Properties

Label 21.30.c.a.20.11
Level $21$
Weight $30$
Character 21.20
Analytic conductor $111.884$
Analytic rank $0$
Dimension $76$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 30 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(111.883889004\)
Analytic rank: \(0\)
Dimension: \(76\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.11
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.12

$q$-expansion

\(f(q)\) \(=\) \(q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} +O(q^{10})\) \(q-23469.1i q^{2} +(-4.70121e6 - 6.82122e6i) q^{3} -1.39279e7 q^{4} +1.98757e10 q^{5} +(-1.60088e11 + 1.10333e11i) q^{6} +(-7.54484e11 - 1.62808e12i) q^{7} -1.22730e13i q^{8} +(-2.44277e13 + 6.41359e13i) q^{9} -4.66464e14i q^{10} -5.73249e14i q^{11} +(6.54778e13 + 9.50050e13i) q^{12} +2.54219e16i q^{13} +(-3.82097e16 + 1.77071e16i) q^{14} +(-9.34397e16 - 1.35576e17i) q^{15} -2.95514e17 q^{16} -7.73767e16 q^{17} +(1.50521e18 + 5.73296e17i) q^{18} -3.43827e18i q^{19} -2.76826e17 q^{20} +(-7.55853e18 + 1.28005e19i) q^{21} -1.34536e19 q^{22} -2.68583e19i q^{23} +(-8.37168e19 + 5.76979e19i) q^{24} +2.08778e20 q^{25} +5.96629e20 q^{26} +(5.52325e20 - 1.34890e20i) q^{27} +(1.05084e19 + 2.26757e19i) q^{28} +9.38030e20i q^{29} +(-3.18185e21 + 2.19294e21i) q^{30} +5.15944e21i q^{31} +3.46426e20i q^{32} +(-3.91025e21 + 2.69496e21i) q^{33} +1.81596e21i q^{34} +(-1.49959e22 - 3.23593e22i) q^{35} +(3.40225e20 - 8.93276e20i) q^{36} -3.88136e22 q^{37} -8.06931e22 q^{38} +(1.73408e23 - 1.19514e23i) q^{39} -2.43934e23i q^{40} -4.34123e23 q^{41} +(3.00415e23 + 1.77392e23i) q^{42} -5.92539e23 q^{43} +7.98413e21i q^{44} +(-4.85516e23 + 1.27474e24i) q^{45} -6.30341e23 q^{46} -1.14886e24 q^{47} +(1.38927e24 + 2.01576e24i) q^{48} +(-2.08141e24 + 2.45673e24i) q^{49} -4.89983e24i q^{50} +(3.63764e23 + 5.27803e23i) q^{51} -3.54072e23i q^{52} +1.25991e25i q^{53} +(-3.16574e24 - 1.29626e25i) q^{54} -1.13937e25i q^{55} +(-1.99815e25 + 9.25979e24i) q^{56} +(-2.34532e25 + 1.61640e25i) q^{57} +2.20147e25 q^{58} -6.30342e25 q^{59} +(1.30141e24 + 1.88829e24i) q^{60} -1.06559e26i q^{61} +1.21087e26 q^{62} +(1.22849e26 - 8.61923e24i) q^{63} -1.50522e26 q^{64} +5.05277e26i q^{65} +(6.32483e25 + 9.17701e25i) q^{66} -2.01956e26 q^{67} +1.07769e24 q^{68} +(-1.83207e26 + 1.26267e26i) q^{69} +(-7.59443e26 + 3.51940e26i) q^{70} +7.89239e26i q^{71} +(7.87141e26 + 2.99801e26i) q^{72} -1.48365e27i q^{73} +9.10920e26i q^{74} +(-9.81508e26 - 1.42412e27i) q^{75} +4.78877e25i q^{76} +(-9.33297e26 + 4.32507e26i) q^{77} +(-2.80488e27 - 4.06974e27i) q^{78} +4.39054e27 q^{79} -5.87354e27 q^{80} +(-3.51671e27 - 3.13338e27i) q^{81} +1.01885e28i q^{82} -4.23602e27 q^{83} +(1.05274e26 - 1.78283e26i) q^{84} -1.53791e27 q^{85} +1.39064e28i q^{86} +(6.39851e27 - 4.40987e27i) q^{87} -7.03548e27 q^{88} +1.28454e28 q^{89} +(2.99171e28 + 1.13946e28i) q^{90} +(4.13890e28 - 1.91804e28i) q^{91} +3.74079e26i q^{92} +(3.51936e28 - 2.42556e28i) q^{93} +2.69627e28i q^{94} -6.83379e28i q^{95} +(2.36305e27 - 1.62862e27i) q^{96} +1.72177e27i q^{97} +(5.76572e28 + 4.88489e28i) q^{98} +(3.67658e28 + 1.40031e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} + O(q^{10}) \) \( 76q - 20401094660q^{4} + 1962751543872q^{7} - 89581451225964q^{9} - 116668222909200048q^{15} + 4964525139713333892q^{16} + 1542346202347854996q^{18} + 33840646982361357348q^{21} - 9870996616978150672q^{22} + \)\(32\!\cdots\!12\)\(q^{25} - \)\(31\!\cdots\!64\)\(q^{28} + \)\(51\!\cdots\!44\)\(q^{30} - \)\(85\!\cdots\!52\)\(q^{36} - \)\(17\!\cdots\!76\)\(q^{37} + \)\(38\!\cdots\!96\)\(q^{39} + \)\(80\!\cdots\!56\)\(q^{42} + \)\(23\!\cdots\!20\)\(q^{43} - \)\(10\!\cdots\!00\)\(q^{46} - \)\(51\!\cdots\!40\)\(q^{49} - \)\(96\!\cdots\!00\)\(q^{51} + \)\(20\!\cdots\!48\)\(q^{57} - \)\(40\!\cdots\!72\)\(q^{58} - \)\(16\!\cdots\!96\)\(q^{60} - \)\(36\!\cdots\!84\)\(q^{63} - \)\(16\!\cdots\!28\)\(q^{64} + \)\(48\!\cdots\!64\)\(q^{67} - \)\(65\!\cdots\!20\)\(q^{70} + \)\(19\!\cdots\!24\)\(q^{72} - \)\(80\!\cdots\!36\)\(q^{78} - \)\(11\!\cdots\!52\)\(q^{79} + \)\(18\!\cdots\!32\)\(q^{81} - \)\(72\!\cdots\!52\)\(q^{84} + \)\(14\!\cdots\!48\)\(q^{85} - \)\(16\!\cdots\!84\)\(q^{88} + \)\(44\!\cdots\!40\)\(q^{91} + \)\(22\!\cdots\!32\)\(q^{93} - \)\(23\!\cdots\!24\)\(q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).

\(n\) \(8\) \(10\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 23469.1i 1.01289i −0.862273 0.506444i \(-0.830960\pi\)
0.862273 0.506444i \(-0.169040\pi\)
\(3\) −4.70121e6 6.82122e6i −0.567481 0.823387i
\(4\) −1.39279e7 −0.0259427
\(5\) 1.98757e10 1.45632 0.728160 0.685407i \(-0.240376\pi\)
0.728160 + 0.685407i \(0.240376\pi\)
\(6\) −1.60088e11 + 1.10333e11i −0.833999 + 0.574795i
\(7\) −7.54484e11 1.62808e12i −0.420464 0.907309i
\(8\) 1.22730e13i 0.986611i
\(9\) −2.44277e13 + 6.41359e13i −0.355931 + 0.934512i
\(10\) 4.66464e14i 1.47509i
\(11\) 5.73249e14i 0.455144i −0.973761 0.227572i \(-0.926921\pi\)
0.973761 0.227572i \(-0.0730787\pi\)
\(12\) 6.54778e13 + 9.50050e13i 0.0147220 + 0.0213608i
\(13\) 2.54219e16i 1.79073i 0.445337 + 0.895363i \(0.353084\pi\)
−0.445337 + 0.895363i \(0.646916\pi\)
\(14\) −3.82097e16 + 1.77071e16i −0.919003 + 0.425883i
\(15\) −9.34397e16 1.35576e17i −0.826434 1.19911i
\(16\) −2.95514e17 −1.02527
\(17\) −7.73767e16 −0.111455 −0.0557276 0.998446i \(-0.517748\pi\)
−0.0557276 + 0.998446i \(0.517748\pi\)
\(18\) 1.50521e18 + 5.73296e17i 0.946557 + 0.360518i
\(19\) 3.43827e18i 0.987217i −0.869684 0.493608i \(-0.835678\pi\)
0.869684 0.493608i \(-0.164322\pi\)
\(20\) −2.76826e17 −0.0377808
\(21\) −7.55853e18 + 1.28005e19i −0.508461 + 0.861085i
\(22\) −1.34536e19 −0.461010
\(23\) 2.68583e19i 0.483087i −0.970390 0.241544i \(-0.922346\pi\)
0.970390 0.241544i \(-0.0776537\pi\)
\(24\) −8.37168e19 + 5.76979e19i −0.812362 + 0.559883i
\(25\) 2.08778e20 1.12087
\(26\) 5.96629e20 1.81381
\(27\) 5.52325e20 1.34890e20i 0.971449 0.237249i
\(28\) 1.05084e19 + 2.26757e19i 0.0109079 + 0.0235380i
\(29\) 9.38030e20i 0.585390i 0.956206 + 0.292695i \(0.0945521\pi\)
−0.956206 + 0.292695i \(0.905448\pi\)
\(30\) −3.18185e21 + 2.19294e21i −1.21457 + 0.837085i
\(31\) 5.15944e21i 1.22422i 0.790775 + 0.612108i \(0.209678\pi\)
−0.790775 + 0.612108i \(0.790322\pi\)
\(32\) 3.46426e20i 0.0518723i
\(33\) −3.91025e21 + 2.69496e21i −0.374760 + 0.258286i
\(34\) 1.81596e21i 0.112892i
\(35\) −1.49959e22 3.23593e22i −0.612330 1.32133i
\(36\) 3.40225e20 8.93276e20i 0.00923380 0.0242437i
\(37\) −3.88136e22 −0.708042 −0.354021 0.935238i \(-0.615186\pi\)
−0.354021 + 0.935238i \(0.615186\pi\)
\(38\) −8.06931e22 −0.999940
\(39\) 1.73408e23 1.19514e23i 1.47446 1.01620i
\(40\) 2.43934e23i 1.43682i
\(41\) −4.34123e23 −1.78751 −0.893753 0.448560i \(-0.851937\pi\)
−0.893753 + 0.448560i \(0.851937\pi\)
\(42\) 3.00415e23 + 1.77392e23i 0.872183 + 0.515014i
\(43\) −5.92539e23 −1.22299 −0.611497 0.791247i \(-0.709432\pi\)
−0.611497 + 0.791247i \(0.709432\pi\)
\(44\) 7.98413e21i 0.0118077i
\(45\) −4.85516e23 + 1.27474e24i −0.518349 + 1.36095i
\(46\) −6.30341e23 −0.489313
\(47\) −1.14886e24 −0.652902 −0.326451 0.945214i \(-0.605853\pi\)
−0.326451 + 0.945214i \(0.605853\pi\)
\(48\) 1.38927e24 + 2.01576e24i 0.581821 + 0.844193i
\(49\) −2.08141e24 + 2.45673e24i −0.646420 + 0.762981i
\(50\) 4.89983e24i 1.13531i
\(51\) 3.63764e23 + 5.27803e23i 0.0632487 + 0.0917708i
\(52\) 3.54072e23i 0.0464562i
\(53\) 1.25991e25i 1.25412i 0.778970 + 0.627061i \(0.215742\pi\)
−0.778970 + 0.627061i \(0.784258\pi\)
\(54\) −3.16574e24 1.29626e25i −0.240307 0.983969i
\(55\) 1.13937e25i 0.662835i
\(56\) −1.99815e25 + 9.25979e24i −0.895162 + 0.414834i
\(57\) −2.34532e25 + 1.61640e25i −0.812861 + 0.560227i
\(58\) 2.20147e25 0.592935
\(59\) −6.30342e25 −1.32502 −0.662509 0.749054i \(-0.730508\pi\)
−0.662509 + 0.749054i \(0.730508\pi\)
\(60\) 1.30141e24 + 1.88829e24i 0.0214399 + 0.0311082i
\(61\) 1.06559e26i 1.38136i −0.723158 0.690682i \(-0.757310\pi\)
0.723158 0.690682i \(-0.242690\pi\)
\(62\) 1.21087e26 1.23999
\(63\) 1.22849e26 8.61923e24i 0.997548 0.0699891i
\(64\) −1.50522e26 −0.972729
\(65\) 5.05277e26i 2.60787i
\(66\) 6.32483e25 + 9.17701e25i 0.261614 + 0.379590i
\(67\) −2.01956e26 −0.671696 −0.335848 0.941916i \(-0.609023\pi\)
−0.335848 + 0.941916i \(0.609023\pi\)
\(68\) 1.07769e24 0.00289145
\(69\) −1.83207e26 + 1.26267e26i −0.397768 + 0.274143i
\(70\) −7.59443e26 + 3.51940e26i −1.33836 + 0.620222i
\(71\) 7.89239e26i 1.13230i 0.824302 + 0.566151i \(0.191568\pi\)
−0.824302 + 0.566151i \(0.808432\pi\)
\(72\) 7.87141e26 + 2.99801e26i 0.922000 + 0.351165i
\(73\) 1.48365e27i 1.42282i −0.702776 0.711412i \(-0.748056\pi\)
0.702776 0.711412i \(-0.251944\pi\)
\(74\) 9.10920e26i 0.717167i
\(75\) −9.81508e26 1.42412e27i −0.636071 0.922907i
\(76\) 4.78877e25i 0.0256110i
\(77\) −9.33297e26 + 4.32507e26i −0.412957 + 0.191372i
\(78\) −2.80488e27 4.06974e27i −1.02930 1.49346i
\(79\) 4.39054e27 1.33944 0.669722 0.742612i \(-0.266413\pi\)
0.669722 + 0.742612i \(0.266413\pi\)
\(80\) −5.87354e27 −1.49312
\(81\) −3.51671e27 3.13338e27i −0.746626 0.665244i
\(82\) 1.01885e28i 1.81054i
\(83\) −4.23602e27 −0.631431 −0.315715 0.948854i \(-0.602244\pi\)
−0.315715 + 0.948854i \(0.602244\pi\)
\(84\) 1.05274e26 1.78283e26i 0.0131908 0.0223388i
\(85\) −1.53791e27 −0.162315
\(86\) 1.39064e28i 1.23876i
\(87\) 6.39851e27 4.40987e27i 0.482003 0.332198i
\(88\) −7.03548e27 −0.449050
\(89\) 1.28454e28 0.695975 0.347987 0.937499i \(-0.386865\pi\)
0.347987 + 0.937499i \(0.386865\pi\)
\(90\) 2.99171e28 + 1.13946e28i 1.37849 + 0.525030i
\(91\) 4.13890e28 1.91804e28i 1.62474 0.752935i
\(92\) 3.74079e26i 0.0125326i
\(93\) 3.51936e28 2.42556e28i 1.00800 0.694719i
\(94\) 2.69627e28i 0.661317i
\(95\) 6.83379e28i 1.43770i
\(96\) 2.36305e27 1.62862e27i 0.0427110 0.0294366i
\(97\) 1.72177e27i 0.0267785i 0.999910 + 0.0133892i \(0.00426205\pi\)
−0.999910 + 0.0133892i \(0.995738\pi\)
\(98\) 5.76572e28 + 4.88489e28i 0.772815 + 0.654752i
\(99\) 3.67658e28 + 1.40031e28i 0.425338 + 0.162000i
\(100\) −2.90783e27 −0.0290783
\(101\) −1.79335e29 −1.55240 −0.776202 0.630484i \(-0.782856\pi\)
−0.776202 + 0.630484i \(0.782856\pi\)
\(102\) 1.23871e28 8.53721e27i 0.0929535 0.0640639i
\(103\) 8.70748e28i 0.567221i −0.958940 0.283611i \(-0.908468\pi\)
0.958940 0.283611i \(-0.0915323\pi\)
\(104\) 3.12003e29 1.76675
\(105\) −1.50231e29 + 2.54418e29i −0.740482 + 1.25401i
\(106\) 2.95690e29 1.27028
\(107\) 8.17895e28i 0.306643i −0.988176 0.153321i \(-0.951003\pi\)
0.988176 0.153321i \(-0.0489970\pi\)
\(108\) −7.69270e27 + 1.87873e27i −0.0252020 + 0.00615487i
\(109\) −2.81481e29 −0.806800 −0.403400 0.915024i \(-0.632172\pi\)
−0.403400 + 0.915024i \(0.632172\pi\)
\(110\) −2.67400e29 −0.671378
\(111\) 1.82471e29 + 2.64756e29i 0.401800 + 0.582992i
\(112\) 2.22961e29 + 4.81122e29i 0.431089 + 0.930237i
\(113\) 4.35011e29i 0.739372i 0.929157 + 0.369686i \(0.120535\pi\)
−0.929157 + 0.369686i \(0.879465\pi\)
\(114\) 3.79355e29 + 5.50425e29i 0.567447 + 0.823338i
\(115\) 5.33828e29i 0.703529i
\(116\) 1.30647e28i 0.0151866i
\(117\) −1.63046e30 6.20997e29i −1.67346 0.637375i
\(118\) 1.47936e30i 1.34210i
\(119\) 5.83795e28 + 1.25976e29i 0.0468629 + 0.101124i
\(120\) −1.66393e30 + 1.14679e30i −1.18306 + 0.815369i
\(121\) 1.25770e30 0.792844
\(122\) −2.50085e30 −1.39917
\(123\) 2.04090e30 + 2.96125e30i 1.01438 + 1.47181i
\(124\) 7.18599e28i 0.0317594i
\(125\) 4.47466e29 0.176021
\(126\) −2.02286e29 2.88316e30i −0.0708912 1.01040i
\(127\) 1.01244e30 0.316385 0.158192 0.987408i \(-0.449433\pi\)
0.158192 + 0.987408i \(0.449433\pi\)
\(128\) 3.71861e30i 1.03714i
\(129\) 2.78565e30 + 4.04184e30i 0.694026 + 1.00700i
\(130\) 1.18584e31 2.64148
\(131\) −2.09552e30 −0.417694 −0.208847 0.977948i \(-0.566971\pi\)
−0.208847 + 0.977948i \(0.566971\pi\)
\(132\) 5.44615e28 3.75350e28i 0.00972226 0.00670062i
\(133\) −5.59779e30 + 2.59412e30i −0.895711 + 0.415089i
\(134\) 4.73974e30i 0.680353i
\(135\) 1.09778e31 2.68103e30i 1.41474 0.345511i
\(136\) 9.49644e29i 0.109963i
\(137\) 1.03686e31i 1.07962i 0.841788 + 0.539809i \(0.181504\pi\)
−0.841788 + 0.539809i \(0.818496\pi\)
\(138\) 2.96336e30 + 4.29969e30i 0.277676 + 0.402894i
\(139\) 1.55704e30i 0.131397i 0.997840 + 0.0656986i \(0.0209276\pi\)
−0.997840 + 0.0656986i \(0.979072\pi\)
\(140\) 2.08861e29 + 4.50695e29i 0.0158855 + 0.0342789i
\(141\) 5.40103e30 + 7.83662e30i 0.370509 + 0.537591i
\(142\) 1.85227e31 1.14690
\(143\) 1.45731e31 0.815039
\(144\) 7.21872e30 1.89531e31i 0.364925 0.958127i
\(145\) 1.86440e31i 0.852516i
\(146\) −3.48200e31 −1.44116
\(147\) 2.65430e31 + 2.64818e30i 0.995060 + 0.0992766i
\(148\) 5.40590e29 0.0183685
\(149\) 1.78985e31i 0.551590i −0.961217 0.275795i \(-0.911059\pi\)
0.961217 0.275795i \(-0.0889410\pi\)
\(150\) −3.34228e31 + 2.30351e31i −0.934802 + 0.644269i
\(151\) 5.02949e31 1.27749 0.638746 0.769418i \(-0.279454\pi\)
0.638746 + 0.769418i \(0.279454\pi\)
\(152\) −4.21979e31 −0.973999
\(153\) 1.89013e30 4.96262e30i 0.0396704 0.104156i
\(154\) 1.01505e31 + 2.19036e31i 0.193838 + 0.418279i
\(155\) 1.02547e32i 1.78285i
\(156\) −2.41521e30 + 1.66457e30i −0.0382514 + 0.0263630i
\(157\) 3.53151e31i 0.509818i −0.966965 0.254909i \(-0.917955\pi\)
0.966965 0.254909i \(-0.0820455\pi\)
\(158\) 1.03042e32i 1.35671i
\(159\) 8.59413e31 5.92310e31i 1.03263 0.711690i
\(160\) 6.88545e30i 0.0755427i
\(161\) −4.37276e31 + 2.02642e31i −0.438310 + 0.203121i
\(162\) −7.35377e31 + 8.25339e31i −0.673817 + 0.756249i
\(163\) 1.19012e32 0.997399 0.498700 0.866775i \(-0.333811\pi\)
0.498700 + 0.866775i \(0.333811\pi\)
\(164\) 6.04641e30 0.0463726
\(165\) −7.77189e31 + 5.35641e31i −0.545770 + 0.376146i
\(166\) 9.94156e31i 0.639569i
\(167\) −4.14758e31 −0.244572 −0.122286 0.992495i \(-0.539022\pi\)
−0.122286 + 0.992495i \(0.539022\pi\)
\(168\) 1.57100e32 + 9.27659e31i 0.849556 + 0.501654i
\(169\) −4.44734e32 −2.20670
\(170\) 3.60934e31i 0.164406i
\(171\) 2.20517e32 + 8.39889e31i 0.922566 + 0.351381i
\(172\) 8.25280e30 0.0317277
\(173\) 1.76776e32 0.624820 0.312410 0.949947i \(-0.398864\pi\)
0.312410 + 0.949947i \(0.398864\pi\)
\(174\) −1.03496e32 1.50167e32i −0.336479 0.488215i
\(175\) −1.57520e32 3.39908e32i −0.471284 1.01697i
\(176\) 1.69403e32i 0.466646i
\(177\) 2.96337e32 + 4.29970e32i 0.751922 + 1.09100i
\(178\) 3.01471e32i 0.704944i
\(179\) 7.22462e32i 1.55756i −0.627295 0.778782i \(-0.715838\pi\)
0.627295 0.778782i \(-0.284162\pi\)
\(180\) 6.76220e30 1.77545e31i 0.0134474 0.0353066i
\(181\) 1.20311e32i 0.220783i 0.993888 + 0.110391i \(0.0352104\pi\)
−0.993888 + 0.110391i \(0.964790\pi\)
\(182\) −4.50147e32 9.71362e32i −0.762639 1.64568i
\(183\) −7.26864e32 + 5.00957e32i −1.13740 + 0.783898i
\(184\) −3.29633e32 −0.476619
\(185\) −7.71446e32 −1.03113
\(186\) −5.69257e32 8.25963e32i −0.703672 1.02099i
\(187\) 4.43561e31i 0.0507282i
\(188\) 1.60012e31 0.0169380
\(189\) −6.36332e32 7.97459e32i −0.623717 0.781650i
\(190\) −1.60383e33 −1.45623
\(191\) 8.95713e32i 0.753676i −0.926279 0.376838i \(-0.877011\pi\)
0.926279 0.376838i \(-0.122989\pi\)
\(192\) 7.07637e32 + 1.02675e33i 0.552005 + 0.800932i
\(193\) 2.16008e33 1.56275 0.781374 0.624063i \(-0.214519\pi\)
0.781374 + 0.624063i \(0.214519\pi\)
\(194\) 4.04085e31 0.0271236
\(195\) 3.44661e33 2.37541e33i 2.14728 1.47992i
\(196\) 2.89896e31 3.42170e31i 0.0167699 0.0197938i
\(197\) 9.51350e32i 0.511187i 0.966784 + 0.255594i \(0.0822709\pi\)
−0.966784 + 0.255594i \(0.917729\pi\)
\(198\) 3.28641e32 8.62861e32i 0.164088 0.430820i
\(199\) 1.72725e33i 0.801651i −0.916154 0.400826i \(-0.868723\pi\)
0.916154 0.400826i \(-0.131277\pi\)
\(200\) 2.56233e33i 1.10586i
\(201\) 9.49439e32 + 1.37759e33i 0.381175 + 0.553066i
\(202\) 4.20883e33i 1.57241i
\(203\) 1.52719e33 7.07729e32i 0.531130 0.246135i
\(204\) −5.06645e30 7.35117e30i −0.00164084 0.00238078i
\(205\) −8.62850e33 −2.60318
\(206\) −2.04357e33 −0.574532
\(207\) 1.72258e33 + 6.56087e32i 0.451451 + 0.171946i
\(208\) 7.51252e33i 1.83598i
\(209\) −1.97098e33 −0.449326
\(210\) 5.97096e33 + 3.52579e33i 1.27018 + 0.750026i
\(211\) 3.23925e33 0.643205 0.321603 0.946875i \(-0.395778\pi\)
0.321603 + 0.946875i \(0.395778\pi\)
\(212\) 1.75479e32i 0.0325352i
\(213\) 5.38357e33 3.71037e33i 0.932322 0.642560i
\(214\) −1.91953e33 −0.310595
\(215\) −1.17771e34 −1.78107
\(216\) −1.65550e33 6.77868e33i −0.234073 0.958442i
\(217\) 8.40000e33 3.89271e33i 1.11074 0.514738i
\(218\) 6.60612e33i 0.817198i
\(219\) −1.01203e34 + 6.97496e33i −1.17153 + 0.807425i
\(220\) 1.58690e32i 0.0171957i
\(221\) 1.96706e33i 0.199586i
\(222\) 6.21358e33 4.28242e33i 0.590506 0.406979i
\(223\) 1.73026e34i 1.54060i 0.637682 + 0.770300i \(0.279893\pi\)
−0.637682 + 0.770300i \(0.720107\pi\)
\(224\) 5.64011e32 2.61373e32i 0.0470643 0.0218104i
\(225\) −5.09996e33 + 1.33902e34i −0.398951 + 1.04746i
\(226\) 1.02093e34 0.748902
\(227\) −4.21542e33 −0.290046 −0.145023 0.989428i \(-0.546326\pi\)
−0.145023 + 0.989428i \(0.546326\pi\)
\(228\) 3.26653e32 2.25130e32i 0.0210878 0.0145338i
\(229\) 1.88113e34i 1.13974i 0.821736 + 0.569868i \(0.193006\pi\)
−0.821736 + 0.569868i \(0.806994\pi\)
\(230\) −1.25285e34 −0.712597
\(231\) 7.33785e33 + 4.33292e33i 0.391918 + 0.231423i
\(232\) 1.15124e34 0.577553
\(233\) 2.37783e34i 1.12078i 0.828229 + 0.560389i \(0.189348\pi\)
−0.828229 + 0.560389i \(0.810652\pi\)
\(234\) −1.45743e34 + 3.82653e34i −0.645589 + 1.69502i
\(235\) −2.28343e34 −0.950834
\(236\) 8.77931e32 0.0343745
\(237\) −2.06408e34 2.99488e34i −0.760109 1.10288i
\(238\) 2.95654e33 1.37011e33i 0.102428 0.0474669i
\(239\) 4.11101e34i 1.34023i −0.742258 0.670115i \(-0.766245\pi\)
0.742258 0.670115i \(-0.233755\pi\)
\(240\) 2.76127e34 + 4.00647e34i 0.847317 + 1.22942i
\(241\) 3.28350e34i 0.948614i −0.880359 0.474307i \(-0.842699\pi\)
0.880359 0.474307i \(-0.157301\pi\)
\(242\) 2.95170e34i 0.803062i
\(243\) −4.84072e33 + 3.87189e34i −0.124056 + 0.992275i
\(244\) 1.48414e33i 0.0358363i
\(245\) −4.13695e34 + 4.88291e34i −0.941395 + 1.11114i
\(246\) 6.94979e34 4.78982e34i 1.49078 1.02745i
\(247\) 8.74073e34 1.76784
\(248\) 6.33218e34 1.20782
\(249\) 1.99144e34 + 2.88948e34i 0.358325 + 0.519912i
\(250\) 1.05016e34i 0.178290i
\(251\) 1.41605e34 0.226887 0.113443 0.993544i \(-0.463812\pi\)
0.113443 + 0.993544i \(0.463812\pi\)
\(252\) −1.71102e33 + 1.20047e32i −0.0258790 + 0.00181570i
\(253\) −1.53965e34 −0.219874
\(254\) 2.37611e34i 0.320462i
\(255\) 7.23005e33 + 1.04904e34i 0.0921104 + 0.133648i
\(256\) 6.46138e33 0.0777761
\(257\) 6.39890e34 0.727906 0.363953 0.931417i \(-0.381427\pi\)
0.363953 + 0.931417i \(0.381427\pi\)
\(258\) 9.48583e34 6.53767e34i 1.01998 0.702970i
\(259\) 2.92842e34 + 6.31918e34i 0.297706 + 0.642413i
\(260\) 7.03743e33i 0.0676551i
\(261\) −6.01614e34 2.29139e34i −0.547055 0.208359i
\(262\) 4.91800e34i 0.423078i
\(263\) 1.20189e35i 0.978374i 0.872179 + 0.489187i \(0.162706\pi\)
−0.872179 + 0.489187i \(0.837294\pi\)
\(264\) 3.30753e34 + 4.79906e34i 0.254828 + 0.369742i
\(265\) 2.50416e35i 1.82640i
\(266\) 6.08817e34 + 1.31375e35i 0.420439 + 0.907255i
\(267\) −6.03890e34 8.76215e34i −0.394952 0.573056i
\(268\) 2.81282e33 0.0174256
\(269\) −2.28523e35 −1.34129 −0.670643 0.741780i \(-0.733982\pi\)
−0.670643 + 0.741780i \(0.733982\pi\)
\(270\) −6.29213e34 2.57640e35i −0.349964 1.43297i
\(271\) 2.80968e35i 1.48116i −0.671968 0.740581i \(-0.734551\pi\)
0.671968 0.740581i \(-0.265449\pi\)
\(272\) 2.28659e34 0.114272
\(273\) −3.25412e35 1.92152e35i −1.54197 0.910515i
\(274\) 2.43341e35 1.09353
\(275\) 1.19682e35i 0.510156i
\(276\) 2.55168e33 1.75862e33i 0.0103191 0.00711199i
\(277\) −3.34384e35 −1.28319 −0.641593 0.767046i \(-0.721726\pi\)
−0.641593 + 0.767046i \(0.721726\pi\)
\(278\) 3.65424e34 0.133091
\(279\) −3.30905e35 1.26033e35i −1.14404 0.435736i
\(280\) −3.97145e35 + 1.84044e35i −1.30364 + 0.604131i
\(281\) 2.59745e35i 0.809666i −0.914391 0.404833i \(-0.867330\pi\)
0.914391 0.404833i \(-0.132670\pi\)
\(282\) 1.83918e35 1.26757e35i 0.544519 0.375285i
\(283\) 3.56363e35i 1.00228i −0.865366 0.501140i \(-0.832914\pi\)
0.865366 0.501140i \(-0.167086\pi\)
\(284\) 1.09924e34i 0.0293749i
\(285\) −4.66148e35 + 3.21271e35i −1.18379 + 0.815869i
\(286\) 3.42017e35i 0.825543i
\(287\) 3.27539e35 + 7.06790e35i 0.751581 + 1.62182i
\(288\) −2.22184e34 8.46238e33i −0.0484753 0.0184630i
\(289\) −4.75981e35 −0.987578
\(290\) 4.37557e35 0.863503
\(291\) 1.17446e34 8.09441e33i 0.0220490 0.0151963i
\(292\) 2.06641e34i 0.0369118i
\(293\) 5.56455e35 0.945910 0.472955 0.881087i \(-0.343187\pi\)
0.472955 + 0.881087i \(0.343187\pi\)
\(294\) 6.21505e34 6.22941e35i 0.100556 1.00788i
\(295\) −1.25285e36 −1.92965
\(296\) 4.76359e35i 0.698562i
\(297\) −7.73254e34 3.16619e35i −0.107983 0.442149i
\(298\) −4.20062e35 −0.558699
\(299\) 6.82790e35 0.865077
\(300\) 1.36703e34 + 1.98349e34i 0.0165014 + 0.0239427i
\(301\) 4.47061e35 + 9.64703e35i 0.514225 + 1.10963i
\(302\) 1.18038e36i 1.29396i
\(303\) 8.43091e35 + 1.22328e36i 0.880960 + 1.27823i
\(304\) 1.01606e36i 1.01216i
\(305\) 2.11794e36i 2.01171i
\(306\) −1.16468e35 4.43597e34i −0.105499 0.0401817i
\(307\) 8.46425e35i 0.731277i −0.930757 0.365639i \(-0.880851\pi\)
0.930757 0.365639i \(-0.119149\pi\)
\(308\) 1.29988e34 6.02390e33i 0.0107132 0.00496469i
\(309\) −5.93956e35 + 4.09357e35i −0.467042 + 0.321887i
\(310\) 2.40669e36 1.80583
\(311\) 1.53663e36 1.10038 0.550192 0.835038i \(-0.314554\pi\)
0.550192 + 0.835038i \(0.314554\pi\)
\(312\) −1.46679e36 2.12824e36i −1.00260 1.45472i
\(313\) 2.33745e36i 1.52528i −0.646824 0.762639i \(-0.723903\pi\)
0.646824 0.762639i \(-0.276097\pi\)
\(314\) −8.28813e35 −0.516388
\(315\) 2.44171e36 1.71313e35i 1.45275 0.101927i
\(316\) −6.11508e34 −0.0347488
\(317\) 9.66443e35i 0.524586i 0.964988 + 0.262293i \(0.0844787\pi\)
−0.964988 + 0.262293i \(0.915521\pi\)
\(318\) −1.39010e36 2.01696e36i −0.720862 1.04594i
\(319\) 5.37724e35 0.266437
\(320\) −2.99174e36 −1.41660
\(321\) −5.57904e35 + 3.84509e35i −0.252485 + 0.174014i
\(322\) 4.75582e35 + 1.02625e36i 0.205739 + 0.443959i
\(323\) 2.66042e35i 0.110031i
\(324\) 4.89802e34 + 4.36413e34i 0.0193695 + 0.0172582i
\(325\) 5.30753e36i 2.00717i
\(326\) 2.79310e36i 1.01025i
\(327\) 1.32330e36 + 1.92005e36i 0.457843 + 0.664308i
\(328\) 5.32800e36i 1.76357i
\(329\) 8.66796e35 + 1.87044e36i 0.274522 + 0.592384i
\(330\) 1.25710e36 + 1.82399e36i 0.380994 + 0.552804i
\(331\) −5.63257e36 −1.63381 −0.816903 0.576775i \(-0.804311\pi\)
−0.816903 + 0.576775i \(0.804311\pi\)
\(332\) 5.89987e34 0.0163810
\(333\) 9.48126e35 2.48935e36i 0.252014 0.661674i
\(334\) 9.73400e35i 0.247724i
\(335\) −4.01402e36 −0.978205
\(336\) 2.23365e36 3.78271e36i 0.521310 0.882844i
\(337\) 4.78446e36 1.06955 0.534773 0.844996i \(-0.320397\pi\)
0.534773 + 0.844996i \(0.320397\pi\)
\(338\) 1.04375e37i 2.23514i
\(339\) 2.96731e36 2.04508e36i 0.608789 0.419580i
\(340\) 2.14198e34 0.00421087
\(341\) 2.95764e36 0.557194
\(342\) 1.97114e36 5.17533e36i 0.355910 0.934457i
\(343\) 5.57015e36 + 1.53515e36i 0.964056 + 0.265697i
\(344\) 7.27223e36i 1.20662i
\(345\) −3.64135e36 + 2.50963e36i −0.579277 + 0.399240i
\(346\) 4.14878e36i 0.632873i
\(347\) 1.75513e36i 0.256762i 0.991725 + 0.128381i \(0.0409781\pi\)
−0.991725 + 0.128381i \(0.959022\pi\)
\(348\) −8.91175e34 + 6.14201e34i −0.0125044 + 0.00861810i
\(349\) 8.95480e36i 1.20528i −0.798014 0.602639i \(-0.794116\pi\)
0.798014 0.602639i \(-0.205884\pi\)
\(350\) −7.97733e36 + 3.69684e36i −1.03008 + 0.477358i
\(351\) 3.42915e36 + 1.40411e37i 0.424848 + 1.73960i
\(352\) 1.98588e35 0.0236094
\(353\) −1.46102e37 −1.66695 −0.833473 0.552560i \(-0.813651\pi\)
−0.833473 + 0.552560i \(0.813651\pi\)
\(354\) 1.00910e37 6.95476e36i 1.10506 0.761613i
\(355\) 1.56866e37i 1.64899i
\(356\) −1.78909e35 −0.0180554
\(357\) 5.84854e35 9.90457e35i 0.0566707 0.0959725i
\(358\) −1.69555e37 −1.57764
\(359\) 1.05987e37i 0.947071i −0.880775 0.473535i \(-0.842978\pi\)
0.880775 0.473535i \(-0.157022\pi\)
\(360\) 1.56449e37 + 5.95874e36i 1.34273 + 0.511409i
\(361\) 3.08130e35 0.0254027
\(362\) 2.82358e36 0.223628
\(363\) −5.91269e36 8.57902e36i −0.449924 0.652817i
\(364\) −5.76460e35 + 2.67142e35i −0.0421501 + 0.0195331i
\(365\) 2.94886e37i 2.07209i
\(366\) 1.17570e37 + 1.70588e37i 0.794001 + 1.15206i
\(367\) 1.41449e37i 0.918207i 0.888383 + 0.459103i \(0.151829\pi\)
−0.888383 + 0.459103i \(0.848171\pi\)
\(368\) 7.93701e36i 0.495295i
\(369\) 1.06046e37 2.78429e37i 0.636228 1.67045i
\(370\) 1.81051e37i 1.04442i
\(371\) 2.05124e37 9.50583e36i 1.13788 0.527313i
\(372\) −4.90172e35 + 3.37828e35i −0.0261503 + 0.0180229i
\(373\) 2.24839e36 0.115370 0.0576850 0.998335i \(-0.481628\pi\)
0.0576850 + 0.998335i \(0.481628\pi\)
\(374\) 1.04100e36 0.0513820
\(375\) −2.10363e36 3.05227e36i −0.0998887 0.144934i
\(376\) 1.41000e37i 0.644160i
\(377\) −2.38465e37 −1.04827
\(378\) −1.87157e37 + 1.49341e37i −0.791724 + 0.631756i
\(379\) 7.15894e36 0.291461 0.145730 0.989324i \(-0.453447\pi\)
0.145730 + 0.989324i \(0.453447\pi\)
\(380\) 9.51801e35i 0.0372979i
\(381\) −4.75969e36 6.90607e36i −0.179542 0.260507i
\(382\) −2.10216e37 −0.763390
\(383\) −2.50212e37 −0.874833 −0.437416 0.899259i \(-0.644106\pi\)
−0.437416 + 0.899259i \(0.644106\pi\)
\(384\) 2.53655e37 1.74820e37i 0.853965 0.588556i
\(385\) −1.85499e37 + 8.59637e36i −0.601397 + 0.278698i
\(386\) 5.06952e37i 1.58289i
\(387\) 1.44743e37 3.80030e37i 0.435301 1.14290i
\(388\) 2.39806e34i 0.000694705i
\(389\) 5.39063e37i 1.50442i −0.658922 0.752211i \(-0.728987\pi\)
0.658922 0.752211i \(-0.271013\pi\)
\(390\) −5.57488e37 8.08887e37i −1.49899 2.17496i
\(391\) 2.07821e36i 0.0538426i
\(392\) 3.01514e37 + 2.55452e37i 0.752766 + 0.637766i
\(393\) 9.85148e36 + 1.42940e37i 0.237033 + 0.343924i
\(394\) 2.23273e37 0.517776
\(395\) 8.72648e37 1.95066
\(396\) −5.12069e35 1.95034e35i −0.0110344 0.00420271i
\(397\) 4.27254e37i 0.887614i 0.896122 + 0.443807i \(0.146372\pi\)
−0.896122 + 0.443807i \(0.853628\pi\)
\(398\) −4.05370e37 −0.811983
\(399\) 4.40114e37 + 2.59883e37i 0.850078 + 0.501962i
\(400\) −6.16967e37 −1.14919
\(401\) 3.95033e37i 0.709644i −0.934934 0.354822i \(-0.884542\pi\)
0.934934 0.354822i \(-0.115458\pi\)
\(402\) 3.23308e37 2.22825e37i 0.560194 0.386088i
\(403\) −1.31163e38 −2.19223
\(404\) 2.49775e36 0.0402735
\(405\) −6.98969e37 6.22781e37i −1.08733 0.968807i
\(406\) −1.66098e37 3.58418e37i −0.249308 0.537976i
\(407\) 2.22498e37i 0.322261i
\(408\) 6.47773e36 4.46447e36i 0.0905421 0.0624019i
\(409\) 4.52233e37i 0.610062i 0.952342 + 0.305031i \(0.0986668\pi\)
−0.952342 + 0.305031i \(0.901333\pi\)
\(410\) 2.02503e38i 2.63673i
\(411\) 7.07262e37 4.87447e37i 0.888943 0.612662i
\(412\) 1.21277e36i 0.0147152i
\(413\) 4.75583e37 + 1.02625e38i 0.557122 + 1.20220i
\(414\) 1.53978e37 4.04275e37i 0.174162 0.457269i
\(415\) −8.41938e37 −0.919565
\(416\) −8.80680e36 −0.0928892
\(417\) 1.06209e37 7.31999e36i 0.108191 0.0745655i
\(418\) 4.62572e37i 0.455117i
\(419\) −7.07947e36 −0.0672818 −0.0336409 0.999434i \(-0.510710\pi\)
−0.0336409 + 0.999434i \(0.510710\pi\)
\(420\) 2.09240e36 3.54350e36i 0.0192101 0.0325325i
\(421\) 1.12032e38 0.993695 0.496847 0.867838i \(-0.334491\pi\)
0.496847 + 0.867838i \(0.334491\pi\)
\(422\) 7.60224e37i 0.651495i
\(423\) 2.80640e37 7.36832e37i 0.232388 0.610145i
\(424\) 1.54629e38 1.23733
\(425\) −1.61545e37 −0.124927
\(426\) −8.70792e37 1.26348e38i −0.650841 0.944338i
\(427\) −1.73487e38 + 8.03972e37i −1.25333 + 0.580814i
\(428\) 1.13915e36i 0.00795513i
\(429\) −6.85110e37 9.94060e37i −0.462519 0.671092i
\(430\) 2.76398e38i 1.80402i
\(431\) 1.65534e38i 1.04464i 0.852750 + 0.522319i \(0.174933\pi\)
−0.852750 + 0.522319i \(0.825067\pi\)
\(432\) −1.63220e38 + 3.98618e37i −0.995997 + 0.243244i
\(433\) 1.72286e38i 1.01666i −0.861163 0.508330i \(-0.830263\pi\)
0.861163 0.508330i \(-0.169737\pi\)
\(434\) −9.13585e37 1.97140e38i −0.521372 1.12506i
\(435\) 1.27175e38 8.76492e37i 0.701950 0.483786i
\(436\) 3.92044e36 0.0209305
\(437\) −9.23462e37 −0.476912
\(438\) 1.63696e38 + 2.37515e38i 0.817831 + 1.18663i
\(439\) 2.02612e38i 0.979332i 0.871910 + 0.489666i \(0.162881\pi\)
−0.871910 + 0.489666i \(0.837119\pi\)
\(440\) −1.39835e38 −0.653961
\(441\) −1.06720e38 1.93506e38i −0.482934 0.875657i
\(442\) −4.61651e37 −0.202158
\(443\) 6.37635e37i 0.270220i 0.990831 + 0.135110i \(0.0431388\pi\)
−0.990831 + 0.135110i \(0.956861\pi\)
\(444\) −2.54143e36 3.68748e36i −0.0104238 0.0151244i
\(445\) 2.55311e38 1.01356
\(446\) 4.06075e38 1.56045
\(447\) −1.22090e38 + 8.41446e37i −0.454171 + 0.313017i
\(448\) 1.13567e38 + 2.45063e38i 0.408997 + 0.882566i
\(449\) 2.27296e38i 0.792536i 0.918135 + 0.396268i \(0.129695\pi\)
−0.918135 + 0.396268i \(0.870305\pi\)
\(450\) 3.14255e38 + 1.19691e38i 1.06096 + 0.404093i
\(451\) 2.48861e38i 0.813573i
\(452\) 6.05878e36i 0.0191813i
\(453\) −2.36447e38 3.43072e38i −0.724952 1.05187i
\(454\) 9.89322e37i 0.293784i
\(455\) 8.22634e38 3.81224e38i 2.36614 1.09651i
\(456\) 1.98381e38 + 2.87841e38i 0.552726 + 0.801978i
\(457\) −1.56674e38 −0.422875 −0.211438 0.977391i \(-0.567815\pi\)
−0.211438 + 0.977391i \(0.567815\pi\)
\(458\) 4.41485e38 1.15443
\(459\) −4.27370e37 + 1.04373e37i −0.108273 + 0.0264427i
\(460\) 7.43508e36i 0.0182514i
\(461\) −6.49971e38 −1.54607 −0.773037 0.634360i \(-0.781264\pi\)
−0.773037 + 0.634360i \(0.781264\pi\)
\(462\) 1.01690e38 1.72213e38i 0.234406 0.396969i
\(463\) 1.98052e38 0.442441 0.221220 0.975224i \(-0.428996\pi\)
0.221220 + 0.975224i \(0.428996\pi\)
\(464\) 2.77201e38i 0.600183i
\(465\) 6.99497e38 4.82096e38i 1.46797 1.01173i
\(466\) 5.58055e38 1.13522
\(467\) 1.84901e38 0.364624 0.182312 0.983241i \(-0.441642\pi\)
0.182312 + 0.983241i \(0.441642\pi\)
\(468\) 2.27088e37 + 8.64917e36i 0.0434139 + 0.0165352i
\(469\) 1.52373e38 + 3.28802e38i 0.282424 + 0.609436i
\(470\) 5.35902e38i 0.963088i
\(471\) −2.40892e38 + 1.66023e38i −0.419777 + 0.289312i
\(472\) 7.73619e38i 1.30728i
\(473\) 3.39672e38i 0.556638i
\(474\) −7.02871e38 + 4.84421e38i −1.11709 + 0.769906i
\(475\) 7.17834e38i 1.10654i
\(476\) −8.13101e35 1.75457e36i −0.00121575 0.00262344i
\(477\) −8.08055e38 3.07767e38i −1.17199 0.446381i
\(478\) −9.64817e38 −1.35750
\(479\) −5.59195e38 −0.763305 −0.381652 0.924306i \(-0.624645\pi\)
−0.381652 + 0.924306i \(0.624645\pi\)
\(480\) 4.69672e37 3.23699e37i 0.0622009 0.0428690i
\(481\) 9.86715e38i 1.26791i
\(482\) −7.70608e38 −0.960840
\(483\) 3.43799e38 + 2.03010e38i 0.415979 + 0.245631i
\(484\) −1.75170e37 −0.0205685
\(485\) 3.42214e37i 0.0389980i
\(486\) 9.08698e38 + 1.13607e38i 1.00506 + 0.125655i
\(487\) −1.68468e39 −1.80862 −0.904309 0.426877i \(-0.859614\pi\)
−0.904309 + 0.426877i \(0.859614\pi\)
\(488\) −1.30780e39 −1.36287
\(489\) −5.59498e38 8.11804e38i −0.566005 0.821245i
\(490\) 1.14598e39 + 9.70905e38i 1.12547 + 0.953528i
\(491\) 1.10505e39i 1.05366i 0.849972 + 0.526828i \(0.176619\pi\)
−0.849972 + 0.526828i \(0.823381\pi\)
\(492\) −2.84254e37 4.12439e37i −0.0263156 0.0381826i
\(493\) 7.25816e37i 0.0652448i
\(494\) 2.05137e39i 1.79062i
\(495\) 7.30745e38 + 2.78322e38i 0.619428 + 0.235924i
\(496\) 1.52468e39i 1.25515i
\(497\) 1.28495e39 5.95468e38i 1.02735 0.476092i
\(498\) 6.78136e38 4.67373e38i 0.526612 0.362943i
\(499\) −6.45263e38 −0.486720 −0.243360 0.969936i \(-0.578250\pi\)
−0.243360 + 0.969936i \(0.578250\pi\)
\(500\) −6.23225e36 −0.00456646
\(501\) 1.94986e38 + 2.82915e38i 0.138790 + 0.201377i
\(502\) 3.32334e38i 0.229811i
\(503\) −1.83229e39 −1.23100 −0.615499 0.788138i \(-0.711045\pi\)
−0.615499 + 0.788138i \(0.711045\pi\)
\(504\) −1.05784e38 1.50773e39i −0.0690520 0.984192i
\(505\) −3.56440e39 −2.26080
\(506\) 3.61342e38i 0.222708i
\(507\) 2.09079e39 + 3.03363e39i 1.25226 + 1.81697i
\(508\) −1.41011e37 −0.00820786
\(509\) −1.09277e39 −0.618190 −0.309095 0.951031i \(-0.600026\pi\)
−0.309095 + 0.951031i \(0.600026\pi\)
\(510\) 2.46201e38 1.69683e38i 0.135370 0.0932975i
\(511\) −2.41551e39 + 1.11939e39i −1.29094 + 0.598246i
\(512\) 1.84477e39i 0.958359i
\(513\) −4.63788e38 1.89904e39i −0.234216 0.959031i
\(514\) 1.50177e39i 0.737287i
\(515\) 1.73067e39i 0.826056i
\(516\) −3.87981e37 5.62941e37i −0.0180049 0.0261242i
\(517\) 6.58582e38i 0.297164i
\(518\) 1.48305e39 6.87275e38i 0.650692 0.301543i
\(519\) −8.31061e38 1.20583e39i −0.354573 0.514468i
\(520\) 6.20127e39 2.57295
\(521\) 3.12908e38 0.126261 0.0631305 0.998005i \(-0.479892\pi\)
0.0631305 + 0.998005i \(0.479892\pi\)
\(522\) −5.37768e38 + 1.41193e39i −0.211044 + 0.554105i
\(523\) 3.64988e39i 1.39317i −0.717474 0.696586i \(-0.754702\pi\)
0.717474 0.696586i \(-0.245298\pi\)
\(524\) 2.91861e37 0.0108361
\(525\) −1.57805e39 + 2.67245e39i −0.569917 + 0.965162i
\(526\) 2.82072e39 0.990983
\(527\) 3.99220e38i 0.136445i
\(528\) 1.15553e39 7.96398e38i 0.384230 0.264812i
\(529\) 2.36969e39 0.766627
\(530\) 5.87703e39 1.84994
\(531\) 1.53978e39 4.04275e39i 0.471615 1.23825i
\(532\) 7.79653e37 3.61305e37i 0.0232371 0.0107685i
\(533\) 1.10362e40i 3.20093i
\(534\) −2.05640e39 + 1.41728e39i −0.580442 + 0.400043i
\(535\) 1.62562e39i 0.446570i
\(536\) 2.47861e39i 0.662703i
\(537\) −4.92807e39 + 3.39644e39i −1.28248 + 0.883888i
\(538\) 5.36323e39i 1.35857i
\(539\) 1.40832e39 + 1.19317e39i 0.347267 + 0.294215i
\(540\) −1.52898e38 + 3.73410e37i −0.0367021 + 0.00896347i
\(541\) 1.94010e39 0.453382 0.226691 0.973967i \(-0.427209\pi\)
0.226691 + 0.973967i \(0.427209\pi\)
\(542\) −6.59407e39 −1.50025
\(543\) 8.20665e38 5.65605e38i 0.181789 0.125290i
\(544\) 2.68053e37i 0.00578145i
\(545\) −5.59463e39 −1.17496
\(546\) −4.50964e39 + 7.63713e39i −0.922250 + 1.56184i
\(547\) 2.66457e39 0.530654 0.265327 0.964158i \(-0.414520\pi\)
0.265327 + 0.964158i \(0.414520\pi\)
\(548\) 1.44412e38i 0.0280082i
\(549\) 6.83427e39 + 2.60299e39i 1.29090 + 0.491670i
\(550\) −2.80882e39 −0.516731
\(551\) 3.22520e39 0.577907
\(552\) 1.54967e39 + 2.24850e39i 0.270472 + 0.392442i
\(553\) −3.31259e39 7.14816e39i −0.563188 1.21529i
\(554\) 7.84770e39i 1.29972i
\(555\) 3.62673e39 + 5.26220e39i 0.585149 + 0.849023i
\(556\) 2.16863e37i 0.00340880i
\(557\) 5.86087e39i 0.897557i −0.893643 0.448779i \(-0.851859\pi\)
0.893643 0.448779i \(-0.148141\pi\)
\(558\) −2.95788e39 + 7.76605e39i −0.441352 + 1.15879i
\(559\) 1.50635e40i 2.19005i
\(560\) 4.43149e39 + 9.56261e39i 0.627803 + 1.35472i
\(561\) 3.02562e38 2.08527e38i 0.0417689 0.0287873i
\(562\) −6.09599e39 −0.820101
\(563\) −2.96898e39 −0.389256 −0.194628 0.980877i \(-0.562350\pi\)
−0.194628 + 0.980877i \(0.562350\pi\)
\(564\) −7.52247e37 1.09147e38i −0.00961200 0.0139465i
\(565\) 8.64614e39i 1.07676i
\(566\) −8.36352e39 −1.01520
\(567\) −2.44811e39 + 8.08958e39i −0.289652 + 0.957132i
\(568\) 9.68633e39 1.11714
\(569\) 9.01376e39i 1.01339i 0.862124 + 0.506697i \(0.169134\pi\)
−0.862124 + 0.506697i \(0.830866\pi\)
\(570\) 7.53993e39 + 1.09401e40i 0.826384 + 1.19904i
\(571\) −6.18707e39 −0.661092 −0.330546 0.943790i \(-0.607233\pi\)
−0.330546 + 0.943790i \(0.607233\pi\)
\(572\) −2.02972e38 −0.0211443
\(573\) −6.10985e39 + 4.21093e39i −0.620567 + 0.427697i
\(574\) 1.65877e40 7.68705e39i 1.64272 0.761268i
\(575\) 5.60742e39i 0.541477i
\(576\) 3.67691e39 9.65390e39i 0.346224 0.909027i
\(577\) 5.79829e39i 0.532416i 0.963916 + 0.266208i \(0.0857707\pi\)
−0.963916 + 0.266208i \(0.914229\pi\)
\(578\) 1.11709e40i 1.00031i
\(579\) −1.01550e40 1.47344e40i −0.886830 1.28675i
\(580\) 2.59671e38i 0.0221165i
\(581\) 3.19601e39 + 6.89660e39i 0.265494 + 0.572903i
\(582\) −1.89969e38 2.75635e38i −0.0153921 0.0223332i
\(583\) 7.22242e39 0.570806
\(584\) −1.82089e40 −1.40377
\(585\) −3.24064e40 1.23427e40i −2.43709 0.928221i
\(586\) 1.30595e40i 0.958101i
\(587\) 2.32280e40 1.66249 0.831245 0.555907i \(-0.187629\pi\)
0.831245 + 0.555907i \(0.187629\pi\)
\(588\) −3.69688e38 3.68835e37i −0.0258145 0.00257550i
\(589\) 1.77395e40 1.20857
\(590\) 2.94032e40i 1.95452i
\(591\) 6.48937e39 4.47249e39i 0.420905 0.290089i
\(592\) 1.14700e40 0.725934
\(593\) 2.10136e40 1.29780 0.648899 0.760875i \(-0.275230\pi\)
0.648899 + 0.760875i \(0.275230\pi\)
\(594\) −7.43077e39 + 1.81476e39i −0.447848 + 0.109374i
\(595\) 1.16033e39 + 2.50385e39i 0.0682474 + 0.147269i
\(596\) 2.49288e38i 0.0143097i
\(597\) −1.17819e40 + 8.12016e39i −0.660069 + 0.454922i
\(598\) 1.60245e40i 0.876226i
\(599\) 1.68953e40i 0.901728i −0.892593 0.450864i \(-0.851116\pi\)
0.892593 0.450864i \(-0.148884\pi\)
\(600\) −1.74782e40 + 1.20460e40i −0.910550 + 0.627555i
\(601\) 7.63589e39i 0.388311i 0.980971 + 0.194156i \(0.0621966\pi\)
−0.980971 + 0.194156i \(0.937803\pi\)
\(602\) 2.26407e40 1.04921e40i 1.12393 0.520852i
\(603\) 4.93333e39 1.29527e40i 0.239078 0.627709i
\(604\) −7.00500e38 −0.0331415
\(605\) 2.49975e40 1.15463
\(606\) 2.87093e40 1.97866e40i 1.29470 0.892314i
\(607\) 1.38282e40i 0.608878i 0.952532 + 0.304439i \(0.0984690\pi\)
−0.952532 + 0.304439i \(0.901531\pi\)
\(608\) 1.19111e39 0.0512093
\(609\) −1.20072e40 7.09013e39i −0.504071 0.297648i
\(610\) −4.97060e40 −2.03764
\(611\) 2.92062e40i 1.16917i
\(612\) −2.63255e37 + 6.91187e37i −0.00102916 + 0.00270209i
\(613\) 1.09697e40 0.418812 0.209406 0.977829i \(-0.432847\pi\)
0.209406 + 0.977829i \(0.432847\pi\)
\(614\) −1.98648e40 −0.740702
\(615\) 4.05643e40 + 5.88569e40i 1.47725 + 2.14342i
\(616\) 5.30816e39 + 1.14544e40i 0.188809 + 0.407428i
\(617\) 4.32531e39i 0.150273i −0.997173 0.0751367i \(-0.976061\pi\)
0.997173 0.0751367i \(-0.0239393\pi\)
\(618\) 9.60723e39 + 1.39396e40i 0.326036 + 0.473062i
\(619\) 4.58735e40i 1.52071i −0.649506 0.760357i \(-0.725024\pi\)
0.649506 0.760357i \(-0.274976\pi\)
\(620\) 1.42826e39i 0.0462518i
\(621\) −3.62292e39 1.48345e40i −0.114612 0.469294i
\(622\) 3.60634e40i 1.11457i
\(623\) −9.69167e39 2.09134e40i −0.292632 0.631464i
\(624\) −5.12445e40 + 3.53179e40i −1.51172 + 1.04188i
\(625\) −2.99942e40 −0.864524
\(626\) −5.48578e40 −1.54494
\(627\) 9.26600e39 + 1.34445e40i 0.254984 + 0.369969i
\(628\) 4.91863e38i 0.0132260i
\(629\) 3.00327e39 0.0789150
\(630\) −4.02056e39 5.73047e40i −0.103240 1.47147i
\(631\) −1.09303e40 −0.274288 −0.137144 0.990551i \(-0.543792\pi\)
−0.137144 + 0.990551i \(0.543792\pi\)
\(632\) 5.38851e40i 1.32151i
\(633\) −1.52284e40 2.20957e40i −0.365007 0.529606i
\(634\) 2.26815e40 0.531347
\(635\) 2.01229e40 0.460757
\(636\) −1.19698e39 + 8.24961e38i −0.0267891 + 0.0184631i
\(637\) −6.24547e40 5.29134e40i −1.36629 1.15756i
\(638\) 1.26199e40i 0.269871i
\(639\) −5.06186e40 1.92793e40i −1.05815 0.403021i
\(640\) 7.39099e40i 1.51040i
\(641\) 2.14381e40i 0.428297i −0.976801 0.214149i \(-0.931302\pi\)
0.976801 0.214149i \(-0.0686977\pi\)
\(642\) 9.02409e39 + 1.30935e40i 0.176257 + 0.255740i
\(643\) 5.85246e40i 1.11758i −0.829309 0.558791i \(-0.811266\pi\)
0.829309 0.558791i \(-0.188734\pi\)
\(644\) 6.09033e38 2.82237e38i 0.0113709 0.00526949i
\(645\) 5.53666e40 + 8.03342e40i 1.01072 + 1.46651i
\(646\) 6.24376e39 0.111449
\(647\) −1.08177e41 −1.88809 −0.944045 0.329817i \(-0.893013\pi\)
−0.944045 + 0.329817i \(0.893013\pi\)
\(648\) −3.84560e40 + 4.31606e40i −0.656337 + 0.736630i
\(649\) 3.61342e40i 0.603074i
\(650\) 1.24563e41 2.03304
\(651\) −6.60432e40 3.89978e40i −1.05415 0.622466i
\(652\) −1.65758e39 −0.0258752
\(653\) 1.08910e40i 0.166275i 0.996538 + 0.0831375i \(0.0264941\pi\)
−0.996538 + 0.0831375i \(0.973506\pi\)
\(654\) 4.50618e40 3.10567e40i 0.672870 0.463744i
\(655\) −4.16499e40 −0.608296
\(656\) 1.28289e41 1.83267
\(657\) 9.51555e40 + 3.62422e40i 1.32965 + 0.506427i
\(658\) 4.38975e40 2.03429e40i 0.600019 0.278060i
\(659\) 7.93936e40i 1.06157i 0.847508 + 0.530783i \(0.178102\pi\)
−0.847508 + 0.530783i \(0.821898\pi\)
\(660\) 1.08246e39 7.46034e38i 0.0141587 0.00975824i
\(661\) 2.45659e39i 0.0314349i −0.999876 0.0157174i \(-0.994997\pi\)
0.999876 0.0157174i \(-0.00500323\pi\)
\(662\) 1.32191e41i 1.65486i
\(663\) −1.34178e40 + 9.24756e39i −0.164336 + 0.113261i
\(664\) 5.19887e40i 0.622977i
\(665\) −1.11260e41 + 5.15599e40i −1.30444 + 0.604502i
\(666\) −5.84227e40 2.22517e40i −0.670201 0.255262i
\(667\) 2.51939e40 0.282795
\(668\) 5.77669e38 0.00634484
\(669\) 1.18024e41 8.13429e40i 1.26851 0.874260i
\(670\) 9.42054e40i 0.990812i
\(671\) −6.10849e40 −0.628720
\(672\) −4.43441e39 2.61847e39i −0.0446665 0.0263751i
\(673\) −1.64622e40 −0.162281 −0.0811406 0.996703i \(-0.525856\pi\)
−0.0811406 + 0.996703i \(0.525856\pi\)
\(674\) 1.12287e41i 1.08333i
\(675\) 1.15313e41 2.81620e40i 1.08887 0.265925i
\(676\) 6.19420e39 0.0572477
\(677\) −1.26236e41 −1.14195 −0.570975 0.820967i \(-0.693435\pi\)
−0.570975 + 0.820967i \(0.693435\pi\)
\(678\) −4.79962e40 6.96401e40i −0.424987 0.616636i
\(679\) 2.80319e39 1.29905e39i 0.0242963 0.0112594i
\(680\) 1.88748e40i 0.160141i
\(681\) 1.98176e40 + 2.87543e40i 0.164595 + 0.238820i
\(682\) 6.94131e40i 0.564376i
\(683\) 5.39341e40i 0.429302i 0.976691 + 0.214651i \(0.0688615\pi\)
−0.976691 + 0.214651i \(0.931139\pi\)
\(684\) −3.07132e39 1.16979e39i −0.0239338 0.00911576i
\(685\) 2.06082e41i 1.57227i
\(686\) 3.60287e40 1.30727e41i 0.269122 0.976482i
\(687\) 1.28316e41 8.84359e40i 0.938444 0.646779i
\(688\) 1.75103e41 1.25390
\(689\) −3.20293e41 −2.24579
\(690\) 5.88989e40 + 8.54593e40i 0.404385 + 0.586743i
\(691\) 7.81794e40i 0.525606i 0.964849 + 0.262803i \(0.0846470\pi\)
−0.964849 + 0.262803i \(0.915353\pi\)
\(692\) −2.46211e39 −0.0162095
\(693\) −4.94096e39 7.04230e40i −0.0318551 0.454028i
\(694\) 4.11913e40 0.260072
\(695\) 3.09473e40i 0.191356i
\(696\) −5.41224e40 7.85289e40i −0.327750 0.475549i
\(697\) 3.35910e40 0.199227
\(698\) −2.10161e41 −1.22081
\(699\) 1.62197e41 1.11787e41i 0.922834 0.636020i
\(700\) 2.19391e39 + 4.73419e39i 0.0122264 + 0.0263830i
\(701\) 3.07719e41i 1.67974i −0.542785 0.839872i \(-0.682630\pi\)
0.542785 0.839872i \(-0.317370\pi\)
\(702\) 3.29533e41 8.04792e40i 1.76202 0.430324i
\(703\) 1.33452e41i 0.698991i
\(704\) 8.62868e40i 0.442732i
\(705\) 1.07349e41 + 1.55758e41i 0.539580 + 0.782904i
\(706\) 3.42887e41i 1.68843i
\(707\) 1.35305e41 + 2.91972e41i 0.652730 + 1.40851i
\(708\) −4.12734e39 5.98856e39i −0.0195069 0.0283035i
\(709\) −4.46581e40 −0.206790 −0.103395 0.994640i \(-0.532971\pi\)
−0.103395 + 0.994640i \(0.532971\pi\)
\(710\) 3.68152e41 1.67025
\(711\) −1.07251e41 + 2.81591e41i −0.476750 + 1.25173i
\(712\) 1.57652e41i 0.686656i
\(713\) 1.38574e41 0.591403
\(714\) −2.32451e40 1.37260e40i −0.0972094 0.0574011i
\(715\) 2.89649e41 1.18696
\(716\) 1.00623e40i 0.0404074i
\(717\) −2.80421e41 + 1.93267e41i −1.10353 + 0.760554i
\(718\) −2.48742e41 −0.959277
\(719\) 6.81653e40 0.257629 0.128814 0.991669i \(-0.458883\pi\)
0.128814 + 0.991669i \(0.458883\pi\)
\(720\) 1.43477e41 3.76705e41i 0.531448 1.39534i
\(721\) −1.41765e41 + 6.56965e40i −0.514645 + 0.238496i
\(722\) 7.23153e39i 0.0257300i
\(723\) −2.23975e41 + 1.54364e41i −0.781076 + 0.538320i
\(724\) 1.67567e39i 0.00572769i
\(725\) 1.95840e41i 0.656145i
\(726\) −2.01342e41 + 1.38765e41i −0.661231 + 0.455722i
\(727\) 8.26628e40i 0.266110i 0.991109 + 0.133055i \(0.0424787\pi\)
−0.991109 + 0.133055i \(0.957521\pi\)
\(728\) −2.35401e41 5.07967e41i −0.742855 1.60299i
\(729\) 2.86867e41 1.49006e41i 0.887426 0.460951i
\(730\) −6.92071e41 −2.09879
\(731\) 4.58487e40 0.136309
\(732\) 1.01237e40 6.97726e39i 0.0295071 0.0203364i
\(733\) 1.95437e41i 0.558469i 0.960223 + 0.279235i \(0.0900807\pi\)
−0.960223 + 0.279235i \(0.909919\pi\)
\(734\) 3.31967e41 0.930041
\(735\) 5.27561e41 + 5.26344e40i 1.44913 + 0.144578i
\(736\) 9.30443e39 0.0250589
\(737\) 1.15771e41i 0.305719i
\(738\) −6.53448e41 2.48881e41i −1.69197 0.644428i
\(739\) 5.29225e41 1.34368 0.671841 0.740696i \(-0.265504\pi\)
0.671841 + 0.740696i \(0.265504\pi\)
\(740\) 1.07446e40 0.0267504
\(741\) −4.10920e41 5.96224e41i −1.00321 1.45561i
\(742\) −2.23093e41 4.81408e41i −0.534109 1.15254i
\(743\) 4.92649e41i 1.15664i 0.815809 + 0.578322i \(0.196292\pi\)
−0.815809 + 0.578322i \(0.803708\pi\)
\(744\) −2.97689e41 4.31932e41i −0.685417 0.994506i
\(745\) 3.55745e41i 0.803291i
\(746\) 5.27676e40i 0.116857i
\(747\) 1.03476e41 2.71681e41i 0.224746 0.590080i
\(748\) 6.17785e38i 0.00131603i
\(749\) −1.33160e41 + 6.17089e40i −0.278220 + 0.128932i
\(750\) −7.16340e40 + 4.93704e40i −0.146802 + 0.101176i
\(751\) −3.73723e41 −0.751226 −0.375613 0.926777i \(-0.622568\pi\)
−0.375613 + 0.926777i \(0.622568\pi\)
\(752\) 3.39504e41 0.669400
\(753\) −6.65714e40 9.65917e40i −0.128754 0.186815i
\(754\) 5.59656e41i