Properties

Label 21.30.c.a.20.4
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 20.4
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.3

$q$-expansion

\(f(q)\) \(=\) \(q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +O(q^{10})\) \(q+40537.3i q^{2} +(-896293. - 8.23572e6i) q^{3} -1.10640e9 q^{4} +2.53522e10 q^{5} +(3.33854e11 - 3.63333e10i) q^{6} +(3.38830e11 + 1.76213e12i) q^{7} -2.30873e13i q^{8} +(-6.70237e13 + 1.47632e13i) q^{9} +1.02771e15i q^{10} +1.41931e15i q^{11} +(9.91662e14 + 9.11203e15i) q^{12} +2.20140e16i q^{13} +(-7.14320e16 + 1.37353e16i) q^{14} +(-2.27230e16 - 2.08794e17i) q^{15} +3.41903e17 q^{16} +9.03848e17 q^{17} +(-5.98462e17 - 2.71696e18i) q^{18} -2.84158e17i q^{19} -2.80498e19 q^{20} +(1.42087e19 - 4.36989e18i) q^{21} -5.75350e19 q^{22} +3.67708e19i q^{23} +(-1.90141e20 + 2.06930e19i) q^{24} +4.56470e20 q^{25} -8.92390e20 q^{26} +(1.81659e20 + 5.38756e20i) q^{27} +(-3.74882e20 - 1.94963e21i) q^{28} -1.16157e21i q^{29} +(8.46394e21 - 9.21130e20i) q^{30} -1.18888e21i q^{31} +1.46491e21i q^{32} +(1.16890e22 - 1.27212e21i) q^{33} +3.66396e22i q^{34} +(8.59008e21 + 4.46739e22i) q^{35} +(7.41553e22 - 1.63341e22i) q^{36} -1.35607e21 q^{37} +1.15190e22 q^{38} +(1.81301e23 - 1.97310e22i) q^{39} -5.85315e23i q^{40} +1.70731e23 q^{41} +(1.77144e23 + 5.75983e23i) q^{42} -6.75136e23 q^{43} -1.57033e24i q^{44} +(-1.69920e24 + 3.74280e23i) q^{45} -1.49059e24 q^{46} +1.96537e24 q^{47} +(-3.06445e23 - 2.81582e24i) q^{48} +(-2.99029e24 + 1.19412e24i) q^{49} +1.85041e25i q^{50} +(-8.10112e23 - 7.44384e24i) q^{51} -2.43564e25i q^{52} -1.77266e24i q^{53} +(-2.18397e25 + 7.36395e24i) q^{54} +3.59826e25i q^{55} +(4.06829e25 - 7.82268e24i) q^{56} +(-2.34025e24 + 2.54689e23i) q^{57} +4.70870e25 q^{58} -4.83190e25 q^{59} +(2.51408e25 + 2.31010e26i) q^{60} +7.56453e25i q^{61} +4.81939e25 q^{62} +(-4.87243e25 - 1.13102e26i) q^{63} +1.24174e26 q^{64} +5.58105e26i q^{65} +(5.15682e25 + 4.73842e26i) q^{66} -1.04824e26 q^{67} -1.00002e27 q^{68} +(3.02834e26 - 3.29574e25i) q^{69} +(-1.81096e27 + 3.48219e26i) q^{70} -2.52140e26i q^{71} +(3.40844e26 + 1.54740e27i) q^{72} -9.99284e26i q^{73} -5.49714e25i q^{74} +(-4.09131e26 - 3.75936e27i) q^{75} +3.14394e26i q^{76} +(-2.50101e27 + 4.80904e26i) q^{77} +(7.99843e26 + 7.34948e27i) q^{78} -2.17559e27 q^{79} +8.66800e27 q^{80} +(4.27422e27 - 1.97897e27i) q^{81} +6.92096e27i q^{82} +6.73274e27 q^{83} +(-1.57206e28 + 4.83486e27i) q^{84} +2.29145e28 q^{85} -2.73682e28i q^{86} +(-9.56638e27 + 1.04111e27i) q^{87} +3.27681e28 q^{88} -8.13678e27 q^{89} +(-1.51723e28 - 6.88810e28i) q^{90} +(-3.87916e28 + 7.45901e27i) q^{91} -4.06833e28i q^{92} +(-9.79126e27 + 1.06558e27i) q^{93} +7.96709e28i q^{94} -7.20404e27i q^{95} +(1.20646e28 - 1.31299e27i) q^{96} +1.01638e29i q^{97} +(-4.84066e28 - 1.21219e29i) q^{98} +(-2.09536e28 - 9.51273e28i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 40537.3i 1.74952i 0.484552 + 0.874762i \(0.338983\pi\)
−0.484552 + 0.874762i \(0.661017\pi\)
\(3\) −896293. 8.23572e6i −0.108191 0.994130i
\(4\) −1.10640e9 −2.06084
\(5\) 2.53522e10 1.85759 0.928797 0.370589i \(-0.120844\pi\)
0.928797 + 0.370589i \(0.120844\pi\)
\(6\) 3.33854e11 3.63333e10i 1.73926 0.189283i
\(7\) 3.38830e11 + 1.76213e12i 0.188825 + 0.982011i
\(8\) 2.30873e13i 1.85596i
\(9\) −6.70237e13 + 1.47632e13i −0.976589 + 0.215112i
\(10\) 1.02771e15i 3.24991i
\(11\) 1.41931e15i 1.12689i 0.826152 + 0.563447i \(0.190525\pi\)
−0.826152 + 0.563447i \(0.809475\pi\)
\(12\) 9.91662e14 + 9.11203e15i 0.222964 + 2.04874i
\(13\) 2.20140e16i 1.55068i 0.631546 + 0.775338i \(0.282421\pi\)
−0.631546 + 0.775338i \(0.717579\pi\)
\(14\) −7.14320e16 + 1.37353e16i −1.71805 + 0.330354i
\(15\) −2.27230e16 2.08794e17i −0.200975 1.84669i
\(16\) 3.41903e17 1.18621
\(17\) 9.03848e17 1.30193 0.650963 0.759110i \(-0.274365\pi\)
0.650963 + 0.759110i \(0.274365\pi\)
\(18\) −5.98462e17 2.71696e18i −0.376344 1.70857i
\(19\) 2.84158e17i 0.0815893i −0.999168 0.0407947i \(-0.987011\pi\)
0.999168 0.0407947i \(-0.0129889\pi\)
\(20\) −2.80498e19 −3.82820
\(21\) 1.42087e19 4.36989e18i 0.955817 0.293962i
\(22\) −5.75350e19 −1.97153
\(23\) 3.67708e19i 0.661377i 0.943740 + 0.330689i \(0.107281\pi\)
−0.943740 + 0.330689i \(0.892719\pi\)
\(24\) −1.90141e20 + 2.06930e19i −1.84507 + 0.200799i
\(25\) 4.56470e20 2.45066
\(26\) −8.92390e20 −2.71295
\(27\) 1.81659e20 + 5.38756e20i 0.319508 + 0.947584i
\(28\) −3.74882e20 1.94963e21i −0.389138 2.02376i
\(29\) 1.16157e21i 0.724895i −0.932004 0.362448i \(-0.881941\pi\)
0.932004 0.362448i \(-0.118059\pi\)
\(30\) 8.46394e21 9.21130e20i 3.23083 0.351611i
\(31\) 1.18888e21i 0.282093i −0.990003 0.141047i \(-0.954953\pi\)
0.990003 0.141047i \(-0.0450468\pi\)
\(32\) 1.46491e21i 0.219350i
\(33\) 1.16890e22 1.27212e21i 1.12028 0.121920i
\(34\) 3.66396e22i 2.27775i
\(35\) 8.59008e21 + 4.46739e22i 0.350761 + 1.82418i
\(36\) 7.41553e22 1.63341e22i 2.01259 0.443311i
\(37\) −1.35607e21 −0.0247375 −0.0123688 0.999924i \(-0.503937\pi\)
−0.0123688 + 0.999924i \(0.503937\pi\)
\(38\) 1.15190e22 0.142743
\(39\) 1.81301e23 1.97310e22i 1.54157 0.167769i
\(40\) 5.85315e23i 3.44762i
\(41\) 1.70731e23 0.702984 0.351492 0.936191i \(-0.385674\pi\)
0.351492 + 0.936191i \(0.385674\pi\)
\(42\) 1.77144e23 + 5.75983e23i 0.514293 + 1.67223i
\(43\) −6.75136e23 −1.39347 −0.696737 0.717327i \(-0.745365\pi\)
−0.696737 + 0.717327i \(0.745365\pi\)
\(44\) 1.57033e24i 2.32235i
\(45\) −1.69920e24 + 3.74280e23i −1.81411 + 0.399591i
\(46\) −1.49059e24 −1.15710
\(47\) 1.96537e24 1.11693 0.558464 0.829528i \(-0.311391\pi\)
0.558464 + 0.829528i \(0.311391\pi\)
\(48\) −3.06445e23 2.81582e24i −0.128338 1.17925i
\(49\) −2.99029e24 + 1.19412e24i −0.928690 + 0.370857i
\(50\) 1.85041e25i 4.28748i
\(51\) −8.10112e23 7.44384e24i −0.140857 1.29428i
\(52\) 2.43564e25i 3.19569i
\(53\) 1.77266e24i 0.176451i −0.996101 0.0882257i \(-0.971880\pi\)
0.996101 0.0882257i \(-0.0281197\pi\)
\(54\) −2.18397e25 + 7.36395e24i −1.65782 + 0.558987i
\(55\) 3.59826e25i 2.09331i
\(56\) 4.06829e25 7.82268e24i 1.82257 0.350452i
\(57\) −2.34025e24 + 2.54689e23i −0.0811104 + 0.00882724i
\(58\) 4.70870e25 1.26822
\(59\) −4.83190e25 −1.01570 −0.507848 0.861447i \(-0.669559\pi\)
−0.507848 + 0.861447i \(0.669559\pi\)
\(60\) 2.51408e25 + 2.31010e26i 0.414177 + 3.80573i
\(61\) 7.56453e25i 0.980617i 0.871549 + 0.490309i \(0.163116\pi\)
−0.871549 + 0.490309i \(0.836884\pi\)
\(62\) 4.81939e25 0.493529
\(63\) −4.87243e25 1.13102e26i −0.395647 0.918403i
\(64\) 1.24174e26 0.802457
\(65\) 5.58105e26i 2.88053i
\(66\) 5.15682e25 + 4.73842e26i 0.213302 + 1.95996i
\(67\) −1.04824e26 −0.348639 −0.174319 0.984689i \(-0.555773\pi\)
−0.174319 + 0.984689i \(0.555773\pi\)
\(68\) −1.00002e27 −2.68306
\(69\) 3.02834e26 3.29574e25i 0.657495 0.0715552i
\(70\) −1.81096e27 + 3.48219e26i −3.19144 + 0.613664i
\(71\) 2.52140e26i 0.361739i −0.983507 0.180869i \(-0.942109\pi\)
0.983507 0.180869i \(-0.0578911\pi\)
\(72\) 3.40844e26 + 1.54740e27i 0.399240 + 1.81251i
\(73\) 9.99284e26i 0.958313i −0.877729 0.479157i \(-0.840943\pi\)
0.877729 0.479157i \(-0.159057\pi\)
\(74\) 5.49714e25i 0.0432789i
\(75\) −4.09131e26 3.75936e27i −0.265139 2.43627i
\(76\) 3.14394e26i 0.168142i
\(77\) −2.50101e27 + 4.80904e26i −1.10662 + 0.212786i
\(78\) 7.99843e26 + 7.34948e27i 0.293517 + 2.69702i
\(79\) −2.17559e27 −0.663720 −0.331860 0.943329i \(-0.607676\pi\)
−0.331860 + 0.943329i \(0.607676\pi\)
\(80\) 8.66800e27 2.20350
\(81\) 4.27422e27 1.97897e27i 0.907454 0.420152i
\(82\) 6.92096e27i 1.22989i
\(83\) 6.73274e27 1.00360 0.501798 0.864985i \(-0.332672\pi\)
0.501798 + 0.864985i \(0.332672\pi\)
\(84\) −1.57206e28 + 4.83486e27i −1.96978 + 0.605807i
\(85\) 2.29145e28 2.41845
\(86\) 2.73682e28i 2.43792i
\(87\) −9.56638e27 + 1.04111e27i −0.720640 + 0.0784273i
\(88\) 3.27681e28 2.09147
\(89\) −8.13678e27 −0.440857 −0.220428 0.975403i \(-0.570746\pi\)
−0.220428 + 0.975403i \(0.570746\pi\)
\(90\) −1.51723e28 6.88810e28i −0.699094 3.17382i
\(91\) −3.87916e28 + 7.45901e27i −1.52278 + 0.292807i
\(92\) 4.06833e28i 1.36299i
\(93\) −9.79126e27 + 1.06558e27i −0.280437 + 0.0305200i
\(94\) 7.96709e28i 1.95409i
\(95\) 7.20404e27i 0.151560i
\(96\) 1.20646e28 1.31299e27i 0.218062 0.0237317i
\(97\) 1.01638e29i 1.58075i 0.612621 + 0.790377i \(0.290115\pi\)
−0.612621 + 0.790377i \(0.709885\pi\)
\(98\) −4.84066e28 1.21219e29i −0.648823 1.62477i
\(99\) −2.09536e28 9.51273e28i −0.242409 1.10051i
\(100\) −5.05040e29 −5.05040
\(101\) 2.70459e28 0.234121 0.117061 0.993125i \(-0.462653\pi\)
0.117061 + 0.993125i \(0.462653\pi\)
\(102\) 3.01753e29 3.28398e28i 2.26438 0.246432i
\(103\) 7.33945e28i 0.478106i −0.971007 0.239053i \(-0.923163\pi\)
0.971007 0.239053i \(-0.0768369\pi\)
\(104\) 5.08246e29 2.87800
\(105\) 3.60222e29 1.10786e29i 1.77552 0.546061i
\(106\) 7.18589e28 0.308706
\(107\) 2.13042e29i 0.798732i 0.916792 + 0.399366i \(0.130770\pi\)
−0.916792 + 0.399366i \(0.869230\pi\)
\(108\) −2.00988e29 5.96082e29i −0.658454 1.95282i
\(109\) 7.01375e28 0.201033 0.100516 0.994935i \(-0.467951\pi\)
0.100516 + 0.994935i \(0.467951\pi\)
\(110\) −1.45864e30 −3.66230
\(111\) 1.21543e27 + 1.11682e28i 0.00267638 + 0.0245923i
\(112\) 1.15847e29 + 6.02477e29i 0.223987 + 1.16488i
\(113\) 3.32301e29i 0.564800i 0.959297 + 0.282400i \(0.0911305\pi\)
−0.959297 + 0.282400i \(0.908869\pi\)
\(114\) −1.03244e28 9.48674e28i −0.0154435 0.141905i
\(115\) 9.32221e29i 1.22857i
\(116\) 1.28517e30i 1.49389i
\(117\) −3.24998e29 1.47546e30i −0.333569 1.51437i
\(118\) 1.95872e30i 1.77699i
\(119\) 3.06251e29 + 1.59270e30i 0.245836 + 1.27850i
\(120\) −4.82049e30 + 5.24614e29i −3.42739 + 0.373002i
\(121\) −4.28128e29 −0.269890
\(122\) −3.06646e30 −1.71561
\(123\) −1.53025e29 1.40609e30i −0.0760566 0.698857i
\(124\) 1.31538e30i 0.581348i
\(125\) 6.85031e30 2.69473
\(126\) 4.58486e30 1.97515e30i 1.60677 0.692194i
\(127\) −1.74410e28 −0.00545026 −0.00272513 0.999996i \(-0.500867\pi\)
−0.00272513 + 0.999996i \(0.500867\pi\)
\(128\) 5.82016e30i 1.62327i
\(129\) 6.05120e29 + 5.56023e30i 0.150761 + 1.38529i
\(130\) −2.26241e31 −5.03955
\(131\) −6.50358e29 −0.129634 −0.0648170 0.997897i \(-0.520646\pi\)
−0.0648170 + 0.997897i \(0.520646\pi\)
\(132\) −1.29328e31 + 1.40747e30i −2.30871 + 0.251257i
\(133\) 5.00724e29 9.62813e28i 0.0801216 0.0154061i
\(134\) 4.24928e30i 0.609952i
\(135\) 4.60545e30 + 1.36587e31i 0.593516 + 1.76023i
\(136\) 2.08674e31i 2.41632i
\(137\) 1.06805e31i 1.11209i −0.831151 0.556047i \(-0.812317\pi\)
0.831151 0.556047i \(-0.187683\pi\)
\(138\) 1.33600e30 + 1.22761e31i 0.125188 + 1.15030i
\(139\) 6.22380e30i 0.525220i 0.964902 + 0.262610i \(0.0845832\pi\)
−0.964902 + 0.262610i \(0.915417\pi\)
\(140\) −9.50410e30 4.94273e31i −0.722860 3.75933i
\(141\) −1.76155e30 1.61862e31i −0.120842 1.11037i
\(142\) 1.02211e31 0.632871
\(143\) −3.12447e31 −1.74745
\(144\) −2.29156e31 + 5.04759e30i −1.15844 + 0.255169i
\(145\) 2.94484e31i 1.34656i
\(146\) 4.05083e31 1.67659
\(147\) 1.25146e31 + 2.35569e31i 0.469156 + 0.883115i
\(148\) 1.50036e30 0.0509800
\(149\) 7.49140e30i 0.230867i 0.993315 + 0.115434i \(0.0368257\pi\)
−0.993315 + 0.115434i \(0.963174\pi\)
\(150\) 1.52394e32 1.65851e31i 4.26232 0.463868i
\(151\) −3.37654e31 −0.857643 −0.428821 0.903389i \(-0.641071\pi\)
−0.428821 + 0.903389i \(0.641071\pi\)
\(152\) −6.56046e30 −0.151427
\(153\) −6.05792e31 + 1.33437e31i −1.27145 + 0.280060i
\(154\) −1.94946e31 1.01384e32i −0.372274 1.93606i
\(155\) 3.01407e31i 0.524015i
\(156\) −2.00593e32 + 2.18305e31i −3.17693 + 0.345746i
\(157\) 2.00568e31i 0.289545i −0.989465 0.144772i \(-0.953755\pi\)
0.989465 0.144772i \(-0.0462450\pi\)
\(158\) 8.81927e31i 1.16119i
\(159\) −1.45991e31 + 1.58882e30i −0.175416 + 0.0190905i
\(160\) 3.71387e31i 0.407462i
\(161\) −6.47949e31 + 1.24590e31i −0.649480 + 0.124885i
\(162\) 8.02222e31 + 1.73266e32i 0.735067 + 1.58761i
\(163\) −1.57676e32 −1.32144 −0.660719 0.750634i \(-0.729748\pi\)
−0.660719 + 0.750634i \(0.729748\pi\)
\(164\) −1.88897e32 −1.44874
\(165\) 2.96343e32 3.22510e31i 2.08102 0.226478i
\(166\) 2.72927e32i 1.75582i
\(167\) −1.17503e32 −0.692885 −0.346443 0.938071i \(-0.612611\pi\)
−0.346443 + 0.938071i \(0.612611\pi\)
\(168\) −1.00889e32 3.28041e32i −0.545582 1.77396i
\(169\) −2.83080e32 −1.40460
\(170\) 9.28894e32i 4.23114i
\(171\) 4.19510e30 + 1.90453e31i 0.0175509 + 0.0796793i
\(172\) 7.46973e32 2.87172
\(173\) 4.13553e31 0.146171 0.0730857 0.997326i \(-0.476715\pi\)
0.0730857 + 0.997326i \(0.476715\pi\)
\(174\) −4.22038e31 3.87796e32i −0.137210 1.26078i
\(175\) 1.54666e32 + 8.04359e32i 0.462745 + 2.40657i
\(176\) 4.85266e32i 1.33674i
\(177\) 4.33080e31 + 3.97942e32i 0.109889 + 1.00973i
\(178\) 3.29843e32i 0.771290i
\(179\) 4.08045e32i 0.879709i 0.898069 + 0.439855i \(0.144970\pi\)
−0.898069 + 0.439855i \(0.855030\pi\)
\(180\) 1.88000e33 4.14105e32i 3.73858 0.823492i
\(181\) 2.24904e32i 0.412723i −0.978476 0.206361i \(-0.933838\pi\)
0.978476 0.206361i \(-0.0661622\pi\)
\(182\) −3.02368e32 1.57251e33i −0.512273 2.66414i
\(183\) 6.22994e32 6.78004e31i 0.974861 0.106094i
\(184\) 8.48940e32 1.22749
\(185\) −3.43793e31 −0.0459523
\(186\) −4.31959e31 3.96912e32i −0.0533955 0.490632i
\(187\) 1.28284e33i 1.46713i
\(188\) −2.17449e33 −2.30181
\(189\) −8.87807e32 + 5.02653e32i −0.870206 + 0.492688i
\(190\) 2.92033e32 0.265158
\(191\) 1.73131e33i 1.45677i −0.685167 0.728386i \(-0.740271\pi\)
0.685167 0.728386i \(-0.259729\pi\)
\(192\) −1.11296e32 1.02266e33i −0.0868187 0.797747i
\(193\) −2.27621e33 −1.64676 −0.823382 0.567488i \(-0.807915\pi\)
−0.823382 + 0.567488i \(0.807915\pi\)
\(194\) −4.12012e33 −2.76557
\(195\) 4.59639e33 5.00225e32i 2.86362 0.311648i
\(196\) 3.30847e33 1.32118e33i 1.91388 0.764275i
\(197\) 3.08387e33i 1.65705i 0.559953 + 0.828524i \(0.310819\pi\)
−0.559953 + 0.828524i \(0.689181\pi\)
\(198\) 3.85621e33 8.49402e32i 1.92537 0.424100i
\(199\) 2.22436e33i 1.03237i −0.856477 0.516185i \(-0.827352\pi\)
0.856477 0.516185i \(-0.172648\pi\)
\(200\) 1.05387e34i 4.54832i
\(201\) 9.39529e31 + 8.63300e32i 0.0377196 + 0.346592i
\(202\) 1.09637e33i 0.409601i
\(203\) 2.04684e33 3.93575e32i 0.711855 0.136879i
\(204\) 8.96311e32 + 8.23589e33i 0.290283 + 2.66731i
\(205\) 4.32840e33 1.30586
\(206\) 2.97522e33 0.836458
\(207\) −5.42856e32 2.46451e33i −0.142270 0.645894i
\(208\) 7.52667e33i 1.83943i
\(209\) 4.03309e32 0.0919425
\(210\) 4.49098e33 + 1.46024e34i 0.955348 + 3.10632i
\(211\) 5.33777e33 1.05990 0.529949 0.848029i \(-0.322211\pi\)
0.529949 + 0.848029i \(0.322211\pi\)
\(212\) 1.96128e33i 0.363638i
\(213\) −2.07655e33 + 2.25991e32i −0.359615 + 0.0391369i
\(214\) −8.63617e33 −1.39740
\(215\) −1.71162e34 −2.58851
\(216\) 1.24384e34 4.19401e33i 1.75868 0.592994i
\(217\) 2.09496e33 4.02827e32i 0.277019 0.0532663i
\(218\) 2.84319e33i 0.351711i
\(219\) −8.22982e33 + 8.95651e32i −0.952688 + 0.103681i
\(220\) 3.98113e34i 4.31397i
\(221\) 1.98973e34i 2.01886i
\(222\) −4.52729e32 + 4.92704e31i −0.0430249 + 0.00468240i
\(223\) 1.01051e33i 0.0899746i −0.998988 0.0449873i \(-0.985675\pi\)
0.998988 0.0449873i \(-0.0143247\pi\)
\(224\) −2.58136e33 + 4.96356e32i −0.215404 + 0.0414187i
\(225\) −3.05943e34 + 6.73897e33i −2.39328 + 0.527166i
\(226\) −1.34706e34 −0.988132
\(227\) −2.00462e34 −1.37930 −0.689649 0.724144i \(-0.742235\pi\)
−0.689649 + 0.724144i \(0.742235\pi\)
\(228\) 2.58926e33 2.81789e32i 0.167155 0.0181915i
\(229\) 2.74288e34i 1.66185i 0.556382 + 0.830927i \(0.312189\pi\)
−0.556382 + 0.830927i \(0.687811\pi\)
\(230\) −3.77897e34 −2.14942
\(231\) 6.20222e33 + 2.01665e34i 0.331264 + 1.07710i
\(232\) −2.68176e34 −1.34538
\(233\) 1.74777e34i 0.823804i −0.911228 0.411902i \(-0.864865\pi\)
0.911228 0.411902i \(-0.135135\pi\)
\(234\) 5.98113e34 1.31746e34i 2.64944 0.583588i
\(235\) 4.98265e34 2.07480
\(236\) 5.34603e34 2.09319
\(237\) 1.94997e33 + 1.79176e34i 0.0718086 + 0.659824i
\(238\) −6.45637e34 + 1.24146e34i −2.23678 + 0.430097i
\(239\) 3.55379e34i 1.15857i 0.815125 + 0.579285i \(0.196668\pi\)
−0.815125 + 0.579285i \(0.803332\pi\)
\(240\) −7.76906e33 7.13872e34i −0.238400 2.19057i
\(241\) 5.61592e34i 1.62246i −0.584728 0.811229i \(-0.698799\pi\)
0.584728 0.811229i \(-0.301201\pi\)
\(242\) 1.73552e34i 0.472179i
\(243\) −2.01292e34 3.34276e34i −0.515865 0.856670i
\(244\) 8.36943e34i 2.02089i
\(245\) −7.58106e34 + 3.02737e34i −1.72513 + 0.688901i
\(246\) 5.69991e34 6.20321e33i 1.22267 0.133063i
\(247\) 6.25548e33 0.126519
\(248\) −2.74480e34 −0.523554
\(249\) −6.03450e33 5.54489e34i −0.108580 0.997706i
\(250\) 2.77693e35i 4.71449i
\(251\) 1.02385e35 1.64047 0.820237 0.572024i \(-0.193842\pi\)
0.820237 + 0.572024i \(0.193842\pi\)
\(252\) 5.39088e34 + 1.25137e35i 0.815364 + 1.89268i
\(253\) −5.21891e34 −0.745302
\(254\) 7.07011e32i 0.00953537i
\(255\) −2.05381e34 1.88718e35i −0.261655 2.40425i
\(256\) −1.69268e35 −2.03749
\(257\) 1.38355e35 1.57385 0.786927 0.617046i \(-0.211671\pi\)
0.786927 + 0.617046i \(0.211671\pi\)
\(258\) −2.25397e35 + 2.45299e34i −2.42361 + 0.263761i
\(259\) −4.59476e32 2.38957e33i −0.00467107 0.0242925i
\(260\) 6.17489e35i 5.93630i
\(261\) 1.71486e34 + 7.78529e34i 0.155934 + 0.707925i
\(262\) 2.63638e34i 0.226798i
\(263\) 1.90296e35i 1.54907i 0.632531 + 0.774535i \(0.282016\pi\)
−0.632531 + 0.774535i \(0.717984\pi\)
\(264\) −2.93698e34 2.69869e35i −0.226279 2.07920i
\(265\) 4.49408e34i 0.327775i
\(266\) 3.90299e33 + 2.02980e34i 0.0269534 + 0.140175i
\(267\) 7.29294e33 + 6.70122e34i 0.0476968 + 0.438269i
\(268\) 1.15978e35 0.718488
\(269\) 8.92185e34 0.523657 0.261828 0.965114i \(-0.415675\pi\)
0.261828 + 0.965114i \(0.415675\pi\)
\(270\) −5.53685e35 + 1.86693e35i −3.07956 + 1.03837i
\(271\) 1.16122e35i 0.612152i 0.952007 + 0.306076i \(0.0990162\pi\)
−0.952007 + 0.306076i \(0.900984\pi\)
\(272\) 3.09028e35 1.54436
\(273\) 9.61989e34 + 3.12791e35i 0.455839 + 1.48216i
\(274\) 4.32957e35 1.94564
\(275\) 6.47872e35i 2.76163i
\(276\) −3.35057e35 + 3.64642e34i −1.35499 + 0.147464i
\(277\) −2.67170e35 −1.02525 −0.512626 0.858612i \(-0.671327\pi\)
−0.512626 + 0.858612i \(0.671327\pi\)
\(278\) −2.52296e35 −0.918885
\(279\) 1.75517e34 + 7.96830e34i 0.0606817 + 0.275489i
\(280\) 1.03140e36 1.98322e35i 3.38560 0.650998i
\(281\) 8.53294e34i 0.265985i 0.991117 + 0.132993i \(0.0424586\pi\)
−0.991117 + 0.132993i \(0.957541\pi\)
\(282\) 6.56147e35 7.14084e34i 1.94262 0.211416i
\(283\) 4.51797e34i 0.127069i 0.997980 + 0.0635345i \(0.0202373\pi\)
−0.997980 + 0.0635345i \(0.979763\pi\)
\(284\) 2.78968e35i 0.745485i
\(285\) −5.93305e34 + 6.45693e33i −0.150670 + 0.0163974i
\(286\) 1.26658e36i 3.05720i
\(287\) 5.78486e34 + 3.00849e35i 0.132741 + 0.690338i
\(288\) −2.16268e34 9.81838e34i −0.0471847 0.214214i
\(289\) 3.34973e35 0.695009
\(290\) 1.19376e36 2.35584
\(291\) 8.37059e35 9.10971e34i 1.57148 0.171024i
\(292\) 1.10561e36i 1.97493i
\(293\) −6.15925e34 −0.104700 −0.0523501 0.998629i \(-0.516671\pi\)
−0.0523501 + 0.998629i \(0.516671\pi\)
\(294\) −9.54935e35 + 5.07310e35i −1.54503 + 0.820800i
\(295\) −1.22499e36 −1.88675
\(296\) 3.13080e34i 0.0459119i
\(297\) −7.64661e35 + 2.57830e35i −1.06783 + 0.360051i
\(298\) −3.03681e35 −0.403908
\(299\) −8.09474e35 −1.02558
\(300\) 4.52664e35 + 4.15937e36i 0.546409 + 5.02076i
\(301\) −2.28756e35 1.18968e36i −0.263123 1.36841i
\(302\) 1.36876e36i 1.50047i
\(303\) −2.42410e34 2.22742e35i −0.0253299 0.232747i
\(304\) 9.71546e34i 0.0967824i
\(305\) 1.91778e36i 1.82159i
\(306\) −5.40918e35 2.45572e36i −0.489972 2.22443i
\(307\) 4.68306e35i 0.404598i −0.979324 0.202299i \(-0.935159\pi\)
0.979324 0.202299i \(-0.0648412\pi\)
\(308\) 2.76712e36 5.32074e35i 2.28057 0.438517i
\(309\) −6.04457e35 + 6.57830e34i −0.475299 + 0.0517268i
\(310\) 1.22182e36 0.916777
\(311\) −1.53662e36 −1.10037 −0.550186 0.835042i \(-0.685443\pi\)
−0.550186 + 0.835042i \(0.685443\pi\)
\(312\) −4.55537e35 4.18577e36i −0.311374 2.86110i
\(313\) 1.19248e36i 0.778141i −0.921208 0.389071i \(-0.872796\pi\)
0.921208 0.389071i \(-0.127204\pi\)
\(314\) 8.13048e35 0.506566
\(315\) −1.23527e36 2.86739e36i −0.734952 1.70602i
\(316\) 2.40708e36 1.36782
\(317\) 6.75081e34i 0.0366435i 0.999832 + 0.0183217i \(0.00583231\pi\)
−0.999832 + 0.0183217i \(0.994168\pi\)
\(318\) −6.44066e34 5.91809e35i −0.0333993 0.306894i
\(319\) 1.64863e36 0.816880
\(320\) 3.14809e36 1.49064
\(321\) 1.75456e36 1.90948e35i 0.794044 0.0864157i
\(322\) −5.05056e35 2.62661e36i −0.218489 1.13628i
\(323\) 2.56836e35i 0.106223i
\(324\) −4.72902e36 + 2.18954e36i −1.87011 + 0.865866i
\(325\) 1.00488e37i 3.80017i
\(326\) 6.39178e36i 2.31189i
\(327\) −6.28638e34 5.77633e35i −0.0217499 0.199853i
\(328\) 3.94171e36i 1.30471i
\(329\) 6.65926e35 + 3.46324e36i 0.210904 + 1.09684i
\(330\) 1.30737e36 + 1.20129e37i 0.396228 + 3.64080i
\(331\) 4.49145e36 1.30281 0.651405 0.758730i \(-0.274180\pi\)
0.651405 + 0.758730i \(0.274180\pi\)
\(332\) −7.44912e36 −2.06825
\(333\) 9.08887e34 2.00199e34i 0.0241584 0.00532134i
\(334\) 4.76327e36i 1.21222i
\(335\) −2.65752e36 −0.647629
\(336\) 4.85800e36 1.49408e36i 1.13380 0.348702i
\(337\) −4.28477e36 −0.957842 −0.478921 0.877858i \(-0.658972\pi\)
−0.478921 + 0.877858i \(0.658972\pi\)
\(338\) 1.14753e37i 2.45738i
\(339\) 2.73674e36 2.97839e35i 0.561485 0.0611064i
\(340\) −2.53527e37 −4.98403
\(341\) 1.68739e36 0.317889
\(342\) −7.72047e35 + 1.70058e35i −0.139401 + 0.0307057i
\(343\) −3.11740e36 4.86468e36i −0.539545 0.841957i
\(344\) 1.55871e37i 2.58623i
\(345\) 7.67751e36 8.35543e35i 1.22136 0.132920i
\(346\) 1.67643e36i 0.255731i
\(347\) 1.36597e36i 0.199831i −0.994996 0.0999157i \(-0.968143\pi\)
0.994996 0.0999157i \(-0.0318573\pi\)
\(348\) 1.05843e37 1.15189e36i 1.48512 0.161626i
\(349\) 6.00688e36i 0.808500i 0.914648 + 0.404250i \(0.132467\pi\)
−0.914648 + 0.404250i \(0.867533\pi\)
\(350\) −3.26066e37 + 6.26973e36i −4.21035 + 0.809585i
\(351\) −1.18602e37 + 3.99904e36i −1.46940 + 0.495453i
\(352\) −2.07916e36 −0.247184
\(353\) 4.96737e36 0.566752 0.283376 0.959009i \(-0.408546\pi\)
0.283376 + 0.959009i \(0.408546\pi\)
\(354\) −1.61315e37 + 1.75559e36i −1.76656 + 0.192254i
\(355\) 6.39230e36i 0.671964i
\(356\) 9.00256e36 0.908534
\(357\) 1.28425e37 3.94972e36i 1.24440 0.382716i
\(358\) −1.65411e37 −1.53907
\(359\) 2.42934e36i 0.217080i 0.994092 + 0.108540i \(0.0346175\pi\)
−0.994092 + 0.108540i \(0.965382\pi\)
\(360\) 8.64114e36 + 3.92300e37i 0.741626 + 3.36691i
\(361\) 1.20491e37 0.993343
\(362\) 9.11702e36 0.722069
\(363\) 3.83728e35 + 3.52594e36i 0.0291997 + 0.268305i
\(364\) 4.29192e37 8.25268e36i 3.13820 0.603427i
\(365\) 2.53341e37i 1.78016i
\(366\) 2.74845e36 + 2.52545e37i 0.185614 + 1.70554i
\(367\) 1.82108e37i 1.18214i −0.806618 0.591072i \(-0.798705\pi\)
0.806618 0.591072i \(-0.201295\pi\)
\(368\) 1.25720e37i 0.784535i
\(369\) −1.14430e37 + 2.52053e36i −0.686526 + 0.151220i
\(370\) 1.39365e36i 0.0803947i
\(371\) 3.12366e36 6.00630e35i 0.173277 0.0333185i
\(372\) 1.08331e37 1.17896e36i 0.577936 0.0628968i
\(373\) 2.96683e37 1.52235 0.761175 0.648547i \(-0.224623\pi\)
0.761175 + 0.648547i \(0.224623\pi\)
\(374\) −5.20029e37 −2.56678
\(375\) −6.13988e36 5.64172e37i −0.291546 2.67891i
\(376\) 4.53752e37i 2.07298i
\(377\) 2.55709e37 1.12408
\(378\) −2.03762e37 3.59893e37i −0.861969 1.52245i
\(379\) 7.48995e36 0.304937 0.152469 0.988308i \(-0.451278\pi\)
0.152469 + 0.988308i \(0.451278\pi\)
\(380\) 7.97058e36i 0.312340i
\(381\) 1.56322e34 + 1.43639e35i 0.000589670 + 0.00541827i
\(382\) 7.01827e37 2.54866
\(383\) −3.26768e37 −1.14250 −0.571251 0.820776i \(-0.693542\pi\)
−0.571251 + 0.820776i \(0.693542\pi\)
\(384\) 4.79332e37 5.21657e36i 1.61374 0.175623i
\(385\) −6.34060e37 + 1.21920e37i −2.05565 + 0.395270i
\(386\) 9.22714e37i 2.88105i
\(387\) 4.52501e37 9.96719e36i 1.36085 0.299753i
\(388\) 1.12452e38i 3.25768i
\(389\) 2.80009e37i 0.781452i 0.920507 + 0.390726i \(0.127776\pi\)
−0.920507 + 0.390726i \(0.872224\pi\)
\(390\) 2.02778e37 + 1.86325e38i 0.545235 + 5.00997i
\(391\) 3.32352e37i 0.861064i
\(392\) 2.75691e37 + 6.90379e37i 0.688296 + 1.72361i
\(393\) 5.82911e35 + 5.35616e36i 0.0140252 + 0.128873i
\(394\) −1.25012e38 −2.89905
\(395\) −5.51561e37 −1.23292
\(396\) 2.31831e37 + 1.05249e38i 0.499565 + 2.26798i
\(397\) 7.23184e37i 1.50240i −0.660073 0.751201i \(-0.729475\pi\)
0.660073 0.751201i \(-0.270525\pi\)
\(398\) 9.01696e37 1.80616
\(399\) −1.24174e36 4.03752e36i −0.0239841 0.0779845i
\(400\) 1.56068e38 2.90700
\(401\) 6.54810e37i 1.17631i −0.808748 0.588155i \(-0.799855\pi\)
0.808748 0.588155i \(-0.200145\pi\)
\(402\) −3.49959e37 + 3.80860e36i −0.606372 + 0.0659914i
\(403\) 2.61720e37 0.437435
\(404\) −2.99237e37 −0.482486
\(405\) 1.08361e38 5.01713e37i 1.68568 0.780473i
\(406\) 1.59545e37 + 8.29735e37i 0.239472 + 1.24541i
\(407\) 1.92468e36i 0.0278766i
\(408\) −1.71858e38 + 1.87033e37i −2.40214 + 0.261425i
\(409\) 9.85984e36i 0.133009i 0.997786 + 0.0665046i \(0.0211847\pi\)
−0.997786 + 0.0665046i \(0.978815\pi\)
\(410\) 1.75462e38i 2.28463i
\(411\) −8.79612e37 + 9.57282e36i −1.10557 + 0.120319i
\(412\) 8.12040e37i 0.985298i
\(413\) −1.63719e37 8.51444e37i −0.191789 0.997425i
\(414\) 9.99048e37 2.20059e37i 1.13001 0.248905i
\(415\) 1.70690e38 1.86428
\(416\) −3.22486e37 −0.340140
\(417\) 5.12575e37 5.57835e36i 0.522137 0.0568241i
\(418\) 1.63491e37i 0.160856i
\(419\) −5.25615e37 −0.499533 −0.249767 0.968306i \(-0.580354\pi\)
−0.249767 + 0.968306i \(0.580354\pi\)
\(420\) −3.98551e38 + 1.22574e38i −3.65906 + 1.12534i
\(421\) 3.20373e37 0.284162 0.142081 0.989855i \(-0.454621\pi\)
0.142081 + 0.989855i \(0.454621\pi\)
\(422\) 2.16379e38i 1.85432i
\(423\) −1.31726e38 + 2.90152e37i −1.09078 + 0.240265i
\(424\) −4.09260e37 −0.327487
\(425\) 4.12580e38 3.19057
\(426\) −9.16106e36 8.41778e37i −0.0684710 0.629156i
\(427\) −1.33297e38 + 2.56309e37i −0.962977 + 0.185165i
\(428\) 2.35711e38i 1.64606i
\(429\) 2.80044e37 + 2.57323e38i 0.189058 + 1.73719i
\(430\) 6.93845e38i 4.52866i
\(431\) 2.30202e37i 0.145274i 0.997358 + 0.0726371i \(0.0231415\pi\)
−0.997358 + 0.0726371i \(0.976859\pi\)
\(432\) 6.21096e37 + 1.84202e38i 0.379005 + 1.12404i
\(433\) 3.08651e37i 0.182135i −0.995845 0.0910676i \(-0.970972\pi\)
0.995845 0.0910676i \(-0.0290279\pi\)
\(434\) 1.63295e37 + 8.49240e37i 0.0931908 + 0.484651i
\(435\) −2.42529e38 + 2.63944e37i −1.33866 + 0.145686i
\(436\) −7.76005e37 −0.414295
\(437\) 1.04487e37 0.0539613
\(438\) −3.63073e37 3.33615e38i −0.181393 1.66675i
\(439\) 3.14943e38i 1.52229i 0.648585 + 0.761143i \(0.275361\pi\)
−0.648585 + 0.761143i \(0.724639\pi\)
\(440\) 8.30743e38 3.88511
\(441\) 1.82791e38 1.24181e38i 0.827173 0.561947i
\(442\) −8.06585e38 −3.53205
\(443\) 3.05724e38i 1.29561i −0.761805 0.647807i \(-0.775686\pi\)
0.761805 0.647807i \(-0.224314\pi\)
\(444\) −1.34476e36 1.23565e37i −0.00551559 0.0506808i
\(445\) −2.06285e38 −0.818933
\(446\) 4.09634e37 0.157413
\(447\) 6.16970e37 6.71449e36i 0.229512 0.0249778i
\(448\) 4.20739e37 + 2.18811e38i 0.151524 + 0.788021i
\(449\) 2.65621e38i 0.926170i 0.886314 + 0.463085i \(0.153258\pi\)
−0.886314 + 0.463085i \(0.846742\pi\)
\(450\) −2.73180e38 1.24021e39i −0.922290 4.18711i
\(451\) 2.42319e38i 0.792188i
\(452\) 3.67659e38i 1.16396i
\(453\) 3.02637e37 + 2.78082e38i 0.0927893 + 0.852608i
\(454\) 8.12621e38i 2.41311i
\(455\) −9.83453e38 + 1.89102e38i −2.82871 + 0.543916i
\(456\) 5.88009e36 + 5.40301e37i 0.0163830 + 0.150538i
\(457\) 3.78952e38 1.02282 0.511410 0.859337i \(-0.329123\pi\)
0.511410 + 0.859337i \(0.329123\pi\)
\(458\) −1.11189e39 −2.90745
\(459\) 1.64192e38 + 4.86954e38i 0.415975 + 1.23368i
\(460\) 1.03141e39i 2.53188i
\(461\) 6.92235e38 1.64661 0.823304 0.567600i \(-0.192128\pi\)
0.823304 + 0.567600i \(0.192128\pi\)
\(462\) −8.17498e38 + 2.51422e38i −1.88442 + 0.579554i
\(463\) 7.45245e38 1.66485 0.832424 0.554139i \(-0.186952\pi\)
0.832424 + 0.554139i \(0.186952\pi\)
\(464\) 3.97145e38i 0.859881i
\(465\) −2.48230e38 + 2.70149e37i −0.520939 + 0.0566938i
\(466\) 7.08500e38 1.44127
\(467\) 4.66425e38 0.919787 0.459893 0.887974i \(-0.347888\pi\)
0.459893 + 0.887974i \(0.347888\pi\)
\(468\) 3.59579e38 + 1.63246e39i 0.687432 + 3.12088i
\(469\) −3.55174e37 1.84713e38i −0.0658318 0.342367i
\(470\) 2.01983e39i 3.62991i
\(471\) −1.65182e38 + 1.79767e37i −0.287845 + 0.0313262i
\(472\) 1.11556e39i 1.88509i
\(473\) 9.58227e38i 1.57030i
\(474\) −7.26330e38 + 7.90465e37i −1.15438 + 0.125631i
\(475\) 1.29710e38i 0.199947i
\(476\) −3.38837e38 1.76217e39i −0.506629 2.63479i
\(477\) 2.61702e37 + 1.18810e38i 0.0379568 + 0.172321i
\(478\) −1.44061e39 −2.02695
\(479\) −8.86151e38 −1.20960 −0.604802 0.796376i \(-0.706748\pi\)
−0.604802 + 0.796376i \(0.706748\pi\)
\(480\) 3.05864e38 3.32872e37i 0.405071 0.0440838i
\(481\) 2.98525e37i 0.0383599i
\(482\) 2.27654e39 2.83853
\(483\) 1.60684e38 + 5.22466e38i 0.194420 + 0.632156i
\(484\) 4.73683e38 0.556199
\(485\) 2.57674e39i 2.93640i
\(486\) 1.35506e39 8.15984e38i 1.49877 0.902518i
\(487\) 1.52650e39 1.63880 0.819399 0.573223i \(-0.194307\pi\)
0.819399 + 0.573223i \(0.194307\pi\)
\(488\) 1.74645e39 1.81999
\(489\) 1.41324e38 + 1.29858e39i 0.142968 + 1.31368i
\(490\) −1.22721e39 3.07316e39i −1.20525 3.01816i
\(491\) 9.61324e38i 0.916617i 0.888793 + 0.458309i \(0.151545\pi\)
−0.888793 + 0.458309i \(0.848455\pi\)
\(492\) 1.69307e38 + 1.55570e39i 0.156740 + 1.44023i
\(493\) 1.04988e39i 0.943760i
\(494\) 2.53580e38i 0.221348i
\(495\) −5.31220e38 2.41169e39i −0.450297 2.04431i
\(496\) 4.06481e38i 0.334623i
\(497\) 4.44303e38 8.54324e37i 0.355231 0.0683054i
\(498\) 2.24775e39 2.44623e38i 1.74551 0.189964i
\(499\) −2.19901e39 −1.65871 −0.829354 0.558723i \(-0.811291\pi\)
−0.829354 + 0.558723i \(0.811291\pi\)
\(500\) −7.57921e39 −5.55340
\(501\) 1.05317e38 + 9.67724e38i 0.0749641 + 0.688818i
\(502\) 4.15043e39i 2.87005i
\(503\) −1.09841e39 −0.737954 −0.368977 0.929438i \(-0.620292\pi\)
−0.368977 + 0.929438i \(0.620292\pi\)
\(504\) −2.61123e39 + 1.12492e39i −1.70452 + 0.734306i
\(505\) 6.85673e38 0.434902
\(506\) 2.11561e39i 1.30392i
\(507\) 2.53723e38 + 2.33137e39i 0.151965 + 1.39635i
\(508\) 1.92968e37 0.0112321
\(509\) −6.04238e38 −0.341822 −0.170911 0.985286i \(-0.554671\pi\)
−0.170911 + 0.985286i \(0.554671\pi\)
\(510\) 7.65011e39 8.32561e38i 4.20630 0.457771i
\(511\) 1.76087e39 3.38587e38i 0.941074 0.180954i
\(512\) 3.73700e39i 1.94137i
\(513\) 1.53092e38 5.16198e37i 0.0773127 0.0260684i
\(514\) 5.60854e39i 2.75350i
\(515\) 1.86071e39i 0.888126i
\(516\) −6.69507e38 6.15186e39i −0.310695 2.85487i
\(517\) 2.78947e39i 1.25866i
\(518\) 9.68666e37 1.86259e37i 0.0425004 0.00817215i
\(519\) −3.70665e37 3.40591e38i −0.0158145 0.145313i
\(520\) 1.28852e40 5.34615
\(521\) −2.48661e38 −0.100337 −0.0501684 0.998741i \(-0.515976\pi\)
−0.0501684 + 0.998741i \(0.515976\pi\)
\(522\) −3.15595e39 + 6.95157e38i −1.23853 + 0.272810i
\(523\) 1.18620e39i 0.452777i −0.974037 0.226389i \(-0.927308\pi\)
0.974037 0.226389i \(-0.0726919\pi\)
\(524\) 7.19559e38 0.267154
\(525\) 6.48585e39 1.99472e39i 2.34238 0.720399i
\(526\) −7.71408e39 −2.71014
\(527\) 1.07456e39i 0.367264i
\(528\) 3.99651e39 4.34940e38i 1.32889 0.144623i
\(529\) 1.73897e39 0.562580
\(530\) 1.82178e39 0.573451
\(531\) 3.23852e39 7.13345e38i 0.991918 0.218489i
\(532\) −5.54003e38 + 1.06526e38i −0.165118 + 0.0317495i
\(533\) 3.75847e39i 1.09010i
\(534\) −2.71650e39 + 2.95636e38i −0.766762 + 0.0834467i
\(535\) 5.40109e39i 1.48372i
\(536\) 2.42010e39i 0.647060i
\(537\) 3.36054e39 3.65728e38i 0.874545 0.0951767i
\(538\) 3.61668e39i 0.916151i
\(539\) −1.69483e39 4.24415e39i −0.417916 1.04654i
\(540\) −5.09548e39 1.51120e40i −1.22314 3.62754i
\(541\) −1.96022e39 −0.458084 −0.229042 0.973417i \(-0.573559\pi\)
−0.229042 + 0.973417i \(0.573559\pi\)
\(542\) −4.70727e39 −1.07098
\(543\) −1.85225e39 + 2.01580e38i −0.410300 + 0.0446529i
\(544\) 1.32406e39i 0.285577i
\(545\) 1.77814e39 0.373437
\(546\) −1.26797e40 + 3.89965e39i −2.59308 + 0.797503i
\(547\) 5.39261e39 1.07395 0.536973 0.843599i \(-0.319568\pi\)
0.536973 + 0.843599i \(0.319568\pi\)
\(548\) 1.18169e40i 2.29185i
\(549\) −1.11677e39 5.07003e39i −0.210943 0.957661i
\(550\) −2.62630e40 −4.83154
\(551\) −3.30071e38 −0.0591437
\(552\) −7.60899e38 6.99163e39i −0.132804 1.22029i
\(553\) −7.37155e38 3.83368e39i −0.125327 0.651780i
\(554\) 1.08304e40i 1.79370i
\(555\) 3.08139e37 + 2.83138e38i 0.00497163 + 0.0456826i
\(556\) 6.88604e39i 1.08239i
\(557\) 1.86146e39i 0.285071i −0.989790 0.142536i \(-0.954474\pi\)
0.989790 0.142536i \(-0.0455256\pi\)
\(558\) −3.23014e39 + 7.11498e38i −0.481975 + 0.106164i
\(559\) 1.48625e40i 2.16083i
\(560\) 2.93698e39 + 1.52741e40i 0.416077 + 2.16387i
\(561\) 1.05651e40 1.14980e39i 1.45852 0.158731i
\(562\) −3.45903e39 −0.465348
\(563\) −9.81277e38 −0.128653 −0.0643265 0.997929i \(-0.520490\pi\)
−0.0643265 + 0.997929i \(0.520490\pi\)
\(564\) 1.94898e39 + 1.79085e40i 0.249035 + 2.28830i
\(565\) 8.42457e39i 1.04917i
\(566\) −1.83146e39 −0.222310
\(567\) 4.93544e39 + 6.86120e39i 0.583944 + 0.811794i
\(568\) −5.82123e39 −0.671373
\(569\) 1.20996e40i 1.36033i −0.733061 0.680163i \(-0.761909\pi\)
0.733061 0.680163i \(-0.238091\pi\)
\(570\) −2.61747e38 2.40510e39i −0.0286877 0.263601i
\(571\) 1.66810e40 1.78238 0.891189 0.453633i \(-0.149872\pi\)
0.891189 + 0.453633i \(0.149872\pi\)
\(572\) 3.45693e40 3.60121
\(573\) −1.42586e40 + 1.55176e39i −1.44822 + 0.157610i
\(574\) −1.21956e40 + 2.34503e39i −1.20776 + 0.232234i
\(575\) 1.67848e40i 1.62081i
\(576\) −8.32261e39 + 1.83321e39i −0.783671 + 0.172618i
\(577\) 1.46760e40i 1.34760i −0.738916 0.673798i \(-0.764662\pi\)
0.738916 0.673798i \(-0.235338\pi\)
\(578\) 1.35789e40i 1.21594i
\(579\) 2.04015e39 + 1.87462e40i 0.178165 + 1.63710i
\(580\) 3.25819e40i 2.77504i
\(581\) 2.28125e39 + 1.18640e40i 0.189504 + 0.985543i
\(582\) 3.69283e39 + 3.39321e40i 0.299210 + 2.74934i
\(583\) 2.51595e39 0.198842
\(584\) −2.30708e40 −1.77859
\(585\) −8.23943e39 3.74062e40i −0.619636 2.81309i
\(586\) 2.49680e39i 0.183176i
\(587\) 1.75156e40 1.25364 0.626819 0.779165i \(-0.284356\pi\)
0.626819 + 0.779165i \(0.284356\pi\)
\(588\) −1.38462e40 2.60635e40i −0.966854 1.81996i
\(589\) −3.37830e38 −0.0230158
\(590\) 4.96580e40i 3.30092i
\(591\) 2.53978e40 2.76405e39i 1.64732 0.179278i
\(592\) −4.63644e38 −0.0293440
\(593\) −2.04282e40 −1.26164 −0.630822 0.775928i \(-0.717282\pi\)
−0.630822 + 0.775928i \(0.717282\pi\)
\(594\) −1.04517e40 3.09973e40i −0.629919 1.86819i
\(595\) 7.76413e39 + 4.03784e40i 0.456664 + 2.37494i
\(596\) 8.28851e39i 0.475780i
\(597\) −1.83192e40 + 1.99368e39i −1.02631 + 0.111693i
\(598\) 3.28139e40i 1.79428i
\(599\) 3.07821e40i 1.64289i −0.570287 0.821445i \(-0.693168\pi\)
0.570287 0.821445i \(-0.306832\pi\)
\(600\) −8.67936e40 + 9.44574e39i −4.52162 + 0.492088i
\(601\) 2.87869e40i 1.46391i 0.681351 + 0.731957i \(0.261393\pi\)
−0.681351 + 0.731957i \(0.738607\pi\)
\(602\) 4.82263e40 9.27316e39i 2.39406 0.460340i
\(603\) 7.02568e39 1.54754e39i 0.340477 0.0749964i
\(604\) 3.73582e40 1.76746
\(605\) −1.08540e40 −0.501345
\(606\) 9.02937e39 9.82666e38i 0.407197 0.0443152i
\(607\) 6.50759e39i 0.286539i 0.989684 + 0.143270i \(0.0457616\pi\)
−0.989684 + 0.143270i \(0.954238\pi\)
\(608\) 4.16267e38 0.0178966
\(609\) −5.07594e39 1.65044e40i −0.213091 0.692867i
\(610\) −7.77415e40 −3.18692
\(611\) 4.32658e40i 1.73200i
\(612\) 6.70251e40 1.47635e40i 2.62024 0.577158i
\(613\) 2.10947e40 0.805370 0.402685 0.915339i \(-0.368077\pi\)
0.402685 + 0.915339i \(0.368077\pi\)
\(614\) 1.89839e40 0.707854
\(615\) −3.87951e39 3.56474e40i −0.141282 1.29819i
\(616\) 1.11028e40 + 5.77416e40i 0.394923 + 2.05385i
\(617\) 2.77271e40i 0.963317i −0.876359 0.481659i \(-0.840035\pi\)
0.876359 0.481659i \(-0.159965\pi\)
\(618\) −2.66667e39 2.45031e40i −0.0904973 0.831548i
\(619\) 3.62054e39i 0.120021i 0.998198 + 0.0600107i \(0.0191135\pi\)
−0.998198 + 0.0600107i \(0.980887\pi\)
\(620\) 3.33478e40i 1.07991i
\(621\) −1.98105e40 + 6.67973e39i −0.626710 + 0.211315i
\(622\) 6.22903e40i 1.92513i
\(623\) −2.75698e39 1.43381e40i −0.0832448 0.432926i
\(624\) 6.19875e40 6.74610e39i 1.82864 0.199011i
\(625\) 8.86463e40 2.55506
\(626\) 4.83400e40 1.36138
\(627\) −3.61483e38 3.32154e39i −0.00994736 0.0914028i
\(628\) 2.21909e40i 0.596705i
\(629\) −1.22568e39 −0.0322064
\(630\) 1.16236e41 5.00745e40i 2.98472 1.28582i
\(631\) −3.16287e40 −0.793699 −0.396849 0.917884i \(-0.629896\pi\)
−0.396849 + 0.917884i \(0.629896\pi\)
\(632\) 5.02286e40i 1.23184i
\(633\) −4.78421e39 4.39604e40i −0.114672 1.05368i
\(634\) −2.73660e39 −0.0641086
\(635\) −4.42168e38 −0.0101244
\(636\) 1.61525e40 1.75788e39i 0.361503 0.0393424i
\(637\) −2.62875e40 6.58285e40i −0.575079 1.44010i
\(638\) 6.68311e40i 1.42915i
\(639\) 3.72239e39 + 1.68993e40i 0.0778144 + 0.353270i
\(640\) 1.47554e41i 3.01537i
\(641\) 3.32279e40i 0.663838i −0.943308 0.331919i \(-0.892304\pi\)
0.943308 0.331919i \(-0.107696\pi\)
\(642\) 7.74053e39 + 7.11250e40i 0.151187 + 1.38920i
\(643\) 6.25407e40i 1.19427i 0.802140 + 0.597136i \(0.203695\pi\)
−0.802140 + 0.597136i \(0.796305\pi\)
\(644\) 7.16893e40 1.37847e40i 1.33847 0.257367i
\(645\) 1.53411e40 + 1.40964e41i 0.280054 + 2.57331i
\(646\) 1.04114e40 0.185840
\(647\) −2.46712e40 −0.430604 −0.215302 0.976547i \(-0.569074\pi\)
−0.215302 + 0.976547i \(0.569074\pi\)
\(648\) −4.56892e40 9.86804e40i −0.779787 1.68420i
\(649\) 6.85796e40i 1.14458i
\(650\) −4.07350e41 −6.64850
\(651\) −5.19527e39 1.68924e40i −0.0829246 0.269630i
\(652\) 1.74454e41 2.72327
\(653\) 8.56660e40i 1.30788i 0.756547 + 0.653939i \(0.226885\pi\)
−0.756547 + 0.653939i \(0.773115\pi\)
\(654\) 2.34157e40 2.54833e39i 0.349647 0.0380521i
\(655\) −1.64880e40 −0.240807
\(656\) 5.83733e40 0.833889
\(657\) 1.47527e40 + 6.69757e40i 0.206145 + 0.935879i
\(658\) −1.40390e41 + 2.69949e40i −1.91894 + 0.368982i
\(659\) 2.34042e39i 0.0312935i 0.999878 + 0.0156468i \(0.00498073\pi\)
−0.999878 + 0.0156468i \(0.995019\pi\)
\(660\) −3.27875e41 + 3.56826e40i −4.28865 + 0.466734i
\(661\) 4.64889e40i 0.594878i −0.954741 0.297439i \(-0.903868\pi\)
0.954741 0.297439i \(-0.0961325\pi\)
\(662\) 1.82072e41i 2.27930i
\(663\) 1.63869e41 1.78338e40i 2.00701 0.218423i
\(664\) 1.55441e41i 1.86264i
\(665\) 1.26945e40 2.44094e39i 0.148833 0.0286183i
\(666\) 8.11555e38 + 3.68438e39i 0.00930982 + 0.0422657i
\(667\) 4.27119e40 0.479429
\(668\) 1.30006e41 1.42792
\(669\) −8.32227e39 + 9.05713e38i −0.0894465 + 0.00973446i
\(670\) 1.07729e41i 1.13304i
\(671\) −1.07364e41 −1.10505
\(672\) 6.40150e39 + 2.08145e40i 0.0644803 + 0.209658i
\(673\) −1.84928e41 −1.82299 −0.911497 0.411307i \(-0.865072\pi\)
−0.911497 + 0.411307i \(0.865072\pi\)
\(674\) 1.73693e41i 1.67577i
\(675\) 8.29217e40 + 2.45926e41i 0.783003 + 2.32220i
\(676\) 3.13201e41 2.89465
\(677\) −1.58660e41 −1.43527 −0.717633 0.696422i \(-0.754774\pi\)
−0.717633 + 0.696422i \(0.754774\pi\)
\(678\) 1.20736e40 + 1.10940e41i 0.106907 + 0.982332i
\(679\) −1.79099e41 + 3.44378e40i −1.55232 + 0.298486i
\(680\) 5.29036e41i 4.48855i
\(681\) 1.79673e40 + 1.65095e41i 0.149228 + 1.37120i
\(682\) 6.84021e40i 0.556155i
\(683\) 1.21940e41i 0.970609i −0.874345 0.485304i \(-0.838709\pi\)
0.874345 0.485304i \(-0.161291\pi\)
\(684\) −4.64147e39 2.10718e40i −0.0361695 0.164206i
\(685\) 2.70773e41i 2.06582i
\(686\) 1.97201e41 1.26371e41i 1.47302 0.943948i
\(687\) 2.25896e41 2.45843e40i 1.65210 0.179798i
\(688\) −2.30831e41 −1.65296
\(689\) 3.90234e40 0.273619
\(690\) 3.38707e40 + 3.11226e41i 0.232548 + 2.13680i
\(691\) 1.29754e41i 0.872348i 0.899862 + 0.436174i \(0.143667\pi\)
−0.899862 + 0.436174i \(0.856333\pi\)
\(692\) −4.57557e40 −0.301236
\(693\) 1.60527e41 6.91549e40i 1.03494 0.445852i
\(694\) 5.53727e40 0.349610
\(695\) 1.57787e41i 0.975645i
\(696\) 2.40364e40 + 2.20862e41i 0.145558 + 1.33748i
\(697\) 1.54314e41 0.915232
\(698\) −2.43503e41 −1.41449
\(699\) −1.43942e41 + 1.56652e40i −0.818969 + 0.0891283i
\(700\) −1.71123e41 8.89946e41i −0.953643 4.95955i
\(701\) 1.30986e41i 0.715013i 0.933911 + 0.357507i \(0.116373\pi\)
−0.933911 + 0.357507i \(0.883627\pi\)
\(702\) −1.62110e41 4.80781e41i −0.866808 2.57074i
\(703\) 3.85338e38i 0.00201832i
\(704\) 1.76242e41i 0.904284i
\(705\) −4.46591e40 4.10357e41i −0.224475 2.06262i
\(706\) 2.01364e41i 0.991547i
\(707\) 9.16394e39 + 4.76583e40i 0.0442080 + 0.229910i
\(708\) −4.79161e40 4.40284e41i −0.226464 2.08090i
\(709\) 2.32302e41 1.07568 0.537840 0.843047i \(-0.319241\pi\)
0.537840 + 0.843047i \(0.319241\pi\)
\(710\) 2.59127e41 1.17562
\(711\) 1.45816e41 3.21188e40i 0.648182 0.142774i
\(712\) 1.87857e41i 0.818213i
\(713\) 4.37160e40 0.186570
\(714\) 1.60111e41 + 5.20601e41i 0.669571 + 2.17711i
\(715\) −7.92123e41 −3.24605
\(716\) 4.51463e41i 1.81294i
\(717\) 2.92680e41 3.18524e40i 1.15177 0.125347i
\(718\) −9.84790e40 −0.379786
\(719\) −9.86131e40 −0.372705 −0.186353 0.982483i \(-0.559667\pi\)
−0.186353 + 0.982483i \(0.559667\pi\)
\(720\) −5.80961e41 + 1.27968e41i −2.15192 + 0.474001i
\(721\) 1.29331e41 2.48682e40i 0.469505 0.0902784i
\(722\) 4.88437e41i 1.73788i
\(723\) −4.62511e41 + 5.03351e40i −1.61293 + 0.175536i
\(724\) 2.48835e41i 0.850555i
\(725\) 5.30223e41i 1.77647i
\(726\) −1.42932e41 + 1.55553e40i −0.469407 + 0.0510855i
\(727\) 9.34355e40i 0.300790i 0.988626 + 0.150395i \(0.0480545\pi\)
−0.988626 + 0.150395i \(0.951946\pi\)
\(728\) 1.72209e41 + 8.95595e41i 0.543438 + 2.82622i
\(729\) −2.57258e41 + 1.95739e41i −0.795830 + 0.605521i
\(730\) 1.02698e42 3.11443
\(731\) −6.10220e41 −1.81420
\(732\) −6.89283e41 + 7.50146e40i −2.00903 + 0.218643i
\(733\) 3.34929e41i 0.957072i 0.878068 + 0.478536i \(0.158832\pi\)
−0.878068 + 0.478536i \(0.841168\pi\)
\(734\) 7.38217e41 2.06819
\(735\) 3.17274e41 + 5.97220e41i 0.871501 + 1.64047i
\(736\) −5.38660e40 −0.145073
\(737\) 1.48777e41i 0.392879i
\(738\) −1.02176e41 4.63868e41i −0.264564 1.20110i
\(739\) −3.87117e41 −0.982875 −0.491437 0.870913i \(-0.663528\pi\)
−0.491437 + 0.870913i \(0.663528\pi\)
\(740\) 3.80374e40 0.0947002
\(741\) −5.60674e39 5.15183e40i −0.0136882 0.125776i
\(742\) 2.43479e40 + 1.26625e41i 0.0582915 + 0.303153i
\(743\) 7.69793e40i 0.180733i 0.995909 + 0.0903663i \(0.0288038\pi\)
−0.995909 + 0.0903663i \(0.971196\pi\)
\(744\) 2.46015e40 + 2.26054e41i 0.0566439 + 0.520481i
\(745\) 1.89924e41i 0.428857i
\(746\) 1.20267e42i 2.66339i
\(747\) −4.51253e41 + 9.93969e40i −0.980102 + 0.215886i
\(748\) 1.41934e42i 3.02352i
\(749\) −3.75408e41 + 7.21851e40i −0.784364 + 0.150821i
\(750\) 2.28700e42 2.48894e41i 4.68682 0.510067i
\(751\) 6.59473e41 1.32562 0.662809 0.748789i \(-0.269364\pi\)
0.662809 + 0.748789i \(0.269364\pi\)
\(752\) 6.71966e41 1.32492
\(753\) −9.17673e40 8.43217e41i −0.177485 1.63084i
\(754\) 1.03658e42i