Properties

Label 43.11.b.b.42.18
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 42.18
Character \(\chi\) \(=\) 43.42
Dual form 43.11.b.b.42.17

$q$-expansion

\(f(q)\) \(=\) \(q+0.846054i q^{2} +54.5873i q^{3} +1023.28 q^{4} +4881.88i q^{5} -46.1839 q^{6} +30624.2i q^{7} +1732.11i q^{8} +56069.2 q^{9} +O(q^{10})\) \(q+0.846054i q^{2} +54.5873i q^{3} +1023.28 q^{4} +4881.88i q^{5} -46.1839 q^{6} +30624.2i q^{7} +1732.11i q^{8} +56069.2 q^{9} -4130.34 q^{10} -179422. q^{11} +55858.4i q^{12} -338315. q^{13} -25909.7 q^{14} -266489. q^{15} +1.04638e6 q^{16} +766203. q^{17} +47437.6i q^{18} -3.89726e6i q^{19} +4.99555e6i q^{20} -1.67169e6 q^{21} -151801. i q^{22} +3.13921e6 q^{23} -94551.5 q^{24} -1.40672e7 q^{25} -286232. i q^{26} +6.28400e6i q^{27} +3.13372e7i q^{28} -1.81741e7i q^{29} -225464. i q^{30} -2.96757e7 q^{31} +2.65898e6i q^{32} -9.79419e6i q^{33} +648249. i q^{34} -1.49504e8 q^{35} +5.73747e7 q^{36} +8.05730e7i q^{37} +3.29729e6 q^{38} -1.84677e7i q^{39} -8.45598e6 q^{40} +4.52023e7 q^{41} -1.41434e6i q^{42} +(1.20044e8 + 8.48586e7i) q^{43} -1.83600e8 q^{44} +2.73723e8i q^{45} +2.65594e6i q^{46} +1.36443e8 q^{47} +5.71190e7i q^{48} -6.55365e8 q^{49} -1.19016e7i q^{50} +4.18250e7i q^{51} -3.46192e8 q^{52} -3.81746e8 q^{53} -5.31660e6 q^{54} -8.75919e8i q^{55} -5.30445e7 q^{56} +2.12741e8 q^{57} +1.53763e7 q^{58} +1.06201e9 q^{59} -2.72694e8 q^{60} +7.22078e8i q^{61} -2.51072e7i q^{62} +1.71707e9i q^{63} +1.06924e9 q^{64} -1.65161e9i q^{65} +8.28642e6 q^{66} +1.44131e9 q^{67} +7.84044e8 q^{68} +1.71361e8i q^{69} -1.26488e8i q^{70} +3.79857e8i q^{71} +9.71183e7i q^{72} -1.13814e9i q^{73} -6.81691e7 q^{74} -7.67889e8i q^{75} -3.98800e9i q^{76} -5.49466e9i q^{77} +1.56247e7 q^{78} -4.58342e9 q^{79} +5.10829e9i q^{80} +2.96780e9 q^{81} +3.82436e7i q^{82} +6.19566e9 q^{83} -1.71062e9 q^{84} +3.74051e9i q^{85} +(-7.17950e7 + 1.01563e8i) q^{86} +9.92077e8 q^{87} -3.10780e8i q^{88} +7.46570e9i q^{89} -2.31585e8 q^{90} -1.03606e10i q^{91} +3.21231e9 q^{92} -1.61992e9i q^{93} +1.15438e8i q^{94} +1.90259e10 q^{95} -1.45146e8 q^{96} -3.79259e9 q^{97} -5.54474e8i q^{98} -1.00601e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} + O(q^{10}) \) \( 34q - 16156q^{4} + 12798q^{6} - 790716q^{9} - 254122q^{10} - 218200q^{11} - 191008q^{13} - 1380228q^{14} - 512732q^{15} + 2224308q^{16} - 1070678q^{17} + 17857352q^{21} + 8915254q^{23} - 39666730q^{24} - 82938284q^{25} - 55042410q^{31} - 179227232q^{35} + 394381042q^{36} + 709061882q^{38} + 433255366q^{40} + 80370626q^{41} + 1585062q^{43} + 324477888q^{44} - 544910502q^{47} - 2479345922q^{49} - 987059452q^{52} - 915886820q^{53} - 297150836q^{54} + 2172449592q^{56} - 2398069428q^{57} + 930519014q^{58} + 3394816764q^{59} - 5474941192q^{60} + 2925325476q^{64} + 455136192q^{66} + 3405920388q^{67} + 664008226q^{68} + 16264108918q^{74} - 17800086268q^{78} - 13853150858q^{79} + 20444701546q^{81} + 113867236q^{83} - 30401949428q^{84} + 19291204884q^{86} - 5221634730q^{87} - 6984391876q^{90} + 41423783058q^{92} + 4107406010q^{95} + 33148445474q^{96} + 15795117154q^{97} + 1345877600q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.846054i 0.0264392i 0.999913 + 0.0132196i \(0.00420805\pi\)
−0.999913 + 0.0132196i \(0.995792\pi\)
\(3\) 54.5873i 0.224639i 0.993672 + 0.112320i \(0.0358281\pi\)
−0.993672 + 0.112320i \(0.964172\pi\)
\(4\) 1023.28 0.999301
\(5\) 4881.88i 1.56220i 0.624404 + 0.781101i \(0.285342\pi\)
−0.624404 + 0.781101i \(0.714658\pi\)
\(6\) −46.1839 −0.00593928
\(7\) 30624.2i 1.82211i 0.412287 + 0.911054i \(0.364730\pi\)
−0.412287 + 0.911054i \(0.635270\pi\)
\(8\) 1732.11i 0.0528599i
\(9\) 56069.2 0.949537
\(10\) −4130.34 −0.0413034
\(11\) −179422. −1.11407 −0.557036 0.830488i \(-0.688061\pi\)
−0.557036 + 0.830488i \(0.688061\pi\)
\(12\) 55858.4i 0.224482i
\(13\) −338315. −0.911179 −0.455590 0.890190i \(-0.650572\pi\)
−0.455590 + 0.890190i \(0.650572\pi\)
\(14\) −25909.7 −0.0481751
\(15\) −266489. −0.350932
\(16\) 1.04638e6 0.997903
\(17\) 766203. 0.539634 0.269817 0.962912i \(-0.413037\pi\)
0.269817 + 0.962912i \(0.413037\pi\)
\(18\) 47437.6i 0.0251050i
\(19\) 3.89726e6i 1.57395i −0.616985 0.786975i \(-0.711646\pi\)
0.616985 0.786975i \(-0.288354\pi\)
\(20\) 4.99555e6i 1.56111i
\(21\) −1.67169e6 −0.409317
\(22\) 151801.i 0.0294552i
\(23\) 3.13921e6 0.487732 0.243866 0.969809i \(-0.421584\pi\)
0.243866 + 0.969809i \(0.421584\pi\)
\(24\) −94551.5 −0.0118744
\(25\) −1.40672e7 −1.44048
\(26\) 286232.i 0.0240908i
\(27\) 6.28400e6i 0.437943i
\(28\) 3.13372e7i 1.82083i
\(29\) 1.81741e7i 0.886060i −0.896507 0.443030i \(-0.853903\pi\)
0.896507 0.443030i \(-0.146097\pi\)
\(30\) 225464.i 0.00927836i
\(31\) −2.96757e7 −1.03656 −0.518278 0.855212i \(-0.673427\pi\)
−0.518278 + 0.855212i \(0.673427\pi\)
\(32\) 2.65898e6i 0.0792437i
\(33\) 9.79419e6i 0.250264i
\(34\) 648249.i 0.0142675i
\(35\) −1.49504e8 −2.84650
\(36\) 5.73747e7 0.948873
\(37\) 8.05730e7i 1.16193i 0.813928 + 0.580966i \(0.197325\pi\)
−0.813928 + 0.580966i \(0.802675\pi\)
\(38\) 3.29729e6 0.0416140
\(39\) 1.84677e7i 0.204687i
\(40\) −8.45598e6 −0.0825779
\(41\) 4.52023e7 0.390159 0.195079 0.980787i \(-0.437504\pi\)
0.195079 + 0.980787i \(0.437504\pi\)
\(42\) 1.41434e6i 0.0108220i
\(43\) 1.20044e8 + 8.48586e7i 0.816577 + 0.577237i
\(44\) −1.83600e8 −1.11329
\(45\) 2.73723e8i 1.48337i
\(46\) 2.65594e6i 0.0128952i
\(47\) 1.36443e8 0.594925 0.297463 0.954733i \(-0.403860\pi\)
0.297463 + 0.954733i \(0.403860\pi\)
\(48\) 5.71190e7i 0.224168i
\(49\) −6.55365e8 −2.32008
\(50\) 1.19016e7i 0.0380850i
\(51\) 4.18250e7i 0.121223i
\(52\) −3.46192e8 −0.910542
\(53\) −3.81746e8 −0.912842 −0.456421 0.889764i \(-0.650869\pi\)
−0.456421 + 0.889764i \(0.650869\pi\)
\(54\) −5.31660e6 −0.0115789
\(55\) 8.75919e8i 1.74041i
\(56\) −5.30445e7 −0.0963165
\(57\) 2.12741e8 0.353571
\(58\) 1.53763e7 0.0234267
\(59\) 1.06201e9 1.48548 0.742740 0.669580i \(-0.233526\pi\)
0.742740 + 0.669580i \(0.233526\pi\)
\(60\) −2.72694e8 −0.350687
\(61\) 7.22078e8i 0.854939i 0.904030 + 0.427470i \(0.140595\pi\)
−0.904030 + 0.427470i \(0.859405\pi\)
\(62\) 2.51072e7i 0.0274057i
\(63\) 1.71707e9i 1.73016i
\(64\) 1.06924e9 0.995808
\(65\) 1.65161e9i 1.42345i
\(66\) 8.28642e6 0.00661679
\(67\) 1.44131e9 1.06753 0.533767 0.845631i \(-0.320776\pi\)
0.533767 + 0.845631i \(0.320776\pi\)
\(68\) 7.84044e8 0.539257
\(69\) 1.71361e8i 0.109564i
\(70\) 1.26488e8i 0.0752592i
\(71\) 3.79857e8i 0.210537i 0.994444 + 0.105268i \(0.0335702\pi\)
−0.994444 + 0.105268i \(0.966430\pi\)
\(72\) 9.71183e7i 0.0501925i
\(73\) 1.13814e9i 0.549013i −0.961585 0.274507i \(-0.911485\pi\)
0.961585 0.274507i \(-0.0885145\pi\)
\(74\) −6.81691e7 −0.0307206
\(75\) 7.67889e8i 0.323588i
\(76\) 3.98800e9i 1.57285i
\(77\) 5.49466e9i 2.02996i
\(78\) 1.56247e7 0.00541175
\(79\) −4.58342e9 −1.48955 −0.744773 0.667318i \(-0.767442\pi\)
−0.744773 + 0.667318i \(0.767442\pi\)
\(80\) 5.10829e9i 1.55893i
\(81\) 2.96780e9 0.851158
\(82\) 3.82436e7i 0.0103155i
\(83\) 6.19566e9 1.57289 0.786443 0.617663i \(-0.211920\pi\)
0.786443 + 0.617663i \(0.211920\pi\)
\(84\) −1.71062e9 −0.409031
\(85\) 3.74051e9i 0.843018i
\(86\) −7.17950e7 + 1.01563e8i −0.0152617 + 0.0215896i
\(87\) 9.92077e8 0.199044
\(88\) 3.10780e8i 0.0588898i
\(89\) 7.46570e9i 1.33697i 0.743727 + 0.668483i \(0.233056\pi\)
−0.743727 + 0.668483i \(0.766944\pi\)
\(90\) −2.31585e8 −0.0392191
\(91\) 1.03606e10i 1.66027i
\(92\) 3.21231e9 0.487391
\(93\) 1.61992e9i 0.232851i
\(94\) 1.15438e8i 0.0157293i
\(95\) 1.90259e10 2.45883
\(96\) −1.45146e8 −0.0178012
\(97\) −3.79259e9 −0.441649 −0.220825 0.975314i \(-0.570875\pi\)
−0.220825 + 0.975314i \(0.570875\pi\)
\(98\) 5.54474e8i 0.0613410i
\(99\) −1.00601e10 −1.05785
\(100\) −1.43947e10 −1.43947
\(101\) −1.53422e9 −0.145976 −0.0729878 0.997333i \(-0.523253\pi\)
−0.0729878 + 0.997333i \(0.523253\pi\)
\(102\) −3.53862e7 −0.00320504
\(103\) −2.62038e9 −0.226036 −0.113018 0.993593i \(-0.536052\pi\)
−0.113018 + 0.993593i \(0.536052\pi\)
\(104\) 5.85999e8i 0.0481649i
\(105\) 8.16101e9i 0.639436i
\(106\) 3.22978e8i 0.0241348i
\(107\) −1.32447e10 −0.944326 −0.472163 0.881511i \(-0.656527\pi\)
−0.472163 + 0.881511i \(0.656527\pi\)
\(108\) 6.43032e9i 0.437637i
\(109\) −2.14660e8 −0.0139514 −0.00697570 0.999976i \(-0.502220\pi\)
−0.00697570 + 0.999976i \(0.502220\pi\)
\(110\) 7.41075e8 0.0460149
\(111\) −4.39827e9 −0.261016
\(112\) 3.20444e10i 1.81829i
\(113\) 1.52894e10i 0.829846i 0.909857 + 0.414923i \(0.136191\pi\)
−0.909857 + 0.414923i \(0.863809\pi\)
\(114\) 1.79990e8i 0.00934813i
\(115\) 1.53253e10i 0.761937i
\(116\) 1.85973e10i 0.885441i
\(117\) −1.89690e10 −0.865199
\(118\) 8.98514e8i 0.0392749i
\(119\) 2.34643e10i 0.983272i
\(120\) 4.61589e8i 0.0185502i
\(121\) 6.25498e9 0.241157
\(122\) −6.10918e8 −0.0226039
\(123\) 2.46747e9i 0.0876450i
\(124\) −3.03667e10 −1.03583
\(125\) 2.09996e10i 0.688113i
\(126\) −1.45274e9 −0.0457440
\(127\) −1.09606e10 −0.331754 −0.165877 0.986146i \(-0.553045\pi\)
−0.165877 + 0.986146i \(0.553045\pi\)
\(128\) 3.62743e9i 0.105572i
\(129\) −4.63221e9 + 6.55287e9i −0.129670 + 0.183435i
\(130\) 1.39735e9 0.0376348
\(131\) 4.01825e10i 1.04155i −0.853694 0.520776i \(-0.825643\pi\)
0.853694 0.520776i \(-0.174357\pi\)
\(132\) 1.00222e10i 0.250089i
\(133\) 1.19350e11 2.86791
\(134\) 1.21942e9i 0.0282248i
\(135\) −3.06777e10 −0.684155
\(136\) 1.32715e9i 0.0285250i
\(137\) 1.58617e10i 0.328661i −0.986405 0.164330i \(-0.947454\pi\)
0.986405 0.164330i \(-0.0525463\pi\)
\(138\) −1.44981e8 −0.00289678
\(139\) −2.51826e10 −0.485318 −0.242659 0.970112i \(-0.578020\pi\)
−0.242659 + 0.970112i \(0.578020\pi\)
\(140\) −1.52985e11 −2.84451
\(141\) 7.44807e9i 0.133644i
\(142\) −3.21380e8 −0.00556643
\(143\) 6.07012e10 1.01512
\(144\) 5.86696e10 0.947546
\(145\) 8.87239e10 1.38421
\(146\) 9.62931e8 0.0145155
\(147\) 3.57746e10i 0.521181i
\(148\) 8.24491e10i 1.16112i
\(149\) 2.12604e10i 0.289495i 0.989469 + 0.144747i \(0.0462369\pi\)
−0.989469 + 0.144747i \(0.953763\pi\)
\(150\) 6.49675e8 0.00855540
\(151\) 1.47453e10i 0.187831i −0.995580 0.0939157i \(-0.970062\pi\)
0.995580 0.0939157i \(-0.0299384\pi\)
\(152\) 6.75049e9 0.0831988
\(153\) 4.29604e10 0.512403
\(154\) 4.64878e9 0.0536705
\(155\) 1.44873e11i 1.61931i
\(156\) 1.88977e10i 0.204544i
\(157\) 6.49091e10i 0.680467i −0.940341 0.340233i \(-0.889494\pi\)
0.940341 0.340233i \(-0.110506\pi\)
\(158\) 3.87782e9i 0.0393824i
\(159\) 2.08385e10i 0.205060i
\(160\) −1.29808e10 −0.123795
\(161\) 9.61358e10i 0.888701i
\(162\) 2.51092e9i 0.0225039i
\(163\) 1.68483e11i 1.46426i 0.681167 + 0.732128i \(0.261473\pi\)
−0.681167 + 0.732128i \(0.738527\pi\)
\(164\) 4.62548e10 0.389886
\(165\) 4.78141e10 0.390964
\(166\) 5.24186e9i 0.0415858i
\(167\) 8.66424e10 0.667034 0.333517 0.942744i \(-0.391765\pi\)
0.333517 + 0.942744i \(0.391765\pi\)
\(168\) 2.89556e9i 0.0216365i
\(169\) −2.34018e10 −0.169752
\(170\) −3.16468e9 −0.0222887
\(171\) 2.18516e11i 1.49452i
\(172\) 1.22839e11 + 8.68345e10i 0.816006 + 0.576833i
\(173\) 1.37685e11 0.888496 0.444248 0.895904i \(-0.353471\pi\)
0.444248 + 0.895904i \(0.353471\pi\)
\(174\) 8.39351e8i 0.00526256i
\(175\) 4.30795e11i 2.62470i
\(176\) −1.87744e11 −1.11174
\(177\) 5.79720e10i 0.333697i
\(178\) −6.31639e9 −0.0353483
\(179\) 2.72920e11i 1.48515i −0.669763 0.742575i \(-0.733604\pi\)
0.669763 0.742575i \(-0.266396\pi\)
\(180\) 2.80097e11i 1.48233i
\(181\) 2.81034e11 1.44666 0.723328 0.690505i \(-0.242612\pi\)
0.723328 + 0.690505i \(0.242612\pi\)
\(182\) 8.76563e9 0.0438961
\(183\) −3.94163e10 −0.192053
\(184\) 5.43747e9i 0.0257815i
\(185\) −3.93348e11 −1.81517
\(186\) 1.37054e9 0.00615639
\(187\) −1.37474e11 −0.601191
\(188\) 1.39620e11 0.594509
\(189\) −1.92442e11 −0.797979
\(190\) 1.60970e10i 0.0650094i
\(191\) 4.74206e11i 1.86552i 0.360495 + 0.932761i \(0.382608\pi\)
−0.360495 + 0.932761i \(0.617392\pi\)
\(192\) 5.83670e10i 0.223698i
\(193\) −3.33550e11 −1.24559 −0.622794 0.782386i \(-0.714002\pi\)
−0.622794 + 0.782386i \(0.714002\pi\)
\(194\) 3.20874e9i 0.0116769i
\(195\) 9.01571e10 0.319762
\(196\) −6.70624e11 −2.31846
\(197\) 4.59036e11 1.54709 0.773545 0.633742i \(-0.218482\pi\)
0.773545 + 0.633742i \(0.218482\pi\)
\(198\) 8.51137e9i 0.0279688i
\(199\) 3.09195e11i 0.990756i 0.868677 + 0.495378i \(0.164971\pi\)
−0.868677 + 0.495378i \(0.835029\pi\)
\(200\) 2.43659e10i 0.0761435i
\(201\) 7.86770e10i 0.239810i
\(202\) 1.29803e9i 0.00385948i
\(203\) 5.56567e11 1.61450
\(204\) 4.27989e10i 0.121138i
\(205\) 2.20672e11i 0.609507i
\(206\) 2.21699e9i 0.00597622i
\(207\) 1.76013e11 0.463120
\(208\) −3.54005e11 −0.909269
\(209\) 6.99255e11i 1.75349i
\(210\) 6.90465e9 0.0169062
\(211\) 5.38365e11i 1.28725i −0.765339 0.643627i \(-0.777429\pi\)
0.765339 0.643627i \(-0.222571\pi\)
\(212\) −3.90635e11 −0.912204
\(213\) −2.07354e10 −0.0472949
\(214\) 1.12057e10i 0.0249672i
\(215\) −4.14270e11 + 5.86039e11i −0.901760 + 1.27566i
\(216\) −1.08846e10 −0.0231496
\(217\) 9.08793e11i 1.88872i
\(218\) 1.81614e8i 0.000368864i
\(219\) 6.21283e10 0.123330
\(220\) 8.96314e11i 1.73919i
\(221\) −2.59218e11 −0.491703
\(222\) 3.72117e9i 0.00690105i
\(223\) 8.51101e10i 0.154332i −0.997018 0.0771661i \(-0.975413\pi\)
0.997018 0.0771661i \(-0.0245872\pi\)
\(224\) −8.14290e10 −0.144391
\(225\) −7.88734e11 −1.36779
\(226\) −1.29356e10 −0.0219405
\(227\) 5.77929e11i 0.958837i 0.877586 + 0.479419i \(0.159152\pi\)
−0.877586 + 0.479419i \(0.840848\pi\)
\(228\) 2.17694e11 0.353324
\(229\) 3.46320e11 0.549920 0.274960 0.961456i \(-0.411335\pi\)
0.274960 + 0.961456i \(0.411335\pi\)
\(230\) −1.29660e10 −0.0201450
\(231\) 2.99939e11 0.456009
\(232\) 3.14796e10 0.0468371
\(233\) 5.72808e11i 0.834121i −0.908879 0.417061i \(-0.863060\pi\)
0.908879 0.417061i \(-0.136940\pi\)
\(234\) 1.60488e10i 0.0228752i
\(235\) 6.66099e11i 0.929393i
\(236\) 1.08673e12 1.48444
\(237\) 2.50197e11i 0.334611i
\(238\) −1.98521e10 −0.0259969
\(239\) 3.40057e11 0.436076 0.218038 0.975940i \(-0.430034\pi\)
0.218038 + 0.975940i \(0.430034\pi\)
\(240\) −2.78848e11 −0.350196
\(241\) 1.25721e12i 1.54641i 0.634158 + 0.773204i \(0.281347\pi\)
−0.634158 + 0.773204i \(0.718653\pi\)
\(242\) 5.29205e9i 0.00637599i
\(243\) 5.33068e11i 0.629146i
\(244\) 7.38891e11i 0.854342i
\(245\) 3.19941e12i 3.62443i
\(246\) −2.08762e9 −0.00231726
\(247\) 1.31850e12i 1.43415i
\(248\) 5.14017e10i 0.0547922i
\(249\) 3.38205e11i 0.353332i
\(250\) 1.77668e10 0.0181932
\(251\) 1.80908e12 1.81589 0.907945 0.419089i \(-0.137650\pi\)
0.907945 + 0.419089i \(0.137650\pi\)
\(252\) 1.75705e12i 1.72895i
\(253\) −5.63245e11 −0.543369
\(254\) 9.27326e9i 0.00877130i
\(255\) −2.04185e11 −0.189375
\(256\) 1.09183e12 0.993017
\(257\) 8.85258e11i 0.789595i −0.918768 0.394797i \(-0.870815\pi\)
0.918768 0.394797i \(-0.129185\pi\)
\(258\) −5.54408e9 3.91910e9i −0.00484988 0.00342837i
\(259\) −2.46748e12 −2.11717
\(260\) 1.69007e12i 1.42245i
\(261\) 1.01901e12i 0.841347i
\(262\) 3.39966e10 0.0275378
\(263\) 2.32424e12i 1.84715i −0.383413 0.923577i \(-0.625252\pi\)
0.383413 0.923577i \(-0.374748\pi\)
\(264\) 1.69647e10 0.0132290
\(265\) 1.86364e12i 1.42604i
\(266\) 1.00977e11i 0.0758251i
\(267\) −4.07533e11 −0.300335
\(268\) 1.47487e12 1.06679
\(269\) −8.13151e10 −0.0577311 −0.0288656 0.999583i \(-0.509189\pi\)
−0.0288656 + 0.999583i \(0.509189\pi\)
\(270\) 2.59550e10i 0.0180885i
\(271\) 1.01982e12 0.697711 0.348856 0.937177i \(-0.386570\pi\)
0.348856 + 0.937177i \(0.386570\pi\)
\(272\) 8.01738e11 0.538503
\(273\) 5.65558e11 0.372961
\(274\) 1.34199e10 0.00868953
\(275\) 2.52396e12 1.60479
\(276\) 1.75351e11i 0.109487i
\(277\) 2.04163e12i 1.25192i 0.779854 + 0.625961i \(0.215293\pi\)
−0.779854 + 0.625961i \(0.784707\pi\)
\(278\) 2.13058e10i 0.0128314i
\(279\) −1.66389e12 −0.984248
\(280\) 2.58957e11i 0.150466i
\(281\) 1.27867e12 0.729836 0.364918 0.931040i \(-0.381097\pi\)
0.364918 + 0.931040i \(0.381097\pi\)
\(282\) −6.30147e9 −0.00353343
\(283\) 7.72221e11 0.425412 0.212706 0.977116i \(-0.431772\pi\)
0.212706 + 0.977116i \(0.431772\pi\)
\(284\) 3.88702e11i 0.210390i
\(285\) 1.03858e12i 0.552349i
\(286\) 5.13565e10i 0.0268389i
\(287\) 1.38428e12i 0.710911i
\(288\) 1.49087e11i 0.0752448i
\(289\) −1.42893e12 −0.708795
\(290\) 7.50652e10i 0.0365973i
\(291\) 2.07028e11i 0.0992118i
\(292\) 1.16464e12i 0.548629i
\(293\) −1.94950e12 −0.902788 −0.451394 0.892325i \(-0.649073\pi\)
−0.451394 + 0.892325i \(0.649073\pi\)
\(294\) 3.02673e10 0.0137796
\(295\) 5.18458e12i 2.32062i
\(296\) −1.39562e11 −0.0614196
\(297\) 1.12749e12i 0.487900i
\(298\) −1.79875e10 −0.00765400
\(299\) −1.06204e12 −0.444412
\(300\) 7.85768e11i 0.323361i
\(301\) −2.59873e12 + 3.67624e12i −1.05179 + 1.48789i
\(302\) 1.24753e10 0.00496611
\(303\) 8.37489e10i 0.0327919i
\(304\) 4.07800e12i 1.57065i
\(305\) −3.52510e12 −1.33559
\(306\) 3.63468e10i 0.0135475i
\(307\) 3.18628e12 1.16840 0.584201 0.811609i \(-0.301408\pi\)
0.584201 + 0.811609i \(0.301408\pi\)
\(308\) 5.62260e12i 2.02854i
\(309\) 1.43040e11i 0.0507767i
\(310\) 1.22571e11 0.0428132
\(311\) 2.38175e12 0.818641 0.409321 0.912391i \(-0.365766\pi\)
0.409321 + 0.912391i \(0.365766\pi\)
\(312\) 3.19881e10 0.0108197
\(313\) 1.24263e12i 0.413638i 0.978379 + 0.206819i \(0.0663112\pi\)
−0.978379 + 0.206819i \(0.933689\pi\)
\(314\) 5.49166e10 0.0179910
\(315\) −8.38255e12 −2.70286
\(316\) −4.69014e12 −1.48850
\(317\) −1.03858e12 −0.324447 −0.162224 0.986754i \(-0.551867\pi\)
−0.162224 + 0.986754i \(0.551867\pi\)
\(318\) 1.76305e10 0.00542163
\(319\) 3.26084e12i 0.987135i
\(320\) 5.21991e12i 1.55565i
\(321\) 7.22991e11i 0.212133i
\(322\) −8.13361e10 −0.0234965
\(323\) 2.98609e12i 0.849357i
\(324\) 3.03691e12 0.850563
\(325\) 4.75912e12 1.31253
\(326\) −1.42545e11 −0.0387137
\(327\) 1.17177e10i 0.00313403i
\(328\) 7.82955e10i 0.0206238i
\(329\) 4.17846e12i 1.08402i
\(330\) 4.04533e10i 0.0103368i
\(331\) 3.52483e12i 0.887153i −0.896236 0.443577i \(-0.853709\pi\)
0.896236 0.443577i \(-0.146291\pi\)
\(332\) 6.33992e12 1.57179
\(333\) 4.51766e12i 1.10330i
\(334\) 7.33042e10i 0.0176358i
\(335\) 7.03628e12i 1.66771i
\(336\) −1.74922e12 −0.408459
\(337\) −6.83158e12 −1.57171 −0.785854 0.618412i \(-0.787776\pi\)
−0.785854 + 0.618412i \(0.787776\pi\)
\(338\) 1.97992e10i 0.00448811i
\(339\) −8.34606e11 −0.186416
\(340\) 3.82761e12i 0.842428i
\(341\) 5.32448e12 1.15480
\(342\) 1.84876e11 0.0395140
\(343\) 1.14194e13i 2.40533i
\(344\) −1.46985e11 + 2.07929e11i −0.0305127 + 0.0431642i
\(345\) −8.36566e11 −0.171161
\(346\) 1.16489e11i 0.0234911i
\(347\) 8.64593e12i 1.71856i −0.511507 0.859279i \(-0.670913\pi\)
0.511507 0.859279i \(-0.329087\pi\)
\(348\) 1.01518e12 0.198905
\(349\) 5.68975e12i 1.09892i 0.835520 + 0.549460i \(0.185166\pi\)
−0.835520 + 0.549460i \(0.814834\pi\)
\(350\) 3.64476e11 0.0693951
\(351\) 2.12597e12i 0.399044i
\(352\) 4.77080e11i 0.0882832i
\(353\) −1.01878e12 −0.185868 −0.0929342 0.995672i \(-0.529625\pi\)
−0.0929342 + 0.995672i \(0.529625\pi\)
\(354\) −4.90475e10 −0.00882268
\(355\) −1.85442e12 −0.328901
\(356\) 7.63953e12i 1.33603i
\(357\) −1.28086e12 −0.220881
\(358\) 2.30905e11 0.0392662
\(359\) 2.44894e12 0.410682 0.205341 0.978691i \(-0.434170\pi\)
0.205341 + 0.978691i \(0.434170\pi\)
\(360\) −4.74120e11 −0.0784108
\(361\) −9.05753e12 −1.47732
\(362\) 2.37770e11i 0.0382484i
\(363\) 3.41443e11i 0.0541733i
\(364\) 1.06018e13i 1.65911i
\(365\) 5.55628e12 0.857670
\(366\) 3.33484e10i 0.00507773i
\(367\) −5.29017e12 −0.794584 −0.397292 0.917692i \(-0.630050\pi\)
−0.397292 + 0.917692i \(0.630050\pi\)
\(368\) 3.28480e12 0.486710
\(369\) 2.53446e12 0.370470
\(370\) 3.32794e11i 0.0479917i
\(371\) 1.16907e13i 1.66330i
\(372\) 1.65764e12i 0.232688i
\(373\) 4.24662e12i 0.588165i 0.955780 + 0.294083i \(0.0950141\pi\)
−0.955780 + 0.294083i \(0.904986\pi\)
\(374\) 1.16310e11i 0.0158950i
\(375\) 1.14631e12 0.154577
\(376\) 2.36335e11i 0.0314477i
\(377\) 6.14857e12i 0.807360i
\(378\) 1.62817e11i 0.0210979i
\(379\) −1.42309e13 −1.81986 −0.909929 0.414764i \(-0.863864\pi\)
−0.909929 + 0.414764i \(0.863864\pi\)
\(380\) 1.94689e13 2.45711
\(381\) 5.98310e11i 0.0745249i
\(382\) −4.01204e11 −0.0493229
\(383\) 4.75530e12i 0.577011i 0.957478 + 0.288505i \(0.0931583\pi\)
−0.957478 + 0.288505i \(0.906842\pi\)
\(384\) −1.98012e11 −0.0237156
\(385\) 2.68243e13 3.17121
\(386\) 2.82201e11i 0.0329323i
\(387\) 6.73076e12 + 4.75796e12i 0.775370 + 0.548108i
\(388\) −3.88090e12 −0.441341
\(389\) 1.25209e13i 1.40568i −0.711349 0.702839i \(-0.751915\pi\)
0.711349 0.702839i \(-0.248085\pi\)
\(390\) 7.62778e10i 0.00845425i
\(391\) 2.40527e12 0.263197
\(392\) 1.13517e12i 0.122639i
\(393\) 2.19346e12 0.233973
\(394\) 3.88369e11i 0.0409038i
\(395\) 2.23757e13i 2.32697i
\(396\) −1.02943e13 −1.05711
\(397\) 1.80073e13 1.82598 0.912992 0.407978i \(-0.133766\pi\)
0.912992 + 0.407978i \(0.133766\pi\)
\(398\) −2.61596e11 −0.0261948
\(399\) 6.51501e12i 0.644245i
\(400\) −1.47196e13 −1.43746
\(401\) −4.77325e12 −0.460355 −0.230177 0.973149i \(-0.573931\pi\)
−0.230177 + 0.973149i \(0.573931\pi\)
\(402\) −6.65651e10 −0.00634039
\(403\) 1.00397e13 0.944488
\(404\) −1.56994e12 −0.145874
\(405\) 1.44885e13i 1.32968i
\(406\) 4.70886e11i 0.0426860i
\(407\) 1.44566e13i 1.29448i
\(408\) −7.24457e10 −0.00640784
\(409\) 9.20218e12i 0.804034i −0.915632 0.402017i \(-0.868309\pi\)
0.915632 0.402017i \(-0.131691\pi\)
\(410\) −1.86701e11 −0.0161149
\(411\) 8.65850e11 0.0738301
\(412\) −2.68140e12 −0.225878
\(413\) 3.25230e13i 2.70670i
\(414\) 1.48917e11i 0.0122445i
\(415\) 3.02465e13i 2.45717i
\(416\) 8.99570e11i 0.0722052i
\(417\) 1.37465e12i 0.109021i
\(418\) −5.91608e11 −0.0463610
\(419\) 1.75815e13i 1.36140i −0.732562 0.680700i \(-0.761676\pi\)
0.732562 0.680700i \(-0.238324\pi\)
\(420\) 8.35103e12i 0.638989i
\(421\) 1.52384e13i 1.15220i −0.817379 0.576100i \(-0.804574\pi\)
0.817379 0.576100i \(-0.195426\pi\)
\(422\) 4.55486e11 0.0340340
\(423\) 7.65026e12 0.564904
\(424\) 6.61228e11i 0.0482528i
\(425\) −1.07783e13 −0.777330
\(426\) 1.75433e10i 0.00125044i
\(427\) −2.21131e13 −1.55779
\(428\) −1.35531e13 −0.943666
\(429\) 3.31352e12i 0.228036i
\(430\) −4.95821e11 3.50495e11i −0.0337274 0.0238418i
\(431\) 8.76785e12 0.589531 0.294766 0.955570i \(-0.404758\pi\)
0.294766 + 0.955570i \(0.404758\pi\)
\(432\) 6.57543e12i 0.437024i
\(433\) 9.25042e12i 0.607746i 0.952713 + 0.303873i \(0.0982798\pi\)
−0.952713 + 0.303873i \(0.901720\pi\)
\(434\) 7.68889e11 0.0499361
\(435\) 4.84320e12i 0.310947i
\(436\) −2.19658e11 −0.0139416
\(437\) 1.22343e13i 0.767666i
\(438\) 5.25639e10i 0.00326075i
\(439\) 2.41481e13 1.48102 0.740510 0.672045i \(-0.234584\pi\)
0.740510 + 0.672045i \(0.234584\pi\)
\(440\) 1.51719e12 0.0919977
\(441\) −3.67458e13 −2.20300
\(442\) 2.19312e11i 0.0130002i
\(443\) −8.01561e12 −0.469805 −0.234903 0.972019i \(-0.575477\pi\)
−0.234903 + 0.972019i \(0.575477\pi\)
\(444\) −4.50068e12 −0.260833
\(445\) −3.64467e13 −2.08861
\(446\) 7.20077e10 0.00408042
\(447\) −1.16055e12 −0.0650319
\(448\) 3.27446e13i 1.81447i
\(449\) 2.13102e13i 1.16777i −0.811838 0.583883i \(-0.801533\pi\)
0.811838 0.583883i \(-0.198467\pi\)
\(450\) 6.67312e11i 0.0361632i
\(451\) −8.11031e12 −0.434665
\(452\) 1.56454e13i 0.829266i
\(453\) 8.04905e11 0.0421943
\(454\) −4.88959e11 −0.0253509
\(455\) 5.05792e13 2.59367
\(456\) 3.68491e11i 0.0186897i
\(457\) 1.95013e13i 0.978323i −0.872193 0.489161i \(-0.837303\pi\)
0.872193 0.489161i \(-0.162697\pi\)
\(458\) 2.93005e11i 0.0145395i
\(459\) 4.81482e12i 0.236329i
\(460\) 1.56821e13i 0.761404i
\(461\) 1.21083e13 0.581541 0.290770 0.956793i \(-0.406088\pi\)
0.290770 + 0.956793i \(0.406088\pi\)
\(462\) 2.53765e11i 0.0120565i
\(463\) 2.45524e13i 1.15395i −0.816761 0.576977i \(-0.804232\pi\)
0.816761 0.576977i \(-0.195768\pi\)
\(464\) 1.90170e13i 0.884202i
\(465\) 7.90825e12 0.363760
\(466\) 4.84626e11 0.0220535
\(467\) 1.20191e13i 0.541113i 0.962704 + 0.270556i \(0.0872076\pi\)
−0.962704 + 0.270556i \(0.912792\pi\)
\(468\) −1.94107e13 −0.864594
\(469\) 4.41388e13i 1.94516i
\(470\) −5.63556e11 −0.0245724
\(471\) 3.54321e12 0.152860
\(472\) 1.83951e12i 0.0785223i
\(473\) −2.15385e13 1.52255e13i −0.909726 0.643083i
\(474\) 2.11680e11 0.00884683
\(475\) 5.48233e13i 2.26724i
\(476\) 2.40107e13i 0.982584i
\(477\) −2.14042e13 −0.866778
\(478\) 2.87707e11i 0.0115295i
\(479\) 4.15981e13 1.64967 0.824833 0.565377i \(-0.191269\pi\)
0.824833 + 0.565377i \(0.191269\pi\)
\(480\) 7.08588e11i 0.0278091i
\(481\) 2.72590e13i 1.05873i
\(482\) −1.06367e12 −0.0408858
\(483\) −5.24780e12 −0.199637
\(484\) 6.40062e12 0.240988
\(485\) 1.85150e13i 0.689946i
\(486\) −4.51005e11 −0.0166341
\(487\) −8.49956e12 −0.310278 −0.155139 0.987893i \(-0.549583\pi\)
−0.155139 + 0.987893i \(0.549583\pi\)
\(488\) −1.25072e12 −0.0451920
\(489\) −9.19702e12 −0.328929
\(490\) 2.70688e12 0.0958271
\(491\) 5.57689e12i 0.195427i 0.995215 + 0.0977135i \(0.0311529\pi\)
−0.995215 + 0.0977135i \(0.968847\pi\)
\(492\) 2.52493e12i 0.0875837i
\(493\) 1.39251e13i 0.478148i
\(494\) −1.11552e12 −0.0379178
\(495\) 4.91121e13i 1.65258i
\(496\) −3.10520e13 −1.03438
\(497\) −1.16328e13 −0.383621
\(498\) −2.86139e11 −0.00934181
\(499\) 2.12718e13i 0.687545i −0.939053 0.343772i \(-0.888295\pi\)
0.939053 0.343772i \(-0.111705\pi\)
\(500\) 2.14885e13i 0.687632i
\(501\) 4.72958e12i 0.149842i
\(502\) 1.53058e12i 0.0480107i
\(503\) 1.61237e13i 0.500753i 0.968148 + 0.250377i \(0.0805545\pi\)
−0.968148 + 0.250377i \(0.919446\pi\)
\(504\) −2.97417e12 −0.0914561
\(505\) 7.48987e12i 0.228043i
\(506\) 4.76536e11i 0.0143662i
\(507\) 1.27744e12i 0.0381330i
\(508\) −1.12158e13 −0.331522
\(509\) 4.96346e13 1.45277 0.726383 0.687290i \(-0.241200\pi\)
0.726383 + 0.687290i \(0.241200\pi\)
\(510\) 1.72751e11i 0.00500692i
\(511\) 3.48547e13 1.00036
\(512\) 4.63824e12i 0.131827i
\(513\) 2.44903e13 0.689300
\(514\) 7.48976e11 0.0208763
\(515\) 1.27924e13i 0.353115i
\(516\) −4.74007e12 + 6.70545e12i −0.129579 + 0.183307i
\(517\) −2.44810e13 −0.662789
\(518\) 2.08762e12i 0.0559762i
\(519\) 7.51585e12i 0.199591i
\(520\) 2.86078e12 0.0752433
\(521\) 5.19063e13i 1.35217i 0.736823 + 0.676086i \(0.236325\pi\)
−0.736823 + 0.676086i \(0.763675\pi\)
\(522\) 8.62136e11 0.0222445
\(523\) 2.70715e13i 0.691836i 0.938265 + 0.345918i \(0.112432\pi\)
−0.938265 + 0.345918i \(0.887568\pi\)
\(524\) 4.11181e13i 1.04082i
\(525\) 2.35160e13 0.589612
\(526\) 1.96644e12 0.0488373
\(527\) −2.27376e13 −0.559360
\(528\) 1.02484e13i 0.249740i
\(529\) −3.15719e13 −0.762117
\(530\) 1.57674e12 0.0377035
\(531\) 5.95458e13 1.41052
\(532\) 1.22129e14 2.86590
\(533\) −1.52926e13 −0.355505
\(534\) 3.44795e11i 0.00794062i
\(535\) 6.46589e13i 1.47523i
\(536\) 2.49650e12i 0.0564298i
\(537\) 1.48980e13 0.333623
\(538\) 6.87970e10i 0.00152636i
\(539\) 1.17587e14 2.58473
\(540\) −3.13920e13 −0.683677
\(541\) −4.82709e11 −0.0104160 −0.00520798 0.999986i \(-0.501658\pi\)
−0.00520798 + 0.999986i \(0.501658\pi\)
\(542\) 8.62820e11i 0.0184469i
\(543\) 1.53409e13i 0.324976i
\(544\) 2.03732e12i 0.0427626i
\(545\) 1.04794e12i 0.0217949i
\(546\) 4.78493e11i 0.00986080i
\(547\) 5.07801e13 1.03695 0.518474 0.855093i \(-0.326500\pi\)
0.518474 + 0.855093i \(0.326500\pi\)
\(548\) 1.62311e13i 0.328431i
\(549\) 4.04864e13i 0.811797i
\(550\) 2.13541e12i 0.0424295i
\(551\) −7.08292e13 −1.39461
\(552\) −2.96817e11 −0.00579153
\(553\) 1.40363e14i 2.71411i
\(554\) −1.72733e12 −0.0330998
\(555\) 2.14718e13i 0.407759i
\(556\) −2.57689e13 −0.484978
\(557\) 1.93646e13 0.361188 0.180594 0.983558i \(-0.442198\pi\)
0.180594 + 0.983558i \(0.442198\pi\)
\(558\) 1.40774e12i 0.0260227i
\(559\) −4.06125e13 2.87089e13i −0.744048 0.525966i
\(560\) −1.56437e14 −2.84053
\(561\) 7.50434e12i 0.135051i
\(562\) 1.08182e12i 0.0192963i
\(563\) 1.67892e13 0.296817 0.148409 0.988926i \(-0.452585\pi\)
0.148409 + 0.988926i \(0.452585\pi\)
\(564\) 7.62149e12i 0.133550i
\(565\) −7.46409e13 −1.29639
\(566\) 6.53341e11i 0.0112475i
\(567\) 9.08866e13i 1.55090i
\(568\) −6.57955e11 −0.0111290
\(569\) −7.06796e13 −1.18504 −0.592520 0.805556i \(-0.701867\pi\)
−0.592520 + 0.805556i \(0.701867\pi\)
\(570\) −8.78692e11 −0.0146037
\(571\) 3.18030e13i 0.523947i 0.965075 + 0.261974i \(0.0843733\pi\)
−0.965075 + 0.261974i \(0.915627\pi\)
\(572\) 6.21146e13 1.01441
\(573\) −2.58857e13 −0.419070
\(574\) −1.17118e12 −0.0187959
\(575\) −4.41598e13 −0.702567
\(576\) 5.99515e13 0.945557
\(577\) 2.25287e13i 0.352255i −0.984367 0.176128i \(-0.943643\pi\)
0.984367 0.176128i \(-0.0563571\pi\)
\(578\) 1.20895e12i 0.0187400i
\(579\) 1.82076e13i 0.279808i
\(580\) 9.07898e13 1.38324
\(581\) 1.89737e14i 2.86597i
\(582\) 1.75157e11 0.00262308
\(583\) 6.84939e13 1.01697
\(584\) 1.97139e12 0.0290208
\(585\) 9.26046e13i 1.35162i
\(586\) 1.64939e12i 0.0238690i
\(587\) 9.42670e13i 1.35260i −0.736627 0.676300i \(-0.763582\pi\)
0.736627 0.676300i \(-0.236418\pi\)
\(588\) 3.66076e13i 0.520816i
\(589\) 1.15654e14i 1.63149i
\(590\) −4.38644e12 −0.0613553
\(591\) 2.50576e13i 0.347537i
\(592\) 8.43098e13i 1.15950i
\(593\) 1.31494e14i 1.79321i 0.442832 + 0.896605i \(0.353974\pi\)
−0.442832 + 0.896605i \(0.646026\pi\)
\(594\) 9.53918e11 0.0128997
\(595\) −1.14550e14 −1.53607
\(596\) 2.17554e13i 0.289292i
\(597\) −1.68781e13 −0.222563
\(598\) 8.98544e11i 0.0117499i
\(599\) 1.15805e12 0.0150174 0.00750868 0.999972i \(-0.497610\pi\)
0.00750868 + 0.999972i \(0.497610\pi\)
\(600\) 1.33007e12 0.0171048
\(601\) 3.04760e13i 0.388674i 0.980935 + 0.194337i \(0.0622555\pi\)
−0.980935 + 0.194337i \(0.937745\pi\)
\(602\) −3.11030e12 2.19866e12i −0.0393387 0.0278084i
\(603\) 8.08129e13 1.01366
\(604\) 1.50886e13i 0.187700i
\(605\) 3.05361e13i 0.376735i
\(606\) 7.08561e10 0.000866991
\(607\) 1.14536e14i 1.38995i −0.719035 0.694974i \(-0.755416\pi\)
0.719035 0.694974i \(-0.244584\pi\)
\(608\) 1.03627e13 0.124726
\(609\) 3.03815e13i 0.362680i
\(610\) 2.98243e12i 0.0353119i
\(611\) −4.61607e13 −0.542083
\(612\) 4.39607e13 0.512044
\(613\) −3.22409e13 −0.372481 −0.186241 0.982504i \(-0.559630\pi\)
−0.186241 + 0.982504i \(0.559630\pi\)
\(614\) 2.69577e12i 0.0308916i
\(615\) −1.20459e13 −0.136919
\(616\) 9.51738e12 0.107304
\(617\) −1.54437e14 −1.72713 −0.863567 0.504235i \(-0.831775\pi\)
−0.863567 + 0.504235i \(0.831775\pi\)
\(618\) 1.21019e11 0.00134249
\(619\) 1.73772e13 0.191217 0.0956086 0.995419i \(-0.469520\pi\)
0.0956086 + 0.995419i \(0.469520\pi\)
\(620\) 1.48246e14i 1.61818i
\(621\) 1.97268e13i 0.213599i
\(622\) 2.01509e12i 0.0216442i
\(623\) −2.28631e14 −2.43610
\(624\) 1.93242e13i 0.204258i
\(625\) −3.48572e13 −0.365504
\(626\) −1.05133e12 −0.0109363
\(627\) −3.81705e13 −0.393904
\(628\) 6.64204e13i 0.679991i
\(629\) 6.17353e13i 0.627018i
\(630\) 7.09209e12i 0.0714614i
\(631\) 6.14662e12i 0.0614454i 0.999528 + 0.0307227i \(0.00978088\pi\)
−0.999528 + 0.0307227i \(0.990219\pi\)
\(632\) 7.93900e12i 0.0787373i
\(633\) 2.93879e13 0.289168
\(634\) 8.78696e11i 0.00857813i
\(635\) 5.35084e13i 0.518266i
\(636\) 2.13237e13i 0.204917i
\(637\) 2.21719e14 2.11401
\(638\) −2.75885e12 −0.0260991
\(639\) 2.12983e13i 0.199913i
\(640\) −1.77087e13 −0.164925
\(641\) 9.01040e13i 0.832633i −0.909220 0.416317i \(-0.863321\pi\)
0.909220 0.416317i \(-0.136679\pi\)
\(642\) 6.11690e11 0.00560862
\(643\) 5.02415e13 0.457096 0.228548 0.973533i \(-0.426602\pi\)
0.228548 + 0.973533i \(0.426602\pi\)
\(644\) 9.83742e13i 0.888080i
\(645\) −3.19903e13 2.26139e13i −0.286563 0.202571i
\(646\) 2.52639e12 0.0224563
\(647\) 1.07660e14i 0.949583i −0.880098 0.474791i \(-0.842524\pi\)
0.880098 0.474791i \(-0.157476\pi\)
\(648\) 5.14057e12i 0.0449921i
\(649\) −1.90548e14 −1.65493
\(650\) 4.02648e12i 0.0347023i
\(651\) 4.96086e13 0.424280
\(652\) 1.72406e14i 1.46323i
\(653\) 2.03675e14i 1.71542i 0.514132 + 0.857711i \(0.328114\pi\)
−0.514132 + 0.857711i \(0.671886\pi\)
\(654\) 9.91381e9 8.28613e−5
\(655\) 1.96166e14 1.62711
\(656\) 4.72987e13 0.389341
\(657\) 6.38148e13i 0.521309i
\(658\) −3.53520e12 −0.0286606
\(659\) 9.42998e13 0.758723 0.379362 0.925248i \(-0.376144\pi\)
0.379362 + 0.925248i \(0.376144\pi\)
\(660\) 4.89274e13 0.390690
\(661\) −2.15781e14 −1.71004 −0.855018 0.518598i \(-0.826454\pi\)
−0.855018 + 0.518598i \(0.826454\pi\)
\(662\) 2.98220e12 0.0234556
\(663\) 1.41500e13i 0.110456i
\(664\) 1.07316e13i 0.0831426i
\(665\) 5.82654e14i 4.48025i
\(666\) −3.82219e12 −0.0291703
\(667\) 5.70524e13i 0.432160i
\(668\) 8.86598e13 0.666568
\(669\) 4.64593e12 0.0346691
\(670\) −5.95308e12 −0.0440928
\(671\) 1.29557e14i 0.952464i
\(672\) 4.44499e12i 0.0324358i
\(673\) 1.04309e14i 0.755519i −0.925904 0.377759i \(-0.876695\pi\)
0.925904 0.377759i \(-0.123305\pi\)
\(674\) 5.77989e12i 0.0415547i
\(675\) 8.83980e13i 0.630846i
\(676\) −2.39467e13 −0.169634
\(677\) 1.52663e14i 1.07347i −0.843750 0.536737i \(-0.819657\pi\)
0.843750 0.536737i \(-0.180343\pi\)
\(678\) 7.06122e11i 0.00492869i
\(679\) 1.16145e14i 0.804733i
\(680\) −6.47900e12 −0.0445618
\(681\) −3.15476e13 −0.215393
\(682\) 4.50480e12i 0.0305319i
\(683\) 7.96363e13 0.535806 0.267903 0.963446i \(-0.413669\pi\)
0.267903 + 0.963446i \(0.413669\pi\)
\(684\) 2.23604e14i 1.49348i
\(685\) 7.74351e13 0.513435
\(686\) 9.66146e12 0.0635949
\(687\) 1.89047e13i 0.123534i
\(688\) 1.25611e14 + 8.87942e13i 0.814865 + 0.576026i
\(689\) 1.29150e14 0.831763
\(690\) 7.07780e11i 0.00452536i
\(691\) 1.80567e14i 1.14617i 0.819496 + 0.573085i \(0.194253\pi\)
−0.819496 + 0.573085i \(0.805747\pi\)
\(692\) 1.40891e14 0.887875
\(693\) 3.08081e14i 1.92752i
\(694\) 7.31492e12 0.0454373
\(695\) 1.22938e14i 0.758164i
\(696\) 1.71839e12i 0.0105214i
\(697\) 3.46341e13 0.210543
\(698\) −4.81384e12 −0.0290546
\(699\) 3.12681e13 0.187376
\(700\) 4.40826e14i 2.62287i
\(701\) −6.31483e13 −0.373054 −0.186527 0.982450i \(-0.559723\pi\)
−0.186527 + 0.982450i \(0.559723\pi\)
\(702\) 1.79868e12 0.0105504
\(703\) 3.14014e14 1.82882
\(704\) −1.91846e14 −1.10940
\(705\) −3.63606e13 −0.208778
\(706\) 8.61941e11i 0.00491421i
\(707\) 4.69842e13i 0.265983i
\(708\) 5.93219e13i 0.333464i
\(709\) 1.41239e14 0.788358 0.394179 0.919034i \(-0.371029\pi\)
0.394179 + 0.919034i \(0.371029\pi\)
\(710\) 1.56894e12i 0.00869589i
\(711\) −2.56989e14 −1.41438
\(712\) −1.29314e13 −0.0706719
\(713\) −9.31583e13 −0.505561
\(714\) 1.08367e12i 0.00583993i
\(715\) 2.96336e14i 1.58582i
\(716\) 2.79275e14i 1.48411i
\(717\) 1.85628e13i 0.0979599i
\(718\) 2.07193e12i 0.0108581i
\(719\) −8.58193e13 −0.446623 −0.223311 0.974747i \(-0.571687\pi\)
−0.223311 + 0.974747i \(0.571687\pi\)
\(720\) 2.86418e14i 1.48026i
\(721\) 8.02470e13i 0.411863i
\(722\) 7.66316e12i 0.0390591i
\(723\) −6.86280e13 −0.347384
\(724\) 2.87577e14 1.44564
\(725\) 2.55658e14i 1.27635i
\(726\) −2.88879e11 −0.00143230
\(727\) 1.46830e14i 0.723005i −0.932371 0.361503i \(-0.882264\pi\)
0.932371 0.361503i \(-0.117736\pi\)
\(728\) 1.79457e13 0.0877616
\(729\) 1.46147e14 0.709827
\(730\) 4.70092e12i 0.0226761i
\(731\) 9.19779e13 + 6.50190e13i 0.440653 + 0.311496i
\(732\) −4.03341e13 −0.191919
\(733\) 6.49570e13i 0.306977i 0.988150 + 0.153488i \(0.0490508\pi\)
−0.988150 + 0.153488i \(0.950949\pi\)
\(734\) 4.47577e12i 0.0210082i
\(735\) 1.74647e14 0.814190
\(736\) 8.34709e12i 0.0386497i
\(737\) −2.58603e14 −1.18931
\(738\) 2.14429e12i 0.00979493i
\(739\) 2.94890e14i 1.33794i 0.743288 + 0.668972i \(0.233265\pi\)
−0.743288 + 0.668972i \(0.766735\pi\)
\(740\) −4.02507e14 −1.81390
\(741\) −7.19733e13 −0.322167
\(742\) 9.89094e12 0.0439762
\(743\) 1.44160e14i 0.636651i 0.947981 + 0.318326i \(0.103120\pi\)
−0.947981 + 0.318326i \(0.896880\pi\)
\(744\) 2.80588e12 0.0123085
\(745\) −1.03791e14 −0.452249
\(746\) −3.59287e12 −0.0155506
\(747\) 3.47386e14 1.49351
\(748\) −1.40675e14 −0.600771
\(749\) 4.05607e14i 1.72066i
\(750\) 9.69841e11i 0.00408690i
\(751\) 8.92427e12i 0.0373571i 0.999826 + 0.0186785i \(0.00594591\pi\)
−0.999826 + 0.0186785i \(0.994054\pi\)
\(752\) 1.42771e14 0.593678
\(753\) 9.87530e13i 0.407920i
\(754\) −5.20202e12 −0.0213459
\(755\) 7.19847e13 0.293431
\(756\) −1.96923e14 −0.797421
\(757\) 9.64872e13i 0.388142i −0.980988 0.194071i \(-0.937831\pi\)
0.980988 0.194071i \(-0.0621691\pi\)
\(758\) 1.20401e13i 0.0481156i
\(759\) 3.07461e13i 0.122062i
\(760\) 3.29551e13i 0.129973i
\(761\) 1.69309e14i 0.663370i −0.943390 0.331685i \(-0.892383\pi\)
0.943390 0.331685i \(-0.107617\pi\)
\(762\) 5.06203e11 0.00197038
\(763\) 6.57377e12i 0.0254210i
\(764\) 4.85248e14i 1.86422i
\(765\) 2.09728e14i 0.800477i
\(766\) −4.02324e12 −0.0152557
\(767\) −3.59292e14 −1.35354
\(768\) 5.96003e13i 0.223071i
\(769\) −3.58143e14 −1.33176 −0.665878 0.746061i \(-0.731943\pi\)
−0.665878 + 0.746061i \(0.731943\pi\)
\(770\) 2.26948e13i 0.0838442i
\(771\) 4.83239e13 0.177374
\(772\) −3.41316e14 −1.24472
\(773\) 1.36760e14i 0.495522i 0.968821 + 0.247761i \(0.0796948\pi\)
−0.968821 + 0.247761i \(0.920305\pi\)
\(774\) −4.02549e12 + 5.69459e12i −0.0144915 + 0.0205002i
\(775\) 4.17452e14 1.49313
\(776\) 6.56920e12i 0.0233455i
\(777\) 1.34693e14i 0.475599i
\(778\) 1.05933e13 0.0371650
\(779\) 1.76165e14i 0.614090i