Properties

Label 45.4.j.a.4.5
Level $45$
Weight $4$
Character 45.4
Analytic conductor $2.655$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,4,Mod(4,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 4.5
Character \(\chi\) \(=\) 45.4
Dual form 45.4.j.a.34.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.31667 + 1.33753i) q^{2} +(-5.14958 - 0.694136i) q^{3} +(-0.422017 + 0.730954i) q^{4} +(7.31972 - 8.45113i) q^{5} +(12.8583 - 5.27964i) q^{6} +(13.3501 - 7.70766i) q^{7} -23.6584i q^{8} +(26.0363 + 7.14902i) q^{9} +O(q^{10})\) \(q+(-2.31667 + 1.33753i) q^{2} +(-5.14958 - 0.694136i) q^{3} +(-0.422017 + 0.730954i) q^{4} +(7.31972 - 8.45113i) q^{5} +(12.8583 - 5.27964i) q^{6} +(13.3501 - 7.70766i) q^{7} -23.6584i q^{8} +(26.0363 + 7.14902i) q^{9} +(-5.65374 + 29.3689i) q^{10} +(-22.2799 - 38.5899i) q^{11} +(2.68059 - 3.47117i) q^{12} +(24.2689 + 14.0117i) q^{13} +(-20.6185 + 35.7123i) q^{14} +(-43.5597 + 38.4389i) q^{15} +(28.2677 + 48.9610i) q^{16} -92.6615i q^{17} +(-69.8798 + 18.2625i) q^{18} -49.5811 q^{19} +(3.08835 + 8.91690i) q^{20} +(-74.0974 + 30.4245i) q^{21} +(103.230 + 59.6001i) q^{22} +(0.799176 + 0.461404i) q^{23} +(-16.4221 + 121.831i) q^{24} +(-17.8434 - 123.720i) q^{25} -74.9642 q^{26} +(-129.114 - 54.8872i) q^{27} +13.0110i q^{28} +(94.9247 + 164.414i) q^{29} +(49.5004 - 147.313i) q^{30} +(149.590 - 259.098i) q^{31} +(32.9360 + 19.0156i) q^{32} +(87.9454 + 214.187i) q^{33} +(123.938 + 214.666i) q^{34} +(32.5802 - 169.241i) q^{35} +(-16.2134 + 16.0144i) q^{36} +57.8330i q^{37} +(114.863 - 66.3163i) q^{38} +(-115.249 - 89.0001i) q^{39} +(-199.940 - 173.173i) q^{40} +(143.940 - 249.311i) q^{41} +(130.966 - 169.591i) q^{42} +(0.512647 - 0.295977i) q^{43} +37.6099 q^{44} +(250.996 - 167.708i) q^{45} -2.46857 q^{46} +(-518.145 + 299.151i) q^{47} +(-111.581 - 271.750i) q^{48} +(-52.6839 + 91.2513i) q^{49} +(206.817 + 262.753i) q^{50} +(-64.3197 + 477.168i) q^{51} +(-20.4838 + 11.8263i) q^{52} +146.339i q^{53} +(372.528 - 45.5382i) q^{54} +(-489.211 - 94.1769i) q^{55} +(-182.351 - 315.840i) q^{56} +(255.322 + 34.4160i) q^{57} +(-439.819 - 253.930i) q^{58} +(-96.5330 + 167.200i) q^{59} +(-9.71415 - 48.0620i) q^{60} +(283.076 + 490.303i) q^{61} +800.326i q^{62} +(402.689 - 105.240i) q^{63} -554.019 q^{64} +(296.056 - 102.538i) q^{65} +(-490.223 - 378.571i) q^{66} +(307.580 + 177.581i) q^{67} +(67.7313 + 39.1047i) q^{68} +(-3.79514 - 2.93078i) q^{69} +(150.888 + 435.653i) q^{70} -320.703 q^{71} +(169.134 - 615.977i) q^{72} -636.782i q^{73} +(-77.3535 - 133.980i) q^{74} +(6.00734 + 649.491i) q^{75} +(20.9240 - 36.2415i) q^{76} +(-594.875 - 343.452i) q^{77} +(386.034 + 52.0353i) q^{78} +(-143.883 - 249.212i) q^{79} +(620.688 + 119.487i) q^{80} +(626.783 + 372.269i) q^{81} +770.097i q^{82} +(246.867 - 142.529i) q^{83} +(9.03144 - 67.0014i) q^{84} +(-783.094 - 678.256i) q^{85} +(-0.791757 + 1.37136i) q^{86} +(-374.696 - 912.556i) q^{87} +(-912.973 + 527.105i) q^{88} +331.615 q^{89} +(-357.161 + 724.240i) q^{90} +431.988 q^{91} +(-0.674531 + 0.389441i) q^{92} +(-950.175 + 1230.41i) q^{93} +(800.248 - 1386.07i) q^{94} +(-362.920 + 419.016i) q^{95} +(-156.407 - 120.784i) q^{96} +(1577.58 - 910.814i) q^{97} -281.866i q^{98} +(-304.207 - 1164.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 54 q^{4} + 3 q^{5} - 12 q^{6} - 18 q^{9} - 20 q^{10} + 90 q^{11} - 102 q^{14} - 87 q^{15} - 146 q^{16} - 8 q^{19} - 6 q^{20} + 30 q^{21} + 462 q^{24} + 71 q^{25} - 936 q^{26} - 516 q^{29} - 66 q^{30} - 38 q^{31} + 212 q^{34} - 534 q^{35} + 864 q^{36} + 330 q^{39} + 44 q^{40} + 576 q^{41} + 3288 q^{44} + 1053 q^{45} - 580 q^{46} - 4 q^{49} + 558 q^{50} + 1260 q^{51} - 3726 q^{54} + 30 q^{55} + 2430 q^{56} - 2202 q^{59} - 5052 q^{60} - 20 q^{61} + 644 q^{64} + 339 q^{65} - 5052 q^{66} + 1452 q^{69} + 636 q^{70} - 5904 q^{71} - 4080 q^{74} + 2283 q^{75} + 396 q^{76} - 218 q^{79} + 2532 q^{80} + 198 q^{81} + 4662 q^{84} - 704 q^{85} + 6108 q^{86} + 8148 q^{89} + 6408 q^{90} - 1884 q^{91} - 1078 q^{94} - 1692 q^{95} + 11874 q^{96} - 1602 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31667 + 1.33753i −0.819068 + 0.472889i −0.850095 0.526630i \(-0.823455\pi\)
0.0310272 + 0.999519i \(0.490122\pi\)
\(3\) −5.14958 0.694136i −0.991037 0.133587i
\(4\) −0.422017 + 0.730954i −0.0527521 + 0.0913693i
\(5\) 7.31972 8.45113i 0.654696 0.755892i
\(6\) 12.8583 5.27964i 0.874898 0.359234i
\(7\) 13.3501 7.70766i 0.720835 0.416175i −0.0942246 0.995551i \(-0.530037\pi\)
0.815060 + 0.579376i \(0.196704\pi\)
\(8\) 23.6584i 1.04556i
\(9\) 26.0363 + 7.14902i 0.964309 + 0.264779i
\(10\) −5.65374 + 29.3689i −0.178787 + 0.928726i
\(11\) −22.2799 38.5899i −0.610694 1.05775i −0.991124 0.132944i \(-0.957557\pi\)
0.380429 0.924810i \(-0.375776\pi\)
\(12\) 2.68059 3.47117i 0.0644850 0.0835034i
\(13\) 24.2689 + 14.0117i 0.517768 + 0.298933i 0.736021 0.676959i \(-0.236702\pi\)
−0.218253 + 0.975892i \(0.570036\pi\)
\(14\) −20.6185 + 35.7123i −0.393609 + 0.681750i
\(15\) −43.5597 + 38.4389i −0.749805 + 0.661659i
\(16\) 28.2677 + 48.9610i 0.441682 + 0.765016i
\(17\) 92.6615i 1.32198i −0.750394 0.660991i \(-0.770136\pi\)
0.750394 0.660991i \(-0.229864\pi\)
\(18\) −69.8798 + 18.2625i −0.915045 + 0.239140i
\(19\) −49.5811 −0.598667 −0.299334 0.954149i \(-0.596764\pi\)
−0.299334 + 0.954149i \(0.596764\pi\)
\(20\) 3.08835 + 8.91690i 0.0345288 + 0.0996940i
\(21\) −74.0974 + 30.4245i −0.769970 + 0.316150i
\(22\) 103.230 + 59.6001i 1.00040 + 0.577581i
\(23\) 0.799176 + 0.461404i 0.00724520 + 0.00418302i 0.503618 0.863926i \(-0.332002\pi\)
−0.496373 + 0.868109i \(0.665335\pi\)
\(24\) −16.4221 + 121.831i −0.139673 + 1.03619i
\(25\) −17.8434 123.720i −0.142747 0.989759i
\(26\) −74.9642 −0.565449
\(27\) −129.114 54.8872i −0.920295 0.391224i
\(28\) 13.0110i 0.0878163i
\(29\) 94.9247 + 164.414i 0.607830 + 1.05279i 0.991597 + 0.129363i \(0.0412933\pi\)
−0.383767 + 0.923430i \(0.625373\pi\)
\(30\) 49.5004 147.313i 0.301250 0.896518i
\(31\) 149.590 259.098i 0.866683 1.50114i 0.00131648 0.999999i \(-0.499581\pi\)
0.865366 0.501140i \(-0.167086\pi\)
\(32\) 32.9360 + 19.0156i 0.181947 + 0.105047i
\(33\) 87.9454 + 214.187i 0.463919 + 1.12985i
\(34\) 123.938 + 214.666i 0.625151 + 1.08279i
\(35\) 32.5802 169.241i 0.157345 0.817342i
\(36\) −16.2134 + 16.0144i −0.0750619 + 0.0741406i
\(37\) 57.8330i 0.256965i 0.991712 + 0.128482i \(0.0410105\pi\)
−0.991712 + 0.128482i \(0.958989\pi\)
\(38\) 114.863 66.3163i 0.490349 0.283103i
\(39\) −115.249 89.0001i −0.473194 0.365421i
\(40\) −199.940 173.173i −0.790332 0.684525i
\(41\) 143.940 249.311i 0.548284 0.949656i −0.450108 0.892974i \(-0.648615\pi\)
0.998392 0.0566817i \(-0.0180520\pi\)
\(42\) 130.966 169.591i 0.481154 0.623059i
\(43\) 0.512647 0.295977i 0.00181809 0.00104967i −0.499091 0.866550i \(-0.666333\pi\)
0.500909 + 0.865500i \(0.332999\pi\)
\(44\) 37.6099 0.128862
\(45\) 250.996 167.708i 0.831473 0.555565i
\(46\) −2.46857 −0.00791242
\(47\) −518.145 + 299.151i −1.60807 + 0.928418i −0.618266 + 0.785969i \(0.712164\pi\)
−0.989802 + 0.142449i \(0.954502\pi\)
\(48\) −111.581 271.750i −0.335528 0.817162i
\(49\) −52.6839 + 91.2513i −0.153597 + 0.266039i
\(50\) 206.817 + 262.753i 0.584966 + 0.743176i
\(51\) −64.3197 + 477.168i −0.176599 + 1.31013i
\(52\) −20.4838 + 11.8263i −0.0546267 + 0.0315387i
\(53\) 146.339i 0.379267i 0.981855 + 0.189634i \(0.0607301\pi\)
−0.981855 + 0.189634i \(0.939270\pi\)
\(54\) 372.528 45.5382i 0.938790 0.114759i
\(55\) −489.211 94.1769i −1.19937 0.230888i
\(56\) −182.351 315.840i −0.435136 0.753678i
\(57\) 255.322 + 34.4160i 0.593301 + 0.0799739i
\(58\) −439.819 253.930i −0.995708 0.574873i
\(59\) −96.5330 + 167.200i −0.213009 + 0.368942i −0.952655 0.304054i \(-0.901660\pi\)
0.739646 + 0.672996i \(0.234993\pi\)
\(60\) −9.71415 48.0620i −0.0209015 0.103413i
\(61\) 283.076 + 490.303i 0.594167 + 1.02913i 0.993664 + 0.112393i \(0.0358517\pi\)
−0.399496 + 0.916735i \(0.630815\pi\)
\(62\) 800.326i 1.63938i
\(63\) 402.689 105.240i 0.805302 0.210459i
\(64\) −554.019 −1.08207
\(65\) 296.056 102.538i 0.564942 0.195666i
\(66\) −490.223 378.571i −0.914276 0.706044i
\(67\) 307.580 + 177.581i 0.560849 + 0.323806i 0.753486 0.657464i \(-0.228371\pi\)
−0.192637 + 0.981270i \(0.561704\pi\)
\(68\) 67.7313 + 39.1047i 0.120789 + 0.0697373i
\(69\) −3.79514 2.93078i −0.00662147 0.00511339i
\(70\) 150.888 + 435.653i 0.257636 + 0.743865i
\(71\) −320.703 −0.536062 −0.268031 0.963410i \(-0.586373\pi\)
−0.268031 + 0.963410i \(0.586373\pi\)
\(72\) 169.134 615.977i 0.276842 1.00824i
\(73\) 636.782i 1.02095i −0.859891 0.510477i \(-0.829469\pi\)
0.859891 0.510477i \(-0.170531\pi\)
\(74\) −77.3535 133.980i −0.121516 0.210471i
\(75\) 6.00734 + 649.491i 0.00924891 + 0.999957i
\(76\) 20.9240 36.2415i 0.0315809 0.0546998i
\(77\) −594.875 343.452i −0.880420 0.508311i
\(78\) 386.034 + 52.0353i 0.560381 + 0.0755364i
\(79\) −143.883 249.212i −0.204912 0.354918i 0.745193 0.666849i \(-0.232358\pi\)
−0.950105 + 0.311931i \(0.899024\pi\)
\(80\) 620.688 + 119.487i 0.867438 + 0.166989i
\(81\) 626.783 + 372.269i 0.859785 + 0.510657i
\(82\) 770.097i 1.03711i
\(83\) 246.867 142.529i 0.326472 0.188489i −0.327801 0.944747i \(-0.606308\pi\)
0.654274 + 0.756258i \(0.272974\pi\)
\(84\) 9.03144 67.0014i 0.0117311 0.0870292i
\(85\) −783.094 678.256i −0.999277 0.865496i
\(86\) −0.791757 + 1.37136i −0.000992759 + 0.00171951i
\(87\) −374.696 912.556i −0.461743 1.12456i
\(88\) −912.973 + 527.105i −1.10595 + 0.638518i
\(89\) 331.615 0.394957 0.197478 0.980307i \(-0.436725\pi\)
0.197478 + 0.980307i \(0.436725\pi\)
\(90\) −357.161 + 724.240i −0.418312 + 0.848240i
\(91\) 431.988 0.497634
\(92\) −0.674531 + 0.389441i −0.000764399 + 0.000441326i
\(93\) −950.175 + 1230.41i −1.05945 + 1.37191i
\(94\) 800.248 1386.07i 0.878078 1.52088i
\(95\) −362.920 + 419.016i −0.391945 + 0.452528i
\(96\) −156.407 120.784i −0.166284 0.128411i
\(97\) 1577.58 910.814i 1.65133 0.953393i 0.674798 0.738003i \(-0.264231\pi\)
0.976528 0.215391i \(-0.0691024\pi\)
\(98\) 281.866i 0.290538i
\(99\) −304.207 1164.02i −0.308828 1.18170i
\(100\) 97.9638 + 39.1692i 0.0979638 + 0.0391692i
\(101\) 573.683 + 993.648i 0.565184 + 0.978927i 0.997033 + 0.0769812i \(0.0245281\pi\)
−0.431849 + 0.901946i \(0.642139\pi\)
\(102\) −489.219 1191.47i −0.474901 1.15660i
\(103\) 1370.52 + 791.272i 1.31108 + 0.756955i 0.982276 0.187442i \(-0.0600197\pi\)
0.328808 + 0.944397i \(0.393353\pi\)
\(104\) 331.493 574.162i 0.312553 0.541358i
\(105\) −285.251 + 848.905i −0.265120 + 0.788997i
\(106\) −195.733 339.019i −0.179351 0.310646i
\(107\) 385.387i 0.348194i −0.984728 0.174097i \(-0.944299\pi\)
0.984728 0.174097i \(-0.0557007\pi\)
\(108\) 94.6082 71.2130i 0.0842934 0.0634488i
\(109\) 203.502 0.178825 0.0894126 0.995995i \(-0.471501\pi\)
0.0894126 + 0.995995i \(0.471501\pi\)
\(110\) 1259.31 436.158i 1.09155 0.378055i
\(111\) 40.1440 297.816i 0.0343270 0.254661i
\(112\) 754.750 + 435.755i 0.636761 + 0.367634i
\(113\) 57.1707 + 33.0075i 0.0475944 + 0.0274786i 0.523608 0.851959i \(-0.324586\pi\)
−0.476014 + 0.879438i \(0.657919\pi\)
\(114\) −637.529 + 261.770i −0.523773 + 0.215062i
\(115\) 9.74913 3.37659i 0.00790532 0.00273799i
\(116\) −160.239 −0.128257
\(117\) 531.704 + 538.311i 0.420137 + 0.425358i
\(118\) 516.464i 0.402918i
\(119\) −714.203 1237.04i −0.550175 0.952932i
\(120\) 909.401 + 1030.55i 0.691805 + 0.783967i
\(121\) −327.286 + 566.876i −0.245895 + 0.425903i
\(122\) −1311.59 757.247i −0.973327 0.561950i
\(123\) −914.286 + 1183.93i −0.670231 + 0.867901i
\(124\) 126.259 + 218.687i 0.0914386 + 0.158376i
\(125\) −1176.18 754.799i −0.841607 0.540090i
\(126\) −792.138 + 782.415i −0.560073 + 0.553199i
\(127\) 1821.52i 1.27270i 0.771399 + 0.636352i \(0.219557\pi\)
−0.771399 + 0.636352i \(0.780443\pi\)
\(128\) 1019.99 588.893i 0.704339 0.406650i
\(129\) −2.84536 + 1.16831i −0.00194202 + 0.000797394i
\(130\) −548.717 + 633.532i −0.370197 + 0.427419i
\(131\) −119.129 + 206.337i −0.0794530 + 0.137617i −0.903014 0.429611i \(-0.858651\pi\)
0.823561 + 0.567228i \(0.191984\pi\)
\(132\) −193.675 26.1064i −0.127707 0.0172142i
\(133\) −661.910 + 382.154i −0.431541 + 0.249150i
\(134\) −950.083 −0.612498
\(135\) −1408.94 + 689.400i −0.898237 + 0.439512i
\(136\) −2192.22 −1.38221
\(137\) −1773.17 + 1023.74i −1.10578 + 0.638424i −0.937734 0.347355i \(-0.887080\pi\)
−0.168048 + 0.985779i \(0.553747\pi\)
\(138\) 12.7121 + 1.71353i 0.00784150 + 0.00105699i
\(139\) −1089.68 + 1887.39i −0.664934 + 1.15170i 0.314369 + 0.949301i \(0.398207\pi\)
−0.979303 + 0.202399i \(0.935126\pi\)
\(140\) 109.958 + 95.2372i 0.0663797 + 0.0574930i
\(141\) 2875.88 1180.84i 1.71768 0.705281i
\(142\) 742.964 428.950i 0.439071 0.253498i
\(143\) 1248.71i 0.730228i
\(144\) 385.964 + 1476.85i 0.223359 + 0.854660i
\(145\) 2084.31 + 401.246i 1.19374 + 0.229805i
\(146\) 851.716 + 1475.22i 0.482798 + 0.836231i
\(147\) 334.641 433.336i 0.187760 0.243136i
\(148\) −42.2733 24.4065i −0.0234787 0.0135554i
\(149\) 77.9741 135.055i 0.0428717 0.0742560i −0.843793 0.536668i \(-0.819683\pi\)
0.886665 + 0.462412i \(0.153016\pi\)
\(150\) −882.632 1496.62i −0.480444 0.814659i
\(151\) −807.071 1397.89i −0.434957 0.753368i 0.562335 0.826909i \(-0.309903\pi\)
−0.997292 + 0.0735418i \(0.976570\pi\)
\(152\) 1173.01i 0.625943i
\(153\) 662.439 2412.57i 0.350033 1.27480i
\(154\) 1837.51 0.961498
\(155\) −1094.71 3160.73i −0.567286 1.63791i
\(156\) 113.692 46.6820i 0.0583502 0.0239587i
\(157\) 856.073 + 494.254i 0.435172 + 0.251247i 0.701548 0.712623i \(-0.252493\pi\)
−0.266375 + 0.963869i \(0.585826\pi\)
\(158\) 666.658 + 384.895i 0.335674 + 0.193801i
\(159\) 101.579 753.583i 0.0506650 0.375868i
\(160\) 401.785 139.157i 0.198525 0.0687585i
\(161\) 14.2254 0.00696347
\(162\) −1949.97 24.0828i −0.945706 0.0116798i
\(163\) 2974.11i 1.42914i −0.699564 0.714570i \(-0.746622\pi\)
0.699564 0.714570i \(-0.253378\pi\)
\(164\) 121.490 + 210.427i 0.0578462 + 0.100193i
\(165\) 2453.86 + 824.551i 1.15777 + 0.389037i
\(166\) −381.274 + 660.386i −0.178269 + 0.308770i
\(167\) 2112.20 + 1219.48i 0.978724 + 0.565067i 0.901885 0.431977i \(-0.142184\pi\)
0.0768396 + 0.997043i \(0.475517\pi\)
\(168\) 719.793 + 1753.02i 0.330555 + 0.805051i
\(169\) −705.847 1222.56i −0.321278 0.556469i
\(170\) 2721.36 + 523.884i 1.22776 + 0.236353i
\(171\) −1290.91 354.456i −0.577300 0.158514i
\(172\) 0.499628i 0.000221490i
\(173\) −2298.08 + 1326.79i −1.00994 + 0.583089i −0.911174 0.412022i \(-0.864823\pi\)
−0.0987652 + 0.995111i \(0.531489\pi\)
\(174\) 2088.62 + 1612.93i 0.909989 + 0.702733i
\(175\) −1191.80 1514.14i −0.514810 0.654046i
\(176\) 1259.60 2181.69i 0.539466 0.934382i
\(177\) 613.164 794.003i 0.260385 0.337180i
\(178\) −768.244 + 443.546i −0.323496 + 0.186771i
\(179\) 2102.30 0.877841 0.438921 0.898526i \(-0.355361\pi\)
0.438921 + 0.898526i \(0.355361\pi\)
\(180\) 16.6622 + 254.242i 0.00689961 + 0.105278i
\(181\) 1597.36 0.655973 0.327987 0.944682i \(-0.393630\pi\)
0.327987 + 0.944682i \(0.393630\pi\)
\(182\) −1000.78 + 577.798i −0.407596 + 0.235326i
\(183\) −1117.39 2721.35i −0.451364 1.09928i
\(184\) 10.9161 18.9072i 0.00437360 0.00757531i
\(185\) 488.754 + 423.321i 0.194238 + 0.168234i
\(186\) 555.535 4121.34i 0.218999 1.62469i
\(187\) −3575.79 + 2064.49i −1.39833 + 0.807327i
\(188\) 504.987i 0.195904i
\(189\) −2146.73 + 262.418i −0.826199 + 0.100995i
\(190\) 280.318 1456.14i 0.107034 0.555997i
\(191\) 1703.71 + 2950.92i 0.645426 + 1.11791i 0.984203 + 0.177044i \(0.0566535\pi\)
−0.338777 + 0.940867i \(0.610013\pi\)
\(192\) 2852.96 + 384.564i 1.07237 + 0.144550i
\(193\) −709.387 409.565i −0.264574 0.152752i 0.361845 0.932238i \(-0.382147\pi\)
−0.626419 + 0.779486i \(0.715480\pi\)
\(194\) −2436.49 + 4220.12i −0.901698 + 1.56179i
\(195\) −1595.74 + 322.526i −0.586017 + 0.118444i
\(196\) −44.4670 77.0191i −0.0162052 0.0280682i
\(197\) 359.979i 0.130190i −0.997879 0.0650950i \(-0.979265\pi\)
0.997879 0.0650950i \(-0.0207350\pi\)
\(198\) 2261.66 + 2289.77i 0.811764 + 0.821851i
\(199\) 1338.34 0.476745 0.238372 0.971174i \(-0.423386\pi\)
0.238372 + 0.971174i \(0.423386\pi\)
\(200\) −2927.01 + 422.145i −1.03485 + 0.149251i
\(201\) −1460.64 1127.97i −0.512566 0.395826i
\(202\) −2658.07 1534.64i −0.925848 0.534538i
\(203\) 2534.50 + 1463.30i 0.876291 + 0.505927i
\(204\) −321.644 248.387i −0.110390 0.0852480i
\(205\) −1053.36 3041.34i −0.358878 1.03618i
\(206\) −4233.41 −1.43182
\(207\) 17.5090 + 17.7266i 0.00587904 + 0.00595210i
\(208\) 1584.31i 0.528135i
\(209\) 1104.66 + 1913.33i 0.365603 + 0.633242i
\(210\) −474.605 2348.17i −0.155956 0.771614i
\(211\) −534.114 + 925.113i −0.174265 + 0.301836i −0.939907 0.341431i \(-0.889088\pi\)
0.765642 + 0.643267i \(0.222422\pi\)
\(212\) −106.967 61.7574i −0.0346534 0.0200071i
\(213\) 1651.49 + 222.611i 0.531258 + 0.0716107i
\(214\) 515.468 + 892.816i 0.164657 + 0.285195i
\(215\) 1.25109 6.49891i 0.000396855 0.00206150i
\(216\) −1298.54 + 3054.62i −0.409049 + 0.962225i
\(217\) 4611.96i 1.44277i
\(218\) −471.448 + 272.190i −0.146470 + 0.0845645i
\(219\) −442.013 + 3279.16i −0.136386 + 1.01180i
\(220\) 275.294 317.847i 0.0843651 0.0974055i
\(221\) 1298.34 2248.79i 0.395185 0.684480i
\(222\) 305.337 + 743.635i 0.0923104 + 0.224818i
\(223\) −1315.35 + 759.415i −0.394987 + 0.228046i −0.684319 0.729183i \(-0.739900\pi\)
0.289332 + 0.957229i \(0.406567\pi\)
\(224\) 586.263 0.174872
\(225\) 419.900 3348.78i 0.124415 0.992230i
\(226\) −176.594 −0.0519774
\(227\) 3667.72 2117.56i 1.07240 0.619152i 0.143566 0.989641i \(-0.454143\pi\)
0.928837 + 0.370489i \(0.120810\pi\)
\(228\) −132.907 + 172.104i −0.0386050 + 0.0499907i
\(229\) −2768.26 + 4794.77i −0.798829 + 1.38361i 0.121550 + 0.992585i \(0.461213\pi\)
−0.920379 + 0.391027i \(0.872120\pi\)
\(230\) −18.0693 + 20.8622i −0.00518023 + 0.00598094i
\(231\) 2824.96 + 2181.56i 0.804626 + 0.621367i
\(232\) 3889.78 2245.76i 1.10076 0.635524i
\(233\) 6337.30i 1.78185i 0.454154 + 0.890923i \(0.349941\pi\)
−0.454154 + 0.890923i \(0.650059\pi\)
\(234\) −1951.79 535.920i −0.545268 0.149719i
\(235\) −1264.51 + 6568.61i −0.351011 + 1.82336i
\(236\) −81.4771 141.122i −0.0224733 0.0389249i
\(237\) 567.948 + 1383.21i 0.155663 + 0.379111i
\(238\) 3309.15 + 1910.54i 0.901262 + 0.520344i
\(239\) 1271.43 2202.19i 0.344110 0.596016i −0.641082 0.767473i \(-0.721514\pi\)
0.985192 + 0.171457i \(0.0548474\pi\)
\(240\) −3113.34 1046.15i −0.837355 0.281370i
\(241\) −1025.71 1776.58i −0.274157 0.474854i 0.695765 0.718269i \(-0.255065\pi\)
−0.969922 + 0.243415i \(0.921732\pi\)
\(242\) 1751.02i 0.465124i
\(243\) −2969.26 2352.10i −0.783862 0.620935i
\(244\) −477.852 −0.125374
\(245\) 385.545 + 1113.17i 0.100537 + 0.290278i
\(246\) 534.552 3965.68i 0.138544 1.02781i
\(247\) −1203.28 694.713i −0.309971 0.178962i
\(248\) −6129.82 3539.05i −1.56953 0.906170i
\(249\) −1370.20 + 562.605i −0.348726 + 0.143187i
\(250\) 3734.40 + 175.441i 0.944736 + 0.0443834i
\(251\) −2770.89 −0.696801 −0.348401 0.937346i \(-0.613275\pi\)
−0.348401 + 0.937346i \(0.613275\pi\)
\(252\) −93.0162 + 338.760i −0.0232519 + 0.0846821i
\(253\) 41.1201i 0.0102182i
\(254\) −2436.34 4219.86i −0.601848 1.04243i
\(255\) 3561.81 + 4036.31i 0.874702 + 0.991229i
\(256\) 640.748 1109.81i 0.156433 0.270949i
\(257\) −369.581 213.378i −0.0897036 0.0517904i 0.454477 0.890758i \(-0.349826\pi\)
−0.544181 + 0.838968i \(0.683159\pi\)
\(258\) 5.02913 6.51235i 0.00121356 0.00157148i
\(259\) 445.757 + 772.074i 0.106942 + 0.185229i
\(260\) −49.9897 + 259.676i −0.0119240 + 0.0619402i
\(261\) 1296.09 + 4959.37i 0.307379 + 1.17616i
\(262\) 637.355i 0.150290i
\(263\) 3258.32 1881.19i 0.763943 0.441063i −0.0667669 0.997769i \(-0.521268\pi\)
0.830710 + 0.556706i \(0.187935\pi\)
\(264\) 5067.31 2080.64i 1.18133 0.485056i
\(265\) 1236.73 + 1071.16i 0.286685 + 0.248305i
\(266\) 1022.29 1770.65i 0.235641 0.408142i
\(267\) −1707.68 230.186i −0.391417 0.0527609i
\(268\) −259.608 + 149.885i −0.0591719 + 0.0341629i
\(269\) 1980.25 0.448839 0.224420 0.974493i \(-0.427951\pi\)
0.224420 + 0.974493i \(0.427951\pi\)
\(270\) 2341.95 3481.61i 0.527877 0.784756i
\(271\) 5659.70 1.26864 0.634321 0.773070i \(-0.281280\pi\)
0.634321 + 0.773070i \(0.281280\pi\)
\(272\) 4536.80 2619.32i 1.01134 0.583896i
\(273\) −2224.56 299.859i −0.493174 0.0664772i
\(274\) 2738.57 4743.34i 0.603807 1.04582i
\(275\) −4376.79 + 3445.04i −0.959747 + 0.755431i
\(276\) 3.74388 1.53724i 0.000816503 0.000335257i
\(277\) −5343.00 + 3084.78i −1.15895 + 0.669121i −0.951053 0.309029i \(-0.899996\pi\)
−0.207900 + 0.978150i \(0.566663\pi\)
\(278\) 5829.95i 1.25776i
\(279\) 5747.07 5676.53i 1.23322 1.21808i
\(280\) −4003.97 770.795i −0.854581 0.164514i
\(281\) −1671.73 2895.52i −0.354900 0.614705i 0.632201 0.774805i \(-0.282152\pi\)
−0.987101 + 0.160100i \(0.948818\pi\)
\(282\) −5083.06 + 6582.20i −1.07338 + 1.38994i
\(283\) 4419.60 + 2551.66i 0.928333 + 0.535973i 0.886284 0.463142i \(-0.153278\pi\)
0.0420490 + 0.999116i \(0.486611\pi\)
\(284\) 135.342 234.419i 0.0282784 0.0489796i
\(285\) 2159.74 1905.84i 0.448884 0.396114i
\(286\) 1670.19 + 2892.86i 0.345317 + 0.598106i
\(287\) 4437.76i 0.912727i
\(288\) 721.590 + 730.556i 0.147639 + 0.149474i
\(289\) −3673.14 −0.747638
\(290\) −5365.35 + 1858.28i −1.08643 + 0.376282i
\(291\) −8756.08 + 3595.26i −1.76389 + 0.724253i
\(292\) 465.458 + 268.733i 0.0932839 + 0.0538575i
\(293\) −3576.93 2065.14i −0.713195 0.411764i 0.0990477 0.995083i \(-0.468420\pi\)
−0.812243 + 0.583319i \(0.801754\pi\)
\(294\) −195.653 + 1451.49i −0.0388120 + 0.287934i
\(295\) 706.436 + 2039.67i 0.139425 + 0.402557i
\(296\) 1368.23 0.268672
\(297\) 758.550 + 6205.37i 0.148200 + 1.21236i
\(298\) 417.172i 0.0810943i
\(299\) 12.9301 + 22.3956i 0.00250089 + 0.00433167i
\(300\) −477.284 269.705i −0.0918533 0.0519048i
\(301\) 4.56258 7.90261i 0.000873696 0.00151329i
\(302\) 3739.44 + 2158.97i 0.712519 + 0.411373i
\(303\) −2264.50 5515.08i −0.429347 1.04565i
\(304\) −1401.54 2427.54i −0.264421 0.457990i
\(305\) 6215.65 + 1196.56i 1.16691 + 0.224639i
\(306\) 1692.23 + 6475.16i 0.316138 + 1.20967i
\(307\) 3382.52i 0.628830i 0.949286 + 0.314415i \(0.101808\pi\)
−0.949286 + 0.314415i \(0.898192\pi\)
\(308\) 502.095 289.884i 0.0928880 0.0536289i
\(309\) −6508.37 5026.05i −1.19821 0.925313i
\(310\) 6763.66 + 5858.16i 1.23919 + 1.07329i
\(311\) 3010.61 5214.53i 0.548926 0.950767i −0.449423 0.893319i \(-0.648370\pi\)
0.998348 0.0574482i \(-0.0182964\pi\)
\(312\) −2105.60 + 2726.59i −0.382070 + 0.494753i
\(313\) 8827.35 5096.47i 1.59409 0.920350i 0.601499 0.798874i \(-0.294571\pi\)
0.992594 0.121476i \(-0.0387628\pi\)
\(314\) −2644.32 −0.475247
\(315\) 2058.18 4173.50i 0.368144 0.746509i
\(316\) 242.884 0.0432382
\(317\) 4677.05 2700.30i 0.828673 0.478435i −0.0247250 0.999694i \(-0.507871\pi\)
0.853398 + 0.521260i \(0.174538\pi\)
\(318\) 772.616 + 1881.67i 0.136246 + 0.331820i
\(319\) 4229.82 7326.27i 0.742397 1.28587i
\(320\) −4055.26 + 4682.09i −0.708425 + 0.817927i
\(321\) −267.511 + 1984.58i −0.0465141 + 0.345074i
\(322\) −32.9556 + 19.0269i −0.00570355 + 0.00329295i
\(323\) 4594.25i 0.791428i
\(324\) −536.624 + 301.046i −0.0920138 + 0.0516197i
\(325\) 1300.48 3252.56i 0.221962 0.555137i
\(326\) 3977.96 + 6890.03i 0.675825 + 1.17056i
\(327\) −1047.95 141.258i −0.177222 0.0238887i
\(328\) −5898.29 3405.38i −0.992923 0.573265i
\(329\) −4611.51 + 7987.37i −0.772768 + 1.33847i
\(330\) −6787.65 + 1371.90i −1.13227 + 0.228850i
\(331\) 1151.45 + 1994.37i 0.191206 + 0.331179i 0.945650 0.325185i \(-0.105427\pi\)
−0.754444 + 0.656365i \(0.772093\pi\)
\(332\) 240.598i 0.0397727i
\(333\) −413.449 + 1505.76i −0.0680387 + 0.247793i
\(334\) −6524.37 −1.06886
\(335\) 3752.17 1299.55i 0.611948 0.211947i
\(336\) −3584.17 2767.86i −0.581942 0.449402i
\(337\) −8284.68 4783.16i −1.33916 0.773162i −0.352473 0.935822i \(-0.614659\pi\)
−0.986682 + 0.162660i \(0.947993\pi\)
\(338\) 3270.43 + 1888.19i 0.526296 + 0.303857i
\(339\) −271.493 209.659i −0.0434970 0.0335903i
\(340\) 826.253 286.171i 0.131794 0.0456465i
\(341\) −13331.4 −2.11711
\(342\) 3464.71 905.475i 0.547808 0.143165i
\(343\) 6911.73i 1.08804i
\(344\) −7.00232 12.1284i −0.00109750 0.00190092i
\(345\) −52.5478 + 10.6208i −0.00820022 + 0.00165740i
\(346\) 3549.26 6147.50i 0.551472 0.955178i
\(347\) 70.5999 + 40.7609i 0.0109222 + 0.00630593i 0.505451 0.862855i \(-0.331326\pi\)
−0.494529 + 0.869161i \(0.664659\pi\)
\(348\) 825.165 + 111.228i 0.127108 + 0.0171334i
\(349\) 46.7859 + 81.0356i 0.00717591 + 0.0124290i 0.869591 0.493773i \(-0.164382\pi\)
−0.862415 + 0.506202i \(0.831049\pi\)
\(350\) 4786.22 + 1913.69i 0.730955 + 0.292260i
\(351\) −2364.39 3141.15i −0.359549 0.477670i
\(352\) 1694.66i 0.256607i
\(353\) −5781.08 + 3337.71i −0.871659 + 0.503253i −0.867899 0.496740i \(-0.834530\pi\)
−0.00376007 + 0.999993i \(0.501197\pi\)
\(354\) −358.496 + 2659.57i −0.0538245 + 0.399307i
\(355\) −2347.46 + 2710.30i −0.350958 + 0.405206i
\(356\) −139.947 + 242.396i −0.0208348 + 0.0360869i
\(357\) 2819.17 + 6865.97i 0.417945 + 1.01789i
\(358\) −4870.35 + 2811.90i −0.719012 + 0.415122i
\(359\) 8334.50 1.22529 0.612644 0.790359i \(-0.290106\pi\)
0.612644 + 0.790359i \(0.290106\pi\)
\(360\) −3967.69 5938.16i −0.580877 0.869356i
\(361\) −4400.72 −0.641598
\(362\) −3700.57 + 2136.53i −0.537287 + 0.310203i
\(363\) 2078.88 2691.99i 0.300586 0.389237i
\(364\) −182.306 + 315.764i −0.0262512 + 0.0454685i
\(365\) −5381.53 4661.07i −0.771732 0.668415i
\(366\) 6228.51 + 4809.93i 0.889534 + 0.686937i
\(367\) 108.912 62.8805i 0.0154909 0.00894369i −0.492235 0.870463i \(-0.663820\pi\)
0.507725 + 0.861519i \(0.330486\pi\)
\(368\) 52.1713i 0.00739026i
\(369\) 5530.00 5462.13i 0.780164 0.770588i
\(370\) −1698.49 326.973i −0.238649 0.0459419i
\(371\) 1127.93 + 1953.63i 0.157841 + 0.273389i
\(372\) −498.382 1213.79i −0.0694621 0.169172i
\(373\) −1243.40 717.879i −0.172603 0.0996525i 0.411210 0.911541i \(-0.365106\pi\)
−0.583813 + 0.811888i \(0.698440\pi\)
\(374\) 5522.63 9565.48i 0.763552 1.32251i
\(375\) 5532.91 + 4703.33i 0.761915 + 0.647677i
\(376\) 7077.42 + 12258.5i 0.970718 + 1.68133i
\(377\) 5320.21i 0.726803i
\(378\) 4622.28 3479.26i 0.628953 0.473422i
\(379\) 2125.04 0.288010 0.144005 0.989577i \(-0.454002\pi\)
0.144005 + 0.989577i \(0.454002\pi\)
\(380\) −153.124 442.109i −0.0206713 0.0596835i
\(381\) 1264.38 9380.05i 0.170016 1.26130i
\(382\) −7893.90 4557.54i −1.05730 0.610430i
\(383\) 6114.80 + 3530.38i 0.815800 + 0.471002i 0.848966 0.528447i \(-0.177226\pi\)
−0.0331659 + 0.999450i \(0.510559\pi\)
\(384\) −5661.30 + 2324.54i −0.752349 + 0.308915i
\(385\) −7256.88 + 2513.40i −0.960636 + 0.332714i
\(386\) 2191.22 0.288939
\(387\) 15.4634 4.04123i 0.00203113 0.000530820i
\(388\) 1537.51i 0.201174i
\(389\) −4909.56 8503.61i −0.639909 1.10836i −0.985452 0.169952i \(-0.945639\pi\)
0.345543 0.938403i \(-0.387695\pi\)
\(390\) 3265.42 2881.54i 0.423977 0.374135i
\(391\) 42.7544 74.0528i 0.00552988 0.00957803i
\(392\) 2158.85 + 1246.42i 0.278160 + 0.160596i
\(393\) 756.691 979.859i 0.0971247 0.125769i
\(394\) 481.483 + 833.954i 0.0615654 + 0.106634i
\(395\) −3159.31 608.191i −0.402435 0.0774720i
\(396\) 979.225 + 268.874i 0.124262 + 0.0341198i
\(397\) 10995.5i 1.39005i −0.718987 0.695023i \(-0.755394\pi\)
0.718987 0.695023i \(-0.244606\pi\)
\(398\) −3100.49 + 1790.07i −0.390486 + 0.225447i
\(399\) 3673.83 1508.48i 0.460956 0.189269i
\(400\) 5553.07 4370.90i 0.694133 0.546363i
\(401\) 3265.90 5656.71i 0.406712 0.704446i −0.587807 0.809001i \(-0.700009\pi\)
0.994519 + 0.104555i \(0.0333419\pi\)
\(402\) 4892.53 + 659.487i 0.607008 + 0.0818215i
\(403\) 7260.77 4192.01i 0.897481 0.518161i
\(404\) −968.415 −0.119259
\(405\) 7733.97 2572.12i 0.948899 0.315580i
\(406\) −7828.82 −0.956989
\(407\) 2231.77 1288.51i 0.271805 0.156927i
\(408\) 11289.0 + 1521.70i 1.36983 + 0.184645i
\(409\) −2502.67 + 4334.75i −0.302565 + 0.524058i −0.976716 0.214535i \(-0.931176\pi\)
0.674151 + 0.738593i \(0.264510\pi\)
\(410\) 6508.19 + 5636.90i 0.783943 + 0.678991i
\(411\) 9841.70 4041.01i 1.18116 0.484984i
\(412\) −1156.77 + 667.860i −0.138325 + 0.0798619i
\(413\) 2976.17i 0.354596i
\(414\) −64.2726 17.6479i −0.00763002 0.00209504i
\(415\) 602.469 3129.58i 0.0712627 0.370181i
\(416\) 532.880 + 922.975i 0.0628043 + 0.108780i
\(417\) 6921.52 8962.87i 0.812826 1.05255i
\(418\) −5118.27 2955.04i −0.598907 0.345779i
\(419\) −36.7472 + 63.6481i −0.00428453 + 0.00742103i −0.868160 0.496285i \(-0.834697\pi\)
0.863875 + 0.503706i \(0.168030\pi\)
\(420\) −500.130 566.758i −0.0581044 0.0658451i
\(421\) −2515.40 4356.81i −0.291195 0.504365i 0.682897 0.730514i \(-0.260720\pi\)
−0.974093 + 0.226149i \(0.927386\pi\)
\(422\) 2857.58i 0.329632i
\(423\) −15629.2 + 4084.57i −1.79650 + 0.469501i
\(424\) 3462.13 0.396547
\(425\) −11464.1 + 1653.39i −1.30844 + 0.188709i
\(426\) −4123.70 + 1693.20i −0.469000 + 0.192572i
\(427\) 7558.17 + 4363.71i 0.856594 + 0.494555i
\(428\) 281.700 + 162.640i 0.0318143 + 0.0183680i
\(429\) −866.776 + 6430.34i −0.0975486 + 0.723683i
\(430\) 5.79413 + 16.7292i 0.000649809 + 0.00187617i
\(431\) −1951.29 −0.218075 −0.109037 0.994038i \(-0.534777\pi\)
−0.109037 + 0.994038i \(0.534777\pi\)
\(432\) −962.413 7873.08i −0.107185 0.876838i
\(433\) 3805.50i 0.422357i −0.977448 0.211178i \(-0.932270\pi\)
0.977448 0.211178i \(-0.0677301\pi\)
\(434\) 6168.64 + 10684.4i 0.682268 + 1.18172i
\(435\) −10454.8 3513.05i −1.15234 0.387213i
\(436\) −85.8812 + 148.751i −0.00943340 + 0.0163391i
\(437\) −39.6240 22.8769i −0.00433747 0.00250424i
\(438\) −3361.98 8187.95i −0.366762 0.893231i
\(439\) 5952.18 + 10309.5i 0.647111 + 1.12083i 0.983810 + 0.179217i \(0.0573565\pi\)
−0.336698 + 0.941613i \(0.609310\pi\)
\(440\) −2228.07 + 11573.9i −0.241407 + 1.25401i
\(441\) −2024.05 + 1999.21i −0.218557 + 0.215874i
\(442\) 6946.29i 0.747514i
\(443\) −7853.51 + 4534.23i −0.842283 + 0.486292i −0.858040 0.513583i \(-0.828318\pi\)
0.0157565 + 0.999876i \(0.494984\pi\)
\(444\) 200.748 + 155.027i 0.0214574 + 0.0165704i
\(445\) 2427.33 2802.53i 0.258577 0.298545i
\(446\) 2031.48 3518.63i 0.215681 0.373570i
\(447\) −495.281 + 641.353i −0.0524071 + 0.0678634i
\(448\) −7396.18 + 4270.19i −0.779993 + 0.450329i
\(449\) −7332.48 −0.770693 −0.385346 0.922772i \(-0.625918\pi\)
−0.385346 + 0.922772i \(0.625918\pi\)
\(450\) 3506.33 + 8319.65i 0.367311 + 0.871538i
\(451\) −12827.9 −1.33934
\(452\) −48.2539 + 27.8594i −0.00502140 + 0.00289911i
\(453\) 3185.75 + 7758.75i 0.330419 + 0.804720i
\(454\) −5664.61 + 9811.40i −0.585580 + 1.01425i
\(455\) 3162.03 3650.79i 0.325799 0.376158i
\(456\) 814.226 6040.49i 0.0836176 0.620333i
\(457\) −1013.62 + 585.214i −0.103753 + 0.0599019i −0.550979 0.834519i \(-0.685745\pi\)
0.447226 + 0.894421i \(0.352412\pi\)
\(458\) 14810.5i 1.51103i
\(459\) −5085.93 + 11963.9i −0.517191 + 1.21661i
\(460\) −1.64616 + 8.55115i −0.000166854 + 0.000866738i
\(461\) 7373.89 + 12771.9i 0.744981 + 1.29034i 0.950204 + 0.311629i \(0.100875\pi\)
−0.205223 + 0.978715i \(0.565792\pi\)
\(462\) −9462.40 1275.48i −0.952881 0.128443i
\(463\) −1806.10 1042.75i −0.181289 0.104667i 0.406609 0.913602i \(-0.366711\pi\)
−0.587898 + 0.808935i \(0.700044\pi\)
\(464\) −5366.60 + 9295.23i −0.536936 + 0.930000i
\(465\) 3443.33 + 17036.3i 0.343399 + 1.69901i
\(466\) −8476.34 14681.4i −0.842615 1.45945i
\(467\) 9943.76i 0.985315i −0.870223 0.492658i \(-0.836025\pi\)
0.870223 0.492658i \(-0.163975\pi\)
\(468\) −617.869 + 161.475i −0.0610278 + 0.0159491i
\(469\) 5474.95 0.539040
\(470\) −5856.27 16908.7i −0.574744 1.65944i
\(471\) −4065.34 3139.43i −0.397709 0.307128i
\(472\) 3955.68 + 2283.81i 0.385752 + 0.222714i
\(473\) −22.8434 13.1887i −0.00222059 0.00128206i
\(474\) −3165.84 2444.80i −0.306776 0.236906i
\(475\) 884.693 + 6134.16i 0.0854579 + 0.592536i
\(476\) 1205.62 0.116092
\(477\) −1046.18 + 3810.13i −0.100422 + 0.365731i
\(478\) 6802.34i 0.650903i
\(479\) −1332.10 2307.26i −0.127067 0.220087i 0.795472 0.605990i \(-0.207223\pi\)
−0.922539 + 0.385904i \(0.873890\pi\)
\(480\) −2165.62 + 437.709i −0.205930 + 0.0416220i
\(481\) −810.336 + 1403.54i −0.0768153 + 0.133048i
\(482\) 4752.47 + 2743.84i 0.449106 + 0.259292i
\(483\) −73.2548 9.87436i −0.00690105 0.000930226i
\(484\) −276.240 478.463i −0.0259429 0.0449345i
\(485\) 3850.01 19999.2i 0.360453 1.87241i
\(486\) 10024.8 + 1477.56i 0.935669 + 0.137909i
\(487\) 3071.50i 0.285797i 0.989737 + 0.142898i \(0.0456422\pi\)
−0.989737 + 0.142898i \(0.954358\pi\)
\(488\) 11599.8 6697.12i 1.07602 0.621239i
\(489\) −2064.43 + 15315.4i −0.190914 + 1.41633i
\(490\) −2382.09 2063.18i −0.219616 0.190214i
\(491\) −8044.80 + 13934.0i −0.739423 + 1.28072i 0.213332 + 0.976980i \(0.431568\pi\)
−0.952755 + 0.303739i \(0.901765\pi\)
\(492\) −479.558 1167.94i −0.0439434 0.107022i
\(493\) 15234.9 8795.86i 1.39177 0.803541i
\(494\) 3716.80 0.338516
\(495\) −12064.0 5949.40i −1.09543 0.540214i
\(496\) 16914.3 1.53119
\(497\) −4281.40 + 2471.87i −0.386413 + 0.223096i
\(498\) 2421.80 3136.05i 0.217918 0.282189i
\(499\) 6030.29 10444.8i 0.540987 0.937018i −0.457860 0.889024i \(-0.651384\pi\)
0.998848 0.0479936i \(-0.0152827\pi\)
\(500\) 1048.09 541.198i 0.0937442 0.0484062i
\(501\) −10030.5 7745.96i −0.894467 0.690747i
\(502\) 6419.25 3706.16i 0.570727 0.329510i
\(503\) 1324.90i 0.117444i 0.998274 + 0.0587222i \(0.0187026\pi\)
−0.998274 + 0.0587222i \(0.981297\pi\)
\(504\) −2489.79 9526.96i −0.220048 0.841993i
\(505\) 12596.7 + 2424.95i 1.10999 + 0.213681i
\(506\) 54.9995 + 95.2619i 0.00483207 + 0.00836939i
\(507\) 2786.19 + 6785.64i 0.244061 + 0.594400i
\(508\) −1331.45 768.710i −0.116286 0.0671378i
\(509\) −6060.53 + 10497.2i −0.527757 + 0.914102i 0.471719 + 0.881749i \(0.343634\pi\)
−0.999476 + 0.0323536i \(0.989700\pi\)
\(510\) −13650.2 4586.78i −1.18518 0.398247i
\(511\) −4908.10 8501.08i −0.424895 0.735940i
\(512\) 12850.4i 1.10920i
\(513\) 6401.60 + 2721.37i 0.550951 + 0.234213i
\(514\) 1141.60 0.0979644
\(515\) 16719.0 5790.59i 1.43054 0.495463i
\(516\) 0.346810 2.57288i 2.95881e−5 0.000219505i
\(517\) 23088.4 + 13330.1i 1.96408 + 1.13396i
\(518\) −2065.35 1192.43i −0.175186 0.101143i
\(519\) 12755.1 5237.26i 1.07878 0.442948i
\(520\) −2425.89 7004.20i −0.204581 0.590682i
\(521\) 17997.6 1.51342 0.756708 0.653753i \(-0.226807\pi\)
0.756708 + 0.653753i \(0.226807\pi\)
\(522\) −9635.94 9755.68i −0.807957 0.817997i
\(523\) 6451.03i 0.539357i 0.962950 + 0.269679i \(0.0869174\pi\)
−0.962950 + 0.269679i \(0.913083\pi\)
\(524\) −100.549 174.156i −0.00838263 0.0145191i
\(525\) 5086.26 + 8624.44i 0.422824 + 0.716955i
\(526\) −5032.32 + 8716.23i −0.417147 + 0.722520i
\(527\) −24008.4 13861.2i −1.98448 1.14574i
\(528\) −8000.81 + 10360.5i −0.659452 + 0.853942i
\(529\) −6083.07 10536.2i −0.499965 0.865965i
\(530\) −4297.81 827.361i −0.352235 0.0678081i
\(531\) −3708.68 + 3663.16i −0.303094 + 0.299374i
\(532\) 645.101i 0.0525727i
\(533\) 6986.53 4033.67i 0.567768 0.327801i
\(534\) 4264.02 1750.81i 0.345547 0.141882i
\(535\) −3256.96 2820.93i −0.263197 0.227961i
\(536\) 4201.28 7276.84i 0.338559 0.586402i
\(537\) −10826.0 1459.29i −0.869973 0.117268i
\(538\) −4587.59 + 2648.64i −0.367630 + 0.212251i
\(539\) 4695.17 0.375204
\(540\) 90.6752 1320.81i 0.00722600 0.105256i
\(541\) −520.899 −0.0413959 −0.0206980 0.999786i \(-0.506589\pi\)
−0.0206980 + 0.999786i \(0.506589\pi\)
\(542\) −13111.7 + 7570.03i −1.03910 + 0.599927i
\(543\) −8225.76 1108.79i −0.650094 0.0876292i
\(544\) 1762.01 3051.89i 0.138871 0.240531i
\(545\) 1489.58 1719.82i 0.117076 0.135173i
\(546\) 5554.65 2280.74i 0.435379 0.178767i
\(547\) −7013.36 + 4049.16i −0.548207 + 0.316508i −0.748399 0.663249i \(-0.769177\pi\)
0.200191 + 0.979757i \(0.435844\pi\)
\(548\) 1728.14i 0.134713i
\(549\) 3865.09 + 14789.4i 0.300470 + 1.14972i
\(550\) 5531.74 13835.1i 0.428862 1.07260i
\(551\) −4706.47 8151.84i −0.363888 0.630273i
\(552\) −69.3373 + 89.7868i −0.00534636 + 0.00692315i
\(553\) −3841.68 2218.00i −0.295416 0.170559i
\(554\) 8251.99 14292.9i 0.632840 1.09611i
\(555\) −2223.04 2519.19i −0.170023 0.192673i
\(556\) −919.730 1593.02i −0.0701533 0.121509i
\(557\) 6687.22i 0.508701i 0.967112 + 0.254351i \(0.0818617\pi\)
−0.967112 + 0.254351i \(0.918138\pi\)
\(558\) −5721.55 + 20837.6i −0.434072 + 1.58087i
\(559\) 16.5885 0.00125513
\(560\) 9207.19 3188.89i 0.694776 0.240634i
\(561\) 19846.9 8149.15i 1.49365 0.613293i
\(562\) 7745.69 + 4471.98i 0.581374 + 0.335657i
\(563\) −2102.31 1213.77i −0.157375 0.0908602i 0.419245 0.907873i \(-0.362295\pi\)
−0.576619 + 0.817013i \(0.695628\pi\)
\(564\) −350.530 + 2600.47i −0.0261701 + 0.194148i
\(565\) 697.424 241.551i 0.0519307 0.0179861i
\(566\) −13651.7 −1.01382
\(567\) 11236.9 + 138.779i 0.832286 + 0.0102790i
\(568\) 7587.30i 0.560486i
\(569\) 1276.83 + 2211.53i 0.0940727 + 0.162939i 0.909221 0.416313i \(-0.136678\pi\)
−0.815149 + 0.579252i \(0.803345\pi\)
\(570\) −2454.28 + 7303.93i −0.180348 + 0.536716i
\(571\) −4518.07 + 7825.53i −0.331130 + 0.573535i −0.982734 0.185025i \(-0.940763\pi\)
0.651603 + 0.758560i \(0.274097\pi\)
\(572\) 912.752 + 526.977i 0.0667204 + 0.0385210i
\(573\) −6725.07 16378.6i −0.490303 1.19411i
\(574\) 5935.65 + 10280.8i 0.431619 + 0.747585i
\(575\) 42.8249 107.107i 0.00310595 0.00776812i
\(576\) −14424.6 3960.69i −1.04345 0.286508i
\(577\) 5427.02i 0.391560i −0.980648 0.195780i \(-0.937276\pi\)
0.980648 0.195780i \(-0.0627238\pi\)
\(578\) 8509.48 4912.95i 0.612366 0.353550i
\(579\) 3368.75 + 2601.50i 0.241797 + 0.186726i
\(580\) −1172.91 + 1354.20i −0.0839695 + 0.0969487i
\(581\) 2197.13 3805.54i 0.156889 0.271739i
\(582\) 15476.2 20040.6i 1.10225 1.42733i
\(583\) 5647.20 3260.41i 0.401171 0.231616i
\(584\) −15065.2 −1.06747
\(585\) 8441.27 553.214i 0.596587 0.0390984i
\(586\) 11048.8 0.778874
\(587\) −4624.04 + 2669.69i −0.325136 + 0.187717i −0.653679 0.756772i \(-0.726776\pi\)
0.328544 + 0.944489i \(0.393442\pi\)
\(588\) 175.525 + 427.482i 0.0123104 + 0.0299814i
\(589\) −7416.84 + 12846.3i −0.518855 + 0.898683i
\(590\) −4364.71 3780.37i −0.304563 0.263789i
\(591\) −249.874 + 1853.74i −0.0173916 + 0.129023i
\(592\) −2831.56 + 1634.80i −0.196582 + 0.113497i
\(593\) 4617.67i 0.319772i 0.987135 + 0.159886i \(0.0511127\pi\)
−0.987135 + 0.159886i \(0.948887\pi\)
\(594\) −10057.2 13361.2i −0.694700 0.922926i
\(595\) −15682.1 3018.93i −1.08051 0.208007i
\(596\) 65.8128 + 113.991i 0.00452315 + 0.00783432i
\(597\) −6891.87 928.988i −0.472472 0.0636867i
\(598\) −59.9095 34.5888i −0.00409680 0.00236529i
\(599\) 5444.19 9429.61i 0.371358 0.643211i −0.618417 0.785850i \(-0.712226\pi\)
0.989775 + 0.142639i \(0.0455589\pi\)
\(600\) 15365.9 142.124i 1.04552 0.00967031i
\(601\) 5636.61 + 9762.89i 0.382566 + 0.662623i 0.991428 0.130653i \(-0.0417072\pi\)
−0.608863 + 0.793276i \(0.708374\pi\)
\(602\) 24.4104i 0.00165264i
\(603\) 6738.73 + 6822.47i 0.455095 + 0.460750i
\(604\) 1362.39 0.0917795
\(605\) 2395.10 + 6915.32i 0.160950 + 0.464707i
\(606\) 12622.7 + 9747.81i 0.846142 + 0.653428i
\(607\) 8854.84 + 5112.34i 0.592103 + 0.341851i 0.765929 0.642926i \(-0.222280\pi\)
−0.173825 + 0.984776i \(0.555613\pi\)
\(608\) −1633.00 942.813i −0.108926 0.0628884i
\(609\) −12035.9 9294.65i −0.800852 0.618453i
\(610\) −16000.1 + 5541.59i −1.06201 + 0.367824i
\(611\) −16766.4 −1.11014
\(612\) 1483.92 + 1502.36i 0.0980126 + 0.0992306i
\(613\) 7119.74i 0.469109i −0.972103 0.234554i \(-0.924637\pi\)
0.972103 0.234554i \(-0.0753631\pi\)
\(614\) −4524.23 7836.20i −0.297367 0.515054i
\(615\) 3313.27 + 16392.8i 0.217242 + 1.07483i
\(616\) −8125.50 + 14073.8i −0.531470 + 0.920533i
\(617\) 4640.99 + 2679.48i 0.302819 + 0.174832i 0.643708 0.765271i \(-0.277395\pi\)
−0.340890 + 0.940103i \(0.610728\pi\)
\(618\) 21800.3 + 2938.56i 1.41899 + 0.191272i
\(619\) −10798.6 18703.7i −0.701183 1.21448i −0.968051 0.250752i \(-0.919322\pi\)
0.266869 0.963733i \(-0.414011\pi\)
\(620\) 2772.33 + 533.696i 0.179580 + 0.0345706i
\(621\) −77.8595 103.438i −0.00503123 0.00668411i
\(622\) 16107.1i 1.03832i
\(623\) 4427.08 2555.98i 0.284699 0.164371i
\(624\) 1099.73 8158.52i 0.0705517 0.523401i
\(625\) −14988.2 + 4415.16i −0.959247 + 0.282570i
\(626\) −13633.4 + 23613.7i −0.870447 + 1.50766i
\(627\) −4360.43 10619.6i −0.277733 0.676406i
\(628\) −722.554 + 417.167i −0.0459125 + 0.0265076i
\(629\) 5358.89 0.339703
\(630\) 814.067 + 12421.5i 0.0514813 + 0.785532i
\(631\) −1384.23 −0.0873305 −0.0436652 0.999046i \(-0.513903\pi\)
−0.0436652 + 0.999046i \(0.513903\pi\)
\(632\) −5895.95 + 3404.03i −0.371089 + 0.214248i
\(633\) 3392.62 4393.20i 0.213025 0.275851i
\(634\) −7223.47 + 12511.4i −0.452493 + 0.783741i
\(635\) 15393.9 + 13333.0i 0.962028 + 0.833234i
\(636\) 507.967 + 392.274i 0.0316701 + 0.0244571i
\(637\) −2557.16 + 1476.38i −0.159056 + 0.0918309i
\(638\) 22630.1i 1.40429i
\(639\) −8349.93 2292.71i −0.516930 0.141938i
\(640\) 2489.25 12930.6i 0.153744 0.798637i
\(641\) 811.571 + 1405.68i 0.0500080 + 0.0866164i 0.889946 0.456066i \(-0.150742\pi\)
−0.839938 + 0.542683i \(0.817409\pi\)
\(642\) −2034.71 4955.43i −0.125083 0.304635i
\(643\) −24396.6 14085.4i −1.49628 0.863879i −0.496292 0.868156i \(-0.665305\pi\)
−0.999991 + 0.00427672i \(0.998639\pi\)
\(644\) −6.00335 + 10.3981i −0.000367337 + 0.000636247i
\(645\) −10.9537 + 32.5982i −0.000668686 + 0.00199001i
\(646\) −6144.96 10643.4i −0.374257 0.648233i
\(647\) 16695.3i 1.01447i 0.861808 + 0.507235i \(0.169332\pi\)
−0.861808 + 0.507235i \(0.830668\pi\)
\(648\) 8807.27 14828.7i 0.533923 0.898958i
\(649\) 8602.97 0.520333
\(650\) 1337.61 + 9274.56i 0.0807161 + 0.559659i
\(651\) −3201.33 + 23749.6i −0.192734 + 1.42983i
\(652\) 2173.93 + 1255.12i 0.130580 + 0.0753901i
\(653\) −3888.42 2244.98i −0.233025 0.134537i 0.378942 0.925421i \(-0.376288\pi\)
−0.611967 + 0.790883i \(0.709621\pi\)
\(654\) 2616.69 1074.42i 0.156454 0.0642401i
\(655\) 871.795 + 2517.11i 0.0520059 + 0.150155i
\(656\) 16275.4 0.968669
\(657\) 4552.37 16579.5i 0.270327 0.984516i
\(658\) 24672.2i 1.46173i
\(659\) −7650.45 13251.0i −0.452229 0.783284i 0.546295 0.837593i \(-0.316038\pi\)
−0.998524 + 0.0543086i \(0.982705\pi\)
\(660\) −1638.28 + 1445.68i −0.0966210 + 0.0852624i
\(661\) 10317.4 17870.3i 0.607113 1.05155i −0.384600 0.923083i \(-0.625661\pi\)
0.991714 0.128468i \(-0.0410059\pi\)
\(662\) −5335.06 3080.20i −0.313222 0.180839i
\(663\) −8246.88 + 10679.1i −0.483080 + 0.625554i
\(664\) −3372.00 5840.47i −0.197077 0.341347i
\(665\) −1615.36 + 8391.15i −0.0941971 + 0.489316i
\(666\) −1056.18 4041.36i −0.0614504 0.235134i
\(667\) 175.195i 0.0101703i
\(668\) −1782.77 + 1029.28i −0.103259 + 0.0596169i
\(669\) 7300.61 2997.64i 0.421910 0.173237i
\(670\) −6954.35 + 8029.28i −0.401000 + 0.462982i
\(671\) 12613.8 21847.8i 0.725709 1.25697i
\(672\) −3019.01 406.946i −0.173305 0.0233606i
\(673\) −15202.1 + 8776.92i −0.870723 + 0.502712i −0.867588 0.497283i \(-0.834331\pi\)
−0.00313453 + 0.999995i \(0.500998\pi\)
\(674\) 25590.5 1.46248
\(675\) −4486.82 + 16953.3i −0.255848 + 0.966717i
\(676\) 1191.52 0.0677922
\(677\) −13148.6 + 7591.32i −0.746440 + 0.430958i −0.824406 0.565998i \(-0.808491\pi\)
0.0779659 + 0.996956i \(0.475157\pi\)
\(678\) 909.387 + 122.581i 0.0515115 + 0.00694348i
\(679\) 14040.5 24318.8i 0.793556 1.37448i
\(680\) −16046.4 + 18526.7i −0.904930 + 1.04481i
\(681\) −20357.1 + 8358.65i −1.14550 + 0.470344i
\(682\) 30884.5 17831.2i 1.73406 1.00116i
\(683\) 1735.90i 0.0972510i 0.998817 + 0.0486255i \(0.0154841\pi\)
−0.998817 + 0.0486255i \(0.984516\pi\)
\(684\) 803.877 794.010i 0.0449371 0.0443856i
\(685\) −4327.34 + 22478.8i −0.241371 + 1.25383i
\(686\) −9244.67 16012.2i −0.514523 0.891181i
\(687\) 17583.6 22769.5i 0.976501 1.26450i
\(688\) 28.9827 + 16.7331i 0.00160604 + 0.000927246i
\(689\) −2050.45 + 3551.48i −0.113376 + 0.196373i
\(690\) 107.530 94.8892i 0.00593277 0.00523532i
\(691\) 13824.0 + 23943.8i 0.761055 + 1.31819i 0.942307 + 0.334750i \(0.108652\pi\)
−0.181252 + 0.983437i \(0.558015\pi\)
\(692\) 2239.72i 0.123037i
\(693\) −13033.0 13195.0i −0.714408 0.723285i
\(694\) −218.076 −0.0119280
\(695\) 7974.39 + 23024.2i 0.435232 + 1.25663i
\(696\) −21589.6 + 8864.70i −1.17579 + 0.482781i
\(697\) −23101.5 13337.7i −1.25543 0.724822i
\(698\) −216.775 125.155i −0.0117551 0.00678682i
\(699\) 4398.95 32634.4i 0.238031 1.76588i
\(700\) 1609.72 232.161i 0.0869170 0.0125355i
\(701\) 19116.9 1.03001 0.515005 0.857187i \(-0.327790\pi\)
0.515005 + 0.857187i \(0.327790\pi\)
\(702\) 9678.91 + 4114.57i 0.520380 + 0.221217i
\(703\) 2867.42i 0.153836i
\(704\) 12343.5 + 21379.5i 0.660812 + 1.14456i
\(705\) 11071.2 32947.9i 0.591441 1.76013i
\(706\) 8928.58 15464.8i 0.475965 0.824396i
\(707\) 15317.4 + 8843.51i 0.814809 + 0.470430i
\(708\) 321.614 + 783.277i 0.0170720 + 0.0415782i
\(709\) −5022.64 8699.47i −0.266050 0.460812i 0.701788 0.712385i \(-0.252385\pi\)
−0.967838 + 0.251574i \(0.919052\pi\)
\(710\) 1813.17 9418.68i 0.0958410 0.497855i
\(711\) −1964.56 7517.19i −0.103624 0.396507i
\(712\) 7845.47i 0.412952i
\(713\) 239.098 138.043i 0.0125586 0.00725070i
\(714\) −15714.6 12135.5i −0.823673 0.636077i
\(715\) −10553.0 9140.23i −0.551974 0.478077i
\(716\) −887.207 + 1536.69i −0.0463080 + 0.0802077i
\(717\) −8075.97 + 10457.8i −0.420645 + 0.544705i
\(718\) −19308.3 + 11147.7i −1.00359 + 0.579425i
\(719\) −22559.7 −1.17014 −0.585072 0.810981i \(-0.698934\pi\)
−0.585072 + 0.810981i \(0.698934\pi\)
\(720\) 15306.2 + 7548.32i 0.792263 + 0.390707i
\(721\) 24395.4 1.26010
\(722\) 10195.0 5886.10i 0.525512 0.303404i
\(723\) 4048.79 + 9860.64i 0.208266 + 0.507222i
\(724\) −674.114 + 1167.60i −0.0346040 + 0.0599358i
\(725\) 18647.6 14677.8i 0.955246 0.751889i
\(726\) −1215.45 + 9017.03i −0.0621343 + 0.460955i
\(727\) −3176.64 + 1834.04i −0.162057 + 0.0935635i −0.578835 0.815445i \(-0.696492\pi\)
0.416778 + 0.909008i \(0.363159\pi\)
\(728\) 10220.1i 0.520307i
\(729\) 13657.8 + 14173.4i 0.693887 + 0.720084i
\(730\) 18701.6 + 3600.20i 0.948187 + 0.182533i
\(731\) −27.4256 47.5026i −0.00138765 0.00240348i
\(732\) 2460.74 + 331.694i 0.124251 + 0.0167483i
\(733\) 27217.8 + 15714.2i 1.37150 + 0.791838i 0.991117 0.132989i \(-0.0424576\pi\)
0.380387 + 0.924828i \(0.375791\pi\)
\(734\) −168.209 + 291.347i −0.00845875 + 0.0146510i
\(735\) −1212.70 5999.99i −0.0608587 0.301106i
\(736\) 17.5478 + 30.3936i 0.000878830 + 0.00152218i
\(737\) 15826.0i 0.790987i
\(738\) −5505.44 + 20050.5i −0.274604 + 1.00009i
\(739\) −17467.0 −0.869465 −0.434732 0.900560i \(-0.643157\pi\)
−0.434732 + 0.900560i \(0.643157\pi\)
\(740\) −515.691 + 178.608i −0.0256178 + 0.00887267i
\(741\) 5714.15 + 4412.72i 0.283286 + 0.218766i
\(742\) −5226.09 3017.28i −0.258566 0.149283i
\(743\) 21644.9 + 12496.7i 1.06874 + 0.617038i 0.927837 0.372985i \(-0.121666\pi\)
0.140904 + 0.990023i \(0.454999\pi\)
\(744\) 29109.4 + 22479.6i 1.43441 + 1.10772i
\(745\) −570.620 1647.54i −0.0280616 0.0810215i
\(746\) 3840.74 0.188498
\(747\) 7446.47 1946.07i 0.364728 0.0953187i
\(748\) 3484.99i 0.170353i
\(749\) −2970.43 5144.94i −0.144910 0.250991i
\(750\) −19108.8 3495.63i −0.930339 0.170190i
\(751\) 4674.02 8095.64i 0.227107 0.393361i −0.729842 0.683615i \(-0.760407\pi\)
0.956950 + 0.290254i \(0.0937399\pi\)
\(752\) −29293.5 16912.6i −1.42051 0.820132i
\(753\) 14268.9 + 1923.38i 0.690556 + 0.0930833i
\(754\) −7115.95 12325.2i −0.343697 0.595301i
\(755\) −17721.3 3411.48i −0.854230 0.164446i
\(756\) 714.140 1679.91i 0.0343558 0.0808169i
\(757\) 11708.4i 0.562153i 0.959685 + 0.281076i \(0.0906915\pi\)
−0.959685 + 0.281076i \(0.909309\pi\)
\(758\) −4923.02 + 2842.31i −0.235900 + 0.136197i
\(759\) −28.5430 + 211.751i −0.00136501 + 0.0101266i
\(760\) 9913.24 + 8586.08i 0.473146 + 0.409802i
\(761\) −9705.34 + 16810.1i −0.462310 + 0.800745i −0.999076 0.0429866i \(-0.986313\pi\)
0.536765 + 0.843732i \(0.319646\pi\)
\(762\) 9616.95 + 23421.6i 0.457199 + 1.11349i
\(763\) 2716.76 1568.52i 0.128904 0.0744225i
\(764\) −2875.98 −0.136190
\(765\) −15540.1 23257.7i −0.734447 1.09919i
\(766\) −18888.0 −0.890927
\(767\) −4685.50 + 2705.17i −0.220578 + 0.127351i
\(768\) −4069.94 + 5270.28i −0.191226 + 0.247624i
\(769\) −4928.83 + 8536.98i −0.231129 + 0.400327i −0.958141 0.286298i \(-0.907575\pi\)
0.727012 + 0.686625i \(0.240909\pi\)
\(770\) 13450.1 15529.0i 0.629489 0.726789i
\(771\) 1755.07 + 1355.34i 0.0819811 + 0.0633094i
\(772\) 598.746 345.686i 0.0279137 0.0161160i
\(773\) 27574.5i 1.28303i −0.767108 0.641517i \(-0.778305\pi\)
0.767108 0.641517i \(-0.221695\pi\)
\(774\) −30.4183 + 30.0450i −0.00141262 + 0.00139528i
\(775\) −34724.7 13884.1i −1.60948 0.643525i
\(776\) −21548.4 37322.9i −0.996831 1.72656i
\(777\) −1759.54 4285.27i −0.0812395 0.197855i
\(778\) 22747.7 + 13133.4i 1.04826 + 0.605212i
\(779\) −7136.70 + 12361.1i −0.328240 + 0.568528i
\(780\) 437.677 1302.52i 0.0200915 0.0597921i
\(781\) 7145.22 + 12375.9i 0.327370 + 0.567022i
\(782\) 228.741i 0.0104601i
\(783\) −3231.85 26438.3i −0.147505 1.20668i
\(784\) −5957.01 −0.271365
\(785\) 10443.2 3616.99i 0.474821 0.164453i
\(786\) −442.411 + 3282.11i −0.0200767 + 0.148943i
\(787\) 10199.2 + 5888.51i 0.461959 + 0.266712i 0.712868 0.701298i \(-0.247396\pi\)
−0.250908 + 0.968011i \(0.580729\pi\)
\(788\) 263.128 + 151.917i 0.0118954 + 0.00686779i
\(789\) −18084.8 + 7425.64i −0.816016 + 0.335057i
\(790\) 8132.56 2816.69i 0.366257 0.126852i
\(791\) 1017.64 0.0457436
\(792\) −27538.8 + 7197.04i −1.23554 + 0.322898i
\(793\) 15865.5i 0.710466i
\(794\) 14706.8 + 25473.0i 0.657338 + 1.13854i
\(795\) −5625.10 6374.48i −0.250946 0.284377i
\(796\) −564.800 + 978.263i −0.0251493 + 0.0435598i
\(797\) 21356.0 + 12329.9i 0.949146 + 0.547990i 0.892816 0.450422i \(-0.148727\pi\)
0.0563307 + 0.998412i \(0.482060\pi\)
\(798\) −6493.42 + 8408.51i −0.288051 + 0.373005i
\(799\) 27719.8 + 48012.1i 1.22735 + 2.12584i
\(800\) 1764.92 4414.14i 0.0779991 0.195079i
\(801\) 8634.05 + 2370.72i 0.380860 + 0.104576i
\(802\) 17473.0i 0.769318i
\(803\) −24573.3 + 14187.4i −1.07992 + 0.623491i
\(804\) 1440.91 591.640i 0.0632053 0.0259521i
\(805\) 104.126 120.221i 0.00455895 0.00526363i
\(806\) −11213.9 + 19423.0i −0.490065 + 0.848818i
\(807\) −10197.4 1374.56i −0.444817 0.0599589i
\(808\) 23508.1 13572.4i 1.02353 0.590935i
\(809\) −19263.0 −0.837144 −0.418572 0.908184i \(-0.637469\pi\)
−0.418572 + 0.908184i \(0.637469\pi\)
\(810\) −14476.8 + 16303.2i −0.627978 + 0.707205i
\(811\) −13597.4 −0.588741 −0.294370 0.955691i \(-0.595110\pi\)
−0.294370 + 0.955691i \(0.595110\pi\)
\(812\) −2139.20 + 1235.07i −0.0924524 + 0.0533774i
\(813\) −29145.1 3928.60i −1.25727 0.169474i
\(814\) −3446.85 + 5970.12i −0.148418 + 0.257067i
\(815\) −25134.6 21769.6i −1.08028 0.935652i
\(816\) −25180.8 + 10339.3i −1.08027 + 0.443562i
\(817\) −25.4176 + 14.6748i −0.00108843 + 0.000628406i
\(818\) 13389.6i 0.572318i
\(819\) 11247.4 + 3088.29i 0.479873 + 0.131763i
\(820\) 2667.62 + 513.538i 0.113607 + 0.0218701i
\(821\) −14336.8 24832.1i −0.609449 1.05560i −0.991331 0.131386i \(-0.958057\pi\)
0.381882 0.924211i \(-0.375276\pi\)
\(822\) −17395.0 + 22525.3i −0.738103 + 0.955790i
\(823\) 7307.19 + 4218.81i 0.309493 + 0.178686i 0.646700 0.762745i \(-0.276149\pi\)
−0.337207 + 0.941431i \(0.609482\pi\)
\(824\) 18720.2 32424.3i 0.791443 1.37082i
\(825\) 24930.0 14702.4i 1.05206 0.620451i
\(826\) −3980.73 6894.82i −0.167684 0.290438i
\(827\) 11315.7i 0.475799i −0.971290 0.237900i \(-0.923541\pi\)
0.971290 0.237900i \(-0.0764590\pi\)
\(828\) −20.3464 + 5.31738i −0.000853971 + 0.000223178i
\(829\) −6773.57 −0.283783 −0.141891 0.989882i \(-0.545318\pi\)
−0.141891 + 0.989882i \(0.545318\pi\)
\(830\) 2790.19 + 8056.04i 0.116685 + 0.336903i
\(831\) 29655.5 12176.6i 1.23795 0.508304i
\(832\) −13445.4 7762.72i −0.560260 0.323466i
\(833\) 8455.47 + 4881.77i 0.351698 + 0.203053i
\(834\) −4046.78 + 30021.8i −0.168020 + 1.24649i
\(835\) 25766.7 8924.24i 1.06790 0.369864i
\(836\) −1864.74 −0.0771452
\(837\) −33535.3 + 25242.5i −1.38489 + 1.04242i
\(838\) 196.602i 0.00810443i
\(839\) 4456.94 + 7719.65i 0.183398 + 0.317654i 0.943035 0.332692i \(-0.107957\pi\)
−0.759638 + 0.650347i \(0.774624\pi\)
\(840\) 20083.7 + 6748.57i 0.824945 + 0.277200i
\(841\) −5826.91 + 10092.5i −0.238916 + 0.413814i
\(842\) 11654.7 + 6728.87i 0.477018 + 0.275406i
\(843\) 6598.81 + 16071.1i 0.269603 + 0.656605i
\(844\) −450.810 780.826i −0.0183857 0.0318450i
\(845\) −15498.6 2983.61i −0.630970 0.121467i
\(846\) 30744.6 30367.2i 1.24943 1.23410i
\(847\) 10090.4i 0.409341i
\(848\) −7164.90 + 4136.66i −0.290146 + 0.167516i
\(849\) −20987.9 16207.8i −0.848414 0.655182i
\(850\) 24347.0 19163.9i 0.982466 0.773314i
\(851\) −26.6844 + 46.2187i −0.00107489 + 0.00186176i
\(852\) −859.673 + 1113.21i −0.0345680 + 0.0447630i
\(853\) −27426.4 + 15834.6i −1.10089 + 0.635600i −0.936455 0.350787i \(-0.885914\pi\)
−0.164437 + 0.986388i \(0.552581\pi\)
\(854\) −23346.4 −0.935478
\(855\) −12444.7 + 8315.14i −0.497776 + 0.332598i
\(856\) −9117.63 −0.364059
\(857\) 38152.6 22027.4i 1.52073 0.877995i 0.521031 0.853538i \(-0.325548\pi\)
0.999701 0.0244574i \(-0.00778582\pi\)
\(858\) −6592.75 16056.3i −0.262323 0.638875i
\(859\) 9534.70 16514.6i 0.378719 0.655961i −0.612157 0.790736i \(-0.709698\pi\)
0.990876 + 0.134775i \(0.0430313\pi\)
\(860\) 4.22243 + 3.65714i 0.000167423 + 0.000145009i
\(861\) −3080.41 + 22852.6i −0.121928 + 0.904547i
\(862\) 4520.50 2609.91i 0.178618 0.103125i
\(863\) 6256.14i 0.246769i −0.992359 0.123384i \(-0.960625\pi\)
0.992359 0.123384i \(-0.0393748\pi\)
\(864\) −3208.78 4262.94i −0.126348 0.167857i
\(865\) −5608.35 + 29133.1i −0.220451 + 1.14515i
\(866\) 5089.97 + 8816.09i 0.199728 + 0.345939i
\(867\) 18915.2 + 2549.66i 0.740937 + 0.0998744i
\(868\) 3371.13 + 1946.32i 0.131824 + 0.0761089i
\(869\) −6411.38 + 11104.8i −0.250277 + 0.433493i
\(870\) 28919.2 5845.06i 1.12696 0.227777i
\(871\) 4976.42 + 8619.41i 0.193593 + 0.335313i
\(872\) 4814.52i 0.186973i
\(873\) 47585.8 12436.1i 1.84483 0.482130i
\(874\) 122.394 0.00473690
\(875\) −21519.8 1010.99i −0.831432 0.0390604i
\(876\) −2210.38 1706.95i −0.0852532 0.0658362i
\(877\) 6025.33 + 3478.73i 0.231997 + 0.133943i 0.611493 0.791250i \(-0.290569\pi\)
−0.379496 + 0.925193i \(0.623903\pi\)
\(878\) −27578.5 15922.5i −1.06006 0.612024i
\(879\) 16986.2 + 13117.5i 0.651797 + 0.503346i
\(880\) −9217.85 26614.4i −0.353106 1.01951i
\(881\) 10626.4 0.406371 0.203186 0.979140i \(-0.434871\pi\)
0.203186 + 0.979140i \(0.434871\pi\)
\(882\) 2015.06 7338.76i 0.0769283 0.280169i
\(883\) 31013.5i 1.18198i −0.806679 0.590990i \(-0.798737\pi\)
0.806679 0.590990i \(-0.201263\pi\)
\(884\) 1095.84 + 1898.06i 0.0416936 + 0.0722155i
\(885\) −2222.04 10993.8i −0.0843988 0.417574i
\(886\) 12129.3 21008.6i 0.459925 0.796613i
\(887\) −8138.36 4698.69i −0.308072 0.177865i 0.337992 0.941149i \(-0.390252\pi\)
−0.646063 + 0.763284i \(0.723586\pi\)
\(888\) −7045.83 949.740i −0.266264 0.0358910i
\(889\) 14039.6 + 24317.4i 0.529667 + 0.917410i
\(890\) −1874.87 + 9739.17i −0.0706131 + 0.366806i
\(891\) 401.158 32481.6i 0.0150834 1.22130i
\(892\) 1281.94i 0.0481195i
\(893\) 25690.2 14832.2i 0.962697 0.555814i
\(894\) 289.574 2148.26i 0.0108331 0.0803675i
\(895\) 15388.3 17766.9i 0.574719 0.663554i
\(896\) 9077.97 15723.5i 0.338475 0.586256i
\(897\) −51.0389 124.303i −0.00189982 0.00462693i
\(898\) 16987.0 9807.42i 0.631250 0.364452i
\(899\) 56799.2 2.10718
\(900\) 2270.60 + 1720.17i 0.0840962 + 0.0637099i
\(901\) 13560.0 0.501385
\(902\) 29718.0 17157.7i 1.09701 0.633357i
\(903\) −28.9808 + 37.5281i −0.00106802 + 0.00138301i
\(904\) 780.903 1352.56i 0.0287306 0.0497628i
\(905\) 11692.3 13499.5i 0.429463 0.495845i
\(906\) −17757.9 13713.5i −0.651178 0.502869i
\(907\) −23868.1 + 13780.2i −0.873788 + 0.504482i −0.868605 0.495505i \(-0.834983\pi\)
−0.00518301 + 0.999987i \(0.501650\pi\)
\(908\) 3574.58i 0.130646i
\(909\) 7833.00 + 29972.2i 0.285813 + 1.09364i
\(910\) −2442.35 + 12687.0i −0.0889705 + 0.462165i
\(911\) 17935.0 + 31064.4i 0.652266 + 1.12976i 0.982572 + 0.185884i \(0.0595148\pi\)
−0.330306 + 0.943874i \(0.607152\pi\)
\(912\) 5532.31 + 13473.7i 0.200869 + 0.489208i
\(913\) −11000.4 6351.06i −0.398750 0.230218i
\(914\) 1565.49 2711.50i 0.0566539 0.0981274i
\(915\) −31177.4 10476.3i −1.12644 0.378509i
\(916\) −2336.50 4046.94i −0.0842798 0.145977i
\(917\) 3672.82i 0.132265i
\(918\) −4219.63 34519.0i −0.151709 1.24106i
\(919\) −3081.79 −0.110619 −0.0553095 0.998469i \(-0.517615\pi\)
−0.0553095 + 0.998469i \(0.517615\pi\)
\(920\) −79.8846 230.648i −0.00286274 0.00826549i
\(921\) 2347.93 17418.6i 0.0840032 0.623194i
\(922\) −34165.8 19725.6i −1.22038 0.704586i
\(923\) −7783.11 4493.58i −0.277556 0.160247i
\(924\) −2786.80 + 1144.26i −0.0992195 + 0.0407396i
\(925\) 7155.09 1031.94i 0.254333 0.0366809i
\(926\) 5578.86 0.197984
\(927\) 30026.6 + 30399.7i 1.06387 + 1.07709i
\(928\) 7220.20i 0.255404i
\(929\) −2135.02 3697.96i −0.0754011 0.130599i 0.825860 0.563876i \(-0.190690\pi\)
−0.901261 + 0.433277i \(0.857357\pi\)
\(930\) −30763.7 34862.0i −1.08471 1.22921i
\(931\) 2612.13 4524.33i 0.0919538 0.159269i
\(932\) −4632.27 2674.44i −0.162806 0.0939961i
\(933\) −19123.0 + 24762.9i −0.671016 + 0.868917i
\(934\) 13300.1 + 23036.4i 0.465945 + 0.807040i
\(935\) −8726.57 + 45331.0i −0.305229 + 1.58554i
\(936\) 12735.6 12579.2i 0.444738 0.439279i
\(937\) 49225.3i 1.71624i −0.513446 0.858122i \(-0.671631\pi\)
0.513446 0.858122i \(-0.328369\pi\)
\(938\) −12683.7 + 7322.92i −0.441510 + 0.254906i
\(939\) −48994.8 + 20117.3i −1.70275 + 0.699152i
\(940\) −4267.71 3696.36i −0.148082 0.128258i
\(941\) −17284.9 + 29938.3i −0.598800 + 1.03715i 0.394199 + 0.919025i \(0.371022\pi\)
−0.992999 + 0.118127i \(0.962311\pi\)
\(942\) 13617.1 + 1835.52i 0.470988 + 0.0634867i
\(943\) 230.067 132.829i 0.00794486 0.00458697i
\(944\) −10915.1 −0.376329
\(945\) −13495.7 + 20063.1i −0.464567 + 0.690639i
\(946\) 70.5610 0.00242509
\(947\) −23679.2 + 13671.2i −0.812534 + 0.469117i −0.847835 0.530260i \(-0.822094\pi\)
0.0353008 + 0.999377i \(0.488761\pi\)
\(948\) −1250.75 168.594i −0.0428506 0.00577604i
\(949\) 8922.37 15454.0i 0.305197 0.528618i
\(950\) −10254.2 13027.6i −0.350200 0.444915i
\(951\) −25959.2 + 10658.9i −0.885158 + 0.363447i
\(952\) −29266.2 + 16896.9i −0.996349 + 0.575242i
\(953\) 45941.5i 1.56158i 0.624791 + 0.780792i \(0.285184\pi\)
−0.624791 + 0.780792i \(0.714816\pi\)
\(954\) −2672.51 10226.1i −0.0906979 0.347047i
\(955\) 37409.3 + 7201.59i 1.26758 + 0.244019i
\(956\) 1073.13 + 1858.72i 0.0363050 + 0.0628822i
\(957\) −26867.2 + 34791.1i −0.907518 + 1.17517i
\(958\) 6172.08 + 3563.45i 0.208153 + 0.120177i
\(959\) −15781.3 + 27334.0i −0.531391 + 0.920397i
\(960\) 24132.9 21295.9i 0.811340 0.715960i
\(961\) −29858.9 51717.1i −1.00228 1.73600i
\(962\) 4335.40i 0.145300i
\(963\) 2755.14 10034.1i 0.0921944 0.335767i
\(964\) 1731.47 0.0578494
\(965\) −8653.80 + 2997.23i −0.288680 + 0.0999835i
\(966\) 182.915 75.1050i 0.00609232 0.00250151i
\(967\) −40996.6 23669.4i −1.36335 0.787132i −0.373284 0.927717i \(-0.621768\pi\)
−0.990069 + 0.140585i \(0.955102\pi\)
\(968\) 13411.4 + 7743.05i 0.445307 + 0.257098i
\(969\) 3189.04 23658.5i 0.105724 0.784334i
\(970\) 17830.4 + 51481.1i 0.590205 + 1.70408i
\(971\) 50168.3 1.65806 0.829031 0.559202i \(-0.188893\pi\)
0.829031 + 0.559202i \(0.188893\pi\)
\(972\) 2972.36 1177.77i 0.0980848 0.0388652i
\(973\) 33595.7i 1.10691i
\(974\) −4108.23 7115.66i −0.135150 0.234087i
\(975\) −8954.66 + 15846.6i −0.294132 + 0.520511i
\(976\) −16003.8 + 27719.4i −0.524867 + 0.909096i
\(977\) 41259.3 + 23821.0i 1.35108 + 0.780044i 0.988400 0.151872i \(-0.0485301\pi\)
0.362675 + 0.931916i \(0.381863\pi\)
\(978\) −15702.2 38242.0i −0.513396 1.25035i
\(979\) −7388.35 12797.0i −0.241198 0.417767i
\(980\) −976.385 187.962i −0.0318260 0.00612675i
\(981\) 5298.45 + 1454.84i 0.172443 + 0.0473491i
\(982\) 43040.7i 1.39866i
\(983\) −9663.22 + 5579.06i −0.313539 + 0.181022i −0.648509 0.761207i \(-0.724607\pi\)
0.334970 + 0.942229i \(0.391274\pi\)
\(984\) 28009.9 + 21630.5i 0.907443 + 0.700768i
\(985\) −3042.23 2634.95i −0.0984097 0.0852349i
\(986\) −23529.5 + 40754.3i −0.759971 + 1.31631i
\(987\) 29291.7 37930.6i 0.944644 1.22325i
\(988\) 1015.61 586.361i 0.0327032 0.0188812i
\(989\) 0.546260 1.75632e−5
\(990\) 35905.8 2353.15i 1.15269 0.0755436i
\(991\) −57670.7 −1.84861 −0.924304 0.381658i \(-0.875353\pi\)
−0.924304 + 0.381658i \(0.875353\pi\)
\(992\) 9853.79 5689.09i 0.315381 0.182085i
\(993\) −4545.11 11069.4i −0.145252 0.353753i
\(994\) 6612.41 11453.0i 0.210999 0.365461i
\(995\) 9796.25 11310.5i 0.312123 0.360368i
\(996\) 167.008 1238.98i 0.00531310 0.0394163i
\(997\) 44800.2 25865.4i 1.42311 0.821630i 0.426543 0.904467i \(-0.359731\pi\)
0.996563 + 0.0828370i \(0.0263981\pi\)
\(998\) 32262.8i 1.02331i
\(999\) 3174.29 7467.04i 0.100531 0.236483i
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 45.4.j.a.4.5 32
3.2 odd 2 135.4.j.a.64.12 32
5.2 odd 4 225.4.e.g.76.5 32
5.3 odd 4 225.4.e.g.76.12 32
5.4 even 2 inner 45.4.j.a.4.12 yes 32
9.2 odd 6 135.4.j.a.19.5 32
9.4 even 3 405.4.b.e.244.5 16
9.5 odd 6 405.4.b.f.244.12 16
9.7 even 3 inner 45.4.j.a.34.12 yes 32
15.14 odd 2 135.4.j.a.64.5 32
45.4 even 6 405.4.b.e.244.12 16
45.7 odd 12 225.4.e.g.151.5 32
45.13 odd 12 2025.4.a.bk.1.5 16
45.14 odd 6 405.4.b.f.244.5 16
45.22 odd 12 2025.4.a.bk.1.12 16
45.23 even 12 2025.4.a.bl.1.12 16
45.29 odd 6 135.4.j.a.19.12 32
45.32 even 12 2025.4.a.bl.1.5 16
45.34 even 6 inner 45.4.j.a.34.5 yes 32
45.43 odd 12 225.4.e.g.151.12 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.j.a.4.5 32 1.1 even 1 trivial
45.4.j.a.4.12 yes 32 5.4 even 2 inner
45.4.j.a.34.5 yes 32 45.34 even 6 inner
45.4.j.a.34.12 yes 32 9.7 even 3 inner
135.4.j.a.19.5 32 9.2 odd 6
135.4.j.a.19.12 32 45.29 odd 6
135.4.j.a.64.5 32 15.14 odd 2
135.4.j.a.64.12 32 3.2 odd 2
225.4.e.g.76.5 32 5.2 odd 4
225.4.e.g.76.12 32 5.3 odd 4
225.4.e.g.151.5 32 45.7 odd 12
225.4.e.g.151.12 32 45.43 odd 12
405.4.b.e.244.5 16 9.4 even 3
405.4.b.e.244.12 16 45.4 even 6
405.4.b.f.244.5 16 45.14 odd 6
405.4.b.f.244.12 16 9.5 odd 6
2025.4.a.bk.1.5 16 45.13 odd 12
2025.4.a.bk.1.12 16 45.22 odd 12
2025.4.a.bl.1.5 16 45.32 even 12
2025.4.a.bl.1.12 16 45.23 even 12