Properties

Label 43.11.b.b.42.3
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 42.3
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.32

$q$-expansion

\(f(q)\) \(=\) \(q-57.1045i q^{2} +18.6474i q^{3} -2236.92 q^{4} +2202.14i q^{5} +1064.85 q^{6} +1818.95i q^{7} +69263.1i q^{8} +58701.3 q^{9} +O(q^{10})\) \(q-57.1045i q^{2} +18.6474i q^{3} -2236.92 q^{4} +2202.14i q^{5} +1064.85 q^{6} +1818.95i q^{7} +69263.1i q^{8} +58701.3 q^{9} +125752. q^{10} +84875.6 q^{11} -41712.7i q^{12} -196611. q^{13} +103870. q^{14} -41064.1 q^{15} +1.66462e6 q^{16} +562240. q^{17} -3.35210e6i q^{18} -2.47979e6i q^{19} -4.92600e6i q^{20} -33918.6 q^{21} -4.84678e6i q^{22} +4.25931e6 q^{23} -1.29157e6 q^{24} +4.91622e6 q^{25} +1.12273e7i q^{26} +2.19573e6i q^{27} -4.06884e6i q^{28} +7153.04i q^{29} +2.34494e6i q^{30} +9.25813e6 q^{31} -2.41321e7i q^{32} +1.58271e6i q^{33} -3.21064e7i q^{34} -4.00557e6 q^{35} -1.31310e8 q^{36} -2.64139e7i q^{37} -1.41607e8 q^{38} -3.66627e6i q^{39} -1.52527e8 q^{40} -1.16242e8 q^{41} +1.93690e6i q^{42} +(8.45157e7 - 1.20285e8i) q^{43} -1.89860e8 q^{44} +1.29268e8i q^{45} -2.43225e8i q^{46} +3.14889e7 q^{47} +3.10409e7i q^{48} +2.79167e8 q^{49} -2.80738e8i q^{50} +1.04843e7i q^{51} +4.39802e8 q^{52} +2.99781e8 q^{53} +1.25386e8 q^{54} +1.86908e8i q^{55} -1.25986e8 q^{56} +4.62416e7 q^{57} +408471. q^{58} +6.98652e6 q^{59} +9.18569e7 q^{60} -1.07131e9i q^{61} -5.28681e8i q^{62} +1.06775e8i q^{63} +3.26525e8 q^{64} -4.32964e8i q^{65} +9.03797e7 q^{66} +1.30677e9 q^{67} -1.25768e9 q^{68} +7.94249e7i q^{69} +2.28736e8i q^{70} -1.39477e9i q^{71} +4.06583e9i q^{72} +7.73274e8i q^{73} -1.50835e9 q^{74} +9.16747e7i q^{75} +5.54709e9i q^{76} +1.54384e8i q^{77} -2.09361e8 q^{78} -2.98734e8 q^{79} +3.66573e9i q^{80} +3.42531e9 q^{81} +6.63792e9i q^{82} +3.52379e9 q^{83} +7.58731e7 q^{84} +1.23813e9i q^{85} +(-6.86883e9 - 4.82622e9i) q^{86} -133385. q^{87} +5.87875e9i q^{88} -8.07639e9i q^{89} +7.38179e9 q^{90} -3.57625e8i q^{91} -9.52772e9 q^{92} +1.72640e8i q^{93} -1.79815e9i q^{94} +5.46083e9 q^{95} +4.50000e8 q^{96} -7.54869e9 q^{97} -1.59417e10i q^{98} +4.98231e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 57.1045i 1.78451i −0.451528 0.892257i \(-0.649121\pi\)
0.451528 0.892257i \(-0.350879\pi\)
\(3\) 18.6474i 0.0767382i 0.999264 + 0.0383691i \(0.0122163\pi\)
−0.999264 + 0.0383691i \(0.987784\pi\)
\(4\) −2236.92 −2.18449
\(5\) 2202.14i 0.704683i 0.935871 + 0.352342i \(0.114615\pi\)
−0.935871 + 0.352342i \(0.885385\pi\)
\(6\) 1064.85 0.136940
\(7\) 1818.95i 0.108226i 0.998535 + 0.0541128i \(0.0172331\pi\)
−0.998535 + 0.0541128i \(0.982767\pi\)
\(8\) 69263.1i 2.11374i
\(9\) 58701.3 0.994111
\(10\) 125752. 1.25752
\(11\) 84875.6 0.527011 0.263505 0.964658i \(-0.415121\pi\)
0.263505 + 0.964658i \(0.415121\pi\)
\(12\) 41712.7i 0.167634i
\(13\) −196611. −0.529530 −0.264765 0.964313i \(-0.585294\pi\)
−0.264765 + 0.964313i \(0.585294\pi\)
\(14\) 103870. 0.193130
\(15\) −41064.1 −0.0540761
\(16\) 1.66462e6 1.58751
\(17\) 562240. 0.395983 0.197992 0.980204i \(-0.436558\pi\)
0.197992 + 0.980204i \(0.436558\pi\)
\(18\) 3.35210e6i 1.77401i
\(19\) 2.47979e6i 1.00149i −0.865595 0.500745i \(-0.833059\pi\)
0.865595 0.500745i \(-0.166941\pi\)
\(20\) 4.92600e6i 1.53937i
\(21\) −33918.6 −0.00830503
\(22\) 4.84678e6i 0.940458i
\(23\) 4.25931e6 0.661759 0.330879 0.943673i \(-0.392655\pi\)
0.330879 + 0.943673i \(0.392655\pi\)
\(24\) −1.29157e6 −0.162205
\(25\) 4.91622e6 0.503421
\(26\) 1.12273e7i 0.944953i
\(27\) 2.19573e6i 0.153024i
\(28\) 4.06884e6i 0.236418i
\(29\) 7153.04i 0.000348739i 1.00000 0.000174370i \(5.55036e-5\pi\)
−1.00000 0.000174370i \(0.999944\pi\)
\(30\) 2.34494e6i 0.0964996i
\(31\) 9.25813e6 0.323381 0.161691 0.986841i \(-0.448305\pi\)
0.161691 + 0.986841i \(0.448305\pi\)
\(32\) 2.41321e7i 0.719192i
\(33\) 1.58271e6i 0.0404419i
\(34\) 3.21064e7i 0.706638i
\(35\) −4.00557e6 −0.0762648
\(36\) −1.31310e8 −2.17163
\(37\) 2.64139e7i 0.380911i −0.981696 0.190455i \(-0.939004\pi\)
0.981696 0.190455i \(-0.0609964\pi\)
\(38\) −1.41607e8 −1.78717
\(39\) 3.66627e6i 0.0406352i
\(40\) −1.52527e8 −1.48952
\(41\) −1.16242e8 −1.00333 −0.501664 0.865063i \(-0.667279\pi\)
−0.501664 + 0.865063i \(0.667279\pi\)
\(42\) 1.93690e6i 0.0148204i
\(43\) 8.45157e7 1.20285e8i 0.574904 0.818221i
\(44\) −1.89860e8 −1.15125
\(45\) 1.29268e8i 0.700534i
\(46\) 2.43225e8i 1.18092i
\(47\) 3.14889e7 0.137299 0.0686496 0.997641i \(-0.478131\pi\)
0.0686496 + 0.997641i \(0.478131\pi\)
\(48\) 3.10409e7i 0.121823i
\(49\) 2.79167e8 0.988287
\(50\) 2.80738e8i 0.898362i
\(51\) 1.04843e7i 0.0303870i
\(52\) 4.39802e8 1.15675
\(53\) 2.99781e8 0.716844 0.358422 0.933560i \(-0.383315\pi\)
0.358422 + 0.933560i \(0.383315\pi\)
\(54\) 1.25386e8 0.273074
\(55\) 1.86908e8i 0.371376i
\(56\) −1.25986e8 −0.228761
\(57\) 4.62416e7 0.0768526
\(58\) 408471. 0.000622330
\(59\) 6.98652e6 0.00977239 0.00488620 0.999988i \(-0.498445\pi\)
0.00488620 + 0.999988i \(0.498445\pi\)
\(60\) 9.18569e7 0.118129
\(61\) 1.07131e9i 1.26843i −0.773158 0.634214i \(-0.781324\pi\)
0.773158 0.634214i \(-0.218676\pi\)
\(62\) 5.28681e8i 0.577079i
\(63\) 1.06775e8i 0.107588i
\(64\) 3.26525e8 0.304100
\(65\) 4.32964e8i 0.373151i
\(66\) 9.03797e7 0.0721691
\(67\) 1.30677e9 0.967888 0.483944 0.875099i \(-0.339204\pi\)
0.483944 + 0.875099i \(0.339204\pi\)
\(68\) −1.25768e9 −0.865022
\(69\) 7.94249e7i 0.0507822i
\(70\) 2.28736e8i 0.136096i
\(71\) 1.39477e9i 0.773055i −0.922278 0.386528i \(-0.873674\pi\)
0.922278 0.386528i \(-0.126326\pi\)
\(72\) 4.06583e9i 2.10129i
\(73\) 7.73274e8i 0.373009i 0.982454 + 0.186504i \(0.0597158\pi\)
−0.982454 + 0.186504i \(0.940284\pi\)
\(74\) −1.50835e9 −0.679741
\(75\) 9.16747e7i 0.0386316i
\(76\) 5.54709e9i 2.18775i
\(77\) 1.54384e8i 0.0570361i
\(78\) −2.09361e8 −0.0725140
\(79\) −2.98734e8 −0.0970844 −0.0485422 0.998821i \(-0.515458\pi\)
−0.0485422 + 0.998821i \(0.515458\pi\)
\(80\) 3.66573e9i 1.11869i
\(81\) 3.42531e9 0.982368
\(82\) 6.63792e9i 1.79045i
\(83\) 3.52379e9 0.894582 0.447291 0.894389i \(-0.352389\pi\)
0.447291 + 0.894389i \(0.352389\pi\)
\(84\) 7.58731e7 0.0181423
\(85\) 1.23813e9i 0.279043i
\(86\) −6.86883e9 4.82622e9i −1.46013 1.02592i
\(87\) −133385. −2.67616e−5
\(88\) 5.87875e9i 1.11396i
\(89\) 8.07639e9i 1.44633i −0.690676 0.723164i \(-0.742687\pi\)
0.690676 0.723164i \(-0.257313\pi\)
\(90\) 7.38179e9 1.25011
\(91\) 3.57625e8i 0.0573087i
\(92\) −9.52772e9 −1.44561
\(93\) 1.72640e8i 0.0248157i
\(94\) 1.79815e9i 0.245012i
\(95\) 5.46083e9 0.705734
\(96\) 4.50000e8 0.0551895
\(97\) −7.54869e9 −0.879049 −0.439524 0.898231i \(-0.644853\pi\)
−0.439524 + 0.898231i \(0.644853\pi\)
\(98\) 1.59417e10i 1.76361i
\(99\) 4.98231e9 0.523907
\(100\) −1.09972e10 −1.09972
\(101\) 3.95675e9 0.376471 0.188236 0.982124i \(-0.439723\pi\)
0.188236 + 0.982124i \(0.439723\pi\)
\(102\) 5.98700e8 0.0542261
\(103\) 1.14870e10 0.990876 0.495438 0.868643i \(-0.335008\pi\)
0.495438 + 0.868643i \(0.335008\pi\)
\(104\) 1.36179e10i 1.11929i
\(105\) 7.46934e7i 0.00585242i
\(106\) 1.71188e10i 1.27922i
\(107\) 7.45115e9 0.531257 0.265628 0.964076i \(-0.414421\pi\)
0.265628 + 0.964076i \(0.414421\pi\)
\(108\) 4.91168e9i 0.334281i
\(109\) 1.68687e10 1.09635 0.548175 0.836363i \(-0.315323\pi\)
0.548175 + 0.836363i \(0.315323\pi\)
\(110\) 1.06733e10 0.662725
\(111\) 4.92549e8 0.0292304
\(112\) 3.02786e9i 0.171809i
\(113\) 1.10472e10i 0.599596i 0.954003 + 0.299798i \(0.0969192\pi\)
−0.954003 + 0.299798i \(0.903081\pi\)
\(114\) 2.64060e9i 0.137144i
\(115\) 9.37957e9i 0.466331i
\(116\) 1.60008e7i 0.000761818i
\(117\) −1.15413e10 −0.526412
\(118\) 3.98961e8i 0.0174390i
\(119\) 1.02268e9i 0.0428555i
\(120\) 2.84422e9i 0.114303i
\(121\) −1.87336e10 −0.722260
\(122\) −6.11765e10 −2.26353
\(123\) 2.16760e9i 0.0769935i
\(124\) −2.07097e10 −0.706424
\(125\) 3.23314e10i 1.05944i
\(126\) 6.09730e9 0.191993
\(127\) −4.21274e10 −1.27510 −0.637552 0.770407i \(-0.720053\pi\)
−0.637552 + 0.770407i \(0.720053\pi\)
\(128\) 4.33573e10i 1.26186i
\(129\) 2.24301e9 + 1.57600e9i 0.0627888 + 0.0441170i
\(130\) −2.47241e10 −0.665893
\(131\) 2.65584e9i 0.0688407i 0.999407 + 0.0344203i \(0.0109585\pi\)
−0.999407 + 0.0344203i \(0.989042\pi\)
\(132\) 3.54039e9i 0.0883449i
\(133\) 4.51061e9 0.108387
\(134\) 7.46224e10i 1.72721i
\(135\) −4.83530e9 −0.107834
\(136\) 3.89424e10i 0.837006i
\(137\) 1.39044e10i 0.288104i 0.989570 + 0.144052i \(0.0460133\pi\)
−0.989570 + 0.144052i \(0.953987\pi\)
\(138\) 4.53552e9 0.0906215
\(139\) 2.23725e10 0.431162 0.215581 0.976486i \(-0.430835\pi\)
0.215581 + 0.976486i \(0.430835\pi\)
\(140\) 8.96013e9 0.166600
\(141\) 5.87185e8i 0.0105361i
\(142\) −7.96475e10 −1.37953
\(143\) −1.66875e10 −0.279068
\(144\) 9.77156e10 1.57816
\(145\) −1.57520e7 −0.000245751
\(146\) 4.41574e10 0.665639
\(147\) 5.20573e9i 0.0758394i
\(148\) 5.90856e10i 0.832096i
\(149\) 9.63861e10i 1.31245i 0.754565 + 0.656225i \(0.227848\pi\)
−0.754565 + 0.656225i \(0.772152\pi\)
\(150\) 5.23503e9 0.0689387
\(151\) 8.29933e10i 1.05720i 0.848870 + 0.528601i \(0.177283\pi\)
−0.848870 + 0.528601i \(0.822717\pi\)
\(152\) 1.71758e11 2.11689
\(153\) 3.30042e10 0.393651
\(154\) 8.81603e9 0.101782
\(155\) 2.03877e10i 0.227882i
\(156\) 8.20116e9i 0.0887671i
\(157\) 1.42899e11i 1.49807i 0.662532 + 0.749034i \(0.269482\pi\)
−0.662532 + 0.749034i \(0.730518\pi\)
\(158\) 1.70591e10i 0.173249i
\(159\) 5.59013e9i 0.0550093i
\(160\) 5.31421e10 0.506803
\(161\) 7.74746e9i 0.0716192i
\(162\) 1.95600e11i 1.75305i
\(163\) 1.25418e11i 1.08999i −0.838440 0.544993i \(-0.816532\pi\)
0.838440 0.544993i \(-0.183468\pi\)
\(164\) 2.60023e11 2.19176
\(165\) −3.48534e9 −0.0284987
\(166\) 2.01224e11i 1.59639i
\(167\) 5.76436e10 0.443781 0.221891 0.975072i \(-0.428777\pi\)
0.221891 + 0.975072i \(0.428777\pi\)
\(168\) 2.34931e9i 0.0175547i
\(169\) −9.92027e10 −0.719598
\(170\) 7.07026e10 0.497956
\(171\) 1.45567e11i 0.995593i
\(172\) −1.89055e11 + 2.69069e11i −1.25587 + 1.78740i
\(173\) 1.26919e11 0.819021 0.409511 0.912305i \(-0.365699\pi\)
0.409511 + 0.912305i \(0.365699\pi\)
\(174\) 7.61690e6i 4.77565e-5i
\(175\) 8.94235e9i 0.0544831i
\(176\) 1.41286e11 0.836635
\(177\) 1.30280e8i 0.000749915i
\(178\) −4.61198e11 −2.58099
\(179\) 2.41061e11i 1.31179i 0.754854 + 0.655893i \(0.227708\pi\)
−0.754854 + 0.655893i \(0.772292\pi\)
\(180\) 2.89162e11i 1.53031i
\(181\) −2.48789e11 −1.28067 −0.640336 0.768095i \(-0.721205\pi\)
−0.640336 + 0.768095i \(0.721205\pi\)
\(182\) −2.04220e10 −0.102268
\(183\) 1.99771e10 0.0973368
\(184\) 2.95013e11i 1.39879i
\(185\) 5.81669e10 0.268421
\(186\) 9.85851e9 0.0442840
\(187\) 4.77204e10 0.208688
\(188\) −7.04380e10 −0.299929
\(189\) −3.99392e9 −0.0165612
\(190\) 3.11838e11i 1.25939i
\(191\) 1.27186e11i 0.500347i 0.968201 + 0.250174i \(0.0804877\pi\)
−0.968201 + 0.250174i \(0.919512\pi\)
\(192\) 6.08884e9i 0.0233361i
\(193\) −1.33168e11 −0.497293 −0.248647 0.968594i \(-0.579986\pi\)
−0.248647 + 0.968594i \(0.579986\pi\)
\(194\) 4.31064e11i 1.56867i
\(195\) 8.07363e9 0.0286349
\(196\) −6.24473e11 −2.15890
\(197\) 3.13724e11 1.05734 0.528672 0.848826i \(-0.322690\pi\)
0.528672 + 0.848826i \(0.322690\pi\)
\(198\) 2.84512e11i 0.934920i
\(199\) 4.99495e11i 1.60054i 0.599642 + 0.800268i \(0.295310\pi\)
−0.599642 + 0.800268i \(0.704690\pi\)
\(200\) 3.40513e11i 1.06410i
\(201\) 2.43678e10i 0.0742739i
\(202\) 2.25948e11i 0.671818i
\(203\) −1.30110e7 −3.77425e−5
\(204\) 2.34525e10i 0.0663802i
\(205\) 2.55980e11i 0.707028i
\(206\) 6.55957e11i 1.76823i
\(207\) 2.50027e11 0.657862
\(208\) −3.27283e11 −0.840634
\(209\) 2.10474e11i 0.527796i
\(210\) −4.26532e9 −0.0104437
\(211\) 4.50429e11i 1.07700i 0.842627 + 0.538498i \(0.181008\pi\)
−0.842627 + 0.538498i \(0.818992\pi\)
\(212\) −6.70586e11 −1.56594
\(213\) 2.60088e10 0.0593228
\(214\) 4.25494e11i 0.948035i
\(215\) 2.64885e11 + 1.86115e11i 0.576587 + 0.405125i
\(216\) −1.52083e11 −0.323454
\(217\) 1.68401e10i 0.0349981i
\(218\) 9.63279e11i 1.95645i
\(219\) −1.44195e10 −0.0286240
\(220\) 4.18097e11i 0.811267i
\(221\) −1.10542e11 −0.209685
\(222\) 2.81267e10i 0.0521620i
\(223\) 7.34909e11i 1.33263i −0.745671 0.666315i \(-0.767871\pi\)
0.745671 0.666315i \(-0.232129\pi\)
\(224\) 4.38950e10 0.0778350
\(225\) 2.88589e11 0.500457
\(226\) 6.30842e11 1.06999
\(227\) 8.22389e11i 1.36442i −0.731156 0.682210i \(-0.761019\pi\)
0.731156 0.682210i \(-0.238981\pi\)
\(228\) −1.03439e11 −0.167884
\(229\) 8.77283e11 1.39304 0.696518 0.717539i \(-0.254732\pi\)
0.696518 + 0.717539i \(0.254732\pi\)
\(230\) 5.35615e11 0.832173
\(231\) −2.87886e9 −0.00437684
\(232\) −4.95442e8 −0.000737144
\(233\) 6.34864e11i 0.924488i −0.886753 0.462244i \(-0.847044\pi\)
0.886753 0.462244i \(-0.152956\pi\)
\(234\) 6.59060e11i 0.939389i
\(235\) 6.93428e10i 0.0967524i
\(236\) −1.56283e10 −0.0213477
\(237\) 5.57061e9i 0.00745008i
\(238\) 5.83998e10 0.0764763
\(239\) −7.00573e9 −0.00898388 −0.00449194 0.999990i \(-0.501430\pi\)
−0.00449194 + 0.999990i \(0.501430\pi\)
\(240\) −6.83562e10 −0.0858464
\(241\) 1.92126e11i 0.236321i −0.992995 0.118160i \(-0.962300\pi\)
0.992995 0.118160i \(-0.0376997\pi\)
\(242\) 1.06977e12i 1.28888i
\(243\) 1.93529e11i 0.228410i
\(244\) 2.39643e12i 2.77087i
\(245\) 6.14763e11i 0.696430i
\(246\) −1.23780e11 −0.137396
\(247\) 4.87553e11i 0.530319i
\(248\) 6.41247e11i 0.683544i
\(249\) 6.57095e10i 0.0686486i
\(250\) 1.84627e12 1.89058
\(251\) −7.65495e11 −0.768375 −0.384188 0.923255i \(-0.625518\pi\)
−0.384188 + 0.923255i \(0.625518\pi\)
\(252\) 2.38846e11i 0.235026i
\(253\) 3.61511e11 0.348754
\(254\) 2.40566e12i 2.27544i
\(255\) −2.30878e10 −0.0214132
\(256\) −2.14153e12 −1.94771
\(257\) 2.15015e12i 1.91780i −0.283745 0.958900i \(-0.591577\pi\)
0.283745 0.958900i \(-0.408423\pi\)
\(258\) 8.99964e10 1.28086e11i 0.0787275 0.112048i
\(259\) 4.80454e10 0.0412243
\(260\) 9.68504e11i 0.815145i
\(261\) 4.19893e8i 0.000346686i
\(262\) 1.51660e11 0.122847
\(263\) 9.92900e11i 0.789090i −0.918877 0.394545i \(-0.870902\pi\)
0.918877 0.394545i \(-0.129098\pi\)
\(264\) −1.09623e11 −0.0854836
\(265\) 6.60158e11i 0.505148i
\(266\) 2.57576e11i 0.193418i
\(267\) 1.50603e11 0.110989
\(268\) −2.92314e12 −2.11434
\(269\) 3.87961e11 0.275440 0.137720 0.990471i \(-0.456023\pi\)
0.137720 + 0.990471i \(0.456023\pi\)
\(270\) 2.76117e11i 0.192431i
\(271\) 1.29080e11 0.0883107 0.0441554 0.999025i \(-0.485940\pi\)
0.0441554 + 0.999025i \(0.485940\pi\)
\(272\) 9.35918e11 0.628627
\(273\) 6.66876e9 0.00439776
\(274\) 7.94004e11 0.514126
\(275\) 4.17268e11 0.265308
\(276\) 1.77667e11i 0.110933i
\(277\) 1.08344e12i 0.664364i 0.943215 + 0.332182i \(0.107785\pi\)
−0.943215 + 0.332182i \(0.892215\pi\)
\(278\) 1.27757e12i 0.769415i
\(279\) 5.43464e11 0.321477
\(280\) 2.77438e11i 0.161204i
\(281\) −5.74014e11 −0.327635 −0.163818 0.986491i \(-0.552381\pi\)
−0.163818 + 0.986491i \(0.552381\pi\)
\(282\) 3.35309e10 0.0188018
\(283\) −2.28530e12 −1.25896 −0.629478 0.777018i \(-0.716731\pi\)
−0.629478 + 0.777018i \(0.716731\pi\)
\(284\) 3.11998e12i 1.68873i
\(285\) 1.01830e11i 0.0541567i
\(286\) 9.52928e11i 0.498001i
\(287\) 2.11438e11i 0.108586i
\(288\) 1.41658e12i 0.714957i
\(289\) −1.69988e12 −0.843197
\(290\) 8.99508e8i 0.000438546i
\(291\) 1.40763e11i 0.0674566i
\(292\) 1.72975e12i 0.814834i
\(293\) −1.26450e12 −0.585572 −0.292786 0.956178i \(-0.594582\pi\)
−0.292786 + 0.956178i \(0.594582\pi\)
\(294\) 2.97270e11 0.135336
\(295\) 1.53853e10i 0.00688644i
\(296\) 1.82950e12 0.805146
\(297\) 1.86364e11i 0.0806456i
\(298\) 5.50407e12 2.34209
\(299\) −8.37425e11 −0.350421
\(300\) 2.05069e11i 0.0843904i
\(301\) 2.18793e11 + 1.53730e11i 0.0885525 + 0.0622193i
\(302\) 4.73929e12 1.88659
\(303\) 7.37830e10i 0.0288897i
\(304\) 4.12792e12i 1.58988i
\(305\) 2.35917e12 0.893840
\(306\) 1.88469e12i 0.702477i
\(307\) 2.50470e11 0.0918469 0.0459235 0.998945i \(-0.485377\pi\)
0.0459235 + 0.998945i \(0.485377\pi\)
\(308\) 3.45345e11i 0.124595i
\(309\) 2.14202e11i 0.0760380i
\(310\) 1.16423e12 0.406658
\(311\) −4.53328e12 −1.55815 −0.779077 0.626928i \(-0.784312\pi\)
−0.779077 + 0.626928i \(0.784312\pi\)
\(312\) 2.53937e11 0.0858922
\(313\) 3.19354e12i 1.06304i −0.847045 0.531522i \(-0.821620\pi\)
0.847045 0.531522i \(-0.178380\pi\)
\(314\) 8.16018e12 2.67332
\(315\) −2.35132e11 −0.0758157
\(316\) 6.68244e11 0.212080
\(317\) −4.16251e12 −1.30035 −0.650173 0.759786i \(-0.725304\pi\)
−0.650173 + 0.759786i \(0.725304\pi\)
\(318\) 3.19221e11 0.0981649
\(319\) 6.07119e8i 0.000183789i
\(320\) 7.19053e11i 0.214295i
\(321\) 1.38944e11i 0.0407677i
\(322\) 4.42414e11 0.127806
\(323\) 1.39424e12i 0.396574i
\(324\) −7.66213e12 −2.14597
\(325\) −9.66582e11 −0.266577
\(326\) −7.16192e12 −1.94510
\(327\) 3.14557e11i 0.0841320i
\(328\) 8.05126e12i 2.12077i
\(329\) 5.72766e10i 0.0148593i
\(330\) 1.99028e11i 0.0508563i
\(331\) 2.33766e12i 0.588358i −0.955750 0.294179i \(-0.904954\pi\)
0.955750 0.294179i \(-0.0950461\pi\)
\(332\) −7.88244e12 −1.95421
\(333\) 1.55053e12i 0.378668i
\(334\) 3.29171e12i 0.791934i
\(335\) 2.87768e12i 0.682055i
\(336\) −5.64617e10 −0.0131843
\(337\) −6.43508e12 −1.48049 −0.740244 0.672339i \(-0.765290\pi\)
−0.740244 + 0.672339i \(0.765290\pi\)
\(338\) 5.66492e12i 1.28413i
\(339\) −2.06001e11 −0.0460119
\(340\) 2.76959e12i 0.609567i
\(341\) 7.85790e11 0.170426
\(342\) −8.31251e12 −1.77665
\(343\) 1.02160e12i 0.215184i
\(344\) 8.33134e12 + 5.85381e12i 1.72951 + 1.21520i
\(345\) −1.74904e11 −0.0357854
\(346\) 7.24762e12i 1.46155i
\(347\) 6.74519e12i 1.34075i 0.742024 + 0.670373i \(0.233866\pi\)
−0.742024 + 0.670373i \(0.766134\pi\)
\(348\) 2.98372e8 5.84605e−5
\(349\) 3.87004e12i 0.747462i 0.927537 + 0.373731i \(0.121922\pi\)
−0.927537 + 0.373731i \(0.878078\pi\)
\(350\) 5.10648e11 0.0972258
\(351\) 4.31705e11i 0.0810310i
\(352\) 2.04823e12i 0.379022i
\(353\) 2.15226e12 0.392665 0.196332 0.980537i \(-0.437097\pi\)
0.196332 + 0.980537i \(0.437097\pi\)
\(354\) 7.43958e9 0.00133823
\(355\) 3.07147e12 0.544759
\(356\) 1.80662e13i 3.15949i
\(357\) −1.90704e10 −0.00328865
\(358\) 1.37657e13 2.34090
\(359\) 6.07414e12 1.01862 0.509310 0.860583i \(-0.329901\pi\)
0.509310 + 0.860583i \(0.329901\pi\)
\(360\) −8.95351e12 −1.48075
\(361\) −1.82909e10 −0.00298331
\(362\) 1.42070e13i 2.28538i
\(363\) 3.49332e11i 0.0554249i
\(364\) 7.99977e11i 0.125190i
\(365\) −1.70285e12 −0.262853
\(366\) 1.14078e12i 0.173699i
\(367\) −2.68441e12 −0.403198 −0.201599 0.979468i \(-0.564614\pi\)
−0.201599 + 0.979468i \(0.564614\pi\)
\(368\) 7.09015e12 1.05055
\(369\) −6.82354e12 −0.997419
\(370\) 3.32159e12i 0.479002i
\(371\) 5.45286e11i 0.0775809i
\(372\) 3.86181e11i 0.0542097i
\(373\) 8.55286e12i 1.18459i −0.805722 0.592294i \(-0.798222\pi\)
0.805722 0.592294i \(-0.201778\pi\)
\(374\) 2.72505e12i 0.372406i
\(375\) −6.02896e11 −0.0812992
\(376\) 2.18102e12i 0.290215i
\(377\) 1.40636e9i 0.000184668i
\(378\) 2.28071e11i 0.0295536i
\(379\) 1.36576e13 1.74654 0.873269 0.487238i \(-0.161996\pi\)
0.873269 + 0.487238i \(0.161996\pi\)
\(380\) −1.22154e13 −1.54167
\(381\) 7.85565e11i 0.0978492i
\(382\) 7.26287e12 0.892877
\(383\) 5.32035e12i 0.645574i −0.946472 0.322787i \(-0.895380\pi\)
0.946472 0.322787i \(-0.104620\pi\)
\(384\) 8.08500e11 0.0968331
\(385\) −3.39975e11 −0.0401924
\(386\) 7.60447e12i 0.887427i
\(387\) 4.96118e12 7.06091e12i 0.571518 0.813403i
\(388\) 1.68858e13 1.92027
\(389\) 7.76096e12i 0.871299i −0.900116 0.435650i \(-0.856519\pi\)
0.900116 0.435650i \(-0.143481\pi\)
\(390\) 4.61040e11i 0.0510994i
\(391\) 2.39475e12 0.262045
\(392\) 1.93359e13i 2.08898i
\(393\) −4.95244e10 −0.00528271
\(394\) 1.79150e13i 1.88685i
\(395\) 6.57853e11i 0.0684138i
\(396\) −1.11450e13 −1.14447
\(397\) −8.18970e12 −0.830454 −0.415227 0.909718i \(-0.636298\pi\)
−0.415227 + 0.909718i \(0.636298\pi\)
\(398\) 2.85234e13 2.85618
\(399\) 8.41110e10i 0.00831741i
\(400\) 8.18366e12 0.799186
\(401\) 1.19369e13 1.15125 0.575626 0.817713i \(-0.304758\pi\)
0.575626 + 0.817713i \(0.304758\pi\)
\(402\) 1.39151e12 0.132543
\(403\) −1.82025e12 −0.171240
\(404\) −8.85093e12 −0.822398
\(405\) 7.54299e12i 0.692259i
\(406\) 7.42986e8i 6.73520e-5i
\(407\) 2.24189e12i 0.200744i
\(408\) −7.26174e11 −0.0642303
\(409\) 2.10211e13i 1.83670i −0.395766 0.918351i \(-0.629521\pi\)
0.395766 0.918351i \(-0.370479\pi\)
\(410\) −1.46176e13 −1.26170
\(411\) −2.59281e11 −0.0221086
\(412\) −2.56954e13 −2.16456
\(413\) 1.27081e10i 0.00105762i
\(414\) 1.42776e13i 1.17396i
\(415\) 7.75987e12i 0.630397i
\(416\) 4.74463e12i 0.380834i
\(417\) 4.17189e11i 0.0330866i
\(418\) −1.20190e13 −0.941860
\(419\) 1.65091e13i 1.27836i 0.769056 + 0.639181i \(0.220727\pi\)
−0.769056 + 0.639181i \(0.779273\pi\)
\(420\) 1.67083e11i 0.0127846i
\(421\) 2.29197e13i 1.73300i 0.499176 + 0.866501i \(0.333636\pi\)
−0.499176 + 0.866501i \(0.666364\pi\)
\(422\) 2.57215e13 1.92192
\(423\) 1.84844e12 0.136491
\(424\) 2.07637e13i 1.51522i
\(425\) 2.76410e12 0.199346
\(426\) 1.48522e12i 0.105862i
\(427\) 1.94866e12 0.137276
\(428\) −1.66676e13 −1.16053
\(429\) 3.11177e11i 0.0214152i
\(430\) 1.06280e13 1.51261e13i 0.722951 1.02893i
\(431\) 2.74183e13 1.84355 0.921773 0.387731i \(-0.126741\pi\)
0.921773 + 0.387731i \(0.126741\pi\)
\(432\) 3.65507e12i 0.242928i
\(433\) 1.02469e13i 0.673216i 0.941645 + 0.336608i \(0.109280\pi\)
−0.941645 + 0.336608i \(0.890720\pi\)
\(434\) 9.61642e11 0.0624547
\(435\) 2.93733e8i 1.88585e-5i
\(436\) −3.77340e13 −2.39497
\(437\) 1.05622e13i 0.662745i
\(438\) 8.23419e11i 0.0510799i
\(439\) −2.04098e13 −1.25175 −0.625873 0.779925i \(-0.715257\pi\)
−0.625873 + 0.779925i \(0.715257\pi\)
\(440\) −1.29458e13 −0.784992
\(441\) 1.63874e13 0.982467
\(442\) 6.31246e12i 0.374186i
\(443\) 1.64922e13 0.966630 0.483315 0.875447i \(-0.339433\pi\)
0.483315 + 0.875447i \(0.339433\pi\)
\(444\) −1.10179e12 −0.0638535
\(445\) 1.77853e13 1.01920
\(446\) −4.19666e13 −2.37810
\(447\) −1.79735e12 −0.100715
\(448\) 5.93932e11i 0.0329114i
\(449\) 4.44530e11i 0.0243596i −0.999926 0.0121798i \(-0.996123\pi\)
0.999926 0.0121798i \(-0.00387704\pi\)
\(450\) 1.64797e13i 0.893072i
\(451\) −9.86609e12 −0.528764
\(452\) 2.47116e13i 1.30981i
\(453\) −1.54761e12 −0.0811278
\(454\) −4.69621e13 −2.43483
\(455\) 7.87538e11 0.0403845
\(456\) 3.20283e12i 0.162446i
\(457\) 3.80983e12i 0.191128i −0.995423 0.0955641i \(-0.969534\pi\)
0.995423 0.0955641i \(-0.0304655\pi\)
\(458\) 5.00968e13i 2.48589i
\(459\) 1.23453e12i 0.0605951i
\(460\) 2.09813e13i 1.01869i
\(461\) −3.28817e13 −1.57924 −0.789622 0.613594i \(-0.789723\pi\)
−0.789622 + 0.613594i \(0.789723\pi\)
\(462\) 1.64396e11i 0.00781054i
\(463\) 3.09113e13i 1.45282i 0.687262 + 0.726410i \(0.258812\pi\)
−0.687262 + 0.726410i \(0.741188\pi\)
\(464\) 1.19071e10i 0.000553627i
\(465\) −3.80177e11 −0.0174872
\(466\) −3.62536e13 −1.64976
\(467\) 2.24409e11i 0.0101031i −0.999987 0.00505156i \(-0.998392\pi\)
0.999987 0.00505156i \(-0.00160797\pi\)
\(468\) 2.58169e13 1.14994
\(469\) 2.37695e12i 0.104750i
\(470\) 3.95978e12 0.172656
\(471\) −2.66470e12 −0.114959
\(472\) 4.83908e11i 0.0206563i
\(473\) 7.17332e12 1.02093e13i 0.302980 0.431211i
\(474\) −3.18107e11 −0.0132948
\(475\) 1.21912e13i 0.504172i
\(476\) 2.28766e12i 0.0936175i
\(477\) 1.75975e13 0.712623
\(478\) 4.00058e11i 0.0160319i
\(479\) −1.96576e13 −0.779566 −0.389783 0.920907i \(-0.627450\pi\)
−0.389783 + 0.920907i \(0.627450\pi\)
\(480\) 9.90962e11i 0.0388911i
\(481\) 5.19325e12i 0.201704i
\(482\) −1.09713e13 −0.421718
\(483\) −1.44470e11 −0.00549593
\(484\) 4.19054e13 1.57777
\(485\) 1.66232e13i 0.619451i
\(486\) 1.10514e13 0.407600
\(487\) 3.32804e13 1.21491 0.607454 0.794355i \(-0.292191\pi\)
0.607454 + 0.794355i \(0.292191\pi\)
\(488\) 7.42022e13 2.68113
\(489\) 2.33871e12 0.0836436
\(490\) 3.51057e13 1.24279
\(491\) 2.31126e13i 0.809918i 0.914335 + 0.404959i \(0.132714\pi\)
−0.914335 + 0.404959i \(0.867286\pi\)
\(492\) 4.84875e12i 0.168192i
\(493\) 4.02172e9i 0.000138095i
\(494\) 2.78415e13 0.946362
\(495\) 1.09717e13i 0.369189i
\(496\) 1.54113e13 0.513371
\(497\) 2.53701e12 0.0836643
\(498\) 3.75231e12 0.122504
\(499\) 8.58315e11i 0.0277424i 0.999904 + 0.0138712i \(0.00441548\pi\)
−0.999904 + 0.0138712i \(0.995585\pi\)
\(500\) 7.23228e13i 2.31433i
\(501\) 1.07490e12i 0.0340550i
\(502\) 4.37131e13i 1.37118i
\(503\) 3.88625e12i 0.120696i −0.998177 0.0603478i \(-0.980779\pi\)
0.998177 0.0603478i \(-0.0192210\pi\)
\(504\) −7.39553e12 −0.227414
\(505\) 8.71330e12i 0.265293i
\(506\) 2.06439e13i 0.622357i
\(507\) 1.84987e12i 0.0552206i
\(508\) 9.42355e13 2.78545
\(509\) −5.83701e13 −1.70845 −0.854223 0.519906i \(-0.825967\pi\)
−0.854223 + 0.519906i \(0.825967\pi\)
\(510\) 1.31842e12i 0.0382122i
\(511\) −1.40654e12 −0.0403691
\(512\) 7.78932e13i 2.21386i
\(513\) 5.44496e12 0.153253
\(514\) −1.22783e14 −3.42234
\(515\) 2.52959e13i 0.698254i
\(516\) −5.01743e12 3.52537e12i −0.137162 0.0963733i
\(517\) 2.67264e12 0.0723581
\(518\) 2.74361e12i 0.0735653i
\(519\) 2.36670e12i 0.0628502i
\(520\) 2.99884e13 0.788744
\(521\) 1.80423e13i 0.470006i −0.971995 0.235003i \(-0.924490\pi\)
0.971995 0.235003i \(-0.0755100\pi\)
\(522\) 2.39777e10 0.000618665
\(523\) 6.85020e13i 1.75063i 0.483552 + 0.875316i \(0.339347\pi\)
−0.483552 + 0.875316i \(0.660653\pi\)
\(524\) 5.94089e12i 0.150382i
\(525\) −1.66751e11 −0.00418093
\(526\) −5.66990e13 −1.40814
\(527\) 5.20529e12 0.128054
\(528\) 2.63461e12i 0.0642018i
\(529\) −2.32848e13 −0.562075
\(530\) 3.76980e13 0.901444
\(531\) 4.10118e11 0.00971484
\(532\) −1.00899e13 −0.236770
\(533\) 2.28544e13 0.531292
\(534\) 8.60013e12i 0.198061i
\(535\) 1.64084e13i 0.374368i
\(536\) 9.05109e13i 2.04586i
\(537\) −4.49516e12 −0.100664
\(538\) 2.21543e13i 0.491526i
\(539\) 2.36944e13 0.520838
\(540\) 1.08162e13 0.235562
\(541\) −6.10736e13 −1.31785 −0.658926 0.752207i \(-0.728989\pi\)
−0.658926 + 0.752207i \(0.728989\pi\)
\(542\) 7.37106e12i 0.157592i
\(543\) 4.63926e12i 0.0982765i
\(544\) 1.35680e13i 0.284788i
\(545\) 3.71472e13i 0.772580i
\(546\) 3.80816e11i 0.00784787i
\(547\) −7.67144e13 −1.56653 −0.783267 0.621685i \(-0.786448\pi\)
−0.783267 + 0.621685i \(0.786448\pi\)
\(548\) 3.11030e13i 0.629362i
\(549\) 6.28872e13i 1.26096i
\(550\) 2.38278e13i 0.473447i
\(551\) 1.77380e10 0.000349259
\(552\) −5.50121e12 −0.107340
\(553\) 5.43382e11i 0.0105070i
\(554\) 6.18693e13 1.18557
\(555\) 1.08466e12i 0.0205982i
\(556\) −5.00455e13 −0.941870
\(557\) −2.21154e13 −0.412496 −0.206248 0.978500i \(-0.566125\pi\)
−0.206248 + 0.978500i \(0.566125\pi\)
\(558\) 3.10342e13i 0.573680i
\(559\) −1.66167e13 + 2.36494e13i −0.304429 + 0.433273i
\(560\) −6.66777e12 −0.121071
\(561\) 8.89861e11i 0.0160143i
\(562\) 3.27787e13i 0.584670i
\(563\) 2.34950e13 0.415369 0.207685 0.978196i \(-0.433407\pi\)
0.207685 + 0.978196i \(0.433407\pi\)
\(564\) 1.31348e12i 0.0230160i
\(565\) −2.43273e13 −0.422525
\(566\) 1.30501e14i 2.24662i
\(567\) 6.23045e12i 0.106317i
\(568\) 9.66059e13 1.63404
\(569\) 1.92419e11 0.00322616 0.00161308 0.999999i \(-0.499487\pi\)
0.00161308 + 0.999999i \(0.499487\pi\)
\(570\) 5.81496e12 0.0966434
\(571\) 6.65935e13i 1.09711i 0.836114 + 0.548556i \(0.184822\pi\)
−0.836114 + 0.548556i \(0.815178\pi\)
\(572\) 3.73285e13 0.609621
\(573\) −2.37168e12 −0.0383957
\(574\) −1.20740e13 −0.193773
\(575\) 2.09397e13 0.333143
\(576\) 1.91675e13 0.302310
\(577\) 6.72009e13i 1.05074i −0.850873 0.525371i \(-0.823926\pi\)
0.850873 0.525371i \(-0.176074\pi\)
\(578\) 9.70707e13i 1.50470i
\(579\) 2.48323e12i 0.0381614i
\(580\) 3.52359e10 0.000536840
\(581\) 6.40960e12i 0.0968166i
\(582\) −8.03821e12 −0.120377
\(583\) 2.54441e13 0.377785
\(584\) −5.35593e13 −0.788444
\(585\) 2.54155e13i 0.370954i
\(586\) 7.22085e13i 1.04496i
\(587\) 9.27329e12i 0.133059i −0.997784 0.0665293i \(-0.978807\pi\)
0.997784 0.0665293i \(-0.0211926\pi\)
\(588\) 1.16448e13i 0.165670i
\(589\) 2.29582e13i 0.323863i
\(590\) 8.78567e11 0.0122890
\(591\) 5.85012e12i 0.0811386i
\(592\) 4.39691e13i 0.604699i
\(593\) 1.26589e14i 1.72632i −0.504927 0.863162i \(-0.668481\pi\)
0.504927 0.863162i \(-0.331519\pi\)
\(594\) 1.06422e13 0.143913
\(595\) −2.25209e12 −0.0301996
\(596\) 2.15608e14i 2.86704i
\(597\) −9.31427e12 −0.122822
\(598\) 4.78207e13i 0.625331i
\(599\) 9.12594e13 1.18343 0.591716 0.806146i \(-0.298451\pi\)
0.591716 + 0.806146i \(0.298451\pi\)
\(600\) −6.34967e12 −0.0816572
\(601\) 8.65963e13i 1.10440i −0.833711 0.552201i \(-0.813788\pi\)
0.833711 0.552201i \(-0.186212\pi\)
\(602\) 8.77864e12 1.24940e13i 0.111031 0.158023i
\(603\) 7.67090e13 0.962188
\(604\) 1.85649e14i 2.30945i
\(605\) 4.12538e13i 0.508964i
\(606\) 4.21334e12 0.0515541
\(607\) 2.96451e13i 0.359758i −0.983689 0.179879i \(-0.942429\pi\)
0.983689 0.179879i \(-0.0575706\pi\)
\(608\) −5.98425e13 −0.720264
\(609\) 2.42621e8i 2.89629e-6i
\(610\) 1.34719e14i 1.59507i
\(611\) −6.19105e12 −0.0727040
\(612\) −7.38277e13 −0.859928
\(613\) −2.80351e13 −0.323891 −0.161946 0.986800i \(-0.551777\pi\)
−0.161946 + 0.986800i \(0.551777\pi\)
\(614\) 1.43030e13i 0.163902i
\(615\) 4.77336e12 0.0542561
\(616\) −1.06931e13 −0.120559
\(617\) 1.75598e13 0.196378 0.0981891 0.995168i \(-0.468695\pi\)
0.0981891 + 0.995168i \(0.468695\pi\)
\(618\) 1.22319e13 0.135691
\(619\) −4.13205e13 −0.454686 −0.227343 0.973815i \(-0.573004\pi\)
−0.227343 + 0.973815i \(0.573004\pi\)
\(620\) 4.56056e13i 0.497805i
\(621\) 9.35230e12i 0.101265i
\(622\) 2.58870e14i 2.78055i
\(623\) 1.46905e13 0.156530
\(624\) 6.10297e12i 0.0645087i
\(625\) −2.31882e13 −0.243146
\(626\) −1.82366e14 −1.89702
\(627\) 3.92478e12 0.0405021
\(628\) 3.19654e14i 3.27252i
\(629\) 1.48509e13i 0.150834i
\(630\) 1.34271e13i 0.135294i
\(631\) 1.03967e14i 1.03932i 0.854373 + 0.519660i \(0.173941\pi\)
−0.854373 + 0.519660i \(0.826059\pi\)
\(632\) 2.06912e13i 0.205211i
\(633\) −8.39932e12 −0.0826467
\(634\) 2.37698e14i 2.32049i
\(635\) 9.27702e13i 0.898545i
\(636\) 1.25047e13i 0.120167i
\(637\) −5.48872e13 −0.523328
\(638\) 3.46692e10 0.000327975
\(639\) 8.18747e13i 0.768503i
\(640\) 9.54787e13 0.889215
\(641\) 8.81924e13i 0.814969i 0.913212 + 0.407484i \(0.133594\pi\)
−0.913212 + 0.407484i \(0.866406\pi\)
\(642\) 7.93434e12 0.0727505
\(643\) 1.86707e14 1.69866 0.849329 0.527865i \(-0.177007\pi\)
0.849329 + 0.527865i \(0.177007\pi\)
\(644\) 1.73304e13i 0.156452i
\(645\) −3.47056e12 + 4.93941e12i −0.0310886 + 0.0442462i
\(646\) −7.96171e13 −0.707691
\(647\) 4.89851e13i 0.432058i 0.976387 + 0.216029i \(0.0693106\pi\)
−0.976387 + 0.216029i \(0.930689\pi\)
\(648\) 2.37247e14i 2.07647i
\(649\) 5.92985e11 0.00515016
\(650\) 5.51961e13i 0.475710i
\(651\) −3.14023e11 −0.00268569
\(652\) 2.80549e14i 2.38107i
\(653\) 1.63337e14i 1.37569i −0.725859 0.687844i \(-0.758558\pi\)
0.725859 0.687844i \(-0.241442\pi\)
\(654\) 1.79626e13 0.150135
\(655\) −5.84852e12 −0.0485109
\(656\) −1.93499e14 −1.59279
\(657\) 4.53921e13i 0.370812i
\(658\) 3.27075e12 0.0265166
\(659\) 1.48601e14 1.19562 0.597811 0.801637i \(-0.296037\pi\)
0.597811 + 0.801637i \(0.296037\pi\)
\(660\) 7.79642e12 0.0622552
\(661\) −2.25306e13 −0.178552 −0.0892761 0.996007i \(-0.528455\pi\)
−0.0892761 + 0.996007i \(0.528455\pi\)
\(662\) −1.33491e14 −1.04993
\(663\) 2.06132e12i 0.0160908i
\(664\) 2.44069e14i 1.89091i
\(665\) 9.93297e12i 0.0763785i
\(666\) −8.85420e13 −0.675738
\(667\) 3.04670e10i 0.000230781i
\(668\) −1.28944e14 −0.969436
\(669\) 1.37041e13 0.102264
\(670\) 1.64329e14 1.21714
\(671\) 9.09281e13i 0.668475i
\(672\) 8.18527e11i 0.00597292i
\(673\) 1.63307e14i 1.18285i −0.806361 0.591424i \(-0.798566\pi\)
0.806361 0.591424i \(-0.201434\pi\)
\(674\) 3.67472e14i 2.64195i
\(675\) 1.07947e13i 0.0770358i
\(676\) 2.21908e14 1.57196
\(677\) 2.03834e13i 0.143329i −0.997429 0.0716643i \(-0.977169\pi\)
0.997429 0.0716643i \(-0.0228310\pi\)
\(678\) 1.17635e13i 0.0821088i
\(679\) 1.37307e13i 0.0951356i
\(680\) −8.57565e13 −0.589824
\(681\) 1.53354e13 0.104703
\(682\) 4.48721e13i 0.304127i
\(683\) −2.61360e14 −1.75847 −0.879235 0.476389i \(-0.841946\pi\)
−0.879235 + 0.476389i \(0.841946\pi\)
\(684\) 3.25621e14i 2.17486i
\(685\) −3.06194e13 −0.203022
\(686\) 5.83377e13 0.383998
\(687\) 1.63590e13i 0.106899i
\(688\) 1.40687e14 2.00230e14i 0.912665 1.29893i
\(689\) −5.89401e13 −0.379590
\(690\) 9.98782e12i 0.0638595i
\(691\) 1.06175e14i 0.673957i −0.941512 0.336979i \(-0.890595\pi\)
0.941512 0.336979i \(-0.109405\pi\)
\(692\) −2.83907e14 −1.78914
\(693\) 9.06256e12i 0.0567002i
\(694\) 3.85180e14 2.39258
\(695\) 4.92673e13i 0.303833i
\(696\) 9.23868e9i 5.65671e-5i
\(697\) −6.53557e13 −0.397301
\(698\) 2.20997e14 1.33386
\(699\) 1.18385e13 0.0709435
\(700\) 2.00033e13i 0.119018i
\(701\) −1.75520e14 −1.03690 −0.518449 0.855109i \(-0.673490\pi\)
−0.518449 + 0.855109i \(0.673490\pi\)
\(702\) −2.46523e13 −0.144601
\(703\) −6.55008e13 −0.381478
\(704\) 2.77140e13 0.160264
\(705\) −1.29306e12 −0.00742460
\(706\) 1.22904e14i 0.700716i
\(707\) 7.19712e12i 0.0407438i
\(708\) 2.91426e11i 0.00163818i
\(709\) −1.11019e14 −0.619678 −0.309839 0.950789i \(-0.600275\pi\)
−0.309839 + 0.950789i \(0.600275\pi\)
\(710\) 1.75395e14i 0.972130i
\(711\) −1.75361e13 −0.0965127
\(712\) 5.59395e14 3.05716
\(713\) 3.94332e13 0.214001
\(714\) 1.08900e12i 0.00586865i
\(715\) 3.67481e13i 0.196655i
\(716\) 5.39235e14i 2.86558i
\(717\) 1.30638e11i 0.000689406i
\(718\) 3.46860e14i 1.81774i
\(719\) 2.29173e14 1.19267 0.596333 0.802737i \(-0.296624\pi\)
0.596333 + 0.802737i \(0.296624\pi\)
\(720\) 2.15183e14i 1.11210i
\(721\) 2.08942e13i 0.107238i
\(722\) 1.04449e12i 0.00532377i
\(723\) 3.58265e12 0.0181348
\(724\) 5.56521e14 2.79762
\(725\) 3.51659e10i 0.000175563i
\(726\) −1.99484e13 −0.0989065
\(727\) 2.63433e14i 1.29717i 0.761142 + 0.648586i \(0.224639\pi\)
−0.761142 + 0.648586i \(0.775361\pi\)
\(728\) 2.47702e13 0.121136
\(729\) 1.98652e14 0.964841
\(730\) 9.72405e13i 0.469065i
\(731\) 4.75181e13 6.76292e13i 0.227652 0.324002i
\(732\) −4.46872e13 −0.212631
\(733\) 6.84831e13i 0.323641i −0.986820 0.161820i \(-0.948263\pi\)
0.986820 0.161820i \(-0.0517365\pi\)
\(734\) 1.53292e14i 0.719512i
\(735\) −1.14637e13 −0.0534427
\(736\) 1.02786e14i 0.475932i
\(737\) 1.10913e14 0.510087
\(738\) 3.89654e14i 1.77991i
\(739\) 3.18534e14i 1.44522i 0.691256 + 0.722610i \(0.257058\pi\)
−0.691256 + 0.722610i \(0.742942\pi\)
\(740\) −1.30115e14 −0.586364
\(741\) −9.09159e12 −0.0406957
\(742\) 3.11382e13 0.138444
\(743\) 1.06741e14i 0.471396i 0.971826 + 0.235698i \(0.0757376\pi\)
−0.971826 + 0.235698i \(0.924262\pi\)
\(744\) −1.19576e13 −0.0524539
\(745\) −2.12255e14 −0.924862
\(746\) −4.88406e14 −2.11391
\(747\) 2.06851e14 0.889314
\(748\) −1.06747e14 −0.455876
\(749\) 1.35532e13i 0.0574956i
\(750\) 3.44281e13i 0.145080i
\(751\) 3.69630e14i 1.54728i 0.633628 + 0.773638i \(0.281565\pi\)
−0.633628 + 0.773638i \(0.718435\pi\)
\(752\) 5.24171e13 0.217964
\(753\) 1.42745e13i 0.0589637i
\(754\) −8.03097e10 −0.000329542
\(755\) −1.82762e14 −0.744993
\(756\) 8.93408e12 0.0361777
\(757\) 7.07825e13i 0.284739i −0.989814 0.142369i \(-0.954528\pi\)
0.989814 0.142369i \(-0.0454721\pi\)
\(758\) 7.79909e14i 3.11672i
\(759\) 6.74124e12i 0.0267628i
\(760\) 3.78234e14i 1.49174i
\(761\) 2.27363e14i 0.890833i −0.895323 0.445417i \(-0.853056\pi\)
0.895323 0.445417i \(-0.146944\pi\)
\(762\) −4.48593e13 −0.174613
\(763\) 3.06833e13i 0.118653i
\(764\) 2.84504e14i 1.09300i
\(765\) 7.26797e13i 0.277400i
\(766\) −3.03816e14 −1.15204
\(767\) −1.37362e12 −0.00517477
\(768\) 3.99340e13i 0.149464i
\(769\) −2.60420e14 −0.968374 −0.484187 0.874965i \(-0.660885\pi\)
−0.484187 + 0.874965i \(0.660885\pi\)
\(770\) 1.94141e13i 0.0717238i
\(771\) 4.00947e13 0.147168
\(772\) 2.97885e14 1.08633
\(773\) 1.78304e14i 0.646045i 0.946391 + 0.323023i \(0.104699\pi\)
−0.946391 + 0.323023i \(0.895301\pi\)
\(774\) −4.03209e14 2.83305e14i −1.45153 1.01988i
\(775\) 4.55151e13 0.162797
\(776\) 5.22845e14i 1.85808i
\(777\) 8.95921e11i 0.00316348i
\(778\) −4.43185e14 −1.55485
\(779\) 2.88255e14i 1.00482i
\(780\) −1.80601e13 −0.0625527