Properties

Label 252.8.k.e.37.6
Level $252$
Weight $8$
Character 252.37
Analytic conductor $78.721$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(78.7210264220\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} - 993183560713460 x^{9} + 4531523101103784409 x^{8} - 25038421018919762700 x^{7} + 77467785793463920028824 x^{6} - 352418565495722251364640 x^{5} + 967025470523891143640719680 x^{4} - 1651641278575894088053178880 x^{3} + 7200793191683961412674394484736 x^{2} + 21939035854717669821876654243840 x + 34494438285389383231614325978300416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{13}\cdot 7^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.6
Root \(62.2223 - 107.772i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.8.k.e.109.6

$q$-expansion

\(f(q)\) \(=\) \(q+(135.624 - 234.907i) q^{5} +(87.0016 + 903.313i) q^{7} +O(q^{10})\) \(q+(135.624 - 234.907i) q^{5} +(87.0016 + 903.313i) q^{7} +(2753.41 + 4769.04i) q^{11} +8802.63 q^{13} +(-3420.94 - 5925.24i) q^{17} +(13231.5 - 22917.6i) q^{19} +(-41328.3 + 71582.8i) q^{23} +(2274.86 + 3940.17i) q^{25} -233335. q^{29} +(19823.7 + 34335.7i) q^{31} +(223994. + 102073. i) q^{35} +(-115873. + 200699. i) q^{37} +403925. q^{41} -122932. q^{43} +(52674.9 - 91235.6i) q^{47} +(-808404. + 157179. i) q^{49} +(-665248. - 1.15224e6i) q^{53} +1.49371e6 q^{55} +(429413. + 743764. i) q^{59} +(525507. - 910205. i) q^{61} +(1.19385e6 - 2.06780e6i) q^{65} +(2.21180e6 + 3.83096e6i) q^{67} -154446. q^{71} +(1.07857e6 + 1.86813e6i) q^{73} +(-4.06838e6 + 2.90210e6i) q^{77} +(-954414. + 1.65309e6i) q^{79} +8.56018e6 q^{83} -1.85584e6 q^{85} +(-5.54046e6 + 9.59637e6i) q^{89} +(765843. + 7.95153e6i) q^{91} +(-3.58900e6 - 6.21634e6i) q^{95} +1.13502e6 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 1680q^{7} + O(q^{10}) \) \( 16q + 1680q^{7} - 28280q^{13} + 42224q^{19} - 80460q^{25} + 164752q^{31} - 647980q^{37} + 1341440q^{43} + 230104q^{49} - 323120q^{55} - 4319336q^{61} - 3905760q^{67} + 6471780q^{73} - 6093104q^{79} + 456400q^{85} + 15969856q^{91} - 27141240q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 135.624 234.907i 0.485223 0.840430i −0.514633 0.857410i \(-0.672072\pi\)
0.999856 + 0.0169803i \(0.00540526\pi\)
\(6\) 0 0
\(7\) 87.0016 + 903.313i 0.0958703 + 0.995394i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2753.41 + 4769.04i 0.623729 + 1.08033i 0.988785 + 0.149345i \(0.0477164\pi\)
−0.365056 + 0.930985i \(0.618950\pi\)
\(12\) 0 0
\(13\) 8802.63 1.11125 0.555624 0.831434i \(-0.312479\pi\)
0.555624 + 0.831434i \(0.312479\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3420.94 5925.24i −0.168878 0.292506i 0.769147 0.639071i \(-0.220681\pi\)
−0.938026 + 0.346565i \(0.887348\pi\)
\(18\) 0 0
\(19\) 13231.5 22917.6i 0.442558 0.766533i −0.555320 0.831636i \(-0.687404\pi\)
0.997879 + 0.0651034i \(0.0207377\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −41328.3 + 71582.8i −0.708273 + 1.22676i 0.257224 + 0.966352i \(0.417192\pi\)
−0.965497 + 0.260413i \(0.916141\pi\)
\(24\) 0 0
\(25\) 2274.86 + 3940.17i 0.0291182 + 0.0504342i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −233335. −1.77659 −0.888295 0.459274i \(-0.848110\pi\)
−0.888295 + 0.459274i \(0.848110\pi\)
\(30\) 0 0
\(31\) 19823.7 + 34335.7i 0.119514 + 0.207005i 0.919575 0.392914i \(-0.128533\pi\)
−0.800061 + 0.599919i \(0.795200\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 223994. + 102073.i 0.883077 + 0.402415i
\(36\) 0 0
\(37\) −115873. + 200699.i −0.376078 + 0.651386i −0.990488 0.137601i \(-0.956061\pi\)
0.614410 + 0.788987i \(0.289394\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 403925. 0.915287 0.457643 0.889136i \(-0.348694\pi\)
0.457643 + 0.889136i \(0.348694\pi\)
\(42\) 0 0
\(43\) −122932. −0.235791 −0.117895 0.993026i \(-0.537615\pi\)
−0.117895 + 0.993026i \(0.537615\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 52674.9 91235.6i 0.0740050 0.128180i −0.826648 0.562719i \(-0.809755\pi\)
0.900653 + 0.434539i \(0.143089\pi\)
\(48\) 0 0
\(49\) −808404. + 157179.i −0.981618 + 0.190857i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −665248. 1.15224e6i −0.613788 1.06311i −0.990596 0.136820i \(-0.956312\pi\)
0.376808 0.926291i \(-0.377022\pi\)
\(54\) 0 0
\(55\) 1.49371e6 1.21059
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 429413. + 743764.i 0.272203 + 0.471469i 0.969426 0.245385i \(-0.0789145\pi\)
−0.697223 + 0.716855i \(0.745581\pi\)
\(60\) 0 0
\(61\) 525507. 910205.i 0.296431 0.513434i −0.678886 0.734244i \(-0.737537\pi\)
0.975317 + 0.220810i \(0.0708701\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.19385e6 2.06780e6i 0.539202 0.933926i
\(66\) 0 0
\(67\) 2.21180e6 + 3.83096e6i 0.898432 + 1.55613i 0.829499 + 0.558508i \(0.188626\pi\)
0.0689321 + 0.997621i \(0.478041\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −154446. −0.0512121 −0.0256060 0.999672i \(-0.508152\pi\)
−0.0256060 + 0.999672i \(0.508152\pi\)
\(72\) 0 0
\(73\) 1.07857e6 + 1.86813e6i 0.324502 + 0.562054i 0.981411 0.191916i \(-0.0614700\pi\)
−0.656910 + 0.753969i \(0.728137\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.06838e6 + 2.90210e6i −1.01556 + 0.724427i
\(78\) 0 0
\(79\) −954414. + 1.65309e6i −0.217792 + 0.377227i −0.954133 0.299384i \(-0.903219\pi\)
0.736341 + 0.676611i \(0.236552\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 8.56018e6 1.64327 0.821637 0.570012i \(-0.193061\pi\)
0.821637 + 0.570012i \(0.193061\pi\)
\(84\) 0 0
\(85\) −1.85584e6 −0.327774
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.54046e6 + 9.59637e6i −0.833069 + 1.44292i 0.0625233 + 0.998044i \(0.480085\pi\)
−0.895593 + 0.444875i \(0.853248\pi\)
\(90\) 0 0
\(91\) 765843. + 7.95153e6i 0.106536 + 1.10613i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.58900e6 6.21634e6i −0.429478 0.743878i
\(96\) 0 0
\(97\) 1.13502e6 0.126270 0.0631352 0.998005i \(-0.479890\pi\)
0.0631352 + 0.998005i \(0.479890\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.16132e6 7.20762e6i −0.401889 0.696092i 0.592065 0.805890i \(-0.298313\pi\)
−0.993954 + 0.109798i \(0.964980\pi\)
\(102\) 0 0
\(103\) −5.20374e6 + 9.01315e6i −0.469230 + 0.812730i −0.999381 0.0351731i \(-0.988802\pi\)
0.530151 + 0.847903i \(0.322135\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.54590e6 + 1.30699e7i −0.595481 + 1.03140i 0.397998 + 0.917386i \(0.369705\pi\)
−0.993479 + 0.114017i \(0.963628\pi\)
\(108\) 0 0
\(109\) 1.33676e7 + 2.31534e7i 0.988694 + 1.71247i 0.624205 + 0.781261i \(0.285423\pi\)
0.364489 + 0.931208i \(0.381244\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −54643.3 −0.00356256 −0.00178128 0.999998i \(-0.500567\pi\)
−0.00178128 + 0.999998i \(0.500567\pi\)
\(114\) 0 0
\(115\) 1.12102e7 + 1.94167e7i 0.687340 + 1.19051i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 5.05472e6 3.60568e6i 0.274968 0.196143i
\(120\) 0 0
\(121\) −5.41890e6 + 9.38582e6i −0.278075 + 0.481641i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.24253e7 1.02696
\(126\) 0 0
\(127\) 2.99538e7 1.29760 0.648798 0.760961i \(-0.275272\pi\)
0.648798 + 0.760961i \(0.275272\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.29309e7 3.97174e7i 0.891191 1.54359i 0.0527416 0.998608i \(-0.483204\pi\)
0.838449 0.544980i \(-0.183463\pi\)
\(132\) 0 0
\(133\) 2.18529e7 + 9.95828e6i 0.805431 + 0.367032i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −1.37558e7 2.38257e7i −0.457049 0.791631i 0.541755 0.840537i \(-0.317760\pi\)
−0.998803 + 0.0489051i \(0.984427\pi\)
\(138\) 0 0
\(139\) 1.41540e7 0.447021 0.223510 0.974702i \(-0.428248\pi\)
0.223510 + 0.974702i \(0.428248\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.42372e7 + 4.19801e7i 0.693117 + 1.20051i
\(144\) 0 0
\(145\) −3.16458e7 + 5.48121e7i −0.862041 + 1.49310i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.57625e7 + 2.73014e7i −0.390367 + 0.676135i −0.992498 0.122262i \(-0.960985\pi\)
0.602131 + 0.798397i \(0.294319\pi\)
\(150\) 0 0
\(151\) −5.45008e6 9.43982e6i −0.128820 0.223123i 0.794400 0.607396i \(-0.207786\pi\)
−0.923220 + 0.384272i \(0.874452\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.07543e7 0.231964
\(156\) 0 0
\(157\) 4.48305e7 + 7.76486e7i 0.924537 + 1.60135i 0.792304 + 0.610127i \(0.208881\pi\)
0.132233 + 0.991219i \(0.457785\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −6.82573e7 3.11046e7i −1.28902 0.587400i
\(162\) 0 0
\(163\) −4.56018e7 + 7.89846e7i −0.824755 + 1.42852i 0.0773509 + 0.997004i \(0.475354\pi\)
−0.902106 + 0.431514i \(0.857980\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −4.72822e7 −0.785579 −0.392789 0.919628i \(-0.628490\pi\)
−0.392789 + 0.919628i \(0.628490\pi\)
\(168\) 0 0
\(169\) 1.47378e7 0.234872
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.07168e7 1.85621e7i 0.157364 0.272562i −0.776553 0.630051i \(-0.783034\pi\)
0.933917 + 0.357489i \(0.116367\pi\)
\(174\) 0 0
\(175\) −3.36129e6 + 2.39771e6i −0.0474103 + 0.0338192i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.11093e7 + 3.65624e7i 0.275099 + 0.476485i 0.970160 0.242465i \(-0.0779561\pi\)
−0.695061 + 0.718951i \(0.744623\pi\)
\(180\) 0 0
\(181\) 4.62466e6 0.0579702 0.0289851 0.999580i \(-0.490772\pi\)
0.0289851 + 0.999580i \(0.490772\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.14304e7 + 5.44390e7i 0.364963 + 0.632134i
\(186\) 0 0
\(187\) 1.88385e7 3.26292e7i 0.210669 0.364889i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.94101e7 + 1.54863e8i −0.928474 + 1.60816i −0.142597 + 0.989781i \(0.545545\pi\)
−0.785877 + 0.618383i \(0.787788\pi\)
\(192\) 0 0
\(193\) 2.05863e7 + 3.56566e7i 0.206124 + 0.357017i 0.950490 0.310754i \(-0.100582\pi\)
−0.744366 + 0.667771i \(0.767248\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.97492e7 0.836370 0.418185 0.908362i \(-0.362666\pi\)
0.418185 + 0.908362i \(0.362666\pi\)
\(198\) 0 0
\(199\) −1.51247e7 2.61968e7i −0.136051 0.235647i 0.789948 0.613174i \(-0.210108\pi\)
−0.925998 + 0.377527i \(0.876774\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.03005e7 2.10775e8i −0.170322 1.76841i
\(204\) 0 0
\(205\) 5.47819e7 9.48850e7i 0.444118 0.769235i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.45726e8 1.10415
\(210\) 0 0
\(211\) 4.15724e7 0.304661 0.152331 0.988330i \(-0.451322\pi\)
0.152331 + 0.988330i \(0.451322\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.66726e7 + 2.88777e7i −0.114411 + 0.198166i
\(216\) 0 0
\(217\) −2.92912e7 + 2.08943e7i −0.194593 + 0.138809i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3.01133e7 5.21577e7i −0.187666 0.325047i
\(222\) 0 0
\(223\) 1.48057e7 0.0894052 0.0447026 0.999000i \(-0.485766\pi\)
0.0447026 + 0.999000i \(0.485766\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −9.63163e7 1.66825e8i −0.546524 0.946607i −0.998509 0.0545820i \(-0.982617\pi\)
0.451985 0.892025i \(-0.350716\pi\)
\(228\) 0 0
\(229\) 1.58823e7 2.75090e7i 0.0873956 0.151374i −0.819014 0.573774i \(-0.805479\pi\)
0.906409 + 0.422400i \(0.138812\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.65294e6 + 4.59502e6i −0.0137398 + 0.0237981i −0.872814 0.488054i \(-0.837707\pi\)
0.859074 + 0.511852i \(0.171040\pi\)
\(234\) 0 0
\(235\) −1.42879e7 2.47474e7i −0.0718178 0.124392i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −5.84527e7 −0.276957 −0.138478 0.990365i \(-0.544221\pi\)
−0.138478 + 0.990365i \(0.544221\pi\)
\(240\) 0 0
\(241\) −1.49460e8 2.58872e8i −0.687803 1.19131i −0.972547 0.232707i \(-0.925242\pi\)
0.284743 0.958604i \(-0.408092\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −7.27163e7 + 2.11217e8i −0.315901 + 0.917589i
\(246\) 0 0
\(247\) 1.16472e8 2.01735e8i 0.491792 0.851808i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2.54841e8 1.01721 0.508606 0.860999i \(-0.330161\pi\)
0.508606 + 0.860999i \(0.330161\pi\)
\(252\) 0 0
\(253\) −4.55175e8 −1.76708
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.67755e8 2.90560e8i 0.616467 1.06775i −0.373659 0.927566i \(-0.621897\pi\)
0.990125 0.140185i \(-0.0447698\pi\)
\(258\) 0 0
\(259\) −1.91375e8 8.72088e7i −0.684440 0.311897i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.52202e8 2.63622e8i −0.515912 0.893585i −0.999829 0.0184718i \(-0.994120\pi\)
0.483918 0.875114i \(-0.339213\pi\)
\(264\) 0 0
\(265\) −3.60894e8 −1.19129
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.75579e8 + 4.77317e8i 0.863204 + 1.49511i 0.868819 + 0.495129i \(0.164879\pi\)
−0.00561523 + 0.999984i \(0.501787\pi\)
\(270\) 0 0
\(271\) 3.05360e8 5.28899e8i 0.932008 1.61429i 0.152124 0.988361i \(-0.451389\pi\)
0.779884 0.625924i \(-0.215278\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.25272e7 + 2.16978e7i −0.0363237 + 0.0629146i
\(276\) 0 0
\(277\) −8.96395e7 1.55260e8i −0.253408 0.438915i 0.711054 0.703137i \(-0.248218\pi\)
−0.964462 + 0.264222i \(0.914885\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.22014e8 −0.328048 −0.164024 0.986456i \(-0.552447\pi\)
−0.164024 + 0.986456i \(0.552447\pi\)
\(282\) 0 0
\(283\) −1.24497e8 2.15635e8i −0.326518 0.565546i 0.655300 0.755368i \(-0.272542\pi\)
−0.981818 + 0.189823i \(0.939209\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.51421e7 + 3.64871e8i 0.0877488 + 0.911071i
\(288\) 0 0
\(289\) 1.81764e8 3.14824e8i 0.442960 0.767229i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −4.74504e8 −1.10205 −0.551027 0.834487i \(-0.685764\pi\)
−0.551027 + 0.834487i \(0.685764\pi\)
\(294\) 0 0
\(295\) 2.32954e8 0.528316
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.63798e8 + 6.30117e8i −0.787067 + 1.36324i
\(300\) 0 0
\(301\) −1.06953e7 1.11046e8i −0.0226053 0.234705i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.42543e8 2.46891e8i −0.287670 0.498260i
\(306\) 0 0
\(307\) 3.83066e8 0.755595 0.377798 0.925888i \(-0.376682\pi\)
0.377798 + 0.925888i \(0.376682\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.36877e8 4.10282e8i −0.446540 0.773431i 0.551618 0.834097i \(-0.314011\pi\)
−0.998158 + 0.0606664i \(0.980677\pi\)
\(312\) 0 0
\(313\) −1.10694e8 + 1.91728e8i −0.204042 + 0.353411i −0.949827 0.312776i \(-0.898741\pi\)
0.745785 + 0.666187i \(0.232075\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.36623e8 4.09843e8i 0.417205 0.722620i −0.578452 0.815716i \(-0.696343\pi\)
0.995657 + 0.0930963i \(0.0296764\pi\)
\(318\) 0 0
\(319\) −6.42466e8 1.11278e9i −1.10811 1.91930i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.81056e8 −0.298954
\(324\) 0 0
\(325\) 2.00248e7 + 3.46839e7i 0.0323575 + 0.0560449i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 8.69970e7 + 3.96442e7i 0.134685 + 0.0613754i
\(330\) 0 0
\(331\) −4.58900e7 + 7.94838e7i −0.0695537 + 0.120471i −0.898705 0.438554i \(-0.855491\pi\)
0.829151 + 0.559024i \(0.188824\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.19989e9 1.74376
\(336\) 0 0
\(337\) 4.12466e8 0.587061 0.293530 0.955950i \(-0.405170\pi\)
0.293530 + 0.955950i \(0.405170\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.09166e8 + 1.89080e8i −0.149089 + 0.258230i
\(342\) 0 0
\(343\) −2.12315e8 7.16567e8i −0.284086 0.958799i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.94162e8 + 8.55913e8i 0.634916 + 1.09971i 0.986533 + 0.163562i \(0.0522985\pi\)
−0.351617 + 0.936144i \(0.614368\pi\)
\(348\) 0 0
\(349\) −1.13371e9 −1.42762 −0.713812 0.700337i \(-0.753033\pi\)
−0.713812 + 0.700337i \(0.753033\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −5.88180e8 1.01876e9i −0.711703 1.23271i −0.964217 0.265113i \(-0.914591\pi\)
0.252514 0.967593i \(-0.418743\pi\)
\(354\) 0 0
\(355\) −2.09466e7 + 3.62805e7i −0.0248493 + 0.0430402i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.65381e8 6.32858e8i 0.416788 0.721898i −0.578827 0.815451i \(-0.696489\pi\)
0.995614 + 0.0935532i \(0.0298225\pi\)
\(360\) 0 0
\(361\) 9.67926e7 + 1.67650e8i 0.108285 + 0.187555i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.85118e8 0.629822
\(366\) 0 0
\(367\) 3.06230e8 + 5.30405e8i 0.323382 + 0.560114i 0.981184 0.193077i \(-0.0618468\pi\)
−0.657802 + 0.753191i \(0.728513\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.82959e8 7.01174e8i 0.999371 0.712882i
\(372\) 0 0
\(373\) −2.75024e8 + 4.76356e8i −0.274404 + 0.475281i −0.969985 0.243167i \(-0.921814\pi\)
0.695581 + 0.718448i \(0.255147\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.05396e9 −1.97423
\(378\) 0 0
\(379\) 1.77173e8 0.167171 0.0835853 0.996501i \(-0.473363\pi\)
0.0835853 + 0.996501i \(0.473363\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.41656e8 2.45356e8i 0.128837 0.223152i −0.794389 0.607409i \(-0.792209\pi\)
0.923226 + 0.384257i \(0.125542\pi\)
\(384\) 0 0
\(385\) 1.29955e8 + 1.34929e9i 0.116060 + 1.20501i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 7.25354e8 + 1.25635e9i 0.624779 + 1.08215i 0.988584 + 0.150673i \(0.0481442\pi\)
−0.363805 + 0.931475i \(0.618523\pi\)
\(390\) 0 0
\(391\) 5.65527e8 0.478448
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 2.58882e8 + 4.48398e8i 0.211355 + 0.366078i
\(396\) 0 0
\(397\) −5.93238e8 + 1.02752e9i −0.475842 + 0.824182i −0.999617 0.0276745i \(-0.991190\pi\)
0.523775 + 0.851856i \(0.324523\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 2.92674e8 5.06926e8i 0.226662 0.392590i −0.730155 0.683282i \(-0.760552\pi\)
0.956817 + 0.290692i \(0.0938854\pi\)
\(402\) 0 0
\(403\) 1.74501e8 + 3.02245e8i 0.132810 + 0.230034i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.27619e9 −0.938283
\(408\) 0 0
\(409\) 1.05156e9 + 1.82135e9i 0.759978 + 1.31632i 0.942861 + 0.333187i \(0.108124\pi\)
−0.182882 + 0.983135i \(0.558543\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.34492e8 + 4.52603e8i −0.443201 + 0.316149i
\(414\) 0 0
\(415\) 1.16096e9 2.01085e9i 0.797353 1.38106i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.71830e9 −1.80530 −0.902648 0.430380i \(-0.858380\pi\)
−0.902648 + 0.430380i \(0.858380\pi\)
\(420\) 0 0
\(421\) 5.29822e8 0.346053 0.173027 0.984917i \(-0.444645\pi\)
0.173027 + 0.984917i \(0.444645\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.55643e7 2.69582e7i 0.00983488 0.0170345i
\(426\) 0 0
\(427\) 8.67919e8 + 3.95508e8i 0.539488 + 0.245843i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.01224e8 + 1.75325e8i 0.0608995 + 0.105481i 0.894868 0.446331i \(-0.147270\pi\)
−0.833968 + 0.551812i \(0.813936\pi\)
\(432\) 0 0
\(433\) −6.56435e8 −0.388584 −0.194292 0.980944i \(-0.562241\pi\)
−0.194292 + 0.980944i \(0.562241\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.09367e9 + 1.89429e9i 0.626904 + 1.08583i
\(438\) 0 0
\(439\) 4.19575e8 7.26724e8i 0.236692 0.409962i −0.723071 0.690774i \(-0.757270\pi\)
0.959763 + 0.280811i \(0.0906035\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.11299e7 + 1.05880e8i −0.0334072 + 0.0578630i −0.882246 0.470789i \(-0.843969\pi\)
0.848838 + 0.528652i \(0.177303\pi\)
\(444\) 0 0
\(445\) 1.50284e9 + 2.60299e9i 0.808448 + 1.40027i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.95736e9 1.02049 0.510244 0.860030i \(-0.329555\pi\)
0.510244 + 0.860030i \(0.329555\pi\)
\(450\) 0 0
\(451\) 1.11217e9 + 1.92633e9i 0.570891 + 0.988812i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.97174e9 + 8.98515e8i 0.981318 + 0.447183i
\(456\) 0 0
\(457\) −1.37930e9 + 2.38901e9i −0.676007 + 1.17088i 0.300167 + 0.953887i \(0.402958\pi\)
−0.976174 + 0.216991i \(0.930376\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.05133e9 −0.499788 −0.249894 0.968273i \(-0.580396\pi\)
−0.249894 + 0.968273i \(0.580396\pi\)
\(462\) 0 0
\(463\) 1.67036e9 0.782127 0.391063 0.920364i \(-0.372107\pi\)
0.391063 + 0.920364i \(0.372107\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.73863e8 1.51357e9i 0.397040 0.687693i −0.596319 0.802747i \(-0.703371\pi\)
0.993359 + 0.115054i \(0.0367041\pi\)
\(468\) 0 0
\(469\) −3.26812e9 + 2.33125e9i −1.46283 + 1.04348i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.38483e8 5.86269e8i −0.147070 0.254732i
\(474\) 0 0
\(475\) 1.20399e8 0.0515460
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −9.61974e8 1.66619e9i −0.399935 0.692707i 0.593783 0.804625i \(-0.297634\pi\)
−0.993717 + 0.111918i \(0.964301\pi\)
\(480\) 0 0
\(481\) −1.01999e9 + 1.76668e9i −0.417916 + 0.723851i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.53935e8 2.66624e8i 0.0612692 0.106121i
\(486\) 0 0
\(487\) 1.71220e9 + 2.96562e9i 0.671743 + 1.16349i 0.977409 + 0.211355i \(0.0677875\pi\)
−0.305666 + 0.952139i \(0.598879\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.92888e9 −1.11665 −0.558325 0.829622i \(-0.688556\pi\)
−0.558325 + 0.829622i \(0.688556\pi\)
\(492\) 0 0
\(493\) 7.98225e8 + 1.38257e9i 0.300028 + 0.519663i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.34370e7 1.39513e8i −0.00490972 0.0509762i
\(498\) 0 0
\(499\) 1.54754e9 2.68042e9i 0.557559 0.965721i −0.440140 0.897929i \(-0.645071\pi\)
0.997699 0.0677918i \(-0.0215953\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.54605e9 0.892029 0.446014 0.895026i \(-0.352843\pi\)
0.446014 + 0.895026i \(0.352843\pi\)
\(504\) 0 0
\(505\) −2.25750e9 −0.780023
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.01304e8 + 1.75463e8i −0.0340496 + 0.0589757i −0.882548 0.470222i \(-0.844174\pi\)
0.848498 + 0.529198i \(0.177507\pi\)
\(510\) 0 0
\(511\) −1.59367e9 + 1.13681e9i −0.528355 + 0.376891i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.41150e9 + 2.44480e9i 0.455362 + 0.788710i
\(516\) 0 0
\(517\) 5.80141e8 0.184636
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −2.74740e9 4.75864e9i −0.851119 1.47418i −0.880199 0.474604i \(-0.842591\pi\)
0.0290803 0.999577i \(-0.490742\pi\)
\(522\) 0 0
\(523\) 1.84283e9 3.19187e9i 0.563286 0.975640i −0.433921 0.900951i \(-0.642870\pi\)
0.997207 0.0746890i \(-0.0237964\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.35632e8 2.34921e8i 0.0403668 0.0699173i
\(528\) 0 0
\(529\) −1.71365e9 2.96813e9i −0.503301 0.871743i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.55560e9 1.01711
\(534\) 0 0
\(535\) 2.04681e9 + 3.54518e9i 0.577882 + 1.00092i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.97546e9 3.42253e9i −0.818452 0.941428i
\(540\) 0 0
\(541\) −7.06594e8 + 1.22386e9i −0.191858 + 0.332308i −0.945866 0.324557i \(-0.894785\pi\)
0.754008 + 0.656865i \(0.228118\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 7.25188e9 1.91895
\(546\) 0 0
\(547\) 5.40167e9 1.41115 0.705574 0.708637i \(-0.250689\pi\)
0.705574 + 0.708637i \(0.250689\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.08736e9 + 5.34747e9i −0.786244 + 1.36181i
\(552\) 0 0
\(553\) −1.57630e9 7.18312e8i −0.396369 0.180624i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −2.85131e9 4.93861e9i −0.699118 1.21091i −0.968772 0.247951i \(-0.920243\pi\)
0.269654 0.962957i \(-0.413091\pi\)
\(558\) 0 0
\(559\) −1.08213e9 −0.262022
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.78880e9 + 4.83035e9i 0.658626 + 1.14077i 0.980972 + 0.194151i \(0.0621952\pi\)
−0.322346 + 0.946622i \(0.604471\pi\)
\(564\) 0 0
\(565\) −7.41094e6 + 1.28361e7i −0.00172864 + 0.00299408i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.19424e9 + 2.06848e9i −0.271767 + 0.470714i −0.969314 0.245824i \(-0.920941\pi\)
0.697547 + 0.716539i \(0.254275\pi\)
\(570\) 0 0
\(571\) −2.78817e9 4.82925e9i −0.626747 1.08556i −0.988200 0.153168i \(-0.951053\pi\)
0.361453 0.932390i \(-0.382281\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.76065e8 −0.0824946
\(576\) 0 0
\(577\) 3.88721e9 + 6.73285e9i 0.842409 + 1.45909i 0.887853 + 0.460128i \(0.152196\pi\)
−0.0454440 + 0.998967i \(0.514470\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 7.44750e8 + 7.73252e9i 0.157541 + 1.63570i
\(582\) 0 0
\(583\) 3.66340e9 6.34519e9i 0.765675 1.32619i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.89217e8 −0.120238 −0.0601190 0.998191i \(-0.519148\pi\)
−0.0601190 + 0.998191i \(0.519148\pi\)
\(588\) 0 0
\(589\) 1.04919e9 0.211568
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.58290e8 + 1.48660e9i −0.169022 + 0.292754i −0.938076 0.346429i \(-0.887394\pi\)
0.769054 + 0.639183i \(0.220727\pi\)
\(594\) 0 0
\(595\) −1.61461e8 1.67641e9i −0.0314238 0.326265i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.84213e9 6.65477e9i −0.730430 1.26514i −0.956700 0.291076i \(-0.905987\pi\)
0.226270 0.974065i \(-0.427347\pi\)
\(600\) 0 0
\(601\) −1.01577e10 −1.90869 −0.954344 0.298709i \(-0.903444\pi\)
−0.954344 + 0.298709i \(0.903444\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.46986e9 + 2.54588e9i 0.269857 + 0.467406i
\(606\) 0 0
\(607\) 1.12929e9 1.95598e9i 0.204948 0.354981i −0.745168 0.666877i \(-0.767631\pi\)
0.950116 + 0.311896i \(0.100964\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.63678e8 8.03113e8i 0.0822379 0.142440i
\(612\) 0 0
\(613\) −3.16951e9 5.48975e9i −0.555752 0.962590i −0.997845 0.0656207i \(-0.979097\pi\)
0.442093 0.896969i \(-0.354236\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.51460e9 −1.11658 −0.558290 0.829646i \(-0.688542\pi\)
−0.558290 + 0.829646i \(0.688542\pi\)
\(618\) 0 0
\(619\) −4.99392e9 8.64972e9i −0.846299 1.46583i −0.884488 0.466563i \(-0.845492\pi\)
0.0381887 0.999271i \(-0.487841\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −9.15055e9 4.16987e9i −1.51614 0.690899i
\(624\) 0 0
\(625\) 2.86368e9 4.96005e9i 0.469186 0.812654i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.58558e9 0.254046
\(630\) 0 0
\(631\) −6.90293e8 −0.109378 −0.0546891 0.998503i \(-0.517417\pi\)
−0.0546891 + 0.998503i \(0.517417\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.06245e9 7.03637e9i 0.629622 1.09054i
\(636\) 0 0
\(637\) −7.11609e9 + 1.38359e9i −1.09082 + 0.212090i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 4.03158e8 + 6.98291e8i 0.0604606 + 0.104721i 0.894671 0.446725i \(-0.147410\pi\)
−0.834211 + 0.551446i \(0.814076\pi\)
\(642\) 0 0
\(643\) −7.24540e9 −1.07479 −0.537395 0.843331i \(-0.680592\pi\)
−0.537395 + 0.843331i \(0.680592\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.06148e9 + 8.76675e9i 0.734705 + 1.27255i 0.954853 + 0.297079i \(0.0960126\pi\)
−0.220148 + 0.975466i \(0.570654\pi\)
\(648\) 0 0
\(649\) −2.36469e9 + 4.09577e9i −0.339562 + 0.588138i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.23757e9 + 9.07174e9i −0.736095 + 1.27495i 0.218146 + 0.975916i \(0.429999\pi\)
−0.954241 + 0.299038i \(0.903334\pi\)
\(654\) 0 0
\(655\) −6.21994e9 1.07733e10i −0.864852 1.49797i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.86587e9 0.798424 0.399212 0.916859i \(-0.369284\pi\)
0.399212 + 0.916859i \(0.369284\pi\)
\(660\) 0 0
\(661\) 3.88047e9 + 6.72116e9i 0.522611 + 0.905189i 0.999654 + 0.0263091i \(0.00837541\pi\)
−0.477043 + 0.878880i \(0.658291\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 5.30305e9 3.78282e9i 0.699278 0.498816i
\(666\) 0 0
\(667\) 9.64335e9 1.67028e10i 1.25831 2.17946i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 5.78774e9 0.739571
\(672\) 0 0
\(673\) 3.37850e9 0.427239 0.213620 0.976917i \(-0.431475\pi\)
0.213620 + 0.976917i \(0.431475\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.21681e9 1.24999e10i 0.893891 1.54827i 0.0587208 0.998274i \(-0.481298\pi\)
0.835171 0.549991i \(-0.185369\pi\)
\(678\) 0 0
\(679\) 9.87483e7 + 1.02528e9i 0.0121056 + 0.125689i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.49427e9 + 2.58816e9i 0.179456 + 0.310827i 0.941694 0.336470i \(-0.109233\pi\)
−0.762238 + 0.647296i \(0.775900\pi\)
\(684\) 0 0
\(685\) −7.46243e9 −0.887081
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.85594e9 1.01428e10i −0.682070 1.18138i
\(690\) 0 0
\(691\) 5.72440e9 9.91495e9i 0.660019 1.14319i −0.320591 0.947218i \(-0.603881\pi\)
0.980610 0.195969i \(-0.0627852\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.91962e9 3.32488e9i 0.216904 0.375690i
\(696\) 0 0
\(697\) −1.38180e9 2.39335e9i −0.154572 0.267727i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.77015e9 0.303732 0.151866 0.988401i \(-0.451472\pi\)
0.151866 + 0.988401i \(0.451472\pi\)
\(702\) 0 0
\(703\) 3.06635e9 + 5.31107e9i 0.332873 + 0.576552i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.14869e9 4.38605e9i 0.654357 0.466773i
\(708\) 0 0
\(709\) 9.01249e8 1.56101e9i 0.0949692 0.164492i −0.814627 0.579986i \(-0.803058\pi\)
0.909596 + 0.415494i \(0.136391\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.27713e9 −0.338595
\(714\) 0 0
\(715\) 1.31486e10 1.34526
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −4.56454e9 + 7.90602e9i −0.457979 + 0.793244i −0.998854 0.0478595i \(-0.984760\pi\)
0.540875 + 0.841103i \(0.318093\pi\)
\(720\) 0 0
\(721\) −8.59442e9 3.91645e9i −0.853972 0.389152i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −5.30805e8 9.19381e8i −0.0517311 0.0896009i
\(726\) 0 0
\(727\) −1.21081e10 −1.16871 −0.584354 0.811499i \(-0.698652\pi\)
−0.584354 + 0.811499i \(0.698652\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.20544e8 + 7.28404e8i 0.0398200 + 0.0689702i
\(732\) 0 0
\(733\) 6.82100e9 1.18143e10i 0.639711 1.10801i −0.345785 0.938314i \(-0.612387\pi\)
0.985496 0.169699i \(-0.0542795\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.21800e10 + 2.10964e10i −1.12076 + 1.94121i
\(738\) 0 0
\(739\) −2.37583e9 4.11506e9i −0.216551 0.375077i 0.737200 0.675674i \(-0.236147\pi\)
−0.953751 + 0.300597i \(0.902814\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.47115e9 −0.399907 −0.199953 0.979805i \(-0.564079\pi\)
−0.199953 + 0.979805i \(0.564079\pi\)
\(744\) 0 0
\(745\) 4.27554e9 + 7.40545e9i 0.378830 + 0.656152i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.24627e10 5.67921e9i −1.08374 0.493857i
\(750\) 0 0
\(751\) 7.08632e9 1.22739e10i 0.610494 1.05741i −0.380663 0.924714i \(-0.624304\pi\)
0.991157 0.132693i \(-0.0423623\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.95664e9 −0.250026
\(756\) 0 0
\(757\) −1.37310e10 −1.15045 −0.575223 0.817997i \(-0.695085\pi\)
−0.575223 + 0.817997i \(0.695085\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.17090e8 + 5.49216e8i −0.0260817 + 0.0451749i −0.878772 0.477242i \(-0.841636\pi\)
0.852690 + 0.522417i \(0.174970\pi\)
\(762\) 0 0
\(763\) −1.97518e10 + 1.40895e10i −1.60979 + 1.14831i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.77996e9 + 6.54709e9i 0.302485 + 0.523919i
\(768\) 0 0
\(769\) 8.38079e9 0.664573 0.332287 0.943178i \(-0.392180\pi\)
0.332287 + 0.943178i \(0.392180\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.91233e9 6.77635e9i −0.304654 0.527676i 0.672530 0.740070i \(-0.265207\pi\)
−0.977184 + 0.212393i \(0.931874\pi\)
\(774\) 0 0
\(775\) −9.01925e7 + 1.56218e8i −0.00696008 + 0.0120552i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 5.34452e9 9.25698e9i 0.405068 0.701598i
\(780\) 0 0
\(781\) −4.25252e8 7.36559e8i −0.0319425 0.0553260i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.43203e10 1.79443
\(786\) 0 0
\(787\) 1.28524e10 + 2.22609e10i 0.939878 + 1.62792i 0.765696 + 0.643202i \(0.222395\pi\)
0.174181 + 0.984714i \(0.444272\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.75406e6 4.93600e7i −0.000341544 0.00354615i
\(792\) 0 0
\(793\) 4.62585e9 8.01220e9i