Properties

Label 6.11.b.a.5.1
Level $6$
Weight $11$
Character 6.5
Analytic conductor $3.812$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.81214351604\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{85})\)
Defining polynomial: \(x^{4} - 2 x^{3} - 37 x^{2} + 38 x + 531\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{11}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.1
Root \(-4.10977 + 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 6.5
Dual form 6.11.b.a.5.3

$q$-expansion

\(f(q)\) \(=\) \(q-22.6274i q^{2} +(-200.269 + 137.627i) q^{3} -512.000 q^{4} +3630.47i q^{5} +(3114.15 + 4531.57i) q^{6} -23226.5 q^{7} +11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +O(q^{10})\) \(q-22.6274i q^{2} +(-200.269 + 137.627i) q^{3} -512.000 q^{4} +3630.47i q^{5} +(3114.15 + 4531.57i) q^{6} -23226.5 q^{7} +11585.2i q^{8} +(21166.4 - 55125.0i) q^{9} +82148.2 q^{10} -62442.7i q^{11} +(102538. - 70465.2i) q^{12} -170161. q^{13} +525556. i q^{14} +(-499653. - 727072. i) q^{15} +262144. q^{16} +2.66626e6i q^{17} +(-1.24734e6 - 478941. i) q^{18} +766825. q^{19} -1.85880e6i q^{20} +(4.65156e6 - 3.19661e6i) q^{21} -1.41292e6 q^{22} -1.40327e6i q^{23} +(-1.59445e6 - 2.32016e6i) q^{24} -3.41471e6 q^{25} +3.85029e6i q^{26} +(3.34774e6 + 1.39529e7i) q^{27} +1.18920e7 q^{28} -4.83245e6i q^{29} +(-1.64518e7 + 1.13058e7i) q^{30} -4.18297e7 q^{31} -5.93164e6i q^{32} +(8.59382e6 + 1.25053e7i) q^{33} +6.03306e7 q^{34} -8.43233e7i q^{35} +(-1.08372e7 + 2.82240e7i) q^{36} +5.01619e7 q^{37} -1.73513e7i q^{38} +(3.40779e7 - 2.34188e7i) q^{39} -4.20599e7 q^{40} +1.49239e8i q^{41} +(-7.23310e7 - 1.05253e8i) q^{42} -1.98719e8 q^{43} +3.19706e7i q^{44} +(2.00130e8 + 7.68440e7i) q^{45} -3.17523e7 q^{46} +1.55059e8i q^{47} +(-5.24993e7 + 3.60782e7i) q^{48} +2.56996e8 q^{49} +7.72661e7i q^{50} +(-3.66951e8 - 5.33970e8i) q^{51} +8.71222e7 q^{52} -4.21541e7i q^{53} +(3.15718e8 - 7.57507e7i) q^{54} +2.26696e8 q^{55} -2.69085e8i q^{56} +(-1.53571e8 + 1.05536e8i) q^{57} -1.09346e8 q^{58} -2.92026e8i q^{59} +(2.55822e8 + 3.72261e8i) q^{60} -5.30727e8 q^{61} +9.46499e8i q^{62} +(-4.91622e8 + 1.28036e9i) q^{63} -1.34218e8 q^{64} -6.17764e8i q^{65} +(2.82963e8 - 1.94456e8i) q^{66} +5.22093e8 q^{67} -1.36513e9i q^{68} +(1.93128e8 + 2.81031e8i) q^{69} -1.90802e9 q^{70} -5.71364e8i q^{71} +(6.38636e8 + 2.45218e8i) q^{72} +2.18588e9 q^{73} -1.13503e9i q^{74} +(6.83861e8 - 4.69958e8i) q^{75} -3.92615e8 q^{76} +1.45033e9i q^{77} +(-5.29906e8 - 7.71095e8i) q^{78} +1.96592e9 q^{79} +9.51707e8i q^{80} +(-2.59075e9 - 2.33360e9i) q^{81} +3.37689e9 q^{82} +2.18558e9i q^{83} +(-2.38160e9 + 1.63666e9i) q^{84} -9.67979e9 q^{85} +4.49650e9i q^{86} +(6.65078e8 + 9.67791e8i) q^{87} +7.23413e8 q^{88} +2.38742e8i q^{89} +(1.73878e9 - 4.52842e9i) q^{90} +3.95224e9 q^{91} +7.18473e8i q^{92} +(8.37720e9 - 5.75692e9i) q^{93} +3.50858e9 q^{94} +2.78394e9i q^{95} +(8.16356e8 + 1.18792e9i) q^{96} -8.84112e9 q^{97} -5.81517e9i q^{98} +(-3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} + O(q^{10}) \) \( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} - 53760 q^{10} - 43008 q^{12} + 275240 q^{13} - 1180800 q^{15} + 1048576 q^{16} - 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} + 7730688 q^{22} - 2752512 q^{24} - 33732380 q^{25} + 34619508 q^{27} + 23097344 q^{28} - 85731840 q^{30} - 21785848 q^{31} + 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} - 71014168 q^{37} + 217287240 q^{39} + 27525120 q^{40} - 145233408 q^{42} - 470688664 q^{43} + 312318720 q^{45} + 188814336 q^{46} + 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} - 140922880 q^{52} + 481662720 q^{54} + 2701359360 q^{55} - 1058753208 q^{57} - 1564177920 q^{58} + 604569600 q^{60} - 1184038744 q^{61} - 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} - 297365848 q^{67} + 596268288 q^{69} - 3962250240 q^{70} + 1488715776 q^{72} + 6534269000 q^{73} - 5150031180 q^{75} + 803188736 q^{76} - 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} + 8378668032 q^{82} - 4929540096 q^{84} - 12880512000 q^{85} + 210268800 q^{87} - 3958112256 q^{88} - 9243763200 q^{90} + 8317232080 q^{91} + 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} - 39176355064 q^{97} - 2626912512 q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 22.6274i 0.707107i
\(3\) −200.269 + 137.627i −0.824153 + 0.566368i
\(4\) −512.000 −0.500000
\(5\) 3630.47i 1.16175i 0.813992 + 0.580876i \(0.197290\pi\)
−0.813992 + 0.580876i \(0.802710\pi\)
\(6\) 3114.15 + 4531.57i 0.400483 + 0.582764i
\(7\) −23226.5 −1.38196 −0.690978 0.722876i \(-0.742820\pi\)
−0.690978 + 0.722876i \(0.742820\pi\)
\(8\) 11585.2i 0.353553i
\(9\) 21166.4 55125.0i 0.358455 0.933547i
\(10\) 82148.2 0.821482
\(11\) 62442.7i 0.387720i −0.981029 0.193860i \(-0.937899\pi\)
0.981029 0.193860i \(-0.0621007\pi\)
\(12\) 102538. 70465.2i 0.412076 0.283184i
\(13\) −170161. −0.458292 −0.229146 0.973392i \(-0.573593\pi\)
−0.229146 + 0.973392i \(0.573593\pi\)
\(14\) 525556.i 0.977190i
\(15\) −499653. 727072.i −0.657979 0.957460i
\(16\) 262144. 0.250000
\(17\) 2.66626e6i 1.87784i 0.344139 + 0.938919i \(0.388171\pi\)
−0.344139 + 0.938919i \(0.611829\pi\)
\(18\) −1.24734e6 478941.i −0.660117 0.253466i
\(19\) 766825. 0.309691 0.154845 0.987939i \(-0.450512\pi\)
0.154845 + 0.987939i \(0.450512\pi\)
\(20\) 1.85880e6i 0.580876i
\(21\) 4.65156e6 3.19661e6i 1.13894 0.782695i
\(22\) −1.41292e6 −0.274159
\(23\) 1.40327e6i 0.218022i −0.994041 0.109011i \(-0.965232\pi\)
0.994041 0.109011i \(-0.0347684\pi\)
\(24\) −1.59445e6 2.32016e6i −0.200241 0.291382i
\(25\) −3.41471e6 −0.349667
\(26\) 3.85029e6i 0.324061i
\(27\) 3.34774e6 + 1.39529e7i 0.233310 + 0.972402i
\(28\) 1.18920e7 0.690978
\(29\) 4.83245e6i 0.235601i −0.993037 0.117801i \(-0.962416\pi\)
0.993037 0.117801i \(-0.0375844\pi\)
\(30\) −1.64518e7 + 1.13058e7i −0.677027 + 0.465261i
\(31\) −4.18297e7 −1.46109 −0.730544 0.682865i \(-0.760734\pi\)
−0.730544 + 0.682865i \(0.760734\pi\)
\(32\) 5.93164e6i 0.176777i
\(33\) 8.59382e6 + 1.25053e7i 0.219592 + 0.319540i
\(34\) 6.03306e7 1.32783
\(35\) 8.43233e7i 1.60549i
\(36\) −1.08372e7 + 2.82240e7i −0.179227 + 0.466774i
\(37\) 5.01619e7 0.723378 0.361689 0.932299i \(-0.382200\pi\)
0.361689 + 0.932299i \(0.382200\pi\)
\(38\) 1.73513e7i 0.218985i
\(39\) 3.40779e7 2.34188e7i 0.377702 0.259562i
\(40\) −4.20599e7 −0.410741
\(41\) 1.49239e8i 1.28814i 0.764967 + 0.644069i \(0.222755\pi\)
−0.764967 + 0.644069i \(0.777245\pi\)
\(42\) −7.23310e7 1.05253e8i −0.553449 0.805354i
\(43\) −1.98719e8 −1.35175 −0.675876 0.737015i \(-0.736235\pi\)
−0.675876 + 0.737015i \(0.736235\pi\)
\(44\) 3.19706e7i 0.193860i
\(45\) 2.00130e8 + 7.68440e7i 1.08455 + 0.416435i
\(46\) −3.17523e7 −0.154165
\(47\) 1.55059e8i 0.676093i 0.941129 + 0.338047i \(0.109766\pi\)
−0.941129 + 0.338047i \(0.890234\pi\)
\(48\) −5.24993e7 + 3.60782e7i −0.206038 + 0.141592i
\(49\) 2.56996e8 0.909802
\(50\) 7.72661e7i 0.247252i
\(51\) −3.66951e8 5.33970e8i −1.06355 1.54762i
\(52\) 8.71222e7 0.229146
\(53\) 4.21541e7i 0.100800i −0.998729 0.0503999i \(-0.983950\pi\)
0.998729 0.0503999i \(-0.0160496\pi\)
\(54\) 3.15718e8 7.57507e7i 0.687592 0.164975i
\(55\) 2.26696e8 0.450434
\(56\) 2.69085e8i 0.488595i
\(57\) −1.53571e8 + 1.05536e8i −0.255233 + 0.175399i
\(58\) −1.09346e8 −0.166595
\(59\) 2.92026e8i 0.408471i −0.978922 0.204236i \(-0.934529\pi\)
0.978922 0.204236i \(-0.0654708\pi\)
\(60\) 2.55822e8 + 3.72261e8i 0.328989 + 0.478730i
\(61\) −5.30727e8 −0.628379 −0.314190 0.949360i \(-0.601733\pi\)
−0.314190 + 0.949360i \(0.601733\pi\)
\(62\) 9.46499e8i 1.03315i
\(63\) −4.91622e8 + 1.28036e9i −0.495369 + 1.29012i
\(64\) −1.34218e8 −0.125000
\(65\) 6.17764e8i 0.532421i
\(66\) 2.82963e8 1.94456e8i 0.225949 0.155275i
\(67\) 5.22093e8 0.386700 0.193350 0.981130i \(-0.438065\pi\)
0.193350 + 0.981130i \(0.438065\pi\)
\(68\) 1.36513e9i 0.938919i
\(69\) 1.93128e8 + 2.81031e8i 0.123481 + 0.179684i
\(70\) −1.90802e9 −1.13525
\(71\) 5.71364e8i 0.316681i −0.987385 0.158340i \(-0.949386\pi\)
0.987385 0.158340i \(-0.0506143\pi\)
\(72\) 6.38636e8 + 2.45218e8i 0.330059 + 0.126733i
\(73\) 2.18588e9 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(74\) 1.13503e9i 0.511506i
\(75\) 6.83861e8 4.69958e8i 0.288179 0.198040i
\(76\) −3.92615e8 −0.154845
\(77\) 1.45033e9i 0.535812i
\(78\) −5.29906e8 7.71095e8i −0.183538 0.267076i
\(79\) 1.96592e9 0.638897 0.319449 0.947604i \(-0.396502\pi\)
0.319449 + 0.947604i \(0.396502\pi\)
\(80\) 9.51707e8i 0.290438i
\(81\) −2.59075e9 2.33360e9i −0.743020 0.669269i
\(82\) 3.37689e9 0.910851
\(83\) 2.18558e9i 0.554850i 0.960747 + 0.277425i \(0.0894810\pi\)
−0.960747 + 0.277425i \(0.910519\pi\)
\(84\) −2.38160e9 + 1.63666e9i −0.569471 + 0.391348i
\(85\) −9.67979e9 −2.18158
\(86\) 4.49650e9i 0.955833i
\(87\) 6.65078e8 + 9.67791e8i 0.133437 + 0.194171i
\(88\) 7.23413e8 0.137080
\(89\) 2.38742e8i 0.0427542i 0.999771 + 0.0213771i \(0.00680506\pi\)
−0.999771 + 0.0213771i \(0.993195\pi\)
\(90\) 1.73878e9 4.52842e9i 0.294464 0.766892i
\(91\) 3.95224e9 0.633339
\(92\) 7.18473e8i 0.109011i
\(93\) 8.37720e9 5.75692e9i 1.20416 0.827514i
\(94\) 3.50858e9 0.478070
\(95\) 2.78394e9i 0.359784i
\(96\) 8.16356e8 + 1.18792e9i 0.100121 + 0.145691i
\(97\) −8.84112e9 −1.02955 −0.514776 0.857324i \(-0.672125\pi\)
−0.514776 + 0.857324i \(0.672125\pi\)
\(98\) 5.81517e9i 0.643327i
\(99\) −3.44215e9 1.32169e9i −0.361955 0.138980i
\(100\) 1.74833e9 0.174833
\(101\) 1.67928e10i 1.59778i −0.601477 0.798890i \(-0.705421\pi\)
0.601477 0.798890i \(-0.294579\pi\)
\(102\) −1.20824e10 + 8.30314e9i −1.09434 + 0.752041i
\(103\) 8.36865e9 0.721887 0.360944 0.932588i \(-0.382455\pi\)
0.360944 + 0.932588i \(0.382455\pi\)
\(104\) 1.97135e9i 0.162031i
\(105\) 1.16052e10 + 1.68873e10i 0.909297 + 1.32317i
\(106\) −9.53837e8 −0.0712763
\(107\) 1.43555e10i 1.02353i 0.859126 + 0.511764i \(0.171008\pi\)
−0.859126 + 0.511764i \(0.828992\pi\)
\(108\) −1.71404e9 7.14389e9i −0.116655 0.486201i
\(109\) −4.72564e9 −0.307134 −0.153567 0.988138i \(-0.549076\pi\)
−0.153567 + 0.988138i \(0.549076\pi\)
\(110\) 5.12956e9i 0.318505i
\(111\) −1.00459e10 + 6.90365e9i −0.596174 + 0.409698i
\(112\) −6.08870e9 −0.345489
\(113\) 1.32158e10i 0.717303i 0.933472 + 0.358651i \(0.116763\pi\)
−0.933472 + 0.358651i \(0.883237\pi\)
\(114\) 2.38801e9 + 3.47492e9i 0.124026 + 0.180477i
\(115\) 5.09452e9 0.253288
\(116\) 2.47422e9i 0.117801i
\(117\) −3.60169e9 + 9.38011e9i −0.164277 + 0.427837i
\(118\) −6.60779e9 −0.288833
\(119\) 6.19280e10i 2.59509i
\(120\) 8.42330e9 5.78859e9i 0.338513 0.232631i
\(121\) 2.20383e10 0.849673
\(122\) 1.20090e10i 0.444331i
\(123\) −2.05393e10 2.98879e10i −0.729560 1.06162i
\(124\) 2.14168e10 0.730544
\(125\) 2.30568e10i 0.755526i
\(126\) 2.89713e10 + 1.11241e10i 0.912253 + 0.350279i
\(127\) −3.17814e10 −0.961953 −0.480976 0.876733i \(-0.659718\pi\)
−0.480976 + 0.876733i \(0.659718\pi\)
\(128\) 3.03700e9i 0.0883883i
\(129\) 3.97973e10 2.73492e10i 1.11405 0.765589i
\(130\) −1.39784e10 −0.376479
\(131\) 5.01094e10i 1.29886i 0.760421 + 0.649430i \(0.224993\pi\)
−0.760421 + 0.649430i \(0.775007\pi\)
\(132\) −4.40004e9 6.40273e9i −0.109796 0.159770i
\(133\) −1.78107e10 −0.427979
\(134\) 1.18136e10i 0.273438i
\(135\) −5.06557e10 + 1.21539e10i −1.12969 + 0.271048i
\(136\) −3.08893e10 −0.663916
\(137\) 2.74744e10i 0.569279i 0.958635 + 0.284639i \(0.0918738\pi\)
−0.958635 + 0.284639i \(0.908126\pi\)
\(138\) 6.35900e9 4.36999e9i 0.127056 0.0873142i
\(139\) 6.32488e10 1.21893 0.609464 0.792814i \(-0.291385\pi\)
0.609464 + 0.792814i \(0.291385\pi\)
\(140\) 4.31735e10i 0.802745i
\(141\) −2.13403e10 3.10534e10i −0.382917 0.557204i
\(142\) −1.29285e10 −0.223927
\(143\) 1.06253e10i 0.177689i
\(144\) 5.54864e9 1.44507e10i 0.0896137 0.233387i
\(145\) 1.75441e10 0.273710
\(146\) 4.94607e10i 0.745583i
\(147\) −5.14684e10 + 3.53697e10i −0.749815 + 0.515282i
\(148\) −2.56829e10 −0.361689
\(149\) 3.38479e10i 0.460893i −0.973085 0.230446i \(-0.925981\pi\)
0.973085 0.230446i \(-0.0740186\pi\)
\(150\) −1.06339e10 1.54740e10i −0.140035 0.203773i
\(151\) 1.22386e11 1.55901 0.779503 0.626399i \(-0.215472\pi\)
0.779503 + 0.626399i \(0.215472\pi\)
\(152\) 8.88385e9i 0.109492i
\(153\) 1.46978e11 + 5.64351e10i 1.75305 + 0.673120i
\(154\) 3.28171e10 0.378876
\(155\) 1.51862e11i 1.69742i
\(156\) −1.74479e10 + 1.19904e10i −0.188851 + 0.129781i
\(157\) −1.58971e11 −1.66656 −0.833279 0.552853i \(-0.813539\pi\)
−0.833279 + 0.552853i \(0.813539\pi\)
\(158\) 4.44838e10i 0.451769i
\(159\) 5.80155e9 + 8.44215e9i 0.0570898 + 0.0830745i
\(160\) 2.15347e10 0.205371
\(161\) 3.25930e10i 0.301297i
\(162\) −5.28033e10 + 5.86220e10i −0.473245 + 0.525395i
\(163\) −9.20831e10 −0.800280 −0.400140 0.916454i \(-0.631038\pi\)
−0.400140 + 0.916454i \(0.631038\pi\)
\(164\) 7.64102e10i 0.644069i
\(165\) −4.54003e10 + 3.11996e10i −0.371226 + 0.255111i
\(166\) 4.94540e10 0.392338
\(167\) 2.12416e11i 1.63533i 0.575697 + 0.817663i \(0.304731\pi\)
−0.575697 + 0.817663i \(0.695269\pi\)
\(168\) 3.70334e10 + 5.38894e10i 0.276725 + 0.402677i
\(169\) −1.08904e11 −0.789968
\(170\) 2.19029e11i 1.54261i
\(171\) 1.62309e10 4.22713e10i 0.111010 0.289111i
\(172\) 1.01744e11 0.675876
\(173\) 3.04132e11i 1.96260i −0.192482 0.981300i \(-0.561654\pi\)
0.192482 0.981300i \(-0.438346\pi\)
\(174\) 2.18986e10 1.50490e10i 0.137300 0.0943542i
\(175\) 7.93119e10 0.483224
\(176\) 1.63690e10i 0.0969300i
\(177\) 4.01908e10 + 5.84837e10i 0.231345 + 0.336642i
\(178\) 5.40212e9 0.0302318
\(179\) 7.07114e9i 0.0384791i −0.999815 0.0192395i \(-0.993875\pi\)
0.999815 0.0192395i \(-0.00612451\pi\)
\(180\) −1.02467e11 3.93442e10i −0.542275 0.208218i
\(181\) −1.27309e11 −0.655337 −0.327669 0.944793i \(-0.606263\pi\)
−0.327669 + 0.944793i \(0.606263\pi\)
\(182\) 8.94290e10i 0.447838i
\(183\) 1.06288e11 7.30425e10i 0.517880 0.355894i
\(184\) 1.62572e10 0.0770825
\(185\) 1.82111e11i 0.840386i
\(186\) −1.30264e11 1.89554e11i −0.585141 0.851470i
\(187\) 1.66488e11 0.728075
\(188\) 7.93900e10i 0.338047i
\(189\) −7.77563e10 3.24078e11i −0.322424 1.34382i
\(190\) 6.29934e10 0.254406
\(191\) 2.06460e11i 0.812209i 0.913827 + 0.406105i \(0.133113\pi\)
−0.913827 + 0.406105i \(0.866887\pi\)
\(192\) 2.68797e10 1.84720e10i 0.103019 0.0707960i
\(193\) 3.11606e11 1.16364 0.581821 0.813317i \(-0.302340\pi\)
0.581821 + 0.813317i \(0.302340\pi\)
\(194\) 2.00052e11i 0.728004i
\(195\) 8.50212e10 + 1.23719e11i 0.301546 + 0.438796i
\(196\) −1.31582e11 −0.454901
\(197\) 1.51694e11i 0.511255i 0.966775 + 0.255628i \(0.0822821\pi\)
−0.966775 + 0.255628i \(0.917718\pi\)
\(198\) −2.99063e10 + 7.78870e10i −0.0982737 + 0.255941i
\(199\) −1.11692e11 −0.357895 −0.178947 0.983859i \(-0.557269\pi\)
−0.178947 + 0.983859i \(0.557269\pi\)
\(200\) 3.95603e10i 0.123626i
\(201\) −1.04559e11 + 7.18543e10i −0.318700 + 0.219014i
\(202\) −3.79978e11 −1.12980
\(203\) 1.12241e11i 0.325591i
\(204\) 1.87879e11 + 2.73392e11i 0.531773 + 0.773812i
\(205\) −5.41807e11 −1.49650
\(206\) 1.89361e11i 0.510451i
\(207\) −7.73551e10 2.97021e10i −0.203534 0.0781512i
\(208\) −4.46066e10 −0.114573
\(209\) 4.78826e10i 0.120073i
\(210\) 3.82117e11 2.62596e11i 0.935621 0.642970i
\(211\) 1.53066e11 0.365987 0.182994 0.983114i \(-0.441421\pi\)
0.182994 + 0.983114i \(0.441421\pi\)
\(212\) 2.15829e10i 0.0503999i
\(213\) 7.86354e10 + 1.14427e11i 0.179358 + 0.260993i
\(214\) 3.24828e11 0.723744
\(215\) 7.21444e11i 1.57040i
\(216\) −1.61648e11 + 3.87843e10i −0.343796 + 0.0824874i
\(217\) 9.71560e11 2.01916
\(218\) 1.06929e11i 0.217177i
\(219\) −4.37763e11 + 3.00836e11i −0.868998 + 0.597186i
\(220\) −1.16069e11 −0.225217
\(221\) 4.53693e11i 0.860598i
\(222\) 1.56212e11 + 2.27312e11i 0.289700 + 0.421559i
\(223\) −6.05759e11 −1.09844 −0.549219 0.835678i \(-0.685075\pi\)
−0.549219 + 0.835678i \(0.685075\pi\)
\(224\) 1.37771e11i 0.244298i
\(225\) −7.22772e10 + 1.88236e11i −0.125340 + 0.326430i
\(226\) 2.99040e11 0.507210
\(227\) 6.70588e11i 1.11257i −0.830992 0.556284i \(-0.812227\pi\)
0.830992 0.556284i \(-0.187773\pi\)
\(228\) 7.86286e10 5.40345e10i 0.127616 0.0876995i
\(229\) 3.53356e11 0.561094 0.280547 0.959840i \(-0.409484\pi\)
0.280547 + 0.959840i \(0.409484\pi\)
\(230\) 1.15276e11i 0.179102i
\(231\) −1.99605e11 2.90456e11i −0.303467 0.441591i
\(232\) 5.59851e10 0.0832976
\(233\) 1.12390e12i 1.63662i 0.574779 + 0.818309i \(0.305088\pi\)
−0.574779 + 0.818309i \(0.694912\pi\)
\(234\) 2.12248e11 + 8.14969e10i 0.302527 + 0.116161i
\(235\) −5.62936e11 −0.785452
\(236\) 1.49517e11i 0.204236i
\(237\) −3.93714e11 + 2.70565e11i −0.526549 + 0.361851i
\(238\) −1.40127e12 −1.83500
\(239\) 2.64603e11i 0.339317i 0.985503 + 0.169658i \(0.0542665\pi\)
−0.985503 + 0.169658i \(0.945734\pi\)
\(240\) −1.30981e11 1.90597e11i −0.164495 0.239365i
\(241\) 8.86768e11 1.09075 0.545375 0.838192i \(-0.316387\pi\)
0.545375 + 0.838192i \(0.316387\pi\)
\(242\) 4.98671e11i 0.600810i
\(243\) 8.40014e11 + 1.10789e11i 0.991414 + 0.130757i
\(244\) 2.71732e11 0.314190
\(245\) 9.33019e11i 1.05696i
\(246\) −6.76286e11 + 4.64752e11i −0.750680 + 0.515877i
\(247\) −1.30483e11 −0.141929
\(248\) 4.84607e11i 0.516573i
\(249\) −3.00795e11 4.37704e11i −0.314249 0.457281i
\(250\) 5.21716e11 0.534237
\(251\) 8.59494e11i 0.862729i 0.902178 + 0.431364i \(0.141968\pi\)
−0.902178 + 0.431364i \(0.858032\pi\)
\(252\) 2.51710e11 6.55546e11i 0.247684 0.645060i
\(253\) −8.76237e10 −0.0845316
\(254\) 7.19130e11i 0.680203i
\(255\) 1.93856e12 1.33220e12i 1.79796 1.23558i
\(256\) 6.87195e10 0.0625000
\(257\) 2.17900e12i 1.94353i −0.235954 0.971764i \(-0.575821\pi\)
0.235954 0.971764i \(-0.424179\pi\)
\(258\) −6.18841e11 9.00510e11i −0.541353 0.787753i
\(259\) −1.16509e12 −0.999677
\(260\) 3.16295e11i 0.266211i
\(261\) −2.66389e11 1.02286e11i −0.219945 0.0844524i
\(262\) 1.13385e12 0.918433
\(263\) 1.37942e12i 1.09627i 0.836391 + 0.548134i \(0.184661\pi\)
−0.836391 + 0.548134i \(0.815339\pi\)
\(264\) −1.44877e11 + 9.95615e10i −0.112975 + 0.0776375i
\(265\) 1.53039e11 0.117104
\(266\) 4.03010e11i 0.302627i
\(267\) −3.28574e10 4.78126e10i −0.0242146 0.0352360i
\(268\) −2.67312e11 −0.193350
\(269\) 1.18129e12i 0.838680i −0.907829 0.419340i \(-0.862262\pi\)
0.907829 0.419340i \(-0.137738\pi\)
\(270\) 2.75011e11 + 1.14621e12i 0.191660 + 0.798812i
\(271\) −1.42251e12 −0.973213 −0.486606 0.873621i \(-0.661765\pi\)
−0.486606 + 0.873621i \(0.661765\pi\)
\(272\) 6.98944e11i 0.469459i
\(273\) −7.91511e11 + 5.43937e11i −0.521968 + 0.358703i
\(274\) 6.21674e11 0.402541
\(275\) 2.13224e11i 0.135573i
\(276\) −9.88815e10 1.43888e11i −0.0617404 0.0898418i
\(277\) 5.29960e11 0.324971 0.162485 0.986711i \(-0.448049\pi\)
0.162485 + 0.986711i \(0.448049\pi\)
\(278\) 1.43116e12i 0.861913i
\(279\) −8.85385e11 + 2.30587e12i −0.523734 + 1.36400i
\(280\) 9.76905e11 0.567626
\(281\) 2.28441e12i 1.30389i 0.758265 + 0.651946i \(0.226047\pi\)
−0.758265 + 0.651946i \(0.773953\pi\)
\(282\) −7.02659e11 + 4.82876e11i −0.394003 + 0.270764i
\(283\) 2.31274e12 1.27408 0.637038 0.770833i \(-0.280160\pi\)
0.637038 + 0.770833i \(0.280160\pi\)
\(284\) 2.92539e11i 0.158340i
\(285\) −3.83146e11 5.57537e11i −0.203770 0.296517i
\(286\) 2.40423e11 0.125645
\(287\) 3.46630e12i 1.78015i
\(288\) −3.26982e11 1.25551e11i −0.165029 0.0633665i
\(289\) −5.09295e12 −2.52627
\(290\) 3.96978e11i 0.193542i
\(291\) 1.77060e12 1.21678e12i 0.848509 0.583106i
\(292\) −1.11917e12 −0.527207
\(293\) 1.05989e12i 0.490822i −0.969419 0.245411i \(-0.921077\pi\)
0.969419 0.245411i \(-0.0789229\pi\)
\(294\) 8.00326e11 + 1.16460e12i 0.364360 + 0.530199i
\(295\) 1.06019e12 0.474542
\(296\) 5.81138e11i 0.255753i
\(297\) 8.71257e11 2.09042e11i 0.377020 0.0904588i
\(298\) −7.65890e11 −0.325900
\(299\) 2.38781e11i 0.0999179i
\(300\) −3.50137e11 + 2.40618e11i −0.144089 + 0.0990200i
\(301\) 4.61555e12 1.86806
\(302\) 2.76928e12i 1.10238i
\(303\) 2.31115e12 + 3.36308e12i 0.904931 + 1.31681i
\(304\) 2.01019e11 0.0774227
\(305\) 1.92679e12i 0.730020i
\(306\) 1.27698e12 3.32573e12i 0.475968 1.23959i
\(307\) 6.89209e11 0.252731 0.126366 0.991984i \(-0.459669\pi\)
0.126366 + 0.991984i \(0.459669\pi\)
\(308\) 7.42567e11i 0.267906i
\(309\) −1.67598e12 + 1.15176e12i −0.594945 + 0.408854i
\(310\) −3.43624e12 −1.20026
\(311\) 1.95674e12i 0.672559i 0.941762 + 0.336280i \(0.109169\pi\)
−0.941762 + 0.336280i \(0.890831\pi\)
\(312\) 2.71312e11 + 3.94801e11i 0.0917690 + 0.133538i
\(313\) −2.48821e11 −0.0828256 −0.0414128 0.999142i \(-0.513186\pi\)
−0.0414128 + 0.999142i \(0.513186\pi\)
\(314\) 3.59711e12i 1.17843i
\(315\) −4.64832e12 1.78482e12i −1.49880 0.575495i
\(316\) −1.00655e12 −0.319449
\(317\) 4.63675e12i 1.44850i 0.689539 + 0.724249i \(0.257813\pi\)
−0.689539 + 0.724249i \(0.742187\pi\)
\(318\) 1.91024e11 1.31274e11i 0.0587425 0.0403686i
\(319\) −3.01751e11 −0.0913473
\(320\) 4.87274e11i 0.145219i
\(321\) −1.97571e12 2.87497e12i −0.579694 0.843544i
\(322\) 7.37496e11 0.213049
\(323\) 2.04456e12i 0.581549i
\(324\) 1.32646e12 + 1.19480e12i 0.371510 + 0.334634i
\(325\) 5.81050e11 0.160249
\(326\) 2.08360e12i 0.565883i
\(327\) 9.46400e11 6.50378e11i 0.253125 0.173951i
\(328\) −1.72897e12 −0.455426
\(329\) 3.60147e12i 0.934331i
\(330\) 7.05967e11 + 1.02729e12i 0.180391 + 0.262497i
\(331\) −1.41443e12 −0.355994 −0.177997 0.984031i \(-0.556962\pi\)
−0.177997 + 0.984031i \(0.556962\pi\)
\(332\) 1.11902e12i 0.277425i
\(333\) 1.06175e12 2.76518e12i 0.259298 0.675308i
\(334\) 4.80642e12 1.15635
\(335\) 1.89545e12i 0.449249i
\(336\) 1.21938e12 8.37971e11i 0.284736 0.195674i
\(337\) 8.67755e11 0.199640 0.0998201 0.995006i \(-0.468173\pi\)
0.0998201 + 0.995006i \(0.468173\pi\)
\(338\) 2.46421e12i 0.558592i
\(339\) −1.81886e12 2.64672e12i −0.406257 0.591167i
\(340\) 4.95605e12 1.09079
\(341\) 2.61196e12i 0.566493i
\(342\) −9.56490e11 3.67264e11i −0.204432 0.0784961i
\(343\) 5.91785e11 0.124650
\(344\) 2.30221e12i 0.477917i
\(345\) −1.02028e12 + 7.01146e11i −0.208748 + 0.143454i
\(346\) −6.88173e12 −1.38777
\(347\) 5.20712e12i 1.03502i −0.855676 0.517512i \(-0.826858\pi\)
0.855676 0.517512i \(-0.173142\pi\)
\(348\) −3.40520e11 4.95509e11i −0.0667185 0.0970857i
\(349\) 1.11953e12 0.216226 0.108113 0.994139i \(-0.465519\pi\)
0.108113 + 0.994139i \(0.465519\pi\)
\(350\) 1.79462e12i 0.341691i
\(351\) −5.69653e11 2.37424e12i −0.106924 0.445644i
\(352\) −3.70388e11 −0.0685398
\(353\) 3.73952e12i 0.682248i −0.940018 0.341124i \(-0.889192\pi\)
0.940018 0.341124i \(-0.110808\pi\)
\(354\) 1.32334e12 9.09413e11i 0.238042 0.163586i
\(355\) 2.07432e12 0.367904
\(356\) 1.22236e11i 0.0213771i
\(357\) 8.52299e12 + 1.24023e13i 1.46977 + 2.13875i
\(358\) −1.60002e11 −0.0272088
\(359\) 3.54489e12i 0.594471i −0.954804 0.297235i \(-0.903935\pi\)
0.954804 0.297235i \(-0.0960646\pi\)
\(360\) −8.90257e11 + 2.31855e12i −0.147232 + 0.383446i
\(361\) −5.54305e12 −0.904092
\(362\) 2.88066e12i 0.463393i
\(363\) −4.41360e12 + 3.03308e12i −0.700260 + 0.481228i
\(364\) −2.02355e12 −0.316670
\(365\) 7.93577e12i 1.22497i
\(366\) −1.65276e12 2.40503e12i −0.251655 0.366197i
\(367\) −1.01161e13 −1.51944 −0.759722 0.650248i \(-0.774665\pi\)
−0.759722 + 0.650248i \(0.774665\pi\)
\(368\) 3.67858e11i 0.0545056i
\(369\) 8.22679e12 + 3.15885e12i 1.20254 + 0.461739i
\(370\) 4.12071e12 0.594242
\(371\) 9.79093e11i 0.139301i
\(372\) −4.28913e12 + 2.94754e12i −0.602080 + 0.413757i
\(373\) 3.81055e12 0.527769 0.263885 0.964554i \(-0.414996\pi\)
0.263885 + 0.964554i \(0.414996\pi\)
\(374\) 3.76720e12i 0.514827i
\(375\) −3.17325e12 4.61757e12i −0.427906 0.622669i
\(376\) −1.79639e12 −0.239035
\(377\) 8.22293e11i 0.107974i
\(378\) −7.33304e12 + 1.75943e12i −0.950222 + 0.227988i
\(379\) 1.11052e13 1.42014 0.710069 0.704132i \(-0.248664\pi\)
0.710069 + 0.704132i \(0.248664\pi\)
\(380\) 1.42538e12i 0.179892i
\(381\) 6.36482e12 4.37399e12i 0.792796 0.544819i
\(382\) 4.67165e12 0.574319
\(383\) 4.29169e12i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838472\pi\)
\(384\) −4.17974e11 6.08217e11i −0.0500603 0.0728455i
\(385\) −5.26537e12 −0.622480
\(386\) 7.05084e12i 0.822820i
\(387\) −4.20617e12 + 1.09544e13i −0.484542 + 1.26192i
\(388\) 4.52665e12 0.514776
\(389\) 1.50554e13i 1.69023i −0.534588 0.845113i \(-0.679533\pi\)
0.534588 0.845113i \(-0.320467\pi\)
\(390\) 2.79944e12 1.92381e12i 0.310276 0.213225i
\(391\) 3.74148e12 0.409411
\(392\) 2.97736e12i 0.321663i
\(393\) −6.89642e12 1.00354e13i −0.735633 1.07046i
\(394\) 3.43245e12 0.361512
\(395\) 7.13723e12i 0.742240i
\(396\) 1.76238e12 + 6.76703e11i 0.180977 + 0.0694900i
\(397\) −1.11669e13 −1.13235 −0.566174 0.824286i \(-0.691577\pi\)
−0.566174 + 0.824286i \(0.691577\pi\)
\(398\) 2.52729e12i 0.253070i
\(399\) 3.56693e12 2.45124e12i 0.352720 0.242394i
\(400\) −8.95146e11 −0.0874166
\(401\) 1.15685e13i 1.11572i 0.829935 + 0.557861i \(0.188378\pi\)
−0.829935 + 0.557861i \(0.811622\pi\)
\(402\) 1.62588e12 + 2.36590e12i 0.154867 + 0.225355i
\(403\) 7.11777e12 0.669605
\(404\) 8.59793e12i 0.798890i
\(405\) 8.47206e12 9.40565e12i 0.777524 0.863205i
\(406\) 2.53973e12 0.230227
\(407\) 3.13224e12i 0.280468i
\(408\) 6.18616e12 4.25121e12i 0.547168 0.376021i
\(409\) −1.07411e13 −0.938498 −0.469249 0.883066i \(-0.655475\pi\)
−0.469249 + 0.883066i \(0.655475\pi\)
\(410\) 1.22597e13i 1.05818i
\(411\) −3.78123e12 5.50227e12i −0.322421 0.469172i
\(412\) −4.28475e12 −0.360944
\(413\) 6.78275e12i 0.564489i
\(414\) −6.72082e11 + 1.75035e12i −0.0552612 + 0.143920i
\(415\) −7.93468e12 −0.644598
\(416\) 1.00933e12i 0.0810153i
\(417\) −1.26668e13 + 8.70477e12i −1.00458 + 0.690362i
\(418\) −1.08346e12 −0.0849047
\(419\) 8.81717e12i 0.682746i 0.939928 + 0.341373i \(0.110892\pi\)
−0.939928 + 0.341373i \(0.889108\pi\)
\(420\) −5.94186e12 8.64632e12i −0.454649 0.661584i
\(421\) −5.69741e12 −0.430792 −0.215396 0.976527i \(-0.569104\pi\)
−0.215396 + 0.976527i \(0.569104\pi\)
\(422\) 3.46348e12i 0.258792i
\(423\) 8.54761e12 + 3.28203e12i 0.631165 + 0.242349i
\(424\) 4.88365e11 0.0356381
\(425\) 9.10451e12i 0.656617i
\(426\) 2.58918e12 1.77932e12i 0.184550 0.126825i
\(427\) 1.23269e13 0.868392
\(428\) 7.35003e12i 0.511764i
\(429\) −1.46233e12 2.12792e12i −0.100637 0.146443i
\(430\) −1.63244e13 −1.11044
\(431\) 1.80323e13i 1.21245i 0.795293 + 0.606226i \(0.207317\pi\)
−0.795293 + 0.606226i \(0.792683\pi\)
\(432\) 8.77590e11 + 3.65767e12i 0.0583274 + 0.243101i
\(433\) 2.06339e13 1.35563 0.677816 0.735232i \(-0.262927\pi\)
0.677816 + 0.735232i \(0.262927\pi\)
\(434\) 2.19839e13i 1.42776i
\(435\) −3.51354e12 + 2.41455e12i −0.225579 + 0.155021i
\(436\) 2.41953e12 0.153567
\(437\) 1.07606e12i 0.0675195i
\(438\) 6.80715e12 + 9.90545e12i 0.422275 + 0.614474i
\(439\) 1.95313e13 1.19787 0.598935 0.800798i \(-0.295591\pi\)
0.598935 + 0.800798i \(0.295591\pi\)
\(440\) 2.62633e12i 0.159253i
\(441\) 5.43969e12 1.41669e13i 0.326123 0.849343i
\(442\) −1.02659e13 −0.608535
\(443\) 2.97469e13i 1.74351i −0.489946 0.871753i \(-0.662984\pi\)
0.489946 0.871753i \(-0.337016\pi\)
\(444\) 5.14349e12 3.53467e12i 0.298087 0.204849i
\(445\) −8.66747e11 −0.0496698
\(446\) 1.37068e13i 0.776713i
\(447\) 4.65839e12 + 6.77868e12i 0.261035 + 0.379846i
\(448\) 3.11741e12 0.172744
\(449\) 1.37505e13i 0.753509i −0.926313 0.376754i \(-0.877040\pi\)
0.926313 0.376754i \(-0.122960\pi\)
\(450\) 4.25930e12 + 1.63545e12i 0.230821 + 0.0886285i
\(451\) 9.31887e12 0.499437
\(452\) 6.76651e12i 0.358651i
\(453\) −2.45102e13 + 1.68437e13i −1.28486 + 0.882971i
\(454\) −1.51737e13 −0.786704
\(455\) 1.43485e13i 0.735783i
\(456\) −1.22266e12 1.77916e12i −0.0620129 0.0902383i
\(457\) 4.10224e11 0.0205798 0.0102899 0.999947i \(-0.496725\pi\)
0.0102899 + 0.999947i \(0.496725\pi\)
\(458\) 7.99554e12i 0.396753i
\(459\) −3.72021e13 + 8.92594e12i −1.82601 + 0.438118i
\(460\) −2.60840e12 −0.126644
\(461\) 2.10914e11i 0.0101298i −0.999987 0.00506490i \(-0.998388\pi\)
0.999987 0.00506490i \(-0.00161221\pi\)
\(462\) −6.57226e12 + 4.51654e12i −0.312252 + 0.214583i
\(463\) −1.96738e13 −0.924660 −0.462330 0.886708i \(-0.652987\pi\)
−0.462330 + 0.886708i \(0.652987\pi\)
\(464\) 1.26680e12i 0.0589003i
\(465\) 2.09003e13 + 3.04132e13i 0.961365 + 1.39893i
\(466\) 2.54309e13 1.15726
\(467\) 1.21902e13i 0.548815i −0.961614 0.274407i \(-0.911518\pi\)
0.961614 0.274407i \(-0.0884817\pi\)
\(468\) 1.84406e12 4.80261e12i 0.0821385 0.213919i
\(469\) −1.21264e13 −0.534402
\(470\) 1.27378e13i 0.555399i
\(471\) 3.18370e13 2.18788e13i 1.37350 0.943885i
\(472\) 3.38319e12 0.144416
\(473\) 1.24085e13i 0.524101i
\(474\) 6.12218e12 + 8.90872e12i 0.255867 + 0.372326i
\(475\) −2.61849e12 −0.108289
\(476\) 3.17071e13i 1.29754i
\(477\) −2.32374e12 8.92250e11i −0.0941014 0.0361322i
\(478\) 5.98729e12 0.239933
\(479\) 5.00886e12i 0.198637i 0.995056 + 0.0993187i \(0.0316663\pi\)
−0.995056 + 0.0993187i \(0.968334\pi\)
\(480\) −4.31273e12 + 2.96376e12i −0.169257 + 0.116315i
\(481\) −8.53558e12 −0.331518
\(482\) 2.00653e13i 0.771276i
\(483\) −4.48569e12 6.52737e12i −0.170645 0.248315i
\(484\) −1.12836e13 −0.424837
\(485\) 3.20975e13i 1.19608i
\(486\) 2.50686e12 1.90074e13i 0.0924590 0.701036i
\(487\) −4.17000e13 −1.52227 −0.761134 0.648595i \(-0.775357\pi\)
−0.761134 + 0.648595i \(0.775357\pi\)
\(488\) 6.14859e12i 0.222166i
\(489\) 1.84414e13 1.26732e13i 0.659553 0.453253i
\(490\) 2.11118e13 0.747386
\(491\) 2.10340e12i 0.0737081i −0.999321 0.0368540i \(-0.988266\pi\)
0.999321 0.0368540i \(-0.0117337\pi\)
\(492\) 1.05161e13 + 1.53026e13i 0.364780 + 0.530811i
\(493\) 1.28846e13 0.442421
\(494\) 2.95250e12i 0.100359i
\(495\) 4.79835e12 1.24966e13i 0.161460 0.420501i
\(496\) −1.09654e13 −0.365272
\(497\) 1.32708e13i 0.437639i
\(498\) −9.90410e12 + 6.80622e12i −0.323347 + 0.222208i
\(499\) 2.74482e13 0.887179 0.443589 0.896230i \(-0.353705\pi\)
0.443589 + 0.896230i \(0.353705\pi\)
\(500\) 1.18051e13i 0.377763i
\(501\) −2.92342e13 4.25403e13i −0.926197 1.34776i
\(502\) 1.94481e13 0.610041
\(503\) 2.26985e13i 0.704949i 0.935822 + 0.352474i \(0.114660\pi\)
−0.935822 + 0.352474i \(0.885340\pi\)
\(504\) −1.48333e13 5.69556e12i −0.456127 0.175139i
\(505\) 6.09659e13 1.85622
\(506\) 1.98270e12i 0.0597729i
\(507\) 2.18101e13 1.49882e13i 0.651055 0.447413i
\(508\) 1.62721e13 0.480976
\(509\) 4.21460e13i 1.23358i 0.787127 + 0.616791i \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(510\) −3.01443e13 4.38647e13i −0.873685 1.27135i
\(511\) −5.07703e13 −1.45715
\(512\) 1.55494e12i 0.0441942i
\(513\) 2.56713e12 + 1.06994e13i 0.0722539 + 0.301144i
\(514\) −4.93051e13 −1.37428
\(515\) 3.03822e13i 0.838653i
\(516\) −2.03762e13 + 1.40028e13i −0.557025 + 0.382795i
\(517\) 9.68227e12 0.262135
\(518\) 2.63629e13i 0.706878i
\(519\) 4.18569e13 + 6.09083e13i 1.11155 + 1.61748i
\(520\) 7.15694e12 0.188239
\(521\) 6.54420e13i 1.70478i 0.522907 + 0.852390i \(0.324848\pi\)
−0.522907 + 0.852390i \(0.675152\pi\)
\(522\) −2.31446e12 + 6.02770e12i −0.0597169 + 0.155525i
\(523\) −6.14531e13 −1.57049 −0.785245 0.619185i \(-0.787463\pi\)
−0.785245 + 0.619185i \(0.787463\pi\)
\(524\) 2.56560e13i 0.649430i
\(525\) −1.58837e13 + 1.09155e13i −0.398250 + 0.273682i
\(526\) 3.12126e13 0.775178
\(527\) 1.11529e14i 2.74369i
\(528\) 2.25282e12 + 3.27820e12i 0.0548980 + 0.0798851i
\(529\) 3.94574e13 0.952466
\(530\) 3.46288e12i 0.0828053i
\(531\) −1.60979e13 6.18114e12i −0.381327 0.146418i
\(532\) 9.11907e12 0.213990
\(533\) 2.53946e13i 0.590343i
\(534\) −1.08188e12 + 7.43479e11i −0.0249156 + 0.0171223i
\(535\) −5.21173e13 −1.18909
\(536\) 6.04857e12i 0.136719i
\(537\) 9.73183e11 + 1.41613e12i 0.0217933 + 0.0317126i
\(538\) −2.67296e13 −0.593036
\(539\) 1.60475e13i 0.352748i
\(540\) 2.59357e13 6.22278e12i 0.564845 0.135524i
\(541\) 1.50207e13 0.324118 0.162059 0.986781i \(-0.448187\pi\)
0.162059 + 0.986781i \(0.448187\pi\)
\(542\) 3.21877e13i 0.688166i
\(543\) 2.54960e13 1.75211e13i 0.540098 0.371162i
\(544\) 1.58153e13 0.331958
\(545\) 1.71563e13i 0.356814i
\(546\) 1.23079e13 + 1.79099e13i 0.253641 + 0.369087i
\(547\) 7.15097e13 1.46025 0.730127 0.683312i \(-0.239461\pi\)
0.730127 + 0.683312i \(0.239461\pi\)
\(548\) 1.40669e13i 0.284639i
\(549\) −1.12336e13 + 2.92563e13i −0.225245 + 0.586621i
\(550\) 4.82470e12 0.0958644
\(551\) 3.70565e12i 0.0729636i
\(552\) −3.25581e12 + 2.23743e12i −0.0635278 + 0.0436571i
\(553\) −4.56616e13 −0.882928
\(554\) 1.19916e13i 0.229789i
\(555\) −2.50635e13 3.64713e13i −0.475967 0.692606i
\(556\) −3.23834e13 −0.609464
\(557\) 7.34107e13i 1.36925i −0.728895 0.684626i \(-0.759966\pi\)
0.728895 0.684626i \(-0.240034\pi\)
\(558\) 5.21758e13 + 2.00340e13i 0.964490 + 0.370336i
\(559\) 3.38141e13 0.619497
\(560\) 2.21048e13i 0.401372i
\(561\) −3.33425e13 + 2.29134e13i −0.600045 + 0.412358i
\(562\) 5.16902e13 0.921991
\(563\) 4.77347e13i 0.843902i 0.906619 + 0.421951i \(0.138655\pi\)
−0.906619 + 0.421951i \(0.861345\pi\)
\(564\) 1.09262e13 + 1.58994e13i 0.191459 + 0.278602i
\(565\) −4.79797e13 −0.833327
\(566\) 5.23314e13i 0.900907i
\(567\) 6.01742e13 + 5.42013e13i 1.02682 + 0.924900i
\(568\) 6.61939e12 0.111963
\(569\) 1.90951e13i 0.320156i 0.987104 + 0.160078i \(0.0511745\pi\)
−0.987104 + 0.160078i \(0.948825\pi\)
\(570\) −1.26156e13 + 8.66961e12i −0.209669 + 0.144087i
\(571\) −2.09448e13 −0.345060 −0.172530 0.985004i \(-0.555194\pi\)
−0.172530 + 0.985004i \(0.555194\pi\)
\(572\) 5.44014e12i 0.0888444i
\(573\) −2.84145e13 4.13475e13i −0.460009 0.669385i
\(574\) −7.84334e13 −1.25876
\(575\) 4.79175e12i 0.0762351i
\(576\) −2.84091e12 + 7.39876e12i −0.0448069 + 0.116693i
\(577\) 3.56688e13 0.557711 0.278855 0.960333i \(-0.410045\pi\)
0.278855 + 0.960333i \(0.410045\pi\)
\(578\) 1.15240e14i 1.78635i
\(579\) −6.24051e13 + 4.28856e13i −0.959019 + 0.659050i
\(580\) −8.98258e12 −0.136855
\(581\) 5.07634e13i 0.766778i
\(582\) −2.75326e13 4.00642e13i −0.412318 0.599986i
\(583\) −2.63221e12 −0.0390821
\(584\) 2.53239e13i 0.372792i
\(585\) −3.40542e13 1.30758e13i −0.497040 0.190849i
\(586\) −2.39826e13 −0.347064
\(587\) 1.29418e14i 1.85697i 0.371375 + 0.928483i \(0.378886\pi\)
−0.371375 + 0.928483i \(0.621114\pi\)
\(588\) 2.63518e13 1.81093e13i 0.374908 0.257641i
\(589\) −3.20761e13 −0.452486
\(590\) 2.39894e13i 0.335552i
\(591\) −2.08773e13 3.03797e13i −0.289559 0.421352i
\(592\) 1.31496e13 0.180845
\(593\) 3.96596e13i 0.540848i −0.962741 0.270424i \(-0.912836\pi\)
0.962741 0.270424i \(-0.0871639\pi\)
\(594\) −4.73007e12 1.97143e13i −0.0639640 0.266593i
\(595\) 2.24828e14 3.01485
\(596\) 1.73301e13i 0.230446i
\(597\) 2.23684e13 1.53718e13i 0.294960 0.202700i
\(598\) 5.40299e12 0.0706526
\(599\) 4.57555e13i 0.593347i 0.954979 + 0.296674i \(0.0958774\pi\)
−0.954979 + 0.296674i \(0.904123\pi\)
\(600\) 5.44458e12 + 7.92270e12i 0.0700177 + 0.101887i
\(601\) 1.06033e14 1.35229 0.676143 0.736770i \(-0.263650\pi\)
0.676143 + 0.736770i \(0.263650\pi\)
\(602\) 1.04438e14i 1.32092i
\(603\) 1.10508e13 2.87804e13i 0.138614 0.361003i
\(604\) −6.26617e13 −0.779503
\(605\) 8.00096e13i 0.987109i
\(606\) 7.60979e13 5.22954e13i 0.931128 0.639883i
\(607\) −9.55067e13 −1.15902 −0.579509 0.814966i \(-0.696756\pi\)
−0.579509 + 0.814966i \(0.696756\pi\)
\(608\) 4.54853e12i 0.0547461i
\(609\) −1.54475e13 2.24784e13i −0.184404 0.268336i
\(610\) −4.35983e13 −0.516202
\(611\) 2.63849e13i 0.309848i
\(612\) −7.52526e13 2.88948e13i −0.876525 0.336560i
\(613\) −5.18411e13 −0.598924 −0.299462 0.954108i \(-0.596807\pi\)
−0.299462 + 0.954108i \(0.596807\pi\)
\(614\) 1.55950e13i 0.178708i
\(615\) 1.08507e14 7.45675e13i 1.23334 0.847567i
\(616\) −1.68024e13 −0.189438
\(617\) 8.05443e13i 0.900760i −0.892837 0.450380i \(-0.851289\pi\)
0.892837 0.450380i \(-0.148711\pi\)
\(618\) 2.60612e13 + 3.79231e13i 0.289103 + 0.420690i
\(619\) −5.14946e13 −0.566642 −0.283321 0.959025i \(-0.591436\pi\)
−0.283321 + 0.959025i \(0.591436\pi\)
\(620\) 7.77532e13i 0.848711i
\(621\) 1.95797e13 4.69777e12i 0.212005 0.0508667i
\(622\) 4.42759e13 0.475571
\(623\) 5.54515e12i 0.0590844i
\(624\) 8.93332e12 6.13909e12i 0.0944256 0.0648905i
\(625\) −1.17054e14 −1.22740
\(626\) 5.63017e12i 0.0585665i
\(627\) 6.58996e12 + 9.58941e12i 0.0680057 + 0.0989587i
\(628\) 8.13933e13 0.833279
\(629\) 1.33745e14i 1.35839i
\(630\) −4.03859e13 + 1.05180e14i −0.406937 + 1.05981i
\(631\) −1.02922e13 −0.102887 −0.0514435 0.998676i \(-0.516382\pi\)
−0.0514435 + 0.998676i \(0.516382\pi\)
\(632\) 2.27757e13i 0.225884i
\(633\) −3.06543e13 + 2.10660e13i −0.301629 + 0.207283i
\(634\) 1.04918e14 1.02424
\(635\) 1.15381e14i 1.11755i
\(636\) −2.97040e12 4.32238e12i −0.0285449 0.0415372i
\(637\) −4.37307e13 −0.416955
\(638\) 6.82785e12i 0.0645923i
\(639\) −3.14965e13 1.20937e13i −0.295636 0.113516i
\(640\) −1.10257e13 −0.102685
\(641\) 4.62451e13i 0.427342i 0.976906 + 0.213671i \(0.0685420\pi\)
−0.976906 + 0.213671i \(0.931458\pi\)
\(642\) −6.50531e13 + 4.47053e13i −0.596476 + 0.409906i
\(643\) 2.73102e13 0.248468 0.124234 0.992253i \(-0.460353\pi\)
0.124234 + 0.992253i \(0.460353\pi\)
\(644\) 1.66876e13i 0.150649i
\(645\) 9.92905e13 + 1.44483e14i 0.889424 + 1.29425i
\(646\) 4.62630e13 0.411217
\(647\) 1.34984e13i 0.119059i −0.998227 0.0595293i \(-0.981040\pi\)
0.998227 0.0595293i \(-0.0189600\pi\)
\(648\) 2.70353e13 3.00145e13i 0.236622 0.262697i
\(649\) −1.82349e13 −0.158372
\(650\) 1.31476e13i 0.113313i
\(651\) −1.94573e14 + 1.33713e14i −1.66410 + 1.14359i
\(652\) 4.71466e13 0.400140
\(653\) 8.41840e13i 0.709029i −0.935051 0.354514i \(-0.884646\pi\)
0.935051 0.354514i \(-0.115354\pi\)
\(654\) −1.47164e13 2.14146e13i −0.123002 0.178987i
\(655\) −1.81921e14 −1.50895
\(656\) 3.91220e13i 0.322034i
\(657\) 4.62671e13 1.20496e14i 0.377960 0.984345i
\(658\) −8.14920e13 −0.660672
\(659\) 1.65464e14i 1.33130i −0.746264 0.665650i \(-0.768154\pi\)
0.746264 0.665650i \(-0.231846\pi\)
\(660\) 2.32449e13 1.59742e13i 0.185613 0.127556i
\(661\) 2.01681e14 1.59830 0.799148 0.601135i \(-0.205284\pi\)
0.799148 + 0.601135i \(0.205284\pi\)
\(662\) 3.20050e13i 0.251726i
\(663\) 6.24405e13 + 9.08606e13i 0.487415 + 0.709264i
\(664\) −2.53204e13 −0.196169
\(665\) 6.46612e13i 0.497205i
\(666\) −6.25688e13 2.40246e13i −0.477515 0.183352i
\(667\) −6.78122e12 −0.0513664
\(668\) 1.08757e14i 0.817663i
\(669\) 1.21315e14 8.33691e13i 0.905281 0.622120i
\(670\) 4.28890e13 0.317667
\(671\) 3.31400e13i 0.243635i
\(672\) −1.89611e13 2.75914e13i −0.138362 0.201338i
\(673\) 6.04368e12 0.0437750 0.0218875 0.999760i \(-0.493032\pi\)
0.0218875 + 0.999760i \(0.493032\pi\)
\(674\) 1.96351e13i 0.141167i
\(675\) −1.14316e13 4.76452e13i −0.0815806 0.340017i
\(676\) 5.57588e13 0.394984
\(677\) 1.21474e14i 0.854164i 0.904213 + 0.427082i \(0.140458\pi\)
−0.904213 + 0.427082i \(0.859542\pi\)
\(678\) −5.98885e13 + 4.11561e13i −0.418018 + 0.287267i
\(679\) 2.05349e14 1.42280
\(680\) 1.12143e14i 0.771305i
\(681\) 9.22913e13 + 1.34298e14i 0.630123 + 0.916926i
\(682\) 5.91019e13 0.400571
\(683\) 1.51629e14i 1.02019i −0.860119 0.510094i \(-0.829611\pi\)
0.860119 0.510094i \(-0.170389\pi\)
\(684\) −8.31024e12 + 2.16429e13i −0.0555051 + 0.144556i
\(685\) −9.97450e13 −0.661360
\(686\) 1.33906e13i 0.0881410i
\(687\) −7.07663e13 + 4.86315e13i −0.462427 + 0.317785i
\(688\) −5.20930e13 −0.337938
\(689\) 7.17296e12i 0.0461958i
\(690\) 1.58651e13 + 2.30862e13i 0.101437 + 0.147607i
\(691\) 6.62249e13 0.420369 0.210185 0.977662i \(-0.432593\pi\)
0.210185 + 0.977662i \(0.432593\pi\)
\(692\) 1.55716e14i 0.981300i
\(693\) 7.99493e13 + 3.06982e13i 0.500205 + 0.192064i
\(694\) −1.17824e14 −0.731873
\(695\) 2.29623e14i 1.41609i
\(696\) −1.12121e13 + 7.70509e12i −0.0686500 + 0.0471771i
\(697\) −3.97909e14 −2.41891
\(698\) 2.53321e13i 0.152895i
\(699\) −1.54679e14 2.25082e14i −0.926928 1.34882i
\(700\) −4.06077e13 −0.241612
\(701\) 5.78990e13i 0.342043i 0.985267 + 0.171022i \(0.0547068\pi\)
−0.985267 + 0.171022i \(0.945293\pi\)
\(702\) −5.37228e13 + 1.28898e13i −0.315118 + 0.0756066i
\(703\) 3.84654e13 0.224024
\(704\) 8.38091e12i 0.0484650i
\(705\) 1.12739e14 7.74754e13i 0.647332 0.444855i
\(706\) −8.46157e13 −0.482422
\(707\) 3.90039e14i 2.20806i
\(708\) −2.05777e13 2.99437e13i −0.115672 0.168321i
\(709\) 2.70077e14 1.50750 0.753750 0.657162i \(-0.228243\pi\)
0.753750 + 0.657162i \(0.228243\pi\)
\(710\) 4.69366e13i 0.260148i
\(711\) 4.16115e13 1.08372e14i 0.229016 0.596441i
\(712\) −2.76588e12 −0.0151159
\(713\) 5.86983e13i 0.318550i
\(714\) 2.80631e14 1.92853e14i 1.51232 1.03929i
\(715\) −3.85748e13 −0.206430
\(716\) 3.62043e12i 0.0192395i
\(717\) −3.64166e13 5.29918e13i −0.192178 0.279649i
\(718\) −8.02117e13 −0.420354
\(719\) 1.48102e14i 0.770755i −0.922759 0.385377i \(-0.874071\pi\)
0.922759 0.385377i \(-0.125929\pi\)
\(720\) 5.24629e13 + 2.01442e13i 0.271137 + 0.104109i
\(721\) −1.94375e14 −0.997616
\(722\) 1.25425e14i 0.639289i
\(723\) −1.77592e14 + 1.22044e14i −0.898944 + 0.617765i
\(724\) 6.51820e13 0.327669
\(725\) 1.65014e13i 0.0823819i
\(726\) 6.86307e13 + 9.98683e13i 0.340279 + 0.495159i
\(727\) 5.21602e13 0.256842 0.128421 0.991720i \(-0.459009\pi\)
0.128421 + 0.991720i \(0.459009\pi\)
\(728\) 4.57876e13i 0.223919i
\(729\) −1.83476e14 + 9.34214e13i −0.891133 + 0.453742i
\(730\) 1.79566e14 0.866183
\(731\) 5.29837e14i 2.53837i
\(732\) −5.44195e13 + 3.73978e13i −0.258940 + 0.177947i
\(733\) 3.21782e14 1.52069 0.760346 0.649518i \(-0.225029\pi\)
0.760346 + 0.649518i \(0.225029\pi\)
\(734\) 2.28902e14i 1.07441i
\(735\) −1.28409e14 1.86855e14i −0.598630 0.871099i
\(736\) −8.32367e12 −0.0385413
\(737\) 3.26009e13i 0.149931i
\(738\) 7.14765e13 1.86151e14i 0.326499 0.850322i
\(739\) 1.66542e14 0.755617 0.377809 0.925884i \(-0.376678\pi\)
0.377809 + 0.925884i \(0.376678\pi\)
\(740\) 9.32411e13i 0.420193i
\(741\) 2.61318e13 1.79581e13i 0.116971 0.0803839i
\(742\) 2.21543e13 0.0985007
\(743\) 1.13631e14i 0.501825i 0.968010 + 0.250912i \(0.0807306\pi\)
−0.968010 + 0.250912i \(0.919269\pi\)
\(744\) 6.66953e13 + 9.70519e13i 0.292570 + 0.425735i
\(745\) 1.22884e14 0.535443
\(746\) 8.62230e13i 0.373189i
\(747\) 1.20480e14 + 4.62608e13i 0.517979 + 0.198889i
\(748\) −8.52421e13 −0.364037
\(749\) 3.33429e14i 1.41447i
\(750\) −1.04484e14 + 7.18025e13i −0.440293 + 0.302575i
\(751\) −1.64956e14 −0.690508 −0.345254 0.938509i \(-0.612207\pi\)
−0.345254 + 0.938509i \(0.612207\pi\)
\(752\) 4.06477e13i 0.169023i
\(753\) −1.18290e14 1.72130e14i −0.488622 0.711020i
\(754\) 1.86064e13 0.0763493
\(755\) 4.44320e14i 1.81118i
\(756\) 3.98112e13 + 1.65928e14i 0.161212 + 0.671909i
\(757\) −2.67990e14 −1.07805 −0.539026 0.842289i \(-0.681207\pi\)
−0.539026 + 0.842289i \(0.681207\pi\)
\(758\) 2.51282e14i 1.00419i
\(759\) 1.75483e13 1.20594e13i 0.0696669 0.0478760i
\(760\) −3.22526e13 −0.127203
\(761\) 1.29795e14i 0.508550i −0.967132 0.254275i \(-0.918163\pi\)
0.967132 0.254275i \(-0.0818368\pi\)
\(762\) −9.89720e13 1.44020e14i −0.385245 0.560591i
\(763\) 1.09760e14 0.424446
\(764\) 1.05707e14i 0.406105i
\(765\) −2.04886e14 + 5.33599e14i −0.781998 + 2.03661i
\(766\) −9.71099e13 −0.368230
\(767\) 4.96913e13i 0.187199i
\(768\) −1.37624e13 + 9.45768e12i −0.0515095 + 0.0353980i
\(769\) −2.19185e14 −0.815041