Properties

Label 378.2.v.b.79.4
Level $378$
Weight $2$
Character 378.79
Analytic conductor $3.018$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [378,2,Mod(67,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.v (of order \(9\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(12\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 79.4
Character \(\chi\) \(=\) 378.79
Dual form 378.2.v.b.67.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +O(q^{10})\) \(q+(0.766044 + 0.642788i) q^{2} +(-1.07856 + 1.35526i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.620533 + 3.51922i) q^{5} +(-1.69736 + 0.344903i) q^{6} +(-0.670349 + 2.55942i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.673434 - 2.92344i) q^{9} +(-1.78675 + 3.09475i) q^{10} +(0.735962 - 4.17385i) q^{11} +(-1.52196 - 0.826833i) q^{12} +(-0.585610 - 3.32116i) q^{13} +(-2.15868 + 1.52974i) q^{14} +(-5.43872 - 2.95469i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(1.28580 - 2.22707i) q^{17} +(1.36327 - 2.67236i) q^{18} +(3.01921 + 5.22942i) q^{19} +(-3.35800 + 1.22221i) q^{20} +(-2.74566 - 3.66897i) q^{21} +(3.24668 - 2.72429i) q^{22} +(-1.75410 + 1.47186i) q^{23} +(-0.634407 - 1.61168i) q^{24} +(-7.30136 + 2.65748i) q^{25} +(1.68620 - 2.92058i) q^{26} +(4.68834 + 2.24042i) q^{27} +(-2.63694 - 0.215726i) q^{28} +(-0.315874 + 1.79141i) q^{29} +(-2.26706 - 5.75936i) q^{30} +(1.79383 + 10.1733i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(4.86285 + 5.49914i) q^{33} +(2.41652 - 0.879540i) q^{34} +(-9.42313 - 0.770898i) q^{35} +(2.76208 - 1.17085i) q^{36} +7.16828 q^{37} +(-1.04856 + 5.94668i) q^{38} +(5.13263 + 2.78840i) q^{39} +(-3.35800 - 1.22221i) q^{40} +(-1.32145 - 7.49429i) q^{41} +(0.255073 - 4.57547i) q^{42} +(-2.13929 - 1.79507i) q^{43} +4.23824 q^{44} +(9.87032 - 4.18405i) q^{45} -2.28981 q^{46} +(-0.550684 + 3.12308i) q^{47} +(0.549987 - 1.64241i) q^{48} +(-6.10127 - 3.43141i) q^{49} +(-7.30136 - 2.65748i) q^{50} +(1.63144 + 4.14461i) q^{51} +(3.16901 - 1.15343i) q^{52} +(4.04351 + 7.00356i) q^{53} +(2.15136 + 4.72987i) q^{54} +15.1454 q^{55} +(-1.88135 - 1.86025i) q^{56} +(-10.3436 - 1.54843i) q^{57} +(-1.39347 + 1.16926i) q^{58} +(-5.98431 - 2.17811i) q^{59} +(1.96538 - 5.86917i) q^{60} +(0.904765 - 5.13118i) q^{61} +(-5.16512 + 8.94625i) q^{62} +(7.93374 + 0.236123i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(11.3245 - 4.12177i) q^{65} +(0.190379 + 7.33837i) q^{66} +(-1.43204 + 1.20163i) q^{67} +(2.41652 + 0.879540i) q^{68} +(-0.102857 - 3.96474i) q^{69} +(-6.72301 - 6.64761i) q^{70} +(-3.31293 - 5.73817i) q^{71} +(2.86849 + 0.878508i) q^{72} +12.1719 q^{73} +(5.49122 + 4.60768i) q^{74} +(4.27337 - 12.7614i) q^{75} +(-4.62570 + 3.88142i) q^{76} +(10.1893 + 4.68157i) q^{77} +(2.13947 + 5.43523i) q^{78} +(2.65034 + 2.22390i) q^{79} +(-1.78675 - 3.09475i) q^{80} +(-8.09297 + 3.93748i) q^{81} +(3.80495 - 6.59037i) q^{82} +(0.275388 - 1.56180i) q^{83} +(3.13645 - 3.34106i) q^{84} +(8.63544 + 3.14304i) q^{85} +(-0.484937 - 2.75021i) q^{86} +(-2.08713 - 2.36023i) q^{87} +(3.24668 + 2.72429i) q^{88} +(-2.58297 - 4.47383i) q^{89} +(10.2506 + 3.13935i) q^{90} +(8.89280 + 0.727513i) q^{91} +(-1.75410 - 1.47186i) q^{92} +(-15.7222 - 8.54138i) q^{93} +(-2.42933 + 2.03845i) q^{94} +(-16.5300 + 13.8703i) q^{95} +(1.47704 - 0.904635i) q^{96} +(14.6758 + 12.3145i) q^{97} +(-2.46817 - 6.55043i) q^{98} +(-12.6976 + 0.659271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 72 q + 3 q^{6} + 6 q^{7} - 36 q^{8} + 24 q^{9} - 6 q^{10} + 12 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} - 12 q^{17} - 18 q^{19} - 30 q^{21} - 6 q^{22} + 30 q^{23} + 6 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} - 18 q^{35} + 9 q^{36} - 24 q^{39} - 6 q^{41} + 12 q^{42} + 24 q^{43} + 51 q^{45} + 45 q^{47} - 6 q^{48} - 12 q^{49} + 6 q^{50} - 51 q^{51} + 6 q^{52} - 15 q^{53} + 27 q^{54} + 72 q^{55} - 3 q^{56} - 63 q^{57} + 3 q^{58} - 30 q^{59} - 3 q^{60} + 9 q^{61} - 24 q^{62} - 39 q^{63} - 36 q^{64} + 9 q^{65} - 6 q^{67} + 9 q^{68} - 21 q^{69} - 33 q^{70} + 12 q^{71} - 12 q^{72} + 132 q^{73} - 18 q^{74} - 30 q^{75} - 33 q^{77} + 30 q^{78} - 9 q^{79} - 6 q^{80} + 36 q^{81} - 33 q^{82} - 18 q^{83} + 15 q^{84} + 21 q^{85} - 12 q^{86} - 39 q^{87} - 6 q^{88} - 36 q^{89} + 69 q^{90} + 39 q^{91} + 30 q^{92} - 66 q^{93} - 9 q^{94} - 33 q^{95} - 48 q^{97} - 12 q^{98} - 54 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766044 + 0.642788i 0.541675 + 0.454519i
\(3\) −1.07856 + 1.35526i −0.622705 + 0.782457i
\(4\) 0.173648 + 0.984808i 0.0868241 + 0.492404i
\(5\) 0.620533 + 3.51922i 0.277511 + 1.57384i 0.730872 + 0.682515i \(0.239114\pi\)
−0.453361 + 0.891327i \(0.649775\pi\)
\(6\) −1.69736 + 0.344903i −0.692946 + 0.140806i
\(7\) −0.670349 + 2.55942i −0.253368 + 0.967370i
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) −0.673434 2.92344i −0.224478 0.974479i
\(10\) −1.78675 + 3.09475i −0.565021 + 0.978645i
\(11\) 0.735962 4.17385i 0.221901 1.25846i −0.646621 0.762811i \(-0.723818\pi\)
0.868522 0.495651i \(-0.165070\pi\)
\(12\) −1.52196 0.826833i −0.439351 0.238686i
\(13\) −0.585610 3.32116i −0.162419 0.921123i −0.951686 0.307073i \(-0.900650\pi\)
0.789267 0.614050i \(-0.210461\pi\)
\(14\) −2.15868 + 1.52974i −0.576932 + 0.408840i
\(15\) −5.43872 2.95469i −1.40427 0.762898i
\(16\) −0.939693 + 0.342020i −0.234923 + 0.0855050i
\(17\) 1.28580 2.22707i 0.311853 0.540145i −0.666911 0.745138i \(-0.732384\pi\)
0.978763 + 0.204993i \(0.0657171\pi\)
\(18\) 1.36327 2.67236i 0.321326 0.629881i
\(19\) 3.01921 + 5.22942i 0.692654 + 1.19971i 0.970965 + 0.239221i \(0.0768920\pi\)
−0.278311 + 0.960491i \(0.589775\pi\)
\(20\) −3.35800 + 1.22221i −0.750871 + 0.273295i
\(21\) −2.74566 3.66897i −0.599152 0.800635i
\(22\) 3.24668 2.72429i 0.692194 0.580820i
\(23\) −1.75410 + 1.47186i −0.365755 + 0.306905i −0.807079 0.590443i \(-0.798953\pi\)
0.441325 + 0.897347i \(0.354509\pi\)
\(24\) −0.634407 1.61168i −0.129498 0.328984i
\(25\) −7.30136 + 2.65748i −1.46027 + 0.531496i
\(26\) 1.68620 2.92058i 0.330690 0.572772i
\(27\) 4.68834 + 2.24042i 0.902271 + 0.431168i
\(28\) −2.63694 0.215726i −0.498335 0.0407684i
\(29\) −0.315874 + 1.79141i −0.0586563 + 0.332657i −0.999988 0.00482527i \(-0.998464\pi\)
0.941332 + 0.337482i \(0.109575\pi\)
\(30\) −2.26706 5.75936i −0.413906 1.05151i
\(31\) 1.79383 + 10.1733i 0.322181 + 1.82718i 0.528787 + 0.848755i \(0.322647\pi\)
−0.206606 + 0.978424i \(0.566242\pi\)
\(32\) −0.939693 0.342020i −0.166116 0.0604612i
\(33\) 4.86285 + 5.49914i 0.846514 + 0.957278i
\(34\) 2.41652 0.879540i 0.414429 0.150840i
\(35\) −9.42313 0.770898i −1.59280 0.130306i
\(36\) 2.76208 1.17085i 0.460347 0.195142i
\(37\) 7.16828 1.17846 0.589229 0.807966i \(-0.299431\pi\)
0.589229 + 0.807966i \(0.299431\pi\)
\(38\) −1.04856 + 5.94668i −0.170099 + 0.964679i
\(39\) 5.13263 + 2.78840i 0.821879 + 0.446502i
\(40\) −3.35800 1.22221i −0.530946 0.193249i
\(41\) −1.32145 7.49429i −0.206375 1.17041i −0.895261 0.445542i \(-0.853011\pi\)
0.688886 0.724870i \(-0.258100\pi\)
\(42\) 0.255073 4.57547i 0.0393586 0.706011i
\(43\) −2.13929 1.79507i −0.326238 0.273746i 0.464927 0.885349i \(-0.346081\pi\)
−0.791165 + 0.611603i \(0.790525\pi\)
\(44\) 4.23824 0.638938
\(45\) 9.87032 4.18405i 1.47138 0.623721i
\(46\) −2.28981 −0.337614
\(47\) −0.550684 + 3.12308i −0.0803255 + 0.455549i 0.917942 + 0.396714i \(0.129850\pi\)
−0.998268 + 0.0588345i \(0.981262\pi\)
\(48\) 0.549987 1.64241i 0.0793837 0.237062i
\(49\) −6.10127 3.43141i −0.871609 0.490201i
\(50\) −7.30136 2.65748i −1.03257 0.375824i
\(51\) 1.63144 + 4.14461i 0.228448 + 0.580362i
\(52\) 3.16901 1.15343i 0.439463 0.159951i
\(53\) 4.04351 + 7.00356i 0.555418 + 0.962012i 0.997871 + 0.0652206i \(0.0207751\pi\)
−0.442453 + 0.896792i \(0.645892\pi\)
\(54\) 2.15136 + 4.72987i 0.292764 + 0.643653i
\(55\) 15.1454 2.04220
\(56\) −1.88135 1.86025i −0.251406 0.248586i
\(57\) −10.3436 1.54843i −1.37004 0.205094i
\(58\) −1.39347 + 1.16926i −0.182972 + 0.153531i
\(59\) −5.98431 2.17811i −0.779091 0.283566i −0.0782972 0.996930i \(-0.524948\pi\)
−0.700793 + 0.713364i \(0.747171\pi\)
\(60\) 1.96538 5.86917i 0.253730 0.757706i
\(61\) 0.904765 5.13118i 0.115843 0.656980i −0.870486 0.492193i \(-0.836195\pi\)
0.986329 0.164787i \(-0.0526936\pi\)
\(62\) −5.16512 + 8.94625i −0.655971 + 1.13617i
\(63\) 7.93374 + 0.236123i 0.999557 + 0.0297487i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 11.3245 4.12177i 1.40463 0.511243i
\(66\) 0.190379 + 7.33837i 0.0234341 + 0.903291i
\(67\) −1.43204 + 1.20163i −0.174952 + 0.146802i −0.726059 0.687633i \(-0.758650\pi\)
0.551107 + 0.834435i \(0.314206\pi\)
\(68\) 2.41652 + 0.879540i 0.293046 + 0.106660i
\(69\) −0.102857 3.96474i −0.0123825 0.477298i
\(70\) −6.72301 6.64761i −0.803553 0.794542i
\(71\) −3.31293 5.73817i −0.393173 0.680996i 0.599693 0.800230i \(-0.295289\pi\)
−0.992866 + 0.119234i \(0.961956\pi\)
\(72\) 2.86849 + 0.878508i 0.338055 + 0.103533i
\(73\) 12.1719 1.42462 0.712309 0.701866i \(-0.247649\pi\)
0.712309 + 0.701866i \(0.247649\pi\)
\(74\) 5.49122 + 4.60768i 0.638342 + 0.535632i
\(75\) 4.27337 12.7614i 0.493446 1.47356i
\(76\) −4.62570 + 3.88142i −0.530604 + 0.445229i
\(77\) 10.1893 + 4.68157i 1.16118 + 0.533514i
\(78\) 2.13947 + 5.43523i 0.242247 + 0.615419i
\(79\) 2.65034 + 2.22390i 0.298187 + 0.250208i 0.779589 0.626291i \(-0.215428\pi\)
−0.481402 + 0.876500i \(0.659872\pi\)
\(80\) −1.78675 3.09475i −0.199765 0.346003i
\(81\) −8.09297 + 3.93748i −0.899219 + 0.437498i
\(82\) 3.80495 6.59037i 0.420187 0.727785i
\(83\) 0.275388 1.56180i 0.0302278 0.171430i −0.965957 0.258704i \(-0.916704\pi\)
0.996184 + 0.0872741i \(0.0278156\pi\)
\(84\) 3.13645 3.34106i 0.342215 0.364539i
\(85\) 8.63544 + 3.14304i 0.936645 + 0.340911i
\(86\) −0.484937 2.75021i −0.0522921 0.296563i
\(87\) −2.08713 2.36023i −0.223764 0.253043i
\(88\) 3.24668 + 2.72429i 0.346097 + 0.290410i
\(89\) −2.58297 4.47383i −0.273794 0.474225i 0.696036 0.718007i \(-0.254945\pi\)
−0.969830 + 0.243782i \(0.921612\pi\)
\(90\) 10.2506 + 3.13935i 1.08050 + 0.330917i
\(91\) 8.89280 + 0.727513i 0.932219 + 0.0762640i
\(92\) −1.75410 1.47186i −0.182877 0.153452i
\(93\) −15.7222 8.54138i −1.63031 0.885700i
\(94\) −2.42933 + 2.03845i −0.250566 + 0.210250i
\(95\) −16.5300 + 13.8703i −1.69594 + 1.42306i
\(96\) 1.47704 0.904635i 0.150749 0.0923290i
\(97\) 14.6758 + 12.3145i 1.49010 + 1.25034i 0.894504 + 0.447060i \(0.147529\pi\)
0.595597 + 0.803284i \(0.296916\pi\)
\(98\) −2.46817 6.55043i −0.249323 0.661693i
\(99\) −12.6976 + 0.659271i −1.27616 + 0.0662592i
\(100\) −3.88497 6.72897i −0.388497 0.672897i
\(101\) −6.46670 5.42621i −0.643461 0.539928i 0.261618 0.965171i \(-0.415744\pi\)
−0.905079 + 0.425244i \(0.860188\pi\)
\(102\) −1.41435 + 4.22363i −0.140041 + 0.418202i
\(103\) 3.50065 + 19.8532i 0.344929 + 1.95619i 0.287250 + 0.957856i \(0.407259\pi\)
0.0576796 + 0.998335i \(0.481630\pi\)
\(104\) 3.16901 + 1.15343i 0.310747 + 0.113103i
\(105\) 11.2081 11.9393i 1.09380 1.16516i
\(106\) −1.40429 + 7.96415i −0.136397 + 0.773547i
\(107\) 3.04619 5.27616i 0.294487 0.510066i −0.680379 0.732861i \(-0.738185\pi\)
0.974865 + 0.222795i \(0.0715180\pi\)
\(108\) −1.39226 + 5.00616i −0.133970 + 0.481718i
\(109\) −5.46649 9.46824i −0.523595 0.906893i −0.999623 0.0274630i \(-0.991257\pi\)
0.476028 0.879430i \(-0.342076\pi\)
\(110\) 11.6020 + 9.73525i 1.10621 + 0.928220i
\(111\) −7.73140 + 9.71485i −0.733832 + 0.922093i
\(112\) −0.245452 2.63434i −0.0231930 0.248922i
\(113\) 3.76639 3.16038i 0.354312 0.297303i −0.448207 0.893930i \(-0.647937\pi\)
0.802519 + 0.596627i \(0.203493\pi\)
\(114\) −6.92834 7.83489i −0.648898 0.733805i
\(115\) −6.26828 5.25971i −0.584520 0.490471i
\(116\) −1.81905 −0.168894
\(117\) −9.31483 + 3.94857i −0.861156 + 0.365046i
\(118\) −3.18418 5.51517i −0.293128 0.507712i
\(119\) 4.83808 + 4.78382i 0.443506 + 0.438532i
\(120\) 5.27820 3.23272i 0.481831 0.295106i
\(121\) −6.54274 2.38136i −0.594795 0.216488i
\(122\) 3.99135 3.34914i 0.361360 0.303217i
\(123\) 11.5819 + 6.29212i 1.04431 + 0.567341i
\(124\) −9.70725 + 3.53315i −0.871737 + 0.317286i
\(125\) −4.94921 8.57228i −0.442671 0.766728i
\(126\) 5.92582 + 5.28059i 0.527914 + 0.470432i
\(127\) 2.75557 4.77279i 0.244517 0.423517i −0.717478 0.696581i \(-0.754704\pi\)
0.961996 + 0.273064i \(0.0880371\pi\)
\(128\) 0.173648 0.984808i 0.0153485 0.0870455i
\(129\) 4.74012 0.963191i 0.417345 0.0848042i
\(130\) 11.3245 + 4.12177i 0.993223 + 0.361504i
\(131\) 2.24615 1.88474i 0.196247 0.164671i −0.539369 0.842070i \(-0.681337\pi\)
0.735616 + 0.677399i \(0.236893\pi\)
\(132\) −4.57117 + 5.74389i −0.397870 + 0.499942i
\(133\) −15.4082 + 4.22189i −1.33606 + 0.366084i
\(134\) −1.86940 −0.161491
\(135\) −4.97524 + 17.8895i −0.428201 + 1.53969i
\(136\) 1.28580 + 2.22707i 0.110257 + 0.190970i
\(137\) 15.2235 5.54091i 1.30063 0.473392i 0.403431 0.915010i \(-0.367818\pi\)
0.897203 + 0.441618i \(0.145595\pi\)
\(138\) 2.46969 3.10328i 0.210234 0.264169i
\(139\) −13.9917 5.09257i −1.18676 0.431946i −0.328176 0.944617i \(-0.606434\pi\)
−0.858585 + 0.512671i \(0.828656\pi\)
\(140\) −0.877122 9.41383i −0.0741304 0.795614i
\(141\) −3.63863 4.11474i −0.306428 0.346523i
\(142\) 1.15057 6.52521i 0.0965537 0.547583i
\(143\) −14.2930 −1.19524
\(144\) 1.63270 + 2.51680i 0.136058 + 0.209734i
\(145\) −6.50037 −0.539827
\(146\) 9.32425 + 7.82397i 0.771680 + 0.647517i
\(147\) 11.2310 4.56781i 0.926317 0.376746i
\(148\) 1.24476 + 7.05938i 0.102319 + 0.580278i
\(149\) −6.78584 2.46984i −0.555918 0.202338i 0.0487561 0.998811i \(-0.484474\pi\)
−0.604674 + 0.796473i \(0.706697\pi\)
\(150\) 11.4765 7.02897i 0.937051 0.573913i
\(151\) 1.41821 8.04308i 0.115412 0.654536i −0.871133 0.491048i \(-0.836614\pi\)
0.986545 0.163489i \(-0.0522748\pi\)
\(152\) −6.03842 −0.489780
\(153\) −7.37662 2.25917i −0.596364 0.182643i
\(154\) 4.79619 + 10.1358i 0.386488 + 0.816769i
\(155\) −34.6889 + 12.6257i −2.78628 + 1.01412i
\(156\) −1.85477 + 5.53885i −0.148500 + 0.443463i
\(157\) 16.1435 + 5.87575i 1.28839 + 0.468936i 0.893198 0.449663i \(-0.148456\pi\)
0.395192 + 0.918599i \(0.370678\pi\)
\(158\) 0.600783 + 3.40721i 0.0477958 + 0.271063i
\(159\) −13.8528 2.07375i −1.09859 0.164459i
\(160\) 0.620533 3.51922i 0.0490574 0.278218i
\(161\) −2.59126 5.47614i −0.204220 0.431580i
\(162\) −8.73054 2.18578i −0.685936 0.171731i
\(163\) 5.52476 9.56917i 0.432733 0.749515i −0.564375 0.825519i \(-0.690883\pi\)
0.997108 + 0.0760035i \(0.0242160\pi\)
\(164\) 7.15097 2.60274i 0.558397 0.203240i
\(165\) −16.3351 + 20.5258i −1.27169 + 1.59793i
\(166\) 1.21487 1.01940i 0.0942920 0.0791204i
\(167\) 15.1547 12.7163i 1.17270 0.984014i 0.172703 0.984974i \(-0.444750\pi\)
1.00000 0.000959417i \(0.000305392\pi\)
\(168\) 4.55025 0.543325i 0.351060 0.0419184i
\(169\) 1.52885 0.556457i 0.117604 0.0428044i
\(170\) 4.59482 + 7.95846i 0.352407 + 0.610386i
\(171\) 13.2547 12.3481i 1.01361 0.944286i
\(172\) 1.39632 2.41850i 0.106468 0.184409i
\(173\) −18.2070 + 6.62682i −1.38426 + 0.503828i −0.923466 0.383681i \(-0.874656\pi\)
−0.460790 + 0.887509i \(0.652434\pi\)
\(174\) −0.0817105 3.14962i −0.00619446 0.238772i
\(175\) −1.90714 20.4687i −0.144167 1.54729i
\(176\) 0.735962 + 4.17385i 0.0554752 + 0.314616i
\(177\) 9.40631 5.76105i 0.707021 0.433027i
\(178\) 0.897055 5.08745i 0.0672371 0.381320i
\(179\) 10.9281 18.9280i 0.816805 1.41475i −0.0912195 0.995831i \(-0.529076\pi\)
0.908025 0.418917i \(-0.137590\pi\)
\(180\) 5.83445 + 8.99382i 0.434874 + 0.670360i
\(181\) 2.48406 4.30251i 0.184638 0.319803i −0.758816 0.651305i \(-0.774222\pi\)
0.943455 + 0.331502i \(0.107555\pi\)
\(182\) 6.34465 + 6.27349i 0.470296 + 0.465022i
\(183\) 5.97822 + 6.76045i 0.441923 + 0.499747i
\(184\) −0.397622 2.25502i −0.0293131 0.166243i
\(185\) 4.44816 + 25.2267i 0.327035 + 1.85471i
\(186\) −6.55358 16.6491i −0.480532 1.22077i
\(187\) −8.34917 7.00578i −0.610552 0.512314i
\(188\) −3.17126 −0.231288
\(189\) −8.87699 + 10.4976i −0.645706 + 0.763586i
\(190\) −21.5783 −1.56546
\(191\) 12.7309 + 10.6825i 0.921173 + 0.772956i 0.974212 0.225636i \(-0.0724461\pi\)
−0.0530384 + 0.998592i \(0.516891\pi\)
\(192\) 1.71296 + 0.256429i 0.123622 + 0.0185062i
\(193\) −0.318916 1.80866i −0.0229560 0.130190i 0.971176 0.238364i \(-0.0766110\pi\)
−0.994132 + 0.108173i \(0.965500\pi\)
\(194\) 3.32673 + 18.8668i 0.238845 + 1.35456i
\(195\) −6.62803 + 19.7931i −0.474643 + 1.41742i
\(196\) 2.31980 6.60443i 0.165700 0.471745i
\(197\) 5.53938 9.59449i 0.394665 0.683579i −0.598394 0.801202i \(-0.704194\pi\)
0.993058 + 0.117623i \(0.0375274\pi\)
\(198\) −10.1507 7.65683i −0.721379 0.544147i
\(199\) 4.99889 8.65832i 0.354362 0.613772i −0.632647 0.774440i \(-0.718032\pi\)
0.987008 + 0.160668i \(0.0513649\pi\)
\(200\) 1.34924 7.65190i 0.0954055 0.541071i
\(201\) −0.0839723 3.23680i −0.00592295 0.228306i
\(202\) −1.46588 8.31343i −0.103139 0.584931i
\(203\) −4.37323 2.00932i −0.306940 0.141027i
\(204\) −3.79835 + 2.32636i −0.265938 + 0.162878i
\(205\) 25.5540 9.30091i 1.78477 0.649604i
\(206\) −10.0797 + 17.4586i −0.702287 + 1.21640i
\(207\) 5.48417 + 4.13679i 0.381176 + 0.287527i
\(208\) 1.68620 + 2.92058i 0.116917 + 0.202506i
\(209\) 24.0488 8.75306i 1.66349 0.605462i
\(210\) 16.2604 1.94157i 1.12207 0.133981i
\(211\) −15.4658 + 12.9774i −1.06471 + 0.893398i −0.994563 0.104139i \(-0.966791\pi\)
−0.0701473 + 0.997537i \(0.522347\pi\)
\(212\) −6.19501 + 5.19823i −0.425475 + 0.357016i
\(213\) 11.3499 + 1.69907i 0.777680 + 0.116418i
\(214\) 5.72497 2.08372i 0.391351 0.142440i
\(215\) 4.98976 8.64251i 0.340299 0.589415i
\(216\) −4.28443 + 2.94001i −0.291518 + 0.200043i
\(217\) −27.2402 2.22850i −1.84919 0.151281i
\(218\) 1.89849 10.7669i 0.128582 0.729226i
\(219\) −13.1281 + 16.4961i −0.887116 + 1.11470i
\(220\) 2.62996 + 14.9153i 0.177312 + 1.00559i
\(221\) −8.14944 2.96615i −0.548191 0.199525i
\(222\) −12.1672 + 2.47236i −0.816608 + 0.165934i
\(223\) −23.0056 + 8.37336i −1.54057 + 0.560722i −0.966182 0.257861i \(-0.916982\pi\)
−0.574388 + 0.818583i \(0.694760\pi\)
\(224\) 1.50530 2.17580i 0.100577 0.145376i
\(225\) 12.6860 + 19.5554i 0.845730 + 1.30370i
\(226\) 4.91667 0.327052
\(227\) −2.47362 + 14.0286i −0.164180 + 0.931111i 0.785726 + 0.618575i \(0.212290\pi\)
−0.949906 + 0.312536i \(0.898821\pi\)
\(228\) −0.271242 10.4553i −0.0179635 0.692421i
\(229\) −18.1896 6.62047i −1.20200 0.437493i −0.338079 0.941118i \(-0.609777\pi\)
−0.863922 + 0.503625i \(0.831999\pi\)
\(230\) −1.42090 8.05834i −0.0936916 0.531352i
\(231\) −17.3344 + 8.75974i −1.14052 + 0.576348i
\(232\) −1.39347 1.16926i −0.0914858 0.0767657i
\(233\) −14.4577 −0.947157 −0.473579 0.880752i \(-0.657038\pi\)
−0.473579 + 0.880752i \(0.657038\pi\)
\(234\) −9.67367 2.96267i −0.632387 0.193676i
\(235\) −11.3325 −0.739252
\(236\) 1.10586 6.27162i 0.0719851 0.408248i
\(237\) −5.87249 + 1.19329i −0.381459 + 0.0775124i
\(238\) 0.631204 + 6.77448i 0.0409149 + 0.439124i
\(239\) 4.16230 + 1.51495i 0.269237 + 0.0979941i 0.473111 0.881003i \(-0.343131\pi\)
−0.203874 + 0.978997i \(0.565353\pi\)
\(240\) 6.12129 + 0.916352i 0.395127 + 0.0591502i
\(241\) −6.97073 + 2.53714i −0.449024 + 0.163431i −0.556627 0.830763i \(-0.687905\pi\)
0.107603 + 0.994194i \(0.465683\pi\)
\(242\) −3.48132 6.02982i −0.223788 0.387612i
\(243\) 3.39243 15.2148i 0.217625 0.976033i
\(244\) 5.21034 0.333558
\(245\) 8.28983 23.6010i 0.529618 1.50781i
\(246\) 4.82778 + 12.2648i 0.307808 + 0.781973i
\(247\) 15.5997 13.0897i 0.992582 0.832876i
\(248\) −9.70725 3.53315i −0.616411 0.224355i
\(249\) 1.81962 + 2.05771i 0.115314 + 0.130402i
\(250\) 1.71884 9.74804i 0.108709 0.616520i
\(251\) 7.82057 13.5456i 0.493630 0.854993i −0.506343 0.862332i \(-0.669003\pi\)
0.999973 + 0.00733960i \(0.00233629\pi\)
\(252\) 1.14514 + 7.85421i 0.0721373 + 0.494769i
\(253\) 4.85238 + 8.40457i 0.305067 + 0.528391i
\(254\) 5.17878 1.88492i 0.324946 0.118270i
\(255\) −13.5734 + 8.31328i −0.850001 + 0.520598i
\(256\) 0.766044 0.642788i 0.0478778 0.0401742i
\(257\) 3.23052 + 1.17581i 0.201514 + 0.0733452i 0.440805 0.897603i \(-0.354693\pi\)
−0.239291 + 0.970948i \(0.576915\pi\)
\(258\) 4.25027 + 2.30905i 0.264610 + 0.143755i
\(259\) −4.80525 + 18.3467i −0.298584 + 1.14001i
\(260\) 6.02563 + 10.4367i 0.373694 + 0.647257i
\(261\) 5.44980 0.282958i 0.337334 0.0175147i
\(262\) 2.93214 0.181148
\(263\) 14.1176 + 11.8461i 0.870527 + 0.730459i 0.964209 0.265143i \(-0.0854192\pi\)
−0.0936820 + 0.995602i \(0.529864\pi\)
\(264\) −7.19382 + 1.46178i −0.442749 + 0.0899664i
\(265\) −22.1379 + 18.5759i −1.35992 + 1.14111i
\(266\) −14.5172 6.67006i −0.890104 0.408967i
\(267\) 8.84905 + 1.32470i 0.541553 + 0.0810701i
\(268\) −1.43204 1.20163i −0.0874759 0.0734010i
\(269\) 2.60573 + 4.51325i 0.158874 + 0.275178i 0.934463 0.356060i \(-0.115880\pi\)
−0.775589 + 0.631238i \(0.782547\pi\)
\(270\) −15.3104 + 10.5062i −0.931763 + 0.639384i
\(271\) −7.42537 + 12.8611i −0.451059 + 0.781257i −0.998452 0.0556184i \(-0.982287\pi\)
0.547393 + 0.836876i \(0.315620\pi\)
\(272\) −0.446554 + 2.53254i −0.0270763 + 0.153558i
\(273\) −10.5774 + 11.2674i −0.640170 + 0.681931i
\(274\) 15.2235 + 5.54091i 0.919687 + 0.334739i
\(275\) 5.71838 + 32.4306i 0.344832 + 1.95564i
\(276\) 3.88664 0.789764i 0.233948 0.0475382i
\(277\) −4.85881 4.07703i −0.291938 0.244965i 0.485041 0.874491i \(-0.338805\pi\)
−0.776979 + 0.629526i \(0.783249\pi\)
\(278\) −7.44483 12.8948i −0.446511 0.773380i
\(279\) 28.5330 12.0952i 1.70823 0.724120i
\(280\) 5.37918 7.77522i 0.321468 0.464658i
\(281\) 6.51650 + 5.46799i 0.388742 + 0.326193i 0.816123 0.577879i \(-0.196119\pi\)
−0.427381 + 0.904072i \(0.640564\pi\)
\(282\) −0.142451 5.49094i −0.00848285 0.326981i
\(283\) 4.04102 3.39082i 0.240214 0.201563i −0.514731 0.857352i \(-0.672108\pi\)
0.754945 + 0.655789i \(0.227664\pi\)
\(284\) 5.07571 4.25903i 0.301188 0.252727i
\(285\) −0.969286 37.3622i −0.0574155 2.21314i
\(286\) −10.9491 9.18736i −0.647432 0.543260i
\(287\) 20.0669 + 1.64165i 1.18451 + 0.0969038i
\(288\) −0.367054 + 2.97746i −0.0216289 + 0.175449i
\(289\) 5.19343 + 8.99528i 0.305496 + 0.529134i
\(290\) −4.97957 4.17836i −0.292411 0.245362i
\(291\) −32.5179 + 6.60762i −1.90623 + 0.387345i
\(292\) 2.11364 + 11.9870i 0.123691 + 0.701487i
\(293\) −24.2167 8.81416i −1.41476 0.514929i −0.482234 0.876043i \(-0.660174\pi\)
−0.932522 + 0.361114i \(0.882397\pi\)
\(294\) 11.5396 + 3.72000i 0.673001 + 0.216955i
\(295\) 3.95178 22.4117i 0.230082 1.30486i
\(296\) −3.58414 + 6.20792i −0.208324 + 0.360828i
\(297\) 12.8016 17.9196i 0.742824 1.03980i
\(298\) −3.61067 6.25386i −0.209161 0.362277i
\(299\) 5.91551 + 4.96370i 0.342103 + 0.287058i
\(300\) 13.3096 + 1.99244i 0.768432 + 0.115034i
\(301\) 6.02842 4.27201i 0.347472 0.246234i
\(302\) 6.25640 5.24975i 0.360016 0.302089i
\(303\) 14.3286 2.91156i 0.823156 0.167265i
\(304\) −4.62570 3.88142i −0.265302 0.222615i
\(305\) 18.6192 1.06613
\(306\) −4.19865 6.47223i −0.240021 0.369992i
\(307\) −12.7518 22.0867i −0.727783 1.26056i −0.957818 0.287374i \(-0.907218\pi\)
0.230036 0.973182i \(-0.426116\pi\)
\(308\) −2.84110 + 10.8474i −0.161886 + 0.618089i
\(309\) −30.6818 16.6685i −1.74542 0.948237i
\(310\) −34.6889 12.6257i −1.97020 0.717093i
\(311\) 5.05181 4.23898i 0.286462 0.240370i −0.488221 0.872720i \(-0.662354\pi\)
0.774683 + 0.632350i \(0.217909\pi\)
\(312\) −4.98114 + 3.05079i −0.282002 + 0.172717i
\(313\) −22.3439 + 8.13252i −1.26295 + 0.459677i −0.884759 0.466049i \(-0.845677\pi\)
−0.378194 + 0.925726i \(0.623455\pi\)
\(314\) 8.58977 + 14.8779i 0.484749 + 0.839609i
\(315\) 4.09218 + 28.0671i 0.230568 + 1.58140i
\(316\) −1.72989 + 2.99625i −0.0973138 + 0.168552i
\(317\) 4.58962 26.0290i 0.257779 1.46194i −0.531060 0.847334i \(-0.678206\pi\)
0.788838 0.614601i \(-0.210683\pi\)
\(318\) −9.27885 10.4930i −0.520332 0.588416i
\(319\) 7.24460 + 2.63682i 0.405620 + 0.147634i
\(320\) 2.73746 2.29701i 0.153029 0.128407i
\(321\) 3.86506 + 9.81901i 0.215726 + 0.548044i
\(322\) 1.53497 5.86059i 0.0855407 0.326598i
\(323\) 15.5284 0.864024
\(324\) −5.28299 7.28629i −0.293500 0.404794i
\(325\) 13.1017 + 22.6927i 0.726749 + 1.25877i
\(326\) 10.3832 3.77916i 0.575070 0.209308i
\(327\) 18.7278 + 2.80354i 1.03565 + 0.155036i
\(328\) 7.15097 + 2.60274i 0.394846 + 0.143712i
\(329\) −7.62413 3.50299i −0.420332 0.193126i
\(330\) −25.7072 + 5.22369i −1.41513 + 0.287554i
\(331\) 1.36963 7.76758i 0.0752819 0.426945i −0.923752 0.382992i \(-0.874894\pi\)
0.999034 0.0439529i \(-0.0139951\pi\)
\(332\) 1.58590 0.0870374
\(333\) −4.82736 20.9560i −0.264538 1.14838i
\(334\) 19.7830 1.08248
\(335\) −5.11741 4.29402i −0.279594 0.234607i
\(336\) 3.83494 + 2.50864i 0.209213 + 0.136857i
\(337\) −0.904111 5.12747i −0.0492501 0.279311i 0.950230 0.311549i \(-0.100848\pi\)
−0.999480 + 0.0322377i \(0.989737\pi\)
\(338\) 1.52885 + 0.556457i 0.0831587 + 0.0302673i
\(339\) 0.220854 + 8.51306i 0.0119952 + 0.462366i
\(340\) −1.59576 + 9.05003i −0.0865425 + 0.490807i
\(341\) 43.7820 2.37093
\(342\) 18.0909 0.939295i 0.978243 0.0507912i
\(343\) 12.8724 13.3155i 0.695044 0.718967i
\(344\) 2.62422 0.955139i 0.141489 0.0514976i
\(345\) 13.8889 2.82223i 0.747755 0.151944i
\(346\) −18.2070 6.62682i −0.978817 0.356260i
\(347\) −0.607976 3.44800i −0.0326379 0.185098i 0.964130 0.265429i \(-0.0855136\pi\)
−0.996768 + 0.0803304i \(0.974402\pi\)
\(348\) 1.96194 2.46527i 0.105171 0.132152i
\(349\) −0.112862 + 0.640070i −0.00604134 + 0.0342622i −0.987679 0.156491i \(-0.949982\pi\)
0.981638 + 0.190753i \(0.0610929\pi\)
\(350\) 11.6961 16.9058i 0.625181 0.903654i
\(351\) 4.69524 16.8827i 0.250613 0.901133i
\(352\) −2.11912 + 3.67042i −0.112949 + 0.195634i
\(353\) −8.02159 + 2.91962i −0.426946 + 0.155396i −0.546551 0.837426i \(-0.684060\pi\)
0.119605 + 0.992822i \(0.461837\pi\)
\(354\) 10.9088 + 1.63304i 0.579795 + 0.0867949i
\(355\) 18.1381 15.2197i 0.962670 0.807776i
\(356\) 3.95733 3.32060i 0.209738 0.175991i
\(357\) −11.7014 + 1.39722i −0.619306 + 0.0739485i
\(358\) 20.5381 7.47527i 1.08547 0.395080i
\(359\) 9.31447 + 16.1331i 0.491599 + 0.851474i 0.999953 0.00967360i \(-0.00307925\pi\)
−0.508354 + 0.861148i \(0.669746\pi\)
\(360\) −1.31167 + 10.6400i −0.0691310 + 0.560776i
\(361\) −8.73124 + 15.1229i −0.459539 + 0.795944i
\(362\) 4.66850 1.69919i 0.245371 0.0893077i
\(363\) 10.2841 6.29865i 0.539774 0.330593i
\(364\) 0.827759 + 8.88403i 0.0433863 + 0.465650i
\(365\) 7.55309 + 42.8357i 0.395347 + 2.24212i
\(366\) 0.234045 + 9.02153i 0.0122337 + 0.471563i
\(367\) −1.99519 + 11.3153i −0.104148 + 0.590653i 0.887409 + 0.460983i \(0.152503\pi\)
−0.991557 + 0.129670i \(0.958608\pi\)
\(368\) 1.14491 1.98304i 0.0596824 0.103373i
\(369\) −21.0192 + 8.91007i −1.09422 + 0.463840i
\(370\) −12.8080 + 22.1840i −0.665854 + 1.15329i
\(371\) −20.6356 + 5.65420i −1.07135 + 0.293552i
\(372\) 5.68149 16.9665i 0.294572 0.879672i
\(373\) −1.59415 9.04089i −0.0825421 0.468119i −0.997860 0.0653873i \(-0.979172\pi\)
0.915318 0.402732i \(-0.131939\pi\)
\(374\) −1.89260 10.7335i −0.0978641 0.555015i
\(375\) 16.9556 + 2.53824i 0.875585 + 0.131074i
\(376\) −2.42933 2.03845i −0.125283 0.105125i
\(377\) 6.13454 0.315945
\(378\) −13.5479 + 2.33559i −0.696828 + 0.120130i
\(379\) 29.4786 1.51421 0.757107 0.653291i \(-0.226612\pi\)
0.757107 + 0.653291i \(0.226612\pi\)
\(380\) −16.5300 13.8703i −0.847969 0.711530i
\(381\) 3.49631 + 8.88222i 0.179121 + 0.455050i
\(382\) 2.88585 + 16.3665i 0.147653 + 0.837382i
\(383\) 1.43914 + 8.16177i 0.0735366 + 0.417047i 0.999247 + 0.0388125i \(0.0123575\pi\)
−0.925710 + 0.378234i \(0.876531\pi\)
\(384\) 1.14738 + 1.29751i 0.0585518 + 0.0662132i
\(385\) −10.1527 + 38.7633i −0.517428 + 1.97556i
\(386\) 0.918281 1.59051i 0.0467393 0.0809548i
\(387\) −3.80712 + 7.46293i −0.193527 + 0.379362i
\(388\) −9.57894 + 16.5912i −0.486297 + 0.842291i
\(389\) 3.82567 21.6964i 0.193969 1.10005i −0.719910 0.694067i \(-0.755817\pi\)
0.913879 0.405986i \(-0.133072\pi\)
\(390\) −17.8001 + 10.9020i −0.901345 + 0.552044i
\(391\) 1.02253 + 5.79903i 0.0517113 + 0.293270i
\(392\) 6.02232 3.56815i 0.304173 0.180219i
\(393\) 0.131710 + 5.07691i 0.00664390 + 0.256096i
\(394\) 10.4106 3.78916i 0.524480 0.190895i
\(395\) −6.18176 + 10.7071i −0.311038 + 0.538734i
\(396\) −2.85417 12.3902i −0.143427 0.622632i
\(397\) 9.27464 + 16.0642i 0.465481 + 0.806237i 0.999223 0.0394107i \(-0.0125481\pi\)
−0.533742 + 0.845647i \(0.679215\pi\)
\(398\) 9.39483 3.41944i 0.470920 0.171401i
\(399\) 10.8969 25.4356i 0.545527 1.27337i
\(400\) 5.95212 4.99442i 0.297606 0.249721i
\(401\) 0.307478 0.258005i 0.0153547 0.0128841i −0.635078 0.772448i \(-0.719032\pi\)
0.650433 + 0.759564i \(0.274588\pi\)
\(402\) 2.01625 2.53351i 0.100561 0.126360i
\(403\) 32.7367 11.9152i 1.63073 0.593537i
\(404\) 4.22084 7.31071i 0.209995 0.363721i
\(405\) −18.8788 26.0376i −0.938096 1.29382i
\(406\) −2.05852 4.35029i −0.102163 0.215901i
\(407\) 5.27558 29.9193i 0.261501 1.48305i
\(408\) −4.40506 0.659435i −0.218083 0.0326469i
\(409\) −3.11053 17.6407i −0.153806 0.872277i −0.959869 0.280448i \(-0.909517\pi\)
0.806063 0.591829i \(-0.201594\pi\)
\(410\) 25.5540 + 9.30091i 1.26202 + 0.459339i
\(411\) −8.91008 + 26.6080i −0.439502 + 1.31247i
\(412\) −18.9437 + 6.89493i −0.933288 + 0.339689i
\(413\) 9.58627 13.8563i 0.471710 0.681822i
\(414\) 1.54204 + 6.69412i 0.0757870 + 0.328998i
\(415\) 5.66721 0.278193
\(416\) −0.585610 + 3.32116i −0.0287119 + 0.162833i
\(417\) 21.9926 13.4697i 1.07698 0.659615i
\(418\) 24.0488 + 8.75306i 1.17627 + 0.428126i
\(419\) −3.74670 21.2486i −0.183038 1.03806i −0.928450 0.371457i \(-0.878858\pi\)
0.745412 0.666604i \(-0.232253\pi\)
\(420\) 13.7042 + 8.96462i 0.668695 + 0.437429i
\(421\) 8.86652 + 7.43990i 0.432128 + 0.362598i 0.832754 0.553643i \(-0.186763\pi\)
−0.400626 + 0.916242i \(0.631207\pi\)
\(422\) −20.1892 −0.982794
\(423\) 9.50099 0.493300i 0.461954 0.0239851i
\(424\) −8.08701 −0.392740
\(425\) −3.46970 + 19.6777i −0.168305 + 0.954507i
\(426\) 7.60237 + 8.59712i 0.368336 + 0.416532i
\(427\) 12.5263 + 5.75536i 0.606192 + 0.278521i
\(428\) 5.72497 + 2.08372i 0.276727 + 0.100720i
\(429\) 15.4158 19.3707i 0.744281 0.935224i
\(430\) 9.37768 3.41320i 0.452232 0.164599i
\(431\) −12.2662 21.2456i −0.590840 1.02336i −0.994120 0.108288i \(-0.965463\pi\)
0.403280 0.915077i \(-0.367870\pi\)
\(432\) −5.17187 0.501796i −0.248832 0.0241427i
\(433\) 16.3713 0.786753 0.393377 0.919377i \(-0.371307\pi\)
0.393377 + 0.919377i \(0.371307\pi\)
\(434\) −19.4348 19.2168i −0.932899 0.922437i
\(435\) 7.01102 8.80966i 0.336152 0.422391i
\(436\) 8.37515 7.02759i 0.401097 0.336560i
\(437\) −12.9930 4.72906i −0.621538 0.226222i
\(438\) −20.6602 + 4.19814i −0.987183 + 0.200595i
\(439\) 3.65877 20.7499i 0.174623 0.990338i −0.763954 0.645270i \(-0.776745\pi\)
0.938578 0.345068i \(-0.112144\pi\)
\(440\) −7.57268 + 13.1163i −0.361013 + 0.625294i
\(441\) −5.92271 + 20.1475i −0.282034 + 0.959404i
\(442\) −4.33623 7.51057i −0.206253 0.357241i
\(443\) −18.9032 + 6.88019i −0.898117 + 0.326888i −0.749498 0.662007i \(-0.769705\pi\)
−0.148619 + 0.988895i \(0.547483\pi\)
\(444\) −10.9098 5.92697i −0.517757 0.281282i
\(445\) 14.1416 11.8662i 0.670374 0.562511i
\(446\) −23.0056 8.37336i −1.08935 0.396490i
\(447\) 10.6662 6.53268i 0.504493 0.308985i
\(448\) 2.55170 0.699171i 0.120556 0.0330327i
\(449\) 6.10832 + 10.5799i 0.288270 + 0.499298i 0.973397 0.229126i \(-0.0735867\pi\)
−0.685127 + 0.728423i \(0.740253\pi\)
\(450\) −2.85199 + 23.1347i −0.134444 + 1.09058i
\(451\) −32.2526 −1.51871
\(452\) 3.76639 + 3.16038i 0.177156 + 0.148652i
\(453\) 9.37080 + 10.5969i 0.440279 + 0.497888i
\(454\) −10.9123 + 9.15652i −0.512141 + 0.429737i
\(455\) 2.95800 + 31.7471i 0.138673 + 1.48833i
\(456\) 6.51277 8.18360i 0.304988 0.383232i
\(457\) −14.7782 12.4004i −0.691295 0.580065i 0.227988 0.973664i \(-0.426785\pi\)
−0.919282 + 0.393599i \(0.871230\pi\)
\(458\) −9.67848 16.7636i −0.452245 0.783312i
\(459\) 11.0179 7.56055i 0.514269 0.352896i
\(460\) 4.09133 7.08639i 0.190759 0.330405i
\(461\) −2.70552 + 15.3438i −0.126009 + 0.714630i 0.854695 + 0.519130i \(0.173744\pi\)
−0.980704 + 0.195500i \(0.937367\pi\)
\(462\) −18.9096 4.43201i −0.879754 0.206196i
\(463\) 11.9099 + 4.33484i 0.553499 + 0.201457i 0.603600 0.797287i \(-0.293732\pi\)
−0.0501015 + 0.998744i \(0.515954\pi\)
\(464\) −0.315874 1.79141i −0.0146641 0.0831642i
\(465\) 20.3029 60.6299i 0.941522 2.81164i
\(466\) −11.0753 9.29325i −0.513052 0.430501i
\(467\) 1.22127 + 2.11530i 0.0565135 + 0.0978842i 0.892898 0.450259i \(-0.148668\pi\)
−0.836385 + 0.548143i \(0.815335\pi\)
\(468\) −5.50609 8.48765i −0.254519 0.392342i
\(469\) −2.11550 4.47071i −0.0976846 0.206438i
\(470\) −8.68122 7.28441i −0.400435 0.336005i
\(471\) −25.3748 + 15.5412i −1.16921 + 0.716102i
\(472\) 4.87845 4.09351i 0.224549 0.188419i
\(473\) −9.06680 + 7.60795i −0.416892 + 0.349814i
\(474\) −5.26562 2.86065i −0.241858 0.131394i
\(475\) −35.9414 30.1584i −1.64910 1.38376i
\(476\) −3.87102 + 5.59528i −0.177428 + 0.256459i
\(477\) 17.7514 16.5374i 0.812782 0.757194i
\(478\) 2.21471 + 3.83599i 0.101299 + 0.175454i
\(479\) −27.8263 23.3490i −1.27142 1.06684i −0.994367 0.105988i \(-0.966200\pi\)
−0.277048 0.960856i \(-0.589356\pi\)
\(480\) 4.10016 + 4.63665i 0.187146 + 0.211633i
\(481\) −4.19782 23.8070i −0.191404 1.08551i
\(482\) −6.97073 2.53714i −0.317508 0.115563i
\(483\) 10.2164 + 2.39450i 0.464861 + 0.108954i
\(484\) 1.20905 6.85686i 0.0549568 0.311676i
\(485\) −34.2304 + 59.2888i −1.55432 + 2.69217i
\(486\) 12.3787 9.47463i 0.561508 0.429778i
\(487\) −14.0709 24.3714i −0.637611 1.10437i −0.985955 0.167008i \(-0.946589\pi\)
0.348344 0.937367i \(-0.386744\pi\)
\(488\) 3.99135 + 3.34914i 0.180680 + 0.151608i
\(489\) 7.00990 + 17.8083i 0.316999 + 0.805321i
\(490\) 21.5208 12.7508i 0.972210 0.576022i
\(491\) −20.3127 + 17.0443i −0.916698 + 0.769201i −0.973381 0.229192i \(-0.926392\pi\)
0.0566838 + 0.998392i \(0.481947\pi\)
\(492\) −4.18534 + 12.4986i −0.188690 + 0.563480i
\(493\) 3.58345 + 3.00687i 0.161391 + 0.135423i
\(494\) 20.3639 0.916216
\(495\) −10.1994 44.2765i −0.458429 1.99008i
\(496\) −5.16512 8.94625i −0.231921 0.401698i
\(497\) 16.9072 4.63262i 0.758392 0.207801i
\(498\) 0.0712376 + 2.74593i 0.00319223 + 0.123048i
\(499\) −15.2890 5.56474i −0.684429 0.249112i −0.0236811 0.999720i \(-0.507539\pi\)
−0.660748 + 0.750608i \(0.729761\pi\)
\(500\) 7.58263 6.36258i 0.339105 0.284543i
\(501\) 0.888641 + 34.2536i 0.0397016 + 1.53034i
\(502\) 14.6979 5.34959i 0.655998 0.238764i
\(503\) 12.7106 + 22.0155i 0.566739 + 0.981621i 0.996886 + 0.0788616i \(0.0251285\pi\)
−0.430147 + 0.902759i \(0.641538\pi\)
\(504\) −4.17136 + 6.75276i −0.185807 + 0.300792i
\(505\) 15.0832 26.1249i 0.671193 1.16254i
\(506\) −1.68521 + 9.55733i −0.0749169 + 0.424875i
\(507\) −0.894813 + 2.67216i −0.0397400 + 0.118675i
\(508\) 5.17878 + 1.88492i 0.229771 + 0.0836299i
\(509\) 22.4015 18.7971i 0.992928 0.833166i 0.00693932 0.999976i \(-0.497791\pi\)
0.985989 + 0.166810i \(0.0533467\pi\)
\(510\) −15.7415 2.35649i −0.697046 0.104347i
\(511\) −8.15945 + 31.1531i −0.360953 + 1.37813i
\(512\) 1.00000 0.0441942
\(513\) 2.43899 + 31.2816i 0.107684 + 1.38112i
\(514\) 1.71892 + 2.97726i 0.0758184 + 0.131321i
\(515\) −67.6953 + 24.6391i −2.98301 + 1.08573i
\(516\) 1.77167 + 4.50085i 0.0779935 + 0.198139i
\(517\) 12.6300 + 4.59694i 0.555466 + 0.202173i
\(518\) −15.4740 + 10.9656i −0.679890 + 0.481801i
\(519\) 10.6563 31.8226i 0.467759 1.39686i
\(520\) −2.09268 + 11.8682i −0.0917701 + 0.520454i
\(521\) −32.0183 −1.40275 −0.701375 0.712793i \(-0.747430\pi\)
−0.701375 + 0.712793i \(0.747430\pi\)
\(522\) 4.35667 + 3.28630i 0.190686 + 0.143838i
\(523\) −11.4164 −0.499203 −0.249602 0.968349i \(-0.580300\pi\)
−0.249602 + 0.968349i \(0.580300\pi\)
\(524\) 2.24615 + 1.88474i 0.0981236 + 0.0823354i
\(525\) 29.7973 + 19.4920i 1.30046 + 0.850699i
\(526\) 3.20019 + 18.1492i 0.139535 + 0.791343i
\(527\) 24.9632 + 9.08586i 1.08741 + 0.395786i
\(528\) −6.45040 3.50431i −0.280718 0.152506i
\(529\) −3.08343 + 17.4870i −0.134062 + 0.760304i
\(530\) −28.8990 −1.25529
\(531\) −2.33753 + 18.9616i −0.101440 + 0.822862i
\(532\) −6.83335 14.4410i −0.296263 0.626097i
\(533\) −24.1159 + 8.77746i −1.04457 + 0.380194i
\(534\) 5.92727 + 6.70284i 0.256498 + 0.290060i
\(535\) 20.4582 + 7.44618i 0.884486 + 0.321927i
\(536\) −0.324618 1.84100i −0.0140213 0.0795190i
\(537\) 13.8657 + 35.2253i 0.598351 + 1.52008i
\(538\) −0.904960 + 5.13228i −0.0390156 + 0.221268i
\(539\) −18.8125 + 22.9404i −0.810311 + 0.988111i
\(540\) −18.4817 1.79317i −0.795326 0.0771658i
\(541\) −8.61153 + 14.9156i −0.370239 + 0.641272i −0.989602 0.143832i \(-0.954057\pi\)
0.619363 + 0.785104i \(0.287391\pi\)
\(542\) −13.9551 + 5.07925i −0.599424 + 0.218173i
\(543\) 3.15181 + 8.00703i 0.135257 + 0.343615i
\(544\) −1.96996 + 1.65300i −0.0844615 + 0.0708716i
\(545\) 29.9287 25.1131i 1.28200 1.07573i
\(546\) −15.3452 + 1.83230i −0.656715 + 0.0784154i
\(547\) 17.2209 6.26790i 0.736313 0.267996i 0.0534785 0.998569i \(-0.482969\pi\)
0.682835 + 0.730573i \(0.260747\pi\)
\(548\) 8.10027 + 14.0301i 0.346026 + 0.599335i
\(549\) −15.6100 + 0.810484i −0.666218 + 0.0345906i
\(550\) −16.4654 + 28.5190i −0.702088 + 1.21605i
\(551\) −10.3217 + 3.75680i −0.439721 + 0.160045i
\(552\) 3.48499 + 1.89329i 0.148331 + 0.0805838i
\(553\) −7.46855 + 5.29255i −0.317595 + 0.225062i
\(554\) −1.10140 6.24637i −0.0467941 0.265383i
\(555\) −38.9863 21.1801i −1.65487 0.899044i
\(556\) 2.58556 14.6635i 0.109652 0.621869i
\(557\) −16.4685 + 28.5242i −0.697792 + 1.20861i 0.271438 + 0.962456i \(0.412501\pi\)
−0.969230 + 0.246155i \(0.920833\pi\)
\(558\) 29.6322 + 9.07520i 1.25443 + 0.384184i
\(559\) −4.70894 + 8.15612i −0.199167 + 0.344967i
\(560\) 9.11851 2.49849i 0.385327 0.105581i
\(561\) 18.4997 3.75912i 0.781057 0.158710i
\(562\) 1.47717 + 8.37745i 0.0623107 + 0.353381i
\(563\) −2.82269 16.0083i −0.118962 0.674668i −0.984712 0.174191i \(-0.944269\pi\)
0.865750 0.500477i \(-0.166842\pi\)
\(564\) 3.42038 4.29787i 0.144024 0.180973i
\(565\) 13.4592 + 11.2936i 0.566234 + 0.475126i
\(566\) 5.27518 0.221732
\(567\) −4.65256 23.3528i −0.195389 0.980726i
\(568\) 6.62587 0.278015
\(569\) −10.7885 9.05266i −0.452279 0.379507i 0.388002 0.921659i \(-0.373165\pi\)
−0.840281 + 0.542152i \(0.817610\pi\)
\(570\) 23.2734 29.2441i 0.974817 1.22490i
\(571\) −1.10444 6.26360i −0.0462194 0.262124i 0.952938 0.303165i \(-0.0980434\pi\)
−0.999157 + 0.0410418i \(0.986932\pi\)
\(572\) −2.48195 14.0758i −0.103776 0.588541i
\(573\) −28.2084 + 5.73194i −1.17842 + 0.239455i
\(574\) 14.3169 + 14.1563i 0.597575 + 0.590873i
\(575\) 8.89586 15.4081i 0.370983 0.642561i
\(576\) −2.19505 + 2.04493i −0.0914606 + 0.0852054i
\(577\) −4.40925 + 7.63704i −0.183559 + 0.317934i −0.943090 0.332537i \(-0.892095\pi\)
0.759531 + 0.650471i \(0.225429\pi\)
\(578\) −1.80366 + 10.2291i −0.0750223 + 0.425473i
\(579\) 2.79517 + 1.51853i 0.116163 + 0.0631079i
\(580\) −1.12878 6.40162i −0.0468699 0.265813i
\(581\) 3.81271 + 1.75179i 0.158178 + 0.0726764i
\(582\) −29.1574 15.8404i −1.20861 0.656604i
\(583\) 32.2076 11.7226i 1.33390 0.485501i
\(584\) −6.08597 + 10.5412i −0.251839 + 0.436198i
\(585\) −19.6760 30.3307i −0.813504 1.25402i
\(586\) −12.8854 22.3182i −0.532293 0.921958i
\(587\) −35.6777 + 12.9856i −1.47258 + 0.535974i −0.948799 0.315882i \(-0.897700\pi\)
−0.523777 + 0.851855i \(0.675478\pi\)
\(588\) 6.44865 + 10.2672i 0.265938 + 0.423411i
\(589\) −47.7845 + 40.0960i −1.96893 + 1.65213i
\(590\) 17.4332 14.6282i 0.717713 0.602233i
\(591\) 7.02845 + 17.8555i 0.289112 + 0.734476i
\(592\) −6.73598 + 2.45170i −0.276847 + 0.100764i
\(593\) −10.9811 + 19.0198i −0.450939 + 0.781049i −0.998445 0.0557527i \(-0.982244\pi\)
0.547506 + 0.836802i \(0.315578\pi\)
\(594\) 21.3251 5.49847i 0.874978 0.225605i
\(595\) −13.8331 + 19.9948i −0.567103 + 0.819706i
\(596\) 1.25397 7.11163i 0.0513647 0.291304i
\(597\) 6.34266 + 16.1133i 0.259588 + 0.659472i
\(598\) 1.34094 + 7.60483i 0.0548350 + 0.310985i
\(599\) −36.5041 13.2864i −1.49152 0.542868i −0.537669 0.843156i \(-0.680695\pi\)
−0.953849 + 0.300288i \(0.902917\pi\)
\(600\) 8.91505 + 10.0816i 0.363956 + 0.411578i
\(601\) 35.2616 12.8342i 1.43835 0.523516i 0.499037 0.866581i \(-0.333687\pi\)
0.939312 + 0.343064i \(0.111465\pi\)
\(602\) 7.36403 + 0.602445i 0.300135 + 0.0245538i
\(603\) 4.47726 + 3.37727i 0.182328 + 0.137533i
\(604\) 8.16716 0.332317
\(605\) 4.32055 24.5030i 0.175655 0.996190i
\(606\) 12.8479 + 6.97986i 0.521909 + 0.283537i
\(607\) −7.93473 2.88800i −0.322061 0.117220i 0.175931 0.984403i \(-0.443707\pi\)
−0.497991 + 0.867182i \(0.665929\pi\)
\(608\) −1.04856 5.94668i −0.0425247 0.241170i
\(609\) 7.43992 3.75967i 0.301481 0.152350i
\(610\) 14.2631 + 11.9682i 0.577497 + 0.484577i
\(611\) 10.6947 0.432663
\(612\) 0.943917 7.65685i 0.0381556 0.309510i
\(613\) 31.0659 1.25474 0.627370 0.778721i \(-0.284131\pi\)
0.627370 + 0.778721i \(0.284131\pi\)
\(614\) 4.42865 25.1161i 0.178726 1.01360i
\(615\) −14.9564 + 44.6638i −0.603098 + 1.80102i
\(616\) −9.14900 + 6.48339i −0.368624 + 0.261223i
\(617\) −1.58599 0.577253i −0.0638495 0.0232393i 0.309898 0.950770i \(-0.399705\pi\)
−0.373747 + 0.927531i \(0.621927\pi\)
\(618\) −12.7893 32.4907i −0.514461 1.30697i
\(619\) −10.8615 + 3.95325i −0.436560 + 0.158895i −0.550945 0.834542i \(-0.685732\pi\)
0.114385 + 0.993436i \(0.463510\pi\)
\(620\) −18.4576 31.9695i −0.741275 1.28393i
\(621\) −11.5214 + 2.97068i −0.462338 + 0.119209i
\(622\) 6.59468 0.264422
\(623\) 13.1819 3.61187i 0.528121 0.144707i
\(624\) −5.77678 0.864780i −0.231256 0.0346189i
\(625\) −2.66405 + 2.23540i −0.106562 + 0.0894161i
\(626\) −22.3439 8.13252i −0.893042 0.325041i
\(627\) −14.0754 + 42.0330i −0.562117 + 1.67864i
\(628\) −2.98320 + 16.9185i −0.119042 + 0.675123i
\(629\) 9.21699 15.9643i 0.367506 0.636538i
\(630\) −14.9064 + 24.1310i −0.593884 + 0.961403i
\(631\) −20.7060 35.8638i −0.824291 1.42771i −0.902460 0.430774i \(-0.858241\pi\)
0.0781684 0.996940i \(-0.475093\pi\)
\(632\) −3.25112 + 1.18331i −0.129323 + 0.0470696i
\(633\) −0.906886 34.9569i −0.0360455 1.38941i
\(634\) 20.2470 16.9892i 0.804110 0.674729i
\(635\) 18.5064 + 6.73578i 0.734404 + 0.267301i
\(636\) −0.363264 14.0024i −0.0144044 0.555231i
\(637\) −7.82329 + 22.2727i −0.309970 + 0.882478i
\(638\) 3.85477 + 6.67666i 0.152612 + 0.264332i
\(639\) −14.5441 + 13.5494i −0.575357 + 0.536007i
\(640\) 3.57351 0.141255
\(641\) 37.1288 + 31.1547i 1.46650 + 1.23054i 0.919314 + 0.393526i \(0.128745\pi\)
0.547184 + 0.837012i \(0.315700\pi\)
\(642\) −3.35073 + 10.0062i −0.132243 + 0.394914i
\(643\) −14.2836 + 11.9854i −0.563291 + 0.472658i −0.879412 0.476061i \(-0.842064\pi\)
0.316121 + 0.948719i \(0.397620\pi\)
\(644\) 4.94297 3.50281i 0.194780 0.138030i
\(645\) 6.33108 + 16.0838i 0.249286 + 0.633300i
\(646\) 11.8955 + 9.98147i 0.468020 + 0.392716i
\(647\) −7.77304 13.4633i −0.305590 0.529297i 0.671803 0.740730i \(-0.265520\pi\)
−0.977392 + 0.211433i \(0.932187\pi\)
\(648\) 0.636527 8.97746i 0.0250051 0.352668i
\(649\) −13.4953 + 23.3746i −0.529738 + 0.917533i
\(650\) −4.55016 + 25.8052i −0.178472 + 1.01216i
\(651\) 32.4003 34.5139i 1.26987 1.35271i
\(652\) 10.3832 + 3.77916i 0.406636 + 0.148003i
\(653\) −0.238128 1.35049i −0.00931865 0.0528487i 0.979794 0.200010i \(-0.0640975\pi\)
−0.989113 + 0.147161i \(0.952986\pi\)
\(654\) 12.5443 + 14.1856i 0.490519 + 0.554702i
\(655\) 8.02663 + 6.73515i 0.313627 + 0.263164i
\(656\) 3.80495 + 6.59037i 0.148558 + 0.257311i
\(657\) −8.19700 35.5839i −0.319795 1.38826i
\(658\) −3.58875 7.58414i −0.139904 0.295661i
\(659\) 21.0943 + 17.7002i 0.821718 + 0.689503i 0.953374 0.301792i \(-0.0975850\pi\)
−0.131656 + 0.991295i \(0.542029\pi\)
\(660\) −23.0506 12.5227i −0.897242 0.487445i
\(661\) −5.63017 + 4.72427i −0.218988 + 0.183753i −0.745682 0.666302i \(-0.767876\pi\)
0.526693 + 0.850055i \(0.323432\pi\)
\(662\) 6.04210 5.06993i 0.234833 0.197048i
\(663\) 12.8095 7.84541i 0.497481 0.304691i
\(664\) 1.21487 + 1.01940i 0.0471460 + 0.0395602i
\(665\) −24.4190 51.6050i −0.946929 2.00116i
\(666\) 9.77230 19.1562i 0.378669 0.742288i
\(667\) −2.08264 3.60723i −0.0806400 0.139673i
\(668\) 15.1547 + 12.7163i 0.586351 + 0.492007i
\(669\) 13.4648 40.2096i 0.520580 1.55459i
\(670\) −1.16002 6.57882i −0.0448156 0.254162i
\(671\) −20.7509 7.55271i −0.801079 0.291569i
\(672\) 1.32521 + 4.38678i 0.0511212 + 0.169224i
\(673\) −3.58323 + 20.3215i −0.138123 + 0.783336i 0.834510 + 0.550992i \(0.185751\pi\)
−0.972634 + 0.232344i \(0.925361\pi\)
\(674\) 2.60328 4.50902i 0.100275 0.173681i
\(675\) −40.1851 3.89893i −1.54673 0.150070i
\(676\) 0.813486 + 1.40900i 0.0312879 + 0.0541923i
\(677\) 24.7375 + 20.7572i 0.950739 + 0.797765i 0.979422 0.201823i \(-0.0646867\pi\)
−0.0286825 + 0.999589i \(0.509131\pi\)
\(678\) −5.30291 + 6.66335i −0.203657 + 0.255904i
\(679\) −41.3558 + 29.3065i −1.58709 + 1.12468i
\(680\) −7.03967 + 5.90699i −0.269959 + 0.226523i
\(681\) −16.3444 18.4830i −0.626319 0.708271i
\(682\) 33.5390 + 28.1425i 1.28427 + 1.07763i
\(683\) −22.3000 −0.853286 −0.426643 0.904420i \(-0.640304\pi\)
−0.426643 + 0.904420i \(0.640304\pi\)
\(684\) 14.4622 + 10.9091i 0.552976 + 0.417118i
\(685\) 28.9464 + 50.1366i 1.10598 + 1.91562i
\(686\) 18.4198 1.92602i 0.703273 0.0735358i
\(687\) 28.5909 17.5110i 1.09081 0.668086i
\(688\) 2.62422 + 0.955139i 0.100048 + 0.0364143i
\(689\) 20.8920 17.5305i 0.795922 0.667858i
\(690\) 12.4536 + 6.76569i 0.474102 + 0.257565i
\(691\) 16.0011 5.82393i 0.608711 0.221553i −0.0192281 0.999815i \(-0.506121\pi\)
0.627939 + 0.778262i \(0.283899\pi\)
\(692\) −9.68777 16.7797i −0.368274 0.637869i
\(693\) 6.82447 32.9404i 0.259240 1.25130i
\(694\) 1.75060 3.03212i 0.0664517 0.115098i
\(695\) 9.23953 52.4000i 0.350475 1.98764i
\(696\) 3.08758 0.627395i 0.117034 0.0237813i
\(697\) −18.3895 6.69322i −0.696551 0.253524i
\(698\) −0.497886 + 0.417776i −0.0188453 + 0.0158131i
\(699\) 15.5935 19.5939i 0.589799 0.741110i
\(700\) 19.8266 5.43252i 0.749373 0.205330i
\(701\) −4.91861 −0.185773 −0.0928867 0.995677i \(-0.529609\pi\)
−0.0928867 + 0.995677i \(0.529609\pi\)
\(702\) 14.4488 9.91488i 0.545334 0.374213i
\(703\) 21.6425 + 37.4860i 0.816264 + 1.41381i
\(704\) −3.98264 + 1.44956i −0.150101 + 0.0546324i
\(705\) 12.2228 15.3585i 0.460336 0.578433i
\(706\) −8.02159 2.91962i −0.301897 0.109881i
\(707\) 18.2229 12.9136i 0.685342 0.485664i
\(708\) 7.30692 + 8.26301i 0.274611 + 0.310543i
\(709\) −2.71149 + 15.3776i −0.101832 + 0.577519i 0.890606 + 0.454775i \(0.150280\pi\)
−0.992438 + 0.122744i \(0.960831\pi\)
\(710\) 23.6776 0.888604
\(711\) 4.71660 9.24576i 0.176886 0.346743i
\(712\) 5.16593 0.193601
\(713\) −18.1203 15.2047i −0.678609 0.569420i
\(714\) −9.86194 6.45122i −0.369074 0.241431i
\(715\) −8.86927 50.3001i −0.331692 1.88112i
\(716\) 20.5381 + 7.47527i 0.767546 + 0.279364i
\(717\) −6.54242 + 4.00701i −0.244331 + 0.149645i
\(718\) −3.23488 + 18.3459i −0.120725 + 0.684664i
\(719\) −19.9026 −0.742240 −0.371120 0.928585i \(-0.621026\pi\)
−0.371120 + 0.928585i \(0.621026\pi\)
\(720\) −7.84404 + 7.30757i −0.292330 + 0.272337i
\(721\) −53.1593 4.34891i −1.97975 0.161962i
\(722\) −16.4094 + 5.97252i −0.610693 + 0.222274i
\(723\) 4.07985 12.1836i 0.151731 0.453112i
\(724\) 4.66850 + 1.69919i 0.173503 + 0.0631501i
\(725\) −2.45432 13.9192i −0.0911513 0.516945i
\(726\) 11.9267 + 1.78543i 0.442643 + 0.0662633i
\(727\) 0.456609 2.58956i 0.0169347 0.0960414i −0.975169 0.221462i \(-0.928917\pi\)
0.992104 + 0.125421i \(0.0400281\pi\)
\(728\) −5.07645 + 7.33764i −0.188146 + 0.271951i
\(729\) 16.9611 + 21.0077i 0.628188 + 0.778062i
\(730\) −21.7483 + 37.6691i −0.804939 + 1.39420i
\(731\) −6.74846 + 2.45624i −0.249601 + 0.0908473i
\(732\) −5.61964 + 7.06134i −0.207708 + 0.260995i
\(733\) 32.4848 27.2579i 1.19985 1.00680i 0.200218 0.979751i \(-0.435835\pi\)
0.999634 0.0270437i \(-0.00860933\pi\)
\(734\) −8.80172 + 7.38552i −0.324877 + 0.272605i
\(735\) 23.0443 + 36.6898i 0.850002 + 1.35332i
\(736\) 2.15172 0.783162i 0.0793134 0.0288677i
\(737\) 3.96147 + 6.86147i 0.145923 + 0.252746i
\(738\) −21.8289 6.68536i −0.803533 0.246092i
\(739\) −0.211003 + 0.365468i −0.00776186 + 0.0134439i −0.869880 0.493263i \(-0.835804\pi\)
0.862118 + 0.506707i \(0.169137\pi\)
\(740\) −24.0711 + 8.76116i −0.884870 + 0.322067i
\(741\) 0.914735 + 35.2595i 0.0336036 + 1.29529i
\(742\) −19.4422 8.93294i −0.713747 0.327939i
\(743\) −7.01750 39.7982i −0.257447 1.46006i −0.789712 0.613477i \(-0.789770\pi\)
0.532265 0.846578i \(-0.321341\pi\)
\(744\) 15.2581 9.34510i 0.559390 0.342608i
\(745\) 4.48108 25.4135i 0.164174 0.931077i
\(746\) 4.59018 7.95042i 0.168058 0.291086i
\(747\) −4.75129 + 0.246691i −0.173841 + 0.00902596i
\(748\) 5.44953 9.43887i 0.199255 0.345119i
\(749\) 11.4619 + 11.3334i 0.418809 + 0.414112i
\(750\) 11.3572 + 12.8433i 0.414707 + 0.468970i
\(751\) −3.92766 22.2748i −0.143322 0.812821i −0.968699 0.248238i \(-0.920148\pi\)
0.825377 0.564582i \(-0.190963\pi\)
\(752\) −0.550684 3.12308i −0.0200814 0.113887i
\(753\) 9.92286 + 25.2086i 0.361609 + 0.918652i
\(754\) 4.69933 + 3.94320i 0.171139 + 0.143603i
\(755\) 29.1854 1.06216
\(756\) −11.8796 6.91925i −0.432056 0.251651i
\(757\) −2.49660 −0.0907406 −0.0453703 0.998970i \(-0.514447\pi\)
−0.0453703 + 0.998970i \(0.514447\pi\)
\(758\) 22.5819 + 18.9485i 0.820212 + 0.688240i
\(759\) −16.6239 2.48859i −0.603410 0.0903299i
\(760\) −3.74704 21.2505i −0.135919 0.770836i
\(761\) 0.837007 + 4.74690i 0.0303415 + 0.172075i 0.996213 0.0869467i \(-0.0277110\pi\)
−0.965871 + 0.259022i \(0.916600\pi\)
\(762\) −3.03105 + 9.05156i −0.109803 + 0.327903i
\(763\) 27.8977 7.64403i 1.00996 0.276732i
\(764\) −8.30948 + 14.3924i −0.300627 + 0.520700i
\(765\) 3.37309 27.3618i 0.121954 0.989268i
\(766\) −4.14384 + 7.17734i −0.149723 + 0.259328i
\(767\) −3.72938 + 21.1504i −0.134660 + 0.763695i
\(768\) 0.0449194 + 1.73147i 0.00162089 + 0.0624790i
\(769\) 0.959984 + 5.44434i 0.0346179 + 0.196328i 0.997212 0.0746194i \(-0.0237742\pi\)
−0.962594 + 0.270947i \(0.912663\pi\)
\(770\) −32.6940 + 23.1684i −1.17821 + 0.834932i
\(771\) −5.07782 + 3.11000i −0.182873 + 0.112004i
\(772\) 1.72580 0.628141i 0.0621130 0.0226073i
\(773\) −3.30380 + 5.72235i −0.118829 + 0.205819i −0.919304 0.393548i \(-0.871248\pi\)
0.800475 + 0.599367i \(0.204581\pi\)
\(774\) −7.71350 + 3.26977i −0.277256 + 0.117529i
\(775\) −40.1327 69.5119i −1.44161 2.49694i
\(776\) −18.0025 + 6.55238i −0.646253 + 0.235217i
\(777\) −19.6817 26.3002i −0.706076 0.943516i
\(778\) 16.8768 14.1613i 0.605064 0.507709i
\(779\) 35.2011 29.5372i 1.26121 1.05828i
\(780\) −20.6434 3.09030i −0.739151 0.110650i
\(781\) −26.3884 + 9.60461i −0.944253 + 0.343680i
\(782\) −2.94425 + 5.09958i −0.105286 + 0.182361i
\(783\) −5.49443 + 7.69105i −0.196355 + 0.274856i
\(784\) 6.90692 + 1.13771i 0.246676 + 0.0406326i
\(785\) −10.6605 + 60.4585i −0.380488 + 2.15786i
\(786\) −3.16248 + 3.97380i −0.112802 + 0.141741i
\(787\) −4.16624 23.6279i −0.148510 0.842244i −0.964481 0.264151i \(-0.914908\pi\)
0.815971 0.578093i \(-0.196203\pi\)
\(788\) 10.4106 + 3.78916i 0.370864 + 0.134983i
\(789\) −31.2810 + 6.35629i −1.11363 + 0.226290i
\(790\) −11.6179 + 4.22857i −0.413347 + 0.150446i
\(791\) 5.56394 + 11.7583i 0.197831 + 0.418078i
\(792\) 5.77786 11.3261i 0.205307 0.402455i
\(793\) −17.5713 −0.623975
\(794\) −3.22105 + 18.2675i −0.114311 + 0.648289i
\(795\) −1.29813 50.0377i −0.0460398 1.77465i
\(796\) 9.39483 + 3.41944i 0.332991 + 0.121199i
\(797\) 5.25048 + 29.7770i 0.185982 + 1.05475i 0.924688 + 0.380726i \(0.124326\pi\)
−0.738706 + 0.674028i \(0.764563\pi\)
\(798\) 24.6972 12.4804i 0.874271 0.441802i
\(799\) 6.24727 + 5.24208i 0.221013 + 0.185452i
\(800\) 7.76995 0.274709
\(801\) −11.3395 + 10.5640i −0.400662 + 0.373259i
\(802\) 0.401384 0.0141734
\(803\) 8.95808 50.8038i 0.316124 1.79283i
\(804\) 3.17305 0.644762i 0.111905 0.0227390i
\(805\) 17.6637 12.5173i 0.622565 0.441178i
\(806\) 32.7367 + 11.9152i 1.15310 + 0.419694i
\(807\) −8.92704 1.33637i −0.314247 0.0470425i
\(808\) 7.93258 2.88722i 0.279067 0.101572i
\(809\) 19.0848 + 33.0558i 0.670984 + 1.16218i 0.977625 + 0.210354i \(0.0674615\pi\)
−0.306641 + 0.951825i \(0.599205\pi\)
\(810\) 2.27463 32.0810i 0.0799224 1.12721i
\(811\) 39.4404 1.38494 0.692470 0.721447i \(-0.256522\pi\)
0.692470 + 0.721447i \(0.256522\pi\)
\(812\) 1.21940 4.65570i 0.0427924 0.163383i
\(813\) −9.42142 23.9347i −0.330424 0.839427i
\(814\) 23.2731 19.5285i 0.815722 0.684472i
\(815\) 37.1043 + 13.5049i 1.29971 + 0.473054i
\(816\) −2.95060 3.33668i −0.103292 0.116807i
\(817\) 2.92825 16.6069i 0.102447 0.581003i
\(818\) 8.95642 15.5130i 0.313154 0.542399i
\(819\) −3.86187 26.4875i −0.134945 0.925548i
\(820\) 13.5970 + 23.5507i 0.474828 + 0.822427i
\(821\) 28.0603 10.2131i 0.979310 0.356440i 0.197738 0.980255i \(-0.436640\pi\)
0.781572 + 0.623815i \(0.214418\pi\)
\(822\) −23.9288 + 14.6556i −0.834612 + 0.511172i
\(823\) 0.156228 0.131091i 0.00544577 0.00456954i −0.640061 0.768324i \(-0.721091\pi\)
0.645506 + 0.763755i \(0.276646\pi\)
\(824\) −18.9437 6.89493i −0.659934 0.240196i
\(825\) −50.1193 27.2283i −1.74493 0.947968i
\(826\) 16.2501 4.45258i 0.565415 0.154925i
\(827\) −10.1906 17.6506i −0.354362 0.613773i 0.632647 0.774441i \(-0.281969\pi\)
−0.987009 + 0.160668i \(0.948635\pi\)
\(828\) −3.12163 + 6.11920i −0.108484 + 0.212657i
\(829\) 23.3577 0.811247 0.405624 0.914040i \(-0.367054\pi\)
0.405624 + 0.914040i \(0.367054\pi\)
\(830\) 4.34134 + 3.64282i 0.150690 + 0.126444i
\(831\) 10.7659 2.18763i 0.373465 0.0758880i
\(832\) −2.58340 + 2.16773i −0.0895634 + 0.0751526i
\(833\) −15.4870 + 9.17586i −0.536593 + 0.317925i
\(834\) 25.5055 + 3.81815i 0.883182 + 0.132212i
\(835\) 54.1553 + 45.4417i 1.87412 + 1.57257i
\(836\) 12.7961 + 22.1635i 0.442563 + 0.766541i
\(837\) −14.3824 + 51.7148i −0.497127 + 1.78753i
\(838\) 10.7882 18.6857i 0.372672 0.645486i
\(839\) 2.87441 16.3016i 0.0992358 0.562794i −0.894131 0.447806i \(-0.852206\pi\)
0.993367 0.114989i \(-0.0366832\pi\)
\(840\) 4.73566 + 15.6762i 0.163396 + 0.540879i
\(841\) 24.1417 + 8.78686i 0.832473 + 0.302995i
\(842\) 2.00988 + 11.3986i 0.0692650 + 0.392821i
\(843\) −14.4389 + 2.93398i −0.497303 + 0.101052i
\(844\) −15.4658 12.9774i −0.532355 0.446699i
\(845\) 2.90700 + 5.03507i 0.100004 + 0.173212i
\(846\) 7.59527 + 5.72923i 0.261131 + 0.196975i
\(847\) 10.4808 15.1493i 0.360126 0.520536i
\(848\) −6.19501 5.19823i −0.212737 0.178508i
\(849\) 0.236958 + 9.13381i 0.00813238 + 0.313471i
\(850\) −15.3065 + 12.8437i −0.525009 + 0.440535i
\(851\) −12.5739 + 10.5507i −0.431027 + 0.361674i
\(852\) 0.297630 + 11.4725i 0.0101966 + 0.393041i
\(853\) −32.9561 27.6534i −1.12839 0.946836i −0.129397 0.991593i \(-0.541304\pi\)
−0.998998 + 0.0447572i \(0.985749\pi\)
\(854\) 5.89626 + 12.4606i 0.201766 + 0.426394i
\(855\) 51.6807 + 38.9836i 1.76744 + 1.33321i
\(856\) 3.04619 + 5.27616i 0.104117 + 0.180336i
\(857\) −12.2834 10.3070i −0.419593 0.352080i 0.408416 0.912796i \(-0.366081\pi\)
−0.828008 + 0.560716i \(0.810526\pi\)
\(858\) 24.2604 4.92970i 0.828236 0.168297i
\(859\) 6.44783 + 36.5675i 0.219997 + 1.24767i 0.872021 + 0.489468i \(0.162809\pi\)
−0.652024 + 0.758198i \(0.726080\pi\)
\(860\) 9.37768 + 3.41320i 0.319776 + 0.116389i
\(861\) −23.8681 + 25.4251i −0.813423 + 0.866486i
\(862\) 4.25999 24.1596i 0.145096 0.822879i
\(863\) −8.50835 + 14.7369i −0.289627 + 0.501650i −0.973721 0.227745i \(-0.926865\pi\)
0.684093 + 0.729394i \(0.260198\pi\)
\(864\) −3.63933 3.70881i −0.123813 0.126176i
\(865\) −34.6193 59.9624i −1.17709 2.03878i
\(866\) 12.5411 + 10.5233i 0.426165 + 0.357595i
\(867\) −17.7923 2.66349i −0.604258 0.0904570i
\(868\) −2.53557 27.2134i −0.0860630 0.923682i
\(869\) 11.2328 9.42541i 0.381046 0.319735i
\(870\) 11.0335 2.24200i 0.374070 0.0760109i
\(871\) 4.82941 + 4.05235i 0.163638 + 0.137309i
\(872\) 10.9330 0.370238
\(873\) 26.1174 51.1967i 0.883939 1.73275i
\(874\) −6.91342 11.9744i −0.233850 0.405040i
\(875\) 25.2578 6.92069i 0.853868 0.233962i
\(876\) −18.5251 10.0642i −0.625907 0.340036i
\(877\) −40.9308 14.8976i −1.38213 0.503056i −0.459310 0.888276i \(-0.651903\pi\)
−0.922825 + 0.385220i \(0.874126\pi\)
\(878\) 16.1405 13.5435i 0.544717 0.457072i
\(879\) 38.0645 23.3133i 1.28388 0.786337i
\(880\) −14.2320 + 5.18002i −0.479760 + 0.174618i
\(881\) −5.49845 9.52359i −0.185247 0.320858i 0.758412 0.651775i \(-0.225975\pi\)
−0.943660 + 0.330917i \(0.892642\pi\)
\(882\) −17.4876 + 11.6268i −0.588839 + 0.391496i
\(883\) −17.2558 + 29.8879i −0.580703 + 1.00581i 0.414693 + 0.909961i \(0.363889\pi\)
−0.995396 + 0.0958457i \(0.969444\pi\)
\(884\) 1.50596 8.54070i 0.0506508 0.287255i
\(885\) 26.1113 + 29.5279i 0.877722 + 0.992570i
\(886\) −18.9032 6.88019i −0.635065 0.231145i
\(887\) −10.1293 + 8.49952i −0.340110 + 0.285386i −0.796804 0.604238i \(-0.793478\pi\)
0.456694 + 0.889624i \(0.349033\pi\)
\(888\) −4.54761 11.5530i −0.152608 0.387694i
\(889\) 10.3684 + 10.2521i 0.347744 + 0.343844i
\(890\) 18.4605 0.618797
\(891\) 10.4783 + 36.6767i 0.351037 + 1.22871i
\(892\) −12.2410 21.2021i −0.409860 0.709899i
\(893\) −17.9946 + 6.54948i −0.602165 + 0.219170i
\(894\) 12.3699 + 1.85176i 0.413711 + 0.0619322i
\(895\) 73.3931 + 26.7129i 2.45326 + 0.892914i
\(896\) 2.40413 + 1.10460i 0.0803164 + 0.0369022i
\(897\) −13.1073 + 2.66339i −0.437639 + 0.0889281i
\(898\) −2.12140 + 12.0310i −0.0707920 + 0.401481i
\(899\) −18.7912 −0.626721
\(900\) −17.0555 + 15.8890i −0.568515 + 0.529633i
\(901\) 20.7966 0.692835
\(902\) −24.7069 20.7315i −0.822650 0.690285i
\(903\) −0.712326 + 12.7776i −0.0237047 + 0.425213i
\(904\) 0.853771 + 4.84198i 0.0283960 + 0.161042i
\(905\) 16.6829 + 6.07208i 0.554559 + 0.201843i
\(906\) 0.366864 + 14.1412i 0.0121882 + 0.469809i
\(907\) −0.920700 + 5.22155i −0.0305713 + 0.173379i −0.996271 0.0862848i \(-0.972501\pi\)
0.965699 + 0.259663i \(0.0836116\pi\)
\(908\) −14.2450 −0.472738
\(909\) −11.5083 + 22.5592i −0.381706 + 0.748241i
\(910\) −18.1407 + 26.2211i −0.601359 + 0.869221i
\(911\) 39.5736 14.4036i 1.31113 0.477213i 0.410525 0.911849i \(-0.365345\pi\)
0.900606 + 0.434636i \(0.143123\pi\)
\(912\) 10.2494 2.08267i 0.339391 0.0689641i
\(913\) −6.31606 2.29886i −0.209031 0.0760810i
\(914\) −3.34994 18.9985i −0.110806 0.628414i
\(915\) −20.0818 + 25.2337i −0.663884 + 0.834201i
\(916\) 3.36130 19.0629i 0.111060 0.629855i
\(917\) 3.31815 + 7.01228i 0.109575 + 0.231566i
\(918\) 13.3000 + 1.29042i 0.438965 + 0.0425902i
\(919\) −1.88056 + 3.25723i −0.0620340 + 0.107446i −0.895374 0.445314i \(-0.853092\pi\)
0.833340 + 0.552760i \(0.186425\pi\)
\(920\) 7.68918 2.79863i 0.253505 0.0922682i
\(921\) 43.6867 + 6.53986i 1.43953 + 0.215496i
\(922\) −11.9353 + 10.0149i −0.393069 + 0.329824i
\(923\) −17.1173 + 14.3631i −0.563422 + 0.472767i
\(924\) −11.6368 15.5500i −0.382821 0.511556i
\(925\) −52.3382 + 19.0496i −1.72087 + 0.626346i
\(926\) 6.33711 + 10.9762i 0.208250 + 0.360700i
\(927\) 55.6820 23.6037i 1.82884 0.775248i
\(928\) 0.909523 1.57534i 0.0298566 0.0517131i
\(929\) −39.3542 + 14.3237i −1.29117 + 0.469947i −0.894110 0.447847i \(-0.852191\pi\)
−0.397058 + 0.917794i \(0.629969\pi\)
\(930\) 54.5250 33.3948i 1.78795 1.09506i
\(931\) −0.476705 42.2662i −0.0156234 1.38522i
\(932\) −2.51056 14.2381i −0.0822361 0.466384i
\(933\) 0.296229 + 11.4185i 0.00969810 + 0.373824i
\(934\) −0.424141 + 2.40542i −0.0138783 + 0.0787079i
\(935\) 19.4739 33.7298i 0.636866 1.10308i
\(936\) 1.23785 10.0412i 0.0404604 0.328206i
\(937\) −3.70662 + 6.42005i −0.121090 + 0.209734i −0.920198 0.391454i \(-0.871972\pi\)
0.799108 + 0.601188i \(0.205306\pi\)
\(938\) 1.25315 4.78458i 0.0409168 0.156222i
\(939\) 13.0775 39.0531i 0.426769 1.27445i
\(940\) −1.96787 11.1604i −0.0641849 0.364011i
\(941\) −5.44171 30.8615i −0.177395 1.00605i −0.935344 0.353741i \(-0.884910\pi\)
0.757949 0.652314i \(-0.226202\pi\)
\(942\) −29.4279 4.40534i −0.958814 0.143534i
\(943\) 13.3485 + 11.2007i 0.434687 + 0.364746i
\(944\) 6.36837 0.207273
\(945\) −42.4517 24.7260i −1.38095 0.804336i
\(946\) −11.8359 −0.384817
\(947\) −22.0761 18.5240i −0.717376 0.601950i 0.209282 0.977855i \(-0.432887\pi\)
−0.926658 + 0.375905i \(0.877332\pi\)
\(948\) −2.19491 5.57606i −0.0712873 0.181102i
\(949\) −7.12801 40.4249i −0.231385 1.31225i
\(950\) −8.14725 46.2054i −0.264332 1.49910i
\(951\) 30.3258 + 34.2939i 0.983381 + 1.11205i
\(952\) −6.56196 + 1.79799i −0.212674 + 0.0582732i
\(953\) −10.4605 + 18.1180i −0.338848 + 0.586901i −0.984216 0.176970i \(-0.943370\pi\)
0.645369 + 0.763871i \(0.276704\pi\)
\(954\) 24.2284 1.25796i 0.784423 0.0407280i
\(955\) −29.6940 + 51.4315i −0.960875 + 1.66428i
\(956\) −0.769161 + 4.36213i −0.0248765 + 0.141081i
\(957\) −11.3873 + 6.97433i −0.368098 + 0.225448i
\(958\) −6.30771 35.7728i −0.203793 1.15577i
\(959\) 3.97645 + 42.6778i 0.128406 + 1.37814i
\(960\) 0.160520 + 6.18741i 0.00518076 + 0.199698i
\(961\) −71.1478 + 25.8957i −2.29509 + 0.835344i
\(962\) 12.0871 20.9355i 0.389705 0.674988i
\(963\) −17.4759 5.35221i −0.563154 0.172473i
\(964\) −3.70905 6.42426i −0.119460 0.206911i
\(965\) 6.16717 2.24467i 0.198528 0.0722584i
\(966\) 6.28704 + 8.40126i 0.202282 + 0.270306i
\(967\) 2.48476 2.08496i 0.0799045 0.0670478i −0.601961 0.798526i \(-0.705614\pi\)
0.681865 + 0.731478i \(0.261169\pi\)
\(968\) 5.33369 4.47550i 0.171431 0.143848i
\(969\) −16.7483 + 21.0450i −0.538032 + 0.676062i
\(970\) −64.3321 + 23.4150i −2.06558 + 0.751810i
\(971\) −6.98231 + 12.0937i −0.224073 + 0.388106i −0.956041 0.293233i \(-0.905269\pi\)
0.731968 + 0.681339i \(0.238602\pi\)
\(972\) 15.5728 + 0.698864i 0.499497 + 0.0224161i
\(973\) 22.4133 32.3969i 0.718539 1.03860i
\(974\) 4.88676 27.7142i 0.156582 0.888019i
\(975\) −44.8853 6.71929i −1.43748 0.215190i
\(976\) 0.904765 + 5.13118i 0.0289608 + 0.164245i
\(977\) 25.2902 + 9.20490i 0.809107 + 0.294491i 0.713255 0.700905i \(-0.247220\pi\)
0.0958518 + 0.995396i \(0.469443\pi\)
\(978\) −6.07709 + 18.1479i −0.194324 + 0.580305i
\(979\) −20.5740 + 7.48834i −0.657549 + 0.239328i
\(980\) 24.6819 + 4.06563i 0.788436 + 0.129872i
\(981\) −23.9985 + 22.3572i −0.766213 + 0.713810i
\(982\) −26.5163 −0.846169
\(983\) −6.45820 + 36.6263i −0.205985 + 1.16820i 0.689898 + 0.723906i \(0.257655\pi\)
−0.895883 + 0.444290i \(0.853456\pi\)
\(984\) −11.2401 + 6.88419i −0.358321 + 0.219460i
\(985\) 37.2025 + 13.5406i 1.18537 + 0.431439i
\(986\) 0.812303 + 4.60680i 0.0258690 + 0.146710i
\(987\) 12.9705 6.55448i 0.412856 0.208631i
\(988\) 15.5997 + 13.0897i 0.496291 + 0.416438i
\(989\) 6.39462 0.203337
\(990\) 20.6472 40.4738i 0.656211 1.28634i
\(991\) 21.3969 0.679694 0.339847 0.940481i \(-0.389625\pi\)
0.339847 + 0.940481i \(0.389625\pi\)
\(992\) 1.79383 10.1733i 0.0569541 0.323003i
\(993\) 9.04982 + 10.2340i 0.287187 + 0.324765i
\(994\) 15.9295 + 7.31896i 0.505252 + 0.232143i
\(995\) 33.5725 + 12.2194i 1.06432 + 0.387381i
\(996\) −1.71048 + 2.14930i −0.0541986 + 0.0681030i
\(997\) 26.8727 9.78085i 0.851066 0.309763i 0.120591 0.992702i \(-0.461521\pi\)
0.730475 + 0.682940i \(0.239299\pi\)
\(998\) −8.13510 14.0904i −0.257512 0.446024i
\(999\) 33.6074 + 16.0599i 1.06329 + 0.508114i
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 378.2.v.b.79.4 yes 72
7.4 even 3 378.2.w.a.25.12 yes 72
27.13 even 9 378.2.w.a.121.12 yes 72
189.67 even 9 inner 378.2.v.b.67.4 72
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.v.b.67.4 72 189.67 even 9 inner
378.2.v.b.79.4 yes 72 1.1 even 1 trivial
378.2.w.a.25.12 yes 72 7.4 even 3
378.2.w.a.121.12 yes 72 27.13 even 9