Properties

Label 3.17.b.a.2.3
Level 3
Weight 17
Character 3.2
Analytic conductor 4.870
Analytic rank 0
Dimension 4
CM No
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: No
Analytic conductor: \(4.8697363157\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 3^{8} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 2.3
Root \(33.1293i\)
Character \(\chi\) = 3.2
Dual form 3.17.b.a.2.2

$q$-expansion

\(f(q)\) \(=\) \(q+198.776i q^{2} +(4343.70 - 4917.21i) q^{3} +26024.2 q^{4} +482304. i q^{5} +(977423. + 863422. i) q^{6} +5.53804e6 q^{7} +1.81999e7i q^{8} +(-5.31128e6 - 4.27178e7i) q^{9} +O(q^{10})\) \(q+198.776i q^{2} +(4343.70 - 4917.21i) q^{3} +26024.2 q^{4} +482304. i q^{5} +(977423. + 863422. i) q^{6} +5.53804e6 q^{7} +1.81999e7i q^{8} +(-5.31128e6 - 4.27178e7i) q^{9} -9.58704e7 q^{10} -1.03813e8i q^{11} +(1.13041e8 - 1.27967e8i) q^{12} -7.54564e7 q^{13} +1.10083e9i q^{14} +(2.37159e9 + 2.09499e9i) q^{15} -1.91219e9 q^{16} -7.90639e9i q^{17} +(8.49126e9 - 1.05575e9i) q^{18} -3.27620e10 q^{19} +1.25516e10i q^{20} +(2.40556e10 - 2.72317e10i) q^{21} +2.06354e10 q^{22} +4.02817e10i q^{23} +(8.94931e10 + 7.90551e10i) q^{24} -8.00297e10 q^{25} -1.49989e10i q^{26} +(-2.33123e11 - 1.59437e11i) q^{27} +1.44123e11 q^{28} -6.12299e11i q^{29} +(-4.16432e11 + 4.71416e11i) q^{30} +5.76962e11 q^{31} +8.12655e11i q^{32} +(-5.10469e11 - 4.50931e11i) q^{33} +1.57160e12 q^{34} +2.67102e12i q^{35} +(-1.38222e11 - 1.11170e12i) q^{36} -2.03746e11 q^{37} -6.51230e12i q^{38} +(-3.27760e11 + 3.71035e11i) q^{39} -8.77792e12 q^{40} +2.51630e12i q^{41} +(5.41300e12 + 4.78166e12i) q^{42} +2.81005e12 q^{43} -2.70164e12i q^{44} +(2.06030e13 - 2.56165e12i) q^{45} -8.00702e12 q^{46} +1.80566e13i q^{47} +(-8.30597e12 + 9.40263e12i) q^{48} -2.56309e12 q^{49} -1.59080e13i q^{50} +(-3.88774e13 - 3.43430e13i) q^{51} -1.96369e12 q^{52} -2.59324e13i q^{53} +(3.16921e13 - 4.63392e13i) q^{54} +5.00693e13 q^{55} +1.00792e14i q^{56} +(-1.42308e14 + 1.61098e14i) q^{57} +1.21710e14 q^{58} -1.63379e14i q^{59} +(6.17188e13 + 5.45203e13i) q^{60} +7.04936e13 q^{61} +1.14686e14i q^{62} +(-2.94141e13 - 2.36573e14i) q^{63} -2.86853e14 q^{64} -3.63930e13i q^{65} +(8.96341e13 - 1.01469e14i) q^{66} -1.75368e14 q^{67} -2.05757e14i q^{68} +(1.98074e14 + 1.74972e14i) q^{69} -5.30934e14 q^{70} +6.72953e14i q^{71} +(7.77462e14 - 9.66650e13i) q^{72} +1.04423e15 q^{73} -4.04998e13i q^{74} +(-3.47625e14 + 3.93523e14i) q^{75} -8.52605e14 q^{76} -5.74918e14i q^{77} +(-7.37528e13 - 6.51507e13i) q^{78} +4.55899e13 q^{79} -9.22256e14i q^{80} +(-1.79660e15 + 4.53772e14i) q^{81} -5.00180e14 q^{82} -3.65326e14i q^{83} +(6.26027e14 - 7.08683e14i) q^{84} +3.81329e15 q^{85} +5.58570e14i q^{86} +(-3.01081e15 - 2.65964e15i) q^{87} +1.88938e15 q^{88} +6.68789e15i q^{89} +(5.09195e14 + 4.09537e15i) q^{90} -4.17880e14 q^{91} +1.04830e15i q^{92} +(2.50615e15 - 2.83704e15i) q^{93} -3.58921e15 q^{94} -1.58013e16i q^{95} +(3.99600e15 + 3.52993e15i) q^{96} -5.40349e15 q^{97} -5.09480e14i q^{98} +(-4.43465e15 + 5.51378e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} + O(q^{10}) \) \( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} - 18646560q^{10} + 572494608q^{12} - 1580730424q^{13} + 6829958880q^{15} - 14561268608q^{16} + 42304978080q^{18} - 56117116360q^{19} + 124455437064q^{21} - 173545812000q^{22} + 100515572352q^{24} - 8074048700q^{25} - 317983667652q^{27} + 746852001056q^{28} - 1762329117600q^{30} + 2471781156248q^{31} - 3610697951520q^{33} + 2721261612672q^{34} - 1219654126512q^{36} + 370563213896q^{37} + 7022170227384q^{39} - 11795287092480q^{40} + 27587883687840q^{42} - 28065022062664q^{43} + 18795326443200q^{45} - 43994579504832q^{46} + 41041959355008q^{48} + 29478262537164q^{49} - 82841575222656q^{51} + 42193089120416q^{52} - 107063660756304q^{54} + 290253653236800q^{55} - 335129108488344q^{57} + 8796421982880q^{58} + 56126440892160q^{60} + 362269793083208q^{61} - 266698363786344q^{63} - 653949742779392q^{64} + 1332768950045280q^{66} - 26774405363464q^{67} + 58823173290816q^{69} - 2292362286177600q^{70} + 2397649754476800q^{72} + 317628887539976q^{73} - 1511365865026500q^{75} - 2008642200508384q^{76} + 1538179445855520q^{78} + 4794017165184920q^{79} - 6444192852054396q^{81} + 1589112481320000q^{82} - 1210523902199136q^{84} + 7999994092573440q^{85} - 8850169595242080q^{87} - 3370289894104320q^{88} + 3549134645307360q^{90} + 9328538231657008q^{91} - 2064207396761784q^{93} - 12859596129667968q^{94} + 15507630559798272q^{96} - 13833795002601784q^{97} + 18943177097338560q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 198.776i 0.776468i 0.921561 + 0.388234i \(0.126915\pi\)
−0.921561 + 0.388234i \(0.873085\pi\)
\(3\) 4343.70 4917.21i 0.662048 0.749461i
\(4\) 26024.2 0.397098
\(5\) 482304.i 1.23470i 0.786689 + 0.617350i \(0.211794\pi\)
−0.786689 + 0.617350i \(0.788206\pi\)
\(6\) 977423. + 863422.i 0.581933 + 0.514059i
\(7\) 5.53804e6 0.960664 0.480332 0.877087i \(-0.340516\pi\)
0.480332 + 0.877087i \(0.340516\pi\)
\(8\) 1.81999e7i 1.08480i
\(9\) −5.31128e6 4.27178e7i −0.123384 0.992359i
\(10\) −9.58704e7 −0.958704
\(11\) 1.03813e8i 0.484293i −0.970240 0.242147i \(-0.922148\pi\)
0.970240 0.242147i \(-0.0778515\pi\)
\(12\) 1.13041e8 1.27967e8i 0.262898 0.297609i
\(13\) −7.54564e7 −0.0925016 −0.0462508 0.998930i \(-0.514727\pi\)
−0.0462508 + 0.998930i \(0.514727\pi\)
\(14\) 1.10083e9i 0.745925i
\(15\) 2.37159e9 + 2.09499e9i 0.925359 + 0.817431i
\(16\) −1.91219e9 −0.445216
\(17\) 7.90639e9i 1.13341i −0.823921 0.566705i \(-0.808218\pi\)
0.823921 0.566705i \(-0.191782\pi\)
\(18\) 8.49126e9 1.05575e9i 0.770535 0.0958038i
\(19\) −3.27620e10 −1.92904 −0.964521 0.264004i \(-0.914957\pi\)
−0.964521 + 0.264004i \(0.914957\pi\)
\(20\) 1.25516e10i 0.490296i
\(21\) 2.40556e10 2.72317e10i 0.636006 0.719980i
\(22\) 2.06354e10 0.376038
\(23\) 4.02817e10i 0.514381i 0.966361 + 0.257191i \(0.0827968\pi\)
−0.966361 + 0.257191i \(0.917203\pi\)
\(24\) 8.94931e10 + 7.90551e10i 0.813017 + 0.718191i
\(25\) −8.00297e10 −0.524483
\(26\) 1.49989e10i 0.0718245i
\(27\) −2.33123e11 1.59437e11i −0.825421 0.564518i
\(28\) 1.44123e11 0.381477
\(29\) 6.12299e11i 1.22400i −0.790859 0.611998i \(-0.790366\pi\)
0.790859 0.611998i \(-0.209634\pi\)
\(30\) −4.16432e11 + 4.71416e11i −0.634709 + 0.718512i
\(31\) 5.76962e11 0.676477 0.338239 0.941060i \(-0.390169\pi\)
0.338239 + 0.941060i \(0.390169\pi\)
\(32\) 8.12655e11i 0.739106i
\(33\) −5.10469e11 4.50931e11i −0.362959 0.320626i
\(34\) 1.57160e12 0.880056
\(35\) 2.67102e12i 1.18613i
\(36\) −1.38222e11 1.11170e12i −0.0489955 0.394063i
\(37\) −2.03746e11 −0.0580063 −0.0290032 0.999579i \(-0.509233\pi\)
−0.0290032 + 0.999579i \(0.509233\pi\)
\(38\) 6.51230e12i 1.49784i
\(39\) −3.27760e11 + 3.71035e11i −0.0612405 + 0.0693264i
\(40\) −8.77792e12 −1.33940
\(41\) 2.51630e12i 0.315131i 0.987509 + 0.157566i \(0.0503646\pi\)
−0.987509 + 0.157566i \(0.949635\pi\)
\(42\) 5.41300e12 + 4.78166e12i 0.559042 + 0.493838i
\(43\) 2.81005e12 0.240418 0.120209 0.992749i \(-0.461644\pi\)
0.120209 + 0.992749i \(0.461644\pi\)
\(44\) 2.70164e12i 0.192312i
\(45\) 2.06030e13 2.56165e12i 1.22527 0.152342i
\(46\) −8.00702e12 −0.399400
\(47\) 1.80566e13i 0.758320i 0.925331 + 0.379160i \(0.123787\pi\)
−0.925331 + 0.379160i \(0.876213\pi\)
\(48\) −8.30597e12 + 9.40263e12i −0.294754 + 0.333672i
\(49\) −2.56309e12 −0.0771250
\(50\) 1.59080e13i 0.407244i
\(51\) −3.88774e13 3.43430e13i −0.849447 0.750372i
\(52\) −1.96369e12 −0.0367322
\(53\) 2.59324e13i 0.416519i −0.978074 0.208260i \(-0.933220\pi\)
0.978074 0.208260i \(-0.0667799\pi\)
\(54\) 3.16921e13 4.63392e13i 0.438330 0.640913i
\(55\) 5.00693e13 0.597957
\(56\) 1.00792e14i 1.04213i
\(57\) −1.42308e14 + 1.61098e14i −1.27712 + 1.44574i
\(58\) 1.21710e14 0.950393
\(59\) 1.63379e14i 1.11270i −0.830947 0.556352i \(-0.812201\pi\)
0.830947 0.556352i \(-0.187799\pi\)
\(60\) 6.17188e13 + 5.45203e13i 0.367458 + 0.324600i
\(61\) 7.04936e13 0.367715 0.183857 0.982953i \(-0.441142\pi\)
0.183857 + 0.982953i \(0.441142\pi\)
\(62\) 1.14686e14i 0.525263i
\(63\) −2.94141e13 2.36573e14i −0.118531 0.953323i
\(64\) −2.86853e14 −1.01911
\(65\) 3.63930e13i 0.114212i
\(66\) 8.96341e13 1.01469e14i 0.248955 0.281826i
\(67\) −1.75368e14 −0.431869 −0.215934 0.976408i \(-0.569280\pi\)
−0.215934 + 0.976408i \(0.569280\pi\)
\(68\) 2.05757e14i 0.450074i
\(69\) 1.98074e14 + 1.74972e14i 0.385509 + 0.340545i
\(70\) −5.30934e14 −0.920993
\(71\) 6.72953e14i 1.04212i 0.853520 + 0.521060i \(0.174463\pi\)
−0.853520 + 0.521060i \(0.825537\pi\)
\(72\) 7.77462e14 9.66650e13i 1.07651 0.133847i
\(73\) 1.04423e15 1.29483 0.647416 0.762137i \(-0.275850\pi\)
0.647416 + 0.762137i \(0.275850\pi\)
\(74\) 4.04998e13i 0.0450401i
\(75\) −3.47625e14 + 3.93523e14i −0.347233 + 0.393079i
\(76\) −8.52605e14 −0.766018
\(77\) 5.74918e14i 0.465243i
\(78\) −7.37528e13 6.51507e13i −0.0538297 0.0475513i
\(79\) 4.55899e13 0.0300505 0.0150252 0.999887i \(-0.495217\pi\)
0.0150252 + 0.999887i \(0.495217\pi\)
\(80\) 9.22256e14i 0.549708i
\(81\) −1.79660e15 + 4.53772e14i −0.969553 + 0.244883i
\(82\) −5.00180e14 −0.244689
\(83\) 3.65326e14i 0.162202i −0.996706 0.0811009i \(-0.974156\pi\)
0.996706 0.0811009i \(-0.0258436\pi\)
\(84\) 6.26027e14 7.08683e14i 0.252556 0.285902i
\(85\) 3.81329e15 1.39942
\(86\) 5.58570e14i 0.186677i
\(87\) −3.01081e15 2.65964e15i −0.917337 0.810344i
\(88\) 1.88938e15 0.525362
\(89\) 6.68789e15i 1.69891i 0.527665 + 0.849453i \(0.323068\pi\)
−0.527665 + 0.849453i \(0.676932\pi\)
\(90\) 5.09195e14 + 4.09537e15i 0.118289 + 0.951379i
\(91\) −4.17880e14 −0.0888630
\(92\) 1.04830e15i 0.204260i
\(93\) 2.50615e15 2.83704e15i 0.447861 0.506994i
\(94\) −3.58921e15 −0.588811
\(95\) 1.58013e16i 2.38179i
\(96\) 3.99600e15 + 3.52993e15i 0.553931 + 0.489324i
\(97\) −5.40349e15 −0.689446 −0.344723 0.938704i \(-0.612027\pi\)
−0.344723 + 0.938704i \(0.612027\pi\)
\(98\) 5.09480e14i 0.0598851i
\(99\) −4.43465e15 + 5.51378e14i −0.480593 + 0.0597541i
\(100\) −2.08271e15 −0.208271
\(101\) 1.22011e16i 1.12675i 0.826202 + 0.563374i \(0.190497\pi\)
−0.826202 + 0.563374i \(0.809503\pi\)
\(102\) 6.82655e15 7.72789e15i 0.582640 0.659568i
\(103\) −9.05312e15 −0.714662 −0.357331 0.933978i \(-0.616313\pi\)
−0.357331 + 0.933978i \(0.616313\pi\)
\(104\) 1.37330e15i 0.100346i
\(105\) 1.31340e16 + 1.16021e16i 0.888959 + 0.785276i
\(106\) 5.15473e15 0.323414
\(107\) 6.69296e14i 0.0389537i −0.999810 0.0194768i \(-0.993800\pi\)
0.999810 0.0194768i \(-0.00620006\pi\)
\(108\) −6.06684e15 4.14921e15i −0.327773 0.224169i
\(109\) 2.32335e16 1.16601 0.583004 0.812469i \(-0.301877\pi\)
0.583004 + 0.812469i \(0.301877\pi\)
\(110\) 9.95256e15i 0.464294i
\(111\) −8.85012e14 + 1.00186e15i −0.0384030 + 0.0434735i
\(112\) −1.05898e16 −0.427703
\(113\) 7.46562e15i 0.280827i 0.990093 + 0.140413i \(0.0448431\pi\)
−0.990093 + 0.140413i \(0.955157\pi\)
\(114\) −3.20224e16 2.82875e16i −1.12257 0.991642i
\(115\) −1.94280e16 −0.635106
\(116\) 1.59346e16i 0.486046i
\(117\) 4.00770e14 + 3.22333e15i 0.0114132 + 0.0917948i
\(118\) 3.24757e16 0.863979
\(119\) 4.37859e16i 1.08883i
\(120\) −3.81286e16 + 4.31629e16i −0.886750 + 1.00383i
\(121\) 3.51727e16 0.765460
\(122\) 1.40124e16i 0.285519i
\(123\) 1.23732e16 + 1.09301e16i 0.236179 + 0.208632i
\(124\) 1.50150e16 0.268628
\(125\) 3.49951e16i 0.587121i
\(126\) 4.70249e16 5.84680e15i 0.740225 0.0920352i
\(127\) −3.26265e16 −0.482104 −0.241052 0.970512i \(-0.577492\pi\)
−0.241052 + 0.970512i \(0.577492\pi\)
\(128\) 3.76130e15i 0.0521986i
\(129\) 1.22060e16 1.38176e16i 0.159168 0.180184i
\(130\) 7.23404e15 0.0886817
\(131\) 8.12417e16i 0.936717i 0.883538 + 0.468359i \(0.155154\pi\)
−0.883538 + 0.468359i \(0.844846\pi\)
\(132\) −1.32845e16 1.17351e16i −0.144130 0.127320i
\(133\) −1.81437e17 −1.85316
\(134\) 3.48589e16i 0.335332i
\(135\) 7.68970e16 1.12436e17i 0.697010 1.01915i
\(136\) 1.43896e17 1.22952
\(137\) 1.67072e17i 1.34629i −0.739511 0.673145i \(-0.764943\pi\)
0.739511 0.673145i \(-0.235057\pi\)
\(138\) −3.47801e16 + 3.93723e16i −0.264422 + 0.299335i
\(139\) −1.60035e17 −1.14841 −0.574203 0.818713i \(-0.694688\pi\)
−0.574203 + 0.818713i \(0.694688\pi\)
\(140\) 6.95111e16i 0.471010i
\(141\) 8.87881e16 + 7.84324e16i 0.568332 + 0.502045i
\(142\) −1.33767e17 −0.809173
\(143\) 7.83332e15i 0.0447979i
\(144\) 1.01562e16 + 8.16844e16i 0.0549325 + 0.441814i
\(145\) 2.95315e17 1.51127
\(146\) 2.07568e17i 1.00540i
\(147\) −1.11333e16 + 1.26033e16i −0.0510604 + 0.0578022i
\(148\) −5.30233e15 −0.0230342
\(149\) 5.03915e16i 0.207428i 0.994607 + 0.103714i \(0.0330726\pi\)
−0.994607 + 0.103714i \(0.966927\pi\)
\(150\) −7.82229e16 6.90994e16i −0.305214 0.269615i
\(151\) 2.76836e17 1.02425 0.512127 0.858910i \(-0.328858\pi\)
0.512127 + 0.858910i \(0.328858\pi\)
\(152\) 5.96267e17i 2.09263i
\(153\) −3.37744e17 + 4.19931e16i −1.12475 + 0.139845i
\(154\) 1.14280e17 0.361246
\(155\) 2.78271e17i 0.835246i
\(156\) −8.52969e15 + 9.65590e15i −0.0243185 + 0.0275293i
\(157\) −3.20791e17 −0.869011 −0.434506 0.900669i \(-0.643077\pi\)
−0.434506 + 0.900669i \(0.643077\pi\)
\(158\) 9.06216e15i 0.0233332i
\(159\) −1.27515e17 1.12642e17i −0.312165 0.275756i
\(160\) −3.91947e17 −0.912573
\(161\) 2.23081e17i 0.494147i
\(162\) −9.01990e16 3.57121e17i −0.190144 0.752827i
\(163\) 8.96440e17 1.79895 0.899477 0.436967i \(-0.143947\pi\)
0.899477 + 0.436967i \(0.143947\pi\)
\(164\) 6.54847e16i 0.125138i
\(165\) 2.17486e17 2.46201e17i 0.395876 0.448145i
\(166\) 7.26179e16 0.125945
\(167\) 1.19275e17i 0.197159i −0.995129 0.0985795i \(-0.968570\pi\)
0.995129 0.0985795i \(-0.0314299\pi\)
\(168\) 4.95616e17 + 4.37810e17i 0.781036 + 0.689940i
\(169\) −6.59723e17 −0.991443
\(170\) 7.57989e17i 1.08660i
\(171\) 1.74008e17 + 1.39952e18i 0.238013 + 1.91430i
\(172\) 7.31292e16 0.0954693
\(173\) 1.37077e18i 1.70843i −0.519922 0.854214i \(-0.674039\pi\)
0.519922 0.854214i \(-0.325961\pi\)
\(174\) 5.28673e17 5.98476e17i 0.629206 0.712283i
\(175\) −4.43207e17 −0.503852
\(176\) 1.98509e17i 0.215615i
\(177\) −8.03369e17 7.09668e17i −0.833928 0.736664i
\(178\) −1.32939e18 −1.31915
\(179\) 1.29943e17i 0.123290i −0.998098 0.0616451i \(-0.980365\pi\)
0.998098 0.0616451i \(-0.0196347\pi\)
\(180\) 5.36176e17 6.66650e16i 0.486550 0.0604948i
\(181\) 1.06449e18 0.924090 0.462045 0.886857i \(-0.347116\pi\)
0.462045 + 0.886857i \(0.347116\pi\)
\(182\) 8.30645e16i 0.0689992i
\(183\) 3.06203e17 3.46632e17i 0.243445 0.275588i
\(184\) −7.33125e17 −0.558001
\(185\) 9.82676e16i 0.0716204i
\(186\) 5.63936e17 + 4.98161e17i 0.393664 + 0.347749i
\(187\) −8.20783e17 −0.548903
\(188\) 4.69908e17i 0.301127i
\(189\) −1.29104e18 8.82965e17i −0.792952 0.542312i
\(190\) 3.14091e18 1.84938
\(191\) 2.28288e18i 1.28889i 0.764649 + 0.644447i \(0.222912\pi\)
−0.764649 + 0.644447i \(0.777088\pi\)
\(192\) −1.24600e18 + 1.41052e18i −0.674698 + 0.763782i
\(193\) 1.20324e18 0.625019 0.312509 0.949915i \(-0.398830\pi\)
0.312509 + 0.949915i \(0.398830\pi\)
\(194\) 1.07408e18i 0.535332i
\(195\) −1.78952e17 1.58080e17i −0.0855972 0.0756137i
\(196\) −6.67023e16 −0.0306261
\(197\) 1.11597e18i 0.491951i 0.969276 + 0.245976i \(0.0791083\pi\)
−0.969276 + 0.245976i \(0.920892\pi\)
\(198\) −1.09601e17 8.81500e17i −0.0463971 0.373165i
\(199\) 1.79444e18 0.729632 0.364816 0.931080i \(-0.381132\pi\)
0.364816 + 0.931080i \(0.381132\pi\)
\(200\) 1.45654e18i 0.568960i
\(201\) −7.61746e17 + 8.62322e17i −0.285918 + 0.323669i
\(202\) −2.42528e18 −0.874884
\(203\) 3.39094e18i 1.17585i
\(204\) −1.01175e18 8.93748e17i −0.337313 0.297971i
\(205\) −1.21362e18 −0.389093
\(206\) 1.79954e18i 0.554912i
\(207\) 1.72075e18 2.13947e17i 0.510451 0.0634664i
\(208\) 1.44287e17 0.0411832
\(209\) 3.40111e18i 0.934223i
\(210\) −2.30622e18 + 2.61072e18i −0.609742 + 0.690248i
\(211\) −1.86500e18 −0.474699 −0.237350 0.971424i \(-0.576279\pi\)
−0.237350 + 0.971424i \(0.576279\pi\)
\(212\) 6.74869e17i 0.165399i
\(213\) 3.30905e18 + 2.92311e18i 0.781029 + 0.689934i
\(214\) 1.33040e17 0.0302463
\(215\) 1.35530e18i 0.296843i
\(216\) 2.90174e18 4.24283e18i 0.612390 0.895418i
\(217\) 3.19523e18 0.649867
\(218\) 4.61825e18i 0.905368i
\(219\) 4.53582e18 5.13470e18i 0.857241 0.970426i
\(220\) 1.30301e18 0.237447
\(221\) 5.96588e17i 0.104842i
\(222\) −1.99146e17 1.75919e17i −0.0337558 0.0298187i
\(223\) −1.06591e19 −1.74293 −0.871465 0.490458i \(-0.836829\pi\)
−0.871465 + 0.490458i \(0.836829\pi\)
\(224\) 4.50051e18i 0.710032i
\(225\) 4.25060e17 + 3.41869e18i 0.0647128 + 0.520475i
\(226\) −1.48398e18 −0.218053
\(227\) 8.51142e18i 1.20724i −0.797271 0.603622i \(-0.793724\pi\)
0.797271 0.603622i \(-0.206276\pi\)
\(228\) −3.70346e18 + 4.19244e18i −0.507141 + 0.574101i
\(229\) −2.44574e18 −0.323390 −0.161695 0.986841i \(-0.551696\pi\)
−0.161695 + 0.986841i \(0.551696\pi\)
\(230\) 3.86182e18i 0.493139i
\(231\) −2.82699e18 2.49727e18i −0.348682 0.308013i
\(232\) 1.11438e19 1.32779
\(233\) 8.15863e18i 0.939226i −0.882872 0.469613i \(-0.844393\pi\)
0.882872 0.469613i \(-0.155607\pi\)
\(234\) −6.40720e17 + 7.96634e16i −0.0712757 + 0.00886200i
\(235\) −8.70877e18 −0.936298
\(236\) 4.25180e18i 0.441852i
\(237\) 1.98029e17 2.24175e17i 0.0198949 0.0225217i
\(238\) 8.70357e18 0.845438
\(239\) 1.59803e19i 1.50107i 0.660828 + 0.750537i \(0.270205\pi\)
−0.660828 + 0.750537i \(0.729795\pi\)
\(240\) −4.53493e18 4.00600e18i −0.411985 0.363933i
\(241\) 1.54187e19 1.35491 0.677456 0.735564i \(-0.263083\pi\)
0.677456 + 0.735564i \(0.263083\pi\)
\(242\) 6.99148e18i 0.594355i
\(243\) −5.57260e18 + 1.08053e19i −0.458361 + 0.888766i
\(244\) 1.83454e18 0.146019
\(245\) 1.23619e18i 0.0952261i
\(246\) −2.17263e18 + 2.45949e18i −0.161996 + 0.183385i
\(247\) 2.47210e18 0.178440
\(248\) 1.05007e19i 0.733844i
\(249\) −1.79639e18 1.58687e18i −0.121564 0.107385i
\(250\) −6.95618e18 −0.455880
\(251\) 2.32208e19i 1.47396i −0.675912 0.736982i \(-0.736250\pi\)
0.675912 0.736982i \(-0.263750\pi\)
\(252\) −7.65477e17 6.15661e18i −0.0470682 0.378563i
\(253\) 4.18175e18 0.249111
\(254\) 6.48536e18i 0.374338i
\(255\) 1.65638e19 1.87508e19i 0.926484 1.04881i
\(256\) −1.80516e19 −0.978577
\(257\) 2.25664e19i 1.18576i 0.805290 + 0.592881i \(0.202010\pi\)
−0.805290 + 0.592881i \(0.797990\pi\)
\(258\) 2.74661e18 + 2.42626e18i 0.139907 + 0.123589i
\(259\) −1.12835e18 −0.0557246
\(260\) 9.47097e17i 0.0453532i
\(261\) −2.61561e19 + 3.25209e18i −1.21464 + 0.151022i
\(262\) −1.61489e19 −0.727331
\(263\) 2.26673e18i 0.0990272i −0.998773 0.0495136i \(-0.984233\pi\)
0.998773 0.0495136i \(-0.0157671\pi\)
\(264\) 8.20691e18 9.29050e18i 0.347815 0.393739i
\(265\) 1.25073e19 0.514276
\(266\) 3.60653e19i 1.43892i
\(267\) 3.28858e19 + 2.90502e19i 1.27326 + 1.12476i
\(268\) −4.56381e18 −0.171494
\(269\) 2.50953e19i 0.915323i 0.889126 + 0.457662i \(0.151313\pi\)
−0.889126 + 0.457662i \(0.848687\pi\)
\(270\) 2.23496e19 + 1.52853e19i 0.791335 + 0.541206i
\(271\) −4.19713e19 −1.44277 −0.721387 0.692532i \(-0.756495\pi\)
−0.721387 + 0.692532i \(0.756495\pi\)
\(272\) 1.51185e19i 0.504612i
\(273\) −1.81515e18 + 2.05481e18i −0.0588316 + 0.0665993i
\(274\) 3.32098e19 1.04535
\(275\) 8.30809e18i 0.254004i
\(276\) 5.15471e18 + 4.55349e18i 0.153085 + 0.135230i
\(277\) 4.25589e19 1.22787 0.613934 0.789357i \(-0.289586\pi\)
0.613934 + 0.789357i \(0.289586\pi\)
\(278\) 3.18110e19i 0.891700i
\(279\) −3.06440e18 2.46465e19i −0.0834666 0.671308i
\(280\) −4.86124e19 −1.28672
\(281\) 1.12360e19i 0.289041i −0.989502 0.144520i \(-0.953836\pi\)
0.989502 0.144520i \(-0.0461639\pi\)
\(282\) −1.55905e19 + 1.76489e19i −0.389822 + 0.441291i
\(283\) 1.09842e19 0.266978 0.133489 0.991050i \(-0.457382\pi\)
0.133489 + 0.991050i \(0.457382\pi\)
\(284\) 1.75131e19i 0.413824i
\(285\) −7.76982e19 6.86360e19i −1.78506 1.57686i
\(286\) −1.55708e18 −0.0347841
\(287\) 1.39354e19i 0.302735i
\(288\) 3.47148e19 4.31624e18i 0.733458 0.0911939i
\(289\) −1.38498e19 −0.284618
\(290\) 5.87014e19i 1.17345i
\(291\) −2.34711e19 + 2.65701e19i −0.456446 + 0.516713i
\(292\) 2.71752e19 0.514175
\(293\) 9.07495e19i 1.67072i −0.549704 0.835359i \(-0.685260\pi\)
0.549704 0.835359i \(-0.314740\pi\)
\(294\) −2.50522e18 2.21303e18i −0.0448815 0.0396468i
\(295\) 7.87983e19 1.37385
\(296\) 3.70817e18i 0.0629254i
\(297\) −1.65515e19 + 2.42011e19i −0.273392 + 0.399746i
\(298\) −1.00166e19 −0.161061
\(299\) 3.03951e18i 0.0475811i
\(300\) −9.04666e18 + 1.02411e19i −0.137885 + 0.156091i
\(301\) 1.55622e19 0.230960
\(302\) 5.50283e19i 0.795300i
\(303\) 5.99953e19 + 5.29978e19i 0.844454 + 0.745962i
\(304\) 6.26471e19 0.858840
\(305\) 3.39994e19i 0.454017i
\(306\) −8.34720e18 6.71353e19i −0.108585 0.873332i
\(307\) −9.03091e19 −1.14452 −0.572262 0.820071i \(-0.693934\pi\)
−0.572262 + 0.820071i \(0.693934\pi\)
\(308\) 1.49618e19i 0.184747i
\(309\) −3.93240e19 + 4.45161e19i −0.473141 + 0.535611i
\(310\) −5.53136e19 −0.648542
\(311\) 2.45372e19i 0.280377i 0.990125 + 0.140188i \(0.0447708\pi\)
−0.990125 + 0.140188i \(0.955229\pi\)
\(312\) −6.75282e18 5.96521e18i −0.0752053 0.0664338i
\(313\) −3.08699e19 −0.335104 −0.167552 0.985863i \(-0.553586\pi\)
−0.167552 + 0.985863i \(0.553586\pi\)
\(314\) 6.37655e19i 0.674759i
\(315\) 1.14100e20 1.41865e19i 1.17707 0.146350i
\(316\) 1.18644e18 0.0119330
\(317\) 1.73419e20i 1.70068i −0.526235 0.850339i \(-0.676397\pi\)
0.526235 0.850339i \(-0.323603\pi\)
\(318\) 2.23906e19 2.53469e19i 0.214116 0.242386i
\(319\) −6.35644e19 −0.592773
\(320\) 1.38351e20i 1.25829i
\(321\) −3.29107e18 2.90722e18i −0.0291942 0.0257892i
\(322\) −4.43432e19 −0.383690
\(323\) 2.59029e20i 2.18640i
\(324\) −4.67551e19 + 1.18091e19i −0.385007 + 0.0972423i
\(325\) 6.03876e18 0.0485155
\(326\) 1.78190e20i 1.39683i
\(327\) 1.00919e20 1.14244e20i 0.771954 0.873878i
\(328\) −4.57965e19 −0.341855
\(329\) 9.99980e19i 0.728491i
\(330\) 4.89389e19 + 4.32309e19i 0.347970 + 0.307385i
\(331\) 2.49632e19 0.173251 0.0866256 0.996241i \(-0.472392\pi\)
0.0866256 + 0.996241i \(0.472392\pi\)
\(332\) 9.50731e18i 0.0644100i
\(333\) 1.08215e18 + 8.70358e18i 0.00715706 + 0.0575631i
\(334\) 2.37089e19 0.153088
\(335\) 8.45808e19i 0.533228i
\(336\) −4.59987e19 + 5.20721e19i −0.283160 + 0.320547i
\(337\) 2.29644e20 1.38043 0.690217 0.723602i \(-0.257515\pi\)
0.690217 + 0.723602i \(0.257515\pi\)
\(338\) 1.31137e20i 0.769824i
\(339\) 3.67100e19 + 3.24284e19i 0.210469 + 0.185921i
\(340\) 9.92377e19 0.555707
\(341\) 5.98959e19i 0.327614i
\(342\) −2.78191e20 + 3.45886e19i −1.48639 + 0.184810i
\(343\) −1.98240e20 −1.03476
\(344\) 5.11427e19i 0.260805i
\(345\) −8.43896e19 + 9.55318e19i −0.420471 + 0.475987i
\(346\) 2.72476e20 1.32654
\(347\) 2.23524e20i 1.06338i −0.846939 0.531690i \(-0.821557\pi\)
0.846939 0.531690i \(-0.178443\pi\)
\(348\) −7.83539e19 6.92151e19i −0.364273 0.321786i
\(349\) −2.27023e20 −1.03149 −0.515747 0.856741i \(-0.672486\pi\)
−0.515747 + 0.856741i \(0.672486\pi\)
\(350\) 8.80989e19i 0.391225i
\(351\) 1.75906e19 + 1.20305e19i 0.0763528 + 0.0522188i
\(352\) 8.43638e19 0.357944
\(353\) 2.03750e20i 0.845085i 0.906343 + 0.422543i \(0.138862\pi\)
−0.906343 + 0.422543i \(0.861138\pi\)
\(354\) 1.41065e20 1.59690e20i 0.571996 0.647519i
\(355\) −3.24568e20 −1.28671
\(356\) 1.74047e20i 0.674631i
\(357\) −2.15305e20 1.90193e20i −0.816033 0.720855i
\(358\) 2.58295e19 0.0957309
\(359\) 3.04784e20i 1.10468i −0.833619 0.552341i \(-0.813735\pi\)
0.833619 0.552341i \(-0.186265\pi\)
\(360\) 4.66220e19 + 3.74973e20i 0.165261 + 1.32917i
\(361\) 7.84909e20 2.72121
\(362\) 2.11595e20i 0.717526i
\(363\) 1.52780e20 1.72952e20i 0.506771 0.573683i
\(364\) −1.08750e19 −0.0352873
\(365\) 5.03637e20i 1.59873i
\(366\) 6.89021e19 + 6.08657e19i 0.213985 + 0.189027i
\(367\) −3.27286e20 −0.994486 −0.497243 0.867611i \(-0.665654\pi\)
−0.497243 + 0.867611i \(0.665654\pi\)
\(368\) 7.70261e19i 0.229011i
\(369\) 1.07491e20 1.33648e19i 0.312723 0.0388822i
\(370\) 1.95332e19 0.0556109
\(371\) 1.43614e20i 0.400135i
\(372\) 6.52205e19 7.38318e19i 0.177844 0.201326i
\(373\) −4.63340e20 −1.23660 −0.618300 0.785942i \(-0.712178\pi\)
−0.618300 + 0.785942i \(0.712178\pi\)
\(374\) 1.63152e20i 0.426205i
\(375\) 1.72079e20 + 1.52008e20i 0.440024 + 0.388702i
\(376\) −3.28629e20 −0.822627
\(377\) 4.62019e19i 0.113222i
\(378\) 1.75512e20 2.56628e20i 0.421088 0.615702i
\(379\) 9.70265e19 0.227917 0.113959 0.993486i \(-0.463647\pi\)
0.113959 + 0.993486i \(0.463647\pi\)
\(380\) 4.11215e20i 0.945803i
\(381\) −1.41720e20 + 1.60432e20i −0.319176 + 0.361318i
\(382\) −4.53782e20 −1.00078
\(383\) 1.93222e20i 0.417317i 0.977989 + 0.208659i \(0.0669098\pi\)
−0.977989 + 0.208659i \(0.933090\pi\)
\(384\) −1.84951e19 1.63380e19i −0.0391208 0.0345580i
\(385\) 2.77285e20 0.574435
\(386\) 2.39175e20i 0.485307i
\(387\) −1.49250e19 1.20039e20i −0.0296637 0.238581i
\(388\) −1.40621e20 −0.273777
\(389\) 8.17463e20i 1.55909i −0.626346 0.779545i \(-0.715450\pi\)
0.626346 0.779545i \(-0.284550\pi\)
\(390\) 3.14225e19 3.55713e19i 0.0587116 0.0664635i
\(391\) 3.18483e20 0.583005
\(392\) 4.66481e19i 0.0836653i
\(393\) 3.99483e20 + 3.52889e20i 0.702033 + 0.620152i
\(394\) −2.21828e20 −0.381984
\(395\) 2.19882e19i 0.0371033i
\(396\) −1.15408e20 + 1.43492e19i −0.190842 + 0.0237282i
\(397\) 7.89790e20 1.27993 0.639967 0.768402i \(-0.278948\pi\)
0.639967 + 0.768402i \(0.278948\pi\)
\(398\) 3.56691e20i 0.566536i
\(399\) −7.88109e20 + 8.92166e20i −1.22688 + 1.38887i
\(400\) 1.53032e20 0.233508
\(401\) 1.03439e21i 1.54713i 0.633714 + 0.773567i \(0.281530\pi\)
−0.633714 + 0.773567i \(0.718470\pi\)
\(402\) −1.71409e20 1.51417e20i −0.251319 0.222006i
\(403\) −4.35354e19 −0.0625752
\(404\) 3.17523e20i 0.447429i
\(405\) −2.18857e20 8.66509e20i −0.302356 1.19711i
\(406\) 6.74036e20 0.913009
\(407\) 2.11514e19i 0.0280921i
\(408\) 6.25040e20 7.07567e20i 0.814005 0.921481i
\(409\) 1.88705e20 0.240989 0.120495 0.992714i \(-0.461552\pi\)
0.120495 + 0.992714i \(0.461552\pi\)
\(410\) 2.41239e20i 0.302118i
\(411\) −8.21528e20 7.25710e20i −1.00899 0.891309i
\(412\) −2.35600e20 −0.283790
\(413\) 9.04798e20i 1.06893i
\(414\) 4.25276e19 + 3.42042e20i 0.0492797 + 0.396349i
\(415\) 1.76198e20 0.200271
\(416\) 6.13200e19i 0.0683685i
\(417\) −6.95142e20 + 7.86924e20i −0.760300 + 0.860686i
\(418\) −6.76058e20 −0.725394
\(419\) 4.80232e20i 0.505520i −0.967529 0.252760i \(-0.918662\pi\)
0.967529 0.252760i \(-0.0813384\pi\)
\(420\) 3.41801e20 + 3.01935e20i 0.353004 + 0.311831i
\(421\) −9.58853e20 −0.971617 −0.485809 0.874065i \(-0.661475\pi\)
−0.485809 + 0.874065i \(0.661475\pi\)
\(422\) 3.70716e20i 0.368589i
\(423\) 7.71338e20 9.59036e19i 0.752526 0.0935647i
\(424\) 4.71968e20 0.451841
\(425\) 6.32746e20i 0.594454i
\(426\) −5.81042e20 + 6.57760e20i −0.535712 + 0.606444i
\(427\) 3.90396e20 0.353250
\(428\) 1.74179e19i 0.0154684i
\(429\) 3.85181e19 + 3.40256e19i 0.0335743 + 0.0296584i
\(430\) −2.69401e20 −0.230489
\(431\) 3.66306e20i 0.307628i 0.988100 + 0.153814i \(0.0491556\pi\)
−0.988100 + 0.153814i \(0.950844\pi\)
\(432\) 4.45775e20 + 3.04873e20i 0.367490 + 0.251332i
\(433\) −1.35950e20 −0.110021 −0.0550107 0.998486i \(-0.517519\pi\)
−0.0550107 + 0.998486i \(0.517519\pi\)
\(434\) 6.35135e20i 0.504601i
\(435\) 1.28276e21 1.45213e21i 1.00053 1.13264i
\(436\) 6.04632e20 0.463019
\(437\) 1.31971e21i 0.992263i
\(438\) 1.02065e21 + 9.01611e20i 0.753505 + 0.665620i
\(439\) 4.40467e20 0.319299 0.159649 0.987174i \(-0.448964\pi\)
0.159649 + 0.987174i \(0.448964\pi\)
\(440\) 9.11258e20i 0.648664i
\(441\) 1.36133e19 + 1.09490e20i 0.00951599 + 0.0765356i
\(442\) −1.18587e20 −0.0814066
\(443\) 1.63123e21i 1.09973i 0.835254 + 0.549865i \(0.185321\pi\)
−0.835254 + 0.549865i \(0.814679\pi\)
\(444\) −2.30317e19 + 2.60727e19i −0.0152497 + 0.0172632i
\(445\) −3.22560e21 −2.09764
\(446\) 2.11876e21i 1.35333i
\(447\) 2.47786e20 + 2.18886e20i 0.155459 + 0.137327i
\(448\) −1.58860e21 −0.979020
\(449\) 2.11301e20i 0.127918i 0.997953 + 0.0639588i \(0.0203726\pi\)
−0.997953 + 0.0639588i \(0.979627\pi\)
\(450\) −6.79553e20 + 8.44917e19i −0.404132 + 0.0502474i
\(451\) 2.61224e20 0.152616
\(452\) 1.94287e20i 0.111516i
\(453\) 1.20249e21 1.36126e21i 0.678105 0.767638i
\(454\) 1.69186e21 0.937386
\(455\) 2.01546e20i 0.109719i
\(456\) −2.93197e21 2.59000e21i −1.56834 1.38542i
\(457\) 1.57273e21 0.826657 0.413329 0.910582i \(-0.364366\pi\)
0.413329 + 0.910582i \(0.364366\pi\)
\(458\) 4.86154e20i 0.251102i
\(459\) −1.26057e21 + 1.84316e21i −0.639830 + 0.935540i
\(460\) −5.05599e20 −0.252199
\(461\) 1.48905e21i 0.729963i −0.931015 0.364981i \(-0.881075\pi\)
0.931015 0.364981i \(-0.118925\pi\)
\(462\) 4.96397e20 5.61938e20i 0.239163 0.270740i
\(463\) 5.50698e20 0.260775 0.130387 0.991463i \(-0.458378\pi\)
0.130387 + 0.991463i \(0.458378\pi\)
\(464\) 1.17083e21i 0.544942i
\(465\) 1.36832e21 + 1.20873e21i 0.625985 + 0.552973i
\(466\) 1.62174e21 0.729279
\(467\) 4.29729e21i 1.89959i 0.312878 + 0.949793i \(0.398707\pi\)
−0.312878 + 0.949793i \(0.601293\pi\)
\(468\) 1.04297e19 + 8.38846e19i 0.00453217 + 0.0364515i
\(469\) −9.71194e20 −0.414881
\(470\) 1.73109e21i 0.727005i
\(471\) −1.39342e21 + 1.57740e21i −0.575327 + 0.651290i
\(472\) 2.97349e21 1.20706
\(473\) 2.91718e20i 0.116433i
\(474\) 4.45606e19 + 3.93633e19i 0.0174874 + 0.0154477i
\(475\) 2.62194e21 1.01175
\(476\) 1.13949e21i 0.432370i
\(477\) −1.10777e21 + 1.37734e20i −0.413337 + 0.0513919i
\(478\) −3.17650e21 −1.16554
\(479\) 2.49777e21i 0.901297i −0.892702 0.450648i \(-0.851193\pi\)
0.892702 0.450648i \(-0.148807\pi\)
\(480\) −1.70250e21 + 1.92729e21i −0.604168 + 0.683938i
\(481\) 1.53739e19 0.00536568
\(482\) 3.06486e21i 1.05205i
\(483\) 1.09694e21 + 9.68999e20i 0.370344 + 0.327149i
\(484\) 9.15341e20 0.303962
\(485\) 2.60613e21i 0.851258i
\(486\) −2.14784e21 1.10770e21i −0.690098 0.355902i
\(487\) −6.06848e20 −0.191800 −0.0958999 0.995391i \(-0.530573\pi\)
−0.0958999 + 0.995391i \(0.530573\pi\)
\(488\) 1.28298e21i 0.398897i
\(489\) 3.89386e21 4.40799e21i 1.19099 1.34825i
\(490\) 2.45724e20 0.0739400
\(491\) 3.25851e21i 0.964645i −0.875994 0.482322i \(-0.839793\pi\)
0.875994 0.482322i \(-0.160207\pi\)
\(492\) 3.22002e20 + 2.84446e20i 0.0937860 + 0.0828474i
\(493\) −4.84108e21 −1.38729
\(494\) 4.91394e20i 0.138553i
\(495\) −2.65932e20 2.13885e21i −0.0737784 0.593388i
\(496\) −1.10326e21 −0.301178
\(497\) 3.72684e21i 1.00113i
\(498\) 3.15430e20 3.57078e20i 0.0833814 0.0943905i
\(499\) −1.08927e21 −0.283355 −0.141678 0.989913i \(-0.545250\pi\)
−0.141678 + 0.989913i \(0.545250\pi\)
\(500\) 9.10720e20i 0.233144i
\(501\) −5.86499e20 5.18094e20i −0.147763 0.130529i
\(502\) 4.61573e21 1.14449
\(503\) 3.04610e20i 0.0743361i −0.999309 0.0371680i \(-0.988166\pi\)
0.999309 0.0371680i \(-0.0118337\pi\)
\(504\) 4.30561e21 5.35334e20i 1.03417 0.128582i
\(505\) −5.88463e21 −1.39120
\(506\) 8.31230e20i 0.193427i
\(507\) −2.86564e21 + 3.24400e21i −0.656383 + 0.743048i
\(508\) −8.49079e20 −0.191442
\(509\) 5.82783e21i 1.29350i 0.762704 + 0.646748i \(0.223871\pi\)
−0.762704 + 0.646748i \(0.776129\pi\)
\(510\) 3.72720e21 + 3.29248e21i 0.814368 + 0.719385i
\(511\) 5.78298e21 1.24390
\(512\) 3.83471e21i 0.812032i
\(513\) 7.63759e21 + 5.22346e21i 1.59227 + 1.08898i
\(514\) −4.48566e21 −0.920706
\(515\) 4.36636e21i 0.882392i
\(516\) 3.17651e20 3.59592e20i 0.0632053 0.0715505i
\(517\) 1.87450e21 0.367250
\(518\) 2.24289e20i 0.0432684i
\(519\) −6.74038e21 5.95422e21i −1.28040 1.13106i
\(520\) 6.62350e20 0.123897
\(521\) 8.10069e20i 0.149218i −0.997213 0.0746088i \(-0.976229\pi\)
0.997213 0.0746088i \(-0.0237708\pi\)
\(522\) −6.46438e20 5.19920e21i −0.117263 0.943131i
\(523\) −1.43005e21 −0.255468 −0.127734 0.991808i \(-0.540770\pi\)
−0.127734 + 0.991808i \(0.540770\pi\)
\(524\) 2.11425e21i 0.371968i
\(525\) −1.92516e21 + 2.17935e21i −0.333574 + 0.377617i
\(526\) 4.50572e20 0.0768914
\(527\) 4.56168e21i 0.766726i
\(528\) 9.76112e20 + 8.62264e20i 0.161595 + 0.142748i
\(529\) 4.51000e21 0.735412
\(530\) 2.48615e21i 0.399319i
\(531\) −6.97918e21 + 8.67751e20i −1.10420 + 0.137290i
\(532\) −4.72176e21 −0.735886
\(533\) 1.89871e20i 0.0291502i
\(534\) −5.77447e21 + 6.53690e21i −0.873338 + 0.988648i
\(535\) 3.22805e20 0.0480961
\(536\) 3.19169e21i 0.468492i
\(537\) −6.38957e20 5.64433e20i −0.0924012 0.0816241i
\(538\) −4.98834e21 −0.710719
\(539\) 2.66081e20i 0.0373511i
\(540\) 2.00118e21 2.92607e21i 0.276781 0.404701i
\(541\) 1.23948e22 1.68913 0.844563 0.535456i \(-0.179860\pi\)
0.844563 + 0.535456i \(0.179860\pi\)
\(542\) 8.34288e21i 1.12027i
\(543\) 4.62384e21 5.23434e21i 0.611792 0.692570i
\(544\) 6.42517e21 0.837710
\(545\) 1.12056e22i 1.43967i
\(546\) −4.08446e20 3.60807e20i −0.0517122 0.0456808i
\(547\) 3.91673e21 0.488680 0.244340 0.969690i \(-0.421429\pi\)
0.244340 + 0.969690i \(0.421429\pi\)
\(548\) 4.34791e21i 0.534609i
\(549\) −3.74411e20 3.01133e21i −0.0453702 0.364905i
\(550\) −1.65145e21 −0.197226
\(551\) 2.00602e22i 2.36114i
\(552\) −3.18447e21 + 3.60493e21i −0.369424 + 0.418200i
\(553\) 2.52478e20 0.0288684
\(554\) 8.45967e21i 0.953401i
\(555\) −4.83203e20 4.26845e20i −0.0536767 0.0474162i
\(556\) −4.16477e21 −0.456029
\(557\) 4.96525e21i 0.535919i −0.963430 0.267960i \(-0.913651\pi\)
0.963430 0.267960i \(-0.0863494\pi\)
\(558\) 4.89913e21 6.09129e20i 0.521249 0.0648091i
\(559\) −2.12036e20 −0.0222390
\(560\) 5.10749e21i 0.528084i
\(561\) −3.56523e21 + 4.03597e21i −0.363400 + 0.411381i
\(562\) 2.23343e21 0.224431
\(563\) 1.04818e22i 1.03841i −0.854650 0.519205i \(-0.826228\pi\)
0.854650 0.519205i \(-0.173772\pi\)
\(564\) 2.31064e21 + 2.04114e21i 0.225683 + 0.199361i
\(565\) −3.60070e21 −0.346736
\(566\) 2.18338e21i 0.207300i
\(567\) −9.94964e21 + 2.51301e21i −0.931414 + 0.235250i
\(568\) −1.22477e22 −1.13049
\(569\) 1.83294e22i 1.66821i −0.551606 0.834105i \(-0.685985\pi\)
0.551606 0.834105i \(-0.314015\pi\)
\(570\) 1.36432e22 1.54445e22i 1.22438 1.38604i
\(571\) −5.87637e21 −0.520020 −0.260010 0.965606i \(-0.583726\pi\)
−0.260010 + 0.965606i \(0.583726\pi\)
\(572\) 2.03856e20i 0.0177891i
\(573\) 1.12254e22 + 9.91616e21i 0.965976 + 0.853310i
\(574\) −2.77001e21 −0.235064
\(575\) 3.22373e21i 0.269784i
\(576\) 1.52356e21 + 1.22537e22i 0.125742 + 1.01132i
\(577\) −1.18497e22 −0.964496 −0.482248 0.876035i \(-0.660180\pi\)
−0.482248 + 0.876035i \(0.660180\pi\)
\(578\) 2.75301e21i 0.220996i
\(579\) 5.22650e21 5.91658e21i 0.413793 0.468427i
\(580\) 7.68533e21 0.600121
\(581\) 2.02319e21i 0.155821i
\(582\) −5.28149e21 4.66549e21i −0.401211 0.354416i
\(583\) −2.69211e21 −0.201718
\(584\) 1.90049e22i 1.40464i
\(585\) −1.55463e21 + 1.93293e20i −0.113339 + 0.0140919i
\(586\) 1.80388e22 1.29726
\(587\) 3.83504e21i 0.272060i 0.990705 + 0.136030i \(0.0434344\pi\)
−0.990705 + 0.136030i \(0.956566\pi\)
\(588\) −2.89735e20 + 3.27990e20i −0.0202760 + 0.0229531i
\(589\) −1.89024e22 −1.30495
\(590\) 1.56632e22i 1.06675i
\(591\) 5.48746e21 + 4.84743e21i 0.368698 + 0.325696i
\(592\) 3.89601e20 0.0258253
\(593\) 1.40261e21i 0.0917274i 0.998948 + 0.0458637i \(0.0146040\pi\)
−0.998948 + 0.0458637i \(0.985396\pi\)
\(594\) −4.81060e21 3.29004e21i −0.310390 0.212280i
\(595\) 2.11181e22 1.34437
\(596\) 1.31140e21i 0.0823691i
\(597\) 7.79450e21 8.82364e21i 0.483052 0.546831i
\(598\) 6.04181e20 0.0369452
\(599\) 1.21866e22i 0.735306i −0.929963 0.367653i \(-0.880161\pi\)
0.929963 0.367653i \(-0.119839\pi\)
\(600\) −7.16210e21 6.32676e21i −0.426413 0.376679i
\(601\) 7.79610e21 0.458017 0.229009 0.973424i \(-0.426452\pi\)
0.229009 + 0.973424i \(0.426452\pi\)
\(602\) 3.09338e21i 0.179333i
\(603\) 9.31429e20 + 7.49134e21i 0.0532858 + 0.428569i
\(604\) 7.20444e21 0.406729
\(605\) 1.69639e22i 0.945113i
\(606\) −1.05347e22 + 1.19256e22i −0.579215 + 0.655691i
\(607\) −1.39324e22 −0.755991 −0.377995 0.925807i \(-0.623387\pi\)
−0.377995 + 0.925807i \(0.623387\pi\)
\(608\) 2.66242e22i 1.42577i
\(609\) −1.66740e22 1.47292e22i −0.881253 0.778468i
\(610\) −6.75825e21 −0.352530
\(611\) 1.36248e21i 0.0701459i
\(612\) −8.78951e21 + 1.09284e21i −0.446635 + 0.0555320i
\(613\) 2.18069e22 1.09373 0.546866 0.837220i \(-0.315821\pi\)
0.546866 + 0.837220i \(0.315821\pi\)
\(614\) 1.79513e22i 0.888686i
\(615\) −5.27161e21 + 5.96764e21i −0.257598 + 0.291610i
\(616\) 1.04635e22 0.504696
\(617\) 1.41464e22i 0.673540i −0.941587 0.336770i \(-0.890666\pi\)
0.941587 0.336770i \(-0.109334\pi\)
\(618\) −8.84873e21 7.81666e21i −0.415885 0.367378i
\(619\) −1.06168e22 −0.492571 −0.246285 0.969197i \(-0.579210\pi\)
−0.246285 + 0.969197i \(0.579210\pi\)
\(620\) 7.24178e21i 0.331674i
\(621\) 6.42237e21 9.39060e21i 0.290377 0.424581i
\(622\) −4.87740e21 −0.217703
\(623\) 3.70378e22i 1.63208i
\(624\) 6.26738e20 7.09489e20i 0.0272653 0.0308652i
\(625\) −2.90899e22 −1.24940
\(626\) 6.13618e21i 0.260198i
\(627\) 1.67240e22 + 1.47734e22i 0.700164 + 0.618501i
\(628\) −8.34833e21 −0.345082
\(629\) 1.61090e21i 0.0657450i
\(630\) 2.81994e21 + 2.26803e22i 0.113636 + 0.913955i
\(631\) 4.92516e22 1.95968 0.979841 0.199781i \(-0.0640232\pi\)
0.979841 + 0.199781i \(0.0640232\pi\)
\(632\) 8.29733e20i 0.0325988i
\(633\) −8.10099e21 + 9.17059e21i −0.314274 + 0.355769i
\(634\) 3.44715e22 1.32052
\(635\) 1.57359e22i 0.595254i
\(636\) −3.31847e21 2.93143e21i −0.123960 0.109502i
\(637\) 1.93401e20 0.00713418
\(638\) 1.26351e22i 0.460269i
\(639\) 2.87471e22 3.57424e21i 1.03416 0.128581i
\(640\) 1.81409e21 0.0644495
\(641\) 5.24245e21i 0.183937i 0.995762 + 0.0919686i \(0.0293160\pi\)
−0.995762 + 0.0919686i \(0.970684\pi\)
\(642\) 5.77885e20 6.54186e20i 0.0200245 0.0226684i
\(643\) −3.35417e22 −1.14788 −0.573941 0.818897i \(-0.694586\pi\)
−0.573941 + 0.818897i \(0.694586\pi\)
\(644\) 5.80551e21i 0.196225i
\(645\) 6.66430e21 + 5.88701e21i 0.222473 + 0.196525i
\(646\) −5.14888e22 −1.69767
\(647\) 1.65630e22i 0.539393i 0.962945 + 0.269697i \(0.0869235\pi\)
−0.962945 + 0.269697i \(0.913077\pi\)
\(648\) −8.25864e21 3.26980e22i −0.265649 1.05177i
\(649\) −1.69608e22 −0.538875
\(650\) 1.20036e21i 0.0376707i
\(651\) 1.38791e22 1.57116e22i 0.430244 0.487050i
\(652\) 2.33291e22 0.714361
\(653\) 4.29848e22i 1.30020i 0.759849 + 0.650099i \(0.225273\pi\)
−0.759849 + 0.650099i \(0.774727\pi\)
\(654\) 2.27089e22 + 2.00603e22i 0.678539 + 0.599398i
\(655\) −3.91832e22 −1.15656
\(656\) 4.81164e21i 0.140301i
\(657\) −5.54620e21 4.46072e22i −0.159762 1.28494i
\(658\) −1.98772e22 −0.565650
\(659\) 1.66575e22i 0.468303i −0.972200 0.234151i \(-0.924769\pi\)
0.972200 0.234151i \(-0.0752312\pi\)
\(660\) 5.65989e21 6.40719e21i 0.157202 0.177957i
\(661\) −6.24453e21 −0.171352 −0.0856758 0.996323i \(-0.527305\pi\)
−0.0856758 + 0.996323i \(0.527305\pi\)
\(662\) 4.96208e21i 0.134524i
\(663\) 2.93355e21 + 2.59140e21i 0.0785752 + 0.0694106i
\(664\) 6.64891e21 0.175957
\(665\) 8.75080e22i 2.28810i
\(666\) −1.73006e21 + 2.15106e20i −0.0446959 + 0.00555723i
\(667\) 2.46645e22 0.629600
\(668\) 3.10403e21i 0.0782914i
\(669\) −4.62997e22 + 5.24129e22i −1.15390 + 1.30626i
\(670\) 1.68126e22 0.414035
\(671\) 7.31812e21i 0.178082i
\(672\) 2.21300e22 + 1.95489e22i 0.532142 + 0.470076i
\(673\) 6.40128e22 1.52106 0.760530 0.649303i \(-0.224939\pi\)
0.760530 + 0.649303i \(0.224939\pi\)
\(674\) 4.56477e22i 1.07186i
\(675\) 1.86568e22 + 1.27597e22i 0.432919 + 0.296080i
\(676\) −1.71688e22 −0.393700
\(677\) 2.51675e22i 0.570336i −0.958478 0.285168i \(-0.907951\pi\)
0.958478 0.285168i \(-0.0920494\pi\)
\(678\) −6.44598e21 + 7.29707e21i −0.144361 + 0.163422i
\(679\) −2.99247e22 −0.662326
\(680\) 6.94016e22i 1.51809i
\(681\) −4.18525e22 3.69710e22i −0.904782 0.799254i
\(682\) 1.19058e22 0.254381
\(683\) 6.35355e22i 1.34169i 0.741599 + 0.670843i \(0.234068\pi\)
−0.741599 + 0.670843i \(0.765932\pi\)
\(684\) 4.52843e21 + 3.64214e22i 0.0945145 + 0.760165i
\(685\) 8.05795e22 1.66226
\(686\) 3.94052e22i 0.803454i
\(687\) −1.06236e22 + 1.20262e22i −0.214100 + 0.242368i
\(688\) −5.37334e21 −0.107038
\(689\) 1.95676e21i 0.0385287i
\(690\) −1.89894e22 1.67746e22i −0.369589 0.326482i
\(691\) −5.74302e22 −1.10488 −0.552441 0.833552i \(-0.686303\pi\)
−0.552441 + 0.833552i \(0.686303\pi\)
\(692\) 3.56732e22i 0.678413i
\(693\) −2.45592e22 + 3.05355e21i −0.461688 + 0.0574036i
\(694\) 4.44312e22 0.825681
\(695\) 7.71854e22i 1.41794i
\(696\) 4.84054e22 5.47965e22i 0.879063 0.995129i
\(697\) 1.98949e22 0.357173
\(698\) 4.51267e22i 0.800922i
\(699\) −4.01178e22 3.54386e22i −0.703913 0.621813i
\(700\) −1.15341e22 −0.200078
\(701\) 5.88811e22i 1.00979i 0.863180 + 0.504896i \(0.168469\pi\)
−0.863180 + 0.504896i \(0.831531\pi\)
\(702\) −2.39137e21 + 3.49659e21i −0.0405462 + 0.0592855i
\(703\) 6.67513e21 0.111897
\(704\) 2.97790e22i 0.493547i
\(705\) −3.78283e22 + 4.28229e22i −0.619874 + 0.701719i
\(706\) −4.05006e22 −0.656182
\(707\) 6.75700e22i 1.08243i
\(708\) −2.09070e22 1.84685e22i −0.331151 0.292527i
\(709\) 5.30257e22 0.830456 0.415228 0.909717i \(-0.363702\pi\)
0.415228 + 0.909717i \(0.363702\pi\)
\(710\) 6.45163e22i 0.999086i
\(711\) −2.42141e20 1.94750e21i −0.00370775 0.0298209i
\(712\) −1.21719e23 −1.84297
\(713\) 2.32410e22i 0.347967i
\(714\) 3.78057e22 4.27973e22i 0.559721 0.633623i
\(715\) −3.77805e21 −0.0553120
\(716\) 3.38166e21i 0.0489582i
\(717\) 7.85787e22 + 6.94137e22i 1.12500 + 0.993784i
\(718\) 6.05837e22 0.857749
\(719\) 1.00941e23i 1.41330i −0.707562 0.706651i \(-0.750205\pi\)
0.707562 0.706651i \(-0.249795\pi\)
\(720\) −3.93968e22 + 4.89836e21i −0.545507 + 0.0678252i
\(721\) −5.01365e22 −0.686550
\(722\) 1.56021e23i 2.11293i
\(723\) 6.69741e22 7.58170e22i 0.897017 1.01545i
\(724\) 2.77026e22 0.366954
\(725\) 4.90022e22i 0.641965i
\(726\) 3.43786e22 + 3.03689e22i 0.445446 + 0.393492i
\(727\) 7.22307e22 0.925649 0.462824 0.886450i \(-0.346836\pi\)
0.462824 + 0.886450i \(0.346836\pi\)
\(728\) 7.60540e21i 0.0963987i
\(729\) 2.89264e22 + 7.43367e22i 0.362639 + 0.931930i
\(730\) −1.00111e23 −1.24136
\(731\) 2.22173e22i 0.272492i
\(732\) 7.96869e21 9.02082e21i 0.0966714 0.109435i
\(733\) 6.69461e22 0.803329 0.401664 0.915787i \(-0.368432\pi\)
0.401664 + 0.915787i \(0.368432\pi\)
\(734\) 6.50565e22i 0.772186i
\(735\) −6.07861e21 5.36963e21i −0.0713683 0.0630443i
\(736\) −3.27351e22 −0.380182
\(737\) 1.82054e22i 0.209151i
\(738\) 2.65659e21 + 2.13666e22i 0.0301908 + 0.242820i
\(739\) −1.18482e23 −1.33197 −0.665986 0.745964i \(-0.731989\pi\)
−0.665986 + 0.745964i \(0.731989\pi\)
\(740\) 2.55734e21i 0.0284403i
\(741\) 1.07381e22 1.21559e22i 0.118136 0.133734i
\(742\) 2.85471e22 0.310692
\(743\) 9.49194e22i 1.02199i −0.859585 0.510993i \(-0.829278\pi\)
0.859585 0.510993i \(-0.170722\pi\)
\(744\) 5.16340e22 + 4.56117e22i 0.549987 + 0.485840i
\(745\) −2.43040e22 −0.256111
\(746\) 9.21007e22i 0.960180i
\(747\) −1.56059e22 + 1.94035e21i −0.160962 + 0.0200131i
\(748\) −2.13602e22 −0.217968
\(749\) 3.70659e21i 0.0374214i
\(750\) −3.02156e22 + 3.42050e22i −0.301815 + 0.341665i
\(751\) −1.45353e23 −1.43649 −0.718246 0.695789i \(-0.755055\pi\)
−0.718246 + 0.695789i \(0.755055\pi\)
\(752\) 3.45276e22i 0.337616i
\(753\) −1.14182e23 1.00864e23i −1.10468 0.975836i
\(754\) −9.18382e21 −0.0879129
\(755\) 1.33519e23i 1.26464i
\(756\) −3.35984e22 2.29785e22i −0.314879 0.215351i
\(757\) 6.76777e22 0.627594 0.313797 0.949490i \(-0.398399\pi\)
0.313797 + 0.949490i \(0.398399\pi\)
\(758\) 1.92865e22i 0.176970i
\(759\) 1.81642e22 2.05625e22i 0.164924 0.186699i
\(760\) 2.87582e23 2.58377
\(761\) 4.27404e22i 0.379981i 0.981786 + 0.189990i \(0.0608456\pi\)
−0.981786 + 0.189990i \(0.939154\pi\)
\(762\) −3.18899e22 2.81705e22i −0.280552 0.247830i
\(763\) 1.28668e23 1.12014
\(764\) 5.94102e22i 0.511817i
\(765\) −2.02534e22 1.62895e23i −0.172666 1.38873i
\(766\) −3.84079e22 −0.324034
\(767\) 1.23280e22i 0.102927i
\(768\) −7.84105e22 + 8.87634e22i −0.647865 + 0.733406i
\(769\) −8.99380e22 −0.735415 −0.367708 0.929941i \(-0.619857\pi\)
−0.367708 + 0.929941i \(0.619857\pi\)
\(770\) 5.51176e22i 0.446031i
\(771\) 1.10964e23 + 9.80217e22i 0.888683 + 0.785032i
\(772\) 3.13133e22 0.248193
\(773\) 9.93303e22i 0.779194i 0.920985 + 0.389597i \(0.127386\pi\)
−0.920985 + 0.389597i \(0.872614\pi\)
\(774\) 2.38609e22 2.96672e21i 0.185250 0.0230329i
\(775\) −4.61741e22 −0.354801