Properties

Label 287.3.q.a.73.10
Level $287$
Weight $3$
Character 287.73
Analytic conductor $7.820$
Analytic rank $0$
Dimension $216$
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] = [287,3,Mod(73,287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(287, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("287.73");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 287 = 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 287.q (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: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(216\)
Relative dimension: \(54\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 73.10
Character \(\chi\) \(=\) 287.73
Dual form 287.3.q.a.173.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.27032 + 1.31077i) q^{2} +(4.22026 - 1.13082i) q^{3} +(1.43624 - 2.48764i) q^{4} +(-0.688501 - 1.19252i) q^{5} +(-8.09911 + 8.09911i) q^{6} +(4.55185 + 5.31796i) q^{7} -2.95585i q^{8} +(8.73764 - 5.04468i) q^{9} +O(q^{10})\) \(q+(-2.27032 + 1.31077i) q^{2} +(4.22026 - 1.13082i) q^{3} +(1.43624 - 2.48764i) q^{4} +(-0.688501 - 1.19252i) q^{5} +(-8.09911 + 8.09911i) q^{6} +(4.55185 + 5.31796i) q^{7} -2.95585i q^{8} +(8.73764 - 5.04468i) q^{9} +(3.12624 + 1.80493i) q^{10} +(1.84953 + 6.90255i) q^{11} +(3.24824 - 12.1226i) q^{12} +(-1.89334 - 1.89334i) q^{13} +(-17.3048 - 6.10705i) q^{14} +(-4.25417 - 4.25417i) q^{15} +(9.61939 + 16.6613i) q^{16} +(2.96941 + 11.0820i) q^{17} +(-13.2248 + 22.9061i) q^{18} +(21.1030 + 5.65453i) q^{19} -3.95541 q^{20} +(25.2236 + 17.2959i) q^{21} +(-13.2467 - 13.2467i) q^{22} +(-4.96498 - 8.59959i) q^{23} +(-3.34252 - 12.4745i) q^{24} +(11.5519 - 20.0085i) q^{25} +(6.78023 + 1.81676i) q^{26} +(3.36550 - 3.36550i) q^{27} +(19.7667 - 3.68549i) q^{28} +(32.7263 - 32.7263i) q^{29} +(15.2346 + 4.08209i) q^{30} +(7.70768 + 4.45003i) q^{31} +(-33.4389 - 19.3059i) q^{32} +(15.6110 + 27.0391i) q^{33} +(-21.2674 - 21.2674i) q^{34} +(3.20782 - 9.08958i) q^{35} -28.9814i q^{36} +(23.3739 + 40.4848i) q^{37} +(-55.3224 + 14.8236i) q^{38} +(-10.1314 - 5.84938i) q^{39} +(-3.52490 + 2.03510i) q^{40} +(-25.3209 + 32.2467i) q^{41} +(-79.9366 - 6.20484i) q^{42} -1.74946i q^{43} +(19.8274 + 5.31274i) q^{44} +(-12.0317 - 6.94653i) q^{45} +(22.5442 + 13.0159i) q^{46} +(53.5048 + 14.3366i) q^{47} +(59.4372 + 59.4372i) q^{48} +(-7.56140 + 48.4131i) q^{49} +60.5677i q^{50} +(25.0634 + 43.4110i) q^{51} +(-7.42924 + 1.99066i) q^{52} +(-0.233821 - 0.872632i) q^{53} +(-3.22937 + 12.0522i) q^{54} +(6.95801 - 6.95801i) q^{55} +(15.7191 - 13.4546i) q^{56} +95.4544 q^{57} +(-31.4026 + 117.196i) q^{58} +(-90.5579 - 52.2836i) q^{59} +(-16.6929 + 4.47284i) q^{60} +(30.9579 + 53.6207i) q^{61} -23.3319 q^{62} +(66.5998 + 23.5038i) q^{63} +24.2675 q^{64} +(-0.954278 + 3.56142i) q^{65} +(-70.8841 - 40.9249i) q^{66} +(-28.8444 + 7.72884i) q^{67} +(31.8327 + 8.52955i) q^{68} +(-30.6781 - 30.6781i) q^{69} +(4.63158 + 24.8410i) q^{70} +(-30.7997 + 30.7997i) q^{71} +(-14.9113 - 25.8271i) q^{72} +(8.60551 - 14.9052i) q^{73} +(-106.132 - 61.2756i) q^{74} +(26.1262 - 97.5044i) q^{75} +(44.3754 - 44.3754i) q^{76} +(-28.2887 + 41.2551i) q^{77} +30.6688 q^{78} +(-31.0558 - 8.32138i) q^{79} +(13.2459 - 22.9426i) q^{80} +(-35.0046 + 60.6297i) q^{81} +(15.2185 - 106.400i) q^{82} -89.3470i q^{83} +(79.2530 - 37.9062i) q^{84} +(11.1710 - 11.1710i) q^{85} +(2.29314 + 3.97183i) q^{86} +(101.106 - 175.121i) q^{87} +(20.4029 - 5.46694i) q^{88} +(32.3439 - 120.709i) q^{89} +36.4212 q^{90} +(1.45052 - 18.6869i) q^{91} -28.5236 q^{92} +(37.5606 + 10.0643i) q^{93} +(-140.265 + 37.5839i) q^{94} +(-7.78630 - 29.0589i) q^{95} +(-162.952 - 43.6629i) q^{96} +(-9.59968 + 9.59968i) q^{97} +(-46.2916 - 119.824i) q^{98} +(50.9817 + 50.9817i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 216 q - 6 q^{3} + 204 q^{4} - 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 216 q - 6 q^{3} + 204 q^{4} - 4 q^{7} - 12 q^{10} - 10 q^{11} - 30 q^{12} - 74 q^{14} + 16 q^{15} - 372 q^{16} + 48 q^{17} - 36 q^{18} - 78 q^{19} - 80 q^{22} - 4 q^{23} + 108 q^{24} - 464 q^{25} + 36 q^{26} + 56 q^{28} - 120 q^{29} - 188 q^{30} - 84 q^{31} + 22 q^{35} - 104 q^{37} - 24 q^{38} + 240 q^{40} + 320 q^{42} + 118 q^{44} + 180 q^{45} - 282 q^{47} + 112 q^{51} - 306 q^{52} - 244 q^{53} + 54 q^{54} + 510 q^{56} - 344 q^{57} - 116 q^{58} + 252 q^{59} + 236 q^{60} - 30 q^{63} - 840 q^{64} - 52 q^{65} + 828 q^{66} - 294 q^{67} + 78 q^{68} - 282 q^{70} + 336 q^{71} + 548 q^{72} + 42 q^{75} - 1528 q^{78} + 8 q^{79} + 792 q^{81} - 342 q^{82} + 4 q^{85} - 212 q^{86} + 252 q^{88} + 396 q^{89} - 352 q^{92} + 118 q^{93} + 576 q^{94} + 278 q^{95} + 138 q^{96} + 780 q^{98} + 40 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).

\(n\) \(206\) \(211\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.27032 + 1.31077i −1.13516 + 0.655385i −0.945228 0.326412i \(-0.894160\pi\)
−0.189933 + 0.981797i \(0.560827\pi\)
\(3\) 4.22026 1.13082i 1.40675 0.376939i 0.525989 0.850492i \(-0.323695\pi\)
0.880765 + 0.473553i \(0.157029\pi\)
\(4\) 1.43624 2.48764i 0.359060 0.621909i
\(5\) −0.688501 1.19252i −0.137700 0.238504i 0.788926 0.614489i \(-0.210638\pi\)
−0.926626 + 0.375985i \(0.877304\pi\)
\(6\) −8.09911 + 8.09911i −1.34985 + 1.34985i
\(7\) 4.55185 + 5.31796i 0.650264 + 0.759709i
\(8\) 2.95585i 0.369481i
\(9\) 8.73764 5.04468i 0.970849 0.560520i
\(10\) 3.12624 + 1.80493i 0.312624 + 0.180493i
\(11\) 1.84953 + 6.90255i 0.168139 + 0.627504i 0.997619 + 0.0689674i \(0.0219705\pi\)
−0.829480 + 0.558537i \(0.811363\pi\)
\(12\) 3.24824 12.1226i 0.270687 1.01022i
\(13\) −1.89334 1.89334i −0.145642 0.145642i 0.630526 0.776168i \(-0.282839\pi\)
−0.776168 + 0.630526i \(0.782839\pi\)
\(14\) −17.3048 6.10705i −1.23606 0.436218i
\(15\) −4.25417 4.25417i −0.283612 0.283612i
\(16\) 9.61939 + 16.6613i 0.601212 + 1.04133i
\(17\) 2.96941 + 11.0820i 0.174671 + 0.651881i 0.996607 + 0.0823019i \(0.0262272\pi\)
−0.821936 + 0.569579i \(0.807106\pi\)
\(18\) −13.2248 + 22.9061i −0.734713 + 1.27256i
\(19\) 21.1030 + 5.65453i 1.11068 + 0.297607i 0.767108 0.641518i \(-0.221695\pi\)
0.343576 + 0.939125i \(0.388362\pi\)
\(20\) −3.95541 −0.197770
\(21\) 25.2236 + 17.2959i 1.20112 + 0.823614i
\(22\) −13.2467 13.2467i −0.602122 0.602122i
\(23\) −4.96498 8.59959i −0.215869 0.373895i 0.737672 0.675159i \(-0.235925\pi\)
−0.953541 + 0.301264i \(0.902592\pi\)
\(24\) −3.34252 12.4745i −0.139272 0.519769i
\(25\) 11.5519 20.0085i 0.462077 0.800341i
\(26\) 6.78023 + 1.81676i 0.260778 + 0.0698753i
\(27\) 3.36550 3.36550i 0.124648 0.124648i
\(28\) 19.7667 3.68549i 0.705953 0.131624i
\(29\) 32.7263 32.7263i 1.12849 1.12849i 0.138072 0.990422i \(-0.455909\pi\)
0.990422 0.138072i \(-0.0440906\pi\)
\(30\) 15.2346 + 4.08209i 0.507820 + 0.136070i
\(31\) 7.70768 + 4.45003i 0.248635 + 0.143549i 0.619139 0.785281i \(-0.287482\pi\)
−0.370504 + 0.928831i \(0.620815\pi\)
\(32\) −33.4389 19.3059i −1.04496 0.603310i
\(33\) 15.6110 + 27.0391i 0.473061 + 0.819366i
\(34\) −21.2674 21.2674i −0.625513 0.625513i
\(35\) 3.20782 9.08958i 0.0916519 0.259702i
\(36\) 28.9814i 0.805040i
\(37\) 23.3739 + 40.4848i 0.631727 + 1.09418i 0.987199 + 0.159496i \(0.0509869\pi\)
−0.355472 + 0.934687i \(0.615680\pi\)
\(38\) −55.3224 + 14.8236i −1.45585 + 0.390094i
\(39\) −10.1314 5.84938i −0.259780 0.149984i
\(40\) −3.52490 + 2.03510i −0.0881226 + 0.0508776i
\(41\) −25.3209 + 32.2467i −0.617583 + 0.786506i
\(42\) −79.9366 6.20484i −1.90325 0.147734i
\(43\) 1.74946i 0.0406851i −0.999793 0.0203425i \(-0.993524\pi\)
0.999793 0.0203425i \(-0.00647568\pi\)
\(44\) 19.8274 + 5.31274i 0.450623 + 0.120744i
\(45\) −12.0317 6.94653i −0.267372 0.154367i
\(46\) 22.5442 + 13.0159i 0.490091 + 0.282954i
\(47\) 53.5048 + 14.3366i 1.13840 + 0.305033i 0.778307 0.627884i \(-0.216079\pi\)
0.360092 + 0.932917i \(0.382745\pi\)
\(48\) 59.4372 + 59.4372i 1.23827 + 1.23827i
\(49\) −7.56140 + 48.4131i −0.154314 + 0.988022i
\(50\) 60.5677i 1.21135i
\(51\) 25.0634 + 43.4110i 0.491438 + 0.851196i
\(52\) −7.42924 + 1.99066i −0.142870 + 0.0382819i
\(53\) −0.233821 0.872632i −0.00441172 0.0164648i 0.963685 0.267042i \(-0.0860463\pi\)
−0.968097 + 0.250577i \(0.919380\pi\)
\(54\) −3.22937 + 12.0522i −0.0598032 + 0.223189i
\(55\) 6.95801 6.95801i 0.126509 0.126509i
\(56\) 15.7191 13.4546i 0.280698 0.240260i
\(57\) 95.4544 1.67464
\(58\) −31.4026 + 117.196i −0.541424 + 2.02062i
\(59\) −90.5579 52.2836i −1.53488 0.886163i −0.999126 0.0417887i \(-0.986694\pi\)
−0.535753 0.844375i \(-0.679972\pi\)
\(60\) −16.6929 + 4.47284i −0.278214 + 0.0745473i
\(61\) 30.9579 + 53.6207i 0.507507 + 0.879028i 0.999962 + 0.00869034i \(0.00276626\pi\)
−0.492455 + 0.870338i \(0.663900\pi\)
\(62\) −23.3319 −0.376321
\(63\) 66.5998 + 23.5038i 1.05714 + 0.373076i
\(64\) 24.2675 0.379179
\(65\) −0.954278 + 3.56142i −0.0146812 + 0.0547910i
\(66\) −70.8841 40.9249i −1.07400 0.620075i
\(67\) −28.8444 + 7.72884i −0.430514 + 0.115356i −0.467567 0.883957i \(-0.654869\pi\)
0.0370536 + 0.999313i \(0.488203\pi\)
\(68\) 31.8327 + 8.52955i 0.468128 + 0.125435i
\(69\) −30.6781 30.6781i −0.444610 0.444610i
\(70\) 4.63158 + 24.8410i 0.0661655 + 0.354871i
\(71\) −30.7997 + 30.7997i −0.433798 + 0.433798i −0.889918 0.456120i \(-0.849239\pi\)
0.456120 + 0.889918i \(0.349239\pi\)
\(72\) −14.9113 25.8271i −0.207101 0.358710i
\(73\) 8.60551 14.9052i 0.117884 0.204181i −0.801045 0.598604i \(-0.795722\pi\)
0.918929 + 0.394423i \(0.129056\pi\)
\(74\) −106.132 61.2756i −1.43422 0.828049i
\(75\) 26.1262 97.5044i 0.348350 1.30006i
\(76\) 44.3754 44.3754i 0.583886 0.583886i
\(77\) −28.2887 + 41.2551i −0.367386 + 0.535780i
\(78\) 30.6688 0.393189
\(79\) −31.0558 8.32138i −0.393112 0.105334i 0.0568480 0.998383i \(-0.481895\pi\)
−0.449960 + 0.893049i \(0.648562\pi\)
\(80\) 13.2459 22.9426i 0.165574 0.286783i
\(81\) −35.0046 + 60.6297i −0.432155 + 0.748514i
\(82\) 15.2185 106.400i 0.185591 1.29757i
\(83\) 89.3470i 1.07647i −0.842795 0.538235i \(-0.819091\pi\)
0.842795 0.538235i \(-0.180909\pi\)
\(84\) 79.2530 37.9062i 0.943488 0.451264i
\(85\) 11.1710 11.1710i 0.131424 0.131424i
\(86\) 2.29314 + 3.97183i 0.0266644 + 0.0461841i
\(87\) 101.106 175.121i 1.16214 2.01289i
\(88\) 20.4029 5.46694i 0.231851 0.0621243i
\(89\) 32.3439 120.709i 0.363414 1.35628i −0.506144 0.862449i \(-0.668929\pi\)
0.869558 0.493831i \(-0.164404\pi\)
\(90\) 36.4212 0.404680
\(91\) 1.45052 18.6869i 0.0159397 0.205351i
\(92\) −28.5236 −0.310039
\(93\) 37.5606 + 10.0643i 0.403877 + 0.108219i
\(94\) −140.265 + 37.5839i −1.49218 + 0.399829i
\(95\) −7.78630 29.0589i −0.0819611 0.305883i
\(96\) −162.952 43.6629i −1.69742 0.454822i
\(97\) −9.59968 + 9.59968i −0.0989657 + 0.0989657i −0.754856 0.655890i \(-0.772293\pi\)
0.655890 + 0.754856i \(0.272293\pi\)
\(98\) −46.2916 119.824i −0.472363 1.22270i
\(99\) 50.9817 + 50.9817i 0.514966 + 0.514966i
\(100\) −33.1827 57.4741i −0.331827 0.574741i
\(101\) −37.0499 138.272i −0.366831 1.36903i −0.864922 0.501907i \(-0.832632\pi\)
0.498090 0.867125i \(-0.334035\pi\)
\(102\) −113.804 65.7046i −1.11572 0.644163i
\(103\) 2.45624 + 4.25433i 0.0238470 + 0.0413042i 0.877703 0.479206i \(-0.159075\pi\)
−0.853856 + 0.520510i \(0.825742\pi\)
\(104\) −5.59643 + 5.59643i −0.0538119 + 0.0538119i
\(105\) 3.25918 41.9879i 0.0310398 0.399884i
\(106\) 1.67467 + 1.67467i 0.0157988 + 0.0157988i
\(107\) −78.9809 136.799i −0.738139 1.27849i −0.953332 0.301923i \(-0.902372\pi\)
0.215194 0.976571i \(-0.430962\pi\)
\(108\) −3.53849 13.2058i −0.0327638 0.122276i
\(109\) −11.9978 + 3.21479i −0.110071 + 0.0294935i −0.313434 0.949610i \(-0.601480\pi\)
0.203363 + 0.979103i \(0.434813\pi\)
\(110\) −6.67657 + 24.9173i −0.0606961 + 0.226521i
\(111\) 144.425 + 144.425i 1.30112 + 1.30112i
\(112\) −44.8180 + 126.995i −0.400161 + 1.13388i
\(113\) −59.9043 −0.530126 −0.265063 0.964231i \(-0.585393\pi\)
−0.265063 + 0.964231i \(0.585393\pi\)
\(114\) −216.712 + 125.119i −1.90098 + 1.09753i
\(115\) −6.83678 + 11.8417i −0.0594503 + 0.102971i
\(116\) −34.4085 128.414i −0.296625 1.10702i
\(117\) −26.0946 6.99204i −0.223031 0.0597610i
\(118\) 274.127 2.32311
\(119\) −45.4172 + 66.2347i −0.381657 + 0.556594i
\(120\) −12.5747 + 12.5747i −0.104789 + 0.104789i
\(121\) 60.5647 34.9670i 0.500534 0.288984i
\(122\) −140.569 81.1575i −1.15220 0.665225i
\(123\) −70.3957 + 164.723i −0.572323 + 1.33921i
\(124\) 22.1401 12.7826i 0.178549 0.103086i
\(125\) −66.2391 −0.529913
\(126\) −182.011 + 33.9358i −1.44453 + 0.269332i
\(127\) −35.8001 −0.281890 −0.140945 0.990017i \(-0.545014\pi\)
−0.140945 + 0.990017i \(0.545014\pi\)
\(128\) 78.6605 45.4147i 0.614535 0.354802i
\(129\) −1.97832 7.38318i −0.0153358 0.0572339i
\(130\) −2.50168 9.33640i −0.0192437 0.0718184i
\(131\) −25.2556 43.7440i −0.192791 0.333924i 0.753383 0.657582i \(-0.228421\pi\)
−0.946174 + 0.323658i \(0.895087\pi\)
\(132\) 89.6846 0.679429
\(133\) 65.9870 + 137.963i 0.496143 + 1.03732i
\(134\) 55.3554 55.3554i 0.413100 0.413100i
\(135\) −6.33058 1.69627i −0.0468932 0.0125650i
\(136\) 32.7566 8.77712i 0.240858 0.0645376i
\(137\) −101.489 + 27.1939i −0.740796 + 0.198496i −0.609432 0.792838i \(-0.708602\pi\)
−0.131364 + 0.991334i \(0.541936\pi\)
\(138\) 109.861 + 29.4371i 0.796094 + 0.213313i
\(139\) 182.983i 1.31642i −0.752833 0.658211i \(-0.771313\pi\)
0.752833 0.658211i \(-0.228687\pi\)
\(140\) −18.0044 21.0347i −0.128603 0.150248i
\(141\) 242.016 1.71643
\(142\) 29.5538 110.296i 0.208126 0.776735i
\(143\) 9.56709 16.5707i 0.0669027 0.115879i
\(144\) 168.102 + 97.0535i 1.16737 + 0.673982i
\(145\) −61.5589 16.4947i −0.424544 0.113756i
\(146\) 45.1194i 0.309037i
\(147\) 22.8352 + 212.866i 0.155341 + 1.44807i
\(148\) 134.282 0.907310
\(149\) −49.8420 + 186.013i −0.334510 + 1.24841i 0.569890 + 0.821721i \(0.306986\pi\)
−0.904400 + 0.426687i \(0.859681\pi\)
\(150\) 68.4909 + 255.612i 0.456606 + 1.70408i
\(151\) 14.2200 + 53.0698i 0.0941723 + 0.351456i 0.996893 0.0787721i \(-0.0250999\pi\)
−0.902720 + 0.430228i \(0.858433\pi\)
\(152\) 16.7139 62.3773i 0.109960 0.410377i
\(153\) 81.8506 + 81.8506i 0.534971 + 0.534971i
\(154\) 10.1485 130.742i 0.0658992 0.848976i
\(155\) 12.2554i 0.0790671i
\(156\) −29.1023 + 16.8022i −0.186553 + 0.107706i
\(157\) −181.743 + 48.6979i −1.15760 + 0.310178i −0.786006 0.618218i \(-0.787855\pi\)
−0.371592 + 0.928396i \(0.621188\pi\)
\(158\) 81.4141 21.8148i 0.515279 0.138069i
\(159\) −1.97357 3.41833i −0.0124124 0.0214989i
\(160\) 53.1686i 0.332304i
\(161\) 23.1325 65.5476i 0.143680 0.407128i
\(162\) 183.532i 1.13291i
\(163\) −22.4087 38.8131i −0.137477 0.238117i 0.789064 0.614311i \(-0.210566\pi\)
−0.926541 + 0.376194i \(0.877233\pi\)
\(164\) 43.8514 + 109.303i 0.267386 + 0.666483i
\(165\) 21.4964 37.2329i 0.130281 0.225654i
\(166\) 117.113 + 202.846i 0.705503 + 1.22197i
\(167\) −88.8802 88.8802i −0.532217 0.532217i 0.389015 0.921231i \(-0.372815\pi\)
−0.921231 + 0.389015i \(0.872815\pi\)
\(168\) 51.1240 74.5572i 0.304310 0.443793i
\(169\) 161.831i 0.957577i
\(170\) −10.7192 + 40.0045i −0.0630539 + 0.235320i
\(171\) 212.916 57.0506i 1.24512 0.333629i
\(172\) −4.35202 2.51264i −0.0253024 0.0146084i
\(173\) −9.10749 15.7746i −0.0526444 0.0911829i 0.838502 0.544898i \(-0.183432\pi\)
−0.891147 + 0.453715i \(0.850098\pi\)
\(174\) 530.108i 3.04660i
\(175\) 158.987 29.6430i 0.908498 0.169389i
\(176\) −97.2139 + 97.2139i −0.552352 + 0.552352i
\(177\) −441.301 118.246i −2.49323 0.668058i
\(178\) 84.7908 + 316.443i 0.476353 + 1.77777i
\(179\) 185.798 49.7843i 1.03798 0.278125i 0.300701 0.953718i \(-0.402779\pi\)
0.737274 + 0.675594i \(0.236113\pi\)
\(180\) −34.5609 + 19.9538i −0.192005 + 0.110854i
\(181\) −237.148 + 237.148i −1.31021 + 1.31021i −0.388948 + 0.921260i \(0.627161\pi\)
−0.921260 + 0.388948i \(0.872839\pi\)
\(182\) 21.2011 + 44.3266i 0.116490 + 0.243553i
\(183\) 191.286 + 191.286i 1.04528 + 1.04528i
\(184\) −25.4191 + 14.6757i −0.138147 + 0.0797593i
\(185\) 32.1859 55.7476i 0.173978 0.301338i
\(186\) −98.4666 + 26.3841i −0.529391 + 0.141850i
\(187\) −71.0019 + 40.9930i −0.379689 + 0.219214i
\(188\) 112.510 112.510i 0.598456 0.598456i
\(189\) 33.2169 + 2.57836i 0.175751 + 0.0136421i
\(190\) 55.7669 + 55.7669i 0.293510 + 0.293510i
\(191\) −57.6586 + 215.185i −0.301877 + 1.12662i 0.633723 + 0.773560i \(0.281526\pi\)
−0.935600 + 0.353061i \(0.885141\pi\)
\(192\) 102.415 27.4420i 0.533412 0.142927i
\(193\) −0.516936 1.92923i −0.00267843 0.00999603i 0.964574 0.263814i \(-0.0849804\pi\)
−0.967252 + 0.253818i \(0.918314\pi\)
\(194\) 9.21138 34.3773i 0.0474813 0.177203i
\(195\) 16.1092i 0.0826114i
\(196\) 109.574 + 88.3427i 0.559052 + 0.450728i
\(197\) 25.3724i 0.128794i −0.997924 0.0643970i \(-0.979488\pi\)
0.997924 0.0643970i \(-0.0205124\pi\)
\(198\) −182.570 48.9195i −0.922071 0.247068i
\(199\) −18.3123 68.3423i −0.0920215 0.343429i 0.904530 0.426411i \(-0.140222\pi\)
−0.996551 + 0.0829821i \(0.973556\pi\)
\(200\) −59.1422 34.1458i −0.295711 0.170729i
\(201\) −112.991 + 65.2354i −0.562145 + 0.324554i
\(202\) 265.358 + 265.358i 1.31366 + 1.31366i
\(203\) 323.003 + 25.0721i 1.59115 + 0.123508i
\(204\) 143.988 0.705823
\(205\) 55.8883 + 7.99373i 0.272626 + 0.0389938i
\(206\) −11.1529 6.43913i −0.0541403 0.0312579i
\(207\) −86.7643 50.0934i −0.419151 0.241997i
\(208\) 13.3327 49.7583i 0.0640995 0.239223i
\(209\) 156.123i 0.746999i
\(210\) 47.6371 + 99.5980i 0.226843 + 0.474276i
\(211\) −222.867 222.867i −1.05624 1.05624i −0.998321 0.0579182i \(-0.981554\pi\)
−0.0579182 0.998321i \(-0.518446\pi\)
\(212\) −2.50662 0.671646i −0.0118237 0.00316814i
\(213\) −95.1539 + 164.811i −0.446732 + 0.773763i
\(214\) 358.624 + 207.052i 1.67581 + 0.967531i
\(215\) −2.08626 + 1.20450i −0.00970355 + 0.00560235i
\(216\) −9.94792 9.94792i −0.0460552 0.0460552i
\(217\) 11.4191 + 61.2450i 0.0526225 + 0.282235i
\(218\) 23.0249 23.0249i 0.105619 0.105619i
\(219\) 19.4625 72.6350i 0.0888699 0.331667i
\(220\) −7.31565 27.3024i −0.0332530 0.124102i
\(221\) 15.3599 26.6041i 0.0695017 0.120381i
\(222\) −517.198 138.583i −2.32972 0.624247i
\(223\) 142.000i 0.636771i −0.947961 0.318385i \(-0.896859\pi\)
0.947961 0.318385i \(-0.103141\pi\)
\(224\) −49.5403 265.704i −0.221162 1.18618i
\(225\) 233.103i 1.03601i
\(226\) 136.002 78.5208i 0.601779 0.347437i
\(227\) 82.6955 + 308.624i 0.364297 + 1.35958i 0.868371 + 0.495915i \(0.165167\pi\)
−0.504073 + 0.863661i \(0.668166\pi\)
\(228\) 137.095 237.456i 0.601295 1.04147i
\(229\) 329.405 + 88.2637i 1.43845 + 0.385431i 0.891990 0.452055i \(-0.149309\pi\)
0.546458 + 0.837486i \(0.315976\pi\)
\(230\) 35.8458i 0.155851i
\(231\) −72.7338 + 206.097i −0.314865 + 0.892193i
\(232\) −96.7341 96.7341i −0.416957 0.416957i
\(233\) −342.883 91.8752i −1.47160 0.394314i −0.568121 0.822945i \(-0.692330\pi\)
−0.903480 + 0.428630i \(0.858996\pi\)
\(234\) 68.4082 18.3299i 0.292343 0.0783330i
\(235\) −19.7415 73.6762i −0.0840063 0.313516i
\(236\) −260.125 + 150.184i −1.10223 + 0.636371i
\(237\) −140.474 −0.592716
\(238\) 16.2933 209.906i 0.0684592 0.881956i
\(239\) 32.3582 32.3582i 0.135390 0.135390i −0.636164 0.771554i \(-0.719480\pi\)
0.771554 + 0.636164i \(0.219480\pi\)
\(240\) 29.9574 111.803i 0.124822 0.465844i
\(241\) 178.773 309.643i 0.741795 1.28483i −0.209883 0.977727i \(-0.567308\pi\)
0.951677 0.307100i \(-0.0993585\pi\)
\(242\) −91.6675 + 158.773i −0.378791 + 0.656086i
\(243\) −90.2541 + 336.833i −0.371416 + 1.38614i
\(244\) 177.852 0.728901
\(245\) 62.9395 24.3153i 0.256896 0.0992463i
\(246\) −56.0931 466.247i −0.228021 1.89531i
\(247\) −29.2492 50.6612i −0.118418 0.205106i
\(248\) 13.1536 22.7827i 0.0530388 0.0918659i
\(249\) −101.035 377.068i −0.405763 1.51433i
\(250\) 150.384 86.8243i 0.601536 0.347297i
\(251\) 2.42083 0.00964474 0.00482237 0.999988i \(-0.498465\pi\)
0.00482237 + 0.999988i \(0.498465\pi\)
\(252\) 154.122 131.919i 0.611596 0.523488i
\(253\) 50.1762 50.1762i 0.198325 0.198325i
\(254\) 81.2777 46.9257i 0.319991 0.184747i
\(255\) 34.5123 59.7770i 0.135342 0.234420i
\(256\) −167.591 + 290.277i −0.654654 + 1.13389i
\(257\) −11.2815 + 42.1031i −0.0438968 + 0.163825i −0.984395 0.175974i \(-0.943692\pi\)
0.940498 + 0.339799i \(0.110359\pi\)
\(258\) 14.1691 + 14.1691i 0.0549188 + 0.0549188i
\(259\) −108.902 + 308.582i −0.420471 + 1.19144i
\(260\) 7.48894 + 7.48894i 0.0288036 + 0.0288036i
\(261\) 120.857 451.045i 0.463054 1.72814i
\(262\) 114.677 + 66.2086i 0.437697 + 0.252705i
\(263\) −434.077 + 116.311i −1.65048 + 0.442246i −0.959748 0.280862i \(-0.909380\pi\)
−0.690735 + 0.723108i \(0.742713\pi\)
\(264\) 79.9234 46.1438i 0.302740 0.174787i
\(265\) −0.879644 + 0.879644i −0.00331941 + 0.00331941i
\(266\) −330.650 226.727i −1.24305 0.852359i
\(267\) 545.998i 2.04494i
\(268\) −22.2009 + 82.8549i −0.0828392 + 0.309160i
\(269\) 86.6551 + 50.0303i 0.322138 + 0.185986i 0.652345 0.757922i \(-0.273785\pi\)
−0.330207 + 0.943908i \(0.607119\pi\)
\(270\) 16.5959 4.44685i 0.0614662 0.0164698i
\(271\) −63.3651 + 36.5838i −0.233819 + 0.134996i −0.612333 0.790600i \(-0.709769\pi\)
0.378513 + 0.925596i \(0.376435\pi\)
\(272\) −156.076 + 156.076i −0.573809 + 0.573809i
\(273\) −15.0099 80.5040i −0.0549814 0.294886i
\(274\) 194.768 194.768i 0.710831 0.710831i
\(275\) 159.476 + 42.7313i 0.579911 + 0.155387i
\(276\) −120.377 + 32.2549i −0.436148 + 0.116866i
\(277\) 144.360 250.039i 0.521155 0.902666i −0.478543 0.878064i \(-0.658835\pi\)
0.999697 0.0246021i \(-0.00783188\pi\)
\(278\) 239.848 + 415.429i 0.862764 + 1.49435i
\(279\) 89.7959 0.321849
\(280\) −26.8674 9.48182i −0.0959551 0.0338636i
\(281\) 165.126 + 165.126i 0.587639 + 0.587639i 0.936991 0.349353i \(-0.113598\pi\)
−0.349353 + 0.936991i \(0.613598\pi\)
\(282\) −549.454 + 317.228i −1.94842 + 1.12492i
\(283\) −87.9204 50.7609i −0.310673 0.179367i 0.336555 0.941664i \(-0.390738\pi\)
−0.647228 + 0.762297i \(0.724072\pi\)
\(284\) 32.3828 + 120.854i 0.114024 + 0.425543i
\(285\) −65.7205 113.831i −0.230598 0.399408i
\(286\) 50.1610i 0.175388i
\(287\) −286.744 + 12.1267i −0.999107 + 0.0422532i
\(288\) −389.569 −1.35267
\(289\) 136.288 78.6862i 0.471586 0.272270i
\(290\) 161.379 43.2414i 0.556480 0.149108i
\(291\) −29.6577 + 51.3686i −0.101916 + 0.176524i
\(292\) −24.7191 42.8148i −0.0846546 0.146626i
\(293\) 128.345 128.345i 0.438037 0.438037i −0.453314 0.891351i \(-0.649758\pi\)
0.891351 + 0.453314i \(0.149758\pi\)
\(294\) −330.862 453.343i −1.12538 1.54198i
\(295\) 143.989i 0.488099i
\(296\) 119.667 69.0897i 0.404280 0.233411i
\(297\) 29.4552 + 17.0060i 0.0991757 + 0.0572591i
\(298\) −130.663 487.640i −0.438466 1.63638i
\(299\) −6.88157 + 25.6824i −0.0230153 + 0.0858942i
\(300\) −205.032 205.032i −0.683440 0.683440i
\(301\) 9.30355 7.96327i 0.0309088 0.0264560i
\(302\) −101.846 101.846i −0.337239 0.337239i
\(303\) −312.721 541.648i −1.03208 1.78762i
\(304\) 108.786 + 405.996i 0.357850 + 1.33551i
\(305\) 42.6291 73.8358i 0.139768 0.242085i
\(306\) −293.115 78.5398i −0.957891 0.256666i
\(307\) 256.378 0.835107 0.417554 0.908652i \(-0.362888\pi\)
0.417554 + 0.908652i \(0.362888\pi\)
\(308\) 61.9984 + 129.624i 0.201293 + 0.420858i
\(309\) 15.1768 + 15.1768i 0.0491160 + 0.0491160i
\(310\) 16.0640 + 27.8237i 0.0518194 + 0.0897539i
\(311\) 145.821 + 544.211i 0.468878 + 1.74988i 0.643702 + 0.765276i \(0.277398\pi\)
−0.174824 + 0.984600i \(0.555936\pi\)
\(312\) −17.2899 + 29.9470i −0.0554163 + 0.0959838i
\(313\) 339.355 + 90.9298i 1.08420 + 0.290511i 0.756315 0.654207i \(-0.226998\pi\)
0.327885 + 0.944718i \(0.393664\pi\)
\(314\) 348.783 348.783i 1.11077 1.11077i
\(315\) −17.8253 95.6039i −0.0565882 0.303504i
\(316\) −65.3041 + 65.3041i −0.206659 + 0.206659i
\(317\) 311.565 + 83.4837i 0.982856 + 0.263355i 0.714247 0.699894i \(-0.246769\pi\)
0.268609 + 0.963249i \(0.413436\pi\)
\(318\) 8.96129 + 5.17380i 0.0281802 + 0.0162698i
\(319\) 286.424 + 165.367i 0.897879 + 0.518391i
\(320\) −16.7082 28.9394i −0.0522130 0.0904356i
\(321\) −488.014 488.014i −1.52029 1.52029i
\(322\) 33.3997 + 179.135i 0.103726 + 0.556321i
\(323\) 250.654i 0.776017i
\(324\) 100.550 + 174.157i 0.310339 + 0.537523i
\(325\) −59.7548 + 16.0112i −0.183861 + 0.0492654i
\(326\) 101.750 + 58.7454i 0.312117 + 0.180201i
\(327\) −46.9984 + 27.1345i −0.143726 + 0.0829802i
\(328\) 95.3165 + 74.8447i 0.290599 + 0.228185i
\(329\) 167.304 + 349.794i 0.508524 + 1.06320i
\(330\) 112.707i 0.341538i
\(331\) −178.424 47.8085i −0.539045 0.144437i −0.0209830 0.999780i \(-0.506680\pi\)
−0.518062 + 0.855343i \(0.673346\pi\)
\(332\) −222.263 128.324i −0.669467 0.386517i
\(333\) 408.465 + 235.828i 1.22662 + 0.708191i
\(334\) 318.288 + 85.2850i 0.952958 + 0.255344i
\(335\) 29.0762 + 29.0762i 0.0867946 + 0.0867946i
\(336\) −45.5357 + 586.634i −0.135523 + 1.74593i
\(337\) 125.196i 0.371501i 0.982597 + 0.185751i \(0.0594717\pi\)
−0.982597 + 0.185751i \(0.940528\pi\)
\(338\) 212.123 + 367.407i 0.627582 + 1.08700i
\(339\) −252.812 + 67.7407i −0.745757 + 0.199825i
\(340\) −11.7452 43.8337i −0.0345447 0.128923i
\(341\) −16.4610 + 61.4331i −0.0482726 + 0.180156i
\(342\) −408.607 + 408.607i −1.19476 + 1.19476i
\(343\) −291.877 + 180.158i −0.850954 + 0.525241i
\(344\) −5.17114 −0.0150324
\(345\) −15.4623 + 57.7060i −0.0448182 + 0.167264i
\(346\) 41.3539 + 23.8757i 0.119520 + 0.0690048i
\(347\) −247.911 + 66.4274i −0.714440 + 0.191434i −0.597689 0.801728i \(-0.703914\pi\)
−0.116750 + 0.993161i \(0.537248\pi\)
\(348\) −290.425 503.031i −0.834556 1.44549i
\(349\) 588.398 1.68595 0.842977 0.537949i \(-0.180801\pi\)
0.842977 + 0.537949i \(0.180801\pi\)
\(350\) −322.097 + 275.695i −0.920276 + 0.787700i
\(351\) −12.7441 −0.0363080
\(352\) 71.4139 266.520i 0.202880 0.757160i
\(353\) −20.9838 12.1150i −0.0594442 0.0343202i 0.469983 0.882675i \(-0.344260\pi\)
−0.529428 + 0.848355i \(0.677593\pi\)
\(354\) 1156.89 309.988i 3.26805 0.875671i
\(355\) 57.9348 + 15.5236i 0.163197 + 0.0437284i
\(356\) −253.827 253.827i −0.712996 0.712996i
\(357\) −116.773 + 330.886i −0.327097 + 0.926852i
\(358\) −356.564 + 356.564i −0.995990 + 0.995990i
\(359\) 219.000 + 379.320i 0.610029 + 1.05660i 0.991235 + 0.132111i \(0.0421755\pi\)
−0.381206 + 0.924490i \(0.624491\pi\)
\(360\) −20.5329 + 35.5640i −0.0570358 + 0.0987889i
\(361\) 100.728 + 58.1551i 0.279024 + 0.161094i
\(362\) 227.555 849.247i 0.628605 2.34599i
\(363\) 216.057 216.057i 0.595200 0.595200i
\(364\) −44.4030 30.4472i −0.121986 0.0836463i
\(365\) −23.6996 −0.0649305
\(366\) −685.012 183.548i −1.87162 0.501498i
\(367\) −294.581 + 510.229i −0.802673 + 1.39027i 0.115177 + 0.993345i \(0.463256\pi\)
−0.917851 + 0.396926i \(0.870077\pi\)
\(368\) 95.5201 165.446i 0.259566 0.449581i
\(369\) −58.5704 + 409.496i −0.158727 + 1.10975i
\(370\) 168.753i 0.456090i
\(371\) 3.57631 5.21554i 0.00963964 0.0140581i
\(372\) 78.9824 78.9824i 0.212318 0.212318i
\(373\) −270.125 467.870i −0.724195 1.25434i −0.959305 0.282373i \(-0.908878\pi\)
0.235110 0.971969i \(-0.424455\pi\)
\(374\) 107.465 186.134i 0.287339 0.497685i
\(375\) −279.546 + 74.9042i −0.745457 + 0.199745i
\(376\) 42.3767 158.152i 0.112704 0.420617i
\(377\) −123.924 −0.328712
\(378\) −78.7926 + 37.6860i −0.208446 + 0.0996984i
\(379\) −309.771 −0.817338 −0.408669 0.912683i \(-0.634007\pi\)
−0.408669 + 0.912683i \(0.634007\pi\)
\(380\) −83.4709 22.3660i −0.219660 0.0588578i
\(381\) −151.086 + 40.4833i −0.396551 + 0.106255i
\(382\) −151.154 564.115i −0.395692 1.47674i
\(383\) −264.883 70.9753i −0.691602 0.185314i −0.104136 0.994563i \(-0.533208\pi\)
−0.587466 + 0.809249i \(0.699874\pi\)
\(384\) 280.612 280.612i 0.730761 0.730761i
\(385\) 68.6743 + 5.33063i 0.178375 + 0.0138458i
\(386\) 3.70239 + 3.70239i 0.00959169 + 0.00959169i
\(387\) −8.82546 15.2861i −0.0228048 0.0394991i
\(388\) 10.0931 + 37.6679i 0.0260131 + 0.0970823i
\(389\) −230.477 133.066i −0.592486 0.342072i 0.173594 0.984817i \(-0.444462\pi\)
−0.766080 + 0.642745i \(0.777795\pi\)
\(390\) −21.1155 36.5731i −0.0541423 0.0937772i
\(391\) 80.5575 80.5575i 0.206029 0.206029i
\(392\) 143.102 + 22.3503i 0.365055 + 0.0570162i
\(393\) −156.052 156.052i −0.397078 0.397078i
\(394\) 33.2574 + 57.6036i 0.0844097 + 0.146202i
\(395\) 11.4586 + 42.7639i 0.0290090 + 0.108263i
\(396\) 200.046 53.6021i 0.505166 0.135359i
\(397\) 7.69477 28.7173i 0.0193823 0.0723357i −0.955557 0.294805i \(-0.904745\pi\)
0.974940 + 0.222470i \(0.0714118\pi\)
\(398\) 131.156 + 131.156i 0.329537 + 0.329537i
\(399\) 434.494 + 507.623i 1.08896 + 1.27224i
\(400\) 444.490 1.11123
\(401\) 647.605 373.895i 1.61497 0.932406i 0.626780 0.779196i \(-0.284372\pi\)
0.988194 0.153210i \(-0.0489611\pi\)
\(402\) 171.017 296.211i 0.425416 0.736843i
\(403\) −6.16785 23.0187i −0.0153048 0.0571184i
\(404\) −397.184 106.425i −0.983128 0.263428i
\(405\) 96.4027 0.238031
\(406\) −766.183 + 366.460i −1.88715 + 0.902612i
\(407\) −236.217 + 236.217i −0.580387 + 0.580387i
\(408\) 128.316 74.0835i 0.314501 0.181577i
\(409\) −424.853 245.289i −1.03876 0.599728i −0.119278 0.992861i \(-0.538058\pi\)
−0.919482 + 0.393133i \(0.871391\pi\)
\(410\) −137.362 + 55.1084i −0.335030 + 0.134411i
\(411\) −397.559 + 229.531i −0.967297 + 0.558469i
\(412\) 14.1110 0.0342499
\(413\) −134.163 719.570i −0.324851 1.74230i
\(414\) 262.644 0.634406
\(415\) −106.548 + 61.5155i −0.256742 + 0.148230i
\(416\) 26.7585 + 99.8640i 0.0643232 + 0.240058i
\(417\) −206.920 772.235i −0.496210 1.85188i
\(418\) −204.641 354.449i −0.489572 0.847963i
\(419\) 118.680 0.283247 0.141623 0.989921i \(-0.454768\pi\)
0.141623 + 0.989921i \(0.454768\pi\)
\(420\) −99.7697 68.4123i −0.237547 0.162886i
\(421\) −391.632 + 391.632i −0.930241 + 0.930241i −0.997721 0.0674794i \(-0.978504\pi\)
0.0674794 + 0.997721i \(0.478504\pi\)
\(422\) 798.106 + 213.852i 1.89125 + 0.506758i
\(423\) 539.829 144.647i 1.27619 0.341954i
\(424\) −2.57937 + 0.691140i −0.00608342 + 0.00163005i
\(425\) 256.037 + 68.6048i 0.602439 + 0.161423i
\(426\) 498.900i 1.17113i
\(427\) −144.237 + 408.706i −0.337792 + 0.957158i
\(428\) −453.741 −1.06014
\(429\) 21.6372 80.7513i 0.0504365 0.188231i
\(430\) 3.15766 5.46922i 0.00734339 0.0127191i
\(431\) 121.231 + 69.9930i 0.281279 + 0.162397i 0.634002 0.773331i \(-0.281411\pi\)
−0.352723 + 0.935728i \(0.614744\pi\)
\(432\) 88.4477 + 23.6995i 0.204740 + 0.0548599i
\(433\) 40.5223i 0.0935851i −0.998905 0.0467925i \(-0.985100\pi\)
0.998905 0.0467925i \(-0.0149000\pi\)
\(434\) −106.203 124.078i −0.244708 0.285894i
\(435\) −278.447 −0.640108
\(436\) −9.23442 + 34.4633i −0.0211799 + 0.0790443i
\(437\) −56.1492 209.552i −0.128488 0.479524i
\(438\) 51.0217 + 190.416i 0.116488 + 0.434739i
\(439\) −26.0996 + 97.4051i −0.0594525 + 0.221880i −0.989260 0.146167i \(-0.953306\pi\)
0.929808 + 0.368046i \(0.119973\pi\)
\(440\) −20.5668 20.5668i −0.0467428 0.0467428i
\(441\) 178.160 + 461.161i 0.403990 + 1.04572i
\(442\) 80.5331i 0.182202i
\(443\) 269.880 155.815i 0.609211 0.351728i −0.163446 0.986552i \(-0.552261\pi\)
0.772656 + 0.634824i \(0.218928\pi\)
\(444\) 566.705 151.848i 1.27636 0.342000i
\(445\) −166.216 + 44.5376i −0.373520 + 0.100084i
\(446\) 186.129 + 322.385i 0.417330 + 0.722837i
\(447\) 841.385i 1.88229i
\(448\) 110.462 + 129.053i 0.246566 + 0.288066i
\(449\) 192.321i 0.428331i 0.976797 + 0.214165i \(0.0687031\pi\)
−0.976797 + 0.214165i \(0.931297\pi\)
\(450\) 305.545 + 529.219i 0.678988 + 1.17604i
\(451\) −269.417 115.137i −0.597376 0.255293i
\(452\) −86.0368 + 149.020i −0.190347 + 0.329691i
\(453\) 120.024 + 207.888i 0.264954 + 0.458914i
\(454\) −592.280 592.280i −1.30458 1.30458i
\(455\) −23.2832 + 11.1362i −0.0511719 + 0.0244752i
\(456\) 282.149i 0.618747i
\(457\) 101.221 377.762i 0.221490 0.826612i −0.762291 0.647235i \(-0.775925\pi\)
0.983780 0.179377i \(-0.0574081\pi\)
\(458\) −863.548 + 231.387i −1.88548 + 0.505212i
\(459\) 47.2900 + 27.3029i 0.103028 + 0.0594834i
\(460\) 19.6385 + 34.0149i 0.0426924 + 0.0739454i
\(461\) 529.367i 1.14830i −0.818749 0.574151i \(-0.805332\pi\)
0.818749 0.574151i \(-0.194668\pi\)
\(462\) −105.016 563.243i −0.227308 1.21914i
\(463\) −287.564 + 287.564i −0.621088 + 0.621088i −0.945810 0.324722i \(-0.894729\pi\)
0.324722 + 0.945810i \(0.394729\pi\)
\(464\) 860.070 + 230.455i 1.85360 + 0.496670i
\(465\) −13.8586 51.7210i −0.0298035 0.111228i
\(466\) 898.882 240.855i 1.92893 0.516856i
\(467\) −143.101 + 82.6196i −0.306427 + 0.176916i −0.645326 0.763907i \(-0.723279\pi\)
0.338900 + 0.940823i \(0.389945\pi\)
\(468\) −54.8718 + 54.8718i −0.117247 + 0.117247i
\(469\) −172.397 118.213i −0.367584 0.252053i
\(470\) 141.392 + 141.392i 0.300834 + 0.300834i
\(471\) −711.935 + 411.036i −1.51154 + 0.872687i
\(472\) −154.542 + 267.675i −0.327420 + 0.567109i
\(473\) 12.0757 3.23568i 0.0255301 0.00684076i
\(474\) 318.920 184.129i 0.672828 0.388457i
\(475\) 356.919 356.919i 0.751409 0.751409i
\(476\) 99.5379 + 208.110i 0.209113 + 0.437207i
\(477\) −6.44519 6.44519i −0.0135119 0.0135119i
\(478\) −31.0493 + 115.878i −0.0649568 + 0.242422i
\(479\) 767.938 205.768i 1.60321 0.429579i 0.657200 0.753716i \(-0.271741\pi\)
0.946010 + 0.324137i \(0.105074\pi\)
\(480\) 60.1239 + 224.386i 0.125258 + 0.467470i
\(481\) 32.3968 120.906i 0.0673529 0.251365i
\(482\) 937.319i 1.94465i
\(483\) 23.5029 302.786i 0.0486602 0.626887i
\(484\) 200.884i 0.415049i
\(485\) 18.0572 + 4.83841i 0.0372313 + 0.00997610i
\(486\) −236.605 883.022i −0.486841 1.81692i
\(487\) −547.427 316.057i −1.12408 0.648988i −0.181640 0.983365i \(-0.558141\pi\)
−0.942439 + 0.334377i \(0.891474\pi\)
\(488\) 158.495 91.5070i 0.324784 0.187514i
\(489\) −138.461 138.461i −0.283152 0.283152i
\(490\) −111.021 + 137.703i −0.226574 + 0.281026i
\(491\) 172.010 0.350326 0.175163 0.984539i \(-0.443955\pi\)
0.175163 + 0.984539i \(0.443955\pi\)
\(492\) 308.666 + 411.700i 0.627370 + 0.836790i
\(493\) 459.850 + 265.495i 0.932759 + 0.538529i
\(494\) 132.810 + 76.6781i 0.268847 + 0.155219i
\(495\) 25.6957 95.8976i 0.0519104 0.193732i
\(496\) 171.226i 0.345215i
\(497\) −303.987 23.5961i −0.611643 0.0474770i
\(498\) 723.631 + 723.631i 1.45307 + 1.45307i
\(499\) 882.662 + 236.509i 1.76886 + 0.473965i 0.988482 0.151340i \(-0.0483588\pi\)
0.780380 + 0.625305i \(0.215025\pi\)
\(500\) −95.1352 + 164.779i −0.190270 + 0.329558i
\(501\) −475.605 274.590i −0.949311 0.548085i
\(502\) −5.49606 + 3.17315i −0.0109483 + 0.00632102i
\(503\) −449.661 449.661i −0.893957 0.893957i 0.100936 0.994893i \(-0.467816\pi\)
−0.994893 + 0.100936i \(0.967816\pi\)
\(504\) 69.4737 196.859i 0.137845 0.390593i
\(505\) −139.383 + 139.383i −0.276007 + 0.276007i
\(506\) −48.1466 + 179.686i −0.0951514 + 0.355110i
\(507\) −183.000 682.967i −0.360948 1.34708i
\(508\) −51.4175 + 89.0577i −0.101215 + 0.175310i
\(509\) −97.7145 26.1825i −0.191973 0.0514391i 0.161551 0.986864i \(-0.448350\pi\)
−0.353525 + 0.935425i \(0.615017\pi\)
\(510\) 180.951i 0.354805i
\(511\) 118.436 22.0823i 0.231773 0.0432140i
\(512\) 515.378i 1.00660i
\(513\) 90.0526 51.9919i 0.175541 0.101349i
\(514\) −29.5749 110.375i −0.0575386 0.214737i
\(515\) 3.38224 5.85822i 0.00656747 0.0113752i
\(516\) −21.2080 5.68267i −0.0411008 0.0110129i
\(517\) 395.835i 0.765639i
\(518\) −157.237 843.325i −0.303547 1.62804i
\(519\) −56.2742 56.2742i −0.108428 0.108428i
\(520\) 10.5270 + 2.82070i 0.0202442 + 0.00542443i
\(521\) 226.787 60.7674i 0.435292 0.116636i −0.0345173 0.999404i \(-0.510989\pi\)
0.469809 + 0.882768i \(0.344323\pi\)
\(522\) 316.832 + 1182.43i 0.606957 + 2.26520i
\(523\) 11.8519 6.84270i 0.0226614 0.0130836i −0.488627 0.872493i \(-0.662502\pi\)
0.511288 + 0.859410i \(0.329169\pi\)
\(524\) −145.092 −0.276894
\(525\) 637.447 304.887i 1.21418 0.580737i
\(526\) 833.038 833.038i 1.58372 1.58372i
\(527\) −26.4279 + 98.6303i −0.0501478 + 0.187154i
\(528\) −300.337 + 520.199i −0.568820 + 0.985226i
\(529\) 215.198 372.734i 0.406802 0.704601i
\(530\) 0.844063 3.15009i 0.00159257 0.00594356i
\(531\) −1055.02 −1.98685
\(532\) 437.976 + 33.9966i 0.823264 + 0.0639034i
\(533\) 108.995 13.1130i 0.204494 0.0246022i
\(534\) 715.678 + 1239.59i 1.34022 + 2.32133i
\(535\) −108.757 + 188.372i −0.203284 + 0.352098i
\(536\) 22.8453 + 85.2597i 0.0426218 + 0.159067i
\(537\) 727.818 420.206i 1.35534 0.782506i
\(538\) −262.313 −0.487571
\(539\) −348.159 + 37.3486i −0.645934 + 0.0692924i
\(540\) −13.3119 + 13.3119i −0.0246517 + 0.0246517i
\(541\) 10.8549 6.26710i 0.0200646 0.0115843i −0.489934 0.871759i \(-0.662979\pi\)
0.509999 + 0.860175i \(0.329646\pi\)
\(542\) 95.9060 166.114i 0.176948 0.306484i
\(543\) −732.655 + 1269.00i −1.34927 + 2.33701i
\(544\) 114.654 427.896i 0.210762 0.786573i
\(545\) 12.0942 + 12.0942i 0.0221912 + 0.0221912i
\(546\) 139.600 + 163.095i 0.255677 + 0.298709i
\(547\) −702.818 702.818i −1.28486 1.28486i −0.937868 0.346991i \(-0.887203\pi\)
−0.346991 0.937868i \(-0.612797\pi\)
\(548\) −78.1139 + 291.525i −0.142544 + 0.531980i
\(549\) 540.999 + 312.346i 0.985425 + 0.568936i
\(550\) −418.072 + 112.022i −0.760130 + 0.203676i
\(551\) 875.676 505.572i 1.58925 0.917553i
\(552\) −90.6797 + 90.6797i −0.164275 + 0.164275i
\(553\) −97.1085 203.031i −0.175603 0.367145i
\(554\) 756.891i 1.36623i
\(555\) 72.7926 271.666i 0.131158 0.489488i
\(556\) −455.195 262.807i −0.818695 0.472674i
\(557\) 330.017 88.4279i 0.592491 0.158757i 0.0498995 0.998754i \(-0.484110\pi\)
0.542591 + 0.839997i \(0.317443\pi\)
\(558\) −203.866 + 117.702i −0.365350 + 0.210935i
\(559\) −3.31233 + 3.31233i −0.00592545 + 0.00592545i
\(560\) 182.301 33.9899i 0.325538 0.0606963i
\(561\) −253.291 + 253.291i −0.451499 + 0.451499i
\(562\) −591.333 158.447i −1.05219 0.281935i
\(563\) 309.973 83.0569i 0.550573 0.147526i 0.0272012 0.999630i \(-0.491341\pi\)
0.523372 + 0.852104i \(0.324674\pi\)
\(564\) 347.593 602.049i 0.616300 1.06746i
\(565\) 41.2442 + 71.4370i 0.0729985 + 0.126437i
\(566\) 266.143 0.470218
\(567\) −481.761 + 89.8241i −0.849667 + 0.158420i
\(568\) 91.0391 + 91.0391i 0.160280 + 0.160280i
\(569\) −969.450 + 559.712i −1.70378 + 0.983677i −0.761919 + 0.647672i \(0.775743\pi\)
−0.941860 + 0.336006i \(0.890924\pi\)
\(570\) 298.413 + 172.289i 0.523532 + 0.302261i
\(571\) 149.256 + 557.033i 0.261395 + 0.975539i 0.964420 + 0.264374i \(0.0851654\pi\)
−0.703025 + 0.711165i \(0.748168\pi\)
\(572\) −27.4813 47.5989i −0.0480441 0.0832149i
\(573\) 973.337i 1.69867i
\(574\) 635.105 403.387i 1.10645 0.702764i
\(575\) −229.420 −0.398992
\(576\) 212.040 122.421i 0.368125 0.212537i
\(577\) −778.916 + 208.710i −1.34994 + 0.361715i −0.860113 0.510104i \(-0.829607\pi\)
−0.489828 + 0.871819i \(0.662940\pi\)
\(578\) −206.279 + 357.286i −0.356884 + 0.618141i
\(579\) −4.36321 7.55731i −0.00753578 0.0130523i
\(580\) −129.446 + 129.446i −0.223183 + 0.223183i
\(581\) 475.144 406.694i 0.817804 0.699989i
\(582\) 155.498i 0.267178i
\(583\) 5.59093 3.22792i 0.00958993 0.00553675i
\(584\) −44.0575 25.4366i −0.0754409 0.0435558i
\(585\) 9.62805 + 35.9324i 0.0164582 + 0.0614229i
\(586\) −123.153 + 459.614i −0.210159 + 0.784325i
\(587\) −266.998 266.998i −0.454851 0.454851i 0.442110 0.896961i \(-0.354230\pi\)
−0.896961 + 0.442110i \(0.854230\pi\)
\(588\) 562.331 + 248.921i 0.956346 + 0.423335i
\(589\) 137.492 + 137.492i 0.233433 + 0.233433i
\(590\) −188.737 326.902i −0.319893 0.554071i
\(591\) −28.6915 107.078i −0.0485474 0.181182i
\(592\) −449.685 + 778.878i −0.759604 + 1.31567i
\(593\) 570.836 + 152.955i 0.962625 + 0.257935i 0.705711 0.708500i \(-0.250628\pi\)
0.256914 + 0.966434i \(0.417294\pi\)
\(594\) −89.1636 −0.150107
\(595\) 110.256 + 8.55828i 0.185304 + 0.0143837i
\(596\) 391.147 + 391.147i 0.656288 + 0.656288i
\(597\) −154.565 267.715i −0.258903 0.448433i
\(598\) −18.0403 67.3274i −0.0301678 0.112588i
\(599\) −427.955 + 741.240i −0.714449 + 1.23746i 0.248722 + 0.968575i \(0.419989\pi\)
−0.963172 + 0.268888i \(0.913344\pi\)
\(600\) −288.208 77.2251i −0.480347 0.128709i
\(601\) 467.742 467.742i 0.778274 0.778274i −0.201264 0.979537i \(-0.564505\pi\)
0.979537 + 0.201264i \(0.0645048\pi\)
\(602\) −10.6840 + 30.2740i −0.0177476 + 0.0502890i
\(603\) −213.043 + 213.043i −0.353304 + 0.353304i
\(604\) 152.442 + 40.8467i 0.252387 + 0.0676269i
\(605\) −83.3977 48.1497i −0.137847 0.0795862i
\(606\) 1419.95 + 819.811i 2.34316 + 1.35282i
\(607\) 352.014 + 609.707i 0.579925 + 1.00446i 0.995487 + 0.0948944i \(0.0302514\pi\)
−0.415563 + 0.909565i \(0.636415\pi\)
\(608\) −596.494 596.494i −0.981076 0.981076i
\(609\) 1391.51 259.446i 2.28491 0.426019i
\(610\) 223.508i 0.366407i
\(611\) −74.1589 128.447i −0.121373 0.210224i
\(612\) 321.172 86.0577i 0.524790 0.140617i
\(613\) −976.559 563.817i −1.59308 0.919766i −0.992774 0.119997i \(-0.961711\pi\)
−0.600308 0.799769i \(-0.704955\pi\)
\(614\) −582.060 + 336.053i −0.947981 + 0.547317i
\(615\) 244.903 29.4637i 0.398216 0.0479085i
\(616\) 121.944 + 83.6171i 0.197961 + 0.135742i
\(617\) 1137.22i 1.84314i 0.388216 + 0.921568i \(0.373091\pi\)
−0.388216 + 0.921568i \(0.626909\pi\)
\(618\) −54.3496 14.5629i −0.0879444 0.0235646i
\(619\) 777.315 + 448.783i 1.25576 + 0.725013i 0.972247 0.233956i \(-0.0751672\pi\)
0.283512 + 0.958969i \(0.408501\pi\)
\(620\) −30.4870 17.6017i −0.0491726 0.0283898i
\(621\) −45.6516 12.2323i −0.0735131 0.0196978i
\(622\) −1044.40 1044.40i −1.67909 1.67909i
\(623\) 789.150 377.445i 1.26669 0.605851i
\(624\) 225.070i 0.360689i
\(625\) −243.193 421.222i −0.389108 0.673955i
\(626\) −889.632 + 238.376i −1.42114 + 0.380793i
\(627\) 176.546 + 658.879i 0.281573 + 1.05084i
\(628\) −139.884 + 522.052i −0.222744 + 0.831294i
\(629\) −379.245 + 379.245i −0.602933 + 0.602933i
\(630\) 165.784 + 193.687i 0.263149 + 0.307439i
\(631\) 1102.72 1.74757 0.873787 0.486309i \(-0.161657\pi\)
0.873787 + 0.486309i \(0.161657\pi\)
\(632\) −24.5967 + 91.7963i −0.0389189 + 0.145247i
\(633\) −1192.58 688.534i −1.88401 1.08773i
\(634\) −816.781 + 218.856i −1.28830 + 0.345199i
\(635\) 24.6484 + 42.6923i 0.0388164 + 0.0672319i
\(636\) −11.3381 −0.0178272
\(637\) 105.979 77.3462i 0.166372 0.121423i
\(638\) −867.031 −1.35898
\(639\) −113.742 + 424.491i −0.178000 + 0.664305i
\(640\) −108.316 62.5361i −0.169243 0.0977127i
\(641\) 982.828 263.348i 1.53327 0.410839i 0.609187 0.793026i \(-0.291496\pi\)
0.924085 + 0.382187i \(0.124829\pi\)
\(642\) 1747.62 + 468.274i 2.72216 + 0.729399i
\(643\) 193.588 + 193.588i 0.301071 + 0.301071i 0.841433 0.540362i \(-0.181713\pi\)
−0.540362 + 0.841433i \(0.681713\pi\)
\(644\) −129.835 151.687i −0.201607 0.235539i
\(645\) −7.44250 + 7.44250i −0.0115388 + 0.0115388i
\(646\) −328.549 569.064i −0.508590 0.880904i
\(647\) 566.209 980.703i 0.875130 1.51577i 0.0185066 0.999829i \(-0.494109\pi\)
0.856624 0.515942i \(-0.172558\pi\)
\(648\) 179.212 + 103.468i 0.276562 + 0.159673i
\(649\) 193.401 721.781i 0.297998 1.11214i
\(650\) 114.675 114.675i 0.176424 0.176424i
\(651\) 117.448 + 245.557i 0.180412 + 0.377200i
\(652\) −128.737 −0.197450
\(653\) 195.416 + 52.3616i 0.299259 + 0.0801863i 0.405324 0.914173i \(-0.367159\pi\)
−0.106065 + 0.994359i \(0.533825\pi\)
\(654\) 71.1343 123.208i 0.108768 0.188392i
\(655\) −34.7770 + 60.2356i −0.0530947 + 0.0919627i
\(656\) −780.843 111.684i −1.19031 0.170251i
\(657\) 173.648i 0.264305i
\(658\) −838.334 574.847i −1.27406 0.873628i
\(659\) −927.089 + 927.089i −1.40681 + 1.40681i −0.631155 + 0.775657i \(0.717419\pi\)
−0.775657 + 0.631155i \(0.782581\pi\)
\(660\) −61.7479 106.951i −0.0935575 0.162046i
\(661\) 216.131 374.350i 0.326976 0.566339i −0.654934 0.755686i \(-0.727304\pi\)
0.981910 + 0.189347i \(0.0606370\pi\)
\(662\) 467.745 125.332i 0.706564 0.189323i
\(663\) 34.7384 129.645i 0.0523958 0.195544i
\(664\) −264.096 −0.397735
\(665\) 119.092 173.679i 0.179086 0.261171i
\(666\) −1236.46 −1.85655
\(667\) −443.919 118.948i −0.665545 0.178332i
\(668\) −348.755 + 93.4486i −0.522088 + 0.139893i
\(669\) −160.576 599.276i −0.240023 0.895779i
\(670\) −104.125 27.9001i −0.155410 0.0416419i
\(671\) −312.862 + 312.862i −0.466262 + 0.466262i
\(672\) −509.536 1065.32i −0.758238 1.58530i
\(673\) −823.957 823.957i −1.22430 1.22430i −0.966087 0.258218i \(-0.916865\pi\)
−0.258218 0.966087i \(-0.583135\pi\)
\(674\) −164.103 284.235i −0.243477 0.421714i
\(675\) −28.4607 106.217i −0.0421640 0.157358i
\(676\) −402.576 232.427i −0.595526 0.343827i
\(677\) −11.0885 19.2059i −0.0163789 0.0283691i 0.857720 0.514117i \(-0.171880\pi\)
−0.874099 + 0.485748i \(0.838547\pi\)
\(678\) 485.171 485.171i 0.715592 0.715592i
\(679\) −94.7469 7.35445i −0.139539 0.0108313i
\(680\) −33.0199 33.0199i −0.0485586 0.0485586i
\(681\) 697.993 + 1208.96i 1.02495 + 1.77527i
\(682\) −43.1531 161.049i −0.0632743 0.236143i
\(683\) −816.683 + 218.830i −1.19573 + 0.320395i −0.801148 0.598466i \(-0.795777\pi\)
−0.394581 + 0.918861i \(0.629110\pi\)
\(684\) 163.876 611.595i 0.239585 0.894145i
\(685\) 102.305 + 102.305i 0.149350 + 0.149350i
\(686\) 426.509 791.599i 0.621734 1.15394i
\(687\) 1489.98 2.16883
\(688\) 29.1482 16.8287i 0.0423666 0.0244604i
\(689\) −1.20949 + 2.09490i −0.00175543 + 0.00304049i
\(690\) −40.5350 151.279i −0.0587464 0.219245i
\(691\) −146.483 39.2500i −0.211987 0.0568018i 0.151263 0.988494i \(-0.451666\pi\)
−0.363250 + 0.931692i \(0.618333\pi\)
\(692\) −52.3221 −0.0756100
\(693\) −39.0578 + 503.179i −0.0563604 + 0.726088i
\(694\) 475.765 475.765i 0.685541 0.685541i
\(695\) −218.210 + 125.984i −0.313972 + 0.181272i
\(696\) −517.632 298.855i −0.743723 0.429389i
\(697\) −432.546 184.852i −0.620582 0.265211i
\(698\) −1335.85 + 771.255i −1.91383 + 1.10495i
\(699\) −1550.95 −2.21881
\(700\) 154.602 438.077i 0.220861 0.625824i
\(701\) 1148.58 1.63849 0.819244 0.573445i \(-0.194393\pi\)
0.819244 + 0.573445i \(0.194393\pi\)
\(702\) 28.9332 16.7046i 0.0412154 0.0237957i
\(703\) 264.337 + 986.518i 0.376013 + 1.40330i
\(704\) 44.8834 + 167.507i 0.0637549 + 0.237937i
\(705\) −166.628 288.609i −0.236352 0.409374i
\(706\) 63.5200 0.0899717
\(707\) 566.681 826.424i 0.801529 1.16892i
\(708\) −927.968 + 927.968i −1.31069 + 1.31069i
\(709\) 868.708 + 232.770i 1.22526 + 0.328307i 0.812732 0.582638i \(-0.197980\pi\)
0.412527 + 0.910945i \(0.364646\pi\)
\(710\) −151.878 + 40.6957i −0.213913 + 0.0573179i
\(711\) −313.333 + 83.9574i −0.440694 + 0.118084i
\(712\) −356.797 95.6035i −0.501120 0.134275i
\(713\) 88.3772i 0.123951i
\(714\) −168.603 904.281i −0.236138 1.26650i
\(715\) −26.3478 −0.0368501
\(716\) 143.004 533.699i 0.199727 0.745390i
\(717\) 99.9689 173.151i 0.139427 0.241494i
\(718\) −994.402 574.118i −1.38496 0.799608i
\(719\) 1294.74 + 346.925i 1.80075 + 0.482511i 0.994096 0.108507i \(-0.0346071\pi\)
0.806658 + 0.591018i \(0.201274\pi\)
\(720\) 267.286i 0.371230i
\(721\) −11.4439 + 32.4272i −0.0158723 + 0.0449753i
\(722\) −304.912 −0.422316
\(723\) 404.318 1508.93i 0.559222 2.08705i
\(724\) 249.337 + 930.538i 0.344388 + 1.28527i
\(725\) −276.754 1032.86i −0.381729 1.42463i
\(726\) −207.318 + 773.722i −0.285562 + 1.06573i
\(727\) 482.853 + 482.853i 0.664171 + 0.664171i 0.956361 0.292189i \(-0.0943837\pi\)
−0.292189 + 0.956361i \(0.594384\pi\)
\(728\) −55.2357 4.28751i −0.0758732 0.00588943i
\(729\) 893.503i 1.22566i
\(730\) 53.8057 31.0648i 0.0737065 0.0425545i
\(731\) 19.3875 5.19486i 0.0265218 0.00710651i
\(732\) 750.582 201.118i 1.02538 0.274751i
\(733\) 217.674 + 377.022i 0.296963 + 0.514355i 0.975440 0.220267i \(-0.0706929\pi\)
−0.678477 + 0.734622i \(0.737360\pi\)
\(734\) 1544.51i 2.10424i
\(735\) 238.125 173.790i 0.323980 0.236449i
\(736\) 383.414i 0.520943i
\(737\) −106.697 184.805i −0.144773 0.250753i
\(738\) −403.782 1006.46i −0.547130 1.36377i
\(739\) 331.794 574.684i 0.448977 0.777651i −0.549343 0.835597i \(-0.685122\pi\)
0.998320 + 0.0579460i \(0.0184551\pi\)
\(740\) −92.4533 160.134i −0.124937 0.216397i
\(741\) −180.728 180.728i −0.243897 0.243897i
\(742\) −1.28299 + 16.5287i −0.00172909 + 0.0222758i
\(743\) 31.4583i 0.0423396i −0.999776 0.0211698i \(-0.993261\pi\)
0.999776 0.0211698i \(-0.00673906\pi\)
\(744\) 29.7486 111.023i 0.0399847 0.149225i
\(745\) 256.140 68.6325i 0.343812 0.0921241i
\(746\) 1226.54 + 708.143i 1.64415 + 0.949253i
\(747\) −450.727 780.682i −0.603383 1.04509i
\(748\) 235.503i 0.314843i
\(749\) 367.982 1042.70i 0.491298 1.39213i
\(750\) 536.478 536.478i 0.715304 0.715304i
\(751\) −879.545 235.673i −1.17117 0.313813i −0.379749 0.925090i \(-0.623989\pi\)
−0.791417 + 0.611277i \(0.790656\pi\)
\(752\) 275.818 + 1029.37i 0.366779 + 1.36884i
\(753\) 10.2165 2.73751i 0.0135678 0.00363548i
\(754\) 281.348 162.436i 0.373141 0.215433i
\(755\) 53.4962 53.4962i 0.0708560 0.0708560i
\(756\) 54.1214 78.9284i 0.0715891 0.104403i
\(757\) −162.067 162.067i −0.214091 0.214091i 0.591912 0.806003i \(-0.298373\pi\)
−0.806003 + 0.591912i \(0.798373\pi\)
\(758\) 703.280 406.039i 0.927810 0.535671i
\(759\) 155.017 268.497i 0.204238 0.353751i
\(760\) −85.8936 + 23.0151i −0.113018 + 0.0302831i
\(761\) −491.357 + 283.685i −0.645673 + 0.372779i −0.786796 0.617213i \(-0.788262\pi\)
0.141124 + 0.989992i \(0.454929\pi\)
\(762\) 289.949 289.949i 0.380510 0.380510i
\(763\) −71.7081 49.1704i −0.0939818 0.0644435i
\(764\) 452.490 + 452.490i 0.592265 + 0.592265i
\(765\) 41.2542 153.963i 0.0539270 0.201258i
\(766\) 694.403 186.065i 0.906531 0.242904i
\(767\) 72.4663 + 270.448i 0.0944802 + 0.352605i
\(768\) −379.030 + 1414.56i −0.493528 + 1.84187i
\(769\) 1046.38i 1.36071i 0.732884 + 0.680354i \(0.238174\pi\)
−0.732884 + 0.680354i \(0.761826\pi\)
\(770\) −162.900 + 77.9139i −0.211558 + 0.101187i
\(771\) 190.443i 0.247008i
\(772\) −5.54168 1.48489i −0.00717834 0.00192343i
\(773\) 117.203 + 437.407i 0.151621 + 0.565856i 0.999371 + 0.0354609i \(0.0112899\pi\)
−0.847750 + 0.530396i \(0.822043\pi\)
\(774\) 40.0732 + 23.1363i 0.0517742 + 0.0298919i
\(775\) 178.077 102.813i 0.229777 0.132662i
\(776\) 28.3752 + 28.3752i 0.0365660 + 0.0365660i
\(777\) −110.646 + 1425.44i −0.142401 + 1.83455i
\(778\) 697.676 0.896756
\(779\) −716.687 + 537.325i −0.920009 + 0.689763i
\(780\) 40.0739 + 23.1367i 0.0513768 + 0.0296624i
\(781\) −269.561 155.631i −0.345149 0.199272i
\(782\) −77.2990 + 288.484i −0.0988478 + 0.368905i
\(783\) 220.281i 0.281330i
\(784\) −879.360 + 339.722i −1.12163 + 0.433319i
\(785\) 183.203 + 183.203i 0.233380 + 0.233380i
\(786\) 558.835 + 149.739i 0.710986 + 0.190508i
\(787\) 579.829 1004.29i 0.736759 1.27610i −0.217189 0.976130i \(-0.569689\pi\)
0.953947 0.299974i \(-0.0969780\pi\)
\(788\) −63.1174 36.4409i −0.0800982 0.0462447i
\(789\) −1700.39 + 981.723i −2.15512 + 1.24426i
\(790\) −82.0683 82.0683i −0.103884 0.103884i
\(791\) −272.675 318.569i −0.344722 0.402742i
\(792\) 150.694 150.694i 0.190270 0.190270i
\(793\) 42.9084 160.136i 0.0541090 0.201937i
\(794\) 20.1722 + 75.2835i 0.0254057 + 0.0948155i
\(795\) −2.71761 + 4.70705i −0.00341838 + 0.00592081i
\(796\) −196.312 52.6016i −0.246623 0.0660824i
\(797\) 133.090i 0.166988i 0.996508 + 0.0834941i \(0.0266080\pi\)
−0.996508 + 0.0834941i \(0.973392\pi\)
\(798\) −1651.82 582.945i −2.06995 0.730508i
\(799\) 635.510i 0.795382i
\(800\) −772.567 + 446.042i −0.965709 + 0.557552i
\(801\) −326.329 1217.88i −0.407402 1.52044i
\(802\) −980.180 + 1697.72i −1.22217 + 2.11686i
\(803\) 118.800 + 31.8323i 0.147945 + 0.0396418i
\(804\) 374.775i 0.466138i
\(805\) −94.0934 + 17.5437i −0.116886 + 0.0217934i
\(806\) 44.1752 + 44.1752i 0.0548080 + 0.0548080i
\(807\) 422.282 + 113.150i 0.523274 + 0.140211i
\(808\) −408.712 + 109.514i −0.505831 + 0.135537i
\(809\) −282.035 1052.57i −0.348622 1.30108i −0.888323 0.459219i \(-0.848129\pi\)
0.539701 0.841857i \(-0.318537\pi\)
\(810\) −218.865 + 126.362i −0.270204 + 0.156002i
\(811\) −473.165 −0.583434 −0.291717 0.956505i \(-0.594227\pi\)
−0.291717 + 0.956505i \(0.594227\pi\)
\(812\) 526.279 767.504i 0.648127 0.945202i
\(813\) −226.048 + 226.048i −0.278041 + 0.278041i
\(814\) 226.662 845.916i 0.278455 1.03921i
\(815\) −30.8569 + 53.4457i −0.0378612 + 0.0655775i
\(816\) −482.188 + 835.175i −0.590917 + 1.02350i
\(817\) 9.89237 36.9188i 0.0121082 0.0451883i
\(818\) 1286.07 1.57221
\(819\) −81.5954 170.597i −0.0996281 0.208299i
\(820\) 100.154 127.549i 0.122140 0.155548i
\(821\) 168.879 + 292.506i 0.205699 + 0.356280i 0.950355 0.311168i \(-0.100720\pi\)
−0.744657 + 0.667448i \(0.767387\pi\)
\(822\) 601.725 1042.22i 0.732025 1.26790i
\(823\) −8.95347 33.4148i −0.0108791 0.0406012i 0.960273 0.279062i \(-0.0900237\pi\)
−0.971152 + 0.238461i \(0.923357\pi\)
\(824\) 12.5752 7.26027i 0.0152611 0.00881100i
\(825\) 721.350 0.874364
\(826\) 1247.79 + 1457.80i 1.51064 + 1.76489i
\(827\) −640.935 + 640.935i −0.775012 + 0.775012i −0.978978 0.203966i \(-0.934617\pi\)
0.203966 + 0.978978i \(0.434617\pi\)
\(828\) −249.229 + 143.892i −0.301001 + 0.173783i
\(829\) 482.254 835.289i 0.581730 1.00759i −0.413544 0.910484i \(-0.635709\pi\)
0.995274 0.0971025i \(-0.0309575\pi\)
\(830\) 161.265 279.320i 0.194296 0.336530i
\(831\) 326.489 1218.47i 0.392887 1.46627i
\(832\) −45.9466 45.9466i −0.0552243 0.0552243i
\(833\) −558.966 + 59.9629i −0.671027 + 0.0719842i
\(834\) 1482.00 + 1482.00i 1.77697 + 1.77697i
\(835\) −44.7972 + 167.185i −0.0536493 + 0.200222i
\(836\) 388.377 + 224.229i 0.464566 + 0.268217i
\(837\) 40.9168 10.9636i 0.0488851 0.0130987i
\(838\) −269.443 + 155.563i −0.321531 + 0.185636i
\(839\) −895.054 + 895.054i −1.06681 + 1.06681i −0.0692080 + 0.997602i \(0.522047\pi\)
−0.997602 + 0.0692080i \(0.977953\pi\)
\(840\) −124.110 9.63365i −0.147750 0.0114686i
\(841\) 1301.03i 1.54700i
\(842\) 375.790 1402.47i 0.446307 1.66564i
\(843\) 883.605 + 510.149i 1.04817 + 0.605159i
\(844\) −874.501 + 234.322i −1.03614 + 0.277632i
\(845\) −192.986 + 111.420i −0.228386 + 0.131859i
\(846\) −1035.99 + 1035.99i −1.22457 + 1.22457i
\(847\) 461.634 + 162.916i 0.545023 + 0.192345i
\(848\) 12.2900 12.2900i 0.0144929 0.0144929i
\(849\) −428.448 114.802i −0.504651 0.135221i
\(850\) −671.210 + 179.850i −0.789659 + 0.211589i
\(851\) 232.102 402.012i 0.272740 0.472399i
\(852\) 273.327 + 473.417i 0.320807 + 0.555654i
\(853\) 1053.07 1.23455 0.617277 0.786746i \(-0.288236\pi\)
0.617277 + 0.786746i \(0.288236\pi\)
\(854\) −208.256 1116.96i −0.243859 1.30791i
\(855\) −214.627 214.627i −0.251025 0.251025i
\(856\) −404.357 + 233.455i −0.472379 + 0.272728i
\(857\) 185.003 + 106.812i 0.215873 + 0.124634i 0.604038 0.796956i \(-0.293558\pi\)
−0.388165 + 0.921590i \(0.626891\pi\)
\(858\) 56.7229 + 211.693i 0.0661106 + 0.246728i
\(859\) −538.522 932.748i −0.626918 1.08585i −0.988167 0.153384i \(-0.950983\pi\)
0.361249 0.932469i \(-0.382350\pi\)
\(860\) 6.91982i 0.00804631i
\(861\) −1196.42 + 375.432i −1.38957 + 0.436042i
\(862\) −366.979 −0.425730
\(863\) 406.780 234.854i 0.471355 0.272137i −0.245452 0.969409i \(-0.578936\pi\)
0.716807 + 0.697272i \(0.245603\pi\)
\(864\) −177.513 + 47.5644i −0.205455 + 0.0550514i
\(865\) −12.5410 + 21.7217i −0.0144983 + 0.0251118i
\(866\) 53.1155 + 91.9987i 0.0613343 + 0.106234i
\(867\) 486.193 486.193i 0.560777 0.560777i
\(868\) 168.756 + 59.5559i 0.194419 + 0.0686128i
\(869\) 229.755i 0.264390i
\(870\) 632.164 364.980i 0.726625 0.419517i
\(871\) 69.2457 + 39.9790i 0.0795014 + 0.0459001i
\(872\) 9.50244 + 35.4636i 0.0108973 + 0.0406692i
\(873\) −35.4512 + 132.306i −0.0406085 + 0.151553i
\(874\) 402.151 + 402.151i 0.460127 + 0.460127i
\(875\) −301.510 352.257i −0.344583 0.402579i
\(876\) −152.737 152.737i −0.174357 0.174357i
\(877\) −90.2595 156.334i −0.102918 0.178260i 0.809967 0.586475i \(-0.199485\pi\)
−0.912886 + 0.408215i \(0.866151\pi\)
\(878\) −68.4212 255.352i −0.0779285 0.290833i
\(879\) 396.514 686.783i 0.451097 0.781323i
\(880\) 182.861 + 48.9975i 0.207797 + 0.0556790i
\(881\) −547.119 −0.621020 −0.310510 0.950570i \(-0.600500\pi\)
−0.310510 + 0.950570i \(0.600500\pi\)
\(882\) −1008.96 813.457i −1.14394 0.922286i
\(883\) −1059.75 1059.75i −1.20017 1.20017i −0.974114 0.226057i \(-0.927416\pi\)
−0.226057 0.974114i \(-0.572584\pi\)
\(884\) −44.1209 76.4196i −0.0499105 0.0864476i
\(885\) 162.825 + 607.673i 0.183984 + 0.686636i
\(886\) −408.477 + 707.502i −0.461035 + 0.798535i
\(887\) −180.833 48.4541i −0.203871 0.0546269i 0.155439 0.987846i \(-0.450321\pi\)
−0.359309 + 0.933219i \(0.616988\pi\)
\(888\) 426.898 426.898i 0.480741 0.480741i
\(889\) −162.957 190.383i −0.183303 0.214155i
\(890\) 318.986 318.986i 0.358411 0.358411i
\(891\) −483.241 129.484i −0.542358 0.145324i
\(892\) −353.244 203.946i −0.396014 0.228639i
\(893\) 1048.04 + 605.089i 1.17362 + 0.677591i
\(894\) −1102.86 1910.21i −1.23363 2.13670i
\(895\) −187.291 187.291i −0.209263 0.209263i
\(896\) 599.564 + 211.593i 0.669156 + 0.236153i
\(897\) 116.168i 0.129507i
\(898\) −252.088 436.629i −0.280722 0.486224i
\(899\) 397.877 106.611i 0.442578 0.118588i
\(900\) −579.876 334.792i −0.644307 0.371991i
\(901\) 8.97618 5.18240i 0.00996247 0.00575183i
\(902\) 762.581 91.7445i 0.845433 0.101712i
\(903\) 30.2584 44.1277i 0.0335088 0.0488679i
\(904\) 177.068i 0.195872i
\(905\) 446.079 + 119.527i 0.492905 + 0.132074i
\(906\) −544.988 314.649i −0.601532 0.347294i
\(907\) 798.516 + 461.023i 0.880393 + 0.508295i 0.870788 0.491659i \(-0.163609\pi\)
0.00960473 + 0.999954i \(0.496943\pi\)
\(908\) 886.515 + 237.541i 0.976338 + 0.261609i
\(909\) −1021.27 1021.27i −1.12351 1.12351i
\(910\) 38.2633 55.8017i 0.0420476 0.0613205i
\(911\) 1019.61i 1.11922i 0.828756 + 0.559611i \(0.189049\pi\)
−0.828756 + 0.559611i \(0.810951\pi\)
\(912\) 918.213 + 1590.39i 1.00681 + 1.74385i
\(913\) 616.722 165.250i 0.675490 0.180997i
\(914\) 265.355 + 990.317i 0.290322 + 1.08350i
\(915\) 96.4114 359.812i 0.105368 0.393238i
\(916\) 692.672 692.672i 0.756192 0.756192i
\(917\) 117.669 333.424i 0.128320 0.363603i
\(918\) −143.151 −0.155938
\(919\) −381.662 + 1424.38i −0.415302 + 1.54993i 0.368929 + 0.929457i \(0.379724\pi\)
−0.784231 + 0.620469i \(0.786942\pi\)
\(920\) 35.0021 + 20.2085i 0.0380458 + 0.0219658i
\(921\) 1081.98 289.916i 1.17479 0.314784i
\(922\) 693.879 + 1201.83i 0.752580 + 1.30351i
\(923\) 116.629 0.126358
\(924\) 408.231 + 476.939i 0.441808 + 0.516168i
\(925\) 1080.05 1.16763
\(926\) 275.932 1029.79i 0.297983 1.11209i
\(927\) 42.9234 + 24.7819i 0.0463036 + 0.0267334i
\(928\) −1726.14 + 462.519i −1.86007 + 0.498404i
\(929\) −1496.71 401.044i −1.61110 0.431694i −0.662732 0.748857i \(-0.730603\pi\)
−0.948371 + 0.317163i \(0.897270\pi\)
\(930\) 99.2579 + 99.2579i 0.106729 + 0.106729i
\(931\) −433.321 + 978.905i −0.465436 + 1.05146i
\(932\) −721.014 + 721.014i −0.773620 + 0.773620i
\(933\) 1230.81 + 2131.82i 1.31919 + 2.28491i
\(934\) 216.591 375.146i 0.231896 0.401655i
\(935\) 97.7698 + 56.4474i 0.104567 + 0.0603715i
\(936\) −20.6674 + 77.1318i −0.0220806 + 0.0824058i
\(937\) −168.298 + 168.298i −0.179613 + 0.179613i −0.791187 0.611574i \(-0.790537\pi\)
0.611574 + 0.791187i \(0.290537\pi\)
\(938\) 546.347 + 42.4085i 0.582459 + 0.0452116i
\(939\) 1534.99 1.63471
\(940\) −211.633 56.7069i −0.225142 0.0603265i
\(941\) 87.6964 151.895i 0.0931949 0.161418i −0.815659 0.578533i \(-0.803625\pi\)
0.908854 + 0.417115i \(0.136959\pi\)
\(942\) 1077.55 1866.37i 1.14389 1.98128i
\(943\) 403.026 + 57.6451i 0.427388 + 0.0611295i
\(944\) 2011.75i 2.13109i
\(945\) −19.7951 41.3870i −0.0209472 0.0437957i
\(946\) −23.1745 + 23.1745i −0.0244974 + 0.0244974i
\(947\) −9.92472 17.1901i −0.0104802 0.0181522i 0.860738 0.509049i \(-0.170003\pi\)
−0.871218 + 0.490896i \(0.836669\pi\)
\(948\) −201.754 + 349.448i −0.212820 + 0.368616i
\(949\) −44.5138 + 11.9274i −0.0469060 + 0.0125684i
\(950\) −342.482 + 1278.16i −0.360507 + 1.34543i
\(951\) 1409.29 1.48191
\(952\) 195.780 + 134.246i 0.205651 + 0.141015i
\(953\) −906.154 −0.950844 −0.475422 0.879758i \(-0.657705\pi\)
−0.475422 + 0.879758i \(0.657705\pi\)
\(954\) 23.0808 + 6.18449i 0.0241937 + 0.00648269i
\(955\) 296.310 79.3960i 0.310272 0.0831371i
\(956\) −34.0214 126.970i −0.0355872 0.132813i
\(957\) 1395.78 + 373.999i 1.45850 + 0.390803i
\(958\) −1473.75 + 1473.75i −1.53836 + 1.53836i
\(959\) −606.579 415.932i −0.632512 0.433715i
\(960\) −103.238 103.238i −0.107540 0.107540i
\(961\) −440.894 763.652i −0.458787 0.794643i
\(962\) 84.9294 + 316.961i 0.0882842 + 0.329481i
\(963\) −1380.21 796.866i −1.43324 0.827483i
\(964\) −513.520 889.443i −0.532697 0.922658i
\(965\) −1.94474 + 1.94474i −0.00201527 + 0.00201527i
\(966\) 343.524 + 718.229i 0.355615 + 0.743509i
\(967\) −250.645 250.645i −0.259198 0.259198i 0.565530 0.824728i \(-0.308672\pi\)
−0.824728 + 0.565530i \(0.808672\pi\)
\(968\) −103.357 179.020i −0.106774 0.184938i
\(969\) 283.443 + 1057.82i 0.292511 + 1.09167i
\(970\) −47.3376 + 12.6841i −0.0488017 + 0.0130764i
\(971\) −143.866 + 536.916i −0.148163 + 0.552952i 0.851431 + 0.524466i \(0.175735\pi\)
−0.999594 + 0.0284856i \(0.990932\pi\)
\(972\) 708.292 + 708.292i 0.728696 + 0.728696i
\(973\) 973.095 832.909i 1.00010 0.856021i
\(974\) 1657.11 1.70135
\(975\) −234.075 + 135.143i −0.240077 + 0.138609i
\(976\) −595.593 + 1031.60i −0.610239 + 1.05696i
\(977\) 267.816 + 999.502i 0.274120 + 1.02303i 0.956428 + 0.291967i \(0.0943097\pi\)
−0.682308 + 0.731065i \(0.739024\pi\)
\(978\) 495.842 + 132.861i 0.506996 + 0.135849i
\(979\) 893.020 0.912176
\(980\) 29.9084 191.493i 0.0305188 0.195401i
\(981\) −88.6146 + 88.6146i −0.0903309 + 0.0903309i
\(982\) −390.518 + 225.466i −0.397676 + 0.229598i
\(983\) −383.319 221.310i −0.389948 0.225137i 0.292189 0.956360i \(-0.405616\pi\)
−0.682138 + 0.731224i \(0.738950\pi\)
\(984\) 486.896 + 208.079i 0.494813 + 0.211462i
\(985\) −30.2571 + 17.4689i −0.0307179 + 0.0177350i
\(986\) −1392.01 −1.41178
\(987\) 1101.62 + 1287.03i 1.11613 + 1.30398i
\(988\) −168.036 −0.170076
\(989\) −15.0446 + 8.68602i −0.0152120 + 0.00878263i
\(990\) 67.3623 + 251.399i 0.0680427 + 0.253939i
\(991\) 215.949 + 805.931i 0.217910 + 0.813250i 0.985122 + 0.171857i \(0.0549766\pi\)
−0.767212 + 0.641393i \(0.778357\pi\)
\(992\) −171.824 297.608i −0.173210 0.300008i
\(993\) −807.058 −0.812747
\(994\) 721.077 344.886i 0.725429 0.346968i
\(995\) −68.8915 + 68.8915i −0.0692377 + 0.0692377i
\(996\) −1083.12 290.221i −1.08747 0.291386i
\(997\) 792.403 212.324i 0.794787 0.212963i 0.161493 0.986874i \(-0.448369\pi\)
0.633294 + 0.773911i \(0.281702\pi\)
\(998\) −2313.94 + 620.017i −2.31857 + 0.621260i
\(999\) 214.917 + 57.5867i 0.215132 + 0.0576444i
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 287.3.q.a.73.10 216
7.5 odd 6 inner 287.3.q.a.278.45 yes 216
41.9 even 4 inner 287.3.q.a.255.45 yes 216
287.173 odd 12 inner 287.3.q.a.173.10 yes 216
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
287.3.q.a.73.10 216 1.1 even 1 trivial
287.3.q.a.173.10 yes 216 287.173 odd 12 inner
287.3.q.a.255.45 yes 216 41.9 even 4 inner
287.3.q.a.278.45 yes 216 7.5 odd 6 inner