Properties

Label 55.2.b.a.34.1
Level $55$
Weight $2$
Character 55.34
Analytic conductor $0.439$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,2,Mod(34,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, 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("55.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 55.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: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 55.34
Dual form 55.2.b.a.34.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +O(q^{10})\) \(q-2.52434i q^{2} +0.792287i q^{3} -4.37228 q^{4} +(0.686141 - 2.12819i) q^{5} +2.00000 q^{6} +3.46410i q^{7} +5.98844i q^{8} +2.37228 q^{9} +(-5.37228 - 1.73205i) q^{10} -1.00000 q^{11} -3.46410i q^{12} +8.74456 q^{14} +(1.68614 + 0.543620i) q^{15} +6.37228 q^{16} +1.58457i q^{17} -5.98844i q^{18} -4.00000 q^{19} +(-3.00000 + 9.30506i) q^{20} -2.74456 q^{21} +2.52434i q^{22} -0.792287i q^{23} -4.74456 q^{24} +(-4.05842 - 2.92048i) q^{25} +4.25639i q^{27} -15.1460i q^{28} -8.74456 q^{29} +(1.37228 - 4.25639i) q^{30} +3.37228 q^{31} -4.10891i q^{32} -0.792287i q^{33} +4.00000 q^{34} +(7.37228 + 2.37686i) q^{35} -10.3723 q^{36} -1.08724i q^{37} +10.0974i q^{38} +(12.7446 + 4.10891i) q^{40} +8.74456 q^{41} +6.92820i q^{42} -3.46410i q^{43} +4.37228 q^{44} +(1.62772 - 5.04868i) q^{45} -2.00000 q^{46} -6.63325i q^{47} +5.04868i q^{48} -5.00000 q^{49} +(-7.37228 + 10.2448i) q^{50} -1.25544 q^{51} -10.0974i q^{53} +10.7446 q^{54} +(-0.686141 + 2.12819i) q^{55} -20.7446 q^{56} -3.16915i q^{57} +22.0742i q^{58} +7.37228 q^{59} +(-7.37228 - 2.37686i) q^{60} -0.744563 q^{61} -8.51278i q^{62} +8.21782i q^{63} +2.37228 q^{64} -2.00000 q^{66} +9.30506i q^{67} -6.92820i q^{68} +0.627719 q^{69} +(6.00000 - 18.6101i) q^{70} -10.1168 q^{71} +14.2063i q^{72} +6.92820i q^{73} -2.74456 q^{74} +(2.31386 - 3.21543i) q^{75} +17.4891 q^{76} -3.46410i q^{77} -1.25544 q^{79} +(4.37228 - 13.5615i) q^{80} +3.74456 q^{81} -22.0742i q^{82} -6.63325i q^{83} +12.0000 q^{84} +(3.37228 + 1.08724i) q^{85} -8.74456 q^{86} -6.92820i q^{87} -5.98844i q^{88} -1.37228 q^{89} +(-12.7446 - 4.10891i) q^{90} +3.46410i q^{92} +2.67181i q^{93} -16.7446 q^{94} +(-2.74456 + 8.51278i) q^{95} +3.25544 q^{96} +5.84096i q^{97} +12.6217i q^{98} -2.37228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{4} - 3 q^{5} + 8 q^{6} - 2 q^{9} - 10 q^{10} - 4 q^{11} + 12 q^{14} + q^{15} + 14 q^{16} - 16 q^{19} - 12 q^{20} + 12 q^{21} + 4 q^{24} + q^{25} - 12 q^{29} - 6 q^{30} + 2 q^{31} + 16 q^{34} + 18 q^{35} - 30 q^{36} + 28 q^{40} + 12 q^{41} + 6 q^{44} + 18 q^{45} - 8 q^{46} - 20 q^{49} - 18 q^{50} - 28 q^{51} + 20 q^{54} + 3 q^{55} - 60 q^{56} + 18 q^{59} - 18 q^{60} + 20 q^{61} - 2 q^{64} - 8 q^{66} + 14 q^{69} + 24 q^{70} - 6 q^{71} + 12 q^{74} + 15 q^{75} + 24 q^{76} - 28 q^{79} + 6 q^{80} - 8 q^{81} + 48 q^{84} + 2 q^{85} - 12 q^{86} + 6 q^{89} - 28 q^{90} - 44 q^{94} + 12 q^{95} + 36 q^{96} + 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/55\mathbb{Z}\right)^\times\).

\(n\) \(12\) \(46\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.52434i 1.78498i −0.451071 0.892488i \(-0.648958\pi\)
0.451071 0.892488i \(-0.351042\pi\)
\(3\) 0.792287i 0.457427i 0.973494 + 0.228714i \(0.0734519\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −4.37228 −2.18614
\(5\) 0.686141 2.12819i 0.306851 0.951757i
\(6\) 2.00000 0.816497
\(7\) 3.46410i 1.30931i 0.755929 + 0.654654i \(0.227186\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 5.98844i 2.11723i
\(9\) 2.37228 0.790760
\(10\) −5.37228 1.73205i −1.69886 0.547723i
\(11\) −1.00000 −0.301511
\(12\) 3.46410i 1.00000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 8.74456 2.33708
\(15\) 1.68614 + 0.543620i 0.435360 + 0.140362i
\(16\) 6.37228 1.59307
\(17\) 1.58457i 0.384316i 0.981364 + 0.192158i \(0.0615486\pi\)
−0.981364 + 0.192158i \(0.938451\pi\)
\(18\) 5.98844i 1.41149i
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −3.00000 + 9.30506i −0.670820 + 2.08068i
\(21\) −2.74456 −0.598913
\(22\) 2.52434i 0.538191i
\(23\) 0.792287i 0.165203i −0.996583 0.0826016i \(-0.973677\pi\)
0.996583 0.0826016i \(-0.0263229\pi\)
\(24\) −4.74456 −0.968480
\(25\) −4.05842 2.92048i −0.811684 0.584096i
\(26\) 0 0
\(27\) 4.25639i 0.819142i
\(28\) 15.1460i 2.86233i
\(29\) −8.74456 −1.62382 −0.811912 0.583779i \(-0.801573\pi\)
−0.811912 + 0.583779i \(0.801573\pi\)
\(30\) 1.37228 4.25639i 0.250543 0.777107i
\(31\) 3.37228 0.605680 0.302840 0.953041i \(-0.402065\pi\)
0.302840 + 0.953041i \(0.402065\pi\)
\(32\) 4.10891i 0.726360i
\(33\) 0.792287i 0.137919i
\(34\) 4.00000 0.685994
\(35\) 7.37228 + 2.37686i 1.24614 + 0.401763i
\(36\) −10.3723 −1.72871
\(37\) 1.08724i 0.178741i −0.995998 0.0893706i \(-0.971514\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 10.0974i 1.63801i
\(39\) 0 0
\(40\) 12.7446 + 4.10891i 2.01509 + 0.649676i
\(41\) 8.74456 1.36567 0.682836 0.730572i \(-0.260747\pi\)
0.682836 + 0.730572i \(0.260747\pi\)
\(42\) 6.92820i 1.06904i
\(43\) 3.46410i 0.528271i −0.964486 0.264135i \(-0.914913\pi\)
0.964486 0.264135i \(-0.0850865\pi\)
\(44\) 4.37228 0.659146
\(45\) 1.62772 5.04868i 0.242646 0.752612i
\(46\) −2.00000 −0.294884
\(47\) 6.63325i 0.967559i −0.875190 0.483779i \(-0.839264\pi\)
0.875190 0.483779i \(-0.160736\pi\)
\(48\) 5.04868i 0.728714i
\(49\) −5.00000 −0.714286
\(50\) −7.37228 + 10.2448i −1.04260 + 1.44884i
\(51\) −1.25544 −0.175796
\(52\) 0 0
\(53\) 10.0974i 1.38698i −0.720467 0.693489i \(-0.756073\pi\)
0.720467 0.693489i \(-0.243927\pi\)
\(54\) 10.7446 1.46215
\(55\) −0.686141 + 2.12819i −0.0925192 + 0.286966i
\(56\) −20.7446 −2.77211
\(57\) 3.16915i 0.419764i
\(58\) 22.0742i 2.89849i
\(59\) 7.37228 0.959789 0.479895 0.877326i \(-0.340675\pi\)
0.479895 + 0.877326i \(0.340675\pi\)
\(60\) −7.37228 2.37686i −0.951757 0.306851i
\(61\) −0.744563 −0.0953315 −0.0476657 0.998863i \(-0.515178\pi\)
−0.0476657 + 0.998863i \(0.515178\pi\)
\(62\) 8.51278i 1.08112i
\(63\) 8.21782i 1.03535i
\(64\) 2.37228 0.296535
\(65\) 0 0
\(66\) −2.00000 −0.246183
\(67\) 9.30506i 1.13679i 0.822754 + 0.568397i \(0.192436\pi\)
−0.822754 + 0.568397i \(0.807564\pi\)
\(68\) 6.92820i 0.840168i
\(69\) 0.627719 0.0755684
\(70\) 6.00000 18.6101i 0.717137 2.22434i
\(71\) −10.1168 −1.20065 −0.600324 0.799757i \(-0.704962\pi\)
−0.600324 + 0.799757i \(0.704962\pi\)
\(72\) 14.2063i 1.67422i
\(73\) 6.92820i 0.810885i 0.914121 + 0.405442i \(0.132883\pi\)
−0.914121 + 0.405442i \(0.867117\pi\)
\(74\) −2.74456 −0.319049
\(75\) 2.31386 3.21543i 0.267181 0.371286i
\(76\) 17.4891 2.00614
\(77\) 3.46410i 0.394771i
\(78\) 0 0
\(79\) −1.25544 −0.141248 −0.0706239 0.997503i \(-0.522499\pi\)
−0.0706239 + 0.997503i \(0.522499\pi\)
\(80\) 4.37228 13.5615i 0.488836 1.51622i
\(81\) 3.74456 0.416063
\(82\) 22.0742i 2.43769i
\(83\) 6.63325i 0.728094i −0.931381 0.364047i \(-0.881395\pi\)
0.931381 0.364047i \(-0.118605\pi\)
\(84\) 12.0000 1.30931
\(85\) 3.37228 + 1.08724i 0.365775 + 0.117928i
\(86\) −8.74456 −0.942950
\(87\) 6.92820i 0.742781i
\(88\) 5.98844i 0.638370i
\(89\) −1.37228 −0.145462 −0.0727308 0.997352i \(-0.523171\pi\)
−0.0727308 + 0.997352i \(0.523171\pi\)
\(90\) −12.7446 4.10891i −1.34339 0.433117i
\(91\) 0 0
\(92\) 3.46410i 0.361158i
\(93\) 2.67181i 0.277054i
\(94\) −16.7446 −1.72707
\(95\) −2.74456 + 8.51278i −0.281586 + 0.873393i
\(96\) 3.25544 0.332257
\(97\) 5.84096i 0.593060i 0.955024 + 0.296530i \(0.0958295\pi\)
−0.955024 + 0.296530i \(0.904171\pi\)
\(98\) 12.6217i 1.27498i
\(99\) −2.37228 −0.238423
\(100\) 17.7446 + 12.7692i 1.77446 + 1.27692i
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 3.16915i 0.313792i
\(103\) 10.3923i 1.02398i 0.858990 + 0.511992i \(0.171092\pi\)
−0.858990 + 0.511992i \(0.828908\pi\)
\(104\) 0 0
\(105\) −1.88316 + 5.84096i −0.183777 + 0.570020i
\(106\) −25.4891 −2.47572
\(107\) 6.63325i 0.641260i −0.947204 0.320630i \(-0.896105\pi\)
0.947204 0.320630i \(-0.103895\pi\)
\(108\) 18.6101i 1.79076i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 5.37228 + 1.73205i 0.512227 + 0.165145i
\(111\) 0.861407 0.0817611
\(112\) 22.0742i 2.08582i
\(113\) 0.497333i 0.0467852i 0.999726 + 0.0233926i \(0.00744677\pi\)
−0.999726 + 0.0233926i \(0.992553\pi\)
\(114\) −8.00000 −0.749269
\(115\) −1.68614 0.543620i −0.157233 0.0506929i
\(116\) 38.2337 3.54991
\(117\) 0 0
\(118\) 18.6101i 1.71320i
\(119\) −5.48913 −0.503187
\(120\) −3.25544 + 10.0974i −0.297179 + 0.921758i
\(121\) 1.00000 0.0909091
\(122\) 1.87953i 0.170164i
\(123\) 6.92820i 0.624695i
\(124\) −14.7446 −1.32410
\(125\) −9.00000 + 6.63325i −0.804984 + 0.593296i
\(126\) 20.7446 1.84807
\(127\) 8.21782i 0.729214i −0.931162 0.364607i \(-0.881203\pi\)
0.931162 0.364607i \(-0.118797\pi\)
\(128\) 14.2063i 1.25567i
\(129\) 2.74456 0.241645
\(130\) 0 0
\(131\) −2.74456 −0.239794 −0.119897 0.992786i \(-0.538256\pi\)
−0.119897 + 0.992786i \(0.538256\pi\)
\(132\) 3.46410i 0.301511i
\(133\) 13.8564i 1.20150i
\(134\) 23.4891 2.02915
\(135\) 9.05842 + 2.92048i 0.779625 + 0.251355i
\(136\) −9.48913 −0.813686
\(137\) 14.3537i 1.22632i 0.789958 + 0.613161i \(0.210102\pi\)
−0.789958 + 0.613161i \(0.789898\pi\)
\(138\) 1.58457i 0.134888i
\(139\) 16.2337 1.37692 0.688462 0.725273i \(-0.258286\pi\)
0.688462 + 0.725273i \(0.258286\pi\)
\(140\) −32.2337 10.3923i −2.72424 0.878310i
\(141\) 5.25544 0.442588
\(142\) 25.5383i 2.14313i
\(143\) 0 0
\(144\) 15.1168 1.25974
\(145\) −6.00000 + 18.6101i −0.498273 + 1.54549i
\(146\) 17.4891 1.44741
\(147\) 3.96143i 0.326734i
\(148\) 4.75372i 0.390754i
\(149\) 11.4891 0.941226 0.470613 0.882340i \(-0.344033\pi\)
0.470613 + 0.882340i \(0.344033\pi\)
\(150\) −8.11684 5.84096i −0.662738 0.476913i
\(151\) −12.2337 −0.995563 −0.497782 0.867302i \(-0.665852\pi\)
−0.497782 + 0.867302i \(0.665852\pi\)
\(152\) 23.9538i 1.94291i
\(153\) 3.75906i 0.303902i
\(154\) −8.74456 −0.704657
\(155\) 2.31386 7.17687i 0.185854 0.576460i
\(156\) 0 0
\(157\) 24.4511i 1.95141i −0.219090 0.975705i \(-0.570309\pi\)
0.219090 0.975705i \(-0.429691\pi\)
\(158\) 3.16915i 0.252124i
\(159\) 8.00000 0.634441
\(160\) −8.74456 2.81929i −0.691318 0.222885i
\(161\) 2.74456 0.216302
\(162\) 9.45254i 0.742662i
\(163\) 3.46410i 0.271329i 0.990755 + 0.135665i \(0.0433170\pi\)
−0.990755 + 0.135665i \(0.956683\pi\)
\(164\) −38.2337 −2.98555
\(165\) −1.68614 0.543620i −0.131266 0.0423208i
\(166\) −16.7446 −1.29963
\(167\) 15.7359i 1.21768i −0.793292 0.608842i \(-0.791635\pi\)
0.793292 0.608842i \(-0.208365\pi\)
\(168\) 16.4356i 1.26804i
\(169\) 13.0000 1.00000
\(170\) 2.74456 8.51278i 0.210498 0.652900i
\(171\) −9.48913 −0.725652
\(172\) 15.1460i 1.15487i
\(173\) 8.51278i 0.647214i 0.946192 + 0.323607i \(0.104896\pi\)
−0.946192 + 0.323607i \(0.895104\pi\)
\(174\) −17.4891 −1.32585
\(175\) 10.1168 14.0588i 0.764762 1.06274i
\(176\) −6.37228 −0.480329
\(177\) 5.84096i 0.439034i
\(178\) 3.46410i 0.259645i
\(179\) −12.8614 −0.961307 −0.480653 0.876911i \(-0.659600\pi\)
−0.480653 + 0.876911i \(0.659600\pi\)
\(180\) −7.11684 + 22.0742i −0.530458 + 1.64532i
\(181\) 24.1168 1.79259 0.896295 0.443457i \(-0.146248\pi\)
0.896295 + 0.443457i \(0.146248\pi\)
\(182\) 0 0
\(183\) 0.589907i 0.0436072i
\(184\) 4.74456 0.349774
\(185\) −2.31386 0.746000i −0.170118 0.0548470i
\(186\) 6.74456 0.494535
\(187\) 1.58457i 0.115876i
\(188\) 29.0024i 2.11522i
\(189\) −14.7446 −1.07251
\(190\) 21.4891 + 6.92820i 1.55899 + 0.502625i
\(191\) −19.3723 −1.40173 −0.700865 0.713294i \(-0.747202\pi\)
−0.700865 + 0.713294i \(0.747202\pi\)
\(192\) 1.87953i 0.135643i
\(193\) 16.4356i 1.18306i 0.806282 + 0.591532i \(0.201477\pi\)
−0.806282 + 0.591532i \(0.798523\pi\)
\(194\) 14.7446 1.05860
\(195\) 0 0
\(196\) 21.8614 1.56153
\(197\) 8.51278i 0.606510i 0.952909 + 0.303255i \(0.0980734\pi\)
−0.952909 + 0.303255i \(0.901927\pi\)
\(198\) 5.98844i 0.425580i
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 17.4891 24.3036i 1.23667 1.71853i
\(201\) −7.37228 −0.520001
\(202\) 15.1460i 1.06567i
\(203\) 30.2921i 2.12609i
\(204\) 5.48913 0.384316
\(205\) 6.00000 18.6101i 0.419058 1.29979i
\(206\) 26.2337 1.82779
\(207\) 1.87953i 0.130636i
\(208\) 0 0
\(209\) 4.00000 0.276686
\(210\) 14.7446 + 4.75372i 1.01747 + 0.328038i
\(211\) 1.48913 0.102516 0.0512578 0.998685i \(-0.483677\pi\)
0.0512578 + 0.998685i \(0.483677\pi\)
\(212\) 44.1485i 3.03213i
\(213\) 8.01544i 0.549209i
\(214\) −16.7446 −1.14463
\(215\) −7.37228 2.37686i −0.502785 0.162101i
\(216\) −25.4891 −1.73432
\(217\) 11.6819i 0.793021i
\(218\) 25.2434i 1.70970i
\(219\) −5.48913 −0.370921
\(220\) 3.00000 9.30506i 0.202260 0.627347i
\(221\) 0 0
\(222\) 2.17448i 0.145942i
\(223\) 2.37686i 0.159166i 0.996828 + 0.0795832i \(0.0253589\pi\)
−0.996828 + 0.0795832i \(0.974641\pi\)
\(224\) 14.2337 0.951028
\(225\) −9.62772 6.92820i −0.641848 0.461880i
\(226\) 1.25544 0.0835105
\(227\) 16.7306i 1.11045i 0.831701 + 0.555224i \(0.187368\pi\)
−0.831701 + 0.555224i \(0.812632\pi\)
\(228\) 13.8564i 0.917663i
\(229\) −14.6277 −0.966627 −0.483313 0.875447i \(-0.660567\pi\)
−0.483313 + 0.875447i \(0.660567\pi\)
\(230\) −1.37228 + 4.25639i −0.0904856 + 0.280658i
\(231\) 2.74456 0.180579
\(232\) 52.3663i 3.43801i
\(233\) 3.75906i 0.246264i 0.992390 + 0.123132i \(0.0392938\pi\)
−0.992390 + 0.123132i \(0.960706\pi\)
\(234\) 0 0
\(235\) −14.1168 4.55134i −0.920881 0.296897i
\(236\) −32.2337 −2.09823
\(237\) 0.994667i 0.0646105i
\(238\) 13.8564i 0.898177i
\(239\) 14.7446 0.953746 0.476873 0.878972i \(-0.341770\pi\)
0.476873 + 0.878972i \(0.341770\pi\)
\(240\) 10.7446 + 3.46410i 0.693559 + 0.223607i
\(241\) 16.7446 1.07861 0.539306 0.842110i \(-0.318687\pi\)
0.539306 + 0.842110i \(0.318687\pi\)
\(242\) 2.52434i 0.162271i
\(243\) 15.7359i 1.00946i
\(244\) 3.25544 0.208408
\(245\) −3.43070 + 10.6410i −0.219180 + 0.679827i
\(246\) 17.4891 1.11507
\(247\) 0 0
\(248\) 20.1947i 1.28236i
\(249\) 5.25544 0.333050
\(250\) 16.7446 + 22.7190i 1.05902 + 1.43688i
\(251\) −22.1168 −1.39600 −0.698001 0.716096i \(-0.745927\pi\)
−0.698001 + 0.716096i \(0.745927\pi\)
\(252\) 35.9306i 2.26342i
\(253\) 0.792287i 0.0498107i
\(254\) −20.7446 −1.30163
\(255\) −0.861407 + 2.67181i −0.0539434 + 0.167316i
\(256\) −31.1168 −1.94480
\(257\) 10.6873i 0.666653i 0.942811 + 0.333326i \(0.108171\pi\)
−0.942811 + 0.333326i \(0.891829\pi\)
\(258\) 6.92820i 0.431331i
\(259\) 3.76631 0.234027
\(260\) 0 0
\(261\) −20.7446 −1.28406
\(262\) 6.92820i 0.428026i
\(263\) 27.4179i 1.69066i −0.534246 0.845329i \(-0.679405\pi\)
0.534246 0.845329i \(-0.320595\pi\)
\(264\) 4.74456 0.292008
\(265\) −21.4891 6.92820i −1.32007 0.425596i
\(266\) −34.9783 −2.14465
\(267\) 1.08724i 0.0665380i
\(268\) 40.6844i 2.48519i
\(269\) 11.4891 0.700504 0.350252 0.936655i \(-0.386096\pi\)
0.350252 + 0.936655i \(0.386096\pi\)
\(270\) 7.37228 22.8665i 0.448663 1.39161i
\(271\) 13.4891 0.819406 0.409703 0.912219i \(-0.365632\pi\)
0.409703 + 0.912219i \(0.365632\pi\)
\(272\) 10.0974i 0.612242i
\(273\) 0 0
\(274\) 36.2337 2.18896
\(275\) 4.05842 + 2.92048i 0.244732 + 0.176112i
\(276\) −2.74456 −0.165203
\(277\) 11.6819i 0.701899i −0.936394 0.350949i \(-0.885859\pi\)
0.936394 0.350949i \(-0.114141\pi\)
\(278\) 40.9793i 2.45778i
\(279\) 8.00000 0.478947
\(280\) −14.2337 + 44.1485i −0.850626 + 2.63838i
\(281\) −0.510875 −0.0304762 −0.0152381 0.999884i \(-0.504851\pi\)
−0.0152381 + 0.999884i \(0.504851\pi\)
\(282\) 13.2665i 0.790009i
\(283\) 15.1460i 0.900338i −0.892943 0.450169i \(-0.851364\pi\)
0.892943 0.450169i \(-0.148636\pi\)
\(284\) 44.2337 2.62479
\(285\) −6.74456 2.17448i −0.399513 0.128805i
\(286\) 0 0
\(287\) 30.2921i 1.78808i
\(288\) 9.74749i 0.574377i
\(289\) 14.4891 0.852301
\(290\) 46.9783 + 15.1460i 2.75866 + 0.889405i
\(291\) −4.62772 −0.271282
\(292\) 30.2921i 1.77271i
\(293\) 3.16915i 0.185144i −0.995706 0.0925718i \(-0.970491\pi\)
0.995706 0.0925718i \(-0.0295088\pi\)
\(294\) −10.0000 −0.583212
\(295\) 5.05842 15.6896i 0.294513 0.913487i
\(296\) 6.51087 0.378437
\(297\) 4.25639i 0.246981i
\(298\) 29.0024i 1.68007i
\(299\) 0 0
\(300\) −10.1168 + 14.0588i −0.584096 + 0.811684i
\(301\) 12.0000 0.691669
\(302\) 30.8820i 1.77706i
\(303\) 4.75372i 0.273094i
\(304\) −25.4891 −1.46190
\(305\) −0.510875 + 1.58457i −0.0292526 + 0.0907324i
\(306\) 9.48913 0.542457
\(307\) 31.5817i 1.80246i 0.433340 + 0.901231i \(0.357335\pi\)
−0.433340 + 0.901231i \(0.642665\pi\)
\(308\) 15.1460i 0.863025i
\(309\) −8.23369 −0.468398
\(310\) −18.1168 5.84096i −1.02897 0.331744i
\(311\) 5.48913 0.311260 0.155630 0.987815i \(-0.450259\pi\)
0.155630 + 0.987815i \(0.450259\pi\)
\(312\) 0 0
\(313\) 21.8719i 1.23627i 0.786072 + 0.618135i \(0.212112\pi\)
−0.786072 + 0.618135i \(0.787888\pi\)
\(314\) −61.7228 −3.48322
\(315\) 17.4891 + 5.63858i 0.985401 + 0.317698i
\(316\) 5.48913 0.308787
\(317\) 32.9639i 1.85144i 0.378215 + 0.925718i \(0.376538\pi\)
−0.378215 + 0.925718i \(0.623462\pi\)
\(318\) 20.1947i 1.13246i
\(319\) 8.74456 0.489602
\(320\) 1.62772 5.04868i 0.0909922 0.282230i
\(321\) 5.25544 0.293330
\(322\) 6.92820i 0.386094i
\(323\) 6.33830i 0.352672i
\(324\) −16.3723 −0.909571
\(325\) 0 0
\(326\) 8.74456 0.484317
\(327\) 7.92287i 0.438136i
\(328\) 52.3663i 2.89144i
\(329\) 22.9783 1.26683
\(330\) −1.37228 + 4.25639i −0.0755416 + 0.234306i
\(331\) −14.1168 −0.775932 −0.387966 0.921674i \(-0.626822\pi\)
−0.387966 + 0.921674i \(0.626822\pi\)
\(332\) 29.0024i 1.59172i
\(333\) 2.57924i 0.141342i
\(334\) −39.7228 −2.17354
\(335\) 19.8030 + 6.38458i 1.08195 + 0.348827i
\(336\) −17.4891 −0.954110
\(337\) 32.4665i 1.76856i −0.466952 0.884282i \(-0.654648\pi\)
0.466952 0.884282i \(-0.345352\pi\)
\(338\) 32.8164i 1.78498i
\(339\) −0.394031 −0.0214008
\(340\) −14.7446 4.75372i −0.799636 0.257807i
\(341\) −3.37228 −0.182619
\(342\) 23.9538i 1.29527i
\(343\) 6.92820i 0.374088i
\(344\) 20.7446 1.11847
\(345\) 0.430703 1.33591i 0.0231883 0.0719228i
\(346\) 21.4891 1.15526
\(347\) 22.6641i 1.21667i −0.793679 0.608337i \(-0.791837\pi\)
0.793679 0.608337i \(-0.208163\pi\)
\(348\) 30.2921i 1.62382i
\(349\) −15.4891 −0.829114 −0.414557 0.910023i \(-0.636063\pi\)
−0.414557 + 0.910023i \(0.636063\pi\)
\(350\) −35.4891 25.5383i −1.89697 1.36508i
\(351\) 0 0
\(352\) 4.10891i 0.219006i
\(353\) 25.0410i 1.33280i −0.745595 0.666399i \(-0.767835\pi\)
0.745595 0.666399i \(-0.232165\pi\)
\(354\) 14.7446 0.783665
\(355\) −6.94158 + 21.5306i −0.368421 + 1.14273i
\(356\) 6.00000 0.317999
\(357\) 4.34896i 0.230172i
\(358\) 32.4665i 1.71591i
\(359\) −29.4891 −1.55638 −0.778188 0.628031i \(-0.783861\pi\)
−0.778188 + 0.628031i \(0.783861\pi\)
\(360\) 30.2337 + 9.74749i 1.59346 + 0.513738i
\(361\) −3.00000 −0.157895
\(362\) 60.8791i 3.19973i
\(363\) 0.792287i 0.0415843i
\(364\) 0 0
\(365\) 14.7446 + 4.75372i 0.771766 + 0.248821i
\(366\) −1.48913 −0.0778378
\(367\) 25.7407i 1.34365i 0.740708 + 0.671827i \(0.234490\pi\)
−0.740708 + 0.671827i \(0.765510\pi\)
\(368\) 5.04868i 0.263180i
\(369\) 20.7446 1.07992
\(370\) −1.88316 + 5.84096i −0.0979006 + 0.303657i
\(371\) 34.9783 1.81598
\(372\) 11.6819i 0.605680i
\(373\) 11.6819i 0.604867i 0.953170 + 0.302434i \(0.0977990\pi\)
−0.953170 + 0.302434i \(0.902201\pi\)
\(374\) −4.00000 −0.206835
\(375\) −5.25544 7.13058i −0.271390 0.368222i
\(376\) 39.7228 2.04855
\(377\) 0 0
\(378\) 37.2203i 1.91440i
\(379\) 0.627719 0.0322437 0.0161219 0.999870i \(-0.494868\pi\)
0.0161219 + 0.999870i \(0.494868\pi\)
\(380\) 12.0000 37.2203i 0.615587 1.90936i
\(381\) 6.51087 0.333562
\(382\) 48.9022i 2.50205i
\(383\) 10.8896i 0.556435i 0.960518 + 0.278217i \(0.0897435\pi\)
−0.960518 + 0.278217i \(0.910256\pi\)
\(384\) 11.2554 0.574377
\(385\) −7.37228 2.37686i −0.375726 0.121136i
\(386\) 41.4891 2.11174
\(387\) 8.21782i 0.417735i
\(388\) 25.5383i 1.29651i
\(389\) −18.8614 −0.956311 −0.478156 0.878275i \(-0.658695\pi\)
−0.478156 + 0.878275i \(0.658695\pi\)
\(390\) 0 0
\(391\) 1.25544 0.0634902
\(392\) 29.9422i 1.51231i
\(393\) 2.17448i 0.109688i
\(394\) 21.4891 1.08261
\(395\) −0.861407 + 2.67181i −0.0433421 + 0.134434i
\(396\) 10.3723 0.521227
\(397\) 16.4356i 0.824881i −0.910984 0.412441i \(-0.864676\pi\)
0.910984 0.412441i \(-0.135324\pi\)
\(398\) 20.1947i 1.01227i
\(399\) 10.9783 0.549600
\(400\) −25.8614 18.6101i −1.29307 0.930506i
\(401\) −11.4891 −0.573740 −0.286870 0.957970i \(-0.592615\pi\)
−0.286870 + 0.957970i \(0.592615\pi\)
\(402\) 18.6101i 0.928189i
\(403\) 0 0
\(404\) −26.2337 −1.30517
\(405\) 2.56930 7.96916i 0.127669 0.395991i
\(406\) −76.4674 −3.79501
\(407\) 1.08724i 0.0538925i
\(408\) 7.51811i 0.372202i
\(409\) −27.4891 −1.35925 −0.679625 0.733560i \(-0.737857\pi\)
−0.679625 + 0.733560i \(0.737857\pi\)
\(410\) −46.9783 15.1460i −2.32009 0.748009i
\(411\) −11.3723 −0.560953
\(412\) 45.4381i 2.23857i
\(413\) 25.5383i 1.25666i
\(414\) −4.74456 −0.233183
\(415\) −14.1168 4.55134i −0.692969 0.223417i
\(416\) 0 0
\(417\) 12.8617i 0.629842i
\(418\) 10.0974i 0.493878i
\(419\) 22.9783 1.12256 0.561280 0.827626i \(-0.310309\pi\)
0.561280 + 0.827626i \(0.310309\pi\)
\(420\) 8.23369 25.5383i 0.401763 1.24614i
\(421\) 8.51087 0.414795 0.207397 0.978257i \(-0.433501\pi\)
0.207397 + 0.978257i \(0.433501\pi\)
\(422\) 3.75906i 0.182988i
\(423\) 15.7359i 0.765107i
\(424\) 60.4674 2.93656
\(425\) 4.62772 6.43087i 0.224477 0.311943i
\(426\) −20.2337 −0.980325
\(427\) 2.57924i 0.124818i
\(428\) 29.0024i 1.40189i
\(429\) 0 0
\(430\) −6.00000 + 18.6101i −0.289346 + 0.897460i
\(431\) −25.7228 −1.23902 −0.619512 0.784987i \(-0.712670\pi\)
−0.619512 + 0.784987i \(0.712670\pi\)
\(432\) 27.1229i 1.30495i
\(433\) 29.2048i 1.40349i −0.712426 0.701747i \(-0.752404\pi\)
0.712426 0.701747i \(-0.247596\pi\)
\(434\) 29.4891 1.41552
\(435\) −14.7446 4.75372i −0.706948 0.227924i
\(436\) 43.7228 2.09394
\(437\) 3.16915i 0.151601i
\(438\) 13.8564i 0.662085i
\(439\) −21.4891 −1.02562 −0.512810 0.858502i \(-0.671395\pi\)
−0.512810 + 0.858502i \(0.671395\pi\)
\(440\) −12.7446 4.10891i −0.607573 0.195885i
\(441\) −11.8614 −0.564829
\(442\) 0 0
\(443\) 31.6742i 1.50489i 0.658656 + 0.752444i \(0.271125\pi\)
−0.658656 + 0.752444i \(0.728875\pi\)
\(444\) −3.76631 −0.178741
\(445\) −0.941578 + 2.92048i −0.0446351 + 0.138444i
\(446\) 6.00000 0.284108
\(447\) 9.10268i 0.430542i
\(448\) 8.21782i 0.388256i
\(449\) −6.86141 −0.323810 −0.161905 0.986806i \(-0.551764\pi\)
−0.161905 + 0.986806i \(0.551764\pi\)
\(450\) −17.4891 + 24.3036i −0.824445 + 1.14568i
\(451\) −8.74456 −0.411765
\(452\) 2.17448i 0.102279i
\(453\) 9.69259i 0.455398i
\(454\) 42.2337 1.98213
\(455\) 0 0
\(456\) 18.9783 0.888738
\(457\) 20.7846i 0.972263i −0.873886 0.486132i \(-0.838408\pi\)
0.873886 0.486132i \(-0.161592\pi\)
\(458\) 36.9253i 1.72541i
\(459\) −6.74456 −0.314809
\(460\) 7.37228 + 2.37686i 0.343734 + 0.110822i
\(461\) 2.23369 0.104033 0.0520166 0.998646i \(-0.483435\pi\)
0.0520166 + 0.998646i \(0.483435\pi\)
\(462\) 6.92820i 0.322329i
\(463\) 30.0897i 1.39839i 0.714933 + 0.699193i \(0.246457\pi\)
−0.714933 + 0.699193i \(0.753543\pi\)
\(464\) −55.7228 −2.58687
\(465\) 5.68614 + 1.83324i 0.263688 + 0.0850145i
\(466\) 9.48913 0.439575
\(467\) 7.72049i 0.357262i −0.983916 0.178631i \(-0.942833\pi\)
0.983916 0.178631i \(-0.0571668\pi\)
\(468\) 0 0
\(469\) −32.2337 −1.48841
\(470\) −11.4891 + 35.6357i −0.529954 + 1.64375i
\(471\) 19.3723 0.892628
\(472\) 44.1485i 2.03210i
\(473\) 3.46410i 0.159280i
\(474\) −2.51087 −0.115328
\(475\) 16.2337 + 11.6819i 0.744853 + 0.536003i
\(476\) 24.0000 1.10004
\(477\) 23.9538i 1.09677i
\(478\) 37.2203i 1.70241i
\(479\) 5.48913 0.250805 0.125402 0.992106i \(-0.459978\pi\)
0.125402 + 0.992106i \(0.459978\pi\)
\(480\) 2.23369 6.92820i 0.101953 0.316228i
\(481\) 0 0
\(482\) 42.2689i 1.92530i
\(483\) 2.17448i 0.0989423i
\(484\) −4.37228 −0.198740
\(485\) 12.4307 + 4.00772i 0.564449 + 0.181981i
\(486\) 39.7228 1.80186
\(487\) 7.13058i 0.323118i −0.986863 0.161559i \(-0.948348\pi\)
0.986863 0.161559i \(-0.0516521\pi\)
\(488\) 4.45877i 0.201839i
\(489\) −2.74456 −0.124113
\(490\) 26.8614 + 8.66025i 1.21347 + 0.391230i
\(491\) 6.51087 0.293832 0.146916 0.989149i \(-0.453065\pi\)
0.146916 + 0.989149i \(0.453065\pi\)
\(492\) 30.2921i 1.36567i
\(493\) 13.8564i 0.624061i
\(494\) 0 0
\(495\) −1.62772 + 5.04868i −0.0731605 + 0.226921i
\(496\) 21.4891 0.964890
\(497\) 35.0458i 1.57202i
\(498\) 13.2665i 0.594486i
\(499\) 20.0000 0.895323 0.447661 0.894203i \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 39.3505 29.0024i 1.75981 1.29703i
\(501\) 12.4674 0.557001
\(502\) 55.8304i 2.49183i
\(503\) 13.5615i 0.604675i −0.953201 0.302338i \(-0.902233\pi\)
0.953201 0.302338i \(-0.0977670\pi\)
\(504\) −49.2119 −2.19207
\(505\) 4.11684 12.7692i 0.183197 0.568220i
\(506\) 2.00000 0.0889108
\(507\) 10.2997i 0.457427i
\(508\) 35.9306i 1.59416i
\(509\) −22.6277 −1.00296 −0.501478 0.865170i \(-0.667210\pi\)
−0.501478 + 0.865170i \(0.667210\pi\)
\(510\) 6.74456 + 2.17448i 0.298654 + 0.0962876i
\(511\) −24.0000 −1.06170
\(512\) 50.1369i 2.21576i
\(513\) 17.0256i 0.751697i
\(514\) 26.9783 1.18996
\(515\) 22.1168 + 7.13058i 0.974585 + 0.314211i
\(516\) −12.0000 −0.528271
\(517\) 6.63325i 0.291730i
\(518\) 9.50744i 0.417733i
\(519\) −6.74456 −0.296053
\(520\) 0 0
\(521\) −21.6060 −0.946575 −0.473287 0.880908i \(-0.656933\pi\)
−0.473287 + 0.880908i \(0.656933\pi\)
\(522\) 52.3663i 2.29201i
\(523\) 29.0024i 1.26819i −0.773256 0.634094i \(-0.781373\pi\)
0.773256 0.634094i \(-0.218627\pi\)
\(524\) 12.0000 0.524222
\(525\) 11.1386 + 8.01544i 0.486128 + 0.349823i
\(526\) −69.2119 −3.01778
\(527\) 5.34363i 0.232772i
\(528\) 5.04868i 0.219715i
\(529\) 22.3723 0.972708
\(530\) −17.4891 + 54.2458i −0.759679 + 2.35629i
\(531\) 17.4891 0.758963
\(532\) 60.5841i 2.62665i
\(533\) 0 0
\(534\) −2.74456 −0.118769
\(535\) −14.1168 4.55134i −0.610324 0.196772i
\(536\) −55.7228 −2.40686
\(537\) 10.1899i 0.439728i
\(538\) 29.0024i 1.25038i
\(539\) 5.00000 0.215365
\(540\) −39.6060 12.7692i −1.70437 0.549497i
\(541\) 34.2337 1.47182 0.735911 0.677079i \(-0.236754\pi\)
0.735911 + 0.677079i \(0.236754\pi\)
\(542\) 34.0511i 1.46262i
\(543\) 19.1075i 0.819980i
\(544\) 6.51087 0.279151
\(545\) −6.86141 + 21.2819i −0.293910 + 0.911618i
\(546\) 0 0
\(547\) 29.0024i 1.24005i −0.784580 0.620027i \(-0.787122\pi\)
0.784580 0.620027i \(-0.212878\pi\)
\(548\) 62.7586i 2.68091i
\(549\) −1.76631 −0.0753844
\(550\) 7.37228 10.2448i 0.314355 0.436841i
\(551\) 34.9783 1.49012
\(552\) 3.75906i 0.159996i
\(553\) 4.34896i 0.184937i
\(554\) −29.4891 −1.25287
\(555\) 0.591046 1.83324i 0.0250885 0.0778167i
\(556\) −70.9783 −3.01015
\(557\) 0.994667i 0.0421454i −0.999778 0.0210727i \(-0.993292\pi\)
0.999778 0.0210727i \(-0.00670814\pi\)
\(558\) 20.1947i 0.854910i
\(559\) 0 0
\(560\) 46.9783 + 15.1460i 1.98519 + 0.640036i
\(561\) 1.25544 0.0530046
\(562\) 1.28962i 0.0543994i
\(563\) 18.9051i 0.796754i 0.917222 + 0.398377i \(0.130426\pi\)
−0.917222 + 0.398377i \(0.869574\pi\)
\(564\) −22.9783 −0.967559
\(565\) 1.05842 + 0.341241i 0.0445281 + 0.0143561i
\(566\) −38.2337 −1.60708
\(567\) 12.9715i 0.544754i
\(568\) 60.5841i 2.54205i
\(569\) 27.2554 1.14261 0.571304 0.820739i \(-0.306438\pi\)
0.571304 + 0.820739i \(0.306438\pi\)
\(570\) −5.48913 + 17.0256i −0.229914 + 0.713122i
\(571\) 1.48913 0.0623180 0.0311590 0.999514i \(-0.490080\pi\)
0.0311590 + 0.999514i \(0.490080\pi\)
\(572\) 0 0
\(573\) 15.3484i 0.641189i
\(574\) 76.4674 3.19169
\(575\) −2.31386 + 3.21543i −0.0964946 + 0.134093i
\(576\) 5.62772 0.234488
\(577\) 21.8719i 0.910537i 0.890354 + 0.455269i \(0.150457\pi\)
−0.890354 + 0.455269i \(0.849543\pi\)
\(578\) 36.5754i 1.52134i
\(579\) −13.0217 −0.541165
\(580\) 26.2337 81.3687i 1.08929 3.37865i
\(581\) 22.9783 0.953298
\(582\) 11.6819i 0.484231i
\(583\) 10.0974i 0.418190i
\(584\) −41.4891 −1.71683
\(585\) 0 0
\(586\) −8.00000 −0.330477
\(587\) 41.2743i 1.70357i −0.523890 0.851786i \(-0.675520\pi\)
0.523890 0.851786i \(-0.324480\pi\)
\(588\) 17.3205i 0.714286i
\(589\) −13.4891 −0.555810
\(590\) −39.6060 12.7692i −1.63055 0.525698i
\(591\) −6.74456 −0.277434
\(592\) 6.92820i 0.284747i
\(593\) 22.7739i 0.935214i 0.883937 + 0.467607i \(0.154884\pi\)
−0.883937 + 0.467607i \(0.845116\pi\)
\(594\) −10.7446 −0.440855
\(595\) −3.76631 + 11.6819i −0.154404 + 0.478912i
\(596\) −50.2337 −2.05765
\(597\) 6.33830i 0.259409i
\(598\) 0 0
\(599\) −10.9783 −0.448559 −0.224280 0.974525i \(-0.572003\pi\)
−0.224280 + 0.974525i \(0.572003\pi\)
\(600\) 19.2554 + 13.8564i 0.786100 + 0.565685i
\(601\) −38.4674 −1.56912 −0.784558 0.620055i \(-0.787110\pi\)
−0.784558 + 0.620055i \(0.787110\pi\)
\(602\) 30.2921i 1.23461i
\(603\) 22.0742i 0.898932i
\(604\) 53.4891 2.17644
\(605\) 0.686141 2.12819i 0.0278956 0.0865234i
\(606\) 12.0000 0.487467
\(607\) 3.46410i 0.140604i 0.997526 + 0.0703018i \(0.0223962\pi\)
−0.997526 + 0.0703018i \(0.977604\pi\)
\(608\) 16.4356i 0.666554i
\(609\) 24.0000 0.972529
\(610\) 4.00000 + 1.28962i 0.161955 + 0.0522152i
\(611\) 0 0
\(612\) 16.4356i 0.664372i
\(613\) 4.34896i 0.175653i 0.996136 + 0.0878265i \(0.0279921\pi\)
−0.996136 + 0.0878265i \(0.972008\pi\)
\(614\) 79.7228 3.21735
\(615\) 14.7446 + 4.75372i 0.594558 + 0.191689i
\(616\) 20.7446 0.835822
\(617\) 17.0256i 0.685423i −0.939441 0.342712i \(-0.888655\pi\)
0.939441 0.342712i \(-0.111345\pi\)
\(618\) 20.7846i 0.836080i
\(619\) −14.1168 −0.567404 −0.283702 0.958913i \(-0.591563\pi\)
−0.283702 + 0.958913i \(0.591563\pi\)
\(620\) −10.1168 + 31.3793i −0.406302 + 1.26022i
\(621\) 3.37228 0.135325
\(622\) 13.8564i 0.555591i
\(623\) 4.75372i 0.190454i
\(624\) 0 0
\(625\) 7.94158 + 23.7051i 0.317663 + 0.948204i
\(626\) 55.2119 2.20671
\(627\) 3.16915i 0.126564i
\(628\) 106.907i 4.26606i
\(629\) 1.72281 0.0686931
\(630\) 14.2337 44.1485i 0.567084 1.75892i
\(631\) 23.6060 0.939739 0.469869 0.882736i \(-0.344301\pi\)
0.469869 + 0.882736i \(0.344301\pi\)
\(632\) 7.51811i 0.299054i
\(633\) 1.17981i 0.0468934i
\(634\) 83.2119 3.30477
\(635\) −17.4891 5.63858i −0.694035 0.223760i
\(636\) −34.9783 −1.38698
\(637\) 0 0
\(638\) 22.0742i 0.873927i
\(639\) −24.0000 −0.949425
\(640\) −30.2337 9.74749i −1.19509 0.385304i
\(641\) −25.3723 −1.00214 −0.501072 0.865405i \(-0.667061\pi\)
−0.501072 + 0.865405i \(0.667061\pi\)
\(642\) 13.2665i 0.523587i
\(643\) 30.4944i 1.20258i 0.799030 + 0.601292i \(0.205347\pi\)
−0.799030 + 0.601292i \(0.794653\pi\)
\(644\) −12.0000 −0.472866
\(645\) 1.88316 5.84096i 0.0741492 0.229988i
\(646\) −16.0000 −0.629512
\(647\) 21.9817i 0.864188i −0.901829 0.432094i \(-0.857775\pi\)
0.901829 0.432094i \(-0.142225\pi\)
\(648\) 22.4241i 0.880901i
\(649\) −7.37228 −0.289387
\(650\) 0 0
\(651\) −9.25544 −0.362749
\(652\) 15.1460i 0.593164i
\(653\) 30.7894i 1.20488i 0.798163 + 0.602441i \(0.205805\pi\)
−0.798163 + 0.602441i \(0.794195\pi\)
\(654\) −20.0000 −0.782062
\(655\) −1.88316 + 5.84096i −0.0735810 + 0.228225i
\(656\) 55.7228 2.17561
\(657\) 16.4356i 0.641216i
\(658\) 58.0049i 2.26127i
\(659\) −21.2554 −0.827994 −0.413997 0.910278i \(-0.635868\pi\)
−0.413997 + 0.910278i \(0.635868\pi\)
\(660\) 7.37228 + 2.37686i 0.286966 + 0.0925192i
\(661\) −16.3505 −0.635962 −0.317981 0.948097i \(-0.603005\pi\)
−0.317981 + 0.948097i \(0.603005\pi\)
\(662\) 35.6357i 1.38502i
\(663\) 0 0
\(664\) 39.7228 1.54154
\(665\) −29.4891 9.50744i −1.14354 0.368683i
\(666\) −6.51087 −0.252291
\(667\) 6.92820i 0.268261i
\(668\) 68.8019i 2.66203i
\(669\) −1.88316 −0.0728070
\(670\) 16.1168 49.9894i 0.622648 1.93126i
\(671\) 0.744563 0.0287435
\(672\) 11.2772i 0.435026i
\(673\) 18.6101i 0.717368i −0.933459 0.358684i \(-0.883226\pi\)
0.933459 0.358684i \(-0.116774\pi\)
\(674\) −81.9565 −3.15685
\(675\) 12.4307 17.2742i 0.478458 0.664885i
\(676\) −56.8397 −2.18614
\(677\) 50.0820i 1.92481i 0.271623 + 0.962404i \(0.412440\pi\)
−0.271623 + 0.962404i \(0.587560\pi\)
\(678\) 0.994667i 0.0381999i
\(679\) −20.2337 −0.776498
\(680\) −6.51087 + 20.1947i −0.249681 + 0.774431i
\(681\) −13.2554 −0.507949
\(682\) 8.51278i 0.325971i
\(683\) 17.9104i 0.685323i −0.939459 0.342661i \(-0.888672\pi\)
0.939459 0.342661i \(-0.111328\pi\)
\(684\) 41.4891 1.58638
\(685\) 30.5475 + 9.84868i 1.16716 + 0.376299i
\(686\) 17.4891 0.667738
\(687\) 11.5894i 0.442161i
\(688\) 22.0742i 0.841572i
\(689\) 0 0
\(690\) −3.37228 1.08724i −0.128381 0.0413905i
\(691\) 44.8614 1.70661 0.853304 0.521413i \(-0.174595\pi\)
0.853304 + 0.521413i \(0.174595\pi\)
\(692\) 37.2203i 1.41490i
\(693\) 8.21782i 0.312169i
\(694\) −57.2119 −2.17174
\(695\) 11.1386 34.5484i 0.422511 1.31050i
\(696\) 41.4891 1.57264
\(697\) 13.8564i 0.524849i
\(698\) 39.0998i 1.47995i
\(699\) −2.97825 −0.112648
\(700\) −44.2337 + 61.4690i −1.67188 + 2.32331i
\(701\) −12.5109 −0.472529 −0.236265 0.971689i \(-0.575923\pi\)
−0.236265 + 0.971689i \(0.575923\pi\)
\(702\) 0 0
\(703\) 4.34896i 0.164024i
\(704\) −2.37228 −0.0894087
\(705\) 3.60597 11.1846i 0.135809 0.421236i
\(706\) −63.2119 −2.37901
\(707\) 20.7846i 0.781686i
\(708\) 25.5383i 0.959789i
\(709\) −23.8832 −0.896951 −0.448475 0.893795i \(-0.648033\pi\)
−0.448475 + 0.893795i \(0.648033\pi\)
\(710\) 54.3505 + 17.5229i 2.03974 + 0.657622i
\(711\) −2.97825 −0.111693
\(712\) 8.21782i 0.307976i
\(713\) 2.67181i 0.100060i
\(714\) −10.9783 −0.410851
\(715\) 0 0
\(716\) 56.2337 2.10155
\(717\) 11.6819i 0.436269i
\(718\) 74.4405i 2.77810i
\(719\) 30.3505 1.13188 0.565942 0.824445i \(-0.308513\pi\)
0.565942 + 0.824445i \(0.308513\pi\)
\(720\) 10.3723 32.1716i 0.386552 1.19896i
\(721\) −36.0000 −1.34071
\(722\) 7.57301i 0.281838i
\(723\) 13.2665i 0.493386i
\(724\) −105.446 −3.91886
\(725\) 35.4891 + 25.5383i 1.31803 + 0.948470i
\(726\) 2.00000 0.0742270
\(727\) 14.0588i 0.521412i 0.965418 + 0.260706i \(0.0839552\pi\)
−0.965418 + 0.260706i \(0.916045\pi\)
\(728\) 0 0
\(729\) −1.23369 −0.0456921
\(730\) 12.0000 37.2203i 0.444140 1.37758i
\(731\) 5.48913 0.203023
\(732\) 2.57924i 0.0953315i
\(733\) 9.50744i 0.351165i 0.984465 + 0.175583i \(0.0561809\pi\)
−0.984465 + 0.175583i \(0.943819\pi\)
\(734\) 64.9783 2.39839
\(735\) −8.43070 2.71810i −0.310971 0.100259i
\(736\) −3.25544 −0.119997
\(737\) 9.30506i 0.342756i
\(738\) 52.3663i 1.92763i
\(739\) 10.7446 0.395245 0.197623 0.980278i \(-0.436678\pi\)
0.197623 + 0.980278i \(0.436678\pi\)
\(740\) 10.1168 + 3.26172i 0.371903 + 0.119903i
\(741\) 0 0
\(742\) 88.2969i 3.24148i
\(743\) 11.3870i 0.417747i −0.977943 0.208874i \(-0.933020\pi\)
0.977943 0.208874i \(-0.0669798\pi\)
\(744\) −16.0000 −0.586588
\(745\) 7.88316 24.4511i 0.288816 0.895819i
\(746\) 29.4891 1.07967
\(747\) 15.7359i 0.575748i
\(748\) 6.92820i 0.253320i
\(749\) 22.9783 0.839607
\(750\) −18.0000 + 13.2665i −0.657267 + 0.484424i
\(751\) 27.3723 0.998829 0.499414 0.866363i \(-0.333549\pi\)
0.499414 + 0.866363i \(0.333549\pi\)
\(752\) 42.2689i 1.54139i
\(753\) 17.5229i 0.638570i
\(754\) 0 0
\(755\) −8.39403 + 26.0357i −0.305490 + 0.947535i
\(756\) 64.4674 2.34466
\(757\) 39.7995i 1.44654i 0.690567 + 0.723269i \(0.257361\pi\)
−0.690567 + 0.723269i \(0.742639\pi\)
\(758\) 1.58457i 0.0575543i
\(759\) −0.627719 −0.0227847
\(760\) −50.9783 16.4356i −1.84918 0.596184i
\(761\) 32.7446 1.18699 0.593495 0.804838i \(-0.297748\pi\)
0.593495 + 0.804838i \(0.297748\pi\)
\(762\) 16.4356i 0.595401i
\(763\) 34.6410i 1.25409i
\(764\) 84.7011 3.06438
\(765\) 8.00000 + 2.57924i 0.289241 + 0.0932526i
\(766\) 27.4891 0.993222
\(767\) 0 0
\(768\) 24.6535i 0.889605i
\(769\) −29.2119 −1.05341 −0.526705 0.850048i \(-0.676573\pi\)
−0.526705 + 0.850048i \(0.676573\pi\)
\(770\) −6.00000 + 18.6101i −0.216225 + 0.670662i
\(771\) −8.46738 −0.304945
\(772\) 71.8613i 2.58634i
\(773\) 17.6155i 0.633584i 0.948495 + 0.316792i \(0.102606\pi\)
−0.948495 + 0.316792i \(0.897394\pi\)
\(774\) −20.7446 −0.745648
\(775\) −13.6861 9.84868i −0.491621 0.353775i
\(776\) −34.9783 −1.25565
\(777\) 2.98400i 0.107050i
\(778\) 47.6126i 1.70699i
\(779\) −34.9783 −1.25323
\(780\) 0 0
\(781\) 10.1168 0.362009
\(782\) 3.16915i 0.113328i