Properties

Label 175.2.x.a.108.15
Level $175$
Weight $2$
Character 175.108
Analytic conductor $1.397$
Analytic rank $0$
Dimension $288$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [175,2,Mod(3,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(60))
 
chi = DirichletCharacter(H, H._module([21, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.x (of order \(60\), degree \(16\), 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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(288\)
Relative dimension: \(18\) over \(\Q(\zeta_{60})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label 108.15
Character \(\chi\) \(=\) 175.108
Dual form 175.2.x.a.47.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0938876 + 1.79148i) q^{2} +(-2.61479 - 2.11742i) q^{3} +(-1.21155 + 0.127339i) q^{4} +(1.96760 + 1.06233i) q^{5} +(3.54782 - 4.88315i) q^{6} +(-1.70162 + 2.02595i) q^{7} +(0.219393 + 1.38519i) q^{8} +(1.72995 + 8.13875i) q^{9} +O(q^{10})\) \(q+(0.0938876 + 1.79148i) q^{2} +(-2.61479 - 2.11742i) q^{3} +(-1.21155 + 0.127339i) q^{4} +(1.96760 + 1.06233i) q^{5} +(3.54782 - 4.88315i) q^{6} +(-1.70162 + 2.02595i) q^{7} +(0.219393 + 1.38519i) q^{8} +(1.72995 + 8.13875i) q^{9} +(-1.71842 + 3.62466i) q^{10} +(2.72413 + 0.579032i) q^{11} +(3.43759 + 2.23239i) q^{12} +(0.649129 + 1.27399i) q^{13} +(-3.78922 - 2.85821i) q^{14} +(-2.89546 - 6.94401i) q^{15} +(-4.84416 + 1.02966i) q^{16} +(1.22658 + 0.470838i) q^{17} +(-14.4180 + 3.86330i) q^{18} +(0.229521 - 2.18375i) q^{19} +(-2.51913 - 1.03652i) q^{20} +(8.73917 - 1.69441i) q^{21} +(-0.781564 + 4.93460i) q^{22} +(-1.79534 + 0.0940899i) q^{23} +(2.35936 - 4.08653i) q^{24} +(2.74289 + 4.18049i) q^{25} +(-2.22138 + 1.28252i) q^{26} +(8.12718 - 15.9505i) q^{27} +(1.80362 - 2.67123i) q^{28} +(-1.22410 - 1.68484i) q^{29} +(12.1682 - 5.83912i) q^{30} +(1.74585 + 3.92124i) q^{31} +(-1.57345 - 5.87221i) q^{32} +(-5.89698 - 7.28217i) q^{33} +(-0.728339 + 2.24160i) q^{34} +(-5.50035 + 2.17858i) q^{35} +(-3.13230 - 9.64024i) q^{36} +(0.0698212 - 0.107515i) q^{37} +(3.93370 + 0.206156i) q^{38} +(1.00022 - 4.70569i) q^{39} +(-1.03986 + 2.95857i) q^{40} +(-6.08777 - 1.97804i) q^{41} +(3.85600 + 15.4970i) q^{42} +(2.62278 + 2.62278i) q^{43} +(-3.37416 - 0.354639i) q^{44} +(-5.24223 + 17.8516i) q^{45} +(-0.337121 - 3.20749i) q^{46} +(-2.63321 - 6.85976i) q^{47} +(14.8467 + 7.56475i) q^{48} +(-1.20897 - 6.89481i) q^{49} +(-7.23176 + 5.30634i) q^{50} +(-2.21028 - 3.82831i) q^{51} +(-0.948683 - 1.46084i) q^{52} +(7.79381 - 9.62456i) q^{53} +(29.3381 + 13.0621i) q^{54} +(4.74488 + 4.03324i) q^{55} +(-3.17965 - 1.91259i) q^{56} +(-5.22405 + 5.22405i) q^{57} +(2.90343 - 2.35115i) q^{58} +(0.660191 + 0.733216i) q^{59} +(4.39224 + 8.04432i) q^{60} +(5.97461 + 5.37956i) q^{61} +(-6.86092 + 3.49581i) q^{62} +(-19.4324 - 10.3443i) q^{63} +(0.952259 - 0.309408i) q^{64} +(-0.0761742 + 3.19629i) q^{65} +(12.4922 - 11.2481i) q^{66} +(-1.09944 + 2.86414i) q^{67} +(-1.54602 - 0.414254i) q^{68} +(4.89367 + 3.55546i) q^{69} +(-4.41929 - 9.64924i) q^{70} +(4.78252 - 3.47471i) q^{71} +(-10.8942 + 4.18189i) q^{72} +(-1.03177 + 0.670038i) q^{73} +(0.199167 + 0.114989i) q^{74} +(1.67975 - 16.7390i) q^{75} +2.67495i q^{76} +(-5.80853 + 4.53367i) q^{77} +(8.52407 + 1.35008i) q^{78} +(3.47703 - 7.80955i) q^{79} +(-10.6252 - 3.12016i) q^{80} +(-32.2210 + 14.3457i) q^{81} +(2.97205 - 11.0918i) q^{82} +(-6.21112 + 0.983744i) q^{83} +(-10.3722 + 3.16570i) q^{84} +(1.91322 + 2.22945i) q^{85} +(-4.45241 + 4.94491i) q^{86} +(-0.366720 + 6.99743i) q^{87} +(-0.204415 + 3.90048i) q^{88} +(2.11663 - 2.35076i) q^{89} +(-32.4730 - 7.71533i) q^{90} +(-3.68561 - 0.852738i) q^{91} +(2.16317 - 0.342612i) q^{92} +(3.73786 - 13.9499i) q^{93} +(12.0419 - 5.36140i) q^{94} +(2.77148 - 4.05292i) q^{95} +(-8.31966 + 18.6863i) q^{96} +(13.4042 + 2.12301i) q^{97} +(12.2384 - 2.81319i) q^{98} +23.1727i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0938876 + 1.79148i 0.0663886 + 1.26677i 0.805259 + 0.592923i \(0.202026\pi\)
−0.738871 + 0.673847i \(0.764641\pi\)
\(3\) −2.61479 2.11742i −1.50965 1.22249i −0.904570 0.426326i \(-0.859808\pi\)
−0.605080 0.796164i \(-0.706859\pi\)
\(4\) −1.21155 + 0.127339i −0.605776 + 0.0636696i
\(5\) 1.96760 + 1.06233i 0.879937 + 0.475090i
\(6\) 3.54782 4.88315i 1.44839 1.99354i
\(7\) −1.70162 + 2.02595i −0.643152 + 0.765738i
\(8\) 0.219393 + 1.38519i 0.0775670 + 0.489739i
\(9\) 1.72995 + 8.13875i 0.576648 + 2.71292i
\(10\) −1.71842 + 3.62466i −0.543412 + 1.14622i
\(11\) 2.72413 + 0.579032i 0.821357 + 0.174585i 0.599377 0.800467i \(-0.295415\pi\)
0.221979 + 0.975051i \(0.428748\pi\)
\(12\) 3.43759 + 2.23239i 0.992346 + 0.644437i
\(13\) 0.649129 + 1.27399i 0.180036 + 0.353341i 0.963334 0.268306i \(-0.0864639\pi\)
−0.783298 + 0.621647i \(0.786464\pi\)
\(14\) −3.78922 2.85821i −1.01271 0.763889i
\(15\) −2.89546 6.94401i −0.747604 1.79293i
\(16\) −4.84416 + 1.02966i −1.21104 + 0.257414i
\(17\) 1.22658 + 0.470838i 0.297488 + 0.114195i 0.502534 0.864557i \(-0.332401\pi\)
−0.205046 + 0.978752i \(0.565734\pi\)
\(18\) −14.4180 + 3.86330i −3.39836 + 0.910588i
\(19\) 0.229521 2.18375i 0.0526558 0.500986i −0.936131 0.351652i \(-0.885620\pi\)
0.988787 0.149335i \(-0.0477132\pi\)
\(20\) −2.51913 1.03652i −0.563294 0.231773i
\(21\) 8.73917 1.69441i 1.90704 0.369750i
\(22\) −0.781564 + 4.93460i −0.166630 + 1.05206i
\(23\) −1.79534 + 0.0940899i −0.374355 + 0.0196191i −0.238586 0.971121i \(-0.576684\pi\)
−0.135769 + 0.990741i \(0.543350\pi\)
\(24\) 2.35936 4.08653i 0.481602 0.834159i
\(25\) 2.74289 + 4.18049i 0.548579 + 0.836099i
\(26\) −2.22138 + 1.28252i −0.435649 + 0.251522i
\(27\) 8.12718 15.9505i 1.56408 3.06967i
\(28\) 1.80362 2.67123i 0.340852 0.504815i
\(29\) −1.22410 1.68484i −0.227311 0.312866i 0.680094 0.733125i \(-0.261939\pi\)
−0.907404 + 0.420259i \(0.861939\pi\)
\(30\) 12.1682 5.83912i 2.22160 1.06607i
\(31\) 1.74585 + 3.92124i 0.313563 + 0.704275i 0.999732 0.0231680i \(-0.00737526\pi\)
−0.686168 + 0.727443i \(0.740709\pi\)
\(32\) −1.57345 5.87221i −0.278150 1.03807i
\(33\) −5.89698 7.28217i −1.02653 1.26766i
\(34\) −0.728339 + 2.24160i −0.124909 + 0.384430i
\(35\) −5.50035 + 2.17858i −0.929728 + 0.368246i
\(36\) −3.13230 9.64024i −0.522050 1.60671i
\(37\) 0.0698212 0.107515i 0.0114785 0.0176754i −0.832885 0.553446i \(-0.813312\pi\)
0.844363 + 0.535771i \(0.179979\pi\)
\(38\) 3.93370 + 0.206156i 0.638130 + 0.0334430i
\(39\) 1.00022 4.70569i 0.160164 0.753513i
\(40\) −1.03986 + 2.95857i −0.164416 + 0.467791i
\(41\) −6.08777 1.97804i −0.950749 0.308917i −0.207729 0.978186i \(-0.566607\pi\)
−0.743020 + 0.669269i \(0.766607\pi\)
\(42\) 3.85600 + 15.4970i 0.594993 + 2.39124i
\(43\) 2.62278 + 2.62278i 0.399970 + 0.399970i 0.878222 0.478253i \(-0.158730\pi\)
−0.478253 + 0.878222i \(0.658730\pi\)
\(44\) −3.37416 0.354639i −0.508674 0.0534638i
\(45\) −5.24223 + 17.8516i −0.781466 + 2.66116i
\(46\) −0.337121 3.20749i −0.0497058 0.472919i
\(47\) −2.63321 6.85976i −0.384094 1.00060i −0.980256 0.197734i \(-0.936642\pi\)
0.596162 0.802864i \(-0.296692\pi\)
\(48\) 14.8467 + 7.56475i 2.14293 + 1.09188i
\(49\) −1.20897 6.89481i −0.172711 0.984973i
\(50\) −7.23176 + 5.30634i −1.02273 + 0.750430i
\(51\) −2.21028 3.82831i −0.309501 0.536071i
\(52\) −0.948683 1.46084i −0.131559 0.202582i
\(53\) 7.79381 9.62456i 1.07056 1.32203i 0.126610 0.991953i \(-0.459590\pi\)
0.943952 0.330082i \(-0.107076\pi\)
\(54\) 29.3381 + 13.0621i 3.99241 + 1.77753i
\(55\) 4.74488 + 4.03324i 0.639799 + 0.543842i
\(56\) −3.17965 1.91259i −0.424899 0.255580i
\(57\) −5.22405 + 5.22405i −0.691943 + 0.691943i
\(58\) 2.90343 2.35115i 0.381238 0.308721i
\(59\) 0.660191 + 0.733216i 0.0859495 + 0.0954566i 0.784585 0.620021i \(-0.212876\pi\)
−0.698636 + 0.715477i \(0.746209\pi\)
\(60\) 4.39224 + 8.04432i 0.567036 + 1.03852i
\(61\) 5.97461 + 5.37956i 0.764971 + 0.688783i 0.956184 0.292766i \(-0.0945756\pi\)
−0.191213 + 0.981548i \(0.561242\pi\)
\(62\) −6.86092 + 3.49581i −0.871337 + 0.443968i
\(63\) −19.4324 10.3443i −2.44826 1.30326i
\(64\) 0.952259 0.309408i 0.119032 0.0386760i
\(65\) −0.0761742 + 3.19629i −0.00944824 + 0.396451i
\(66\) 12.4922 11.2481i 1.53769 1.38454i
\(67\) −1.09944 + 2.86414i −0.134318 + 0.349911i −0.984199 0.177063i \(-0.943340\pi\)
0.849881 + 0.526974i \(0.176674\pi\)
\(68\) −1.54602 0.414254i −0.187482 0.0502357i
\(69\) 4.89367 + 3.55546i 0.589129 + 0.428027i
\(70\) −4.41929 9.64924i −0.528207 1.15330i
\(71\) 4.78252 3.47471i 0.567581 0.412372i −0.266645 0.963795i \(-0.585915\pi\)
0.834226 + 0.551423i \(0.185915\pi\)
\(72\) −10.8942 + 4.18189i −1.28389 + 0.492840i
\(73\) −1.03177 + 0.670038i −0.120759 + 0.0784221i −0.603605 0.797283i \(-0.706270\pi\)
0.482846 + 0.875705i \(0.339603\pi\)
\(74\) 0.199167 + 0.114989i 0.0231527 + 0.0133672i
\(75\) 1.67975 16.7390i 0.193961 1.93285i
\(76\) 2.67495i 0.306838i
\(77\) −5.80853 + 4.53367i −0.661944 + 0.516660i
\(78\) 8.52407 + 1.35008i 0.965160 + 0.152866i
\(79\) 3.47703 7.80955i 0.391197 0.878643i −0.605377 0.795939i \(-0.706978\pi\)
0.996574 0.0827041i \(-0.0263556\pi\)
\(80\) −10.6252 3.12016i −1.18793 0.348844i
\(81\) −32.2210 + 14.3457i −3.58011 + 1.59397i
\(82\) 2.97205 11.0918i 0.328208 1.22489i
\(83\) −6.21112 + 0.983744i −0.681759 + 0.107980i −0.487702 0.873010i \(-0.662165\pi\)
−0.194057 + 0.980990i \(0.562165\pi\)
\(84\) −10.3722 + 3.16570i −1.13170 + 0.345406i
\(85\) 1.91322 + 2.22945i 0.207518 + 0.241818i
\(86\) −4.45241 + 4.94491i −0.480116 + 0.533223i
\(87\) −0.366720 + 6.99743i −0.0393165 + 0.750203i
\(88\) −0.204415 + 3.90048i −0.0217907 + 0.415792i
\(89\) 2.11663 2.35076i 0.224362 0.249180i −0.620445 0.784250i \(-0.713048\pi\)
0.844808 + 0.535070i \(0.179715\pi\)
\(90\) −32.4730 7.71533i −3.42295 0.813267i
\(91\) −3.68561 0.852738i −0.386357 0.0893913i
\(92\) 2.16317 0.342612i 0.225526 0.0357198i
\(93\) 3.73786 13.9499i 0.387598 1.44654i
\(94\) 12.0419 5.36140i 1.24203 0.552987i
\(95\) 2.77148 4.05292i 0.284348 0.415820i
\(96\) −8.31966 + 18.6863i −0.849122 + 1.90716i
\(97\) 13.4042 + 2.12301i 1.36099 + 0.215559i 0.793876 0.608080i \(-0.208060\pi\)
0.567113 + 0.823640i \(0.308060\pi\)
\(98\) 12.2384 2.81319i 1.23627 0.284175i
\(99\) 23.1727i 2.32895i
\(100\) −3.85550 4.71561i −0.385550 0.471561i
\(101\) −9.71050 5.60636i −0.966231 0.557854i −0.0681459 0.997675i \(-0.521708\pi\)
−0.898085 + 0.439822i \(0.855042\pi\)
\(102\) 6.65084 4.31911i 0.658531 0.427655i
\(103\) −12.2217 + 4.69146i −1.20424 + 0.462263i −0.875990 0.482329i \(-0.839791\pi\)
−0.328246 + 0.944592i \(0.606458\pi\)
\(104\) −1.62230 + 1.17867i −0.159080 + 0.115578i
\(105\) 18.9952 + 5.95000i 1.85374 + 0.580661i
\(106\) 17.9740 + 13.0589i 1.74579 + 1.26839i
\(107\) 15.4822 + 4.14844i 1.49672 + 0.401045i 0.912000 0.410190i \(-0.134538\pi\)
0.584720 + 0.811235i \(0.301204\pi\)
\(108\) −7.81538 + 20.3598i −0.752035 + 1.95912i
\(109\) 1.17356 1.05667i 0.112406 0.101211i −0.611011 0.791622i \(-0.709237\pi\)
0.723417 + 0.690411i \(0.242570\pi\)
\(110\) −6.78000 + 8.87904i −0.646448 + 0.846583i
\(111\) −0.410222 + 0.133289i −0.0389366 + 0.0126513i
\(112\) 6.15688 11.5661i 0.581770 1.09290i
\(113\) 18.3623 9.35606i 1.72738 0.880144i 0.752138 0.659006i \(-0.229023\pi\)
0.975242 0.221138i \(-0.0709773\pi\)
\(114\) −9.84928 8.86833i −0.922469 0.830595i
\(115\) −3.63247 1.72212i −0.338729 0.160589i
\(116\) 1.69761 + 1.88539i 0.157619 + 0.175054i
\(117\) −9.24571 + 7.48703i −0.854766 + 0.692176i
\(118\) −1.25156 + 1.25156i −0.115215 + 0.115215i
\(119\) −3.04106 + 1.68380i −0.278774 + 0.154353i
\(120\) 8.98353 5.53422i 0.820080 0.505203i
\(121\) −2.96338 1.31938i −0.269398 0.119944i
\(122\) −9.07646 + 11.2085i −0.821744 + 1.01477i
\(123\) 11.7299 + 18.0625i 1.05765 + 1.62864i
\(124\) −2.61451 4.52847i −0.234790 0.406669i
\(125\) 0.955835 + 11.1394i 0.0854925 + 0.996339i
\(126\) 16.7071 35.7841i 1.48839 3.18790i
\(127\) 1.98097 + 1.00935i 0.175783 + 0.0895657i 0.539668 0.841878i \(-0.318550\pi\)
−0.363885 + 0.931444i \(0.618550\pi\)
\(128\) −3.71359 9.67424i −0.328238 0.855090i
\(129\) −1.30450 12.4115i −0.114855 1.09277i
\(130\) −5.73325 + 0.163627i −0.502839 + 0.0143511i
\(131\) 6.04593 + 0.635453i 0.528235 + 0.0555198i 0.364893 0.931050i \(-0.381106\pi\)
0.163343 + 0.986569i \(0.447772\pi\)
\(132\) 8.07181 + 8.07181i 0.702561 + 0.702561i
\(133\) 4.03362 + 4.18091i 0.349759 + 0.362531i
\(134\) −5.23429 1.70072i −0.452174 0.146920i
\(135\) 32.9358 22.7504i 2.83466 1.95804i
\(136\) −0.383099 + 1.80234i −0.0328505 + 0.154549i
\(137\) 7.87810 + 0.412874i 0.673071 + 0.0352742i 0.385810 0.922578i \(-0.373922\pi\)
0.287261 + 0.957852i \(0.407255\pi\)
\(138\) −5.91009 + 9.10074i −0.503100 + 0.774706i
\(139\) 0.106015 + 0.326280i 0.00899206 + 0.0276747i 0.955452 0.295147i \(-0.0953686\pi\)
−0.946460 + 0.322822i \(0.895369\pi\)
\(140\) 6.38654 3.33987i 0.539761 0.282270i
\(141\) −7.63965 + 23.5124i −0.643375 + 1.98010i
\(142\) 6.67390 + 8.24158i 0.560061 + 0.691618i
\(143\) 1.03063 + 3.84638i 0.0861859 + 0.321650i
\(144\) −16.7603 37.6441i −1.39669 3.13701i
\(145\) −0.618690 4.61549i −0.0513794 0.383295i
\(146\) −1.29723 1.78549i −0.107360 0.147768i
\(147\) −11.4380 + 20.5884i −0.943387 + 1.69810i
\(148\) −0.0709012 + 0.139151i −0.00582804 + 0.0114382i
\(149\) −16.0367 + 9.25881i −1.31378 + 0.758511i −0.982720 0.185098i \(-0.940740\pi\)
−0.331060 + 0.943610i \(0.607406\pi\)
\(150\) 30.1453 + 1.43767i 2.46135 + 0.117385i
\(151\) −7.73899 + 13.4043i −0.629790 + 1.09083i 0.357803 + 0.933797i \(0.383526\pi\)
−0.987594 + 0.157032i \(0.949808\pi\)
\(152\) 3.07526 0.161168i 0.249437 0.0130724i
\(153\) −1.71013 + 10.7973i −0.138256 + 0.872912i
\(154\) −8.66735 9.98023i −0.698435 0.804230i
\(155\) −0.730535 + 9.57010i −0.0586780 + 0.768689i
\(156\) −0.612606 + 5.82855i −0.0490477 + 0.466658i
\(157\) 1.82818 0.489859i 0.145904 0.0390950i −0.185128 0.982714i \(-0.559270\pi\)
0.331032 + 0.943620i \(0.392603\pi\)
\(158\) 14.3171 + 5.49583i 1.13901 + 0.437225i
\(159\) −40.7584 + 8.66346i −3.23235 + 0.687057i
\(160\) 3.14232 13.2257i 0.248422 1.04558i
\(161\) 2.86437 3.79738i 0.225744 0.299276i
\(162\) −28.7253 56.3765i −2.25687 4.42936i
\(163\) 8.26033 + 5.36432i 0.646999 + 0.420166i 0.825990 0.563685i \(-0.190617\pi\)
−0.178991 + 0.983851i \(0.557283\pi\)
\(164\) 7.62753 + 1.62128i 0.595610 + 0.126601i
\(165\) −3.86681 20.5930i −0.301031 1.60316i
\(166\) −2.34551 11.0347i −0.182047 0.856463i
\(167\) −1.14630 7.23746i −0.0887035 0.560052i −0.991513 0.130010i \(-0.958499\pi\)
0.902809 0.430041i \(-0.141501\pi\)
\(168\) 4.26438 + 11.7337i 0.329004 + 0.905272i
\(169\) 6.43953 8.86326i 0.495349 0.681789i
\(170\) −3.81440 + 3.63682i −0.292551 + 0.278932i
\(171\) 18.1701 1.90975i 1.38950 0.146042i
\(172\) −3.51161 2.84365i −0.267758 0.216826i
\(173\) −0.967106 18.4535i −0.0735277 1.40299i −0.747513 0.664247i \(-0.768752\pi\)
0.673985 0.738745i \(-0.264581\pi\)
\(174\) −12.5702 −0.952945
\(175\) −13.1369 1.55664i −0.993053 0.117671i
\(176\) −13.7923 −1.03964
\(177\) −0.173737 3.31510i −0.0130589 0.249179i
\(178\) 4.41007 + 3.57120i 0.330548 + 0.267673i
\(179\) 14.7567 1.55100i 1.10297 0.115927i 0.464500 0.885573i \(-0.346234\pi\)
0.638471 + 0.769646i \(0.279567\pi\)
\(180\) 4.07803 22.2957i 0.303959 1.66182i
\(181\) 6.60847 9.09578i 0.491204 0.676084i −0.489406 0.872056i \(-0.662786\pi\)
0.980609 + 0.195972i \(0.0627863\pi\)
\(182\) 1.18163 6.68277i 0.0875885 0.495360i
\(183\) −4.23158 26.7172i −0.312808 1.97499i
\(184\) −0.524217 2.46625i −0.0386458 0.181814i
\(185\) 0.251597 0.137373i 0.0184978 0.0100999i
\(186\) 25.3419 + 5.38660i 1.85816 + 0.394964i
\(187\) 3.06872 + 1.99285i 0.224407 + 0.145732i
\(188\) 4.06379 + 7.97564i 0.296383 + 0.581684i
\(189\) 18.4856 + 43.6070i 1.34463 + 3.17194i
\(190\) 7.52094 + 4.58453i 0.545626 + 0.332597i
\(191\) −8.70186 + 1.84964i −0.629645 + 0.133835i −0.511671 0.859182i \(-0.670973\pi\)
−0.117974 + 0.993017i \(0.537640\pi\)
\(192\) −3.14510 1.20729i −0.226978 0.0871288i
\(193\) −15.1345 + 4.05528i −1.08941 + 0.291905i −0.758444 0.651739i \(-0.774040\pi\)
−0.330962 + 0.943644i \(0.607373\pi\)
\(194\) −2.54486 + 24.2127i −0.182710 + 1.73837i
\(195\) 6.96705 8.19633i 0.498921 0.586952i
\(196\) 2.34272 + 8.19947i 0.167337 + 0.585677i
\(197\) 1.05759 6.67734i 0.0753500 0.475741i −0.920942 0.389701i \(-0.872579\pi\)
0.996292 0.0860406i \(-0.0274215\pi\)
\(198\) −41.5136 + 2.17563i −2.95024 + 0.154616i
\(199\) 5.26451 9.11840i 0.373191 0.646387i −0.616863 0.787070i \(-0.711597\pi\)
0.990055 + 0.140684i \(0.0449301\pi\)
\(200\) −5.18901 + 4.71660i −0.366918 + 0.333514i
\(201\) 8.93939 5.16116i 0.630536 0.364040i
\(202\) 9.13200 17.9226i 0.642526 1.26103i
\(203\) 5.49636 + 0.386972i 0.385769 + 0.0271601i
\(204\) 3.16536 + 4.35675i 0.221620 + 0.305033i
\(205\) −9.87695 10.3592i −0.689836 0.723519i
\(206\) −9.55213 21.4544i −0.665528 1.49480i
\(207\) −3.87162 14.4491i −0.269096 1.00428i
\(208\) −4.45625 5.50301i −0.308986 0.381565i
\(209\) 1.88971 5.81592i 0.130714 0.402296i
\(210\) −8.87591 + 34.5882i −0.612496 + 2.38681i
\(211\) −4.67742 14.3956i −0.322007 0.991035i −0.972774 0.231757i \(-0.925552\pi\)
0.650767 0.759278i \(-0.274448\pi\)
\(212\) −8.21703 + 12.6531i −0.564348 + 0.869020i
\(213\) −19.8627 1.04096i −1.36097 0.0713254i
\(214\) −5.97828 + 28.1256i −0.408667 + 1.92263i
\(215\) 2.37431 + 7.94684i 0.161927 + 0.541970i
\(216\) 23.8775 + 7.75827i 1.62466 + 0.527883i
\(217\) −10.9150 3.13545i −0.740959 0.212848i
\(218\) 2.00320 + 2.00320i 0.135674 + 0.135674i
\(219\) 4.11661 + 0.432673i 0.278175 + 0.0292373i
\(220\) −6.26226 4.28227i −0.422201 0.288711i
\(221\) 0.196364 + 1.86828i 0.0132089 + 0.125674i
\(222\) −0.277300 0.722392i −0.0186112 0.0484838i
\(223\) −20.3102 10.3485i −1.36007 0.692990i −0.386694 0.922208i \(-0.626383\pi\)
−0.973375 + 0.229218i \(0.926383\pi\)
\(224\) 14.5743 + 6.80453i 0.973783 + 0.454647i
\(225\) −29.2790 + 29.5558i −1.95193 + 1.97038i
\(226\) 18.4852 + 32.0173i 1.22962 + 2.12976i
\(227\) 7.24773 + 11.1605i 0.481049 + 0.740750i 0.992981 0.118276i \(-0.0377366\pi\)
−0.511932 + 0.859026i \(0.671070\pi\)
\(228\) 5.66399 6.99444i 0.375107 0.463218i
\(229\) −0.872146 0.388305i −0.0576331 0.0256599i 0.377718 0.925921i \(-0.376709\pi\)
−0.435351 + 0.900261i \(0.643376\pi\)
\(230\) 2.74411 6.66919i 0.180941 0.439753i
\(231\) 24.7878 + 0.444475i 1.63092 + 0.0292443i
\(232\) 2.06526 2.06526i 0.135591 0.135591i
\(233\) 4.75032 3.84673i 0.311204 0.252008i −0.460975 0.887413i \(-0.652500\pi\)
0.772179 + 0.635405i \(0.219167\pi\)
\(234\) −14.2809 15.8606i −0.933575 1.03684i
\(235\) 2.10624 16.2946i 0.137396 1.06294i
\(236\) −0.893223 0.804262i −0.0581439 0.0523530i
\(237\) −25.6278 + 13.0580i −1.66470 + 0.848209i
\(238\) −3.30201 5.28993i −0.214038 0.342895i
\(239\) 2.06560 0.671155i 0.133613 0.0434134i −0.241447 0.970414i \(-0.577622\pi\)
0.375060 + 0.927001i \(0.377622\pi\)
\(240\) 21.1760 + 30.6565i 1.36690 + 1.97887i
\(241\) −15.5961 + 14.0428i −1.00463 + 0.904575i −0.995441 0.0953831i \(-0.969592\pi\)
−0.00919128 + 0.999958i \(0.502926\pi\)
\(242\) 2.08542 5.43272i 0.134056 0.349228i
\(243\) 62.7520 + 16.8143i 4.02554 + 1.07864i
\(244\) −7.92359 5.75682i −0.507256 0.368543i
\(245\) 4.94581 14.8506i 0.315976 0.948767i
\(246\) −31.2573 + 22.7098i −1.99289 + 1.44792i
\(247\) 2.93106 1.12513i 0.186499 0.0715902i
\(248\) −5.04863 + 3.27862i −0.320589 + 0.208193i
\(249\) 18.3238 + 10.5792i 1.16122 + 0.670432i
\(250\) −19.8663 + 2.75821i −1.25646 + 0.174445i
\(251\) 17.9887i 1.13544i 0.823223 + 0.567718i \(0.192174\pi\)
−0.823223 + 0.567718i \(0.807826\pi\)
\(252\) 24.8607 + 10.0581i 1.56607 + 0.633602i
\(253\) −4.94523 0.783248i −0.310904 0.0492424i
\(254\) −1.62225 + 3.64364i −0.101789 + 0.228622i
\(255\) −0.281994 9.88064i −0.0176592 0.618750i
\(256\) 18.8120 8.37563i 1.17575 0.523477i
\(257\) 6.02980 22.5035i 0.376129 1.40373i −0.475560 0.879683i \(-0.657755\pi\)
0.851689 0.524048i \(-0.175579\pi\)
\(258\) 22.1125 3.50228i 1.37667 0.218043i
\(259\) 0.0990117 + 0.324405i 0.00615228 + 0.0201575i
\(260\) −0.314724 3.88217i −0.0195184 0.240762i
\(261\) 11.5948 12.8774i 0.717702 0.797088i
\(262\) −0.570765 + 10.8908i −0.0352620 + 0.672838i
\(263\) 0.346091 6.60381i 0.0213409 0.407208i −0.966983 0.254841i \(-0.917977\pi\)
0.988324 0.152368i \(-0.0486898\pi\)
\(264\) 8.79343 9.76610i 0.541198 0.601062i
\(265\) 25.5596 10.6576i 1.57011 0.654694i
\(266\) −7.11133 + 7.61869i −0.436023 + 0.467132i
\(267\) −10.5121 + 1.66495i −0.643329 + 0.101893i
\(268\) 0.967314 3.61006i 0.0590881 0.220520i
\(269\) 9.31881 4.14900i 0.568178 0.252969i −0.102481 0.994735i \(-0.532678\pi\)
0.670659 + 0.741766i \(0.266011\pi\)
\(270\) 43.8492 + 56.8679i 2.66858 + 3.46087i
\(271\) 1.50441 3.37895i 0.0913861 0.205257i −0.862069 0.506790i \(-0.830832\pi\)
0.953456 + 0.301534i \(0.0974985\pi\)
\(272\) −6.42653 1.01786i −0.389665 0.0617169i
\(273\) 7.83150 + 10.0337i 0.473984 + 0.607267i
\(274\) 14.1522i 0.854968i
\(275\) 5.05137 + 12.9764i 0.304609 + 0.782509i
\(276\) −6.38169 3.68447i −0.384132 0.221779i
\(277\) −11.2107 + 7.28032i −0.673587 + 0.437432i −0.835587 0.549358i \(-0.814872\pi\)
0.162000 + 0.986791i \(0.448205\pi\)
\(278\) −0.574572 + 0.220558i −0.0344605 + 0.0132282i
\(279\) −28.8938 + 20.9925i −1.72982 + 1.25679i
\(280\) −4.22448 7.14106i −0.252461 0.426760i
\(281\) −17.6179 12.8001i −1.05099 0.763592i −0.0785934 0.996907i \(-0.525043\pi\)
−0.972401 + 0.233314i \(0.925043\pi\)
\(282\) −42.8394 11.4788i −2.55105 0.683552i
\(283\) −7.15018 + 18.6269i −0.425034 + 1.10725i 0.539195 + 0.842181i \(0.318729\pi\)
−0.964229 + 0.265070i \(0.914605\pi\)
\(284\) −5.35181 + 4.81879i −0.317572 + 0.285943i
\(285\) −15.8285 + 4.72916i −0.937602 + 0.280131i
\(286\) −6.79396 + 2.20749i −0.401735 + 0.130532i
\(287\) 14.3665 8.96766i 0.848026 0.529344i
\(288\) 45.0705 22.9646i 2.65580 1.35320i
\(289\) −11.3507 10.2202i −0.667686 0.601187i
\(290\) 8.21048 1.54171i 0.482136 0.0905323i
\(291\) −30.5538 33.9335i −1.79110 1.98922i
\(292\) 1.16472 0.943171i 0.0681601 0.0551949i
\(293\) −16.9470 + 16.9470i −0.990054 + 0.990054i −0.999951 0.00989737i \(-0.996850\pi\)
0.00989737 + 0.999951i \(0.496850\pi\)
\(294\) −37.9576 18.5579i −2.21373 1.08232i
\(295\) 0.520071 + 2.14402i 0.0302797 + 0.124830i
\(296\) 0.164247 + 0.0731276i 0.00954668 + 0.00425046i
\(297\) 31.3754 38.7453i 1.82058 2.24823i
\(298\) −18.0927 27.8602i −1.04808 1.61390i
\(299\) −1.28528 2.22617i −0.0743296 0.128743i
\(300\) 0.0964201 + 20.4940i 0.00556682 + 1.18322i
\(301\) −9.77659 + 0.850652i −0.563513 + 0.0490308i
\(302\) −24.7402 12.6058i −1.42364 0.725381i
\(303\) 13.5199 + 35.2206i 0.776700 + 2.02337i
\(304\) 1.13668 + 10.8148i 0.0651928 + 0.620268i
\(305\) 6.04075 + 16.9319i 0.345892 + 0.969516i
\(306\) −19.5038 2.04993i −1.11496 0.117187i
\(307\) 4.38282 + 4.38282i 0.250141 + 0.250141i 0.821028 0.570888i \(-0.193401\pi\)
−0.570888 + 0.821028i \(0.693401\pi\)
\(308\) 6.46003 6.23244i 0.368094 0.355126i
\(309\) 41.8908 + 13.6112i 2.38309 + 0.774312i
\(310\) −17.2133 0.410227i −0.977647 0.0232994i
\(311\) −1.09488 + 5.15101i −0.0620850 + 0.292087i −0.998226 0.0595378i \(-0.981037\pi\)
0.936141 + 0.351625i \(0.114371\pi\)
\(312\) 6.73771 + 0.353109i 0.381448 + 0.0199908i
\(313\) −13.6444 + 21.0106i −0.771229 + 1.18759i 0.206650 + 0.978415i \(0.433744\pi\)
−0.977879 + 0.209173i \(0.932923\pi\)
\(314\) 1.04922 + 3.22916i 0.0592107 + 0.182232i
\(315\) −27.2462 40.9971i −1.53515 2.30993i
\(316\) −3.21815 + 9.90444i −0.181035 + 0.557168i
\(317\) −1.51082 1.86570i −0.0848559 0.104788i 0.732950 0.680283i \(-0.238143\pi\)
−0.817806 + 0.575494i \(0.804810\pi\)
\(318\) −19.3472 72.2045i −1.08493 4.04903i
\(319\) −2.35905 5.29851i −0.132081 0.296660i
\(320\) 2.20236 + 0.402827i 0.123116 + 0.0225187i
\(321\) −31.6987 43.6296i −1.76925 2.43516i
\(322\) 7.07188 + 4.77494i 0.394100 + 0.266097i
\(323\) 1.30972 2.57047i 0.0728747 0.143025i
\(324\) 37.2107 21.4836i 2.06726 1.19353i
\(325\) −3.54541 + 6.20809i −0.196664 + 0.344363i
\(326\) −8.83454 + 15.3019i −0.489300 + 0.847493i
\(327\) −5.30602 + 0.278077i −0.293424 + 0.0153777i
\(328\) 1.40434 8.86668i 0.0775419 0.489580i
\(329\) 18.3783 + 6.33794i 1.01323 + 0.349422i
\(330\) 36.5289 8.86074i 2.01085 0.487768i
\(331\) −3.01739 + 28.7085i −0.165851 + 1.57796i 0.522535 + 0.852618i \(0.324987\pi\)
−0.688385 + 0.725345i \(0.741680\pi\)
\(332\) 7.39983 1.98278i 0.406118 0.108819i
\(333\) 0.995827 + 0.382262i 0.0545710 + 0.0209478i
\(334\) 12.8582 2.73309i 0.703568 0.149548i
\(335\) −5.20594 + 4.46751i −0.284431 + 0.244086i
\(336\) −40.5892 + 17.2063i −2.21432 + 0.938681i
\(337\) 6.89117 + 13.5247i 0.375386 + 0.736737i 0.998987 0.0450065i \(-0.0143308\pi\)
−0.623601 + 0.781743i \(0.714331\pi\)
\(338\) 16.4830 + 10.7042i 0.896555 + 0.582230i
\(339\) −67.8242 14.4165i −3.68371 0.782996i
\(340\) −2.60187 2.45747i −0.141106 0.133275i
\(341\) 2.48540 + 11.6929i 0.134592 + 0.633205i
\(342\) 5.12723 + 32.3720i 0.277249 + 1.75048i
\(343\) 16.0258 + 9.28302i 0.865311 + 0.501236i
\(344\) −3.05763 + 4.20846i −0.164856 + 0.226905i
\(345\) 5.85170 + 12.1944i 0.315045 + 0.656526i
\(346\) 32.9683 3.46511i 1.77239 0.186285i
\(347\) 3.59527 + 2.91139i 0.193004 + 0.156292i 0.720952 0.692985i \(-0.243705\pi\)
−0.527948 + 0.849277i \(0.677038\pi\)
\(348\) −0.446748 8.52445i −0.0239482 0.456959i
\(349\) 31.6205 1.69260 0.846302 0.532703i \(-0.178824\pi\)
0.846302 + 0.532703i \(0.178824\pi\)
\(350\) 1.55531 23.6806i 0.0831347 1.26578i
\(351\) 25.5963 1.36623
\(352\) −0.886099 16.9078i −0.0472292 0.901187i
\(353\) −9.63035 7.79850i −0.512572 0.415072i 0.337829 0.941207i \(-0.390307\pi\)
−0.850401 + 0.526135i \(0.823641\pi\)
\(354\) 5.92264 0.622495i 0.314785 0.0330852i
\(355\) 13.1014 1.75619i 0.695349 0.0932091i
\(356\) −2.26507 + 3.11760i −0.120048 + 0.165232i
\(357\) 11.5170 + 2.03642i 0.609546 + 0.107779i
\(358\) 4.16406 + 26.2908i 0.220077 + 1.38951i
\(359\) −3.65927 17.2155i −0.193129 0.908601i −0.962812 0.270174i \(-0.912919\pi\)
0.769683 0.638427i \(-0.220414\pi\)
\(360\) −25.8779 3.34499i −1.36389 0.176296i
\(361\) 13.8687 + 2.94789i 0.729933 + 0.155152i
\(362\) 16.9154 + 10.9850i 0.889053 + 0.577358i
\(363\) 4.95494 + 9.72461i 0.260067 + 0.510410i
\(364\) 4.57390 + 0.563814i 0.239737 + 0.0295519i
\(365\) −2.74191 + 0.222284i −0.143518 + 0.0116349i
\(366\) 47.4661 10.0892i 2.48109 0.527372i
\(367\) 0.369868 + 0.141979i 0.0193070 + 0.00741125i 0.368002 0.929825i \(-0.380042\pi\)
−0.348695 + 0.937236i \(0.613375\pi\)
\(368\) 8.60004 2.30437i 0.448308 0.120124i
\(369\) 5.56724 52.9687i 0.289819 2.75744i
\(370\) 0.269724 + 0.437835i 0.0140223 + 0.0227619i
\(371\) 6.23679 + 32.1673i 0.323798 + 1.67004i
\(372\) −2.75225 + 17.3770i −0.142697 + 0.900956i
\(373\) −33.1559 + 1.73763i −1.71675 + 0.0899709i −0.885120 0.465363i \(-0.845924\pi\)
−0.831627 + 0.555334i \(0.812590\pi\)
\(374\) −3.28205 + 5.68467i −0.169711 + 0.293947i
\(375\) 21.0874 31.1511i 1.08895 1.60864i
\(376\) 8.92436 5.15248i 0.460239 0.265719i
\(377\) 1.35186 2.65317i 0.0696242 0.136645i
\(378\) −76.3856 + 37.2107i −3.92885 + 1.91391i
\(379\) −3.47916 4.78865i −0.178712 0.245976i 0.710258 0.703942i \(-0.248578\pi\)
−0.888970 + 0.457965i \(0.848578\pi\)
\(380\) −2.84169 + 5.26324i −0.145776 + 0.269998i
\(381\) −3.04260 6.83379i −0.155877 0.350106i
\(382\) −4.13059 15.4156i −0.211340 0.788730i
\(383\) −9.12314 11.2661i −0.466171 0.575673i 0.488791 0.872401i \(-0.337438\pi\)
−0.954962 + 0.296728i \(0.904105\pi\)
\(384\) −10.7741 + 33.1593i −0.549814 + 1.69215i
\(385\) −16.2451 + 2.74985i −0.827929 + 0.140145i
\(386\) −8.68591 26.7325i −0.442101 1.36065i
\(387\) −16.8089 + 25.8834i −0.854443 + 1.31573i
\(388\) −16.5102 0.865264i −0.838179 0.0439271i
\(389\) −1.71681 + 8.07695i −0.0870457 + 0.409518i 0.912953 + 0.408064i \(0.133796\pi\)
−0.999999 + 0.00145363i \(0.999537\pi\)
\(390\) 15.3377 + 11.7118i 0.776655 + 0.593051i
\(391\) −2.24642 0.729907i −0.113607 0.0369130i
\(392\) 9.28538 3.18733i 0.468983 0.160984i
\(393\) −14.4633 14.4633i −0.729578 0.729578i
\(394\) 12.0616 + 1.26773i 0.607657 + 0.0638673i
\(395\) 15.1378 11.6723i 0.761663 0.587297i
\(396\) −2.95080 28.0750i −0.148283 1.41082i
\(397\) 1.44779 + 3.77161i 0.0726623 + 0.189292i 0.965102 0.261876i \(-0.0843410\pi\)
−0.892439 + 0.451167i \(0.851008\pi\)
\(398\) 16.8297 + 8.57518i 0.843599 + 0.429835i
\(399\) −1.69433 19.4731i −0.0848227 0.974872i
\(400\) −17.5915 17.4267i −0.879574 0.871336i
\(401\) 1.96532 + 3.40403i 0.0981433 + 0.169989i 0.910916 0.412592i \(-0.135376\pi\)
−0.812773 + 0.582581i \(0.802043\pi\)
\(402\) 10.0854 + 15.5302i 0.503016 + 0.774576i
\(403\) −3.86233 + 4.76958i −0.192396 + 0.237590i
\(404\) 12.4787 + 5.55587i 0.620838 + 0.276415i
\(405\) −78.6380 6.00284i −3.90755 0.298284i
\(406\) −0.177214 + 9.88297i −0.00879496 + 0.490483i
\(407\) 0.252457 0.252457i 0.0125138 0.0125138i
\(408\) 4.81802 3.90156i 0.238528 0.193156i
\(409\) 26.3067 + 29.2166i 1.30078 + 1.44467i 0.825029 + 0.565090i \(0.191158\pi\)
0.475755 + 0.879578i \(0.342175\pi\)
\(410\) 17.6310 18.6670i 0.870735 0.921897i
\(411\) −19.7254 17.7608i −0.972980 0.876075i
\(412\) 14.2098 7.24024i 0.700065 0.356701i
\(413\) −2.60886 + 0.0898600i −0.128373 + 0.00442172i
\(414\) 25.5218 8.29253i 1.25433 0.407555i
\(415\) −13.2661 4.66267i −0.651205 0.228881i
\(416\) 6.45975 5.81639i 0.316715 0.285172i
\(417\) 0.413664 1.07763i 0.0202572 0.0527719i
\(418\) 10.5965 + 2.83934i 0.518294 + 0.138876i
\(419\) −6.94468 5.04561i −0.339270 0.246494i 0.405084 0.914280i \(-0.367242\pi\)
−0.744354 + 0.667786i \(0.767242\pi\)
\(420\) −23.7714 4.78990i −1.15992 0.233723i
\(421\) −13.9780 + 10.1556i −0.681246 + 0.494954i −0.873771 0.486338i \(-0.838332\pi\)
0.192525 + 0.981292i \(0.438332\pi\)
\(422\) 25.3504 9.73109i 1.23404 0.473702i
\(423\) 51.2746 33.2981i 2.49305 1.61901i
\(424\) 15.0417 + 8.68436i 0.730492 + 0.421750i
\(425\) 1.39603 + 6.41915i 0.0677174 + 0.311375i
\(426\) 35.6814i 1.72877i
\(427\) −21.0653 + 2.95031i −1.01942 + 0.142775i
\(428\) −19.2858 3.05456i −0.932212 0.147648i
\(429\) 5.44949 12.2398i 0.263104 0.590941i
\(430\) −14.0137 + 4.99964i −0.675801 + 0.241104i
\(431\) 32.6655 14.5436i 1.57344 0.700542i 0.579973 0.814635i \(-0.303063\pi\)
0.993470 + 0.114093i \(0.0363963\pi\)
\(432\) −22.9458 + 85.6349i −1.10398 + 4.12011i
\(433\) 11.0735 1.75387i 0.532157 0.0842855i 0.115428 0.993316i \(-0.463176\pi\)
0.416730 + 0.909030i \(0.363176\pi\)
\(434\) 4.59233 19.8484i 0.220439 0.952756i
\(435\) −8.15516 + 13.3786i −0.391010 + 0.641453i
\(436\) −1.28727 + 1.42966i −0.0616490 + 0.0684681i
\(437\) −0.206600 + 3.94217i −0.00988304 + 0.188580i
\(438\) −0.388628 + 7.41546i −0.0185693 + 0.354324i
\(439\) −11.0215 + 12.2406i −0.526027 + 0.584212i −0.946342 0.323166i \(-0.895253\pi\)
0.420315 + 0.907378i \(0.361919\pi\)
\(440\) −4.54582 + 7.45742i −0.216713 + 0.355518i
\(441\) 54.0237 21.7672i 2.57256 1.03653i
\(442\) −3.32855 + 0.527191i −0.158323 + 0.0250759i
\(443\) 2.79602 10.4349i 0.132843 0.495777i −0.867155 0.498039i \(-0.834054\pi\)
0.999997 + 0.00226265i \(0.000720226\pi\)
\(444\) 0.480033 0.213724i 0.0227814 0.0101429i
\(445\) 6.66197 2.37678i 0.315808 0.112670i
\(446\) 16.6324 37.3569i 0.787566 1.76890i
\(447\) 61.5374 + 9.74657i 2.91062 + 0.460997i
\(448\) −0.993538 + 2.45573i −0.0469403 + 0.116022i
\(449\) 23.2598i 1.09770i −0.835921 0.548850i \(-0.815066\pi\)
0.835921 0.548850i \(-0.184934\pi\)
\(450\) −55.6976 49.6778i −2.62561 2.34184i
\(451\) −15.4385 8.91344i −0.726972 0.419718i
\(452\) −21.0555 + 13.6736i −0.990367 + 0.643152i
\(453\) 48.6184 18.6628i 2.28429 0.876857i
\(454\) −19.3134 + 14.0320i −0.906424 + 0.658556i
\(455\) −6.34591 5.59320i −0.297501 0.262213i
\(456\) −8.38243 6.09019i −0.392543 0.285199i
\(457\) 10.2799 + 2.75448i 0.480872 + 0.128849i 0.491109 0.871098i \(-0.336592\pi\)
−0.0102368 + 0.999948i \(0.503259\pi\)
\(458\) 0.613757 1.59889i 0.0286790 0.0747113i
\(459\) 17.4787 15.7379i 0.815836 0.734582i
\(460\) 4.62022 + 1.62388i 0.215419 + 0.0757140i
\(461\) 9.06900 2.94670i 0.422385 0.137241i −0.0901091 0.995932i \(-0.528722\pi\)
0.512494 + 0.858691i \(0.328722\pi\)
\(462\) 1.53100 + 44.4486i 0.0712284 + 2.06794i
\(463\) −27.7199 + 14.1240i −1.28825 + 0.656398i −0.957803 0.287425i \(-0.907201\pi\)
−0.330451 + 0.943823i \(0.607201\pi\)
\(464\) 7.66456 + 6.90120i 0.355818 + 0.320380i
\(465\) 22.1741 23.4769i 1.02830 1.08872i
\(466\) 7.33735 + 8.14896i 0.339896 + 0.377493i
\(467\) −20.1890 + 16.3487i −0.934236 + 0.756529i −0.970069 0.242828i \(-0.921925\pi\)
0.0358334 + 0.999358i \(0.488591\pi\)
\(468\) 10.2483 10.2483i 0.473727 0.473727i
\(469\) −3.93179 7.10111i −0.181553 0.327899i
\(470\) 29.3893 + 2.24343i 1.35563 + 0.103482i
\(471\) −5.81753 2.59013i −0.268058 0.119347i
\(472\) −0.870803 + 1.07535i −0.0400820 + 0.0494971i
\(473\) 5.62612 + 8.66346i 0.258689 + 0.398346i
\(474\) −25.7993 44.6857i −1.18500 2.05248i
\(475\) 9.75870 5.03028i 0.447760 0.230805i
\(476\) 3.46999 2.42726i 0.159047 0.111253i
\(477\) 91.8148 + 46.7820i 4.20391 + 2.14200i
\(478\) 1.39630 + 3.63748i 0.0638652 + 0.166374i
\(479\) 3.16582 + 30.1208i 0.144650 + 1.37625i 0.790347 + 0.612660i \(0.209900\pi\)
−0.645697 + 0.763594i \(0.723433\pi\)
\(480\) −36.2208 + 27.9288i −1.65325 + 1.27477i
\(481\) 0.182296 + 0.0191601i 0.00831199 + 0.000873625i
\(482\) −26.6217 26.6217i −1.21258 1.21258i
\(483\) −15.5304 + 3.86430i −0.706656 + 0.175832i
\(484\) 3.75830 + 1.22115i 0.170832 + 0.0555066i
\(485\) 24.1187 + 18.4170i 1.09517 + 0.836271i
\(486\) −24.2310 + 113.998i −1.09914 + 5.17105i
\(487\) −29.4815 1.54506i −1.33593 0.0700132i −0.629061 0.777356i \(-0.716561\pi\)
−0.706871 + 0.707343i \(0.749894\pi\)
\(488\) −6.14094 + 9.45621i −0.277987 + 0.428063i
\(489\) −10.2405 31.5171i −0.463093 1.42525i
\(490\) 27.0689 + 7.46605i 1.22285 + 0.337282i
\(491\) 9.05539 27.8696i 0.408664 1.25774i −0.509133 0.860688i \(-0.670034\pi\)
0.917797 0.397051i \(-0.129966\pi\)
\(492\) −16.5115 20.3900i −0.744394 0.919250i
\(493\) −0.708172 2.64293i −0.0318945 0.119032i
\(494\) 2.29084 + 5.14531i 0.103070 + 0.231498i
\(495\) −24.6172 + 45.5947i −1.10646 + 2.04933i
\(496\) −12.4947 17.1975i −0.561028 0.772189i
\(497\) −1.09845 + 15.6018i −0.0492721 + 0.699836i
\(498\) −17.2321 + 33.8200i −0.772191 + 1.51551i
\(499\) 3.07718 1.77661i 0.137754 0.0795321i −0.429539 0.903048i \(-0.641324\pi\)
0.567293 + 0.823516i \(0.307991\pi\)
\(500\) −2.57653 13.3743i −0.115226 0.598115i
\(501\) −12.3274 + 21.3516i −0.550747 + 0.953921i
\(502\) −32.2264 + 1.68892i −1.43834 + 0.0753800i
\(503\) −2.66709 + 16.8394i −0.118920 + 0.750830i 0.854100 + 0.520109i \(0.174109\pi\)
−0.973020 + 0.230721i \(0.925891\pi\)
\(504\) 10.0655 29.1871i 0.448351 1.30010i
\(505\) −13.1506 21.3469i −0.585192 0.949923i
\(506\) 0.938879 8.93283i 0.0417382 0.397113i
\(507\) −35.6052 + 9.54039i −1.58128 + 0.423704i
\(508\) −2.52858 0.970631i −0.112188 0.0430648i
\(509\) −15.5878 + 3.31329i −0.690918 + 0.146859i −0.539972 0.841683i \(-0.681565\pi\)
−0.150946 + 0.988542i \(0.548232\pi\)
\(510\) 17.6745 1.43286i 0.782641 0.0634480i
\(511\) 0.398212 3.23047i 0.0176159 0.142907i
\(512\) 7.36205 + 14.4488i 0.325360 + 0.638554i
\(513\) −32.9665 21.4087i −1.45551 0.945217i
\(514\) 40.8808 + 8.68948i 1.80317 + 0.383277i
\(515\) −29.0312 3.75258i −1.27927 0.165358i
\(516\) 3.16095 + 14.8711i 0.139153 + 0.654663i
\(517\) −3.20120 20.2116i −0.140789 0.888905i
\(518\) −0.571870 + 0.207835i −0.0251265 + 0.00913176i
\(519\) −36.5449 + 50.2997i −1.60414 + 2.20791i
\(520\) −4.44418 + 0.595726i −0.194890 + 0.0261243i
\(521\) 22.2886 2.34262i 0.976480 0.102632i 0.397175 0.917743i \(-0.369991\pi\)
0.579305 + 0.815111i \(0.303324\pi\)
\(522\) 24.1582 + 19.5629i 1.05737 + 0.856245i
\(523\) −0.788577 15.0469i −0.0344821 0.657957i −0.960127 0.279564i \(-0.909810\pi\)
0.925645 0.378393i \(-0.123523\pi\)
\(524\) −7.40588 −0.323527
\(525\) 31.0541 + 31.8865i 1.35531 + 1.39164i
\(526\) 11.8631 0.517256
\(527\) 0.295145 + 5.63171i 0.0128567 + 0.245321i
\(528\) 36.0640 + 29.2041i 1.56949 + 1.27094i
\(529\) −19.6596 + 2.06631i −0.854765 + 0.0898395i
\(530\) 21.4927 + 44.7890i 0.933584 + 1.94551i
\(531\) −4.82537 + 6.64155i −0.209403 + 0.288219i
\(532\) −5.41933 4.55176i −0.234958 0.197344i
\(533\) −1.43175 9.03974i −0.0620161 0.391555i
\(534\) −3.96968 18.6759i −0.171785 0.808185i
\(535\) 26.0557 + 24.6097i 1.12649 + 1.06397i
\(536\) −4.20859 0.894564i −0.181784 0.0386393i
\(537\) −41.8699 27.1906i −1.80682 1.17336i
\(538\) 8.30778 + 16.3049i 0.358174 + 0.702956i
\(539\) 0.698911 19.4824i 0.0301042 0.839167i
\(540\) −37.0064 + 31.7573i −1.59250 + 1.36662i
\(541\) 6.83288 1.45237i 0.293768 0.0624424i −0.0586700 0.998277i \(-0.518686\pi\)
0.352438 + 0.935835i \(0.385353\pi\)
\(542\) 6.19458 + 2.37788i 0.266080 + 0.102138i
\(543\) −36.5393 + 9.79068i −1.56805 + 0.420158i
\(544\) 0.834901 7.94356i 0.0357961 0.340577i
\(545\) 3.43163 0.832404i 0.146995 0.0356562i
\(546\) −17.2399 + 14.9720i −0.737801 + 0.640744i
\(547\) 3.34437 21.1155i 0.142995 0.902835i −0.806996 0.590557i \(-0.798908\pi\)
0.949991 0.312278i \(-0.101092\pi\)
\(548\) −9.59731 + 0.502974i −0.409977 + 0.0214860i
\(549\) −33.4472 + 57.9322i −1.42749 + 2.47249i
\(550\) −22.7728 + 10.2678i −0.971036 + 0.437819i
\(551\) −3.96022 + 2.28643i −0.168711 + 0.0974053i
\(552\) −3.85135 + 7.55871i −0.163924 + 0.321720i
\(553\) 9.90519 + 20.3332i 0.421211 + 0.864656i
\(554\) −14.0951 19.4003i −0.598844 0.824239i
\(555\) −0.948751 0.173533i −0.0402722 0.00736607i
\(556\) −0.169991 0.381806i −0.00720922 0.0161922i
\(557\) 9.23180 + 34.4535i 0.391164 + 1.45984i 0.828217 + 0.560407i \(0.189355\pi\)
−0.437053 + 0.899436i \(0.643978\pi\)
\(558\) −40.3206 49.7917i −1.70691 2.10785i
\(559\) −1.63886 + 5.04390i −0.0693166 + 0.213334i
\(560\) 24.4014 16.2168i 1.03115 0.685286i
\(561\) −3.80437 11.7087i −0.160621 0.494340i
\(562\) 21.2771 32.7639i 0.897522 1.38206i
\(563\) −9.46267 0.495918i −0.398804 0.0209004i −0.148120 0.988969i \(-0.547322\pi\)
−0.250684 + 0.968069i \(0.580656\pi\)
\(564\) 6.26178 29.4594i 0.263669 1.24046i
\(565\) 46.0689 + 1.09792i 1.93813 + 0.0461897i
\(566\) −34.0410 11.0606i −1.43085 0.464911i
\(567\) 25.7642 89.6892i 1.08199 3.76659i
\(568\) 5.86238 + 5.86238i 0.245980 + 0.245980i
\(569\) −17.3128 1.81965i −0.725789 0.0762835i −0.265574 0.964091i \(-0.585561\pi\)
−0.460216 + 0.887807i \(0.652228\pi\)
\(570\) −9.95831 27.9125i −0.417108 1.16913i
\(571\) 1.08064 + 10.2816i 0.0452232 + 0.430270i 0.993586 + 0.113082i \(0.0360722\pi\)
−0.948362 + 0.317189i \(0.897261\pi\)
\(572\) −1.73846 4.52885i −0.0726888 0.189361i
\(573\) 26.6700 + 13.5890i 1.11416 + 0.567690i
\(574\) 17.4143 + 24.8953i 0.726857 + 1.03911i
\(575\) −5.31777 7.24734i −0.221767 0.302235i
\(576\) 4.16555 + 7.21494i 0.173565 + 0.300623i
\(577\) −12.6995 19.5555i −0.528687 0.814107i 0.468920 0.883241i \(-0.344643\pi\)
−0.997607 + 0.0691337i \(0.977977\pi\)
\(578\) 17.2436 21.2941i 0.717239 0.885716i
\(579\) 48.1603 + 21.4423i 2.00147 + 0.891113i
\(580\) 1.33731 + 5.51312i 0.0555287 + 0.228920i
\(581\) 8.57595 14.2574i 0.355790 0.591496i
\(582\) 57.9226 57.9226i 2.40097 2.40097i
\(583\) 26.8043 21.7057i 1.11012 0.898958i
\(584\) −1.15449 1.28219i −0.0477733 0.0530576i
\(585\) −26.1456 + 4.90944i −1.08099 + 0.202980i
\(586\) −31.9514 28.7691i −1.31990 1.18844i
\(587\) 35.3817 18.0279i 1.46036 0.744089i 0.470006 0.882663i \(-0.344252\pi\)
0.990352 + 0.138574i \(0.0442519\pi\)
\(588\) 11.2360 26.4004i 0.463364 1.08873i
\(589\) 8.96371 2.91249i 0.369343 0.120007i
\(590\) −3.79214 + 1.13299i −0.156120 + 0.0466446i
\(591\) −16.9041 + 15.2205i −0.695341 + 0.626088i
\(592\) −0.227521 + 0.592713i −0.00935106 + 0.0243603i
\(593\) −7.47928 2.00407i −0.307137 0.0822972i 0.101958 0.994789i \(-0.467489\pi\)
−0.409096 + 0.912491i \(0.634156\pi\)
\(594\) 72.3574 + 52.5707i 2.96886 + 2.15700i
\(595\) −7.77235 + 0.0824135i −0.318635 + 0.00337862i
\(596\) 18.2503 13.2596i 0.747563 0.543136i
\(597\) −33.0730 + 12.6956i −1.35359 + 0.519594i
\(598\) 3.86747 2.51156i 0.158153 0.102705i
\(599\) −28.2706 16.3221i −1.15511 0.666901i −0.204980 0.978766i \(-0.565713\pi\)
−0.950126 + 0.311865i \(0.899046\pi\)
\(600\) 23.5552 1.34563i 0.961636 0.0549350i
\(601\) 7.02390i 0.286511i −0.989686 0.143255i \(-0.954243\pi\)
0.989686 0.143255i \(-0.0457571\pi\)
\(602\) −2.44183 17.4347i −0.0995215 0.710587i
\(603\) −25.2125 3.99327i −1.02673 0.162619i
\(604\) 7.66930 17.2255i 0.312059 0.700897i
\(605\) −4.42912 5.74411i −0.180069 0.233531i
\(606\) −61.8278 + 27.5275i −2.51158 + 1.11823i
\(607\) 0.594770 2.21971i 0.0241410 0.0900954i −0.952804 0.303585i \(-0.901816\pi\)
0.976945 + 0.213490i \(0.0684830\pi\)
\(608\) −13.1846 + 2.08823i −0.534705 + 0.0846890i
\(609\) −13.5524 12.6499i −0.549173 0.512601i
\(610\) −29.7660 + 12.4116i −1.20519 + 0.502531i
\(611\) 7.02995 7.80755i 0.284401 0.315860i
\(612\) 0.696986 13.2993i 0.0281740 0.537592i
\(613\) 0.935899 17.8580i 0.0378006 0.721279i −0.912336 0.409443i \(-0.865723\pi\)
0.950136 0.311835i \(-0.100944\pi\)
\(614\) −7.44025 + 8.26323i −0.300264 + 0.333477i
\(615\) 3.89138 + 48.0008i 0.156916 + 1.93558i
\(616\) −7.55435 7.05127i −0.304373 0.284104i
\(617\) −38.5471 + 6.10525i −1.55185 + 0.245788i −0.872716 0.488229i \(-0.837643\pi\)
−0.679131 + 0.734017i \(0.737643\pi\)
\(618\) −20.4511 + 76.3247i −0.822665 + 3.07023i
\(619\) 23.3635 10.4021i 0.939057 0.418095i 0.120625 0.992698i \(-0.461510\pi\)
0.818432 + 0.574603i \(0.194843\pi\)
\(620\) −0.333568 11.6877i −0.0133964 0.469389i
\(621\) −13.0903 + 29.4013i −0.525295 + 1.17983i
\(622\) −9.33074 1.47784i −0.374128 0.0592561i
\(623\) 1.16082 + 8.28829i 0.0465073 + 0.332063i
\(624\) 23.8250i 0.953762i
\(625\) −9.95307 + 22.9333i −0.398123 + 0.917332i
\(626\) −38.9211 22.4711i −1.55560 0.898127i
\(627\) −17.2559 + 11.2061i −0.689135 + 0.447529i
\(628\) −2.15255 + 0.826288i −0.0858963 + 0.0329725i
\(629\) 0.136263 0.0990011i 0.00543317 0.00394743i
\(630\) 70.8876 52.6602i 2.82423 2.09803i
\(631\) 3.71186 + 2.69683i 0.147767 + 0.107359i 0.659212 0.751957i \(-0.270890\pi\)
−0.511445 + 0.859316i \(0.670890\pi\)
\(632\) 11.5805 + 3.10300i 0.460649 + 0.123431i
\(633\) −18.2510 + 47.5456i −0.725413 + 1.88977i
\(634\) 3.20053 2.88177i 0.127109 0.114450i
\(635\) 2.82548 + 4.09046i 0.112126 + 0.162325i
\(636\) 48.2777 15.6864i 1.91434 0.622005i
\(637\) 7.99912 6.01584i 0.316937 0.238356i
\(638\) 9.27071 4.72366i 0.367031 0.187012i
\(639\) 36.5533 + 32.9127i 1.44603 + 1.30201i
\(640\) 2.97041 22.9801i 0.117416 0.908368i
\(641\) 3.80072 + 4.22113i 0.150119 + 0.166724i 0.813514 0.581545i \(-0.197552\pi\)
−0.663395 + 0.748270i \(0.730885\pi\)
\(642\) 75.1855 60.8840i 2.96733 2.40290i
\(643\) 18.1847 18.1847i 0.717133 0.717133i −0.250884 0.968017i \(-0.580721\pi\)
0.968017 + 0.250884i \(0.0807212\pi\)
\(644\) −2.98678 + 4.96548i −0.117696 + 0.195667i
\(645\) 10.6184 25.8067i 0.418100 1.01614i
\(646\) 4.72791 + 2.10500i 0.186017 + 0.0828202i
\(647\) −27.0230 + 33.3707i −1.06238 + 1.31194i −0.114464 + 0.993427i \(0.536515\pi\)
−0.947920 + 0.318508i \(0.896818\pi\)
\(648\) −26.9406 41.4849i −1.05833 1.62968i
\(649\) 1.37389 + 2.37965i 0.0539300 + 0.0934094i
\(650\) −11.4546 5.76867i −0.449285 0.226266i
\(651\) 21.9014 + 31.3102i 0.858384 + 1.22714i
\(652\) −10.6909 5.44729i −0.418688 0.213332i
\(653\) −9.22908 24.0426i −0.361162 0.940859i −0.986973 0.160885i \(-0.948565\pi\)
0.625811 0.779975i \(-0.284768\pi\)
\(654\) −0.996339 9.47954i −0.0389600 0.370679i
\(655\) 11.2209 + 7.67311i 0.438437 + 0.299813i
\(656\) 31.5268 + 3.31360i 1.23091 + 0.129374i
\(657\) −7.23818 7.23818i −0.282388 0.282388i
\(658\) −9.62881 + 33.5194i −0.375370 + 1.30672i
\(659\) 10.3796 + 3.37253i 0.404331 + 0.131375i 0.504120 0.863634i \(-0.331817\pi\)
−0.0997894 + 0.995009i \(0.531817\pi\)
\(660\) 7.30713 + 24.4571i 0.284430 + 0.951989i
\(661\) 7.03787 33.1106i 0.273741 1.28785i −0.599425 0.800431i \(-0.704604\pi\)
0.873167 0.487422i \(-0.162063\pi\)
\(662\) −51.7141 2.71022i −2.00993 0.105336i
\(663\) 3.44247 5.30094i 0.133694 0.205871i
\(664\) −2.72535 8.38775i −0.105764 0.325508i
\(665\) 3.49501 + 12.5114i 0.135531 + 0.485172i
\(666\) −0.591320 + 1.81990i −0.0229132 + 0.0705196i
\(667\) 2.35621 + 2.90968i 0.0912329 + 0.112663i
\(668\) 2.31042 + 8.62260i 0.0893927 + 0.333618i
\(669\) 31.1947 + 70.0643i 1.20606 + 2.70884i
\(670\) −8.49225 8.90691i −0.328084 0.344104i
\(671\) 13.1607 + 18.1141i 0.508063 + 0.699289i
\(672\) −23.7006 48.6522i −0.914270 1.87680i
\(673\) 11.8073 23.1732i 0.455139 0.893261i −0.543413 0.839466i \(-0.682868\pi\)
0.998552 0.0537956i \(-0.0171320\pi\)
\(674\) −23.5822 + 13.6152i −0.908354 + 0.524439i
\(675\) 88.9729 9.77486i 3.42457 0.376235i
\(676\) −6.67319 + 11.5583i −0.256661 + 0.444550i
\(677\) 0.946766 0.0496179i 0.0363872 0.00190697i −0.0341337 0.999417i \(-0.510867\pi\)
0.0705208 + 0.997510i \(0.477534\pi\)
\(678\) 19.4590 122.860i 0.747320 4.71839i
\(679\) −27.1100 + 23.5437i −1.04039 + 0.903524i
\(680\) −2.66847 + 3.13930i −0.102331 + 0.120387i
\(681\) 4.68018 44.5289i 0.179345 1.70635i
\(682\) −20.7142 + 5.55036i −0.793189 + 0.212534i
\(683\) 11.9315 + 4.58007i 0.456546 + 0.175251i 0.575763 0.817617i \(-0.304705\pi\)
−0.119217 + 0.992868i \(0.538039\pi\)
\(684\) −21.7708 + 4.62752i −0.832427 + 0.176938i
\(685\) 15.0623 + 9.18154i 0.575502 + 0.350809i
\(686\) −15.1258 + 29.5815i −0.577504 + 1.12943i
\(687\) 1.45828 + 2.86203i 0.0556368 + 0.109193i
\(688\) −15.4057 10.0046i −0.587337 0.381421i
\(689\) 17.3208 + 3.68164i 0.659868 + 0.140259i
\(690\) −21.2967 + 11.6281i −0.810752 + 0.442675i
\(691\) 0.556217 + 2.61679i 0.0211595 + 0.0995476i 0.987460 0.157869i \(-0.0504622\pi\)
−0.966301 + 0.257416i \(0.917129\pi\)
\(692\) 3.52155 + 22.2342i 0.133869 + 0.845218i
\(693\) −46.9469 39.4312i −1.78336 1.49787i
\(694\) −4.87815 + 6.71420i −0.185172 + 0.254868i
\(695\) −0.138024 + 0.754612i −0.00523554 + 0.0286241i
\(696\) −9.77323 + 1.02721i −0.370453 + 0.0389362i
\(697\) −6.53577 5.29256i −0.247560 0.200470i
\(698\) 2.96877 + 56.6475i 0.112370 + 2.14414i
\(699\) −20.5662 −0.777886
\(700\) 16.1142 + 0.213115i 0.609060 + 0.00805500i
\(701\) 29.0119 1.09576 0.547882 0.836556i \(-0.315434\pi\)
0.547882 + 0.836556i \(0.315434\pi\)
\(702\) 2.40318 + 45.8554i 0.0907021 + 1.73070i
\(703\) −0.218761 0.177149i −0.00825072 0.00668130i
\(704\) 2.77324 0.291479i 0.104520 0.0109855i
\(705\) −40.0098 + 38.1472i −1.50686 + 1.43671i
\(706\) 13.0667 17.9848i 0.491772 0.676867i
\(707\) 27.8818 10.1331i 1.04860 0.381095i
\(708\) 0.632635 + 3.99430i 0.0237759 + 0.150115i
\(709\) −8.26415 38.8798i −0.310367 1.46016i −0.806149 0.591713i \(-0.798452\pi\)
0.495782 0.868447i \(-0.334881\pi\)
\(710\) 4.37625 + 23.3060i 0.164238 + 0.874660i
\(711\) 69.5751 + 14.7886i 2.60927 + 0.554617i
\(712\) 3.72062 + 2.41620i 0.139436 + 0.0905508i
\(713\) −3.50334 6.87569i −0.131201 0.257497i
\(714\) −2.56690 + 20.8238i −0.0960638 + 0.779310i
\(715\) −2.05826 + 8.66301i −0.0769747 + 0.323978i
\(716\) −17.6811 + 3.75823i −0.660772 + 0.140452i
\(717\) −6.82224 2.61881i −0.254781 0.0978013i
\(718\) 30.4978 8.17185i 1.13817 0.304971i
\(719\) 1.21225 11.5338i 0.0452092 0.430137i −0.948384 0.317123i \(-0.897283\pi\)
0.993593 0.113013i \(-0.0360503\pi\)
\(720\) 7.01319 91.8736i 0.261366 3.42393i
\(721\) 11.2920 32.7436i 0.420535 1.21944i
\(722\) −3.97899 + 25.1224i −0.148083 + 0.934957i
\(723\) 70.5149 3.69553i 2.62248 0.137438i
\(724\) −6.84826 + 11.8615i −0.254513 + 0.440830i
\(725\) 3.68586 9.73869i 0.136889 0.361686i
\(726\) −16.9563 + 9.78971i −0.629306 + 0.363330i
\(727\) −7.77204 + 15.2535i −0.288249 + 0.565721i −0.989040 0.147646i \(-0.952830\pi\)
0.700791 + 0.713366i \(0.252830\pi\)
\(728\) 0.372609 5.29236i 0.0138098 0.196148i
\(729\) −66.2863 91.2353i −2.45505 3.37909i
\(730\) −0.655650 4.89122i −0.0242667 0.181032i
\(731\) 1.98213 + 4.45194i 0.0733117 + 0.164661i
\(732\) 8.52893 + 31.8304i 0.315238 + 1.17649i
\(733\) 28.3876 + 35.0558i 1.04852 + 1.29482i 0.954166 + 0.299277i \(0.0967455\pi\)
0.0943550 + 0.995539i \(0.469921\pi\)
\(734\) −0.219627 + 0.675942i −0.00810658 + 0.0249495i
\(735\) −44.3771 + 28.3587i −1.63687 + 1.04603i
\(736\) 3.37740 + 10.3946i 0.124493 + 0.383149i
\(737\) −4.65346 + 7.16570i −0.171412 + 0.263952i
\(738\) 95.4152 + 5.00050i 3.51228 + 0.184071i
\(739\) 1.55619 7.32130i 0.0572454 0.269318i −0.940211 0.340591i \(-0.889373\pi\)
0.997457 + 0.0712729i \(0.0227061\pi\)
\(740\) −0.287330 + 0.198473i −0.0105625 + 0.00729603i
\(741\) −10.0465 3.26429i −0.369066 0.119917i
\(742\) −57.0415 + 14.1932i −2.09406 + 0.521049i
\(743\) 12.2018 + 12.2018i 0.447641 + 0.447641i 0.894569 0.446929i \(-0.147482\pi\)
−0.446929 + 0.894569i \(0.647482\pi\)
\(744\) 20.1433 + 2.11715i 0.738490 + 0.0776184i
\(745\) −41.3898 + 1.18127i −1.51641 + 0.0432783i
\(746\) −6.22586 59.2351i −0.227945 2.16875i
\(747\) −18.7513 48.8489i −0.686076 1.78729i
\(748\) −3.97169 2.02368i −0.145219 0.0739930i
\(749\) −34.7494 + 24.3071i −1.26971 + 0.888163i
\(750\) 57.7865 + 34.8531i 2.11007 + 1.27266i
\(751\) 7.41010 + 12.8347i 0.270398 + 0.468344i 0.968964 0.247203i \(-0.0795113\pi\)
−0.698566 + 0.715546i \(0.746178\pi\)
\(752\) 19.8189 + 30.5184i 0.722721 + 1.11289i
\(753\) 38.0895 47.0367i 1.38806 1.71411i
\(754\) 4.88003 + 2.17273i 0.177720 + 0.0791262i
\(755\) −29.4671 + 18.1530i −1.07242 + 0.660653i
\(756\) −27.9491 50.4782i −1.01650 1.83587i
\(757\) 34.1428 34.1428i 1.24094 1.24094i 0.281332 0.959610i \(-0.409224\pi\)
0.959610 0.281332i \(-0.0907762\pi\)
\(758\) 8.25213 6.68244i 0.299731 0.242717i
\(759\) 11.2723 + 12.5191i 0.409158 + 0.454416i
\(760\) 6.22210 + 2.94984i 0.225699 + 0.107002i
\(761\) 19.1966 + 17.2847i 0.695877 + 0.626570i 0.939198 0.343375i \(-0.111570\pi\)
−0.243321 + 0.969946i \(0.578237\pi\)
\(762\) 11.9570 6.09237i 0.433155 0.220703i
\(763\) 0.143826 + 4.17563i 0.00520686 + 0.151168i
\(764\) 10.3072 3.34902i 0.372903 0.121163i
\(765\) −14.8352 + 19.4281i −0.536368 + 0.702424i
\(766\) 19.3265 17.4017i 0.698297 0.628749i
\(767\) −0.505559 + 1.31703i −0.0182547 + 0.0475551i
\(768\) −66.9241 17.9323i −2.41491 0.647074i
\(769\) 4.99641 + 3.63011i 0.180175 + 0.130905i 0.674217 0.738533i \(-0.264481\pi\)
−0.494042 + 0.869438i \(0.664481\pi\)
\(770\) −6.45153 28.8447i −0.232497 1.03949i
\(771\) −63.4160 + 46.0744i −2.28387 + 1.65933i
\(772\) 17.8199 6.84040i 0.641351 0.246191i
\(773\) −35.9087 + 23.3194i −1.29155 + 0.838739i −0.993279 0.115743i \(-0.963075\pi\)
−0.298266 + 0.954483i \(0.596408\pi\)
\(774\) −47.9478 27.6827i −1.72345 0.995033i
\(775\) −11.6040 + 18.0540i −0.416829 + 0.648520i
\(776\) 19.0331i 0.683249i
\(777\) 0.428005 1.05790i 0.0153546 0.0379519i
\(778\) −14.6309 2.31731i −0.524544 0.0830795i
\(779\) −5.71680 + 12.8402i −0.204826 + 0.460046i
\(780\) −7.39723 + 10.8175i −0.264863 + 0.387327i
\(781\) 15.0402 6.69633i 0.538181 0.239613i
\(782\) 1.09671 4.09296i 0.0392181 0.146364i
\(783\) −36.8225 + 5.83211i −1.31593 + 0.208422i
\(784\) 12.9557 + 32.1547i 0.462705 + 1.14838i
\(785\) 4.11751 + 0.978289i 0.146960 + 0.0349166i
\(786\) 24.5529 27.2687i 0.875772 0.972643i
\(787\) 1.73452 33.0967i 0.0618291 1.17977i −0.774875 0.632114i \(-0.782187\pi\)
0.836704 0.547655i \(-0.184479\pi\)
\(788\) −0.431034 + 8.22463i −0.0153550 + 0.292990i
\(789\) −14.8880 + 16.5348i −0.530026 + 0.588653i
\(790\) 22.3320 + 26.0232i 0.794535 + 0.925862i
\(791\) −12.2907 + 53.1216i −0.437008 + 1.88879i
\(792\) −32.0986 + 5.08393i −1.14058 + 0.180649i
\(793\) −2.97520 + 11.1036i −0.105653 + 0.394301i
\(794\) −6.62085 + 2.94779i −0.234965 + 0.104613i
\(795\) −89.3996 26.2528i −3.17068 0.931090i
\(796\) −5.21710 + 11.7178i −0.184915 + 0.415327i
\(797\) −30.0160 4.75407i −1.06322 0.168398i −0.399769 0.916616i \(-0.630910\pi\)
−0.663452 + 0.748218i \(0.730910\pi\)
\(798\) 34.7266 4.86364i 1.22931 0.172171i
\(799\) 9.65383i 0.341528i
\(800\) 20.2329 22.6847i 0.715342 0.802024i
\(801\) 22.7939 + 13.1601i 0.805382 + 0.464988i
\(802\) −5.91374 + 3.84043i −0.208822 + 0.135610i
\(803\) −3.19865 + 1.22785i −0.112878 + 0.0433298i
\(804\) −10.1733 + 7.39135i −0.358786 + 0.260673i
\(805\) 9.67002 4.42881i 0.340823 0.156095i
\(806\) −8.90724 6.47149i −0.313744 0.227948i
\(807\) −33.1519 8.88302i −1.16700 0.312697i
\(808\) 5.63546 14.6809i 0.198255 0.516472i
\(809\) −34.3619 + 30.9396i −1.20810 + 1.08778i −0.214279 + 0.976773i \(0.568740\pi\)
−0.993820 + 0.111004i \(0.964593\pi\)
\(810\) 3.37086 141.442i 0.118440 4.96977i
\(811\) −50.5167 + 16.4139i −1.77388 + 0.576369i −0.998481 0.0550996i \(-0.982452\pi\)
−0.775401 + 0.631469i \(0.782452\pi\)
\(812\) −6.70841 + 0.231066i −0.235419 + 0.00810881i
\(813\) −11.0883 + 5.64979i −0.388885 + 0.198147i
\(814\) 0.475975 + 0.428570i 0.0166829 + 0.0150214i
\(815\) 10.5543 + 19.3301i 0.369702 + 0.677102i
\(816\) 14.6488 + 16.2691i 0.512810 + 0.569533i
\(817\) 6.32947 5.12550i 0.221440 0.179319i
\(818\) −49.8712 + 49.8712i −1.74370 + 1.74370i
\(819\) 0.564322 31.4715i 0.0197190 1.09970i
\(820\) 13.2856 + 11.2930i 0.463953 + 0.394369i
\(821\) −16.1959 7.21089i −0.565241 0.251662i 0.104163 0.994560i \(-0.466784\pi\)
−0.669404 + 0.742899i \(0.733450\pi\)
\(822\) 29.9662 37.0052i 1.04519 1.29070i
\(823\) −15.2848 23.5365i −0.532795 0.820432i 0.465102 0.885257i \(-0.346018\pi\)
−0.997897 + 0.0648249i \(0.979351\pi\)
\(824\) −9.17990 15.9001i −0.319797 0.553905i
\(825\) 14.2683 44.6265i 0.496757 1.55370i
\(826\) −0.405922 4.66528i −0.0141238 0.162326i
\(827\) −44.0345 22.4367i −1.53123 0.780200i −0.533388 0.845871i \(-0.679081\pi\)
−0.997841 + 0.0656703i \(0.979081\pi\)
\(828\) 6.53060 + 17.0128i 0.226954 + 0.591236i
\(829\) −3.75520 35.7283i −0.130423 1.24090i −0.842462 0.538756i \(-0.818894\pi\)
0.712038 0.702141i \(-0.247772\pi\)
\(830\) 7.10757 24.2037i 0.246707 0.840122i
\(831\) 44.7291 + 4.70122i 1.55164 + 0.163084i
\(832\) 1.01232 + 1.01232i 0.0350959 + 0.0350959i
\(833\) 1.76344 9.02624i 0.0610996 0.312741i
\(834\) 1.96940 + 0.639896i 0.0681946 + 0.0221578i
\(835\) 5.43314 15.4582i 0.188022 0.534952i
\(836\) −1.54888 + 7.28693i −0.0535693 + 0.252024i
\(837\) 76.7345 + 4.02148i 2.65233 + 0.139003i
\(838\) 8.38710 12.9150i 0.289728 0.446141i
\(839\) −12.2133 37.5885i −0.421649 1.29770i −0.906167 0.422920i \(-0.861005\pi\)
0.484519 0.874781i \(-0.338995\pi\)
\(840\) −4.07448 + 27.6174i −0.140583 + 0.952889i
\(841\) 7.62125 23.4558i 0.262802 0.808821i
\(842\) −19.5060 24.0879i −0.672220 0.830122i
\(843\) 18.9639 + 70.7741i 0.653150 + 2.43759i
\(844\) 7.50007 + 16.8454i 0.258163 + 0.579844i
\(845\) 22.0862 10.5984i 0.759787 0.364596i
\(846\) 64.4670 + 88.7312i 2.21642 + 3.05064i
\(847\) 7.71555 3.75858i 0.265110 0.129146i
\(848\) −27.8445 + 54.6478i −0.956183 + 1.87661i
\(849\) 58.1370 33.5654i 1.99526 1.15196i
\(850\) −11.3687 + 3.10364i −0.389944 + 0.106454i
\(851\) −0.115237 + 0.199596i −0.00395027 + 0.00684207i
\(852\) 24.1973 1.26812i 0.828984 0.0434452i
\(853\) −8.40569 + 53.0714i −0.287805 + 1.81713i 0.243444 + 0.969915i \(0.421723\pi\)
−0.531249 + 0.847215i \(0.678277\pi\)
\(854\) −7.26319 37.4611i −0.248541 1.28189i
\(855\) 37.7802 + 15.5450i 1.29205 + 0.531629i
\(856\) −2.34970 + 22.3559i −0.0803112 + 0.764110i
\(857\) −33.7704 + 9.04875i −1.15357 + 0.309099i −0.784397 0.620260i \(-0.787027\pi\)
−0.369178 + 0.929359i \(0.620361\pi\)
\(858\) 22.4389 + 8.61350i 0.766053 + 0.294060i
\(859\) 17.6446 3.75048i 0.602027 0.127965i 0.103192 0.994661i \(-0.467094\pi\)
0.498836 + 0.866697i \(0.333761\pi\)
\(860\) −3.88854 9.32567i −0.132598 0.318003i
\(861\) −56.5536 6.97123i −1.92734 0.237579i
\(862\) 29.1216 + 57.1543i 0.991884 + 1.94668i
\(863\) −33.4803 21.7424i −1.13968 0.740120i −0.170233 0.985404i \(-0.554452\pi\)
−0.969451 + 0.245284i \(0.921119\pi\)
\(864\) −106.452 22.6272i −3.62158 0.769791i
\(865\) 17.7009 37.3364i 0.601848 1.26948i
\(866\) 4.18169 + 19.6733i 0.142099 + 0.668525i
\(867\) 8.03923 + 50.7577i 0.273027 + 1.72382i
\(868\) 13.6234 + 2.40886i 0.462408 + 0.0817619i
\(869\) 13.9939 19.2609i 0.474710 0.653382i
\(870\) −24.7331 13.3538i −0.838532 0.452735i
\(871\) −4.36256 + 0.458524i −0.147820 + 0.0155365i
\(872\) 1.72116 + 1.39377i 0.0582860 + 0.0471990i
\(873\) 5.90982 + 112.766i 0.200017 + 3.81655i
\(874\) −7.08173 −0.239543
\(875\) −24.1944 17.0186i −0.817920 0.575333i
\(876\) −5.04258 −0.170373
\(877\) −0.192873 3.68024i −0.00651286 0.124273i −0.999951 0.00990186i \(-0.996848\pi\)
0.993438 0.114371i \(-0.0364852\pi\)
\(878\) −22.9636 18.5956i −0.774985 0.627570i
\(879\) 80.1966 8.42901i 2.70497 0.284303i
\(880\) −27.1378 14.6521i −0.914814 0.493921i
\(881\) −2.33356 + 3.21186i −0.0786195 + 0.108210i −0.846515 0.532364i \(-0.821304\pi\)
0.767896 + 0.640575i \(0.221304\pi\)
\(882\) 44.0677 + 94.7388i 1.48384 + 3.19002i
\(883\) −1.62857 10.2824i −0.0548057 0.346030i −0.999819 0.0189993i \(-0.993952\pi\)
0.945014 0.327031i \(-0.106048\pi\)
\(884\) −0.475810 2.23851i −0.0160032 0.0752893i
\(885\) 3.17990 6.70736i 0.106891 0.225466i
\(886\) 18.9564 + 4.02932i 0.636854 + 0.135367i
\(887\) 40.1413 + 26.0680i 1.34781 + 0.875279i 0.998102 0.0615788i \(-0.0196135\pi\)
0.349710 + 0.936858i \(0.386280\pi\)
\(888\) −0.274631 0.538993i −0.00921601 0.0180874i
\(889\) −5.41576 + 2.29581i −0.181639 + 0.0769991i
\(890\) 4.88344 + 11.7117i 0.163693 + 0.392576i
\(891\) −96.0809 + 20.4226i −3.21883 + 0.684184i
\(892\) 25.9246 + 9.95153i 0.868020 + 0.333202i
\(893\) −15.5844 + 4.17582i −0.521511 + 0.139738i
\(894\) −11.6832 + 111.158i −0.390745 + 3.71769i
\(895\) 30.6830 + 12.6248i 1.02562 + 0.422002i
\(896\) 25.9187 + 8.93832i 0.865883 + 0.298608i
\(897\) −1.35299 + 8.54243i −0.0451749 + 0.285223i
\(898\) 41.6696 2.18381i 1.39053 0.0728747i
\(899\) 4.46954 7.74147i 0.149067 0.258192i
\(900\) 31.7094 39.5367i 1.05698 1.31789i
\(901\) 14.0913 8.13562i 0.469450 0.271037i
\(902\) 14.5188 28.4947i 0.483423 0.948771i
\(903\) 27.3649 + 18.4768i 0.910648 + 0.614870i
\(904\) 16.9885 + 23.3826i 0.565028 + 0.777695i
\(905\) 22.6656 10.8764i 0.753429 0.361545i
\(906\) 37.9988 + 85.3468i 1.26243 + 2.83546i
\(907\) −1.60740 5.99891i −0.0533730 0.199191i 0.934091 0.357035i \(-0.116212\pi\)
−0.987464 + 0.157844i \(0.949546\pi\)
\(908\) −10.2022 12.5986i −0.338571 0.418101i
\(909\) 28.8302 88.7301i 0.956236 2.94299i
\(910\) 9.42431 11.8937i 0.312413 0.394273i
\(911\) 13.3336 + 41.0366i 0.441762 + 1.35960i 0.885996 + 0.463693i \(0.153476\pi\)
−0.444234 + 0.895911i \(0.646524\pi\)
\(912\) 19.9272 30.6851i 0.659854 1.01609i
\(913\) −17.4895 0.916587i −0.578819 0.0303346i
\(914\) −3.96945 + 18.6748i −0.131298 + 0.617708i
\(915\) 20.0565 57.0640i 0.663047 1.88648i
\(916\) 1.10610 + 0.359393i 0.0365465 + 0.0118747i
\(917\) −11.5753 + 11.1675i −0.382249 + 0.368782i
\(918\) 29.8352 + 29.8352i 0.984708 + 0.984708i
\(919\) −37.6803 3.96036i −1.24296 0.130640i −0.539874 0.841746i \(-0.681528\pi\)
−0.703085 + 0.711106i \(0.748195\pi\)
\(920\) 1.58853 5.40948i 0.0523722 0.178345i
\(921\) −2.17990 20.7404i −0.0718302 0.683419i
\(922\) 6.13042 + 15.9703i 0.201895 + 0.525954i
\(923\) 7.53121 + 3.83734i 0.247893 + 0.126308i
\(924\) −30.0883 + 2.61795i −0.989832 + 0.0861243i
\(925\) 0.640979 0.00301567i 0.0210753 9.91547e-5i
\(926\) −27.9055 48.3337i −0.917031 1.58834i
\(927\) −59.3254 91.3531i −1.94850 3.00043i
\(928\) −7.96764 + 9.83921i −0.261551 + 0.322988i
\(929\) −18.8136 8.37634i −0.617253 0.274819i 0.0741964 0.997244i \(-0.476361\pi\)
−0.691449 + 0.722425i \(0.743027\pi\)
\(930\) 44.1404 + 37.5203i 1.44742 + 1.23034i
\(931\) −15.3340 + 1.05759i −0.502552 + 0.0346611i
\(932\) −5.26542 + 5.26542i −0.172475 + 0.172475i
\(933\) 13.7697 11.1505i 0.450800 0.365051i
\(934\) −31.1840 34.6333i −1.02037 1.13324i
\(935\) 3.92095 + 7.18115i 0.128229 + 0.234849i
\(936\) −12.3994 11.1645i −0.405287 0.364922i
\(937\) −32.8384 + 16.7320i −1.07278 + 0.546610i −0.898899 0.438156i \(-0.855632\pi\)
−0.173884 + 0.984766i \(0.555632\pi\)
\(938\) 12.3524 7.71044i 0.403319 0.251755i
\(939\) 80.1655 26.0473i 2.61610 0.850023i
\(940\) −0.476879 + 20.0100i −0.0155541 + 0.652654i
\(941\) 10.5157 9.46840i 0.342803 0.308661i −0.479688 0.877439i \(-0.659250\pi\)
0.822491 + 0.568778i \(0.192584\pi\)
\(942\) 4.09398 10.6652i 0.133389 0.347491i
\(943\) 11.1157 + 2.97845i 0.361978 + 0.0969917i
\(944\) −3.95303 2.87204i −0.128660 0.0934770i
\(945\) −9.95297 + 105.439i −0.323770 + 3.42993i
\(946\) −14.9922 + 10.8925i −0.487439 + 0.354145i
\(947\) −6.08066 + 2.33415i −0.197595 + 0.0758495i −0.455153 0.890413i \(-0.650415\pi\)
0.257558 + 0.966263i \(0.417082\pi\)
\(948\) 29.3866 19.0839i 0.954432 0.619816i
\(949\) −1.52337 0.879519i −0.0494507 0.0285504i
\(950\) 9.92788 + 17.0103i 0.322103 + 0.551886i
\(951\) 8.07745i 0.261929i
\(952\) −2.99957 3.84304i −0.0972165 0.124554i
\(953\) 22.4339 + 3.55319i 0.726706 + 0.115099i 0.508817 0.860875i \(-0.330083\pi\)
0.217889 + 0.975974i \(0.430083\pi\)
\(954\) −75.1888 + 168.877i −2.43433 + 5.46759i
\(955\) −19.0867 5.60494i −0.617632 0.181372i
\(956\) −2.41712 + 1.07617i −0.0781753 + 0.0348059i
\(957\) −5.05073 + 18.8496i −0.163267 + 0.609321i
\(958\) −53.6636 + 8.49948i −1.73379 + 0.274606i
\(959\) −14.2420 + 15.2581i −0.459898 + 0.492710i
\(960\) −4.90575 5.71661i −0.158333 0.184503i
\(961\) 8.41493 9.34573i 0.271449 0.301475i
\(962\) −0.0172096 + 0.328379i −0.000554861 + 0.0105874i
\(963\) −6.97979 + 133.182i −0.224921 + 4.29174i
\(964\) 17.1073 18.9996i 0.550988 0.611934i
\(965\) −34.0867 8.09874i −1.09729 0.260708i
\(966\) −8.38094 27.4596i −0.269652 0.883497i
\(967\) 14.8670 2.35470i 0.478090 0.0757220i 0.0872612 0.996185i \(-0.472189\pi\)
0.390829 + 0.920463i \(0.372189\pi\)
\(968\) 1.17745 4.39431i 0.0378447 0.141238i
\(969\) −8.86738 + 3.94801i −0.284861 + 0.126828i
\(970\) −30.7292 + 44.9374i −0.986656 + 1.44285i
\(971\) 19.2083 43.1426i 0.616425 1.38451i −0.287897 0.957661i \(-0.592956\pi\)
0.904322 0.426851i \(-0.140377\pi\)
\(972\) −78.1685 12.3807i −2.50725 0.397110i
\(973\) −0.841426 0.340424i −0.0269749 0.0109135i
\(974\) 52.9606i 1.69697i
\(975\) 22.4156 8.72576i 0.717874 0.279448i
\(976\) −34.4811 19.9076i −1.10371 0.637228i
\(977\) −14.1121 + 9.16452i −0.451487 + 0.293199i −0.750282 0.661118i \(-0.770082\pi\)
0.298795 + 0.954317i \(0.403415\pi\)
\(978\) 55.5009 21.3048i 1.77472 0.681252i
\(979\) 7.12715 5.17818i 0.227785 0.165495i
\(980\) −4.10105 + 18.6220i −0.131003 + 0.594859i
\(981\) 10.6302 + 7.72329i 0.339396 + 0.246586i
\(982\) 50.7782 + 13.6060i 1.62040 + 0.434184i
\(983\) 14.2858 37.2158i 0.455646 1.18700i −0.492823 0.870129i \(-0.664035\pi\)
0.948469 0.316869i \(-0.102632\pi\)
\(984\) −22.4465 + 20.2109i −0.715569 + 0.644301i
\(985\) 9.17448 12.0148i 0.292323 0.382824i
\(986\) 4.66828 1.51682i 0.148668 0.0483053i
\(987\) −34.6353 55.4868i −1.10245 1.76617i
\(988\) −3.40786 + 1.73639i −0.108418 + 0.0552419i
\(989\) −4.95556 4.46200i −0.157578 0.141883i
\(990\) −83.9933 39.8205i −2.66948 1.26558i
\(991\) 23.0510 + 25.6007i 0.732239 + 0.813234i 0.988154 0.153465i \(-0.0490433\pi\)
−0.255915 + 0.966699i \(0.582377\pi\)
\(992\) 20.2793 16.4219i 0.643869 0.521395i
\(993\) 68.6777 68.6777i 2.17942 2.17942i
\(994\) −28.0535 0.503033i −0.889803 0.0159552i
\(995\) 20.0452 12.3487i 0.635477 0.391480i
\(996\) −23.5474 10.4840i −0.746127 0.332197i
\(997\) −4.61203 + 5.69539i −0.146065 + 0.180375i −0.844927 0.534881i \(-0.820356\pi\)
0.698863 + 0.715256i \(0.253690\pi\)
\(998\) 3.47168 + 5.34592i 0.109894 + 0.169222i
\(999\) −1.14747 1.98748i −0.0363044 0.0628810i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 175.2.x.a.108.15 yes 288
5.2 odd 4 875.2.bb.b.857.4 288
5.3 odd 4 875.2.bb.a.857.15 288
5.4 even 2 875.2.bb.c.143.4 288
7.5 odd 6 inner 175.2.x.a.33.15 288
25.3 odd 20 875.2.bb.c.507.4 288
25.4 even 10 875.2.bb.a.493.4 288
25.21 even 5 875.2.bb.b.493.15 288
25.22 odd 20 inner 175.2.x.a.122.15 yes 288
35.12 even 12 875.2.bb.b.607.15 288
35.19 odd 6 875.2.bb.c.768.4 288
35.33 even 12 875.2.bb.a.607.4 288
175.47 even 60 inner 175.2.x.a.47.15 yes 288
175.54 odd 30 875.2.bb.a.243.15 288
175.96 odd 30 875.2.bb.b.243.4 288
175.103 even 60 875.2.bb.c.257.4 288
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.x.a.33.15 288 7.5 odd 6 inner
175.2.x.a.47.15 yes 288 175.47 even 60 inner
175.2.x.a.108.15 yes 288 1.1 even 1 trivial
175.2.x.a.122.15 yes 288 25.22 odd 20 inner
875.2.bb.a.243.15 288 175.54 odd 30
875.2.bb.a.493.4 288 25.4 even 10
875.2.bb.a.607.4 288 35.33 even 12
875.2.bb.a.857.15 288 5.3 odd 4
875.2.bb.b.243.4 288 175.96 odd 30
875.2.bb.b.493.15 288 25.21 even 5
875.2.bb.b.607.15 288 35.12 even 12
875.2.bb.b.857.4 288 5.2 odd 4
875.2.bb.c.143.4 288 5.4 even 2
875.2.bb.c.257.4 288 175.103 even 60
875.2.bb.c.507.4 288 25.3 odd 20
875.2.bb.c.768.4 288 35.19 odd 6