Properties

Label 150.3.j.a.11.16
Level $150$
Weight $3$
Character 150.11
Analytic conductor $4.087$
Analytic rank $0$
Dimension $80$
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] = [150,3,Mod(11,150)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(150, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 8]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("150.11");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 150.j (of order \(10\), degree \(4\), 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: \(4.08720396540\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 11.16
Character \(\chi\) \(=\) 150.11
Dual form 150.3.j.a.41.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.831254 + 1.14412i) q^{2} +(0.178022 + 2.99471i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.93889 - 0.779331i) q^{5} +(-3.27834 + 2.69305i) q^{6} +8.16986 q^{7} +(-2.68999 + 0.874032i) q^{8} +(-8.93662 + 1.06625i) q^{9} +O(q^{10})\) \(q+(0.831254 + 1.14412i) q^{2} +(0.178022 + 2.99471i) q^{3} +(-0.618034 + 1.90211i) q^{4} +(4.93889 - 0.779331i) q^{5} +(-3.27834 + 2.69305i) q^{6} +8.16986 q^{7} +(-2.68999 + 0.874032i) q^{8} +(-8.93662 + 1.06625i) q^{9} +(4.99712 + 5.00288i) q^{10} +(6.71524 + 9.24273i) q^{11} +(-5.80631 - 1.51222i) q^{12} +(-16.0096 - 11.6317i) q^{13} +(6.79123 + 9.34733i) q^{14} +(3.21311 + 14.6518i) q^{15} +(-3.23607 - 2.35114i) q^{16} +(-14.3824 + 4.67311i) q^{17} +(-8.64852 - 9.33826i) q^{18} +(-4.39373 - 13.5225i) q^{19} +(-1.57003 + 9.87598i) q^{20} +(1.45442 + 24.4664i) q^{21} +(-4.99275 + 15.3661i) q^{22} +(-1.26018 - 1.73449i) q^{23} +(-3.09635 - 7.90016i) q^{24} +(23.7853 - 7.69806i) q^{25} -27.9859i q^{26} +(-4.78403 - 26.5728i) q^{27} +(-5.04925 + 15.5400i) q^{28} +(44.8797 + 14.5823i) q^{29} +(-14.0926 + 15.8556i) q^{30} +(-12.3974 - 38.1554i) q^{31} -5.65685i q^{32} +(-26.4839 + 21.7556i) q^{33} +(-17.3020 - 12.5706i) q^{34} +(40.3501 - 6.36703i) q^{35} +(3.49500 - 17.6574i) q^{36} +(42.2525 + 30.6983i) q^{37} +(11.8191 - 16.2676i) q^{38} +(31.9835 - 50.0150i) q^{39} +(-12.6044 + 6.41314i) q^{40} +(12.3449 - 16.9912i) q^{41} +(-26.7836 + 22.0018i) q^{42} -22.1632 q^{43} +(-21.7310 + 7.06082i) q^{44} +(-43.3060 + 12.2307i) q^{45} +(0.936937 - 2.88360i) q^{46} +(35.0106 + 11.3756i) q^{47} +(6.46490 - 10.1097i) q^{48} +17.7467 q^{49} +(28.5791 + 20.8142i) q^{50} +(-16.5550 - 42.2391i) q^{51} +(32.0193 - 23.2634i) q^{52} +(-70.7241 - 22.9797i) q^{53} +(26.4258 - 27.5623i) q^{54} +(40.3690 + 40.4155i) q^{55} +(-21.9769 + 7.14072i) q^{56} +(39.7138 - 15.5653i) q^{57} +(20.6225 + 63.4695i) q^{58} +(4.35141 - 5.98921i) q^{59} +(-29.8552 - 2.94364i) q^{60} +(-6.76561 + 4.91551i) q^{61} +(33.3490 - 45.9010i) q^{62} +(-73.0109 + 8.71112i) q^{63} +(6.47214 - 4.70228i) q^{64} +(-88.1348 - 44.9708i) q^{65} +(-46.9059 - 12.2164i) q^{66} +(-40.3867 - 124.298i) q^{67} -30.2450i q^{68} +(4.96995 - 4.08265i) q^{69} +(40.8258 + 40.8728i) q^{70} +(53.4414 + 17.3642i) q^{71} +(23.1075 - 10.6791i) q^{72} +(-79.1392 + 57.4980i) q^{73} +73.8601i q^{74} +(27.2878 + 69.8597i) q^{75} +28.4368 q^{76} +(54.8626 + 75.5119i) q^{77} +(83.8096 - 4.98210i) q^{78} +(6.64298 - 20.4450i) q^{79} +(-17.8149 - 9.09006i) q^{80} +(78.7262 - 19.0573i) q^{81} +29.7018 q^{82} +(74.5092 - 24.2095i) q^{83} +(-47.4367 - 12.3546i) q^{84} +(-67.3910 + 34.2886i) q^{85} +(-18.4233 - 25.3574i) q^{86} +(-35.6802 + 136.998i) q^{87} +(-26.1424 - 18.9936i) q^{88} +(-31.9182 - 43.9316i) q^{89} +(-49.9917 - 39.3806i) q^{90} +(-130.797 - 95.0292i) q^{91} +(4.07802 - 1.32503i) q^{92} +(112.057 - 43.9193i) q^{93} +(16.0876 + 49.5125i) q^{94} +(-32.2386 - 63.3620i) q^{95} +(16.9407 - 1.00705i) q^{96} +(-10.5214 + 32.3815i) q^{97} +(14.7520 + 20.3044i) q^{98} +(-69.8666 - 75.4386i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 80 q - 4 q^{3} + 40 q^{4} - 8 q^{7} + 20 q^{9} - 12 q^{12} + 40 q^{13} - 60 q^{15} - 80 q^{16} - 32 q^{18} + 60 q^{19} + 60 q^{21} - 8 q^{22} - 180 q^{25} + 182 q^{27} - 24 q^{28} + 20 q^{30} - 180 q^{31} + 26 q^{33} - 120 q^{34} - 40 q^{36} + 128 q^{37} + 220 q^{39} + 128 q^{42} - 56 q^{43} - 100 q^{45} - 120 q^{46} + 24 q^{48} + 440 q^{49} - 20 q^{51} - 80 q^{52} - 120 q^{54} - 792 q^{57} - 100 q^{60} + 200 q^{61} - 574 q^{63} + 160 q^{64} - 160 q^{66} - 732 q^{67} - 220 q^{69} + 280 q^{70} + 64 q^{72} - 400 q^{73} + 590 q^{75} + 80 q^{76} - 260 q^{78} + 400 q^{79} + 140 q^{81} + 448 q^{82} + 180 q^{84} - 200 q^{85} + 310 q^{87} - 64 q^{88} + 440 q^{90} + 340 q^{91} + 348 q^{93} + 160 q^{94} - 276 q^{97} + 180 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.831254 + 1.14412i 0.415627 + 0.572061i
\(3\) 0.178022 + 2.99471i 0.0593407 + 0.998238i
\(4\) −0.618034 + 1.90211i −0.154508 + 0.475528i
\(5\) 4.93889 0.779331i 0.987778 0.155866i
\(6\) −3.27834 + 2.69305i −0.546390 + 0.448841i
\(7\) 8.16986 1.16712 0.583562 0.812069i \(-0.301659\pi\)
0.583562 + 0.812069i \(0.301659\pi\)
\(8\) −2.68999 + 0.874032i −0.336249 + 0.109254i
\(9\) −8.93662 + 1.06625i −0.992957 + 0.118472i
\(10\) 4.99712 + 5.00288i 0.499712 + 0.500288i
\(11\) 6.71524 + 9.24273i 0.610476 + 0.840249i 0.996617 0.0821915i \(-0.0261919\pi\)
−0.386140 + 0.922440i \(0.626192\pi\)
\(12\) −5.80631 1.51222i −0.483859 0.126018i
\(13\) −16.0096 11.6317i −1.23151 0.894745i −0.234508 0.972114i \(-0.575348\pi\)
−0.997002 + 0.0773696i \(0.975348\pi\)
\(14\) 6.79123 + 9.34733i 0.485088 + 0.667666i
\(15\) 3.21311 + 14.6518i 0.214207 + 0.976788i
\(16\) −3.23607 2.35114i −0.202254 0.146946i
\(17\) −14.3824 + 4.67311i −0.846021 + 0.274889i −0.699779 0.714360i \(-0.746718\pi\)
−0.146243 + 0.989249i \(0.546718\pi\)
\(18\) −8.64852 9.33826i −0.480473 0.518792i
\(19\) −4.39373 13.5225i −0.231249 0.711711i −0.997597 0.0692850i \(-0.977928\pi\)
0.766348 0.642426i \(-0.222072\pi\)
\(20\) −1.57003 + 9.87598i −0.0785013 + 0.493799i
\(21\) 1.45442 + 24.4664i 0.0692579 + 1.16507i
\(22\) −4.99275 + 15.3661i −0.226943 + 0.698460i
\(23\) −1.26018 1.73449i −0.0547903 0.0754124i 0.780743 0.624853i \(-0.214841\pi\)
−0.835533 + 0.549440i \(0.814841\pi\)
\(24\) −3.09635 7.90016i −0.129015 0.329174i
\(25\) 23.7853 7.69806i 0.951411 0.307922i
\(26\) 27.9859i 1.07638i
\(27\) −4.78403 26.5728i −0.177186 0.984177i
\(28\) −5.04925 + 15.5400i −0.180330 + 0.555000i
\(29\) 44.8797 + 14.5823i 1.54758 + 0.502838i 0.953455 0.301537i \(-0.0974996\pi\)
0.594122 + 0.804375i \(0.297500\pi\)
\(30\) −14.0926 + 15.8556i −0.469753 + 0.528519i
\(31\) −12.3974 38.1554i −0.399918 1.23082i −0.925065 0.379808i \(-0.875990\pi\)
0.525148 0.851011i \(-0.324010\pi\)
\(32\) 5.65685i 0.176777i
\(33\) −26.4839 + 21.7556i −0.802542 + 0.659262i
\(34\) −17.3020 12.5706i −0.508883 0.369725i
\(35\) 40.3501 6.36703i 1.15286 0.181915i
\(36\) 3.49500 17.6574i 0.0970834 0.490484i
\(37\) 42.2525 + 30.6983i 1.14196 + 0.829682i 0.987391 0.158300i \(-0.0506012\pi\)
0.154569 + 0.987982i \(0.450601\pi\)
\(38\) 11.8191 16.2676i 0.311029 0.428095i
\(39\) 31.9835 50.0150i 0.820089 1.28243i
\(40\) −12.6044 + 6.41314i −0.315111 + 0.160329i
\(41\) 12.3449 16.9912i 0.301094 0.414421i −0.631484 0.775389i \(-0.717554\pi\)
0.932578 + 0.360968i \(0.117554\pi\)
\(42\) −26.7836 + 22.0018i −0.637704 + 0.523853i
\(43\) −22.1632 −0.515423 −0.257712 0.966222i \(-0.582968\pi\)
−0.257712 + 0.966222i \(0.582968\pi\)
\(44\) −21.7310 + 7.06082i −0.493886 + 0.160473i
\(45\) −43.3060 + 12.2307i −0.962356 + 0.271793i
\(46\) 0.936937 2.88360i 0.0203682 0.0626869i
\(47\) 35.0106 + 11.3756i 0.744906 + 0.242035i 0.656788 0.754075i \(-0.271915\pi\)
0.0881183 + 0.996110i \(0.471915\pi\)
\(48\) 6.46490 10.1097i 0.134685 0.210618i
\(49\) 17.7467 0.362177
\(50\) 28.5791 + 20.8142i 0.571583 + 0.416285i
\(51\) −16.5550 42.2391i −0.324608 0.828218i
\(52\) 32.0193 23.2634i 0.615755 0.447372i
\(53\) −70.7241 22.9797i −1.33442 0.433579i −0.446995 0.894536i \(-0.647506\pi\)
−0.887422 + 0.460958i \(0.847506\pi\)
\(54\) 26.4258 27.5623i 0.489366 0.510412i
\(55\) 40.3690 + 40.4155i 0.733982 + 0.734827i
\(56\) −21.9769 + 7.14072i −0.392444 + 0.127513i
\(57\) 39.7138 15.5653i 0.696734 0.273075i
\(58\) 20.6225 + 63.4695i 0.355560 + 1.09430i
\(59\) 4.35141 5.98921i 0.0737528 0.101512i −0.770547 0.637383i \(-0.780017\pi\)
0.844300 + 0.535871i \(0.180017\pi\)
\(60\) −29.8552 2.94364i −0.497587 0.0490606i
\(61\) −6.76561 + 4.91551i −0.110912 + 0.0805821i −0.641859 0.766823i \(-0.721836\pi\)
0.530947 + 0.847405i \(0.321836\pi\)
\(62\) 33.3490 45.9010i 0.537888 0.740339i
\(63\) −73.0109 + 8.71112i −1.15890 + 0.138272i
\(64\) 6.47214 4.70228i 0.101127 0.0734732i
\(65\) −88.1348 44.9708i −1.35592 0.691858i
\(66\) −46.9059 12.2164i −0.710696 0.185096i
\(67\) −40.3867 124.298i −0.602787 1.85519i −0.511341 0.859378i \(-0.670851\pi\)
−0.0914465 0.995810i \(-0.529149\pi\)
\(68\) 30.2450i 0.444780i
\(69\) 4.96995 4.08265i 0.0720282 0.0591688i
\(70\) 40.8258 + 40.8728i 0.583226 + 0.583897i
\(71\) 53.4414 + 17.3642i 0.752696 + 0.244566i 0.660141 0.751142i \(-0.270497\pi\)
0.0925552 + 0.995708i \(0.470497\pi\)
\(72\) 23.1075 10.6791i 0.320938 0.148321i
\(73\) −79.1392 + 57.4980i −1.08410 + 0.787643i −0.978393 0.206754i \(-0.933710\pi\)
−0.105705 + 0.994398i \(0.533710\pi\)
\(74\) 73.8601i 0.998110i
\(75\) 27.2878 + 69.8597i 0.363837 + 0.931463i
\(76\) 28.4368 0.374168
\(77\) 54.8626 + 75.5119i 0.712501 + 0.980674i
\(78\) 83.8096 4.98210i 1.07448 0.0638731i
\(79\) 6.64298 20.4450i 0.0840884 0.258797i −0.900168 0.435542i \(-0.856557\pi\)
0.984257 + 0.176745i \(0.0565567\pi\)
\(80\) −17.8149 9.09006i −0.222686 0.113626i
\(81\) 78.7262 19.0573i 0.971929 0.235276i
\(82\) 29.7018 0.362217
\(83\) 74.5092 24.2095i 0.897701 0.291681i 0.176413 0.984316i \(-0.443551\pi\)
0.721288 + 0.692636i \(0.243551\pi\)
\(84\) −47.4367 12.3546i −0.564723 0.147079i
\(85\) −67.3910 + 34.2886i −0.792835 + 0.403395i
\(86\) −18.4233 25.3574i −0.214224 0.294854i
\(87\) −35.6802 + 136.998i −0.410118 + 1.57469i
\(88\) −26.1424 18.9936i −0.297073 0.215836i
\(89\) −31.9182 43.9316i −0.358631 0.493613i 0.591136 0.806572i \(-0.298680\pi\)
−0.949767 + 0.312959i \(0.898680\pi\)
\(90\) −49.9917 39.3806i −0.555463 0.437562i
\(91\) −130.797 95.0292i −1.43732 1.04428i
\(92\) 4.07802 1.32503i 0.0443263 0.0144025i
\(93\) 112.057 43.9193i 1.20492 0.472250i
\(94\) 16.0876 + 49.5125i 0.171144 + 0.526728i
\(95\) −32.2386 63.3620i −0.339354 0.666968i
\(96\) 16.9407 1.00705i 0.176465 0.0104901i
\(97\) −10.5214 + 32.3815i −0.108468 + 0.333830i −0.990529 0.137306i \(-0.956156\pi\)
0.882061 + 0.471136i \(0.156156\pi\)
\(98\) 14.7520 + 20.3044i 0.150530 + 0.207187i
\(99\) −69.8666 75.4386i −0.705723 0.762007i
\(100\) −0.0575303 + 50.0000i −0.000575303 + 0.500000i
\(101\) 16.9106i 0.167431i 0.996490 + 0.0837156i \(0.0266787\pi\)
−0.996490 + 0.0837156i \(0.973321\pi\)
\(102\) 34.5653 54.0524i 0.338876 0.529925i
\(103\) −44.2048 + 136.048i −0.429173 + 1.32086i 0.469769 + 0.882789i \(0.344337\pi\)
−0.898942 + 0.438068i \(0.855663\pi\)
\(104\) 53.2323 + 17.2962i 0.511849 + 0.166310i
\(105\) 26.2506 + 119.703i 0.250006 + 1.14003i
\(106\) −32.4982 100.019i −0.306586 0.943576i
\(107\) 85.3363i 0.797536i 0.917052 + 0.398768i \(0.130562\pi\)
−0.917052 + 0.398768i \(0.869438\pi\)
\(108\) 53.5011 + 7.32312i 0.495381 + 0.0678067i
\(109\) 11.7410 + 8.53034i 0.107716 + 0.0782600i 0.640339 0.768092i \(-0.278794\pi\)
−0.532623 + 0.846352i \(0.678794\pi\)
\(110\) −12.6834 + 79.7826i −0.115303 + 0.725296i
\(111\) −84.4106 + 131.999i −0.760456 + 1.18918i
\(112\) −26.4382 19.2085i −0.236056 0.171504i
\(113\) −113.560 + 156.302i −1.00496 + 1.38321i −0.0827241 + 0.996572i \(0.526362\pi\)
−0.922234 + 0.386633i \(0.873638\pi\)
\(114\) 50.8208 + 32.4988i 0.445797 + 0.285077i
\(115\) −7.57562 7.58434i −0.0658750 0.0659508i
\(116\) −55.4744 + 76.3539i −0.478227 + 0.658224i
\(117\) 155.474 + 86.8776i 1.32884 + 0.742543i
\(118\) 10.4695 0.0887247
\(119\) −117.502 + 38.1787i −0.987411 + 0.320829i
\(120\) −21.4494 36.6050i −0.178745 0.305041i
\(121\) −2.94264 + 9.05652i −0.0243194 + 0.0748473i
\(122\) −11.2479 3.65466i −0.0921958 0.0299562i
\(123\) 53.0816 + 33.9445i 0.431558 + 0.275972i
\(124\) 80.2379 0.647080
\(125\) 111.474 56.5565i 0.891789 0.452452i
\(126\) −70.6572 76.2923i −0.560772 0.605495i
\(127\) −0.932755 + 0.677686i −0.00734453 + 0.00533611i −0.591451 0.806341i \(-0.701445\pi\)
0.584107 + 0.811677i \(0.301445\pi\)
\(128\) 10.7600 + 3.49613i 0.0840623 + 0.0273135i
\(129\) −3.94554 66.3725i −0.0305856 0.514515i
\(130\) −21.8103 138.219i −0.167771 1.06322i
\(131\) −104.160 + 33.8437i −0.795116 + 0.258349i −0.678281 0.734802i \(-0.737275\pi\)
−0.116835 + 0.993151i \(0.537275\pi\)
\(132\) −25.0137 63.8211i −0.189498 0.483493i
\(133\) −35.8961 110.477i −0.269896 0.830654i
\(134\) 108.640 149.530i 0.810747 1.11590i
\(135\) −44.3368 127.512i −0.328421 0.944532i
\(136\) 34.6040 25.1413i 0.254441 0.184862i
\(137\) −45.0126 + 61.9546i −0.328559 + 0.452223i −0.941056 0.338250i \(-0.890165\pi\)
0.612497 + 0.790473i \(0.290165\pi\)
\(138\) 8.80234 + 2.29251i 0.0637851 + 0.0166124i
\(139\) 160.437 116.564i 1.15422 0.838593i 0.165188 0.986262i \(-0.447177\pi\)
0.989037 + 0.147669i \(0.0471770\pi\)
\(140\) −12.8269 + 80.6854i −0.0916207 + 0.576324i
\(141\) −27.8341 + 106.872i −0.197405 + 0.757956i
\(142\) 24.5566 + 75.5776i 0.172934 + 0.532237i
\(143\) 226.082i 1.58100i
\(144\) 31.4264 + 17.5608i 0.218239 + 0.121950i
\(145\) 233.020 + 37.0443i 1.60704 + 0.255478i
\(146\) −131.569 42.7495i −0.901161 0.292805i
\(147\) 3.15930 + 53.1462i 0.0214918 + 0.361539i
\(148\) −84.5050 + 61.3965i −0.570980 + 0.414841i
\(149\) 85.8938i 0.576468i 0.957560 + 0.288234i \(0.0930682\pi\)
−0.957560 + 0.288234i \(0.906932\pi\)
\(150\) −57.2450 + 89.2917i −0.381633 + 0.595278i
\(151\) 209.411 1.38683 0.693414 0.720540i \(-0.256106\pi\)
0.693414 + 0.720540i \(0.256106\pi\)
\(152\) 23.6382 + 32.5352i 0.155514 + 0.214047i
\(153\) 123.547 57.0970i 0.807496 0.373183i
\(154\) −40.7901 + 125.539i −0.264871 + 0.815189i
\(155\) −90.9653 178.784i −0.586873 1.15344i
\(156\) 75.3672 + 91.7471i 0.483123 + 0.588123i
\(157\) −246.358 −1.56916 −0.784579 0.620029i \(-0.787121\pi\)
−0.784579 + 0.620029i \(0.787121\pi\)
\(158\) 28.9136 9.39459i 0.182997 0.0594595i
\(159\) 56.2270 215.889i 0.353629 1.35779i
\(160\) −4.40856 27.9386i −0.0275535 0.174616i
\(161\) −10.2955 14.1705i −0.0639471 0.0880156i
\(162\) 87.2454 + 74.2310i 0.538552 + 0.458216i
\(163\) −10.7251 7.79226i −0.0657984 0.0478053i 0.554400 0.832250i \(-0.312948\pi\)
−0.620198 + 0.784445i \(0.712948\pi\)
\(164\) 24.6897 + 33.9825i 0.150547 + 0.207210i
\(165\) −113.846 + 128.088i −0.689977 + 0.776293i
\(166\) 89.6347 + 65.1234i 0.539968 + 0.392310i
\(167\) −36.7045 + 11.9260i −0.219787 + 0.0714132i −0.416841 0.908980i \(-0.636863\pi\)
0.197053 + 0.980393i \(0.436863\pi\)
\(168\) −25.2968 64.5433i −0.150576 0.384186i
\(169\) 68.7885 + 211.709i 0.407033 + 1.25272i
\(170\) −95.2494 48.6010i −0.560291 0.285888i
\(171\) 53.6834 + 116.161i 0.313938 + 0.679302i
\(172\) 13.6976 42.1569i 0.0796373 0.245098i
\(173\) −169.211 232.898i −0.978096 1.34623i −0.937849 0.347044i \(-0.887185\pi\)
−0.0402475 0.999190i \(-0.512815\pi\)
\(174\) −186.402 + 73.0574i −1.07127 + 0.419870i
\(175\) 194.323 62.8921i 1.11041 0.359384i
\(176\) 45.6986i 0.259651i
\(177\) 18.7106 + 11.9650i 0.105710 + 0.0675990i
\(178\) 23.7310 73.0366i 0.133320 0.410318i
\(179\) −164.926 53.5877i −0.921375 0.299373i −0.190344 0.981717i \(-0.560960\pi\)
−0.731031 + 0.682345i \(0.760960\pi\)
\(180\) 3.50045 89.9319i 0.0194470 0.499622i
\(181\) −20.0567 61.7281i −0.110810 0.341039i 0.880240 0.474529i \(-0.157382\pi\)
−0.991050 + 0.133490i \(0.957382\pi\)
\(182\) 228.641i 1.25627i
\(183\) −15.9250 19.3860i −0.0870217 0.105934i
\(184\) 4.90587 + 3.56432i 0.0266623 + 0.0193713i
\(185\) 232.605 + 118.687i 1.25732 + 0.641549i
\(186\) 143.397 + 91.6994i 0.770953 + 0.493008i
\(187\) −139.773 101.551i −0.747451 0.543055i
\(188\) −43.2755 + 59.5636i −0.230189 + 0.316828i
\(189\) −39.0849 217.096i −0.206798 1.14866i
\(190\) 45.6954 89.5549i 0.240502 0.471341i
\(191\) 36.9984 50.9239i 0.193709 0.266618i −0.701104 0.713059i \(-0.747309\pi\)
0.894813 + 0.446442i \(0.147309\pi\)
\(192\) 15.2342 + 18.5451i 0.0793446 + 0.0965890i
\(193\) 13.0256 0.0674899 0.0337450 0.999430i \(-0.489257\pi\)
0.0337450 + 0.999430i \(0.489257\pi\)
\(194\) −45.7944 + 14.8795i −0.236054 + 0.0766985i
\(195\) 118.985 271.944i 0.610178 1.39459i
\(196\) −10.9680 + 33.7562i −0.0559594 + 0.172225i
\(197\) −167.244 54.3408i −0.848954 0.275842i −0.147946 0.988995i \(-0.547266\pi\)
−0.701008 + 0.713154i \(0.747266\pi\)
\(198\) 28.2342 142.645i 0.142597 0.720427i
\(199\) −296.281 −1.48885 −0.744423 0.667708i \(-0.767276\pi\)
−0.744423 + 0.667708i \(0.767276\pi\)
\(200\) −57.2539 + 41.4968i −0.286270 + 0.207484i
\(201\) 365.046 143.074i 1.81615 0.711813i
\(202\) −19.3478 + 14.0570i −0.0957809 + 0.0695889i
\(203\) 366.661 + 119.135i 1.80621 + 0.586874i
\(204\) 90.5751 5.38428i 0.443996 0.0263935i
\(205\) 47.7281 93.5387i 0.232820 0.456286i
\(206\) −192.401 + 62.5150i −0.933988 + 0.303471i
\(207\) 13.1111 + 14.1568i 0.0633388 + 0.0683902i
\(208\) 24.4605 + 75.2818i 0.117599 + 0.361932i
\(209\) 95.4800 131.417i 0.456842 0.628789i
\(210\) −115.134 + 129.538i −0.548259 + 0.616847i
\(211\) 113.481 82.4489i 0.537826 0.390753i −0.285451 0.958393i \(-0.592143\pi\)
0.823277 + 0.567640i \(0.192143\pi\)
\(212\) 87.4198 120.323i 0.412358 0.567562i
\(213\) −42.4870 + 163.133i −0.199469 + 0.765882i
\(214\) −97.6352 + 70.9362i −0.456239 + 0.331477i
\(215\) −109.462 + 17.2725i −0.509124 + 0.0803371i
\(216\) 36.0945 + 67.2992i 0.167104 + 0.311571i
\(217\) −101.285 311.724i −0.466753 1.43652i
\(218\) 20.5240i 0.0941469i
\(219\) −186.278 226.763i −0.850587 1.03545i
\(220\) −101.824 + 51.8082i −0.462837 + 0.235492i
\(221\) 284.612 + 92.4762i 1.28784 + 0.418444i
\(222\) −221.190 + 13.1487i −0.996351 + 0.0592285i
\(223\) 184.655 134.160i 0.828051 0.601614i −0.0909562 0.995855i \(-0.528992\pi\)
0.919007 + 0.394241i \(0.128992\pi\)
\(224\) 46.2157i 0.206320i
\(225\) −204.352 + 94.1557i −0.908231 + 0.418470i
\(226\) −273.226 −1.20897
\(227\) −56.8890 78.3009i −0.250612 0.344938i 0.665113 0.746742i \(-0.268383\pi\)
−0.915726 + 0.401804i \(0.868383\pi\)
\(228\) 5.06238 + 85.1601i 0.0222034 + 0.373509i
\(229\) −100.673 + 309.839i −0.439619 + 1.35301i 0.448659 + 0.893703i \(0.351902\pi\)
−0.888278 + 0.459306i \(0.848098\pi\)
\(230\) 2.38015 14.9720i 0.0103485 0.0650954i
\(231\) −216.370 + 177.741i −0.936665 + 0.769439i
\(232\) −133.472 −0.575309
\(233\) −156.948 + 50.9955i −0.673596 + 0.218865i −0.625790 0.779992i \(-0.715223\pi\)
−0.0478067 + 0.998857i \(0.515223\pi\)
\(234\) 29.8399 + 250.099i 0.127521 + 1.06880i
\(235\) 181.779 + 28.8982i 0.773527 + 0.122971i
\(236\) 8.70283 + 11.9784i 0.0368764 + 0.0507560i
\(237\) 62.4095 + 16.2542i 0.263331 + 0.0685830i
\(238\) −141.355 102.700i −0.593929 0.431514i
\(239\) 187.217 + 257.682i 0.783334 + 1.07817i 0.994906 + 0.100805i \(0.0321417\pi\)
−0.211572 + 0.977362i \(0.567858\pi\)
\(240\) 24.0507 54.9688i 0.100211 0.229037i
\(241\) 242.269 + 176.019i 1.00527 + 0.730369i 0.963211 0.268747i \(-0.0866095\pi\)
0.0420552 + 0.999115i \(0.486609\pi\)
\(242\) −12.8079 + 4.16152i −0.0529250 + 0.0171964i
\(243\) 71.0863 + 232.370i 0.292536 + 0.956254i
\(244\) −5.16847 15.9069i −0.0211823 0.0651923i
\(245\) 87.6488 13.8305i 0.357750 0.0564511i
\(246\) 5.28758 + 88.9484i 0.0214942 + 0.361579i
\(247\) −86.9474 + 267.597i −0.352014 + 1.08339i
\(248\) 66.6981 + 91.8021i 0.268944 + 0.370170i
\(249\) 85.7648 + 218.824i 0.344437 + 0.878810i
\(250\) 157.370 + 80.5267i 0.629482 + 0.322107i
\(251\) 299.580i 1.19355i 0.802410 + 0.596774i \(0.203551\pi\)
−0.802410 + 0.596774i \(0.796449\pi\)
\(252\) 28.5537 144.259i 0.113308 0.572456i
\(253\) 7.56900 23.2950i 0.0299170 0.0920750i
\(254\) −1.55071 0.503857i −0.00610517 0.00198369i
\(255\) −114.682 195.713i −0.449732 0.767500i
\(256\) 4.94427 + 15.2169i 0.0193136 + 0.0594410i
\(257\) 59.2537i 0.230559i 0.993333 + 0.115280i \(0.0367764\pi\)
−0.993333 + 0.115280i \(0.963224\pi\)
\(258\) 72.6585 59.6865i 0.281622 0.231343i
\(259\) 345.197 + 250.801i 1.33281 + 0.968342i
\(260\) 140.010 139.849i 0.538499 0.537880i
\(261\) −416.621 82.4634i −1.59625 0.315952i
\(262\) −125.305 91.0394i −0.478263 0.347479i
\(263\) −274.001 + 377.130i −1.04183 + 1.43396i −0.146147 + 0.989263i \(0.546687\pi\)
−0.895683 + 0.444693i \(0.853313\pi\)
\(264\) 52.2264 81.6703i 0.197827 0.309357i
\(265\) −367.208 58.3765i −1.38569 0.220289i
\(266\) 96.5604 132.904i 0.363009 0.499639i
\(267\) 125.880 103.407i 0.471462 0.387290i
\(268\) 261.388 0.975330
\(269\) −377.993 + 122.817i −1.40518 + 0.456570i −0.910862 0.412712i \(-0.864582\pi\)
−0.494316 + 0.869282i \(0.664582\pi\)
\(270\) 109.034 156.721i 0.403830 0.580450i
\(271\) 13.1622 40.5090i 0.0485689 0.149480i −0.923831 0.382801i \(-0.874959\pi\)
0.972400 + 0.233321i \(0.0749594\pi\)
\(272\) 57.5294 + 18.6924i 0.211505 + 0.0687222i
\(273\) 261.301 408.615i 0.957145 1.49676i
\(274\) −108.301 −0.395258
\(275\) 230.875 + 168.147i 0.839546 + 0.611443i
\(276\) 4.69406 + 11.9766i 0.0170075 + 0.0433936i
\(277\) −284.186 + 206.473i −1.02594 + 0.745391i −0.967493 0.252900i \(-0.918616\pi\)
−0.0584498 + 0.998290i \(0.518616\pi\)
\(278\) 266.728 + 86.6652i 0.959454 + 0.311745i
\(279\) 151.474 + 327.761i 0.542919 + 1.17477i
\(280\) −102.976 + 52.3945i −0.367773 + 0.187123i
\(281\) 451.488 146.697i 1.60672 0.522055i 0.637962 0.770068i \(-0.279778\pi\)
0.968757 + 0.248013i \(0.0797776\pi\)
\(282\) −145.412 + 56.9920i −0.515644 + 0.202099i
\(283\) 32.6173 + 100.386i 0.115256 + 0.354720i 0.992000 0.126236i \(-0.0402897\pi\)
−0.876745 + 0.480956i \(0.840290\pi\)
\(284\) −66.0572 + 90.9200i −0.232596 + 0.320141i
\(285\) 184.012 107.825i 0.645655 0.378334i
\(286\) 258.666 187.932i 0.904426 0.657104i
\(287\) 100.856 138.816i 0.351414 0.483680i
\(288\) 6.03162 + 50.5531i 0.0209431 + 0.175532i
\(289\) −48.7916 + 35.4492i −0.168829 + 0.122662i
\(290\) 151.316 + 297.397i 0.521779 + 1.02551i
\(291\) −98.8464 25.7439i −0.339678 0.0884671i
\(292\) −60.4569 186.067i −0.207044 0.637217i
\(293\) 304.284i 1.03851i −0.854619 0.519256i \(-0.826209\pi\)
0.854619 0.519256i \(-0.173791\pi\)
\(294\) −58.1796 + 47.7926i −0.197890 + 0.162560i
\(295\) 16.8236 32.9712i 0.0570291 0.111767i
\(296\) −140.490 45.6481i −0.474629 0.154216i
\(297\) 213.479 222.660i 0.718786 0.749698i
\(298\) −98.2730 + 71.3995i −0.329775 + 0.239596i
\(299\) 42.4265i 0.141895i
\(300\) −149.746 + 8.72881i −0.499153 + 0.0290960i
\(301\) −181.070 −0.601563
\(302\) 174.074 + 239.592i 0.576403 + 0.793350i
\(303\) −50.6423 + 3.01045i −0.167136 + 0.00993549i
\(304\) −17.5749 + 54.0900i −0.0578122 + 0.177928i
\(305\) −29.5838 + 29.5498i −0.0969962 + 0.0968846i
\(306\) 168.025 + 93.8907i 0.549101 + 0.306832i
\(307\) 254.233 0.828120 0.414060 0.910250i \(-0.364110\pi\)
0.414060 + 0.910250i \(0.364110\pi\)
\(308\) −177.539 + 57.6859i −0.576426 + 0.187292i
\(309\) −415.295 108.161i −1.34400 0.350036i
\(310\) 128.935 252.690i 0.415920 0.815129i
\(311\) −8.14763 11.2142i −0.0261982 0.0360587i 0.795717 0.605669i \(-0.207094\pi\)
−0.821915 + 0.569610i \(0.807094\pi\)
\(312\) −42.3207 + 162.495i −0.135643 + 0.520816i
\(313\) −88.0914 64.0022i −0.281442 0.204480i 0.438104 0.898924i \(-0.355650\pi\)
−0.719546 + 0.694445i \(0.755650\pi\)
\(314\) −204.786 281.864i −0.652184 0.897655i
\(315\) −353.804 + 99.9230i −1.12319 + 0.317216i
\(316\) 34.7831 + 25.2714i 0.110073 + 0.0799728i
\(317\) 31.5232 10.2425i 0.0994421 0.0323107i −0.258873 0.965911i \(-0.583351\pi\)
0.358315 + 0.933601i \(0.383351\pi\)
\(318\) 293.743 115.128i 0.923720 0.362039i
\(319\) 166.598 + 512.735i 0.522250 + 1.60732i
\(320\) 28.3005 28.2680i 0.0884392 0.0883375i
\(321\) −255.558 + 15.1918i −0.796130 + 0.0473263i
\(322\) 7.65465 23.5586i 0.0237722 0.0731633i
\(323\) 126.384 + 173.953i 0.391283 + 0.538554i
\(324\) −12.4063 + 161.524i −0.0382909 + 0.498532i
\(325\) −470.335 153.420i −1.44718 0.472061i
\(326\) 18.7482i 0.0575099i
\(327\) −23.4558 + 36.6795i −0.0717302 + 0.112170i
\(328\) −18.3567 + 56.4962i −0.0559656 + 0.172244i
\(329\) 286.032 + 92.9374i 0.869397 + 0.282484i
\(330\) −241.184 23.7800i −0.730860 0.0720606i
\(331\) −7.95277 24.4761i −0.0240265 0.0739460i 0.938324 0.345756i \(-0.112378\pi\)
−0.962351 + 0.271810i \(0.912378\pi\)
\(332\) 156.687i 0.471949i
\(333\) −410.327 229.287i −1.23221 0.688549i
\(334\) −44.1556 32.0809i −0.132202 0.0960506i
\(335\) −296.335 582.418i −0.884581 1.73856i
\(336\) 52.8174 82.5945i 0.157195 0.245817i
\(337\) 203.661 + 147.968i 0.604335 + 0.439075i 0.847415 0.530931i \(-0.178158\pi\)
−0.243080 + 0.970006i \(0.578158\pi\)
\(338\) −185.041 + 254.687i −0.547458 + 0.753511i
\(339\) −488.297 312.255i −1.44040 0.921106i
\(340\) −23.5709 149.377i −0.0693261 0.439344i
\(341\) 269.408 370.809i 0.790054 1.08742i
\(342\) −88.2774 + 157.979i −0.258121 + 0.461928i
\(343\) −255.335 −0.744418
\(344\) 59.6189 19.3714i 0.173311 0.0563121i
\(345\) 21.3643 24.0370i 0.0619255 0.0696724i
\(346\) 125.807 387.196i 0.363605 1.11906i
\(347\) −47.2702 15.3590i −0.136225 0.0442623i 0.240111 0.970745i \(-0.422816\pi\)
−0.376336 + 0.926483i \(0.622816\pi\)
\(348\) −238.534 152.537i −0.685442 0.438325i
\(349\) −53.4503 −0.153153 −0.0765764 0.997064i \(-0.524399\pi\)
−0.0765764 + 0.997064i \(0.524399\pi\)
\(350\) 233.488 + 170.050i 0.667108 + 0.485856i
\(351\) −232.496 + 481.067i −0.662381 + 1.37056i
\(352\) 52.2848 37.9871i 0.148536 0.107918i
\(353\) 616.363 + 200.268i 1.74607 + 0.567332i 0.995611 0.0935856i \(-0.0298329\pi\)
0.750458 + 0.660918i \(0.229833\pi\)
\(354\) 1.86381 + 31.3532i 0.00526499 + 0.0885684i
\(355\) 277.474 + 44.1112i 0.781616 + 0.124257i
\(356\) 103.289 33.5607i 0.290139 0.0942717i
\(357\) −135.252 345.088i −0.378858 0.966633i
\(358\) −75.7845 233.241i −0.211689 0.651510i
\(359\) 271.831 374.144i 0.757190 1.04218i −0.240252 0.970710i \(-0.577230\pi\)
0.997443 0.0714725i \(-0.0227698\pi\)
\(360\) 105.803 70.7513i 0.293897 0.196531i
\(361\) 128.502 93.3621i 0.355961 0.258621i
\(362\) 53.9524 74.2591i 0.149040 0.205136i
\(363\) −27.6455 7.20011i −0.0761585 0.0198350i
\(364\) 261.593 190.058i 0.718662 0.522139i
\(365\) −346.050 + 345.652i −0.948081 + 0.946991i
\(366\) 8.94229 34.3348i 0.0244325 0.0938110i
\(367\) −85.5299 263.234i −0.233052 0.717259i −0.997374 0.0724246i \(-0.976926\pi\)
0.764322 0.644834i \(-0.223074\pi\)
\(368\) 8.57577i 0.0233037i
\(369\) −92.2044 + 165.007i −0.249876 + 0.447173i
\(370\) 57.5615 + 364.787i 0.155572 + 0.985911i
\(371\) −577.806 187.741i −1.55743 0.506040i
\(372\) 14.2841 + 240.290i 0.0383982 + 0.645940i
\(373\) 109.956 79.8879i 0.294789 0.214177i −0.430553 0.902565i \(-0.641682\pi\)
0.725342 + 0.688388i \(0.241682\pi\)
\(374\) 244.333i 0.653296i
\(375\) 189.215 + 323.763i 0.504574 + 0.863368i
\(376\) −104.121 −0.276917
\(377\) −548.891 755.484i −1.45594 2.00394i
\(378\) 215.895 225.180i 0.571151 0.595714i
\(379\) 53.8748 165.809i 0.142150 0.437492i −0.854484 0.519478i \(-0.826126\pi\)
0.996633 + 0.0819862i \(0.0261263\pi\)
\(380\) 140.446 22.1617i 0.369595 0.0583202i
\(381\) −2.19553 2.67269i −0.00576254 0.00701494i
\(382\) 89.0183 0.233032
\(383\) 609.024 197.884i 1.59014 0.516668i 0.625497 0.780227i \(-0.284896\pi\)
0.964643 + 0.263559i \(0.0848962\pi\)
\(384\) −8.55439 + 32.8454i −0.0222771 + 0.0855350i
\(385\) 329.809 + 330.189i 0.856647 + 0.857633i
\(386\) 10.8275 + 14.9028i 0.0280506 + 0.0386084i
\(387\) 198.064 23.6315i 0.511794 0.0610634i
\(388\) −55.0907 40.0258i −0.141986 0.103159i
\(389\) −145.995 200.945i −0.375308 0.516567i 0.579026 0.815309i \(-0.303433\pi\)
−0.954334 + 0.298742i \(0.903433\pi\)
\(390\) 410.044 89.9215i 1.05139 0.230568i
\(391\) 26.2298 + 19.0570i 0.0670838 + 0.0487393i
\(392\) −47.7384 + 15.5112i −0.121782 + 0.0395693i
\(393\) −119.895 305.905i −0.305076 0.778385i
\(394\) −76.8495 236.519i −0.195050 0.600301i
\(395\) 16.8755 106.153i 0.0427229 0.268741i
\(396\) 186.673 86.2705i 0.471396 0.217855i
\(397\) 93.2252 286.918i 0.234824 0.722714i −0.762321 0.647200i \(-0.775940\pi\)
0.997145 0.0755146i \(-0.0240600\pi\)
\(398\) −246.284 338.981i −0.618805 0.851712i
\(399\) 324.457 127.166i 0.813174 0.318712i
\(400\) −95.0700 31.0111i −0.237675 0.0775278i
\(401\) 380.590i 0.949103i 0.880228 + 0.474551i \(0.157390\pi\)
−0.880228 + 0.474551i \(0.842610\pi\)
\(402\) 467.141 + 298.726i 1.16204 + 0.743100i
\(403\) −245.333 + 755.057i −0.608767 + 1.87359i
\(404\) −32.1658 10.4513i −0.0796183 0.0258695i
\(405\) 373.968 155.476i 0.923378 0.383891i
\(406\) 168.483 + 518.537i 0.414983 + 1.27719i
\(407\) 596.675i 1.46603i
\(408\) 81.4512 + 99.1534i 0.199635 + 0.243023i
\(409\) −308.301 223.994i −0.753791 0.547661i 0.143208 0.989693i \(-0.454258\pi\)
−0.897000 + 0.442031i \(0.854258\pi\)
\(410\) 146.694 23.1475i 0.357790 0.0564574i
\(411\) −193.549 123.771i −0.470923 0.301145i
\(412\) −231.459 168.165i −0.561794 0.408168i
\(413\) 35.5505 48.9310i 0.0860786 0.118477i
\(414\) −5.29841 + 26.7686i −0.0127981 + 0.0646585i
\(415\) 349.125 177.635i 0.841266 0.428037i
\(416\) −65.7987 + 90.5642i −0.158170 + 0.217702i
\(417\) 377.639 + 459.712i 0.905608 + 1.10243i
\(418\) 229.725 0.549582
\(419\) 92.3572 30.0087i 0.220423 0.0716198i −0.196724 0.980459i \(-0.563030\pi\)
0.417147 + 0.908839i \(0.363030\pi\)
\(420\) −243.913 24.0491i −0.580746 0.0572598i
\(421\) −77.2950 + 237.890i −0.183599 + 0.565059i −0.999921 0.0125374i \(-0.996009\pi\)
0.816323 + 0.577596i \(0.196009\pi\)
\(422\) 188.663 + 61.3004i 0.447070 + 0.145262i
\(423\) −325.006 64.3296i −0.768335 0.152079i
\(424\) 210.332 0.496067
\(425\) −306.115 + 221.868i −0.720270 + 0.522041i
\(426\) −221.962 + 86.9946i −0.521037 + 0.204213i
\(427\) −55.2741 + 40.1590i −0.129448 + 0.0940492i
\(428\) −162.319 52.7408i −0.379251 0.123226i
\(429\) 677.052 40.2477i 1.57821 0.0938174i
\(430\) −110.752 110.880i −0.257563 0.257860i
\(431\) −135.416 + 43.9993i −0.314190 + 0.102087i −0.461867 0.886949i \(-0.652820\pi\)
0.147677 + 0.989036i \(0.452820\pi\)
\(432\) −46.9949 + 97.2393i −0.108785 + 0.225091i
\(433\) 97.0856 + 298.799i 0.224216 + 0.690066i 0.998370 + 0.0570692i \(0.0181756\pi\)
−0.774154 + 0.632997i \(0.781824\pi\)
\(434\) 272.457 375.005i 0.627781 0.864067i
\(435\) −69.4541 + 704.424i −0.159665 + 1.61937i
\(436\) −23.4820 + 17.0607i −0.0538578 + 0.0391300i
\(437\) −17.9177 + 24.6616i −0.0410016 + 0.0564339i
\(438\) 104.600 401.623i 0.238813 0.916948i
\(439\) 150.083 109.042i 0.341875 0.248387i −0.403577 0.914946i \(-0.632233\pi\)
0.745453 + 0.666559i \(0.232233\pi\)
\(440\) −143.917 73.4336i −0.327084 0.166894i
\(441\) −158.595 + 18.9224i −0.359626 + 0.0429079i
\(442\) 130.781 + 402.503i 0.295885 + 0.910640i
\(443\) 495.077i 1.11755i −0.829318 0.558777i \(-0.811271\pi\)
0.829318 0.558777i \(-0.188729\pi\)
\(444\) −198.909 242.138i −0.447993 0.545357i
\(445\) −191.878 192.098i −0.431186 0.431682i
\(446\) 306.991 + 99.7474i 0.688321 + 0.223649i
\(447\) −257.227 + 15.2910i −0.575453 + 0.0342080i
\(448\) 52.8765 38.4170i 0.118028 0.0857522i
\(449\) 844.252i 1.88029i 0.340770 + 0.940147i \(0.389312\pi\)
−0.340770 + 0.940147i \(0.610688\pi\)
\(450\) −277.594 155.536i −0.616876 0.345636i
\(451\) 239.944 0.532027
\(452\) −227.120 312.604i −0.502479 0.691603i
\(453\) 37.2798 + 627.126i 0.0822953 + 1.38438i
\(454\) 42.2967 130.176i 0.0931646 0.286731i
\(455\) −720.049 367.405i −1.58253 0.807484i
\(456\) −93.2254 + 76.5816i −0.204442 + 0.167942i
\(457\) 537.204 1.17550 0.587751 0.809042i \(-0.300013\pi\)
0.587751 + 0.809042i \(0.300013\pi\)
\(458\) −438.178 + 142.373i −0.956722 + 0.310858i
\(459\) 192.983 + 359.823i 0.420443 + 0.783928i
\(460\) 19.1083 9.72231i 0.0415397 0.0211354i
\(461\) 262.691 + 361.563i 0.569829 + 0.784302i 0.992534 0.121965i \(-0.0389195\pi\)
−0.422706 + 0.906267i \(0.638920\pi\)
\(462\) −383.215 99.8060i −0.829470 0.216030i
\(463\) 275.587 + 200.226i 0.595221 + 0.432453i 0.844179 0.536061i \(-0.180088\pi\)
−0.248958 + 0.968514i \(0.580088\pi\)
\(464\) −110.949 152.708i −0.239114 0.329112i
\(465\) 519.212 304.242i 1.11658 0.654285i
\(466\) −188.809 137.178i −0.405169 0.294372i
\(467\) −518.469 + 168.461i −1.11021 + 0.360729i −0.806024 0.591883i \(-0.798385\pi\)
−0.304187 + 0.952612i \(0.598385\pi\)
\(468\) −261.339 + 242.036i −0.558417 + 0.517172i
\(469\) −329.954 1015.49i −0.703527 2.16523i
\(470\) 118.041 + 231.999i 0.251152 + 0.493615i
\(471\) −43.8571 737.771i −0.0931150 1.56639i
\(472\) −6.47052 + 19.9142i −0.0137087 + 0.0421911i
\(473\) −148.831 204.849i −0.314654 0.433084i
\(474\) 33.2814 + 84.9155i 0.0702139 + 0.179147i
\(475\) −208.603 287.813i −0.439164 0.605923i
\(476\) 247.098i 0.519113i
\(477\) 656.536 + 129.951i 1.37639 + 0.272434i
\(478\) −139.195 + 428.398i −0.291203 + 0.896231i
\(479\) 435.593 + 141.533i 0.909379 + 0.295475i 0.726103 0.687586i \(-0.241330\pi\)
0.183276 + 0.983061i \(0.441330\pi\)
\(480\) 82.8832 18.1761i 0.172673 0.0378668i
\(481\) −319.375 982.935i −0.663981 2.04352i
\(482\) 423.502i 0.878635i
\(483\) 40.6038 33.3547i 0.0840658 0.0690573i
\(484\) −15.4079 11.1945i −0.0318345 0.0231291i
\(485\) −26.7281 + 168.128i −0.0551095 + 0.346657i
\(486\) −206.769 + 274.490i −0.425450 + 0.564794i
\(487\) 202.292 + 146.974i 0.415385 + 0.301795i 0.775778 0.631006i \(-0.217358\pi\)
−0.360393 + 0.932800i \(0.617358\pi\)
\(488\) 13.9032 19.1360i 0.0284901 0.0392132i
\(489\) 21.4263 33.5059i 0.0438165 0.0685192i
\(490\) 88.6823 + 88.7843i 0.180984 + 0.181193i
\(491\) −208.550 + 287.044i −0.424745 + 0.584611i −0.966737 0.255773i \(-0.917670\pi\)
0.541992 + 0.840383i \(0.317670\pi\)
\(492\) −97.3725 + 79.9883i −0.197912 + 0.162578i
\(493\) −713.621 −1.44751
\(494\) −378.439 + 122.962i −0.766071 + 0.248911i
\(495\) −403.855 318.134i −0.815869 0.642695i
\(496\) −49.5898 + 152.622i −0.0999794 + 0.307705i
\(497\) 436.609 + 141.863i 0.878489 + 0.285438i
\(498\) −179.069 + 280.024i −0.359576 + 0.562296i
\(499\) −65.2143 −0.130690 −0.0653450 0.997863i \(-0.520815\pi\)
−0.0653450 + 0.997863i \(0.520815\pi\)
\(500\) 38.6824 + 246.989i 0.0773648 + 0.493978i
\(501\) −42.2492 107.796i −0.0843297 0.215162i
\(502\) −342.757 + 249.027i −0.682782 + 0.496070i
\(503\) 256.839 + 83.4520i 0.510614 + 0.165908i 0.552981 0.833194i \(-0.313490\pi\)
−0.0423676 + 0.999102i \(0.513490\pi\)
\(504\) 188.785 87.2468i 0.374574 0.173109i
\(505\) 13.1789 + 83.5194i 0.0260969 + 0.165385i
\(506\) 32.9441 10.7042i 0.0651069 0.0211545i
\(507\) −621.763 + 243.691i −1.22636 + 0.480653i
\(508\) −0.712562 2.19304i −0.00140268 0.00431701i
\(509\) 254.598 350.425i 0.500194 0.688457i −0.482034 0.876153i \(-0.660102\pi\)
0.982227 + 0.187695i \(0.0601018\pi\)
\(510\) 128.590 293.897i 0.252137 0.576268i
\(511\) −646.556 + 469.751i −1.26528 + 0.919277i
\(512\) −13.3001 + 18.3060i −0.0259767 + 0.0357538i
\(513\) −338.311 + 181.446i −0.659475 + 0.353695i
\(514\) −67.7935 + 49.2549i −0.131894 + 0.0958266i
\(515\) −112.296 + 706.378i −0.218050 + 1.37161i
\(516\) 128.686 + 33.5156i 0.249392 + 0.0649527i
\(517\) 129.963 + 399.984i 0.251378 + 0.773663i
\(518\) 603.427i 1.16492i
\(519\) 667.341 548.198i 1.28582 1.05626i
\(520\) 276.388 + 43.9386i 0.531515 + 0.0844972i
\(521\) −304.188 98.8367i −0.583854 0.189706i 0.00217230 0.999998i \(-0.499309\pi\)
−0.586026 + 0.810292i \(0.699309\pi\)
\(522\) −251.970 545.214i −0.482701 1.04447i
\(523\) 318.145 231.146i 0.608308 0.441962i −0.240510 0.970647i \(-0.577315\pi\)
0.848818 + 0.528685i \(0.177315\pi\)
\(524\) 219.041i 0.418017i
\(525\) 222.938 + 570.744i 0.424643 + 1.08713i
\(526\) −659.248 −1.25332
\(527\) 356.609 + 490.830i 0.676677 + 0.931366i
\(528\) 136.854 8.13536i 0.259194 0.0154079i
\(529\) 162.050 498.737i 0.306332 0.942793i
\(530\) −238.453 468.656i −0.449911 0.884257i
\(531\) −32.5009 + 58.1629i −0.0612070 + 0.109535i
\(532\) 232.325 0.436701
\(533\) −395.274 + 128.432i −0.741601 + 0.240961i
\(534\) 222.948 + 58.0655i 0.417506 + 0.108737i
\(535\) 66.5053 + 421.467i 0.124309 + 0.787788i
\(536\) 217.280 + 299.061i 0.405373 + 0.557949i
\(537\) 131.119 503.446i 0.244170 0.937516i
\(538\) −454.726 330.378i −0.845216 0.614085i
\(539\) 119.173 + 164.028i 0.221100 + 0.304319i
\(540\) 269.943 5.52701i 0.499895 0.0102352i
\(541\) 87.3140 + 63.4374i 0.161394 + 0.117259i 0.665551 0.746353i \(-0.268197\pi\)
−0.504157 + 0.863612i \(0.668197\pi\)
\(542\) 57.2884 18.6141i 0.105698 0.0343434i
\(543\) 181.288 71.0530i 0.333863 0.130853i
\(544\) 26.4351 + 81.3589i 0.0485940 + 0.149557i
\(545\) 64.6355 + 32.9803i 0.118597 + 0.0605143i
\(546\) 684.713 40.7031i 1.25405 0.0745478i
\(547\) −53.3464 + 164.183i −0.0975254 + 0.300152i −0.987904 0.155069i \(-0.950440\pi\)
0.890378 + 0.455222i \(0.150440\pi\)
\(548\) −90.0253 123.909i −0.164280 0.226112i
\(549\) 55.2205 51.1418i 0.100584 0.0931545i
\(550\) −0.464756 + 403.922i −0.000845010 + 0.734404i
\(551\) 670.957i 1.21771i
\(552\) −9.80077 + 15.3262i −0.0177550 + 0.0277648i
\(553\) 54.2722 167.033i 0.0981415 0.302048i
\(554\) −472.461 153.512i −0.852819 0.277098i
\(555\) −314.024 + 717.713i −0.565808 + 1.29318i
\(556\) 122.563 + 377.211i 0.220437 + 0.678436i
\(557\) 909.017i 1.63199i −0.578061 0.815994i \(-0.696190\pi\)
0.578061 0.815994i \(-0.303810\pi\)
\(558\) −249.086 + 445.758i −0.446390 + 0.798850i
\(559\) 354.825 + 257.795i 0.634749 + 0.461172i
\(560\) −145.545 74.2645i −0.259902 0.132615i
\(561\) 279.234 436.659i 0.497744 0.778359i
\(562\) 543.141 + 394.615i 0.966443 + 0.702162i
\(563\) 308.779 424.997i 0.548452 0.754880i −0.441349 0.897336i \(-0.645500\pi\)
0.989801 + 0.142456i \(0.0454999\pi\)
\(564\) −186.080 118.994i −0.329929 0.210982i
\(565\) −439.050 + 860.461i −0.777080 + 1.52294i
\(566\) −87.7404 + 120.764i −0.155018 + 0.213364i
\(567\) 643.182 155.696i 1.13436 0.274596i
\(568\) −158.934 −0.279813
\(569\) −571.702 + 185.757i −1.00475 + 0.326463i −0.764762 0.644313i \(-0.777143\pi\)
−0.239987 + 0.970776i \(0.577143\pi\)
\(570\) 276.326 + 120.902i 0.484782 + 0.212109i
\(571\) 52.1997 160.654i 0.0914180 0.281356i −0.894886 0.446296i \(-0.852743\pi\)
0.986304 + 0.164940i \(0.0527430\pi\)
\(572\) 430.034 + 139.727i 0.751808 + 0.244277i
\(573\) 159.089 + 101.734i 0.277643 + 0.177546i
\(574\) 242.660 0.422752
\(575\) −43.3259 31.5543i −0.0753493 0.0548771i
\(576\) −52.8252 + 48.9234i −0.0917104 + 0.0849365i
\(577\) 444.674 323.074i 0.770665 0.559921i −0.131498 0.991316i \(-0.541979\pi\)
0.902163 + 0.431396i \(0.141979\pi\)
\(578\) −81.1165 26.3563i −0.140340 0.0455992i
\(579\) 2.31884 + 39.0078i 0.00400490 + 0.0673710i
\(580\) −214.477 + 420.337i −0.369788 + 0.724718i
\(581\) 608.730 197.788i 1.04773 0.340427i
\(582\) −52.7123 134.492i −0.0905709 0.231086i
\(583\) −262.535 807.998i −0.450317 1.38593i
\(584\) 162.629 223.839i 0.278474 0.383287i
\(585\) 835.577 + 307.913i 1.42834 + 0.526347i
\(586\) 348.138 252.937i 0.594092 0.431633i
\(587\) −575.392 + 791.960i −0.980225 + 1.34916i −0.0435176 + 0.999053i \(0.513856\pi\)
−0.936708 + 0.350112i \(0.886144\pi\)
\(588\) −103.043 26.8368i −0.175242 0.0456408i
\(589\) −461.486 + 335.289i −0.783507 + 0.569251i
\(590\) 51.7078 8.15922i 0.0876404 0.0138292i
\(591\) 132.962 510.521i 0.224978 0.863826i
\(592\) −64.5561 198.683i −0.109047 0.335614i
\(593\) 116.765i 0.196905i −0.995142 0.0984527i \(-0.968611\pi\)
0.995142 0.0984527i \(-0.0313893\pi\)
\(594\) 432.206 + 59.1594i 0.727620 + 0.0995950i
\(595\) −550.575 + 280.133i −0.925337 + 0.470812i
\(596\) −163.380 53.0853i −0.274127 0.0890693i
\(597\) −52.7445 887.275i −0.0883492 1.48622i
\(598\) −48.5411 + 35.2672i −0.0811724 + 0.0589752i
\(599\) 355.503i 0.593494i 0.954956 + 0.296747i \(0.0959018\pi\)
−0.954956 + 0.296747i \(0.904098\pi\)
\(600\) −134.464 164.072i −0.224106 0.273453i
\(601\) −83.5556 −0.139028 −0.0695138 0.997581i \(-0.522145\pi\)
−0.0695138 + 0.997581i \(0.522145\pi\)
\(602\) −150.515 207.167i −0.250026 0.344131i
\(603\) 493.453 + 1067.74i 0.818330 + 1.77071i
\(604\) −129.423 + 398.323i −0.214277 + 0.659476i
\(605\) −7.47536 + 47.0225i −0.0123560 + 0.0777231i
\(606\) −45.5409 55.4385i −0.0751500 0.0914827i
\(607\) 863.021 1.42178 0.710890 0.703303i \(-0.248292\pi\)
0.710890 + 0.703303i \(0.248292\pi\)
\(608\) −76.4948 + 24.8547i −0.125814 + 0.0408794i
\(609\) −291.503 + 1119.25i −0.478658 + 1.83786i
\(610\) −58.4003 9.28414i −0.0957382 0.0152199i
\(611\) −428.189 589.352i −0.700800 0.964569i
\(612\) 32.2488 + 270.288i 0.0526941 + 0.441647i
\(613\) 118.032 + 85.7549i 0.192547 + 0.139894i 0.679882 0.733321i \(-0.262031\pi\)
−0.487335 + 0.873215i \(0.662031\pi\)
\(614\) 211.332 + 290.874i 0.344189 + 0.473736i
\(615\) 288.618 + 126.280i 0.469298 + 0.205334i
\(616\) −213.580 155.175i −0.346721 0.251907i
\(617\) −265.234 + 86.1796i −0.429876 + 0.139675i −0.515960 0.856613i \(-0.672565\pi\)
0.0860839 + 0.996288i \(0.472565\pi\)
\(618\) −221.466 565.058i −0.358360 0.914333i
\(619\) −283.216 871.650i −0.457539 1.40816i −0.868129 0.496339i \(-0.834677\pi\)
0.410590 0.911820i \(-0.365323\pi\)
\(620\) 396.286 62.5319i 0.639172 0.100858i
\(621\) −40.0614 + 41.7843i −0.0645111 + 0.0672855i
\(622\) 6.05773 18.6438i 0.00973912 0.0299739i
\(623\) −260.767 358.915i −0.418567 0.576108i
\(624\) −221.093 + 86.6541i −0.354316 + 0.138869i
\(625\) 506.480 366.201i 0.810367 0.585922i
\(626\) 153.989i 0.245990i
\(627\) 410.553 + 262.540i 0.654790 + 0.418724i
\(628\) 152.258 468.600i 0.242448 0.746179i
\(629\) −751.147 244.063i −1.19419 0.388017i
\(630\) −408.425 321.734i −0.648294 0.510689i
\(631\) −251.644 774.479i −0.398801 1.22738i −0.925961 0.377618i \(-0.876743\pi\)
0.527160 0.849766i \(-0.323257\pi\)
\(632\) 60.8031i 0.0962074i
\(633\) 267.113 + 325.166i 0.421980 + 0.513690i
\(634\) 37.9224 + 27.5522i 0.0598145 + 0.0434578i
\(635\) −4.07863 + 4.07394i −0.00642305 + 0.00641566i
\(636\) 375.896 + 240.377i 0.591031 + 0.377952i
\(637\) −284.118 206.424i −0.446024 0.324056i
\(638\) −448.147 + 616.821i −0.702425 + 0.966804i
\(639\) −496.100 98.1950i −0.776369 0.153670i
\(640\) 55.8670 + 8.88141i 0.0872922 + 0.0138772i
\(641\) 82.1393 113.055i 0.128142 0.176373i −0.740125 0.672469i \(-0.765234\pi\)
0.868267 + 0.496096i \(0.165234\pi\)
\(642\) −229.815 279.761i −0.357967 0.435765i
\(643\) 731.126 1.13705 0.568527 0.822665i \(-0.307513\pi\)
0.568527 + 0.822665i \(0.307513\pi\)
\(644\) 33.3169 10.8253i 0.0517343 0.0168095i
\(645\) −71.2127 324.731i −0.110407 0.503460i
\(646\) −93.9662 + 289.198i −0.145459 + 0.447675i
\(647\) 298.529 + 96.9980i 0.461405 + 0.149920i 0.530490 0.847691i \(-0.322008\pi\)
−0.0690849 + 0.997611i \(0.522008\pi\)
\(648\) −195.116 + 120.073i −0.301105 + 0.185298i
\(649\) 84.5774 0.130320
\(650\) −215.437 665.652i −0.331441 1.02408i
\(651\) 915.494 358.815i 1.40629 0.551175i
\(652\) 21.4503 15.5845i 0.0328992 0.0239027i
\(653\) −851.933 276.810i −1.30464 0.423905i −0.427449 0.904039i \(-0.640588\pi\)
−0.877195 + 0.480135i \(0.840588\pi\)
\(654\) −61.4636 + 3.65373i −0.0939810 + 0.00558675i
\(655\) −488.061 + 248.326i −0.745131 + 0.379123i
\(656\) −79.8976 + 25.9603i −0.121795 + 0.0395737i
\(657\) 645.929 598.219i 0.983149 0.910532i
\(658\) 131.433 + 404.510i 0.199747 + 0.614757i
\(659\) 141.835 195.218i 0.215227 0.296234i −0.687729 0.725967i \(-0.741392\pi\)
0.902956 + 0.429733i \(0.141392\pi\)
\(660\) −173.278 295.711i −0.262542 0.448047i
\(661\) −747.195 + 542.869i −1.13040 + 0.821284i −0.985753 0.168199i \(-0.946205\pi\)
−0.144648 + 0.989483i \(0.546205\pi\)
\(662\) 21.3929 29.4448i 0.0323156 0.0444786i
\(663\) −226.272 + 868.795i −0.341286 + 1.31040i
\(664\) −179.269 + 130.247i −0.269984 + 0.196155i
\(665\) −263.385 517.659i −0.396068 0.778434i
\(666\) −78.7534 660.059i −0.118248 0.991080i
\(667\) −31.2636 96.2195i −0.0468720 0.144257i
\(668\) 77.1868i 0.115549i
\(669\) 434.643 + 529.107i 0.649691 + 0.790892i
\(670\) 420.028 823.180i 0.626907 1.22863i
\(671\) −90.8655 29.5240i −0.135418 0.0440000i
\(672\) 138.403 8.22742i 0.205957 0.0122432i
\(673\) 490.766 356.562i 0.729221 0.529810i −0.160096 0.987102i \(-0.551180\pi\)
0.889317 + 0.457291i \(0.151180\pi\)
\(674\) 356.012i 0.528208i
\(675\) −318.349 595.214i −0.471627 0.881798i
\(676\) −445.209 −0.658593
\(677\) −684.375 941.961i −1.01089 1.39138i −0.918396 0.395663i \(-0.870515\pi\)
−0.0924975 0.995713i \(-0.529485\pi\)
\(678\) −48.6403 818.235i −0.0717409 1.20684i
\(679\) −85.9584 + 264.553i −0.126596 + 0.389621i
\(680\) 151.312 151.138i 0.222518 0.222262i
\(681\) 224.361 184.305i 0.329459 0.270639i
\(682\) 648.198 0.950437
\(683\) 724.002 235.243i 1.06003 0.344426i 0.273435 0.961891i \(-0.411840\pi\)
0.786598 + 0.617465i \(0.211840\pi\)
\(684\) −254.129 + 30.3207i −0.371533 + 0.0443286i
\(685\) −174.029 + 341.067i −0.254058 + 0.497908i
\(686\) −212.249 292.135i −0.309400 0.425853i
\(687\) −945.801 246.328i −1.37671 0.358556i
\(688\) 71.7216 + 52.1088i 0.104247 + 0.0757396i
\(689\) 864.975 + 1190.54i 1.25541 + 1.72792i
\(690\) 45.2604 + 4.46254i 0.0655948 + 0.00646745i
\(691\) 67.3344 + 48.9213i 0.0974449 + 0.0707979i 0.635441 0.772150i \(-0.280818\pi\)
−0.537996 + 0.842947i \(0.680818\pi\)
\(692\) 547.577 177.919i 0.791296 0.257108i
\(693\) −570.800 616.323i −0.823666 0.889356i
\(694\) −21.7209 66.8502i −0.0312982 0.0963259i
\(695\) 701.540 700.733i 1.00941 1.00825i
\(696\) −23.7609 399.709i −0.0341392 0.574295i
\(697\) −98.1463 + 302.063i −0.140812 + 0.433376i
\(698\) −44.4308 61.1537i −0.0636544 0.0876128i
\(699\) −180.657 460.936i −0.258451 0.659422i
\(700\) −0.470015 + 408.493i −0.000671450 + 0.583561i
\(701\) 367.659i 0.524478i 0.965003 + 0.262239i \(0.0844609\pi\)
−0.965003 + 0.262239i \(0.915539\pi\)
\(702\) −743.662 + 133.885i −1.05935 + 0.190720i
\(703\) 229.471 706.239i 0.326417 1.00461i
\(704\) 86.9239 + 28.2433i 0.123471 + 0.0401183i
\(705\) −54.1810 + 549.520i −0.0768525 + 0.779461i
\(706\) 283.222 + 871.668i 0.401165 + 1.23466i
\(707\) 138.157i 0.195413i
\(708\) −34.3226 + 28.1949i −0.0484783 + 0.0398233i
\(709\) 309.214 + 224.657i 0.436128 + 0.316865i 0.784094 0.620642i \(-0.213128\pi\)
−0.347967 + 0.937507i \(0.613128\pi\)
\(710\) 180.183 + 354.132i 0.253778 + 0.498777i
\(711\) −37.5663 + 189.792i −0.0528358 + 0.266937i
\(712\) 124.257 + 90.2782i 0.174519 + 0.126795i
\(713\) −50.5570 + 69.5858i −0.0709075 + 0.0975958i
\(714\) 282.394 441.601i 0.395510 0.618488i
\(715\) −176.193 1116.60i −0.246424 1.56167i
\(716\) 203.860 280.589i 0.284720 0.391884i
\(717\) −738.355 + 606.534i −1.02978 + 0.845933i
\(718\) 654.027 0.910901
\(719\) −190.863 + 62.0152i −0.265456 + 0.0862520i −0.438721 0.898623i \(-0.644568\pi\)
0.173265 + 0.984875i \(0.444568\pi\)
\(720\) 168.897 + 62.2392i 0.234580 + 0.0864434i
\(721\) −361.147 + 1111.50i −0.500897 + 1.54160i
\(722\) 213.635 + 69.4144i 0.295894 + 0.0961418i
\(723\) −483.997 + 756.862i −0.669428 + 1.04684i
\(724\) 129.810 0.179295
\(725\) 1179.73 + 1.35741i 1.62722 + 0.00187229i
\(726\) −14.7427 37.6150i −0.0203067 0.0518113i
\(727\) −454.130 + 329.945i −0.624664 + 0.453845i −0.854547 0.519373i \(-0.826165\pi\)
0.229884 + 0.973218i \(0.426165\pi\)
\(728\) 434.900 + 141.308i 0.597391 + 0.194104i
\(729\) −683.226 + 254.250i −0.937210 + 0.348765i
\(730\) −683.123 108.599i −0.935785 0.148766i
\(731\) 318.759 103.571i 0.436059 0.141684i
\(732\) 46.7165 18.3099i 0.0638204 0.0250135i
\(733\) 157.971 + 486.184i 0.215513 + 0.663280i 0.999117 + 0.0420193i \(0.0133791\pi\)
−0.783604 + 0.621260i \(0.786621\pi\)
\(734\) 230.075 316.671i 0.313454 0.431432i
\(735\) 57.0219 + 260.021i 0.0775808 + 0.353770i
\(736\) −9.81174 + 7.12864i −0.0133312 + 0.00968566i
\(737\) 877.643 1207.97i 1.19083 1.63904i
\(738\) −265.434 + 31.6695i −0.359666 + 0.0429127i
\(739\) 358.558 260.508i 0.485194 0.352514i −0.318139 0.948044i \(-0.603058\pi\)
0.803333 + 0.595530i \(0.203058\pi\)
\(740\) −369.513 + 369.088i −0.499342 + 0.498768i
\(741\) −816.854 212.745i −1.10237 0.287105i
\(742\) −265.505 817.142i −0.357824 1.10127i
\(743\) 853.716i 1.14901i 0.818500 + 0.574506i \(0.194806\pi\)
−0.818500 + 0.574506i \(0.805194\pi\)
\(744\) −263.047 + 216.084i −0.353558 + 0.290436i
\(745\) 66.9397 + 424.220i 0.0898520 + 0.569423i
\(746\) 182.803 + 59.3963i 0.245044 + 0.0796198i
\(747\) −640.046 + 295.796i −0.856823 + 0.395979i
\(748\) 279.547 203.103i 0.373725 0.271527i
\(749\) 697.186i 0.930823i
\(750\) −213.139 + 485.615i −0.284185 + 0.647487i
\(751\) 595.126 0.792445 0.396222 0.918155i \(-0.370321\pi\)
0.396222 + 0.918155i \(0.370321\pi\)
\(752\) −86.5509 119.127i −0.115094 0.158414i
\(753\) −897.157 + 53.3319i −1.19144 + 0.0708260i
\(754\) 408.098 1256.00i 0.541245 1.66578i
\(755\) 1034.26 163.200i 1.36988 0.216160i
\(756\) 437.097 + 59.8289i 0.578171 + 0.0791387i
\(757\) −109.179 −0.144226 −0.0721129 0.997396i \(-0.522974\pi\)
−0.0721129 + 0.997396i \(0.522974\pi\)
\(758\) 234.490 76.1904i 0.309354 0.100515i
\(759\) 71.1092 + 18.5200i 0.0936881 + 0.0244005i
\(760\) 142.102 + 142.266i 0.186977 + 0.187192i
\(761\) −80.5362 110.849i −0.105829 0.145662i 0.752817 0.658230i \(-0.228694\pi\)
−0.858647 + 0.512568i \(0.828694\pi\)
\(762\) 1.23285 4.73364i 0.00161791 0.00621212i
\(763\) 95.9224 + 69.6917i 0.125717 + 0.0913391i
\(764\) 73.9968 + 101.848i 0.0968545 + 0.133309i
\(765\) 565.687 378.280i 0.739460 0.494483i
\(766\) 732.657 + 532.306i 0.956471 + 0.694917i
\(767\) −139.329 + 45.2708i −0.181655 + 0.0590232i
\(768\) −44.6901 + 17.5156i −0.0581902 + 0.0228068i
\(769\) −404.111 1243.73i −0.525502 1.61733i −0.763322 0.646019i \(-0.776433\pi\)
0.237820 0.971309i \(-0.423567\pi\)
\(770\) −103.621 + 651.813i −0.134573 + 0.846510i
\(771\) −177.448 + 10.5485i −0.230153 + 0.0136815i
\(772\) −8.05023 + 24.7761i −0.0104278 + 0.0320934i
\(773\) 683.328 + 940.521i 0.883995 + 1.21672i 0.975298 + 0.220892i \(0.0708969\pi\)
−0.0913029 + 0.995823i \(0.529103\pi\)
\(774\) 191.679 + 206.966i 0.247647 + 0.267398i
\(775\) −588.599 812.101i −0.759483 1.04787i
\(776\) 96.3022i 0.124101i
\(777\) −689.623 + 1078.41i −0.887546 + 1.38792i
\(778\) 108.547 334.072i 0.139520 0.429398i
\(779\) −284.004 92.2785i −0.364575 0.118458i
\(780\) 443.732 + 394.393i 0.568887 + 0.505632i
\(781\) 198.380 + 610.550i 0.254007 + 0.781754i
\(782\) 45.8513i 0.0586334i
\(783\) 172.787 1262.34i 0.220673 1.61219i
\(784\) −57.4294 41.7249i −0.0732518 0.0532205i
\(785\) −1216.73 + 191.994i −1.54998 + 0.244579i
\(786\) 250.330 391.459i 0.318486 0.498040i
\(787\) −252.611 183.532i −0.320979 0.233205i 0.415614 0.909541i \(-0.363567\pi\)
−0.736593 + 0.676336i \(0.763567\pi\)
\(788\) 206.725 284.532i 0.262341 0.361082i
\(789\) −1178.18 753.418i −1.49325 0.954902i
\(790\) 135.480 68.9321i 0.171493 0.0872559i
\(791\) −927.771 + 1276.97i −1.17291 + 1.61437i
\(792\) 253.877 + 141.864i 0.320551 + 0.179121i
\(793\) 165.491 0.208689
\(794\) 405.763 131.840i 0.511036 0.166046i
\(795\) 109.450 1110.07i 0.137673 1.39632i
\(796\) 183.111 563.559i 0.230040 0.707989i
\(797\) 131.308 + 42.6647i 0.164753 + 0.0535316i 0.390232 0.920716i \(-0.372395\pi\)
−0.225479 + 0.974248i \(0.572395\pi\)
\(798\) 415.199 + 265.511i 0.520300 + 0.332720i
\(799\) −556.695 −0.696739
\(800\) −43.5468 134.550i −0.0544335 0.168187i
\(801\) 332.082 + 358.567i 0.414585 + 0.447649i
\(802\) −435.442 + 316.367i −0.542945 + 0.394473i
\(803\) −1062.88 345.350i −1.32363 0.430074i
\(804\) 46.5329 + 782.784i 0.0578768 + 0.973611i
\(805\) −61.8918 61.9630i −0.0768842 0.0769727i
\(806\) −1067.81 + 346.953i −1.32483 + 0.430463i
\(807\) −435.094 1110.12i −0.539150 1.37561i
\(808\) −14.7804 45.4893i −0.0182925 0.0562986i
\(809\) 85.8547 118.169i 0.106124 0.146068i −0.752651 0.658419i \(-0.771225\pi\)
0.858776 + 0.512351i \(0.171225\pi\)
\(810\) 488.746 + 298.626i 0.603390 + 0.368674i
\(811\) 1036.00 752.698i 1.27743 0.928110i 0.277962 0.960592i \(-0.410341\pi\)
0.999472 + 0.0324815i \(0.0103410\pi\)
\(812\) −453.218 + 623.801i −0.558150 + 0.768228i
\(813\) 123.656 + 32.2054i 0.152098 + 0.0396131i
\(814\) −682.669 + 495.988i −0.838660 + 0.609322i
\(815\) −59.0430 30.1267i −0.0724454 0.0369653i
\(816\) −45.7370 + 175.612i −0.0560503 + 0.215211i
\(817\) 97.3791 + 299.702i 0.119191 + 0.366832i
\(818\) 538.929i 0.658838i
\(819\) 1270.20 + 709.778i 1.55092 + 0.866640i
\(820\) 148.423 + 148.594i 0.181004 + 0.181213i
\(821\) 1289.48 + 418.976i 1.57062 + 0.510324i 0.959618 0.281307i \(-0.0907680\pi\)
0.610999 + 0.791632i \(0.290768\pi\)
\(822\) −19.2799 324.329i −0.0234549 0.394561i
\(823\) −1040.57 + 756.016i −1.26436 + 0.918610i −0.998963 0.0455292i \(-0.985503\pi\)
−0.265396 + 0.964140i \(0.585503\pi\)
\(824\) 404.606i 0.491026i
\(825\) −462.450 + 721.338i −0.560546 + 0.874350i
\(826\) 85.5345 0.103553
\(827\) 711.227 + 978.920i 0.860008 + 1.18370i 0.981567 + 0.191116i \(0.0612106\pi\)
−0.121559 + 0.992584i \(0.538789\pi\)
\(828\) −35.0309 + 16.1895i −0.0423078 + 0.0195525i
\(829\) −376.859 + 1159.85i −0.454595 + 1.39910i 0.417015 + 0.908900i \(0.363076\pi\)
−0.871610 + 0.490200i \(0.836924\pi\)
\(830\) 493.449 + 251.782i 0.594516 + 0.303352i
\(831\) −668.920 814.299i −0.804957 0.979902i
\(832\) −158.312 −0.190279
\(833\) −255.239 + 82.9321i −0.306409 + 0.0995584i
\(834\) −212.054 + 814.203i −0.254261 + 0.976262i
\(835\) −171.985 + 87.5062i −0.205970 + 0.104798i
\(836\) 190.960 + 262.834i 0.228421 + 0.314394i
\(837\) −954.586 + 511.971i −1.14048 + 0.611674i
\(838\) 111.106 + 80.7232i 0.132585 + 0.0963284i
\(839\) −55.8737 76.9036i −0.0665956 0.0916610i 0.774420 0.632672i \(-0.218042\pi\)
−0.841016 + 0.541011i \(0.818042\pi\)
\(840\) −175.239 299.058i −0.208617 0.356021i
\(841\) 1121.16 + 814.572i 1.33313 + 0.968576i
\(842\) −336.427 + 109.312i −0.399557 + 0.129824i
\(843\) 519.691 + 1325.96i 0.616478 + 1.57291i
\(844\) 86.6919 + 266.810i 0.102716 + 0.316126i
\(845\) 504.731 + 992.000i 0.597314 + 1.17396i
\(846\) −196.561 425.320i −0.232342 0.502743i
\(847\) −24.0410 + 73.9905i −0.0283837 + 0.0873560i
\(848\) 174.840 + 240.646i 0.206179 + 0.283781i
\(849\) −294.820 + 115.550i −0.347256 + 0.136102i
\(850\) −508.303 165.804i −0.598003 0.195064i
\(851\) 111.972i 0.131577i
\(852\) −284.039 181.637i −0.333379 0.213189i
\(853\) 376.565 1158.95i 0.441460 1.35867i −0.444860 0.895600i \(-0.646747\pi\)
0.886320 0.463074i \(-0.153253\pi\)
\(854\) −91.8937 29.8581i −0.107604 0.0349626i
\(855\) 355.664 + 531.867i 0.415981 + 0.622067i
\(856\) −74.5867 229.554i −0.0871340 0.268171i
\(857\) 1122.46i 1.30976i 0.755734 + 0.654879i \(0.227280\pi\)
−0.755734 + 0.654879i \(0.772720\pi\)
\(858\) 608.850 + 741.174i 0.709616 + 0.863840i
\(859\) −344.804 250.515i −0.401402 0.291636i 0.368710 0.929545i \(-0.379800\pi\)
−0.770112 + 0.637909i \(0.779800\pi\)
\(860\) 34.7968 218.883i 0.0404614 0.254516i
\(861\) 433.669 + 277.322i 0.503681 + 0.322093i
\(862\) −162.906 118.358i −0.188986 0.137306i
\(863\) 184.161 253.476i 0.213396 0.293715i −0.688878 0.724877i \(-0.741896\pi\)
0.902274 + 0.431162i \(0.141896\pi\)
\(864\) −150.318 + 27.0626i −0.173980 + 0.0313224i
\(865\) −1017.22 1018.39i −1.17597 1.17733i
\(866\) −261.160 + 359.456i −0.301570 + 0.415076i
\(867\) −114.846 139.806i −0.132464 0.161253i
\(868\) 655.533 0.755222
\(869\) 233.577 75.8937i 0.268788 0.0873345i
\(870\) −863.682 + 506.091i −0.992738 + 0.581714i
\(871\) −799.213 + 2459.72i −0.917581 + 2.82402i
\(872\) −39.0390 12.6846i −0.0447695 0.0145465i
\(873\) 59.4989 300.600i 0.0681545 0.344330i
\(874\) −43.1101 −0.0493250
\(875\) 910.724 462.059i 1.04083 0.528067i
\(876\) 546.456 214.175i 0.623808 0.244492i
\(877\) 406.741 295.515i 0.463787 0.336961i −0.331228 0.943551i \(-0.607463\pi\)
0.795015 + 0.606590i \(0.207463\pi\)
\(878\) 249.515 + 81.0722i 0.284185 + 0.0923374i
\(879\) 911.243 54.1693i 1.03668 0.0616260i
\(880\) −35.6143 225.700i −0.0404708 0.256478i
\(881\) −600.757 + 195.198i −0.681903 + 0.221564i −0.629428 0.777058i \(-0.716711\pi\)
−0.0524748 + 0.998622i \(0.516711\pi\)
\(882\) −153.482 165.723i −0.174016 0.187895i
\(883\) −392.777 1208.84i −0.444821 1.36902i −0.882680 0.469974i \(-0.844263\pi\)
0.437860 0.899043i \(-0.355737\pi\)
\(884\) −351.800 + 484.212i −0.397964 + 0.547751i
\(885\) 101.734 + 44.5122i 0.114954 + 0.0502963i
\(886\) 566.429 411.535i 0.639310 0.464486i
\(887\) 996.483 1371.54i 1.12343 1.54627i 0.323449 0.946246i \(-0.395158\pi\)
0.799982 0.600024i \(-0.204842\pi\)
\(888\) 111.692 428.854i 0.125780 0.482944i
\(889\) −7.62048 + 5.53661i −0.00857197 + 0.00622790i
\(890\) 60.2853 379.214i 0.0677363 0.426083i
\(891\) 704.807 + 599.671i 0.791030 + 0.673031i
\(892\) 141.064 + 434.151i 0.158144 + 0.486716i
\(893\) 523.412i 0.586128i
\(894\) −231.316 281.589i −0.258743 0.314976i
\(895\) −856.314 136.132i −0.956776 0.152103i
\(896\) 87.9075 + 28.5629i 0.0981111 + 0.0318782i
\(897\) −127.055 + 7.55285i −0.141645 + 0.00842012i
\(898\) −965.928 + 701.788i −1.07564 + 0.781501i
\(899\) 1893.19i 2.10588i
\(900\) −52.7984 446.892i −0.0586648 0.496547i
\(901\) 1124.57 1.24813
\(902\) 199.455 + 274.526i 0.221125 + 0.304352i
\(903\) −32.2345 542.254i −0.0356972 0.600503i
\(904\) 168.863 519.707i 0.186796 0.574898i
\(905\) −147.164 289.238i −0.162613 0.319600i
\(906\) −686.520 + 563.953i −0.757748 + 0.622465i
\(907\) −1632.25 −1.79962 −0.899808 0.436287i \(-0.856293\pi\)
−0.899808 + 0.436287i \(0.856293\pi\)
\(908\) 184.097 59.8166i 0.202750 0.0658773i
\(909\) −18.0309 151.123i −0.0198360 0.166252i
\(910\) −178.187 1129.23i −0.195810 1.24091i
\(911\) 608.264 + 837.204i 0.667689 + 0.918994i 0.999705 0.0242790i \(-0.00772902\pi\)
−0.332017 + 0.943274i \(0.607729\pi\)
\(912\) −165.113 43.0026i −0.181045 0.0471520i
\(913\) 724.109 + 526.096i 0.793109 + 0.576228i
\(914\) 446.553 + 614.628i 0.488570 + 0.672459i
\(915\) −93.7598 83.3346i −0.102470 0.0910760i
\(916\) −527.130 382.982i −0.575469 0.418103i
\(917\) −850.975 + 276.499i −0.927999 + 0.301525i
\(918\) −251.264 + 519.901i −0.273708 + 0.566341i
\(919\) 466.695 + 1436.34i 0.507829 + 1.56294i 0.795961 + 0.605347i \(0.206966\pi\)
−0.288132 + 0.957591i \(0.593034\pi\)
\(920\) 27.0073 + 13.7805i 0.0293558 + 0.0149788i
\(921\) 45.2591 + 761.355i 0.0491412 + 0.826661i
\(922\) −195.310 + 601.102i −0.211833 + 0.651954i
\(923\) −653.603 899.608i −0.708129 0.974656i
\(924\) −204.359 521.409i −0.221167 0.564296i
\(925\) 1241.31 + 404.904i 1.34195 + 0.437734i
\(926\) 481.744i 0.520242i
\(927\) 249.980 1262.95i 0.269665 1.36240i
\(928\) 82.4900 253.878i 0.0888901 0.273575i
\(929\) −397.912 129.289i −0.428323 0.139170i 0.0869191 0.996215i \(-0.472298\pi\)
−0.515242 + 0.857045i \(0.672298\pi\)
\(930\) 779.688 + 341.140i 0.838374 + 0.366817i
\(931\) −77.9740 239.979i −0.0837529 0.257765i
\(932\) 330.050i 0.354131i
\(933\) 32.1330 26.3962i 0.0344405 0.0282917i
\(934\) −623.719 453.158i −0.667793 0.485180i
\(935\) −769.467 392.621i −0.822960 0.419915i
\(936\) −494.159 97.8107i −0.527947 0.104499i
\(937\) 338.812 + 246.162i 0.361593 + 0.262712i 0.753716 0.657200i \(-0.228259\pi\)
−0.392123 + 0.919913i \(0.628259\pi\)
\(938\) 887.575 1221.64i 0.946242 1.30239i
\(939\) 175.986 275.202i 0.187418 0.293080i
\(940\) −167.313 + 327.904i −0.177993 + 0.348834i
\(941\) −90.7130 + 124.856i −0.0964007 + 0.132684i −0.854493 0.519464i \(-0.826132\pi\)
0.758092 + 0.652148i \(0.226132\pi\)
\(942\) 807.644 663.453i 0.857372 0.704303i
\(943\) −45.0278 −0.0477495
\(944\) −28.1629 + 9.15069i −0.0298336 + 0.00969353i
\(945\) −362.226 1041.75i −0.383308 1.10238i
\(946\) 110.655 340.562i 0.116972 0.360003i
\(947\) 1397.36 + 454.031i 1.47557 + 0.479441i 0.932786 0.360431i \(-0.117371\pi\)
0.542783 + 0.839873i \(0.317371\pi\)
\(948\) −69.4884 + 108.664i −0.0733000 + 0.114625i
\(949\) 1935.79 2.03982
\(950\) 155.892 477.914i 0.164097 0.503067i
\(951\) 36.2851 + 92.5794i 0.0381547 + 0.0973495i
\(952\) 282.710 205.401i 0.296964 0.215757i
\(953\) 1028.70 + 334.245i 1.07943 + 0.350729i 0.794155 0.607716i \(-0.207914\pi\)
0.285278 + 0.958445i \(0.407914\pi\)
\(954\) 397.069 + 859.180i 0.416215 + 0.900608i
\(955\) 143.045 280.342i 0.149785 0.293552i
\(956\) −605.847 + 196.851i −0.633731 + 0.205912i
\(957\) −1505.84 + 590.191i −1.57350 + 0.616709i
\(958\) 200.157 + 616.021i 0.208933 + 0.643028i
\(959\) −367.747 + 506.160i −0.383469 + 0.527800i
\(960\) 89.6927 + 79.7197i 0.0934299 + 0.0830413i
\(961\) −524.673 + 381.197i −0.545966 + 0.396667i
\(962\) 859.117 1182.47i 0.893053 1.22918i
\(963\) −90.9899 762.618i −0.0944859 0.791919i
\(964\) −484.538 + 352.038i −0.502633 + 0.365184i
\(965\) 64.3318 10.1512i 0.0666651 0.0105194i
\(966\) 71.9139 + 18.7295i 0.0744451 + 0.0193887i
\(967\) 285.066 + 877.343i 0.294794 + 0.907283i 0.983291 + 0.182043i \(0.0582711\pi\)
−0.688496 + 0.725240i \(0.741729\pi\)
\(968\) 26.9340i 0.0278243i
\(969\) −498.440 + 409.452i −0.514386 + 0.422551i
\(970\) −214.577 + 109.177i −0.221214 + 0.112554i
\(971\) 150.836 + 49.0095i 0.155341 + 0.0504732i 0.385655 0.922643i \(-0.373975\pi\)
−0.230314 + 0.973116i \(0.573975\pi\)
\(972\) −485.927 8.39830i −0.499925 0.00864023i
\(973\) 1310.75 952.316i 1.34712 0.978742i
\(974\) 353.620i 0.363060i
\(975\) 375.718 1435.83i 0.385352 1.47265i
\(976\) 33.4510 0.0342736
\(977\) −454.644 625.764i −0.465347 0.640496i 0.510260 0.860020i \(-0.329549\pi\)
−0.975607 + 0.219525i \(0.929549\pi\)
\(978\) 56.1455 3.33760i 0.0574085 0.00341268i
\(979\) 191.710 590.022i 0.195822 0.602678i
\(980\) −27.8627 + 175.266i −0.0284314 + 0.178843i
\(981\) −114.020 63.7135i −0.116229 0.0649475i
\(982\) −501.771 −0.510969
\(983\) −239.699 + 77.8830i −0.243845 + 0.0792299i −0.428390 0.903594i \(-0.640919\pi\)
0.184545 + 0.982824i \(0.440919\pi\)
\(984\) −172.458 44.9155i −0.175262 0.0456459i
\(985\) −868.349 138.045i −0.881572 0.140147i
\(986\) −593.200 816.470i −0.601623 0.828063i
\(987\) −227.401 + 873.128i −0.230396 + 0.884628i
\(988\) −455.263 330.768i −0.460792 0.334785i
\(989\) 27.9296 + 38.4418i 0.0282402 + 0.0388693i
\(990\) 28.2782 726.510i 0.0285639 0.733849i
\(991\) −1032.77 750.353i −1.04215 0.757167i −0.0714470 0.997444i \(-0.522762\pi\)
−0.970704 + 0.240277i \(0.922762\pi\)
\(992\) −215.840 + 70.1305i −0.217580 + 0.0706961i
\(993\) 71.8832 28.1736i 0.0723899 0.0283722i
\(994\) 200.624 + 617.459i 0.201835 + 0.621186i
\(995\) −1463.30 + 230.901i −1.47065 + 0.232061i
\(996\) −469.233 + 27.8938i −0.471118 + 0.0280058i
\(997\) −119.525 + 367.860i −0.119884 + 0.368966i −0.992934 0.118664i \(-0.962139\pi\)
0.873050 + 0.487631i \(0.162139\pi\)
\(998\) −54.2096 74.6131i −0.0543182 0.0747627i
\(999\) 613.601 1269.63i 0.614215 1.27090i
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 150.3.j.a.11.16 yes 80
3.2 odd 2 inner 150.3.j.a.11.4 80
25.16 even 5 inner 150.3.j.a.41.4 yes 80
75.41 odd 10 inner 150.3.j.a.41.16 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
150.3.j.a.11.4 80 3.2 odd 2 inner
150.3.j.a.11.16 yes 80 1.1 even 1 trivial
150.3.j.a.41.4 yes 80 25.16 even 5 inner
150.3.j.a.41.16 yes 80 75.41 odd 10 inner