Properties

Label 189.4.f.b.64.1
Level $189$
Weight $4$
Character 189.64
Analytic conductor $11.151$
Analytic rank $0$
Dimension $16$
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] = [189,4,Mod(64,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.64");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + 599392 x^{8} - 1089732 x^{7} + 4808401 x^{6} - 7939134 x^{5} + \cdots + 21307456 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{14} \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 64.1
Root \(-2.47591 - 4.28840i\) of defining polynomial
Character \(\chi\) \(=\) 189.64
Dual form 189.4.f.b.127.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.47591 - 4.28840i) q^{2} +(-8.26023 + 14.3071i) q^{4} +(8.06998 - 13.9776i) q^{5} +(3.50000 + 6.06218i) q^{7} +42.1917 q^{8} +O(q^{10})\) \(q+(-2.47591 - 4.28840i) q^{2} +(-8.26023 + 14.3071i) q^{4} +(8.06998 - 13.9776i) q^{5} +(3.50000 + 6.06218i) q^{7} +42.1917 q^{8} -79.9221 q^{10} +(-15.3185 - 26.5325i) q^{11} +(39.0059 - 67.5603i) q^{13} +(17.3313 - 30.0188i) q^{14} +(-38.3809 - 66.4776i) q^{16} -106.992 q^{17} -49.5081 q^{19} +(133.320 + 230.917i) q^{20} +(-75.8546 + 131.384i) q^{22} +(19.5071 - 33.7873i) q^{23} +(-67.7492 - 117.345i) q^{25} -386.300 q^{26} -115.643 q^{28} +(2.87388 + 4.97771i) q^{29} +(-92.2467 + 159.776i) q^{31} +(-21.2881 + 36.8720i) q^{32} +(264.901 + 458.822i) q^{34} +112.980 q^{35} +91.0901 q^{37} +(122.578 + 212.310i) q^{38} +(340.486 - 589.739i) q^{40} +(-41.4346 + 71.7668i) q^{41} +(45.6371 + 79.0458i) q^{43} +506.139 q^{44} -193.191 q^{46} +(118.982 + 206.083i) q^{47} +(-24.5000 + 42.4352i) q^{49} +(-335.481 + 581.070i) q^{50} +(644.396 + 1116.13i) q^{52} -497.669 q^{53} -494.481 q^{55} +(147.671 + 255.773i) q^{56} +(14.2309 - 24.6487i) q^{58} +(-2.10297 + 3.64245i) q^{59} +(-313.196 - 542.471i) q^{61} +913.577 q^{62} -403.264 q^{64} +(-629.554 - 1090.42i) q^{65} +(339.310 - 587.702i) q^{67} +(883.775 - 1530.74i) q^{68} +(-279.727 - 484.502i) q^{70} -747.071 q^{71} -23.2628 q^{73} +(-225.531 - 390.630i) q^{74} +(408.948 - 708.319i) q^{76} +(107.230 - 185.728i) q^{77} +(-77.0203 - 133.403i) q^{79} -1238.93 q^{80} +410.353 q^{82} +(141.098 + 244.389i) q^{83} +(-863.420 + 1495.49i) q^{85} +(225.986 - 391.420i) q^{86} +(-646.315 - 1119.45i) q^{88} -111.091 q^{89} +546.083 q^{91} +(322.266 + 558.181i) q^{92} +(589.177 - 1020.48i) q^{94} +(-399.530 + 692.006i) q^{95} +(-555.045 - 961.367i) q^{97} +242.639 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 3 q^{2} - 43 q^{4} + 30 q^{5} + 56 q^{7} - 12 q^{8} - 28 q^{10} + 24 q^{11} - 68 q^{13} - 21 q^{14} - 103 q^{16} - 336 q^{17} + 352 q^{19} + 330 q^{20} - 151 q^{22} + 228 q^{23} - 244 q^{25} - 1590 q^{26} - 602 q^{28} + 618 q^{29} - 72 q^{31} + 786 q^{32} + 261 q^{34} + 420 q^{35} + 420 q^{37} + 1032 q^{38} + 375 q^{40} + 420 q^{41} + 2 q^{43} - 774 q^{44} + 804 q^{46} + 570 q^{47} - 392 q^{49} + 1110 q^{50} + 431 q^{52} - 1056 q^{53} - 1676 q^{55} - 42 q^{56} - 37 q^{58} - 150 q^{59} - 578 q^{61} - 2340 q^{62} - 224 q^{64} - 366 q^{65} + 898 q^{67} + 2526 q^{68} - 98 q^{70} - 1764 q^{71} + 1944 q^{73} - 222 q^{74} - 1423 q^{76} - 168 q^{77} + 158 q^{79} - 4950 q^{80} - 422 q^{82} + 2958 q^{83} + 774 q^{85} - 114 q^{86} - 1317 q^{88} - 8760 q^{89} - 952 q^{91} + 4629 q^{92} + 3234 q^{94} + 930 q^{95} + 60 q^{97} - 294 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47591 4.28840i −0.875365 1.51618i −0.856373 0.516357i \(-0.827288\pi\)
−0.0189918 0.999820i \(-0.506046\pi\)
\(3\) 0 0
\(4\) −8.26023 + 14.3071i −1.03253 + 1.78839i
\(5\) 8.06998 13.9776i 0.721801 1.25020i −0.238476 0.971148i \(-0.576648\pi\)
0.960277 0.279048i \(-0.0900187\pi\)
\(6\) 0 0
\(7\) 3.50000 + 6.06218i 0.188982 + 0.327327i
\(8\) 42.1917 1.86463
\(9\) 0 0
\(10\) −79.9221 −2.52736
\(11\) −15.3185 26.5325i −0.419883 0.727259i 0.576044 0.817419i \(-0.304596\pi\)
−0.995927 + 0.0901595i \(0.971262\pi\)
\(12\) 0 0
\(13\) 39.0059 67.5603i 0.832177 1.44137i −0.0641315 0.997941i \(-0.520428\pi\)
0.896308 0.443431i \(-0.146239\pi\)
\(14\) 17.3313 30.0188i 0.330857 0.573061i
\(15\) 0 0
\(16\) −38.3809 66.4776i −0.599701 1.03871i
\(17\) −106.992 −1.52643 −0.763214 0.646146i \(-0.776380\pi\)
−0.763214 + 0.646146i \(0.776380\pi\)
\(18\) 0 0
\(19\) −49.5081 −0.597787 −0.298893 0.954287i \(-0.596617\pi\)
−0.298893 + 0.954287i \(0.596617\pi\)
\(20\) 133.320 + 230.917i 1.49056 + 2.58173i
\(21\) 0 0
\(22\) −75.8546 + 131.384i −0.735102 + 1.27323i
\(23\) 19.5071 33.7873i 0.176848 0.306310i −0.763951 0.645274i \(-0.776743\pi\)
0.940799 + 0.338964i \(0.110076\pi\)
\(24\) 0 0
\(25\) −67.7492 117.345i −0.541993 0.938760i
\(26\) −386.300 −2.91383
\(27\) 0 0
\(28\) −115.643 −0.780518
\(29\) 2.87388 + 4.97771i 0.0184023 + 0.0318737i 0.875080 0.483978i \(-0.160809\pi\)
−0.856678 + 0.515852i \(0.827475\pi\)
\(30\) 0 0
\(31\) −92.2467 + 159.776i −0.534451 + 0.925697i 0.464738 + 0.885448i \(0.346148\pi\)
−0.999190 + 0.0402489i \(0.987185\pi\)
\(32\) −21.2881 + 36.8720i −0.117601 + 0.203691i
\(33\) 0 0
\(34\) 264.901 + 458.822i 1.33618 + 2.31434i
\(35\) 112.980 0.545630
\(36\) 0 0
\(37\) 91.0901 0.404733 0.202366 0.979310i \(-0.435137\pi\)
0.202366 + 0.979310i \(0.435137\pi\)
\(38\) 122.578 + 212.310i 0.523282 + 0.906350i
\(39\) 0 0
\(40\) 340.486 589.739i 1.34589 2.33115i
\(41\) −41.4346 + 71.7668i −0.157829 + 0.273368i −0.934086 0.357049i \(-0.883783\pi\)
0.776256 + 0.630417i \(0.217116\pi\)
\(42\) 0 0
\(43\) 45.6371 + 79.0458i 0.161851 + 0.280334i 0.935533 0.353241i \(-0.114920\pi\)
−0.773682 + 0.633575i \(0.781587\pi\)
\(44\) 506.139 1.73417
\(45\) 0 0
\(46\) −193.191 −0.619227
\(47\) 118.982 + 206.083i 0.369262 + 0.639580i 0.989450 0.144872i \(-0.0462772\pi\)
−0.620188 + 0.784453i \(0.712944\pi\)
\(48\) 0 0
\(49\) −24.5000 + 42.4352i −0.0714286 + 0.123718i
\(50\) −335.481 + 581.070i −0.948884 + 1.64352i
\(51\) 0 0
\(52\) 644.396 + 1116.13i 1.71849 + 2.97652i
\(53\) −497.669 −1.28981 −0.644906 0.764262i \(-0.723104\pi\)
−0.644906 + 0.764262i \(0.723104\pi\)
\(54\) 0 0
\(55\) −494.481 −1.21229
\(56\) 147.671 + 255.773i 0.352381 + 0.610342i
\(57\) 0 0
\(58\) 14.2309 24.6487i 0.0322174 0.0558022i
\(59\) −2.10297 + 3.64245i −0.00464039 + 0.00803740i −0.868336 0.495976i \(-0.834810\pi\)
0.863696 + 0.504013i \(0.168144\pi\)
\(60\) 0 0
\(61\) −313.196 542.471i −0.657387 1.13863i −0.981290 0.192537i \(-0.938328\pi\)
0.323903 0.946090i \(-0.395005\pi\)
\(62\) 913.577 1.87136
\(63\) 0 0
\(64\) −403.264 −0.787626
\(65\) −629.554 1090.42i −1.20133 2.08077i
\(66\) 0 0
\(67\) 339.310 587.702i 0.618706 1.07163i −0.371016 0.928627i \(-0.620990\pi\)
0.989722 0.143004i \(-0.0456763\pi\)
\(68\) 883.775 1530.74i 1.57608 2.72985i
\(69\) 0 0
\(70\) −279.727 484.502i −0.477626 0.827272i
\(71\) −747.071 −1.24875 −0.624374 0.781126i \(-0.714646\pi\)
−0.624374 + 0.781126i \(0.714646\pi\)
\(72\) 0 0
\(73\) −23.2628 −0.0372974 −0.0186487 0.999826i \(-0.505936\pi\)
−0.0186487 + 0.999826i \(0.505936\pi\)
\(74\) −225.531 390.630i −0.354289 0.613647i
\(75\) 0 0
\(76\) 408.948 708.319i 0.617232 1.06908i
\(77\) 107.230 185.728i 0.158701 0.274878i
\(78\) 0 0
\(79\) −77.0203 133.403i −0.109689 0.189987i 0.805955 0.591977i \(-0.201652\pi\)
−0.915644 + 0.401989i \(0.868319\pi\)
\(80\) −1238.93 −1.73146
\(81\) 0 0
\(82\) 410.353 0.552633
\(83\) 141.098 + 244.389i 0.186597 + 0.323195i 0.944113 0.329621i \(-0.106921\pi\)
−0.757517 + 0.652816i \(0.773588\pi\)
\(84\) 0 0
\(85\) −863.420 + 1495.49i −1.10178 + 1.90833i
\(86\) 225.986 391.420i 0.283357 0.490790i
\(87\) 0 0
\(88\) −646.315 1119.45i −0.782925 1.35607i
\(89\) −111.091 −0.132311 −0.0661554 0.997809i \(-0.521073\pi\)
−0.0661554 + 0.997809i \(0.521073\pi\)
\(90\) 0 0
\(91\) 546.083 0.629067
\(92\) 322.266 + 558.181i 0.365202 + 0.632548i
\(93\) 0 0
\(94\) 589.177 1020.48i 0.646478 1.11973i
\(95\) −399.530 + 692.006i −0.431483 + 0.747350i
\(96\) 0 0
\(97\) −555.045 961.367i −0.580993 1.00631i −0.995362 0.0962003i \(-0.969331\pi\)
0.414369 0.910109i \(-0.364002\pi\)
\(98\) 242.639 0.250104
\(99\) 0 0
\(100\) 2238.49 2.23849
\(101\) −699.163 1210.99i −0.688805 1.19305i −0.972225 0.234050i \(-0.924802\pi\)
0.283419 0.958996i \(-0.408531\pi\)
\(102\) 0 0
\(103\) −723.877 + 1253.79i −0.692483 + 1.19942i 0.278539 + 0.960425i \(0.410150\pi\)
−0.971022 + 0.238991i \(0.923183\pi\)
\(104\) 1645.73 2850.48i 1.55170 2.68762i
\(105\) 0 0
\(106\) 1232.18 + 2134.20i 1.12906 + 1.95558i
\(107\) 1063.28 0.960664 0.480332 0.877087i \(-0.340516\pi\)
0.480332 + 0.877087i \(0.340516\pi\)
\(108\) 0 0
\(109\) 1933.34 1.69890 0.849450 0.527669i \(-0.176934\pi\)
0.849450 + 0.527669i \(0.176934\pi\)
\(110\) 1224.29 + 2120.53i 1.06120 + 1.83804i
\(111\) 0 0
\(112\) 268.666 465.343i 0.226666 0.392596i
\(113\) 770.314 1334.22i 0.641284 1.11074i −0.343863 0.939020i \(-0.611736\pi\)
0.985146 0.171716i \(-0.0549311\pi\)
\(114\) 0 0
\(115\) −314.844 545.325i −0.255298 0.442190i
\(116\) −94.9556 −0.0760035
\(117\) 0 0
\(118\) 20.8270 0.0162482
\(119\) −374.471 648.602i −0.288468 0.499641i
\(120\) 0 0
\(121\) 196.184 339.801i 0.147396 0.255298i
\(122\) −1550.89 + 2686.21i −1.15091 + 1.99343i
\(123\) 0 0
\(124\) −1523.96 2639.57i −1.10367 1.91162i
\(125\) −169.442 −0.121243
\(126\) 0 0
\(127\) 1471.23 1.02796 0.513980 0.857802i \(-0.328171\pi\)
0.513980 + 0.857802i \(0.328171\pi\)
\(128\) 1168.75 + 2024.33i 0.807061 + 1.39787i
\(129\) 0 0
\(130\) −3117.43 + 5399.56i −2.10321 + 3.64286i
\(131\) 339.376 587.816i 0.226347 0.392044i −0.730376 0.683045i \(-0.760655\pi\)
0.956723 + 0.291001i \(0.0939884\pi\)
\(132\) 0 0
\(133\) −173.278 300.127i −0.112971 0.195672i
\(134\) −3360.40 −2.16638
\(135\) 0 0
\(136\) −4514.16 −2.84622
\(137\) 909.980 + 1576.13i 0.567480 + 0.982905i 0.996814 + 0.0797591i \(0.0254151\pi\)
−0.429334 + 0.903146i \(0.641252\pi\)
\(138\) 0 0
\(139\) 1459.34 2527.65i 0.890499 1.54239i 0.0512202 0.998687i \(-0.483689\pi\)
0.839279 0.543702i \(-0.182978\pi\)
\(140\) −933.238 + 1616.42i −0.563379 + 0.975800i
\(141\) 0 0
\(142\) 1849.68 + 3203.74i 1.09311 + 1.89332i
\(143\) −2390.06 −1.39767
\(144\) 0 0
\(145\) 92.7686 0.0531311
\(146\) 57.5966 + 99.7602i 0.0326488 + 0.0565494i
\(147\) 0 0
\(148\) −752.425 + 1303.24i −0.417898 + 0.723821i
\(149\) −492.243 + 852.590i −0.270645 + 0.468771i −0.969027 0.246954i \(-0.920570\pi\)
0.698382 + 0.715725i \(0.253904\pi\)
\(150\) 0 0
\(151\) 64.9327 + 112.467i 0.0349943 + 0.0606120i 0.882992 0.469388i \(-0.155525\pi\)
−0.847998 + 0.530000i \(0.822192\pi\)
\(152\) −2088.83 −1.11465
\(153\) 0 0
\(154\) −1061.96 −0.555685
\(155\) 1488.86 + 2578.78i 0.771535 + 1.33634i
\(156\) 0 0
\(157\) 108.515 187.954i 0.0551621 0.0955436i −0.837126 0.547011i \(-0.815766\pi\)
0.892288 + 0.451467i \(0.149099\pi\)
\(158\) −381.390 + 660.587i −0.192036 + 0.332617i
\(159\) 0 0
\(160\) 343.589 + 595.113i 0.169769 + 0.294049i
\(161\) 273.099 0.133685
\(162\) 0 0
\(163\) 40.7178 0.0195660 0.00978302 0.999952i \(-0.496886\pi\)
0.00978302 + 0.999952i \(0.496886\pi\)
\(164\) −684.518 1185.62i −0.325926 0.564521i
\(165\) 0 0
\(166\) 698.691 1210.17i 0.326680 0.565827i
\(167\) 862.994 1494.75i 0.399883 0.692618i −0.593828 0.804592i \(-0.702384\pi\)
0.993711 + 0.111974i \(0.0357174\pi\)
\(168\) 0 0
\(169\) −1944.43 3367.84i −0.885037 1.53293i
\(170\) 8550.99 3.85783
\(171\) 0 0
\(172\) −1507.89 −0.668463
\(173\) −291.438 504.786i −0.128079 0.221839i 0.794853 0.606802i \(-0.207548\pi\)
−0.922932 + 0.384962i \(0.874214\pi\)
\(174\) 0 0
\(175\) 474.244 821.415i 0.204854 0.354818i
\(176\) −1175.88 + 2036.68i −0.503609 + 0.872276i
\(177\) 0 0
\(178\) 275.052 + 476.404i 0.115820 + 0.200607i
\(179\) 3699.88 1.54493 0.772465 0.635058i \(-0.219024\pi\)
0.772465 + 0.635058i \(0.219024\pi\)
\(180\) 0 0
\(181\) 2872.98 1.17982 0.589908 0.807470i \(-0.299164\pi\)
0.589908 + 0.807470i \(0.299164\pi\)
\(182\) −1352.05 2341.82i −0.550663 0.953776i
\(183\) 0 0
\(184\) 823.037 1425.54i 0.329756 0.571154i
\(185\) 735.095 1273.22i 0.292137 0.505995i
\(186\) 0 0
\(187\) 1638.96 + 2838.76i 0.640922 + 1.11011i
\(188\) −3931.27 −1.52509
\(189\) 0 0
\(190\) 3956.79 1.51082
\(191\) −136.646 236.678i −0.0517663 0.0896619i 0.838981 0.544161i \(-0.183152\pi\)
−0.890747 + 0.454499i \(0.849818\pi\)
\(192\) 0 0
\(193\) −422.139 + 731.166i −0.157442 + 0.272697i −0.933945 0.357416i \(-0.883658\pi\)
0.776504 + 0.630113i \(0.216991\pi\)
\(194\) −2748.48 + 4760.51i −1.01716 + 1.76178i
\(195\) 0 0
\(196\) −404.751 701.049i −0.147504 0.255484i
\(197\) −2506.77 −0.906600 −0.453300 0.891358i \(-0.649753\pi\)
−0.453300 + 0.891358i \(0.649753\pi\)
\(198\) 0 0
\(199\) −3938.12 −1.40284 −0.701421 0.712747i \(-0.747451\pi\)
−0.701421 + 0.712747i \(0.747451\pi\)
\(200\) −2858.45 4950.98i −1.01061 1.75044i
\(201\) 0 0
\(202\) −3462.13 + 5996.58i −1.20591 + 2.08870i
\(203\) −20.1172 + 34.8439i −0.00695541 + 0.0120471i
\(204\) 0 0
\(205\) 668.753 + 1158.31i 0.227843 + 0.394635i
\(206\) 7169.01 2.42470
\(207\) 0 0
\(208\) −5988.32 −1.99623
\(209\) 758.393 + 1313.57i 0.251001 + 0.434746i
\(210\) 0 0
\(211\) 33.4253 57.8944i 0.0109057 0.0188892i −0.860521 0.509415i \(-0.829862\pi\)
0.871427 + 0.490526i \(0.163195\pi\)
\(212\) 4110.86 7120.21i 1.33177 2.30669i
\(213\) 0 0
\(214\) −2632.58 4559.76i −0.840931 1.45654i
\(215\) 1473.16 0.467297
\(216\) 0 0
\(217\) −1291.45 −0.404007
\(218\) −4786.76 8290.92i −1.48716 2.57583i
\(219\) 0 0
\(220\) 4084.53 7074.61i 1.25172 2.16805i
\(221\) −4173.31 + 7228.38i −1.27026 + 2.20015i
\(222\) 0 0
\(223\) −1243.80 2154.33i −0.373502 0.646925i 0.616599 0.787277i \(-0.288510\pi\)
−0.990102 + 0.140352i \(0.955177\pi\)
\(224\) −298.033 −0.0888981
\(225\) 0 0
\(226\) −7628.90 −2.24543
\(227\) 1923.36 + 3331.36i 0.562370 + 0.974054i 0.997289 + 0.0735843i \(0.0234438\pi\)
−0.434919 + 0.900470i \(0.643223\pi\)
\(228\) 0 0
\(229\) 2005.94 3474.40i 0.578849 1.00260i −0.416762 0.909015i \(-0.636835\pi\)
0.995612 0.0935809i \(-0.0298314\pi\)
\(230\) −1559.05 + 2700.35i −0.446959 + 0.774155i
\(231\) 0 0
\(232\) 121.254 + 210.018i 0.0343134 + 0.0594325i
\(233\) −5724.20 −1.60946 −0.804732 0.593639i \(-0.797691\pi\)
−0.804732 + 0.593639i \(0.797691\pi\)
\(234\) 0 0
\(235\) 3840.73 1.06613
\(236\) −34.7420 60.1749i −0.00958267 0.0165977i
\(237\) 0 0
\(238\) −1854.31 + 3211.76i −0.505029 + 0.874737i
\(239\) 3059.79 5299.71i 0.828122 1.43435i −0.0713879 0.997449i \(-0.522743\pi\)
0.899510 0.436901i \(-0.143924\pi\)
\(240\) 0 0
\(241\) −246.401 426.780i −0.0658594 0.114072i 0.831216 0.555950i \(-0.187646\pi\)
−0.897075 + 0.441879i \(0.854312\pi\)
\(242\) −1942.94 −0.516102
\(243\) 0 0
\(244\) 10348.3 2.71508
\(245\) 395.429 + 684.903i 0.103114 + 0.178599i
\(246\) 0 0
\(247\) −1931.11 + 3344.78i −0.497464 + 0.861633i
\(248\) −3892.04 + 6741.22i −0.996552 + 1.72608i
\(249\) 0 0
\(250\) 419.523 + 726.636i 0.106132 + 0.183826i
\(251\) 1859.25 0.467548 0.233774 0.972291i \(-0.424892\pi\)
0.233774 + 0.972291i \(0.424892\pi\)
\(252\) 0 0
\(253\) −1195.28 −0.297022
\(254\) −3642.63 6309.23i −0.899840 1.55857i
\(255\) 0 0
\(256\) 4174.37 7230.23i 1.01913 1.76519i
\(257\) 1885.96 3266.57i 0.457753 0.792852i −0.541088 0.840966i \(-0.681988\pi\)
0.998842 + 0.0481134i \(0.0153209\pi\)
\(258\) 0 0
\(259\) 318.815 + 552.204i 0.0764873 + 0.132480i
\(260\) 20801.0 4.96164
\(261\) 0 0
\(262\) −3361.05 −0.792544
\(263\) 20.3689 + 35.2800i 0.00477568 + 0.00827171i 0.868403 0.495858i \(-0.165147\pi\)
−0.863628 + 0.504130i \(0.831813\pi\)
\(264\) 0 0
\(265\) −4016.18 + 6956.22i −0.930988 + 1.61252i
\(266\) −858.043 + 1486.17i −0.197782 + 0.342568i
\(267\) 0 0
\(268\) 5605.56 + 9709.11i 1.27766 + 2.21298i
\(269\) −1404.08 −0.318247 −0.159124 0.987259i \(-0.550867\pi\)
−0.159124 + 0.987259i \(0.550867\pi\)
\(270\) 0 0
\(271\) −222.681 −0.0499148 −0.0249574 0.999689i \(-0.507945\pi\)
−0.0249574 + 0.999689i \(0.507945\pi\)
\(272\) 4106.43 + 7112.55i 0.915400 + 1.58552i
\(273\) 0 0
\(274\) 4506.05 7804.71i 0.993505 1.72080i
\(275\) −2075.64 + 3595.11i −0.455148 + 0.788339i
\(276\) 0 0
\(277\) 2889.62 + 5004.98i 0.626789 + 1.08563i 0.988192 + 0.153221i \(0.0489647\pi\)
−0.361403 + 0.932410i \(0.617702\pi\)
\(278\) −14452.7 −3.11805
\(279\) 0 0
\(280\) 4766.80 1.01740
\(281\) 1885.10 + 3265.09i 0.400198 + 0.693162i 0.993749 0.111633i \(-0.0356082\pi\)
−0.593552 + 0.804796i \(0.702275\pi\)
\(282\) 0 0
\(283\) 2402.06 4160.49i 0.504549 0.873905i −0.495437 0.868644i \(-0.664992\pi\)
0.999986 0.00526120i \(-0.00167470\pi\)
\(284\) 6170.98 10688.4i 1.28937 2.23325i
\(285\) 0 0
\(286\) 5917.56 + 10249.5i 1.22347 + 2.11911i
\(287\) −580.084 −0.119308
\(288\) 0 0
\(289\) 6534.21 1.32998
\(290\) −229.686 397.829i −0.0465091 0.0805562i
\(291\) 0 0
\(292\) 192.156 332.824i 0.0385106 0.0667023i
\(293\) 1493.45 2586.74i 0.297777 0.515764i −0.677850 0.735200i \(-0.737088\pi\)
0.975627 + 0.219436i \(0.0704216\pi\)
\(294\) 0 0
\(295\) 33.9418 + 58.7890i 0.00669888 + 0.0116028i
\(296\) 3843.24 0.754676
\(297\) 0 0
\(298\) 4874.99 0.947653
\(299\) −1521.78 2635.81i −0.294338 0.509808i
\(300\) 0 0
\(301\) −319.460 + 553.321i −0.0611739 + 0.105956i
\(302\) 321.534 556.914i 0.0612657 0.106115i
\(303\) 0 0
\(304\) 1900.16 + 3291.18i 0.358493 + 0.620928i
\(305\) −10109.9 −1.89801
\(306\) 0 0
\(307\) −2881.52 −0.535691 −0.267845 0.963462i \(-0.586312\pi\)
−0.267845 + 0.963462i \(0.586312\pi\)
\(308\) 1771.49 + 3068.30i 0.327726 + 0.567639i
\(309\) 0 0
\(310\) 7372.55 12769.6i 1.35075 2.33957i
\(311\) 3398.84 5886.96i 0.619712 1.07337i −0.369826 0.929101i \(-0.620583\pi\)
0.989538 0.144272i \(-0.0460840\pi\)
\(312\) 0 0
\(313\) −470.871 815.572i −0.0850326 0.147281i 0.820373 0.571829i \(-0.193766\pi\)
−0.905405 + 0.424549i \(0.860433\pi\)
\(314\) −1074.69 −0.193148
\(315\) 0 0
\(316\) 2544.82 0.453029
\(317\) 1816.50 + 3146.27i 0.321845 + 0.557452i 0.980869 0.194670i \(-0.0623636\pi\)
−0.659024 + 0.752122i \(0.729030\pi\)
\(318\) 0 0
\(319\) 88.0473 152.502i 0.0154536 0.0267664i
\(320\) −3254.34 + 5636.68i −0.568509 + 0.984687i
\(321\) 0 0
\(322\) −676.168 1171.16i −0.117023 0.202690i
\(323\) 5296.96 0.912478
\(324\) 0 0
\(325\) −10570.5 −1.80414
\(326\) −100.813 174.614i −0.0171274 0.0296656i
\(327\) 0 0
\(328\) −1748.20 + 3027.96i −0.294293 + 0.509730i
\(329\) −832.874 + 1442.58i −0.139568 + 0.241739i
\(330\) 0 0
\(331\) −1375.17 2381.86i −0.228357 0.395525i 0.728965 0.684551i \(-0.240002\pi\)
−0.957321 + 0.289026i \(0.906669\pi\)
\(332\) −4662.01 −0.770665
\(333\) 0 0
\(334\) −8546.77 −1.40017
\(335\) −5476.45 9485.49i −0.893166 1.54701i
\(336\) 0 0
\(337\) −2916.14 + 5050.90i −0.471372 + 0.816440i −0.999464 0.0327474i \(-0.989574\pi\)
0.528092 + 0.849187i \(0.322908\pi\)
\(338\) −9628.43 + 16676.9i −1.54946 + 2.68374i
\(339\) 0 0
\(340\) −14264.1 24706.1i −2.27523 3.94082i
\(341\) 5652.34 0.897629
\(342\) 0 0
\(343\) −343.000 −0.0539949
\(344\) 1925.51 + 3335.07i 0.301792 + 0.522719i
\(345\) 0 0
\(346\) −1443.15 + 2499.61i −0.224232 + 0.388380i
\(347\) 1704.98 2953.11i 0.263770 0.456863i −0.703471 0.710724i \(-0.748367\pi\)
0.967241 + 0.253862i \(0.0817008\pi\)
\(348\) 0 0
\(349\) −2973.73 5150.66i −0.456104 0.789996i 0.542647 0.839961i \(-0.317422\pi\)
−0.998751 + 0.0499654i \(0.984089\pi\)
\(350\) −4696.74 −0.717289
\(351\) 0 0
\(352\) 1304.41 0.197515
\(353\) −265.847 460.460i −0.0400838 0.0694273i 0.845287 0.534312i \(-0.179429\pi\)
−0.885371 + 0.464885i \(0.846096\pi\)
\(354\) 0 0
\(355\) −6028.85 + 10442.3i −0.901347 + 1.56118i
\(356\) 917.640 1589.40i 0.136615 0.236624i
\(357\) 0 0
\(358\) −9160.57 15866.6i −1.35238 2.34239i
\(359\) 7555.95 1.11083 0.555415 0.831573i \(-0.312559\pi\)
0.555415 + 0.831573i \(0.312559\pi\)
\(360\) 0 0
\(361\) −4407.94 −0.642651
\(362\) −7113.22 12320.5i −1.03277 1.78881i
\(363\) 0 0
\(364\) −4510.77 + 7812.88i −0.649529 + 1.12502i
\(365\) −187.730 + 325.159i −0.0269213 + 0.0466290i
\(366\) 0 0
\(367\) 4851.61 + 8403.24i 0.690060 + 1.19522i 0.971818 + 0.235733i \(0.0757492\pi\)
−0.281758 + 0.959486i \(0.590917\pi\)
\(368\) −2994.79 −0.424224
\(369\) 0 0
\(370\) −7280.11 −1.02290
\(371\) −1741.84 3016.96i −0.243752 0.422190i
\(372\) 0 0
\(373\) −7.09728 + 12.2928i −0.000985210 + 0.00170643i −0.866518 0.499147i \(-0.833647\pi\)
0.865532 + 0.500853i \(0.166980\pi\)
\(374\) 8115.81 14057.0i 1.12208 1.94350i
\(375\) 0 0
\(376\) 5020.05 + 8694.98i 0.688536 + 1.19258i
\(377\) 448.393 0.0612558
\(378\) 0 0
\(379\) −2618.92 −0.354948 −0.177474 0.984126i \(-0.556792\pi\)
−0.177474 + 0.984126i \(0.556792\pi\)
\(380\) −6600.41 11432.2i −0.891037 1.54332i
\(381\) 0 0
\(382\) −676.646 + 1171.98i −0.0906288 + 0.156974i
\(383\) −4344.62 + 7525.10i −0.579633 + 1.00395i 0.415888 + 0.909416i \(0.363471\pi\)
−0.995521 + 0.0945386i \(0.969862\pi\)
\(384\) 0 0
\(385\) −1730.69 2997.63i −0.229101 0.396815i
\(386\) 4180.71 0.551276
\(387\) 0 0
\(388\) 18339.2 2.39957
\(389\) 5302.27 + 9183.80i 0.691094 + 1.19701i 0.971480 + 0.237123i \(0.0762045\pi\)
−0.280385 + 0.959888i \(0.590462\pi\)
\(390\) 0 0
\(391\) −2087.10 + 3614.96i −0.269946 + 0.467560i
\(392\) −1033.70 + 1790.41i −0.133188 + 0.230688i
\(393\) 0 0
\(394\) 6206.53 + 10750.0i 0.793606 + 1.37457i
\(395\) −2486.21 −0.316695
\(396\) 0 0
\(397\) 2918.97 0.369015 0.184508 0.982831i \(-0.440931\pi\)
0.184508 + 0.982831i \(0.440931\pi\)
\(398\) 9750.41 + 16888.2i 1.22800 + 2.12696i
\(399\) 0 0
\(400\) −5200.54 + 9007.60i −0.650068 + 1.12595i
\(401\) 2129.01 3687.56i 0.265132 0.459222i −0.702466 0.711717i \(-0.747918\pi\)
0.967598 + 0.252495i \(0.0812512\pi\)
\(402\) 0 0
\(403\) 7196.34 + 12464.4i 0.889516 + 1.54069i
\(404\) 23101.0 2.84484
\(405\) 0 0
\(406\) 199.233 0.0243541
\(407\) −1395.37 2416.85i −0.169941 0.294346i
\(408\) 0 0
\(409\) 2308.33 3998.14i 0.279070 0.483363i −0.692084 0.721817i \(-0.743307\pi\)
0.971154 + 0.238454i \(0.0766406\pi\)
\(410\) 3311.54 5735.75i 0.398891 0.690899i
\(411\) 0 0
\(412\) −11958.8 20713.2i −1.43002 2.47686i
\(413\) −29.4416 −0.00350781
\(414\) 0 0
\(415\) 4554.63 0.538742
\(416\) 1660.72 + 2876.46i 0.195730 + 0.339014i
\(417\) 0 0
\(418\) 3755.42 6504.58i 0.439434 0.761122i
\(419\) 997.567 1727.84i 0.116311 0.201457i −0.801992 0.597335i \(-0.796226\pi\)
0.918303 + 0.395878i \(0.129560\pi\)
\(420\) 0 0
\(421\) −8281.75 14344.4i −0.958736 1.66058i −0.725577 0.688141i \(-0.758427\pi\)
−0.233160 0.972438i \(-0.574907\pi\)
\(422\) −331.032 −0.0381857
\(423\) 0 0
\(424\) −20997.5 −2.40502
\(425\) 7248.59 + 12554.9i 0.827314 + 1.43295i
\(426\) 0 0
\(427\) 2192.37 3797.30i 0.248469 0.430361i
\(428\) −8782.92 + 15212.5i −0.991912 + 1.71804i
\(429\) 0 0
\(430\) −3647.41 6317.50i −0.409055 0.708505i
\(431\) −1439.27 −0.160852 −0.0804258 0.996761i \(-0.525628\pi\)
−0.0804258 + 0.996761i \(0.525628\pi\)
\(432\) 0 0
\(433\) −6467.98 −0.717856 −0.358928 0.933365i \(-0.616858\pi\)
−0.358928 + 0.933365i \(0.616858\pi\)
\(434\) 3197.52 + 5538.26i 0.353654 + 0.612547i
\(435\) 0 0
\(436\) −15969.8 + 27660.5i −1.75416 + 3.03830i
\(437\) −965.760 + 1672.74i −0.105717 + 0.183108i
\(438\) 0 0
\(439\) 6255.01 + 10834.0i 0.680035 + 1.17785i 0.974970 + 0.222337i \(0.0713686\pi\)
−0.294935 + 0.955517i \(0.595298\pi\)
\(440\) −20863.0 −2.26047
\(441\) 0 0
\(442\) 41330.9 4.44776
\(443\) 3510.58 + 6080.51i 0.376507 + 0.652130i 0.990551 0.137142i \(-0.0437916\pi\)
−0.614044 + 0.789272i \(0.710458\pi\)
\(444\) 0 0
\(445\) −896.506 + 1552.79i −0.0955021 + 0.165415i
\(446\) −6159.07 + 10667.8i −0.653902 + 1.13259i
\(447\) 0 0
\(448\) −1411.43 2444.66i −0.148847 0.257811i
\(449\) −5184.19 −0.544894 −0.272447 0.962171i \(-0.587833\pi\)
−0.272447 + 0.962171i \(0.587833\pi\)
\(450\) 0 0
\(451\) 2538.87 0.265079
\(452\) 12725.9 + 22042.0i 1.32429 + 2.29373i
\(453\) 0 0
\(454\) 9524.13 16496.3i 0.984559 1.70531i
\(455\) 4406.88 7632.94i 0.454061 0.786457i
\(456\) 0 0
\(457\) −1288.14 2231.12i −0.131853 0.228375i 0.792538 0.609822i \(-0.208759\pi\)
−0.924391 + 0.381447i \(0.875426\pi\)
\(458\) −19866.1 −2.02682
\(459\) 0 0
\(460\) 10402.7 1.05441
\(461\) −8952.21 15505.7i −0.904438 1.56653i −0.821670 0.569963i \(-0.806957\pi\)
−0.0827674 0.996569i \(-0.526376\pi\)
\(462\) 0 0
\(463\) −5631.93 + 9754.79i −0.565309 + 0.979144i 0.431712 + 0.902012i \(0.357910\pi\)
−0.997021 + 0.0771323i \(0.975424\pi\)
\(464\) 220.604 382.097i 0.0220717 0.0382293i
\(465\) 0 0
\(466\) 14172.6 + 24547.6i 1.40887 + 2.44023i
\(467\) −9817.00 −0.972755 −0.486377 0.873749i \(-0.661682\pi\)
−0.486377 + 0.873749i \(0.661682\pi\)
\(468\) 0 0
\(469\) 4750.34 0.467698
\(470\) −9509.29 16470.6i −0.933257 1.61645i
\(471\) 0 0
\(472\) −88.7278 + 153.681i −0.00865260 + 0.0149867i
\(473\) 1398.19 2421.73i 0.135917 0.235415i
\(474\) 0 0
\(475\) 3354.13 + 5809.53i 0.323996 + 0.561178i
\(476\) 12372.9 1.19140
\(477\) 0 0
\(478\) −30303.0 −2.89964
\(479\) 3675.86 + 6366.78i 0.350636 + 0.607319i 0.986361 0.164597i \(-0.0526322\pi\)
−0.635725 + 0.771915i \(0.719299\pi\)
\(480\) 0 0
\(481\) 3553.05 6154.07i 0.336809 0.583371i
\(482\) −1220.13 + 2113.33i −0.115302 + 0.199709i
\(483\) 0 0
\(484\) 3241.05 + 5613.67i 0.304381 + 0.527204i
\(485\) −17916.8 −1.67745
\(486\) 0 0
\(487\) 15312.1 1.42476 0.712378 0.701796i \(-0.247618\pi\)
0.712378 + 0.701796i \(0.247618\pi\)
\(488\) −13214.3 22887.8i −1.22578 2.12312i
\(489\) 0 0
\(490\) 1958.09 3391.51i 0.180526 0.312679i
\(491\) −8989.47 + 15570.2i −0.826251 + 1.43111i 0.0747090 + 0.997205i \(0.476197\pi\)
−0.900960 + 0.433903i \(0.857136\pi\)
\(492\) 0 0
\(493\) −307.481 532.573i −0.0280898 0.0486529i
\(494\) 19125.0 1.74185
\(495\) 0 0
\(496\) 14162.0 1.28204
\(497\) −2614.75 4528.88i −0.235991 0.408748i
\(498\) 0 0
\(499\) 9407.52 16294.3i 0.843965 1.46179i −0.0425521 0.999094i \(-0.513549\pi\)
0.886517 0.462696i \(-0.153118\pi\)
\(500\) 1399.63 2424.23i 0.125187 0.216830i
\(501\) 0 0
\(502\) −4603.32 7973.19i −0.409275 0.708886i
\(503\) 6228.19 0.552090 0.276045 0.961145i \(-0.410976\pi\)
0.276045 + 0.961145i \(0.410976\pi\)
\(504\) 0 0
\(505\) −22568.9 −1.98872
\(506\) 2959.40 + 5125.84i 0.260003 + 0.450339i
\(507\) 0 0
\(508\) −12152.7 + 21049.1i −1.06140 + 1.83839i
\(509\) −5901.69 + 10222.0i −0.513925 + 0.890144i 0.485944 + 0.873990i \(0.338476\pi\)
−0.999870 + 0.0161547i \(0.994858\pi\)
\(510\) 0 0
\(511\) −81.4199 141.023i −0.00704854 0.0122084i
\(512\) −22641.4 −1.95433
\(513\) 0 0
\(514\) −18677.8 −1.60281
\(515\) 11683.4 + 20236.2i 0.999670 + 1.73148i
\(516\) 0 0
\(517\) 3645.26 6313.78i 0.310094 0.537098i
\(518\) 1578.71 2734.41i 0.133909 0.231937i
\(519\) 0 0
\(520\) −26562.0 46006.7i −2.24004 3.87986i
\(521\) 7277.82 0.611990 0.305995 0.952033i \(-0.401011\pi\)
0.305995 + 0.952033i \(0.401011\pi\)
\(522\) 0 0
\(523\) 18929.2 1.58263 0.791316 0.611408i \(-0.209397\pi\)
0.791316 + 0.611408i \(0.209397\pi\)
\(524\) 5606.64 + 9710.99i 0.467419 + 0.809593i
\(525\) 0 0
\(526\) 100.863 174.700i 0.00836092 0.0144815i
\(527\) 9869.62 17094.7i 0.815802 1.41301i
\(528\) 0 0
\(529\) 5322.45 + 9218.75i 0.437449 + 0.757685i
\(530\) 39774.7 3.25982
\(531\) 0 0
\(532\) 5725.28 0.466583
\(533\) 3232.39 + 5598.67i 0.262684 + 0.454981i
\(534\) 0 0
\(535\) 8580.63 14862.1i 0.693408 1.20102i
\(536\) 14316.1 24796.2i 1.15366 1.99819i
\(537\) 0 0
\(538\) 3476.38 + 6021.26i 0.278582 + 0.482519i
\(539\) 1501.22 0.119967
\(540\) 0 0
\(541\) 3018.24 0.239860 0.119930 0.992782i \(-0.461733\pi\)
0.119930 + 0.992782i \(0.461733\pi\)
\(542\) 551.337 + 954.944i 0.0436936 + 0.0756796i
\(543\) 0 0
\(544\) 2277.65 3945.00i 0.179510 0.310920i
\(545\) 15602.0 27023.5i 1.22627 2.12396i
\(546\) 0 0
\(547\) 4726.68 + 8186.86i 0.369467 + 0.639936i 0.989482 0.144654i \(-0.0462069\pi\)
−0.620015 + 0.784590i \(0.712874\pi\)
\(548\) −30066.6 −2.34376
\(549\) 0 0
\(550\) 20556.3 1.59368
\(551\) −142.280 246.437i −0.0110006 0.0190537i
\(552\) 0 0
\(553\) 539.142 933.821i 0.0414587 0.0718085i
\(554\) 14308.9 24783.7i 1.09734 1.90065i
\(555\) 0 0
\(556\) 24108.9 + 41757.8i 1.83893 + 3.18512i
\(557\) −6175.74 −0.469793 −0.234896 0.972020i \(-0.575475\pi\)
−0.234896 + 0.972020i \(0.575475\pi\)
\(558\) 0 0
\(559\) 7120.47 0.538755
\(560\) −4336.26 7510.62i −0.327215 0.566753i
\(561\) 0 0
\(562\) 9334.65 16168.1i 0.700638 1.21354i
\(563\) 6329.56 10963.1i 0.473817 0.820675i −0.525734 0.850649i \(-0.676209\pi\)
0.999551 + 0.0299739i \(0.00954242\pi\)
\(564\) 0 0
\(565\) −12432.8 21534.3i −0.925758 1.60346i
\(566\) −23789.1 −1.76666
\(567\) 0 0
\(568\) −31520.2 −2.32845
\(569\) 9605.51 + 16637.2i 0.707704 + 1.22578i 0.965707 + 0.259636i \(0.0836024\pi\)
−0.258002 + 0.966144i \(0.583064\pi\)
\(570\) 0 0
\(571\) 3780.12 6547.37i 0.277046 0.479858i −0.693603 0.720357i \(-0.743978\pi\)
0.970649 + 0.240499i \(0.0773112\pi\)
\(572\) 19742.4 34194.9i 1.44313 2.49958i
\(573\) 0 0
\(574\) 1436.23 + 2487.63i 0.104438 + 0.180892i
\(575\) −5286.36 −0.383402
\(576\) 0 0
\(577\) −14126.1 −1.01920 −0.509598 0.860413i \(-0.670206\pi\)
−0.509598 + 0.860413i \(0.670206\pi\)
\(578\) −16178.1 28021.3i −1.16422 2.01649i
\(579\) 0 0
\(580\) −766.290 + 1327.25i −0.0548594 + 0.0950193i
\(581\) −987.686 + 1710.72i −0.0705269 + 0.122156i
\(582\) 0 0
\(583\) 7623.56 + 13204.4i 0.541571 + 0.938028i
\(584\) −981.497 −0.0695456
\(585\) 0 0
\(586\) −14790.6 −1.04265
\(587\) 5811.15 + 10065.2i 0.408606 + 0.707727i 0.994734 0.102492i \(-0.0326816\pi\)
−0.586128 + 0.810219i \(0.699348\pi\)
\(588\) 0 0
\(589\) 4566.96 7910.21i 0.319488 0.553369i
\(590\) 168.074 291.112i 0.0117279 0.0203134i
\(591\) 0 0
\(592\) −3496.11 6055.45i −0.242719 0.420401i
\(593\) 22182.5 1.53613 0.768064 0.640373i \(-0.221220\pi\)
0.768064 + 0.640373i \(0.221220\pi\)
\(594\) 0 0
\(595\) −12087.9 −0.832865
\(596\) −8132.07 14085.2i −0.558897 0.968038i
\(597\) 0 0
\(598\) −7535.59 + 13052.0i −0.515306 + 0.892537i
\(599\) −11203.2 + 19404.5i −0.764189 + 1.32361i 0.176485 + 0.984303i \(0.443527\pi\)
−0.940674 + 0.339311i \(0.889806\pi\)
\(600\) 0 0
\(601\) −5627.94 9747.88i −0.381977 0.661604i 0.609367 0.792888i \(-0.291423\pi\)
−0.991345 + 0.131284i \(0.958090\pi\)
\(602\) 3163.81 0.214198
\(603\) 0 0
\(604\) −2145.43 −0.144531
\(605\) −3166.41 5484.38i −0.212781 0.368548i
\(606\) 0 0
\(607\) 6156.29 10663.0i 0.411658 0.713012i −0.583413 0.812175i \(-0.698283\pi\)
0.995071 + 0.0991632i \(0.0316166\pi\)
\(608\) 1053.93 1825.47i 0.0703004 0.121764i
\(609\) 0 0
\(610\) 25031.2 + 43355.4i 1.66145 + 2.87772i
\(611\) 18564.0 1.22916
\(612\) 0 0
\(613\) −26835.4 −1.76814 −0.884070 0.467354i \(-0.845207\pi\)
−0.884070 + 0.467354i \(0.845207\pi\)
\(614\) 7134.37 + 12357.1i 0.468925 + 0.812202i
\(615\) 0 0
\(616\) 4524.21 7836.16i 0.295918 0.512545i
\(617\) −10882.7 + 18849.4i −0.710084 + 1.22990i 0.254741 + 0.967009i \(0.418010\pi\)
−0.964825 + 0.262893i \(0.915323\pi\)
\(618\) 0 0
\(619\) −3557.64 6162.01i −0.231007 0.400117i 0.727097 0.686534i \(-0.240869\pi\)
−0.958105 + 0.286418i \(0.907535\pi\)
\(620\) −49193.2 −3.18653
\(621\) 0 0
\(622\) −33660.8 −2.16990
\(623\) −388.820 673.456i −0.0250044 0.0433089i
\(624\) 0 0
\(625\) 7101.25 12299.7i 0.454480 0.787182i
\(626\) −2331.67 + 4038.56i −0.148869 + 0.257849i
\(627\) 0 0
\(628\) 1792.72 + 3105.08i 0.113913 + 0.197303i
\(629\) −9745.88 −0.617796
\(630\) 0 0
\(631\) −11639.8 −0.734345 −0.367173 0.930153i \(-0.619674\pi\)
−0.367173 + 0.930153i \(0.619674\pi\)
\(632\) −3249.61 5628.50i −0.204530 0.354256i
\(633\) 0 0
\(634\) 8994.98 15579.8i 0.563464 0.975948i
\(635\) 11872.8 20564.3i 0.741982 1.28515i
\(636\) 0 0
\(637\) 1911.29 + 3310.45i 0.118882 + 0.205910i
\(638\) −871.988 −0.0541102
\(639\) 0 0
\(640\) 37727.1 2.33015
\(641\) −12837.8 22235.7i −0.791048 1.37014i −0.925318 0.379191i \(-0.876202\pi\)
0.134270 0.990945i \(-0.457131\pi\)
\(642\) 0 0
\(643\) 8573.42 14849.6i 0.525821 0.910748i −0.473727 0.880672i \(-0.657092\pi\)
0.999548 0.0300764i \(-0.00957506\pi\)
\(644\) −2255.86 + 3907.27i −0.138033 + 0.239081i
\(645\) 0 0
\(646\) −13114.8 22715.4i −0.798752 1.38348i
\(647\) 13104.3 0.796263 0.398132 0.917328i \(-0.369659\pi\)
0.398132 + 0.917328i \(0.369659\pi\)
\(648\) 0 0
\(649\) 128.858 0.00779369
\(650\) 26171.5 + 45330.4i 1.57928 + 2.73539i
\(651\) 0 0
\(652\) −336.338 + 582.555i −0.0202025 + 0.0349917i
\(653\) −8373.04 + 14502.5i −0.501780 + 0.869108i 0.498218 + 0.867052i \(0.333988\pi\)
−0.999998 + 0.00205652i \(0.999345\pi\)
\(654\) 0 0
\(655\) −5477.51 9487.33i −0.326754 0.565955i
\(656\) 6361.18 0.378601
\(657\) 0 0
\(658\) 8248.47 0.488691
\(659\) −12133.6 21015.9i −0.717232 1.24228i −0.962092 0.272724i \(-0.912075\pi\)
0.244860 0.969558i \(-0.421258\pi\)
\(660\) 0 0
\(661\) −7233.95 + 12529.6i −0.425670 + 0.737282i −0.996483 0.0837981i \(-0.973295\pi\)
0.570813 + 0.821080i \(0.306628\pi\)
\(662\) −6809.57 + 11794.5i −0.399791 + 0.692458i
\(663\) 0 0
\(664\) 5953.16 + 10311.2i 0.347933 + 0.602638i
\(665\) −5593.42 −0.326170
\(666\) 0 0
\(667\) 224.244 0.0130176
\(668\) 14257.0 + 24693.9i 0.825781 + 1.43029i
\(669\) 0 0
\(670\) −27118.4 + 46970.4i −1.56369 + 2.70839i
\(671\) −9595.41 + 16619.7i −0.552052 + 0.956181i
\(672\) 0 0
\(673\) 7479.13 + 12954.2i 0.428379 + 0.741975i 0.996729 0.0808120i \(-0.0257513\pi\)
−0.568350 + 0.822787i \(0.692418\pi\)
\(674\) 28880.4 1.65049
\(675\) 0 0
\(676\) 64245.6 3.65530
\(677\) −12861.9 22277.4i −0.730165 1.26468i −0.956812 0.290706i \(-0.906110\pi\)
0.226647 0.973977i \(-0.427224\pi\)
\(678\) 0 0
\(679\) 3885.32 6729.57i 0.219595 0.380349i
\(680\) −36429.2 + 63097.2i −2.05440 + 3.55833i
\(681\) 0 0
\(682\) −13994.7 24239.5i −0.785753 1.36096i
\(683\) 2949.64 0.165248 0.0826242 0.996581i \(-0.473670\pi\)
0.0826242 + 0.996581i \(0.473670\pi\)
\(684\) 0 0
\(685\) 29374.1 1.63843
\(686\) 849.236 + 1470.92i 0.0472653 + 0.0818659i
\(687\) 0 0
\(688\) 3503.18 6067.69i 0.194124 0.336233i
\(689\) −19412.0 + 33622.6i −1.07335 + 1.85910i
\(690\) 0 0
\(691\) 4059.96 + 7032.05i 0.223514 + 0.387137i 0.955873 0.293782i \(-0.0949139\pi\)
−0.732359 + 0.680919i \(0.761581\pi\)
\(692\) 9629.38 0.528980
\(693\) 0 0
\(694\) −16885.5 −0.923579
\(695\) −23553.6 40796.1i −1.28553 2.22660i
\(696\) 0 0
\(697\) 4433.16 7678.45i 0.240915 0.417277i
\(698\) −14725.4 + 25505.1i −0.798515 + 1.38307i
\(699\) 0 0
\(700\) 7834.73 + 13570.1i 0.423035 + 0.732719i
\(701\) 15870.9 0.855115 0.427558 0.903988i \(-0.359374\pi\)
0.427558 + 0.903988i \(0.359374\pi\)
\(702\) 0 0
\(703\) −4509.70 −0.241944
\(704\) 6177.43 + 10699.6i 0.330711 + 0.572808i
\(705\) 0 0
\(706\) −1316.42 + 2280.11i −0.0701760 + 0.121548i
\(707\) 4894.14 8476.90i 0.260344 0.450929i
\(708\) 0 0
\(709\) 7436.79 + 12880.9i 0.393928 + 0.682303i 0.992964 0.118419i \(-0.0377827\pi\)
−0.599036 + 0.800722i \(0.704449\pi\)
\(710\) 59707.5 3.15603
\(711\) 0 0
\(712\) −4687.13 −0.246710
\(713\) 3598.93 + 6233.53i 0.189034 + 0.327416i
\(714\) 0 0
\(715\) −19287.7 + 33407.3i −1.00884 + 1.74736i
\(716\) −30561.9 + 52934.7i −1.59518 + 2.76294i
\(717\) 0 0
\(718\) −18707.8 32402.9i −0.972382 1.68421i
\(719\) −31809.4 −1.64992 −0.824959 0.565192i \(-0.808802\pi\)
−0.824959 + 0.565192i \(0.808802\pi\)
\(720\) 0 0
\(721\) −10134.3 −0.523468
\(722\) 10913.7 + 18903.0i 0.562554 + 0.974373i
\(723\) 0 0
\(724\) −23731.4 + 41104.1i −1.21819 + 2.10997i
\(725\) 389.406 674.471i 0.0199478 0.0345506i
\(726\) 0 0
\(727\) −8385.91 14524.8i −0.427808 0.740984i 0.568870 0.822427i \(-0.307381\pi\)
−0.996678 + 0.0814427i \(0.974047\pi\)
\(728\) 23040.2 1.17297
\(729\) 0 0
\(730\) 1859.21 0.0942638
\(731\) −4882.79 8457.24i −0.247054 0.427910i
\(732\) 0 0
\(733\) 15894.2 27529.5i 0.800906 1.38721i −0.118114 0.993000i \(-0.537685\pi\)
0.919020 0.394210i \(-0.128982\pi\)
\(734\) 24024.3 41611.3i 1.20811 2.09251i
\(735\) 0 0
\(736\) 830.537 + 1438.53i 0.0415951 + 0.0720448i
\(737\) −20791.0 −1.03914
\(738\) 0 0
\(739\) −17098.2 −0.851107 −0.425553 0.904933i \(-0.639921\pi\)
−0.425553 + 0.904933i \(0.639921\pi\)
\(740\) 12144.1 + 21034.2i 0.603279 + 1.04491i
\(741\) 0 0
\(742\) −8625.27 + 14939.4i −0.426743 + 0.739141i
\(743\) −308.950 + 535.118i −0.0152548 + 0.0264220i −0.873552 0.486731i \(-0.838189\pi\)
0.858297 + 0.513153i \(0.171523\pi\)
\(744\) 0 0
\(745\) 7944.78 + 13760.8i 0.390704 + 0.676719i
\(746\) 70.2888 0.00344967
\(747\) 0 0
\(748\) −54152.6 −2.64708
\(749\) 3721.47 + 6445.78i 0.181548 + 0.314451i
\(750\) 0 0
\(751\) −13234.5 + 22922.8i −0.643053 + 1.11380i 0.341694 + 0.939811i \(0.388999\pi\)
−0.984747 + 0.173990i \(0.944334\pi\)
\(752\) 9133.26 15819.3i 0.442893 0.767114i
\(753\) 0 0
\(754\) −1110.18 1922.89i −0.0536212 0.0928746i
\(755\) 2096.02 0.101036
\(756\) 0 0
\(757\) 40262.5 1.93311 0.966557 0.256453i \(-0.0825538\pi\)
0.966557 + 0.256453i \(0.0825538\pi\)
\(758\) 6484.21 + 11231.0i 0.310709 + 0.538163i
\(759\) 0 0
\(760\) −16856.8 + 29196.9i −0.804555 + 1.39353i
\(761\) 19445.6 33680.8i 0.926286 1.60438i 0.136807 0.990598i \(-0.456316\pi\)
0.789479 0.613777i \(-0.210351\pi\)
\(762\) 0 0
\(763\) 6766.68 + 11720.2i 0.321062 + 0.556096i
\(764\) 4514.91 0.213801
\(765\) 0 0
\(766\) 43027.5 2.02956
\(767\) 164.057 + 284.154i 0.00772326 + 0.0133771i
\(768\) 0 0
\(769\) −13910.2 + 24093.2i −0.652296 + 1.12981i 0.330268 + 0.943887i \(0.392861\pi\)
−0.982564 + 0.185923i \(0.940473\pi\)
\(770\) −8570.03 + 14843.7i −0.401094 + 0.694715i
\(771\) 0 0
\(772\) −6973.93 12079.2i −0.325126 0.563135i
\(773\) −25952.0 −1.20754 −0.603770 0.797159i \(-0.706335\pi\)
−0.603770 + 0.797159i \(0.706335\pi\)
\(774\) 0 0
\(775\) 24998.5 1.15868
\(776\) −23418.3 40561.7i −1.08333 1.87639i
\(777\) 0 0
\(778\) 26255.8 45476.5i 1.20992 2.09564i
\(779\) 2051.35 3553.04i 0.0943482 0.163416i
\(780\) 0 0
\(781\) 11444.0 + 19821.7i 0.524328 + 0.908163i
\(782\) 20669.8 0.945206
\(783\) 0 0
\(784\) 3761.32 0.171343
\(785\) −1751.43 3033.57i −0.0796322 0.137927i
\(786\) 0 0
\(787\) −21058.2 + 36473.8i −0.953802 + 1.65203i −0.216715 + 0.976235i \(0.569534\pi\)
−0.737087 + 0.675798i \(0.763799\pi\)
\(788\) 20706.5 35864.7i 0.936090 1.62136i
\(789\) 0 0
\(790\) 6155.62 + 10661.8i 0.277224 + 0.480166i
\(791\) 10784.4 0.484765
\(792\) 0 0
\(793\) −48866.0 −2.18825
\(794\) −7227.10 12517.7i −0.323023 0.559492i
\(795\) 0 0
\(796\) 32529.7 56343.2i 1.44847 2.50883i
\(797\) 6485.71 11233.6i 0.288250 0.499264i −0.685142 0.728410i \(-0.740260\pi\)
0.973392 + 0.229145i \(0.0735931\pi\)
\(798\) 0 0
\(799\) −12730.1 22049.1i −0.563652 0.976274i
\(800\) 5769.00 0.254956
\(801\) 0 0
\(802\) −21085.0 −0.928349
\(803\) 356.353 + 617.221i 0.0156605 + 0.0271248i
\(804\) 0 0
\(805\) 2203.91 3817.28i 0.0964937 0.167132i
\(806\) 35634.9 61721.5i 1.55730 2.69733i
\(807\) 0 0
\(808\) −29498.9 51093.5i −1.28436 2.22458i
\(809\) 9053.03 0.393433 0.196717 0.980460i \(-0.436972\pi\)
0.196717 + 0.980460i \(0.436972\pi\)
\(810\) 0 0
\(811\) −2374.82 −0.102825 −0.0514127 0.998677i \(-0.516372\pi\)
−0.0514127 + 0.998677i \(0.516372\pi\)
\(812\) −332.345 575.638i −0.0143633 0.0248780i
\(813\) 0 0
\(814\) −6909.60 + 11967.8i −0.297520 + 0.515320i
\(815\) 328.592 569.138i 0.0141228 0.0244614i
\(816\) 0 0
\(817\) −2259.41 3913.41i −0.0967524 0.167580i
\(818\) −22860.8 −0.977152
\(819\) 0 0
\(820\) −22096.2 −0.941016
\(821\) 2574.93 + 4459.91i 0.109459 + 0.189588i 0.915551 0.402202i \(-0.131755\pi\)
−0.806092 + 0.591790i \(0.798422\pi\)
\(822\) 0 0
\(823\) −1437.48 + 2489.79i −0.0608839 + 0.105454i −0.894861 0.446345i \(-0.852725\pi\)
0.833977 + 0.551799i \(0.186059\pi\)
\(824\) −30541.6 + 52899.6i −1.29122 + 2.23646i
\(825\) 0 0
\(826\) 72.8945 + 126.257i 0.00307061 + 0.00531846i
\(827\) −515.502 −0.0216757 −0.0108378 0.999941i \(-0.503450\pi\)
−0.0108378 + 0.999941i \(0.503450\pi\)
\(828\) 0 0
\(829\) −14698.3 −0.615793 −0.307897 0.951420i \(-0.599625\pi\)
−0.307897 + 0.951420i \(0.599625\pi\)
\(830\) −11276.8 19532.1i −0.471596 0.816829i
\(831\) 0 0
\(832\) −15729.7 + 27244.7i −0.655444 + 1.13526i
\(833\) 2621.30 4540.22i 0.109031 0.188847i
\(834\) 0 0
\(835\) −13928.7 24125.2i −0.577272 0.999864i
\(836\) −25058.0 −1.03666
\(837\) 0 0
\(838\) −9879.53 −0.407259
\(839\) −2205.55 3820.12i −0.0907557 0.157194i 0.817074 0.576533i \(-0.195595\pi\)
−0.907829 + 0.419340i \(0.862262\pi\)
\(840\) 0 0
\(841\) 12178.0 21092.9i 0.499323 0.864852i
\(842\) −41009.7 + 71030.9i −1.67849 + 2.90723i
\(843\) 0 0
\(844\) 552.201 + 956.441i 0.0225208 + 0.0390072i
\(845\) −62765.9 −2.55528
\(846\) 0 0
\(847\) 2746.58 0.111421
\(848\) 19100.9 + 33083.8i 0.773501 + 1.33974i
\(849\) 0 0
\(850\) 35893.7 62169.7i 1.44840 2.50871i
\(851\) 1776.90 3077.68i 0.0715763 0.123974i
\(852\) 0 0
\(853\) −10950.2 18966.3i −0.439540 0.761306i 0.558114 0.829764i \(-0.311525\pi\)
−0.997654 + 0.0684586i \(0.978192\pi\)
\(854\) −21712.4 −0.870004
\(855\) 0 0
\(856\) 44861.5 1.79128
\(857\) 11901.6 + 20614.1i 0.474388 + 0.821664i 0.999570 0.0293263i \(-0.00933618\pi\)
−0.525182 + 0.850990i \(0.676003\pi\)
\(858\) 0 0
\(859\) −22244.1 + 38527.8i −0.883536 + 1.53033i −0.0361535 + 0.999346i \(0.511511\pi\)
−0.847382 + 0.530983i \(0.821823\pi\)
\(860\) −12168.7 + 21076.7i −0.482497 + 0.835710i
\(861\) 0 0
\(862\) 3563.49 + 6172.15i 0.140804 + 0.243880i
\(863\) 34544.3 1.36258 0.681288 0.732016i \(-0.261420\pi\)
0.681288 + 0.732016i \(0.261420\pi\)
\(864\) 0 0
\(865\) −9407.60 −0.369790
\(866\) 16014.1 + 27737.3i 0.628386 + 1.08840i
\(867\) 0 0
\(868\) 10667.7 18477.0i 0.417149 0.722523i
\(869\) −2359.68 + 4087.08i −0.0921134 + 0.159545i
\(870\) 0 0
\(871\) −26470.2 45847.8i −1.02975 1.78357i
\(872\) 81570.8 3.16782
\(873\) 0 0
\(874\) 9564.52 0.370166
\(875\) −593.048 1027.19i −0.0229128 0.0396861i
\(876\) 0 0
\(877\) −16602.3 + 28756.0i −0.639246 + 1.10721i 0.346353 + 0.938104i \(0.387420\pi\)
−0.985599 + 0.169102i \(0.945913\pi\)
\(878\) 30973.6 53647.9i 1.19056 2.06211i
\(879\) 0 0
\(880\) 18978.6 + 32871.9i 0.727010 + 1.25922i
\(881\) −23411.1 −0.895278 −0.447639 0.894214i \(-0.647735\pi\)
−0.447639 + 0.894214i \(0.647735\pi\)
\(882\) 0 0
\(883\) −12881.8 −0.490947 −0.245473 0.969403i \(-0.578943\pi\)
−0.245473 + 0.969403i \(0.578943\pi\)
\(884\) −68944.9 119416.i −2.62316 4.54344i
\(885\) 0 0
\(886\) 17383.7 30109.5i 0.659163 1.14170i
\(887\) 2811.78 4870.15i 0.106438 0.184356i −0.807887 0.589338i \(-0.799389\pi\)
0.914325 + 0.404982i \(0.132722\pi\)
\(888\) 0 0
\(889\) 5149.31 + 8918.88i 0.194266 + 0.336479i
\(890\) 8878.66 0.334397
\(891\) 0 0
\(892\) 41096.3 1.54261
\(893\) −5890.58 10202.8i −0.220740 0.382333i
\(894\) 0 0
\(895\) 29858.0 51715.6i 1.11513 1.93146i
\(896\) −8181.25 + 14170.3i −0.305041 + 0.528346i
\(897\) 0 0
\(898\) 12835.6 + 22231.9i 0.476981 + 0.826155i
\(899\) −1060.42 −0.0393405
\(900\) 0 0
\(901\) 53246.4 1.96881
\(902\) −6286.01 10887.7i −0.232041 0.401907i
\(903\) 0 0
\(904\) 32500.8 56293.1i 1.19575 2.07111i
\(905\) 23184.9 40157.4i 0.851592 1.47500i
\(906\) 0 0
\(907\) −18281.5 31664.5i −0.669269 1.15921i −0.978109 0.208093i \(-0.933274\pi\)
0.308840 0.951114i \(-0.400059\pi\)
\(908\) −63549.6 −2.32265
\(909\) 0 0
\(910\) −43644.1 −1.58988
\(911\) 9963.46 + 17257.2i 0.362354 + 0.627615i 0.988348 0.152213i \(-0.0486400\pi\)
−0.625994 + 0.779828i \(0.715307\pi\)
\(912\) 0 0
\(913\) 4322.83 7487.37i 0.156698 0.271408i
\(914\) −6378.63 + 11048.1i −0.230838 + 0.399824i
\(915\) 0 0
\(916\) 33139.1 + 57398.6i 1.19536 + 2.07042i
\(917\) 4751.26 0.171102
\(918\) 0 0
\(919\) 48298.1 1.73363 0.866816 0.498628i \(-0.166163\pi\)
0.866816 + 0.498628i \(0.166163\pi\)
\(920\) −13283.8 23008.2i −0.476036 0.824519i
\(921\) 0 0
\(922\) −44329.6 + 76781.2i −1.58343 + 2.74258i
\(923\) −29140.2 + 50472.3i −1.03918 + 1.79991i
\(924\) 0 0
\(925\) −6171.28 10689.0i −0.219362 0.379947i
\(926\) 55776.5 1.97941
\(927\) 0 0
\(928\) −244.718 −0.00865652
\(929\) 7808.00 + 13523.9i 0.275751 + 0.477614i 0.970324 0.241808i \(-0.0777403\pi\)
−0.694574 + 0.719422i \(0.744407\pi\)
\(930\) 0 0
\(931\) 1212.95 2100.89i 0.0426990 0.0739569i
\(932\) 47283.2 81896.9i 1.66182 2.87835i
\(933\) 0 0
\(934\) 24306.0 + 42099.2i 0.851516 + 1.47487i
\(935\) 52905.4 1.85047
\(936\) 0 0
\(937\) 25030.1 0.872678 0.436339 0.899782i \(-0.356275\pi\)
0.436339 + 0.899782i \(0.356275\pi\)
\(938\) −11761.4 20371.3i −0.409407 0.709113i
\(939\) 0 0
\(940\) −31725.3 + 54949.8i −1.10081 + 1.90667i
\(941\) 8006.44 13867.6i 0.277367 0.480414i −0.693363 0.720589i \(-0.743872\pi\)
0.970730 + 0.240175i \(0.0772049\pi\)
\(942\) 0 0
\(943\) 1616.54 + 2799.92i 0.0558236 + 0.0966894i
\(944\) 322.855 0.0111314
\(945\) 0 0
\(946\) −13847.1 −0.475908
\(947\) −606.613 1050.69i −0.0208155 0.0360535i 0.855430 0.517918i \(-0.173293\pi\)
−0.876246 + 0.481865i \(0.839960\pi\)
\(948\) 0 0
\(949\) −907.388 + 1571.64i −0.0310380 + 0.0537594i
\(950\) 16609.0 28767.7i 0.567230 0.982471i
\(951\) 0 0
\(952\) −15799.5 27365.6i −0.537885 0.931644i
\(953\) 20143.9 0.684705 0.342352 0.939572i \(-0.388776\pi\)
0.342352 + 0.939572i \(0.388776\pi\)
\(954\) 0 0
\(955\) −4410.92 −0.149460
\(956\) 50549.1 + 87553.5i 1.71012 + 2.96201i
\(957\) 0 0
\(958\) 18202.2 31527.1i 0.613869 1.06325i
\(959\) −6369.86 + 11032.9i −0.214487 + 0.371503i
\(960\) 0 0
\(961\) −2123.40 3677.84i −0.0712767 0.123455i
\(962\) −35188.1 −1.17932
\(963\) 0 0
\(964\) 8141.32 0.272007
\(965\) 6813.31 + 11801.0i 0.227283 + 0.393666i
\(966\) 0 0
\(967\) −13701.4 + 23731.5i −0.455642 + 0.789196i −0.998725 0.0504835i \(-0.983924\pi\)
0.543082 + 0.839679i \(0.317257\pi\)
\(968\) 8277.34 14336.8i 0.274839 0.476035i
\(969\) 0 0
\(970\) 44360.4 + 76834.4i 1.46838 + 2.54330i
\(971\) 25837.8 0.853938 0.426969 0.904266i \(-0.359581\pi\)
0.426969 + 0.904266i \(0.359581\pi\)
\(972\) 0 0
\(973\) 20430.7 0.673154
\(974\) −37911.2 65664.2i −1.24718 2.16018i
\(975\) 0 0
\(976\) −24041.4 + 41641.0i −0.788471 + 1.36567i
\(977\) −11031.0 + 19106.2i −0.361221 + 0.625653i −0.988162 0.153414i \(-0.950973\pi\)
0.626941 + 0.779066i \(0.284307\pi\)
\(978\) 0 0
\(979\) 1701.76 + 2947.53i 0.0555551 + 0.0962243i
\(980\) −13065.3 −0.425874
\(981\) 0 0
\(982\) 89028.3 2.89308
\(983\) −5900.89 10220.6i −0.191464 0.331626i 0.754271 0.656563i \(-0.227990\pi\)
−0.945736 + 0.324937i \(0.894657\pi\)
\(984\) 0 0
\(985\) −20229.6 + 35038.7i −0.654385 + 1.13343i
\(986\) −1522.59 + 2637.20i −0.0491776 + 0.0851781i
\(987\) 0 0
\(988\) −31902.8 55257.3i −1.02729 1.77932i
\(989\) 3560.99 0.114492
\(990\) 0 0
\(991\) −46761.9 −1.49893 −0.749465 0.662044i \(-0.769689\pi\)
−0.749465 + 0.662044i \(0.769689\pi\)
\(992\) −3927.51 6802.65i −0.125704 0.217726i
\(993\) 0 0
\(994\) −12947.8 + 22426.2i −0.413157 + 0.715608i
\(995\) −31780.5 + 55045.5i −1.01257 + 1.75383i
\(996\) 0 0
\(997\) 19130.6 + 33135.1i 0.607695 + 1.05256i 0.991619 + 0.129194i \(0.0412389\pi\)
−0.383925 + 0.923364i \(0.625428\pi\)
\(998\) −93168.6 −2.95511
\(999\) 0 0
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 189.4.f.b.64.1 16
3.2 odd 2 63.4.f.b.22.8 16
9.2 odd 6 63.4.f.b.43.8 yes 16
9.4 even 3 567.4.a.g.1.8 8
9.5 odd 6 567.4.a.i.1.1 8
9.7 even 3 inner 189.4.f.b.127.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.f.b.22.8 16 3.2 odd 2
63.4.f.b.43.8 yes 16 9.2 odd 6
189.4.f.b.64.1 16 1.1 even 1 trivial
189.4.f.b.127.1 16 9.7 even 3 inner
567.4.a.g.1.8 8 9.4 even 3
567.4.a.i.1.1 8 9.5 odd 6