Properties

Label 22.4.c.a.3.1
Level $22$
Weight $4$
Character 22.3
Analytic conductor $1.298$
Analytic rank $0$
Dimension $4$
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] = [22,4,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.29804202013\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 3.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 22.3
Dual form 22.4.c.a.15.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.61803 + 1.17557i) q^{2} +(-3.04508 - 9.37181i) q^{3} +(1.23607 - 3.80423i) q^{4} +(1.30902 + 0.951057i) q^{5} +(15.9443 + 11.5842i) q^{6} +(4.57295 - 14.0741i) q^{7} +(2.47214 + 7.60845i) q^{8} +(-56.7148 + 41.2057i) q^{9} +O(q^{10})\) \(q+(-1.61803 + 1.17557i) q^{2} +(-3.04508 - 9.37181i) q^{3} +(1.23607 - 3.80423i) q^{4} +(1.30902 + 0.951057i) q^{5} +(15.9443 + 11.5842i) q^{6} +(4.57295 - 14.0741i) q^{7} +(2.47214 + 7.60845i) q^{8} +(-56.7148 + 41.2057i) q^{9} -3.23607 q^{10} +(35.5967 + 7.99197i) q^{11} -39.4164 q^{12} +(41.1976 - 29.9318i) q^{13} +(9.14590 + 28.1482i) q^{14} +(4.92705 - 15.1639i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(48.7943 + 35.4511i) q^{17} +(43.3262 - 133.344i) q^{18} +(-8.16970 - 25.1437i) q^{19} +(5.23607 - 3.80423i) q^{20} -145.825 q^{21} +(-66.9919 + 28.9152i) q^{22} -29.1672 q^{23} +(63.7771 - 46.3368i) q^{24} +(-37.8181 - 116.392i) q^{25} +(-31.4721 + 96.8613i) q^{26} +(343.626 + 249.659i) q^{27} +(-47.8885 - 34.7931i) q^{28} +(-46.4352 + 142.913i) q^{29} +(9.85410 + 30.3278i) q^{30} +(-23.7680 + 17.2685i) q^{31} +32.0000 q^{32} +(-33.4959 - 357.942i) q^{33} -120.626 q^{34} +(19.3713 - 14.0741i) q^{35} +(86.6525 + 266.689i) q^{36} +(-69.4746 + 213.821i) q^{37} +(42.7771 + 31.0794i) q^{38} +(-405.965 - 294.951i) q^{39} +(-4.00000 + 12.3107i) q^{40} +(36.9975 + 113.867i) q^{41} +(235.949 - 171.427i) q^{42} +213.974 q^{43} +(74.4033 - 125.539i) q^{44} -113.430 q^{45} +(47.1935 - 34.2881i) q^{46} +(-54.0846 - 166.455i) q^{47} +(-48.7214 + 149.949i) q^{48} +(100.325 + 72.8902i) q^{49} +(198.018 + 143.869i) q^{50} +(183.658 - 565.243i) q^{51} +(-62.9443 - 193.723i) q^{52} +(51.1124 - 37.1353i) q^{53} -849.489 q^{54} +(38.9959 + 44.3161i) q^{55} +118.387 q^{56} +(-210.765 + 153.130i) q^{57} +(-92.8704 - 285.826i) q^{58} +(-80.9712 + 249.204i) q^{59} +(-51.5967 - 37.4872i) q^{60} +(573.568 + 416.722i) q^{61} +(18.1571 - 55.8819i) q^{62} +(320.579 + 986.641i) q^{63} +(-51.7771 + 37.6183i) q^{64} +82.3951 q^{65} +(474.984 + 539.786i) q^{66} -151.692 q^{67} +(195.177 - 141.805i) q^{68} +(88.8166 + 273.349i) q^{69} +(-14.7984 + 45.5447i) q^{70} +(-853.960 - 620.438i) q^{71} +(-453.718 - 329.646i) q^{72} +(-9.74013 + 29.9770i) q^{73} +(-138.949 - 427.642i) q^{74} +(-975.646 + 708.848i) q^{75} -105.751 q^{76} +(275.262 - 464.445i) q^{77} +1003.60 q^{78} +(-52.6797 + 38.2741i) q^{79} +(-8.00000 - 24.6215i) q^{80} +(708.479 - 2180.47i) q^{81} +(-193.721 - 140.747i) q^{82} +(186.532 + 135.523i) q^{83} +(-180.249 + 554.750i) q^{84} +(30.1565 + 92.8123i) q^{85} +(-346.217 + 251.541i) q^{86} +1480.75 q^{87} +(27.1935 + 290.593i) q^{88} -618.952 q^{89} +(183.533 - 133.344i) q^{90} +(-232.868 - 716.695i) q^{91} +(-36.0526 + 110.959i) q^{92} +(234.212 + 170.165i) q^{93} +(283.190 + 205.750i) q^{94} +(13.2188 - 40.6834i) q^{95} +(-97.4427 - 299.898i) q^{96} +(889.913 - 646.559i) q^{97} -248.016 q^{98} +(-2348.18 + 1013.53i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} - q^{3} - 4 q^{4} + 3 q^{5} + 28 q^{6} + 25 q^{7} - 8 q^{8} - 124 q^{9} - 4 q^{10} + 44 q^{11} - 104 q^{12} + 91 q^{13} + 50 q^{14} + 13 q^{15} - 16 q^{16} + 23 q^{17} + 142 q^{18} + 59 q^{19} + 12 q^{20} - 230 q^{21} - 22 q^{22} - 224 q^{23} + 112 q^{24} + 126 q^{25} - 108 q^{26} + 773 q^{27} - 120 q^{28} - 425 q^{29} + 26 q^{30} - 227 q^{31} + 128 q^{32} - 11 q^{33} - 724 q^{34} + 35 q^{35} + 284 q^{36} - 61 q^{37} + 28 q^{38} - 839 q^{39} - 16 q^{40} + 347 q^{41} + 510 q^{42} + 1160 q^{43} + 396 q^{44} - 248 q^{45} - 8 q^{46} + 251 q^{47} - 16 q^{48} + 48 q^{49} + 242 q^{50} - 247 q^{51} - 216 q^{52} - 245 q^{53} - 1144 q^{54} + 33 q^{55} + 80 q^{56} - 331 q^{57} - 850 q^{58} - 827 q^{59} - 108 q^{60} + 1335 q^{61} + 976 q^{62} + 370 q^{63} - 64 q^{64} + 182 q^{65} + 1408 q^{66} - 88 q^{67} + 92 q^{68} - 244 q^{69} - 10 q^{70} - 1665 q^{71} - 992 q^{72} - 153 q^{73} - 122 q^{74} - 1709 q^{75} - 584 q^{76} - 55 q^{77} + 1832 q^{78} + 677 q^{79} - 32 q^{80} + 1376 q^{81} - 596 q^{82} + 887 q^{83} - 560 q^{84} + 181 q^{85} - 240 q^{86} + 1670 q^{87} - 88 q^{88} + 1728 q^{89} + 354 q^{90} - 245 q^{91} + 464 q^{92} + 1033 q^{93} + 292 q^{94} + 73 q^{95} - 32 q^{96} + 2019 q^{97} - 1484 q^{98} - 5654 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/22\mathbb{Z}\right)^\times\).

\(n\) \(13\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.61803 + 1.17557i −0.572061 + 0.415627i
\(3\) −3.04508 9.37181i −0.586027 1.80361i −0.595107 0.803646i \(-0.702890\pi\)
0.00908010 0.999959i \(-0.497110\pi\)
\(4\) 1.23607 3.80423i 0.154508 0.475528i
\(5\) 1.30902 + 0.951057i 0.117082 + 0.0850651i 0.644785 0.764364i \(-0.276947\pi\)
−0.527703 + 0.849429i \(0.676947\pi\)
\(6\) 15.9443 + 11.5842i 1.08487 + 0.788204i
\(7\) 4.57295 14.0741i 0.246916 0.759929i −0.748399 0.663248i \(-0.769177\pi\)
0.995315 0.0966811i \(-0.0308227\pi\)
\(8\) 2.47214 + 7.60845i 0.109254 + 0.336249i
\(9\) −56.7148 + 41.2057i −2.10055 + 1.52614i
\(10\) −3.23607 −0.102333
\(11\) 35.5967 + 7.99197i 0.975711 + 0.219061i
\(12\) −39.4164 −0.948211
\(13\) 41.1976 29.9318i 0.878934 0.638583i −0.0540349 0.998539i \(-0.517208\pi\)
0.932969 + 0.359956i \(0.117208\pi\)
\(14\) 9.14590 + 28.1482i 0.174596 + 0.537351i
\(15\) 4.92705 15.1639i 0.0848106 0.261020i
\(16\) −12.9443 9.40456i −0.202254 0.146946i
\(17\) 48.7943 + 35.4511i 0.696139 + 0.505774i 0.878672 0.477425i \(-0.158430\pi\)
−0.182534 + 0.983200i \(0.558430\pi\)
\(18\) 43.3262 133.344i 0.567338 1.74609i
\(19\) −8.16970 25.1437i −0.0986451 0.303598i 0.889541 0.456855i \(-0.151024\pi\)
−0.988186 + 0.153256i \(0.951024\pi\)
\(20\) 5.23607 3.80423i 0.0585410 0.0425325i
\(21\) −145.825 −1.51531
\(22\) −66.9919 + 28.9152i −0.649214 + 0.280216i
\(23\) −29.1672 −0.264425 −0.132213 0.991221i \(-0.542208\pi\)
−0.132213 + 0.991221i \(0.542208\pi\)
\(24\) 63.7771 46.3368i 0.542435 0.394102i
\(25\) −37.8181 116.392i −0.302545 0.931137i
\(26\) −31.4721 + 96.8613i −0.237392 + 0.730618i
\(27\) 343.626 + 249.659i 2.44929 + 1.77951i
\(28\) −47.8885 34.7931i −0.323217 0.234831i
\(29\) −46.4352 + 142.913i −0.297338 + 0.915112i 0.685088 + 0.728460i \(0.259764\pi\)
−0.982426 + 0.186652i \(0.940236\pi\)
\(30\) 9.85410 + 30.3278i 0.0599702 + 0.184569i
\(31\) −23.7680 + 17.2685i −0.137705 + 0.100049i −0.654505 0.756057i \(-0.727123\pi\)
0.516800 + 0.856106i \(0.327123\pi\)
\(32\) 32.0000 0.176777
\(33\) −33.4959 357.942i −0.176694 1.88817i
\(34\) −120.626 −0.608448
\(35\) 19.3713 14.0741i 0.0935529 0.0679702i
\(36\) 86.6525 + 266.689i 0.401169 + 1.23467i
\(37\) −69.4746 + 213.821i −0.308691 + 0.950053i 0.669583 + 0.742737i \(0.266473\pi\)
−0.978274 + 0.207316i \(0.933527\pi\)
\(38\) 42.7771 + 31.0794i 0.182615 + 0.132677i
\(39\) −405.965 294.951i −1.66683 1.21102i
\(40\) −4.00000 + 12.3107i −0.0158114 + 0.0486624i
\(41\) 36.9975 + 113.867i 0.140928 + 0.433731i 0.996465 0.0840105i \(-0.0267729\pi\)
−0.855537 + 0.517741i \(0.826773\pi\)
\(42\) 235.949 171.427i 0.866852 0.629805i
\(43\) 213.974 0.758853 0.379427 0.925222i \(-0.376121\pi\)
0.379427 + 0.925222i \(0.376121\pi\)
\(44\) 74.4033 125.539i 0.254925 0.430131i
\(45\) −113.430 −0.375757
\(46\) 47.1935 34.2881i 0.151267 0.109902i
\(47\) −54.0846 166.455i −0.167852 0.516595i 0.831383 0.555700i \(-0.187550\pi\)
−0.999235 + 0.0391043i \(0.987550\pi\)
\(48\) −48.7214 + 149.949i −0.146507 + 0.450901i
\(49\) 100.325 + 72.8902i 0.292492 + 0.212508i
\(50\) 198.018 + 143.869i 0.560080 + 0.406922i
\(51\) 183.658 565.243i 0.504261 1.55196i
\(52\) −62.9443 193.723i −0.167862 0.516625i
\(53\) 51.1124 37.1353i 0.132468 0.0962440i −0.519578 0.854423i \(-0.673911\pi\)
0.652046 + 0.758179i \(0.273911\pi\)
\(54\) −849.489 −2.14076
\(55\) 38.9959 + 44.3161i 0.0956038 + 0.108647i
\(56\) 118.387 0.282502
\(57\) −210.765 + 153.130i −0.489763 + 0.355834i
\(58\) −92.8704 285.826i −0.210250 0.647082i
\(59\) −80.9712 + 249.204i −0.178670 + 0.549891i −0.999782 0.0208768i \(-0.993354\pi\)
0.821112 + 0.570767i \(0.193354\pi\)
\(60\) −51.5967 37.4872i −0.111019 0.0806597i
\(61\) 573.568 + 416.722i 1.20390 + 0.874684i 0.994663 0.103180i \(-0.0329019\pi\)
0.209237 + 0.977865i \(0.432902\pi\)
\(62\) 18.1571 55.8819i 0.0371929 0.114468i
\(63\) 320.579 + 986.641i 0.641098 + 1.97310i
\(64\) −51.7771 + 37.6183i −0.101127 + 0.0734732i
\(65\) 82.3951 0.157229
\(66\) 474.984 + 539.786i 0.885855 + 1.00671i
\(67\) −151.692 −0.276599 −0.138299 0.990390i \(-0.544164\pi\)
−0.138299 + 0.990390i \(0.544164\pi\)
\(68\) 195.177 141.805i 0.348069 0.252887i
\(69\) 88.8166 + 273.349i 0.154960 + 0.476919i
\(70\) −14.7984 + 45.5447i −0.0252678 + 0.0777662i
\(71\) −853.960 620.438i −1.42741 1.03708i −0.990491 0.137579i \(-0.956068\pi\)
−0.436924 0.899498i \(-0.643932\pi\)
\(72\) −453.718 329.646i −0.742656 0.539571i
\(73\) −9.74013 + 29.9770i −0.0156164 + 0.0480623i −0.958561 0.284887i \(-0.908044\pi\)
0.942945 + 0.332949i \(0.108044\pi\)
\(74\) −138.949 427.642i −0.218277 0.671789i
\(75\) −975.646 + 708.848i −1.50210 + 1.09134i
\(76\) −105.751 −0.159611
\(77\) 275.262 464.445i 0.407390 0.687382i
\(78\) 1003.60 1.45686
\(79\) −52.6797 + 38.2741i −0.0750245 + 0.0545085i −0.624665 0.780893i \(-0.714765\pi\)
0.549641 + 0.835401i \(0.314765\pi\)
\(80\) −8.00000 24.6215i −0.0111803 0.0344095i
\(81\) 708.479 2180.47i 0.971851 2.99105i
\(82\) −193.721 140.747i −0.260890 0.189547i
\(83\) 186.532 + 135.523i 0.246681 + 0.179224i 0.704255 0.709947i \(-0.251281\pi\)
−0.457573 + 0.889172i \(0.651281\pi\)
\(84\) −180.249 + 554.750i −0.234129 + 0.720574i
\(85\) 30.1565 + 92.8123i 0.0384816 + 0.118434i
\(86\) −346.217 + 251.541i −0.434111 + 0.315400i
\(87\) 1480.75 1.82475
\(88\) 27.1935 + 290.593i 0.0329413 + 0.352015i
\(89\) −618.952 −0.737177 −0.368589 0.929593i \(-0.620159\pi\)
−0.368589 + 0.929593i \(0.620159\pi\)
\(90\) 183.533 133.344i 0.214956 0.156175i
\(91\) −232.868 716.695i −0.268255 0.825605i
\(92\) −36.0526 + 110.959i −0.0408559 + 0.125742i
\(93\) 234.212 + 170.165i 0.261147 + 0.189734i
\(94\) 283.190 + 205.750i 0.310733 + 0.225760i
\(95\) 13.2188 40.6834i 0.0142761 0.0439372i
\(96\) −97.4427 299.898i −0.103596 0.318835i
\(97\) 889.913 646.559i 0.931515 0.676785i −0.0148484 0.999890i \(-0.504727\pi\)
0.946363 + 0.323105i \(0.104727\pi\)
\(98\) −248.016 −0.255647
\(99\) −2348.18 + 1013.53i −2.38384 + 1.02892i
\(100\) −489.528 −0.489528
\(101\) −1091.59 + 793.084i −1.07541 + 0.781335i −0.976878 0.213799i \(-0.931416\pi\)
−0.0985372 + 0.995133i \(0.531416\pi\)
\(102\) 367.317 + 1130.49i 0.356567 + 1.09740i
\(103\) −458.805 + 1412.06i −0.438907 + 1.35082i 0.450123 + 0.892966i \(0.351380\pi\)
−0.889030 + 0.457849i \(0.848620\pi\)
\(104\) 329.580 + 239.454i 0.310750 + 0.225773i
\(105\) −190.887 138.688i −0.177416 0.128900i
\(106\) −39.0464 + 120.172i −0.0357785 + 0.110115i
\(107\) −544.547 1675.94i −0.491994 1.51420i −0.821590 0.570079i \(-0.806913\pi\)
0.329597 0.944122i \(-0.393087\pi\)
\(108\) 1374.50 998.634i 1.22464 0.889756i
\(109\) 688.087 0.604649 0.302325 0.953205i \(-0.402237\pi\)
0.302325 + 0.953205i \(0.402237\pi\)
\(110\) −115.193 25.8626i −0.0998479 0.0224172i
\(111\) 2215.45 1.89442
\(112\) −191.554 + 139.172i −0.161609 + 0.117416i
\(113\) 93.6925 + 288.356i 0.0779987 + 0.240055i 0.982451 0.186519i \(-0.0597204\pi\)
−0.904453 + 0.426574i \(0.859720\pi\)
\(114\) 161.010 495.538i 0.132280 0.407117i
\(115\) −38.1803 27.7396i −0.0309594 0.0224933i
\(116\) 486.276 + 353.300i 0.389220 + 0.282785i
\(117\) −1103.15 + 3395.15i −0.871678 + 2.68275i
\(118\) −161.942 498.407i −0.126339 0.388831i
\(119\) 722.076 524.619i 0.556241 0.404132i
\(120\) 127.554 0.0970337
\(121\) 1203.26 + 568.976i 0.904025 + 0.427480i
\(122\) −1417.94 −1.05225
\(123\) 954.475 693.467i 0.699692 0.508356i
\(124\) 36.3143 + 111.764i 0.0262993 + 0.0809410i
\(125\) 123.691 380.682i 0.0885061 0.272394i
\(126\) −1678.57 1219.55i −1.18682 0.862274i
\(127\) −1832.93 1331.71i −1.28068 0.930470i −0.281109 0.959676i \(-0.590702\pi\)
−0.999573 + 0.0292057i \(0.990702\pi\)
\(128\) 39.5542 121.735i 0.0273135 0.0840623i
\(129\) −651.568 2005.32i −0.444708 1.36867i
\(130\) −133.318 + 96.8613i −0.0899444 + 0.0653484i
\(131\) 1457.48 0.972068 0.486034 0.873940i \(-0.338443\pi\)
0.486034 + 0.873940i \(0.338443\pi\)
\(132\) −1403.10 315.015i −0.925180 0.207716i
\(133\) −391.235 −0.255070
\(134\) 245.443 178.325i 0.158232 0.114962i
\(135\) 212.372 + 653.615i 0.135393 + 0.416698i
\(136\) −149.102 + 458.889i −0.0940103 + 0.289334i
\(137\) 159.260 + 115.709i 0.0993177 + 0.0721585i 0.636336 0.771412i \(-0.280449\pi\)
−0.537018 + 0.843571i \(0.680449\pi\)
\(138\) −465.050 337.878i −0.286867 0.208421i
\(139\) −12.2537 + 37.7129i −0.00747728 + 0.0230127i −0.954726 0.297488i \(-0.903851\pi\)
0.947248 + 0.320501i \(0.103851\pi\)
\(140\) −29.5967 91.0894i −0.0178670 0.0549890i
\(141\) −1395.29 + 1013.74i −0.833368 + 0.605477i
\(142\) 2111.11 1.24761
\(143\) 1705.71 736.224i 0.997475 0.430533i
\(144\) 1121.65 0.649105
\(145\) −196.703 + 142.913i −0.112657 + 0.0818501i
\(146\) −19.4803 59.9541i −0.0110425 0.0339852i
\(147\) 377.615 1162.18i 0.211872 0.652075i
\(148\) 727.548 + 528.595i 0.404082 + 0.293582i
\(149\) 1983.05 + 1440.77i 1.09032 + 0.792165i 0.979453 0.201670i \(-0.0646369\pi\)
0.110868 + 0.993835i \(0.464637\pi\)
\(150\) 745.327 2293.88i 0.405705 1.24863i
\(151\) 853.976 + 2628.27i 0.460236 + 1.41646i 0.864877 + 0.501984i \(0.167396\pi\)
−0.404642 + 0.914475i \(0.632604\pi\)
\(152\) 171.108 124.317i 0.0913074 0.0663387i
\(153\) −4228.15 −2.23415
\(154\) 100.605 + 1075.08i 0.0526427 + 0.562547i
\(155\) −47.5360 −0.0246334
\(156\) −1623.86 + 1179.80i −0.833416 + 0.605512i
\(157\) −1102.59 3393.41i −0.560483 1.72499i −0.681004 0.732280i \(-0.738456\pi\)
0.120521 0.992711i \(-0.461544\pi\)
\(158\) 40.2437 123.858i 0.0202634 0.0623644i
\(159\) −503.667 365.935i −0.251216 0.182519i
\(160\) 41.8885 + 30.4338i 0.0206974 + 0.0150375i
\(161\) −133.380 + 410.502i −0.0652908 + 0.200944i
\(162\) 1416.96 + 4360.95i 0.687202 + 2.11499i
\(163\) 57.4193 41.7176i 0.0275916 0.0200464i −0.573904 0.818923i \(-0.694572\pi\)
0.601496 + 0.798876i \(0.294572\pi\)
\(164\) 478.906 0.228026
\(165\) 296.576 500.409i 0.139930 0.236102i
\(166\) −461.132 −0.215607
\(167\) −2218.99 + 1612.19i −1.02821 + 0.747035i −0.967949 0.251148i \(-0.919192\pi\)
−0.0602564 + 0.998183i \(0.519192\pi\)
\(168\) −360.498 1109.50i −0.165554 0.509523i
\(169\) 122.417 376.761i 0.0557202 0.171489i
\(170\) −157.902 114.722i −0.0712383 0.0517576i
\(171\) 1499.41 + 1089.38i 0.670542 + 0.487177i
\(172\) 264.486 814.004i 0.117249 0.360856i
\(173\) 412.124 + 1268.39i 0.181117 + 0.557421i 0.999860 0.0167395i \(-0.00532860\pi\)
−0.818743 + 0.574160i \(0.805329\pi\)
\(174\) −2395.90 + 1740.73i −1.04387 + 0.758415i
\(175\) −1811.05 −0.782302
\(176\) −385.613 438.222i −0.165152 0.187683i
\(177\) 2582.05 1.09649
\(178\) 1001.49 727.622i 0.421711 0.306391i
\(179\) 1001.56 + 3082.48i 0.418212 + 1.28713i 0.909346 + 0.416041i \(0.136583\pi\)
−0.491134 + 0.871084i \(0.663417\pi\)
\(180\) −140.207 + 431.512i −0.0580577 + 0.178683i
\(181\) −2152.17 1563.65i −0.883811 0.642126i 0.0504458 0.998727i \(-0.483936\pi\)
−0.934257 + 0.356600i \(0.883936\pi\)
\(182\) 1219.31 + 885.883i 0.496602 + 0.360802i
\(183\) 2158.87 6644.32i 0.872068 2.68395i
\(184\) −72.1052 221.917i −0.0288895 0.0889128i
\(185\) −294.299 + 213.821i −0.116958 + 0.0849753i
\(186\) −579.005 −0.228251
\(187\) 1453.59 + 1651.91i 0.568435 + 0.645986i
\(188\) −700.085 −0.271590
\(189\) 5085.10 3694.54i 1.95707 1.42190i
\(190\) 26.4377 + 81.3669i 0.0100947 + 0.0310683i
\(191\) −308.593 + 949.751i −0.116906 + 0.359799i −0.992340 0.123539i \(-0.960576\pi\)
0.875434 + 0.483338i \(0.160576\pi\)
\(192\) 510.217 + 370.694i 0.191780 + 0.139336i
\(193\) −3108.04 2258.12i −1.15918 0.842192i −0.169504 0.985529i \(-0.554217\pi\)
−0.989674 + 0.143337i \(0.954217\pi\)
\(194\) −679.833 + 2092.31i −0.251594 + 0.774325i
\(195\) −250.900 772.191i −0.0921402 0.283578i
\(196\) 401.299 291.561i 0.146246 0.106254i
\(197\) −3386.25 −1.22467 −0.612335 0.790598i \(-0.709770\pi\)
−0.612335 + 0.790598i \(0.709770\pi\)
\(198\) 2607.96 4400.37i 0.936058 1.57940i
\(199\) −4895.30 −1.74381 −0.871906 0.489674i \(-0.837116\pi\)
−0.871906 + 0.489674i \(0.837116\pi\)
\(200\) 792.073 575.475i 0.280040 0.203461i
\(201\) 461.915 + 1421.63i 0.162094 + 0.498875i
\(202\) 833.898 2566.47i 0.290460 0.893943i
\(203\) 1799.02 + 1307.07i 0.622003 + 0.451912i
\(204\) −1923.30 1397.36i −0.660087 0.479581i
\(205\) −59.8632 + 184.240i −0.0203953 + 0.0627701i
\(206\) −917.609 2824.11i −0.310354 0.955171i
\(207\) 1654.21 1201.85i 0.555438 0.403549i
\(208\) −814.768 −0.271606
\(209\) −89.8667 960.327i −0.0297426 0.317834i
\(210\) 471.899 0.155067
\(211\) 1188.79 863.709i 0.387867 0.281802i −0.376714 0.926330i \(-0.622946\pi\)
0.764581 + 0.644528i \(0.222946\pi\)
\(212\) −78.0928 240.345i −0.0252992 0.0778630i
\(213\) −3214.25 + 9892.44i −1.03398 + 3.18225i
\(214\) 2851.28 + 2071.58i 0.910793 + 0.661730i
\(215\) 280.095 + 203.501i 0.0888481 + 0.0645519i
\(216\) −1050.03 + 3231.65i −0.330765 + 1.01799i
\(217\) 134.348 + 413.481i 0.0420283 + 0.129350i
\(218\) −1113.35 + 808.894i −0.345896 + 0.251308i
\(219\) 310.599 0.0958370
\(220\) 216.790 93.5716i 0.0664363 0.0286754i
\(221\) 3071.32 0.934839
\(222\) −3584.67 + 2604.41i −1.08373 + 0.787373i
\(223\) 539.379 + 1660.04i 0.161971 + 0.498495i 0.998800 0.0489686i \(-0.0155934\pi\)
−0.836829 + 0.547464i \(0.815593\pi\)
\(224\) 146.334 450.371i 0.0436490 0.134338i
\(225\) 6940.87 + 5042.83i 2.05655 + 1.49417i
\(226\) −490.580 356.428i −0.144393 0.104908i
\(227\) 730.475 2248.17i 0.213583 0.657341i −0.785668 0.618648i \(-0.787681\pi\)
0.999251 0.0386928i \(-0.0123194\pi\)
\(228\) 322.020 + 991.076i 0.0935364 + 0.287875i
\(229\) 2502.89 1818.46i 0.722253 0.524748i −0.164850 0.986319i \(-0.552714\pi\)
0.887103 + 0.461571i \(0.152714\pi\)
\(230\) 94.3870 0.0270595
\(231\) −5190.88 1165.43i −1.47851 0.331946i
\(232\) −1202.14 −0.340191
\(233\) −2184.39 + 1587.05i −0.614182 + 0.446229i −0.850884 0.525353i \(-0.823933\pi\)
0.236703 + 0.971582i \(0.423933\pi\)
\(234\) −2206.30 6790.30i −0.616369 1.89699i
\(235\) 87.5106 269.330i 0.0242918 0.0747624i
\(236\) 847.941 + 616.065i 0.233882 + 0.169926i
\(237\) 519.112 + 377.157i 0.142278 + 0.103371i
\(238\) −551.617 + 1697.70i −0.150235 + 0.462377i
\(239\) 110.604 + 340.405i 0.0299347 + 0.0921296i 0.964908 0.262590i \(-0.0845765\pi\)
−0.934973 + 0.354719i \(0.884577\pi\)
\(240\) −206.387 + 149.949i −0.0555093 + 0.0403298i
\(241\) 4290.72 1.14685 0.573423 0.819260i \(-0.305615\pi\)
0.573423 + 0.819260i \(0.305615\pi\)
\(242\) −2615.78 + 493.891i −0.694830 + 0.131192i
\(243\) −11124.3 −2.93672
\(244\) 2294.27 1666.89i 0.601950 0.437342i
\(245\) 62.0041 + 190.829i 0.0161685 + 0.0497617i
\(246\) −729.154 + 2244.11i −0.188980 + 0.581622i
\(247\) −1089.17 791.327i −0.280575 0.203850i
\(248\) −190.144 138.148i −0.0486861 0.0353725i
\(249\) 702.094 2160.82i 0.178688 0.549946i
\(250\) 247.382 + 761.363i 0.0625832 + 0.192611i
\(251\) 4362.71 3169.69i 1.09710 0.797088i 0.116514 0.993189i \(-0.462828\pi\)
0.980584 + 0.196101i \(0.0628280\pi\)
\(252\) 4149.66 1.03732
\(253\) −1038.26 233.103i −0.258003 0.0579252i
\(254\) 4531.26 1.11936
\(255\) 777.990 565.243i 0.191057 0.138811i
\(256\) 79.1084 + 243.470i 0.0193136 + 0.0594410i
\(257\) 1259.96 3877.75i 0.305813 0.941196i −0.673560 0.739133i \(-0.735236\pi\)
0.979373 0.202063i \(-0.0647645\pi\)
\(258\) 3411.65 + 2478.71i 0.823257 + 0.598131i
\(259\) 2691.63 + 1955.58i 0.645752 + 0.469167i
\(260\) 101.846 313.450i 0.0242932 0.0747666i
\(261\) −3255.26 10018.7i −0.772014 2.37601i
\(262\) −2358.26 + 1713.37i −0.556082 + 0.404018i
\(263\) −3256.10 −0.763421 −0.381711 0.924282i \(-0.624665\pi\)
−0.381711 + 0.924282i \(0.624665\pi\)
\(264\) 2640.58 1139.73i 0.615592 0.265704i
\(265\) 102.225 0.0236967
\(266\) 633.031 459.924i 0.145916 0.106014i
\(267\) 1884.76 + 5800.70i 0.432006 + 1.32958i
\(268\) −187.502 + 577.070i −0.0427369 + 0.131531i
\(269\) −1666.61 1210.86i −0.377750 0.274452i 0.382667 0.923886i \(-0.375006\pi\)
−0.760417 + 0.649435i \(0.775006\pi\)
\(270\) −1112.00 807.912i −0.250644 0.182104i
\(271\) −1652.93 + 5087.21i −0.370511 + 1.14032i 0.575946 + 0.817488i \(0.304634\pi\)
−0.946457 + 0.322829i \(0.895366\pi\)
\(272\) −298.204 917.778i −0.0664753 0.204590i
\(273\) −6007.62 + 4364.79i −1.33186 + 0.967653i
\(274\) −393.713 −0.0868068
\(275\) −415.999 4445.42i −0.0912207 0.974797i
\(276\) 1149.67 0.250731
\(277\) 6799.60 4940.20i 1.47490 1.07158i 0.495750 0.868465i \(-0.334893\pi\)
0.979155 0.203116i \(-0.0651067\pi\)
\(278\) −24.5073 75.4257i −0.00528723 0.0162724i
\(279\) 636.438 1958.75i 0.136568 0.420314i
\(280\) 154.971 + 112.593i 0.0330759 + 0.0240311i
\(281\) −5691.91 4135.42i −1.20837 0.877930i −0.213285 0.976990i \(-0.568416\pi\)
−0.995081 + 0.0990600i \(0.968416\pi\)
\(282\) 1065.91 3280.53i 0.225085 0.692741i
\(283\) 2334.20 + 7183.92i 0.490295 + 1.50897i 0.824162 + 0.566354i \(0.191646\pi\)
−0.333867 + 0.942620i \(0.608354\pi\)
\(284\) −3415.84 + 2481.75i −0.713707 + 0.518539i
\(285\) −421.530 −0.0876115
\(286\) −1894.42 + 3196.42i −0.391676 + 0.660869i
\(287\) 1771.76 0.364402
\(288\) −1814.87 + 1318.58i −0.371328 + 0.269785i
\(289\) −394.099 1212.91i −0.0802156 0.246878i
\(290\) 150.267 462.476i 0.0304276 0.0936465i
\(291\) −8769.29 6371.26i −1.76655 1.28347i
\(292\) 102.000 + 74.1073i 0.0204421 + 0.0148521i
\(293\) 1008.60 3104.15i 0.201103 0.618930i −0.798748 0.601665i \(-0.794504\pi\)
0.999851 0.0172649i \(-0.00549588\pi\)
\(294\) 755.231 + 2324.36i 0.149816 + 0.461087i
\(295\) −342.999 + 249.204i −0.0676956 + 0.0491837i
\(296\) −1798.60 −0.353180
\(297\) 10236.7 + 11633.3i 1.99998 + 2.27283i
\(298\) −4902.37 −0.952976
\(299\) −1201.62 + 873.026i −0.232412 + 0.168857i
\(300\) 1490.65 + 4587.76i 0.286876 + 0.882915i
\(301\) 978.491 3011.48i 0.187373 0.576675i
\(302\) −4471.48 3248.72i −0.852002 0.619015i
\(303\) 10756.6 + 7815.13i 2.03944 + 1.48174i
\(304\) −130.715 + 402.300i −0.0246613 + 0.0758996i
\(305\) 354.485 + 1090.99i 0.0665500 + 0.204820i
\(306\) 6841.29 4970.49i 1.27807 0.928574i
\(307\) −5505.74 −1.02355 −0.511774 0.859120i \(-0.671012\pi\)
−0.511774 + 0.859120i \(0.671012\pi\)
\(308\) −1426.61 1621.24i −0.263924 0.299932i
\(309\) 14630.6 2.69355
\(310\) 76.9149 55.8819i 0.0140918 0.0102383i
\(311\) −373.968 1150.95i −0.0681857 0.209854i 0.911158 0.412058i \(-0.135190\pi\)
−0.979344 + 0.202203i \(0.935190\pi\)
\(312\) 1240.52 3817.92i 0.225098 0.692780i
\(313\) 3966.86 + 2882.09i 0.716358 + 0.520464i 0.885218 0.465176i \(-0.154009\pi\)
−0.168861 + 0.985640i \(0.554009\pi\)
\(314\) 5773.21 + 4194.48i 1.03758 + 0.753848i
\(315\) −518.708 + 1596.42i −0.0927805 + 0.285549i
\(316\) 80.4875 + 247.715i 0.0143284 + 0.0440983i
\(317\) −6220.65 + 4519.57i −1.10217 + 0.800771i −0.981412 0.191912i \(-0.938531\pi\)
−0.120754 + 0.992682i \(0.538531\pi\)
\(318\) 1245.13 0.219571
\(319\) −2795.10 + 4716.12i −0.490581 + 0.827750i
\(320\) −103.554 −0.0180902
\(321\) −14048.4 + 10206.8i −2.44270 + 1.77472i
\(322\) −266.760 821.003i −0.0461676 0.142089i
\(323\) 492.740 1516.50i 0.0848816 0.261239i
\(324\) −7419.29 5390.43i −1.27217 0.924285i
\(325\) −5041.84 3663.11i −0.860526 0.625209i
\(326\) −43.8644 + 135.001i −0.00745223 + 0.0229356i
\(327\) −2095.28 6448.62i −0.354341 1.09055i
\(328\) −774.885 + 562.987i −0.130445 + 0.0947737i
\(329\) −2590.03 −0.434021
\(330\) 108.395 + 1158.32i 0.0180817 + 0.193223i
\(331\) 3085.35 0.512344 0.256172 0.966631i \(-0.417539\pi\)
0.256172 + 0.966631i \(0.417539\pi\)
\(332\) 746.128 542.094i 0.123341 0.0896122i
\(333\) −4870.40 14989.6i −0.801491 2.46674i
\(334\) 1695.15 5217.15i 0.277709 0.854699i
\(335\) −198.567 144.268i −0.0323848 0.0235289i
\(336\) 1887.59 + 1371.42i 0.306478 + 0.222670i
\(337\) −1785.06 + 5493.84i −0.288541 + 0.888038i 0.696774 + 0.717291i \(0.254618\pi\)
−0.985315 + 0.170747i \(0.945382\pi\)
\(338\) 244.834 + 753.523i 0.0394001 + 0.121261i
\(339\) 2417.12 1756.14i 0.387256 0.281358i
\(340\) 390.354 0.0622645
\(341\) −984.072 + 424.748i −0.156277 + 0.0674528i
\(342\) −3706.74 −0.586075
\(343\) 5591.08 4062.16i 0.880146 0.639464i
\(344\) 528.972 + 1628.01i 0.0829077 + 0.255164i
\(345\) −143.708 + 442.288i −0.0224261 + 0.0690203i
\(346\) −2157.91 1567.81i −0.335289 0.243602i
\(347\) −735.627 534.465i −0.113806 0.0826846i 0.529427 0.848356i \(-0.322407\pi\)
−0.643232 + 0.765671i \(0.722407\pi\)
\(348\) 1830.31 5633.11i 0.281939 0.867719i
\(349\) 3533.36 + 10874.6i 0.541938 + 1.66791i 0.728161 + 0.685406i \(0.240375\pi\)
−0.186223 + 0.982508i \(0.559625\pi\)
\(350\) 2930.35 2129.02i 0.447525 0.325146i
\(351\) 21629.3 3.28913
\(352\) 1139.10 + 255.743i 0.172483 + 0.0387248i
\(353\) 2773.55 0.418190 0.209095 0.977895i \(-0.432948\pi\)
0.209095 + 0.977895i \(0.432948\pi\)
\(354\) −4177.85 + 3035.39i −0.627260 + 0.455731i
\(355\) −527.776 1624.33i −0.0789055 0.242846i
\(356\) −765.067 + 2354.63i −0.113900 + 0.350549i
\(357\) −7115.41 5169.65i −1.05487 0.766406i
\(358\) −5244.23 3810.16i −0.774207 0.562494i
\(359\) −779.606 + 2399.38i −0.114613 + 0.352742i −0.991866 0.127286i \(-0.959373\pi\)
0.877253 + 0.480028i \(0.159373\pi\)
\(360\) −280.413 863.023i −0.0410530 0.126348i
\(361\) 4983.58 3620.79i 0.726576 0.527888i
\(362\) 5320.47 0.772479
\(363\) 1668.32 13009.3i 0.241223 1.88102i
\(364\) −3014.31 −0.434046
\(365\) −41.2599 + 29.9770i −0.00591682 + 0.00429882i
\(366\) 4317.74 + 13288.6i 0.616645 + 1.89784i
\(367\) 1623.66 4997.11i 0.230938 0.710754i −0.766696 0.642010i \(-0.778101\pi\)
0.997634 0.0687443i \(-0.0218993\pi\)
\(368\) 377.548 + 274.305i 0.0534811 + 0.0388563i
\(369\) −6790.26 4933.41i −0.957958 0.695997i
\(370\) 224.825 691.939i 0.0315894 0.0972222i
\(371\) −288.912 889.179i −0.0404300 0.124431i
\(372\) 936.849 680.661i 0.130574 0.0948672i
\(373\) 316.370 0.0439169 0.0219585 0.999759i \(-0.493010\pi\)
0.0219585 + 0.999759i \(0.493010\pi\)
\(374\) −4293.90 964.040i −0.593669 0.133287i
\(375\) −3944.33 −0.543158
\(376\) 1132.76 822.999i 0.155366 0.112880i
\(377\) 2364.62 + 7277.55i 0.323035 + 0.994198i
\(378\) −3884.67 + 11955.8i −0.528587 + 1.62682i
\(379\) −4253.04 3090.01i −0.576422 0.418795i 0.261011 0.965336i \(-0.415944\pi\)
−0.837432 + 0.546541i \(0.815944\pi\)
\(380\) −138.430 100.575i −0.0186876 0.0135773i
\(381\) −6899.04 + 21233.1i −0.927687 + 2.85513i
\(382\) −617.186 1899.50i −0.0826648 0.254416i
\(383\) 1152.22 837.137i 0.153722 0.111686i −0.508265 0.861201i \(-0.669713\pi\)
0.661988 + 0.749515i \(0.269713\pi\)
\(384\) −1261.33 −0.167622
\(385\) 802.036 346.177i 0.106170 0.0458255i
\(386\) 7683.49 1.01316
\(387\) −12135.5 + 8816.94i −1.59401 + 1.15811i
\(388\) −1359.67 4184.62i −0.177904 0.547531i
\(389\) −608.800 + 1873.69i −0.0793506 + 0.244216i −0.982860 0.184351i \(-0.940982\pi\)
0.903510 + 0.428567i \(0.140982\pi\)
\(390\) 1313.73 + 954.481i 0.170573 + 0.123928i
\(391\) −1423.19 1034.01i −0.184077 0.133739i
\(392\) −306.565 + 943.510i −0.0394997 + 0.121567i
\(393\) −4438.16 13659.2i −0.569658 1.75323i
\(394\) 5479.06 3980.77i 0.700587 0.509006i
\(395\) −105.359 −0.0134208
\(396\) 953.177 + 10185.8i 0.120957 + 1.29256i
\(397\) −4148.62 −0.524467 −0.262233 0.965004i \(-0.584459\pi\)
−0.262233 + 0.965004i \(0.584459\pi\)
\(398\) 7920.76 5754.77i 0.997567 0.724775i
\(399\) 1191.34 + 3666.58i 0.149478 + 0.460046i
\(400\) −605.090 + 1862.27i −0.0756362 + 0.232784i
\(401\) 6237.68 + 4531.94i 0.776795 + 0.564375i 0.904015 0.427500i \(-0.140606\pi\)
−0.127220 + 0.991874i \(0.540606\pi\)
\(402\) −2418.62 1757.23i −0.300074 0.218016i
\(403\) −462.308 + 1422.84i −0.0571444 + 0.175872i
\(404\) 1667.80 + 5132.95i 0.205386 + 0.632113i
\(405\) 3001.17 2180.47i 0.368220 0.267528i
\(406\) −4447.43 −0.543650
\(407\) −4181.92 + 7056.09i −0.509312 + 0.859355i
\(408\) 4754.65 0.576937
\(409\) 2828.03 2054.69i 0.341900 0.248405i −0.403563 0.914952i \(-0.632228\pi\)
0.745463 + 0.666547i \(0.232228\pi\)
\(410\) −119.726 368.480i −0.0144216 0.0443852i
\(411\) 599.445 1844.90i 0.0719426 0.221417i
\(412\) 4804.67 + 3490.79i 0.574536 + 0.417425i
\(413\) 3137.04 + 2279.19i 0.373762 + 0.271554i
\(414\) −1263.70 + 3889.28i −0.150019 + 0.461710i
\(415\) 115.283 + 354.805i 0.0136362 + 0.0419679i
\(416\) 1318.32 957.817i 0.155375 0.112887i
\(417\) 390.751 0.0458877
\(418\) 1274.34 + 1448.20i 0.149115 + 0.169459i
\(419\) 6493.78 0.757140 0.378570 0.925573i \(-0.376416\pi\)
0.378570 + 0.925573i \(0.376416\pi\)
\(420\) −763.548 + 554.750i −0.0887079 + 0.0644501i
\(421\) −3078.30 9474.04i −0.356359 1.09676i −0.955217 0.295906i \(-0.904379\pi\)
0.598858 0.800855i \(-0.295621\pi\)
\(422\) −908.157 + 2795.02i −0.104759 + 0.322416i
\(423\) 9926.29 + 7211.87i 1.14098 + 0.828968i
\(424\) 408.899 + 297.083i 0.0468347 + 0.0340274i
\(425\) 2280.93 7019.97i 0.260332 0.801220i
\(426\) −6428.50 19784.9i −0.731131 2.25019i
\(427\) 8487.88 6166.80i 0.961961 0.698905i
\(428\) −7048.76 −0.796062
\(429\) −12093.8 13743.7i −1.36106 1.54675i
\(430\) −692.433 −0.0776561
\(431\) −4447.02 + 3230.95i −0.496996 + 0.361089i −0.807868 0.589363i \(-0.799379\pi\)
0.310872 + 0.950452i \(0.399379\pi\)
\(432\) −2100.05 6463.30i −0.233886 0.719828i
\(433\) 30.3861 93.5189i 0.00337243 0.0103793i −0.949356 0.314202i \(-0.898263\pi\)
0.952729 + 0.303823i \(0.0982631\pi\)
\(434\) −703.455 511.090i −0.0778040 0.0565279i
\(435\) 1938.33 + 1408.28i 0.213645 + 0.155222i
\(436\) 850.522 2617.64i 0.0934234 0.287528i
\(437\) 238.287 + 733.372i 0.0260842 + 0.0802791i
\(438\) −502.559 + 365.131i −0.0548247 + 0.0398325i
\(439\) −1951.20 −0.212131 −0.106065 0.994359i \(-0.533825\pi\)
−0.106065 + 0.994359i \(0.533825\pi\)
\(440\) −240.774 + 406.254i −0.0260874 + 0.0440168i
\(441\) −8693.38 −0.938709
\(442\) −4969.50 + 3610.56i −0.534785 + 0.388544i
\(443\) 2916.72 + 8976.73i 0.312816 + 0.962747i 0.976644 + 0.214863i \(0.0689304\pi\)
−0.663829 + 0.747885i \(0.731070\pi\)
\(444\) 2738.44 8428.06i 0.292704 0.900851i
\(445\) −810.219 588.658i −0.0863102 0.0627080i
\(446\) −2824.23 2051.92i −0.299845 0.217850i
\(447\) 7464.07 22972.0i 0.789795 2.43074i
\(448\) 292.669 + 900.742i 0.0308645 + 0.0949912i
\(449\) −10419.2 + 7569.98i −1.09513 + 0.795656i −0.980258 0.197725i \(-0.936645\pi\)
−0.114869 + 0.993381i \(0.536645\pi\)
\(450\) −17158.8 −1.79749
\(451\) 406.972 + 4348.96i 0.0424913 + 0.454068i
\(452\) 1212.78 0.126205
\(453\) 22031.2 16006.6i 2.28502 1.66017i
\(454\) 1460.95 + 4496.34i 0.151026 + 0.464810i
\(455\) 376.789 1159.64i 0.0388223 0.119483i
\(456\) −1686.12 1225.04i −0.173157 0.125806i
\(457\) 6276.04 + 4559.81i 0.642409 + 0.466738i 0.860677 0.509151i \(-0.170041\pi\)
−0.218268 + 0.975889i \(0.570041\pi\)
\(458\) −1912.04 + 5884.66i −0.195074 + 0.600376i
\(459\) 7916.29 + 24363.8i 0.805013 + 2.47757i
\(460\) −152.721 + 110.959i −0.0154797 + 0.0112467i
\(461\) 13529.3 1.36686 0.683432 0.730014i \(-0.260487\pi\)
0.683432 + 0.730014i \(0.260487\pi\)
\(462\) 9769.07 4216.55i 0.983762 0.424614i
\(463\) −14558.3 −1.46130 −0.730651 0.682752i \(-0.760783\pi\)
−0.730651 + 0.682752i \(0.760783\pi\)
\(464\) 1945.10 1413.20i 0.194610 0.141393i
\(465\) 144.751 + 445.498i 0.0144359 + 0.0444290i
\(466\) 1668.73 5135.82i 0.165885 0.510541i
\(467\) 3748.30 + 2723.30i 0.371415 + 0.269849i 0.757797 0.652490i \(-0.226275\pi\)
−0.386382 + 0.922339i \(0.626275\pi\)
\(468\) 11552.3 + 8393.27i 1.14104 + 0.829015i
\(469\) −693.680 + 2134.93i −0.0682967 + 0.210196i
\(470\) 175.021 + 538.660i 0.0171769 + 0.0528650i
\(471\) −28444.9 + 20666.4i −2.78274 + 2.02178i
\(472\) −2096.23 −0.204421
\(473\) 7616.77 + 1710.07i 0.740421 + 0.166235i
\(474\) −1283.31 −0.124356
\(475\) −2617.57 + 1901.78i −0.252847 + 0.183704i
\(476\) −1103.23 3395.41i −0.106233 0.326950i
\(477\) −1368.64 + 4212.25i −0.131375 + 0.404330i
\(478\) −579.132 420.764i −0.0554160 0.0402621i
\(479\) −15857.6 11521.2i −1.51263 1.09899i −0.964991 0.262281i \(-0.915525\pi\)
−0.547643 0.836712i \(-0.684475\pi\)
\(480\) 157.666 485.245i 0.0149925 0.0461423i
\(481\) 3537.86 + 10888.4i 0.335369 + 1.03216i
\(482\) −6942.54 + 5044.05i −0.656066 + 0.476660i
\(483\) 4253.30 0.400687
\(484\) 3651.82 3874.17i 0.342958 0.363840i
\(485\) 1779.83 0.166634
\(486\) 17999.4 13077.4i 1.67998 1.22058i
\(487\) −1135.70 3495.33i −0.105675 0.325233i 0.884213 0.467083i \(-0.154695\pi\)
−0.989888 + 0.141850i \(0.954695\pi\)
\(488\) −1752.67 + 5394.16i −0.162581 + 0.500373i
\(489\) −565.816 411.089i −0.0523253 0.0380165i
\(490\) −324.658 235.877i −0.0299317 0.0217466i
\(491\) 6356.81 19564.3i 0.584275 1.79821i −0.0178877 0.999840i \(-0.505694\pi\)
0.602163 0.798373i \(-0.294306\pi\)
\(492\) −1458.31 4488.21i −0.133629 0.411269i
\(493\) −7332.19 + 5327.15i −0.669828 + 0.486659i
\(494\) 2692.57 0.245232
\(495\) −4037.72 906.525i −0.366631 0.0823137i
\(496\) 470.062 0.0425532
\(497\) −12637.2 + 9181.48i −1.14056 + 0.828663i
\(498\) 1404.19 + 4321.64i 0.126352 + 0.388870i
\(499\) 299.378 921.390i 0.0268577 0.0826594i −0.936729 0.350055i \(-0.886163\pi\)
0.963587 + 0.267395i \(0.0861630\pi\)
\(500\) −1295.31 941.097i −0.115856 0.0841743i
\(501\) 21866.1 + 15886.7i 1.94991 + 1.41669i
\(502\) −3332.81 + 10257.3i −0.296316 + 0.911967i
\(503\) −3990.19 12280.5i −0.353705 1.08859i −0.956757 0.290890i \(-0.906049\pi\)
0.603052 0.797702i \(-0.293951\pi\)
\(504\) −6714.29 + 4878.22i −0.593409 + 0.431137i
\(505\) −2183.17 −0.192376
\(506\) 1953.96 843.375i 0.171669 0.0740961i
\(507\) −3903.71 −0.341952
\(508\) −7331.74 + 5326.82i −0.640341 + 0.465235i
\(509\) −741.973 2283.56i −0.0646117 0.198855i 0.913539 0.406751i \(-0.133338\pi\)
−0.978151 + 0.207896i \(0.933338\pi\)
\(510\) −594.331 + 1829.16i −0.0516028 + 0.158817i
\(511\) 377.359 + 274.167i 0.0326680 + 0.0237347i
\(512\) −414.217 300.946i −0.0357538 0.0259767i
\(513\) 3470.03 10679.7i 0.298647 0.919140i
\(514\) 2519.91 + 7755.50i 0.216242 + 0.665526i
\(515\) −1943.53 + 1412.06i −0.166295 + 0.120821i
\(516\) −8434.07 −0.719553
\(517\) −594.930 6357.50i −0.0506093 0.540818i
\(518\) −6654.08 −0.564408
\(519\) 10632.1 7724.70i 0.899228 0.653327i
\(520\) 203.692 + 626.899i 0.0171779 + 0.0528680i
\(521\) 4413.81 13584.3i 0.371157 1.14230i −0.574878 0.818239i \(-0.694951\pi\)
0.946035 0.324064i \(-0.105049\pi\)
\(522\) 17044.8 + 12383.7i 1.42917 + 1.03836i
\(523\) 7496.61 + 5446.60i 0.626776 + 0.455379i 0.855282 0.518163i \(-0.173384\pi\)
−0.228506 + 0.973543i \(0.573384\pi\)
\(524\) 1801.55 5544.59i 0.150193 0.462246i
\(525\) 5514.81 + 16972.9i 0.458450 + 1.41096i
\(526\) 5268.48 3827.78i 0.436724 0.317298i
\(527\) −1771.93 −0.146464
\(528\) −2932.71 + 4948.31i −0.241723 + 0.407856i
\(529\) −11316.3 −0.930079
\(530\) −165.403 + 120.172i −0.0135560 + 0.00984898i
\(531\) −5676.35 17470.0i −0.463903 1.42775i
\(532\) −483.593 + 1488.35i −0.0394105 + 0.121293i
\(533\) 4932.44 + 3583.62i 0.400840 + 0.291227i
\(534\) −9868.74 7170.06i −0.799742 0.581046i
\(535\) 881.095 2711.73i 0.0712020 0.219137i
\(536\) −375.003 1154.14i −0.0302195 0.0930061i
\(537\) 25838.6 18772.8i 2.07638 1.50858i
\(538\) 4120.08 0.330166
\(539\) 2988.70 + 3396.44i 0.238835 + 0.271420i
\(540\) 2749.00 0.219071
\(541\) −4262.05 + 3096.56i −0.338706 + 0.246084i −0.744116 0.668051i \(-0.767129\pi\)
0.405410 + 0.914135i \(0.367129\pi\)
\(542\) −3305.87 10174.4i −0.261991 0.806326i
\(543\) −8100.64 + 24931.2i −0.640205 + 1.97035i
\(544\) 1561.42 + 1134.44i 0.123061 + 0.0894091i
\(545\) 900.717 + 654.409i 0.0707935 + 0.0514345i
\(546\) 4589.41 14124.8i 0.359723 1.10711i
\(547\) −5988.10 18429.5i −0.468067 1.44056i −0.855084 0.518489i \(-0.826495\pi\)
0.387018 0.922072i \(-0.373505\pi\)
\(548\) 637.041 462.837i 0.0496588 0.0360793i
\(549\) −49701.1 −3.86374
\(550\) 5899.01 + 6703.81i 0.457336 + 0.519730i
\(551\) 3972.72 0.307157
\(552\) −1860.20 + 1351.51i −0.143433 + 0.104211i
\(553\) 297.771 + 916.445i 0.0228978 + 0.0704723i
\(554\) −5194.44 + 15986.8i −0.398358 + 1.22602i
\(555\) 2900.06 + 2107.01i 0.221803 + 0.161149i
\(556\) 128.322 + 93.2314i 0.00978788 + 0.00711131i
\(557\) −1640.80 + 5049.86i −0.124817 + 0.384146i −0.993868 0.110576i \(-0.964730\pi\)
0.869051 + 0.494723i \(0.164730\pi\)
\(558\) 1272.88 + 3917.51i 0.0965683 + 0.297207i
\(559\) 8815.19 6404.61i 0.666982 0.484591i
\(560\) −383.108 −0.0289094
\(561\) 11055.0 18653.0i 0.831986 1.40380i
\(562\) 14071.2 1.05615
\(563\) 3636.30 2641.93i 0.272206 0.197769i −0.443305 0.896371i \(-0.646194\pi\)
0.715511 + 0.698602i \(0.246194\pi\)
\(564\) 2131.82 + 6561.06i 0.159159 + 0.489842i
\(565\) −151.598 + 466.570i −0.0112881 + 0.0347411i
\(566\) −12222.0 8879.81i −0.907649 0.659446i
\(567\) −27448.4 19942.4i −2.03302 1.47708i
\(568\) 2609.47 8031.12i 0.192766 0.593272i
\(569\) −6870.82 21146.2i −0.506221 1.55799i −0.798709 0.601718i \(-0.794483\pi\)
0.292488 0.956269i \(-0.405517\pi\)
\(570\) 682.050 495.538i 0.0501191 0.0364137i
\(571\) 2370.18 0.173711 0.0868554 0.996221i \(-0.472318\pi\)
0.0868554 + 0.996221i \(0.472318\pi\)
\(572\) −692.387 7398.94i −0.0506122 0.540848i
\(573\) 9840.57 0.717445
\(574\) −2866.76 + 2082.82i −0.208460 + 0.151455i
\(575\) 1103.05 + 3394.83i 0.0800005 + 0.246216i
\(576\) 1386.44 4267.02i 0.100292 0.308668i
\(577\) 11203.3 + 8139.68i 0.808318 + 0.587277i 0.913343 0.407192i \(-0.133492\pi\)
−0.105024 + 0.994470i \(0.533492\pi\)
\(578\) 2063.53 + 1499.24i 0.148498 + 0.107890i
\(579\) −11698.4 + 36004.1i −0.839673 + 2.58425i
\(580\) 300.535 + 924.951i 0.0215156 + 0.0662181i
\(581\) 2760.37 2005.53i 0.197107 0.143207i
\(582\) 21678.9 1.54402
\(583\) 2116.22 913.409i 0.150334 0.0648877i
\(584\) −252.158 −0.0178671
\(585\) −4673.02 + 3395.15i −0.330266 + 0.239952i
\(586\) 2017.20 + 6208.31i 0.142201 + 0.437650i
\(587\) −6142.87 + 18905.8i −0.431931 + 1.32935i 0.464268 + 0.885695i \(0.346317\pi\)
−0.896199 + 0.443652i \(0.853683\pi\)
\(588\) −3954.44 2873.07i −0.277344 0.201502i
\(589\) 628.371 + 456.538i 0.0439585 + 0.0319377i
\(590\) 262.028 806.440i 0.0182840 0.0562722i
\(591\) 10311.4 + 31735.2i 0.717690 + 2.20882i
\(592\) 2910.19 2114.38i 0.202041 0.146791i
\(593\) 23426.3 1.62226 0.811132 0.584863i \(-0.198852\pi\)
0.811132 + 0.584863i \(0.198852\pi\)
\(594\) −30239.1 6789.09i −2.08876 0.468956i
\(595\) 1444.15 0.0995034
\(596\) 7932.20 5763.08i 0.545161 0.396082i
\(597\) 14906.6 + 45877.8i 1.02192 + 3.14515i
\(598\) 917.954 2825.17i 0.0627724 0.193194i
\(599\) 715.720 + 520.001i 0.0488206 + 0.0354702i 0.611928 0.790914i \(-0.290394\pi\)
−0.563107 + 0.826384i \(0.690394\pi\)
\(600\) −7805.17 5670.78i −0.531074 0.385848i
\(601\) −2132.95 + 6564.54i −0.144767 + 0.445546i −0.996981 0.0776468i \(-0.975259\pi\)
0.852214 + 0.523193i \(0.175259\pi\)
\(602\) 1956.98 + 6022.97i 0.132493 + 0.407771i
\(603\) 8603.18 6250.57i 0.581009 0.422128i
\(604\) 11054.1 0.744677
\(605\) 1033.96 + 1889.16i 0.0694814 + 0.126951i
\(606\) −26591.8 −1.78254
\(607\) 15358.8 11158.8i 1.02701 0.746165i 0.0593000 0.998240i \(-0.481113\pi\)
0.967708 + 0.252075i \(0.0811131\pi\)
\(608\) −261.430 804.600i −0.0174382 0.0536691i
\(609\) 6771.40 20840.2i 0.450560 1.38668i
\(610\) −1856.11 1348.54i −0.123199 0.0895095i
\(611\) −7210.45 5238.70i −0.477420 0.346866i
\(612\) −5226.28 + 16084.8i −0.345196 + 1.06240i
\(613\) −5602.31 17242.1i −0.369127 1.13606i −0.947356 0.320182i \(-0.896256\pi\)
0.578229 0.815875i \(-0.303744\pi\)
\(614\) 8908.48 6472.39i 0.585533 0.425414i
\(615\) 1908.95 0.125165
\(616\) 4214.19 + 946.145i 0.275641 + 0.0618852i
\(617\) −15257.7 −0.995549 −0.497774 0.867307i \(-0.665849\pi\)
−0.497774 + 0.867307i \(0.665849\pi\)
\(618\) −23672.8 + 17199.3i −1.54088 + 1.11951i
\(619\) −2351.71 7237.82i −0.152703 0.469972i 0.845218 0.534422i \(-0.179471\pi\)
−0.997921 + 0.0644500i \(0.979471\pi\)
\(620\) −58.7577 + 180.838i −0.00380608 + 0.0117139i
\(621\) −10022.6 7281.84i −0.647653 0.470548i
\(622\) 1958.12 + 1422.66i 0.126227 + 0.0917096i
\(623\) −2830.44 + 8711.19i −0.182021 + 0.560203i
\(624\) 2481.04 + 7635.85i 0.159168 + 0.489869i
\(625\) −11852.2 + 8611.11i −0.758539 + 0.551111i
\(626\) −9806.61 −0.626120
\(627\) −8726.35 + 3766.49i −0.555816 + 0.239903i
\(628\) −14272.2 −0.906881
\(629\) −10970.2 + 7970.29i −0.695404 + 0.505241i
\(630\) −1037.42 3192.84i −0.0656057 0.201914i
\(631\) −8054.72 + 24789.9i −0.508167 + 1.56398i 0.287214 + 0.957866i \(0.407271\pi\)
−0.795381 + 0.606110i \(0.792729\pi\)
\(632\) −421.438 306.193i −0.0265252 0.0192717i
\(633\) −11714.5 8511.07i −0.735559 0.534415i
\(634\) 4752.16 14625.6i 0.297685 0.916180i
\(635\) −1132.82 3486.45i −0.0707944 0.217883i
\(636\) −2014.67 + 1463.74i −0.125608 + 0.0912597i
\(637\) 6314.86 0.392785
\(638\) −1021.57 10916.7i −0.0633926 0.677422i
\(639\) 73997.8 4.58107
\(640\) 167.554 121.735i 0.0103487 0.00751876i
\(641\) −7101.22 21855.3i −0.437568 1.34670i −0.890432 0.455117i \(-0.849598\pi\)
0.452864 0.891580i \(-0.350402\pi\)
\(642\) 10732.0 33029.8i 0.659750 2.03050i
\(643\) −5300.09 3850.74i −0.325062 0.236172i 0.413270 0.910608i \(-0.364386\pi\)
−0.738333 + 0.674437i \(0.764386\pi\)
\(644\) 1396.77 + 1014.82i 0.0854668 + 0.0620952i
\(645\) 1054.26 3244.68i 0.0643588 0.198076i
\(646\) 985.479 + 3032.99i 0.0600204 + 0.184724i
\(647\) 5081.70 3692.07i 0.308783 0.224344i −0.422591 0.906320i \(-0.638879\pi\)
0.731374 + 0.681977i \(0.238879\pi\)
\(648\) 18341.5 1.11192
\(649\) −4873.94 + 8223.72i −0.294790 + 0.497395i
\(650\) 12464.1 0.752127
\(651\) 3465.96 2518.17i 0.208666 0.151605i
\(652\) −87.7289 270.002i −0.00526952 0.0162179i
\(653\) 364.184 1120.84i 0.0218248 0.0671699i −0.939551 0.342409i \(-0.888757\pi\)
0.961376 + 0.275239i \(0.0887571\pi\)
\(654\) 10971.0 + 7970.93i 0.655966 + 0.476587i
\(655\) 1907.87 + 1386.15i 0.113812 + 0.0826890i
\(656\) 591.960 1821.86i 0.0352319 0.108433i
\(657\) −682.816 2101.49i −0.0405467 0.124790i
\(658\) 4190.76 3044.76i 0.248287 0.180391i
\(659\) −15421.0 −0.911561 −0.455781 0.890092i \(-0.650640\pi\)
−0.455781 + 0.890092i \(0.650640\pi\)
\(660\) −1537.08 1746.78i −0.0906526 0.103020i
\(661\) −9587.68 −0.564172 −0.282086 0.959389i \(-0.591026\pi\)
−0.282086 + 0.959389i \(0.591026\pi\)
\(662\) −4992.20 + 3627.04i −0.293092 + 0.212944i
\(663\) −9352.44 28783.8i −0.547841 1.68608i
\(664\) −569.991 + 1754.25i −0.0333132 + 0.102527i
\(665\) −512.133 372.086i −0.0298642 0.0216976i
\(666\) 25501.8 + 18528.1i 1.48374 + 1.07800i
\(667\) 1354.38 4168.36i 0.0786236 0.241979i
\(668\) 3390.31 + 10434.3i 0.196370 + 0.604364i
\(669\) 13915.1 10109.9i 0.804169 0.584263i
\(670\) 490.885 0.0283053
\(671\) 17086.7 + 19417.9i 0.983050 + 1.11717i
\(672\) −4666.39 −0.267872
\(673\) −13066.9 + 9493.66i −0.748428 + 0.543765i −0.895339 0.445385i \(-0.853067\pi\)
0.146911 + 0.989150i \(0.453067\pi\)
\(674\) −3570.12 10987.7i −0.204029 0.627937i
\(675\) 16063.0 49436.9i 0.915950 2.81901i
\(676\) −1281.97 931.406i −0.0729387 0.0529930i
\(677\) 6493.60 + 4717.87i 0.368640 + 0.267832i 0.756647 0.653824i \(-0.226836\pi\)
−0.388007 + 0.921656i \(0.626836\pi\)
\(678\) −1846.51 + 5682.98i −0.104594 + 0.321908i
\(679\) −5030.21 15481.4i −0.284303 0.874995i
\(680\) −631.607 + 458.889i −0.0356191 + 0.0258788i
\(681\) −23293.8 −1.31075
\(682\) 1092.94 1844.10i 0.0613649 0.103540i
\(683\) −17912.7 −1.00353 −0.501765 0.865004i \(-0.667316\pi\)
−0.501765 + 0.865004i \(0.667316\pi\)
\(684\) 5997.63 4357.53i 0.335271 0.243588i
\(685\) 98.4282 + 302.931i 0.00549015 + 0.0168969i
\(686\) −4271.21 + 13145.4i −0.237719 + 0.731625i
\(687\) −24663.8 17919.3i −1.36970 0.995143i
\(688\) −2769.73 2012.33i −0.153481 0.111511i
\(689\) 994.180 3059.77i 0.0549713 0.169184i
\(690\) −287.416 884.577i −0.0158576 0.0488047i
\(691\) −22242.6 + 16160.2i −1.22453 + 0.889672i −0.996468 0.0839750i \(-0.973238\pi\)
−0.228060 + 0.973647i \(0.573238\pi\)
\(692\) 5334.65 0.293053
\(693\) 3526.37 + 37683.2i 0.193298 + 2.06561i
\(694\) 1818.57 0.0994698
\(695\) −51.9073 + 37.7129i −0.00283303 + 0.00205832i
\(696\) 3660.62 + 11266.2i 0.199361 + 0.613570i
\(697\) −2231.43 + 6867.64i −0.121265 + 0.373215i
\(698\) −18500.9 13441.7i −1.00325 0.728905i
\(699\) 21525.2 + 15639.0i 1.16475 + 0.846239i
\(700\) −2238.59 + 6889.66i −0.120872 + 0.372007i
\(701\) 691.682 + 2128.78i 0.0372674 + 0.114697i 0.967960 0.251106i \(-0.0807943\pi\)
−0.930692 + 0.365803i \(0.880794\pi\)
\(702\) −34996.9 + 25426.7i −1.88158 + 1.36705i
\(703\) 5943.85 0.318885
\(704\) −2143.74 + 925.287i −0.114766 + 0.0495356i
\(705\) −2790.59 −0.149077
\(706\) −4487.69 + 3260.50i −0.239230 + 0.173811i
\(707\) 6170.17 + 18989.8i 0.328222 + 1.01016i
\(708\) 3191.59 9822.71i 0.169417 0.521413i
\(709\) −19598.0 14238.8i −1.03811 0.754229i −0.0681922 0.997672i \(-0.521723\pi\)
−0.969915 + 0.243443i \(0.921723\pi\)
\(710\) 2763.47 + 2007.78i 0.146072 + 0.106128i
\(711\) 1410.61 4341.41i 0.0744051 0.228995i
\(712\) −1530.13 4709.27i −0.0805396 0.247875i
\(713\) 693.246 503.672i 0.0364127 0.0264554i
\(714\) 17590.3 0.921988
\(715\) 2933.00 + 658.499i 0.153410 + 0.0344426i
\(716\) 12964.4 0.676682
\(717\) 2853.41 2073.12i 0.148623 0.107981i
\(718\) −1559.21 4798.76i −0.0810436 0.249426i
\(719\) 3011.07 9267.11i 0.156181 0.480674i −0.842098 0.539324i \(-0.818680\pi\)
0.998279 + 0.0586501i \(0.0186796\pi\)
\(720\) 1468.26 + 1066.76i 0.0759985 + 0.0552162i
\(721\) 17775.3 + 12914.5i 0.918151 + 0.667076i
\(722\) −3807.12 + 11717.1i −0.196241 + 0.603969i
\(723\) −13065.6 40211.8i −0.672082 2.06846i
\(724\) −8608.70 + 6254.58i −0.441906 + 0.321063i
\(725\) 18390.0 0.942053
\(726\) 12593.9 + 23010.7i 0.643808 + 1.17632i
\(727\) 14917.2 0.761002 0.380501 0.924781i \(-0.375752\pi\)
0.380501 + 0.924781i \(0.375752\pi\)
\(728\) 4877.26 3543.53i 0.248301 0.180401i
\(729\) 14745.4 + 45381.6i 0.749143 + 2.30563i
\(730\) 31.5197 97.0078i 0.00159808 0.00491838i
\(731\) 10440.7 + 7585.61i 0.528267 + 0.383808i
\(732\) −22608.0 16425.7i −1.14155 0.829386i
\(733\) −2192.28 + 6747.15i −0.110469 + 0.339989i −0.990975 0.134046i \(-0.957203\pi\)
0.880506 + 0.474035i \(0.157203\pi\)
\(734\) 3247.32 + 9994.21i 0.163298 + 0.502579i
\(735\) 1599.60 1162.18i 0.0802752 0.0583234i
\(736\) −933.350 −0.0467442
\(737\) −5399.74 1212.32i −0.269881 0.0605920i
\(738\) 16786.4 0.837286
\(739\) 24019.6 17451.3i 1.19564 0.868681i 0.201788 0.979429i \(-0.435325\pi\)
0.993848 + 0.110749i \(0.0353249\pi\)
\(740\) 449.649 + 1383.88i 0.0223371 + 0.0687465i
\(741\) −4099.56 + 12617.1i −0.203240 + 0.625509i
\(742\) 1512.76 + 1099.09i 0.0748453 + 0.0543783i
\(743\) 15616.2 + 11345.8i 0.771065 + 0.560212i 0.902284 0.431142i \(-0.141889\pi\)
−0.131219 + 0.991353i \(0.541889\pi\)
\(744\) −715.689 + 2202.66i −0.0352667 + 0.108540i
\(745\) 1225.59 + 3771.99i 0.0602715 + 0.185497i
\(746\) −511.897 + 371.915i −0.0251232 + 0.0182531i
\(747\) −16163.5 −0.791687
\(748\) 8080.97 3487.93i 0.395013 0.170497i
\(749\) −26077.5 −1.27217
\(750\) 6382.05 4636.83i 0.310719 0.225751i
\(751\) 3888.27 + 11966.9i 0.188928 + 0.581461i 0.999994 0.00349415i \(-0.00111222\pi\)
−0.811066 + 0.584955i \(0.801112\pi\)
\(752\) −865.353 + 2663.28i −0.0419630 + 0.129149i
\(753\) −42990.5 31234.5i −2.08056 1.51162i
\(754\) −12381.3 8995.54i −0.598011 0.434481i
\(755\) −1381.76 + 4252.63i −0.0666059 + 0.204992i
\(756\) −7769.34 23911.6i −0.373767 1.15034i
\(757\) −2207.59 + 1603.91i −0.105992 + 0.0770079i −0.639519 0.768775i \(-0.720866\pi\)
0.533527 + 0.845783i \(0.320866\pi\)
\(758\) 10514.1 0.503811
\(759\) 976.982 + 10440.2i 0.0467223 + 0.499281i
\(760\) 342.217 0.0163336
\(761\) 17098.3 12422.6i 0.814471 0.591748i −0.100652 0.994922i \(-0.532093\pi\)
0.915123 + 0.403174i \(0.132093\pi\)
\(762\) −13798.1 42466.1i −0.655974 2.01888i
\(763\) 3146.58 9684.19i 0.149298 0.459491i
\(764\) 3231.63 + 2347.91i 0.153032 + 0.111184i
\(765\) −5534.72 4021.21i −0.261579 0.190048i
\(766\) −880.217 + 2709.03i −0.0415190 + 0.127782i
\(767\) 4123.29 + 12690.2i 0.194111 + 0.597414i
\(768\) 2040.87 1482.78i 0.0958899 0.0696681i
\(769\) 10493.4 0.492068 0.246034 0.969261i \(-0.420873\pi\)
0.246034 + 0.969261i \(0.420873\pi\)
\(770\) −890.766 + 1502.98i −0.0416896 + 0.0703422i
\(771\) −40178.2 −1.87676
\(772\) −12432.1 + 9032.48i −0.579589 + 0.421096i
\(773\) −4552.70 14011.8i −0.211836 0.651965i −0.999363 0.0356844i \(-0.988639\pi\)
0.787527 0.616280i \(-0.211361\pi\)
\(774\) 9270.67 28532.2i 0.430527 1.32502i
\(775\) 2908.77 + 2113.35i 0.134821 + 0.0979532i
\(776\) 7119.30 + 5172.48i 0.329340 + 0.239280i
\(777\) 10131.1 31180.4i 0.467763 1.43963i
\(778\) −1217.60 3747.39i −0.0561093 0.172687i
\(779\) 2560.77 1860.51i 0.117778 0.0855709i
\(780\) −3247.72 −0.149086
\(781\) −25439.7 28910.4i −1.16556 1.32458i
\(782\) 3518.33 0.160889
\(783\) −51635.7 + 37515.5i −2.35672 + 1.71226i
\(784\) −613.130 1887.02i −0.0279305 0.0859612i
\(785\) 1784.02 5490.65i 0.0811139 0.249643i
\(786\) 23238.5 + 16883.8i 1.05457 + 0.766188i
\(787\) 20429.3 + 14842.8i 0.925319 + 0.672284i 0.944842 0.327526i \(-0.106215\pi\)
−0.0195232 + 0.999809i \(0.506215\pi\)
\(788\) −4185.63 + 12882.0i −0.189222 + 0.582365i
\(789\) 9915.10 + 30515.5i 0.447385 + 1.37691i
\(790\) 170.475 123.858i 0.00767752 0.00557804i
\(791\) 4486.80 0.201684
\(792\) −13516.4 15360.4i −0.606419 0.689152i
\(793\) 36102.8 1.61671
\(794\) 6712.61 4877.00i 0.300027 0.217983i
\(795\) −311.283 958.031i −0.0138869 0.0427395i
\(796\) −6050.92 + 18622.8i −0.269434 + 0.829232i
\(797\) 23715.1 + 17230.0i 1.05399 + 0.765770i 0.972968 0.230942i \(-0.0741806\pi\)
0.0810250 + 0.996712i \(0.474181\pi\)
\(798\) −6237.96 4532.14i −0.276718 0.201048i
\(799\) 3262.01 10039.4i 0.144432 0.444517i
\(800\) −1210.18 3724.55i −0.0534829 0.164603i
\(801\) 35103.7 25504.3i 1.54848 1.12503i
\(802\) −15420.4 −0.678944
\(803\) −586.293 + 989.243i −0.0257657 + 0.0434740i
\(804\) 5979.15 0.262274
\(805\) −565.007 + 410.502i −0.0247377 + 0.0179730i
\(806\) −924.615 2845.67i −0.0404072 0.124361i
\(807\) −6273.00 + 19306.3i −0.273631 + 0.842149i
\(808\) −8732.69 6344.67i −0.380217 0.276244i
\(809\) −5853.31 4252.68i −0.254378 0.184816i 0.453287 0.891365i \(-0.350251\pi\)
−0.707665 + 0.706548i \(0.750251\pi\)
\(810\) −2292.69 + 7056.16i −0.0994528 + 0.306084i
\(811\) −5857.20 18026.6i −0.253606 0.780518i −0.994101 0.108457i \(-0.965409\pi\)
0.740496 0.672061i \(-0.234591\pi\)
\(812\) 7196.09 5228.26i 0.311001 0.225956i
\(813\) 52709.7 2.27381
\(814\) −1528.44 16333.1i −0.0658131 0.703288i
\(815\) 114.839 0.00493573
\(816\) −7693.19 + 5589.43i −0.330043 + 0.239791i
\(817\) −1748.10 5380.10i −0.0748571 0.230387i
\(818\) −2160.43 + 6649.11i −0.0923442 + 0.284206i
\(819\) 42739.0 + 31051.7i 1.82347 + 1.32483i
\(820\) 626.895 + 455.466i 0.0266977 + 0.0193970i
\(821\) 3984.18 12262.0i 0.169365 0.521253i −0.829966 0.557814i \(-0.811640\pi\)
0.999331 + 0.0365611i \(0.0116404\pi\)
\(822\) 1198.89 + 3689.80i 0.0508711 + 0.156565i
\(823\) 14384.7 10451.1i 0.609257 0.442651i −0.239896 0.970799i \(-0.577113\pi\)
0.849153 + 0.528148i \(0.177113\pi\)
\(824\) −11877.8 −0.502163
\(825\) −40394.9 + 17435.4i −1.70469 + 0.735783i
\(826\) −7755.18 −0.326680
\(827\) −16174.7 + 11751.6i −0.680107 + 0.494127i −0.873393 0.487016i \(-0.838085\pi\)
0.193286 + 0.981142i \(0.438085\pi\)
\(828\) −2527.41 7778.56i −0.106079 0.326478i
\(829\) −1081.28 + 3327.83i −0.0453008 + 0.139421i −0.971149 0.238475i \(-0.923352\pi\)
0.925848 + 0.377896i \(0.123352\pi\)
\(830\) −603.630 438.563i −0.0252437 0.0183406i
\(831\) −67004.0 48681.2i −2.79704 2.03217i
\(832\) −1007.11 + 3099.56i −0.0419654 + 0.129156i
\(833\) 2311.23 + 7113.25i 0.0961339 + 0.295870i
\(834\) −632.249 + 459.356i −0.0262506 + 0.0190722i
\(835\) −4437.97 −0.183931
\(836\) −3764.38 845.157i −0.155734 0.0349645i
\(837\) −12478.5 −0.515317
\(838\) −10507.2 + 7633.89i −0.433131 + 0.314688i
\(839\) 5818.06 + 17906.1i 0.239406 + 0.736816i 0.996506 + 0.0835174i \(0.0266154\pi\)
−0.757100 + 0.653299i \(0.773385\pi\)
\(840\) 583.299 1795.21i 0.0239592 0.0737388i
\(841\) 1463.27 + 1063.13i 0.0599973 + 0.0435906i
\(842\) 16118.2 + 11710.6i 0.659703 + 0.479302i
\(843\) −21424.0 + 65936.2i −0.875304 + 2.69391i
\(844\) −1816.31 5590.04i −0.0740760 0.227982i
\(845\) 518.568 376.761i 0.0211116 0.0153384i
\(846\) −24539.1 −0.997250
\(847\) 13510.3 14332.8i 0.548073 0.581443i
\(848\) −1010.85 −0.0409350
\(849\) 60218.5 43751.3i 2.43427 1.76860i
\(850\) 4561.85 + 14039.9i 0.184083 + 0.566548i
\(851\) 2026.38 6236.56i 0.0816256 0.251218i
\(852\) 33660.0 + 24455.5i 1.35349 + 0.983369i
\(853\) −23396.5 16998.6i −0.939134 0.682321i 0.00907800 0.999959i \(-0.497110\pi\)
−0.948212 + 0.317638i \(0.897110\pi\)
\(854\) −6484.16 + 19956.2i −0.259817 + 0.799634i
\(855\) 926.685 + 2852.04i 0.0370666 + 0.114079i
\(856\) 11405.1 8286.31i 0.455397 0.330865i
\(857\) −13906.3 −0.554294 −0.277147 0.960827i \(-0.589389\pi\)
−0.277147 + 0.960827i \(0.589389\pi\)
\(858\) 35724.9 + 8020.74i 1.42148 + 0.319142i
\(859\) 18829.8 0.747923 0.373962 0.927444i \(-0.377999\pi\)
0.373962 + 0.927444i \(0.377999\pi\)
\(860\) 1120.38 814.004i 0.0444240 0.0322759i
\(861\) −5395.15 16604.6i −0.213549 0.657238i
\(862\) 3397.22 10455.6i 0.134234 0.413130i
\(863\) −21161.8 15374.9i −0.834710 0.606452i 0.0861781 0.996280i \(-0.472535\pi\)
−0.920888 + 0.389828i \(0.872535\pi\)
\(864\) 10996.0 + 7989.07i 0.432977 + 0.314576i
\(865\) −666.831 + 2052.30i −0.0262115 + 0.0806707i
\(866\) 60.7722 + 187.038i 0.00238467 + 0.00733926i
\(867\) −10167.1 + 7386.85i −0.398262 + 0.289355i
\(868\) 1739.04 0.0680032
\(869\) −2181.11 + 941.418i −0.0851429 + 0.0367496i
\(870\) −4791.81 −0.186733
\(871\) −6249.34 + 4540.41i −0.243112 + 0.176631i
\(872\) 1701.04 + 5235.27i 0.0660603 + 0.203313i
\(873\) −23829.3 + 73339.0i −0.923824 + 2.84324i
\(874\) −1247.69 906.498i −0.0482879 0.0350832i
\(875\) −4792.12 3481.68i −0.185146 0.134517i
\(876\) 383.921 1181.59i 0.0148076 0.0455732i
\(877\) 437.333 + 1345.97i 0.0168389 + 0.0518247i 0.959123 0.282990i \(-0.0913263\pi\)
−0.942284 + 0.334815i \(0.891326\pi\)
\(878\) 3157.10 2293.77i 0.121352 0.0881673i
\(879\) −32162.8 −1.23416
\(880\) −88.0000 940.380i −0.00337100 0.0360230i
\(881\) −5355.31 −0.204796 −0.102398 0.994744i \(-0.532651\pi\)
−0.102398 + 0.994744i \(0.532651\pi\)
\(882\) 14066.2 10219.7i 0.536999 0.390153i
\(883\) 15100.2 + 46473.5i 0.575494 + 1.77119i 0.634492 + 0.772929i \(0.281209\pi\)
−0.0589988 + 0.998258i \(0.518791\pi\)
\(884\) 3796.36 11684.0i 0.144441 0.444543i
\(885\) 3379.95 + 2455.68i 0.128379 + 0.0932731i
\(886\) −15272.1 11095.8i −0.579094 0.420736i
\(887\) 3898.08 11997.1i 0.147559 0.454140i −0.849772 0.527150i \(-0.823261\pi\)
0.997331 + 0.0730104i \(0.0232606\pi\)
\(888\) 5476.88 + 16856.1i 0.206973 + 0.636998i
\(889\) −27124.5 + 19707.1i −1.02331 + 0.743480i
\(890\) 2002.97 0.0754379
\(891\) 42645.8 71955.7i 1.60347 2.70551i
\(892\) 6981.87 0.262074
\(893\) −3743.45 + 2719.78i −0.140280 + 0.101919i
\(894\) 14928.1 + 45944.1i 0.558469 + 1.71879i
\(895\) −1620.56 + 4987.56i −0.0605243 + 0.186275i
\(896\) −1532.43 1113.38i −0.0571373 0.0415127i
\(897\) 11840.9 + 8602.88i 0.440752 + 0.320225i
\(898\) 7959.55 24497.0i 0.295783 0.910328i
\(899\) −1364.21 4198.62i −0.0506107 0.155764i
\(900\) 27763.5 20171.3i 1.02828 0.747087i
\(901\) 3810.49 0.140894
\(902\) −5771.01 6558.34i −0.213030 0.242094i
\(903\) −31202.6 −1.14990
\(904\) −1962.32 + 1425.71i −0.0721967 + 0.0524540i
\(905\) −1330.12 4093.68i −0.0488559 0.150363i
\(906\) −16830.3 + 51798.4i −0.617164 + 1.89943i
\(907\) −4524.62 3287.33i −0.165642 0.120346i 0.501876 0.864940i \(-0.332643\pi\)
−0.667518 + 0.744593i \(0.732643\pi\)
\(908\) −7649.64 5557.79i −0.279584 0.203130i
\(909\) 29229.5 89959.2i 1.06654 3.28246i
\(910\) 753.577 + 2319.27i 0.0274515 + 0.0844870i
\(911\) 18282.3 13282.8i 0.664894 0.483074i −0.203418 0.979092i \(-0.565205\pi\)
0.868312 + 0.496018i \(0.165205\pi\)
\(912\) 4168.32 0.151345
\(913\) 5556.83 + 6314.95i 0.201429 + 0.228909i
\(914\) −15515.2 −0.561486
\(915\) 9145.13 6644.32i 0.330414 0.240060i
\(916\) −3824.08 11769.3i −0.137938 0.424530i
\(917\) 6665.00 20512.7i 0.240019 0.738703i
\(918\) −41450.2 30115.4i −1.49026 1.08274i
\(919\) 5500.45 + 3996.31i 0.197436 + 0.143445i 0.682111 0.731249i \(-0.261062\pi\)
−0.484675 + 0.874694i \(0.661062\pi\)
\(920\) 116.669 359.069i 0.00418093 0.0128676i
\(921\) 16765.5 + 51598.8i 0.599827 + 1.84608i
\(922\) −21890.9 + 15904.7i −0.781930 + 0.568105i
\(923\) −53751.9 −1.91686
\(924\) −10849.8 + 18306.8i −0.386291 + 0.651783i
\(925\) 27514.5 0.978022
\(926\) 23555.9 17114.3i 0.835954 0.607356i
\(927\) −32163.7 98989.8i −1.13959 3.50728i
\(928\) −1485.93 + 4573.21i −0.0525624 + 0.161770i
\(929\) 12838.7 + 9327.85i 0.453416 + 0.329426i 0.790943 0.611890i \(-0.209590\pi\)
−0.337527 + 0.941316i \(0.609590\pi\)
\(930\) −757.927 550.666i −0.0267241 0.0194162i
\(931\) 1013.11 3118.03i 0.0356641 0.109763i
\(932\) 3337.46 + 10271.6i 0.117298 + 0.361007i
\(933\) −9647.76 + 7009.51i −0.338535 + 0.245960i
\(934\) −9266.32 −0.324629
\(935\) 331.722 + 3544.83i 0.0116026 + 0.123987i
\(936\) −28559.0 −0.997307
\(937\) −16439.2 + 11943.8i −0.573154 + 0.416421i −0.836250 0.548349i \(-0.815257\pi\)
0.263096 + 0.964770i \(0.415257\pi\)
\(938\) −1387.36 4269.85i −0.0482930 0.148631i
\(939\) 14931.0 45952.8i 0.518907 1.59703i
\(940\) −916.423 665.821i −0.0317983 0.0231028i
\(941\) −1682.78 1222.61i −0.0582964 0.0423548i 0.558255 0.829669i \(-0.311471\pi\)
−0.616552 + 0.787314i \(0.711471\pi\)
\(942\) 21730.0 66878.0i 0.751593 2.31317i
\(943\) −1079.11 3321.17i −0.0372648 0.114689i
\(944\) 3391.76 2464.26i 0.116941 0.0849628i
\(945\) 10170.2 0.350092
\(946\) −14334.5 + 6187.09i −0.492658 + 0.212642i
\(947\) −21613.7 −0.741658 −0.370829 0.928701i \(-0.620926\pi\)
−0.370829 + 0.928701i \(0.620926\pi\)
\(948\) 2076.45 1508.63i 0.0711391 0.0516856i
\(949\) 495.997 + 1526.52i 0.0169660 + 0.0522160i
\(950\) 1999.65 6154.28i 0.0682917 0.210180i
\(951\) 61298.9 + 44536.3i 2.09017 + 1.51860i
\(952\) 5776.61 + 4196.95i 0.196661 + 0.142882i
\(953\) −4733.66 + 14568.7i −0.160900 + 0.495201i −0.998711 0.0507606i \(-0.983835\pi\)
0.837810 + 0.545961i \(0.183835\pi\)
\(954\) −2737.28 8424.49i −0.0928960 0.285905i
\(955\) −1307.22 + 949.751i −0.0442939 + 0.0321814i
\(956\) 1431.69 0.0484354
\(957\) 52709.9 + 11834.1i 1.78043 + 0.399731i
\(958\) 39202.1 1.32209
\(959\) 2356.79 1712.31i 0.0793585 0.0576573i
\(960\) 315.331 + 970.490i 0.0106013 + 0.0326275i
\(961\) −8939.21 + 27512.1i −0.300064 + 0.923502i
\(962\) −18524.5 13458.8i −0.620845 0.451070i
\(963\) 99942.2 + 72612.3i 3.34433 + 2.42980i
\(964\) 5303.63 16322.9i 0.177197 0.545358i
\(965\) −1920.87 5911.84i −0.0640778 0.197211i
\(966\) −6881.98 + 5000.05i −0.229217 + 0.166536i
\(967\) −33356.0 −1.10926 −0.554631 0.832096i \(-0.687141\pi\)
−0.554631 + 0.832096i \(0.687141\pi\)
\(968\) −1354.41 + 10561.5i −0.0449716 + 0.350682i
\(969\) −15712.7 −0.520915
\(970\) −2879.82 + 2092.31i −0.0953251 + 0.0692578i
\(971\) −7568.22 23292.6i −0.250129 0.769819i −0.994750 0.102332i \(-0.967370\pi\)
0.744621 0.667488i \(-0.232630\pi\)
\(972\) −13750.3 + 42319.2i −0.453747 + 1.39649i
\(973\) 474.739 + 344.918i 0.0156418 + 0.0113644i
\(974\) 5946.62 + 4320.47i 0.195628 + 0.142132i
\(975\) −18977.1 + 58405.6i −0.623338 + 1.91844i
\(976\) −3505.34 10788.3i −0.114962 0.353817i
\(977\) −35570.7 + 25843.6i −1.16480 + 0.846276i −0.990377 0.138395i \(-0.955806\pi\)
−0.174422 + 0.984671i \(0.555806\pi\)
\(978\) 1398.77 0.0457340
\(979\) −22032.7 4946.64i −0.719272 0.161487i
\(980\) 802.597 0.0261613
\(981\) −39024.7 + 28353.1i −1.27009 + 0.922777i
\(982\) 12713.6 + 39128.5i 0.413145 + 1.27153i
\(983\) 10717.1 32983.8i 0.347733 1.07021i −0.612371 0.790570i \(-0.709784\pi\)
0.960104 0.279642i \(-0.0902157\pi\)
\(984\) 7635.80 + 5547.73i 0.247378 + 0.179731i
\(985\) −4432.65 3220.51i −0.143387 0.104177i
\(986\) 5601.30 17239.0i 0.180914 0.556797i
\(987\) 7886.86 + 24273.3i 0.254348 + 0.782803i
\(988\) −4356.67 + 3165.31i −0.140288 + 0.101925i
\(989\) −6241.01 −0.200660
\(990\) 7598.86 3279.84i 0.243947 0.105293i
\(991\) 42734.1 1.36982 0.684910 0.728627i \(-0.259841\pi\)
0.684910 + 0.728627i \(0.259841\pi\)
\(992\) −760.576 + 552.591i −0.0243431 + 0.0176863i
\(993\) −9395.14 28915.3i −0.300248 0.924067i
\(994\) 9653.98 29711.9i 0.308054 0.948093i
\(995\) −6408.03 4655.71i −0.204169 0.148337i
\(996\) −7352.42 5341.84i −0.233906 0.169943i
\(997\) 9922.10 30537.1i 0.315182 0.970029i −0.660498 0.750828i \(-0.729655\pi\)
0.975680 0.219202i \(-0.0703452\pi\)
\(998\) 598.755 + 1842.78i 0.0189912 + 0.0584491i
\(999\) −77255.5 + 56129.4i −2.44670 + 1.77763i
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 22.4.c.a.3.1 4
3.2 odd 2 198.4.f.b.91.1 4
4.3 odd 2 176.4.m.a.113.1 4
11.2 odd 10 242.4.a.h.1.1 2
11.3 even 5 242.4.c.f.27.1 4
11.4 even 5 inner 22.4.c.a.15.1 yes 4
11.5 even 5 242.4.c.f.9.1 4
11.6 odd 10 242.4.c.m.9.1 4
11.7 odd 10 242.4.c.j.81.1 4
11.8 odd 10 242.4.c.m.27.1 4
11.9 even 5 242.4.a.k.1.1 2
11.10 odd 2 242.4.c.j.3.1 4
33.2 even 10 2178.4.a.bi.1.2 2
33.20 odd 10 2178.4.a.z.1.2 2
33.26 odd 10 198.4.f.b.37.1 4
44.15 odd 10 176.4.m.a.81.1 4
44.31 odd 10 1936.4.a.bb.1.2 2
44.35 even 10 1936.4.a.bc.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.4.c.a.3.1 4 1.1 even 1 trivial
22.4.c.a.15.1 yes 4 11.4 even 5 inner
176.4.m.a.81.1 4 44.15 odd 10
176.4.m.a.113.1 4 4.3 odd 2
198.4.f.b.37.1 4 33.26 odd 10
198.4.f.b.91.1 4 3.2 odd 2
242.4.a.h.1.1 2 11.2 odd 10
242.4.a.k.1.1 2 11.9 even 5
242.4.c.f.9.1 4 11.5 even 5
242.4.c.f.27.1 4 11.3 even 5
242.4.c.j.3.1 4 11.10 odd 2
242.4.c.j.81.1 4 11.7 odd 10
242.4.c.m.9.1 4 11.6 odd 10
242.4.c.m.27.1 4 11.8 odd 10
1936.4.a.bb.1.2 2 44.31 odd 10
1936.4.a.bc.1.2 2 44.35 even 10
2178.4.a.z.1.2 2 33.20 odd 10
2178.4.a.bi.1.2 2 33.2 even 10