Properties

Label 43.9.b.b.42.9
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.9
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.20

$q$-expansion

\(f(q)\) \(=\) \(q-14.4463i q^{2} -49.3343i q^{3} +47.3041 q^{4} +738.628i q^{5} -712.698 q^{6} -198.404i q^{7} -4381.63i q^{8} +4127.13 q^{9} +O(q^{10})\) \(q-14.4463i q^{2} -49.3343i q^{3} +47.3041 q^{4} +738.628i q^{5} -712.698 q^{6} -198.404i q^{7} -4381.63i q^{8} +4127.13 q^{9} +10670.5 q^{10} +12439.9 q^{11} -2333.71i q^{12} +27835.0 q^{13} -2866.21 q^{14} +36439.7 q^{15} -51188.5 q^{16} -66432.0 q^{17} -59621.8i q^{18} -154260. i q^{19} +34940.1i q^{20} -9788.14 q^{21} -179711. i q^{22} +253326. q^{23} -216164. q^{24} -154946. q^{25} -402113. i q^{26} -527291. i q^{27} -9385.34i q^{28} +332311. i q^{29} -526419. i q^{30} -716916. q^{31} -382211. i q^{32} -613716. i q^{33} +959697. i q^{34} +146547. q^{35} +195230. q^{36} -2.30467e6i q^{37} -2.22849e6 q^{38} -1.37322e6i q^{39} +3.23639e6 q^{40} -126422. q^{41} +141403. i q^{42} +(-149483. + 3.41553e6i) q^{43} +588460. q^{44} +3.04841e6i q^{45} -3.65963e6i q^{46} +3.57846e6 q^{47} +2.52535e6i q^{48} +5.72544e6 q^{49} +2.23840e6i q^{50} +3.27737e6i q^{51} +1.31671e6 q^{52} -4.88694e6 q^{53} -7.61741e6 q^{54} +9.18849e6i q^{55} -869334. q^{56} -7.61030e6 q^{57} +4.80066e6 q^{58} +5.89621e6 q^{59} +1.72374e6 q^{60} +3.89973e6i q^{61} +1.03568e7i q^{62} -818841. i q^{63} -1.86258e7 q^{64} +2.05597e7i q^{65} -8.86593e6 q^{66} +2.99507e7 q^{67} -3.14250e6 q^{68} -1.24977e7i q^{69} -2.11707e6i q^{70} -4.99800e6i q^{71} -1.80835e7i q^{72} +1.46539e7i q^{73} -3.32940e7 q^{74} +7.64416e6i q^{75} -7.29712e6i q^{76} -2.46814e6i q^{77} -1.98379e7 q^{78} -1.87235e7 q^{79} -3.78092e7i q^{80} +1.06456e6 q^{81} +1.82634e6i q^{82} +7.06201e7 q^{83} -463019. q^{84} -4.90685e7i q^{85} +(4.93418e7 + 2.15948e6i) q^{86} +1.63943e7 q^{87} -5.45072e7i q^{88} +1.63314e7i q^{89} +4.40383e7 q^{90} -5.52258e6i q^{91} +1.19834e7 q^{92} +3.53685e7i q^{93} -5.16956e7i q^{94} +1.13941e8 q^{95} -1.88561e7 q^{96} -1.07206e8 q^{97} -8.27114e7i q^{98} +5.13413e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 14.4463i 0.902895i −0.892298 0.451447i \(-0.850908\pi\)
0.892298 0.451447i \(-0.149092\pi\)
\(3\) 49.3343i 0.609065i −0.952502 0.304533i \(-0.901500\pi\)
0.952502 0.304533i \(-0.0985003\pi\)
\(4\) 47.3041 0.184781
\(5\) 738.628i 1.18180i 0.806743 + 0.590902i \(0.201228\pi\)
−0.806743 + 0.590902i \(0.798772\pi\)
\(6\) −712.698 −0.549922
\(7\) 198.404i 0.0826341i −0.999146 0.0413171i \(-0.986845\pi\)
0.999146 0.0413171i \(-0.0131554\pi\)
\(8\) 4381.63i 1.06973i
\(9\) 4127.13 0.629040
\(10\) 10670.5 1.06705
\(11\) 12439.9 0.849665 0.424833 0.905272i \(-0.360333\pi\)
0.424833 + 0.905272i \(0.360333\pi\)
\(12\) 2333.71i 0.112544i
\(13\) 27835.0 0.974580 0.487290 0.873240i \(-0.337986\pi\)
0.487290 + 0.873240i \(0.337986\pi\)
\(14\) −2866.21 −0.0746099
\(15\) 36439.7 0.719796
\(16\) −51188.5 −0.781074
\(17\) −66432.0 −0.795393 −0.397696 0.917517i \(-0.630190\pi\)
−0.397696 + 0.917517i \(0.630190\pi\)
\(18\) 59621.8i 0.567956i
\(19\) 154260.i 1.18369i −0.806051 0.591846i \(-0.798399\pi\)
0.806051 0.591846i \(-0.201601\pi\)
\(20\) 34940.1i 0.218376i
\(21\) −9788.14 −0.0503296
\(22\) 179711.i 0.767158i
\(23\) 253326. 0.905250 0.452625 0.891701i \(-0.350488\pi\)
0.452625 + 0.891701i \(0.350488\pi\)
\(24\) −216164. −0.651537
\(25\) −154946. −0.396662
\(26\) 402113.i 0.879943i
\(27\) 527291.i 0.992191i
\(28\) 9385.34i 0.0152692i
\(29\) 332311.i 0.469843i 0.972014 + 0.234921i \(0.0754832\pi\)
−0.972014 + 0.234921i \(0.924517\pi\)
\(30\) 526419.i 0.649900i
\(31\) −716916. −0.776285 −0.388143 0.921599i \(-0.626883\pi\)
−0.388143 + 0.921599i \(0.626883\pi\)
\(32\) 382211.i 0.364505i
\(33\) 613716.i 0.517501i
\(34\) 959697.i 0.718156i
\(35\) 146547. 0.0976574
\(36\) 195230. 0.116235
\(37\) 2.30467e6i 1.22971i −0.788641 0.614854i \(-0.789215\pi\)
0.788641 0.614854i \(-0.210785\pi\)
\(38\) −2.22849e6 −1.06875
\(39\) 1.37322e6i 0.593583i
\(40\) 3.23639e6 1.26422
\(41\) −126422. −0.0447392 −0.0223696 0.999750i \(-0.507121\pi\)
−0.0223696 + 0.999750i \(0.507121\pi\)
\(42\) 141403.i 0.0454423i
\(43\) −149483. + 3.41553e6i −0.0437239 + 0.999044i
\(44\) 588460. 0.157002
\(45\) 3.04841e6i 0.743402i
\(46\) 3.65963e6i 0.817346i
\(47\) 3.57846e6 0.733339 0.366670 0.930351i \(-0.380498\pi\)
0.366670 + 0.930351i \(0.380498\pi\)
\(48\) 2.52535e6i 0.475725i
\(49\) 5.72544e6 0.993172
\(50\) 2.23840e6i 0.358144i
\(51\) 3.27737e6i 0.484446i
\(52\) 1.31671e6 0.180084
\(53\) −4.88694e6 −0.619346 −0.309673 0.950843i \(-0.600220\pi\)
−0.309673 + 0.950843i \(0.600220\pi\)
\(54\) −7.61741e6 −0.895844
\(55\) 9.18849e6i 1.00414i
\(56\) −869334. −0.0883964
\(57\) −7.61030e6 −0.720946
\(58\) 4.80066e6 0.424218
\(59\) 5.89621e6 0.486592 0.243296 0.969952i \(-0.421771\pi\)
0.243296 + 0.969952i \(0.421771\pi\)
\(60\) 1.72374e6 0.133005
\(61\) 3.89973e6i 0.281653i 0.990034 + 0.140827i \(0.0449760\pi\)
−0.990034 + 0.140827i \(0.955024\pi\)
\(62\) 1.03568e7i 0.700904i
\(63\) 818841.i 0.0519801i
\(64\) −1.86258e7 −1.11018
\(65\) 2.05597e7i 1.15176i
\(66\) −8.86593e6 −0.467249
\(67\) 2.99507e7 1.48630 0.743152 0.669122i \(-0.233330\pi\)
0.743152 + 0.669122i \(0.233330\pi\)
\(68\) −3.14250e6 −0.146974
\(69\) 1.24977e7i 0.551357i
\(70\) 2.11707e6i 0.0881743i
\(71\) 4.99800e6i 0.196681i −0.995153 0.0983407i \(-0.968647\pi\)
0.995153 0.0983407i \(-0.0313535\pi\)
\(72\) 1.80835e7i 0.672904i
\(73\) 1.46539e7i 0.516014i 0.966143 + 0.258007i \(0.0830657\pi\)
−0.966143 + 0.258007i \(0.916934\pi\)
\(74\) −3.32940e7 −1.11030
\(75\) 7.64416e6i 0.241593i
\(76\) 7.29712e6i 0.218724i
\(77\) 2.46814e6i 0.0702113i
\(78\) −1.98379e7 −0.535942
\(79\) −1.87235e7 −0.480705 −0.240352 0.970686i \(-0.577263\pi\)
−0.240352 + 0.970686i \(0.577263\pi\)
\(80\) 3.78092e7i 0.923077i
\(81\) 1.06456e6 0.0247304
\(82\) 1.82634e6i 0.0403948i
\(83\) 7.06201e7 1.48804 0.744022 0.668155i \(-0.232916\pi\)
0.744022 + 0.668155i \(0.232916\pi\)
\(84\) −463019. −0.00929997
\(85\) 4.90685e7i 0.939999i
\(86\) 4.93418e7 + 2.15948e6i 0.902031 + 0.0394781i
\(87\) 1.63943e7 0.286165
\(88\) 5.45072e7i 0.908914i
\(89\) 1.63314e7i 0.260294i 0.991495 + 0.130147i \(0.0415449\pi\)
−0.991495 + 0.130147i \(0.958455\pi\)
\(90\) 4.40383e7 0.671214
\(91\) 5.52258e6i 0.0805335i
\(92\) 1.19834e7 0.167274
\(93\) 3.53685e7i 0.472808i
\(94\) 5.16956e7i 0.662128i
\(95\) 1.13941e8 1.39889
\(96\) −1.88561e7 −0.222007
\(97\) −1.07206e8 −1.21097 −0.605484 0.795858i \(-0.707020\pi\)
−0.605484 + 0.795858i \(0.707020\pi\)
\(98\) 8.27114e7i 0.896729i
\(99\) 5.13413e7 0.534473
\(100\) −7.32959e6 −0.0732959
\(101\) −1.00294e8 −0.963808 −0.481904 0.876224i \(-0.660055\pi\)
−0.481904 + 0.876224i \(0.660055\pi\)
\(102\) 4.73460e7 0.437404
\(103\) −2.18778e8 −1.94382 −0.971908 0.235360i \(-0.924373\pi\)
−0.971908 + 0.235360i \(0.924373\pi\)
\(104\) 1.21962e8i 1.04254i
\(105\) 7.22980e6i 0.0594797i
\(106\) 7.05983e7i 0.559205i
\(107\) −1.66714e6 −0.0127186 −0.00635928 0.999980i \(-0.502024\pi\)
−0.00635928 + 0.999980i \(0.502024\pi\)
\(108\) 2.49430e7i 0.183339i
\(109\) −2.10448e8 −1.49087 −0.745434 0.666579i \(-0.767758\pi\)
−0.745434 + 0.666579i \(0.767758\pi\)
\(110\) 1.32740e8 0.906631
\(111\) −1.13699e8 −0.748973
\(112\) 1.01560e7i 0.0645434i
\(113\) 2.55631e8i 1.56783i 0.620868 + 0.783915i \(0.286780\pi\)
−0.620868 + 0.783915i \(0.713220\pi\)
\(114\) 1.09941e8i 0.650938i
\(115\) 1.87114e8i 1.06983i
\(116\) 1.57196e7i 0.0868182i
\(117\) 1.14879e8 0.613049
\(118\) 8.51785e7i 0.439341i
\(119\) 1.31804e7i 0.0657266i
\(120\) 1.59665e8i 0.769989i
\(121\) −5.96066e7 −0.278069
\(122\) 5.63367e7 0.254303
\(123\) 6.23695e6i 0.0272491i
\(124\) −3.39130e7 −0.143443
\(125\) 1.74079e8i 0.713027i
\(126\) −1.18292e7 −0.0469326
\(127\) 2.08712e8 0.802292 0.401146 0.916014i \(-0.368612\pi\)
0.401146 + 0.916014i \(0.368612\pi\)
\(128\) 1.71228e8i 0.637874i
\(129\) 1.68503e8 + 7.37466e6i 0.608483 + 0.0266307i
\(130\) 2.97012e8 1.03992
\(131\) 4.36493e8i 1.48215i 0.671423 + 0.741074i \(0.265683\pi\)
−0.671423 + 0.741074i \(0.734317\pi\)
\(132\) 2.90312e7i 0.0956247i
\(133\) −3.06059e7 −0.0978133
\(134\) 4.32677e8i 1.34198i
\(135\) 3.89472e8 1.17258
\(136\) 2.91080e8i 0.850858i
\(137\) 7.48994e7i 0.212616i 0.994333 + 0.106308i \(0.0339029\pi\)
−0.994333 + 0.106308i \(0.966097\pi\)
\(138\) −1.80545e8 −0.497817
\(139\) −2.26715e8 −0.607324 −0.303662 0.952780i \(-0.598209\pi\)
−0.303662 + 0.952780i \(0.598209\pi\)
\(140\) 6.93227e6 0.0180453
\(141\) 1.76541e8i 0.446651i
\(142\) −7.22027e7 −0.177582
\(143\) 3.46266e8 0.828066
\(144\) −2.11261e8 −0.491327
\(145\) −2.45454e8 −0.555262
\(146\) 2.11695e8 0.465906
\(147\) 2.82460e8i 0.604906i
\(148\) 1.09020e8i 0.227227i
\(149\) 3.64612e8i 0.739751i 0.929081 + 0.369875i \(0.120600\pi\)
−0.929081 + 0.369875i \(0.879400\pi\)
\(150\) 1.10430e8 0.218133
\(151\) 6.29194e8i 1.21025i 0.796129 + 0.605127i \(0.206878\pi\)
−0.796129 + 0.605127i \(0.793122\pi\)
\(152\) −6.75909e8 −1.26623
\(153\) −2.74173e8 −0.500334
\(154\) −3.56555e7 −0.0633934
\(155\) 5.29534e8i 0.917418i
\(156\) 6.49588e7i 0.109683i
\(157\) 6.81816e8i 1.12220i −0.827750 0.561098i \(-0.810379\pi\)
0.827750 0.561098i \(-0.189621\pi\)
\(158\) 2.70485e8i 0.434026i
\(159\) 2.41094e8i 0.377222i
\(160\) 2.82312e8 0.430774
\(161\) 5.02611e7i 0.0748046i
\(162\) 1.53790e7i 0.0223289i
\(163\) 8.22150e8i 1.16466i −0.812951 0.582332i \(-0.802140\pi\)
0.812951 0.582332i \(-0.197860\pi\)
\(164\) −5.98029e6 −0.00826698
\(165\) 4.53308e8 0.611586
\(166\) 1.02020e9i 1.34355i
\(167\) −5.41132e8 −0.695725 −0.347862 0.937546i \(-0.613092\pi\)
−0.347862 + 0.937546i \(0.613092\pi\)
\(168\) 4.28880e7i 0.0538392i
\(169\) −4.09451e7 −0.0501944
\(170\) −7.08859e8 −0.848720
\(171\) 6.36651e8i 0.744589i
\(172\) −7.07117e6 + 1.61568e8i −0.00807937 + 0.184605i
\(173\) 3.97704e8 0.443992 0.221996 0.975048i \(-0.428743\pi\)
0.221996 + 0.975048i \(0.428743\pi\)
\(174\) 2.36837e8i 0.258377i
\(175\) 3.07420e7i 0.0327778i
\(176\) −6.36782e8 −0.663652
\(177\) 2.90885e8i 0.296366i
\(178\) 2.35929e8 0.235018
\(179\) 9.87563e8i 0.961951i 0.876734 + 0.480975i \(0.159717\pi\)
−0.876734 + 0.480975i \(0.840283\pi\)
\(180\) 1.44202e8i 0.137367i
\(181\) −1.27942e9 −1.19206 −0.596031 0.802962i \(-0.703256\pi\)
−0.596031 + 0.802962i \(0.703256\pi\)
\(182\) −7.97810e7 −0.0727133
\(183\) 1.92390e8 0.171545
\(184\) 1.10998e9i 0.968376i
\(185\) 1.70230e9 1.45328
\(186\) 5.10945e8 0.426896
\(187\) −8.26410e8 −0.675817
\(188\) 1.69276e8 0.135508
\(189\) −1.04617e8 −0.0819888
\(190\) 1.64602e9i 1.26305i
\(191\) 3.56434e8i 0.267822i −0.990993 0.133911i \(-0.957246\pi\)
0.990993 0.133911i \(-0.0427536\pi\)
\(192\) 9.18890e8i 0.676174i
\(193\) 1.31721e9 0.949347 0.474674 0.880162i \(-0.342566\pi\)
0.474674 + 0.880162i \(0.342566\pi\)
\(194\) 1.54873e9i 1.09338i
\(195\) 1.01430e9 0.701499
\(196\) 2.70836e8 0.183520
\(197\) 1.33673e9 0.887519 0.443759 0.896146i \(-0.353644\pi\)
0.443759 + 0.896146i \(0.353644\pi\)
\(198\) 7.41692e8i 0.482573i
\(199\) 1.52102e9i 0.969890i 0.874545 + 0.484945i \(0.161160\pi\)
−0.874545 + 0.484945i \(0.838840\pi\)
\(200\) 6.78916e8i 0.424323i
\(201\) 1.47760e9i 0.905256i
\(202\) 1.44888e9i 0.870217i
\(203\) 6.59319e7 0.0388250
\(204\) 1.55033e8i 0.0895166i
\(205\) 9.33791e7i 0.0528730i
\(206\) 3.16054e9i 1.75506i
\(207\) 1.04551e9 0.569438
\(208\) −1.42483e9 −0.761219
\(209\) 1.91899e9i 1.00574i
\(210\) −1.04444e8 −0.0537039
\(211\) 9.39023e8i 0.473747i −0.971541 0.236873i \(-0.923877\pi\)
0.971541 0.236873i \(-0.0761227\pi\)
\(212\) −2.31172e8 −0.114444
\(213\) −2.46573e8 −0.119792
\(214\) 2.40841e7i 0.0114835i
\(215\) −2.52281e9 1.10413e8i −1.18067 0.0516731i
\(216\) −2.31039e9 −1.06138
\(217\) 1.42239e8i 0.0641477i
\(218\) 3.04020e9i 1.34610i
\(219\) 7.22939e8 0.314286
\(220\) 4.34653e8i 0.185546i
\(221\) −1.84913e9 −0.775174
\(222\) 1.64254e9i 0.676243i
\(223\) 1.73592e9i 0.701958i 0.936383 + 0.350979i \(0.114151\pi\)
−0.936383 + 0.350979i \(0.885849\pi\)
\(224\) −7.58324e7 −0.0301205
\(225\) −6.39483e8 −0.249516
\(226\) 3.69292e9 1.41559
\(227\) 6.10500e8i 0.229923i 0.993370 + 0.114961i \(0.0366745\pi\)
−0.993370 + 0.114961i \(0.963326\pi\)
\(228\) −3.59998e8 −0.133217
\(229\) −4.14557e9 −1.50745 −0.753724 0.657192i \(-0.771744\pi\)
−0.753724 + 0.657192i \(0.771744\pi\)
\(230\) 2.70310e9 0.965943
\(231\) −1.21764e8 −0.0427633
\(232\) 1.45606e9 0.502606
\(233\) 6.91935e8i 0.234769i 0.993087 + 0.117385i \(0.0374511\pi\)
−0.993087 + 0.117385i \(0.962549\pi\)
\(234\) 1.65957e9i 0.553519i
\(235\) 2.64315e9i 0.866664i
\(236\) 2.78915e8 0.0899132
\(237\) 9.23710e8i 0.292781i
\(238\) 1.90408e8 0.0593442
\(239\) 2.94993e9 0.904106 0.452053 0.891991i \(-0.350692\pi\)
0.452053 + 0.891991i \(0.350692\pi\)
\(240\) −1.86529e9 −0.562214
\(241\) 6.00192e9i 1.77919i −0.456752 0.889594i \(-0.650987\pi\)
0.456752 0.889594i \(-0.349013\pi\)
\(242\) 8.61096e8i 0.251067i
\(243\) 3.51208e9i 1.00725i
\(244\) 1.84473e8i 0.0520443i
\(245\) 4.22897e9i 1.17373i
\(246\) 9.01010e7 0.0246031
\(247\) 4.29382e9i 1.15360i
\(248\) 3.14126e9i 0.830418i
\(249\) 3.48399e9i 0.906316i
\(250\) 2.51480e9 0.643788
\(251\) −5.22577e9 −1.31661 −0.658303 0.752753i \(-0.728725\pi\)
−0.658303 + 0.752753i \(0.728725\pi\)
\(252\) 3.87345e7i 0.00960496i
\(253\) 3.15136e9 0.769160
\(254\) 3.01512e9i 0.724385i
\(255\) −2.42076e9 −0.572521
\(256\) −2.29459e9 −0.534251
\(257\) 7.78874e9i 1.78540i 0.450656 + 0.892698i \(0.351190\pi\)
−0.450656 + 0.892698i \(0.648810\pi\)
\(258\) 1.06537e8 2.43424e9i 0.0240447 0.549396i
\(259\) −4.57257e8 −0.101616
\(260\) 9.72557e8i 0.212824i
\(261\) 1.37149e9i 0.295550i
\(262\) 6.30571e9 1.33822
\(263\) 4.65449e9i 0.972858i −0.873720 0.486429i \(-0.838299\pi\)
0.873720 0.486429i \(-0.161701\pi\)
\(264\) −2.68907e9 −0.553588
\(265\) 3.60963e9i 0.731947i
\(266\) 4.42142e8i 0.0883151i
\(267\) 8.05699e8 0.158536
\(268\) 1.41679e9 0.274642
\(269\) −5.29425e9 −1.01110 −0.505551 0.862797i \(-0.668711\pi\)
−0.505551 + 0.862797i \(0.668711\pi\)
\(270\) 5.62643e9i 1.05871i
\(271\) 1.58476e9 0.293823 0.146912 0.989150i \(-0.453067\pi\)
0.146912 + 0.989150i \(0.453067\pi\)
\(272\) 3.40055e9 0.621261
\(273\) −2.72453e8 −0.0490502
\(274\) 1.08202e9 0.191970
\(275\) −1.92752e9 −0.337030
\(276\) 5.91190e8i 0.101880i
\(277\) 9.51951e9i 1.61695i −0.588533 0.808473i \(-0.700294\pi\)
0.588533 0.808473i \(-0.299706\pi\)
\(278\) 3.27519e9i 0.548349i
\(279\) −2.95880e9 −0.488314
\(280\) 6.42114e8i 0.104467i
\(281\) 6.79176e9 1.08932 0.544662 0.838656i \(-0.316658\pi\)
0.544662 + 0.838656i \(0.316658\pi\)
\(282\) −2.55036e9 −0.403279
\(283\) 6.59772e9 1.02860 0.514302 0.857609i \(-0.328051\pi\)
0.514302 + 0.857609i \(0.328051\pi\)
\(284\) 2.36426e8i 0.0363431i
\(285\) 5.62118e9i 0.852017i
\(286\) 5.00226e9i 0.747657i
\(287\) 2.50828e7i 0.00369698i
\(288\) 1.57743e9i 0.229288i
\(289\) −2.56255e9 −0.367350
\(290\) 3.54591e9i 0.501343i
\(291\) 5.28893e9i 0.737558i
\(292\) 6.93188e8i 0.0953498i
\(293\) 2.95135e9 0.400452 0.200226 0.979750i \(-0.435832\pi\)
0.200226 + 0.979750i \(0.435832\pi\)
\(294\) −4.08051e9 −0.546167
\(295\) 4.35511e9i 0.575057i
\(296\) −1.00982e10 −1.31546
\(297\) 6.55947e9i 0.843030i
\(298\) 5.26729e9 0.667917
\(299\) 7.05133e9 0.882239
\(300\) 3.61600e8i 0.0446420i
\(301\) 6.77657e8 + 2.96582e7i 0.0825551 + 0.00361309i
\(302\) 9.08953e9 1.09273
\(303\) 4.94794e9i 0.587022i
\(304\) 7.89633e9i 0.924551i
\(305\) −2.88045e9 −0.332859
\(306\) 3.96079e9i 0.451748i
\(307\) −2.01113e9 −0.226405 −0.113202 0.993572i \(-0.536111\pi\)
−0.113202 + 0.993572i \(0.536111\pi\)
\(308\) 1.16753e8i 0.0129737i
\(309\) 1.07933e10i 1.18391i
\(310\) −7.64982e9 −0.828332
\(311\) −1.19451e9 −0.127687 −0.0638435 0.997960i \(-0.520336\pi\)
−0.0638435 + 0.997960i \(0.520336\pi\)
\(312\) −6.01693e9 −0.634975
\(313\) 6.10803e9i 0.636390i −0.948025 0.318195i \(-0.896923\pi\)
0.948025 0.318195i \(-0.103077\pi\)
\(314\) −9.84972e9 −1.01322
\(315\) 6.04819e8 0.0614304
\(316\) −8.85697e8 −0.0888254
\(317\) −4.65744e9 −0.461223 −0.230611 0.973046i \(-0.574073\pi\)
−0.230611 + 0.973046i \(0.574073\pi\)
\(318\) 3.48292e9 0.340592
\(319\) 4.13393e9i 0.399209i
\(320\) 1.37575e10i 1.31202i
\(321\) 8.22474e7i 0.00774643i
\(322\) −7.26087e8 −0.0675406
\(323\) 1.02478e10i 0.941500i
\(324\) 5.03581e7 0.00456972
\(325\) −4.31292e9 −0.386579
\(326\) −1.18770e10 −1.05157
\(327\) 1.03823e10i 0.908036i
\(328\) 5.53935e8i 0.0478590i
\(329\) 7.09983e8i 0.0605988i
\(330\) 6.54862e9i 0.552197i
\(331\) 1.46486e10i 1.22035i 0.792266 + 0.610176i \(0.208901\pi\)
−0.792266 + 0.610176i \(0.791099\pi\)
\(332\) 3.34062e9 0.274963
\(333\) 9.51168e9i 0.773535i
\(334\) 7.81736e9i 0.628166i
\(335\) 2.21224e10i 1.75652i
\(336\) 5.01040e8 0.0393111
\(337\) 1.59260e10 1.23477 0.617387 0.786660i \(-0.288191\pi\)
0.617387 + 0.786660i \(0.288191\pi\)
\(338\) 5.91505e8i 0.0453202i
\(339\) 1.26114e10 0.954911
\(340\) 2.32114e9i 0.173694i
\(341\) −8.91840e9 −0.659583
\(342\) −9.19725e9 −0.672285
\(343\) 2.27971e9i 0.164704i
\(344\) 1.49656e10 + 6.54980e8i 1.06871 + 0.0467729i
\(345\) 9.23113e9 0.651596
\(346\) 5.74535e9i 0.400878i
\(347\) 1.08692e10i 0.749688i 0.927088 + 0.374844i \(0.122304\pi\)
−0.927088 + 0.374844i \(0.877696\pi\)
\(348\) 7.75517e8 0.0528779
\(349\) 3.33672e9i 0.224915i −0.993657 0.112458i \(-0.964128\pi\)
0.993657 0.112458i \(-0.0358722\pi\)
\(350\) 4.44109e8 0.0295949
\(351\) 1.46771e10i 0.966970i
\(352\) 4.75469e9i 0.309707i
\(353\) 2.37900e10 1.53213 0.766065 0.642764i \(-0.222212\pi\)
0.766065 + 0.642764i \(0.222212\pi\)
\(354\) −4.20222e9 −0.267588
\(355\) 3.69166e9 0.232439
\(356\) 7.72542e8i 0.0480975i
\(357\) 6.50246e8 0.0400318
\(358\) 1.42666e10 0.868540
\(359\) 8.83406e9 0.531842 0.265921 0.963995i \(-0.414324\pi\)
0.265921 + 0.963995i \(0.414324\pi\)
\(360\) 1.33570e10 0.795241
\(361\) −6.81256e9 −0.401127
\(362\) 1.84829e10i 1.07631i
\(363\) 2.94065e9i 0.169362i
\(364\) 2.61241e8i 0.0148811i
\(365\) −1.08238e10 −0.609827
\(366\) 2.77933e9i 0.154887i
\(367\) −3.31879e10 −1.82943 −0.914714 0.404101i \(-0.867584\pi\)
−0.914714 + 0.404101i \(0.867584\pi\)
\(368\) −1.29674e10 −0.707068
\(369\) −5.21761e8 −0.0281427
\(370\) 2.45919e10i 1.31215i
\(371\) 9.69591e8i 0.0511791i
\(372\) 1.67307e9i 0.0873662i
\(373\) 6.01756e8i 0.0310874i 0.999879 + 0.0155437i \(0.00494792\pi\)
−0.999879 + 0.0155437i \(0.995052\pi\)
\(374\) 1.19386e10i 0.610192i
\(375\) 8.58806e9 0.434280
\(376\) 1.56795e10i 0.784477i
\(377\) 9.24986e9i 0.457899i
\(378\) 1.51133e9i 0.0740273i
\(379\) −2.14209e10 −1.03820 −0.519099 0.854714i \(-0.673732\pi\)
−0.519099 + 0.854714i \(0.673732\pi\)
\(380\) 5.38986e9 0.258489
\(381\) 1.02967e10i 0.488648i
\(382\) −5.14916e9 −0.241815
\(383\) 1.03097e10i 0.479128i −0.970881 0.239564i \(-0.922996\pi\)
0.970881 0.239564i \(-0.0770045\pi\)
\(384\) 8.44741e9 0.388507
\(385\) 1.82304e9 0.0829761
\(386\) 1.90288e10i 0.857160i
\(387\) −6.16937e8 + 1.40963e10i −0.0275041 + 0.628438i
\(388\) −5.07128e9 −0.223764
\(389\) 8.19319e9i 0.357812i −0.983866 0.178906i \(-0.942744\pi\)
0.983866 0.178906i \(-0.0572558\pi\)
\(390\) 1.46529e10i 0.633379i
\(391\) −1.68290e10 −0.720030
\(392\) 2.50867e10i 1.06243i
\(393\) 2.15340e10 0.902725
\(394\) 1.93108e10i 0.801336i
\(395\) 1.38297e10i 0.568099i
\(396\) 2.42865e9 0.0987607
\(397\) −1.88316e10 −0.758098 −0.379049 0.925377i \(-0.623749\pi\)
−0.379049 + 0.925377i \(0.623749\pi\)
\(398\) 2.19731e10 0.875709
\(399\) 1.50992e9i 0.0595747i
\(400\) 7.93146e9 0.309823
\(401\) −6.25242e9 −0.241808 −0.120904 0.992664i \(-0.538579\pi\)
−0.120904 + 0.992664i \(0.538579\pi\)
\(402\) −2.13458e10 −0.817351
\(403\) −1.99553e10 −0.756552
\(404\) −4.74432e9 −0.178094
\(405\) 7.86315e8i 0.0292265i
\(406\) 9.52473e8i 0.0350549i
\(407\) 2.86700e10i 1.04484i
\(408\) 1.43602e10 0.518228
\(409\) 3.02005e10i 1.07925i 0.841906 + 0.539624i \(0.181433\pi\)
−0.841906 + 0.539624i \(0.818567\pi\)
\(410\) −1.34898e9 −0.0477388
\(411\) 3.69511e9 0.129497
\(412\) −1.03491e10 −0.359181
\(413\) 1.16984e9i 0.0402091i
\(414\) 1.51038e10i 0.514143i
\(415\) 5.21620e10i 1.75858i
\(416\) 1.06388e10i 0.355239i
\(417\) 1.11848e10i 0.369900i
\(418\) −2.77223e10 −0.908079
\(419\) 5.63631e9i 0.182868i 0.995811 + 0.0914342i \(0.0291451\pi\)
−0.995811 + 0.0914342i \(0.970855\pi\)
\(420\) 3.41999e8i 0.0109907i
\(421\) 2.23614e10i 0.711821i −0.934520 0.355911i \(-0.884171\pi\)
0.934520 0.355911i \(-0.115829\pi\)
\(422\) −1.35654e10 −0.427743
\(423\) 1.47688e10 0.461299
\(424\) 2.14127e10i 0.662535i
\(425\) 1.02934e10 0.315502
\(426\) 3.56207e9i 0.108159i
\(427\) 7.73724e8 0.0232742
\(428\) −7.88627e7 −0.00235015
\(429\) 1.70828e10i 0.504346i
\(430\) −1.59506e9 + 3.64453e10i −0.0466554 + 1.06602i
\(431\) −3.86516e10 −1.12010 −0.560052 0.828457i \(-0.689219\pi\)
−0.560052 + 0.828457i \(0.689219\pi\)
\(432\) 2.69912e10i 0.774975i
\(433\) 4.84787e10i 1.37911i −0.724232 0.689556i \(-0.757806\pi\)
0.724232 0.689556i \(-0.242194\pi\)
\(434\) 2.05483e9 0.0579186
\(435\) 1.21093e10i 0.338191i
\(436\) −9.95506e9 −0.275485
\(437\) 3.90781e10i 1.07154i
\(438\) 1.04438e10i 0.283767i
\(439\) 4.03504e10 1.08640 0.543200 0.839603i \(-0.317213\pi\)
0.543200 + 0.839603i \(0.317213\pi\)
\(440\) 4.02605e10 1.07416
\(441\) 2.36296e10 0.624744
\(442\) 2.67132e10i 0.699900i
\(443\) 5.75175e10 1.49343 0.746715 0.665144i \(-0.231630\pi\)
0.746715 + 0.665144i \(0.231630\pi\)
\(444\) −5.37844e9 −0.138396
\(445\) −1.20628e10 −0.307616
\(446\) 2.50777e10 0.633794
\(447\) 1.79878e10 0.450556
\(448\) 3.69544e9i 0.0917390i
\(449\) 5.96814e10i 1.46843i −0.678916 0.734216i \(-0.737550\pi\)
0.678916 0.734216i \(-0.262450\pi\)
\(450\) 9.23817e9i 0.225287i
\(451\) −1.57269e9 −0.0380133
\(452\) 1.20924e10i 0.289706i
\(453\) 3.10408e10 0.737124
\(454\) 8.81948e9 0.207596
\(455\) 4.07913e9 0.0951749
\(456\) 3.33455e10i 0.771219i
\(457\) 5.34965e10i 1.22648i 0.789897 + 0.613240i \(0.210134\pi\)
−0.789897 + 0.613240i \(0.789866\pi\)
\(458\) 5.98882e10i 1.36107i
\(459\) 3.50290e10i 0.789182i
\(460\) 8.85124e9i 0.197685i
\(461\) −3.98268e10 −0.881804 −0.440902 0.897555i \(-0.645341\pi\)
−0.440902 + 0.897555i \(0.645341\pi\)
\(462\) 1.75904e9i 0.0386107i
\(463\) 5.57576e10i 1.21333i 0.794957 + 0.606666i \(0.207494\pi\)
−0.794957 + 0.606666i \(0.792506\pi\)
\(464\) 1.70105e10i 0.366982i
\(465\) −2.61242e10 −0.558767
\(466\) 9.99591e9 0.211972
\(467\) 3.57499e10i 0.751635i 0.926694 + 0.375818i \(0.122638\pi\)
−0.926694 + 0.375818i \(0.877362\pi\)
\(468\) 5.43422e9 0.113280
\(469\) 5.94235e9i 0.122819i
\(470\) 3.81838e10 0.782506
\(471\) −3.36369e10 −0.683490
\(472\) 2.58350e10i 0.520524i
\(473\) −1.85957e9 + 4.24890e10i −0.0371507 + 0.848852i
\(474\) 1.33442e10 0.264350
\(475\) 2.39020e10i 0.469526i
\(476\) 6.23487e8i 0.0121451i
\(477\) −2.01690e10 −0.389593
\(478\) 4.26156e10i 0.816313i
\(479\) 1.36640e10 0.259559 0.129779 0.991543i \(-0.458573\pi\)
0.129779 + 0.991543i \(0.458573\pi\)
\(480\) 1.39277e10i 0.262369i
\(481\) 6.41505e10i 1.19845i
\(482\) −8.67056e10 −1.60642
\(483\) −2.47959e9 −0.0455609
\(484\) −2.81964e9 −0.0513821
\(485\) 7.91854e10i 1.43113i
\(486\) −5.07366e10 −0.909444
\(487\) −4.93586e10 −0.877499 −0.438750 0.898609i \(-0.644579\pi\)
−0.438750 + 0.898609i \(0.644579\pi\)
\(488\) 1.70871e10 0.301294
\(489\) −4.05602e10 −0.709356
\(490\) 6.10930e10 1.05976
\(491\) 3.03520e10i 0.522229i 0.965308 + 0.261114i \(0.0840900\pi\)
−0.965308 + 0.261114i \(0.915910\pi\)
\(492\) 2.95033e8i 0.00503513i
\(493\) 2.20761e10i 0.373709i
\(494\) −6.20299e10 −1.04158
\(495\) 3.79221e10i 0.631643i
\(496\) 3.66978e10 0.606337
\(497\) −9.91626e8 −0.0162526
\(498\) −5.03308e10 −0.818308
\(499\) 9.99001e10i 1.61125i 0.592423 + 0.805627i \(0.298171\pi\)
−0.592423 + 0.805627i \(0.701829\pi\)
\(500\) 8.23464e9i 0.131754i
\(501\) 2.66964e10i 0.423742i
\(502\) 7.54932e10i 1.18876i
\(503\) 4.91660e8i 0.00768057i −0.999993 0.00384028i \(-0.998778\pi\)
0.999993 0.00384028i \(-0.00122240\pi\)
\(504\) −3.58785e9 −0.0556048
\(505\) 7.40801e10i 1.13903i
\(506\) 4.55256e10i 0.694470i
\(507\) 2.02000e9i 0.0305716i
\(508\) 9.87292e9 0.148249
\(509\) −5.80539e10 −0.864888 −0.432444 0.901661i \(-0.642349\pi\)
−0.432444 + 0.901661i \(0.642349\pi\)
\(510\) 3.49711e10i 0.516926i
\(511\) 2.90740e9 0.0426403
\(512\) 7.69827e10i 1.12025i
\(513\) −8.13399e10 −1.17445
\(514\) 1.12519e11 1.61202
\(515\) 1.61596e11i 2.29721i
\(516\) 7.97086e9 + 3.48851e8i 0.112436 + 0.00492086i
\(517\) 4.45159e10 0.623093
\(518\) 6.60568e9i 0.0917484i
\(519\) 1.96204e10i 0.270420i
\(520\) 9.00848e10 1.23208
\(521\) 1.29089e11i 1.75202i −0.482292 0.876011i \(-0.660196\pi\)
0.482292 0.876011i \(-0.339804\pi\)
\(522\) 1.98130e10 0.266850
\(523\) 1.17907e11i 1.57592i −0.615729 0.787958i \(-0.711138\pi\)
0.615729 0.787958i \(-0.288862\pi\)
\(524\) 2.06479e10i 0.273874i
\(525\) 1.51664e9 0.0199638
\(526\) −6.72403e10 −0.878388
\(527\) 4.76262e10 0.617452
\(528\) 3.14152e10i 0.404207i
\(529\) −1.41368e10 −0.180522
\(530\) −5.21459e10 −0.660871
\(531\) 2.43344e10 0.306086
\(532\) −1.44778e9 −0.0180741
\(533\) −3.51896e9 −0.0436019
\(534\) 1.16394e10i 0.143141i
\(535\) 1.23140e9i 0.0150309i
\(536\) 1.31233e11i 1.58995i
\(537\) 4.87207e10 0.585891
\(538\) 7.64823e10i 0.912919i
\(539\) 7.12241e10 0.843863
\(540\) 1.84236e10 0.216670
\(541\) 1.00163e11 1.16928 0.584638 0.811294i \(-0.301237\pi\)
0.584638 + 0.811294i \(0.301237\pi\)
\(542\) 2.28939e10i 0.265292i
\(543\) 6.31192e10i 0.726043i
\(544\) 2.53910e10i 0.289925i
\(545\) 1.55443e11i 1.76192i
\(546\) 3.93594e9i 0.0442871i
\(547\) 1.44716e11 1.61647 0.808235 0.588859i \(-0.200423\pi\)
0.808235 + 0.588859i \(0.200423\pi\)
\(548\) 3.54304e9i 0.0392875i
\(549\) 1.60947e10i 0.177171i
\(550\) 2.78456e10i 0.304303i
\(551\) 5.12622e10 0.556149
\(552\) −5.47601e10 −0.589804
\(553\) 3.71483e9i 0.0397226i
\(554\) −1.37522e11 −1.45993
\(555\) 8.39815e10i 0.885140i
\(556\) −1.07245e10 −0.112222
\(557\) −5.90654e10 −0.613639 −0.306819 0.951768i \(-0.599265\pi\)
−0.306819 + 0.951768i \(0.599265\pi\)
\(558\) 4.27438e10i 0.440896i
\(559\) −4.16087e9 + 9.50712e10i −0.0426125 + 0.973648i
\(560\) −7.50152e9 −0.0762777
\(561\) 4.07704e10i 0.411617i
\(562\) 9.81159e10i 0.983545i
\(563\) −6.86390e9 −0.0683183 −0.0341592 0.999416i \(-0.510875\pi\)
−0.0341592 + 0.999416i \(0.510875\pi\)
\(564\) 8.35110e9i 0.0825329i
\(565\) −1.88816e11 −1.85287
\(566\) 9.53128e10i 0.928721i
\(567\) 2.11214e8i 0.00204357i
\(568\) −2.18994e10 −0.210396
\(569\) 1.96344e11 1.87313 0.936567 0.350488i \(-0.113984\pi\)
0.936567 + 0.350488i \(0.113984\pi\)
\(570\) −8.12054e10 −0.769281
\(571\) 8.07361e10i 0.759493i −0.925091 0.379746i \(-0.876011\pi\)
0.925091 0.379746i \(-0.123989\pi\)
\(572\) 1.63798e10 0.153011
\(573\) −1.75844e10 −0.163121
\(574\) 3.62353e8 0.00333799
\(575\) −3.92519e10 −0.359079
\(576\) −7.68711e10 −0.698350
\(577\) 3.65362e10i 0.329625i 0.986325 + 0.164812i \(0.0527019\pi\)
−0.986325 + 0.164812i \(0.947298\pi\)
\(578\) 3.70194e10i 0.331679i
\(579\) 6.49835e10i 0.578214i
\(580\) −1.16110e10 −0.102602
\(581\) 1.40113e10i 0.122963i
\(582\) 7.64056e10 0.665937
\(583\) −6.07933e10 −0.526237
\(584\) 6.42078e10 0.551997
\(585\) 8.48525e10i 0.724504i
\(586\) 4.26362e10i 0.361566i
\(587\) 2.20512e11i 1.85729i 0.370968 + 0.928646i \(0.379026\pi\)
−0.370968 + 0.928646i \(0.620974\pi\)
\(588\) 1.33615e10i 0.111775i
\(589\) 1.10591e11i 0.918883i
\(590\) 6.29153e10 0.519216
\(591\) 6.59464e10i 0.540557i
\(592\) 1.17973e11i 0.960494i
\(593\) 4.75066e10i 0.384181i 0.981377 + 0.192090i \(0.0615266\pi\)
−0.981377 + 0.192090i \(0.938473\pi\)
\(594\) −9.47602e10 −0.761167
\(595\) −9.73542e9 −0.0776760
\(596\) 1.72476e10i 0.136692i
\(597\) 7.50384e10 0.590726
\(598\) 1.01866e11i 0.796569i
\(599\) −1.31062e11 −1.01805 −0.509026 0.860751i \(-0.669994\pi\)
−0.509026 + 0.860751i \(0.669994\pi\)
\(600\) 3.34939e10 0.258440
\(601\) 9.34024e10i 0.715913i 0.933738 + 0.357956i \(0.116526\pi\)
−0.933738 + 0.357956i \(0.883474\pi\)
\(602\) 4.28451e8 9.78964e9i 0.00326224 0.0745385i
\(603\) 1.23610e11 0.934944
\(604\) 2.97634e10i 0.223633i
\(605\) 4.40271e10i 0.328624i
\(606\) 7.14795e10 0.530019
\(607\) 1.69612e11i 1.24940i 0.780866 + 0.624699i \(0.214778\pi\)
−0.780866 + 0.624699i \(0.785222\pi\)
\(608\) −5.89599e10 −0.431462
\(609\) 3.25270e9i 0.0236470i
\(610\) 4.16119e10i 0.300537i
\(611\) 9.96064e10 0.714698
\(612\) −1.29695e10 −0.0924524
\(613\) 3.40764e10 0.241330 0.120665 0.992693i \(-0.461497\pi\)
0.120665 + 0.992693i \(0.461497\pi\)
\(614\) 2.90534e10i 0.204420i
\(615\) −4.60679e9 −0.0322031
\(616\) −1.08145e10 −0.0751073
\(617\) −1.79585e11 −1.23916 −0.619582 0.784932i \(-0.712698\pi\)
−0.619582 + 0.784932i \(0.712698\pi\)
\(618\) 1.55923e11 1.06895
\(619\) −3.84231e10 −0.261716 −0.130858 0.991401i \(-0.541773\pi\)
−0.130858 + 0.991401i \(0.541773\pi\)
\(620\) 2.50491e10i 0.169522i
\(621\) 1.33577e11i 0.898182i
\(622\) 1.72562e10i 0.115288i
\(623\) 3.24023e9 0.0215091
\(624\) 7.02930e10i 0.463632i
\(625\) −1.89105e11 −1.23932
\(626\) −8.82384e10 −0.574593
\(627\) −9.46717e10 −0.612562
\(628\) 3.22527e10i 0.207361i
\(629\) 1.53104e11i 0.978101i
\(630\) 8.73740e9i 0.0554651i
\(631\) 1.33200e11i 0.840208i −0.907476 0.420104i \(-0.861994\pi\)
0.907476 0.420104i \(-0.138006\pi\)
\(632\) 8.20393e10i 0.514226i
\(633\) −4.63260e10 −0.288543
\(634\) 6.72829e10i 0.416435i
\(635\) 1.54160e11i 0.948152i
\(636\) 1.14047e10i 0.0697037i
\(637\) 1.59367e11 0.967925
\(638\) 5.97200e10 0.360443
\(639\) 2.06274e10i 0.123720i
\(640\) −1.26474e11 −0.753843
\(641\) 3.22936e11i 1.91286i −0.291956 0.956432i \(-0.594306\pi\)
0.291956 0.956432i \(-0.405694\pi\)
\(642\) 1.18817e9 0.00699421
\(643\) −8.28778e10 −0.484836 −0.242418 0.970172i \(-0.577940\pi\)
−0.242418 + 0.970172i \(0.577940\pi\)
\(644\) 2.37755e9i 0.0138225i
\(645\) −5.44713e9 + 1.24461e11i −0.0314723 + 0.719108i
\(646\) 1.48043e11 0.850075
\(647\) 1.35729e11i 0.774560i 0.921962 + 0.387280i \(0.126585\pi\)
−0.921962 + 0.387280i \(0.873415\pi\)
\(648\) 4.66451e9i 0.0264549i
\(649\) 7.33486e10 0.413440
\(650\) 6.23059e10i 0.349040i
\(651\) 7.01727e9 0.0390701
\(652\) 3.88910e10i 0.215208i
\(653\) 2.27648e11i 1.25202i 0.779816 + 0.626009i \(0.215313\pi\)
−0.779816 + 0.626009i \(0.784687\pi\)
\(654\) 1.49986e11 0.819861
\(655\) −3.22406e11 −1.75161
\(656\) 6.47137e9 0.0349446
\(657\) 6.04784e10i 0.324593i
\(658\) −1.02566e10 −0.0547144
\(659\) 1.34412e11 0.712685 0.356343 0.934355i \(-0.384024\pi\)
0.356343 + 0.934355i \(0.384024\pi\)
\(660\) 2.14433e10 0.113010
\(661\) 3.17172e11 1.66146 0.830729 0.556678i \(-0.187924\pi\)
0.830729 + 0.556678i \(0.187924\pi\)
\(662\) 2.11619e11 1.10185
\(663\) 9.12256e10i 0.472131i
\(664\) 3.09431e11i 1.59181i
\(665\) 2.26063e10i 0.115596i
\(666\) −1.37409e11 −0.698421
\(667\) 8.41830e10i 0.425325i
\(668\) −2.55977e10 −0.128557
\(669\) 8.56405e10 0.427538
\(670\) 3.19587e11 1.58595
\(671\) 4.85124e10i 0.239311i
\(672\) 3.74114e9i 0.0183454i
\(673\) 1.83900e11i 0.896439i −0.893924 0.448219i \(-0.852058\pi\)
0.893924 0.448219i \(-0.147942\pi\)
\(674\) 2.30072e11i 1.11487i
\(675\) 8.17018e10i 0.393565i
\(676\) −1.93687e9 −0.00927499
\(677\) 2.28590e11i 1.08818i −0.839025 0.544092i \(-0.816874\pi\)
0.839025 0.544092i \(-0.183126\pi\)
\(678\) 1.82188e11i 0.862184i
\(679\) 2.12702e10i 0.100067i
\(680\) −2.15000e11 −1.00555
\(681\) 3.01186e10 0.140038
\(682\) 1.28838e11i 0.595534i
\(683\) −2.31405e11 −1.06338 −0.531692 0.846938i \(-0.678443\pi\)
−0.531692 + 0.846938i \(0.678443\pi\)
\(684\) 3.01162e10i 0.137586i
\(685\) −5.53228e10 −0.251271
\(686\) −3.29335e10 −0.148710
\(687\) 2.04519e11i 0.918134i
\(688\) 7.65183e9 1.74836e11i 0.0341516 0.780327i
\(689\) −1.36028e11 −0.603603
\(690\) 1.33356e11i 0.588322i
\(691\) 5.16820e10i 0.226687i −0.993556 0.113344i \(-0.963844\pi\)
0.993556 0.113344i \(-0.0361561\pi\)
\(692\) 1.88130e10 0.0820415
\(693\) 1.01863e10i 0.0441657i
\(694\) 1.57020e11 0.676889
\(695\) 1.67458e11i 0.717738i
\(696\) 7.18337e10i 0.306120i
\(697\) 8.39849e9 0.0355852
\(698\) −4.82034e10 −0.203075
\(699\) 3.41361e10 0.142990
\(700\) 1.45422e9i 0.00605674i
\(701\) 4.23537e11 1.75396 0.876979 0.480530i \(-0.159556\pi\)
0.876979 + 0.480530i \(0.159556\pi\)
\(702\) −2.12030e11 −0.873072
\(703\) −3.55519e11 −1.45560
\(704\) −2.31704e11 −0.943284
\(705\) 1.30398e11 0.527855
\(706\) 3.43678e11i 1.38335i
\(707\) 1.98988e10i 0.0796434i
\(708\) 1.37601e10i 0.0547630i
\(709\) 9.66397e10 0.382446 0.191223 0.981547i \(-0.438755\pi\)
0.191223 + 0.981547i \(0.438755\pi\)
\(710\) 5.33309e10i 0.209868i
\(711\) −7.72743e10 −0.302382
\(712\) 7.15581e10 0.278445
\(713\) −1.81614e11 −0.702733
\(714\) 9.39365e9i 0.0361445i
\(715\) 2.55761e11i 0.978613i
\(716\) 4.67157e10i 0.177751i
\(717\) 1.45532e11i 0.550660i
\(718\) 1.27620e11i 0.480197i
\(719\) 1.22535e11 0.458506 0.229253 0.973367i \(-0.426372\pi\)
0.229253 + 0.973367i \(0.426372\pi\)
\(720\) 1.56044e11i 0.580652i
\(721\) 4.34066e10i 0.160626i
\(722\) 9.84164e10i 0.362175i
\(723\) −2.96100e11 −1.08364
\(724\) −6.05217e10 −0.220271
\(725\) 5.14903e10i 0.186369i
\(726\) 4.24816e10 0.152916
\(727\) 2.91321e11i 1.04288i −0.853289 0.521439i \(-0.825395\pi\)
0.853289 0.521439i \(-0.174605\pi\)
\(728\) −2.41979e10 −0.0861493
\(729\) −1.66281e11 −0.588753
\(730\) 1.56363e11i 0.550610i
\(731\) 9.93048e9 2.26901e11i 0.0347777 0.794632i
\(732\) 9.10084e9 0.0316984
\(733\) 3.02333e11i 1.04730i 0.851934 + 0.523649i \(0.175430\pi\)
−0.851934 + 0.523649i \(0.824570\pi\)
\(734\) 4.79443e11i 1.65178i
\(735\) 2.08633e11 0.714881
\(736\) 9.68241e10i 0.329968i
\(737\) 3.72585e11 1.26286
\(738\) 7.53752e9i 0.0254099i
\(739\) 4.15049e11i 1.39162i 0.718224 + 0.695812i \(0.244955\pi\)
−0.718224 + 0.695812i \(0.755045\pi\)
\(740\) 8.05255e10 0.268538
\(741\) −2.11833e11 −0.702619
\(742\) 1.40070e10 0.0462094
\(743\) 5.51999e11i 1.81127i −0.424059 0.905634i \(-0.639395\pi\)
0.424059 0.905634i \(-0.360605\pi\)
\(744\) 1.54972e11 0.505779
\(745\) −2.69312e11 −0.874241
\(746\) 8.69315e9 0.0280687
\(747\) 2.91458e11 0.936039
\(748\) −3.90926e10 −0.124879
\(749\) 3.30769e8i 0.00105099i
\(750\) 1.24066e11i 0.392109i
\(751\) 3.96084e11i 1.24517i −0.782554 0.622583i \(-0.786083\pi\)
0.782554 0.622583i \(-0.213917\pi\)
\(752\) −1.83176e11 −0.572793
\(753\) 2.57810e11i 0.801899i
\(754\) 1.33626e11 0.413435
\(755\) −4.64740e11 −1.43028
\(756\) −4.94880e9 −0.0151500
\(757\) 3.94309e11i 1.20075i 0.799718 + 0.600376i \(0.204982\pi\)
−0.799718 + 0.600376i \(0.795018\pi\)
\(758\) 3.09452e11i 0.937383i
\(759\) 1.55470e11i 0.468468i
\(760\) 4.99245e11i 1.49644i
\(761\) 2.99271e11i 0.892330i 0.894951 + 0.446165i \(0.147210\pi\)
−0.894951 + 0.446165i \(0.852790\pi\)
\(762\) −1.48749e11 −0.441198
\(763\) 4.17539e10i 0.123197i
\(764\) 1.68608e10i 0.0494885i
\(765\) 2.02512e11i 0.591297i
\(766\) −1.48937e11 −0.432602
\(767\) 1.64121e11 0.474223
\(768\) 1.13202e11i 0.325394i
\(769\) −2.06441e11 −0.590324 −0.295162 0.955447i \(-0.595374\pi\)
−0.295162 + 0.955447i \(0.595374\pi\)
\(770\) 2.63362e10i 0.0749186i
\(771\) 3.84252e11 1.08742
\(772\) 6.23093e10 0.175422
\(773\) 5.73479e11i 1.60620i 0.595844 + 0.803100i \(0.296818\pi\)
−0.595844 + 0.803100i \(0.703182\pi\)
\(774\) 2.03640e11 + 8.91247e9i 0.567413 + 0.0248333i
\(775\) 1.11083e11 0.307923
\(776\) 4.69737e11i 1.29541i
\(777\) 2.25585e10i 0.0618907i
\(778\) −1.18361e11 −0.323066
\(779\) 1.95019e10i 0.0529574i
\(780\) 4.79804e10 0.129624
\(781\) 6.21749e10i 0.167113i
\(782\) 2.43116e11i