Properties

Label 5.18.b.a.4.6
Level 5
Weight 18
Character 5.4
Analytic conductor 9.161
Analytic rank 0
Dimension 8
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 18 \)
Character orbit: \([\chi]\) = 5.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(9.16110436723\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 4.6
Root \(137.667i\)
Character \(\chi\) = 5.4
Dual form 5.18.b.a.4.3

$q$-expansion

\(f(q)\) \(=\) \(q+275.335i q^{2} -2990.60i q^{3} +55262.8 q^{4} +(-756669. - 436339. i) q^{5} +823415. q^{6} -2.43909e7i q^{7} +5.13044e7i q^{8} +1.20196e8 q^{9} +O(q^{10})\) \(q+275.335i q^{2} -2990.60i q^{3} +55262.8 q^{4} +(-756669. - 436339. i) q^{5} +823415. q^{6} -2.43909e7i q^{7} +5.13044e7i q^{8} +1.20196e8 q^{9} +(1.20139e8 - 2.08337e8i) q^{10} +8.41139e8 q^{11} -1.65269e8i q^{12} -4.01580e9i q^{13} +6.71566e9 q^{14} +(-1.30491e9 + 2.26289e9i) q^{15} -6.88248e9 q^{16} +8.60868e9i q^{17} +3.30943e10i q^{18} -6.64861e10 q^{19} +(-4.18157e10 - 2.41133e10i) q^{20} -7.29433e10 q^{21} +2.31595e11i q^{22} -5.12783e11i q^{23} +1.53431e11 q^{24} +(3.82157e11 + 6.60328e11i) q^{25} +1.10569e12 q^{26} -7.45665e11i q^{27} -1.34791e12i q^{28} +1.63558e11 q^{29} +(-6.23053e11 - 3.59288e11i) q^{30} -3.12692e12 q^{31} +4.82959e12i q^{32} -2.51551e12i q^{33} -2.37027e12 q^{34} +(-1.06427e13 + 1.84558e13i) q^{35} +6.64240e12 q^{36} -2.41839e12i q^{37} -1.83059e13i q^{38} -1.20096e13 q^{39} +(2.23861e13 - 3.88205e13i) q^{40} +4.43989e13 q^{41} -2.00838e13i q^{42} +7.24471e13i q^{43} +4.64837e13 q^{44} +(-9.09490e13 - 5.24464e13i) q^{45} +1.41187e14 q^{46} +5.71958e13i q^{47} +2.05827e13i q^{48} -3.62285e14 q^{49} +(-1.81811e14 + 1.05221e14i) q^{50} +2.57451e13 q^{51} -2.21925e14i q^{52} +3.35911e14i q^{53} +2.05308e14 q^{54} +(-6.36464e14 - 3.67021e14i) q^{55} +1.25136e15 q^{56} +1.98833e14i q^{57} +4.50331e13i q^{58} -2.43892e14 q^{59} +(-7.21132e13 + 1.25054e14i) q^{60} +2.41050e15 q^{61} -8.60950e14i q^{62} -2.93170e15i q^{63} -2.23185e15 q^{64} +(-1.75225e15 + 3.03863e15i) q^{65} +6.92606e14 q^{66} +2.63132e15i q^{67} +4.75740e14i q^{68} -1.53353e15 q^{69} +(-5.08153e15 - 2.93030e15i) q^{70} +4.51149e15 q^{71} +6.16661e15i q^{72} +2.61026e15i q^{73} +6.65866e14 q^{74} +(1.97477e15 - 1.14288e15i) q^{75} -3.67421e15 q^{76} -2.05161e16i q^{77} -3.30667e15i q^{78} +7.48386e15 q^{79} +(5.20776e15 + 3.00309e15i) q^{80} +1.32922e16 q^{81} +1.22245e16i q^{82} +2.07744e15i q^{83} -4.03105e15 q^{84} +(3.75630e15 - 6.51393e15i) q^{85} -1.99472e16 q^{86} -4.89135e14i q^{87} +4.31541e16i q^{88} +2.77854e15 q^{89} +(1.44403e16 - 2.50414e16i) q^{90} -9.79490e16 q^{91} -2.83378e16i q^{92} +9.35136e15i q^{93} -1.57480e16 q^{94} +(5.03080e16 + 2.90105e16i) q^{95} +1.44434e16 q^{96} +5.77968e16i q^{97} -9.97495e16i q^{98} +1.01102e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + O(q^{10}) \) \( 8q - 579096q^{4} + 379200q^{5} + 357816q^{6} - 234916344q^{9} + 329570200q^{10} + 463296576q^{11} - 29937907992q^{14} + 30646226400q^{15} + 30848001568q^{16} - 20615713280q^{19} - 47558579400q^{20} - 75039699024q^{21} + 1768741136160q^{24} - 1789249435000q^{25} - 838901194224q^{26} - 4079017824720q^{29} + 2416984007400q^{30} + 11329328658496q^{31} - 36406243632832q^{34} + 4019663899200q^{35} + 59729752432728q^{36} + 40318460422272q^{39} - 209747532172000q^{40} + 97217252847456q^{41} - 116357853210912q^{44} - 366841998003600q^{45} + 1081224261700136q^{46} - 856574357621656q^{49} - 1283266301910000q^{50} + 2468309514424896q^{51} - 3408409774777680q^{54} - 2042713226757600q^{55} + 8363016326678880q^{56} - 1091409512240640q^{59} - 11479379108104800q^{60} + 8064731010774976q^{61} - 3616160324265856q^{64} - 11989509557901600q^{65} + 27318846906958752q^{66} - 12078989597365008q^{69} - 13190931213697800q^{70} + 25241492058140736q^{71} - 29902523510328912q^{74} + 3839235716880000q^{75} + 20767634734678560q^{76} + 3229852337730880q^{79} + 1263407265391200q^{80} - 49353541005202632q^{81} + 101439947332382688q^{84} + 25693702369787200q^{85} - 165112838769552744q^{86} + 92963987535626640q^{89} + 206315814421823400q^{90} - 225591670236809664q^{91} + 162612564681867848q^{94} + 204319715505252000q^{95} - 654303222993538944q^{96} - 56327331239952768q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 275.335i 0.760512i 0.924881 + 0.380256i \(0.124164\pi\)
−0.924881 + 0.380256i \(0.875836\pi\)
\(3\) 2990.60i 0.263164i −0.991305 0.131582i \(-0.957994\pi\)
0.991305 0.131582i \(-0.0420057\pi\)
\(4\) 55262.8 0.421622
\(5\) −756669. 436339.i −0.866285 0.499550i
\(6\) 823415. 0.200140
\(7\) 2.43909e7i 1.59917i −0.600554 0.799584i \(-0.705053\pi\)
0.600554 0.799584i \(-0.294947\pi\)
\(8\) 5.13044e7i 1.08116i
\(9\) 1.20196e8 0.930744
\(10\) 1.20139e8 2.08337e8i 0.379913 0.658820i
\(11\) 8.41139e8 1.18312 0.591561 0.806260i \(-0.298512\pi\)
0.591561 + 0.806260i \(0.298512\pi\)
\(12\) 1.65269e8i 0.110956i
\(13\) 4.01580e9i 1.36538i −0.730707 0.682691i \(-0.760810\pi\)
0.730707 0.682691i \(-0.239190\pi\)
\(14\) 6.71566e9 1.21619
\(15\) −1.30491e9 + 2.26289e9i −0.131464 + 0.227975i
\(16\) −6.88248e9 −0.400613
\(17\) 8.60868e9i 0.299310i 0.988738 + 0.149655i \(0.0478163\pi\)
−0.988738 + 0.149655i \(0.952184\pi\)
\(18\) 3.30943e10i 0.707842i
\(19\) −6.64861e10 −0.898101 −0.449051 0.893506i \(-0.648238\pi\)
−0.449051 + 0.893506i \(0.648238\pi\)
\(20\) −4.18157e10 2.41133e10i −0.365245 0.210621i
\(21\) −7.29433e10 −0.420844
\(22\) 2.31595e11i 0.899779i
\(23\) 5.12783e11i 1.36536i −0.730718 0.682680i \(-0.760814\pi\)
0.730718 0.682680i \(-0.239186\pi\)
\(24\) 1.53431e11 0.284523
\(25\) 3.82157e11 + 6.60328e11i 0.500900 + 0.865505i
\(26\) 1.10569e12 1.03839
\(27\) 7.45665e11i 0.508103i
\(28\) 1.34791e12i 0.674244i
\(29\) 1.63558e11 0.0607139 0.0303570 0.999539i \(-0.490336\pi\)
0.0303570 + 0.999539i \(0.490336\pi\)
\(30\) −6.23053e11 3.59288e11i −0.173378 0.0999797i
\(31\) −3.12692e12 −0.658480 −0.329240 0.944246i \(-0.606793\pi\)
−0.329240 + 0.944246i \(0.606793\pi\)
\(32\) 4.82959e12i 0.776489i
\(33\) 2.51551e12i 0.311356i
\(34\) −2.37027e12 −0.227629
\(35\) −1.06427e13 + 1.84558e13i −0.798864 + 1.38534i
\(36\) 6.64240e12 0.392422
\(37\) 2.41839e12i 0.113191i −0.998397 0.0565954i \(-0.981975\pi\)
0.998397 0.0565954i \(-0.0180245\pi\)
\(38\) 1.83059e13i 0.683016i
\(39\) −1.20096e13 −0.359320
\(40\) 2.23861e13 3.88205e13i 0.540093 0.936593i
\(41\) 4.43989e13 0.868379 0.434189 0.900822i \(-0.357035\pi\)
0.434189 + 0.900822i \(0.357035\pi\)
\(42\) 2.00838e13i 0.320057i
\(43\) 7.24471e13i 0.945234i 0.881268 + 0.472617i \(0.156691\pi\)
−0.881268 + 0.472617i \(0.843309\pi\)
\(44\) 4.64837e13 0.498830
\(45\) −9.09490e13 5.24464e13i −0.806290 0.464953i
\(46\) 1.41187e14 1.03837
\(47\) 5.71958e13i 0.350374i 0.984535 + 0.175187i \(0.0560531\pi\)
−0.984535 + 0.175187i \(0.943947\pi\)
\(48\) 2.05827e13i 0.105427i
\(49\) −3.62285e14 −1.55734
\(50\) −1.81811e14 + 1.05221e14i −0.658227 + 0.380941i
\(51\) 2.57451e13 0.0787677
\(52\) 2.21925e14i 0.575675i
\(53\) 3.35911e14i 0.741104i 0.928812 + 0.370552i \(0.120832\pi\)
−0.928812 + 0.370552i \(0.879168\pi\)
\(54\) 2.05308e14 0.386418
\(55\) −6.36464e14 3.67021e14i −1.02492 0.591029i
\(56\) 1.25136e15 1.72896
\(57\) 1.98833e14i 0.236348i
\(58\) 4.50331e13i 0.0461736i
\(59\) −2.43892e14 −0.216249 −0.108125 0.994137i \(-0.534485\pi\)
−0.108125 + 0.994137i \(0.534485\pi\)
\(60\) −7.21132e13 + 1.25054e14i −0.0554280 + 0.0961194i
\(61\) 2.41050e15 1.60992 0.804960 0.593329i \(-0.202187\pi\)
0.804960 + 0.593329i \(0.202187\pi\)
\(62\) 8.60950e14i 0.500782i
\(63\) 2.93170e15i 1.48842i
\(64\) −2.23185e15 −0.991142
\(65\) −1.75225e15 + 3.03863e15i −0.682076 + 1.18281i
\(66\) 6.92606e14 0.236790
\(67\) 2.63132e15i 0.791659i 0.918324 + 0.395829i \(0.129543\pi\)
−0.918324 + 0.395829i \(0.870457\pi\)
\(68\) 4.75740e14i 0.126196i
\(69\) −1.53353e15 −0.359314
\(70\) −5.08153e15 2.93030e15i −1.05356 0.607546i
\(71\) 4.51149e15 0.829133 0.414566 0.910019i \(-0.363933\pi\)
0.414566 + 0.910019i \(0.363933\pi\)
\(72\) 6.16661e15i 1.00628i
\(73\) 2.61026e15i 0.378826i 0.981898 + 0.189413i \(0.0606585\pi\)
−0.981898 + 0.189413i \(0.939342\pi\)
\(74\) 6.65866e14 0.0860830
\(75\) 1.97477e15 1.14288e15i 0.227770 0.131819i
\(76\) −3.67421e15 −0.378659
\(77\) 2.05161e16i 1.89201i
\(78\) 3.30667e15i 0.273267i
\(79\) 7.48386e15 0.555003 0.277501 0.960725i \(-0.410494\pi\)
0.277501 + 0.960725i \(0.410494\pi\)
\(80\) 5.20776e15 + 3.00309e15i 0.347045 + 0.200126i
\(81\) 1.32922e16 0.797030
\(82\) 1.22245e16i 0.660412i
\(83\) 2.07744e15i 0.101243i 0.998718 + 0.0506214i \(0.0161202\pi\)
−0.998718 + 0.0506214i \(0.983880\pi\)
\(84\) −4.03105e15 −0.177437
\(85\) 3.75630e15 6.51393e15i 0.149520 0.259288i
\(86\) −1.99472e16 −0.718862
\(87\) 4.89135e14i 0.0159777i
\(88\) 4.31541e16i 1.27915i
\(89\) 2.77854e15 0.0748173 0.0374086 0.999300i \(-0.488090\pi\)
0.0374086 + 0.999300i \(0.488090\pi\)
\(90\) 1.44403e16 2.50414e16i 0.353602 0.613193i
\(91\) −9.79490e16 −2.18348
\(92\) 2.83378e16i 0.575665i
\(93\) 9.35136e15i 0.173289i
\(94\) −1.57480e16 −0.266464
\(95\) 5.03080e16 + 2.90105e16i 0.778012 + 0.448646i
\(96\) 1.44434e16 0.204344
\(97\) 5.77968e16i 0.748762i 0.927275 + 0.374381i \(0.122145\pi\)
−0.927275 + 0.374381i \(0.877855\pi\)
\(98\) 9.97495e16i 1.18438i
\(99\) 1.01102e17 1.10119
\(100\) 2.11190e16 + 3.64916e16i 0.211190 + 0.364916i
\(101\) −6.77981e16 −0.622997 −0.311499 0.950247i \(-0.600831\pi\)
−0.311499 + 0.950247i \(0.600831\pi\)
\(102\) 7.08852e15i 0.0599038i
\(103\) 9.15022e16i 0.711729i −0.934537 0.355865i \(-0.884186\pi\)
0.934537 0.355865i \(-0.115814\pi\)
\(104\) 2.06029e17 1.47620
\(105\) 5.51939e16 + 3.18280e16i 0.364571 + 0.210233i
\(106\) −9.24880e16 −0.563619
\(107\) 3.51736e16i 0.197904i −0.995092 0.0989519i \(-0.968451\pi\)
0.995092 0.0989519i \(-0.0315490\pi\)
\(108\) 4.12076e16i 0.214227i
\(109\) −3.76273e17 −1.80875 −0.904375 0.426739i \(-0.859662\pi\)
−0.904375 + 0.426739i \(0.859662\pi\)
\(110\) 1.01054e17 1.75241e17i 0.449484 0.779465i
\(111\) −7.23242e15 −0.0297878
\(112\) 1.67870e17i 0.640648i
\(113\) 3.30695e17i 1.17020i 0.810960 + 0.585101i \(0.198945\pi\)
−0.810960 + 0.585101i \(0.801055\pi\)
\(114\) −5.47456e16 −0.179746
\(115\) −2.23747e17 + 3.88007e17i −0.682065 + 1.18279i
\(116\) 9.03866e15 0.0255983
\(117\) 4.82686e17i 1.27082i
\(118\) 6.71518e16i 0.164460i
\(119\) 2.09973e17 0.478647
\(120\) −1.16096e17 6.69478e16i −0.246478 0.142133i
\(121\) 2.02067e17 0.399779
\(122\) 6.63695e17i 1.22436i
\(123\) 1.32779e17i 0.228526i
\(124\) −1.72803e17 −0.277630
\(125\) −1.03934e15 6.66399e17i −0.00155963 0.999999i
\(126\) 8.07198e17 1.13196
\(127\) 7.69744e17i 1.00929i −0.863328 0.504643i \(-0.831624\pi\)
0.863328 0.504643i \(-0.168376\pi\)
\(128\) 1.85170e16i 0.0227136i
\(129\) 2.16660e17 0.248752
\(130\) −8.36642e17 4.82455e17i −0.899541 0.518727i
\(131\) 1.50692e18 1.51804 0.759022 0.651065i \(-0.225678\pi\)
0.759022 + 0.651065i \(0.225678\pi\)
\(132\) 1.39014e17i 0.131274i
\(133\) 1.62165e18i 1.43621i
\(134\) −7.24494e17 −0.602066
\(135\) −3.25363e17 + 5.64222e17i −0.253823 + 0.440162i
\(136\) −4.41664e17 −0.323602
\(137\) 3.94985e17i 0.271929i 0.990714 + 0.135965i \(0.0434134\pi\)
−0.990714 + 0.135965i \(0.956587\pi\)
\(138\) 4.22233e17i 0.273263i
\(139\) −7.47149e17 −0.454759 −0.227380 0.973806i \(-0.573016\pi\)
−0.227380 + 0.973806i \(0.573016\pi\)
\(140\) −5.88145e17 + 1.01992e18i −0.336819 + 0.584088i
\(141\) 1.71050e17 0.0922061
\(142\) 1.24217e18i 0.630565i
\(143\) 3.37785e18i 1.61541i
\(144\) −8.27250e17 −0.372869
\(145\) −1.23759e17 7.13666e16i −0.0525956 0.0303296i
\(146\) −7.18695e17 −0.288101
\(147\) 1.08345e18i 0.409836i
\(148\) 1.33647e17i 0.0477237i
\(149\) −9.58107e17 −0.323095 −0.161548 0.986865i \(-0.551649\pi\)
−0.161548 + 0.986865i \(0.551649\pi\)
\(150\) 3.14673e17 + 5.43724e17i 0.100250 + 0.173222i
\(151\) 3.59671e18 1.08293 0.541466 0.840723i \(-0.317870\pi\)
0.541466 + 0.840723i \(0.317870\pi\)
\(152\) 3.41103e18i 0.970991i
\(153\) 1.03473e18i 0.278581i
\(154\) 5.64880e18 1.43890
\(155\) 2.36605e18 + 1.36440e18i 0.570432 + 0.328944i
\(156\) −6.63687e17 −0.151497
\(157\) 1.64813e18i 0.356323i −0.984001 0.178162i \(-0.942985\pi\)
0.984001 0.178162i \(-0.0570150\pi\)
\(158\) 2.06057e18i 0.422086i
\(159\) 1.00457e18 0.195032
\(160\) 2.10734e18 3.65440e18i 0.387895 0.672661i
\(161\) −1.25072e19 −2.18344
\(162\) 3.65981e18i 0.606151i
\(163\) 3.35481e18i 0.527318i −0.964616 0.263659i \(-0.915071\pi\)
0.964616 0.263659i \(-0.0849294\pi\)
\(164\) 2.45361e18 0.366127
\(165\) −1.09761e18 + 1.90341e18i −0.155538 + 0.269723i
\(166\) −5.71991e17 −0.0769964
\(167\) 5.47912e17i 0.0700843i 0.999386 + 0.0350422i \(0.0111566\pi\)
−0.999386 + 0.0350422i \(0.988843\pi\)
\(168\) 3.74231e18i 0.455000i
\(169\) −7.47627e18 −0.864267
\(170\) 1.79351e18 + 1.03424e18i 0.197191 + 0.113712i
\(171\) −7.99140e18 −0.835903
\(172\) 4.00363e18i 0.398531i
\(173\) 2.01070e19i 1.90527i 0.304121 + 0.952634i \(0.401637\pi\)
−0.304121 + 0.952634i \(0.598363\pi\)
\(174\) 1.34676e17 0.0121513
\(175\) 1.61060e19 9.32114e18i 1.38409 0.801024i
\(176\) −5.78912e18 −0.473975
\(177\) 7.29381e17i 0.0569091i
\(178\) 7.65029e17i 0.0568994i
\(179\) 4.53989e18 0.321955 0.160977 0.986958i \(-0.448535\pi\)
0.160977 + 0.986958i \(0.448535\pi\)
\(180\) −5.02610e18 2.89833e18i −0.339950 0.196034i
\(181\) 4.15934e18 0.268384 0.134192 0.990955i \(-0.457156\pi\)
0.134192 + 0.990955i \(0.457156\pi\)
\(182\) 2.69688e19i 1.66056i
\(183\) 7.20885e18i 0.423674i
\(184\) 2.63080e19 1.47617
\(185\) −1.05524e18 + 1.82992e18i −0.0565445 + 0.0980556i
\(186\) −2.57475e18 −0.131788
\(187\) 7.24110e18i 0.354120i
\(188\) 3.16080e18i 0.147725i
\(189\) −1.81874e19 −0.812543
\(190\) −7.98759e18 + 1.38515e19i −0.341201 + 0.591687i
\(191\) 3.00403e19 1.22721 0.613607 0.789612i \(-0.289718\pi\)
0.613607 + 0.789612i \(0.289718\pi\)
\(192\) 6.67457e18i 0.260833i
\(193\) 4.96197e19i 1.85531i −0.373438 0.927655i \(-0.621821\pi\)
0.373438 0.927655i \(-0.378179\pi\)
\(194\) −1.59135e19 −0.569442
\(195\) 9.08733e18 + 5.24028e18i 0.311273 + 0.179498i
\(196\) −2.00209e19 −0.656608
\(197\) 5.07587e19i 1.59422i 0.603836 + 0.797109i \(0.293638\pi\)
−0.603836 + 0.797109i \(0.706362\pi\)
\(198\) 2.78369e19i 0.837464i
\(199\) −3.21936e18 −0.0927936 −0.0463968 0.998923i \(-0.514774\pi\)
−0.0463968 + 0.998923i \(0.514774\pi\)
\(200\) −3.38778e19 + 1.96063e19i −0.935750 + 0.541553i
\(201\) 7.86922e18 0.208336
\(202\) 1.86672e19i 0.473797i
\(203\) 3.98932e18i 0.0970918i
\(204\) 1.42275e18 0.0332102
\(205\) −3.35952e19 1.93729e19i −0.752264 0.433798i
\(206\) 2.51937e19 0.541279
\(207\) 6.16347e19i 1.27080i
\(208\) 2.76387e19i 0.546990i
\(209\) −5.59240e19 −1.06256
\(210\) −8.76335e18 + 1.51968e19i −0.159884 + 0.277261i
\(211\) 9.47490e19 1.66025 0.830126 0.557576i \(-0.188269\pi\)
0.830126 + 0.557576i \(0.188269\pi\)
\(212\) 1.85634e19i 0.312466i
\(213\) 1.34920e19i 0.218198i
\(214\) 9.68450e18 0.150508
\(215\) 3.16115e19 5.48185e19i 0.472191 0.818842i
\(216\) 3.82559e19 0.549341
\(217\) 7.62684e19i 1.05302i
\(218\) 1.03601e20i 1.37558i
\(219\) 7.80624e18 0.0996935
\(220\) −3.51728e19 2.02826e19i −0.432129 0.249191i
\(221\) 3.45708e19 0.408672
\(222\) 1.99134e18i 0.0226540i
\(223\) 1.31328e20i 1.43802i 0.694999 + 0.719011i \(0.255405\pi\)
−0.694999 + 0.719011i \(0.744595\pi\)
\(224\) 1.17798e20 1.24174
\(225\) 4.59339e19 + 7.93691e19i 0.466210 + 0.805564i
\(226\) −9.10518e19 −0.889953
\(227\) 1.40184e20i 1.31971i −0.751392 0.659856i \(-0.770617\pi\)
0.751392 0.659856i \(-0.229383\pi\)
\(228\) 1.09881e19i 0.0996496i
\(229\) −2.03342e20 −1.77675 −0.888375 0.459119i \(-0.848165\pi\)
−0.888375 + 0.459119i \(0.848165\pi\)
\(230\) −1.06832e20 6.16053e19i −0.899526 0.518718i
\(231\) −6.13554e19 −0.497910
\(232\) 8.39124e18i 0.0656415i
\(233\) 1.39686e20i 1.05348i 0.850027 + 0.526740i \(0.176586\pi\)
−0.850027 + 0.526740i \(0.823414\pi\)
\(234\) 1.32900e20 0.966475
\(235\) 2.49567e19 4.32783e19i 0.175029 0.303524i
\(236\) −1.34781e19 −0.0911754
\(237\) 2.23812e19i 0.146057i
\(238\) 5.78130e19i 0.364017i
\(239\) −7.58670e19 −0.460968 −0.230484 0.973076i \(-0.574031\pi\)
−0.230484 + 0.973076i \(0.574031\pi\)
\(240\) 8.98104e18 1.55743e19i 0.0526661 0.0913300i
\(241\) −2.19191e20 −1.24073 −0.620365 0.784313i \(-0.713016\pi\)
−0.620365 + 0.784313i \(0.713016\pi\)
\(242\) 5.56362e19i 0.304037i
\(243\) 1.36047e20i 0.717853i
\(244\) 1.33211e20 0.678777
\(245\) 2.74130e20 + 1.58079e20i 1.34910 + 0.777969i
\(246\) 3.65587e19 0.173797
\(247\) 2.66995e20i 1.22625i
\(248\) 1.60425e20i 0.711922i
\(249\) 6.21278e18 0.0266435
\(250\) 1.83483e20 2.86165e17i 0.760511 0.00118611i
\(251\) 3.03839e19 0.121735 0.0608676 0.998146i \(-0.480613\pi\)
0.0608676 + 0.998146i \(0.480613\pi\)
\(252\) 1.62014e20i 0.627549i
\(253\) 4.31322e20i 1.61539i
\(254\) 2.11937e20 0.767574
\(255\) −1.94805e19 1.12336e19i −0.0682353 0.0393484i
\(256\) −2.97632e20 −1.00842
\(257\) 2.96660e20i 0.972361i −0.873858 0.486180i \(-0.838390\pi\)
0.873858 0.486180i \(-0.161610\pi\)
\(258\) 5.96540e19i 0.189179i
\(259\) −5.89866e19 −0.181011
\(260\) −9.68343e19 + 1.67923e20i −0.287578 + 0.498698i
\(261\) 1.96591e19 0.0565091
\(262\) 4.14907e20i 1.15449i
\(263\) 3.43830e20i 0.926233i 0.886297 + 0.463116i \(0.153269\pi\)
−0.886297 + 0.463116i \(0.846731\pi\)
\(264\) 1.29057e20 0.336625
\(265\) 1.46571e20 2.54173e20i 0.370218 0.642008i
\(266\) −4.46498e20 −1.09226
\(267\) 8.30950e18i 0.0196892i
\(268\) 1.45414e20i 0.333781i
\(269\) −1.76686e20 −0.392923 −0.196462 0.980511i \(-0.562945\pi\)
−0.196462 + 0.980511i \(0.562945\pi\)
\(270\) −1.55350e20 8.95836e19i −0.334749 0.193035i
\(271\) 1.00224e20 0.209282 0.104641 0.994510i \(-0.466631\pi\)
0.104641 + 0.994510i \(0.466631\pi\)
\(272\) 5.92491e19i 0.119907i
\(273\) 2.92926e20i 0.574613i
\(274\) −1.08753e20 −0.206806
\(275\) 3.21447e20 + 5.55427e20i 0.592626 + 1.02400i
\(276\) −8.47470e19 −0.151495
\(277\) 1.22541e20i 0.212424i 0.994343 + 0.106212i \(0.0338722\pi\)
−0.994343 + 0.106212i \(0.966128\pi\)
\(278\) 2.05716e20i 0.345850i
\(279\) −3.75845e20 −0.612877
\(280\) −9.46866e20 5.46017e20i −1.49777 0.863700i
\(281\) 6.75283e20 1.03629 0.518146 0.855292i \(-0.326622\pi\)
0.518146 + 0.855292i \(0.326622\pi\)
\(282\) 4.70959e19i 0.0701238i
\(283\) 6.87359e20i 0.993114i −0.868004 0.496557i \(-0.834597\pi\)
0.868004 0.496557i \(-0.165403\pi\)
\(284\) 2.49318e20 0.349581
\(285\) 8.67586e19 1.50451e20i 0.118068 0.204745i
\(286\) 9.30039e20 1.22854
\(287\) 1.08293e21i 1.38868i
\(288\) 5.80500e20i 0.722713i
\(289\) 7.53131e20 0.910414
\(290\) 1.96497e19 3.40752e19i 0.0230660 0.0399995i
\(291\) 1.72847e20 0.197047
\(292\) 1.44250e20i 0.159721i
\(293\) 1.22015e21i 1.31231i 0.754625 + 0.656156i \(0.227819\pi\)
−0.754625 + 0.656156i \(0.772181\pi\)
\(294\) −2.98311e20 −0.311685
\(295\) 1.84545e20 + 1.06419e20i 0.187334 + 0.108027i
\(296\) 1.24074e20 0.122377
\(297\) 6.27208e20i 0.601148i
\(298\) 2.63800e20i 0.245718i
\(299\) −2.05924e21 −1.86424
\(300\) 1.09132e20 6.31585e19i 0.0960328 0.0555778i
\(301\) 1.76705e21 1.51159
\(302\) 9.90299e20i 0.823583i
\(303\) 2.02757e20i 0.163951i
\(304\) 4.57589e20 0.359791
\(305\) −1.82395e21 1.05180e21i −1.39465 0.804235i
\(306\) −2.84898e20 −0.211864
\(307\) 1.90026e21i 1.37448i 0.726431 + 0.687239i \(0.241177\pi\)
−0.726431 + 0.687239i \(0.758823\pi\)
\(308\) 1.13378e21i 0.797714i
\(309\) −2.73646e20 −0.187302
\(310\) −3.75666e20 + 6.51454e20i −0.250165 + 0.433820i
\(311\) −1.43465e21 −0.929569 −0.464785 0.885424i \(-0.653868\pi\)
−0.464785 + 0.885424i \(0.653868\pi\)
\(312\) 6.16148e20i 0.388482i
\(313\) 2.00027e21i 1.22733i −0.789566 0.613665i \(-0.789694\pi\)
0.789566 0.613665i \(-0.210306\pi\)
\(314\) 4.53787e20 0.270988
\(315\) −1.27921e21 + 2.21833e21i −0.743538 + 1.28939i
\(316\) 4.13579e20 0.234001
\(317\) 1.13693e21i 0.626226i 0.949716 + 0.313113i \(0.101372\pi\)
−0.949716 + 0.313113i \(0.898628\pi\)
\(318\) 2.76594e20i 0.148324i
\(319\) 1.37575e20 0.0718320
\(320\) 1.68877e21 + 9.73844e20i 0.858612 + 0.495125i
\(321\) −1.05190e20 −0.0520813
\(322\) 3.44367e21i 1.66053i
\(323\) 5.72358e20i 0.268810i
\(324\) 7.34565e20 0.336045
\(325\) 2.65175e21 1.53467e21i 1.18174 0.683920i
\(326\) 9.23695e20 0.401032
\(327\) 1.12528e21i 0.475998i
\(328\) 2.27786e21i 0.938856i
\(329\) 1.39506e21 0.560308
\(330\) −5.24074e20 3.02211e20i −0.205127 0.118288i
\(331\) −1.84600e21 −0.704195 −0.352097 0.935963i \(-0.614531\pi\)
−0.352097 + 0.935963i \(0.614531\pi\)
\(332\) 1.14805e20i 0.0426862i
\(333\) 2.90682e20i 0.105352i
\(334\) −1.50859e20 −0.0533000
\(335\) 1.14815e21 1.99104e21i 0.395473 0.685802i
\(336\) 5.02031e20 0.168596
\(337\) 6.86430e20i 0.224772i 0.993665 + 0.112386i \(0.0358493\pi\)
−0.993665 + 0.112386i \(0.964151\pi\)
\(338\) 2.05848e21i 0.657285i
\(339\) 9.88975e20 0.307956
\(340\) 2.07584e20 3.59978e20i 0.0630409 0.109321i
\(341\) −2.63018e21 −0.779063
\(342\) 2.20031e21i 0.635714i
\(343\) 3.16238e21i 0.891280i
\(344\) −3.71686e21 −1.02195
\(345\) 1.16037e21 + 6.69137e20i 0.311268 + 0.179495i
\(346\) −5.53616e21 −1.44898
\(347\) 8.26157e20i 0.210990i −0.994420 0.105495i \(-0.966357\pi\)
0.994420 0.105495i \(-0.0336427\pi\)
\(348\) 2.70310e19i 0.00673656i
\(349\) 3.10029e21 0.754026 0.377013 0.926208i \(-0.376951\pi\)
0.377013 + 0.926208i \(0.376951\pi\)
\(350\) 2.56643e21 + 4.43454e21i 0.609188 + 1.05262i
\(351\) −2.99445e21 −0.693755
\(352\) 4.06235e21i 0.918682i
\(353\) 2.62238e21i 0.578909i 0.957192 + 0.289455i \(0.0934739\pi\)
−0.957192 + 0.289455i \(0.906526\pi\)
\(354\) −2.00824e20 −0.0432801
\(355\) −3.41371e21 1.96854e21i −0.718266 0.414193i
\(356\) 1.53550e20 0.0315446
\(357\) 6.27946e20i 0.125963i
\(358\) 1.24999e21i 0.244850i
\(359\) 4.39853e21 0.841403 0.420702 0.907199i \(-0.361784\pi\)
0.420702 + 0.907199i \(0.361784\pi\)
\(360\) 2.69073e21 4.66609e21i 0.502689 0.871729i
\(361\) −1.05999e21 −0.193414
\(362\) 1.14521e21i 0.204109i
\(363\) 6.04302e20i 0.105208i
\(364\) −5.41294e21 −0.920601
\(365\) 1.13896e21 1.97510e21i 0.189242 0.328171i
\(366\) 1.98485e21 0.322209
\(367\) 6.17095e21i 0.978793i −0.872061 0.489396i \(-0.837217\pi\)
0.872061 0.489396i \(-0.162783\pi\)
\(368\) 3.52922e21i 0.546981i
\(369\) 5.33659e21 0.808239
\(370\) −5.03840e20 2.90543e20i −0.0745724 0.0430027i
\(371\) 8.19317e21 1.18515
\(372\) 5.16783e20i 0.0730622i
\(373\) 8.48385e21i 1.17238i −0.810174 0.586190i \(-0.800627\pi\)
0.810174 0.586190i \(-0.199373\pi\)
\(374\) −1.99373e21 −0.269313
\(375\) −1.99293e21 + 3.10823e18i −0.263164 + 0.000410438i
\(376\) −2.93440e21 −0.378811
\(377\) 6.56816e20i 0.0828976i
\(378\) 5.00763e21i 0.617948i
\(379\) 5.99241e21 0.723050 0.361525 0.932362i \(-0.382256\pi\)
0.361525 + 0.932362i \(0.382256\pi\)
\(380\) 2.78016e21 + 1.60320e21i 0.328027 + 0.189159i
\(381\) −2.30199e21 −0.265608
\(382\) 8.27113e21i 0.933311i
\(383\) 2.17350e21i 0.239866i −0.992782 0.119933i \(-0.961732\pi\)
0.992782 0.119933i \(-0.0382680\pi\)
\(384\) 5.53769e19 0.00597741
\(385\) −8.95198e21 + 1.55239e22i −0.945154 + 1.63902i
\(386\) 1.36620e22 1.41099
\(387\) 8.70789e21i 0.879771i
\(388\) 3.19401e21i 0.315694i
\(389\) −1.86409e22 −1.80258 −0.901289 0.433218i \(-0.857378\pi\)
−0.901289 + 0.433218i \(0.857378\pi\)
\(390\) −1.44283e21 + 2.50206e21i −0.136510 + 0.236727i
\(391\) 4.41439e21 0.408665
\(392\) 1.85868e22i 1.68373i
\(393\) 4.50659e21i 0.399495i
\(394\) −1.39756e22 −1.21242
\(395\) −5.66280e21 3.26550e21i −0.480791 0.277252i
\(396\) 5.58718e21 0.464284
\(397\) 7.16091e21i 0.582437i 0.956657 + 0.291218i \(0.0940607\pi\)
−0.956657 + 0.291218i \(0.905939\pi\)
\(398\) 8.86401e20i 0.0705706i
\(399\) 4.84971e21 0.377961
\(400\) −2.63019e21 4.54470e21i −0.200667 0.346733i
\(401\) −2.30431e21 −0.172113 −0.0860566 0.996290i \(-0.527427\pi\)
−0.0860566 + 0.996290i \(0.527427\pi\)
\(402\) 2.16667e21i 0.158442i
\(403\) 1.25571e22i 0.899077i
\(404\) −3.74672e21 −0.262669
\(405\) −1.00578e22 5.79991e21i −0.690455 0.398156i
\(406\) 1.09840e21 0.0738394
\(407\) 2.03420e21i 0.133919i
\(408\) 1.32084e21i 0.0851605i
\(409\) 1.97605e22 1.24782 0.623908 0.781498i \(-0.285544\pi\)
0.623908 + 0.781498i \(0.285544\pi\)
\(410\) 5.33404e21 9.24994e21i 0.329909 0.572105i
\(411\) 1.18124e21 0.0715621
\(412\) 5.05667e21i 0.300081i
\(413\) 5.94873e21i 0.345819i
\(414\) 1.69702e22 0.966459
\(415\) 9.06467e20 1.57193e21i 0.0505759 0.0877052i
\(416\) 1.93947e22 1.06020
\(417\) 2.23442e21i 0.119676i
\(418\) 1.53978e22i 0.808092i
\(419\) −2.45016e21 −0.126001 −0.0630006 0.998013i \(-0.520067\pi\)
−0.0630006 + 0.998013i \(0.520067\pi\)
\(420\) 3.05017e21 + 1.75890e21i 0.153711 + 0.0886386i
\(421\) 4.22696e21 0.208752 0.104376 0.994538i \(-0.466716\pi\)
0.104376 + 0.994538i \(0.466716\pi\)
\(422\) 2.60877e22i 1.26264i
\(423\) 6.87473e21i 0.326109i
\(424\) −1.72337e22 −0.801253
\(425\) −5.68456e21 + 3.28986e21i −0.259054 + 0.149924i
\(426\) 3.71483e21 0.165942
\(427\) 5.87943e22i 2.57453i
\(428\) 1.94379e21i 0.0834406i
\(429\) −1.01018e22 −0.425119
\(430\) 1.50934e22 + 8.70374e21i 0.622739 + 0.359107i
\(431\) −2.22344e22 −0.899432 −0.449716 0.893172i \(-0.648475\pi\)
−0.449716 + 0.893172i \(0.648475\pi\)
\(432\) 5.13203e21i 0.203553i
\(433\) 2.10672e22i 0.819333i 0.912235 + 0.409667i \(0.134355\pi\)
−0.912235 + 0.409667i \(0.865645\pi\)
\(434\) −2.09993e22 −0.800835
\(435\) −2.13429e20 + 3.70113e20i −0.00798167 + 0.0138413i
\(436\) −2.07939e22 −0.762608
\(437\) 3.40929e22i 1.22623i
\(438\) 2.14933e21i 0.0758181i
\(439\) 4.37524e22 1.51375 0.756874 0.653560i \(-0.226725\pi\)
0.756874 + 0.653560i \(0.226725\pi\)
\(440\) 1.88298e22 3.26534e22i 0.638997 1.10810i
\(441\) −4.35454e22 −1.44949
\(442\) 9.51854e21i 0.310800i
\(443\) 2.24729e22i 0.719827i −0.932986 0.359914i \(-0.882806\pi\)
0.932986 0.359914i \(-0.117194\pi\)
\(444\) −3.99684e20 −0.0125592
\(445\) −2.10244e21 1.21239e21i −0.0648131 0.0373749i
\(446\) −3.61591e22 −1.09363
\(447\) 2.86531e21i 0.0850272i
\(448\) 5.44369e22i 1.58500i
\(449\) −2.31598e22 −0.661670 −0.330835 0.943689i \(-0.607330\pi\)
−0.330835 + 0.943689i \(0.607330\pi\)
\(450\) −2.18531e22 + 1.26472e22i −0.612641 + 0.354558i
\(451\) 3.73456e22 1.02740
\(452\) 1.82751e22i 0.493383i
\(453\) 1.07563e22i 0.284989i
\(454\) 3.85976e22 1.00366
\(455\) 7.41150e22 + 4.27389e22i 1.89151 + 1.09075i
\(456\) −1.02010e22 −0.255530
\(457\) 7.37859e22i 1.81420i −0.420912 0.907101i \(-0.638290\pi\)
0.420912 0.907101i \(-0.361710\pi\)
\(458\) 5.59872e22i 1.35124i
\(459\) 6.41920e21 0.152080
\(460\) −1.23649e22 + 2.14424e22i −0.287573 + 0.498690i
\(461\) 7.16140e21 0.163508 0.0817542 0.996653i \(-0.473948\pi\)
0.0817542 + 0.996653i \(0.473948\pi\)
\(462\) 1.68933e22i 0.378667i
\(463\) 6.96956e22i 1.53379i −0.641771 0.766897i \(-0.721800\pi\)
0.641771 0.766897i \(-0.278200\pi\)
\(464\) −1.12568e21 −0.0243228
\(465\) 4.08036e21 7.07589e21i 0.0865662 0.150117i
\(466\) −3.84603e22 −0.801184
\(467\) 7.30135e22i 1.49352i 0.665096 + 0.746758i \(0.268391\pi\)
−0.665096 + 0.746758i \(0.731609\pi\)
\(468\) 2.66746e22i 0.535806i
\(469\) 6.41802e22 1.26600
\(470\) 1.19160e22 + 6.87146e21i 0.230834 + 0.133112i
\(471\) −4.92889e21 −0.0937716
\(472\) 1.25127e22i 0.233800i
\(473\) 6.09381e22i 1.11833i
\(474\) 6.16232e21 0.111078
\(475\) −2.54081e22 4.39026e22i −0.449859 0.777311i
\(476\) 1.16037e22 0.201808
\(477\) 4.03753e22i 0.689779i
\(478\) 2.08888e22i 0.350572i
\(479\) −8.82520e22 −1.45503 −0.727516 0.686091i \(-0.759325\pi\)
−0.727516 + 0.686091i \(0.759325\pi\)
\(480\) −1.09288e22 6.30219e21i −0.177020 0.102080i
\(481\) −9.71177e21 −0.154549
\(482\) 6.03508e22i 0.943590i
\(483\) 3.74041e22i 0.574604i
\(484\) 1.11668e22 0.168556
\(485\) 2.52190e22 4.37330e22i 0.374044 0.648641i
\(486\) 3.74585e22 0.545936
\(487\) 8.68662e22i 1.24410i 0.782978 + 0.622049i \(0.213699\pi\)
−0.782978 + 0.622049i \(0.786301\pi\)
\(488\) 1.23670e23i 1.74058i
\(489\) −1.00329e22 −0.138771
\(490\) −4.35246e22 + 7.54774e22i −0.591654 + 1.02601i
\(491\) 1.69753e22 0.226790 0.113395 0.993550i \(-0.463827\pi\)
0.113395 + 0.993550i \(0.463827\pi\)
\(492\) 7.33775e21i 0.0963517i
\(493\) 1.40802e21i 0.0181723i
\(494\) −7.35130e22 −0.932578
\(495\) −7.65007e22 4.41147e22i −0.953940 0.550097i
\(496\) 2.15210e22 0.263796
\(497\) 1.10039e23i 1.32592i
\(498\) 1.71059e21i 0.0202627i
\(499\) −8.59451e22 −1.00084 −0.500422 0.865781i \(-0.666822\pi\)
−0.500422 + 0.865781i \(0.666822\pi\)
\(500\) −5.74366e19 3.68271e22i −0.000657573 0.421621i
\(501\) 1.63858e21 0.0184437
\(502\) 8.36573e21i 0.0925811i
\(503\) 8.57709e22i 0.933281i −0.884447 0.466640i \(-0.845464\pi\)
0.884447 0.466640i \(-0.154536\pi\)
\(504\) 1.50409e23 1.60922
\(505\) 5.13007e22 + 2.95829e22i 0.539693 + 0.311218i
\(506\) 1.18758e23 1.22852
\(507\) 2.23585e22i 0.227444i
\(508\) 4.25382e22i 0.425537i
\(509\) −1.19520e23 −1.17582 −0.587908 0.808928i \(-0.700048\pi\)
−0.587908 + 0.808928i \(0.700048\pi\)
\(510\) 3.09300e21 5.36366e21i 0.0299249 0.0518937i
\(511\) 6.36666e22 0.605806
\(512\) 7.95213e22i 0.744199i
\(513\) 4.95764e22i 0.456328i
\(514\) 8.16808e22 0.739492
\(515\) −3.99259e22 + 6.92368e22i −0.355544 + 0.616561i
\(516\) 1.19732e22 0.104879
\(517\) 4.81096e22i 0.414536i
\(518\) 1.62411e22i 0.137661i
\(519\) 6.01320e22 0.501398
\(520\) −1.55895e23 8.98982e22i −1.27881 0.737433i
\(521\) 2.19068e23 1.76791 0.883953 0.467576i \(-0.154872\pi\)
0.883953 + 0.467576i \(0.154872\pi\)
\(522\) 5.41282e21i 0.0429759i
\(523\) 1.41671e23i 1.10667i 0.832959 + 0.553334i \(0.186645\pi\)
−0.832959 + 0.553334i \(0.813355\pi\)
\(524\) 8.32767e22 0.640040
\(525\) −2.78758e22 4.81665e22i −0.210801 0.364243i
\(526\) −9.46684e22 −0.704411
\(527\) 2.69187e22i 0.197090i
\(528\) 1.73129e22i 0.124733i
\(529\) −1.21896e23 −0.864206
\(530\) 6.99828e22 + 4.03561e22i 0.488255 + 0.281556i
\(531\) −2.93149e22 −0.201273
\(532\) 8.96172e22i 0.605540i
\(533\) 1.78297e23i 1.18567i
\(534\) 2.28789e21 0.0149739
\(535\) −1.53476e22 + 2.66147e22i −0.0988628 + 0.171441i
\(536\) −1.34998e23 −0.855910
\(537\) 1.35770e22i 0.0847270i
\(538\) 4.86478e22i 0.298823i
\(539\) −3.04732e23 −1.84252
\(540\) −1.79805e22 + 3.11805e22i −0.107017 + 0.185582i
\(541\) −8.41450e22 −0.493005 −0.246503 0.969142i \(-0.579281\pi\)
−0.246503 + 0.969142i \(0.579281\pi\)
\(542\) 2.75951e22i 0.159161i
\(543\) 1.24389e22i 0.0706290i
\(544\) −4.15764e22 −0.232411
\(545\) 2.84714e23 + 1.64183e23i 1.56689 + 0.903560i
\(546\) −8.06527e22 −0.437000
\(547\) 3.89693e22i 0.207889i 0.994583 + 0.103944i \(0.0331464\pi\)
−0.994583 + 0.103944i \(0.966854\pi\)
\(548\) 2.18280e22i 0.114651i
\(549\) 2.89734e23 1.49842
\(550\) −1.52928e23 + 8.85054e22i −0.778763 + 0.450699i
\(551\) −1.08743e22 −0.0545272
\(552\) 7.86767e22i 0.388476i
\(553\) 1.82538e23i 0.887543i
\(554\) −3.37398e22 −0.161551
\(555\) 5.47255e21 + 3.15579e21i 0.0258047 + 0.0148805i
\(556\) −4.12896e22 −0.191736
\(557\) 2.32989e23i 1.06553i 0.846263 + 0.532766i \(0.178847\pi\)
−0.846263 + 0.532766i \(0.821153\pi\)
\(558\) 1.03483e23i 0.466100i
\(559\) 2.90933e23 1.29060
\(560\) 7.32481e22 1.27022e23i 0.320036 0.554984i
\(561\) 2.16552e22 0.0931918
\(562\) 1.85929e23i 0.788113i
\(563\) 9.12208e22i 0.380866i 0.981700 + 0.190433i \(0.0609892\pi\)
−0.981700 + 0.190433i \(0.939011\pi\)
\(564\) 9.45268e21 0.0388761
\(565\) 1.44295e23 2.50227e23i 0.584574 1.01373i
\(566\) 1.89254e23 0.755275
\(567\) 3.24209e23i 1.27458i
\(568\) 2.31460e23i 0.896425i
\(569\) −9.35509e22 −0.356939 −0.178469 0.983945i \(-0.557115\pi\)
−0.178469 + 0.983945i \(0.557115\pi\)
\(570\) 4.14243e22 + 2.38876e22i 0.155711 + 0.0897919i
\(571\) −4.28288e23 −1.58609 −0.793047 0.609161i \(-0.791506\pi\)
−0.793047 + 0.609161i \(0.791506\pi\)
\(572\) 1.86669e23i 0.681094i
\(573\) 8.98383e22i 0.322959i
\(574\) 2.98168e23 1.05611
\(575\) 3.38605e23 1.95963e23i 1.18173 0.683909i
\(576\) −2.68261e23 −0.922500
\(577\) 2.90787e23i 0.985329i −0.870219 0.492664i \(-0.836023\pi\)
0.870219 0.492664i \(-0.163977\pi\)
\(578\) 2.07363e23i 0.692380i
\(579\) −1.48392e23 −0.488252
\(580\) −6.83927e21 3.94392e21i −0.0221754 0.0127876i
\(581\) 5.06706e22 0.161904
\(582\) 4.75907e22i 0.149857i
\(583\) 2.82548e23i 0.876818i
\(584\) −1.33918e23 −0.409571
\(585\) −2.10614e23 + 3.65233e23i −0.634838 + 1.10089i
\(586\) −3.35948e23 −0.998028
\(587\) 1.26868e23i 0.371473i 0.982600 + 0.185737i \(0.0594671\pi\)
−0.982600 + 0.185737i \(0.940533\pi\)
\(588\) 5.98743e22i 0.172796i
\(589\) 2.07897e23 0.591382
\(590\) −2.93009e22 + 5.08117e22i −0.0821560 + 0.142469i
\(591\) 1.51799e23 0.419541
\(592\) 1.66445e22i 0.0453458i
\(593\) 1.32480e23i 0.355784i 0.984050 + 0.177892i \(0.0569278\pi\)
−0.984050 + 0.177892i \(0.943072\pi\)
\(594\) 1.72692e23 0.457181
\(595\) −1.58880e23 9.16195e22i −0.414645 0.239108i
\(596\) −5.29477e22 −0.136224
\(597\) 9.62780e21i 0.0244200i
\(598\) 5.66979e23i 1.41777i
\(599\) −5.93521e23 −1.46321 −0.731607 0.681727i \(-0.761229\pi\)
−0.731607 + 0.681727i \(0.761229\pi\)
\(600\) 5.86346e22 + 1.01315e23i 0.142518 + 0.246256i
\(601\) −1.72671e21 −0.00413797 −0.00206898 0.999998i \(-0.500659\pi\)
−0.00206898 + 0.999998i \(0.500659\pi\)
\(602\) 4.86530e23i 1.14958i
\(603\) 3.16276e23i 0.736832i
\(604\) 1.98764e23 0.456588
\(605\) −1.52898e23 8.81698e22i −0.346323 0.199710i
\(606\) −5.58260e22 −0.124686
\(607\) 2.08633e23i 0.459492i 0.973251 + 0.229746i \(0.0737896\pi\)
−0.973251 + 0.229746i \(0.926210\pi\)
\(608\) 3.21101e23i 0.697366i
\(609\) −1.19304e22 −0.0255511
\(610\) 2.89596e23 5.02198e23i 0.611630 1.06065i
\(611\) 2.29687e23 0.478395
\(612\) 5.71823e22i 0.117456i
\(613\) 1.08017e23i 0.218816i 0.993997 + 0.109408i \(0.0348954\pi\)
−0.993997 + 0.109408i \(0.965105\pi\)
\(614\) −5.23209e23 −1.04531
\(615\) −5.79367e22 + 1.00470e23i −0.114160 + 0.197969i
\(616\) 1.05257e24 2.04557
\(617\) 9.73966e23i 1.86690i −0.358714 0.933448i \(-0.616785\pi\)
0.358714 0.933448i \(-0.383215\pi\)
\(618\) 7.53442e22i 0.142445i
\(619\) 3.73326e23 0.696174 0.348087 0.937462i \(-0.386831\pi\)
0.348087 + 0.937462i \(0.386831\pi\)
\(620\) 1.30754e23 + 7.54004e22i 0.240506 + 0.138690i
\(621\) −3.82364e23 −0.693743
\(622\) 3.95008e23i 0.706948i
\(623\) 6.77711e22i 0.119645i
\(624\) 8.26562e22 0.143948
\(625\) −2.89989e23 + 5.04697e23i −0.498198 + 0.867063i
\(626\) 5.50744e23 0.933400
\(627\) 1.67246e23i 0.279629i
\(628\) 9.10802e22i 0.150234i
\(629\) 2.08191e22 0.0338791
\(630\) −6.10782e23 3.52212e23i −0.980599 0.565470i
\(631\) 1.00811e24 1.59683 0.798417 0.602105i \(-0.205671\pi\)
0.798417 + 0.602105i \(0.205671\pi\)
\(632\) 3.83955e23i 0.600047i
\(633\) 2.83356e23i 0.436919i
\(634\) −3.13037e23 −0.476252
\(635\) −3.35869e23 + 5.82441e23i −0.504189 + 0.874330i
\(636\) 5.55156e22 0.0822299
\(637\) 1.45486e24i 2.12636i
\(638\) 3.78791e22i 0.0546291i
\(639\) 5.42265e23 0.771711
\(640\) 8.07968e21 1.40112e22i 0.0113466 0.0196764i
\(641\) −9.24099e23 −1.28064 −0.640318 0.768110i \(-0.721197\pi\)
−0.640318 + 0.768110i \(0.721197\pi\)
\(642\) 2.89624e22i 0.0396084i
\(643\) 1.41354e24i 1.90772i −0.300245 0.953862i \(-0.597068\pi\)
0.300245 0.953862i \(-0.402932\pi\)
\(644\) −6.91185e23 −0.920586
\(645\) −1.63940e23 9.45372e22i −0.215490 0.124264i
\(646\) 1.57590e23 0.204434
\(647\) 9.10189e23i 1.16532i −0.812716 0.582660i \(-0.802012\pi\)
0.812716 0.582660i \(-0.197988\pi\)
\(648\) 6.81949e23i 0.861717i
\(649\) −2.05147e23 −0.255850
\(650\) 4.22547e23 + 7.30118e23i 0.520129 + 0.898731i
\(651\) 2.28088e23 0.277118
\(652\) 1.85396e23i 0.222329i
\(653\) 9.48371e23i 1.12258i 0.827620 + 0.561288i \(0.189694\pi\)
−0.827620 + 0.561288i \(0.810306\pi\)
\(654\) −3.09829e23 −0.362002
\(655\) −1.14024e24 6.57528e23i −1.31506 0.758338i
\(656\) −3.05574e23 −0.347884
\(657\) 3.13744e23i 0.352590i
\(658\) 3.84107e23i 0.426121i
\(659\) −1.24301e23 −0.136128 −0.0680641 0.997681i \(-0.521682\pi\)
−0.0680641 + 0.997681i \(0.521682\pi\)
\(660\) −6.06572e22 + 1.05188e23i −0.0655781 + 0.113721i
\(661\) −4.05632e23 −0.432932 −0.216466 0.976290i \(-0.569453\pi\)
−0.216466 + 0.976290i \(0.569453\pi\)
\(662\) 5.08267e23i 0.535548i
\(663\) 1.03387e23i 0.107548i
\(664\) −1.06582e23 −0.109460
\(665\) 7.07591e23 1.22706e24i 0.717461 1.24417i
\(666\) 8.00348e22 0.0801213
\(667\) 8.38696e22i 0.0828963i
\(668\) 3.02792e22i 0.0295491i
\(669\) 3.92748e23 0.378436
\(670\) 5.48202e23 + 3.16125e23i 0.521561 + 0.300762i
\(671\) 2.02757e24 1.90473
\(672\) 3.52286e23i 0.326781i
\(673\) 1.59557e24i 1.46147i 0.682664 + 0.730733i \(0.260821\pi\)
−0.682664 + 0.730733i \(0.739179\pi\)
\(674\) −1.88998e23 −0.170942
\(675\) 4.92384e23 2.84961e23i 0.439766 0.254509i
\(676\) −4.13160e23 −0.364394
\(677\) 3.21368e23i 0.279897i −0.990159 0.139949i \(-0.955306\pi\)
0.990159 0.139949i \(-0.0446938\pi\)
\(678\) 2.72299e23i 0.234204i
\(679\) 1.40971e24 1.19740
\(680\) 3.34193e23 + 1.92715e23i 0.280332 + 0.161655i
\(681\) −4.19234e23 −0.347301
\(682\) 7.24179e23i 0.592486i
\(683\) 6.20239e23i 0.501168i −0.968095 0.250584i \(-0.919377\pi\)
0.968095 0.250584i \(-0.0806226\pi\)
\(684\) −4.41627e23 −0.352435
\(685\) 1.72347e23 2.98873e23i 0.135842 0.235568i
\(686\) −8.70713e23 −0.677829
\(687\) 6.08115e23i 0.467577i
\(688\) 4.98616e23i 0.378673i
\(689\) 1.34895e24 1.01189
\(690\) −1.84237e23 + 3.19491e23i −0.136508 + 0.236723i
\(691\) −2.58392e24 −1.89111 −0.945553 0.325468i \(-0.894478\pi\)
−0.945553 + 0.325468i \(0.894478\pi\)
\(692\) 1.11117e24i 0.803302i
\(693\) 2.46597e24i 1.76098i
\(694\) 2.27470e23 0.160461
\(695\) 5.65345e23 + 3.26010e23i 0.393951 + 0.227175i
\(696\) 2.50948e22 0.0172745
\(697\) 3.82216e23i 0.259914i
\(698\) 8.53618e23i 0.573446i
\(699\) 4.17743e23 0.277238
\(700\) 8.90062e23 5.15112e23i 0.583562 0.337729i
\(701\) −1.45739e24 −0.944002 −0.472001 0.881598i \(-0.656468\pi\)
−0.472001 + 0.881598i \(0.656468\pi\)
\(702\) 8.24475e23i 0.527609i
\(703\) 1.60789e23i 0.101657i
\(704\) −1.87730e24 −1.17264
\(705\) −1.29428e23 7.46355e22i −0.0798767 0.0460615i
\(706\) −7.22032e23 −0.440267
\(707\) 1.65366e24i 0.996277i
\(708\) 4.03077e22i 0.0239941i
\(709\) −1.40022e24 −0.823572 −0.411786 0.911280i \(-0.635095\pi\)
−0.411786 + 0.911280i \(0.635095\pi\)
\(710\) 5.42007e23 9.39912e23i 0.314999 0.546249i
\(711\) 8.99533e23 0.516566
\(712\) 1.42552e23i 0.0808895i
\(713\) 1.60343e24i 0.899062i
\(714\) 1.72895e23 0.0957962
\(715\) −1.47389e24 + 2.55591e24i −0.806980 + 1.39941i
\(716\) 2.50887e23 0.135743
\(717\) 2.26888e23i 0.121310i
\(718\) 1.21107e24i 0.639897i
\(719\) 2.68849e24 1.40383 0.701913 0.712262i \(-0.252329\pi\)
0.701913 + 0.712262i \(0.252329\pi\)
\(720\) 6.25955e23 + 3.60961e23i 0.323011 + 0.186266i
\(721\) −2.23182e24 −1.13818
\(722\) 2.91851e23i 0.147094i
\(723\) 6.55511e23i 0.326516i
\(724\) 2.29857e23 0.113156
\(725\) 6.25047e22 + 1.08002e23i 0.0304116 + 0.0525482i
\(726\) 1.66385e23 0.0800117
\(727\) 3.76032e24i 1.78724i −0.448825 0.893620i \(-0.648157\pi\)
0.448825 0.893620i \(-0.351843\pi\)
\(728\) 5.02522e24i 2.36069i
\(729\) 1.30970e24 0.608116
\(730\) 5.43814e23 + 3.13595e23i 0.249578 + 0.143921i
\(731\) −6.23674e23 −0.282918
\(732\) 3.98381e23i 0.178630i
\(733\) 7.16715e23i 0.317660i −0.987306 0.158830i \(-0.949228\pi\)
0.987306 0.158830i \(-0.0507722\pi\)
\(734\) 1.69908e24 0.744384
\(735\) 4.72750e23 8.19811e23i 0.204734 0.355035i
\(736\) 2.47653e24 1.06019
\(737\) 2.21331e24i 0.936629i
\(738\) 1.46935e24i 0.614675i
\(739\) −4.16628e24 −1.72294 −0.861471 0.507807i \(-0.830456\pi\)
−0.861471 + 0.507807i \(0.830456\pi\)
\(740\) −5.83153e22 + 1.01126e23i −0.0238404 + 0.0413424i
\(741\) 7.98475e23 0.322706
\(742\) 2.25586e24i 0.901321i
\(743\) 4.05156e24i 1.60036i −0.599761 0.800179i \(-0.704738\pi\)
0.599761 0.800179i \(-0.295262\pi\)
\(744\) −4.79766e23 −0.187353
\(745\) 7.24970e23 + 4.18059e23i 0.279893 + 0.161402i
\(746\) 2.33590e24 0.891608
\(747\) 2.49701e23i 0.0942313i
\(748\) 4.00163e23i 0.149305i
\(749\) −8.57914e23 −0.316482
\(750\) −8.55804e20 5.48723e23i −0.000312143 0.200139i
\(751\) 2.96073e24 1.06772 0.533862 0.845571i \(-0.320740\pi\)
0.533862 + 0.845571i \(0.320740\pi\)
\(752\) 3.93649e23i 0.140365i
\(753\) 9.08659e22i 0.0320364i
\(754\) 1.80844e23 0.0630446
\(755\) −2.72152e24 1.56938e24i −0.938128 0.540978i
\(756\) −1.00509e24 −0.342586
\(757\) 1.79219e24i 0.604046i −0.953301 0.302023i \(-0.902338\pi\)
0.953301 0.302023i \(-0.0976620\pi\)
\(758\) 1.64992e24i 0.549888i
\(759\) −1.28991e24 −0.425113
\(760\) −1.48837e24 + 2.58102e24i −0.485058 + 0.841155i
\(761\) 5.85997e23 0.188854 0.0944269 0.995532i \(-0.469898\pi\)
0.0944269 + 0.995532i \(0.469898\pi\)
\(762\) 6.33818e23i 0.201998i
\(763\) 9.17764e24i 2.89249i
\(764\) 1.66011e24 0.517420
\(765\) 4.51494e23 7.82951e23i 0.139165 0.241331i
\(766\) 5.98439e23 0.182421
\(767\) 9.79421e23i 0.295263i
\(768\) 8.90097e23i 0.265379i
\(769\) −1.30761e23 −0.0385571 −0.0192785 0.999814i \(-0.506137\pi\)
−0.0192785 + 0.999814i \(0.506137\pi\)
\(770\) −4.27427e24 2.46479e24i −1.24650 0.718801i
\(771\) −8.87190e23 −0.255891
\(772\) 2.74212e24i 0.782239i
\(773\) 1.87689e24i 0.529559i 0.964309 + 0.264779i \(0.0852992\pi\)
−0.964309 + 0.264779i \(0.914701\pi\)
\(774\) −2.39758e24 −0.669076
\(775\) −1.19497e24