Properties

Label 273.2.bn.c.146.4
Level $273$
Weight $2$
Character 273.146
Analytic conductor $2.180$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(146,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.146");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.bn (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 146.4
Character \(\chi\) \(=\) 273.146
Dual form 273.2.bn.c.230.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.01386 + 1.16270i) q^{2} +(1.06546 + 1.36557i) q^{3} +(1.70376 - 2.95099i) q^{4} +0.993521 q^{5} +(-3.73345 - 1.51126i) q^{6} +(2.52966 - 0.775133i) q^{7} +3.27304i q^{8} +(-0.729580 + 2.90993i) q^{9} +O(q^{10})\) \(q+(-2.01386 + 1.16270i) q^{2} +(1.06546 + 1.36557i) q^{3} +(1.70376 - 2.95099i) q^{4} +0.993521 q^{5} +(-3.73345 - 1.51126i) q^{6} +(2.52966 - 0.775133i) q^{7} +3.27304i q^{8} +(-0.729580 + 2.90993i) q^{9} +(-2.00081 + 1.15517i) q^{10} +(2.81046 - 1.62262i) q^{11} +(5.84509 - 0.817568i) q^{12} +(2.75926 - 2.32088i) q^{13} +(-4.19313 + 4.50225i) q^{14} +(1.05856 + 1.35672i) q^{15} +(-0.398062 - 0.689463i) q^{16} +(1.72639 - 2.99020i) q^{17} +(-1.91412 - 6.70849i) q^{18} +(1.33408 + 0.770230i) q^{19} +(1.69272 - 2.93187i) q^{20} +(3.75376 + 2.62856i) q^{21} +(-3.77325 + 6.53546i) q^{22} +(-4.81226 + 2.77836i) q^{23} +(-4.46958 + 3.48730i) q^{24} -4.01292 q^{25} +(-2.85828 + 7.88213i) q^{26} +(-4.75107 + 2.10413i) q^{27} +(2.02251 - 8.78564i) q^{28} +(-2.42166 + 1.39814i) q^{29} +(-3.70926 - 1.50147i) q^{30} +0.253865i q^{31} +(-4.06579 - 2.34739i) q^{32} +(5.21025 + 2.10905i) q^{33} +8.02913i q^{34} +(2.51327 - 0.770110i) q^{35} +(7.34417 + 7.11080i) q^{36} +(0.572688 + 0.991924i) q^{37} -3.58220 q^{38} +(6.10922 + 1.29516i) q^{39} +3.25183i q^{40} +(1.42995 + 2.47675i) q^{41} +(-10.6158 - 0.929046i) q^{42} +(-5.92223 + 10.2576i) q^{43} -11.0582i q^{44} +(-0.724852 + 2.89108i) q^{45} +(6.46082 - 11.1905i) q^{46} -6.13878 q^{47} +(0.517392 - 1.27818i) q^{48} +(5.79834 - 3.92164i) q^{49} +(8.08146 - 4.66583i) q^{50} +(5.92274 - 0.828430i) q^{51} +(-2.14779 - 12.0968i) q^{52} +1.06449i q^{53} +(7.12151 - 9.76151i) q^{54} +(2.79225 - 1.61211i) q^{55} +(2.53704 + 8.27968i) q^{56} +(0.369604 + 2.64243i) q^{57} +(3.25125 - 5.63134i) q^{58} +(7.26527 - 12.5838i) q^{59} +(5.80721 - 0.812271i) q^{60} +(-10.5869 - 6.11236i) q^{61} +(-0.295169 - 0.511248i) q^{62} +(0.409998 + 7.92666i) q^{63} +12.5095 q^{64} +(2.74138 - 2.30584i) q^{65} +(-12.9449 + 1.81064i) q^{66} +(-4.97057 - 8.60928i) q^{67} +(-5.88271 - 10.1891i) q^{68} +(-8.92134 - 3.61126i) q^{69} +(-4.16596 + 4.47308i) q^{70} +(3.62686 + 2.09397i) q^{71} +(-9.52433 - 2.38794i) q^{72} +8.34583i q^{73} +(-2.30663 - 1.33173i) q^{74} +(-4.27561 - 5.47993i) q^{75} +(4.54589 - 2.62457i) q^{76} +(5.85176 - 6.28315i) q^{77} +(-13.8090 + 4.49493i) q^{78} +7.85176 q^{79} +(-0.395482 - 0.684996i) q^{80} +(-7.93543 - 4.24606i) q^{81} +(-5.75944 - 3.32521i) q^{82} +9.49585 q^{83} +(14.1523 - 6.59889i) q^{84} +(1.71521 - 2.97082i) q^{85} -27.5432i q^{86} +(-4.48945 - 1.81728i) q^{87} +(5.31090 + 9.19875i) q^{88} +(1.72349 + 2.98518i) q^{89} +(-1.90171 - 6.66502i) q^{90} +(5.18100 - 8.00982i) q^{91} +18.9346i q^{92} +(-0.346671 + 0.270483i) q^{93} +(12.3626 - 7.13758i) q^{94} +(1.32543 + 0.765239i) q^{95} +(-1.12642 - 8.05319i) q^{96} +(-6.67981 - 3.85659i) q^{97} +(-7.11734 + 14.6394i) q^{98} +(2.67126 + 9.36208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 64 q + 32 q^{4} - 4 q^{7} - 10 q^{9} - 18 q^{15} - 16 q^{16} + 8 q^{18} - 44 q^{21} - 32 q^{22} + 48 q^{25} + 40 q^{28} - 40 q^{30} - 6 q^{36} + 12 q^{37} - 12 q^{42} + 40 q^{43} - 36 q^{46} - 24 q^{49} - 28 q^{51} - 68 q^{57} - 116 q^{60} + 4 q^{63} - 48 q^{64} - 28 q^{67} - 64 q^{70} + 62 q^{72} - 2 q^{78} + 56 q^{79} + 10 q^{81} + 28 q^{85} + 80 q^{88} - 16 q^{91} + 46 q^{93} - 32 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.01386 + 1.16270i −1.42401 + 0.822155i −0.996639 0.0819189i \(-0.973895\pi\)
−0.427376 + 0.904074i \(0.640562\pi\)
\(3\) 1.06546 + 1.36557i 0.615145 + 0.788414i
\(4\) 1.70376 2.95099i 0.851878 1.47550i
\(5\) 0.993521 0.444316 0.222158 0.975011i \(-0.428690\pi\)
0.222158 + 0.975011i \(0.428690\pi\)
\(6\) −3.73345 1.51126i −1.52417 0.616968i
\(7\) 2.52966 0.775133i 0.956121 0.292973i
\(8\) 3.27304i 1.15719i
\(9\) −0.729580 + 2.90993i −0.243193 + 0.969978i
\(10\) −2.00081 + 1.15517i −0.632712 + 0.365297i
\(11\) 2.81046 1.62262i 0.847386 0.489238i −0.0123823 0.999923i \(-0.503941\pi\)
0.859768 + 0.510685i \(0.170608\pi\)
\(12\) 5.84509 0.817568i 1.68733 0.236012i
\(13\) 2.75926 2.32088i 0.765281 0.643696i
\(14\) −4.19313 + 4.50225i −1.12066 + 1.20328i
\(15\) 1.05856 + 1.35672i 0.273319 + 0.350305i
\(16\) −0.398062 0.689463i −0.0995154 0.172366i
\(17\) 1.72639 2.99020i 0.418712 0.725230i −0.577099 0.816675i \(-0.695815\pi\)
0.995810 + 0.0914447i \(0.0291485\pi\)
\(18\) −1.91412 6.70849i −0.451162 1.58121i
\(19\) 1.33408 + 0.770230i 0.306058 + 0.176703i 0.645161 0.764046i \(-0.276790\pi\)
−0.339103 + 0.940749i \(0.610123\pi\)
\(20\) 1.69272 2.93187i 0.378503 0.655587i
\(21\) 3.75376 + 2.62856i 0.819137 + 0.573598i
\(22\) −3.77325 + 6.53546i −0.804460 + 1.39337i
\(23\) −4.81226 + 2.77836i −1.00343 + 0.579328i −0.909260 0.416228i \(-0.863352\pi\)
−0.0941659 + 0.995557i \(0.530018\pi\)
\(24\) −4.46958 + 3.48730i −0.912349 + 0.711843i
\(25\) −4.01292 −0.802583
\(26\) −2.85828 + 7.88213i −0.560554 + 1.54581i
\(27\) −4.75107 + 2.10413i −0.914343 + 0.404940i
\(28\) 2.02251 8.78564i 0.382219 1.66033i
\(29\) −2.42166 + 1.39814i −0.449690 + 0.259629i −0.707699 0.706514i \(-0.750267\pi\)
0.258009 + 0.966143i \(0.416934\pi\)
\(30\) −3.70926 1.50147i −0.677215 0.274129i
\(31\) 0.253865i 0.0455955i 0.999740 + 0.0227977i \(0.00725737\pi\)
−0.999740 + 0.0227977i \(0.992743\pi\)
\(32\) −4.06579 2.34739i −0.718737 0.414963i
\(33\) 5.21025 + 2.10905i 0.906987 + 0.367138i
\(34\) 8.02913i 1.37698i
\(35\) 2.51327 0.770110i 0.424820 0.130172i
\(36\) 7.34417 + 7.11080i 1.22403 + 1.18513i
\(37\) 0.572688 + 0.991924i 0.0941493 + 0.163071i 0.909253 0.416243i \(-0.136654\pi\)
−0.815104 + 0.579315i \(0.803320\pi\)
\(38\) −3.58220 −0.581109
\(39\) 6.10922 + 1.29516i 0.978258 + 0.207392i
\(40\) 3.25183i 0.514160i
\(41\) 1.42995 + 2.47675i 0.223321 + 0.386803i 0.955814 0.293971i \(-0.0949770\pi\)
−0.732494 + 0.680774i \(0.761644\pi\)
\(42\) −10.6158 0.929046i −1.63805 0.143355i
\(43\) −5.92223 + 10.2576i −0.903131 + 1.56427i −0.0797249 + 0.996817i \(0.525404\pi\)
−0.823406 + 0.567452i \(0.807929\pi\)
\(44\) 11.0582i 1.66709i
\(45\) −0.724852 + 2.89108i −0.108055 + 0.430977i
\(46\) 6.46082 11.1905i 0.952596 1.64994i
\(47\) −6.13878 −0.895433 −0.447716 0.894176i \(-0.647763\pi\)
−0.447716 + 0.894176i \(0.647763\pi\)
\(48\) 0.517392 1.27818i 0.0746791 0.184489i
\(49\) 5.79834 3.92164i 0.828334 0.560235i
\(50\) 8.08146 4.66583i 1.14289 0.659848i
\(51\) 5.92274 0.828430i 0.829350 0.116003i
\(52\) −2.14779 12.0968i −0.297845 1.67752i
\(53\) 1.06449i 0.146219i 0.997324 + 0.0731093i \(0.0232922\pi\)
−0.997324 + 0.0731093i \(0.976708\pi\)
\(54\) 7.12151 9.76151i 0.969114 1.32837i
\(55\) 2.79225 1.61211i 0.376507 0.217376i
\(56\) 2.53704 + 8.27968i 0.339026 + 1.10642i
\(57\) 0.369604 + 2.64243i 0.0489553 + 0.349999i
\(58\) 3.25125 5.63134i 0.426911 0.739431i
\(59\) 7.26527 12.5838i 0.945857 1.63827i 0.191832 0.981428i \(-0.438557\pi\)
0.754025 0.656846i \(-0.228110\pi\)
\(60\) 5.80721 0.812271i 0.749708 0.104864i
\(61\) −10.5869 6.11236i −1.35552 0.782607i −0.366500 0.930418i \(-0.619444\pi\)
−0.989016 + 0.147811i \(0.952777\pi\)
\(62\) −0.295169 0.511248i −0.0374866 0.0649286i
\(63\) 0.409998 + 7.92666i 0.0516549 + 0.998665i
\(64\) 12.5095 1.56369
\(65\) 2.74138 2.30584i 0.340027 0.286004i
\(66\) −12.9449 + 1.81064i −1.59341 + 0.222874i
\(67\) −4.97057 8.60928i −0.607252 1.05179i −0.991691 0.128641i \(-0.958939\pi\)
0.384439 0.923150i \(-0.374395\pi\)
\(68\) −5.88271 10.1891i −0.713383 1.23562i
\(69\) −8.92134 3.61126i −1.07400 0.434744i
\(70\) −4.16596 + 4.47308i −0.497928 + 0.534635i
\(71\) 3.62686 + 2.09397i 0.430429 + 0.248508i 0.699529 0.714604i \(-0.253393\pi\)
−0.269100 + 0.963112i \(0.586726\pi\)
\(72\) −9.52433 2.38794i −1.12245 0.281422i
\(73\) 8.34583i 0.976806i 0.872618 + 0.488403i \(0.162420\pi\)
−0.872618 + 0.488403i \(0.837580\pi\)
\(74\) −2.30663 1.33173i −0.268140 0.154811i
\(75\) −4.27561 5.47993i −0.493705 0.632768i
\(76\) 4.54589 2.62457i 0.521449 0.301059i
\(77\) 5.85176 6.28315i 0.666870 0.716032i
\(78\) −13.8090 + 4.49493i −1.56356 + 0.508950i
\(79\) 7.85176 0.883392 0.441696 0.897165i \(-0.354377\pi\)
0.441696 + 0.897165i \(0.354377\pi\)
\(80\) −0.395482 0.684996i −0.0442163 0.0765848i
\(81\) −7.93543 4.24606i −0.881714 0.471784i
\(82\) −5.75944 3.32521i −0.636024 0.367209i
\(83\) 9.49585 1.04230 0.521152 0.853464i \(-0.325502\pi\)
0.521152 + 0.853464i \(0.325502\pi\)
\(84\) 14.1523 6.59889i 1.54415 0.719997i
\(85\) 1.71521 2.97082i 0.186040 0.322231i
\(86\) 27.5432i 2.97006i
\(87\) −4.48945 1.81728i −0.481320 0.194833i
\(88\) 5.31090 + 9.19875i 0.566144 + 0.980590i
\(89\) 1.72349 + 2.98518i 0.182690 + 0.316429i 0.942796 0.333371i \(-0.108186\pi\)
−0.760106 + 0.649800i \(0.774853\pi\)
\(90\) −1.90171 6.66502i −0.200458 0.702555i
\(91\) 5.18100 8.00982i 0.543116 0.839658i
\(92\) 18.9346i 1.97407i
\(93\) −0.346671 + 0.270483i −0.0359481 + 0.0280478i
\(94\) 12.3626 7.13758i 1.27511 0.736185i
\(95\) 1.32543 + 0.765239i 0.135987 + 0.0785119i
\(96\) −1.12642 8.05319i −0.114965 0.821925i
\(97\) −6.67981 3.85659i −0.678232 0.391578i 0.120956 0.992658i \(-0.461404\pi\)
−0.799189 + 0.601080i \(0.794737\pi\)
\(98\) −7.11734 + 14.6394i −0.718960 + 1.47880i
\(99\) 2.67126 + 9.36208i 0.268472 + 0.940925i
\(100\) −6.83704 + 11.8421i −0.683704 + 1.18421i
\(101\) 6.75250 + 11.6957i 0.671899 + 1.16376i 0.977365 + 0.211560i \(0.0678544\pi\)
−0.305466 + 0.952203i \(0.598812\pi\)
\(102\) −10.9644 + 8.55473i −1.08563 + 0.847045i
\(103\) 12.3378i 1.21568i 0.794059 + 0.607841i \(0.207964\pi\)
−0.794059 + 0.607841i \(0.792036\pi\)
\(104\) 7.59633 + 9.03118i 0.744882 + 0.885580i
\(105\) 3.72943 + 2.61153i 0.363955 + 0.254859i
\(106\) −1.23768 2.14373i −0.120214 0.208218i
\(107\) 5.39056 3.11224i 0.521125 0.300872i −0.216270 0.976334i \(-0.569389\pi\)
0.737395 + 0.675462i \(0.236056\pi\)
\(108\) −1.88539 + 17.6053i −0.181421 + 1.69407i
\(109\) −14.8132 −1.41884 −0.709422 0.704784i \(-0.751044\pi\)
−0.709422 + 0.704784i \(0.751044\pi\)
\(110\) −3.74880 + 6.49312i −0.357434 + 0.619094i
\(111\) −0.744368 + 1.83891i −0.0706523 + 0.174541i
\(112\) −1.54138 1.43555i −0.145647 0.135647i
\(113\) −14.9870 8.65278i −1.40986 0.813985i −0.414488 0.910055i \(-0.636039\pi\)
−0.995375 + 0.0960701i \(0.969373\pi\)
\(114\) −3.81670 4.89175i −0.357466 0.458154i
\(115\) −4.78108 + 2.76036i −0.445838 + 0.257405i
\(116\) 9.52839i 0.884689i
\(117\) 4.74050 + 9.72253i 0.438260 + 0.898848i
\(118\) 33.7894i 3.11057i
\(119\) 2.04938 8.90236i 0.187866 0.816078i
\(120\) −4.44062 + 3.46471i −0.405371 + 0.316283i
\(121\) −0.234209 + 0.405662i −0.0212917 + 0.0368784i
\(122\) 28.4274 2.57370
\(123\) −1.85862 + 4.59158i −0.167586 + 0.414009i
\(124\) 0.749153 + 0.432524i 0.0672760 + 0.0388418i
\(125\) −8.95452 −0.800916
\(126\) −10.0420 15.4865i −0.894615 1.37965i
\(127\) −5.38117 9.32045i −0.477501 0.827057i 0.522166 0.852844i \(-0.325124\pi\)
−0.999667 + 0.0257872i \(0.991791\pi\)
\(128\) −17.0608 + 9.85006i −1.50798 + 0.870631i
\(129\) −20.3174 + 2.84185i −1.78885 + 0.250211i
\(130\) −2.83976 + 7.83106i −0.249063 + 0.686829i
\(131\) 9.18252 0.802281 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(132\) 15.1008 11.7821i 1.31435 1.02550i
\(133\) 3.97179 + 0.914331i 0.344398 + 0.0792826i
\(134\) 20.0201 + 11.5586i 1.72947 + 0.998511i
\(135\) −4.72028 + 2.09050i −0.406257 + 0.179921i
\(136\) 9.78705 + 5.65055i 0.839232 + 0.484531i
\(137\) 1.07228 + 0.619079i 0.0916108 + 0.0528915i 0.545106 0.838367i \(-0.316490\pi\)
−0.453495 + 0.891259i \(0.649823\pi\)
\(138\) 22.1652 3.10030i 1.88682 0.263915i
\(139\) 10.5917 + 6.11510i 0.898373 + 0.518676i 0.876672 0.481089i \(-0.159758\pi\)
0.0217011 + 0.999765i \(0.493092\pi\)
\(140\) 2.00941 8.72872i 0.169826 0.737711i
\(141\) −6.54064 8.38295i −0.550821 0.705972i
\(142\) −9.73866 −0.817250
\(143\) 3.98889 11.0000i 0.333568 0.919864i
\(144\) 2.29671 0.655315i 0.191392 0.0546096i
\(145\) −2.40597 + 1.38909i −0.199805 + 0.115357i
\(146\) −9.70372 16.8073i −0.803086 1.39099i
\(147\) 11.5332 + 3.73969i 0.951242 + 0.308445i
\(148\) 3.90288 0.320815
\(149\) −8.39830 4.84876i −0.688015 0.397226i 0.114853 0.993383i \(-0.463360\pi\)
−0.802868 + 0.596157i \(0.796694\pi\)
\(150\) 14.9820 + 6.06455i 1.22328 + 0.495169i
\(151\) 4.84486 0.394269 0.197135 0.980376i \(-0.436836\pi\)
0.197135 + 0.980376i \(0.436836\pi\)
\(152\) −2.52100 + 4.36649i −0.204480 + 0.354169i
\(153\) 7.44174 + 7.20528i 0.601629 + 0.582512i
\(154\) −4.47918 + 19.4573i −0.360943 + 1.56791i
\(155\) 0.252220i 0.0202588i
\(156\) 14.2306 15.8216i 1.13936 1.26674i
\(157\) 20.7117i 1.65297i −0.562958 0.826486i \(-0.690337\pi\)
0.562958 0.826486i \(-0.309663\pi\)
\(158\) −15.8124 + 9.12927i −1.25796 + 0.726285i
\(159\) −1.45364 + 1.13417i −0.115281 + 0.0899457i
\(160\) −4.03945 2.33218i −0.319346 0.184375i
\(161\) −10.0198 + 10.7584i −0.789669 + 0.847884i
\(162\) 20.9177 0.675578i 1.64345 0.0530784i
\(163\) −0.175873 + 0.304621i −0.0137754 + 0.0238597i −0.872831 0.488023i \(-0.837718\pi\)
0.859056 + 0.511882i \(0.171052\pi\)
\(164\) 9.74515 0.760968
\(165\) 5.17649 + 2.09538i 0.402989 + 0.163125i
\(166\) −19.1233 + 11.0409i −1.48426 + 0.856937i
\(167\) −8.43594 14.6115i −0.652793 1.13067i −0.982442 0.186567i \(-0.940264\pi\)
0.329649 0.944103i \(-0.393069\pi\)
\(168\) −8.60338 + 12.2862i −0.663765 + 0.947901i
\(169\) 2.22704 12.8078i 0.171311 0.985217i
\(170\) 7.97710i 0.611816i
\(171\) −3.21463 + 3.32013i −0.245829 + 0.253897i
\(172\) 20.1801 + 34.9529i 1.53872 + 2.66513i
\(173\) −10.3357 + 17.9020i −0.785809 + 1.36106i 0.142705 + 0.989765i \(0.454420\pi\)
−0.928515 + 0.371296i \(0.878913\pi\)
\(174\) 11.1541 1.56015i 0.845589 0.118275i
\(175\) −10.1513 + 3.11054i −0.767367 + 0.235135i
\(176\) −2.23747 1.29181i −0.168656 0.0973735i
\(177\) 24.9250 3.48633i 1.87348 0.262048i
\(178\) −6.94176 4.00783i −0.520307 0.300399i
\(179\) 4.34650 2.50945i 0.324873 0.187565i −0.328690 0.944438i \(-0.606607\pi\)
0.653562 + 0.756873i \(0.273274\pi\)
\(180\) 7.29658 + 7.06473i 0.543855 + 0.526574i
\(181\) 12.6750i 0.942123i −0.882100 0.471062i \(-0.843871\pi\)
0.882100 0.471062i \(-0.156129\pi\)
\(182\) −1.12076 + 22.1546i −0.0830765 + 1.64221i
\(183\) −2.93309 20.9697i −0.216820 1.55012i
\(184\) −9.09369 15.7507i −0.670396 1.16116i
\(185\) 0.568977 + 0.985497i 0.0418320 + 0.0724552i
\(186\) 0.383655 0.947791i 0.0281310 0.0694954i
\(187\) 11.2051i 0.819399i
\(188\) −10.4590 + 18.1155i −0.762800 + 1.32121i
\(189\) −10.3876 + 9.00544i −0.755586 + 0.655049i
\(190\) −3.55899 −0.258196
\(191\) 1.58695 + 0.916224i 0.114827 + 0.0662957i 0.556314 0.830972i \(-0.312215\pi\)
−0.441486 + 0.897268i \(0.645549\pi\)
\(192\) 13.3284 + 17.0826i 0.961895 + 1.23283i
\(193\) −2.36521 4.09667i −0.170252 0.294885i 0.768256 0.640143i \(-0.221125\pi\)
−0.938508 + 0.345258i \(0.887791\pi\)
\(194\) 17.9363 1.28775
\(195\) 6.06963 + 1.28677i 0.434656 + 0.0921477i
\(196\) −1.69378 23.7924i −0.120984 1.69946i
\(197\) −18.4409 + 10.6468i −1.31386 + 0.758556i −0.982733 0.185031i \(-0.940762\pi\)
−0.331125 + 0.943587i \(0.607428\pi\)
\(198\) −16.2649 15.7480i −1.15589 1.11917i
\(199\) −2.28678 1.32027i −0.162105 0.0935916i 0.416753 0.909020i \(-0.363168\pi\)
−0.578858 + 0.815428i \(0.696501\pi\)
\(200\) 13.1344i 0.928745i
\(201\) 6.46065 15.9605i 0.455699 1.12577i
\(202\) −27.1972 15.7023i −1.91359 1.10481i
\(203\) −5.04222 + 5.41393i −0.353894 + 0.379984i
\(204\) 7.64622 18.8894i 0.535343 1.32252i
\(205\) 1.42068 + 2.46070i 0.0992249 + 0.171863i
\(206\) −14.3452 24.8467i −0.999480 1.73115i
\(207\) −4.57392 16.0304i −0.317909 1.11419i
\(208\) −2.69852 0.978556i −0.187108 0.0678506i
\(209\) 4.99916 0.345799
\(210\) −10.5470 0.923026i −0.727811 0.0636949i
\(211\) −6.46256 11.1935i −0.444901 0.770592i 0.553144 0.833086i \(-0.313428\pi\)
−0.998045 + 0.0624940i \(0.980095\pi\)
\(212\) 3.14130 + 1.81363i 0.215745 + 0.124561i
\(213\) 1.00482 + 7.18379i 0.0688489 + 0.492225i
\(214\) −7.23723 + 12.5352i −0.494727 + 0.856892i
\(215\) −5.88385 + 10.1911i −0.401276 + 0.695030i
\(216\) −6.88691 15.5504i −0.468595 1.05807i
\(217\) 0.196779 + 0.642191i 0.0133582 + 0.0435948i
\(218\) 29.8317 17.2233i 2.02046 1.16651i
\(219\) −11.3968 + 8.89217i −0.770127 + 0.600877i
\(220\) 10.9865i 0.740713i
\(221\) −2.17632 12.2575i −0.146395 0.824528i
\(222\) −0.639047 4.56878i −0.0428901 0.306636i
\(223\) −5.68065 + 3.27973i −0.380405 + 0.219627i −0.677994 0.735067i \(-0.737151\pi\)
0.297590 + 0.954694i \(0.403817\pi\)
\(224\) −12.1046 2.78656i −0.808773 0.186185i
\(225\) 2.92774 11.6773i 0.195183 0.778488i
\(226\) 40.2424 2.67689
\(227\) −9.01102 + 15.6075i −0.598082 + 1.03591i 0.395021 + 0.918672i \(0.370737\pi\)
−0.993104 + 0.117237i \(0.962596\pi\)
\(228\) 8.42752 + 3.41136i 0.558126 + 0.225923i
\(229\) 8.97041i 0.592781i 0.955067 + 0.296391i \(0.0957831\pi\)
−0.955067 + 0.296391i \(0.904217\pi\)
\(230\) 6.41896 11.1180i 0.423253 0.733096i
\(231\) 14.8149 + 1.29654i 0.974751 + 0.0853059i
\(232\) −4.57618 7.92618i −0.300441 0.520380i
\(233\) 23.3691i 1.53096i 0.643459 + 0.765481i \(0.277499\pi\)
−0.643459 + 0.765481i \(0.722501\pi\)
\(234\) −20.8511 14.0680i −1.36308 0.919656i
\(235\) −6.09900 −0.397855
\(236\) −24.7565 42.8795i −1.61151 2.79122i
\(237\) 8.36575 + 10.7222i 0.543414 + 0.696479i
\(238\) 6.22364 + 20.3109i 0.403419 + 1.31656i
\(239\) 13.2727i 0.858538i −0.903177 0.429269i \(-0.858771\pi\)
0.903177 0.429269i \(-0.141229\pi\)
\(240\) 0.514040 1.26990i 0.0331811 0.0819715i
\(241\) 23.7299 + 13.7005i 1.52858 + 0.882525i 0.999422 + 0.0340009i \(0.0108249\pi\)
0.529157 + 0.848524i \(0.322508\pi\)
\(242\) 1.08926i 0.0700205i
\(243\) −2.65660 15.3604i −0.170421 0.985371i
\(244\) −36.0751 + 20.8279i −2.30947 + 1.33337i
\(245\) 5.76077 3.89623i 0.368042 0.248921i
\(246\) −1.59564 11.4078i −0.101735 0.727337i
\(247\) 5.46868 0.970966i 0.347964 0.0617811i
\(248\) −0.830910 −0.0527628
\(249\) 10.1175 + 12.9673i 0.641169 + 0.821768i
\(250\) 18.0332 10.4114i 1.14052 0.658478i
\(251\) −0.205761 + 0.356389i −0.0129875 + 0.0224951i −0.872446 0.488710i \(-0.837468\pi\)
0.859459 + 0.511205i \(0.170801\pi\)
\(252\) 24.0901 + 12.2952i 1.51753 + 0.774525i
\(253\) −9.01645 + 15.6169i −0.566859 + 0.981829i
\(254\) 21.6738 + 12.5134i 1.35994 + 0.785160i
\(255\) 5.88437 0.823062i 0.368493 0.0515422i
\(256\) 10.3959 18.0062i 0.649743 1.12539i
\(257\) −2.08991 3.61983i −0.130365 0.225799i 0.793452 0.608633i \(-0.208282\pi\)
−0.923817 + 0.382833i \(0.874948\pi\)
\(258\) 37.6122 29.3462i 2.34163 1.82702i
\(259\) 2.21758 + 2.06532i 0.137794 + 0.128333i
\(260\) −2.13387 12.0184i −0.132337 0.745349i
\(261\) −2.30172 8.06692i −0.142473 0.499330i
\(262\) −18.4923 + 10.6765i −1.14246 + 0.659599i
\(263\) 20.6659 11.9315i 1.27431 0.735726i 0.298518 0.954404i \(-0.403508\pi\)
0.975797 + 0.218678i \(0.0701744\pi\)
\(264\) −6.90300 + 17.0534i −0.424850 + 1.04956i
\(265\) 1.05759i 0.0649673i
\(266\) −9.06173 + 2.77668i −0.555610 + 0.170249i
\(267\) −2.24016 + 5.53416i −0.137096 + 0.338685i
\(268\) −33.8746 −2.06922
\(269\) −4.67279 + 8.09350i −0.284905 + 0.493470i −0.972586 0.232543i \(-0.925295\pi\)
0.687681 + 0.726013i \(0.258629\pi\)
\(270\) 7.07536 9.69826i 0.430593 0.590217i
\(271\) 18.9748 10.9551i 1.15264 0.665474i 0.203107 0.979156i \(-0.434896\pi\)
0.949528 + 0.313682i \(0.101563\pi\)
\(272\) −2.74884 −0.166673
\(273\) 16.4582 1.45913i 0.996093 0.0883108i
\(274\) −2.87922 −0.173940
\(275\) −11.2781 + 6.51144i −0.680098 + 0.392655i
\(276\) −25.8566 + 20.1741i −1.55638 + 1.21434i
\(277\) −4.70935 + 8.15684i −0.282958 + 0.490097i −0.972112 0.234518i \(-0.924649\pi\)
0.689154 + 0.724615i \(0.257982\pi\)
\(278\) −28.4402 −1.70573
\(279\) −0.738730 0.185215i −0.0442266 0.0110885i
\(280\) 2.52060 + 8.22603i 0.150635 + 0.491599i
\(281\) 1.80220i 0.107510i 0.998554 + 0.0537552i \(0.0171191\pi\)
−0.998554 + 0.0537552i \(0.982881\pi\)
\(282\) 22.9188 + 9.27728i 1.36480 + 0.552454i
\(283\) 21.3714 12.3388i 1.27040 0.733466i 0.295337 0.955393i \(-0.404568\pi\)
0.975063 + 0.221928i \(0.0712349\pi\)
\(284\) 12.3586 7.13523i 0.733347 0.423398i
\(285\) 0.367209 + 2.62531i 0.0217516 + 0.155510i
\(286\) 4.75663 + 26.7903i 0.281265 + 1.58414i
\(287\) 5.53709 + 5.15692i 0.326844 + 0.304403i
\(288\) 9.79706 10.1186i 0.577297 0.596243i
\(289\) 2.53914 + 4.39792i 0.149361 + 0.258701i
\(290\) 3.23019 5.59485i 0.189683 0.328541i
\(291\) −1.85063 13.2308i −0.108486 0.775605i
\(292\) 24.6285 + 14.2193i 1.44127 + 0.832120i
\(293\) 12.1793 21.0952i 0.711523 1.23239i −0.252762 0.967528i \(-0.581339\pi\)
0.964285 0.264866i \(-0.0853277\pi\)
\(294\) −27.5744 + 5.87847i −1.60817 + 0.342839i
\(295\) 7.21819 12.5023i 0.420260 0.727911i
\(296\) −3.24661 + 1.87443i −0.188705 + 0.108949i
\(297\) −9.93848 + 13.6228i −0.576689 + 0.790472i
\(298\) 22.5507 1.30633
\(299\) −6.83005 + 18.8349i −0.394992 + 1.08925i
\(300\) −23.4558 + 3.28083i −1.35422 + 0.189419i
\(301\) −7.03021 + 30.5387i −0.405214 + 1.76022i
\(302\) −9.75687 + 5.63313i −0.561445 + 0.324150i
\(303\) −8.77676 + 21.6823i −0.504212 + 1.24562i
\(304\) 1.22640i 0.0703386i
\(305\) −10.5183 6.07275i −0.602277 0.347725i
\(306\) −23.3642 5.85789i −1.33564 0.334873i
\(307\) 17.9759i 1.02594i 0.858407 + 0.512969i \(0.171454\pi\)
−0.858407 + 0.512969i \(0.828546\pi\)
\(308\) −8.57157 27.9735i −0.488411 1.59394i
\(309\) −16.8482 + 13.1455i −0.958461 + 0.747821i
\(310\) −0.293257 0.507936i −0.0166559 0.0288488i
\(311\) −28.6085 −1.62224 −0.811118 0.584882i \(-0.801141\pi\)
−0.811118 + 0.584882i \(0.801141\pi\)
\(312\) −4.23913 + 19.9957i −0.239993 + 1.13204i
\(313\) 0.862233i 0.0487363i −0.999703 0.0243681i \(-0.992243\pi\)
0.999703 0.0243681i \(-0.00775739\pi\)
\(314\) 24.0815 + 41.7104i 1.35900 + 2.35386i
\(315\) 0.407341 + 7.87530i 0.0229511 + 0.443723i
\(316\) 13.3775 23.1705i 0.752543 1.30344i
\(317\) 12.9621i 0.728024i −0.931394 0.364012i \(-0.881407\pi\)
0.931394 0.364012i \(-0.118593\pi\)
\(318\) 1.60872 3.97421i 0.0902123 0.222863i
\(319\) −4.53731 + 7.85886i −0.254041 + 0.440012i
\(320\) 12.4284 0.694771
\(321\) 9.99344 + 4.04523i 0.557779 + 0.225783i
\(322\) 7.66956 33.3160i 0.427408 1.85663i
\(323\) 4.60628 2.65944i 0.256300 0.147975i
\(324\) −26.0501 + 16.1831i −1.44723 + 0.899064i
\(325\) −11.0727 + 9.31349i −0.614202 + 0.516620i
\(326\) 0.817952i 0.0453022i
\(327\) −15.7829 20.2285i −0.872795 1.11864i
\(328\) −8.10649 + 4.68029i −0.447606 + 0.258426i
\(329\) −15.5290 + 4.75837i −0.856142 + 0.262337i
\(330\) −12.8610 + 1.79891i −0.707976 + 0.0990266i
\(331\) −2.99634 + 5.18982i −0.164694 + 0.285258i −0.936547 0.350543i \(-0.885997\pi\)
0.771853 + 0.635802i \(0.219330\pi\)
\(332\) 16.1786 28.0222i 0.887917 1.53792i
\(333\) −3.30426 + 0.942796i −0.181072 + 0.0516649i
\(334\) 33.9776 + 19.6170i 1.85917 + 1.07339i
\(335\) −4.93836 8.55350i −0.269812 0.467328i
\(336\) 0.318067 3.63440i 0.0173520 0.198273i
\(337\) −0.309894 −0.0168810 −0.00844050 0.999964i \(-0.502687\pi\)
−0.00844050 + 0.999964i \(0.502687\pi\)
\(338\) 10.4067 + 28.3826i 0.566052 + 1.54381i
\(339\) −4.15214 29.6851i −0.225513 1.61227i
\(340\) −5.84459 10.1231i −0.316967 0.549004i
\(341\) 0.411926 + 0.713477i 0.0223070 + 0.0386369i
\(342\) 2.61350 10.4240i 0.141322 0.563663i
\(343\) 11.6280 14.4149i 0.627854 0.778331i
\(344\) −33.5735 19.3837i −1.81016 1.04510i
\(345\) −8.86353 3.58786i −0.477197 0.193164i
\(346\) 48.0694i 2.58423i
\(347\) 14.1898 + 8.19250i 0.761750 + 0.439796i 0.829924 0.557877i \(-0.188384\pi\)
−0.0681740 + 0.997673i \(0.521717\pi\)
\(348\) −13.0117 + 10.1521i −0.697501 + 0.544212i
\(349\) 13.5833 7.84235i 0.727100 0.419791i −0.0902604 0.995918i \(-0.528770\pi\)
0.817360 + 0.576127i \(0.195437\pi\)
\(350\) 16.8267 18.0672i 0.899424 0.965730i
\(351\) −8.22600 + 16.8325i −0.439072 + 0.898452i
\(352\) −15.2357 −0.812064
\(353\) 6.04590 + 10.4718i 0.321791 + 0.557358i 0.980858 0.194726i \(-0.0623819\pi\)
−0.659067 + 0.752084i \(0.729049\pi\)
\(354\) −46.1419 + 36.0013i −2.45241 + 1.91345i
\(355\) 3.60336 + 2.08040i 0.191247 + 0.110416i
\(356\) 11.7457 0.622519
\(357\) 14.3404 6.68656i 0.758973 0.353890i
\(358\) −5.83550 + 10.1074i −0.308416 + 0.534192i
\(359\) 8.64784i 0.456416i −0.973612 0.228208i \(-0.926713\pi\)
0.973612 0.228208i \(-0.0732866\pi\)
\(360\) −9.46262 2.37247i −0.498724 0.125040i
\(361\) −8.31349 14.3994i −0.437552 0.757863i
\(362\) 14.7372 + 25.5256i 0.774572 + 1.34160i
\(363\) −0.803502 + 0.112388i −0.0421729 + 0.00589884i
\(364\) −14.8098 28.9359i −0.776243 1.51665i
\(365\) 8.29176i 0.434010i
\(366\) 30.2884 + 38.8197i 1.58320 + 2.02914i
\(367\) −8.18828 + 4.72751i −0.427425 + 0.246774i −0.698249 0.715855i \(-0.746037\pi\)
0.270824 + 0.962629i \(0.412704\pi\)
\(368\) 3.83115 + 2.21192i 0.199713 + 0.115304i
\(369\) −8.25043 + 2.35408i −0.429500 + 0.122548i
\(370\) −2.29168 1.32310i −0.119139 0.0687848i
\(371\) 0.825120 + 2.69279i 0.0428381 + 0.139803i
\(372\) 0.207552 + 1.48386i 0.0107611 + 0.0769347i
\(373\) −0.0165941 + 0.0287419i −0.000859212 + 0.00148820i −0.866455 0.499256i \(-0.833607\pi\)
0.865595 + 0.500744i \(0.166940\pi\)
\(374\) 13.0282 + 22.5655i 0.673673 + 1.16684i
\(375\) −9.54070 12.2280i −0.492680 0.631454i
\(376\) 20.0925i 1.03619i
\(377\) −3.43706 + 9.47822i −0.177018 + 0.488153i
\(378\) 10.4485 30.2134i 0.537414 1.55401i
\(379\) 10.3805 + 17.9796i 0.533211 + 0.923548i 0.999248 + 0.0387829i \(0.0123481\pi\)
−0.466037 + 0.884765i \(0.654319\pi\)
\(380\) 4.51643 2.60756i 0.231688 0.133765i
\(381\) 6.99433 17.2790i 0.358330 0.885228i
\(382\) −4.26119 −0.218021
\(383\) 6.40969 11.1019i 0.327520 0.567281i −0.654499 0.756063i \(-0.727120\pi\)
0.982019 + 0.188781i \(0.0604538\pi\)
\(384\) −31.6286 12.8029i −1.61404 0.653346i
\(385\) 5.81384 6.24244i 0.296301 0.318144i
\(386\) 9.52642 + 5.50008i 0.484882 + 0.279947i
\(387\) −25.5282 24.7170i −1.29767 1.25644i
\(388\) −22.7616 + 13.1414i −1.15554 + 0.667153i
\(389\) 31.4927i 1.59675i 0.602164 + 0.798373i \(0.294305\pi\)
−0.602164 + 0.798373i \(0.705695\pi\)
\(390\) −13.7195 + 4.46580i −0.694715 + 0.226135i
\(391\) 19.1862i 0.970286i
\(392\) 12.8357 + 18.9782i 0.648301 + 0.958544i
\(393\) 9.78363 + 12.5394i 0.493519 + 0.632529i
\(394\) 24.7582 42.8825i 1.24730 2.16039i
\(395\) 7.80088 0.392505
\(396\) 32.1786 + 8.06784i 1.61704 + 0.405424i
\(397\) −18.6659 10.7768i −0.936815 0.540870i −0.0478544 0.998854i \(-0.515238\pi\)
−0.888960 + 0.457984i \(0.848572\pi\)
\(398\) 6.14034 0.307787
\(399\) 2.98321 + 6.39796i 0.149347 + 0.320298i
\(400\) 1.59739 + 2.76676i 0.0798694 + 0.138338i
\(401\) 19.9477 11.5168i 0.996141 0.575122i 0.0890368 0.996028i \(-0.471621\pi\)
0.907104 + 0.420906i \(0.138288\pi\)
\(402\) 5.54653 + 39.6541i 0.276636 + 1.97777i
\(403\) 0.589189 + 0.700479i 0.0293496 + 0.0348934i
\(404\) 46.0185 2.28950
\(405\) −7.88401 4.21854i −0.391760 0.209621i
\(406\) 3.85953 16.7655i 0.191545 0.832058i
\(407\) 3.21903 + 1.85851i 0.159562 + 0.0921229i
\(408\) 2.71149 + 19.3854i 0.134239 + 0.959719i
\(409\) −0.944364 0.545229i −0.0466958 0.0269598i 0.476470 0.879191i \(-0.341916\pi\)
−0.523166 + 0.852231i \(0.675249\pi\)
\(410\) −5.72212 3.30367i −0.282595 0.163157i
\(411\) 0.297073 + 2.12388i 0.0146535 + 0.104763i
\(412\) 36.4089 + 21.0207i 1.79374 + 1.03561i
\(413\) 8.62452 37.4643i 0.424385 1.84350i
\(414\) 27.8498 + 26.9649i 1.36874 + 1.32525i
\(415\) 9.43432 0.463113
\(416\) −16.6666 + 2.95916i −0.817147 + 0.145085i
\(417\) 2.93440 + 20.9791i 0.143698 + 1.02735i
\(418\) −10.0676 + 5.81254i −0.492423 + 0.284301i
\(419\) 6.71289 + 11.6271i 0.327946 + 0.568019i 0.982104 0.188339i \(-0.0603103\pi\)
−0.654158 + 0.756358i \(0.726977\pi\)
\(420\) 14.0606 6.55613i 0.686089 0.319906i
\(421\) −14.8776 −0.725088 −0.362544 0.931967i \(-0.618092\pi\)
−0.362544 + 0.931967i \(0.618092\pi\)
\(422\) 26.0294 + 15.0281i 1.26709 + 0.731556i
\(423\) 4.47873 17.8634i 0.217763 0.868550i
\(424\) −3.48411 −0.169204
\(425\) −6.92787 + 11.9994i −0.336051 + 0.582057i
\(426\) −10.3762 13.2988i −0.502727 0.644331i
\(427\) −31.5192 7.25591i −1.52532 0.351138i
\(428\) 21.2100i 1.02523i
\(429\) 19.2713 6.27293i 0.930426 0.302860i
\(430\) 27.3647i 1.31964i
\(431\) 12.0692 6.96815i 0.581352 0.335644i −0.180318 0.983608i \(-0.557713\pi\)
0.761671 + 0.647964i \(0.224379\pi\)
\(432\) 3.34194 + 2.43811i 0.160789 + 0.117304i
\(433\) −33.2539 19.1991i −1.59808 0.922652i −0.991857 0.127357i \(-0.959351\pi\)
−0.606223 0.795295i \(-0.707316\pi\)
\(434\) −1.14296 1.06449i −0.0548640 0.0510971i
\(435\) −4.46036 1.80550i −0.213858 0.0865673i
\(436\) −25.2380 + 43.7136i −1.20868 + 2.09350i
\(437\) −8.55991 −0.409476
\(438\) 12.6127 31.1587i 0.602658 1.48882i
\(439\) 30.1873 17.4287i 1.44076 0.831825i 0.442863 0.896589i \(-0.353963\pi\)
0.997901 + 0.0647643i \(0.0206295\pi\)
\(440\) 5.27649 + 9.13915i 0.251547 + 0.435692i
\(441\) 7.18137 + 19.7339i 0.341970 + 0.939711i
\(442\) 18.6346 + 22.1545i 0.886359 + 1.05378i
\(443\) 29.2218i 1.38837i 0.719798 + 0.694184i \(0.244234\pi\)
−0.719798 + 0.694184i \(0.755766\pi\)
\(444\) 4.15838 + 5.32967i 0.197348 + 0.252935i
\(445\) 1.71233 + 2.96584i 0.0811721 + 0.140594i
\(446\) 7.62669 13.2098i 0.361134 0.625503i
\(447\) −2.32674 16.6347i −0.110051 0.786793i
\(448\) 31.6448 9.69652i 1.49507 0.458118i
\(449\) −30.5053 17.6122i −1.43963 0.831173i −0.441809 0.897109i \(-0.645663\pi\)
−0.997824 + 0.0659365i \(0.978997\pi\)
\(450\) 7.68119 + 26.9206i 0.362095 + 1.26905i
\(451\) 8.03763 + 4.64053i 0.378477 + 0.218514i
\(452\) −51.0686 + 29.4845i −2.40206 + 1.38683i
\(453\) 5.16202 + 6.61601i 0.242533 + 0.310847i
\(454\) 41.9086i 1.96687i
\(455\) 5.14743 7.95792i 0.241315 0.373073i
\(456\) −8.64879 + 1.20973i −0.405017 + 0.0566508i
\(457\) −8.52070 14.7583i −0.398581 0.690363i 0.594970 0.803748i \(-0.297164\pi\)
−0.993551 + 0.113385i \(0.963831\pi\)
\(458\) −10.4299 18.0652i −0.487358 0.844130i
\(459\) −1.91044 + 17.8392i −0.0891715 + 0.832662i
\(460\) 18.8119i 0.877110i
\(461\) 8.40395 14.5561i 0.391411 0.677944i −0.601225 0.799080i \(-0.705320\pi\)
0.992636 + 0.121136i \(0.0386538\pi\)
\(462\) −31.3427 + 14.6143i −1.45819 + 0.679920i
\(463\) 22.3885 1.04048 0.520241 0.854020i \(-0.325842\pi\)
0.520241 + 0.854020i \(0.325842\pi\)
\(464\) 1.92794 + 1.11310i 0.0895022 + 0.0516741i
\(465\) −0.344425 + 0.268731i −0.0159723 + 0.0124621i
\(466\) −27.1713 47.0621i −1.25869 2.18011i
\(467\) 35.3675 1.63661 0.818305 0.574784i \(-0.194914\pi\)
0.818305 + 0.574784i \(0.194914\pi\)
\(468\) 36.7678 + 2.57564i 1.69959 + 0.119059i
\(469\) −19.2472 17.9257i −0.888752 0.827731i
\(470\) 12.2825 7.09133i 0.566551 0.327099i
\(471\) 28.2833 22.0675i 1.30323 1.01682i
\(472\) 41.1874 + 23.7795i 1.89580 + 1.09454i
\(473\) 38.4381i 1.76739i
\(474\) −29.3141 11.8660i −1.34644 0.545025i
\(475\) −5.35354 3.09087i −0.245637 0.141819i
\(476\) −22.7792 21.2152i −1.04408 0.972396i
\(477\) −3.09759 0.776629i −0.141829 0.0355594i
\(478\) 15.4322 + 26.7293i 0.705852 + 1.22257i
\(479\) 2.19131 + 3.79546i 0.100124 + 0.173419i 0.911735 0.410778i \(-0.134743\pi\)
−0.811612 + 0.584197i \(0.801410\pi\)
\(480\) −1.11912 8.00101i −0.0510807 0.365194i
\(481\) 3.88233 + 1.40784i 0.177019 + 0.0641920i
\(482\) −63.7183 −2.90229
\(483\) −25.3671 2.22002i −1.15424 0.101014i
\(484\) 0.798071 + 1.38230i 0.0362759 + 0.0628318i
\(485\) −6.63653 3.83160i −0.301349 0.173984i
\(486\) 23.2096 + 27.8449i 1.05281 + 1.26307i
\(487\) 10.9910 19.0370i 0.498049 0.862647i −0.501948 0.864898i \(-0.667383\pi\)
0.999997 + 0.00225101i \(0.000716520\pi\)
\(488\) 20.0060 34.6514i 0.905629 1.56860i
\(489\) −0.603368 + 0.0843947i −0.0272852 + 0.00381646i
\(490\) −7.07123 + 14.5445i −0.319445 + 0.657055i
\(491\) −31.4002 + 18.1289i −1.41707 + 0.818147i −0.996041 0.0888997i \(-0.971665\pi\)
−0.421031 + 0.907046i \(0.638332\pi\)
\(492\) 10.3831 + 13.3077i 0.468106 + 0.599958i
\(493\) 9.65498i 0.434839i
\(494\) −9.88421 + 8.31384i −0.444712 + 0.374057i
\(495\) 2.65395 + 9.30142i 0.119286 + 0.418068i
\(496\) 0.175030 0.101054i 0.00785910 0.00453745i
\(497\) 10.7978 + 2.48573i 0.484348 + 0.111500i
\(498\) −35.4523 14.3507i −1.58865 0.643069i
\(499\) 4.30900 0.192897 0.0964486 0.995338i \(-0.469252\pi\)
0.0964486 + 0.995338i \(0.469252\pi\)
\(500\) −15.2563 + 26.4247i −0.682283 + 1.18175i
\(501\) 10.9649 27.0879i 0.489874 1.21020i
\(502\) 0.956957i 0.0427111i
\(503\) −2.12701 + 3.68409i −0.0948387 + 0.164265i −0.909541 0.415614i \(-0.863567\pi\)
0.814703 + 0.579879i \(0.196900\pi\)
\(504\) −25.9443 + 1.34194i −1.15565 + 0.0597748i
\(505\) 6.70875 + 11.6199i 0.298535 + 0.517078i
\(506\) 41.9338i 1.86419i
\(507\) 19.8628 10.6051i 0.882140 0.470987i
\(508\) −36.6728 −1.62709
\(509\) 7.02933 + 12.1752i 0.311570 + 0.539654i 0.978702 0.205284i \(-0.0658119\pi\)
−0.667133 + 0.744939i \(0.732479\pi\)
\(510\) −10.8933 + 8.49930i −0.482364 + 0.376355i
\(511\) 6.46913 + 21.1121i 0.286177 + 0.933944i
\(512\) 8.94911i 0.395498i
\(513\) −7.95896 0.852341i −0.351397 0.0376318i
\(514\) 8.41759 + 4.85990i 0.371284 + 0.214361i
\(515\) 12.2579i 0.540147i
\(516\) −26.2296 + 64.7984i −1.15470 + 2.85259i
\(517\) −17.2528 + 9.96090i −0.758777 + 0.438080i
\(518\) −6.86725 1.58088i −0.301729 0.0694600i
\(519\) −35.4587 + 4.95971i −1.55647 + 0.217707i
\(520\) 7.54711 + 8.97266i 0.330963 + 0.393477i
\(521\) 7.14275 0.312930 0.156465 0.987684i \(-0.449990\pi\)
0.156465 + 0.987684i \(0.449990\pi\)
\(522\) 14.0148 + 13.5694i 0.613410 + 0.593918i
\(523\) −23.1547 + 13.3684i −1.01248 + 0.584558i −0.911918 0.410372i \(-0.865399\pi\)
−0.100566 + 0.994930i \(0.532065\pi\)
\(524\) 15.6448 27.0976i 0.683446 1.18376i
\(525\) −15.0635 10.5482i −0.657426 0.460361i
\(526\) −27.7455 + 48.0566i −1.20976 + 2.09537i
\(527\) 0.759106 + 0.438270i 0.0330672 + 0.0190914i
\(528\) −0.619888 4.43180i −0.0269772 0.192869i
\(529\) 3.93858 6.82182i 0.171243 0.296601i
\(530\) −1.22966 2.12984i −0.0534132 0.0925144i
\(531\) 31.3175 + 30.3223i 1.35906 + 1.31588i
\(532\) 9.46515 10.1629i 0.410366 0.440619i
\(533\) 9.69383 + 3.51525i 0.419886 + 0.152262i
\(534\) −1.92320 13.7497i −0.0832251 0.595006i
\(535\) 5.35564 3.09208i 0.231544 0.133682i
\(536\) 28.1785 16.2689i 1.21713 0.702709i
\(537\) 8.05788 + 3.26174i 0.347723 + 0.140754i
\(538\) 21.7323i 0.936944i
\(539\) 9.93267 20.4301i 0.427830 0.879987i
\(540\) −1.87317 + 17.4912i −0.0806084 + 0.752702i
\(541\) −28.3425 −1.21854 −0.609270 0.792963i \(-0.708538\pi\)
−0.609270 + 0.792963i \(0.708538\pi\)
\(542\) −25.4750 + 44.1241i −1.09425 + 1.89529i
\(543\) 17.3086 13.5047i 0.742783 0.579543i
\(544\) −14.0383 + 8.10502i −0.601887 + 0.347500i
\(545\) −14.7172 −0.630415
\(546\) −31.4479 + 22.0744i −1.34585 + 0.944699i
\(547\) −16.6146 −0.710389 −0.355194 0.934792i \(-0.615585\pi\)
−0.355194 + 0.934792i \(0.615585\pi\)
\(548\) 3.65380 2.10952i 0.156082 0.0901143i
\(549\) 25.5105 26.3478i 1.08876 1.12450i
\(550\) 15.1417 26.2263i 0.645646 1.11829i
\(551\) −4.30757 −0.183509
\(552\) 11.8198 29.1999i 0.503084 1.24283i
\(553\) 19.8623 6.08616i 0.844629 0.258810i
\(554\) 21.9023i 0.930541i
\(555\) −0.739545 + 1.82699i −0.0313919 + 0.0775514i
\(556\) 36.0912 20.8373i 1.53061 0.883698i
\(557\) 12.6092 7.27991i 0.534267 0.308459i −0.208485 0.978026i \(-0.566853\pi\)
0.742752 + 0.669566i \(0.233520\pi\)
\(558\) 1.70305 0.485927i 0.0720958 0.0205709i
\(559\) 7.46567 + 42.0482i 0.315764 + 1.77845i
\(560\) −1.53140 1.42625i −0.0647134 0.0602702i
\(561\) 15.3014 11.9386i 0.646026 0.504049i
\(562\) −2.09543 3.62939i −0.0883902 0.153096i
\(563\) −5.51013 + 9.54383i −0.232224 + 0.402224i −0.958462 0.285219i \(-0.907934\pi\)
0.726238 + 0.687443i \(0.241267\pi\)
\(564\) −35.8817 + 5.01887i −1.51089 + 0.211333i
\(565\) −14.8899 8.59671i −0.626424 0.361666i
\(566\) −28.6927 + 49.6973i −1.20605 + 2.08893i
\(567\) −23.3652 4.59006i −0.981245 0.192764i
\(568\) −6.85365 + 11.8709i −0.287573 + 0.498090i
\(569\) 16.6811 9.63084i 0.699308 0.403746i −0.107781 0.994175i \(-0.534375\pi\)
0.807090 + 0.590429i \(0.201041\pi\)
\(570\) −3.79196 4.86005i −0.158828 0.203565i
\(571\) 22.2001 0.929046 0.464523 0.885561i \(-0.346226\pi\)
0.464523 + 0.885561i \(0.346226\pi\)
\(572\) −25.6647 30.5125i −1.07310 1.27579i
\(573\) 0.439661 + 3.14329i 0.0183671 + 0.131313i
\(574\) −17.1469 3.94732i −0.715698 0.164758i
\(575\) 19.3112 11.1493i 0.805333 0.464959i
\(576\) −9.12668 + 36.4018i −0.380278 + 1.51674i
\(577\) 29.5912i 1.23190i 0.787787 + 0.615948i \(0.211227\pi\)
−0.787787 + 0.615948i \(0.788773\pi\)
\(578\) −10.2269 5.90453i −0.425385 0.245596i
\(579\) 3.07425 7.59472i 0.127762 0.315626i
\(580\) 9.46665i 0.393081i
\(581\) 24.0213 7.36054i 0.996569 0.305367i
\(582\) 19.1104 + 24.4933i 0.792153 + 1.01528i
\(583\) 1.72726 + 2.99170i 0.0715358 + 0.123904i
\(584\) −27.3163 −1.13035
\(585\) 4.70979 + 9.65954i 0.194726 + 0.399373i
\(586\) 56.6437i 2.33993i
\(587\) −15.3668 26.6162i −0.634258 1.09857i −0.986672 0.162722i \(-0.947973\pi\)
0.352414 0.935844i \(-0.385361\pi\)
\(588\) 30.6856 27.6629i 1.26545 1.14080i
\(589\) −0.195534 + 0.338675i −0.00805685 + 0.0139549i
\(590\) 33.5705i 1.38207i
\(591\) −34.1871 13.8385i −1.40627 0.569242i
\(592\) 0.455930 0.789694i 0.0187386 0.0324562i
\(593\) −1.66886 −0.0685320 −0.0342660 0.999413i \(-0.510909\pi\)
−0.0342660 + 0.999413i \(0.510909\pi\)
\(594\) 4.17550 38.9898i 0.171323 1.59977i
\(595\) 2.03610 8.84468i 0.0834720 0.362597i
\(596\) −28.6173 + 16.5222i −1.17221 + 0.676776i
\(597\) −0.633548 4.52946i −0.0259294 0.185379i
\(598\) −8.14463 45.8722i −0.333059 1.87585i
\(599\) 26.2751i 1.07357i −0.843719 0.536785i \(-0.819639\pi\)
0.843719 0.536785i \(-0.180361\pi\)
\(600\) 17.9360 13.9943i 0.732236 0.571313i
\(601\) 10.4226 6.01747i 0.425145 0.245458i −0.272131 0.962260i \(-0.587728\pi\)
0.697276 + 0.716803i \(0.254395\pi\)
\(602\) −21.3496 69.6748i −0.870145 2.83973i
\(603\) 28.6789 8.18288i 1.16789 0.333232i
\(604\) 8.25446 14.2972i 0.335869 0.581743i
\(605\) −0.232692 + 0.403034i −0.00946026 + 0.0163856i
\(606\) −7.53494 53.8700i −0.306086 2.18832i
\(607\) −9.90743 5.72005i −0.402130 0.232170i 0.285273 0.958446i \(-0.407916\pi\)
−0.687403 + 0.726277i \(0.741249\pi\)
\(608\) −3.61606 6.26319i −0.146650 0.254006i
\(609\) −12.7654 1.11717i −0.517281 0.0452701i
\(610\) 28.2432 1.14353
\(611\) −16.9385 + 14.2474i −0.685258 + 0.576386i
\(612\) 33.9416 9.68449i 1.37201 0.391472i
\(613\) 13.0562 + 22.6140i 0.527335 + 0.913370i 0.999492 + 0.0318564i \(0.0101419\pi\)
−0.472158 + 0.881514i \(0.656525\pi\)
\(614\) −20.9006 36.2009i −0.843481 1.46095i
\(615\) −1.84658 + 4.56183i −0.0744612 + 0.183951i
\(616\) 20.5650 + 19.1530i 0.828588 + 0.771698i
\(617\) 26.2287 + 15.1431i 1.05593 + 0.609639i 0.924303 0.381660i \(-0.124648\pi\)
0.131624 + 0.991300i \(0.457981\pi\)
\(618\) 18.6456 46.0627i 0.750038 1.85291i
\(619\) 17.4602i 0.701786i 0.936416 + 0.350893i \(0.114122\pi\)
−0.936416 + 0.350893i \(0.885878\pi\)
\(620\) 0.744299 + 0.429721i 0.0298918 + 0.0172580i
\(621\) 17.0173 23.3258i 0.682883 0.936032i
\(622\) 57.6134 33.2631i 2.31009 1.33373i
\(623\) 6.67376 + 6.21555i 0.267379 + 0.249021i
\(624\) −1.53888 4.72763i −0.0616044 0.189257i
\(625\) 11.1681 0.446723
\(626\) 1.00252 + 1.73642i 0.0400688 + 0.0694012i
\(627\) 5.32642 + 6.82672i 0.212717 + 0.272633i
\(628\) −61.1200 35.2877i −2.43895 1.40813i
\(629\) 3.95474 0.157686
\(630\) −9.97696 15.3861i −0.397492 0.612998i
\(631\) 15.6357 27.0818i 0.622446 1.07811i −0.366583 0.930385i \(-0.619472\pi\)
0.989029 0.147722i \(-0.0471942\pi\)
\(632\) 25.6991i 1.02226i
\(633\) 8.39991 20.7513i 0.333866 0.824792i
\(634\) 15.0711 + 26.1039i 0.598549 + 1.03672i
\(635\) −5.34630 9.26006i −0.212161 0.367474i
\(636\) 0.870292 + 6.22202i 0.0345093 + 0.246719i
\(637\) 6.89748 24.2781i 0.273288 0.961932i
\(638\) 21.1022i 0.835444i
\(639\) −8.73939 + 9.02621i −0.345725 + 0.357071i
\(640\) −16.9503 + 9.78624i −0.670018 + 0.386835i
\(641\) 19.6915 + 11.3689i 0.777766 + 0.449043i 0.835638 0.549281i \(-0.185098\pi\)
−0.0578722 + 0.998324i \(0.518432\pi\)
\(642\) −24.8288 + 3.47287i −0.979914 + 0.137063i
\(643\) 14.1454 + 8.16683i 0.557839 + 0.322068i 0.752278 0.658846i \(-0.228955\pi\)
−0.194439 + 0.980915i \(0.562289\pi\)
\(644\) 14.6768 + 47.8981i 0.578348 + 1.88745i
\(645\) −20.1858 + 2.82344i −0.794814 + 0.111173i
\(646\) −6.18428 + 10.7115i −0.243317 + 0.421438i
\(647\) −9.43158 16.3360i −0.370794 0.642233i 0.618894 0.785474i \(-0.287581\pi\)
−0.989688 + 0.143241i \(0.954248\pi\)
\(648\) 13.8975 25.9730i 0.545946 1.02032i
\(649\) 47.1551i 1.85100i
\(650\) 11.4700 31.6303i 0.449891 1.24064i
\(651\) −0.667298 + 0.952947i −0.0261535 + 0.0373489i
\(652\) 0.599289 + 1.03800i 0.0234700 + 0.0406512i
\(653\) −24.9249 + 14.3904i −0.975387 + 0.563140i −0.900874 0.434080i \(-0.857073\pi\)
−0.0745126 + 0.997220i \(0.523740\pi\)
\(654\) 55.3042 + 22.3865i 2.16257 + 0.875382i
\(655\) 9.12302 0.356466
\(656\) 1.13842 1.97179i 0.0444477 0.0769857i
\(657\) −24.2858 6.08895i −0.947480 0.237553i
\(658\) 25.7407 27.6383i 1.00348 1.07745i
\(659\) −16.6013 9.58474i −0.646693 0.373369i 0.140495 0.990081i \(-0.455131\pi\)
−0.787188 + 0.616713i \(0.788464\pi\)
\(660\) 15.0029 11.7058i 0.583988 0.455646i
\(661\) −3.87309 + 2.23613i −0.150646 + 0.0869753i −0.573428 0.819256i \(-0.694387\pi\)
0.422782 + 0.906231i \(0.361053\pi\)
\(662\) 13.9354i 0.541616i
\(663\) 14.4197 16.0318i 0.560015 0.622624i
\(664\) 31.0803i 1.20615i
\(665\) 3.94606 + 0.908407i 0.153021 + 0.0352265i
\(666\) 5.55812 5.74053i 0.215373 0.222441i
\(667\) 7.76910 13.4565i 0.300821 0.521037i
\(668\) −57.4912 −2.22440
\(669\) −10.5312 4.26292i −0.407161 0.164814i
\(670\) 19.8904 + 11.4837i 0.768432 + 0.443654i
\(671\) −39.6721 −1.53153
\(672\) −9.09175 19.4987i −0.350722 0.752178i
\(673\) 0.348930 + 0.604365i 0.0134503 + 0.0232965i 0.872672 0.488307i \(-0.162385\pi\)
−0.859222 + 0.511603i \(0.829052\pi\)
\(674\) 0.624083 0.360315i 0.0240388 0.0138788i
\(675\) 19.0656 8.44370i 0.733837 0.324998i
\(676\) −34.0015 28.3934i −1.30775 1.09205i
\(677\) 15.5029 0.595823 0.297912 0.954593i \(-0.403710\pi\)
0.297912 + 0.954593i \(0.403710\pi\)
\(678\) 42.8768 + 54.9540i 1.64667 + 2.11050i
\(679\) −19.8870 4.57812i −0.763193 0.175692i
\(680\) 9.72363 + 5.61394i 0.372884 + 0.215285i
\(681\) −30.9141 + 4.32405i −1.18463 + 0.165698i
\(682\) −1.65912 0.957896i −0.0635311 0.0366797i
\(683\) −29.1164 16.8103i −1.11411 0.643230i −0.174217 0.984707i \(-0.555739\pi\)
−0.939890 + 0.341477i \(0.889073\pi\)
\(684\) 4.32074 + 15.1431i 0.165207 + 0.579010i
\(685\) 1.06533 + 0.615068i 0.0407041 + 0.0235005i
\(686\) −6.65697 + 42.5495i −0.254164 + 1.62455i
\(687\) −12.2498 + 9.55764i −0.467357 + 0.364647i
\(688\) 9.42965 0.359502
\(689\) 2.47055 + 2.93720i 0.0941204 + 0.111898i
\(690\) 22.0215 3.08021i 0.838346 0.117262i
\(691\) −13.1236 + 7.57692i −0.499246 + 0.288240i −0.728402 0.685150i \(-0.759737\pi\)
0.229156 + 0.973390i \(0.426403\pi\)
\(692\) 35.2191 + 61.0012i 1.33883 + 2.31892i
\(693\) 14.0142 + 21.6123i 0.532357 + 0.820983i
\(694\) −38.1018 −1.44632
\(695\) 10.5230 + 6.07548i 0.399161 + 0.230456i
\(696\) 5.94803 14.6942i 0.225460 0.556981i
\(697\) 9.87462 0.374028
\(698\) −18.2366 + 31.5868i −0.690267 + 1.19558i
\(699\) −31.9122 + 24.8989i −1.20703 + 0.941763i
\(700\) −8.11617 + 35.2561i −0.306762 + 1.33255i
\(701\) 32.2808i 1.21923i 0.792697 + 0.609615i \(0.208676\pi\)
−0.792697 + 0.609615i \(0.791324\pi\)
\(702\) −3.00517 43.4627i −0.113423 1.64039i
\(703\) 1.76441i 0.0665458i
\(704\) 35.1575 20.2982i 1.32505 0.765016i
\(705\) −6.49826 8.32863i −0.244739 0.313674i
\(706\) −24.3512 14.0592i −0.916469 0.529124i
\(707\) 26.1472 + 24.3520i 0.983367 + 0.915850i
\(708\) 32.1780 79.4933i 1.20932 2.98754i
\(709\) −13.5154 + 23.4093i −0.507581 + 0.879155i 0.492381 + 0.870380i \(0.336127\pi\)
−0.999961 + 0.00877549i \(0.997207\pi\)
\(710\) −9.67555 −0.363117
\(711\) −5.72848 + 22.8481i −0.214835 + 0.856871i
\(712\) −9.77062 + 5.64107i −0.366169 + 0.211408i
\(713\) −0.705328 1.22166i −0.0264147 0.0457517i
\(714\) −21.1050 + 30.1394i −0.789836 + 1.12794i
\(715\) 3.96304 10.9287i 0.148209 0.408710i
\(716\) 17.1020i 0.639132i
\(717\) 18.1248 14.1415i 0.676883 0.528125i
\(718\) 10.0549 + 17.4155i 0.375244 + 0.649942i
\(719\) −7.06963 + 12.2450i −0.263653 + 0.456660i −0.967210 0.253979i \(-0.918261\pi\)
0.703557 + 0.710639i \(0.251594\pi\)
\(720\) 2.28183 0.651069i 0.0850387 0.0242639i
\(721\) 9.56346 + 31.2105i 0.356162 + 1.16234i
\(722\) 33.4844 + 19.3322i 1.24616 + 0.719472i
\(723\) 6.57434 + 47.0023i 0.244502 + 1.74803i
\(724\) −37.4038 21.5951i −1.39010 0.802575i
\(725\) 9.71791 5.61064i 0.360914 0.208374i
\(726\) 1.48747 1.16057i 0.0552051 0.0430727i
\(727\) 2.05755i 0.0763102i 0.999272 + 0.0381551i \(0.0121481\pi\)
−0.999272 + 0.0381551i \(0.987852\pi\)
\(728\) 26.2165 + 16.9576i 0.971647 + 0.628491i
\(729\) 18.1453 19.9937i 0.672047 0.740508i
\(730\) −9.64085 16.6984i −0.356824 0.618037i
\(731\) 20.4482 + 35.4173i 0.756303 + 1.30996i
\(732\) −66.8787 27.0717i −2.47191 1.00060i
\(733\) 8.27890i 0.305788i −0.988243 0.152894i \(-0.951141\pi\)
0.988243 0.152894i \(-0.0488593\pi\)
\(734\) 10.9934 19.0411i 0.405773 0.702819i
\(735\) 11.4585 + 3.71546i 0.422652 + 0.137047i
\(736\) 26.0876 0.961600
\(737\) −27.9392 16.1307i −1.02915 0.594182i
\(738\) 13.8781 14.3336i 0.510861 0.527626i
\(739\) 25.6935 + 44.5024i 0.945151 + 1.63705i 0.755450 + 0.655207i \(0.227419\pi\)
0.189701 + 0.981842i \(0.439248\pi\)
\(740\) 3.87759 0.142543
\(741\) 7.15260 + 6.43335i 0.262757 + 0.236335i
\(742\) −4.79259 4.46354i −0.175942 0.163862i
\(743\) −24.6284 + 14.2192i −0.903527 + 0.521651i −0.878343 0.478031i \(-0.841351\pi\)
−0.0251840 + 0.999683i \(0.508017\pi\)
\(744\) −0.885303 1.13467i −0.0324568 0.0415990i
\(745\) −8.34388 4.81734i −0.305696 0.176494i
\(746\) 0.0771762i 0.00282562i
\(747\) −6.92798 + 27.6323i −0.253482 + 1.01101i
\(748\) −33.0662 19.0908i −1.20902 0.698028i
\(749\) 11.2239 12.0513i 0.410112 0.440345i
\(750\) 33.4312 + 13.5326i 1.22074 + 0.494140i
\(751\) 11.0996 + 19.2251i 0.405032 + 0.701535i 0.994325 0.106384i \(-0.0339272\pi\)
−0.589294 + 0.807919i \(0.700594\pi\)
\(752\) 2.44361 + 4.23246i 0.0891094 + 0.154342i
\(753\) −0.705906 + 0.0987370i −0.0257246 + 0.00359818i
\(754\) −4.09859 23.0841i −0.149262 0.840673i
\(755\) 4.81347 0.175180
\(756\) 8.87706 + 45.9968i 0.322855 + 1.67289i
\(757\) 3.40501 + 5.89765i 0.123757 + 0.214354i 0.921246 0.388979i \(-0.127172\pi\)
−0.797489 + 0.603333i \(0.793839\pi\)
\(758\) −41.8098 24.1389i −1.51860 0.876764i
\(759\) −30.9328 + 4.32665i −1.12279 + 0.157047i
\(760\) −2.50466 + 4.33820i −0.0908536 + 0.157363i
\(761\) 8.91462 15.4406i 0.323155 0.559720i −0.657982 0.753033i \(-0.728590\pi\)
0.981137 + 0.193313i \(0.0619233\pi\)
\(762\) 6.00470 + 42.9298i 0.217527 + 1.55518i
\(763\) −37.4723 + 11.4822i −1.35659 + 0.415683i
\(764\) 5.40754 3.12205i 0.195638 0.112952i
\(765\) 7.39352 + 7.15859i 0.267313 + 0.258819i
\(766\) 29.8103i 1.07709i
\(767\) −9.15873 51.5838i −0.330703 1.86258i
\(768\) 35.6652 4.98859i 1.28696 0.180010i
\(769\) 32.8631 18.9735i 1.18507 0.684203i 0.227891 0.973687i \(-0.426817\pi\)
0.957183 + 0.289484i \(0.0934837\pi\)
\(770\) −4.45016 + 19.3312i −0.160373 + 0.696647i
\(771\) 2.71643 6.71073i 0.0978297 0.241681i
\(772\) −16.1190 −0.580135
\(773\) 14.3153 24.7948i 0.514885 0.891807i −0.484966 0.874533i \(-0.661168\pi\)
0.999851 0.0172738i \(-0.00549870\pi\)
\(774\) 80.1488 + 20.0949i 2.88089 + 0.722298i
\(775\) 1.01874i 0.0365942i
\(776\) 12.6228 21.8633i 0.453132 0.784847i
\(777\) −0.457600 + 5.22878i −0.0164163 + 0.187582i
\(778\) −36.6167 63.4220i −1.31277 2.27379i
\(779\) 4.40556i 0.157846i
\(780\) 14.1384 15.7191i 0.506237 0.562834i
\(781\) 13.5909 0.486319
\(782\) −22.3078 38.6383i −0.797726 1.38170i
\(783\) 8.56358 11.7382i 0.306037 0.419488i
\(784\) −5.01192 2.43668i −0.178997 0.0870244i
\(785\) 20.5775i 0.734441i
\(786\) −34.2825 13.8772i −1.22282 0.494982i
\(787\) 31.9616 + 18.4530i 1.13931 + 0.657779i 0.946259 0.323410i \(-0.104829\pi\)
0.193048 + 0.981189i \(0.438163\pi\)
\(788\) 72.5585i 2.58479i
\(789\) 38.3121 + 15.5083i 1.36395 + 0.552109i
\(790\) −15.7099 + 9.07011i −0.558933 + 0.322700i
\(791\) −44.6191 10.2716i −1.58647 0.365216i
\(792\) −30.6425 + 8.74315i −1.08883 + 0.310674i
\(793\) −43.3981 + 7.70535i −1.54111 + 0.273625i
\(794\) 50.1207 1.77872
\(795\) −1.44422 + 1.12682i −0.0512211 + 0.0399643i
\(796\) −7.79223 + 4.49884i −0.276188 + 0.159457i
\(797\) 9.40846 16.2959i 0.333265 0.577232i −0.649885 0.760032i \(-0.725183\pi\)
0.983150 + 0.182801i \(0.0585164\pi\)
\(798\) −13.4467 9.41601i −0.476008 0.333323i
\(799\) −10.5979 + 18.3562i −0.374928 + 0.649395i
\(800\) 16.3157 + 9.41987i 0.576847 + 0.333043i
\(801\) −9.94410 + 2.83733i −0.351358 + 0.100252i
\(802\) −26.7813 + 46.3865i −0.945680 + 1.63797i
\(803\) 13.5421 + 23.4556i 0.477891 + 0.827731i
\(804\) −36.0921 46.2582i −1.27287 1.63140i
\(805\) −9.95486 + 10.6887i −0.350863 + 0.376728i
\(806\) −2.00100 0.725616i −0.0704820 0.0255587i
\(807\) −16.0309 + 2.24229i −0.564316 + 0.0789324i
\(808\) −38.2804 + 22.1012i −1.34670 + 0.777518i
\(809\) −6.06225 + 3.50004i −0.213137 + 0.123055i −0.602769 0.797916i \(-0.705936\pi\)
0.389631 + 0.920971i \(0.372602\pi\)
\(810\) 20.7822 0.671201i 0.730213 0.0235836i
\(811\) 18.2312i 0.640186i −0.947386 0.320093i \(-0.896286\pi\)
0.947386 0.320093i \(-0.103714\pi\)
\(812\) 7.38577 + 24.1036i 0.259190 + 0.845870i
\(813\) 35.1769 + 14.2392i 1.23371 + 0.499391i
\(814\) −8.64358 −0.302957
\(815\) −0.174733 + 0.302647i −0.00612064 + 0.0106013i
\(816\) −2.92879 3.75374i −0.102528 0.131407i
\(817\) −15.8014 + 9.12296i −0.552822 + 0.319172i
\(818\) 2.53576 0.0886606
\(819\) 19.5281 + 20.9202i 0.682367 + 0.731010i
\(820\) 9.68201 0.338110
\(821\) 35.7015 20.6123i 1.24599 0.719373i 0.275684 0.961248i \(-0.411096\pi\)
0.970307 + 0.241875i \(0.0777624\pi\)
\(822\) −3.06770 3.93179i −0.106998 0.137137i
\(823\) −0.377035 + 0.653044i −0.0131426 + 0.0227637i −0.872522 0.488575i \(-0.837517\pi\)
0.859379 + 0.511339i \(0.170850\pi\)
\(824\) −40.3822 −1.40678
\(825\) −20.9083 8.46344i −0.727933 0.294659i
\(826\) 26.1913 + 85.4756i 0.911311 + 2.97408i
\(827\) 3.14508i 0.109365i 0.998504 + 0.0546826i \(0.0174147\pi\)
−0.998504 + 0.0546826i \(0.982585\pi\)
\(828\) −55.0985 13.8143i −1.91480 0.480080i
\(829\) −18.0808 + 10.4390i −0.627973 + 0.362561i −0.779967 0.625821i \(-0.784764\pi\)
0.151993 + 0.988382i \(0.451431\pi\)
\(830\) −18.9994 + 10.9693i −0.659479 + 0.380751i
\(831\) −16.1564 + 2.25984i −0.560459 + 0.0783930i
\(832\) 34.5170 29.0330i 1.19666 1.00654i
\(833\) −1.71628 24.1085i −0.0594657 0.835309i
\(834\) −30.3019 38.8371i −1.04927 1.34482i
\(835\) −8.38128 14.5168i −0.290046 0.502375i
\(836\) 8.51736 14.7525i 0.294579 0.510226i
\(837\) −0.534165 1.20613i −0.0184634 0.0416899i
\(838\) −27.0376 15.6102i −0.934000 0.539245i
\(839\) −11.0796 + 19.1904i −0.382510 + 0.662527i −0.991420 0.130712i \(-0.958274\pi\)
0.608910 + 0.793239i \(0.291607\pi\)
\(840\) −8.54763 + 12.2066i −0.294921 + 0.421167i
\(841\) −10.5904 + 18.3431i −0.365186 + 0.632520i
\(842\) 29.9613 17.2982i 1.03254 0.596135i
\(843\) −2.46104 + 1.92018i −0.0847627 + 0.0661345i
\(844\) −44.0426 −1.51601
\(845\) 2.21261 12.7248i 0.0761163 0.437748i
\(846\) 11.7503 + 41.1819i 0.403985 + 1.41586i
\(847\) −0.278027 + 1.20773i −0.00955312 + 0.0414981i
\(848\) 0.733925 0.423732i 0.0252031 0.0145510i
\(849\) 39.6200 + 16.0377i 1.35975 + 0.550413i
\(850\) 32.2202i 1.10514i
\(851\) −5.51185 3.18227i −0.188944 0.109087i
\(852\) 22.9113 + 9.27422i 0.784927 + 0.317730i
\(853\) 1.85108i 0.0633799i 0.999498 + 0.0316899i \(0.0100889\pi\)
−0.999498 + 0.0316899i \(0.989911\pi\)
\(854\) 71.9117 22.0350i 2.46077 0.754023i
\(855\) −3.19381 + 3.29862i −0.109226 + 0.112810i
\(856\) 10.1865 + 17.6435i 0.348167 + 0.603044i
\(857\) 20.7097 0.707429 0.353714 0.935354i \(-0.384919\pi\)
0.353714 + 0.935354i \(0.384919\pi\)
\(858\) −31.5161 + 35.0396i −1.07594 + 1.19623i
\(859\) 47.4101i 1.61761i 0.588077 + 0.808805i \(0.299885\pi\)
−0.588077 + 0.808805i \(0.700115\pi\)
\(860\) 20.0493 + 34.7264i 0.683676 + 1.18416i
\(861\) −1.14259 + 13.0558i −0.0389393 + 0.444941i
\(862\) −16.2038 + 28.0658i −0.551903 + 0.955924i
\(863\) 2.98037i 0.101453i −0.998713 0.0507265i \(-0.983846\pi\)
0.998713 0.0507265i \(-0.0161537\pi\)
\(864\) 24.2561 + 2.59763i 0.825208 + 0.0883732i
\(865\) −10.2687 + 17.7860i −0.349147 + 0.604741i
\(866\) 89.2916 3.03425
\(867\) −3.30032 + 8.15320i −0.112085 + 0.276897i
\(868\) 2.23037 + 0.513444i 0.0757035 + 0.0174274i
\(869\) 22.0671 12.7404i 0.748574 0.432189i
\(870\) 11.0818 1.55004i 0.375709 0.0525514i
\(871\) −33.6962 12.2192i −1.14175 0.414031i
\(872\) 48.4841i 1.64188i
\(873\) 16.0959 16.6241i 0.544763 0.562641i
\(874\) 17.2385 9.95263i 0.583100 0.336653i
\(875\) −22.6519 + 6.94094i −0.765773 + 0.234647i
\(876\) 6.82329 + 48.7821i 0.230537 + 1.64819i
\(877\) 19.6907 34.1054i 0.664909 1.15166i −0.314401 0.949290i \(-0.601804\pi\)
0.979310 0.202366i \(-0.0648631\pi\)
\(878\) −40.5287 + 70.1978i −1.36778 + 2.36906i
\(879\) 41.7836 5.84439i 1.40933 0.197126i
\(880\) −2.22297 1.28344i −0.0749365 0.0432646i
\(881\) 2.05629 + 3.56160i 0.0692782 + 0.119993i 0.898584 0.438802i \(-0.144597\pi\)
−0.829306 + 0.558795i \(0.811264\pi\)
\(882\) −37.4070 31.3916i −1.25956 1.05701i
\(883\) 22.4900 0.756847 0.378424 0.925633i \(-0.376466\pi\)
0.378424 + 0.925633i \(0.376466\pi\)
\(884\) −39.8797 14.4615i −1.34130 0.486392i
\(885\) 24.7635 3.46374i 0.832416 0.116432i
\(886\) −33.9762 58.8485i −1.14145 1.97706i
\(887\) 27.1826 + 47.0817i 0.912704 + 1.58085i 0.810229 + 0.586114i \(0.199343\pi\)
0.102475 + 0.994736i \(0.467324\pi\)
\(888\) −6.01881 2.43635i −0.201978 0.0817584i
\(889\) −20.8371 19.4064i −0.698854 0.650871i
\(890\) −6.89678 3.98186i −0.231181 0.133472i
\(891\) −29.1919 + 0.942809i −0.977967 + 0.0315853i
\(892\) 22.3514i 0.748381i
\(893\) −8.18961 4.72827i −0.274055 0.158226i
\(894\) 24.0269 + 30.7946i 0.803580 + 1.02993i
\(895\) 4.31834 2.49319i 0.144346 0.0833383i
\(896\) −35.5229 + 38.1417i −1.18674 + 1.27422i
\(897\) −32.9976 + 10.7409i −1.10176 + 0.358630i
\(898\) 81.9112 2.73341
\(899\) −0.354940 0.614774i −0.0118379 0.0205038i
\(900\) −29.4715 28.5351i −0.982385 0.951169i
\(901\) 3.18303 + 1.83772i 0.106042 + 0.0612235i
\(902\) −21.5822 −0.718610
\(903\) −49.1933 + 22.9376i −1.63705 + 0.763316i
\(904\) 28.3209 49.0532i 0.941939 1.63149i
\(905\) 12.5928i 0.418600i
\(906\) −18.0880 7.32183i −0.600935 0.243252i
\(907\) 27.4601 + 47.5623i 0.911799 + 1.57928i 0.811522 + 0.584322i \(0.198640\pi\)
0.100277 + 0.994960i \(0.468027\pi\)
\(908\) 30.7052 + 53.1829i 1.01899 + 1.76494i
\(909\) −38.9601 + 11.1164i −1.29223 + 0.368708i
\(910\) −1.11350 + 22.0111i −0.0369122 + 0.729660i
\(911\) 22.6915i 0.751804i −0.926659 0.375902i \(-0.877333\pi\)
0.926659 0.375902i \(-0.122667\pi\)
\(912\) 1.67473 1.30668i 0.0554560 0.0432685i
\(913\) 26.6877 15.4082i 0.883234 0.509936i
\(914\) 34.3190 + 19.8141i 1.13517 + 0.655391i
\(915\) −2.91408 20.8338i −0.0963366 0.688745i
\(916\) 26.4716 + 15.2834i 0.874647 + 0.504978i
\(917\) 23.2286 7.11767i 0.767077 0.235046i
\(918\) −16.8943 38.1469i −0.557596 1.25904i
\(919\) 6.94934 12.0366i 0.229238 0.397051i −0.728345 0.685211i \(-0.759710\pi\)
0.957582 + 0.288160i \(0.0930434\pi\)
\(920\) −9.03477 15.6487i −0.297868 0.515922i
\(921\) −24.5474 + 19.1526i −0.808864 + 0.631101i
\(922\) 39.0852i 1.28720i
\(923\) 14.8673 2.63970i 0.489363 0.0868866i
\(924\) 29.0671 41.5098i 0.956238 1.36557i
\(925\) −2.29815 3.98051i −0.0755627 0.130878i
\(926\) −45.0873 + 26.0312i −1.48166 + 0.855437i
\(927\) −35.9023 9.00143i −1.17918 0.295646i
\(928\) 13.1279 0.430946
\(929\) 9.13212 15.8173i 0.299615 0.518949i −0.676433 0.736504i \(-0.736475\pi\)
0.976048 + 0.217556i \(0.0698084\pi\)
\(930\) 0.381169 0.941650i 0.0124990 0.0308779i
\(931\) 10.7560 0.765720i 0.352514 0.0250954i
\(932\) 68.9621 + 39.8153i 2.25893 + 1.30419i
\(933\) −30.4812 39.0669i −0.997911 1.27899i
\(934\) −71.2251 + 41.1218i −2.33056 + 1.34555i
\(935\) 11.1325i 0.364072i
\(936\) −31.8223 + 15.5159i −1.04014 + 0.507152i
\(937\) 25.2955i 0.826369i 0.910647 + 0.413185i \(0.135584\pi\)
−0.910647 + 0.413185i \(0.864416\pi\)
\(938\) 59.6034 + 13.7211i 1.94612 + 0.448009i
\(939\) 1.17744 0.918677i 0.0384244 0.0299799i
\(940\) −10.3912 + 17.9981i −0.338924 + 0.587034i
\(941\) −38.2972 −1.24845 −0.624226 0.781244i \(-0.714586\pi\)
−0.624226 + 0.781244i \(0.714586\pi\)
\(942\) −31.3007 + 77.3260i −1.01983 + 2.51942i
\(943\) −13.7626 7.94583i −0.448172 0.258752i
\(944\) −11.5681 −0.376510
\(945\) −10.3203 + 8.94709i −0.335719 + 0.291049i
\(946\) −44.6921 77.4090i −1.45307 2.51678i
\(947\) 13.1262 7.57839i 0.426543 0.246265i −0.271330 0.962486i \(-0.587463\pi\)
0.697873 + 0.716222i \(0.254130\pi\)
\(948\) 45.8942 6.41935i 1.49057 0.208491i
\(949\) 19.3697 + 23.0283i 0.628766 + 0.747531i
\(950\) 14.3751 0.466388
\(951\) 17.7007 13.8106i 0.573984 0.447840i
\(952\) 29.1378 + 6.70771i 0.944362 + 0.217398i
\(953\) −8.75300 5.05355i −0.283538 0.163700i 0.351486 0.936193i \(-0.385676\pi\)
−0.635024 + 0.772493i \(0.719010\pi\)
\(954\) 7.14110 2.03755i 0.231202 0.0659683i
\(955\) 1.57666 + 0.910288i 0.0510197 + 0.0294562i
\(956\) −39.1676 22.6134i −1.26677 0.731370i
\(957\) −15.5662 + 2.17728i −0.503183 + 0.0703816i
\(958\) −8.82599 5.09569i −0.285155 0.164634i
\(959\) 3.19236 + 0.734902i 0.103087 + 0.0237312i
\(960\) 13.2420 + 16.9720i 0.427385 + 0.547767i
\(961\) 30.9356 0.997921
\(962\) −9.45537 + 1.67881i −0.304853 + 0.0541269i
\(963\) 5.12358 + 17.9568i 0.165105 + 0.578650i
\(964\) 80.8600 46.6846i 2.60433 1.50361i
\(965\) −2.34989 4.07012i −0.0756455 0.131022i
\(966\) 53.6671 25.0236i 1.72671 0.805122i
\(967\) 23.0574 0.741476 0.370738 0.928737i \(-0.379105\pi\)
0.370738 + 0.928737i \(0.379105\pi\)
\(968\) −1.32775 0.766576i −0.0426755 0.0246387i
\(969\) 8.53948 + 3.45668i 0.274328 + 0.111045i
\(970\) 17.8201 0.572168
\(971\) −9.19702 + 15.9297i −0.295147 + 0.511209i −0.975019 0.222122i \(-0.928702\pi\)
0.679872 + 0.733330i \(0.262035\pi\)
\(972\) −49.8547 18.3308i −1.59909 0.587961i
\(973\) 31.5333 + 7.25916i 1.01091 + 0.232718i
\(974\) 51.1170i 1.63790i
\(975\) −24.5158 5.19739i −0.785134 0.166450i
\(976\) 9.73238i 0.311526i
\(977\) −37.1628 + 21.4560i −1.18894 + 0.686437i −0.958067 0.286545i \(-0.907493\pi\)
−0.230878 + 0.972983i \(0.574160\pi\)
\(978\) 1.11697 0.871497i 0.0357169 0.0278674i
\(979\) 9.68763 + 5.59315i 0.309618 + 0.178758i
\(980\) −1.68281 23.6382i −0.0537552 0.755095i
\(981\) 10.8074 43.1054i 0.345053 1.37625i
\(982\) 42.1571 73.0182i 1.34529 2.33011i
\(983\) 26.4607 0.843967 0.421983 0.906604i \(-0.361334\pi\)
0.421983 + 0.906604i \(0.361334\pi\)
\(984\) −15.0284 6.08334i −0.479089 0.193930i
\(985\) −18.3214 + 10.5779i −0.583768 + 0.337039i
\(986\) −11.2259 19.4438i −0.357505 0.619216i
\(987\) −23.0435 16.1361i −0.733482 0.513619i
\(988\) 6.45199 17.7923i 0.205265 0.566049i
\(989\) 65.8163i 2.09284i
\(990\) −16.1595 15.6460i −0.513582 0.497263i
\(991\) −11.0247 19.0953i −0.350210 0.606582i 0.636076 0.771627i \(-0.280557\pi\)
−0.986286 + 0.165045i \(0.947223\pi\)
\(992\) 0.595919 1.03216i 0.0189204 0.0327712i
\(993\) −10.2796 + 1.43783i −0.326212 + 0.0456282i
\(994\) −24.6355 + 7.54875i −0.781390 + 0.239432i
\(995\) −2.27196 1.31172i −0.0720260 0.0415842i
\(996\) 55.5041 7.76350i 1.75871 0.245996i
\(997\) −0.997512 0.575914i −0.0315915 0.0182394i 0.484121 0.875001i \(-0.339139\pi\)
−0.515713 + 0.856762i \(0.672473\pi\)
\(998\) −8.67772 + 5.01008i −0.274688 + 0.158591i
\(999\) −4.80802 3.50769i −0.152119 0.110978i
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 273.2.bn.c.146.4 yes 64
3.2 odd 2 inner 273.2.bn.c.146.29 yes 64
7.6 odd 2 inner 273.2.bn.c.146.3 64
13.9 even 3 inner 273.2.bn.c.230.30 yes 64
21.20 even 2 inner 273.2.bn.c.146.30 yes 64
39.35 odd 6 inner 273.2.bn.c.230.3 yes 64
91.48 odd 6 inner 273.2.bn.c.230.29 yes 64
273.230 even 6 inner 273.2.bn.c.230.4 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.bn.c.146.3 64 7.6 odd 2 inner
273.2.bn.c.146.4 yes 64 1.1 even 1 trivial
273.2.bn.c.146.29 yes 64 3.2 odd 2 inner
273.2.bn.c.146.30 yes 64 21.20 even 2 inner
273.2.bn.c.230.3 yes 64 39.35 odd 6 inner
273.2.bn.c.230.4 yes 64 273.230 even 6 inner
273.2.bn.c.230.29 yes 64 91.48 odd 6 inner
273.2.bn.c.230.30 yes 64 13.9 even 3 inner