Properties

Label 21.22.c.b.20.50
Level $21$
Weight $22$
Character 21.20
Analytic conductor $58.690$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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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 20.50
Character \(\chi\) \(=\) 21.20
Dual form 21.22.c.b.20.49

$q$-expansion

\(f(q)\) \(=\) \(q+247.072i q^{2} +(-16209.6 + 100983. i) q^{3} +2.03611e6 q^{4} +3.48005e7 q^{5} +(-2.49501e7 - 4.00494e6i) q^{6} +(7.14474e8 - 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} +O(q^{10})\) \(q+247.072i q^{2} +(-16209.6 + 100983. i) q^{3} +2.03611e6 q^{4} +3.48005e7 q^{5} +(-2.49501e7 - 4.00494e6i) q^{6} +(7.14474e8 - 2.19256e8i) q^{7} +1.02121e9i q^{8} +(-9.93485e9 - 3.27379e9i) q^{9} +8.59823e9i q^{10} +9.21376e10i q^{11} +(-3.30045e10 + 2.05613e11i) q^{12} +1.67572e11i q^{13} +(5.41720e10 + 1.76527e11i) q^{14} +(-5.64102e11 + 3.51427e12i) q^{15} +4.01771e12 q^{16} -7.92508e12 q^{17} +(8.08863e11 - 2.45462e12i) q^{18} +3.32012e13i q^{19} +7.08576e13 q^{20} +(1.05598e13 + 7.57039e13i) q^{21} -2.27646e13 q^{22} -3.78679e14i q^{23} +(-1.03125e14 - 1.65535e13i) q^{24} +7.34238e14 q^{25} -4.14025e13 q^{26} +(4.91638e14 - 9.50186e14i) q^{27} +(1.45475e15 - 4.46428e14i) q^{28} +2.17759e15i q^{29} +(-8.68277e14 - 1.39374e14i) q^{30} +3.73514e15i q^{31} +3.13430e15i q^{32} +(-9.30435e15 - 1.49351e15i) q^{33} -1.95807e15i q^{34} +(2.48640e16 - 7.63021e15i) q^{35} +(-2.02284e16 - 6.66579e15i) q^{36} -1.35512e16 q^{37} -8.20309e15 q^{38} +(-1.69220e16 - 2.71628e15i) q^{39} +3.55387e16i q^{40} +6.54994e16 q^{41} +(-1.87043e16 + 2.60904e15i) q^{42} +4.14672e15 q^{43} +1.87602e17i q^{44} +(-3.45738e17 - 1.13930e17i) q^{45} +9.35610e16 q^{46} +4.66357e17 q^{47} +(-6.51255e16 + 4.05721e17i) q^{48} +(4.62400e17 - 3.13305e17i) q^{49} +1.81410e17i q^{50} +(1.28462e17 - 8.00299e17i) q^{51} +3.41196e17i q^{52} -1.25598e18i q^{53} +(2.34764e17 + 1.21470e17i) q^{54} +3.20643e18i q^{55} +(2.23907e17 + 7.29630e17i) q^{56} +(-3.35276e18 - 5.38178e17i) q^{57} -5.38023e17 q^{58} -5.49943e17 q^{59} +(-1.14857e18 + 7.15542e18i) q^{60} +7.00101e18i q^{61} -9.22849e17 q^{62} +(-7.81599e18 - 1.60766e17i) q^{63} +7.65136e18 q^{64} +5.83161e18i q^{65} +(3.69006e17 - 2.29884e18i) q^{66} -1.30709e19 q^{67} -1.61363e19 q^{68} +(3.82402e19 + 6.13824e18i) q^{69} +(1.88521e18 + 6.14321e18i) q^{70} -3.38969e19i q^{71} +(3.34324e18 - 1.01456e19i) q^{72} +5.69462e19i q^{73} -3.34811e18i q^{74} +(-1.19017e19 + 7.41457e19i) q^{75} +6.76012e19i q^{76} +(2.02017e19 + 6.58299e19i) q^{77} +(6.71118e17 - 4.18095e18i) q^{78} -5.19511e19 q^{79} +1.39818e20 q^{80} +(8.79835e19 + 6.50493e19i) q^{81} +1.61831e19i q^{82} -1.77530e20 q^{83} +(2.15009e19 + 1.54141e20i) q^{84} -2.75797e20 q^{85} +1.02454e18i q^{86} +(-2.19900e20 - 3.52979e19i) q^{87} -9.40921e19 q^{88} +4.40189e20 q^{89} +(2.81488e19 - 8.54222e19i) q^{90} +(3.67412e19 + 1.19726e20i) q^{91} -7.71031e20i q^{92} +(-3.77186e20 - 6.05451e19i) q^{93} +1.15224e20i q^{94} +1.15542e21i q^{95} +(-3.16512e20 - 5.08058e19i) q^{96} -5.59451e20i q^{97} +(7.74089e19 + 1.14246e20i) q^{98} +(3.01639e20 - 9.15373e20i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 247.072i 0.170612i 0.996355 + 0.0853058i \(0.0271867\pi\)
−0.996355 + 0.0853058i \(0.972813\pi\)
\(3\) −16209.6 + 100983.i −0.158489 + 0.987361i
\(4\) 2.03611e6 0.970892
\(5\) 3.48005e7 1.59368 0.796839 0.604192i \(-0.206504\pi\)
0.796839 + 0.604192i \(0.206504\pi\)
\(6\) −2.49501e7 4.00494e6i −0.168455 0.0270401i
\(7\) 7.14474e8 2.19256e8i 0.955998 0.293374i
\(8\) 1.02121e9i 0.336257i
\(9\) −9.93485e9 3.27379e9i −0.949762 0.312972i
\(10\) 8.59823e9i 0.271900i
\(11\) 9.21376e10i 1.07106i 0.844516 + 0.535530i \(0.179888\pi\)
−0.844516 + 0.535530i \(0.820112\pi\)
\(12\) −3.30045e10 + 2.05613e11i −0.153876 + 0.958620i
\(13\) 1.67572e11i 0.337130i 0.985691 + 0.168565i \(0.0539133\pi\)
−0.985691 + 0.168565i \(0.946087\pi\)
\(14\) 5.41720e10 + 1.76527e11i 0.0500530 + 0.163104i
\(15\) −5.64102e11 + 3.51427e12i −0.252580 + 1.57353i
\(16\) 4.01771e12 0.913522
\(17\) −7.92508e12 −0.953432 −0.476716 0.879057i \(-0.658173\pi\)
−0.476716 + 0.879057i \(0.658173\pi\)
\(18\) 8.08863e11 2.45462e12i 0.0533966 0.162041i
\(19\) 3.32012e13i 1.24234i 0.783675 + 0.621171i \(0.213343\pi\)
−0.783675 + 0.621171i \(0.786657\pi\)
\(20\) 7.08576e13 1.54729
\(21\) 1.05598e13 + 7.57039e13i 0.138151 + 0.990411i
\(22\) −2.27646e13 −0.182735
\(23\) 3.78679e14i 1.90603i −0.302928 0.953013i \(-0.597964\pi\)
0.302928 0.953013i \(-0.402036\pi\)
\(24\) −1.03125e14 1.65535e13i −0.332007 0.0532930i
\(25\) 7.34238e14 1.53981
\(26\) −4.14025e13 −0.0575183
\(27\) 4.91638e14 9.50186e14i 0.459543 0.888156i
\(28\) 1.45475e15 4.46428e14i 0.928170 0.284834i
\(29\) 2.17759e15i 0.961165i 0.876950 + 0.480583i \(0.159575\pi\)
−0.876950 + 0.480583i \(0.840425\pi\)
\(30\) −8.68277e14 1.39374e14i −0.268463 0.0430932i
\(31\) 3.73514e15i 0.818482i 0.912426 + 0.409241i \(0.134206\pi\)
−0.912426 + 0.409241i \(0.865794\pi\)
\(32\) 3.13430e15i 0.492115i
\(33\) −9.30435e15 1.49351e15i −1.05752 0.169751i
\(34\) 1.95807e15i 0.162667i
\(35\) 2.48640e16 7.63021e15i 1.52355 0.467544i
\(36\) −2.02284e16 6.66579e15i −0.922116 0.303862i
\(37\) −1.35512e16 −0.463296 −0.231648 0.972800i \(-0.574412\pi\)
−0.231648 + 0.972800i \(0.574412\pi\)
\(38\) −8.20309e15 −0.211958
\(39\) −1.69220e16 2.71628e15i −0.332869 0.0534314i
\(40\) 3.55387e16i 0.535885i
\(41\) 6.54994e16 0.762092 0.381046 0.924556i \(-0.375564\pi\)
0.381046 + 0.924556i \(0.375564\pi\)
\(42\) −1.87043e16 + 2.60904e15i −0.168976 + 0.0235702i
\(43\) 4.14672e15 0.0292608 0.0146304 0.999893i \(-0.495343\pi\)
0.0146304 + 0.999893i \(0.495343\pi\)
\(44\) 1.87602e17i 1.03988i
\(45\) −3.45738e17 1.13930e17i −1.51362 0.498776i
\(46\) 9.35610e16 0.325190
\(47\) 4.66357e17 1.29327 0.646637 0.762798i \(-0.276175\pi\)
0.646637 + 0.762798i \(0.276175\pi\)
\(48\) −6.51255e16 + 4.05721e17i −0.144783 + 0.901976i
\(49\) 4.62400e17 3.13305e17i 0.827863 0.560930i
\(50\) 1.81410e17i 0.262709i
\(51\) 1.28462e17 8.00299e17i 0.151108 0.941382i
\(52\) 3.41196e17i 0.327317i
\(53\) 1.25598e18i 0.986476i −0.869894 0.493238i \(-0.835813\pi\)
0.869894 0.493238i \(-0.164187\pi\)
\(54\) 2.34764e17 + 1.21470e17i 0.151530 + 0.0784034i
\(55\) 3.20643e18i 1.70692i
\(56\) 2.23907e17 + 7.29630e17i 0.0986491 + 0.321461i
\(57\) −3.35276e18 5.38178e17i −1.22664 0.196898i
\(58\) −5.38023e17 −0.163986
\(59\) −5.49943e17 −0.140079 −0.0700393 0.997544i \(-0.522312\pi\)
−0.0700393 + 0.997544i \(0.522312\pi\)
\(60\) −1.14857e18 + 7.15542e18i −0.245228 + 1.52773i
\(61\) 7.00101e18i 1.25660i 0.777971 + 0.628301i \(0.216249\pi\)
−0.777971 + 0.628301i \(0.783751\pi\)
\(62\) −9.22849e17 −0.139643
\(63\) −7.81599e18 1.60766e17i −0.999789 0.0205645i
\(64\) 7.65136e18 0.829562
\(65\) 5.83161e18i 0.537277i
\(66\) 3.69006e17 2.29884e18i 0.0289615 0.180426i
\(67\) −1.30709e19 −0.876032 −0.438016 0.898967i \(-0.644319\pi\)
−0.438016 + 0.898967i \(0.644319\pi\)
\(68\) −1.61363e19 −0.925679
\(69\) 3.82402e19 + 6.13824e18i 1.88194 + 0.302084i
\(70\) 1.88521e18 + 6.14321e18i 0.0797684 + 0.259936i
\(71\) 3.38969e19i 1.23580i −0.786258 0.617898i \(-0.787984\pi\)
0.786258 0.617898i \(-0.212016\pi\)
\(72\) 3.34324e18 1.01456e19i 0.105239 0.319364i
\(73\) 5.69462e19i 1.55087i 0.631430 + 0.775433i \(0.282468\pi\)
−0.631430 + 0.775433i \(0.717532\pi\)
\(74\) 3.34811e18i 0.0790436i
\(75\) −1.19017e19 + 7.41457e19i −0.244043 + 1.52035i
\(76\) 6.76012e19i 1.20618i
\(77\) 2.02017e19 + 6.58299e19i 0.314221 + 1.02393i
\(78\) 6.71118e17 4.18095e18i 0.00911602 0.0567913i
\(79\) −5.19511e19 −0.617320 −0.308660 0.951172i \(-0.599881\pi\)
−0.308660 + 0.951172i \(0.599881\pi\)
\(80\) 1.39818e20 1.45586
\(81\) 8.79835e19 + 6.50493e19i 0.804098 + 0.594497i
\(82\) 1.61831e19i 0.130022i
\(83\) −1.77530e20 −1.25589 −0.627946 0.778257i \(-0.716104\pi\)
−0.627946 + 0.778257i \(0.716104\pi\)
\(84\) 2.15009e19 + 1.54141e20i 0.134130 + 0.961582i
\(85\) −2.75797e20 −1.51946
\(86\) 1.02454e18i 0.00499223i
\(87\) −2.19900e20 3.52979e19i −0.949017 0.152334i
\(88\) −9.40921e19 −0.360151
\(89\) 4.40189e20 1.49639 0.748194 0.663480i \(-0.230921\pi\)
0.748194 + 0.663480i \(0.230921\pi\)
\(90\) 2.81488e19 8.54222e19i 0.0850970 0.258240i
\(91\) 3.67412e19 + 1.19726e20i 0.0989052 + 0.322296i
\(92\) 7.71031e20i 1.85055i
\(93\) −3.77186e20 6.05451e19i −0.808137 0.129720i
\(94\) 1.15224e20i 0.220648i
\(95\) 1.15542e21i 1.97989i
\(96\) −3.16512e20 5.08058e19i −0.485895 0.0779948i
\(97\) 5.59451e20i 0.770297i −0.922855 0.385149i \(-0.874150\pi\)
0.922855 0.385149i \(-0.125850\pi\)
\(98\) 7.74089e19 + 1.14246e20i 0.0957012 + 0.141243i
\(99\) 3.01639e20 9.15373e20i 0.335211 1.01725i
\(100\) 1.49499e21 1.49499
\(101\) −7.90626e20 −0.712191 −0.356095 0.934450i \(-0.615892\pi\)
−0.356095 + 0.934450i \(0.615892\pi\)
\(102\) 1.97732e20 + 3.17395e19i 0.160611 + 0.0257809i
\(103\) 3.92142e20i 0.287509i 0.989613 + 0.143755i \(0.0459176\pi\)
−0.989613 + 0.143755i \(0.954082\pi\)
\(104\) −1.71127e20 −0.113362
\(105\) 3.67487e20 + 2.63453e21i 0.220168 + 1.57840i
\(106\) 3.10318e20 0.168304
\(107\) 1.59873e21i 0.785678i −0.919607 0.392839i \(-0.871493\pi\)
0.919607 0.392839i \(-0.128507\pi\)
\(108\) 1.00103e21 1.93468e21i 0.446166 0.862303i
\(109\) −6.51658e20 −0.263658 −0.131829 0.991272i \(-0.542085\pi\)
−0.131829 + 0.991272i \(0.542085\pi\)
\(110\) −7.92221e20 −0.291221
\(111\) 2.19659e20 1.36844e21i 0.0734273 0.457440i
\(112\) 2.87055e21 8.80907e20i 0.873325 0.268004i
\(113\) 6.17950e21i 1.71250i −0.516565 0.856248i \(-0.672789\pi\)
0.516565 0.856248i \(-0.327211\pi\)
\(114\) 1.32969e20 8.28374e20i 0.0335930 0.209279i
\(115\) 1.31782e22i 3.03759i
\(116\) 4.43382e21i 0.933187i
\(117\) 5.48598e20 1.66481e21i 0.105512 0.320194i
\(118\) 1.35876e20i 0.0238990i
\(119\) −5.66226e21 + 1.73762e21i −0.911479 + 0.279712i
\(120\) −3.58881e21 5.76069e20i −0.529112 0.0849319i
\(121\) −1.08909e21 −0.147169
\(122\) −1.72975e21 −0.214391
\(123\) −1.06172e21 + 6.61434e21i −0.120783 + 0.752459i
\(124\) 7.60514e21i 0.794657i
\(125\) 8.95767e21 0.860281
\(126\) 3.97207e19 1.93111e21i 0.00350854 0.170576i
\(127\) 1.92143e21 0.156202 0.0781008 0.996945i \(-0.475114\pi\)
0.0781008 + 0.996945i \(0.475114\pi\)
\(128\) 8.46355e21i 0.633648i
\(129\) −6.72167e19 + 4.18749e20i −0.00463751 + 0.0288910i
\(130\) −1.44083e21 −0.0916657
\(131\) 3.30217e21 0.193843 0.0969215 0.995292i \(-0.469100\pi\)
0.0969215 + 0.995292i \(0.469100\pi\)
\(132\) −1.89447e22 3.04095e21i −1.02674 0.164810i
\(133\) 7.27956e21 + 2.37214e22i 0.364471 + 1.18768i
\(134\) 3.22946e21i 0.149461i
\(135\) 1.71092e22 3.30669e22i 0.732363 1.41543i
\(136\) 8.09319e21i 0.320598i
\(137\) 1.54231e22i 0.565725i −0.959160 0.282863i \(-0.908716\pi\)
0.959160 0.282863i \(-0.0912841\pi\)
\(138\) −1.51659e21 + 9.44809e21i −0.0515391 + 0.321080i
\(139\) 1.70092e22i 0.535830i −0.963443 0.267915i \(-0.913665\pi\)
0.963443 0.267915i \(-0.0863347\pi\)
\(140\) 5.06259e22 1.55359e22i 1.47920 0.453934i
\(141\) −7.55945e21 + 4.70942e22i −0.204970 + 1.27693i
\(142\) 8.37497e21 0.210841
\(143\) −1.54397e22 −0.361086
\(144\) −3.99154e22 1.31532e22i −0.867629 0.285907i
\(145\) 7.57814e22i 1.53179i
\(146\) −1.40698e22 −0.264596
\(147\) 2.41432e22 + 5.17731e22i 0.422633 + 0.906301i
\(148\) −2.75916e22 −0.449810
\(149\) 6.09708e22i 0.926117i 0.886328 + 0.463059i \(0.153248\pi\)
−0.886328 + 0.463059i \(0.846752\pi\)
\(150\) −1.83193e22 2.94058e21i −0.259389 0.0416365i
\(151\) −1.02653e23 −1.35554 −0.677770 0.735274i \(-0.737053\pi\)
−0.677770 + 0.735274i \(0.737053\pi\)
\(152\) −3.39055e22 −0.417746
\(153\) 7.87345e22 + 2.59451e22i 0.905534 + 0.298397i
\(154\) −1.62647e22 + 4.99128e21i −0.174695 + 0.0536098i
\(155\) 1.29985e23i 1.30440i
\(156\) −3.44550e22 5.53064e21i −0.323180 0.0518761i
\(157\) 6.98052e22i 0.612268i 0.951988 + 0.306134i \(0.0990355\pi\)
−0.951988 + 0.306134i \(0.900964\pi\)
\(158\) 1.28357e22i 0.105322i
\(159\) 1.26833e23 + 2.03589e22i 0.974007 + 0.156346i
\(160\) 1.09075e23i 0.784272i
\(161\) −8.30276e22 2.70556e23i −0.559179 1.82216i
\(162\) −1.60719e22 + 2.17383e22i −0.101428 + 0.137188i
\(163\) 3.10704e23 1.83813 0.919066 0.394103i \(-0.128945\pi\)
0.919066 + 0.394103i \(0.128945\pi\)
\(164\) 1.33364e23 0.739908
\(165\) −3.23796e23 5.19750e22i −1.68535 0.270529i
\(166\) 4.38627e22i 0.214270i
\(167\) −2.26403e23 −1.03839 −0.519194 0.854656i \(-0.673768\pi\)
−0.519194 + 0.854656i \(0.673768\pi\)
\(168\) −7.73098e22 + 1.07838e22i −0.333033 + 0.0464542i
\(169\) 2.18984e23 0.886343
\(170\) 6.81417e22i 0.259238i
\(171\) 1.08694e23 3.29849e23i 0.388818 1.17993i
\(172\) 8.44317e21 0.0284091
\(173\) 1.54465e23 0.489041 0.244521 0.969644i \(-0.421369\pi\)
0.244521 + 0.969644i \(0.421369\pi\)
\(174\) 8.72113e21 5.43312e22i 0.0259900 0.161913i
\(175\) 5.24594e23 1.60986e23i 1.47205 0.451740i
\(176\) 3.70182e23i 0.978437i
\(177\) 8.91436e21 5.55350e22i 0.0222009 0.138308i
\(178\) 1.08758e23i 0.255301i
\(179\) 1.69966e23i 0.376188i 0.982151 + 0.188094i \(0.0602310\pi\)
−0.982151 + 0.188094i \(0.939769\pi\)
\(180\) −7.03959e23 2.31973e23i −1.46956 0.484257i
\(181\) 2.21194e23i 0.435660i −0.975987 0.217830i \(-0.930102\pi\)
0.975987 0.217830i \(-0.0698978\pi\)
\(182\) −2.95810e22 + 9.07774e21i −0.0549874 + 0.0168744i
\(183\) −7.06984e23 1.13484e23i −1.24072 0.199157i
\(184\) 3.86712e23 0.640915
\(185\) −4.71587e23 −0.738344
\(186\) 1.49590e22 9.31922e22i 0.0221318 0.137878i
\(187\) 7.30198e23i 1.02118i
\(188\) 9.49552e23 1.25563
\(189\) 1.42929e23 7.86677e23i 0.178760 0.983893i
\(190\) −2.85472e23 −0.337793
\(191\) 1.22833e23i 0.137552i −0.997632 0.0687758i \(-0.978091\pi\)
0.997632 0.0687758i \(-0.0219093\pi\)
\(192\) −1.24025e23 + 7.72658e23i −0.131476 + 0.819077i
\(193\) −8.35000e23 −0.838175 −0.419087 0.907946i \(-0.637650\pi\)
−0.419087 + 0.907946i \(0.637650\pi\)
\(194\) 1.38225e23 0.131422
\(195\) −5.88894e23 9.45280e22i −0.530486 0.0851524i
\(196\) 9.41495e23 6.37923e23i 0.803766 0.544602i
\(197\) 1.49542e24i 1.21023i −0.796138 0.605115i \(-0.793127\pi\)
0.796138 0.605115i \(-0.206873\pi\)
\(198\) 2.26163e23 + 7.45267e22i 0.173555 + 0.0571910i
\(199\) 3.32350e23i 0.241901i 0.992659 + 0.120951i \(0.0385942\pi\)
−0.992659 + 0.120951i \(0.961406\pi\)
\(200\) 7.49813e23i 0.517772i
\(201\) 2.11874e23 1.31994e24i 0.138841 0.864960i
\(202\) 1.95342e23i 0.121508i
\(203\) 4.77450e23 + 1.55583e24i 0.281981 + 0.918872i
\(204\) 2.61563e23 1.62950e24i 0.146710 0.913979i
\(205\) 2.27941e24 1.21453
\(206\) −9.68872e22 −0.0490525
\(207\) −1.23972e24 + 3.76212e24i −0.596532 + 1.81027i
\(208\) 6.73258e23i 0.307976i
\(209\) −3.05908e24 −1.33062
\(210\) −6.50920e23 + 9.07958e22i −0.269293 + 0.0375632i
\(211\) 2.82664e24 1.11251 0.556256 0.831011i \(-0.312238\pi\)
0.556256 + 0.831011i \(0.312238\pi\)
\(212\) 2.55731e24i 0.957761i
\(213\) 3.42301e24 + 5.49455e23i 1.22018 + 0.195860i
\(214\) 3.95001e23 0.134046
\(215\) 1.44308e23 0.0466323
\(216\) 9.70342e23 + 5.02067e23i 0.298649 + 0.154525i
\(217\) 8.18951e23 + 2.66866e24i 0.240121 + 0.782467i
\(218\) 1.61006e23i 0.0449832i
\(219\) −5.75060e24 9.23074e23i −1.53126 0.245795i
\(220\) 6.52865e24i 1.65724i
\(221\) 1.32802e24i 0.321431i
\(222\) 3.38103e23 + 5.42716e22i 0.0780446 + 0.0125275i
\(223\) 4.24179e24i 0.934004i 0.884256 + 0.467002i \(0.154666\pi\)
−0.884256 + 0.467002i \(0.845334\pi\)
\(224\) 6.87214e23 + 2.23938e24i 0.144374 + 0.470461i
\(225\) −7.29454e24 2.40374e24i −1.46245 0.481916i
\(226\) 1.52678e24 0.292172
\(227\) −3.16057e23 −0.0577422 −0.0288711 0.999583i \(-0.509191\pi\)
−0.0288711 + 0.999583i \(0.509191\pi\)
\(228\) −6.82659e24 1.09579e24i −1.19093 0.191166i
\(229\) 3.56596e24i 0.594161i 0.954853 + 0.297080i \(0.0960129\pi\)
−0.954853 + 0.297080i \(0.903987\pi\)
\(230\) 3.25597e24 0.518249
\(231\) −6.97517e24 + 9.72956e23i −1.06079 + 0.147968i
\(232\) −2.22379e24 −0.323199
\(233\) 1.60294e23i 0.0222679i −0.999938 0.0111339i \(-0.996456\pi\)
0.999938 0.0111339i \(-0.00354412\pi\)
\(234\) 4.11328e23 + 1.35543e23i 0.0546288 + 0.0180016i
\(235\) 1.62294e25 2.06106
\(236\) −1.11974e24 −0.136001
\(237\) 8.42107e23 5.24619e24i 0.0978385 0.609518i
\(238\) −4.29317e23 1.39899e24i −0.0477222 0.155509i
\(239\) 7.82157e24i 0.831986i 0.909368 + 0.415993i \(0.136566\pi\)
−0.909368 + 0.415993i \(0.863434\pi\)
\(240\) −2.26640e24 + 1.41193e25i −0.230738 + 1.43746i
\(241\) 1.45971e25i 1.42261i −0.702882 0.711306i \(-0.748104\pi\)
0.702882 0.711306i \(-0.251896\pi\)
\(242\) 2.69083e23i 0.0251088i
\(243\) −7.99506e24 + 7.83043e24i −0.714424 + 0.699713i
\(244\) 1.42548e25i 1.22002i
\(245\) 1.60917e25 1.09032e25i 1.31935 0.893941i
\(246\) −1.63422e24 2.62321e23i −0.128378 0.0206070i
\(247\) −5.56361e24 −0.418831
\(248\) −3.81437e24 −0.275220
\(249\) 2.87769e24 1.79276e25i 0.199045 1.24002i
\(250\) 2.21319e24i 0.146774i
\(251\) −1.07792e25 −0.685508 −0.342754 0.939425i \(-0.611360\pi\)
−0.342754 + 0.939425i \(0.611360\pi\)
\(252\) −1.59142e25 3.27336e23i −0.970686 0.0199659i
\(253\) 3.48906e25 2.04147
\(254\) 4.74731e23i 0.0266498i
\(255\) 4.47055e24 2.78508e25i 0.240818 1.50026i
\(256\) 1.39550e25 0.721454
\(257\) 2.56886e25 1.27480 0.637401 0.770533i \(-0.280010\pi\)
0.637401 + 0.770533i \(0.280010\pi\)
\(258\) −1.03461e23 1.66074e22i −0.00492913 0.000791214i
\(259\) −9.68194e24 + 2.97117e24i −0.442910 + 0.135919i
\(260\) 1.18738e25i 0.521637i
\(261\) 7.12899e24 2.16341e25i 0.300817 0.912878i
\(262\) 8.15873e23i 0.0330719i
\(263\) 1.48951e25i 0.580105i −0.957011 0.290053i \(-0.906327\pi\)
0.957011 0.290053i \(-0.0936728\pi\)
\(264\) 1.52520e24 9.50172e24i 0.0570800 0.355599i
\(265\) 4.37088e25i 1.57212i
\(266\) −5.86090e24 + 1.79858e24i −0.202631 + 0.0621830i
\(267\) −7.13529e24 + 4.44517e25i −0.237161 + 1.47747i
\(268\) −2.66138e25 −0.850532
\(269\) −5.79749e25 −1.78173 −0.890863 0.454273i \(-0.849899\pi\)
−0.890863 + 0.454273i \(0.849899\pi\)
\(270\) 8.16992e24 + 4.22722e24i 0.241490 + 0.124950i
\(271\) 2.99675e25i 0.852066i −0.904708 0.426033i \(-0.859911\pi\)
0.904708 0.426033i \(-0.140089\pi\)
\(272\) −3.18407e25 −0.870982
\(273\) −1.26859e25 + 1.76953e24i −0.333897 + 0.0465748i
\(274\) 3.81062e24 0.0965193
\(275\) 6.76509e25i 1.64923i
\(276\) 7.78612e25 + 1.24981e25i 1.82716 + 0.293291i
\(277\) 1.61099e25 0.363962 0.181981 0.983302i \(-0.441749\pi\)
0.181981 + 0.983302i \(0.441749\pi\)
\(278\) 4.20249e24 0.0914189
\(279\) 1.22281e25 3.71080e25i 0.256161 0.777363i
\(280\) 7.79207e24 + 2.53915e25i 0.157215 + 0.512305i
\(281\) 3.88973e25i 0.755967i −0.925812 0.377983i \(-0.876618\pi\)
0.925812 0.377983i \(-0.123382\pi\)
\(282\) −1.16357e25 1.86773e24i −0.217859 0.0349702i
\(283\) 6.67261e25i 1.20376i −0.798588 0.601878i \(-0.794419\pi\)
0.798588 0.601878i \(-0.205581\pi\)
\(284\) 6.90177e25i 1.19982i
\(285\) −1.16678e26 1.87289e25i −1.95487 0.313791i
\(286\) 3.81473e24i 0.0616056i
\(287\) 4.67976e25 1.43611e25i 0.728558 0.223578i
\(288\) 1.02611e25 3.11388e25i 0.154018 0.467392i
\(289\) −6.28509e24 −0.0909671
\(290\) −1.87235e25 −0.261341
\(291\) 5.64951e25 + 9.06847e24i 0.760561 + 0.122084i
\(292\) 1.15948e26i 1.50572i
\(293\) 2.91436e25 0.365118 0.182559 0.983195i \(-0.441562\pi\)
0.182559 + 0.983195i \(0.441562\pi\)
\(294\) −1.27917e25 + 5.96512e24i −0.154626 + 0.0721061i
\(295\) −1.91383e25 −0.223240
\(296\) 1.38386e25i 0.155786i
\(297\) 8.75479e25 + 4.52983e25i 0.951268 + 0.492198i
\(298\) −1.50642e25 −0.158006
\(299\) 6.34562e25 0.642579
\(300\) −2.42331e25 + 1.50969e26i −0.236939 + 1.47609i
\(301\) 2.96272e24 9.09193e23i 0.0279732 0.00858436i
\(302\) 2.53626e25i 0.231271i
\(303\) 1.28157e25 7.98399e25i 0.112874 0.703189i
\(304\) 1.33393e26i 1.13491i
\(305\) 2.43639e26i 2.00262i
\(306\) −6.41030e24 + 1.94531e25i −0.0509100 + 0.154495i
\(307\) 1.50702e26i 1.15655i 0.815842 + 0.578276i \(0.196274\pi\)
−0.815842 + 0.578276i \(0.803726\pi\)
\(308\) 4.11328e25 + 1.34037e26i 0.305075 + 0.994126i
\(309\) −3.95997e25 6.35646e24i −0.283875 0.0455671i
\(310\) −3.21156e25 −0.222545
\(311\) −7.43049e25 −0.497775 −0.248888 0.968532i \(-0.580065\pi\)
−0.248888 + 0.968532i \(0.580065\pi\)
\(312\) 2.77390e24 1.72810e25i 0.0179667 0.111930i
\(313\) 2.26853e26i 1.42079i −0.703803 0.710395i \(-0.748516\pi\)
0.703803 0.710395i \(-0.251484\pi\)
\(314\) −1.72469e25 −0.104460
\(315\) −2.72000e26 5.59472e24i −1.59334 0.0327731i
\(316\) −1.05778e26 −0.599351
\(317\) 1.87990e26i 1.03042i −0.857065 0.515209i \(-0.827714\pi\)
0.857065 0.515209i \(-0.172286\pi\)
\(318\) −5.03013e24 + 3.13369e25i −0.0266744 + 0.166177i
\(319\) −2.00638e26 −1.02947
\(320\) 2.66271e26 1.32205
\(321\) 1.61445e26 + 2.59147e25i 0.775748 + 0.124521i
\(322\) 6.68469e25 2.05138e25i 0.310881 0.0954024i
\(323\) 2.63122e26i 1.18449i
\(324\) 1.79144e26 + 1.32447e26i 0.780692 + 0.577193i
\(325\) 1.23038e26i 0.519116i
\(326\) 7.67662e25i 0.313607i
\(327\) 1.05631e25 6.58065e25i 0.0417869 0.260326i
\(328\) 6.68889e25i 0.256259i
\(329\) 3.33200e26 1.02251e26i 1.23637 0.379413i
\(330\) 1.28416e25 8.00010e25i 0.0461553 0.287540i
\(331\) −4.01134e26 −1.39667 −0.698337 0.715769i \(-0.746076\pi\)
−0.698337 + 0.715769i \(0.746076\pi\)
\(332\) −3.61470e26 −1.21933
\(333\) 1.34629e26 + 4.43637e25i 0.440021 + 0.144998i
\(334\) 5.59379e25i 0.177161i
\(335\) −4.54874e26 −1.39611
\(336\) 4.24263e25 + 3.04156e26i 0.126204 + 0.904763i
\(337\) 9.72732e25 0.280465 0.140233 0.990119i \(-0.455215\pi\)
0.140233 + 0.990119i \(0.455215\pi\)
\(338\) 5.41048e25i 0.151221i
\(339\) 6.24025e26 + 1.00167e26i 1.69085 + 0.271412i
\(340\) −5.61552e26 −1.47523
\(341\) −3.44147e26 −0.876643
\(342\) 8.14965e25 + 2.68552e25i 0.201310 + 0.0663368i
\(343\) 2.61678e26 3.25232e26i 0.626873 0.779121i
\(344\) 4.23469e24i 0.00983915i
\(345\) 1.33078e27 + 2.13614e26i 2.99920 + 0.481425i
\(346\) 3.81639e25i 0.0834361i
\(347\) 1.17581e26i 0.249390i 0.992195 + 0.124695i \(0.0397953\pi\)
−0.992195 + 0.124695i \(0.960205\pi\)
\(348\) −4.47741e26 7.18704e25i −0.921392 0.147900i
\(349\) 3.71476e26i 0.741761i −0.928681 0.370881i \(-0.879056\pi\)
0.928681 0.370881i \(-0.120944\pi\)
\(350\) 3.97751e25 + 1.29612e26i 0.0770721 + 0.251150i
\(351\) 1.59225e26 + 8.23850e25i 0.299424 + 0.154926i
\(352\) −2.88787e26 −0.527084
\(353\) −4.02575e26 −0.713202 −0.356601 0.934257i \(-0.616064\pi\)
−0.356601 + 0.934257i \(0.616064\pi\)
\(354\) 1.37212e25 + 2.20249e24i 0.0235970 + 0.00378773i
\(355\) 1.17963e27i 1.96946i
\(356\) 8.96272e26 1.45283
\(357\) −8.36874e25 5.99959e26i −0.131718 0.944290i
\(358\) −4.19939e25 −0.0641821
\(359\) 8.57792e26i 1.27318i −0.771202 0.636591i \(-0.780344\pi\)
0.771202 0.636591i \(-0.219656\pi\)
\(360\) 1.16346e26 3.53072e26i 0.167717 0.508964i
\(361\) −3.88111e26 −0.543414
\(362\) 5.46508e25 0.0743287
\(363\) 1.76537e25 1.09980e26i 0.0233247 0.145309i
\(364\) 7.48091e25 + 2.43775e26i 0.0960263 + 0.312914i
\(365\) 1.98175e27i 2.47158i
\(366\) 2.80386e25 1.74676e26i 0.0339786 0.211681i
\(367\) 1.01208e27i 1.19185i −0.803039 0.595927i \(-0.796785\pi\)
0.803039 0.595927i \(-0.203215\pi\)
\(368\) 1.52142e27i 1.74120i
\(369\) −6.50727e26 2.14432e26i −0.723806 0.238513i
\(370\) 1.16516e26i 0.125970i
\(371\) −2.75381e26 8.97365e26i −0.289406 0.943069i
\(372\) −7.67992e26 1.23276e26i −0.784613 0.125944i
\(373\) −8.85286e25 −0.0879308 −0.0439654 0.999033i \(-0.513999\pi\)
−0.0439654 + 0.999033i \(0.513999\pi\)
\(374\) 1.80411e26 0.174226
\(375\) −1.45200e26 + 9.04574e26i −0.136345 + 0.849407i
\(376\) 4.76250e26i 0.434873i
\(377\) −3.64905e26 −0.324038
\(378\) 1.94366e26 + 3.53137e25i 0.167864 + 0.0304985i
\(379\) −1.60854e26 −0.135120 −0.0675601 0.997715i \(-0.521521\pi\)
−0.0675601 + 0.997715i \(0.521521\pi\)
\(380\) 2.35256e27i 1.92226i
\(381\) −3.11456e25 + 1.94032e26i −0.0247562 + 0.154227i
\(382\) 3.03487e25 0.0234679
\(383\) 2.47683e27 1.86341 0.931705 0.363216i \(-0.118321\pi\)
0.931705 + 0.363216i \(0.118321\pi\)
\(384\) −8.54676e26 1.37191e26i −0.625639 0.100426i
\(385\) 7.03030e26 + 2.29091e27i 0.500767 + 1.63182i
\(386\) 2.06305e26i 0.143002i
\(387\) −4.11971e25 1.35755e25i −0.0277908 0.00915780i
\(388\) 1.13910e27i 0.747875i
\(389\) 1.99655e26i 0.127588i 0.997963 + 0.0637940i \(0.0203201\pi\)
−0.997963 + 0.0637940i \(0.979680\pi\)
\(390\) 2.33552e25 1.45499e26i 0.0145280 0.0905071i
\(391\) 3.00106e27i 1.81727i
\(392\) 3.19951e26 + 4.72209e26i 0.188617 + 0.278375i
\(393\) −5.35268e25 + 3.33463e26i −0.0307220 + 0.191393i
\(394\) 3.69477e26 0.206479
\(395\) −1.80793e27 −0.983810
\(396\) 6.14170e26 1.86380e27i 0.325454 0.987642i
\(397\) 1.03765e26i 0.0535487i −0.999642 0.0267743i \(-0.991476\pi\)
0.999642 0.0267743i \(-0.00852355\pi\)
\(398\) −8.21143e25 −0.0412712
\(399\) −2.51346e27 + 3.50599e26i −1.23043 + 0.171631i
\(400\) 2.94996e27 1.40665
\(401\) 2.10386e27i 0.977240i −0.872497 0.488620i \(-0.837500\pi\)
0.872497 0.488620i \(-0.162500\pi\)
\(402\) 3.26121e26 + 5.23482e25i 0.147572 + 0.0236880i
\(403\) −6.25906e26 −0.275935
\(404\) −1.60980e27 −0.691460
\(405\) 3.06187e27 + 2.26375e27i 1.28147 + 0.947437i
\(406\) −3.84403e26 + 1.17965e26i −0.156770 + 0.0481092i
\(407\) 1.24857e27i 0.496217i
\(408\) 8.17276e26 + 1.31187e26i 0.316546 + 0.0508113i
\(409\) 1.90621e26i 0.0719576i −0.999353 0.0359788i \(-0.988545\pi\)
0.999353 0.0359788i \(-0.0114549\pi\)
\(410\) 5.63180e26i 0.207213i
\(411\) 1.55747e27 + 2.50002e26i 0.558575 + 0.0896612i
\(412\) 7.98442e26i 0.279140i
\(413\) −3.92920e26 + 1.20578e26i −0.133915 + 0.0410954i
\(414\) −9.29515e26 3.06299e26i −0.308854 0.101775i
\(415\) −6.17814e27 −2.00149
\(416\) −5.25223e26 −0.165907
\(417\) 1.71764e27 + 2.75712e26i 0.529058 + 0.0849232i
\(418\) 7.55813e26i 0.227020i
\(419\) 2.23604e27 0.654988 0.327494 0.944853i \(-0.393796\pi\)
0.327494 + 0.944853i \(0.393796\pi\)
\(420\) 7.48243e26 + 5.36419e27i 0.213759 + 1.53245i
\(421\) 9.55945e26 0.266361 0.133181 0.991092i \(-0.457481\pi\)
0.133181 + 0.991092i \(0.457481\pi\)
\(422\) 6.98383e26i 0.189807i
\(423\) −4.63318e27 1.52676e27i −1.22830 0.404758i
\(424\) 1.28262e27 0.331709
\(425\) −5.81889e27 −1.46810
\(426\) −1.35755e26 + 8.45731e26i −0.0334160 + 0.208176i
\(427\) 1.53501e27 + 5.00204e27i 0.368654 + 1.20131i
\(428\) 3.25518e27i 0.762809i
\(429\) 2.50272e26 1.55915e27i 0.0572282 0.356523i
\(430\) 3.56545e25i 0.00795601i
\(431\) 8.11612e27i 1.76741i 0.468044 + 0.883705i \(0.344959\pi\)
−0.468044 + 0.883705i \(0.655041\pi\)
\(432\) 1.97526e27 3.81757e27i 0.419803 0.811350i
\(433\) 2.10911e27i 0.437499i 0.975781 + 0.218749i \(0.0701977\pi\)
−0.975781 + 0.218749i \(0.929802\pi\)
\(434\) −6.59351e26 + 2.02340e26i −0.133498 + 0.0409675i
\(435\) −7.65264e27 1.22839e27i −1.51243 0.242771i
\(436\) −1.32685e27 −0.255984
\(437\) 1.25726e28 2.36794
\(438\) 2.28066e26 1.42081e27i 0.0419355 0.261252i
\(439\) 7.48107e27i 1.34303i −0.740991 0.671515i \(-0.765644\pi\)
0.740991 0.671515i \(-0.234356\pi\)
\(440\) −3.27445e27 −0.573965
\(441\) −5.61957e27 + 1.59884e27i −0.961829 + 0.273652i
\(442\) 3.28118e26 0.0548398
\(443\) 1.77997e27i 0.290518i 0.989394 + 0.145259i \(0.0464016\pi\)
−0.989394 + 0.145259i \(0.953598\pi\)
\(444\) 4.47249e26 2.78629e27i 0.0712899 0.444125i
\(445\) 1.53188e28 2.38476
\(446\) −1.04803e27 −0.159352
\(447\) −6.15702e27 9.88312e26i −0.914412 0.146779i
\(448\) 5.46669e27 1.67760e27i 0.793059 0.243372i
\(449\) 6.70454e27i 0.950128i −0.879951 0.475064i \(-0.842425\pi\)
0.879951 0.475064i \(-0.157575\pi\)
\(450\) 5.93898e26 1.80228e27i 0.0822205 0.249511i
\(451\) 6.03496e27i 0.816246i
\(452\) 1.25821e28i 1.66265i
\(453\) 1.66396e27 1.03662e28i 0.214838 1.33841i
\(454\) 7.80888e25i 0.00985150i
\(455\) 1.27861e27 + 4.16653e27i 0.157623 + 0.513635i
\(456\) 5.49595e26 3.42389e27i 0.0662082 0.412466i
\(457\) 4.82928e27 0.568542 0.284271 0.958744i \(-0.408249\pi\)
0.284271 + 0.958744i \(0.408249\pi\)
\(458\) −8.81049e26 −0.101371
\(459\) −3.89627e27 + 7.53030e27i −0.438143 + 0.846796i
\(460\) 2.68323e28i 2.94917i
\(461\) 1.23732e28 1.32930 0.664648 0.747157i \(-0.268582\pi\)
0.664648 + 0.747157i \(0.268582\pi\)
\(462\) −2.40390e26 1.72337e27i −0.0252451 0.180983i
\(463\) 1.82176e28 1.87022 0.935108 0.354364i \(-0.115302\pi\)
0.935108 + 0.354364i \(0.115302\pi\)
\(464\) 8.74895e27i 0.878046i
\(465\) −1.31263e28 2.10700e27i −1.28791 0.206732i
\(466\) 3.96041e25 0.00379916
\(467\) −8.95927e27 −0.840321 −0.420161 0.907450i \(-0.638026\pi\)
−0.420161 + 0.907450i \(0.638026\pi\)
\(468\) 1.11700e27 3.38973e27i 0.102441 0.310873i
\(469\) −9.33882e27 + 2.86587e27i −0.837485 + 0.257005i
\(470\) 4.00984e27i 0.351641i
\(471\) −7.04915e27 1.13151e27i −0.604529 0.0970377i
\(472\) 5.61609e26i 0.0471024i
\(473\) 3.82069e26i 0.0313401i
\(474\) 1.29619e27 + 2.08061e26i 0.103991 + 0.0166924i
\(475\) 2.43776e28i 1.91297i
\(476\) −1.15290e28 + 3.53798e27i −0.884947 + 0.271570i
\(477\) −4.11182e27 + 1.24780e28i −0.308739 + 0.936918i
\(478\) −1.93249e27 −0.141947
\(479\) −3.71334e27 −0.266834 −0.133417 0.991060i \(-0.542595\pi\)
−0.133417 + 0.991060i \(0.542595\pi\)
\(480\) −1.10148e28 1.76807e27i −0.774360 0.124298i
\(481\) 2.27080e27i 0.156191i
\(482\) 3.60653e27 0.242714
\(483\) 2.86675e28 3.99878e27i 1.88775 0.263319i
\(484\) −2.21750e27 −0.142885
\(485\) 1.94692e28i 1.22761i
\(486\) −1.93468e27 1.97536e27i −0.119379 0.121889i
\(487\) −1.08522e28 −0.655334 −0.327667 0.944793i \(-0.606262\pi\)
−0.327667 + 0.944793i \(0.606262\pi\)
\(488\) −7.14952e27 −0.422541
\(489\) −5.03638e27 + 3.13759e28i −0.291324 + 1.81490i
\(490\) 2.69387e27 + 3.97582e27i 0.152517 + 0.225096i
\(491\) 1.43543e28i 0.795472i 0.917500 + 0.397736i \(0.130204\pi\)
−0.917500 + 0.397736i \(0.869796\pi\)
\(492\) −2.16178e27 + 1.34675e28i −0.117267 + 0.730556i
\(493\) 1.72576e28i 0.916406i
\(494\) 1.37461e27i 0.0714574i
\(495\) 1.04972e28 3.18555e28i 0.534219 1.62117i
\(496\) 1.50067e28i 0.747701i
\(497\) −7.43209e27 2.42184e28i −0.362551 1.18142i
\(498\) 4.42940e27 + 7.10997e26i 0.211561 + 0.0339594i
\(499\) 1.12880e28 0.527912 0.263956 0.964535i \(-0.414973\pi\)
0.263956 + 0.964535i \(0.414973\pi\)
\(500\) 1.82388e28 0.835239
\(501\) 3.66991e27 2.28629e28i 0.164573 1.02526i
\(502\) 2.66324e27i 0.116956i
\(503\) −1.02864e28 −0.442386 −0.221193 0.975230i \(-0.570995\pi\)
−0.221193 + 0.975230i \(0.570995\pi\)
\(504\) 1.64176e26 7.98179e27i 0.00691495 0.336186i
\(505\) −2.75142e28 −1.13500
\(506\) 8.62049e27i 0.348298i
\(507\) −3.54964e27 + 2.21137e28i −0.140476 + 0.875141i
\(508\) 3.91224e27 0.151655
\(509\) −8.65416e27 −0.328616 −0.164308 0.986409i \(-0.552539\pi\)
−0.164308 + 0.986409i \(0.552539\pi\)
\(510\) 6.88116e27 + 1.10455e27i 0.255962 + 0.0410864i
\(511\) 1.24858e28 + 4.06865e28i 0.454984 + 1.48262i
\(512\) 2.11972e28i 0.756736i
\(513\) 3.15473e28 + 1.63230e28i 1.10339 + 0.570909i
\(514\) 6.34693e27i 0.217496i
\(515\) 1.36467e28i 0.458197i
\(516\) −1.36860e26 + 8.52618e26i −0.00450252 + 0.0280500i
\(517\) 4.29690e28i 1.38517i
\(518\) −7.34093e26 2.39214e27i −0.0231894 0.0755655i
\(519\) −2.50381e27 + 1.55983e28i −0.0775076 + 0.482860i
\(520\) −5.95531e27 −0.180663
\(521\) 4.59585e28 1.36637 0.683187 0.730244i \(-0.260593\pi\)
0.683187 + 0.730244i \(0.260593\pi\)
\(522\) 5.34518e27 + 1.76138e27i 0.155748 + 0.0513230i
\(523\) 5.26887e28i 1.50470i −0.658764 0.752349i \(-0.728921\pi\)
0.658764 0.752349i \(-0.271079\pi\)
\(524\) 6.72356e27 0.188201
\(525\) 7.75342e27 + 5.55847e28i 0.212726 + 1.52504i
\(526\) 3.68015e27 0.0989728
\(527\) 2.96013e28i 0.780367i
\(528\) −3.73822e28 6.00051e27i −0.966070 0.155071i
\(529\) −1.03926e29 −2.63294
\(530\) 1.07992e28 0.268223
\(531\) 5.46360e27 + 1.80040e27i 0.133041 + 0.0438406i
\(532\) 1.48220e28 + 4.82993e28i 0.353862 + 1.15310i
\(533\) 1.09759e28i 0.256924i
\(534\) −1.09828e28 1.76293e27i −0.252074 0.0404624i
\(535\) 5.56365e28i 1.25212i
\(536\) 1.33482e28i 0.294572i
\(537\) −1.71637e28 2.75508e27i −0.371433 0.0596217i
\(538\) 1.43240e28i 0.303983i
\(539\) 2.88672e28 + 4.26044e28i 0.600789 + 0.886691i
\(540\) 3.48363e28 6.73279e28i 0.711045 1.37423i
\(541\) 2.60992e28 0.522464 0.261232 0.965276i \(-0.415871\pi\)
0.261232 + 0.965276i \(0.415871\pi\)
\(542\) 7.40413e27 0.145372
\(543\) 2.23368e28 + 3.58546e27i 0.430153 + 0.0690473i
\(544\) 2.48396e28i 0.469198i
\(545\) −2.26780e28 −0.420186
\(546\) −4.37203e26 3.13433e27i −0.00794621 0.0569668i
\(547\) −8.15351e28 −1.45371 −0.726855 0.686791i \(-0.759019\pi\)
−0.726855 + 0.686791i \(0.759019\pi\)
\(548\) 3.14031e28i 0.549258i
\(549\) 2.29199e28 6.95540e28i 0.393280 1.19347i
\(550\) −1.67147e28 −0.281377
\(551\) −7.22988e28 −1.19410
\(552\) −6.26845e27 + 3.90514e28i −0.101578 + 0.632814i
\(553\) −3.71177e28 + 1.13906e28i −0.590157 + 0.181106i
\(554\) 3.98031e27i 0.0620961i
\(555\) 7.64424e27 4.76224e28i 0.117019 0.729012i
\(556\) 3.46325e28i 0.520233i
\(557\) 8.12529e28i 1.19773i 0.800850 + 0.598865i \(0.204382\pi\)
−0.800850 + 0.598865i \(0.795618\pi\)
\(558\) 9.16836e27 + 3.02122e27i 0.132627 + 0.0437041i
\(559\) 6.94876e26i 0.00986469i
\(560\) 9.98966e28 3.06560e28i 1.39180 0.427112i
\(561\) 7.37377e28 + 1.18362e28i 1.00828 + 0.161846i
\(562\) 9.61043e27 0.128977
\(563\) −1.36835e29 −1.80243 −0.901215 0.433372i \(-0.857324\pi\)
−0.901215 + 0.433372i \(0.857324\pi\)
\(564\) −1.53919e28 + 9.58888e28i −0.199003 + 1.23976i
\(565\) 2.15050e29i 2.72917i
\(566\) 1.64862e28 0.205375
\(567\) 7.71244e28 + 2.71851e28i 0.943126 + 0.332437i
\(568\) 3.46159e28 0.415545
\(569\) 9.33152e28i 1.09970i 0.835264 + 0.549849i \(0.185315\pi\)
−0.835264 + 0.549849i \(0.814685\pi\)
\(570\) 4.62738e27 2.88278e28i 0.0535364 0.333523i
\(571\) 1.49938e29 1.70307 0.851536 0.524296i \(-0.175671\pi\)
0.851536 + 0.524296i \(0.175671\pi\)
\(572\) −3.14369e28 −0.350576
\(573\) 1.24041e28 + 1.99108e27i 0.135813 + 0.0218004i
\(574\) 3.54824e27 + 1.15624e28i 0.0381450 + 0.124300i
\(575\) 2.78041e29i 2.93492i
\(576\) −7.60151e28 2.50490e28i −0.787887 0.259629i
\(577\) 6.52072e28i 0.663666i −0.943338 0.331833i \(-0.892333\pi\)
0.943338 0.331833i \(-0.107667\pi\)
\(578\) 1.55287e27i 0.0155200i
\(579\) 1.35350e28 8.43209e28i 0.132841 0.827581i
\(580\) 1.54299e29i 1.48720i
\(581\) −1.26841e29 + 3.89245e28i −1.20063 + 0.368446i
\(582\) −2.24057e27 + 1.39584e28i −0.0208289 + 0.129761i
\(583\) 1.15723e29 1.05657
\(584\) −5.81542e28 −0.521490
\(585\) 1.90915e28 5.79361e28i 0.168152 0.510285i
\(586\) 7.20057e27i 0.0622934i
\(587\) 8.71061e28 0.740199 0.370099 0.928992i \(-0.379324\pi\)
0.370099 + 0.928992i \(0.379324\pi\)
\(588\) 4.91582e28 + 1.05416e29i 0.410331 + 0.879920i
\(589\) −1.24011e29 −1.01683
\(590\) 4.72854e27i 0.0380874i
\(591\) 1.51012e29 + 2.42402e28i 1.19493 + 0.191808i
\(592\) −5.44447e28 −0.423231
\(593\) 2.35881e29 1.80143 0.900716 0.434408i \(-0.143042\pi\)
0.900716 + 0.434408i \(0.143042\pi\)
\(594\) −1.11920e28 + 2.16306e28i −0.0839747 + 0.162297i
\(595\) −1.97049e29 + 6.04700e28i −1.45260 + 0.445771i
\(596\) 1.24143e29i 0.899160i
\(597\) −3.35617e28 5.38725e27i −0.238844 0.0383387i
\(598\) 1.56783e28i 0.109631i
\(599\) 1.72970e29i 1.18848i −0.804290 0.594238i \(-0.797454\pi\)
0.804290 0.594238i \(-0.202546\pi\)
\(600\) −7.57185e28 1.21542e28i −0.511227 0.0820611i
\(601\) 2.72534e28i 0.180817i 0.995905 + 0.0904084i \(0.0288172\pi\)
−0.995905 + 0.0904084i \(0.971183\pi\)
\(602\) 2.24636e26 + 7.32006e26i 0.00146459 + 0.00477256i
\(603\) 1.29857e29 + 4.27914e28i 0.832023 + 0.274173i
\(604\) −2.09012e29 −1.31608
\(605\) −3.79008e28 −0.234540
\(606\) 1.97262e28 + 3.16641e27i 0.119972 + 0.0192577i
\(607\) 2.01615e29i 1.20515i −0.798061 0.602576i \(-0.794141\pi\)
0.798061 0.602576i \(-0.205859\pi\)
\(608\) −1.04063e29 −0.611375
\(609\) −1.64852e29 + 2.29950e28i −0.951949 + 0.132786i
\(610\) −6.01963e28 −0.341670
\(611\) 7.81486e28i 0.436002i
\(612\) 1.60312e29 + 5.28269e28i 0.879176 + 0.289711i
\(613\) 1.72405e29 0.929428 0.464714 0.885461i \(-0.346157\pi\)
0.464714 + 0.885461i \(0.346157\pi\)
\(614\) −3.72342e28 −0.197321
\(615\) −3.69484e28 + 2.30182e29i −0.192489 + 1.19918i
\(616\) −6.72264e28 + 2.06302e28i −0.344304 + 0.105659i
\(617\) 2.50226e29i 1.25991i 0.776633 + 0.629954i \(0.216926\pi\)
−0.776633 + 0.629954i \(0.783074\pi\)
\(618\) 1.57050e27 9.78398e27i 0.00777427 0.0484325i
\(619\) 1.67096e29i 0.813233i 0.913599 + 0.406616i \(0.133291\pi\)
−0.913599 + 0.406616i \(0.866709\pi\)
\(620\) 2.64663e29i 1.26643i
\(621\) −3.59816e29 1.86173e29i −1.69285 0.875901i
\(622\) 1.83587e28i 0.0849263i
\(623\) 3.14503e29 9.65140e28i 1.43054 0.439001i
\(624\) −6.79878e28 1.09132e28i −0.304083 0.0488108i
\(625\) −3.83803e28 −0.168798
\(626\) 5.60492e28 0.242403
\(627\) 4.95865e28 3.08916e29i 0.210889 1.31380i
\(628\) 1.42131e29i 0.594446i
\(629\) 1.07394e29 0.441721
\(630\) 1.38230e27 6.72037e28i 0.00559148 0.271843i
\(631\) 1.18588e27 0.00471774 0.00235887 0.999997i \(-0.499249\pi\)
0.00235887 + 0.999997i \(0.499249\pi\)
\(632\) 5.30532e28i 0.207578i
\(633\) −4.58187e28 + 2.85443e29i −0.176321 + 1.09845i
\(634\) 4.64472e28 0.175801
\(635\) 6.68667e28 0.248935
\(636\) 2.58245e29 + 4.14530e28i 0.945656 + 0.151795i
\(637\) 5.25013e28 + 7.74855e28i 0.189106 + 0.279098i
\(638\) 4.95721e28i 0.175639i
\(639\) −1.10971e29 + 3.36760e29i −0.386769 + 1.17371i
\(640\) 2.94536e29i 1.00983i
\(641\) 3.71900e29i 1.25434i −0.778881 0.627172i \(-0.784212\pi\)
0.778881 0.627172i \(-0.215788\pi\)
\(642\) −6.40281e27 + 3.98885e28i −0.0212448 + 0.132352i
\(643\) 3.90743e29i 1.27549i 0.770249 + 0.637743i \(0.220132\pi\)
−0.770249 + 0.637743i \(0.779868\pi\)
\(644\) −1.69053e29 5.50882e29i −0.542902 1.76912i
\(645\) −2.33917e27 + 1.45727e28i −0.00739070 + 0.0460429i
\(646\) 6.50101e28 0.202088
\(647\) −3.08437e29 −0.943347 −0.471673 0.881773i \(-0.656350\pi\)
−0.471673 + 0.881773i \(0.656350\pi\)
\(648\) −6.64292e28 + 8.98499e28i −0.199904 + 0.270384i
\(649\) 5.06704e28i 0.150033i
\(650\) −3.03993e28 −0.0885672
\(651\) −2.82764e29 + 3.94424e28i −0.810633 + 0.113074i
\(652\) 6.32626e29 1.78463
\(653\) 8.04579e28i 0.223347i −0.993745 0.111674i \(-0.964379\pi\)
0.993745 0.111674i \(-0.0356211\pi\)
\(654\) 1.62589e28 + 2.60985e27i 0.0444146 + 0.00712934i
\(655\) 1.14917e29 0.308923
\(656\) 2.63158e29 0.696188
\(657\) 1.86430e29 5.65752e29i 0.485377 1.47295i
\(658\) 2.52635e28 + 8.23243e28i 0.0647323 + 0.210939i
\(659\) 5.58260e29i 1.40780i 0.710301 + 0.703898i \(0.248559\pi\)
−0.710301 + 0.703898i \(0.751441\pi\)
\(660\) −6.59283e29 1.05827e29i −1.63629 0.262654i
\(661\) 2.91146e29i 0.711207i −0.934637 0.355603i \(-0.884275\pi\)
0.934637 0.355603i \(-0.115725\pi\)
\(662\) 9.91090e28i 0.238289i
\(663\) 1.34108e29 + 2.15267e28i 0.317368 + 0.0509432i
\(664\) 1.81296e29i 0.422302i
\(665\) 2.53332e29 + 8.25517e29i 0.580849 + 1.89277i
\(666\) −1.09610e28 + 3.32630e28i −0.0247384 + 0.0750727i
\(667\) 8.24609e29 1.83201
\(668\) −4.60981e29 −1.00816
\(669\) −4.28350e29 6.87578e28i −0.922199 0.148029i
\(670\) 1.12387e29i 0.238193i
\(671\) −6.45056e29 −1.34589
\(672\) −2.37279e29 + 3.30977e28i −0.487396 + 0.0679861i
\(673\) −2.98874e29 −0.604408 −0.302204 0.953243i \(-0.597722\pi\)
−0.302204 + 0.953243i \(0.597722\pi\)
\(674\) 2.40335e28i 0.0478506i
\(675\) 3.60979e29 6.97663e29i 0.707608 1.36759i
\(676\) 4.45875e29 0.860543
\(677\) −2.07189e29 −0.393719 −0.196859 0.980432i \(-0.563074\pi\)
−0.196859 + 0.980432i \(0.563074\pi\)
\(678\) −2.47485e28 + 1.54179e29i −0.0463060 + 0.288479i
\(679\) −1.22663e29 3.99713e29i −0.225985 0.736403i
\(680\) 2.81647e29i 0.510930i
\(681\) 5.12315e27 3.19164e28i 0.00915151 0.0570124i
\(682\) 8.50291e28i 0.149565i
\(683\) 5.00451e28i 0.0866851i 0.999060 + 0.0433426i \(0.0138007\pi\)
−0.999060 + 0.0433426i \(0.986199\pi\)
\(684\) 2.21312e29 6.71608e29i 0.377500 1.14558i
\(685\) 5.36731e29i 0.901584i
\(686\) 8.03558e28 + 6.46534e28i 0.132927 + 0.106952i
\(687\) −3.60102e29 5.78028e28i −0.586651 0.0941679i
\(688\) 1.66603e28 0.0267304
\(689\) 2.10468e29 0.332571
\(690\) −5.27780e28 + 3.28798e29i −0.0821367 + 0.511698i
\(691\) 4.80820e29i 0.736993i 0.929629 + 0.368496i \(0.120127\pi\)
−0.929629 + 0.368496i \(0.879873\pi\)
\(692\) 3.14507e29 0.474806
\(693\) 1.48126e28 7.20146e29i 0.0220258 1.07083i
\(694\) −2.90511e28 −0.0425489
\(695\) 5.91927e29i 0.853941i
\(696\) 3.60467e28 2.24565e29i 0.0512234 0.319114i
\(697\) −5.19088e29 −0.726603
\(698\) 9.17814e28 0.126553
\(699\) 1.61869e28 + 2.59829e27i 0.0219864 + 0.00352921i
\(700\) 1.06813e30 3.27785e29i 1.42920 0.438590i
\(701\) 1.10836e30i 1.46097i −0.682931 0.730483i \(-0.739295\pi\)
0.682931 0.730483i \(-0.260705\pi\)
\(702\) −2.03550e28 + 3.93401e28i −0.0264321 + 0.0510852i
\(703\) 4.49915e29i 0.575572i
\(704\) 7.04978e29i 0.888510i
\(705\) −2.63073e29 + 1.63890e30i −0.326656 + 2.03501i
\(706\) 9.94650e28i 0.121681i
\(707\) −5.64881e29 + 1.73349e29i −0.680853 + 0.208938i
\(708\) 1.81506e28 1.13075e29i 0.0215547 0.134282i
\(709\) 3.69654e29 0.432523 0.216262 0.976335i \(-0.430614\pi\)
0.216262 + 0.976335i \(0.430614\pi\)
\(710\) 2.91453e29 0.336013
\(711\) 5.16127e29 + 1.70077e29i 0.586308 + 0.193204i
\(712\) 4.49527e29i 0.503171i
\(713\) 1.41442e30 1.56005
\(714\) 1.48233e29 2.06768e28i 0.161107 0.0224725i
\(715\) −5.37310e29 −0.575455
\(716\) 3.46069e29i 0.365238i
\(717\) −7.89847e29 1.26785e29i −0.821471 0.131861i
\(718\) 2.11936e29 0.217220
\(719\) −5.12329e28 −0.0517482 −0.0258741 0.999665i \(-0.508237\pi\)
−0.0258741 + 0.999665i \(0.508237\pi\)
\(720\) −1.38908e30 4.57737e29i −1.38272 0.455643i
\(721\) 8.59793e28 + 2.80175e29i 0.0843478 + 0.274858i
\(722\) 9.58914e28i 0.0927127i
\(723\) 1.47406e30 + 2.36613e29i 1.40463 + 0.225468i
\(724\) 4.50374e29i 0.422979i
\(725\) 1.59887e30i 1.48001i
\(726\) 2.71729e28 + 4.36173e27i 0.0247914 + 0.00397946i
\(727\) 3.90953e29i 0.351571i −0.984428 0.175785i \(-0.943753\pi\)
0.984428 0.175785i \(-0.0562465\pi\)
\(728\) −1.22266e29 + 3.75206e28i −0.108374 + 0.0332576i
\(729\) −6.61145e29 9.34295e29i −0.577641 0.816291i
\(730\) −4.89636e29 −0.421681
\(731\) −3.28631e28 −0.0278982
\(732\) −1.43950e30 2.31065e29i −1.20460 0.193360i
\(733\) 2.37201e30i 1.95670i 0.206956 + 0.978350i \(0.433644\pi\)
−0.206956 + 0.978350i \(0.566356\pi\)
\(734\) 2.50058e29 0.203344
\(735\) 8.40196e29 + 1.80173e30i 0.673541 + 1.44435i
\(736\) 1.18690e30 0.937984
\(737\) 1.20432e30i 0.938283i
\(738\) 5.29801e28 1.60777e29i 0.0406931 0.123490i
\(739\) −2.08219e30 −1.57671 −0.788357 0.615217i \(-0.789068\pi\)
−0.788357 + 0.615217i \(0.789068\pi\)
\(740\) −9.60202e29 −0.716852
\(741\) 9.01839e28 5.61831e29i 0.0663801 0.413537i
\(742\) 2.21714e29 6.80390e28i 0.160899 0.0493761i
\(743\) 3.31867e29i 0.237455i 0.992927 + 0.118728i \(0.0378815\pi\)
−0.992927 + 0.118728i \(0.962118\pi\)
\(744\) 6.18294e28 3.85187e29i 0.0436194 0.271742i
\(745\) 2.12181e30i 1.47593i
\(746\) 2.18730e28i 0.0150020i
\(747\) 1.76373e30 + 5.81197e29i 1.19280 + 0.393058i
\(748\) 1.48676e30i 0.991458i
\(749\) −3.50530e29 1.14225e30i −0.230498 0.751107i
\(750\) −2.23495e29 3.58749e28i −0.144919 0.0232620i
\(751\) −1.43488e30 −0.917481 −0.458740 0.888570i \(-0.651699\pi\)
−0.458740 + 0.888570i \(0.651699\pi\)
\(752\) 1.87369e30 1.18144
\(753\) 1.74727e29 1.08852e30i 0.108645 0.676844i
\(754\) 9.01578e28i 0.0552846i
\(755\) −3.57236e30 −2.16029
\(756\) 2.91018e29 1.60176e30i 0.173557 0.955253i
\(757\) 2.39650e29 0.140952 0.0704758 0.997513i \(-0.477548\pi\)
0.0704758 + 0.997513i \(0.477548\pi\)
\(758\) 3.97426e28i 0.0230531i
\(759\) −5.65562e29 + 3.52336e30i −0.323550 + 2.01567i
\(760\) −1.17993e30 −0.665753
\(761\) 1.91913e30