Properties

Label 2005.2.a.g.1.7
Level $2005$
Weight $2$
Character 2005.1
Self dual yes
Analytic conductor $16.010$
Analytic rank $0$
Dimension $37$
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] = [2005,2,Mod(1,2005)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2005, 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("2005.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2005 = 5 \cdot 401 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2005.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: \(16.0100056053\)
Analytic rank: \(0\)
Dimension: \(37\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 2005.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.88267 q^{2} +2.47026 q^{3} +1.54444 q^{4} +1.00000 q^{5} -4.65067 q^{6} +0.359672 q^{7} +0.857674 q^{8} +3.10216 q^{9} +O(q^{10})\) \(q-1.88267 q^{2} +2.47026 q^{3} +1.54444 q^{4} +1.00000 q^{5} -4.65067 q^{6} +0.359672 q^{7} +0.857674 q^{8} +3.10216 q^{9} -1.88267 q^{10} +5.16983 q^{11} +3.81515 q^{12} +3.84899 q^{13} -0.677142 q^{14} +2.47026 q^{15} -4.70359 q^{16} +0.331790 q^{17} -5.84034 q^{18} +6.07013 q^{19} +1.54444 q^{20} +0.888481 q^{21} -9.73307 q^{22} +4.55195 q^{23} +2.11867 q^{24} +1.00000 q^{25} -7.24638 q^{26} +0.252368 q^{27} +0.555490 q^{28} -8.88940 q^{29} -4.65067 q^{30} +3.86039 q^{31} +7.13995 q^{32} +12.7708 q^{33} -0.624651 q^{34} +0.359672 q^{35} +4.79109 q^{36} -0.0839175 q^{37} -11.4280 q^{38} +9.50800 q^{39} +0.857674 q^{40} -3.28822 q^{41} -1.67271 q^{42} -12.0070 q^{43} +7.98447 q^{44} +3.10216 q^{45} -8.56982 q^{46} -9.56754 q^{47} -11.6191 q^{48} -6.87064 q^{49} -1.88267 q^{50} +0.819607 q^{51} +5.94453 q^{52} +3.98325 q^{53} -0.475125 q^{54} +5.16983 q^{55} +0.308481 q^{56} +14.9948 q^{57} +16.7358 q^{58} +8.52046 q^{59} +3.81515 q^{60} -2.90830 q^{61} -7.26783 q^{62} +1.11576 q^{63} -4.03497 q^{64} +3.84899 q^{65} -24.0432 q^{66} -5.56751 q^{67} +0.512429 q^{68} +11.2445 q^{69} -0.677142 q^{70} -5.78381 q^{71} +2.66064 q^{72} +16.4780 q^{73} +0.157989 q^{74} +2.47026 q^{75} +9.37493 q^{76} +1.85944 q^{77} -17.9004 q^{78} -6.53012 q^{79} -4.70359 q^{80} -8.68307 q^{81} +6.19063 q^{82} +1.94202 q^{83} +1.37220 q^{84} +0.331790 q^{85} +22.6052 q^{86} -21.9591 q^{87} +4.43403 q^{88} +13.9230 q^{89} -5.84034 q^{90} +1.38437 q^{91} +7.03021 q^{92} +9.53615 q^{93} +18.0125 q^{94} +6.07013 q^{95} +17.6375 q^{96} -0.131070 q^{97} +12.9351 q^{98} +16.0376 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.88267 −1.33125 −0.665623 0.746288i \(-0.731834\pi\)
−0.665623 + 0.746288i \(0.731834\pi\)
\(3\) 2.47026 1.42620 0.713101 0.701061i \(-0.247290\pi\)
0.713101 + 0.701061i \(0.247290\pi\)
\(4\) 1.54444 0.772218
\(5\) 1.00000 0.447214
\(6\) −4.65067 −1.89863
\(7\) 0.359672 0.135943 0.0679715 0.997687i \(-0.478347\pi\)
0.0679715 + 0.997687i \(0.478347\pi\)
\(8\) 0.857674 0.303234
\(9\) 3.10216 1.03405
\(10\) −1.88267 −0.595352
\(11\) 5.16983 1.55876 0.779381 0.626550i \(-0.215534\pi\)
0.779381 + 0.626550i \(0.215534\pi\)
\(12\) 3.81515 1.10134
\(13\) 3.84899 1.06752 0.533759 0.845636i \(-0.320779\pi\)
0.533759 + 0.845636i \(0.320779\pi\)
\(14\) −0.677142 −0.180974
\(15\) 2.47026 0.637817
\(16\) −4.70359 −1.17590
\(17\) 0.331790 0.0804710 0.0402355 0.999190i \(-0.487189\pi\)
0.0402355 + 0.999190i \(0.487189\pi\)
\(18\) −5.84034 −1.37658
\(19\) 6.07013 1.39258 0.696292 0.717759i \(-0.254832\pi\)
0.696292 + 0.717759i \(0.254832\pi\)
\(20\) 1.54444 0.345347
\(21\) 0.888481 0.193882
\(22\) −9.73307 −2.07510
\(23\) 4.55195 0.949148 0.474574 0.880216i \(-0.342602\pi\)
0.474574 + 0.880216i \(0.342602\pi\)
\(24\) 2.11867 0.432472
\(25\) 1.00000 0.200000
\(26\) −7.24638 −1.42113
\(27\) 0.252368 0.0485683
\(28\) 0.555490 0.104978
\(29\) −8.88940 −1.65072 −0.825360 0.564607i \(-0.809028\pi\)
−0.825360 + 0.564607i \(0.809028\pi\)
\(30\) −4.65067 −0.849092
\(31\) 3.86039 0.693347 0.346673 0.937986i \(-0.387311\pi\)
0.346673 + 0.937986i \(0.387311\pi\)
\(32\) 7.13995 1.26218
\(33\) 12.7708 2.22311
\(34\) −0.624651 −0.107127
\(35\) 0.359672 0.0607956
\(36\) 4.79109 0.798516
\(37\) −0.0839175 −0.0137959 −0.00689797 0.999976i \(-0.502196\pi\)
−0.00689797 + 0.999976i \(0.502196\pi\)
\(38\) −11.4280 −1.85387
\(39\) 9.50800 1.52250
\(40\) 0.857674 0.135610
\(41\) −3.28822 −0.513534 −0.256767 0.966473i \(-0.582657\pi\)
−0.256767 + 0.966473i \(0.582657\pi\)
\(42\) −1.67271 −0.258105
\(43\) −12.0070 −1.83105 −0.915527 0.402256i \(-0.868226\pi\)
−0.915527 + 0.402256i \(0.868226\pi\)
\(44\) 7.98447 1.20370
\(45\) 3.10216 0.462443
\(46\) −8.56982 −1.26355
\(47\) −9.56754 −1.39557 −0.697784 0.716308i \(-0.745831\pi\)
−0.697784 + 0.716308i \(0.745831\pi\)
\(48\) −11.6191 −1.67707
\(49\) −6.87064 −0.981519
\(50\) −1.88267 −0.266249
\(51\) 0.819607 0.114768
\(52\) 5.94453 0.824358
\(53\) 3.98325 0.547142 0.273571 0.961852i \(-0.411795\pi\)
0.273571 + 0.961852i \(0.411795\pi\)
\(54\) −0.475125 −0.0646563
\(55\) 5.16983 0.697100
\(56\) 0.308481 0.0412225
\(57\) 14.9948 1.98611
\(58\) 16.7358 2.19752
\(59\) 8.52046 1.10927 0.554635 0.832094i \(-0.312858\pi\)
0.554635 + 0.832094i \(0.312858\pi\)
\(60\) 3.81515 0.492534
\(61\) −2.90830 −0.372370 −0.186185 0.982515i \(-0.559612\pi\)
−0.186185 + 0.982515i \(0.559612\pi\)
\(62\) −7.26783 −0.923016
\(63\) 1.11576 0.140573
\(64\) −4.03497 −0.504371
\(65\) 3.84899 0.477409
\(66\) −24.0432 −2.95951
\(67\) −5.56751 −0.680180 −0.340090 0.940393i \(-0.610458\pi\)
−0.340090 + 0.940393i \(0.610458\pi\)
\(68\) 0.512429 0.0621412
\(69\) 11.2445 1.35368
\(70\) −0.677142 −0.0809339
\(71\) −5.78381 −0.686412 −0.343206 0.939260i \(-0.611513\pi\)
−0.343206 + 0.939260i \(0.611513\pi\)
\(72\) 2.66064 0.313560
\(73\) 16.4780 1.92861 0.964303 0.264802i \(-0.0853068\pi\)
0.964303 + 0.264802i \(0.0853068\pi\)
\(74\) 0.157989 0.0183658
\(75\) 2.47026 0.285241
\(76\) 9.37493 1.07538
\(77\) 1.85944 0.211903
\(78\) −17.9004 −2.02682
\(79\) −6.53012 −0.734696 −0.367348 0.930084i \(-0.619734\pi\)
−0.367348 + 0.930084i \(0.619734\pi\)
\(80\) −4.70359 −0.525877
\(81\) −8.68307 −0.964786
\(82\) 6.19063 0.683641
\(83\) 1.94202 0.213164 0.106582 0.994304i \(-0.466009\pi\)
0.106582 + 0.994304i \(0.466009\pi\)
\(84\) 1.37220 0.149720
\(85\) 0.331790 0.0359877
\(86\) 22.6052 2.43759
\(87\) −21.9591 −2.35426
\(88\) 4.43403 0.472669
\(89\) 13.9230 1.47584 0.737918 0.674890i \(-0.235809\pi\)
0.737918 + 0.674890i \(0.235809\pi\)
\(90\) −5.84034 −0.615626
\(91\) 1.38437 0.145122
\(92\) 7.03021 0.732950
\(93\) 9.53615 0.988853
\(94\) 18.0125 1.85785
\(95\) 6.07013 0.622782
\(96\) 17.6375 1.80012
\(97\) −0.131070 −0.0133081 −0.00665407 0.999978i \(-0.502118\pi\)
−0.00665407 + 0.999978i \(0.502118\pi\)
\(98\) 12.9351 1.30664
\(99\) 16.0376 1.61184
\(100\) 1.54444 0.154444
\(101\) −7.81189 −0.777312 −0.388656 0.921383i \(-0.627061\pi\)
−0.388656 + 0.921383i \(0.627061\pi\)
\(102\) −1.54305 −0.152784
\(103\) −13.8492 −1.36460 −0.682302 0.731070i \(-0.739021\pi\)
−0.682302 + 0.731070i \(0.739021\pi\)
\(104\) 3.30118 0.323707
\(105\) 0.888481 0.0867068
\(106\) −7.49914 −0.728381
\(107\) 5.38180 0.520278 0.260139 0.965571i \(-0.416232\pi\)
0.260139 + 0.965571i \(0.416232\pi\)
\(108\) 0.389767 0.0375053
\(109\) 5.90613 0.565705 0.282852 0.959163i \(-0.408719\pi\)
0.282852 + 0.959163i \(0.408719\pi\)
\(110\) −9.73307 −0.928012
\(111\) −0.207298 −0.0196758
\(112\) −1.69175 −0.159855
\(113\) 3.00127 0.282335 0.141168 0.989986i \(-0.454914\pi\)
0.141168 + 0.989986i \(0.454914\pi\)
\(114\) −28.2302 −2.64400
\(115\) 4.55195 0.424472
\(116\) −13.7291 −1.27472
\(117\) 11.9402 1.10387
\(118\) −16.0412 −1.47671
\(119\) 0.119336 0.0109395
\(120\) 2.11867 0.193408
\(121\) 15.7271 1.42974
\(122\) 5.47537 0.495717
\(123\) −8.12276 −0.732404
\(124\) 5.96213 0.535415
\(125\) 1.00000 0.0894427
\(126\) −2.10060 −0.187137
\(127\) −5.65507 −0.501806 −0.250903 0.968012i \(-0.580728\pi\)
−0.250903 + 0.968012i \(0.580728\pi\)
\(128\) −6.68339 −0.590734
\(129\) −29.6604 −2.61146
\(130\) −7.24638 −0.635549
\(131\) −1.04380 −0.0911974 −0.0455987 0.998960i \(-0.514520\pi\)
−0.0455987 + 0.998960i \(0.514520\pi\)
\(132\) 19.7237 1.71673
\(133\) 2.18325 0.189312
\(134\) 10.4818 0.905488
\(135\) 0.252368 0.0217204
\(136\) 0.284568 0.0244015
\(137\) −20.1434 −1.72097 −0.860484 0.509477i \(-0.829839\pi\)
−0.860484 + 0.509477i \(0.829839\pi\)
\(138\) −21.1696 −1.80208
\(139\) −20.2698 −1.71926 −0.859632 0.510913i \(-0.829307\pi\)
−0.859632 + 0.510913i \(0.829307\pi\)
\(140\) 0.555490 0.0469475
\(141\) −23.6343 −1.99036
\(142\) 10.8890 0.913784
\(143\) 19.8986 1.66401
\(144\) −14.5913 −1.21594
\(145\) −8.88940 −0.738224
\(146\) −31.0226 −2.56745
\(147\) −16.9722 −1.39985
\(148\) −0.129605 −0.0106535
\(149\) 2.66820 0.218587 0.109294 0.994010i \(-0.465141\pi\)
0.109294 + 0.994010i \(0.465141\pi\)
\(150\) −4.65067 −0.379726
\(151\) 0.152848 0.0124386 0.00621929 0.999981i \(-0.498020\pi\)
0.00621929 + 0.999981i \(0.498020\pi\)
\(152\) 5.20619 0.422278
\(153\) 1.02927 0.0832114
\(154\) −3.50071 −0.282095
\(155\) 3.86039 0.310074
\(156\) 14.6845 1.17570
\(157\) 12.4116 0.990557 0.495278 0.868734i \(-0.335066\pi\)
0.495278 + 0.868734i \(0.335066\pi\)
\(158\) 12.2940 0.978062
\(159\) 9.83966 0.780336
\(160\) 7.13995 0.564462
\(161\) 1.63721 0.129030
\(162\) 16.3473 1.28437
\(163\) 5.45902 0.427583 0.213792 0.976879i \(-0.431419\pi\)
0.213792 + 0.976879i \(0.431419\pi\)
\(164\) −5.07846 −0.396561
\(165\) 12.7708 0.994205
\(166\) −3.65617 −0.283774
\(167\) 8.71943 0.674730 0.337365 0.941374i \(-0.390464\pi\)
0.337365 + 0.941374i \(0.390464\pi\)
\(168\) 0.762027 0.0587916
\(169\) 1.81475 0.139596
\(170\) −0.624651 −0.0479086
\(171\) 18.8305 1.44001
\(172\) −18.5441 −1.41397
\(173\) 25.9281 1.97128 0.985638 0.168872i \(-0.0540125\pi\)
0.985638 + 0.168872i \(0.0540125\pi\)
\(174\) 41.3417 3.13410
\(175\) 0.359672 0.0271886
\(176\) −24.3167 −1.83294
\(177\) 21.0477 1.58204
\(178\) −26.2124 −1.96470
\(179\) 7.47024 0.558352 0.279176 0.960240i \(-0.409939\pi\)
0.279176 + 0.960240i \(0.409939\pi\)
\(180\) 4.79109 0.357107
\(181\) −17.2665 −1.28341 −0.641705 0.766952i \(-0.721773\pi\)
−0.641705 + 0.766952i \(0.721773\pi\)
\(182\) −2.60632 −0.193193
\(183\) −7.18425 −0.531075
\(184\) 3.90409 0.287813
\(185\) −0.0839175 −0.00616974
\(186\) −17.9534 −1.31641
\(187\) 1.71530 0.125435
\(188\) −14.7765 −1.07768
\(189\) 0.0907696 0.00660252
\(190\) −11.4280 −0.829077
\(191\) −18.5808 −1.34446 −0.672228 0.740344i \(-0.734663\pi\)
−0.672228 + 0.740344i \(0.734663\pi\)
\(192\) −9.96740 −0.719335
\(193\) −7.18286 −0.517034 −0.258517 0.966007i \(-0.583234\pi\)
−0.258517 + 0.966007i \(0.583234\pi\)
\(194\) 0.246761 0.0177164
\(195\) 9.50800 0.680882
\(196\) −10.6113 −0.757947
\(197\) 15.2620 1.08737 0.543685 0.839290i \(-0.317029\pi\)
0.543685 + 0.839290i \(0.317029\pi\)
\(198\) −30.1936 −2.14576
\(199\) −3.03183 −0.214921 −0.107460 0.994209i \(-0.534272\pi\)
−0.107460 + 0.994209i \(0.534272\pi\)
\(200\) 0.857674 0.0606467
\(201\) −13.7532 −0.970075
\(202\) 14.7072 1.03479
\(203\) −3.19726 −0.224404
\(204\) 1.26583 0.0886259
\(205\) −3.28822 −0.229660
\(206\) 26.0735 1.81663
\(207\) 14.1209 0.981471
\(208\) −18.1041 −1.25529
\(209\) 31.3815 2.17071
\(210\) −1.67271 −0.115428
\(211\) −8.63615 −0.594537 −0.297269 0.954794i \(-0.596076\pi\)
−0.297269 + 0.954794i \(0.596076\pi\)
\(212\) 6.15189 0.422513
\(213\) −14.2875 −0.978963
\(214\) −10.1321 −0.692618
\(215\) −12.0070 −0.818873
\(216\) 0.216449 0.0147275
\(217\) 1.38847 0.0942557
\(218\) −11.1193 −0.753093
\(219\) 40.7049 2.75058
\(220\) 7.98447 0.538313
\(221\) 1.27706 0.0859043
\(222\) 0.390273 0.0261934
\(223\) 10.1783 0.681589 0.340794 0.940138i \(-0.389304\pi\)
0.340794 + 0.940138i \(0.389304\pi\)
\(224\) 2.56804 0.171584
\(225\) 3.10216 0.206811
\(226\) −5.65039 −0.375858
\(227\) 25.3332 1.68143 0.840713 0.541481i \(-0.182136\pi\)
0.840713 + 0.541481i \(0.182136\pi\)
\(228\) 23.1585 1.53371
\(229\) −20.1348 −1.33055 −0.665273 0.746601i \(-0.731685\pi\)
−0.665273 + 0.746601i \(0.731685\pi\)
\(230\) −8.56982 −0.565077
\(231\) 4.59329 0.302216
\(232\) −7.62421 −0.500554
\(233\) −4.71918 −0.309164 −0.154582 0.987980i \(-0.549403\pi\)
−0.154582 + 0.987980i \(0.549403\pi\)
\(234\) −22.4794 −1.46953
\(235\) −9.56754 −0.624117
\(236\) 13.1593 0.856599
\(237\) −16.1311 −1.04783
\(238\) −0.224669 −0.0145631
\(239\) 4.76557 0.308259 0.154129 0.988051i \(-0.450743\pi\)
0.154129 + 0.988051i \(0.450743\pi\)
\(240\) −11.6191 −0.750007
\(241\) 7.37790 0.475253 0.237626 0.971357i \(-0.423631\pi\)
0.237626 + 0.971357i \(0.423631\pi\)
\(242\) −29.6090 −1.90334
\(243\) −22.2065 −1.42455
\(244\) −4.49169 −0.287551
\(245\) −6.87064 −0.438949
\(246\) 15.2924 0.975011
\(247\) 23.3639 1.48661
\(248\) 3.31096 0.210246
\(249\) 4.79728 0.304015
\(250\) −1.88267 −0.119070
\(251\) 29.2656 1.84723 0.923616 0.383320i \(-0.125219\pi\)
0.923616 + 0.383320i \(0.125219\pi\)
\(252\) 1.72322 0.108553
\(253\) 23.5328 1.47950
\(254\) 10.6466 0.668028
\(255\) 0.819607 0.0513258
\(256\) 20.6525 1.29078
\(257\) −2.09085 −0.130424 −0.0652118 0.997871i \(-0.520772\pi\)
−0.0652118 + 0.997871i \(0.520772\pi\)
\(258\) 55.8407 3.47649
\(259\) −0.0301827 −0.00187546
\(260\) 5.94453 0.368664
\(261\) −27.5764 −1.70693
\(262\) 1.96513 0.121406
\(263\) −9.51589 −0.586775 −0.293387 0.955994i \(-0.594783\pi\)
−0.293387 + 0.955994i \(0.594783\pi\)
\(264\) 10.9532 0.674122
\(265\) 3.98325 0.244689
\(266\) −4.11034 −0.252021
\(267\) 34.3934 2.10484
\(268\) −8.59867 −0.525248
\(269\) 15.0493 0.917574 0.458787 0.888546i \(-0.348284\pi\)
0.458787 + 0.888546i \(0.348284\pi\)
\(270\) −0.475125 −0.0289152
\(271\) −13.1023 −0.795907 −0.397954 0.917405i \(-0.630280\pi\)
−0.397954 + 0.917405i \(0.630280\pi\)
\(272\) −1.56061 −0.0946256
\(273\) 3.41976 0.206973
\(274\) 37.9234 2.29103
\(275\) 5.16983 0.311752
\(276\) 17.3664 1.04533
\(277\) −3.73137 −0.224196 −0.112098 0.993697i \(-0.535757\pi\)
−0.112098 + 0.993697i \(0.535757\pi\)
\(278\) 38.1614 2.28877
\(279\) 11.9756 0.716958
\(280\) 0.308481 0.0184353
\(281\) −6.95712 −0.415027 −0.207513 0.978232i \(-0.566537\pi\)
−0.207513 + 0.978232i \(0.566537\pi\)
\(282\) 44.4955 2.64967
\(283\) 12.6825 0.753899 0.376950 0.926234i \(-0.376973\pi\)
0.376950 + 0.926234i \(0.376973\pi\)
\(284\) −8.93274 −0.530060
\(285\) 14.9948 0.888214
\(286\) −37.4625 −2.21521
\(287\) −1.18268 −0.0698114
\(288\) 22.1493 1.30516
\(289\) −16.8899 −0.993524
\(290\) 16.7358 0.982759
\(291\) −0.323776 −0.0189801
\(292\) 25.4492 1.48930
\(293\) −10.2431 −0.598410 −0.299205 0.954189i \(-0.596721\pi\)
−0.299205 + 0.954189i \(0.596721\pi\)
\(294\) 31.9531 1.86354
\(295\) 8.52046 0.496081
\(296\) −0.0719738 −0.00418339
\(297\) 1.30470 0.0757064
\(298\) −5.02333 −0.290994
\(299\) 17.5204 1.01323
\(300\) 3.81515 0.220268
\(301\) −4.31859 −0.248919
\(302\) −0.287762 −0.0165588
\(303\) −19.2974 −1.10860
\(304\) −28.5514 −1.63753
\(305\) −2.90830 −0.166529
\(306\) −1.93777 −0.110775
\(307\) 13.7117 0.782567 0.391284 0.920270i \(-0.372031\pi\)
0.391284 + 0.920270i \(0.372031\pi\)
\(308\) 2.87179 0.163635
\(309\) −34.2111 −1.94620
\(310\) −7.26783 −0.412785
\(311\) 2.48910 0.141144 0.0705721 0.997507i \(-0.477518\pi\)
0.0705721 + 0.997507i \(0.477518\pi\)
\(312\) 8.15476 0.461672
\(313\) 18.9284 1.06989 0.534947 0.844885i \(-0.320332\pi\)
0.534947 + 0.844885i \(0.320332\pi\)
\(314\) −23.3670 −1.31868
\(315\) 1.11576 0.0628659
\(316\) −10.0854 −0.567346
\(317\) 21.3008 1.19637 0.598187 0.801357i \(-0.295888\pi\)
0.598187 + 0.801357i \(0.295888\pi\)
\(318\) −18.5248 −1.03882
\(319\) −45.9567 −2.57308
\(320\) −4.03497 −0.225561
\(321\) 13.2944 0.742022
\(322\) −3.08232 −0.171771
\(323\) 2.01401 0.112063
\(324\) −13.4105 −0.745026
\(325\) 3.84899 0.213504
\(326\) −10.2775 −0.569219
\(327\) 14.5897 0.806810
\(328\) −2.82022 −0.155721
\(329\) −3.44117 −0.189718
\(330\) −24.0432 −1.32353
\(331\) −22.7554 −1.25075 −0.625374 0.780325i \(-0.715053\pi\)
−0.625374 + 0.780325i \(0.715053\pi\)
\(332\) 2.99932 0.164609
\(333\) −0.260326 −0.0142658
\(334\) −16.4158 −0.898232
\(335\) −5.56751 −0.304186
\(336\) −4.17905 −0.227986
\(337\) 14.5814 0.794298 0.397149 0.917754i \(-0.370000\pi\)
0.397149 + 0.917754i \(0.370000\pi\)
\(338\) −3.41657 −0.185837
\(339\) 7.41390 0.402668
\(340\) 0.512429 0.0277904
\(341\) 19.9576 1.08076
\(342\) −35.4516 −1.91700
\(343\) −4.98887 −0.269374
\(344\) −10.2981 −0.555237
\(345\) 11.2445 0.605383
\(346\) −48.8140 −2.62426
\(347\) 10.2104 0.548121 0.274060 0.961712i \(-0.411633\pi\)
0.274060 + 0.961712i \(0.411633\pi\)
\(348\) −33.9144 −1.81800
\(349\) −4.69795 −0.251475 −0.125738 0.992064i \(-0.540130\pi\)
−0.125738 + 0.992064i \(0.540130\pi\)
\(350\) −0.677142 −0.0361948
\(351\) 0.971363 0.0518475
\(352\) 36.9123 1.96743
\(353\) 33.2339 1.76886 0.884432 0.466669i \(-0.154546\pi\)
0.884432 + 0.466669i \(0.154546\pi\)
\(354\) −39.6259 −2.10609
\(355\) −5.78381 −0.306973
\(356\) 21.5032 1.13967
\(357\) 0.294789 0.0156019
\(358\) −14.0640 −0.743304
\(359\) 19.1315 1.00972 0.504861 0.863201i \(-0.331544\pi\)
0.504861 + 0.863201i \(0.331544\pi\)
\(360\) 2.66064 0.140228
\(361\) 17.8465 0.939288
\(362\) 32.5071 1.70853
\(363\) 38.8500 2.03910
\(364\) 2.13808 0.112066
\(365\) 16.4780 0.862499
\(366\) 13.5256 0.706992
\(367\) −17.6567 −0.921672 −0.460836 0.887485i \(-0.652450\pi\)
−0.460836 + 0.887485i \(0.652450\pi\)
\(368\) −21.4105 −1.11610
\(369\) −10.2006 −0.531022
\(370\) 0.157989 0.00821344
\(371\) 1.43266 0.0743802
\(372\) 14.7280 0.763611
\(373\) −23.8902 −1.23699 −0.618493 0.785790i \(-0.712256\pi\)
−0.618493 + 0.785790i \(0.712256\pi\)
\(374\) −3.22934 −0.166985
\(375\) 2.47026 0.127563
\(376\) −8.20583 −0.423183
\(377\) −34.2152 −1.76217
\(378\) −0.170889 −0.00878958
\(379\) −21.4359 −1.10109 −0.550544 0.834806i \(-0.685580\pi\)
−0.550544 + 0.834806i \(0.685580\pi\)
\(380\) 9.37493 0.480924
\(381\) −13.9695 −0.715677
\(382\) 34.9814 1.78980
\(383\) 37.9957 1.94149 0.970744 0.240118i \(-0.0771860\pi\)
0.970744 + 0.240118i \(0.0771860\pi\)
\(384\) −16.5097 −0.842506
\(385\) 1.85944 0.0947659
\(386\) 13.5229 0.688300
\(387\) −37.2478 −1.89341
\(388\) −0.202429 −0.0102768
\(389\) −19.1324 −0.970054 −0.485027 0.874499i \(-0.661190\pi\)
−0.485027 + 0.874499i \(0.661190\pi\)
\(390\) −17.9004 −0.906422
\(391\) 1.51029 0.0763789
\(392\) −5.89277 −0.297630
\(393\) −2.57846 −0.130066
\(394\) −28.7332 −1.44756
\(395\) −6.53012 −0.328566
\(396\) 24.7691 1.24470
\(397\) 23.5575 1.18232 0.591158 0.806556i \(-0.298671\pi\)
0.591158 + 0.806556i \(0.298671\pi\)
\(398\) 5.70793 0.286113
\(399\) 5.39319 0.269997
\(400\) −4.70359 −0.235179
\(401\) −1.00000 −0.0499376
\(402\) 25.8927 1.29141
\(403\) 14.8586 0.740161
\(404\) −12.0650 −0.600255
\(405\) −8.68307 −0.431465
\(406\) 6.01938 0.298737
\(407\) −0.433839 −0.0215046
\(408\) 0.702956 0.0348015
\(409\) −14.9218 −0.737836 −0.368918 0.929462i \(-0.620272\pi\)
−0.368918 + 0.929462i \(0.620272\pi\)
\(410\) 6.19063 0.305734
\(411\) −49.7594 −2.45445
\(412\) −21.3892 −1.05377
\(413\) 3.06457 0.150798
\(414\) −26.5850 −1.30658
\(415\) 1.94202 0.0953299
\(416\) 27.4816 1.34740
\(417\) −50.0717 −2.45202
\(418\) −59.0810 −2.88975
\(419\) −39.2555 −1.91775 −0.958877 0.283822i \(-0.908398\pi\)
−0.958877 + 0.283822i \(0.908398\pi\)
\(420\) 1.37220 0.0669566
\(421\) 1.33621 0.0651229 0.0325614 0.999470i \(-0.489634\pi\)
0.0325614 + 0.999470i \(0.489634\pi\)
\(422\) 16.2590 0.791476
\(423\) −29.6801 −1.44309
\(424\) 3.41633 0.165912
\(425\) 0.331790 0.0160942
\(426\) 26.8986 1.30324
\(427\) −1.04603 −0.0506211
\(428\) 8.31184 0.401768
\(429\) 49.1547 2.37321
\(430\) 22.6052 1.09012
\(431\) 4.64440 0.223713 0.111856 0.993724i \(-0.464320\pi\)
0.111856 + 0.993724i \(0.464320\pi\)
\(432\) −1.18704 −0.0571113
\(433\) −33.0190 −1.58679 −0.793397 0.608704i \(-0.791690\pi\)
−0.793397 + 0.608704i \(0.791690\pi\)
\(434\) −2.61403 −0.125478
\(435\) −21.9591 −1.05286
\(436\) 9.12165 0.436848
\(437\) 27.6309 1.32177
\(438\) −76.6338 −3.66170
\(439\) 0.233804 0.0111589 0.00557944 0.999984i \(-0.498224\pi\)
0.00557944 + 0.999984i \(0.498224\pi\)
\(440\) 4.43403 0.211384
\(441\) −21.3138 −1.01494
\(442\) −2.40428 −0.114360
\(443\) −39.3825 −1.87112 −0.935559 0.353170i \(-0.885104\pi\)
−0.935559 + 0.353170i \(0.885104\pi\)
\(444\) −0.320158 −0.0151940
\(445\) 13.9230 0.660014
\(446\) −19.1623 −0.907363
\(447\) 6.59113 0.311750
\(448\) −1.45126 −0.0685657
\(449\) −22.5649 −1.06490 −0.532451 0.846461i \(-0.678729\pi\)
−0.532451 + 0.846461i \(0.678729\pi\)
\(450\) −5.84034 −0.275316
\(451\) −16.9996 −0.800478
\(452\) 4.63527 0.218025
\(453\) 0.377573 0.0177399
\(454\) −47.6941 −2.23839
\(455\) 1.38437 0.0649004
\(456\) 12.8606 0.602254
\(457\) 14.7318 0.689124 0.344562 0.938764i \(-0.388027\pi\)
0.344562 + 0.938764i \(0.388027\pi\)
\(458\) 37.9071 1.77128
\(459\) 0.0837333 0.00390834
\(460\) 7.03021 0.327785
\(461\) −26.5125 −1.23481 −0.617404 0.786646i \(-0.711816\pi\)
−0.617404 + 0.786646i \(0.711816\pi\)
\(462\) −8.64764 −0.402325
\(463\) −24.6790 −1.14693 −0.573466 0.819230i \(-0.694401\pi\)
−0.573466 + 0.819230i \(0.694401\pi\)
\(464\) 41.8121 1.94108
\(465\) 9.53615 0.442229
\(466\) 8.88466 0.411574
\(467\) 5.32908 0.246600 0.123300 0.992369i \(-0.460652\pi\)
0.123300 + 0.992369i \(0.460652\pi\)
\(468\) 18.4409 0.852431
\(469\) −2.00248 −0.0924658
\(470\) 18.0125 0.830854
\(471\) 30.6599 1.41273
\(472\) 7.30778 0.336368
\(473\) −62.0743 −2.85418
\(474\) 30.3694 1.39491
\(475\) 6.07013 0.278517
\(476\) 0.184306 0.00844766
\(477\) 12.3567 0.565775
\(478\) −8.97197 −0.410369
\(479\) 27.1255 1.23940 0.619698 0.784841i \(-0.287255\pi\)
0.619698 + 0.784841i \(0.287255\pi\)
\(480\) 17.6375 0.805038
\(481\) −0.322998 −0.0147274
\(482\) −13.8901 −0.632679
\(483\) 4.04432 0.184023
\(484\) 24.2896 1.10407
\(485\) −0.131070 −0.00595158
\(486\) 41.8075 1.89643
\(487\) −8.85228 −0.401135 −0.200568 0.979680i \(-0.564279\pi\)
−0.200568 + 0.979680i \(0.564279\pi\)
\(488\) −2.49438 −0.112915
\(489\) 13.4852 0.609820
\(490\) 12.9351 0.584349
\(491\) 5.50856 0.248598 0.124299 0.992245i \(-0.460332\pi\)
0.124299 + 0.992245i \(0.460332\pi\)
\(492\) −12.5451 −0.565576
\(493\) −2.94942 −0.132835
\(494\) −43.9864 −1.97904
\(495\) 16.0376 0.720839
\(496\) −18.1577 −0.815305
\(497\) −2.08027 −0.0933130
\(498\) −9.03168 −0.404719
\(499\) −29.3998 −1.31611 −0.658057 0.752968i \(-0.728622\pi\)
−0.658057 + 0.752968i \(0.728622\pi\)
\(500\) 1.54444 0.0690693
\(501\) 21.5392 0.962301
\(502\) −55.0975 −2.45912
\(503\) 30.0406 1.33945 0.669723 0.742611i \(-0.266413\pi\)
0.669723 + 0.742611i \(0.266413\pi\)
\(504\) 0.956958 0.0426263
\(505\) −7.81189 −0.347624
\(506\) −44.3045 −1.96957
\(507\) 4.48290 0.199093
\(508\) −8.73389 −0.387504
\(509\) −22.8233 −1.01162 −0.505812 0.862644i \(-0.668807\pi\)
−0.505812 + 0.862644i \(0.668807\pi\)
\(510\) −1.54305 −0.0683273
\(511\) 5.92667 0.262181
\(512\) −25.5151 −1.12762
\(513\) 1.53191 0.0676353
\(514\) 3.93637 0.173626
\(515\) −13.8492 −0.610270
\(516\) −45.8087 −2.01661
\(517\) −49.4625 −2.17536
\(518\) 0.0568240 0.00249671
\(519\) 64.0490 2.81144
\(520\) 3.30118 0.144766
\(521\) 22.2596 0.975211 0.487605 0.873064i \(-0.337871\pi\)
0.487605 + 0.873064i \(0.337871\pi\)
\(522\) 51.9171 2.27235
\(523\) 11.5568 0.505344 0.252672 0.967552i \(-0.418691\pi\)
0.252672 + 0.967552i \(0.418691\pi\)
\(524\) −1.61209 −0.0704243
\(525\) 0.888481 0.0387765
\(526\) 17.9153 0.781142
\(527\) 1.28084 0.0557943
\(528\) −60.0686 −2.61415
\(529\) −2.27971 −0.0991180
\(530\) −7.49914 −0.325742
\(531\) 26.4319 1.14705
\(532\) 3.37190 0.146190
\(533\) −12.6564 −0.548208
\(534\) −64.7514 −2.80207
\(535\) 5.38180 0.232675
\(536\) −4.77511 −0.206253
\(537\) 18.4534 0.796323
\(538\) −28.3329 −1.22152
\(539\) −35.5200 −1.52996
\(540\) 0.389767 0.0167729
\(541\) −41.4991 −1.78418 −0.892092 0.451853i \(-0.850763\pi\)
−0.892092 + 0.451853i \(0.850763\pi\)
\(542\) 24.6673 1.05955
\(543\) −42.6527 −1.83040
\(544\) 2.36897 0.101569
\(545\) 5.90613 0.252991
\(546\) −6.43826 −0.275532
\(547\) −2.73715 −0.117032 −0.0585160 0.998286i \(-0.518637\pi\)
−0.0585160 + 0.998286i \(0.518637\pi\)
\(548\) −31.1102 −1.32896
\(549\) −9.02203 −0.385051
\(550\) −9.73307 −0.415019
\(551\) −53.9598 −2.29876
\(552\) 9.64411 0.410480
\(553\) −2.34870 −0.0998768
\(554\) 7.02493 0.298461
\(555\) −0.207298 −0.00879929
\(556\) −31.3055 −1.32765
\(557\) −43.1801 −1.82960 −0.914801 0.403905i \(-0.867652\pi\)
−0.914801 + 0.403905i \(0.867652\pi\)
\(558\) −22.5460 −0.954449
\(559\) −46.2150 −1.95469
\(560\) −1.69175 −0.0714894
\(561\) 4.23723 0.178896
\(562\) 13.0979 0.552503
\(563\) −9.14382 −0.385366 −0.192683 0.981261i \(-0.561719\pi\)
−0.192683 + 0.981261i \(0.561719\pi\)
\(564\) −36.5016 −1.53700
\(565\) 3.00127 0.126264
\(566\) −23.8770 −1.00363
\(567\) −3.12305 −0.131156
\(568\) −4.96063 −0.208143
\(569\) 9.36512 0.392606 0.196303 0.980543i \(-0.437106\pi\)
0.196303 + 0.980543i \(0.437106\pi\)
\(570\) −28.2302 −1.18243
\(571\) 21.7699 0.911041 0.455520 0.890225i \(-0.349453\pi\)
0.455520 + 0.890225i \(0.349453\pi\)
\(572\) 30.7322 1.28498
\(573\) −45.8992 −1.91747
\(574\) 2.22659 0.0929363
\(575\) 4.55195 0.189830
\(576\) −12.5171 −0.521547
\(577\) 38.2125 1.59081 0.795404 0.606080i \(-0.207259\pi\)
0.795404 + 0.606080i \(0.207259\pi\)
\(578\) 31.7981 1.32263
\(579\) −17.7435 −0.737395
\(580\) −13.7291 −0.570070
\(581\) 0.698488 0.0289782
\(582\) 0.609563 0.0252672
\(583\) 20.5927 0.852864
\(584\) 14.1328 0.584818
\(585\) 11.9402 0.493667
\(586\) 19.2844 0.796632
\(587\) −8.61476 −0.355569 −0.177785 0.984069i \(-0.556893\pi\)
−0.177785 + 0.984069i \(0.556893\pi\)
\(588\) −26.2125 −1.08099
\(589\) 23.4331 0.965543
\(590\) −16.0412 −0.660406
\(591\) 37.7009 1.55081
\(592\) 0.394713 0.0162226
\(593\) 34.9986 1.43722 0.718611 0.695413i \(-0.244778\pi\)
0.718611 + 0.695413i \(0.244778\pi\)
\(594\) −2.45632 −0.100784
\(595\) 0.119336 0.00489228
\(596\) 4.12086 0.168797
\(597\) −7.48940 −0.306521
\(598\) −32.9852 −1.34886
\(599\) −44.8538 −1.83268 −0.916339 0.400404i \(-0.868870\pi\)
−0.916339 + 0.400404i \(0.868870\pi\)
\(600\) 2.11867 0.0864945
\(601\) 34.1735 1.39396 0.696982 0.717088i \(-0.254526\pi\)
0.696982 + 0.717088i \(0.254526\pi\)
\(602\) 8.13046 0.331373
\(603\) −17.2713 −0.703343
\(604\) 0.236064 0.00960530
\(605\) 15.7271 0.639399
\(606\) 36.3305 1.47583
\(607\) −8.06230 −0.327239 −0.163619 0.986524i \(-0.552317\pi\)
−0.163619 + 0.986524i \(0.552317\pi\)
\(608\) 43.3404 1.75768
\(609\) −7.89806 −0.320046
\(610\) 5.47537 0.221691
\(611\) −36.8254 −1.48980
\(612\) 1.58964 0.0642574
\(613\) −34.7708 −1.40438 −0.702190 0.711989i \(-0.747794\pi\)
−0.702190 + 0.711989i \(0.747794\pi\)
\(614\) −25.8145 −1.04179
\(615\) −8.12276 −0.327541
\(616\) 1.59479 0.0642561
\(617\) 9.44795 0.380360 0.190180 0.981749i \(-0.439093\pi\)
0.190180 + 0.981749i \(0.439093\pi\)
\(618\) 64.4082 2.59088
\(619\) 25.7746 1.03597 0.517984 0.855390i \(-0.326683\pi\)
0.517984 + 0.855390i \(0.326683\pi\)
\(620\) 5.96213 0.239445
\(621\) 1.14877 0.0460985
\(622\) −4.68615 −0.187898
\(623\) 5.00771 0.200630
\(624\) −44.7217 −1.79030
\(625\) 1.00000 0.0400000
\(626\) −35.6358 −1.42429
\(627\) 77.5204 3.09587
\(628\) 19.1690 0.764926
\(629\) −0.0278430 −0.00111017
\(630\) −2.10060 −0.0836901
\(631\) 20.0942 0.799937 0.399969 0.916529i \(-0.369021\pi\)
0.399969 + 0.916529i \(0.369021\pi\)
\(632\) −5.60071 −0.222784
\(633\) −21.3335 −0.847930
\(634\) −40.1024 −1.59267
\(635\) −5.65507 −0.224414
\(636\) 15.1967 0.602590
\(637\) −26.4450 −1.04779
\(638\) 86.5211 3.42540
\(639\) −17.9423 −0.709788
\(640\) −6.68339 −0.264184
\(641\) −4.91683 −0.194203 −0.0971015 0.995274i \(-0.530957\pi\)
−0.0971015 + 0.995274i \(0.530957\pi\)
\(642\) −25.0290 −0.987814
\(643\) 43.2595 1.70599 0.852994 0.521922i \(-0.174785\pi\)
0.852994 + 0.521922i \(0.174785\pi\)
\(644\) 2.52857 0.0996394
\(645\) −29.6604 −1.16788
\(646\) −3.79171 −0.149183
\(647\) −35.4758 −1.39470 −0.697348 0.716732i \(-0.745637\pi\)
−0.697348 + 0.716732i \(0.745637\pi\)
\(648\) −7.44725 −0.292555
\(649\) 44.0493 1.72909
\(650\) −7.24638 −0.284226
\(651\) 3.42988 0.134428
\(652\) 8.43111 0.330188
\(653\) −18.8927 −0.739330 −0.369665 0.929165i \(-0.620528\pi\)
−0.369665 + 0.929165i \(0.620528\pi\)
\(654\) −27.4675 −1.07406
\(655\) −1.04380 −0.0407847
\(656\) 15.4665 0.603864
\(657\) 51.1175 1.99428
\(658\) 6.47858 0.252561
\(659\) 15.4408 0.601489 0.300744 0.953705i \(-0.402765\pi\)
0.300744 + 0.953705i \(0.402765\pi\)
\(660\) 19.7237 0.767744
\(661\) −46.9182 −1.82491 −0.912454 0.409179i \(-0.865815\pi\)
−0.912454 + 0.409179i \(0.865815\pi\)
\(662\) 42.8408 1.66505
\(663\) 3.15466 0.122517
\(664\) 1.66562 0.0646385
\(665\) 2.18325 0.0846629
\(666\) 0.490107 0.0189912
\(667\) −40.4641 −1.56678
\(668\) 13.4666 0.521039
\(669\) 25.1430 0.972084
\(670\) 10.4818 0.404946
\(671\) −15.0354 −0.580436
\(672\) 6.34370 0.244714
\(673\) 35.9705 1.38656 0.693281 0.720668i \(-0.256165\pi\)
0.693281 + 0.720668i \(0.256165\pi\)
\(674\) −27.4519 −1.05741
\(675\) 0.252368 0.00971365
\(676\) 2.80277 0.107799
\(677\) −35.8881 −1.37929 −0.689646 0.724146i \(-0.742234\pi\)
−0.689646 + 0.724146i \(0.742234\pi\)
\(678\) −13.9579 −0.536050
\(679\) −0.0471422 −0.00180915
\(680\) 0.284568 0.0109127
\(681\) 62.5796 2.39805
\(682\) −37.5735 −1.43876
\(683\) 8.62788 0.330137 0.165068 0.986282i \(-0.447216\pi\)
0.165068 + 0.986282i \(0.447216\pi\)
\(684\) 29.0826 1.11200
\(685\) −20.1434 −0.769641
\(686\) 9.39239 0.358603
\(687\) −49.7381 −1.89763
\(688\) 56.4761 2.15313
\(689\) 15.3315 0.584084
\(690\) −21.1696 −0.805914
\(691\) −9.07301 −0.345154 −0.172577 0.984996i \(-0.555209\pi\)
−0.172577 + 0.984996i \(0.555209\pi\)
\(692\) 40.0443 1.52226
\(693\) 5.76829 0.219119
\(694\) −19.2227 −0.729684
\(695\) −20.2698 −0.768879
\(696\) −18.8337 −0.713891
\(697\) −1.09100 −0.0413246
\(698\) 8.84467 0.334776
\(699\) −11.6576 −0.440931
\(700\) 0.555490 0.0209955
\(701\) 27.3340 1.03239 0.516195 0.856471i \(-0.327348\pi\)
0.516195 + 0.856471i \(0.327348\pi\)
\(702\) −1.82875 −0.0690219
\(703\) −0.509390 −0.0192120
\(704\) −20.8601 −0.786194
\(705\) −23.6343 −0.890118
\(706\) −62.5685 −2.35480
\(707\) −2.80971 −0.105670
\(708\) 32.5069 1.22168
\(709\) 29.4217 1.10495 0.552477 0.833528i \(-0.313683\pi\)
0.552477 + 0.833528i \(0.313683\pi\)
\(710\) 10.8890 0.408657
\(711\) −20.2575 −0.759715
\(712\) 11.9414 0.447523
\(713\) 17.5723 0.658089
\(714\) −0.554990 −0.0207700
\(715\) 19.8986 0.744167
\(716\) 11.5373 0.431170
\(717\) 11.7722 0.439640
\(718\) −36.0183 −1.34419
\(719\) −37.3915 −1.39447 −0.697234 0.716844i \(-0.745586\pi\)
−0.697234 + 0.716844i \(0.745586\pi\)
\(720\) −14.5913 −0.543786
\(721\) −4.98117 −0.185509
\(722\) −33.5990 −1.25042
\(723\) 18.2253 0.677807
\(724\) −26.6670 −0.991072
\(725\) −8.88940 −0.330144
\(726\) −73.1417 −2.71454
\(727\) −10.8008 −0.400579 −0.200289 0.979737i \(-0.564188\pi\)
−0.200289 + 0.979737i \(0.564188\pi\)
\(728\) 1.18734 0.0440058
\(729\) −28.8066 −1.06691
\(730\) −31.0226 −1.14820
\(731\) −3.98382 −0.147347
\(732\) −11.0956 −0.410106
\(733\) −9.70111 −0.358319 −0.179159 0.983820i \(-0.557338\pi\)
−0.179159 + 0.983820i \(0.557338\pi\)
\(734\) 33.2417 1.22697
\(735\) −16.9722 −0.626030
\(736\) 32.5007 1.19799
\(737\) −28.7831 −1.06024
\(738\) 19.2044 0.706922
\(739\) 14.9881 0.551347 0.275673 0.961251i \(-0.411099\pi\)
0.275673 + 0.961251i \(0.411099\pi\)
\(740\) −0.129605 −0.00476438
\(741\) 57.7148 2.12021
\(742\) −2.69723 −0.0990184
\(743\) 45.6383 1.67431 0.837153 0.546969i \(-0.184218\pi\)
0.837153 + 0.546969i \(0.184218\pi\)
\(744\) 8.17891 0.299853
\(745\) 2.66820 0.0977552
\(746\) 44.9772 1.64673
\(747\) 6.02445 0.220423
\(748\) 2.64917 0.0968633
\(749\) 1.93568 0.0707282
\(750\) −4.65067 −0.169818
\(751\) 44.6761 1.63026 0.815128 0.579281i \(-0.196667\pi\)
0.815128 + 0.579281i \(0.196667\pi\)
\(752\) 45.0018 1.64105
\(753\) 72.2936 2.63453
\(754\) 64.4159 2.34589
\(755\) 0.152848 0.00556270
\(756\) 0.140188 0.00509859
\(757\) −30.1368 −1.09534 −0.547670 0.836695i \(-0.684485\pi\)
−0.547670 + 0.836695i \(0.684485\pi\)
\(758\) 40.3566 1.46582
\(759\) 58.1321 2.11006
\(760\) 5.20619 0.188848
\(761\) −48.6214 −1.76253 −0.881263 0.472627i \(-0.843306\pi\)
−0.881263 + 0.472627i \(0.843306\pi\)
\(762\) 26.2998 0.952743
\(763\) 2.12427 0.0769036
\(764\) −28.6968 −1.03821
\(765\) 1.02927 0.0372133
\(766\) −71.5332 −2.58460
\(767\) 32.7952 1.18417
\(768\) 51.0170 1.84092
\(769\) −7.22344 −0.260484 −0.130242 0.991482i \(-0.541575\pi\)
−0.130242 + 0.991482i \(0.541575\pi\)
\(770\) −3.50071 −0.126157
\(771\) −5.16493 −0.186010
\(772\) −11.0935 −0.399263
\(773\) 17.2166 0.619238 0.309619 0.950861i \(-0.399798\pi\)
0.309619 + 0.950861i \(0.399798\pi\)
\(774\) 70.1251 2.52060
\(775\) 3.86039 0.138669
\(776\) −0.112415 −0.00403548
\(777\) −0.0745591 −0.00267479
\(778\) 36.0200 1.29138
\(779\) −19.9599 −0.715139
\(780\) 14.6845 0.525790
\(781\) −29.9013 −1.06995
\(782\) −2.84338 −0.101679
\(783\) −2.24340 −0.0801726
\(784\) 32.3166 1.15417
\(785\) 12.4116 0.442990
\(786\) 4.85438 0.173150
\(787\) −44.7451 −1.59499 −0.797495 0.603325i \(-0.793842\pi\)
−0.797495 + 0.603325i \(0.793842\pi\)
\(788\) 23.5711 0.839687
\(789\) −23.5067 −0.836860
\(790\) 12.2940 0.437402
\(791\) 1.07947 0.0383815
\(792\) 13.7551 0.488765
\(793\) −11.1940 −0.397512
\(794\) −44.3509 −1.57395
\(795\) 9.83966 0.348977
\(796\) −4.68247 −0.165966
\(797\) 5.42828 0.192280 0.0961399 0.995368i \(-0.469350\pi\)
0.0961399 + 0.995368i \(0.469350\pi\)
\(798\) −10.1536 −0.359433
\(799\) −3.17442 −0.112303
\(800\) 7.13995 0.252435
\(801\) 43.1915 1.52610
\(802\) 1.88267 0.0664793
\(803\) 85.1885 3.00624
\(804\) −21.2409 −0.749110
\(805\) 1.63721 0.0577040
\(806\) −27.9738 −0.985337
\(807\) 37.1757 1.30865
\(808\) −6.70005 −0.235707
\(809\) 23.0741 0.811243 0.405621 0.914041i \(-0.367055\pi\)
0.405621 + 0.914041i \(0.367055\pi\)
\(810\) 16.3473 0.574387
\(811\) 5.36379 0.188348 0.0941741 0.995556i \(-0.469979\pi\)
0.0941741 + 0.995556i \(0.469979\pi\)
\(812\) −4.93797 −0.173289
\(813\) −32.3660 −1.13513
\(814\) 0.816775 0.0286279
\(815\) 5.45902 0.191221
\(816\) −3.85509 −0.134955
\(817\) −72.8842 −2.54990
\(818\) 28.0928 0.982242
\(819\) 4.29455 0.150064
\(820\) −5.07846 −0.177347
\(821\) 16.0163 0.558974 0.279487 0.960150i \(-0.409836\pi\)
0.279487 + 0.960150i \(0.409836\pi\)
\(822\) 93.6804 3.26748
\(823\) −8.92417 −0.311077 −0.155538 0.987830i \(-0.549711\pi\)
−0.155538 + 0.987830i \(0.549711\pi\)
\(824\) −11.8781 −0.413794
\(825\) 12.7708 0.444622
\(826\) −5.76956 −0.200749
\(827\) −30.6036 −1.06419 −0.532096 0.846684i \(-0.678596\pi\)
−0.532096 + 0.846684i \(0.678596\pi\)
\(828\) 21.8088 0.757910
\(829\) −2.52311 −0.0876314 −0.0438157 0.999040i \(-0.513951\pi\)
−0.0438157 + 0.999040i \(0.513951\pi\)
\(830\) −3.65617 −0.126908
\(831\) −9.21744 −0.319749
\(832\) −15.5306 −0.538425
\(833\) −2.27961 −0.0789839
\(834\) 94.2683 3.26424
\(835\) 8.71943 0.301748
\(836\) 48.4668 1.67626
\(837\) 0.974240 0.0336746
\(838\) 73.9050 2.55300
\(839\) −12.9948 −0.448631 −0.224315 0.974517i \(-0.572015\pi\)
−0.224315 + 0.974517i \(0.572015\pi\)
\(840\) 0.762027 0.0262924
\(841\) 50.0214 1.72488
\(842\) −2.51564 −0.0866946
\(843\) −17.1859 −0.591912
\(844\) −13.3380 −0.459112
\(845\) 1.81475 0.0624293
\(846\) 55.8777 1.92111
\(847\) 5.65660 0.194363
\(848\) −18.7356 −0.643383
\(849\) 31.3291 1.07521
\(850\) −0.624651 −0.0214254
\(851\) −0.381989 −0.0130944
\(852\) −22.0661 −0.755973
\(853\) −38.7716 −1.32751 −0.663757 0.747948i \(-0.731039\pi\)
−0.663757 + 0.747948i \(0.731039\pi\)
\(854\) 1.96933 0.0673892
\(855\) 18.8305 0.643990
\(856\) 4.61583 0.157766
\(857\) −5.83115 −0.199188 −0.0995941 0.995028i \(-0.531754\pi\)
−0.0995941 + 0.995028i \(0.531754\pi\)
\(858\) −92.5420 −3.15933
\(859\) −9.47873 −0.323410 −0.161705 0.986839i \(-0.551699\pi\)
−0.161705 + 0.986839i \(0.551699\pi\)
\(860\) −18.5441 −0.632348
\(861\) −2.92152 −0.0995653
\(862\) −8.74385 −0.297817
\(863\) −23.6659 −0.805597 −0.402799 0.915289i \(-0.631963\pi\)
−0.402799 + 0.915289i \(0.631963\pi\)
\(864\) 1.80189 0.0613017
\(865\) 25.9281 0.881581
\(866\) 62.1639 2.11241
\(867\) −41.7224 −1.41697
\(868\) 2.14441 0.0727860
\(869\) −33.7596 −1.14522
\(870\) 41.3417 1.40161
\(871\) −21.4293 −0.726105
\(872\) 5.06553 0.171541
\(873\) −0.406601 −0.0137613
\(874\) −52.0199 −1.75960
\(875\) 0.359672 0.0121591
\(876\) 62.8661 2.12405
\(877\) 29.9042 1.00979 0.504897 0.863179i \(-0.331530\pi\)
0.504897 + 0.863179i \(0.331530\pi\)
\(878\) −0.440176 −0.0148552
\(879\) −25.3032 −0.853454
\(880\) −24.3167 −0.819717
\(881\) 16.5853 0.558774 0.279387 0.960179i \(-0.409869\pi\)
0.279387 + 0.960179i \(0.409869\pi\)
\(882\) 40.1269 1.35114
\(883\) 17.0913 0.575169 0.287584 0.957755i \(-0.407148\pi\)
0.287584 + 0.957755i \(0.407148\pi\)
\(884\) 1.97234 0.0663369
\(885\) 21.0477 0.707512
\(886\) 74.1441 2.49092
\(887\) 45.7489 1.53610 0.768049 0.640391i \(-0.221227\pi\)
0.768049 + 0.640391i \(0.221227\pi\)
\(888\) −0.177794 −0.00596637
\(889\) −2.03397 −0.0682170
\(890\) −26.2124 −0.878642
\(891\) −44.8900 −1.50387
\(892\) 15.7197 0.526335
\(893\) −58.0762 −1.94345
\(894\) −12.4089 −0.415016
\(895\) 7.47024 0.249703
\(896\) −2.40383 −0.0803062
\(897\) 43.2800 1.44508
\(898\) 42.4822 1.41765
\(899\) −34.3166 −1.14452
\(900\) 4.79109 0.159703
\(901\) 1.32161 0.0440291
\(902\) 32.0045 1.06563
\(903\) −10.6680 −0.355009
\(904\) 2.57411 0.0856136
\(905\) −17.2665 −0.573958
\(906\) −0.710844 −0.0236162
\(907\) −52.0051 −1.72680 −0.863400 0.504520i \(-0.831670\pi\)
−0.863400 + 0.504520i \(0.831670\pi\)
\(908\) 39.1256 1.29843
\(909\) −24.2337 −0.803783
\(910\) −2.60632 −0.0863985
\(911\) 18.5204 0.613608 0.306804 0.951773i \(-0.400740\pi\)
0.306804 + 0.951773i \(0.400740\pi\)
\(912\) −70.5292 −2.33546
\(913\) 10.0399 0.332272
\(914\) −27.7351 −0.917394
\(915\) −7.18425 −0.237504
\(916\) −31.0969 −1.02747
\(917\) −0.375426 −0.0123977
\(918\) −0.157642 −0.00520296
\(919\) 41.1033 1.35587 0.677937 0.735120i \(-0.262874\pi\)
0.677937 + 0.735120i \(0.262874\pi\)
\(920\) 3.90409 0.128714
\(921\) 33.8714 1.11610
\(922\) 49.9142 1.64384
\(923\) −22.2619 −0.732758
\(924\) 7.09405 0.233377
\(925\) −0.0839175 −0.00275919
\(926\) 46.4624 1.52685
\(927\) −42.9625 −1.41107
\(928\) −63.4698 −2.08350
\(929\) 39.6944 1.30233 0.651166 0.758935i \(-0.274280\pi\)
0.651166 + 0.758935i \(0.274280\pi\)
\(930\) −17.9534 −0.588715
\(931\) −41.7056 −1.36685
\(932\) −7.28848 −0.238742
\(933\) 6.14872 0.201300
\(934\) −10.0329 −0.328286
\(935\) 1.71530 0.0560963
\(936\) 10.2408 0.334731
\(937\) 9.73210 0.317934 0.158967 0.987284i \(-0.449184\pi\)
0.158967 + 0.987284i \(0.449184\pi\)
\(938\) 3.77000 0.123095
\(939\) 46.7579 1.52589
\(940\) −14.7765 −0.481955
\(941\) 42.3982 1.38214 0.691071 0.722787i \(-0.257139\pi\)
0.691071 + 0.722787i \(0.257139\pi\)
\(942\) −57.7224 −1.88070
\(943\) −14.9678 −0.487420
\(944\) −40.0768 −1.30439
\(945\) 0.0907696 0.00295274
\(946\) 116.865 3.79962
\(947\) 36.3265 1.18045 0.590227 0.807237i \(-0.299038\pi\)
0.590227 + 0.807237i \(0.299038\pi\)
\(948\) −24.9134 −0.809150
\(949\) 63.4238 2.05882
\(950\) −11.4280 −0.370774
\(951\) 52.6185 1.70627
\(952\) 0.102351 0.00331722
\(953\) −44.4553 −1.44005 −0.720025 0.693948i \(-0.755870\pi\)
−0.720025 + 0.693948i \(0.755870\pi\)
\(954\) −23.2636 −0.753186
\(955\) −18.5808 −0.601259
\(956\) 7.36011 0.238043
\(957\) −113.525 −3.66973
\(958\) −51.0683 −1.64994
\(959\) −7.24502 −0.233954
\(960\) −9.96740 −0.321696
\(961\) −16.0974 −0.519270
\(962\) 0.608098 0.0196059
\(963\) 16.6952 0.537995
\(964\) 11.3947 0.366999
\(965\) −7.18286 −0.231225
\(966\) −7.61412 −0.244980
\(967\) −37.5166 −1.20645 −0.603226 0.797571i \(-0.706118\pi\)
−0.603226 + 0.797571i \(0.706118\pi\)
\(968\) 13.4887 0.433545
\(969\) 4.97512 0.159824
\(970\) 0.246761 0.00792303
\(971\) 29.2648 0.939153 0.469576 0.882892i \(-0.344407\pi\)
0.469576 + 0.882892i \(0.344407\pi\)
\(972\) −34.2966 −1.10006
\(973\) −7.29048 −0.233722
\(974\) 16.6659 0.534010
\(975\) 9.50800 0.304500
\(976\) 13.6795 0.437869
\(977\) −48.6799 −1.55741 −0.778703 0.627392i \(-0.784122\pi\)
−0.778703 + 0.627392i \(0.784122\pi\)
\(978\) −25.3881 −0.811821
\(979\) 71.9796 2.30048
\(980\) −10.6113 −0.338964
\(981\) 18.3218 0.584969
\(982\) −10.3708 −0.330945
\(983\) −12.9095 −0.411750 −0.205875 0.978578i \(-0.566004\pi\)
−0.205875 + 0.978578i \(0.566004\pi\)
\(984\) −6.96668 −0.222089
\(985\) 15.2620 0.486286
\(986\) 5.55277 0.176836
\(987\) −8.50057 −0.270576
\(988\) 36.0840 1.14799
\(989\) −54.6554 −1.73794
\(990\) −30.1936 −0.959614
\(991\) −28.6531 −0.910194 −0.455097 0.890442i \(-0.650395\pi\)
−0.455097 + 0.890442i \(0.650395\pi\)
\(992\) 27.5630 0.875126
\(993\) −56.2115 −1.78382
\(994\) 3.91646 0.124223
\(995\) −3.03183 −0.0961155
\(996\) 7.40909 0.234766
\(997\) −24.0393 −0.761332 −0.380666 0.924713i \(-0.624305\pi\)
−0.380666 + 0.924713i \(0.624305\pi\)
\(998\) 55.3500 1.75207
\(999\) −0.0211781 −0.000670045 0
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 2005.2.a.g.1.7 37
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2005.2.a.g.1.7 37 1.1 even 1 trivial