Properties

Label 5.18.b.a.4.2
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 4.2
Root \(-256.320i\)
Character \(\chi\) = 5.4
Dual form 5.18.b.a.4.7

$q$-expansion

\(f(q)\) \(=\) \(q-512.640i q^{2} +18245.5i q^{3} -131728. q^{4} +(346646. - 801733. i) q^{5} +9.35337e6 q^{6} -1.34806e7i q^{7} +336370. i q^{8} -2.03757e8 q^{9} +O(q^{10})\) \(q-512.640i q^{2} +18245.5i q^{3} -131728. q^{4} +(346646. - 801733. i) q^{5} +9.35337e6 q^{6} -1.34806e7i q^{7} +336370. i q^{8} -2.03757e8 q^{9} +(-4.11001e8 - 1.77705e8i) q^{10} +8.20239e8 q^{11} -2.40344e9i q^{12} -2.92679e9i q^{13} -6.91067e9 q^{14} +(1.46280e10 + 6.32472e9i) q^{15} -1.70934e10 q^{16} -3.73919e10i q^{17} +1.04454e11i q^{18} +3.00949e10 q^{19} +(-4.56630e10 + 1.05611e11i) q^{20} +2.45959e11 q^{21} -4.20488e11i q^{22} +4.40887e11i q^{23} -6.13723e9 q^{24} +(-5.22613e11 - 5.55835e11i) q^{25} -1.50039e12 q^{26} -1.36143e12i q^{27} +1.77577e12i q^{28} +1.80846e12 q^{29} +(3.24231e12 - 7.49891e12i) q^{30} +2.90970e12 q^{31} +8.80687e12i q^{32} +1.49657e13i q^{33} -1.91686e13 q^{34} +(-1.08078e13 - 4.67297e12i) q^{35} +2.68406e13 q^{36} +3.31096e12i q^{37} -1.54279e13i q^{38} +5.34006e13 q^{39} +(2.69679e11 + 1.16601e11i) q^{40} -7.87183e13 q^{41} -1.26089e14i q^{42} +4.61355e12i q^{43} -1.08049e14 q^{44} +(-7.06316e13 + 1.63359e14i) q^{45} +2.26016e14 q^{46} +1.39204e14i q^{47} -3.11878e14i q^{48} +5.09053e13 q^{49} +(-2.84943e14 + 2.67913e14i) q^{50} +6.82233e14 q^{51} +3.85540e14i q^{52} +4.39747e13i q^{53} -6.97923e14 q^{54} +(2.84332e14 - 6.57613e14i) q^{55} +4.53445e12 q^{56} +5.49096e14i q^{57} -9.27089e14i q^{58} -3.18887e14 q^{59} +(-1.92692e15 - 8.33143e14i) q^{60} +7.17560e14 q^{61} -1.49163e15i q^{62} +2.74676e15i q^{63} +2.27429e15 q^{64} +(-2.34650e15 - 1.01456e15i) q^{65} +7.67200e15 q^{66} -2.87655e15i q^{67} +4.92556e15i q^{68} -8.04420e15 q^{69} +(-2.39556e15 + 5.54052e15i) q^{70} -3.39253e14 q^{71} -6.85378e13i q^{72} +8.49295e15i q^{73} +1.69733e15 q^{74} +(1.01415e16 - 9.53533e15i) q^{75} -3.96434e15 q^{76} -1.10573e16i q^{77} -2.73753e16i q^{78} +1.05825e16 q^{79} +(-5.92536e15 + 1.37044e16i) q^{80} -1.47335e15 q^{81} +4.03542e16i q^{82} -2.86866e16i q^{83} -3.23997e16 q^{84} +(-2.99783e16 - 1.29617e16i) q^{85} +2.36509e15 q^{86} +3.29962e16i q^{87} +2.75904e14i q^{88} +6.62578e16 q^{89} +(8.37445e16 + 3.62086e16i) q^{90} -3.94547e16 q^{91} -5.80772e16i q^{92} +5.30888e16i q^{93} +7.13616e16 q^{94} +(1.04323e16 - 2.41281e16i) q^{95} -1.60686e17 q^{96} +2.94405e16i q^{97} -2.60961e16i q^{98} -1.67130e17 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 512.640i 1.41598i −0.706221 0.707991i \(-0.749602\pi\)
0.706221 0.707991i \(-0.250398\pi\)
\(3\) 18245.5i 1.60555i 0.596280 + 0.802777i \(0.296645\pi\)
−0.596280 + 0.802777i \(0.703355\pi\)
\(4\) −131728. −1.00501
\(5\) 346646. 801733.i 0.396863 0.917878i
\(6\) 9.35337e6 2.27343
\(7\) 1.34806e7i 0.883841i −0.897054 0.441921i \(-0.854297\pi\)
0.897054 0.441921i \(-0.145703\pi\)
\(8\) 336370.i 0.00708846i
\(9\) −2.03757e8 −1.57780
\(10\) −4.11001e8 1.77705e8i −1.29970 0.561951i
\(11\) 8.20239e8 1.15373 0.576863 0.816841i \(-0.304277\pi\)
0.576863 + 0.816841i \(0.304277\pi\)
\(12\) 2.40344e9i 1.61359i
\(13\) 2.92679e9i 0.995114i −0.867431 0.497557i \(-0.834231\pi\)
0.867431 0.497557i \(-0.165769\pi\)
\(14\) −6.91067e9 −1.25150
\(15\) 1.46280e10 + 6.32472e9i 1.47370 + 0.637185i
\(16\) −1.70934e10 −0.994969
\(17\) 3.73919e10i 1.30005i −0.759911 0.650027i \(-0.774758\pi\)
0.759911 0.650027i \(-0.225242\pi\)
\(18\) 1.04454e11i 2.23414i
\(19\) 3.00949e10 0.406525 0.203262 0.979124i \(-0.434846\pi\)
0.203262 + 0.979124i \(0.434846\pi\)
\(20\) −4.56630e10 + 1.05611e11i −0.398850 + 0.922473i
\(21\) 2.45959e11 1.41905
\(22\) 4.20488e11i 1.63365i
\(23\) 4.40887e11i 1.17393i 0.809614 + 0.586963i \(0.199677\pi\)
−0.809614 + 0.586963i \(0.800323\pi\)
\(24\) −6.13723e9 −0.0113809
\(25\) −5.22613e11 5.55835e11i −0.684999 0.728544i
\(26\) −1.50039e12 −1.40906
\(27\) 1.36143e12i 0.927690i
\(28\) 1.77577e12i 0.888266i
\(29\) 1.80846e12 0.671314 0.335657 0.941984i \(-0.391042\pi\)
0.335657 + 0.941984i \(0.391042\pi\)
\(30\) 3.24231e12 7.49891e12i 0.902242 2.08674i
\(31\) 2.90970e12 0.612736 0.306368 0.951913i \(-0.400886\pi\)
0.306368 + 0.951913i \(0.400886\pi\)
\(32\) 8.80687e12i 1.41595i
\(33\) 1.49657e13i 1.85237i
\(34\) −1.91686e13 −1.84085
\(35\) −1.08078e13 4.67297e12i −0.811258 0.350764i
\(36\) 2.68406e13 1.58570
\(37\) 3.31096e12i 0.154967i 0.996994 + 0.0774834i \(0.0246885\pi\)
−0.996994 + 0.0774834i \(0.975312\pi\)
\(38\) 1.54279e13i 0.575632i
\(39\) 5.34006e13 1.59771
\(40\) 2.69679e11 + 1.16601e11i 0.00650634 + 0.00281315i
\(41\) −7.87183e13 −1.53962 −0.769809 0.638275i \(-0.779648\pi\)
−0.769809 + 0.638275i \(0.779648\pi\)
\(42\) 1.26089e14i 2.00936i
\(43\) 4.61355e12i 0.0601940i 0.999547 + 0.0300970i \(0.00958162\pi\)
−0.999547 + 0.0300970i \(0.990418\pi\)
\(44\) −1.08049e14 −1.15950
\(45\) −7.06316e13 + 1.63359e14i −0.626171 + 1.44823i
\(46\) 2.26016e14 1.66226
\(47\) 1.39204e14i 0.852746i 0.904547 + 0.426373i \(0.140209\pi\)
−0.904547 + 0.426373i \(0.859791\pi\)
\(48\) 3.11878e14i 1.59748i
\(49\) 5.09053e13 0.218824
\(50\) −2.84943e14 + 2.67913e14i −1.03160 + 0.969947i
\(51\) 6.82233e14 2.08731
\(52\) 3.85540e14i 1.00010i
\(53\) 4.39747e13i 0.0970194i 0.998823 + 0.0485097i \(0.0154472\pi\)
−0.998823 + 0.0485097i \(0.984553\pi\)
\(54\) −6.97923e14 −1.31359
\(55\) 2.84332e14 6.57613e14i 0.457871 1.05898i
\(56\) 4.53445e12 0.00626508
\(57\) 5.49096e14i 0.652697i
\(58\) 9.27089e14i 0.950569i
\(59\) −3.18887e14 −0.282745 −0.141372 0.989957i \(-0.545151\pi\)
−0.141372 + 0.989957i \(0.545151\pi\)
\(60\) −1.92692e15 8.33143e14i −1.48108 0.640375i
\(61\) 7.17560e14 0.479242 0.239621 0.970867i \(-0.422977\pi\)
0.239621 + 0.970867i \(0.422977\pi\)
\(62\) 1.49163e15i 0.867623i
\(63\) 2.74676e15i 1.39453i
\(64\) 2.27429e15 1.00999
\(65\) −2.34650e15 1.01456e15i −0.913393 0.394924i
\(66\) 7.67200e15 2.62292
\(67\) 2.87655e15i 0.865438i −0.901529 0.432719i \(-0.857554\pi\)
0.901529 0.432719i \(-0.142446\pi\)
\(68\) 4.92556e15i 1.30656i
\(69\) −8.04420e15 −1.88480
\(70\) −2.39556e15 + 5.54052e15i −0.496676 + 1.14873i
\(71\) −3.39253e14 −0.0623488 −0.0311744 0.999514i \(-0.509925\pi\)
−0.0311744 + 0.999514i \(0.509925\pi\)
\(72\) 6.85378e13i 0.0111842i
\(73\) 8.49295e15i 1.23258i 0.787520 + 0.616289i \(0.211365\pi\)
−0.787520 + 0.616289i \(0.788635\pi\)
\(74\) 1.69733e15 0.219430
\(75\) 1.01415e16 9.53533e15i 1.16972 1.09980i
\(76\) −3.96434e15 −0.408560
\(77\) 1.10573e16i 1.01971i
\(78\) 2.73753e16i 2.26233i
\(79\) 1.05825e16 0.784800 0.392400 0.919795i \(-0.371645\pi\)
0.392400 + 0.919795i \(0.371645\pi\)
\(80\) −5.92536e15 + 1.37044e16i −0.394866 + 0.913260i
\(81\) −1.47335e15 −0.0883454
\(82\) 4.03542e16i 2.18007i
\(83\) 2.86866e16i 1.39803i −0.715108 0.699014i \(-0.753623\pi\)
0.715108 0.699014i \(-0.246377\pi\)
\(84\) −3.23997e16 −1.42616
\(85\) −2.99783e16 1.29617e16i −1.19329 0.515943i
\(86\) 2.36509e15 0.0852337
\(87\) 3.29962e16i 1.07783i
\(88\) 2.75904e14i 0.00817814i
\(89\) 6.62578e16 1.78411 0.892055 0.451926i \(-0.149263\pi\)
0.892055 + 0.451926i \(0.149263\pi\)
\(90\) 8.37445e16 + 3.62086e16i 2.05067 + 0.886647i
\(91\) −3.94547e16 −0.879523
\(92\) 5.80772e16i 1.17980i
\(93\) 5.30888e16i 0.983780i
\(94\) 7.13616e16 1.20747
\(95\) 1.04323e16 2.41281e16i 0.161335 0.373140i
\(96\) −1.60686e17 −2.27338
\(97\) 2.94405e16i 0.381405i 0.981648 + 0.190702i \(0.0610765\pi\)
−0.981648 + 0.190702i \(0.938923\pi\)
\(98\) 2.60961e16i 0.309852i
\(99\) −1.67130e17 −1.82035
\(100\) 6.88429e16 + 7.32191e16i 0.688429 + 0.732191i
\(101\) 3.97485e16 0.365249 0.182625 0.983183i \(-0.441541\pi\)
0.182625 + 0.983183i \(0.441541\pi\)
\(102\) 3.49740e17i 2.95559i
\(103\) 1.45599e17i 1.13251i 0.824229 + 0.566256i \(0.191609\pi\)
−0.824229 + 0.566256i \(0.808391\pi\)
\(104\) 9.84483e14 0.00705383
\(105\) 8.52607e16 1.97194e17i 0.563170 1.30252i
\(106\) 2.25432e16 0.137378
\(107\) 1.76418e17i 0.992612i 0.868148 + 0.496306i \(0.165311\pi\)
−0.868148 + 0.496306i \(0.834689\pi\)
\(108\) 1.79338e17i 0.932334i
\(109\) 2.43800e17 1.17195 0.585974 0.810330i \(-0.300712\pi\)
0.585974 + 0.810330i \(0.300712\pi\)
\(110\) −3.37119e17 1.45760e17i −1.49950 0.648337i
\(111\) −6.04100e16 −0.248808
\(112\) 2.30429e17i 0.879395i
\(113\) 1.83084e17i 0.647864i −0.946080 0.323932i \(-0.894995\pi\)
0.946080 0.323932i \(-0.105005\pi\)
\(114\) 2.81489e17 0.924208
\(115\) 3.53474e17 + 1.52832e17i 1.07752 + 0.465888i
\(116\) −2.38225e17 −0.674675
\(117\) 5.96355e17i 1.57009i
\(118\) 1.63474e17i 0.400361i
\(119\) −5.04063e17 −1.14904
\(120\) −2.12744e15 + 4.92042e15i −0.00451666 + 0.0104463i
\(121\) 1.67345e17 0.331082
\(122\) 3.67850e17i 0.678598i
\(123\) 1.43625e18i 2.47194i
\(124\) −3.83289e17 −0.615803
\(125\) −6.26793e17 + 2.26319e17i −0.940565 + 0.339614i
\(126\) 1.40810e18 1.97462
\(127\) 2.96492e16i 0.0388760i −0.999811 0.0194380i \(-0.993812\pi\)
0.999811 0.0194380i \(-0.00618770\pi\)
\(128\) 1.15574e16i 0.0141767i
\(129\) −8.41764e16 −0.0966447
\(130\) −5.20103e17 + 1.20291e18i −0.559205 + 1.29335i
\(131\) 1.21062e18 1.21956 0.609779 0.792572i \(-0.291258\pi\)
0.609779 + 0.792572i \(0.291258\pi\)
\(132\) 1.97140e18i 1.86164i
\(133\) 4.05696e17i 0.359304i
\(134\) −1.47464e18 −1.22544
\(135\) −1.09150e18 4.71933e17i −0.851506 0.368166i
\(136\) 1.25775e16 0.00921538
\(137\) 1.52381e18i 1.04907i 0.851388 + 0.524537i \(0.175762\pi\)
−0.851388 + 0.524537i \(0.824238\pi\)
\(138\) 4.12378e18i 2.66884i
\(139\) 1.00912e18 0.614208 0.307104 0.951676i \(-0.400640\pi\)
0.307104 + 0.951676i \(0.400640\pi\)
\(140\) 1.42369e18 + 6.15562e17i 0.815320 + 0.352520i
\(141\) −2.53984e18 −1.36913
\(142\) 1.73915e17i 0.0882848i
\(143\) 2.40066e18i 1.14809i
\(144\) 3.48291e18 1.56986
\(145\) 6.26895e17 1.44990e18i 0.266420 0.616184i
\(146\) 4.35383e18 1.74531
\(147\) 9.28791e17i 0.351334i
\(148\) 4.36146e17i 0.155743i
\(149\) −1.64103e18 −0.553393 −0.276696 0.960957i \(-0.589240\pi\)
−0.276696 + 0.960957i \(0.589240\pi\)
\(150\) −4.88819e18 5.19893e18i −1.55730 1.65630i
\(151\) 2.07485e16 0.00624716 0.00312358 0.999995i \(-0.499006\pi\)
0.00312358 + 0.999995i \(0.499006\pi\)
\(152\) 1.01230e16i 0.00288164i
\(153\) 7.61887e18i 2.05123i
\(154\) −5.66840e18 −1.44389
\(155\) 1.00863e18 2.33280e18i 0.243172 0.562417i
\(156\) −7.03437e18 −1.60571
\(157\) 1.83892e18i 0.397572i −0.980043 0.198786i \(-0.936300\pi\)
0.980043 0.198786i \(-0.0636999\pi\)
\(158\) 5.42503e18i 1.11126i
\(159\) −8.02340e17 −0.155770
\(160\) 7.06076e18 + 3.05286e18i 1.29967 + 0.561937i
\(161\) 5.94340e18 1.03756
\(162\) 7.55300e17i 0.125095i
\(163\) 5.45886e18i 0.858039i −0.903295 0.429020i \(-0.858859\pi\)
0.903295 0.429020i \(-0.141141\pi\)
\(164\) 1.03694e19 1.54732
\(165\) 1.19985e19 + 5.18778e18i 1.70025 + 0.735136i
\(166\) −1.47059e19 −1.97958
\(167\) 5.91125e17i 0.0756118i −0.999285 0.0378059i \(-0.987963\pi\)
0.999285 0.0378059i \(-0.0120369\pi\)
\(168\) 8.27332e16i 0.0100589i
\(169\) 8.43308e16 0.00974876
\(170\) −6.64471e18 + 1.53681e19i −0.730567 + 1.68968i
\(171\) −6.13206e18 −0.641415
\(172\) 6.07734e17i 0.0604953i
\(173\) 1.31685e19i 1.24780i 0.781506 + 0.623898i \(0.214452\pi\)
−0.781506 + 0.623898i \(0.785548\pi\)
\(174\) 1.69152e19 1.52619
\(175\) −7.49296e18 + 7.04511e18i −0.643917 + 0.605431i
\(176\) −1.40207e19 −1.14792
\(177\) 5.81824e18i 0.453961i
\(178\) 3.39664e19i 2.52627i
\(179\) −1.56562e19 −1.11029 −0.555145 0.831754i \(-0.687337\pi\)
−0.555145 + 0.831754i \(0.687337\pi\)
\(180\) 9.30417e18 2.15190e19i 0.629306 1.45548i
\(181\) 1.63176e19 1.05290 0.526450 0.850206i \(-0.323523\pi\)
0.526450 + 0.850206i \(0.323523\pi\)
\(182\) 2.02261e19i 1.24539i
\(183\) 1.30922e19i 0.769448i
\(184\) −1.48301e17 −0.00832133
\(185\) 2.65450e18 + 1.14773e18i 0.142241 + 0.0615006i
\(186\) 2.72155e19 1.39301
\(187\) 3.06703e19i 1.49991i
\(188\) 1.83371e19i 0.857015i
\(189\) −1.83528e19 −0.819931
\(190\) −1.23690e19 5.34800e18i −0.528360 0.228447i
\(191\) −4.29371e19 −1.75408 −0.877040 0.480417i \(-0.840485\pi\)
−0.877040 + 0.480417i \(0.840485\pi\)
\(192\) 4.14955e19i 1.62159i
\(193\) 1.05930e19i 0.396080i 0.980194 + 0.198040i \(0.0634576\pi\)
−0.980194 + 0.198040i \(0.936542\pi\)
\(194\) 1.50924e19 0.540062
\(195\) 1.85111e19 4.28131e19i 0.634071 1.46650i
\(196\) −6.70565e18 −0.219920
\(197\) 2.04072e19i 0.640945i 0.947258 + 0.320473i \(0.103842\pi\)
−0.947258 + 0.320473i \(0.896158\pi\)
\(198\) 8.56775e19i 2.57758i
\(199\) 2.52073e19 0.726566 0.363283 0.931679i \(-0.381656\pi\)
0.363283 + 0.931679i \(0.381656\pi\)
\(200\) 1.86966e17 1.75791e17i 0.00516425 0.00485559i
\(201\) 5.24840e19 1.38951
\(202\) 2.03767e19i 0.517187i
\(203\) 2.43790e19i 0.593335i
\(204\) −8.98693e19 −2.09775
\(205\) −2.72873e19 + 6.31111e19i −0.611017 + 1.41318i
\(206\) 7.46401e19 1.60362
\(207\) 8.98340e19i 1.85222i
\(208\) 5.00289e19i 0.990107i
\(209\) 2.46850e19 0.469018
\(210\) −1.01089e20 4.37081e19i −1.84434 0.797439i
\(211\) 5.82521e19 1.02073 0.510365 0.859958i \(-0.329510\pi\)
0.510365 + 0.859958i \(0.329510\pi\)
\(212\) 5.79271e18i 0.0975051i
\(213\) 6.18984e18i 0.100104i
\(214\) 9.04387e19 1.40552
\(215\) 3.69884e18 + 1.59927e18i 0.0552507 + 0.0238888i
\(216\) 4.57943e17 0.00657590
\(217\) 3.92243e19i 0.541561i
\(218\) 1.24982e20i 1.65946i
\(219\) −1.54958e20 −1.97897
\(220\) −3.74546e19 + 8.66261e19i −0.460163 + 1.06428i
\(221\) −1.09438e20 −1.29370
\(222\) 3.09686e19i 0.352307i
\(223\) 7.59414e19i 0.831548i −0.909468 0.415774i \(-0.863511\pi\)
0.909468 0.415774i \(-0.136489\pi\)
\(224\) 1.18722e20 1.25147
\(225\) 1.06486e20 + 1.13255e20i 1.08079 + 1.14950i
\(226\) −9.38564e19 −0.917365
\(227\) 2.04064e20i 1.92109i 0.278125 + 0.960545i \(0.410287\pi\)
−0.278125 + 0.960545i \(0.589713\pi\)
\(228\) 7.23314e19i 0.655965i
\(229\) −2.06891e20 −1.80775 −0.903877 0.427792i \(-0.859292\pi\)
−0.903877 + 0.427792i \(0.859292\pi\)
\(230\) 7.83476e19 1.81205e20i 0.659689 1.52575i
\(231\) 2.01745e20 1.63720
\(232\) 6.08311e17i 0.00475859i
\(233\) 1.17415e19i 0.0885519i −0.999019 0.0442759i \(-0.985902\pi\)
0.999019 0.0442759i \(-0.0140981\pi\)
\(234\) 3.05716e20 2.22322
\(235\) 1.11604e20 + 4.82544e19i 0.782717 + 0.338423i
\(236\) 4.20063e19 0.284160
\(237\) 1.93083e20i 1.26004i
\(238\) 2.58403e20i 1.62702i
\(239\) −2.08822e20 −1.26880 −0.634402 0.773003i \(-0.718754\pi\)
−0.634402 + 0.773003i \(0.718754\pi\)
\(240\) −2.50043e20 1.08111e20i −1.46629 0.633979i
\(241\) 1.13616e20 0.643123 0.321562 0.946889i \(-0.395792\pi\)
0.321562 + 0.946889i \(0.395792\pi\)
\(242\) 8.57876e19i 0.468807i
\(243\) 2.02697e20i 1.06953i
\(244\) −9.45229e19 −0.481641
\(245\) 1.76461e19 4.08124e19i 0.0868434 0.200854i
\(246\) −7.36281e20 −3.50022
\(247\) 8.80814e19i 0.404539i
\(248\) 9.78734e17i 0.00434335i
\(249\) 5.23401e20 2.24461
\(250\) 1.16020e20 + 3.21319e20i 0.480887 + 1.33182i
\(251\) −1.87124e20 −0.749725 −0.374862 0.927080i \(-0.622310\pi\)
−0.374862 + 0.927080i \(0.622310\pi\)
\(252\) 3.61826e20i 1.40151i
\(253\) 3.61633e20i 1.35439i
\(254\) −1.51994e19 −0.0550477
\(255\) 2.36493e20 5.46969e20i 0.828374 1.91589i
\(256\) 2.92171e20 0.989913
\(257\) 3.72191e20i 1.21993i −0.792429 0.609964i \(-0.791184\pi\)
0.792429 0.609964i \(-0.208816\pi\)
\(258\) 4.31522e19i 0.136847i
\(259\) 4.46335e19 0.136966
\(260\) 3.09100e20 + 1.33646e20i 0.917965 + 0.396901i
\(261\) −3.68487e20 −1.05920
\(262\) 6.20614e20i 1.72687i
\(263\) 4.29984e20i 1.15832i 0.815214 + 0.579160i \(0.196619\pi\)
−0.815214 + 0.579160i \(0.803381\pi\)
\(264\) −5.03399e18 −0.0131304
\(265\) 3.52560e19 + 1.52437e19i 0.0890519 + 0.0385034i
\(266\) −2.07976e20 −0.508768
\(267\) 1.20890e21i 2.86448i
\(268\) 3.78922e20i 0.869770i
\(269\) −7.19281e20 −1.59957 −0.799787 0.600285i \(-0.795054\pi\)
−0.799787 + 0.600285i \(0.795054\pi\)
\(270\) −2.41932e20 + 5.59548e20i −0.521316 + 1.20572i
\(271\) 3.85312e19 0.0804588 0.0402294 0.999190i \(-0.487191\pi\)
0.0402294 + 0.999190i \(0.487191\pi\)
\(272\) 6.39156e20i 1.29351i
\(273\) 7.19870e20i 1.41212i
\(274\) 7.81167e20 1.48547
\(275\) −4.28668e20 4.55917e20i −0.790301 0.840539i
\(276\) 1.05965e21 1.89424
\(277\) 1.09040e21i 1.89019i −0.326792 0.945096i \(-0.605968\pi\)
0.326792 0.945096i \(-0.394032\pi\)
\(278\) 5.17314e20i 0.869707i
\(279\) −5.92872e20 −0.966775
\(280\) 1.57185e18 3.63542e18i 0.00248638 0.00575057i
\(281\) 1.21849e21 1.86989 0.934947 0.354786i \(-0.115446\pi\)
0.934947 + 0.354786i \(0.115446\pi\)
\(282\) 1.30203e21i 1.93866i
\(283\) 5.78122e20i 0.835285i −0.908611 0.417643i \(-0.862856\pi\)
0.908611 0.417643i \(-0.137144\pi\)
\(284\) 4.46892e19 0.0626610
\(285\) 4.40228e20 + 1.90342e20i 0.599097 + 0.259032i
\(286\) −1.23068e21 −1.62567
\(287\) 1.06117e21i 1.36078i
\(288\) 1.79447e21i 2.23408i
\(289\) −5.70912e20 −0.690140
\(290\) −7.43278e20 3.21371e20i −0.872506 0.377246i
\(291\) −5.37157e20 −0.612365
\(292\) 1.11876e21i 1.23875i
\(293\) 6.74703e20i 0.725668i 0.931854 + 0.362834i \(0.118191\pi\)
−0.931854 + 0.362834i \(0.881809\pi\)
\(294\) 4.76136e20 0.497483
\(295\) −1.10541e20 + 2.55662e20i −0.112211 + 0.259525i
\(296\) −1.11371e18 −0.00109848
\(297\) 1.11670e21i 1.07030i
\(298\) 8.41258e20i 0.783594i
\(299\) 1.29038e21 1.16819
\(300\) −1.33592e21 + 1.25607e21i −1.17557 + 1.10531i
\(301\) 6.21932e19 0.0532020
\(302\) 1.06365e19i 0.00884587i
\(303\) 7.25231e20i 0.586427i
\(304\) −5.14425e20 −0.404480
\(305\) 2.48739e20 5.75292e20i 0.190193 0.439886i
\(306\) 3.90574e21 2.90450
\(307\) 1.91771e20i 0.138710i −0.997592 0.0693548i \(-0.977906\pi\)
0.997592 0.0693548i \(-0.0220941\pi\)
\(308\) 1.45655e21i 1.02481i
\(309\) −2.65653e21 −1.81831
\(310\) −1.19589e21 5.17066e20i −0.796372 0.344328i
\(311\) 2.70588e21 1.75325 0.876627 0.481171i \(-0.159788\pi\)
0.876627 + 0.481171i \(0.159788\pi\)
\(312\) 1.79624e19i 0.0113253i
\(313\) 1.59470e21i 0.978477i 0.872150 + 0.489239i \(0.162725\pi\)
−0.872150 + 0.489239i \(0.837275\pi\)
\(314\) −9.42705e20 −0.562955
\(315\) 2.20217e21 + 9.52153e20i 1.28000 + 0.553436i
\(316\) −1.39402e21 −0.788729
\(317\) 1.14239e21i 0.629234i −0.949219 0.314617i \(-0.898124\pi\)
0.949219 0.314617i \(-0.101876\pi\)
\(318\) 4.11312e20i 0.220567i
\(319\) 1.48337e21 0.774512
\(320\) 7.88372e20 1.82337e21i 0.400826 0.927045i
\(321\) −3.21882e21 −1.59369
\(322\) 3.04683e21i 1.46917i
\(323\) 1.12530e21i 0.528504i
\(324\) 1.94082e20 0.0887876
\(325\) −1.62681e21 + 1.52958e21i −0.724984 + 0.681652i
\(326\) −2.79843e21 −1.21497
\(327\) 4.44825e21i 1.88162i
\(328\) 2.64785e19i 0.0109135i
\(329\) 1.87655e21 0.753692
\(330\) 2.65946e21 6.15090e21i 1.04094 2.40752i
\(331\) −1.23995e21 −0.473006 −0.236503 0.971631i \(-0.576001\pi\)
−0.236503 + 0.971631i \(0.576001\pi\)
\(332\) 3.77884e21i 1.40503i
\(333\) 6.74632e20i 0.244507i
\(334\) −3.03035e20 −0.107065
\(335\) −2.30623e21 9.97143e20i −0.794366 0.343460i
\(336\) −4.20429e21 −1.41191
\(337\) 5.46590e21i 1.78981i −0.446255 0.894906i \(-0.647243\pi\)
0.446255 0.894906i \(-0.352757\pi\)
\(338\) 4.32314e19i 0.0138041i
\(339\) 3.34046e21 1.04018
\(340\) 3.94899e21 + 1.70742e21i 1.19926 + 0.518526i
\(341\) 2.38665e21 0.706929
\(342\) 3.14354e21i 0.908233i
\(343\) 3.82222e21i 1.07725i
\(344\) −1.55186e18 −0.000426683
\(345\) −2.78849e21 + 6.44930e21i −0.748008 + 1.73002i
\(346\) 6.75069e21 1.76686
\(347\) 3.32900e21i 0.850185i 0.905150 + 0.425093i \(0.139759\pi\)
−0.905150 + 0.425093i \(0.860241\pi\)
\(348\) 4.34653e21i 1.08323i
\(349\) 1.29318e21 0.314517 0.157258 0.987558i \(-0.449734\pi\)
0.157258 + 0.987558i \(0.449734\pi\)
\(350\) 3.61161e21 + 3.84119e21i 0.857279 + 0.911775i
\(351\) −3.98461e21 −0.923157
\(352\) 7.22374e21i 1.63361i
\(353\) 1.41320e21i 0.311974i −0.987759 0.155987i \(-0.950144\pi\)
0.987759 0.155987i \(-0.0498558\pi\)
\(354\) −2.98266e21 −0.642801
\(355\) −1.17601e20 + 2.71991e20i −0.0247439 + 0.0572286i
\(356\) −8.72801e21 −1.79304
\(357\) 9.19687e21i 1.84485i
\(358\) 8.02601e21i 1.57215i
\(359\) −6.70882e21 −1.28334 −0.641672 0.766979i \(-0.721759\pi\)
−0.641672 + 0.766979i \(0.721759\pi\)
\(360\) −5.49491e19 2.37583e19i −0.0102657 0.00443859i
\(361\) −4.57468e21 −0.834737
\(362\) 8.36504e21i 1.49089i
\(363\) 3.05328e21i 0.531570i
\(364\) 5.19730e21 0.883926
\(365\) 6.80908e21 + 2.94404e21i 1.13136 + 0.489164i
\(366\) 6.71161e21 1.08953
\(367\) 1.37823e21i 0.218606i 0.994009 + 0.109303i \(0.0348618\pi\)
−0.994009 + 0.109303i \(0.965138\pi\)
\(368\) 7.53627e21i 1.16802i
\(369\) 1.60394e22 2.42921
\(370\) 5.88372e20 1.36081e21i 0.0870838 0.201410i
\(371\) 5.92804e20 0.0857497
\(372\) 6.99329e21i 0.988705i
\(373\) 5.63938e21i 0.779303i −0.920962 0.389652i \(-0.872595\pi\)
0.920962 0.389652i \(-0.127405\pi\)
\(374\) −1.57228e22 −2.12384
\(375\) −4.12929e21 1.14361e22i −0.545268 1.51013i
\(376\) −4.68240e19 −0.00604466
\(377\) 5.29298e21i 0.668034i
\(378\) 9.40839e21i 1.16101i
\(379\) −7.95543e21 −0.959910 −0.479955 0.877293i \(-0.659347\pi\)
−0.479955 + 0.877293i \(0.659347\pi\)
\(380\) −1.37422e21 + 3.17835e21i −0.162142 + 0.375008i
\(381\) 5.40964e20 0.0624175
\(382\) 2.20113e22i 2.48375i
\(383\) 9.82389e21i 1.08416i 0.840326 + 0.542081i \(0.182363\pi\)
−0.840326 + 0.542081i \(0.817637\pi\)
\(384\) 2.10871e20 0.0227615
\(385\) −8.86498e21 3.83295e21i −0.935969 0.404685i
\(386\) 5.43042e21 0.560843
\(387\) 9.40045e20i 0.0949742i
\(388\) 3.87815e21i 0.383314i
\(389\) 1.88950e21 0.182716 0.0913579 0.995818i \(-0.470879\pi\)
0.0913579 + 0.995818i \(0.470879\pi\)
\(390\) −2.19477e22 9.48954e21i −2.07654 0.897834i
\(391\) 1.64856e22 1.52617
\(392\) 1.71230e19i 0.00155113i
\(393\) 2.20884e22i 1.95807i
\(394\) 1.04616e22 0.907567
\(395\) 3.66839e21 8.48436e21i 0.311458 0.720351i
\(396\) 2.20157e22 1.82946
\(397\) 2.38867e22i 1.94284i 0.237364 + 0.971421i \(0.423716\pi\)
−0.237364 + 0.971421i \(0.576284\pi\)
\(398\) 1.29223e22i 1.02881i
\(399\) 7.40212e21 0.576881
\(400\) 8.93325e21 + 9.50112e21i 0.681553 + 0.724878i
\(401\) −5.01330e21 −0.374452 −0.187226 0.982317i \(-0.559950\pi\)
−0.187226 + 0.982317i \(0.559950\pi\)
\(402\) 2.69054e22i 1.96752i
\(403\) 8.51606e21i 0.609742i
\(404\) −5.23600e21 −0.367078
\(405\) −5.10731e20 + 1.18124e21i −0.0350610 + 0.0810903i
\(406\) −1.24977e22 −0.840152
\(407\) 2.71578e21i 0.178789i
\(408\) 2.29482e20i 0.0147958i
\(409\) −1.79789e22 −1.13531 −0.567657 0.823265i \(-0.692150\pi\)
−0.567657 + 0.823265i \(0.692150\pi\)
\(410\) 3.23533e22 + 1.39886e22i 2.00104 + 0.865190i
\(411\) −2.78027e22 −1.68434
\(412\) 1.91795e22i 1.13818i
\(413\) 4.29877e21i 0.249901i
\(414\) −4.60525e22 −2.62271
\(415\) −2.29990e22 9.94409e21i −1.28322 0.554825i
\(416\) 2.57758e22 1.40903
\(417\) 1.84118e22i 0.986143i
\(418\) 1.26545e22i 0.664122i
\(419\) 3.00683e22 1.54628 0.773142 0.634233i \(-0.218684\pi\)
0.773142 + 0.634233i \(0.218684\pi\)
\(420\) −1.12312e22 + 2.59760e22i −0.565989 + 1.30904i
\(421\) 1.89938e22 0.938026 0.469013 0.883191i \(-0.344610\pi\)
0.469013 + 0.883191i \(0.344610\pi\)
\(422\) 2.98624e22i 1.44534i
\(423\) 2.83638e22i 1.34546i
\(424\) −1.47918e19 −0.000687718
\(425\) −2.07837e22 + 1.95415e22i −0.947146 + 0.890536i
\(426\) −3.17316e21 −0.141746
\(427\) 9.67311e21i 0.423574i
\(428\) 2.32392e22i 0.997581i
\(429\) 4.38013e22 1.84332
\(430\) 8.19849e20 1.89617e21i 0.0338261 0.0782341i
\(431\) 1.12764e22 0.456155 0.228077 0.973643i \(-0.426756\pi\)
0.228077 + 0.973643i \(0.426756\pi\)
\(432\) 2.32715e22i 0.923023i
\(433\) 8.94358e21i 0.347828i −0.984761 0.173914i \(-0.944359\pi\)
0.984761 0.173914i \(-0.0556414\pi\)
\(434\) −2.01080e22 −0.766841
\(435\) 2.64542e22 + 1.14380e22i 0.989317 + 0.427751i
\(436\) −3.21153e22 −1.17781
\(437\) 1.32684e22i 0.477230i
\(438\) 7.94377e22i 2.80218i
\(439\) 3.08777e22 1.06831 0.534154 0.845387i \(-0.320630\pi\)
0.534154 + 0.845387i \(0.320630\pi\)
\(440\) 2.21201e20 + 9.56407e19i 0.00750653 + 0.00324560i
\(441\) −1.03723e22 −0.345261
\(442\) 5.61024e22i 1.83186i
\(443\) 3.82645e21i 0.122564i −0.998120 0.0612822i \(-0.980481\pi\)
0.998120 0.0612822i \(-0.0195190\pi\)
\(444\) 7.95770e21 0.250053
\(445\) 2.29680e22 5.31211e22i 0.708048 1.63760i
\(446\) −3.89306e22 −1.17746
\(447\) 2.99414e22i 0.888501i
\(448\) 3.06587e22i 0.892668i
\(449\) −5.61218e22 −1.60339 −0.801693 0.597736i \(-0.796067\pi\)
−0.801693 + 0.597736i \(0.796067\pi\)
\(450\) 5.80593e22 5.45892e22i 1.62767 1.53038i
\(451\) −6.45678e22 −1.77630
\(452\) 2.41173e22i 0.651108i
\(453\) 3.78566e20i 0.0100301i
\(454\) 1.04612e23 2.72023
\(455\) −1.36768e22 + 3.16322e22i −0.349050 + 0.807294i
\(456\) −1.84699e20 −0.00462662
\(457\) 1.57770e22i 0.387915i 0.981010 + 0.193957i \(0.0621324\pi\)
−0.981010 + 0.193957i \(0.937868\pi\)
\(458\) 1.06061e23i 2.55975i
\(459\) −5.09064e22 −1.20605
\(460\) −4.65624e22 2.01322e22i −1.08291 0.468220i
\(461\) 1.26163e22 0.288055 0.144027 0.989574i \(-0.453995\pi\)
0.144027 + 0.989574i \(0.453995\pi\)
\(462\) 1.03423e23i 2.31824i
\(463\) 5.01130e22i 1.10284i −0.834228 0.551420i \(-0.814086\pi\)
0.834228 0.551420i \(-0.185914\pi\)
\(464\) −3.09128e22 −0.667937
\(465\) 4.25631e22 + 1.84030e22i 0.902990 + 0.390426i
\(466\) −6.01916e21 −0.125388
\(467\) 1.34110e22i 0.274326i 0.990548 + 0.137163i \(0.0437985\pi\)
−0.990548 + 0.137163i \(0.956202\pi\)
\(468\) 7.85567e22i 1.57795i
\(469\) −3.87775e22 −0.764910
\(470\) 2.47372e22 5.72129e22i 0.479202 1.10831i
\(471\) 3.35520e22 0.638323
\(472\) 1.07264e20i 0.00200422i
\(473\) 3.78421e21i 0.0694474i
\(474\) 9.89823e22 1.78419
\(475\) −1.57280e22 1.67278e22i −0.278469 0.296171i
\(476\) 6.63993e22 1.15479
\(477\) 8.96018e21i 0.153077i
\(478\) 1.07051e23i 1.79660i
\(479\) −9.41455e22 −1.55220 −0.776100 0.630609i \(-0.782805\pi\)
−0.776100 + 0.630609i \(0.782805\pi\)
\(480\) −5.57010e22 + 1.28827e23i −0.902220 + 2.08668i
\(481\) 9.69047e21 0.154210
\(482\) 5.82441e22i 0.910651i
\(483\) 1.08440e23i 1.66586i
\(484\) −2.20440e22 −0.332740
\(485\) 2.36035e22 + 1.02054e22i 0.350083 + 0.151365i
\(486\) −1.03911e23 −1.51444
\(487\) 9.22452e22i 1.32114i −0.750766 0.660568i \(-0.770316\pi\)
0.750766 0.660568i \(-0.229684\pi\)
\(488\) 2.41366e20i 0.00339709i
\(489\) 9.95995e22 1.37763
\(490\) −2.09221e22 9.04609e21i −0.284406 0.122969i
\(491\) 5.46994e22 0.730786 0.365393 0.930853i \(-0.380935\pi\)
0.365393 + 0.930853i \(0.380935\pi\)
\(492\) 1.89195e23i 2.48431i
\(493\) 6.76217e22i 0.872745i
\(494\) −4.51541e22 −0.572819
\(495\) −5.79348e22 + 1.33993e23i −0.722429 + 1.67086i
\(496\) −4.97367e22 −0.609653
\(497\) 4.57332e21i 0.0551065i
\(498\) 2.68317e23i 3.17832i
\(499\) 1.31366e23 1.52978 0.764889 0.644162i \(-0.222794\pi\)
0.764889 + 0.644162i \(0.222794\pi\)
\(500\) 8.25662e22 2.98125e22i 0.945274 0.341314i
\(501\) 1.07854e22 0.121399
\(502\) 9.59271e22i 1.06160i
\(503\) 2.61038e22i 0.284038i −0.989864 0.142019i \(-0.954641\pi\)
0.989864 0.142019i \(-0.0453594\pi\)
\(504\) −9.23928e20 −0.00988504
\(505\) 1.37787e22 3.18677e22i 0.144954 0.335254i
\(506\) 1.85387e23 1.91779
\(507\) 1.53866e21i 0.0156521i
\(508\) 3.90564e21i 0.0390706i
\(509\) −1.64322e22 −0.161657 −0.0808285 0.996728i \(-0.525757\pi\)
−0.0808285 + 0.996728i \(0.525757\pi\)
\(510\) −2.80398e23 1.21236e23i −2.71287 1.17296i
\(511\) 1.14490e23 1.08940
\(512\) 1.51293e23i 1.41588i
\(513\) 4.09720e22i 0.377129i
\(514\) −1.90800e23 −1.72740
\(515\) 1.16732e23 + 5.04714e22i 1.03951 + 0.449452i
\(516\) 1.10884e22 0.0971285
\(517\) 1.14180e23i 0.983835i
\(518\) 2.28809e22i 0.193942i
\(519\) −2.40265e23 −2.00340
\(520\) 3.41267e20 7.89293e20i 0.00279940 0.00647455i
\(521\) −8.34710e22 −0.673620 −0.336810 0.941573i \(-0.609348\pi\)
−0.336810 + 0.941573i \(0.609348\pi\)
\(522\) 1.88901e23i 1.49981i
\(523\) 1.83965e23i 1.43704i 0.695505 + 0.718522i \(0.255181\pi\)
−0.695505 + 0.718522i \(0.744819\pi\)
\(524\) −1.59473e23 −1.22566
\(525\) −1.28541e23 1.36713e23i −0.972051 1.03384i
\(526\) 2.20427e23 1.64016
\(527\) 1.08799e23i 0.796590i
\(528\) 2.55814e23i 1.84305i
\(529\) −5.33313e22 −0.378102
\(530\) 7.81451e21 1.80737e22i 0.0545201 0.126096i
\(531\) 6.49755e22 0.446115
\(532\) 5.34416e22i 0.361102i
\(533\) 2.30392e23i 1.53209i
\(534\) 6.19733e23 4.05606
\(535\) 1.41440e23 + 6.11544e22i 0.911097 + 0.393931i
\(536\) 9.67584e20 0.00613463
\(537\) 2.85655e23i 1.78263i
\(538\) 3.68732e23i 2.26497i
\(539\) 4.17545e22 0.252463
\(540\) 1.43782e23 + 6.21669e22i 0.855769 + 0.370009i
\(541\) −3.23384e23 −1.89471 −0.947353 0.320192i \(-0.896253\pi\)
−0.947353 + 0.320192i \(0.896253\pi\)
\(542\) 1.97527e22i 0.113928i
\(543\) 2.97722e23i 1.69049i
\(544\) 3.29305e23 1.84081
\(545\) 8.45122e22 1.95462e23i 0.465103 1.07570i
\(546\) −3.69035e23 −1.99954
\(547\) 1.81693e23i 0.969272i −0.874716 0.484636i \(-0.838952\pi\)
0.874716 0.484636i \(-0.161048\pi\)
\(548\) 2.00729e23i 1.05433i
\(549\) −1.46208e23 −0.756148
\(550\) −2.33722e23 + 2.19752e23i −1.19019 + 1.11905i
\(551\) 5.44254e22 0.272906
\(552\) 2.70582e21i 0.0133603i
\(553\) 1.42658e23i 0.693639i
\(554\) −5.58981e23 −2.67648
\(555\) −2.09409e22 + 4.84327e22i −0.0987425 + 0.228375i
\(556\) −1.32929e23 −0.617283
\(557\) 3.53126e23i 1.61496i 0.589898 + 0.807478i \(0.299168\pi\)
−0.589898 + 0.807478i \(0.700832\pi\)
\(558\) 3.03930e23i 1.36894i
\(559\) 1.35029e22 0.0598999
\(560\) 1.84743e23 + 7.98772e22i 0.807177 + 0.348999i
\(561\) 5.59594e23 2.40818
\(562\) 6.24646e23i 2.64774i
\(563\) 2.98124e23i 1.24473i −0.782727 0.622365i \(-0.786172\pi\)
0.782727 0.622365i \(-0.213828\pi\)
\(564\) 3.34569e23 1.37598
\(565\) −1.46785e23 6.34653e22i −0.594660 0.257113i
\(566\) −2.96369e23 −1.18275
\(567\) 1.98616e22i 0.0780833i
\(568\) 1.14115e20i 0.000441957i
\(569\) −2.50456e23 −0.955602 −0.477801 0.878468i \(-0.658566\pi\)
−0.477801 + 0.878468i \(0.658566\pi\)
\(570\) 9.75768e22 2.25679e23i 0.366784 0.848310i
\(571\) 6.51987e22 0.241453 0.120726 0.992686i \(-0.461478\pi\)
0.120726 + 0.992686i \(0.461478\pi\)
\(572\) 3.16235e23i 1.15384i
\(573\) 7.83409e23i 2.81627i
\(574\) 5.43996e23 1.92684
\(575\) 2.45060e23 2.30413e23i 0.855256 0.804139i
\(576\) −4.63403e23 −1.59356
\(577\) 2.02985e23i 0.687811i 0.939004 + 0.343905i \(0.111750\pi\)
−0.939004 + 0.343905i \(0.888250\pi\)
\(578\) 2.92672e23i 0.977226i
\(579\) −1.93275e23 −0.635928
\(580\) −8.25797e22 + 1.90993e23i −0.267753 + 0.619269i
\(581\) −3.86711e23 −1.23563
\(582\) 2.75368e23i 0.867099i
\(583\) 3.60698e22i 0.111934i
\(584\) −2.85677e21 −0.00873708
\(585\) 4.78117e23 + 2.06724e23i 1.44115 + 0.623111i
\(586\) 3.45880e23 1.02753
\(587\) 4.32091e23i 1.26518i 0.774488 + 0.632589i \(0.218008\pi\)
−0.774488 + 0.632589i \(0.781992\pi\)
\(588\) 1.22348e23i 0.353093i
\(589\) 8.75670e22 0.249092
\(590\) 1.31063e23 + 5.66676e22i 0.367483 + 0.158889i
\(591\) −3.72339e23 −1.02907
\(592\) 5.65956e22i 0.154187i
\(593\) 2.09720e23i 0.563215i −0.959530 0.281608i \(-0.909132\pi\)
0.959530 0.281608i \(-0.0908676\pi\)
\(594\) −5.72464e23 −1.51553
\(595\) −1.74731e23 + 4.04124e23i −0.456012 + 1.05468i
\(596\) 2.16170e23 0.556163
\(597\) 4.59919e23i 1.16654i
\(598\) 6.61502e23i 1.65414i
\(599\) 4.27137e23 1.05303 0.526514 0.850167i \(-0.323499\pi\)
0.526514 + 0.850167i \(0.323499\pi\)
\(600\) 3.20740e21 + 3.41128e21i 0.00779591 + 0.00829148i
\(601\) −2.36643e23 −0.567102 −0.283551 0.958957i \(-0.591513\pi\)
−0.283551 + 0.958957i \(0.591513\pi\)
\(602\) 3.18827e22i 0.0753330i
\(603\) 5.86118e23i 1.36549i
\(604\) −2.73316e21 −0.00627843
\(605\) 5.80093e22 1.34166e23i 0.131394 0.303893i
\(606\) 3.71783e23 0.830371
\(607\) 2.71884e23i 0.598798i −0.954128 0.299399i \(-0.903214\pi\)
0.954128 0.299399i \(-0.0967861\pi\)
\(608\) 2.65042e23i 0.575618i
\(609\) 4.44807e23 0.952631
\(610\) −2.94918e23 1.27514e23i −0.622870 0.269311i
\(611\) 4.07420e23 0.848579
\(612\) 1.00362e24i 2.06149i
\(613\) 4.19323e22i 0.0849444i 0.999098 + 0.0424722i \(0.0135234\pi\)
−0.999098 + 0.0424722i \(0.986477\pi\)
\(614\) −9.83095e22 −0.196410
\(615\) −1.15149e24 4.97871e23i −2.26894 0.981021i
\(616\) 3.71933e21 0.00722818
\(617\) 2.53421e23i 0.485757i −0.970057 0.242879i \(-0.921908\pi\)
0.970057 0.242879i \(-0.0780917\pi\)
\(618\) 1.36184e24i 2.57469i
\(619\) 1.42452e23 0.265642 0.132821 0.991140i \(-0.457596\pi\)
0.132821 + 0.991140i \(0.457596\pi\)
\(620\) −1.32865e23 + 3.07295e23i −0.244390 + 0.565232i
\(621\) 6.00236e23 1.08904
\(622\) 1.38714e24i 2.48258i
\(623\) 8.93191e23i 1.57687i
\(624\) −9.12801e23 −1.58967
\(625\) −3.58277e22 + 5.80973e23i −0.0615516 + 0.998104i
\(626\) 8.17505e23 1.38551
\(627\) 4.50390e23i 0.753034i
\(628\) 2.42238e23i 0.399562i
\(629\) 1.23803e23 0.201465
\(630\) 4.88112e23 1.12892e24i 0.783655 1.81246i
\(631\) −7.06224e23 −1.11865 −0.559323 0.828950i \(-0.688939\pi\)
−0.559323 + 0.828950i \(0.688939\pi\)
\(632\) 3.55964e21i 0.00556303i
\(633\) 1.06284e24i 1.63884i
\(634\) −5.85638e23 −0.890985
\(635\) −2.37708e22 1.02778e22i −0.0356834 0.0154284i
\(636\) 1.05691e23 0.156550
\(637\) 1.48989e23i 0.217755i
\(638\) 7.60435e23i 1.09670i
\(639\) 6.91254e22 0.0983740
\(640\) −9.26598e21 4.00633e21i −0.0130125 0.00562623i
\(641\) 1.55017e23 0.214826 0.107413 0.994214i \(-0.465743\pi\)
0.107413 + 0.994214i \(0.465743\pi\)
\(642\) 1.65010e24i 2.25664i
\(643\) 1.13817e23i 0.153608i 0.997046 + 0.0768041i \(0.0244716\pi\)
−0.997046 + 0.0768041i \(0.975528\pi\)
\(644\) −7.82913e23 −1.04276
\(645\) −2.91794e22 + 6.74870e22i −0.0383547 + 0.0887080i
\(646\) −5.76876e23 −0.748353
\(647\) 5.81112e23i 0.744001i 0.928233 + 0.372000i \(0.121328\pi\)
−0.928233 + 0.372000i \(0.878672\pi\)
\(648\) 4.95591e20i 0.000626233i
\(649\) −2.61563e23 −0.326210
\(650\) 7.84123e23 + 8.33968e23i 0.965208 + 1.02656i
\(651\) 7.15666e23 0.869505
\(652\) 7.19085e23i 0.862335i
\(653\) 1.22090e24i 1.44517i 0.691282 + 0.722585i \(0.257046\pi\)
−0.691282 + 0.722585i \(0.742954\pi\)
\(654\) 2.28035e24 2.66435
\(655\) 4.19657e23 9.70596e23i 0.483997 1.11941i
\(656\) 1.34557e24 1.53187
\(657\) 1.73050e24i 1.94476i
\(658\) 9.61993e23i 1.06721i
\(659\) −8.05650e23 −0.882308 −0.441154 0.897431i \(-0.645431\pi\)
−0.441154 + 0.897431i \(0.645431\pi\)
\(660\) −1.58054e24 6.83376e23i −1.70876 0.738816i
\(661\) 1.62925e22 0.0173891 0.00869453 0.999962i \(-0.497232\pi\)
0.00869453 + 0.999962i \(0.497232\pi\)
\(662\) 6.35649e23i 0.669768i
\(663\) 1.99675e24i 2.07711i
\(664\) 9.64931e21 0.00990986
\(665\) −3.25260e23 1.40633e23i −0.329797 0.142594i
\(666\) −3.45844e23 −0.346217
\(667\) 7.97326e23i 0.788073i
\(668\) 7.78679e22i 0.0759903i
\(669\) 1.38559e24 1.33509
\(670\) −5.11176e23 + 1.18226e24i −0.486334 + 1.12481i
\(671\) 5.88571e23 0.552914
\(672\) 2.16613e24i 2.00931i
\(673\) 9.71208e22i 0.0889578i −0.999010 0.0444789i \(-0.985837\pi\)
0.999010 0.0444789i \(-0.0141628\pi\)
\(674\) −2.80204e24 −2.53434
\(675\) −7.56729e23 + 7.11500e23i −0.675863 + 0.635467i
\(676\) −1.11087e22 −0.00979756
\(677\) 6.85083e23i 0.596677i −0.954460 0.298339i \(-0.903568\pi\)
0.954460 0.298339i \(-0.0964325\pi\)
\(678\) 1.71245e24i 1.47288i
\(679\) 3.96875e23 0.337101
\(680\) 4.35993e21 1.00838e22i 0.00365725 0.00845860i
\(681\) −3.72325e24 −3.08441
\(682\) 1.22349e24i 1.00100i
\(683\) 2.54919e23i 0.205981i −0.994682 0.102990i \(-0.967159\pi\)
0.994682 0.102990i \(-0.0328410\pi\)
\(684\) 8.07765e23 0.644626
\(685\) 1.22169e24 + 5.28222e23i 0.962922 + 0.416339i
\(686\) −1.95942e24 −1.52536
\(687\) 3.77482e24i 2.90245i
\(688\) 7.88614e22i 0.0598912i
\(689\) 1.28705e23 0.0965453
\(690\) 3.30617e24 + 1.42949e24i 2.44967 + 1.05917i
\(691\) 2.08545e24 1.52628 0.763142 0.646231i \(-0.223656\pi\)
0.763142 + 0.646231i \(0.223656\pi\)
\(692\) 1.73466e24i 1.25404i
\(693\) 2.25300e24i 1.60890i
\(694\) 1.70658e24 1.20385
\(695\) 3.49806e23 8.09042e23i 0.243756 0.563768i
\(696\) −1.10989e22 −0.00764016
\(697\) 2.94342e24i 2.00159i
\(698\) 6.62938e23i 0.445350i
\(699\) 2.14229e23 0.142175
\(700\) 9.87033e23 9.28040e23i 0.647140 0.608462i
\(701\) −1.58460e24 −1.02640 −0.513201 0.858268i \(-0.671541\pi\)
−0.513201 + 0.858268i \(0.671541\pi\)
\(702\) 2.04267e24i 1.30717i
\(703\) 9.96429e22i 0.0629979i
\(704\) 1.86546e24 1.16525
\(705\) −8.80425e23 + 2.03628e24i −0.543357 + 1.25669i
\(706\) −7.24463e23 −0.441750
\(707\) 5.35832e23i 0.322823i
\(708\) 7.66426e23i 0.456234i
\(709\) 6.54139e23 0.384749 0.192374 0.981322i \(-0.438381\pi\)
0.192374 + 0.981322i \(0.438381\pi\)
\(710\) 1.39433e23 + 6.02869e22i 0.0810347 + 0.0350370i
\(711\) −2.15627e24 −1.23826
\(712\) 2.22871e22i 0.0126466i
\(713\) 1.28285e24i 0.719306i
\(714\) −4.71469e24 −2.61227
\(715\) −1.92469e24 8.32180e23i −1.05380 0.455634i
\(716\) 2.06237e24 1.11585
\(717\) 3.81006e24i 2.03713i
\(718\) 3.43921e24i 1.81719i
\(719\) −9.39757e23 −0.490704 −0.245352 0.969434i \(-0.578904\pi\)
−0.245352 + 0.969434i \(0.578904\pi\)
\(720\) 1.20734e24 2.79237e24i 0.623021 1.44094i
\(721\) 1.96276e24 1.00096
\(722\) 2.34517e24i 1.18197i
\(723\) 2.07298e24i 1.03257i
\(724\) −2.14948e24 −1.05817
\(725\) −9.45125e23 1.00520e24i −0.459850 0.489082i
\(726\) 1.56524e24 0.752694
\(727\) 3.68851e24i 1.75311i 0.481303 + 0.876555i \(0.340164\pi\)
−0.481303 + 0.876555i \(0.659836\pi\)
\(728\) 1.32714e22i 0.00623446i
\(729\) 3.50804e24 1.62885
\(730\) 1.50924e24 3.49061e24i 0.692648 1.60198i
\(731\) 1.72509e23 0.0782555
\(732\) 1.72462e24i 0.773300i
\(733\) 1.51915e24i 0.673314i −0.941627 0.336657i \(-0.890704\pi\)
0.941627 0.336657i \(-0.109296\pi\)
\(734\) 7.06538e23 0.309542
\(735\) 7.44643e23 + 3.21961e23i 0.322482 + 0.139432i
\(736\) −3.88284e24 −1.66222
\(737\) 2.35946e24i 0.998478i
\(738\) 8.22246e24i 3.43972i
\(739\) 2.81865e24 1.16564 0.582819 0.812602i \(-0.301950\pi\)
0.582819 + 0.812602i \(0.301950\pi\)
\(740\) −3.49673e23 1.51188e23i −0.142953 0.0618085i
\(741\) 1.60709e24 0.649508
\(742\) 3.03895e23i 0.121420i
\(743\) 2.00449e23i 0.0791769i 0.999216 + 0.0395884i \(0.0126047\pi\)
−0.999216 + 0.0395884i \(0.987395\pi\)
\(744\) −1.78575e22 −0.00697349
\(745\) −5.68856e23 + 1.31567e24i −0.219621 + 0.507947i
\(746\) −2.89098e24 −1.10348
\(747\) 5.84511e24i 2.20581i
\(748\) 4.04014e24i 1.50741i
\(749\) 2.37821e24 0.877312
\(750\) −5.86262e24 + 2.11684e24i −2.13831 + 0.772090i
\(751\) −1.04857e24 −0.378146 −0.189073 0.981963i \(-0.560548\pi\)
−0.189073 + 0.981963i \(0.560548\pi\)
\(752\) 2.37947e24i 0.848456i
\(753\) 3.41416e24i 1.20372i
\(754\) −2.71339e24 −0.945924
\(755\) 7.19238e21 1.66348e22i 0.00247927 0.00573413i
\(756\) 2.41758e24 0.824035
\(757\) 9.69171e23i 0.326652i −0.986572 0.163326i \(-0.947778\pi\)
0.986572 0.163326i \(-0.0522222\pi\)
\(758\) 4.07827e24i 1.35922i
\(759\) −6.59816e24 −2.17454
\(760\) 8.11596e21 + 3.50910e21i 0.00264499 + 0.00114362i
\(761\) 5.85969e23 0.188845 0.0944224 0.995532i \(-0.469900\pi\)
0.0944224 + 0.995532i \(0.469900\pi\)
\(762\) 2.77320e23i 0.0883821i
\(763\) 3.28656e24i 1.03582i
\(764\) 5.65603e24 1.76286
\(765\) 6.10830e24 + 2.64105e24i 1.88277 + 0.814056i
\(766\) 5.03612e24 1.53515
\(767\) 9.33313e23i 0.281363i
\(768\) 5.33080e24i 1.58936i
\(769\) −4.42159e24 −1.30378 −0.651891 0.758313i \(-0.726024\pi\)
−0.651891 + 0.758313i \(0.726024\pi\)
\(770\) −1.96493e24 + 4.54455e24i −0.573027 + 1.32532i
\(771\) 6.79080e24 1.95866
\(772\) 1.39540e24i 0.398063i
\(773\) 2.69572e24i 0.760587i −0.924866 0.380293i \(-0.875823\pi\)
0.924866 0.380293i \(-0.124177\pi\)
\(774\) −4.81905e23 −0.134482
\(775\) −1.52065e24