Properties

Label 287.3.k.a.124.11
Level $287$
Weight $3$
Character 287.124
Analytic conductor $7.820$
Analytic rank $0$
Dimension $108$
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] = [287,3,Mod(124,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.124");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.k (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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.11
Character \(\chi\) \(=\) 287.124
Dual form 287.3.k.a.206.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31543 + 2.27839i) q^{2} +(-0.740318 + 0.427423i) q^{3} +(-1.46069 - 2.52999i) q^{4} +(-2.81050 - 1.62264i) q^{5} -2.24897i q^{6} +(-0.616116 + 6.97283i) q^{7} -2.83768 q^{8} +(-4.13462 + 7.16137i) q^{9} +O(q^{10})\) \(q+(-1.31543 + 2.27839i) q^{2} +(-0.740318 + 0.427423i) q^{3} +(-1.46069 - 2.52999i) q^{4} +(-2.81050 - 1.62264i) q^{5} -2.24897i q^{6} +(-0.616116 + 6.97283i) q^{7} -2.83768 q^{8} +(-4.13462 + 7.16137i) q^{9} +(7.39401 - 4.26893i) q^{10} +(5.33528 + 9.24098i) q^{11} +(2.16275 + 1.24867i) q^{12} -8.63725i q^{13} +(-15.0763 - 10.5760i) q^{14} +2.77422 q^{15} +(9.57552 - 16.5853i) q^{16} +(2.92114 - 1.68652i) q^{17} +(-10.8776 - 18.8405i) q^{18} +(-21.5923 - 12.4663i) q^{19} +9.48073i q^{20} +(-2.52423 - 5.42546i) q^{21} -28.0727 q^{22} +(5.18948 - 8.98844i) q^{23} +(2.10078 - 1.21289i) q^{24} +(-7.23406 - 12.5298i) q^{25} +(19.6790 + 11.3617i) q^{26} -14.7625i q^{27} +(18.5412 - 8.62640i) q^{28} -34.4810 q^{29} +(-3.64928 + 6.32074i) q^{30} +(44.0915 - 25.4563i) q^{31} +(19.5164 + 33.8035i) q^{32} +(-7.89961 - 4.56084i) q^{33} +8.87396i q^{34} +(13.0460 - 18.5974i) q^{35} +24.1576 q^{36} +(-2.14020 + 3.70694i) q^{37} +(56.8060 - 32.7970i) q^{38} +(3.69176 + 6.39431i) q^{39} +(7.97529 + 4.60453i) q^{40} +6.40312i q^{41} +(15.6817 + 1.38563i) q^{42} -6.38866 q^{43} +(15.5864 - 26.9965i) q^{44} +(23.2407 - 13.4180i) q^{45} +(13.6528 + 23.6473i) q^{46} +(-26.2931 - 15.1803i) q^{47} +16.3712i q^{48} +(-48.2408 - 8.59214i) q^{49} +38.0635 q^{50} +(-1.44171 + 2.49712i) q^{51} +(-21.8522 + 12.6164i) q^{52} +(33.9460 + 58.7962i) q^{53} +(33.6347 + 19.4190i) q^{54} -34.6290i q^{55} +(1.74834 - 19.7866i) q^{56} +21.3135 q^{57} +(45.3573 - 78.5611i) q^{58} +(2.95415 - 1.70558i) q^{59} +(-4.05228 - 7.01876i) q^{60} +(-30.3606 - 17.5287i) q^{61} +133.943i q^{62} +(-47.3876 - 33.2422i) q^{63} -26.0856 q^{64} +(-14.0152 + 24.2750i) q^{65} +(20.7827 - 11.9989i) q^{66} +(12.5915 + 21.8090i) q^{67} +(-8.53376 - 4.92697i) q^{68} +8.87241i q^{69} +(25.2110 + 54.1874i) q^{70} -111.814 q^{71} +(11.7327 - 20.3216i) q^{72} +(-41.8375 + 24.1549i) q^{73} +(-5.63056 - 9.75241i) q^{74} +(10.7110 + 6.18400i) q^{75} +72.8377i q^{76} +(-67.7229 + 31.5085i) q^{77} -19.4249 q^{78} +(38.0116 - 65.8380i) q^{79} +(-53.8240 + 31.0753i) q^{80} +(-30.9017 - 53.5234i) q^{81} +(-14.5888 - 8.42284i) q^{82} +96.9071i q^{83} +(-10.0393 + 14.3112i) q^{84} -10.9465 q^{85} +(8.40382 - 14.5558i) q^{86} +(25.5269 - 14.7380i) q^{87} +(-15.1398 - 26.2229i) q^{88} +(-98.9342 - 57.1197i) q^{89} +70.6017i q^{90} +(60.2261 + 5.32155i) q^{91} -30.3209 q^{92} +(-21.7612 + 37.6914i) q^{93} +(69.1731 - 39.9371i) q^{94} +(40.4567 + 70.0731i) q^{95} +(-28.8967 - 16.6835i) q^{96} -17.9041i q^{97} +(83.0334 - 98.6088i) q^{98} -88.2374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 2 q^{2} - 6 q^{3} - 106 q^{4} - 6 q^{5} - 4 q^{7} - 4 q^{8} + 164 q^{9} + 48 q^{10} + 6 q^{11} + 18 q^{12} + 38 q^{14} - 56 q^{15} - 202 q^{16} + 48 q^{17} + 32 q^{18} - 78 q^{19} - 104 q^{21} - 48 q^{22} - 16 q^{23} + 248 q^{25} + 144 q^{26} + 168 q^{29} - 64 q^{30} + 30 q^{31} - 104 q^{32} + 24 q^{33} - 54 q^{35} - 524 q^{36} + 76 q^{37} - 24 q^{38} - 34 q^{39} - 288 q^{40} + 190 q^{42} - 112 q^{43} + 102 q^{44} + 6 q^{45} - 68 q^{46} + 294 q^{47} + 68 q^{49} - 264 q^{50} - 36 q^{51} - 306 q^{52} + 152 q^{53} + 102 q^{54} - 438 q^{56} + 256 q^{57} - 164 q^{58} - 138 q^{59} + 280 q^{60} + 282 q^{61} + 442 q^{63} + 796 q^{64} + 76 q^{65} - 240 q^{66} - 158 q^{67} - 738 q^{68} - 82 q^{70} - 48 q^{71} - 374 q^{72} + 48 q^{73} + 34 q^{74} - 258 q^{75} - 184 q^{77} + 432 q^{78} + 128 q^{79} + 12 q^{80} - 262 q^{81} + 628 q^{84} - 196 q^{85} + 316 q^{86} + 438 q^{87} + 76 q^{88} - 24 q^{89} + 370 q^{91} - 592 q^{92} - 90 q^{93} - 264 q^{94} - 250 q^{95} - 102 q^{96} - 100 q^{98} + 168 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31543 + 2.27839i −0.657713 + 1.13919i 0.323493 + 0.946231i \(0.395143\pi\)
−0.981206 + 0.192962i \(0.938191\pi\)
\(3\) −0.740318 + 0.427423i −0.246773 + 0.142474i −0.618286 0.785954i \(-0.712172\pi\)
0.371513 + 0.928428i \(0.378839\pi\)
\(4\) −1.46069 2.52999i −0.365173 0.632499i
\(5\) −2.81050 1.62264i −0.562100 0.324529i 0.191888 0.981417i \(-0.438539\pi\)
−0.753988 + 0.656888i \(0.771872\pi\)
\(6\) 2.24897i 0.374829i
\(7\) −0.616116 + 6.97283i −0.0880165 + 0.996119i
\(8\) −2.83768 −0.354709
\(9\) −4.13462 + 7.16137i −0.459402 + 0.795708i
\(10\) 7.39401 4.26893i 0.739401 0.426893i
\(11\) 5.33528 + 9.24098i 0.485026 + 0.840089i 0.999852 0.0172056i \(-0.00547697\pi\)
−0.514826 + 0.857294i \(0.672144\pi\)
\(12\) 2.16275 + 1.24867i 0.180230 + 0.104056i
\(13\) 8.63725i 0.664404i −0.943208 0.332202i \(-0.892208\pi\)
0.943208 0.332202i \(-0.107792\pi\)
\(14\) −15.0763 10.5760i −1.07688 0.755428i
\(15\) 2.77422 0.184948
\(16\) 9.57552 16.5853i 0.598470 1.03658i
\(17\) 2.92114 1.68652i 0.171832 0.0992070i −0.411618 0.911357i \(-0.635036\pi\)
0.583449 + 0.812150i \(0.301703\pi\)
\(18\) −10.8776 18.8405i −0.604310 1.04670i
\(19\) −21.5923 12.4663i −1.13643 0.656121i −0.190889 0.981612i \(-0.561137\pi\)
−0.945545 + 0.325491i \(0.894471\pi\)
\(20\) 9.48073i 0.474037i
\(21\) −2.52423 5.42546i −0.120201 0.258355i
\(22\) −28.0727 −1.27603
\(23\) 5.18948 8.98844i 0.225630 0.390802i −0.730879 0.682508i \(-0.760889\pi\)
0.956508 + 0.291706i \(0.0942228\pi\)
\(24\) 2.10078 1.21289i 0.0875326 0.0505370i
\(25\) −7.23406 12.5298i −0.289362 0.501190i
\(26\) 19.6790 + 11.3617i 0.756884 + 0.436987i
\(27\) 14.7625i 0.546760i
\(28\) 18.5412 8.62640i 0.662185 0.308086i
\(29\) −34.4810 −1.18900 −0.594501 0.804095i \(-0.702650\pi\)
−0.594501 + 0.804095i \(0.702650\pi\)
\(30\) −3.64928 + 6.32074i −0.121643 + 0.210691i
\(31\) 44.0915 25.4563i 1.42231 0.821170i 0.425811 0.904812i \(-0.359989\pi\)
0.996496 + 0.0836424i \(0.0266553\pi\)
\(32\) 19.5164 + 33.8035i 0.609889 + 1.05636i
\(33\) −7.89961 4.56084i −0.239382 0.138207i
\(34\) 8.87396i 0.260999i
\(35\) 13.0460 18.5974i 0.372743 0.531355i
\(36\) 24.1576 0.671045
\(37\) −2.14020 + 3.70694i −0.0578433 + 0.100188i −0.893497 0.449069i \(-0.851756\pi\)
0.835654 + 0.549257i \(0.185089\pi\)
\(38\) 56.8060 32.7970i 1.49490 0.863079i
\(39\) 3.69176 + 6.39431i 0.0946605 + 0.163957i
\(40\) 7.97529 + 4.60453i 0.199382 + 0.115113i
\(41\) 6.40312i 0.156174i
\(42\) 15.6817 + 1.38563i 0.373374 + 0.0329911i
\(43\) −6.38866 −0.148574 −0.0742868 0.997237i \(-0.523668\pi\)
−0.0742868 + 0.997237i \(0.523668\pi\)
\(44\) 15.5864 26.9965i 0.354237 0.613556i
\(45\) 23.2407 13.4180i 0.516460 0.298178i
\(46\) 13.6528 + 23.6473i 0.296799 + 0.514071i
\(47\) −26.2931 15.1803i −0.559427 0.322985i 0.193489 0.981103i \(-0.438020\pi\)
−0.752915 + 0.658117i \(0.771353\pi\)
\(48\) 16.3712i 0.341066i
\(49\) −48.2408 8.59214i −0.984506 0.175350i
\(50\) 38.0635 0.761270
\(51\) −1.44171 + 2.49712i −0.0282689 + 0.0489631i
\(52\) −21.8522 + 12.6164i −0.420234 + 0.242622i
\(53\) 33.9460 + 58.7962i 0.640491 + 1.10936i 0.985323 + 0.170698i \(0.0546023\pi\)
−0.344833 + 0.938664i \(0.612064\pi\)
\(54\) 33.6347 + 19.4190i 0.622865 + 0.359612i
\(55\) 34.6290i 0.629619i
\(56\) 1.74834 19.7866i 0.0312203 0.353333i
\(57\) 21.3135 0.373921
\(58\) 45.3573 78.5611i 0.782022 1.35450i
\(59\) 2.95415 1.70558i 0.0500703 0.0289081i −0.474756 0.880118i \(-0.657464\pi\)
0.524826 + 0.851209i \(0.324130\pi\)
\(60\) −4.05228 7.01876i −0.0675380 0.116979i
\(61\) −30.3606 17.5287i −0.497715 0.287356i 0.230055 0.973178i \(-0.426110\pi\)
−0.727769 + 0.685822i \(0.759443\pi\)
\(62\) 133.943i 2.16038i
\(63\) −47.3876 33.2422i −0.752185 0.527655i
\(64\) −26.0856 −0.407587
\(65\) −14.0152 + 24.2750i −0.215618 + 0.373461i
\(66\) 20.7827 11.9989i 0.314889 0.181802i
\(67\) 12.5915 + 21.8090i 0.187932 + 0.325508i 0.944561 0.328337i \(-0.106488\pi\)
−0.756628 + 0.653845i \(0.773155\pi\)
\(68\) −8.53376 4.92697i −0.125497 0.0724554i
\(69\) 8.87241i 0.128586i
\(70\) 25.2110 + 54.1874i 0.360157 + 0.774105i
\(71\) −111.814 −1.57484 −0.787421 0.616415i \(-0.788584\pi\)
−0.787421 + 0.616415i \(0.788584\pi\)
\(72\) 11.7327 20.3216i 0.162954 0.282245i
\(73\) −41.8375 + 24.1549i −0.573117 + 0.330889i −0.758393 0.651797i \(-0.774015\pi\)
0.185277 + 0.982686i \(0.440682\pi\)
\(74\) −5.63056 9.75241i −0.0760886 0.131789i
\(75\) 10.7110 + 6.18400i 0.142813 + 0.0824534i
\(76\) 72.8377i 0.958391i
\(77\) −67.7229 + 31.5085i −0.879519 + 0.409201i
\(78\) −19.4249 −0.249038
\(79\) 38.0116 65.8380i 0.481160 0.833393i −0.518607 0.855013i \(-0.673549\pi\)
0.999766 + 0.0216200i \(0.00688239\pi\)
\(80\) −53.8240 + 31.0753i −0.672800 + 0.388441i
\(81\) −30.9017 53.5234i −0.381503 0.660782i
\(82\) −14.5888 8.42284i −0.177912 0.102718i
\(83\) 96.9071i 1.16756i 0.811913 + 0.583778i \(0.198426\pi\)
−0.811913 + 0.583778i \(0.801574\pi\)
\(84\) −10.0393 + 14.3112i −0.119515 + 0.170371i
\(85\) −10.9465 −0.128782
\(86\) 8.40382 14.5558i 0.0977188 0.169254i
\(87\) 25.5269 14.7380i 0.293413 0.169402i
\(88\) −15.1398 26.2229i −0.172043 0.297987i
\(89\) −98.9342 57.1197i −1.11162 0.641794i −0.172372 0.985032i \(-0.555143\pi\)
−0.939249 + 0.343238i \(0.888476\pi\)
\(90\) 70.6017i 0.784463i
\(91\) 60.2261 + 5.32155i 0.661825 + 0.0584785i
\(92\) −30.3209 −0.329575
\(93\) −21.7612 + 37.6914i −0.233991 + 0.405284i
\(94\) 69.1731 39.9371i 0.735885 0.424863i
\(95\) 40.4567 + 70.0731i 0.425860 + 0.737611i
\(96\) −28.8967 16.6835i −0.301008 0.173787i
\(97\) 17.9041i 0.184578i −0.995732 0.0922890i \(-0.970582\pi\)
0.995732 0.0922890i \(-0.0294184\pi\)
\(98\) 83.0334 98.6088i 0.847280 1.00621i
\(99\) −88.2374 −0.891287
\(100\) −21.1335 + 36.6043i −0.211335 + 0.366043i
\(101\) −10.7587 + 6.21151i −0.106521 + 0.0615001i −0.552314 0.833636i \(-0.686255\pi\)
0.445793 + 0.895136i \(0.352922\pi\)
\(102\) −3.79293 6.56955i −0.0371856 0.0644074i
\(103\) 10.0055 + 5.77666i 0.0971405 + 0.0560841i 0.547783 0.836620i \(-0.315472\pi\)
−0.450643 + 0.892704i \(0.648805\pi\)
\(104\) 24.5097i 0.235670i
\(105\) −1.70924 + 19.3442i −0.0162785 + 0.184230i
\(106\) −178.614 −1.68504
\(107\) −90.8985 + 157.441i −0.849519 + 1.47141i 0.0321194 + 0.999484i \(0.489774\pi\)
−0.881638 + 0.471926i \(0.843559\pi\)
\(108\) −37.3491 + 21.5635i −0.345825 + 0.199662i
\(109\) 29.7295 + 51.4930i 0.272748 + 0.472413i 0.969564 0.244836i \(-0.0787342\pi\)
−0.696817 + 0.717249i \(0.745401\pi\)
\(110\) 78.8983 + 45.5519i 0.717257 + 0.414108i
\(111\) 3.65908i 0.0329647i
\(112\) 109.747 + 76.9870i 0.979883 + 0.687384i
\(113\) −78.7413 −0.696826 −0.348413 0.937341i \(-0.613279\pi\)
−0.348413 + 0.937341i \(0.613279\pi\)
\(114\) −28.0364 + 48.5604i −0.245933 + 0.425968i
\(115\) −29.1701 + 16.8413i −0.253653 + 0.146447i
\(116\) 50.3662 + 87.2368i 0.434191 + 0.752042i
\(117\) 61.8546 + 35.7117i 0.528671 + 0.305229i
\(118\) 8.97424i 0.0760529i
\(119\) 9.96005 + 21.4077i 0.0836979 + 0.179896i
\(120\) −7.87233 −0.0656028
\(121\) 3.56956 6.18266i 0.0295005 0.0510963i
\(122\) 79.8743 46.1154i 0.654707 0.377995i
\(123\) −2.73684 4.74035i −0.0222507 0.0385394i
\(124\) −128.808 74.3675i −1.03878 0.599738i
\(125\) 128.085i 1.02468i
\(126\) 138.074 64.2396i 1.09582 0.509838i
\(127\) −184.890 −1.45582 −0.727912 0.685671i \(-0.759509\pi\)
−0.727912 + 0.685671i \(0.759509\pi\)
\(128\) −43.7521 + 75.7809i −0.341813 + 0.592038i
\(129\) 4.72964 2.73066i 0.0366639 0.0211679i
\(130\) −36.8719 63.8639i −0.283630 0.491261i
\(131\) 36.8304 + 21.2640i 0.281148 + 0.162321i 0.633943 0.773380i \(-0.281435\pi\)
−0.352795 + 0.935701i \(0.614769\pi\)
\(132\) 26.6480i 0.201878i
\(133\) 100.229 142.879i 0.753599 1.07427i
\(134\) −66.2525 −0.494422
\(135\) −23.9543 + 41.4901i −0.177439 + 0.307334i
\(136\) −8.28924 + 4.78579i −0.0609503 + 0.0351896i
\(137\) 35.5312 + 61.5418i 0.259352 + 0.449210i 0.966068 0.258286i \(-0.0831578\pi\)
−0.706717 + 0.707497i \(0.749824\pi\)
\(138\) −20.2148 11.6710i −0.146484 0.0845725i
\(139\) 227.344i 1.63557i −0.575523 0.817786i \(-0.695201\pi\)
0.575523 0.817786i \(-0.304799\pi\)
\(140\) −66.1076 5.84123i −0.472197 0.0417230i
\(141\) 25.9536 0.184068
\(142\) 147.083 254.755i 1.03579 1.79405i
\(143\) 79.8166 46.0822i 0.558158 0.322253i
\(144\) 79.1823 + 137.148i 0.549877 + 0.952415i
\(145\) 96.9090 + 55.9504i 0.668338 + 0.385865i
\(146\) 127.096i 0.870520i
\(147\) 39.3860 14.2583i 0.267932 0.0969952i
\(148\) 12.5047 0.0844913
\(149\) −23.7000 + 41.0496i −0.159060 + 0.275500i −0.934530 0.355884i \(-0.884180\pi\)
0.775470 + 0.631385i \(0.217513\pi\)
\(150\) −28.1791 + 16.2692i −0.187861 + 0.108461i
\(151\) −100.321 173.761i −0.664378 1.15074i −0.979453 0.201670i \(-0.935363\pi\)
0.315075 0.949067i \(-0.397970\pi\)
\(152\) 61.2718 + 35.3753i 0.403104 + 0.232732i
\(153\) 27.8924i 0.182304i
\(154\) 17.2960 195.746i 0.112312 1.27108i
\(155\) −165.226 −1.06597
\(156\) 10.7850 18.6803i 0.0691349 0.119745i
\(157\) 102.521 59.1907i 0.653002 0.377011i −0.136604 0.990626i \(-0.543619\pi\)
0.789605 + 0.613615i \(0.210285\pi\)
\(158\) 100.003 + 173.210i 0.632930 + 1.09627i
\(159\) −50.2617 29.0186i −0.316111 0.182507i
\(160\) 126.673i 0.791705i
\(161\) 59.4776 + 41.7233i 0.369426 + 0.259151i
\(162\) 162.596 1.00368
\(163\) −39.0763 + 67.6821i −0.239732 + 0.415227i −0.960637 0.277806i \(-0.910393\pi\)
0.720906 + 0.693033i \(0.243726\pi\)
\(164\) 16.1999 9.35300i 0.0987797 0.0570305i
\(165\) 14.8012 + 25.6365i 0.0897044 + 0.155373i
\(166\) −220.792 127.474i −1.33007 0.767917i
\(167\) 162.093i 0.970619i 0.874342 + 0.485310i \(0.161293\pi\)
−0.874342 + 0.485310i \(0.838707\pi\)
\(168\) 7.16294 + 15.3957i 0.0426365 + 0.0916410i
\(169\) 94.3979 0.558567
\(170\) 14.3993 24.9403i 0.0847016 0.146707i
\(171\) 178.552 103.087i 1.04416 0.602847i
\(172\) 9.33187 + 16.1633i 0.0542551 + 0.0939726i
\(173\) 82.9106 + 47.8685i 0.479252 + 0.276696i 0.720105 0.693865i \(-0.244094\pi\)
−0.240853 + 0.970562i \(0.577427\pi\)
\(174\) 77.5469i 0.445672i
\(175\) 91.8249 42.7221i 0.524714 0.244126i
\(176\) 204.352 1.16109
\(177\) −1.45801 + 2.52534i −0.00823732 + 0.0142675i
\(178\) 260.281 150.273i 1.46225 0.844233i
\(179\) −144.889 250.955i −0.809436 1.40198i −0.913255 0.407388i \(-0.866440\pi\)
0.103820 0.994596i \(-0.466894\pi\)
\(180\) −67.8950 39.1992i −0.377195 0.217773i
\(181\) 321.597i 1.77678i 0.459088 + 0.888391i \(0.348176\pi\)
−0.459088 + 0.888391i \(0.651824\pi\)
\(182\) −91.3475 + 130.218i −0.501910 + 0.715484i
\(183\) 29.9687 0.163763
\(184\) −14.7261 + 25.5063i −0.0800329 + 0.138621i
\(185\) 12.0301 6.94557i 0.0650274 0.0375436i
\(186\) −57.2504 99.1606i −0.307798 0.533122i
\(187\) 31.1702 + 17.9961i 0.166685 + 0.0962358i
\(188\) 88.6950i 0.471782i
\(189\) 102.937 + 9.09543i 0.544638 + 0.0481240i
\(190\) −212.871 −1.12037
\(191\) 105.692 183.063i 0.553360 0.958447i −0.444669 0.895695i \(-0.646679\pi\)
0.998029 0.0627526i \(-0.0199879\pi\)
\(192\) 19.3116 11.1496i 0.100581 0.0580707i
\(193\) −90.5625 156.859i −0.469236 0.812740i 0.530146 0.847907i \(-0.322137\pi\)
−0.999381 + 0.0351662i \(0.988804\pi\)
\(194\) 40.7924 + 23.5515i 0.210270 + 0.121399i
\(195\) 23.9616i 0.122880i
\(196\) 48.7269 + 134.599i 0.248607 + 0.686732i
\(197\) 72.3346 0.367181 0.183590 0.983003i \(-0.441228\pi\)
0.183590 + 0.983003i \(0.441228\pi\)
\(198\) 116.070 201.039i 0.586211 1.01535i
\(199\) −204.816 + 118.251i −1.02923 + 0.594225i −0.916763 0.399431i \(-0.869208\pi\)
−0.112464 + 0.993656i \(0.535874\pi\)
\(200\) 20.5279 + 35.5554i 0.102640 + 0.177777i
\(201\) −18.6434 10.7638i −0.0927531 0.0535510i
\(202\) 32.6831i 0.161798i
\(203\) 21.2443 240.431i 0.104652 1.18439i
\(204\) 8.42360 0.0412921
\(205\) 10.3900 17.9960i 0.0506829 0.0877853i
\(206\) −26.3229 + 15.1975i −0.127781 + 0.0737745i
\(207\) 42.9131 + 74.3276i 0.207309 + 0.359070i
\(208\) −143.251 82.7062i −0.688708 0.397626i
\(209\) 266.045i 1.27294i
\(210\) −41.8251 29.3401i −0.199167 0.139715i
\(211\) −211.016 −1.00007 −0.500037 0.866004i \(-0.666680\pi\)
−0.500037 + 0.866004i \(0.666680\pi\)
\(212\) 99.1694 171.766i 0.467780 0.810219i
\(213\) 82.7778 47.7918i 0.388628 0.224375i
\(214\) −239.141 414.204i −1.11748 1.93553i
\(215\) 17.9553 + 10.3665i 0.0835132 + 0.0482164i
\(216\) 41.8913i 0.193941i
\(217\) 150.337 + 323.127i 0.692796 + 1.48906i
\(218\) −156.428 −0.717560
\(219\) 20.6487 35.7646i 0.0942863 0.163309i
\(220\) −87.6112 + 50.5824i −0.398233 + 0.229920i
\(221\) −14.5669 25.2306i −0.0659135 0.114166i
\(222\) 8.33681 + 4.81326i 0.0375532 + 0.0216813i
\(223\) 179.692i 0.805794i 0.915245 + 0.402897i \(0.131997\pi\)
−0.915245 + 0.402897i \(0.868003\pi\)
\(224\) −247.730 + 115.258i −1.10594 + 0.514545i
\(225\) 119.640 0.531735
\(226\) 103.578 179.403i 0.458312 0.793819i
\(227\) 237.200 136.948i 1.04494 0.603294i 0.123709 0.992319i \(-0.460521\pi\)
0.921227 + 0.389025i \(0.127188\pi\)
\(228\) −31.1325 53.9231i −0.136546 0.236505i
\(229\) 311.597 + 179.900i 1.36068 + 0.785591i 0.989715 0.143054i \(-0.0456923\pi\)
0.370969 + 0.928645i \(0.379026\pi\)
\(230\) 88.6142i 0.385279i
\(231\) 36.6691 52.2726i 0.158741 0.226289i
\(232\) 97.8460 0.421750
\(233\) −178.266 + 308.766i −0.765091 + 1.32518i 0.175108 + 0.984549i \(0.443973\pi\)
−0.940199 + 0.340627i \(0.889361\pi\)
\(234\) −162.730 + 93.9523i −0.695428 + 0.401506i
\(235\) 49.2644 + 85.3285i 0.209636 + 0.363100i
\(236\) −8.63020 4.98265i −0.0365686 0.0211129i
\(237\) 64.9881i 0.274211i
\(238\) −61.8767 5.46739i −0.259986 0.0229722i
\(239\) −198.688 −0.831330 −0.415665 0.909518i \(-0.636451\pi\)
−0.415665 + 0.909518i \(0.636451\pi\)
\(240\) 26.5646 46.0112i 0.110686 0.191713i
\(241\) −73.4752 + 42.4209i −0.304876 + 0.176020i −0.644631 0.764493i \(-0.722989\pi\)
0.339755 + 0.940514i \(0.389656\pi\)
\(242\) 9.39098 + 16.2657i 0.0388057 + 0.0672135i
\(243\) 160.817 + 92.8476i 0.661797 + 0.382089i
\(244\) 102.416i 0.419738i
\(245\) 121.639 + 102.426i 0.496485 + 0.418065i
\(246\) 14.4005 0.0585384
\(247\) −107.675 + 186.498i −0.435929 + 0.755052i
\(248\) −125.117 + 72.2366i −0.504506 + 0.291277i
\(249\) −41.4203 71.7421i −0.166347 0.288121i
\(250\) −291.828 168.487i −1.16731 0.673947i
\(251\) 108.607i 0.432698i −0.976316 0.216349i \(-0.930585\pi\)
0.976316 0.216349i \(-0.0694148\pi\)
\(252\) −14.8839 + 168.447i −0.0590631 + 0.668441i
\(253\) 110.749 0.437744
\(254\) 243.209 421.250i 0.957514 1.65846i
\(255\) 8.10387 4.67877i 0.0317799 0.0183481i
\(256\) −167.277 289.731i −0.653424 1.13176i
\(257\) −156.396 90.2955i −0.608546 0.351344i 0.163850 0.986485i \(-0.447609\pi\)
−0.772396 + 0.635141i \(0.780942\pi\)
\(258\) 14.3679i 0.0556897i
\(259\) −24.5293 17.2072i −0.0947076 0.0664370i
\(260\) 81.8875 0.314952
\(261\) 142.566 246.931i 0.546230 0.946098i
\(262\) −96.8953 + 55.9425i −0.369829 + 0.213521i
\(263\) 34.7339 + 60.1609i 0.132068 + 0.228749i 0.924474 0.381246i \(-0.124505\pi\)
−0.792406 + 0.609995i \(0.791172\pi\)
\(264\) 22.4165 + 12.9422i 0.0849111 + 0.0490234i
\(265\) 220.329i 0.831430i
\(266\) 193.689 + 416.306i 0.728153 + 1.56506i
\(267\) 97.6570 0.365757
\(268\) 36.7845 63.7126i 0.137256 0.237734i
\(269\) −290.015 + 167.440i −1.07812 + 0.622455i −0.930389 0.366573i \(-0.880531\pi\)
−0.147734 + 0.989027i \(0.547198\pi\)
\(270\) −63.0203 109.154i −0.233408 0.404275i
\(271\) −259.826 150.010i −0.958766 0.553544i −0.0629732 0.998015i \(-0.520058\pi\)
−0.895793 + 0.444471i \(0.853392\pi\)
\(272\) 64.5972i 0.237490i
\(273\) −46.8610 + 21.8024i −0.171652 + 0.0798622i
\(274\) −186.955 −0.682316
\(275\) 77.1915 133.700i 0.280696 0.486180i
\(276\) 22.4471 12.9599i 0.0813302 0.0469560i
\(277\) −71.7616 124.295i −0.259067 0.448718i 0.706925 0.707288i \(-0.250082\pi\)
−0.965992 + 0.258571i \(0.916748\pi\)
\(278\) 517.978 + 299.055i 1.86323 + 1.07574i
\(279\) 421.008i 1.50899i
\(280\) −37.0204 + 52.7734i −0.132216 + 0.188477i
\(281\) −194.772 −0.693138 −0.346569 0.938024i \(-0.612653\pi\)
−0.346569 + 0.938024i \(0.612653\pi\)
\(282\) −34.1401 + 59.1324i −0.121064 + 0.209689i
\(283\) −333.054 + 192.289i −1.17687 + 0.679466i −0.955288 0.295676i \(-0.904455\pi\)
−0.221581 + 0.975142i \(0.571122\pi\)
\(284\) 163.326 + 282.888i 0.575090 + 0.996085i
\(285\) −59.9016 34.5842i −0.210181 0.121348i
\(286\) 242.471i 0.847800i
\(287\) −44.6479 3.94506i −0.155568 0.0137459i
\(288\) −322.772 −1.12074
\(289\) −138.811 + 240.428i −0.480316 + 0.831932i
\(290\) −254.953 + 147.197i −0.879149 + 0.507577i
\(291\) 7.65261 + 13.2547i 0.0262976 + 0.0455488i
\(292\) 122.223 + 70.5658i 0.418574 + 0.241664i
\(293\) 392.535i 1.33971i −0.742492 0.669855i \(-0.766356\pi\)
0.742492 0.669855i \(-0.233644\pi\)
\(294\) −19.3235 + 108.492i −0.0657262 + 0.369021i
\(295\) −11.0702 −0.0375260
\(296\) 6.07320 10.5191i 0.0205176 0.0355375i
\(297\) 136.420 78.7623i 0.459327 0.265193i
\(298\) −62.3512 107.995i −0.209232 0.362401i
\(299\) −77.6354 44.8228i −0.259650 0.149909i
\(300\) 36.1317i 0.120439i
\(301\) 3.93616 44.5471i 0.0130769 0.147997i
\(302\) 527.860 1.74788
\(303\) 5.30988 9.19698i 0.0175244 0.0303531i
\(304\) −413.514 + 238.743i −1.36024 + 0.785338i
\(305\) 56.8856 + 98.5288i 0.186510 + 0.323045i
\(306\) −63.5497 36.6905i −0.207679 0.119903i
\(307\) 242.848i 0.791037i 0.918458 + 0.395519i \(0.129435\pi\)
−0.918458 + 0.395519i \(0.870565\pi\)
\(308\) 178.639 + 125.314i 0.579996 + 0.406865i
\(309\) −9.87630 −0.0319621
\(310\) 217.342 376.448i 0.701104 1.21435i
\(311\) 428.372 247.321i 1.37740 0.795244i 0.385556 0.922684i \(-0.374010\pi\)
0.991846 + 0.127441i \(0.0406763\pi\)
\(312\) −10.4760 18.1450i −0.0335770 0.0581570i
\(313\) 230.240 + 132.929i 0.735590 + 0.424693i 0.820464 0.571698i \(-0.193715\pi\)
−0.0848734 + 0.996392i \(0.527049\pi\)
\(314\) 311.444i 0.991859i
\(315\) 79.2427 + 170.321i 0.251564 + 0.540700i
\(316\) −222.093 −0.702826
\(317\) −306.001 + 530.009i −0.965303 + 1.67195i −0.256502 + 0.966544i \(0.582570\pi\)
−0.708800 + 0.705409i \(0.750763\pi\)
\(318\) 132.231 76.3436i 0.415821 0.240074i
\(319\) −183.966 318.638i −0.576696 0.998867i
\(320\) 73.3135 + 42.3276i 0.229105 + 0.132274i
\(321\) 155.408i 0.484138i
\(322\) −173.300 + 80.6289i −0.538199 + 0.250400i
\(323\) −84.0985 −0.260367
\(324\) −90.2759 + 156.362i −0.278629 + 0.482600i
\(325\) −108.223 + 62.4824i −0.332993 + 0.192253i
\(326\) −102.804 178.062i −0.315349 0.546201i
\(327\) −44.0186 25.4142i −0.134613 0.0777191i
\(328\) 18.1700i 0.0553963i
\(329\) 122.049 173.984i 0.370970 0.528828i
\(330\) −77.8797 −0.235999
\(331\) 10.1039 17.5004i 0.0305253 0.0528714i −0.850359 0.526203i \(-0.823615\pi\)
0.880884 + 0.473331i \(0.156949\pi\)
\(332\) 245.174 141.552i 0.738477 0.426360i
\(333\) −17.6978 30.6536i −0.0531467 0.0920528i
\(334\) −369.311 213.222i −1.10572 0.638389i
\(335\) 81.7258i 0.243957i
\(336\) −114.154 10.0865i −0.339743 0.0300195i
\(337\) 318.992 0.946564 0.473282 0.880911i \(-0.343069\pi\)
0.473282 + 0.880911i \(0.343069\pi\)
\(338\) −124.173 + 215.075i −0.367377 + 0.636316i
\(339\) 58.2936 33.6558i 0.171958 0.0992798i
\(340\) 15.9894 + 27.6945i 0.0470277 + 0.0814544i
\(341\) 470.481 + 271.633i 1.37971 + 0.796576i
\(342\) 542.412i 1.58600i
\(343\) 89.6335 331.081i 0.261322 0.965252i
\(344\) 18.1290 0.0527005
\(345\) 14.3968 24.9359i 0.0417297 0.0722780i
\(346\) −218.126 + 125.935i −0.630421 + 0.363974i
\(347\) −131.772 228.236i −0.379747 0.657740i 0.611279 0.791415i \(-0.290655\pi\)
−0.991025 + 0.133675i \(0.957322\pi\)
\(348\) −74.5740 43.0553i −0.214293 0.123722i
\(349\) 87.8079i 0.251599i −0.992056 0.125799i \(-0.959850\pi\)
0.992056 0.125799i \(-0.0401495\pi\)
\(350\) −23.4515 + 265.410i −0.0670043 + 0.758315i
\(351\) −127.508 −0.363270
\(352\) −208.251 + 360.702i −0.591623 + 1.02472i
\(353\) 419.174 242.010i 1.18746 0.685582i 0.229734 0.973253i \(-0.426214\pi\)
0.957729 + 0.287671i \(0.0928811\pi\)
\(354\) −3.83580 6.64379i −0.0108356 0.0187678i
\(355\) 314.253 + 181.434i 0.885219 + 0.511081i
\(356\) 333.737i 0.937464i
\(357\) −16.5237 11.5913i −0.0462850 0.0324687i
\(358\) 762.363 2.12951
\(359\) 208.514 361.157i 0.580819 1.00601i −0.414563 0.910021i \(-0.636066\pi\)
0.995382 0.0959882i \(-0.0306011\pi\)
\(360\) −65.9496 + 38.0760i −0.183193 + 0.105767i
\(361\) 130.317 + 225.716i 0.360989 + 0.625251i
\(362\) −732.723 423.038i −2.02410 1.16861i
\(363\) 6.10284i 0.0168122i
\(364\) −74.5084 160.145i −0.204693 0.439958i
\(365\) 156.779 0.429532
\(366\) −39.4216 + 68.2802i −0.107709 + 0.186558i
\(367\) −200.173 + 115.570i −0.545429 + 0.314904i −0.747276 0.664513i \(-0.768639\pi\)
0.201847 + 0.979417i \(0.435306\pi\)
\(368\) −99.3840 172.138i −0.270065 0.467767i
\(369\) −45.8551 26.4745i −0.124269 0.0717466i
\(370\) 36.5455i 0.0987717i
\(371\) −430.891 + 200.475i −1.16143 + 0.540363i
\(372\) 127.146 0.341789
\(373\) −86.3786 + 149.612i −0.231578 + 0.401105i −0.958273 0.285856i \(-0.907722\pi\)
0.726695 + 0.686961i \(0.241055\pi\)
\(374\) −82.0041 + 47.3451i −0.219262 + 0.126591i
\(375\) −54.7466 94.8239i −0.145991 0.252864i
\(376\) 74.6112 + 43.0768i 0.198434 + 0.114566i
\(377\) 297.821i 0.789977i
\(378\) −156.128 + 222.565i −0.413038 + 0.588796i
\(379\) 565.822 1.49293 0.746467 0.665423i \(-0.231749\pi\)
0.746467 + 0.665423i \(0.231749\pi\)
\(380\) 118.190 204.710i 0.311025 0.538712i
\(381\) 136.877 79.0260i 0.359257 0.207417i
\(382\) 278.059 + 481.613i 0.727904 + 1.26077i
\(383\) −277.603 160.274i −0.724812 0.418470i 0.0917092 0.995786i \(-0.470767\pi\)
−0.816521 + 0.577315i \(0.804100\pi\)
\(384\) 74.8026i 0.194798i
\(385\) 241.462 + 21.3355i 0.627175 + 0.0554168i
\(386\) 476.513 1.23449
\(387\) 26.4147 45.7516i 0.0682550 0.118221i
\(388\) −45.2972 + 26.1523i −0.116745 + 0.0674030i
\(389\) 103.496 + 179.260i 0.266057 + 0.460824i 0.967840 0.251567i \(-0.0809459\pi\)
−0.701783 + 0.712390i \(0.747613\pi\)
\(390\) 54.5938 + 31.5197i 0.139984 + 0.0808199i
\(391\) 35.0086i 0.0895361i
\(392\) 136.892 + 24.3817i 0.349214 + 0.0621983i
\(393\) −36.3549 −0.0925061
\(394\) −95.1508 + 164.806i −0.241499 + 0.418289i
\(395\) −213.663 + 123.359i −0.540920 + 0.312300i
\(396\) 128.888 + 223.240i 0.325474 + 0.563738i
\(397\) 352.446 + 203.485i 0.887773 + 0.512556i 0.873214 0.487338i \(-0.162032\pi\)
0.0145598 + 0.999894i \(0.495365\pi\)
\(398\) 622.201i 1.56332i
\(399\) −13.1316 + 148.616i −0.0329113 + 0.372470i
\(400\) −277.080 −0.692699
\(401\) 291.875 505.542i 0.727867 1.26070i −0.229916 0.973210i \(-0.573845\pi\)
0.957783 0.287492i \(-0.0928215\pi\)
\(402\) 49.0479 28.3178i 0.122010 0.0704424i
\(403\) −219.872 380.830i −0.545588 0.944987i
\(404\) 31.4302 + 18.1462i 0.0777974 + 0.0449164i
\(405\) 200.570i 0.495234i
\(406\) 519.848 + 364.671i 1.28041 + 0.898205i
\(407\) −45.6743 −0.112222
\(408\) 4.09111 7.08602i 0.0100272 0.0173677i
\(409\) −369.314 + 213.224i −0.902968 + 0.521329i −0.878162 0.478363i \(-0.841230\pi\)
−0.0248063 + 0.999692i \(0.507897\pi\)
\(410\) 27.3345 + 47.3448i 0.0666696 + 0.115475i
\(411\) −52.6087 30.3737i −0.128002 0.0739019i
\(412\) 33.7517i 0.0819216i
\(413\) 10.0726 + 21.6496i 0.0243889 + 0.0524203i
\(414\) −225.796 −0.545401
\(415\) 157.246 272.358i 0.378905 0.656283i
\(416\) 291.969 168.568i 0.701849 0.405213i
\(417\) 97.1722 + 168.307i 0.233027 + 0.403614i
\(418\) 606.152 + 349.962i 1.45013 + 0.837230i
\(419\) 766.420i 1.82916i −0.404400 0.914582i \(-0.632520\pi\)
0.404400 0.914582i \(-0.367480\pi\)
\(420\) 51.4373 23.9315i 0.122470 0.0569798i
\(421\) −138.782 −0.329649 −0.164825 0.986323i \(-0.552706\pi\)
−0.164825 + 0.986323i \(0.552706\pi\)
\(422\) 277.575 480.775i 0.657762 1.13928i
\(423\) 217.424 125.530i 0.514004 0.296760i
\(424\) −96.3278 166.845i −0.227188 0.393501i
\(425\) −42.2633 24.4007i −0.0994431 0.0574135i
\(426\) 251.466i 0.590296i
\(427\) 140.930 200.900i 0.330048 0.470491i
\(428\) 531.099 1.24089
\(429\) −39.3931 + 68.2309i −0.0918255 + 0.159046i
\(430\) −47.2379 + 27.2728i −0.109855 + 0.0634251i
\(431\) 393.063 + 680.805i 0.911979 + 1.57959i 0.811265 + 0.584678i \(0.198779\pi\)
0.100714 + 0.994915i \(0.467887\pi\)
\(432\) −244.841 141.359i −0.566761 0.327220i
\(433\) 571.792i 1.32054i −0.751030 0.660268i \(-0.770443\pi\)
0.751030 0.660268i \(-0.229557\pi\)
\(434\) −933.964 82.5246i −2.15199 0.190149i
\(435\) −95.6579 −0.219903
\(436\) 86.8514 150.431i 0.199200 0.345025i
\(437\) −224.105 + 129.387i −0.512827 + 0.296081i
\(438\) 54.3237 + 94.0914i 0.124027 + 0.214821i
\(439\) −518.777 299.516i −1.18172 0.682269i −0.225311 0.974287i \(-0.572340\pi\)
−0.956413 + 0.292018i \(0.905673\pi\)
\(440\) 98.2659i 0.223332i
\(441\) 260.989 309.945i 0.591812 0.702823i
\(442\) 76.6466 0.173409
\(443\) −142.116 + 246.151i −0.320802 + 0.555646i −0.980654 0.195750i \(-0.937286\pi\)
0.659851 + 0.751396i \(0.270619\pi\)
\(444\) −9.25746 + 5.34480i −0.0208501 + 0.0120378i
\(445\) 185.370 + 321.070i 0.416561 + 0.721505i
\(446\) −409.408 236.372i −0.917955 0.529982i
\(447\) 40.5197i 0.0906480i
\(448\) 16.0717 181.890i 0.0358744 0.406005i
\(449\) −170.899 −0.380622 −0.190311 0.981724i \(-0.560950\pi\)
−0.190311 + 0.981724i \(0.560950\pi\)
\(450\) −157.378 + 272.587i −0.349729 + 0.605748i
\(451\) −59.1711 + 34.1625i −0.131200 + 0.0757483i
\(452\) 115.017 + 199.215i 0.254462 + 0.440741i
\(453\) 148.539 + 85.7591i 0.327901 + 0.189314i
\(454\) 720.579i 1.58718i
\(455\) −160.631 112.682i −0.353034 0.247652i
\(456\) −60.4808 −0.132633
\(457\) 356.186 616.932i 0.779401 1.34996i −0.152887 0.988244i \(-0.548857\pi\)
0.932288 0.361718i \(-0.117810\pi\)
\(458\) −819.765 + 473.291i −1.78988 + 1.03339i
\(459\) −24.8973 43.1234i −0.0542424 0.0939507i
\(460\) 85.2170 + 49.2001i 0.185254 + 0.106957i
\(461\) 172.115i 0.373352i −0.982422 0.186676i \(-0.940228\pi\)
0.982422 0.186676i \(-0.0597715\pi\)
\(462\) 70.8618 + 152.307i 0.153380 + 0.329669i
\(463\) −151.835 −0.327937 −0.163968 0.986466i \(-0.552429\pi\)
−0.163968 + 0.986466i \(0.552429\pi\)
\(464\) −330.174 + 571.878i −0.711582 + 1.23250i
\(465\) 122.320 70.6212i 0.263053 0.151874i
\(466\) −468.992 812.318i −1.00642 1.74317i
\(467\) −429.229 247.815i −0.919119 0.530654i −0.0357654 0.999360i \(-0.511387\pi\)
−0.883354 + 0.468706i \(0.844720\pi\)
\(468\) 208.656i 0.445845i
\(469\) −159.829 + 74.3612i −0.340786 + 0.158553i
\(470\) −259.215 −0.551521
\(471\) −50.5989 + 87.6398i −0.107429 + 0.186072i
\(472\) −8.38291 + 4.83988i −0.0177604 + 0.0102540i
\(473\) −34.0853 59.0375i −0.0720620 0.124815i
\(474\) −148.068 85.4871i −0.312380 0.180352i
\(475\) 360.728i 0.759427i
\(476\) 39.6127 56.4689i 0.0832200 0.118632i
\(477\) −561.415 −1.17697
\(478\) 261.359 452.688i 0.546777 0.947045i
\(479\) −580.212 + 334.986i −1.21130 + 0.699344i −0.963042 0.269350i \(-0.913191\pi\)
−0.248257 + 0.968694i \(0.579858\pi\)
\(480\) 54.1429 + 93.7782i 0.112798 + 0.195371i
\(481\) 32.0178 + 18.4855i 0.0665650 + 0.0384313i
\(482\) 223.206i 0.463084i
\(483\) −61.8658 5.46643i −0.128087 0.0113177i
\(484\) −20.8561 −0.0430911
\(485\) −29.0519 + 50.3194i −0.0599009 + 0.103751i
\(486\) −423.085 + 244.268i −0.870546 + 0.502610i
\(487\) −406.384 703.877i −0.834463 1.44533i −0.894467 0.447135i \(-0.852444\pi\)
0.0600030 0.998198i \(-0.480889\pi\)
\(488\) 86.1535 + 49.7408i 0.176544 + 0.101928i
\(489\) 66.8083i 0.136622i
\(490\) −393.372 + 142.406i −0.802801 + 0.290625i
\(491\) 436.038 0.888062 0.444031 0.896011i \(-0.353548\pi\)
0.444031 + 0.896011i \(0.353548\pi\)
\(492\) −7.99537 + 13.8484i −0.0162507 + 0.0281471i
\(493\) −100.724 + 58.1529i −0.204308 + 0.117957i
\(494\) −283.276 490.648i −0.573433 0.993215i
\(495\) 247.991 + 143.178i 0.500993 + 0.289248i
\(496\) 975.028i 1.96578i
\(497\) 68.8902 779.659i 0.138612 1.56873i
\(498\) 217.942 0.437634
\(499\) −100.403 + 173.903i −0.201208 + 0.348503i −0.948918 0.315523i \(-0.897820\pi\)
0.747710 + 0.664026i \(0.231153\pi\)
\(500\) 324.055 187.093i 0.648110 0.374187i
\(501\) −69.2824 120.001i −0.138288 0.239522i
\(502\) 247.449 + 142.865i 0.492926 + 0.284591i
\(503\) 290.866i 0.578261i −0.957290 0.289131i \(-0.906634\pi\)
0.957290 0.289131i \(-0.0933662\pi\)
\(504\) 134.471 + 94.3307i 0.266807 + 0.187164i
\(505\) 40.3163 0.0798342
\(506\) −145.683 + 252.330i −0.287910 + 0.498675i
\(507\) −69.8845 + 40.3478i −0.137839 + 0.0795815i
\(508\) 270.067 + 467.770i 0.531628 + 0.920806i
\(509\) 275.851 + 159.263i 0.541948 + 0.312894i 0.745868 0.666094i \(-0.232035\pi\)
−0.203920 + 0.978988i \(0.565368\pi\)
\(510\) 24.6183i 0.0482712i
\(511\) −142.651 306.608i −0.279161 0.600016i
\(512\) 530.143 1.03544
\(513\) −184.034 + 318.756i −0.358741 + 0.621358i
\(514\) 411.456 237.554i 0.800498 0.462168i
\(515\) −18.7469 32.4706i −0.0364018 0.0630497i
\(516\) −13.8171 7.97731i −0.0267773 0.0154599i
\(517\) 323.965i 0.626624i
\(518\) 71.4710 33.2523i 0.137975 0.0641937i
\(519\) −81.8403 −0.157688
\(520\) 39.7705 68.8846i 0.0764818 0.132470i
\(521\) −475.647 + 274.615i −0.912950 + 0.527092i −0.881379 0.472410i \(-0.843384\pi\)
−0.0315708 + 0.999502i \(0.510051\pi\)
\(522\) 375.070 + 649.640i 0.718525 + 1.24452i
\(523\) 66.5620 + 38.4296i 0.127270 + 0.0734792i 0.562283 0.826945i \(-0.309923\pi\)
−0.435014 + 0.900424i \(0.643256\pi\)
\(524\) 124.241i 0.237101i
\(525\) −49.7192 + 70.8760i −0.0947033 + 0.135002i
\(526\) −182.760 −0.347452
\(527\) 85.8649 148.722i 0.162931 0.282206i
\(528\) −151.286 + 87.3449i −0.286526 + 0.165426i
\(529\) 210.639 + 364.837i 0.398183 + 0.689672i
\(530\) 501.994 + 289.827i 0.947159 + 0.546843i
\(531\) 28.2077i 0.0531218i
\(532\) −507.885 44.8765i −0.954671 0.0843542i
\(533\) 55.3054 0.103762
\(534\) −128.461 + 222.500i −0.240563 + 0.416667i
\(535\) 510.941 294.992i 0.955029 0.551386i
\(536\) −35.7305 61.8870i −0.0666613 0.115461i
\(537\) 214.528 + 123.858i 0.399493 + 0.230648i
\(538\) 881.022i 1.63759i
\(539\) −177.978 491.634i −0.330201 0.912122i
\(540\) 139.960 0.259184
\(541\) −473.959 + 820.922i −0.876080 + 1.51742i −0.0204724 + 0.999790i \(0.506517\pi\)
−0.855608 + 0.517625i \(0.826816\pi\)
\(542\) 683.563 394.655i 1.26119 0.728146i
\(543\) −137.458 238.084i −0.253146 0.438461i
\(544\) 114.020 + 65.8297i 0.209596 + 0.121010i
\(545\) 192.962i 0.354058i
\(546\) 11.9680 135.447i 0.0219194 0.248071i
\(547\) −124.560 −0.227714 −0.113857 0.993497i \(-0.536321\pi\)
−0.113857 + 0.993497i \(0.536321\pi\)
\(548\) 103.800 179.787i 0.189416 0.328079i
\(549\) 251.059 144.949i 0.457302 0.264024i
\(550\) 203.079 + 351.744i 0.369235 + 0.639534i
\(551\) 744.523 + 429.851i 1.35122 + 0.780128i
\(552\) 25.1770i 0.0456105i
\(553\) 435.658 + 305.612i 0.787809 + 0.552645i
\(554\) 377.589 0.681568
\(555\) −5.93739 + 10.2839i −0.0106980 + 0.0185295i
\(556\) −575.180 + 332.080i −1.03450 + 0.597267i
\(557\) 30.1591 + 52.2371i 0.0541456 + 0.0937829i 0.891828 0.452375i \(-0.149423\pi\)
−0.837682 + 0.546158i \(0.816090\pi\)
\(558\) −959.218 553.805i −1.71903 0.992481i
\(559\) 55.1805i 0.0987129i
\(560\) −183.521 394.452i −0.327716 0.704378i
\(561\) −30.7678 −0.0548445
\(562\) 256.208 443.765i 0.455886 0.789618i
\(563\) 175.101 101.094i 0.311014 0.179564i −0.336366 0.941731i \(-0.609198\pi\)
0.647380 + 0.762167i \(0.275865\pi\)
\(564\) −37.9103 65.6625i −0.0672168 0.116423i
\(565\) 221.303 + 127.769i 0.391686 + 0.226140i
\(566\) 1011.77i 1.78757i
\(567\) 392.249 182.496i 0.691796 0.321863i
\(568\) 317.291 0.558611
\(569\) −96.8566 + 167.760i −0.170222 + 0.294834i −0.938498 0.345286i \(-0.887782\pi\)
0.768275 + 0.640120i \(0.221115\pi\)
\(570\) 157.592 90.9860i 0.276478 0.159625i
\(571\) 340.375 + 589.547i 0.596104 + 1.03248i 0.993390 + 0.114787i \(0.0366187\pi\)
−0.397286 + 0.917695i \(0.630048\pi\)
\(572\) −233.175 134.624i −0.407649 0.235356i
\(573\) 180.700i 0.315358i
\(574\) 67.7194 96.5357i 0.117978 0.168181i
\(575\) −150.164 −0.261155
\(576\) 107.854 186.808i 0.187246 0.324320i
\(577\) 636.220 367.322i 1.10263 0.636606i 0.165723 0.986172i \(-0.447004\pi\)
0.936912 + 0.349566i \(0.113671\pi\)
\(578\) −365.192 632.531i −0.631820 1.09434i
\(579\) 134.090 + 77.4170i 0.231589 + 0.133708i
\(580\) 326.905i 0.563630i
\(581\) −675.717 59.7060i −1.16302 0.102764i
\(582\) −40.2658 −0.0691852
\(583\) −362.223 + 627.389i −0.621309 + 1.07614i
\(584\) 118.721 68.5438i 0.203290 0.117369i
\(585\) −115.895 200.736i −0.198111 0.343138i
\(586\) 894.345 + 516.351i 1.52619 + 0.881144i
\(587\) 462.339i 0.787631i 0.919190 + 0.393815i \(0.128845\pi\)
−0.919190 + 0.393815i \(0.871155\pi\)
\(588\) −93.6043 78.8194i −0.159191 0.134047i
\(589\) −1269.38 −2.15515
\(590\) 14.5620 25.2221i 0.0246813 0.0427493i
\(591\) −53.5506 + 30.9174i −0.0906101 + 0.0523138i
\(592\) 40.9871 + 70.9918i 0.0692350 + 0.119919i
\(593\) −44.0297 25.4206i −0.0742491 0.0428677i 0.462416 0.886663i \(-0.346983\pi\)
−0.536665 + 0.843795i \(0.680316\pi\)
\(594\) 414.424i 0.697683i
\(595\) 6.74429 76.3279i 0.0113349 0.128282i
\(596\) 138.474 0.232338
\(597\) 101.086 175.086i 0.169324 0.293277i
\(598\) 204.247 117.922i 0.341551 0.197194i
\(599\) 232.893 + 403.383i 0.388803 + 0.673427i 0.992289 0.123947i \(-0.0395552\pi\)
−0.603485 + 0.797374i \(0.706222\pi\)
\(600\) −30.3944 17.5482i −0.0506573 0.0292470i
\(601\) 764.479i 1.27201i 0.771684 + 0.636006i \(0.219415\pi\)
−0.771684 + 0.636006i \(0.780585\pi\)
\(602\) 96.3177 + 67.5665i 0.159996 + 0.112237i
\(603\) −208.244 −0.345346
\(604\) −293.077 + 507.624i −0.485226 + 0.840437i
\(605\) −20.0645 + 11.5842i −0.0331644 + 0.0191475i
\(606\) 13.9695 + 24.1959i 0.0230520 + 0.0399272i
\(607\) −536.851 309.951i −0.884433 0.510628i −0.0123157 0.999924i \(-0.503920\pi\)
−0.872118 + 0.489296i \(0.837254\pi\)
\(608\) 973.191i 1.60064i
\(609\) 87.0379 + 187.075i 0.142919 + 0.307184i
\(610\) −299.315 −0.490681
\(611\) −131.116 + 227.100i −0.214593 + 0.371685i
\(612\) 70.5677 40.7423i 0.115307 0.0665724i
\(613\) 428.807 + 742.715i 0.699522 + 1.21161i 0.968632 + 0.248498i \(0.0799369\pi\)
−0.269111 + 0.963109i \(0.586730\pi\)
\(614\) −553.302 319.449i −0.901144 0.520275i
\(615\) 17.7637i 0.0288840i
\(616\) 192.176 89.4109i 0.311974 0.145148i
\(617\) 272.951 0.442384 0.221192 0.975230i \(-0.429005\pi\)
0.221192 + 0.975230i \(0.429005\pi\)
\(618\) 12.9916 22.5020i 0.0210219 0.0364110i
\(619\) 405.926 234.362i 0.655778 0.378613i −0.134889 0.990861i \(-0.543068\pi\)
0.790666 + 0.612247i \(0.209734\pi\)
\(620\) 241.344 + 418.020i 0.389264 + 0.674226i
\(621\) −132.692 76.6099i −0.213675 0.123365i
\(622\) 1301.33i 2.09217i
\(623\) 459.241 654.659i 0.737144 1.05082i
\(624\) 141.402 0.226606
\(625\) 26.9853 46.7399i 0.0431764 0.0747838i
\(626\) −605.727 + 349.717i −0.967615 + 0.558653i
\(627\) 113.714 + 196.958i 0.181361 + 0.314127i
\(628\) −299.504 172.919i −0.476917 0.275348i
\(629\) 14.4380i 0.0229538i
\(630\) −492.294 43.4988i −0.781419 0.0690457i
\(631\) 817.942 1.29626 0.648132 0.761528i \(-0.275551\pi\)
0.648132 + 0.761528i \(0.275551\pi\)
\(632\) −107.865 + 186.827i −0.170672 + 0.295612i
\(633\) 156.219 90.1929i 0.246791 0.142485i
\(634\) −805.043 1394.38i −1.26978 2.19933i
\(635\) 519.632 + 300.010i 0.818318 + 0.472456i
\(636\) 169.549i 0.266586i
\(637\) −74.2125 + 416.668i −0.116503 + 0.654110i
\(638\) 967.975 1.51720
\(639\) 462.308 800.740i 0.723486 1.25311i
\(640\) 245.931 141.988i 0.384267 0.221856i
\(641\) 246.502 + 426.954i 0.384559 + 0.666075i 0.991708 0.128513i \(-0.0410203\pi\)
−0.607149 + 0.794588i \(0.707687\pi\)
\(642\) 354.080 + 204.428i 0.551527 + 0.318424i
\(643\) 13.7996i 0.0214613i 0.999942 + 0.0107307i \(0.00341574\pi\)
−0.999942 + 0.0107307i \(0.996584\pi\)
\(644\) 18.6812 211.423i 0.0290081 0.328296i
\(645\) −17.7235 −0.0274784
\(646\) 110.625 191.609i 0.171247 0.296608i
\(647\) 523.870 302.456i 0.809691 0.467475i −0.0371577 0.999309i \(-0.511830\pi\)
0.846848 + 0.531834i \(0.178497\pi\)
\(648\) 87.6891 + 151.882i 0.135323 + 0.234386i
\(649\) 31.5224 + 18.1995i 0.0485707 + 0.0280423i
\(650\) 328.764i 0.505791i
\(651\) −249.409 174.959i −0.383116 0.268755i
\(652\) 228.314 0.350174
\(653\) −204.388 + 354.010i −0.312999 + 0.542129i −0.979010 0.203812i \(-0.934667\pi\)
0.666012 + 0.745941i \(0.268000\pi\)
\(654\) 115.806 66.8609i 0.177074 0.102234i
\(655\) −69.0078 119.525i −0.105355 0.182481i
\(656\) 106.198 + 61.3133i 0.161887 + 0.0934654i
\(657\) 399.485i 0.608045i
\(658\) 235.856 + 506.939i 0.358444 + 0.770424i
\(659\) −427.176 −0.648219 −0.324110 0.946020i \(-0.605065\pi\)
−0.324110 + 0.946020i \(0.605065\pi\)
\(660\) 43.2401 74.8941i 0.0655153 0.113476i
\(661\) 533.521 308.028i 0.807142 0.466003i −0.0388207 0.999246i \(-0.512360\pi\)
0.845962 + 0.533243i \(0.179027\pi\)
\(662\) 26.5818 + 46.0411i 0.0401538 + 0.0695485i
\(663\) 21.5682 + 12.4524i 0.0325313 + 0.0187820i
\(664\) 274.991i 0.414143i
\(665\) −513.534 + 238.925i −0.772231 + 0.359285i
\(666\) 93.1208 0.139821
\(667\) −178.939 + 309.931i −0.268274 + 0.464664i
\(668\) 410.095 236.769i 0.613915 0.354444i
\(669\) −76.8045 133.029i −0.114805 0.198848i
\(670\) 186.203 + 107.504i 0.277915 + 0.160454i
\(671\) 374.082i 0.557499i
\(672\) 134.135 191.213i 0.199606 0.284543i
\(673\) −383.624 −0.570021 −0.285011 0.958524i \(-0.591997\pi\)
−0.285011 + 0.958524i \(0.591997\pi\)
\(674\) −419.610 + 726.787i −0.622567 + 1.07832i
\(675\) −184.971 + 106.793i −0.274031 + 0.158212i
\(676\) −137.886 238.826i −0.203974 0.353293i
\(677\) 977.315 + 564.253i 1.44360 + 0.833461i 0.998088 0.0618160i \(-0.0196892\pi\)
0.445510 + 0.895277i \(0.353023\pi\)
\(678\) 177.087i 0.261190i
\(679\) 124.842 + 11.0310i 0.183862 + 0.0162459i
\(680\) 31.0625 0.0456802
\(681\) −117.069 + 202.770i −0.171908 + 0.297753i
\(682\) −1237.77 + 714.625i −1.81491 + 1.04784i
\(683\) 363.784 + 630.092i 0.532626 + 0.922535i 0.999274 + 0.0380923i \(0.0121281\pi\)
−0.466648 + 0.884443i \(0.654539\pi\)
\(684\) −521.618 301.156i −0.762599 0.440287i
\(685\) 230.618i 0.336668i
\(686\) 636.425 + 639.733i 0.927733 + 0.932555i
\(687\) −307.574 −0.447706
\(688\) −61.1748 + 105.958i −0.0889169 + 0.154009i
\(689\) 507.838 293.200i 0.737065 0.425544i
\(690\) 37.8757 + 65.6027i 0.0548924 + 0.0950764i
\(691\) −19.5488 11.2865i −0.0282906 0.0163336i 0.485788 0.874077i \(-0.338533\pi\)
−0.514079 + 0.857743i \(0.671866\pi\)
\(692\) 279.684i 0.404168i
\(693\) 54.3645 615.265i 0.0784480 0.887828i
\(694\) 693.346 0.999057
\(695\) −368.899 + 638.952i −0.530790 + 0.919355i
\(696\) −72.4372 + 41.8216i −0.104076 + 0.0600885i
\(697\) 10.7990 + 18.7044i 0.0154935 + 0.0268356i
\(698\) 200.060 + 115.505i 0.286619 + 0.165480i
\(699\) 304.780i 0.436023i
\(700\) −242.215 169.913i −0.346021 0.242732i
\(701\) −226.918 −0.323707 −0.161853 0.986815i \(-0.551747\pi\)
−0.161853 + 0.986815i \(0.551747\pi\)
\(702\) 167.727 290.512i 0.238927 0.413834i
\(703\) 92.4236 53.3608i 0.131470 0.0759044i
\(704\) −139.174 241.056i −0.197690 0.342409i
\(705\) −72.9427 42.1135i −0.103465 0.0597354i
\(706\) 1273.39i 1.80367i
\(707\) −36.6832 78.8453i −0.0518858 0.111521i
\(708\) 8.51879 0.0120322
\(709\) −528.978 + 916.217i −0.746090 + 1.29227i 0.203593 + 0.979056i \(0.434738\pi\)
−0.949684 + 0.313211i \(0.898595\pi\)
\(710\) −826.753 + 477.326i −1.16444 + 0.672290i
\(711\) 314.327 + 544.431i 0.442092 + 0.765725i
\(712\) 280.743 + 162.087i 0.394302 + 0.227650i
\(713\) 528.419i 0.741121i
\(714\) 48.1453 22.3999i 0.0674304 0.0313724i
\(715\) −299.100 −0.418321
\(716\) −423.277 + 733.137i −0.591168 + 1.02393i
\(717\) 147.092 84.9238i 0.205150 0.118443i
\(718\) 548.570 + 950.151i 0.764025 + 1.32333i
\(719\) −955.001 551.370i −1.32823 0.766857i −0.343208 0.939259i \(-0.611514\pi\)
−0.985027 + 0.172403i \(0.944847\pi\)
\(720\) 513.938i 0.713803i
\(721\) −46.4442 + 66.2074i −0.0644164 + 0.0918271i
\(722\) −685.690 −0.949709
\(723\) 36.2633 62.8100i 0.0501568 0.0868741i
\(724\) 813.640 469.755i 1.12381 0.648833i
\(725\) 249.438 + 432.039i 0.344052 + 0.595916i
\(726\) −13.9046 8.02784i −0.0191524 0.0110576i
\(727\) 323.401i 0.444843i 0.974951 + 0.222422i \(0.0713961\pi\)
−0.974951 + 0.222422i \(0.928604\pi\)
\(728\) −170.902 15.1008i −0.234756 0.0207429i
\(729\) 397.490 0.545254
\(730\) −206.231 + 357.203i −0.282509 + 0.489319i
\(731\) −18.6622 + 10.7746i −0.0255296 + 0.0147395i
\(732\) −43.7750 75.8205i −0.0598019 0.103580i
\(733\) 726.564 + 419.482i 0.991220 + 0.572281i 0.905639 0.424050i \(-0.139392\pi\)
0.0855813 + 0.996331i \(0.472725\pi\)
\(734\) 608.094i 0.828465i
\(735\) −133.831 23.8365i −0.182082 0.0324306i
\(736\) 405.121 0.550436
\(737\) −134.358 + 232.715i −0.182304 + 0.315759i
\(738\) 120.638 69.6505i 0.163466 0.0943773i
\(739\) 148.154 + 256.611i 0.200479 + 0.347240i 0.948683 0.316229i \(-0.102417\pi\)
−0.748204 + 0.663469i \(0.769083\pi\)
\(740\) −35.1445 20.2907i −0.0474926 0.0274198i
\(741\) 184.090i 0.248435i
\(742\) 110.047 1245.44i 0.148311 1.67850i
\(743\) 419.334 0.564379 0.282190 0.959359i \(-0.408939\pi\)
0.282190 + 0.959359i \(0.408939\pi\)
\(744\) 61.7511 106.956i 0.0829988 0.143758i
\(745\) 133.218 76.9132i 0.178816 0.103239i
\(746\) −227.249 393.607i −0.304624 0.527624i
\(747\) −693.988 400.674i −0.929033 0.536378i
\(748\) 105.147i 0.140571i
\(749\) −1041.80 730.822i −1.39093 0.975730i
\(750\) 288.060 0.384081
\(751\) −683.529 + 1183.91i −0.910158 + 1.57644i −0.0963185 + 0.995351i \(0.530707\pi\)
−0.813840 + 0.581090i \(0.802627\pi\)
\(752\) −503.540 + 290.719i −0.669600 + 0.386594i
\(753\) 46.4211 + 80.4038i 0.0616483 + 0.106778i
\(754\) −678.552 391.762i −0.899936 0.519578i
\(755\) 651.142i 0.862439i
\(756\) −127.347 273.715i −0.168449 0.362057i
\(757\) −850.445 −1.12344 −0.561720 0.827327i \(-0.689860\pi\)
−0.561720 + 0.827327i \(0.689860\pi\)
\(758\) −744.297 + 1289.16i −0.981922 + 1.70074i
\(759\) −81.9897 + 47.3368i −0.108023 + 0.0623673i
\(760\) −114.803 198.845i −0.151057 0.261638i
\(761\) −1303.98 752.856i −1.71351 0.989298i −0.929712 0.368286i \(-0.879945\pi\)
−0.783801 0.621011i \(-0.786722\pi\)
\(762\) 415.812i 0.545685i
\(763\) −377.369 + 175.573i −0.494586 + 0.230109i
\(764\) −617.533 −0.808289
\(765\) 45.2595 78.3917i 0.0591627 0.102473i
\(766\) 730.333 421.658i 0.953437 0.550467i
\(767\) −14.7315 25.5157i −0.0192066 0.0332669i
\(768\) 247.676 + 142.996i 0.322494 + 0.186192i
\(769\) 240.121i 0.312251i 0.987737 + 0.156126i \(0.0499004\pi\)
−0.987737 + 0.156126i \(0.950100\pi\)
\(770\) −366.236 + 522.079i −0.475632 + 0.678025i
\(771\) 154.377 0.200230
\(772\) −264.568 + 458.245i −0.342705 + 0.593582i
\(773\) −351.926 + 203.184i −0.455273 + 0.262852i −0.710054 0.704147i \(-0.751330\pi\)
0.254782 + 0.966999i \(0.417996\pi\)
\(774\) 69.4932 + 120.366i 0.0897844 + 0.155511i
\(775\) −637.921 368.304i −0.823124 0.475231i
\(776\) 50.8059i 0.0654716i
\(777\) 25.5142 + 2.25442i 0.0328368 + 0.00290144i
\(778\) −544.566 −0.699956
\(779\) 79.8232 138.258i 0.102469 0.177481i
\(780\) −60.6228 + 35.0006i −0.0777215 + 0.0448725i
\(781\) −596.558 1033.27i −0.763839 1.32301i
\(782\) 79.7631 + 46.0513i 0.101999 + 0.0588891i
\(783\) 509.027i 0.650099i
\(784\) −604.434 + 717.814i −0.770962 + 0.915579i
\(785\) −384.181 −0.489403
\(786\) 47.8222 82.8305i 0.0608425 0.105382i
\(787\) 396.123 228.702i 0.503333 0.290600i −0.226756 0.973952i \(-0.572812\pi\)
0.730089 + 0.683352i \(0.239479\pi\)
\(788\) −105.659 183.006i −0.134084 0.232241i
\(789\) −51.4283 29.6921i −0.0651816 0.0376326i
\(790\) 649.076i 0.821616i
\(791\) 48.5138 549.050i 0.0613322 0.694122i
\(792\) 250.389 0.316148
\(793\) −151.400 + 262.232i −0.190920 + 0.330684i
\(794\) −927.234 + 535.339i −1.16780 + 0.674230i
\(795\) 94.1736 + 163.114i 0.118457 + 0.205174i
\(796\) 598.347 + 345.456i 0.751693 + 0.433990i
\(797\) 980.899i 1.23074i 0.788239 + 0.615369i \(0.210993\pi\)
−0.788239 + 0.615369i \(0.789007\pi\)
\(798\) −321.330 225.412i −0.402669 0.282471i
\(799\) −102.407 −0.128170
\(800\) 282.366 489.073i 0.352958 0.611341i
\(801\) 818.110 472.336i 1.02136 0.589683i
\(802\) 767.879 + 1330.01i 0.957455 + 1.65836i
\(803\) −446.430 257.746i −0.555952 0.320979i
\(804\) 62.8901i 0.0782216i
\(805\) −99.4598 213.774i −0.123553 0.265558i
\(806\) 1156.90 1.43536
\(807\) 143.136 247.918i 0.177368 0.307210i
\(808\) 30.5296 17.6263i 0.0377841 0.0218147i
\(809\) 687.444 + 1190.69i 0.849746 + 1.47180i 0.881435 + 0.472305i \(0.156578\pi\)
−0.0316893 + 0.999498i \(0.510089\pi\)
\(810\) −456.976 263.835i −0.564167 0.325722i
\(811\) 224.419i 0.276718i 0.990382 + 0.138359i \(0.0441828\pi\)
−0.990382 + 0.138359i \(0.955817\pi\)
\(812\) −639.319 + 297.447i −0.787339 + 0.366314i
\(813\) 256.471 0.315463
\(814\) 60.0812 104.064i 0.0738098 0.127842i
\(815\) 219.648 126.814i 0.269506 0.155600i
\(816\) 27.6103 + 47.8225i 0.0338362 + 0.0586060i
\(817\) 137.946 + 79.6430i 0.168844 + 0.0974822i
\(818\) 1121.92i 1.37154i
\(819\) −287.122 + 409.299i −0.350576 + 0.499755i
\(820\) −60.7063 −0.0740321
\(821\) −247.168 + 428.107i −0.301057 + 0.521446i −0.976376 0.216080i \(-0.930673\pi\)
0.675319 + 0.737526i \(0.264006\pi\)
\(822\) 138.406 79.9086i 0.168377 0.0972124i
\(823\) 586.983 + 1016.68i 0.713223 + 1.23534i 0.963641 + 0.267201i \(0.0860988\pi\)
−0.250417 + 0.968138i \(0.580568\pi\)
\(824\) −28.3923 16.3923i −0.0344566 0.0198936i
\(825\) 131.974i 0.159968i
\(826\) −62.5759 5.52917i −0.0757578 0.00669391i
\(827\) −444.014 −0.536898 −0.268449 0.963294i \(-0.586511\pi\)
−0.268449 + 0.963294i \(0.586511\pi\)
\(828\) 125.366 217.140i 0.151408 0.262246i
\(829\) 251.653 145.292i 0.303563 0.175262i −0.340480 0.940252i \(-0.610589\pi\)
0.644042 + 0.764990i \(0.277256\pi\)
\(830\) 413.690 + 716.533i 0.498422 + 0.863292i
\(831\) 106.253 + 61.3451i 0.127861 + 0.0738208i
\(832\) 225.308i 0.270802i
\(833\) −155.409 + 56.2602i −0.186565 + 0.0675392i
\(834\) −511.291 −0.613059
\(835\) 263.020 455.564i 0.314994 0.545585i
\(836\) −673.092 + 388.610i −0.805134 + 0.464844i
\(837\) −375.799 650.903i −0.448983 0.777661i
\(838\) 1746.20 + 1008.17i 2.08377 + 1.20307i
\(839\) 52.3089i 0.0623467i 0.999514 + 0.0311733i \(0.00992439\pi\)
−0.999514 + 0.0311733i \(0.990076\pi\)
\(840\) 4.85027 54.8925i 0.00577413 0.0653482i
\(841\) 347.942 0.413724
\(842\) 182.558 316.200i 0.216815 0.375534i
\(843\) 144.193 83.2499i 0.171048 0.0987543i
\(844\) 308.229 + 533.868i 0.365200 + 0.632545i
\(845\) −265.305 153.174i −0.313971 0.181271i
\(846\) 660.499i 0.780732i
\(847\) 40.9114 + 28.6992i 0.0483015 + 0.0338833i
\(848\) 1300.20 1.53326
\(849\) 164.377 284.710i 0.193613 0.335347i
\(850\) 111.189 64.1948i 0.130810 0.0755233i
\(851\) 22.2131 + 38.4742i 0.0261023 + 0.0452105i
\(852\) −241.826 139.618i −0.283833 0.163871i
\(853\) 992.792i 1.16388i 0.813231 + 0.581941i \(0.197707\pi\)
−0.813231 + 0.581941i \(0.802293\pi\)
\(854\) 272.343 + 585.362i 0.318903 + 0.685436i
\(855\) −669.092 −0.782564
\(856\) 257.941 446.766i 0.301332 0.521923i
\(857\) −342.250 + 197.598i −0.399358 + 0.230570i −0.686207 0.727406i \(-0.740726\pi\)
0.286849 + 0.957976i \(0.407392\pi\)
\(858\) −103.638 179.505i −0.120790 0.209214i
\(859\) −736.922 425.462i −0.857884 0.495300i 0.00541904 0.999985i \(-0.498275\pi\)
−0.863303 + 0.504686i \(0.831608\pi\)
\(860\) 60.5692i 0.0704293i
\(861\) 34.7399 16.1629i 0.0403483 0.0187723i
\(862\) −2068.18 −2.39928
\(863\) −166.810 + 288.924i −0.193291 + 0.334790i −0.946339 0.323176i \(-0.895249\pi\)
0.753048 + 0.657966i \(0.228583\pi\)
\(864\) 499.025 288.112i 0.577575 0.333463i
\(865\) −155.347 269.069i −0.179592 0.311062i
\(866\) 1302.76 + 752.150i 1.50434 + 0.868533i
\(867\) 237.324i 0.273731i
\(868\) 597.913 852.340i 0.688840 0.981959i
\(869\) 811.211 0.933499
\(870\) 125.831 217.946i 0.144633 0.250512i
\(871\) 188.370 108.756i 0.216269 0.124863i
\(872\) −84.3627 146.121i −0.0967463 0.167569i
\(873\) 128.218 + 74.0265i 0.146870 + 0.0847956i
\(874\) 680.797i 0.778944i
\(875\) −893.118 78.9154i −1.02071 0.0901890i
\(876\) −120.646 −0.137723
\(877\) 563.918 976.734i 0.643008 1.11372i −0.341750 0.939791i \(-0.611020\pi\)
0.984758 0.173931i \(-0.0556471\pi\)
\(878\) 1364.83 787.982i 1.55447 0.897474i
\(879\) 167.778 + 290.601i 0.190874 + 0.330604i
\(880\) −574.333 331.591i −0.652651 0.376808i
\(881\) 1303.89i 1.48002i −0.672598 0.740008i \(-0.734822\pi\)
0.672598 0.740008i \(-0.265178\pi\)
\(882\) 362.863 + 1002.34i 0.411409 + 1.13644i
\(883\) 692.546 0.784310 0.392155 0.919899i \(-0.371730\pi\)
0.392155 + 0.919899i \(0.371730\pi\)
\(884\) −42.5555 + 73.7083i −0.0481397 + 0.0833804i
\(885\) 8.19545 4.73164i 0.00926039 0.00534649i
\(886\) −373.885 647.588i −0.421992 0.730912i
\(887\) −786.305 453.973i −0.886477 0.511808i −0.0136885 0.999906i \(-0.504357\pi\)
−0.872789 + 0.488099i \(0.837691\pi\)
\(888\) 10.3833i 0.0116929i
\(889\) 113.913 1289.20i 0.128137 1.45017i
\(890\) −975.361 −1.09591
\(891\) 329.739 571.124i 0.370077 0.640993i
\(892\) 454.620 262.475i 0.509664 0.294255i
\(893\) 378.484 + 655.554i 0.423835 + 0.734103i
\(894\) 92.3194 + 53.3006i 0.103266 + 0.0596204i
\(895\) 940.412i 1.05074i
\(896\) −501.451 351.766i −0.559655 0.392596i
\(897\) 76.6332 0.0854328
\(898\) 224.805 389.374i 0.250340 0.433602i
\(899\) −1520.32 + 877.758i −1.69113 + 0.976372i
\(900\) −174.758 302.689i −0.194175 0.336321i
\(901\) 198.322 + 114.501i 0.220113 + 0.127082i
\(902\) 179.753i 0.199283i
\(903\) 16.1264 + 34.6614i 0.0178587 + 0.0383847i
\(904\) 223.442 0.247171
\(905\) 521.838 903.850i 0.576616 0.998729i
\(906\) −390.784 + 225.620i −0.431329 + 0.249028i
\(907\) −594.166 1029.13i −0.655090 1.13465i −0.981871 0.189549i \(-0.939297\pi\)
0.326782 0.945100i \(-0.394036\pi\)
\(908\) −692.954 400.077i −0.763165 0.440614i
\(909\) 102.729i 0.113013i
\(910\) 468.030 217.754i 0.514319 0.239290i
\(911\) 1096.66 1.20379 0.601897 0.798574i \(-0.294412\pi\)
0.601897 + 0.798574i \(0.294412\pi\)
\(912\) 204.088 353.491i 0.223781 0.387600i
\(913\) −895.517 + 517.027i −0.980851 + 0.566294i
\(914\) 937.073 + 1623.06i 1.02524 + 1.77577i
\(915\) −84.2269 48.6284i −0.0920513 0.0531458i
\(916\) 1051.12i 1.14751i
\(917\) −170.962 + 243.711i −0.186436 + 0.265770i
\(918\) 131.002 0.142704
\(919\) −371.006 + 642.601i −0.403706 + 0.699240i −0.994170 0.107825i \(-0.965612\pi\)
0.590464 + 0.807064i \(0.298945\pi\)
\(920\) 82.7752 47.7903i 0.0899730 0.0519460i
\(921\) −103.799 179.785i −0.112702 0.195206i
\(922\) 392.145 + 226.405i 0.425320 + 0.245559i
\(923\) 965.764i 1.04633i
\(924\) −185.812 16.4182i −0.201095 0.0177686i
\(925\) 61.9294 0.0669507
\(926\) 199.727 345.938i 0.215688 0.373583i
\(927\) −82.7376 + 47.7686i −0.0892531 + 0.0515303i
\(928\) −672.947 1165.58i −0.725159 1.25601i
\(929\) −616.054 355.679i −0.663136 0.382862i 0.130335 0.991470i \(-0.458395\pi\)
−0.793471 + 0.608608i \(0.791728\pi\)
\(930\) 371.588i 0.399557i
\(931\) 934.516 + 786.908i 1.00378 + 0.845229i
\(932\) 1041.57 1.11756
\(933\) −211.421 + 366.192i −0.226603 + 0.392489i
\(934\) 1129.24 651.966i 1.20903 0.698036i
\(935\) −58.4025 101.156i −0.0624626 0.108188i
\(936\) −175.523 101.338i −0.187525 0.108267i
\(937\) 71.4737i 0.0762793i 0.999272 + 0.0381397i \(0.0121432\pi\)
−0.999272 + 0.0381397i \(0.987857\pi\)
\(938\) 40.8192 461.968i 0.0435173 0.492503i
\(939\) −227.268 −0.242031
\(940\) 143.920 249.277i 0.153107 0.265189i
\(941\) 8.28924 4.78580i 0.00880897 0.00508586i −0.495589 0.868557i \(-0.665048\pi\)
0.504398 + 0.863471i \(0.331714\pi\)
\(942\) −133.118 230.568i −0.141314 0.244764i
\(943\) 57.5541 + 33.2289i 0.0610330 + 0.0352374i
\(944\) 65.3272i 0.0692025i
\(945\) −274.545 192.592i −0.290524 0.203801i
\(946\) 179.347 0.189584
\(947\) −99.0022 + 171.477i −0.104543 + 0.181074i −0.913551 0.406723i \(-0.866671\pi\)
0.809008 + 0.587797i \(0.200005\pi\)
\(948\) 164.420 94.9277i 0.173438 0.100135i
\(949\) 208.632 + 361.361i 0.219844 + 0.380781i
\(950\) −821.877 474.511i −0.865133 0.499485i
\(951\) 523.167i 0.550123i
\(952\) −28.2634 60.7481i −0.0296884 0.0638110i
\(953\) −255.788 −0.268403 −0.134201 0.990954i \(-0.542847\pi\)
−0.134201 + 0.990954i \(0.542847\pi\)
\(954\) 738.500 1279.12i 0.774109 1.34080i
\(955\) −594.093 + 343.000i −0.622087 + 0.359162i
\(956\) 290.222 + 502.679i 0.303580 + 0.525815i
\(957\) 272.387 + 157.263i 0.284626 + 0.164329i
\(958\) 1762.60i 1.83987i
\(959\) −451.012 + 209.836i −0.470294 + 0.218807i
\(960\) −72.3671 −0.0753824
\(961\) 815.542 1412.56i 0.848639 1.46989i
\(962\) −84.2340 + 48.6325i −0.0875613 + 0.0505536i
\(963\) −751.662 1301.92i −0.780542 1.35194i
\(964\) 214.649 + 123.928i 0.222665 + 0.128556i
\(965\) 587.803i 0.609122i
\(966\) 93.8346 133.763i 0.0971372 0.138472i
\(967\) 1114.91 1.15296 0.576479 0.817112i \(-0.304426\pi\)
0.576479 + 0.817112i \(0.304426\pi\)
\(968\) −10.1293 + 17.5444i −0.0104641 + 0.0181244i
\(969\) 62.2597 35.9456i 0.0642515 0.0370956i
\(970\) −76.4313 132.383i −0.0787952 0.136477i
\(971\) 75.7157 + 43.7145i 0.0779771 + 0.0450201i 0.538482 0.842637i \(-0.318998\pi\)
−0.460505 + 0.887657i \(0.652331\pi\)
\(972\) 542.487i 0.558115i
\(973\) 1585.23 + 140.070i 1.62922 + 0.143957i
\(974\) 2138.27 2.19535
\(975\) 53.4128 92.5137i 0.0547823 0.0948858i
\(976\) −581.437 + 335.693i −0.595735 + 0.343948i
\(977\) −375.495 650.376i −0.384334 0.665687i 0.607342 0.794440i \(-0.292236\pi\)
−0.991677 + 0.128754i \(0.958902\pi\)
\(978\) 152.215 + 87.8814i 0.155639 + 0.0898583i
\(979\) 1219.00i 1.24515i
\(980\) 81.4598 457.358i 0.0831222 0.466692i
\(981\) −491.681 −0.501204
\(982\) −573.576 + 993.463i −0.584090 + 1.01167i
\(983\) 1418.51 818.974i 1.44304 0.833138i 0.444986 0.895538i \(-0.353209\pi\)
0.998051 + 0.0623999i \(0.0198754\pi\)
\(984\) 7.76627 + 13.4516i 0.00789255 + 0.0136703i
\(985\) −203.296 117.373i −0.206392 0.119161i
\(986\) 305.983i 0.310328i
\(987\) −15.9904 + 180.970i −0.0162010 + 0.183354i
\(988\) 629.118 0.636759
\(989\) −33.1538 + 57.4241i −0.0335226 + 0.0580628i
\(990\) −652.429 + 376.680i −0.659019 + 0.380485i
\(991\) −703.430 1218.38i −0.709819 1.22944i −0.964924 0.262529i \(-0.915444\pi\)
0.255106 0.966913i \(-0.417890\pi\)
\(992\) 1721.02 + 993.631i 1.73490 + 1.00164i
\(993\) 17.2745i 0.0173963i
\(994\) 1685.74 + 1182.54i 1.69592 + 1.18968i
\(995\) 767.515 0.771372
\(996\) −121.005 + 209.586i −0.121491 + 0.210428i
\(997\) 529.811 305.887i 0.531406 0.306807i −0.210183 0.977662i \(-0.567406\pi\)
0.741589 + 0.670855i \(0.234073\pi\)
\(998\) −264.145 457.513i −0.264674 0.458430i
\(999\) 54.7238 + 31.5948i 0.0547786 + 0.0316264i
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 287.3.k.a.124.11 108
7.3 odd 6 inner 287.3.k.a.206.11 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.k.a.124.11 108 1.1 even 1 trivial
287.3.k.a.206.11 yes 108 7.3 odd 6 inner