Properties

Label 6.17.b.a.5.6
Level 6
Weight 17
Character 6.5
Analytic conductor 9.739
Analytic rank 0
Dimension 6
CM No
Inner twists 2

Related objects

Downloads

Learn more about

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 5.6
Root \(-158.486i\)
Character \(\chi\) = 6.5
Dual form 6.17.b.a.5.3

$q$-expansion

\(f(q)\) \(=\) \(q+181.019i q^{2} +(6178.01 - 2208.83i) q^{3} -32768.0 q^{4} -548425. i q^{5} +(399841. + 1.11834e6i) q^{6} -8.81996e6 q^{7} -5.93164e6i q^{8} +(3.32888e7 - 2.72924e7i) q^{9} +O(q^{10})\) \(q+181.019i q^{2} +(6178.01 - 2208.83i) q^{3} -32768.0 q^{4} -548425. i q^{5} +(399841. + 1.11834e6i) q^{6} -8.81996e6 q^{7} -5.93164e6i q^{8} +(3.32888e7 - 2.72924e7i) q^{9} +9.92755e7 q^{10} -2.97767e8i q^{11} +(-2.02441e8 + 7.23790e7i) q^{12} +6.77774e8 q^{13} -1.59658e9i q^{14} +(-1.21138e9 - 3.38817e9i) q^{15} +1.07374e9 q^{16} +3.75977e9i q^{17} +(4.94045e9 + 6.02592e9i) q^{18} -9.70862e8 q^{19} +1.79708e10i q^{20} +(-5.44898e10 + 1.94818e10i) q^{21} +5.39016e10 q^{22} +2.68175e10i q^{23} +(-1.31020e10 - 3.66457e10i) q^{24} -1.48182e11 q^{25} +1.22690e11i q^{26} +(1.45374e11 - 2.42142e11i) q^{27} +2.89012e11 q^{28} -3.75954e11i q^{29} +(6.13325e11 - 2.19283e11i) q^{30} -4.78969e11 q^{31} +1.94368e11i q^{32} +(-6.57717e11 - 1.83961e12i) q^{33} -6.80590e11 q^{34} +4.83709e12i q^{35} +(-1.09081e12 + 8.94316e11i) q^{36} +9.79062e11 q^{37} -1.75745e11i q^{38} +(4.18729e12 - 1.49709e12i) q^{39} -3.25306e12 q^{40} +1.07974e13i q^{41} +(-3.52658e12 - 9.86370e12i) q^{42} +8.94265e12 q^{43} +9.75722e12i q^{44} +(-1.49678e13 - 1.82564e13i) q^{45} -4.85449e12 q^{46} -2.80443e13i q^{47} +(6.63359e12 - 2.37172e12i) q^{48} +4.45588e13 q^{49} -2.68238e13i q^{50} +(8.30469e12 + 2.32279e13i) q^{51} -2.22093e13 q^{52} +7.34316e13i q^{53} +(4.38324e13 + 2.63156e13i) q^{54} -1.63303e14 q^{55} +5.23168e13i q^{56} +(-5.99799e12 + 2.14447e12i) q^{57} +6.80550e13 q^{58} -1.35037e14i q^{59} +(3.96945e13 + 1.11024e14i) q^{60} +4.44549e13 q^{61} -8.67026e13i q^{62} +(-2.93606e14 + 2.40718e14i) q^{63} -3.51844e13 q^{64} -3.71708e14i q^{65} +(3.33004e14 - 1.19059e14i) q^{66} +6.70954e14 q^{67} -1.23200e14i q^{68} +(5.92354e13 + 1.65679e14i) q^{69} -8.75606e14 q^{70} -6.75764e14i q^{71} +(-1.61889e14 - 1.97457e14i) q^{72} +4.82017e14 q^{73} +1.77229e14i q^{74} +(-9.15470e14 + 3.27309e14i) q^{75} +3.18132e13 q^{76} +2.62629e15i q^{77} +(2.71002e14 + 7.57981e14i) q^{78} +3.05638e14 q^{79} -5.88867e14i q^{80} +(3.63274e14 - 1.81706e15i) q^{81} -1.95453e15 q^{82} +1.62564e15i q^{83} +(1.78552e15 - 6.38380e14i) q^{84} +2.06195e15 q^{85} +1.61879e15i q^{86} +(-8.30419e14 - 2.32265e15i) q^{87} -1.76625e15 q^{88} -3.89903e15i q^{89} +(3.30477e15 - 2.70946e15i) q^{90} -5.97794e15 q^{91} -8.78756e14i q^{92} +(-2.95907e15 + 1.05796e15i) q^{93} +5.07657e15 q^{94} +5.32445e14i q^{95} +(4.29326e14 + 1.20081e15i) q^{96} +1.41665e16 q^{97} +8.06600e15i q^{98} +(-8.12676e15 - 9.91231e15i) 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
\(3\) 6178.01 2208.83i 0.941626 0.336661i
\(4\) −32768.0 −0.500000
\(5\) 548425.i 1.40397i −0.712193 0.701984i \(-0.752298\pi\)
0.712193 0.701984i \(-0.247702\pi\)
\(6\) 399841. + 1.11834e6i 0.238055 + 0.665830i
\(7\) −8.81996e6 −1.52997 −0.764984 0.644049i \(-0.777253\pi\)
−0.764984 + 0.644049i \(0.777253\pi\)
\(8\) 5.93164e6i 0.353553i
\(9\) 3.32888e7 2.72924e7i 0.773319 0.634017i
\(10\) 9.92755e7 0.992755
\(11\) 2.97767e8i 1.38910i −0.719442 0.694552i \(-0.755603\pi\)
0.719442 0.694552i \(-0.244397\pi\)
\(12\) −2.02441e8 + 7.23790e7i −0.470813 + 0.168330i
\(13\) 6.77774e8 0.830880 0.415440 0.909621i \(-0.363628\pi\)
0.415440 + 0.909621i \(0.363628\pi\)
\(14\) 1.59658e9i 1.08185i
\(15\) −1.21138e9 3.38817e9i −0.472661 1.32201i
\(16\) 1.07374e9 0.250000
\(17\) 3.75977e9i 0.538976i 0.963004 + 0.269488i \(0.0868545\pi\)
−0.963004 + 0.269488i \(0.913146\pi\)
\(18\) 4.94045e9 + 6.02592e9i 0.448318 + 0.546819i
\(19\) −9.70862e8 −0.0571648 −0.0285824 0.999591i \(-0.509099\pi\)
−0.0285824 + 0.999591i \(0.509099\pi\)
\(20\) 1.79708e10i 0.701984i
\(21\) −5.44898e10 + 1.94818e10i −1.44066 + 0.515080i
\(22\) 5.39016e10 0.982245
\(23\) 2.68175e10i 0.342449i 0.985232 + 0.171224i \(0.0547723\pi\)
−0.985232 + 0.171224i \(0.945228\pi\)
\(24\) −1.31020e10 3.66457e10i −0.119028 0.332915i
\(25\) −1.48182e11 −0.971126
\(26\) 1.22690e11i 0.587521i
\(27\) 1.45374e11 2.42142e11i 0.514728 0.857353i
\(28\) 2.89012e11 0.764984
\(29\) 3.75954e11i 0.751538i −0.926713 0.375769i \(-0.877379\pi\)
0.926713 0.375769i \(-0.122621\pi\)
\(30\) 6.13325e11 2.19283e11i 0.934804 0.334222i
\(31\) −4.78969e11 −0.561583 −0.280791 0.959769i \(-0.590597\pi\)
−0.280791 + 0.959769i \(0.590597\pi\)
\(32\) 1.94368e11i 0.176777i
\(33\) −6.57717e11 1.83961e12i −0.467657 1.30802i
\(34\) −6.80590e11 −0.381114
\(35\) 4.83709e12i 2.14803i
\(36\) −1.09081e12 + 8.94316e11i −0.386659 + 0.317009i
\(37\) 9.79062e11 0.278738 0.139369 0.990241i \(-0.455493\pi\)
0.139369 + 0.990241i \(0.455493\pi\)
\(38\) 1.75745e11i 0.0404216i
\(39\) 4.18729e12 1.49709e12i 0.782378 0.279725i
\(40\) −3.25306e12 −0.496378
\(41\) 1.07974e13i 1.35222i 0.736802 + 0.676109i \(0.236335\pi\)
−0.736802 + 0.676109i \(0.763665\pi\)
\(42\) −3.52658e12 9.86370e12i −0.364217 1.01870i
\(43\) 8.94265e12 0.765100 0.382550 0.923935i \(-0.375046\pi\)
0.382550 + 0.923935i \(0.375046\pi\)
\(44\) 9.75722e12i 0.694552i
\(45\) −1.49678e13 1.82564e13i −0.890140 1.08571i
\(46\) −4.85449e12 −0.242148
\(47\) 2.80443e13i 1.17778i −0.808215 0.588888i \(-0.799566\pi\)
0.808215 0.588888i \(-0.200434\pi\)
\(48\) 6.63359e12 2.37172e12i 0.235406 0.0841652i
\(49\) 4.45588e13 1.34080
\(50\) 2.68238e13i 0.686690i
\(51\) 8.30469e12 + 2.32279e13i 0.181452 + 0.507514i
\(52\) −2.22093e13 −0.415440
\(53\) 7.34316e13i 1.17944i 0.807608 + 0.589720i \(0.200762\pi\)
−0.807608 + 0.589720i \(0.799238\pi\)
\(54\) 4.38324e13 + 2.63156e13i 0.606240 + 0.363968i
\(55\) −1.63303e14 −1.95026
\(56\) 5.23168e13i 0.540925i
\(57\) −5.99799e12 + 2.14447e12i −0.0538279 + 0.0192452i
\(58\) 6.80550e13 0.531417
\(59\) 1.35037e14i 0.919683i −0.888001 0.459841i \(-0.847906\pi\)
0.888001 0.459841i \(-0.152094\pi\)
\(60\) 3.96945e13 + 1.11024e14i 0.236331 + 0.661006i
\(61\) 4.44549e13 0.231890 0.115945 0.993256i \(-0.463010\pi\)
0.115945 + 0.993256i \(0.463010\pi\)
\(62\) 8.67026e13i 0.397099i
\(63\) −2.93606e14 + 2.40718e14i −1.18315 + 0.970026i
\(64\) −3.51844e13 −0.125000
\(65\) 3.71708e14i 1.16653i
\(66\) 3.33004e14 1.19059e14i 0.924907 0.330683i
\(67\) 6.70954e14 1.65232 0.826160 0.563435i \(-0.190521\pi\)
0.826160 + 0.563435i \(0.190521\pi\)
\(68\) 1.23200e14i 0.269488i
\(69\) 5.92354e13 + 1.65679e14i 0.115289 + 0.322459i
\(70\) −8.75606e14 −1.51888
\(71\) 6.75764e14i 1.04647i −0.852187 0.523237i \(-0.824724\pi\)
0.852187 0.523237i \(-0.175276\pi\)
\(72\) −1.61889e14 1.97457e14i −0.224159 0.273410i
\(73\) 4.82017e14 0.597695 0.298847 0.954301i \(-0.403398\pi\)
0.298847 + 0.954301i \(0.403398\pi\)
\(74\) 1.77229e14i 0.197098i
\(75\) −9.15470e14 + 3.27309e14i −0.914438 + 0.326940i
\(76\) 3.18132e13 0.0285824
\(77\) 2.62629e15i 2.12528i
\(78\) 2.71002e14 + 7.57981e14i 0.197795 + 0.553225i
\(79\) 3.05638e14 0.201461 0.100731 0.994914i \(-0.467882\pi\)
0.100731 + 0.994914i \(0.467882\pi\)
\(80\) 5.88867e14i 0.350992i
\(81\) 3.63274e14 1.81706e15i 0.196044 0.980595i
\(82\) −1.95453e15 −0.956162
\(83\) 1.62564e15i 0.721773i 0.932610 + 0.360886i \(0.117526\pi\)
−0.932610 + 0.360886i \(0.882474\pi\)
\(84\) 1.78552e15 6.38380e14i 0.720329 0.257540i
\(85\) 2.06195e15 0.756705
\(86\) 1.61879e15i 0.541008i
\(87\) −8.30419e14 2.32265e15i −0.253013 0.707667i
\(88\) −1.76625e15 −0.491123
\(89\) 3.89903e15i 0.990459i −0.868762 0.495230i \(-0.835084\pi\)
0.868762 0.495230i \(-0.164916\pi\)
\(90\) 3.30477e15 2.70946e15i 0.767716 0.629424i
\(91\) −5.97794e15 −1.27122
\(92\) 8.78756e14i 0.171224i
\(93\) −2.95907e15 + 1.05796e15i −0.528801 + 0.189063i
\(94\) 5.07657e15 0.832813
\(95\) 5.32445e14i 0.0802576i
\(96\) 4.29326e14 + 1.20081e15i 0.0595138 + 0.166458i
\(97\) 1.41665e16 1.80754 0.903769 0.428021i \(-0.140789\pi\)
0.903769 + 0.428021i \(0.140789\pi\)
\(98\) 8.06600e15i 0.948090i
\(99\) −8.12676e15 9.91231e15i −0.880716 1.07422i
\(100\) 4.85563e15 0.485563
\(101\) 8.68808e15i 0.802330i 0.916006 + 0.401165i \(0.131395\pi\)
−0.916006 + 0.401165i \(0.868605\pi\)
\(102\) −4.20469e15 + 1.50331e15i −0.358866 + 0.128306i
\(103\) −2.33033e16 −1.83959 −0.919794 0.392402i \(-0.871644\pi\)
−0.919794 + 0.392402i \(0.871644\pi\)
\(104\) 4.02031e15i 0.293760i
\(105\) 1.06843e16 + 2.98836e16i 0.723156 + 2.02264i
\(106\) −1.32925e16 −0.833990
\(107\) 6.31512e15i 0.367546i −0.982969 0.183773i \(-0.941169\pi\)
0.982969 0.183773i \(-0.0588311\pi\)
\(108\) −4.76363e15 + 7.93451e15i −0.257364 + 0.428677i
\(109\) 2.25696e16 1.13269 0.566347 0.824167i \(-0.308356\pi\)
0.566347 + 0.824167i \(0.308356\pi\)
\(110\) 2.95610e16i 1.37904i
\(111\) 6.04865e15 2.16258e15i 0.262467 0.0938402i
\(112\) −9.47036e15 −0.382492
\(113\) 2.00529e16i 0.754311i −0.926150 0.377155i \(-0.876902\pi\)
0.926150 0.377155i \(-0.123098\pi\)
\(114\) −3.88191e14 1.08575e15i −0.0136084 0.0380621i
\(115\) 1.47074e16 0.480787
\(116\) 1.23193e16i 0.375769i
\(117\) 2.25623e16 1.84981e16i 0.642535 0.526792i
\(118\) 2.44444e16 0.650314
\(119\) 3.31610e16i 0.824616i
\(120\) −2.00974e16 + 7.18546e15i −0.467402 + 0.167111i
\(121\) −4.27154e16 −0.929611
\(122\) 8.04720e15i 0.163971i
\(123\) 2.38495e16 + 6.67061e16i 0.455239 + 1.27328i
\(124\) 1.56949e16 0.280791
\(125\) 2.41626e15i 0.0405381i
\(126\) −4.35745e16 5.31484e16i −0.685912 0.836616i
\(127\) −1.00499e17 −1.48501 −0.742506 0.669839i \(-0.766363\pi\)
−0.742506 + 0.669839i \(0.766363\pi\)
\(128\) 6.36905e15i 0.0883883i
\(129\) 5.52477e16 1.97528e16i 0.720438 0.257579i
\(130\) 6.72864e16 0.824860
\(131\) 8.13030e16i 0.937424i 0.883351 + 0.468712i \(0.155282\pi\)
−0.883351 + 0.468712i \(0.844718\pi\)
\(132\) 2.15521e16 + 6.02802e16i 0.233829 + 0.654008i
\(133\) 8.56297e15 0.0874603
\(134\) 1.21456e17i 1.16837i
\(135\) −1.32797e17 7.97270e16i −1.20370 0.722662i
\(136\) 2.23016e16 0.190557
\(137\) 1.68892e17i 1.36096i 0.732768 + 0.680478i \(0.238228\pi\)
−0.732768 + 0.680478i \(0.761772\pi\)
\(138\) −2.99911e16 + 1.07227e16i −0.228013 + 0.0815217i
\(139\) 1.17875e17 0.845867 0.422934 0.906161i \(-0.361000\pi\)
0.422934 + 0.906161i \(0.361000\pi\)
\(140\) 1.58502e17i 1.07401i
\(141\) −6.19452e16 1.73258e17i −0.396511 1.10902i
\(142\) 1.22326e17 0.739969
\(143\) 2.01819e17i 1.15418i
\(144\) 3.57436e16 2.93050e16i 0.193330 0.158504i
\(145\) −2.06183e17 −1.05513
\(146\) 8.72544e16i 0.422634i
\(147\) 2.75284e17 9.84228e16i 1.26253 0.451395i
\(148\) −3.20819e16 −0.139369
\(149\) 3.69639e16i 0.152156i 0.997102 + 0.0760778i \(0.0242397\pi\)
−0.997102 + 0.0760778i \(0.975760\pi\)
\(150\) −5.92493e16 1.65718e17i −0.231182 0.646605i
\(151\) −2.48497e16 −0.0919403 −0.0459702 0.998943i \(-0.514638\pi\)
−0.0459702 + 0.998943i \(0.514638\pi\)
\(152\) 5.75881e15i 0.0202108i
\(153\) 1.02613e17 + 1.25158e17i 0.341720 + 0.416800i
\(154\) −4.75410e17 −1.50280
\(155\) 2.62678e17i 0.788444i
\(156\) −1.37209e17 + 4.90566e16i −0.391189 + 0.139862i
\(157\) 4.63885e17 1.25665 0.628324 0.777952i \(-0.283741\pi\)
0.628324 + 0.777952i \(0.283741\pi\)
\(158\) 5.53265e16i 0.142454i
\(159\) 1.62198e17 + 4.53661e17i 0.397071 + 1.11059i
\(160\) 1.06596e17 0.248189
\(161\) 2.36529e17i 0.523936i
\(162\) 3.28923e17 + 6.57596e16i 0.693385 + 0.138624i
\(163\) 2.12872e16 0.0427187 0.0213593 0.999772i \(-0.493201\pi\)
0.0213593 + 0.999772i \(0.493201\pi\)
\(164\) 3.53808e17i 0.676109i
\(165\) −1.00889e18 + 3.60708e17i −1.83641 + 0.656576i
\(166\) −2.94273e17 −0.510370
\(167\) 5.29792e16i 0.0875737i −0.999041 0.0437868i \(-0.986058\pi\)
0.999041 0.0437868i \(-0.0139422\pi\)
\(168\) 1.15559e17 + 3.23214e17i 0.182108 + 0.509349i
\(169\) −2.06039e17 −0.309639
\(170\) 3.73253e17i 0.535071i
\(171\) −3.23189e16 + 2.64971e16i −0.0442066 + 0.0362435i
\(172\) −2.93033e17 −0.382550
\(173\) 1.09697e18i 1.36718i −0.729867 0.683590i \(-0.760418\pi\)
0.729867 0.683590i \(-0.239582\pi\)
\(174\) 4.20444e17 1.50322e17i 0.500396 0.178907i
\(175\) 1.30696e18 1.48579
\(176\) 3.19725e17i 0.347276i
\(177\) −2.98275e17 8.34262e17i −0.309621 0.865997i
\(178\) 7.05800e17 0.700360
\(179\) 3.50481e17i 0.332537i 0.986081 + 0.166269i \(0.0531719\pi\)
−0.986081 + 0.166269i \(0.946828\pi\)
\(180\) 4.90465e17 + 5.98227e17i 0.445070 + 0.542857i
\(181\) −1.16227e18 −1.00897 −0.504487 0.863419i \(-0.668318\pi\)
−0.504487 + 0.863419i \(0.668318\pi\)
\(182\) 1.08212e18i 0.898888i
\(183\) 2.74643e17 9.81935e16i 0.218353 0.0780682i
\(184\) 1.59072e17 0.121074
\(185\) 5.36942e17i 0.391339i
\(186\) −1.91512e17 5.35649e17i −0.133688 0.373919i
\(187\) 1.11953e18 0.748694
\(188\) 9.18957e17i 0.588888i
\(189\) −1.28220e18 + 2.13568e18i −0.787518 + 1.31172i
\(190\) −9.63829e16 −0.0567507
\(191\) 5.02220e17i 0.283548i 0.989899 + 0.141774i \(0.0452807\pi\)
−0.989899 + 0.141774i \(0.954719\pi\)
\(192\) −2.17369e17 + 7.77164e16i −0.117703 + 0.0420826i
\(193\) −1.79109e18 −0.930379 −0.465190 0.885211i \(-0.654014\pi\)
−0.465190 + 0.885211i \(0.654014\pi\)
\(194\) 2.56440e18i 1.27812i
\(195\) −8.21041e17 2.29642e18i −0.392725 1.09843i
\(196\) −1.46010e18 −0.670401
\(197\) 2.08085e18i 0.917297i 0.888618 + 0.458649i \(0.151666\pi\)
−0.888618 + 0.458649i \(0.848334\pi\)
\(198\) 1.79432e18 1.47110e18i 0.759589 0.622760i
\(199\) −1.32205e18 −0.537554 −0.268777 0.963202i \(-0.586619\pi\)
−0.268777 + 0.963202i \(0.586619\pi\)
\(200\) 8.78963e17i 0.343345i
\(201\) 4.14516e18 1.48202e18i 1.55587 0.556272i
\(202\) −1.57271e18 −0.567333
\(203\) 3.31590e18i 1.14983i
\(204\) −2.72128e17 7.61131e17i −0.0907261 0.253757i
\(205\) 5.92154e18 1.89847
\(206\) 4.21836e18i 1.30079i
\(207\) 7.31913e17 + 8.92724e17i 0.217119 + 0.264822i
\(208\) 7.27754e17 0.207720
\(209\) 2.89091e17i 0.0794079i
\(210\) −5.40950e18 + 1.93407e18i −1.43022 + 0.511349i
\(211\) −3.76539e18 −0.958409 −0.479204 0.877703i \(-0.659075\pi\)
−0.479204 + 0.877703i \(0.659075\pi\)
\(212\) 2.40621e18i 0.589720i
\(213\) −1.49265e18 4.17488e18i −0.352307 0.985387i
\(214\) 1.14316e18 0.259894
\(215\) 4.90437e18i 1.07418i
\(216\) −1.43630e18 8.62309e17i −0.303120 0.181984i
\(217\) 4.22449e18 0.859203
\(218\) 4.08554e18i 0.800935i
\(219\) 2.97791e18 1.06469e18i 0.562805 0.201220i
\(220\) 5.35111e18 0.975129
\(221\) 2.54827e18i 0.447824i
\(222\) 3.91469e17 + 1.09492e18i 0.0663550 + 0.185592i
\(223\) −7.62525e18 −1.24685 −0.623426 0.781882i \(-0.714260\pi\)
−0.623426 + 0.781882i \(0.714260\pi\)
\(224\) 1.71432e18i 0.270463i
\(225\) −4.93281e18 + 4.04424e18i −0.750990 + 0.615711i
\(226\) 3.62997e18 0.533378
\(227\) 1.03157e19i 1.46316i −0.681755 0.731580i \(-0.738783\pi\)
0.681755 0.731580i \(-0.261217\pi\)
\(228\) 1.96542e17 7.02700e16i 0.0269139 0.00962258i
\(229\) −1.17626e18 −0.155532 −0.0777659 0.996972i \(-0.524779\pi\)
−0.0777659 + 0.996972i \(0.524779\pi\)
\(230\) 2.66232e18i 0.339968i
\(231\) 5.80104e18 + 1.62252e19i 0.715500 + 2.00122i
\(232\) −2.23002e18 −0.265709
\(233\) 1.08482e19i 1.24885i 0.781086 + 0.624423i \(0.214666\pi\)
−0.781086 + 0.624423i \(0.785334\pi\)
\(234\) 3.34851e18 + 4.08422e18i 0.372498 + 0.454341i
\(235\) −1.53802e19 −1.65356
\(236\) 4.42491e18i 0.459841i
\(237\) 1.88824e18 6.75104e17i 0.189701 0.0678241i
\(238\) 6.00278e18 0.583091
\(239\) 5.84823e18i 0.549340i −0.961539 0.274670i \(-0.911431\pi\)
0.961539 0.274670i \(-0.0885687\pi\)
\(240\) −1.30071e18 3.63802e18i −0.118165 0.330503i
\(241\) 6.67037e18 0.586157 0.293078 0.956088i \(-0.405320\pi\)
0.293078 + 0.956088i \(0.405320\pi\)
\(242\) 7.73231e18i 0.657334i
\(243\) −1.76928e18 1.20282e19i −0.145528 0.989354i
\(244\) −1.45670e18 −0.115945
\(245\) 2.44371e19i 1.88244i
\(246\) −1.20751e19 + 4.31723e18i −0.900347 + 0.321902i
\(247\) −6.58025e17 −0.0474971
\(248\) 2.84107e18i 0.198549i
\(249\) 3.59077e18 + 1.00432e19i 0.242993 + 0.679640i
\(250\) 4.37389e17 0.0286647
\(251\) 1.76579e19i 1.12085i 0.828205 + 0.560426i \(0.189363\pi\)
−0.828205 + 0.560426i \(0.810637\pi\)
\(252\) 9.62089e18 7.88783e18i 0.591576 0.485013i
\(253\) 7.98537e18 0.475697
\(254\) 1.81922e19i 1.05006i
\(255\) 1.27387e19 4.55450e18i 0.712533 0.254753i
\(256\) 1.15292e18 0.0625000
\(257\) 3.98050e18i 0.209157i −0.994517 0.104579i \(-0.966651\pi\)
0.994517 0.104579i \(-0.0333494\pi\)
\(258\) 3.57564e18 + 1.00009e19i 0.182136 + 0.509427i
\(259\) −8.63528e18 −0.426460
\(260\) 1.21801e19i 0.583264i
\(261\) −1.02607e19 1.25151e19i −0.476488 0.581178i
\(262\) −1.47174e19 −0.662859
\(263\) 1.01302e19i 0.442559i 0.975210 + 0.221279i \(0.0710233\pi\)
−0.975210 + 0.221279i \(0.928977\pi\)
\(264\) −1.09119e19 + 3.90134e18i −0.462454 + 0.165342i
\(265\) 4.02717e19 1.65590
\(266\) 1.55006e18i 0.0618438i
\(267\) −8.61230e18 2.40882e19i −0.333449 0.932642i
\(268\) −2.19858e19 −0.826160
\(269\) 4.60904e19i 1.68109i 0.541739 + 0.840547i \(0.317766\pi\)
−0.541739 + 0.840547i \(0.682234\pi\)
\(270\) 1.44321e19 2.40388e19i 0.510999 0.851142i
\(271\) 2.83745e19 0.975382 0.487691 0.873016i \(-0.337839\pi\)
0.487691 + 0.873016i \(0.337839\pi\)
\(272\) 4.03702e18i 0.134744i
\(273\) −3.69318e19 + 1.32043e19i −1.19701 + 0.427970i
\(274\) −3.05727e19 −0.962341
\(275\) 4.41237e19i 1.34900i
\(276\) −1.94102e18 5.42896e18i −0.0576446 0.161229i
\(277\) −2.50576e19 −0.722939 −0.361470 0.932384i \(-0.617725\pi\)
−0.361470 + 0.932384i \(0.617725\pi\)
\(278\) 2.13376e19i 0.598118i
\(279\) −1.59443e19 + 1.30722e19i −0.434282 + 0.356053i
\(280\) 2.86919e19 0.759442
\(281\) 3.81217e19i 0.980668i −0.871535 0.490334i \(-0.836875\pi\)
0.871535 0.490334i \(-0.163125\pi\)
\(282\) 3.13631e19 1.12133e19i 0.784198 0.280376i
\(283\) −1.65340e19 −0.401870 −0.200935 0.979605i \(-0.564398\pi\)
−0.200935 + 0.979605i \(0.564398\pi\)
\(284\) 2.21434e19i 0.523237i
\(285\) 1.17608e18 + 3.28945e18i 0.0270196 + 0.0755726i
\(286\) 3.65331e19 0.816128
\(287\) 9.52322e19i 2.06885i
\(288\) 5.30476e18 + 6.47029e18i 0.112079 + 0.136705i
\(289\) 3.45254e19 0.709505
\(290\) 3.73230e19i 0.746093i
\(291\) 8.75205e19 3.12913e19i 1.70202 0.608527i
\(292\) −1.57947e19 −0.298847
\(293\) 7.32082e18i 0.134778i 0.997727 + 0.0673889i \(0.0214668\pi\)
−0.997727 + 0.0673889i \(0.978533\pi\)
\(294\) 1.78164e19 + 4.98318e19i 0.319185 + 0.892746i
\(295\) −7.40579e19 −1.29120
\(296\) 5.80744e18i 0.0985488i
\(297\) −7.21018e19 4.32877e19i −1.19095 0.715011i
\(298\) −6.69119e18 −0.107590
\(299\) 1.81762e19i 0.284534i
\(300\) 2.99981e19 1.07253e19i 0.457219 0.163470i
\(301\) −7.88738e19 −1.17058
\(302\) 4.49828e18i 0.0650116i
\(303\) 1.91905e19 + 5.36751e19i 0.270113 + 0.755495i
\(304\) −1.04246e18 −0.0142912
\(305\) 2.43802e19i 0.325566i
\(306\) −2.26561e19 + 1.85749e19i −0.294722 + 0.241633i
\(307\) 1.46906e20 1.86179 0.930896 0.365284i \(-0.119028\pi\)
0.930896 + 0.365284i \(0.119028\pi\)
\(308\) 8.60583e19i 1.06264i
\(309\) −1.43968e20 + 5.14732e19i −1.73220 + 0.619317i
\(310\) −4.75499e19 −0.557514
\(311\) 1.24018e20i 1.41710i 0.705659 + 0.708552i \(0.250651\pi\)
−0.705659 + 0.708552i \(0.749349\pi\)
\(312\) −8.88020e18 2.48375e19i −0.0988976 0.276612i
\(313\) 1.48074e20 1.60740 0.803700 0.595035i \(-0.202862\pi\)
0.803700 + 0.595035i \(0.202862\pi\)
\(314\) 8.39722e19i 0.888584i
\(315\) 1.32016e20 + 1.61021e20i 1.36189 + 1.66111i
\(316\) −1.00152e19 −0.100731
\(317\) 1.99460e20i 1.95606i −0.208460 0.978031i \(-0.566845\pi\)
0.208460 0.978031i \(-0.433155\pi\)
\(318\) −8.21214e19 + 2.93610e19i −0.785306 + 0.280772i
\(319\) −1.11947e20 −1.04396
\(320\) 1.92960e19i 0.175496i
\(321\) −1.39490e19 3.90148e19i −0.123738 0.346090i
\(322\) 4.28164e19 0.370479
\(323\) 3.65021e18i 0.0308105i
\(324\) −1.19038e19 + 5.95415e19i −0.0980221 + 0.490298i
\(325\) −1.00434e20 −0.806889
\(326\) 3.85340e18i 0.0302067i
\(327\) 1.39435e20 4.98525e19i 1.06657 0.381333i
\(328\) 6.40460e19 0.478081
\(329\) 2.47350e20i 1.80196i
\(330\) −6.52952e19 1.82628e20i −0.464269 1.29854i
\(331\) −1.27378e20 −0.884036 −0.442018 0.897006i \(-0.645737\pi\)
−0.442018 + 0.897006i \(0.645737\pi\)
\(332\) 5.32691e19i 0.360886i
\(333\) 3.25918e19 2.67209e19i 0.215553 0.176725i
\(334\) 9.59026e18 0.0619240
\(335\) 3.67968e20i 2.31980i
\(336\) −5.85080e19 + 2.09184e19i −0.360164 + 0.128770i
\(337\) 2.66631e20 1.60277 0.801386 0.598148i \(-0.204096\pi\)
0.801386 + 0.598148i \(0.204096\pi\)
\(338\) 3.72970e19i 0.218948i
\(339\) −4.42936e19 1.23887e20i −0.253947 0.710279i
\(340\) −6.75660e19 −0.378353
\(341\) 1.42621e20i 0.780097i
\(342\) −4.79649e18 5.85034e18i −0.0256280 0.0312588i
\(343\) −9.98933e19 −0.521415
\(344\) 5.30446e19i 0.270504i
\(345\) 9.08624e19 3.24862e19i 0.452722 0.161862i
\(346\) 1.98573e20 0.966742
\(347\) 1.22916e20i 0.584753i 0.956303 + 0.292377i \(0.0944461\pi\)
−0.956303 + 0.292377i \(0.905554\pi\)
\(348\) 2.72112e19 + 7.61085e19i 0.126507 + 0.353834i
\(349\) −5.33630e19 −0.242458 −0.121229 0.992625i \(-0.538684\pi\)
−0.121229 + 0.992625i \(0.538684\pi\)
\(350\) 2.36585e20i 1.05061i
\(351\) 9.85311e19 1.64118e20i 0.427677 0.712358i
\(352\) 5.78764e19 0.245561
\(353\) 2.08236e20i 0.863689i 0.901948 + 0.431844i \(0.142137\pi\)
−0.901948 + 0.431844i \(0.857863\pi\)
\(354\) 1.51018e20 5.39935e19i 0.612352 0.218935i
\(355\) −3.70606e20 −1.46922
\(356\) 1.27763e20i 0.495230i
\(357\) −7.32470e19 2.04869e20i −0.277616 0.776480i
\(358\) −6.34438e19 −0.235139
\(359\) 5.45140e20i 1.97584i 0.154958 + 0.987921i \(0.450476\pi\)
−0.154958 + 0.987921i \(0.549524\pi\)
\(360\) −1.08291e20 + 8.87837e19i −0.383858 + 0.314712i
\(361\) −2.87499e20 −0.996732
\(362\) 2.10394e20i 0.713452i
\(363\) −2.63896e20 + 9.43511e19i −0.875346 + 0.312964i
\(364\) 1.95885e20 0.635610
\(365\) 2.64350e20i 0.839144i
\(366\) 1.77749e19 + 4.97157e19i 0.0552025 + 0.154399i
\(367\) −4.49668e19 −0.136635 −0.0683177 0.997664i \(-0.521763\pi\)
−0.0683177 + 0.997664i \(0.521763\pi\)
\(368\) 2.87951e19i 0.0856122i
\(369\) 2.94685e20 + 3.59431e20i 0.857329 + 1.04570i
\(370\) 9.71969e19 0.276719
\(371\) 6.47663e20i 1.80450i
\(372\) 9.69629e19 3.46673e19i 0.264400 0.0945315i
\(373\) 5.45992e20 1.45719 0.728593 0.684946i \(-0.240174\pi\)
0.728593 + 0.684946i \(0.240174\pi\)
\(374\) 2.02657e20i 0.529406i
\(375\) −5.33711e18 1.49277e19i −0.0136476 0.0381717i
\(376\) −1.66349e20 −0.416406
\(377\) 2.54812e20i 0.624438i
\(378\) −3.86600e20 2.32102e20i −0.927528 0.556859i
\(379\) −6.86587e19 −0.161281 −0.0806403 0.996743i \(-0.525697\pi\)
−0.0806403 + 0.996743i \(0.525697\pi\)
\(380\) 1.74472e19i 0.0401288i
\(381\) −6.20881e20 + 2.21984e20i −1.39833 + 0.499946i
\(382\) −9.09115e19 −0.200499
\(383\) 4.63825e20i 1.00176i 0.865517 + 0.500880i \(0.166990\pi\)
−0.865517 + 0.500880i \(0.833010\pi\)
\(384\) −1.40682e19 3.93481e19i −0.0297569 0.0832288i
\(385\) 1.44032e21 2.98383
\(386\) 3.24223e20i 0.657877i
\(387\) 2.97690e20 2.44066e20i 0.591667 0.485087i
\(388\) −4.64206e20 −0.903769
\(389\) 6.10357e20i 1.16409i −0.813156 0.582046i \(-0.802252\pi\)
0.813156 0.582046i \(-0.197748\pi\)
\(390\) 4.15696e20 1.48624e20i 0.776710 0.277698i
\(391\) −1.00828e20 −0.184572
\(392\) 2.64307e20i 0.474045i
\(393\) 1.79585e20 + 5.02290e20i 0.315594 + 0.882703i
\(394\) −3.76673e20 −0.648627
\(395\) 1.67620e20i 0.282845i
\(396\) 2.66298e20 + 3.24807e20i 0.440358 + 0.537110i
\(397\) −6.66393e20 −1.07996 −0.539979 0.841679i \(-0.681568\pi\)
−0.539979 + 0.841679i \(0.681568\pi\)
\(398\) 2.39316e20i 0.380108i
\(399\) 5.29021e19 1.89142e19i 0.0823549 0.0294445i
\(400\) −1.59109e20 −0.242782
\(401\) 3.54618e20i 0.530403i 0.964193 + 0.265201i \(0.0854384\pi\)
−0.964193 + 0.265201i \(0.914562\pi\)
\(402\) 2.68275e20 + 7.50354e20i 0.393343 + 1.10016i
\(403\) −3.24633e20 −0.466608
\(404\) 2.84691e20i 0.401165i
\(405\) −9.96522e20 1.99229e20i −1.37672 0.275240i
\(406\) −6.00242e20 −0.813052
\(407\) 2.91532e20i 0.387196i
\(408\) 1.37779e20 4.92605e19i 0.179433 0.0641530i
\(409\) −5.68936e19 −0.0726569 −0.0363284 0.999340i \(-0.511566\pi\)
−0.0363284 + 0.999340i \(0.511566\pi\)
\(410\) 1.07191e21i 1.34242i
\(411\) 3.73054e20 + 1.04342e21i 0.458181 + 1.28151i
\(412\) 7.63604e20 0.919794
\(413\) 1.19102e21i 1.40708i
\(414\) −1.61600e20 + 1.32490e20i −0.187258 + 0.153526i
\(415\) 8.91543e20 1.01335
\(416\) 1.31738e20i 0.146880i
\(417\) 7.28231e20 2.60365e20i 0.796491 0.284770i
\(418\) −5.23310e19 −0.0561499
\(419\) 1.43563e20i 0.151123i −0.997141 0.0755614i \(-0.975925\pi\)
0.997141 0.0755614i \(-0.0240749\pi\)
\(420\) −3.50104e20 9.79224e20i −0.361578 1.01132i
\(421\) −6.44522e20 −0.653102 −0.326551 0.945180i \(-0.605886\pi\)
−0.326551 + 0.945180i \(0.605886\pi\)
\(422\) 6.81609e20i 0.677697i
\(423\) −7.65396e20 9.33564e20i −0.746730 0.910796i
\(424\) 4.35570e20 0.416995
\(425\) 5.57130e20i 0.523414i
\(426\) 7.55734e20 2.70199e20i 0.696774 0.249119i
\(427\) −3.92091e20 −0.354784
\(428\) 2.06934e20i 0.183773i
\(429\) −4.45784e20 1.24684e21i −0.388567 1.08680i
\(430\) 8.87786e20 0.759557
\(431\) 1.78139e20i 0.149603i 0.997198 + 0.0748017i \(0.0238324\pi\)
−0.997198 + 0.0748017i \(0.976168\pi\)
\(432\) 1.56095e20 2.59998e20i 0.128682 0.214338i
\(433\) 7.63467e20 0.617855 0.308928 0.951086i \(-0.400030\pi\)
0.308928 + 0.951086i \(0.400030\pi\)
\(434\) 7.64714e20i 0.607549i
\(435\) −1.27380e21 + 4.55423e20i −0.993542 + 0.355223i
\(436\) −7.39561e20 −0.566347
\(437\) 2.60361e19i 0.0195760i
\(438\) 1.92730e20 + 5.39058e20i 0.142284 + 0.397963i
\(439\) 3.77361e19 0.0273552 0.0136776 0.999906i \(-0.495646\pi\)
0.0136776 + 0.999906i \(0.495646\pi\)
\(440\) 9.68654e20i 0.689520i
\(441\) 1.48331e21 1.21611e21i 1.03687 0.850091i
\(442\) −4.61287e20 −0.316660
\(443\) 1.54395e21i 1.04088i −0.853897 0.520442i \(-0.825767\pi\)
0.853897 0.520442i \(-0.174233\pi\)
\(444\) −1.98202e20 + 7.08635e19i −0.131233 + 0.0469201i
\(445\) −2.13833e21 −1.39057
\(446\) 1.38032e21i 0.881658i
\(447\) 8.16471e19 + 2.28363e20i 0.0512248 + 0.143274i
\(448\) 3.10325e20 0.191246
\(449\) 1.33836e21i 0.810219i 0.914268 + 0.405109i \(0.132767\pi\)
−0.914268 + 0.405109i \(0.867233\pi\)
\(450\) −7.32086e20 8.92934e20i −0.435373 0.531030i
\(451\) 3.21509e21 1.87837
\(452\) 6.57095e20i 0.377155i
\(453\) −1.53522e20 + 5.48889e19i −0.0865734 + 0.0309527i
\(454\) 1.86734e21 1.03461
\(455\) 3.27845e21i 1.78475i
\(456\) 1.27202e19 + 3.55780e19i 0.00680419 + 0.0190310i
\(457\) −1.28524e21 −0.675544 −0.337772 0.941228i \(-0.609673\pi\)
−0.337772 + 0.941228i \(0.609673\pi\)
\(458\) 2.12926e20i 0.109978i
\(459\) 9.10397e20 + 5.46574e20i 0.462093 + 0.277426i
\(460\) −4.81932e20 −0.240394
\(461\) 6.09388e20i 0.298735i 0.988782 + 0.149368i \(0.0477238\pi\)
−0.988782 + 0.149368i \(0.952276\pi\)
\(462\) −2.93708e21 + 1.05010e21i −1.41508 + 0.505935i
\(463\) 2.09033e21 0.989843 0.494922 0.868938i \(-0.335197\pi\)
0.494922 + 0.868938i \(0.335197\pi\)
\(464\) 4.03678e20i 0.187884i
\(465\) 5.80213e20 + 1.62283e21i 0.265438 + 0.742419i
\(466\) −1.96373e21 −0.883068
\(467\) 1.09633e21i 0.484626i 0.970198 + 0.242313i \(0.0779062\pi\)
−0.970198 + 0.242313i \(0.922094\pi\)
\(468\) −7.39322e20 + 6.06144e20i −0.321268 + 0.263396i
\(469\) −5.91779e21 −2.52800
\(470\) 2.78412e21i 1.16924i
\(471\) 2.86589e21 1.02464e21i 1.18329 0.423064i
\(472\) −8.00993e20 −0.325157
\(473\) 2.66282e21i 1.06280i
\(474\) 1.22207e20 + 3.41807e20i 0.0479589 + 0.134139i
\(475\) 1.43864e20 0.0555142
\(476\) 1.08662e21i 0.412308i
\(477\) 2.00412e21 + 2.44445e21i 0.747785 + 0.912083i
\(478\) 1.05864e21 0.388442
\(479\) 1.81172e21i 0.653744i −0.945069 0.326872i \(-0.894005\pi\)
0.945069 0.326872i \(-0.105995\pi\)
\(480\) 6.58553e20 2.35453e20i 0.233701 0.0835555i
\(481\) 6.63583e20 0.231598
\(482\) 1.20747e21i 0.414475i
\(483\) −5.22454e20 1.46128e21i −0.176389 0.493352i
\(484\) 1.39970e21 0.464805
\(485\) 7.76924e21i 2.53772i
\(486\) 2.17734e21 3.20273e20i 0.699579 0.102904i
\(487\) −6.83278e19 −0.0215956 −0.0107978 0.999942i \(-0.503437\pi\)
−0.0107978 + 0.999942i \(0.503437\pi\)
\(488\) 2.63691e20i 0.0819854i
\(489\) 1.31513e20 4.70199e19i 0.0402250 0.0143817i
\(490\) 4.42359e21 1.33109
\(491\) 1.74579e20i 0.0516820i 0.999666 + 0.0258410i \(0.00822636\pi\)
−0.999666 + 0.0258410i \(0.991774\pi\)
\(492\) −7.81502e20 2.18583e21i −0.227619 0.636641i
\(493\) 1.41350e21 0.405061
\(494\) 1.19115e20i 0.0335855i
\(495\) −5.43616e21 + 4.45692e21i −1.50817 + 1.23650i
\(496\) −5.14289e20 −0.140396
\(497\) 5.96021e21i 1.60107i
\(498\) −1.81802e21 + 6.49999e20i −0.480578 + 0.171822i
\(499\) −1.38375e21 −0.359960 −0.179980 0.983670i \(-0.557603\pi\)
−0.179980 + 0.983670i \(0.557603\pi\)
\(500\) 7.91759e19i 0.0202690i
\(501\) −1.17022e20 3.27306e20i −0.0294826 0.0824617i
\(502\) −3.19641e21 −0.792562
\(503\) 6.68741e21i 1.63198i −0.578068 0.815988i \(-0.696193\pi\)
0.578068 0.815988i \(-0.303807\pi\)
\(504\) 1.42785e21 + 1.74157e21i 0.342956 + 0.418308i
\(505\) 4.76476e21 1.12645
\(506\) 1.44551e21i 0.336369i
\(507\) −1.27291e21 + 4.55105e20i −0.291564 + 0.104243i
\(508\) 3.29314e21 0.742506
\(509\) 3.92709e21i 0.871623i −0.900038 0.435812i \(-0.856461\pi\)
0.900038 0.435812i \(-0.143539\pi\)
\(510\) 8.24453e20 + 2.30596e21i 0.180138 + 0.503837i
\(511\) −4.25137e21 −0.914454
\(512\) 2.08701e20i 0.0441942i
\(513\) −1.41139e20 + 2.35086e20i −0.0294244 + 0.0490104i
\(514\) 7.20548e20 0.147897
\(515\) 1.27801e22i 2.58272i
\(516\) −1.81036e21 + 6.47260e20i −0.360219 + 0.128790i
\(517\) −8.35068e21 −1.63605
\(518\) 1.56315e21i 0.301553i
\(519\) −2.42302e21 6.77708e21i −0.460276 1.28737i
\(520\) −2.20484e21 −0.412430
\(521\) 1.00353e22i 1.84854i 0.381743 + 0.924268i \(0.375324\pi\)
−0.381743 + 0.924268i \(0.624676\pi\)
\(522\) 2.26547e21 1.85738e21i 0.410955 0.336928i
\(523\) 6.06629e21 1.08370 0.541851 0.840475i \(-0.317724\pi\)
0.541851 + 0.840475i \(0.317724\pi\)
\(524\) 2.66414e21i 0.468712i
\(525\) 8.07441e21 2.88686e21i 1.39906 0.500208i
\(526\) −1.83376e21 −0.312936
\(527\) 1.80081e21i 0.302680i
\(528\) −7.06218e20 1.97526e21i −0.116914 0.327004i
\(529\) 5.41343e21 0.882729
\(530\) 7.28996e21i 1.17090i
\(531\) −3.68549e21 4.49524e21i −0.583095 0.711208i
\(532\) −2.80591e20 −0.0437302
\(533\) 7.31817e21i 1.12353i
\(534\) 4.36044e21 1.55899e21i 0.659478 0.235784i
\(535\) −3.46337e21 −0.516022
\(536\) 3.97986e21i 0.584183i
\(537\) 7.74153e20 + 2.16527e21i 0.111952 + 0.313126i
\(538\) −8.34325e21 −1.18871
\(539\) 1.32681e22i 1.86251i
\(540\) 4.35148e21 + 2.61249e21i 0.601848 + 0.361331i
\(541\) 1.03705e22 1.41325 0.706626 0.707587i \(-0.250216\pi\)
0.706626 + 0.707587i \(0.250216\pi\)
\(542\) 5.13634e21i 0.689699i
\(543\) −7.18054e21 + 2.56727e21i −0.950076 + 0.339682i
\(544\) −7.30778e20 −0.0952784
\(545\) 1.23777e22i 1.59026i
\(546\) −2.39023e21 6.68536e21i −0.302620 0.846416i
\(547\) 8.78290e21 1.09582 0.547910 0.836537i \(-0.315424\pi\)
0.547910 + 0.836537i \(0.315424\pi\)
\(548\) 5.53425e21i 0.680478i
\(549\) 1.47985e21 1.21328e21i 0.179325 0.147022i
\(550\) −7.98724e21 −0.953884
\(551\) 3.65000e20i 0.0429615i
\(552\) 9.82747e20 3.51363e20i 0.114006 0.0407609i
\(553\) −2.69572e21 −0.308229
\(554\) 4.53591e21i 0.511195i
\(555\) −1.18601e21 3.31723e21i −0.131749 0.368495i
\(556\) −3.86252e21 −0.422934
\(557\) 1.64848e22i 1.77928i 0.456666 + 0.889638i \(0.349043\pi\)
−0.456666 + 0.889638i \(0.650957\pi\)
\(558\) −2.36632e21 2.88623e21i −0.251768 0.307084i
\(559\) 6.06109e21 0.635706
\(560\) 5.19378e21i 0.537006i
\(561\) 6.91649e21 2.47286e21i 0.704990 0.252056i
\(562\) 6.90077e21 0.693437
\(563\) 1.09770e22i 1.08746i 0.839259 + 0.543732i \(0.182989\pi\)
−0.839259 + 0.543732i \(0.817011\pi\)
\(564\) 2.02982e21 + 5.67732e21i 0.198255 + 0.554512i
\(565\) −1.09975e22 −1.05903
\(566\) 2.99297e21i 0.284165i
\(567\) −3.20406e21 + 1.60264e22i −0.299941 + 1.50028i
\(568\) −4.00839e21 −0.369984
\(569\) 7.70777e21i 0.701504i −0.936468 0.350752i \(-0.885926\pi\)
0.936468 0.350752i \(-0.114074\pi\)
\(570\) −5.95454e20 + 2.12894e20i −0.0534379 + 0.0191057i
\(571\) −1.24243e22 −1.09947 −0.549733 0.835340i \(-0.685271\pi\)
−0.549733 + 0.835340i \(0.685271\pi\)
\(572\) 6.61319e21i 0.577089i
\(573\) 1.10932e21 + 3.10272e21i 0.0954596 + 0.266996i
\(574\) 1.72389e22 1.46290
\(575\) 3.97387e21i 0.332561i
\(576\) −1.17125e21 + 9.60265e20i −0.0966649 + 0.0792522i
\(577\) −5.10610e21 −0.415607 −0.207803 0.978171i \(-0.566631\pi\)
−0.207803 + 0.978171i \(0.566631\pi\)
\(578\) 6.24976e21i 0.501696i
\(579\) −1.10654e22 + 3.95623e21i −0.876069 + 0.313222i
\(580\) 6.75619e21 0.527567
\(581\) 1.43381e22i 1.10429i
\(582\) 5.66433e21 + 1.58429e22i 0.430294 + 1.20351i
\(583\) 2.18655e22 1.63836
\(584\) 2.85915e21i 0.211317i
\(585\) −1.01448e22 1.23737e22i −0.739599 0.902099i
\(586\) −1.32521e21 −0.0953024
\(587\) 5.19346e21i 0.368427i −0.982886 0.184214i \(-0.941026\pi\)
0.982886 0.184214i \(-0.0589738\pi\)
\(588\) −9.02052e21 + 3.22512e21i −0.631267 + 0.225698i
\(589\) 4.65013e20 0.0321028
\(590\) 1.34059e22i 0.913020i
\(591\) 4.59624e21 + 1.28555e22i 0.308818 + 0.863751i
\(592\) 1.05126e21 0.0696845
\(593\) 4.29285e21i 0.280743i −0.990099 0.140371i \(-0.955170\pi\)
0.990099 0.140371i \(-0.0448296\pi\)
\(594\) 7.83591e21 1.30518e22i 0.505589 0.842131i
\(595\) −1.81863e22 −1.15773
\(596\) 1.21123e21i 0.0760778i
\(597\) −8.16761e21 + 2.92018e21i −0.506175 + 0.180973i
\(598\) −3.29025e21 −0.201196
\(599\) 1.02183e22i 0.616541i −0.951299 0.308271i \(-0.900250\pi\)
0.951299 0.308271i \(-0.0997503\pi\)
\(600\) 1.94148e21 + 5.43024e21i 0.115591 + 0.323302i
\(601\) −1.64963e22 −0.969150 −0.484575 0.874750i \(-0.661026\pi\)
−0.484575 + 0.874750i \(0.661026\pi\)
\(602\) 1.42777e22i 0.827724i
\(603\) 2.23353e22 1.83119e22i 1.27777 1.04760i
\(604\) 8.14276e20 0.0459702
\(605\) 2.34262e22i 1.30514i
\(606\) −9.71622e21 + 3.47385e21i −0.534215 + 0.190999i
\(607\) 6.96878e21 0.378136 0.189068 0.981964i \(-0.439453\pi\)
0.189068 + 0.981964i \(0.439453\pi\)
\(608\) 1.88705e20i 0.0101054i
\(609\) 7.32427e21 + 2.04857e22i 0.387102 + 1.08271i
\(610\) 4.41329e21 0.230210
\(611\) 1.90077e22i 0.978590i
\(612\) −3.36242e21 4.10119e21i −0.170860 0.208400i
\(613\) 2.71321e22 1.36082 0.680408 0.732833i \(-0.261802\pi\)
0.680408 + 0.732833i \(0.261802\pi\)
\(614\) 2.65927e22i 1.31649i
\(615\) 3.65833e22 1.30797e22i 1.78765 0.639140i
\(616\) 1.55782e22 0.751402
\(617\) 2.67609e22i 1.27415i −0.770803 0.637073i \(-0.780145\pi\)
0.770803 0.637073i \(-0.219855\pi\)
\(618\) −9.31764e21 2.60610e22i −0.437923 1.22485i
\(619\) −2.25075e22 −1.04424 −0.522122 0.852871i \(-0.674859\pi\)
−0.522122 + 0.852871i \(0.674859\pi\)
\(620\) 8.60745e21i 0.394222i
\(621\) 6.49364e21 + 3.89858e21i 0.293600 + 0.176268i
\(622\) −2.24497e22 −1.00204
\(623\) 3.43893e22i 1.51537i
\(624\) 4.49607e21 1.60749e21i 0.195595 0.0699312i
\(625\) −2.39359e22 −1.02804
\(626\) 2.68042e22i 1.13660i
\(627\) 6.38553e20 + 1.78600e21i 0.0267335 + 0.0747725i
\(628\) −1.52006e22 −0.628324
\(629\) 3.68104e21i 0.150233i
\(630\) −2.91479e22 + 2.38974e22i −1.17458 + 0.962998i
\(631\) −1.91478e22 −0.761875 −0.380938 0.924601i \(-0.624399\pi\)
−0.380938 + 0.924601i \(0.624399\pi\)
\(632\) 1.81294e21i 0.0712272i
\(633\) −2.32626e22 + 8.31712e21i −0.902462 + 0.322659i
\(634\) 3.61062e22 1.38314
\(635\) 5.51159e22i 2.08491i
\(636\) −5.31490e21 1.48656e22i −0.198536 0.555296i
\(637\) 3.02008e22 1.11404
\(638\) 2.02645e22i 0.738194i
\(639\) −1.84432e22 2.24954e22i −0.663483 0.809258i
\(640\) −3.49295e21 −0.124094
\(641\) 3.21010e22i 1.12630i 0.826355 + 0.563150i \(0.190411\pi\)
−0.826355 + 0.563150i \(0.809589\pi\)
\(642\) 7.06244e21 2.52505e21i 0.244723 0.0874961i
\(643\) 3.71143e22 1.27015 0.635073 0.772452i \(-0.280970\pi\)
0.635073 + 0.772452i \(0.280970\pi\)
\(644\) 7.75059e21i 0.261968i
\(645\) −1.08329e22 3.02992e22i −0.361633 1.01147i
\(646\) 6.60759e20 0.0217863
\(647\) 1.37787e22i 0.448719i 0.974506 + 0.224360i \(0.0720291\pi\)
−0.974506 + 0.224360i \(0.927971\pi\)
\(648\) −1.07782e22 2.15481e21i −0.346693 0.0693121i
\(649\) −4.02097e22 −1.27754
\(650\) 1.81805e22i 0.570557i
\(651\) 2.60989e22 9.33118e21i 0.809048 0.289260i
\(652\) −6.97539e20 −0.0213593
\(653\) 4.84286e22i 1.46486i −0.680841 0.732431i \(-0.738386\pi\)
0.680841 0.732431i \(-0.261614\pi\)
\(654\) 9.02427e21 + 2.52405e22i 0.269643 + 0.754181i
\(655\) 4.45886e22 1.31611
\(656\) 1.15936e22i 0.338054i
\(657\) 1.60458e22 1.31554e22i 0.462209 0.378949i
\(658\) −4.47751e22 −1.27418
\(659\) 2.62793e22i 0.738807i −0.929269 0.369404i \(-0.879562\pi\)
0.929269 0.369404i \(-0.120438\pi\)
\(660\) 3.30592e22 1.18197e22i 0.918207 0.328288i
\(661\) 6.00724e21 0.164840 0.0824201 0.996598i \(-0.473735\pi\)
0.0824201 + 0.996598i \(0.473735\pi\)
\(662\) 2.30579e22i 0.625108i
\(663\) 5.62871e21 + 1.57432e22i 0.150765 + 0.421683i
\(664\) 9.64273e21 0.255185
\(665\) 4.69614e21i 0.122791i
\(666\) 4.83700e21 + 5.89975e21i 0.124963 + 0.152419i
\(667\) 1.00822e22 0.257363
\(668\) 1.73602e21i 0.0437868i
\(669\) −4.71088e22 + 1.68429e22i −1.17407 + 0.419766i
\(670\) 6.66093e22 1.64035
\(671\) 1.32372e22i 0.322119i
\(672\) −3.78664e21 1.05911e22i −0.0910542 0.254675i
\(673\) −3.45462e22 −0.820881 −0.410440 0.911887i \(-0.634625\pi\)
−0.410440 + 0.911887i \(0.634625\pi\)
\(674\) 4.82654e22i 1.13333i
\(675\) −2.15419e22 + 3.58811e22i −0.499866 + 0.832598i
\(676\) 6.75148e21 0.154819
\(677\) 3.42077e22i 0.775201i −0.921828 0.387600i \(-0.873304\pi\)
0.921828 0.387600i \(-0.126696\pi\)
\(678\) 2.24260e22 8.01799e21i 0.502243 0.179568i
\(679\) −1.24948e23 −2.76547
\(680\) 1.22307e22i 0.267536i
\(681\) −2.27857e22 6.37305e22i −0.492589 1.37775i
\(682\) −2.58172e22 −0.551612
\(683\) 1.76733e22i 0.373209i −0.982435 0.186605i \(-0.940252\pi\)
0.982435 0.186605i \(-0.0597484\pi\)
\(684\) 1.05903e21 8.68258e20i 0.0221033 0.0181217i
\(685\) 9.26245e22 1.91074
\(686\) 1.80826e22i 0.368696i
\(687\) −7.26694e21 + 2.59816e21i −0.146453 + 0.0523615i
\(688\) 9.60209e21 0.191275
\(689\) 4.97700e22i 0.979973i
\(690\) 5.88062e21 + 1.64479e22i 0.114454 + 0.320123i
\(691\) 3.67658e22 0.707325 0.353663 0.935373i \(-0.384936\pi\)
0.353663 + 0.935373i \(0.384936\pi\)
\(692\) 3.59455e22i 0.683590i
\(693\) 7.16777e22 + 8.74262e22i 1.34747 + 1.64352i
\(694\) −2.22502e22 −0.413483
\(695\) 6.46454e22i 1.18757i
\(696\) −1.37771e22 + 4.92575e21i −0.250198 + 0.0894537i
\(697\) −4.05955e22 −0.728813
\(698\) 9.65974e21i 0.171444i
\(699\) 2.39618e22 + 6.70201e22i 0.420438 + 1.17595i
\(700\) −4.28265e22 −0.742896
\(701\) 9.04977e22i 1.55201i 0.630729 + 0.776003i \(0.282756\pi\)
−0.630729 + 0.776003i \(0.717244\pi\)
\(702\) 2.97084e22 + 1.78360e22i 0.503713 + 0.302414i
\(703\) −9.50534e20 −0.0159340
\(704\) 1.04767e22i 0.173638i
\(705\) −9.50191e22 + 3.39723e22i −1.55703 + 0.556689i
\(706\) −3.76947e22 −0.610720
\(707\) 7.66286e22i 1.22754i
\(708\) 9.77387e21 + 2.73371e22i 0.154811 + 0.432999i
\(709\) 1.22712e23 1.92185 0.960923 0.276816i \(-0.0892794\pi\)
0.960923 + 0.276816i \(0.0892794\pi\)
\(710\) 6.70869e22i 1.03889i
\(711\) 1.01743e22 8.34159e21i 0.155794 0.127730i
\(712\) −2.31277e22 −0.350180
\(713\) 1.28448e22i 0.192313i
\(714\) 3.70852e22 1.32591e22i 0.549054 0.196304i
\(715\) −1.10682e23 −1.62043
\(716\) 1.14846e22i 0.166269i
\(717\) −1.29178e22 3.61304e22i −0.184941 0.517273i
\(718\) −9.86808e22 −1.39713
\(719\) 1.80138e22i 0.252217i 0.992016 + 0.126108i \(0.0402487\pi\)
−0.992016 + 0.126108i \(0.959751\pi\)
\(720\) −1.60716e22 1.96027e22i −0.222535 0.271429i
\(721\) 2.05535e23 2.81451
\(722\) 5.20428e22i 0.704796i
\(723\) 4.12096e22 1.47337e22i 0.551940 0.197336i
\(724\) 3.80854e22 0.504487
\(725\) 5.57097e22i 0.729838i
\(726\) −1.70794e22 4.77702e22i −0.221299 0.618963i
\(727\) −7.83484e21 −0.100405 −0.0502024 0.998739i \(-0.515987\pi\)
−0.0502024 + 0.998739i \(0.515987\pi\)
\(728\) 3.54590e22i 0.449444i
\(729\) −3.74990e22 7.04025e22i −0.470109 0.882608i
\(730\) 4.78525e22 0.593365
\(731\) 3.36223e22i 0.412371i
\(732\) −8.99950e21 + 3.21760e21i −0.109177 + 0.0390341i
\(733\) 1.30423e22 0.156503 0.0782513 0.996934i \(-0.475066\pi\)
0.0782513 + 0.996934i \(0.475066\pi\)
\(734\) 8.13985e21i 0.0966158i
\(735\) −5.39775e22 1.50973e23i −0.633745 1.77256i
\(736\) −5.21247e21 −0.0605370
\(737\) 1.99788e23i 2.29525i
\(738\) −6.50640e22 + 5.33437e22i −0.739418 + 0.606223i
\(739\) −7.97130e22 −0.896135 −0.448068 0.894000i \(-0.647888\pi\)
−0.448068 + 0.894000i \(0.647888\pi\)
\(740\) 1.75945e22i 0.195670i
\(741\) −4.06529e21 + 1.45347e21i −0.0447245 + 0.0159904i
\(742\) 1.17240e23 1.27598
\(743\) 1.47795e23i 1.59129i 0.605762 + 0.795646i \(0.292869\pi\)
−0.605762 + 0.795646i \(0.707131\pi\)
\(744\) 6.27545e21 + 1.75522e22i 0.0668438 + 0.186959i
\(745\) 2.02719e22 0.213622
\(746\) 9.88350e22i 1.03039i
\(747\) 4.43676e22 + 5.41158e22i 0.457616 + 0.558160i
\(748\) −3.66849e22 −0.374347
\(749\) 5.56991e22i 0.562333i
\(750\) 2.70219e21 9.66119e20i 0.0269915 0.00965030i
\(751\) −1.09749e21 −0.0108463 −0.00542315 0.999985i \(-0.501726\pi\)
−0.00542315 + 0.999985i \(0.501726\pi\)
\(752\) 3.01124e22i 0.294444i
\(753\) 3.90032e22 + 1.09090e23i 0.377347 + 1.05542i
\(754\) 4.61259e22 0.441544
\(755\) 1.36282e22i 0.129081i
\(756\) 4.20150e22 6.99820e22i 0.393759 0.655861i
\(757\) −2.73479e22 −0.253604 −0.126802 0.991928i \(-0.540471\pi\)
−0.126802 + 0.991928i \(0.540471\pi\)
\(758\) 1.24286e22i 0.114043i
\(759\) 4.93337e22 1.76383e22i 0.447929 0.160149i
\(760\) 3.15827e21 0.0283753
\(761\) 1.88562e23i 1.67640i 0.545363 + 0.838200i \(0.316392\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(762\) −4.01835e22 1.12391e23i −0.353515 0.988766i
\(763\) −1.99063e23 −1.73298
\(764\) 1.64567e22i 0.141774i
\(765\) 6.86399e22 5.62755e22i 0.585174 0.479764i
\(766\) −8.39613e22 −0.708352
\(767\) 9.15249e22i 0.764146i
\(768\) 7.12276e21 2.54661e21i 0.0588516 0.0210413i
\(769\) −1.56339e23 −1.27837 −0.639187 0.769051i \(-0.720729\pi\)
−0.639187 + 0.769051i \(0.720729\pi\)
\(770\) 2.60726e23i 2.10989i
\(771\) −8.79226e21 2.45916e22i −0.0704151 0.196948i
\(772\) 5.86906e22 0.465190
\(773\) 1.68543e22i 0.132213i