Properties

Label 43.11.b.b.42.4
Level 43
Weight 11
Character 43.42
Analytic conductor 27.320
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(27.3203618650\)
Analytic rank: \(0\)
Dimension: \(34\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.4
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.31

$q$-expansion

\(f(q)\) \(=\) \(q-50.9791i q^{2} +197.849i q^{3} -1574.87 q^{4} -5530.45i q^{5} +10086.2 q^{6} +21393.6i q^{7} +28082.7i q^{8} +19904.8 q^{9} +O(q^{10})\) \(q-50.9791i q^{2} +197.849i q^{3} -1574.87 q^{4} -5530.45i q^{5} +10086.2 q^{6} +21393.6i q^{7} +28082.7i q^{8} +19904.8 q^{9} -281938. q^{10} -131052. q^{11} -311586. i q^{12} -588595. q^{13} +1.09063e6 q^{14} +1.09419e6 q^{15} -181032. q^{16} -270179. q^{17} -1.01473e6i q^{18} +2.93766e6i q^{19} +8.70974e6i q^{20} -4.23270e6 q^{21} +6.68092e6i q^{22} +1.08666e7 q^{23} -5.55614e6 q^{24} -2.08203e7 q^{25} +3.00060e7i q^{26} +1.56209e7i q^{27} -3.36921e7i q^{28} -7.43530e6i q^{29} -5.57811e7i q^{30} +4.62840e7 q^{31} +3.79856e7i q^{32} -2.59285e7i q^{33} +1.37735e7i q^{34} +1.18316e8 q^{35} -3.13474e7 q^{36} +6.79130e7i q^{37} +1.49759e8 q^{38} -1.16453e8i q^{39} +1.55310e8 q^{40} +7.10053e7 q^{41} +2.15779e8i q^{42} +(-1.24384e8 + 7.83589e7i) q^{43} +2.06390e8 q^{44} -1.10082e8i q^{45} -5.53971e8i q^{46} -3.33454e8 q^{47} -3.58170e7i q^{48} -1.75210e8 q^{49} +1.06140e9i q^{50} -5.34547e7i q^{51} +9.26959e8 q^{52} -3.32431e8 q^{53} +7.96341e8 q^{54} +7.24778e8i q^{55} -6.00791e8 q^{56} -5.81213e8 q^{57} -3.79045e8 q^{58} -7.48163e7 q^{59} -1.72321e9 q^{60} +7.63592e8i q^{61} -2.35952e9i q^{62} +4.25835e8i q^{63} +1.75109e9 q^{64} +3.25520e9i q^{65} -1.32181e9 q^{66} +5.79974e8 q^{67} +4.25497e8 q^{68} +2.14995e9i q^{69} -6.03166e9i q^{70} +9.90329e8i q^{71} +5.58981e8i q^{72} -8.61773e8i q^{73} +3.46214e9 q^{74} -4.11928e9i q^{75} -4.62643e9i q^{76} -2.80367e9i q^{77} -5.93666e9 q^{78} -4.77088e9 q^{79} +1.00119e9i q^{80} -1.91523e9 q^{81} -3.61979e9i q^{82} -1.89897e9 q^{83} +6.66594e9 q^{84} +1.49422e9i q^{85} +(3.99466e9 + 6.34098e9i) q^{86} +1.47107e9 q^{87} -3.68030e9i q^{88} +1.53171e9i q^{89} -5.61190e9 q^{90} -1.25922e10i q^{91} -1.71135e10 q^{92} +9.15724e9i q^{93} +1.69992e10i q^{94} +1.62466e10 q^{95} -7.51541e9 q^{96} -1.02062e10 q^{97} +8.93206e9i q^{98} -2.60856e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 50.9791i 1.59310i −0.604575 0.796548i \(-0.706657\pi\)
0.604575 0.796548i \(-0.293343\pi\)
\(3\) 197.849i 0.814193i 0.913385 + 0.407097i \(0.133459\pi\)
−0.913385 + 0.407097i \(0.866541\pi\)
\(4\) −1574.87 −1.53796
\(5\) 5530.45i 1.76975i −0.465833 0.884873i \(-0.654245\pi\)
0.465833 0.884873i \(-0.345755\pi\)
\(6\) 10086.2 1.29709
\(7\) 21393.6i 1.27290i 0.771319 + 0.636449i \(0.219597\pi\)
−0.771319 + 0.636449i \(0.780403\pi\)
\(8\) 28082.7i 0.857017i
\(9\) 19904.8 0.337089
\(10\) −281938. −2.81938
\(11\) −131052. −0.813730 −0.406865 0.913488i \(-0.633378\pi\)
−0.406865 + 0.913488i \(0.633378\pi\)
\(12\) 311586.i 1.25219i
\(13\) −588595. −1.58526 −0.792628 0.609705i \(-0.791288\pi\)
−0.792628 + 0.609705i \(0.791288\pi\)
\(14\) 1.09063e6 2.02785
\(15\) 1.09419e6 1.44092
\(16\) −181032. −0.172645
\(17\) −270179. −0.190286 −0.0951432 0.995464i \(-0.530331\pi\)
−0.0951432 + 0.995464i \(0.530331\pi\)
\(18\) 1.01473e6i 0.537016i
\(19\) 2.93766e6i 1.18641i 0.805052 + 0.593204i \(0.202137\pi\)
−0.805052 + 0.593204i \(0.797863\pi\)
\(20\) 8.70974e6i 2.72179i
\(21\) −4.23270e6 −1.03638
\(22\) 6.68092e6i 1.29635i
\(23\) 1.08666e7 1.68832 0.844161 0.536089i \(-0.180099\pi\)
0.844161 + 0.536089i \(0.180099\pi\)
\(24\) −5.55614e6 −0.697778
\(25\) −2.08203e7 −2.13200
\(26\) 3.00060e7i 2.52547i
\(27\) 1.56209e7i 1.08865i
\(28\) 3.36921e7i 1.95766i
\(29\) 7.43530e6i 0.362501i −0.983437 0.181250i \(-0.941986\pi\)
0.983437 0.181250i \(-0.0580144\pi\)
\(30\) 5.57811e7i 2.29552i
\(31\) 4.62840e7 1.61667 0.808337 0.588720i \(-0.200368\pi\)
0.808337 + 0.588720i \(0.200368\pi\)
\(32\) 3.79856e7i 1.13206i
\(33\) 2.59285e7i 0.662534i
\(34\) 1.37735e7i 0.303145i
\(35\) 1.18316e8 2.25270
\(36\) −3.13474e7 −0.518429
\(37\) 6.79130e7i 0.979364i 0.871901 + 0.489682i \(0.162887\pi\)
−0.871901 + 0.489682i \(0.837113\pi\)
\(38\) 1.49759e8 1.89006
\(39\) 1.16453e8i 1.29071i
\(40\) 1.55310e8 1.51670
\(41\) 7.10053e7 0.612874 0.306437 0.951891i \(-0.400863\pi\)
0.306437 + 0.951891i \(0.400863\pi\)
\(42\) 2.15779e8i 1.65106i
\(43\) −1.24384e8 + 7.83589e7i −0.846101 + 0.533023i
\(44\) 2.06390e8 1.25148
\(45\) 1.10082e8i 0.596562i
\(46\) 5.53971e8i 2.68966i
\(47\) −3.33454e8 −1.45394 −0.726971 0.686668i \(-0.759072\pi\)
−0.726971 + 0.686668i \(0.759072\pi\)
\(48\) 3.58170e7i 0.140567i
\(49\) −1.75210e8 −0.620268
\(50\) 1.06140e9i 3.39648i
\(51\) 5.34547e7i 0.154930i
\(52\) 9.26959e8 2.43806
\(53\) −3.32431e8 −0.794919 −0.397459 0.917620i \(-0.630108\pi\)
−0.397459 + 0.917620i \(0.630108\pi\)
\(54\) 7.96341e8 1.73432
\(55\) 7.24778e8i 1.44010i
\(56\) −6.00791e8 −1.09090
\(57\) −5.81213e8 −0.965965
\(58\) −3.79045e8 −0.577498
\(59\) −7.48163e7 −0.104649 −0.0523247 0.998630i \(-0.516663\pi\)
−0.0523247 + 0.998630i \(0.516663\pi\)
\(60\) −1.72321e9 −2.21607
\(61\) 7.63592e8i 0.904091i 0.891995 + 0.452046i \(0.149306\pi\)
−0.891995 + 0.452046i \(0.850694\pi\)
\(62\) 2.35952e9i 2.57552i
\(63\) 4.25835e8i 0.429080i
\(64\) 1.75109e9 1.63083
\(65\) 3.25520e9i 2.80550i
\(66\) −1.32181e9 −1.05548
\(67\) 5.79974e8 0.429570 0.214785 0.976661i \(-0.431095\pi\)
0.214785 + 0.976661i \(0.431095\pi\)
\(68\) 4.25497e8 0.292652
\(69\) 2.14995e9i 1.37462i
\(70\) 6.03166e9i 3.58878i
\(71\) 9.90329e8i 0.548893i 0.961602 + 0.274446i \(0.0884946\pi\)
−0.961602 + 0.274446i \(0.911505\pi\)
\(72\) 5.58981e8i 0.288891i
\(73\) 8.61773e8i 0.415698i −0.978161 0.207849i \(-0.933354\pi\)
0.978161 0.207849i \(-0.0666463\pi\)
\(74\) 3.46214e9 1.56022
\(75\) 4.11928e9i 1.73586i
\(76\) 4.62643e9i 1.82464i
\(77\) 2.80367e9i 1.03580i
\(78\) −5.93666e9 −2.05622
\(79\) −4.77088e9 −1.55047 −0.775235 0.631673i \(-0.782368\pi\)
−0.775235 + 0.631673i \(0.782368\pi\)
\(80\) 1.00119e9i 0.305539i
\(81\) −1.91523e9 −0.549282
\(82\) 3.61979e9i 0.976368i
\(83\) −1.89897e9 −0.482088 −0.241044 0.970514i \(-0.577490\pi\)
−0.241044 + 0.970514i \(0.577490\pi\)
\(84\) 6.66594e9 1.59391
\(85\) 1.49422e9i 0.336759i
\(86\) 3.99466e9 + 6.34098e9i 0.849157 + 1.34792i
\(87\) 1.47107e9 0.295146
\(88\) 3.68030e9i 0.697381i
\(89\) 1.53171e9i 0.274300i 0.990550 + 0.137150i \(0.0437942\pi\)
−0.990550 + 0.137150i \(0.956206\pi\)
\(90\) −5.61190e9 −0.950381
\(91\) 1.25922e10i 2.01787i
\(92\) −1.71135e10 −2.59657
\(93\) 9.15724e9i 1.31628i
\(94\) 1.69992e10i 2.31627i
\(95\) 1.62466e10 2.09964
\(96\) −7.51541e9 −0.921714
\(97\) −1.02062e10 −1.18852 −0.594259 0.804274i \(-0.702555\pi\)
−0.594259 + 0.804274i \(0.702555\pi\)
\(98\) 8.93206e9i 0.988147i
\(99\) −2.60856e9 −0.274300
\(100\) 3.27892e10 3.27892
\(101\) 7.39786e9 0.703881 0.351941 0.936022i \(-0.385522\pi\)
0.351941 + 0.936022i \(0.385522\pi\)
\(102\) −2.72507e9 −0.246818
\(103\) 1.89500e9 0.163464 0.0817320 0.996654i \(-0.473955\pi\)
0.0817320 + 0.996654i \(0.473955\pi\)
\(104\) 1.65294e10i 1.35859i
\(105\) 2.34088e10i 1.83414i
\(106\) 1.69471e10i 1.26638i
\(107\) −3.52939e9 −0.251640 −0.125820 0.992053i \(-0.540156\pi\)
−0.125820 + 0.992053i \(0.540156\pi\)
\(108\) 2.46009e10i 1.67430i
\(109\) −2.09373e10 −1.36078 −0.680391 0.732849i \(-0.738190\pi\)
−0.680391 + 0.732849i \(0.738190\pi\)
\(110\) 3.69485e10 2.29421
\(111\) −1.34365e10 −0.797392
\(112\) 3.87292e9i 0.219760i
\(113\) 1.44266e9i 0.0783016i 0.999233 + 0.0391508i \(0.0124653\pi\)
−0.999233 + 0.0391508i \(0.987535\pi\)
\(114\) 2.96297e10i 1.53888i
\(115\) 6.00974e10i 2.98790i
\(116\) 1.17096e10i 0.557510i
\(117\) −1.17158e10 −0.534373
\(118\) 3.81407e9i 0.166716i
\(119\) 5.78011e9i 0.242215i
\(120\) 3.07280e10i 1.23489i
\(121\) −8.76277e9 −0.337843
\(122\) 3.89272e10 1.44030
\(123\) 1.40483e10i 0.498998i
\(124\) −7.28912e10 −2.48637
\(125\) 6.11374e10i 2.00335i
\(126\) 2.17087e10 0.683566
\(127\) 3.60104e10 1.08996 0.544979 0.838450i \(-0.316538\pi\)
0.544979 + 0.838450i \(0.316538\pi\)
\(128\) 5.03719e10i 1.46602i
\(129\) −1.55032e10 2.46092e10i −0.433984 0.688890i
\(130\) 1.65947e11 4.46943
\(131\) 1.97020e10i 0.510685i 0.966851 + 0.255342i \(0.0821882\pi\)
−0.966851 + 0.255342i \(0.917812\pi\)
\(132\) 4.08340e10i 1.01895i
\(133\) −6.28471e10 −1.51017
\(134\) 2.95665e10i 0.684347i
\(135\) 8.63908e10 1.92663
\(136\) 7.58738e9i 0.163079i
\(137\) 5.16409e10i 1.07002i −0.844847 0.535008i \(-0.820308\pi\)
0.844847 0.535008i \(-0.179692\pi\)
\(138\) 1.09603e11 2.18990
\(139\) −5.56775e10 −1.07302 −0.536508 0.843895i \(-0.680257\pi\)
−0.536508 + 0.843895i \(0.680257\pi\)
\(140\) −1.86332e11 −3.46456
\(141\) 6.59736e10i 1.18379i
\(142\) 5.04861e10 0.874440
\(143\) 7.71366e10 1.28997
\(144\) −3.60340e9 −0.0581969
\(145\) −4.11206e10 −0.641534
\(146\) −4.39324e10 −0.662248
\(147\) 3.46652e10i 0.505018i
\(148\) 1.06954e11i 1.50622i
\(149\) 5.02449e10i 0.684164i −0.939670 0.342082i \(-0.888868\pi\)
0.939670 0.342082i \(-0.111132\pi\)
\(150\) −2.09997e11 −2.76539
\(151\) 1.21272e11i 1.54481i 0.635131 + 0.772404i \(0.280946\pi\)
−0.635131 + 0.772404i \(0.719054\pi\)
\(152\) −8.24976e10 −1.01677
\(153\) −5.37786e9 −0.0641435
\(154\) −1.42929e11 −1.65012
\(155\) 2.55972e11i 2.86110i
\(156\) 1.83398e11i 1.98505i
\(157\) 1.55559e10i 0.163079i −0.996670 0.0815394i \(-0.974016\pi\)
0.996670 0.0815394i \(-0.0259836\pi\)
\(158\) 2.43215e11i 2.47005i
\(159\) 6.57712e10i 0.647218i
\(160\) 2.10077e11 2.00346
\(161\) 2.32476e11i 2.14906i
\(162\) 9.76365e10i 0.875059i
\(163\) 5.97193e9i 0.0519011i 0.999663 + 0.0259506i \(0.00826125\pi\)
−0.999663 + 0.0259506i \(0.991739\pi\)
\(164\) −1.11824e11 −0.942574
\(165\) −1.43397e11 −1.17252
\(166\) 9.68076e10i 0.768014i
\(167\) −2.25335e11 −1.73479 −0.867395 0.497621i \(-0.834207\pi\)
−0.867395 + 0.497621i \(0.834207\pi\)
\(168\) 1.18866e11i 0.888200i
\(169\) 2.08585e11 1.51304
\(170\) 7.61737e10 0.536489
\(171\) 5.84735e10i 0.399925i
\(172\) 1.95888e11 1.23405e11i 1.30127 0.819766i
\(173\) −1.73165e11 −1.11746 −0.558728 0.829351i \(-0.688710\pi\)
−0.558728 + 0.829351i \(0.688710\pi\)
\(174\) 7.49937e10i 0.470195i
\(175\) 4.45421e11i 2.71382i
\(176\) 2.37246e10 0.140487
\(177\) 1.48023e10i 0.0852048i
\(178\) 7.80850e10 0.436986
\(179\) 9.54014e10i 0.519146i −0.965724 0.259573i \(-0.916418\pi\)
0.965724 0.259573i \(-0.0835818\pi\)
\(180\) 1.73365e11i 0.917487i
\(181\) 2.69717e11 1.38840 0.694202 0.719780i \(-0.255757\pi\)
0.694202 + 0.719780i \(0.255757\pi\)
\(182\) −6.41936e11 −3.21466
\(183\) −1.51076e11 −0.736105
\(184\) 3.05165e11i 1.44692i
\(185\) 3.75590e11 1.73322
\(186\) 4.66828e11 2.09697
\(187\) 3.54076e10 0.154842
\(188\) 5.25146e11 2.23610
\(189\) −3.34188e11 −1.38574
\(190\) 8.28237e11i 3.34493i
\(191\) 5.74703e10i 0.226087i 0.993590 + 0.113044i \(0.0360600\pi\)
−0.993590 + 0.113044i \(0.963940\pi\)
\(192\) 3.46452e11i 1.32781i
\(193\) 4.85240e9 0.0181205 0.00906025 0.999959i \(-0.497116\pi\)
0.00906025 + 0.999959i \(0.497116\pi\)
\(194\) 5.20303e11i 1.89342i
\(195\) −6.44037e11 −2.28422
\(196\) 2.75933e11 0.953945
\(197\) −1.37673e11 −0.463999 −0.232000 0.972716i \(-0.574527\pi\)
−0.232000 + 0.972716i \(0.574527\pi\)
\(198\) 1.32982e11i 0.436986i
\(199\) 1.32479e11i 0.424504i 0.977215 + 0.212252i \(0.0680798\pi\)
−0.977215 + 0.212252i \(0.931920\pi\)
\(200\) 5.84691e11i 1.82716i
\(201\) 1.14747e11i 0.349753i
\(202\) 3.77136e11i 1.12135i
\(203\) 1.59068e11 0.461426
\(204\) 8.41841e10i 0.238276i
\(205\) 3.92692e11i 1.08463i
\(206\) 9.66052e10i 0.260414i
\(207\) 2.16298e11 0.569115
\(208\) 1.06554e11 0.273687
\(209\) 3.84987e11i 0.965416i
\(210\) 1.19336e12 2.92196
\(211\) 1.43647e11i 0.343466i 0.985143 + 0.171733i \(0.0549367\pi\)
−0.985143 + 0.171733i \(0.945063\pi\)
\(212\) 5.23536e11 1.22255
\(213\) −1.95936e11 −0.446905
\(214\) 1.79925e11i 0.400887i
\(215\) 4.33360e11 + 6.87900e11i 0.943315 + 1.49738i
\(216\) −4.38678e11 −0.932991
\(217\) 9.90181e11i 2.05786i
\(218\) 1.06737e12i 2.16786i
\(219\) 1.70501e11 0.338459
\(220\) 1.14143e12i 2.21481i
\(221\) 1.59026e11 0.301653
\(222\) 6.84981e11i 1.27032i
\(223\) 1.22924e11i 0.222902i 0.993770 + 0.111451i \(0.0355498\pi\)
−0.993770 + 0.111451i \(0.964450\pi\)
\(224\) −8.12648e11 −1.44099
\(225\) −4.14424e11 −0.718674
\(226\) 7.35453e10 0.124742
\(227\) 6.76953e11i 1.12313i −0.827433 0.561564i \(-0.810200\pi\)
0.827433 0.561564i \(-0.189800\pi\)
\(228\) 9.15334e11 1.48561
\(229\) −2.91880e11 −0.463476 −0.231738 0.972778i \(-0.574441\pi\)
−0.231738 + 0.972778i \(0.574441\pi\)
\(230\) −3.06371e12 −4.76002
\(231\) 5.54704e11 0.843338
\(232\) 2.08804e11 0.310669
\(233\) 6.90403e11i 1.00536i 0.864472 + 0.502681i \(0.167653\pi\)
−0.864472 + 0.502681i \(0.832347\pi\)
\(234\) 5.97263e11i 0.851308i
\(235\) 1.84415e12i 2.57311i
\(236\) 1.17826e11 0.160946
\(237\) 9.43914e11i 1.26238i
\(238\) −2.94665e11 −0.385872
\(239\) −3.17121e11 −0.406664 −0.203332 0.979110i \(-0.565177\pi\)
−0.203332 + 0.979110i \(0.565177\pi\)
\(240\) −1.98084e11 −0.248767
\(241\) 7.71400e11i 0.948843i −0.880298 0.474422i \(-0.842657\pi\)
0.880298 0.474422i \(-0.157343\pi\)
\(242\) 4.46718e11i 0.538216i
\(243\) 5.43474e11i 0.641428i
\(244\) 1.20256e12i 1.39045i
\(245\) 9.68993e11i 1.09772i
\(246\) 7.16171e11 0.794952
\(247\) 1.72909e12i 1.88076i
\(248\) 1.29978e12i 1.38552i
\(249\) 3.75709e11i 0.392513i
\(250\) 3.11673e12 3.19153
\(251\) −1.41940e12 −1.42474 −0.712371 0.701803i \(-0.752379\pi\)
−0.712371 + 0.701803i \(0.752379\pi\)
\(252\) 6.70633e11i 0.659906i
\(253\) −1.42409e12 −1.37384
\(254\) 1.83578e12i 1.73641i
\(255\) −2.95629e11 −0.274187
\(256\) −7.74795e11 −0.704672
\(257\) 1.85716e12i 1.65647i −0.560381 0.828235i \(-0.689345\pi\)
0.560381 0.828235i \(-0.310655\pi\)
\(258\) −1.25456e12 + 7.90340e11i −1.09747 + 0.691378i
\(259\) −1.45290e12 −1.24663
\(260\) 5.12650e12i 4.31474i
\(261\) 1.47998e11i 0.122195i
\(262\) 1.00439e12 0.813570
\(263\) 1.35241e12i 1.07481i −0.843325 0.537403i \(-0.819405\pi\)
0.843325 0.537403i \(-0.180595\pi\)
\(264\) 7.28144e11 0.567803
\(265\) 1.83850e12i 1.40680i
\(266\) 3.20389e12i 2.40585i
\(267\) −3.03047e11 −0.223333
\(268\) −9.13382e11 −0.660660
\(269\) 1.33910e12 0.950721 0.475360 0.879791i \(-0.342318\pi\)
0.475360 + 0.879791i \(0.342318\pi\)
\(270\) 4.40413e12i 3.06931i
\(271\) 2.01872e12 1.38111 0.690557 0.723278i \(-0.257366\pi\)
0.690557 + 0.723278i \(0.257366\pi\)
\(272\) 4.89111e10 0.0328521
\(273\) 2.49134e12 1.64294
\(274\) −2.63260e12 −1.70464
\(275\) 2.72854e12 1.73487
\(276\) 3.38589e12i 2.11411i
\(277\) 3.00986e12i 1.84564i 0.385228 + 0.922822i \(0.374123\pi\)
−0.385228 + 0.922822i \(0.625877\pi\)
\(278\) 2.83839e12i 1.70942i
\(279\) 9.21272e11 0.544963
\(280\) 3.32265e12i 1.93061i
\(281\) −3.85491e11 −0.220030 −0.110015 0.993930i \(-0.535090\pi\)
−0.110015 + 0.993930i \(0.535090\pi\)
\(282\) −3.36327e12 −1.88589
\(283\) 1.81571e12 1.00026 0.500130 0.865950i \(-0.333285\pi\)
0.500130 + 0.865950i \(0.333285\pi\)
\(284\) 1.55964e12i 0.844174i
\(285\) 3.21437e12i 1.70951i
\(286\) 3.93235e12i 2.05505i
\(287\) 1.51906e12i 0.780126i
\(288\) 7.56094e11i 0.381605i
\(289\) −1.94300e12 −0.963791
\(290\) 2.09629e12i 1.02203i
\(291\) 2.01929e12i 0.967684i
\(292\) 1.35718e12i 0.639326i
\(293\) 1.66503e12 0.771052 0.385526 0.922697i \(-0.374020\pi\)
0.385526 + 0.922697i \(0.374020\pi\)
\(294\) −1.76720e12 −0.804543
\(295\) 4.13768e11i 0.185203i
\(296\) −1.90718e12 −0.839332
\(297\) 2.04716e12i 0.885867i
\(298\) −2.56144e12 −1.08994
\(299\) −6.39604e12 −2.67642
\(300\) 6.48732e12i 2.66968i
\(301\) −1.67638e12 2.66102e12i −0.678484 1.07700i
\(302\) 6.18232e12 2.46103
\(303\) 1.46366e12i 0.573095i
\(304\) 5.31810e11i 0.204828i
\(305\) 4.22301e12 1.60001
\(306\) 2.74159e11i 0.102187i
\(307\) 2.43294e11 0.0892154 0.0446077 0.999005i \(-0.485796\pi\)
0.0446077 + 0.999005i \(0.485796\pi\)
\(308\) 4.41542e12i 1.59301i
\(309\) 3.74923e11i 0.133091i
\(310\) −1.30492e13 −4.55801
\(311\) 8.12366e11 0.279222 0.139611 0.990206i \(-0.455415\pi\)
0.139611 + 0.990206i \(0.455415\pi\)
\(312\) 3.27032e12 1.10616
\(313\) 3.63754e12i 1.21084i 0.795907 + 0.605419i \(0.206994\pi\)
−0.795907 + 0.605419i \(0.793006\pi\)
\(314\) −7.93027e11 −0.259800
\(315\) 2.35506e12 0.759362
\(316\) 7.51351e12 2.38455
\(317\) −2.91949e12 −0.912033 −0.456017 0.889971i \(-0.650724\pi\)
−0.456017 + 0.889971i \(0.650724\pi\)
\(318\) −3.35296e12 −1.03108
\(319\) 9.74412e11i 0.294978i
\(320\) 9.68434e12i 2.88616i
\(321\) 6.98285e11i 0.204884i
\(322\) 1.18514e13 3.42366
\(323\) 7.93696e11i 0.225757i
\(324\) 3.01623e12 0.844772
\(325\) 1.22547e13 3.37977
\(326\) 3.04444e11 0.0826835
\(327\) 4.14243e12i 1.10794i
\(328\) 1.99402e12i 0.525244i
\(329\) 7.13378e12i 1.85072i
\(330\) 7.31023e12i 1.86793i
\(331\) 4.66102e12i 1.17312i 0.809907 + 0.586558i \(0.199518\pi\)
−0.809907 + 0.586558i \(0.800482\pi\)
\(332\) 2.99062e12 0.741431
\(333\) 1.35179e12i 0.330133i
\(334\) 1.14874e13i 2.76369i
\(335\) 3.20752e12i 0.760230i
\(336\) 7.66254e11 0.178927
\(337\) −6.14610e12 −1.41400 −0.707001 0.707213i \(-0.749952\pi\)
−0.707001 + 0.707213i \(0.749952\pi\)
\(338\) 1.06335e13i 2.41042i
\(339\) −2.85428e11 −0.0637527
\(340\) 2.35319e12i 0.517920i
\(341\) −6.06561e12 −1.31554
\(342\) 2.98093e12 0.637119
\(343\) 2.29478e12i 0.483360i
\(344\) −2.20053e12 3.49304e12i −0.456810 0.725123i
\(345\) 1.18902e13 2.43273
\(346\) 8.82781e12i 1.78022i
\(347\) 2.05674e12i 0.408820i 0.978885 + 0.204410i \(0.0655276\pi\)
−0.978885 + 0.204410i \(0.934472\pi\)
\(348\) −2.31674e12 −0.453921
\(349\) 2.78036e12i 0.537000i 0.963280 + 0.268500i \(0.0865279\pi\)
−0.963280 + 0.268500i \(0.913472\pi\)
\(350\) −2.27072e13 −4.32337
\(351\) 9.19439e12i 1.72579i
\(352\) 4.97809e12i 0.921190i
\(353\) 5.01751e12 0.915409 0.457704 0.889104i \(-0.348672\pi\)
0.457704 + 0.889104i \(0.348672\pi\)
\(354\) −7.54610e11 −0.135739
\(355\) 5.47697e12 0.971401
\(356\) 2.41224e12i 0.421862i
\(357\) 1.14359e12 0.197210
\(358\) −4.86347e12 −0.827050
\(359\) 1.73968e12 0.291741 0.145870 0.989304i \(-0.453402\pi\)
0.145870 + 0.989304i \(0.453402\pi\)
\(360\) 3.09142e12 0.511264
\(361\) −2.49879e12 −0.407562
\(362\) 1.37499e13i 2.21186i
\(363\) 1.73371e12i 0.275069i
\(364\) 1.98310e13i 3.10340i
\(365\) −4.76599e12 −0.735680
\(366\) 7.70171e12i 1.17269i
\(367\) 2.47571e12 0.371851 0.185925 0.982564i \(-0.440472\pi\)
0.185925 + 0.982564i \(0.440472\pi\)
\(368\) −1.96721e12 −0.291481
\(369\) 1.41334e12 0.206593
\(370\) 1.91472e13i 2.76119i
\(371\) 7.11190e12i 1.01185i
\(372\) 1.44214e13i 2.02439i
\(373\) 6.84223e12i 0.947662i −0.880616 0.473831i \(-0.842871\pi\)
0.880616 0.473831i \(-0.157129\pi\)
\(374\) 1.80505e12i 0.246678i
\(375\) −1.20960e13 −1.63111
\(376\) 9.36431e12i 1.24605i
\(377\) 4.37638e12i 0.574656i
\(378\) 1.70366e13i 2.20762i
\(379\) 1.09466e13 1.39986 0.699929 0.714213i \(-0.253215\pi\)
0.699929 + 0.714213i \(0.253215\pi\)
\(380\) −2.55863e13 −3.22915
\(381\) 7.12462e12i 0.887436i
\(382\) 2.92978e12 0.360179
\(383\) 1.95855e12i 0.237652i 0.992915 + 0.118826i \(0.0379131\pi\)
−0.992915 + 0.118826i \(0.962087\pi\)
\(384\) 9.96603e12 1.19362
\(385\) −1.55056e13 −1.83309
\(386\) 2.47371e11i 0.0288677i
\(387\) −2.47583e12 + 1.55972e12i −0.285211 + 0.179676i
\(388\) 1.60734e13 1.82789
\(389\) 7.18199e11i 0.0806301i 0.999187 + 0.0403150i \(0.0128362\pi\)
−0.999187 + 0.0403150i \(0.987164\pi\)
\(390\) 3.28324e13i 3.63898i
\(391\) −2.93594e12 −0.321265
\(392\) 4.92039e12i 0.531580i
\(393\) −3.89801e12 −0.415796
\(394\) 7.01844e12i 0.739196i
\(395\) 2.63851e13i 2.74394i
\(396\) 4.10814e12 0.421861
\(397\) −2.00526e12 −0.203338 −0.101669 0.994818i \(-0.532418\pi\)
−0.101669 + 0.994818i \(0.532418\pi\)
\(398\) 6.75366e12 0.676276
\(399\) 1.24342e13i 1.22957i
\(400\) 3.76914e12 0.368080
\(401\) 1.26762e13 1.22256 0.611278 0.791416i \(-0.290656\pi\)
0.611278 + 0.791416i \(0.290656\pi\)
\(402\) 5.84971e12 0.557191
\(403\) −2.72425e13 −2.56284
\(404\) −1.16507e13 −1.08254
\(405\) 1.05921e13i 0.972089i
\(406\) 8.10913e12i 0.735096i
\(407\) 8.90014e12i 0.796938i
\(408\) 1.50116e12 0.132778
\(409\) 4.94819e12i 0.432344i −0.976355 0.216172i \(-0.930643\pi\)
0.976355 0.216172i \(-0.0693573\pi\)
\(410\) −2.00191e13 −1.72792
\(411\) 1.02171e13 0.871201
\(412\) −2.98437e12 −0.251401
\(413\) 1.60059e12i 0.133208i
\(414\) 1.10267e13i 0.906656i
\(415\) 1.05021e13i 0.853174i
\(416\) 2.23581e13i 1.79460i
\(417\) 1.10157e13i 0.873642i
\(418\) −1.96263e13 −1.53800
\(419\) 1.99645e13i 1.54592i 0.634453 + 0.772962i \(0.281225\pi\)
−0.634453 + 0.772962i \(0.718775\pi\)
\(420\) 3.68657e13i 2.82082i
\(421\) 1.11863e13i 0.845815i −0.906173 0.422908i \(-0.861009\pi\)
0.906173 0.422908i \(-0.138991\pi\)
\(422\) 7.32300e12 0.547175
\(423\) −6.63733e12 −0.490108
\(424\) 9.33559e12i 0.681259i
\(425\) 5.62522e12 0.405690
\(426\) 9.98862e12i 0.711963i
\(427\) −1.63360e13 −1.15082
\(428\) 5.55832e12 0.387012
\(429\) 1.52614e13i 1.05029i
\(430\) 3.50685e13 2.20923e13i 2.38548 1.50279i
\(431\) −2.48302e12 −0.166953 −0.0834766 0.996510i \(-0.526602\pi\)
−0.0834766 + 0.996510i \(0.526602\pi\)
\(432\) 2.82789e12i 0.187950i
\(433\) 2.28933e13i 1.50407i 0.659122 + 0.752036i \(0.270928\pi\)
−0.659122 + 0.752036i \(0.729072\pi\)
\(434\) 5.04785e13 3.27837
\(435\) 8.13567e12i 0.522333i
\(436\) 3.29735e13 2.09282
\(437\) 3.19225e13i 2.00304i
\(438\) 8.69198e12i 0.539198i
\(439\) 1.49219e13 0.915171 0.457586 0.889166i \(-0.348714\pi\)
0.457586 + 0.889166i \(0.348714\pi\)
\(440\) −2.03537e13 −1.23419
\(441\) −3.48752e12 −0.209086
\(442\) 8.10701e12i 0.480562i
\(443\) 6.06514e12 0.355486 0.177743 0.984077i \(-0.443120\pi\)
0.177743 + 0.984077i \(0.443120\pi\)
\(444\) 2.11607e13 1.22635
\(445\) 8.47104e12 0.485441
\(446\) 6.26657e12 0.355104
\(447\) 9.94089e12 0.557042
\(448\) 3.74622e13i 2.07588i
\(449\) 2.97603e13i 1.63082i −0.578886 0.815408i \(-0.696512\pi\)
0.578886 0.815408i \(-0.303488\pi\)
\(450\) 2.11269e13i 1.14492i
\(451\) −9.30539e12 −0.498715
\(452\) 2.27199e12i 0.120425i
\(453\) −2.39935e13 −1.25777
\(454\) −3.45104e13 −1.78925
\(455\) −6.96403e13 −3.57112
\(456\) 1.63221e13i 0.827849i
\(457\) 1.82891e13i 0.917509i −0.888563 0.458754i \(-0.848296\pi\)
0.888563 0.458754i \(-0.151704\pi\)
\(458\) 1.48798e13i 0.738363i
\(459\) 4.22045e12i 0.207155i
\(460\) 9.46454e13i 4.59526i
\(461\) −6.48572e12 −0.311497 −0.155748 0.987797i \(-0.549779\pi\)
−0.155748 + 0.987797i \(0.549779\pi\)
\(462\) 2.82783e13i 1.34352i
\(463\) 4.91343e12i 0.230930i 0.993312 + 0.115465i \(0.0368358\pi\)
−0.993312 + 0.115465i \(0.963164\pi\)
\(464\) 1.34603e12i 0.0625841i
\(465\) 5.06437e13 2.32949
\(466\) 3.51961e13 1.60164
\(467\) 1.64010e13i 0.738391i −0.929352 0.369195i \(-0.879633\pi\)
0.929352 0.369195i \(-0.120367\pi\)
\(468\) 1.84509e13 0.821842
\(469\) 1.24077e13i 0.546799i
\(470\) 9.40133e13 4.09921
\(471\) 3.07772e12 0.132778
\(472\) 2.10105e12i 0.0896863i
\(473\) 1.63008e13 1.02691e13i 0.688498 0.433737i
\(474\) −4.81199e13 −2.01110
\(475\) 6.11630e13i 2.52942i
\(476\) 9.10291e12i 0.372516i
\(477\) −6.61697e12 −0.267959
\(478\) 1.61666e13i 0.647855i
\(479\) 5.14118e12 0.203885 0.101943 0.994790i \(-0.467494\pi\)
0.101943 + 0.994790i \(0.467494\pi\)
\(480\) 4.15636e13i 1.63120i
\(481\) 3.99732e13i 1.55254i
\(482\) −3.93253e13 −1.51160
\(483\) −4.59952e13 −1.74975
\(484\) 1.38002e13 0.519588
\(485\) 5.64450e13i 2.10338i
\(486\) 2.77058e13 1.02186
\(487\) 1.42608e13 0.520594 0.260297 0.965529i \(-0.416180\pi\)
0.260297 + 0.965529i \(0.416180\pi\)
\(488\) −2.14438e13 −0.774822
\(489\) −1.18154e12 −0.0422576
\(490\) 4.93984e13 1.74877
\(491\) 2.22525e12i 0.0779778i 0.999240 + 0.0389889i \(0.0124137\pi\)
−0.999240 + 0.0389889i \(0.987586\pi\)
\(492\) 2.21243e13i 0.767438i
\(493\) 2.00887e12i 0.0689789i
\(494\) −8.81475e13 −2.99623
\(495\) 1.44265e13i 0.485441i
\(496\) −8.37888e12 −0.279111
\(497\) −2.11867e13 −0.698684
\(498\) −1.91533e13 −0.625312
\(499\) 8.67993e12i 0.280552i 0.990112 + 0.140276i \(0.0447990\pi\)
−0.990112 + 0.140276i \(0.955201\pi\)
\(500\) 9.62833e13i 3.08107i
\(501\) 4.45824e13i 1.41245i
\(502\) 7.23598e13i 2.26975i
\(503\) 2.35785e13i 0.732278i −0.930560 0.366139i \(-0.880680\pi\)
0.930560 0.366139i \(-0.119320\pi\)
\(504\) −1.19586e13 −0.367729
\(505\) 4.09135e13i 1.24569i
\(506\) 7.25990e13i 2.18866i
\(507\) 4.12684e13i 1.23191i
\(508\) −5.67116e13 −1.67631
\(509\) 4.27361e13 1.25085 0.625426 0.780283i \(-0.284925\pi\)
0.625426 + 0.780283i \(0.284925\pi\)
\(510\) 1.50709e13i 0.436806i
\(511\) 1.84364e13 0.529141
\(512\) 1.20825e13i 0.343405i
\(513\) −4.58890e13 −1.29158
\(514\) −9.46763e13 −2.63892
\(515\) 1.04802e13i 0.289290i
\(516\) 2.44155e13 + 3.87563e13i 0.667448 + 1.05948i
\(517\) 4.36999e13 1.18312
\(518\) 7.40676e13i 1.98600i
\(519\) 3.42606e13i 0.909825i
\(520\) −9.14148e13 −2.40436
\(521\) 2.84719e13i 0.741700i −0.928693 0.370850i \(-0.879066\pi\)
0.928693 0.370850i \(-0.120934\pi\)
\(522\) −7.54481e12 −0.194668
\(523\) 5.37208e13i 1.37288i −0.727185 0.686442i \(-0.759172\pi\)
0.727185 0.686442i \(-0.240828\pi\)
\(524\) 3.10280e13i 0.785411i
\(525\) 8.81261e13 2.20957
\(526\) −6.89448e13 −1.71227
\(527\) −1.25050e13 −0.307631
\(528\) 4.69389e12i 0.114383i
\(529\) 7.66570e13 1.85043
\(530\) 9.37249e13 2.24117
\(531\) −1.48920e12 −0.0352761
\(532\) 9.89759e13 2.32258
\(533\) −4.17933e13 −0.971563
\(534\) 1.54490e13i 0.355791i
\(535\) 1.95191e13i 0.445339i
\(536\) 1.62872e13i 0.368149i
\(537\) 1.88751e13 0.422685
\(538\) 6.82663e13i 1.51459i
\(539\) 2.29617e13 0.504731
\(540\) −1.36054e14 −2.96308
\(541\) −7.63520e13 −1.64753 −0.823766 0.566930i \(-0.808131\pi\)
−0.823766 + 0.566930i \(0.808131\pi\)
\(542\) 1.02912e14i 2.20025i
\(543\) 5.33633e13i 1.13043i
\(544\) 1.02629e13i 0.215415i
\(545\) 1.15793e14i 2.40824i
\(546\) 1.27006e14i 2.61736i
\(547\) −1.59858e13 −0.326435 −0.163218 0.986590i \(-0.552187\pi\)
−0.163218 + 0.986590i \(0.552187\pi\)
\(548\) 8.13275e13i 1.64564i
\(549\) 1.51991e13i 0.304759i
\(550\) 1.39099e14i 2.76382i
\(551\) 2.18424e13 0.430073
\(552\) −6.03765e13 −1.17807
\(553\) 1.02066e14i 1.97359i
\(554\) 1.53440e14 2.94029
\(555\) 7.43100e13i 1.41118i
\(556\) 8.76847e13 1.65025
\(557\) −3.99128e13 −0.744451 −0.372226 0.928142i \(-0.621405\pi\)
−0.372226 + 0.928142i \(0.621405\pi\)
\(558\) 4.69656e13i 0.868179i
\(559\) 7.32117e13 4.61216e13i 1.34129 0.844978i
\(560\) −2.14190e13 −0.388919
\(561\) 7.00536e12i 0.126071i
\(562\) 1.96520e13i 0.350530i
\(563\) −9.10884e13 −1.61035 −0.805177 0.593035i \(-0.797930\pi\)
−0.805177 + 0.593035i \(0.797930\pi\)
\(564\) 1.03900e14i 1.82062i
\(565\) 7.97855e12 0.138574
\(566\) 9.25630e13i 1.59351i
\(567\) 4.09736e13i 0.699179i
\(568\) −2.78112e13 −0.470411
\(569\) 1.13563e14 1.90403 0.952017 0.306044i \(-0.0990055\pi\)
0.952017 + 0.306044i \(0.0990055\pi\)
\(570\) 1.63866e14 2.72342
\(571\) 3.43432e13i 0.565797i −0.959150 0.282898i \(-0.908704\pi\)
0.959150 0.282898i \(-0.0912960\pi\)
\(572\) −1.21480e14 −1.98392
\(573\) −1.13704e13 −0.184079
\(574\) 7.74402e13 1.24282
\(575\) −2.26246e14 −3.59950
\(576\) 3.48551e13 0.549736
\(577\) 3.09732e13i 0.484292i −0.970240 0.242146i \(-0.922149\pi\)
0.970240 0.242146i \(-0.0778512\pi\)
\(578\) 9.90522e13i 1.53541i
\(579\) 9.60043e11i 0.0147536i
\(580\) 6.47595e13 0.986651
\(581\) 4.06257e13i 0.613649i
\(582\) −1.02942e14 −1.54161
\(583\) 4.35658e13 0.646850
\(584\) 2.42009e13 0.356261
\(585\) 6.47940e13i 0.945704i
\(586\) 8.48816e13i 1.22836i
\(587\) 2.52840e13i 0.362790i −0.983410 0.181395i \(-0.941939\pi\)
0.983410 0.181395i \(-0.0580613\pi\)
\(588\) 5.45931e13i 0.776696i
\(589\) 1.35967e14i 1.91803i
\(590\) 2.10935e13 0.295046
\(591\) 2.72384e13i 0.377785i
\(592\) 1.22944e13i 0.169083i
\(593\) 8.57912e13i 1.16996i 0.811049 + 0.584978i \(0.198897\pi\)
−0.811049 + 0.584978i \(0.801103\pi\)
\(594\) −1.04362e14 −1.41127
\(595\) −3.19666e13 −0.428659
\(596\) 7.91290e13i 1.05221i
\(597\) −2.62108e13 −0.345628
\(598\) 3.26064e14i 4.26380i
\(599\) −1.40363e14 −1.82020 −0.910101 0.414386i \(-0.863996\pi\)
−0.910101 + 0.414386i \(0.863996\pi\)
\(600\) 1.15681e14 1.48766
\(601\) 5.65527e13i 0.721242i −0.932712 0.360621i \(-0.882565\pi\)
0.932712 0.360621i \(-0.117435\pi\)
\(602\) −1.35656e14 + 8.54602e13i −1.71576 + 1.08089i
\(603\) 1.15442e13 0.144803
\(604\) 1.90987e14i 2.37585i
\(605\) 4.84621e13i 0.597896i
\(606\) 7.46160e13 0.912996
\(607\) 1.13844e14i 1.38156i 0.723067 + 0.690778i \(0.242732\pi\)
−0.723067 + 0.690778i \(0.757268\pi\)
\(608\) −1.11589e14 −1.34308
\(609\) 3.14714e13i 0.375690i
\(610\) 2.15285e14i 2.54897i
\(611\) 1.96269e14 2.30487
\(612\) 8.46942e12 0.0986499
\(613\) −1.16539e13 −0.134639 −0.0673194 0.997731i \(-0.521445\pi\)
−0.0673194 + 0.997731i \(0.521445\pi\)
\(614\) 1.24029e13i 0.142129i
\(615\) 7.76936e13 0.883100
\(616\) 7.87349e13 0.887695
\(617\) 1.26157e14 1.41087 0.705435 0.708775i \(-0.250752\pi\)
0.705435 + 0.708775i \(0.250752\pi\)
\(618\) 1.91132e13 0.212027
\(619\) −3.11922e13 −0.343236 −0.171618 0.985164i \(-0.554899\pi\)
−0.171618 + 0.985164i \(0.554899\pi\)
\(620\) 4.03121e14i 4.40025i
\(621\) 1.69747e14i 1.83799i
\(622\) 4.14137e13i 0.444828i
\(623\) −3.27687e13 −0.349156
\(624\) 2.10817e13i 0.222834i
\(625\) 1.34794e14 1.41342
\(626\) 1.85438e14 1.92898
\(627\) 7.61692e13 0.786035
\(628\) 2.44985e13i 0.250808i
\(629\) 1.83487e13i 0.186360i
\(630\) 1.20059e14i 1.20974i
\(631\) 1.30583e14i 1.30539i 0.757623 + 0.652693i \(0.226361\pi\)
−0.757623 + 0.652693i \(0.773639\pi\)
\(632\) 1.33979e14i 1.32878i
\(633\) −2.84204e13 −0.279648
\(634\) 1.48833e14i 1.45296i
\(635\) 1.99154e14i 1.92895i
\(636\) 1.03581e14i 0.995393i
\(637\) 1.03128e14 0.983284
\(638\) 4.96746e13 0.469928
\(639\) 1.97123e13i 0.185026i
\(640\) −2.78580e14 −2.59448
\(641\) 1.44466e14i 1.33498i −0.744617 0.667492i \(-0.767368\pi\)
0.744617 0.667492i \(-0.232632\pi\)
\(642\) −3.55980e13 −0.326400
\(643\) 1.10913e14 1.00909 0.504544 0.863386i \(-0.331661\pi\)
0.504544 + 0.863386i \(0.331661\pi\)
\(644\) 3.66119e14i 3.30516i
\(645\) −1.36100e14 + 8.57399e13i −1.21916 + 0.768041i
\(646\) −4.04619e13 −0.359653
\(647\) 8.03445e13i 0.708654i −0.935121 0.354327i \(-0.884710\pi\)
0.935121 0.354327i \(-0.115290\pi\)
\(648\) 5.37848e13i 0.470744i
\(649\) 9.80484e12 0.0851563
\(650\) 6.24735e14i 5.38429i
\(651\) −1.95906e14 −1.67550
\(652\) 9.40500e12i 0.0798217i
\(653\) 1.33993e12i 0.0112854i 0.999984 + 0.00564269i \(0.00179613\pi\)
−0.999984 + 0.00564269i \(0.998204\pi\)
\(654\) −2.11177e14 −1.76506
\(655\) 1.08961e14 0.903782
\(656\) −1.28542e13 −0.105810
\(657\) 1.71534e13i 0.140127i
\(658\) −3.63674e14 −2.94837
\(659\) −1.00852e14 −0.811439 −0.405719 0.913998i \(-0.632979\pi\)
−0.405719 + 0.913998i \(0.632979\pi\)
\(660\) 2.25831e14 1.80328
\(661\) 3.71317e13 0.294264 0.147132 0.989117i \(-0.452996\pi\)
0.147132 + 0.989117i \(0.452996\pi\)
\(662\) 2.37615e14 1.86889
\(663\) 3.14632e13i 0.245604i
\(664\) 5.33282e13i 0.413158i
\(665\) 3.47573e14i 2.67263i
\(666\) 6.89132e13 0.525934
\(667\) 8.07966e13i 0.612018i
\(668\) 3.54873e14 2.66803
\(669\) −2.43205e13 −0.181485
\(670\) −1.63516e14 −1.21112
\(671\) 1.00070e14i 0.735687i
\(672\) 1.60782e14i 1.17325i
\(673\) 2.46169e14i 1.78303i 0.452990 + 0.891515i \(0.350357\pi\)
−0.452990 + 0.891515i \(0.649643\pi\)
\(674\) 3.13323e14i 2.25264i
\(675\) 3.25232e14i 2.32100i
\(676\) −3.28494e14 −2.32699
\(677\) 2.33878e14i 1.64454i 0.569095 + 0.822272i \(0.307294\pi\)
−0.569095 + 0.822272i \(0.692706\pi\)
\(678\) 1.45509e13i 0.101564i
\(679\) 2.18348e14i 1.51286i
\(680\) −4.19617e13 −0.288608
\(681\) 1.33934e14 0.914443
\(682\) 3.09220e14i 2.09578i
\(683\) 6.44757e13 0.433803 0.216902 0.976193i \(-0.430405\pi\)
0.216902 + 0.976193i \(0.430405\pi\)
\(684\) 9.20880e13i 0.615067i
\(685\) −2.85597e14 −1.89366
\(686\) 1.16986e14 0.770039
\(687\) 5.77483e13i 0.377359i
\(688\) 2.25175e13 1.41855e13i 0.146075 0.0920240i
\(689\) 1.95667e14 1.26015
\(690\) 6.06152e14i 3.87557i
\(691\) 7.37386e12i 0.0468063i −0.999726 0.0234032i \(-0.992550\pi\)
0.999726 0.0234032i \(-0.00745014\pi\)
\(692\) 2.72713e14 1.71860
\(693\) 5.58065e13i 0.349155i
\(694\) 1.04851e14 0.651290
\(695\) 3.07922e14i 1.89896i
\(696\) 4.13116e13i 0.252945i
\(697\) −1.91842e13 −0.116622
\(698\) 1.41740e14 0.855493
\(699\) −1.36595e14 −0.818560
\(700\) 7.01479e14i 4.17373i
\(701\) 4.68867e13 0.276987 0.138494 0.990363i \(-0.455774\pi\)
0.138494 + 0.990363i \(0.455774\pi\)
\(702\) −4.68722e14 −2.74935
\(703\) −1.99505e14 −1.16192
\(704\) −2.29484e14 −1.32706
\(705\) −3.64864e14 −2.09501
\(706\) 2.55788e14i 1.45833i
\(707\) 1.58267e14i 0.895968i
\(708\) 2.33117e13i 0.131041i
\(709\) 1.01880e14 0.568668 0.284334 0.958725i \(-0.408228\pi\)
0.284334 + 0.958725i \(0.408228\pi\)
\(710\) 2.79211e14i 1.54754i
\(711\) −9.49633e13 −0.522646
\(712\) −4.30145e13 −0.235080
\(713\) 5.02951e14 2.72947
\(714\) 5.82991e13i 0.314174i
\(715\) 4.26600e14i 2.28292i
\(716\) 1.50245e14i 0.798424i
\(717\) 6.27421e13i 0.331103i
\(718\) 8.86873e13i 0.464771i
\(719\) −4.02819e12 −0.0209636 −0.0104818 0.999945i \(-0.503337\pi\)
−0.0104818 + 0.999945i \(0.503337\pi\)
\(720\) 1.99284e13i 0.102994i
\(721\) 4.05408e13i 0.208073i
\(722\) 1.27386e14i 0.649286i
\(723\) 1.52621e14 0.772542
\(724\) −4.24769e14 −2.13531
\(725\) 1.54805e14i 0.772851i
\(726\) −8.83827e13 −0.438212
\(727\) 2.88334e14i 1.41979i 0.704308 + 0.709894i \(0.251257\pi\)
−0.704308 + 0.709894i \(0.748743\pi\)
\(728\) 3.53622e14 1.72935
\(729\) −2.20618e14 −1.07153
\(730\) 2.42966e14i 1.17201i
\(731\) 3.36060e13 2.11710e13i 0.161001 0.101427i
\(732\) 2.37925e14 1.13210
\(733\) 1.60551e14i 0.758739i 0.925245 + 0.379369i \(0.123859\pi\)
−0.925245 + 0.379369i \(0.876141\pi\)
\(734\) 1.26209e14i 0.592394i
\(735\) −1.91714e14 −0.893753
\(736\) 4.12775e14i 1.91128i
\(737\) −7.60068e13 −0.349554
\(738\) 7.20510e13i 0.329123i
\(739\) 3.52502e14i 1.59933i −0.600443 0.799667i \(-0.705009\pi\)
0.600443 0.799667i \(-0.294991\pi\)
\(740\) −5.91504e14 −2.66563
\(741\) 3.42099e14 1.53130
\(742\) −3.62558e14 −1.61198
\(743\) 2.04821e14i 0.904545i 0.891880 + 0.452272i \(0.149386\pi\)
−0.891880 + 0.452272i \(0.850614\pi\)
\(744\) −2.57160e14 −1.12808
\(745\) −2.77877e14 −1.21080
\(746\) −3.48811e14 −1.50972
\(747\) −3.77985e13 −0.162507
\(748\) −5.57623e13 −0.238140
\(749\) 7.55062e13i 0.320312i
\(750\) 6.16642e14i 2.59852i
\(751\) 1.68853e14i 0.706822i 0.935468 + 0.353411i \(0.114978\pi\)
−0.935468 + 0.353411i \(0.885022\pi\)
\(752\) 6.03658e13 0.251016
\(753\) 2.80827e14i 1.16002i
\(754\) 2.23104e14 0.915483
\(755\) 6.70687e14 2.73392
\(756\) 5.26301e14 2.13121
\(757\) 1.93219e14i 0.777267i −0.921392 0.388634i \(-0.872947\pi\)
0.921392 0.388634i \(-0.127053\pi\)
\(758\) 5.58049e14i 2.23011i
\(759\) 2.81756e14i 1.11857i
\(760\) 4.56249e14i 1.79943i
\(761\) 2.44903e14i 0.959558i −0.877389 0.479779i \(-0.840717\pi\)
0.877389 0.479779i \(-0.159283\pi\)
\(762\) 3.63207e14 1.41377
\(763\) 4.47924e14i 1.73214i
\(764\) 9.05081e13i 0.347713i
\(765\) 2.97420e13i 0.113518i
\(766\) 9.98453e13 0.378603
\(767\) 4.40365e13 0.165896
\(768\) 1.53292e14i 0.573739i
\(769\) 3.72779e14 1.38618 0.693090 0.720851i \(-0.256249\pi\)
0.693090 + 0.720851i \(0.256249\pi\)
\(770\) 7.90461e14i 2.92030i
\(771\) 3.67437e14 1.34869
\(772\) −7.64189e12 −0.0278685
\(773\) 5.95281e13i 0.215687i −0.994168 0.107844i \(-0.965605\pi\)
0.994168 0.107844i \(-0.0343946\pi\)
\(774\) 7.95129e13 + 1.26216e14i 0.286242 + 0.454369i
\(775\) −9.63647e14 −3.44675
\(776\) 2.86618e14i 1.01858i
\(777\) 2.87455e14i 1.01500i
\(778\) 3.66131e13 0.128451
\(779\) 2.08590e14i 0.727119i
\(780\) 1.01427e15 3.51303