Properties

Label 225.2.k.c.124.8
Level $225$
Weight $2$
Character 225.124
Analytic conductor $1.797$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,2,Mod(49,225)]
 
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, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), 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: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.8
Root \(2.28087 + 1.31686i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.2.k.c.49.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.28087 + 1.31686i) q^{2} +(0.238330 - 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(-1.55662 - 0.898714i) q^{7} +7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +O(q^{10})\) \(q+(2.28087 + 1.31686i) q^{2} +(0.238330 - 1.71558i) q^{3} +(2.46825 + 4.27513i) q^{4} +(2.80278 - 3.59916i) q^{6} +(-1.55662 - 0.898714i) q^{7} +7.73393i q^{8} +(-2.88640 - 0.817746i) q^{9} +(-0.904062 + 1.56588i) q^{11} +(7.92257 - 3.21558i) q^{12} +(1.70765 - 0.985914i) q^{13} +(-2.36696 - 4.09970i) q^{14} +(-5.24801 + 9.08982i) q^{16} -4.80812i q^{17} +(-5.50664 - 5.66616i) q^{18} -2.96467 q^{19} +(-1.91280 + 2.45630i) q^{21} +(-4.12410 + 2.38105i) q^{22} +(-1.50162 + 0.866963i) q^{23} +(13.2681 + 1.84323i) q^{24} +5.19325 q^{26} +(-2.09082 + 4.75694i) q^{27} -8.87300i q^{28} +(-3.68382 + 6.38057i) q^{29} +(1.31151 + 2.27161i) q^{31} +(-10.5445 + 6.08789i) q^{32} +(2.47092 + 1.92418i) q^{33} +(6.33163 - 10.9667i) q^{34} +(-3.62838 - 14.3581i) q^{36} -11.6351i q^{37} +(-6.76203 - 3.90406i) q^{38} +(-1.28442 - 3.16458i) q^{39} +(1.23324 + 2.13603i) q^{41} +(-7.59746 + 3.08362i) q^{42} +(6.30306 + 3.63907i) q^{43} -8.92580 q^{44} -4.56668 q^{46} +(5.44910 + 3.14604i) q^{47} +(14.3435 + 11.1697i) q^{48} +(-1.88463 - 3.26427i) q^{49} +(-8.24870 - 1.14592i) q^{51} +(8.42983 + 4.86696i) q^{52} +1.72540i q^{53} +(-11.0331 + 8.09664i) q^{54} +(6.95059 - 12.0388i) q^{56} +(-0.706570 + 5.08612i) q^{57} +(-16.8047 + 9.70218i) q^{58} +(5.51300 + 9.54880i) q^{59} +(6.33521 - 10.9729i) q^{61} +6.90833i q^{62} +(3.75810 + 3.86696i) q^{63} -11.0756 q^{64} +(3.10197 + 7.64268i) q^{66} +(-7.88407 + 4.55187i) q^{67} +(20.5554 - 11.8676i) q^{68} +(1.12946 + 2.78277i) q^{69} +1.27460 q^{71} +(6.32439 - 22.3232i) q^{72} -3.58770i q^{73} +(15.3218 - 26.5382i) q^{74} +(-7.31755 - 12.6744i) q^{76} +(2.81456 - 1.62499i) q^{77} +(1.23771 - 8.90941i) q^{78} +(1.05545 - 1.82809i) q^{79} +(7.66258 + 4.72068i) q^{81} +6.49602i q^{82} +(-0.951614 - 0.549415i) q^{83} +(-15.2223 - 2.11470i) q^{84} +(9.58431 + 16.6005i) q^{86} +(10.0684 + 7.84056i) q^{87} +(-12.1104 - 6.99195i) q^{88} +13.2935 q^{89} -3.54422 q^{91} +(-7.41277 - 4.27976i) q^{92} +(4.20969 - 1.70861i) q^{93} +(8.28580 + 14.3514i) q^{94} +(7.93115 + 19.5409i) q^{96} +(-3.31926 - 1.91638i) q^{97} -9.92718i q^{98} +(3.88998 - 3.78046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.28087 + 1.31686i 1.61282 + 0.931162i 0.988713 + 0.149823i \(0.0478703\pi\)
0.624107 + 0.781339i \(0.285463\pi\)
\(3\) 0.238330 1.71558i 0.137600 0.990488i
\(4\) 2.46825 + 4.27513i 1.23412 + 2.13757i
\(5\) 0 0
\(6\) 2.80278 3.59916i 1.14423 1.46935i
\(7\) −1.55662 0.898714i −0.588346 0.339682i 0.176097 0.984373i \(-0.443653\pi\)
−0.764443 + 0.644691i \(0.776986\pi\)
\(8\) 7.73393i 2.73436i
\(9\) −2.88640 0.817746i −0.962133 0.272582i
\(10\) 0 0
\(11\) −0.904062 + 1.56588i −0.272585 + 0.472131i −0.969523 0.245000i \(-0.921212\pi\)
0.696938 + 0.717131i \(0.254545\pi\)
\(12\) 7.92257 3.21558i 2.28705 0.928257i
\(13\) 1.70765 0.985914i 0.473618 0.273443i −0.244135 0.969741i \(-0.578504\pi\)
0.717753 + 0.696298i \(0.245171\pi\)
\(14\) −2.36696 4.09970i −0.632598 1.09569i
\(15\) 0 0
\(16\) −5.24801 + 9.08982i −1.31200 + 2.27246i
\(17\) 4.80812i 1.16614i −0.812421 0.583071i \(-0.801851\pi\)
0.812421 0.583071i \(-0.198149\pi\)
\(18\) −5.50664 5.66616i −1.29793 1.33553i
\(19\) −2.96467 −0.680142 −0.340071 0.940400i \(-0.610451\pi\)
−0.340071 + 0.940400i \(0.610451\pi\)
\(20\) 0 0
\(21\) −1.91280 + 2.45630i −0.417407 + 0.536010i
\(22\) −4.12410 + 2.38105i −0.879261 + 0.507641i
\(23\) −1.50162 + 0.866963i −0.313110 + 0.180774i −0.648317 0.761370i \(-0.724527\pi\)
0.335207 + 0.942144i \(0.391194\pi\)
\(24\) 13.2681 + 1.84323i 2.70835 + 0.376247i
\(25\) 0 0
\(26\) 5.19325 1.01848
\(27\) −2.09082 + 4.75694i −0.402379 + 0.915473i
\(28\) 8.87300i 1.67684i
\(29\) −3.68382 + 6.38057i −0.684069 + 1.18484i 0.289659 + 0.957130i \(0.406458\pi\)
−0.973728 + 0.227713i \(0.926875\pi\)
\(30\) 0 0
\(31\) 1.31151 + 2.27161i 0.235555 + 0.407993i 0.959434 0.281934i \(-0.0909760\pi\)
−0.723879 + 0.689927i \(0.757643\pi\)
\(32\) −10.5445 + 6.08789i −1.86403 + 1.07620i
\(33\) 2.47092 + 1.92418i 0.430132 + 0.334957i
\(34\) 6.33163 10.9667i 1.08587 1.88078i
\(35\) 0 0
\(36\) −3.62838 14.3581i −0.604729 2.39302i
\(37\) 11.6351i 1.91280i −0.292063 0.956399i \(-0.594342\pi\)
0.292063 0.956399i \(-0.405658\pi\)
\(38\) −6.76203 3.90406i −1.09695 0.633322i
\(39\) −1.28442 3.16458i −0.205673 0.506738i
\(40\) 0 0
\(41\) 1.23324 + 2.13603i 0.192600 + 0.333592i 0.946111 0.323842i \(-0.104975\pi\)
−0.753511 + 0.657435i \(0.771641\pi\)
\(42\) −7.59746 + 3.08362i −1.17231 + 0.475813i
\(43\) 6.30306 + 3.63907i 0.961207 + 0.554953i 0.896544 0.442954i \(-0.146069\pi\)
0.0646628 + 0.997907i \(0.479403\pi\)
\(44\) −8.92580 −1.34562
\(45\) 0 0
\(46\) −4.56668 −0.673321
\(47\) 5.44910 + 3.14604i 0.794833 + 0.458897i 0.841661 0.540006i \(-0.181578\pi\)
−0.0468283 + 0.998903i \(0.514911\pi\)
\(48\) 14.3435 + 11.1697i 2.07031 + 1.61221i
\(49\) −1.88463 3.26427i −0.269233 0.466324i
\(50\) 0 0
\(51\) −8.24870 1.14592i −1.15505 0.160461i
\(52\) 8.42983 + 4.86696i 1.16901 + 0.674926i
\(53\) 1.72540i 0.237001i 0.992954 + 0.118501i \(0.0378088\pi\)
−0.992954 + 0.118501i \(0.962191\pi\)
\(54\) −11.0331 + 8.09664i −1.50142 + 1.10181i
\(55\) 0 0
\(56\) 6.95059 12.0388i 0.928811 1.60875i
\(57\) −0.706570 + 5.08612i −0.0935875 + 0.673673i
\(58\) −16.8047 + 9.70218i −2.20656 + 1.27396i
\(59\) 5.51300 + 9.54880i 0.717732 + 1.24315i 0.961896 + 0.273414i \(0.0881529\pi\)
−0.244165 + 0.969734i \(0.578514\pi\)
\(60\) 0 0
\(61\) 6.33521 10.9729i 0.811141 1.40494i −0.100925 0.994894i \(-0.532180\pi\)
0.912066 0.410043i \(-0.134486\pi\)
\(62\) 6.90833i 0.877358i
\(63\) 3.75810 + 3.86696i 0.473476 + 0.487192i
\(64\) −11.0756 −1.38445
\(65\) 0 0
\(66\) 3.10197 + 7.64268i 0.381826 + 0.940748i
\(67\) −7.88407 + 4.55187i −0.963193 + 0.556100i −0.897154 0.441717i \(-0.854369\pi\)
−0.0660386 + 0.997817i \(0.521036\pi\)
\(68\) 20.5554 11.8676i 2.49271 1.43916i
\(69\) 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 \(0.475902\pi\)
\(72\) 6.32439 22.3232i 0.745336 2.63081i
\(73\) 3.58770i 0.419908i −0.977711 0.209954i \(-0.932669\pi\)
0.977711 0.209954i \(-0.0673315\pi\)
\(74\) 15.3218 26.5382i 1.78112 3.08500i
\(75\) 0 0
\(76\) −7.31755 12.6744i −0.839380 1.45385i
\(77\) 2.81456 1.62499i 0.320749 0.185184i
\(78\) 1.23771 8.90941i 0.140143 1.00879i
\(79\) 1.05545 1.82809i 0.118747 0.205676i −0.800524 0.599300i \(-0.795445\pi\)
0.919272 + 0.393624i \(0.128779\pi\)
\(80\) 0 0
\(81\) 7.66258 + 4.72068i 0.851398 + 0.524520i
\(82\) 6.49602i 0.717366i
\(83\) −0.951614 0.549415i −0.104453 0.0603061i 0.446863 0.894602i \(-0.352541\pi\)
−0.551317 + 0.834296i \(0.685874\pi\)
\(84\) −15.2223 2.11470i −1.66089 0.230733i
\(85\) 0 0
\(86\) 9.58431 + 16.6005i 1.03350 + 1.79008i
\(87\) 10.0684 + 7.84056i 1.07944 + 0.840596i
\(88\) −12.1104 6.99195i −1.29097 0.745344i
\(89\) 13.2935 1.40910 0.704552 0.709653i \(-0.251148\pi\)
0.704552 + 0.709653i \(0.251148\pi\)
\(90\) 0 0
\(91\) −3.54422 −0.371535
\(92\) −7.41277 4.27976i −0.772834 0.446196i
\(93\) 4.20969 1.70861i 0.436524 0.177174i
\(94\) 8.28580 + 14.3514i 0.854615 + 1.48024i
\(95\) 0 0
\(96\) 7.93115 + 19.5409i 0.809470 + 1.99438i
\(97\) −3.31926 1.91638i −0.337020 0.194579i 0.321933 0.946762i \(-0.395667\pi\)
−0.658954 + 0.752184i \(0.729001\pi\)
\(98\) 9.92718i 1.00280i
\(99\) 3.88998 3.78046i 0.390957 0.379951i
\(100\) 0 0
\(101\) −3.27618 + 5.67452i −0.325993 + 0.564636i −0.981713 0.190368i \(-0.939032\pi\)
0.655720 + 0.755004i \(0.272365\pi\)
\(102\) −17.3052 13.4761i −1.71347 1.33433i
\(103\) −6.99365 + 4.03779i −0.689105 + 0.397855i −0.803277 0.595606i \(-0.796912\pi\)
0.114172 + 0.993461i \(0.463579\pi\)
\(104\) 7.62499 + 13.2069i 0.747691 + 1.29504i
\(105\) 0 0
\(106\) −2.27211 + 3.93541i −0.220687 + 0.382241i
\(107\) 8.97674i 0.867814i 0.900958 + 0.433907i \(0.142865\pi\)
−0.900958 + 0.433907i \(0.857135\pi\)
\(108\) −25.4972 + 2.80278i −2.45347 + 0.269697i
\(109\) 6.34164 0.607419 0.303710 0.952765i \(-0.401775\pi\)
0.303710 + 0.952765i \(0.401775\pi\)
\(110\) 0 0
\(111\) −19.9609 2.77299i −1.89460 0.263201i
\(112\) 16.3383 9.43292i 1.54382 0.891327i
\(113\) −12.9060 + 7.45127i −1.21409 + 0.700957i −0.963648 0.267174i \(-0.913910\pi\)
−0.250444 + 0.968131i \(0.580577\pi\)
\(114\) −8.30931 + 10.6703i −0.778238 + 0.999367i
\(115\) 0 0
\(116\) −36.3704 −3.37691
\(117\) −5.73519 + 1.44931i −0.530219 + 0.133989i
\(118\) 29.0394i 2.67330i
\(119\) −4.32113 + 7.48441i −0.396117 + 0.686095i
\(120\) 0 0
\(121\) 3.86534 + 6.69497i 0.351395 + 0.608634i
\(122\) 28.8996 16.6852i 2.61645 1.51061i
\(123\) 3.95845 1.60663i 0.356921 0.144865i
\(124\) −6.47428 + 11.2138i −0.581408 + 1.00703i
\(125\) 0 0
\(126\) 3.47948 + 13.7689i 0.309977 + 1.22663i
\(127\) 3.62303i 0.321492i −0.986996 0.160746i \(-0.948610\pi\)
0.986996 0.160746i \(-0.0513899\pi\)
\(128\) −4.17289 2.40922i −0.368835 0.212947i
\(129\) 7.74531 9.94607i 0.681936 0.875703i
\(130\) 0 0
\(131\) −3.64673 6.31631i −0.318616 0.551859i 0.661584 0.749871i \(-0.269885\pi\)
−0.980200 + 0.198012i \(0.936551\pi\)
\(132\) −2.12729 + 15.3129i −0.185157 + 1.33282i
\(133\) 4.61486 + 2.66439i 0.400159 + 0.231032i
\(134\) −23.9767 −2.07127
\(135\) 0 0
\(136\) 37.1857 3.18865
\(137\) −6.17148 3.56310i −0.527265 0.304417i 0.212637 0.977131i \(-0.431795\pi\)
−0.739902 + 0.672715i \(0.765128\pi\)
\(138\) −1.08838 + 7.83449i −0.0926488 + 0.666916i
\(139\) −7.35533 12.7398i −0.623871 1.08058i −0.988758 0.149525i \(-0.952226\pi\)
0.364887 0.931052i \(-0.381108\pi\)
\(140\) 0 0
\(141\) 6.69595 8.59855i 0.563901 0.724128i
\(142\) 2.90721 + 1.67848i 0.243967 + 0.140855i
\(143\) 3.56531i 0.298146i
\(144\) 22.5810 21.9453i 1.88175 1.82878i
\(145\) 0 0
\(146\) 4.72450 8.18308i 0.391003 0.677236i
\(147\) −6.04927 + 2.45525i −0.498935 + 0.202505i
\(148\) 49.7416 28.7183i 4.08873 2.36063i
\(149\) −0.282655 0.489572i −0.0231560 0.0401073i 0.854215 0.519920i \(-0.174038\pi\)
−0.877371 + 0.479812i \(0.840705\pi\)
\(150\) 0 0
\(151\) −0.0766925 + 0.132835i −0.00624115 + 0.0108100i −0.869129 0.494585i \(-0.835320\pi\)
0.862888 + 0.505395i \(0.168653\pi\)
\(152\) 22.9285i 1.85975i
\(153\) −3.93183 + 13.8782i −0.317869 + 1.12198i
\(154\) 8.55953 0.689746
\(155\) 0 0
\(156\) 10.3587 13.3021i 0.829362 1.06502i
\(157\) 9.92525 5.73035i 0.792121 0.457332i −0.0485874 0.998819i \(-0.515472\pi\)
0.840709 + 0.541487i \(0.182139\pi\)
\(158\) 4.81469 2.77976i 0.383036 0.221146i
\(159\) 2.96005 + 0.411214i 0.234747 + 0.0326114i
\(160\) 0 0
\(161\) 3.11661 0.245623
\(162\) 11.2609 + 20.8578i 0.884738 + 1.63875i
\(163\) 22.0595i 1.72783i −0.503637 0.863915i \(-0.668005\pi\)
0.503637 0.863915i \(-0.331995\pi\)
\(164\) −6.08789 + 10.5445i −0.475384 + 0.823389i
\(165\) 0 0
\(166\) −1.44701 2.50629i −0.112310 0.194526i
\(167\) −14.7817 + 8.53421i −1.14384 + 0.660397i −0.947379 0.320115i \(-0.896279\pi\)
−0.196462 + 0.980511i \(0.562945\pi\)
\(168\) −18.9969 14.7935i −1.46564 1.14134i
\(169\) −4.55595 + 7.89113i −0.350457 + 0.607010i
\(170\) 0 0
\(171\) 8.55722 + 2.42435i 0.654387 + 0.185395i
\(172\) 35.9285i 2.73953i
\(173\) −10.3444 5.97233i −0.786468 0.454067i 0.0522497 0.998634i \(-0.483361\pi\)
−0.838718 + 0.544567i \(0.816694\pi\)
\(174\) 12.6398 + 31.1420i 0.958218 + 2.36087i
\(175\) 0 0
\(176\) −9.48906 16.4355i −0.715265 1.23887i
\(177\) 17.6956 7.18221i 1.33008 0.539848i
\(178\) 30.3207 + 17.5056i 2.27263 + 1.31210i
\(179\) −8.54921 −0.638998 −0.319499 0.947587i \(-0.603515\pi\)
−0.319499 + 0.947587i \(0.603515\pi\)
\(180\) 0 0
\(181\) −10.5524 −0.784351 −0.392176 0.919890i \(-0.628277\pi\)
−0.392176 + 0.919890i \(0.628277\pi\)
\(182\) −8.08390 4.66724i −0.599219 0.345959i
\(183\) −17.3150 13.4837i −1.27996 0.996744i
\(184\) −6.70503 11.6135i −0.494301 0.856155i
\(185\) 0 0
\(186\) 11.8518 + 1.64646i 0.869013 + 0.120724i
\(187\) 7.52895 + 4.34684i 0.550571 + 0.317873i
\(188\) 31.0608i 2.26534i
\(189\) 7.52973 5.52569i 0.547708 0.401935i
\(190\) 0 0
\(191\) 8.66862 15.0145i 0.627239 1.08641i −0.360864 0.932618i \(-0.617518\pi\)
0.988103 0.153792i \(-0.0491485\pi\)
\(192\) −2.63964 + 19.0010i −0.190500 + 1.37128i
\(193\) 1.35059 0.779763i 0.0972175 0.0561286i −0.450603 0.892724i \(-0.648791\pi\)
0.547821 + 0.836596i \(0.315458\pi\)
\(194\) −5.04721 8.74202i −0.362369 0.627641i
\(195\) 0 0
\(196\) 9.30346 16.1141i 0.664533 1.15100i
\(197\) 17.9767i 1.28079i −0.768046 0.640395i \(-0.778771\pi\)
0.768046 0.640395i \(-0.221229\pi\)
\(198\) 13.8509 3.50019i 0.984339 0.248748i
\(199\) −11.0225 −0.781362 −0.390681 0.920526i \(-0.627760\pi\)
−0.390681 + 0.920526i \(0.627760\pi\)
\(200\) 0 0
\(201\) 5.93007 + 14.6106i 0.418275 + 1.03055i
\(202\) −14.9451 + 8.62856i −1.05153 + 0.607104i
\(203\) 11.4686 6.62141i 0.804939 0.464732i
\(204\) −15.4609 38.0927i −1.08248 2.66702i
\(205\) 0 0
\(206\) −21.2688 −1.48187
\(207\) 5.04324 1.27445i 0.350529 0.0885806i
\(208\) 20.6964i 1.43503i
\(209\) 2.68025 4.64232i 0.185397 0.321116i
\(210\) 0 0
\(211\) 11.9643 + 20.7227i 0.823655 + 1.42661i 0.902943 + 0.429760i \(0.141402\pi\)
−0.0792886 + 0.996852i \(0.525265\pi\)
\(212\) −7.37630 + 4.25871i −0.506606 + 0.292489i
\(213\) 0.303776 2.18668i 0.0208144 0.149829i
\(214\) −11.8211 + 20.4748i −0.808076 + 1.39963i
\(215\) 0 0
\(216\) −36.7898 16.1703i −2.50323 1.10025i
\(217\) 4.71470i 0.320055i
\(218\) 14.4645 + 8.35107i 0.979658 + 0.565606i
\(219\) −6.15497 0.855056i −0.415914 0.0577793i
\(220\) 0 0
\(221\) −4.74040 8.21061i −0.318874 0.552305i
\(222\) −41.8766 32.6106i −2.81057 2.18868i
\(223\) −18.8020 10.8553i −1.25907 0.726927i −0.286180 0.958176i \(-0.592385\pi\)
−0.972895 + 0.231249i \(0.925719\pi\)
\(224\) 21.8851 1.46226
\(225\) 0 0
\(226\) −39.2492 −2.61082
\(227\) 12.2111 + 7.05010i 0.810481 + 0.467932i 0.847123 0.531397i \(-0.178333\pi\)
−0.0366416 + 0.999328i \(0.511666\pi\)
\(228\) −23.4878 + 9.53312i −1.55552 + 0.631347i
\(229\) 1.83879 + 3.18488i 0.121511 + 0.210463i 0.920364 0.391064i \(-0.127893\pi\)
−0.798853 + 0.601526i \(0.794559\pi\)
\(230\) 0 0
\(231\) −2.11699 5.21587i −0.139288 0.343179i
\(232\) −49.3469 28.4904i −3.23978 1.87049i
\(233\) 5.34164i 0.349943i −0.984574 0.174971i \(-0.944017\pi\)
0.984574 0.174971i \(-0.0559833\pi\)
\(234\) −14.9898 4.24676i −0.979913 0.277619i
\(235\) 0 0
\(236\) −27.2149 + 47.1376i −1.77154 + 3.06840i
\(237\) −2.88469 2.24639i −0.187380 0.145919i
\(238\) −19.7119 + 11.3807i −1.27773 + 0.737698i
\(239\) −11.0167 19.0815i −0.712613 1.23428i −0.963873 0.266362i \(-0.914178\pi\)
0.251260 0.967920i \(-0.419155\pi\)
\(240\) 0 0
\(241\) 9.32358 16.1489i 0.600585 1.04024i −0.392148 0.919902i \(-0.628268\pi\)
0.992733 0.120341i \(-0.0383988\pi\)
\(242\) 20.3605i 1.30882i
\(243\) 9.92491 12.0207i 0.636683 0.771126i
\(244\) 62.5475 4.00420
\(245\) 0 0
\(246\) 11.1444 + 1.54820i 0.710542 + 0.0987095i
\(247\) −5.06263 + 2.92291i −0.322127 + 0.185980i
\(248\) −17.5684 + 10.1431i −1.11560 + 0.644091i
\(249\) −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 \(0.346520\pi\)
\(252\) −7.25586 + 25.6110i −0.457076 + 1.61334i
\(253\) 3.13515i 0.197105i
\(254\) 4.77103 8.26366i 0.299361 0.518508i
\(255\) 0 0
\(256\) 4.73035 + 8.19320i 0.295647 + 0.512075i
\(257\) −19.2335 + 11.1045i −1.19975 + 0.692678i −0.960500 0.278280i \(-0.910236\pi\)
−0.239253 + 0.970957i \(0.576902\pi\)
\(258\) 30.7637 12.4862i 1.91526 0.777357i
\(259\) −10.4566 + 18.1114i −0.649743 + 1.12539i
\(260\) 0 0
\(261\) 15.8507 15.4044i 0.981132 0.953510i
\(262\) 19.2089i 1.18673i
\(263\) −4.97100 2.87001i −0.306525 0.176972i 0.338846 0.940842i \(-0.389964\pi\)
−0.645370 + 0.763870i \(0.723297\pi\)
\(264\) −14.8815 + 19.1099i −0.915892 + 1.17613i
\(265\) 0 0
\(266\) 7.01727 + 12.1543i 0.430256 + 0.745226i
\(267\) 3.16823 22.8059i 0.193892 1.39570i
\(268\) −38.9197 22.4703i −2.37740 1.37259i
\(269\) 15.6162 0.952139 0.476070 0.879408i \(-0.342061\pi\)
0.476070 + 0.879408i \(0.342061\pi\)
\(270\) 0 0
\(271\) −6.75315 −0.410225 −0.205112 0.978738i \(-0.565756\pi\)
−0.205112 + 0.978738i \(0.565756\pi\)
\(272\) 43.7050 + 25.2331i 2.65000 + 1.52998i
\(273\) −0.844693 + 6.08037i −0.0511232 + 0.368001i
\(274\) −9.38423 16.2540i −0.566922 0.981938i
\(275\) 0 0
\(276\) −9.10894 + 11.6972i −0.548294 + 0.704087i
\(277\) 26.2376 + 15.1483i 1.57646 + 0.910172i 0.995347 + 0.0963529i \(0.0307177\pi\)
0.581118 + 0.813820i \(0.302616\pi\)
\(278\) 38.7438i 2.32370i
\(279\) −1.92795 7.62925i −0.115423 0.456751i
\(280\) 0 0
\(281\) −9.31755 + 16.1385i −0.555838 + 0.962740i 0.441999 + 0.897015i \(0.354269\pi\)
−0.997838 + 0.0657249i \(0.979064\pi\)
\(282\) 26.5957 10.7945i 1.58375 0.642805i
\(283\) −4.91354 + 2.83683i −0.292079 + 0.168632i −0.638879 0.769307i \(-0.720602\pi\)
0.346800 + 0.937939i \(0.387268\pi\)
\(284\) 3.14604 + 5.44910i 0.186683 + 0.323345i
\(285\) 0 0
\(286\) −4.69502 + 8.13201i −0.277622 + 0.480856i
\(287\) 4.43332i 0.261690i
\(288\) 35.4141 8.94931i 2.08679 0.527343i
\(289\) −6.11806 −0.359886
\(290\) 0 0
\(291\) −4.07877 + 5.23772i −0.239102 + 0.307040i
\(292\) 15.3379 8.85533i 0.897582 0.518219i
\(293\) 15.8286 9.13867i 0.924720 0.533887i 0.0395819 0.999216i \(-0.487397\pi\)
0.885138 + 0.465329i \(0.154064\pi\)
\(294\) −17.0308 2.36594i −0.993257 0.137985i
\(295\) 0 0
\(296\) 89.9850 5.23027
\(297\) −5.55857 7.57454i −0.322541 0.439520i
\(298\) 1.48887i 0.0862478i
\(299\) −1.70950 + 2.96094i −0.0988631 + 0.171236i
\(300\) 0 0
\(301\) −6.54097 11.3293i −0.377015 0.653009i
\(302\) −0.349852 + 0.201987i −0.0201317 + 0.0116230i
\(303\) 8.95425 + 6.97295i 0.514408 + 0.400585i
\(304\) 15.5586 26.9483i 0.892349 1.54559i
\(305\) 0 0
\(306\) −27.2436 + 26.4766i −1.55741 + 1.51357i
\(307\) 15.5050i 0.884915i 0.896789 + 0.442458i \(0.145893\pi\)
−0.896789 + 0.442458i \(0.854107\pi\)
\(308\) 13.8941 + 8.02174i 0.791688 + 0.457081i
\(309\) 5.26033 + 12.9605i 0.299250 + 0.737295i
\(310\) 0 0
\(311\) −15.2232 26.3673i −0.863228 1.49515i −0.868796 0.495170i \(-0.835106\pi\)
0.00556798 0.999984i \(-0.498228\pi\)
\(312\) 24.4746 9.93365i 1.38560 0.562382i
\(313\) 6.01832 + 3.47468i 0.340176 + 0.196401i 0.660350 0.750958i \(-0.270408\pi\)
−0.320174 + 0.947359i \(0.603741\pi\)
\(314\) 30.1843 1.70340
\(315\) 0 0
\(316\) 10.4205 0.586196
\(317\) −13.9820 8.07253i −0.785309 0.453398i 0.0529995 0.998595i \(-0.483122\pi\)
−0.838308 + 0.545196i \(0.816455\pi\)
\(318\) 6.20998 + 4.83590i 0.348238 + 0.271184i
\(319\) −6.66081 11.5369i −0.372934 0.645940i
\(320\) 0 0
\(321\) 15.4003 + 2.13943i 0.859560 + 0.119411i
\(322\) 7.10858 + 4.10414i 0.396146 + 0.228715i
\(323\) 14.2545i 0.793142i
\(324\) −1.26838 + 44.4104i −0.0704655 + 2.46724i
\(325\) 0 0
\(326\) 29.0493 50.3148i 1.60889 2.78668i
\(327\) 1.51140 10.8796i 0.0835808 0.601642i
\(328\) −16.5199 + 9.53779i −0.912160 + 0.526636i
\(329\) −5.65478 9.79436i −0.311758 0.539981i
\(330\) 0 0
\(331\) −6.31112 + 10.9312i −0.346890 + 0.600832i −0.985695 0.168537i \(-0.946096\pi\)
0.638805 + 0.769369i \(0.279429\pi\)
\(332\) 5.42437i 0.297701i
\(333\) −9.51456 + 33.5835i −0.521394 + 1.84037i
\(334\) −44.9535 −2.45975
\(335\) 0 0
\(336\) −12.2890 30.2777i −0.670419 1.65179i
\(337\) 5.99324 3.46020i 0.326473 0.188489i −0.327801 0.944747i \(-0.606308\pi\)
0.654274 + 0.756258i \(0.272974\pi\)
\(338\) −20.7831 + 11.9991i −1.13045 + 0.652665i
\(339\) 9.70734 + 23.9170i 0.527230 + 1.29900i
\(340\) 0 0
\(341\) −4.74276 −0.256835
\(342\) 16.3254 + 16.7983i 0.882776 + 0.908348i
\(343\) 19.3570i 1.04518i
\(344\) −28.1443 + 48.7474i −1.51744 + 2.62828i
\(345\) 0 0
\(346\) −15.7295 27.2442i −0.845621 1.46466i
\(347\) −11.9566 + 6.90317i −0.641866 + 0.370581i −0.785333 0.619074i \(-0.787508\pi\)
0.143467 + 0.989655i \(0.454175\pi\)
\(348\) −8.66816 + 62.3962i −0.464662 + 3.34479i
\(349\) 3.28384 5.68778i 0.175780 0.304460i −0.764651 0.644445i \(-0.777089\pi\)
0.940431 + 0.339985i \(0.110422\pi\)
\(350\) 0 0
\(351\) 1.11954 + 10.1846i 0.0597564 + 0.543612i
\(352\) 22.0153i 1.17342i
\(353\) 3.05273 + 1.76250i 0.162481 + 0.0938082i 0.579035 0.815302i \(-0.303429\pi\)
−0.416555 + 0.909111i \(0.636763\pi\)
\(354\) 49.8194 + 6.92097i 2.64787 + 0.367846i
\(355\) 0 0
\(356\) 32.8116 + 56.8313i 1.73901 + 3.01205i
\(357\) 11.8102 + 9.19698i 0.625063 + 0.486756i
\(358\) −19.4996 11.2581i −1.03059 0.595010i
\(359\) −22.9285 −1.21012 −0.605061 0.796179i \(-0.706851\pi\)
−0.605061 + 0.796179i \(0.706851\pi\)
\(360\) 0 0
\(361\) −10.2107 −0.537407
\(362\) −24.0686 13.8960i −1.26502 0.730358i
\(363\) 12.4070 5.03568i 0.651196 0.264304i
\(364\) −8.74801 15.1520i −0.458520 0.794181i
\(365\) 0 0
\(366\) −21.7371 53.5560i −1.13621 2.79942i
\(367\) 3.61939 + 2.08966i 0.188931 + 0.109079i 0.591482 0.806318i \(-0.298543\pi\)
−0.402551 + 0.915397i \(0.631876\pi\)
\(368\) 18.1993i 0.948706i
\(369\) −1.81289 7.17392i −0.0943751 0.373459i
\(370\) 0 0
\(371\) 1.55064 2.68578i 0.0805051 0.139439i
\(372\) 17.6951 + 13.7797i 0.917447 + 0.714444i
\(373\) 5.92440 3.42045i 0.306754 0.177104i −0.338719 0.940888i \(-0.609994\pi\)
0.645473 + 0.763783i \(0.276660\pi\)
\(374\) 11.4484 + 19.8292i 0.591982 + 1.02534i
\(375\) 0 0
\(376\) −24.3312 + 42.1429i −1.25479 + 2.17336i
\(377\) 14.5277i 0.748217i
\(378\) 24.4509 2.68776i 1.25762 0.138244i
\(379\) 12.7764 0.656280 0.328140 0.944629i \(-0.393578\pi\)
0.328140 + 0.944629i \(0.393578\pi\)
\(380\) 0 0
\(381\) −6.21558 0.863476i −0.318434 0.0442372i
\(382\) 39.5440 22.8307i 2.02325 1.16812i
\(383\) 6.52515 3.76730i 0.333420 0.192500i −0.323939 0.946078i \(-0.605007\pi\)
0.657358 + 0.753578i \(0.271674\pi\)
\(384\) −5.12773 + 6.58472i −0.261673 + 0.336025i
\(385\) 0 0
\(386\) 4.10736 0.209059
\(387\) −15.2173 15.6581i −0.773538 0.795946i
\(388\) 18.9204i 0.960538i
\(389\) 2.72588 4.72135i 0.138207 0.239382i −0.788611 0.614893i \(-0.789199\pi\)
0.926818 + 0.375511i \(0.122533\pi\)
\(390\) 0 0
\(391\) 4.16847 + 7.22000i 0.210808 + 0.365131i
\(392\) 25.2456 14.5756i 1.27510 0.736177i
\(393\) −11.7052 + 4.75087i −0.590451 + 0.239649i
\(394\) 23.6729 41.0026i 1.19262 2.06568i
\(395\) 0 0
\(396\) 25.7634 + 7.29904i 1.29466 + 0.366791i
\(397\) 5.64549i 0.283339i 0.989914 + 0.141670i \(0.0452470\pi\)
−0.989914 + 0.141670i \(0.954753\pi\)
\(398\) −25.1408 14.5151i −1.26020 0.727574i
\(399\) 5.67082 7.28214i 0.283896 0.364563i
\(400\) 0 0
\(401\) 2.75209 + 4.76676i 0.137433 + 0.238040i 0.926524 0.376235i \(-0.122782\pi\)
−0.789091 + 0.614276i \(0.789448\pi\)
\(402\) −5.71438 + 41.1339i −0.285007 + 2.05157i
\(403\) 4.47922 + 2.58608i 0.223126 + 0.128822i
\(404\) −32.3458 −1.60926
\(405\) 0 0
\(406\) 34.8779 1.73096
\(407\) 18.2192 + 10.5188i 0.903091 + 0.521400i
\(408\) 8.86246 63.7948i 0.438757 3.15831i
\(409\) 16.4265 + 28.4515i 0.812238 + 1.40684i 0.911295 + 0.411755i \(0.135084\pi\)
−0.0990570 + 0.995082i \(0.531583\pi\)
\(410\) 0 0
\(411\) −7.58362 + 9.73844i −0.374072 + 0.480362i
\(412\) −34.5241 19.9325i −1.70088 0.982005i
\(413\) 19.8184i 0.975202i
\(414\) 13.1813 + 3.73439i 0.647824 + 0.183535i
\(415\) 0 0
\(416\) −12.0043 + 20.7920i −0.588558 + 1.01941i
\(417\) −23.6091 + 9.58235i −1.15614 + 0.469250i
\(418\) 12.2266 7.05903i 0.598022 0.345268i
\(419\) 11.4295 + 19.7965i 0.558369 + 0.967124i 0.997633 + 0.0687656i \(0.0219060\pi\)
−0.439264 + 0.898358i \(0.644761\pi\)
\(420\) 0 0
\(421\) −8.97071 + 15.5377i −0.437205 + 0.757262i −0.997473 0.0710498i \(-0.977365\pi\)
0.560267 + 0.828312i \(0.310698\pi\)
\(422\) 63.0212i 3.06782i
\(423\) −13.1556 13.5367i −0.639648 0.658177i
\(424\) −13.3441 −0.648046
\(425\) 0 0
\(426\) 3.57243 4.58750i 0.173085 0.222265i
\(427\) −19.7230 + 11.3871i −0.954463 + 0.551060i
\(428\) −38.3768 + 22.1568i −1.85501 + 1.07099i
\(429\) 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 \(0.547622\pi\)
\(432\) −32.2671 43.9697i −1.55245 2.11549i
\(433\) 3.11806i 0.149844i −0.997189 0.0749221i \(-0.976129\pi\)
0.997189 0.0749221i \(-0.0238708\pi\)
\(434\) 6.20861 10.7536i 0.298023 0.516190i
\(435\) 0 0
\(436\) 15.6528 + 27.1114i 0.749631 + 1.29840i
\(437\) 4.45182 2.57026i 0.212960 0.122952i
\(438\) −12.9127 10.0555i −0.616992 0.480471i
\(439\) 6.75494 11.6999i 0.322396 0.558406i −0.658586 0.752505i \(-0.728845\pi\)
0.980982 + 0.194100i \(0.0621785\pi\)
\(440\) 0 0
\(441\) 2.77044 + 10.9631i 0.131926 + 0.522054i
\(442\) 24.9698i 1.18769i
\(443\) 21.0248 + 12.1387i 0.998918 + 0.576726i 0.907928 0.419126i \(-0.137663\pi\)
0.0909904 + 0.995852i \(0.470997\pi\)
\(444\) −37.4135 92.1799i −1.77557 4.37466i
\(445\) 0 0
\(446\) −28.5899 49.5192i −1.35377 2.34480i
\(447\) −0.907263 + 0.368236i −0.0429121 + 0.0174169i
\(448\) 17.2404 + 9.95377i 0.814534 + 0.470271i
\(449\) 24.1437 1.13941 0.569705 0.821849i \(-0.307057\pi\)
0.569705 + 0.821849i \(0.307057\pi\)
\(450\) 0 0
\(451\) −4.45970 −0.209999
\(452\) −63.7104 36.7832i −2.99668 1.73014i
\(453\) 0.209611 + 0.163230i 0.00984838 + 0.00766924i
\(454\) 18.5680 + 32.1607i 0.871440 + 1.50938i
\(455\) 0 0
\(456\) −39.3357 5.46456i −1.84206 0.255902i
\(457\) −2.44355 1.41078i −0.114304 0.0659937i 0.441758 0.897134i \(-0.354355\pi\)
−0.556062 + 0.831141i \(0.687688\pi\)
\(458\) 9.68573i 0.452585i
\(459\) 22.8720 + 10.0529i 1.06757 + 0.469230i
\(460\) 0 0
\(461\) −10.7286 + 18.5825i −0.499681 + 0.865474i −1.00000 0.000367761i \(-0.999883\pi\)
0.500318 + 0.865841i \(0.333216\pi\)
\(462\) 2.03999 14.6845i 0.0949090 0.683185i
\(463\) −17.1502 + 9.90167i −0.797037 + 0.460170i −0.842434 0.538799i \(-0.818878\pi\)
0.0453970 + 0.998969i \(0.485545\pi\)
\(464\) −38.6655 66.9706i −1.79500 3.10903i
\(465\) 0 0
\(466\) 7.03421 12.1836i 0.325853 0.564395i
\(467\) 22.7210i 1.05140i −0.850669 0.525701i \(-0.823803\pi\)
0.850669 0.525701i \(-0.176197\pi\)
\(468\) −20.3519 20.9415i −0.940767 0.968019i
\(469\) 16.3633 0.755588
\(470\) 0 0
\(471\) −7.46536 18.3932i −0.343986 0.847516i
\(472\) −73.8497 + 42.6372i −3.39921 + 1.96253i
\(473\) −11.3967 + 6.57989i −0.524021 + 0.302544i
\(474\) −3.62141 8.92247i −0.166337 0.409822i
\(475\) 0 0
\(476\) −42.6625 −1.95543
\(477\) 1.41094 4.98018i 0.0646023 0.228027i
\(478\) 58.0300i 2.65423i
\(479\) 10.6440 18.4359i 0.486336 0.842359i −0.513541 0.858065i \(-0.671666\pi\)
0.999877 + 0.0157065i \(0.00499974\pi\)
\(480\) 0 0
\(481\) −11.4712 19.8687i −0.523042 0.905935i
\(482\) 42.5318 24.5557i 1.93727 1.11848i
\(483\) 0.742781 5.34677i 0.0337977 0.243287i
\(484\) −19.0813 + 33.0497i −0.867330 + 1.50226i
\(485\) 0 0
\(486\) 38.4670 14.3478i 1.74490 0.650831i
\(487\) 9.58690i 0.434424i 0.976124 + 0.217212i \(0.0696963\pi\)
−0.976124 + 0.217212i \(0.930304\pi\)
\(488\) 84.8637 + 48.9961i 3.84160 + 2.21795i
\(489\) −37.8447 5.25743i −1.71140 0.237749i
\(490\) 0 0
\(491\) 18.9222 + 32.7742i 0.853945 + 1.47908i 0.877620 + 0.479357i \(0.159130\pi\)
−0.0236745 + 0.999720i \(0.507537\pi\)
\(492\) 16.6390 + 12.9573i 0.750144 + 0.584160i
\(493\) 30.6786 + 17.7123i 1.38169 + 0.797721i
\(494\) −15.3963 −0.692711
\(495\) 0 0
\(496\) −27.5314 −1.23619
\(497\) −1.98407 1.14550i −0.0889977 0.0513829i
\(498\) −4.64459 + 1.88513i −0.208129 + 0.0844745i
\(499\) 8.46266 + 14.6577i 0.378840 + 0.656171i 0.990894 0.134646i \(-0.0429896\pi\)
−0.612053 + 0.790816i \(0.709656\pi\)
\(500\) 0 0
\(501\) 11.1182 + 27.3930i 0.496723 + 1.22383i
\(502\) 33.5126 + 19.3485i 1.49574 + 0.863566i
\(503\) 40.4168i 1.80210i 0.433719 + 0.901048i \(0.357201\pi\)
−0.433719 + 0.901048i \(0.642799\pi\)
\(504\) −29.9068 + 29.0649i −1.33216 + 1.29465i
\(505\) 0 0
\(506\) 4.12856 7.15088i 0.183537 0.317896i
\(507\) 12.4520 + 9.69676i 0.553013 + 0.430648i
\(508\) 15.4889 8.94253i 0.687210 0.396761i
\(509\) −20.7034 35.8593i −0.917660 1.58943i −0.802959 0.596034i \(-0.796742\pi\)
−0.114701 0.993400i \(-0.536591\pi\)
\(510\) 0 0
\(511\) −3.22431 + 5.58467i −0.142635 + 0.247051i
\(512\) 34.5537i 1.52707i
\(513\) 6.19860 14.1028i 0.273675 0.622652i
\(514\) −58.4922 −2.57998
\(515\) 0 0
\(516\) 61.6381 + 8.56285i 2.71347 + 0.376959i
\(517\) −9.85265 + 5.68843i −0.433319 + 0.250177i
\(518\) −47.7004 + 27.5398i −2.09584 + 1.21003i
\(519\) −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 \(0.621689\pi\)
\(522\) 56.4389 14.2624i 2.47026 0.624248i
\(523\) 9.57651i 0.418751i 0.977835 + 0.209376i \(0.0671432\pi\)
−0.977835 + 0.209376i \(0.932857\pi\)
\(524\) 18.0021 31.1805i 0.786424 1.36213i
\(525\) 0 0
\(526\) −7.55880 13.0922i −0.329579 0.570848i
\(527\) 10.9222 6.30592i 0.475777 0.274690i
\(528\) −30.4579 + 12.3621i −1.32551 + 0.537992i
\(529\) −9.99675 + 17.3149i −0.434641 + 0.752821i
\(530\) 0 0
\(531\) −8.10422 32.0699i −0.351693 1.39171i
\(532\) 26.3055i 1.14049i
\(533\) 4.21189 + 2.43174i 0.182437 + 0.105330i
\(534\) 37.2586 47.8452i 1.61234 2.07047i
\(535\) 0 0
\(536\) −35.2038 60.9748i −1.52057 2.63371i
\(537\) −2.03753 + 14.6668i −0.0879260 + 0.632920i
\(538\) 35.6187 + 20.5644i 1.53563 + 0.886596i
\(539\) 6.81528 0.293555
\(540\) 0 0
\(541\) −0.833751 −0.0358458 −0.0179229 0.999839i \(-0.505705\pi\)
−0.0179229 + 0.999839i \(0.505705\pi\)
\(542\) −15.4031 8.89297i −0.661619 0.381986i
\(543\) −2.51495 + 18.1034i −0.107927 + 0.776891i
\(544\) 29.2713 + 50.6994i 1.25500 + 2.17372i
\(545\) 0 0
\(546\) −9.93365 + 12.7562i −0.425121 + 0.545915i
\(547\) −24.5319 14.1635i −1.04891 0.605587i −0.126565 0.991958i \(-0.540395\pi\)
−0.922343 + 0.386371i \(0.873728\pi\)
\(548\) 35.1785i 1.50275i
\(549\) −27.2590 + 26.4916i −1.16339 + 1.13063i
\(550\) 0 0
\(551\) 10.9213 18.9163i 0.465264 0.805861i
\(552\) −21.5218 + 8.73515i −0.916027 + 0.371793i
\(553\) −3.28586 + 1.89709i −0.139729 + 0.0806727i
\(554\) 39.8964 + 69.1026i 1.69504 + 2.93589i
\(555\) 0 0
\(556\) 36.3096 62.8901i 1.53987 2.66713i
\(557\) 11.5042i 0.487448i −0.969845 0.243724i \(-0.921631\pi\)
0.969845 0.243724i \(-0.0783690\pi\)
\(558\) 5.64926 19.9402i 0.239152 0.844135i
\(559\) 14.3512 0.606993
\(560\) 0 0
\(561\) 9.25171 11.8805i 0.390608 0.501595i
\(562\) −42.5043 + 24.5398i −1.79293 + 1.03515i
\(563\) 28.5840 16.5030i 1.20467 0.695517i 0.243080 0.970006i \(-0.421842\pi\)
0.961590 + 0.274490i \(0.0885089\pi\)
\(564\) 53.2872 + 7.40273i 2.24380 + 0.311711i
\(565\) 0 0
\(566\) −14.9429 −0.628095
\(567\) −7.68517 14.2348i −0.322747 0.597804i
\(568\) 9.85769i 0.413619i
\(569\) −13.5044 + 23.3903i −0.566135 + 0.980574i 0.430809 + 0.902443i \(0.358228\pi\)
−0.996943 + 0.0781305i \(0.975105\pi\)
\(570\) 0 0
\(571\) 12.2122 + 21.1521i 0.511064 + 0.885189i 0.999918 + 0.0128232i \(0.00408185\pi\)
−0.488854 + 0.872366i \(0.662585\pi\)
\(572\) −15.2422 + 8.80007i −0.637307 + 0.367950i
\(573\) −23.6925 18.4501i −0.989768 0.770763i
\(574\) 5.83807 10.1118i 0.243676 0.422060i
\(575\) 0 0
\(576\) 31.9685 + 9.05701i 1.33202 + 0.377375i
\(577\) 14.7976i 0.616033i −0.951381 0.308017i \(-0.900335\pi\)
0.951381 0.308017i \(-0.0996653\pi\)
\(578\) −13.9545 8.05663i −0.580431 0.335112i
\(579\) −1.01586 2.50288i −0.0422175 0.104016i
\(580\) 0 0
\(581\) 0.987533 + 1.71046i 0.0409698 + 0.0709617i
\(582\) −16.2005 + 6.57538i −0.671532 + 0.272558i
\(583\) −2.70177 1.55987i −0.111896 0.0646030i
\(584\) 27.7470 1.14818
\(585\) 0 0
\(586\) 48.1375 1.98854
\(587\) 26.4813 + 15.2890i 1.09300 + 0.631044i 0.934374 0.356295i \(-0.115960\pi\)
0.158626 + 0.987339i \(0.449294\pi\)
\(588\) −25.4276 19.8013i −1.04862 0.816590i
\(589\) −3.88821 6.73457i −0.160211 0.277493i
\(590\) 0 0
\(591\) −30.8405 4.28440i −1.26861 0.176237i
\(592\) 105.761 + 61.0611i 4.34675 + 2.50960i
\(593\) 5.09990i 0.209428i −0.994502 0.104714i \(-0.966607\pi\)
0.994502 0.104714i \(-0.0333927\pi\)
\(594\) −2.70376 24.5964i −0.110936 1.00920i
\(595\) 0 0
\(596\) 1.39532 2.41677i 0.0571547 0.0989949i
\(597\) −2.62698 + 18.9099i −0.107515 + 0.773929i
\(598\) −7.79831 + 4.50236i −0.318897 + 0.184115i
\(599\) −0.282655 0.489572i −0.0115490 0.0200034i 0.860193 0.509968i \(-0.170343\pi\)
−0.871742 + 0.489965i \(0.837010\pi\)
\(600\) 0 0
\(601\) 5.50480 9.53459i 0.224546 0.388924i −0.731637 0.681694i \(-0.761244\pi\)
0.956183 + 0.292770i \(0.0945769\pi\)
\(602\) 34.4542i 1.40425i
\(603\) 26.4788 6.69134i 1.07830 0.272492i
\(604\) −0.757185 −0.0308094
\(605\) 0 0
\(606\) 11.2411 + 27.6959i 0.456638 + 1.12507i
\(607\) 16.5396 9.54913i 0.671321 0.387587i −0.125256 0.992124i \(-0.539975\pi\)
0.796577 + 0.604537i \(0.206642\pi\)
\(608\) 31.2611 18.0486i 1.26780 0.731967i
\(609\) −8.62621 21.2534i −0.349552 0.861229i
\(610\) 0 0
\(611\) 12.4069 0.501929
\(612\) −69.0357 + 17.4457i −2.79060 + 0.705200i
\(613\) 9.33918i 0.377206i 0.982053 + 0.188603i \(0.0603959\pi\)
−0.982053 + 0.188603i \(0.939604\pi\)
\(614\) −20.4179 + 35.3648i −0.823999 + 1.42721i
\(615\) 0 0
\(616\) 12.5675 + 21.7676i 0.506360 + 0.877041i
\(617\) 21.1444 12.2077i 0.851241 0.491464i −0.00982861 0.999952i \(-0.503129\pi\)
0.861069 + 0.508488i \(0.169795\pi\)
\(618\) −5.06900 + 36.4883i −0.203905 + 1.46777i
\(619\) 19.7431 34.1961i 0.793544 1.37446i −0.130216 0.991486i \(-0.541567\pi\)
0.923760 0.382973i \(-0.125100\pi\)
\(620\) 0 0
\(621\) −0.984464 8.95580i −0.0395052 0.359384i
\(622\) 80.1874i 3.21522i
\(623\) −20.6928 11.9470i −0.829040 0.478647i
\(624\) 35.5062 + 4.93256i 1.42138 + 0.197461i
\(625\) 0 0
\(626\) 9.15135 + 15.8506i 0.365761 + 0.633517i
\(627\) −7.32547 5.70457i −0.292551 0.227819i
\(628\) 48.9960 + 28.2879i 1.95515 + 1.12881i
\(629\) −55.9430 −2.23059
\(630\) 0 0
\(631\) 42.1634 1.67850 0.839249 0.543747i \(-0.182995\pi\)
0.839249 + 0.543747i \(0.182995\pi\)
\(632\) 14.1383 + 8.16277i 0.562393 + 0.324698i
\(633\) 38.4029 15.5868i 1.52638 0.619518i
\(634\) −21.2608 36.8248i −0.844375 1.46250i
\(635\) 0 0
\(636\) 5.54814 + 13.6696i 0.219998 + 0.542034i
\(637\) −6.43658 3.71616i −0.255027 0.147240i
\(638\) 35.0855i 1.38905i
\(639\) −3.67901 1.04230i −0.145539 0.0412328i
\(640\) 0 0
\(641\) −17.6577 + 30.5841i −0.697438 + 1.20800i 0.271913 + 0.962322i \(0.412344\pi\)
−0.969352 + 0.245677i \(0.920990\pi\)
\(642\) 32.3087 + 25.1598i 1.27512 + 0.992978i
\(643\) 12.2936 7.09771i 0.484812 0.279906i −0.237608 0.971361i \(-0.576363\pi\)
0.722420 + 0.691455i \(0.243030\pi\)
\(644\) 7.69256 + 13.3239i 0.303129 + 0.525036i
\(645\) 0 0
\(646\) −18.7712 + 32.5127i −0.738544 + 1.27919i
\(647\) 17.4897i 0.687593i −0.939044 0.343796i \(-0.888287\pi\)
0.939044 0.343796i \(-0.111713\pi\)
\(648\) −36.5094 + 59.2618i −1.43422 + 2.32803i
\(649\) −19.9364 −0.782572
\(650\) 0 0
\(651\) −8.08842 1.12365i −0.317010 0.0440395i
\(652\) 94.3072 54.4483i 3.69335 2.13236i
\(653\) −9.50650 + 5.48858i −0.372018 + 0.214785i −0.674340 0.738421i \(-0.735572\pi\)
0.302322 + 0.953206i \(0.402238\pi\)
\(654\) 17.7742 22.8246i 0.695026 0.892512i
\(655\) 0 0
\(656\) −25.8882 −1.01077
\(657\) −2.93383 + 10.3555i −0.114459 + 0.404007i
\(658\) 29.7862i 1.16119i
\(659\) −7.89381 + 13.6725i −0.307499 + 0.532604i −0.977815 0.209472i \(-0.932825\pi\)
0.670316 + 0.742076i \(0.266159\pi\)
\(660\) 0 0
\(661\) −24.9466 43.2088i −0.970311 1.68063i −0.694614 0.719383i \(-0.744425\pi\)
−0.275697 0.961245i \(-0.588909\pi\)
\(662\) −28.7897 + 16.6217i −1.11894 + 0.646022i
\(663\) −15.2157 + 6.17567i −0.590929 + 0.239843i
\(664\) 4.24913 7.35972i 0.164898 0.285612i
\(665\) 0 0
\(666\) −65.9263 + 64.0703i −2.55459 + 2.48267i
\(667\) 12.7750i 0.494649i
\(668\) −72.9698 42.1291i −2.82328 1.63002i
\(669\) −23.1042 + 29.6691i −0.893261 + 1.14707i
\(670\) 0 0
\(671\) 11.4549 + 19.8404i 0.442210 + 0.765929i
\(672\) 5.21587 37.5455i 0.201207 1.44835i
\(673\) −24.9757 14.4197i −0.962743 0.555840i −0.0657266 0.997838i \(-0.520937\pi\)
−0.897016 + 0.441998i \(0.854270\pi\)
\(674\) 18.2264 0.702055
\(675\) 0 0
\(676\) −44.9809 −1.73003
\(677\) 9.06176 + 5.23181i 0.348272 + 0.201075i 0.663924 0.747800i \(-0.268890\pi\)
−0.315652 + 0.948875i \(0.602223\pi\)
\(678\) −9.35426 + 67.3349i −0.359248 + 2.58598i
\(679\) 3.44455 + 5.96614i 0.132190 + 0.228959i
\(680\) 0 0
\(681\) 15.0053 19.2689i 0.575003 0.738385i
\(682\) −10.8176 6.24556i −0.414228 0.239155i
\(683\) 16.1875i 0.619396i −0.950835 0.309698i \(-0.899772\pi\)
0.950835 0.309698i \(-0.100228\pi\)
\(684\) 10.7569 + 42.5672i 0.411302 + 1.62760i
\(685\) 0 0
\(686\) −25.4904 + 44.1507i −0.973229 + 1.68568i
\(687\) 5.90214 2.39553i 0.225181 0.0913953i
\(688\) −66.1570 + 38.1958i −2.52221 + 1.45620i
\(689\) 1.70109 + 2.94638i 0.0648065 + 0.112248i
\(690\) 0 0
\(691\) −4.94181 + 8.55946i −0.187995 + 0.325617i −0.944582 0.328276i \(-0.893532\pi\)
0.756586 + 0.653894i \(0.226866\pi\)
\(692\) 58.9648i 2.24150i
\(693\) −9.45276 + 2.38876i −0.359081 + 0.0907415i
\(694\) −36.3621 −1.38029
\(695\) 0 0
\(696\) −60.6383 + 77.8682i −2.29849 + 2.95158i
\(697\) 10.2703 5.92957i 0.389016 0.224598i
\(698\) 14.9800 8.64872i 0.567002 0.327359i
\(699\) −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 \(0.188143\pi\)
\(702\) −10.8582 + 24.7040i −0.409815 + 0.932391i
\(703\) 34.4942i 1.30097i
\(704\) 10.0130 17.3430i 0.377379 0.653640i
\(705\) 0 0
\(706\) 4.64193 + 8.04005i 0.174701 + 0.302591i
\(707\) 10.1995 5.88870i 0.383593 0.221467i
\(708\) 74.3820 + 57.9236i 2.79545 + 2.17690i
\(709\) 12.6130 21.8464i 0.473692 0.820458i −0.525855 0.850574i \(-0.676254\pi\)
0.999546 + 0.0301162i \(0.00958774\pi\)
\(710\) 0 0
\(711\) −4.54136 + 4.41351i −0.170314 + 0.165520i
\(712\) 102.811i 3.85299i
\(713\) −3.93880 2.27407i −0.147509 0.0851645i
\(714\) 14.8264 + 36.5295i 0.554865 + 1.36708i
\(715\) 0 0
\(716\) −21.1016 36.5490i −0.788603 1.36590i
\(717\) −35.3614 + 14.3523i −1.32060 + 0.535998i
\(718\) −52.2971 30.1937i −1.95171 1.12682i
\(719\) 36.8600 1.37465 0.687323 0.726352i \(-0.258786\pi\)
0.687323 + 0.726352i \(0.258786\pi\)
\(720\) 0 0
\(721\) 14.5153 0.540576
\(722\) −23.2893 13.4461i −0.866740 0.500412i
\(723\) −25.4826 19.8441i −0.947708 0.738009i
\(724\) −26.0459 45.1128i −0.967988 1.67660i
\(725\) 0 0
\(726\) 34.9300 + 4.85252i 1.29637 + 0.180094i
\(727\) −33.1213 19.1226i −1.22840 0.709217i −0.261705 0.965148i \(-0.584285\pi\)
−0.966695 + 0.255931i \(0.917618\pi\)
\(728\) 27.4107i 1.01591i
\(729\) −18.2569 19.8918i −0.676183 0.736734i
\(730\) 0 0
\(731\) 17.4971 30.3059i 0.647154 1.12090i
\(732\) 14.9070 107.305i 0.550977 3.96611i
\(733\) 34.2801 19.7916i 1.26616 0.731020i 0.291903 0.956448i \(-0.405711\pi\)
0.974260 + 0.225428i \(0.0723781\pi\)
\(734\) 5.50358 + 9.53248i 0.203141 + 0.351850i
\(735\) 0 0
\(736\) 10.5559 18.2834i 0.389097 0.673936i
\(737\) 16.4607i 0.606338i
\(738\) 5.31210 18.7501i 0.195541 0.690201i
\(739\) 8.24773 0.303398 0.151699 0.988427i \(-0.451526\pi\)
0.151699 + 0.988427i \(0.451526\pi\)
\(740\) 0 0
\(741\) 3.80790 + 9.38194i 0.139887 + 0.344654i
\(742\) 7.07361 4.08395i 0.259680 0.149927i
\(743\) 1.13292 0.654091i 0.0415627 0.0239963i −0.479075 0.877774i \(-0.659028\pi\)
0.520637 + 0.853778i \(0.325694\pi\)
\(744\) 13.2142 + 32.5574i 0.484458 + 1.19361i
\(745\) 0 0
\(746\) 18.0171 0.659651
\(747\) 2.29746 + 2.36401i 0.0840595 + 0.0864946i
\(748\) 42.9164i 1.56918i
\(749\) 8.06752 13.9734i 0.294781 0.510575i
\(750\) 0 0
\(751\) −14.2234 24.6357i −0.519020 0.898969i −0.999756 0.0221034i \(-0.992964\pi\)
0.480736 0.876866i \(-0.340370\pi\)
\(752\) −57.1939 + 33.0209i −2.08565 + 1.20415i
\(753\) 3.50176 25.2068i 0.127611 0.918585i
\(754\) −19.1310 + 33.1359i −0.696711 + 1.20674i
\(755\) 0 0
\(756\) 42.2083 + 18.5518i 1.53510 + 0.674724i
\(757\) 38.2012i 1.38845i 0.719760 + 0.694223i \(0.244252\pi\)
−0.719760 + 0.694223i \(0.755748\pi\)
\(758\) 29.1414 + 16.8248i 1.05846 + 0.611103i
\(759\) −5.37859 0.747201i −0.195231 0.0271217i
\(760\) 0 0
\(761\) −11.0952 19.2174i −0.402200 0.696632i 0.591791 0.806092i \(-0.298421\pi\)
−0.993991 + 0.109460i \(0.965088\pi\)
\(762\) −13.0398 10.1545i −0.472384 0.367860i
\(763\) −9.87152 5.69932i −0.357373 0.206329i
\(764\) 85.5852 3.09637
\(765\) 0 0
\(766\) 19.8440 0.716994
\(767\) 18.8286 + 10.8707i 0.679861 + 0.392518i
\(768\) 15.1834 6.16258i 0.547885 0.222373i
\(769\) −8.45652 14.6471i −0.304950 0.528189i 0.672300 0.740279i \(-0.265306\pi\)
−0.977250 + 0.212090i \(0.931973\pi\)
\(770\) 0 0
\(771\) 14.4666 + 35.6431i 0.521003 + 1.28365i
\(772\) 6.66718 + 3.84930i 0.239957 + 0.138539i
\(773\) 38.6464i 1.39001i −0.719003 0.695007i \(-0.755401\pi\)
0.719003 0.695007i \(-0.244599\pi\)
\(774\) −14.0891 55.7532i −0.506423 2.00401i
\(775\) 0