Properties

Label 6018.2.a.x.1.4
Level $6018$
Weight $2$
Character 6018.1
Self dual yes
Analytic conductor $48.054$
Analytic rank $0$
Dimension $10$
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] = [6018,2,Mod(1,6018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6018.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} - 34x^{8} + 30x^{7} + 341x^{6} - 276x^{5} - 1032x^{4} + 1176x^{3} + 416x^{2} - 896x + 272 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-0.976160\) of defining polynomial
Character \(\chi\) \(=\) 6018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.976160 q^{5} +1.00000 q^{6} -3.87477 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.976160 q^{5} +1.00000 q^{6} -3.87477 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.976160 q^{10} -0.0200581 q^{11} -1.00000 q^{12} +4.09284 q^{13} +3.87477 q^{14} +0.976160 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} +4.76012 q^{19} -0.976160 q^{20} +3.87477 q^{21} +0.0200581 q^{22} -0.204808 q^{23} +1.00000 q^{24} -4.04711 q^{25} -4.09284 q^{26} -1.00000 q^{27} -3.87477 q^{28} -6.91994 q^{29} -0.976160 q^{30} +1.87253 q^{31} -1.00000 q^{32} +0.0200581 q^{33} -1.00000 q^{34} +3.78240 q^{35} +1.00000 q^{36} -0.0763691 q^{37} -4.76012 q^{38} -4.09284 q^{39} +0.976160 q^{40} +1.72765 q^{41} -3.87477 q^{42} +0.671491 q^{43} -0.0200581 q^{44} -0.976160 q^{45} +0.204808 q^{46} +10.7654 q^{47} -1.00000 q^{48} +8.01388 q^{49} +4.04711 q^{50} -1.00000 q^{51} +4.09284 q^{52} -3.54134 q^{53} +1.00000 q^{54} +0.0195800 q^{55} +3.87477 q^{56} -4.76012 q^{57} +6.91994 q^{58} -1.00000 q^{59} +0.976160 q^{60} -6.17734 q^{61} -1.87253 q^{62} -3.87477 q^{63} +1.00000 q^{64} -3.99526 q^{65} -0.0200581 q^{66} -2.36212 q^{67} +1.00000 q^{68} +0.204808 q^{69} -3.78240 q^{70} -10.9512 q^{71} -1.00000 q^{72} +3.32488 q^{73} +0.0763691 q^{74} +4.04711 q^{75} +4.76012 q^{76} +0.0777208 q^{77} +4.09284 q^{78} -9.33941 q^{79} -0.976160 q^{80} +1.00000 q^{81} -1.72765 q^{82} -2.90996 q^{83} +3.87477 q^{84} -0.976160 q^{85} -0.671491 q^{86} +6.91994 q^{87} +0.0200581 q^{88} -13.8917 q^{89} +0.976160 q^{90} -15.8588 q^{91} -0.204808 q^{92} -1.87253 q^{93} -10.7654 q^{94} -4.64664 q^{95} +1.00000 q^{96} +6.56510 q^{97} -8.01388 q^{98} -0.0200581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + q^{5} + 10 q^{6} + 10 q^{7} - 10 q^{8} + 10 q^{9} - q^{10} + 2 q^{11} - 10 q^{12} - 10 q^{14} - q^{15} + 10 q^{16} + 10 q^{17} - 10 q^{18} + 15 q^{19} + q^{20} - 10 q^{21} - 2 q^{22} + 19 q^{23} + 10 q^{24} + 19 q^{25} - 10 q^{27} + 10 q^{28} - q^{29} + q^{30} + 15 q^{31} - 10 q^{32} - 2 q^{33} - 10 q^{34} - 14 q^{35} + 10 q^{36} + q^{37} - 15 q^{38} - q^{40} - 5 q^{41} + 10 q^{42} + 26 q^{43} + 2 q^{44} + q^{45} - 19 q^{46} + 14 q^{47} - 10 q^{48} + 20 q^{49} - 19 q^{50} - 10 q^{51} - 2 q^{53} + 10 q^{54} + 4 q^{55} - 10 q^{56} - 15 q^{57} + q^{58} - 10 q^{59} - q^{60} + 4 q^{61} - 15 q^{62} + 10 q^{63} + 10 q^{64} - 20 q^{65} + 2 q^{66} + 15 q^{67} + 10 q^{68} - 19 q^{69} + 14 q^{70} + 14 q^{71} - 10 q^{72} + 43 q^{73} - q^{74} - 19 q^{75} + 15 q^{76} + 20 q^{77} + q^{80} + 10 q^{81} + 5 q^{82} - 4 q^{83} - 10 q^{84} + q^{85} - 26 q^{86} + q^{87} - 2 q^{88} - 22 q^{89} - q^{90} - q^{91} + 19 q^{92} - 15 q^{93} - 14 q^{94} - 37 q^{95} + 10 q^{96} + 37 q^{97} - 20 q^{98} + 2 q^{99}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −0.976160 −0.436552 −0.218276 0.975887i \(-0.570043\pi\)
−0.218276 + 0.975887i \(0.570043\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.87477 −1.46453 −0.732264 0.681021i \(-0.761536\pi\)
−0.732264 + 0.681021i \(0.761536\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 0.976160 0.308689
\(11\) −0.0200581 −0.00604776 −0.00302388 0.999995i \(-0.500963\pi\)
−0.00302388 + 0.999995i \(0.500963\pi\)
\(12\) −1.00000 −0.288675
\(13\) 4.09284 1.13515 0.567574 0.823322i \(-0.307882\pi\)
0.567574 + 0.823322i \(0.307882\pi\)
\(14\) 3.87477 1.03558
\(15\) 0.976160 0.252043
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 4.76012 1.09205 0.546024 0.837770i \(-0.316141\pi\)
0.546024 + 0.837770i \(0.316141\pi\)
\(20\) −0.976160 −0.218276
\(21\) 3.87477 0.845545
\(22\) 0.0200581 0.00427641
\(23\) −0.204808 −0.0427054 −0.0213527 0.999772i \(-0.506797\pi\)
−0.0213527 + 0.999772i \(0.506797\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.04711 −0.809422
\(26\) −4.09284 −0.802671
\(27\) −1.00000 −0.192450
\(28\) −3.87477 −0.732264
\(29\) −6.91994 −1.28500 −0.642500 0.766285i \(-0.722103\pi\)
−0.642500 + 0.766285i \(0.722103\pi\)
\(30\) −0.976160 −0.178222
\(31\) 1.87253 0.336315 0.168158 0.985760i \(-0.446218\pi\)
0.168158 + 0.985760i \(0.446218\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.0200581 0.00349167
\(34\) −1.00000 −0.171499
\(35\) 3.78240 0.639342
\(36\) 1.00000 0.166667
\(37\) −0.0763691 −0.0125550 −0.00627750 0.999980i \(-0.501998\pi\)
−0.00627750 + 0.999980i \(0.501998\pi\)
\(38\) −4.76012 −0.772194
\(39\) −4.09284 −0.655378
\(40\) 0.976160 0.154344
\(41\) 1.72765 0.269814 0.134907 0.990858i \(-0.456926\pi\)
0.134907 + 0.990858i \(0.456926\pi\)
\(42\) −3.87477 −0.597891
\(43\) 0.671491 0.102401 0.0512007 0.998688i \(-0.483695\pi\)
0.0512007 + 0.998688i \(0.483695\pi\)
\(44\) −0.0200581 −0.00302388
\(45\) −0.976160 −0.145517
\(46\) 0.204808 0.0301973
\(47\) 10.7654 1.57029 0.785145 0.619312i \(-0.212588\pi\)
0.785145 + 0.619312i \(0.212588\pi\)
\(48\) −1.00000 −0.144338
\(49\) 8.01388 1.14484
\(50\) 4.04711 0.572348
\(51\) −1.00000 −0.140028
\(52\) 4.09284 0.567574
\(53\) −3.54134 −0.486440 −0.243220 0.969971i \(-0.578204\pi\)
−0.243220 + 0.969971i \(0.578204\pi\)
\(54\) 1.00000 0.136083
\(55\) 0.0195800 0.00264016
\(56\) 3.87477 0.517789
\(57\) −4.76012 −0.630494
\(58\) 6.91994 0.908633
\(59\) −1.00000 −0.130189
\(60\) 0.976160 0.126022
\(61\) −6.17734 −0.790928 −0.395464 0.918482i \(-0.629416\pi\)
−0.395464 + 0.918482i \(0.629416\pi\)
\(62\) −1.87253 −0.237811
\(63\) −3.87477 −0.488176
\(64\) 1.00000 0.125000
\(65\) −3.99526 −0.495551
\(66\) −0.0200581 −0.00246899
\(67\) −2.36212 −0.288579 −0.144290 0.989535i \(-0.546090\pi\)
−0.144290 + 0.989535i \(0.546090\pi\)
\(68\) 1.00000 0.121268
\(69\) 0.204808 0.0246560
\(70\) −3.78240 −0.452083
\(71\) −10.9512 −1.29967 −0.649837 0.760074i \(-0.725163\pi\)
−0.649837 + 0.760074i \(0.725163\pi\)
\(72\) −1.00000 −0.117851
\(73\) 3.32488 0.389147 0.194574 0.980888i \(-0.437668\pi\)
0.194574 + 0.980888i \(0.437668\pi\)
\(74\) 0.0763691 0.00887773
\(75\) 4.04711 0.467320
\(76\) 4.76012 0.546024
\(77\) 0.0777208 0.00885710
\(78\) 4.09284 0.463422
\(79\) −9.33941 −1.05077 −0.525383 0.850866i \(-0.676078\pi\)
−0.525383 + 0.850866i \(0.676078\pi\)
\(80\) −0.976160 −0.109138
\(81\) 1.00000 0.111111
\(82\) −1.72765 −0.190787
\(83\) −2.90996 −0.319409 −0.159705 0.987165i \(-0.551054\pi\)
−0.159705 + 0.987165i \(0.551054\pi\)
\(84\) 3.87477 0.422773
\(85\) −0.976160 −0.105879
\(86\) −0.671491 −0.0724088
\(87\) 6.91994 0.741895
\(88\) 0.0200581 0.00213820
\(89\) −13.8917 −1.47252 −0.736261 0.676698i \(-0.763410\pi\)
−0.736261 + 0.676698i \(0.763410\pi\)
\(90\) 0.976160 0.102896
\(91\) −15.8588 −1.66246
\(92\) −0.204808 −0.0213527
\(93\) −1.87253 −0.194172
\(94\) −10.7654 −1.11036
\(95\) −4.64664 −0.476736
\(96\) 1.00000 0.102062
\(97\) 6.56510 0.666584 0.333292 0.942824i \(-0.391840\pi\)
0.333292 + 0.942824i \(0.391840\pi\)
\(98\) −8.01388 −0.809524
\(99\) −0.0200581 −0.00201592
\(100\) −4.04711 −0.404711
\(101\) 2.28999 0.227862 0.113931 0.993489i \(-0.463656\pi\)
0.113931 + 0.993489i \(0.463656\pi\)
\(102\) 1.00000 0.0990148
\(103\) 9.40392 0.926596 0.463298 0.886203i \(-0.346666\pi\)
0.463298 + 0.886203i \(0.346666\pi\)
\(104\) −4.09284 −0.401336
\(105\) −3.78240 −0.369125
\(106\) 3.54134 0.343965
\(107\) −10.6637 −1.03090 −0.515451 0.856919i \(-0.672376\pi\)
−0.515451 + 0.856919i \(0.672376\pi\)
\(108\) −1.00000 −0.0962250
\(109\) −10.2720 −0.983879 −0.491940 0.870629i \(-0.663712\pi\)
−0.491940 + 0.870629i \(0.663712\pi\)
\(110\) −0.0195800 −0.00186688
\(111\) 0.0763691 0.00724864
\(112\) −3.87477 −0.366132
\(113\) −14.4538 −1.35970 −0.679848 0.733353i \(-0.737954\pi\)
−0.679848 + 0.733353i \(0.737954\pi\)
\(114\) 4.76012 0.445827
\(115\) 0.199925 0.0186431
\(116\) −6.91994 −0.642500
\(117\) 4.09284 0.378383
\(118\) 1.00000 0.0920575
\(119\) −3.87477 −0.355200
\(120\) −0.976160 −0.0891108
\(121\) −10.9996 −0.999963
\(122\) 6.17734 0.559270
\(123\) −1.72765 −0.155777
\(124\) 1.87253 0.168158
\(125\) 8.83143 0.789907
\(126\) 3.87477 0.345192
\(127\) 11.0071 0.976724 0.488362 0.872641i \(-0.337594\pi\)
0.488362 + 0.872641i \(0.337594\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.671491 −0.0591215
\(130\) 3.99526 0.350408
\(131\) 9.73289 0.850367 0.425183 0.905107i \(-0.360210\pi\)
0.425183 + 0.905107i \(0.360210\pi\)
\(132\) 0.0200581 0.00174584
\(133\) −18.4444 −1.59933
\(134\) 2.36212 0.204056
\(135\) 0.976160 0.0840145
\(136\) −1.00000 −0.0857493
\(137\) 17.5945 1.50320 0.751602 0.659617i \(-0.229282\pi\)
0.751602 + 0.659617i \(0.229282\pi\)
\(138\) −0.204808 −0.0174344
\(139\) 18.6395 1.58098 0.790489 0.612476i \(-0.209826\pi\)
0.790489 + 0.612476i \(0.209826\pi\)
\(140\) 3.78240 0.319671
\(141\) −10.7654 −0.906607
\(142\) 10.9512 0.919008
\(143\) −0.0820947 −0.00686510
\(144\) 1.00000 0.0833333
\(145\) 6.75497 0.560970
\(146\) −3.32488 −0.275169
\(147\) −8.01388 −0.660974
\(148\) −0.0763691 −0.00627750
\(149\) 11.1125 0.910374 0.455187 0.890396i \(-0.349572\pi\)
0.455187 + 0.890396i \(0.349572\pi\)
\(150\) −4.04711 −0.330445
\(151\) 15.4133 1.25432 0.627159 0.778891i \(-0.284218\pi\)
0.627159 + 0.778891i \(0.284218\pi\)
\(152\) −4.76012 −0.386097
\(153\) 1.00000 0.0808452
\(154\) −0.0777208 −0.00626292
\(155\) −1.82788 −0.146819
\(156\) −4.09284 −0.327689
\(157\) −1.24776 −0.0995818 −0.0497909 0.998760i \(-0.515855\pi\)
−0.0497909 + 0.998760i \(0.515855\pi\)
\(158\) 9.33941 0.743003
\(159\) 3.54134 0.280847
\(160\) 0.976160 0.0771722
\(161\) 0.793584 0.0625432
\(162\) −1.00000 −0.0785674
\(163\) 7.89843 0.618653 0.309327 0.950956i \(-0.399896\pi\)
0.309327 + 0.950956i \(0.399896\pi\)
\(164\) 1.72765 0.134907
\(165\) −0.0195800 −0.00152430
\(166\) 2.90996 0.225856
\(167\) −23.7000 −1.83396 −0.916980 0.398934i \(-0.869380\pi\)
−0.916980 + 0.398934i \(0.869380\pi\)
\(168\) −3.87477 −0.298945
\(169\) 3.75130 0.288562
\(170\) 0.976160 0.0748681
\(171\) 4.76012 0.364016
\(172\) 0.671491 0.0512007
\(173\) 24.3272 1.84956 0.924780 0.380501i \(-0.124249\pi\)
0.924780 + 0.380501i \(0.124249\pi\)
\(174\) −6.91994 −0.524599
\(175\) 15.6816 1.18542
\(176\) −0.0200581 −0.00151194
\(177\) 1.00000 0.0751646
\(178\) 13.8917 1.04123
\(179\) −26.2696 −1.96348 −0.981741 0.190222i \(-0.939079\pi\)
−0.981741 + 0.190222i \(0.939079\pi\)
\(180\) −0.976160 −0.0727587
\(181\) −10.5798 −0.786390 −0.393195 0.919455i \(-0.628630\pi\)
−0.393195 + 0.919455i \(0.628630\pi\)
\(182\) 15.8588 1.17553
\(183\) 6.17734 0.456642
\(184\) 0.204808 0.0150986
\(185\) 0.0745485 0.00548091
\(186\) 1.87253 0.137300
\(187\) −0.0200581 −0.00146680
\(188\) 10.7654 0.785145
\(189\) 3.87477 0.281848
\(190\) 4.64664 0.337103
\(191\) 18.5956 1.34553 0.672767 0.739854i \(-0.265106\pi\)
0.672767 + 0.739854i \(0.265106\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −10.0613 −0.724226 −0.362113 0.932134i \(-0.617945\pi\)
−0.362113 + 0.932134i \(0.617945\pi\)
\(194\) −6.56510 −0.471346
\(195\) 3.99526 0.286107
\(196\) 8.01388 0.572420
\(197\) 12.4837 0.889424 0.444712 0.895674i \(-0.353306\pi\)
0.444712 + 0.895674i \(0.353306\pi\)
\(198\) 0.0200581 0.00142547
\(199\) 12.8824 0.913208 0.456604 0.889670i \(-0.349066\pi\)
0.456604 + 0.889670i \(0.349066\pi\)
\(200\) 4.04711 0.286174
\(201\) 2.36212 0.166611
\(202\) −2.28999 −0.161123
\(203\) 26.8132 1.88192
\(204\) −1.00000 −0.0700140
\(205\) −1.68647 −0.117788
\(206\) −9.40392 −0.655202
\(207\) −0.204808 −0.0142351
\(208\) 4.09284 0.283787
\(209\) −0.0954792 −0.00660444
\(210\) 3.78240 0.261010
\(211\) 21.2253 1.46121 0.730606 0.682799i \(-0.239237\pi\)
0.730606 + 0.682799i \(0.239237\pi\)
\(212\) −3.54134 −0.243220
\(213\) 10.9512 0.750367
\(214\) 10.6637 0.728958
\(215\) −0.655483 −0.0447036
\(216\) 1.00000 0.0680414
\(217\) −7.25561 −0.492543
\(218\) 10.2720 0.695708
\(219\) −3.32488 −0.224674
\(220\) 0.0195800 0.00132008
\(221\) 4.09284 0.275314
\(222\) −0.0763691 −0.00512556
\(223\) 24.7471 1.65719 0.828595 0.559848i \(-0.189140\pi\)
0.828595 + 0.559848i \(0.189140\pi\)
\(224\) 3.87477 0.258894
\(225\) −4.04711 −0.269807
\(226\) 14.4538 0.961451
\(227\) 0.782040 0.0519058 0.0259529 0.999663i \(-0.491738\pi\)
0.0259529 + 0.999663i \(0.491738\pi\)
\(228\) −4.76012 −0.315247
\(229\) 1.67635 0.110776 0.0553882 0.998465i \(-0.482360\pi\)
0.0553882 + 0.998465i \(0.482360\pi\)
\(230\) −0.199925 −0.0131827
\(231\) −0.0777208 −0.00511365
\(232\) 6.91994 0.454316
\(233\) −2.77060 −0.181508 −0.0907539 0.995873i \(-0.528928\pi\)
−0.0907539 + 0.995873i \(0.528928\pi\)
\(234\) −4.09284 −0.267557
\(235\) −10.5087 −0.685513
\(236\) −1.00000 −0.0650945
\(237\) 9.33941 0.606660
\(238\) 3.87477 0.251164
\(239\) −0.488210 −0.0315796 −0.0157898 0.999875i \(-0.505026\pi\)
−0.0157898 + 0.999875i \(0.505026\pi\)
\(240\) 0.976160 0.0630109
\(241\) −18.6888 −1.20385 −0.601925 0.798553i \(-0.705599\pi\)
−0.601925 + 0.798553i \(0.705599\pi\)
\(242\) 10.9996 0.707081
\(243\) −1.00000 −0.0641500
\(244\) −6.17734 −0.395464
\(245\) −7.82283 −0.499782
\(246\) 1.72765 0.110151
\(247\) 19.4824 1.23964
\(248\) −1.87253 −0.118905
\(249\) 2.90996 0.184411
\(250\) −8.83143 −0.558549
\(251\) −9.79196 −0.618063 −0.309032 0.951052i \(-0.600005\pi\)
−0.309032 + 0.951052i \(0.600005\pi\)
\(252\) −3.87477 −0.244088
\(253\) 0.00410806 0.000258272 0
\(254\) −11.0071 −0.690648
\(255\) 0.976160 0.0611295
\(256\) 1.00000 0.0625000
\(257\) −5.93389 −0.370146 −0.185073 0.982725i \(-0.559252\pi\)
−0.185073 + 0.982725i \(0.559252\pi\)
\(258\) 0.671491 0.0418052
\(259\) 0.295913 0.0183872
\(260\) −3.99526 −0.247776
\(261\) −6.91994 −0.428334
\(262\) −9.73289 −0.601300
\(263\) 0.685091 0.0422445 0.0211223 0.999777i \(-0.493276\pi\)
0.0211223 + 0.999777i \(0.493276\pi\)
\(264\) −0.0200581 −0.00123449
\(265\) 3.45692 0.212357
\(266\) 18.4444 1.13090
\(267\) 13.8917 0.850161
\(268\) −2.36212 −0.144290
\(269\) 5.05267 0.308067 0.154034 0.988066i \(-0.450774\pi\)
0.154034 + 0.988066i \(0.450774\pi\)
\(270\) −0.976160 −0.0594072
\(271\) −19.1778 −1.16497 −0.582485 0.812841i \(-0.697920\pi\)
−0.582485 + 0.812841i \(0.697920\pi\)
\(272\) 1.00000 0.0606339
\(273\) 15.8588 0.959819
\(274\) −17.5945 −1.06293
\(275\) 0.0811775 0.00489519
\(276\) 0.204808 0.0123280
\(277\) 5.02496 0.301921 0.150960 0.988540i \(-0.451763\pi\)
0.150960 + 0.988540i \(0.451763\pi\)
\(278\) −18.6395 −1.11792
\(279\) 1.87253 0.112105
\(280\) −3.78240 −0.226042
\(281\) −29.8736 −1.78211 −0.891055 0.453895i \(-0.850034\pi\)
−0.891055 + 0.453895i \(0.850034\pi\)
\(282\) 10.7654 0.641068
\(283\) 9.35241 0.555943 0.277971 0.960589i \(-0.410338\pi\)
0.277971 + 0.960589i \(0.410338\pi\)
\(284\) −10.9512 −0.649837
\(285\) 4.64664 0.275243
\(286\) 0.0820947 0.00485436
\(287\) −6.69427 −0.395150
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −6.75497 −0.396665
\(291\) −6.56510 −0.384853
\(292\) 3.32488 0.194574
\(293\) −19.7447 −1.15350 −0.576749 0.816921i \(-0.695679\pi\)
−0.576749 + 0.816921i \(0.695679\pi\)
\(294\) 8.01388 0.467379
\(295\) 0.976160 0.0568342
\(296\) 0.0763691 0.00443887
\(297\) 0.0200581 0.00116389
\(298\) −11.1125 −0.643732
\(299\) −0.838244 −0.0484769
\(300\) 4.04711 0.233660
\(301\) −2.60188 −0.149970
\(302\) −15.4133 −0.886936
\(303\) −2.28999 −0.131556
\(304\) 4.76012 0.273012
\(305\) 6.03008 0.345281
\(306\) −1.00000 −0.0571662
\(307\) 26.3420 1.50342 0.751708 0.659497i \(-0.229230\pi\)
0.751708 + 0.659497i \(0.229230\pi\)
\(308\) 0.0777208 0.00442855
\(309\) −9.40392 −0.534970
\(310\) 1.82788 0.103817
\(311\) 22.5144 1.27668 0.638338 0.769756i \(-0.279622\pi\)
0.638338 + 0.769756i \(0.279622\pi\)
\(312\) 4.09284 0.231711
\(313\) 16.9101 0.955814 0.477907 0.878411i \(-0.341396\pi\)
0.477907 + 0.878411i \(0.341396\pi\)
\(314\) 1.24776 0.0704150
\(315\) 3.78240 0.213114
\(316\) −9.33941 −0.525383
\(317\) −1.50973 −0.0847947 −0.0423974 0.999101i \(-0.513500\pi\)
−0.0423974 + 0.999101i \(0.513500\pi\)
\(318\) −3.54134 −0.198588
\(319\) 0.138801 0.00777137
\(320\) −0.976160 −0.0545690
\(321\) 10.6637 0.595191
\(322\) −0.793584 −0.0442247
\(323\) 4.76012 0.264860
\(324\) 1.00000 0.0555556
\(325\) −16.5642 −0.918814
\(326\) −7.89843 −0.437454
\(327\) 10.2720 0.568043
\(328\) −1.72765 −0.0953937
\(329\) −41.7134 −2.29973
\(330\) 0.0195800 0.00107784
\(331\) 14.9957 0.824239 0.412120 0.911130i \(-0.364789\pi\)
0.412120 + 0.911130i \(0.364789\pi\)
\(332\) −2.90996 −0.159705
\(333\) −0.0763691 −0.00418500
\(334\) 23.7000 1.29681
\(335\) 2.30581 0.125980
\(336\) 3.87477 0.211386
\(337\) −32.0030 −1.74331 −0.871657 0.490117i \(-0.836954\pi\)
−0.871657 + 0.490117i \(0.836954\pi\)
\(338\) −3.75130 −0.204044
\(339\) 14.4538 0.785021
\(340\) −0.976160 −0.0529397
\(341\) −0.0375594 −0.00203395
\(342\) −4.76012 −0.257398
\(343\) −3.92855 −0.212122
\(344\) −0.671491 −0.0362044
\(345\) −0.199925 −0.0107636
\(346\) −24.3272 −1.30784
\(347\) 7.08683 0.380441 0.190220 0.981741i \(-0.439080\pi\)
0.190220 + 0.981741i \(0.439080\pi\)
\(348\) 6.91994 0.370948
\(349\) 35.6085 1.90608 0.953040 0.302845i \(-0.0979365\pi\)
0.953040 + 0.302845i \(0.0979365\pi\)
\(350\) −15.6816 −0.838219
\(351\) −4.09284 −0.218459
\(352\) 0.0200581 0.00106910
\(353\) 32.3000 1.71916 0.859579 0.511003i \(-0.170726\pi\)
0.859579 + 0.511003i \(0.170726\pi\)
\(354\) −1.00000 −0.0531494
\(355\) 10.6902 0.567376
\(356\) −13.8917 −0.736261
\(357\) 3.87477 0.205075
\(358\) 26.2696 1.38839
\(359\) −25.2748 −1.33395 −0.666976 0.745079i \(-0.732412\pi\)
−0.666976 + 0.745079i \(0.732412\pi\)
\(360\) 0.976160 0.0514482
\(361\) 3.65879 0.192568
\(362\) 10.5798 0.556061
\(363\) 10.9996 0.577329
\(364\) −15.8588 −0.831228
\(365\) −3.24561 −0.169883
\(366\) −6.17734 −0.322895
\(367\) 16.9270 0.883580 0.441790 0.897119i \(-0.354344\pi\)
0.441790 + 0.897119i \(0.354344\pi\)
\(368\) −0.204808 −0.0106763
\(369\) 1.72765 0.0899381
\(370\) −0.0745485 −0.00387559
\(371\) 13.7219 0.712405
\(372\) −1.87253 −0.0970859
\(373\) −1.60953 −0.0833383 −0.0416691 0.999131i \(-0.513268\pi\)
−0.0416691 + 0.999131i \(0.513268\pi\)
\(374\) 0.0200581 0.00103718
\(375\) −8.83143 −0.456053
\(376\) −10.7654 −0.555181
\(377\) −28.3222 −1.45867
\(378\) −3.87477 −0.199297
\(379\) −5.76769 −0.296266 −0.148133 0.988967i \(-0.547326\pi\)
−0.148133 + 0.988967i \(0.547326\pi\)
\(380\) −4.64664 −0.238368
\(381\) −11.0071 −0.563912
\(382\) −18.5956 −0.951436
\(383\) 29.1366 1.48881 0.744405 0.667728i \(-0.232733\pi\)
0.744405 + 0.667728i \(0.232733\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.0758679 −0.00386659
\(386\) 10.0613 0.512105
\(387\) 0.671491 0.0341338
\(388\) 6.56510 0.333292
\(389\) 15.2183 0.771600 0.385800 0.922582i \(-0.373925\pi\)
0.385800 + 0.922582i \(0.373925\pi\)
\(390\) −3.99526 −0.202308
\(391\) −0.204808 −0.0103576
\(392\) −8.01388 −0.404762
\(393\) −9.73289 −0.490960
\(394\) −12.4837 −0.628918
\(395\) 9.11676 0.458714
\(396\) −0.0200581 −0.00100796
\(397\) 34.3140 1.72217 0.861086 0.508459i \(-0.169785\pi\)
0.861086 + 0.508459i \(0.169785\pi\)
\(398\) −12.8824 −0.645735
\(399\) 18.4444 0.923376
\(400\) −4.04711 −0.202356
\(401\) −15.4362 −0.770845 −0.385422 0.922740i \(-0.625944\pi\)
−0.385422 + 0.922740i \(0.625944\pi\)
\(402\) −2.36212 −0.117812
\(403\) 7.66394 0.381768
\(404\) 2.28999 0.113931
\(405\) −0.976160 −0.0485058
\(406\) −26.8132 −1.33072
\(407\) 0.00153182 7.59296e−5 0
\(408\) 1.00000 0.0495074
\(409\) 26.4843 1.30956 0.654781 0.755819i \(-0.272761\pi\)
0.654781 + 0.755819i \(0.272761\pi\)
\(410\) 1.68647 0.0832886
\(411\) −17.5945 −0.867875
\(412\) 9.40392 0.463298
\(413\) 3.87477 0.190665
\(414\) 0.204808 0.0100658
\(415\) 2.84058 0.139439
\(416\) −4.09284 −0.200668
\(417\) −18.6395 −0.912779
\(418\) 0.0954792 0.00467004
\(419\) 33.8253 1.65248 0.826238 0.563321i \(-0.190477\pi\)
0.826238 + 0.563321i \(0.190477\pi\)
\(420\) −3.78240 −0.184562
\(421\) 8.88019 0.432794 0.216397 0.976305i \(-0.430569\pi\)
0.216397 + 0.976305i \(0.430569\pi\)
\(422\) −21.2253 −1.03323
\(423\) 10.7654 0.523430
\(424\) 3.54134 0.171983
\(425\) −4.04711 −0.196314
\(426\) −10.9512 −0.530590
\(427\) 23.9358 1.15834
\(428\) −10.6637 −0.515451
\(429\) 0.0820947 0.00396357
\(430\) 0.655483 0.0316102
\(431\) −1.60947 −0.0775256 −0.0387628 0.999248i \(-0.512342\pi\)
−0.0387628 + 0.999248i \(0.512342\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 10.3342 0.496631 0.248315 0.968679i \(-0.420123\pi\)
0.248315 + 0.968679i \(0.420123\pi\)
\(434\) 7.25561 0.348281
\(435\) −6.75497 −0.323876
\(436\) −10.2720 −0.491940
\(437\) −0.974910 −0.0466363
\(438\) 3.32488 0.158869
\(439\) 5.92289 0.282684 0.141342 0.989961i \(-0.454858\pi\)
0.141342 + 0.989961i \(0.454858\pi\)
\(440\) −0.0195800 −0.000933438 0
\(441\) 8.01388 0.381613
\(442\) −4.09284 −0.194676
\(443\) −3.78046 −0.179615 −0.0898076 0.995959i \(-0.528625\pi\)
−0.0898076 + 0.995959i \(0.528625\pi\)
\(444\) 0.0763691 0.00362432
\(445\) 13.5606 0.642833
\(446\) −24.7471 −1.17181
\(447\) −11.1125 −0.525605
\(448\) −3.87477 −0.183066
\(449\) −25.1981 −1.18917 −0.594586 0.804032i \(-0.702684\pi\)
−0.594586 + 0.804032i \(0.702684\pi\)
\(450\) 4.04711 0.190783
\(451\) −0.0346535 −0.00163177
\(452\) −14.4538 −0.679848
\(453\) −15.4133 −0.724181
\(454\) −0.782040 −0.0367030
\(455\) 15.4807 0.725749
\(456\) 4.76012 0.222913
\(457\) 13.0744 0.611594 0.305797 0.952097i \(-0.401077\pi\)
0.305797 + 0.952097i \(0.401077\pi\)
\(458\) −1.67635 −0.0783308
\(459\) −1.00000 −0.0466760
\(460\) 0.199925 0.00932156
\(461\) 2.93939 0.136901 0.0684505 0.997655i \(-0.478194\pi\)
0.0684505 + 0.997655i \(0.478194\pi\)
\(462\) 0.0777208 0.00361590
\(463\) 37.6944 1.75181 0.875903 0.482488i \(-0.160267\pi\)
0.875903 + 0.482488i \(0.160267\pi\)
\(464\) −6.91994 −0.321250
\(465\) 1.82788 0.0847661
\(466\) 2.77060 0.128345
\(467\) −15.4296 −0.713999 −0.356999 0.934105i \(-0.616200\pi\)
−0.356999 + 0.934105i \(0.616200\pi\)
\(468\) 4.09284 0.189191
\(469\) 9.15270 0.422632
\(470\) 10.5087 0.484731
\(471\) 1.24776 0.0574936
\(472\) 1.00000 0.0460287
\(473\) −0.0134689 −0.000619299 0
\(474\) −9.33941 −0.428973
\(475\) −19.2648 −0.883928
\(476\) −3.87477 −0.177600
\(477\) −3.54134 −0.162147
\(478\) 0.488210 0.0223302
\(479\) 16.5292 0.755237 0.377618 0.925961i \(-0.376743\pi\)
0.377618 + 0.925961i \(0.376743\pi\)
\(480\) −0.976160 −0.0445554
\(481\) −0.312566 −0.0142518
\(482\) 18.6888 0.851250
\(483\) −0.793584 −0.0361093
\(484\) −10.9996 −0.499982
\(485\) −6.40858 −0.290999
\(486\) 1.00000 0.0453609
\(487\) −4.64275 −0.210383 −0.105192 0.994452i \(-0.533546\pi\)
−0.105192 + 0.994452i \(0.533546\pi\)
\(488\) 6.17734 0.279635
\(489\) −7.89843 −0.357180
\(490\) 7.82283 0.353399
\(491\) −10.2849 −0.464152 −0.232076 0.972698i \(-0.574552\pi\)
−0.232076 + 0.972698i \(0.574552\pi\)
\(492\) −1.72765 −0.0778886
\(493\) −6.91994 −0.311658
\(494\) −19.4824 −0.876555
\(495\) 0.0195800 0.000880053 0
\(496\) 1.87253 0.0840789
\(497\) 42.4336 1.90341
\(498\) −2.90996 −0.130398
\(499\) −2.71766 −0.121659 −0.0608295 0.998148i \(-0.519375\pi\)
−0.0608295 + 0.998148i \(0.519375\pi\)
\(500\) 8.83143 0.394954
\(501\) 23.7000 1.05884
\(502\) 9.79196 0.437037
\(503\) 44.1857 1.97014 0.985071 0.172147i \(-0.0550703\pi\)
0.985071 + 0.172147i \(0.0550703\pi\)
\(504\) 3.87477 0.172596
\(505\) −2.23540 −0.0994738
\(506\) −0.00410806 −0.000182626 0
\(507\) −3.75130 −0.166601
\(508\) 11.0071 0.488362
\(509\) −32.5057 −1.44079 −0.720394 0.693565i \(-0.756039\pi\)
−0.720394 + 0.693565i \(0.756039\pi\)
\(510\) −0.976160 −0.0432251
\(511\) −12.8831 −0.569917
\(512\) −1.00000 −0.0441942
\(513\) −4.76012 −0.210165
\(514\) 5.93389 0.261733
\(515\) −9.17974 −0.404507
\(516\) −0.671491 −0.0295608
\(517\) −0.215933 −0.00949673
\(518\) −0.295913 −0.0130017
\(519\) −24.3272 −1.06784
\(520\) 3.99526 0.175204
\(521\) −15.6998 −0.687821 −0.343911 0.939002i \(-0.611752\pi\)
−0.343911 + 0.939002i \(0.611752\pi\)
\(522\) 6.91994 0.302878
\(523\) 14.6944 0.642542 0.321271 0.946987i \(-0.395890\pi\)
0.321271 + 0.946987i \(0.395890\pi\)
\(524\) 9.73289 0.425183
\(525\) −15.6816 −0.684403
\(526\) −0.685091 −0.0298714
\(527\) 1.87253 0.0815685
\(528\) 0.0200581 0.000872918 0
\(529\) −22.9581 −0.998176
\(530\) −3.45692 −0.150159
\(531\) −1.00000 −0.0433963
\(532\) −18.4444 −0.799667
\(533\) 7.07100 0.306279
\(534\) −13.8917 −0.601155
\(535\) 10.4095 0.450042
\(536\) 2.36212 0.102028
\(537\) 26.2696 1.13362
\(538\) −5.05267 −0.217836
\(539\) −0.160743 −0.00692371
\(540\) 0.976160 0.0420072
\(541\) 40.9475 1.76047 0.880234 0.474539i \(-0.157385\pi\)
0.880234 + 0.474539i \(0.157385\pi\)
\(542\) 19.1778 0.823759
\(543\) 10.5798 0.454022
\(544\) −1.00000 −0.0428746
\(545\) 10.0271 0.429514
\(546\) −15.8588 −0.678695
\(547\) 43.1212 1.84373 0.921864 0.387514i \(-0.126666\pi\)
0.921864 + 0.387514i \(0.126666\pi\)
\(548\) 17.5945 0.751602
\(549\) −6.17734 −0.263643
\(550\) −0.0811775 −0.00346142
\(551\) −32.9398 −1.40328
\(552\) −0.204808 −0.00871720
\(553\) 36.1881 1.53887
\(554\) −5.02496 −0.213490
\(555\) −0.0745485 −0.00316441
\(556\) 18.6395 0.790489
\(557\) −40.9288 −1.73421 −0.867105 0.498125i \(-0.834022\pi\)
−0.867105 + 0.498125i \(0.834022\pi\)
\(558\) −1.87253 −0.0792703
\(559\) 2.74830 0.116241
\(560\) 3.78240 0.159836
\(561\) 0.0200581 0.000846855 0
\(562\) 29.8736 1.26014
\(563\) −3.58242 −0.150981 −0.0754906 0.997147i \(-0.524052\pi\)
−0.0754906 + 0.997147i \(0.524052\pi\)
\(564\) −10.7654 −0.453304
\(565\) 14.1092 0.593579
\(566\) −9.35241 −0.393111
\(567\) −3.87477 −0.162725
\(568\) 10.9512 0.459504
\(569\) 17.1405 0.718567 0.359284 0.933228i \(-0.383021\pi\)
0.359284 + 0.933228i \(0.383021\pi\)
\(570\) −4.64664 −0.194627
\(571\) 22.8089 0.954522 0.477261 0.878762i \(-0.341630\pi\)
0.477261 + 0.878762i \(0.341630\pi\)
\(572\) −0.0820947 −0.00343255
\(573\) −18.5956 −0.776844
\(574\) 6.69427 0.279413
\(575\) 0.828880 0.0345667
\(576\) 1.00000 0.0416667
\(577\) −22.8241 −0.950178 −0.475089 0.879938i \(-0.657584\pi\)
−0.475089 + 0.879938i \(0.657584\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 10.0613 0.418132
\(580\) 6.75497 0.280485
\(581\) 11.2754 0.467784
\(582\) 6.56510 0.272132
\(583\) 0.0710327 0.00294187
\(584\) −3.32488 −0.137584
\(585\) −3.99526 −0.165184
\(586\) 19.7447 0.815647
\(587\) −21.6300 −0.892767 −0.446384 0.894842i \(-0.647288\pi\)
−0.446384 + 0.894842i \(0.647288\pi\)
\(588\) −8.01388 −0.330487
\(589\) 8.91345 0.367272
\(590\) −0.976160 −0.0401879
\(591\) −12.4837 −0.513509
\(592\) −0.0763691 −0.00313875
\(593\) 37.4157 1.53648 0.768238 0.640164i \(-0.221134\pi\)
0.768238 + 0.640164i \(0.221134\pi\)
\(594\) −0.0200581 −0.000822995 0
\(595\) 3.78240 0.155063
\(596\) 11.1125 0.455187
\(597\) −12.8824 −0.527241
\(598\) 0.838244 0.0342784
\(599\) −22.2390 −0.908660 −0.454330 0.890833i \(-0.650121\pi\)
−0.454330 + 0.890833i \(0.650121\pi\)
\(600\) −4.04711 −0.165223
\(601\) −3.99369 −0.162906 −0.0814531 0.996677i \(-0.525956\pi\)
−0.0814531 + 0.996677i \(0.525956\pi\)
\(602\) 2.60188 0.106045
\(603\) −2.36212 −0.0961931
\(604\) 15.4133 0.627159
\(605\) 10.7374 0.436536
\(606\) 2.28999 0.0930245
\(607\) −10.8577 −0.440701 −0.220351 0.975421i \(-0.570720\pi\)
−0.220351 + 0.975421i \(0.570720\pi\)
\(608\) −4.76012 −0.193049
\(609\) −26.8132 −1.08653
\(610\) −6.03008 −0.244151
\(611\) 44.0609 1.78251
\(612\) 1.00000 0.0404226
\(613\) 19.0462 0.769270 0.384635 0.923069i \(-0.374327\pi\)
0.384635 + 0.923069i \(0.374327\pi\)
\(614\) −26.3420 −1.06308
\(615\) 1.68647 0.0680049
\(616\) −0.0777208 −0.00313146
\(617\) 29.4380 1.18513 0.592565 0.805522i \(-0.298115\pi\)
0.592565 + 0.805522i \(0.298115\pi\)
\(618\) 9.40392 0.378281
\(619\) 14.2727 0.573669 0.286835 0.957980i \(-0.407397\pi\)
0.286835 + 0.957980i \(0.407397\pi\)
\(620\) −1.82788 −0.0734096
\(621\) 0.204808 0.00821865
\(622\) −22.5144 −0.902746
\(623\) 53.8274 2.15655
\(624\) −4.09284 −0.163845
\(625\) 11.6147 0.464587
\(626\) −16.9101 −0.675862
\(627\) 0.0954792 0.00381307
\(628\) −1.24776 −0.0497909
\(629\) −0.0763691 −0.00304504
\(630\) −3.78240 −0.150694
\(631\) 4.18663 0.166667 0.0833336 0.996522i \(-0.473443\pi\)
0.0833336 + 0.996522i \(0.473443\pi\)
\(632\) 9.33941 0.371502
\(633\) −21.2253 −0.843632
\(634\) 1.50973 0.0599589
\(635\) −10.7447 −0.426391
\(636\) 3.54134 0.140423
\(637\) 32.7995 1.29956
\(638\) −0.138801 −0.00549519
\(639\) −10.9512 −0.433225
\(640\) 0.976160 0.0385861
\(641\) 20.7493 0.819549 0.409775 0.912187i \(-0.365607\pi\)
0.409775 + 0.912187i \(0.365607\pi\)
\(642\) −10.6637 −0.420864
\(643\) −39.7523 −1.56768 −0.783840 0.620963i \(-0.786742\pi\)
−0.783840 + 0.620963i \(0.786742\pi\)
\(644\) 0.793584 0.0312716
\(645\) 0.655483 0.0258096
\(646\) −4.76012 −0.187285
\(647\) 0.414841 0.0163091 0.00815453 0.999967i \(-0.497404\pi\)
0.00815453 + 0.999967i \(0.497404\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 0.0200581 0.000787351 0
\(650\) 16.5642 0.649700
\(651\) 7.25561 0.284370
\(652\) 7.89843 0.309327
\(653\) 32.0099 1.25265 0.626323 0.779564i \(-0.284559\pi\)
0.626323 + 0.779564i \(0.284559\pi\)
\(654\) −10.2720 −0.401667
\(655\) −9.50086 −0.371229
\(656\) 1.72765 0.0674535
\(657\) 3.32488 0.129716
\(658\) 41.7134 1.62616
\(659\) −21.5527 −0.839574 −0.419787 0.907623i \(-0.637895\pi\)
−0.419787 + 0.907623i \(0.637895\pi\)
\(660\) −0.0195800 −0.000762149 0
\(661\) −6.61164 −0.257163 −0.128582 0.991699i \(-0.541042\pi\)
−0.128582 + 0.991699i \(0.541042\pi\)
\(662\) −14.9957 −0.582825
\(663\) −4.09284 −0.158953
\(664\) 2.90996 0.112928
\(665\) 18.0047 0.698192
\(666\) 0.0763691 0.00295924
\(667\) 1.41726 0.0548764
\(668\) −23.7000 −0.916980
\(669\) −24.7471 −0.956779
\(670\) −2.30581 −0.0890813
\(671\) 0.123906 0.00478334
\(672\) −3.87477 −0.149473
\(673\) −19.9294 −0.768224 −0.384112 0.923287i \(-0.625492\pi\)
−0.384112 + 0.923287i \(0.625492\pi\)
\(674\) 32.0030 1.23271
\(675\) 4.04711 0.155773
\(676\) 3.75130 0.144281
\(677\) −20.8723 −0.802187 −0.401093 0.916037i \(-0.631370\pi\)
−0.401093 + 0.916037i \(0.631370\pi\)
\(678\) −14.4538 −0.555094
\(679\) −25.4383 −0.976231
\(680\) 0.976160 0.0374340
\(681\) −0.782040 −0.0299679
\(682\) 0.0375594 0.00143822
\(683\) 10.6419 0.407201 0.203601 0.979054i \(-0.434736\pi\)
0.203601 + 0.979054i \(0.434736\pi\)
\(684\) 4.76012 0.182008
\(685\) −17.1751 −0.656227
\(686\) 3.92855 0.149993
\(687\) −1.67635 −0.0639568
\(688\) 0.671491 0.0256004
\(689\) −14.4941 −0.552182
\(690\) 0.199925 0.00761102
\(691\) −34.3588 −1.30707 −0.653535 0.756896i \(-0.726715\pi\)
−0.653535 + 0.756896i \(0.726715\pi\)
\(692\) 24.3272 0.924780
\(693\) 0.0777208 0.00295237
\(694\) −7.08683 −0.269012
\(695\) −18.1951 −0.690180
\(696\) −6.91994 −0.262300
\(697\) 1.72765 0.0654395
\(698\) −35.6085 −1.34780
\(699\) 2.77060 0.104794
\(700\) 15.6816 0.592710
\(701\) −1.29257 −0.0488198 −0.0244099 0.999702i \(-0.507771\pi\)
−0.0244099 + 0.999702i \(0.507771\pi\)
\(702\) 4.09284 0.154474
\(703\) −0.363527 −0.0137107
\(704\) −0.0200581 −0.000755969 0
\(705\) 10.5087 0.395781
\(706\) −32.3000 −1.21563
\(707\) −8.87319 −0.333711
\(708\) 1.00000 0.0375823
\(709\) −7.83101 −0.294100 −0.147050 0.989129i \(-0.546978\pi\)
−0.147050 + 0.989129i \(0.546978\pi\)
\(710\) −10.6902 −0.401195
\(711\) −9.33941 −0.350255
\(712\) 13.8917 0.520615
\(713\) −0.383508 −0.0143625
\(714\) −3.87477 −0.145010
\(715\) 0.0801375 0.00299697
\(716\) −26.2696 −0.981741
\(717\) 0.488210 0.0182325
\(718\) 25.2748 0.943247
\(719\) −17.6553 −0.658432 −0.329216 0.944255i \(-0.606784\pi\)
−0.329216 + 0.944255i \(0.606784\pi\)
\(720\) −0.976160 −0.0363793
\(721\) −36.4381 −1.35703
\(722\) −3.65879 −0.136166
\(723\) 18.6888 0.695043
\(724\) −10.5798 −0.393195
\(725\) 28.0058 1.04011
\(726\) −10.9996 −0.408233
\(727\) 38.4302 1.42530 0.712649 0.701521i \(-0.247495\pi\)
0.712649 + 0.701521i \(0.247495\pi\)
\(728\) 15.8588 0.587767
\(729\) 1.00000 0.0370370
\(730\) 3.24561 0.120125
\(731\) 0.671491 0.0248360
\(732\) 6.17734 0.228321
\(733\) 21.0258 0.776605 0.388302 0.921532i \(-0.373062\pi\)
0.388302 + 0.921532i \(0.373062\pi\)
\(734\) −16.9270 −0.624785
\(735\) 7.82283 0.288549
\(736\) 0.204808 0.00754931
\(737\) 0.0473798 0.00174526
\(738\) −1.72765 −0.0635958
\(739\) 25.9626 0.955051 0.477526 0.878618i \(-0.341534\pi\)
0.477526 + 0.878618i \(0.341534\pi\)
\(740\) 0.0745485 0.00274046
\(741\) −19.4824 −0.715704
\(742\) −13.7219 −0.503747
\(743\) −49.2105 −1.80536 −0.902679 0.430315i \(-0.858402\pi\)
−0.902679 + 0.430315i \(0.858402\pi\)
\(744\) 1.87253 0.0686501
\(745\) −10.8476 −0.397426
\(746\) 1.60953 0.0589291
\(747\) −2.90996 −0.106470
\(748\) −0.0200581 −0.000733398 0
\(749\) 41.3196 1.50978
\(750\) 8.83143 0.322478
\(751\) 11.4941 0.419427 0.209714 0.977763i \(-0.432747\pi\)
0.209714 + 0.977763i \(0.432747\pi\)
\(752\) 10.7654 0.392572
\(753\) 9.79196 0.356839
\(754\) 28.3222 1.03143
\(755\) −15.0459 −0.547575
\(756\) 3.87477 0.140924
\(757\) −22.4832 −0.817167 −0.408583 0.912721i \(-0.633977\pi\)
−0.408583 + 0.912721i \(0.633977\pi\)
\(758\) 5.76769 0.209492
\(759\) −0.00410806 −0.000149113 0
\(760\) 4.64664 0.168551
\(761\) 22.8630 0.828784 0.414392 0.910099i \(-0.363994\pi\)
0.414392 + 0.910099i \(0.363994\pi\)
\(762\) 11.0071 0.398746
\(763\) 39.8017 1.44092
\(764\) 18.5956 0.672767
\(765\) −0.976160 −0.0352931
\(766\) −29.1366 −1.05275
\(767\) −4.09284 −0.147784
\(768\) −1.00000 −0.0360844
\(769\) 40.5926 1.46381 0.731903 0.681409i \(-0.238633\pi\)
0.731903 + 0.681409i \(0.238633\pi\)
\(770\) 0.0758679 0.00273409
\(771\) 5.93389 0.213704
\(772\) −10.0613 −0.362113
\(773\) −53.2082 −1.91377 −0.956883 0.290474i \(-0.906187\pi\)
−0.956883 + 0.290474i \(0.906187\pi\)
\(774\) −0.671491 −0.0241363
\(775\) −7.57832 −0.272221
\(776\) −6.56510 −0.235673
\(777\) −0.295913 −0.0106158
\(778\) −15.2183 −0.545604
\(779\) 8.22385 0.294650
\(780\) 3.99526 0.143053
\(781\) 0.219662 0.00786011
\(782\) 0.204808 0.00732391
\(783\) 6.91994 0.247298
\(784\) 8.01388 0.286210
\(785\) 1.21801 0.0434726
\(786\) 9.73289 0.347161
\(787\) 3.24829 0.115789 0.0578945 0.998323i \(-0.481561\pi\)
0.0578945 + 0.998323i \(0.481561\pi\)
\(788\) 12.4837 0.444712
\(789\) −0.685091 −0.0243899
\(790\) −9.11676 −0.324360
\(791\) 56.0051 1.99131
\(792\) 0.0200581 0.000712735 0
\(793\) −25.2829 −0.897820
\(794\) −34.3140 −1.21776
\(795\) −3.45692 −0.122604
\(796\) 12.8824 0.456604
\(797\) 21.3316 0.755603 0.377802 0.925887i \(-0.376680\pi\)
0.377802 + 0.925887i \(0.376680\pi\)
\(798\) −18.4444 −0.652925
\(799\) 10.7654 0.380851
\(800\) 4.04711 0.143087
\(801\) −13.8917 −0.490841
\(802\) 15.4362 0.545070
\(803\) −0.0666908 −0.00235347
\(804\) 2.36212 0.0833057
\(805\) −0.774665 −0.0273034
\(806\) −7.66394 −0.269951
\(807\) −5.05267 −0.177863
\(808\) −2.28999 −0.0805615
\(809\) −21.3886 −0.751982 −0.375991 0.926623i \(-0.622698\pi\)
−0.375991 + 0.926623i \(0.622698\pi\)
\(810\) 0.976160 0.0342988
\(811\) 25.7158 0.903003 0.451501 0.892270i \(-0.350889\pi\)
0.451501 + 0.892270i \(0.350889\pi\)
\(812\) 26.8132 0.940959
\(813\) 19.1778 0.672596
\(814\) −0.00153182 −5.36903e−5 0
\(815\) −7.71014 −0.270074
\(816\) −1.00000 −0.0350070
\(817\) 3.19638 0.111827
\(818\) −26.4843 −0.926000
\(819\) −15.8588 −0.554152
\(820\) −1.68647 −0.0588940
\(821\) 7.09093 0.247475 0.123738 0.992315i \(-0.460512\pi\)
0.123738 + 0.992315i \(0.460512\pi\)
\(822\) 17.5945 0.613680
\(823\) −26.0126 −0.906744 −0.453372 0.891321i \(-0.649779\pi\)
−0.453372 + 0.891321i \(0.649779\pi\)
\(824\) −9.40392 −0.327601
\(825\) −0.0811775 −0.00282624
\(826\) −3.87477 −0.134821
\(827\) −20.7693 −0.722218 −0.361109 0.932524i \(-0.617602\pi\)
−0.361109 + 0.932524i \(0.617602\pi\)
\(828\) −0.204808 −0.00711756
\(829\) 53.2093 1.84803 0.924017 0.382351i \(-0.124886\pi\)
0.924017 + 0.382351i \(0.124886\pi\)
\(830\) −2.84058 −0.0985981
\(831\) −5.02496 −0.174314
\(832\) 4.09284 0.141894
\(833\) 8.01388 0.277664
\(834\) 18.6395 0.645432
\(835\) 23.1350 0.800619
\(836\) −0.0954792 −0.00330222
\(837\) −1.87253 −0.0647239
\(838\) −33.8253 −1.16848
\(839\) 22.9755 0.793204 0.396602 0.917991i \(-0.370189\pi\)
0.396602 + 0.917991i \(0.370189\pi\)
\(840\) 3.78240 0.130505
\(841\) 18.8856 0.651227
\(842\) −8.88019 −0.306032
\(843\) 29.8736 1.02890
\(844\) 21.2253 0.730606
\(845\) −3.66187 −0.125972
\(846\) −10.7654 −0.370121
\(847\) 42.6210 1.46447
\(848\) −3.54134 −0.121610
\(849\) −9.35241 −0.320974
\(850\) 4.04711 0.138815
\(851\) 0.0156410 0.000536166 0
\(852\) 10.9512 0.375184
\(853\) 12.4322 0.425671 0.212836 0.977088i \(-0.431730\pi\)
0.212836 + 0.977088i \(0.431730\pi\)
\(854\) −23.9358 −0.819067
\(855\) −4.64664 −0.158912
\(856\) 10.6637 0.364479
\(857\) −13.0859 −0.447005 −0.223502 0.974703i \(-0.571749\pi\)
−0.223502 + 0.974703i \(0.571749\pi\)
\(858\) −0.0820947 −0.00280267
\(859\) 35.5786 1.21393 0.606964 0.794730i \(-0.292387\pi\)
0.606964 + 0.794730i \(0.292387\pi\)
\(860\) −0.655483 −0.0223518
\(861\) 6.69427 0.228140
\(862\) 1.60947 0.0548189
\(863\) 27.3570 0.931243 0.465621 0.884984i \(-0.345831\pi\)
0.465621 + 0.884984i \(0.345831\pi\)
\(864\) 1.00000 0.0340207
\(865\) −23.7472 −0.807430
\(866\) −10.3342 −0.351171
\(867\) −1.00000 −0.0339618
\(868\) −7.25561 −0.246272
\(869\) 0.187331 0.00635477
\(870\) 6.75497 0.229015
\(871\) −9.66779 −0.327580
\(872\) 10.2720 0.347854
\(873\) 6.56510 0.222195
\(874\) 0.974910 0.0329768
\(875\) −34.2198 −1.15684
\(876\) −3.32488 −0.112337
\(877\) −7.62407 −0.257446 −0.128723 0.991681i \(-0.541088\pi\)
−0.128723 + 0.991681i \(0.541088\pi\)
\(878\) −5.92289 −0.199888
\(879\) 19.7447 0.665973
\(880\) 0.0195800 0.000660040 0
\(881\) −17.0712 −0.575142 −0.287571 0.957759i \(-0.592848\pi\)
−0.287571 + 0.957759i \(0.592848\pi\)
\(882\) −8.01388 −0.269841
\(883\) 24.7219 0.831958 0.415979 0.909374i \(-0.363439\pi\)
0.415979 + 0.909374i \(0.363439\pi\)
\(884\) 4.09284 0.137657
\(885\) −0.976160 −0.0328133
\(886\) 3.78046 0.127007
\(887\) 25.8472 0.867865 0.433933 0.900945i \(-0.357126\pi\)
0.433933 + 0.900945i \(0.357126\pi\)
\(888\) −0.0763691 −0.00256278
\(889\) −42.6501 −1.43044
\(890\) −13.5606 −0.454551
\(891\) −0.0200581 −0.000671973 0
\(892\) 24.7471 0.828595
\(893\) 51.2445 1.71483
\(894\) 11.1125 0.371659
\(895\) 25.6433 0.857162
\(896\) 3.87477 0.129447
\(897\) 0.838244 0.0279882
\(898\) 25.1981 0.840872
\(899\) −12.9578 −0.432166
\(900\) −4.04711 −0.134904
\(901\) −3.54134 −0.117979
\(902\) 0.0346535 0.00115384
\(903\) 2.60188 0.0865850
\(904\) 14.4538 0.480725
\(905\) 10.3276 0.343300
\(906\) 15.4133 0.512073
\(907\) −26.1380 −0.867898 −0.433949 0.900937i \(-0.642880\pi\)
−0.433949 + 0.900937i \(0.642880\pi\)
\(908\) 0.782040 0.0259529
\(909\) 2.28999 0.0759542
\(910\) −15.4807 −0.513182
\(911\) 4.23218 0.140218 0.0701092 0.997539i \(-0.477665\pi\)
0.0701092 + 0.997539i \(0.477665\pi\)
\(912\) −4.76012 −0.157623
\(913\) 0.0583683 0.00193171
\(914\) −13.0744 −0.432462
\(915\) −6.03008 −0.199348
\(916\) 1.67635 0.0553882
\(917\) −37.7128 −1.24539
\(918\) 1.00000 0.0330049
\(919\) −14.6891 −0.484547 −0.242274 0.970208i \(-0.577893\pi\)
−0.242274 + 0.970208i \(0.577893\pi\)
\(920\) −0.199925 −0.00659134
\(921\) −26.3420 −0.867997
\(922\) −2.93939 −0.0968036
\(923\) −44.8217 −1.47532
\(924\) −0.0777208 −0.00255683
\(925\) 0.309074 0.0101623
\(926\) −37.6944 −1.23871
\(927\) 9.40392 0.308865
\(928\) 6.91994 0.227158
\(929\) 4.80777 0.157738 0.0788689 0.996885i \(-0.474869\pi\)
0.0788689 + 0.996885i \(0.474869\pi\)
\(930\) −1.82788 −0.0599387
\(931\) 38.1471 1.25022
\(932\) −2.77060 −0.0907539
\(933\) −22.5144 −0.737089
\(934\) 15.4296 0.504874
\(935\) 0.0195800 0.000640333 0
\(936\) −4.09284 −0.133779
\(937\) −55.8126 −1.82332 −0.911658 0.410949i \(-0.865197\pi\)
−0.911658 + 0.410949i \(0.865197\pi\)
\(938\) −9.15270 −0.298846
\(939\) −16.9101 −0.551839
\(940\) −10.5087 −0.342757
\(941\) 30.8389 1.00532 0.502661 0.864484i \(-0.332355\pi\)
0.502661 + 0.864484i \(0.332355\pi\)
\(942\) −1.24776 −0.0406541
\(943\) −0.353837 −0.0115225
\(944\) −1.00000 −0.0325472
\(945\) −3.78240 −0.123042
\(946\) 0.0134689 0.000437910 0
\(947\) 30.7117 0.997997 0.498999 0.866603i \(-0.333701\pi\)
0.498999 + 0.866603i \(0.333701\pi\)
\(948\) 9.33941 0.303330
\(949\) 13.6082 0.441740
\(950\) 19.2648 0.625031
\(951\) 1.50973 0.0489563
\(952\) 3.87477 0.125582
\(953\) 35.9992 1.16613 0.583065 0.812426i \(-0.301853\pi\)
0.583065 + 0.812426i \(0.301853\pi\)
\(954\) 3.54134 0.114655
\(955\) −18.1523 −0.587396
\(956\) −0.488210 −0.0157898
\(957\) −0.138801 −0.00448680
\(958\) −16.5292 −0.534033
\(959\) −68.1749 −2.20148
\(960\) 0.976160 0.0315054
\(961\) −27.4936 −0.886892
\(962\) 0.312566 0.0100775
\(963\) −10.6637 −0.343634
\(964\) −18.6888 −0.601925
\(965\) 9.82141 0.316162
\(966\) 0.793584 0.0255331
\(967\) −57.8042 −1.85886 −0.929430 0.369000i \(-0.879700\pi\)
−0.929430 + 0.369000i \(0.879700\pi\)
\(968\) 10.9996 0.353540
\(969\) −4.76012 −0.152917
\(970\) 6.40858 0.205767
\(971\) −43.8980 −1.40875 −0.704377 0.709826i \(-0.748773\pi\)
−0.704377 + 0.709826i \(0.748773\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −72.2237 −2.31539
\(974\) 4.64275 0.148763
\(975\) 16.5642 0.530478
\(976\) −6.17734 −0.197732
\(977\) 32.1070 1.02719 0.513597 0.858032i \(-0.328313\pi\)
0.513597 + 0.858032i \(0.328313\pi\)
\(978\) 7.89843 0.252564
\(979\) 0.278642 0.00890545
\(980\) −7.82283 −0.249891
\(981\) −10.2720 −0.327960
\(982\) 10.2849 0.328205
\(983\) 38.8987 1.24067 0.620337 0.784335i \(-0.286996\pi\)
0.620337 + 0.784335i \(0.286996\pi\)
\(984\) 1.72765 0.0550756
\(985\) −12.1861 −0.388280
\(986\) 6.91994 0.220376
\(987\) 41.7134 1.32775
\(988\) 19.4824 0.619818
\(989\) −0.137527 −0.00437309
\(990\) −0.0195800 −0.000622292 0
\(991\) 58.3009 1.85199 0.925994 0.377538i \(-0.123229\pi\)
0.925994 + 0.377538i \(0.123229\pi\)
\(992\) −1.87253 −0.0594527
\(993\) −14.9957 −0.475875
\(994\) −42.4336 −1.34591
\(995\) −12.5753 −0.398663
\(996\) 2.90996 0.0922055
\(997\) −42.3174 −1.34021 −0.670103 0.742268i \(-0.733750\pi\)
−0.670103 + 0.742268i \(0.733750\pi\)
\(998\) 2.71766 0.0860259
\(999\) 0.0763691 0.00241621
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 6018.2.a.x.1.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6018.2.a.x.1.4 10 1.1 even 1 trivial