Properties

Label 21.22.c.b.20.2
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 22 \)
Character orbit: \([\chi]\) \(=\) 21.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(58.6902423003\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 20.2
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.1

$q$-expansion

\(f(q)\) \(=\) \(q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +O(q^{10})\) \(q+1223.76i q^{2} +(-94027.5 + 40239.2i) q^{3} +599559. q^{4} +3.45471e7 q^{5} +(-4.92432e7 - 1.15067e8i) q^{6} +(-6.99978e8 - 2.61872e8i) q^{7} +3.30013e9i q^{8} +(7.22197e9 - 7.56717e9i) q^{9} +4.22775e10i q^{10} -1.38407e11i q^{11} +(-5.63750e10 + 2.41257e10i) q^{12} -1.98416e11i q^{13} +(3.20469e11 - 8.56606e11i) q^{14} +(-3.24838e12 + 1.39015e12i) q^{15} -2.78121e12 q^{16} -1.12113e13 q^{17} +(9.26042e12 + 8.83798e12i) q^{18} +1.31763e13i q^{19} +2.07130e13 q^{20} +(7.63546e13 - 3.54339e12i) q^{21} +1.69378e14 q^{22} +2.41160e14i q^{23} +(-1.32795e14 - 3.10303e14i) q^{24} +7.16668e14 q^{25} +2.42815e14 q^{26} +(-3.74567e14 + 1.00213e15i) q^{27} +(-4.19678e14 - 1.57008e14i) q^{28} +2.94084e15i q^{29} +(-1.70121e15 - 3.97524e15i) q^{30} +5.22972e15i q^{31} +3.51734e15i q^{32} +(5.56940e15 + 1.30141e16i) q^{33} -1.37200e16i q^{34} +(-2.41822e16 - 9.04692e15i) q^{35} +(4.33000e15 - 4.53696e15i) q^{36} +1.95264e16 q^{37} -1.61247e16 q^{38} +(7.98411e15 + 1.86566e16i) q^{39} +1.14010e17i q^{40} -8.86426e16 q^{41} +(4.33626e15 + 9.34399e16i) q^{42} -2.83588e16 q^{43} -8.29834e16i q^{44} +(2.49499e17 - 2.61424e17i) q^{45} -2.95123e17 q^{46} -5.37703e17 q^{47} +(2.61510e17 - 1.11914e17i) q^{48} +(4.21392e17 + 3.66609e17i) q^{49} +8.77031e17i q^{50} +(1.05417e18 - 4.51135e17i) q^{51} -1.18962e17i q^{52} +1.93110e18i q^{53} +(-1.22637e18 - 4.58381e17i) q^{54} -4.78158e18i q^{55} +(8.64211e17 - 2.31002e18i) q^{56} +(-5.30204e17 - 1.23894e18i) q^{57} -3.59888e18 q^{58} -1.38432e18 q^{59} +(-1.94759e18 + 8.33475e17i) q^{60} +2.80127e18i q^{61} -6.39993e18 q^{62} +(-7.03685e18 + 3.40562e18i) q^{63} -1.01370e19 q^{64} -6.85472e18i q^{65} +(-1.59262e19 + 6.81562e18i) q^{66} +1.55480e19 q^{67} -6.72185e18 q^{68} +(-9.70408e18 - 2.26757e19i) q^{69} +(1.10713e19 - 2.95933e19i) q^{70} +1.31437e19i q^{71} +(2.49727e19 + 2.38335e19i) q^{72} +3.15045e19i q^{73} +2.38956e19i q^{74} +(-6.73865e19 + 2.88381e19i) q^{75} +7.89997e18i q^{76} +(-3.62450e19 + 9.68821e19i) q^{77} +(-2.28312e19 + 9.77065e18i) q^{78} -6.56128e18 q^{79} -9.60829e19 q^{80} +(-5.10520e18 - 1.09300e20i) q^{81} -1.08477e20i q^{82} -1.99817e20 q^{83} +(4.57791e19 - 2.12447e18i) q^{84} -3.87320e20 q^{85} -3.47045e19i q^{86} +(-1.18337e20 - 2.76519e20i) q^{87} +4.56763e20 q^{88} +7.23185e19 q^{89} +(3.19921e20 + 3.05327e20i) q^{90} +(-5.19597e19 + 1.38887e20i) q^{91} +1.44590e20i q^{92} +(-2.10440e20 - 4.91737e20i) q^{93} -6.58020e20i q^{94} +4.55204e20i q^{95} +(-1.41535e20 - 3.30726e20i) q^{96} -6.71547e19i q^{97} +(-4.48642e20 + 5.15684e20i) q^{98} +(-1.04735e21 - 9.99575e20i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} + O(q^{10}) \) \( 52q - 58720260q^{4} + 1422287188q^{7} + 10150644696q^{9} - 687153165468q^{15} + 36241782390404q^{16} + 36759093002772q^{18} + 79412641656180q^{21} + 228880341648112q^{22} + 4502168959229812q^{25} - 328465100861772q^{28} - 2422487119598196q^{30} + 94669723666911312q^{36} - 111253244635261912q^{37} - 198389110134084780q^{39} - 125754675449474820q^{42} + 808208758088766656q^{43} - 1124214920076830456q^{46} + 760563680048831596q^{49} + 4341973540932052200q^{51} - 13080454499124088812q^{57} - 10814528487339424568q^{58} + 13643758017961015644q^{60} - 38182310822257441896q^{63} - 30480555033993680900q^{64} - 25547251957658589040q^{67} + 73727169165159410040q^{70} + 39846964674222889428q^{72} + 45848199464273536260q^{78} + 199210197493083963080q^{79} + 235499606962845306588q^{81} - 373919224753720758924q^{84} - 570842672309470848672q^{85} - 1060053674241923431168q^{88} - 923077800435233893128q^{91} - 2832166256981601869904q^{93} + 1525182290356701596928q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1223.76i 0.845049i 0.906351 + 0.422525i \(0.138856\pi\)
−0.906351 + 0.422525i \(0.861144\pi\)
\(3\) −94027.5 + 40239.2i −0.919351 + 0.393437i
\(4\) 599559. 0.285892
\(5\) 3.45471e7 1.58208 0.791038 0.611768i \(-0.209541\pi\)
0.791038 + 0.611768i \(0.209541\pi\)
\(6\) −4.92432e7 1.15067e8i −0.332474 0.776897i
\(7\) −6.99978e8 2.61872e8i −0.936602 0.350396i
\(8\) 3.30013e9i 1.08664i
\(9\) 7.22197e9 7.56717e9i 0.690414 0.723415i
\(10\) 4.22775e10i 1.33693i
\(11\) 1.38407e11i 1.60893i −0.594002 0.804463i \(-0.702453\pi\)
0.594002 0.804463i \(-0.297547\pi\)
\(12\) −5.63750e10 + 2.41257e10i −0.262835 + 0.112481i
\(13\) 1.98416e11i 0.399183i −0.979879 0.199592i \(-0.936038\pi\)
0.979879 0.199592i \(-0.0639616\pi\)
\(14\) 3.20469e11 8.56606e11i 0.296102 0.791474i
\(15\) −3.24838e12 + 1.39015e12i −1.45448 + 0.622448i
\(16\) −2.78121e12 −0.632374
\(17\) −1.12113e13 −1.34879 −0.674394 0.738372i \(-0.735595\pi\)
−0.674394 + 0.738372i \(0.735595\pi\)
\(18\) 9.26042e12 + 8.83798e12i 0.611321 + 0.583434i
\(19\) 1.31763e13i 0.493039i 0.969138 + 0.246519i \(0.0792869\pi\)
−0.969138 + 0.246519i \(0.920713\pi\)
\(20\) 2.07130e13 0.452302
\(21\) 7.63546e13 3.54339e12i 0.998925 0.0463571i
\(22\) 1.69378e14 1.35962
\(23\) 2.41160e14i 1.21384i 0.794761 + 0.606922i \(0.207596\pi\)
−0.794761 + 0.606922i \(0.792404\pi\)
\(24\) −1.32795e14 3.10303e14i −0.427526 0.999006i
\(25\) 7.16668e14 1.50296
\(26\) 2.42815e14 0.337330
\(27\) −3.74567e14 + 1.00213e15i −0.350115 + 0.936707i
\(28\) −4.19678e14 1.57008e14i −0.267767 0.100175i
\(29\) 2.94084e15i 1.29805i 0.760767 + 0.649026i \(0.224823\pi\)
−0.760767 + 0.649026i \(0.775177\pi\)
\(30\) −1.70121e15 3.97524e15i −0.525999 1.22911i
\(31\) 5.22972e15i 1.14599i 0.819559 + 0.572995i \(0.194218\pi\)
−0.819559 + 0.572995i \(0.805782\pi\)
\(32\) 3.51734e15i 0.552255i
\(33\) 5.56940e15 + 1.30141e16i 0.633012 + 1.47917i
\(34\) 1.37200e16i 1.13979i
\(35\) −2.41822e16 9.04692e15i −1.48177 0.554353i
\(36\) 4.33000e15 4.53696e15i 0.197384 0.206818i
\(37\) 1.95264e16 0.667580 0.333790 0.942648i \(-0.391672\pi\)
0.333790 + 0.942648i \(0.391672\pi\)
\(38\) −1.61247e16 −0.416642
\(39\) 7.98411e15 + 1.86566e16i 0.157054 + 0.366990i
\(40\) 1.14010e17i 1.71915i
\(41\) −8.86426e16 −1.03136 −0.515682 0.856780i \(-0.672461\pi\)
−0.515682 + 0.856780i \(0.672461\pi\)
\(42\) 4.33626e15 + 9.34399e16i 0.0391740 + 0.844141i
\(43\) −2.83588e16 −0.200110 −0.100055 0.994982i \(-0.531902\pi\)
−0.100055 + 0.994982i \(0.531902\pi\)
\(44\) 8.29834e16i 0.459979i
\(45\) 2.49499e17 2.61424e17i 1.09229 1.14450i
\(46\) −2.95123e17 −1.02576
\(47\) −5.37703e17 −1.49113 −0.745564 0.666434i \(-0.767820\pi\)
−0.745564 + 0.666434i \(0.767820\pi\)
\(48\) 2.61510e17 1.11914e17i 0.581374 0.248800i
\(49\) 4.21392e17 + 3.66609e17i 0.754445 + 0.656363i
\(50\) 8.77031e17i 1.27008i
\(51\) 1.05417e18 4.51135e17i 1.24001 0.530664i
\(52\) 1.18962e17i 0.114123i
\(53\) 1.93110e18i 1.51673i 0.651831 + 0.758364i \(0.274001\pi\)
−0.651831 + 0.758364i \(0.725999\pi\)
\(54\) −1.22637e18 4.58381e17i −0.791563 0.295864i
\(55\) 4.78158e18i 2.54544i
\(56\) 8.64211e17 2.31002e18i 0.380755 1.01775i
\(57\) −5.30204e17 1.23894e18i −0.193980 0.453276i
\(58\) −3.59888e18 −1.09692
\(59\) −1.38432e18 −0.352606 −0.176303 0.984336i \(-0.556414\pi\)
−0.176303 + 0.984336i \(0.556414\pi\)
\(60\) −1.94759e18 + 8.33475e17i −0.415825 + 0.177953i
\(61\) 2.80127e18i 0.502796i 0.967884 + 0.251398i \(0.0808903\pi\)
−0.967884 + 0.251398i \(0.919110\pi\)
\(62\) −6.39993e18 −0.968417
\(63\) −7.03685e18 + 3.40562e18i −0.900124 + 0.435633i
\(64\) −1.01370e19 −1.09906
\(65\) 6.85472e18i 0.631538i
\(66\) −1.59262e19 + 6.81562e18i −1.24997 + 0.534926i
\(67\) 1.55480e19 1.04205 0.521026 0.853541i \(-0.325549\pi\)
0.521026 + 0.853541i \(0.325549\pi\)
\(68\) −6.72185e18 −0.385608
\(69\) −9.70408e18 2.26757e19i −0.477572 1.11595i
\(70\) 1.10713e19 2.95933e19i 0.468456 1.25217i
\(71\) 1.31437e19i 0.479188i 0.970873 + 0.239594i \(0.0770143\pi\)
−0.970873 + 0.239594i \(0.922986\pi\)
\(72\) 2.49727e19 + 2.38335e19i 0.786093 + 0.750233i
\(73\) 3.15045e19i 0.857991i 0.903307 + 0.428996i \(0.141132\pi\)
−0.903307 + 0.428996i \(0.858868\pi\)
\(74\) 2.38956e19i 0.564138i
\(75\) −6.73865e19 + 2.88381e19i −1.38175 + 0.591322i
\(76\) 7.89997e18i 0.140956i
\(77\) −3.62450e19 + 9.68821e19i −0.563762 + 1.50692i
\(78\) −2.28312e19 + 9.77065e18i −0.310124 + 0.132718i
\(79\) −6.56128e18 −0.0779658 −0.0389829 0.999240i \(-0.512412\pi\)
−0.0389829 + 0.999240i \(0.512412\pi\)
\(80\) −9.60829e19 −1.00046
\(81\) −5.10520e18 1.09300e20i −0.0466573 0.998911i
\(82\) 1.08477e20i 0.871553i
\(83\) −1.99817e20 −1.41355 −0.706776 0.707438i \(-0.749851\pi\)
−0.706776 + 0.707438i \(0.749851\pi\)
\(84\) 4.57791e19 2.12447e18i 0.285585 0.0132531i
\(85\) −3.87320e20 −2.13388
\(86\) 3.47045e19i 0.169103i
\(87\) −1.18337e20 2.76519e20i −0.510702 1.19337i
\(88\) 4.56763e20 1.74833
\(89\) 7.23185e19 0.245841 0.122921 0.992417i \(-0.460774\pi\)
0.122921 + 0.992417i \(0.460774\pi\)
\(90\) 3.19921e20 + 3.05327e20i 0.967156 + 0.923036i
\(91\) −5.19597e19 + 1.38887e20i −0.139872 + 0.373876i
\(92\) 1.44590e20i 0.347028i
\(93\) −2.10440e20 4.91737e20i −0.450875 1.05357i
\(94\) 6.58020e20i 1.26008i
\(95\) 4.55204e20i 0.780024i
\(96\) −1.41535e20 3.30726e20i −0.217278 0.507716i
\(97\) 6.71547e19i 0.0924641i −0.998931 0.0462320i \(-0.985279\pi\)
0.998931 0.0462320i \(-0.0147214\pi\)
\(98\) −4.48642e20 + 5.15684e20i −0.554659 + 0.637543i
\(99\) −1.04735e21 9.99575e20i −1.16392 1.11083i
\(100\) 4.29685e20 0.429685
\(101\) 1.32040e21 1.18941 0.594704 0.803945i \(-0.297269\pi\)
0.594704 + 0.803945i \(0.297269\pi\)
\(102\) 5.52082e20 + 1.29006e21i 0.448437 + 1.04787i
\(103\) 9.37344e20i 0.687240i 0.939109 + 0.343620i \(0.111653\pi\)
−0.939109 + 0.343620i \(0.888347\pi\)
\(104\) 6.54801e20 0.433769
\(105\) 2.63783e21 1.22414e20i 1.58037 0.0733403i
\(106\) −2.36320e21 −1.28171
\(107\) 1.56246e21i 0.767857i −0.923363 0.383928i \(-0.874571\pi\)
0.923363 0.383928i \(-0.125429\pi\)
\(108\) −2.24575e20 + 6.00835e20i −0.100095 + 0.267797i
\(109\) 2.46852e21 0.998754 0.499377 0.866385i \(-0.333562\pi\)
0.499377 + 0.866385i \(0.333562\pi\)
\(110\) 5.85152e21 2.15102
\(111\) −1.83601e21 + 7.85724e20i −0.613740 + 0.262651i
\(112\) 1.94679e21 + 7.28320e20i 0.592282 + 0.221581i
\(113\) 1.13111e21i 0.313461i 0.987641 + 0.156730i \(0.0500954\pi\)
−0.987641 + 0.156730i \(0.949905\pi\)
\(114\) 1.51616e21 6.48843e20i 0.383040 0.163923i
\(115\) 8.33139e21i 1.92039i
\(116\) 1.76320e21i 0.371102i
\(117\) −1.50145e21 1.43296e21i −0.288775 0.275602i
\(118\) 1.69407e21i 0.297969i
\(119\) 7.84769e21 + 2.93593e21i 1.26328 + 0.472610i
\(120\) −4.58767e21 1.07201e22i −0.676378 1.58050i
\(121\) −1.17564e22 −1.58864
\(122\) −3.42809e21 −0.424887
\(123\) 8.33484e21 3.56690e21i 0.948186 0.405777i
\(124\) 3.13552e21i 0.327629i
\(125\) 8.28547e21 0.795724
\(126\) −4.16767e21 8.61143e21i −0.368131 0.760649i
\(127\) 5.14526e21 0.418281 0.209140 0.977886i \(-0.432933\pi\)
0.209140 + 0.977886i \(0.432933\pi\)
\(128\) 5.02889e21i 0.376502i
\(129\) 2.66651e21 1.14114e21i 0.183972 0.0787309i
\(130\) 8.38855e21 0.533681
\(131\) −1.92037e22 −1.12729 −0.563647 0.826016i \(-0.690602\pi\)
−0.563647 + 0.826016i \(0.690602\pi\)
\(132\) 3.33918e21 + 7.80272e21i 0.180973 + 0.422882i
\(133\) 3.45050e21 9.22313e21i 0.172759 0.461781i
\(134\) 1.90271e22i 0.880585i
\(135\) −1.29402e22 + 3.46207e22i −0.553908 + 1.48194i
\(136\) 3.69989e22i 1.46565i
\(137\) 1.79781e22i 0.659446i 0.944078 + 0.329723i \(0.106955\pi\)
−0.944078 + 0.329723i \(0.893045\pi\)
\(138\) 2.77496e22 1.18755e22i 0.943033 0.403572i
\(139\) 4.29132e22i 1.35187i −0.736961 0.675935i \(-0.763740\pi\)
0.736961 0.675935i \(-0.236260\pi\)
\(140\) −1.44987e22 5.42416e21i −0.423627 0.158485i
\(141\) 5.05588e22 2.16367e22i 1.37087 0.586666i
\(142\) −1.60848e22 −0.404937
\(143\) −2.74623e22 −0.642257
\(144\) −2.00858e22 + 2.10459e22i −0.436600 + 0.457469i
\(145\) 1.01597e23i 2.05361i
\(146\) −3.85540e22 −0.725045
\(147\) −5.43745e22 1.75148e22i −0.951838 0.306601i
\(148\) 1.17072e22 0.190856
\(149\) 7.26126e22i 1.10295i −0.834191 0.551475i \(-0.814065\pi\)
0.834191 0.551475i \(-0.185935\pi\)
\(150\) −3.52910e22 8.24650e22i −0.499696 1.16765i
\(151\) −4.63871e22 −0.612546 −0.306273 0.951944i \(-0.599082\pi\)
−0.306273 + 0.951944i \(0.599082\pi\)
\(152\) −4.34836e22 −0.535757
\(153\) −8.09680e22 + 8.48381e22i −0.931222 + 0.975733i
\(154\) −1.18561e23 4.43552e22i −1.27342 0.476406i
\(155\) 1.80672e23i 1.81304i
\(156\) 4.78694e21 + 1.11857e22i 0.0449004 + 0.104919i
\(157\) 9.02342e22i 0.791453i 0.918368 + 0.395726i \(0.129507\pi\)
−0.918368 + 0.395726i \(0.870493\pi\)
\(158\) 8.02945e21i 0.0658850i
\(159\) −7.77058e22 1.81576e23i −0.596738 1.39441i
\(160\) 1.21514e23i 0.873709i
\(161\) 6.31530e22 1.68807e23i 0.425327 1.13689i
\(162\) 1.33757e23 6.24755e21i 0.844129 0.0394277i
\(163\) 4.02213e22 0.237950 0.118975 0.992897i \(-0.462039\pi\)
0.118975 + 0.992897i \(0.462039\pi\)
\(164\) −5.31464e22 −0.294859
\(165\) 1.92407e23 + 4.49600e23i 1.00147 + 2.34016i
\(166\) 2.44528e23i 1.19452i
\(167\) −5.26157e22 −0.241320 −0.120660 0.992694i \(-0.538501\pi\)
−0.120660 + 0.992694i \(0.538501\pi\)
\(168\) 1.16936e22 + 2.51980e23i 0.0503735 + 1.08547i
\(169\) 2.07695e23 0.840653
\(170\) 4.73987e23i 1.80324i
\(171\) 9.97074e22 + 9.51590e22i 0.356671 + 0.340401i
\(172\) −1.70028e22 −0.0572099
\(173\) 3.02093e23 0.956436 0.478218 0.878241i \(-0.341283\pi\)
0.478218 + 0.878241i \(0.341283\pi\)
\(174\) 3.38394e23 1.44816e23i 1.00845 0.431568i
\(175\) −5.01652e23 1.87675e23i −1.40768 0.526632i
\(176\) 3.84940e23i 1.01744i
\(177\) 1.30164e23 5.57037e22i 0.324168 0.138728i
\(178\) 8.85006e22i 0.207748i
\(179\) 5.35659e23i 1.18558i −0.805356 0.592791i \(-0.798026\pi\)
0.805356 0.592791i \(-0.201974\pi\)
\(180\) 1.49589e23 1.56739e23i 0.312276 0.327202i
\(181\) 8.67409e22i 0.170844i −0.996345 0.0854218i \(-0.972776\pi\)
0.996345 0.0854218i \(-0.0272238\pi\)
\(182\) −1.69965e23 6.35863e22i −0.315943 0.118199i
\(183\) −1.12721e23 2.63396e23i −0.197819 0.462246i
\(184\) −7.95860e23 −1.31901
\(185\) 6.74580e23 1.05616
\(186\) 6.01769e23 2.57528e23i 0.890316 0.381012i
\(187\) 1.55173e24i 2.17010i
\(188\) −3.22384e23 −0.426301
\(189\) 5.24618e23 6.03379e23i 0.656136 0.754642i
\(190\) −5.57061e23 −0.659159
\(191\) 4.88545e23i 0.547084i 0.961860 + 0.273542i \(0.0881953\pi\)
−0.961860 + 0.273542i \(0.911805\pi\)
\(192\) 9.53157e23 4.07905e23i 1.01042 0.432410i
\(193\) 8.38721e23 0.841910 0.420955 0.907082i \(-0.361695\pi\)
0.420955 + 0.907082i \(0.361695\pi\)
\(194\) 8.21813e22 0.0781367
\(195\) 2.75828e23 + 6.44532e23i 0.248471 + 0.580606i
\(196\) 2.52649e23 + 2.19804e23i 0.215690 + 0.187649i
\(197\) 1.14045e24i 0.922955i −0.887152 0.461478i \(-0.847319\pi\)
0.887152 0.461478i \(-0.152681\pi\)
\(198\) 1.22324e24 1.28171e24i 0.938702 0.983570i
\(199\) 5.50546e23i 0.400716i −0.979723 0.200358i \(-0.935790\pi\)
0.979723 0.200358i \(-0.0642105\pi\)
\(200\) 2.36510e24i 1.63318i
\(201\) −1.46194e24 + 6.25639e23i −0.958012 + 0.409982i
\(202\) 1.61585e24i 1.00511i
\(203\) 7.70122e23 2.05852e24i 0.454832 1.21576i
\(204\) 6.32039e23 2.70482e23i 0.354509 0.151712i
\(205\) −3.06235e24 −1.63169
\(206\) −1.14709e24 −0.580751
\(207\) 1.82490e24 + 1.74165e24i 0.878113 + 0.838055i
\(208\) 5.51838e23i 0.252433i
\(209\) 1.82370e24 0.793263
\(210\) 1.49805e23 + 3.22808e24i 0.0619762 + 1.33549i
\(211\) −4.11913e24 −1.62121 −0.810605 0.585593i \(-0.800862\pi\)
−0.810605 + 0.585593i \(0.800862\pi\)
\(212\) 1.15781e24i 0.433620i
\(213\) −5.28892e23 1.23587e24i −0.188530 0.440542i
\(214\) 1.91208e24 0.648877
\(215\) −9.79717e23 −0.316590
\(216\) −3.30715e24 1.23612e24i −1.01786 0.380449i
\(217\) 1.36952e24 3.66069e24i 0.401550 1.07334i
\(218\) 3.02088e24i 0.843996i
\(219\) −1.26772e24 2.96229e24i −0.337566 0.788795i
\(220\) 2.86684e24i 0.727721i
\(221\) 2.22451e24i 0.538414i
\(222\) −9.61539e23 2.24684e24i −0.221953 0.518641i
\(223\) 8.67661e24i 1.91051i 0.295787 + 0.955254i \(0.404418\pi\)
−0.295787 + 0.955254i \(0.595582\pi\)
\(224\) 9.21092e23 2.46206e24i 0.193508 0.517243i
\(225\) 5.17576e24 5.42315e24i 1.03767 1.08726i
\(226\) −1.38422e24 −0.264890
\(227\) 1.73350e23 0.0316702 0.0158351 0.999875i \(-0.494959\pi\)
0.0158351 + 0.999875i \(0.494959\pi\)
\(228\) −3.17888e23 7.42814e23i −0.0554573 0.129588i
\(229\) 1.02017e25i 1.69981i −0.526936 0.849905i \(-0.676659\pi\)
0.526936 0.849905i \(-0.323341\pi\)
\(230\) −1.01956e25 −1.62283
\(231\) −4.90431e23 1.05680e25i −0.0745851 1.60720i
\(232\) −9.70515e24 −1.41052
\(233\) 1.18566e25i 1.64711i 0.567234 + 0.823557i \(0.308014\pi\)
−0.567234 + 0.823557i \(0.691986\pi\)
\(234\) 1.75360e24 1.83742e24i 0.232897 0.244029i
\(235\) −1.85761e25 −2.35908
\(236\) −8.29979e23 −0.100807
\(237\) 6.16941e23 2.64021e23i 0.0716780 0.0306747i
\(238\) −3.59288e24 + 9.60370e24i −0.399379 + 1.06753i
\(239\) 6.52754e23i 0.0694339i −0.999397 0.0347170i \(-0.988947\pi\)
0.999397 0.0347170i \(-0.0110530\pi\)
\(240\) 9.03443e24 3.86629e24i 0.919777 0.393620i
\(241\) 1.09066e24i 0.106295i 0.998587 + 0.0531474i \(0.0169253\pi\)
−0.998587 + 0.0531474i \(0.983075\pi\)
\(242\) 1.43870e25i 1.34248i
\(243\) 4.87816e24 + 1.00718e25i 0.435903 + 0.899993i
\(244\) 1.67953e24i 0.143745i
\(245\) 1.45579e25 + 1.26653e25i 1.19359 + 1.03842i
\(246\) 4.36504e24 + 1.01999e25i 0.342902 + 0.801263i
\(247\) 2.61440e24 0.196813
\(248\) −1.72588e25 −1.24528
\(249\) 1.87882e25 8.04045e24i 1.29955 0.556144i
\(250\) 1.01394e25i 0.672426i
\(251\) −7.60023e24 −0.483340 −0.241670 0.970359i \(-0.577695\pi\)
−0.241670 + 0.970359i \(0.577695\pi\)
\(252\) −4.21901e24 + 2.04187e24i −0.257338 + 0.124544i
\(253\) 3.33783e25 1.95299
\(254\) 6.29657e24i 0.353468i
\(255\) 3.64187e25 1.55854e25i 1.96179 0.839550i
\(256\) −1.51047e25 −0.780894
\(257\) 1.51964e25 0.754126 0.377063 0.926188i \(-0.376934\pi\)
0.377063 + 0.926188i \(0.376934\pi\)
\(258\) 1.39648e24 + 3.26317e24i 0.0665315 + 0.155465i
\(259\) −1.36680e25 5.11340e24i −0.625256 0.233917i
\(260\) 4.10981e24i 0.180552i
\(261\) 2.22538e25 + 2.12386e25i 0.939029 + 0.896193i
\(262\) 2.35008e25i 0.952619i
\(263\) 2.96038e25i 1.15296i −0.817113 0.576478i \(-0.804427\pi\)
0.817113 0.576478i \(-0.195573\pi\)
\(264\) −4.29482e25 + 1.83797e25i −1.60733 + 0.687857i
\(265\) 6.67139e25i 2.39958i
\(266\) 1.12869e25 + 4.22260e24i 0.390228 + 0.145990i
\(267\) −6.79992e24 + 2.91004e24i −0.226014 + 0.0967231i
\(268\) 9.32194e24 0.297914
\(269\) 2.14097e25 0.657979 0.328989 0.944334i \(-0.393292\pi\)
0.328989 + 0.944334i \(0.393292\pi\)
\(270\) −4.23675e25 1.58358e25i −1.25231 0.468079i
\(271\) 3.15046e25i 0.895770i 0.894091 + 0.447885i \(0.147823\pi\)
−0.894091 + 0.447885i \(0.852177\pi\)
\(272\) 3.11811e25 0.852938
\(273\) −7.03066e23 1.51500e25i −0.0185050 0.398754i
\(274\) −2.20010e25 −0.557264
\(275\) 9.91922e25i 2.41816i
\(276\) −5.81817e24 1.35954e25i −0.136534 0.319041i
\(277\) −5.47081e25 −1.23599 −0.617994 0.786183i \(-0.712054\pi\)
−0.617994 + 0.786183i \(0.712054\pi\)
\(278\) 5.25155e25 1.14240
\(279\) 3.95742e25 + 3.77689e25i 0.829026 + 0.791207i
\(280\) 2.98560e25 7.98046e25i 0.602383 1.61016i
\(281\) 1.52007e24i 0.0295425i 0.999891 + 0.0147712i \(0.00470201\pi\)
−0.999891 + 0.0147712i \(0.995298\pi\)
\(282\) 2.64782e25 + 6.18720e25i 0.495761 + 1.15845i
\(283\) 2.48723e25i 0.448703i −0.974508 0.224351i \(-0.927974\pi\)
0.974508 0.224351i \(-0.0720263\pi\)
\(284\) 7.88043e24i 0.136996i
\(285\) −1.83170e25 4.28017e25i −0.306891 0.717117i
\(286\) 3.36073e25i 0.542739i
\(287\) 6.20478e25 + 2.32130e25i 0.965977 + 0.361386i
\(288\) 2.66163e25 + 2.54021e25i 0.399509 + 0.381284i
\(289\) 5.66021e25 0.819229
\(290\) −1.24331e26 −1.73541
\(291\) 2.70225e24 + 6.31438e24i 0.0363788 + 0.0850070i
\(292\) 1.88888e25i 0.245293i
\(293\) −1.45882e26 −1.82764 −0.913821 0.406116i \(-0.866883\pi\)
−0.913821 + 0.406116i \(0.866883\pi\)
\(294\) 2.14340e25 6.65414e25i 0.259093 0.804350i
\(295\) −4.78242e25 −0.557849
\(296\) 6.44396e25i 0.725420i
\(297\) 1.38702e26 + 5.18429e25i 1.50709 + 0.563309i
\(298\) 8.88605e25 0.932047
\(299\) 4.78501e25 0.484547
\(300\) −4.04022e25 + 1.72901e25i −0.395031 + 0.169054i
\(301\) 1.98506e25 + 7.42638e24i 0.187424 + 0.0701179i
\(302\) 5.67667e25i 0.517632i
\(303\) −1.24154e26 + 5.31318e25i −1.09348 + 0.467958i
\(304\) 3.66461e25i 0.311785i
\(305\) 9.67759e25i 0.795461i
\(306\) −1.03822e26 9.90855e25i −0.824542 0.786928i
\(307\) 1.28667e26i 0.987445i 0.869619 + 0.493723i \(0.164364\pi\)
−0.869619 + 0.493723i \(0.835636\pi\)
\(308\) −2.17310e25 + 5.80865e25i −0.161175 + 0.430817i
\(309\) −3.77180e25 8.81361e25i −0.270386 0.631815i
\(310\) −2.21099e26 −1.53211
\(311\) −1.53383e26 −1.02752 −0.513762 0.857933i \(-0.671749\pi\)
−0.513762 + 0.857933i \(0.671749\pi\)
\(312\) −6.15692e25 + 2.63486e25i −0.398787 + 0.170661i
\(313\) 6.75251e25i 0.422912i −0.977388 0.211456i \(-0.932180\pi\)
0.977388 0.211456i \(-0.0678205\pi\)
\(314\) −1.10425e26 −0.668816
\(315\) −2.43103e26 + 1.17655e26i −1.42406 + 0.689204i
\(316\) −3.93388e24 −0.0222898
\(317\) 2.10670e24i 0.0115473i 0.999983 + 0.00577365i \(0.00183782\pi\)
−0.999983 + 0.00577365i \(0.998162\pi\)
\(318\) 2.22206e26 9.50933e25i 1.17834 0.504273i
\(319\) 4.07034e26 2.08847
\(320\) −3.50205e26 −1.73879
\(321\) 6.28722e25 + 1.46914e26i 0.302104 + 0.705930i
\(322\) 2.06579e26 + 7.72843e25i 0.960727 + 0.359422i
\(323\) 1.47724e26i 0.665005i
\(324\) −3.06087e24 6.55317e25i −0.0133389 0.285581i
\(325\) 1.42199e26i 0.599958i
\(326\) 4.92213e25i 0.201080i
\(327\) −2.32109e26 + 9.93312e25i −0.918206 + 0.392947i
\(328\) 2.92532e26i 1.12072i
\(329\) 3.76380e26 + 1.40809e26i 1.39659 + 0.522485i
\(330\) −5.50203e26 + 2.35460e26i −1.97755 + 0.846294i
\(331\) 6.10254e25 0.212479 0.106240 0.994341i \(-0.466119\pi\)
0.106240 + 0.994341i \(0.466119\pi\)
\(332\) −1.19802e26 −0.404123
\(333\) 1.41019e26 1.47759e26i 0.460906 0.482937i
\(334\) 6.43891e25i 0.203927i
\(335\) 5.37139e26 1.64860
\(336\) −2.12358e26 + 9.85490e24i −0.631694 + 0.0293150i
\(337\) 3.60725e26 1.04007 0.520034 0.854146i \(-0.325919\pi\)
0.520034 + 0.854146i \(0.325919\pi\)
\(338\) 2.54170e26i 0.710393i
\(339\) −4.55151e25 1.06356e26i −0.123327 0.288180i
\(340\) −2.32221e26 −0.610060
\(341\) 7.23832e26 1.84381
\(342\) −1.16452e26 + 1.22018e26i −0.287655 + 0.301405i
\(343\) −1.98961e26 3.66969e26i −0.476627 0.879105i
\(344\) 9.35879e25i 0.217448i
\(345\) −3.35248e26 7.83380e26i −0.755555 1.76552i
\(346\) 3.69689e26i 0.808236i
\(347\) 7.67821e26i 1.62855i 0.580481 + 0.814274i \(0.302865\pi\)
−0.580481 + 0.814274i \(0.697135\pi\)
\(348\) −7.09498e25 1.65790e26i −0.146006 0.341173i
\(349\) 2.40328e26i 0.479884i −0.970787 0.239942i \(-0.922872\pi\)
0.970787 0.239942i \(-0.0771285\pi\)
\(350\) 2.29670e26 6.13902e26i 0.445030 1.18956i
\(351\) 1.98839e26 + 7.43203e25i 0.373918 + 0.139760i
\(352\) 4.86826e26 0.888537
\(353\) 1.97397e25 0.0349708 0.0174854 0.999847i \(-0.494434\pi\)
0.0174854 + 0.999847i \(0.494434\pi\)
\(354\) 6.81681e25 + 1.59289e26i 0.117232 + 0.273938i
\(355\) 4.54078e26i 0.758111i
\(356\) 4.33592e25 0.0702840
\(357\) −8.56038e26 + 3.97261e25i −1.34734 + 0.0625258i
\(358\) 6.55520e26 1.00188
\(359\) 7.21127e26i 1.07034i −0.844746 0.535168i \(-0.820248\pi\)
0.844746 0.535168i \(-0.179752\pi\)
\(360\) 8.62734e26 + 8.23378e26i 1.24366 + 1.18692i
\(361\) 5.40594e26 0.756913
\(362\) 1.06150e26 0.144371
\(363\) 1.10542e27 4.73066e26i 1.46052 0.625032i
\(364\) −3.11529e25 + 8.32710e25i −0.0399884 + 0.106888i
\(365\) 1.08839e27i 1.35741i
\(366\) 3.22335e26 1.37943e26i 0.390621 0.167167i
\(367\) 2.53576e26i 0.298616i 0.988791 + 0.149308i \(0.0477047\pi\)
−0.988791 + 0.149308i \(0.952295\pi\)
\(368\) 6.70717e26i 0.767604i
\(369\) −6.40174e26 + 6.70774e26i −0.712068 + 0.746104i
\(370\) 8.25525e26i 0.892508i
\(371\) 5.05700e26 1.35173e27i 0.531456 1.42057i
\(372\) −1.26171e26 2.94825e26i −0.128902 0.301206i
\(373\) −4.36853e26 −0.433903 −0.216952 0.976182i \(-0.569611\pi\)
−0.216952 + 0.976182i \(0.569611\pi\)
\(374\) −1.89895e27 −1.83384
\(375\) −7.79062e26 + 3.33400e26i −0.731550 + 0.313067i
\(376\) 1.77449e27i 1.62032i
\(377\) 5.83510e26 0.518161
\(378\) 7.38392e26 + 6.42007e26i 0.637710 + 0.554467i
\(379\) 9.77018e26 0.820712 0.410356 0.911925i \(-0.365404\pi\)
0.410356 + 0.911925i \(0.365404\pi\)
\(380\) 2.72922e26i 0.223003i
\(381\) −4.83795e26 + 2.07041e26i −0.384547 + 0.164567i
\(382\) −5.97863e26 −0.462313
\(383\) −1.58081e27 −1.18930 −0.594652 0.803984i \(-0.702710\pi\)
−0.594652 + 0.803984i \(0.702710\pi\)
\(384\) 2.02358e26 + 4.72853e26i 0.148130 + 0.346138i
\(385\) −1.25216e27 + 3.34700e27i −0.891913 + 2.38407i
\(386\) 1.02639e27i 0.711455i
\(387\) −2.04807e26 + 2.14596e26i −0.138159 + 0.144763i
\(388\) 4.02632e25i 0.0264347i
\(389\) 4.76046e26i 0.304213i −0.988364 0.152107i \(-0.951394\pi\)
0.988364 0.152107i \(-0.0486057\pi\)
\(390\) −7.88754e26 + 3.37548e26i −0.490640 + 0.209970i
\(391\) 2.70373e27i 1.63722i
\(392\) −1.20986e27 + 1.39065e27i −0.713232 + 0.819812i
\(393\) 1.80568e27 7.72742e26i 1.03638 0.443520i
\(394\) 1.39564e27 0.779943
\(395\) −2.26674e26 −0.123348
\(396\) −6.27950e26 5.99304e26i −0.332756 0.317576i
\(397\) 3.21025e27i 1.65668i −0.560225 0.828340i \(-0.689285\pi\)
0.560225 0.828340i \(-0.310715\pi\)
\(398\) 6.73737e26 0.338624
\(399\) 4.66888e25 + 1.00607e27i 0.0228558 + 0.492509i
\(400\) −1.99320e27 −0.950434
\(401\) 2.46908e27i 1.14688i 0.819247 + 0.573441i \(0.194392\pi\)
−0.819247 + 0.573441i \(0.805608\pi\)
\(402\) −7.65633e26 1.78907e27i −0.346455 0.809567i
\(403\) 1.03766e27 0.457460
\(404\) 7.91657e26 0.340042
\(405\) −1.76370e26 3.77600e27i −0.0738154 1.58035i
\(406\) 2.51914e27 + 9.42446e26i 1.02737 + 0.384355i
\(407\) 2.70259e27i 1.07409i
\(408\) 1.48880e27 + 3.47891e27i 0.576642 + 1.34745i
\(409\) 1.42944e26i 0.0539597i 0.999636 + 0.0269799i \(0.00858900\pi\)
−0.999636 + 0.0269799i \(0.991411\pi\)
\(410\) 3.74758e27i 1.37886i
\(411\) −7.23426e26 1.69044e27i −0.259451 0.606262i
\(412\) 5.61993e26i 0.196476i
\(413\) 9.68991e26 + 3.62513e26i 0.330251 + 0.123552i
\(414\) −2.13137e27 + 2.23324e27i −0.708198 + 0.742049i
\(415\) −6.90309e27 −2.23634
\(416\) 6.97898e26 0.220451
\(417\) 1.72679e27 + 4.03502e27i 0.531877 + 1.24284i
\(418\) 2.23177e27i 0.670346i
\(419\) −1.51781e27 −0.444601 −0.222301 0.974978i \(-0.571357\pi\)
−0.222301 + 0.974978i \(0.571357\pi\)
\(420\) 1.58154e27 7.33943e25i 0.451816 0.0209674i
\(421\) −5.17334e26 −0.144148 −0.0720741 0.997399i \(-0.522962\pi\)
−0.0720741 + 0.997399i \(0.522962\pi\)
\(422\) 5.04083e27i 1.37000i
\(423\) −3.88328e27 + 4.06889e27i −1.02950 + 1.07870i
\(424\) −6.37288e27 −1.64814
\(425\) −8.03481e27 −2.02718
\(426\) 1.51241e27 6.47238e26i 0.372279 0.159317i
\(427\) 7.33574e26 1.96083e27i 0.176178 0.470920i
\(428\) 9.36788e26i 0.219524i
\(429\) 2.58221e27 1.10506e27i 0.590460 0.252688i
\(430\) 1.19894e27i 0.267534i
\(431\) 1.93756e27i 0.421933i 0.977493 + 0.210966i \(0.0676611\pi\)
−0.977493 + 0.210966i \(0.932339\pi\)
\(432\) 1.04175e27 2.78713e27i 0.221403 0.592349i
\(433\) 3.70466e27i 0.768468i 0.923236 + 0.384234i \(0.125534\pi\)
−0.923236 + 0.384234i \(0.874466\pi\)
\(434\) 4.47981e27 + 1.67596e27i 0.907021 + 0.339330i
\(435\) −4.08820e27 9.55295e27i −0.807969 1.88799i
\(436\) 1.48002e27 0.285536
\(437\) −3.17760e27 −0.598473
\(438\) 3.62514e27 1.55138e27i 0.666571 0.285260i
\(439\) 2.42257e27i 0.434910i −0.976070 0.217455i \(-0.930224\pi\)
0.976070 0.217455i \(-0.0697756\pi\)
\(440\) 1.57798e28 2.76598
\(441\) 5.81748e27 5.41108e26i 0.995702 0.0926144i
\(442\) −2.72228e27 −0.454986
\(443\) 4.87788e27i 0.796145i 0.917354 + 0.398073i \(0.130321\pi\)
−0.917354 + 0.398073i \(0.869679\pi\)
\(444\) −1.10080e27 + 4.71088e26i −0.175463 + 0.0750898i
\(445\) 2.49840e27 0.388939
\(446\) −1.06181e28 −1.61447
\(447\) 2.92187e27 + 6.82758e27i 0.433942 + 1.01400i
\(448\) 7.09568e27 + 2.65460e27i 1.02938 + 0.385105i
\(449\) 1.25132e28i 1.77330i 0.462440 + 0.886650i \(0.346974\pi\)
−0.462440 + 0.886650i \(0.653026\pi\)
\(450\) 6.63665e27 + 6.33390e27i 0.918792 + 0.876879i
\(451\) 1.22688e28i 1.65939i
\(452\) 6.78170e26i 0.0896159i
\(453\) 4.36166e27 1.86658e27i 0.563145 0.240999i
\(454\) 2.12139e26i 0.0267629i
\(455\) −1.79506e27 + 4.79815e27i −0.221289 + 0.591500i
\(456\) 4.08865e27 1.74974e27i 0.492549 0.210787i
\(457\) 3.85988e27 0.454416 0.227208 0.973846i \(-0.427040\pi\)
0.227208 + 0.973846i \(0.427040\pi\)
\(458\) 1.24845e28 1.43642
\(459\) 4.19940e27 1.12352e28i 0.472230 1.26342i
\(460\) 4.99516e27i 0.549025i
\(461\) 1.14925e28 1.23468 0.617338 0.786698i \(-0.288211\pi\)
0.617338 + 0.786698i \(0.288211\pi\)
\(462\) 1.29328e28 6.00171e26i 1.35816 0.0630281i
\(463\) −9.73227e27 −0.999111 −0.499556 0.866282i \(-0.666503\pi\)
−0.499556 + 0.866282i \(0.666503\pi\)
\(464\) 8.17908e27i 0.820854i
\(465\) −7.27009e27 1.69881e28i −0.713319 1.66682i
\(466\) −1.45097e28 −1.39189
\(467\) −1.54696e28 −1.45094 −0.725472 0.688252i \(-0.758378\pi\)
−0.725472 + 0.688252i \(0.758378\pi\)
\(468\) −9.00208e26 8.59143e26i −0.0825585 0.0787923i
\(469\) −1.08833e28 4.07158e27i −0.975987 0.365131i
\(470\) 2.27327e28i 1.99354i
\(471\) −3.63095e27 8.48450e27i −0.311387 0.727623i
\(472\) 4.56843e27i 0.383156i
\(473\) 3.92507e27i 0.321963i
\(474\) 3.23098e26 + 7.54989e26i 0.0259216 + 0.0605714i
\(475\) 9.44304e27i 0.741018i
\(476\) 4.70515e27 + 1.76026e27i 0.361161 + 0.135115i
\(477\) 1.46129e28 + 1.39463e28i 1.09722 + 1.04717i
\(478\) 7.98815e26 0.0586751
\(479\) 1.75617e28 1.26196 0.630978 0.775801i \(-0.282654\pi\)
0.630978 + 0.775801i \(0.282654\pi\)
\(480\) −4.88962e27 1.14257e28i −0.343750 0.803245i
\(481\) 3.87435e27i 0.266487i
\(482\) −1.33471e27 −0.0898243
\(483\) 8.54523e26 + 1.84137e28i 0.0562703 + 1.21254i
\(484\) −7.04863e27 −0.454181
\(485\) 2.32000e27i 0.146285i
\(486\) −1.23254e28 + 5.96971e27i −0.760539 + 0.368360i
\(487\) 1.24697e28 0.753013 0.376506 0.926414i \(-0.377125\pi\)
0.376506 + 0.926414i \(0.377125\pi\)
\(488\) −9.24457e27 −0.546359
\(489\) −3.78190e27 + 1.61847e27i −0.218760 + 0.0936185i
\(490\) −1.54993e28 + 1.78154e28i −0.877512 + 1.00864i
\(491\) 1.80793e28i 1.00190i 0.865475 + 0.500952i \(0.167017\pi\)
−0.865475 + 0.500952i \(0.832983\pi\)
\(492\) 4.99722e27 2.13857e27i 0.271079 0.116008i
\(493\) 3.29707e28i 1.75080i
\(494\) 3.19940e27i 0.166317i
\(495\) −3.61830e28 3.45325e28i −1.84141 1.75741i
\(496\) 1.45449e28i 0.724694i
\(497\) 3.44197e27 9.20031e27i 0.167905 0.448808i
\(498\) 9.83960e27 + 2.29923e28i 0.469969 + 1.09818i
\(499\) −1.50235e28 −0.702611 −0.351305 0.936261i \(-0.614262\pi\)
−0.351305 + 0.936261i \(0.614262\pi\)
\(500\) 4.96763e27 0.227491
\(501\) 4.94732e27 2.11721e27i 0.221857 0.0949442i
\(502\) 9.30087e27i 0.408446i
\(503\) 8.00712e27 0.344360 0.172180 0.985066i \(-0.444919\pi\)
0.172180 + 0.985066i \(0.444919\pi\)
\(504\) −1.12390e28 2.32225e28i −0.473377 0.978113i
\(505\) 4.56160e28 1.88173
\(506\) 4.08472e28i 1.65037i
\(507\) −1.95291e28 + 8.35749e27i −0.772855 + 0.330744i
\(508\) 3.08488e27 0.119583
\(509\) −4.61539e28 −1.75255 −0.876277 0.481807i \(-0.839981\pi\)
−0.876277 + 0.481807i \(0.839981\pi\)
\(510\) 1.90728e28 + 4.45678e28i 0.709461 + 1.65781i
\(511\) 8.25014e27 2.20525e28i 0.300637 0.803596i
\(512\) 2.90309e28i 1.03640i
\(513\) −1.32044e28 4.93541e27i −0.461833 0.172620i
\(514\) 1.85968e28i 0.637273i
\(515\) 3.23826e28i 1.08727i
\(516\) 1.59873e27 6.84178e26i 0.0525960 0.0225085i
\(517\) 7.44221e28i 2.39911i
\(518\) 6.25759e27 1.67264e28i 0.197672 0.528372i
\(519\) −2.84050e28 + 1.21560e28i −0.879301 + 0.376298i
\(520\) 2.26215e28 0.686256
\(521\) −3.96504e28 −1.17883 −0.589416 0.807830i \(-0.700642\pi\)
−0.589416 + 0.807830i \(0.700642\pi\)
\(522\) −2.59910e28 + 2.72334e28i −0.757327 + 0.793526i
\(523\) 3.10901e28i 0.887881i −0.896056 0.443940i \(-0.853580\pi\)
0.896056 0.443940i \(-0.146420\pi\)
\(524\) −1.15138e28 −0.322284
\(525\) 5.47209e28 2.53943e27i 1.50135 0.0696729i
\(526\) 3.62280e28 0.974304
\(527\) 5.86321e28i 1.54570i
\(528\) −1.54897e28 3.61949e28i −0.400300 0.935388i
\(529\) −1.86866e28 −0.473419
\(530\) −8.16420e28 −2.02776
\(531\) −9.99749e27 + 1.04754e28i −0.243444 + 0.255080i
\(532\) 2.06878e27 5.52981e27i 0.0493904 0.132019i
\(533\) 1.75881e28i 0.411703i
\(534\) −3.56119e27 8.32149e27i −0.0817358 0.190993i
\(535\) 5.39786e28i 1.21481i
\(536\) 5.13105e28i 1.13234i
\(537\) 2.15545e28 + 5.03667e28i 0.466453 + 1.08997i
\(538\) 2.62004e28i 0.556025i
\(539\) 5.07414e28 5.83238e28i 1.05604 1.21385i
\(540\) −7.75843e27 + 2.07571e28i −0.158358 + 0.423675i
\(541\) −5.02334e28 −1.00559 −0.502795 0.864406i \(-0.667695\pi\)
−0.502795 + 0.864406i \(0.667695\pi\)
\(542\) −3.85541e28 −0.756970
\(543\) 3.49038e27 + 8.15603e27i 0.0672163 + 0.157065i
\(544\) 3.94341e28i 0.744875i
\(545\) 8.52803e28 1.58010
\(546\) 1.85400e28 8.60386e26i 0.336967 0.0156376i
\(547\) −3.14126e28 −0.560062 −0.280031 0.959991i \(-0.590345\pi\)
−0.280031 + 0.959991i \(0.590345\pi\)
\(548\) 1.07790e28i 0.188530i
\(549\) 2.11977e28 + 2.02307e28i 0.363730 + 0.347137i
\(550\) 1.21388e29 2.04346
\(551\) −3.87494e28 −0.639990
\(552\) 7.48327e28 3.20247e28i 1.21264 0.518950i
\(553\) 4.59275e27 + 1.71822e27i 0.0730229 + 0.0273189i
\(554\) 6.69497e28i 1.04447i
\(555\) −6.34290e28 + 2.71445e28i −0.970983 + 0.415533i
\(556\) 2.57290e28i 0.386489i
\(557\) 8.26677e28i 1.21859i −0.792945 0.609293i \(-0.791453\pi\)
0.792945 0.609293i \(-0.208547\pi\)
\(558\) −4.62201e28 + 4.84294e28i −0.668609 + 0.700567i
\(559\) 5.62686e27i 0.0798808i
\(560\) 6.72559e28 + 2.51614e28i 0.937035 + 0.350558i
\(561\) −6.24404e28 1.45905e29i −0.853799 1.99509i
\(562\) −1.86020e27 −0.0249649
\(563\) 1.30474e29 1.71865 0.859323 0.511433i \(-0.170885\pi\)
0.859323 + 0.511433i \(0.170885\pi\)
\(564\) 3.03130e28 1.29725e28i 0.391921 0.167723i
\(565\) 3.90768e28i 0.495918i
\(566\) 3.04378e28 0.379176
\(567\) −2.50490e28 + 7.78444e28i −0.306315 + 0.951930i
\(568\) −4.33760e28 −0.520705
\(569\) 9.08661e28i 1.07084i −0.844587 0.535418i \(-0.820154\pi\)
0.844587 0.535418i \(-0.179846\pi\)
\(570\) 5.23791e28 2.24157e28i 0.605999 0.259338i
\(571\) 9.49646e28 1.07865 0.539327 0.842096i \(-0.318679\pi\)
0.539327 + 0.842096i \(0.318679\pi\)
\(572\) −1.64653e28 −0.183616
\(573\) −1.96586e28 4.59366e28i −0.215243 0.502962i
\(574\) −2.84072e28 + 7.59318e28i −0.305389 + 0.816298i
\(575\) 1.72832e29i 1.82436i
\(576\) −7.32092e28 + 7.67085e28i −0.758804 + 0.795073i
\(577\) 5.39460e28i 0.549052i −0.961580 0.274526i \(-0.911479\pi\)
0.961580 0.274526i \(-0.0885209\pi\)
\(578\) 6.92675e28i 0.692289i
\(579\) −7.88628e28 + 3.37494e28i −0.774011 + 0.331239i
\(580\) 6.09137e28i 0.587112i
\(581\) 1.39867e29 + 5.23263e28i 1.32393 + 0.495303i
\(582\) −7.72730e27 + 3.30691e27i −0.0718351 + 0.0307419i
\(583\) 2.67278e29 2.44030
\(584\) −1.03969e29 −0.932329
\(585\) −5.18709e28 4.95046e28i −0.456864 0.436023i
\(586\) 1.78525e29i 1.54445i
\(587\) 1.58353e29 1.34563 0.672817 0.739809i \(-0.265084\pi\)
0.672817 + 0.739809i \(0.265084\pi\)
\(588\) −3.26007e28 1.05012e28i −0.272123 0.0876548i
\(589\) −6.89084e28 −0.565017
\(590\) 5.85254e28i 0.471409i
\(591\) 4.58907e28 + 1.07234e29i 0.363125 + 0.848520i
\(592\) −5.43069e28 −0.422160
\(593\) 1.48490e28 0.113402 0.0567012 0.998391i \(-0.481942\pi\)
0.0567012 + 0.998391i \(0.481942\pi\)
\(594\) −6.34433e28 + 1.69738e29i −0.476023 + 1.27357i
\(595\) 2.71115e29 + 1.01428e29i 1.99860 + 0.747705i
\(596\) 4.35355e28i 0.315325i
\(597\) 2.21535e28 + 5.17664e28i 0.157657 + 0.368399i
\(598\) 5.85572e28i 0.409466i
\(599\) 7.20867e28i 0.495306i −0.968849 0.247653i \(-0.920341\pi\)
0.968849 0.247653i \(-0.0796593\pi\)
\(600\) −9.51696e28 2.22384e29i −0.642555 1.50147i
\(601\) 5.80781e28i 0.385328i 0.981265 + 0.192664i \(0.0617128\pi\)
−0.981265 + 0.192664i \(0.938287\pi\)
\(602\) −9.08812e27 + 2.42924e28i −0.0592531 + 0.158382i
\(603\) 1.12287e29 1.17654e29i 0.719447 0.753835i
\(604\) −2.78118e28 −0.175122
\(605\) −4.06149e29 −2.51335
\(606\) −6.50206e28 1.51935e29i −0.395447 0.924048i
\(607\) 1.15339e29i 0.689438i −0.938706 0.344719i \(-0.887974\pi\)
0.938706 0.344719i \(-0.112026\pi\)
\(608\) −4.63456e28 −0.272283
\(609\) 1.04205e28 + 2.24546e29i 0.0601738 + 1.29666i
\(610\) −1.18431e29 −0.672204
\(611\) 1.06689e29i 0.595233i
\(612\) −4.85451e28 + 5.08654e28i −0.266229 + 0.278954i
\(613\) −2.77828e29 −1.49776 −0.748878 0.662708i \(-0.769407\pi\)
−0.748878 + 0.662708i \(0.769407\pi\)
\(614\) −1.57457e29 −0.834440
\(615\) 2.87945e29 1.23226e29i 1.50010 0.641970i
\(616\) −3.19724e29 1.19613e29i −1.63749 0.612607i
\(617\) 1.84076e29i 0.926836i 0.886140 + 0.463418i \(0.153377\pi\)
−0.886140 + 0.463418i \(0.846623\pi\)
\(618\) 1.07858e29 4.61578e28i 0.533915 0.228489i
\(619\) 2.28968e29i 1.11435i 0.830394 + 0.557177i \(0.188115\pi\)
−0.830394 + 0.557177i \(0.811885\pi\)
\(620\) 1.08323e29i 0.518334i
\(621\) −2.41673e29 9.03307e28i −1.13702 0.424985i
\(622\) 1.87704e29i 0.868309i
\(623\) −5.06214e28 1.89382e28i −0.230255 0.0861417i
\(624\) −2.22055e28 5.18879e28i −0.0993167 0.232075i
\(625\) −5.54945e28 −0.244067
\(626\) 8.26347e28 0.357381
\(627\) −1.71478e29 + 7.33841e28i −0.729288 + 0.312099i
\(628\) 5.41007e28i 0.226270i
\(629\) −2.18917e29 −0.900424
\(630\) −1.43981e29 2.97500e29i −0.582411 1.20340i
\(631\) 3.78698e29 1.50656 0.753278 0.657703i \(-0.228472\pi\)
0.753278 + 0.657703i \(0.228472\pi\)
\(632\) 2.16531e28i 0.0847210i
\(633\) 3.87311e29 1.65750e29i 1.49046 0.637845i
\(634\) −2.57810e27 −0.00975803
\(635\) 1.77754e29 0.661752
\(636\) −4.65892e28 1.08866e29i −0.170602 0.398649i
\(637\) 7.27412e28 8.36112e28i 0.262009 0.301162i
\(638\) 4.98112e29i 1.76486i
\(639\) 9.94608e28 + 9.49236e28i 0.346651 + 0.330838i
\(640\) 1.73734e29i 0.595654i
\(641\) 1.64616e29i 0.555218i −0.960694 0.277609i \(-0.910458\pi\)
0.960694 0.277609i \(-0.0895420\pi\)
\(642\) −1.79788e29 + 7.69406e28i −0.596546 + 0.255292i
\(643\) 2.84507e29i 0.928705i −0.885650 0.464353i \(-0.846287\pi\)
0.885650 0.464353i \(-0.153713\pi\)
\(644\) 3.78639e28 1.01210e29i 0.121597 0.325027i
\(645\) 9.21203e28 3.94230e28i 0.291057 0.124558i
\(646\) 1.80779e29 0.561962
\(647\) −3.09210e29 −0.945713 −0.472856 0.881140i \(-0.656777\pi\)
−0.472856 + 0.881140i \(0.656777\pi\)
\(648\) 3.60704e29 1.68478e28i 1.08546 0.0506998i
\(649\) 1.91600e29i 0.567316i
\(650\) 1.74017e29 0.506994
\(651\) 1.85309e28 + 3.99313e29i 0.0531247 + 1.14476i
\(652\) 2.41150e28 0.0680280
\(653\) 1.03787e29i 0.288108i 0.989570 + 0.144054i \(0.0460139\pi\)
−0.989570 + 0.144054i \(0.953986\pi\)
\(654\) −1.21558e29 2.84046e29i −0.332060 0.775929i
\(655\) −6.63434e29 −1.78346
\(656\) 2.46534e29 0.652208
\(657\) 2.38400e29 + 2.27525e29i 0.620683 + 0.592369i
\(658\) −1.72317e29 + 4.60600e29i −0.441526 + 1.18019i
\(659\) 6.06577e29i 1.52964i −0.644244 0.764820i \(-0.722828\pi\)
0.644244 0.764820i \(-0.277172\pi\)
\(660\) 1.15359e29 + 2.69562e29i 0.286313 + 0.669032i
\(661\) 1.05277e29i 0.257170i 0.991699 + 0.128585i \(0.0410434\pi\)
−0.991699 + 0.128585i \(0.958957\pi\)
\(662\) 7.46806e28i 0.179556i
\(663\) −8.95126e28 2.09165e29i −0.211832 0.494992i
\(664\) 6.59421e29i 1.53602i
\(665\) 1.19205e29 3.18633e29i 0.273318 0.730572i
\(666\) 1.80822e29 + 1.72573e29i 0.408105 + 0.389488i
\(667\) −7.09212e29 −1.57563
\(668\) −3.15462e28 −0.0689913
\(669\) −3.49139e29 8.15839e29i −0.751665 1.75643i
\(670\) 6.57331e29i 1.39315i
\(671\) 3.87717e29 0.808962
\(672\) 1.24633e28 + 2.68565e29i 0.0256009 + 0.551661i
\(673\) 5.79956e28 0.117284 0.0586418 0.998279i \(-0.481323\pi\)
0.0586418 + 0.998279i \(0.481323\pi\)
\(674\) 4.41441e29i 0.878909i
\(675\) −2.68440e29 + 7.18193e29i −0.526209 + 1.40783i
\(676\) 1.24526e29 0.240336
\(677\) −1.55680e29 −0.295837 −0.147919 0.989000i \(-0.547257\pi\)
−0.147919 + 0.989000i \(0.547257\pi\)
\(678\) 1.30154e29 5.56997e28i 0.243527 0.104218i
\(679\) −1.75859e28 + 4.70068e28i −0.0323991 + 0.0866020i
\(680\) 1.27821e30i 2.31877i
\(681\) −1.62996e28 + 6.97544e27i −0.0291161 + 0.0124603i
\(682\) 8.85798e29i 1.55811i
\(683\) 4.88251e29i 0.845718i 0.906196 + 0.422859i \(0.138973\pi\)
−0.906196 + 0.422859i \(0.861027\pi\)
\(684\) 5.97805e28 + 5.70534e28i 0.101969 + 0.0973178i
\(685\) 6.21094e29i 1.04329i
\(686\) 4.49082e29 2.43481e29i 0.742887 0.402774i
\(687\) 4.10508e29 + 9.59241e29i 0.668769 + 1.56272i
\(688\) 7.88719e28 0.126545
\(689\) 3.83162e29 0.605453
\(690\) 9.58670e29 4.10264e29i 1.49195 0.638481i
\(691\) 4.46432e29i 0.684283i −0.939649 0.342141i \(-0.888848\pi\)
0.939649 0.342141i \(-0.111152\pi\)
\(692\) 1.81122e29 0.273437
\(693\) 4.71363e29 + 9.73952e29i 0.700901 + 1.44823i
\(694\) −9.39630e29 −1.37620
\(695\) 1.48253e30i 2.13876i
\(696\) 9.12550e29 3.90527e29i 1.29676 0.554950i
\(697\) 9.93802e29 1.39109
\(698\) 2.94104e29 0.405526
\(699\) −4.77100e29 1.11485e30i −0.648036 1.51428i
\(700\) −3.00770e29 1.12522e29i −0.402443 0.150560i
\(701\) 1.85634e29i 0.244692i 0.992488 + 0.122346i \(0.0390417\pi\)
−0.992488 + 0.122346i \(0.960958\pi\)
\(702\) −9.09503e28 + 2.43331e29i −0.118104 + 0.315979i
\(703\) 2.57285e29i 0.329143i
\(704\) 1.40304e30i 1.76830i
\(705\) 1.74666e30 7.47487e29i 2.16882 0.928149i
\(706\) 2.41567e28i 0.0295521i
\(707\) −9.24251e29 3.45775e29i −1.11400 0.416764i
\(708\) 7.80408e28 3.33977e28i 0.0926771 0.0396613i
\(709\) 2.39282e28 0.0279978 0.0139989 0.999902i \(-0.495544\pi\)
0.0139989 + 0.999902i \(0.495544\pi\)
\(710\) −5.55683e29 −0.640641
\(711\) −4.73854e28 + 4.96504e28i −0.0538287 + 0.0564016i
\(712\) 2.38661e29i 0.267141i
\(713\) −1.26120e30 −1.39105
\(714\) −4.86153e28 1.04759e30i −0.0528374 1.13857i
\(715\) −9.48745e29 −1.01610
\(716\) 3.21159e29i 0.338949i
\(717\) 2.62663e28 + 6.13768e28i 0.0273179 + 0.0638342i
\(718\) 8.82487e29 0.904486
\(719\) 1.27733e30 1.29018 0.645091 0.764106i \(-0.276820\pi\)
0.645091 + 0.764106i \(0.276820\pi\)
\(720\) −6.93908e29 + 7.27076e29i −0.690734 + 0.723750i
\(721\) 2.45464e29 6.56120e29i 0.240806 0.643670i
\(722\) 6.61559e29i 0.639629i
\(723\) −4.38874e28 1.02552e29i −0.0418203 0.0977222i
\(724\) 5.20063e28i 0.0488428i
\(725\) 2.10760e30i 1.95092i
\(726\) 5.78920e29 + 1.35277e30i 0.528183 + 1.23421i
\(727\) 4.55339e29i 0.409472i −0.978817 0.204736i \(-0.934366\pi\)
0.978817 0.204736i \(-0.0656335\pi\)
\(728\) −4.58346e29 1.71474e29i −0.406269 0.151991i
\(729\) −8.63960e29 7.50729e29i −0.754840 0.655909i
\(730\) −1.33193e30 −1.14708
\(731\) 3.17940e29 0.269907
\(732\) −6.75827e28 1.57922e29i −0.0565548 0.132152i
\(733\) 1.30029e30i 1.07262i −0.844020 0.536312i \(-0.819817\pi\)
0.844020 0.536312i \(-0.180183\pi\)
\(734\) −3.10316e29 −0.252346
\(735\) −1.87848e30 6.05087e29i −1.50588 0.485066i
\(736\) −8.48242e29 −0.670352
\(737\) 2.15196e30i 1.67658i
\(738\) −8.20867e29 7.83421e29i −0.630494 0.601732i
\(739\) 7.52338e27 0.00569700 0.00284850 0.999996i \(-0.499093\pi\)
0.00284850 + 0.999996i \(0.499093\pi\)
\(740\) 4.04450e29 0.301948
\(741\) −2.45825e29 + 1.05201e29i −0.180940 + 0.0774336i
\(742\) 1.65419e30 + 6.18856e29i 1.20045 + 0.449106i
\(743\) 1.12099e30i 0.802086i 0.916059 + 0.401043i \(0.131352\pi\)
−0.916059 + 0.401043i \(0.868648\pi\)
\(744\) 1.62280e30 6.94478e29i 1.14485 0.489940i
\(745\) 2.50856e30i 1.74495i
\(746\) 5.34604e29i 0.366669i
\(747\) −1.44307e30 + 1.51205e30i −0.975936 + 1.02258i
\(748\) 9.30355e29i 0.620414i
\(749\) −4.09165e29 + 1.09369e30i −0.269054 + 0.719176i
\(750\) −4.08003e29 9.53386e29i −0.264557 0.618195i
\(751\) 6.89593e29 0.440934 0.220467 0.975394i \(-0.429242\pi\)
0.220467 + 0.975394i \(0.429242\pi\)
\(752\) 1.49546e30 0.942950
\(753\) 7.14630e29 3.05827e29i 0.444359 0.190164i
\(754\) 7.14078e29i 0.437871i
\(755\) −1.60254e30 −0.969094
\(756\) 3.14539e29 3.61761e29i 0.187584 0.215746i
\(757\) 3.24718e30 1.90985 0.954926 0.296844i \(-0.0959343\pi\)
0.954926 + 0.296844i \(0.0959343\pi\)
\(758\) 1.19564e30i 0.693542i
\(759\) −3.13848e30 + 1.34312e30i −1.79548 + 0.768378i
\(760\) −1.50223e30 −0.847607
\(761\) −2.08186e30