Properties

Label 1155.2.k.a.769.16
Level $1155$
Weight $2$
Character 1155.769
Analytic conductor $9.223$
Analytic rank $0$
Dimension $48$
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] = [1155,2,Mod(769,1155)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1155.769");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.k (of order \(2\), degree \(1\), 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: \(9.22272143346\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 769.16
Character \(\chi\) \(=\) 1155.769
Dual form 1155.2.k.a.769.15

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.17317 q^{2} -1.00000 q^{3} -0.623669 q^{4} +(-2.20931 + 0.344884i) q^{5} +1.17317 q^{6} +(-1.71739 - 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.17317 q^{2} -1.00000 q^{3} -0.623669 q^{4} +(-2.20931 + 0.344884i) q^{5} +1.17317 q^{6} +(-1.71739 - 2.01260i) q^{7} +3.07801 q^{8} +1.00000 q^{9} +(2.59190 - 0.404608i) q^{10} +(1.48217 - 2.96702i) q^{11} +0.623669 q^{12} +3.43348i q^{13} +(2.01480 + 2.36113i) q^{14} +(2.20931 - 0.344884i) q^{15} -2.36370 q^{16} +3.10231i q^{17} -1.17317 q^{18} +5.32112 q^{19} +(1.37788 - 0.215094i) q^{20} +(1.71739 + 2.01260i) q^{21} +(-1.73883 + 3.48082i) q^{22} -5.88666i q^{23} -3.07801 q^{24} +(4.76211 - 1.52391i) q^{25} -4.02806i q^{26} -1.00000 q^{27} +(1.07109 + 1.25520i) q^{28} +5.81504i q^{29} +(-2.59190 + 0.404608i) q^{30} +0.722644i q^{31} -3.38301 q^{32} +(-1.48217 + 2.96702i) q^{33} -3.63954i q^{34} +(4.48837 + 3.85416i) q^{35} -0.623669 q^{36} -1.11476i q^{37} -6.24259 q^{38} -3.43348i q^{39} +(-6.80029 + 1.06156i) q^{40} -3.34512 q^{41} +(-2.01480 - 2.36113i) q^{42} +7.30051 q^{43} +(-0.924381 + 1.85044i) q^{44} +(-2.20931 + 0.344884i) q^{45} +6.90606i q^{46} -6.60481 q^{47} +2.36370 q^{48} +(-1.10113 + 6.91285i) q^{49} +(-5.58677 + 1.78781i) q^{50} -3.10231i q^{51} -2.14136i q^{52} -11.7433i q^{53} +1.17317 q^{54} +(-2.25129 + 7.06624i) q^{55} +(-5.28616 - 6.19481i) q^{56} -5.32112 q^{57} -6.82204i q^{58} -14.7567i q^{59} +(-1.37788 + 0.215094i) q^{60} -5.25854 q^{61} -0.847785i q^{62} +(-1.71739 - 2.01260i) q^{63} +8.69624 q^{64} +(-1.18415 - 7.58563i) q^{65} +(1.73883 - 3.48082i) q^{66} -1.98202i q^{67} -1.93481i q^{68} +5.88666i q^{69} +(-5.26562 - 4.52159i) q^{70} -14.9478 q^{71} +3.07801 q^{72} +7.27698i q^{73} +1.30781i q^{74} +(-4.76211 + 1.52391i) q^{75} -3.31862 q^{76} +(-8.51688 + 2.11252i) q^{77} +4.02806i q^{78} -11.5312i q^{79} +(5.22214 - 0.815202i) q^{80} +1.00000 q^{81} +3.92440 q^{82} +7.39391i q^{83} +(-1.07109 - 1.25520i) q^{84} +(-1.06994 - 6.85396i) q^{85} -8.56475 q^{86} -5.81504i q^{87} +(4.56212 - 9.13252i) q^{88} +3.65152i q^{89} +(2.59190 - 0.404608i) q^{90} +(6.91023 - 5.89663i) q^{91} +3.67133i q^{92} -0.722644i q^{93} +7.74857 q^{94} +(-11.7560 + 1.83517i) q^{95} +3.38301 q^{96} +3.77353 q^{97} +(1.29181 - 8.10996i) q^{98} +(1.48217 - 2.96702i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(232\) \(386\) \(661\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17317 −0.829557 −0.414779 0.909922i \(-0.636141\pi\)
−0.414779 + 0.909922i \(0.636141\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.623669 −0.311835
\(5\) −2.20931 + 0.344884i −0.988034 + 0.154237i
\(6\) 1.17317 0.478945
\(7\) −1.71739 2.01260i −0.649113 0.760692i
\(8\) 3.07801 1.08824
\(9\) 1.00000 0.333333
\(10\) 2.59190 0.404608i 0.819631 0.127948i
\(11\) 1.48217 2.96702i 0.446890 0.894589i
\(12\) 0.623669 0.180038
\(13\) 3.43348i 0.952276i 0.879371 + 0.476138i \(0.157964\pi\)
−0.879371 + 0.476138i \(0.842036\pi\)
\(14\) 2.01480 + 2.36113i 0.538477 + 0.631037i
\(15\) 2.20931 0.344884i 0.570442 0.0890488i
\(16\) −2.36370 −0.590924
\(17\) 3.10231i 0.752420i 0.926534 + 0.376210i \(0.122773\pi\)
−0.926534 + 0.376210i \(0.877227\pi\)
\(18\) −1.17317 −0.276519
\(19\) 5.32112 1.22075 0.610375 0.792113i \(-0.291019\pi\)
0.610375 + 0.792113i \(0.291019\pi\)
\(20\) 1.37788 0.215094i 0.308103 0.0480965i
\(21\) 1.71739 + 2.01260i 0.374766 + 0.439186i
\(22\) −1.73883 + 3.48082i −0.370721 + 0.742113i
\(23\) 5.88666i 1.22745i −0.789519 0.613726i \(-0.789670\pi\)
0.789519 0.613726i \(-0.210330\pi\)
\(24\) −3.07801 −0.628297
\(25\) 4.76211 1.52391i 0.952422 0.304783i
\(26\) 4.02806i 0.789968i
\(27\) −1.00000 −0.192450
\(28\) 1.07109 + 1.25520i 0.202416 + 0.237210i
\(29\) 5.81504i 1.07983i 0.841721 + 0.539913i \(0.181543\pi\)
−0.841721 + 0.539913i \(0.818457\pi\)
\(30\) −2.59190 + 0.404608i −0.473214 + 0.0738711i
\(31\) 0.722644i 0.129791i 0.997892 + 0.0648954i \(0.0206714\pi\)
−0.997892 + 0.0648954i \(0.979329\pi\)
\(32\) −3.38301 −0.598036
\(33\) −1.48217 + 2.96702i −0.258012 + 0.516491i
\(34\) 3.63954i 0.624176i
\(35\) 4.48837 + 3.85416i 0.758673 + 0.651472i
\(36\) −0.623669 −0.103945
\(37\) 1.11476i 0.183266i −0.995793 0.0916331i \(-0.970791\pi\)
0.995793 0.0916331i \(-0.0292087\pi\)
\(38\) −6.24259 −1.01268
\(39\) 3.43348i 0.549797i
\(40\) −6.80029 + 1.06156i −1.07522 + 0.167847i
\(41\) −3.34512 −0.522420 −0.261210 0.965282i \(-0.584122\pi\)
−0.261210 + 0.965282i \(0.584122\pi\)
\(42\) −2.01480 2.36113i −0.310890 0.364330i
\(43\) 7.30051 1.11332 0.556659 0.830741i \(-0.312083\pi\)
0.556659 + 0.830741i \(0.312083\pi\)
\(44\) −0.924381 + 1.85044i −0.139356 + 0.278964i
\(45\) −2.20931 + 0.344884i −0.329345 + 0.0514123i
\(46\) 6.90606i 1.01824i
\(47\) −6.60481 −0.963410 −0.481705 0.876333i \(-0.659982\pi\)
−0.481705 + 0.876333i \(0.659982\pi\)
\(48\) 2.36370 0.341170
\(49\) −1.10113 + 6.91285i −0.157304 + 0.987550i
\(50\) −5.58677 + 1.78781i −0.790089 + 0.252835i
\(51\) 3.10231i 0.434410i
\(52\) 2.14136i 0.296953i
\(53\) 11.7433i 1.61307i −0.591186 0.806535i \(-0.701340\pi\)
0.591186 0.806535i \(-0.298660\pi\)
\(54\) 1.17317 0.159648
\(55\) −2.25129 + 7.06624i −0.303563 + 0.952811i
\(56\) −5.28616 6.19481i −0.706392 0.827817i
\(57\) −5.32112 −0.704800
\(58\) 6.82204i 0.895777i
\(59\) 14.7567i 1.92116i −0.278003 0.960580i \(-0.589672\pi\)
0.278003 0.960580i \(-0.410328\pi\)
\(60\) −1.37788 + 0.215094i −0.177884 + 0.0277685i
\(61\) −5.25854 −0.673287 −0.336643 0.941632i \(-0.609292\pi\)
−0.336643 + 0.941632i \(0.609292\pi\)
\(62\) 0.847785i 0.107669i
\(63\) −1.71739 2.01260i −0.216371 0.253564i
\(64\) 8.69624 1.08703
\(65\) −1.18415 7.58563i −0.146876 0.940881i
\(66\) 1.73883 3.48082i 0.214036 0.428459i
\(67\) 1.98202i 0.242142i −0.992644 0.121071i \(-0.961367\pi\)
0.992644 0.121071i \(-0.0386329\pi\)
\(68\) 1.93481i 0.234631i
\(69\) 5.88666i 0.708670i
\(70\) −5.26562 4.52159i −0.629363 0.540433i
\(71\) −14.9478 −1.77398 −0.886990 0.461788i \(-0.847208\pi\)
−0.886990 + 0.461788i \(0.847208\pi\)
\(72\) 3.07801 0.362747
\(73\) 7.27698i 0.851706i 0.904792 + 0.425853i \(0.140026\pi\)
−0.904792 + 0.425853i \(0.859974\pi\)
\(74\) 1.30781i 0.152030i
\(75\) −4.76211 + 1.52391i −0.549881 + 0.175966i
\(76\) −3.31862 −0.380672
\(77\) −8.51688 + 2.11252i −0.970589 + 0.240744i
\(78\) 4.02806i 0.456088i
\(79\) 11.5312i 1.29736i −0.761061 0.648680i \(-0.775321\pi\)
0.761061 0.648680i \(-0.224679\pi\)
\(80\) 5.22214 0.815202i 0.583853 0.0911424i
\(81\) 1.00000 0.111111
\(82\) 3.92440 0.433378
\(83\) 7.39391i 0.811587i 0.913965 + 0.405794i \(0.133005\pi\)
−0.913965 + 0.405794i \(0.866995\pi\)
\(84\) −1.07109 1.25520i −0.116865 0.136953i
\(85\) −1.06994 6.85396i −0.116051 0.743417i
\(86\) −8.56475 −0.923561
\(87\) 5.81504i 0.623438i
\(88\) 4.56212 9.13252i 0.486324 0.973529i
\(89\) 3.65152i 0.387060i 0.981094 + 0.193530i \(0.0619937\pi\)
−0.981094 + 0.193530i \(0.938006\pi\)
\(90\) 2.59190 0.404608i 0.273210 0.0426495i
\(91\) 6.91023 5.89663i 0.724389 0.618135i
\(92\) 3.67133i 0.382762i
\(93\) 0.722644i 0.0749347i
\(94\) 7.74857 0.799204
\(95\) −11.7560 + 1.83517i −1.20614 + 0.188285i
\(96\) 3.38301 0.345277
\(97\) 3.77353 0.383144 0.191572 0.981479i \(-0.438641\pi\)
0.191572 + 0.981479i \(0.438641\pi\)
\(98\) 1.29181 8.10996i 0.130492 0.819229i
\(99\) 1.48217 2.96702i 0.148963 0.298196i
\(100\) −2.96998 + 0.950419i −0.296998 + 0.0950419i
\(101\) −15.2917 −1.52158 −0.760791 0.648997i \(-0.775189\pi\)
−0.760791 + 0.648997i \(0.775189\pi\)
\(102\) 3.63954i 0.360368i
\(103\) −1.35140 −0.133158 −0.0665789 0.997781i \(-0.521208\pi\)
−0.0665789 + 0.997781i \(0.521208\pi\)
\(104\) 10.5683i 1.03631i
\(105\) −4.48837 3.85416i −0.438020 0.376127i
\(106\) 13.7769i 1.33813i
\(107\) −1.77552 −0.171646 −0.0858228 0.996310i \(-0.527352\pi\)
−0.0858228 + 0.996310i \(0.527352\pi\)
\(108\) 0.623669 0.0600126
\(109\) 1.93909i 0.185731i 0.995679 + 0.0928656i \(0.0296027\pi\)
−0.995679 + 0.0928656i \(0.970397\pi\)
\(110\) 2.64114 8.28991i 0.251823 0.790411i
\(111\) 1.11476i 0.105809i
\(112\) 4.05940 + 4.75718i 0.383577 + 0.449511i
\(113\) 17.3740i 1.63441i 0.576350 + 0.817203i \(0.304477\pi\)
−0.576350 + 0.817203i \(0.695523\pi\)
\(114\) 6.24259 0.584672
\(115\) 2.03022 + 13.0055i 0.189319 + 1.21276i
\(116\) 3.62666i 0.336727i
\(117\) 3.43348i 0.317425i
\(118\) 17.3122i 1.59371i
\(119\) 6.24371 5.32788i 0.572360 0.488406i
\(120\) 6.80029 1.06156i 0.620779 0.0969066i
\(121\) −6.60637 8.79522i −0.600579 0.799565i
\(122\) 6.16916 0.558530
\(123\) 3.34512 0.301620
\(124\) 0.450691i 0.0404733i
\(125\) −9.99541 + 5.00918i −0.894016 + 0.448034i
\(126\) 2.01480 + 2.36113i 0.179492 + 0.210346i
\(127\) 6.23748 0.553487 0.276743 0.960944i \(-0.410745\pi\)
0.276743 + 0.960944i \(0.410745\pi\)
\(128\) −3.43617 −0.303717
\(129\) −7.30051 −0.642774
\(130\) 1.38922 + 8.89924i 0.121842 + 0.780515i
\(131\) −2.79723 −0.244395 −0.122198 0.992506i \(-0.538994\pi\)
−0.122198 + 0.992506i \(0.538994\pi\)
\(132\) 0.924381 1.85044i 0.0804571 0.161060i
\(133\) −9.13845 10.7093i −0.792405 0.928614i
\(134\) 2.32525i 0.200871i
\(135\) 2.20931 0.344884i 0.190147 0.0296829i
\(136\) 9.54894i 0.818815i
\(137\) 18.1264i 1.54865i −0.632791 0.774323i \(-0.718091\pi\)
0.632791 0.774323i \(-0.281909\pi\)
\(138\) 6.90606i 0.587882i
\(139\) −12.5540 −1.06481 −0.532407 0.846489i \(-0.678712\pi\)
−0.532407 + 0.846489i \(0.678712\pi\)
\(140\) −2.79926 2.40372i −0.236581 0.203152i
\(141\) 6.60481 0.556225
\(142\) 17.5364 1.47162
\(143\) 10.1872 + 5.08899i 0.851896 + 0.425562i
\(144\) −2.36370 −0.196975
\(145\) −2.00552 12.8472i −0.166549 1.06690i
\(146\) 8.53714i 0.706539i
\(147\) 1.10113 6.91285i 0.0908194 0.570162i
\(148\) 0.695245i 0.0571488i
\(149\) 3.14282i 0.257470i −0.991679 0.128735i \(-0.958908\pi\)
0.991679 0.128735i \(-0.0410916\pi\)
\(150\) 5.58677 1.78781i 0.456158 0.145974i
\(151\) 0.939283i 0.0764378i 0.999269 + 0.0382189i \(0.0121684\pi\)
−0.999269 + 0.0382189i \(0.987832\pi\)
\(152\) 16.3785 1.32847
\(153\) 3.10231i 0.250807i
\(154\) 9.99176 2.47835i 0.805159 0.199711i
\(155\) −0.249229 1.59655i −0.0200185 0.128238i
\(156\) 2.14136i 0.171446i
\(157\) −12.9739 −1.03543 −0.517715 0.855553i \(-0.673217\pi\)
−0.517715 + 0.855553i \(0.673217\pi\)
\(158\) 13.5281i 1.07623i
\(159\) 11.7433i 0.931307i
\(160\) 7.47411 1.16675i 0.590880 0.0922393i
\(161\) −11.8475 + 10.1097i −0.933713 + 0.796756i
\(162\) −1.17317 −0.0921730
\(163\) 9.34655i 0.732078i 0.930599 + 0.366039i \(0.119286\pi\)
−0.930599 + 0.366039i \(0.880714\pi\)
\(164\) 2.08625 0.162909
\(165\) 2.25129 7.06624i 0.175262 0.550106i
\(166\) 8.67432i 0.673258i
\(167\) 24.2687i 1.87797i −0.343964 0.938983i \(-0.611770\pi\)
0.343964 0.938983i \(-0.388230\pi\)
\(168\) 5.28616 + 6.19481i 0.407836 + 0.477940i
\(169\) 1.21121 0.0931702
\(170\) 1.25522 + 8.04087i 0.0962710 + 0.616707i
\(171\) 5.32112 0.406916
\(172\) −4.55311 −0.347171
\(173\) 0.0905291i 0.00688280i −0.999994 0.00344140i \(-0.998905\pi\)
0.999994 0.00344140i \(-0.00109543\pi\)
\(174\) 6.82204i 0.517177i
\(175\) −11.2454 6.96707i −0.850075 0.526661i
\(176\) −3.50339 + 7.01313i −0.264078 + 0.528634i
\(177\) 14.7567i 1.10918i
\(178\) 4.28385i 0.321088i
\(179\) −22.0633 −1.64909 −0.824543 0.565799i \(-0.808568\pi\)
−0.824543 + 0.565799i \(0.808568\pi\)
\(180\) 1.37788 0.215094i 0.102701 0.0160322i
\(181\) 5.43785i 0.404192i −0.979366 0.202096i \(-0.935225\pi\)
0.979366 0.202096i \(-0.0647753\pi\)
\(182\) −8.10688 + 6.91776i −0.600922 + 0.512778i
\(183\) 5.25854 0.388722
\(184\) 18.1192i 1.33577i
\(185\) 0.384465 + 2.46286i 0.0282664 + 0.181073i
\(186\) 0.847785i 0.0621626i
\(187\) 9.20460 + 4.59813i 0.673107 + 0.336249i
\(188\) 4.11922 0.300425
\(189\) 1.71739 + 2.01260i 0.124922 + 0.146395i
\(190\) 13.7918 2.15297i 1.00056 0.156193i
\(191\) −18.9758 −1.37304 −0.686521 0.727110i \(-0.740863\pi\)
−0.686521 + 0.727110i \(0.740863\pi\)
\(192\) −8.69624 −0.627597
\(193\) −16.3232 −1.17497 −0.587484 0.809235i \(-0.699882\pi\)
−0.587484 + 0.809235i \(0.699882\pi\)
\(194\) −4.42700 −0.317840
\(195\) 1.18415 + 7.58563i 0.0847990 + 0.543218i
\(196\) 0.686739 4.31133i 0.0490528 0.307952i
\(197\) 16.1111 1.14787 0.573933 0.818902i \(-0.305417\pi\)
0.573933 + 0.818902i \(0.305417\pi\)
\(198\) −1.73883 + 3.48082i −0.123574 + 0.247371i
\(199\) 24.4971i 1.73656i 0.496078 + 0.868278i \(0.334773\pi\)
−0.496078 + 0.868278i \(0.665227\pi\)
\(200\) 14.6578 4.69063i 1.03647 0.331677i
\(201\) 1.98202i 0.139801i
\(202\) 17.9398 1.26224
\(203\) 11.7034 9.98670i 0.821414 0.700929i
\(204\) 1.93481i 0.135464i
\(205\) 7.39042 1.15368i 0.516169 0.0805765i
\(206\) 1.58543 0.110462
\(207\) 5.88666i 0.409151i
\(208\) 8.11571i 0.562723i
\(209\) 7.88678 15.7879i 0.545540 1.09207i
\(210\) 5.26562 + 4.52159i 0.363363 + 0.312019i
\(211\) 13.0894i 0.901112i 0.892748 + 0.450556i \(0.148774\pi\)
−0.892748 + 0.450556i \(0.851226\pi\)
\(212\) 7.32396i 0.503012i
\(213\) 14.9478 1.02421
\(214\) 2.08298 0.142390
\(215\) −16.1291 + 2.51783i −1.10000 + 0.171715i
\(216\) −3.07801 −0.209432
\(217\) 1.45439 1.24106i 0.0987307 0.0842489i
\(218\) 2.27489i 0.154075i
\(219\) 7.27698i 0.491733i
\(220\) 1.40406 4.40700i 0.0946616 0.297120i
\(221\) −10.6517 −0.716512
\(222\) 1.30781i 0.0877744i
\(223\) −4.59749 −0.307871 −0.153935 0.988081i \(-0.549195\pi\)
−0.153935 + 0.988081i \(0.549195\pi\)
\(224\) 5.80995 + 6.80864i 0.388193 + 0.454921i
\(225\) 4.76211 1.52391i 0.317474 0.101594i
\(226\) 20.3826i 1.35583i
\(227\) 18.9902i 1.26042i 0.776424 + 0.630211i \(0.217032\pi\)
−0.776424 + 0.630211i \(0.782968\pi\)
\(228\) 3.31862 0.219781
\(229\) 19.7583i 1.30566i −0.757503 0.652831i \(-0.773581\pi\)
0.757503 0.652831i \(-0.226419\pi\)
\(230\) −2.38179 15.2576i −0.157051 1.00606i
\(231\) 8.51688 2.11252i 0.560370 0.138994i
\(232\) 17.8988i 1.17511i
\(233\) 19.0700 1.24932 0.624660 0.780897i \(-0.285238\pi\)
0.624660 + 0.780897i \(0.285238\pi\)
\(234\) 4.02806i 0.263323i
\(235\) 14.5921 2.27789i 0.951882 0.148593i
\(236\) 9.20331i 0.599085i
\(237\) 11.5312i 0.749031i
\(238\) −7.32494 + 6.25051i −0.474805 + 0.405161i
\(239\) 23.1560i 1.49784i 0.662661 + 0.748919i \(0.269427\pi\)
−0.662661 + 0.748919i \(0.730573\pi\)
\(240\) −5.22214 + 0.815202i −0.337088 + 0.0526211i
\(241\) 15.7072 1.01179 0.505896 0.862595i \(-0.331162\pi\)
0.505896 + 0.862595i \(0.331162\pi\)
\(242\) 7.75041 + 10.3183i 0.498215 + 0.663285i
\(243\) −1.00000 −0.0641500
\(244\) 3.27959 0.209954
\(245\) 0.0485958 15.6524i 0.00310467 0.999995i
\(246\) −3.92440 −0.250211
\(247\) 18.2700i 1.16249i
\(248\) 2.22431i 0.141244i
\(249\) 7.39391i 0.468570i
\(250\) 11.7263 5.87662i 0.741638 0.371670i
\(251\) 27.7124i 1.74919i −0.484854 0.874595i \(-0.661127\pi\)
0.484854 0.874595i \(-0.338873\pi\)
\(252\) 1.07109 + 1.25520i 0.0674720 + 0.0790700i
\(253\) −17.4658 8.72500i −1.09807 0.548536i
\(254\) −7.31763 −0.459149
\(255\) 1.06994 + 6.85396i 0.0670021 + 0.429212i
\(256\) −13.3613 −0.835079
\(257\) −8.14674 −0.508180 −0.254090 0.967181i \(-0.581776\pi\)
−0.254090 + 0.967181i \(0.581776\pi\)
\(258\) 8.56475 0.533218
\(259\) −2.24358 + 1.91449i −0.139409 + 0.118961i
\(260\) 0.738521 + 4.73092i 0.0458011 + 0.293399i
\(261\) 5.81504i 0.359942i
\(262\) 3.28163 0.202740
\(263\) 11.5514 0.712293 0.356146 0.934430i \(-0.384090\pi\)
0.356146 + 0.934430i \(0.384090\pi\)
\(264\) −4.56212 + 9.13252i −0.280779 + 0.562067i
\(265\) 4.05009 + 25.9447i 0.248795 + 1.59377i
\(266\) 10.7210 + 12.5638i 0.657345 + 0.770338i
\(267\) 3.65152i 0.223469i
\(268\) 1.23613i 0.0755084i
\(269\) 16.9804i 1.03531i −0.855589 0.517656i \(-0.826805\pi\)
0.855589 0.517656i \(-0.173195\pi\)
\(270\) −2.59190 + 0.404608i −0.157738 + 0.0246237i
\(271\) 18.3679 1.11577 0.557885 0.829918i \(-0.311613\pi\)
0.557885 + 0.829918i \(0.311613\pi\)
\(272\) 7.33292i 0.444623i
\(273\) −6.91023 + 5.89663i −0.418226 + 0.356880i
\(274\) 21.2654i 1.28469i
\(275\) 2.53676 16.3879i 0.152972 0.988230i
\(276\) 3.67133i 0.220988i
\(277\) −11.6755 −0.701514 −0.350757 0.936467i \(-0.614076\pi\)
−0.350757 + 0.936467i \(0.614076\pi\)
\(278\) 14.7280 0.883324
\(279\) 0.722644i 0.0432636i
\(280\) 13.8153 + 11.8632i 0.825620 + 0.708959i
\(281\) 7.54255i 0.449951i 0.974364 + 0.224975i \(0.0722302\pi\)
−0.974364 + 0.224975i \(0.927770\pi\)
\(282\) −7.74857 −0.461421
\(283\) 4.89738i 0.291119i −0.989350 0.145559i \(-0.953502\pi\)
0.989350 0.145559i \(-0.0464982\pi\)
\(284\) 9.32250 0.553189
\(285\) 11.7560 1.83517i 0.696366 0.108706i
\(286\) −11.9513 5.97025i −0.706696 0.353028i
\(287\) 5.74489 + 6.73240i 0.339110 + 0.397401i
\(288\) −3.38301 −0.199345
\(289\) 7.37569 0.433864
\(290\) 2.35281 + 15.0720i 0.138162 + 0.885058i
\(291\) −3.77353 −0.221208
\(292\) 4.53843i 0.265592i
\(293\) 7.63128i 0.445824i −0.974839 0.222912i \(-0.928444\pi\)
0.974839 0.222912i \(-0.0715563\pi\)
\(294\) −1.29181 + 8.10996i −0.0753399 + 0.472982i
\(295\) 5.08936 + 32.6022i 0.296314 + 1.89817i
\(296\) 3.43126i 0.199438i
\(297\) −1.48217 + 2.96702i −0.0860040 + 0.172164i
\(298\) 3.68706i 0.213586i
\(299\) 20.2117 1.16887
\(300\) 2.96998 0.950419i 0.171472 0.0548724i
\(301\) −12.5378 14.6930i −0.722669 0.846891i
\(302\) 1.10194i 0.0634095i
\(303\) 15.2917 0.878486
\(304\) −12.5775 −0.721370
\(305\) 11.6177 1.81359i 0.665230 0.103846i
\(306\) 3.63954i 0.208059i
\(307\) 29.9896i 1.71160i −0.517310 0.855798i \(-0.673067\pi\)
0.517310 0.855798i \(-0.326933\pi\)
\(308\) 5.31172 1.31752i 0.302663 0.0750725i
\(309\) 1.35140 0.0768787
\(310\) 0.292388 + 1.87302i 0.0166065 + 0.106380i
\(311\) 10.3684i 0.587939i −0.955815 0.293969i \(-0.905024\pi\)
0.955815 0.293969i \(-0.0949764\pi\)
\(312\) 10.5683i 0.598312i
\(313\) −17.3488 −0.980614 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(314\) 15.2206 0.858948
\(315\) 4.48837 + 3.85416i 0.252891 + 0.217157i
\(316\) 7.19165i 0.404562i
\(317\) 20.0871i 1.12821i −0.825704 0.564103i \(-0.809222\pi\)
0.825704 0.564103i \(-0.190778\pi\)
\(318\) 13.7769i 0.772572i
\(319\) 17.2533 + 8.61885i 0.966000 + 0.482563i
\(320\) −19.2127 + 2.99920i −1.07402 + 0.167660i
\(321\) 1.77552 0.0990996
\(322\) 13.8991 11.8604i 0.774568 0.660955i
\(323\) 16.5078i 0.918516i
\(324\) −0.623669 −0.0346483
\(325\) 5.23233 + 16.3506i 0.290237 + 0.906969i
\(326\) 10.9651i 0.607301i
\(327\) 1.93909i 0.107232i
\(328\) −10.2963 −0.568520
\(329\) 11.3430 + 13.2928i 0.625362 + 0.732858i
\(330\) −2.64114 + 8.28991i −0.145390 + 0.456344i
\(331\) −17.1491 −0.942598 −0.471299 0.881973i \(-0.656215\pi\)
−0.471299 + 0.881973i \(0.656215\pi\)
\(332\) 4.61136i 0.253081i
\(333\) 1.11476i 0.0610887i
\(334\) 28.4713i 1.55788i
\(335\) 0.683568 + 4.37890i 0.0373473 + 0.239245i
\(336\) −4.05940 4.75718i −0.221458 0.259525i
\(337\) −26.9388 −1.46745 −0.733724 0.679448i \(-0.762219\pi\)
−0.733724 + 0.679448i \(0.762219\pi\)
\(338\) −1.42096 −0.0772900
\(339\) 17.3740i 0.943625i
\(340\) 0.667287 + 4.27461i 0.0361887 + 0.231823i
\(341\) 2.14410 + 1.07108i 0.116109 + 0.0580021i
\(342\) −6.24259 −0.337560
\(343\) 15.8039 9.65595i 0.853329 0.521372i
\(344\) 22.4711 1.21156
\(345\) −2.03022 13.0055i −0.109303 0.700190i
\(346\) 0.106206i 0.00570968i
\(347\) −27.4275 −1.47238 −0.736192 0.676773i \(-0.763378\pi\)
−0.736192 + 0.676773i \(0.763378\pi\)
\(348\) 3.62666i 0.194409i
\(349\) 3.35671 0.179681 0.0898403 0.995956i \(-0.471364\pi\)
0.0898403 + 0.995956i \(0.471364\pi\)
\(350\) 13.1928 + 8.17356i 0.705186 + 0.436895i
\(351\) 3.43348i 0.183266i
\(352\) −5.01417 + 10.0374i −0.267256 + 0.534997i
\(353\) 17.3099 0.921312 0.460656 0.887579i \(-0.347614\pi\)
0.460656 + 0.887579i \(0.347614\pi\)
\(354\) 17.3122i 0.920130i
\(355\) 33.0244 5.15527i 1.75275 0.273613i
\(356\) 2.27734i 0.120699i
\(357\) −6.24371 + 5.32788i −0.330452 + 0.281981i
\(358\) 25.8840 1.36801
\(359\) 1.11316i 0.0587501i −0.999568 0.0293751i \(-0.990648\pi\)
0.999568 0.0293751i \(-0.00935171\pi\)
\(360\) −6.80029 + 1.06156i −0.358407 + 0.0559491i
\(361\) 9.31434 0.490228
\(362\) 6.37952i 0.335300i
\(363\) 6.60637 + 8.79522i 0.346745 + 0.461629i
\(364\) −4.30970 + 3.67755i −0.225890 + 0.192756i
\(365\) −2.50972 16.0771i −0.131365 0.841514i
\(366\) −6.16916 −0.322467
\(367\) 3.68482 0.192346 0.0961731 0.995365i \(-0.469340\pi\)
0.0961731 + 0.995365i \(0.469340\pi\)
\(368\) 13.9143i 0.725332i
\(369\) −3.34512 −0.174140
\(370\) −0.451043 2.88936i −0.0234486 0.150211i
\(371\) −23.6346 + 20.1679i −1.22705 + 1.04707i
\(372\) 0.450691i 0.0233672i
\(373\) 4.82270 0.249710 0.124855 0.992175i \(-0.460153\pi\)
0.124855 + 0.992175i \(0.460153\pi\)
\(374\) −10.7986 5.39440i −0.558381 0.278938i
\(375\) 9.99541 5.00918i 0.516161 0.258673i
\(376\) −20.3297 −1.04842
\(377\) −19.9658 −1.02829
\(378\) −2.01480 2.36113i −0.103630 0.121443i
\(379\) −15.4604 −0.794148 −0.397074 0.917787i \(-0.629974\pi\)
−0.397074 + 0.917787i \(0.629974\pi\)
\(380\) 7.33187 1.14454i 0.376117 0.0587137i
\(381\) −6.23748 −0.319556
\(382\) 22.2619 1.13902
\(383\) 4.92470 0.251640 0.125820 0.992053i \(-0.459844\pi\)
0.125820 + 0.992053i \(0.459844\pi\)
\(384\) 3.43617 0.175351
\(385\) 18.0879 7.60456i 0.921843 0.387564i
\(386\) 19.1499 0.974704
\(387\) 7.30051 0.371106
\(388\) −2.35344 −0.119478
\(389\) −8.29383 −0.420514 −0.210257 0.977646i \(-0.567430\pi\)
−0.210257 + 0.977646i \(0.567430\pi\)
\(390\) −1.38922 8.89924i −0.0703456 0.450630i
\(391\) 18.2622 0.923560
\(392\) −3.38928 + 21.2778i −0.171185 + 1.07469i
\(393\) 2.79723 0.141102
\(394\) −18.9011 −0.952221
\(395\) 3.97693 + 25.4760i 0.200101 + 1.28184i
\(396\) −0.924381 + 1.85044i −0.0464519 + 0.0929880i
\(397\) −32.3860 −1.62541 −0.812704 0.582677i \(-0.802005\pi\)
−0.812704 + 0.582677i \(0.802005\pi\)
\(398\) 28.7393i 1.44057i
\(399\) 9.13845 + 10.7093i 0.457495 + 0.536135i
\(400\) −11.2562 + 3.60207i −0.562809 + 0.180104i
\(401\) −18.6858 −0.933124 −0.466562 0.884488i \(-0.654508\pi\)
−0.466562 + 0.884488i \(0.654508\pi\)
\(402\) 2.32525i 0.115973i
\(403\) −2.48118 −0.123597
\(404\) 9.53698 0.474482
\(405\) −2.20931 + 0.344884i −0.109782 + 0.0171374i
\(406\) −13.7300 + 11.7161i −0.681410 + 0.581461i
\(407\) −3.30753 1.65227i −0.163948 0.0818998i
\(408\) 9.54894i 0.472743i
\(409\) 7.69234 0.380362 0.190181 0.981749i \(-0.439093\pi\)
0.190181 + 0.981749i \(0.439093\pi\)
\(410\) −8.67022 + 1.35346i −0.428192 + 0.0668429i
\(411\) 18.1264i 0.894111i
\(412\) 0.842830 0.0415232
\(413\) −29.6994 + 25.3431i −1.46141 + 1.24705i
\(414\) 6.90606i 0.339414i
\(415\) −2.55004 16.3354i −0.125177 0.801876i
\(416\) 11.6155i 0.569496i
\(417\) 12.5540 0.614771
\(418\) −9.25255 + 18.5219i −0.452557 + 0.905934i
\(419\) 7.32643i 0.357919i 0.983856 + 0.178960i \(0.0572732\pi\)
−0.983856 + 0.178960i \(0.942727\pi\)
\(420\) 2.79926 + 2.40372i 0.136590 + 0.117290i
\(421\) −1.91887 −0.0935201 −0.0467601 0.998906i \(-0.514890\pi\)
−0.0467601 + 0.998906i \(0.514890\pi\)
\(422\) 15.3561i 0.747524i
\(423\) −6.60481 −0.321137
\(424\) 36.1461i 1.75541i
\(425\) 4.72765 + 14.7735i 0.229325 + 0.716621i
\(426\) −17.5364 −0.849639
\(427\) 9.03097 + 10.5833i 0.437039 + 0.512164i
\(428\) 1.10733 0.0535251
\(429\) −10.1872 5.08899i −0.491842 0.245699i
\(430\) 18.9222 2.95385i 0.912509 0.142447i
\(431\) 7.47238i 0.359932i 0.983673 + 0.179966i \(0.0575988\pi\)
−0.983673 + 0.179966i \(0.942401\pi\)
\(432\) 2.36370 0.113723
\(433\) 13.5598 0.651644 0.325822 0.945431i \(-0.394359\pi\)
0.325822 + 0.945431i \(0.394359\pi\)
\(434\) −1.70625 + 1.45598i −0.0819028 + 0.0698893i
\(435\) 2.00552 + 12.8472i 0.0961571 + 0.615977i
\(436\) 1.20935i 0.0579175i
\(437\) 31.3236i 1.49841i
\(438\) 8.53714i 0.407920i
\(439\) −30.6807 −1.46431 −0.732156 0.681137i \(-0.761486\pi\)
−0.732156 + 0.681137i \(0.761486\pi\)
\(440\) −6.92949 + 21.7500i −0.330350 + 1.03689i
\(441\) −1.10113 + 6.91285i −0.0524346 + 0.329183i
\(442\) 12.4963 0.594387
\(443\) 29.3213i 1.39310i 0.717509 + 0.696549i \(0.245282\pi\)
−0.717509 + 0.696549i \(0.754718\pi\)
\(444\) 0.695245i 0.0329949i
\(445\) −1.25935 8.06733i −0.0596990 0.382428i
\(446\) 5.39365 0.255397
\(447\) 3.14282i 0.148650i
\(448\) −14.9349 17.5021i −0.705606 0.826895i
\(449\) 14.5550 0.686892 0.343446 0.939173i \(-0.388406\pi\)
0.343446 + 0.939173i \(0.388406\pi\)
\(450\) −5.58677 + 1.78781i −0.263363 + 0.0842783i
\(451\) −4.95802 + 9.92503i −0.233464 + 0.467352i
\(452\) 10.8356i 0.509665i
\(453\) 0.939283i 0.0441314i
\(454\) 22.2787i 1.04559i
\(455\) −13.2332 + 15.4107i −0.620381 + 0.722466i
\(456\) −16.3785 −0.766993
\(457\) −20.6452 −0.965741 −0.482870 0.875692i \(-0.660406\pi\)
−0.482870 + 0.875692i \(0.660406\pi\)
\(458\) 23.1798i 1.08312i
\(459\) 3.10231i 0.144803i
\(460\) −1.26618 8.11111i −0.0590361 0.378182i
\(461\) −7.59495 −0.353732 −0.176866 0.984235i \(-0.556596\pi\)
−0.176866 + 0.984235i \(0.556596\pi\)
\(462\) −9.99176 + 2.47835i −0.464859 + 0.115303i
\(463\) 28.5815i 1.32829i −0.747602 0.664147i \(-0.768795\pi\)
0.747602 0.664147i \(-0.231205\pi\)
\(464\) 13.7450i 0.638095i
\(465\) 0.249229 + 1.59655i 0.0115577 + 0.0740380i
\(466\) −22.3724 −1.03638
\(467\) 22.0580 1.02072 0.510360 0.859961i \(-0.329512\pi\)
0.510360 + 0.859961i \(0.329512\pi\)
\(468\) 2.14136i 0.0989843i
\(469\) −3.98901 + 3.40391i −0.184196 + 0.157178i
\(470\) −17.1190 + 2.67236i −0.789640 + 0.123267i
\(471\) 12.9739 0.597806
\(472\) 45.4214i 2.09069i
\(473\) 10.8206 21.6607i 0.497530 0.995962i
\(474\) 13.5281i 0.621364i
\(475\) 25.3398 8.10893i 1.16267 0.372063i
\(476\) −3.89401 + 3.32284i −0.178482 + 0.152302i
\(477\) 11.7433i 0.537690i
\(478\) 27.1660i 1.24254i
\(479\) −30.3084 −1.38483 −0.692413 0.721501i \(-0.743452\pi\)
−0.692413 + 0.721501i \(0.743452\pi\)
\(480\) −7.47411 + 1.16675i −0.341145 + 0.0532544i
\(481\) 3.82752 0.174520
\(482\) −18.4273 −0.839339
\(483\) 11.8475 10.1097i 0.539080 0.460007i
\(484\) 4.12019 + 5.48531i 0.187281 + 0.249332i
\(485\) −8.33691 + 1.30143i −0.378559 + 0.0590950i
\(486\) 1.17317 0.0532161
\(487\) 10.1505i 0.459965i −0.973195 0.229982i \(-0.926133\pi\)
0.973195 0.229982i \(-0.0738668\pi\)
\(488\) −16.1858 −0.732699
\(489\) 9.34655i 0.422665i
\(490\) −0.0570112 + 18.3629i −0.00257550 + 0.829553i
\(491\) 34.2469i 1.54554i −0.634685 0.772771i \(-0.718870\pi\)
0.634685 0.772771i \(-0.281130\pi\)
\(492\) −2.08625 −0.0940554
\(493\) −18.0400 −0.812482
\(494\) 21.4338i 0.964352i
\(495\) −2.25129 + 7.06624i −0.101188 + 0.317604i
\(496\) 1.70811i 0.0766965i
\(497\) 25.6713 + 30.0840i 1.15151 + 1.34945i
\(498\) 8.67432i 0.388706i
\(499\) 3.09687 0.138635 0.0693174 0.997595i \(-0.477918\pi\)
0.0693174 + 0.997595i \(0.477918\pi\)
\(500\) 6.23383 3.12407i 0.278785 0.139713i
\(501\) 24.2687i 1.08424i
\(502\) 32.5114i 1.45105i
\(503\) 19.8339i 0.884350i −0.896929 0.442175i \(-0.854207\pi\)
0.896929 0.442175i \(-0.145793\pi\)
\(504\) −5.28616 6.19481i −0.235464 0.275939i
\(505\) 33.7842 5.27387i 1.50337 0.234684i
\(506\) 20.4904 + 10.2359i 0.910908 + 0.455042i
\(507\) −1.21121 −0.0537918
\(508\) −3.89013 −0.172596
\(509\) 1.89918i 0.0841798i −0.999114 0.0420899i \(-0.986598\pi\)
0.999114 0.0420899i \(-0.0134016\pi\)
\(510\) −1.25522 8.04087i −0.0555821 0.356056i
\(511\) 14.6457 12.4974i 0.647886 0.552854i
\(512\) 22.5474 0.996463
\(513\) −5.32112 −0.234933
\(514\) 9.55753 0.421564
\(515\) 2.98567 0.466078i 0.131564 0.0205379i
\(516\) 4.55311 0.200439
\(517\) −9.78941 + 19.5966i −0.430538 + 0.861856i
\(518\) 2.63210 2.24602i 0.115648 0.0986846i
\(519\) 0.0905291i 0.00397379i
\(520\) −3.64484 23.3487i −0.159837 1.02391i
\(521\) 8.01305i 0.351058i 0.984474 + 0.175529i \(0.0561636\pi\)
−0.984474 + 0.175529i \(0.943836\pi\)
\(522\) 6.82204i 0.298592i
\(523\) 5.57803i 0.243910i −0.992536 0.121955i \(-0.961084\pi\)
0.992536 0.121955i \(-0.0389164\pi\)
\(524\) 1.74455 0.0762109
\(525\) 11.2454 + 6.96707i 0.490791 + 0.304068i
\(526\) −13.5518 −0.590888
\(527\) −2.24186 −0.0976572
\(528\) 3.50339 7.01313i 0.152465 0.305207i
\(529\) −11.6527 −0.506640
\(530\) −4.75145 30.4375i −0.206390 1.32212i
\(531\) 14.7567i 0.640387i
\(532\) 5.69938 + 6.67906i 0.247099 + 0.289574i
\(533\) 11.4854i 0.497488i
\(534\) 4.28385i 0.185380i
\(535\) 3.92267 0.612348i 0.169592 0.0264741i
\(536\) 6.10068i 0.263509i
\(537\) 22.0633 0.952100
\(538\) 19.9209i 0.858850i
\(539\) 18.8785 + 13.5130i 0.813154 + 0.582048i
\(540\) −1.37788 + 0.215094i −0.0592945 + 0.00925617i
\(541\) 12.9502i 0.556774i −0.960469 0.278387i \(-0.910200\pi\)
0.960469 0.278387i \(-0.0897997\pi\)
\(542\) −21.5487 −0.925595
\(543\) 5.43785i 0.233360i
\(544\) 10.4951i 0.449975i
\(545\) −0.668762 4.28406i −0.0286466 0.183509i
\(546\) 8.10688 6.91776i 0.346942 0.296053i
\(547\) −9.04582 −0.386771 −0.193386 0.981123i \(-0.561947\pi\)
−0.193386 + 0.981123i \(0.561947\pi\)
\(548\) 11.3049i 0.482922i
\(549\) −5.25854 −0.224429
\(550\) −2.97605 + 19.2259i −0.126899 + 0.819794i
\(551\) 30.9425i 1.31820i
\(552\) 18.1192i 0.771205i
\(553\) −23.2077 + 19.8036i −0.986891 + 0.842134i
\(554\) 13.6974 0.581946
\(555\) −0.384465 2.46286i −0.0163196 0.104543i
\(556\) 7.82953 0.332046
\(557\) −35.0800 −1.48639 −0.743193 0.669077i \(-0.766690\pi\)
−0.743193 + 0.669077i \(0.766690\pi\)
\(558\) 0.847785i 0.0358896i
\(559\) 25.0662i 1.06019i
\(560\) −10.6091 9.11007i −0.448318 0.384971i
\(561\) −9.20460 4.59813i −0.388618 0.194133i
\(562\) 8.84870i 0.373260i
\(563\) 0.289494i 0.0122007i 0.999981 + 0.00610035i \(0.00194181\pi\)
−0.999981 + 0.00610035i \(0.998058\pi\)
\(564\) −4.11922 −0.173450
\(565\) −5.99201 38.3845i −0.252086 1.61485i
\(566\) 5.74546i 0.241500i
\(567\) −1.71739 2.01260i −0.0721237 0.0845213i
\(568\) −46.0096 −1.93052
\(569\) 3.15902i 0.132433i 0.997805 + 0.0662165i \(0.0210928\pi\)
−0.997805 + 0.0662165i \(0.978907\pi\)
\(570\) −13.7918 + 2.15297i −0.577676 + 0.0901780i
\(571\) 13.2386i 0.554020i −0.960867 0.277010i \(-0.910656\pi\)
0.960867 0.277010i \(-0.0893435\pi\)
\(572\) −6.35344 3.17384i −0.265651 0.132705i
\(573\) 18.9758 0.792726
\(574\) −6.73974 7.89825i −0.281311 0.329667i
\(575\) −8.97076 28.0329i −0.374106 1.16905i
\(576\) 8.69624 0.362343
\(577\) −30.8410 −1.28393 −0.641964 0.766734i \(-0.721880\pi\)
−0.641964 + 0.766734i \(0.721880\pi\)
\(578\) −8.65294 −0.359915
\(579\) 16.3232 0.678369
\(580\) 1.25078 + 8.01242i 0.0519358 + 0.332698i
\(581\) 14.8810 12.6982i 0.617368 0.526812i
\(582\) 4.42700 0.183505
\(583\) −34.8427 17.4056i −1.44304 0.720865i
\(584\) 22.3986i 0.926862i
\(585\) −1.18415 7.58563i −0.0489587 0.313627i
\(586\) 8.95280i 0.369837i
\(587\) −35.0865 −1.44818 −0.724088 0.689708i \(-0.757739\pi\)
−0.724088 + 0.689708i \(0.757739\pi\)
\(588\) −0.686739 + 4.31133i −0.0283206 + 0.177796i
\(589\) 3.84528i 0.158442i
\(590\) −5.97069 38.2479i −0.245809 1.57464i
\(591\) −16.1111 −0.662721
\(592\) 2.63497i 0.108296i
\(593\) 41.1114i 1.68824i −0.536151 0.844122i \(-0.680122\pi\)
0.536151 0.844122i \(-0.319878\pi\)
\(594\) 1.73883 3.48082i 0.0713452 0.142820i
\(595\) −11.9568 + 13.9243i −0.490181 + 0.570841i
\(596\) 1.96008i 0.0802880i
\(597\) 24.4971i 1.00260i
\(598\) −23.7118 −0.969648
\(599\) 11.6236 0.474927 0.237464 0.971396i \(-0.423684\pi\)
0.237464 + 0.971396i \(0.423684\pi\)
\(600\) −14.6578 + 4.69063i −0.598404 + 0.191494i
\(601\) −24.3506 −0.993282 −0.496641 0.867956i \(-0.665433\pi\)
−0.496641 + 0.867956i \(0.665433\pi\)
\(602\) 14.7090 + 17.2374i 0.599495 + 0.702545i
\(603\) 1.98202i 0.0807141i
\(604\) 0.585802i 0.0238360i
\(605\) 17.6289 + 17.1529i 0.716715 + 0.697366i
\(606\) −17.9398 −0.728754
\(607\) 14.1378i 0.573834i 0.957955 + 0.286917i \(0.0926305\pi\)
−0.957955 + 0.286917i \(0.907370\pi\)
\(608\) −18.0014 −0.730052
\(609\) −11.7034 + 9.98670i −0.474244 + 0.404682i
\(610\) −13.6296 + 2.12765i −0.551846 + 0.0861460i
\(611\) 22.6775i 0.917432i
\(612\) 1.93481i 0.0782102i
\(613\) 3.49651 0.141223 0.0706114 0.997504i \(-0.477505\pi\)
0.0706114 + 0.997504i \(0.477505\pi\)
\(614\) 35.1829i 1.41987i
\(615\) −7.39042 + 1.15368i −0.298010 + 0.0465209i
\(616\) −26.2151 + 6.50238i −1.05624 + 0.261988i
\(617\) 3.42766i 0.137992i 0.997617 + 0.0689961i \(0.0219796\pi\)
−0.997617 + 0.0689961i \(0.978020\pi\)
\(618\) −1.58543 −0.0637753
\(619\) 0.639680i 0.0257109i 0.999917 + 0.0128555i \(0.00409213\pi\)
−0.999917 + 0.0128555i \(0.995908\pi\)
\(620\) 0.155436 + 0.995717i 0.00624247 + 0.0399889i
\(621\) 5.88666i 0.236223i
\(622\) 12.1639i 0.487729i
\(623\) 7.34905 6.27109i 0.294433 0.251246i
\(624\) 8.11571i 0.324888i
\(625\) 20.3554 14.5141i 0.814215 0.580564i
\(626\) 20.3531 0.813475
\(627\) −7.88678 + 15.7879i −0.314968 + 0.630506i
\(628\) 8.09142 0.322883
\(629\) 3.45834 0.137893
\(630\) −5.26562 4.52159i −0.209788 0.180144i
\(631\) 44.9853 1.79084 0.895418 0.445226i \(-0.146877\pi\)
0.895418 + 0.445226i \(0.146877\pi\)
\(632\) 35.4931i 1.41184i
\(633\) 13.0894i 0.520257i
\(634\) 23.5657i 0.935912i
\(635\) −13.7805 + 2.15121i −0.546864 + 0.0853682i
\(636\) 7.32396i 0.290414i
\(637\) −23.7351 3.78070i −0.940421 0.149797i
\(638\) −20.2411 10.1114i −0.801352 0.400314i
\(639\) −14.9478 −0.591327
\(640\) 7.59156 1.18508i 0.300083 0.0468444i
\(641\) 26.6120 1.05111 0.525556 0.850759i \(-0.323857\pi\)
0.525556 + 0.850759i \(0.323857\pi\)
\(642\) −2.08298 −0.0822088
\(643\) −32.0498 −1.26392 −0.631960 0.775001i \(-0.717749\pi\)
−0.631960 + 0.775001i \(0.717749\pi\)
\(644\) 7.38892 6.30511i 0.291164 0.248456i
\(645\) 16.1291 2.51783i 0.635083 0.0991396i
\(646\) 19.3664i 0.761962i
\(647\) −2.30057 −0.0904447 −0.0452223 0.998977i \(-0.514400\pi\)
−0.0452223 + 0.998977i \(0.514400\pi\)
\(648\) 3.07801 0.120916
\(649\) −43.7834 21.8719i −1.71865 0.858547i
\(650\) −6.13842 19.1821i −0.240768 0.752382i
\(651\) −1.45439 + 1.24106i −0.0570022 + 0.0486411i
\(652\) 5.82916i 0.228287i
\(653\) 30.8146i 1.20587i 0.797791 + 0.602934i \(0.206002\pi\)
−0.797791 + 0.602934i \(0.793998\pi\)
\(654\) 2.27489i 0.0889551i
\(655\) 6.17995 0.964721i 0.241471 0.0376948i
\(656\) 7.90686 0.308711
\(657\) 7.27698i 0.283902i
\(658\) −13.3073 15.5948i −0.518774 0.607948i
\(659\) 42.0492i 1.63801i 0.573789 + 0.819003i \(0.305473\pi\)
−0.573789 + 0.819003i \(0.694527\pi\)
\(660\) −1.40406 + 4.40700i −0.0546529 + 0.171542i
\(661\) 10.9191i 0.424704i −0.977193 0.212352i \(-0.931888\pi\)
0.977193 0.212352i \(-0.0681124\pi\)
\(662\) 20.1188 0.781939
\(663\) 10.6517 0.413678
\(664\) 22.7586i 0.883203i
\(665\) 23.8832 + 20.5085i 0.926149 + 0.795284i
\(666\) 1.30781i 0.0506766i
\(667\) 34.2311 1.32543
\(668\) 15.1356i 0.585615i
\(669\) 4.59749 0.177749
\(670\) −0.801942 5.13720i −0.0309817 0.198467i
\(671\) −7.79402 + 15.6022i −0.300885 + 0.602315i
\(672\) −5.80995 6.80864i −0.224124 0.262649i
\(673\) −16.5791 −0.639078 −0.319539 0.947573i \(-0.603528\pi\)
−0.319539 + 0.947573i \(0.603528\pi\)
\(674\) 31.6038 1.21733
\(675\) −4.76211 + 1.52391i −0.183294 + 0.0586555i
\(676\) −0.755396 −0.0290537
\(677\) 38.2674i 1.47074i 0.677667 + 0.735369i \(0.262991\pi\)
−0.677667 + 0.735369i \(0.737009\pi\)
\(678\) 20.3826i 0.782791i
\(679\) −6.48064 7.59461i −0.248704 0.291455i
\(680\) −3.29328 21.0966i −0.126292 0.809017i
\(681\) 18.9902i 0.727705i
\(682\) −2.51539 1.25656i −0.0963194 0.0481161i
\(683\) 2.74520i 0.105042i −0.998620 0.0525211i \(-0.983274\pi\)
0.998620 0.0525211i \(-0.0167257\pi\)
\(684\) −3.31862 −0.126891
\(685\) 6.25152 + 40.0469i 0.238858 + 1.53011i
\(686\) −18.5407 + 11.3281i −0.707886 + 0.432508i
\(687\) 19.7583i 0.753825i
\(688\) −17.2562 −0.657886
\(689\) 40.3205 1.53609
\(690\) 2.38179 + 15.2576i 0.0906732 + 0.580848i
\(691\) 18.2714i 0.695079i 0.937665 + 0.347539i \(0.112983\pi\)
−0.937665 + 0.347539i \(0.887017\pi\)
\(692\) 0.0564602i 0.00214630i
\(693\) −8.51688 + 2.11252i −0.323530 + 0.0802481i
\(694\) 32.1771 1.22143
\(695\) 27.7356 4.32967i 1.05207 0.164234i
\(696\) 17.8988i 0.678451i
\(697\) 10.3776i 0.393080i
\(698\) −3.93799 −0.149055
\(699\) −19.0700 −0.721295
\(700\) 7.01344 + 4.34515i 0.265083 + 0.164231i
\(701\) 8.67328i 0.327585i 0.986495 + 0.163793i \(0.0523728\pi\)
−0.986495 + 0.163793i \(0.947627\pi\)
\(702\) 4.02806i 0.152029i
\(703\) 5.93180i 0.223722i
\(704\) 12.8893 25.8019i 0.485782 0.972445i
\(705\) −14.5921 + 2.27789i −0.549569 + 0.0857905i
\(706\) −20.3075 −0.764281
\(707\) 26.2619 + 30.7761i 0.987679 + 1.15746i
\(708\) 9.20331i 0.345882i
\(709\) −26.4116 −0.991907 −0.495954 0.868349i \(-0.665181\pi\)
−0.495954 + 0.868349i \(0.665181\pi\)
\(710\) −38.7433 + 6.04802i −1.45401 + 0.226978i
\(711\) 11.5312i 0.432453i
\(712\) 11.2394i 0.421215i
\(713\) 4.25396 0.159312
\(714\) 7.32494 6.25051i 0.274129 0.233920i
\(715\) −24.2618 7.72975i −0.907339 0.289076i
\(716\) 13.7602 0.514242
\(717\) 23.1560i 0.864777i
\(718\) 1.30592i 0.0487366i
\(719\) 52.5438i 1.95955i −0.200091 0.979777i \(-0.564124\pi\)
0.200091 0.979777i \(-0.435876\pi\)
\(720\) 5.22214 0.815202i 0.194618 0.0303808i
\(721\) 2.32089 + 2.71984i 0.0864345 + 0.101292i
\(722\) −10.9273 −0.406673
\(723\) −15.7072 −0.584158
\(724\) 3.39142i 0.126041i
\(725\) 8.86162 + 27.6918i 0.329112 + 1.02845i
\(726\) −7.75041 10.3183i −0.287645 0.382948i
\(727\) 30.1240 1.11724 0.558619 0.829424i \(-0.311331\pi\)
0.558619 + 0.829424i \(0.311331\pi\)
\(728\) 21.2698 18.1499i 0.788310 0.672681i
\(729\) 1.00000 0.0370370
\(730\) 2.94433 + 18.8612i 0.108974 + 0.698084i
\(731\) 22.6484i 0.837682i
\(732\) −3.27959 −0.121217
\(733\) 12.6817i 0.468408i 0.972187 + 0.234204i \(0.0752484\pi\)
−0.972187 + 0.234204i \(0.924752\pi\)
\(734\) −4.32293 −0.159562
\(735\) −0.0485958 + 15.6524i −0.00179248 + 0.577347i
\(736\) 19.9146i 0.734061i
\(737\) −5.88068 2.93768i −0.216618 0.108211i
\(738\) 3.92440 0.144459
\(739\) 16.2962i 0.599464i −0.954023 0.299732i \(-0.903103\pi\)
0.954023 0.299732i \(-0.0968973\pi\)
\(740\) −0.239779 1.53601i −0.00881445 0.0564649i
\(741\) 18.2700i 0.671164i
\(742\) 27.7275 23.6604i 1.01791 0.868601i
\(743\) −3.73982 −0.137201 −0.0686003 0.997644i \(-0.521853\pi\)
−0.0686003 + 0.997644i \(0.521853\pi\)
\(744\) 2.22431i 0.0815471i
\(745\) 1.08391 + 6.94346i 0.0397114 + 0.254389i
\(746\) −5.65786 −0.207149
\(747\) 7.39391i 0.270529i
\(748\) −5.74063 2.86772i −0.209898 0.104854i
\(749\) 3.04926 + 3.57340i 0.111417 + 0.130569i
\(750\) −11.7263 + 5.87662i −0.428185 + 0.214584i
\(751\) −21.8888 −0.798735 −0.399367 0.916791i \(-0.630770\pi\)
−0.399367 + 0.916791i \(0.630770\pi\)
\(752\) 15.6118 0.569302
\(753\) 27.7124i 1.00990i
\(754\) 23.4233 0.853027
\(755\) −0.323944 2.07517i −0.0117895 0.0755231i
\(756\) −1.07109 1.25520i −0.0389550 0.0456511i
\(757\) 49.3842i 1.79490i −0.441118 0.897449i \(-0.645418\pi\)
0.441118 0.897449i \(-0.354582\pi\)
\(758\) 18.1377 0.658791
\(759\) 17.4658 + 8.72500i 0.633969 + 0.316697i
\(760\) −36.1852 + 5.64868i −1.31257 + 0.204899i
\(761\) 26.4800 0.959898 0.479949 0.877296i \(-0.340655\pi\)
0.479949 + 0.877296i \(0.340655\pi\)
\(762\) 7.31763 0.265090
\(763\) 3.90262 3.33018i 0.141284 0.120561i
\(764\) 11.8346 0.428162
\(765\) −1.06994 6.85396i −0.0386837 0.247806i
\(766\) −5.77751 −0.208750
\(767\) 50.6669 1.82948
\(768\) 13.3613 0.482133
\(769\) −2.91216 −0.105015 −0.0525075 0.998621i \(-0.516721\pi\)
−0.0525075 + 0.998621i \(0.516721\pi\)
\(770\) −21.2202 + 8.92145i −0.764721 + 0.321507i
\(771\) 8.14674 0.293398
\(772\) 10.1803 0.366396
\(773\) −46.6347 −1.67733 −0.838666 0.544646i \(-0.816664\pi\)
−0.838666 + 0.544646i \(0.816664\pi\)
\(774\) −8.56475 −0.307854
\(775\) 1.10125 + 3.44131i 0.0395580 + 0.123616i
\(776\) 11.6150 0.416954
\(777\) 2.24358 1.91449i 0.0804879 0.0686819i
\(778\) 9.73008 0.348840
\(779\) −17.7998 −0.637744
\(780\) −0.738521 4.73092i −0.0264433 0.169394i
\(781\) −22.1552 + 44.3505i −0.792774 + 1.58698i
\(782\) −21.4247 −0.766146
\(783\) 5.81504i 0.207813i
\(784\) 2.60273 16.3399i 0.0929546 0.583567i
\(785\) 28.6634 4.47450i 1.02304 0.159702i
\(786\) −3.28163 −0.117052
\(787\) 23.3539i 0.832478i −0.909255 0.416239i \(-0.863348\pi\)
0.909255 0.416239i \(-0.136652\pi\)
\(788\) −10.0480 −0.357945
\(789\) −11.5514 −0.411242
\(790\) −4.66562 29.8877i −0.165995 1.06336i
\(791\) 34.9669 29.8379i 1.24328 1.06091i
\(792\) 4.56212 9.13252i 0.162108 0.324510i
\(793\) 18.0551i 0.641155i
\(794\) 37.9943 1.34837
\(795\) −4.05009 25.9447i −0.143642 0.920163i
\(796\) 15.2781i 0.541518i
\(797\) 31.0609 1.10023 0.550117 0.835087i \(-0.314583\pi\)
0.550117 + 0.835087i \(0.314583\pi\)
\(798\) −10.7210 12.5638i −0.379518 0.444755i
\(799\) 20.4901i 0.724889i
\(800\) −16.1102 + 5.15541i −0.569583 + 0.182271i
\(801\) 3.65152i 0.129020i
\(802\) 21.9216 0.774080
\(803\) 21.5909 + 10.7857i 0.761927 + 0.380619i
\(804\) 1.23613i 0.0435948i
\(805\) 22.6881 26.4215i 0.799651 0.931235i
\(806\) 2.91085 0.102530
\(807\) 16.9804i 0.597737i
\(808\) −47.0681 −1.65585
\(809\) 34.0603i 1.19750i 0.800938 + 0.598748i \(0.204335\pi\)
−0.800938 + 0.598748i \(0.795665\pi\)
\(810\) 2.59190 0.404608i 0.0910701 0.0142165i
\(811\) 52.8198 1.85475 0.927377 0.374129i \(-0.122058\pi\)
0.927377 + 0.374129i \(0.122058\pi\)
\(812\) −7.29902 + 6.22840i −0.256146 + 0.218574i
\(813\) −18.3679 −0.644190
\(814\) 3.88029 + 1.93839i 0.136004 + 0.0679405i
\(815\) −3.22348 20.6494i −0.112914 0.723318i
\(816\) 7.33292i 0.256703i
\(817\) 38.8469 1.35908
\(818\) −9.02443 −0.315532
\(819\) 6.91023 5.89663i 0.241463 0.206045i
\(820\) −4.60918 + 0.719515i −0.160959 + 0.0251266i
\(821\) 7.76941i 0.271154i −0.990767 0.135577i \(-0.956711\pi\)
0.990767 0.135577i \(-0.0432888\pi\)
\(822\) 21.2654i 0.741716i
\(823\) 1.80568i 0.0629422i 0.999505 + 0.0314711i \(0.0100192\pi\)
−0.999505 + 0.0314711i \(0.989981\pi\)
\(824\) −4.15964 −0.144908
\(825\) −2.53676 + 16.3879i −0.0883185 + 0.570555i
\(826\) 34.8425 29.7318i 1.21232 1.03450i
\(827\) −52.6701 −1.83152 −0.915760 0.401726i \(-0.868411\pi\)
−0.915760 + 0.401726i \(0.868411\pi\)
\(828\) 3.67133i 0.127587i
\(829\) 7.36227i 0.255702i 0.991793 + 0.127851i \(0.0408079\pi\)
−0.991793 + 0.127851i \(0.959192\pi\)
\(830\) 2.99164 + 19.1643i 0.103841 + 0.665202i
\(831\) 11.6755 0.405019
\(832\) 29.8584i 1.03515i
\(833\) −21.4458 3.41603i −0.743053 0.118359i
\(834\) −14.7280 −0.509987
\(835\) 8.36988 + 53.6170i 0.289652 + 1.85549i
\(836\) −4.91875 + 9.84640i −0.170118 + 0.340545i
\(837\) 0.722644i 0.0249782i
\(838\) 8.59516i 0.296915i
\(839\) 17.7190i 0.611728i −0.952075 0.305864i \(-0.901055\pi\)
0.952075 0.305864i \(-0.0989454\pi\)
\(840\) −13.8153 11.8632i −0.476672 0.409318i
\(841\) −4.81467 −0.166023
\(842\) 2.25117 0.0775803
\(843\) 7.54255i 0.259779i
\(844\) 8.16346i 0.280998i
\(845\) −2.67594 + 0.417728i −0.0920553 + 0.0143703i
\(846\) 7.74857 0.266401
\(847\) −6.35553 + 28.4008i −0.218379 + 0.975864i
\(848\) 27.7577i 0.953203i
\(849\) 4.89738i 0.168078i
\(850\) −5.54634 17.3319i −0.190238 0.594478i
\(851\) −6.56224 −0.224951
\(852\) −9.32250 −0.319384
\(853\) 40.5291i 1.38769i 0.720125 + 0.693844i \(0.244084\pi\)
−0.720125 + 0.693844i \(0.755916\pi\)
\(854\) −10.5949 12.4161i −0.362549 0.424869i
\(855\) −11.7560 + 1.83517i −0.402047 + 0.0627616i
\(856\) −5.46506 −0.186792
\(857\) 33.2959i 1.13737i −0.822556 0.568683i \(-0.807453\pi\)
0.822556 0.568683i \(-0.192547\pi\)
\(858\) 11.9513 + 5.97025i 0.408011 + 0.203821i
\(859\) 49.0304i 1.67289i −0.548048 0.836447i \(-0.684629\pi\)
0.548048 0.836447i \(-0.315371\pi\)
\(860\) 10.0592 1.57030i 0.343017 0.0535466i
\(861\) −5.74489 6.73240i −0.195785 0.229439i
\(862\) 8.76638i 0.298584i
\(863\) 10.0731i 0.342891i 0.985194 + 0.171446i \(0.0548438\pi\)
−0.985194 + 0.171446i \(0.945156\pi\)
\(864\) 3.38301 0.115092
\(865\) 0.0312221 + 0.200007i 0.00106158 + 0.00680044i
\(866\) −15.9080 −0.540576
\(867\) −7.37569 −0.250491
\(868\) −0.907061 + 0.774014i −0.0307877 + 0.0262717i
\(869\) −34.2132 17.0911i −1.16060 0.579777i
\(870\) −2.35281 15.0720i −0.0797679 0.510989i
\(871\) 6.80522 0.230586
\(872\) 5.96855i 0.202121i
\(873\) 3.77353 0.127715
\(874\) 36.7480i 1.24302i
\(875\) 27.2475 + 11.5140i 0.921134 + 0.389246i
\(876\) 4.53843i 0.153339i
\(877\) 15.1073 0.510136 0.255068 0.966923i \(-0.417902\pi\)
0.255068 + 0.966923i \(0.417902\pi\)
\(878\) 35.9937 1.21473
\(879\) 7.63128i 0.257397i
\(880\) 5.32136 16.7024i 0.179383 0.563039i
\(881\) 28.6024i 0.963639i −0.876271 0.481819i \(-0.839976\pi\)
0.876271 0.481819i \(-0.160024\pi\)
\(882\) 1.29181 8.10996i 0.0434975 0.273076i
\(883\) 12.6564i 0.425921i 0.977061 + 0.212960i \(0.0683106\pi\)
−0.977061 + 0.212960i \(0.931689\pi\)
\(884\) 6.64315 0.223433
\(885\) −5.08936 32.6022i −0.171077 1.09591i
\(886\) 34.3989i 1.15565i
\(887\) 11.2443i 0.377547i 0.982021 + 0.188774i \(0.0604512\pi\)
−0.982021 + 0.188774i \(0.939549\pi\)
\(888\) 3.43126i 0.115146i
\(889\) −10.7122 12.5536i −0.359276 0.421033i
\(890\) 1.47743 + 9.46436i 0.0495237 + 0.317246i
\(891\) 1.48217 2.96702i 0.0496544 0.0993988i
\(892\) 2.86732 0.0960048
\(893\) −35.1450 −1.17608
\(894\) 3.68706i 0.123314i
\(895\) 48.7446 7.60928i 1.62935 0.254350i
\(896\) 5.90125 + 6.91563i 0.197147 + 0.231035i
\(897\) −20.2117 −0.674850
\(898\) −17.0755 −0.569816
\(899\) −4.20220 −0.140151
\(900\) −2.96998 + 0.950419i −0.0989994 + 0.0316806i
\(901\) 36.4314 1.21371
\(902\) 5.81661 11.6438i 0.193672 0.387695i
\(903\) 12.5378 + 14.6930i 0.417233 + 0.488953i
\(904\) 53.4773i 1.77863i
\(905\) 1.87543 + 12.0139i 0.0623413 + 0.399355i
\(906\) 1.10194i 0.0366095i
\(907\) 46.9653i 1.55946i 0.626117 + 0.779729i \(0.284643\pi\)
−0.626117 + 0.779729i \(0.715357\pi\)
\(908\) 11.8436i 0.393043i
\(909\) −15.2917 −0.507194
\(910\) 15.5248 18.0794i 0.514642 0.599327i
\(911\) 7.80180 0.258485 0.129243 0.991613i \(-0.458745\pi\)
0.129243 + 0.991613i \(0.458745\pi\)
\(912\) 12.5775 0.416483
\(913\) 21.9379 + 10.9590i 0.726037 + 0.362690i
\(914\) 24.2203 0.801137
\(915\) −11.6177 + 1.81359i −0.384071 + 0.0599553i
\(916\) 12.3226i 0.407151i
\(917\) 4.80394 + 5.62971i 0.158640 + 0.185909i
\(918\) 3.63954i 0.120123i
\(919\) 28.8139i 0.950484i 0.879855 + 0.475242i \(0.157639\pi\)
−0.879855 + 0.475242i \(0.842361\pi\)
\(920\) 6.24903 + 40.0310i 0.206024 + 1.31978i
\(921\) 29.9896i 0.988190i
\(922\) 8.91017 0.293441
\(923\) 51.3231i 1.68932i
\(924\) −5.31172 + 1.31752i −0.174743 + 0.0433431i
\(925\) −1.69881 5.30863i −0.0558564 0.174547i
\(926\) 33.5310i 1.10190i
\(927\) −1.35140 −0.0443859
\(928\) 19.6723i 0.645775i
\(929\) 0.852646i 0.0279744i 0.999902 + 0.0139872i \(0.00445241\pi\)
−0.999902 + 0.0139872i \(0.995548\pi\)
\(930\) −0.292388 1.87302i −0.00958778 0.0614188i
\(931\) −5.85923 + 36.7841i −0.192028 + 1.20555i
\(932\) −11.8934 −0.389581
\(933\) 10.3684i 0.339447i
\(934\) −25.8778 −0.846746
\(935\) −21.9216 6.98418i −0.716914 0.228407i
\(936\) 10.5683i 0.345436i
\(937\) 16.0248i 0.523507i 0.965135 + 0.261754i \(0.0843008\pi\)
−0.965135 + 0.261754i \(0.915699\pi\)
\(938\) 4.67980 3.99336i 0.152801 0.130388i
\(939\) 17.3488 0.566157
\(940\) −9.10063 + 1.42065i −0.296830 + 0.0463366i
\(941\) −29.0243 −0.946164 −0.473082 0.881018i \(-0.656859\pi\)
−0.473082 + 0.881018i \(0.656859\pi\)
\(942\) −15.2206 −0.495914
\(943\) 19.6916i 0.641246i
\(944\) 34.8804i 1.13526i
\(945\) −4.48837 3.85416i −0.146007 0.125376i
\(946\) −12.6944 + 25.4117i −0.412730 + 0.826207i
\(947\) 11.9719i 0.389035i 0.980899 + 0.194518i \(0.0623142\pi\)
−0.980899 + 0.194518i \(0.937686\pi\)
\(948\) 7.19165i 0.233574i
\(949\) −24.9854 −0.811059
\(950\) −29.7279 + 9.51316i −0.964500 + 0.308648i
\(951\) 20.0871i 0.651370i
\(952\) 19.2182 16.3993i 0.622866 0.531504i
\(953\) 27.7753 0.899730 0.449865 0.893096i \(-0.351472\pi\)
0.449865 + 0.893096i \(0.351472\pi\)
\(954\) 13.7769i 0.446045i
\(955\) 41.9235 6.54446i 1.35661 0.211774i
\(956\) 14.4417i 0.467078i
\(957\) −17.2533 8.61885i −0.557720 0.278608i
\(958\) 35.5570 1.14879
\(959\) −36.4813 + 31.1302i −1.17804 + 1.00525i
\(960\) 19.2127 2.99920i 0.620087 0.0967987i
\(961\) 30.4778 0.983154
\(962\) −4.49034 −0.144774
\(963\) −1.77552 −0.0572152
\(964\) −9.79612 −0.315512
\(965\) 36.0630 5.62961i 1.16091 0.181224i
\(966\) −13.8991 + 11.8604i −0.447197 + 0.381602i
\(967\) 50.2899 1.61722 0.808608 0.588348i \(-0.200222\pi\)
0.808608 + 0.588348i \(0.200222\pi\)
\(968\) −20.3345 27.0718i −0.653576 0.870120i
\(969\) 16.5078i 0.530306i
\(970\) 9.78062 1.52680i 0.314037 0.0490227i
\(971\) 43.1696i 1.38538i 0.721237 + 0.692688i \(0.243574\pi\)
−0.721237 + 0.692688i \(0.756426\pi\)
\(972\) 0.623669 0.0200042
\(973\) 21.5601 + 25.2661i 0.691185 + 0.809995i
\(974\) 11.9083i 0.381567i
\(975\) −5.23233 16.3506i −0.167569 0.523639i
\(976\) 12.4296 0.397861
\(977\) 34.3037i 1.09747i 0.835996 + 0.548736i \(0.184891\pi\)
−0.835996 + 0.548736i \(0.815109\pi\)
\(978\) 10.9651i 0.350625i
\(979\) 10.8341 + 5.41215i 0.346260 + 0.172973i
\(980\) −0.0303077 + 9.76192i −0.000968145 + 0.311833i
\(981\) 1.93909i 0.0619104i
\(982\) 40.1775i 1.28212i
\(983\) 50.9060 1.62365 0.811825 0.583901i \(-0.198474\pi\)
0.811825 + 0.583901i \(0.198474\pi\)
\(984\) 10.2963 0.328235
\(985\) −35.5944 + 5.55646i −1.13413 + 0.177044i
\(986\) 21.1641 0.674001
\(987\) −11.3430 13.2928i −0.361053 0.423116i
\(988\) 11.3944i 0.362505i
\(989\) 42.9756i 1.36654i
\(990\) 2.64114 8.28991i 0.0839411 0.263470i
\(991\) 39.1588 1.24392 0.621960 0.783049i \(-0.286336\pi\)
0.621960 + 0.783049i \(0.286336\pi\)
\(992\) 2.44471i 0.0776196i
\(993\) 17.1491 0.544209
\(994\) −30.1168 35.2937i −0.955247 1.11945i
\(995\) −8.44868 54.1218i −0.267841 1.71578i
\(996\) 4.61136i 0.146116i
\(997\) 27.4294i 0.868698i −0.900745 0.434349i \(-0.856978\pi\)
0.900745 0.434349i \(-0.143022\pi\)
\(998\) −3.63316 −0.115006
\(999\) 1.11476i 0.0352696i
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 1155.2.k.a.769.16 yes 48
5.4 even 2 1155.2.k.b.769.33 yes 48
7.6 odd 2 1155.2.k.b.769.15 yes 48
11.10 odd 2 inner 1155.2.k.a.769.33 yes 48
35.34 odd 2 inner 1155.2.k.a.769.34 yes 48
55.54 odd 2 1155.2.k.b.769.16 yes 48
77.76 even 2 1155.2.k.b.769.34 yes 48
385.384 even 2 inner 1155.2.k.a.769.15 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1155.2.k.a.769.15 48 385.384 even 2 inner
1155.2.k.a.769.16 yes 48 1.1 even 1 trivial
1155.2.k.a.769.33 yes 48 11.10 odd 2 inner
1155.2.k.a.769.34 yes 48 35.34 odd 2 inner
1155.2.k.b.769.15 yes 48 7.6 odd 2
1155.2.k.b.769.16 yes 48 55.54 odd 2
1155.2.k.b.769.33 yes 48 5.4 even 2
1155.2.k.b.769.34 yes 48 77.76 even 2