\(538\) 48.6801 2.09875
\(539\) 11.4934 0.495055
\(540\) 160.826 6.92084
\(541\) 0.825893 0.0355079 0.0177540 0.999842i \(-0.494348\pi\)
0.0177540 + 0.999842i \(0.494348\pi\)
\(542\) −27.9067 −1.19869
\(543\) −24.0279 −1.03113
\(544\) −5.88886 −0.252483
\(545\) −14.9600 −0.640815
\(546\) 69.2399 2.96320
\(547\) −20.8830 −0.892891 −0.446445 0.894811i \(-0.647310\pi\)
−0.446445 + 0.894811i \(0.647310\pi\)
\(548\) 67.6928 2.89169
\(549\) 0.450299 0.0192183
\(550\) 30.5941 1.30454
\(551\) −1.97839 −0.0842821
\(552\) −109.223 −4.64886
\(553\) −17.2627 −0.734085
\(554\) 25.8102 1.09657
\(555\) −86.5284 −3.67293
\(556\) −101.296 −4.29592
\(557\) 27.2966 1.15659 0.578297 0.815826i \(-0.303717\pi\)
0.578297 + 0.815826i \(0.303717\pi\)
\(558\) 58.5505 2.47864
\(559\) 43.6608 1.84666
\(560\) −54.8903 −2.31954
\(561\) 5.01789 0.211855
\(562\) −59.9496 −2.52882
\(563\) −10.4374 −0.439885 −0.219942 0.975513i \(-0.570587\pi\)
−0.219942 + 0.975513i \(0.570587\pi\)
\(564\) 66.0671 2.78192
\(565\) 21.9535 0.923589
\(566\) −83.7207 −3.51904
\(567\) 27.0227 1.13485
\(568\) 25.1968 1.05723
\(569\) 19.2063 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(570\) 65.9463 2.76219
\(571\) 23.6850 0.991185 0.495593 0.868555i \(-0.334951\pi\)
0.495593 + 0.868555i \(0.334951\pi\)
\(572\) −71.7448 −2.99980
\(573\) 19.0115 0.794216
\(574\) 6.01528 0.251073
\(575\) −17.1296 −0.714354
\(576\) 64.7910 2.69962
\(577\) 33.3582 1.38872 0.694360 0.719628i \(-0.255688\pi\)
0.694360 + 0.719628i \(0.255688\pi\)
\(578\) 43.9429 1.82778
\(579\) −57.8116 −2.40257
\(580\) −10.3782 −0.430932
\(581\) 12.0075 0.498154
\(582\) 45.5961 1.89002
\(583\) −3.15693 −0.130747
\(584\) 29.9792 1.24055
\(585\) −90.3422 −3.73519
\(586\) 9.92699 0.410080
\(587\) −3.41715 −0.141041 −0.0705204 0.997510i \(-0.522466\pi\)
−0.0705204 + 0.997510i \(0.522466\pi\)
\(588\) 55.1942 2.27617
\(589\) 9.29421 0.382961
\(590\) 60.7166 2.49966
\(591\) 56.4393 2.32160
\(592\) −96.2398 −3.95543
\(593\) 35.2315 1.44679 0.723393 0.690437i \(-0.242582\pi\)
0.723393 + 0.690437i \(0.242582\pi\)
\(594\) −92.4036 −3.79136
\(595\) −2.77217 −0.113648
\(596\) 108.325 4.43718
\(597\) −12.3353 −0.504851
\(598\) 56.5879 2.31405
\(599\) 6.46616 0.264200 0.132100 0.991236i \(-0.457828\pi\)
0.132100 + 0.991236i \(0.457828\pi\)
\(600\) 86.8722 3.54654
\(601\) 23.2793 0.949583 0.474791 0.880098i \(-0.342524\pi\)
0.474791 + 0.880098i \(0.342524\pi\)
\(602\) −45.2396 −1.84383
\(603\) 100.655 4.09897
\(604\) −4.89340 −0.199110
\(605\) 3.04776 0.123909
\(606\) 28.6941 1.16562
\(607\) −20.2975 −0.823849 −0.411925 0.911218i \(-0.635143\pi\)
−0.411925 + 0.911218i \(0.635143\pi\)
\(608\) 31.5654 1.28014
\(609\) −4.08506 −0.165535
\(610\) 0.528223 0.0213871
\(611\) −20.2391 −0.818785
\(612\) 16.5656 0.669623
\(613\) −26.6543 −1.07656 −0.538279 0.842767i \(-0.680925\pi\)
−0.538279 + 0.842767i \(0.680925\pi\)
\(614\) 88.1364 3.55690
\(615\) −11.4170 −0.460376
\(616\) 43.9557 1.77103
\(617\) −10.0512 −0.404645 −0.202322 0.979319i \(-0.564849\pi\)
−0.202322 + 0.979319i \(0.564849\pi\)
\(618\) 23.8547 0.959577
\(619\) 40.5056 1.62806 0.814030 0.580823i \(-0.197269\pi\)
0.814030 + 0.580823i \(0.197269\pi\)
\(620\) 48.7555 1.95807
\(621\) 51.7367 2.07612
\(622\) −2.59905 −0.104212
\(623\) −9.83939 −0.394207
\(624\) −146.166 −5.85133
\(625\) −29.8313 −1.19325
\(626\) 23.7780 0.950359
\(627\) −26.8968 −1.07415
\(628\) 44.2215 1.76463
\(629\) −4.86048 −0.193800
\(630\) 93.6090 3.72947
\(631\) −44.4387 −1.76908 −0.884539 0.466466i \(-0.845527\pi\)
−0.884539 + 0.466466i \(0.845527\pi\)
\(632\) 71.5498 2.84610
\(633\) 64.1431 2.54946
\(634\) 26.3006 1.04453
\(635\) 8.07791 0.320562
\(636\) −15.1604 −0.601148
\(637\) −16.9082 −0.669929
\(638\) 5.96287 0.236072
\(639\) −21.8856 −0.865780
\(640\) 8.32598 0.329113
\(641\) −17.7327 −0.700399 −0.350199 0.936675i \(-0.613886\pi\)
−0.350199 + 0.936675i \(0.613886\pi\)
\(642\) −38.0736 −1.50265
\(643\) −8.44158 −0.332903 −0.166452 0.986050i \(-0.553231\pi\)
−0.166452 + 0.986050i \(0.553231\pi\)
\(644\) −41.6224 −1.64015
\(645\) 85.8645 3.38091
\(646\) 3.70434 0.145745
\(647\) 38.0905 1.49749 0.748745 0.662858i \(-0.230657\pi\)
0.748745 + 0.662858i \(0.230657\pi\)
\(648\) −112.003 −4.39988
\(649\) −24.7638 −0.972065
\(650\) −45.0079 −1.76535
\(651\) 19.1911 0.752159
\(652\) 54.9174 2.15073
\(653\) 10.5246 0.411858 0.205929 0.978567i \(-0.433978\pi\)
0.205929 + 0.978567i \(0.433978\pi\)
\(654\) 41.2771 1.61406
\(655\) 37.5213 1.46608
\(656\) −12.6983 −0.495786
\(657\) −26.0395 −1.01590
\(658\) 20.9709 0.817531
\(659\) 45.7967 1.78399 0.891994 0.452048i \(-0.149306\pi\)
0.891994 + 0.452048i \(0.149306\pi\)
\(660\) −141.095 −5.49212
\(661\) 19.0341 0.740342 0.370171 0.928964i \(-0.379299\pi\)
0.370171 + 0.928964i \(0.379299\pi\)
\(662\) 47.3490 1.84027
\(663\) −7.38196 −0.286692
\(664\) −49.7682 −1.93138
\(665\) 14.8593 0.576221
\(666\) 164.126 6.35974
\(667\) −3.33861 −0.129271
\(668\) −74.1101 −2.86741
\(669\) 71.8758 2.77888
\(670\) 118.073 4.56155
\(671\) −0.215441 −0.00831699
\(672\) 65.1776 2.51428
\(673\) 25.3296 0.976385 0.488193 0.872736i \(-0.337656\pi\)
0.488193 + 0.872736i \(0.337656\pi\)
\(674\) −54.3983 −2.09534
\(675\) −41.1494 −1.58384
\(676\) 41.9317 1.61276
\(677\) 39.8768 1.53259 0.766295 0.642489i \(-0.222098\pi\)
0.766295 + 0.642489i \(0.222098\pi\)
\(678\) −60.5733 −2.32631
\(679\) 10.2739 0.394277
\(680\) 11.4900 0.440622
\(681\) 25.9819 0.995629
\(682\) −28.0128 −1.07267
\(683\) −48.3416 −1.84974 −0.924871 0.380282i \(-0.875827\pi\)
−0.924871 + 0.380282i \(0.875827\pi\)
\(684\) −88.7945 −3.39514
\(685\) −40.7820 −1.55820
\(686\) 51.2049 1.95501
\(687\) 38.2255 1.45840
\(688\) 95.5013 3.64095
\(689\) 4.64425 0.176932
\(690\) 111.287 4.23663
\(691\) −9.15136 −0.348134 −0.174067 0.984734i \(-0.555691\pi\)
−0.174067 + 0.984734i \(0.555691\pi\)
\(692\) 108.390 4.12037
\(693\) −38.1793 −1.45031
\(694\) −29.1163 −1.10524
\(695\) 61.0267 2.31488
\(696\) 16.9316 0.641792
\(697\) −0.641314 −0.0242915
\(698\) −20.1432 −0.762432
\(699\) 33.2127 1.25622
\(700\) 33.1049 1.25125
\(701\) 48.3637 1.82667 0.913335 0.407209i \(-0.133498\pi\)
0.913335 + 0.407209i \(0.133498\pi\)
\(702\) 135.938 5.13063
\(703\) 26.0531 0.982610
\(704\) −30.9985 −1.16830
\(705\) −39.8026 −1.49905
\(706\) −41.2244 −1.55150
\(707\) 6.46549 0.243160
\(708\) −118.922 −4.46937
\(709\) 30.8439 1.15837 0.579183 0.815198i \(-0.303372\pi\)
0.579183 + 0.815198i \(0.303372\pi\)
\(710\) −25.6729 −0.963485
\(711\) −62.1472 −2.33070
\(712\) 40.7820 1.52837
\(713\) 15.6844 0.587384
\(714\) 7.64889 0.286253
\(715\) 43.2232 1.61646
\(716\) −32.1224 −1.20047
\(717\) 58.8153 2.19650
\(718\) −30.7067 −1.14596
\(719\) −39.3826 −1.46872 −0.734362 0.678758i \(-0.762518\pi\)
−0.734362 + 0.678758i \(0.762518\pi\)
\(720\) −197.610 −7.36448
\(721\) 5.37506 0.200178
\(722\) 30.0291 1.11757
\(723\) −6.15348 −0.228851
\(724\) 37.9513 1.41045
\(725\) 2.65540 0.0986192
\(726\) −8.40930 −0.312098
\(727\) −39.4690 −1.46382 −0.731912 0.681399i \(-0.761372\pi\)
−0.731912 + 0.681399i \(0.761372\pi\)
\(728\) −64.6645 −2.39663
\(729\) −6.33230 −0.234530
\(730\) −30.5457 −1.13055
\(731\) 4.82319 0.178392
\(732\) −1.03460 −0.0382400
\(733\) −16.4915 −0.609128 −0.304564 0.952492i \(-0.598511\pi\)
−0.304564 + 0.952492i \(0.598511\pi\)
\(734\) −46.4777 −1.71552
\(735\) −33.2522 −1.22652
\(736\) 53.2678 1.96348
\(737\) −48.1570 −1.77389
\(738\) 21.6555 0.797150
\(739\) −37.9285 −1.39522 −0.697612 0.716476i \(-0.745754\pi\)
−0.697612 + 0.716476i \(0.745754\pi\)
\(740\) 136.669 5.02405
\(741\) 39.5687 1.45359
\(742\) −4.81218 −0.176661
\(743\) 7.36474 0.270186 0.135093 0.990833i \(-0.456867\pi\)
0.135093 + 0.990833i \(0.456867\pi\)
\(744\) −79.5427 −2.91618
\(745\) −65.2614 −2.39099
\(746\) 59.5456 2.18012
\(747\) 43.2280 1.58163
\(748\) −7.92561 −0.289789
\(749\) −8.57894 −0.313468
\(750\) 31.3876 1.14611
\(751\) 26.8126 0.978405 0.489202 0.872170i \(-0.337288\pi\)
0.489202 + 0.872170i \(0.337288\pi\)
\(752\) −44.2698 −1.61435
\(753\) 2.06243 0.0751592
\(754\) −8.77216 −0.319463
\(755\) 2.94807 0.107291
\(756\) −99.9870 −3.63649
\(757\) 12.9176 0.469499 0.234750 0.972056i \(-0.424573\pi\)
0.234750 + 0.972056i \(0.424573\pi\)
\(758\) 15.6643 0.568952
\(759\) −45.3894 −1.64753
\(760\) −61.5885 −2.23405
\(761\) 15.2719 0.553605 0.276802 0.960927i \(-0.410725\pi\)
0.276802 + 0.960927i \(0.410725\pi\)
\(762\) −22.2883 −0.807421
\(763\) 9.30077 0.336710
\(764\) −30.0281 −1.08638
\(765\) −9.98005 −0.360830
\(766\) −42.2100 −1.52511
\(767\) 36.4308 1.31544
\(768\) 37.8695 1.36650
\(769\) 18.3002 0.659921 0.329960 0.943995i \(-0.392965\pi\)
0.329960 + 0.943995i \(0.392965\pi\)
\(770\) −44.7862 −1.61398
\(771\) 49.8129 1.79397
\(772\) 91.3117 3.28638
\(773\) −8.64714 −0.311016 −0.155508 0.987835i \(-0.549701\pi\)
−0.155508 + 0.987835i \(0.549701\pi\)
\(774\) −162.866 −5.85411
\(775\) −12.4747 −0.448106
\(776\) −42.5831 −1.52864
\(777\) 53.7956 1.92991
\(778\) 26.4769 0.949242
\(779\) 3.43756 0.123163
\(780\) 207.569 7.43217
\(781\) 10.4709 0.374679
\(782\) 6.25123 0.223543
\(783\) −8.02014 −0.286616
\(784\) −36.9842 −1.32086
\(785\) −26.6416 −0.950879
\(786\) −103.528 −3.69271
\(787\) −7.44912 −0.265533 −0.132766 0.991147i \(-0.542386\pi\)
−0.132766 + 0.991147i \(0.542386\pi\)
\(788\) −89.1442 −3.17563
\(789\) 31.5035 1.12155
\(790\) −72.9017 −2.59373
\(791\) −13.6487 −0.485291
\(792\) 158.244 5.62296
\(793\) 0.316941 0.0112549
\(794\) −8.90026 −0.315858
\(795\) 9.13349 0.323931
\(796\) 19.4833 0.690566
\(797\) 48.1292 1.70482 0.852412 0.522870i \(-0.175139\pi\)
0.852412 + 0.522870i \(0.175139\pi\)
\(798\) −40.9995 −1.45137
\(799\) −2.23580 −0.0790968
\(800\) −42.3672 −1.49791
\(801\) −35.4226 −1.25160
\(802\) −4.83732 −0.170812
\(803\) 12.4583 0.439645
\(804\) −231.263 −8.15600
\(805\) 25.0758 0.883804
\(806\) 41.2105 1.45158
\(807\) 57.4425 2.02207
\(808\) −26.7979 −0.942748
\(809\) 6.18950 0.217611 0.108806 0.994063i \(-0.465297\pi\)
0.108806 + 0.994063i \(0.465297\pi\)
\(810\) 114.119 4.00973
\(811\) 28.2244 0.991094 0.495547 0.868581i \(-0.334968\pi\)
0.495547 + 0.868581i \(0.334968\pi\)
\(812\) 6.45224 0.226429
\(813\) −32.9299 −1.15490
\(814\) −78.5241 −2.75227
\(815\) −33.0854 −1.15893
\(816\) −16.1469 −0.565254
\(817\) −25.8532 −0.904488
\(818\) 37.2269 1.30161
\(819\) 56.1667 1.96262
\(820\) 18.0327 0.629731
\(821\) 49.0116 1.71052 0.855258 0.518203i \(-0.173399\pi\)
0.855258 + 0.518203i \(0.173399\pi\)
\(822\) 112.525 3.92475
\(823\) −30.8178 −1.07424 −0.537121 0.843505i \(-0.680488\pi\)
−0.537121 + 0.843505i \(0.680488\pi\)
\(824\) −22.2784 −0.776104
\(825\) 36.1011 1.25688
\(826\) −37.7481 −1.31342
\(827\) 31.6319 1.09995 0.549974 0.835182i \(-0.314638\pi\)
0.549974 + 0.835182i \(0.314638\pi\)
\(828\) −149.844 −5.20745
\(829\) 1.49897 0.0520612 0.0260306 0.999661i \(-0.491713\pi\)
0.0260306 + 0.999661i \(0.491713\pi\)
\(830\) 50.7085 1.76012
\(831\) 30.4561 1.05651
\(832\) 45.6028 1.58099
\(833\) −1.86784 −0.0647169
\(834\) −168.383 −5.83063
\(835\) 44.6482 1.54512
\(836\) 42.4827 1.46930
\(837\) 37.6776 1.30233
\(838\) 4.54581 0.157032
\(839\) 9.02087 0.311435 0.155718 0.987802i \(-0.450231\pi\)
0.155718 + 0.987802i \(0.450231\pi\)
\(840\) −127.171 −4.38781
\(841\) −28.4825 −0.982154
\(842\) 49.2381 1.69686
\(843\) −70.7406 −2.43644
\(844\) −101.312 −3.48731
\(845\) −25.2621 −0.869042
\(846\) 75.4970 2.59564
\(847\) −1.89483 −0.0651070
\(848\) 10.1586 0.348847
\(849\) −98.7905 −3.39048
\(850\) −4.97199 −0.170538
\(851\) 43.9656 1.50712
\(852\) 50.2840 1.72270
\(853\) 51.1432 1.75111 0.875556 0.483117i \(-0.160495\pi\)
0.875556 + 0.483117i \(0.160495\pi\)
\(854\) −0.328402 −0.0112377
\(855\) 53.4949 1.82949
\(856\) 35.5577 1.21534
\(857\) 9.49639 0.324390 0.162195 0.986759i \(-0.448143\pi\)
0.162195 + 0.986759i \(0.448143\pi\)
\(858\) −119.260 −4.07148
\(859\) 5.28903 0.180460 0.0902298 0.995921i \(-0.471240\pi\)
0.0902298 + 0.995921i \(0.471240\pi\)
\(860\) −135.620 −4.62462
\(861\) 7.09803 0.241900
\(862\) −81.1644 −2.76447
\(863\) 20.2943 0.690826 0.345413 0.938451i \(-0.387739\pi\)
0.345413 + 0.938451i \(0.387739\pi\)
\(864\) 127.962 4.35336
\(865\) −65.3004 −2.22028
\(866\) −21.1379 −0.718296
\(867\) 51.8527 1.76101
\(868\) −30.3118 −1.02885
\(869\) 29.7336 1.00864
\(870\) −17.2515 −0.584882
\(871\) 70.8452 2.40050
\(872\) −38.5495 −1.30545
\(873\) 36.9870 1.25182
\(874\) −33.5077 −1.13342
\(875\) 7.07242 0.239091
\(876\) 59.8281 2.02140
\(877\) 52.5660 1.77503 0.887513 0.460782i \(-0.152431\pi\)
0.887513 + 0.460782i \(0.152431\pi\)
\(878\) −15.7513 −0.531580
\(879\) 11.7139 0.395099
\(880\) 94.5441 3.18708
\(881\) −9.22078 −0.310656 −0.155328 0.987863i \(-0.549643\pi\)
−0.155328 + 0.987863i \(0.549643\pi\)
\(882\) 63.0722 2.12375
\(883\) 27.5680 0.927738 0.463869 0.885904i \(-0.346461\pi\)
0.463869 + 0.885904i \(0.346461\pi\)
\(884\) 11.6596 0.392155
\(885\) 71.6456 2.40834
\(886\) 32.9149 1.10580
\(887\) 53.3759 1.79219 0.896093 0.443866i \(-0.146393\pi\)
0.896093 + 0.443866i \(0.146393\pi\)
\(888\) −222.970 −7.48238
\(889\) −5.02212 −0.168436
\(890\) −41.5525 −1.39284
\(891\) −46.5444 −1.55930
\(892\) −113.526 −3.80112
\(893\) 11.9843 0.401039
\(894\) 180.067 6.02235
\(895\) 19.3524 0.646880
\(896\) −5.17634 −0.172929
\(897\) 66.7737 2.22951
\(898\) 35.1108 1.17166
\(899\) −2.43136 −0.0810905
\(900\) 119.180 3.97268
\(901\) 0.513047 0.0170921
\(902\) −10.3608 −0.344978
\(903\) −53.3828 −1.77647
\(904\) 56.5706 1.88151
\(905\) −22.8641 −0.760027
\(906\) −8.13422 −0.270241
\(907\) −50.0678 −1.66247 −0.831237 0.555918i \(-0.812367\pi\)
−0.831237 + 0.555918i \(0.812367\pi\)
\(908\) −41.0377 −1.36188
\(909\) 23.2763 0.772026
\(910\) 65.8863 2.18411
\(911\) −24.3099 −0.805424 −0.402712 0.915327i \(-0.631932\pi\)
−0.402712 + 0.915327i \(0.631932\pi\)
\(912\) 86.5503 2.86597
\(913\) −20.6819 −0.684472
\(914\) 61.3441 2.02908
\(915\) 0.623304 0.0206058
\(916\) −60.3761 −1.99488
\(917\) −23.3274 −0.770337
\(918\) 15.0169 0.495633
\(919\) −11.5013 −0.379394 −0.189697 0.981843i \(-0.560751\pi\)
−0.189697 + 0.981843i \(0.560751\pi\)
\(920\) −103.933 −3.42657
\(921\) 104.001 3.42695
\(922\) −36.0162 −1.18613
\(923\) −15.4041 −0.507031
\(924\) 87.7202 2.88578
\(925\) −34.9686 −1.14976
\(926\) −16.2300 −0.533351
\(927\) 19.3507 0.635559
\(928\) −8.25749 −0.271066
\(929\) −29.0660 −0.953626 −0.476813 0.879005i \(-0.658208\pi\)
−0.476813 + 0.879005i \(0.658208\pi\)
\(930\) 81.0455 2.65759
\(931\) 10.0120 0.328130
\(932\) −52.4584 −1.71833
\(933\) −3.06688 −0.100405
\(934\) −1.80390 −0.0590255
\(935\) 4.77484 0.156154
\(936\) −232.798 −7.60923
\(937\) −47.8839 −1.56430 −0.782150 0.623090i \(-0.785877\pi\)
−0.782150 + 0.623090i \(0.785877\pi\)
\(938\) −73.4070 −2.39682
\(939\) 28.0580 0.915639
\(940\) 62.8671 2.05050
\(941\) 31.6061 1.03033 0.515165 0.857091i \(-0.327731\pi\)
0.515165 + 0.857091i \(0.327731\pi\)
\(942\) 73.5086 2.39504
\(943\) 5.80103 0.188907
\(944\) 79.6867 2.59358
\(945\) 60.2380 1.95954
\(946\) 77.9216 2.53345
\(947\) −39.1461 −1.27208 −0.636039 0.771657i \(-0.719428\pi\)
−0.636039 + 0.771657i \(0.719428\pi\)
\(948\) 142.789 4.63756
\(949\) −18.3278 −0.594946
\(950\) 26.6508 0.864666
\(951\) 31.0348 1.00637
\(952\) −7.14345 −0.231521
\(953\) −17.0366 −0.551870 −0.275935 0.961176i \(-0.588987\pi\)
−0.275935 + 0.961176i \(0.588987\pi\)
\(954\) −17.3243 −0.560894
\(955\) 18.0907 0.585400
\(956\) −92.8971 −3.00451
\(957\) 7.03620 0.227448
\(958\) 74.5961 2.41009
\(959\) 25.3546 0.818743
\(960\) 89.6837 2.89453
\(961\) −19.5778 −0.631541
\(962\) 115.519 3.72449
\(963\) −30.8849 −0.995252
\(964\) 9.71925 0.313036
\(965\) −55.0115 −1.77088
\(966\) −69.1883 −2.22610
\(967\) −4.90118 −0.157611 −0.0788057 0.996890i \(-0.525111\pi\)
−0.0788057 + 0.996890i \(0.525111\pi\)
\(968\) 7.85361 0.252425
\(969\) 4.37113 0.140421
\(970\) 43.3876 1.39309
\(971\) 18.3675 0.589441 0.294721 0.955583i \(-0.404773\pi\)
0.294721 + 0.955583i \(0.404773\pi\)
\(972\) −59.8595 −1.92000
\(973\) −37.9409 −1.21633
\(974\) −10.7017 −0.342904
\(975\) −53.1093 −1.70086
\(976\) 0.693260 0.0221907
\(977\) 14.6595 0.469001 0.234500 0.972116i \(-0.424655\pi\)
0.234500 + 0.972116i \(0.424655\pi\)
\(978\) 91.2883 2.91908
\(979\) 16.9476 0.541646
\(980\) 52.5208 1.67772
\(981\) 33.4836 1.06905
\(982\) 100.554 3.20881
\(983\) 50.6466 1.61537 0.807687 0.589611i \(-0.200719\pi\)
0.807687 + 0.589611i \(0.200719\pi\)
\(984\) −29.4197 −0.937866
\(985\) 53.7056 1.71120
\(986\) −0.969055 −0.0308610
\(987\) 24.7457 0.787664
\(988\) −62.4976 −1.98831
\(989\) −43.6283 −1.38730
\(990\) −161.234 −5.12435
\(991\) 5.89768 0.187346 0.0936730 0.995603i \(-0.470139\pi\)
0.0936730 + 0.995603i \(0.470139\pi\)
\(992\) 38.7926 1.23167
\(993\) 55.8719 1.77304
\(994\) 15.9611 0.506255
\(995\) −11.7378 −0.372115
\(996\) −99.3200 −3.14708
\(997\) −13.2462 −0.419510 −0.209755 0.977754i \(-0.567267\pi\)
−0.209755 + 0.977754i \(0.567267\pi\)
\(998\) 81.4584 2.57852
\(999\) 105.616 3.34154
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 8003.2.a.d.1.9 179
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8003.2.a.d.1.9 179 1.1 even 1 trivial