Properties

Label 43.7.b.b.42.13
Level 43
Weight 7
Character 43.42
Analytic conductor 9.892
Analytic rank 0
Dimension 20
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{15} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.13
Root \(6.90119i\) of \(x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + 80362197690736 x^{8} + 2545997652841536 x^{6} + 40210452531479040 x^{4} + 212033222410436608 x^{2} + 64236717122519040\)
Character \(\chi\) \(=\) 43.42
Dual form 43.7.b.b.42.8

$q$-expansion

\(f(q)\) \(=\) \(q+6.90119i q^{2} +11.0801i q^{3} +16.3736 q^{4} -107.518i q^{5} -76.4660 q^{6} +594.412i q^{7} +554.673i q^{8} +606.231 q^{9} +O(q^{10})\) \(q+6.90119i q^{2} +11.0801i q^{3} +16.3736 q^{4} -107.518i q^{5} -76.4660 q^{6} +594.412i q^{7} +554.673i q^{8} +606.231 q^{9} +742.004 q^{10} -326.752 q^{11} +181.422i q^{12} -3327.43 q^{13} -4102.15 q^{14} +1191.32 q^{15} -2779.99 q^{16} +1730.37 q^{17} +4183.71i q^{18} +6997.69i q^{19} -1760.47i q^{20} -6586.16 q^{21} -2254.98i q^{22} -7593.56 q^{23} -6145.85 q^{24} +4064.80 q^{25} -22963.2i q^{26} +14794.5i q^{27} +9732.68i q^{28} -10036.1i q^{29} +8221.51i q^{30} +25812.1 q^{31} +16313.8i q^{32} -3620.46i q^{33} +11941.6i q^{34} +63910.2 q^{35} +9926.19 q^{36} -37980.1i q^{37} -48292.4 q^{38} -36868.3i q^{39} +59637.6 q^{40} -18315.7 q^{41} -45452.3i q^{42} +(61156.1 + 50806.4i) q^{43} -5350.12 q^{44} -65180.9i q^{45} -52404.6i q^{46} +130402. q^{47} -30802.7i q^{48} -235677. q^{49} +28051.9i q^{50} +19172.7i q^{51} -54482.1 q^{52} +272103. q^{53} -102100. q^{54} +35131.9i q^{55} -329705. q^{56} -77535.3 q^{57} +69261.1 q^{58} +216781. q^{59} +19506.2 q^{60} -344144. i q^{61} +178134. i q^{62} +360351. i q^{63} -290504. q^{64} +357760. i q^{65} +24985.5 q^{66} -227534. q^{67} +28332.4 q^{68} -84137.6i q^{69} +441056. i q^{70} -281680. i q^{71} +336260. i q^{72} -294591. i q^{73} +262108. q^{74} +45038.5i q^{75} +114578. i q^{76} -194226. i q^{77} +254435. q^{78} -497124. q^{79} +298900. i q^{80} +278017. q^{81} -126400. i q^{82} -143881. q^{83} -107839. q^{84} -186046. i q^{85} +(-350625. + 422050. i) q^{86} +111201. q^{87} -181241. i q^{88} -523099. i q^{89} +449826. q^{90} -1.97786e6i q^{91} -124334. q^{92} +286002. i q^{93} +899926. i q^{94} +752380. q^{95} -180760. q^{96} -430866. q^{97} -1.62645e6i q^{98} -198087. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.90119i 0.862648i 0.902197 + 0.431324i \(0.141953\pi\)
−0.902197 + 0.431324i \(0.858047\pi\)
\(3\) 11.0801i 0.410375i 0.978723 + 0.205188i \(0.0657804\pi\)
−0.978723 + 0.205188i \(0.934220\pi\)
\(4\) 16.3736 0.255838
\(5\) 107.518i 0.860147i −0.902794 0.430074i \(-0.858488\pi\)
0.902794 0.430074i \(-0.141512\pi\)
\(6\) −76.4660 −0.354009
\(7\) 594.412i 1.73298i 0.499194 + 0.866490i \(0.333629\pi\)
−0.499194 + 0.866490i \(0.666371\pi\)
\(8\) 554.673i 1.08335i
\(9\) 606.231 0.831592
\(10\) 742.004 0.742004
\(11\) −326.752 −0.245494 −0.122747 0.992438i \(-0.539170\pi\)
−0.122747 + 0.992438i \(0.539170\pi\)
\(12\) 181.422i 0.104989i
\(13\) −3327.43 −1.51453 −0.757266 0.653106i \(-0.773466\pi\)
−0.757266 + 0.653106i \(0.773466\pi\)
\(14\) −4102.15 −1.49495
\(15\) 1191.32 0.352983
\(16\) −2779.99 −0.678709
\(17\) 1730.37 0.352202 0.176101 0.984372i \(-0.443651\pi\)
0.176101 + 0.984372i \(0.443651\pi\)
\(18\) 4183.71i 0.717372i
\(19\) 6997.69i 1.02022i 0.860109 + 0.510110i \(0.170395\pi\)
−0.860109 + 0.510110i \(0.829605\pi\)
\(20\) 1760.47i 0.220058i
\(21\) −6586.16 −0.711172
\(22\) 2254.98i 0.211775i
\(23\) −7593.56 −0.624111 −0.312055 0.950064i \(-0.601017\pi\)
−0.312055 + 0.950064i \(0.601017\pi\)
\(24\) −6145.85 −0.444578
\(25\) 4064.80 0.260147
\(26\) 22963.2i 1.30651i
\(27\) 14794.5i 0.751640i
\(28\) 9732.68i 0.443362i
\(29\) 10036.1i 0.411502i −0.978604 0.205751i \(-0.934036\pi\)
0.978604 0.205751i \(-0.0659637\pi\)
\(30\) 8221.51i 0.304500i
\(31\) 25812.1 0.866440 0.433220 0.901288i \(-0.357377\pi\)
0.433220 + 0.901288i \(0.357377\pi\)
\(32\) 16313.8i 0.497859i
\(33\) 3620.46i 0.100745i
\(34\) 11941.6i 0.303826i
\(35\) 63910.2 1.49062
\(36\) 9926.19 0.212753
\(37\) 37980.1i 0.749809i −0.927063 0.374905i \(-0.877675\pi\)
0.927063 0.374905i \(-0.122325\pi\)
\(38\) −48292.4 −0.880091
\(39\) 36868.3i 0.621527i
\(40\) 59637.6 0.931837
\(41\) −18315.7 −0.265749 −0.132874 0.991133i \(-0.542421\pi\)
−0.132874 + 0.991133i \(0.542421\pi\)
\(42\) 45452.3i 0.613491i
\(43\) 61156.1 + 50806.4i 0.769191 + 0.639019i
\(44\) −5350.12 −0.0628066
\(45\) 65180.9i 0.715292i
\(46\) 52404.6i 0.538388i
\(47\) 130402. 1.25600 0.627999 0.778214i \(-0.283874\pi\)
0.627999 + 0.778214i \(0.283874\pi\)
\(48\) 30802.7i 0.278525i
\(49\) −235677. −2.00322
\(50\) 28051.9i 0.224415i
\(51\) 19172.7i 0.144535i
\(52\) −54482.1 −0.387475
\(53\) 272103. 1.82771 0.913853 0.406045i \(-0.133092\pi\)
0.913853 + 0.406045i \(0.133092\pi\)
\(54\) −102100. −0.648401
\(55\) 35131.9i 0.211161i
\(56\) −329705. −1.87742
\(57\) −77535.3 −0.418673
\(58\) 69261.1 0.354981
\(59\) 216781. 1.05552 0.527759 0.849394i \(-0.323032\pi\)
0.527759 + 0.849394i \(0.323032\pi\)
\(60\) 19506.2 0.0903064
\(61\) 344144.i 1.51618i −0.652151 0.758089i \(-0.726133\pi\)
0.652151 0.758089i \(-0.273867\pi\)
\(62\) 178134.i 0.747433i
\(63\) 360351.i 1.44113i
\(64\) −290504. −1.10819
\(65\) 357760.i 1.30272i
\(66\) 24985.5 0.0869071
\(67\) −227534. −0.756524 −0.378262 0.925699i \(-0.623478\pi\)
−0.378262 + 0.925699i \(0.623478\pi\)
\(68\) 28332.4 0.0901065
\(69\) 84137.6i 0.256120i
\(70\) 441056.i 1.28588i
\(71\) 281680.i 0.787013i −0.919322 0.393506i \(-0.871262\pi\)
0.919322 0.393506i \(-0.128738\pi\)
\(72\) 336260.i 0.900902i
\(73\) 294591.i 0.757270i −0.925546 0.378635i \(-0.876394\pi\)
0.925546 0.378635i \(-0.123606\pi\)
\(74\) 262108. 0.646822
\(75\) 45038.5i 0.106758i
\(76\) 114578.i 0.261011i
\(77\) 194226.i 0.425436i
\(78\) 254435. 0.536159
\(79\) −497124. −1.00828 −0.504142 0.863621i \(-0.668191\pi\)
−0.504142 + 0.863621i \(0.668191\pi\)
\(80\) 298900.i 0.583790i
\(81\) 278017. 0.523138
\(82\) 126400.i 0.229248i
\(83\) −143881. −0.251634 −0.125817 0.992053i \(-0.540155\pi\)
−0.125817 + 0.992053i \(0.540155\pi\)
\(84\) −107839. −0.181945
\(85\) 186046.i 0.302945i
\(86\) −350625. + 422050.i −0.551248 + 0.663542i
\(87\) 111201. 0.168870
\(88\) 181241.i 0.265955i
\(89\) 523099.i 0.742017i −0.928629 0.371009i \(-0.879012\pi\)
0.928629 0.371009i \(-0.120988\pi\)
\(90\) 449826. 0.617045
\(91\) 1.97786e6i 2.62466i
\(92\) −124334. −0.159671
\(93\) 286002.i 0.355565i
\(94\) 899926.i 1.08349i
\(95\) 752380. 0.877539
\(96\) −180760. −0.204309
\(97\) −430866. −0.472093 −0.236046 0.971742i \(-0.575852\pi\)
−0.236046 + 0.971742i \(0.575852\pi\)
\(98\) 1.62645e6i 1.72807i
\(99\) −198087. −0.204151
\(100\) 66555.4 0.0665554
\(101\) 842018. 0.817254 0.408627 0.912701i \(-0.366008\pi\)
0.408627 + 0.912701i \(0.366008\pi\)
\(102\) −132314. −0.124683
\(103\) 104065. 0.0952343 0.0476171 0.998866i \(-0.484837\pi\)
0.0476171 + 0.998866i \(0.484837\pi\)
\(104\) 1.84564e6i 1.64076i
\(105\) 708134.i 0.611713i
\(106\) 1.87784e6i 1.57667i
\(107\) 837014. 0.683253 0.341627 0.939836i \(-0.389022\pi\)
0.341627 + 0.939836i \(0.389022\pi\)
\(108\) 242240.i 0.192298i
\(109\) 2.47342e6 1.90993 0.954967 0.296711i \(-0.0958899\pi\)
0.954967 + 0.296711i \(0.0958899\pi\)
\(110\) −242452. −0.182158
\(111\) 420824. 0.307703
\(112\) 1.65246e6i 1.17619i
\(113\) 2.68260e6i 1.85918i 0.368597 + 0.929589i \(0.379838\pi\)
−0.368597 + 0.929589i \(0.620162\pi\)
\(114\) 535086.i 0.361168i
\(115\) 816447.i 0.536827i
\(116\) 164328.i 0.105278i
\(117\) −2.01719e6 −1.25947
\(118\) 1.49605e6i 0.910541i
\(119\) 1.02855e6i 0.610359i
\(120\) 660792.i 0.382403i
\(121\) −1.66479e6 −0.939733
\(122\) 2.37500e6 1.30793
\(123\) 202940.i 0.109057i
\(124\) 422638. 0.221668
\(125\) 2.11702e6i 1.08391i
\(126\) −2.48685e6 −1.24319
\(127\) 899817. 0.439281 0.219641 0.975581i \(-0.429512\pi\)
0.219641 + 0.975581i \(0.429512\pi\)
\(128\) 960739.i 0.458116i
\(129\) −562942. + 677617.i −0.262237 + 0.315657i
\(130\) −2.46897e6 −1.12379
\(131\) 1.57065e6i 0.698662i −0.936999 0.349331i \(-0.886409\pi\)
0.936999 0.349331i \(-0.113591\pi\)
\(132\) 59280.0i 0.0257743i
\(133\) −4.15951e6 −1.76802
\(134\) 1.57026e6i 0.652614i
\(135\) 1.59068e6 0.646521
\(136\) 959789.i 0.381557i
\(137\) 2.54070e6i 0.988080i 0.869439 + 0.494040i \(0.164480\pi\)
−0.869439 + 0.494040i \(0.835520\pi\)
\(138\) 580649. 0.220941
\(139\) −4.18653e6 −1.55887 −0.779434 0.626484i \(-0.784493\pi\)
−0.779434 + 0.626484i \(0.784493\pi\)
\(140\) 1.04644e6 0.381356
\(141\) 1.44487e6i 0.515431i
\(142\) 1.94393e6 0.678915
\(143\) 1.08724e6 0.371808
\(144\) −1.68532e6 −0.564409
\(145\) −1.07907e6 −0.353952
\(146\) 2.03303e6 0.653258
\(147\) 2.61133e6i 0.822072i
\(148\) 621872.i 0.191830i
\(149\) 3.45889e6i 1.04563i 0.852446 + 0.522815i \(0.175118\pi\)
−0.852446 + 0.522815i \(0.824882\pi\)
\(150\) −310819. −0.0920945
\(151\) 6.00850e6i 1.74516i 0.488472 + 0.872579i \(0.337554\pi\)
−0.488472 + 0.872579i \(0.662446\pi\)
\(152\) −3.88143e6 −1.10525
\(153\) 1.04900e6 0.292888
\(154\) 1.34039e6 0.367002
\(155\) 2.77528e6i 0.745266i
\(156\) 603668.i 0.159010i
\(157\) 3.21178e6i 0.829940i −0.909835 0.414970i \(-0.863792\pi\)
0.909835 0.414970i \(-0.136208\pi\)
\(158\) 3.43074e6i 0.869795i
\(159\) 3.01494e6i 0.750045i
\(160\) 1.75404e6 0.428232
\(161\) 4.51370e6i 1.08157i
\(162\) 1.91865e6i 0.451284i
\(163\) 2.40767e6i 0.555947i 0.960589 + 0.277974i \(0.0896628\pi\)
−0.960589 + 0.277974i \(0.910337\pi\)
\(164\) −299894. −0.0679886
\(165\) −389266. −0.0866551
\(166\) 992950.i 0.217072i
\(167\) 473244. 0.101610 0.0508049 0.998709i \(-0.483821\pi\)
0.0508049 + 0.998709i \(0.483821\pi\)
\(168\) 3.65317e6i 0.770446i
\(169\) 6.24497e6 1.29381
\(170\) 1.28394e6 0.261335
\(171\) 4.24221e6i 0.848407i
\(172\) 1.00135e6 + 831885.i 0.196788 + 0.163485i
\(173\) 2.36439e6 0.456648 0.228324 0.973585i \(-0.426675\pi\)
0.228324 + 0.973585i \(0.426675\pi\)
\(174\) 767422.i 0.145676i
\(175\) 2.41616e6i 0.450829i
\(176\) 908369. 0.166619
\(177\) 2.40197e6i 0.433159i
\(178\) 3.61001e6 0.640100
\(179\) 5.36583e6i 0.935573i −0.883841 0.467787i \(-0.845052\pi\)
0.883841 0.467787i \(-0.154948\pi\)
\(180\) 1.06725e6i 0.182999i
\(181\) −1.32962e6 −0.224228 −0.112114 0.993695i \(-0.535762\pi\)
−0.112114 + 0.993695i \(0.535762\pi\)
\(182\) 1.36496e7 2.26415
\(183\) 3.81316e6 0.622202
\(184\) 4.21194e6i 0.676128i
\(185\) −4.08356e6 −0.644946
\(186\) −1.97375e6 −0.306728
\(187\) −565402. −0.0864634
\(188\) 2.13515e6 0.321332
\(189\) −8.79405e6 −1.30258
\(190\) 5.19232e6i 0.757008i
\(191\) 1.27305e7i 1.82703i −0.406807 0.913514i \(-0.633358\pi\)
0.406807 0.913514i \(-0.366642\pi\)
\(192\) 3.21883e6i 0.454772i
\(193\) −3.87363e6 −0.538823 −0.269411 0.963025i \(-0.586829\pi\)
−0.269411 + 0.963025i \(0.586829\pi\)
\(194\) 2.97349e6i 0.407250i
\(195\) −3.96402e6 −0.534604
\(196\) −3.85888e6 −0.512499
\(197\) −7.79358e6 −1.01939 −0.509693 0.860356i \(-0.670241\pi\)
−0.509693 + 0.860356i \(0.670241\pi\)
\(198\) 1.36704e6i 0.176110i
\(199\) 2.68474e6i 0.340678i −0.985386 0.170339i \(-0.945514\pi\)
0.985386 0.170339i \(-0.0544862\pi\)
\(200\) 2.25463e6i 0.281829i
\(201\) 2.52111e6i 0.310459i
\(202\) 5.81092e6i 0.705003i
\(203\) 5.96559e6 0.713124
\(204\) 313926.i 0.0369775i
\(205\) 1.96927e6i 0.228583i
\(206\) 718172.i 0.0821537i
\(207\) −4.60345e6 −0.519006
\(208\) 9.25023e6 1.02793
\(209\) 2.28651e6i 0.250458i
\(210\) −4.88696e6 −0.527693
\(211\) 1.89548e6i 0.201777i −0.994898 0.100888i \(-0.967831\pi\)
0.994898 0.100888i \(-0.0321685\pi\)
\(212\) 4.45532e6 0.467596
\(213\) 3.12106e6 0.322970
\(214\) 5.77639e6i 0.589407i
\(215\) 5.46263e6 6.57540e6i 0.549650 0.661618i
\(216\) −8.20613e6 −0.814287
\(217\) 1.53430e7i 1.50152i
\(218\) 1.70695e7i 1.64760i
\(219\) 3.26411e6 0.310765
\(220\) 575236.i 0.0540229i
\(221\) −5.75768e6 −0.533421
\(222\) 2.90419e6i 0.265440i
\(223\) 5.86386e6i 0.528772i 0.964417 + 0.264386i \(0.0851694\pi\)
−0.964417 + 0.264386i \(0.914831\pi\)
\(224\) −9.69715e6 −0.862780
\(225\) 2.46420e6 0.216336
\(226\) −1.85131e7 −1.60382
\(227\) 1.08262e7i 0.925551i −0.886476 0.462775i \(-0.846854\pi\)
0.886476 0.462775i \(-0.153146\pi\)
\(228\) −1.26953e6 −0.107112
\(229\) −4.16761e6 −0.347041 −0.173520 0.984830i \(-0.555514\pi\)
−0.173520 + 0.984830i \(0.555514\pi\)
\(230\) −5.63445e6 −0.463093
\(231\) 2.15204e6 0.174588
\(232\) 5.56677e6 0.445799
\(233\) 2.22514e7i 1.75909i 0.475812 + 0.879547i \(0.342154\pi\)
−0.475812 + 0.879547i \(0.657846\pi\)
\(234\) 1.39210e7i 1.08648i
\(235\) 1.40206e7i 1.08034i
\(236\) 3.54950e6 0.270042
\(237\) 5.50820e6i 0.413775i
\(238\) −7.09823e6 −0.526525
\(239\) 2.26230e7 1.65713 0.828567 0.559891i \(-0.189157\pi\)
0.828567 + 0.559891i \(0.189157\pi\)
\(240\) −3.31185e6 −0.239573
\(241\) 1.73057e7i 1.23634i 0.786045 + 0.618170i \(0.212126\pi\)
−0.786045 + 0.618170i \(0.787874\pi\)
\(242\) 1.14891e7i 0.810659i
\(243\) 1.38657e7i 0.966323i
\(244\) 5.63488e6i 0.387896i
\(245\) 2.53396e7i 1.72306i
\(246\) 1.40053e6 0.0940776
\(247\) 2.32843e7i 1.54516i
\(248\) 1.43173e7i 0.938654i
\(249\) 1.59422e6i 0.103264i
\(250\) 1.46099e7 0.935035
\(251\) −2.40761e7 −1.52253 −0.761264 0.648442i \(-0.775421\pi\)
−0.761264 + 0.648442i \(0.775421\pi\)
\(252\) 5.90025e6i 0.368696i
\(253\) 2.48121e6 0.153215
\(254\) 6.20980e6i 0.378945i
\(255\) 2.06142e6 0.124321
\(256\) −1.19620e7 −0.712993
\(257\) 9.76539e6i 0.575294i −0.957736 0.287647i \(-0.907127\pi\)
0.957736 0.287647i \(-0.0928730\pi\)
\(258\) −4.67636e6 3.88497e6i −0.272301 0.226219i
\(259\) 2.25758e7 1.29940
\(260\) 5.85782e6i 0.333285i
\(261\) 6.08420e6i 0.342202i
\(262\) 1.08394e7 0.602699
\(263\) 7.57778e6i 0.416557i 0.978070 + 0.208279i \(0.0667861\pi\)
−0.978070 + 0.208279i \(0.933214\pi\)
\(264\) 2.00817e6 0.109141
\(265\) 2.92561e7i 1.57210i
\(266\) 2.87056e7i 1.52518i
\(267\) 5.79601e6 0.304506
\(268\) −3.72556e6 −0.193547
\(269\) −8.27452e6 −0.425095 −0.212548 0.977151i \(-0.568176\pi\)
−0.212548 + 0.977151i \(0.568176\pi\)
\(270\) 1.09776e7i 0.557720i
\(271\) −1.77022e7 −0.889445 −0.444723 0.895668i \(-0.646698\pi\)
−0.444723 + 0.895668i \(0.646698\pi\)
\(272\) −4.81041e6 −0.239043
\(273\) 2.19150e7 1.07709
\(274\) −1.75339e7 −0.852365
\(275\) −1.32818e6 −0.0638645
\(276\) 1.37764e6i 0.0655251i
\(277\) 3.35720e7i 1.57957i −0.613385 0.789784i \(-0.710193\pi\)
0.613385 0.789784i \(-0.289807\pi\)
\(278\) 2.88920e7i 1.34475i
\(279\) 1.56481e7 0.720525
\(280\) 3.54493e7i 1.61486i
\(281\) 3.12675e7 1.40921 0.704604 0.709601i \(-0.251125\pi\)
0.704604 + 0.709601i \(0.251125\pi\)
\(282\) −9.97129e6 −0.444635
\(283\) 4.43759e7 1.95789 0.978945 0.204124i \(-0.0654346\pi\)
0.978945 + 0.204124i \(0.0654346\pi\)
\(284\) 4.61213e6i 0.201348i
\(285\) 8.33647e6i 0.360120i
\(286\) 7.50328e6i 0.320740i
\(287\) 1.08871e7i 0.460537i
\(288\) 9.88995e6i 0.414016i
\(289\) −2.11434e7 −0.875954
\(290\) 7.44684e6i 0.305336i
\(291\) 4.77405e6i 0.193735i
\(292\) 4.82352e6i 0.193738i
\(293\) 2.10928e6 0.0838553 0.0419276 0.999121i \(-0.486650\pi\)
0.0419276 + 0.999121i \(0.486650\pi\)
\(294\) 1.80213e7 0.709159
\(295\) 2.33080e7i 0.907901i
\(296\) 2.10665e7 0.812303
\(297\) 4.83415e6i 0.184523i
\(298\) −2.38705e7 −0.902011
\(299\) 2.52670e7 0.945236
\(300\) 737443.i 0.0273127i
\(301\) −3.02000e7 + 3.63519e7i −1.10741 + 1.33299i
\(302\) −4.14658e7 −1.50546
\(303\) 9.32967e6i 0.335381i
\(304\) 1.94535e7i 0.692433i
\(305\) −3.70018e7 −1.30414
\(306\) 7.23936e6i 0.252660i
\(307\) 1.34969e7 0.466466 0.233233 0.972421i \(-0.425070\pi\)
0.233233 + 0.972421i \(0.425070\pi\)
\(308\) 3.18017e6i 0.108843i
\(309\) 1.15305e6i 0.0390818i
\(310\) 1.91527e7 0.642902
\(311\) −4.02057e7 −1.33662 −0.668308 0.743885i \(-0.732981\pi\)
−0.668308 + 0.743885i \(0.732981\pi\)
\(312\) 2.04499e7 0.673329
\(313\) 2.75678e6i 0.0899021i −0.998989 0.0449510i \(-0.985687\pi\)
0.998989 0.0449510i \(-0.0143132\pi\)
\(314\) 2.21651e7 0.715946
\(315\) 3.87443e7 1.23959
\(316\) −8.13972e6 −0.257957
\(317\) 1.69320e7 0.531532 0.265766 0.964038i \(-0.414375\pi\)
0.265766 + 0.964038i \(0.414375\pi\)
\(318\) −2.08067e7 −0.647025
\(319\) 3.27932e6i 0.101021i
\(320\) 3.12346e7i 0.953203i
\(321\) 9.27423e6i 0.280390i
\(322\) 3.11499e7 0.933016
\(323\) 1.21086e7i 0.359323i
\(324\) 4.55214e6 0.133838
\(325\) −1.35253e7 −0.394001
\(326\) −1.66158e7 −0.479587
\(327\) 2.74058e7i 0.783790i
\(328\) 1.01592e7i 0.287898i
\(329\) 7.75123e7i 2.17662i
\(330\) 2.68640e6i 0.0747529i
\(331\) 1.17055e6i 0.0322778i −0.999870 0.0161389i \(-0.994863\pi\)
0.999870 0.0161389i \(-0.00513740\pi\)
\(332\) −2.35585e6 −0.0643775
\(333\) 2.30247e7i 0.623536i
\(334\) 3.26595e6i 0.0876536i
\(335\) 2.44641e7i 0.650722i
\(336\) 1.83095e7 0.482679
\(337\) −1.71166e7 −0.447228 −0.223614 0.974678i \(-0.571785\pi\)
−0.223614 + 0.974678i \(0.571785\pi\)
\(338\) 4.30977e7i 1.11610i
\(339\) −2.97236e7 −0.762961
\(340\) 3.04625e6i 0.0775049i
\(341\) −8.43416e6 −0.212706
\(342\) −2.92763e7 −0.731877
\(343\) 7.01572e7i 1.73856i
\(344\) −2.81810e7 + 3.39217e7i −0.692278 + 0.833301i
\(345\) −9.04634e6 −0.220301
\(346\) 1.63171e7i 0.393927i
\(347\) 4.50028e7i 1.07709i −0.842597 0.538544i \(-0.818974\pi\)
0.842597 0.538544i \(-0.181026\pi\)
\(348\) 1.82077e6 0.0432034
\(349\) 4.97760e7i 1.17097i −0.810685 0.585483i \(-0.800905\pi\)
0.810685 0.585483i \(-0.199095\pi\)
\(350\) −1.66744e7 −0.388907
\(351\) 4.92277e7i 1.13838i
\(352\) 5.33059e6i 0.122221i
\(353\) −6.55699e7 −1.49067 −0.745333 0.666693i \(-0.767709\pi\)
−0.745333 + 0.666693i \(0.767709\pi\)
\(354\) −1.65764e7 −0.373664
\(355\) −3.02858e7 −0.676947
\(356\) 8.56503e6i 0.189836i
\(357\) −1.13965e7 −0.250476
\(358\) 3.70306e7 0.807071
\(359\) 4.55309e7 0.984063 0.492031 0.870577i \(-0.336254\pi\)
0.492031 + 0.870577i \(0.336254\pi\)
\(360\) 3.61541e7 0.774909
\(361\) −1.92179e6 −0.0408493
\(362\) 9.17593e6i 0.193430i
\(363\) 1.84461e7i 0.385643i
\(364\) 3.23848e7i 0.671486i
\(365\) −3.16740e7 −0.651364
\(366\) 2.63153e7i 0.536742i
\(367\) −6.30366e7 −1.27525 −0.637623 0.770348i \(-0.720082\pi\)
−0.637623 + 0.770348i \(0.720082\pi\)
\(368\) 2.11100e7 0.423590
\(369\) −1.11035e7 −0.220995
\(370\) 2.81814e7i 0.556362i
\(371\) 1.61742e8i 3.16738i
\(372\) 4.68288e6i 0.0909671i
\(373\) 2.47114e7i 0.476179i 0.971243 + 0.238089i \(0.0765211\pi\)
−0.971243 + 0.238089i \(0.923479\pi\)
\(374\) 3.90194e6i 0.0745875i
\(375\) 2.34568e7 0.444810
\(376\) 7.23303e7i 1.36068i
\(377\) 3.33945e7i 0.623233i
\(378\) 6.06894e7i 1.12367i
\(379\) 5.77691e7 1.06115 0.530577 0.847637i \(-0.321975\pi\)
0.530577 + 0.847637i \(0.321975\pi\)
\(380\) 1.23192e7 0.224508
\(381\) 9.97008e6i 0.180270i
\(382\) 8.78556e7 1.57608
\(383\) 8.68330e7i 1.54557i −0.634668 0.772785i \(-0.718863\pi\)
0.634668 0.772785i \(-0.281137\pi\)
\(384\) 1.06451e7 0.188000
\(385\) −2.08828e7 −0.365937
\(386\) 2.67326e7i 0.464815i
\(387\) 3.70747e7 + 3.08004e7i 0.639653 + 0.531403i
\(388\) −7.05484e6 −0.120779
\(389\) 6.43558e6i 0.109330i −0.998505 0.0546650i \(-0.982591\pi\)
0.998505 0.0546650i \(-0.0174091\pi\)
\(390\) 2.73565e7i 0.461176i
\(391\) −1.31396e7 −0.219813
\(392\) 1.30724e8i 2.17018i
\(393\) 1.74031e7 0.286713
\(394\) 5.37850e7i 0.879371i
\(395\) 5.34499e7i 0.867273i
\(396\) −3.24341e6 −0.0522295
\(397\) 1.21619e8 1.94370 0.971850 0.235601i \(-0.0757060\pi\)
0.971850 + 0.235601i \(0.0757060\pi\)
\(398\) 1.85279e7 0.293885
\(399\) 4.60879e7i 0.725552i
\(400\) −1.13001e7 −0.176564
\(401\) 1.77372e7 0.275075 0.137538 0.990497i \(-0.456081\pi\)
0.137538 + 0.990497i \(0.456081\pi\)
\(402\) 1.73987e7 0.267817
\(403\) −8.58879e7 −1.31225
\(404\) 1.37869e7 0.209084
\(405\) 2.98919e7i 0.449975i
\(406\) 4.11697e7i 0.615176i
\(407\) 1.24101e7i 0.184074i
\(408\) −1.06346e7 −0.156581
\(409\) 3.42591e7i 0.500732i 0.968151 + 0.250366i \(0.0805510\pi\)
−0.968151 + 0.250366i \(0.919449\pi\)
\(410\) −1.35903e7 −0.197187
\(411\) −2.81513e7 −0.405483
\(412\) 1.70392e6 0.0243645
\(413\) 1.28857e8i 1.82919i
\(414\) 3.17692e7i 0.447719i
\(415\) 1.54699e7i 0.216442i
\(416\) 5.42832e7i 0.754024i
\(417\) 4.63872e7i 0.639721i
\(418\) 1.57796e7 0.216057
\(419\) 7.43380e7i 1.01058i −0.862951 0.505288i \(-0.831386\pi\)
0.862951 0.505288i \(-0.168614\pi\)
\(420\) 1.15947e7i 0.156499i
\(421\) 6.57042e7i 0.880535i 0.897867 + 0.440268i \(0.145116\pi\)
−0.897867 + 0.440268i \(0.854884\pi\)
\(422\) 1.30810e7 0.174062
\(423\) 7.90534e7 1.04448
\(424\) 1.50929e8i 1.98004i
\(425\) 7.03359e6 0.0916242
\(426\) 2.15390e7i 0.278610i
\(427\) 2.04563e8 2.62751
\(428\) 1.37050e7 0.174802
\(429\) 1.20468e7i 0.152581i
\(430\) 4.53781e7 + 3.76986e7i 0.570743 + 0.474155i
\(431\) −7.65329e7 −0.955908 −0.477954 0.878385i \(-0.658621\pi\)
−0.477954 + 0.878385i \(0.658621\pi\)
\(432\) 4.11287e7i 0.510145i
\(433\) 1.00323e8i 1.23577i −0.786269 0.617884i \(-0.787990\pi\)
0.786269 0.617884i \(-0.212010\pi\)
\(434\) −1.05885e8 −1.29529
\(435\) 1.19562e7i 0.145253i
\(436\) 4.04988e7 0.488633
\(437\) 5.31374e7i 0.636730i
\(438\) 2.25262e7i 0.268081i
\(439\) 3.20358e7 0.378653 0.189327 0.981914i \(-0.439369\pi\)
0.189327 + 0.981914i \(0.439369\pi\)
\(440\) −1.94867e7 −0.228760
\(441\) −1.42875e8 −1.66586
\(442\) 3.97348e7i 0.460155i
\(443\) −8.21035e7 −0.944388 −0.472194 0.881495i \(-0.656538\pi\)
−0.472194 + 0.881495i \(0.656538\pi\)
\(444\) 6.89042e6 0.0787221
\(445\) −5.62428e7 −0.638244
\(446\) −4.04676e7 −0.456145
\(447\) −3.83250e7 −0.429101
\(448\) 1.72679e8i 1.92047i
\(449\) 4.47173e7i 0.494011i −0.969014 0.247005i \(-0.920553\pi\)
0.969014 0.247005i \(-0.0794465\pi\)
\(450\) 1.70059e7i 0.186622i
\(451\) 5.98469e6 0.0652397
\(452\) 4.39239e7i 0.475648i
\(453\) −6.65749e7 −0.716170
\(454\) 7.47139e7 0.798425
\(455\) −2.12657e8 −2.25759
\(456\) 4.30068e7i 0.453568i
\(457\) 1.04216e8i 1.09191i 0.837816 + 0.545953i \(0.183832\pi\)
−0.837816 + 0.545953i \(0.816168\pi\)
\(458\) 2.87614e7i 0.299374i
\(459\) 2.56000e7i 0.264729i
\(460\) 1.33682e7i 0.137341i
\(461\) 5.88536e6 0.0600717 0.0300359 0.999549i \(-0.490438\pi\)
0.0300359 + 0.999549i \(0.490438\pi\)
\(462\) 1.48517e7i 0.150608i
\(463\) 8.38526e7i 0.844838i 0.906401 + 0.422419i \(0.138819\pi\)
−0.906401 + 0.422419i \(0.861181\pi\)
\(464\) 2.79003e7i 0.279290i
\(465\) 3.07504e7 0.305839
\(466\) −1.53561e8 −1.51748
\(467\) 5.43691e7i 0.533828i −0.963720 0.266914i \(-0.913996\pi\)
0.963720 0.266914i \(-0.0860040\pi\)
\(468\) −3.30287e7 −0.322221
\(469\) 1.35249e8i 1.31104i
\(470\) 9.67585e7 0.931957
\(471\) 3.55869e7 0.340587
\(472\) 1.20243e8i 1.14349i
\(473\) −1.99829e7 1.66011e7i −0.188832 0.156875i
\(474\) 3.80131e7 0.356942
\(475\) 2.84442e7i 0.265407i
\(476\) 1.68411e7i 0.156153i
\(477\) 1.64957e8 1.51991
\(478\) 1.56126e8i 1.42952i
\(479\) −2.39565e7 −0.217980 −0.108990 0.994043i \(-0.534762\pi\)
−0.108990 + 0.994043i \(0.534762\pi\)
\(480\) 1.94350e7i 0.175736i
\(481\) 1.26376e8i 1.13561i
\(482\) −1.19430e8 −1.06653
\(483\) 5.00124e7 0.443850
\(484\) −2.72587e7 −0.240419
\(485\) 4.63260e7i 0.406069i
\(486\) −9.56896e7 −0.833597
\(487\) 7.69776e6 0.0666465 0.0333233 0.999445i \(-0.489391\pi\)
0.0333233 + 0.999445i \(0.489391\pi\)
\(488\) 1.90887e8 1.64255
\(489\) −2.66773e7 −0.228147
\(490\) −1.74873e8 −1.48640
\(491\) 1.38326e8i 1.16858i 0.811544 + 0.584292i \(0.198628\pi\)
−0.811544 + 0.584292i \(0.801372\pi\)
\(492\) 3.32286e6i 0.0279008i
\(493\) 1.73662e7i 0.144932i
\(494\) 1.60689e8 1.33293
\(495\) 2.12980e7i 0.175600i
\(496\) −7.17575e7 −0.588061
\(497\) 1.67434e8 1.36388
\(498\) 1.10020e7 0.0890808
\(499\) 2.71530e7i 0.218532i 0.994013 + 0.109266i \(0.0348501\pi\)
−0.994013 + 0.109266i \(0.965150\pi\)
\(500\) 3.46632e7i 0.277306i
\(501\) 5.24361e6i 0.0416982i
\(502\) 1.66154e8i 1.31341i
\(503\) 4.39907e7i 0.345666i 0.984951 + 0.172833i \(0.0552921\pi\)
−0.984951 + 0.172833i \(0.944708\pi\)
\(504\) −1.99877e8 −1.56125
\(505\) 9.05324e7i 0.702959i
\(506\) 1.71233e7i 0.132171i
\(507\) 6.91951e7i 0.530948i
\(508\) 1.47333e7 0.112385
\(509\) 9.94585e7 0.754203 0.377102 0.926172i \(-0.376921\pi\)
0.377102 + 0.926172i \(0.376921\pi\)
\(510\) 1.42262e7i 0.107246i
\(511\) 1.75108e8 1.31233
\(512\) 1.44040e8i 1.07318i
\(513\) −1.03528e8 −0.766838
\(514\) 6.73927e7 0.496277
\(515\) 1.11889e7i 0.0819155i
\(516\) −9.21740e6 + 1.10951e7i −0.0670902 + 0.0807570i
\(517\) −4.26090e7 −0.308340
\(518\) 1.55800e8i 1.12093i
\(519\) 2.61978e7i 0.187397i
\(520\) −1.98440e8 −1.41130
\(521\) 1.64109e7i 0.116043i 0.998315 + 0.0580216i \(0.0184792\pi\)
−0.998315 + 0.0580216i \(0.981521\pi\)
\(522\) 4.19882e7 0.295200
\(523\) 1.31984e8i 0.922603i −0.887243 0.461302i \(-0.847383\pi\)
0.887243 0.461302i \(-0.152617\pi\)
\(524\) 2.57173e7i 0.178744i
\(525\) −2.67714e7 −0.185009
\(526\) −5.22957e7 −0.359343
\(527\) 4.46644e7 0.305162
\(528\) 1.00648e7i 0.0683763i
\(529\) −9.03738e7 −0.610486
\(530\) 2.01902e8 1.35617
\(531\) 1.31420e8 0.877761
\(532\) −6.81063e7 −0.452327
\(533\) 6.09441e7 0.402485
\(534\) 3.99993e7i 0.262681i
\(535\) 8.99944e7i 0.587698i
\(536\) 1.26207e8i 0.819578i
\(537\) 5.94541e7 0.383936
\(538\) 5.71040e7i 0.366708i
\(539\) 7.70079e7 0.491778
\(540\) 2.60453e7 0.165404
\(541\) 1.85731e8 1.17299 0.586493 0.809954i \(-0.300508\pi\)
0.586493 + 0.809954i \(0.300508\pi\)
\(542\) 1.22166e8i 0.767279i
\(543\) 1.47323e7i 0.0920178i
\(544\) 2.82289e7i 0.175347i
\(545\) 2.65938e8i 1.64282i
\(546\) 1.51239e8i 0.929153i
\(547\) −1.99821e8 −1.22090 −0.610450 0.792055i \(-0.709011\pi\)
−0.610450 + 0.792055i \(0.709011\pi\)
\(548\) 4.16005e7i 0.252788i
\(549\) 2.08631e8i 1.26084i
\(550\) 9.16603e6i 0.0550926i
\(551\) 7.02296e7 0.419822
\(552\) 4.66689e7 0.277466
\(553\) 2.95496e8i 1.74734i
\(554\) 2.31687e8 1.36261
\(555\) 4.52464e7i 0.264670i
\(556\) −6.85486e7 −0.398817
\(557\) −7.45441e7 −0.431368 −0.215684 0.976463i \(-0.569198\pi\)
−0.215684 + 0.976463i \(0.569198\pi\)
\(558\) 1.07990e8i 0.621559i
\(559\) −2.03493e8 1.69055e8i −1.16497 0.967815i
\(560\) −1.77670e8 −1.01170
\(561\) 6.26472e6i 0.0354824i
\(562\) 2.15783e8i 1.21565i
\(563\) −2.84802e8 −1.59595 −0.797973 0.602693i \(-0.794094\pi\)
−0.797973 + 0.602693i \(0.794094\pi\)
\(564\) 2.36577e7i 0.131867i
\(565\) 2.88429e8 1.59917
\(566\) 3.06247e8i 1.68897i
\(567\) 1.65257e8i 0.906587i
\(568\) 1.56241e8 0.852607
\(569\) 7.04148e7 0.382232 0.191116 0.981567i \(-0.438789\pi\)
0.191116 + 0.981567i \(0.438789\pi\)
\(570\) −5.75316e7 −0.310657
\(571\) 1.43310e8i 0.769780i −0.922962 0.384890i \(-0.874239\pi\)
0.922962 0.384890i \(-0.125761\pi\)
\(572\) 1.78021e7 0.0951227
\(573\) 1.41056e8 0.749767
\(574\) 7.51336e7 0.397282
\(575\) −3.08663e7 −0.162361
\(576\) −1.76113e8 −0.921559
\(577\) 3.52177e7i 0.183330i 0.995790 + 0.0916651i \(0.0292189\pi\)
−0.995790 + 0.0916651i \(0.970781\pi\)
\(578\) 1.45915e8i 0.755640i
\(579\) 4.29203e7i 0.221120i
\(580\) −1.76682e7 −0.0905543
\(581\) 8.55247e7i 0.436077i
\(582\) 3.29466e7 0.167125
\(583\) −8.89104e7 −0.448691
\(584\) 1.63402e8 0.820386
\(585\) 2.16885e8i 1.08333i
\(586\) 1.45565e7i 0.0723376i
\(587\) 1.60114e8i 0.791617i −0.918333 0.395809i \(-0.870464\pi\)
0.918333 0.395809i \(-0.129536\pi\)
\(588\) 4.27569e7i 0.210317i
\(589\) 1.80625e8i 0.883959i
\(590\) 1.60853e8 0.783200
\(591\) 8.63539e7i 0.418331i
\(592\) 1.05584e8i 0.508903i
\(593\) 2.06554e8i 0.990533i −0.868741 0.495266i \(-0.835070\pi\)
0.868741 0.495266i \(-0.164930\pi\)
\(594\) 3.33613e7 0.159178
\(595\) 1.10588e8 0.524998
\(596\) 5.66346e7i 0.267512i
\(597\) 2.97473e7 0.139806
\(598\) 1.74372e8i 0.815407i
\(599\) 1.21447e8 0.565075 0.282537 0.959256i \(-0.408824\pi\)
0.282537 + 0.959256i \(0.408824\pi\)
\(600\) −2.49816e7 −0.115656
\(601\) 3.10614e8i 1.43086i 0.698684 + 0.715430i \(0.253769\pi\)
−0.698684 + 0.715430i \(0.746231\pi\)
\(602\) −2.50871e8 2.08416e8i −1.14990 0.955302i
\(603\) −1.37938e8 −0.629119
\(604\) 9.83808e7i 0.446478i
\(605\) 1.78996e8i 0.808308i
\(606\) −6.43858e7 −0.289316
\(607\) 4.20257e8i 1.87909i 0.342421 + 0.939547i \(0.388753\pi\)
−0.342421 + 0.939547i \(0.611247\pi\)
\(608\) −1.14159e8 −0.507926
\(609\) 6.60995e7i 0.292649i
\(610\) 2.55356e8i 1.12501i
\(611\) −4.33902e8 −1.90225
\(612\) 1.71760e7 0.0749319
\(613\) −4.00813e8 −1.74004 −0.870022 0.493014i \(-0.835895\pi\)
−0.870022 + 0.493014i \(0.835895\pi\)
\(614\) 9.31449e7i 0.402396i
\(615\) −2.18198e7 −0.0938048
\(616\) 1.07732e8 0.460894
\(617\) 2.59681e8 1.10556 0.552782 0.833326i \(-0.313566\pi\)
0.552782 + 0.833326i \(0.313566\pi\)
\(618\) −7.95744e6 −0.0337138
\(619\) −1.81356e8 −0.764644 −0.382322 0.924029i \(-0.624875\pi\)
−0.382322 + 0.924029i \(0.624875\pi\)
\(620\) 4.54413e7i 0.190667i
\(621\) 1.12343e8i 0.469107i
\(622\) 2.77467e8i 1.15303i
\(623\) 3.10937e8 1.28590
\(624\) 1.02494e8i 0.421836i
\(625\) −1.64106e8 −0.672177
\(626\) 1.90251e7 0.0775539
\(627\) 2.53348e7 0.102782
\(628\) 5.25884e7i 0.212330i
\(629\) 6.57195e7i 0.264084i
\(630\) 2.67382e8i 1.06933i
\(631\) 2.84986e8i 1.13432i 0.823608 + 0.567160i \(0.191958\pi\)
−0.823608 + 0.567160i \(0.808042\pi\)
\(632\) 2.75741e8i 1.09232i
\(633\) 2.10021e7 0.0828042
\(634\) 1.16851e8i 0.458526i
\(635\) 9.67468e7i 0.377847i
\(636\) 4.93655e7i 0.191890i
\(637\) 7.84198e8 3.03394
\(638\) −2.26312e7 −0.0871457
\(639\) 1.70763e8i 0.654473i
\(640\) −1.03297e8 −0.394047
\(641\) 3.06450e8i 1.16355i 0.813350 + 0.581775i \(0.197641\pi\)
−0.813350 + 0.581775i \(0.802359\pi\)
\(642\) −6.40032e7 −0.241878
\(643\) −3.24019e8 −1.21882 −0.609408 0.792857i \(-0.708593\pi\)
−0.609408 + 0.792857i \(0.708593\pi\)
\(644\) 7.39056e7i 0.276707i
\(645\) 7.28563e7 + 6.05266e7i 0.271511 + 0.225563i
\(646\) −8.35636e7 −0.309970
\(647\) 3.47049e8i 1.28138i 0.767800 + 0.640690i \(0.221352\pi\)
−0.767800 + 0.640690i \(0.778648\pi\)
\(648\) 1.54209e8i 0.566739i
\(649\) −7.08338e7 −0.259123
\(650\) 9.33408e7i 0.339884i
\(651\) −1.70003e8 −0.616188
\(652\) 3.94222e7i 0.142232i
\(653\) 1.64007e8i 0.589011i −0.955650 0.294505i \(-0.904845\pi\)
0.955650 0.294505i \(-0.0951549\pi\)
\(654\) −1.89133e8 −0.676135
\(655\) −1.68874e8 −0.600952
\(656\) 5.09174e7 0.180366
\(657\) 1.78590e8i 0.629740i
\(658\) −5.34927e8 −1.87766
\(659\) 8.42317e7 0.294320 0.147160 0.989113i \(-0.452987\pi\)
0.147160 + 0.989113i \(0.452987\pi\)
\(660\) −6.37369e6 −0.0221697
\(661\) 3.01790e7 0.104496 0.0522481 0.998634i \(-0.483361\pi\)
0.0522481 + 0.998634i \(0.483361\pi\)
\(662\) 8.07816e6 0.0278444
\(663\) 6.37958e7i 0.218903i
\(664\) 7.98070e7i 0.272607i
\(665\) 4.47224e8i 1.52076i
\(666\) 1.58898e8 0.537892
\(667\) 7.62098e7i 0.256823i
\(668\) 7.74872e6 0.0259956
\(669\) −6.49723e7 −0.216995
\(670\) −1.68832e8 −0.561344
\(671\) 1.12450e8i 0.372212i
\(672\) 1.07446e8i 0.354063i
\(673\) 2.18792e8i 0.717772i −0.933381 0.358886i \(-0.883157\pi\)
0.933381 0.358886i \(-0.116843\pi\)
\(674\) 1.18125e8i 0.385800i
\(675\) 6.01368e7i 0.195537i
\(676\) 1.02253e8 0.331006
\(677\) 5.58092e8i 1.79862i −0.437312 0.899310i \(-0.644069\pi\)
0.437312 0.899310i \(-0.355931\pi\)
\(678\) 2.05128e8i 0.658167i
\(679\) 2.56112e8i 0.818127i
\(680\) 1.03195e8 0.328195
\(681\) 1.19956e8 0.379823
\(682\) 5.82057e7i 0.183490i
\(683\) 4.01935e8 1.26152 0.630759 0.775979i \(-0.282744\pi\)
0.630759 + 0.775979i \(0.282744\pi\)
\(684\) 6.94604e7i 0.217055i
\(685\) 2.73172e8 0.849894
\(686\) 4.84168e8 1.49977
\(687\) 4.61776e7i 0.142417i
\(688\) −1.70014e8 1.41242e8i −0.522057 0.433708i
\(689\) −9.05405e8 −2.76812
\(690\) 6.24305e7i 0.190042i
\(691\) 3.35495e8i 1.01684i −0.861109 0.508420i \(-0.830230\pi\)
0.861109 0.508420i \(-0.169770\pi\)
\(692\) 3.87137e7 0.116828
\(693\) 1.17745e8i 0.353789i
\(694\) 3.10573e8 0.929149
\(695\) 4.50128e8i 1.34086i
\(696\) 6.16805e7i 0.182945i
\(697\) −3.16928e7 −0.0935972
\(698\) 3.43514e8 1.01013
\(699\) −2.46548e8 −0.721889
\(700\) 3.95614e7i 0.115339i
\(701\) −2.59344e8 −0.752873 −0.376436 0.926443i \(-0.622851\pi\)
−0.376436 + 0.926443i \(0.622851\pi\)
\(702\) 3.39730e8 0.982025
\(703\) 2.65773e8 0.764971
\(704\) 9.49230e7 0.272053
\(705\) 1.55350e8 0.443346
\(706\) 4.52510e8i 1.28592i
\(707\) 5.00506e8i 1.41629i
\(708\) 3.93289e7i 0.110818i
\(709\) 1.30606e8 0.366458 0.183229 0.983070i \(-0.441345\pi\)
0.183229 + 0.983070i \(0.441345\pi\)
\(710\) 2.09008e8i 0.583967i
\(711\) −3.01372e8 −0.838482
\(712\) 2.90149e8 0.803862
\(713\) −1.96006e8 −0.540754
\(714\) 7.86493e7i 0.216073i
\(715\) 1.16899e8i 0.319810i
\(716\) 8.78580e7i 0.239355i
\(717\) 2.50666e8i 0.680046i
\(718\) 3.14217e8i 0.848900i
\(719\) 4.57584e8 1.23107 0.615537 0.788108i \(-0.288939\pi\)
0.615537 + 0.788108i \(0.288939\pi\)
\(720\) 1.81203e8i 0.485475i
\(721\) 6.18575e7i 0.165039i
\(722\) 1.32626e7i 0.0352386i
\(723\) −1.91749e8 −0.507363
\(724\) −2.17706e7 −0.0573661
\(725\) 4.07948e7i 0.107051i
\(726\) 1.27300e8 0.332674
\(727\) 3.80141e8i 0.989330i 0.869084 + 0.494665i \(0.164709\pi\)
−0.869084 + 0.494665i \(0.835291\pi\)
\(728\) 1.09707e9 2.84341
\(729\) 4.90408e7 0.126583
\(730\) 2.18588e8i 0.561898i
\(731\) 1.05823e8 + 8.79138e7i 0.270911 + 0.225064i
\(732\) 6.24352e7 0.159183
\(733\) 3.54939e8i 0.901242i −0.892715 0.450621i \(-0.851203\pi\)
0.892715 0.450621i \(-0.148797\pi\)
\(734\) 4.35027e8i 1.10009i
\(735\) −2.80766e8 −0.707103
\(736\) 1.23880e8i 0.310719i
\(737\) 7.43474e7 0.185722
\(738\) 7.66275e7i 0.190641i
\(739\) 3.35280e7i 0.0830757i −0.999137 0.0415378i \(-0.986774\pi\)
0.999137 0.0415378i \(-0.0132257\pi\)
\(740\) −6.68626e7 −0.165002
\(741\) 2.57993e8 0.634094
\(742\) −1.11621e9 −2.73233
\(743\) 4.64197e8i 1.13171i 0.824504 + 0.565856i \(0.191454\pi\)
−0.824504 + 0.565856i \(0.808546\pi\)
\(744\) −1.58637e8 −0.385200
\(745\) 3.71894e8 0.899396
\(746\) −1.70538e8 −0.410775
\(747\) −8.72251e7 −0.209257
\(748\) −9.25767e6 −0.0221206
\(749\) 4.97532e8i 1.18406i
\(750\) 1.61880e8i 0.383715i
\(751\) 3.26025e8i 0.769716i −0.922976 0.384858i \(-0.874250\pi\)
0.922976 0.384858i \(-0.125750\pi\)
\(752\) −3.62515e8 −0.852458
\(753\) 2.66766e8i 0.624808i
\(754\) −2.30461e8 −0.537631
\(755\) 6.46024e8 1.50109
\(756\) −1.43990e8 −0.333248
\(757\) 6.61201e8i 1.52421i −0.647451 0.762107i \(-0.724165\pi\)
0.647451 0.762107i \(-0.275835\pi\)
\(758\) 3.98675e8i 0.915402i
\(759\) 2.74921e7i 0.0628758i
\(760\) 4.17325e8i 0.950679i
\(761\) 8.45615e8i 1.91875i −0.282131 0.959376i \(-0.591041\pi\)
0.282131 0.959376i \(-0.408959\pi\)
\(762\) −6.88054e7 −0.155510
\(763\) 1.47023e9i 3.30988i
\(764\) 2.08444e8i 0.467423i
\(765\) 1.12787e8i 0.251927i
\(766\) 5.99251e8 1.33328
\(767\) −7.21325e8 −1.59862
\(768\) 1.32541e8i 0.292595i
\(769\) 1.38008e8 0.303477 0.151738 0.988421i \(-0.451513\pi\)
0.151738 + 0.988421i \(0.451513\pi\)
\(770\) 1.44116e8i 0.315675i
\(771\) 1.08202e8 0.236086
\(772\) −6.34253e7 −0.137851
\(773\) 6.00044e8i 1.29911i −0.760317 0.649553i \(-0.774956\pi\)
0.760317 0.649553i \(-0.225044\pi\)
\(774\) −2.12560e8 + 2.55859e8i −0.458414 + 0.551796i
\(775\) 1.04921e8 0.225402
\(776\) 2.38990e8i 0.511440i
\(777\) 2.50143e8i 0.533244i
\(778\) 4.44132e7 0.0943133
\(779\) 1.28167e8i 0.271122i
\(780\) −6.49054e7 −0.136772
\(781\) 9.20397e7i 0.193207i
\(782\) 9.06791e7i 0.189621i
\(783\) 1.48480e8