Properties

Label 42.4.e.b.25.1
Level $42$
Weight $4$
Character 42.25
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 25.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 42.25
Dual form 42.4.e.b.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(7.50000 + 12.9904i) q^{5} +6.00000 q^{6} +(17.5000 - 6.06218i) q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-15.0000 + 25.9808i) q^{10} +(4.50000 - 7.79423i) q^{11} +(6.00000 + 10.3923i) q^{12} -88.0000 q^{13} +(28.0000 + 24.2487i) q^{14} +45.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} +(42.0000 - 72.7461i) q^{17} +(9.00000 - 15.5885i) q^{18} +(-52.0000 - 90.0666i) q^{19} -60.0000 q^{20} +(10.5000 - 54.5596i) q^{21} +18.0000 q^{22} +(42.0000 + 72.7461i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-50.0000 + 86.6025i) q^{25} +(-88.0000 - 152.420i) q^{26} -27.0000 q^{27} +(-14.0000 + 72.7461i) q^{28} +51.0000 q^{29} +(45.0000 + 77.9423i) q^{30} +(-92.5000 + 160.215i) q^{31} +(16.0000 - 27.7128i) q^{32} +(-13.5000 - 23.3827i) q^{33} +168.000 q^{34} +(210.000 + 181.865i) q^{35} +36.0000 q^{36} +(-22.0000 - 38.1051i) q^{37} +(104.000 - 180.133i) q^{38} +(-132.000 + 228.631i) q^{39} +(-60.0000 - 103.923i) q^{40} -168.000 q^{41} +(105.000 - 36.3731i) q^{42} +326.000 q^{43} +(18.0000 + 31.1769i) q^{44} +(67.5000 - 116.913i) q^{45} +(-84.0000 + 145.492i) q^{46} +(69.0000 + 119.512i) q^{47} -48.0000 q^{48} +(269.500 - 212.176i) q^{49} -200.000 q^{50} +(-126.000 - 218.238i) q^{51} +(176.000 - 304.841i) q^{52} +(-319.500 + 553.390i) q^{53} +(-27.0000 - 46.7654i) q^{54} +135.000 q^{55} +(-140.000 + 48.4974i) q^{56} -312.000 q^{57} +(51.0000 + 88.3346i) q^{58} +(-79.5000 + 137.698i) q^{59} +(-90.0000 + 155.885i) q^{60} +(-361.000 - 625.270i) q^{61} -370.000 q^{62} +(-126.000 - 109.119i) q^{63} +64.0000 q^{64} +(-660.000 - 1143.15i) q^{65} +(27.0000 - 46.7654i) q^{66} +(83.0000 - 143.760i) q^{67} +(168.000 + 290.985i) q^{68} +252.000 q^{69} +(-105.000 + 545.596i) q^{70} +1086.00 q^{71} +(36.0000 + 62.3538i) q^{72} +(-109.000 + 188.794i) q^{73} +(44.0000 - 76.2102i) q^{74} +(150.000 + 259.808i) q^{75} +416.000 q^{76} +(31.5000 - 163.679i) q^{77} -528.000 q^{78} +(291.500 + 504.893i) q^{79} +(120.000 - 207.846i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-168.000 - 290.985i) q^{82} -597.000 q^{83} +(168.000 + 145.492i) q^{84} +1260.00 q^{85} +(326.000 + 564.649i) q^{86} +(76.5000 - 132.502i) q^{87} +(-36.0000 + 62.3538i) q^{88} +(519.000 + 898.934i) q^{89} +270.000 q^{90} +(-1540.00 + 533.472i) q^{91} -336.000 q^{92} +(277.500 + 480.644i) q^{93} +(-138.000 + 239.023i) q^{94} +(780.000 - 1351.00i) q^{95} +(-48.0000 - 83.1384i) q^{96} -169.000 q^{97} +(637.000 + 254.611i) q^{98} -81.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} + 3 q^{3} - 4 q^{4} + 15 q^{5} + 12 q^{6} + 35 q^{7} - 16 q^{8} - 9 q^{9} - 30 q^{10} + 9 q^{11} + 12 q^{12} - 176 q^{13} + 56 q^{14} + 90 q^{15} - 16 q^{16} + 84 q^{17} + 18 q^{18} - 104 q^{19} - 120 q^{20} + 21 q^{21} + 36 q^{22} + 84 q^{23} - 24 q^{24} - 100 q^{25} - 176 q^{26} - 54 q^{27} - 28 q^{28} + 102 q^{29} + 90 q^{30} - 185 q^{31} + 32 q^{32} - 27 q^{33} + 336 q^{34} + 420 q^{35} + 72 q^{36} - 44 q^{37} + 208 q^{38} - 264 q^{39} - 120 q^{40} - 336 q^{41} + 210 q^{42} + 652 q^{43} + 36 q^{44} + 135 q^{45} - 168 q^{46} + 138 q^{47} - 96 q^{48} + 539 q^{49} - 400 q^{50} - 252 q^{51} + 352 q^{52} - 639 q^{53} - 54 q^{54} + 270 q^{55} - 280 q^{56} - 624 q^{57} + 102 q^{58} - 159 q^{59} - 180 q^{60} - 722 q^{61} - 740 q^{62} - 252 q^{63} + 128 q^{64} - 1320 q^{65} + 54 q^{66} + 166 q^{67} + 336 q^{68} + 504 q^{69} - 210 q^{70} + 2172 q^{71} + 72 q^{72} - 218 q^{73} + 88 q^{74} + 300 q^{75} + 832 q^{76} + 63 q^{77} - 1056 q^{78} + 583 q^{79} + 240 q^{80} - 81 q^{81} - 336 q^{82} - 1194 q^{83} + 336 q^{84} + 2520 q^{85} + 652 q^{86} + 153 q^{87} - 72 q^{88} + 1038 q^{89} + 540 q^{90} - 3080 q^{91} - 672 q^{92} + 555 q^{93} - 276 q^{94} + 1560 q^{95} - 96 q^{96} - 338 q^{97} + 1274 q^{98} - 162 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 7.50000 + 12.9904i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 6.00000 0.408248
\(7\) 17.5000 6.06218i 0.944911 0.327327i
\(8\) −8.00000 −0.353553
\(9\) −4.50000 7.79423i −0.166667 0.288675i
\(10\) −15.0000 + 25.9808i −0.474342 + 0.821584i
\(11\) 4.50000 7.79423i 0.123346 0.213641i −0.797739 0.603002i \(-0.793971\pi\)
0.921085 + 0.389362i \(0.127304\pi\)
\(12\) 6.00000 + 10.3923i 0.144338 + 0.250000i
\(13\) −88.0000 −1.87745 −0.938723 0.344671i \(-0.887990\pi\)
−0.938723 + 0.344671i \(0.887990\pi\)
\(14\) 28.0000 + 24.2487i 0.534522 + 0.462910i
\(15\) 45.0000 0.774597
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 42.0000 72.7461i 0.599206 1.03785i −0.393733 0.919225i \(-0.628817\pi\)
0.992939 0.118630i \(-0.0378502\pi\)
\(18\) 9.00000 15.5885i 0.117851 0.204124i
\(19\) −52.0000 90.0666i −0.627875 1.08751i −0.987977 0.154598i \(-0.950592\pi\)
0.360103 0.932913i \(-0.382742\pi\)
\(20\) −60.0000 −0.670820
\(21\) 10.5000 54.5596i 0.109109 0.566947i
\(22\) 18.0000 0.174437
\(23\) 42.0000 + 72.7461i 0.380765 + 0.659505i 0.991172 0.132583i \(-0.0423272\pi\)
−0.610406 + 0.792088i \(0.708994\pi\)
\(24\) −12.0000 + 20.7846i −0.102062 + 0.176777i
\(25\) −50.0000 + 86.6025i −0.400000 + 0.692820i
\(26\) −88.0000 152.420i −0.663778 1.14970i
\(27\) −27.0000 −0.192450
\(28\) −14.0000 + 72.7461i −0.0944911 + 0.490990i
\(29\) 51.0000 0.326568 0.163284 0.986579i \(-0.447791\pi\)
0.163284 + 0.986579i \(0.447791\pi\)
\(30\) 45.0000 + 77.9423i 0.273861 + 0.474342i
\(31\) −92.5000 + 160.215i −0.535919 + 0.928239i 0.463199 + 0.886254i \(0.346701\pi\)
−0.999118 + 0.0419848i \(0.986632\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) −13.5000 23.3827i −0.0712136 0.123346i
\(34\) 168.000 0.847405
\(35\) 210.000 + 181.865i 1.01419 + 0.878310i
\(36\) 36.0000 0.166667
\(37\) −22.0000 38.1051i −0.0977507 0.169309i 0.813003 0.582260i \(-0.197831\pi\)
−0.910753 + 0.412951i \(0.864498\pi\)
\(38\) 104.000 180.133i 0.443974 0.768986i
\(39\) −132.000 + 228.631i −0.541972 + 0.938723i
\(40\) −60.0000 103.923i −0.237171 0.410792i
\(41\) −168.000 −0.639932 −0.319966 0.947429i \(-0.603671\pi\)
−0.319966 + 0.947429i \(0.603671\pi\)
\(42\) 105.000 36.3731i 0.385758 0.133631i
\(43\) 326.000 1.15615 0.578076 0.815983i \(-0.303804\pi\)
0.578076 + 0.815983i \(0.303804\pi\)
\(44\) 18.0000 + 31.1769i 0.0616728 + 0.106820i
\(45\) 67.5000 116.913i 0.223607 0.387298i
\(46\) −84.0000 + 145.492i −0.269242 + 0.466341i
\(47\) 69.0000 + 119.512i 0.214142 + 0.370905i 0.953007 0.302949i \(-0.0979711\pi\)
−0.738865 + 0.673854i \(0.764638\pi\)
\(48\) −48.0000 −0.144338
\(49\) 269.500 212.176i 0.785714 0.618590i
\(50\) −200.000 −0.565685
\(51\) −126.000 218.238i −0.345952 0.599206i
\(52\) 176.000 304.841i 0.469362 0.812958i
\(53\) −319.500 + 553.390i −0.828051 + 1.43423i 0.0715141 + 0.997440i \(0.477217\pi\)
−0.899565 + 0.436787i \(0.856116\pi\)
\(54\) −27.0000 46.7654i −0.0680414 0.117851i
\(55\) 135.000 0.330971
\(56\) −140.000 + 48.4974i −0.334077 + 0.115728i
\(57\) −312.000 −0.725007
\(58\) 51.0000 + 88.3346i 0.115459 + 0.199981i
\(59\) −79.5000 + 137.698i −0.175424 + 0.303843i −0.940308 0.340325i \(-0.889463\pi\)
0.764884 + 0.644168i \(0.222796\pi\)
\(60\) −90.0000 + 155.885i −0.193649 + 0.335410i
\(61\) −361.000 625.270i −0.757726 1.31242i −0.944007 0.329924i \(-0.892977\pi\)
0.186281 0.982497i \(-0.440357\pi\)
\(62\) −370.000 −0.757904
\(63\) −126.000 109.119i −0.251976 0.218218i
\(64\) 64.0000 0.125000
\(65\) −660.000 1143.15i −1.25943 2.18140i
\(66\) 27.0000 46.7654i 0.0503556 0.0872185i
\(67\) 83.0000 143.760i 0.151344 0.262136i −0.780378 0.625309i \(-0.784973\pi\)
0.931722 + 0.363173i \(0.118306\pi\)
\(68\) 168.000 + 290.985i 0.299603 + 0.518927i
\(69\) 252.000 0.439670
\(70\) −105.000 + 545.596i −0.179284 + 0.931589i
\(71\) 1086.00 1.81527 0.907637 0.419755i \(-0.137884\pi\)
0.907637 + 0.419755i \(0.137884\pi\)
\(72\) 36.0000 + 62.3538i 0.0589256 + 0.102062i
\(73\) −109.000 + 188.794i −0.174760 + 0.302693i −0.940078 0.340959i \(-0.889248\pi\)
0.765318 + 0.643652i \(0.222582\pi\)
\(74\) 44.0000 76.2102i 0.0691202 0.119720i
\(75\) 150.000 + 259.808i 0.230940 + 0.400000i
\(76\) 416.000 0.627875
\(77\) 31.5000 163.679i 0.0466202 0.242246i
\(78\) −528.000 −0.766464
\(79\) 291.500 + 504.893i 0.415143 + 0.719049i 0.995443 0.0953535i \(-0.0303981\pi\)
−0.580300 + 0.814403i \(0.697065\pi\)
\(80\) 120.000 207.846i 0.167705 0.290474i
\(81\) −40.5000 + 70.1481i −0.0555556 + 0.0962250i
\(82\) −168.000 290.985i −0.226250 0.391876i
\(83\) −597.000 −0.789509 −0.394755 0.918787i \(-0.629170\pi\)
−0.394755 + 0.918787i \(0.629170\pi\)
\(84\) 168.000 + 145.492i 0.218218 + 0.188982i
\(85\) 1260.00 1.60784
\(86\) 326.000 + 564.649i 0.408761 + 0.707996i
\(87\) 76.5000 132.502i 0.0942720 0.163284i
\(88\) −36.0000 + 62.3538i −0.0436092 + 0.0755334i
\(89\) 519.000 + 898.934i 0.618134 + 1.07064i 0.989826 + 0.142283i \(0.0454443\pi\)
−0.371692 + 0.928356i \(0.621222\pi\)
\(90\) 270.000 0.316228
\(91\) −1540.00 + 533.472i −1.77402 + 0.614539i
\(92\) −336.000 −0.380765
\(93\) 277.500 + 480.644i 0.309413 + 0.535919i
\(94\) −138.000 + 239.023i −0.151421 + 0.262270i
\(95\) 780.000 1351.00i 0.842382 1.45905i
\(96\) −48.0000 83.1384i −0.0510310 0.0883883i
\(97\) −169.000 −0.176901 −0.0884503 0.996081i \(-0.528191\pi\)
−0.0884503 + 0.996081i \(0.528191\pi\)
\(98\) 637.000 + 254.611i 0.656599 + 0.262445i
\(99\) −81.0000 −0.0822304
\(100\) −200.000 346.410i −0.200000 0.346410i
\(101\) −321.000 + 555.988i −0.316244 + 0.547752i −0.979701 0.200463i \(-0.935755\pi\)
0.663457 + 0.748215i \(0.269089\pi\)
\(102\) 252.000 436.477i 0.244625 0.423702i
\(103\) −232.000 401.836i −0.221938 0.384408i 0.733458 0.679735i \(-0.237905\pi\)
−0.955396 + 0.295326i \(0.904572\pi\)
\(104\) 704.000 0.663778
\(105\) 787.500 272.798i 0.731925 0.253546i
\(106\) −1278.00 −1.17104
\(107\) −196.500 340.348i −0.177536 0.307502i 0.763500 0.645808i \(-0.223479\pi\)
−0.941036 + 0.338306i \(0.890146\pi\)
\(108\) 54.0000 93.5307i 0.0481125 0.0833333i
\(109\) −7.00000 + 12.1244i −0.00615118 + 0.0106542i −0.869085 0.494663i \(-0.835291\pi\)
0.862933 + 0.505318i \(0.168625\pi\)
\(110\) 135.000 + 233.827i 0.117016 + 0.202677i
\(111\) −132.000 −0.112873
\(112\) −224.000 193.990i −0.188982 0.163663i
\(113\) −2184.00 −1.81817 −0.909086 0.416608i \(-0.863219\pi\)
−0.909086 + 0.416608i \(0.863219\pi\)
\(114\) −312.000 540.400i −0.256329 0.443974i
\(115\) −630.000 + 1091.19i −0.510850 + 0.884819i
\(116\) −102.000 + 176.669i −0.0816419 + 0.141408i
\(117\) 396.000 + 685.892i 0.312908 + 0.541972i
\(118\) −318.000 −0.248087
\(119\) 294.000 1527.67i 0.226478 1.17682i
\(120\) −360.000 −0.273861
\(121\) 625.000 + 1082.53i 0.469572 + 0.813322i
\(122\) 722.000 1250.54i 0.535794 0.928022i
\(123\) −252.000 + 436.477i −0.184732 + 0.319966i
\(124\) −370.000 640.859i −0.267960 0.464120i
\(125\) 375.000 0.268328
\(126\) 63.0000 327.358i 0.0445435 0.231455i
\(127\) −373.000 −0.260617 −0.130309 0.991473i \(-0.541597\pi\)
−0.130309 + 0.991473i \(0.541597\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 489.000 846.973i 0.333752 0.578076i
\(130\) 1320.00 2286.31i 0.890551 1.54248i
\(131\) 586.500 + 1015.85i 0.391166 + 0.677519i 0.992604 0.121400i \(-0.0387385\pi\)
−0.601438 + 0.798920i \(0.705405\pi\)
\(132\) 108.000 0.0712136
\(133\) −1456.00 1260.93i −0.949257 0.822081i
\(134\) 332.000 0.214033
\(135\) −202.500 350.740i −0.129099 0.223607i
\(136\) −336.000 + 581.969i −0.211851 + 0.366937i
\(137\) −15.0000 + 25.9808i −0.00935428 + 0.0162021i −0.870665 0.491877i \(-0.836311\pi\)
0.861310 + 0.508079i \(0.169644\pi\)
\(138\) 252.000 + 436.477i 0.155447 + 0.269242i
\(139\) −82.0000 −0.0500370 −0.0250185 0.999687i \(-0.507964\pi\)
−0.0250185 + 0.999687i \(0.507964\pi\)
\(140\) −1050.00 + 363.731i −0.633866 + 0.219578i
\(141\) 414.000 0.247270
\(142\) 1086.00 + 1881.01i 0.641796 + 1.11162i
\(143\) −396.000 + 685.892i −0.231575 + 0.401099i
\(144\) −72.0000 + 124.708i −0.0416667 + 0.0721688i
\(145\) 382.500 + 662.509i 0.219068 + 0.379437i
\(146\) −436.000 −0.247148
\(147\) −147.000 1018.45i −0.0824786 0.571429i
\(148\) 176.000 0.0977507
\(149\) 717.000 + 1241.88i 0.394221 + 0.682811i 0.993001 0.118102i \(-0.0376811\pi\)
−0.598780 + 0.800913i \(0.704348\pi\)
\(150\) −300.000 + 519.615i −0.163299 + 0.282843i
\(151\) 1335.50 2313.15i 0.719745 1.24663i −0.241356 0.970437i \(-0.577592\pi\)
0.961101 0.276198i \(-0.0890745\pi\)
\(152\) 416.000 + 720.533i 0.221987 + 0.384493i
\(153\) −756.000 −0.399470
\(154\) 315.000 109.119i 0.164827 0.0570979i
\(155\) −2775.00 −1.43802
\(156\) −528.000 914.523i −0.270986 0.469362i
\(157\) −1126.00 + 1950.29i −0.572386 + 0.991401i 0.423934 + 0.905693i \(0.360649\pi\)
−0.996320 + 0.0857085i \(0.972685\pi\)
\(158\) −583.000 + 1009.79i −0.293551 + 0.508444i
\(159\) 958.500 + 1660.17i 0.478075 + 0.828051i
\(160\) 480.000 0.237171
\(161\) 1176.00 + 1018.45i 0.575663 + 0.498539i
\(162\) −162.000 −0.0785674
\(163\) −838.000 1451.46i −0.402682 0.697466i 0.591366 0.806403i \(-0.298589\pi\)
−0.994049 + 0.108937i \(0.965255\pi\)
\(164\) 336.000 581.969i 0.159983 0.277098i
\(165\) 202.500 350.740i 0.0955431 0.165485i
\(166\) −597.000 1034.03i −0.279134 0.483474i
\(167\) 3030.00 1.40400 0.702001 0.712176i \(-0.252290\pi\)
0.702001 + 0.712176i \(0.252290\pi\)
\(168\) −84.0000 + 436.477i −0.0385758 + 0.200446i
\(169\) 5547.00 2.52481
\(170\) 1260.00 + 2182.38i 0.568456 + 0.984595i
\(171\) −468.000 + 810.600i −0.209292 + 0.362504i
\(172\) −652.000 + 1129.30i −0.289038 + 0.500628i
\(173\) −1719.00 2977.40i −0.755452 1.30848i −0.945149 0.326638i \(-0.894084\pi\)
0.189698 0.981843i \(-0.439249\pi\)
\(174\) 306.000 0.133321
\(175\) −350.000 + 1818.65i −0.151186 + 0.785584i
\(176\) −144.000 −0.0616728
\(177\) 238.500 + 413.094i 0.101281 + 0.175424i
\(178\) −1038.00 + 1797.87i −0.437086 + 0.757056i
\(179\) 606.000 1049.62i 0.253042 0.438282i −0.711320 0.702869i \(-0.751902\pi\)
0.964362 + 0.264587i \(0.0852355\pi\)
\(180\) 270.000 + 467.654i 0.111803 + 0.193649i
\(181\) 3032.00 1.24512 0.622560 0.782572i \(-0.286093\pi\)
0.622560 + 0.782572i \(0.286093\pi\)
\(182\) −2464.00 2133.89i −1.00354 0.869089i
\(183\) −2166.00 −0.874947
\(184\) −336.000 581.969i −0.134621 0.233170i
\(185\) 330.000 571.577i 0.131146 0.227152i
\(186\) −555.000 + 961.288i −0.218788 + 0.378952i
\(187\) −378.000 654.715i −0.147819 0.256030i
\(188\) −552.000 −0.214142
\(189\) −472.500 + 163.679i −0.181848 + 0.0629941i
\(190\) 3120.00 1.19131
\(191\) −1260.00 2182.38i −0.477332 0.826763i 0.522331 0.852743i \(-0.325063\pi\)
−0.999662 + 0.0259799i \(0.991729\pi\)
\(192\) 96.0000 166.277i 0.0360844 0.0625000i
\(193\) −182.500 + 316.099i −0.0680655 + 0.117893i −0.898050 0.439894i \(-0.855016\pi\)
0.829984 + 0.557787i \(0.188349\pi\)
\(194\) −169.000 292.717i −0.0625438 0.108329i
\(195\) −3960.00 −1.45426
\(196\) 196.000 + 1357.93i 0.0714286 + 0.494872i
\(197\) −1590.00 −0.575040 −0.287520 0.957775i \(-0.592831\pi\)
−0.287520 + 0.957775i \(0.592831\pi\)
\(198\) −81.0000 140.296i −0.0290728 0.0503556i
\(199\) 2690.00 4659.22i 0.958236 1.65971i 0.231455 0.972846i \(-0.425652\pi\)
0.726782 0.686868i \(-0.241015\pi\)
\(200\) 400.000 692.820i 0.141421 0.244949i
\(201\) −249.000 431.281i −0.0873786 0.151344i
\(202\) −1284.00 −0.447237
\(203\) 892.500 309.171i 0.308577 0.106894i
\(204\) 1008.00 0.345952
\(205\) −1260.00 2182.38i −0.429279 0.743533i
\(206\) 464.000 803.672i 0.156934 0.271818i
\(207\) 378.000 654.715i 0.126922 0.219835i
\(208\) 704.000 + 1219.36i 0.234681 + 0.406479i
\(209\) −936.000 −0.309782
\(210\) 1260.00 + 1091.19i 0.414039 + 0.358569i
\(211\) −5362.00 −1.74946 −0.874728 0.484614i \(-0.838960\pi\)
−0.874728 + 0.484614i \(0.838960\pi\)
\(212\) −1278.00 2213.56i −0.414025 0.717113i
\(213\) 1629.00 2821.51i 0.524025 0.907637i
\(214\) 393.000 680.696i 0.125537 0.217437i
\(215\) 2445.00 + 4234.86i 0.775570 + 1.34333i
\(216\) 216.000 0.0680414
\(217\) −647.500 + 3364.51i −0.202558 + 1.05252i
\(218\) −28.0000 −0.00869908
\(219\) 327.000 + 566.381i 0.100898 + 0.174760i
\(220\) −270.000 + 467.654i −0.0827427 + 0.143315i
\(221\) −3696.00 + 6401.66i −1.12498 + 1.94852i
\(222\) −132.000 228.631i −0.0399066 0.0691202i
\(223\) −1573.00 −0.472358 −0.236179 0.971710i \(-0.575895\pi\)
−0.236179 + 0.971710i \(0.575895\pi\)
\(224\) 112.000 581.969i 0.0334077 0.173591i
\(225\) 900.000 0.266667
\(226\) −2184.00 3782.80i −0.642821 1.11340i
\(227\) −460.500 + 797.609i −0.134645 + 0.233212i −0.925462 0.378841i \(-0.876323\pi\)
0.790817 + 0.612053i \(0.209656\pi\)
\(228\) 624.000 1080.80i 0.181252 0.313937i
\(229\) −2026.00 3509.13i −0.584637 1.01262i −0.994921 0.100663i \(-0.967904\pi\)
0.410284 0.911958i \(-0.365430\pi\)
\(230\) −2520.00 −0.722452
\(231\) −378.000 327.358i −0.107665 0.0932405i
\(232\) −408.000 −0.115459
\(233\) 234.000 + 405.300i 0.0657933 + 0.113957i 0.897046 0.441938i \(-0.145709\pi\)
−0.831252 + 0.555895i \(0.812376\pi\)
\(234\) −792.000 + 1371.78i −0.221259 + 0.383232i
\(235\) −1035.00 + 1792.67i −0.287302 + 0.497622i
\(236\) −318.000 550.792i −0.0877120 0.151922i
\(237\) 1749.00 0.479366
\(238\) 2940.00 1018.45i 0.800722 0.277378i
\(239\) 4932.00 1.33483 0.667415 0.744686i \(-0.267401\pi\)
0.667415 + 0.744686i \(0.267401\pi\)
\(240\) −360.000 623.538i −0.0968246 0.167705i
\(241\) 768.500 1331.08i 0.205408 0.355778i −0.744854 0.667227i \(-0.767481\pi\)
0.950263 + 0.311449i \(0.100814\pi\)
\(242\) −1250.00 + 2165.06i −0.332037 + 0.575106i
\(243\) 121.500 + 210.444i 0.0320750 + 0.0555556i
\(244\) 2888.00 0.757726
\(245\) 4777.50 + 1909.59i 1.24581 + 0.497955i
\(246\) −1008.00 −0.261251
\(247\) 4576.00 + 7925.86i 1.17880 + 2.04174i
\(248\) 740.000 1281.72i 0.189476 0.328182i
\(249\) −895.500 + 1551.05i −0.227912 + 0.394755i
\(250\) 375.000 + 649.519i 0.0948683 + 0.164317i
\(251\) 5319.00 1.33758 0.668789 0.743452i \(-0.266813\pi\)
0.668789 + 0.743452i \(0.266813\pi\)
\(252\) 630.000 218.238i 0.157485 0.0545545i
\(253\) 756.000 0.187863
\(254\) −373.000 646.055i −0.0921421 0.159595i
\(255\) 1890.00 3273.58i 0.464143 0.803919i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2673.00 4629.77i −0.648783 1.12372i −0.983414 0.181375i \(-0.941945\pi\)
0.334631 0.942349i \(-0.391388\pi\)
\(258\) 1956.00 0.471997
\(259\) −616.000 533.472i −0.147785 0.127986i
\(260\) 5280.00 1.25943
\(261\) −229.500 397.506i −0.0544279 0.0942720i
\(262\) −1173.00 + 2031.70i −0.276596 + 0.479079i
\(263\) −387.000 + 670.304i −0.0907355 + 0.157159i −0.907821 0.419358i \(-0.862255\pi\)
0.817085 + 0.576517i \(0.195588\pi\)
\(264\) 108.000 + 187.061i 0.0251778 + 0.0436092i
\(265\) −9585.00 −2.22189
\(266\) 728.000 3782.80i 0.167807 0.871948i
\(267\) 3114.00 0.713759
\(268\) 332.000 + 575.041i 0.0756721 + 0.131068i
\(269\) −1207.50 + 2091.45i −0.273690 + 0.474045i −0.969804 0.243887i \(-0.921578\pi\)
0.696114 + 0.717931i \(0.254911\pi\)
\(270\) 405.000 701.481i 0.0912871 0.158114i
\(271\) 237.500 + 411.362i 0.0532365 + 0.0922084i 0.891416 0.453187i \(-0.149713\pi\)
−0.838179 + 0.545395i \(0.816380\pi\)
\(272\) −1344.00 −0.299603
\(273\) −924.000 + 4801.24i −0.204846 + 1.06441i
\(274\) −60.0000 −0.0132290
\(275\) 450.000 + 779.423i 0.0986764 + 0.170913i
\(276\) −504.000 + 872.954i −0.109918 + 0.190383i
\(277\) −1864.00 + 3228.54i −0.404321 + 0.700304i −0.994242 0.107156i \(-0.965825\pi\)
0.589921 + 0.807461i \(0.299159\pi\)
\(278\) −82.0000 142.028i −0.0176908 0.0306413i
\(279\) 1665.00 0.357279
\(280\) −1680.00 1454.92i −0.358569 0.310530i
\(281\) 1602.00 0.340097 0.170049 0.985436i \(-0.445608\pi\)
0.170049 + 0.985436i \(0.445608\pi\)
\(282\) 414.000 + 717.069i 0.0874232 + 0.151421i
\(283\) −343.000 + 594.093i −0.0720468 + 0.124789i −0.899798 0.436306i \(-0.856286\pi\)
0.827751 + 0.561095i \(0.189620\pi\)
\(284\) −2172.00 + 3762.01i −0.453819 + 0.786037i
\(285\) −2340.00 4053.00i −0.486350 0.842382i
\(286\) −1584.00 −0.327496
\(287\) −2940.00 + 1018.45i −0.604678 + 0.209467i
\(288\) −288.000 −0.0589256
\(289\) −1071.50 1855.89i −0.218095 0.377751i
\(290\) −765.000 + 1325.02i −0.154905 + 0.268303i
\(291\) −253.500 + 439.075i −0.0510668 + 0.0884503i
\(292\) −436.000 755.174i −0.0873800 0.151347i
\(293\) −1101.00 −0.219526 −0.109763 0.993958i \(-0.535009\pi\)
−0.109763 + 0.993958i \(0.535009\pi\)
\(294\) 1617.00 1273.06i 0.320767 0.252538i
\(295\) −2385.00 −0.470712
\(296\) 176.000 + 304.841i 0.0345601 + 0.0598599i
\(297\) −121.500 + 210.444i −0.0237379 + 0.0411152i
\(298\) −1434.00 + 2483.76i −0.278756 + 0.482820i
\(299\) −3696.00 6401.66i −0.714867 1.23819i
\(300\) −1200.00 −0.230940
\(301\) 5705.00 1976.27i 1.09246 0.378440i
\(302\) 5342.00 1.01787
\(303\) 963.000 + 1667.96i 0.182584 + 0.316244i
\(304\) −832.000 + 1441.07i −0.156969 + 0.271878i
\(305\) 5415.00 9379.06i 1.01660 1.76080i
\(306\) −756.000 1309.43i −0.141234 0.244625i
\(307\) 2780.00 0.516818 0.258409 0.966036i \(-0.416802\pi\)
0.258409 + 0.966036i \(0.416802\pi\)
\(308\) 504.000 + 436.477i 0.0932405 + 0.0807486i
\(309\) −1392.00 −0.256272
\(310\) −2775.00 4806.44i −0.508417 0.880605i
\(311\) −2148.00 + 3720.45i −0.391646 + 0.678351i −0.992667 0.120883i \(-0.961428\pi\)
0.601021 + 0.799233i \(0.294761\pi\)
\(312\) 1056.00 1829.05i 0.191616 0.331889i
\(313\) −2744.50 4753.61i −0.495618 0.858435i 0.504370 0.863488i \(-0.331725\pi\)
−0.999987 + 0.00505298i \(0.998392\pi\)
\(314\) −4504.00 −0.809476
\(315\) 472.500 2455.18i 0.0845154 0.439155i
\(316\) −2332.00 −0.415143
\(317\) −2245.50 3889.32i −0.397854 0.689104i 0.595607 0.803276i \(-0.296912\pi\)
−0.993461 + 0.114172i \(0.963578\pi\)
\(318\) −1917.00 + 3320.34i −0.338050 + 0.585520i
\(319\) 229.500 397.506i 0.0402807 0.0697682i
\(320\) 480.000 + 831.384i 0.0838525 + 0.145237i
\(321\) −1179.00 −0.205001
\(322\) −588.000 + 3055.34i −0.101764 + 0.528780i
\(323\) −8736.00 −1.50490
\(324\) −162.000 280.592i −0.0277778 0.0481125i
\(325\) 4400.00 7621.02i 0.750979 1.30073i
\(326\) 1676.00 2902.92i 0.284739 0.493183i
\(327\) 21.0000 + 36.3731i 0.00355138 + 0.00615118i
\(328\) 1344.00 0.226250
\(329\) 1932.00 + 1673.16i 0.323753 + 0.280378i
\(330\) 810.000 0.135118
\(331\) 1982.00 + 3432.92i 0.329126 + 0.570062i 0.982339 0.187112i \(-0.0599127\pi\)
−0.653213 + 0.757174i \(0.726579\pi\)
\(332\) 1194.00 2068.07i 0.197377 0.341868i
\(333\) −198.000 + 342.946i −0.0325836 + 0.0564364i
\(334\) 3030.00 + 5248.11i 0.496390 + 0.859773i
\(335\) 2490.00 0.406099
\(336\) −840.000 + 290.985i −0.136386 + 0.0472456i
\(337\) 161.000 0.0260244 0.0130122 0.999915i \(-0.495858\pi\)
0.0130122 + 0.999915i \(0.495858\pi\)
\(338\) 5547.00 + 9607.69i 0.892654 + 1.54612i
\(339\) −3276.00 + 5674.20i −0.524861 + 0.909086i
\(340\) −2520.00 + 4364.77i −0.401959 + 0.696214i
\(341\) 832.500 + 1441.93i 0.132206 + 0.228988i
\(342\) −1872.00 −0.295983
\(343\) 3430.00 5346.84i 0.539949 0.841698i
\(344\) −2608.00 −0.408761
\(345\) 1890.00 + 3273.58i 0.294940 + 0.510850i
\(346\) 3438.00 5954.79i 0.534185 0.925236i
\(347\) 2958.00 5123.41i 0.457619 0.792619i −0.541216 0.840884i \(-0.682036\pi\)
0.998835 + 0.0482646i \(0.0153691\pi\)
\(348\) 306.000 + 530.008i 0.0471360 + 0.0816419i
\(349\) −142.000 −0.0217796 −0.0108898 0.999941i \(-0.503466\pi\)
−0.0108898 + 0.999941i \(0.503466\pi\)
\(350\) −3500.00 + 1212.44i −0.534522 + 0.185164i
\(351\) 2376.00 0.361315
\(352\) −144.000 249.415i −0.0218046 0.0377667i
\(353\) 2220.00 3845.15i 0.334727 0.579764i −0.648705 0.761040i \(-0.724689\pi\)
0.983432 + 0.181275i \(0.0580225\pi\)
\(354\) −477.000 + 826.188i −0.0716166 + 0.124044i
\(355\) 8145.00 + 14107.6i 1.21772 + 2.10916i
\(356\) −4152.00 −0.618134
\(357\) −3528.00 3055.34i −0.523030 0.452957i
\(358\) 2424.00 0.357856
\(359\) −1143.00 1979.73i −0.168037 0.291048i 0.769693 0.638415i \(-0.220409\pi\)
−0.937730 + 0.347366i \(0.887076\pi\)
\(360\) −540.000 + 935.307i −0.0790569 + 0.136931i
\(361\) −1978.50 + 3426.86i −0.288453 + 0.499615i
\(362\) 3032.00 + 5251.58i 0.440217 + 0.762477i
\(363\) 3750.00 0.542215
\(364\) 1232.00 6401.66i 0.177402 0.921808i
\(365\) −3270.00 −0.468930
\(366\) −2166.00 3751.62i −0.309341 0.535794i
\(367\) 1434.50 2484.63i 0.204033 0.353396i −0.745791 0.666180i \(-0.767928\pi\)
0.949824 + 0.312784i \(0.101262\pi\)
\(368\) 672.000 1163.94i 0.0951914 0.164876i
\(369\) 756.000 + 1309.43i 0.106655 + 0.184732i
\(370\) 1320.00 0.185469
\(371\) −2236.50 + 11621.2i −0.312974 + 1.62626i
\(372\) −2220.00 −0.309413
\(373\) 1532.00 + 2653.50i 0.212665 + 0.368346i 0.952548 0.304390i \(-0.0984524\pi\)
−0.739883 + 0.672736i \(0.765119\pi\)
\(374\) 756.000 1309.43i 0.104524 0.181040i
\(375\) 562.500 974.279i 0.0774597 0.134164i
\(376\) −552.000 956.092i −0.0757107 0.131135i
\(377\) −4488.00 −0.613113
\(378\) −756.000 654.715i −0.102869 0.0890871i
\(379\) −6040.00 −0.818612 −0.409306 0.912397i \(-0.634229\pi\)
−0.409306 + 0.912397i \(0.634229\pi\)
\(380\) 3120.00 + 5404.00i 0.421191 + 0.729524i
\(381\) −559.500 + 969.082i −0.0752337 + 0.130309i
\(382\) 2520.00 4364.77i 0.337525 0.584610i
\(383\) −921.000 1595.22i −0.122874 0.212825i 0.798026 0.602623i \(-0.205878\pi\)
−0.920900 + 0.389799i \(0.872545\pi\)
\(384\) 384.000 0.0510310
\(385\) 2362.50 818.394i 0.312738 0.108336i
\(386\) −730.000 −0.0962591
\(387\) −1467.00 2540.92i −0.192692 0.333752i
\(388\) 338.000 585.433i 0.0442251 0.0766002i
\(389\) −3915.00 + 6780.98i −0.510279 + 0.883828i 0.489650 + 0.871919i \(0.337124\pi\)
−0.999929 + 0.0119097i \(0.996209\pi\)
\(390\) −3960.00 6858.92i −0.514160 0.890551i
\(391\) 7056.00 0.912627
\(392\) −2156.00 + 1697.41i −0.277792 + 0.218704i
\(393\) 3519.00 0.451680
\(394\) −1590.00 2753.96i −0.203307 0.352138i
\(395\) −4372.50 + 7573.39i −0.556973 + 0.964706i
\(396\) 162.000 280.592i 0.0205576 0.0356068i
\(397\) 7382.00 + 12786.0i 0.933229 + 1.61640i 0.777762 + 0.628559i \(0.216355\pi\)
0.155467 + 0.987841i \(0.450312\pi\)
\(398\) 10760.0 1.35515
\(399\) −5460.00 + 1891.40i −0.685067 + 0.237314i
\(400\) 1600.00 0.200000
\(401\) −3132.00 5424.78i −0.390036 0.675563i 0.602417 0.798181i \(-0.294204\pi\)
−0.992454 + 0.122618i \(0.960871\pi\)
\(402\) 498.000 862.561i 0.0617860 0.107017i
\(403\) 8140.00 14098.9i 1.00616 1.74272i
\(404\) −1284.00 2223.95i −0.158122 0.273876i
\(405\) −1215.00 −0.149071
\(406\) 1428.00 + 1236.68i 0.174558 + 0.151171i
\(407\) −396.000 −0.0482285
\(408\) 1008.00 + 1745.91i 0.122312 + 0.211851i
\(409\) −2375.50 + 4114.49i −0.287191 + 0.497429i −0.973138 0.230222i \(-0.926055\pi\)
0.685948 + 0.727651i \(0.259388\pi\)
\(410\) 2520.00 4364.77i 0.303546 0.525757i
\(411\) 45.0000 + 77.9423i 0.00540070 + 0.00935428i
\(412\) 1856.00 0.221938
\(413\) −556.500 + 2891.66i −0.0663041 + 0.344526i
\(414\) 1512.00 0.179495
\(415\) −4477.50 7755.26i −0.529619 0.917327i
\(416\) −1408.00 + 2438.73i −0.165944 + 0.287424i
\(417\) −123.000 + 213.042i −0.0144445 + 0.0250185i
\(418\) −936.000 1621.20i −0.109525 0.189702i
\(419\) −4704.00 −0.548462 −0.274231 0.961664i \(-0.588423\pi\)
−0.274231 + 0.961664i \(0.588423\pi\)
\(420\) −630.000 + 3273.58i −0.0731925 + 0.380319i
\(421\) −4474.00 −0.517932 −0.258966 0.965886i \(-0.583382\pi\)
−0.258966 + 0.965886i \(0.583382\pi\)
\(422\) −5362.00 9287.26i −0.618526 1.07132i
\(423\) 621.000 1075.60i 0.0713807 0.123635i
\(424\) 2556.00 4427.12i 0.292760 0.507076i
\(425\) 4200.00 + 7274.61i 0.479365 + 0.830284i
\(426\) 6516.00 0.741083
\(427\) −10108.0 8753.78i −1.14557 0.992097i
\(428\) 1572.00 0.177536
\(429\) 1188.00 + 2057.68i 0.133700 + 0.231575i
\(430\) −4890.00 + 8469.73i −0.548411 + 0.949876i
\(431\) 6402.00 11088.6i 0.715484 1.23925i −0.247289 0.968942i \(-0.579540\pi\)
0.962773 0.270312i \(-0.0871270\pi\)
\(432\) 216.000 + 374.123i 0.0240563 + 0.0416667i
\(433\) −5074.00 −0.563143 −0.281571 0.959540i \(-0.590856\pi\)
−0.281571 + 0.959540i \(0.590856\pi\)
\(434\) −6475.00 + 2243.01i −0.716152 + 0.248082i
\(435\) 2295.00 0.252958
\(436\) −28.0000 48.4974i −0.00307559 0.00532708i
\(437\) 4368.00 7565.60i 0.478146 0.828173i
\(438\) −654.000 + 1132.76i −0.0713455 + 0.123574i
\(439\) 633.500 + 1097.25i 0.0688731 + 0.119292i 0.898406 0.439167i \(-0.144726\pi\)
−0.829532 + 0.558459i \(0.811393\pi\)
\(440\) −1080.00 −0.117016
\(441\) −2866.50 1145.75i −0.309524 0.123718i
\(442\) −14784.0 −1.59096
\(443\) 3466.50 + 6004.15i 0.371780 + 0.643941i 0.989839 0.142190i \(-0.0454144\pi\)
−0.618060 + 0.786131i \(0.712081\pi\)
\(444\) 264.000 457.261i 0.0282182 0.0488754i
\(445\) −7785.00 + 13484.0i −0.829313 + 1.43641i
\(446\) −1573.00 2724.52i −0.167004 0.289259i
\(447\) 4302.00 0.455207
\(448\) 1120.00 387.979i 0.118114 0.0409159i
\(449\) 11688.0 1.22849 0.614244 0.789116i \(-0.289461\pi\)
0.614244 + 0.789116i \(0.289461\pi\)
\(450\) 900.000 + 1558.85i 0.0942809 + 0.163299i
\(451\) −756.000 + 1309.43i −0.0789327 + 0.136715i
\(452\) 4368.00 7565.60i 0.454543 0.787292i
\(453\) −4006.50 6939.46i −0.415545 0.719745i
\(454\) −1842.00 −0.190417
\(455\) −18480.0 16004.1i −1.90408 1.64898i
\(456\) 2496.00 0.256329
\(457\) −275.500 477.180i −0.0281999 0.0488436i 0.851581 0.524223i \(-0.175644\pi\)
−0.879781 + 0.475379i \(0.842311\pi\)
\(458\) 4052.00 7018.27i 0.413401 0.716031i
\(459\) −1134.00 + 1964.15i −0.115317 + 0.199735i
\(460\) −2520.00 4364.77i −0.255425 0.442409i
\(461\) 13386.0 1.35238 0.676191 0.736726i \(-0.263629\pi\)
0.676191 + 0.736726i \(0.263629\pi\)
\(462\) 189.000 982.073i 0.0190326 0.0988965i
\(463\) −6376.00 −0.639995 −0.319998 0.947418i \(-0.603682\pi\)
−0.319998 + 0.947418i \(0.603682\pi\)
\(464\) −408.000 706.677i −0.0408210 0.0707040i
\(465\) −4162.50 + 7209.66i −0.415121 + 0.719011i
\(466\) −468.000 + 810.600i −0.0465229 + 0.0805801i
\(467\) −2850.00 4936.34i −0.282403 0.489137i 0.689573 0.724216i \(-0.257798\pi\)
−0.971976 + 0.235080i \(0.924465\pi\)
\(468\) −3168.00 −0.312908
\(469\) 581.000 3018.96i 0.0572027 0.297234i
\(470\) −4140.00 −0.406306
\(471\) 3378.00 + 5850.87i 0.330467 + 0.572386i
\(472\) 636.000 1101.58i 0.0620218 0.107425i
\(473\) 1467.00 2540.92i 0.142606 0.247001i
\(474\) 1749.00 + 3029.36i 0.169481 + 0.293551i
\(475\) 10400.0 1.00460
\(476\) 4704.00 + 4073.78i 0.452957 + 0.392272i
\(477\) 5751.00 0.552034
\(478\) 4932.00 + 8542.47i 0.471934 + 0.817414i
\(479\) −9897.00 + 17142.1i −0.944062 + 1.63516i −0.186442 + 0.982466i \(0.559696\pi\)
−0.757619 + 0.652697i \(0.773638\pi\)
\(480\) 720.000 1247.08i 0.0684653 0.118585i
\(481\) 1936.00 + 3353.25i 0.183522 + 0.317869i
\(482\) 3074.00 0.290491
\(483\) 4410.00 1527.67i 0.415449 0.143916i
\(484\) −5000.00 −0.469572
\(485\) −1267.50 2195.37i −0.118668 0.205540i
\(486\) −243.000 + 420.888i −0.0226805 + 0.0392837i
\(487\) −7967.50 + 13800.1i −0.741359 + 1.28407i 0.210517 + 0.977590i \(0.432485\pi\)
−0.951877 + 0.306482i \(0.900848\pi\)
\(488\) 2888.00 + 5002.16i 0.267897 + 0.464011i
\(489\) −5028.00 −0.464978
\(490\) 1470.00 + 10184.5i 0.135526 + 0.938953i
\(491\) 9963.00 0.915731 0.457865 0.889021i \(-0.348614\pi\)
0.457865 + 0.889021i \(0.348614\pi\)
\(492\) −1008.00 1745.91i −0.0923662 0.159983i
\(493\) 2142.00 3710.05i 0.195681 0.338930i
\(494\) −9152.00 + 15851.7i −0.833538 + 1.44373i
\(495\) −607.500 1052.22i −0.0551618 0.0955431i
\(496\) 2960.00 0.267960
\(497\) 19005.0 6583.53i 1.71527 0.594188i
\(498\) −3582.00 −0.322316
\(499\) −9571.00 16577.5i −0.858631 1.48719i −0.873235 0.487299i \(-0.837982\pi\)
0.0146043 0.999893i \(-0.495351\pi\)
\(500\) −750.000 + 1299.04i −0.0670820 + 0.116190i
\(501\) 4545.00 7872.17i 0.405301 0.702001i
\(502\) 5319.00 + 9212.78i 0.472906 + 0.819096i
\(503\) −12192.0 −1.08074 −0.540372 0.841426i \(-0.681717\pi\)
−0.540372 + 0.841426i \(0.681717\pi\)
\(504\) 1008.00 + 872.954i 0.0890871 + 0.0771517i
\(505\) −9630.00 −0.848573
\(506\) 756.000 + 1309.43i 0.0664196 + 0.115042i
\(507\) 8320.50 14411.5i 0.728849 1.26240i
\(508\) 746.000 1292.11i 0.0651543 0.112851i
\(509\) 9904.50 + 17155.1i 0.862494 + 1.49388i 0.869515 + 0.493907i \(0.164432\pi\)
−0.00702091 + 0.999975i \(0.502235\pi\)
\(510\) 7560.00 0.656397
\(511\) −763.000 + 3964.66i −0.0660531 + 0.343222i
\(512\) −512.000 −0.0441942
\(513\) 1404.00 + 2431.80i 0.120835 + 0.209292i
\(514\) 5346.00 9259.54i 0.458759 0.794593i
\(515\) 3480.00 6027.54i 0.297761 0.515738i
\(516\) 1956.00 + 3387.89i 0.166876 + 0.289038i
\(517\) 1242.00 0.105654
\(518\) 308.000 1600.41i 0.0261250 0.135749i
\(519\) −10314.0 −0.872321
\(520\) 5280.00 + 9145.23i 0.445276 + 0.771240i
\(521\) 897.000 1553.65i 0.0754286 0.130646i −0.825844 0.563899i \(-0.809301\pi\)
0.901273 + 0.433253i \(0.142634\pi\)
\(522\) 459.000 795.011i 0.0384864 0.0666603i
\(523\) 3224.00 + 5584.13i 0.269552 + 0.466878i 0.968746 0.248054i \(-0.0797911\pi\)
−0.699194 + 0.714932i \(0.746458\pi\)
\(524\) −4692.00 −0.391166
\(525\) 4200.00 + 3637.31i 0.349149 + 0.302372i
\(526\) −1548.00 −0.128319
\(527\) 7770.00 + 13458.0i 0.642251 + 1.11241i
\(528\) −216.000 + 374.123i −0.0178034 + 0.0308364i
\(529\) 2555.50 4426.26i 0.210035 0.363792i
\(530\) −9585.00 16601.7i −0.785558 1.36063i
\(531\) 1431.00 0.116949
\(532\) 7280.00 2521.87i 0.593286 0.205520i
\(533\) 14784.0 1.20144
\(534\) 3114.00 + 5393.61i 0.252352 + 0.437086i
\(535\) 2947.50 5105.22i 0.238190 0.412557i
\(536\) −664.000 + 1150.08i −0.0535083 + 0.0926790i
\(537\) −1818.00 3148.87i −0.146094 0.253042i
\(538\) −4830.00 −0.387056
\(539\) −441.000 3055.34i −0.0352416 0.244161i
\(540\) 1620.00 0.129099
\(541\) −3631.00 6289.08i −0.288556 0.499794i 0.684909 0.728628i \(-0.259842\pi\)
−0.973465 + 0.228835i \(0.926509\pi\)
\(542\) −475.000 + 822.724i −0.0376439 + 0.0652012i
\(543\) 4548.00 7877.37i 0.359435 0.622560i
\(544\) −1344.00 2327.88i −0.105926 0.183469i
\(545\) −210.000 −0.0165053
\(546\) −9240.00 + 3200.83i −0.724241 + 0.250884i
\(547\) 14204.0 1.11027 0.555136 0.831759i \(-0.312666\pi\)
0.555136 + 0.831759i \(0.312666\pi\)
\(548\) −60.0000 103.923i −0.00467714 0.00810104i
\(549\) −3249.00 + 5627.43i −0.252575 + 0.437474i
\(550\) −900.000 + 1558.85i −0.0697748 + 0.120853i
\(551\) −2652.00 4593.40i −0.205044 0.355146i
\(552\) −2016.00 −0.155447
\(553\) 8162.00 + 7068.50i 0.627638 + 0.543550i
\(554\) −7456.00 −0.571796
\(555\) −990.000 1714.73i −0.0757174 0.131146i
\(556\) 164.000 284.056i 0.0125093 0.0216667i
\(557\) −7912.50 + 13704.9i −0.601909 + 1.04254i 0.390623 + 0.920551i \(0.372260\pi\)
−0.992532 + 0.121986i \(0.961074\pi\)
\(558\) 1665.00 + 2883.86i 0.126317 + 0.218788i
\(559\) −28688.0 −2.17061
\(560\) 840.000 4364.77i 0.0633866 0.329366i
\(561\) −2268.00 −0.170686
\(562\) 1602.00 + 2774.75i 0.120243 + 0.208266i
\(563\) −529.500 + 917.121i −0.0396372 + 0.0686537i −0.885163 0.465280i \(-0.845954\pi\)
0.845526 + 0.533934i \(0.179287\pi\)
\(564\) −828.000 + 1434.14i −0.0618175 + 0.107071i
\(565\) −16380.0 28371.0i −1.21967 2.11252i
\(566\) −1372.00 −0.101890
\(567\) −283.500 + 1473.11i −0.0209980 + 0.109109i
\(568\) −8688.00 −0.641796
\(569\) −1980.00 3429.46i −0.145880 0.252672i 0.783821 0.620987i \(-0.213268\pi\)
−0.929701 + 0.368315i \(0.879935\pi\)
\(570\) 4680.00 8106.00i 0.343901 0.595654i
\(571\) 1265.00 2191.04i 0.0927121 0.160582i −0.815939 0.578138i \(-0.803780\pi\)
0.908651 + 0.417555i \(0.137113\pi\)
\(572\) −1584.00 2743.57i −0.115787 0.200550i
\(573\) −7560.00 −0.551175
\(574\) −4704.00 4073.78i −0.342058 0.296231i
\(575\) −8400.00 −0.609225
\(576\) −288.000 498.831i −0.0208333 0.0360844i
\(577\) −5915.50 + 10245.9i −0.426803 + 0.739245i −0.996587 0.0825498i \(-0.973694\pi\)
0.569784 + 0.821795i \(0.307027\pi\)
\(578\) 2143.00 3711.78i 0.154216 0.267111i
\(579\) 547.500 + 948.298i 0.0392976 + 0.0680655i
\(580\) −3060.00 −0.219068
\(581\) −10447.5 + 3619.12i −0.746016 + 0.258428i
\(582\) −1014.00 −0.0722193
\(583\) 2875.50 + 4980.51i 0.204273 + 0.353811i
\(584\) 872.000 1510.35i 0.0617870 0.107018i
\(585\) −5940.00 + 10288.4i −0.419810 + 0.727132i
\(586\) −1101.00 1906.99i −0.0776141 0.134432i
\(587\) 4809.00 0.338141 0.169070 0.985604i \(-0.445923\pi\)
0.169070 + 0.985604i \(0.445923\pi\)
\(588\) 3822.00 + 1527.67i 0.268055 + 0.107143i
\(589\) 19240.0 1.34596
\(590\) −2385.00 4130.94i −0.166422 0.288251i
\(591\) −2385.00 + 4130.94i −0.166000 + 0.287520i
\(592\) −352.000 + 609.682i −0.0244377 + 0.0423273i
\(593\) −10902.0 18882.8i −0.754960 1.30763i −0.945394 0.325930i \(-0.894323\pi\)
0.190434 0.981700i \(-0.439011\pi\)
\(594\) −486.000 −0.0335704
\(595\) 22050.0 7638.34i 1.51926 0.526288i
\(596\) −5736.00 −0.394221
\(597\) −8070.00 13977.7i −0.553238 0.958236i
\(598\) 7392.00 12803.3i 0.505487 0.875530i
\(599\) −7083.00 + 12268.1i −0.483144 + 0.836831i −0.999813 0.0193549i \(-0.993839\pi\)
0.516668 + 0.856186i \(0.327172\pi\)
\(600\) −1200.00 2078.46i −0.0816497 0.141421i
\(601\) 5891.00 0.399832 0.199916 0.979813i \(-0.435933\pi\)
0.199916 + 0.979813i \(0.435933\pi\)
\(602\) 9128.00 + 7905.08i 0.617989 + 0.535194i
\(603\) −1494.00 −0.100896
\(604\) 5342.00 + 9252.62i 0.359872 + 0.623317i
\(605\) −9375.00 + 16238.0i −0.629997 + 1.09119i
\(606\) −1926.00 + 3335.93i −0.129106 + 0.223619i
\(607\) 1368.50 + 2370.31i 0.0915086 + 0.158497i 0.908146 0.418653i \(-0.137498\pi\)
−0.816638 + 0.577151i \(0.804164\pi\)
\(608\) −3328.00 −0.221987
\(609\) 535.500 2782.54i 0.0356315 0.185146i
\(610\) 21660.0 1.43768
\(611\) −6072.00 10517.0i −0.402041 0.696355i
\(612\) 1512.00 2618.86i 0.0998676 0.172976i
\(613\) 13094.0 22679.5i 0.862743 1.49432i −0.00652719 0.999979i \(-0.502078\pi\)
0.869271 0.494337i \(-0.164589\pi\)
\(614\) 2780.00 + 4815.10i 0.182723 + 0.316485i
\(615\) −7560.00 −0.495689
\(616\) −252.000 + 1309.43i −0.0164827 + 0.0856468i
\(617\) −2358.00 −0.153857 −0.0769283 0.997037i \(-0.524511\pi\)
−0.0769283 + 0.997037i \(0.524511\pi\)
\(618\) −1392.00 2411.01i −0.0906059 0.156934i
\(619\) −6883.00 + 11921.7i −0.446932 + 0.774110i −0.998185 0.0602291i \(-0.980817\pi\)
0.551252 + 0.834339i \(0.314150\pi\)
\(620\) 5550.00 9612.88i 0.359505 0.622682i
\(621\) −1134.00 1964.15i −0.0732783 0.126922i
\(622\) −8592.00 −0.553871
\(623\) 14532.0 + 12585.1i 0.934530 + 0.809327i
\(624\) 4224.00 0.270986
\(625\) 9062.50 + 15696.7i 0.580000 + 1.00459i
\(626\) 5489.00 9507.23i 0.350455 0.607005i
\(627\) −1404.00 + 2431.80i −0.0894264 + 0.154891i
\(628\) −4504.00 7801.16i −0.286193 0.495701i
\(629\) −3696.00 −0.234291
\(630\) 4725.00 1636.79i 0.298807 0.103510i
\(631\) 21287.0 1.34298 0.671491 0.741012i \(-0.265654\pi\)
0.671491 + 0.741012i \(0.265654\pi\)
\(632\) −2332.00 4039.14i −0.146775 0.254222i
\(633\) −8043.00 + 13930.9i −0.505025 + 0.874728i
\(634\) 4491.00 7778.64i 0.281326 0.487270i
\(635\) −2797.50 4845.41i −0.174827 0.302810i
\(636\) −7668.00 −0.478075
\(637\) −23716.0 + 18671.5i −1.47514 + 1.16137i
\(638\) 918.000 0.0569655
\(639\) −4887.00 8464.53i −0.302546 0.524025i
\(640\) −960.000 + 1662.77i −0.0592927 + 0.102698i
\(641\) −10713.0 + 18555.5i −0.660122 + 1.14336i 0.320462 + 0.947262i \(0.396162\pi\)
−0.980583 + 0.196103i \(0.937171\pi\)
\(642\) −1179.00 2042.09i −0.0724788 0.125537i
\(643\) 9962.00 0.610984 0.305492 0.952195i \(-0.401179\pi\)
0.305492 + 0.952195i \(0.401179\pi\)
\(644\) −5880.00 + 2036.89i −0.359790 + 0.124635i
\(645\) 14670.0 0.895551
\(646\) −8736.00 15131.2i −0.532064 0.921562i
\(647\) 9087.00 15739.1i 0.552159 0.956367i −0.445960 0.895053i \(-0.647137\pi\)
0.998119 0.0613142i \(-0.0195292\pi\)
\(648\) 324.000 561.184i 0.0196419 0.0340207i
\(649\) 715.500 + 1239.28i 0.0432755 + 0.0749555i
\(650\) 17600.0 1.06204
\(651\) 7770.00 + 6729.02i 0.467788 + 0.405117i
\(652\) 6704.00 0.402682
\(653\) 9583.50 + 16599.1i 0.574321 + 0.994752i 0.996115 + 0.0880610i \(0.0280670\pi\)
−0.421795 + 0.906691i \(0.638600\pi\)
\(654\) −42.0000 + 72.7461i −0.00251121 + 0.00434954i
\(655\) −8797.50 + 15237.7i −0.524804 + 0.908988i
\(656\) 1344.00 + 2327.88i 0.0799914 + 0.138549i
\(657\) 1962.00 0.116507
\(658\) −966.000 + 5019.48i −0.0572319 + 0.297386i
\(659\) 13080.0 0.773178 0.386589 0.922252i \(-0.373653\pi\)
0.386589 + 0.922252i \(0.373653\pi\)
\(660\) 810.000 + 1402.96i 0.0477715 + 0.0827427i
\(661\) 7595.00 13154.9i 0.446916 0.774081i −0.551268 0.834328i \(-0.685856\pi\)
0.998183 + 0.0602477i \(0.0191891\pi\)
\(662\) −3964.00 + 6865.85i −0.232727 + 0.403095i
\(663\) 11088.0 + 19205.0i 0.649506 + 1.12498i
\(664\) 4776.00 0.279134
\(665\) 5460.00 28371.0i 0.318391 1.65441i
\(666\) −792.000 −0.0460801
\(667\) 2142.00 + 3710.05i 0.124346 + 0.215373i
\(668\) −6060.00 + 10496.2i −0.351001 + 0.607951i
\(669\) −2359.50 + 4086.77i −0.136358 + 0.236179i
\(670\) 2490.00 + 4312.81i 0.143578 + 0.248684i
\(671\) −6498.00 −0.373849
\(672\) −1344.00 1163.94i −0.0771517 0.0668153i
\(673\) 4397.00 0.251845 0.125923 0.992040i \(-0.459811\pi\)
0.125923 + 0.992040i \(0.459811\pi\)
\(674\) 161.000 + 278.860i 0.00920102 + 0.0159366i
\(675\) 1350.00 2338.27i 0.0769800 0.133333i
\(676\) −11094.0 + 19215.4i −0.631202 + 1.09327i
\(677\) −2014.50 3489.22i −0.114363 0.198082i 0.803162 0.595761i \(-0.203149\pi\)
−0.917525 + 0.397679i \(0.869816\pi\)
\(678\) −13104.0 −0.742266
\(679\) −2957.50 + 1024.51i −0.167155 + 0.0579043i
\(680\) −10080.0 −0.568456
\(681\) 1381.50 + 2392.83i 0.0777374 + 0.134645i
\(682\) −1665.00 + 2883.86i −0.0934841 + 0.161919i
\(683\) −7510.50 + 13008.6i −0.420763 + 0.728783i −0.996014 0.0891936i \(-0.971571\pi\)
0.575251 + 0.817977i \(0.304904\pi\)
\(684\) −1872.00 3242.40i −0.104646 0.181252i
\(685\) −450.000 −0.0251002
\(686\) 12691.0 + 594.093i 0.706333 + 0.0330650i
\(687\) −12156.0 −0.675081
\(688\) −2608.00 4517.19i −0.144519 0.250314i
\(689\) 28116.0 48698.3i 1.55462 2.69268i
\(690\) −3780.00 + 6547.15i −0.208554 + 0.361226i
\(691\) 6992.00 + 12110.5i 0.384932 + 0.666722i 0.991760 0.128111i \(-0.0408915\pi\)
−0.606828 + 0.794834i \(0.707558\pi\)
\(692\) 13752.0 0.755452
\(693\) −1417.50 + 491.036i −0.0777004 + 0.0269162i
\(694\) 11832.0 0.647171
\(695\) −615.000 1065.21i −0.0335659 0.0581378i
\(696\) −612.000 + 1060.02i −0.0333302 + 0.0577296i
\(697\) −7056.00 + 12221.4i −0.383451 + 0.664156i
\(698\) −142.000 245.951i −0.00770026 0.0133372i
\(699\) 1404.00 0.0759716
\(700\) −5600.00 4849.74i −0.302372 0.261861i
\(701\) −31053.0 −1.67312 −0.836559 0.547877i \(-0.815436\pi\)
−0.836559 + 0.547877i \(0.815436\pi\)
\(702\) 2376.00 + 4115.35i 0.127744 + 0.221259i
\(703\) −2288.00 + 3962.93i −0.122750 + 0.212610i
\(704\) 288.000 498.831i 0.0154182 0.0267051i
\(705\) 3105.00 + 5378.02i 0.165874 + 0.287302i
\(706\) 8880.00 0.473376
\(707\) −2247.00 + 11675.8i −0.119529 + 0.621092i
\(708\) −1908.00 −0.101281
\(709\) −7543.00 13064.9i −0.399553 0.692047i 0.594117 0.804378i \(-0.297501\pi\)
−0.993671 + 0.112332i \(0.964168\pi\)
\(710\) −16290.0 + 28215.1i −0.861060 + 1.49140i
\(711\) 2623.50 4544.04i 0.138381 0.239683i
\(712\) −4152.00 7191.47i −0.218543 0.378528i
\(713\) −15540.0 −0.816238
\(714\) 1764.00 9166.01i 0.0924594 0.480433i
\(715\) −11880.0 −0.621380
\(716\) 2424.00 + 4198.49i 0.126521 + 0.219141i
\(717\) 7398.00 12813.7i 0.385332 0.667415i
\(718\) 2286.00 3959.47i 0.118820 0.205802i
\(719\) 3189.00 + 5523.51i 0.165410 + 0.286498i 0.936801 0.349863i \(-0.113772\pi\)
−0.771391 + 0.636362i \(0.780439\pi\)
\(720\) −2160.00 −0.111803
\(721\) −6496.00 5625.70i −0.335539 0.290585i
\(722\) −7914.00 −0.407934
\(723\) −2305.50 3993.24i −0.118593 0.205408i
\(724\) −6064.00 + 10503.2i −0.311280 + 0.539153i
\(725\) −2550.00 + 4416.73i −0.130627 + 0.226253i
\(726\) 3750.00 + 6495.19i 0.191702 + 0.332037i
\(727\) −7363.00 −0.375624 −0.187812 0.982205i \(-0.560140\pi\)
−0.187812 + 0.982205i \(0.560140\pi\)
\(728\) 12320.0 4267.77i 0.627211 0.217272i
\(729\) 729.000 0.0370370
\(730\) −3270.00 5663.81i −0.165792 0.287160i
\(731\) 13692.0 23715.2i 0.692773 1.19992i
\(732\) 4332.00 7503.24i 0.218737 0.378863i
\(733\) −16405.0 28414.3i −0.826647 1.43180i −0.900654 0.434537i \(-0.856912\pi\)
0.0740064 0.997258i \(-0.476421\pi\)
\(734\) 5738.00 0.288547
\(735\) 12127.5 9547.93i 0.608612 0.479157i
\(736\) 2688.00 0.134621
\(737\) −747.000 1293.84i −0.0373353 0.0646666i
\(738\) −1512.00 + 2618.86i −0.0754167 + 0.130625i
\(739\) 12017.0 20814.1i 0.598177 1.03607i −0.394914 0.918718i \(-0.629225\pi\)
0.993090 0.117354i \(-0.0374412\pi\)
\(740\) 1320.00 + 2286.31i 0.0655732 + 0.113576i
\(741\) 27456.0 1.36116
\(742\) −22365.0 + 7747.46i −1.10653 + 0.383313i
\(743\) −8022.00 −0.396095 −0.198048 0.980192i \(-0.563460\pi\)
−0.198048 + 0.980192i \(0.563460\pi\)
\(744\) −2220.00 3845.15i −0.109394 0.189476i
\(745\) −10755.0 + 18628.2i −0.528903 + 0.916087i
\(746\) −3064.00 + 5307.00i −0.150377 + 0.260460i
\(747\) 2686.50 + 4653.15i 0.131585 + 0.227912i
\(748\) 3024.00 0.147819
\(749\) −5502.00 4764.87i −0.268409 0.232449i
\(750\) 2250.00 0.109545
\(751\) −14759.5 25564.2i −0.717153 1.24215i −0.962123 0.272615i \(-0.912112\pi\)
0.244970 0.969531i \(-0.421222\pi\)
\(752\) 1104.00 1912.18i 0.0535356 0.0927263i
\(753\) 7978.50 13819.2i 0.386126 0.668789i
\(754\) −4488.00 7773.44i −0.216768 0.375454i
\(755\) 40065.0 1.93128
\(756\) 378.000 1964.15i 0.0181848 0.0944911i
\(757\) −3742.00 −0.179664 −0.0898318 0.995957i \(-0.528633\pi\)
−0.0898318 + 0.995957i \(0.528633\pi\)
\(758\) −6040.00 10461.6i −0.289423 0.501295i
\(759\) 1134.00 1964.15i 0.0542313 0.0939314i
\(760\) −6240.00 + 10808.0i −0.297827 + 0.515852i
\(761\) 5448.00 + 9436.21i 0.259514 + 0.449491i 0.966112 0.258124i \(-0.0831044\pi\)
−0.706598 + 0.707615i \(0.749771\pi\)
\(762\) −2238.00 −0.106397
\(763\) −49.0000 + 254.611i −0.00232493 + 0.0120807i
\(764\) 10080.0 0.477332
\(765\) −5670.00 9820.73i −0.267973 0.464143i
\(766\) 1842.00 3190.44i 0.0868853 0.150490i
\(767\) 6996.00 12117.4i 0.329349 0.570450i
\(768\) 384.000 + 665.108i 0.0180422 + 0.0312500i
\(769\) 17285.0 0.810550 0.405275 0.914195i \(-0.367176\pi\)
0.405275 + 0.914195i \(0.367176\pi\)
\(770\) 3780.00 + 3273.58i 0.176911 + 0.153210i
\(771\) −16038.0 −0.749150
\(772\) −730.000 1264.40i −0.0340327 0.0589464i
\(773\) −5913.00 + 10241.6i −0.275130 + 0.476540i −0.970168 0.242434i \(-0.922054\pi\)
0.695038 + 0.718973i \(0.255388\pi\)
\(774\) 2934.00 5081.84i 0.136254 0.235999i
\(775\) −9250.00 16021.5i −0.428735 0.742591i
\(776\) 1352.00 0.0625438
\(777\) −2310.00 + 800.207i −0.106655 + 0.0369463i
\(778\) −15660.0 −0.721643
\(779\) 8736.00 + 15131.2i 0.401797 + 0.695932i
\(780\) 7920.00 13717.8i 0.363566 0.629715i
\(781\) 4887.00 8464.53i 0.223906 0.387817i
\(782\) 7056.00 + 12221.4i 0.322662 + 0.558868i
\(783\) −1377.00 −0.0628480
\(784\) −5096.00 2036.89i −0.232143 0.0927884i
\(785\) −33780.0 −1.53587
\(786\) 3519.00 + 6095.09i 0.159693 + 0.276596i
\(787\) −8857.00 + 15340.8i −0.401166 + 0.694841i −0.993867 0.110582i \(-0.964728\pi\)
0.592701 + 0.805423i \(0.298062\pi\)
\(788\) 3180.00 5507.92i 0.143760 0.248999i
\(789\) 1161.00 + 2010.91i 0.0523862 + 0.0907355i
\(790\) −17490.0 −0.787679
\(791\) −38220.0 + 13239.8i −1.71801 + 0.595136i
\(792\) 648.000 0.0290728
\(793\) 31768.0 + 55023.8i 1.42259 + 2.46400i
\(794\) −14764.0 + 25572.0i −0.659893 + 1.14297i
\(795\) −14377.5 + 24902.6i −0.641406 + 1.11095i
\(796\) 10760.0 + 18636.9i 0.479118 + 0.829857i
\(797\) −24939.0 −1.10839 −0.554194 0.832388i \(-0.686973\pi\)
−0.554194 + 0.832388i \(0.686973\pi\)
\(798\) −8736.00 7565.60i −0.387533 0.335613i
\(799\) 11592.0 0.513261
\(800\) 1600.00 + 2771.28i 0.0707107 + 0.122474i
\(801\) 4671.00 8090.41i 0.206045 0.356880i
\(802\) 6264.00 10849.6i 0.275797 0.477695i
\(803\) 981.000 + 1699.14i 0.0431118 + 0.0746717i
\(804\) 1992.00 0.0873786
\(805\) −4410.00 + 22915.0i −0.193083 + 1.00329i
\(806\) 32560.0 1.42292
\(807\) 3622.50 + 6274.35i 0.158015 + 0.273690i
\(808\) 2568.00 4447.91i 0.111809 0.193659i
\(809\) 14532.0 25170.2i 0.631543 1.09386i −0.355694 0.934602i \(-0.615755\pi\)
0.987236 0.159261i \(-0.0509112\pi\)
\(810\) −1215.00 2104.44i −0.0527046 0.0912871i
\(811\) −15370.0 −0.665492 −0.332746 0.943017i \(-0.607975\pi\)
−0.332746 + 0.943017i \(0.607975\pi\)
\(812\) −714.000 + 3710.05i −0.0308577 + 0.160342i
\(813\) 1425.00 0.0614722
\(814\) −396.000 685.892i −0.0170513 0.0295338i
\(815\) 12570.0 21771.9i 0.540255 0.935749i
\(816\) −2016.00 + 3491.81i −0.0864879 + 0.149801i
\(817\) −16952.0 29361.7i −0.725918 1.25733i
\(818\) −9502.00 −0.406149
\(819\) 11088.0 + 9602.49i 0.473072 + 0.409692i
\(820\) 10080.0 0.429279
\(821\) −22015.5 38132.0i −0.935866 1.62097i −0.773082 0.634306i \(-0.781286\pi\)
−0.162785 0.986662i \(-0.552048\pi\)
\(822\) −90.0000 + 155.885i −0.00381887 + 0.00661448i
\(823\) 2096.00 3630.38i 0.0887752 0.153763i −0.818218 0.574907i \(-0.805038\pi\)
0.906994 + 0.421144i \(0.138371\pi\)
\(824\) 1856.00 + 3214.69i 0.0784670 + 0.135909i
\(825\) 2700.00 0.113942
\(826\) −5565.00 + 1927.77i −0.234420 + 0.0812056i
\(827\) 33195.0 1.39577 0.697886 0.716209i \(-0.254124\pi\)
0.697886 + 0.716209i \(0.254124\pi\)
\(828\) 1512.00 + 2618.86i 0.0634609 + 0.109918i
\(829\) −8224.00 + 14244.4i −0.344549 + 0.596777i −0.985272 0.170996i \(-0.945302\pi\)
0.640723 + 0.767773i \(0.278635\pi\)
\(830\) 8955.00 15510.5i 0.374497 0.648648i
\(831\) 5592.00 + 9685.63i 0.233435 + 0.404321i
\(832\) −5632.00 −0.234681
\(833\) −4116.00 28516.5i −0.171202 1.18612i
\(834\) −492.000 −0.0204275
\(835\) 22725.0 + 39360.9i 0.941834 + 1.63130i
\(836\) 1872.00 3242.40i 0.0774455 0.134140i
\(837\) 2497.50 4325.80i 0.103138 0.178640i
\(838\) −4704.00 8147.57i −0.193910 0.335863i
\(839\) 16860.0 0.693769 0.346884 0.937908i \(-0.387240\pi\)
0.346884 + 0.937908i \(0.387240\pi\)
\(840\) −6300.00 + 2182.38i −0.258775 + 0.0896421i
\(841\) −21788.0 −0.893354
\(842\) −4474.00 7749.20i −0.183117 0.317167i
\(843\) 2403.00 4162.12i 0.0981776 0.170049i
\(844\) 10724.0 18574.5i 0.437364 0.757537i
\(845\) 41602.5 + 72057.6i 1.69369 + 2.93356i
\(846\) 2484.00 0.100948
\(847\) 17500.0 + 15155.4i 0.709926 + 0.614814i
\(848\) 10224.0 0.414025
\(849\) 1029.00 + 1782.28i 0.0415962 + 0.0720468i
\(850\) −8400.00 + 14549.2i −0.338962 + 0.587099i
\(851\) 1848.00 3200.83i 0.0744402 0.128934i
\(852\) 6516.00 + 11286.0i 0.262012 + 0.453819i
\(853\) 29054.0 1.16623 0.583113 0.812391i \(-0.301835\pi\)
0.583113 + 0.812391i \(0.301835\pi\)
\(854\) 5054.00 26261.4i 0.202511 1.05228i
\(855\) −14040.0 −0.561588
\(856\) 1572.00 + 2722.78i 0.0627685 + 0.108718i
\(857\) −20979.0 + 36336.7i −0.836207 + 1.44835i 0.0568378 + 0.998383i \(0.481898\pi\)
−0.893044 + 0.449969i \(0.851435\pi\)
\(858\) −2376.00 + 4115.35i −0.0945400 + 0.163748i
\(859\) −2773.00 4802.98i −0.110144 0.190775i 0.805684 0.592345i \(-0.201798\pi\)
−0.915828 + 0.401570i \(0.868464\pi\)
\(860\) −19560.0 −0.775570
\(861\) −1764.00 + 9166.01i −0.0698223 + 0.362807i
\(862\) 25608.0 1.01185
\(863\) 16269.0 + 28178.7i 0.641719 + 1.11149i 0.985049 + 0.172275i \(0.0551116\pi\)
−0.343330 + 0.939215i \(0.611555\pi\)
\(864\) −432.000 + 748.246i −0.0170103 + 0.0294628i
\(865\) 25785.0 44660.9i 1.01354 1.75551i
\(866\) −5074.00 8788.43i −0.199101 0.344853i
\(867\) −6429.00 −0.251834
\(868\) −10360.0 8972.02i −0.405117 0.350841i
\(869\) 5247.00 0.204824
\(870\) 2295.00 + 3975.06i 0.0894342 + 0.154905i
\(871\) −7304.00 + 12650.9i −0.284141 + 0.492146i
\(872\) 56.0000 96.9948i 0.00217477 0.00376681i
\(873\) 760.500 + 1317.22i 0.0294834 + 0.0510668i
\(874\) 17472.0 0.676200
\(875\) 6562.50 2273.32i 0.253546 0.0878310i
\(876\) −2616.00 −0.100898
\(877\) −16048.0 27796.0i −0.617905 1.07024i −0.989867 0.141995i \(-0.954648\pi\)
0.371963 0.928248i \(-0.378685\pi\)
\(878\) −1267.00 + 2194.51i −0.0487007 + 0.0843520i
\(879\) −1651.50 + 2860.48i −0.0633717 + 0.109763i
\(880\) −1080.00 1870.61i −0.0413714 0.0716573i
\(881\) −8490.00 −0.324671 −0.162336 0.986736i \(-0.551903\pi\)
−0.162336 + 0.986736i \(0.551903\pi\)
\(882\) −882.000 6110.68i −0.0336718 0.233285i
\(883\) −48352.0 −1.84278 −0.921390 0.388640i \(-0.872945\pi\)
−0.921390 + 0.388640i \(0.872945\pi\)
\(884\) −14784.0 25606.6i −0.562488 0.974258i
\(885\) −3577.50 + 6196.41i −0.135883 + 0.235356i
\(886\) −6933.00 + 12008.3i −0.262888 + 0.455335i
\(887\) −7746.00 13416.5i −0.293219 0.507870i 0.681350 0.731958i \(-0.261393\pi\)
−0.974569 + 0.224088i \(0.928060\pi\)
\(888\) 1056.00 0.0399066
\(889\) −6527.50 + 2261.19i −0.246260 + 0.0853070i
\(890\) −31140.0 −1.17283
\(891\) 364.500 + 631.333i 0.0137051 + 0.0237379i
\(892\) 3146.00 5449.03i 0.118090 0.204537i
\(893\) 7176.00 12429.2i 0.268909 0.465764i
\(894\) 4302.00 + 7451.28i 0.160940 + 0.278756i
\(895\) 18180.0 0.678984
\(896\) 1792.00 + 1551.92i 0.0668153 + 0.0578638i
\(897\) −22176.0 −0.825457
\(898\) 11688.0 + 20244.2i 0.434336 + 0.752292i
\(899\) −4717.50 + 8170.95i −0.175014 + 0.303133i
\(900\) −1800.00 + 3117.69i −0.0666667 + 0.115470i
\(901\) 26838.0 + 46484.8i 0.992346 + 1.71879i
\(902\) −3024.00 −0.111628
\(903\) 3423.00 17786.4i 0.126147 0.655477i
\(904\) 17472.0 0.642821
\(905\) 22740.0 + 39386.8i 0.835252 + 1.44670i
\(906\) 8013.00 13878.9i 0.293835 0.508936i
\(907\) 4058.00 7028.66i 0.148560 0.257313i −0.782136 0.623108i \(-0.785870\pi\)
0.930695 + 0.365795i \(0.119203\pi\)
\(908\) −1842.00 3190.44i −0.0673226 0.116606i
\(909\) 5778.00 0.210830
\(910\) 9240.00 48012.4i 0.336597 1.74901i
\(911\) −4446.00 −0.161693 −0.0808466 0.996727i \(-0.525762\pi\)
−0.0808466 + 0.996727i \(0.525762\pi\)
\(912\) 2496.00 + 4323.20i 0.0906259 + 0.156969i
\(913\) −2686.50 + 4653.15i −0.0973824 + 0.168671i
\(914\) 551.000 954.360i 0.0199403 0.0345377i
\(915\) −16245.0 28137.2i −0.586932 1.01660i
\(916\) 16208.0 0.584637
\(917\) 16422.0 + 14221.9i 0.591387 + 0.512156i
\(918\) −4536.00 −0.163083
\(919\) −13252.0 22953.1i −0.475673 0.823889i 0.523939 0.851756i \(-0.324462\pi\)
−0.999612 + 0.0278666i \(0.991129\pi\)
\(920\) 5040.00 8729.54i 0.180613 0.312831i
\(921\) 4170.00 7222.65i 0.149192 0.258409i
\(922\) 13386.0 + 23185.2i 0.478139 + 0.828162i
\(923\) −95568.0 −3.40808
\(924\) 1890.00 654.715i 0.0672905 0.0233101i
\(925\) 4400.00 0.156401
\(926\) −6376.00 11043.6i −0.226273 0.391916i
\(927\) −2088.00 + 3616.52i −0.0739794 + 0.128136i
\(928\) 816.000 1413.35i 0.0288648 0.0499953i
\(929\) 2715.00 + 4702.52i 0.0958840 + 0.166076i 0.909977 0.414658i \(-0.136099\pi\)
−0.814093 + 0.580734i \(0.802766\pi\)
\(930\) −16650.0 −0.587070
\(931\) −33124.0 13239.8i −1.16605 0.466076i
\(932\) −1872.00 −0.0657933
\(933\) 6444.00 + 11161.3i 0.226117 + 0.391646i
\(934\) 5700.00 9872.69i 0.199689 0.345872i
\(935\) 5670.00 9820.73i 0.198320 0.343500i
\(936\) −3168.00 5487.14i −0.110630 0.191616i
\(937\) 33803.0 1.17854 0.589272 0.807935i \(-0.299415\pi\)
0.589272 + 0.807935i \(0.299415\pi\)
\(938\) 5810.00 2012.64i 0.202242 0.0700588i
\(939\) −16467.0 −0.572290
\(940\) −4140.00 7170.69i −0.143651 0.248811i
\(941\) 24241.5 41987.5i 0.839798 1.45457i −0.0502645 0.998736i \(-0.516006\pi\)
0.890063 0.455838i \(-0.150660\pi\)
\(942\) −6756.00 + 11701.7i −0.233676 + 0.404738i
\(943\) −7056.00 12221.4i −0.243664 0.422038i
\(944\) 2544.00 0.0877120
\(945\) −5670.00 4910.36i −0.195180 0.169031i
\(946\) 5868.00 0.201676
\(947\) −18648.0 32299.3i −0.639893 1.10833i −0.985456 0.169931i \(-0.945645\pi\)
0.345563 0.938396i \(-0.387688\pi\)
\(948\) −3498.00 + 6058.71i −0.119842 + 0.207572i
\(949\) 9592.00 16613.8i 0.328103 0.568291i
\(950\) 10400.0 + 18013.3i 0.355180 + 0.615189i
\(951\) −13473.0 −0.459403
\(952\) −2352.00 + 12221.4i −0.0800722 + 0.416067i
\(953\) −38478.0 −1.30790 −0.653948 0.756540i \(-0.726888\pi\)
−0.653948 + 0.756540i \(0.726888\pi\)
\(954\) 5751.00 + 9961.02i 0.195173 + 0.338050i
\(955\) 18900.0 32735.8i 0.640408 1.10922i
\(956\) −9864.00 + 17084.9i −0.333708 + 0.577999i
\(957\) −688.500 1192.52i −0.0232561 0.0402807i
\(958\) −39588.0 −1.33510
\(959\) −105.000 + 545.596i −0.00353559 + 0.0183714i
\(960\) 2880.00 0.0968246
\(961\) −2217.00 3839.96i −0.0744184 0.128897i
\(962\) −3872.00 + 6706.50i −0.129770 + 0.224767i
\(963\) −1768.50 + 3063.13i −0.0591787 + 0.102501i
\(964\) 3074.00 + 5324.32i 0.102704 + 0.177889i
\(965\) −5475.00 −0.182639
\(966\) 7056.00 + 6110.68i 0.235014 + 0.203528i
\(967\) 27257.0 0.906438 0.453219 0.891399i \(-0.350275\pi\)
0.453219 + 0.891399i \(0.350275\pi\)
\(968\) −5000.00 8660.25i −0.166019 0.287553i
\(969\) −13104.0 + 22696.8i −0.434428 + 0.752452i
\(970\) 2535.00 4390.75i 0.0839113 0.145339i
\(971\) −17170.5 29740.2i −0.567485 0.982912i −0.996814 0.0797641i \(-0.974583\pi\)
0.429329 0.903148i \(-0.358750\pi\)
\(972\) −972.000 −0.0320750
\(973\) −1435.00 + 497.099i −0.0472806 + 0.0163785i
\(974\) −31870.0 −1.04844
\(975\) −13200.0 22863.1i −0.433578 0.750979i
\(976\) −5776.00 + 10004.3i −0.189432 + 0.328105i
\(977\) −13713.0 + 23751.6i −0.449046 + 0.777770i −0.998324 0.0578693i \(-0.981569\pi\)
0.549278 + 0.835639i \(0.314903\pi\)
\(978\) −5028.00 8708.75i −0.164394 0.284739i
\(979\) 9342.00 0.304976
\(980\) −16170.0 + 12730.6i −0.527073 + 0.414963i
\(981\) 126.000 0.00410079
\(982\) 9963.00 + 17256.4i 0.323760 + 0.560768i
\(983\) −6162.00 + 10672.9i −0.199936 + 0.346300i −0.948508 0.316755i \(-0.897407\pi\)
0.748571 + 0.663054i \(0.230740\pi\)
\(984\) 2016.00 3491.81i 0.0653127 0.113125i
\(985\) −11925.0 20654.7i −0.385748 0.668136i
\(986\) 8568.00 0.276735
\(987\) 7245.00 2509.74i 0.233648 0.0809382i
\(988\) −36608.0 −1.17880
\(989\) 13692.0 + 23715.2i 0.440223 + 0.762488i
\(990\) 1215.00 2104.44i 0.0390053 0.0675591i
\(991\) −23798.5 + 41220.2i −0.762850 + 1.32129i 0.178526 + 0.983935i \(0.442867\pi\)
−0.941376 + 0.337360i \(0.890466\pi\)
\(992\) 2960.00 + 5126.87i 0.0947380 + 0.164091i
\(993\) 11892.0 0.380042
\(994\) 30408.0 + 26334.1i 0.970305 + 0.840309i
\(995\) 80700.0 2.57122
\(996\) −3582.00 6204.21i −0.113956 0.197377i
\(997\) 5621.00 9735.86i 0.178555 0.309266i −0.762831 0.646598i \(-0.776191\pi\)
0.941386 + 0.337332i \(0.109525\pi\)
\(998\) 19142.0 33154.9i 0.607144 1.05160i
\(999\) 594.000 + 1028.84i 0.0188121 + 0.0325836i
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.b.25.1 2
3.2 odd 2 126.4.g.a.109.1 2
4.3 odd 2 336.4.q.d.193.1 2
7.2 even 3 inner 42.4.e.b.37.1 yes 2
7.3 odd 6 294.4.a.g.1.1 1
7.4 even 3 294.4.a.a.1.1 1
7.5 odd 6 294.4.e.e.79.1 2
7.6 odd 2 294.4.e.e.67.1 2
21.2 odd 6 126.4.g.a.37.1 2
21.5 even 6 882.4.g.l.667.1 2
21.11 odd 6 882.4.a.r.1.1 1
21.17 even 6 882.4.a.h.1.1 1
21.20 even 2 882.4.g.l.361.1 2
28.3 even 6 2352.4.a.q.1.1 1
28.11 odd 6 2352.4.a.u.1.1 1
28.23 odd 6 336.4.q.d.289.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.4.e.b.25.1 2 1.1 even 1 trivial
42.4.e.b.37.1 yes 2 7.2 even 3 inner
126.4.g.a.37.1 2 21.2 odd 6
126.4.g.a.109.1 2 3.2 odd 2
294.4.a.a.1.1 1 7.4 even 3
294.4.a.g.1.1 1 7.3 odd 6
294.4.e.e.67.1 2 7.6 odd 2
294.4.e.e.79.1 2 7.5 odd 6
336.4.q.d.193.1 2 4.3 odd 2
336.4.q.d.289.1 2 28.23 odd 6
882.4.a.h.1.1 1 21.17 even 6
882.4.a.r.1.1 1 21.11 odd 6
882.4.g.l.361.1 2 21.20 even 2
882.4.g.l.667.1 2 21.5 even 6
2352.4.a.q.1.1 1 28.3 even 6
2352.4.a.u.1.1 1 28.11 odd 6