Properties

Label 42.4.e.a.37.1
Level $42$
Weight $4$
Character 42.37
Analytic conductor $2.478$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [42,4,Mod(25,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("42.25");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), 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: \(2.47808022024\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 42.37
Dual form 42.4.e.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} -6.00000 q^{6} +(-3.50000 - 18.1865i) q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(3.00000 - 5.19615i) q^{5} -6.00000 q^{6} +(-3.50000 - 18.1865i) q^{7} -8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(-6.00000 - 10.3923i) q^{10} +(15.0000 + 25.9808i) q^{11} +(-6.00000 + 10.3923i) q^{12} +53.0000 q^{13} +(-35.0000 - 12.1244i) q^{14} -18.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(42.0000 + 72.7461i) q^{17} +(9.00000 + 15.5885i) q^{18} +(48.5000 - 84.0045i) q^{19} -24.0000 q^{20} +(-42.0000 + 36.3731i) q^{21} +60.0000 q^{22} +(-42.0000 + 72.7461i) q^{23} +(12.0000 + 20.7846i) q^{24} +(44.5000 + 77.0763i) q^{25} +(53.0000 - 91.7987i) q^{26} +27.0000 q^{27} +(-56.0000 + 48.4974i) q^{28} -180.000 q^{29} +(-18.0000 + 31.1769i) q^{30} +(-89.5000 - 155.019i) q^{31} +(16.0000 + 27.7128i) q^{32} +(45.0000 - 77.9423i) q^{33} +168.000 q^{34} +(-105.000 - 36.3731i) q^{35} +36.0000 q^{36} +(72.5000 - 125.574i) q^{37} +(-97.0000 - 168.009i) q^{38} +(-79.5000 - 137.698i) q^{39} +(-24.0000 + 41.5692i) q^{40} +126.000 q^{41} +(21.0000 + 109.119i) q^{42} -325.000 q^{43} +(60.0000 - 103.923i) q^{44} +(27.0000 + 46.7654i) q^{45} +(84.0000 + 145.492i) q^{46} +(183.000 - 316.965i) q^{47} +48.0000 q^{48} +(-318.500 + 127.306i) q^{49} +178.000 q^{50} +(126.000 - 218.238i) q^{51} +(-106.000 - 183.597i) q^{52} +(384.000 + 665.108i) q^{53} +(27.0000 - 46.7654i) q^{54} +180.000 q^{55} +(28.0000 + 145.492i) q^{56} -291.000 q^{57} +(-180.000 + 311.769i) q^{58} +(132.000 + 228.631i) q^{59} +(36.0000 + 62.3538i) q^{60} +(-409.000 + 708.409i) q^{61} -358.000 q^{62} +(157.500 + 54.5596i) q^{63} +64.0000 q^{64} +(159.000 - 275.396i) q^{65} +(-90.0000 - 155.885i) q^{66} +(261.500 + 452.931i) q^{67} +(168.000 - 290.985i) q^{68} +252.000 q^{69} +(-168.000 + 145.492i) q^{70} -342.000 q^{71} +(36.0000 - 62.3538i) q^{72} +(21.5000 + 37.2391i) q^{73} +(-145.000 - 251.147i) q^{74} +(133.500 - 231.229i) q^{75} -388.000 q^{76} +(420.000 - 363.731i) q^{77} -318.000 q^{78} +(585.500 - 1014.12i) q^{79} +(48.0000 + 83.1384i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(126.000 - 218.238i) q^{82} -810.000 q^{83} +(210.000 + 72.7461i) q^{84} +504.000 q^{85} +(-325.000 + 562.917i) q^{86} +(270.000 + 467.654i) q^{87} +(-120.000 - 207.846i) q^{88} +(300.000 - 519.615i) q^{89} +108.000 q^{90} +(-185.500 - 963.886i) q^{91} +336.000 q^{92} +(-268.500 + 465.056i) q^{93} +(-366.000 - 633.931i) q^{94} +(-291.000 - 504.027i) q^{95} +(48.0000 - 83.1384i) q^{96} +386.000 q^{97} +(-98.0000 + 678.964i) q^{98} -270.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} - 12 q^{6} - 7 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 3 q^{3} - 4 q^{4} + 6 q^{5} - 12 q^{6} - 7 q^{7} - 16 q^{8} - 9 q^{9} - 12 q^{10} + 30 q^{11} - 12 q^{12} + 106 q^{13} - 70 q^{14} - 36 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} + 97 q^{19} - 48 q^{20} - 84 q^{21} + 120 q^{22} - 84 q^{23} + 24 q^{24} + 89 q^{25} + 106 q^{26} + 54 q^{27} - 112 q^{28} - 360 q^{29} - 36 q^{30} - 179 q^{31} + 32 q^{32} + 90 q^{33} + 336 q^{34} - 210 q^{35} + 72 q^{36} + 145 q^{37} - 194 q^{38} - 159 q^{39} - 48 q^{40} + 252 q^{41} + 42 q^{42} - 650 q^{43} + 120 q^{44} + 54 q^{45} + 168 q^{46} + 366 q^{47} + 96 q^{48} - 637 q^{49} + 356 q^{50} + 252 q^{51} - 212 q^{52} + 768 q^{53} + 54 q^{54} + 360 q^{55} + 56 q^{56} - 582 q^{57} - 360 q^{58} + 264 q^{59} + 72 q^{60} - 818 q^{61} - 716 q^{62} + 315 q^{63} + 128 q^{64} + 318 q^{65} - 180 q^{66} + 523 q^{67} + 336 q^{68} + 504 q^{69} - 336 q^{70} - 684 q^{71} + 72 q^{72} + 43 q^{73} - 290 q^{74} + 267 q^{75} - 776 q^{76} + 840 q^{77} - 636 q^{78} + 1171 q^{79} + 96 q^{80} - 81 q^{81} + 252 q^{82} - 1620 q^{83} + 420 q^{84} + 1008 q^{85} - 650 q^{86} + 540 q^{87} - 240 q^{88} + 600 q^{89} + 216 q^{90} - 371 q^{91} + 672 q^{92} - 537 q^{93} - 732 q^{94} - 582 q^{95} + 96 q^{96} + 772 q^{97} - 196 q^{98} - 540 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.353553 0.612372i
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −2.00000 3.46410i −0.250000 0.433013i
\(5\) 3.00000 5.19615i 0.268328 0.464758i −0.700102 0.714043i \(-0.746862\pi\)
0.968430 + 0.249285i \(0.0801955\pi\)
\(6\) −6.00000 −0.408248
\(7\) −3.50000 18.1865i −0.188982 0.981981i
\(8\) −8.00000 −0.353553
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) −6.00000 10.3923i −0.189737 0.328634i
\(11\) 15.0000 + 25.9808i 0.411152 + 0.712136i 0.995016 0.0997155i \(-0.0317933\pi\)
−0.583864 + 0.811851i \(0.698460\pi\)
\(12\) −6.00000 + 10.3923i −0.144338 + 0.250000i
\(13\) 53.0000 1.13074 0.565368 0.824839i \(-0.308734\pi\)
0.565368 + 0.824839i \(0.308734\pi\)
\(14\) −35.0000 12.1244i −0.668153 0.231455i
\(15\) −18.0000 −0.309839
\(16\) −8.00000 + 13.8564i −0.125000 + 0.216506i
\(17\) 42.0000 + 72.7461i 0.599206 + 1.03785i 0.992939 + 0.118630i \(0.0378502\pi\)
−0.393733 + 0.919225i \(0.628817\pi\)
\(18\) 9.00000 + 15.5885i 0.117851 + 0.204124i
\(19\) 48.5000 84.0045i 0.585614 1.01431i −0.409185 0.912452i \(-0.634187\pi\)
0.994799 0.101861i \(-0.0324798\pi\)
\(20\) −24.0000 −0.268328
\(21\) −42.0000 + 36.3731i −0.436436 + 0.377964i
\(22\) 60.0000 0.581456
\(23\) −42.0000 + 72.7461i −0.380765 + 0.659505i −0.991172 0.132583i \(-0.957673\pi\)
0.610406 + 0.792088i \(0.291006\pi\)
\(24\) 12.0000 + 20.7846i 0.102062 + 0.176777i
\(25\) 44.5000 + 77.0763i 0.356000 + 0.616610i
\(26\) 53.0000 91.7987i 0.399775 0.692431i
\(27\) 27.0000 0.192450
\(28\) −56.0000 + 48.4974i −0.377964 + 0.327327i
\(29\) −180.000 −1.15259 −0.576296 0.817241i \(-0.695502\pi\)
−0.576296 + 0.817241i \(0.695502\pi\)
\(30\) −18.0000 + 31.1769i −0.109545 + 0.189737i
\(31\) −89.5000 155.019i −0.518538 0.898134i −0.999768 0.0215397i \(-0.993143\pi\)
0.481230 0.876594i \(-0.340190\pi\)
\(32\) 16.0000 + 27.7128i 0.0883883 + 0.153093i
\(33\) 45.0000 77.9423i 0.237379 0.411152i
\(34\) 168.000 0.847405
\(35\) −105.000 36.3731i −0.507093 0.175662i
\(36\) 36.0000 0.166667
\(37\) 72.5000 125.574i 0.322133 0.557951i −0.658795 0.752323i \(-0.728933\pi\)
0.980928 + 0.194372i \(0.0622668\pi\)
\(38\) −97.0000 168.009i −0.414092 0.717228i
\(39\) −79.5000 137.698i −0.326415 0.565368i
\(40\) −24.0000 + 41.5692i −0.0948683 + 0.164317i
\(41\) 126.000 0.479949 0.239974 0.970779i \(-0.422861\pi\)
0.239974 + 0.970779i \(0.422861\pi\)
\(42\) 21.0000 + 109.119i 0.0771517 + 0.400892i
\(43\) −325.000 −1.15261 −0.576303 0.817236i \(-0.695505\pi\)
−0.576303 + 0.817236i \(0.695505\pi\)
\(44\) 60.0000 103.923i 0.205576 0.356068i
\(45\) 27.0000 + 46.7654i 0.0894427 + 0.154919i
\(46\) 84.0000 + 145.492i 0.269242 + 0.466341i
\(47\) 183.000 316.965i 0.567942 0.983705i −0.428827 0.903387i \(-0.641073\pi\)
0.996769 0.0803184i \(-0.0255937\pi\)
\(48\) 48.0000 0.144338
\(49\) −318.500 + 127.306i −0.928571 + 0.371154i
\(50\) 178.000 0.503460
\(51\) 126.000 218.238i 0.345952 0.599206i
\(52\) −106.000 183.597i −0.282684 0.489623i
\(53\) 384.000 + 665.108i 0.995216 + 1.72376i 0.582217 + 0.813034i \(0.302186\pi\)
0.413000 + 0.910731i \(0.364481\pi\)
\(54\) 27.0000 46.7654i 0.0680414 0.117851i
\(55\) 180.000 0.441294
\(56\) 28.0000 + 145.492i 0.0668153 + 0.347183i
\(57\) −291.000 −0.676209
\(58\) −180.000 + 311.769i −0.407503 + 0.705815i
\(59\) 132.000 + 228.631i 0.291270 + 0.504495i 0.974110 0.226073i \(-0.0725888\pi\)
−0.682840 + 0.730568i \(0.739255\pi\)
\(60\) 36.0000 + 62.3538i 0.0774597 + 0.134164i
\(61\) −409.000 + 708.409i −0.858477 + 1.48693i 0.0149048 + 0.999889i \(0.495255\pi\)
−0.873382 + 0.487036i \(0.838078\pi\)
\(62\) −358.000 −0.733323
\(63\) 157.500 + 54.5596i 0.314970 + 0.109109i
\(64\) 64.0000 0.125000
\(65\) 159.000 275.396i 0.303408 0.525518i
\(66\) −90.0000 155.885i −0.167852 0.290728i
\(67\) 261.500 + 452.931i 0.476826 + 0.825886i 0.999647 0.0265560i \(-0.00845402\pi\)
−0.522822 + 0.852442i \(0.675121\pi\)
\(68\) 168.000 290.985i 0.299603 0.518927i
\(69\) 252.000 0.439670
\(70\) −168.000 + 145.492i −0.286855 + 0.248424i
\(71\) −342.000 −0.571661 −0.285831 0.958280i \(-0.592269\pi\)
−0.285831 + 0.958280i \(0.592269\pi\)
\(72\) 36.0000 62.3538i 0.0589256 0.102062i
\(73\) 21.5000 + 37.2391i 0.0344710 + 0.0597056i 0.882746 0.469850i \(-0.155692\pi\)
−0.848275 + 0.529556i \(0.822359\pi\)
\(74\) −145.000 251.147i −0.227783 0.394531i
\(75\) 133.500 231.229i 0.205537 0.356000i
\(76\) −388.000 −0.585614
\(77\) 420.000 363.731i 0.621603 0.538324i
\(78\) −318.000 −0.461621
\(79\) 585.500 1014.12i 0.833847 1.44427i −0.0611191 0.998130i \(-0.519467\pi\)
0.894966 0.446135i \(-0.147200\pi\)
\(80\) 48.0000 + 83.1384i 0.0670820 + 0.116190i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) 126.000 218.238i 0.169687 0.293907i
\(83\) −810.000 −1.07119 −0.535597 0.844474i \(-0.679913\pi\)
−0.535597 + 0.844474i \(0.679913\pi\)
\(84\) 210.000 + 72.7461i 0.272772 + 0.0944911i
\(85\) 504.000 0.643135
\(86\) −325.000 + 562.917i −0.407508 + 0.705824i
\(87\) 270.000 + 467.654i 0.332725 + 0.576296i
\(88\) −120.000 207.846i −0.145364 0.251778i
\(89\) 300.000 519.615i 0.357303 0.618866i −0.630207 0.776428i \(-0.717030\pi\)
0.987509 + 0.157561i \(0.0503631\pi\)
\(90\) 108.000 0.126491
\(91\) −185.500 963.886i −0.213689 1.11036i
\(92\) 336.000 0.380765
\(93\) −268.500 + 465.056i −0.299378 + 0.518538i
\(94\) −366.000 633.931i −0.401596 0.695585i
\(95\) −291.000 504.027i −0.314273 0.544337i
\(96\) 48.0000 83.1384i 0.0510310 0.0883883i
\(97\) 386.000 0.404045 0.202022 0.979381i \(-0.435249\pi\)
0.202022 + 0.979381i \(0.435249\pi\)
\(98\) −98.0000 + 678.964i −0.101015 + 0.699854i
\(99\) −270.000 −0.274101
\(100\) 178.000 308.305i 0.178000 0.308305i
\(101\) −309.000 535.204i −0.304422 0.527275i 0.672710 0.739906i \(-0.265130\pi\)
−0.977133 + 0.212631i \(0.931797\pi\)
\(102\) −252.000 436.477i −0.244625 0.423702i
\(103\) −737.500 + 1277.39i −0.705515 + 1.22199i 0.260991 + 0.965341i \(0.415951\pi\)
−0.966505 + 0.256646i \(0.917382\pi\)
\(104\) −424.000 −0.399775
\(105\) 63.0000 + 327.358i 0.0585540 + 0.304256i
\(106\) 1536.00 1.40745
\(107\) −942.000 + 1631.59i −0.851090 + 1.47413i 0.0291364 + 0.999575i \(0.490724\pi\)
−0.880226 + 0.474555i \(0.842609\pi\)
\(108\) −54.0000 93.5307i −0.0481125 0.0833333i
\(109\) −206.500 357.668i −0.181460 0.314298i 0.760918 0.648848i \(-0.224749\pi\)
−0.942378 + 0.334550i \(0.891416\pi\)
\(110\) 180.000 311.769i 0.156021 0.270237i
\(111\) −435.000 −0.371967
\(112\) 280.000 + 96.9948i 0.236228 + 0.0818317i
\(113\) −882.000 −0.734262 −0.367131 0.930169i \(-0.619660\pi\)
−0.367131 + 0.930169i \(0.619660\pi\)
\(114\) −291.000 + 504.027i −0.239076 + 0.414092i
\(115\) 252.000 + 436.477i 0.204340 + 0.353928i
\(116\) 360.000 + 623.538i 0.288148 + 0.499087i
\(117\) −238.500 + 413.094i −0.188456 + 0.326415i
\(118\) 528.000 0.411918
\(119\) 1176.00 1018.45i 0.905914 0.784544i
\(120\) 144.000 0.109545
\(121\) 215.500 373.257i 0.161908 0.280433i
\(122\) 818.000 + 1416.82i 0.607035 + 1.05142i
\(123\) −189.000 327.358i −0.138549 0.239974i
\(124\) −358.000 + 620.074i −0.259269 + 0.449067i
\(125\) 1284.00 0.918756
\(126\) 252.000 218.238i 0.178174 0.154303i
\(127\) 2483.00 1.73489 0.867443 0.497536i \(-0.165762\pi\)
0.867443 + 0.497536i \(0.165762\pi\)
\(128\) 64.0000 110.851i 0.0441942 0.0765466i
\(129\) 487.500 + 844.375i 0.332729 + 0.576303i
\(130\) −318.000 550.792i −0.214542 0.371597i
\(131\) −1059.00 + 1834.24i −0.706300 + 1.22335i 0.259921 + 0.965630i \(0.416304\pi\)
−0.966220 + 0.257717i \(0.917030\pi\)
\(132\) −360.000 −0.237379
\(133\) −1697.50 588.031i −1.10671 0.383374i
\(134\) 1046.00 0.674333
\(135\) 81.0000 140.296i 0.0516398 0.0894427i
\(136\) −336.000 581.969i −0.211851 0.366937i
\(137\) −1506.00 2608.47i −0.939170 1.62669i −0.767024 0.641618i \(-0.778263\pi\)
−0.172146 0.985071i \(-0.555070\pi\)
\(138\) 252.000 436.477i 0.155447 0.269242i
\(139\) −37.0000 −0.0225777 −0.0112888 0.999936i \(-0.503593\pi\)
−0.0112888 + 0.999936i \(0.503593\pi\)
\(140\) 84.0000 + 436.477i 0.0507093 + 0.263493i
\(141\) −1098.00 −0.655803
\(142\) −342.000 + 592.361i −0.202113 + 0.350069i
\(143\) 795.000 + 1376.98i 0.464904 + 0.805237i
\(144\) −72.0000 124.708i −0.0416667 0.0721688i
\(145\) −540.000 + 935.307i −0.309273 + 0.535676i
\(146\) 86.0000 0.0487494
\(147\) 808.500 + 636.529i 0.453632 + 0.357143i
\(148\) −580.000 −0.322133
\(149\) 822.000 1423.75i 0.451952 0.782804i −0.546555 0.837423i \(-0.684061\pi\)
0.998507 + 0.0546191i \(0.0173945\pi\)
\(150\) −267.000 462.458i −0.145336 0.251730i
\(151\) −544.000 942.236i −0.293179 0.507802i 0.681380 0.731930i \(-0.261380\pi\)
−0.974560 + 0.224128i \(0.928047\pi\)
\(152\) −388.000 + 672.036i −0.207046 + 0.358614i
\(153\) −756.000 −0.399470
\(154\) −210.000 1091.19i −0.109885 0.570979i
\(155\) −1074.00 −0.556553
\(156\) −318.000 + 550.792i −0.163208 + 0.282684i
\(157\) −253.000 438.209i −0.128609 0.222757i 0.794529 0.607226i \(-0.207718\pi\)
−0.923138 + 0.384469i \(0.874385\pi\)
\(158\) −1171.00 2028.23i −0.589619 1.02125i
\(159\) 1152.00 1995.32i 0.574588 0.995216i
\(160\) 192.000 0.0948683
\(161\) 1470.00 + 509.223i 0.719579 + 0.249270i
\(162\) −162.000 −0.0785674
\(163\) −922.000 + 1596.95i −0.443047 + 0.767379i −0.997914 0.0645596i \(-0.979436\pi\)
0.554867 + 0.831939i \(0.312769\pi\)
\(164\) −252.000 436.477i −0.119987 0.207824i
\(165\) −270.000 467.654i −0.127391 0.220647i
\(166\) −810.000 + 1402.96i −0.378724 + 0.655969i
\(167\) 162.000 0.0750655 0.0375327 0.999295i \(-0.488050\pi\)
0.0375327 + 0.999295i \(0.488050\pi\)
\(168\) 336.000 290.985i 0.154303 0.133631i
\(169\) 612.000 0.278562
\(170\) 504.000 872.954i 0.227383 0.393838i
\(171\) 436.500 + 756.040i 0.195205 + 0.338104i
\(172\) 650.000 + 1125.83i 0.288151 + 0.499093i
\(173\) 1362.00 2359.05i 0.598560 1.03674i −0.394473 0.918907i \(-0.629073\pi\)
0.993034 0.117830i \(-0.0375937\pi\)
\(174\) 1080.00 0.470544
\(175\) 1246.00 1079.07i 0.538221 0.466113i
\(176\) −480.000 −0.205576
\(177\) 396.000 685.892i 0.168165 0.291270i
\(178\) −600.000 1039.23i −0.252651 0.437605i
\(179\) 627.000 + 1086.00i 0.261811 + 0.453470i 0.966723 0.255825i \(-0.0823469\pi\)
−0.704912 + 0.709295i \(0.749014\pi\)
\(180\) 108.000 187.061i 0.0447214 0.0774597i
\(181\) −1807.00 −0.742062 −0.371031 0.928620i \(-0.620996\pi\)
−0.371031 + 0.928620i \(0.620996\pi\)
\(182\) −1855.00 642.591i −0.755504 0.261714i
\(183\) 2454.00 0.991284
\(184\) 336.000 581.969i 0.134621 0.233170i
\(185\) −435.000 753.442i −0.172875 0.299428i
\(186\) 537.000 + 930.111i 0.211692 + 0.366662i
\(187\) −1260.00 + 2182.38i −0.492729 + 0.853432i
\(188\) −1464.00 −0.567942
\(189\) −94.5000 491.036i −0.0363696 0.188982i
\(190\) −1164.00 −0.444450
\(191\) −357.000 + 618.342i −0.135244 + 0.234250i −0.925691 0.378281i \(-0.876515\pi\)
0.790447 + 0.612531i \(0.209849\pi\)
\(192\) −96.0000 166.277i −0.0360844 0.0625000i
\(193\) 1854.50 + 3212.09i 0.691657 + 1.19799i 0.971295 + 0.237880i \(0.0764524\pi\)
−0.279637 + 0.960106i \(0.590214\pi\)
\(194\) 386.000 668.572i 0.142851 0.247426i
\(195\) −954.000 −0.350345
\(196\) 1078.00 + 848.705i 0.392857 + 0.309295i
\(197\) −1044.00 −0.377573 −0.188787 0.982018i \(-0.560455\pi\)
−0.188787 + 0.982018i \(0.560455\pi\)
\(198\) −270.000 + 467.654i −0.0969094 + 0.167852i
\(199\) 68.0000 + 117.779i 0.0242231 + 0.0419556i 0.877883 0.478875i \(-0.158955\pi\)
−0.853660 + 0.520831i \(0.825622\pi\)
\(200\) −356.000 616.610i −0.125865 0.218005i
\(201\) 784.500 1358.79i 0.275295 0.476826i
\(202\) −1236.00 −0.430518
\(203\) 630.000 + 3273.58i 0.217819 + 1.13182i
\(204\) −1008.00 −0.345952
\(205\) 378.000 654.715i 0.128784 0.223060i
\(206\) 1475.00 + 2554.77i 0.498874 + 0.864076i
\(207\) −378.000 654.715i −0.126922 0.219835i
\(208\) −424.000 + 734.390i −0.141342 + 0.244811i
\(209\) 2910.00 0.963105
\(210\) 630.000 + 218.238i 0.207020 + 0.0717137i
\(211\) 1484.00 0.484184 0.242092 0.970253i \(-0.422166\pi\)
0.242092 + 0.970253i \(0.422166\pi\)
\(212\) 1536.00 2660.43i 0.497608 0.861882i
\(213\) 513.000 + 888.542i 0.165024 + 0.285831i
\(214\) 1884.00 + 3263.18i 0.601811 + 1.04237i
\(215\) −975.000 + 1688.75i −0.309277 + 0.535683i
\(216\) −216.000 −0.0680414
\(217\) −2506.00 + 2170.26i −0.783956 + 0.678925i
\(218\) −826.000 −0.256623
\(219\) 64.5000 111.717i 0.0199019 0.0344710i
\(220\) −360.000 623.538i −0.110324 0.191086i
\(221\) 2226.00 + 3855.55i 0.677543 + 1.17354i
\(222\) −435.000 + 753.442i −0.131510 + 0.227783i
\(223\) −2032.00 −0.610192 −0.305096 0.952322i \(-0.598689\pi\)
−0.305096 + 0.952322i \(0.598689\pi\)
\(224\) 448.000 387.979i 0.133631 0.115728i
\(225\) −801.000 −0.237333
\(226\) −882.000 + 1527.67i −0.259601 + 0.449642i
\(227\) −3099.00 5367.63i −0.906114 1.56944i −0.819415 0.573201i \(-0.805702\pi\)
−0.0866989 0.996235i \(-0.527632\pi\)
\(228\) 582.000 + 1008.05i 0.169052 + 0.292807i
\(229\) 2295.50 3975.92i 0.662406 1.14732i −0.317576 0.948233i \(-0.602869\pi\)
0.979982 0.199088i \(-0.0637978\pi\)
\(230\) 1008.00 0.288981
\(231\) −1575.00 545.596i −0.448603 0.155401i
\(232\) 1440.00 0.407503
\(233\) −2265.00 + 3923.10i −0.636846 + 1.10305i 0.349275 + 0.937020i \(0.386428\pi\)
−0.986121 + 0.166029i \(0.946905\pi\)
\(234\) 477.000 + 826.188i 0.133258 + 0.230810i
\(235\) −1098.00 1901.79i −0.304790 0.527912i
\(236\) 528.000 914.523i 0.145635 0.252247i
\(237\) −3513.00 −0.962843
\(238\) −588.000 3055.34i −0.160144 0.832135i
\(239\) 1530.00 0.414090 0.207045 0.978331i \(-0.433615\pi\)
0.207045 + 0.978331i \(0.433615\pi\)
\(240\) 144.000 249.415i 0.0387298 0.0670820i
\(241\) −2767.00 4792.58i −0.739577 1.28099i −0.952686 0.303957i \(-0.901692\pi\)
0.213108 0.977029i \(-0.431641\pi\)
\(242\) −431.000 746.514i −0.114486 0.198296i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) 3272.00 0.858477
\(245\) −294.000 + 2036.89i −0.0766652 + 0.531152i
\(246\) −756.000 −0.195938
\(247\) 2570.50 4452.24i 0.662174 1.14692i
\(248\) 716.000 + 1240.15i 0.183331 + 0.317538i
\(249\) 1215.00 + 2104.44i 0.309227 + 0.535597i
\(250\) 1284.00 2223.95i 0.324829 0.562621i
\(251\) −468.000 −0.117689 −0.0588444 0.998267i \(-0.518742\pi\)
−0.0588444 + 0.998267i \(0.518742\pi\)
\(252\) −126.000 654.715i −0.0314970 0.163663i
\(253\) −2520.00 −0.626210
\(254\) 2483.00 4300.68i 0.613375 1.06240i
\(255\) −756.000 1309.43i −0.185657 0.321568i
\(256\) −128.000 221.703i −0.0312500 0.0541266i
\(257\) 1245.00 2156.40i 0.302183 0.523396i −0.674447 0.738323i \(-0.735618\pi\)
0.976630 + 0.214927i \(0.0689514\pi\)
\(258\) 1950.00 0.470549
\(259\) −2537.50 879.016i −0.608774 0.210886i
\(260\) −1272.00 −0.303408
\(261\) 810.000 1402.96i 0.192099 0.332725i
\(262\) 2118.00 + 3668.48i 0.499429 + 0.865037i
\(263\) −786.000 1361.39i −0.184285 0.319190i 0.759051 0.651032i \(-0.225663\pi\)
−0.943335 + 0.331841i \(0.892330\pi\)
\(264\) −360.000 + 623.538i −0.0839260 + 0.145364i
\(265\) 4608.00 1.06818
\(266\) −2716.00 + 2352.12i −0.626048 + 0.542173i
\(267\) −1800.00 −0.412578
\(268\) 1046.00 1811.73i 0.238413 0.412943i
\(269\) −903.000 1564.04i −0.204672 0.354503i 0.745356 0.666667i \(-0.232280\pi\)
−0.950028 + 0.312164i \(0.898946\pi\)
\(270\) −162.000 280.592i −0.0365148 0.0632456i
\(271\) 3056.00 5293.15i 0.685014 1.18648i −0.288418 0.957504i \(-0.593129\pi\)
0.973432 0.228975i \(-0.0735372\pi\)
\(272\) −1344.00 −0.299603
\(273\) −2226.00 + 1927.77i −0.493493 + 0.427378i
\(274\) −6024.00 −1.32819
\(275\) −1335.00 + 2312.29i −0.292740 + 0.507041i
\(276\) −504.000 872.954i −0.109918 0.190383i
\(277\) 2115.50 + 3664.15i 0.458874 + 0.794793i 0.998902 0.0468542i \(-0.0149196\pi\)
−0.540028 + 0.841647i \(0.681586\pi\)
\(278\) −37.0000 + 64.0859i −0.00798242 + 0.0138260i
\(279\) 1611.00 0.345692
\(280\) 840.000 + 290.985i 0.179284 + 0.0621059i
\(281\) −3816.00 −0.810119 −0.405060 0.914290i \(-0.632749\pi\)
−0.405060 + 0.914290i \(0.632749\pi\)
\(282\) −1098.00 + 1901.79i −0.231862 + 0.401596i
\(283\) 1998.50 + 3461.50i 0.419783 + 0.727085i 0.995917 0.0902699i \(-0.0287730\pi\)
−0.576135 + 0.817355i \(0.695440\pi\)
\(284\) 684.000 + 1184.72i 0.142915 + 0.247536i
\(285\) −873.000 + 1512.08i −0.181446 + 0.314273i
\(286\) 3180.00 0.657473
\(287\) −441.000 2291.50i −0.0907018 0.471300i
\(288\) −288.000 −0.0589256
\(289\) −1071.50 + 1855.89i −0.218095 + 0.377751i
\(290\) 1080.00 + 1870.61i 0.218689 + 0.378780i
\(291\) −579.000 1002.86i −0.116638 0.202022i
\(292\) 86.0000 148.956i 0.0172355 0.0298528i
\(293\) 4608.00 0.918779 0.459389 0.888235i \(-0.348068\pi\)
0.459389 + 0.888235i \(0.348068\pi\)
\(294\) 1911.00 763.834i 0.379088 0.151523i
\(295\) 1584.00 0.312624
\(296\) −580.000 + 1004.59i −0.113891 + 0.197265i
\(297\) 405.000 + 701.481i 0.0791262 + 0.137051i
\(298\) −1644.00 2847.49i −0.319578 0.553526i
\(299\) −2226.00 + 3855.55i −0.430545 + 0.745726i
\(300\) −1068.00 −0.205537
\(301\) 1137.50 + 5910.62i 0.217822 + 1.13184i
\(302\) −2176.00 −0.414618
\(303\) −927.000 + 1605.61i −0.175758 + 0.304422i
\(304\) 776.000 + 1344.07i 0.146403 + 0.253578i
\(305\) 2454.00 + 4250.45i 0.460707 + 0.797968i
\(306\) −756.000 + 1309.43i −0.141234 + 0.244625i
\(307\) −631.000 −0.117306 −0.0586532 0.998278i \(-0.518681\pi\)
−0.0586532 + 0.998278i \(0.518681\pi\)
\(308\) −2100.00 727.461i −0.388502 0.134581i
\(309\) 4425.00 0.814658
\(310\) −1074.00 + 1860.22i −0.196771 + 0.340818i
\(311\) −1947.00 3372.30i −0.354998 0.614874i 0.632120 0.774871i \(-0.282185\pi\)
−0.987118 + 0.159997i \(0.948852\pi\)
\(312\) 636.000 + 1101.58i 0.115405 + 0.199888i
\(313\) 1092.50 1892.27i 0.197290 0.341716i −0.750359 0.661031i \(-0.770119\pi\)
0.947649 + 0.319314i \(0.103453\pi\)
\(314\) −1012.00 −0.181880
\(315\) 756.000 654.715i 0.135225 0.117108i
\(316\) −4684.00 −0.833847
\(317\) −1752.00 + 3034.55i −0.310417 + 0.537658i −0.978453 0.206471i \(-0.933802\pi\)
0.668036 + 0.744129i \(0.267135\pi\)
\(318\) −2304.00 3990.65i −0.406295 0.703724i
\(319\) −2700.00 4676.54i −0.473890 0.820802i
\(320\) 192.000 332.554i 0.0335410 0.0580948i
\(321\) 5652.00 0.982754
\(322\) 2352.00 2036.89i 0.407055 0.352520i
\(323\) 8148.00 1.40361
\(324\) −162.000 + 280.592i −0.0277778 + 0.0481125i
\(325\) 2358.50 + 4085.04i 0.402542 + 0.697223i
\(326\) 1844.00 + 3193.90i 0.313281 + 0.542619i
\(327\) −619.500 + 1073.01i −0.104766 + 0.181460i
\(328\) −1008.00 −0.169687
\(329\) −6405.00 2218.76i −1.07331 0.371806i
\(330\) −1080.00 −0.180158
\(331\) −1472.50 + 2550.44i −0.244519 + 0.423520i −0.961996 0.273062i \(-0.911964\pi\)
0.717477 + 0.696582i \(0.245297\pi\)
\(332\) 1620.00 + 2805.92i 0.267798 + 0.463840i
\(333\) 652.500 + 1130.16i 0.107378 + 0.185984i
\(334\) 162.000 280.592i 0.0265397 0.0459680i
\(335\) 3138.00 0.511783
\(336\) −168.000 872.954i −0.0272772 0.141737i
\(337\) 4277.00 0.691344 0.345672 0.938355i \(-0.387651\pi\)
0.345672 + 0.938355i \(0.387651\pi\)
\(338\) 612.000 1060.02i 0.0984864 0.170583i
\(339\) 1323.00 + 2291.50i 0.211963 + 0.367131i
\(340\) −1008.00 1745.91i −0.160784 0.278486i
\(341\) 2685.00 4650.56i 0.426396 0.738539i
\(342\) 1746.00 0.276061
\(343\) 3430.00 + 5346.84i 0.539949 + 0.841698i
\(344\) 2600.00 0.407508
\(345\) 756.000 1309.43i 0.117976 0.204340i
\(346\) −2724.00 4718.11i −0.423246 0.733084i
\(347\) −3594.00 6224.99i −0.556012 0.963040i −0.997824 0.0659329i \(-0.978998\pi\)
0.441812 0.897107i \(-0.354336\pi\)
\(348\) 1080.00 1870.61i 0.166362 0.288148i
\(349\) −9406.00 −1.44267 −0.721335 0.692587i \(-0.756471\pi\)
−0.721335 + 0.692587i \(0.756471\pi\)
\(350\) −623.000 3237.20i −0.0951450 0.494388i
\(351\) 1431.00 0.217610
\(352\) −480.000 + 831.384i −0.0726821 + 0.125889i
\(353\) −1695.00 2935.83i −0.255569 0.442658i 0.709481 0.704724i \(-0.248929\pi\)
−0.965050 + 0.262066i \(0.915596\pi\)
\(354\) −792.000 1371.78i −0.118911 0.205959i
\(355\) −1026.00 + 1777.08i −0.153393 + 0.265684i
\(356\) −2400.00 −0.357303
\(357\) −4410.00 1527.67i −0.653787 0.226478i
\(358\) 2508.00 0.370257
\(359\) 2406.00 4167.31i 0.353715 0.612653i −0.633182 0.774003i \(-0.718251\pi\)
0.986897 + 0.161350i \(0.0515848\pi\)
\(360\) −216.000 374.123i −0.0316228 0.0547723i
\(361\) −1275.00 2208.36i −0.185887 0.321966i
\(362\) −1807.00 + 3129.82i −0.262359 + 0.454418i
\(363\) −1293.00 −0.186956
\(364\) −2968.00 + 2570.36i −0.427378 + 0.370120i
\(365\) 258.000 0.0369982
\(366\) 2454.00 4250.45i 0.350472 0.607035i
\(367\) 3549.50 + 6147.91i 0.504857 + 0.874437i 0.999984 + 0.00561709i \(0.00178798\pi\)
−0.495128 + 0.868820i \(0.664879\pi\)
\(368\) −672.000 1163.94i −0.0951914 0.164876i
\(369\) −567.000 + 982.073i −0.0799914 + 0.138549i
\(370\) −1740.00 −0.244482
\(371\) 10752.0 9311.51i 1.50463 1.30304i
\(372\) 2148.00 0.299378
\(373\) −1481.50 + 2566.03i −0.205655 + 0.356204i −0.950341 0.311210i \(-0.899266\pi\)
0.744687 + 0.667414i \(0.232599\pi\)
\(374\) 2520.00 + 4364.77i 0.348412 + 0.603467i
\(375\) −1926.00 3335.93i −0.265222 0.459378i
\(376\) −1464.00 + 2535.72i −0.200798 + 0.347792i
\(377\) −9540.00 −1.30328
\(378\) −945.000 327.358i −0.128586 0.0445435i
\(379\) −11899.0 −1.61269 −0.806346 0.591444i \(-0.798558\pi\)
−0.806346 + 0.591444i \(0.798558\pi\)
\(380\) −1164.00 + 2016.11i −0.157137 + 0.272169i
\(381\) −3724.50 6451.02i −0.500819 0.867443i
\(382\) 714.000 + 1236.68i 0.0956320 + 0.165639i
\(383\) −1284.00 + 2223.95i −0.171304 + 0.296707i −0.938876 0.344256i \(-0.888131\pi\)
0.767572 + 0.640963i \(0.221465\pi\)
\(384\) −384.000 −0.0510310
\(385\) −630.000 3273.58i −0.0833968 0.433343i
\(386\) 7418.00 0.978151
\(387\) 1462.50 2533.12i 0.192101 0.332729i
\(388\) −772.000 1337.14i −0.101011 0.174957i
\(389\) 5073.00 + 8786.69i 0.661212 + 1.14525i 0.980298 + 0.197526i \(0.0632908\pi\)
−0.319086 + 0.947726i \(0.603376\pi\)
\(390\) −954.000 + 1652.38i −0.123866 + 0.214542i
\(391\) −7056.00 −0.912627
\(392\) 2548.00 1018.45i 0.328300 0.131223i
\(393\) 6354.00 0.815565
\(394\) −1044.00 + 1808.26i −0.133492 + 0.231215i
\(395\) −3513.00 6084.69i −0.447489 0.775074i
\(396\) 540.000 + 935.307i 0.0685253 + 0.118689i
\(397\) 3114.50 5394.47i 0.393734 0.681967i −0.599205 0.800596i \(-0.704517\pi\)
0.992939 + 0.118629i \(0.0378499\pi\)
\(398\) 272.000 0.0342566
\(399\) 1018.50 + 5292.28i 0.127791 + 0.664024i
\(400\) −1424.00 −0.178000
\(401\) 1236.00 2140.81i 0.153922 0.266601i −0.778744 0.627342i \(-0.784143\pi\)
0.932666 + 0.360741i \(0.117476\pi\)
\(402\) −1569.00 2717.59i −0.194663 0.337167i
\(403\) −4743.50 8215.98i −0.586329 1.01555i
\(404\) −1236.00 + 2140.81i −0.152211 + 0.263637i
\(405\) −486.000 −0.0596285
\(406\) 6300.00 + 2182.38i 0.770108 + 0.266773i
\(407\) 4350.00 0.529783
\(408\) −1008.00 + 1745.91i −0.122312 + 0.211851i
\(409\) 3537.50 + 6127.13i 0.427673 + 0.740751i 0.996666 0.0815915i \(-0.0260003\pi\)
−0.568993 + 0.822342i \(0.692667\pi\)
\(410\) −756.000 1309.43i −0.0910639 0.157727i
\(411\) −4518.00 + 7825.41i −0.542230 + 0.939170i
\(412\) 5900.00 0.705515
\(413\) 3696.00 3200.83i 0.440359 0.381362i
\(414\) −1512.00 −0.179495
\(415\) −2430.00 + 4208.88i −0.287431 + 0.497846i
\(416\) 848.000 + 1468.78i 0.0999438 + 0.173108i
\(417\) 55.5000 + 96.1288i 0.00651762 + 0.0112888i
\(418\) 2910.00 5040.27i 0.340509 0.589779i
\(419\) −4158.00 −0.484801 −0.242400 0.970176i \(-0.577935\pi\)
−0.242400 + 0.970176i \(0.577935\pi\)
\(420\) 1008.00 872.954i 0.117108 0.101419i
\(421\) −6595.00 −0.763469 −0.381735 0.924272i \(-0.624673\pi\)
−0.381735 + 0.924272i \(0.624673\pi\)
\(422\) 1484.00 2570.36i 0.171185 0.296501i
\(423\) 1647.00 + 2852.69i 0.189314 + 0.327902i
\(424\) −3072.00 5320.86i −0.351862 0.609443i
\(425\) −3738.00 + 6474.41i −0.426634 + 0.738953i
\(426\) 2052.00 0.233380
\(427\) 14315.0 + 4958.86i 1.62237 + 0.562005i
\(428\) 7536.00 0.851090
\(429\) 2385.00 4130.94i 0.268412 0.464904i
\(430\) 1950.00 + 3377.50i 0.218692 + 0.378785i
\(431\) −759.000 1314.63i −0.0848254 0.146922i 0.820491 0.571659i \(-0.193700\pi\)
−0.905317 + 0.424737i \(0.860367\pi\)
\(432\) −216.000 + 374.123i −0.0240563 + 0.0416667i
\(433\) 8567.00 0.950817 0.475408 0.879765i \(-0.342300\pi\)
0.475408 + 0.879765i \(0.342300\pi\)
\(434\) 1253.00 + 6510.78i 0.138585 + 0.720109i
\(435\) 3240.00 0.357117
\(436\) −826.000 + 1430.67i −0.0907299 + 0.157149i
\(437\) 4074.00 + 7056.37i 0.445963 + 0.772431i
\(438\) −129.000 223.435i −0.0140727 0.0243747i
\(439\) −5320.00 + 9214.51i −0.578382 + 1.00179i 0.417283 + 0.908777i \(0.362982\pi\)
−0.995665 + 0.0930106i \(0.970351\pi\)
\(440\) −1440.00 −0.156021
\(441\) 441.000 3055.34i 0.0476190 0.329914i
\(442\) 8904.00 0.958190
\(443\) −3516.00 + 6089.89i −0.377088 + 0.653136i −0.990637 0.136520i \(-0.956408\pi\)
0.613549 + 0.789657i \(0.289741\pi\)
\(444\) 870.000 + 1506.88i 0.0929918 + 0.161067i
\(445\) −1800.00 3117.69i −0.191749 0.332119i
\(446\) −2032.00 + 3519.53i −0.215735 + 0.373665i
\(447\) −4932.00 −0.521869
\(448\) −224.000 1163.94i −0.0236228 0.122748i
\(449\) −14814.0 −1.55705 −0.778525 0.627613i \(-0.784032\pi\)
−0.778525 + 0.627613i \(0.784032\pi\)
\(450\) −801.000 + 1387.37i −0.0839100 + 0.145336i
\(451\) 1890.00 + 3273.58i 0.197332 + 0.341789i
\(452\) 1764.00 + 3055.34i 0.183565 + 0.317945i
\(453\) −1632.00 + 2826.71i −0.169267 + 0.293179i
\(454\) −12396.0 −1.28144
\(455\) −5565.00 1927.77i −0.573387 0.198627i
\(456\) 2328.00 0.239076
\(457\) 5625.50 9743.65i 0.575820 0.997350i −0.420132 0.907463i \(-0.638016\pi\)
0.995952 0.0898866i \(-0.0286505\pi\)
\(458\) −4591.00 7951.85i −0.468392 0.811278i
\(459\) 1134.00 + 1964.15i 0.115317 + 0.199735i
\(460\) 1008.00 1745.91i 0.102170 0.176964i
\(461\) −3852.00 −0.389166 −0.194583 0.980886i \(-0.562335\pi\)
−0.194583 + 0.980886i \(0.562335\pi\)
\(462\) −2520.00 + 2182.38i −0.253768 + 0.219770i
\(463\) −475.000 −0.0476784 −0.0238392 0.999716i \(-0.507589\pi\)
−0.0238392 + 0.999716i \(0.507589\pi\)
\(464\) 1440.00 2494.15i 0.144074 0.249543i
\(465\) 1611.00 + 2790.33i 0.160663 + 0.278277i
\(466\) 4530.00 + 7846.19i 0.450318 + 0.779974i
\(467\) −2967.00 + 5138.99i −0.293997 + 0.509217i −0.974751 0.223295i \(-0.928319\pi\)
0.680754 + 0.732512i \(0.261652\pi\)
\(468\) 1908.00 0.188456
\(469\) 7322.00 6341.04i 0.720892 0.624311i
\(470\) −4392.00 −0.431038
\(471\) −759.000 + 1314.63i −0.0742524 + 0.128609i
\(472\) −1056.00 1829.05i −0.102980 0.178366i
\(473\) −4875.00 8443.75i −0.473896 0.820812i
\(474\) −3513.00 + 6084.69i −0.340417 + 0.589619i
\(475\) 8633.00 0.833914
\(476\) −5880.00 2036.89i −0.566196 0.196136i
\(477\) −6912.00 −0.663477
\(478\) 1530.00 2650.04i 0.146403 0.253577i
\(479\) 6684.00 + 11577.0i 0.637578 + 1.10432i 0.985963 + 0.166966i \(0.0533969\pi\)
−0.348385 + 0.937352i \(0.613270\pi\)
\(480\) −288.000 498.831i −0.0273861 0.0474342i
\(481\) 3842.50 6655.41i 0.364247 0.630895i
\(482\) −11068.0 −1.04592
\(483\) −882.000 4583.01i −0.0830898 0.431747i
\(484\) −1724.00 −0.161908
\(485\) 1158.00 2005.71i 0.108417 0.187783i
\(486\) 243.000 + 420.888i 0.0226805 + 0.0392837i
\(487\) −3326.50 5761.67i −0.309524 0.536111i 0.668734 0.743501i \(-0.266836\pi\)
−0.978258 + 0.207390i \(0.933503\pi\)
\(488\) 3272.00 5667.27i 0.303517 0.525708i
\(489\) 5532.00 0.511586
\(490\) 3234.00 + 2546.11i 0.298158 + 0.234738i
\(491\) 15444.0 1.41951 0.709754 0.704450i \(-0.248806\pi\)
0.709754 + 0.704450i \(0.248806\pi\)
\(492\) −756.000 + 1309.43i −0.0692746 + 0.119987i
\(493\) −7560.00 13094.3i −0.690640 1.19622i
\(494\) −5141.00 8904.47i −0.468228 0.810994i
\(495\) −810.000 + 1402.96i −0.0735491 + 0.127391i
\(496\) 2864.00 0.259269
\(497\) 1197.00 + 6219.79i 0.108034 + 0.561360i
\(498\) 4860.00 0.437313
\(499\) −341.500 + 591.495i −0.0306366 + 0.0530641i −0.880937 0.473233i \(-0.843087\pi\)
0.850301 + 0.526297i \(0.176420\pi\)
\(500\) −2568.00 4447.91i −0.229689 0.397833i
\(501\) −243.000 420.888i −0.0216695 0.0375327i
\(502\) −468.000 + 810.600i −0.0416093 + 0.0720694i
\(503\) 9882.00 0.875977 0.437989 0.898980i \(-0.355691\pi\)
0.437989 + 0.898980i \(0.355691\pi\)
\(504\) −1260.00 436.477i −0.111359 0.0385758i
\(505\) −3708.00 −0.326740
\(506\) −2520.00 + 4364.77i −0.221399 + 0.383474i
\(507\) −918.000 1590.02i −0.0804138 0.139281i
\(508\) −4966.00 8601.36i −0.433722 0.751228i
\(509\) −2103.00 + 3642.50i −0.183131 + 0.317193i −0.942945 0.332948i \(-0.891957\pi\)
0.759814 + 0.650141i \(0.225290\pi\)
\(510\) −3024.00 −0.262559
\(511\) 602.000 521.347i 0.0521153 0.0451332i
\(512\) −512.000 −0.0441942
\(513\) 1309.50 2268.12i 0.112701 0.195205i
\(514\) −2490.00 4312.81i −0.213675 0.370097i
\(515\) 4425.00 + 7664.32i 0.378619 + 0.655787i
\(516\) 1950.00 3377.50i 0.166364 0.288151i
\(517\) 10980.0 0.934042
\(518\) −4060.00 + 3516.06i −0.344375 + 0.298237i
\(519\) −8172.00 −0.691158
\(520\) −1272.00 + 2203.17i −0.107271 + 0.185799i
\(521\) −4530.00 7846.19i −0.380927 0.659785i 0.610268 0.792195i \(-0.291062\pi\)
−0.991195 + 0.132410i \(0.957728\pi\)
\(522\) −1620.00 2805.92i −0.135834 0.235272i
\(523\) 7839.50 13578.4i 0.655444 1.13526i −0.326338 0.945253i \(-0.605815\pi\)
0.981782 0.190010i \(-0.0608520\pi\)
\(524\) 8472.00 0.706300
\(525\) −4672.50 1618.60i −0.388428 0.134555i
\(526\) −3144.00 −0.260618
\(527\) 7518.00 13021.6i 0.621422 1.07633i
\(528\) 720.000 + 1247.08i 0.0593447 + 0.102788i
\(529\) 2555.50 + 4426.26i 0.210035 + 0.363792i
\(530\) 4608.00 7981.29i 0.377658 0.654123i
\(531\) −2376.00 −0.194180
\(532\) 1358.00 + 7056.37i 0.110671 + 0.575061i
\(533\) 6678.00 0.542695
\(534\) −1800.00 + 3117.69i −0.145868 + 0.252651i
\(535\) 5652.00 + 9789.55i 0.456743 + 0.791101i
\(536\) −2092.00 3623.45i −0.168583 0.291995i
\(537\) 1881.00 3257.99i 0.151157 0.261811i
\(538\) −3612.00 −0.289451
\(539\) −8085.00 6365.29i −0.646096 0.508668i
\(540\) −648.000 −0.0516398
\(541\) 3855.50 6677.92i 0.306397 0.530696i −0.671174 0.741300i \(-0.734210\pi\)
0.977571 + 0.210604i \(0.0675431\pi\)
\(542\) −6112.00 10586.3i −0.484378 0.838967i
\(543\) 2710.50 + 4694.72i 0.214215 + 0.371031i
\(544\) −1344.00 + 2327.88i −0.105926 + 0.183469i
\(545\) −2478.00 −0.194763
\(546\) 1113.00 + 5783.32i 0.0872381 + 0.453302i
\(547\) 4292.00 0.335489 0.167745 0.985830i \(-0.446352\pi\)
0.167745 + 0.985830i \(0.446352\pi\)
\(548\) −6024.00 + 10433.9i −0.469585 + 0.813345i
\(549\) −3681.00 6375.68i −0.286159 0.495642i
\(550\) 2670.00 + 4624.58i 0.206999 + 0.358532i
\(551\) −8730.00 + 15120.8i −0.674974 + 1.16909i
\(552\) −2016.00 −0.155447
\(553\) −20492.5 7098.81i −1.57582 0.545881i
\(554\) 8462.00 0.648946
\(555\) −1305.00 + 2260.33i −0.0998093 + 0.172875i
\(556\) 74.0000 + 128.172i 0.00564442 + 0.00977643i
\(557\) 4929.00 + 8537.28i 0.374952 + 0.649436i 0.990320 0.138804i \(-0.0443258\pi\)
−0.615368 + 0.788240i \(0.710992\pi\)
\(558\) 1611.00 2790.33i 0.122221 0.211692i
\(559\) −17225.0 −1.30329
\(560\) 1344.00 1163.94i 0.101419 0.0878310i
\(561\) 7560.00 0.568954
\(562\) −3816.00 + 6609.51i −0.286420 + 0.496095i
\(563\) 6945.00 + 12029.1i 0.519888 + 0.900472i 0.999733 + 0.0231188i \(0.00735960\pi\)
−0.479845 + 0.877353i \(0.659307\pi\)
\(564\) 2196.00 + 3803.58i 0.163951 + 0.283971i
\(565\) −2646.00 + 4583.01i −0.197023 + 0.341254i
\(566\) 7994.00 0.593662
\(567\) −1134.00 + 982.073i −0.0839921 + 0.0727393i
\(568\) 2736.00 0.202113
\(569\) −9519.00 + 16487.4i −0.701331 + 1.21474i 0.266669 + 0.963788i \(0.414077\pi\)
−0.967999 + 0.250952i \(0.919256\pi\)
\(570\) 1746.00 + 3024.16i 0.128302 + 0.222225i
\(571\) 4026.50 + 6974.10i 0.295103 + 0.511133i 0.975009 0.222166i \(-0.0713127\pi\)
−0.679906 + 0.733299i \(0.737979\pi\)
\(572\) 3180.00 5507.92i 0.232452 0.402618i
\(573\) 2142.00 0.156166
\(574\) −4410.00 1527.67i −0.320679 0.111087i
\(575\) −7476.00 −0.542210
\(576\) −288.000 + 498.831i −0.0208333 + 0.0360844i
\(577\) 8568.50 + 14841.1i 0.618217 + 1.07078i 0.989811 + 0.142388i \(0.0454781\pi\)
−0.371594 + 0.928395i \(0.621189\pi\)
\(578\) 2143.00 + 3711.78i 0.154216 + 0.267111i
\(579\) 5563.50 9636.26i 0.399328 0.691657i
\(580\) 4320.00 0.309273
\(581\) 2835.00 + 14731.1i 0.202437 + 1.05189i
\(582\) −2316.00 −0.164951
\(583\) −11520.0 + 19953.2i −0.818370 + 1.41746i
\(584\) −172.000 297.913i −0.0121873 0.0211091i
\(585\) 1431.00 + 2478.56i 0.101136 + 0.175173i
\(586\) 4608.00 7981.29i 0.324837 0.562635i
\(587\) 18144.0 1.27578 0.637890 0.770127i \(-0.279807\pi\)
0.637890 + 0.770127i \(0.279807\pi\)
\(588\) 588.000 4073.78i 0.0412393 0.285714i
\(589\) −17363.0 −1.21465
\(590\) 1584.00 2743.57i 0.110529 0.191442i
\(591\) 1566.00 + 2712.39i 0.108996 + 0.188787i
\(592\) 1160.00 + 2009.18i 0.0805333 + 0.139488i
\(593\) 12351.0 21392.6i 0.855303 1.48143i −0.0210603 0.999778i \(-0.506704\pi\)
0.876363 0.481650i \(-0.159962\pi\)
\(594\) 1620.00 0.111901
\(595\) −1764.00 9166.01i −0.121541 0.631546i
\(596\) −6576.00 −0.451952
\(597\) 204.000 353.338i 0.0139852 0.0242231i
\(598\) 4452.00 + 7711.09i 0.304441 + 0.527308i
\(599\) 1086.00 + 1881.01i 0.0740781 + 0.128307i 0.900685 0.434473i \(-0.143065\pi\)
−0.826607 + 0.562780i \(0.809732\pi\)
\(600\) −1068.00 + 1849.83i −0.0726682 + 0.125865i
\(601\) 4175.00 0.283364 0.141682 0.989912i \(-0.454749\pi\)
0.141682 + 0.989912i \(0.454749\pi\)
\(602\) 11375.0 + 3940.42i 0.770117 + 0.266776i
\(603\) −4707.00 −0.317884
\(604\) −2176.00 + 3768.94i −0.146590 + 0.253901i
\(605\) −1293.00 2239.54i −0.0868891 0.150496i
\(606\) 1854.00 + 3211.22i 0.124280 + 0.215259i
\(607\) −1130.50 + 1958.08i −0.0755940 + 0.130933i −0.901344 0.433103i \(-0.857419\pi\)
0.825750 + 0.564036i \(0.190752\pi\)
\(608\) 3104.00 0.207046
\(609\) 7560.00 6547.15i 0.503032 0.435639i
\(610\) 9816.00 0.651538
\(611\) 9699.00 16799.2i 0.642192 1.11231i
\(612\) 1512.00 + 2618.86i 0.0998676 + 0.172976i
\(613\) 8159.00 + 14131.8i 0.537584 + 0.931123i 0.999033 + 0.0439561i \(0.0139962\pi\)
−0.461450 + 0.887166i \(0.652670\pi\)
\(614\) −631.000 + 1092.92i −0.0414741 + 0.0718352i
\(615\) −2268.00 −0.148707
\(616\) −3360.00 + 2909.85i −0.219770 + 0.190326i
\(617\) −26550.0 −1.73235 −0.866177 0.499737i \(-0.833430\pi\)
−0.866177 + 0.499737i \(0.833430\pi\)
\(618\) 4425.00 7664.32i 0.288025 0.498874i
\(619\) −9962.50 17255.6i −0.646893 1.12045i −0.983861 0.178935i \(-0.942735\pi\)
0.336968 0.941516i \(-0.390599\pi\)
\(620\) 2148.00 + 3720.45i 0.139138 + 0.240995i
\(621\) −1134.00 + 1964.15i −0.0732783 + 0.126922i
\(622\) −7788.00 −0.502042
\(623\) −10500.0 3637.31i −0.675239 0.233909i
\(624\) 2544.00 0.163208
\(625\) −1710.50 + 2962.67i −0.109472 + 0.189611i
\(626\) −2185.00 3784.53i −0.139505 0.241630i
\(627\) −4365.00 7560.40i −0.278024 0.481552i
\(628\) −1012.00 + 1752.84i −0.0643045 + 0.111379i
\(629\) 12180.0 0.772096
\(630\) −378.000 1964.15i −0.0239046 0.124212i
\(631\) −6832.00 −0.431026 −0.215513 0.976501i \(-0.569142\pi\)
−0.215513 + 0.976501i \(0.569142\pi\)
\(632\) −4684.00 + 8112.93i −0.294809 + 0.510625i
\(633\) −2226.00 3855.55i −0.139772 0.242092i
\(634\) 3504.00 + 6069.11i 0.219498 + 0.380181i
\(635\) 7449.00 12902.0i 0.465519 0.806303i
\(636\) −9216.00 −0.574588
\(637\) −16880.5 + 6747.20i −1.04997 + 0.419677i
\(638\) −10800.0 −0.670182
\(639\) 1539.00 2665.63i 0.0952768 0.165024i
\(640\) −384.000 665.108i −0.0237171 0.0410792i
\(641\) −5106.00 8843.85i −0.314625 0.544947i 0.664732 0.747082i \(-0.268546\pi\)
−0.979358 + 0.202134i \(0.935212\pi\)
\(642\) 5652.00 9789.55i 0.347456 0.601811i
\(643\) 3779.00 0.231772 0.115886 0.993263i \(-0.463029\pi\)
0.115886 + 0.993263i \(0.463029\pi\)
\(644\) −1176.00 6110.68i −0.0719579 0.373904i
\(645\) 5850.00 0.357122
\(646\) 8148.00 14112.7i 0.496252 0.859534i
\(647\) −8499.00 14720.7i −0.516430 0.894483i −0.999818 0.0190767i \(-0.993927\pi\)
0.483388 0.875406i \(-0.339406\pi\)
\(648\) 324.000 + 561.184i 0.0196419 + 0.0340207i
\(649\) −3960.00 + 6858.92i −0.239512 + 0.414848i
\(650\) 9434.00 0.569280
\(651\) 9397.50 + 3255.39i 0.565771 + 0.195989i
\(652\) 7376.00 0.443047
\(653\) 10875.0 18836.1i 0.651718 1.12881i −0.330988 0.943635i \(-0.607382\pi\)
0.982706 0.185173i \(-0.0592846\pi\)
\(654\) 1239.00 + 2146.01i 0.0740806 + 0.128311i
\(655\) 6354.00 + 11005.5i 0.379040 + 0.656517i
\(656\) −1008.00 + 1745.91i −0.0599936 + 0.103912i
\(657\) −387.000 −0.0229807
\(658\) −10248.0 + 8875.03i −0.607156 + 0.525813i
\(659\) −10944.0 −0.646916 −0.323458 0.946243i \(-0.604845\pi\)
−0.323458 + 0.946243i \(0.604845\pi\)
\(660\) −1080.00 + 1870.61i −0.0636954 + 0.110324i
\(661\) −5477.50 9487.31i −0.322315 0.558266i 0.658650 0.752449i \(-0.271128\pi\)
−0.980965 + 0.194184i \(0.937794\pi\)
\(662\) 2945.00 + 5100.89i 0.172901 + 0.299474i
\(663\) 6678.00 11566.6i 0.391180 0.677543i
\(664\) 6480.00 0.378724
\(665\) −8148.00 + 7056.37i −0.475137 + 0.411480i
\(666\) 2610.00 0.151855
\(667\) 7560.00 13094.3i 0.438867 0.760140i
\(668\) −324.000 561.184i −0.0187664 0.0325043i
\(669\) 3048.00 + 5279.29i 0.176147 + 0.305096i
\(670\) 3138.00 5435.18i 0.180943 0.313402i
\(671\) −24540.0 −1.41186
\(672\) −1680.00 581.969i −0.0964396 0.0334077i
\(673\) 25103.0 1.43782 0.718908 0.695106i \(-0.244642\pi\)
0.718908 + 0.695106i \(0.244642\pi\)
\(674\) 4277.00 7407.98i 0.244427 0.423360i
\(675\) 1201.50 + 2081.06i 0.0685122 + 0.118667i
\(676\) −1224.00 2120.03i −0.0696404 0.120621i
\(677\) 2802.00 4853.21i 0.159069 0.275515i −0.775464 0.631391i \(-0.782484\pi\)
0.934533 + 0.355876i \(0.115817\pi\)
\(678\) 5292.00 0.299761
\(679\) −1351.00 7020.00i −0.0763573 0.396764i
\(680\) −4032.00 −0.227383
\(681\) −9297.00 + 16102.9i −0.523145 + 0.906114i
\(682\) −5370.00 9301.11i −0.301507 0.522226i
\(683\) −5484.00 9498.57i −0.307232 0.532141i 0.670524 0.741888i \(-0.266069\pi\)
−0.977756 + 0.209747i \(0.932736\pi\)
\(684\) 1746.00 3024.16i 0.0976023 0.169052i
\(685\) −18072.0 −1.00802
\(686\) 12691.0 594.093i 0.706333 0.0330650i
\(687\) −13773.0 −0.764880
\(688\) 2600.00 4503.33i 0.144076 0.249546i
\(689\) 20352.0 + 35250.7i 1.12533 + 1.94912i
\(690\) −1512.00 2618.86i −0.0834215 0.144490i
\(691\) −4202.50 + 7278.94i −0.231361 + 0.400729i −0.958209 0.286069i \(-0.907651\pi\)
0.726848 + 0.686799i \(0.240985\pi\)
\(692\) −10896.0 −0.598560
\(693\) 945.000 + 4910.36i 0.0518003 + 0.269162i
\(694\) −14376.0 −0.786319
\(695\) −111.000 + 192.258i −0.00605823 + 0.0104932i
\(696\) −2160.00 3741.23i −0.117636 0.203751i
\(697\) 5292.00 + 9166.01i 0.287588 + 0.498117i
\(698\) −9406.00 + 16291.7i −0.510061 + 0.883451i
\(699\) 13590.0 0.735366
\(700\) −6230.00 2158.14i −0.336388 0.116528i
\(701\) 468.000 0.0252156 0.0126078 0.999921i \(-0.495987\pi\)
0.0126078 + 0.999921i \(0.495987\pi\)
\(702\) 1431.00 2478.56i 0.0769368 0.133258i
\(703\) −7032.50 12180.6i −0.377291 0.653488i
\(704\) 960.000 + 1662.77i 0.0513940 + 0.0890170i
\(705\) −3294.00 + 5705.38i −0.175971 + 0.304790i
\(706\) −6780.00 −0.361429
\(707\) −8652.00 + 7492.85i −0.460243 + 0.398582i
\(708\) −3168.00 −0.168165
\(709\) 12533.0 21707.8i 0.663874 1.14986i −0.315715 0.948854i \(-0.602244\pi\)
0.979589 0.201010i \(-0.0644222\pi\)
\(710\) 2052.00 + 3554.17i 0.108465 + 0.187867i
\(711\) 5269.50 + 9127.04i 0.277949 + 0.481422i
\(712\) −2400.00 + 4156.92i −0.126326 + 0.218802i
\(713\) 15036.0 0.789765
\(714\) −7056.00 + 6110.68i −0.369838 + 0.320289i
\(715\) 9540.00 0.498987
\(716\) 2508.00 4343.98i 0.130906 0.226735i
\(717\) −2295.00 3975.06i −0.119537 0.207045i
\(718\) −4812.00 8334.63i −0.250115 0.433211i
\(719\) −5541.00 + 9597.29i −0.287405 + 0.497801i −0.973190 0.230004i \(-0.926126\pi\)
0.685784 + 0.727805i \(0.259459\pi\)
\(720\) −864.000 −0.0447214
\(721\) 25812.5 + 8941.71i 1.33330 + 0.461868i
\(722\) −5100.00 −0.262884
\(723\) −8301.00 + 14377.8i −0.426995 + 0.739577i
\(724\) 3614.00 + 6259.63i 0.185516 + 0.321322i
\(725\) −8010.00 13873.7i −0.410323 0.710700i
\(726\) −1293.00 + 2239.54i −0.0660988 + 0.114486i
\(727\) 13481.0 0.687734 0.343867 0.939018i \(-0.388263\pi\)
0.343867 + 0.939018i \(0.388263\pi\)
\(728\) 1484.00 + 7711.09i 0.0755504 + 0.392571i
\(729\) 729.000 0.0370370
\(730\) 258.000 446.869i 0.0130808 0.0226567i
\(731\) −13650.0 23642.5i −0.690648 1.19624i
\(732\) −4908.00 8500.91i −0.247821 0.429238i
\(733\) −12158.5 + 21059.1i −0.612666 + 1.06117i 0.378123 + 0.925755i \(0.376570\pi\)
−0.990789 + 0.135414i \(0.956764\pi\)
\(734\) 14198.0 0.713975
\(735\) 5733.00 2291.50i 0.287707 0.114998i
\(736\) −2688.00 −0.134621
\(737\) −7845.00 + 13587.9i −0.392095 + 0.679129i
\(738\) 1134.00 + 1964.15i 0.0565625 + 0.0979691i
\(739\) 9108.50 + 15776.4i 0.453399 + 0.785309i 0.998595 0.0529992i \(-0.0168781\pi\)
−0.545196 + 0.838309i \(0.683545\pi\)
\(740\) −1740.00 + 3013.77i −0.0864374 + 0.149714i
\(741\) −15423.0 −0.764613
\(742\) −5376.00 27934.5i −0.265983 1.38209i
\(743\) 19782.0 0.976758 0.488379 0.872632i \(-0.337588\pi\)
0.488379 + 0.872632i \(0.337588\pi\)
\(744\) 2148.00 3720.45i 0.105846 0.183331i
\(745\) −4932.00 8542.47i −0.242543 0.420097i
\(746\) 2963.00 + 5132.07i 0.145420 + 0.251874i
\(747\) 3645.00 6313.33i 0.178532 0.309227i
\(748\) 10080.0 0.492729
\(749\) 32970.0 + 11421.1i 1.60841 + 0.557169i
\(750\) −7704.00 −0.375080
\(751\) 2460.50 4261.71i 0.119554 0.207073i −0.800037 0.599951i \(-0.795187\pi\)
0.919591 + 0.392877i \(0.128520\pi\)
\(752\) 2928.00 + 5071.44i 0.141986 + 0.245926i
\(753\) 702.000 + 1215.90i 0.0339738 + 0.0588444i
\(754\) −9540.00 + 16523.8i −0.460778 + 0.798090i
\(755\) −6528.00 −0.314673
\(756\) −1512.00 + 1309.43i −0.0727393 + 0.0629941i
\(757\) 18098.0 0.868934 0.434467 0.900688i \(-0.356937\pi\)
0.434467 + 0.900688i \(0.356937\pi\)
\(758\) −11899.0 + 20609.7i −0.570173 + 0.987569i
\(759\) 3780.00 + 6547.15i 0.180771 + 0.313105i
\(760\) 2328.00 + 4032.21i 0.111112 + 0.192452i
\(761\) 12234.0 21189.9i 0.582762 1.00937i −0.412388 0.911008i \(-0.635305\pi\)
0.995150 0.0983657i \(-0.0313615\pi\)
\(762\) −14898.0 −0.708265
\(763\) −5782.00 + 5007.36i −0.274341 + 0.237587i
\(764\) 2856.00 0.135244
\(765\) −2268.00 + 3928.29i −0.107189 + 0.185657i
\(766\) 2568.00 + 4447.91i 0.121130 + 0.209803i
\(767\) 6996.00 + 12117.4i 0.329349 + 0.570450i
\(768\) −384.000 + 665.108i −0.0180422 + 0.0312500i
\(769\) 21719.0 1.01847 0.509237 0.860626i \(-0.329928\pi\)
0.509237 + 0.860626i \(0.329928\pi\)
\(770\) −6300.00 2182.38i −0.294852 0.102140i
\(771\) −7470.00 −0.348931
\(772\) 7418.00 12848.4i 0.345829 0.598993i
\(773\) 15153.0 + 26245.8i 0.705065 + 1.22121i 0.966668 + 0.256033i \(0.0824157\pi\)
−0.261603 + 0.965176i \(0.584251\pi\)
\(774\) −2925.00 5066.25i −0.135836 0.235275i
\(775\) 7965.50 13796.7i 0.369199 0.639471i
\(776\) −3088.00 −0.142851
\(777\) 1522.50 + 7911.14i 0.0702952 + 0.365265i
\(778\) 20292.0 0.935094
\(779\) 6111.00 10584.6i 0.281065 0.486818i
\(780\) 1908.00 + 3304.75i 0.0875864 + 0.151704i
\(781\) −5130.00 8885.42i −0.235039 0.407100i
\(782\) −7056.00 + 12221.4i −0.322662 + 0.558868i
\(783\) −4860.00 −0.221816
\(784\) 784.000 5431.71i 0.0357143 0.247436i
\(785\) −3036.00 −0.138038
\(786\) 6354.00 11005.5i 0.288346 0.499429i
\(787\) −13648.0 23639.0i −0.618169 1.07070i −0.989820 0.142327i \(-0.954542\pi\)
0.371651 0.928372i \(-0.378792\pi\)
\(788\) 2088.00 + 3616.52i 0.0943933 + 0.163494i
\(789\) −2358.00 + 4084.18i −0.106397 + 0.184285i
\(790\) −14052.0 −0.632845
\(791\) 3087.00 + 16040.5i 0.138762 + 0.721031i
\(792\) 2160.00 0.0969094
\(793\) −21677.0 + 37545.7i −0.970710 + 1.68132i
\(794\) −6229.00 10788.9i −0.278412 0.482223i
\(795\) −6912.00 11971.9i −0.308356 0.534089i
\(796\) 272.000 471.118i 0.0121115 0.0209778i
\(797\) −35100.0 −1.55998 −0.779991 0.625791i \(-0.784776\pi\)
−0.779991 + 0.625791i \(0.784776\pi\)
\(798\) 10185.0 + 3528.19i 0.451811 + 0.156512i
\(799\) 30744.0 1.36126
\(800\) −1424.00 + 2466.44i −0.0629325 + 0.109002i
\(801\) 2700.00 + 4676.54i 0.119101 + 0.206289i
\(802\) −2472.00 4281.63i −0.108840 0.188516i
\(803\) −645.000 + 1117.17i −0.0283456 + 0.0490961i
\(804\) −6276.00 −0.275295
\(805\) 7056.00 6110.68i 0.308933 0.267544i
\(806\) −18974.0 −0.829194
\(807\) −2709.00 + 4692.13i −0.118168 + 0.204672i
\(808\) 2472.00 + 4281.63i 0.107630 + 0.186420i
\(809\) −22197.0 38446.3i −0.964654 1.67083i −0.710542 0.703655i \(-0.751550\pi\)
−0.254112 0.967175i \(-0.581783\pi\)
\(810\) −486.000 + 841.777i −0.0210819 + 0.0365148i
\(811\) −8584.00 −0.371671 −0.185835 0.982581i \(-0.559499\pi\)
−0.185835 + 0.982581i \(0.559499\pi\)
\(812\) 10080.0 8729.54i 0.435639 0.377274i
\(813\) −18336.0 −0.790986
\(814\) 4350.00 7534.42i 0.187306 0.324424i
\(815\) 5532.00 + 9581.71i 0.237764 + 0.411819i
\(816\) 2016.00 + 3491.81i 0.0864879 + 0.149801i
\(817\) −15762.5 + 27301.5i −0.674982 + 1.16910i
\(818\) 14150.0 0.604820
\(819\) 8347.50 + 2891.66i 0.356148 + 0.123373i
\(820\) −3024.00 −0.128784
\(821\) 4917.00 8516.49i 0.209019 0.362031i −0.742387 0.669971i \(-0.766306\pi\)
0.951406 + 0.307940i \(0.0996397\pi\)
\(822\) 9036.00 + 15650.8i 0.383414 + 0.664093i
\(823\) −21928.0 37980.4i −0.928751 1.60864i −0.785415 0.618970i \(-0.787550\pi\)
−0.143336 0.989674i \(-0.545783\pi\)
\(824\) 5900.00 10219.1i 0.249437 0.432038i
\(825\) 8010.00 0.338027
\(826\) −1848.00 9602.49i −0.0778452 0.404496i
\(827\) 13266.0 0.557804 0.278902 0.960320i \(-0.410030\pi\)
0.278902 + 0.960320i \(0.410030\pi\)
\(828\) −1512.00 + 2618.86i −0.0634609 + 0.109918i
\(829\) −8726.50 15114.7i −0.365602 0.633241i 0.623271 0.782006i \(-0.285803\pi\)
−0.988873 + 0.148765i \(0.952470\pi\)
\(830\) 4860.00 + 8417.77i 0.203245 + 0.352030i
\(831\) 6346.50 10992.5i 0.264931 0.458874i
\(832\) 3392.00 0.141342
\(833\) −22638.0 17822.8i −0.941609 0.741325i
\(834\) 222.000 0.00921730
\(835\) 486.000 841.777i 0.0201422 0.0348873i
\(836\) −5820.00 10080.5i −0.240776 0.417037i
\(837\) −2416.50 4185.50i −0.0997927 0.172846i
\(838\) −4158.00 + 7201.87i −0.171403 + 0.296879i
\(839\) −35172.0 −1.44729 −0.723643 0.690175i \(-0.757534\pi\)
−0.723643 + 0.690175i \(0.757534\pi\)
\(840\) −504.000 2618.86i −0.0207020 0.107571i
\(841\) 8011.00 0.328468
\(842\) −6595.00 + 11422.9i −0.269927 + 0.467528i
\(843\) 5724.00 + 9914.26i 0.233861 + 0.405060i
\(844\) −2968.00 5140.73i −0.121046 0.209658i
\(845\) 1836.00 3180.05i 0.0747459 0.129464i
\(846\) 6588.00 0.267731
\(847\) −7542.50 2612.80i −0.305978 0.105994i
\(848\) −12288.0 −0.497608
\(849\) 5995.50 10384.5i 0.242362 0.419783i
\(850\) 7476.00 + 12948.8i 0.301676 + 0.522518i
\(851\) 6090.00 + 10548.2i 0.245314 + 0.424897i
\(852\) 2052.00 3554.17i 0.0825122 0.142915i
\(853\) 3503.00 0.140610 0.0703051 0.997526i \(-0.477603\pi\)
0.0703051 + 0.997526i \(0.477603\pi\)
\(854\) 22904.0 19835.4i 0.917750 0.794795i
\(855\) 5238.00 0.209516
\(856\) 7536.00 13052.7i 0.300906 0.521184i
\(857\) −11424.0 19786.9i −0.455352 0.788692i 0.543357 0.839502i \(-0.317153\pi\)
−0.998708 + 0.0508097i \(0.983820\pi\)
\(858\) −4770.00 8261.88i −0.189796 0.328737i
\(859\) 6728.00 11653.2i 0.267237 0.462868i −0.700910 0.713249i \(-0.747223\pi\)
0.968147 + 0.250382i \(0.0805561\pi\)
\(860\) 7800.00 0.309277
\(861\) −5292.00 + 4583.01i −0.209467 + 0.181404i
\(862\) −3036.00 −0.119961
\(863\) −20355.0 + 35255.9i −0.802888 + 1.39064i 0.114820 + 0.993386i \(0.463371\pi\)
−0.917708 + 0.397256i \(0.869962\pi\)
\(864\) 432.000 + 748.246i 0.0170103 + 0.0294628i
\(865\) −8172.00 14154.3i −0.321221 0.556371i
\(866\) 8567.00 14838.5i 0.336165 0.582254i
\(867\) 6429.00 0.251834
\(868\) 12530.0 + 4340.52i 0.489972 + 0.169731i
\(869\) 35130.0 1.37135
\(870\) 3240.00 5611.84i 0.126260 0.218689i
\(871\) 13859.5 + 24005.4i 0.539163 + 0.933858i
\(872\) 1652.00 + 2861.35i 0.0641557 + 0.111121i
\(873\) −1737.00 + 3008.57i −0.0673408 + 0.116638i
\(874\) 16296.0 0.630687
\(875\) −4494.00 23351.5i −0.173628 0.902200i
\(876\) −516.000 −0.0199019
\(877\) −1453.00 + 2516.67i −0.0559456 + 0.0969007i −0.892642 0.450767i \(-0.851151\pi\)
0.836696 + 0.547667i \(0.184484\pi\)
\(878\) 10640.0 + 18429.0i 0.408978 + 0.708371i
\(879\) −6912.00 11971.9i −0.265229 0.459389i
\(880\) −1440.00 + 2494.15i −0.0551618 + 0.0955431i
\(881\) −19188.0 −0.733780 −0.366890 0.930264i \(-0.619577\pi\)
−0.366890 + 0.930264i \(0.619577\pi\)
\(882\) −4851.00 3819.17i −0.185195 0.145803i
\(883\) −17251.0 −0.657466 −0.328733 0.944423i \(-0.606622\pi\)
−0.328733 + 0.944423i \(0.606622\pi\)
\(884\) 8904.00 15422.2i 0.338771 0.586769i
\(885\) −2376.00 4115.35i −0.0902467 0.156312i
\(886\) 7032.00 + 12179.8i 0.266642 + 0.461837i
\(887\) 1047.00 1813.46i 0.0396334 0.0686471i −0.845528 0.533931i \(-0.820714\pi\)
0.885162 + 0.465284i \(0.154048\pi\)
\(888\) 3480.00 0.131510
\(889\) −8690.50 45157.2i −0.327863 1.70362i
\(890\) −7200.00 −0.271174
\(891\) 1215.00 2104.44i 0.0456835 0.0791262i
\(892\) 4064.00 + 7039.05i 0.152548 + 0.264221i
\(893\) −17751.0 30745.6i −0.665190 1.15214i
\(894\) −4932.00 + 8542.47i −0.184509 + 0.319578i
\(895\) 7524.00 0.281005
\(896\) −2240.00 775.959i −0.0835191 0.0289319i
\(897\) 13356.0 0.497150
\(898\) −14814.0 + 25658.6i −0.550501 + 0.953495i
\(899\) 16110.0 + 27903.3i 0.597662 + 1.03518i
\(900\) 1602.00 + 2774.75i 0.0593333 + 0.102768i
\(901\) −32256.0 + 55869.0i −1.19268 + 2.06578i
\(902\) 7560.00 0.279069
\(903\) 13650.0 11821.2i 0.503038 0.435644i
\(904\) 7056.00 0.259601
\(905\) −5421.00 + 9389.45i −0.199116 + 0.344879i
\(906\) 3264.00 + 5653.41i 0.119690 + 0.207309i
\(907\) 20133.5 + 34872.2i 0.737069 + 1.27664i 0.953809 + 0.300412i \(0.0971242\pi\)
−0.216740 + 0.976229i \(0.569542\pi\)
\(908\) −12396.0 + 21470.5i −0.453057 + 0.784718i
\(909\) 5562.00 0.202948
\(910\) −8904.00 + 7711.09i −0.324357 + 0.280901i
\(911\) 17604.0 0.640227 0.320113 0.947379i \(-0.396279\pi\)
0.320113 + 0.947379i \(0.396279\pi\)
\(912\) 2328.00 4032.21i 0.0845261 0.146403i
\(913\) −12150.0 21044.4i −0.440423 0.762835i
\(914\) −11251.0 19487.3i −0.407166 0.705233i
\(915\) 7362.00 12751.4i 0.265989 0.460707i
\(916\) −18364.0 −0.662406
\(917\) 37065.0 + 12839.7i 1.33478 + 0.462382i
\(918\) 4536.00 0.163083
\(919\) −1754.50 + 3038.88i −0.0629767 + 0.109079i −0.895795 0.444468i \(-0.853393\pi\)
0.832818 + 0.553547i \(0.186726\pi\)
\(920\) −2016.00 3491.81i −0.0722452 0.125132i
\(921\) 946.500 + 1639.39i 0.0338634 + 0.0586532i
\(922\) −3852.00 + 6671.86i −0.137591 + 0.238315i
\(923\) −18126.0 −0.646397
\(924\) 1260.00 + 6547.15i 0.0448603 + 0.233101i
\(925\) 12905.0 0.458718
\(926\) −475.000 + 822.724i −0.0168569 + 0.0291970i
\(927\) −6637.50 11496.5i −0.235172 0.407329i
\(928\) −2880.00 4988.31i −0.101876 0.176454i
\(929\) 17319.0 29997.4i 0.611645 1.05940i −0.379319 0.925266i \(-0.623842\pi\)
0.990963 0.134134i \(-0.0428251\pi\)
\(930\) 6444.00 0.227212
\(931\) −4753.00 + 32929.7i −0.167318 + 1.15921i
\(932\) 18120.0 0.636846
\(933\) −5841.00 + 10116.9i −0.204958 + 0.354998i
\(934\) 5934.00 + 10278.0i 0.207887 + 0.360071i
\(935\) 7560.00 + 13094.3i 0.264426 + 0.458000i
\(936\) 1908.00 3304.75i 0.0666292 0.115405i
\(937\) −17353.0 −0.605014 −0.302507 0.953147i \(-0.597824\pi\)
−0.302507 + 0.953147i \(0.597824\pi\)
\(938\) −3661.00 19023.1i −0.127437 0.662182i
\(939\) −6555.00 −0.227811
\(940\) −4392.00 + 7607.17i −0.152395 + 0.263956i
\(941\) 23460.0 + 40633.9i 0.812725 + 1.40768i 0.910950 + 0.412517i \(0.135350\pi\)
−0.0982252 + 0.995164i \(0.531317\pi\)
\(942\) 1518.00 + 2629.25i 0.0525044 + 0.0909402i
\(943\) −5292.00 + 9166.01i −0.182748 + 0.316529i
\(944\) −4224.00 −0.145635
\(945\) −2835.00 982.073i −0.0975900 0.0338062i
\(946\) −19500.0 −0.670190
\(947\) −9177.00 + 15895.0i −0.314902 + 0.545427i −0.979417 0.201849i \(-0.935305\pi\)
0.664514 + 0.747275i \(0.268638\pi\)
\(948\) 7026.00 + 12169.4i 0.240711 + 0.416923i
\(949\) 1139.50 + 1973.67i 0.0389776 + 0.0675112i
\(950\) 8633.00 14952.8i 0.294833 0.510666i
\(951\) 10512.0 0.358438
\(952\) −9408.00 + 8147.57i −0.320289 + 0.277378i
\(953\) 35568.0 1.20898 0.604491 0.796612i \(-0.293376\pi\)
0.604491 + 0.796612i \(0.293376\pi\)
\(954\) −6912.00 + 11971.9i −0.234575 + 0.406295i
\(955\) 2142.00 + 3710.05i 0.0725796 + 0.125712i
\(956\) −3060.00 5300.08i −0.103522 0.179306i
\(957\) −8100.00 + 14029.6i −0.273601 + 0.473890i
\(958\) 26736.0 0.901671
\(959\) −42168.0 + 36518.6i −1.41989 + 1.22966i
\(960\) −1152.00 −0.0387298
\(961\) −1125.00 + 1948.56i −0.0377631 + 0.0654076i
\(962\) −7685.00 13310.8i −0.257562 0.446110i
\(963\) −8478.00 14684.3i −0.283697 0.491377i
\(964\) −11068.0 + 19170.3i −0.369789 + 0.640493i
\(965\) 22254.0 0.742364
\(966\) −8820.00 3055.34i −0.293767 0.101764i
\(967\) −27343.0 −0.909298 −0.454649 0.890671i \(-0.650235\pi\)
−0.454649 + 0.890671i \(0.650235\pi\)
\(968\) −1724.00 + 2986.06i −0.0572432 + 0.0991482i
\(969\) −12222.0 21169.1i −0.405188 0.701806i
\(970\) −2316.00 4011.43i −0.0766621 0.132783i
\(971\) −25512.0 + 44188.1i −0.843171 + 1.46042i 0.0440291 + 0.999030i \(0.485981\pi\)
−0.887200 + 0.461385i \(0.847353\pi\)
\(972\) 972.000 0.0320750
\(973\) 129.500 + 672.902i 0.00426678 + 0.0221709i
\(974\) −13306.0 −0.437733
\(975\) 7075.50 12255.1i 0.232408 0.402542i
\(976\) −6544.00 11334.5i −0.214619 0.371731i
\(977\) 1113.00 + 1927.77i 0.0364463 + 0.0631268i 0.883673 0.468104i \(-0.155063\pi\)
−0.847227 + 0.531231i \(0.821730\pi\)
\(978\) 5532.00 9581.71i 0.180873 0.313281i
\(979\) 18000.0 0.587623
\(980\) 7644.00 3055.34i 0.249162 0.0995910i
\(981\) 3717.00 0.120973
\(982\) 15444.0 26749.8i 0.501872 0.869267i
\(983\) −17652.0 30574.2i −0.572748 0.992029i −0.996282 0.0861487i \(-0.972544\pi\)
0.423534 0.905880i \(-0.360789\pi\)
\(984\) 1512.00 + 2618.86i 0.0489846 + 0.0848437i
\(985\) −3132.00 + 5424.78i −0.101314 + 0.175480i
\(986\) −30240.0 −0.976712
\(987\) 3843.00 + 19968.8i 0.123935 + 0.643986i
\(988\) −20564.0 −0.662174
\(989\) 13650.0 23642.5i 0.438872 0.760149i
\(990\) 1620.00 + 2805.92i 0.0520071 + 0.0900789i
\(991\) 1170.50 + 2027.37i 0.0375198 + 0.0649863i 0.884176 0.467155i \(-0.154721\pi\)
−0.846656 + 0.532141i \(0.821388\pi\)
\(992\) 2864.00 4960.59i 0.0916654 0.158769i
\(993\) 8835.00 0.282347
\(994\) 11970.0 + 4146.53i 0.381957 + 0.132314i
\(995\) 816.000 0.0259989
\(996\) 4860.00 8417.77i 0.154613 0.267798i
\(997\) −14507.5 25127.7i −0.460840 0.798198i 0.538163 0.842841i \(-0.319118\pi\)
−0.999003 + 0.0446429i \(0.985785\pi\)
\(998\) 683.000 + 1182.99i 0.0216633 + 0.0375220i
\(999\) 1957.50 3390.49i 0.0619946 0.107378i
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 42.4.e.a.37.1 yes 2
3.2 odd 2 126.4.g.b.37.1 2
4.3 odd 2 336.4.q.f.289.1 2
7.2 even 3 294.4.a.d.1.1 1
7.3 odd 6 294.4.e.i.67.1 2
7.4 even 3 inner 42.4.e.a.25.1 2
7.5 odd 6 294.4.a.c.1.1 1
7.6 odd 2 294.4.e.i.79.1 2
21.2 odd 6 882.4.a.o.1.1 1
21.5 even 6 882.4.a.l.1.1 1
21.11 odd 6 126.4.g.b.109.1 2
21.17 even 6 882.4.g.g.361.1 2
21.20 even 2 882.4.g.g.667.1 2
28.11 odd 6 336.4.q.f.193.1 2
28.19 even 6 2352.4.a.bf.1.1 1
28.23 odd 6 2352.4.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.a.25.1 2 7.4 even 3 inner
42.4.e.a.37.1 yes 2 1.1 even 1 trivial
126.4.g.b.37.1 2 3.2 odd 2
126.4.g.b.109.1 2 21.11 odd 6
294.4.a.c.1.1 1 7.5 odd 6
294.4.a.d.1.1 1 7.2 even 3
294.4.e.i.67.1 2 7.3 odd 6
294.4.e.i.79.1 2 7.6 odd 2
336.4.q.f.193.1 2 28.11 odd 6
336.4.q.f.289.1 2 4.3 odd 2
882.4.a.l.1.1 1 21.5 even 6
882.4.a.o.1.1 1 21.2 odd 6
882.4.g.g.361.1 2 21.17 even 6
882.4.g.g.667.1 2 21.20 even 2
2352.4.a.f.1.1 1 28.23 odd 6
2352.4.a.bf.1.1 1 28.19 even 6