Properties

Label 637.2.f.l.393.6
Level $637$
Weight $2$
Character 637.393
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(295,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: 16.0.468066644398978174550016.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 8x^{14} + 45x^{12} + 124x^{10} + 248x^{8} + 250x^{6} + 177x^{4} + 14x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.6
Root \(0.141226 - 0.244611i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.l.295.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.760387 + 1.31703i) q^{2} +(1.06311 + 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} +0.589391 q^{5} +(-1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +O(q^{10})\) \(q+(0.760387 + 1.31703i) q^{2} +(1.06311 + 1.84135i) q^{3} +(-0.156376 + 0.270851i) q^{4} +0.589391 q^{5} +(-1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 + 1.31703i) q^{9} +(0.448165 + 0.776245i) q^{10} +(-0.760387 - 1.31703i) q^{11} -0.664976 q^{12} +(3.32565 + 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} +(2.26384 + 3.92109i) q^{16} +(-2.39740 + 4.15241i) q^{17} -2.31275 q^{18} +(-0.841957 + 1.45831i) q^{19} +(-0.0921666 + 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +(-0.886972 - 1.53628i) q^{23} +(2.72785 + 4.72477i) q^{24} -4.65262 q^{25} +(0.694354 + 5.43908i) q^{26} +3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 + 1.65046i) q^{30} -6.08640 q^{31} +(-0.876873 + 1.51879i) q^{32} +(1.61674 - 2.80028i) q^{33} -7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +(-0.704563 - 1.22034i) q^{37} -2.56085 q^{38} +(0.970785 + 7.60445i) q^{39} +1.51233 q^{40} +(-0.677729 - 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +0.475625 q^{44} +(-0.448165 + 0.776245i) q^{45} +(1.34888 - 2.33633i) q^{46} -0.464832 q^{47} +(-4.81341 + 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} -10.1947 q^{51} +(-0.897307 + 0.682948i) q^{52} +8.24681 q^{53} +(2.39153 + 4.14225i) q^{54} +(-0.448165 - 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 - 9.07763i) q^{58} +(5.93782 - 10.2846i) q^{59} -0.391931 q^{60} +(-1.24009 + 2.14789i) q^{61} +(-4.62802 - 8.01596i) q^{62} +6.38833 q^{64} +(1.96011 + 0.820936i) q^{65} +4.91740 q^{66} +(3.78642 + 6.55827i) q^{67} +(-0.749790 - 1.29867i) q^{68} +(1.88589 - 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 + 3.37939i) q^{72} -16.3712 q^{73} +(1.07148 - 1.85586i) q^{74} +(-4.94622 - 8.56711i) q^{75} +(-0.263323 - 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} -14.9623 q^{79} +(1.33429 + 2.31106i) q^{80} +(5.62478 + 9.74241i) q^{81} +(1.03067 - 1.78518i) q^{82} +10.1222 q^{83} +(-1.41300 + 2.44740i) q^{85} +17.5795 q^{86} +(7.32746 - 12.6915i) q^{87} +(-1.95109 - 3.37939i) q^{88} +(-8.24250 - 14.2764i) q^{89} -1.36312 q^{90} +0.554804 q^{92} +(-6.47049 - 11.2072i) q^{93} +(-0.353452 - 0.612196i) q^{94} +(-0.496242 + 0.859516i) q^{95} -3.72883 q^{96} +(0.486935 - 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.760387 + 1.31703i 0.537675 + 0.931280i 0.999029 + 0.0440636i \(0.0140304\pi\)
−0.461354 + 0.887216i \(0.652636\pi\)
\(3\) 1.06311 + 1.84135i 0.613784 + 1.06311i 0.990596 + 0.136816i \(0.0436869\pi\)
−0.376812 + 0.926290i \(0.622980\pi\)
\(4\) −0.156376 + 0.270851i −0.0781880 + 0.135426i
\(5\) 0.589391 0.263584 0.131792 0.991277i \(-0.457927\pi\)
0.131792 + 0.991277i \(0.457927\pi\)
\(6\) −1.61674 + 2.80028i −0.660032 + 1.14321i
\(7\) 0 0
\(8\) 2.56592 0.907190
\(9\) −0.760387 + 1.31703i −0.253462 + 0.439009i
\(10\) 0.448165 + 0.776245i 0.141722 + 0.245470i
\(11\) −0.760387 1.31703i −0.229265 0.397099i 0.728325 0.685232i \(-0.240299\pi\)
−0.957591 + 0.288132i \(0.906966\pi\)
\(12\) −0.664976 −0.191962
\(13\) 3.32565 + 1.39285i 0.922370 + 0.386308i
\(14\) 0 0
\(15\) 0.626585 + 1.08528i 0.161784 + 0.280217i
\(16\) 2.26384 + 3.92109i 0.565961 + 0.980274i
\(17\) −2.39740 + 4.15241i −0.581454 + 1.00711i 0.413853 + 0.910344i \(0.364183\pi\)
−0.995307 + 0.0967643i \(0.969151\pi\)
\(18\) −2.31275 −0.545121
\(19\) −0.841957 + 1.45831i −0.193158 + 0.334560i −0.946295 0.323304i \(-0.895206\pi\)
0.753137 + 0.657864i \(0.228540\pi\)
\(20\) −0.0921666 + 0.159637i −0.0206091 + 0.0356960i
\(21\) 0 0
\(22\) 1.15638 2.00290i 0.246540 0.427020i
\(23\) −0.886972 1.53628i −0.184946 0.320337i 0.758612 0.651543i \(-0.225878\pi\)
−0.943558 + 0.331206i \(0.892544\pi\)
\(24\) 2.72785 + 4.72477i 0.556819 + 0.964439i
\(25\) −4.65262 −0.930524
\(26\) 0.694354 + 5.43908i 0.136174 + 1.06669i
\(27\) 3.14515 0.605284
\(28\) 0 0
\(29\) −3.44625 5.96909i −0.639953 1.10843i −0.985443 0.170009i \(-0.945620\pi\)
0.345489 0.938423i \(-0.387713\pi\)
\(30\) −0.952894 + 1.65046i −0.173974 + 0.301332i
\(31\) −6.08640 −1.09315 −0.546575 0.837410i \(-0.684069\pi\)
−0.546575 + 0.837410i \(0.684069\pi\)
\(32\) −0.876873 + 1.51879i −0.155011 + 0.268486i
\(33\) 1.61674 2.80028i 0.281439 0.487466i
\(34\) −7.29179 −1.25053
\(35\) 0 0
\(36\) −0.237812 0.411903i −0.0396354 0.0686505i
\(37\) −0.704563 1.22034i −0.115830 0.200623i 0.802282 0.596946i \(-0.203619\pi\)
−0.918111 + 0.396323i \(0.870286\pi\)
\(38\) −2.56085 −0.415425
\(39\) 0.970785 + 7.60445i 0.155450 + 1.21769i
\(40\) 1.51233 0.239121
\(41\) −0.677729 1.17386i −0.105843 0.183326i 0.808239 0.588855i \(-0.200421\pi\)
−0.914082 + 0.405528i \(0.867088\pi\)
\(42\) 0 0
\(43\) 5.77978 10.0109i 0.881408 1.52664i 0.0316319 0.999500i \(-0.489930\pi\)
0.849776 0.527144i \(-0.176737\pi\)
\(44\) 0.475625 0.0717031
\(45\) −0.448165 + 0.776245i −0.0668085 + 0.115716i
\(46\) 1.34888 2.33633i 0.198882 0.344474i
\(47\) −0.464832 −0.0678027 −0.0339013 0.999425i \(-0.510793\pi\)
−0.0339013 + 0.999425i \(0.510793\pi\)
\(48\) −4.81341 + 8.33707i −0.694756 + 1.20335i
\(49\) 0 0
\(50\) −3.53779 6.12763i −0.500319 0.866578i
\(51\) −10.1947 −1.42755
\(52\) −0.897307 + 0.682948i −0.124434 + 0.0947078i
\(53\) 8.24681 1.13279 0.566393 0.824135i \(-0.308338\pi\)
0.566393 + 0.824135i \(0.308338\pi\)
\(54\) 2.39153 + 4.14225i 0.325446 + 0.563689i
\(55\) −0.448165 0.776245i −0.0604306 0.104669i
\(56\) 0 0
\(57\) −3.58035 −0.474230
\(58\) 5.24097 9.07763i 0.688173 1.19195i
\(59\) 5.93782 10.2846i 0.773038 1.33894i −0.162852 0.986651i \(-0.552069\pi\)
0.935890 0.352291i \(-0.114597\pi\)
\(60\) −0.391931 −0.0505981
\(61\) −1.24009 + 2.14789i −0.158777 + 0.275009i −0.934428 0.356153i \(-0.884088\pi\)
0.775651 + 0.631162i \(0.217422\pi\)
\(62\) −4.62802 8.01596i −0.587759 1.01803i
\(63\) 0 0
\(64\) 6.38833 0.798541
\(65\) 1.96011 + 0.820936i 0.243122 + 0.101825i
\(66\) 4.91740 0.605290
\(67\) 3.78642 + 6.55827i 0.462585 + 0.801220i 0.999089 0.0426774i \(-0.0135888\pi\)
−0.536504 + 0.843898i \(0.680255\pi\)
\(68\) −0.749790 1.29867i −0.0909254 0.157487i
\(69\) 1.88589 3.26646i 0.227034 0.393235i
\(70\) 0 0
\(71\) −3.30235 + 5.71984i −0.391917 + 0.678821i −0.992702 0.120590i \(-0.961521\pi\)
0.600785 + 0.799411i \(0.294855\pi\)
\(72\) −1.95109 + 3.37939i −0.229939 + 0.398265i
\(73\) −16.3712 −1.91610 −0.958049 0.286604i \(-0.907474\pi\)
−0.958049 + 0.286604i \(0.907474\pi\)
\(74\) 1.07148 1.85586i 0.124557 0.215739i
\(75\) −4.94622 8.56711i −0.571141 0.989245i
\(76\) −0.263323 0.456090i −0.0302053 0.0523171i
\(77\) 0 0
\(78\) −9.27710 + 7.06087i −1.05042 + 0.799486i
\(79\) −14.9623 −1.68339 −0.841696 0.539951i \(-0.818443\pi\)
−0.841696 + 0.539951i \(0.818443\pi\)
\(80\) 1.33429 + 2.31106i 0.149178 + 0.258384i
\(81\) 5.62478 + 9.74241i 0.624976 + 1.08249i
\(82\) 1.03067 1.78518i 0.113819 0.197140i
\(83\) 10.1222 1.11105 0.555526 0.831499i \(-0.312517\pi\)
0.555526 + 0.831499i \(0.312517\pi\)
\(84\) 0 0
\(85\) −1.41300 + 2.44740i −0.153262 + 0.265457i
\(86\) 17.5795 1.89564
\(87\) 7.32746 12.6915i 0.785586 1.36068i
\(88\) −1.95109 3.37939i −0.207987 0.360244i
\(89\) −8.24250 14.2764i −0.873703 1.51330i −0.858138 0.513419i \(-0.828379\pi\)
−0.0155650 0.999879i \(-0.504955\pi\)
\(90\) −1.36312 −0.143685
\(91\) 0 0
\(92\) 0.554804 0.0578423
\(93\) −6.47049 11.2072i −0.670958 1.16213i
\(94\) −0.353452 0.612196i −0.0364558 0.0631432i
\(95\) −0.496242 + 0.859516i −0.0509133 + 0.0881845i
\(96\) −3.72883 −0.380573
\(97\) 0.486935 0.843396i 0.0494407 0.0856338i −0.840246 0.542205i \(-0.817589\pi\)
0.889687 + 0.456572i \(0.150923\pi\)
\(98\) 0 0
\(99\) 2.31275 0.232440
\(100\) 0.727557 1.26017i 0.0727557 0.126017i
\(101\) 1.47012 + 2.54632i 0.146282 + 0.253368i 0.929851 0.367937i \(-0.119936\pi\)
−0.783568 + 0.621305i \(0.786603\pi\)
\(102\) −7.75195 13.4268i −0.767557 1.32945i
\(103\) 0.528682 0.0520926 0.0260463 0.999661i \(-0.491708\pi\)
0.0260463 + 0.999661i \(0.491708\pi\)
\(104\) 8.53336 + 3.57395i 0.836765 + 0.350455i
\(105\) 0 0
\(106\) 6.27076 + 10.8613i 0.609070 + 1.05494i
\(107\) 9.66119 + 16.7337i 0.933983 + 1.61771i 0.776438 + 0.630194i \(0.217024\pi\)
0.157545 + 0.987512i \(0.449642\pi\)
\(108\) −0.491825 + 0.851866i −0.0473259 + 0.0819709i
\(109\) −5.73240 −0.549064 −0.274532 0.961578i \(-0.588523\pi\)
−0.274532 + 0.961578i \(0.588523\pi\)
\(110\) 0.681558 1.18049i 0.0649840 0.112556i
\(111\) 1.49805 2.59470i 0.142189 0.246278i
\(112\) 0 0
\(113\) −2.57480 + 4.45968i −0.242216 + 0.419531i −0.961345 0.275346i \(-0.911208\pi\)
0.719129 + 0.694877i \(0.244541\pi\)
\(114\) −2.72245 4.71543i −0.254981 0.441640i
\(115\) −0.522774 0.905470i −0.0487489 0.0844355i
\(116\) 2.15564 0.200147
\(117\) −4.36321 + 3.32087i −0.403379 + 0.307015i
\(118\) 18.0602 1.66257
\(119\) 0 0
\(120\) 1.60777 + 2.78474i 0.146769 + 0.254211i
\(121\) 4.34362 7.52338i 0.394875 0.683943i
\(122\) −3.77178 −0.341481
\(123\) 1.44099 2.49588i 0.129930 0.225045i
\(124\) 0.951766 1.64851i 0.0854711 0.148040i
\(125\) −5.68917 −0.508855
\(126\) 0 0
\(127\) 4.50166 + 7.79710i 0.399457 + 0.691881i 0.993659 0.112436i \(-0.0358652\pi\)
−0.594202 + 0.804316i \(0.702532\pi\)
\(128\) 6.61135 + 11.4512i 0.584366 + 1.01215i
\(129\) 24.5781 2.16398
\(130\) 0.409246 + 3.20575i 0.0358933 + 0.281163i
\(131\) 6.79840 0.593979 0.296989 0.954881i \(-0.404017\pi\)
0.296989 + 0.954881i \(0.404017\pi\)
\(132\) 0.505639 + 0.875793i 0.0440102 + 0.0762280i
\(133\) 0 0
\(134\) −5.75829 + 9.97364i −0.497440 + 0.861592i
\(135\) 1.85372 0.159543
\(136\) −6.15153 + 10.6548i −0.527490 + 0.913639i
\(137\) 7.03779 12.1898i 0.601279 1.04145i −0.391349 0.920242i \(-0.627991\pi\)
0.992628 0.121203i \(-0.0386753\pi\)
\(138\) 5.73602 0.488283
\(139\) −8.64313 + 14.9703i −0.733101 + 1.26977i 0.222451 + 0.974944i \(0.428594\pi\)
−0.955552 + 0.294824i \(0.904739\pi\)
\(140\) 0 0
\(141\) −0.494165 0.855919i −0.0416162 0.0720814i
\(142\) −10.0443 −0.842896
\(143\) −0.694354 5.43908i −0.0580648 0.454839i
\(144\) −6.88559 −0.573799
\(145\) −2.03119 3.51813i −0.168681 0.292165i
\(146\) −12.4484 21.5613i −1.03024 1.78442i
\(147\) 0 0
\(148\) 0.440707 0.0362259
\(149\) 8.56260 14.8309i 0.701475 1.21499i −0.266473 0.963842i \(-0.585858\pi\)
0.967949 0.251148i \(-0.0808082\pi\)
\(150\) 7.52209 13.0286i 0.614176 1.06378i
\(151\) 15.7975 1.28558 0.642789 0.766043i \(-0.277777\pi\)
0.642789 + 0.766043i \(0.277777\pi\)
\(152\) −2.16040 + 3.74191i −0.175231 + 0.303509i
\(153\) −3.64590 6.31488i −0.294753 0.510528i
\(154\) 0 0
\(155\) −3.58727 −0.288137
\(156\) −2.21148 0.926214i −0.177060 0.0741565i
\(157\) −3.78351 −0.301957 −0.150979 0.988537i \(-0.548242\pi\)
−0.150979 + 0.988537i \(0.548242\pi\)
\(158\) −11.3771 19.7058i −0.905117 1.56771i
\(159\) 8.76722 + 15.1853i 0.695286 + 1.20427i
\(160\) −0.516821 + 0.895161i −0.0408583 + 0.0707687i
\(161\) 0 0
\(162\) −8.55402 + 14.8160i −0.672067 + 1.16406i
\(163\) −0.857757 + 1.48568i −0.0671847 + 0.116367i −0.897661 0.440687i \(-0.854735\pi\)
0.830476 + 0.557054i \(0.188068\pi\)
\(164\) 0.423922 0.0331027
\(165\) 0.952894 1.65046i 0.0741827 0.128488i
\(166\) 7.69677 + 13.3312i 0.597385 + 1.03470i
\(167\) −6.32605 10.9570i −0.489524 0.847881i 0.510403 0.859935i \(-0.329496\pi\)
−0.999927 + 0.0120542i \(0.996163\pi\)
\(168\) 0 0
\(169\) 9.11992 + 9.26429i 0.701532 + 0.712638i
\(170\) −4.29772 −0.329620
\(171\) −1.28043 2.21776i −0.0979166 0.169596i
\(172\) 1.80764 + 3.13092i 0.137831 + 0.238730i
\(173\) 5.74371 9.94839i 0.436686 0.756362i −0.560746 0.827988i \(-0.689485\pi\)
0.997432 + 0.0716259i \(0.0228188\pi\)
\(174\) 22.2868 1.68956
\(175\) 0 0
\(176\) 3.44280 5.96310i 0.259510 0.449485i
\(177\) 25.2501 1.89792
\(178\) 12.5350 21.7112i 0.939536 1.62732i
\(179\) 1.09225 + 1.89184i 0.0816389 + 0.141403i 0.903954 0.427630i \(-0.140651\pi\)
−0.822315 + 0.569032i \(0.807318\pi\)
\(180\) −0.140165 0.242772i −0.0104472 0.0180952i
\(181\) −11.5981 −0.862081 −0.431041 0.902333i \(-0.641853\pi\)
−0.431041 + 0.902333i \(0.641853\pi\)
\(182\) 0 0
\(183\) −5.27337 −0.389819
\(184\) −2.27590 3.94198i −0.167782 0.290606i
\(185\) −0.415264 0.719258i −0.0305308 0.0528809i
\(186\) 9.84014 17.0436i 0.721514 1.24970i
\(187\) 7.29179 0.533229
\(188\) 0.0726885 0.125900i 0.00530135 0.00918221i
\(189\) 0 0
\(190\) −1.50934 −0.109499
\(191\) −8.87961 + 15.3799i −0.642506 + 1.11285i 0.342365 + 0.939567i \(0.388772\pi\)
−0.984871 + 0.173286i \(0.944561\pi\)
\(192\) 6.79147 + 11.7632i 0.490132 + 0.848934i
\(193\) −11.3189 19.6050i −0.814756 1.41120i −0.909503 0.415697i \(-0.863538\pi\)
0.0947474 0.995501i \(-0.469796\pi\)
\(194\) 1.48103 0.106332
\(195\) 0.572172 + 4.48200i 0.0409741 + 0.320962i
\(196\) 0 0
\(197\) −10.0032 17.3260i −0.712696 1.23442i −0.963842 0.266476i \(-0.914141\pi\)
0.251146 0.967949i \(-0.419193\pi\)
\(198\) 1.75859 + 3.04596i 0.124977 + 0.216467i
\(199\) 0.924426 1.60115i 0.0655309 0.113503i −0.831398 0.555677i \(-0.812459\pi\)
0.896929 + 0.442174i \(0.145793\pi\)
\(200\) −11.9383 −0.844162
\(201\) −8.05073 + 13.9443i −0.567854 + 0.983553i
\(202\) −2.23572 + 3.87237i −0.157304 + 0.272459i
\(203\) 0 0
\(204\) 1.59421 2.76126i 0.111617 0.193327i
\(205\) −0.399447 0.691863i −0.0278986 0.0483218i
\(206\) 0.402003 + 0.696289i 0.0280088 + 0.0485127i
\(207\) 2.69777 0.187508
\(208\) 2.06725 + 16.1934i 0.143338 + 1.12281i
\(209\) 2.56085 0.177138
\(210\) 0 0
\(211\) 8.08474 + 14.0032i 0.556576 + 0.964019i 0.997779 + 0.0666110i \(0.0212187\pi\)
−0.441203 + 0.897407i \(0.645448\pi\)
\(212\) −1.28960 + 2.23366i −0.0885702 + 0.153408i
\(213\) −14.0430 −0.962210
\(214\) −14.6925 + 25.4481i −1.00436 + 1.73960i
\(215\) 3.40655 5.90032i 0.232325 0.402399i
\(216\) 8.07020 0.549108
\(217\) 0 0
\(218\) −4.35884 7.54973i −0.295218 0.511332i
\(219\) −17.4043 30.1451i −1.17607 2.03701i
\(220\) 0.280329 0.0188998
\(221\) −13.7566 + 10.4703i −0.925369 + 0.704306i
\(222\) 4.55639 0.305805
\(223\) 6.21589 + 10.7662i 0.416247 + 0.720961i 0.995558 0.0941455i \(-0.0300119\pi\)
−0.579312 + 0.815106i \(0.696679\pi\)
\(224\) 0 0
\(225\) 3.53779 6.12763i 0.235853 0.408509i
\(226\) −7.83136 −0.520934
\(227\) −0.617487 + 1.06952i −0.0409841 + 0.0709865i −0.885790 0.464087i \(-0.846383\pi\)
0.844806 + 0.535073i \(0.179716\pi\)
\(228\) 0.559881 0.969743i 0.0370790 0.0642228i
\(229\) 6.55514 0.433176 0.216588 0.976263i \(-0.430507\pi\)
0.216588 + 0.976263i \(0.430507\pi\)
\(230\) 0.795020 1.37702i 0.0524221 0.0907977i
\(231\) 0 0
\(232\) −8.84282 15.3162i −0.580559 1.00556i
\(233\) 6.29887 0.412653 0.206326 0.978483i \(-0.433849\pi\)
0.206326 + 0.978483i \(0.433849\pi\)
\(234\) −7.69141 3.22132i −0.502803 0.210585i
\(235\) −0.273968 −0.0178717
\(236\) 1.85706 + 3.21653i 0.120885 + 0.209378i
\(237\) −15.9065 27.5509i −1.03324 1.78962i
\(238\) 0 0
\(239\) −18.9193 −1.22379 −0.611895 0.790939i \(-0.709592\pi\)
−0.611895 + 0.790939i \(0.709592\pi\)
\(240\) −2.83698 + 4.91380i −0.183126 + 0.317184i
\(241\) −11.1484 + 19.3096i −0.718131 + 1.24384i 0.243609 + 0.969874i \(0.421669\pi\)
−0.961740 + 0.273965i \(0.911665\pi\)
\(242\) 13.2113 0.849257
\(243\) −7.24176 + 12.5431i −0.464559 + 0.804640i
\(244\) −0.387839 0.671757i −0.0248289 0.0430048i
\(245\) 0 0
\(246\) 4.38285 0.279440
\(247\) −4.83127 + 3.67711i −0.307406 + 0.233969i
\(248\) −15.6172 −0.991695
\(249\) 10.7609 + 18.6385i 0.681947 + 1.18117i
\(250\) −4.32597 7.49280i −0.273598 0.473886i
\(251\) 3.47657 6.02160i 0.219439 0.380080i −0.735197 0.677853i \(-0.762910\pi\)
0.954637 + 0.297773i \(0.0962438\pi\)
\(252\) 0 0
\(253\) −1.34888 + 2.33633i −0.0848036 + 0.146884i
\(254\) −6.84600 + 11.8576i −0.429556 + 0.744013i
\(255\) −6.00869 −0.376279
\(256\) −3.66603 + 6.34975i −0.229127 + 0.396860i
\(257\) −10.5776 18.3209i −0.659811 1.14283i −0.980664 0.195697i \(-0.937303\pi\)
0.320853 0.947129i \(-0.396030\pi\)
\(258\) 18.6888 + 32.3700i 1.16352 + 2.01527i
\(259\) 0 0
\(260\) −0.528865 + 0.402523i −0.0327988 + 0.0249634i
\(261\) 10.4819 0.648816
\(262\) 5.16941 + 8.95368i 0.319367 + 0.553160i
\(263\) 4.21496 + 7.30053i 0.259906 + 0.450170i 0.966216 0.257732i \(-0.0829752\pi\)
−0.706311 + 0.707902i \(0.749642\pi\)
\(264\) 4.14844 7.18530i 0.255319 0.442225i
\(265\) 4.86060 0.298584
\(266\) 0 0
\(267\) 17.5253 30.3547i 1.07253 1.85768i
\(268\) −2.36842 −0.144674
\(269\) 2.91519 5.04926i 0.177743 0.307859i −0.763364 0.645968i \(-0.776454\pi\)
0.941107 + 0.338109i \(0.109787\pi\)
\(270\) 1.40955 + 2.44141i 0.0857823 + 0.148579i
\(271\) −9.21497 15.9608i −0.559769 0.969549i −0.997515 0.0704502i \(-0.977556\pi\)
0.437746 0.899099i \(-0.355777\pi\)
\(272\) −21.7093 −1.31632
\(273\) 0 0
\(274\) 21.4058 1.29317
\(275\) 3.53779 + 6.12763i 0.213337 + 0.369510i
\(276\) 0.589815 + 1.02159i 0.0355027 + 0.0614925i
\(277\) 3.09154 5.35470i 0.185752 0.321733i −0.758077 0.652165i \(-0.773861\pi\)
0.943830 + 0.330432i \(0.107194\pi\)
\(278\) −26.2885 −1.57668
\(279\) 4.62802 8.01596i 0.277072 0.479903i
\(280\) 0 0
\(281\) −5.64049 −0.336483 −0.168242 0.985746i \(-0.553809\pi\)
−0.168242 + 0.985746i \(0.553809\pi\)
\(282\) 0.751513 1.30166i 0.0447520 0.0775127i
\(283\) 8.22771 + 14.2508i 0.489086 + 0.847123i 0.999921 0.0125564i \(-0.00399694\pi\)
−0.510835 + 0.859679i \(0.670664\pi\)
\(284\) −1.03282 1.78889i −0.0612864 0.106151i
\(285\) −2.11023 −0.124999
\(286\) 6.63545 5.05029i 0.392362 0.298630i
\(287\) 0 0
\(288\) −1.33353 2.30973i −0.0785787 0.136102i
\(289\) −2.99502 5.18752i −0.176177 0.305148i
\(290\) 3.08898 5.35028i 0.181391 0.314179i
\(291\) 2.07065 0.121384
\(292\) 2.56005 4.43414i 0.149816 0.259489i
\(293\) −15.3086 + 26.5152i −0.894335 + 1.54903i −0.0597104 + 0.998216i \(0.519018\pi\)
−0.834625 + 0.550819i \(0.814316\pi\)
\(294\) 0 0
\(295\) 3.49970 6.06166i 0.203760 0.352923i
\(296\) −1.80785 3.13130i −0.105079 0.182003i
\(297\) −2.39153 4.14225i −0.138771 0.240358i
\(298\) 26.0435 1.50866
\(299\) −0.809947 6.34456i −0.0468404 0.366915i
\(300\) 3.09388 0.178625
\(301\) 0 0
\(302\) 12.0122 + 20.8057i 0.691223 + 1.19723i
\(303\) −3.12578 + 5.41401i −0.179571 + 0.311027i
\(304\) −7.62424 −0.437280
\(305\) −0.730896 + 1.26595i −0.0418510 + 0.0724880i
\(306\) 5.54458 9.60350i 0.316963 0.548995i
\(307\) −9.96020 −0.568459 −0.284229 0.958756i \(-0.591738\pi\)
−0.284229 + 0.958756i \(0.591738\pi\)
\(308\) 0 0
\(309\) 0.562044 + 0.973489i 0.0319736 + 0.0553799i
\(310\) −2.72771 4.72454i −0.154924 0.268336i
\(311\) 27.7468 1.57337 0.786687 0.617352i \(-0.211795\pi\)
0.786687 + 0.617352i \(0.211795\pi\)
\(312\) 2.49096 + 19.5124i 0.141023 + 1.10467i
\(313\) −16.5227 −0.933920 −0.466960 0.884278i \(-0.654651\pi\)
−0.466960 + 0.884278i \(0.654651\pi\)
\(314\) −2.87693 4.98300i −0.162355 0.281207i
\(315\) 0 0
\(316\) 2.33975 4.05256i 0.131621 0.227974i
\(317\) 23.6793 1.32996 0.664980 0.746861i \(-0.268440\pi\)
0.664980 + 0.746861i \(0.268440\pi\)
\(318\) −13.3330 + 23.0934i −0.747675 + 1.29501i
\(319\) −5.24097 + 9.07763i −0.293438 + 0.508250i
\(320\) 3.76523 0.210483
\(321\) −20.5417 + 35.5793i −1.14653 + 1.98584i
\(322\) 0 0
\(323\) −4.03701 6.99230i −0.224625 0.389062i
\(324\) −3.51832 −0.195462
\(325\) −15.4730 6.48041i −0.858287 0.359469i
\(326\) −2.60891 −0.144494
\(327\) −6.09414 10.5554i −0.337007 0.583713i
\(328\) −1.73900 3.01203i −0.0960202 0.166312i
\(329\) 0 0
\(330\) 2.89827 0.159545
\(331\) −3.97604 + 6.88671i −0.218543 + 0.378528i −0.954363 0.298650i \(-0.903464\pi\)
0.735820 + 0.677178i \(0.236797\pi\)
\(332\) −1.58286 + 2.74160i −0.0868710 + 0.150465i
\(333\) 2.14296 0.117434
\(334\) 9.62049 16.6632i 0.526410 0.911768i
\(335\) 2.23168 + 3.86539i 0.121930 + 0.211189i
\(336\) 0 0
\(337\) −7.91326 −0.431063 −0.215531 0.976497i \(-0.569148\pi\)
−0.215531 + 0.976497i \(0.569148\pi\)
\(338\) −5.26667 + 19.0556i −0.286469 + 1.03649i
\(339\) −10.9491 −0.594674
\(340\) −0.441920 0.765427i −0.0239665 0.0415111i
\(341\) 4.62802 + 8.01596i 0.250621 + 0.434089i
\(342\) 1.94724 3.37271i 0.105294 0.182375i
\(343\) 0 0
\(344\) 14.8305 25.6871i 0.799605 1.38496i
\(345\) 1.11153 1.92522i 0.0598426 0.103650i
\(346\) 17.4698 0.939180
\(347\) −3.56786 + 6.17971i −0.191533 + 0.331744i −0.945758 0.324871i \(-0.894679\pi\)
0.754226 + 0.656615i \(0.228012\pi\)
\(348\) 2.29168 + 3.96930i 0.122847 + 0.212777i
\(349\) 0.688402 + 1.19235i 0.0368493 + 0.0638249i 0.883862 0.467748i \(-0.154935\pi\)
−0.847013 + 0.531573i \(0.821601\pi\)
\(350\) 0 0
\(351\) 10.4597 + 4.38073i 0.558296 + 0.233826i
\(352\) 2.66705 0.142154
\(353\) 0.346608 + 0.600342i 0.0184481 + 0.0319530i 0.875102 0.483938i \(-0.160794\pi\)
−0.856654 + 0.515891i \(0.827461\pi\)
\(354\) 19.1999 + 33.2551i 1.02046 + 1.76749i
\(355\) −1.94638 + 3.37123i −0.103303 + 0.178926i
\(356\) 5.15571 0.273252
\(357\) 0 0
\(358\) −1.66107 + 2.87706i −0.0877904 + 0.152057i
\(359\) −5.80365 −0.306305 −0.153152 0.988203i \(-0.548943\pi\)
−0.153152 + 0.988203i \(0.548943\pi\)
\(360\) −1.14996 + 1.99178i −0.0606081 + 0.104976i
\(361\) 8.08222 + 13.9988i 0.425380 + 0.736780i
\(362\) −8.81905 15.2750i −0.463519 0.802839i
\(363\) 18.4709 0.969472
\(364\) 0 0
\(365\) −9.64902 −0.505053
\(366\) −4.00980 6.94518i −0.209596 0.363030i
\(367\) 3.67578 + 6.36664i 0.191874 + 0.332336i 0.945871 0.324542i \(-0.105210\pi\)
−0.753997 + 0.656878i \(0.771877\pi\)
\(368\) 4.01593 6.95580i 0.209345 0.362596i
\(369\) 2.06134 0.107309
\(370\) 0.631522 1.09383i 0.0328313 0.0568654i
\(371\) 0 0
\(372\) 4.04731 0.209843
\(373\) −9.19942 + 15.9339i −0.476328 + 0.825024i −0.999632 0.0271216i \(-0.991366\pi\)
0.523304 + 0.852146i \(0.324699\pi\)
\(374\) 5.54458 + 9.60350i 0.286704 + 0.496585i
\(375\) −6.04819 10.4758i −0.312327 0.540966i
\(376\) −1.19272 −0.0615099
\(377\) −3.14698 24.6512i −0.162078 1.26960i
\(378\) 0 0
\(379\) 2.42550 + 4.20110i 0.124590 + 0.215796i 0.921573 0.388206i \(-0.126905\pi\)
−0.796983 + 0.604002i \(0.793572\pi\)
\(380\) −0.155201 0.268815i −0.00796162 0.0137899i
\(381\) −9.57147 + 16.5783i −0.490361 + 0.849331i
\(382\) −27.0078 −1.38184
\(383\) −11.4103 + 19.7631i −0.583037 + 1.00985i 0.412080 + 0.911148i \(0.364802\pi\)
−0.995117 + 0.0987019i \(0.968531\pi\)
\(384\) −14.0571 + 24.3476i −0.717349 + 1.24249i
\(385\) 0 0
\(386\) 17.2136 29.8148i 0.876147 1.51753i
\(387\) 8.78973 + 15.2243i 0.446807 + 0.773893i
\(388\) 0.152290 + 0.263773i 0.00773134 + 0.0133911i
\(389\) −20.3122 −1.02987 −0.514933 0.857230i \(-0.672183\pi\)
−0.514933 + 0.857230i \(0.672183\pi\)
\(390\) −5.46784 + 4.16162i −0.276875 + 0.210732i
\(391\) 8.50569 0.430151
\(392\) 0 0
\(393\) 7.22741 + 12.5182i 0.364575 + 0.631462i
\(394\) 15.2125 26.3489i 0.766397 1.32744i
\(395\) −8.81866 −0.443715
\(396\) −0.361659 + 0.626411i −0.0181740 + 0.0314783i
\(397\) −17.0689 + 29.5641i −0.856662 + 1.48378i 0.0184326 + 0.999830i \(0.494132\pi\)
−0.875095 + 0.483952i \(0.839201\pi\)
\(398\) 2.81169 0.140937
\(399\) 0 0
\(400\) −10.5328 18.2434i −0.526640 0.912168i
\(401\) 1.51298 + 2.62056i 0.0755547 + 0.130865i 0.901327 0.433139i \(-0.142594\pi\)
−0.825773 + 0.564003i \(0.809261\pi\)
\(402\) −24.4867 −1.22128
\(403\) −20.2412 8.47746i −1.00829 0.422292i
\(404\) −0.919564 −0.0457500
\(405\) 3.31520 + 5.74209i 0.164734 + 0.285327i
\(406\) 0 0
\(407\) −1.07148 + 1.85586i −0.0531114 + 0.0919916i
\(408\) −26.1589 −1.29506
\(409\) 2.69162 4.66203i 0.133092 0.230523i −0.791775 0.610813i \(-0.790843\pi\)
0.924867 + 0.380291i \(0.124176\pi\)
\(410\) 0.607469 1.05217i 0.0300008 0.0519628i
\(411\) 29.9276 1.47622
\(412\) −0.0826731 + 0.143194i −0.00407301 + 0.00705466i
\(413\) 0 0
\(414\) 2.05135 + 3.55304i 0.100818 + 0.174622i
\(415\) 5.96592 0.292856
\(416\) −5.03162 + 3.82961i −0.246696 + 0.187762i
\(417\) −36.7543 −1.79986
\(418\) 1.94724 + 3.37271i 0.0952425 + 0.164965i
\(419\) 2.94117 + 5.09426i 0.143686 + 0.248871i 0.928882 0.370376i \(-0.120771\pi\)
−0.785196 + 0.619247i \(0.787438\pi\)
\(420\) 0 0
\(421\) −28.7614 −1.40174 −0.700872 0.713287i \(-0.747206\pi\)
−0.700872 + 0.713287i \(0.747206\pi\)
\(422\) −12.2951 + 21.2957i −0.598514 + 1.03666i
\(423\) 0.353452 0.612196i 0.0171854 0.0297660i
\(424\) 21.1607 1.02765
\(425\) 11.1542 19.3196i 0.541057 0.937138i
\(426\) −10.6781 18.4950i −0.517356 0.896087i
\(427\) 0 0
\(428\) −6.04311 −0.292105
\(429\) 9.27710 7.06087i 0.447903 0.340902i
\(430\) 10.3612 0.499661
\(431\) −4.19294 7.26238i −0.201967 0.349817i 0.747195 0.664605i \(-0.231400\pi\)
−0.949162 + 0.314788i \(0.898067\pi\)
\(432\) 7.12013 + 12.3324i 0.342567 + 0.593344i
\(433\) −13.7996 + 23.9017i −0.663168 + 1.14864i 0.316611 + 0.948556i \(0.397455\pi\)
−0.979779 + 0.200085i \(0.935878\pi\)
\(434\) 0 0
\(435\) 4.31874 7.48028i 0.207068 0.358652i
\(436\) 0.896409 1.55263i 0.0429302 0.0743573i
\(437\) 2.98717 0.142896
\(438\) 26.4679 45.8438i 1.26469 2.19050i
\(439\) 15.5869 + 26.9973i 0.743921 + 1.28851i 0.950697 + 0.310121i \(0.100369\pi\)
−0.206776 + 0.978388i \(0.566297\pi\)
\(440\) −1.14996 1.99178i −0.0548221 0.0949546i
\(441\) 0 0
\(442\) −24.2500 10.1564i −1.15345 0.483090i
\(443\) −23.5883 −1.12071 −0.560357 0.828251i \(-0.689336\pi\)
−0.560357 + 0.828251i \(0.689336\pi\)
\(444\) 0.468518 + 0.811497i 0.0222349 + 0.0385119i
\(445\) −4.85806 8.41440i −0.230294 0.398881i
\(446\) −9.45296 + 16.3730i −0.447611 + 0.775284i
\(447\) 36.4118 1.72222
\(448\) 0 0
\(449\) −1.41328 + 2.44787i −0.0666968 + 0.115522i −0.897445 0.441125i \(-0.854579\pi\)
0.830749 + 0.556648i \(0.187913\pi\)
\(450\) 10.7604 0.507248
\(451\) −1.03067 + 1.78518i −0.0485324 + 0.0840607i
\(452\) −0.805272 1.39477i −0.0378768 0.0656046i
\(453\) 16.7944 + 29.0887i 0.789068 + 1.36671i
\(454\) −1.87812 −0.0881444
\(455\) 0 0
\(456\) −9.18691 −0.430217
\(457\) 18.8716 + 32.6866i 0.882776 + 1.52901i 0.848242 + 0.529609i \(0.177661\pi\)
0.0345338 + 0.999404i \(0.489005\pi\)
\(458\) 4.98444 + 8.63330i 0.232908 + 0.403408i
\(459\) −7.54017 + 13.0599i −0.351945 + 0.609586i
\(460\) 0.326997 0.0152463
\(461\) 17.3293 30.0152i 0.807106 1.39795i −0.107754 0.994178i \(-0.534366\pi\)
0.914860 0.403771i \(-0.132301\pi\)
\(462\) 0 0
\(463\) 18.5114 0.860296 0.430148 0.902758i \(-0.358461\pi\)
0.430148 + 0.902758i \(0.358461\pi\)
\(464\) 15.6036 27.0262i 0.724377 1.25466i
\(465\) −3.81365 6.60543i −0.176854 0.306320i
\(466\) 4.78958 + 8.29579i 0.221873 + 0.384295i
\(467\) −6.62783 −0.306700 −0.153350 0.988172i \(-0.549006\pi\)
−0.153350 + 0.988172i \(0.549006\pi\)
\(468\) −0.217161 1.70108i −0.0100383 0.0786326i
\(469\) 0 0
\(470\) −0.208321 0.360823i −0.00960915 0.0166435i
\(471\) −4.02227 6.96678i −0.185337 0.321012i
\(472\) 15.2360 26.3895i 0.701293 1.21468i
\(473\) −17.5795 −0.808305
\(474\) 24.1902 41.8987i 1.11109 1.92447i
\(475\) 3.91730 6.78497i 0.179738 0.311316i
\(476\) 0 0
\(477\) −6.27076 + 10.8613i −0.287118 + 0.497304i
\(478\) −14.3860 24.9173i −0.658001 1.13969i
\(479\) −8.72630 15.1144i −0.398715 0.690594i 0.594853 0.803835i \(-0.297210\pi\)
−0.993568 + 0.113240i \(0.963877\pi\)
\(480\) −2.19774 −0.100313
\(481\) −0.643379 5.03978i −0.0293355 0.229794i
\(482\) −33.9083 −1.54448
\(483\) 0 0
\(484\) 1.35848 + 2.35295i 0.0617489 + 0.106952i
\(485\) 0.286995 0.497090i 0.0130318 0.0225717i
\(486\) −22.0261 −0.999126
\(487\) 17.7569 30.7558i 0.804641 1.39368i −0.111892 0.993720i \(-0.535691\pi\)
0.916533 0.399959i \(-0.130976\pi\)
\(488\) −3.18196 + 5.51132i −0.144041 + 0.249486i
\(489\) −3.64754 −0.164948
\(490\) 0 0
\(491\) 14.9059 + 25.8178i 0.672695 + 1.16514i 0.977137 + 0.212611i \(0.0681966\pi\)
−0.304442 + 0.952531i \(0.598470\pi\)
\(492\) 0.450674 + 0.780590i 0.0203179 + 0.0351917i
\(493\) 33.0481 1.48841
\(494\) −8.51650 3.56689i −0.383175 0.160482i
\(495\) 1.36312 0.0612675
\(496\) −13.7787 23.8653i −0.618680 1.07159i
\(497\) 0 0
\(498\) −16.3649 + 28.3449i −0.733331 + 1.27017i
\(499\) −7.50966 −0.336178 −0.168089 0.985772i \(-0.553760\pi\)
−0.168089 + 0.985772i \(0.553760\pi\)
\(500\) 0.889649 1.54092i 0.0397863 0.0689119i
\(501\) 13.4505 23.2970i 0.600925 1.04083i
\(502\) 10.5742 0.471948
\(503\) 0.492171 0.852466i 0.0219448 0.0380096i −0.854844 0.518884i \(-0.826348\pi\)
0.876789 + 0.480875i \(0.159681\pi\)
\(504\) 0 0
\(505\) 0.866474 + 1.50078i 0.0385576 + 0.0667837i
\(506\) −4.10269 −0.182387
\(507\) −7.36339 + 26.6419i −0.327019 + 1.18321i
\(508\) −2.81580 −0.124931
\(509\) 6.48958 + 11.2403i 0.287646 + 0.498217i 0.973247 0.229760i \(-0.0737941\pi\)
−0.685602 + 0.727977i \(0.740461\pi\)
\(510\) −4.56893 7.91362i −0.202316 0.350421i
\(511\) 0 0
\(512\) 15.2950 0.675949
\(513\) −2.64808 + 4.58661i −0.116916 + 0.202504i
\(514\) 16.0861 27.8619i 0.709527 1.22894i
\(515\) 0.311600 0.0137308
\(516\) −3.84342 + 6.65699i −0.169197 + 0.293058i
\(517\) 0.353452 + 0.612196i 0.0155448 + 0.0269244i
\(518\) 0 0
\(519\) 24.4247 1.07212
\(520\) 5.02949 + 2.10646i 0.220558 + 0.0923742i
\(521\) 19.4146 0.850569 0.425285 0.905060i \(-0.360174\pi\)
0.425285 + 0.905060i \(0.360174\pi\)
\(522\) 7.97033 + 13.8050i 0.348852 + 0.604229i
\(523\) 13.6360 + 23.6182i 0.596259 + 1.03275i 0.993368 + 0.114979i \(0.0366801\pi\)
−0.397109 + 0.917771i \(0.629987\pi\)
\(524\) −1.06311 + 1.84135i −0.0464420 + 0.0804399i
\(525\) 0 0
\(526\) −6.41000 + 11.1024i −0.279489 + 0.484090i
\(527\) 14.5915 25.2732i 0.635616 1.10092i
\(528\) 14.6402 0.637134
\(529\) 9.92656 17.1933i 0.431590 0.747535i
\(530\) 3.69593 + 6.40154i 0.160541 + 0.278065i
\(531\) 9.03008 + 15.6406i 0.391872 + 0.678742i
\(532\) 0 0
\(533\) −0.618874 4.84783i −0.0268064 0.209983i
\(534\) 53.3040 2.30669
\(535\) 5.69422 + 9.86268i 0.246183 + 0.426401i
\(536\) 9.71566 + 16.8280i 0.419652 + 0.726859i
\(537\) −2.32236 + 4.02245i −0.100217 + 0.173582i
\(538\) 8.86670 0.382271
\(539\) 0 0
\(540\) −0.289878 + 0.502083i −0.0124743 + 0.0216062i
\(541\) −30.0990 −1.29406 −0.647029 0.762465i \(-0.723989\pi\)
−0.647029 + 0.762465i \(0.723989\pi\)
\(542\) 14.0139 24.2727i 0.601947 1.04260i
\(543\) −12.3300 21.3562i −0.529132 0.916483i
\(544\) −4.20442 7.28228i −0.180263 0.312225i
\(545\) −3.37863 −0.144724
\(546\) 0 0
\(547\) −26.1451 −1.11788 −0.558942 0.829207i \(-0.688793\pi\)
−0.558942 + 0.829207i \(0.688793\pi\)
\(548\) 2.20108 + 3.81238i 0.0940255 + 0.162857i
\(549\) −1.88589 3.26646i −0.0804878 0.139409i
\(550\) −5.38018 + 9.31874i −0.229411 + 0.397352i
\(551\) 11.6064 0.494449
\(552\) 4.83905 8.38147i 0.205963 0.356739i
\(553\) 0 0
\(554\) 9.40305 0.399497
\(555\) 0.882938 1.52929i 0.0374786 0.0649149i
\(556\) −2.70316 4.68200i −0.114639 0.198561i
\(557\) −8.95317 15.5073i −0.379358 0.657067i 0.611611 0.791159i \(-0.290522\pi\)
−0.990969 + 0.134091i \(0.957188\pi\)
\(558\) 14.0763 0.595899
\(559\) 33.1652 25.2423i 1.40274 1.06764i
\(560\) 0 0
\(561\) 7.75195 + 13.4268i 0.327287 + 0.566878i
\(562\) −4.28895 7.42868i −0.180919 0.313360i
\(563\) −15.8275 + 27.4140i −0.667048 + 1.15536i 0.311678 + 0.950188i \(0.399109\pi\)
−0.978726 + 0.205173i \(0.934224\pi\)
\(564\) 0.309102 0.0130155
\(565\) −1.51756 + 2.62850i −0.0638443 + 0.110582i
\(566\) −12.5125 + 21.6722i −0.525939 + 0.910953i
\(567\) 0 0
\(568\) −8.47358 + 14.6767i −0.355544 + 0.615820i
\(569\) 13.0555 + 22.6129i 0.547317 + 0.947981i 0.998457 + 0.0555278i \(0.0176841\pi\)
−0.451140 + 0.892453i \(0.648983\pi\)
\(570\) −1.60459 2.77923i −0.0672089 0.116409i
\(571\) 13.3041 0.556760 0.278380 0.960471i \(-0.410203\pi\)
0.278380 + 0.960471i \(0.410203\pi\)
\(572\) 1.58176 + 0.662475i 0.0661368 + 0.0276995i
\(573\) −37.7599 −1.57744
\(574\) 0 0
\(575\) 4.12674 + 7.14773i 0.172097 + 0.298081i
\(576\) −4.85760 + 8.41361i −0.202400 + 0.350567i
\(577\) 16.7713 0.698198 0.349099 0.937086i \(-0.386488\pi\)
0.349099 + 0.937086i \(0.386488\pi\)
\(578\) 4.55474 7.88904i 0.189452 0.328141i
\(579\) 24.0665 41.6844i 1.00017 1.73234i
\(580\) 1.27052 0.0527554
\(581\) 0 0
\(582\) 1.57450 + 2.72711i 0.0652650 + 0.113042i
\(583\) −6.27076 10.8613i −0.259708 0.449828i
\(584\) −42.0071 −1.73827
\(585\) −2.57164 + 1.95729i −0.106324 + 0.0809241i
\(586\) −46.5617 −1.92345
\(587\) −5.03261 8.71673i −0.207718 0.359778i 0.743277 0.668983i \(-0.233270\pi\)
−0.950995 + 0.309205i \(0.899937\pi\)
\(588\) 0 0
\(589\) 5.12448 8.87587i 0.211151 0.365724i
\(590\) 10.6445 0.438227
\(591\) 21.2688 36.8387i 0.874883 1.51534i
\(592\) 3.19004 5.52532i 0.131110 0.227089i
\(593\) −39.4322 −1.61929 −0.809643 0.586923i \(-0.800339\pi\)
−0.809643 + 0.586923i \(0.800339\pi\)
\(594\) 3.63697 6.29942i 0.149227 0.258468i
\(595\) 0 0
\(596\) 2.67797 + 4.63838i 0.109694 + 0.189995i
\(597\) 3.93105 0.160887
\(598\) 7.74009 5.89104i 0.316516 0.240902i
\(599\) 13.7720 0.562709 0.281355 0.959604i \(-0.409216\pi\)
0.281355 + 0.959604i \(0.409216\pi\)
\(600\) −12.6916 21.9825i −0.518133 0.897433i
\(601\) 16.6312 + 28.8060i 0.678399 + 1.17502i 0.975463 + 0.220164i \(0.0706592\pi\)
−0.297064 + 0.954858i \(0.596007\pi\)
\(602\) 0 0
\(603\) −11.5166 −0.468991
\(604\) −2.47034 + 4.27876i −0.100517 + 0.174100i
\(605\) 2.56009 4.43421i 0.104083 0.180276i
\(606\) −9.50720 −0.386204
\(607\) 21.9824 38.0747i 0.892240 1.54540i 0.0550554 0.998483i \(-0.482466\pi\)
0.837184 0.546921i \(-0.184200\pi\)
\(608\) −1.47658 2.55751i −0.0598831 0.103721i
\(609\) 0 0
\(610\) −2.22305 −0.0900088
\(611\) −1.54587 0.647442i −0.0625391 0.0261927i
\(612\) 2.28052 0.0921846
\(613\) −1.35045 2.33906i −0.0545443 0.0944736i 0.837464 0.546492i \(-0.184037\pi\)
−0.892008 + 0.452019i \(0.850704\pi\)
\(614\) −7.57361 13.1179i −0.305646 0.529394i
\(615\) 0.849310 1.47105i 0.0342475 0.0593184i
\(616\) 0 0
\(617\) −3.00208 + 5.19975i −0.120859 + 0.209334i −0.920107 0.391668i \(-0.871898\pi\)
0.799248 + 0.601002i \(0.205232\pi\)
\(618\) −0.854742 + 1.48046i −0.0343828 + 0.0595527i
\(619\) 13.3641 0.537148 0.268574 0.963259i \(-0.413448\pi\)
0.268574 + 0.963259i \(0.413448\pi\)
\(620\) 0.560963 0.971616i 0.0225288 0.0390210i
\(621\) −2.78966 4.83183i −0.111945 0.193895i
\(622\) 21.0983 + 36.5433i 0.845963 + 1.46525i
\(623\) 0 0
\(624\) −27.6201 + 21.0218i −1.10569 + 0.841547i
\(625\) 19.9099 0.796398
\(626\) −12.5637 21.7609i −0.502145 0.869741i
\(627\) 2.72245 + 4.71543i 0.108724 + 0.188316i
\(628\) 0.591650 1.02477i 0.0236094 0.0408927i
\(629\) 6.75647 0.269398
\(630\) 0 0
\(631\) −20.2228 + 35.0270i −0.805059 + 1.39440i 0.111192 + 0.993799i \(0.464533\pi\)
−0.916251 + 0.400604i \(0.868800\pi\)
\(632\) −38.3921 −1.52716
\(633\) −17.1899 + 29.7737i −0.683236 + 1.18340i
\(634\) 18.0054 + 31.1863i 0.715086 + 1.23857i
\(635\) 2.65324 + 4.59554i 0.105291 + 0.182369i
\(636\) −5.48393 −0.217452
\(637\) 0 0
\(638\) −15.9407 −0.631097
\(639\) −5.02213 8.69859i −0.198672 0.344111i
\(640\) 3.89667 + 6.74923i 0.154029 + 0.266787i
\(641\) −5.10991 + 8.85062i −0.201829 + 0.349578i −0.949118 0.314921i \(-0.898022\pi\)
0.747289 + 0.664500i \(0.231355\pi\)
\(642\) −62.4786 −2.46584
\(643\) 15.9014 27.5420i 0.627088 1.08615i −0.361045 0.932548i \(-0.617580\pi\)
0.988133 0.153600i \(-0.0490868\pi\)
\(644\) 0 0
\(645\) 14.4861 0.570389
\(646\) 6.13937 10.6337i 0.241550 0.418378i
\(647\) −17.2617 29.8981i −0.678626 1.17541i −0.975395 0.220465i \(-0.929243\pi\)
0.296769 0.954949i \(-0.404091\pi\)
\(648\) 14.4328 + 24.9983i 0.566972 + 0.982025i
\(649\) −18.0602 −0.708923
\(650\) −3.23057 25.3060i −0.126713 0.992582i
\(651\) 0 0
\(652\) −0.268265 0.464649i −0.0105061 0.0181970i
\(653\) −5.05899 8.76244i −0.197974 0.342901i 0.749898 0.661554i \(-0.230103\pi\)
−0.947871 + 0.318653i \(0.896769\pi\)
\(654\) 9.26781 16.0523i 0.362400 0.627695i
\(655\) 4.00692 0.156563
\(656\) 3.06855 5.31488i 0.119807 0.207511i
\(657\) 12.4484 21.5613i 0.485659 0.841185i
\(658\) 0 0
\(659\) 17.3841 30.1101i 0.677187 1.17292i −0.298637 0.954367i \(-0.596532\pi\)
0.975824 0.218556i \(-0.0701345\pi\)
\(660\) 0.298019 + 0.516185i 0.0116004 + 0.0200925i
\(661\) −8.28076 14.3427i −0.322084 0.557866i 0.658834 0.752289i \(-0.271050\pi\)
−0.980918 + 0.194422i \(0.937717\pi\)
\(662\) −12.0933 −0.470020
\(663\) −33.9042 14.1998i −1.31673 0.551474i
\(664\) 25.9727 1.00794
\(665\) 0 0
\(666\) 1.62948 + 2.82234i 0.0631411 + 0.109364i
\(667\) −6.11346 + 10.5888i −0.236714 + 0.410001i
\(668\) 3.95697 0.153100
\(669\) −13.2163 + 22.8913i −0.510972 + 0.885029i
\(670\) −3.39388 + 5.87838i −0.131117 + 0.227102i
\(671\) 3.77178 0.145608
\(672\) 0 0
\(673\) 20.9437 + 36.2756i 0.807321 + 1.39832i 0.914713 + 0.404104i \(0.132417\pi\)
−0.107393 + 0.994217i \(0.534250\pi\)
\(674\) −6.01714 10.4220i −0.231771 0.401440i
\(675\) −14.6332 −0.563231
\(676\) −3.93538 + 1.02143i −0.151361 + 0.0392857i
\(677\) 31.5715 1.21339 0.606696 0.794934i \(-0.292495\pi\)
0.606696 + 0.794934i \(0.292495\pi\)
\(678\) −8.32556 14.4203i −0.319741 0.553808i
\(679\) 0 0
\(680\) −3.62566 + 6.27983i −0.139038 + 0.240820i
\(681\) −2.62582 −0.100621
\(682\) −7.03817 + 12.1905i −0.269505 + 0.466797i
\(683\) 13.1338 22.7484i 0.502551 0.870444i −0.497445 0.867496i \(-0.665728\pi\)
0.999996 0.00294809i \(-0.000938408\pi\)
\(684\) 0.800911 0.0306236
\(685\) 4.14801 7.18457i 0.158487 0.274508i
\(686\) 0 0
\(687\) 6.96880 + 12.0703i 0.265876 + 0.460512i
\(688\) 52.3381 1.99537
\(689\) 27.4260 + 11.4866i 1.04485 + 0.437604i
\(690\) 3.38076 0.128703
\(691\) 3.05047 + 5.28358i 0.116046 + 0.200997i 0.918197 0.396124i \(-0.129645\pi\)
−0.802152 + 0.597120i \(0.796311\pi\)
\(692\) 1.79635 + 3.11138i 0.0682872 + 0.118277i
\(693\) 0 0
\(694\) −10.8518 −0.411929
\(695\) −5.09419 + 8.82339i −0.193234 + 0.334690i
\(696\) 18.8017 32.5655i 0.712677 1.23439i
\(697\) 6.49914 0.246172
\(698\) −1.04690 + 1.81329i −0.0396259 + 0.0686341i
\(699\) 6.69636 + 11.5984i 0.253280 + 0.438693i
\(700\) 0 0
\(701\) −20.5701 −0.776921 −0.388461 0.921465i \(-0.626993\pi\)
−0.388461 + 0.921465i \(0.626993\pi\)
\(702\) 2.18385 + 17.1067i 0.0824240 + 0.645652i
\(703\) 2.37285 0.0894936
\(704\) −4.85760 8.41361i −0.183078 0.317100i
\(705\) −0.291257 0.504471i −0.0109694 0.0189995i
\(706\) −0.527111 + 0.912984i −0.0198381 + 0.0343606i
\(707\) 0 0
\(708\) −3.94851 + 6.83902i −0.148394 + 0.257026i
\(709\) 21.5764 37.3715i 0.810320 1.40352i −0.102320 0.994751i \(-0.532627\pi\)
0.912640 0.408764i \(-0.134040\pi\)
\(710\) −5.92000 −0.222174
\(711\) 11.3771 19.7058i 0.426676 0.739025i
\(712\) −21.1496 36.6322i −0.792615 1.37285i
\(713\) 5.39847 + 9.35042i 0.202174 + 0.350176i
\(714\) 0 0
\(715\) −0.409246 3.20575i −0.0153050 0.119888i
\(716\) −0.683209 −0.0255327
\(717\) −20.1132 34.8372i −0.751143 1.30102i
\(718\) −4.41302 7.64357i −0.164692 0.285255i
\(719\) 14.1042 24.4292i 0.525999 0.911057i −0.473542 0.880771i \(-0.657025\pi\)
0.999541 0.0302857i \(-0.00964171\pi\)
\(720\) −4.05831 −0.151244
\(721\) 0 0
\(722\) −12.2912 + 21.2890i −0.457432 + 0.792295i
\(723\) −47.4076 −1.76311
\(724\) 1.81367 3.14136i 0.0674044 0.116748i
\(725\) 16.0341 + 27.7719i 0.595492 + 1.03142i
\(726\) 14.0450 + 24.3267i 0.521260 + 0.902850i
\(727\) −19.5116 −0.723646 −0.361823 0.932247i \(-0.617845\pi\)
−0.361823 + 0.932247i \(0.617845\pi\)
\(728\) 0 0
\(729\) 2.95370 0.109396
\(730\) −7.33698 12.7080i −0.271554 0.470345i
\(731\) 27.7128 + 48.0000i 1.02500 + 1.77535i
\(732\) 0.824628 1.42830i 0.0304791 0.0527914i
\(733\) 20.3666 0.752259 0.376129 0.926567i \(-0.377255\pi\)
0.376129 + 0.926567i \(0.377255\pi\)
\(734\) −5.59003 + 9.68222i −0.206332 + 0.357377i
\(735\) 0 0
\(736\) 3.11105 0.114675
\(737\) 5.75829 9.97364i 0.212109 0.367384i
\(738\) 1.56742 + 2.71485i 0.0576975 + 0.0999349i
\(739\) 5.20995 + 9.02391i 0.191651 + 0.331950i 0.945798 0.324757i \(-0.105282\pi\)
−0.754146 + 0.656706i \(0.771949\pi\)
\(740\) 0.259749 0.00954856
\(741\) −11.9070 4.98691i −0.437415 0.183199i
\(742\) 0 0
\(743\) 8.70470 + 15.0770i 0.319344 + 0.553121i 0.980351 0.197259i \(-0.0632040\pi\)
−0.661007 + 0.750380i \(0.729871\pi\)
\(744\) −16.6028 28.7568i −0.608687 1.05428i
\(745\) 5.04672 8.74118i 0.184898 0.320252i
\(746\) −27.9805 −1.02444
\(747\) −7.69677 + 13.3312i −0.281610 + 0.487763i
\(748\) −1.14026 + 1.97499i −0.0416921 + 0.0722128i
\(749\) 0 0
\(750\) 9.19792 15.9313i 0.335861 0.581728i
\(751\) 0.907626 + 1.57205i 0.0331197 + 0.0573651i 0.882110 0.471043i \(-0.156122\pi\)
−0.848990 + 0.528408i \(0.822789\pi\)
\(752\) −1.05231 1.82265i −0.0383737 0.0664652i
\(753\) 14.7839 0.538754
\(754\) 30.0734 22.8891i 1.09521 0.833573i
\(755\) 9.31088 0.338858
\(756\) 0 0
\(757\) −26.7814 46.3867i −0.973385 1.68595i −0.685165 0.728388i \(-0.740270\pi\)
−0.288220 0.957564i \(-0.593063\pi\)
\(758\) −3.68864 + 6.38892i −0.133978 + 0.232056i
\(759\) −5.73602 −0.208204
\(760\) −1.27332 + 2.20545i −0.0461881 + 0.0800001i
\(761\) −1.84083 + 3.18841i −0.0667300 + 0.115580i −0.897460 0.441096i \(-0.854590\pi\)
0.830730 + 0.556675i \(0.187923\pi\)
\(762\) −29.1121 −1.05462
\(763\) 0 0
\(764\) −2.77711 4.81010i −0.100472 0.174023i
\(765\) −2.14886 3.72193i −0.0776922 0.134567i
\(766\) −34.7048 −1.25394
\(767\) 34.0721 25.9325i 1.23027 0.936369i
\(768\) −15.5895 −0.562538
\(769\) −2.61897 4.53619i −0.0944424 0.163579i 0.814933 0.579555i \(-0.196773\pi\)
−0.909376 + 0.415976i \(0.863440\pi\)
\(770\) 0 0
\(771\) 22.4902 38.9541i 0.809963 1.40290i
\(772\) 7.08004 0.254816
\(773\) 20.3069 35.1726i 0.730388 1.26507i −0.226329 0.974051i \(-0.572672\pi\)
0.956717 0.291019i \(-0.0939942\pi\)
\(774\) −13.3672 + 23.1527i −0.480474 + 0.832205i
\(775\) 28.3177 1.01720
\(776\) 1.24944 2.16409i 0.0448522 0.0776862i