Properties

Label 21.30.c.a.20.2
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 20.2
Character \(\chi\) \(=\) 21.20
Dual form 21.30.c.a.20.1

$q$-expansion

\(f(q)\) \(=\) \(q+27459.9i q^{2} +(-7.86336e6 + 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 - 2.15927e11i) q^{6} +(-1.78867e12 + 1.43352e11i) q^{7} +8.77881e12i q^{8} +(5.50345e13 - 4.10041e13i) q^{9} +O(q^{10})\) \(q+27459.9i q^{2} +(-7.86336e6 + 2.60729e6i) q^{3} -2.17175e8 q^{4} -2.60713e10 q^{5} +(-7.15959e10 - 2.15927e11i) q^{6} +(-1.78867e12 + 1.43352e11i) q^{7} +8.77881e12i q^{8} +(5.50345e13 - 4.10041e13i) q^{9} -7.15915e14i q^{10} -1.84525e15i q^{11} +(1.70773e15 - 5.66239e14i) q^{12} +1.93886e14i q^{13} +(-3.93643e15 - 4.91168e16i) q^{14} +(2.05008e17 - 6.79754e16i) q^{15} -3.57660e17 q^{16} -8.05269e16 q^{17} +(1.12597e18 + 1.51124e18i) q^{18} +5.95624e18i q^{19} +5.66204e18 q^{20} +(1.36912e19 - 5.79082e18i) q^{21} +5.06704e19 q^{22} -6.15339e19i q^{23} +(-2.28889e19 - 6.90309e19i) q^{24} +4.93447e20 q^{25} -5.32409e18 q^{26} +(-3.25846e20 + 4.65921e20i) q^{27} +(3.88456e20 - 3.11325e19i) q^{28} +9.13257e20i q^{29} +(1.86660e21 + 5.62950e21i) q^{30} -3.13598e21i q^{31} -5.10823e21i q^{32} +(4.81110e21 + 1.45099e22i) q^{33} -2.21126e21i q^{34} +(4.66330e22 - 3.73737e21i) q^{35} +(-1.19521e22 + 8.90508e21i) q^{36} -2.79899e22 q^{37} -1.63558e23 q^{38} +(-5.05517e20 - 1.52460e21i) q^{39} -2.28875e23i q^{40} +2.23493e23 q^{41} +(1.59015e23 + 3.75960e23i) q^{42} +5.48297e23 q^{43} +4.00743e23i q^{44} +(-1.43482e24 + 1.06903e24i) q^{45} +1.68972e24 q^{46} -1.11402e24 q^{47} +(2.81241e24 - 9.32524e23i) q^{48} +(3.17881e24 - 5.12820e23i) q^{49} +1.35500e25i q^{50} +(6.33212e23 - 2.09957e23i) q^{51} -4.21073e22i q^{52} -1.03543e25i q^{53} +(-1.27941e25 - 8.94770e24i) q^{54} +4.81080e25i q^{55} +(-1.25846e24 - 1.57024e25i) q^{56} +(-1.55296e25 - 4.68361e25i) q^{57} -2.50780e25 q^{58} -9.54320e24 q^{59} +(-4.45227e25 + 1.47626e25i) q^{60} +8.43183e25i q^{61} +8.61137e25 q^{62} +(-9.25607e25 + 8.12323e25i) q^{63} -5.17459e25 q^{64} -5.05486e24i q^{65} +(-3.98439e26 + 1.32112e26i) q^{66} +2.14590e26 q^{67} +1.74884e25 q^{68} +(1.60437e26 + 4.83863e26i) q^{69} +(1.02628e26 + 1.28054e27i) q^{70} -7.65917e26i q^{71} +(3.59967e26 + 4.83137e26i) q^{72} -7.98935e26i q^{73} -7.68601e26i q^{74} +(-3.88015e27 + 1.28656e27i) q^{75} -1.29355e27i q^{76} +(2.64520e26 + 3.30055e27i) q^{77} +(4.18652e25 - 1.38815e25i) q^{78} -2.93271e27 q^{79} +9.32466e27 q^{80} +(1.34745e27 - 4.51328e27i) q^{81} +6.13708e27i q^{82} -5.11580e27 q^{83} +(-2.97340e27 + 1.25762e27i) q^{84} +2.09944e27 q^{85} +1.50562e28i q^{86} +(-2.38113e27 - 7.18127e27i) q^{87} +1.61991e28 q^{88} +2.50441e28 q^{89} +(-2.93555e28 - 3.94000e28i) q^{90} +(-2.77939e25 - 3.46799e26i) q^{91} +1.33637e28i q^{92} +(8.17641e27 + 2.46593e28i) q^{93} -3.05909e28i q^{94} -1.55287e29i q^{95} +(1.33186e28 + 4.01679e28i) q^{96} -1.08394e29i q^{97} +(1.40820e28 + 8.72897e28i) q^{98} +(-7.56629e28 - 1.01552e29i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 27459.9i 1.18512i 0.805525 + 0.592562i \(0.201884\pi\)
−0.805525 + 0.592562i \(0.798116\pi\)
\(3\) −7.86336e6 + 2.60729e6i −0.949183 + 0.314725i
\(4\) −2.17175e8 −0.404521
\(5\) −2.60713e10 −1.91028 −0.955141 0.296153i \(-0.904296\pi\)
−0.955141 + 0.296153i \(0.904296\pi\)
\(6\) −7.15959e10 2.15927e11i −0.372988 1.12490i
\(7\) −1.78867e12 + 1.43352e11i −0.996804 + 0.0798881i
\(8\) 8.77881e12i 0.705717i
\(9\) 5.50345e13 4.10041e13i 0.801896 0.597463i
\(10\) 7.15915e14i 2.26392i
\(11\) 1.84525e15i 1.46508i −0.680724 0.732540i \(-0.738335\pi\)
0.680724 0.732540i \(-0.261665\pi\)
\(12\) 1.70773e15 5.66239e14i 0.383964 0.127313i
\(13\) 1.93886e14i 0.0136574i 0.999977 + 0.00682870i \(0.00217366\pi\)
−0.999977 + 0.00682870i \(0.997826\pi\)
\(14\) −3.93643e15 4.91168e16i −0.0946773 1.18134i
\(15\) 2.05008e17 6.79754e16i 1.81321 0.601213i
\(16\) −3.57660e17 −1.24088
\(17\) −8.05269e16 −0.115993 −0.0579964 0.998317i \(-0.518471\pi\)
−0.0579964 + 0.998317i \(0.518471\pi\)
\(18\) 1.12597e18 + 1.51124e18i 0.708068 + 0.950347i
\(19\) 5.95624e18i 1.71019i 0.518469 + 0.855096i \(0.326502\pi\)
−0.518469 + 0.855096i \(0.673498\pi\)
\(20\) 5.66204e18 0.772748
\(21\) 1.36912e19 5.79082e18i 0.921006 0.389547i
\(22\) 5.06704e19 1.73630
\(23\) 6.15339e19i 1.10678i −0.832922 0.553390i \(-0.813334\pi\)
0.832922 0.553390i \(-0.186666\pi\)
\(24\) −2.28889e19 6.90309e19i −0.222107 0.669855i
\(25\) 4.93447e20 2.64917
\(26\) −5.32409e18 −0.0161857
\(27\) −3.25846e20 + 4.65921e20i −0.573110 + 0.819479i
\(28\) 3.88456e20 3.11325e19i 0.403228 0.0323164i
\(29\) 9.13257e20i 0.569931i 0.958538 + 0.284965i \(0.0919821\pi\)
−0.958538 + 0.284965i \(0.908018\pi\)
\(30\) 1.86660e21 + 5.62950e21i 0.712513 + 2.14888i
\(31\) 3.13598e21i 0.744096i −0.928214 0.372048i \(-0.878656\pi\)
0.928214 0.372048i \(-0.121344\pi\)
\(32\) 5.10823e21i 0.764885i
\(33\) 4.81110e21 + 1.45099e22i 0.461097 + 1.39063i
\(34\) 2.21126e21i 0.137466i
\(35\) 4.66330e22 3.73737e21i 1.90418 0.152609i
\(36\) −1.19521e22 + 8.90508e21i −0.324384 + 0.241686i
\(37\) −2.79899e22 −0.510595 −0.255298 0.966863i \(-0.582173\pi\)
−0.255298 + 0.966863i \(0.582173\pi\)
\(38\) −1.63558e23 −2.02679
\(39\) −5.05517e20 1.52460e21i −0.00429832 0.0129634i
\(40\) 2.28875e23i 1.34812i
\(41\) 2.23493e23 0.920232 0.460116 0.887859i \(-0.347808\pi\)
0.460116 + 0.887859i \(0.347808\pi\)
\(42\) 1.59015e23 + 3.75960e23i 0.461662 + 1.09151i
\(43\) 5.48297e23 1.13168 0.565840 0.824515i \(-0.308552\pi\)
0.565840 + 0.824515i \(0.308552\pi\)
\(44\) 4.00743e23i 0.592655i
\(45\) −1.43482e24 + 1.06903e24i −1.53185 + 1.14132i
\(46\) 1.68972e24 1.31167
\(47\) −1.11402e24 −0.633103 −0.316552 0.948575i \(-0.602525\pi\)
−0.316552 + 0.948575i \(0.602525\pi\)
\(48\) 2.81241e24 9.32524e23i 1.17783 0.390537i
\(49\) 3.17881e24 5.12820e23i 0.987236 0.159265i
\(50\) 1.35500e25i 3.13960i
\(51\) 6.33212e23 2.09957e23i 0.110098 0.0365059i
\(52\) 4.21073e22i 0.00552470i
\(53\) 1.03543e25i 1.03067i −0.856988 0.515336i \(-0.827667\pi\)
0.856988 0.515336i \(-0.172333\pi\)
\(54\) −1.27941e25 8.94770e24i −0.971184 0.679207i
\(55\) 4.81080e25i 2.79871i
\(56\) −1.25846e24 1.57024e25i −0.0563784 0.703462i
\(57\) −1.55296e25 4.68361e25i −0.538240 1.62329i
\(58\) −2.50780e25 −0.675439
\(59\) −9.54320e24 −0.200604 −0.100302 0.994957i \(-0.531981\pi\)
−0.100302 + 0.994957i \(0.531981\pi\)
\(60\) −4.45227e25 + 1.47626e25i −0.733479 + 0.243203i
\(61\) 8.43183e25i 1.09305i 0.837444 + 0.546524i \(0.184049\pi\)
−0.837444 + 0.546524i \(0.815951\pi\)
\(62\) 8.61137e25 0.881846
\(63\) −9.25607e25 + 8.12323e25i −0.751603 + 0.659615i
\(64\) −5.17459e25 −0.334400
\(65\) 5.05486e24i 0.0260895i
\(66\) −3.98439e26 + 1.32112e26i −1.64807 + 0.546458i
\(67\) 2.14590e26 0.713716 0.356858 0.934159i \(-0.383848\pi\)
0.356858 + 0.934159i \(0.383848\pi\)
\(68\) 1.74884e25 0.0469215
\(69\) 1.60437e26 + 4.83863e26i 0.348331 + 1.05054i
\(70\) 1.02628e26 + 1.28054e27i 0.180860 + 2.25669i
\(71\) 7.65917e26i 1.09884i −0.835545 0.549422i \(-0.814848\pi\)
0.835545 0.549422i \(-0.185152\pi\)
\(72\) 3.59967e26 + 4.83137e26i 0.421640 + 0.565912i
\(73\) 7.98935e26i 0.766178i −0.923711 0.383089i \(-0.874860\pi\)
0.923711 0.383089i \(-0.125140\pi\)
\(74\) 7.68601e26i 0.605119i
\(75\) −3.88015e27 + 1.28656e27i −2.51455 + 0.833761i
\(76\) 1.29355e27i 0.691808i
\(77\) 2.64520e26 + 3.30055e27i 0.117042 + 1.46040i
\(78\) 4.18652e25 1.38815e25i 0.0153632 0.00509405i
\(79\) −2.93271e27 −0.894697 −0.447349 0.894360i \(-0.647632\pi\)
−0.447349 + 0.894360i \(0.647632\pi\)
\(80\) 9.32466e27 2.37044
\(81\) 1.34745e27 4.51328e27i 0.286076 0.958207i
\(82\) 6.13708e27i 1.09059i
\(83\) −5.11580e27 −0.762573 −0.381286 0.924457i \(-0.624519\pi\)
−0.381286 + 0.924457i \(0.624519\pi\)
\(84\) −2.97340e27 + 1.25762e27i −0.372566 + 0.157580i
\(85\) 2.09944e27 0.221579
\(86\) 1.50562e28i 1.34118i
\(87\) −2.38113e27 7.18127e27i −0.179371 0.540969i
\(88\) 1.61991e28 1.03393
\(89\) 2.50441e28 1.35691 0.678454 0.734643i \(-0.262650\pi\)
0.678454 + 0.734643i \(0.262650\pi\)
\(90\) −2.93555e28 3.94000e28i −1.35261 1.81543i
\(91\) −2.77939e25 3.46799e26i −0.00109106 0.0136137i
\(92\) 1.33637e28i 0.447715i
\(93\) 8.17641e27 + 2.46593e28i 0.234186 + 0.706283i
\(94\) 3.05909e28i 0.750306i
\(95\) 1.55287e29i 3.26695i
\(96\) 1.33186e28 + 4.01679e28i 0.240728 + 0.726015i
\(97\) 1.08394e29i 1.68584i −0.538042 0.842918i \(-0.680836\pi\)
0.538042 0.842918i \(-0.319164\pi\)
\(98\) 1.40820e28 + 8.72897e28i 0.188749 + 1.17000i
\(99\) −7.56629e28 1.01552e29i −0.875331 1.17484i
\(100\) −1.07165e29 −1.07165
\(101\) −6.79883e28 −0.588538 −0.294269 0.955723i \(-0.595076\pi\)
−0.294269 + 0.955723i \(0.595076\pi\)
\(102\) 5.76540e27 + 1.73879e28i 0.0432640 + 0.130480i
\(103\) 1.35130e29i 0.880261i −0.897934 0.440130i \(-0.854932\pi\)
0.897934 0.440130i \(-0.145068\pi\)
\(104\) −1.70209e27 −0.00963826
\(105\) −3.56948e29 + 1.50974e29i −1.75938 + 0.744145i
\(106\) 2.84328e29 1.22147
\(107\) 2.32027e29i 0.869908i 0.900453 + 0.434954i \(0.143235\pi\)
−0.900453 + 0.434954i \(0.856765\pi\)
\(108\) 7.07657e28 1.01187e29i 0.231835 0.331496i
\(109\) 1.37524e29 0.394180 0.197090 0.980385i \(-0.436851\pi\)
0.197090 + 0.980385i \(0.436851\pi\)
\(110\) −1.32104e30 −3.31683
\(111\) 2.20095e29 7.29779e28i 0.484648 0.160697i
\(112\) 6.39738e29 5.12713e28i 1.23692 0.0991318i
\(113\) 1.01708e29i 0.172869i −0.996258 0.0864344i \(-0.972453\pi\)
0.996258 0.0864344i \(-0.0275473\pi\)
\(114\) 1.28611e30 4.26443e29i 1.92380 0.637882i
\(115\) 1.60427e30i 2.11426i
\(116\) 1.98337e29i 0.230549i
\(117\) 7.95013e27 + 1.06704e28i 0.00815979 + 0.0109518i
\(118\) 2.62055e29i 0.237741i
\(119\) 1.44036e29 1.15437e28i 0.115622 0.00926645i
\(120\) 5.96743e29 + 1.79972e30i 0.424287 + 1.27961i
\(121\) −1.81864e30 −1.14646
\(122\) −2.31537e30 −1.29540
\(123\) −1.75740e30 + 5.82710e29i −0.873468 + 0.289620i
\(124\) 6.81058e29i 0.301002i
\(125\) −8.00864e30 −3.15039
\(126\) −2.23063e30 2.54171e30i −0.781727 0.890744i
\(127\) −3.24278e30 −1.01336 −0.506679 0.862135i \(-0.669127\pi\)
−0.506679 + 0.862135i \(0.669127\pi\)
\(128\) 4.16340e30i 1.16119i
\(129\) −4.31146e30 + 1.42957e30i −1.07417 + 0.356168i
\(130\) 1.38806e29 0.0309193
\(131\) 2.26554e30 0.451583 0.225791 0.974176i \(-0.427503\pi\)
0.225791 + 0.974176i \(0.427503\pi\)
\(132\) −1.04485e30 3.15119e30i −0.186523 0.562538i
\(133\) −8.53839e29 1.06538e31i −0.136624 1.70473i
\(134\) 5.89262e30i 0.845842i
\(135\) 8.49522e30 1.21472e31i 1.09480 1.56543i
\(136\) 7.06930e29i 0.0818582i
\(137\) 8.13564e30i 0.847117i 0.905869 + 0.423558i \(0.139219\pi\)
−0.905869 + 0.423558i \(0.860781\pi\)
\(138\) −1.32868e31 + 4.40558e30i −1.24502 + 0.412816i
\(139\) 8.04462e30i 0.678877i −0.940628 0.339438i \(-0.889763\pi\)
0.940628 0.339438i \(-0.110237\pi\)
\(140\) −1.01275e31 + 8.11664e29i −0.770278 + 0.0617334i
\(141\) 8.75995e30 2.90458e30i 0.600931 0.199253i
\(142\) 2.10320e31 1.30227
\(143\) 3.57768e29 0.0200092
\(144\) −1.96836e31 + 1.46655e31i −0.995060 + 0.741382i
\(145\) 2.38098e31i 1.08873i
\(146\) 2.19387e31 0.908017
\(147\) −2.36590e31 + 1.23206e31i −0.886943 + 0.461880i
\(148\) 6.07872e30 0.206546
\(149\) 2.94023e31i 0.906109i −0.891483 0.453054i \(-0.850334\pi\)
0.891483 0.453054i \(-0.149666\pi\)
\(150\) −3.53288e31 1.06549e32i −0.988111 2.98006i
\(151\) 1.57029e31 0.398855 0.199428 0.979913i \(-0.436092\pi\)
0.199428 + 0.979913i \(0.436092\pi\)
\(152\) −5.22887e31 −1.20691
\(153\) −4.43175e30 + 3.30193e30i −0.0930143 + 0.0693015i
\(154\) −9.06328e31 + 7.26370e30i −1.73075 + 0.138710i
\(155\) 8.17591e31i 1.42143i
\(156\) 1.09786e29 + 3.31105e29i 0.00173876 + 0.00524395i
\(157\) 2.67475e31i 0.386134i −0.981186 0.193067i \(-0.938157\pi\)
0.981186 0.193067i \(-0.0618435\pi\)
\(158\) 8.05319e31i 1.06033i
\(159\) 2.69966e31 + 8.14195e31i 0.324378 + 0.978295i
\(160\) 1.33178e32i 1.46114i
\(161\) 8.82101e30 + 1.10064e32i 0.0884185 + 1.10324i
\(162\) 1.23934e32 + 3.70009e31i 1.13559 + 0.339035i
\(163\) 1.09229e32 0.915412 0.457706 0.889104i \(-0.348671\pi\)
0.457706 + 0.889104i \(0.348671\pi\)
\(164\) −4.85371e31 −0.372253
\(165\) −1.25432e32 3.78291e32i −0.880825 2.65649i
\(166\) 1.40479e32i 0.903744i
\(167\) −1.79477e32 −1.05832 −0.529162 0.848521i \(-0.677494\pi\)
−0.529162 + 0.848521i \(0.677494\pi\)
\(168\) 5.08365e31 + 1.20193e32i 0.274910 + 0.649970i
\(169\) 2.01501e32 0.999813
\(170\) 5.76504e31i 0.262599i
\(171\) 2.44230e32 + 3.27798e32i 1.02178 + 1.37140i
\(172\) −1.19077e32 −0.457788
\(173\) −1.76120e31 −0.0622502 −0.0311251 0.999515i \(-0.509909\pi\)
−0.0311251 + 0.999515i \(0.509909\pi\)
\(174\) 1.97197e32 6.53855e31i 0.641115 0.212578i
\(175\) −8.82616e32 + 7.07366e31i −2.64071 + 0.211637i
\(176\) 6.59973e32i 1.81799i
\(177\) 7.50416e31 2.48819e31i 0.190410 0.0631352i
\(178\) 6.87709e32i 1.60810i
\(179\) 1.46675e32i 0.316219i −0.987422 0.158110i \(-0.949460\pi\)
0.987422 0.158110i \(-0.0505400\pi\)
\(180\) 3.11607e32 2.32167e32i 0.619664 0.461689i
\(181\) 3.40067e31i 0.0624058i −0.999513 0.0312029i \(-0.990066\pi\)
0.999513 0.0312029i \(-0.00993380\pi\)
\(182\) 9.52307e30 7.63219e29i 0.0161340 0.00129305i
\(183\) −2.19842e32 6.63025e32i −0.344009 1.03750i
\(184\) 5.40195e32 0.781073
\(185\) 7.29733e32 0.975380
\(186\) −6.77143e32 + 2.24524e32i −0.837034 + 0.277539i
\(187\) 1.48592e32i 0.169939i
\(188\) 2.41938e32 0.256103
\(189\) 5.16042e32 8.80091e32i 0.505812 0.862644i
\(190\) 4.26416e33 3.87174
\(191\) 2.40802e32i 0.202617i 0.994855 + 0.101308i \(0.0323029\pi\)
−0.994855 + 0.101308i \(0.967697\pi\)
\(192\) 4.06897e32 1.34917e32i 0.317407 0.105244i
\(193\) −1.66406e33 −1.20389 −0.601947 0.798536i \(-0.705608\pi\)
−0.601947 + 0.798536i \(0.705608\pi\)
\(194\) 2.97649e33 1.99793
\(195\) 1.31795e31 + 3.97482e31i 0.00821101 + 0.0247637i
\(196\) −6.90358e32 + 1.11372e32i −0.399357 + 0.0644262i
\(197\) 2.90596e33i 1.56146i 0.624870 + 0.780728i \(0.285152\pi\)
−0.624870 + 0.780728i \(0.714848\pi\)
\(198\) 2.78862e33 2.07769e33i 1.39233 1.03738i
\(199\) 1.38700e33i 0.643732i −0.946785 0.321866i \(-0.895690\pi\)
0.946785 0.321866i \(-0.104310\pi\)
\(200\) 4.33188e33i 1.86957i
\(201\) −1.68740e33 + 5.59499e32i −0.677447 + 0.224624i
\(202\) 1.86695e33i 0.697490i
\(203\) −1.30917e32 1.63352e33i −0.0455307 0.568109i
\(204\) −1.37518e32 + 4.55975e31i −0.0445371 + 0.0147674i
\(205\) −5.82674e33 −1.75790
\(206\) 3.71065e33 1.04322
\(207\) −2.52314e33 3.38649e33i −0.661260 0.887522i
\(208\) 6.93453e31i 0.0169472i
\(209\) 1.09908e34 2.50557
\(210\) −4.14573e33 9.80175e33i −0.881905 2.08509i
\(211\) 3.16343e33 0.628148 0.314074 0.949398i \(-0.398306\pi\)
0.314074 + 0.949398i \(0.398306\pi\)
\(212\) 2.24870e33i 0.416928i
\(213\) 1.99697e33 + 6.02268e33i 0.345833 + 1.04300i
\(214\) −6.37143e33 −1.03095
\(215\) −1.42948e34 −2.16183
\(216\) −4.09023e33 2.86054e33i −0.578320 0.404454i
\(217\) 4.49549e32 + 5.60925e33i 0.0594444 + 0.741718i
\(218\) 3.77640e33i 0.467153i
\(219\) 2.08306e33 + 6.28231e33i 0.241135 + 0.727243i
\(220\) 1.04479e34i 1.13214i
\(221\) 1.56130e31i 0.00158416i
\(222\) 2.00396e33 + 6.04378e33i 0.190446 + 0.574369i
\(223\) 1.87524e34i 1.66969i 0.550486 + 0.834845i \(0.314443\pi\)
−0.550486 + 0.834845i \(0.685557\pi\)
\(224\) 7.32275e32 + 9.13696e33i 0.0611052 + 0.762440i
\(225\) 2.71566e34 2.02334e34i 2.12436 1.58278i
\(226\) 2.79288e33 0.204871
\(227\) −1.65372e34 −1.13786 −0.568929 0.822387i \(-0.692642\pi\)
−0.568929 + 0.822387i \(0.692642\pi\)
\(228\) 3.37266e33 + 1.01716e34i 0.217729 + 0.656653i
\(229\) 9.33470e33i 0.565569i 0.959183 + 0.282785i \(0.0912582\pi\)
−0.959183 + 0.282785i \(0.908742\pi\)
\(230\) −4.40531e34 −2.50566
\(231\) −1.06855e34 2.52637e34i −0.570718 1.34935i
\(232\) −8.01731e33 −0.402210
\(233\) 1.40299e34i 0.661291i 0.943755 + 0.330645i \(0.107266\pi\)
−0.943755 + 0.330645i \(0.892734\pi\)
\(234\) −2.93008e32 + 2.18310e32i −0.0129793 + 0.00967037i
\(235\) 2.90440e34 1.20941
\(236\) 2.07255e33 0.0811485
\(237\) 2.30609e34 7.64642e33i 0.849231 0.281584i
\(238\) 3.16988e32 + 3.95522e33i 0.0109819 + 0.137027i
\(239\) 1.47077e34i 0.479484i 0.970837 + 0.239742i \(0.0770628\pi\)
−0.970837 + 0.239742i \(0.922937\pi\)
\(240\) −7.33232e34 + 2.43121e34i −2.24998 + 0.746036i
\(241\) 2.73665e33i 0.0790629i 0.999218 + 0.0395315i \(0.0125865\pi\)
−0.999218 + 0.0395315i \(0.987413\pi\)
\(242\) 4.99396e34i 1.35870i
\(243\) 1.17192e33 + 3.90027e34i 0.0300335 + 0.999549i
\(244\) 1.83118e34i 0.442160i
\(245\) −8.28755e34 + 1.33699e34i −1.88590 + 0.304242i
\(246\) −1.60012e34 4.82581e34i −0.343236 1.03517i
\(247\) −1.15483e33 −0.0233568
\(248\) 2.75302e34 0.525121
\(249\) 4.02274e34 1.33384e34i 0.723821 0.240001i
\(250\) 2.19917e35i 3.73360i
\(251\) 2.11420e34 0.338748 0.169374 0.985552i \(-0.445825\pi\)
0.169374 + 0.985552i \(0.445825\pi\)
\(252\) 2.01019e34 1.76417e34i 0.304039 0.266828i
\(253\) −1.13546e35 −1.62152
\(254\) 8.90463e34i 1.20096i
\(255\) −1.65086e34 + 5.47384e33i −0.210319 + 0.0697365i
\(256\) 8.65457e34 1.04176
\(257\) −7.36616e34 −0.837936 −0.418968 0.908001i \(-0.637608\pi\)
−0.418968 + 0.908001i \(0.637608\pi\)
\(258\) −3.92559e34 1.18392e35i −0.422103 1.27303i
\(259\) 5.00649e34 4.01241e33i 0.508963 0.0407905i
\(260\) 1.09779e33i 0.0105537i
\(261\) 3.74473e34 + 5.02606e34i 0.340513 + 0.457026i
\(262\) 6.22114e34i 0.535182i
\(263\) 2.37182e35i 1.93074i 0.260883 + 0.965370i \(0.415986\pi\)
−0.260883 + 0.965370i \(0.584014\pi\)
\(264\) −1.27379e35 + 4.22358e34i −0.981391 + 0.325404i
\(265\) 2.69950e35i 1.96887i
\(266\) 2.92552e35 2.34463e34i 2.02031 0.161916i
\(267\) −1.96931e35 + 6.52972e34i −1.28795 + 0.427053i
\(268\) −4.66037e34 −0.288713
\(269\) 8.81222e34 0.517223 0.258611 0.965981i \(-0.416735\pi\)
0.258611 + 0.965981i \(0.416735\pi\)
\(270\) 3.33560e35 + 2.33278e35i 1.85524 + 1.29748i
\(271\) 1.51177e35i 0.796951i −0.917179 0.398476i \(-0.869539\pi\)
0.917179 0.398476i \(-0.130461\pi\)
\(272\) 2.88013e34 0.143934
\(273\) 1.12276e33 + 2.65454e33i 0.00532020 + 0.0125785i
\(274\) −2.23404e35 −1.00394
\(275\) 9.10533e35i 3.88125i
\(276\) −3.48429e34 1.05083e35i −0.140907 0.424964i
\(277\) 1.02040e35 0.391574 0.195787 0.980646i \(-0.437274\pi\)
0.195787 + 0.980646i \(0.437274\pi\)
\(278\) 2.20904e35 0.804554
\(279\) −1.28588e35 1.72587e35i −0.444570 0.596688i
\(280\) 3.28096e34 + 4.09382e35i 0.107699 + 1.34381i
\(281\) 2.27657e35i 0.709641i 0.934934 + 0.354821i \(0.115458\pi\)
−0.934934 + 0.354821i \(0.884542\pi\)
\(282\) 7.97594e34 + 2.40547e35i 0.236140 + 0.712178i
\(283\) 1.56973e35i 0.441490i 0.975332 + 0.220745i \(0.0708488\pi\)
−0.975332 + 0.220745i \(0.929151\pi\)
\(284\) 1.66338e35i 0.444505i
\(285\) 4.04878e35 + 1.22108e36i 1.02819 + 3.10093i
\(286\) 9.82428e33i 0.0237134i
\(287\) −3.99755e35 + 3.20381e34i −0.917290 + 0.0735155i
\(288\) −2.09459e35 2.81129e35i −0.456990 0.613358i
\(289\) −4.75484e35 −0.986546
\(290\) 6.53815e35 1.29028
\(291\) 2.82615e35 + 8.52342e35i 0.530575 + 1.60017i
\(292\) 1.73509e35i 0.309935i
\(293\) 3.63411e35 0.617758 0.308879 0.951101i \(-0.400046\pi\)
0.308879 + 0.951101i \(0.400046\pi\)
\(294\) −3.38321e35 6.49675e35i −0.547385 1.05114i
\(295\) 2.48804e35 0.383210
\(296\) 2.45718e35i 0.360336i
\(297\) 8.59741e35 + 6.01267e35i 1.20060 + 0.839652i
\(298\) 8.07384e35 1.07385
\(299\) 1.19306e34 0.0151157
\(300\) 8.42673e35 2.79409e35i 1.01719 0.337274i
\(301\) −9.80726e35 + 7.85995e34i −1.12806 + 0.0904077i
\(302\) 4.31201e35i 0.472693i
\(303\) 5.34616e35 1.77265e35i 0.558630 0.185227i
\(304\) 2.13031e36i 2.12215i
\(305\) 2.19829e36i 2.08803i
\(306\) −9.06708e34 1.21695e35i −0.0821309 0.110234i
\(307\) 1.68415e36i 1.45503i 0.686090 + 0.727517i \(0.259326\pi\)
−0.686090 + 0.727517i \(0.740674\pi\)
\(308\) −5.74473e34 7.16799e35i −0.0473461 0.590761i
\(309\) 3.52323e35 + 1.06257e36i 0.277040 + 0.835528i
\(310\) −2.24510e36 −1.68457
\(311\) −2.55264e36 −1.82795 −0.913974 0.405773i \(-0.867002\pi\)
−0.913974 + 0.405773i \(0.867002\pi\)
\(312\) 1.33841e34 4.43784e33i 0.00914847 0.00303340i
\(313\) 1.65771e36i 1.08172i −0.841112 0.540862i \(-0.818098\pi\)
0.841112 0.540862i \(-0.181902\pi\)
\(314\) 7.34484e35 0.457617
\(315\) 2.41318e36 2.11783e36i 1.43577 1.26005i
\(316\) 6.36912e35 0.361923
\(317\) 1.10890e36i 0.601910i 0.953638 + 0.300955i \(0.0973054\pi\)
−0.953638 + 0.300955i \(0.902695\pi\)
\(318\) −2.23577e36 + 7.41325e35i −1.15940 + 0.384428i
\(319\) 1.68519e36 0.834994
\(320\) 1.34908e36 0.638798
\(321\) −6.04961e35 1.82451e36i −0.273782 0.825701i
\(322\) −3.02235e36 + 2.42224e35i −1.30748 + 0.104787i
\(323\) 4.79637e35i 0.198370i
\(324\) −2.92634e35 + 9.80173e35i −0.115724 + 0.387615i
\(325\) 9.56725e34i 0.0361808i
\(326\) 2.99941e36i 1.08488i
\(327\) −1.08140e36 + 3.58565e35i −0.374149 + 0.124058i
\(328\) 1.96200e36i 0.649423i
\(329\) 1.99262e36 1.59697e35i 0.631080 0.0505774i
\(330\) 1.03878e37 3.44434e36i 3.14827 1.04389i
\(331\) −4.19132e34 −0.0121575 −0.00607876 0.999982i \(-0.501935\pi\)
−0.00607876 + 0.999982i \(0.501935\pi\)
\(332\) 1.11103e36 0.308476
\(333\) −1.54041e36 + 1.14770e36i −0.409444 + 0.305062i
\(334\) 4.92841e36i 1.25425i
\(335\) −5.59464e36 −1.36340
\(336\) −4.89681e36 + 2.07115e36i −1.14286 + 0.483383i
\(337\) 2.76289e36 0.617631 0.308816 0.951122i \(-0.400067\pi\)
0.308816 + 0.951122i \(0.400067\pi\)
\(338\) 5.53319e36i 1.18490i
\(339\) 2.65181e35 + 7.99764e35i 0.0544061 + 0.164084i
\(340\) −4.55946e35 −0.0896333
\(341\) −5.78667e36 −1.09016
\(342\) −9.00131e36 + 6.70654e36i −1.62528 + 1.21093i
\(343\) −5.61234e36 + 1.37296e36i −0.971357 + 0.237625i
\(344\) 4.81340e36i 0.798646i
\(345\) −4.18279e36 1.26149e37i −0.665410 2.00682i
\(346\) 4.83625e35i 0.0737743i
\(347\) 6.10380e36i 0.892941i 0.894798 + 0.446471i \(0.147319\pi\)
−0.894798 + 0.446471i \(0.852681\pi\)
\(348\) 5.17122e35 + 1.55960e36i 0.0725595 + 0.218833i
\(349\) 7.10404e36i 0.956174i −0.878312 0.478087i \(-0.841330\pi\)
0.878312 0.478087i \(-0.158670\pi\)
\(350\) −1.94242e36 2.42366e37i −0.250817 3.12957i
\(351\) −9.03355e34 6.31770e34i −0.0111919 0.00782719i
\(352\) −9.42597e36 −1.12062
\(353\) 1.68355e36 0.192085 0.0960423 0.995377i \(-0.469382\pi\)
0.0960423 + 0.995377i \(0.469382\pi\)
\(354\) 6.83255e35 + 2.06064e36i 0.0748230 + 0.225660i
\(355\) 1.99684e37i 2.09910i
\(356\) −5.43896e36 −0.548897
\(357\) −1.10251e36 + 4.66317e35i −0.106830 + 0.0451847i
\(358\) 4.02769e36 0.374759
\(359\) 3.39910e36i 0.303734i −0.988401 0.151867i \(-0.951471\pi\)
0.988401 0.151867i \(-0.0485286\pi\)
\(360\) −9.38481e36 1.25960e37i −0.805451 1.08105i
\(361\) −2.33470e37 −1.92476
\(362\) 9.33820e35 0.0739586
\(363\) 1.43006e37 4.74172e36i 1.08820 0.360819i
\(364\) 6.03616e33 + 7.53162e34i 0.000441357 + 0.00550704i
\(365\) 2.08293e37i 1.46362i
\(366\) 1.82066e37 6.03684e36i 1.22957 0.407694i
\(367\) 1.85685e37i 1.20536i −0.797981 0.602682i \(-0.794099\pi\)
0.797981 0.602682i \(-0.205901\pi\)
\(368\) 2.20083e37i 1.37338i
\(369\) 1.22998e37 9.16412e36i 0.737930 0.549804i
\(370\) 2.00384e37i 1.15595i
\(371\) 1.48431e36 + 1.85204e37i 0.0823383 + 1.02738i
\(372\) −1.77572e36 5.35540e36i −0.0947329 0.285706i
\(373\) −8.33812e34 −0.00427848 −0.00213924 0.999998i \(-0.500681\pi\)
−0.00213924 + 0.999998i \(0.500681\pi\)
\(374\) −4.08033e36 −0.201399
\(375\) 6.29748e37 2.08809e37i 2.99029 0.991505i
\(376\) 9.77978e36i 0.446792i
\(377\) −1.77068e35 −0.00778377
\(378\) 2.41672e37 + 1.41705e37i 1.02234 + 0.599450i
\(379\) 1.91804e36 0.0780888 0.0390444 0.999237i \(-0.487569\pi\)
0.0390444 + 0.999237i \(0.487569\pi\)
\(380\) 3.37245e37i 1.32155i
\(381\) 2.54991e37 8.45486e36i 0.961863 0.318929i
\(382\) −6.61239e36 −0.240126
\(383\) −3.60082e36 −0.125898 −0.0629490 0.998017i \(-0.520051\pi\)
−0.0629490 + 0.998017i \(0.520051\pi\)
\(384\) 1.08552e37 + 3.27383e37i 0.365456 + 1.10218i
\(385\) −6.89638e36 8.60496e37i −0.223584 2.78977i
\(386\) 4.56949e37i 1.42676i
\(387\) 3.01752e37 2.24825e37i 0.907490 0.676137i
\(388\) 2.35405e37i 0.681956i
\(389\) 2.94788e37i 0.822699i −0.911478 0.411350i \(-0.865058\pi\)
0.911478 0.411350i \(-0.134942\pi\)
\(390\) −1.09148e36 + 3.61907e35i −0.0293480 + 0.00973107i
\(391\) 4.95513e36i 0.128379i
\(392\) 4.50195e36 + 2.79061e37i 0.112396 + 0.696709i
\(393\) −1.78147e37 + 5.90691e36i −0.428634 + 0.142124i
\(394\) −7.97975e37 −1.85052
\(395\) 7.64595e37 1.70912
\(396\) 1.64321e37 + 2.20547e37i 0.354090 + 0.475248i
\(397\) 2.63789e37i 0.548018i 0.961727 + 0.274009i \(0.0883499\pi\)
−0.961727 + 0.274009i \(0.911650\pi\)
\(398\) 3.80868e37 0.762903
\(399\) 3.44915e37 + 8.15483e37i 0.666201 + 1.57510i
\(400\) −1.76486e38 −3.28732
\(401\) 3.97992e37i 0.714958i −0.933921 0.357479i \(-0.883636\pi\)
0.933921 0.357479i \(-0.116364\pi\)
\(402\) −1.53638e37 4.63358e37i −0.266208 0.802859i
\(403\) 6.08023e35 0.0101624
\(404\) 1.47654e37 0.238076
\(405\) −3.51298e37 + 1.17667e38i −0.546485 + 1.83044i
\(406\) 4.48563e37 3.59497e36i 0.673280 0.0539595i
\(407\) 5.16484e37i 0.748063i
\(408\) 1.84317e36 + 5.55884e36i 0.0257628 + 0.0776984i
\(409\) 4.93049e37i 0.665124i 0.943081 + 0.332562i \(0.107913\pi\)
−0.943081 + 0.332562i \(0.892087\pi\)
\(410\) 1.60002e38i 2.08333i
\(411\) −2.12120e37 6.39734e37i −0.266609 0.804069i
\(412\) 2.93469e37i 0.356084i
\(413\) 1.70697e37 1.36804e36i 0.199963 0.0160259i
\(414\) 9.29926e37 6.92853e37i 1.05182 0.783675i
\(415\) 1.33375e38 1.45673
\(416\) 9.90415e35 0.0104463
\(417\) 2.09747e37 + 6.32577e37i 0.213659 + 0.644378i
\(418\) 3.01805e38i 2.96941i
\(419\) 6.58531e37 0.625854 0.312927 0.949777i \(-0.398691\pi\)
0.312927 + 0.949777i \(0.398691\pi\)
\(420\) 7.75203e37 3.27879e37i 0.711706 0.301022i
\(421\) −2.19764e38 −1.94924 −0.974622 0.223856i \(-0.928135\pi\)
−0.974622 + 0.223856i \(0.928135\pi\)
\(422\) 8.68674e37i 0.744434i
\(423\) −6.13095e37 + 4.56795e37i −0.507683 + 0.378256i
\(424\) 9.08983e37 0.727362
\(425\) −3.97357e37 −0.307285
\(426\) −1.65382e38 + 5.48366e37i −1.23609 + 0.409856i
\(427\) −1.20872e37 1.50818e38i −0.0873215 1.08955i
\(428\) 5.03905e37i 0.351896i
\(429\) −2.81326e36 + 9.32806e35i −0.0189924 + 0.00629739i
\(430\) 3.92534e38i 2.56203i
\(431\) 1.17334e38i 0.740464i 0.928939 + 0.370232i \(0.120722\pi\)
−0.928939 + 0.370232i \(0.879278\pi\)
\(432\) 1.16542e38 1.66641e38i 0.711163 1.01688i
\(433\) 2.48867e38i 1.46856i 0.678844 + 0.734282i \(0.262481\pi\)
−0.678844 + 0.734282i \(0.737519\pi\)
\(434\) −1.54029e38 + 1.23446e37i −0.879028 + 0.0704490i
\(435\) 6.20790e37 + 1.87225e38i 0.342650 + 1.03340i
\(436\) −2.98669e37 −0.159454
\(437\) 3.66511e38 1.89281
\(438\) −1.72512e38 + 5.72005e37i −0.861874 + 0.285776i
\(439\) 1.35398e38i 0.654451i −0.944946 0.327225i \(-0.893886\pi\)
0.944946 0.327225i \(-0.106114\pi\)
\(440\) −4.22331e38 −1.97510
\(441\) 1.53916e38 1.58567e38i 0.696506 0.717551i
\(442\) 4.28732e35 0.00187743
\(443\) 3.89269e38i 1.64967i −0.565376 0.824833i \(-0.691269\pi\)
0.565376 0.824833i \(-0.308731\pi\)
\(444\) −4.77992e37 + 1.58490e37i −0.196050 + 0.0650053i
\(445\) −6.52932e38 −2.59208
\(446\) −5.14938e38 −1.97879
\(447\) 7.66603e37 + 2.31201e38i 0.285175 + 0.860063i
\(448\) 9.25566e37 7.41787e36i 0.333331 0.0267146i
\(449\) 3.93055e38i 1.37051i −0.728304 0.685254i \(-0.759691\pi\)
0.728304 0.685254i \(-0.240309\pi\)
\(450\) 5.55606e38 + 7.45717e38i 1.87580 + 2.51764i
\(451\) 4.12400e38i 1.34821i
\(452\) 2.20884e37i 0.0699290i
\(453\) −1.23478e38 + 4.09421e37i −0.378586 + 0.125530i
\(454\) 4.54111e38i 1.34850i
\(455\) 7.24623e35 + 9.04149e36i 0.00208424 + 0.0260061i
\(456\) 4.11165e38 1.36332e38i 1.14558 0.379846i
\(457\) −4.02004e38 −1.08504 −0.542520 0.840043i \(-0.682530\pi\)
−0.542520 + 0.840043i \(0.682530\pi\)
\(458\) −2.56330e38 −0.670270
\(459\) 2.62394e37 3.75191e37i 0.0664767 0.0950537i
\(460\) 3.48408e38i 0.855262i
\(461\) −1.92578e38 −0.458081 −0.229040 0.973417i \(-0.573559\pi\)
−0.229040 + 0.973417i \(0.573559\pi\)
\(462\) 6.93740e38 2.93423e38i 1.59915 0.676372i
\(463\) 7.75241e38 1.73186 0.865929 0.500166i \(-0.166728\pi\)
0.865929 + 0.500166i \(0.166728\pi\)
\(464\) 3.26636e38i 0.707218i
\(465\) −2.13170e38 6.42901e38i −0.447360 1.34920i
\(466\) −3.85258e38 −0.783712
\(467\) −4.16159e37 −0.0820663 −0.0410331 0.999158i \(-0.513065\pi\)
−0.0410331 + 0.999158i \(0.513065\pi\)
\(468\) −1.72657e36 2.31735e36i −0.00330080 0.00443024i
\(469\) −3.83832e38 + 3.07619e37i −0.711434 + 0.0570174i
\(470\) 7.97544e38i 1.43330i
\(471\) 6.97385e37 + 2.10325e38i 0.121526 + 0.366512i
\(472\) 8.37780e37i 0.141570i
\(473\) 1.01175e39i 1.65800i
\(474\) 2.09970e38 + 6.33251e38i 0.333712 + 1.00644i
\(475\) 2.93909e39i 4.53060i
\(476\) −3.12811e37 + 2.50700e36i −0.0467716 + 0.00374847i
\(477\) −4.24568e38 5.69843e38i −0.615788 0.826491i
\(478\) −4.03871e38 −0.568248
\(479\) 1.11054e39 1.51589 0.757946 0.652317i \(-0.226203\pi\)
0.757946 + 0.652317i \(0.226203\pi\)
\(480\) −3.47234e38 1.04723e39i −0.459859 1.38689i
\(481\) 5.42686e36i 0.00697340i
\(482\) −7.51483e37 −0.0936994
\(483\) −3.56332e38 8.42475e38i −0.431143 1.01935i
\(484\) 3.94964e38 0.463766
\(485\) 2.82597e39i 3.22042i
\(486\) −1.07101e39 + 3.21807e37i −1.18459 + 0.0355935i
\(487\) −9.46464e38 −1.01610 −0.508048 0.861329i \(-0.669633\pi\)
−0.508048 + 0.861329i \(0.669633\pi\)
\(488\) −7.40214e38 −0.771383
\(489\) −8.58905e38 + 2.84791e38i −0.868893 + 0.288103i
\(490\) −3.67135e38 2.27575e39i −0.360565 2.23502i
\(491\) 2.79679e38i 0.266673i −0.991071 0.133336i \(-0.957431\pi\)
0.991071 0.133336i \(-0.0425691\pi\)
\(492\) 3.81664e38 1.26550e38i 0.353336 0.117157i
\(493\) 7.35417e37i 0.0661079i
\(494\) 3.17116e37i 0.0276807i
\(495\) 1.97263e39 + 2.64760e39i 1.67213 + 2.24428i
\(496\) 1.12162e39i 0.923337i
\(497\) 1.09796e38 + 1.36998e39i 0.0877845 + 1.09533i
\(498\) 3.66270e38 + 1.10464e39i 0.284431 + 0.857818i
\(499\) 2.38891e39 1.80195 0.900975 0.433872i \(-0.142853\pi\)
0.900975 + 0.433872i \(0.142853\pi\)
\(500\) 1.73928e39 1.27440
\(501\) 1.41129e39 4.67947e38i 1.00454 0.333081i
\(502\) 5.80556e38i 0.401458i
\(503\) 2.00686e39 1.34828 0.674142 0.738602i \(-0.264514\pi\)
0.674142 + 0.738602i \(0.264514\pi\)
\(504\) −7.13123e38 8.12573e38i −0.465502 0.530419i
\(505\) 1.77254e39 1.12427
\(506\) 3.11795e39i 1.92170i
\(507\) −1.58447e39 + 5.25370e38i −0.949006 + 0.314666i
\(508\) 7.04251e38 0.409924
\(509\) 2.23697e39 1.26547 0.632737 0.774367i \(-0.281932\pi\)
0.632737 + 0.774367i \(0.281932\pi\)
\(510\) −1.50311e38 4.53326e38i −0.0826464 0.249254i
\(511\) 1.14529e38 + 1.42903e39i 0.0612085 + 0.763730i
\(512\) 1.41328e38i 0.0734198i
\(513\) −2.77514e39 1.94082e39i −1.40147 0.980128i
\(514\) 2.02274e39i 0.993059i
\(515\) 3.52301e39i 1.68155i
\(516\) 9.36343e38 3.10467e38i 0.434524 0.144077i
\(517\) 2.05565e39i 0.927547i
\(518\) 1.10180e38 + 1.37478e39i 0.0483418 + 0.603185i
\(519\) 1.38490e38 4.59197e37i 0.0590869 0.0195917i
\(520\) 4.43756e37 0.0184118
\(521\) 2.75049e39 1.10985 0.554923 0.831901i \(-0.312748\pi\)
0.554923 + 0.831901i \(0.312748\pi\)
\(522\) −1.38015e39 + 1.02830e39i −0.541632 + 0.403550i
\(523\) 2.90751e39i 1.10980i −0.831916 0.554902i \(-0.812756\pi\)
0.831916 0.554902i \(-0.187244\pi\)
\(524\) −4.92019e38 −0.182674
\(525\) 6.75590e39 2.85746e39i 2.43991 1.03198i
\(526\) −6.51300e39 −2.28817
\(527\) 2.52531e38i 0.0863098i
\(528\) −1.72074e39 5.18960e39i −0.572168 1.72561i
\(529\) −6.95367e38 −0.224961
\(530\) −7.41279e39 −2.33336
\(531\) −5.25205e38 + 3.91311e38i −0.160864 + 0.119854i
\(532\) 1.85433e38 + 2.31374e39i 0.0552672 + 0.689597i
\(533\) 4.33321e37i 0.0125680i
\(534\) −1.79306e39 5.40770e39i −0.506111 1.52639i
\(535\) 6.04923e39i 1.66177i
\(536\) 1.88385e39i 0.503681i
\(537\) 3.82426e38 + 1.15336e39i 0.0995221 + 0.300150i
\(538\) 2.41983e39i 0.612973i
\(539\) −9.46281e38 5.86569e39i −0.233337 1.44638i
\(540\) −1.84495e39 + 2.63806e39i −0.442870 + 0.633251i
\(541\) 5.32128e39 1.24353 0.621764 0.783205i \(-0.286416\pi\)
0.621764 + 0.783205i \(0.286416\pi\)
\(542\) 4.15131e39 0.944487
\(543\) 8.86652e37 + 2.67407e38i 0.0196406 + 0.0592345i
\(544\) 4.11350e38i 0.0887212i
\(545\) −3.58543e39 −0.752995
\(546\) −7.28933e37 + 3.08309e37i −0.0149071 + 0.00630510i
\(547\) −4.81769e39 −0.959451 −0.479726 0.877419i \(-0.659264\pi\)
−0.479726 + 0.877419i \(0.659264\pi\)
\(548\) 1.76686e39i 0.342676i
\(549\) 3.45740e39 + 4.64041e39i 0.653056 + 0.876511i
\(550\) 2.50032e40 4.59977
\(551\) −5.43958e39 −0.974692
\(552\) −4.24774e39 + 1.40844e39i −0.741382 + 0.245823i
\(553\) 5.24566e39 4.20409e38i 0.891838 0.0714756i
\(554\) 2.80201e39i 0.464064i
\(555\) −5.73815e39 + 1.90263e39i −0.925814 + 0.306977i
\(556\) 1.74709e39i 0.274620i
\(557\) 9.50433e39i 1.45553i 0.685827 + 0.727765i \(0.259441\pi\)
−0.685827 + 0.727765i \(0.740559\pi\)
\(558\) 4.73922e39 3.53102e39i 0.707150 0.526871i
\(559\) 1.06307e38i 0.0154558i
\(560\) −1.66788e40 + 1.33671e39i −2.36286 + 0.189370i
\(561\) −3.87423e38 1.16843e39i −0.0534840 0.161303i
\(562\) −6.25143e39 −0.841013
\(563\) 3.75617e39 0.492463 0.246231 0.969211i \(-0.420808\pi\)
0.246231 + 0.969211i \(0.420808\pi\)
\(564\) −1.90245e39 + 6.30802e38i −0.243089 + 0.0806021i
\(565\) 2.65165e39i 0.330228i
\(566\) −4.31045e39 −0.523220
\(567\) −1.76317e39 + 8.26595e39i −0.208612 + 0.977998i
\(568\) 6.72384e39 0.775473
\(569\) 2.36168e39i 0.265518i 0.991148 + 0.132759i \(0.0423836\pi\)
−0.991148 + 0.132759i \(0.957616\pi\)
\(570\) −3.35306e40 + 1.11179e40i −3.67499 + 1.21853i
\(571\) −3.21874e39 −0.343924 −0.171962 0.985104i \(-0.555011\pi\)
−0.171962 + 0.985104i \(0.555011\pi\)
\(572\) −7.76984e37 −0.00809412
\(573\) −6.27839e38 1.89351e39i −0.0637686 0.192320i
\(574\) −8.79763e38 1.09772e40i −0.0871251 1.08710i
\(575\) 3.03637e40i 2.93205i
\(576\) −2.84781e39 + 2.12179e39i −0.268154 + 0.199792i
\(577\) 6.93567e39i 0.636853i 0.947948 + 0.318426i \(0.103154\pi\)
−0.947948 + 0.318426i \(0.896846\pi\)
\(578\) 1.30567e40i 1.16918i
\(579\) 1.30851e40 4.33869e39i 1.14271 0.378895i
\(580\) 5.17090e39i 0.440413i
\(581\) 9.15050e39 7.33360e38i 0.760135 0.0609205i
\(582\) −2.34052e40 + 7.76058e39i −1.89640 + 0.628797i
\(583\) −1.91063e40 −1.51002
\(584\) 7.01370e39 0.540705
\(585\) −2.07270e38 2.78191e38i −0.0155875 0.0209210i
\(586\) 9.97924e39i 0.732120i
\(587\) 1.82904e40 1.30909 0.654547 0.756022i \(-0.272860\pi\)
0.654547 + 0.756022i \(0.272860\pi\)
\(588\) 5.13816e39 2.67572e39i 0.358787 0.186840i
\(589\) 1.86787e40 1.27255
\(590\) 6.83212e39i 0.454152i
\(591\) −7.57669e39 2.28506e40i −0.491429 1.48211i
\(592\) 1.00109e40 0.633589
\(593\) −2.48997e40 −1.53781 −0.768903 0.639366i \(-0.779197\pi\)
−0.768903 + 0.639366i \(0.779197\pi\)
\(594\) −1.65107e40 + 2.36084e40i −0.995092 + 1.42286i
\(595\) −3.75521e39 + 3.00958e38i −0.220871 + 0.0177015i
\(596\) 6.38545e39i 0.366540i
\(597\) 3.61630e39 + 1.09064e40i 0.202599 + 0.611020i
\(598\) 3.27612e38i 0.0179140i
\(599\) 3.33529e39i 0.178010i −0.996031 0.0890051i \(-0.971631\pi\)
0.996031 0.0890051i \(-0.0283688\pi\)
\(600\) −1.12945e40 3.40631e40i −0.588400 1.77456i
\(601\) 2.82826e40i 1.43827i −0.694873 0.719133i \(-0.744539\pi\)
0.694873 0.719133i \(-0.255461\pi\)
\(602\) −2.15833e39 2.69306e40i −0.107144 1.33690i
\(603\) 1.18099e40 8.79908e39i 0.572326 0.426419i
\(604\) −3.41029e39 −0.161345
\(605\) 4.74142e40 2.19006
\(606\) 4.86769e39 + 1.46805e40i 0.219518 + 0.662046i
\(607\) 1.30309e40i 0.573771i 0.957965 + 0.286885i \(0.0926199\pi\)
−0.957965 + 0.286885i \(0.907380\pi\)
\(608\) 3.04259e40 1.30810
\(609\) 5.28851e39 + 1.25036e40i 0.222015 + 0.524910i
\(610\) 6.03647e40 2.47457
\(611\) 2.15993e38i 0.00864654i
\(612\) 9.62467e38 7.17098e38i 0.0376262 0.0280339i
\(613\) −1.11135e40 −0.424302 −0.212151 0.977237i \(-0.568047\pi\)
−0.212151 + 0.977237i \(0.568047\pi\)
\(614\) −4.62465e40 −1.72440
\(615\) 4.58177e40 1.51920e40i 1.66857 0.553255i
\(616\) −2.89749e40 + 2.32217e39i −1.03063 + 0.0825989i
\(617\) 5.19429e40i 1.80464i 0.431064 + 0.902322i \(0.358138\pi\)
−0.431064 + 0.902322i \(0.641862\pi\)
\(618\) −2.91782e40 + 9.67474e39i −0.990205 + 0.328327i
\(619\) 8.01138e39i 0.265578i 0.991144 + 0.132789i \(0.0423933\pi\)
−0.991144 + 0.132789i \(0.957607\pi\)
\(620\) 1.77561e40i 0.574999i
\(621\) 2.86699e40 + 2.00506e40i 0.906982 + 0.634306i
\(622\) 7.00952e40i 2.16635i
\(623\) −4.47957e40 + 3.59012e39i −1.35257 + 0.108401i
\(624\) 1.80803e38 + 5.45287e38i 0.00533372 + 0.0160860i
\(625\) 1.16884e41 3.36895
\(626\) 4.55206e40 1.28198
\(627\) −8.64243e40 + 2.86561e40i −2.37824 + 0.788565i
\(628\) 5.80890e39i 0.156199i
\(629\) 2.25394e39 0.0592254
\(630\) 5.81554e40 + 6.62656e40i 1.49332 + 1.70157i
\(631\) −4.96300e40 −1.24543 −0.622714 0.782450i \(-0.713970\pi\)
−0.622714 + 0.782450i \(0.713970\pi\)
\(632\) 2.57457e40i 0.631403i
\(633\) −2.48752e40 + 8.24797e39i −0.596228 + 0.197694i
\(634\) −3.04502e40 −0.713338
\(635\) 8.45434e40 1.93580
\(636\) −5.86300e39 1.76823e40i −0.131218 0.395741i
\(637\) 9.94286e37 + 6.16326e38i 0.00217515 + 0.0134831i
\(638\) 4.62751e40i 0.989572i
\(639\) −3.14058e40 4.21518e40i −0.656518 0.881159i
\(640\) 1.08545e41i 2.21820i
\(641\) 6.33546e38i 0.0126572i −0.999980 0.00632859i \(-0.997986\pi\)
0.999980 0.00632859i \(-0.00201446\pi\)
\(642\) 5.01008e40 1.66122e40i 0.978559 0.324465i
\(643\) 3.01539e40i 0.575817i 0.957658 + 0.287909i \(0.0929599\pi\)
−0.957658 + 0.287909i \(0.907040\pi\)
\(644\) −1.91571e39 2.39032e40i −0.0357671 0.446284i
\(645\) 1.12405e41 3.72707e40i 2.05197 0.680381i
\(646\) 1.31708e40 0.235093
\(647\) −8.84082e40 −1.54305 −0.771526 0.636198i \(-0.780506\pi\)
−0.771526 + 0.636198i \(0.780506\pi\)
\(648\) 3.96212e40 + 1.18290e40i 0.676223 + 0.201889i
\(649\) 1.76096e40i 0.293901i
\(650\) −2.62716e39 −0.0428788
\(651\) −1.81599e40 4.29354e40i −0.289861 0.685317i
\(652\) −2.37218e40 −0.370303
\(653\) 6.37221e40i 0.972857i −0.873720 0.486428i \(-0.838299\pi\)
0.873720 0.486428i \(-0.161701\pi\)
\(654\) −9.84617e39 2.96952e40i −0.147025 0.443413i
\(655\) −5.90654e40 −0.862650
\(656\) −7.99344e40 −1.14190
\(657\) −3.27596e40 4.39689e40i −0.457763 0.614396i
\(658\) 4.38527e39 + 5.47172e40i 0.0599405 + 0.747908i
\(659\) 2.02299e39i 0.0270493i −0.999909 0.0135246i \(-0.995695\pi\)
0.999909 0.0135246i \(-0.00430516\pi\)
\(660\) 2.72407e40 + 8.21554e40i 0.356312 + 1.07461i
\(661\) 8.62348e40i 1.10347i 0.834019 + 0.551736i \(0.186035\pi\)
−0.834019 + 0.551736i \(0.813965\pi\)
\(662\) 1.15093e39i 0.0144082i
\(663\) 4.07077e37 + 1.22771e38i 0.000498575 + 0.00150366i
\(664\) 4.49106e40i 0.538161i
\(665\) 2.22607e40 + 2.77758e41i 0.260990 + 3.25651i
\(666\) −3.15158e40 4.22995e40i −0.361536 0.485243i
\(667\) 5.61963e40 0.630788
\(668\) 3.89779e40 0.428114
\(669\) −4.88929e40 1.47457e41i −0.525493 1.58484i
\(670\) 1.53628e41i 1.61580i
\(671\) 1.55588e41 1.60140
\(672\) −2.95809e40 6.99380e40i −0.297959 0.704464i
\(673\) −1.47463e41 −1.45367 −0.726833 0.686815i \(-0.759008\pi\)
−0.726833 + 0.686815i \(0.759008\pi\)
\(674\) 7.58686e40i 0.731970i
\(675\) −1.60788e41 + 2.29907e41i −1.51827 + 2.17094i
\(676\) −4.37610e40 −0.404445
\(677\) −1.68380e41 −1.52320 −0.761598 0.648050i \(-0.775585\pi\)
−0.761598 + 0.648050i \(0.775585\pi\)
\(678\) −2.19614e40 + 7.28186e39i −0.194460 + 0.0644780i
\(679\) 1.55385e40 + 1.93882e41i 0.134678 + 1.68045i
\(680\) 1.84306e40i 0.156372i
\(681\) 1.30038e41 4.31174e40i 1.08003 0.358112i
\(682\) 1.58901e41i 1.29198i
\(683\) 1.93052e41i 1.53665i −0.640060 0.768325i \(-0.721091\pi\)
0.640060 0.768325i \(-0.278909\pi\)
\(684\) −5.30408e40 7.11898e40i −0.413330 0.554759i
\(685\) 2.12106e41i 1.61823i
\(686\) −3.77012e40 1.54114e41i −0.281615 1.15118i
\(687\) −2.43383e40 7.34021e40i −0.177999 0.536829i
\(688\) −1.96104e41 −1.40428
\(689\) 2.00755e39 0.0140763
\(690\) 3.46405e41 1.14859e41i 2.37833 0.788594i
\(691\) 2.46113e41i 1.65464i −0.561732 0.827319i \(-0.689865\pi\)
0.561732 0.827319i \(-0.310135\pi\)
\(692\) 3.82490e39 0.0251815
\(693\) 1.49894e41 + 1.70798e41i 0.966389 + 1.10116i
\(694\) −1.67610e41 −1.05825
\(695\) 2.09734e41i 1.29685i
\(696\) 6.30430e40 2.09035e40i 0.381771 0.126586i
\(697\) −1.79972e40 −0.106740
\(698\) 1.95076e41 1.13319
\(699\) −3.65799e40 1.10322e41i −0.208125 0.627686i
\(700\) 1.91682e41 1.53622e40i 1.06822 0.0856117i
\(701\) 1.77281e41i 0.967725i 0.875144 + 0.483862i \(0.160766\pi\)
−0.875144 + 0.483862i \(0.839234\pi\)
\(702\) 1.73483e39 2.48061e39i 0.00927619 0.0132638i
\(703\) 1.66715e41i 0.873216i
\(704\) 9.54841e40i 0.489923i
\(705\) −2.28383e41 + 7.57260e40i −1.14795 + 0.380630i
\(706\) 4.62301e40i 0.227644i
\(707\) 1.21609e41 9.74625e39i 0.586657 0.0470171i
\(708\) −1.62972e40 + 5.40374e39i −0.0770248 + 0.0255395i
\(709\) 1.85949e41 0.861039 0.430519 0.902581i \(-0.358330\pi\)
0.430519 + 0.902581i \(0.358330\pi\)
\(710\) −5.48332e41 −2.48770
\(711\) −1.61400e41 + 1.20253e41i −0.717454 + 0.534549i
\(712\) 2.19857e41i 0.957593i
\(713\) −1.92969e41 −0.823550
\(714\) −1.28050e40 3.02749e40i −0.0535495 0.126607i
\(715\) −9.32747e39 −0.0382232
\(716\) 3.18543e40i 0.127917i
\(717\) −3.83471e40 1.15652e41i −0.150906 0.455118i
\(718\) 9.33389e40 0.359963
\(719\) −2.21601e41 −0.837537 −0.418768 0.908093i \(-0.637538\pi\)
−0.418768 + 0.908093i \(0.637538\pi\)
\(720\) 5.13178e41 3.82350e41i 1.90084 1.41625i
\(721\) 1.93711e40 + 2.41703e41i 0.0703223 + 0.877447i
\(722\) 6.41106e41i 2.28108i
\(723\) −7.13525e39 2.15193e40i −0.0248831 0.0750452i
\(724\) 7.38541e39i 0.0252444i
\(725\) 4.50644e41i 1.50985i
\(726\) 1.30207e41 + 3.92693e41i 0.427616 + 1.28965i
\(727\) 2.56606e41i 0.826072i 0.910715 + 0.413036i \(0.135532\pi\)
−0.910715 + 0.413036i \(0.864468\pi\)
\(728\) 3.04448e39 2.43998e38i 0.00960745 0.000769982i
\(729\) −1.10907e41 3.03637e41i −0.343090 0.939302i
\(730\) −5.71969e41 −1.73457
\(731\) −4.41527e40 −0.131267
\(732\) 4.77443e40 + 1.43993e41i 0.139159 + 0.419691i
\(733\) 2.64459e41i 0.755703i −0.925866 0.377851i \(-0.876663\pi\)
0.925866 0.377851i \(-0.123337\pi\)
\(734\) 5.09888e41 1.42851
\(735\) 6.16821e41 3.21213e41i 1.69431 0.882320i
\(736\) −3.14330e41 −0.846559
\(737\) 3.95973e41i 1.04565i
\(738\) 2.51646e41 + 3.37751e41i 0.651587 + 0.874540i
\(739\) −5.53934e41 −1.40642 −0.703208 0.710985i \(-0.748250\pi\)
−0.703208 + 0.710985i \(0.748250\pi\)
\(740\) −1.58480e41 −0.394562
\(741\) 9.08086e39 3.01098e39i 0.0221699 0.00735096i
\(742\) −5.08570e41 + 4.07589e40i −1.21757 + 0.0975812i
\(743\) 4.83025e41i 1.13405i −0.823701 0.567024i \(-0.808094\pi\)
0.823701 0.567024i \(-0.191906\pi\)
\(744\) −2.16480e41 + 7.17792e40i −0.498436 + 0.165269i
\(745\) 7.66555e41i 1.73092i
\(746\) 2.28964e39i 0.00507054i
\(747\) −2.81545e41 + 2.09769e41i −0.611504 + 0.455609i
\(748\) 3.22706e40i 0.0687438i
\(749\) −3.32615e40 4.15020e41i −0.0694952 0.867127i
\(750\) 5.73386e41 + 1.72928e42i 1.17506 + 3.54387i
\(751\) 1.98960e41 0.399933 0.199966 0.979803i \(-0.435917\pi\)
0.199966 + 0.979803i \(0.435917\pi\)
\(752\) 3.98441e41 0.785607
\(753\) −1.66247e41 + 5.51232e40i −0.321533 + 0.106612i
\(754\)