Properties

Label 1805.2.b.j.1084.1
Level $1805$
Weight $2$
Character 1805.1084
Analytic conductor $14.413$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1805,2,Mod(1084,1805)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1805.1084");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.b (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(14.4129975648\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 22x^{14} + 190x^{12} + 820x^{10} + 1862x^{8} + 2154x^{6} + 1163x^{4} + 256x^{2} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1084.1
Root \(-2.61137i\) of defining polynomial
Character \(\chi\) \(=\) 1805.1084
Dual form 1805.2.b.j.1084.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.61137i q^{2} +0.146779i q^{3} -4.81924 q^{4} +(0.948930 + 2.02473i) q^{5} +0.383293 q^{6} -1.14057i q^{7} +7.36208i q^{8} +2.97846 q^{9} +O(q^{10})\) \(q-2.61137i q^{2} +0.146779i q^{3} -4.81924 q^{4} +(0.948930 + 2.02473i) q^{5} +0.383293 q^{6} -1.14057i q^{7} +7.36208i q^{8} +2.97846 q^{9} +(5.28732 - 2.47801i) q^{10} -5.36995 q^{11} -0.707361i q^{12} -2.41565i q^{13} -2.97846 q^{14} +(-0.297187 + 0.139283i) q^{15} +9.58662 q^{16} +5.74451i q^{17} -7.77785i q^{18} +(-4.57313 - 9.75767i) q^{20} +0.167412 q^{21} +14.0229i q^{22} -1.23526i q^{23} -1.08060 q^{24} +(-3.19906 + 3.84266i) q^{25} -6.30815 q^{26} +0.877509i q^{27} +5.49670i q^{28} +3.91460 q^{29} +(0.363718 + 0.776064i) q^{30} +6.48369 q^{31} -10.3100i q^{32} -0.788193i q^{33} +15.0010 q^{34} +(2.30935 - 1.08232i) q^{35} -14.3539 q^{36} +7.37637i q^{37} +0.354565 q^{39} +(-14.9062 + 6.98610i) q^{40} +4.86252 q^{41} -0.437173i q^{42} +7.59744i q^{43} +25.8791 q^{44} +(2.82635 + 6.03057i) q^{45} -3.22572 q^{46} -7.85368i q^{47} +1.40711i q^{48} +5.69909 q^{49} +(10.0346 + 8.35393i) q^{50} -0.843170 q^{51} +11.6416i q^{52} +0.0179026i q^{53} +2.29150 q^{54} +(-5.09571 - 10.8727i) q^{55} +8.39699 q^{56} -10.2225i q^{58} +13.0250 q^{59} +(1.43222 - 0.671237i) q^{60} -0.0189653 q^{61} -16.9313i q^{62} -3.39715i q^{63} -7.75004 q^{64} +(4.89104 - 2.29228i) q^{65} -2.05826 q^{66} +7.07711i q^{67} -27.6842i q^{68} +0.181310 q^{69} +(-2.82635 - 6.03057i) q^{70} -2.73751 q^{71} +21.9276i q^{72} +5.58836i q^{73} +19.2624 q^{74} +(-0.564019 - 0.469554i) q^{75} +6.12482i q^{77} -0.925901i q^{78} +9.56774 q^{79} +(9.09703 + 19.4103i) q^{80} +8.80657 q^{81} -12.6978i q^{82} -0.390810i q^{83} -0.806797 q^{84} +(-11.6311 + 5.45114i) q^{85} +19.8397 q^{86} +0.574579i q^{87} -39.5340i q^{88} +3.57717 q^{89} +(15.7480 - 7.38063i) q^{90} -2.75522 q^{91} +5.95303i q^{92} +0.951666i q^{93} -20.5088 q^{94} +1.51329 q^{96} +14.7430i q^{97} -14.8824i q^{98} -15.9942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 12 q^{4} + 4 q^{5} - 10 q^{6} - 6 q^{9} + 16 q^{10} - 22 q^{11} + 6 q^{14} - 10 q^{15} + 8 q^{16} - 14 q^{20} + 20 q^{21} + 14 q^{24} + 4 q^{25} - 16 q^{26} + 2 q^{29} - 12 q^{30} - 16 q^{31} - 8 q^{34} - 10 q^{35} + 18 q^{36} + 36 q^{39} - 38 q^{40} - 26 q^{41} + 64 q^{44} - 2 q^{45} - 2 q^{46} + 20 q^{49} + 48 q^{50} + 38 q^{51} + 12 q^{54} - 10 q^{55} - 6 q^{56} + 10 q^{59} + 10 q^{60} - 30 q^{61} + 16 q^{64} + 36 q^{65} + 4 q^{66} + 68 q^{69} + 2 q^{70} + 20 q^{71} + 40 q^{74} + 32 q^{75} + 12 q^{79} + 40 q^{80} - 48 q^{81} - 2 q^{84} - 2 q^{85} + 20 q^{86} - 30 q^{90} + 86 q^{91} - 38 q^{94} + 22 q^{96} + 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1805\mathbb{Z}\right)^\times\).

\(n\) \(362\) \(1446\)
\(\chi(n)\) \(-1\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61137i 1.84652i −0.384180 0.923258i \(-0.625516\pi\)
0.384180 0.923258i \(-0.374484\pi\)
\(3\) 0.146779i 0.0847426i 0.999102 + 0.0423713i \(0.0134912\pi\)
−0.999102 + 0.0423713i \(0.986509\pi\)
\(4\) −4.81924 −2.40962
\(5\) 0.948930 + 2.02473i 0.424375 + 0.905487i
\(6\) 0.383293 0.156479
\(7\) 1.14057i 0.431096i −0.976493 0.215548i \(-0.930846\pi\)
0.976493 0.215548i \(-0.0691538\pi\)
\(8\) 7.36208i 2.60289i
\(9\) 2.97846 0.992819
\(10\) 5.28732 2.47801i 1.67200 0.783614i
\(11\) −5.36995 −1.61910 −0.809550 0.587051i \(-0.800289\pi\)
−0.809550 + 0.587051i \(0.800289\pi\)
\(12\) 0.707361i 0.204198i
\(13\) 2.41565i 0.669980i −0.942222 0.334990i \(-0.891267\pi\)
0.942222 0.334990i \(-0.108733\pi\)
\(14\) −2.97846 −0.796026
\(15\) −0.297187 + 0.139283i −0.0767333 + 0.0359626i
\(16\) 9.58662 2.39665
\(17\) 5.74451i 1.39325i 0.717436 + 0.696624i \(0.245315\pi\)
−0.717436 + 0.696624i \(0.754685\pi\)
\(18\) 7.77785i 1.83326i
\(19\) 0 0
\(20\) −4.57313 9.75767i −1.02258 2.18188i
\(21\) 0.167412 0.0365322
\(22\) 14.0229i 2.98969i
\(23\) 1.23526i 0.257570i −0.991673 0.128785i \(-0.958892\pi\)
0.991673 0.128785i \(-0.0411077\pi\)
\(24\) −1.08060 −0.220576
\(25\) −3.19906 + 3.84266i −0.639812 + 0.768531i
\(26\) −6.30815 −1.23713
\(27\) 0.877509i 0.168877i
\(28\) 5.49670i 1.03878i
\(29\) 3.91460 0.726923 0.363461 0.931609i \(-0.381595\pi\)
0.363461 + 0.931609i \(0.381595\pi\)
\(30\) 0.363718 + 0.776064i 0.0664055 + 0.141689i
\(31\) 6.48369 1.16450 0.582252 0.813008i \(-0.302172\pi\)
0.582252 + 0.813008i \(0.302172\pi\)
\(32\) 10.3100i 1.82257i
\(33\) 0.788193i 0.137207i
\(34\) 15.0010 2.57265
\(35\) 2.30935 1.08232i 0.390352 0.182946i
\(36\) −14.3539 −2.39232
\(37\) 7.37637i 1.21267i 0.795210 + 0.606334i \(0.207361\pi\)
−0.795210 + 0.606334i \(0.792639\pi\)
\(38\) 0 0
\(39\) 0.354565 0.0567759
\(40\) −14.9062 + 6.98610i −2.35688 + 1.10460i
\(41\) 4.86252 0.759398 0.379699 0.925110i \(-0.376028\pi\)
0.379699 + 0.925110i \(0.376028\pi\)
\(42\) 0.437173i 0.0674573i
\(43\) 7.59744i 1.15860i 0.815115 + 0.579299i \(0.196674\pi\)
−0.815115 + 0.579299i \(0.803326\pi\)
\(44\) 25.8791 3.90142
\(45\) 2.82635 + 6.03057i 0.421327 + 0.898984i
\(46\) −3.22572 −0.475607
\(47\) 7.85368i 1.14558i −0.819703 0.572788i \(-0.805862\pi\)
0.819703 0.572788i \(-0.194138\pi\)
\(48\) 1.40711i 0.203099i
\(49\) 5.69909 0.814156
\(50\) 10.0346 + 8.35393i 1.41910 + 1.18142i
\(51\) −0.843170 −0.118067
\(52\) 11.6416i 1.61440i
\(53\) 0.0179026i 0.00245911i 0.999999 + 0.00122955i \(0.000391379\pi\)
−0.999999 + 0.00122955i \(0.999609\pi\)
\(54\) 2.29150 0.311833
\(55\) −5.09571 10.8727i −0.687105 1.46607i
\(56\) 8.39699 1.12210
\(57\) 0 0
\(58\) 10.2225i 1.34227i
\(59\) 13.0250 1.69571 0.847857 0.530225i \(-0.177892\pi\)
0.847857 + 0.530225i \(0.177892\pi\)
\(60\) 1.43222 0.671237i 0.184898 0.0866563i
\(61\) −0.0189653 −0.00242826 −0.00121413 0.999999i \(-0.500386\pi\)
−0.00121413 + 0.999999i \(0.500386\pi\)
\(62\) 16.9313i 2.15028i
\(63\) 3.39715i 0.428000i
\(64\) −7.75004 −0.968754
\(65\) 4.89104 2.29228i 0.606658 0.284323i
\(66\) −2.05826 −0.253355
\(67\) 7.07711i 0.864606i 0.901728 + 0.432303i \(0.142299\pi\)
−0.901728 + 0.432303i \(0.857701\pi\)
\(68\) 27.6842i 3.35720i
\(69\) 0.181310 0.0218271
\(70\) −2.82635 6.03057i −0.337813 0.720791i
\(71\) −2.73751 −0.324883 −0.162442 0.986718i \(-0.551937\pi\)
−0.162442 + 0.986718i \(0.551937\pi\)
\(72\) 21.9276i 2.58420i
\(73\) 5.58836i 0.654068i 0.945013 + 0.327034i \(0.106049\pi\)
−0.945013 + 0.327034i \(0.893951\pi\)
\(74\) 19.2624 2.23921
\(75\) −0.564019 0.469554i −0.0651273 0.0542194i
\(76\) 0 0
\(77\) 6.12482i 0.697988i
\(78\) 0.925901i 0.104838i
\(79\) 9.56774 1.07645 0.538227 0.842800i \(-0.319094\pi\)
0.538227 + 0.842800i \(0.319094\pi\)
\(80\) 9.09703 + 19.4103i 1.01708 + 2.17014i
\(81\) 8.80657 0.978508
\(82\) 12.6978i 1.40224i
\(83\) 0.390810i 0.0428970i −0.999770 0.0214485i \(-0.993172\pi\)
0.999770 0.0214485i \(-0.00682779\pi\)
\(84\) −0.806797 −0.0880288
\(85\) −11.6311 + 5.45114i −1.26157 + 0.591259i
\(86\) 19.8397 2.13937
\(87\) 0.574579i 0.0616014i
\(88\) 39.5340i 4.21434i
\(89\) 3.57717 0.379179 0.189590 0.981863i \(-0.439284\pi\)
0.189590 + 0.981863i \(0.439284\pi\)
\(90\) 15.7480 7.38063i 1.65999 0.777987i
\(91\) −2.75522 −0.288826
\(92\) 5.95303i 0.620646i
\(93\) 0.951666i 0.0986832i
\(94\) −20.5088 −2.11532
\(95\) 0 0
\(96\) 1.51329 0.154450
\(97\) 14.7430i 1.49693i 0.663176 + 0.748463i \(0.269208\pi\)
−0.663176 + 0.748463i \(0.730792\pi\)
\(98\) 14.8824i 1.50335i
\(99\) −15.9942 −1.60747
\(100\) 15.4171 18.5187i 1.54171 1.85187i
\(101\) −10.5437 −1.04914 −0.524569 0.851368i \(-0.675774\pi\)
−0.524569 + 0.851368i \(0.675774\pi\)
\(102\) 2.20183i 0.218013i
\(103\) 9.12063i 0.898682i −0.893360 0.449341i \(-0.851659\pi\)
0.893360 0.449341i \(-0.148341\pi\)
\(104\) 17.7842 1.74388
\(105\) 0.158862 + 0.338963i 0.0155033 + 0.0330794i
\(106\) 0.0467502 0.00454078
\(107\) 3.56368i 0.344514i −0.985052 0.172257i \(-0.944894\pi\)
0.985052 0.172257i \(-0.0551060\pi\)
\(108\) 4.22893i 0.406929i
\(109\) −10.6645 −1.02147 −0.510736 0.859737i \(-0.670627\pi\)
−0.510736 + 0.859737i \(0.670627\pi\)
\(110\) −28.3926 + 13.3068i −2.70713 + 1.26875i
\(111\) −1.08269 −0.102765
\(112\) 10.9342i 1.03319i
\(113\) 12.8769i 1.21135i −0.795711 0.605676i \(-0.792903\pi\)
0.795711 0.605676i \(-0.207097\pi\)
\(114\) 0 0
\(115\) 2.50107 1.17218i 0.233226 0.109306i
\(116\) −18.8654 −1.75161
\(117\) 7.19490i 0.665169i
\(118\) 34.0131i 3.13116i
\(119\) 6.55203 0.600624
\(120\) −1.02541 2.18791i −0.0936067 0.199728i
\(121\) 17.8363 1.62149
\(122\) 0.0495254i 0.00448382i
\(123\) 0.713713i 0.0643534i
\(124\) −31.2465 −2.80602
\(125\) −10.8160 2.83083i −0.967415 0.253197i
\(126\) −8.87120 −0.790309
\(127\) 7.57260i 0.671960i 0.941869 + 0.335980i \(0.109067\pi\)
−0.941869 + 0.335980i \(0.890933\pi\)
\(128\) 0.381857i 0.0337517i
\(129\) −1.11514 −0.0981827
\(130\) −5.98599 12.7723i −0.525006 1.12020i
\(131\) 11.2785 0.985406 0.492703 0.870197i \(-0.336009\pi\)
0.492703 + 0.870197i \(0.336009\pi\)
\(132\) 3.79849i 0.330616i
\(133\) 0 0
\(134\) 18.4809 1.59651
\(135\) −1.77672 + 0.832695i −0.152916 + 0.0716670i
\(136\) −42.2915 −3.62647
\(137\) 13.8445i 1.18282i 0.806373 + 0.591408i \(0.201428\pi\)
−0.806373 + 0.591408i \(0.798572\pi\)
\(138\) 0.473467i 0.0403042i
\(139\) 1.97238 0.167295 0.0836475 0.996495i \(-0.473343\pi\)
0.0836475 + 0.996495i \(0.473343\pi\)
\(140\) −11.1293 + 5.21598i −0.940600 + 0.440831i
\(141\) 1.15275 0.0970791
\(142\) 7.14866i 0.599902i
\(143\) 12.9719i 1.08477i
\(144\) 28.5533 2.37944
\(145\) 3.71468 + 7.92601i 0.308488 + 0.658219i
\(146\) 14.5933 1.20775
\(147\) 0.836504i 0.0689937i
\(148\) 35.5485i 2.92207i
\(149\) −11.1782 −0.915753 −0.457876 0.889016i \(-0.651390\pi\)
−0.457876 + 0.889016i \(0.651390\pi\)
\(150\) −1.22618 + 1.47286i −0.100117 + 0.120259i
\(151\) 10.4524 0.850603 0.425301 0.905052i \(-0.360168\pi\)
0.425301 + 0.905052i \(0.360168\pi\)
\(152\) 0 0
\(153\) 17.1098i 1.38324i
\(154\) 15.9942 1.28885
\(155\) 6.15257 + 13.1277i 0.494186 + 1.05444i
\(156\) −1.70874 −0.136808
\(157\) 5.62072i 0.448583i 0.974522 + 0.224291i \(0.0720067\pi\)
−0.974522 + 0.224291i \(0.927993\pi\)
\(158\) 24.9849i 1.98769i
\(159\) −0.00262771 −0.000208391
\(160\) 20.8750 9.78350i 1.65032 0.773453i
\(161\) −1.40891 −0.111037
\(162\) 22.9972i 1.80683i
\(163\) 5.97258i 0.467808i −0.972260 0.233904i \(-0.924850\pi\)
0.972260 0.233904i \(-0.0751502\pi\)
\(164\) −23.4337 −1.82986
\(165\) 1.59588 0.747940i 0.124239 0.0582271i
\(166\) −1.02055 −0.0792100
\(167\) 10.2447i 0.792756i −0.918087 0.396378i \(-0.870267\pi\)
0.918087 0.396378i \(-0.129733\pi\)
\(168\) 1.23250i 0.0950893i
\(169\) 7.16464 0.551126
\(170\) 14.2349 + 30.3730i 1.09177 + 2.32950i
\(171\) 0 0
\(172\) 36.6139i 2.79178i
\(173\) 2.49506i 0.189696i 0.995492 + 0.0948479i \(0.0302365\pi\)
−0.995492 + 0.0948479i \(0.969764\pi\)
\(174\) 1.50044 0.113748
\(175\) 4.38283 + 3.64876i 0.331311 + 0.275821i
\(176\) −51.4796 −3.88042
\(177\) 1.91179i 0.143699i
\(178\) 9.34131i 0.700161i
\(179\) −22.5409 −1.68478 −0.842392 0.538865i \(-0.818853\pi\)
−0.842392 + 0.538865i \(0.818853\pi\)
\(180\) −13.6209 29.0628i −1.01524 2.16621i
\(181\) −6.81802 −0.506779 −0.253390 0.967364i \(-0.581545\pi\)
−0.253390 + 0.967364i \(0.581545\pi\)
\(182\) 7.19490i 0.533322i
\(183\) 0.00278370i 0.000205777i
\(184\) 9.09410 0.670426
\(185\) −14.9352 + 6.99966i −1.09805 + 0.514625i
\(186\) 2.48515 0.182220
\(187\) 30.8477i 2.25581i
\(188\) 37.8488i 2.76041i
\(189\) 1.00086 0.0728021
\(190\) 0 0
\(191\) −4.97452 −0.359944 −0.179972 0.983672i \(-0.557601\pi\)
−0.179972 + 0.983672i \(0.557601\pi\)
\(192\) 1.13754i 0.0820948i
\(193\) 7.01693i 0.505090i 0.967585 + 0.252545i \(0.0812675\pi\)
−0.967585 + 0.252545i \(0.918733\pi\)
\(194\) 38.4995 2.76410
\(195\) 0.336458 + 0.717899i 0.0240942 + 0.0514098i
\(196\) −27.4653 −1.96181
\(197\) 22.0852i 1.57351i 0.617266 + 0.786754i \(0.288240\pi\)
−0.617266 + 0.786754i \(0.711760\pi\)
\(198\) 41.7666i 2.96822i
\(199\) −2.40961 −0.170812 −0.0854062 0.996346i \(-0.527219\pi\)
−0.0854062 + 0.996346i \(0.527219\pi\)
\(200\) −28.2899 23.5518i −2.00040 1.66536i
\(201\) −1.03877 −0.0732690
\(202\) 27.5335i 1.93725i
\(203\) 4.46489i 0.313374i
\(204\) 4.06344 0.284498
\(205\) 4.61419 + 9.84529i 0.322269 + 0.687625i
\(206\) −23.8173 −1.65943
\(207\) 3.67917i 0.255720i
\(208\) 23.1579i 1.60571i
\(209\) 0 0
\(210\) 0.885158 0.414847i 0.0610817 0.0286272i
\(211\) 19.0046 1.30833 0.654166 0.756351i \(-0.273020\pi\)
0.654166 + 0.756351i \(0.273020\pi\)
\(212\) 0.0862768i 0.00592552i
\(213\) 0.401808i 0.0275315i
\(214\) −9.30609 −0.636151
\(215\) −15.3828 + 7.20944i −1.04910 + 0.491680i
\(216\) −6.46029 −0.439567
\(217\) 7.39512i 0.502014i
\(218\) 27.8489i 1.88617i
\(219\) −0.820251 −0.0554274
\(220\) 24.5574 + 52.3982i 1.65566 + 3.53268i
\(221\) 13.8767 0.933449
\(222\) 2.82731i 0.189757i
\(223\) 22.0446i 1.47622i 0.674683 + 0.738108i \(0.264280\pi\)
−0.674683 + 0.738108i \(0.735720\pi\)
\(224\) −11.7593 −0.785704
\(225\) −9.52827 + 11.4452i −0.635218 + 0.763012i
\(226\) −33.6262 −2.23678
\(227\) 11.7969i 0.782990i −0.920180 0.391495i \(-0.871958\pi\)
0.920180 0.391495i \(-0.128042\pi\)
\(228\) 0 0
\(229\) 1.19467 0.0789463 0.0394731 0.999221i \(-0.487432\pi\)
0.0394731 + 0.999221i \(0.487432\pi\)
\(230\) −3.06099 6.53122i −0.201835 0.430656i
\(231\) −0.898992 −0.0591493
\(232\) 28.8196i 1.89210i
\(233\) 15.6081i 1.02252i 0.859426 + 0.511260i \(0.170821\pi\)
−0.859426 + 0.511260i \(0.829179\pi\)
\(234\) −18.7885 −1.22825
\(235\) 15.9016 7.45259i 1.03730 0.486153i
\(236\) −62.7708 −4.08603
\(237\) 1.40434i 0.0912216i
\(238\) 17.1098i 1.10906i
\(239\) −1.05474 −0.0682255 −0.0341128 0.999418i \(-0.510861\pi\)
−0.0341128 + 0.999418i \(0.510861\pi\)
\(240\) −2.84902 + 1.33525i −0.183903 + 0.0861900i
\(241\) 9.59410 0.618010 0.309005 0.951060i \(-0.400004\pi\)
0.309005 + 0.951060i \(0.400004\pi\)
\(242\) 46.5772i 2.99410i
\(243\) 3.92514i 0.251798i
\(244\) 0.0913985 0.00585119
\(245\) 5.40804 + 11.5391i 0.345507 + 0.737208i
\(246\) 1.86377 0.118830
\(247\) 0 0
\(248\) 47.7334i 3.03108i
\(249\) 0.0573625 0.00363520
\(250\) −7.39233 + 28.2446i −0.467532 + 1.78635i
\(251\) −15.1640 −0.957142 −0.478571 0.878049i \(-0.658845\pi\)
−0.478571 + 0.878049i \(0.658845\pi\)
\(252\) 16.3717i 1.03132i
\(253\) 6.63329i 0.417031i
\(254\) 19.7748 1.24078
\(255\) −0.800110 1.70719i −0.0501048 0.106909i
\(256\) −16.4972 −1.03108
\(257\) 23.0689i 1.43900i −0.694493 0.719499i \(-0.744371\pi\)
0.694493 0.719499i \(-0.255629\pi\)
\(258\) 2.91204i 0.181296i
\(259\) 8.41329 0.522777
\(260\) −23.5711 + 11.0471i −1.46182 + 0.685110i
\(261\) 11.6595 0.721703
\(262\) 29.4523i 1.81957i
\(263\) 3.05610i 0.188447i −0.995551 0.0942235i \(-0.969963\pi\)
0.995551 0.0942235i \(-0.0300368\pi\)
\(264\) 5.80274 0.357134
\(265\) −0.0362479 + 0.0169883i −0.00222669 + 0.00104358i
\(266\) 0 0
\(267\) 0.525052i 0.0321327i
\(268\) 34.1063i 2.08337i
\(269\) 1.05451 0.0642948 0.0321474 0.999483i \(-0.489765\pi\)
0.0321474 + 0.999483i \(0.489765\pi\)
\(270\) 2.17447 + 4.63967i 0.132334 + 0.282361i
\(271\) −1.67598 −0.101809 −0.0509043 0.998704i \(-0.516210\pi\)
−0.0509043 + 0.998704i \(0.516210\pi\)
\(272\) 55.0704i 3.33913i
\(273\) 0.404408i 0.0244759i
\(274\) 36.1531 2.18409
\(275\) 17.1788 20.6349i 1.03592 1.24433i
\(276\) −0.873776 −0.0525952
\(277\) 13.8944i 0.834834i 0.908715 + 0.417417i \(0.137065\pi\)
−0.908715 + 0.417417i \(0.862935\pi\)
\(278\) 5.15061i 0.308913i
\(279\) 19.3114 1.15614
\(280\) 7.96816 + 17.0016i 0.476189 + 1.01604i
\(281\) 1.25004 0.0745713 0.0372856 0.999305i \(-0.488129\pi\)
0.0372856 + 0.999305i \(0.488129\pi\)
\(282\) 3.01026i 0.179258i
\(283\) 15.7261i 0.934819i 0.884041 + 0.467409i \(0.154813\pi\)
−0.884041 + 0.467409i \(0.845187\pi\)
\(284\) 13.1927 0.782846
\(285\) 0 0
\(286\) 33.8744 2.00304
\(287\) 5.54606i 0.327374i
\(288\) 30.7080i 1.80948i
\(289\) −15.9994 −0.941140
\(290\) 20.6977 9.70040i 1.21541 0.569627i
\(291\) −2.16396 −0.126854
\(292\) 26.9316i 1.57606i
\(293\) 11.9316i 0.697051i 0.937299 + 0.348526i \(0.113318\pi\)
−0.937299 + 0.348526i \(0.886682\pi\)
\(294\) 2.18442 0.127398
\(295\) 12.3598 + 26.3722i 0.719618 + 1.53545i
\(296\) −54.3055 −3.15644
\(297\) 4.71218i 0.273428i
\(298\) 29.1904i 1.69095i
\(299\) −2.98396 −0.172567
\(300\) 2.71815 + 2.26289i 0.156932 + 0.130648i
\(301\) 8.66544 0.499467
\(302\) 27.2950i 1.57065i
\(303\) 1.54759i 0.0889067i
\(304\) 0 0
\(305\) −0.0179968 0.0383996i −0.00103049 0.00219876i
\(306\) 44.6799 2.55418
\(307\) 24.3857i 1.39176i −0.718156 0.695882i \(-0.755014\pi\)
0.718156 0.695882i \(-0.244986\pi\)
\(308\) 29.5170i 1.68189i
\(309\) 1.33871 0.0761567
\(310\) 34.2813 16.0666i 1.94705 0.912523i
\(311\) −5.06773 −0.287364 −0.143682 0.989624i \(-0.545894\pi\)
−0.143682 + 0.989624i \(0.545894\pi\)
\(312\) 2.61034i 0.147781i
\(313\) 18.9537i 1.07133i −0.844431 0.535664i \(-0.820061\pi\)
0.844431 0.535664i \(-0.179939\pi\)
\(314\) 14.6778 0.828315
\(315\) 6.87830 3.22366i 0.387549 0.181632i
\(316\) −46.1093 −2.59385
\(317\) 12.1377i 0.681720i −0.940114 0.340860i \(-0.889282\pi\)
0.940114 0.340860i \(-0.110718\pi\)
\(318\) 0.00686192i 0.000384798i
\(319\) −21.0212 −1.17696
\(320\) −7.35424 15.6917i −0.411115 0.877194i
\(321\) 0.523072 0.0291950
\(322\) 3.67917i 0.205032i
\(323\) 0 0
\(324\) −42.4410 −2.35783
\(325\) 9.28251 + 7.72781i 0.514901 + 0.428662i
\(326\) −15.5966 −0.863815
\(327\) 1.56532i 0.0865623i
\(328\) 35.7983i 1.97663i
\(329\) −8.95769 −0.493853
\(330\) −1.95315 4.16742i −0.107517 0.229409i
\(331\) 19.3649 1.06439 0.532197 0.846621i \(-0.321367\pi\)
0.532197 + 0.846621i \(0.321367\pi\)
\(332\) 1.88341i 0.103366i
\(333\) 21.9702i 1.20396i
\(334\) −26.7526 −1.46384
\(335\) −14.3292 + 6.71568i −0.782889 + 0.366917i
\(336\) 1.60491 0.0875551
\(337\) 4.13312i 0.225146i 0.993643 + 0.112573i \(0.0359091\pi\)
−0.993643 + 0.112573i \(0.964091\pi\)
\(338\) 18.7095i 1.01766i
\(339\) 1.89005 0.102653
\(340\) 56.0530 26.2704i 3.03990 1.42471i
\(341\) −34.8171 −1.88545
\(342\) 0 0
\(343\) 14.4842i 0.782076i
\(344\) −55.9330 −3.01570
\(345\) 0.172050 + 0.367104i 0.00926288 + 0.0197642i
\(346\) 6.51552 0.350276
\(347\) 4.77587i 0.256382i 0.991749 + 0.128191i \(0.0409171\pi\)
−0.991749 + 0.128191i \(0.959083\pi\)
\(348\) 2.76904i 0.148436i
\(349\) −0.557017 −0.0298165 −0.0149082 0.999889i \(-0.504746\pi\)
−0.0149082 + 0.999889i \(0.504746\pi\)
\(350\) 9.52827 11.4452i 0.509307 0.611771i
\(351\) 2.11975 0.113144
\(352\) 55.3643i 2.95093i
\(353\) 24.4841i 1.30316i −0.758580 0.651580i \(-0.774107\pi\)
0.758580 0.651580i \(-0.225893\pi\)
\(354\) 4.99240 0.265343
\(355\) −2.59771 5.54273i −0.137872 0.294177i
\(356\) −17.2393 −0.913679
\(357\) 0.961697i 0.0508984i
\(358\) 58.8625i 3.11098i
\(359\) −20.9706 −1.10679 −0.553393 0.832921i \(-0.686667\pi\)
−0.553393 + 0.832921i \(0.686667\pi\)
\(360\) −44.3975 + 20.8078i −2.33996 + 1.09667i
\(361\) 0 0
\(362\) 17.8044i 0.935776i
\(363\) 2.61799i 0.137409i
\(364\) 13.2781 0.695961
\(365\) −11.3149 + 5.30296i −0.592250 + 0.277570i
\(366\) −0.00726927 −0.000379971
\(367\) 21.4343i 1.11886i −0.828877 0.559431i \(-0.811020\pi\)
0.828877 0.559431i \(-0.188980\pi\)
\(368\) 11.8420i 0.617306i
\(369\) 14.4828 0.753945
\(370\) 18.2787 + 39.0012i 0.950264 + 2.02758i
\(371\) 0.0204192 0.00106011
\(372\) 4.58631i 0.237789i
\(373\) 27.7981i 1.43933i −0.694321 0.719666i \(-0.744295\pi\)
0.694321 0.719666i \(-0.255705\pi\)
\(374\) −80.5547 −4.16539
\(375\) 0.415504 1.58756i 0.0214566 0.0819813i
\(376\) 57.8194 2.98181
\(377\) 9.45630i 0.487024i
\(378\) 2.61362i 0.134430i
\(379\) 1.97507 0.101452 0.0507261 0.998713i \(-0.483846\pi\)
0.0507261 + 0.998713i \(0.483846\pi\)
\(380\) 0 0
\(381\) −1.11150 −0.0569436
\(382\) 12.9903i 0.664642i
\(383\) 10.0103i 0.511504i −0.966742 0.255752i \(-0.917677\pi\)
0.966742 0.255752i \(-0.0823231\pi\)
\(384\) 0.0560484 0.00286021
\(385\) −12.4011 + 5.81203i −0.632019 + 0.296208i
\(386\) 18.3238 0.932656
\(387\) 22.6286i 1.15028i
\(388\) 71.0502i 3.60703i
\(389\) −12.0247 −0.609678 −0.304839 0.952404i \(-0.598603\pi\)
−0.304839 + 0.952404i \(0.598603\pi\)
\(390\) 1.87470 0.878615i 0.0949291 0.0444904i
\(391\) 7.09597 0.358859
\(392\) 41.9572i 2.11916i
\(393\) 1.65544i 0.0835059i
\(394\) 57.6727 2.90551
\(395\) 9.07912 + 19.3721i 0.456820 + 0.974715i
\(396\) 77.0797 3.87340
\(397\) 1.87227i 0.0939666i −0.998896 0.0469833i \(-0.985039\pi\)
0.998896 0.0469833i \(-0.0149608\pi\)
\(398\) 6.29237i 0.315408i
\(399\) 0 0
\(400\) −30.6682 + 36.8381i −1.53341 + 1.84190i
\(401\) −23.5289 −1.17498 −0.587489 0.809232i \(-0.699883\pi\)
−0.587489 + 0.809232i \(0.699883\pi\)
\(402\) 2.71260i 0.135292i
\(403\) 15.6623i 0.780196i
\(404\) 50.8127 2.52803
\(405\) 8.35682 + 17.8309i 0.415254 + 0.886026i
\(406\) −11.6595 −0.578649
\(407\) 39.6107i 1.96343i
\(408\) 6.20749i 0.307316i
\(409\) 16.0211 0.792193 0.396097 0.918209i \(-0.370364\pi\)
0.396097 + 0.918209i \(0.370364\pi\)
\(410\) 25.7097 12.0494i 1.26971 0.595075i
\(411\) −2.03207 −0.100235
\(412\) 43.9545i 2.16548i
\(413\) 14.8560i 0.731016i
\(414\) −9.60767 −0.472191
\(415\) 0.791285 0.370852i 0.0388427 0.0182044i
\(416\) −24.9054 −1.22109
\(417\) 0.289503i 0.0141770i
\(418\) 0 0
\(419\) 10.2305 0.499794 0.249897 0.968272i \(-0.419603\pi\)
0.249897 + 0.968272i \(0.419603\pi\)
\(420\) −0.765594 1.63355i −0.0373572 0.0797089i
\(421\) 25.6300 1.24913 0.624565 0.780973i \(-0.285276\pi\)
0.624565 + 0.780973i \(0.285276\pi\)
\(422\) 49.6281i 2.41586i
\(423\) 23.3918i 1.13735i
\(424\) −0.131800 −0.00640078
\(425\) −22.0742 18.3770i −1.07075 0.891417i
\(426\) −1.04927 −0.0508373
\(427\) 0.0216313i 0.00104681i
\(428\) 17.1743i 0.830149i
\(429\) −1.90400 −0.0919259
\(430\) 18.8265 + 40.1701i 0.907895 + 1.93717i
\(431\) −26.3929 −1.27130 −0.635650 0.771978i \(-0.719268\pi\)
−0.635650 + 0.771978i \(0.719268\pi\)
\(432\) 8.41234i 0.404739i
\(433\) 11.1339i 0.535061i 0.963549 + 0.267531i \(0.0862077\pi\)
−0.963549 + 0.267531i \(0.913792\pi\)
\(434\) −19.3114 −0.926976
\(435\) −1.16337 + 0.545236i −0.0557792 + 0.0261420i
\(436\) 51.3948 2.46136
\(437\) 0 0
\(438\) 2.14198i 0.102348i
\(439\) −32.5878 −1.55533 −0.777666 0.628677i \(-0.783597\pi\)
−0.777666 + 0.628677i \(0.783597\pi\)
\(440\) 80.0457 37.5150i 3.81603 1.78846i
\(441\) 16.9745 0.808309
\(442\) 36.2372i 1.72363i
\(443\) 41.7702i 1.98456i 0.124013 + 0.992281i \(0.460424\pi\)
−0.124013 + 0.992281i \(0.539576\pi\)
\(444\) 5.21776 0.247624
\(445\) 3.39449 + 7.24281i 0.160914 + 0.343342i
\(446\) 57.5666 2.72586
\(447\) 1.64072i 0.0776033i
\(448\) 8.83948i 0.417626i
\(449\) 40.0139 1.88837 0.944187 0.329409i \(-0.106849\pi\)
0.944187 + 0.329409i \(0.106849\pi\)
\(450\) 29.8876 + 24.8818i 1.40891 + 1.17294i
\(451\) −26.1115 −1.22954
\(452\) 62.0567i 2.91890i
\(453\) 1.53419i 0.0720823i
\(454\) −30.8061 −1.44580
\(455\) −2.61452 5.57858i −0.122570 0.261528i
\(456\) 0 0
\(457\) 30.1103i 1.40850i 0.709953 + 0.704249i \(0.248716\pi\)
−0.709953 + 0.704249i \(0.751284\pi\)
\(458\) 3.11973i 0.145776i
\(459\) −5.04086 −0.235287
\(460\) −12.0533 + 5.64901i −0.561987 + 0.263386i
\(461\) −19.8065 −0.922479 −0.461239 0.887276i \(-0.652595\pi\)
−0.461239 + 0.887276i \(0.652595\pi\)
\(462\) 2.34760i 0.109220i
\(463\) 17.0673i 0.793186i 0.917994 + 0.396593i \(0.129808\pi\)
−0.917994 + 0.396593i \(0.870192\pi\)
\(464\) 37.5278 1.74218
\(465\) −1.92687 + 0.903065i −0.0893563 + 0.0418786i
\(466\) 40.7585 1.88810
\(467\) 24.1262i 1.11643i 0.829697 + 0.558214i \(0.188513\pi\)
−0.829697 + 0.558214i \(0.811487\pi\)
\(468\) 34.6740i 1.60281i
\(469\) 8.07196 0.372728
\(470\) −19.4615 41.5249i −0.897690 1.91540i
\(471\) −0.825001 −0.0380141
\(472\) 95.8913i 4.41376i
\(473\) 40.7979i 1.87589i
\(474\) 3.66724 0.168442
\(475\) 0 0
\(476\) −31.5758 −1.44728
\(477\) 0.0533220i 0.00244145i
\(478\) 2.75432i 0.125979i
\(479\) 32.5068 1.48527 0.742637 0.669695i \(-0.233575\pi\)
0.742637 + 0.669695i \(0.233575\pi\)
\(480\) 1.43601 + 3.06400i 0.0655445 + 0.139852i
\(481\) 17.8187 0.812464
\(482\) 25.0537i 1.14117i
\(483\) 0.206797i 0.00940960i
\(484\) −85.9576 −3.90717
\(485\) −29.8506 + 13.9901i −1.35545 + 0.635258i
\(486\) 10.2500 0.464949
\(487\) 30.4975i 1.38197i −0.722868 0.690986i \(-0.757177\pi\)
0.722868 0.690986i \(-0.242823\pi\)
\(488\) 0.139624i 0.00632049i
\(489\) 0.876646 0.0396433
\(490\) 30.1329 14.1224i 1.36127 0.637984i
\(491\) −19.4673 −0.878548 −0.439274 0.898353i \(-0.644764\pi\)
−0.439274 + 0.898353i \(0.644764\pi\)
\(492\) 3.43956i 0.155067i
\(493\) 22.4875i 1.01278i
\(494\) 0 0
\(495\) −15.1773 32.3838i −0.682171 1.45555i
\(496\) 62.1567 2.79092
\(497\) 3.12234i 0.140056i
\(498\) 0.149795i 0.00671246i
\(499\) −1.81090 −0.0810670 −0.0405335 0.999178i \(-0.512906\pi\)
−0.0405335 + 0.999178i \(0.512906\pi\)
\(500\) 52.1251 + 13.6424i 2.33110 + 0.610108i
\(501\) 1.50370 0.0671802
\(502\) 39.5987i 1.76738i
\(503\) 26.5154i 1.18226i 0.806575 + 0.591132i \(0.201319\pi\)
−0.806575 + 0.591132i \(0.798681\pi\)
\(504\) 25.0101 1.11404
\(505\) −10.0052 21.3482i −0.445228 0.949981i
\(506\) 17.3220 0.770055
\(507\) 1.05162i 0.0467039i
\(508\) 36.4942i 1.61917i
\(509\) 11.3299 0.502191 0.251095 0.967962i \(-0.419209\pi\)
0.251095 + 0.967962i \(0.419209\pi\)
\(510\) −4.45811 + 2.08938i −0.197408 + 0.0925194i
\(511\) 6.37393 0.281966
\(512\) 42.3167i 1.87015i
\(513\) 0 0
\(514\) −60.2414 −2.65713
\(515\) 18.4668 8.65484i 0.813745 0.381378i
\(516\) 5.37414 0.236583
\(517\) 42.1738i 1.85480i
\(518\) 21.9702i 0.965315i
\(519\) −0.366221 −0.0160753
\(520\) 16.8760 + 36.0082i 0.740060 + 1.57906i
\(521\) −25.1821 −1.10325 −0.551624 0.834093i \(-0.685992\pi\)
−0.551624 + 0.834093i \(0.685992\pi\)
\(522\) 30.4472i 1.33264i
\(523\) 2.56239i 0.112045i −0.998429 0.0560227i \(-0.982158\pi\)
0.998429 0.0560227i \(-0.0178419\pi\)
\(524\) −54.3538 −2.37446
\(525\) −0.535560 + 0.643305i −0.0233738 + 0.0280761i
\(526\) −7.98060 −0.347971
\(527\) 37.2456i 1.62244i
\(528\) 7.55610i 0.328837i
\(529\) 21.4741 0.933658
\(530\) 0.0443627 + 0.0946565i 0.00192699 + 0.00411162i
\(531\) 38.7945 1.68354
\(532\) 0 0
\(533\) 11.7461i 0.508782i
\(534\) 1.37110 0.0593335
\(535\) 7.21550 3.38169i 0.311953 0.146203i
\(536\) −52.1022 −2.25047
\(537\) 3.30852i 0.142773i
\(538\) 2.75372i 0.118721i
\(539\) −30.6038 −1.31820
\(540\) 8.56244 4.01296i 0.368469 0.172690i
\(541\) 27.1770 1.16843 0.584215 0.811599i \(-0.301402\pi\)
0.584215 + 0.811599i \(0.301402\pi\)
\(542\) 4.37660i 0.187991i
\(543\) 1.00074i 0.0429458i
\(544\) 59.2260 2.53929
\(545\) −10.1199 21.5927i −0.433487 0.924930i
\(546\) −1.05606 −0.0451951
\(547\) 15.6526i 0.669259i −0.942350 0.334629i \(-0.891389\pi\)
0.942350 0.334629i \(-0.108611\pi\)
\(548\) 66.7200i 2.85014i
\(549\) −0.0564874 −0.00241082
\(550\) −53.8852 44.8602i −2.29767 1.91284i
\(551\) 0 0
\(552\) 1.33482i 0.0568136i
\(553\) 10.9127i 0.464055i
\(554\) 36.2834 1.54153
\(555\) −1.02740 2.19216i −0.0436107 0.0930520i
\(556\) −9.50537 −0.403118
\(557\) 38.7469i 1.64176i −0.571101 0.820880i \(-0.693484\pi\)
0.571101 0.820880i \(-0.306516\pi\)
\(558\) 50.4291i 2.13484i
\(559\) 18.3528 0.776239
\(560\) 22.1389 10.3758i 0.935538 0.438459i
\(561\) 4.52778 0.191163
\(562\) 3.26432i 0.137697i
\(563\) 38.8502i 1.63734i 0.574265 + 0.818670i \(0.305288\pi\)
−0.574265 + 0.818670i \(0.694712\pi\)
\(564\) −5.55539 −0.233924
\(565\) 26.0722 12.2192i 1.09686 0.514067i
\(566\) 41.0666 1.72616
\(567\) 10.0445i 0.421831i
\(568\) 20.1538i 0.845635i
\(569\) 19.2093 0.805294 0.402647 0.915355i \(-0.368090\pi\)
0.402647 + 0.915355i \(0.368090\pi\)
\(570\) 0 0
\(571\) −8.84542 −0.370169 −0.185085 0.982723i \(-0.559256\pi\)
−0.185085 + 0.982723i \(0.559256\pi\)
\(572\) 62.5148i 2.61387i
\(573\) 0.730153i 0.0305026i
\(574\) −14.4828 −0.604500
\(575\) 4.74668 + 3.95168i 0.197950 + 0.164796i
\(576\) −23.0831 −0.961797
\(577\) 15.0333i 0.625845i −0.949779 0.312922i \(-0.898692\pi\)
0.949779 0.312922i \(-0.101308\pi\)
\(578\) 41.7802i 1.73783i
\(579\) −1.02993 −0.0428026
\(580\) −17.9020 38.1974i −0.743338 1.58606i
\(581\) −0.445748 −0.0184927
\(582\) 5.65089i 0.234237i
\(583\) 0.0961358i 0.00398154i
\(584\) −41.1419 −1.70247
\(585\) 14.5677 6.82746i 0.602302 0.282281i
\(586\) 31.1578 1.28712
\(587\) 42.7945i 1.76632i 0.469073 + 0.883159i \(0.344588\pi\)
−0.469073 + 0.883159i \(0.655412\pi\)
\(588\) 4.03132i 0.166249i
\(589\) 0 0
\(590\) 68.8674 32.2761i 2.83523 1.32879i
\(591\) −3.24164 −0.133343
\(592\) 70.7145i 2.90635i
\(593\) 30.9216i 1.26980i 0.772595 + 0.634900i \(0.218959\pi\)
−0.772595 + 0.634900i \(0.781041\pi\)
\(594\) −12.3052 −0.504890
\(595\) 6.21742 + 13.2661i 0.254889 + 0.543857i
\(596\) 53.8704 2.20662
\(597\) 0.353678i 0.0144751i
\(598\) 7.79221i 0.318647i
\(599\) −18.2839 −0.747058 −0.373529 0.927618i \(-0.621852\pi\)
−0.373529 + 0.927618i \(0.621852\pi\)
\(600\) 3.45689 4.15236i 0.141127 0.169519i
\(601\) −40.5660 −1.65472 −0.827361 0.561670i \(-0.810159\pi\)
−0.827361 + 0.561670i \(0.810159\pi\)
\(602\) 22.6286i 0.922275i
\(603\) 21.0788i 0.858397i
\(604\) −50.3726 −2.04963
\(605\) 16.9254 + 36.1138i 0.688117 + 1.46823i
\(606\) −4.04133 −0.164168
\(607\) 9.33324i 0.378825i −0.981898 0.189412i \(-0.939342\pi\)
0.981898 0.189412i \(-0.0606583\pi\)
\(608\) 0 0
\(609\) 0.655350 0.0265561
\(610\) −0.100276 + 0.0469962i −0.00406004 + 0.00190282i
\(611\) −18.9717 −0.767514
\(612\) 82.4561i 3.33309i
\(613\) 40.6646i 1.64243i 0.570621 + 0.821213i \(0.306702\pi\)
−0.570621 + 0.821213i \(0.693298\pi\)
\(614\) −63.6800 −2.56991
\(615\) −1.44508 + 0.677264i −0.0582711 + 0.0273099i
\(616\) −45.0914 −1.81678
\(617\) 18.4246i 0.741745i −0.928684 0.370872i \(-0.879059\pi\)
0.928684 0.370872i \(-0.120941\pi\)
\(618\) 3.49587i 0.140625i
\(619\) 2.68372 0.107868 0.0539340 0.998545i \(-0.482824\pi\)
0.0539340 + 0.998545i \(0.482824\pi\)
\(620\) −29.6507 63.2657i −1.19080 2.54081i
\(621\) 1.08395 0.0434975
\(622\) 13.2337i 0.530623i
\(623\) 4.08003i 0.163463i
\(624\) 3.39908 0.136072
\(625\) −4.53200 24.5858i −0.181280 0.983432i
\(626\) −49.4952 −1.97823
\(627\) 0 0
\(628\) 27.0876i 1.08091i
\(629\) −42.3736 −1.68955
\(630\) −8.41815 17.9618i −0.335387 0.715615i
\(631\) −18.6512 −0.742492 −0.371246 0.928535i \(-0.621069\pi\)
−0.371246 + 0.928535i \(0.621069\pi\)
\(632\) 70.4385i 2.80189i
\(633\) 2.78947i 0.110872i
\(634\) −31.6959 −1.25881
\(635\) −15.3325 + 7.18587i −0.608451 + 0.285163i
\(636\) 0.0126636 0.000502144
\(637\) 13.7670i 0.545469i
\(638\) 54.8941i 2.17328i
\(639\) −8.15357 −0.322550
\(640\) 0.773157 0.362356i 0.0305617 0.0143234i
\(641\) 4.88420 0.192914 0.0964572 0.995337i \(-0.469249\pi\)
0.0964572 + 0.995337i \(0.469249\pi\)
\(642\) 1.36593i 0.0539091i
\(643\) 3.68757i 0.145424i 0.997353 + 0.0727118i \(0.0231653\pi\)
−0.997353 + 0.0727118i \(0.976835\pi\)
\(644\) 6.78986 0.267558
\(645\) −1.05819 2.25786i −0.0416662 0.0889031i
\(646\) 0 0
\(647\) 26.3559i 1.03616i 0.855333 + 0.518079i \(0.173353\pi\)
−0.855333 + 0.518079i \(0.826647\pi\)
\(648\) 64.8347i 2.54695i
\(649\) −69.9437 −2.74553
\(650\) 20.1802 24.2400i 0.791531 0.950773i
\(651\) 1.08544 0.0425419
\(652\) 28.7833i 1.12724i
\(653\) 23.9281i 0.936379i −0.883628 0.468189i \(-0.844907\pi\)
0.883628 0.468189i \(-0.155093\pi\)
\(654\) −4.08762 −0.159839
\(655\) 10.7025 + 22.8359i 0.418181 + 0.892272i
\(656\) 46.6151 1.82001
\(657\) 16.6447i 0.649371i
\(658\) 23.3918i 0.911908i
\(659\) 5.97176 0.232627 0.116313 0.993213i \(-0.462892\pi\)
0.116313 + 0.993213i \(0.462892\pi\)
\(660\) −7.69092 + 3.60451i −0.299369 + 0.140305i
\(661\) −11.3007 −0.439545 −0.219773 0.975551i \(-0.570532\pi\)
−0.219773 + 0.975551i \(0.570532\pi\)
\(662\) 50.5690i 1.96542i
\(663\) 2.03680i 0.0791029i
\(664\) 2.87718 0.111656
\(665\) 0 0
\(666\) 57.3723 2.22313
\(667\) 4.83555i 0.187233i
\(668\) 49.3715i 1.91024i
\(669\) −3.23567 −0.125098
\(670\) 17.5371 + 37.4189i 0.677518 + 1.44562i
\(671\) 0.101843 0.00393160
\(672\) 1.72602i 0.0665826i
\(673\) 22.9796i 0.885798i 0.896571 + 0.442899i \(0.146050\pi\)
−0.896571 + 0.442899i \(0.853950\pi\)
\(674\) 10.7931 0.415735
\(675\) −3.37196 2.80721i −0.129787 0.108049i
\(676\) −34.5281 −1.32801
\(677\) 30.2320i 1.16191i −0.813936 0.580955i \(-0.802679\pi\)
0.813936 0.580955i \(-0.197321\pi\)
\(678\) 4.93561i 0.189551i
\(679\) 16.8155 0.645319
\(680\) −40.1317 85.6289i −1.53898 3.28372i
\(681\) 1.73154 0.0663526
\(682\) 90.9202i 3.48151i
\(683\) 38.7762i 1.48373i −0.670549 0.741866i \(-0.733941\pi\)
0.670549 0.741866i \(-0.266059\pi\)
\(684\) 0 0
\(685\) −28.0314 + 13.1375i −1.07102 + 0.501957i
\(686\) −37.8237 −1.44412
\(687\) 0.175352i 0.00669011i
\(688\) 72.8338i 2.77676i
\(689\) 0.0432463 0.00164755
\(690\) 0.958642 0.449287i 0.0364949 0.0171041i
\(691\) −34.4907 −1.31209 −0.656044 0.754723i \(-0.727771\pi\)
−0.656044 + 0.754723i \(0.727771\pi\)
\(692\) 12.0243i 0.457095i
\(693\) 18.2425i 0.692975i
\(694\) 12.4716 0.473414
\(695\) 1.87165 + 3.99353i 0.0709957 + 0.151483i
\(696\) −4.23010 −0.160341
\(697\) 27.9328i 1.05803i
\(698\) 1.45458i 0.0550566i
\(699\) −2.29093 −0.0866511
\(700\) −21.1219 17.5843i −0.798333 0.664623i
\(701\) −2.43041 −0.0917952 −0.0458976 0.998946i \(-0.514615\pi\)
−0.0458976 + 0.998946i \(0.514615\pi\)
\(702\) 5.53546i 0.208922i
\(703\) 0 0
\(704\) 41.6173 1.56851
\(705\) 1.09388 + 2.33401i 0.0411979 + 0.0879039i
\(706\) −63.9371 −2.40630
\(707\) 12.0259i 0.452279i
\(708\) 9.21340i 0.346261i
\(709\) 14.9095 0.559939 0.279969 0.960009i \(-0.409676\pi\)
0.279969 + 0.960009i \(0.409676\pi\)
\(710\) −14.4741 + 6.78358i −0.543203 + 0.254583i
\(711\) 28.4971 1.06872
\(712\) 26.3354i 0.986962i
\(713\) 8.00905i 0.299941i
\(714\) 2.51135 0.0939848
\(715\) −26.2646 + 12.3094i −0.982241 + 0.460347i
\(716\) 108.630 4.05969
\(717\) 0.154813i 0.00578161i
\(718\) 54.7619i 2.04370i
\(719\) 47.2596 1.76248 0.881242 0.472665i \(-0.156708\pi\)
0.881242 + 0.472665i \(0.156708\pi\)
\(720\) 27.0951 + 57.8128i 1.00978 + 2.15455i
\(721\) −10.4027 −0.387419
\(722\) 0 0
\(723\) 1.40821i 0.0523718i
\(724\) 32.8577 1.22115
\(725\) −12.5230 + 15.0425i −0.465094 + 0.558663i
\(726\) 6.83654 0.253728
\(727\) 41.1123i 1.52477i −0.647123 0.762386i \(-0.724028\pi\)
0.647123 0.762386i \(-0.275972\pi\)
\(728\) 20.2842i 0.751782i
\(729\) 25.8436 0.957170
\(730\) 13.8480 + 29.5474i 0.512537 + 1.09360i
\(731\) −43.6436 −1.61422
\(732\) 0.0134153i 0.000495845i
\(733\) 25.6070i 0.945816i 0.881112 + 0.472908i \(0.156796\pi\)
−0.881112 + 0.472908i \(0.843204\pi\)
\(734\) −55.9729 −2.06600
\(735\) −1.69370 + 0.793784i −0.0624729 + 0.0292792i
\(736\) −12.7356 −0.469440
\(737\) 38.0037i 1.39988i
\(738\) 37.8199i 1.39217i
\(739\) −10.4997 −0.386237 −0.193119 0.981175i \(-0.561860\pi\)
−0.193119 + 0.981175i \(0.561860\pi\)
\(740\) 71.9762 33.7331i 2.64590 1.24005i
\(741\) 0 0
\(742\) 0.0533220i 0.00195751i
\(743\) 4.64951i 0.170574i 0.996356 + 0.0852871i \(0.0271807\pi\)
−0.996356 + 0.0852871i \(0.972819\pi\)
\(744\) −7.00624 −0.256861
\(745\) −10.6073 22.6328i −0.388622 0.829202i
\(746\) −72.5911 −2.65775
\(747\) 1.16401i 0.0425889i
\(748\) 148.663i 5.43564i
\(749\) −4.06464 −0.148519
\(750\) −4.14570 1.08503i −0.151380 0.0396199i
\(751\) −52.7364 −1.92438 −0.962190 0.272381i \(-0.912189\pi\)
−0.962190 + 0.272381i \(0.912189\pi\)
\(752\) 75.2902i 2.74555i
\(753\) 2.22575i 0.0811107i
\(754\) −24.6939 −0.899298
\(755\) 9.91858 + 21.1633i 0.360974 + 0.770210i
\(756\) −4.82340 −0.175425
\(757\) 13.3049i 0.483575i −0.970329 0.241788i \(-0.922266\pi\)
0.970329 0.241788i \(-0.0777337\pi\)
\(758\) 5.15762i 0.187333i
\(759\) −0.973624 −0.0353403
\(760\) 0 0
\(761\) −20.3115 −0.736292 −0.368146 0.929768i \(-0.620007\pi\)
−0.368146 + 0.929768i \(0.620007\pi\)
\(762\) 2.90252i 0.105147i
\(763\) 12.1636i 0.440353i
\(764\) 23.9734 0.867328
\(765\) −34.6427 + 16.2360i −1.25251 + 0.587013i
\(766\) −26.1407 −0.944501
\(767\) 31.4639i 1.13610i
\(768\) 2.42144i 0.0873762i
\(769\) 21.2618 0.766721 0.383360 0.923599i \(-0.374767\pi\)
0.383360 + 0.923599i \(0.374767\pi\)
\(770\) 15.1773 + 32.3838i 0.546953 + 1.16703i
\(771\) 3.38602 0.121945
\(772\) 33.8163i 1.21707i
\(773\) 36.0232i 1.29566i −0.761783 0.647832i \(-0.775676\pi\)
0.761783 0.647832i \(-0.224324\pi\)
\(774\) 59.0917 2.12401
\(775\) −20.7417 + 24.9146i −0.745065 + 0.894958i
\(776\) −108.539 −3.89633
\(777\) 1.23489i 0.0443014i
\(778\) 31.4010i 1.12578i
\(779\) 0 0
\(780\) −1.62147 3.45973i −0.0580580 0.123878i
\(781\) 14.7003 0.526018
\(782\) 18.5302i 0.662638i
\(783\) 3.43510i 0.122760i
\(784\) 54.6350 1.95125
\(785\) −11.3804 + 5.33368i −0.406186 + 0.190367i
\(786\) 4.32296 0.154195
\(787\) 41.0609i 1.46366i 0.681486 + 0.731831i \(0.261334\pi\)
−0.681486 + 0.731831i \(0.738666\pi\)
\(788\) 106.434i 3.79156i
\(789\) 0.448570 0.0159695
\(790\) 50.5876 23.7089i 1.79983 0.843525i
\(791\) −14.6870 −0.522210
\(792\) 117.750i 4.18407i
\(793\) 0.0458135i 0.00162689i
\(794\) −4.88919 −0.173511
\(795\) −0.00249352 0.00532041i −8.84359e−5 0.000188695i
\(796\) 11.6125 0.411593
\(797\) 33.9392i 1.20219i 0.799179 + 0.601093i \(0.205268\pi\)
−0.799179 + 0.601093i \(0.794732\pi\)
\(798\) 0 0
\(799\) 45.1155 1.59607
\(800\) 39.6179 + 32.9824i 1.40070 + 1.16610i
\(801\) 10.6545 0.376456
\(802\) 61.4426i 2.16961i
\(803\) 30.0092i 1.05900i
\(804\) 5.00607 0.176551
\(805\) −1.33695 2.85265i −0.0471214 0.100543i
\(806\) −40.9001 −1.44064
\(807\) 0.154780i 0.00544851i
\(808\) 77.6237i 2.73079i
\(809\) 51.3707 1.80610 0.903048 0.429539i \(-0.141324\pi\)
0.903048 + 0.429539i \(0.141324\pi\)
\(810\) 46.5631 21.8227i 1.63606 0.766773i
\(811\) −20.6118 −0.723779 −0.361890 0.932221i \(-0.617868\pi\)
−0.361890 + 0.932221i \(0.617868\pi\)
\(812\) 21.5174i 0.755112i
\(813\) 0.245998i 0.00862752i
\(814\) −103.438 −3.62551
\(815\) 12.0929 5.66756i 0.423594 0.198526i
\(816\) −8.08315 −0.282967
\(817\) 0 0
\(818\) 41.8370i 1.46280i
\(819\) −8.20631 −0.286752
\(820\) −22.2369 47.4468i −0.776547 1.65692i
\(821\) 38.7002 1.35065 0.675323 0.737522i \(-0.264004\pi\)
0.675323 + 0.737522i \(0.264004\pi\)
\(822\) 5.30650i 0.185085i
\(823\) 18.7887i 0.654932i 0.944863 + 0.327466i \(0.106195\pi\)
−0.944863 + 0.327466i \(0.893805\pi\)
\(824\) 67.1468 2.33917
\(825\) 3.02875 + 2.52148i 0.105448 + 0.0877866i
\(826\) −38.7945 −1.34983
\(827\) 36.8031i 1.27977i −0.768471 0.639885i \(-0.778982\pi\)
0.768471 0.639885i \(-0.221018\pi\)
\(828\) 17.7308i 0.616189i
\(829\) −22.6730 −0.787466 −0.393733 0.919225i \(-0.628816\pi\)
−0.393733 + 0.919225i \(0.628816\pi\)
\(830\) −0.968430 2.06634i −0.0336147 0.0717236i
\(831\) −2.03940 −0.0707460
\(832\) 18.7214i 0.649047i
\(833\) 32.7385i 1.13432i
\(834\) 0.755998 0.0261781
\(835\) 20.7427 9.72147i 0.717830 0.336425i
\(836\) 0 0
\(837\) 5.68950i 0.196658i
\(838\) 26.7157i 0.922878i
\(839\) −2.70578 −0.0934139 −0.0467070 0.998909i \(-0.514873\pi\)
−0.0467070 + 0.998909i \(0.514873\pi\)
\(840\) −2.49548 + 1.16955i −0.0861021 + 0.0403535i
\(841\) −13.6759 −0.471583
\(842\) 66.9293i 2.30654i
\(843\) 0.183479i 0.00631937i
\(844\) −91.5879 −3.15259
\(845\) 6.79874 + 14.5065i 0.233884 + 0.499037i
\(846\) −61.0847 −2.10013
\(847\) 20.3436i 0.699016i
\(848\) 0.171625i 0.00589363i
\(849\) −2.30825 −0.0792190
\(850\) −47.9892 + 57.6438i −1.64602 + 1.97716i
\(851\) 9.11175 0.312347
\(852\) 1.93641i 0.0663404i
\(853\) 28.0139i 0.959178i −0.877493 0.479589i \(-0.840786\pi\)
0.877493 0.479589i \(-0.159214\pi\)
\(854\) 0.0564874 0.00193296
\(855\) 0 0
\(856\) 26.2361 0.896732
\(857\) 37.9069i 1.29487i 0.762119 + 0.647437i \(0.224159\pi\)
−0.762119 + 0.647437i \(0.775841\pi\)
\(858\) 4.97204i 0.169743i
\(859\) 25.5377 0.871336 0.435668 0.900107i \(-0.356512\pi\)
0.435668 + 0.900107i \(0.356512\pi\)
\(860\) 74.1333 34.7441i 2.52792 1.18476i
\(861\) 0.814042 0.0277425
\(862\) 68.9215i 2.34747i
\(863\) 46.3212i 1.57679i −0.615169 0.788395i \(-0.710912\pi\)
0.615169 0.788395i \(-0.289088\pi\)
\(864\) 9.04714 0.307790
\(865\) −5.05182 + 2.36764i −0.171767 + 0.0805021i
\(866\) 29.0747 0.987999
\(867\) 2.34836i 0.0797546i
\(868\) 35.6389i 1.20966i
\(869\) −51.3783 −1.74289
\(870\) 1.42381 + 3.03798i 0.0482717 + 0.102997i
\(871\) 17.0958 0.579269
\(872\) 78.5128i 2.65878i
\(873\) 43.9114i 1.48618i
\(874\) 0 0
\(875\) −3.22876 + 12.3365i −0.109152 + 0.417049i
\(876\) 3.95299 0.133559
\(877\) 43.7693i 1.47798i −0.673715 0.738992i \(-0.735302\pi\)
0.673715 0.738992i \(-0.264698\pi\)
\(878\) 85.0988i 2.87195i
\(879\) −1.75130 −0.0590700
\(880\) −48.8506 104.232i −1.64675 3.51367i
\(881\) −34.6665 −1.16795 −0.583973 0.811773i \(-0.698503\pi\)
−0.583973 + 0.811773i \(0.698503\pi\)
\(882\) 44.3267i 1.49256i
\(883\) 43.5573i 1.46582i −0.680325 0.732910i \(-0.738161\pi\)
0.680325 0.732910i \(-0.261839\pi\)
\(884\) −66.8753 −2.24926
\(885\) −3.87087 + 1.81416i −0.130118 + 0.0609823i
\(886\) 109.077 3.66452
\(887\) 48.2351i 1.61957i 0.586723 + 0.809787i \(0.300418\pi\)
−0.586723 + 0.809787i \(0.699582\pi\)
\(888\) 7.97087i 0.267485i
\(889\) 8.63710 0.289679
\(890\) 18.9136 8.86426i 0.633987 0.297131i
\(891\) −47.2908 −1.58430
\(892\) 106.238i 3.55712i
\(893\) 0 0
\(894\) −4.28452 −0.143296
\(895\) −21.3897 45.6392i −0.714979 1.52555i
\(896\) −0.435536 −0.0145502
\(897\) 0.437981i 0.0146238i
\(898\) 104.491i 3.48691i
\(899\) 25.3810 0.846505
\(900\) 45.9190 55.1571i 1.53063 1.83857i
\(901\) −0.102841 −0.00342615
\(902\) 68.1867i 2.27037i
\(903\) 1.27190i 0.0423262i
\(904\) 94.8005 3.15302
\(905\) −6.46982 13.8046i −0.215064 0.458882i
\(906\) 4.00632 0.133101
\(907\) 44.1877i 1.46723i −0.679567 0.733613i \(-0.737832\pi\)
0.679567 0.733613i \(-0.262168\pi\)
\(908\) 56.8523i 1.88671i
\(909\) −31.4040 −1.04160
\(910\) −14.5677 + 6.82746i −0.482916 + 0.226328i
\(911\) −33.6536 −1.11499 −0.557496 0.830180i \(-0.688238\pi\)
−0.557496 + 0.830180i \(0.688238\pi\)
\(912\) 0 0
\(913\) 2.09863i 0.0694545i
\(914\) 78.6290 2.60082
\(915\) 0.00563624 0.00264154i 0.000186328 8.73266e-5i
\(916\) −5.75742 −0.190231
\(917\) 12.8639i 0.424805i
\(918\) 13.1635i 0.434461i
\(919\) −4.04484 −0.133427 −0.0667134 0.997772i \(-0.521251\pi\)
−0.0667134 + 0.997772i \(0.521251\pi\)
\(920\) 8.62966 + 18.4131i 0.284512 + 0.607062i
\(921\) 3.57929 0.117942
\(922\) 51.7220i 1.70337i
\(923\) 6.61287i 0.217665i
\(924\) 4.33246 0.142527
\(925\) −28.3449 23.5975i −0.931973 0.775880i
\(926\) 44.5691 1.46463
\(927\) 27.1654i 0.892229i
\(928\) 40.3596i 1.32487i
\(929\) 40.2101 1.31925 0.659625 0.751594i \(-0.270715\pi\)
0.659625 + 0.751594i \(0.270715\pi\)
\(930\) 2.35824 + 5.03176i 0.0773296 + 0.164998i
\(931\) 0 0
\(932\) 75.2192i 2.46389i
\(933\) 0.743833i 0.0243520i
\(934\) 63.0024 2.06150
\(935\) 62.4583 29.2723i 2.04260 0.957307i
\(936\) 52.9695 1.73136
\(937\) 13.1716i 0.430297i 0.976581 + 0.215149i \(0.0690236\pi\)
−0.976581 + 0.215149i \(0.930976\pi\)
\(938\) 21.0788i 0.688249i
\(939\) 2.78200 0.0907872
\(940\) −76.6335 + 35.9158i −2.49951 + 1.17145i
\(941\) 33.9107 1.10546 0.552729 0.833361i \(-0.313586\pi\)
0.552729 + 0.833361i \(0.313586\pi\)
\(942\) 2.15438i 0.0701936i
\(943\) 6.00648i 0.195598i
\(944\) 124.866 4.06404
\(945\) 0.949749 + 2.02648i 0.0308953 + 0.0659213i
\(946\) −106.538 −3.46386
\(947\) 34.4561i 1.11967i −0.828603 0.559836i \(-0.810864\pi\)
0.828603 0.559836i \(-0.189136\pi\)
\(948\) 6.76785i 0.219810i
\(949\) 13.4995 0.438213
\(950\) 0 0
\(951\) 1.78155 0.0577707
\(952\) 48.2366i 1.56336i
\(953\) 6.03770i 0.195580i −0.995207 0.0977902i \(-0.968823\pi\)
0.995207 0.0977902i \(-0.0311774\pi\)
\(954\) 0.139243 0.00450817
\(955\) −4.72047 10.0721i −0.152751 0.325924i
\(956\) 5.08305 0.164398
\(957\) 3.08546i 0.0997388i
\(958\) 84.8872i 2.74258i
\(959\) 15.7907 0.509907
\(960\) 2.30321 1.07944i 0.0743357 0.0348389i
\(961\) 11.0382 0.356072
\(962\) 46.5313i 1.50023i
\(963\) 10.6143i 0.342040i
\(964\) −46.2363 −1.48917
\(965\) −14.2074 + 6.65858i −0.457352 + 0.214347i
\(966\) −0.540023 −0.0173750
\(967\) 12.5734i 0.404334i 0.979351 + 0.202167i \(0.0647983\pi\)
−0.979351 + 0.202167i \(0.935202\pi\)
\(968\) 131.313i 4.22055i
\(969\) 0 0
\(970\) 36.5333 + 77.9510i 1.17301 + 2.50286i
\(971\) −20.5595 −0.659787 −0.329894 0.944018i \(-0.607013\pi\)
−0.329894 + 0.944018i \(0.607013\pi\)
\(972\) 18.9162i 0.606738i
\(973\) 2.24964i 0.0721202i
\(974\) −79.6401 −2.55183
\(975\) −1.13428 + 1.36247i −0.0363259 + 0.0436340i
\(976\) −0.181813 −0.00581970
\(977\) 1.26370i 0.0404295i −0.999796 0.0202147i \(-0.993565\pi\)
0.999796 0.0202147i \(-0.00643499\pi\)
\(978\) 2.28924i 0.0732020i
\(979\) −19.2092 −0.613930
\(980\) −26.0627 55.6098i −0.832541 1.77639i
\(981\) −31.7637 −1.01414
\(982\) 50.8364i 1.62225i
\(983\) 35.5329i 1.13332i −0.823950 0.566662i \(-0.808235\pi\)
0.823950 0.566662i \(-0.191765\pi\)
\(984\) −5.25442 −0.167505
\(985\) −44.7166 + 20.9574i −1.42479 + 0.667757i
\(986\) 58.7230 1.87012
\(987\) 1.31480i 0.0418504i
\(988\) 0 0
\(989\) 9.38483 0.298420
\(990\) −84.5661 + 39.6336i −2.68769 + 1.25964i
\(991\) 4.48854 0.142583 0.0712916 0.997456i \(-0.477288\pi\)
0.0712916 + 0.997456i \(0.477288\pi\)
\(992\) 66.8470i 2.12239i
\(993\) 2.84236i 0.0901995i
\(994\) 8.15357 0.258615
\(995\) −2.28655 4.87880i −0.0724885 0.154668i
\(996\) −0.276444 −0.00875946
\(997\) 8.36943i 0.265063i −0.991179 0.132531i \(-0.957690\pi\)
0.991179 0.132531i \(-0.0423105\pi\)
\(998\) 4.72892i 0.149691i
\(999\) −6.47283 −0.204791
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 1805.2.b.j.1084.1 yes 16
5.2 odd 4 9025.2.a.ck.1.16 16
5.3 odd 4 9025.2.a.ck.1.1 16
5.4 even 2 inner 1805.2.b.j.1084.16 yes 16
19.18 odd 2 1805.2.b.i.1084.16 yes 16
95.18 even 4 9025.2.a.cl.1.16 16
95.37 even 4 9025.2.a.cl.1.1 16
95.94 odd 2 1805.2.b.i.1084.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1805.2.b.i.1084.1 16 95.94 odd 2
1805.2.b.i.1084.16 yes 16 19.18 odd 2
1805.2.b.j.1084.1 yes 16 1.1 even 1 trivial
1805.2.b.j.1084.16 yes 16 5.4 even 2 inner
9025.2.a.ck.1.1 16 5.3 odd 4
9025.2.a.ck.1.16 16 5.2 odd 4
9025.2.a.cl.1.1 16 95.37 even 4
9025.2.a.cl.1.16 16 95.18 even 4