Properties

Label 150.11.b.a.149.2
Level $150$
Weight $11$
Character 150.149
Analytic conductor $95.304$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 150.b (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(95.3035879011\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.3421020160000.10
Defining polynomial: \(x^{8} + 967 x^{4} + 194481\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{26}\cdot 3^{8} \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 149.2
Root \(-3.61315 + 3.61315i\) of defining polynomial
Character \(\chi\) \(=\) 150.149
Dual form 150.11.b.a.149.1

$q$-expansion

\(f(q)\) \(=\) \(q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +O(q^{10})\) \(q-22.6274 q^{2} +(-137.627 + 200.269i) q^{3} +512.000 q^{4} +(3114.15 - 4531.57i) q^{6} -23226.5i q^{7} -11585.2 q^{8} +(-21166.4 - 55125.0i) q^{9} +62442.7i q^{11} +(-70465.2 + 102538. i) q^{12} +170161. i q^{13} +525556. i q^{14} +262144. q^{16} +2.66626e6 q^{17} +(478941. + 1.24734e6i) q^{18} -766825. q^{19} +(4.65156e6 + 3.19661e6i) q^{21} -1.41292e6i q^{22} +1.40327e6 q^{23} +(1.59445e6 - 2.32016e6i) q^{24} -3.85029e6i q^{26} +(1.39529e7 + 3.34774e6i) q^{27} -1.18920e7i q^{28} -4.83245e6i q^{29} -4.18297e7 q^{31} -5.93164e6 q^{32} +(-1.25053e7 - 8.59382e6i) q^{33} -6.03306e7 q^{34} +(-1.08372e7 - 2.82240e7i) q^{36} +5.01619e7i q^{37} +1.73513e7 q^{38} +(-3.40779e7 - 2.34188e7i) q^{39} -1.49239e8i q^{41} +(-1.05253e8 - 7.23310e7i) q^{42} +1.98719e8i q^{43} +3.19706e7i q^{44} -3.17523e7 q^{46} +1.55059e8 q^{47} +(-3.60782e7 + 5.24993e7i) q^{48} -2.56996e8 q^{49} +(-3.66951e8 + 5.33970e8i) q^{51} +8.71222e7i q^{52} +4.21541e7 q^{53} +(-3.15718e8 - 7.57507e7i) q^{54} +2.69085e8i q^{56} +(1.05536e8 - 1.53571e8i) q^{57} +1.09346e8i q^{58} -2.92026e8i q^{59} -5.30727e8 q^{61} +9.46499e8 q^{62} +(-1.28036e9 + 4.91622e8i) q^{63} +1.34218e8 q^{64} +(2.82963e8 + 1.94456e8i) q^{66} +5.22093e8i q^{67} +1.36513e9 q^{68} +(-1.93128e8 + 2.81031e8i) q^{69} +5.71364e8i q^{71} +(2.45218e8 + 6.38636e8i) q^{72} -2.18588e9i q^{73} -1.13503e9i q^{74} -3.92615e8 q^{76} +1.45033e9 q^{77} +(7.71095e8 + 5.29906e8i) q^{78} -1.96592e9 q^{79} +(-2.59075e9 + 2.33360e9i) q^{81} +3.37689e9i q^{82} -2.18558e9 q^{83} +(2.38160e9 + 1.63666e9i) q^{84} -4.49650e9i q^{86} +(9.67791e8 + 6.65078e8i) q^{87} -7.23413e8i q^{88} +2.38742e8i q^{89} +3.95224e9 q^{91} +7.18473e8 q^{92} +(5.75692e9 - 8.37720e9i) q^{93} -3.50858e9 q^{94} +(8.16356e8 - 1.18792e9i) q^{96} -8.84112e9i q^{97} +5.81517e9 q^{98} +(3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + O(q^{10}) \) \( 8 q + 4096 q^{4} + 10752 q^{6} - 318024 q^{9} + 2097152 q^{16} + 3137456 q^{19} + 19256016 q^{21} + 5505024 q^{24} - 43571696 q^{31} - 302174208 q^{34} - 162828288 q^{36} - 434574480 q^{39} + 377628672 q^{46} + 100116840 q^{49} - 1417153536 q^{51} - 963325440 q^{54} - 2368077488 q^{61} + 1073741824 q^{64} + 6246890496 q^{66} - 1192536576 q^{69} + 1606377472 q^{76} - 398565136 q^{79} + 2917929096 q^{81} + 9859080192 q^{84} + 16634464160 q^{91} - 17010954240 q^{94} + 2818572288 q^{96} + 5253825024 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.6274 −0.707107
\(3\) −137.627 + 200.269i −0.566368 + 0.824153i
\(4\) 512.000 0.500000
\(5\) 0 0
\(6\) 3114.15 4531.57i 0.400483 0.582764i
\(7\) 23226.5i 1.38196i −0.722876 0.690978i \(-0.757180\pi\)
0.722876 0.690978i \(-0.242820\pi\)
\(8\) −11585.2 −0.353553
\(9\) −21166.4 55125.0i −0.358455 0.933547i
\(10\) 0 0
\(11\) 62442.7i 0.387720i 0.981029 + 0.193860i \(0.0621007\pi\)
−0.981029 + 0.193860i \(0.937899\pi\)
\(12\) −70465.2 + 102538.i −0.283184 + 0.412076i
\(13\) 170161.i 0.458292i 0.973392 + 0.229146i \(0.0735933\pi\)
−0.973392 + 0.229146i \(0.926407\pi\)
\(14\) 525556.i 0.977190i
\(15\) 0 0
\(16\) 262144. 0.250000
\(17\) 2.66626e6 1.87784 0.938919 0.344139i \(-0.111829\pi\)
0.938919 + 0.344139i \(0.111829\pi\)
\(18\) 478941. + 1.24734e6i 0.253466 + 0.660117i
\(19\) −766825. −0.309691 −0.154845 0.987939i \(-0.549488\pi\)
−0.154845 + 0.987939i \(0.549488\pi\)
\(20\) 0 0
\(21\) 4.65156e6 + 3.19661e6i 1.13894 + 0.782695i
\(22\) 1.41292e6i 0.274159i
\(23\) 1.40327e6 0.218022 0.109011 0.994041i \(-0.465232\pi\)
0.109011 + 0.994041i \(0.465232\pi\)
\(24\) 1.59445e6 2.32016e6i 0.200241 0.291382i
\(25\) 0 0
\(26\) 3.85029e6i 0.324061i
\(27\) 1.39529e7 + 3.34774e6i 0.972402 + 0.233310i
\(28\) 1.18920e7i 0.690978i
\(29\) 4.83245e6i 0.235601i −0.993037 0.117801i \(-0.962416\pi\)
0.993037 0.117801i \(-0.0375844\pi\)
\(30\) 0 0
\(31\) −4.18297e7 −1.46109 −0.730544 0.682865i \(-0.760734\pi\)
−0.730544 + 0.682865i \(0.760734\pi\)
\(32\) −5.93164e6 −0.176777
\(33\) −1.25053e7 8.59382e6i −0.319540 0.219592i
\(34\) −6.03306e7 −1.32783
\(35\) 0 0
\(36\) −1.08372e7 2.82240e7i −0.179227 0.466774i
\(37\) 5.01619e7i 0.723378i 0.932299 + 0.361689i \(0.117800\pi\)
−0.932299 + 0.361689i \(0.882200\pi\)
\(38\) 1.73513e7 0.218985
\(39\) −3.40779e7 2.34188e7i −0.377702 0.259562i
\(40\) 0 0
\(41\) 1.49239e8i 1.28814i −0.764967 0.644069i \(-0.777245\pi\)
0.764967 0.644069i \(-0.222755\pi\)
\(42\) −1.05253e8 7.23310e7i −0.805354 0.553449i
\(43\) 1.98719e8i 1.35175i 0.737015 + 0.675876i \(0.236235\pi\)
−0.737015 + 0.675876i \(0.763765\pi\)
\(44\) 3.19706e7i 0.193860i
\(45\) 0 0
\(46\) −3.17523e7 −0.154165
\(47\) 1.55059e8 0.676093 0.338047 0.941129i \(-0.390234\pi\)
0.338047 + 0.941129i \(0.390234\pi\)
\(48\) −3.60782e7 + 5.24993e7i −0.141592 + 0.206038i
\(49\) −2.56996e8 −0.909802
\(50\) 0 0
\(51\) −3.66951e8 + 5.33970e8i −1.06355 + 1.54762i
\(52\) 8.71222e7i 0.229146i
\(53\) 4.21541e7 0.100800 0.0503999 0.998729i \(-0.483950\pi\)
0.0503999 + 0.998729i \(0.483950\pi\)
\(54\) −3.15718e8 7.57507e7i −0.687592 0.164975i
\(55\) 0 0
\(56\) 2.69085e8i 0.488595i
\(57\) 1.05536e8 1.53571e8i 0.175399 0.255233i
\(58\) 1.09346e8i 0.166595i
\(59\) 2.92026e8i 0.408471i −0.978922 0.204236i \(-0.934529\pi\)
0.978922 0.204236i \(-0.0654708\pi\)
\(60\) 0 0
\(61\) −5.30727e8 −0.628379 −0.314190 0.949360i \(-0.601733\pi\)
−0.314190 + 0.949360i \(0.601733\pi\)
\(62\) 9.46499e8 1.03315
\(63\) −1.28036e9 + 4.91622e8i −1.29012 + 0.495369i
\(64\) 1.34218e8 0.125000
\(65\) 0 0
\(66\) 2.82963e8 + 1.94456e8i 0.225949 + 0.155275i
\(67\) 5.22093e8i 0.386700i 0.981130 + 0.193350i \(0.0619353\pi\)
−0.981130 + 0.193350i \(0.938065\pi\)
\(68\) 1.36513e9 0.938919
\(69\) −1.93128e8 + 2.81031e8i −0.123481 + 0.179684i
\(70\) 0 0
\(71\) 5.71364e8i 0.316681i 0.987385 + 0.158340i \(0.0506143\pi\)
−0.987385 + 0.158340i \(0.949386\pi\)
\(72\) 2.45218e8 + 6.38636e8i 0.126733 + 0.330059i
\(73\) 2.18588e9i 1.05441i −0.849737 0.527207i \(-0.823239\pi\)
0.849737 0.527207i \(-0.176761\pi\)
\(74\) 1.13503e9i 0.511506i
\(75\) 0 0
\(76\) −3.92615e8 −0.154845
\(77\) 1.45033e9 0.535812
\(78\) 7.71095e8 + 5.29906e8i 0.267076 + 0.183538i
\(79\) −1.96592e9 −0.638897 −0.319449 0.947604i \(-0.603498\pi\)
−0.319449 + 0.947604i \(0.603498\pi\)
\(80\) 0 0
\(81\) −2.59075e9 + 2.33360e9i −0.743020 + 0.669269i
\(82\) 3.37689e9i 0.910851i
\(83\) −2.18558e9 −0.554850 −0.277425 0.960747i \(-0.589481\pi\)
−0.277425 + 0.960747i \(0.589481\pi\)
\(84\) 2.38160e9 + 1.63666e9i 0.569471 + 0.391348i
\(85\) 0 0
\(86\) 4.49650e9i 0.955833i
\(87\) 9.67791e8 + 6.65078e8i 0.194171 + 0.133437i
\(88\) 7.23413e8i 0.137080i
\(89\) 2.38742e8i 0.0427542i 0.999771 + 0.0213771i \(0.00680506\pi\)
−0.999771 + 0.0213771i \(0.993195\pi\)
\(90\) 0 0
\(91\) 3.95224e9 0.633339
\(92\) 7.18473e8 0.109011
\(93\) 5.75692e9 8.37720e9i 0.827514 1.20416i
\(94\) −3.50858e9 −0.478070
\(95\) 0 0
\(96\) 8.16356e8 1.18792e9i 0.100121 0.145691i
\(97\) 8.84112e9i 1.02955i −0.857324 0.514776i \(-0.827875\pi\)
0.857324 0.514776i \(-0.172125\pi\)
\(98\) 5.81517e9 0.643327
\(99\) 3.44215e9 1.32169e9i 0.361955 0.138980i
\(100\) 0 0
\(101\) 1.67928e10i 1.59778i 0.601477 + 0.798890i \(0.294579\pi\)
−0.601477 + 0.798890i \(0.705421\pi\)
\(102\) 8.30314e9 1.20824e10i 0.752041 1.09434i
\(103\) 8.36865e9i 0.721887i −0.932588 0.360944i \(-0.882455\pi\)
0.932588 0.360944i \(-0.117545\pi\)
\(104\) 1.97135e9i 0.162031i
\(105\) 0 0
\(106\) −9.53837e8 −0.0712763
\(107\) 1.43555e10 1.02353 0.511764 0.859126i \(-0.328992\pi\)
0.511764 + 0.859126i \(0.328992\pi\)
\(108\) 7.14389e9 + 1.71404e9i 0.486201 + 0.116655i
\(109\) 4.72564e9 0.307134 0.153567 0.988138i \(-0.450924\pi\)
0.153567 + 0.988138i \(0.450924\pi\)
\(110\) 0 0
\(111\) −1.00459e10 6.90365e9i −0.596174 0.409698i
\(112\) 6.08870e9i 0.345489i
\(113\) −1.32158e10 −0.717303 −0.358651 0.933472i \(-0.616763\pi\)
−0.358651 + 0.933472i \(0.616763\pi\)
\(114\) −2.38801e9 + 3.47492e9i −0.124026 + 0.180477i
\(115\) 0 0
\(116\) 2.47422e9i 0.117801i
\(117\) 9.38011e9 3.60169e9i 0.427837 0.164277i
\(118\) 6.60779e9i 0.288833i
\(119\) 6.19280e10i 2.59509i
\(120\) 0 0
\(121\) 2.20383e10 0.849673
\(122\) 1.20090e10 0.444331
\(123\) 2.98879e10 + 2.05393e10i 1.06162 + 0.729560i
\(124\) −2.14168e10 −0.730544
\(125\) 0 0
\(126\) 2.89713e10 1.11241e10i 0.912253 0.350279i
\(127\) 3.17814e10i 0.961953i −0.876733 0.480976i \(-0.840282\pi\)
0.876733 0.480976i \(-0.159718\pi\)
\(128\) −3.03700e9 −0.0883883
\(129\) −3.97973e10 2.73492e10i −1.11405 0.765589i
\(130\) 0 0
\(131\) 5.01094e10i 1.29886i −0.760421 0.649430i \(-0.775007\pi\)
0.760421 0.649430i \(-0.224993\pi\)
\(132\) −6.40273e9 4.40004e9i −0.159770 0.109796i
\(133\) 1.78107e10i 0.427979i
\(134\) 1.18136e10i 0.273438i
\(135\) 0 0
\(136\) −3.08893e10 −0.663916
\(137\) 2.74744e10 0.569279 0.284639 0.958635i \(-0.408126\pi\)
0.284639 + 0.958635i \(0.408126\pi\)
\(138\) 4.36999e9 6.35900e9i 0.0873142 0.127056i
\(139\) −6.32488e10 −1.21893 −0.609464 0.792814i \(-0.708615\pi\)
−0.609464 + 0.792814i \(0.708615\pi\)
\(140\) 0 0
\(141\) −2.13403e10 + 3.10534e10i −0.382917 + 0.557204i
\(142\) 1.29285e10i 0.223927i
\(143\) −1.06253e10 −0.177689
\(144\) −5.54864e9 1.44507e10i −0.0896137 0.233387i
\(145\) 0 0
\(146\) 4.94607e10i 0.745583i
\(147\) 3.53697e10 5.14684e10i 0.515282 0.749815i
\(148\) 2.56829e10i 0.361689i
\(149\) 3.38479e10i 0.460893i −0.973085 0.230446i \(-0.925981\pi\)
0.973085 0.230446i \(-0.0740186\pi\)
\(150\) 0 0
\(151\) 1.22386e11 1.55901 0.779503 0.626399i \(-0.215472\pi\)
0.779503 + 0.626399i \(0.215472\pi\)
\(152\) 8.88385e9 0.109492
\(153\) −5.64351e10 1.46978e11i −0.673120 1.75305i
\(154\) −3.28171e10 −0.378876
\(155\) 0 0
\(156\) −1.74479e10 1.19904e10i −0.188851 0.129781i
\(157\) 1.58971e11i 1.66656i −0.552853 0.833279i \(-0.686461\pi\)
0.552853 0.833279i \(-0.313539\pi\)
\(158\) 4.44838e10 0.451769
\(159\) −5.80155e9 + 8.44215e9i −0.0570898 + 0.0830745i
\(160\) 0 0
\(161\) 3.25930e10i 0.301297i
\(162\) 5.86220e10 5.28033e10i 0.525395 0.473245i
\(163\) 9.20831e10i 0.800280i 0.916454 + 0.400140i \(0.131038\pi\)
−0.916454 + 0.400140i \(0.868962\pi\)
\(164\) 7.64102e10i 0.644069i
\(165\) 0 0
\(166\) 4.94540e10 0.392338
\(167\) 2.12416e11 1.63533 0.817663 0.575697i \(-0.195269\pi\)
0.817663 + 0.575697i \(0.195269\pi\)
\(168\) −5.38894e10 3.70334e10i −0.402677 0.276725i
\(169\) 1.08904e11 0.789968
\(170\) 0 0
\(171\) 1.62309e10 + 4.22713e10i 0.111010 + 0.289111i
\(172\) 1.01744e11i 0.675876i
\(173\) 3.04132e11 1.96260 0.981300 0.192482i \(-0.0616538\pi\)
0.981300 + 0.192482i \(0.0616538\pi\)
\(174\) −2.18986e10 1.50490e10i −0.137300 0.0943542i
\(175\) 0 0
\(176\) 1.63690e10i 0.0969300i
\(177\) 5.84837e10 + 4.01908e10i 0.336642 + 0.231345i
\(178\) 5.40212e9i 0.0302318i
\(179\) 7.07114e9i 0.0384791i −0.999815 0.0192395i \(-0.993875\pi\)
0.999815 0.0192395i \(-0.00612451\pi\)
\(180\) 0 0
\(181\) −1.27309e11 −0.655337 −0.327669 0.944793i \(-0.606263\pi\)
−0.327669 + 0.944793i \(0.606263\pi\)
\(182\) −8.94290e10 −0.447838
\(183\) 7.30425e10 1.06288e11i 0.355894 0.517880i
\(184\) −1.62572e10 −0.0770825
\(185\) 0 0
\(186\) −1.30264e11 + 1.89554e11i −0.585141 + 0.851470i
\(187\) 1.66488e11i 0.728075i
\(188\) 7.93900e10 0.338047
\(189\) 7.77563e10 3.24078e11i 0.322424 1.34382i
\(190\) 0 0
\(191\) 2.06460e11i 0.812209i −0.913827 0.406105i \(-0.866887\pi\)
0.913827 0.406105i \(-0.133113\pi\)
\(192\) −1.84720e10 + 2.68797e10i −0.0707960 + 0.103019i
\(193\) 3.11606e11i 1.16364i −0.813317 0.581821i \(-0.802340\pi\)
0.813317 0.581821i \(-0.197660\pi\)
\(194\) 2.00052e11i 0.728004i
\(195\) 0 0
\(196\) −1.31582e11 −0.454901
\(197\) 1.51694e11 0.511255 0.255628 0.966775i \(-0.417718\pi\)
0.255628 + 0.966775i \(0.417718\pi\)
\(198\) −7.78870e10 + 2.99063e10i −0.255941 + 0.0982737i
\(199\) 1.11692e11 0.357895 0.178947 0.983859i \(-0.442731\pi\)
0.178947 + 0.983859i \(0.442731\pi\)
\(200\) 0 0
\(201\) −1.04559e11 7.18543e10i −0.318700 0.219014i
\(202\) 3.79978e11i 1.12980i
\(203\) −1.12241e11 −0.325591
\(204\) −1.87879e11 + 2.73392e11i −0.531773 + 0.773812i
\(205\) 0 0
\(206\) 1.89361e11i 0.510451i
\(207\) −2.97021e10 7.73551e10i −0.0781512 0.203534i
\(208\) 4.46066e10i 0.114573i
\(209\) 4.78826e10i 0.120073i
\(210\) 0 0
\(211\) 1.53066e11 0.365987 0.182994 0.983114i \(-0.441421\pi\)
0.182994 + 0.983114i \(0.441421\pi\)
\(212\) 2.15829e10 0.0503999
\(213\) −1.14427e11 7.86354e10i −0.260993 0.179358i
\(214\) −3.24828e11 −0.723744
\(215\) 0 0
\(216\) −1.61648e11 3.87843e10i −0.343796 0.0824874i
\(217\) 9.71560e11i 2.01916i
\(218\) −1.06929e11 −0.217177
\(219\) 4.37763e11 + 3.00836e11i 0.868998 + 0.597186i
\(220\) 0 0
\(221\) 4.53693e11i 0.860598i
\(222\) 2.27312e11 + 1.56212e11i 0.421559 + 0.289700i
\(223\) 6.05759e11i 1.09844i 0.835678 + 0.549219i \(0.185075\pi\)
−0.835678 + 0.549219i \(0.814925\pi\)
\(224\) 1.37771e11i 0.244298i
\(225\) 0 0
\(226\) 2.99040e11 0.507210
\(227\) −6.70588e11 −1.11257 −0.556284 0.830992i \(-0.687773\pi\)
−0.556284 + 0.830992i \(0.687773\pi\)
\(228\) 5.40345e10 7.86286e10i 0.0876995 0.127616i
\(229\) −3.53356e11 −0.561094 −0.280547 0.959840i \(-0.590516\pi\)
−0.280547 + 0.959840i \(0.590516\pi\)
\(230\) 0 0
\(231\) −1.99605e11 + 2.90456e11i −0.303467 + 0.441591i
\(232\) 5.59851e10i 0.0832976i
\(233\) −1.12390e12 −1.63662 −0.818309 0.574779i \(-0.805088\pi\)
−0.818309 + 0.574779i \(0.805088\pi\)
\(234\) −2.12248e11 + 8.14969e10i −0.302527 + 0.116161i
\(235\) 0 0
\(236\) 1.49517e11i 0.204236i
\(237\) 2.70565e11 3.93714e11i 0.361851 0.526549i
\(238\) 1.40127e12i 1.83500i
\(239\) 2.64603e11i 0.339317i 0.985503 + 0.169658i \(0.0542665\pi\)
−0.985503 + 0.169658i \(0.945734\pi\)
\(240\) 0 0
\(241\) 8.86768e11 1.09075 0.545375 0.838192i \(-0.316387\pi\)
0.545375 + 0.838192i \(0.316387\pi\)
\(242\) −4.98671e11 −0.600810
\(243\) −1.10789e11 8.40014e11i −0.130757 0.991414i
\(244\) −2.71732e11 −0.314190
\(245\) 0 0
\(246\) −6.76286e11 4.64752e11i −0.750680 0.515877i
\(247\) 1.30483e11i 0.141929i
\(248\) 4.84607e11 0.516573
\(249\) 3.00795e11 4.37704e11i 0.314249 0.457281i
\(250\) 0 0
\(251\) 8.59494e11i 0.862729i −0.902178 0.431364i \(-0.858032\pi\)
0.902178 0.431364i \(-0.141968\pi\)
\(252\) −6.55546e11 + 2.51710e11i −0.645060 + 0.247684i
\(253\) 8.76237e10i 0.0845316i
\(254\) 7.19130e11i 0.680203i
\(255\) 0 0
\(256\) 6.87195e10 0.0625000
\(257\) −2.17900e12 −1.94353 −0.971764 0.235954i \(-0.924179\pi\)
−0.971764 + 0.235954i \(0.924179\pi\)
\(258\) 9.00510e11 + 6.18841e11i 0.787753 + 0.541353i
\(259\) 1.16509e12 0.999677
\(260\) 0 0
\(261\) −2.66389e11 + 1.02286e11i −0.219945 + 0.0844524i
\(262\) 1.13385e12i 0.918433i
\(263\) −1.37942e12 −1.09627 −0.548134 0.836391i \(-0.684661\pi\)
−0.548134 + 0.836391i \(0.684661\pi\)
\(264\) 1.44877e11 + 9.95615e10i 0.112975 + 0.0776375i
\(265\) 0 0
\(266\) 4.03010e11i 0.302627i
\(267\) −4.78126e10 3.28574e10i −0.0352360 0.0242146i
\(268\) 2.67312e11i 0.193350i
\(269\) 1.18129e12i 0.838680i −0.907829 0.419340i \(-0.862262\pi\)
0.907829 0.419340i \(-0.137738\pi\)
\(270\) 0 0
\(271\) −1.42251e12 −0.973213 −0.486606 0.873621i \(-0.661765\pi\)
−0.486606 + 0.873621i \(0.661765\pi\)
\(272\) 6.98944e11 0.469459
\(273\) −5.43937e11 + 7.91511e11i −0.358703 + 0.521968i
\(274\) −6.21674e11 −0.402541
\(275\) 0 0
\(276\) −9.88815e10 + 1.43888e11i −0.0617404 + 0.0898418i
\(277\) 5.29960e11i 0.324971i 0.986711 + 0.162485i \(0.0519510\pi\)
−0.986711 + 0.162485i \(0.948049\pi\)
\(278\) 1.43116e12 0.861913
\(279\) 8.85385e11 + 2.30587e12i 0.523734 + 1.36400i
\(280\) 0 0
\(281\) 2.28441e12i 1.30389i −0.758265 0.651946i \(-0.773953\pi\)
0.758265 0.651946i \(-0.226047\pi\)
\(282\) 4.82876e11 7.02659e11i 0.270764 0.394003i
\(283\) 2.31274e12i 1.27408i −0.770833 0.637038i \(-0.780160\pi\)
0.770833 0.637038i \(-0.219840\pi\)
\(284\) 2.92539e11i 0.158340i
\(285\) 0 0
\(286\) 2.40423e11 0.125645
\(287\) −3.46630e12 −1.78015
\(288\) 1.25551e11 + 3.26982e11i 0.0633665 + 0.165029i
\(289\) 5.09295e12 2.52627
\(290\) 0 0
\(291\) 1.77060e12 + 1.21678e12i 0.848509 + 0.583106i
\(292\) 1.11917e12i 0.527207i
\(293\) 1.05989e12 0.490822 0.245411 0.969419i \(-0.421077\pi\)
0.245411 + 0.969419i \(0.421077\pi\)
\(294\) −8.00326e11 + 1.16460e12i −0.364360 + 0.530199i
\(295\) 0 0
\(296\) 5.81138e11i 0.255753i
\(297\) −2.09042e11 + 8.71257e11i −0.0904588 + 0.377020i
\(298\) 7.65890e11i 0.325900i
\(299\) 2.38781e11i 0.0999179i
\(300\) 0 0
\(301\) 4.61555e12 1.86806
\(302\) −2.76928e12 −1.10238
\(303\) −3.36308e12 2.31115e12i −1.31681 0.904931i
\(304\) −2.01019e11 −0.0774227
\(305\) 0 0
\(306\) 1.27698e12 + 3.32573e12i 0.475968 + 1.23959i
\(307\) 6.89209e11i 0.252731i 0.991984 + 0.126366i \(0.0403313\pi\)
−0.991984 + 0.126366i \(0.959669\pi\)
\(308\) 7.42567e11 0.267906
\(309\) 1.67598e12 + 1.15176e12i 0.594945 + 0.408854i
\(310\) 0 0
\(311\) 1.95674e12i 0.672559i −0.941762 0.336280i \(-0.890831\pi\)
0.941762 0.336280i \(-0.109169\pi\)
\(312\) 3.94801e11 + 2.71312e11i 0.133538 + 0.0917690i
\(313\) 2.48821e11i 0.0828256i 0.999142 + 0.0414128i \(0.0131859\pi\)
−0.999142 + 0.0414128i \(0.986814\pi\)
\(314\) 3.59711e12i 1.17843i
\(315\) 0 0
\(316\) −1.00655e12 −0.319449
\(317\) 4.63675e12 1.44850 0.724249 0.689539i \(-0.242187\pi\)
0.724249 + 0.689539i \(0.242187\pi\)
\(318\) 1.31274e11 1.91024e11i 0.0403686 0.0587425i
\(319\) 3.01751e11 0.0913473
\(320\) 0 0
\(321\) −1.97571e12 + 2.87497e12i −0.579694 + 0.843544i
\(322\) 7.37496e11i 0.213049i
\(323\) −2.04456e12 −0.581549
\(324\) −1.32646e12 + 1.19480e12i −0.371510 + 0.334634i
\(325\) 0 0
\(326\) 2.08360e12i 0.565883i
\(327\) −6.50378e11 + 9.46400e11i −0.173951 + 0.253125i
\(328\) 1.72897e12i 0.455426i
\(329\) 3.60147e12i 0.934331i
\(330\) 0 0
\(331\) −1.41443e12 −0.355994 −0.177997 0.984031i \(-0.556962\pi\)
−0.177997 + 0.984031i \(0.556962\pi\)
\(332\) −1.11902e12 −0.277425
\(333\) 2.76518e12 1.06175e12i 0.675308 0.259298i
\(334\) −4.80642e12 −1.15635
\(335\) 0 0
\(336\) 1.21938e12 + 8.37971e11i 0.284736 + 0.195674i
\(337\) 8.67755e11i 0.199640i 0.995006 + 0.0998201i \(0.0318267\pi\)
−0.995006 + 0.0998201i \(0.968173\pi\)
\(338\) −2.46421e12 −0.558592
\(339\) 1.81886e12 2.64672e12i 0.406257 0.591167i
\(340\) 0 0
\(341\) 2.61196e12i 0.566493i
\(342\) −3.67264e11 9.56490e11i −0.0784961 0.204432i
\(343\) 5.91785e11i 0.124650i
\(344\) 2.30221e12i 0.477917i
\(345\) 0 0
\(346\) −6.88173e12 −1.38777
\(347\) −5.20712e12 −1.03502 −0.517512 0.855676i \(-0.673142\pi\)
−0.517512 + 0.855676i \(0.673142\pi\)
\(348\) 4.95509e11 + 3.40520e11i 0.0970857 + 0.0667185i
\(349\) −1.11953e12 −0.216226 −0.108113 0.994139i \(-0.534481\pi\)
−0.108113 + 0.994139i \(0.534481\pi\)
\(350\) 0 0
\(351\) −5.69653e11 + 2.37424e12i −0.106924 + 0.445644i
\(352\) 3.70388e11i 0.0685398i
\(353\) 3.73952e12 0.682248 0.341124 0.940018i \(-0.389192\pi\)
0.341124 + 0.940018i \(0.389192\pi\)
\(354\) −1.32334e12 9.09413e11i −0.238042 0.163586i
\(355\) 0 0
\(356\) 1.22236e11i 0.0213771i
\(357\) 1.24023e13 + 8.52299e12i 2.13875 + 1.46977i
\(358\) 1.60002e11i 0.0272088i
\(359\) 3.54489e12i 0.594471i −0.954804 0.297235i \(-0.903935\pi\)
0.954804 0.297235i \(-0.0960646\pi\)
\(360\) 0 0
\(361\) −5.54305e12 −0.904092
\(362\) 2.88066e12 0.463393
\(363\) −3.03308e12 + 4.41360e12i −0.481228 + 0.700260i
\(364\) 2.02355e12 0.316670
\(365\) 0 0
\(366\) −1.65276e12 + 2.40503e12i −0.251655 + 0.366197i
\(367\) 1.01161e13i 1.51944i −0.650248 0.759722i \(-0.725335\pi\)
0.650248 0.759722i \(-0.274665\pi\)
\(368\) 3.67858e11 0.0545056
\(369\) −8.22679e12 + 3.15885e12i −1.20254 + 0.461739i
\(370\) 0 0
\(371\) 9.79093e11i 0.139301i
\(372\) 2.94754e12 4.28913e12i 0.413757 0.602080i
\(373\) 3.81055e12i 0.527769i −0.964554 0.263885i \(-0.914996\pi\)
0.964554 0.263885i \(-0.0850038\pi\)
\(374\) 3.76720e12i 0.514827i
\(375\) 0 0
\(376\) −1.79639e12 −0.239035
\(377\) 8.22293e11 0.107974
\(378\) −1.75943e12 + 7.33304e12i −0.227988 + 0.950222i
\(379\) −1.11052e13 −1.42014 −0.710069 0.704132i \(-0.751336\pi\)
−0.710069 + 0.704132i \(0.751336\pi\)
\(380\) 0 0
\(381\) 6.36482e12 + 4.37399e12i 0.792796 + 0.544819i
\(382\) 4.67165e12i 0.574319i
\(383\) 4.29169e12 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(384\) 4.17974e11 6.08217e11i 0.0500603 0.0728455i
\(385\) 0 0
\(386\) 7.05084e12i 0.822820i
\(387\) 1.09544e13 4.20617e12i 1.26192 0.484542i
\(388\) 4.52665e12i 0.514776i
\(389\) 1.50554e13i 1.69023i −0.534588 0.845113i \(-0.679533\pi\)
0.534588 0.845113i \(-0.320467\pi\)
\(390\) 0 0
\(391\) 3.74148e12 0.409411
\(392\) 2.97736e12 0.321663
\(393\) 1.00354e13 + 6.89642e12i 1.07046 + 0.735633i
\(394\) −3.43245e12 −0.361512
\(395\) 0 0
\(396\) 1.76238e12 6.76703e11i 0.180977 0.0694900i
\(397\) 1.11669e13i 1.13235i −0.824286 0.566174i \(-0.808423\pi\)
0.824286 0.566174i \(-0.191577\pi\)
\(398\) −2.52729e12 −0.253070
\(399\) −3.56693e12 2.45124e12i −0.352720 0.242394i
\(400\) 0 0
\(401\) 1.15685e13i 1.11572i −0.829935 0.557861i \(-0.811622\pi\)
0.829935 0.557861i \(-0.188378\pi\)
\(402\) 2.36590e12 + 1.62588e12i 0.225355 + 0.154867i
\(403\) 7.11777e12i 0.669605i
\(404\) 8.59793e12i 0.798890i
\(405\) 0 0
\(406\) 2.53973e12 0.230227
\(407\) −3.13224e12 −0.280468
\(408\) 4.25121e12 6.18616e12i 0.376021 0.547168i
\(409\) 1.07411e13 0.938498 0.469249 0.883066i \(-0.344525\pi\)
0.469249 + 0.883066i \(0.344525\pi\)
\(410\) 0 0
\(411\) −3.78123e12 + 5.50227e12i −0.322421 + 0.469172i
\(412\) 4.28475e12i 0.360944i
\(413\) −6.78275e12 −0.564489
\(414\) 6.72082e11 + 1.75035e12i 0.0552612 + 0.143920i
\(415\) 0 0
\(416\) 1.00933e12i 0.0810153i
\(417\) 8.70477e12 1.26668e13i 0.690362 1.00458i
\(418\) 1.08346e12i 0.0849047i
\(419\) 8.81717e12i 0.682746i 0.939928 + 0.341373i \(0.110892\pi\)
−0.939928 + 0.341373i \(0.889108\pi\)
\(420\) 0 0
\(421\) −5.69741e12 −0.430792 −0.215396 0.976527i \(-0.569104\pi\)
−0.215396 + 0.976527i \(0.569104\pi\)
\(422\) −3.46348e12 −0.258792
\(423\) −3.28203e12 8.54761e12i −0.242349 0.631165i
\(424\) −4.88365e11 −0.0356381
\(425\) 0 0
\(426\) 2.58918e12 + 1.77932e12i 0.184550 + 0.126825i
\(427\) 1.23269e13i 0.868392i
\(428\) 7.35003e12 0.511764
\(429\) 1.46233e12 2.12792e12i 0.100637 0.146443i
\(430\) 0 0
\(431\) 1.80323e13i 1.21245i −0.795293 0.606226i \(-0.792683\pi\)
0.795293 0.606226i \(-0.207317\pi\)
\(432\) 3.65767e12 + 8.77590e11i 0.243101 + 0.0583274i
\(433\) 2.06339e13i 1.35563i −0.735232 0.677816i \(-0.762927\pi\)
0.735232 0.677816i \(-0.237073\pi\)
\(434\) 2.19839e13i 1.42776i
\(435\) 0 0
\(436\) 2.41953e12 0.153567
\(437\) −1.07606e12 −0.0675195
\(438\) −9.90545e12 6.80715e12i −0.614474 0.422275i
\(439\) −1.95313e13 −1.19787 −0.598935 0.800798i \(-0.704409\pi\)
−0.598935 + 0.800798i \(0.704409\pi\)
\(440\) 0 0
\(441\) 5.43969e12 + 1.41669e13i 0.326123 + 0.849343i
\(442\) 1.02659e13i 0.608535i
\(443\) 2.97469e13 1.74351 0.871753 0.489946i \(-0.162984\pi\)
0.871753 + 0.489946i \(0.162984\pi\)
\(444\) −5.14349e12 3.53467e12i −0.298087 0.204849i
\(445\) 0 0
\(446\) 1.37068e13i 0.776713i
\(447\) 6.77868e12 + 4.65839e12i 0.379846 + 0.261035i
\(448\) 3.11741e12i 0.172744i
\(449\) 1.37505e13i 0.753509i −0.926313 0.376754i \(-0.877040\pi\)
0.926313 0.376754i \(-0.122960\pi\)
\(450\) 0 0
\(451\) 9.31887e12 0.499437
\(452\) −6.76651e12 −0.358651
\(453\) −1.68437e13 + 2.45102e13i −0.882971 + 1.28486i
\(454\) 1.51737e13 0.786704
\(455\) 0 0
\(456\) −1.22266e12 + 1.77916e12i −0.0620129 + 0.0902383i
\(457\) 4.10224e11i 0.0205798i 0.999947 + 0.0102899i \(0.00327543\pi\)
−0.999947 + 0.0102899i \(0.996725\pi\)
\(458\) 7.99554e12 0.396753
\(459\) 3.72021e13 + 8.92594e12i 1.82601 + 0.438118i
\(460\) 0 0
\(461\) 2.10914e11i 0.0101298i 0.999987 + 0.00506490i \(0.00161221\pi\)
−0.999987 + 0.00506490i \(0.998388\pi\)
\(462\) 4.51654e12 6.57226e12i 0.214583 0.312252i
\(463\) 1.96738e13i 0.924660i 0.886708 + 0.462330i \(0.152987\pi\)
−0.886708 + 0.462330i \(0.847013\pi\)
\(464\) 1.26680e12i 0.0589003i
\(465\) 0 0
\(466\) 2.54309e13 1.15726
\(467\) −1.21902e13 −0.548815 −0.274407 0.961614i \(-0.588482\pi\)
−0.274407 + 0.961614i \(0.588482\pi\)
\(468\) 4.80261e12 1.84406e12i 0.213919 0.0821385i
\(469\) 1.21264e13 0.534402
\(470\) 0 0
\(471\) 3.18370e13 + 2.18788e13i 1.37350 + 0.943885i
\(472\) 3.38319e12i 0.144416i
\(473\) −1.24085e13 −0.524101
\(474\) −6.12218e12 + 8.90872e12i −0.255867 + 0.372326i
\(475\) 0 0
\(476\) 3.17071e13i 1.29754i
\(477\) −8.92250e11 2.32374e12i −0.0361322 0.0941014i
\(478\) 5.98729e12i 0.239933i
\(479\) 5.00886e12i 0.198637i 0.995056 + 0.0993187i \(0.0316663\pi\)
−0.995056 + 0.0993187i \(0.968334\pi\)
\(480\) 0 0
\(481\) −8.53558e12 −0.331518
\(482\) −2.00653e13 −0.771276
\(483\) 6.52737e12 + 4.48569e12i 0.248315 + 0.170645i
\(484\) 1.12836e13 0.424837
\(485\) 0 0
\(486\) 2.50686e12 + 1.90074e13i 0.0924590 + 0.701036i
\(487\) 4.17000e13i 1.52227i −0.648595 0.761134i \(-0.724643\pi\)
0.648595 0.761134i \(-0.275357\pi\)
\(488\) 6.14859e12 0.222166
\(489\) −1.84414e13 1.26732e13i −0.659553 0.453253i
\(490\) 0 0
\(491\) 2.10340e12i 0.0737081i 0.999321 + 0.0368540i \(0.0117337\pi\)
−0.999321 + 0.0368540i \(0.988266\pi\)
\(492\) 1.53026e13 + 1.05161e13i 0.530811 + 0.364780i
\(493\) 1.28846e13i 0.442421i
\(494\) 2.95250e12i 0.100359i
\(495\) 0 0
\(496\) −1.09654e13 −0.365272
\(497\) 1.32708e13 0.437639
\(498\) −6.80622e12 + 9.90410e12i −0.222208 + 0.323347i
\(499\) −2.74482e13 −0.887179 −0.443589 0.896230i \(-0.646295\pi\)
−0.443589 + 0.896230i \(0.646295\pi\)
\(500\) 0 0
\(501\) −2.92342e13 + 4.25403e13i −0.926197 + 1.34776i
\(502\) 1.94481e13i 0.610041i
\(503\) −2.26985e13 −0.704949 −0.352474 0.935822i \(-0.614660\pi\)
−0.352474 + 0.935822i \(0.614660\pi\)
\(504\) 1.48333e13 5.69556e12i 0.456127 0.175139i
\(505\) 0 0
\(506\) 1.98270e12i 0.0597729i
\(507\) −1.49882e13 + 2.18101e13i −0.447413 + 0.651055i
\(508\) 1.62721e13i 0.480976i
\(509\) 4.21460e13i 1.23358i 0.787127 + 0.616791i \(0.211567\pi\)
−0.787127 + 0.616791i \(0.788433\pi\)
\(510\) 0 0
\(511\) −5.07703e13 −1.45715
\(512\) −1.55494e12 −0.0441942
\(513\) −1.06994e13 2.56713e12i −0.301144 0.0722539i
\(514\) 4.93051e13 1.37428
\(515\) 0 0
\(516\) −2.03762e13 1.40028e13i −0.557025 0.382795i
\(517\) 9.68227e12i 0.262135i
\(518\) −2.63629e13 −0.706878
\(519\) −4.18569e13 + 6.09083e13i −1.11155 + 1.61748i
\(520\) 0 0
\(521\) 6.54420e13i 1.70478i −0.522907 0.852390i \(-0.675152\pi\)
0.522907 0.852390i \(-0.324848\pi\)
\(522\) 6.02770e12 2.31446e12i 0.155525 0.0597169i
\(523\) 6.14531e13i 1.57049i 0.619185 + 0.785245i \(0.287463\pi\)
−0.619185 + 0.785245i \(0.712537\pi\)
\(524\) 2.56560e13i 0.649430i
\(525\) 0 0
\(526\) 3.12126e13 0.775178
\(527\) −1.11529e14 −2.74369
\(528\) −3.27820e12 2.25282e12i −0.0798851 0.0548980i
\(529\) −3.94574e13 −0.952466
\(530\) 0 0
\(531\) −1.60979e13 + 6.18114e12i −0.381327 + 0.146418i
\(532\) 9.11907e12i 0.213990i
\(533\) 2.53946e13 0.590343
\(534\) 1.08188e12 + 7.43479e11i 0.0249156 + 0.0171223i
\(535\) 0 0
\(536\) 6.04857e12i 0.136719i
\(537\) 1.41613e12 + 9.73183e11i 0.0317126 + 0.0217933i
\(538\) 2.67296e13i 0.593036i
\(539\) 1.60475e13i 0.352748i
\(540\) 0 0
\(541\) 1.50207e13 0.324118 0.162059 0.986781i \(-0.448187\pi\)
0.162059 + 0.986781i \(0.448187\pi\)
\(542\) 3.21877e13 0.688166
\(543\) 1.75211e13 2.54960e13i 0.371162 0.540098i
\(544\) −1.58153e13 −0.331958
\(545\) 0 0
\(546\) 1.23079e13 1.79099e13i 0.253641 0.369087i
\(547\) 7.15097e13i 1.46025i 0.683312 + 0.730127i \(0.260539\pi\)
−0.683312 + 0.730127i \(0.739461\pi\)
\(548\) 1.40669e13 0.284639
\(549\) 1.12336e13 + 2.92563e13i 0.225245 + 0.586621i
\(550\) 0 0
\(551\) 3.70565e12i 0.0729636i
\(552\) 2.23743e12 3.25581e12i 0.0436571 0.0635278i
\(553\) 4.56616e13i 0.882928i
\(554\) 1.19916e13i 0.229789i
\(555\) 0 0
\(556\) −3.23834e13 −0.609464
\(557\) −7.34107e13 −1.36925 −0.684626 0.728895i \(-0.740034\pi\)
−0.684626 + 0.728895i \(0.740034\pi\)
\(558\) −2.00340e13 5.21758e13i −0.370336 0.964490i
\(559\) −3.38141e13 −0.619497
\(560\) 0 0
\(561\) −3.33425e13 2.29134e13i −0.600045 0.412358i
\(562\) 5.16902e13i 0.921991i
\(563\) −4.77347e13 −0.843902 −0.421951 0.906619i \(-0.638655\pi\)
−0.421951 + 0.906619i \(0.638655\pi\)
\(564\) −1.09262e13 + 1.58994e13i −0.191459 + 0.278602i
\(565\) 0 0
\(566\) 5.23314e13i 0.900907i
\(567\) 5.42013e13 + 6.01742e13i 0.924900 + 1.02682i
\(568\) 6.61939e12i 0.111963i
\(569\) 1.90951e13i 0.320156i 0.987104 + 0.160078i \(0.0511745\pi\)
−0.987104 + 0.160078i \(0.948825\pi\)
\(570\) 0 0
\(571\) −2.09448e13 −0.345060 −0.172530 0.985004i \(-0.555194\pi\)
−0.172530 + 0.985004i \(0.555194\pi\)
\(572\) −5.44014e12 −0.0888444
\(573\) 4.13475e13 + 2.84145e13i 0.669385 + 0.460009i
\(574\) 7.84334e13 1.25876
\(575\) 0 0
\(576\) −2.84091e12 7.39876e12i −0.0448069 0.116693i
\(577\) 3.56688e13i 0.557711i 0.960333 + 0.278855i \(0.0899550\pi\)
−0.960333 + 0.278855i \(0.910045\pi\)
\(578\) −1.15240e14 −1.78635
\(579\) 6.24051e13 + 4.28856e13i 0.959019 + 0.659050i
\(580\) 0 0
\(581\) 5.07634e13i 0.766778i
\(582\) −4.00642e13 2.75326e13i −0.599986 0.412318i
\(583\) 2.63221e12i 0.0390821i
\(584\) 2.53239e13i 0.372792i
\(585\) 0 0
\(586\) −2.39826e13 −0.347064
\(587\) 1.29418e14 1.85697 0.928483 0.371375i \(-0.121114\pi\)
0.928483 + 0.371375i \(0.121114\pi\)
\(588\) 1.81093e13 2.63518e13i 0.257641 0.374908i
\(589\) 3.20761e13 0.452486
\(590\) 0 0
\(591\) −2.08773e13 + 3.03797e13i −0.289559 + 0.421352i
\(592\) 1.31496e13i 0.180845i
\(593\) 3.96596e13 0.540848 0.270424 0.962741i \(-0.412836\pi\)
0.270424 + 0.962741i \(0.412836\pi\)
\(594\) 4.73007e12 1.97143e13i 0.0639640 0.266593i
\(595\) 0 0
\(596\) 1.73301e13i 0.230446i
\(597\) −1.53718e13 + 2.23684e13i −0.202700 + 0.294960i
\(598\) 5.40299e12i 0.0706526i
\(599\) 4.57555e13i 0.593347i 0.954979 + 0.296674i \(0.0958774\pi\)
−0.954979 + 0.296674i \(0.904123\pi\)
\(600\) 0 0
\(601\) 1.06033e14 1.35229 0.676143 0.736770i \(-0.263650\pi\)
0.676143 + 0.736770i \(0.263650\pi\)
\(602\) −1.04438e14 −1.32092
\(603\) 2.87804e13 1.10508e13i 0.361003 0.138614i
\(604\) 6.26617e13 0.779503
\(605\) 0 0
\(606\) 7.60979e13 + 5.22954e13i 0.931128 + 0.639883i
\(607\) 9.55067e13i 1.15902i −0.814966 0.579509i \(-0.803244\pi\)
0.814966 0.579509i \(-0.196756\pi\)
\(608\) 4.54853e12 0.0547461
\(609\) 1.54475e13 2.24784e13i 0.184404 0.268336i
\(610\) 0 0
\(611\) 2.63849e13i 0.309848i
\(612\) −2.88948e13 7.52526e13i −0.336560 0.876525i
\(613\) 5.18411e13i 0.598924i 0.954108 + 0.299462i \(0.0968072\pi\)
−0.954108 + 0.299462i \(0.903193\pi\)
\(614\) 1.55950e13i 0.178708i
\(615\) 0 0
\(616\) −1.68024e13 −0.189438
\(617\) −8.05443e13 −0.900760 −0.450380 0.892837i \(-0.648711\pi\)
−0.450380 + 0.892837i \(0.648711\pi\)
\(618\) −3.79231e13 2.60612e13i −0.420690 0.289103i
\(619\) 5.14946e13 0.566642 0.283321 0.959025i \(-0.408564\pi\)
0.283321 + 0.959025i \(0.408564\pi\)
\(620\) 0 0
\(621\) 1.95797e13 + 4.69777e12i 0.212005 + 0.0508667i
\(622\) 4.42759e13i 0.475571i
\(623\) 5.54515e12 0.0590844
\(624\) −8.93332e12 6.13909e12i −0.0944256 0.0648905i
\(625\) 0 0
\(626\) 5.63017e12i 0.0585665i
\(627\) 9.58941e12 + 6.58996e12i 0.0989587 + 0.0680057i
\(628\) 8.13933e13i 0.833279i
\(629\) 1.33745e14i 1.35839i
\(630\) 0 0
\(631\) −1.02922e13 −0.102887 −0.0514435 0.998676i \(-0.516382\pi\)
−0.0514435 + 0.998676i \(0.516382\pi\)
\(632\) 2.27757e13 0.225884
\(633\) −2.10660e13 + 3.06543e13i −0.207283 + 0.301629i
\(634\) −1.04918e14 −1.02424
\(635\) 0 0
\(636\) −2.97040e12 + 4.32238e12i −0.0285449 + 0.0415372i
\(637\) 4.37307e13i 0.416955i
\(638\) −6.82785e12 −0.0645923
\(639\) 3.14965e13 1.20937e13i 0.295636 0.113516i
\(640\) 0 0
\(641\) 4.62451e13i 0.427342i −0.976906 0.213671i \(-0.931458\pi\)
0.976906 0.213671i \(-0.0685420\pi\)
\(642\) 4.47053e13 6.50531e13i 0.409906 0.596476i
\(643\) 2.73102e13i 0.248468i −0.992253 0.124234i \(-0.960353\pi\)
0.992253 0.124234i \(-0.0396474\pi\)
\(644\) 1.66876e13i 0.150649i
\(645\) 0 0
\(646\) 4.62630e13 0.411217
\(647\) −1.34984e13 −0.119059 −0.0595293 0.998227i \(-0.518960\pi\)
−0.0595293 + 0.998227i \(0.518960\pi\)
\(648\) 3.00145e13 2.70353e13i 0.262697 0.236622i
\(649\) 1.82349e13 0.158372
\(650\) 0 0
\(651\) −1.94573e14 1.33713e14i −1.66410 1.14359i
\(652\) 4.71466e13i 0.400140i
\(653\) 8.41840e13 0.709029 0.354514 0.935051i \(-0.384646\pi\)
0.354514 + 0.935051i \(0.384646\pi\)
\(654\) 1.47164e13 2.14146e13i 0.123002 0.178987i
\(655\) 0 0
\(656\) 3.91220e13i 0.322034i
\(657\) −1.20496e14 + 4.62671e13i −0.984345 + 0.377960i
\(658\) 8.14920e13i 0.660672i
\(659\) 1.65464e14i 1.33130i −0.746264 0.665650i \(-0.768154\pi\)
0.746264 0.665650i \(-0.231846\pi\)
\(660\) 0 0
\(661\) 2.01681e14 1.59830 0.799148 0.601135i \(-0.205284\pi\)
0.799148 + 0.601135i \(0.205284\pi\)
\(662\) 3.20050e13 0.251726
\(663\) −9.08606e13 6.24405e13i −0.709264 0.487415i
\(664\) 2.53204e13 0.196169
\(665\) 0 0
\(666\) −6.25688e13 + 2.40246e13i −0.477515 + 0.183352i
\(667\) 6.78122e12i 0.0513664i
\(668\) 1.08757e14 0.817663
\(669\) −1.21315e14 8.33691e13i −0.905281 0.622120i
\(670\) 0 0
\(671\) 3.31400e13i 0.243635i
\(672\) −2.75914e13 1.89611e13i −0.201338 0.138362i
\(673\) 6.04368e12i 0.0437750i −0.999760 0.0218875i \(-0.993032\pi\)
0.999760 0.0218875i \(-0.00696757\pi\)
\(674\) 1.96351e13i 0.141167i
\(675\) 0 0
\(676\) 5.57588e13 0.394984
\(677\) 1.21474e14 0.854164 0.427082 0.904213i \(-0.359542\pi\)
0.427082 + 0.904213i \(0.359542\pi\)
\(678\) −4.11561e13 + 5.98885e13i −0.287267 + 0.418018i
\(679\) −2.05349e14 −1.42280
\(680\) 0 0
\(681\) 9.22913e13 1.34298e14i 0.630123 0.916926i
\(682\) 5.91019e13i 0.400571i
\(683\) 1.51629e14 1.02019 0.510094 0.860119i \(-0.329611\pi\)
0.510094 + 0.860119i \(0.329611\pi\)
\(684\) 8.31024e12 + 2.16429e13i 0.0555051 + 0.144556i
\(685\) 0 0
\(686\) 1.33906e13i 0.0881410i
\(687\) 4.86315e13 7.07663e13i 0.317785 0.462427i
\(688\) 5.20930e13i 0.337938i
\(689\) 7.17296e12i 0.0461958i
\(690\) 0 0
\(691\) 6.62249e13 0.420369 0.210185 0.977662i \(-0.432593\pi\)
0.210185 + 0.977662i \(0.432593\pi\)
\(692\) 1.55716e14 0.981300
\(693\) −3.06982e13 7.99493e13i −0.192064 0.500205i
\(694\) 1.17824e14 0.731873
\(695\) 0 0
\(696\) −1.12121e13 7.70509e12i −0.0686500 0.0471771i
\(697\) 3.97909e14i 2.41891i
\(698\) 2.53321e13 0.152895
\(699\) 1.54679e14 2.25082e14i 0.926928 1.34882i
\(700\) 0 0
\(701\) 5.78990e13i 0.342043i −0.985267 0.171022i \(-0.945293\pi\)
0.985267 0.171022i \(-0.0547068\pi\)
\(702\) 1.28898e13 5.37228e13i 0.0756066 0.315118i
\(703\) 3.84654e13i 0.224024i
\(704\) 8.38091e12i 0.0484650i
\(705\) 0 0
\(706\) −8.46157e13 −0.482422
\(707\) 3.90039e14 2.20806
\(708\) 2.99437e13 + 2.05777e13i 0.168321 + 0.115672i
\(709\) −2.70077e14 −1.50750 −0.753750 0.657162i \(-0.771757\pi\)
−0.753750 + 0.657162i \(0.771757\pi\)
\(710\) 0 0
\(711\) 4.16115e13 + 1.08372e14i 0.229016 + 0.596441i
\(712\) 2.76588e12i 0.0151159i
\(713\) −5.86983e13 −0.318550
\(714\) −2.80631e14 1.92853e14i −1.51232 1.03929i
\(715\) 0 0
\(716\) 3.62043e12i 0.0192395i
\(717\) −5.29918e13 3.64166e13i −0.279649 0.192178i
\(718\) 8.02117e13i 0.420354i
\(719\) 1.48102e14i 0.770755i −0.922759 0.385377i \(-0.874071\pi\)
0.922759 0.385377i \(-0.125929\pi\)
\(720\) 0 0
\(721\) −1.94375e14 −0.997616
\(722\) 1.25425e14 0.639289
\(723\) −1.22044e14 + 1.77592e14i −0.617765 + 0.898944i
\(724\) −6.51820e13 −0.327669
\(725\) 0 0
\(726\) 6.86307e13 9.98683e13i 0.340279 0.495159i
\(727\) 5.21602e13i 0.256842i 0.991720 + 0.128421i \(0.0409910\pi\)
−0.991720 + 0.128421i \(0.959009\pi\)
\(728\) −4.57876e13 −0.223919
\(729\) 1.83476e14 + 9.34214e13i 0.891133 + 0.453742i
\(730\) 0 0
\(731\) 5.29837e14i 2.53837i
\(732\) 3.73978e13 5.44195e13i 0.177947 0.258940i
\(733\) 3.21782e14i 1.52069i −0.649518 0.760346i \(-0.725029\pi\)
0.649518 0.760346i \(-0.274971\pi\)
\(734\) 2.28902e14i 1.07441i
\(735\) 0 0
\(736\) −8.32367e12 −0.0385413
\(737\) −3.26009e13 −0.149931
\(738\) 1.86151e14 7.14765e13i 0.850322 0.326499i
\(739\) −1.66542e14 −0.755617 −0.377809 0.925884i \(-0.623322\pi\)
−0.377809 + 0.925884i \(0.623322\pi\)
\(740\) 0 0
\(741\) 2.61318e13 + 1.79581e13i 0.116971 + 0.0803839i
\(742\) 2.21543e13i 0.0985007i
\(743\) −1.13631e14 −0.501825 −0.250912 0.968010i \(-0.580731\pi\)
−0.250912 + 0.968010i \(0.580731\pi\)
\(744\) −6.66953e13 + 9.70519e13i −0.292570 + 0.425735i
\(745\) 0 0
\(746\) 8.62230e13i 0.373189i
\(747\) 4.62608e13 + 1.20480e14i 0.198889 + 0.517979i
\(748\) 8.52421e13i 0.364037i
\(749\) 3.33429e14i 1.41447i
\(750\) 0 0
\(751\) −1.64956e14 −0.690508 −0.345254 0.938509i \(-0.612207\pi\)
−0.345254 + 0.938509i \(0.612207\pi\)
\(752\) 4.06477e13 0.169023
\(753\) 1.72130e14 + 1.18290e14i 0.711020 + 0.488622i
\(754\) −1.86064e13 −0.0763493
\(755\) 0 0
\(756\) 3.98112e13 1.65928e14i 0.161212 0.671909i
\(757\) 2.67990e14i 1.07805i −0.842289 0.539026i \(-0.818793\pi\)
0.842289 0.539026i \(-0.181207\pi\)
\(758\) 2.51282e14 1.00419
\(759\) −1.75483e13 1.20594e13i −0.0696669 0.0478760i
\(760\) 0 0
\(761\) 1.29795e14i 0.508550i 0.967132 + 0.254275i \(0.0818368\pi\)
−0.967132 + 0.254275i \(0.918163\pi\)
\(762\) −1.44020e14 9.89720e13i −0.560591 0.385245i
\(763\) 1.09760e14i 0.424446i
\(764\) 1.05707e14i 0.406105i
\(765\) 0 0
\(766\) −9.71099e13 −0.368230
\(767\) 4.96913e13 0.187199
\(768\) −9.45768e12 + 1.37624e13i −0.0353980 + 0.0515095i
\(769\) 2.19185e14 0.815041 0.407521 0.913196i \(-0.366393\pi\)
0.407521 + 0.913196i \(0.366393\pi\)
\(770\) 0 0
\(771\) 2.99890e14 4.36386e14i 1.10075 1.60176i
\(772\) 1.59542e14i 0.581821i
\(773\) −4.05042e14 −1.46758 −0.733792 0.679374i \(-0.762251\pi\)
−0.733792 + 0.679374i \(0.762251\pi\)
\(774\) −2.47870e14 + 9.51747e13i −0.892315 + 0.342623i
\(775\) 0