Properties

Label 105.4.g.b.104.38
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(104,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.104");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\), degree \(1\), 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: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 104.38
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.37

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+5.11138 q^{2} +(-1.51783 + 4.96953i) q^{3} +18.1262 q^{4} +(10.9509 - 2.25323i) q^{5} +(-7.75821 + 25.4011i) q^{6} +(-11.4695 - 14.5413i) q^{7} +51.7589 q^{8} +(-22.3924 - 15.0858i) q^{9} +O(q^{10})\) \(q+5.11138 q^{2} +(-1.51783 + 4.96953i) q^{3} +18.1262 q^{4} +(10.9509 - 2.25323i) q^{5} +(-7.75821 + 25.4011i) q^{6} +(-11.4695 - 14.5413i) q^{7} +51.7589 q^{8} +(-22.3924 - 15.0858i) q^{9} +(55.9744 - 11.5171i) q^{10} +55.4308i q^{11} +(-27.5125 + 90.0786i) q^{12} -20.9550 q^{13} +(-58.6250 - 74.3263i) q^{14} +(-5.42417 + 57.8410i) q^{15} +119.550 q^{16} -96.8237i q^{17} +(-114.456 - 77.1093i) q^{18} +33.1970i q^{19} +(198.499 - 40.8425i) q^{20} +(89.6723 - 34.9267i) q^{21} +283.328i q^{22} -111.288 q^{23} +(-78.5612 + 257.217i) q^{24} +(114.846 - 49.3500i) q^{25} -107.109 q^{26} +(108.957 - 88.3818i) q^{27} +(-207.899 - 263.579i) q^{28} -156.784i q^{29} +(-27.7250 + 295.647i) q^{30} -80.4962i q^{31} +196.992 q^{32} +(-275.465 - 84.1346i) q^{33} -494.903i q^{34} +(-158.367 - 133.398i) q^{35} +(-405.889 - 273.448i) q^{36} +180.365i q^{37} +169.683i q^{38} +(31.8061 - 104.136i) q^{39} +(566.808 - 116.625i) q^{40} -36.5837 q^{41} +(458.349 - 178.524i) q^{42} -52.5826i q^{43} +1004.75i q^{44} +(-279.209 - 114.748i) q^{45} -568.835 q^{46} +259.660i q^{47} +(-181.456 + 594.105i) q^{48} +(-79.9009 + 333.564i) q^{49} +(587.021 - 252.247i) q^{50} +(481.168 + 146.962i) q^{51} -379.834 q^{52} +191.690 q^{53} +(556.921 - 451.753i) q^{54} +(124.898 + 607.019i) q^{55} +(-593.648 - 752.643i) q^{56} +(-164.973 - 50.3875i) q^{57} -801.380i q^{58} +705.237 q^{59} +(-98.3196 + 1048.44i) q^{60} +427.079i q^{61} -411.447i q^{62} +(37.4617 + 498.642i) q^{63} +50.5057 q^{64} +(-229.476 + 47.2164i) q^{65} +(-1408.00 - 430.044i) q^{66} +306.444i q^{67} -1755.05i q^{68} +(168.916 - 553.048i) q^{69} +(-809.473 - 681.846i) q^{70} -513.791i q^{71} +(-1159.00 - 780.824i) q^{72} -360.633 q^{73} +921.916i q^{74} +(70.9295 + 645.635i) q^{75} +601.736i q^{76} +(806.038 - 635.764i) q^{77} +(162.573 - 532.280i) q^{78} +85.9838 q^{79} +(1309.18 - 269.373i) q^{80} +(273.837 + 675.614i) q^{81} -186.993 q^{82} +886.893i q^{83} +(1625.42 - 633.089i) q^{84} +(-218.166 - 1060.31i) q^{85} -268.770i q^{86} +(779.140 + 237.971i) q^{87} +2869.03i q^{88} -1417.80 q^{89} +(-1427.14 - 586.523i) q^{90} +(240.343 + 304.713i) q^{91} -2017.23 q^{92} +(400.028 + 122.180i) q^{93} +1327.22i q^{94} +(74.8006 + 363.538i) q^{95} +(-299.001 + 978.958i) q^{96} +1055.44 q^{97} +(-408.404 + 1704.97i) q^{98} +(836.218 - 1241.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.11138 1.80715 0.903573 0.428435i \(-0.140935\pi\)
0.903573 + 0.428435i \(0.140935\pi\)
\(3\) −1.51783 + 4.96953i −0.292107 + 0.956386i
\(4\) 18.1262 2.26578
\(5\) 10.9509 2.25323i 0.979481 0.201535i
\(6\) −7.75821 + 25.4011i −0.527879 + 1.72833i
\(7\) −11.4695 14.5413i −0.619295 0.785158i
\(8\) 51.7589 2.28744
\(9\) −22.3924 15.0858i −0.829347 0.558733i
\(10\) 55.9744 11.5171i 1.77007 0.364204i
\(11\) 55.4308i 1.51936i 0.650294 + 0.759682i \(0.274646\pi\)
−0.650294 + 0.759682i \(0.725354\pi\)
\(12\) −27.5125 + 90.0786i −0.661848 + 2.16695i
\(13\) −20.9550 −0.447066 −0.223533 0.974696i \(-0.571759\pi\)
−0.223533 + 0.974696i \(0.571759\pi\)
\(14\) −58.6250 74.3263i −1.11916 1.41890i
\(15\) −5.42417 + 57.8410i −0.0933676 + 0.995632i
\(16\) 119.550 1.86796
\(17\) 96.8237i 1.38136i −0.723158 0.690682i \(-0.757310\pi\)
0.723158 0.690682i \(-0.242690\pi\)
\(18\) −114.456 77.1093i −1.49875 1.00971i
\(19\) 33.1970i 0.400838i 0.979710 + 0.200419i \(0.0642303\pi\)
−0.979710 + 0.200419i \(0.935770\pi\)
\(20\) 198.499 40.8425i 2.21928 0.456634i
\(21\) 89.6723 34.9267i 0.931814 0.362935i
\(22\) 283.328i 2.74571i
\(23\) −111.288 −1.00892 −0.504460 0.863435i \(-0.668308\pi\)
−0.504460 + 0.863435i \(0.668308\pi\)
\(24\) −78.5612 + 257.217i −0.668177 + 2.18767i
\(25\) 114.846 49.3500i 0.918767 0.394800i
\(26\) −107.109 −0.807914
\(27\) 108.957 88.3818i 0.776623 0.629966i
\(28\) −207.899 263.579i −1.40318 1.77899i
\(29\) 156.784i 1.00393i −0.864888 0.501965i \(-0.832611\pi\)
0.864888 0.501965i \(-0.167389\pi\)
\(30\) −27.7250 + 295.647i −0.168729 + 1.79925i
\(31\) 80.4962i 0.466372i −0.972432 0.233186i \(-0.925085\pi\)
0.972432 0.233186i \(-0.0749152\pi\)
\(32\) 196.992 1.08824
\(33\) −275.465 84.1346i −1.45310 0.443817i
\(34\) 494.903i 2.49633i
\(35\) −158.367 133.398i −0.764825 0.644238i
\(36\) −405.889 273.448i −1.87911 1.26596i
\(37\) 180.365i 0.801402i 0.916209 + 0.400701i \(0.131233\pi\)
−0.916209 + 0.400701i \(0.868767\pi\)
\(38\) 169.683i 0.724372i
\(39\) 31.8061 104.136i 0.130591 0.427568i
\(40\) 566.808 116.625i 2.24050 0.461000i
\(41\) −36.5837 −0.139351 −0.0696757 0.997570i \(-0.522196\pi\)
−0.0696757 + 0.997570i \(0.522196\pi\)
\(42\) 458.349 178.524i 1.68392 0.655876i
\(43\) 52.5826i 0.186483i −0.995644 0.0932416i \(-0.970277\pi\)
0.995644 0.0932416i \(-0.0297229\pi\)
\(44\) 1004.75i 3.44254i
\(45\) −279.209 114.748i −0.924935 0.380126i
\(46\) −568.835 −1.82326
\(47\) 259.660i 0.805858i 0.915231 + 0.402929i \(0.132008\pi\)
−0.915231 + 0.402929i \(0.867992\pi\)
\(48\) −181.456 + 594.105i −0.545644 + 1.78649i
\(49\) −79.9009 + 333.564i −0.232947 + 0.972489i
\(50\) 587.021 252.247i 1.66035 0.713461i
\(51\) 481.168 + 146.962i 1.32112 + 0.403506i
\(52\) −379.834 −1.01295
\(53\) 191.690 0.496804 0.248402 0.968657i \(-0.420095\pi\)
0.248402 + 0.968657i \(0.420095\pi\)
\(54\) 556.921 451.753i 1.40347 1.13844i
\(55\) 124.898 + 607.019i 0.306206 + 1.48819i
\(56\) −593.648 752.643i −1.41660 1.79600i
\(57\) −164.973 50.3875i −0.383356 0.117087i
\(58\) 801.380i 1.81425i
\(59\) 705.237 1.55617 0.778085 0.628159i \(-0.216191\pi\)
0.778085 + 0.628159i \(0.216191\pi\)
\(60\) −98.3196 + 1048.44i −0.211550 + 2.25588i
\(61\) 427.079i 0.896423i 0.893928 + 0.448212i \(0.147939\pi\)
−0.893928 + 0.448212i \(0.852061\pi\)
\(62\) 411.447i 0.842803i
\(63\) 37.4617 + 498.642i 0.0749164 + 0.997190i
\(64\) 50.5057 0.0986440
\(65\) −229.476 + 47.2164i −0.437893 + 0.0900996i
\(66\) −1408.00 430.044i −2.62596 0.802041i
\(67\) 306.444i 0.558777i 0.960178 + 0.279388i \(0.0901317\pi\)
−0.960178 + 0.279388i \(0.909868\pi\)
\(68\) 1755.05i 3.12986i
\(69\) 168.916 553.048i 0.294712 0.964916i
\(70\) −809.473 681.846i −1.38215 1.16423i
\(71\) 513.791i 0.858814i −0.903111 0.429407i \(-0.858723\pi\)
0.903111 0.429407i \(-0.141277\pi\)
\(72\) −1159.00 780.824i −1.89708 1.27807i
\(73\) −360.633 −0.578204 −0.289102 0.957298i \(-0.593357\pi\)
−0.289102 + 0.957298i \(0.593357\pi\)
\(74\) 921.916i 1.44825i
\(75\) 70.9295 + 645.635i 0.109203 + 0.994019i
\(76\) 601.736i 0.908208i
\(77\) 806.038 635.764i 1.19294 0.940935i
\(78\) 162.573 532.280i 0.235997 0.772677i
\(79\) 85.9838 0.122455 0.0612274 0.998124i \(-0.480499\pi\)
0.0612274 + 0.998124i \(0.480499\pi\)
\(80\) 1309.18 269.373i 1.82963 0.376460i
\(81\) 273.837 + 675.614i 0.375634 + 0.926768i
\(82\) −186.993 −0.251828
\(83\) 886.893i 1.17288i 0.809992 + 0.586440i \(0.199471\pi\)
−0.809992 + 0.586440i \(0.800529\pi\)
\(84\) 1625.42 633.089i 2.11128 0.822329i
\(85\) −218.166 1060.31i −0.278394 1.35302i
\(86\) 268.770i 0.337002i
\(87\) 779.140 + 237.971i 0.960145 + 0.293255i
\(88\) 2869.03i 3.47545i
\(89\) −1417.80 −1.68861 −0.844305 0.535863i \(-0.819986\pi\)
−0.844305 + 0.535863i \(0.819986\pi\)
\(90\) −1427.14 586.523i −1.67149 0.686943i
\(91\) 240.343 + 304.713i 0.276866 + 0.351018i
\(92\) −2017.23 −2.28598
\(93\) 400.028 + 122.180i 0.446032 + 0.136231i
\(94\) 1327.22i 1.45630i
\(95\) 74.8006 + 363.538i 0.0807830 + 0.392613i
\(96\) −299.001 + 978.958i −0.317882 + 1.04078i
\(97\) 1055.44 1.10478 0.552392 0.833584i \(-0.313715\pi\)
0.552392 + 0.833584i \(0.313715\pi\)
\(98\) −408.404 + 1704.97i −0.420970 + 1.75743i
\(99\) 836.218 1241.23i 0.848920 1.26008i
\(100\) 2081.72 894.528i 2.08172 0.894528i
\(101\) 740.746 0.729772 0.364886 0.931052i \(-0.381108\pi\)
0.364886 + 0.931052i \(0.381108\pi\)
\(102\) 2459.43 + 751.179i 2.38745 + 0.729194i
\(103\) −935.584 −0.895008 −0.447504 0.894282i \(-0.647687\pi\)
−0.447504 + 0.894282i \(0.647687\pi\)
\(104\) −1084.61 −1.02264
\(105\) 903.298 584.533i 0.839551 0.543281i
\(106\) 979.799 0.897797
\(107\) 794.752 0.718052 0.359026 0.933328i \(-0.383109\pi\)
0.359026 + 0.933328i \(0.383109\pi\)
\(108\) 1974.98 1602.03i 1.75965 1.42736i
\(109\) −202.134 −0.177623 −0.0888117 0.996048i \(-0.528307\pi\)
−0.0888117 + 0.996048i \(0.528307\pi\)
\(110\) 638.403 + 3102.70i 0.553358 + 2.68937i
\(111\) −896.330 273.764i −0.766449 0.234095i
\(112\) −1371.17 1738.41i −1.15682 1.46665i
\(113\) 1457.83 1.21364 0.606818 0.794841i \(-0.292446\pi\)
0.606818 + 0.794841i \(0.292446\pi\)
\(114\) −843.242 257.550i −0.692779 0.211594i
\(115\) −1218.71 + 250.758i −0.988218 + 0.203333i
\(116\) 2841.89i 2.27468i
\(117\) 469.232 + 316.123i 0.370773 + 0.249791i
\(118\) 3604.73 2.81223
\(119\) −1407.95 + 1110.52i −1.08459 + 0.855472i
\(120\) −280.749 + 2993.78i −0.213573 + 2.27745i
\(121\) −1741.57 −1.30847
\(122\) 2182.96i 1.61997i
\(123\) 55.5278 181.803i 0.0407055 0.133274i
\(124\) 1459.09i 1.05669i
\(125\) 1146.47 799.203i 0.820349 0.571863i
\(126\) 191.481 + 2548.75i 0.135385 + 1.80207i
\(127\) 1189.69i 0.831242i 0.909538 + 0.415621i \(0.136436\pi\)
−0.909538 + 0.415621i \(0.863564\pi\)
\(128\) −1317.78 −0.909975
\(129\) 261.311 + 79.8116i 0.178350 + 0.0544730i
\(130\) −1172.94 + 241.341i −0.791337 + 0.162823i
\(131\) 531.346 0.354381 0.177190 0.984177i \(-0.443299\pi\)
0.177190 + 0.984177i \(0.443299\pi\)
\(132\) −4993.13 1525.04i −3.29239 1.00559i
\(133\) 482.729 380.753i 0.314721 0.248237i
\(134\) 1566.35i 1.00979i
\(135\) 994.038 1213.37i 0.633727 0.773557i
\(136\) 5011.48i 3.15979i
\(137\) −1269.32 −0.791572 −0.395786 0.918343i \(-0.629528\pi\)
−0.395786 + 0.918343i \(0.629528\pi\)
\(138\) 863.396 2826.84i 0.532588 1.74374i
\(139\) 1566.53i 0.955910i 0.878384 + 0.477955i \(0.158622\pi\)
−0.878384 + 0.477955i \(0.841378\pi\)
\(140\) −2870.59 2417.99i −1.73292 1.45970i
\(141\) −1290.39 394.120i −0.770711 0.235397i
\(142\) 2626.18i 1.55200i
\(143\) 1161.55i 0.679257i
\(144\) −2677.00 1803.50i −1.54919 1.04369i
\(145\) −353.270 1716.93i −0.202327 0.983331i
\(146\) −1843.33 −1.04490
\(147\) −1536.38 903.363i −0.862029 0.506858i
\(148\) 3269.34i 1.81580i
\(149\) 1112.59i 0.611723i −0.952076 0.305862i \(-0.901055\pi\)
0.952076 0.305862i \(-0.0989445\pi\)
\(150\) 362.547 + 3300.08i 0.197346 + 1.79634i
\(151\) 1252.15 0.674822 0.337411 0.941357i \(-0.390449\pi\)
0.337411 + 0.941357i \(0.390449\pi\)
\(152\) 1718.24i 0.916892i
\(153\) −1460.66 + 2168.11i −0.771815 + 1.14563i
\(154\) 4119.96 3249.63i 2.15582 1.70041i
\(155\) −181.377 881.509i −0.0939905 0.456803i
\(156\) 576.524 1887.59i 0.295890 0.968773i
\(157\) 226.625 0.115202 0.0576009 0.998340i \(-0.481655\pi\)
0.0576009 + 0.998340i \(0.481655\pi\)
\(158\) 439.496 0.221294
\(159\) −290.953 + 952.607i −0.145120 + 0.475136i
\(160\) 2157.25 443.869i 1.06591 0.219318i
\(161\) 1276.42 + 1618.28i 0.624819 + 0.792161i
\(162\) 1399.69 + 3453.32i 0.678825 + 1.67480i
\(163\) 1843.89i 0.886042i 0.896511 + 0.443021i \(0.146093\pi\)
−0.896511 + 0.443021i \(0.853907\pi\)
\(164\) −663.123 −0.315739
\(165\) −3206.17 300.666i −1.51273 0.141859i
\(166\) 4533.24i 2.11957i
\(167\) 2144.68i 0.993774i −0.867815 0.496887i \(-0.834476\pi\)
0.867815 0.496887i \(-0.165524\pi\)
\(168\) 4641.34 1807.77i 2.13147 0.830192i
\(169\) −1757.89 −0.800132
\(170\) −1115.13 5419.65i −0.503098 2.44511i
\(171\) 500.804 743.360i 0.223962 0.332434i
\(172\) 953.123i 0.422529i
\(173\) 3462.67i 1.52175i −0.648901 0.760873i \(-0.724771\pi\)
0.648901 0.760873i \(-0.275229\pi\)
\(174\) 3982.48 + 1216.36i 1.73512 + 0.529954i
\(175\) −2034.84 1103.99i −0.878968 0.476880i
\(176\) 6626.72i 2.83811i
\(177\) −1070.43 + 3504.69i −0.454568 + 1.48830i
\(178\) −7246.90 −3.05156
\(179\) 3089.42i 1.29002i 0.764173 + 0.645011i \(0.223147\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(180\) −5061.00 2079.95i −2.09569 0.861281i
\(181\) 2791.07i 1.14618i −0.819493 0.573090i \(-0.805745\pi\)
0.819493 0.573090i \(-0.194255\pi\)
\(182\) 1228.48 + 1557.51i 0.500337 + 0.634340i
\(183\) −2122.38 648.233i −0.857326 0.261851i
\(184\) −5760.14 −2.30784
\(185\) 406.405 + 1975.17i 0.161511 + 0.784958i
\(186\) 2044.69 + 624.507i 0.806045 + 0.246188i
\(187\) 5367.01 2.09880
\(188\) 4706.65i 1.82589i
\(189\) −2534.87 570.687i −0.975582 0.219637i
\(190\) 382.334 + 1858.18i 0.145987 + 0.709509i
\(191\) 3188.41i 1.20788i −0.797029 0.603941i \(-0.793596\pi\)
0.797029 0.603941i \(-0.206404\pi\)
\(192\) −76.6591 + 250.989i −0.0288146 + 0.0943417i
\(193\) 1762.45i 0.657327i −0.944447 0.328664i \(-0.893402\pi\)
0.944447 0.328664i \(-0.106598\pi\)
\(194\) 5394.77 1.99651
\(195\) 113.663 1212.06i 0.0417415 0.445113i
\(196\) −1448.30 + 6046.25i −0.527806 + 2.20344i
\(197\) 1135.69 0.410735 0.205367 0.978685i \(-0.434161\pi\)
0.205367 + 0.978685i \(0.434161\pi\)
\(198\) 4274.23 6344.38i 1.53412 2.27715i
\(199\) 1200.54i 0.427658i −0.976871 0.213829i \(-0.931407\pi\)
0.976871 0.213829i \(-0.0685935\pi\)
\(200\) 5944.29 2554.30i 2.10162 0.903081i
\(201\) −1522.88 465.130i −0.534406 0.163223i
\(202\) 3786.23 1.31880
\(203\) −2279.84 + 1798.23i −0.788244 + 0.621729i
\(204\) 8721.75 + 2663.86i 2.99336 + 0.914254i
\(205\) −400.625 + 82.4315i −0.136492 + 0.0280842i
\(206\) −4782.13 −1.61741
\(207\) 2492.00 + 1678.87i 0.836744 + 0.563717i
\(208\) −2505.16 −0.835103
\(209\) −1840.14 −0.609019
\(210\) 4617.10 2987.77i 1.51719 0.981789i
\(211\) −835.608 −0.272633 −0.136317 0.990665i \(-0.543526\pi\)
−0.136317 + 0.990665i \(0.543526\pi\)
\(212\) 3474.61 1.12565
\(213\) 2553.30 + 779.848i 0.821357 + 0.250865i
\(214\) 4062.28 1.29762
\(215\) −118.481 575.829i −0.0375829 0.182657i
\(216\) 5639.50 4574.54i 1.77648 1.44101i
\(217\) −1170.52 + 923.252i −0.366176 + 0.288822i
\(218\) −1033.19 −0.320991
\(219\) 547.380 1792.17i 0.168897 0.552986i
\(220\) 2263.93 + 11002.9i 0.693793 + 3.37190i
\(221\) 2028.94i 0.617562i
\(222\) −4581.48 1399.31i −1.38509 0.423044i
\(223\) −2734.39 −0.821115 −0.410557 0.911835i \(-0.634666\pi\)
−0.410557 + 0.911835i \(0.634666\pi\)
\(224\) −2259.40 2864.53i −0.673941 0.854440i
\(225\) −3316.16 627.479i −0.982565 0.185920i
\(226\) 7451.50 2.19322
\(227\) 2207.95i 0.645579i −0.946471 0.322790i \(-0.895379\pi\)
0.946471 0.322790i \(-0.104621\pi\)
\(228\) −2990.34 913.333i −0.868597 0.265294i
\(229\) 1720.95i 0.496610i 0.968682 + 0.248305i \(0.0798735\pi\)
−0.968682 + 0.248305i \(0.920126\pi\)
\(230\) −6229.27 + 1281.72i −1.78585 + 0.367452i
\(231\) 1936.01 + 4970.61i 0.551430 + 1.41577i
\(232\) 8114.94i 2.29643i
\(233\) −2915.58 −0.819767 −0.409884 0.912138i \(-0.634431\pi\)
−0.409884 + 0.912138i \(0.634431\pi\)
\(234\) 2398.42 + 1615.82i 0.670041 + 0.451409i
\(235\) 585.075 + 2843.52i 0.162409 + 0.789323i
\(236\) 12783.3 3.52593
\(237\) −130.509 + 427.299i −0.0357699 + 0.117114i
\(238\) −7196.55 + 5676.29i −1.96001 + 1.54596i
\(239\) 6597.22i 1.78552i −0.450536 0.892758i \(-0.648767\pi\)
0.450536 0.892758i \(-0.351233\pi\)
\(240\) −648.457 + 6914.86i −0.174407 + 1.85980i
\(241\) 5492.27i 1.46800i −0.679149 0.734000i \(-0.737651\pi\)
0.679149 0.734000i \(-0.262349\pi\)
\(242\) −8901.83 −2.36459
\(243\) −3773.12 + 335.372i −0.996073 + 0.0885356i
\(244\) 7741.31i 2.03109i
\(245\) −123.392 + 3832.87i −0.0321765 + 0.999482i
\(246\) 283.824 929.266i 0.0735607 0.240845i
\(247\) 695.643i 0.179201i
\(248\) 4166.39i 1.06680i
\(249\) −4407.44 1346.15i −1.12173 0.342606i
\(250\) 5860.06 4085.03i 1.48249 1.03344i
\(251\) 3852.51 0.968798 0.484399 0.874847i \(-0.339038\pi\)
0.484399 + 0.874847i \(0.339038\pi\)
\(252\) 679.039 + 9038.48i 0.169744 + 2.25941i
\(253\) 6168.78i 1.53292i
\(254\) 6080.95i 1.50218i
\(255\) 5600.38 + 525.188i 1.37533 + 0.128975i
\(256\) −7139.74 −1.74310
\(257\) 445.140i 0.108043i 0.998540 + 0.0540215i \(0.0172040\pi\)
−0.998540 + 0.0540215i \(0.982796\pi\)
\(258\) 1335.66 + 407.947i 0.322304 + 0.0984406i
\(259\) 2622.75 2068.70i 0.629227 0.496304i
\(260\) −4159.54 + 855.854i −0.992167 + 0.204146i
\(261\) −2365.21 + 3510.76i −0.560929 + 0.832607i
\(262\) 2715.91 0.640418
\(263\) 5539.14 1.29870 0.649350 0.760490i \(-0.275041\pi\)
0.649350 + 0.760490i \(0.275041\pi\)
\(264\) −14257.7 4354.71i −3.32388 1.01520i
\(265\) 2099.18 431.922i 0.486610 0.100124i
\(266\) 2467.41 1946.18i 0.568747 0.448600i
\(267\) 2151.98 7045.78i 0.493254 1.61496i
\(268\) 5554.66i 1.26606i
\(269\) −6822.25 −1.54632 −0.773160 0.634211i \(-0.781325\pi\)
−0.773160 + 0.634211i \(0.781325\pi\)
\(270\) 5080.90 6201.99i 1.14524 1.39793i
\(271\) 3566.70i 0.799490i 0.916626 + 0.399745i \(0.130901\pi\)
−0.916626 + 0.399745i \(0.869099\pi\)
\(272\) 11575.2i 2.58034i
\(273\) −1879.08 + 731.888i −0.416583 + 0.162256i
\(274\) −6487.98 −1.43049
\(275\) 2735.51 + 6366.00i 0.599845 + 1.39594i
\(276\) 3061.81 10024.7i 0.667751 2.18628i
\(277\) 4554.17i 0.987847i 0.869505 + 0.493923i \(0.164438\pi\)
−0.869505 + 0.493923i \(0.835562\pi\)
\(278\) 8007.14i 1.72747i
\(279\) −1214.35 + 1802.50i −0.260578 + 0.386785i
\(280\) −8196.88 6904.51i −1.74949 1.47366i
\(281\) 4934.61i 1.04759i −0.851843 0.523797i \(-0.824515\pi\)
0.851843 0.523797i \(-0.175485\pi\)
\(282\) −6595.67 2014.50i −1.39279 0.425396i
\(283\) 456.724 0.0959344 0.0479672 0.998849i \(-0.484726\pi\)
0.0479672 + 0.998849i \(0.484726\pi\)
\(284\) 9313.08i 1.94588i
\(285\) −1920.15 180.066i −0.399087 0.0374253i
\(286\) 5937.12i 1.22752i
\(287\) 419.596 + 531.975i 0.0862996 + 0.109413i
\(288\) −4411.12 2971.79i −0.902528 0.608035i
\(289\) −4461.83 −0.908168
\(290\) −1805.70 8775.86i −0.365635 1.77702i
\(291\) −1601.99 + 5245.05i −0.322715 + 1.05660i
\(292\) −6536.90 −1.31008
\(293\) 2102.29i 0.419171i −0.977790 0.209585i \(-0.932789\pi\)
0.977790 0.209585i \(-0.0672114\pi\)
\(294\) −7853.01 4617.43i −1.55781 0.915966i
\(295\) 7723.00 1589.06i 1.52424 0.313623i
\(296\) 9335.50i 1.83316i
\(297\) 4899.07 + 6039.58i 0.957148 + 1.17997i
\(298\) 5686.86i 1.10547i
\(299\) 2332.04 0.451054
\(300\) 1285.68 + 11702.9i 0.247430 + 2.25222i
\(301\) −764.622 + 603.097i −0.146419 + 0.115488i
\(302\) 6400.19 1.21950
\(303\) −1124.33 + 3681.16i −0.213171 + 0.697944i
\(304\) 3968.69i 0.748750i
\(305\) 962.308 + 4676.91i 0.180661 + 0.878030i
\(306\) −7466.01 + 11082.0i −1.39478 + 2.07032i
\(307\) −2780.68 −0.516944 −0.258472 0.966019i \(-0.583219\pi\)
−0.258472 + 0.966019i \(0.583219\pi\)
\(308\) 14610.4 11524.0i 2.70294 2.13195i
\(309\) 1420.06 4649.41i 0.261438 0.855973i
\(310\) −927.085 4505.72i −0.169854 0.825510i
\(311\) −440.562 −0.0803280 −0.0401640 0.999193i \(-0.512788\pi\)
−0.0401640 + 0.999193i \(0.512788\pi\)
\(312\) 1646.25 5389.97i 0.298719 0.978036i
\(313\) 6998.87 1.26390 0.631948 0.775010i \(-0.282255\pi\)
0.631948 + 0.775010i \(0.282255\pi\)
\(314\) 1158.37 0.208186
\(315\) 1533.80 + 5376.18i 0.274348 + 0.961630i
\(316\) 1558.56 0.277455
\(317\) 10112.3 1.79168 0.895839 0.444379i \(-0.146576\pi\)
0.895839 + 0.444379i \(0.146576\pi\)
\(318\) −1487.17 + 4869.14i −0.262253 + 0.858640i
\(319\) 8690.64 1.52534
\(320\) 553.085 113.801i 0.0966199 0.0198802i
\(321\) −1206.30 + 3949.54i −0.209748 + 0.686735i
\(322\) 6524.26 + 8271.62i 1.12914 + 1.43155i
\(323\) 3214.26 0.553703
\(324\) 4963.63 + 12246.3i 0.851102 + 2.09985i
\(325\) −2406.59 + 1034.13i −0.410750 + 0.176502i
\(326\) 9424.84i 1.60121i
\(327\) 306.806 1004.51i 0.0518850 0.169877i
\(328\) −1893.53 −0.318758
\(329\) 3775.81 2978.17i 0.632726 0.499064i
\(330\) −16388.0 1536.82i −2.73372 0.256361i
\(331\) 5030.87 0.835413 0.417706 0.908582i \(-0.362834\pi\)
0.417706 + 0.908582i \(0.362834\pi\)
\(332\) 16076.0i 2.65748i
\(333\) 2720.96 4038.81i 0.447770 0.664641i
\(334\) 10962.3i 1.79589i
\(335\) 690.489 + 3355.84i 0.112613 + 0.547311i
\(336\) 10720.3 4175.47i 1.74059 0.677948i
\(337\) 3231.43i 0.522335i 0.965293 + 0.261168i \(0.0841075\pi\)
−0.965293 + 0.261168i \(0.915892\pi\)
\(338\) −8985.24 −1.44595
\(339\) −2212.73 + 7244.71i −0.354511 + 1.16070i
\(340\) −3954.53 19219.4i −0.630778 3.06564i
\(341\) 4461.97 0.708590
\(342\) 2559.80 3799.60i 0.404731 0.600756i
\(343\) 5766.89 2663.95i 0.907821 0.419357i
\(344\) 2721.62i 0.426569i
\(345\) 603.645 6437.00i 0.0942004 1.00451i
\(346\) 17699.0i 2.75002i
\(347\) −8184.28 −1.26615 −0.633077 0.774089i \(-0.718208\pi\)
−0.633077 + 0.774089i \(0.718208\pi\)
\(348\) 14122.8 + 4313.51i 2.17547 + 0.664449i
\(349\) 11214.5i 1.72005i −0.510248 0.860027i \(-0.670446\pi\)
0.510248 0.860027i \(-0.329554\pi\)
\(350\) −10400.8 5642.92i −1.58842 0.861791i
\(351\) −2283.19 + 1852.04i −0.347202 + 0.281637i
\(352\) 10919.4i 1.65343i
\(353\) 804.207i 0.121257i 0.998160 + 0.0606284i \(0.0193105\pi\)
−0.998160 + 0.0606284i \(0.980690\pi\)
\(354\) −5471.38 + 17913.8i −0.821470 + 2.68957i
\(355\) −1157.69 5626.49i −0.173081 0.841192i
\(356\) −25699.3 −3.82601
\(357\) −3381.73 8682.41i −0.501345 1.28718i
\(358\) 15791.2i 2.33126i
\(359\) 4210.90i 0.619060i −0.950890 0.309530i \(-0.899828\pi\)
0.950890 0.309530i \(-0.100172\pi\)
\(360\) −14451.6 5939.25i −2.11573 0.869516i
\(361\) 5756.96 0.839329
\(362\) 14266.2i 2.07131i
\(363\) 2643.41 8654.79i 0.382213 1.25140i
\(364\) 4356.51 + 5523.29i 0.627316 + 0.795328i
\(365\) −3949.27 + 812.590i −0.566340 + 0.116528i
\(366\) −10848.3 3313.37i −1.54931 0.473203i
\(367\) −12710.6 −1.80787 −0.903935 0.427670i \(-0.859334\pi\)
−0.903935 + 0.427670i \(0.859334\pi\)
\(368\) −13304.4 −1.88462
\(369\) 819.195 + 551.894i 0.115571 + 0.0778603i
\(370\) 2077.29 + 10095.8i 0.291873 + 1.41853i
\(371\) −2198.59 2787.43i −0.307668 0.390070i
\(372\) 7250.99 + 2214.65i 1.01061 + 0.308668i
\(373\) 10529.6i 1.46167i 0.682555 + 0.730835i \(0.260869\pi\)
−0.682555 + 0.730835i \(0.739131\pi\)
\(374\) 27432.8 3.79283
\(375\) 2231.51 + 6910.48i 0.307292 + 0.951615i
\(376\) 13439.7i 1.84335i
\(377\) 3285.39i 0.448823i
\(378\) −12956.7 2917.00i −1.76302 0.396916i
\(379\) −7340.38 −0.994855 −0.497428 0.867505i \(-0.665722\pi\)
−0.497428 + 0.867505i \(0.665722\pi\)
\(380\) 1355.85 + 6589.57i 0.183036 + 0.889573i
\(381\) −5912.19 1805.75i −0.794988 0.242811i
\(382\) 16297.2i 2.18282i
\(383\) 12222.6i 1.63067i 0.578991 + 0.815334i \(0.303447\pi\)
−0.578991 + 0.815334i \(0.696553\pi\)
\(384\) 2000.17 6548.76i 0.265810 0.870287i
\(385\) 7394.34 8778.40i 0.978832 1.16205i
\(386\) 9008.57i 1.18789i
\(387\) −793.251 + 1177.45i −0.104194 + 0.154659i
\(388\) 19131.2 2.50319
\(389\) 1069.72i 0.139426i 0.997567 + 0.0697131i \(0.0222084\pi\)
−0.997567 + 0.0697131i \(0.977792\pi\)
\(390\) 580.976 6195.28i 0.0754330 0.804385i
\(391\) 10775.3i 1.39369i
\(392\) −4135.58 + 17264.9i −0.532853 + 2.22451i
\(393\) −806.493 + 2640.54i −0.103517 + 0.338925i
\(394\) 5804.95 0.742257
\(395\) 941.603 193.742i 0.119942 0.0246790i
\(396\) 15157.5 22498.7i 1.92346 2.85506i
\(397\) −11929.8 −1.50816 −0.754082 0.656780i \(-0.771918\pi\)
−0.754082 + 0.656780i \(0.771918\pi\)
\(398\) 6136.40i 0.772839i
\(399\) 1159.46 + 2976.85i 0.145478 + 0.373506i
\(400\) 13729.8 5899.77i 1.71622 0.737471i
\(401\) 5198.65i 0.647402i 0.946159 + 0.323701i \(0.104927\pi\)
−0.946159 + 0.323701i \(0.895073\pi\)
\(402\) −7784.02 2377.45i −0.965750 0.294967i
\(403\) 1686.80i 0.208499i
\(404\) 13426.9 1.65350
\(405\) 4521.09 + 6781.59i 0.554703 + 0.832049i
\(406\) −11653.1 + 9191.44i −1.42447 + 1.12355i
\(407\) −9997.79 −1.21762
\(408\) 24904.7 + 7606.59i 3.02198 + 0.922996i
\(409\) 16413.0i 1.98428i 0.125136 + 0.992140i \(0.460063\pi\)
−0.125136 + 0.992140i \(0.539937\pi\)
\(410\) −2047.75 + 421.339i −0.246661 + 0.0507523i
\(411\) 1926.61 6307.92i 0.231223 0.757048i
\(412\) −16958.6 −2.02789
\(413\) −8088.72 10255.1i −0.963729 1.22184i
\(414\) 12737.6 + 8581.33i 1.51212 + 1.01872i
\(415\) 1998.38 + 9712.30i 0.236377 + 1.14881i
\(416\) −4127.97 −0.486515
\(417\) −7784.92 2377.73i −0.914219 0.279228i
\(418\) −9405.64 −1.10059
\(419\) −8997.49 −1.04906 −0.524530 0.851392i \(-0.675759\pi\)
−0.524530 + 0.851392i \(0.675759\pi\)
\(420\) 16373.4 10595.4i 1.90223 1.23095i
\(421\) 2279.63 0.263901 0.131950 0.991256i \(-0.457876\pi\)
0.131950 + 0.991256i \(0.457876\pi\)
\(422\) −4271.11 −0.492688
\(423\) 3917.18 5814.41i 0.450260 0.668336i
\(424\) 9921.64 1.13641
\(425\) −4778.25 11119.8i −0.545363 1.26915i
\(426\) 13050.9 + 3986.10i 1.48431 + 0.453350i
\(427\) 6210.29 4898.38i 0.703834 0.555150i
\(428\) 14405.8 1.62694
\(429\) 5772.35 + 1763.04i 0.649631 + 0.198416i
\(430\) −605.601 2943.28i −0.0679178 0.330087i
\(431\) 14695.9i 1.64240i −0.570638 0.821202i \(-0.693304\pi\)
0.570638 0.821202i \(-0.306696\pi\)
\(432\) 13025.8 10566.0i 1.45070 1.17675i
\(433\) 3577.42 0.397043 0.198522 0.980097i \(-0.436386\pi\)
0.198522 + 0.980097i \(0.436386\pi\)
\(434\) −5982.98 + 4719.09i −0.661734 + 0.521944i
\(435\) 9068.51 + 850.421i 0.999545 + 0.0937346i
\(436\) −3663.93 −0.402455
\(437\) 3694.43i 0.404413i
\(438\) 2797.87 9160.48i 0.305222 0.999326i
\(439\) 7413.92i 0.806030i 0.915193 + 0.403015i \(0.132038\pi\)
−0.915193 + 0.403015i \(0.867962\pi\)
\(440\) 6464.60 + 31418.6i 0.700427 + 3.40414i
\(441\) 6821.25 6263.92i 0.736557 0.676376i
\(442\) 10370.7i 1.11602i
\(443\) −5151.58 −0.552503 −0.276252 0.961085i \(-0.589092\pi\)
−0.276252 + 0.961085i \(0.589092\pi\)
\(444\) −16247.1 4962.30i −1.73660 0.530406i
\(445\) −15526.2 + 3194.63i −1.65396 + 0.340314i
\(446\) −13976.5 −1.48387
\(447\) 5529.04 + 1688.72i 0.585043 + 0.178689i
\(448\) −579.276 734.421i −0.0610897 0.0774511i
\(449\) 5031.60i 0.528855i 0.964406 + 0.264427i \(0.0851830\pi\)
−0.964406 + 0.264427i \(0.914817\pi\)
\(450\) −16950.1 3207.28i −1.77564 0.335984i
\(451\) 2027.86i 0.211726i
\(452\) 26424.9 2.74982
\(453\) −1900.55 + 6222.57i −0.197120 + 0.645391i
\(454\) 11285.7i 1.16666i
\(455\) 3318.57 + 2795.35i 0.341928 + 0.288017i
\(456\) −8538.84 2608.00i −0.876903 0.267830i
\(457\) 1781.33i 0.182335i 0.995836 + 0.0911673i \(0.0290598\pi\)
−0.995836 + 0.0911673i \(0.970940\pi\)
\(458\) 8796.44i 0.897447i
\(459\) −8557.45 10549.6i −0.870213 1.07280i
\(460\) −22090.5 + 4545.28i −2.23908 + 0.460706i
\(461\) 17966.1 1.81511 0.907556 0.419931i \(-0.137946\pi\)
0.907556 + 0.419931i \(0.137946\pi\)
\(462\) 9895.71 + 25406.7i 0.996515 + 2.55850i
\(463\) 7730.37i 0.775941i −0.921672 0.387971i \(-0.873176\pi\)
0.921672 0.387971i \(-0.126824\pi\)
\(464\) 18743.4i 1.87530i
\(465\) 4655.98 + 436.625i 0.464335 + 0.0435441i
\(466\) −14902.6 −1.48144
\(467\) 7613.81i 0.754443i 0.926123 + 0.377222i \(0.123121\pi\)
−0.926123 + 0.377222i \(0.876879\pi\)
\(468\) 8505.39 + 5730.10i 0.840089 + 0.565970i
\(469\) 4456.10 3514.76i 0.438728 0.346048i
\(470\) 2990.54 + 14534.3i 0.293497 + 1.42642i
\(471\) −343.979 + 1126.22i −0.0336512 + 0.110177i
\(472\) 36502.3 3.55965
\(473\) 2914.70 0.283336
\(474\) −667.081 + 2184.09i −0.0646414 + 0.211642i
\(475\) 1638.27 + 3812.54i 0.158251 + 0.368277i
\(476\) −25520.7 + 20129.5i −2.45744 + 1.93831i
\(477\) −4292.39 2891.79i −0.412023 0.277581i
\(478\) 33720.9i 3.22669i
\(479\) 1660.45 0.158388 0.0791939 0.996859i \(-0.474765\pi\)
0.0791939 + 0.996859i \(0.474765\pi\)
\(480\) −1068.52 + 11394.2i −0.101606 + 1.08348i
\(481\) 3779.55i 0.358280i
\(482\) 28073.1i 2.65289i
\(483\) −9979.45 + 3886.92i −0.940126 + 0.366172i
\(484\) −31568.1 −2.96470
\(485\) 11558.1 2378.16i 1.08212 0.222653i
\(486\) −19285.8 + 1714.21i −1.80005 + 0.159997i
\(487\) 1783.16i 0.165920i −0.996553 0.0829599i \(-0.973563\pi\)
0.996553 0.0829599i \(-0.0264373\pi\)
\(488\) 22105.1i 2.05051i
\(489\) −9163.28 2798.72i −0.847398 0.258819i
\(490\) −630.705 + 19591.3i −0.0581477 + 1.80621i
\(491\) 4975.18i 0.457284i 0.973511 + 0.228642i \(0.0734286\pi\)
−0.973511 + 0.228642i \(0.926571\pi\)
\(492\) 1006.51 3295.41i 0.0922295 0.301968i
\(493\) −15180.4 −1.38679
\(494\) 3555.69i 0.323842i
\(495\) 6360.59 15476.8i 0.577550 1.40531i
\(496\) 9623.28i 0.871166i
\(497\) −7471.21 + 5892.93i −0.674305 + 0.531859i
\(498\) −22528.1 6880.70i −2.02712 0.619140i
\(499\) −7878.69 −0.706811 −0.353406 0.935470i \(-0.614976\pi\)
−0.353406 + 0.935470i \(0.614976\pi\)
\(500\) 20781.2 14486.5i 1.85873 1.29571i
\(501\) 10658.0 + 3255.26i 0.950431 + 0.290288i
\(502\) 19691.6 1.75076
\(503\) 3798.11i 0.336678i −0.985729 0.168339i \(-0.946160\pi\)
0.985729 0.168339i \(-0.0538404\pi\)
\(504\) 1938.98 + 25809.1i 0.171367 + 2.28101i
\(505\) 8111.86 1669.07i 0.714798 0.147075i
\(506\) 31531.0i 2.77020i
\(507\) 2668.18 8735.88i 0.233724 0.765234i
\(508\) 21564.5i 1.88341i
\(509\) −12066.4 −1.05075 −0.525377 0.850870i \(-0.676076\pi\)
−0.525377 + 0.850870i \(0.676076\pi\)
\(510\) 28625.7 + 2684.44i 2.48542 + 0.233076i
\(511\) 4136.28 + 5244.08i 0.358079 + 0.453982i
\(512\) −25951.6 −2.24006
\(513\) 2934.01 + 3617.05i 0.252514 + 0.311300i
\(514\) 2275.28i 0.195249i
\(515\) −10245.5 + 2108.09i −0.876644 + 0.180376i
\(516\) 4736.57 + 1446.68i 0.404101 + 0.123424i
\(517\) −14393.2 −1.22439
\(518\) 13405.9 10573.9i 1.13711 0.896894i
\(519\) 17207.8 + 5255.75i 1.45538 + 0.444512i
\(520\) −11877.4 + 2443.87i −1.00165 + 0.206098i
\(521\) 671.033 0.0564270 0.0282135 0.999602i \(-0.491018\pi\)
0.0282135 + 0.999602i \(0.491018\pi\)
\(522\) −12089.5 + 17944.8i −1.01368 + 1.50464i
\(523\) 8833.34 0.738538 0.369269 0.929323i \(-0.379608\pi\)
0.369269 + 0.929323i \(0.379608\pi\)
\(524\) 9631.28 0.802947
\(525\) 8574.86 8436.52i 0.712834 0.701333i
\(526\) 28312.6 2.34694
\(527\) −7793.94 −0.644230
\(528\) −32931.7 10058.2i −2.71433 0.829032i
\(529\) 218.010 0.0179181
\(530\) 10729.7 2207.72i 0.879376 0.180938i
\(531\) −15791.9 10639.1i −1.29061 0.869484i
\(532\) 8750.04 6901.61i 0.713087 0.562449i
\(533\) 766.609 0.0622993
\(534\) 10999.6 36013.7i 0.891382 2.91847i
\(535\) 8703.27 1790.76i 0.703318 0.144713i
\(536\) 15861.2i 1.27817i
\(537\) −15352.9 4689.22i −1.23376 0.376824i
\(538\) −34871.1 −2.79443
\(539\) −18489.7 4428.97i −1.47757 0.353932i
\(540\) 18018.1 21993.8i 1.43588 1.75271i
\(541\) −16688.3 −1.32623 −0.663113 0.748519i \(-0.730765\pi\)
−0.663113 + 0.748519i \(0.730765\pi\)
\(542\) 18230.8i 1.44480i
\(543\) 13870.3 + 4236.37i 1.09619 + 0.334807i
\(544\) 19073.5i 1.50325i
\(545\) −2213.56 + 455.456i −0.173979 + 0.0357974i
\(546\) −9604.69 + 3740.96i −0.752826 + 0.293220i
\(547\) 19572.5i 1.52991i −0.644086 0.764953i \(-0.722762\pi\)
0.644086 0.764953i \(-0.277238\pi\)
\(548\) −23008.0 −1.79352
\(549\) 6442.82 9563.30i 0.500862 0.743446i
\(550\) 13982.2 + 32539.0i 1.08401 + 2.52267i
\(551\) 5204.75 0.402413
\(552\) 8742.92 28625.2i 0.674136 2.20719i
\(553\) −986.192 1250.32i −0.0758357 0.0961464i
\(554\) 23278.1i 1.78518i
\(555\) −10432.5 978.332i −0.797901 0.0748250i
\(556\) 28395.3i 2.16588i
\(557\) 23150.1 1.76104 0.880521 0.474008i \(-0.157193\pi\)
0.880521 + 0.474008i \(0.157193\pi\)
\(558\) −6207.00 + 9213.27i −0.470902 + 0.698976i
\(559\) 1101.87i 0.0833704i
\(560\) −18932.7 15947.6i −1.42866 1.20341i
\(561\) −8146.22 + 26671.5i −0.613073 + 2.00726i
\(562\) 25222.7i 1.89316i
\(563\) 5111.84i 0.382661i 0.981526 + 0.191331i \(0.0612803\pi\)
−0.981526 + 0.191331i \(0.938720\pi\)
\(564\) −23389.8 7143.91i −1.74626 0.533356i
\(565\) 15964.6 3284.82i 1.18873 0.244590i
\(566\) 2334.49 0.173367
\(567\) 6683.55 11730.9i 0.495032 0.868875i
\(568\) 26593.2i 1.96448i
\(569\) 1896.42i 0.139723i 0.997557 + 0.0698613i \(0.0222557\pi\)
−0.997557 + 0.0698613i \(0.977744\pi\)
\(570\) −9814.60 920.387i −0.721208 0.0676329i
\(571\) −17070.6 −1.25111 −0.625554 0.780181i \(-0.715127\pi\)
−0.625554 + 0.780181i \(0.715127\pi\)
\(572\) 21054.5i 1.53904i
\(573\) 15844.9 + 4839.47i 1.15520 + 0.352831i
\(574\) 2144.72 + 2719.13i 0.155956 + 0.197725i
\(575\) −12781.0 + 5492.06i −0.926962 + 0.398321i
\(576\) −1130.94 761.919i −0.0818101 0.0551157i
\(577\) −4537.92 −0.327411 −0.163705 0.986509i \(-0.552345\pi\)
−0.163705 + 0.986509i \(0.552345\pi\)
\(578\) −22806.1 −1.64119
\(579\) 8758.56 + 2675.11i 0.628658 + 0.192010i
\(580\) −6403.44 31121.4i −0.458428 2.22801i
\(581\) 12896.6 10172.2i 0.920897 0.726359i
\(582\) −8188.35 + 26809.5i −0.583193 + 1.90943i
\(583\) 10625.5i 0.754826i
\(584\) −18665.9 −1.32261
\(585\) 5850.82 + 2404.55i 0.413507 + 0.169942i
\(586\) 10745.6i 0.757503i
\(587\) 15763.7i 1.10841i 0.832380 + 0.554205i \(0.186978\pi\)
−0.832380 + 0.554205i \(0.813022\pi\)
\(588\) −27848.7 16374.5i −1.95316 1.14843i
\(589\) 2672.23 0.186940
\(590\) 39475.2 8122.31i 2.75452 0.566763i
\(591\) −1723.79 + 5643.85i −0.119978 + 0.392821i
\(592\) 21562.6i 1.49699i
\(593\) 2405.31i 0.166567i −0.996526 0.0832834i \(-0.973459\pi\)
0.996526 0.0832834i \(-0.0265407\pi\)
\(594\) 25041.0 + 30870.6i 1.72971 + 2.13238i
\(595\) −12916.1 + 15333.7i −0.889928 + 1.05650i
\(596\) 20167.0i 1.38603i
\(597\) 5966.10 + 1822.21i 0.409006 + 0.124922i
\(598\) 11919.9 0.815120
\(599\) 8892.20i 0.606553i 0.952903 + 0.303277i \(0.0980806\pi\)
−0.952903 + 0.303277i \(0.901919\pi\)
\(600\) 3671.23 + 33417.3i 0.249795 + 2.27376i
\(601\) 2916.97i 0.197980i −0.995088 0.0989898i \(-0.968439\pi\)
0.995088 0.0989898i \(-0.0315611\pi\)
\(602\) −3908.27 + 3082.66i −0.264600 + 0.208704i
\(603\) 4622.95 6862.00i 0.312207 0.463420i
\(604\) 22696.6 1.52900
\(605\) −19071.8 + 3924.17i −1.28162 + 0.263703i
\(606\) −5746.86 + 18815.8i −0.385232 + 1.26129i
\(607\) 12105.3 0.809458 0.404729 0.914437i \(-0.367366\pi\)
0.404729 + 0.914437i \(0.367366\pi\)
\(608\) 6539.55i 0.436207i
\(609\) −5475.93 14059.1i −0.364361 0.935477i
\(610\) 4918.72 + 23905.5i 0.326481 + 1.58673i
\(611\) 5441.17i 0.360272i
\(612\) −26476.3 + 39299.7i −1.74876 + 2.59574i
\(613\) 11262.7i 0.742083i −0.928616 0.371041i \(-0.879001\pi\)
0.928616 0.371041i \(-0.120999\pi\)
\(614\) −14213.1 −0.934194
\(615\) 198.436 2116.03i 0.0130109 0.138743i
\(616\) 41719.6 32906.4i 2.72878 2.15233i
\(617\) 5183.80 0.338236 0.169118 0.985596i \(-0.445908\pi\)
0.169118 + 0.985596i \(0.445908\pi\)
\(618\) 7258.46 23764.9i 0.472456 1.54687i
\(619\) 26124.4i 1.69633i −0.529734 0.848164i \(-0.677708\pi\)
0.529734 0.848164i \(-0.322292\pi\)
\(620\) −3287.67 15978.4i −0.212961 1.03501i
\(621\) −12125.6 + 9835.83i −0.783550 + 0.635585i
\(622\) −2251.88 −0.145164
\(623\) 16261.4 + 20616.7i 1.04575 + 1.32583i
\(624\) 3802.41 12449.4i 0.243939 0.798680i
\(625\) 10754.2 11335.3i 0.688266 0.725459i
\(626\) 35773.9 2.28405
\(627\) 2793.02 9144.61i 0.177899 0.582457i
\(628\) 4107.86 0.261021
\(629\) 17463.6 1.10703
\(630\) 7839.82 + 27479.7i 0.495787 + 1.73781i
\(631\) −10304.6 −0.650110 −0.325055 0.945695i \(-0.605383\pi\)
−0.325055 + 0.945695i \(0.605383\pi\)
\(632\) 4450.42 0.280108
\(633\) 1268.31 4152.58i 0.0796380 0.260743i
\(634\) 51687.7 3.23782
\(635\) 2680.64 + 13028.2i 0.167525 + 0.814186i
\(636\) −5273.87 + 17267.2i −0.328809 + 1.07655i
\(637\) 1674.32 6989.82i 0.104143 0.434767i
\(638\) 44421.1 2.75650
\(639\) −7750.95 + 11505.0i −0.479848 + 0.712255i
\(640\) −14431.0 + 2969.27i −0.891303 + 0.183392i
\(641\) 23841.8i 1.46910i −0.678552 0.734552i \(-0.737392\pi\)
0.678552 0.734552i \(-0.262608\pi\)
\(642\) −6165.85 + 20187.6i −0.379045 + 1.24103i
\(643\) −8773.65 −0.538101 −0.269050 0.963126i \(-0.586710\pi\)
−0.269050 + 0.963126i \(0.586710\pi\)
\(644\) 23136.6 + 29333.2i 1.41570 + 1.79486i
\(645\) 3041.43 + 285.217i 0.185669 + 0.0174115i
\(646\) 16429.3 1.00062
\(647\) 8008.70i 0.486638i 0.969946 + 0.243319i \(0.0782362\pi\)
−0.969946 + 0.243319i \(0.921764\pi\)
\(648\) 14173.5 + 34969.0i 0.859240 + 2.11993i
\(649\) 39091.8i 2.36439i
\(650\) −12301.0 + 5285.82i −0.742285 + 0.318964i
\(651\) −2811.47 7218.28i −0.169263 0.434573i
\(652\) 33422.8i 2.00757i
\(653\) −4305.61 −0.258027 −0.129014 0.991643i \(-0.541181\pi\)
−0.129014 + 0.991643i \(0.541181\pi\)
\(654\) 1568.20 5134.44i 0.0937638 0.306992i
\(655\) 5818.73 1197.25i 0.347109 0.0714202i
\(656\) −4373.56 −0.260303
\(657\) 8075.43 + 5440.44i 0.479532 + 0.323062i
\(658\) 19299.6 15222.6i 1.14343 0.901882i
\(659\) 24759.2i 1.46355i 0.681545 + 0.731777i \(0.261309\pi\)
−0.681545 + 0.731777i \(0.738691\pi\)
\(660\) −58115.7 5449.93i −3.42750 0.321422i
\(661\) 10995.7i 0.647022i 0.946224 + 0.323511i \(0.104863\pi\)
−0.946224 + 0.323511i \(0.895137\pi\)
\(662\) 25714.7 1.50971
\(663\) −10082.9 3079.59i −0.590627 0.180394i
\(664\) 45904.5i 2.68289i
\(665\) 4428.41 5257.31i 0.258235 0.306571i
\(666\) 13907.8 20643.9i 0.809186 1.20110i
\(667\) 17448.1i 1.01288i
\(668\) 38874.9i 2.25167i
\(669\) 4150.35 13588.6i 0.239853 0.785302i
\(670\) 3529.35 + 17153.0i 0.203509 + 0.989071i
\(671\) −23673.3 −1.36199
\(672\) 17664.7 6880.29i 1.01404 0.394960i
\(673\) 18477.5i 1.05833i 0.848520 + 0.529163i \(0.177494\pi\)
−0.848520 + 0.529163i \(0.822506\pi\)
\(674\) 16517.0i 0.943936i
\(675\) 8151.64 15527.3i 0.464825 0.885403i
\(676\) −31863.9 −1.81292
\(677\) 6639.83i 0.376942i −0.982079 0.188471i \(-0.939647\pi\)
0.982079 0.188471i \(-0.0603531\pi\)
\(678\) −11310.1 + 37030.4i −0.640653 + 2.09756i
\(679\) −12105.4 15347.6i −0.684187 0.867430i
\(680\) −11292.0 54880.4i −0.636809 3.09495i
\(681\) 10972.4 + 3351.29i 0.617423 + 0.188578i
\(682\) 22806.8 1.28052
\(683\) −6422.87 −0.359830 −0.179915 0.983682i \(-0.557582\pi\)
−0.179915 + 0.983682i \(0.557582\pi\)
\(684\) 9077.67 13474.3i 0.507446 0.753220i
\(685\) −13900.2 + 2860.07i −0.775330 + 0.159530i
\(686\) 29476.8 13616.4i 1.64057 0.757840i
\(687\) −8552.32 2612.11i −0.474951 0.145063i
\(688\) 6286.23i 0.348343i
\(689\) −4016.85 −0.222104
\(690\) 3085.46 32902.0i 0.170234 1.81530i
\(691\) 33292.1i 1.83284i −0.400221 0.916419i \(-0.631067\pi\)
0.400221 0.916419i \(-0.368933\pi\)
\(692\) 62765.1i 3.44793i
\(693\) −27640.1 + 2076.53i −1.51509 + 0.113825i
\(694\) −41833.0 −2.28812
\(695\) 3529.76 + 17155.0i 0.192650 + 0.936296i
\(696\) 40327.4 + 12317.1i 2.19627 + 0.670803i
\(697\) 3542.17i 0.192495i
\(698\) 57321.6i 3.10839i
\(699\) 4425.35 14489.0i 0.239460 0.784014i
\(700\) −36883.9 20011.2i −1.99154 1.08050i
\(701\) 21719.6i 1.17024i 0.810946 + 0.585121i \(0.198953\pi\)
−0.810946 + 0.585121i \(0.801047\pi\)
\(702\) −11670.3 + 9466.47i −0.627444 + 0.508958i
\(703\) −5987.59 −0.321232
\(704\) 2799.57i 0.149876i
\(705\) −15019.0 1408.44i −0.802338 0.0752411i
\(706\) 4110.61i 0.219129i
\(707\) −8495.99 10771.4i −0.451944 0.572987i
\(708\) −19402.8 + 63526.8i −1.02995 + 3.37215i
\(709\) 9450.02 0.500568 0.250284 0.968172i \(-0.419476\pi\)
0.250284 + 0.968172i \(0.419476\pi\)
\(710\) −5917.40 28759.1i −0.312783 1.52016i
\(711\) −1925.38 1297.13i −0.101558 0.0684196i
\(712\) −73383.6 −3.86259
\(713\) 8958.26i 0.470532i
\(714\) −17285.3 44379.1i −0.906004 2.32611i
\(715\) −2617.24 12720.1i −0.136894 0.665319i
\(716\) 55999.4i 2.92290i
\(717\) 32785.0 + 10013.5i 1.70764 + 0.521562i
\(718\) 21523.5i 1.11873i
\(719\) 29056.2 1.50711 0.753555 0.657385i \(-0.228338\pi\)
0.753555 + 0.657385i \(0.228338\pi\)
\(720\) −33379.3 13718.1i −1.72774 0.710061i
\(721\) 10730.7 + 13604.6i 0.554274 + 0.702723i
\(722\) 29426.0 1.51679
\(723\) 27294.0 + 8336.34i 1.40398 + 0.428813i
\(724\) 50591.4i 2.59698i
\(725\) −7737.27 18005.9i −0.396352 0.922378i
\(726\) 13511.5 44237.9i 0.690714 2.26146i
\(727\) −3457.74 −0.176397 −0.0881983 0.996103i \(-0.528111\pi\)
−0.0881983 + 0.996103i \(0.528111\pi\)
\(728\) 12439.9 + 15771.6i 0.633314 + 0.802932i
\(729\) 4060.32 19259.7i 0.206286 0.978492i
\(730\) −20186.2 + 4153.45i −1.02346 + 0.210584i
\(731\) −5091.25 −0.257601
\(732\) −38470.7 11750.0i −1.94251 0.593296i
\(733\) 22212.1 1.11927 0.559634 0.828740i \(-0.310942\pi\)
0.559634 + 0.828740i \(0.310942\pi\)
\(734\) −64968.7 −3.26708
\(735\) −18860.3 6430.85i −0.946492 0.322729i
\(736\) −21922.9 −1.09794
\(737\) −16986.4 −0.848986
\(738\) 4187.22 + 2820.94i 0.208853 + 0.140705i
\(739\) −35565.7 −1.77037 −0.885186 0.465237i \(-0.845969\pi\)
−0.885186 + 0.465237i \(0.845969\pi\)
\(740\) 7366.58 + 35802.3i 0.365947 + 1.77854i
\(741\) 3457.01 + 1055.87i 0.171385 + 0.0523459i
\(742\) −11237.8 14247.6i −0.556001 0.704913i
\(743\) −20992.4 −1.03652 −0.518262 0.855222i \(-0.673421\pi\)
−0.518262 + 0.855222i \(0.673421\pi\)
\(744\) 20705.0 + 6323.88i 1.02027 + 0.311619i
\(745\) −2506.92 12183.9i −0.123284 0.599172i
\(746\) 53820.8i 2.64145i
\(747\) 13379.5 19859.6i 0.655328 0.972725i
\(748\) 97283.6 4.75540
\(749\) −9115.41 11556.8i −0.444686 0.563785i
\(750\) 11406.1 + 35322.1i 0.555322 + 1.71971i
\(751\) 5971.01 0.290127 0.145063 0.989422i \(-0.453661\pi\)
0.145063 + 0.989422i \(0.453661\pi\)
\(752\) 31042.3i 1.50531i
\(753\) −5847.46 + 19145.1i −0.282992 + 0.926545i
\(754\) 16792.9i 0.811089i
\(755\) 13712.2 2821.38i 0.660976 0.136001i
\(756\) −45947.6 10344.4i −2.21045 0.497648i
\(757\) 23358.2i 1.12149i 0.827988 + 0.560745i \(0.189485\pi\)
−0.827988 + 0.560745i \(0.810515\pi\)
\(758\) −37519.5 −1.79785
\(759\) 30655.9 + 9363.17i 1.46606 + 0.447775i
\(760\) 3871.59 + 18816.3i 0.184786 + 0.898079i
\(761\) −428.292 −0.0204015 −0.0102008 0.999948i \(-0.503247\pi\)
−0.0102008 + 0.999948i \(0.503247\pi\)
\(762\) −30219.4 9229.85i −1.43666 0.438796i
\(763\) 2318.38 + 2939.30i 0.110001 + 0.139463i
\(764\) 57793.8i 2.73679i
\(765\) −11110.4 + 27034.1i −0.525093 + 1.27767i
\(766\) 62474.4i 2.94686i
\(767\) −14778.2 −0.695711
\(768\) 10836.9 35481.1i 0.509171 1.66708i
\(769\) 16393.0i 0.768720i −0.923183 0.384360i \(-0.874422\pi\)
0.923183 0.384360i \(-0.125578\pi\)
\(770\) 37795.3 44869.7i 1.76889 2.09999i
\(771\) −2212.13 675.647i −0.103331 0.0315601i
\(772\) 31946.6i 1.48936i
\(773\) 22894.4i 1.06527i −0.846344 0.532636i \(-0.821201\pi\)
0.846344 0.532636i \(-0.178799\pi\)
\(774\) −4054.61 + 6018.39i −0.188294 + 0.279492i
\(775\) −3972.49 9244.66i −0.184124 0.428488i
\(776\) 54628.5 2.52713
\(777\) 6299.57 + 16173.8i 0.290857 + 0.746758i
\(778\) 5467.73i 0.251963i
\(779\) 1214.47i 0.0558573i
\(780\) 2060.28 21970.0i 0.0945769 1.00853i
\(781\) 28479.8 1.30485
\(782\) 55076.7i 2.51859i
\(783\) −13856.8 17082.7i −0.632442 0.779675i
\(784\) −9552.12 + 39877.4i −0.435136 + 1.81657i
\(785\) 2481.76 510.640i 0.112838 0.0232172i
\(786\) −4122.29 + 13496.8i −0.187070 + 0.612486i
\(787\) −37222.3 −1.68594 −0.842969 0.537963i \(-0.819194\pi\)
−0.842969 + 0.537963i \(0.819194\pi\)
\(788\) 20585.8 0.930632
\(789\) −8407.48 + 27526.9i −0.379359 + 1.24206i
\(790\) 4812.89 990.286i 0.216753 0.0445985i
\(791\) −16720.5 21198.7i −0.751598 0.952896i
\(792\) 43281.7 64244.5i 1.94185 2.88236i
\(793\) 8949.42i 0.400761i
\(794\) −60977.9 −2.72547
\(795\) −1039.76 + 11087.5i −0.0463854 + 0.494634i
\(796\) 21761.2i 0.968976i
\(797\) 10475.1i 0.465554i −0.972530 0.232777i \(-0.925219\pi\)
0.972530 0.232777i \(-0.0747812\pi\)
\(798\) 5926.45 + 15215.8i 0.262900 + 0.674981i
\(799\) 25141.3 1.11318
\(800\) 22623.7 9721.57i 0.999838 0.429637i
\(801\) 31747.9 + 21388.6i 1.40044 + 0.943483i
\(802\) 26572.3i 1.16995i
\(803\) 19990.2i 0.878502i
\(804\) −27604.0 8431.04i −1.21084 0.369825i
\(805\) 17624.3 + 14845.6i 0.771647 + 0.649984i
\(806\) 8621.85i 0.376789i
\(807\) 10355.0 33903.4i 0.451691 1.47888i
\(808\) 38340.2 1.66931
\(809\) 8052.55i 0.349954i 0.984573 + 0.174977i \(0.0559850\pi\)
−0.984573 + 0.174977i \(0.944015\pi\)
\(810\) 23109.0 + 34663.3i 1.00243 + 1.50363i
\(811\) 11903.9i 0.515416i 0.966223 + 0.257708i \(0.0829672\pi\)
−0.966223 + 0.257708i \(0.917033\pi\)
\(812\) −41324.9 + 32595.1i −1.78598 + 1.40870i
\(813\) −17724.8 5413.66i −0.764621 0.233537i
\(814\) −51102.5 −2.20042
\(815\) 4154.72 + 20192.4i 0.178569 + 0.867862i
\(816\) 57523.4 + 17569.2i 2.46780 + 0.753734i
\(817\) 1745.59 0.0747495
\(818\) 83893.0i 3.58588i
\(819\) −785.010 10449.0i −0.0334926 0.445810i
\(820\) −7261.81 + 1494.17i −0.309260 + 0.0636325i
\(821\) 16286.9i 0.692346i 0.938171 + 0.346173i \(0.112519\pi\)
−0.938171 + 0.346173i \(0.887481\pi\)
\(822\) 9847.65 32242.2i 0.417855 1.36810i
\(823\) 6282.68i 0.266100i 0.991109 + 0.133050i \(0.0424771\pi\)
−0.991109 + 0.133050i \(0.957523\pi\)
\(824\) −48424.8 −2.04728
\(825\) −35788.0 + 3931.68i −1.51028 + 0.165919i
\(826\) −41344.5 52417.7i −1.74160 2.20804i
\(827\) 11366.9 0.477953 0.238977 0.971025i \(-0.423188\pi\)
0.238977 + 0.971025i \(0.423188\pi\)
\(828\) 45170.5 + 30431.5i 1.89587 + 1.27726i
\(829\) 9728.24i 0.407570i 0.979016 + 0.203785i \(0.0653244\pi\)
−0.979016 + 0.203785i \(0.934676\pi\)
\(830\) 10214.5 + 49643.3i 0.427167 + 2.07608i
\(831\) −22632.1 6912.46i −0.944762 0.288557i
\(832\) −1058.35 −0.0441004
\(833\) 32296.9 + 7736.30i 1.34336 + 0.321785i
\(834\) −39791.7 12153.5i −1.65213 0.504605i
\(835\) −4832.46 23486.2i −0.200280 0.973383i
\(836\) −33354.7 −1.37990
\(837\) −7114.40 8770.64i −0.293799 0.362195i
\(838\) −45989.6 −1.89580
\(839\) 12992.1 0.534610 0.267305 0.963612i \(-0.413867\pi\)
0.267305 + 0.963612i \(0.413867\pi\)
\(840\) 46753.6 30254.7i 1.92042 1.24272i
\(841\) −192.087 −0.00787596
\(842\) 11652.0 0.476907
\(843\) 24522.7 + 7489.91i 1.00190 + 0.306010i
\(844\) −15146.4 −0.617726
\(845\) −19250.5 + 3960.93i −0.783714 + 0.161255i
\(846\) 20022.2 29719.7i 0.813685 1.20778i
\(847\) 19975.0 + 25324.8i 0.810328 + 1.02736i
\(848\) 22916.4 0.928011
\(849\) −693.230 + 2269.70i −0.0280231 + 0.0917503i
\(850\) −24423.5 56837.5i −0.985550 2.29354i
\(851\) 20072.5i 0.808550i
\(852\) 46281.6 + 14135.7i 1.86101 + 0.568404i
\(853\) 10335.1 0.414849 0.207424 0.978251i \(-0.433492\pi\)
0.207424 + 0.978251i \(0.433492\pi\)
\(854\) 31743.2 25037.5i 1.27193 1.00324i
\(855\) 3809.30 9268.91i 0.152369 0.370749i
\(856\) 41135.4 1.64250
\(857\) 21299.4i 0.848977i −0.905433 0.424489i \(-0.860454\pi\)
0.905433 0.424489i \(-0.139546\pi\)
\(858\) 29504.7 + 9011.55i 1.17398 + 0.358566i
\(859\) 12245.3i 0.486386i 0.969978 + 0.243193i \(0.0781948\pi\)
−0.969978 + 0.243193i \(0.921805\pi\)
\(860\) −2147.61 10437.6i −0.0851545 0.413859i
\(861\) −3280.54 + 1277.75i −0.129850 + 0.0505755i
\(862\) 75116.3i 2.96806i
\(863\) −24644.7 −0.972092 −0.486046 0.873933i \(-0.661561\pi\)
−0.486046 + 0.873933i \(0.661561\pi\)
\(864\) 21463.7 17410.5i 0.845151 0.685553i
\(865\) −7802.21 37919.5i −0.306685 1.49052i
\(866\) 18285.5 0.717515
\(867\) 6772.31 22173.2i 0.265282 0.868559i
\(868\) −21217.1 + 16735.0i −0.829673 + 0.654406i
\(869\) 4766.15i 0.186054i
\(870\) 46352.6 + 4346.82i 1.80632 + 0.169392i
\(871\) 6421.52i 0.249810i
\(872\) −10462.2 −0.406303
\(873\) −23633.9 15922.2i −0.916250 0.617280i
\(874\) 18883.6i 0.730833i
\(875\) −24771.0 7504.78i −0.957041 0.289952i
\(876\) 9921.91 32485.3i 0.382683 1.25294i
\(877\) 41124.6i 1.58344i 0.610883 + 0.791721i \(0.290815\pi\)
−0.610883 + 0.791721i \(0.709185\pi\)
\(878\) 37895.4i 1.45661i
\(879\) 10447.4 + 3190.92i 0.400889 + 0.122443i
\(880\) 14931.6 + 72568.8i 0.571980 + 2.77988i
\(881\) 40650.0 1.55452 0.777261 0.629179i \(-0.216609\pi\)
0.777261 + 0.629179i \(0.216609\pi\)
\(882\) 34866.0 32017.3i 1.33106 1.22231i
\(883\) 31725.7i 1.20912i −0.796559 0.604561i \(-0.793349\pi\)
0.796559 0.604561i \(-0.206651\pi\)
\(884\) 36776.9i 1.39926i
\(885\) −3825.33 + 40791.6i −0.145296 + 1.54937i
\(886\) −26331.7 −0.998454
\(887\) 6747.77i 0.255432i −0.991811 0.127716i \(-0.959235\pi\)
0.991811 0.127716i \(-0.0407646\pi\)
\(888\) −46393.0 14169.7i −1.75321 0.535478i
\(889\) 17299.7 13645.1i 0.652657 0.514784i
\(890\) −79360.3 + 16329.0i −2.98895 + 0.614998i
\(891\) −37449.8 + 15179.0i −1.40810 + 0.570725i
\(892\) −49564.2 −1.86046
\(893\) −8619.95 −0.323019
\(894\) 28261.0 + 8631.70i 1.05726 + 0.322916i
\(895\) 6961.18 + 33832.0i 0.259985 + 1.26355i
\(896\) 15114.3 + 19162.3i 0.563543 + 0.714474i
\(897\) −3539.64 + 11589.1i −0.131756 + 0.431381i
\(898\) 25718.4i 0.955718i
\(899\) −12620.5 −0.468205
\(900\) −60109.3 11373.8i −2.22627 0.421252i
\(901\) 18560.1i 0.686268i
\(902\) 10365.2i 0.382619i
\(903\) −1836.54 4715.21i −0.0676812 0.173768i
\(904\) 75455.4 2.77612
\(905\) −6288.92 30564.8i −0.230996 1.12266i
\(906\) −9714.41 + 31805.9i −0.356225 + 1.16631i
\(907\) 49852.4i 1.82505i 0.409020 + 0.912525i \(0.365871\pi\)
−0.409020 + 0.912525i \(0.634129\pi\)
\(908\) 40021.7i 1.46274i
\(909\) −16587.1 11174.7i −0.605234 0.407748i
\(910\) 16962.5 + 14288.1i 0.617913 + 0.520489i
\(911\) 14687.9i 0.534175i −0.963672 0.267087i \(-0.913939\pi\)
0.963672 0.267087i \(-0.0860612\pi\)
\(912\) −19722.5 6023.80i −0.716093 0.218715i
\(913\) −49161.1 −1.78203
\(914\) 9105.03i 0.329505i
\(915\) −24702.6 2316.55i −0.892507 0.0836969i
\(916\) 31194.3i 1.12521i
\(917\) −6094.27 7726.47i −0.219466 0.278245i
\(918\) −43740.4 53923.2i −1.57260 1.93870i
\(919\) 48920.4 1.75597 0.877984 0.478689i \(-0.158888\pi\)
0.877984 + 0.478689i \(0.158888\pi\)
\(920\) −63078.9 + 12978.9i −2.26049 + 0.465112i
\(921\) 4220.61 13818.7i 0.151003 0.494398i
\(922\) 91831.7 3.28017
\(923\) 10766.5i 0.383947i
\(924\) 35092.6 + 90098.2i 1.24942 + 3.20781i
\(925\) 8901.03 + 20714.2i 0.316394 + 0.736302i
\(926\) 39512.8i 1.40224i
\(927\) 20950.0 + 14114.0i 0.742273 + 0.500071i
\(928\) 30885.1i 1.09252i
\(929\) 34688.5 1.22507 0.612537 0.790442i \(-0.290149\pi\)
0.612537 + 0.790442i \(0.290149\pi\)
\(930\) 23798.5 + 2231.76i 0.839121 + 0.0786905i
\(931\) −11073.3 2652.47i −0.389811 0.0933741i
\(932\) −52848.3 −1.85741
\(933\) 668.699 2189.39i 0.0234643 0.0768245i
\(934\) 38917.1i 1.36339i
\(935\) 58773.8 12093.1i 2.05573 0.422982i
\(936\) 24286.9 + 16362.1i 0.848122 + 0.571382i
\(937\) 29779.4 1.03826 0.519130 0.854695i \(-0.326256\pi\)
0.519130 + 0.854695i \(0.326256\pi\)
\(938\) 22776.8 17965.3i 0.792846 0.625359i
\(939\) −10623.1 + 34781.1i −0.369193 + 1.20877i
\(940\) 10605.2 + 51542.3i 0.367982 + 1.78843i
\(941\) 18023.5 0.624389 0.312195 0.950018i \(-0.398936\pi\)
0.312195 + 0.950018i \(0.398936\pi\)
\(942\) −1758.21 + 5756.54i −0.0608127 + 0.199107i
\(943\) 4071.32 0.140594
\(944\) 84310.8 2.90687
\(945\) −29045.1 537.894i −0.999829 0.0185161i
\(946\) 14898.1 0.512029
\(947\) 34592.1 1.18700 0.593501 0.804833i \(-0.297745\pi\)
0.593501 + 0.804833i \(0.297745\pi\)
\(948\) −2365.63 + 7745.30i −0.0810465 + 0.265354i
\(949\) 7557.05 0.258495
\(950\) 8373.84 + 19487.3i 0.285982 + 0.665529i
\(951\) −15348.7 + 50253.2i −0.523361 + 1.71354i
\(952\) −72873.7 + 57479.2i −2.48093 + 1.95684i
\(953\) 41901.5 1.42426 0.712132 0.702046i \(-0.247730\pi\)
0.712132 + 0.702046i \(0.247730\pi\)
\(954\) −21940.0 14781.1i −0.744586 0.501629i
\(955\) −7184.24 34916.1i −0.243431 1.18310i
\(956\) 119582.i 4.04558i
\(957\) −13190.9 + 43188.3i −0.445561 + 1.45881i
\(958\) 8487.17 0.286230
\(959\) 14558.5 + 18457.6i 0.490217 + 0.621509i
\(960\) −273.952 + 2921.30i −0.00921015 + 0.0982131i
\(961\) 23311.4 0.782497
\(962\) 19318.7i 0.647464i
\(963\) −17796.4 11989.5i −0.595514 0.401200i
\(964\) 99554.0i 3.32616i
\(965\) −3971.22 19300.5i −0.132475 0.643840i
\(966\) −51008.8 + 19867.5i −1.69894 + 0.661726i
\(967\) 1876.37i 0.0623993i −0.999513 0.0311996i \(-0.990067\pi\)
0.999513 0.0311996i \(-0.00993277\pi\)
\(968\) −90141.8 −2.99304
\(969\) −4878.70 + 15973.3i −0.161740 + 0.529554i
\(970\) 59077.8 12155.7i 1.95554 0.402366i
\(971\) −42968.7 −1.42011 −0.710057 0.704144i \(-0.751331\pi\)
−0.710057 + 0.704144i \(0.751331\pi\)
\(972\) −68392.3 + 6079.02i −2.25688 + 0.200602i
\(973\) 22779.5 17967.4i 0.750541 0.591991i
\(974\) 9114.43i 0.299841i
\(975\) −1486.32 13529.3i −0.0488210 0.444393i
\(976\) 51057.0i 1.67448i
\(977\) −18443.6 −0.603954 −0.301977 0.953315i \(-0.597647\pi\)
−0.301977 + 0.953315i \(0.597647\pi\)
\(978\) −46837.0 14305.3i −1.53137 0.467723i
\(979\) 78589.6i 2.56561i
\(980\) −2236.63 + 69475.4i −0.0729048 + 2.26460i
\(981\) 4526.27 + 3049.36i 0.147312 + 0.0992442i
\(982\) 25430.0i 0.826379i
\(983\) 17892.5i 0.580550i −0.956943 0.290275i \(-0.906253\pi\)
0.956943 0.290275i \(-0.0937468\pi\)
\(984\) 2874.06 9409.94i 0.0931113 0.304855i
\(985\) 12436.9 2558.98i 0.402307 0.0827775i
\(986\) −77592.6 −2.50614
\(987\) 9069.08 + 23284.3i 0.292474 + 0.750911i
\(988\) 12609.4i 0.406029i
\(989\) 5851.81i 0.188146i
\(990\) 32511.4 79107.7i 1.04372 2.53960i
\(991\) 26347.5 0.844557 0.422278 0.906466i \(-0.361230\pi\)
0.422278 + 0.906466i \(0.361230\pi\)
\(992\) 15857.1i 0.507524i
\(993\) −7636.01 + 25001.0i −0.244030 + 0.798977i
\(994\) −38188.2 + 30121.0i −1.21857 + 0.961147i
\(995\) −2705.09 13147.0i −0.0861881 0.418883i
\(996\) −79890.1 24400.6i −2.54158 0.776269i
\(997\) 37680.0 1.19693 0.598463 0.801150i \(-0.295778\pi\)
0.598463 + 0.801150i \(0.295778\pi\)
\(998\) −40271.0 −1.27731
\(999\) 15941.0 + 19652.1i 0.504856 + 0.622387i
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 105.4.g.b.104.38 yes 40
3.2 odd 2 inner 105.4.g.b.104.1 40
5.4 even 2 inner 105.4.g.b.104.3 yes 40
7.6 odd 2 inner 105.4.g.b.104.39 yes 40
15.14 odd 2 inner 105.4.g.b.104.40 yes 40
21.20 even 2 inner 105.4.g.b.104.4 yes 40
35.34 odd 2 inner 105.4.g.b.104.2 yes 40
105.104 even 2 inner 105.4.g.b.104.37 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.g.b.104.1 40 3.2 odd 2 inner
105.4.g.b.104.2 yes 40 35.34 odd 2 inner
105.4.g.b.104.3 yes 40 5.4 even 2 inner
105.4.g.b.104.4 yes 40 21.20 even 2 inner
105.4.g.b.104.37 yes 40 105.104 even 2 inner
105.4.g.b.104.38 yes 40 1.1 even 1 trivial
105.4.g.b.104.39 yes 40 7.6 odd 2 inner
105.4.g.b.104.40 yes 40 15.14 odd 2 inner