Properties

Label 143.4.o.a.32.10
Level $143$
Weight $4$
Character 143.32
Analytic conductor $8.437$
Analytic rank $0$
Dimension $160$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [143,4,Mod(32,143)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(143, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("143.32");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 143 = 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 143.o (of order \(12\), 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: \(8.43727313082\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(40\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 32.10
Character \(\chi\) \(=\) 143.32
Dual form 143.4.o.a.76.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.10849 + 0.832916i) q^{2} +(-2.01807 + 3.49539i) q^{3} +(2.04073 - 1.17821i) q^{4} +(-2.38665 + 2.38665i) q^{5} +(3.36176 - 12.5463i) q^{6} +(25.0107 + 6.70161i) q^{7} +(12.8423 - 12.8423i) q^{8} +(5.35482 + 9.27482i) q^{9} +O(q^{10})\) \(q+(-3.10849 + 0.832916i) q^{2} +(-2.01807 + 3.49539i) q^{3} +(2.04073 - 1.17821i) q^{4} +(-2.38665 + 2.38665i) q^{5} +(3.36176 - 12.5463i) q^{6} +(25.0107 + 6.70161i) q^{7} +(12.8423 - 12.8423i) q^{8} +(5.35482 + 9.27482i) q^{9} +(5.43099 - 9.40675i) q^{10} +(6.74689 + 35.8536i) q^{11} +9.51086i q^{12} +(45.6359 + 10.6941i) q^{13} -83.3274 q^{14} +(-3.52587 - 13.1587i) q^{15} +(-38.6493 + 66.9426i) q^{16} +(-41.8500 - 72.4863i) q^{17} +(-24.3705 - 24.3705i) q^{18} +(-3.43769 + 12.8296i) q^{19} +(-2.05852 + 7.68250i) q^{20} +(-73.8981 + 73.8981i) q^{21} +(-50.8356 - 105.831i) q^{22} +(39.0245 + 22.5308i) q^{23} +(18.9723 + 70.8057i) q^{24} +113.608i q^{25} +(-150.766 + 4.76832i) q^{26} -152.201 q^{27} +(58.9360 - 15.7919i) q^{28} +(-36.6188 - 21.1419i) q^{29} +(21.9202 + 37.9669i) q^{30} +(-11.5908 + 11.5908i) q^{31} +(26.7783 - 99.9381i) q^{32} +(-138.938 - 48.7719i) q^{33} +(190.465 + 190.465i) q^{34} +(-75.6863 + 43.6975i) q^{35} +(21.8555 + 12.6183i) q^{36} +(-99.8493 + 26.7545i) q^{37} -42.7440i q^{38} +(-129.476 + 137.934i) q^{39} +61.3004i q^{40} +(-219.612 + 58.8449i) q^{41} +(168.160 - 291.262i) q^{42} +(50.6613 + 87.7479i) q^{43} +(56.0118 + 65.2181i) q^{44} +(-34.9159 - 9.35568i) q^{45} +(-140.073 - 37.5325i) q^{46} +(372.861 + 372.861i) q^{47} +(-155.994 - 270.189i) q^{48} +(283.579 + 163.724i) q^{49} +(-94.6257 - 353.148i) q^{50} +337.824 q^{51} +(105.730 - 31.9451i) q^{52} -228.175 q^{53} +(473.115 - 126.771i) q^{54} +(-101.673 - 69.4676i) q^{55} +(407.260 - 235.132i) q^{56} +(-37.9071 - 37.9071i) q^{57} +(131.439 + 35.2189i) q^{58} +(157.628 - 588.275i) q^{59} +(-22.6991 - 22.6991i) q^{60} +(721.596 - 416.614i) q^{61} +(26.3757 - 45.6841i) q^{62} +(71.7718 + 267.856i) q^{63} -285.429i q^{64} +(-134.440 + 83.3939i) q^{65} +(472.510 + 35.8830i) q^{66} +(52.4039 + 195.574i) q^{67} +(-170.809 - 98.6165i) q^{68} +(-157.508 + 90.9373i) q^{69} +(198.873 - 198.873i) q^{70} +(-643.820 - 172.511i) q^{71} +(187.879 + 50.3420i) q^{72} +(-159.599 + 159.599i) q^{73} +(288.096 - 166.332i) q^{74} +(-397.104 - 229.268i) q^{75} +(8.10066 + 30.2321i) q^{76} +(-71.5320 + 941.939i) q^{77} +(287.588 - 536.609i) q^{78} +1104.62i q^{79} +(-67.5262 - 252.011i) q^{80} +(162.572 - 281.582i) q^{81} +(633.648 - 365.837i) q^{82} +(-757.803 - 757.803i) q^{83} +(-63.7380 + 237.874i) q^{84} +(272.881 + 73.1182i) q^{85} +(-230.567 - 230.567i) q^{86} +(147.798 - 85.3315i) q^{87} +(547.090 + 373.798i) q^{88} +(-1081.56 + 289.804i) q^{89} +116.328 q^{90} +(1069.72 + 573.302i) q^{91} +106.184 q^{92} +(-17.1234 - 63.9055i) q^{93} +(-1469.59 - 848.470i) q^{94} +(-22.4153 - 38.8244i) q^{95} +(295.283 + 295.283i) q^{96} +(-441.945 - 118.419i) q^{97} +(-1017.87 - 272.737i) q^{98} +(-296.407 + 254.566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 160 q - 4 q^{3} - 12 q^{4} - 8 q^{5} - 652 q^{9} - 80 q^{11} - 64 q^{14} - 76 q^{15} + 940 q^{16} + 68 q^{20} + 28 q^{22} - 240 q^{23} + 496 q^{26} + 824 q^{27} - 280 q^{31} - 266 q^{33} + 2212 q^{34} - 2760 q^{36} + 328 q^{37} + 1164 q^{42} + 104 q^{44} + 896 q^{45} + 4 q^{47} + 2080 q^{48} - 12 q^{49} - 6528 q^{53} + 682 q^{55} - 1356 q^{56} + 1096 q^{58} - 1392 q^{59} + 4 q^{60} - 1880 q^{66} + 304 q^{67} - 12 q^{69} - 1932 q^{70} - 5076 q^{71} + 8832 q^{75} - 10876 q^{78} + 4588 q^{80} - 4624 q^{81} - 7716 q^{82} + 5608 q^{86} + 10152 q^{88} + 7268 q^{89} - 1008 q^{91} + 8120 q^{92} + 2740 q^{93} + 2728 q^{97} - 6996 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).

\(n\) \(67\) \(79\)
\(\chi(n)\) \(e\left(\frac{5}{12}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.10849 + 0.832916i −1.09902 + 0.294480i −0.762364 0.647149i \(-0.775961\pi\)
−0.336652 + 0.941629i \(0.609295\pi\)
\(3\) −2.01807 + 3.49539i −0.388377 + 0.672689i −0.992231 0.124406i \(-0.960297\pi\)
0.603854 + 0.797095i \(0.293631\pi\)
\(4\) 2.04073 1.17821i 0.255091 0.147277i
\(5\) −2.38665 + 2.38665i −0.213469 + 0.213469i −0.805739 0.592271i \(-0.798232\pi\)
0.592271 + 0.805739i \(0.298232\pi\)
\(6\) 3.36176 12.5463i 0.228739 0.853665i
\(7\) 25.0107 + 6.70161i 1.35045 + 0.361853i 0.860302 0.509785i \(-0.170275\pi\)
0.490151 + 0.871638i \(0.336942\pi\)
\(8\) 12.8423 12.8423i 0.567556 0.567556i
\(9\) 5.35482 + 9.27482i 0.198327 + 0.343512i
\(10\) 5.43099 9.40675i 0.171743 0.297468i
\(11\) 6.74689 + 35.8536i 0.184933 + 0.982751i
\(12\) 9.51086i 0.228796i
\(13\) 45.6359 + 10.6941i 0.973625 + 0.228155i
\(14\) −83.3274 −1.59073
\(15\) −3.52587 13.1587i −0.0606916 0.226504i
\(16\) −38.6493 + 66.9426i −0.603896 + 1.04598i
\(17\) −41.8500 72.4863i −0.597065 1.03415i −0.993252 0.115978i \(-0.963000\pi\)
0.396186 0.918170i \(-0.370333\pi\)
\(18\) −24.3705 24.3705i −0.319122 0.319122i
\(19\) −3.43769 + 12.8296i −0.0415084 + 0.154911i −0.983569 0.180530i \(-0.942219\pi\)
0.942061 + 0.335441i \(0.108885\pi\)
\(20\) −2.05852 + 7.68250i −0.0230149 + 0.0858929i
\(21\) −73.8981 + 73.8981i −0.767899 + 0.767899i
\(22\) −50.8356 105.831i −0.492645 1.02560i
\(23\) 39.0245 + 22.5308i 0.353790 + 0.204261i 0.666353 0.745636i \(-0.267854\pi\)
−0.312563 + 0.949897i \(0.601188\pi\)
\(24\) 18.9723 + 70.8057i 0.161363 + 0.602215i
\(25\) 113.608i 0.908862i
\(26\) −150.766 + 4.76832i −1.13722 + 0.0359671i
\(27\) −152.201 −1.08486
\(28\) 58.9360 15.7919i 0.397781 0.106585i
\(29\) −36.6188 21.1419i −0.234481 0.135378i 0.378157 0.925742i \(-0.376558\pi\)
−0.612638 + 0.790364i \(0.709891\pi\)
\(30\) 21.9202 + 37.9669i 0.133402 + 0.231059i
\(31\) −11.5908 + 11.5908i −0.0671539 + 0.0671539i −0.739886 0.672732i \(-0.765121\pi\)
0.672732 + 0.739886i \(0.265121\pi\)
\(32\) 26.7783 99.9381i 0.147931 0.552085i
\(33\) −138.938 48.7719i −0.732909 0.257276i
\(34\) 190.465 + 190.465i 0.960720 + 0.960720i
\(35\) −75.6863 + 43.6975i −0.365524 + 0.211035i
\(36\) 21.8555 + 12.6183i 0.101183 + 0.0584178i
\(37\) −99.8493 + 26.7545i −0.443652 + 0.118876i −0.473728 0.880671i \(-0.657092\pi\)
0.0300755 + 0.999548i \(0.490425\pi\)
\(38\) 42.7440i 0.182473i
\(39\) −129.476 + 137.934i −0.531611 + 0.566336i
\(40\) 61.3004i 0.242311i
\(41\) −219.612 + 58.8449i −0.836528 + 0.224147i −0.651560 0.758597i \(-0.725885\pi\)
−0.184968 + 0.982744i \(0.559218\pi\)
\(42\) 168.160 291.262i 0.617802 1.07006i
\(43\) 50.6613 + 87.7479i 0.179669 + 0.311196i 0.941767 0.336265i \(-0.109164\pi\)
−0.762098 + 0.647462i \(0.775831\pi\)
\(44\) 56.0118 + 65.2181i 0.191911 + 0.223455i
\(45\) −34.9159 9.35568i −0.115666 0.0309925i
\(46\) −140.073 37.5325i −0.448971 0.120302i
\(47\) 372.861 + 372.861i 1.15718 + 1.15718i 0.985080 + 0.172097i \(0.0550541\pi\)
0.172097 + 0.985080i \(0.444946\pi\)
\(48\) −155.994 270.189i −0.469079 0.812468i
\(49\) 283.579 + 163.724i 0.826760 + 0.477330i
\(50\) −94.6257 353.148i −0.267642 0.998854i
\(51\) 337.824 0.927546
\(52\) 105.730 31.9451i 0.281965 0.0851920i
\(53\) −228.175 −0.591362 −0.295681 0.955287i \(-0.595547\pi\)
−0.295681 + 0.955287i \(0.595547\pi\)
\(54\) 473.115 126.771i 1.19227 0.319469i
\(55\) −101.673 69.4676i −0.249264 0.170309i
\(56\) 407.260 235.132i 0.971830 0.561086i
\(57\) −37.9071 37.9071i −0.0880862 0.0880862i
\(58\) 131.439 + 35.2189i 0.297564 + 0.0797321i
\(59\) 157.628 588.275i 0.347820 1.29808i −0.541462 0.840725i \(-0.682129\pi\)
0.889282 0.457358i \(-0.151204\pi\)
\(60\) −22.6991 22.6991i −0.0488407 0.0488407i
\(61\) 721.596 416.614i 1.51460 0.874458i 0.514751 0.857339i \(-0.327884\pi\)
0.999853 0.0171181i \(-0.00544914\pi\)
\(62\) 26.3757 45.6841i 0.0540277 0.0935787i
\(63\) 71.7718 + 267.856i 0.143530 + 0.535662i
\(64\) 285.429i 0.557479i
\(65\) −134.440 + 83.3939i −0.256542 + 0.159134i
\(66\) 472.510 + 35.8830i 0.881241 + 0.0669225i
\(67\) 52.4039 + 195.574i 0.0955545 + 0.356614i 0.997103 0.0760638i \(-0.0242353\pi\)
−0.901548 + 0.432678i \(0.857569\pi\)
\(68\) −170.809 98.6165i −0.304612 0.175868i
\(69\) −157.508 + 90.9373i −0.274808 + 0.158660i
\(70\) 198.873 198.873i 0.339570 0.339570i
\(71\) −643.820 172.511i −1.07616 0.288356i −0.323138 0.946352i \(-0.604738\pi\)
−0.753022 + 0.657996i \(0.771405\pi\)
\(72\) 187.879 + 50.3420i 0.307524 + 0.0824008i
\(73\) −159.599 + 159.599i −0.255885 + 0.255885i −0.823378 0.567493i \(-0.807913\pi\)
0.567493 + 0.823378i \(0.307913\pi\)
\(74\) 288.096 166.332i 0.452574 0.261294i
\(75\) −397.104 229.268i −0.611381 0.352981i
\(76\) 8.10066 + 30.2321i 0.0122264 + 0.0456297i
\(77\) −71.5320 + 941.939i −0.105868 + 1.39408i
\(78\) 287.588 536.609i 0.417474 0.778961i
\(79\) 1104.62i 1.57315i 0.617492 + 0.786577i \(0.288149\pi\)
−0.617492 + 0.786577i \(0.711851\pi\)
\(80\) −67.5262 252.011i −0.0943708 0.352196i
\(81\) 162.572 281.582i 0.223006 0.386258i
\(82\) 633.648 365.837i 0.853350 0.492682i
\(83\) −757.803 757.803i −1.00216 1.00216i −0.999998 0.00216706i \(-0.999310\pi\)
−0.00216706 0.999998i \(-0.500690\pi\)
\(84\) −63.7380 + 237.874i −0.0827903 + 0.308978i
\(85\) 272.881 + 73.1182i 0.348213 + 0.0933034i
\(86\) −230.567 230.567i −0.289100 0.289100i
\(87\) 147.798 85.3315i 0.182134 0.105155i
\(88\) 547.090 + 373.798i 0.662727 + 0.452807i
\(89\) −1081.56 + 289.804i −1.28815 + 0.345159i −0.836958 0.547267i \(-0.815668\pi\)
−0.451193 + 0.892426i \(0.649001\pi\)
\(90\) 116.328 0.136245
\(91\) 1069.72 + 573.302i 1.23228 + 0.660422i
\(92\) 106.184 0.120331
\(93\) −17.1234 63.9055i −0.0190926 0.0712547i
\(94\) −1469.59 848.470i −1.61252 0.930989i
\(95\) −22.4153 38.8244i −0.0242080 0.0419295i
\(96\) 295.283 + 295.283i 0.313929 + 0.313929i
\(97\) −441.945 118.419i −0.462605 0.123955i 0.0199862 0.999800i \(-0.493638\pi\)
−0.482592 + 0.875846i \(0.660304\pi\)
\(98\) −1017.87 272.737i −1.04919 0.281128i
\(99\) −296.407 + 254.566i −0.300910 + 0.258432i
\(100\) 133.854 + 231.843i 0.133854 + 0.231843i
\(101\) 350.297 606.731i 0.345107 0.597743i −0.640266 0.768153i \(-0.721176\pi\)
0.985373 + 0.170410i \(0.0545093\pi\)
\(102\) −1050.12 + 281.379i −1.01939 + 0.273144i
\(103\) 1457.16i 1.39397i 0.717087 + 0.696983i \(0.245475\pi\)
−0.717087 + 0.696983i \(0.754525\pi\)
\(104\) 723.409 448.734i 0.682078 0.423096i
\(105\) 352.738i 0.327845i
\(106\) 709.277 190.050i 0.649916 0.174144i
\(107\) 105.787 + 61.0764i 0.0955781 + 0.0551820i 0.547027 0.837115i \(-0.315759\pi\)
−0.451449 + 0.892297i \(0.649093\pi\)
\(108\) −310.601 + 179.326i −0.276737 + 0.159774i
\(109\) 388.435 + 388.435i 0.341333 + 0.341333i 0.856868 0.515535i \(-0.172407\pi\)
−0.515535 + 0.856868i \(0.672407\pi\)
\(110\) 373.908 + 131.254i 0.324098 + 0.113769i
\(111\) 107.985 403.005i 0.0923376 0.344609i
\(112\) −1415.27 + 1415.27i −1.19402 + 1.19402i
\(113\) 668.440 + 1157.77i 0.556474 + 0.963842i 0.997787 + 0.0664884i \(0.0211795\pi\)
−0.441313 + 0.897353i \(0.645487\pi\)
\(114\) 149.407 + 86.2602i 0.122748 + 0.0708685i
\(115\) −146.911 + 39.3647i −0.119126 + 0.0319198i
\(116\) −99.6388 −0.0797520
\(117\) 145.186 + 480.530i 0.114722 + 0.379701i
\(118\) 1959.94i 1.52904i
\(119\) −560.924 2093.40i −0.432099 1.61262i
\(120\) −214.269 123.708i −0.163000 0.0941080i
\(121\) −1239.96 + 483.800i −0.931600 + 0.363486i
\(122\) −1896.07 + 1896.07i −1.40706 + 1.40706i
\(123\) 237.506 886.383i 0.174107 0.649776i
\(124\) −9.99723 + 37.3102i −0.00724014 + 0.0270206i
\(125\) −569.474 569.474i −0.407482 0.407482i
\(126\) −446.203 772.846i −0.315484 0.546434i
\(127\) 278.594 482.539i 0.194655 0.337153i −0.752132 0.659012i \(-0.770975\pi\)
0.946787 + 0.321860i \(0.104308\pi\)
\(128\) 451.965 + 1686.76i 0.312097 + 1.16476i
\(129\) −408.951 −0.279117
\(130\) 348.445 371.206i 0.235082 0.250438i
\(131\) 1746.14i 1.16459i −0.812977 0.582295i \(-0.802155\pi\)
0.812977 0.582295i \(-0.197845\pi\)
\(132\) −340.998 + 64.1687i −0.224849 + 0.0423119i
\(133\) −171.958 + 297.840i −0.112110 + 0.194181i
\(134\) −325.793 564.291i −0.210032 0.363786i
\(135\) 363.251 363.251i 0.231583 0.231583i
\(136\) −1468.34 393.442i −0.925805 0.248069i
\(137\) −291.452 + 1087.71i −0.181755 + 0.678319i 0.813547 + 0.581499i \(0.197534\pi\)
−0.995302 + 0.0968198i \(0.969133\pi\)
\(138\) 413.868 413.868i 0.255296 0.255296i
\(139\) 1229.20 709.677i 0.750066 0.433051i −0.0756520 0.997134i \(-0.524104\pi\)
0.825718 + 0.564084i \(0.190770\pi\)
\(140\) −102.970 + 178.349i −0.0621612 + 0.107666i
\(141\) −2055.75 + 550.837i −1.22784 + 0.328999i
\(142\) 2144.99 1.26763
\(143\) −75.5228 + 1708.36i −0.0441646 + 0.999024i
\(144\) −827.841 −0.479075
\(145\) 137.855 36.9381i 0.0789532 0.0211555i
\(146\) 363.178 629.043i 0.205869 0.356575i
\(147\) −1144.56 + 660.812i −0.642189 + 0.370768i
\(148\) −172.243 + 172.243i −0.0956639 + 0.0956639i
\(149\) −402.553 + 1502.35i −0.221332 + 0.826021i 0.762509 + 0.646977i \(0.223967\pi\)
−0.983841 + 0.179044i \(0.942700\pi\)
\(150\) 1425.35 + 381.922i 0.775864 + 0.207892i
\(151\) 1199.02 1199.02i 0.646191 0.646191i −0.305879 0.952070i \(-0.598950\pi\)
0.952070 + 0.305879i \(0.0989504\pi\)
\(152\) 120.614 + 208.910i 0.0643626 + 0.111479i
\(153\) 448.198 776.302i 0.236828 0.410198i
\(154\) −562.200 2987.58i −0.294178 1.56329i
\(155\) 55.3265i 0.0286705i
\(156\) −101.710 + 434.037i −0.0522010 + 0.222761i
\(157\) 1139.05 0.579019 0.289509 0.957175i \(-0.406508\pi\)
0.289509 + 0.957175i \(0.406508\pi\)
\(158\) −920.054 3433.69i −0.463263 1.72892i
\(159\) 460.471 797.560i 0.229671 0.397802i
\(160\) 174.607 + 302.428i 0.0862743 + 0.149432i
\(161\) 825.039 + 825.039i 0.403864 + 0.403864i
\(162\) −270.817 + 1010.70i −0.131342 + 0.490175i
\(163\) 984.142 3672.87i 0.472908 1.76492i −0.156333 0.987704i \(-0.549967\pi\)
0.629240 0.777211i \(-0.283366\pi\)
\(164\) −378.837 + 378.837i −0.180379 + 0.180379i
\(165\) 447.998 215.195i 0.211373 0.101533i
\(166\) 2986.81 + 1724.43i 1.39651 + 0.806277i
\(167\) −924.483 3450.22i −0.428375 1.59872i −0.756441 0.654062i \(-0.773063\pi\)
0.328065 0.944655i \(-0.393603\pi\)
\(168\) 1898.05i 0.871652i
\(169\) 1968.27 + 976.073i 0.895890 + 0.444275i
\(170\) −909.148 −0.410167
\(171\) −137.401 + 36.8164i −0.0614461 + 0.0164644i
\(172\) 206.772 + 119.380i 0.0916640 + 0.0529222i
\(173\) 2203.00 + 3815.71i 0.968158 + 1.67690i 0.700880 + 0.713279i \(0.252791\pi\)
0.267277 + 0.963620i \(0.413876\pi\)
\(174\) −388.355 + 388.355i −0.169202 + 0.169202i
\(175\) −761.355 + 2841.41i −0.328874 + 1.22738i
\(176\) −2660.90 934.063i −1.13962 0.400044i
\(177\) 1738.15 + 1738.15i 0.738121 + 0.738121i
\(178\) 3120.64 1801.70i 1.31406 0.758670i
\(179\) 1187.91 + 685.842i 0.496027 + 0.286381i 0.727071 0.686562i \(-0.240881\pi\)
−0.231045 + 0.972943i \(0.574214\pi\)
\(180\) −82.2768 + 22.0460i −0.0340697 + 0.00912895i
\(181\) 1375.63i 0.564914i 0.959280 + 0.282457i \(0.0911495\pi\)
−0.959280 + 0.282457i \(0.908850\pi\)
\(182\) −3802.72 891.114i −1.54877 0.362933i
\(183\) 3363.02i 1.35848i
\(184\) 790.514 211.817i 0.316725 0.0848663i
\(185\) 174.452 302.159i 0.0693295 0.120082i
\(186\) 106.456 + 184.387i 0.0419662 + 0.0726877i
\(187\) 2316.54 1989.53i 0.905893 0.778015i
\(188\) 1200.22 + 321.597i 0.465611 + 0.124760i
\(189\) −3806.66 1019.99i −1.46505 0.392558i
\(190\) 102.015 + 102.015i 0.0389524 + 0.0389524i
\(191\) −1731.80 2999.56i −0.656065 1.13634i −0.981626 0.190817i \(-0.938886\pi\)
0.325561 0.945521i \(-0.394447\pi\)
\(192\) 997.687 + 576.015i 0.375010 + 0.216512i
\(193\) −85.3228 318.429i −0.0318221 0.118762i 0.948188 0.317710i \(-0.102914\pi\)
−0.980010 + 0.198949i \(0.936247\pi\)
\(194\) 1472.41 0.544913
\(195\) −20.1851 638.216i −0.00741273 0.234377i
\(196\) 771.609 0.281199
\(197\) 126.769 33.9676i 0.0458472 0.0122847i −0.235823 0.971796i \(-0.575778\pi\)
0.281670 + 0.959511i \(0.409112\pi\)
\(198\) 709.346 1038.20i 0.254601 0.372633i
\(199\) 4437.07 2561.74i 1.58058 0.912548i 0.585806 0.810452i \(-0.300778\pi\)
0.994774 0.102097i \(-0.0325552\pi\)
\(200\) 1458.99 + 1458.99i 0.515831 + 0.515831i
\(201\) −789.362 211.509i −0.277002 0.0742224i
\(202\) −583.535 + 2177.78i −0.203254 + 0.758556i
\(203\) −774.179 774.179i −0.267669 0.267669i
\(204\) 689.407 398.029i 0.236609 0.136606i
\(205\) 383.695 664.580i 0.130724 0.226421i
\(206\) −1213.69 4529.57i −0.410496 1.53199i
\(207\) 482.593i 0.162041i
\(208\) −2479.69 + 2641.67i −0.826614 + 0.880608i
\(209\) −483.181 36.6934i −0.159916 0.0121442i
\(210\) 293.801 + 1096.48i 0.0965438 + 0.360306i
\(211\) −3920.65 2263.59i −1.27919 0.738539i −0.302488 0.953153i \(-0.597817\pi\)
−0.976699 + 0.214614i \(0.931151\pi\)
\(212\) −465.642 + 268.839i −0.150851 + 0.0870939i
\(213\) 1902.26 1902.26i 0.611930 0.611930i
\(214\) −379.710 101.743i −0.121292 0.0325000i
\(215\) −330.335 88.5129i −0.104784 0.0280769i
\(216\) −1954.62 + 1954.62i −0.615717 + 0.615717i
\(217\) −367.572 + 212.218i −0.114988 + 0.0663884i
\(218\) −1530.98 883.911i −0.475646 0.274615i
\(219\) −235.779 879.941i −0.0727511 0.271511i
\(220\) −289.334 21.9724i −0.0886676 0.00673353i
\(221\) −1134.68 3755.53i −0.345371 1.14310i
\(222\) 1342.68i 0.405922i
\(223\) 644.429 + 2405.04i 0.193516 + 0.722213i 0.992646 + 0.121054i \(0.0386274\pi\)
−0.799130 + 0.601159i \(0.794706\pi\)
\(224\) 1339.49 2320.07i 0.399547 0.692036i
\(225\) −1053.69 + 608.349i −0.312205 + 0.180252i
\(226\) −3042.17 3042.17i −0.895406 0.895406i
\(227\) −598.196 + 2232.50i −0.174906 + 0.652758i 0.821662 + 0.569975i \(0.193047\pi\)
−0.996568 + 0.0827823i \(0.973619\pi\)
\(228\) −122.021 32.6953i −0.0354431 0.00949694i
\(229\) 3796.17 + 3796.17i 1.09545 + 1.09545i 0.994936 + 0.100514i \(0.0320488\pi\)
0.100514 + 0.994936i \(0.467951\pi\)
\(230\) 423.883 244.729i 0.121522 0.0701607i
\(231\) −3148.09 2150.93i −0.896663 0.612644i
\(232\) −741.783 + 198.760i −0.209916 + 0.0562467i
\(233\) 1947.13 0.547470 0.273735 0.961805i \(-0.411741\pi\)
0.273735 + 0.961805i \(0.411741\pi\)
\(234\) −851.549 1372.79i −0.237895 0.383514i
\(235\) −1779.78 −0.494042
\(236\) −371.439 1386.23i −0.102452 0.382355i
\(237\) −3861.07 2229.19i −1.05824 0.610977i
\(238\) 3487.25 + 6040.09i 0.949768 + 1.64505i
\(239\) 3724.72 + 3724.72i 1.00808 + 1.00808i 0.999967 + 0.00811746i \(0.00258390\pi\)
0.00811746 + 0.999967i \(0.497416\pi\)
\(240\) 1017.15 + 272.545i 0.273570 + 0.0733029i
\(241\) −2608.09 698.835i −0.697103 0.186788i −0.107170 0.994241i \(-0.534179\pi\)
−0.589932 + 0.807453i \(0.700846\pi\)
\(242\) 3451.43 2536.67i 0.916803 0.673815i
\(243\) −1398.55 2422.37i −0.369207 0.639485i
\(244\) 981.721 1700.39i 0.257575 0.446132i
\(245\) −1067.56 + 286.051i −0.278382 + 0.0745923i
\(246\) 2953.13i 0.765385i
\(247\) −294.084 + 548.728i −0.0757574 + 0.141355i
\(248\) 297.706i 0.0762273i
\(249\) 4178.11 1119.52i 1.06336 0.284927i
\(250\) 2244.52 + 1295.88i 0.567825 + 0.327834i
\(251\) 4213.65 2432.75i 1.05961 0.611769i 0.134289 0.990942i \(-0.457125\pi\)
0.925326 + 0.379173i \(0.123792\pi\)
\(252\) 462.058 + 462.058i 0.115504 + 0.115504i
\(253\) −544.516 + 1551.18i −0.135310 + 0.385462i
\(254\) −464.091 + 1732.01i −0.114644 + 0.427858i
\(255\) −806.269 + 806.269i −0.198002 + 0.198002i
\(256\) −1668.14 2889.30i −0.407260 0.705395i
\(257\) 2758.87 + 1592.84i 0.669625 + 0.386608i 0.795935 0.605383i \(-0.206980\pi\)
−0.126309 + 0.991991i \(0.540313\pi\)
\(258\) 1271.22 340.622i 0.306754 0.0821946i
\(259\) −2676.60 −0.642147
\(260\) −176.100 + 328.584i −0.0420048 + 0.0783765i
\(261\) 452.844i 0.107396i
\(262\) 1454.39 + 5427.86i 0.342949 + 1.27990i
\(263\) 5840.35 + 3371.93i 1.36932 + 0.790578i 0.990841 0.135032i \(-0.0431137\pi\)
0.378479 + 0.925610i \(0.376447\pi\)
\(264\) −2410.63 + 1157.94i −0.561986 + 0.269949i
\(265\) 544.573 544.573i 0.126237 0.126237i
\(266\) 286.453 1069.06i 0.0660285 0.246422i
\(267\) 1169.69 4365.33i 0.268104 1.00058i
\(268\) 337.370 + 337.370i 0.0768961 + 0.0768961i
\(269\) 162.455 + 281.381i 0.0368219 + 0.0637773i 0.883849 0.467772i \(-0.154943\pi\)
−0.847027 + 0.531550i \(0.821610\pi\)
\(270\) −826.603 + 1431.72i −0.186316 + 0.322710i
\(271\) −110.934 414.010i −0.0248662 0.0928019i 0.952378 0.304921i \(-0.0986301\pi\)
−0.977244 + 0.212119i \(0.931963\pi\)
\(272\) 6469.90 1.44226
\(273\) −4162.68 + 2582.13i −0.922846 + 0.572445i
\(274\) 3623.90i 0.799007i
\(275\) −4073.25 + 766.499i −0.893185 + 0.168079i
\(276\) −214.287 + 371.156i −0.0467340 + 0.0809456i
\(277\) −3267.90 5660.16i −0.708840 1.22775i −0.965288 0.261189i \(-0.915885\pi\)
0.256447 0.966558i \(-0.417448\pi\)
\(278\) −3229.84 + 3229.84i −0.696809 + 0.696809i
\(279\) −169.569 45.4360i −0.0363866 0.00974976i
\(280\) −410.811 + 1533.17i −0.0876809 + 0.327230i
\(281\) 1601.55 1601.55i 0.340002 0.340002i −0.516366 0.856368i \(-0.672716\pi\)
0.856368 + 0.516366i \(0.172716\pi\)
\(282\) 5931.47 3424.54i 1.25253 0.723150i
\(283\) −1744.01 + 3020.71i −0.366327 + 0.634497i −0.988988 0.147994i \(-0.952718\pi\)
0.622661 + 0.782492i \(0.286052\pi\)
\(284\) −1517.12 + 406.510i −0.316987 + 0.0849364i
\(285\) 180.942 0.0376073
\(286\) −1188.16 5373.32i −0.245655 1.11095i
\(287\) −5887.01 −1.21080
\(288\) 1070.30 286.786i 0.218987 0.0586773i
\(289\) −1046.34 + 1812.32i −0.212974 + 0.368882i
\(290\) −397.753 + 229.643i −0.0805410 + 0.0465003i
\(291\) 1305.79 1305.79i 0.263048 0.263048i
\(292\) −137.656 + 513.739i −0.0275880 + 0.102960i
\(293\) 270.052 + 72.3603i 0.0538452 + 0.0144278i 0.285641 0.958337i \(-0.407793\pi\)
−0.231796 + 0.972764i \(0.574460\pi\)
\(294\) 3007.45 3007.45i 0.596592 0.596592i
\(295\) 1027.81 + 1780.21i 0.202851 + 0.351349i
\(296\) −938.708 + 1625.89i −0.184329 + 0.319267i
\(297\) −1026.88 5456.95i −0.200626 1.06614i
\(298\) 5005.32i 0.972988i
\(299\) 1539.97 + 1445.55i 0.297855 + 0.279592i
\(300\) −1080.51 −0.207944
\(301\) 679.024 + 2534.15i 0.130028 + 0.485269i
\(302\) −2728.45 + 4725.82i −0.519883 + 0.900464i
\(303\) 1413.84 + 2448.85i 0.268063 + 0.464299i
\(304\) −725.984 725.984i −0.136967 0.136967i
\(305\) −727.887 + 2716.51i −0.136651 + 0.509990i
\(306\) −746.623 + 2786.44i −0.139482 + 0.520555i
\(307\) 550.112 550.112i 0.102269 0.102269i −0.654121 0.756390i \(-0.726961\pi\)
0.756390 + 0.654121i \(0.226961\pi\)
\(308\) 963.829 + 2006.52i 0.178309 + 0.371208i
\(309\) −5093.36 2940.65i −0.937706 0.541385i
\(310\) 46.0823 + 171.982i 0.00844291 + 0.0315094i
\(311\) 3858.82i 0.703581i −0.936079 0.351791i \(-0.885573\pi\)
0.936079 0.351791i \(-0.114427\pi\)
\(312\) 108.614 + 3434.17i 0.0197085 + 0.623147i
\(313\) 7171.08 1.29499 0.647497 0.762068i \(-0.275816\pi\)
0.647497 + 0.762068i \(0.275816\pi\)
\(314\) −3540.71 + 948.731i −0.636350 + 0.170510i
\(315\) −810.573 467.985i −0.144986 0.0837078i
\(316\) 1301.48 + 2254.22i 0.231689 + 0.401297i
\(317\) −2845.97 + 2845.97i −0.504244 + 0.504244i −0.912754 0.408510i \(-0.866049\pi\)
0.408510 + 0.912754i \(0.366049\pi\)
\(318\) −767.068 + 2862.74i −0.135267 + 0.504825i
\(319\) 510.950 1455.56i 0.0896793 0.255472i
\(320\) 681.220 + 681.220i 0.119004 + 0.119004i
\(321\) −426.972 + 246.512i −0.0742407 + 0.0428629i
\(322\) −3251.81 1877.43i −0.562783 0.324923i
\(323\) 1073.84 287.734i 0.184984 0.0495664i
\(324\) 766.177i 0.131375i
\(325\) −1214.94 + 5184.59i −0.207362 + 0.884891i
\(326\) 12236.8i 2.07893i
\(327\) −2141.62 + 573.845i −0.362177 + 0.0970450i
\(328\) −2064.63 + 3576.04i −0.347561 + 0.601993i
\(329\) 6826.75 + 11824.3i 1.14398 + 1.98144i
\(330\) −1213.36 + 1042.08i −0.202403 + 0.173832i
\(331\) −9646.98 2584.90i −1.60195 0.429242i −0.656320 0.754483i \(-0.727888\pi\)
−0.945631 + 0.325241i \(0.894555\pi\)
\(332\) −2439.32 653.615i −0.403239 0.108048i
\(333\) −782.819 782.819i −0.128823 0.128823i
\(334\) 5747.48 + 9954.93i 0.941582 + 1.63087i
\(335\) −591.837 341.697i −0.0965239 0.0557281i
\(336\) −2090.82 7803.04i −0.339475 1.26694i
\(337\) −3330.67 −0.538377 −0.269189 0.963088i \(-0.586755\pi\)
−0.269189 + 0.963088i \(0.586755\pi\)
\(338\) −6931.33 1394.70i −1.11543 0.224443i
\(339\) −5395.83 −0.864487
\(340\) 643.025 172.298i 0.102567 0.0274828i
\(341\) −493.774 337.370i −0.0784146 0.0535766i
\(342\) 396.443 228.886i 0.0626818 0.0361893i
\(343\) −284.739 284.739i −0.0448234 0.0448234i
\(344\) 1777.50 + 476.279i 0.278594 + 0.0746490i
\(345\) 158.881 592.952i 0.0247938 0.0925318i
\(346\) −10026.2 10026.2i −1.55783 1.55783i
\(347\) 6880.80 3972.63i 1.06450 0.614588i 0.137824 0.990457i \(-0.455989\pi\)
0.926673 + 0.375869i \(0.122656\pi\)
\(348\) 201.078 348.277i 0.0309738 0.0536482i
\(349\) −1680.46 6271.57i −0.257745 0.961918i −0.966543 0.256506i \(-0.917429\pi\)
0.708798 0.705412i \(-0.249238\pi\)
\(350\) 9466.64i 1.44575i
\(351\) −6945.83 1627.66i −1.05624 0.247516i
\(352\) 3763.81 + 285.828i 0.569920 + 0.0432804i
\(353\) 1290.33 + 4815.59i 0.194554 + 0.726085i 0.992382 + 0.123200i \(0.0393156\pi\)
−0.797828 + 0.602885i \(0.794018\pi\)
\(354\) −6850.75 3955.28i −1.02857 0.593844i
\(355\) 1948.30 1124.85i 0.291281 0.168171i
\(356\) −1865.72 + 1865.72i −0.277762 + 0.277762i
\(357\) 8449.23 + 2263.96i 1.25261 + 0.335635i
\(358\) −4263.86 1142.50i −0.629474 0.168667i
\(359\) 2680.85 2680.85i 0.394121 0.394121i −0.482032 0.876154i \(-0.660101\pi\)
0.876154 + 0.482032i \(0.160101\pi\)
\(360\) −568.550 + 328.252i −0.0832367 + 0.0480567i
\(361\) 5787.29 + 3341.29i 0.843751 + 0.487140i
\(362\) −1145.78 4276.11i −0.166356 0.620850i
\(363\) 811.248 5310.48i 0.117299 0.767846i
\(364\) 2858.48 90.4060i 0.411607 0.0130180i
\(365\) 761.813i 0.109247i
\(366\) −2801.11 10453.9i −0.400045 1.49299i
\(367\) −3487.15 + 6039.91i −0.495988 + 0.859076i −0.999989 0.00462668i \(-0.998527\pi\)
0.504001 + 0.863703i \(0.331861\pi\)
\(368\) −3016.54 + 1741.60i −0.427305 + 0.246704i
\(369\) −1721.76 1721.76i −0.242903 0.242903i
\(370\) −290.607 + 1084.56i −0.0408323 + 0.152388i
\(371\) −5706.81 1529.14i −0.798606 0.213986i
\(372\) −110.239 110.239i −0.0153645 0.0153645i
\(373\) 4077.79 2354.31i 0.566059 0.326814i −0.189515 0.981878i \(-0.560691\pi\)
0.755574 + 0.655063i \(0.227358\pi\)
\(374\) −5543.81 + 8113.90i −0.766480 + 1.12182i
\(375\) 3139.77 841.299i 0.432365 0.115852i
\(376\) 9576.80 1.31353
\(377\) −1445.04 1356.44i −0.197409 0.185305i
\(378\) 12682.5 1.72571
\(379\) 309.042 + 1153.36i 0.0418851 + 0.156317i 0.983701 0.179812i \(-0.0575489\pi\)
−0.941816 + 0.336129i \(0.890882\pi\)
\(380\) −91.4870 52.8200i −0.0123505 0.00713055i
\(381\) 1124.44 + 1947.59i 0.151199 + 0.261885i
\(382\) 7881.65 + 7881.65i 1.05565 + 1.05565i
\(383\) 6952.30 + 1862.86i 0.927535 + 0.248532i 0.690803 0.723043i \(-0.257257\pi\)
0.236732 + 0.971575i \(0.423924\pi\)
\(384\) −6807.97 1824.19i −0.904734 0.242423i
\(385\) −2077.36 2418.80i −0.274992 0.320191i
\(386\) 530.449 + 918.765i 0.0699460 + 0.121150i
\(387\) −542.564 + 939.749i −0.0712664 + 0.123437i
\(388\) −1041.41 + 279.046i −0.136262 + 0.0365113i
\(389\) 2904.83i 0.378613i −0.981918 0.189307i \(-0.939376\pi\)
0.981918 0.189307i \(-0.0606240\pi\)
\(390\) 594.325 + 1967.07i 0.0771662 + 0.255401i
\(391\) 3771.65i 0.487828i
\(392\) 5744.41 1539.21i 0.740144 0.198321i
\(393\) 6103.46 + 3523.83i 0.783407 + 0.452300i
\(394\) −365.767 + 211.175i −0.0467692 + 0.0270022i
\(395\) −2636.34 2636.34i −0.335819 0.335819i
\(396\) −304.953 + 868.730i −0.0386982 + 0.110241i
\(397\) −1256.38 + 4688.88i −0.158831 + 0.592766i 0.839916 + 0.542717i \(0.182604\pi\)
−0.998747 + 0.0500488i \(0.984062\pi\)
\(398\) −11658.8 + 11658.8i −1.46835 + 1.46835i
\(399\) −694.046 1202.12i −0.0870820 0.150831i
\(400\) −7605.20 4390.87i −0.950650 0.548858i
\(401\) 9212.81 2468.56i 1.14730 0.307417i 0.365415 0.930845i \(-0.380927\pi\)
0.781881 + 0.623428i \(0.214260\pi\)
\(402\) 2629.89 0.326286
\(403\) −652.911 + 405.004i −0.0807043 + 0.0500612i
\(404\) 1650.90i 0.203305i
\(405\) 284.037 + 1060.04i 0.0348492 + 0.130059i
\(406\) 3051.35 + 1761.70i 0.372995 + 0.215349i
\(407\) −1632.92 3399.45i −0.198872 0.414015i
\(408\) 4338.45 4338.45i 0.526435 0.526435i
\(409\) −460.562 + 1718.84i −0.0556805 + 0.207802i −0.988162 0.153416i \(-0.950972\pi\)
0.932481 + 0.361219i \(0.117639\pi\)
\(410\) −639.172 + 2385.42i −0.0769914 + 0.287336i
\(411\) −3213.82 3213.82i −0.385708 0.385708i
\(412\) 1716.85 + 2973.67i 0.205299 + 0.355588i
\(413\) 7884.78 13656.8i 0.939430 1.62714i
\(414\) −401.960 1500.13i −0.0477180 0.178086i
\(415\) 3617.22 0.427862
\(416\) 2290.81 4274.40i 0.269990 0.503773i
\(417\) 5728.70i 0.672748i
\(418\) 1532.53 288.389i 0.179326 0.0337453i
\(419\) −1476.39 + 2557.19i −0.172140 + 0.298155i −0.939168 0.343459i \(-0.888401\pi\)
0.767028 + 0.641614i \(0.221735\pi\)
\(420\) −415.601 719.842i −0.0482839 0.0836302i
\(421\) 6412.85 6412.85i 0.742383 0.742383i −0.230653 0.973036i \(-0.574086\pi\)
0.973036 + 0.230653i \(0.0740863\pi\)
\(422\) 14072.6 + 3770.75i 1.62333 + 0.434970i
\(423\) −1461.61 + 5454.82i −0.168005 + 0.627003i
\(424\) −2930.29 + 2930.29i −0.335631 + 0.335631i
\(425\) 8235.01 4754.48i 0.939898 0.542650i
\(426\) −4328.73 + 7497.59i −0.492319 + 0.852721i
\(427\) 20839.6 5583.96i 2.36183 0.632850i
\(428\) 287.844 0.0325081
\(429\) −5818.99 3711.57i −0.654880 0.417707i
\(430\) 1100.56 0.123428
\(431\) 13386.3 3586.84i 1.49604 0.400864i 0.584271 0.811559i \(-0.301381\pi\)
0.911773 + 0.410695i \(0.134714\pi\)
\(432\) 5882.47 10188.7i 0.655140 1.13474i
\(433\) −4957.55 + 2862.24i −0.550219 + 0.317669i −0.749210 0.662332i \(-0.769567\pi\)
0.198992 + 0.980001i \(0.436233\pi\)
\(434\) 965.832 965.832i 0.106824 0.106824i
\(435\) −149.087 + 556.400i −0.0164326 + 0.0613272i
\(436\) 1250.35 + 335.030i 0.137342 + 0.0368005i
\(437\) −423.215 + 423.215i −0.0463276 + 0.0463276i
\(438\) 1465.83 + 2538.90i 0.159909 + 0.276971i
\(439\) 7555.01 13085.7i 0.821368 1.42265i −0.0832949 0.996525i \(-0.526544\pi\)
0.904663 0.426127i \(-0.140122\pi\)
\(440\) −2197.84 + 413.587i −0.238131 + 0.0448113i
\(441\) 3506.85i 0.378669i
\(442\) 6655.19 + 10728.9i 0.716188 + 1.15457i
\(443\) 5032.80 0.539764 0.269882 0.962893i \(-0.413015\pi\)
0.269882 + 0.962893i \(0.413015\pi\)
\(444\) −254.459 949.653i −0.0271984 0.101506i
\(445\) 1889.65 3272.98i 0.201299 0.348660i
\(446\) −4006.39 6939.28i −0.425355 0.736736i
\(447\) −4438.92 4438.92i −0.469695 0.469695i
\(448\) 1912.83 7138.79i 0.201725 0.752849i
\(449\) −4482.05 + 16727.2i −0.471094 + 1.75815i 0.164758 + 0.986334i \(0.447316\pi\)
−0.635851 + 0.771811i \(0.719351\pi\)
\(450\) 2768.68 2768.68i 0.290038 0.290038i
\(451\) −3591.50 7476.86i −0.374982 0.780647i
\(452\) 2728.21 + 1575.13i 0.283903 + 0.163912i
\(453\) 1771.34 + 6610.74i 0.183720 + 0.685651i
\(454\) 7437.93i 0.768897i
\(455\) −3921.32 + 1184.78i −0.404032 + 0.122073i
\(456\) −973.631 −0.0999878
\(457\) −12391.8 + 3320.37i −1.26841 + 0.339869i −0.829421 0.558623i \(-0.811330\pi\)
−0.438988 + 0.898493i \(0.644663\pi\)
\(458\) −14962.2 8638.45i −1.52650 0.881328i
\(459\) 6369.61 + 11032.5i 0.647730 + 1.12190i
\(460\) −253.425 + 253.425i −0.0256870 + 0.0256870i
\(461\) 1264.38 4718.73i 0.127740 0.476731i −0.872183 0.489180i \(-0.837296\pi\)
0.999923 + 0.0124491i \(0.00396278\pi\)
\(462\) 11577.3 + 4064.03i 1.16586 + 0.409255i
\(463\) −7285.39 7285.39i −0.731276 0.731276i 0.239596 0.970873i \(-0.422985\pi\)
−0.970873 + 0.239596i \(0.922985\pi\)
\(464\) 2830.59 1634.24i 0.283204 0.163508i
\(465\) 193.388 + 111.653i 0.0192863 + 0.0111350i
\(466\) −6052.62 + 1621.79i −0.601678 + 0.161219i
\(467\) 867.762i 0.0859855i 0.999075 + 0.0429928i \(0.0136892\pi\)
−0.999075 + 0.0429928i \(0.986311\pi\)
\(468\) 862.452 + 809.571i 0.0851856 + 0.0799624i
\(469\) 5242.64i 0.516168i
\(470\) 5532.41 1482.41i 0.542960 0.145486i
\(471\) −2298.67 + 3981.42i −0.224877 + 0.389499i
\(472\) −5530.52 9579.14i −0.539328 0.934143i
\(473\) −2804.27 + 2408.41i −0.272602 + 0.234121i
\(474\) 13858.8 + 3713.46i 1.34295 + 0.359841i
\(475\) −1457.54 390.548i −0.140793 0.0377254i
\(476\) −3611.17 3611.17i −0.347726 0.347726i
\(477\) −1221.83 2116.28i −0.117283 0.203140i
\(478\) −14680.6 8475.86i −1.40476 0.811039i
\(479\) 2539.31 + 9476.83i 0.242221 + 0.903982i 0.974760 + 0.223257i \(0.0716688\pi\)
−0.732538 + 0.680726i \(0.761665\pi\)
\(480\) −1409.47 −0.134028
\(481\) −4842.83 + 153.166i −0.459073 + 0.0145192i
\(482\) 8689.27 0.821132
\(483\) −4548.82 + 1218.85i −0.428526 + 0.114823i
\(484\) −1960.40 + 2448.24i −0.184110 + 0.229925i
\(485\) 1337.39 772.145i 0.125212 0.0722913i
\(486\) 6365.01 + 6365.01i 0.594080 + 0.594080i
\(487\) −9103.97 2439.40i −0.847105 0.226981i −0.190943 0.981601i \(-0.561155\pi\)
−0.656162 + 0.754620i \(0.727821\pi\)
\(488\) 3916.69 14617.3i 0.363320 1.35593i
\(489\) 10852.1 + 10852.1i 1.00357 + 1.00357i
\(490\) 3080.23 1778.37i 0.283980 0.163956i
\(491\) 4432.94 7678.07i 0.407445 0.705716i −0.587157 0.809473i \(-0.699753\pi\)
0.994603 + 0.103757i \(0.0330864\pi\)
\(492\) −559.665 2088.70i −0.0512839 0.191394i
\(493\) 3539.15i 0.323317i
\(494\) 457.110 1950.66i 0.0416323 0.177661i
\(495\) 99.8612 1314.98i 0.00906753 0.119402i
\(496\) −327.942 1223.90i −0.0296876 0.110796i
\(497\) −14946.3 8629.25i −1.34896 0.778823i
\(498\) −12055.1 + 6960.04i −1.08475 + 0.626279i
\(499\) −285.291 + 285.291i −0.0255939 + 0.0255939i −0.719788 0.694194i \(-0.755761\pi\)
0.694194 + 0.719788i \(0.255761\pi\)
\(500\) −1833.10 491.179i −0.163958 0.0439323i
\(501\) 13925.5 + 3731.33i 1.24181 + 0.332742i
\(502\) −11071.8 + 11071.8i −0.984379 + 0.984379i
\(503\) −16006.5 + 9241.35i −1.41888 + 0.819188i −0.996200 0.0870930i \(-0.972242\pi\)
−0.422675 + 0.906281i \(0.638909\pi\)
\(504\) 4361.61 + 2518.18i 0.385480 + 0.222557i
\(505\) 612.021 + 2284.09i 0.0539298 + 0.201269i
\(506\) 400.617 5275.36i 0.0351969 0.463475i
\(507\) −7383.86 + 4910.10i −0.646802 + 0.430109i
\(508\) 1312.97i 0.114673i
\(509\) 4989.51 + 18621.1i 0.434491 + 1.62154i 0.742281 + 0.670089i \(0.233744\pi\)
−0.307790 + 0.951454i \(0.599589\pi\)
\(510\) 1834.72 3177.83i 0.159300 0.275915i
\(511\) −5061.25 + 2922.11i −0.438154 + 0.252968i
\(512\) −2286.41 2286.41i −0.197355 0.197355i
\(513\) 523.220 1952.68i 0.0450306 0.168057i
\(514\) −9902.61 2653.40i −0.849777 0.227697i
\(515\) −3477.74 3477.74i −0.297568 0.297568i
\(516\) −834.558 + 481.832i −0.0712003 + 0.0411075i
\(517\) −10852.7 + 15884.0i −0.923217 + 1.35122i
\(518\) 8320.18 2229.39i 0.705729 0.189100i
\(519\) −17783.2 −1.50404
\(520\) −655.554 + 2797.50i −0.0552845 + 0.235920i
\(521\) −16928.4 −1.42351 −0.711753 0.702429i \(-0.752099\pi\)
−0.711753 + 0.702429i \(0.752099\pi\)
\(522\) 377.181 + 1407.66i 0.0316260 + 0.118030i
\(523\) 12567.6 + 7255.92i 1.05075 + 0.606653i 0.922860 0.385135i \(-0.125845\pi\)
0.127893 + 0.991788i \(0.459179\pi\)
\(524\) −2057.33 3563.40i −0.171517 0.297076i
\(525\) −8395.39 8395.39i −0.697914 0.697914i
\(526\) −20963.2 5617.06i −1.73771 0.465619i
\(527\) 1325.25 + 355.100i 0.109542 + 0.0293518i
\(528\) 8634.78 7415.87i 0.711706 0.611240i
\(529\) −5068.23 8778.43i −0.416555 0.721495i
\(530\) −1239.21 + 2146.38i −0.101562 + 0.175911i
\(531\) 6300.22 1688.14i 0.514889 0.137964i
\(532\) 810.414i 0.0660449i
\(533\) −10651.5 + 336.878i −0.865605 + 0.0273768i
\(534\) 14543.8i 1.17860i
\(535\) −398.246 + 106.710i −0.0321826 + 0.00862329i
\(536\) 3184.62 + 1838.64i 0.256631 + 0.148166i
\(537\) −4794.57 + 2768.15i −0.385291 + 0.222448i
\(538\) −739.357 739.357i −0.0592490 0.0592490i
\(539\) −3956.83 + 11271.9i −0.316201 + 0.900773i
\(540\) 313.309 1169.28i 0.0249679 0.0931814i
\(541\) −7145.93 + 7145.93i −0.567888 + 0.567888i −0.931536 0.363648i \(-0.881531\pi\)
0.363648 + 0.931536i \(0.381531\pi\)
\(542\) 689.671 + 1194.55i 0.0546567 + 0.0946682i
\(543\) −4808.35 2776.10i −0.380011 0.219400i
\(544\) −8364.82 + 2241.35i −0.659262 + 0.176649i
\(545\) −1854.12 −0.145728
\(546\) 10788.9 11493.7i 0.845648 0.900886i
\(547\) 8606.06i 0.672703i −0.941737 0.336352i \(-0.890807\pi\)
0.941737 0.336352i \(-0.109193\pi\)
\(548\) 686.787 + 2563.12i 0.0535366 + 0.199801i
\(549\) 7728.03 + 4461.78i 0.600773 + 0.346856i
\(550\) 12023.2 5775.32i 0.932129 0.447746i
\(551\) 397.127 397.127i 0.0307045 0.0307045i
\(552\) −854.923 + 3190.62i −0.0659202 + 0.246018i
\(553\) −7402.71 + 27627.3i −0.569250 + 2.12447i
\(554\) 14872.6 + 14872.6i 1.14057 + 1.14057i
\(555\) 704.111 + 1219.56i 0.0538519 + 0.0932743i
\(556\) 1672.30 2896.52i 0.127557 0.220935i
\(557\) 2542.54 + 9488.88i 0.193413 + 0.721826i 0.992672 + 0.120839i \(0.0385586\pi\)
−0.799259 + 0.600986i \(0.794775\pi\)
\(558\) 564.949 0.0428605
\(559\) 1373.59 + 4546.23i 0.103929 + 0.343981i
\(560\) 6755.52i 0.509773i
\(561\) 2279.26 + 12112.2i 0.171534 + 0.911547i
\(562\) −3644.44 + 6312.35i −0.273543 + 0.473791i
\(563\) −4334.39 7507.39i −0.324463 0.561987i 0.656940 0.753943i \(-0.271850\pi\)
−0.981404 + 0.191956i \(0.938517\pi\)
\(564\) −3546.22 + 3546.22i −0.264757 + 0.264757i
\(565\) −4358.54 1167.87i −0.324540 0.0869602i
\(566\) 2905.23 10842.5i 0.215752 0.805199i
\(567\) 5953.09 5953.09i 0.440928 0.440928i
\(568\) −10483.6 + 6052.71i −0.774440 + 0.447123i
\(569\) 6981.61 12092.5i 0.514384 0.890938i −0.485477 0.874249i \(-0.661354\pi\)
0.999861 0.0166891i \(-0.00531255\pi\)
\(570\) −562.456 + 150.710i −0.0413310 + 0.0110746i
\(571\) 3023.61 0.221601 0.110801 0.993843i \(-0.464659\pi\)
0.110801 + 0.993843i \(0.464659\pi\)
\(572\) 1858.70 + 3575.29i 0.135867 + 0.261346i
\(573\) 13979.5 1.01920
\(574\) 18299.7 4903.39i 1.33069 0.356557i
\(575\) −2559.67 + 4433.49i −0.185645 + 0.321546i
\(576\) 2647.30 1528.42i 0.191501 0.110563i
\(577\) 9374.86 9374.86i 0.676396 0.676396i −0.282787 0.959183i \(-0.591259\pi\)
0.959183 + 0.282787i \(0.0912588\pi\)
\(578\) 1743.03 6505.08i 0.125433 0.468124i
\(579\) 1285.22 + 344.374i 0.0922487 + 0.0247180i
\(580\) 237.803 237.803i 0.0170245 0.0170245i
\(581\) −13874.7 24031.7i −0.990740 1.71601i
\(582\) −2971.43 + 5146.66i −0.211632 + 0.366557i
\(583\) −1539.47 8180.88i −0.109362 0.581162i
\(584\) 4099.24i 0.290459i
\(585\) −1493.37 800.350i −0.105544 0.0565648i
\(586\) −899.724 −0.0634253
\(587\) −378.243 1411.62i −0.0265959 0.0992571i 0.951352 0.308106i \(-0.0996951\pi\)
−0.977948 + 0.208849i \(0.933028\pi\)
\(588\) −1557.16 + 2697.08i −0.109211 + 0.189159i
\(589\) −108.860 188.551i −0.00761546 0.0131904i
\(590\) −4677.69 4677.69i −0.326402 0.326402i
\(591\) −137.098 + 511.655i −0.00954221 + 0.0356120i
\(592\) 2068.09 7718.22i 0.143578 0.535839i
\(593\) −1624.76 + 1624.76i −0.112514 + 0.112514i −0.761122 0.648608i \(-0.775351\pi\)
0.648608 + 0.761122i \(0.275351\pi\)
\(594\) 7737.24 + 16107.6i 0.534449 + 1.11263i
\(595\) 6334.94 + 3657.48i 0.436483 + 0.252004i
\(596\) 948.588 + 3540.18i 0.0651941 + 0.243308i
\(597\) 20679.1i 1.41765i
\(598\) −5990.99 3210.79i −0.409682 0.219564i
\(599\) −22915.4 −1.56310 −0.781550 0.623842i \(-0.785571\pi\)
−0.781550 + 0.623842i \(0.785571\pi\)
\(600\) −8044.08 + 2155.40i −0.547330 + 0.146657i
\(601\) −8010.26 4624.73i −0.543670 0.313888i 0.202895 0.979200i \(-0.434965\pi\)
−0.746565 + 0.665313i \(0.768298\pi\)
\(602\) −4221.47 7311.80i −0.285805 0.495028i
\(603\) −1533.30 + 1533.30i −0.103550 + 0.103550i
\(604\) 1034.17 3859.57i 0.0696685 0.260006i
\(605\) 1804.69 4114.01i 0.121274 0.276460i
\(606\) −6434.59 6434.59i −0.431333 0.431333i
\(607\) 4055.57 2341.48i 0.271187 0.156570i −0.358240 0.933630i \(-0.616623\pi\)
0.629427 + 0.777060i \(0.283290\pi\)
\(608\) 1190.11 + 687.112i 0.0793840 + 0.0458323i
\(609\) 4268.41 1143.72i 0.284014 0.0761013i
\(610\) 9050.50i 0.600728i
\(611\) 13028.4 + 21003.2i 0.862640 + 1.39067i
\(612\) 2112.29i 0.139517i
\(613\) 10219.6 2738.35i 0.673357 0.180425i 0.0940902 0.995564i \(-0.470006\pi\)
0.579266 + 0.815138i \(0.303339\pi\)
\(614\) −1251.82 + 2168.21i −0.0822789 + 0.142511i
\(615\) 1548.65 + 2682.33i 0.101541 + 0.175873i
\(616\) 11178.1 + 13015.3i 0.731131 + 0.851304i
\(617\) −8367.47 2242.06i −0.545967 0.146291i −0.0247156 0.999695i \(-0.507868\pi\)
−0.521252 + 0.853403i \(0.674535\pi\)
\(618\) 18281.9 + 4898.63i 1.18998 + 0.318854i
\(619\) 567.451 + 567.451i 0.0368461 + 0.0368461i 0.725290 0.688444i \(-0.241706\pi\)
−0.688444 + 0.725290i \(0.741706\pi\)
\(620\) −65.1865 112.906i −0.00422250 0.00731359i
\(621\) −5939.57 3429.21i −0.383811 0.221593i
\(622\) 3214.08 + 11995.1i 0.207191 + 0.773247i
\(623\) −28992.8 −1.86448
\(624\) −4229.48 13998.5i −0.271338 0.898062i
\(625\) −11482.7 −0.734893
\(626\) −22291.2 + 5972.91i −1.42322 + 0.381350i
\(627\) 1103.35 1614.86i 0.0702768 0.102857i
\(628\) 2324.49 1342.04i 0.147702 0.0852760i
\(629\) 6118.03 + 6118.03i 0.387825 + 0.387825i
\(630\) 2909.45 + 779.584i 0.183992 + 0.0493006i
\(631\) 3924.84 14647.7i 0.247615 0.924113i −0.724435 0.689343i \(-0.757899\pi\)
0.972051 0.234771i \(-0.0754339\pi\)
\(632\) 14185.9 + 14185.9i 0.892854 + 0.892854i
\(633\) 15824.2 9136.13i 0.993613 0.573663i
\(634\) 6476.19 11217.1i 0.405682 0.702662i
\(635\) 486.746 + 1816.56i 0.0304188 + 0.113524i
\(636\) 2170.14i 0.135301i
\(637\) 11190.5 + 10504.3i 0.696048 + 0.653370i
\(638\) −375.921 + 4950.16i −0.0233274 + 0.307177i
\(639\) −1847.53 6895.08i −0.114377 0.426862i
\(640\) −5104.39 2947.02i −0.315263 0.182017i
\(641\) 16357.7 9444.14i 1.00794 0.581936i 0.0973543 0.995250i \(-0.468962\pi\)
0.910589 + 0.413314i \(0.135629\pi\)
\(642\) 1121.91 1121.91i 0.0689694 0.0689694i
\(643\) 27570.8 + 7387.59i 1.69096 + 0.453092i 0.970638 0.240547i \(-0.0773267\pi\)
0.720324 + 0.693638i \(0.243993\pi\)
\(644\) 2655.75 + 711.606i 0.162502 + 0.0435423i
\(645\) 976.025 976.025i 0.0595828 0.0595828i
\(646\) −3098.35 + 1788.84i −0.188704 + 0.108949i
\(647\) 16461.1 + 9503.84i 1.00024 + 0.577488i 0.908319 0.418279i \(-0.137367\pi\)
0.0919192 + 0.995766i \(0.470700\pi\)
\(648\) −1528.38 5703.98i −0.0926547 0.345792i
\(649\) 22155.3 + 1682.50i 1.34002 + 0.101763i
\(650\) −541.718 17128.2i −0.0326891 1.03357i
\(651\) 1713.08i 0.103135i
\(652\) −2319.06 8654.85i −0.139297 0.519862i
\(653\) −84.5439 + 146.434i −0.00506655 + 0.00877553i −0.868548 0.495606i \(-0.834946\pi\)
0.863481 + 0.504381i \(0.168279\pi\)
\(654\) 6179.23 3567.58i 0.369460 0.213308i
\(655\) 4167.44 + 4167.44i 0.248604 + 0.248604i
\(656\) 4548.63 16975.7i 0.270723 1.01035i
\(657\) −2334.87 625.627i −0.138648 0.0371507i
\(658\) −31069.5 31069.5i −1.84075 1.84075i
\(659\) −6253.62 + 3610.53i −0.369661 + 0.213424i −0.673310 0.739360i \(-0.735128\pi\)
0.303649 + 0.952784i \(0.401795\pi\)
\(660\) 660.696 966.993i 0.0389660 0.0570305i
\(661\) −12232.5 + 3277.70i −0.719804 + 0.192871i −0.600084 0.799937i \(-0.704866\pi\)
−0.119720 + 0.992808i \(0.538200\pi\)
\(662\) 32140.5 1.88697
\(663\) 15416.9 + 3612.74i 0.903082 + 0.211625i
\(664\) −19463.9 −1.13757
\(665\) −300.437 1121.25i −0.0175195 0.0653835i
\(666\) 3085.40 + 1781.36i 0.179515 + 0.103643i
\(667\) −952.688 1650.10i −0.0553047 0.0957905i
\(668\) −5951.71 5951.71i −0.344729 0.344729i
\(669\) −9707.06 2601.00i −0.560982 0.150315i
\(670\) 2124.32 + 569.210i 0.122492 + 0.0328217i
\(671\) 19805.6 + 23061.0i 1.13947 + 1.32676i
\(672\) 5406.37 + 9364.10i 0.310350 + 0.537542i
\(673\) 3013.58 5219.68i 0.172608 0.298966i −0.766723 0.641978i \(-0.778114\pi\)
0.939331 + 0.343012i \(0.111447\pi\)
\(674\) 10353.3 2774.17i 0.591685 0.158541i
\(675\) 17291.2i 0.985985i
\(676\) 5166.73 327.147i 0.293965 0.0186133i
\(677\) 13615.1i 0.772924i −0.922305 0.386462i \(-0.873697\pi\)
0.922305 0.386462i \(-0.126303\pi\)
\(678\) 16772.9 4494.27i 0.950085 0.254574i
\(679\) −10259.8 5923.48i −0.579873 0.334790i
\(680\) 4443.44 2565.42i 0.250585 0.144676i
\(681\) −6596.25 6596.25i −0.371173 0.371173i
\(682\) 1815.89 + 637.438i 0.101956 + 0.0357900i
\(683\) −564.463 + 2106.61i −0.0316231 + 0.118019i −0.979933 0.199326i \(-0.936125\pi\)
0.948310 + 0.317345i \(0.102791\pi\)
\(684\) −237.020 + 237.020i −0.0132495 + 0.0132495i
\(685\) −1900.40 3291.59i −0.106001 0.183599i
\(686\) 1122.27 + 647.942i 0.0624613 + 0.0360620i
\(687\) −20930.0 + 5608.18i −1.16234 + 0.311449i
\(688\) −7832.10 −0.434006
\(689\) −10413.0 2440.13i −0.575765 0.134922i
\(690\) 1975.52i 0.108995i
\(691\) −8621.98 32177.7i −0.474668 1.77148i −0.622656 0.782496i \(-0.713946\pi\)
0.147988 0.988989i \(-0.452720\pi\)
\(692\) 8991.46 + 5191.22i 0.493937 + 0.285174i
\(693\) −9119.36 + 4380.47i −0.499879 + 0.240116i
\(694\) −18080.0 + 18080.0i −0.988915 + 0.988915i
\(695\) −1239.91 + 4627.42i −0.0676728 + 0.252558i
\(696\) 802.222 2993.93i 0.0436899 0.163053i
\(697\) 13456.2 + 13456.2i 0.731263 + 0.731263i
\(698\) 10447.4 + 18095.4i 0.566532 + 0.981262i
\(699\) −3929.43 + 6805.97i −0.212625 + 0.368277i
\(700\) 1794.08 + 6695.59i 0.0968711 + 0.361528i
\(701\) −23379.8 −1.25969 −0.629845 0.776721i \(-0.716882\pi\)
−0.629845 + 0.776721i \(0.716882\pi\)
\(702\) 22946.7 725.743i 1.23372 0.0390191i
\(703\) 1373.00i 0.0736611i
\(704\) 10233.7 1925.76i 0.547863 0.103096i
\(705\) 3591.71 6221.02i 0.191875 0.332336i
\(706\) −8021.96 13894.4i −0.427635 0.740686i
\(707\) 12827.2 12827.2i 0.682345 0.682345i
\(708\) 5595.00 + 1499.18i 0.296996 + 0.0795798i
\(709\) 8325.55 31071.4i 0.441005 1.64585i −0.285268 0.958448i \(-0.592083\pi\)
0.726273 0.687406i \(-0.241251\pi\)
\(710\) −5119.35 + 5119.35i −0.270600 + 0.270600i
\(711\) −10245.1 + 5915.03i −0.540397 + 0.311998i
\(712\) −10168.0 + 17611.5i −0.535201 + 0.926995i
\(713\) −713.476 + 191.175i −0.0374753 + 0.0100415i
\(714\) −28150.0 −1.47547
\(715\) −3897.02 4257.51i −0.203833 0.222688i
\(716\) 3232.27 0.168709
\(717\) −20536.1 + 5502.63i −1.06964 + 0.286610i
\(718\) −6100.45 + 10566.3i −0.317085 + 0.549207i
\(719\) 32494.6 18760.8i 1.68546 0.973100i 0.727537 0.686068i \(-0.240665\pi\)
0.957921 0.287032i \(-0.0926685\pi\)
\(720\) 1975.77 1975.77i 0.102267 0.102267i
\(721\) −9765.33 + 36444.7i −0.504411 + 1.88249i
\(722\) −20772.7 5566.03i −1.07075 0.286906i
\(723\) 7706.00 7706.00i 0.396389 0.396389i
\(724\) 1620.78 + 2807.28i 0.0831988 + 0.144105i
\(725\) 2401.88 4160.19i 0.123040 0.213111i
\(726\) 1901.44 + 17183.3i 0.0972023 + 0.878417i
\(727\) 16139.3i 0.823348i 0.911331 + 0.411674i \(0.135056\pi\)
−0.911331 + 0.411674i \(0.864944\pi\)
\(728\) 21100.2 6375.16i 1.07421 0.324559i
\(729\) 20068.4 1.01958
\(730\) 634.527 + 2368.09i 0.0321711 + 0.120064i
\(731\) 4240.35 7344.50i 0.214549 0.371609i
\(732\) 3962.35 + 6863.00i 0.200072 + 0.346535i
\(733\) −12081.0 12081.0i −0.608763 0.608763i 0.333860 0.942623i \(-0.391649\pi\)
−0.942623 + 0.333860i \(0.891649\pi\)
\(734\) 5809.00 21679.5i 0.292117 1.09020i
\(735\) 1154.54 4308.80i 0.0579399 0.216235i
\(736\) 3296.70 3296.70i 0.165106 0.165106i
\(737\) −6658.47 + 3198.38i −0.332792 + 0.159856i
\(738\) 6786.14 + 3917.98i 0.338484 + 0.195424i
\(739\) 5265.53 + 19651.2i 0.262105 + 0.978189i 0.963999 + 0.265907i \(0.0856714\pi\)
−0.701894 + 0.712282i \(0.747662\pi\)
\(740\) 822.167i 0.0408425i
\(741\) −1324.54 2135.31i −0.0656656 0.105860i
\(742\) 19013.2 0.940695
\(743\) −18704.0 + 5011.71i −0.923528 + 0.247459i −0.689093 0.724673i \(-0.741991\pi\)
−0.234435 + 0.972132i \(0.575324\pi\)
\(744\) −1040.60 600.791i −0.0512772 0.0296049i
\(745\) −2624.83 4546.34i −0.129082 0.223577i
\(746\) −10714.8 + 10714.8i −0.525867 + 0.525867i
\(747\) 2970.59 11086.4i 0.145499 0.543011i
\(748\) 2383.33 6789.46i 0.116501 0.331882i
\(749\) 2236.51 + 2236.51i 0.109106 + 0.109106i
\(750\) −9059.20 + 5230.33i −0.441060 + 0.254646i
\(751\) 22274.1 + 12859.9i 1.08228 + 0.624855i 0.931511 0.363714i \(-0.118491\pi\)
0.150770 + 0.988569i \(0.451825\pi\)
\(752\) −39371.1 + 10549.4i −1.90920 + 0.511568i
\(753\) 19637.8i 0.950388i
\(754\) 5621.68 + 3012.87i 0.271525 + 0.145520i
\(755\) 5723.29i 0.275883i
\(756\) −8970.13 + 2403.54i −0.431535 + 0.115629i
\(757\) 12094.4 20948.1i 0.580686 1.00578i −0.414713 0.909952i \(-0.636118\pi\)
0.995398 0.0958246i \(-0.0305488\pi\)
\(758\) −1921.31 3327.80i −0.0920647 0.159461i
\(759\) −4323.12 5033.68i −0.206745 0.240726i
\(760\) −786.461 210.731i −0.0375367 0.0100579i
\(761\) −2151.19 576.409i −0.102471 0.0274570i 0.207219 0.978295i \(-0.433559\pi\)
−0.309690 + 0.950838i \(0.600225\pi\)
\(762\) −5117.49 5117.49i −0.243290 0.243290i
\(763\) 7111.91 + 12318.2i 0.337442 + 0.584467i
\(764\) −7068.25 4080.86i −0.334712 0.193246i
\(765\) 783.070 + 2922.46i 0.0370091 + 0.138120i
\(766\) −23162.7 −1.09256
\(767\) 13484.6 25160.8i 0.634811 1.18449i
\(768\) 13465.7 0.632682
\(769\) 8221.79 2203.02i 0.385547 0.103307i −0.0608390 0.998148i \(-0.519378\pi\)
0.446386 + 0.894841i \(0.352711\pi\)
\(770\) 8472.10 + 5788.55i 0.396511 + 0.270915i
\(771\) −11135.2 + 6428.89i −0.520134 + 0.300300i
\(772\) −549.298 549.298i −0.0256084 0.0256084i
\(773\) −26636.0 7137.10i −1.23937 0.332087i −0.421147 0.906992i \(-0.638372\pi\)
−0.818220 + 0.574905i \(0.805039\pi\)
\(774\) 903.821 3373.11i 0.0419731 0.156646i
\(775\) −1316.81 1316.81i −0.0610337 0.0610337i
\(776\) −7196.38 + 4154.83i −0.332906 + 0.192203i
\(777\) 5401.56 9355.78i 0.249395 0.431965i
\(778\) 2419.48 + 9029.62i 0.111494 + 0.416102i
\(779\) 3019.83i 0.138892i
\(780\) −793.147 1278.64i −0.0364093 0.0586958i
\(781\) 1841.36 24247.2i 0.0843649 1.11092i
\(782\) 3141.47 + 11724.1i 0.143656 + 0.536131i
\(783\) 5573.43 + 3217.82i 0.254378 + 0.146865i
\(784\) −21920.2 + 12655.7i −0.998553 + 0.576515i
\(785\) −2718.51 + 2718.51i −0.123602 + 0.123602i
\(786\) −21907.6 5870.12i −0.994170 0.266387i
\(787\) 42172.7 + 11300.2i 1.91016 + 0.511826i 0.993757 + 0.111569i \(0.0355876\pi\)
0.916403 + 0.400257i \(0.131079\pi\)
\(788\) 218.679 218.679i 0.00988595 0.00988595i
\(789\) −23572.4 + 13609.5i −1.06363 + 0.614084i
\(790\) 10390.9 + 5999.17i 0.467963 + 0.270178i
\(791\) 8959.25 + 33436.4i 0.402723 + 1.50298i
\(792\) −537.343 + 7075.78i −0.0241082 + 0.317458i
\(793\) 37386.0 11295.7i 1.67417 0.505828i
\(794\) 15621.8i 0.698231i
\(795\) 804.513 + 3002.48i 0.0358907 + 0.133946i
\(796\) 6036.57 10455.6i 0.268794 0.465566i
\(797\) −1848.77 + 1067.39i −0.0821665 + 0.0474388i −0.540520 0.841331i \(-0.681773\pi\)
0.458354 + 0.888770i \(0.348439\pi\)
\(798\) 3158.70 + 3158.70i 0.140121 + 0.140121i
\(799\) 11423.1 42631.5i 0.505781 1.88760i
\(800\) 11353.8 + 3042.23i 0.501770 + 0.134449i
\(801\) −8479.45 8479.45i −0.374041 0.374041i
\(802\) −26581.8 + 15347.0i −1.17037 + 0.675712i
\(803\) −6798.98 4645.39i −0.298793 0.204150i
\(804\) −1860.08 + 498.406i −0.0815919 + 0.0218625i
\(805\) −3938.16 −0.172425
\(806\) 1692.23 1802.77i 0.0739532 0.0787839i
\(807\) −1311.38 −0.0572031
\(808\) −3293.22 12290.5i −0.143385 0.535120i
\(809\) 29654.6 + 17121.1i 1.28875 + 0.744062i 0.978432 0.206570i \(-0.0662301\pi\)
0.310321 + 0.950632i \(0.399563\pi\)
\(810\) −1765.85 3058.54i −0.0765996 0.132674i
\(811\) −7610.42 7610.42i −0.329517 0.329517i 0.522886 0.852403i \(-0.324855\pi\)
−0.852403 + 0.522886i \(0.824855\pi\)
\(812\) −2492.04 667.740i −0.107701 0.0288585i
\(813\) 1671.00 + 447.743i 0.0720843 + 0.0193149i
\(814\) 7907.36 + 9207.04i 0.340482 + 0.396446i
\(815\) 6417.05 + 11114.7i 0.275803 + 0.477705i
\(816\) −13056.7 + 22614.8i −0.560141 + 0.970193i
\(817\) −1299.93 + 348.315i −0.0556656 + 0.0149156i
\(818\) 5726.60i 0.244775i
\(819\) 410.883 + 12991.4i 0.0175304 + 0.554280i
\(820\) 1808.30i 0.0770106i
\(821\) 7912.57 2120.17i 0.336359 0.0901271i −0.0866864 0.996236i \(-0.527628\pi\)
0.423045 + 0.906109i \(0.360961\pi\)
\(822\) 12667.0 + 7313.27i 0.537483 + 0.310316i
\(823\) −17371.0 + 10029.2i −0.735742 + 0.424781i −0.820519 0.571619i \(-0.806316\pi\)
0.0847770 + 0.996400i \(0.472982\pi\)
\(824\) 18713.4 + 18713.4i 0.791155 + 0.791155i
\(825\) 5540.87 15784.4i 0.233828 0.666114i
\(826\) −13134.7 + 49019.4i −0.553287 + 2.06490i
\(827\) 24922.4 24922.4i 1.04793 1.04793i 0.0491360 0.998792i \(-0.484353\pi\)
0.998792 0.0491360i \(-0.0156468\pi\)
\(828\) 568.599 + 984.842i 0.0238649 + 0.0413353i
\(829\) −21834.8 12606.4i −0.914783 0.528150i −0.0328163 0.999461i \(-0.510448\pi\)
−0.881967 + 0.471311i \(0.843781\pi\)
\(830\) −11244.1 + 3012.84i −0.470226 + 0.125997i
\(831\) 26379.3 1.10119
\(832\) 3052.42 13025.8i 0.127192 0.542775i
\(833\) 27407.4i 1.13999i
\(834\) −4771.53 17807.6i −0.198111 0.739360i
\(835\) 10440.9 + 6028.05i 0.432721 + 0.249831i
\(836\) −1029.27 + 494.410i −0.0425816 + 0.0204540i
\(837\) 1764.13 1764.13i 0.0728524 0.0728524i
\(838\) 2459.43 9178.70i 0.101384 0.378369i
\(839\) 6734.64 25134.0i 0.277122 1.03423i −0.677283 0.735722i \(-0.736843\pi\)
0.954406 0.298512i \(-0.0964904\pi\)
\(840\) −4529.98 4529.98i −0.186070 0.186070i
\(841\) −11300.5 19573.1i −0.463346 0.802538i
\(842\) −14592.9 + 25275.6i −0.597273 + 1.03451i
\(843\) 2366.01 + 8830.09i 0.0966665 + 0.360764i
\(844\) −10668.0 −0.435079
\(845\) −7027.13 + 2368.03i −0.286083 + 0.0964057i
\(846\) 18173.6i 0.738560i
\(847\) −34254.5 + 3790.48i −1.38961 + 0.153769i
\(848\) 8818.79 15274.6i 0.357121 0.618552i
\(849\) −7039.05 12192.0i −0.284546 0.492848i
\(850\) −21638.3 + 21638.3i −0.873162 + 0.873162i
\(851\) −4499.37 1205.60i −0.181241 0.0485635i
\(852\) 1640.73 6123.28i 0.0659747 0.246221i
\(853\) 13596.6 13596.6i 0.545766 0.545766i −0.379448 0.925213i \(-0.623886\pi\)
0.925213 + 0.379448i \(0.123886\pi\)
\(854\) −60128.7 + 34715.3i −2.40932 + 1.39102i
\(855\) 240.060 415.795i 0.00960218 0.0166315i
\(856\) 2142.92 574.194i 0.0855649 0.0229270i
\(857\) 18617.4 0.742074 0.371037 0.928618i \(-0.379002\pi\)
0.371037 + 0.928618i \(0.379002\pi\)
\(858\) 21179.7 + 6690.63i 0.842729 + 0.266217i
\(859\) −16309.7 −0.647823 −0.323912 0.946087i \(-0.604998\pi\)
−0.323912 + 0.946087i \(0.604998\pi\)
\(860\) −778.410 + 208.574i −0.0308646 + 0.00827015i
\(861\) 11880.4 20577.4i 0.470247 0.814491i
\(862\) −38623.5 + 22299.3i −1.52613 + 0.881111i
\(863\) −13244.7 + 13244.7i −0.522426 + 0.522426i −0.918303 0.395878i \(-0.870440\pi\)
0.395878 + 0.918303i \(0.370440\pi\)
\(864\) −4075.69 + 15210.7i −0.160484 + 0.598933i
\(865\) −14364.6 3848.98i −0.564637 0.151294i
\(866\) 13026.5 13026.5i 0.511152 0.511152i
\(867\) −4223.18 7314.75i −0.165429 0.286531i
\(868\) −500.076 + 866.157i −0.0195549 + 0.0338702i
\(869\) −39604.5 + 7452.73i −1.54602 + 0.290928i
\(870\) 1853.74i 0.0722387i
\(871\) 300.004 + 9485.61i 0.0116708 + 0.369010i
\(872\) 9976.83 0.387452
\(873\) −1268.22 4733.07i −0.0491670 0.183494i
\(874\) 963.056 1668.06i 0.0372721 0.0645573i
\(875\) −10426.6 18059.3i −0.402837 0.697734i
\(876\) −1517.92 1517.92i −0.0585454 0.0585454i
\(877\) 2079.87 7762.18i 0.0800824 0.298871i −0.914255 0.405139i \(-0.867223\pi\)
0.994338 + 0.106267i \(0.0338899\pi\)
\(878\) −12585.4 + 46969.2i −0.483754 + 1.80539i
\(879\) −797.911 + 797.911i −0.0306176 + 0.0306176i
\(880\) 8579.92 4121.35i 0.328669 0.157876i
\(881\) 7395.80 + 4269.97i 0.282827 + 0.163290i 0.634703 0.772756i \(-0.281123\pi\)
−0.351875 + 0.936047i \(0.614456\pi\)
\(882\) −2920.91 10901.0i −0.111511 0.416163i
\(883\) 40320.5i 1.53669i 0.640038 + 0.768343i \(0.278918\pi\)
−0.640038 + 0.768343i \(0.721082\pi\)
\(884\) −6740.40 6327.11i −0.256453 0.240728i
\(885\) −8296.72 −0.315131
\(886\) −15644.4 + 4191.90i −0.593209 + 0.158950i
\(887\) 40913.3 + 23621.3i 1.54874 + 0.894166i 0.998238 + 0.0593337i \(0.0188976\pi\)
0.550504 + 0.834833i \(0.314436\pi\)
\(888\) −3788.75 6562.30i −0.143178 0.247992i
\(889\) 10201.6 10201.6i 0.384872 0.384872i
\(890\) −3147.85 + 11747.9i −0.118557 + 0.442462i
\(891\) 11192.6 + 3928.97i 0.420837 + 0.147728i
\(892\) 4148.76 + 4148.76i 0.155729 + 0.155729i
\(893\) −6065.44 + 3501.88i −0.227292 + 0.131227i
\(894\) 17495.6 + 10101.1i 0.654518 + 0.377886i
\(895\) −4472.00 + 1198.27i −0.167020 + 0.0447527i
\(896\) 45215.9i 1.68589i
\(897\) −8160.51 + 2465.59i −0.303759 + 0.0917768i
\(898\) 55729.6i 2.07096i
\(899\) 669.494 179.390i 0.0248375 0.00665518i
\(900\) −1433.53 + 2482.95i −0.0530938 + 0.0919611i
\(901\) 9549.10 + 16539.5i 0.353082 + 0.611556i
\(902\) 17391.7 + 20250.3i 0.641996 + 0.747518i
\(903\) −10228.2 2740.63i −0.376935 0.100999i
\(904\) 23452.8 + 6284.17i 0.862865 + 0.231204i
\(905\) −3283.14 3283.14i −0.120592 0.120592i
\(906\) −11012.4 19074.0i −0.403821 0.699439i
\(907\) 17689.9 + 10213.3i 0.647612 + 0.373899i 0.787541 0.616262i \(-0.211354\pi\)
−0.139928 + 0.990162i \(0.544687\pi\)
\(908\) 1409.61 + 5260.72i 0.0515192 + 0.192272i
\(909\) 7503.10 0.273776
\(910\) 11202.5 6948.99i 0.408089 0.253139i
\(911\) −23581.1 −0.857604 −0.428802 0.903398i \(-0.641064\pi\)
−0.428802 + 0.903398i \(0.641064\pi\)
\(912\) 4002.68 1072.52i 0.145331 0.0389414i
\(913\) 22057.1 32282.8i 0.799545 1.17021i
\(914\) 35754.1 20642.6i 1.29392 0.747043i
\(915\) −8026.35 8026.35i −0.289992 0.289992i
\(916\) 12219.7 + 3274.25i 0.440774 + 0.118105i
\(917\) 11702.0 43672.3i 0.421410 1.57272i
\(918\) −28989.0 28989.0i −1.04224 1.04224i
\(919\) 16382.8 9458.61i 0.588051 0.339511i −0.176276 0.984341i \(-0.556405\pi\)
0.764326 + 0.644830i \(0.223072\pi\)
\(920\) −1381.15 + 2392.22i −0.0494946 + 0.0857272i
\(921\) 812.695 + 3033.02i 0.0290763 + 0.108514i
\(922\) 15721.2i 0.561551i
\(923\) −27536.4 14757.8i −0.981986 0.526282i
\(924\) −8958.65 680.331i −0.318959 0.0242221i
\(925\) −3039.52 11343.7i −0.108042 0.403219i
\(926\) 28714.7 + 16578.4i 1.01903 + 0.588337i
\(927\) −13514.9 + 7802.85i −0.478844 + 0.276461i
\(928\) −3093.47 + 3093.47i −0.109427 + 0.109427i
\(929\) −5354.35 1434.69i −0.189096 0.0506682i 0.163028 0.986621i \(-0.447874\pi\)
−0.352124 + 0.935953i \(0.614541\pi\)
\(930\) −694.140 185.994i −0.0244750 0.00655806i
\(931\) −3075.37 + 3075.37i −0.108261 + 0.108261i
\(932\) 3973.56 2294.13i 0.139655 0.0806297i
\(933\) 13488.1 + 7787.36i 0.473291 + 0.273255i
\(934\) −722.773 2697.43i −0.0253210 0.0944994i
\(935\) −780.454 + 10277.1i −0.0272979 + 0.359461i
\(936\) 8035.65 + 4306.60i 0.280613 + 0.150391i
\(937\) 28049.3i 0.977940i 0.872301 + 0.488970i \(0.162627\pi\)
−0.872301 + 0.488970i \(0.837373\pi\)
\(938\) −4366.68 16296.7i −0.152001 0.567276i
\(939\) −14471.7 + 25065.7i −0.502946 + 0.871128i
\(940\) −3632.04 + 2096.96i −0.126026 + 0.0727609i
\(941\) −3918.47 3918.47i −0.135748 0.135748i 0.635968 0.771715i \(-0.280601\pi\)
−0.771715 + 0.635968i \(0.780601\pi\)
\(942\) 3829.20 14290.8i 0.132444 0.494288i
\(943\) −9896.07 2651.64i −0.341740 0.0915689i
\(944\) 33288.5 + 33288.5i 1.14772 + 1.14772i
\(945\) 11519.5 6650.81i 0.396540 0.228943i
\(946\) 6711.03 9822.24i 0.230650 0.337578i
\(947\) 9793.81 2624.24i 0.336068 0.0900490i −0.0868389 0.996222i \(-0.527677\pi\)
0.422906 + 0.906173i \(0.361010\pi\)
\(948\) −10505.9 −0.359931
\(949\) −8990.20 + 5576.66i −0.307518 + 0.190755i
\(950\) 4856.05 0.165843
\(951\) −4204.42 15691.1i −0.143362 0.535036i
\(952\) −34087.7 19680.5i −1.16049 0.670010i
\(953\) 21987.1 + 38082.8i 0.747357 + 1.29446i 0.949085 + 0.315020i \(0.102011\pi\)
−0.201728 + 0.979442i \(0.564656\pi\)
\(954\) 5560.73 + 5560.73i 0.188716 + 0.188716i
\(955\) 11292.1 + 3025.71i 0.382622 + 0.102523i
\(956\) 11989.7 + 3212.62i 0.405621 + 0.108686i
\(957\) 4056.62 + 4723.38i 0.137024 + 0.159546i
\(958\) −15786.8 27343.6i −0.532410 0.922161i
\(959\) −14578.9 + 25251.3i −0.490903 + 0.850269i
\(960\) −3755.88 + 1006.38i −0.126271 + 0.0338343i
\(961\) 29522.3i 0.990981i
\(962\) 14926.3 4509.78i 0.500253 0.151145i
\(963\) 1308.21i 0.0437763i
\(964\) −6145.78 + 1646.76i −0.205334 + 0.0550191i
\(965\) 963.615 + 556.343i 0.0321449 + 0.0185589i
\(966\) 13124.7 7577.56i 0.437144 0.252385i
\(967\) −34333.1 34333.1i −1.14176 1.14176i −0.988129 0.153626i \(-0.950905\pi\)
−0.153626 0.988129i \(-0.549095\pi\)
\(968\) −9710.85 + 22137.1i −0.322436 + 0.735034i
\(969\) −1161.33 + 4334.15i −0.0385009 + 0.143687i
\(970\) −3514.14 + 3514.14i −0.116322 + 0.116322i
\(971\) −2808.36 4864.23i −0.0928164 0.160763i 0.815879 0.578223i \(-0.196254\pi\)
−0.908695 + 0.417460i \(0.862920\pi\)
\(972\) −5708.13 3295.59i −0.188363 0.108751i
\(973\) 35499.1 9511.95i 1.16963 0.313401i
\(974\) 30331.4 0.997823
\(975\) −15670.4 14709.5i −0.514721 0.483161i
\(976\) 64407.4i 2.11233i
\(977\) 8620.69 + 32172.9i 0.282293 + 1.05353i 0.950795 + 0.309822i \(0.100269\pi\)
−0.668502 + 0.743711i \(0.733064\pi\)
\(978\) −42772.3 24694.6i −1.39847 0.807409i
\(979\) −17687.7 36822.6i −0.577427 1.20210i
\(980\) −1841.56 + 1841.56i −0.0600271 + 0.0600271i
\(981\) −1522.67 + 5682.66i −0.0495565 + 0.184948i
\(982\) −7384.53 + 27559.4i −0.239969 + 0.895577i
\(983\) 15478.7 + 15478.7i 0.502230 + 0.502230i 0.912130 0.409900i \(-0.134436\pi\)
−0.409900 + 0.912130i \(0.634436\pi\)
\(984\) −8333.10 14433.4i −0.269969 0.467600i
\(985\) −221.484 + 383.622i −0.00716454 + 0.0124093i
\(986\) −2947.82 11001.4i −0.0952106 0.355331i
\(987\) −55107.3 −1.77719
\(988\) 46.3751 + 1466.30i 0.00149331 + 0.0472158i
\(989\) 4565.76i 0.146797i
\(990\) 784.851 + 4170.77i 0.0251962 + 0.133895i
\(991\) −2900.34 + 5023.54i −0.0929691 + 0.161027i −0.908759 0.417321i \(-0.862969\pi\)
0.815790 + 0.578348i \(0.196302\pi\)
\(992\) 847.982 + 1468.75i 0.0271406 + 0.0470089i
\(993\) 28503.5 28503.5i 0.910907 0.910907i
\(994\) 53647.8 + 14374.9i 1.71188 + 0.458696i
\(995\) −4475.75 + 16703.7i −0.142604 + 0.532205i
\(996\) 7207.36 7207.36i 0.229291 0.229291i
\(997\) −7517.26 + 4340.09i −0.238791 + 0.137866i −0.614621 0.788823i \(-0.710691\pi\)
0.375830 + 0.926689i \(0.377358\pi\)
\(998\) 649.199 1124.45i 0.0205912 0.0356651i
\(999\) 15197.2 4072.07i 0.481299 0.128964i
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 143.4.o.a.32.10 160
11.10 odd 2 inner 143.4.o.a.32.31 yes 160
13.11 odd 12 inner 143.4.o.a.76.31 yes 160
143.76 even 12 inner 143.4.o.a.76.10 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
143.4.o.a.32.10 160 1.1 even 1 trivial
143.4.o.a.32.31 yes 160 11.10 odd 2 inner
143.4.o.a.76.10 yes 160 143.76 even 12 inner
143.4.o.a.76.31 yes 160 13.11 odd 12 inner