Properties

Label 6.17.b.a.5.2
Level 6
Weight 17
Character 6.5
Analytic conductor 9.739
Analytic rank 0
Dimension 6
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 6.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.7394726314\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{27}\cdot 3^{13} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.2
Root \(-172.725i\)
Character \(\chi\) = 6.5
Dual form 6.17.b.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q-181.019i q^{2} +(1479.09 - 6392.11i) q^{3} -32768.0 q^{4} -441421. i q^{5} +(-1.15709e6 - 267744. i) q^{6} +2.81464e6 q^{7} +5.93164e6i q^{8} +(-3.86713e7 - 1.89090e7i) q^{9} +O(q^{10})\) \(q-181.019i q^{2} +(1479.09 - 6392.11i) q^{3} -32768.0 q^{4} -441421. i q^{5} +(-1.15709e6 - 267744. i) q^{6} +2.81464e6 q^{7} +5.93164e6i q^{8} +(-3.86713e7 - 1.89090e7i) q^{9} -7.99057e7 q^{10} +1.92938e8i q^{11} +(-4.84669e7 + 2.09456e8i) q^{12} -1.24215e9 q^{13} -5.09504e8i q^{14} +(-2.82161e9 - 6.52903e8i) q^{15} +1.07374e9 q^{16} -1.41634e9i q^{17} +(-3.42290e9 + 7.00025e9i) q^{18} +2.68017e10 q^{19} +1.44645e10i q^{20} +(4.16311e9 - 1.79915e10i) q^{21} +3.49256e10 q^{22} -1.20426e11i q^{23} +(3.79157e10 + 8.77345e9i) q^{24} -4.22647e10 q^{25} +2.24852e11i q^{26} +(-1.78067e11 + 2.19223e11i) q^{27} -9.22301e10 q^{28} -6.43715e11i q^{29} +(-1.18188e11 + 5.10766e11i) q^{30} -1.14352e12 q^{31} -1.94368e11i q^{32} +(1.23328e12 + 2.85374e11i) q^{33} -2.56386e11 q^{34} -1.24244e12i q^{35} +(1.26718e12 + 6.19611e11i) q^{36} +4.25212e12 q^{37} -4.85163e12i q^{38} +(-1.83725e12 + 7.93992e12i) q^{39} +2.61835e12 q^{40} -3.12148e12i q^{41} +(-3.25681e12 - 7.53604e11i) q^{42} +4.47086e12 q^{43} -6.32221e12i q^{44} +(-8.34684e12 + 1.70703e13i) q^{45} -2.17994e13 q^{46} -1.17679e13i q^{47} +(1.58816e12 - 6.86347e12i) q^{48} -2.53107e13 q^{49} +7.65072e12i q^{50} +(-9.05342e12 - 2.09490e12i) q^{51} +4.07026e13 q^{52} +4.41654e13i q^{53} +(3.96836e13 + 3.22336e13i) q^{54} +8.51671e13 q^{55} +1.66954e13i q^{56} +(3.96422e13 - 1.71319e14i) q^{57} -1.16525e14 q^{58} -1.42767e14i q^{59} +(9.24585e13 + 2.13943e13i) q^{60} +2.29855e13 q^{61} +2.06999e14i q^{62} +(-1.08846e14 - 5.32221e13i) q^{63} -3.51844e13 q^{64} +5.48309e14i q^{65} +(5.16582e13 - 2.23248e14i) q^{66} -1.94559e14 q^{67} +4.64107e13i q^{68} +(-7.69774e14 - 1.78121e14i) q^{69} -2.24906e14 q^{70} -3.85172e13i q^{71} +(1.12162e14 - 2.29384e14i) q^{72} +1.42218e15 q^{73} -7.69717e14i q^{74} +(-6.25133e13 + 2.70160e14i) q^{75} -8.78239e14 q^{76} +5.43052e14i q^{77} +(1.43728e15 + 3.32577e14i) q^{78} +1.03560e15 q^{79} -4.73972e14i q^{80} +(1.13792e15 + 1.46247e15i) q^{81} -5.65048e14 q^{82} -1.75783e15i q^{83} +(-1.36417e14 + 5.89545e14i) q^{84} -6.25204e14 q^{85} -8.09313e14i q^{86} +(-4.11469e15 - 9.52114e14i) q^{87} -1.14444e15 q^{88} -1.35243e15i q^{89} +(3.09006e15 + 1.51094e15i) q^{90} -3.49619e15 q^{91} +3.94611e15i q^{92} +(-1.69137e15 + 7.30951e15i) q^{93} -2.13022e15 q^{94} -1.18308e16i q^{95} +(-1.24242e15 - 2.87488e14i) q^{96} +5.20071e15 q^{97} +4.58173e15i q^{98} +(3.64828e15 - 7.46118e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + O(q^{10}) \) \( 6q + 6006q^{3} - 196608q^{4} + 159744q^{6} - 167892q^{7} - 10215738q^{9} + 39297024q^{10} - 196804608q^{12} + 1763152140q^{13} - 8080218432q^{15} + 6442450944q^{16} - 12549169152q^{18} + 60306979692q^{19} - 155770661748q^{21} + 94233305088q^{22} - 5234491392q^{24} - 75722441466q^{25} + 330190979958q^{27} + 5501485056q^{28} + 987679531008q^{30} - 2846203650132q^{31} + 3282289396416q^{33} - 1812957659136q^{34} + 334749302784q^{36} + 2483836081932q^{37} - 8759076866580q^{39} - 1287684882432q^{40} - 3652917731328q^{42} + 46155081190764q^{43} - 46496752783488q^{45} - 17111605395456q^{46} + 6448893394944q^{48} + 42155513811090q^{49} - 3055668993792q^{51} - 57774969323520q^{52} + 240022278328320q^{54} - 155561818958208q^{55} + 27052692784332q^{57} - 366644114104320q^{58} + 264772597579776q^{60} + 306036501898764q^{61} - 801652315914324q^{63} - 211106232532992q^{64} + 1157574327017472q^{66} + 1979846570008812q^{67} - 2345782552693632q^{69} - 2197723307360256q^{70} + 411211174772736q^{72} + 3864207384753420q^{73} - 3376263465802122q^{75} - 1976139110547456q^{76} + 5837442492456960q^{78} + 1835806484101548q^{79} - 703356001465338q^{81} - 9913023387353088q^{82} + 5104293044158464q^{84} + 2872972366990848q^{85} - 3000080900606400q^{87} - 3087836941123584q^{88} + 12789804912058368q^{90} - 1824281133603240q^{91} - 11156835457641972q^{93} - 4579876939530240q^{94} + 171523813933056q^{96} + 31097493125645196q^{97} - 28794216850745472q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6\mathbb{Z}\right)^\times\).

\(n\) \(5\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 181.019i 0.707107i
\(3\) 1479.09 6392.11i 0.225437 0.974258i
\(4\) −32768.0 −0.500000
\(5\) 441421.i 1.13004i −0.825078 0.565019i \(-0.808869\pi\)
0.825078 0.565019i \(-0.191131\pi\)
\(6\) −1.15709e6 267744.i −0.688904 0.159408i
\(7\) 2.81464e6 0.488246 0.244123 0.969744i \(-0.421500\pi\)
0.244123 + 0.969744i \(0.421500\pi\)
\(8\) 5.93164e6i 0.353553i
\(9\) −3.86713e7 1.89090e7i −0.898356 0.439268i
\(10\) −7.99057e7 −0.799057
\(11\) 1.92938e8i 0.900072i 0.893010 + 0.450036i \(0.148589\pi\)
−0.893010 + 0.450036i \(0.851411\pi\)
\(12\) −4.84669e7 + 2.09456e8i −0.112719 + 0.487129i
\(13\) −1.24215e9 −1.52274 −0.761370 0.648318i \(-0.775473\pi\)
−0.761370 + 0.648318i \(0.775473\pi\)
\(14\) 5.09504e8i 0.345242i
\(15\) −2.82161e9 6.52903e8i −1.10095 0.254752i
\(16\) 1.07374e9 0.250000
\(17\) 1.41634e9i 0.203038i −0.994834 0.101519i \(-0.967630\pi\)
0.994834 0.101519i \(-0.0323703\pi\)
\(18\) −3.42290e9 + 7.00025e9i −0.310609 + 0.635234i
\(19\) 2.68017e10 1.57810 0.789049 0.614330i \(-0.210574\pi\)
0.789049 + 0.614330i \(0.210574\pi\)
\(20\) 1.44645e10i 0.565019i
\(21\) 4.16311e9 1.79915e10i 0.110069 0.475677i
\(22\) 3.49256e10 0.636447
\(23\) 1.20426e11i 1.53779i −0.639376 0.768895i \(-0.720807\pi\)
0.639376 0.768895i \(-0.279193\pi\)
\(24\) 3.79157e10 + 8.77345e9i 0.344452 + 0.0797040i
\(25\) −4.22647e10 −0.276986
\(26\) 2.24852e11i 1.07674i
\(27\) −1.78067e11 + 2.19223e11i −0.630483 + 0.776203i
\(28\) −9.22301e10 −0.244123
\(29\) 6.43715e11i 1.28680i −0.765532 0.643398i \(-0.777524\pi\)
0.765532 0.643398i \(-0.222476\pi\)
\(30\) −1.18188e11 + 5.10766e11i −0.180137 + 0.778488i
\(31\) −1.14352e12 −1.34076 −0.670379 0.742019i \(-0.733869\pi\)
−0.670379 + 0.742019i \(0.733869\pi\)
\(32\) 1.94368e11i 0.176777i
\(33\) 1.23328e12 + 2.85374e11i 0.876902 + 0.202910i
\(34\) −2.56386e11 −0.143570
\(35\) 1.24244e12i 0.551736i
\(36\) 1.26718e12 + 6.19611e11i 0.449178 + 0.219634i
\(37\) 4.25212e12 1.21058 0.605288 0.796007i \(-0.293058\pi\)
0.605288 + 0.796007i \(0.293058\pi\)
\(38\) 4.85163e12i 1.11588i
\(39\) −1.83725e12 + 7.93992e12i −0.343282 + 1.48354i
\(40\) 2.61835e12 0.399529
\(41\) 3.12148e12i 0.390921i −0.980712 0.195461i \(-0.937380\pi\)
0.980712 0.195461i \(-0.0626202\pi\)
\(42\) −3.25681e12 7.53604e11i −0.336355 0.0778303i
\(43\) 4.47086e12 0.382511 0.191255 0.981540i \(-0.438744\pi\)
0.191255 + 0.981540i \(0.438744\pi\)
\(44\) 6.32221e12i 0.450036i
\(45\) −8.34684e12 + 1.70703e13i −0.496389 + 1.01518i
\(46\) −2.17994e13 −1.08738
\(47\) 1.17679e13i 0.494217i −0.968988 0.247108i \(-0.920520\pi\)
0.968988 0.247108i \(-0.0794804\pi\)
\(48\) 1.58816e12 6.86347e12i 0.0563593 0.243564i
\(49\) −2.53107e13 −0.761616
\(50\) 7.65072e12i 0.195858i
\(51\) −9.05342e12 2.09490e12i −0.197811 0.0457723i
\(52\) 4.07026e13 0.761370
\(53\) 4.41654e13i 0.709374i 0.934985 + 0.354687i \(0.115413\pi\)
−0.934985 + 0.354687i \(0.884587\pi\)
\(54\) 3.96836e13 + 3.22336e13i 0.548859 + 0.445819i
\(55\) 8.51671e13 1.01712
\(56\) 1.66954e13i 0.172621i
\(57\) 3.96422e13 1.71319e14i 0.355762 1.53747i
\(58\) −1.16525e14 −0.909902
\(59\) 1.42767e14i 0.972325i −0.873868 0.486163i \(-0.838396\pi\)
0.873868 0.486163i \(-0.161604\pi\)
\(60\) 9.24585e13 + 2.13943e13i 0.550474 + 0.127376i
\(61\) 2.29855e13 0.119899 0.0599496 0.998201i \(-0.480906\pi\)
0.0599496 + 0.998201i \(0.480906\pi\)
\(62\) 2.06999e14i 0.948059i
\(63\) −1.08846e14 5.32221e13i −0.438619 0.214471i
\(64\) −3.51844e13 −0.125000
\(65\) 5.48309e14i 1.72075i
\(66\) 5.16582e13 2.23248e14i 0.143479 0.620063i
\(67\) −1.94559e14 −0.479129 −0.239565 0.970880i \(-0.577005\pi\)
−0.239565 + 0.970880i \(0.577005\pi\)
\(68\) 4.64107e13i 0.101519i
\(69\) −7.69774e14 1.78121e14i −1.49820 0.346675i
\(70\) −2.24906e14 −0.390137
\(71\) 3.85172e13i 0.0596469i −0.999555 0.0298234i \(-0.990505\pi\)
0.999555 0.0298234i \(-0.00949450\pi\)
\(72\) 1.12162e14 2.29384e14i 0.155305 0.317617i
\(73\) 1.42218e15 1.76349 0.881743 0.471731i \(-0.156371\pi\)
0.881743 + 0.471731i \(0.156371\pi\)
\(74\) 7.69717e14i 0.856007i
\(75\) −6.25133e13 + 2.70160e14i −0.0624428 + 0.269855i
\(76\) −8.78239e14 −0.789049
\(77\) 5.43052e14i 0.439456i
\(78\) 1.43728e15 + 3.32577e14i 1.04902 + 0.242737i
\(79\) 1.03560e15 0.682613 0.341307 0.939952i \(-0.389131\pi\)
0.341307 + 0.939952i \(0.389131\pi\)
\(80\) 4.73972e14i 0.282509i
\(81\) 1.13792e15 + 1.46247e15i 0.614088 + 0.789238i
\(82\) −5.65048e14 −0.276423
\(83\) 1.75783e15i 0.780463i −0.920717 0.390232i \(-0.872395\pi\)
0.920717 0.390232i \(-0.127605\pi\)
\(84\) −1.36417e14 + 5.89545e14i −0.0550344 + 0.237839i
\(85\) −6.25204e14 −0.229441
\(86\) 8.09313e14i 0.270476i
\(87\) −4.11469e15 9.52114e14i −1.25367 0.290091i
\(88\) −1.14444e15 −0.318223
\(89\) 1.35243e15i 0.343555i −0.985136 0.171777i \(-0.945049\pi\)
0.985136 0.171777i \(-0.0549510\pi\)
\(90\) 3.09006e15 + 1.51094e15i 0.717838 + 0.351000i
\(91\) −3.49619e15 −0.743472
\(92\) 3.94611e15i 0.768895i
\(93\) −1.69137e15 + 7.30951e15i −0.302257 + 1.30624i
\(94\) −2.13022e15 −0.349464
\(95\) 1.18308e16i 1.78331i
\(96\) −1.24242e15 2.87488e14i −0.172226 0.0398520i
\(97\) 5.20071e15 0.663573 0.331786 0.943355i \(-0.392349\pi\)
0.331786 + 0.943355i \(0.392349\pi\)
\(98\) 4.58173e15i 0.538544i
\(99\) 3.64828e15 7.46118e15i 0.395372 0.808585i
\(100\) 1.38493e15 0.138493
\(101\) 1.01413e16i 0.936530i 0.883588 + 0.468265i \(0.155121\pi\)
−0.883588 + 0.468265i \(0.844879\pi\)
\(102\) −3.79218e14 + 1.63884e15i −0.0323659 + 0.139874i
\(103\) 1.78661e16 1.41037 0.705185 0.709024i \(-0.250864\pi\)
0.705185 + 0.709024i \(0.250864\pi\)
\(104\) 7.36796e15i 0.538370i
\(105\) −7.94182e15 1.83769e15i −0.537533 0.124382i
\(106\) 7.99479e15 0.501603
\(107\) 7.25364e15i 0.422169i 0.977468 + 0.211084i \(0.0676994\pi\)
−0.977468 + 0.211084i \(0.932301\pi\)
\(108\) 5.83490e15 7.18349e15i 0.315241 0.388102i
\(109\) −1.26213e16 −0.633420 −0.316710 0.948522i \(-0.602578\pi\)
−0.316710 + 0.948522i \(0.602578\pi\)
\(110\) 1.54169e16i 0.719209i
\(111\) 6.28928e15 2.71800e16i 0.272909 1.17941i
\(112\) 3.02220e15 0.122061
\(113\) 5.30603e16i 1.99591i 0.0638829 + 0.997957i \(0.479652\pi\)
−0.0638829 + 0.997957i \(0.520348\pi\)
\(114\) −3.10121e16 7.17601e15i −1.08716 0.251562i
\(115\) −5.31585e16 −1.73776
\(116\) 2.10933e16i 0.643398i
\(117\) 4.80354e16 + 2.34878e16i 1.36796 + 0.668890i
\(118\) −2.58436e16 −0.687538
\(119\) 3.98650e15i 0.0991325i
\(120\) 3.87278e15 1.67368e16i 0.0900686 0.389244i
\(121\) 8.72451e15 0.189871
\(122\) 4.16083e15i 0.0847815i
\(123\) −1.99528e16 4.61696e15i −0.380858 0.0881282i
\(124\) 3.74709e16 0.670379
\(125\) 4.86990e16i 0.817034i
\(126\) −9.63423e15 + 1.97032e16i −0.151654 + 0.310150i
\(127\) −1.76909e16 −0.261408 −0.130704 0.991421i \(-0.541724\pi\)
−0.130704 + 0.991421i \(0.541724\pi\)
\(128\) 6.36905e15i 0.0883883i
\(129\) 6.61282e15 2.85782e16i 0.0862321 0.372664i
\(130\) 9.92546e16 1.21676
\(131\) 6.29766e16i 0.726121i −0.931766 0.363060i \(-0.881732\pi\)
0.931766 0.363060i \(-0.118268\pi\)
\(132\) −4.04122e16 9.35113e15i −0.438451 0.101455i
\(133\) 7.54373e16 0.770500
\(134\) 3.52189e16i 0.338795i
\(135\) 9.67695e16 + 7.86025e16i 0.877139 + 0.712469i
\(136\) 8.40124e15 0.0717848
\(137\) 1.05927e16i 0.0853579i 0.999089 + 0.0426790i \(0.0135893\pi\)
−0.999089 + 0.0426790i \(0.986411\pi\)
\(138\) −3.22433e16 + 1.39344e17i −0.245136 + 1.05939i
\(139\) −6.67031e16 −0.478660 −0.239330 0.970938i \(-0.576928\pi\)
−0.239330 + 0.970938i \(0.576928\pi\)
\(140\) 4.07123e16i 0.275868i
\(141\) −7.52219e16 1.74059e16i −0.481495 0.111415i
\(142\) −6.97235e15 −0.0421767
\(143\) 2.39658e17i 1.37058i
\(144\) −4.15230e16 2.03034e16i −0.224589 0.109817i
\(145\) −2.84149e17 −1.45413
\(146\) 2.57442e17i 1.24697i
\(147\) −3.74369e16 + 1.61789e17i −0.171696 + 0.742010i
\(148\) −1.39334e17 −0.605288
\(149\) 6.45793e16i 0.265830i 0.991127 + 0.132915i \(0.0424337\pi\)
−0.991127 + 0.132915i \(0.957566\pi\)
\(150\) 4.89042e16 + 1.13161e16i 0.190817 + 0.0441538i
\(151\) 2.58366e17 0.955918 0.477959 0.878382i \(-0.341377\pi\)
0.477959 + 0.878382i \(0.341377\pi\)
\(152\) 1.58978e17i 0.557942i
\(153\) −2.67817e16 + 5.47718e16i −0.0891880 + 0.182400i
\(154\) 9.83030e16 0.310743
\(155\) 5.04774e17i 1.51511i
\(156\) 6.02029e16 2.60175e17i 0.171641 0.741770i
\(157\) 2.22147e16 0.0601788 0.0300894 0.999547i \(-0.490421\pi\)
0.0300894 + 0.999547i \(0.490421\pi\)
\(158\) 1.87463e17i 0.482680i
\(159\) 2.82310e17 + 6.53247e16i 0.691113 + 0.159919i
\(160\) −8.57981e16 −0.199764
\(161\) 3.38955e17i 0.750819i
\(162\) 2.64736e17 2.05985e17i 0.558075 0.434226i
\(163\) 1.19046e17 0.238898 0.119449 0.992840i \(-0.461887\pi\)
0.119449 + 0.992840i \(0.461887\pi\)
\(164\) 1.02285e17i 0.195461i
\(165\) 1.25970e17 5.44397e17i 0.229295 0.990932i
\(166\) −3.18201e17 −0.551871
\(167\) 7.29738e17i 1.20624i 0.797649 + 0.603122i \(0.206077\pi\)
−0.797649 + 0.603122i \(0.793923\pi\)
\(168\) 1.06719e17 + 2.46941e16i 0.168177 + 0.0389152i
\(169\) 8.77509e17 1.31874
\(170\) 1.13174e17i 0.162239i
\(171\) −1.03646e18 5.06795e17i −1.41769 0.693207i
\(172\) −1.46501e17 −0.191255
\(173\) 4.08345e17i 0.508930i −0.967082 0.254465i \(-0.918101\pi\)
0.967082 0.254465i \(-0.0818994\pi\)
\(174\) −1.72351e17 + 7.44839e17i −0.205126 + 0.886479i
\(175\) −1.18960e17 −0.135237
\(176\) 2.07166e17i 0.225018i
\(177\) −9.12581e17 2.11165e17i −0.947295 0.219198i
\(178\) −2.44817e17 −0.242930
\(179\) 1.33787e18i 1.26937i 0.772771 + 0.634685i \(0.218870\pi\)
−0.772771 + 0.634685i \(0.781130\pi\)
\(180\) 2.73509e17 5.59360e17i 0.248195 0.507588i
\(181\) −1.05868e18 −0.919041 −0.459520 0.888167i \(-0.651979\pi\)
−0.459520 + 0.888167i \(0.651979\pi\)
\(182\) 6.32879e17i 0.525714i
\(183\) 3.39978e16 1.46926e17i 0.0270297 0.116813i
\(184\) 7.14323e17 0.543691
\(185\) 1.87698e18i 1.36800i
\(186\) 1.32316e18 + 3.06171e17i 0.923654 + 0.213728i
\(187\) 2.73267e17 0.182749
\(188\) 3.85612e17i 0.247108i
\(189\) −5.01194e17 + 6.17033e17i −0.307831 + 0.378978i
\(190\) −2.14161e18 −1.26099
\(191\) 1.01818e18i 0.574855i −0.957802 0.287427i \(-0.907200\pi\)
0.957802 0.287427i \(-0.0928000\pi\)
\(192\) −5.20409e16 + 2.24902e17i −0.0281796 + 0.121782i
\(193\) 2.82918e18 1.46961 0.734805 0.678278i \(-0.237274\pi\)
0.734805 + 0.678278i \(0.237274\pi\)
\(194\) 9.41429e17i 0.469217i
\(195\) 3.50485e18 + 8.11000e17i 1.67646 + 0.387922i
\(196\) 8.29382e17 0.380808
\(197\) 3.70725e17i 0.163426i −0.996656 0.0817132i \(-0.973961\pi\)
0.996656 0.0817132i \(-0.0260391\pi\)
\(198\) −1.35062e18 6.60409e17i −0.571756 0.279570i
\(199\) −1.24614e18 −0.506690 −0.253345 0.967376i \(-0.581531\pi\)
−0.253345 + 0.967376i \(0.581531\pi\)
\(200\) 2.50699e17i 0.0979292i
\(201\) −2.87770e17 + 1.24364e18i −0.108013 + 0.466795i
\(202\) 1.83577e18 0.662226
\(203\) 1.81183e18i 0.628273i
\(204\) 2.96662e17 + 6.86458e16i 0.0989057 + 0.0228861i
\(205\) −1.37789e18 −0.441756
\(206\) 3.23412e18i 0.997282i
\(207\) −2.27713e18 + 4.65702e18i −0.675501 + 1.38148i
\(208\) −1.33374e18 −0.380685
\(209\) 5.17108e18i 1.42040i
\(210\) −3.32657e17 + 1.43762e18i −0.0879512 + 0.380094i
\(211\) −1.50137e18 −0.382145 −0.191073 0.981576i \(-0.561197\pi\)
−0.191073 + 0.981576i \(0.561197\pi\)
\(212\) 1.44721e18i 0.354687i
\(213\) −2.46206e17 5.69705e16i −0.0581114 0.0134466i
\(214\) 1.31305e18 0.298518
\(215\) 1.97353e18i 0.432252i
\(216\) −1.30035e18 1.05623e18i −0.274429 0.222909i
\(217\) −3.21860e18 −0.654620
\(218\) 2.28470e18i 0.447895i
\(219\) 2.10354e18 9.09073e18i 0.397555 1.71809i
\(220\) −2.79075e18 −0.508558
\(221\) 1.75930e18i 0.309174i
\(222\) −4.92011e18 1.13848e18i −0.833971 0.192976i
\(223\) 1.86081e17 0.0304273 0.0152137 0.999884i \(-0.495157\pi\)
0.0152137 + 0.999884i \(0.495157\pi\)
\(224\) 5.47076e17i 0.0863105i
\(225\) 1.63443e18 + 7.99184e17i 0.248832 + 0.121671i
\(226\) 9.60494e18 1.41132
\(227\) 2.27536e18i 0.322733i −0.986895 0.161367i \(-0.948410\pi\)
0.986895 0.161367i \(-0.0515902\pi\)
\(228\) −1.29900e18 + 5.61380e18i −0.177881 + 0.768737i
\(229\) 8.00708e18 1.05874 0.529371 0.848390i \(-0.322428\pi\)
0.529371 + 0.848390i \(0.322428\pi\)
\(230\) 9.62271e18i 1.22878i
\(231\) 3.47125e18 + 8.03224e17i 0.428144 + 0.0990698i
\(232\) 3.81829e18 0.454951
\(233\) 4.98299e18i 0.573645i 0.957984 + 0.286822i \(0.0925989\pi\)
−0.957984 + 0.286822i \(0.907401\pi\)
\(234\) 4.25174e18 8.69533e18i 0.472977 0.967296i
\(235\) −5.19462e18 −0.558484
\(236\) 4.67819e18i 0.486163i
\(237\) 1.53175e18 6.61965e18i 0.153886 0.665041i
\(238\) −7.21633e17 −0.0700972
\(239\) 1.29189e19i 1.21350i −0.794892 0.606751i \(-0.792472\pi\)
0.794892 0.606751i \(-0.207528\pi\)
\(240\) −3.02968e18 7.01049e17i −0.275237 0.0636881i
\(241\) −3.12668e18 −0.274756 −0.137378 0.990519i \(-0.543868\pi\)
−0.137378 + 0.990519i \(0.543868\pi\)
\(242\) 1.57930e18i 0.134259i
\(243\) 1.10314e19 5.11055e18i 0.907359 0.420357i
\(244\) −7.53190e17 −0.0599496
\(245\) 1.11727e19i 0.860655i
\(246\) −8.35758e17 + 3.61185e18i −0.0623160 + 0.269307i
\(247\) −3.32917e19 −2.40303
\(248\) 6.78296e18i 0.474030i
\(249\) −1.12362e19 2.59999e18i −0.760372 0.175945i
\(250\) −8.81546e18 −0.577730
\(251\) 1.30882e19i 0.830791i 0.909641 + 0.415395i \(0.136357\pi\)
−0.909641 + 0.415395i \(0.863643\pi\)
\(252\) 3.56666e18 + 1.74398e18i 0.219309 + 0.107235i
\(253\) 2.32348e19 1.38412
\(254\) 3.20239e18i 0.184844i
\(255\) −9.24734e17 + 3.99637e18i −0.0517244 + 0.223534i
\(256\) 1.15292e18 0.0625000
\(257\) 7.73778e18i 0.406585i 0.979118 + 0.203292i \(0.0651642\pi\)
−0.979118 + 0.203292i \(0.934836\pi\)
\(258\) −5.17321e18 1.19705e18i −0.263513 0.0609753i
\(259\) 1.19682e19 0.591059
\(260\) 1.79670e19i 0.860377i
\(261\) −1.21720e19 + 2.48933e19i −0.565248 + 1.15600i
\(262\) −1.14000e19 −0.513445
\(263\) 6.15684e17i 0.0268975i 0.999910 + 0.0134487i \(0.00428100\pi\)
−0.999910 + 0.0134487i \(0.995719\pi\)
\(264\) −1.69273e18 + 7.31539e18i −0.0717394 + 0.310032i
\(265\) 1.94955e19 0.801620
\(266\) 1.36556e19i 0.544826i
\(267\) −8.64490e18 2.00038e18i −0.334711 0.0774500i
\(268\) 6.37530e18 0.239565
\(269\) 5.30026e19i 1.93321i −0.256272 0.966605i \(-0.582494\pi\)
0.256272 0.966605i \(-0.417506\pi\)
\(270\) 1.42286e19 1.75172e19i 0.503792 0.620231i
\(271\) 3.19793e19 1.09930 0.549649 0.835396i \(-0.314762\pi\)
0.549649 + 0.835396i \(0.314762\pi\)
\(272\) 1.52079e18i 0.0507595i
\(273\) −5.17119e18 + 2.23480e19i −0.167606 + 0.724333i
\(274\) 1.91749e18 0.0603572
\(275\) 8.15448e18i 0.249307i
\(276\) 2.52240e19 + 5.83666e18i 0.749102 + 0.173337i
\(277\) −2.34299e19 −0.675976 −0.337988 0.941150i \(-0.609746\pi\)
−0.337988 + 0.941150i \(0.609746\pi\)
\(278\) 1.20745e19i 0.338464i
\(279\) 4.42214e19 + 2.16229e19i 1.20448 + 0.588952i
\(280\) 7.36972e18 0.195068
\(281\) 2.11978e19i 0.545305i 0.962113 + 0.272653i \(0.0879010\pi\)
−0.962113 + 0.272653i \(0.912099\pi\)
\(282\) −3.15080e18 + 1.36166e19i −0.0787822 + 0.340468i
\(283\) −1.42061e19 −0.345291 −0.172645 0.984984i \(-0.555231\pi\)
−0.172645 + 0.984984i \(0.555231\pi\)
\(284\) 1.26213e18i 0.0298234i
\(285\) −7.56240e19 1.74989e19i −1.73740 0.402024i
\(286\) −4.33827e19 −0.969143
\(287\) 8.78584e18i 0.190866i
\(288\) −3.67531e18 + 7.51646e18i −0.0776523 + 0.158808i
\(289\) 4.66552e19 0.958776
\(290\) 5.14365e19i 1.02822i
\(291\) 7.69233e18 3.32435e19i 0.149594 0.646491i
\(292\) −4.66020e19 −0.881743
\(293\) 8.88168e19i 1.63514i −0.575832 0.817568i \(-0.695322\pi\)
0.575832 0.817568i \(-0.304678\pi\)
\(294\) 2.92869e19 + 6.77680e18i 0.524680 + 0.121408i
\(295\) −6.30203e19 −1.09876
\(296\) 2.52221e19i 0.428003i
\(297\) −4.22965e19 3.43559e19i −0.698639 0.567480i
\(298\) 1.16901e19 0.187970
\(299\) 1.49586e20i 2.34165i
\(300\) 2.04844e18 8.85261e18i 0.0312214 0.134928i
\(301\) 1.25839e19 0.186759
\(302\) 4.67693e19i 0.675936i
\(303\) 6.48241e19 + 1.49999e19i 0.912421 + 0.211128i
\(304\) 2.87781e19 0.394525
\(305\) 1.01463e19i 0.135491i
\(306\) 9.91476e18 + 4.84800e18i 0.128977 + 0.0630654i
\(307\) −9.48569e19 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(308\) 1.77947e19i 0.219728i
\(309\) 2.64257e19 1.14202e20i 0.317949 1.37406i
\(310\) 9.13739e19 1.07134
\(311\) 1.90403e19i 0.217566i −0.994066 0.108783i \(-0.965305\pi\)
0.994066 0.108783i \(-0.0346953\pi\)
\(312\) −4.70968e19 1.08979e19i −0.524511 0.121368i
\(313\) 1.33772e20 1.45215 0.726075 0.687616i \(-0.241343\pi\)
0.726075 + 0.687616i \(0.241343\pi\)
\(314\) 4.02129e18i 0.0425528i
\(315\) −2.34934e19 + 4.80468e19i −0.242360 + 0.495656i
\(316\) −3.39345e19 −0.341307
\(317\) 1.62985e20i 1.59836i 0.601094 + 0.799178i \(0.294732\pi\)
−0.601094 + 0.799178i \(0.705268\pi\)
\(318\) 1.18250e19 5.11036e19i 0.113080 0.488691i
\(319\) 1.24197e20 1.15821
\(320\) 1.55311e19i 0.141255i
\(321\) 4.63660e19 + 1.07288e19i 0.411301 + 0.0951724i
\(322\) −6.13575e19 −0.530909
\(323\) 3.79605e19i 0.320414i
\(324\) −3.72873e19 4.79223e19i −0.307044 0.394619i
\(325\) 5.24989e19 0.421777
\(326\) 2.15495e19i 0.168926i
\(327\) −1.86680e19 + 8.06766e19i −0.142796 + 0.617114i
\(328\) 1.85155e19 0.138212
\(329\) 3.31225e19i 0.241299i
\(330\) −9.85464e19 2.28030e19i −0.700695 0.162136i
\(331\) −1.82914e20 −1.26947 −0.634736 0.772729i \(-0.718891\pi\)
−0.634736 + 0.772729i \(0.718891\pi\)
\(332\) 5.76006e19i 0.390232i
\(333\) −1.64435e20 8.04035e19i −1.08753 0.531767i
\(334\) 1.32097e20 0.852944
\(335\) 8.58824e19i 0.541434i
\(336\) 4.47011e18 1.93182e19i 0.0275172 0.118919i
\(337\) −3.00874e20 −1.80861 −0.904306 0.426884i \(-0.859611\pi\)
−0.904306 + 0.426884i \(0.859611\pi\)
\(338\) 1.58846e20i 0.932487i
\(339\) 3.39167e20 + 7.84811e19i 1.94454 + 0.449953i
\(340\) 2.04867e19 0.114720
\(341\) 2.20629e20i 1.20678i
\(342\) −9.17396e19 + 1.87619e20i −0.490172 + 1.00246i
\(343\) −1.64779e20 −0.860102
\(344\) 2.65196e19i 0.135238i
\(345\) −7.86263e19 + 3.39795e20i −0.391756 + 1.69303i
\(346\) −7.39183e19 −0.359868
\(347\) 2.75354e20i 1.30995i −0.755650 0.654976i \(-0.772679\pi\)
0.755650 0.654976i \(-0.227321\pi\)
\(348\) 1.34830e20 + 3.11989e19i 0.626835 + 0.145046i
\(349\) 1.22450e20 0.556358 0.278179 0.960529i \(-0.410269\pi\)
0.278179 + 0.960529i \(0.410269\pi\)
\(350\) 2.15340e19i 0.0956271i
\(351\) 2.21185e20 2.72307e20i 0.960061 1.18196i
\(352\) 3.75011e19 0.159112
\(353\) 4.25336e20i 1.76415i 0.471113 + 0.882073i \(0.343852\pi\)
−0.471113 + 0.882073i \(0.656148\pi\)
\(354\) −3.82250e19 + 1.65195e20i −0.154996 + 0.669839i
\(355\) −1.70023e19 −0.0674032
\(356\) 4.43166e19i 0.171777i
\(357\) −2.54821e19 5.89640e18i −0.0965806 0.0223481i
\(358\) 2.42180e20 0.897581
\(359\) 3.68750e20i 1.33652i −0.743927 0.668261i \(-0.767039\pi\)
0.743927 0.668261i \(-0.232961\pi\)
\(360\) −1.01255e20 4.95105e19i −0.358919 0.175500i
\(361\) 4.29892e20 1.49039
\(362\) 1.91641e20i 0.649860i
\(363\) 1.29044e19 5.57680e19i 0.0428039 0.184983i
\(364\) 1.14563e20 0.371736
\(365\) 6.27780e20i 1.99281i
\(366\) −2.65965e19 6.15425e18i −0.0825991 0.0191129i
\(367\) −1.52019e20 −0.461922 −0.230961 0.972963i \(-0.574187\pi\)
−0.230961 + 0.972963i \(0.574187\pi\)
\(368\) 1.29306e20i 0.384447i
\(369\) −5.90241e19 + 1.20712e20i −0.171719 + 0.351187i
\(370\) −3.39769e20 −0.967320
\(371\) 1.24310e20i 0.346349i
\(372\) 5.54229e19 2.39518e20i 0.151128 0.653122i
\(373\) 1.18257e20 0.315614 0.157807 0.987470i \(-0.449558\pi\)
0.157807 + 0.987470i \(0.449558\pi\)
\(374\) 4.94666e19i 0.129223i
\(375\) −3.11289e20 7.20303e19i −0.796001 0.184190i
\(376\) 6.98032e19 0.174732
\(377\) 7.99588e20i 1.95946i
\(378\) 1.11695e20 + 9.07259e19i 0.267978 + 0.217669i
\(379\) −3.06672e20 −0.720378 −0.360189 0.932879i \(-0.617288\pi\)
−0.360189 + 0.932879i \(0.617288\pi\)
\(380\) 3.87673e20i 0.891656i
\(381\) −2.61664e19 + 1.13082e20i −0.0589311 + 0.254679i
\(382\) −1.84310e20 −0.406484
\(383\) 5.53470e20i 1.19537i 0.801730 + 0.597687i \(0.203913\pi\)
−0.801730 + 0.597687i \(0.796087\pi\)
\(384\) 4.07116e19 + 9.42042e18i 0.0861130 + 0.0199260i
\(385\) 2.39715e20 0.496602
\(386\) 5.12136e20i 1.03917i
\(387\) −1.72894e20 8.45397e19i −0.343631 0.168025i
\(388\) −1.70417e20 −0.331786
\(389\) 1.22013e20i 0.232707i 0.993208 + 0.116353i \(0.0371205\pi\)
−0.993208 + 0.116353i \(0.962879\pi\)
\(390\) 1.46807e20 6.34446e20i 0.274302 1.18543i
\(391\) −1.70564e20 −0.312230
\(392\) 1.50134e20i 0.269272i
\(393\) −4.02553e20 9.31482e19i −0.707429 0.163695i
\(394\) −6.71084e19 −0.115560
\(395\) 4.57135e20i 0.771379i
\(396\) −1.19547e20 + 2.44488e20i −0.197686 + 0.404293i
\(397\) −2.64665e20 −0.428916 −0.214458 0.976733i \(-0.568798\pi\)
−0.214458 + 0.976733i \(0.568798\pi\)
\(398\) 2.25575e20i 0.358284i
\(399\) 1.11579e20 4.82203e20i 0.173699 0.750666i
\(400\) −4.53813e19 −0.0692464
\(401\) 4.93340e20i 0.737889i 0.929451 + 0.368945i \(0.120281\pi\)
−0.929451 + 0.368945i \(0.879719\pi\)
\(402\) 2.25123e20 + 5.20920e19i 0.330074 + 0.0763770i
\(403\) 1.42042e21 2.04163
\(404\) 3.32309e20i 0.468265i
\(405\) 6.45566e20 5.02301e20i 0.891868 0.693943i
\(406\) −3.27976e20 −0.444256
\(407\) 8.20398e20i 1.08961i
\(408\) 1.24262e19 5.37016e19i 0.0161829 0.0699369i
\(409\) 8.22840e20 1.05082 0.525411 0.850849i \(-0.323912\pi\)
0.525411 + 0.850849i \(0.323912\pi\)
\(410\) 2.49424e20i 0.312369i
\(411\) 6.77099e19 + 1.56676e19i 0.0831606 + 0.0192428i
\(412\) −5.85438e20 −0.705185
\(413\) 4.01838e20i 0.474734i
\(414\) 8.43011e20 + 4.12205e20i 0.976856 + 0.477651i
\(415\) −7.75944e20 −0.881953
\(416\) 2.41433e20i 0.269185i
\(417\) −9.86600e19 + 4.26373e20i −0.107908 + 0.466339i
\(418\) 9.36066e20 1.00438
\(419\) 1.34475e21i 1.41556i −0.706430 0.707782i \(-0.749696\pi\)
0.706430 0.707782i \(-0.250304\pi\)
\(420\) 2.60237e20 + 6.02173e19i 0.268767 + 0.0621909i
\(421\) −1.13149e21 −1.14655 −0.573277 0.819362i \(-0.694328\pi\)
−0.573277 + 0.819362i \(0.694328\pi\)
\(422\) 2.71777e20i 0.270217i
\(423\) −2.22520e20 + 4.55081e20i −0.217093 + 0.443983i
\(424\) −2.61973e20 −0.250802
\(425\) 5.98613e19i 0.0562386i
\(426\) −1.03128e19 + 4.45680e19i −0.00950819 + 0.0410910i
\(427\) 6.46961e19 0.0585403
\(428\) 2.37687e20i 0.211084i
\(429\) −1.53192e21 3.54476e20i −1.33529 0.308978i
\(430\) −3.57248e20 −0.305648
\(431\) 4.50754e20i 0.378548i −0.981924 0.189274i \(-0.939386\pi\)
0.981924 0.189274i \(-0.0606135\pi\)
\(432\) −1.91198e20 + 2.35389e20i −0.157621 + 0.194051i
\(433\) 9.42632e18 0.00762849 0.00381425 0.999993i \(-0.498786\pi\)
0.00381425 + 0.999993i \(0.498786\pi\)
\(434\) 5.82629e20i 0.462886i
\(435\) −4.20283e20 + 1.81631e21i −0.327814 + 1.41670i
\(436\) 4.13574e20 0.316710
\(437\) 3.22762e21i 2.42678i
\(438\) −1.64560e21 3.80781e20i −1.21487 0.281114i
\(439\) 6.88142e20 0.498841 0.249420 0.968395i \(-0.419760\pi\)
0.249420 + 0.968395i \(0.419760\pi\)
\(440\) 5.05181e20i 0.359605i
\(441\) 9.78799e20 + 4.78601e20i 0.684202 + 0.334553i
\(442\) 3.18468e20 0.218619
\(443\) 7.22543e20i 0.487118i 0.969886 + 0.243559i \(0.0783149\pi\)
−0.969886 + 0.243559i \(0.921685\pi\)
\(444\) −2.06087e20 + 8.90635e20i −0.136454 + 0.589707i
\(445\) −5.96993e20 −0.388230
\(446\) 3.36843e19i 0.0215154i
\(447\) 4.12798e20 + 9.55188e19i 0.258987 + 0.0599278i
\(448\) −9.90314e19 −0.0610307
\(449\) 1.67231e21i 1.01239i 0.862420 + 0.506193i \(0.168948\pi\)
−0.862420 + 0.506193i \(0.831052\pi\)
\(450\) 1.44668e20 2.95863e20i 0.0860343 0.175951i
\(451\) 6.02253e20 0.351857
\(452\) 1.73868e21i 0.997957i
\(453\) 3.82148e20 1.65151e21i 0.215499 0.931310i
\(454\) −4.11885e20 −0.228207
\(455\) 1.54329e21i 0.840151i
\(456\) 1.01621e21 + 2.35144e20i 0.543579 + 0.125781i
\(457\) −3.48956e20 −0.183417 −0.0917087 0.995786i \(-0.529233\pi\)
−0.0917087 + 0.995786i \(0.529233\pi\)
\(458\) 1.44944e21i 0.748644i
\(459\) 3.10495e20 + 2.52204e20i 0.157599 + 0.128012i
\(460\) 1.74190e21 0.868880
\(461\) 2.25305e20i 0.110449i −0.998474 0.0552246i \(-0.982413\pi\)
0.998474 0.0552246i \(-0.0175875\pi\)
\(462\) 1.45399e20 6.28363e20i 0.0700529 0.302743i
\(463\) 1.94832e20 0.0922599 0.0461300 0.998935i \(-0.485311\pi\)
0.0461300 + 0.998935i \(0.485311\pi\)
\(464\) 6.91184e20i 0.321699i
\(465\) 3.22657e21 + 7.46608e20i 1.47611 + 0.341561i
\(466\) 9.02018e20 0.405628
\(467\) 1.22910e21i 0.543317i 0.962394 + 0.271658i \(0.0875720\pi\)
−0.962394 + 0.271658i \(0.912428\pi\)
\(468\) −1.57402e21 7.69647e20i −0.683981 0.334445i
\(469\) −5.47613e20 −0.233933
\(470\) 9.40326e20i 0.394908i
\(471\) 3.28576e19 1.41999e20i 0.0135665 0.0586296i
\(472\) 8.46842e20 0.343769
\(473\) 8.62601e20i 0.344287i
\(474\) −1.19829e21 2.77276e20i −0.470255 0.108814i
\(475\) −1.13277e21 −0.437111
\(476\) 1.30630e20i 0.0495662i
\(477\) 8.35125e20 1.70793e21i 0.311605 0.637271i
\(478\) −2.33856e21 −0.858076
\(479\) 9.86668e19i 0.0356030i −0.999842 0.0178015i \(-0.994333\pi\)
0.999842 0.0178015i \(-0.00566669\pi\)
\(480\) −1.26903e20 + 5.48431e20i −0.0450343 + 0.194622i
\(481\) −5.28176e21 −1.84339
\(482\) 5.65990e20i 0.194282i
\(483\) −2.16664e21 5.01346e20i −0.731492 0.169263i
\(484\) −2.85885e20 −0.0949354
\(485\) 2.29570e21i 0.749863i
\(486\) −9.25109e20 1.99689e21i −0.297237 0.641600i
\(487\) 4.91198e21 1.55248 0.776238 0.630439i \(-0.217125\pi\)
0.776238 + 0.630439i \(0.217125\pi\)
\(488\) 1.36342e20i 0.0423908i
\(489\) 1.76079e20 7.60952e20i 0.0538564 0.232748i
\(490\) 2.02247e21 0.608575
\(491\) 6.30381e21i 1.86617i 0.359657 + 0.933085i \(0.382894\pi\)
−0.359657 + 0.933085i \(0.617106\pi\)
\(492\) 6.53814e20 + 1.51288e20i 0.190429 + 0.0440641i
\(493\) −9.11722e20 −0.261268
\(494\) 6.02643e21i 1.69920i
\(495\) −3.29352e21 1.61043e21i −0.913732 0.446786i
\(496\) −1.22785e21 −0.335190
\(497\) 1.08412e20i 0.0291223i
\(498\) −4.70649e20 + 2.03398e21i −0.124412 + 0.537664i
\(499\) −6.31209e21 −1.64198 −0.820991 0.570941i \(-0.806579\pi\)
−0.820991 + 0.570941i \(0.806579\pi\)
\(500\) 1.59577e21i 0.408517i
\(501\) 4.66456e21 + 1.07935e21i 1.17519 + 0.271932i
\(502\) 2.36922e21 0.587458
\(503\) 4.03528e21i 0.984758i −0.870381 0.492379i \(-0.836127\pi\)
0.870381 0.492379i \(-0.163873\pi\)
\(504\) 3.15695e20 6.45634e20i 0.0758268 0.155075i
\(505\) 4.47657e21 1.05831
\(506\) 4.20594e21i 0.978721i
\(507\) 1.29792e21 5.60913e21i 0.297292 1.28479i
\(508\) 5.79694e20 0.130704
\(509\) 1.68915e21i 0.374908i −0.982273 0.187454i \(-0.939976\pi\)
0.982273 0.187454i \(-0.0600236\pi\)
\(510\) 7.23420e20 + 1.67395e20i 0.158063 + 0.0365747i
\(511\) 4.00293e21 0.861015
\(512\) 2.08701e20i 0.0441942i
\(513\) −4.77250e21 + 5.87555e21i −0.994964 + 1.22493i
\(514\) 1.40069e21 0.287499
\(515\) 7.88649e21i 1.59377i
\(516\) −2.16689e20 + 9.36452e20i −0.0431161 + 0.186332i
\(517\) 2.27049e21 0.444831
\(518\) 2.16648e21i 0.417942i
\(519\) −2.61018e21 6.03980e20i −0.495829 0.114732i
\(520\) −3.25237e21 −0.608378
\(521\) 3.87836e21i 0.714409i 0.934026 + 0.357204i \(0.116270\pi\)
−0.934026 + 0.357204i \(0.883730\pi\)
\(522\) 4.50617e21 + 2.20337e21i 0.817416 + 0.399690i
\(523\) 1.01818e22 1.81891 0.909455 0.415803i \(-0.136499\pi\)
0.909455 + 0.415803i \(0.136499\pi\)
\(524\) 2.06362e21i 0.363060i
\(525\) −1.75953e20 + 7.60404e20i −0.0304875 + 0.131756i
\(526\) 1.11451e20 0.0190194
\(527\) 1.61962e21i 0.272225i
\(528\) 1.32423e21 + 3.06418e20i 0.219225 + 0.0507274i
\(529\) −8.36976e21 −1.36480
\(530\) 3.52907e21i 0.566831i
\(531\) −2.69958e21 + 5.52098e21i −0.427111 + 0.873494i
\(532\) −2.47193e21 −0.385250
\(533\) 3.87733e21i 0.595272i
\(534\) −3.62107e20 + 1.56489e21i −0.0547654 + 0.236676i
\(535\) 3.20191e21 0.477066
\(536\) 1.15405e21i 0.169398i
\(537\) 8.55178e21 + 1.97883e21i 1.23669 + 0.286163i
\(538\) −9.59449e21 −1.36699
\(539\) 4.88341e21i 0.685509i
\(540\) −3.17094e21 2.57565e21i −0.438570 0.356235i
\(541\) −1.11108e22 −1.51414 −0.757070 0.653333i \(-0.773370\pi\)
−0.757070 + 0.653333i \(0.773370\pi\)
\(542\) 5.78888e21i 0.777320i
\(543\) −1.56588e21 + 6.76717e21i −0.207186 + 0.895383i
\(544\) −2.75292e20 −0.0358924
\(545\) 5.57130e21i 0.715788i
\(546\) 4.04543e21 + 9.36086e20i 0.512181 + 0.118515i
\(547\) −1.91151e21 −0.238494 −0.119247 0.992865i \(-0.538048\pi\)
−0.119247 + 0.992865i \(0.538048\pi\)
\(548\) 3.47103e20i 0.0426790i
\(549\) −8.88881e20 4.34634e20i −0.107712 0.0526678i
\(550\) −1.47612e21 −0.176287
\(551\) 1.72527e22i 2.03069i
\(552\) 1.05655e21 4.56603e21i 0.122568 0.529695i
\(553\) 2.91484e21 0.333283
\(554\) 4.24126e21i 0.477987i
\(555\) −1.19978e22 2.77622e21i −1.33278 0.308397i
\(556\) 2.18573e21 0.239330
\(557\) 1.06013e22i 1.14424i 0.820170 + 0.572120i \(0.193879\pi\)
−0.820170 + 0.572120i \(0.806121\pi\)
\(558\) 3.91416e21 8.00493e21i 0.416452 0.851695i
\(559\) −5.55346e21 −0.582465
\(560\) 1.33406e21i 0.137934i
\(561\) 4.04187e20 1.74675e21i 0.0411983 0.178044i
\(562\) 3.83721e21 0.385589
\(563\) 1.37945e22i 1.36659i 0.730141 + 0.683297i \(0.239455\pi\)
−0.730141 + 0.683297i \(0.760545\pi\)
\(564\) 2.46487e21 + 5.70356e20i 0.240747 + 0.0557074i
\(565\) 2.34219e22 2.25546
\(566\) 2.57159e21i 0.244157i
\(567\) 3.20283e21 + 4.11634e21i 0.299826 + 0.385342i
\(568\) 2.28470e20 0.0210884
\(569\) 1.17330e22i 1.06785i −0.845531 0.533926i \(-0.820716\pi\)
0.845531 0.533926i \(-0.179284\pi\)
\(570\) −3.16764e21 + 1.36894e22i −0.284274 + 1.22853i
\(571\) 6.61823e21 0.585670 0.292835 0.956163i \(-0.405401\pi\)
0.292835 + 0.956163i \(0.405401\pi\)
\(572\) 7.85310e21i 0.685288i
\(573\) −6.50832e21 1.50598e21i −0.560057 0.129594i
\(574\) −1.59041e21 −0.134963
\(575\) 5.08976e21i 0.425946i
\(576\) 1.36063e21 + 6.65302e20i 0.112295 + 0.0549084i
\(577\) 1.60264e22 1.30446 0.652228 0.758023i \(-0.273835\pi\)
0.652228 + 0.758023i \(0.273835\pi\)
\(578\) 8.44549e21i 0.677957i
\(579\) 4.18462e21 1.80844e22i 0.331305 1.43178i
\(580\) 9.31101e21 0.727064
\(581\) 4.94766e21i 0.381058i
\(582\) −6.01771e21 1.39246e21i −0.457138 0.105779i
\(583\) −8.52120e21 −0.638488
\(584\) 8.43587e21i 0.623486i
\(585\) 1.03680e22 2.12038e22i 0.755871 1.54585i
\(586\) −1.60776e22 −1.15622
\(587\) 3.97771e21i 0.282181i −0.989997 0.141091i \(-0.954939\pi\)
0.989997 0.141091i \(-0.0450609\pi\)
\(588\) 1.22673e21 5.30150e21i 0.0858482 0.371005i
\(589\) −3.06483e22 −2.11585
\(590\) 1.14079e22i 0.776944i
\(591\) −2.36971e21 5.48337e20i −0.159219 0.0368424i
\(592\) 4.56568e21 0.302644
\(593\) 1.12212e22i 0.733839i 0.930253 + 0.366919i \(0.119588\pi\)
−0.930253 + 0.366919i \(0.880412\pi\)
\(594\) −6.21909e21 + 7.65648e21i −0.401269 + 0.494012i
\(595\) −1.75972e21 −0.112023
\(596\) 2.11614e21i 0.132915i
\(597\) −1.84316e21 + 7.96545e21i −0.114227 + 0.493646i
\(598\) 2.70780e22 1.65580
\(599\) 1.31221e22i 0.791749i 0.918305 + 0.395874i \(0.129558\pi\)
−0.918305 + 0.395874i \(0.870442\pi\)
\(600\) −1.60249e21 3.70807e20i −0.0954083 0.0220769i
\(601\) −1.55544e22 −0.913816 −0.456908 0.889514i \(-0.651043\pi\)
−0.456908 + 0.889514i \(0.651043\pi\)
\(602\) 2.27792e21i 0.132059i
\(603\) 7.52384e21 + 3.67892e21i 0.430429 + 0.210466i
\(604\) −8.46615e21 −0.477959
\(605\) 3.85118e21i 0.214561i
\(606\) 2.71527e21 1.17344e22i 0.149290 0.645179i
\(607\) −1.22510e22 −0.664756 −0.332378 0.943146i \(-0.607851\pi\)
−0.332378 + 0.943146i \(0.607851\pi\)
\(608\) 5.20940e21i 0.278971i
\(609\) −1.15814e22 2.67986e21i −0.612100 0.141636i
\(610\) −1.83668e21 −0.0958063
\(611\) 1.46175e22i 0.752564i
\(612\) 8.77582e20 1.79476e21i 0.0445940 0.0912002i
\(613\) −6.85336e21 −0.343732 −0.171866 0.985120i \(-0.554980\pi\)
−0.171866 + 0.985120i \(0.554980\pi\)
\(614\) 1.71709e22i 0.850055i
\(615\) −2.03802e21 + 8.80759e21i −0.0995882 + 0.430384i
\(616\) −3.22119e21 −0.155371
\(617\) 2.44104e22i 1.16223i −0.813820 0.581117i \(-0.802616\pi\)
0.813820 0.581117i \(-0.197384\pi\)
\(618\) −2.06728e22 4.78356e21i −0.971609 0.224824i
\(619\) 3.66015e22 1.69814 0.849070 0.528281i \(-0.177163\pi\)
0.849070 + 0.528281i \(0.177163\pi\)
\(620\) 1.65404e22i 0.757554i
\(621\) 2.64001e22 + 2.14438e22i 1.19364 + 0.969549i
\(622\) −3.44666e21 −0.153842
\(623\) 3.80662e21i 0.167739i
\(624\) −1.97273e21 + 8.52543e21i −0.0858205 + 0.370885i
\(625\) −2.79458e22 −1.20026
\(626\) 2.42154e22i 1.02682i
\(627\) 3.30541e22 + 7.64851e21i 1.38384 + 0.320211i
\(628\) −7.27931e20 −0.0300894
\(629\) 6.02247e21i 0.245793i
\(630\) 8.69740e21 + 4.25275e21i 0.350482 + 0.171374i
\(631\) 1.59443e22 0.634413 0.317206 0.948357i \(-0.397255\pi\)
0.317206 + 0.948357i \(0.397255\pi\)
\(632\) 6.14280e21i 0.241340i
\(633\) −2.22067e21 + 9.59692e21i −0.0861497 + 0.372308i
\(634\) 2.95034e22 1.13021
\(635\) 7.80912e21i 0.295401i
\(636\) −9.25073e21 2.14056e21i −0.345557 0.0799596i
\(637\) 3.14396e22 1.15974
\(638\) 2.24821e22i 0.818977i
\(639\) −7.28322e20 + 1.48951e21i −0.0262009 + 0.0535841i
\(640\) 2.81143e21 0.0998822
\(641\) 4.87647e22i 1.71097i −0.517831 0.855483i \(-0.673260\pi\)
0.517831 0.855483i \(-0.326740\pi\)
\(642\) 1.94212e21 8.39315e21i 0.0672971 0.290834i
\(643\) −3.78640e22 −1.29580 −0.647900 0.761725i \(-0.724353\pi\)
−0.647900 + 0.761725i \(0.724353\pi\)
\(644\) 1.11069e22i 0.375410i
\(645\) −1.26150e22 2.91904e21i −0.421125 0.0974456i
\(646\) −6.87158e21 −0.226567
\(647\) 2.51160e22i 0.817932i 0.912550 + 0.408966i \(0.134110\pi\)
−0.912550 + 0.408966i \(0.865890\pi\)
\(648\) −8.67487e21 + 6.74972e21i −0.279038 + 0.217113i
\(649\) 2.75452e22 0.875162
\(650\) 9.50331e21i 0.298241i
\(651\) −4.76061e21 + 2.05736e22i −0.147576 + 0.637769i
\(652\) −3.90088e21 −0.119449
\(653\) 4.06843e22i 1.23061i 0.788289 + 0.615306i \(0.210967\pi\)
−0.788289 + 0.615306i \(0.789033\pi\)
\(654\) 1.46040e22 + 3.37928e21i 0.436365 + 0.100972i
\(655\) −2.77992e22 −0.820544
\(656\) 3.35166e21i 0.0977304i
\(657\) −5.49976e22 2.68921e22i −1.58424 0.774642i
\(658\) −5.99582e21 −0.170624
\(659\) 2.10016e22i 0.590432i −0.955431 0.295216i \(-0.904608\pi\)
0.955431 0.295216i \(-0.0953916\pi\)
\(660\) −4.12778e21 + 1.78388e22i −0.114648 + 0.495466i
\(661\) 3.87747e22 1.06399 0.531994 0.846748i \(-0.321443\pi\)
0.531994 + 0.846748i \(0.321443\pi\)
\(662\) 3.31110e22i 0.897652i
\(663\) 1.12457e22 + 2.60217e21i 0.301215 + 0.0696993i
\(664\) 1.04268e22 0.275935
\(665\) 3.32996e22i 0.870694i
\(666\) −1.45546e22 + 2.97659e22i −0.376016 + 0.768999i
\(667\) −7.75199e22 −1.97882
\(668\) 2.39121e22i 0.603122i
\(669\) 2.75231e20 1.18945e21i 0.00685944 0.0296440i
\(670\) 1.55464e22 0.382852
\(671\) 4.43479e21i 0.107918i
\(672\) −3.49697e21 8.09176e20i −0.0840887 0.0194576i
\(673\) 1.98456e22 0.471568 0.235784 0.971805i \(-0.424234\pi\)
0.235784 + 0.971805i \(0.424234\pi\)
\(674\) 5.44640e22i 1.27888i
\(675\) 7.52594e21 9.26538e21i 0.174635 0.214997i
\(676\) −2.87542e22 −0.659368
\(677\) 3.60090e22i 0.816022i 0.912977 + 0.408011i \(0.133777\pi\)
−0.912977 + 0.408011i \(0.866223\pi\)
\(678\) 1.42066e22 6.13958e22i 0.318165 1.37499i
\(679\) 1.46381e22 0.323987
\(680\) 3.70849e21i 0.0811195i
\(681\) −1.45444e22 3.36547e21i −0.314425 0.0727560i
\(682\) −3.99381e22 −0.853322
\(683\) 4.37055e22i 0.922935i −0.887157 0.461467i \(-0.847323\pi\)
0.887157 0.461467i \(-0.152677\pi\)
\(684\) 3.39626e22 + 1.66067e22i 0.708847 + 0.346604i
\(685\) 4.67586e21 0.0964577
\(686\) 2.98283e22i 0.608184i
\(687\) 1.18432e22 5.11821e22i 0.238680 1.03149i
\(688\) 4.80055e21 0.0956277
\(689\) 5.48599e22i 1.08019i
\(690\) 6.15094e22 + 1.42329e22i 1.19715 + 0.277013i
\(691\) 2.56278e22 0.493046 0.246523 0.969137i \(-0.420712\pi\)
0.246523 + 0.969137i \(0.420712\pi\)
\(692\) 1.33806e22i 0.254465i
\(693\) 1.02686e22 2.10005e22i 0.193039 0.394788i
\(694\) −4.98444e22 −0.926276
\(695\) 2.94441e22i 0.540904i
\(696\) 5.64760e21 2.44069e22i 0.102563 0.443240i
\(697\) −4.42109e21 −0.0793719
\(698\) 2.21658e22i 0.393404i
\(699\) 3.18518e22 + 7.37031e21i 0.558878 + 0.129321i
\(700\) 3.89808e21 0.0676186
\(701\) 1.07149e23i 1.83756i 0.394765 + 0.918782i \(0.370826\pi\)
−0.394765 + 0.918782i \(0.629174\pi\)
\(702\) −4.92928e22 4.00388e22i −0.835769 0.678866i
\(703\) 1.13964e23 1.91041
\(704\) 6.78842e21i 0.112509i
\(705\) −7.68332e21 + 3.32045e22i −0.125903 + 0.544107i
\(706\) 7.69940e22 1.24744
\(707\) 2.85440e22i 0.457257i
\(708\) 2.99035e22 + 6.91947e21i 0.473648 + 0.109599i
\(709\) 1.93543e22 0.303115 0.151557 0.988448i \(-0.451571\pi\)
0.151557 + 0.988448i \(0.451571\pi\)
\(710\) 3.07774e21i 0.0476613i
\(711\) −4.00479e22 1.95822e22i −0.613230 0.299850i
\(712\) 8.02215e21 0.121465
\(713\) 1.37709e23i 2.06180i
\(714\) −1.06736e21 + 4.61276e21i −0.0158025 + 0.0682928i
\(715\) −1.05790e23 −1.54880
\(716\) 4.38392e22i 0.634685i
\(717\) −8.25787e22 1.91082e22i −1.18226 0.273568i
\(718\) −6.67508e22 −0.945064
\(719\) 1.30967e23i 1.83370i −0.399227 0.916852i \(-0.630721\pi\)
0.399227 0.916852i \(-0.369279\pi\)
\(720\) −8.96235e21 + 1.83291e22i −0.124097 + 0.253794i
\(721\) 5.02868e22 0.688607
\(722\) 7.78187e22i 1.05387i
\(723\) −4.62465e21 + 1.99861e22i −0.0619402 + 0.267683i
\(724\) 3.46907e22 0.459520
\(725\) 2.72064e22i 0.356424i
\(726\) −1.00951e22 2.33594e21i −0.130803 0.0302669i
\(727\) −8.27839e22 −1.06089 −0.530445 0.847719i \(-0.677975\pi\)
−0.530445 + 0.847719i \(0.677975\pi\)
\(728\) 2.07382e22i 0.262857i
\(729\) −1.63508e22 7.80726e22i −0.204983 0.978765i
\(730\) −1.13640e23 −1.40913
\(731\) 6.33228e21i 0.0776642i
\(732\) −1.11404e21 + 4.81447e21i −0.0135149 + 0.0584063i
\(733\) 1.45000e22 0.173994 0.0869972 0.996209i \(-0.472273\pi\)
0.0869972 + 0.996209i \(0.472273\pi\)
\(734\) 2.75183e22i 0.326628i
\(735\) 7.14170e22 + 1.65254e22i 0.838500 + 0.194023i
\(736\) −2.34069e22 −0.271845
\(737\) 3.75379e22i 0.431251i
\(738\) 2.18511e22 + 1.06845e22i 0.248327 + 0.121424i
\(739\) 7.61614e22 0.856208 0.428104 0.903729i \(-0.359182\pi\)
0.428104 + 0.903729i \(0.359182\pi\)
\(740\) 6.15048e22i 0.683998i
\(741\) −4.92414e22 + 2.12804e23i −0.541733 + 2.34117i
\(742\) 2.25025e22 0.244906
\(743\) 4.12674e22i 0.444321i −0.975010 0.222160i \(-0.928689\pi\)
0.975010 0.222160i \(-0.0713109\pi\)
\(744\) −4.33574e22 1.00326e22i −0.461827 0.106864i
\(745\) 2.85067e22 0.300398
\(746\) 2.14068e22i 0.223173i
\(747\) −3.32389e22 + 6.79776e22i −0.342832 + 0.701134i
\(748\) −8.95441e21 −0.0913744
\(749\) 2.04164e22i 0.206122i
\(750\) −1.30389e22 + 5.63493e22i −0.130242 + 0.562858i
\(751\) −9.47521e22 −0.936417 −0.468209 0.883618i \(-0.655100\pi\)
−0.468209 + 0.883618i \(0.655100\pi\)
\(752\) 1.26357e22i 0.123554i
\(753\) 8.36614e22 + 1.93587e22i 0.809404 + 0.187291i
\(754\) 1.44741e23 1.38554
\(755\) 1.14048e23i 1.08022i
\(756\) 1.64231e22 2.02189e22i 0.153915 0.189489i
\(757\) 6.67430e22 0.618926 0.309463 0.950911i \(-0.399851\pi\)
0.309463 + 0.950911i \(0.399851\pi\)
\(758\) 5.55136e22i 0.509384i
\(759\) 3.43664e22 1.48519e23i 0.312032 1.34849i
\(760\) 7.01764e22 0.630496
\(761\) 2.20313e23i 1.95867i −0.202234 0.979337i \(-0.564820\pi\)
0.202234 0.979337i \(-0.435180\pi\)
\(762\) 2.04700e22 + 4.73663e21i 0.180085 + 0.0416706i
\(763\) −3.55244e22 −0.309265
\(764\) 3.33638e22i 0.287427i
\(765\) 2.41774e22 + 1.18220e22i 0.206119 + 0.100786i
\(766\) 1.00189e23 0.845257
\(767\) 1.77337e23i 1.48060i
\(768\) 1.70528e21 7.36960e21i 0.0140898 0.0608911i
\(769\) −1.14604e23 −0.937108 −0.468554 0.883435i \(-0.655225\pi\)
−0.468554 + 0.883435i \(0.655225\pi\)
\(770\) 4.33930e22i 0.351151i
\(771\) 4.94607e22 + 1.14449e22i 0.396118 + 0.0916593i
\(772\) −9.27066e22 −0.734805
\(773\) 1.02991e23i 0.807913i