Properties

Label 225.2.e.c.76.1
Level $225$
Weight $2$
Character 225.76
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(76,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, 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("225.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.e (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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.1223810289.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 8x^{6} - 2x^{5} + 23x^{4} - 8x^{3} + 37x^{2} + 15x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 76.1
Root \(1.31686 + 2.28087i\) of defining polynomial
Character \(\chi\) \(=\) 225.76
Dual form 225.2.e.c.151.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31686 - 2.28087i) q^{2} +(-1.71558 + 0.238330i) q^{3} +(-2.46825 + 4.27513i) q^{4} +(2.80278 + 3.59916i) q^{6} +(0.898714 + 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 - 0.817746i) q^{9} +O(q^{10})\) \(q+(-1.31686 - 2.28087i) q^{2} +(-1.71558 + 0.238330i) q^{3} +(-2.46825 + 4.27513i) q^{4} +(2.80278 + 3.59916i) q^{6} +(0.898714 + 1.55662i) q^{7} +7.73393 q^{8} +(2.88640 - 0.817746i) q^{9} +(-0.904062 - 1.56588i) q^{11} +(3.21558 - 7.92257i) q^{12} +(-0.985914 + 1.70765i) q^{13} +(2.36696 - 4.09970i) q^{14} +(-5.24801 - 9.08982i) q^{16} +4.80812 q^{17} +(-5.66616 - 5.50664i) q^{18} +2.96467 q^{19} +(-1.91280 - 2.45630i) q^{21} +(-2.38105 + 4.12410i) q^{22} +(0.866963 - 1.50162i) q^{23} +(-13.2681 + 1.84323i) q^{24} +5.19325 q^{26} +(-4.75694 + 2.09082i) q^{27} -8.87300 q^{28} +(3.68382 + 6.38057i) q^{29} +(1.31151 - 2.27161i) q^{31} +(-6.08789 + 10.5445i) q^{32} +(1.92418 + 2.47092i) q^{33} +(-6.33163 - 10.9667i) q^{34} +(-3.62838 + 14.3581i) q^{36} +11.6351 q^{37} +(-3.90406 - 6.76203i) q^{38} +(1.28442 - 3.16458i) q^{39} +(1.23324 - 2.13603i) q^{41} +(-3.08362 + 7.59746i) q^{42} +(3.63907 + 6.30306i) q^{43} +8.92580 q^{44} -4.56668 q^{46} +(-3.14604 - 5.44910i) q^{47} +(11.1697 + 14.3435i) q^{48} +(1.88463 - 3.26427i) q^{49} +(-8.24870 + 1.14592i) q^{51} +(-4.86696 - 8.42983i) q^{52} +1.72540 q^{53} +(11.0331 + 8.09664i) q^{54} +(6.95059 + 12.0388i) q^{56} +(-5.08612 + 0.706570i) q^{57} +(9.70218 - 16.8047i) q^{58} +(-5.51300 + 9.54880i) q^{59} +(6.33521 + 10.9729i) q^{61} -6.90833 q^{62} +(3.86696 + 3.75810i) q^{63} +11.0756 q^{64} +(3.10197 - 7.64268i) q^{66} +(-4.55187 + 7.88407i) q^{67} +(-11.8676 + 20.5554i) q^{68} +(-1.12946 + 2.78277i) q^{69} +1.27460 q^{71} +(22.3232 - 6.32439i) q^{72} -3.58770 q^{73} +(-15.3218 - 26.5382i) q^{74} +(-7.31755 + 12.6744i) q^{76} +(1.62499 - 2.81456i) q^{77} +(-8.90941 + 1.23771i) q^{78} +(-1.05545 - 1.82809i) q^{79} +(7.66258 - 4.72068i) q^{81} -6.49602 q^{82} +(-0.549415 - 0.951614i) q^{83} +(15.2223 - 2.11470i) q^{84} +(9.58431 - 16.6005i) q^{86} +(-7.84056 - 10.0684i) q^{87} +(-6.99195 - 12.1104i) q^{88} -13.2935 q^{89} -3.54422 q^{91} +(4.27976 + 7.41277i) q^{92} +(-1.70861 + 4.20969i) q^{93} +(-8.28580 + 14.3514i) q^{94} +(7.93115 - 19.5409i) q^{96} +(1.91638 + 3.31926i) q^{97} -9.92718 q^{98} +(-3.88998 - 3.78046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} + q^{3} - 4 q^{4} + 8 q^{6} + q^{7} + 18 q^{8} + 5 q^{9} + q^{11} + 11 q^{12} - 2 q^{13} - 3 q^{14} - 4 q^{16} + 22 q^{17} - 5 q^{18} + 4 q^{19} - 15 q^{21} - 3 q^{22} - 15 q^{23} - 33 q^{24} - 20 q^{26} - 2 q^{27} - 8 q^{28} - q^{29} + 4 q^{31} - 10 q^{32} - 28 q^{33} - 9 q^{34} - 14 q^{36} - 2 q^{37} - 23 q^{38} + 25 q^{39} + 5 q^{41} - 21 q^{42} + 10 q^{43} + 44 q^{44} - 20 q^{47} + 53 q^{48} + 3 q^{49} + 11 q^{51} - 17 q^{52} + 40 q^{53} + 26 q^{54} + 30 q^{56} - 8 q^{57} + 18 q^{58} - 17 q^{59} + 13 q^{61} - 12 q^{62} + 9 q^{63} + 38 q^{64} - 8 q^{66} - 17 q^{67} - 34 q^{68} - 27 q^{69} - 16 q^{71} + 18 q^{72} + 4 q^{73} - 40 q^{74} - 11 q^{76} - 12 q^{77} - 61 q^{78} + 7 q^{79} + 17 q^{81} + 24 q^{82} - 30 q^{83} + 27 q^{84} + 34 q^{86} - 23 q^{87} - 9 q^{88} - 18 q^{89} - 34 q^{91} + 12 q^{92} + 15 q^{93} - 3 q^{94} + 34 q^{96} + 19 q^{97} + 26 q^{98} - 17 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31686 2.28087i −0.931162 1.61282i −0.781339 0.624107i \(-0.785463\pi\)
−0.149823 0.988713i \(-0.547870\pi\)
\(3\) −1.71558 + 0.238330i −0.990488 + 0.137600i
\(4\) −2.46825 + 4.27513i −1.23412 + 2.13757i
\(5\) 0 0
\(6\) 2.80278 + 3.59916i 1.14423 + 1.46935i
\(7\) 0.898714 + 1.55662i 0.339682 + 0.588346i 0.984373 0.176097i \(-0.0563473\pi\)
−0.644691 + 0.764443i \(0.723014\pi\)
\(8\) 7.73393 2.73436
\(9\) 2.88640 0.817746i 0.962133 0.272582i
\(10\) 0 0
\(11\) −0.904062 1.56588i −0.272585 0.472131i 0.696938 0.717131i \(-0.254545\pi\)
−0.969523 + 0.245000i \(0.921212\pi\)
\(12\) 3.21558 7.92257i 0.928257 2.28705i
\(13\) −0.985914 + 1.70765i −0.273443 + 0.473618i −0.969741 0.244135i \(-0.921496\pi\)
0.696298 + 0.717753i \(0.254829\pi\)
\(14\) 2.36696 4.09970i 0.632598 1.09569i
\(15\) 0 0
\(16\) −5.24801 9.08982i −1.31200 2.27246i
\(17\) 4.80812 1.16614 0.583071 0.812421i \(-0.301851\pi\)
0.583071 + 0.812421i \(0.301851\pi\)
\(18\) −5.66616 5.50664i −1.33553 1.29793i
\(19\) 2.96467 0.680142 0.340071 0.940400i \(-0.389549\pi\)
0.340071 + 0.940400i \(0.389549\pi\)
\(20\) 0 0
\(21\) −1.91280 2.45630i −0.417407 0.536010i
\(22\) −2.38105 + 4.12410i −0.507641 + 0.879261i
\(23\) 0.866963 1.50162i 0.180774 0.313110i −0.761370 0.648317i \(-0.775473\pi\)
0.942144 + 0.335207i \(0.108806\pi\)
\(24\) −13.2681 + 1.84323i −2.70835 + 0.376247i
\(25\) 0 0
\(26\) 5.19325 1.01848
\(27\) −4.75694 + 2.09082i −0.915473 + 0.402379i
\(28\) −8.87300 −1.67684
\(29\) 3.68382 + 6.38057i 0.684069 + 1.18484i 0.973728 + 0.227713i \(0.0731247\pi\)
−0.289659 + 0.957130i \(0.593542\pi\)
\(30\) 0 0
\(31\) 1.31151 2.27161i 0.235555 0.407993i −0.723879 0.689927i \(-0.757643\pi\)
0.959434 + 0.281934i \(0.0909760\pi\)
\(32\) −6.08789 + 10.5445i −1.07620 + 1.86403i
\(33\) 1.92418 + 2.47092i 0.334957 + 0.430132i
\(34\) −6.33163 10.9667i −1.08587 1.88078i
\(35\) 0 0
\(36\) −3.62838 + 14.3581i −0.604729 + 2.39302i
\(37\) 11.6351 1.91280 0.956399 0.292063i \(-0.0943417\pi\)
0.956399 + 0.292063i \(0.0943417\pi\)
\(38\) −3.90406 6.76203i −0.633322 1.09695i
\(39\) 1.28442 3.16458i 0.205673 0.506738i
\(40\) 0 0
\(41\) 1.23324 2.13603i 0.192600 0.333592i −0.753511 0.657435i \(-0.771641\pi\)
0.946111 + 0.323842i \(0.104975\pi\)
\(42\) −3.08362 + 7.59746i −0.475813 + 1.17231i
\(43\) 3.63907 + 6.30306i 0.554953 + 0.961207i 0.997907 + 0.0646628i \(0.0205972\pi\)
−0.442954 + 0.896544i \(0.646069\pi\)
\(44\) 8.92580 1.34562
\(45\) 0 0
\(46\) −4.56668 −0.673321
\(47\) −3.14604 5.44910i −0.458897 0.794833i 0.540006 0.841661i \(-0.318422\pi\)
−0.998903 + 0.0468283i \(0.985089\pi\)
\(48\) 11.1697 + 14.3435i 1.61221 + 2.07031i
\(49\) 1.88463 3.26427i 0.269233 0.466324i
\(50\) 0 0
\(51\) −8.24870 + 1.14592i −1.15505 + 0.160461i
\(52\) −4.86696 8.42983i −0.674926 1.16901i
\(53\) 1.72540 0.237001 0.118501 0.992954i \(-0.462191\pi\)
0.118501 + 0.992954i \(0.462191\pi\)
\(54\) 11.0331 + 8.09664i 1.50142 + 1.10181i
\(55\) 0 0
\(56\) 6.95059 + 12.0388i 0.928811 + 1.60875i
\(57\) −5.08612 + 0.706570i −0.673673 + 0.0935875i
\(58\) 9.70218 16.8047i 1.27396 2.20656i
\(59\) −5.51300 + 9.54880i −0.717732 + 1.24315i 0.244165 + 0.969734i \(0.421486\pi\)
−0.961896 + 0.273414i \(0.911847\pi\)
\(60\) 0 0
\(61\) 6.33521 + 10.9729i 0.811141 + 1.40494i 0.912066 + 0.410043i \(0.134486\pi\)
−0.100925 + 0.994894i \(0.532180\pi\)
\(62\) −6.90833 −0.877358
\(63\) 3.86696 + 3.75810i 0.487192 + 0.473476i
\(64\) 11.0756 1.38445
\(65\) 0 0
\(66\) 3.10197 7.64268i 0.381826 0.940748i
\(67\) −4.55187 + 7.88407i −0.556100 + 0.963193i 0.441717 + 0.897154i \(0.354369\pi\)
−0.997817 + 0.0660386i \(0.978964\pi\)
\(68\) −11.8676 + 20.5554i −1.43916 + 2.49271i
\(69\) −1.12946 + 2.78277i −0.135971 + 0.335006i
\(70\) 0 0
\(71\) 1.27460 0.151268 0.0756338 0.997136i \(-0.475902\pi\)
0.0756338 + 0.997136i \(0.475902\pi\)
\(72\) 22.3232 6.32439i 2.63081 0.745336i
\(73\) −3.58770 −0.419908 −0.209954 0.977711i \(-0.567331\pi\)
−0.209954 + 0.977711i \(0.567331\pi\)
\(74\) −15.3218 26.5382i −1.78112 3.08500i
\(75\) 0 0
\(76\) −7.31755 + 12.6744i −0.839380 + 1.45385i
\(77\) 1.62499 2.81456i 0.185184 0.320749i
\(78\) −8.90941 + 1.23771i −1.00879 + 0.140143i
\(79\) −1.05545 1.82809i −0.118747 0.205676i 0.800524 0.599300i \(-0.204555\pi\)
−0.919272 + 0.393624i \(0.871221\pi\)
\(80\) 0 0
\(81\) 7.66258 4.72068i 0.851398 0.524520i
\(82\) −6.49602 −0.717366
\(83\) −0.549415 0.951614i −0.0603061 0.104453i 0.834296 0.551317i \(-0.185874\pi\)
−0.894602 + 0.446863i \(0.852541\pi\)
\(84\) 15.2223 2.11470i 1.66089 0.230733i
\(85\) 0 0
\(86\) 9.58431 16.6005i 1.03350 1.79008i
\(87\) −7.84056 10.0684i −0.840596 1.07944i
\(88\) −6.99195 12.1104i −0.745344 1.29097i
\(89\) −13.2935 −1.40910 −0.704552 0.709653i \(-0.748852\pi\)
−0.704552 + 0.709653i \(0.748852\pi\)
\(90\) 0 0
\(91\) −3.54422 −0.371535
\(92\) 4.27976 + 7.41277i 0.446196 + 0.772834i
\(93\) −1.70861 + 4.20969i −0.177174 + 0.436524i
\(94\) −8.28580 + 14.3514i −0.854615 + 1.48024i
\(95\) 0 0
\(96\) 7.93115 19.5409i 0.809470 1.99438i
\(97\) 1.91638 + 3.31926i 0.194579 + 0.337020i 0.946762 0.321933i \(-0.104333\pi\)
−0.752184 + 0.658954i \(0.770999\pi\)
\(98\) −9.92718 −1.00280
\(99\) −3.88998 3.78046i −0.390957 0.379951i
\(100\) 0 0
\(101\) −3.27618 5.67452i −0.325993 0.564636i 0.655720 0.755004i \(-0.272365\pi\)
−0.981713 + 0.190368i \(0.939032\pi\)
\(102\) 13.4761 + 17.3052i 1.33433 + 1.71347i
\(103\) 4.03779 6.99365i 0.397855 0.689105i −0.595606 0.803277i \(-0.703088\pi\)
0.993461 + 0.114172i \(0.0364214\pi\)
\(104\) −7.62499 + 13.2069i −0.747691 + 1.29504i
\(105\) 0 0
\(106\) −2.27211 3.93541i −0.220687 0.382241i
\(107\) −8.97674 −0.867814 −0.433907 0.900958i \(-0.642865\pi\)
−0.433907 + 0.900958i \(0.642865\pi\)
\(108\) 2.80278 25.4972i 0.269697 2.45347i
\(109\) −6.34164 −0.607419 −0.303710 0.952765i \(-0.598225\pi\)
−0.303710 + 0.952765i \(0.598225\pi\)
\(110\) 0 0
\(111\) −19.9609 + 2.77299i −1.89460 + 0.263201i
\(112\) 9.43292 16.3383i 0.891327 1.54382i
\(113\) 7.45127 12.9060i 0.700957 1.21409i −0.267174 0.963648i \(-0.586090\pi\)
0.968131 0.250444i \(-0.0805767\pi\)
\(114\) 8.30931 + 10.6703i 0.778238 + 0.999367i
\(115\) 0 0
\(116\) −36.3704 −3.37691
\(117\) −1.44931 + 5.73519i −0.133989 + 0.530219i
\(118\) 29.0394 2.67330
\(119\) 4.32113 + 7.48441i 0.396117 + 0.686095i
\(120\) 0 0
\(121\) 3.86534 6.69497i 0.351395 0.608634i
\(122\) 16.6852 28.8996i 1.51061 2.61645i
\(123\) −1.60663 + 3.95845i −0.144865 + 0.356921i
\(124\) 6.47428 + 11.2138i 0.581408 + 1.00703i
\(125\) 0 0
\(126\) 3.47948 13.7689i 0.309977 1.22663i
\(127\) 3.62303 0.321492 0.160746 0.986996i \(-0.448610\pi\)
0.160746 + 0.986996i \(0.448610\pi\)
\(128\) −2.40922 4.17289i −0.212947 0.368835i
\(129\) −7.74531 9.94607i −0.681936 0.875703i
\(130\) 0 0
\(131\) −3.64673 + 6.31631i −0.318616 + 0.551859i −0.980200 0.198012i \(-0.936551\pi\)
0.661584 + 0.749871i \(0.269885\pi\)
\(132\) −15.3129 + 2.12729i −1.33282 + 0.185157i
\(133\) 2.66439 + 4.61486i 0.231032 + 0.400159i
\(134\) 23.9767 2.07127
\(135\) 0 0
\(136\) 37.1857 3.18865
\(137\) 3.56310 + 6.17148i 0.304417 + 0.527265i 0.977131 0.212637i \(-0.0682052\pi\)
−0.672715 + 0.739902i \(0.734872\pi\)
\(138\) 7.83449 1.08838i 0.666916 0.0926488i
\(139\) 7.35533 12.7398i 0.623871 1.08058i −0.364887 0.931052i \(-0.618892\pi\)
0.988758 0.149525i \(-0.0477744\pi\)
\(140\) 0 0
\(141\) 6.69595 + 8.59855i 0.563901 + 0.724128i
\(142\) −1.67848 2.90721i −0.140855 0.243967i
\(143\) 3.56531 0.298146
\(144\) −22.5810 21.9453i −1.88175 1.82878i
\(145\) 0 0
\(146\) 4.72450 + 8.18308i 0.391003 + 0.677236i
\(147\) −2.45525 + 6.04927i −0.202505 + 0.498935i
\(148\) −28.7183 + 49.7416i −2.36063 + 4.08873i
\(149\) 0.282655 0.489572i 0.0231560 0.0401073i −0.854215 0.519920i \(-0.825962\pi\)
0.877371 + 0.479812i \(0.159295\pi\)
\(150\) 0 0
\(151\) −0.0766925 0.132835i −0.00624115 0.0108100i 0.862888 0.505395i \(-0.168653\pi\)
−0.869129 + 0.494585i \(0.835320\pi\)
\(152\) 22.9285 1.85975
\(153\) 13.8782 3.93183i 1.12198 0.317869i
\(154\) −8.55953 −0.689746
\(155\) 0 0
\(156\) 10.3587 + 13.3021i 0.829362 + 1.06502i
\(157\) 5.73035 9.92525i 0.457332 0.792121i −0.541487 0.840709i \(-0.682139\pi\)
0.998819 + 0.0485874i \(0.0154719\pi\)
\(158\) −2.77976 + 4.81469i −0.221146 + 0.383036i
\(159\) −2.96005 + 0.411214i −0.234747 + 0.0326114i
\(160\) 0 0
\(161\) 3.11661 0.245623
\(162\) −20.8578 11.2609i −1.63875 0.884738i
\(163\) −22.0595 −1.72783 −0.863915 0.503637i \(-0.831995\pi\)
−0.863915 + 0.503637i \(0.831995\pi\)
\(164\) 6.08789 + 10.5445i 0.475384 + 0.823389i
\(165\) 0 0
\(166\) −1.44701 + 2.50629i −0.112310 + 0.194526i
\(167\) −8.53421 + 14.7817i −0.660397 + 1.14384i 0.320115 + 0.947379i \(0.396279\pi\)
−0.980511 + 0.196462i \(0.937055\pi\)
\(168\) −14.7935 18.9969i −1.14134 1.46564i
\(169\) 4.55595 + 7.89113i 0.350457 + 0.607010i
\(170\) 0 0
\(171\) 8.55722 2.42435i 0.654387 0.185395i
\(172\) −35.9285 −2.73953
\(173\) −5.97233 10.3444i −0.454067 0.786468i 0.544567 0.838718i \(-0.316694\pi\)
−0.998634 + 0.0522497i \(0.983361\pi\)
\(174\) −12.6398 + 31.1420i −0.958218 + 2.36087i
\(175\) 0 0
\(176\) −9.48906 + 16.4355i −0.715265 + 1.23887i
\(177\) 7.18221 17.6956i 0.539848 1.33008i
\(178\) 17.5056 + 30.3207i 1.31210 + 2.27263i
\(179\) 8.54921 0.638998 0.319499 0.947587i \(-0.396485\pi\)
0.319499 + 0.947587i \(0.396485\pi\)
\(180\) 0 0
\(181\) −10.5524 −0.784351 −0.392176 0.919890i \(-0.628277\pi\)
−0.392176 + 0.919890i \(0.628277\pi\)
\(182\) 4.66724 + 8.08390i 0.345959 + 0.599219i
\(183\) −13.4837 17.3150i −0.996744 1.27996i
\(184\) 6.70503 11.6135i 0.494301 0.856155i
\(185\) 0 0
\(186\) 11.8518 1.64646i 0.869013 0.120724i
\(187\) −4.34684 7.52895i −0.317873 0.550571i
\(188\) 31.0608 2.26534
\(189\) −7.52973 5.52569i −0.547708 0.401935i
\(190\) 0 0
\(191\) 8.66862 + 15.0145i 0.627239 + 1.08641i 0.988103 + 0.153792i \(0.0491485\pi\)
−0.360864 + 0.932618i \(0.617518\pi\)
\(192\) −19.0010 + 2.63964i −1.37128 + 0.190500i
\(193\) −0.779763 + 1.35059i −0.0561286 + 0.0972175i −0.892724 0.450603i \(-0.851209\pi\)
0.836596 + 0.547821i \(0.184542\pi\)
\(194\) 5.04721 8.74202i 0.362369 0.627641i
\(195\) 0 0
\(196\) 9.30346 + 16.1141i 0.664533 + 1.15100i
\(197\) 17.9767 1.28079 0.640395 0.768046i \(-0.278771\pi\)
0.640395 + 0.768046i \(0.278771\pi\)
\(198\) −3.50019 + 13.8509i −0.248748 + 0.984339i
\(199\) 11.0225 0.781362 0.390681 0.920526i \(-0.372240\pi\)
0.390681 + 0.920526i \(0.372240\pi\)
\(200\) 0 0
\(201\) 5.93007 14.6106i 0.418275 1.03055i
\(202\) −8.62856 + 14.9451i −0.607104 + 1.05153i
\(203\) −6.62141 + 11.4686i −0.464732 + 0.804939i
\(204\) 15.4609 38.0927i 1.08248 2.66702i
\(205\) 0 0
\(206\) −21.2688 −1.48187
\(207\) 1.27445 5.04324i 0.0885806 0.350529i
\(208\) 20.6964 1.43503
\(209\) −2.68025 4.64232i −0.185397 0.321116i
\(210\) 0 0
\(211\) 11.9643 20.7227i 0.823655 1.42661i −0.0792886 0.996852i \(-0.525265\pi\)
0.902943 0.429760i \(-0.141402\pi\)
\(212\) −4.25871 + 7.37630i −0.292489 + 0.506606i
\(213\) −2.18668 + 0.303776i −0.149829 + 0.0208144i
\(214\) 11.8211 + 20.4748i 0.808076 + 1.39963i
\(215\) 0 0
\(216\) −36.7898 + 16.1703i −2.50323 + 1.10025i
\(217\) 4.71470 0.320055
\(218\) 8.35107 + 14.4645i 0.565606 + 0.979658i
\(219\) 6.15497 0.855056i 0.415914 0.0577793i
\(220\) 0 0
\(221\) −4.74040 + 8.21061i −0.318874 + 0.552305i
\(222\) 32.6106 + 41.8766i 2.18868 + 2.81057i
\(223\) −10.8553 18.8020i −0.726927 1.25907i −0.958176 0.286180i \(-0.907615\pi\)
0.231249 0.972895i \(-0.425719\pi\)
\(224\) −21.8851 −1.46226
\(225\) 0 0
\(226\) −39.2492 −2.61082
\(227\) −7.05010 12.2111i −0.467932 0.810481i 0.531397 0.847123i \(-0.321667\pi\)
−0.999328 + 0.0366416i \(0.988334\pi\)
\(228\) 9.53312 23.4878i 0.631347 1.55552i
\(229\) −1.83879 + 3.18488i −0.121511 + 0.210463i −0.920364 0.391064i \(-0.872107\pi\)
0.798853 + 0.601526i \(0.205441\pi\)
\(230\) 0 0
\(231\) −2.11699 + 5.21587i −0.139288 + 0.343179i
\(232\) 28.4904 + 49.3469i 1.87049 + 3.23978i
\(233\) −5.34164 −0.349943 −0.174971 0.984574i \(-0.555983\pi\)
−0.174971 + 0.984574i \(0.555983\pi\)
\(234\) 14.9898 4.24676i 0.979913 0.277619i
\(235\) 0 0
\(236\) −27.2149 47.1376i −1.77154 3.06840i
\(237\) 2.24639 + 2.88469i 0.145919 + 0.187380i
\(238\) 11.3807 19.7119i 0.737698 1.27773i
\(239\) 11.0167 19.0815i 0.712613 1.23428i −0.251260 0.967920i \(-0.580845\pi\)
0.963873 0.266362i \(-0.0858218\pi\)
\(240\) 0 0
\(241\) 9.32358 + 16.1489i 0.600585 + 1.04024i 0.992733 + 0.120341i \(0.0383988\pi\)
−0.392148 + 0.919902i \(0.628268\pi\)
\(242\) −20.3605 −1.30882
\(243\) −12.0207 + 9.92491i −0.771126 + 0.636683i
\(244\) −62.5475 −4.00420
\(245\) 0 0
\(246\) 11.1444 1.54820i 0.710542 0.0987095i
\(247\) −2.92291 + 5.06263i −0.185980 + 0.322127i
\(248\) 10.1431 17.5684i 0.644091 1.11560i
\(249\) 1.16936 + 1.50162i 0.0741052 + 0.0951616i
\(250\) 0 0
\(251\) 14.6929 0.927407 0.463704 0.885990i \(-0.346520\pi\)
0.463704 + 0.885990i \(0.346520\pi\)
\(252\) −25.6110 + 7.25586i −1.61334 + 0.457076i
\(253\) −3.13515 −0.197105
\(254\) −4.77103 8.26366i −0.299361 0.518508i
\(255\) 0 0
\(256\) 4.73035 8.19320i 0.295647 0.512075i
\(257\) −11.1045 + 19.2335i −0.692678 + 1.19975i 0.278280 + 0.960500i \(0.410236\pi\)
−0.970957 + 0.239253i \(0.923098\pi\)
\(258\) −12.4862 + 30.7637i −0.777357 + 1.91526i
\(259\) 10.4566 + 18.1114i 0.649743 + 1.12539i
\(260\) 0 0
\(261\) 15.8507 + 15.4044i 0.981132 + 0.953510i
\(262\) 19.2089 1.18673
\(263\) −2.87001 4.97100i −0.176972 0.306525i 0.763870 0.645370i \(-0.223297\pi\)
−0.940842 + 0.338846i \(0.889964\pi\)
\(264\) 14.8815 + 19.1099i 0.915892 + 1.17613i
\(265\) 0 0
\(266\) 7.01727 12.1543i 0.430256 0.745226i
\(267\) 22.8059 3.16823i 1.39570 0.193892i
\(268\) −22.4703 38.9197i −1.37259 2.37740i
\(269\) −15.6162 −0.952139 −0.476070 0.879408i \(-0.657939\pi\)
−0.476070 + 0.879408i \(0.657939\pi\)
\(270\) 0 0
\(271\) −6.75315 −0.410225 −0.205112 0.978738i \(-0.565756\pi\)
−0.205112 + 0.978738i \(0.565756\pi\)
\(272\) −25.2331 43.7050i −1.52998 2.65000i
\(273\) 6.08037 0.844693i 0.368001 0.0511232i
\(274\) 9.38423 16.2540i 0.566922 0.981938i
\(275\) 0 0
\(276\) −9.10894 11.6972i −0.548294 0.704087i
\(277\) −15.1483 26.2376i −0.910172 1.57646i −0.813820 0.581118i \(-0.802616\pi\)
−0.0963529 0.995347i \(-0.530718\pi\)
\(278\) −38.7438 −2.32370
\(279\) 1.92795 7.62925i 0.115423 0.456751i
\(280\) 0 0
\(281\) −9.31755 16.1385i −0.555838 0.962740i −0.997838 0.0657249i \(-0.979064\pi\)
0.441999 0.897015i \(-0.354269\pi\)
\(282\) 10.7945 26.5957i 0.642805 1.58375i
\(283\) 2.83683 4.91354i 0.168632 0.292079i −0.769307 0.638879i \(-0.779398\pi\)
0.937939 + 0.346800i \(0.112732\pi\)
\(284\) −3.14604 + 5.44910i −0.186683 + 0.323345i
\(285\) 0 0
\(286\) −4.69502 8.13201i −0.277622 0.480856i
\(287\) 4.43332 0.261690
\(288\) −8.94931 + 35.4141i −0.527343 + 2.08679i
\(289\) 6.11806 0.359886
\(290\) 0 0
\(291\) −4.07877 5.23772i −0.239102 0.307040i
\(292\) 8.85533 15.3379i 0.518219 0.897582i
\(293\) −9.13867 + 15.8286i −0.533887 + 0.924720i 0.465329 + 0.885138i \(0.345936\pi\)
−0.999216 + 0.0395819i \(0.987397\pi\)
\(294\) 17.0308 2.36594i 0.993257 0.137985i
\(295\) 0 0
\(296\) 89.9850 5.23027
\(297\) 7.57454 + 5.55857i 0.439520 + 0.322541i
\(298\) −1.48887 −0.0862478
\(299\) 1.70950 + 2.96094i 0.0988631 + 0.171236i
\(300\) 0 0
\(301\) −6.54097 + 11.3293i −0.377015 + 0.653009i
\(302\) −0.201987 + 0.349852i −0.0116230 + 0.0201317i
\(303\) 6.97295 + 8.95425i 0.400585 + 0.514408i
\(304\) −15.5586 26.9483i −0.892349 1.54559i
\(305\) 0 0
\(306\) −27.2436 26.4766i −1.55741 1.51357i
\(307\) −15.5050 −0.884915 −0.442458 0.896789i \(-0.645893\pi\)
−0.442458 + 0.896789i \(0.645893\pi\)
\(308\) 8.02174 + 13.8941i 0.457081 + 0.791688i
\(309\) −5.26033 + 12.9605i −0.299250 + 0.737295i
\(310\) 0 0
\(311\) −15.2232 + 26.3673i −0.863228 + 1.49515i 0.00556798 + 0.999984i \(0.498228\pi\)
−0.868796 + 0.495170i \(0.835106\pi\)
\(312\) 9.93365 24.4746i 0.562382 1.38560i
\(313\) 3.47468 + 6.01832i 0.196401 + 0.340176i 0.947359 0.320174i \(-0.103741\pi\)
−0.750958 + 0.660350i \(0.770408\pi\)
\(314\) −30.1843 −1.70340
\(315\) 0 0
\(316\) 10.4205 0.586196
\(317\) 8.07253 + 13.9820i 0.453398 + 0.785309i 0.998595 0.0529995i \(-0.0168782\pi\)
−0.545196 + 0.838308i \(0.683545\pi\)
\(318\) 4.83590 + 6.20998i 0.271184 + 0.348238i
\(319\) 6.66081 11.5369i 0.372934 0.645940i
\(320\) 0 0
\(321\) 15.4003 2.13943i 0.859560 0.119411i
\(322\) −4.10414 7.10858i −0.228715 0.396146i
\(323\) 14.2545 0.793142
\(324\) 1.26838 + 44.4104i 0.0704655 + 2.46724i
\(325\) 0 0
\(326\) 29.0493 + 50.3148i 1.60889 + 2.78668i
\(327\) 10.8796 1.51140i 0.601642 0.0835808i
\(328\) 9.53779 16.5199i 0.526636 0.912160i
\(329\) 5.65478 9.79436i 0.311758 0.539981i
\(330\) 0 0
\(331\) −6.31112 10.9312i −0.346890 0.600832i 0.638805 0.769369i \(-0.279429\pi\)
−0.985695 + 0.168537i \(0.946096\pi\)
\(332\) 5.42437 0.297701
\(333\) 33.5835 9.51456i 1.84037 0.521394i
\(334\) 44.9535 2.45975
\(335\) 0 0
\(336\) −12.2890 + 30.2777i −0.670419 + 1.65179i
\(337\) 3.46020 5.99324i 0.188489 0.326473i −0.756258 0.654274i \(-0.772974\pi\)
0.944747 + 0.327801i \(0.106308\pi\)
\(338\) 11.9991 20.7831i 0.652665 1.13045i
\(339\) −9.70734 + 23.9170i −0.527230 + 1.29900i
\(340\) 0 0
\(341\) −4.74276 −0.256835
\(342\) −16.7983 16.3254i −0.908348 0.882776i
\(343\) 19.3570 1.04518
\(344\) 28.1443 + 48.7474i 1.51744 + 2.62828i
\(345\) 0 0
\(346\) −15.7295 + 27.2442i −0.845621 + 1.46466i
\(347\) −6.90317 + 11.9566i −0.370581 + 0.641866i −0.989655 0.143467i \(-0.954175\pi\)
0.619074 + 0.785333i \(0.287508\pi\)
\(348\) 62.3962 8.66816i 3.34479 0.464662i
\(349\) −3.28384 5.68778i −0.175780 0.304460i 0.764651 0.644445i \(-0.222911\pi\)
−0.940431 + 0.339985i \(0.889578\pi\)
\(350\) 0 0
\(351\) 1.11954 10.1846i 0.0597564 0.543612i
\(352\) 22.0153 1.17342
\(353\) 1.76250 + 3.05273i 0.0938082 + 0.162481i 0.909111 0.416555i \(-0.136763\pi\)
−0.815302 + 0.579035i \(0.803429\pi\)
\(354\) −49.8194 + 6.92097i −2.64787 + 0.367846i
\(355\) 0 0
\(356\) 32.8116 56.8313i 1.73901 3.01205i
\(357\) −9.19698 11.8102i −0.486756 0.625063i
\(358\) −11.2581 19.4996i −0.595010 1.03059i
\(359\) 22.9285 1.21012 0.605061 0.796179i \(-0.293149\pi\)
0.605061 + 0.796179i \(0.293149\pi\)
\(360\) 0 0
\(361\) −10.2107 −0.537407
\(362\) 13.8960 + 24.0686i 0.730358 + 1.26502i
\(363\) −5.03568 + 12.4070i −0.264304 + 0.651196i
\(364\) 8.74801 15.1520i 0.458520 0.794181i
\(365\) 0 0
\(366\) −21.7371 + 53.5560i −1.13621 + 2.79942i
\(367\) −2.08966 3.61939i −0.109079 0.188931i 0.806318 0.591482i \(-0.201457\pi\)
−0.915397 + 0.402551i \(0.868124\pi\)
\(368\) −18.1993 −0.948706
\(369\) 1.81289 7.17392i 0.0943751 0.373459i
\(370\) 0 0
\(371\) 1.55064 + 2.68578i 0.0805051 + 0.139439i
\(372\) −13.7797 17.6951i −0.714444 0.917447i
\(373\) −3.42045 + 5.92440i −0.177104 + 0.306754i −0.940888 0.338719i \(-0.890006\pi\)
0.763783 + 0.645473i \(0.223340\pi\)
\(374\) −11.4484 + 19.8292i −0.591982 + 1.02534i
\(375\) 0 0
\(376\) −24.3312 42.1429i −1.25479 2.17336i
\(377\) −14.5277 −0.748217
\(378\) −2.68776 + 24.4509i −0.138244 + 1.25762i
\(379\) −12.7764 −0.656280 −0.328140 0.944629i \(-0.606422\pi\)
−0.328140 + 0.944629i \(0.606422\pi\)
\(380\) 0 0
\(381\) −6.21558 + 0.863476i −0.318434 + 0.0442372i
\(382\) 22.8307 39.5440i 1.16812 2.02325i
\(383\) −3.76730 + 6.52515i −0.192500 + 0.333420i −0.946078 0.323939i \(-0.894993\pi\)
0.753578 + 0.657358i \(0.228326\pi\)
\(384\) 5.12773 + 6.58472i 0.261673 + 0.336025i
\(385\) 0 0
\(386\) 4.10736 0.209059
\(387\) 15.6581 + 15.2173i 0.795946 + 0.773538i
\(388\) −18.9204 −0.960538
\(389\) −2.72588 4.72135i −0.138207 0.239382i 0.788611 0.614893i \(-0.210801\pi\)
−0.926818 + 0.375511i \(0.877467\pi\)
\(390\) 0 0
\(391\) 4.16847 7.22000i 0.210808 0.365131i
\(392\) 14.5756 25.2456i 0.736177 1.27510i
\(393\) 4.75087 11.7052i 0.239649 0.590451i
\(394\) −23.6729 41.0026i −1.19262 2.06568i
\(395\) 0 0
\(396\) 25.7634 7.29904i 1.29466 0.366791i
\(397\) −5.64549 −0.283339 −0.141670 0.989914i \(-0.545247\pi\)
−0.141670 + 0.989914i \(0.545247\pi\)
\(398\) −14.5151 25.1408i −0.727574 1.26020i
\(399\) −5.67082 7.28214i −0.283896 0.364563i
\(400\) 0 0
\(401\) 2.75209 4.76676i 0.137433 0.238040i −0.789091 0.614276i \(-0.789448\pi\)
0.926524 + 0.376235i \(0.122782\pi\)
\(402\) −41.1339 + 5.71438i −2.05157 + 0.285007i
\(403\) 2.58608 + 4.47922i 0.128822 + 0.223126i
\(404\) 32.3458 1.60926
\(405\) 0 0
\(406\) 34.8779 1.73096
\(407\) −10.5188 18.2192i −0.521400 0.903091i
\(408\) −63.7948 + 8.86246i −3.15831 + 0.438757i
\(409\) −16.4265 + 28.4515i −0.812238 + 1.40684i 0.0990570 + 0.995082i \(0.468417\pi\)
−0.911295 + 0.411755i \(0.864916\pi\)
\(410\) 0 0
\(411\) −7.58362 9.73844i −0.374072 0.480362i
\(412\) 19.9325 + 34.5241i 0.982005 + 1.70088i
\(413\) −19.8184 −0.975202
\(414\) −13.1813 + 3.73439i −0.647824 + 0.183535i
\(415\) 0 0
\(416\) −12.0043 20.7920i −0.588558 1.01941i
\(417\) −9.58235 + 23.6091i −0.469250 + 1.15614i
\(418\) −7.05903 + 12.2266i −0.345268 + 0.598022i
\(419\) −11.4295 + 19.7965i −0.558369 + 0.967124i 0.439264 + 0.898358i \(0.355239\pi\)
−0.997633 + 0.0687656i \(0.978094\pi\)
\(420\) 0 0
\(421\) −8.97071 15.5377i −0.437205 0.757262i 0.560267 0.828312i \(-0.310698\pi\)
−0.997473 + 0.0710498i \(0.977365\pi\)
\(422\) −63.0212 −3.06782
\(423\) −13.5367 13.1556i −0.658177 0.639648i
\(424\) 13.3441 0.648046
\(425\) 0 0
\(426\) 3.57243 + 4.58750i 0.173085 + 0.222265i
\(427\) −11.3871 + 19.7230i −0.551060 + 0.954463i
\(428\) 22.1568 38.3768i 1.07099 1.85501i
\(429\) −6.11656 + 0.849720i −0.295310 + 0.0410249i
\(430\) 0 0
\(431\) −6.18871 −0.298100 −0.149050 0.988830i \(-0.547622\pi\)
−0.149050 + 0.988830i \(0.547622\pi\)
\(432\) 43.9697 + 32.2671i 2.11549 + 1.55245i
\(433\) −3.11806 −0.149844 −0.0749221 0.997189i \(-0.523871\pi\)
−0.0749221 + 0.997189i \(0.523871\pi\)
\(434\) −6.20861 10.7536i −0.298023 0.516190i
\(435\) 0 0
\(436\) 15.6528 27.1114i 0.749631 1.29840i
\(437\) 2.57026 4.45182i 0.122952 0.212960i
\(438\) −10.0555 12.9127i −0.480471 0.616992i
\(439\) −6.75494 11.6999i −0.322396 0.558406i 0.658586 0.752505i \(-0.271155\pi\)
−0.980982 + 0.194100i \(0.937822\pi\)
\(440\) 0 0
\(441\) 2.77044 10.9631i 0.131926 0.522054i
\(442\) 24.9698 1.18769
\(443\) 12.1387 + 21.0248i 0.576726 + 0.998918i 0.995852 + 0.0909904i \(0.0290032\pi\)
−0.419126 + 0.907928i \(0.637663\pi\)
\(444\) 37.4135 92.1799i 1.77557 4.37466i
\(445\) 0 0
\(446\) −28.5899 + 49.5192i −1.35377 + 2.34480i
\(447\) −0.368236 + 0.907263i −0.0174169 + 0.0429121i
\(448\) 9.95377 + 17.2404i 0.470271 + 0.814534i
\(449\) −24.1437 −1.13941 −0.569705 0.821849i \(-0.692943\pi\)
−0.569705 + 0.821849i \(0.692943\pi\)
\(450\) 0 0
\(451\) −4.45970 −0.209999
\(452\) 36.7832 + 63.7104i 1.73014 + 2.99668i
\(453\) 0.163230 + 0.209611i 0.00766924 + 0.00984838i
\(454\) −18.5680 + 32.1607i −0.871440 + 1.50938i
\(455\) 0 0
\(456\) −39.3357 + 5.46456i −1.84206 + 0.255902i
\(457\) 1.41078 + 2.44355i 0.0659937 + 0.114304i 0.897134 0.441758i \(-0.145645\pi\)
−0.831141 + 0.556062i \(0.812312\pi\)
\(458\) 9.68573 0.452585
\(459\) −22.8720 + 10.0529i −1.06757 + 0.469230i
\(460\) 0 0
\(461\) −10.7286 18.5825i −0.499681 0.865474i 0.500318 0.865841i \(-0.333216\pi\)
−1.00000 0.000367761i \(0.999883\pi\)
\(462\) 14.6845 2.03999i 0.683185 0.0949090i
\(463\) 9.90167 17.1502i 0.460170 0.797037i −0.538799 0.842434i \(-0.681122\pi\)
0.998969 + 0.0453970i \(0.0144553\pi\)
\(464\) 38.6655 66.9706i 1.79500 3.10903i
\(465\) 0 0
\(466\) 7.03421 + 12.1836i 0.325853 + 0.564395i
\(467\) 22.7210 1.05140 0.525701 0.850669i \(-0.323803\pi\)
0.525701 + 0.850669i \(0.323803\pi\)
\(468\) −20.9415 20.3519i −0.968019 0.940767i
\(469\) −16.3633 −0.755588
\(470\) 0 0
\(471\) −7.46536 + 18.3932i −0.343986 + 0.847516i
\(472\) −42.6372 + 73.8497i −1.96253 + 3.39921i
\(473\) 6.57989 11.3967i 0.302544 0.524021i
\(474\) 3.62141 8.92247i 0.166337 0.409822i
\(475\) 0 0
\(476\) −42.6625 −1.95543
\(477\) 4.98018 1.41094i 0.228027 0.0646023i
\(478\) −58.0300 −2.65423
\(479\) −10.6440 18.4359i −0.486336 0.842359i 0.513541 0.858065i \(-0.328334\pi\)
−0.999877 + 0.0157065i \(0.995000\pi\)
\(480\) 0 0
\(481\) −11.4712 + 19.8687i −0.523042 + 0.905935i
\(482\) 24.5557 42.5318i 1.11848 1.93727i
\(483\) −5.34677 + 0.742781i −0.243287 + 0.0337977i
\(484\) 19.0813 + 33.0497i 0.867330 + 1.50226i
\(485\) 0 0
\(486\) 38.4670 + 14.3478i 1.74490 + 0.650831i
\(487\) −9.58690 −0.434424 −0.217212 0.976124i \(-0.569696\pi\)
−0.217212 + 0.976124i \(0.569696\pi\)
\(488\) 48.9961 + 84.8637i 2.21795 + 3.84160i
\(489\) 37.8447 5.25743i 1.71140 0.237749i
\(490\) 0 0
\(491\) 18.9222 32.7742i 0.853945 1.47908i −0.0236745 0.999720i \(-0.507537\pi\)
0.877620 0.479357i \(-0.159130\pi\)
\(492\) −12.9573 16.6390i −0.584160 0.750144i
\(493\) 17.7123 + 30.6786i 0.797721 + 1.38169i
\(494\) 15.3963 0.692711
\(495\) 0 0
\(496\) −27.5314 −1.23619
\(497\) 1.14550 + 1.98407i 0.0513829 + 0.0889977i
\(498\) 1.88513 4.64459i 0.0844745 0.208129i
\(499\) −8.46266 + 14.6577i −0.378840 + 0.656171i −0.990894 0.134646i \(-0.957010\pi\)
0.612053 + 0.790816i \(0.290344\pi\)
\(500\) 0 0
\(501\) 11.1182 27.3930i 0.496723 1.22383i
\(502\) −19.3485 33.5126i −0.863566 1.49574i
\(503\) 40.4168 1.80210 0.901048 0.433719i \(-0.142799\pi\)
0.901048 + 0.433719i \(0.142799\pi\)
\(504\) 29.9068 + 29.0649i 1.33216 + 1.29465i
\(505\) 0 0
\(506\) 4.12856 + 7.15088i 0.183537 + 0.317896i
\(507\) −9.69676 12.4520i −0.430648 0.553013i
\(508\) −8.94253 + 15.4889i −0.396761 + 0.687210i
\(509\) 20.7034 35.8593i 0.917660 1.58943i 0.114701 0.993400i \(-0.463409\pi\)
0.802959 0.596034i \(-0.203258\pi\)
\(510\) 0 0
\(511\) −3.22431 5.58467i −0.142635 0.247051i
\(512\) −34.5537 −1.52707
\(513\) −14.1028 + 6.19860i −0.622652 + 0.273675i
\(514\) 58.4922 2.57998
\(515\) 0 0
\(516\) 61.6381 8.56285i 2.71347 0.376959i
\(517\) −5.68843 + 9.85265i −0.250177 + 0.433319i
\(518\) 27.5398 47.7004i 1.21003 2.09584i
\(519\) 12.7113 + 16.3232i 0.557966 + 0.716507i
\(520\) 0 0
\(521\) −17.0301 −0.746103 −0.373052 0.927811i \(-0.621689\pi\)
−0.373052 + 0.927811i \(0.621689\pi\)
\(522\) 14.2624 56.4389i 0.624248 2.47026i
\(523\) 9.57651 0.418751 0.209376 0.977835i \(-0.432857\pi\)
0.209376 + 0.977835i \(0.432857\pi\)
\(524\) −18.0021 31.1805i −0.786424 1.36213i
\(525\) 0 0
\(526\) −7.55880 + 13.0922i −0.329579 + 0.570848i
\(527\) 6.30592 10.9222i 0.274690 0.475777i
\(528\) 12.3621 30.4579i 0.537992 1.32551i
\(529\) 9.99675 + 17.3149i 0.434641 + 0.752821i
\(530\) 0 0
\(531\) −8.10422 + 32.0699i −0.351693 + 1.39171i
\(532\) −26.3055 −1.14049
\(533\) 2.43174 + 4.21189i 0.105330 + 0.182437i
\(534\) −37.2586 47.8452i −1.61234 2.07047i
\(535\) 0 0
\(536\) −35.2038 + 60.9748i −1.52057 + 2.63371i
\(537\) −14.6668 + 2.03753i −0.632920 + 0.0879260i
\(538\) 20.5644 + 35.6187i 0.886596 + 1.53563i
\(539\) −6.81528 −0.293555
\(540\) 0 0
\(541\) −0.833751 −0.0358458 −0.0179229 0.999839i \(-0.505705\pi\)
−0.0179229 + 0.999839i \(0.505705\pi\)
\(542\) 8.89297 + 15.4031i 0.381986 + 0.661619i
\(543\) 18.1034 2.51495i 0.776891 0.107927i
\(544\) −29.2713 + 50.6994i −1.25500 + 2.17372i
\(545\) 0 0
\(546\) −9.93365 12.7562i −0.425121 0.545915i
\(547\) 14.1635 + 24.5319i 0.605587 + 1.04891i 0.991958 + 0.126565i \(0.0403951\pi\)
−0.386371 + 0.922343i \(0.626272\pi\)
\(548\) −35.1785 −1.50275
\(549\) 27.2590 + 26.4916i 1.16339 + 1.13063i
\(550\) 0 0
\(551\) 10.9213 + 18.9163i 0.465264 + 0.805861i
\(552\) −8.73515 + 21.5218i −0.371793 + 0.916027i
\(553\) 1.89709 3.28586i 0.0806727 0.139729i
\(554\) −39.8964 + 69.1026i −1.69504 + 2.93589i
\(555\) 0 0
\(556\) 36.3096 + 62.8901i 1.53987 + 2.66713i
\(557\) 11.5042 0.487448 0.243724 0.969845i \(-0.421631\pi\)
0.243724 + 0.969845i \(0.421631\pi\)
\(558\) −19.9402 + 5.64926i −0.844135 + 0.239152i
\(559\) −14.3512 −0.606993
\(560\) 0 0
\(561\) 9.25171 + 11.8805i 0.390608 + 0.501595i
\(562\) −24.5398 + 42.5043i −1.03515 + 1.79293i
\(563\) −16.5030 + 28.5840i −0.695517 + 1.20467i 0.274490 + 0.961590i \(0.411491\pi\)
−0.970006 + 0.243080i \(0.921842\pi\)
\(564\) −53.2872 + 7.40273i −2.24380 + 0.311711i
\(565\) 0 0
\(566\) −14.9429 −0.628095
\(567\) 14.2348 + 7.68517i 0.597804 + 0.322747i
\(568\) 9.85769 0.413619
\(569\) 13.5044 + 23.3903i 0.566135 + 0.980574i 0.996943 + 0.0781305i \(0.0248951\pi\)
−0.430809 + 0.902443i \(0.641772\pi\)
\(570\) 0 0
\(571\) 12.2122 21.1521i 0.511064 0.885189i −0.488854 0.872366i \(-0.662585\pi\)
0.999918 0.0128232i \(-0.00408185\pi\)
\(572\) −8.80007 + 15.2422i −0.367950 + 0.637307i
\(573\) −18.4501 23.6925i −0.770763 0.989768i
\(574\) −5.83807 10.1118i −0.243676 0.422060i
\(575\) 0 0
\(576\) 31.9685 9.05701i 1.33202 0.377375i
\(577\) 14.7976 0.616033 0.308017 0.951381i \(-0.400335\pi\)
0.308017 + 0.951381i \(0.400335\pi\)
\(578\) −8.05663 13.9545i −0.335112 0.580431i
\(579\) 1.01586 2.50288i 0.0422175 0.104016i
\(580\) 0 0
\(581\) 0.987533 1.71046i 0.0409698 0.0709617i
\(582\) −6.57538 + 16.2005i −0.272558 + 0.671532i
\(583\) −1.55987 2.70177i −0.0646030 0.111896i
\(584\) −27.7470 −1.14818
\(585\) 0 0
\(586\) 48.1375 1.98854
\(587\) −15.2890 26.4813i −0.631044 1.09300i −0.987339 0.158626i \(-0.949294\pi\)
0.356295 0.934374i \(-0.384040\pi\)
\(588\) −19.8013 25.4276i −0.816590 1.04862i
\(589\) 3.88821 6.73457i 0.160211 0.277493i
\(590\) 0 0
\(591\) −30.8405 + 4.28440i −1.26861 + 0.176237i
\(592\) −61.0611 105.761i −2.50960 4.34675i
\(593\) −5.09990 −0.209428 −0.104714 0.994502i \(-0.533393\pi\)
−0.104714 + 0.994502i \(0.533393\pi\)
\(594\) 2.70376 24.5964i 0.110936 1.00920i
\(595\) 0 0
\(596\) 1.39532 + 2.41677i 0.0571547 + 0.0989949i
\(597\) −18.9099 + 2.62698i −0.773929 + 0.107515i
\(598\) 4.50236 7.79831i 0.184115 0.318897i
\(599\) 0.282655 0.489572i 0.0115490 0.0200034i −0.860193 0.509968i \(-0.829657\pi\)
0.871742 + 0.489965i \(0.162990\pi\)
\(600\) 0 0
\(601\) 5.50480 + 9.53459i 0.224546 + 0.388924i 0.956183 0.292770i \(-0.0945769\pi\)
−0.731637 + 0.681694i \(0.761244\pi\)
\(602\) 34.4542 1.40425
\(603\) −6.69134 + 26.4788i −0.272492 + 1.07830i
\(604\) 0.757185 0.0308094
\(605\) 0 0
\(606\) 11.2411 27.6959i 0.456638 1.12507i
\(607\) 9.54913 16.5396i 0.387587 0.671321i −0.604537 0.796577i \(-0.706642\pi\)
0.992124 + 0.125256i \(0.0399753\pi\)
\(608\) −18.0486 + 31.2611i −0.731967 + 1.26780i
\(609\) 8.62621 21.2534i 0.349552 0.861229i
\(610\) 0 0
\(611\) 12.4069 0.501929
\(612\) −17.4457 + 69.0357i −0.705200 + 2.79060i
\(613\) 9.33918 0.377206 0.188603 0.982053i \(-0.439604\pi\)
0.188603 + 0.982053i \(0.439604\pi\)
\(614\) 20.4179 + 35.3648i 0.823999 + 1.42721i
\(615\) 0 0
\(616\) 12.5675 21.7676i 0.506360 0.877041i
\(617\) 12.2077 21.1444i 0.491464 0.851241i −0.508488 0.861069i \(-0.669795\pi\)
0.999952 + 0.00982861i \(0.00312859\pi\)
\(618\) 36.4883 5.06900i 1.46777 0.203905i
\(619\) −19.7431 34.1961i −0.793544 1.37446i −0.923760 0.382973i \(-0.874900\pi\)
0.130216 0.991486i \(-0.458433\pi\)
\(620\) 0 0
\(621\) −0.984464 + 8.95580i −0.0395052 + 0.359384i
\(622\) 80.1874 3.21522
\(623\) −11.9470 20.6928i −0.478647 0.829040i
\(624\) −35.5062 + 4.93256i −1.42138 + 0.197461i
\(625\) 0 0
\(626\) 9.15135 15.8506i 0.365761 0.633517i
\(627\) 5.70457 + 7.32547i 0.227819 + 0.292551i
\(628\) 28.2879 + 48.9960i 1.12881 + 1.95515i
\(629\) 55.9430 2.23059
\(630\) 0 0
\(631\) 42.1634 1.67850 0.839249 0.543747i \(-0.182995\pi\)
0.839249 + 0.543747i \(0.182995\pi\)
\(632\) −8.16277 14.1383i −0.324698 0.562393i
\(633\) −15.5868 + 38.4029i −0.619518 + 1.52638i
\(634\) 21.2608 36.8248i 0.844375 1.46250i
\(635\) 0 0
\(636\) 5.54814 13.6696i 0.219998 0.542034i
\(637\) 3.71616 + 6.43658i 0.147240 + 0.255027i
\(638\) −35.0855 −1.38905
\(639\) 3.67901 1.04230i 0.145539 0.0412328i
\(640\) 0 0
\(641\) −17.6577 30.5841i −0.697438 1.20800i −0.969352 0.245677i \(-0.920990\pi\)
0.271913 0.962322i \(-0.412344\pi\)
\(642\) −25.1598 32.3087i −0.992978 1.27512i
\(643\) −7.09771 + 12.2936i −0.279906 + 0.484812i −0.971361 0.237608i \(-0.923637\pi\)
0.691455 + 0.722420i \(0.256970\pi\)
\(644\) −7.69256 + 13.3239i −0.303129 + 0.525036i
\(645\) 0 0
\(646\) −18.7712 32.5127i −0.738544 1.27919i
\(647\) 17.4897 0.687593 0.343796 0.939044i \(-0.388287\pi\)
0.343796 + 0.939044i \(0.388287\pi\)
\(648\) 59.2618 36.5094i 2.32803 1.43422i
\(649\) 19.9364 0.782572
\(650\) 0 0
\(651\) −8.08842 + 1.12365i −0.317010 + 0.0440395i
\(652\) 54.4483 94.3072i 2.13236 3.69335i
\(653\) 5.48858 9.50650i 0.214785 0.372018i −0.738421 0.674340i \(-0.764428\pi\)
0.953206 + 0.302322i \(0.0977617\pi\)
\(654\) −17.7742 22.8246i −0.695026 0.892512i
\(655\) 0 0
\(656\) −25.8882 −1.01077
\(657\) −10.3555 + 2.93383i −0.404007 + 0.114459i
\(658\) −29.7862 −1.16119
\(659\) 7.89381 + 13.6725i 0.307499 + 0.532604i 0.977815 0.209472i \(-0.0671746\pi\)
−0.670316 + 0.742076i \(0.733841\pi\)
\(660\) 0 0
\(661\) −24.9466 + 43.2088i −0.970311 + 1.68063i −0.275697 + 0.961245i \(0.588909\pi\)
−0.694614 + 0.719383i \(0.744425\pi\)
\(662\) −16.6217 + 28.7897i −0.646022 + 1.11894i
\(663\) 6.17567 15.2157i 0.239843 0.590929i
\(664\) −4.24913 7.35972i −0.164898 0.285612i
\(665\) 0 0
\(666\) −65.9263 64.0703i −2.55459 2.48267i
\(667\) 12.7750 0.494649
\(668\) −42.1291 72.9698i −1.63002 2.82328i
\(669\) 23.1042 + 29.6691i 0.893261 + 1.14707i
\(670\) 0 0
\(671\) 11.4549 19.8404i 0.442210 0.765929i
\(672\) 37.5455 5.21587i 1.44835 0.201207i
\(673\) −14.4197 24.9757i −0.555840 0.962743i −0.997838 0.0657266i \(-0.979063\pi\)
0.441998 0.897016i \(-0.354270\pi\)
\(674\) −18.2264 −0.702055
\(675\) 0 0
\(676\) −44.9809 −1.73003
\(677\) −5.23181 9.06176i −0.201075 0.348272i 0.747800 0.663924i \(-0.231110\pi\)
−0.948875 + 0.315652i \(0.897777\pi\)
\(678\) 67.3349 9.35426i 2.58598 0.359248i
\(679\) −3.44455 + 5.96614i −0.132190 + 0.228959i
\(680\) 0 0
\(681\) 15.0053 + 19.2689i 0.575003 + 0.738385i
\(682\) 6.24556 + 10.8176i 0.239155 + 0.414228i
\(683\) −16.1875 −0.619396 −0.309698 0.950835i \(-0.600228\pi\)
−0.309698 + 0.950835i \(0.600228\pi\)
\(684\) −10.7569 + 42.5672i −0.411302 + 1.62760i
\(685\) 0 0
\(686\) −25.4904 44.1507i −0.973229 1.68568i
\(687\) 2.39553 5.90214i 0.0913953 0.225181i
\(688\) 38.1958 66.1570i 1.45620 2.52221i
\(689\) −1.70109 + 2.94638i −0.0648065 + 0.112248i
\(690\) 0 0
\(691\) −4.94181 8.55946i −0.187995 0.325617i 0.756586 0.653894i \(-0.226866\pi\)
−0.944582 + 0.328276i \(0.893532\pi\)
\(692\) 58.9648 2.24150
\(693\) 2.38876 9.45276i 0.0907415 0.359081i
\(694\) 36.3621 1.38029
\(695\) 0 0
\(696\) −60.6383 77.8682i −2.29849 2.95158i
\(697\) 5.92957 10.2703i 0.224598 0.389016i
\(698\) −8.64872 + 14.9800i −0.327359 + 0.567002i
\(699\) 9.16399 1.27307i 0.346614 0.0481521i
\(700\) 0 0
\(701\) 43.9692 1.66069 0.830346 0.557248i \(-0.188143\pi\)
0.830346 + 0.557248i \(0.188143\pi\)
\(702\) −24.7040 + 10.8582i −0.932391 + 0.409815i
\(703\) 34.4942 1.30097
\(704\) −10.0130 17.3430i −0.377379 0.653640i
\(705\) 0 0
\(706\) 4.64193 8.04005i 0.174701 0.302591i
\(707\) 5.88870 10.1995i 0.221467 0.383593i
\(708\) 57.9236 + 74.3820i 2.17690 + 2.79545i
\(709\) −12.6130 21.8464i −0.473692 0.820458i 0.525855 0.850574i \(-0.323746\pi\)
−0.999546 + 0.0301162i \(0.990412\pi\)
\(710\) 0 0
\(711\) −4.54136 4.41351i −0.170314 0.165520i
\(712\) −102.811 −3.85299
\(713\) −2.27407 3.93880i −0.0851645 0.147509i
\(714\) −14.8264 + 36.5295i −0.554865 + 1.36708i
\(715\) 0 0
\(716\) −21.1016 + 36.5490i −0.788603 + 1.36590i
\(717\) −14.3523 + 35.3614i −0.535998 + 1.32060i
\(718\) −30.1937 52.2971i −1.12682 1.95171i
\(719\) −36.8600 −1.37465 −0.687323 0.726352i \(-0.741214\pi\)
−0.687323 + 0.726352i \(0.741214\pi\)
\(720\) 0 0
\(721\) 14.5153 0.540576
\(722\) 13.4461 + 23.2893i 0.500412 + 0.866740i
\(723\) −19.8441 25.4826i −0.738009 0.947708i
\(724\) 26.0459 45.1128i 0.967988 1.67660i
\(725\) 0 0
\(726\) 34.9300 4.85252i 1.29637 0.180094i
\(727\) 19.1226 + 33.1213i 0.709217 + 1.22840i 0.965148 + 0.261705i \(0.0842847\pi\)
−0.255931 + 0.966695i \(0.582382\pi\)
\(728\) −27.4107 −1.01591
\(729\) 18.2569 19.8918i 0.676183 0.736734i
\(730\) 0 0
\(731\) 17.4971 + 30.3059i 0.647154 + 1.12090i
\(732\) 107.305 14.9070i 3.96611 0.550977i
\(733\) −19.7916 + 34.2801i −0.731020 + 1.26616i 0.225428 + 0.974260i \(0.427622\pi\)
−0.956448 + 0.291903i \(0.905711\pi\)
\(734\) −5.50358 + 9.53248i −0.203141 + 0.351850i
\(735\) 0 0
\(736\) 10.5559 + 18.2834i 0.389097 + 0.673936i
\(737\) 16.4607 0.606338
\(738\) −18.7501 + 5.31210i −0.690201 + 0.195541i
\(739\) −8.24773 −0.303398 −0.151699 0.988427i \(-0.548474\pi\)
−0.151699 + 0.988427i \(0.548474\pi\)
\(740\) 0 0
\(741\) 3.80790 9.38194i 0.139887 0.344654i
\(742\) 4.08395 7.07361i 0.149927 0.259680i
\(743\) −0.654091 + 1.13292i −0.0239963 + 0.0415627i −0.877774 0.479075i \(-0.840972\pi\)
0.853778 + 0.520637i \(0.174306\pi\)
\(744\) −13.2142 + 32.5574i −0.484458 + 1.19361i
\(745\) 0 0
\(746\) 18.0171 0.659651
\(747\) −2.36401 2.29746i −0.0864946 0.0840595i
\(748\) 42.9164 1.56918
\(749\) −8.06752 13.9734i −0.294781 0.510575i
\(750\) 0 0
\(751\) −14.2234 + 24.6357i −0.519020 + 0.898969i 0.480736 + 0.876866i \(0.340370\pi\)
−0.999756 + 0.0221034i \(0.992964\pi\)
\(752\) −33.0209 + 57.1939i −1.20415 + 2.08565i
\(753\) −25.2068 + 3.50176i −0.918585 + 0.127611i
\(754\) 19.1310 + 33.1359i 0.696711 + 1.20674i
\(755\) 0 0
\(756\) 42.2083 18.5518i 1.53510 0.674724i
\(757\) −38.2012 −1.38845 −0.694223 0.719760i \(-0.744252\pi\)
−0.694223 + 0.719760i \(0.744252\pi\)
\(758\) 16.8248 + 29.1414i 0.611103 + 1.05846i
\(759\) 5.37859 0.747201i 0.195231 0.0271217i
\(760\) 0 0
\(761\) −11.0952 + 19.2174i −0.402200 + 0.696632i −0.993991 0.109460i \(-0.965088\pi\)
0.591791 + 0.806092i \(0.298421\pi\)
\(762\) 10.1545 + 13.0398i 0.367860 + 0.472384i
\(763\) −5.69932 9.87152i −0.206329 0.357373i
\(764\) −85.5852 −3.09637
\(765\) 0 0
\(766\) 19.8440 0.716994
\(767\) −10.8707 18.8286i −0.392518 0.679861i
\(768\) −6.16258 + 15.1834i −0.222373 + 0.547885i
\(769\) 8.45652 14.6471i 0.304950 0.528189i −0.672300 0.740279i \(-0.734694\pi\)
0.977250 + 0.212090i \(0.0680270\pi\)
\(770\) 0 0
\(771\) 14.4666 35.6431i 0.521003 1.28365i
\(772\) −3.84930 6.66718i −0.138539 0.239957i
\(773\) −38.6464 −1.39001 −0.695007 0.719003i \(-0.744599\pi\)
−0.695007 + 0.719003i \(0.744599\pi\)
\(774\) 14.0891 55.7532i 0.506423 2.00401i
\(775\) 0 0