Properties

Label 637.2.e.i.79.1
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(79,637)]
 
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([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not 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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.2696112.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(1.17146 - 2.02903i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.i.508.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.17146 + 2.02903i) q^{2} +(-0.573183 - 0.992782i) q^{3} +(-1.74464 - 3.02181i) q^{4} +(-0.671462 + 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 - 1.45999i) q^{9} +O(q^{10})\) \(q+(-1.17146 + 2.02903i) q^{2} +(-0.573183 - 0.992782i) q^{3} +(-1.74464 - 3.02181i) q^{4} +(-0.671462 + 1.16301i) q^{5} +2.68585 q^{6} +3.48929 q^{8} +(0.842923 - 1.45999i) q^{9} +(-1.57318 - 2.72483i) q^{10} +(-0.573183 - 0.992782i) q^{11} +(-2.00000 + 3.46410i) q^{12} -1.00000 q^{13} +1.53948 q^{15} +(-0.598279 + 1.03625i) q^{16} +(2.91611 + 5.05084i) q^{17} +(1.97490 + 3.42063i) q^{18} +(-1.67146 + 2.89506i) q^{19} +4.68585 q^{20} +2.68585 q^{22} +(1.58757 - 2.74975i) q^{23} +(-2.00000 - 3.46410i) q^{24} +(1.59828 + 2.76830i) q^{25} +(1.17146 - 2.02903i) q^{26} -5.37169 q^{27} +10.4893 q^{29} +(-1.80344 + 3.12365i) q^{30} +(0.817827 + 1.41652i) q^{31} +(2.08757 + 3.61577i) q^{32} +(-0.657077 + 1.13809i) q^{33} -13.6644 q^{34} -5.88240 q^{36} +(-4.25903 + 7.37685i) q^{37} +(-3.91611 - 6.78289i) q^{38} +(0.573183 + 0.992782i) q^{39} +(-2.34292 + 4.05806i) q^{40} +0.292731 q^{41} -8.15371 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.13198 + 1.96065i) q^{45} +(3.71955 + 6.44245i) q^{46} +(-5.30712 + 9.19219i) q^{47} +1.37169 q^{48} -7.48929 q^{50} +(3.34292 - 5.79011i) q^{51} +(1.74464 + 3.02181i) q^{52} +(0.391010 + 0.677249i) q^{53} +(6.29273 - 10.8993i) q^{54} +1.53948 q^{55} +3.83221 q^{57} +(-12.2878 + 21.2831i) q^{58} +(6.32150 + 10.9492i) q^{59} +(-2.68585 - 4.65202i) q^{60} +(-1.00000 + 1.73205i) q^{61} -3.83221 q^{62} -12.1751 q^{64} +(0.671462 - 1.16301i) q^{65} +(-1.53948 - 2.66646i) q^{66} +(3.05019 + 5.28309i) q^{67} +(10.1751 - 17.6239i) q^{68} -3.63986 q^{69} +1.53948 q^{71} +(2.94120 - 5.09431i) q^{72} +(-7.65004 - 13.2503i) q^{73} +(-9.97858 - 17.2834i) q^{74} +(1.83221 - 3.17348i) q^{75} +11.6644 q^{76} -2.68585 q^{78} +(-0.441202 + 0.764184i) q^{79} +(-0.803442 - 1.39160i) q^{80} +(0.550192 + 0.952961i) q^{81} +(-0.342923 + 0.593960i) q^{82} +12.1292 q^{83} -7.83221 q^{85} +(9.55176 - 16.5441i) q^{86} +(-6.01228 - 10.4136i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(2.86802 - 4.96755i) q^{89} -5.30429 q^{90} -11.0790 q^{92} +(0.937529 - 1.62385i) q^{93} +(-12.4342 - 21.5366i) q^{94} +(-2.24464 - 3.88784i) q^{95} +(2.39312 - 4.14500i) q^{96} +5.34292 q^{97} -1.93260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - q^{2} - 2 q^{3} - 3 q^{4} + 2 q^{5} - 8 q^{6} + 6 q^{8} - 7 q^{9} - 8 q^{10} - 2 q^{11} - 12 q^{12} - 6 q^{13} - 12 q^{15} + q^{16} + 4 q^{17} + 15 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} + 5 q^{25} + q^{26} + 16 q^{27} + 48 q^{29} - 20 q^{30} - 4 q^{31} - 7 q^{32} - 16 q^{33} - 28 q^{34} - 2 q^{36} - 10 q^{38} + 2 q^{39} - 2 q^{40} - 4 q^{41} + 20 q^{43} - 12 q^{44} + 22 q^{45} + 18 q^{46} - 8 q^{47} - 40 q^{48} - 30 q^{50} + 8 q^{51} + 3 q^{52} - 8 q^{53} + 32 q^{54} - 12 q^{55} - 4 q^{57} - 12 q^{58} - 4 q^{59} + 8 q^{60} - 6 q^{61} + 4 q^{62} - 34 q^{64} - 2 q^{65} + 12 q^{66} + 12 q^{67} + 22 q^{68} + 12 q^{69} - 12 q^{71} + q^{72} - 10 q^{73} - 30 q^{74} - 16 q^{75} + 16 q^{76} + 8 q^{78} + 14 q^{79} - 14 q^{80} - 3 q^{81} + 10 q^{82} + 24 q^{83} - 20 q^{85} + 26 q^{86} - 26 q^{87} - 12 q^{88} + 2 q^{89} + 56 q^{90} - 24 q^{92} + 22 q^{93} - 10 q^{94} - 6 q^{95} - 4 q^{96} + 20 q^{97} + 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17146 + 2.02903i −0.828348 + 1.43474i 0.0709847 + 0.997477i \(0.477386\pi\)
−0.899333 + 0.437264i \(0.855947\pi\)
\(3\) −0.573183 0.992782i −0.330927 0.573183i 0.651767 0.758420i \(-0.274028\pi\)
−0.982694 + 0.185237i \(0.940695\pi\)
\(4\) −1.74464 3.02181i −0.872322 1.51091i
\(5\) −0.671462 + 1.16301i −0.300287 + 0.520112i −0.976201 0.216869i \(-0.930416\pi\)
0.675914 + 0.736980i \(0.263749\pi\)
\(6\) 2.68585 1.09649
\(7\) 0 0
\(8\) 3.48929 1.23365
\(9\) 0.842923 1.45999i 0.280974 0.486662i
\(10\) −1.57318 2.72483i −0.497484 0.861668i
\(11\) −0.573183 0.992782i −0.172821 0.299335i 0.766584 0.642144i \(-0.221955\pi\)
−0.939405 + 0.342809i \(0.888622\pi\)
\(12\) −2.00000 + 3.46410i −0.577350 + 1.00000i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.53948 0.397492
\(16\) −0.598279 + 1.03625i −0.149570 + 0.259062i
\(17\) 2.91611 + 5.05084i 0.707260 + 1.22501i 0.965870 + 0.259028i \(0.0834021\pi\)
−0.258610 + 0.965982i \(0.583265\pi\)
\(18\) 1.97490 + 3.42063i 0.465489 + 0.806251i
\(19\) −1.67146 + 2.89506i −0.383460 + 0.664171i −0.991554 0.129693i \(-0.958601\pi\)
0.608095 + 0.793865i \(0.291934\pi\)
\(20\) 4.68585 1.04779
\(21\) 0 0
\(22\) 2.68585 0.572624
\(23\) 1.58757 2.74975i 0.331031 0.573362i −0.651684 0.758491i \(-0.725937\pi\)
0.982714 + 0.185129i \(0.0592703\pi\)
\(24\) −2.00000 3.46410i −0.408248 0.707107i
\(25\) 1.59828 + 2.76830i 0.319656 + 0.553660i
\(26\) 1.17146 2.02903i 0.229743 0.397926i
\(27\) −5.37169 −1.03378
\(28\) 0 0
\(29\) 10.4893 1.94781 0.973906 0.226952i \(-0.0728760\pi\)
0.973906 + 0.226952i \(0.0728760\pi\)
\(30\) −1.80344 + 3.12365i −0.329262 + 0.570299i
\(31\) 0.817827 + 1.41652i 0.146886 + 0.254414i 0.930075 0.367370i \(-0.119742\pi\)
−0.783189 + 0.621784i \(0.786408\pi\)
\(32\) 2.08757 + 3.61577i 0.369033 + 0.639184i
\(33\) −0.657077 + 1.13809i −0.114382 + 0.198116i
\(34\) −13.6644 −2.34343
\(35\) 0 0
\(36\) −5.88240 −0.980401
\(37\) −4.25903 + 7.37685i −0.700180 + 1.21275i 0.268223 + 0.963357i \(0.413564\pi\)
−0.968403 + 0.249391i \(0.919770\pi\)
\(38\) −3.91611 6.78289i −0.635276 1.10033i
\(39\) 0.573183 + 0.992782i 0.0917827 + 0.158972i
\(40\) −2.34292 + 4.05806i −0.370449 + 0.641636i
\(41\) 0.292731 0.0457169 0.0228584 0.999739i \(-0.492723\pi\)
0.0228584 + 0.999739i \(0.492723\pi\)
\(42\) 0 0
\(43\) −8.15371 −1.24343 −0.621715 0.783244i \(-0.713564\pi\)
−0.621715 + 0.783244i \(0.713564\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) 1.13198 + 1.96065i 0.168746 + 0.292276i
\(46\) 3.71955 + 6.44245i 0.548417 + 0.949887i
\(47\) −5.30712 + 9.19219i −0.774122 + 1.34082i 0.161164 + 0.986928i \(0.448475\pi\)
−0.935286 + 0.353892i \(0.884858\pi\)
\(48\) 1.37169 0.197987
\(49\) 0 0
\(50\) −7.48929 −1.05915
\(51\) 3.34292 5.79011i 0.468103 0.810778i
\(52\) 1.74464 + 3.02181i 0.241939 + 0.419050i
\(53\) 0.391010 + 0.677249i 0.0537093 + 0.0930273i 0.891630 0.452765i \(-0.149562\pi\)
−0.837921 + 0.545792i \(0.816229\pi\)
\(54\) 6.29273 10.8993i 0.856332 1.48321i
\(55\) 1.53948 0.207584
\(56\) 0 0
\(57\) 3.83221 0.507589
\(58\) −12.2878 + 21.2831i −1.61347 + 2.79461i
\(59\) 6.32150 + 10.9492i 0.822989 + 1.42546i 0.903446 + 0.428701i \(0.141029\pi\)
−0.0804572 + 0.996758i \(0.525638\pi\)
\(60\) −2.68585 4.65202i −0.346741 0.600573i
\(61\) −1.00000 + 1.73205i −0.128037 + 0.221766i −0.922916 0.385002i \(-0.874201\pi\)
0.794879 + 0.606768i \(0.207534\pi\)
\(62\) −3.83221 −0.486691
\(63\) 0 0
\(64\) −12.1751 −1.52189
\(65\) 0.671462 1.16301i 0.0832846 0.144253i
\(66\) −1.53948 2.66646i −0.189497 0.328218i
\(67\) 3.05019 + 5.28309i 0.372640 + 0.645432i 0.989971 0.141272i \(-0.0451192\pi\)
−0.617331 + 0.786704i \(0.711786\pi\)
\(68\) 10.1751 17.6239i 1.23392 2.13721i
\(69\) −3.63986 −0.438188
\(70\) 0 0
\(71\) 1.53948 0.182703 0.0913514 0.995819i \(-0.470881\pi\)
0.0913514 + 0.995819i \(0.470881\pi\)
\(72\) 2.94120 5.09431i 0.346624 0.600370i
\(73\) −7.65004 13.2503i −0.895369 1.55083i −0.833347 0.552750i \(-0.813578\pi\)
−0.0620224 0.998075i \(-0.519755\pi\)
\(74\) −9.97858 17.2834i −1.15999 2.00915i
\(75\) 1.83221 3.17348i 0.211566 0.366442i
\(76\) 11.6644 1.33800
\(77\) 0 0
\(78\) −2.68585 −0.304112
\(79\) −0.441202 + 0.764184i −0.0496391 + 0.0859774i −0.889777 0.456395i \(-0.849140\pi\)
0.840138 + 0.542372i \(0.182474\pi\)
\(80\) −0.803442 1.39160i −0.0898276 0.155586i
\(81\) 0.550192 + 0.952961i 0.0611325 + 0.105885i
\(82\) −0.342923 + 0.593960i −0.0378695 + 0.0655919i
\(83\) 12.1292 1.33135 0.665674 0.746243i \(-0.268144\pi\)
0.665674 + 0.746243i \(0.268144\pi\)
\(84\) 0 0
\(85\) −7.83221 −0.849523
\(86\) 9.55176 16.5441i 1.02999 1.78400i
\(87\) −6.01228 10.4136i −0.644584 1.11645i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) 2.86802 4.96755i 0.304009 0.526560i −0.673031 0.739614i \(-0.735008\pi\)
0.977040 + 0.213055i \(0.0683412\pi\)
\(90\) −5.30429 −0.559121
\(91\) 0 0
\(92\) −11.0790 −1.15506
\(93\) 0.937529 1.62385i 0.0972172 0.168385i
\(94\) −12.4342 21.5366i −1.28249 2.22133i
\(95\) −2.24464 3.88784i −0.230296 0.398884i
\(96\) 2.39312 4.14500i 0.244246 0.423047i
\(97\) 5.34292 0.542492 0.271246 0.962510i \(-0.412564\pi\)
0.271246 + 0.962510i \(0.412564\pi\)
\(98\) 0 0
\(99\) −1.93260 −0.194233
\(100\) 5.57686 9.65940i 0.557686 0.965940i
\(101\) 5.57318 + 9.65304i 0.554552 + 0.960513i 0.997938 + 0.0641821i \(0.0204438\pi\)
−0.443386 + 0.896331i \(0.646223\pi\)
\(102\) 7.83221 + 13.5658i 0.775505 + 1.34321i
\(103\) −1.70727 + 2.95708i −0.168222 + 0.291369i −0.937795 0.347190i \(-0.887136\pi\)
0.769573 + 0.638559i \(0.220469\pi\)
\(104\) −3.48929 −0.342153
\(105\) 0 0
\(106\) −1.83221 −0.177960
\(107\) −2.48929 + 4.31157i −0.240649 + 0.416816i −0.960899 0.276898i \(-0.910693\pi\)
0.720251 + 0.693714i \(0.244027\pi\)
\(108\) 9.37169 + 16.2322i 0.901792 + 1.56195i
\(109\) 6.74832 + 11.6884i 0.646372 + 1.11955i 0.983983 + 0.178263i \(0.0570477\pi\)
−0.337611 + 0.941286i \(0.609619\pi\)
\(110\) −1.80344 + 3.12365i −0.171951 + 0.297829i
\(111\) 9.76481 0.926835
\(112\) 0 0
\(113\) 16.4464 1.54715 0.773576 0.633704i \(-0.218466\pi\)
0.773576 + 0.633704i \(0.218466\pi\)
\(114\) −4.48929 + 7.77568i −0.420460 + 0.728259i
\(115\) 2.13198 + 3.69270i 0.198808 + 0.344346i
\(116\) −18.3001 31.6967i −1.69912 2.94296i
\(117\) −0.842923 + 1.45999i −0.0779283 + 0.134976i
\(118\) −29.6216 −2.72689
\(119\) 0 0
\(120\) 5.37169 0.490366
\(121\) 4.84292 8.38819i 0.440266 0.762563i
\(122\) −2.34292 4.05806i −0.212118 0.367400i
\(123\) −0.167788 0.290618i −0.0151290 0.0262041i
\(124\) 2.85363 4.94264i 0.256264 0.443862i
\(125\) −11.0073 −0.984527
\(126\) 0 0
\(127\) 12.0575 1.06993 0.534967 0.844873i \(-0.320324\pi\)
0.534967 + 0.844873i \(0.320324\pi\)
\(128\) 10.0876 17.4722i 0.891623 1.54434i
\(129\) 4.67357 + 8.09486i 0.411485 + 0.712712i
\(130\) 1.57318 + 2.72483i 0.137977 + 0.238984i
\(131\) −1.83221 + 3.17348i −0.160081 + 0.277269i −0.934898 0.354918i \(-0.884509\pi\)
0.774816 + 0.632186i \(0.217842\pi\)
\(132\) 4.58546 0.399113
\(133\) 0 0
\(134\) −14.2927 −1.23470
\(135\) 3.60688 6.24731i 0.310431 0.537683i
\(136\) 10.1751 + 17.6239i 0.872511 + 1.51123i
\(137\) 6.55176 + 11.3480i 0.559755 + 0.969523i 0.997517 + 0.0704325i \(0.0224379\pi\)
−0.437762 + 0.899091i \(0.644229\pi\)
\(138\) 4.26396 7.38540i 0.362973 0.628687i
\(139\) −7.49663 −0.635856 −0.317928 0.948115i \(-0.602987\pi\)
−0.317928 + 0.948115i \(0.602987\pi\)
\(140\) 0 0
\(141\) 12.1678 1.02471
\(142\) −1.80344 + 3.12365i −0.151342 + 0.262131i
\(143\) 0.573183 + 0.992782i 0.0479319 + 0.0830206i
\(144\) 1.00861 + 1.74696i 0.0840505 + 0.145580i
\(145\) −7.04315 + 12.1991i −0.584902 + 1.01308i
\(146\) 35.8469 2.96671
\(147\) 0 0
\(148\) 29.7220 2.44313
\(149\) −1.08389 + 1.87736i −0.0887961 + 0.153799i −0.907002 0.421125i \(-0.861635\pi\)
0.818206 + 0.574925i \(0.194969\pi\)
\(150\) 4.29273 + 7.43523i 0.350500 + 0.607084i
\(151\) −7.45559 12.9135i −0.606727 1.05088i −0.991776 0.127986i \(-0.959149\pi\)
0.385049 0.922896i \(-0.374185\pi\)
\(152\) −5.83221 + 10.1017i −0.473055 + 0.819355i
\(153\) 9.83221 0.794887
\(154\) 0 0
\(155\) −2.19656 −0.176432
\(156\) 2.00000 3.46410i 0.160128 0.277350i
\(157\) 11.4342 + 19.8046i 0.912546 + 1.58058i 0.810456 + 0.585800i \(0.199220\pi\)
0.102090 + 0.994775i \(0.467447\pi\)
\(158\) −1.03370 1.79042i −0.0822369 0.142439i
\(159\) 0.448240 0.776375i 0.0355478 0.0615705i
\(160\) −5.60688 −0.443263
\(161\) 0 0
\(162\) −2.57812 −0.202556
\(163\) −3.53948 + 6.13056i −0.277234 + 0.480183i −0.970696 0.240310i \(-0.922751\pi\)
0.693463 + 0.720493i \(0.256084\pi\)
\(164\) −0.510711 0.884578i −0.0398799 0.0690739i
\(165\) −0.882404 1.52837i −0.0686950 0.118983i
\(166\) −14.2088 + 24.6104i −1.10282 + 1.91014i
\(167\) −2.61423 −0.202295 −0.101148 0.994871i \(-0.532251\pi\)
−0.101148 + 0.994871i \(0.532251\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 9.17513 15.8918i 0.703701 1.21885i
\(171\) 2.81783 + 4.88062i 0.215485 + 0.373230i
\(172\) 14.2253 + 24.6390i 1.08467 + 1.87871i
\(173\) 5.50157 9.52899i 0.418276 0.724476i −0.577490 0.816398i \(-0.695968\pi\)
0.995766 + 0.0919219i \(0.0293010\pi\)
\(174\) 28.1726 2.13576
\(175\) 0 0
\(176\) 1.37169 0.103395
\(177\) 7.24675 12.5517i 0.544699 0.943446i
\(178\) 6.71955 + 11.6386i 0.503651 + 0.872350i
\(179\) −11.9807 20.7512i −0.895478 1.55101i −0.833212 0.552954i \(-0.813500\pi\)
−0.0622667 0.998060i \(-0.519833\pi\)
\(180\) 3.94981 6.84127i 0.294401 0.509918i
\(181\) −6.56090 −0.487668 −0.243834 0.969817i \(-0.578405\pi\)
−0.243834 + 0.969817i \(0.578405\pi\)
\(182\) 0 0
\(183\) 2.29273 0.169484
\(184\) 5.53948 9.59466i 0.408376 0.707328i
\(185\) −5.71955 9.90655i −0.420510 0.728344i
\(186\) 2.19656 + 3.80455i 0.161059 + 0.278963i
\(187\) 3.34292 5.79011i 0.244459 0.423415i
\(188\) 37.0361 2.70114
\(189\) 0 0
\(190\) 10.5181 0.763060
\(191\) 2.19656 3.80455i 0.158937 0.275288i −0.775548 0.631288i \(-0.782527\pi\)
0.934486 + 0.356001i \(0.115860\pi\)
\(192\) 6.97858 + 12.0873i 0.503635 + 0.872322i
\(193\) 4.14637 + 7.18172i 0.298462 + 0.516951i 0.975784 0.218735i \(-0.0701931\pi\)
−0.677322 + 0.735686i \(0.736860\pi\)
\(194\) −6.25903 + 10.8410i −0.449372 + 0.778335i
\(195\) −1.53948 −0.110245
\(196\) 0 0
\(197\) −3.17092 −0.225919 −0.112959 0.993600i \(-0.536033\pi\)
−0.112959 + 0.993600i \(0.536033\pi\)
\(198\) 2.26396 3.92130i 0.160893 0.278674i
\(199\) −6.79851 11.7754i −0.481934 0.834733i 0.517851 0.855471i \(-0.326732\pi\)
−0.999785 + 0.0207372i \(0.993399\pi\)
\(200\) 5.57686 + 9.65940i 0.394343 + 0.683023i
\(201\) 3.49663 6.05635i 0.246634 0.427182i
\(202\) −26.1151 −1.83745
\(203\) 0 0
\(204\) −23.3288 −1.63335
\(205\) −0.196558 + 0.340448i −0.0137282 + 0.0237779i
\(206\) −4.00000 6.92820i −0.278693 0.482711i
\(207\) −2.67639 4.63565i −0.186022 0.322200i
\(208\) 0.598279 1.03625i 0.0414832 0.0718510i
\(209\) 3.83221 0.265080
\(210\) 0 0
\(211\) 9.27552 0.638553 0.319277 0.947662i \(-0.396560\pi\)
0.319277 + 0.947662i \(0.396560\pi\)
\(212\) 1.36435 2.36312i 0.0937037 0.162300i
\(213\) −0.882404 1.52837i −0.0604613 0.104722i
\(214\) −5.83221 10.1017i −0.398682 0.690537i
\(215\) 5.47490 9.48281i 0.373385 0.646722i
\(216\) −18.7434 −1.27533
\(217\) 0 0
\(218\) −31.6216 −2.14168
\(219\) −8.76974 + 15.1896i −0.592604 + 1.02642i
\(220\) −2.68585 4.65202i −0.181080 0.313639i
\(221\) −2.91611 5.05084i −0.196159 0.339756i
\(222\) −11.4391 + 19.8131i −0.767742 + 1.32977i
\(223\) 19.5928 1.31203 0.656016 0.754747i \(-0.272240\pi\)
0.656016 + 0.754747i \(0.272240\pi\)
\(224\) 0 0
\(225\) 5.38890 0.359260
\(226\) −19.2664 + 33.3703i −1.28158 + 2.21976i
\(227\) −9.83221 17.0299i −0.652587 1.13031i −0.982493 0.186300i \(-0.940350\pi\)
0.329906 0.944014i \(-0.392983\pi\)
\(228\) −6.68585 11.5802i −0.442781 0.766919i
\(229\) 3.88240 6.72452i 0.256556 0.444369i −0.708761 0.705449i \(-0.750745\pi\)
0.965317 + 0.261080i \(0.0840787\pi\)
\(230\) −9.99013 −0.658730
\(231\) 0 0
\(232\) 36.6002 2.40292
\(233\) −6.09828 + 10.5625i −0.399512 + 0.691974i −0.993666 0.112377i \(-0.964154\pi\)
0.594154 + 0.804351i \(0.297487\pi\)
\(234\) −1.97490 3.42063i −0.129104 0.223614i
\(235\) −7.12705 12.3444i −0.464917 0.805260i
\(236\) 22.0575 38.2048i 1.43582 2.48692i
\(237\) 1.01156 0.0657077
\(238\) 0 0
\(239\) −10.2927 −0.665781 −0.332891 0.942965i \(-0.608024\pi\)
−0.332891 + 0.942965i \(0.608024\pi\)
\(240\) −0.921039 + 1.59529i −0.0594528 + 0.102975i
\(241\) −2.01438 3.48902i −0.129758 0.224747i 0.793825 0.608147i \(-0.208087\pi\)
−0.923583 + 0.383399i \(0.874753\pi\)
\(242\) 11.3466 + 19.6529i 0.729387 + 1.26334i
\(243\) −7.42682 + 12.8636i −0.476431 + 0.825202i
\(244\) 6.97858 0.446758
\(245\) 0 0
\(246\) 0.786230 0.0501282
\(247\) 1.67146 2.89506i 0.106353 0.184208i
\(248\) 2.85363 + 4.94264i 0.181206 + 0.313858i
\(249\) −6.95222 12.0416i −0.440579 0.763105i
\(250\) 12.8947 22.3342i 0.815531 1.41254i
\(251\) −2.91117 −0.183752 −0.0918758 0.995770i \(-0.529286\pi\)
−0.0918758 + 0.995770i \(0.529286\pi\)
\(252\) 0 0
\(253\) −3.63986 −0.228836
\(254\) −14.1249 + 24.4651i −0.886278 + 1.53508i
\(255\) 4.48929 + 7.77568i 0.281130 + 0.486932i
\(256\) 11.4593 + 19.8480i 0.716204 + 1.24050i
\(257\) −9.79851 + 16.9715i −0.611214 + 1.05865i 0.379822 + 0.925060i \(0.375985\pi\)
−0.991036 + 0.133594i \(0.957348\pi\)
\(258\) −21.8996 −1.36341
\(259\) 0 0
\(260\) −4.68585 −0.290604
\(261\) 8.84166 15.3142i 0.547285 0.947926i
\(262\) −4.29273 7.43523i −0.265206 0.459350i
\(263\) −3.78412 6.55430i −0.233339 0.404155i 0.725450 0.688275i \(-0.241632\pi\)
−0.958789 + 0.284120i \(0.908299\pi\)
\(264\) −2.29273 + 3.97113i −0.141108 + 0.244406i
\(265\) −1.05019 −0.0645128
\(266\) 0 0
\(267\) −6.57560 −0.402420
\(268\) 10.6430 18.4342i 0.650125 1.12605i
\(269\) −4.73604 8.20306i −0.288761 0.500149i 0.684753 0.728775i \(-0.259910\pi\)
−0.973514 + 0.228626i \(0.926577\pi\)
\(270\) 8.45065 + 14.6370i 0.514290 + 0.890777i
\(271\) 14.6858 25.4366i 0.892102 1.54517i 0.0547504 0.998500i \(-0.482564\pi\)
0.837351 0.546665i \(-0.184103\pi\)
\(272\) −6.97858 −0.423138
\(273\) 0 0
\(274\) −30.7005 −1.85469
\(275\) 1.83221 3.17348i 0.110487 0.191368i
\(276\) 6.35027 + 10.9990i 0.382241 + 0.662061i
\(277\) 0.951913 + 1.64876i 0.0571949 + 0.0990645i 0.893205 0.449649i \(-0.148451\pi\)
−0.836010 + 0.548714i \(0.815118\pi\)
\(278\) 8.78202 15.2109i 0.526711 0.912289i
\(279\) 2.75746 0.165085
\(280\) 0 0
\(281\) −20.5756 −1.22744 −0.613719 0.789525i \(-0.710327\pi\)
−0.613719 + 0.789525i \(0.710327\pi\)
\(282\) −14.2541 + 24.6888i −0.848819 + 1.47020i
\(283\) −13.4966 23.3769i −0.802292 1.38961i −0.918104 0.396339i \(-0.870281\pi\)
0.115813 0.993271i \(-0.463053\pi\)
\(284\) −2.68585 4.65202i −0.159376 0.276047i
\(285\) −2.57318 + 4.45688i −0.152422 + 0.264003i
\(286\) −2.68585 −0.158817
\(287\) 0 0
\(288\) 7.03863 0.414756
\(289\) −8.50735 + 14.7352i −0.500432 + 0.866774i
\(290\) −16.5016 28.5816i −0.969005 1.67837i
\(291\) −3.06247 5.30436i −0.179525 0.310947i
\(292\) −26.6932 + 46.2340i −1.56210 + 2.70564i
\(293\) 14.9070 0.870874 0.435437 0.900219i \(-0.356594\pi\)
0.435437 + 0.900219i \(0.356594\pi\)
\(294\) 0 0
\(295\) −16.9786 −0.988531
\(296\) −14.8610 + 25.7400i −0.863777 + 1.49611i
\(297\) 3.07896 + 5.33292i 0.178659 + 0.309447i
\(298\) −2.53948 4.39851i −0.147108 0.254799i
\(299\) −1.58757 + 2.74975i −0.0918114 + 0.159022i
\(300\) −12.7862 −0.738213
\(301\) 0 0
\(302\) 34.9357 2.01033
\(303\) 6.38890 11.0659i 0.367033 0.635720i
\(304\) −2.00000 3.46410i −0.114708 0.198680i
\(305\) −1.34292 2.32601i −0.0768956 0.133187i
\(306\) −11.5181 + 19.9499i −0.658444 + 1.14046i
\(307\) −26.0288 −1.48554 −0.742770 0.669546i \(-0.766488\pi\)
−0.742770 + 0.669546i \(0.766488\pi\)
\(308\) 0 0
\(309\) 3.91431 0.222677
\(310\) 2.57318 4.45688i 0.146147 0.253134i
\(311\) 9.74832 + 16.8846i 0.552776 + 0.957437i 0.998073 + 0.0620536i \(0.0197650\pi\)
−0.445296 + 0.895383i \(0.646902\pi\)
\(312\) 2.00000 + 3.46410i 0.113228 + 0.196116i
\(313\) −1.74097 + 3.01545i −0.0984055 + 0.170443i −0.911025 0.412352i \(-0.864708\pi\)
0.812619 + 0.582795i \(0.198041\pi\)
\(314\) −53.5787 −3.02362
\(315\) 0 0
\(316\) 3.07896 0.173205
\(317\) −2.51071 + 4.34868i −0.141016 + 0.244246i −0.927879 0.372881i \(-0.878370\pi\)
0.786864 + 0.617127i \(0.211703\pi\)
\(318\) 1.05019 + 1.81899i 0.0588918 + 0.102004i
\(319\) −6.01228 10.4136i −0.336623 0.583048i
\(320\) 8.17513 14.1597i 0.457004 0.791554i
\(321\) 5.70727 0.318549
\(322\) 0 0
\(323\) −19.4966 −1.08482
\(324\) 1.91978 3.32515i 0.106654 0.184731i
\(325\) −1.59828 2.76830i −0.0886566 0.153558i
\(326\) −8.29273 14.3634i −0.459292 0.795517i
\(327\) 7.73604 13.3992i 0.427804 0.740978i
\(328\) 1.02142 0.0563986
\(329\) 0 0
\(330\) 4.13481 0.227614
\(331\) 3.07475 5.32562i 0.169004 0.292723i −0.769066 0.639169i \(-0.779278\pi\)
0.938070 + 0.346446i \(0.112612\pi\)
\(332\) −21.1611 36.6520i −1.16136 2.01154i
\(333\) 7.18007 + 12.4362i 0.393465 + 0.681502i
\(334\) 3.06247 5.30436i 0.167571 0.290241i
\(335\) −8.19235 −0.447596
\(336\) 0 0
\(337\) −25.6258 −1.39593 −0.697963 0.716134i \(-0.745910\pi\)
−0.697963 + 0.716134i \(0.745910\pi\)
\(338\) −1.17146 + 2.02903i −0.0637191 + 0.110365i
\(339\) −9.42682 16.3277i −0.511994 0.886800i
\(340\) 13.6644 + 23.6675i 0.741057 + 1.28355i
\(341\) 0.937529 1.62385i 0.0507700 0.0879363i
\(342\) −13.2039 −0.713985
\(343\) 0 0
\(344\) −28.4507 −1.53396
\(345\) 2.44403 4.23318i 0.131582 0.227907i
\(346\) 12.8898 + 22.3257i 0.692957 + 1.20024i
\(347\) 8.35027 + 14.4631i 0.448266 + 0.776419i 0.998273 0.0587404i \(-0.0187084\pi\)
−0.550007 + 0.835160i \(0.685375\pi\)
\(348\) −20.9786 + 36.3360i −1.12457 + 1.94781i
\(349\) 23.5500 1.26060 0.630300 0.776351i \(-0.282932\pi\)
0.630300 + 0.776351i \(0.282932\pi\)
\(350\) 0 0
\(351\) 5.37169 0.286720
\(352\) 2.39312 4.14500i 0.127553 0.220929i
\(353\) −3.82487 6.62486i −0.203577 0.352606i 0.746101 0.665832i \(-0.231923\pi\)
−0.949678 + 0.313227i \(0.898590\pi\)
\(354\) 16.9786 + 29.4078i 0.902401 + 1.56300i
\(355\) −1.03370 + 1.79042i −0.0548632 + 0.0950259i
\(356\) −20.0147 −1.06078
\(357\) 0 0
\(358\) 56.1396 2.96707
\(359\) −9.18741 + 15.9131i −0.484893 + 0.839860i −0.999849 0.0173569i \(-0.994475\pi\)
0.514956 + 0.857216i \(0.327808\pi\)
\(360\) 3.94981 + 6.84127i 0.208173 + 0.360566i
\(361\) 3.91243 + 6.77653i 0.205918 + 0.356660i
\(362\) 7.68585 13.3123i 0.403959 0.699678i
\(363\) −11.1035 −0.582784
\(364\) 0 0
\(365\) 20.5468 1.07547
\(366\) −2.68585 + 4.65202i −0.140391 + 0.243165i
\(367\) 2.66936 + 4.62346i 0.139339 + 0.241343i 0.927247 0.374451i \(-0.122169\pi\)
−0.787907 + 0.615794i \(0.788835\pi\)
\(368\) 1.89962 + 3.29023i 0.0990243 + 0.171515i
\(369\) 0.246750 0.427383i 0.0128453 0.0222487i
\(370\) 26.8009 1.39331
\(371\) 0 0
\(372\) −6.54262 −0.339219
\(373\) −10.7606 + 18.6379i −0.557163 + 0.965034i 0.440569 + 0.897719i \(0.354777\pi\)
−0.997732 + 0.0673152i \(0.978557\pi\)
\(374\) 7.83221 + 13.5658i 0.404994 + 0.701470i
\(375\) 6.30922 + 10.9279i 0.325807 + 0.564314i
\(376\) −18.5181 + 32.0742i −0.954996 + 1.65410i
\(377\) −10.4893 −0.540226
\(378\) 0 0
\(379\) 4.61002 0.236801 0.118400 0.992966i \(-0.462223\pi\)
0.118400 + 0.992966i \(0.462223\pi\)
\(380\) −7.83221 + 13.5658i −0.401784 + 0.695910i
\(381\) −6.91117 11.9705i −0.354070 0.613267i
\(382\) 5.14637 + 8.91377i 0.263311 + 0.456068i
\(383\) −4.16779 + 7.21882i −0.212964 + 0.368865i −0.952641 0.304098i \(-0.901645\pi\)
0.739677 + 0.672962i \(0.234978\pi\)
\(384\) −23.1281 −1.18025
\(385\) 0 0
\(386\) −19.4292 −0.988922
\(387\) −6.87295 + 11.9043i −0.349372 + 0.605130i
\(388\) −9.32150 16.1453i −0.473227 0.819654i
\(389\) 3.22112 + 5.57914i 0.163317 + 0.282873i 0.936056 0.351850i \(-0.114447\pi\)
−0.772739 + 0.634724i \(0.781114\pi\)
\(390\) 1.80344 3.12365i 0.0913209 0.158172i
\(391\) 18.5181 0.936498
\(392\) 0 0
\(393\) 4.20077 0.211901
\(394\) 3.71462 6.43390i 0.187140 0.324135i
\(395\) −0.592500 1.02624i −0.0298119 0.0516358i
\(396\) 3.37169 + 5.83994i 0.169434 + 0.293468i
\(397\) 0.700231 1.21284i 0.0351436 0.0608705i −0.847919 0.530126i \(-0.822144\pi\)
0.883062 + 0.469256i \(0.155478\pi\)
\(398\) 31.8568 1.59684
\(399\) 0 0
\(400\) −3.82487 −0.191243
\(401\) 3.48929 6.04363i 0.174247 0.301804i −0.765654 0.643253i \(-0.777584\pi\)
0.939900 + 0.341449i \(0.110918\pi\)
\(402\) 8.19235 + 14.1896i 0.408597 + 0.707711i
\(403\) −0.817827 1.41652i −0.0407389 0.0705618i
\(404\) 19.4464 33.6822i 0.967497 1.67575i
\(405\) −1.47773 −0.0734291
\(406\) 0 0
\(407\) 9.76481 0.484024
\(408\) 11.6644 20.2034i 0.577475 1.00022i
\(409\) −9.18952 15.9167i −0.454392 0.787031i 0.544261 0.838916i \(-0.316810\pi\)
−0.998653 + 0.0518854i \(0.983477\pi\)
\(410\) −0.460519 0.797643i −0.0227434 0.0393928i
\(411\) 7.51071 13.0089i 0.370476 0.641683i
\(412\) 11.9143 0.586976
\(413\) 0 0
\(414\) 12.5412 0.616365
\(415\) −8.14426 + 14.1063i −0.399786 + 0.692450i
\(416\) −2.08757 3.61577i −0.102351 0.177278i
\(417\) 4.29694 + 7.44252i 0.210422 + 0.364462i
\(418\) −4.48929 + 7.77568i −0.219578 + 0.380321i
\(419\) 30.0393 1.46751 0.733757 0.679412i \(-0.237765\pi\)
0.733757 + 0.679412i \(0.237765\pi\)
\(420\) 0 0
\(421\) −8.31729 −0.405360 −0.202680 0.979245i \(-0.564965\pi\)
−0.202680 + 0.979245i \(0.564965\pi\)
\(422\) −10.8659 + 18.8203i −0.528944 + 0.916159i
\(423\) 8.94698 + 15.4966i 0.435017 + 0.753472i
\(424\) 1.36435 + 2.36312i 0.0662585 + 0.114763i
\(425\) −9.32150 + 16.1453i −0.452159 + 0.783163i
\(426\) 4.13481 0.200332
\(427\) 0 0
\(428\) 17.3717 0.839692
\(429\) 0.657077 1.13809i 0.0317240 0.0549475i
\(430\) 12.8273 + 22.2175i 0.618586 + 1.07142i
\(431\) −4.82487 8.35691i −0.232406 0.402538i 0.726110 0.687579i \(-0.241326\pi\)
−0.958516 + 0.285040i \(0.907993\pi\)
\(432\) 3.21377 5.56641i 0.154623 0.267814i
\(433\) −26.3074 −1.26425 −0.632127 0.774865i \(-0.717818\pi\)
−0.632127 + 0.774865i \(0.717818\pi\)
\(434\) 0 0
\(435\) 16.1481 0.774240
\(436\) 23.5468 40.7843i 1.12769 1.95321i
\(437\) 5.30712 + 9.19219i 0.253874 + 0.439722i
\(438\) −20.5468 35.5881i −0.981765 1.70047i
\(439\) 16.9070 29.2837i 0.806925 1.39764i −0.108058 0.994145i \(-0.534463\pi\)
0.914984 0.403491i \(-0.132203\pi\)
\(440\) 5.37169 0.256085
\(441\) 0 0
\(442\) 13.6644 0.649950
\(443\) −13.2232 + 22.9033i −0.628254 + 1.08817i 0.359648 + 0.933088i \(0.382897\pi\)
−0.987902 + 0.155080i \(0.950436\pi\)
\(444\) −17.0361 29.5074i −0.808498 1.40036i
\(445\) 3.85153 + 6.67104i 0.182580 + 0.316238i
\(446\) −22.9522 + 39.7544i −1.08682 + 1.88243i
\(447\) 2.48508 0.117540
\(448\) 0 0
\(449\) 2.64300 0.124731 0.0623655 0.998053i \(-0.480136\pi\)
0.0623655 + 0.998053i \(0.480136\pi\)
\(450\) −6.31289 + 10.9343i −0.297593 + 0.515446i
\(451\) −0.167788 0.290618i −0.00790084 0.0136847i
\(452\) −28.6932 49.6981i −1.34961 2.33760i
\(453\) −8.54683 + 14.8035i −0.401565 + 0.695531i
\(454\) 46.0722 2.16228
\(455\) 0 0
\(456\) 13.3717 0.626187
\(457\) 16.8445 29.1755i 0.787952 1.36477i −0.139268 0.990255i \(-0.544475\pi\)
0.927220 0.374518i \(-0.122192\pi\)
\(458\) 9.09617 + 15.7550i 0.425036 + 0.736184i
\(459\) −15.6644 27.1316i −0.731153 1.26639i
\(460\) 7.43910 12.8849i 0.346850 0.600761i
\(461\) −33.0790 −1.54064 −0.770320 0.637657i \(-0.779904\pi\)
−0.770320 + 0.637657i \(0.779904\pi\)
\(462\) 0 0
\(463\) −2.51806 −0.117024 −0.0585120 0.998287i \(-0.518636\pi\)
−0.0585120 + 0.998287i \(0.518636\pi\)
\(464\) −6.27552 + 10.8695i −0.291334 + 0.504605i
\(465\) 1.25903 + 2.18070i 0.0583861 + 0.101128i
\(466\) −14.2878 24.7472i −0.661869 1.14639i
\(467\) 1.28780 2.23053i 0.0595922 0.103217i −0.834690 0.550720i \(-0.814353\pi\)
0.894282 + 0.447503i \(0.147687\pi\)
\(468\) 5.88240 0.271914
\(469\) 0 0
\(470\) 33.3963 1.54045
\(471\) 13.1077 22.7033i 0.603972 1.04611i
\(472\) 22.0575 + 38.2048i 1.01528 + 1.75852i
\(473\) 4.67357 + 8.09486i 0.214891 + 0.372202i
\(474\) −1.18500 + 2.05248i −0.0544289 + 0.0942736i
\(475\) −10.6858 −0.490300
\(476\) 0 0
\(477\) 1.31836 0.0603638
\(478\) 12.0575 20.8843i 0.551499 0.955224i
\(479\) 0.256923 + 0.445005i 0.0117391 + 0.0203328i 0.871835 0.489799i \(-0.162930\pi\)
−0.860096 + 0.510132i \(0.829597\pi\)
\(480\) 3.21377 + 5.56641i 0.146688 + 0.254071i
\(481\) 4.25903 7.37685i 0.194195 0.336356i
\(482\) 9.43910 0.429939
\(483\) 0 0
\(484\) −33.7967 −1.53621
\(485\) −3.58757 + 6.21385i −0.162903 + 0.282156i
\(486\) −17.4005 30.1385i −0.789301 1.36711i
\(487\) −18.0288 31.2267i −0.816962 1.41502i −0.907911 0.419163i \(-0.862323\pi\)
0.0909493 0.995856i \(-0.471010\pi\)
\(488\) −3.48929 + 6.04363i −0.157953 + 0.273582i
\(489\) 8.11508 0.366976
\(490\) 0 0
\(491\) −9.22846 −0.416475 −0.208237 0.978078i \(-0.566773\pi\)
−0.208237 + 0.978078i \(0.566773\pi\)
\(492\) −0.585462 + 1.01405i −0.0263947 + 0.0457169i
\(493\) 30.5879 + 52.9798i 1.37761 + 2.38609i
\(494\) 3.91611 + 6.78289i 0.176194 + 0.305177i
\(495\) 1.29766 2.24762i 0.0583257 0.101023i
\(496\) −1.95715 −0.0878788
\(497\) 0 0
\(498\) 32.5770 1.45981
\(499\) −0.501568 + 0.868741i −0.0224533 + 0.0388902i −0.877034 0.480429i \(-0.840481\pi\)
0.854580 + 0.519319i \(0.173814\pi\)
\(500\) 19.2039 + 33.2621i 0.858825 + 1.48753i
\(501\) 1.49843 + 2.59536i 0.0669450 + 0.115952i
\(502\) 3.41033 5.90686i 0.152210 0.263636i
\(503\) 30.3503 1.35325 0.676626 0.736327i \(-0.263441\pi\)
0.676626 + 0.736327i \(0.263441\pi\)
\(504\) 0 0
\(505\) −14.9687 −0.666099
\(506\) 4.26396 7.38540i 0.189556 0.328321i
\(507\) −0.573183 0.992782i −0.0254559 0.0440910i
\(508\) −21.0361 36.4356i −0.933327 1.61657i
\(509\) 5.29977 9.17947i 0.234908 0.406873i −0.724338 0.689445i \(-0.757854\pi\)
0.959246 + 0.282572i \(0.0911877\pi\)
\(510\) −21.0361 −0.931495
\(511\) 0 0
\(512\) −13.3461 −0.589818
\(513\) 8.97858 15.5514i 0.396414 0.686609i
\(514\) −22.9572 39.7630i −1.01260 1.75387i
\(515\) −2.29273 3.97113i −0.101030 0.174989i
\(516\) 16.3074 28.2453i 0.717894 1.24343i
\(517\) 12.1678 0.535139
\(518\) 0 0
\(519\) −12.6136 −0.553676
\(520\) 2.34292 4.05806i 0.102744 0.177958i
\(521\) −8.13229 14.0855i −0.356282 0.617099i 0.631054 0.775739i \(-0.282622\pi\)
−0.987337 + 0.158640i \(0.949289\pi\)
\(522\) 20.7153 + 35.8800i 0.906686 + 1.57043i
\(523\) 3.61110 6.25460i 0.157902 0.273495i −0.776210 0.630475i \(-0.782860\pi\)
0.934112 + 0.356980i \(0.116194\pi\)
\(524\) 12.7862 0.558569
\(525\) 0 0
\(526\) 17.7318 0.773144
\(527\) −4.76974 + 8.26143i −0.207773 + 0.359874i
\(528\) −0.786230 1.36179i −0.0342163 0.0592643i
\(529\) 6.45926 + 11.1878i 0.280837 + 0.486425i
\(530\) 1.23026 2.13087i 0.0534391 0.0925592i
\(531\) 21.3142 0.924955
\(532\) 0 0
\(533\) −0.292731 −0.0126796
\(534\) 7.70306 13.3421i 0.333344 0.577369i
\(535\) −3.34292 5.79011i −0.144527 0.250328i
\(536\) 10.6430 + 18.4342i 0.459708 + 0.796237i
\(537\) −13.7342 + 23.7884i −0.592676 + 1.02655i
\(538\) 22.1923 0.956780
\(539\) 0 0
\(540\) −25.1709 −1.08318
\(541\) −8.67670 + 15.0285i −0.373041 + 0.646125i −0.990032 0.140845i \(-0.955018\pi\)
0.616991 + 0.786970i \(0.288351\pi\)
\(542\) 34.4078 + 59.5961i 1.47794 + 2.55987i
\(543\) 3.76060 + 6.51354i 0.161383 + 0.279523i
\(544\) −12.1751 + 21.0880i −0.522005 + 0.904138i
\(545\) −18.1249 −0.776387
\(546\) 0 0
\(547\) −34.1109 −1.45848 −0.729238 0.684261i \(-0.760125\pi\)
−0.729238 + 0.684261i \(0.760125\pi\)
\(548\) 22.8610 39.5964i 0.976573 1.69147i
\(549\) 1.68585 + 2.91997i 0.0719502 + 0.124621i
\(550\) 4.29273 + 7.43523i 0.183043 + 0.317039i
\(551\) −17.5324 + 30.3671i −0.746907 + 1.29368i
\(552\) −12.7005 −0.540571
\(553\) 0 0
\(554\) −4.46052 −0.189509
\(555\) −6.55669 + 11.3565i −0.278316 + 0.482058i
\(556\) 13.0790 + 22.6534i 0.554672 + 0.960719i
\(557\) 6.61110 + 11.4508i 0.280121 + 0.485184i 0.971414 0.237390i \(-0.0762920\pi\)
−0.691293 + 0.722574i \(0.742959\pi\)
\(558\) −3.23026 + 5.59497i −0.136748 + 0.236854i
\(559\) 8.15371 0.344865
\(560\) 0 0
\(561\) −7.66442 −0.323592
\(562\) 24.1035 41.7485i 1.01675 1.76106i
\(563\) −20.6858 35.8289i −0.871804 1.51001i −0.860128 0.510078i \(-0.829617\pi\)
−0.0116762 0.999932i \(-0.503717\pi\)
\(564\) −21.2285 36.7688i −0.893880 1.54824i
\(565\) −11.0432 + 19.1273i −0.464589 + 0.804692i
\(566\) 63.2432 2.65831
\(567\) 0 0
\(568\) 5.37169 0.225391
\(569\) 1.34082 2.32236i 0.0562100 0.0973586i −0.836551 0.547889i \(-0.815432\pi\)
0.892761 + 0.450530i \(0.148765\pi\)
\(570\) −6.02877 10.4421i −0.252517 0.437373i
\(571\) 14.4658 + 25.0554i 0.605373 + 1.04854i 0.991992 + 0.126298i \(0.0403095\pi\)
−0.386619 + 0.922239i \(0.626357\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) −5.03612 −0.210387
\(574\) 0 0
\(575\) 10.1495 0.423263
\(576\) −10.2627 + 17.7755i −0.427613 + 0.740647i
\(577\) 18.7648 + 32.5016i 0.781189 + 1.35306i 0.931249 + 0.364382i \(0.118720\pi\)
−0.150060 + 0.988677i \(0.547947\pi\)
\(578\) −19.9321 34.5233i −0.829064 1.43598i
\(579\) 4.75325 8.23287i 0.197538 0.342146i
\(580\) 49.1512 2.04089
\(581\) 0 0
\(582\) 14.3503 0.594838
\(583\) 0.448240 0.776375i 0.0185642 0.0321542i
\(584\) −26.6932 46.2340i −1.10457 1.91318i
\(585\) −1.13198 1.96065i −0.0468016 0.0810628i
\(586\) −17.4629 + 30.2467i −0.721387 + 1.24948i
\(587\) −23.0649 −0.951990 −0.475995 0.879448i \(-0.657912\pi\)
−0.475995 + 0.879448i \(0.657912\pi\)
\(588\) 0 0
\(589\) −5.46787 −0.225299
\(590\) 19.8898 34.4501i 0.818848 1.41829i
\(591\) 1.81752 + 3.14804i 0.0747627 + 0.129493i
\(592\) −5.09617 8.82683i −0.209451 0.362781i
\(593\) −5.52510 + 9.56975i −0.226889 + 0.392982i −0.956884 0.290469i \(-0.906189\pi\)
0.729996 + 0.683452i \(0.239522\pi\)
\(594\) −14.4275 −0.591969
\(595\) 0 0
\(596\) 7.56404 0.309835
\(597\) −7.79358 + 13.4989i −0.318970 + 0.552472i
\(598\) −3.71955 6.44245i −0.152104 0.263451i
\(599\) 22.3022 + 38.6285i 0.911242 + 1.57832i 0.812311 + 0.583224i \(0.198209\pi\)
0.0989311 + 0.995094i \(0.468458\pi\)
\(600\) 6.39312 11.0732i 0.260998 0.452062i
\(601\) −47.8715 −1.95272 −0.976359 0.216156i \(-0.930648\pi\)
−0.976359 + 0.216156i \(0.930648\pi\)
\(602\) 0 0
\(603\) 10.2843 0.418809
\(604\) −26.0147 + 45.0588i −1.05852 + 1.83342i
\(605\) 6.50367 + 11.2647i 0.264412 + 0.457975i
\(606\) 14.9687 + 25.9266i 0.608062 + 1.05319i
\(607\) 22.5345 39.0310i 0.914649 1.58422i 0.107235 0.994234i \(-0.465800\pi\)
0.807414 0.589985i \(-0.200866\pi\)
\(608\) −13.9572 −0.566037
\(609\) 0 0
\(610\) 6.29273 0.254785
\(611\) 5.30712 9.19219i 0.214703 0.371876i
\(612\) −17.1537 29.7111i −0.693398 1.20100i
\(613\) 12.7606 + 22.1020i 0.515396 + 0.892691i 0.999840 + 0.0178695i \(0.00568836\pi\)
−0.484445 + 0.874822i \(0.660978\pi\)
\(614\) 30.4917 52.8132i 1.23054 2.13137i
\(615\) 0.450654 0.0181721
\(616\) 0 0
\(617\) 29.2432 1.17729 0.588643 0.808393i \(-0.299663\pi\)
0.588643 + 0.808393i \(0.299663\pi\)
\(618\) −4.58546 + 7.94225i −0.184454 + 0.319484i
\(619\) 2.39312 + 4.14500i 0.0961874 + 0.166601i 0.910104 0.414381i \(-0.136002\pi\)
−0.813916 + 0.580982i \(0.802669\pi\)
\(620\) 3.83221 + 6.63759i 0.153905 + 0.266572i
\(621\) −8.52792 + 14.7708i −0.342214 + 0.592732i
\(622\) −45.6791 −1.83157
\(623\) 0 0
\(624\) −1.37169 −0.0549116
\(625\) −0.600384 + 1.03990i −0.0240154 + 0.0415958i
\(626\) −4.07896 7.06497i −0.163028 0.282373i
\(627\) −2.19656 3.80455i −0.0877221 0.151939i
\(628\) 39.8971 69.1038i 1.59207 2.75754i
\(629\) −49.6791 −1.98084
\(630\) 0 0
\(631\) −28.3931 −1.13031 −0.565156 0.824984i \(-0.691184\pi\)
−0.565156 + 0.824984i \(0.691184\pi\)
\(632\) −1.53948 + 2.66646i −0.0612373 + 0.106066i
\(633\) −5.31657 9.20856i −0.211315 0.366008i
\(634\) −5.88240 10.1886i −0.233620 0.404642i
\(635\) −8.09617 + 14.0230i −0.321287 + 0.556485i
\(636\) −3.12808 −0.124036
\(637\) 0 0
\(638\) 28.1726 1.11536
\(639\) 1.29766 2.24762i 0.0513348 0.0889145i
\(640\) 13.5468 + 23.4638i 0.535485 + 0.927488i
\(641\) −2.98068 5.16269i −0.117730 0.203914i 0.801138 0.598480i \(-0.204228\pi\)
−0.918868 + 0.394566i \(0.870895\pi\)
\(642\) −6.68585 + 11.5802i −0.263869 + 0.457035i
\(643\) −31.1940 −1.23017 −0.615086 0.788460i \(-0.710879\pi\)
−0.615086 + 0.788460i \(0.710879\pi\)
\(644\) 0 0
\(645\) −12.5525 −0.494253
\(646\) 22.8396 39.5593i 0.898610 1.55644i
\(647\) 7.45559 + 12.9135i 0.293109 + 0.507680i 0.974543 0.224199i \(-0.0719767\pi\)
−0.681434 + 0.731880i \(0.738643\pi\)
\(648\) 1.91978 + 3.32515i 0.0754160 + 0.130624i
\(649\) 7.24675 12.5517i 0.284460 0.492699i
\(650\) 7.48929 0.293754
\(651\) 0 0
\(652\) 24.7005 0.967348
\(653\) 1.78623 3.09384i 0.0699006 0.121071i −0.828957 0.559313i \(-0.811065\pi\)
0.898857 + 0.438241i \(0.144398\pi\)
\(654\) 18.1249 + 31.3933i 0.708741 + 1.22758i
\(655\) −2.46052 4.26174i −0.0961404 0.166520i
\(656\) −0.175135 + 0.303342i −0.00683786 + 0.0118435i
\(657\) −25.7936 −1.00630
\(658\) 0 0
\(659\) −3.90383 −0.152071 −0.0760357 0.997105i \(-0.524226\pi\)
−0.0760357 + 0.997105i \(0.524226\pi\)
\(660\) −3.07896 + 5.33292i −0.119848 + 0.207584i
\(661\) 6.89679 + 11.9456i 0.268254 + 0.464630i 0.968411 0.249359i \(-0.0802200\pi\)
−0.700157 + 0.713989i \(0.746887\pi\)
\(662\) 7.20390 + 12.4775i 0.279988 + 0.484953i
\(663\) −3.34292 + 5.79011i −0.129828 + 0.224869i
\(664\) 42.3221 1.64242
\(665\) 0 0
\(666\) −33.6447 −1.30371
\(667\) 16.6525 28.8429i 0.644786 1.11680i
\(668\) 4.56090 + 7.89972i 0.176467 + 0.305649i
\(669\) −11.2303 19.4514i −0.434187 0.752034i
\(670\) 9.59702 16.6225i 0.370765 0.642184i
\(671\) 2.29273 0.0885099
\(672\) 0 0
\(673\) 5.70306 0.219837 0.109918 0.993941i \(-0.464941\pi\)
0.109918 + 0.993941i \(0.464941\pi\)
\(674\) 30.0196 51.9955i 1.15631 2.00279i
\(675\) −8.58546 14.8705i −0.330455 0.572364i
\(676\) −1.74464 3.02181i −0.0671017 0.116224i
\(677\) 17.6307 30.5373i 0.677604 1.17364i −0.298097 0.954536i \(-0.596352\pi\)
0.975701 0.219108i \(-0.0703148\pi\)
\(678\) 44.1726 1.69644
\(679\) 0 0
\(680\) −27.3288 −1.04801
\(681\) −11.2713 + 19.5225i −0.431917 + 0.748103i
\(682\) 2.19656 + 3.80455i 0.0841105 + 0.145684i
\(683\) −0.518058 0.897302i −0.0198229 0.0343343i 0.855944 0.517069i \(-0.172977\pi\)
−0.875767 + 0.482735i \(0.839644\pi\)
\(684\) 9.83221 17.0299i 0.375944 0.651154i
\(685\) −17.5970 −0.672348
\(686\) 0 0
\(687\) −8.90131 −0.339606
\(688\) 4.87819 8.44928i 0.185979 0.322126i
\(689\) −0.391010 0.677249i −0.0148963 0.0258011i
\(690\) 5.72617 + 9.91802i 0.217992 + 0.377573i
\(691\) 1.83925 3.18567i 0.0699684 0.121189i −0.828919 0.559369i \(-0.811043\pi\)
0.898887 + 0.438180i \(0.144377\pi\)
\(692\) −38.3931 −1.45949
\(693\) 0 0
\(694\) −39.1281 −1.48528
\(695\) 5.03370 8.71863i 0.190939 0.330716i
\(696\) −20.9786 36.3360i −0.795191 1.37731i
\(697\) 0.853635 + 1.47854i 0.0323337 + 0.0560036i
\(698\) −27.5879 + 47.7836i −1.04422 + 1.80864i
\(699\) 13.9817 0.528837
\(700\) 0 0
\(701\) −0.0617493 −0.00233224 −0.00116612 0.999999i \(-0.500371\pi\)
−0.00116612 + 0.999999i \(0.500371\pi\)
\(702\) −6.29273 + 10.8993i −0.237504 + 0.411369i
\(703\) −14.2376 24.6603i −0.536981 0.930079i
\(704\) 6.97858 + 12.0873i 0.263015 + 0.455555i
\(705\) −8.17020 + 14.1512i −0.307708 + 0.532965i
\(706\) 17.9227 0.674531
\(707\) 0 0
\(708\) −50.5720 −1.90061
\(709\) 21.4917 37.2247i 0.807138 1.39800i −0.107701 0.994183i \(-0.534349\pi\)
0.914838 0.403820i \(-0.132318\pi\)
\(710\) −2.42188 4.19483i −0.0908917 0.157429i
\(711\) 0.743798 + 1.28830i 0.0278946 + 0.0483149i
\(712\) 10.0073 17.3332i 0.375041 0.649590i
\(713\) 5.19342 0.194495
\(714\) 0 0
\(715\) −1.53948 −0.0575733
\(716\) −41.8041 + 72.4068i −1.56229 + 2.70597i
\(717\) 5.89962 + 10.2184i 0.220325 + 0.381614i
\(718\) −21.5254 37.2831i −0.803321 1.39139i
\(719\) 8.82728 15.2893i 0.329202 0.570195i −0.653152 0.757227i \(-0.726554\pi\)
0.982354 + 0.187033i \(0.0598870\pi\)
\(720\) −2.70896 −0.100957
\(721\) 0 0
\(722\) −18.3331 −0.682286
\(723\) −2.30922 + 3.99969i −0.0858809 + 0.148750i
\(724\) 11.4464 + 19.8258i 0.425404 + 0.736821i
\(725\) 16.7648 + 29.0375i 0.622629 + 1.07843i
\(726\) 13.0073 22.5294i 0.482748 0.836144i
\(727\) 23.8077 0.882977 0.441488 0.897267i \(-0.354451\pi\)
0.441488 + 0.897267i \(0.354451\pi\)
\(728\) 0 0
\(729\) 20.3288 0.752920
\(730\) −24.0698 + 41.6901i −0.890864 + 1.54302i
\(731\) −23.7771 41.1831i −0.879427 1.52321i
\(732\) −4.00000 6.92820i −0.147844 0.256074i
\(733\) 15.6746 27.1492i 0.578954 1.00278i −0.416645 0.909069i \(-0.636794\pi\)
0.995600 0.0937093i \(-0.0298724\pi\)
\(734\) −12.5082 −0.461686
\(735\) 0 0
\(736\) 13.2566 0.488645
\(737\) 3.49663 6.05635i 0.128800 0.223088i
\(738\) 0.578116 + 1.00133i 0.0212807 + 0.0368593i
\(739\) 12.4054 + 21.4868i 0.456340 + 0.790404i 0.998764 0.0497009i \(-0.0158268\pi\)
−0.542424 + 0.840105i \(0.682493\pi\)
\(740\) −19.9572 + 34.5668i −0.733640 + 1.27070i
\(741\) −3.83221 −0.140780
\(742\) 0 0
\(743\) 21.3717 0.784051 0.392026 0.919954i \(-0.371774\pi\)
0.392026 + 0.919954i \(0.371774\pi\)
\(744\) 3.27131 5.66607i 0.119932 0.207728i
\(745\) −1.45559 2.52115i −0.0533286 0.0923678i
\(746\) −25.2113 43.6672i −0.923049 1.59877i
\(747\) 10.2239 17.7084i 0.374075 0.647916i
\(748\) −23.3288 −0.852987
\(749\) 0 0
\(750\) −29.5640 −1.07953
\(751\) −9.61213 + 16.6487i −0.350751 + 0.607519i −0.986381 0.164475i \(-0.947407\pi\)
0.635630 + 0.771994i \(0.280740\pi\)
\(752\) −6.35027 10.9990i −0.231571 0.401092i
\(753\) 1.66863 + 2.89016i 0.0608084 + 0.105323i
\(754\) 12.2878 21.2831i 0.447495 0.775084i
\(755\) 20.0246 0.728768
\(756\) 0 0
\(757\) −19.8610 −0.721860 −0.360930 0.932593i \(-0.617541\pi\)
−0.360930 + 0.932593i \(0.617541\pi\)
\(758\) −5.40046 + 9.35387i −0.196154 + 0.339748i
\(759\) 2.08631 + 3.61359i 0.0757282 + 0.131165i
\(760\) −7.83221 13.5658i −0.284104 0.492083i
\(761\) 3.06037 5.30071i 0.110938 0.192151i −0.805211 0.592989i \(-0.797948\pi\)
0.916149 + 0.400838i \(0.131281\pi\)
\(762\) 32.3847 1.17317
\(763\) 0 0
\(764\) −15.3288 −0.554578
\(765\) −6.60195 + 11.4349i −0.238694 + 0.413430i
\(766\) −9.76481 16.9131i −0.352817 0.611097i
\(767\) −6.32150 10.9492i −0.228256 0.395351i
\(768\) 13.1365 22.7531i 0.474023 0.821031i
\(769\) −3.82800 −0.138041 −0.0690206 0.997615i \(-0.521987\pi\)
−0.0690206 + 0.997615i \(0.521987\pi\)
\(770\) 0 0
\(771\) 22.4653 0.809070
\(772\) 14.4679 25.0591i 0.520710 0.901896i
\(773\) −3.26817 5.66064i −0.117548 0.203599i 0.801247 0.598333i \(-0.204170\pi\)
−0.918795 + 0.394734i \(0.870837\pi\)
\(774\) −16.1028 27.8909i −0.578803 1.00252i
\(775\) −2.61423 + 4.52798i −0.0939060 + 0.162650i
\(776\) 18.6430