Properties

Label 252.8.k.e.37.7
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 37.7
Root \(68.2530 - 118.218i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.8.k.e.109.7

$q$-expansion

\(f(q)\) \(=\) \(q+(161.248 - 279.290i) q^{5} +(-882.807 + 210.227i) q^{7} +O(q^{10})\) \(q+(161.248 - 279.290i) q^{5} +(-882.807 + 210.227i) q^{7} +(-43.6956 - 75.6830i) q^{11} -9602.23 q^{13} +(16188.6 + 28039.5i) q^{17} +(-477.164 + 826.473i) q^{19} +(-4780.44 + 8279.97i) q^{23} +(-12939.6 - 22412.0i) q^{25} +210126. q^{29} +(20813.0 + 36049.2i) q^{31} +(-83636.7 + 280458. i) q^{35} +(-13999.4 + 24247.7i) q^{37} -296416. q^{41} +496225. q^{43} +(308439. - 534233. i) q^{47} +(735152. - 371180. i) q^{49} +(-299978. - 519577. i) q^{53} -28183.4 q^{55} +(-1.20550e6 - 2.08799e6i) q^{59} +(-539414. + 934292. i) q^{61} +(-1.54834e6 + 2.68181e6i) q^{65} +(-1.37198e6 - 2.37633e6i) q^{67} +2.21738e6 q^{71} +(1.33265e6 + 2.30822e6i) q^{73} +(54485.4 + 57627.4i) q^{77} +(1.44755e6 - 2.50723e6i) q^{79} +3.60576e6 q^{83} +1.04415e7 q^{85} +(-466027. + 807183. i) q^{89} +(8.47691e6 - 2.01865e6i) q^{91} +(153884. + 266535. i) q^{95} +1.21978e7 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 1680q^{7} + O(q^{10}) \) \( 16q + 1680q^{7} - 28280q^{13} + 42224q^{19} - 80460q^{25} + 164752q^{31} - 647980q^{37} + 1341440q^{43} + 230104q^{49} - 323120q^{55} - 4319336q^{61} - 3905760q^{67} + 6471780q^{73} - 6093104q^{79} + 456400q^{85} + 15969856q^{91} - 27141240q^{97} + O(q^{100}) \)

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
\(5\) 161.248 279.290i 0.576900 0.999220i −0.418933 0.908017i \(-0.637596\pi\)
0.995832 0.0912024i \(-0.0290710\pi\)
\(6\) 0 0
\(7\) −882.807 + 210.227i −0.972797 + 0.231657i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −43.6956 75.6830i −0.00989836 0.0171445i 0.861034 0.508548i \(-0.169817\pi\)
−0.870932 + 0.491403i \(0.836484\pi\)
\(12\) 0 0
\(13\) −9602.23 −1.21219 −0.606095 0.795392i \(-0.707265\pi\)
−0.606095 + 0.795392i \(0.707265\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 16188.6 + 28039.5i 0.799168 + 1.38420i 0.920158 + 0.391546i \(0.128060\pi\)
−0.120990 + 0.992654i \(0.538607\pi\)
\(18\) 0 0
\(19\) −477.164 + 826.473i −0.0159599 + 0.0276434i −0.873895 0.486115i \(-0.838414\pi\)
0.857935 + 0.513758i \(0.171747\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4780.44 + 8279.97i −0.0819258 + 0.141900i −0.904077 0.427369i \(-0.859440\pi\)
0.822151 + 0.569269i \(0.192774\pi\)
\(24\) 0 0
\(25\) −12939.6 22412.0i −0.165627 0.286874i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 210126. 1.59988 0.799938 0.600083i \(-0.204866\pi\)
0.799938 + 0.600083i \(0.204866\pi\)
\(30\) 0 0
\(31\) 20813.0 + 36049.2i 0.125478 + 0.217335i 0.921920 0.387381i \(-0.126620\pi\)
−0.796441 + 0.604716i \(0.793287\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −83636.7 + 280458.i −0.329730 + 1.10568i
\(36\) 0 0
\(37\) −13999.4 + 24247.7i −0.0454363 + 0.0786980i −0.887849 0.460135i \(-0.847801\pi\)
0.842413 + 0.538833i \(0.181134\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −296416. −0.671674 −0.335837 0.941920i \(-0.609019\pi\)
−0.335837 + 0.941920i \(0.609019\pi\)
\(42\) 0 0
\(43\) 496225. 0.951784 0.475892 0.879504i \(-0.342125\pi\)
0.475892 + 0.879504i \(0.342125\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 308439. 534233.i 0.433339 0.750564i −0.563820 0.825898i \(-0.690669\pi\)
0.997158 + 0.0753335i \(0.0240021\pi\)
\(48\) 0 0
\(49\) 735152. 371180.i 0.892670 0.450711i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −299978. 519577.i −0.276773 0.479385i 0.693808 0.720160i \(-0.255932\pi\)
−0.970581 + 0.240775i \(0.922598\pi\)
\(54\) 0 0
\(55\) −28183.4 −0.0228414
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.20550e6 2.08799e6i −0.764161 1.32357i −0.940689 0.339270i \(-0.889820\pi\)
0.176528 0.984296i \(-0.443513\pi\)
\(60\) 0 0
\(61\) −539414. + 934292.i −0.304276 + 0.527021i −0.977100 0.212781i \(-0.931748\pi\)
0.672824 + 0.739803i \(0.265081\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.54834e6 + 2.68181e6i −0.699312 + 1.21124i
\(66\) 0 0
\(67\) −1.37198e6 2.37633e6i −0.557294 0.965262i −0.997721 0.0674736i \(-0.978506\pi\)
0.440427 0.897789i \(-0.354827\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.21738e6 0.735253 0.367626 0.929974i \(-0.380171\pi\)
0.367626 + 0.929974i \(0.380171\pi\)
\(72\) 0 0
\(73\) 1.33265e6 + 2.30822e6i 0.400947 + 0.694461i 0.993840 0.110820i \(-0.0353477\pi\)
−0.592893 + 0.805281i \(0.702014\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 54485.4 + 57627.4i 0.0136007 + 0.0143851i
\(78\) 0 0
\(79\) 1.44755e6 2.50723e6i 0.330323 0.572136i −0.652252 0.758002i \(-0.726176\pi\)
0.982575 + 0.185866i \(0.0595090\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 3.60576e6 0.692188 0.346094 0.938200i \(-0.387508\pi\)
0.346094 + 0.938200i \(0.387508\pi\)
\(84\) 0 0
\(85\) 1.04415e7 1.84416
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −466027. + 807183.i −0.0700723 + 0.121369i −0.898933 0.438087i \(-0.855656\pi\)
0.828860 + 0.559455i \(0.188990\pi\)
\(90\) 0 0
\(91\) 8.47691e6 2.01865e6i 1.17921 0.280812i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 153884. + 266535.i 0.0184145 + 0.0318949i
\(96\) 0 0
\(97\) 1.21978e7 1.35700 0.678499 0.734601i \(-0.262631\pi\)
0.678499 + 0.734601i \(0.262631\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 9.43499e6 + 1.63419e7i 0.911206 + 1.57826i 0.812362 + 0.583153i \(0.198181\pi\)
0.0988441 + 0.995103i \(0.468485\pi\)
\(102\) 0 0
\(103\) 4.96997e6 8.60824e6i 0.448150 0.776219i −0.550116 0.835089i \(-0.685416\pi\)
0.998266 + 0.0588698i \(0.0187497\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.52906e6 4.38047e6i 0.199580 0.345682i −0.748812 0.662782i \(-0.769376\pi\)
0.948392 + 0.317100i \(0.102709\pi\)
\(108\) 0 0
\(109\) 3.82903e6 + 6.63207e6i 0.283202 + 0.490520i 0.972171 0.234270i \(-0.0752701\pi\)
−0.688970 + 0.724790i \(0.741937\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.32872e7 −0.866284 −0.433142 0.901326i \(-0.642595\pi\)
−0.433142 + 0.901326i \(0.642595\pi\)
\(114\) 0 0
\(115\) 1.54168e6 + 2.67026e6i 0.0945259 + 0.163724i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.01861e7 2.13502e7i −1.09809 1.16141i
\(120\) 0 0
\(121\) 9.73977e6 1.68698e7i 0.499804 0.865686i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.68491e7 0.771599
\(126\) 0 0
\(127\) 2.32145e7 1.00565 0.502824 0.864389i \(-0.332295\pi\)
0.502824 + 0.864389i \(0.332295\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 5.08126e6 8.80099e6i 0.197479 0.342044i −0.750231 0.661176i \(-0.770058\pi\)
0.947710 + 0.319131i \(0.103391\pi\)
\(132\) 0 0
\(133\) 247497. 829928.i 0.00912197 0.0305886i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.08111e7 3.60459e7i −0.691470 1.19766i −0.971356 0.237629i \(-0.923630\pi\)
0.279886 0.960033i \(-0.409703\pi\)
\(138\) 0 0
\(139\) 4.76834e7 1.50597 0.752983 0.658040i \(-0.228614\pi\)
0.752983 + 0.658040i \(0.228614\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 419575. + 726725.i 0.0119987 + 0.0207823i
\(144\) 0 0
\(145\) 3.38824e7 5.86861e7i 0.922968 1.59863i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.92202e7 + 6.79315e7i −0.971311 + 1.68236i −0.279704 + 0.960086i \(0.590236\pi\)
−0.691607 + 0.722274i \(0.743097\pi\)
\(150\) 0 0
\(151\) 3.04543e7 + 5.27484e7i 0.719829 + 1.24678i 0.961067 + 0.276314i \(0.0891129\pi\)
−0.241239 + 0.970466i \(0.577554\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.34243e7 0.289554
\(156\) 0 0
\(157\) 9.46578e6 + 1.63952e7i 0.195213 + 0.338118i 0.946970 0.321321i \(-0.104127\pi\)
−0.751758 + 0.659440i \(0.770794\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.47953e6 8.31459e6i 0.0468251 0.157018i
\(162\) 0 0
\(163\) 3.34950e7 5.80150e7i 0.605791 1.04926i −0.386134 0.922442i \(-0.626190\pi\)
0.991926 0.126819i \(-0.0404767\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 8.86629e7 1.47311 0.736553 0.676380i \(-0.236452\pi\)
0.736553 + 0.676380i \(0.236452\pi\)
\(168\) 0 0
\(169\) 2.94543e7 0.469403
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.44990e7 2.51130e7i 0.212900 0.368754i −0.739721 0.672914i \(-0.765042\pi\)
0.952621 + 0.304160i \(0.0983758\pi\)
\(174\) 0 0
\(175\) 1.61348e7 + 1.70652e7i 0.227578 + 0.240702i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 3.19272e6 + 5.52995e6i 0.0416079 + 0.0720669i 0.886079 0.463534i \(-0.153419\pi\)
−0.844472 + 0.535600i \(0.820085\pi\)
\(180\) 0 0
\(181\) 8.45188e7 1.05944 0.529722 0.848171i \(-0.322296\pi\)
0.529722 + 0.848171i \(0.322296\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.51476e6 + 7.81980e6i 0.0524244 + 0.0908018i
\(186\) 0 0
\(187\) 1.41474e6 2.45040e6i 0.0158209 0.0274026i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.05189e7 + 1.39463e8i −0.836143 + 1.44824i 0.0569526 + 0.998377i \(0.481862\pi\)
−0.893096 + 0.449866i \(0.851472\pi\)
\(192\) 0 0
\(193\) −1.72082e7 2.98055e7i −0.172300 0.298433i 0.766923 0.641739i \(-0.221787\pi\)
−0.939224 + 0.343306i \(0.888453\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.97894e8 1.84417 0.922086 0.386984i \(-0.126483\pi\)
0.922086 + 0.386984i \(0.126483\pi\)
\(198\) 0 0
\(199\) −2.63954e7 4.57181e7i −0.237434 0.411247i 0.722544 0.691325i \(-0.242973\pi\)
−0.959977 + 0.280078i \(0.909640\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.85500e8 + 4.41741e7i −1.55636 + 0.370623i
\(204\) 0 0
\(205\) −4.77967e7 + 8.27863e7i −0.387489 + 0.671150i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 83399.9 0.000631907
\(210\) 0 0
\(211\) −2.95945e7 −0.216881 −0.108441 0.994103i \(-0.534586\pi\)
−0.108441 + 0.994103i \(0.534586\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.00154e7 1.38591e8i 0.549084 0.951042i
\(216\) 0 0
\(217\) −2.59524e7 2.74490e7i −0.172412 0.182355i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.55447e8 2.69242e8i −0.968743 1.67791i
\(222\) 0 0
\(223\) −2.98299e8 −1.80130 −0.900649 0.434548i \(-0.856908\pi\)
−0.900649 + 0.434548i \(0.856908\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.54487e7 + 9.60399e7i 0.314630 + 0.544956i 0.979359 0.202129i \(-0.0647861\pi\)
−0.664728 + 0.747085i \(0.731453\pi\)
\(228\) 0 0
\(229\) −9.28527e7 + 1.60826e8i −0.510940 + 0.884975i 0.488979 + 0.872295i \(0.337369\pi\)
−0.999920 + 0.0126792i \(0.995964\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 697526. 1.20815e6i 0.00361256 0.00625713i −0.864213 0.503125i \(-0.832183\pi\)
0.867826 + 0.496868i \(0.165517\pi\)
\(234\) 0 0
\(235\) −9.94707e7 1.72288e8i −0.499986 0.866001i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.85224e8 −1.35143 −0.675716 0.737162i \(-0.736165\pi\)
−0.675716 + 0.737162i \(0.736165\pi\)
\(240\) 0 0
\(241\) 1.06726e8 + 1.84854e8i 0.491145 + 0.850688i 0.999948 0.0101950i \(-0.00324521\pi\)
−0.508803 + 0.860883i \(0.669912\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.48751e7 2.65173e8i 0.0646218 1.15199i
\(246\) 0 0
\(247\) 4.58184e6 7.93598e6i 0.0193464 0.0335090i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.82490e8 0.728418 0.364209 0.931317i \(-0.381339\pi\)
0.364209 + 0.931317i \(0.381339\pi\)
\(252\) 0 0
\(253\) 835537. 0.00324372
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.34416e8 + 2.32816e8i −0.493954 + 0.855554i −0.999976 0.00696714i \(-0.997782\pi\)
0.506022 + 0.862521i \(0.331116\pi\)
\(258\) 0 0
\(259\) 7.26124e6 2.43491e7i 0.0259694 0.0870829i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.36464e8 + 2.36362e8i 0.462564 + 0.801184i 0.999088 0.0427009i \(-0.0135962\pi\)
−0.536524 + 0.843885i \(0.680263\pi\)
\(264\) 0 0
\(265\) −1.93484e8 −0.638681
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.53736e7 + 9.59099e7i 0.173448 + 0.300421i 0.939623 0.342211i \(-0.111176\pi\)
−0.766175 + 0.642632i \(0.777842\pi\)
\(270\) 0 0
\(271\) −1.66967e8 + 2.89195e8i −0.509609 + 0.882669i 0.490329 + 0.871537i \(0.336877\pi\)
−0.999938 + 0.0111314i \(0.996457\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.13081e6 + 1.95861e6i −0.00327887 + 0.00567916i
\(276\) 0 0
\(277\) −9.31294e7 1.61305e8i −0.263274 0.456003i 0.703836 0.710362i \(-0.251469\pi\)
−0.967110 + 0.254359i \(0.918136\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.16721e7 −0.219584 −0.109792 0.993955i \(-0.535019\pi\)
−0.109792 + 0.993955i \(0.535019\pi\)
\(282\) 0 0
\(283\) −1.70894e8 2.95998e8i −0.448204 0.776311i 0.550066 0.835121i \(-0.314603\pi\)
−0.998269 + 0.0588101i \(0.981269\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.61678e8 6.23148e7i 0.653403 0.155598i
\(288\) 0 0
\(289\) −3.18973e8 + 5.52477e8i −0.777340 + 1.34639i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.40002e8 0.557415 0.278707 0.960376i \(-0.410094\pi\)
0.278707 + 0.960376i \(0.410094\pi\)
\(294\) 0 0
\(295\) −7.77539e8 −1.76338
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.59029e7 7.95062e7i 0.0993096 0.172009i
\(300\) 0 0
\(301\) −4.38070e8 + 1.04320e8i −0.925894 + 0.220488i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.73959e8 + 3.01306e8i 0.351073 + 0.608077i
\(306\) 0 0
\(307\) −8.27000e8 −1.63125 −0.815626 0.578579i \(-0.803607\pi\)
−0.815626 + 0.578579i \(0.803607\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.02576e7 + 5.24076e7i 0.0570391 + 0.0987946i 0.893135 0.449789i \(-0.148501\pi\)
−0.836096 + 0.548583i \(0.815167\pi\)
\(312\) 0 0
\(313\) −6.22813e7 + 1.07874e8i −0.114803 + 0.198844i −0.917701 0.397272i \(-0.869957\pi\)
0.802898 + 0.596116i \(0.203290\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.75504e7 6.50392e7i 0.0662075 0.114675i −0.831021 0.556240i \(-0.812243\pi\)
0.897229 + 0.441566i \(0.145577\pi\)
\(318\) 0 0
\(319\) −9.18157e6 1.59029e7i −0.0158361 0.0274290i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.08985e7 −0.0510186
\(324\) 0 0
\(325\) 1.24249e8 + 2.15206e8i 0.200771 + 0.347746i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.59982e8 + 5.36466e8i −0.247677 + 0.830533i
\(330\) 0 0
\(331\) 3.52636e8 6.10784e8i 0.534477 0.925741i −0.464712 0.885462i \(-0.653842\pi\)
0.999188 0.0402790i \(-0.0128247\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.84916e8 −1.28601
\(336\) 0 0
\(337\) 6.97886e7 0.0993299 0.0496649 0.998766i \(-0.484185\pi\)
0.0496649 + 0.998766i \(0.484185\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.81887e6 3.15038e6i 0.00248406 0.00430252i
\(342\) 0 0
\(343\) −5.70965e8 + 4.82229e8i −0.763977 + 0.645244i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.10440e8 5.37698e8i −0.398863 0.690852i 0.594723 0.803931i \(-0.297262\pi\)
−0.993586 + 0.113079i \(0.963929\pi\)
\(348\) 0 0
\(349\) 8.33992e8 1.05020 0.525101 0.851040i \(-0.324028\pi\)
0.525101 + 0.851040i \(0.324028\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −4.88369e8 8.45880e8i −0.590931 1.02352i −0.994107 0.108400i \(-0.965427\pi\)
0.403177 0.915122i \(-0.367906\pi\)
\(354\) 0 0
\(355\) 3.57550e8 6.19294e8i 0.424167 0.734679i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.02310e8 1.38964e9i 0.915191 1.58516i 0.108570 0.994089i \(-0.465373\pi\)
0.806621 0.591069i \(-0.201294\pi\)
\(360\) 0 0
\(361\) 4.46480e8 + 7.73327e8i 0.499491 + 0.865143i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 8.59553e8 0.925226
\(366\) 0 0
\(367\) −4.20508e7 7.28341e7i −0.0444061 0.0769136i 0.842968 0.537964i \(-0.180806\pi\)
−0.887374 + 0.461050i \(0.847473\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.74051e8 + 3.95622e8i 0.380297 + 0.402228i
\(372\) 0 0
\(373\) 1.20538e8 2.08778e8i 0.120266 0.208307i −0.799607 0.600524i \(-0.794959\pi\)
0.919873 + 0.392218i \(0.128292\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.01768e9 −1.93935
\(378\) 0 0
\(379\) 1.81829e8 0.171564 0.0857818 0.996314i \(-0.472661\pi\)
0.0857818 + 0.996314i \(0.472661\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.76485e8 + 4.78886e8i −0.251464 + 0.435548i −0.963929 0.266159i \(-0.914245\pi\)
0.712465 + 0.701708i \(0.247579\pi\)
\(384\) 0 0
\(385\) 2.48805e7 5.92491e6i 0.0222201 0.00529138i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 6.08116e8 + 1.05329e9i 0.523797 + 0.907242i 0.999616 + 0.0276994i \(0.00881811\pi\)
−0.475820 + 0.879543i \(0.657849\pi\)
\(390\) 0 0
\(391\) −3.09555e8 −0.261890
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.66830e8 8.08574e8i −0.381127 0.660131i
\(396\) 0 0
\(397\) 4.75231e8 8.23124e8i 0.381187 0.660235i −0.610046 0.792366i \(-0.708849\pi\)
0.991232 + 0.132132i \(0.0421822\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.92679e8 + 5.06935e8i −0.226666 + 0.392597i −0.956818 0.290688i \(-0.906116\pi\)
0.730152 + 0.683285i \(0.239449\pi\)
\(402\) 0 0
\(403\) −1.99851e8 3.46153e8i −0.152104 0.263451i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.44685e6 0.00179898
\(408\) 0 0
\(409\) 8.82474e8 + 1.52849e9i 0.637779 + 1.10467i 0.985919 + 0.167224i \(0.0534802\pi\)
−0.348140 + 0.937443i \(0.613186\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.50317e9 + 1.58986e9i 1.04999 + 1.11054i
\(414\) 0 0
\(415\) 5.81424e8 1.00706e9i 0.399323 0.691648i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.29170e9 0.857849 0.428925 0.903340i \(-0.358893\pi\)
0.428925 + 0.903340i \(0.358893\pi\)
\(420\) 0 0
\(421\) 1.69525e9 1.10725 0.553626 0.832765i \(-0.313244\pi\)
0.553626 + 0.832765i \(0.313244\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.18948e8 7.25639e8i 0.264727 0.458521i
\(426\) 0 0
\(427\) 2.79784e8 9.38199e8i 0.173911 0.583173i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 9.23276e8 + 1.59916e9i 0.555471 + 0.962103i 0.997867 + 0.0652836i \(0.0207952\pi\)
−0.442396 + 0.896820i \(0.645871\pi\)
\(432\) 0 0
\(433\) 1.12073e9 0.663425 0.331713 0.943381i \(-0.392374\pi\)
0.331713 + 0.943381i \(0.392374\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.56211e6 7.90181e6i −0.00261506 0.00452941i
\(438\) 0 0
\(439\) 1.16071e8 2.01041e8i 0.0654783 0.113412i −0.831428 0.555633i \(-0.812476\pi\)
0.896906 + 0.442221i \(0.145809\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.09581e8 8.82620e8i 0.278484 0.482348i −0.692524 0.721395i \(-0.743501\pi\)
0.971008 + 0.239046i \(0.0768348\pi\)
\(444\) 0 0
\(445\) 1.50292e8 + 2.60314e8i 0.0808494 + 0.140035i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.68146e9 −1.39801 −0.699004 0.715118i \(-0.746373\pi\)
−0.699004 + 0.715118i \(0.746373\pi\)
\(450\) 0 0
\(451\) 1.29521e7 + 2.24337e7i 0.00664847 + 0.0115155i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.03099e8 2.69303e9i 0.399696 1.34030i
\(456\) 0 0
\(457\) 1.16628e9 2.02005e9i 0.571605 0.990048i −0.424797 0.905289i \(-0.639654\pi\)
0.996401 0.0847596i \(-0.0270122\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 8.24417e8 0.391917 0.195958 0.980612i \(-0.437218\pi\)
0.195958 + 0.980612i \(0.437218\pi\)
\(462\) 0 0
\(463\) 3.26057e9 1.52672 0.763361 0.645972i \(-0.223548\pi\)
0.763361 + 0.645972i \(0.223548\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.09827e9 + 3.63431e9i −0.953350 + 1.65125i −0.215250 + 0.976559i \(0.569057\pi\)
−0.738100 + 0.674691i \(0.764277\pi\)
\(468\) 0 0
\(469\) 1.71076e9 + 1.80941e9i 0.765744 + 0.809903i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −2.16828e7 3.75557e7i −0.00942110 0.0163178i
\(474\) 0 0
\(475\) 2.46972e7 0.0105736
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 1.32849e9 + 2.30101e9i 0.552310 + 0.956629i 0.998107 + 0.0614949i \(0.0195868\pi\)
−0.445798 + 0.895134i \(0.647080\pi\)
\(480\) 0 0
\(481\) 1.34425e8 2.32832e8i 0.0550774 0.0953969i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.96687e9 3.40672e9i 0.782852 1.35594i
\(486\) 0 0
\(487\) −2.31794e9 4.01480e9i −0.909393 1.57512i −0.814909 0.579589i \(-0.803213\pi\)
−0.0944840 0.995526i \(-0.530120\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.02935e9 −0.392442 −0.196221 0.980560i \(-0.562867\pi\)
−0.196221 + 0.980560i \(0.562867\pi\)
\(492\) 0 0
\(493\) 3.40164e9 + 5.89182e9i 1.27857 + 2.21455i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.95752e9 + 4.66154e8i −0.715252 + 0.170327i
\(498\) 0 0
\(499\) 1.39539e9 2.41689e9i 0.502741 0.870773i −0.497254 0.867605i \(-0.665658\pi\)
0.999995 0.00316767i \(-0.00100830\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −4.48508e9 −1.57138 −0.785691 0.618619i \(-0.787692\pi\)
−0.785691 + 0.618619i \(0.787692\pi\)
\(504\) 0 0
\(505\) 6.08551e9 2.10270
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.02092e9 3.50034e9i 0.679262 1.17652i −0.295941 0.955206i \(-0.595633\pi\)
0.975203 0.221310i \(-0.0710333\pi\)
\(510\) 0 0
\(511\) −1.66173e9 1.75756e9i −0.550917 0.582688i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.60280e9 2.77613e9i −0.517075 0.895601i
\(516\) 0 0
\(517\) −5.39097e7 −0.0171574
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.08982e9 1.88762e9i −0.337615 0.584766i 0.646369 0.763025i \(-0.276287\pi\)
−0.983984 + 0.178259i \(0.942954\pi\)
\(522\) 0 0
\(523\) 1.02819e9 1.78088e9i 0.314281 0.544351i −0.665003 0.746841i \(-0.731570\pi\)
0.979284 + 0.202489i \(0.0649032\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −6.73867e8 + 1.16717e9i −0.200557 + 0.347374i
\(528\) 0 0
\(529\) 1.65671e9 + 2.86950e9i 0.486576 + 0.842775i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2.84626e9 0.814196
\(534\) 0 0
\(535\) −8.15615e8 1.41269e9i −0.230275 0.398848i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −6.02149e7 3.94196e7i −0.0165632 0.0108430i
\(540\) 0 0
\(541\) 6.39017e8 1.10681e9i 0.173509 0.300526i −0.766135 0.642679i \(-0.777823\pi\)
0.939644 + 0.342153i \(0.111156\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.46970e9 0.653516
\(546\) 0 0
\(547\) −6.28942e9 −1.64307 −0.821533 0.570161i \(-0.806881\pi\)
−0.821533 + 0.570161i \(0.806881\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.00265e8 + 1.73663e8i −0.0255339 + 0.0442260i
\(552\) 0 0
\(553\) −7.50819e8 + 2.51771e9i −0.188798 + 0.633094i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.33312e7 + 4.04109e7i 0.00572064 + 0.00990844i 0.868872 0.495038i \(-0.164846\pi\)
−0.863151 + 0.504946i \(0.831512\pi\)
\(558\) 0 0
\(559\) −4.76486e9 −1.15374
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.20530e9 + 3.81969e9i 0.520821 + 0.902088i 0.999707 + 0.0242113i \(0.00770745\pi\)
−0.478886 + 0.877877i \(0.658959\pi\)
\(564\) 0 0
\(565\) −2.14255e9 + 3.71100e9i −0.499759 + 0.865609i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −3.77796e9 + 6.54362e9i −0.859734 + 1.48910i 0.0124479 + 0.999923i \(0.496038\pi\)
−0.872182 + 0.489181i \(0.837296\pi\)
\(570\) 0 0
\(571\) −2.57104e9 4.45317e9i −0.577940 1.00102i −0.995715 0.0924705i \(-0.970524\pi\)
0.417776 0.908550i \(-0.362810\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.47428e8 0.0542764
\(576\) 0 0
\(577\) 1.11111e9 + 1.92450e9i 0.240792 + 0.417065i 0.960940 0.276756i \(-0.0892594\pi\)
−0.720148 + 0.693821i \(0.755926\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.18319e9 + 7.58030e8i −0.673359 + 0.160350i
\(582\) 0 0
\(583\) −2.62154e7 + 4.54064e7i −0.00547919 + 0.00949024i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.10248e9 1.85749 0.928745 0.370719i \(-0.120889\pi\)
0.928745 + 0.370719i \(0.120889\pi\)
\(588\) 0 0
\(589\) −3.97249e7 −0.00801049
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 8.33687e7 1.44399e8i 0.0164177 0.0284363i −0.857700 0.514151i \(-0.828107\pi\)
0.874118 + 0.485714i \(0.161441\pi\)
\(594\) 0 0
\(595\) −9.21787e9 + 2.19510e9i −1.79399 + 0.427213i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 6.87795e8 + 1.19130e9i 0.130757 + 0.226478i 0.923969 0.382468i \(-0.124926\pi\)
−0.793212 + 0.608946i \(0.791593\pi\)
\(600\) 0 0
\(601\) −5.27171e9 −0.990584 −0.495292 0.868727i \(-0.664939\pi\)
−0.495292 + 0.868727i \(0.664939\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.14104e9 5.44045e9i −0.576674 0.998828i
\(606\) 0 0
\(607\) 3.64681e9 6.31645e9i 0.661839 1.14634i −0.318293 0.947992i \(-0.603110\pi\)
0.980132 0.198346i \(-0.0635570\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.96171e9 + 5.12983e9i −0.525288 + 0.909826i
\(612\) 0 0
\(613\) 2.79988e9 + 4.84953e9i 0.490939 + 0.850331i 0.999946 0.0104318i \(-0.00332060\pi\)
−0.509007 + 0.860762i \(0.669987\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.11007e10 1.90263 0.951313 0.308226i \(-0.0997352\pi\)
0.951313 + 0.308226i \(0.0997352\pi\)
\(618\) 0 0
\(619\) 4.29620e9 + 7.44124e9i 0.728060 + 1.26104i 0.957702 + 0.287762i \(0.0929111\pi\)
−0.229642 + 0.973275i \(0.573756\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.41720e8 8.10558e8i 0.0400502 0.134300i
\(624\) 0 0
\(625\) 3.72780e9 6.45673e9i 0.610762 1.05787i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −9.06523e8 −0.145245
\(630\) 0 0
\(631\) 1.71493e8 0.0271734 0.0135867 0.999908i \(-0.495675\pi\)
0.0135867 + 0.999908i \(0.495675\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 3.74330e9 6.48358e9i 0.580158 1.00486i
\(636\) 0 0
\(637\) −7.05910e9 + 3.56416e9i −1.08209 + 0.546347i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3.55924e9 6.16479e9i −0.533770 0.924517i −0.999222 0.0394438i \(-0.987441\pi\)
0.465452 0.885073i \(-0.345892\pi\)
\(642\) 0 0
\(643\) −6.98220e9 −1.03575 −0.517874 0.855457i \(-0.673276\pi\)
−0.517874 + 0.855457i \(0.673276\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.19570e8 + 8.99921e8i 0.0754187 + 0.130629i 0.901268 0.433262i \(-0.142637\pi\)
−0.825850 + 0.563890i \(0.809304\pi\)
\(648\) 0 0
\(649\) −1.05350e8 + 1.82471e8i −0.0151279 + 0.0262022i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −5.96396e9 + 1.03299e10i −0.838182 + 1.45177i 0.0532302 + 0.998582i \(0.483048\pi\)
−0.891413 + 0.453192i \(0.850285\pi\)
\(654\) 0 0
\(655\) −1.63869e9 2.83829e9i −0.227852 0.394650i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.23644e10 −1.68295 −0.841477 0.540292i \(-0.818314\pi\)
−0.841477 + 0.540292i \(0.818314\pi\)
\(660\) 0 0
\(661\) 1.48594e9 + 2.57373e9i 0.200123 + 0.346623i 0.948568 0.316574i \(-0.102532\pi\)
−0.748445 + 0.663197i \(0.769199\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.91883e8 2.02948e8i −0.0253023 0.0267614i
\(666\) 0 0
\(667\) −1.00449e9 + 1.73983e9i −0.131071 + 0.227022i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 9.42800e7 0.0120473
\(672\) 0 0
\(673\) −8.24543e9 −1.04270 −0.521351 0.853342i \(-0.674572\pi\)
−0.521351 + 0.853342i \(0.674572\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.34244e9 + 2.32517e9i −0.166278 + 0.288001i −0.937108 0.349039i \(-0.886508\pi\)
0.770831 + 0.637040i \(0.219841\pi\)
\(678\) 0 0
\(679\) −1.07683e10 + 2.56430e9i −1.32008 + 0.314358i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −3.34998e9 5.80234e9i −0.402319 0.696836i 0.591687 0.806168i \(-0.298462\pi\)
−0.994005 + 0.109332i \(0.965129\pi\)
\(684\) 0 0
\(685\) −1.34230e10 −1.59564
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.88046e9 + 4.98910e9i 0.335501 + 0.581105i
\(690\) 0 0
\(691\) −5.57677e9 + 9.65925e9i −0.642998 + 1.11370i 0.341762 + 0.939786i \(0.388976\pi\)
−0.984760 + 0.173919i \(0.944357\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 7.68887e9 1.33175e10i 0.868792 1.50479i
\(696\) 0 0
\(697\) −4.79857e9 8.31136e9i −0.536781 0.929732i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.52110e9 0.715003 0.357502 0.933913i \(-0.383629\pi\)
0.357502 + 0.933913i \(0.383629\pi\)
\(702\) 0 0
\(703\) −1.33600e7 2.31402e7i −0.00145032 0.00251203i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.17648e10 1.24432e10i −1.25203 1.32424i
\(708\) 0 0
\(709\) 1.09662e9 1.89940e9i 0.115556 0.200149i −0.802446 0.596725i \(-0.796468\pi\)
0.918002 + 0.396576i \(0.129802\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.97981e8 −0.0411197
\(714\) 0 0
\(715\) 2.70623e8 0.0276881
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.05874e8 7.02994e8i 0.0407230 0.0705343i −0.844946 0.534852i \(-0.820367\pi\)
0.885669 + 0.464318i \(0.153701\pi\)
\(720\) 0 0
\(721\) −2.57784e9 + 8.64423e9i −0.256143 + 0.858921i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.71894e9 4.70935e9i −0.264982 0.458963i
\(726\) 0 0
\(727\) −1.14066e10 −1.10100 −0.550499 0.834836i \(-0.685562\pi\)
−0.550499 + 0.834836i \(0.685562\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.03318e9 + 1.39139e10i 0.760636 + 1.31746i
\(732\) 0 0
\(733\) 1.76593e9 3.05868e9i 0.165619 0.286860i −0.771256 0.636525i \(-0.780371\pi\)
0.936875 + 0.349665i \(0.113705\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.19899e8 + 2.07670e8i −0.0110326 + 0.0191090i
\(738\) 0 0
\(739\) −6.44886e9 1.11697e10i −0.587797 1.01809i −0.994520 0.104543i \(-0.966662\pi\)
0.406724 0.913551i \(-0.366671\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.49218e10 −1.33463 −0.667316 0.744774i \(-0.732557\pi\)
−0.667316 + 0.744774i \(0.732557\pi\)
\(744\) 0 0
\(745\) 1.26484e10 + 2.19077e10i 1.12070 + 1.94111i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.31178e9 + 4.39879e9i −0.114071 + 0.382513i
\(750\) 0 0
\(751\) 8.59883e9 1.48936e10i 0.740798 1.28310i −0.211335 0.977414i \(-0.567781\pi\)
0.952132 0.305686i \(-0.0988857\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.96428e10 1.66108
\(756\) 0 0
\(757\) 1.66346e10 1.39373 0.696863 0.717204i \(-0.254578\pi\)
0.696863 + 0.717204i \(0.254578\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −4.04941e9 + 7.01378e9i −0.333077 + 0.576907i −0.983114 0.182996i \(-0.941420\pi\)
0.650036 + 0.759903i \(0.274754\pi\)
\(762\) 0 0
\(763\) −4.77453e9 5.04987e9i −0.389130 0.411571i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.15755e10 + 2.00493e10i 0.926308 + 1.60441i
\(768\) 0 0
\(769\) −3.90614e9 −0.309746 −0.154873 0.987934i \(-0.549497\pi\)
−0.154873 + 0.987934i \(0.549497\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.68336e9 + 2.91567e9i 0.131084 + 0.227044i 0.924095 0.382164i \(-0.124821\pi\)
−0.793011 + 0.609208i \(0.791488\pi\)
\(774\) 0 0
\(775\) 5.38624e8 9.32924e8i 0.0415652 0.0719930i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.41439e8 2.44980e8i 0.0107199 0.0185673i
\(780\) 0 0
\(781\) −9.68899e7 1.67818e8i −0.00727779 0.0126055i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 6.10537e9 0.450472
\(786\) 0 0
\(787\) 9.79288e9 + 1.69618e10i 0.716142 + 1.24039i 0.962518 + 0.271220i \(0.0874269\pi\)
−0.246376 + 0.969174i \(0.579240\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.17301e10 2.79334e9i 0.842719 0.200681i
\(792\) 0 0
\(793\) 5.17958e9 8.97129e9i