Properties

Label 4034.2.a.c.1.18
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $0$
Dimension $49$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -0.604236 q^{3} +1.00000 q^{4} -1.43680 q^{5} +0.604236 q^{6} +3.64541 q^{7} -1.00000 q^{8} -2.63490 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -0.604236 q^{3} +1.00000 q^{4} -1.43680 q^{5} +0.604236 q^{6} +3.64541 q^{7} -1.00000 q^{8} -2.63490 q^{9} +1.43680 q^{10} +1.25520 q^{11} -0.604236 q^{12} +5.16126 q^{13} -3.64541 q^{14} +0.868169 q^{15} +1.00000 q^{16} -5.80826 q^{17} +2.63490 q^{18} +6.69723 q^{19} -1.43680 q^{20} -2.20269 q^{21} -1.25520 q^{22} +5.93367 q^{23} +0.604236 q^{24} -2.93559 q^{25} -5.16126 q^{26} +3.40481 q^{27} +3.64541 q^{28} +8.42225 q^{29} -0.868169 q^{30} -2.36368 q^{31} -1.00000 q^{32} -0.758437 q^{33} +5.80826 q^{34} -5.23774 q^{35} -2.63490 q^{36} +7.09569 q^{37} -6.69723 q^{38} -3.11862 q^{39} +1.43680 q^{40} -10.5916 q^{41} +2.20269 q^{42} -6.98296 q^{43} +1.25520 q^{44} +3.78583 q^{45} -5.93367 q^{46} -13.2976 q^{47} -0.604236 q^{48} +6.28900 q^{49} +2.93559 q^{50} +3.50956 q^{51} +5.16126 q^{52} +13.3065 q^{53} -3.40481 q^{54} -1.80348 q^{55} -3.64541 q^{56} -4.04671 q^{57} -8.42225 q^{58} +5.92430 q^{59} +0.868169 q^{60} +4.34325 q^{61} +2.36368 q^{62} -9.60528 q^{63} +1.00000 q^{64} -7.41572 q^{65} +0.758437 q^{66} +3.74536 q^{67} -5.80826 q^{68} -3.58534 q^{69} +5.23774 q^{70} -10.3568 q^{71} +2.63490 q^{72} +12.4391 q^{73} -7.09569 q^{74} +1.77379 q^{75} +6.69723 q^{76} +4.57572 q^{77} +3.11862 q^{78} -0.511714 q^{79} -1.43680 q^{80} +5.84739 q^{81} +10.5916 q^{82} -5.36832 q^{83} -2.20269 q^{84} +8.34533 q^{85} +6.98296 q^{86} -5.08903 q^{87} -1.25520 q^{88} +10.3756 q^{89} -3.78583 q^{90} +18.8149 q^{91} +5.93367 q^{92} +1.42822 q^{93} +13.2976 q^{94} -9.62261 q^{95} +0.604236 q^{96} -12.2990 q^{97} -6.28900 q^{98} -3.30732 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −0.604236 −0.348856 −0.174428 0.984670i \(-0.555808\pi\)
−0.174428 + 0.984670i \(0.555808\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.43680 −0.642558 −0.321279 0.946985i \(-0.604113\pi\)
−0.321279 + 0.946985i \(0.604113\pi\)
\(6\) 0.604236 0.246678
\(7\) 3.64541 1.37783 0.688917 0.724840i \(-0.258086\pi\)
0.688917 + 0.724840i \(0.258086\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.63490 −0.878300
\(10\) 1.43680 0.454357
\(11\) 1.25520 0.378457 0.189228 0.981933i \(-0.439401\pi\)
0.189228 + 0.981933i \(0.439401\pi\)
\(12\) −0.604236 −0.174428
\(13\) 5.16126 1.43148 0.715738 0.698369i \(-0.246090\pi\)
0.715738 + 0.698369i \(0.246090\pi\)
\(14\) −3.64541 −0.974276
\(15\) 0.868169 0.224160
\(16\) 1.00000 0.250000
\(17\) −5.80826 −1.40871 −0.704355 0.709848i \(-0.748764\pi\)
−0.704355 + 0.709848i \(0.748764\pi\)
\(18\) 2.63490 0.621052
\(19\) 6.69723 1.53645 0.768225 0.640179i \(-0.221140\pi\)
0.768225 + 0.640179i \(0.221140\pi\)
\(20\) −1.43680 −0.321279
\(21\) −2.20269 −0.480666
\(22\) −1.25520 −0.267609
\(23\) 5.93367 1.23725 0.618627 0.785684i \(-0.287689\pi\)
0.618627 + 0.785684i \(0.287689\pi\)
\(24\) 0.604236 0.123339
\(25\) −2.93559 −0.587119
\(26\) −5.16126 −1.01221
\(27\) 3.40481 0.655256
\(28\) 3.64541 0.688917
\(29\) 8.42225 1.56397 0.781986 0.623296i \(-0.214207\pi\)
0.781986 + 0.623296i \(0.214207\pi\)
\(30\) −0.868169 −0.158505
\(31\) −2.36368 −0.424529 −0.212264 0.977212i \(-0.568084\pi\)
−0.212264 + 0.977212i \(0.568084\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.758437 −0.132027
\(34\) 5.80826 0.996108
\(35\) −5.23774 −0.885339
\(36\) −2.63490 −0.439150
\(37\) 7.09569 1.16652 0.583262 0.812284i \(-0.301776\pi\)
0.583262 + 0.812284i \(0.301776\pi\)
\(38\) −6.69723 −1.08643
\(39\) −3.11862 −0.499379
\(40\) 1.43680 0.227179
\(41\) −10.5916 −1.65413 −0.827064 0.562108i \(-0.809990\pi\)
−0.827064 + 0.562108i \(0.809990\pi\)
\(42\) 2.20269 0.339882
\(43\) −6.98296 −1.06489 −0.532445 0.846464i \(-0.678727\pi\)
−0.532445 + 0.846464i \(0.678727\pi\)
\(44\) 1.25520 0.189228
\(45\) 3.78583 0.564359
\(46\) −5.93367 −0.874871
\(47\) −13.2976 −1.93965 −0.969827 0.243794i \(-0.921608\pi\)
−0.969827 + 0.243794i \(0.921608\pi\)
\(48\) −0.604236 −0.0872140
\(49\) 6.28900 0.898429
\(50\) 2.93559 0.415156
\(51\) 3.50956 0.491437
\(52\) 5.16126 0.715738
\(53\) 13.3065 1.82779 0.913896 0.405949i \(-0.133059\pi\)
0.913896 + 0.405949i \(0.133059\pi\)
\(54\) −3.40481 −0.463336
\(55\) −1.80348 −0.243181
\(56\) −3.64541 −0.487138
\(57\) −4.04671 −0.536000
\(58\) −8.42225 −1.10590
\(59\) 5.92430 0.771278 0.385639 0.922650i \(-0.373981\pi\)
0.385639 + 0.922650i \(0.373981\pi\)
\(60\) 0.868169 0.112080
\(61\) 4.34325 0.556097 0.278048 0.960567i \(-0.410312\pi\)
0.278048 + 0.960567i \(0.410312\pi\)
\(62\) 2.36368 0.300187
\(63\) −9.60528 −1.21015
\(64\) 1.00000 0.125000
\(65\) −7.41572 −0.919807
\(66\) 0.758437 0.0933572
\(67\) 3.74536 0.457569 0.228785 0.973477i \(-0.426525\pi\)
0.228785 + 0.973477i \(0.426525\pi\)
\(68\) −5.80826 −0.704355
\(69\) −3.58534 −0.431624
\(70\) 5.23774 0.626029
\(71\) −10.3568 −1.22912 −0.614561 0.788869i \(-0.710667\pi\)
−0.614561 + 0.788869i \(0.710667\pi\)
\(72\) 2.63490 0.310526
\(73\) 12.4391 1.45589 0.727943 0.685638i \(-0.240477\pi\)
0.727943 + 0.685638i \(0.240477\pi\)
\(74\) −7.09569 −0.824858
\(75\) 1.77379 0.204820
\(76\) 6.69723 0.768225
\(77\) 4.57572 0.521451
\(78\) 3.11862 0.353114
\(79\) −0.511714 −0.0575723 −0.0287862 0.999586i \(-0.509164\pi\)
−0.0287862 + 0.999586i \(0.509164\pi\)
\(80\) −1.43680 −0.160640
\(81\) 5.84739 0.649710
\(82\) 10.5916 1.16964
\(83\) −5.36832 −0.589250 −0.294625 0.955613i \(-0.595195\pi\)
−0.294625 + 0.955613i \(0.595195\pi\)
\(84\) −2.20269 −0.240333
\(85\) 8.34533 0.905178
\(86\) 6.98296 0.752991
\(87\) −5.08903 −0.545601
\(88\) −1.25520 −0.133805
\(89\) 10.3756 1.09981 0.549907 0.835226i \(-0.314663\pi\)
0.549907 + 0.835226i \(0.314663\pi\)
\(90\) −3.78583 −0.399062
\(91\) 18.8149 1.97234
\(92\) 5.93367 0.618627
\(93\) 1.42822 0.148099
\(94\) 13.2976 1.37154
\(95\) −9.62261 −0.987259
\(96\) 0.604236 0.0616696
\(97\) −12.2990 −1.24877 −0.624386 0.781116i \(-0.714651\pi\)
−0.624386 + 0.781116i \(0.714651\pi\)
\(98\) −6.28900 −0.635285
\(99\) −3.30732 −0.332399
\(100\) −2.93559 −0.293559
\(101\) −6.36043 −0.632887 −0.316443 0.948611i \(-0.602489\pi\)
−0.316443 + 0.948611i \(0.602489\pi\)
\(102\) −3.50956 −0.347498
\(103\) 9.09708 0.896362 0.448181 0.893943i \(-0.352072\pi\)
0.448181 + 0.893943i \(0.352072\pi\)
\(104\) −5.16126 −0.506103
\(105\) 3.16483 0.308856
\(106\) −13.3065 −1.29244
\(107\) −3.27920 −0.317012 −0.158506 0.987358i \(-0.550668\pi\)
−0.158506 + 0.987358i \(0.550668\pi\)
\(108\) 3.40481 0.327628
\(109\) −15.3607 −1.47129 −0.735646 0.677366i \(-0.763121\pi\)
−0.735646 + 0.677366i \(0.763121\pi\)
\(110\) 1.80348 0.171955
\(111\) −4.28747 −0.406949
\(112\) 3.64541 0.344459
\(113\) 6.23554 0.586591 0.293295 0.956022i \(-0.405248\pi\)
0.293295 + 0.956022i \(0.405248\pi\)
\(114\) 4.04671 0.379009
\(115\) −8.52552 −0.795008
\(116\) 8.42225 0.781986
\(117\) −13.5994 −1.25727
\(118\) −5.92430 −0.545376
\(119\) −21.1735 −1.94097
\(120\) −0.868169 −0.0792526
\(121\) −9.42447 −0.856770
\(122\) −4.34325 −0.393220
\(123\) 6.39982 0.577052
\(124\) −2.36368 −0.212264
\(125\) 11.4019 1.01982
\(126\) 9.60528 0.855706
\(127\) −10.1210 −0.898092 −0.449046 0.893509i \(-0.648236\pi\)
−0.449046 + 0.893509i \(0.648236\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.21935 0.371493
\(130\) 7.41572 0.650402
\(131\) 15.4757 1.35211 0.676057 0.736849i \(-0.263687\pi\)
0.676057 + 0.736849i \(0.263687\pi\)
\(132\) −0.758437 −0.0660135
\(133\) 24.4142 2.11698
\(134\) −3.74536 −0.323550
\(135\) −4.89204 −0.421040
\(136\) 5.80826 0.498054
\(137\) 6.90624 0.590040 0.295020 0.955491i \(-0.404674\pi\)
0.295020 + 0.955491i \(0.404674\pi\)
\(138\) 3.58534 0.305204
\(139\) 13.8548 1.17515 0.587573 0.809171i \(-0.300083\pi\)
0.587573 + 0.809171i \(0.300083\pi\)
\(140\) −5.23774 −0.442670
\(141\) 8.03489 0.676660
\(142\) 10.3568 0.869121
\(143\) 6.47842 0.541752
\(144\) −2.63490 −0.219575
\(145\) −12.1011 −1.00494
\(146\) −12.4391 −1.02947
\(147\) −3.80004 −0.313422
\(148\) 7.09569 0.583262
\(149\) −6.32983 −0.518560 −0.259280 0.965802i \(-0.583485\pi\)
−0.259280 + 0.965802i \(0.583485\pi\)
\(150\) −1.77379 −0.144830
\(151\) −8.72970 −0.710413 −0.355207 0.934788i \(-0.615589\pi\)
−0.355207 + 0.934788i \(0.615589\pi\)
\(152\) −6.69723 −0.543217
\(153\) 15.3042 1.23727
\(154\) −4.57572 −0.368722
\(155\) 3.39614 0.272785
\(156\) −3.11862 −0.249690
\(157\) 20.8602 1.66483 0.832413 0.554156i \(-0.186959\pi\)
0.832413 + 0.554156i \(0.186959\pi\)
\(158\) 0.511714 0.0407098
\(159\) −8.04028 −0.637636
\(160\) 1.43680 0.113589
\(161\) 21.6306 1.70473
\(162\) −5.84739 −0.459414
\(163\) −13.1918 −1.03326 −0.516629 0.856209i \(-0.672813\pi\)
−0.516629 + 0.856209i \(0.672813\pi\)
\(164\) −10.5916 −0.827064
\(165\) 1.08973 0.0848350
\(166\) 5.36832 0.416663
\(167\) −5.01703 −0.388229 −0.194115 0.980979i \(-0.562183\pi\)
−0.194115 + 0.980979i \(0.562183\pi\)
\(168\) 2.20269 0.169941
\(169\) 13.6386 1.04913
\(170\) −8.34533 −0.640058
\(171\) −17.6465 −1.34946
\(172\) −6.98296 −0.532445
\(173\) −15.6351 −1.18872 −0.594358 0.804201i \(-0.702594\pi\)
−0.594358 + 0.804201i \(0.702594\pi\)
\(174\) 5.08903 0.385798
\(175\) −10.7014 −0.808953
\(176\) 1.25520 0.0946142
\(177\) −3.57967 −0.269065
\(178\) −10.3756 −0.777686
\(179\) 7.24607 0.541597 0.270798 0.962636i \(-0.412712\pi\)
0.270798 + 0.962636i \(0.412712\pi\)
\(180\) 3.78583 0.282179
\(181\) 10.1106 0.751515 0.375757 0.926718i \(-0.377383\pi\)
0.375757 + 0.926718i \(0.377383\pi\)
\(182\) −18.8149 −1.39465
\(183\) −2.62435 −0.193998
\(184\) −5.93367 −0.437436
\(185\) −10.1951 −0.749560
\(186\) −1.42822 −0.104722
\(187\) −7.29052 −0.533136
\(188\) −13.2976 −0.969827
\(189\) 12.4119 0.902834
\(190\) 9.62261 0.698098
\(191\) −21.2628 −1.53852 −0.769261 0.638935i \(-0.779375\pi\)
−0.769261 + 0.638935i \(0.779375\pi\)
\(192\) −0.604236 −0.0436070
\(193\) 23.2946 1.67678 0.838390 0.545071i \(-0.183497\pi\)
0.838390 + 0.545071i \(0.183497\pi\)
\(194\) 12.2990 0.883015
\(195\) 4.48085 0.320880
\(196\) 6.28900 0.449214
\(197\) −6.08827 −0.433771 −0.216886 0.976197i \(-0.569590\pi\)
−0.216886 + 0.976197i \(0.569590\pi\)
\(198\) 3.30732 0.235041
\(199\) 21.0792 1.49426 0.747132 0.664675i \(-0.231430\pi\)
0.747132 + 0.664675i \(0.231430\pi\)
\(200\) 2.93559 0.207578
\(201\) −2.26308 −0.159626
\(202\) 6.36043 0.447518
\(203\) 30.7025 2.15490
\(204\) 3.50956 0.245718
\(205\) 15.2180 1.06287
\(206\) −9.09708 −0.633824
\(207\) −15.6346 −1.08668
\(208\) 5.16126 0.357869
\(209\) 8.40637 0.581480
\(210\) −3.16483 −0.218394
\(211\) 14.9328 1.02801 0.514007 0.857786i \(-0.328161\pi\)
0.514007 + 0.857786i \(0.328161\pi\)
\(212\) 13.3065 0.913896
\(213\) 6.25793 0.428787
\(214\) 3.27920 0.224162
\(215\) 10.0331 0.684254
\(216\) −3.40481 −0.231668
\(217\) −8.61657 −0.584931
\(218\) 15.3607 1.04036
\(219\) −7.51615 −0.507894
\(220\) −1.80348 −0.121590
\(221\) −29.9779 −2.01653
\(222\) 4.28747 0.287756
\(223\) −0.170298 −0.0114040 −0.00570199 0.999984i \(-0.501815\pi\)
−0.00570199 + 0.999984i \(0.501815\pi\)
\(224\) −3.64541 −0.243569
\(225\) 7.73499 0.515666
\(226\) −6.23554 −0.414782
\(227\) 15.9952 1.06164 0.530819 0.847485i \(-0.321884\pi\)
0.530819 + 0.847485i \(0.321884\pi\)
\(228\) −4.04671 −0.268000
\(229\) 17.4374 1.15230 0.576149 0.817345i \(-0.304555\pi\)
0.576149 + 0.817345i \(0.304555\pi\)
\(230\) 8.52552 0.562156
\(231\) −2.76481 −0.181911
\(232\) −8.42225 −0.552948
\(233\) 15.6646 1.02622 0.513110 0.858323i \(-0.328493\pi\)
0.513110 + 0.858323i \(0.328493\pi\)
\(234\) 13.5994 0.889021
\(235\) 19.1060 1.24634
\(236\) 5.92430 0.385639
\(237\) 0.309196 0.0200844
\(238\) 21.1735 1.37247
\(239\) 14.5533 0.941374 0.470687 0.882300i \(-0.344006\pi\)
0.470687 + 0.882300i \(0.344006\pi\)
\(240\) 0.868169 0.0560401
\(241\) −23.9038 −1.53978 −0.769889 0.638178i \(-0.779688\pi\)
−0.769889 + 0.638178i \(0.779688\pi\)
\(242\) 9.42447 0.605828
\(243\) −13.7476 −0.881911
\(244\) 4.34325 0.278048
\(245\) −9.03606 −0.577293
\(246\) −6.39982 −0.408037
\(247\) 34.5662 2.19939
\(248\) 2.36368 0.150094
\(249\) 3.24373 0.205563
\(250\) −11.4019 −0.721119
\(251\) 1.63167 0.102990 0.0514949 0.998673i \(-0.483601\pi\)
0.0514949 + 0.998673i \(0.483601\pi\)
\(252\) −9.60528 −0.605076
\(253\) 7.44794 0.468248
\(254\) 10.1210 0.635047
\(255\) −5.04255 −0.315777
\(256\) 1.00000 0.0625000
\(257\) 19.3390 1.20633 0.603167 0.797615i \(-0.293905\pi\)
0.603167 + 0.797615i \(0.293905\pi\)
\(258\) −4.21935 −0.262686
\(259\) 25.8667 1.60728
\(260\) −7.41572 −0.459904
\(261\) −22.1918 −1.37364
\(262\) −15.4757 −0.956089
\(263\) 0.734054 0.0452637 0.0226319 0.999744i \(-0.492795\pi\)
0.0226319 + 0.999744i \(0.492795\pi\)
\(264\) 0.758437 0.0466786
\(265\) −19.1189 −1.17446
\(266\) −24.4142 −1.49693
\(267\) −6.26933 −0.383677
\(268\) 3.74536 0.228785
\(269\) −25.4233 −1.55009 −0.775043 0.631908i \(-0.782272\pi\)
−0.775043 + 0.631908i \(0.782272\pi\)
\(270\) 4.89204 0.297720
\(271\) 11.6790 0.709448 0.354724 0.934971i \(-0.384575\pi\)
0.354724 + 0.934971i \(0.384575\pi\)
\(272\) −5.80826 −0.352177
\(273\) −11.3686 −0.688062
\(274\) −6.90624 −0.417221
\(275\) −3.68476 −0.222199
\(276\) −3.58534 −0.215812
\(277\) 18.4363 1.10773 0.553865 0.832606i \(-0.313152\pi\)
0.553865 + 0.832606i \(0.313152\pi\)
\(278\) −13.8548 −0.830954
\(279\) 6.22805 0.372864
\(280\) 5.23774 0.313015
\(281\) 3.55935 0.212333 0.106166 0.994348i \(-0.466142\pi\)
0.106166 + 0.994348i \(0.466142\pi\)
\(282\) −8.03489 −0.478471
\(283\) −18.2571 −1.08527 −0.542635 0.839969i \(-0.682573\pi\)
−0.542635 + 0.839969i \(0.682573\pi\)
\(284\) −10.3568 −0.614561
\(285\) 5.81433 0.344411
\(286\) −6.47842 −0.383077
\(287\) −38.6106 −2.27911
\(288\) 2.63490 0.155263
\(289\) 16.7359 0.984462
\(290\) 12.1011 0.710602
\(291\) 7.43148 0.435641
\(292\) 12.4391 0.727943
\(293\) 12.8218 0.749058 0.374529 0.927215i \(-0.377804\pi\)
0.374529 + 0.927215i \(0.377804\pi\)
\(294\) 3.80004 0.221623
\(295\) −8.51205 −0.495591
\(296\) −7.09569 −0.412429
\(297\) 4.27372 0.247986
\(298\) 6.32983 0.366677
\(299\) 30.6252 1.77110
\(300\) 1.77379 0.102410
\(301\) −25.4557 −1.46724
\(302\) 8.72970 0.502338
\(303\) 3.84320 0.220786
\(304\) 6.69723 0.384113
\(305\) −6.24040 −0.357325
\(306\) −15.3042 −0.874881
\(307\) 28.7357 1.64004 0.820018 0.572338i \(-0.193963\pi\)
0.820018 + 0.572338i \(0.193963\pi\)
\(308\) 4.57572 0.260726
\(309\) −5.49679 −0.312701
\(310\) −3.39614 −0.192888
\(311\) 16.3801 0.928828 0.464414 0.885618i \(-0.346265\pi\)
0.464414 + 0.885618i \(0.346265\pi\)
\(312\) 3.11862 0.176557
\(313\) 17.9921 1.01698 0.508488 0.861069i \(-0.330205\pi\)
0.508488 + 0.861069i \(0.330205\pi\)
\(314\) −20.8602 −1.17721
\(315\) 13.8009 0.777593
\(316\) −0.511714 −0.0287862
\(317\) −12.5951 −0.707409 −0.353705 0.935357i \(-0.615078\pi\)
−0.353705 + 0.935357i \(0.615078\pi\)
\(318\) 8.04028 0.450877
\(319\) 10.5716 0.591896
\(320\) −1.43680 −0.0803198
\(321\) 1.98141 0.110592
\(322\) −21.6306 −1.20543
\(323\) −38.8993 −2.16441
\(324\) 5.84739 0.324855
\(325\) −15.1514 −0.840447
\(326\) 13.1918 0.730624
\(327\) 9.28152 0.513269
\(328\) 10.5916 0.584822
\(329\) −48.4752 −2.67252
\(330\) −1.08973 −0.0599874
\(331\) 29.9652 1.64704 0.823518 0.567290i \(-0.192008\pi\)
0.823518 + 0.567290i \(0.192008\pi\)
\(332\) −5.36832 −0.294625
\(333\) −18.6964 −1.02456
\(334\) 5.01703 0.274519
\(335\) −5.38135 −0.294015
\(336\) −2.20269 −0.120166
\(337\) −8.61063 −0.469051 −0.234526 0.972110i \(-0.575354\pi\)
−0.234526 + 0.972110i \(0.575354\pi\)
\(338\) −13.6386 −0.741844
\(339\) −3.76774 −0.204636
\(340\) 8.34533 0.452589
\(341\) −2.96689 −0.160666
\(342\) 17.6465 0.954215
\(343\) −2.59188 −0.139948
\(344\) 6.98296 0.376496
\(345\) 5.15142 0.277343
\(346\) 15.6351 0.840548
\(347\) 16.3894 0.879827 0.439913 0.898040i \(-0.355009\pi\)
0.439913 + 0.898040i \(0.355009\pi\)
\(348\) −5.08903 −0.272800
\(349\) −22.7834 −1.21957 −0.609784 0.792568i \(-0.708744\pi\)
−0.609784 + 0.792568i \(0.708744\pi\)
\(350\) 10.7014 0.572016
\(351\) 17.5731 0.937984
\(352\) −1.25520 −0.0669024
\(353\) 13.7280 0.730668 0.365334 0.930877i \(-0.380955\pi\)
0.365334 + 0.930877i \(0.380955\pi\)
\(354\) 3.57967 0.190258
\(355\) 14.8806 0.789783
\(356\) 10.3756 0.549907
\(357\) 12.7938 0.677119
\(358\) −7.24607 −0.382967
\(359\) −1.25394 −0.0661802 −0.0330901 0.999452i \(-0.510535\pi\)
−0.0330901 + 0.999452i \(0.510535\pi\)
\(360\) −3.78583 −0.199531
\(361\) 25.8529 1.36068
\(362\) −10.1106 −0.531401
\(363\) 5.69461 0.298889
\(364\) 18.8149 0.986169
\(365\) −17.8725 −0.935491
\(366\) 2.62435 0.137177
\(367\) 37.2407 1.94395 0.971974 0.235089i \(-0.0755381\pi\)
0.971974 + 0.235089i \(0.0755381\pi\)
\(368\) 5.93367 0.309314
\(369\) 27.9077 1.45282
\(370\) 10.1951 0.530019
\(371\) 48.5077 2.51839
\(372\) 1.42822 0.0740497
\(373\) −29.4837 −1.52661 −0.763303 0.646041i \(-0.776424\pi\)
−0.763303 + 0.646041i \(0.776424\pi\)
\(374\) 7.29052 0.376984
\(375\) −6.88944 −0.355769
\(376\) 13.2976 0.685771
\(377\) 43.4694 2.23879
\(378\) −12.4119 −0.638400
\(379\) −18.9379 −0.972774 −0.486387 0.873744i \(-0.661685\pi\)
−0.486387 + 0.873744i \(0.661685\pi\)
\(380\) −9.62261 −0.493630
\(381\) 6.11547 0.313305
\(382\) 21.2628 1.08790
\(383\) −16.9575 −0.866487 −0.433244 0.901277i \(-0.642631\pi\)
−0.433244 + 0.901277i \(0.642631\pi\)
\(384\) 0.604236 0.0308348
\(385\) −6.57441 −0.335063
\(386\) −23.2946 −1.18566
\(387\) 18.3994 0.935293
\(388\) −12.2990 −0.624386
\(389\) 4.38067 0.222109 0.111054 0.993814i \(-0.464577\pi\)
0.111054 + 0.993814i \(0.464577\pi\)
\(390\) −4.48085 −0.226897
\(391\) −34.4643 −1.74293
\(392\) −6.28900 −0.317643
\(393\) −9.35095 −0.471693
\(394\) 6.08827 0.306723
\(395\) 0.735233 0.0369936
\(396\) −3.30732 −0.166199
\(397\) 8.28590 0.415858 0.207929 0.978144i \(-0.433328\pi\)
0.207929 + 0.978144i \(0.433328\pi\)
\(398\) −21.0792 −1.05660
\(399\) −14.7519 −0.738519
\(400\) −2.93559 −0.146780
\(401\) 16.7756 0.837731 0.418866 0.908048i \(-0.362428\pi\)
0.418866 + 0.908048i \(0.362428\pi\)
\(402\) 2.26308 0.112872
\(403\) −12.1996 −0.607703
\(404\) −6.36043 −0.316443
\(405\) −8.40155 −0.417476
\(406\) −30.7025 −1.52374
\(407\) 8.90651 0.441479
\(408\) −3.50956 −0.173749
\(409\) −27.2041 −1.34516 −0.672578 0.740027i \(-0.734813\pi\)
−0.672578 + 0.740027i \(0.734813\pi\)
\(410\) −15.2180 −0.751565
\(411\) −4.17300 −0.205839
\(412\) 9.09708 0.448181
\(413\) 21.5965 1.06269
\(414\) 15.6346 0.768399
\(415\) 7.71323 0.378627
\(416\) −5.16126 −0.253052
\(417\) −8.37156 −0.409957
\(418\) −8.40637 −0.411169
\(419\) 25.3846 1.24012 0.620059 0.784555i \(-0.287108\pi\)
0.620059 + 0.784555i \(0.287108\pi\)
\(420\) 3.16483 0.154428
\(421\) 34.7267 1.69248 0.846238 0.532805i \(-0.178862\pi\)
0.846238 + 0.532805i \(0.178862\pi\)
\(422\) −14.9328 −0.726915
\(423\) 35.0378 1.70360
\(424\) −13.3065 −0.646222
\(425\) 17.0507 0.827080
\(426\) −6.25793 −0.303198
\(427\) 15.8329 0.766209
\(428\) −3.27920 −0.158506
\(429\) −3.91449 −0.188994
\(430\) −10.0331 −0.483841
\(431\) 20.0671 0.966597 0.483299 0.875456i \(-0.339439\pi\)
0.483299 + 0.875456i \(0.339439\pi\)
\(432\) 3.40481 0.163814
\(433\) 7.70027 0.370051 0.185026 0.982734i \(-0.440763\pi\)
0.185026 + 0.982734i \(0.440763\pi\)
\(434\) 8.61657 0.413609
\(435\) 7.31193 0.350580
\(436\) −15.3607 −0.735646
\(437\) 39.7391 1.90098
\(438\) 7.51615 0.359135
\(439\) 6.62499 0.316193 0.158097 0.987424i \(-0.449464\pi\)
0.158097 + 0.987424i \(0.449464\pi\)
\(440\) 1.80348 0.0859774
\(441\) −16.5709 −0.789090
\(442\) 29.9779 1.42591
\(443\) 12.7949 0.607905 0.303953 0.952687i \(-0.401694\pi\)
0.303953 + 0.952687i \(0.401694\pi\)
\(444\) −4.28747 −0.203475
\(445\) −14.9078 −0.706695
\(446\) 0.170298 0.00806383
\(447\) 3.82471 0.180903
\(448\) 3.64541 0.172229
\(449\) 3.90612 0.184341 0.0921706 0.995743i \(-0.470619\pi\)
0.0921706 + 0.995743i \(0.470619\pi\)
\(450\) −7.73499 −0.364631
\(451\) −13.2946 −0.626016
\(452\) 6.23554 0.293295
\(453\) 5.27480 0.247832
\(454\) −15.9952 −0.750691
\(455\) −27.0333 −1.26734
\(456\) 4.04671 0.189505
\(457\) −11.3275 −0.529879 −0.264940 0.964265i \(-0.585352\pi\)
−0.264940 + 0.964265i \(0.585352\pi\)
\(458\) −17.4374 −0.814797
\(459\) −19.7760 −0.923065
\(460\) −8.52552 −0.397504
\(461\) 17.1518 0.798838 0.399419 0.916769i \(-0.369212\pi\)
0.399419 + 0.916769i \(0.369212\pi\)
\(462\) 2.76481 0.128631
\(463\) −36.7951 −1.71001 −0.855007 0.518616i \(-0.826447\pi\)
−0.855007 + 0.518616i \(0.826447\pi\)
\(464\) 8.42225 0.390993
\(465\) −2.05207 −0.0951625
\(466\) −15.6646 −0.725648
\(467\) 30.8429 1.42724 0.713620 0.700533i \(-0.247054\pi\)
0.713620 + 0.700533i \(0.247054\pi\)
\(468\) −13.5994 −0.628633
\(469\) 13.6534 0.630455
\(470\) −19.1060 −0.881296
\(471\) −12.6045 −0.580784
\(472\) −5.92430 −0.272688
\(473\) −8.76500 −0.403015
\(474\) −0.309196 −0.0142018
\(475\) −19.6604 −0.902079
\(476\) −21.1735 −0.970484
\(477\) −35.0613 −1.60535
\(478\) −14.5533 −0.665652
\(479\) 24.7595 1.13129 0.565644 0.824649i \(-0.308627\pi\)
0.565644 + 0.824649i \(0.308627\pi\)
\(480\) −0.868169 −0.0396263
\(481\) 36.6227 1.66985
\(482\) 23.9038 1.08879
\(483\) −13.0700 −0.594706
\(484\) −9.42447 −0.428385
\(485\) 17.6712 0.802408
\(486\) 13.7476 0.623605
\(487\) 32.5380 1.47444 0.737218 0.675654i \(-0.236139\pi\)
0.737218 + 0.675654i \(0.236139\pi\)
\(488\) −4.34325 −0.196610
\(489\) 7.97094 0.360458
\(490\) 9.03606 0.408208
\(491\) −14.6230 −0.659929 −0.329964 0.943993i \(-0.607037\pi\)
−0.329964 + 0.943993i \(0.607037\pi\)
\(492\) 6.39982 0.288526
\(493\) −48.9186 −2.20318
\(494\) −34.5662 −1.55521
\(495\) 4.75198 0.213585
\(496\) −2.36368 −0.106132
\(497\) −37.7546 −1.69353
\(498\) −3.24373 −0.145355
\(499\) −5.96238 −0.266913 −0.133456 0.991055i \(-0.542608\pi\)
−0.133456 + 0.991055i \(0.542608\pi\)
\(500\) 11.4019 0.509908
\(501\) 3.03147 0.135436
\(502\) −1.63167 −0.0728248
\(503\) −3.41382 −0.152215 −0.0761073 0.997100i \(-0.524249\pi\)
−0.0761073 + 0.997100i \(0.524249\pi\)
\(504\) 9.60528 0.427853
\(505\) 9.13869 0.406667
\(506\) −7.44794 −0.331101
\(507\) −8.24096 −0.365994
\(508\) −10.1210 −0.449046
\(509\) −13.1028 −0.580772 −0.290386 0.956910i \(-0.593784\pi\)
−0.290386 + 0.956910i \(0.593784\pi\)
\(510\) 5.04255 0.223288
\(511\) 45.3456 2.00597
\(512\) −1.00000 −0.0441942
\(513\) 22.8028 1.00677
\(514\) −19.3390 −0.853006
\(515\) −13.0707 −0.575965
\(516\) 4.21935 0.185747
\(517\) −16.6911 −0.734076
\(518\) −25.8667 −1.13652
\(519\) 9.44730 0.414690
\(520\) 7.41572 0.325201
\(521\) −33.6475 −1.47412 −0.737061 0.675826i \(-0.763787\pi\)
−0.737061 + 0.675826i \(0.763787\pi\)
\(522\) 22.1918 0.971307
\(523\) −5.33535 −0.233298 −0.116649 0.993173i \(-0.537215\pi\)
−0.116649 + 0.993173i \(0.537215\pi\)
\(524\) 15.4757 0.676057
\(525\) 6.46620 0.282208
\(526\) −0.734054 −0.0320063
\(527\) 13.7288 0.598038
\(528\) −0.758437 −0.0330067
\(529\) 12.2084 0.530800
\(530\) 19.1189 0.830470
\(531\) −15.6099 −0.677413
\(532\) 24.4142 1.05849
\(533\) −54.6659 −2.36784
\(534\) 6.26933 0.271301
\(535\) 4.71157 0.203699
\(536\) −3.74536 −0.161775
\(537\) −4.37834 −0.188939
\(538\) 25.4233 1.09608
\(539\) 7.89395 0.340017
\(540\) −4.89204 −0.210520
\(541\) 23.5305 1.01165 0.505827 0.862635i \(-0.331187\pi\)
0.505827 + 0.862635i \(0.331187\pi\)
\(542\) −11.6790 −0.501656
\(543\) −6.10919 −0.262170
\(544\) 5.80826 0.249027
\(545\) 22.0704 0.945391
\(546\) 11.3686 0.486533
\(547\) −18.4401 −0.788442 −0.394221 0.919016i \(-0.628986\pi\)
−0.394221 + 0.919016i \(0.628986\pi\)
\(548\) 6.90624 0.295020
\(549\) −11.4440 −0.488419
\(550\) 3.68476 0.157119
\(551\) 56.4058 2.40297
\(552\) 3.58534 0.152602
\(553\) −1.86541 −0.0793251
\(554\) −18.4363 −0.783284
\(555\) 6.16026 0.261489
\(556\) 13.8548 0.587573
\(557\) 13.6225 0.577203 0.288602 0.957449i \(-0.406810\pi\)
0.288602 + 0.957449i \(0.406810\pi\)
\(558\) −6.22805 −0.263654
\(559\) −36.0409 −1.52437
\(560\) −5.23774 −0.221335
\(561\) 4.40520 0.185988
\(562\) −3.55935 −0.150142
\(563\) 32.5236 1.37071 0.685353 0.728211i \(-0.259648\pi\)
0.685353 + 0.728211i \(0.259648\pi\)
\(564\) 8.03489 0.338330
\(565\) −8.95925 −0.376919
\(566\) 18.2571 0.767402
\(567\) 21.3161 0.895193
\(568\) 10.3568 0.434560
\(569\) −36.9267 −1.54805 −0.774024 0.633156i \(-0.781759\pi\)
−0.774024 + 0.633156i \(0.781759\pi\)
\(570\) −5.81433 −0.243536
\(571\) 9.27192 0.388018 0.194009 0.981000i \(-0.437851\pi\)
0.194009 + 0.981000i \(0.437851\pi\)
\(572\) 6.47842 0.270876
\(573\) 12.8478 0.536722
\(574\) 38.6106 1.61158
\(575\) −17.4188 −0.726416
\(576\) −2.63490 −0.109787
\(577\) −9.24587 −0.384911 −0.192455 0.981306i \(-0.561645\pi\)
−0.192455 + 0.981306i \(0.561645\pi\)
\(578\) −16.7359 −0.696120
\(579\) −14.0754 −0.584955
\(580\) −12.1011 −0.502472
\(581\) −19.5697 −0.811889
\(582\) −7.43148 −0.308045
\(583\) 16.7023 0.691740
\(584\) −12.4391 −0.514733
\(585\) 19.5397 0.807866
\(586\) −12.8218 −0.529664
\(587\) −4.81423 −0.198705 −0.0993523 0.995052i \(-0.531677\pi\)
−0.0993523 + 0.995052i \(0.531677\pi\)
\(588\) −3.80004 −0.156711
\(589\) −15.8301 −0.652268
\(590\) 8.51205 0.350436
\(591\) 3.67875 0.151324
\(592\) 7.09569 0.291631
\(593\) −21.1738 −0.869503 −0.434752 0.900550i \(-0.643164\pi\)
−0.434752 + 0.900550i \(0.643164\pi\)
\(594\) −4.27372 −0.175353
\(595\) 30.4221 1.24719
\(596\) −6.32983 −0.259280
\(597\) −12.7368 −0.521283
\(598\) −30.6252 −1.25236
\(599\) 21.8533 0.892902 0.446451 0.894808i \(-0.352688\pi\)
0.446451 + 0.894808i \(0.352688\pi\)
\(600\) −1.77379 −0.0724148
\(601\) −13.4413 −0.548280 −0.274140 0.961690i \(-0.588393\pi\)
−0.274140 + 0.961690i \(0.588393\pi\)
\(602\) 25.4557 1.03750
\(603\) −9.86866 −0.401883
\(604\) −8.72970 −0.355207
\(605\) 13.5411 0.550525
\(606\) −3.84320 −0.156119
\(607\) −24.7732 −1.00551 −0.502756 0.864428i \(-0.667681\pi\)
−0.502756 + 0.864428i \(0.667681\pi\)
\(608\) −6.69723 −0.271609
\(609\) −18.5516 −0.751748
\(610\) 6.24040 0.252667
\(611\) −68.6324 −2.77657
\(612\) 15.3042 0.618634
\(613\) 13.4739 0.544204 0.272102 0.962268i \(-0.412281\pi\)
0.272102 + 0.962268i \(0.412281\pi\)
\(614\) −28.7357 −1.15968
\(615\) −9.19528 −0.370790
\(616\) −4.57572 −0.184361
\(617\) −27.9390 −1.12478 −0.562391 0.826872i \(-0.690118\pi\)
−0.562391 + 0.826872i \(0.690118\pi\)
\(618\) 5.49679 0.221113
\(619\) 26.5867 1.06861 0.534304 0.845292i \(-0.320574\pi\)
0.534304 + 0.845292i \(0.320574\pi\)
\(620\) 3.39614 0.136392
\(621\) 20.2030 0.810719
\(622\) −16.3801 −0.656780
\(623\) 37.8234 1.51536
\(624\) −3.11862 −0.124845
\(625\) −1.70432 −0.0681728
\(626\) −17.9921 −0.719111
\(627\) −5.07943 −0.202853
\(628\) 20.8602 0.832413
\(629\) −41.2136 −1.64329
\(630\) −13.8009 −0.549841
\(631\) −17.6145 −0.701223 −0.350612 0.936521i \(-0.614026\pi\)
−0.350612 + 0.936521i \(0.614026\pi\)
\(632\) 0.511714 0.0203549
\(633\) −9.02291 −0.358629
\(634\) 12.5951 0.500214
\(635\) 14.5419 0.577077
\(636\) −8.04028 −0.318818
\(637\) 32.4592 1.28608
\(638\) −10.5716 −0.418534
\(639\) 27.2890 1.07954
\(640\) 1.43680 0.0567947
\(641\) 40.1910 1.58745 0.793724 0.608278i \(-0.208139\pi\)
0.793724 + 0.608278i \(0.208139\pi\)
\(642\) −1.98141 −0.0782001
\(643\) −47.6277 −1.87825 −0.939126 0.343574i \(-0.888363\pi\)
−0.939126 + 0.343574i \(0.888363\pi\)
\(644\) 21.6306 0.852366
\(645\) −6.06239 −0.238706
\(646\) 38.8993 1.53047
\(647\) −10.8067 −0.424854 −0.212427 0.977177i \(-0.568137\pi\)
−0.212427 + 0.977177i \(0.568137\pi\)
\(648\) −5.84739 −0.229707
\(649\) 7.43617 0.291895
\(650\) 15.1514 0.594286
\(651\) 5.20644 0.204057
\(652\) −13.1918 −0.516629
\(653\) 26.5205 1.03783 0.518914 0.854826i \(-0.326336\pi\)
0.518914 + 0.854826i \(0.326336\pi\)
\(654\) −9.28152 −0.362936
\(655\) −22.2355 −0.868812
\(656\) −10.5916 −0.413532
\(657\) −32.7757 −1.27870
\(658\) 48.4752 1.88976
\(659\) 21.3336 0.831038 0.415519 0.909584i \(-0.363600\pi\)
0.415519 + 0.909584i \(0.363600\pi\)
\(660\) 1.08973 0.0424175
\(661\) −25.6443 −0.997447 −0.498724 0.866761i \(-0.666198\pi\)
−0.498724 + 0.866761i \(0.666198\pi\)
\(662\) −29.9652 −1.16463
\(663\) 18.1138 0.703480
\(664\) 5.36832 0.208331
\(665\) −35.0784 −1.36028
\(666\) 18.6964 0.724472
\(667\) 49.9748 1.93503
\(668\) −5.01703 −0.194115
\(669\) 0.102900 0.00397834
\(670\) 5.38135 0.207900
\(671\) 5.45165 0.210459
\(672\) 2.20269 0.0849705
\(673\) −29.2008 −1.12561 −0.562805 0.826590i \(-0.690278\pi\)
−0.562805 + 0.826590i \(0.690278\pi\)
\(674\) 8.61063 0.331669
\(675\) −9.99514 −0.384713
\(676\) 13.6386 0.524563
\(677\) 5.13469 0.197342 0.0986711 0.995120i \(-0.468541\pi\)
0.0986711 + 0.995120i \(0.468541\pi\)
\(678\) 3.76774 0.144699
\(679\) −44.8348 −1.72060
\(680\) −8.34533 −0.320029
\(681\) −9.66487 −0.370359
\(682\) 2.96689 0.113608
\(683\) −36.5170 −1.39728 −0.698642 0.715472i \(-0.746212\pi\)
−0.698642 + 0.715472i \(0.746212\pi\)
\(684\) −17.6465 −0.674732
\(685\) −9.92291 −0.379135
\(686\) 2.59188 0.0989583
\(687\) −10.5363 −0.401986
\(688\) −6.98296 −0.266223
\(689\) 68.6785 2.61644
\(690\) −5.15142 −0.196111
\(691\) −45.0275 −1.71293 −0.856463 0.516208i \(-0.827343\pi\)
−0.856463 + 0.516208i \(0.827343\pi\)
\(692\) −15.6351 −0.594358
\(693\) −12.0565 −0.457990
\(694\) −16.3894 −0.622132
\(695\) −19.9066 −0.755100
\(696\) 5.08903 0.192899
\(697\) 61.5186 2.33018
\(698\) 22.7834 0.862365
\(699\) −9.46511 −0.358003
\(700\) −10.7014 −0.404476
\(701\) 2.23727 0.0845006 0.0422503 0.999107i \(-0.486547\pi\)
0.0422503 + 0.999107i \(0.486547\pi\)
\(702\) −17.5731 −0.663255
\(703\) 47.5215 1.79231
\(704\) 1.25520 0.0473071
\(705\) −11.5446 −0.434793
\(706\) −13.7280 −0.516660
\(707\) −23.1864 −0.872013
\(708\) −3.57967 −0.134532
\(709\) 20.3051 0.762575 0.381287 0.924457i \(-0.375481\pi\)
0.381287 + 0.924457i \(0.375481\pi\)
\(710\) −14.8806 −0.558461
\(711\) 1.34831 0.0505657
\(712\) −10.3756 −0.388843
\(713\) −14.0253 −0.525251
\(714\) −12.7938 −0.478795
\(715\) −9.30821 −0.348107
\(716\) 7.24607 0.270798
\(717\) −8.79363 −0.328404
\(718\) 1.25394 0.0467964
\(719\) −37.7728 −1.40869 −0.704343 0.709860i \(-0.748758\pi\)
−0.704343 + 0.709860i \(0.748758\pi\)
\(720\) 3.78583 0.141090
\(721\) 33.1626 1.23504
\(722\) −25.8529 −0.962147
\(723\) 14.4435 0.537160
\(724\) 10.1106 0.375757
\(725\) −24.7243 −0.918237
\(726\) −5.69461 −0.211347
\(727\) −7.60722 −0.282136 −0.141068 0.990000i \(-0.545054\pi\)
−0.141068 + 0.990000i \(0.545054\pi\)
\(728\) −18.8149 −0.697327
\(729\) −9.23534 −0.342050
\(730\) 17.8725 0.661492
\(731\) 40.5588 1.50012
\(732\) −2.62435 −0.0969988
\(733\) −23.1004 −0.853232 −0.426616 0.904433i \(-0.640294\pi\)
−0.426616 + 0.904433i \(0.640294\pi\)
\(734\) −37.2407 −1.37458
\(735\) 5.45992 0.201392
\(736\) −5.93367 −0.218718
\(737\) 4.70118 0.173170
\(738\) −27.9077 −1.02730
\(739\) −14.6479 −0.538831 −0.269416 0.963024i \(-0.586831\pi\)
−0.269416 + 0.963024i \(0.586831\pi\)
\(740\) −10.1951 −0.374780
\(741\) −20.8861 −0.767271
\(742\) −48.5077 −1.78077
\(743\) −36.8091 −1.35039 −0.675197 0.737637i \(-0.735941\pi\)
−0.675197 + 0.737637i \(0.735941\pi\)
\(744\) −1.42822 −0.0523611
\(745\) 9.09472 0.333205
\(746\) 29.4837 1.07947
\(747\) 14.1450 0.517538
\(748\) −7.29052 −0.266568
\(749\) −11.9540 −0.436791
\(750\) 6.88944 0.251567
\(751\) −22.6642 −0.827030 −0.413515 0.910497i \(-0.635699\pi\)
−0.413515 + 0.910497i \(0.635699\pi\)
\(752\) −13.2976 −0.484914
\(753\) −0.985912 −0.0359286
\(754\) −43.4694 −1.58306
\(755\) 12.5429 0.456482
\(756\) 12.4119 0.451417
\(757\) 23.5313 0.855259 0.427629 0.903954i \(-0.359349\pi\)
0.427629 + 0.903954i \(0.359349\pi\)
\(758\) 18.9379 0.687855
\(759\) −4.50031 −0.163351
\(760\) 9.62261 0.349049
\(761\) 45.9150 1.66442 0.832208 0.554464i \(-0.187077\pi\)
0.832208 + 0.554464i \(0.187077\pi\)
\(762\) −6.11547 −0.221540
\(763\) −55.9962 −2.02720
\(764\) −21.2628 −0.769261
\(765\) −21.9891 −0.795017
\(766\) 16.9575 0.612699
\(767\) 30.5768 1.10407
\(768\) −0.604236 −0.0218035
\(769\) 44.5169 1.60532 0.802660 0.596437i \(-0.203417\pi\)
0.802660 + 0.596437i \(0.203417\pi\)
\(770\) 6.57441 0.236925
\(771\) −11.6853 −0.420837
\(772\) 23.2946 0.838390
\(773\) 0.840719 0.0302386 0.0151193 0.999886i \(-0.495187\pi\)
0.0151193 + 0.999886i \(0.495187\pi\)
\(774\) −18.3994 −0.661352
\(775\) 6.93880 0.249249
\(776\) 12.2990 0.441507
\(777\) −15.6296 −0.560709
\(778\) −4.38067 −0.157054
\(779\) −70.9343 −2.54149
\(780\) 4.48085 0.160440
\(781\) −12.9998 −0.465170
\(782\) 34.4643 1.23244
\(783\) 28.6761 1.02480
\(784\) 6.28900 0.224607
\(785\) −29.9720 −1.06975
\(786\) 9.35095 0.333537
\(787\) −49.6311 −1.76916 −0.884578 0.466392i \(-0.845554\pi\)
−0.884578 + 0.466392i \(0.845554\pi\)
\(788\) −6.08827 −0.216886
\(789\) −0.443542 −0.0157905
\(790\) −0.735233 −0.0261584
\(791\) 22.7311 0.808225
\(792\) 3.30732 0.117521
\(793\) 22.4167 0.796039
\(794\) −8.28590 −0.294056
\(795\) 11.5523 0.409718
\(796\) 21.0792 0.747132
\(797\) −1.52550 −0.0540362 −0.0270181 0.999635i \(-0.508601\pi\)
−0.0270181 + 0.999635i \(0.508601\pi\)
\(798\) 14.7519 0.522212
\(799\) 77.2359 2.73241
\(800\) 2.93559 0.103789
\(801\) −27.3387 −0.965967
\(802\) −16.7756 −0.592365
\(803\) 15.6135 0.550990
\(804\) −2.26308 −0.0798128
\(805\) −31.0790 −1.09539
\(806\) 12.1996 0.429711
\(807\) 15.3617 0.540757
\(808\) 6.36043 0.223759
\(809\) 37.6212 1.32269 0.661346 0.750081i \(-0.269985\pi\)
0.661346 + 0.750081i \(0.269985\pi\)
\(810\) 8.40155 0.295200
\(811\) 32.2386 1.13205 0.566025 0.824388i \(-0.308481\pi\)
0.566025 + 0.824388i \(0.308481\pi\)
\(812\) 30.7025 1.07745
\(813\) −7.05687 −0.247495
\(814\) −8.90651 −0.312173
\(815\) 18.9540 0.663929
\(816\) 3.50956 0.122859
\(817\) −46.7665 −1.63615
\(818\) 27.2041 0.951168
\(819\) −49.5754 −1.73230
\(820\) 15.2180 0.531437
\(821\) −0.740478 −0.0258429 −0.0129214 0.999917i \(-0.504113\pi\)
−0.0129214 + 0.999917i \(0.504113\pi\)
\(822\) 4.17300 0.145550
\(823\) −28.0508 −0.977790 −0.488895 0.872343i \(-0.662600\pi\)
−0.488895 + 0.872343i \(0.662600\pi\)
\(824\) −9.09708 −0.316912
\(825\) 2.22646 0.0775155
\(826\) −21.5965 −0.751438
\(827\) 9.27975 0.322688 0.161344 0.986898i \(-0.448417\pi\)
0.161344 + 0.986898i \(0.448417\pi\)
\(828\) −15.6346 −0.543340
\(829\) 18.4664 0.641364 0.320682 0.947187i \(-0.396088\pi\)
0.320682 + 0.947187i \(0.396088\pi\)
\(830\) −7.71323 −0.267730
\(831\) −11.1399 −0.386438
\(832\) 5.16126 0.178935
\(833\) −36.5281 −1.26563
\(834\) 8.37156 0.289883
\(835\) 7.20848 0.249460
\(836\) 8.40637 0.290740
\(837\) −8.04787 −0.278175
\(838\) −25.3846 −0.876897
\(839\) 26.1233 0.901876 0.450938 0.892555i \(-0.351090\pi\)
0.450938 + 0.892555i \(0.351090\pi\)
\(840\) −3.16483 −0.109197
\(841\) 41.9342 1.44601
\(842\) −34.7267 −1.19676
\(843\) −2.15069 −0.0740736
\(844\) 14.9328 0.514007
\(845\) −19.5960 −0.674124
\(846\) −35.0378 −1.20463
\(847\) −34.3561 −1.18049
\(848\) 13.3065 0.456948
\(849\) 11.0316 0.378603
\(850\) −17.0507 −0.584834
\(851\) 42.1035 1.44329
\(852\) 6.25793 0.214393
\(853\) 17.0664 0.584342 0.292171 0.956366i \(-0.405622\pi\)
0.292171 + 0.956366i \(0.405622\pi\)
\(854\) −15.8329 −0.541792
\(855\) 25.3546 0.867109
\(856\) 3.27920 0.112081
\(857\) −50.0097 −1.70830 −0.854150 0.520027i \(-0.825922\pi\)
−0.854150 + 0.520027i \(0.825922\pi\)
\(858\) 3.91449 0.133639
\(859\) −28.0648 −0.957560 −0.478780 0.877935i \(-0.658921\pi\)
−0.478780 + 0.877935i \(0.658921\pi\)
\(860\) 10.0331 0.342127
\(861\) 23.3299 0.795082
\(862\) −20.0671 −0.683487
\(863\) −25.3345 −0.862397 −0.431198 0.902257i \(-0.641909\pi\)
−0.431198 + 0.902257i \(0.641909\pi\)
\(864\) −3.40481 −0.115834
\(865\) 22.4646 0.763819
\(866\) −7.70027 −0.261666
\(867\) −10.1124 −0.343435
\(868\) −8.61657 −0.292465
\(869\) −0.642303 −0.0217886
\(870\) −7.31193 −0.247898
\(871\) 19.3308 0.654999
\(872\) 15.3607 0.520181
\(873\) 32.4065 1.09680
\(874\) −39.7391 −1.34420
\(875\) 41.5646 1.40514
\(876\) −7.51615 −0.253947
\(877\) 45.4841 1.53589 0.767945 0.640516i \(-0.221279\pi\)
0.767945 + 0.640516i \(0.221279\pi\)
\(878\) −6.62499 −0.223583
\(879\) −7.74740 −0.261313
\(880\) −1.80348 −0.0607952
\(881\) 24.9893 0.841912 0.420956 0.907081i \(-0.361695\pi\)
0.420956 + 0.907081i \(0.361695\pi\)
\(882\) 16.5709 0.557971
\(883\) −41.2111 −1.38686 −0.693432 0.720522i \(-0.743902\pi\)
−0.693432 + 0.720522i \(0.743902\pi\)
\(884\) −29.9779 −1.00827
\(885\) 5.14329 0.172890
\(886\) −12.7949 −0.429854
\(887\) 8.50083 0.285430 0.142715 0.989764i \(-0.454417\pi\)
0.142715 + 0.989764i \(0.454417\pi\)
\(888\) 4.28747 0.143878
\(889\) −36.8951 −1.23742
\(890\) 14.9078 0.499709
\(891\) 7.33964 0.245887
\(892\) −0.170298 −0.00570199
\(893\) −89.0571 −2.98018
\(894\) −3.82471 −0.127917
\(895\) −10.4112 −0.348007
\(896\) −3.64541 −0.121785
\(897\) −18.5049 −0.617859
\(898\) −3.90612 −0.130349
\(899\) −19.9075 −0.663951
\(900\) 7.73499 0.257833
\(901\) −77.2877 −2.57483
\(902\) 13.2946 0.442660
\(903\) 15.3813 0.511857
\(904\) −6.23554 −0.207391
\(905\) −14.5269 −0.482892
\(906\) −5.27480 −0.175244
\(907\) 7.58359 0.251809 0.125904 0.992042i \(-0.459817\pi\)
0.125904 + 0.992042i \(0.459817\pi\)
\(908\) 15.9952 0.530819
\(909\) 16.7591 0.555864
\(910\) 27.0333 0.896147
\(911\) 12.0184 0.398187 0.199094 0.979980i \(-0.436200\pi\)
0.199094 + 0.979980i \(0.436200\pi\)
\(912\) −4.04671 −0.134000
\(913\) −6.73832 −0.223006
\(914\) 11.3275 0.374681
\(915\) 3.77068 0.124655
\(916\) 17.4374 0.576149
\(917\) 56.4151 1.86299
\(918\) 19.7760 0.652706
\(919\) −36.7776 −1.21318 −0.606591 0.795014i \(-0.707463\pi\)
−0.606591 + 0.795014i \(0.707463\pi\)
\(920\) 8.52552 0.281078
\(921\) −17.3632 −0.572136
\(922\) −17.1518 −0.564864
\(923\) −53.4540 −1.75946
\(924\) −2.76481 −0.0909557
\(925\) −20.8301 −0.684889
\(926\) 36.7951 1.20916
\(927\) −23.9699 −0.787274
\(928\) −8.42225 −0.276474
\(929\) −17.2955 −0.567448 −0.283724 0.958906i \(-0.591570\pi\)
−0.283724 + 0.958906i \(0.591570\pi\)
\(930\) 2.05207 0.0672901
\(931\) 42.1189 1.38039
\(932\) 15.6646 0.513110
\(933\) −9.89742 −0.324027
\(934\) −30.8429 −1.00921
\(935\) 10.4751 0.342571
\(936\) 13.5994 0.444510
\(937\) −2.89678 −0.0946336 −0.0473168 0.998880i \(-0.515067\pi\)
−0.0473168 + 0.998880i \(0.515067\pi\)
\(938\) −13.6534 −0.445799
\(939\) −10.8715 −0.354778
\(940\) 19.1060 0.623170
\(941\) −11.1406 −0.363172 −0.181586 0.983375i \(-0.558123\pi\)
−0.181586 + 0.983375i \(0.558123\pi\)
\(942\) 12.6045 0.410677
\(943\) −62.8469 −2.04658
\(944\) 5.92430 0.192819
\(945\) −17.8335 −0.580124
\(946\) 8.76500 0.284975
\(947\) −30.1415 −0.979468 −0.489734 0.871872i \(-0.662906\pi\)
−0.489734 + 0.871872i \(0.662906\pi\)
\(948\) 0.309196 0.0100422
\(949\) 64.2014 2.08407
\(950\) 19.6604 0.637866
\(951\) 7.61040 0.246784
\(952\) 21.1735 0.686236
\(953\) −47.6824 −1.54458 −0.772292 0.635268i \(-0.780890\pi\)
−0.772292 + 0.635268i \(0.780890\pi\)
\(954\) 35.0613 1.13515
\(955\) 30.5505 0.988590
\(956\) 14.5533 0.470687
\(957\) −6.38774 −0.206486
\(958\) −24.7595 −0.799942
\(959\) 25.1760 0.812977
\(960\) 0.868169 0.0280200
\(961\) −25.4130 −0.819775
\(962\) −36.6227 −1.18076
\(963\) 8.64036 0.278432
\(964\) −23.9038 −0.769889
\(965\) −33.4697 −1.07743
\(966\) 13.0700 0.420521
\(967\) 7.62412 0.245175 0.122588 0.992458i \(-0.460881\pi\)
0.122588 + 0.992458i \(0.460881\pi\)
\(968\) 9.42447 0.302914
\(969\) 23.5043 0.755068
\(970\) −17.6712 −0.567388
\(971\) −1.00004 −0.0320927 −0.0160464 0.999871i \(-0.505108\pi\)
−0.0160464 + 0.999871i \(0.505108\pi\)
\(972\) −13.7476 −0.440955
\(973\) 50.5063 1.61916
\(974\) −32.5380 −1.04258
\(975\) 9.15501 0.293195
\(976\) 4.34325 0.139024
\(977\) −3.08999 −0.0988574 −0.0494287 0.998778i \(-0.515740\pi\)
−0.0494287 + 0.998778i \(0.515740\pi\)
\(978\) −7.97094 −0.254883
\(979\) 13.0235 0.416233
\(980\) −9.03606 −0.288646
\(981\) 40.4740 1.29224
\(982\) 14.6230 0.466640
\(983\) 24.2772 0.774321 0.387161 0.922012i \(-0.373456\pi\)
0.387161 + 0.922012i \(0.373456\pi\)
\(984\) −6.39982 −0.204019
\(985\) 8.74765 0.278723
\(986\) 48.9186 1.55789
\(987\) 29.2905 0.932325
\(988\) 34.5662 1.09970
\(989\) −41.4345 −1.31754
\(990\) −4.75198 −0.151028
\(991\) −44.3775 −1.40970 −0.704850 0.709357i \(-0.748985\pi\)
−0.704850 + 0.709357i \(0.748985\pi\)
\(992\) 2.36368 0.0750468
\(993\) −18.1060 −0.574578
\(994\) 37.7546 1.19750
\(995\) −30.2867 −0.960152
\(996\) 3.24373 0.102782
\(997\) −3.52797 −0.111732 −0.0558660 0.998438i \(-0.517792\pi\)
−0.0558660 + 0.998438i \(0.517792\pi\)
\(998\) 5.96238 0.188736
\(999\) 24.1595 0.764372
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 4034.2.a.c.1.18 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.c.1.18 49 1.1 even 1 trivial