Properties

Label 43.7.b.b.42.19
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 42.19
Root \(13.7504i\) 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.42.2

$q$-expansion

\(f(q)\) \(=\) \(q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +O(q^{10})\) \(q+13.7504i q^{2} +14.6903i q^{3} -125.075 q^{4} -125.525i q^{5} -201.998 q^{6} -485.131i q^{7} -839.807i q^{8} +513.196 q^{9} +1726.02 q^{10} -2195.16 q^{11} -1837.38i q^{12} -2487.29 q^{13} +6670.76 q^{14} +1844.00 q^{15} +3542.93 q^{16} -3215.24 q^{17} +7056.67i q^{18} -828.174i q^{19} +15700.0i q^{20} +7126.70 q^{21} -30184.4i q^{22} +11950.0 q^{23} +12337.0 q^{24} -131.499 q^{25} -34201.4i q^{26} +18248.2i q^{27} +60677.6i q^{28} -39650.8i q^{29} +25355.8i q^{30} -41667.8 q^{31} -5030.75i q^{32} -32247.4i q^{33} -44211.0i q^{34} -60896.0 q^{35} -64187.9 q^{36} +67988.4i q^{37} +11387.8 q^{38} -36539.0i q^{39} -105417. q^{40} +15649.2 q^{41} +97995.4i q^{42} +(-67467.7 - 42065.1i) q^{43} +274559. q^{44} -64418.8i q^{45} +164318. i q^{46} +97342.7 q^{47} +52046.6i q^{48} -117703. q^{49} -1808.17i q^{50} -47232.8i q^{51} +311098. q^{52} -74224.0 q^{53} -250921. q^{54} +275547. i q^{55} -407416. q^{56} +12166.1 q^{57} +545216. q^{58} -159976. q^{59} -230637. q^{60} +45475.1i q^{61} -572950. i q^{62} -248967. i q^{63} +295923. q^{64} +312217. i q^{65} +443417. q^{66} +59219.5 q^{67} +402146. q^{68} +175549. i q^{69} -837347. i q^{70} -450995. i q^{71} -430985. i q^{72} -102717. i q^{73} -934870. q^{74} -1931.76i q^{75} +103584. i q^{76} +1.06494e6i q^{77} +502428. q^{78} +2661.35 q^{79} -444726. i q^{80} +106049. q^{81} +215183. i q^{82} -657618. q^{83} -891371. q^{84} +403593. i q^{85} +(578414. - 927711. i) q^{86} +582481. q^{87} +1.84351e6i q^{88} +680976. i q^{89} +885788. q^{90} +1.20666e6i q^{91} -1.49464e6 q^{92} -612111. i q^{93} +1.33851e6i q^{94} -103956. q^{95} +73903.2 q^{96} +1.25659e6 q^{97} -1.61846e6i q^{98} -1.12654e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.7504i 1.71881i 0.511299 + 0.859403i \(0.329165\pi\)
−0.511299 + 0.859403i \(0.670835\pi\)
\(3\) 14.6903i 0.544084i 0.962285 + 0.272042i \(0.0876990\pi\)
−0.962285 + 0.272042i \(0.912301\pi\)
\(4\) −125.075 −1.95429
\(5\) 125.525i 1.00420i −0.864810 0.502100i \(-0.832561\pi\)
0.864810 0.502100i \(-0.167439\pi\)
\(6\) −201.998 −0.935176
\(7\) 485.131i 1.41437i −0.707026 0.707187i \(-0.749964\pi\)
0.707026 0.707187i \(-0.250036\pi\)
\(8\) 839.807i 1.64025i
\(9\) 513.196 0.703972
\(10\) 1726.02 1.72602
\(11\) −2195.16 −1.64925 −0.824626 0.565678i \(-0.808615\pi\)
−0.824626 + 0.565678i \(0.808615\pi\)
\(12\) 1837.38i 1.06330i
\(13\) −2487.29 −1.13213 −0.566066 0.824360i \(-0.691535\pi\)
−0.566066 + 0.824360i \(0.691535\pi\)
\(14\) 6670.76 2.43104
\(15\) 1844.00 0.546369
\(16\) 3542.93 0.864973
\(17\) −3215.24 −0.654435 −0.327218 0.944949i \(-0.606111\pi\)
−0.327218 + 0.944949i \(0.606111\pi\)
\(18\) 7056.67i 1.20999i
\(19\) 828.174i 0.120743i −0.998176 0.0603713i \(-0.980772\pi\)
0.998176 0.0603713i \(-0.0192285\pi\)
\(20\) 15700.0i 1.96250i
\(21\) 7126.70 0.769539
\(22\) 30184.4i 2.83475i
\(23\) 11950.0 0.982164 0.491082 0.871113i \(-0.336602\pi\)
0.491082 + 0.871113i \(0.336602\pi\)
\(24\) 12337.0 0.892433
\(25\) −131.499 −0.00841593
\(26\) 34201.4i 1.94591i
\(27\) 18248.2i 0.927105i
\(28\) 60677.6i 2.76411i
\(29\) 39650.8i 1.62576i −0.582428 0.812882i \(-0.697897\pi\)
0.582428 0.812882i \(-0.302103\pi\)
\(30\) 25355.8i 0.939103i
\(31\) −41667.8 −1.39867 −0.699335 0.714794i \(-0.746520\pi\)
−0.699335 + 0.714794i \(0.746520\pi\)
\(32\) 5030.75i 0.153526i
\(33\) 32247.4i 0.897333i
\(34\) 44211.0i 1.12485i
\(35\) −60896.0 −1.42031
\(36\) −64187.9 −1.37577
\(37\) 67988.4i 1.34224i 0.741350 + 0.671119i \(0.234186\pi\)
−0.741350 + 0.671119i \(0.765814\pi\)
\(38\) 11387.8 0.207533
\(39\) 36539.0i 0.615975i
\(40\) −105417. −1.64714
\(41\) 15649.2 0.227060 0.113530 0.993535i \(-0.463784\pi\)
0.113530 + 0.993535i \(0.463784\pi\)
\(42\) 97995.4i 1.32269i
\(43\) −67467.7 42065.1i −0.848576 0.529074i
\(44\) 274559. 3.22313
\(45\) 64418.8i 0.706928i
\(46\) 164318.i 1.68815i
\(47\) 97342.7 0.937583 0.468792 0.883309i \(-0.344690\pi\)
0.468792 + 0.883309i \(0.344690\pi\)
\(48\) 52046.6i 0.470618i
\(49\) −117703. −1.00046
\(50\) 1808.17i 0.0144654i
\(51\) 47232.8i 0.356068i
\(52\) 311098. 2.21252
\(53\) −74224.0 −0.498559 −0.249280 0.968432i \(-0.580194\pi\)
−0.249280 + 0.968432i \(0.580194\pi\)
\(54\) −250921. −1.59351
\(55\) 275547.i 1.65618i
\(56\) −407416. −2.31993
\(57\) 12166.1 0.0656942
\(58\) 545216. 2.79437
\(59\) −159976. −0.778933 −0.389466 0.921041i \(-0.627341\pi\)
−0.389466 + 0.921041i \(0.627341\pi\)
\(60\) −230637. −1.06777
\(61\) 45475.1i 0.200347i 0.994970 + 0.100174i \(0.0319399\pi\)
−0.994970 + 0.100174i \(0.968060\pi\)
\(62\) 572950.i 2.40404i
\(63\) 248967.i 0.995681i
\(64\) 295923. 1.12886
\(65\) 312217.i 1.13689i
\(66\) 443417. 1.54234
\(67\) 59219.5 0.196898 0.0984488 0.995142i \(-0.468612\pi\)
0.0984488 + 0.995142i \(0.468612\pi\)
\(68\) 402146. 1.27896
\(69\) 175549.i 0.534380i
\(70\) 837347.i 2.44124i
\(71\) 450995.i 1.26008i −0.776564 0.630039i \(-0.783039\pi\)
0.776564 0.630039i \(-0.216961\pi\)
\(72\) 430985.i 1.15469i
\(73\) 102717.i 0.264042i −0.991247 0.132021i \(-0.957853\pi\)
0.991247 0.132021i \(-0.0421466\pi\)
\(74\) −934870. −2.30705
\(75\) 1931.76i 0.00457898i
\(76\) 103584.i 0.235967i
\(77\) 1.06494e6i 2.33266i
\(78\) 502428. 1.05874
\(79\) 2661.35 0.00539784 0.00269892 0.999996i \(-0.499141\pi\)
0.00269892 + 0.999996i \(0.499141\pi\)
\(80\) 444726.i 0.868605i
\(81\) 106049. 0.199549
\(82\) 215183.i 0.390271i
\(83\) −657618. −1.15011 −0.575055 0.818114i \(-0.695020\pi\)
−0.575055 + 0.818114i \(0.695020\pi\)
\(84\) −891371. −1.50391
\(85\) 403593.i 0.657183i
\(86\) 578414. 927711.i 0.909376 1.45854i
\(87\) 582481. 0.884553
\(88\) 1.84351e6i 2.70518i
\(89\) 680976.i 0.965966i 0.875630 + 0.482983i \(0.160447\pi\)
−0.875630 + 0.482983i \(0.839553\pi\)
\(90\) 885788. 1.21507
\(91\) 1.20666e6i 1.60126i
\(92\) −1.49464e6 −1.91944
\(93\) 612111.i 0.760994i
\(94\) 1.33851e6i 1.61152i
\(95\) −103956. −0.121250
\(96\) 73903.2 0.0835313
\(97\) 1.25659e6 1.37682 0.688410 0.725322i \(-0.258309\pi\)
0.688410 + 0.725322i \(0.258309\pi\)
\(98\) 1.61846e6i 1.71959i
\(99\) −1.12654e6 −1.16103
\(100\) 16447.2 0.0164472
\(101\) 667424. 0.647796 0.323898 0.946092i \(-0.395007\pi\)
0.323898 + 0.946092i \(0.395007\pi\)
\(102\) 649472. 0.612012
\(103\) 946502. 0.866184 0.433092 0.901350i \(-0.357423\pi\)
0.433092 + 0.901350i \(0.357423\pi\)
\(104\) 2.08885e6i 1.85698i
\(105\) 894579.i 0.772771i
\(106\) 1.02061e6i 0.856927i
\(107\) −1.85782e6 −1.51654 −0.758269 0.651942i \(-0.773954\pi\)
−0.758269 + 0.651942i \(0.773954\pi\)
\(108\) 2.28239e6i 1.81184i
\(109\) −933301. −0.720680 −0.360340 0.932821i \(-0.617339\pi\)
−0.360340 + 0.932821i \(0.617339\pi\)
\(110\) −3.78889e6 −2.84665
\(111\) −998768. −0.730290
\(112\) 1.71878e6i 1.22340i
\(113\) 618344.i 0.428543i −0.976774 0.214272i \(-0.931262\pi\)
0.976774 0.214272i \(-0.0687377\pi\)
\(114\) 167289.i 0.112916i
\(115\) 1.50002e6i 0.986288i
\(116\) 4.95931e6i 3.17722i
\(117\) −1.27647e6 −0.796989
\(118\) 2.19975e6i 1.33883i
\(119\) 1.55981e6i 0.925616i
\(120\) 1.54860e6i 0.896181i
\(121\) 3.04715e6 1.72003
\(122\) −625303. −0.344358
\(123\) 229891.i 0.123540i
\(124\) 5.21159e6 2.73341
\(125\) 1.94482e6i 0.995748i
\(126\) 3.42341e6 1.71138
\(127\) −1.93152e6 −0.942951 −0.471475 0.881879i \(-0.656278\pi\)
−0.471475 + 0.881879i \(0.656278\pi\)
\(128\) 3.74710e6i 1.78676i
\(129\) 617948. 991119.i 0.287861 0.461697i
\(130\) −4.29313e6 −1.95409
\(131\) 3.53636e6i 1.57305i −0.617560 0.786524i \(-0.711879\pi\)
0.617560 0.786524i \(-0.288121\pi\)
\(132\) 4.03334e6i 1.75365i
\(133\) −401772. −0.170775
\(134\) 814295.i 0.338429i
\(135\) 2.29060e6 0.930998
\(136\) 2.70018e6i 1.07344i
\(137\) 4.20321e6i 1.63463i −0.576191 0.817315i \(-0.695461\pi\)
0.576191 0.817315i \(-0.304539\pi\)
\(138\) −2.41387e6 −0.918496
\(139\) 818972. 0.304947 0.152474 0.988308i \(-0.451276\pi\)
0.152474 + 0.988308i \(0.451276\pi\)
\(140\) 7.61655e6 2.77571
\(141\) 1.42999e6i 0.510124i
\(142\) 6.20139e6 2.16583
\(143\) 5.45999e6 1.86717
\(144\) 1.81822e6 0.608917
\(145\) −4.97716e6 −1.63259
\(146\) 1.41240e6 0.453837
\(147\) 1.72908e6i 0.544332i
\(148\) 8.50363e6i 2.62313i
\(149\) 2.95549e6i 0.893452i 0.894671 + 0.446726i \(0.147410\pi\)
−0.894671 + 0.446726i \(0.852590\pi\)
\(150\) 26562.5 0.00787038
\(151\) 6.37224e6i 1.85081i 0.378983 + 0.925404i \(0.376274\pi\)
−0.378983 + 0.925404i \(0.623726\pi\)
\(152\) −695506. −0.198048
\(153\) −1.65005e6 −0.460704
\(154\) −1.46434e7 −4.00939
\(155\) 5.23034e6i 1.40454i
\(156\) 4.57011e6i 1.20380i
\(157\) 412869.i 0.106687i −0.998576 0.0533437i \(-0.983012\pi\)
0.998576 0.0533437i \(-0.0169879\pi\)
\(158\) 36594.7i 0.00927784i
\(159\) 1.09037e6i 0.271258i
\(160\) −631485. −0.154171
\(161\) 5.79730e6i 1.38915i
\(162\) 1.45822e6i 0.342986i
\(163\) 3.12906e6i 0.722522i −0.932465 0.361261i \(-0.882346\pi\)
0.932465 0.361261i \(-0.117654\pi\)
\(164\) −1.95732e6 −0.443741
\(165\) −4.04786e6 −0.901101
\(166\) 9.04255e6i 1.97682i
\(167\) −2.61032e6 −0.560459 −0.280229 0.959933i \(-0.590411\pi\)
−0.280229 + 0.959933i \(0.590411\pi\)
\(168\) 5.98505e6i 1.26223i
\(169\) 1.35981e6 0.281721
\(170\) −5.54958e6 −1.12957
\(171\) 425015.i 0.0849995i
\(172\) 8.43851e6 + 5.26129e6i 1.65837 + 1.03397i
\(173\) 1.00269e7 1.93654 0.968270 0.249906i \(-0.0803996\pi\)
0.968270 + 0.249906i \(0.0803996\pi\)
\(174\) 8.00937e6i 1.52038i
\(175\) 63794.2i 0.0119033i
\(176\) −7.77728e6 −1.42656
\(177\) 2.35010e6i 0.423805i
\(178\) −9.36373e6 −1.66031
\(179\) 3.42463e6i 0.597111i −0.954392 0.298555i \(-0.903495\pi\)
0.954392 0.298555i \(-0.0965047\pi\)
\(180\) 8.05718e6i 1.38155i
\(181\) 6.31210e6 1.06448 0.532241 0.846593i \(-0.321350\pi\)
0.532241 + 0.846593i \(0.321350\pi\)
\(182\) −1.65921e7 −2.75225
\(183\) −668041. −0.109006
\(184\) 1.00357e7i 1.61099i
\(185\) 8.53423e6 1.34787
\(186\) 8.41680e6 1.30800
\(187\) 7.05795e6 1.07933
\(188\) −1.21751e7 −1.83231
\(189\) 8.85276e6 1.31127
\(190\) 1.42945e6i 0.208405i
\(191\) 8.30483e6i 1.19187i 0.803031 + 0.595937i \(0.203219\pi\)
−0.803031 + 0.595937i \(0.796781\pi\)
\(192\) 4.34719e6i 0.614193i
\(193\) −4.83096e6 −0.671988 −0.335994 0.941864i \(-0.609072\pi\)
−0.335994 + 0.941864i \(0.609072\pi\)
\(194\) 1.72786e7i 2.36649i
\(195\) −4.58656e6 −0.618562
\(196\) 1.47216e7 1.95519
\(197\) −6.48202e6 −0.847835 −0.423918 0.905701i \(-0.639345\pi\)
−0.423918 + 0.905701i \(0.639345\pi\)
\(198\) 1.54905e7i 1.99558i
\(199\) 1.80084e6i 0.228515i 0.993451 + 0.114258i \(0.0364490\pi\)
−0.993451 + 0.114258i \(0.963551\pi\)
\(200\) 110434.i 0.0138042i
\(201\) 869951.i 0.107129i
\(202\) 9.17739e6i 1.11343i
\(203\) −1.92358e7 −2.29944
\(204\) 5.90763e6i 0.695862i
\(205\) 1.96436e6i 0.228013i
\(206\) 1.30148e7i 1.48880i
\(207\) 6.13268e6 0.691416
\(208\) −8.81230e6 −0.979263
\(209\) 1.81797e6i 0.199135i
\(210\) 1.23009e7 1.32824
\(211\) 9.42048e6i 1.00283i 0.865208 + 0.501413i \(0.167186\pi\)
−0.865208 + 0.501413i \(0.832814\pi\)
\(212\) 9.28356e6 0.974332
\(213\) 6.62525e6 0.685588
\(214\) 2.55459e7i 2.60663i
\(215\) −5.28022e6 + 8.46888e6i −0.531296 + 0.852139i
\(216\) 1.53250e7 1.52068
\(217\) 2.02143e7i 1.97824i
\(218\) 1.28333e7i 1.23871i
\(219\) 1.50894e6 0.143661
\(220\) 3.44640e7i 3.23666i
\(221\) 7.99724e6 0.740906
\(222\) 1.37335e7i 1.25523i
\(223\) 5.46983e6i 0.493241i 0.969112 + 0.246620i \(0.0793201\pi\)
−0.969112 + 0.246620i \(0.920680\pi\)
\(224\) −2.44057e6 −0.217144
\(225\) −67484.7 −0.00592458
\(226\) 8.50250e6 0.736583
\(227\) 2.03320e7i 1.73821i −0.494627 0.869106i \(-0.664695\pi\)
0.494627 0.869106i \(-0.335305\pi\)
\(228\) −1.52167e6 −0.128386
\(229\) 1.81978e7 1.51535 0.757676 0.652631i \(-0.226335\pi\)
0.757676 + 0.652631i \(0.226335\pi\)
\(230\) 2.06260e7 1.69524
\(231\) −1.56442e7 −1.26916
\(232\) −3.32990e7 −2.66666
\(233\) 2.02178e7i 1.59833i −0.601111 0.799166i \(-0.705275\pi\)
0.601111 0.799166i \(-0.294725\pi\)
\(234\) 1.75520e7i 1.36987i
\(235\) 1.22189e7i 0.941520i
\(236\) 2.00090e7 1.52226
\(237\) 39095.9i 0.00293688i
\(238\) −2.14481e7 −1.59096
\(239\) −6.37752e6 −0.467152 −0.233576 0.972339i \(-0.575043\pi\)
−0.233576 + 0.972339i \(0.575043\pi\)
\(240\) 6.53315e6 0.472595
\(241\) 6.37244e6i 0.455255i −0.973748 0.227627i \(-0.926903\pi\)
0.973748 0.227627i \(-0.0730968\pi\)
\(242\) 4.18996e7i 2.95641i
\(243\) 1.48608e7i 1.03568i
\(244\) 5.68779e6i 0.391538i
\(245\) 1.47746e7i 1.00466i
\(246\) −3.16110e6 −0.212341
\(247\) 2.05991e6i 0.136697i
\(248\) 3.49929e7i 2.29416i
\(249\) 9.66060e6i 0.625757i
\(250\) 2.67422e7 1.71150
\(251\) −2.68750e7 −1.69952 −0.849761 0.527168i \(-0.823254\pi\)
−0.849761 + 0.527168i \(0.823254\pi\)
\(252\) 3.11395e7i 1.94585i
\(253\) −2.62321e7 −1.61984
\(254\) 2.65593e7i 1.62075i
\(255\) −5.92889e6 −0.357563
\(256\) −3.25853e7 −1.94223
\(257\) 6.95161e6i 0.409530i 0.978811 + 0.204765i \(0.0656431\pi\)
−0.978811 + 0.204765i \(0.934357\pi\)
\(258\) 1.36283e7 + 8.49706e6i 0.793567 + 0.494777i
\(259\) 3.29832e7 1.89843
\(260\) 3.90505e7i 2.22181i
\(261\) 2.03486e7i 1.14449i
\(262\) 4.86265e7 2.70376
\(263\) 5.84259e6i 0.321172i −0.987022 0.160586i \(-0.948662\pi\)
0.987022 0.160586i \(-0.0513385\pi\)
\(264\) −2.70816e7 −1.47185
\(265\) 9.31696e6i 0.500653i
\(266\) 5.52455e6i 0.293530i
\(267\) −1.00037e7 −0.525567
\(268\) −7.40687e6 −0.384796
\(269\) 3.15131e6 0.161895 0.0809476 0.996718i \(-0.474205\pi\)
0.0809476 + 0.996718i \(0.474205\pi\)
\(270\) 3.14968e7i 1.60020i
\(271\) −1.99695e7 −1.00337 −0.501683 0.865051i \(-0.667286\pi\)
−0.501683 + 0.865051i \(0.667286\pi\)
\(272\) −1.13914e7 −0.566069
\(273\) −1.77262e7 −0.871219
\(274\) 5.77961e7 2.80961
\(275\) 288661. 0.0138800
\(276\) 2.19567e7i 1.04434i
\(277\) 2.84620e7i 1.33914i −0.742749 0.669570i \(-0.766479\pi\)
0.742749 0.669570i \(-0.233521\pi\)
\(278\) 1.12612e7i 0.524145i
\(279\) −2.13837e7 −0.984624
\(280\) 5.11408e7i 2.32967i
\(281\) 9.53964e6 0.429945 0.214973 0.976620i \(-0.431034\pi\)
0.214973 + 0.976620i \(0.431034\pi\)
\(282\) −1.96630e7 −0.876805
\(283\) 1.28327e7 0.566186 0.283093 0.959092i \(-0.408639\pi\)
0.283093 + 0.959092i \(0.408639\pi\)
\(284\) 5.64082e7i 2.46256i
\(285\) 1.52715e6i 0.0659700i
\(286\) 7.50774e7i 3.20930i
\(287\) 7.59189e6i 0.321147i
\(288\) 2.58176e6i 0.108078i
\(289\) −1.37998e7 −0.571715
\(290\) 6.84382e7i 2.80611i
\(291\) 1.84596e7i 0.749106i
\(292\) 1.28473e7i 0.516016i
\(293\) 4.00537e7 1.59235 0.796177 0.605063i \(-0.206852\pi\)
0.796177 + 0.605063i \(0.206852\pi\)
\(294\) 2.37757e7 0.935602
\(295\) 2.00810e7i 0.782204i
\(296\) 5.70971e7 2.20160
\(297\) 4.00576e7i 1.52903i
\(298\) −4.06394e7 −1.53567
\(299\) −2.97231e7 −1.11194
\(300\) 241614.i 0.00894867i
\(301\) −2.04071e7 + 3.27306e7i −0.748309 + 1.20020i
\(302\) −8.76212e7 −3.18118
\(303\) 9.80465e6i 0.352455i
\(304\) 2.93416e6i 0.104439i
\(305\) 5.70825e6 0.201189
\(306\) 2.26889e7i 0.791861i
\(307\) 2.94541e7 1.01796 0.508980 0.860779i \(-0.330023\pi\)
0.508980 + 0.860779i \(0.330023\pi\)
\(308\) 1.33197e8i 4.55871i
\(309\) 1.39044e7i 0.471277i
\(310\) −7.19195e7 −2.41414
\(311\) 2.31664e7 0.770154 0.385077 0.922884i \(-0.374175\pi\)
0.385077 + 0.922884i \(0.374175\pi\)
\(312\) −3.06857e7 −1.01035
\(313\) 1.96712e7i 0.641501i −0.947164 0.320751i \(-0.896065\pi\)
0.947164 0.320751i \(-0.103935\pi\)
\(314\) 5.67713e6 0.183375
\(315\) −3.12515e7 −0.999862
\(316\) −332868. −0.0105490
\(317\) −1.88268e7 −0.591014 −0.295507 0.955341i \(-0.595489\pi\)
−0.295507 + 0.955341i \(0.595489\pi\)
\(318\) 1.49931e7 0.466241
\(319\) 8.70396e7i 2.68130i
\(320\) 3.71457e7i 1.13360i
\(321\) 2.72919e7i 0.825124i
\(322\) 7.97155e7 2.38768
\(323\) 2.66278e6i 0.0790182i
\(324\) −1.32640e7 −0.389978
\(325\) 327076. 0.00952794
\(326\) 4.30260e7 1.24188
\(327\) 1.37105e7i 0.392111i
\(328\) 1.31423e7i 0.372434i
\(329\) 4.72239e7i 1.32609i
\(330\) 5.56599e7i 1.54882i
\(331\) 2.14243e7i 0.590777i 0.955377 + 0.295388i \(0.0954490\pi\)
−0.955377 + 0.295388i \(0.904551\pi\)
\(332\) 8.22515e7 2.24766
\(333\) 3.48913e7i 0.944898i
\(334\) 3.58930e7i 0.963320i
\(335\) 7.43352e6i 0.197724i
\(336\) 2.52494e7 0.665631
\(337\) 8.03689e6 0.209990 0.104995 0.994473i \(-0.466517\pi\)
0.104995 + 0.994473i \(0.466517\pi\)
\(338\) 1.86981e7i 0.484224i
\(339\) 9.08364e6 0.233164
\(340\) 5.04793e7i 1.28433i
\(341\) 9.14672e7 2.30676
\(342\) 5.84415e6 0.146098
\(343\) 26029.3i 0.000645029i
\(344\) −3.53266e7 + 5.66598e7i −0.867813 + 1.39187i
\(345\) 2.20357e7 0.536624
\(346\) 1.37874e8i 3.32854i
\(347\) 8.81380e6i 0.210948i 0.994422 + 0.105474i \(0.0336359\pi\)
−0.994422 + 0.105474i \(0.966364\pi\)
\(348\) −7.28537e7 −1.72868
\(349\) 3.08592e7i 0.725953i 0.931798 + 0.362976i \(0.118239\pi\)
−0.931798 + 0.362976i \(0.881761\pi\)
\(350\) −877198. −0.0204594
\(351\) 4.53886e7i 1.04960i
\(352\) 1.10433e7i 0.253204i
\(353\) 1.32889e7 0.302111 0.151055 0.988525i \(-0.451733\pi\)
0.151055 + 0.988525i \(0.451733\pi\)
\(354\) 3.23149e7 0.728439
\(355\) −5.66112e7 −1.26537
\(356\) 8.51730e7i 1.88778i
\(357\) −2.29141e7 −0.503613
\(358\) 4.70902e7 1.02632
\(359\) −1.94769e7 −0.420956 −0.210478 0.977599i \(-0.567502\pi\)
−0.210478 + 0.977599i \(0.567502\pi\)
\(360\) −5.40994e7 −1.15954
\(361\) 4.63600e7 0.985421
\(362\) 8.67943e7i 1.82964i
\(363\) 4.47634e7i 0.935844i
\(364\) 1.50923e8i 3.12933i
\(365\) −1.28935e7 −0.265151
\(366\) 9.18587e6i 0.187360i
\(367\) 6.75278e7 1.36611 0.683053 0.730369i \(-0.260652\pi\)
0.683053 + 0.730369i \(0.260652\pi\)
\(368\) 4.23380e7 0.849545
\(369\) 8.03109e6 0.159844
\(370\) 1.17350e8i 2.31673i
\(371\) 3.60083e7i 0.705150i
\(372\) 7.65597e7i 1.48721i
\(373\) 8.90560e7i 1.71608i −0.513585 0.858039i \(-0.671683\pi\)
0.513585 0.858039i \(-0.328317\pi\)
\(374\) 9.70500e7i 1.85516i
\(375\) 2.85699e7 0.541771
\(376\) 8.17491e7i 1.53787i
\(377\) 9.86231e7i 1.84058i
\(378\) 1.21729e8i 2.25382i
\(379\) −1.05536e8 −1.93857 −0.969284 0.245942i \(-0.920903\pi\)
−0.969284 + 0.245942i \(0.920903\pi\)
\(380\) 1.30023e7 0.236958
\(381\) 2.83746e7i 0.513045i
\(382\) −1.14195e8 −2.04860
\(383\) 1.03036e8i 1.83397i −0.398920 0.916986i \(-0.630615\pi\)
0.398920 0.916986i \(-0.369385\pi\)
\(384\) −5.50460e7 −0.972147
\(385\) 1.33676e8 2.34246
\(386\) 6.64279e7i 1.15502i
\(387\) −3.46241e7 2.15876e7i −0.597374 0.372454i
\(388\) −1.57167e8 −2.69071
\(389\) 1.57030e7i 0.266768i −0.991064 0.133384i \(-0.957416\pi\)
0.991064 0.133384i \(-0.0425843\pi\)
\(390\) 6.30672e7i 1.06319i
\(391\) −3.84221e7 −0.642762
\(392\) 9.88475e7i 1.64100i
\(393\) 5.19500e7 0.855871
\(394\) 8.91306e7i 1.45726i
\(395\) 334065.i 0.00542051i
\(396\) 1.40902e8 2.26899
\(397\) −7.90324e7 −1.26309 −0.631544 0.775340i \(-0.717578\pi\)
−0.631544 + 0.775340i \(0.717578\pi\)
\(398\) −2.47623e7 −0.392774
\(399\) 5.90215e6i 0.0929162i
\(400\) −465892. −0.00727956
\(401\) −4.44435e7 −0.689247 −0.344623 0.938741i \(-0.611993\pi\)
−0.344623 + 0.938741i \(0.611993\pi\)
\(402\) −1.19622e7 −0.184134
\(403\) 1.03640e8 1.58348
\(404\) −8.34780e7 −1.26598
\(405\) 1.33117e7i 0.200387i
\(406\) 2.64501e8i 3.95229i
\(407\) 1.49245e8i 2.21369i
\(408\) −3.96664e7 −0.584039
\(409\) 7.23937e7i 1.05811i 0.848587 + 0.529055i \(0.177454\pi\)
−0.848587 + 0.529055i \(0.822546\pi\)
\(410\) 2.70108e7 0.391910
\(411\) 6.17464e7 0.889377
\(412\) −1.18384e8 −1.69278
\(413\) 7.76095e7i 1.10170i
\(414\) 8.43271e7i 1.18841i
\(415\) 8.25475e7i 1.15494i
\(416\) 1.25130e7i 0.173812i
\(417\) 1.20309e7i 0.165917i
\(418\) −2.49979e7 −0.342275
\(419\) 2.13499e7i 0.290238i −0.989414 0.145119i \(-0.953644\pi\)
0.989414 0.145119i \(-0.0463564\pi\)
\(420\) 1.11889e8i 1.51022i
\(421\) 7.59636e7i 1.01803i −0.860758 0.509014i \(-0.830010\pi\)
0.860758 0.509014i \(-0.169990\pi\)
\(422\) −1.29536e8 −1.72366
\(423\) 4.99558e7 0.660032
\(424\) 6.23338e7i 0.817761i
\(425\) 422801. 0.00550768
\(426\) 9.11002e7i 1.17839i
\(427\) 2.20613e7 0.283366
\(428\) 2.32367e8 2.96376
\(429\) 8.02088e7i 1.01590i
\(430\) −1.16451e8 7.26054e7i −1.46466 0.913195i
\(431\) −2.01234e7 −0.251344 −0.125672 0.992072i \(-0.540109\pi\)
−0.125672 + 0.992072i \(0.540109\pi\)
\(432\) 6.46521e7i 0.801921i
\(433\) 2.28719e7i 0.281733i 0.990029 + 0.140866i \(0.0449888\pi\)
−0.990029 + 0.140866i \(0.955011\pi\)
\(434\) −2.77956e8 −3.40022
\(435\) 7.31158e7i 0.888267i
\(436\) 1.16733e8 1.40842
\(437\) 9.89667e6i 0.118589i
\(438\) 2.07486e7i 0.246926i
\(439\) −1.12643e8 −1.33141 −0.665705 0.746215i \(-0.731869\pi\)
−0.665705 + 0.746215i \(0.731869\pi\)
\(440\) 2.31406e8 2.71654
\(441\) −6.04045e7 −0.704293
\(442\) 1.09966e8i 1.27347i
\(443\) −1.00154e8 −1.15201 −0.576007 0.817445i \(-0.695390\pi\)
−0.576007 + 0.817445i \(0.695390\pi\)
\(444\) 1.24921e8 1.42720
\(445\) 8.54794e7 0.970022
\(446\) −7.52126e7 −0.847785
\(447\) −4.34170e7 −0.486113
\(448\) 1.43561e8i 1.59662i
\(449\) 2.24376e7i 0.247878i −0.992290 0.123939i \(-0.960447\pi\)
0.992290 0.123939i \(-0.0395527\pi\)
\(450\) 927945.i 0.0101832i
\(451\) −3.43524e7 −0.374479
\(452\) 7.73392e7i 0.837500i
\(453\) −9.36100e7 −1.00700
\(454\) 2.79574e8 2.98765
\(455\) 1.51466e8 1.60798
\(456\) 1.02172e7i 0.107755i
\(457\) 2.72646e7i 0.285660i −0.989747 0.142830i \(-0.954380\pi\)
0.989747 0.142830i \(-0.0456203\pi\)
\(458\) 2.50229e8i 2.60460i
\(459\) 5.86723e7i 0.606730i
\(460\) 1.87615e8i 1.92750i
\(461\) 1.10894e8 1.13189 0.565945 0.824443i \(-0.308511\pi\)
0.565945 + 0.824443i \(0.308511\pi\)
\(462\) 2.15115e8i 2.18145i
\(463\) 4.40459e6i 0.0443775i −0.999754 0.0221887i \(-0.992937\pi\)
0.999754 0.0221887i \(-0.00706348\pi\)
\(464\) 1.40480e8i 1.40624i
\(465\) −7.68352e7 −0.764190
\(466\) 2.78004e8 2.74722
\(467\) 1.58915e7i 0.156032i 0.996952 + 0.0780160i \(0.0248585\pi\)
−0.996952 + 0.0780160i \(0.975141\pi\)
\(468\) 1.59654e8 1.55755
\(469\) 2.87292e7i 0.278487i
\(470\) 1.68016e8 1.61829
\(471\) 6.06516e6 0.0580470
\(472\) 1.34349e8i 1.27764i
\(473\) 1.48102e8 + 9.23394e7i 1.39952 + 0.872577i
\(474\) −537586. −0.00504793
\(475\) 108904.i 0.00101616i
\(476\) 1.95093e8i 1.80893i
\(477\) −3.80915e7 −0.350972
\(478\) 8.76938e7i 0.802944i
\(479\) −5.66316e7 −0.515290 −0.257645 0.966240i \(-0.582947\pi\)
−0.257645 + 0.966240i \(0.582947\pi\)
\(480\) 9.27669e6i 0.0838821i
\(481\) 1.69107e8i 1.51959i
\(482\) 8.76239e7 0.782495
\(483\) 8.51640e7 0.755814
\(484\) −3.81121e8 −3.36145
\(485\) 1.57733e8i 1.38260i
\(486\) −2.04343e8 −1.78013
\(487\) −8.26005e7 −0.715147 −0.357574 0.933885i \(-0.616396\pi\)
−0.357574 + 0.933885i \(0.616396\pi\)
\(488\) 3.81903e7 0.328619
\(489\) 4.59668e7 0.393113
\(490\) −2.03158e8 −1.72681
\(491\) 1.04983e8i 0.886898i −0.896300 0.443449i \(-0.853755\pi\)
0.896300 0.443449i \(-0.146245\pi\)
\(492\) 2.87535e7i 0.241433i
\(493\) 1.27487e8i 1.06396i
\(494\) −2.83247e7 −0.234955
\(495\) 1.41409e8i 1.16590i
\(496\) −1.47626e8 −1.20981
\(497\) −2.18792e8 −1.78222
\(498\) 1.32838e8 1.07556
\(499\) 9.42511e7i 0.758551i 0.925284 + 0.379275i \(0.123827\pi\)
−0.925284 + 0.379275i \(0.876173\pi\)
\(500\) 2.43248e8i 1.94598i
\(501\) 3.83463e7i 0.304937i
\(502\) 3.69543e8i 2.92115i
\(503\) 9.27104e6i 0.0728492i −0.999336 0.0364246i \(-0.988403\pi\)
0.999336 0.0364246i \(-0.0115969\pi\)
\(504\) −2.09084e8 −1.63316
\(505\) 8.37784e7i 0.650516i
\(506\) 3.60703e8i 2.78418i
\(507\) 1.99761e7i 0.153280i
\(508\) 2.41585e8 1.84280
\(509\) −2.93942e7 −0.222899 −0.111450 0.993770i \(-0.535549\pi\)
−0.111450 + 0.993770i \(0.535549\pi\)
\(510\) 8.15249e7i 0.614582i
\(511\) −4.98311e7 −0.373454
\(512\) 2.08248e8i 1.55157i
\(513\) 1.51127e7 0.111941
\(514\) −9.55878e7 −0.703903
\(515\) 1.18810e8i 0.869821i
\(516\) −7.72898e7 + 1.23964e8i −0.562565 + 0.902291i
\(517\) −2.13682e8 −1.54631
\(518\) 4.53534e8i 3.26303i
\(519\) 1.47297e8i 1.05364i
\(520\) 2.62202e8 1.86477
\(521\) 4.15492e7i 0.293798i −0.989151 0.146899i \(-0.953071\pi\)
0.989151 0.146899i \(-0.0469293\pi\)
\(522\) 2.79802e8 1.96716
\(523\) 1.31954e8i 0.922397i 0.887297 + 0.461199i \(0.152580\pi\)
−0.887297 + 0.461199i \(0.847420\pi\)
\(524\) 4.42309e8i 3.07420i
\(525\) −937154. −0.00647639
\(526\) 8.03382e7 0.552033
\(527\) 1.33972e8 0.915338
\(528\) 1.14250e8i 0.776169i
\(529\) −5.23372e6 −0.0353544
\(530\) −1.28112e8 −0.860525
\(531\) −8.20992e7 −0.548347
\(532\) 5.02516e7 0.333745
\(533\) −3.89241e7 −0.257061
\(534\) 1.37556e8i 0.903348i
\(535\) 2.33203e8i 1.52291i
\(536\) 4.97329e7i 0.322961i
\(537\) 5.03088e7 0.324879
\(538\) 4.33319e7i 0.278267i
\(539\) 2.58376e8 1.65000
\(540\) −2.86497e8 −1.81944
\(541\) −6.45179e7 −0.407463 −0.203732 0.979027i \(-0.565307\pi\)
−0.203732 + 0.979027i \(0.565307\pi\)
\(542\) 2.74590e8i 1.72459i
\(543\) 9.27266e7i 0.579168i
\(544\) 1.61751e7i 0.100473i
\(545\) 1.17153e8i 0.723706i
\(546\) 2.43743e8i 1.49746i
\(547\) 1.36234e8 0.832383 0.416192 0.909277i \(-0.363365\pi\)
0.416192 + 0.909277i \(0.363365\pi\)
\(548\) 5.25716e8i 3.19455i
\(549\) 2.33376e7i 0.141039i
\(550\) 3.96921e6i 0.0238570i
\(551\) −3.28377e7 −0.196299
\(552\) 1.47427e8 0.876515
\(553\) 1.29110e6i 0.00763457i
\(554\) 3.91365e8 2.30172
\(555\) 1.25370e8i 0.733357i
\(556\) −1.02433e8 −0.595957
\(557\) −2.82425e8 −1.63432 −0.817162 0.576409i \(-0.804454\pi\)
−0.817162 + 0.576409i \(0.804454\pi\)
\(558\) 2.94036e8i 1.69238i
\(559\) 1.67812e8 + 1.04628e8i 0.960699 + 0.598982i
\(560\) −2.15750e8 −1.22853
\(561\) 1.03683e8i 0.587246i
\(562\) 1.31174e8i 0.738992i
\(563\) −5.27513e7 −0.295602 −0.147801 0.989017i \(-0.547220\pi\)
−0.147801 + 0.989017i \(0.547220\pi\)
\(564\) 1.78856e8i 0.996933i
\(565\) −7.76175e7 −0.430343
\(566\) 1.76456e8i 0.973164i
\(567\) 5.14474e7i 0.282237i
\(568\) −3.78749e8 −2.06684
\(569\) −4.29511e7 −0.233151 −0.116576 0.993182i \(-0.537192\pi\)
−0.116576 + 0.993182i \(0.537192\pi\)
\(570\) 2.09990e7 0.113390
\(571\) 2.78688e8i 1.49696i −0.663157 0.748481i \(-0.730784\pi\)
0.663157 0.748481i \(-0.269216\pi\)
\(572\) −6.82908e8 −3.64900
\(573\) −1.22000e8 −0.648480
\(574\) 1.04392e8 0.551990
\(575\) −1.57141e6 −0.00826582
\(576\) 1.51866e8 0.794683
\(577\) 8.60563e7i 0.447976i 0.974592 + 0.223988i \(0.0719077\pi\)
−0.974592 + 0.223988i \(0.928092\pi\)
\(578\) 1.89754e8i 0.982667i
\(579\) 7.09682e7i 0.365618i
\(580\) 6.22517e8 3.19056
\(581\) 3.19031e8i 1.62669i
\(582\) −2.53828e8 −1.28757
\(583\) 1.62933e8 0.822250
\(584\) −8.62623e7 −0.433094
\(585\) 1.60228e8i 0.800336i
\(586\) 5.50756e8i 2.73695i
\(587\) 2.26249e8i 1.11859i −0.828967 0.559297i \(-0.811071\pi\)
0.828967 0.559297i \(-0.188929\pi\)
\(588\) 2.16265e8i 1.06379i
\(589\) 3.45081e7i 0.168879i
\(590\) −2.76123e8 −1.34446
\(591\) 9.52226e7i 0.461294i
\(592\) 2.40878e8i 1.16100i
\(593\) 1.03816e8i 0.497852i 0.968523 + 0.248926i \(0.0800775\pi\)
−0.968523 + 0.248926i \(0.919922\pi\)
\(594\) 5.50810e8 2.62811
\(595\) 1.95795e8 0.929503
\(596\) 3.69658e8i 1.74607i
\(597\) −2.64548e7 −0.124332
\(598\) 4.08706e8i 1.91121i
\(599\) 1.57390e8 0.732313 0.366156 0.930553i \(-0.380673\pi\)
0.366156 + 0.930553i \(0.380673\pi\)
\(600\) −1.62230e6 −0.00751066
\(601\) 7.90290e7i 0.364052i 0.983294 + 0.182026i \(0.0582655\pi\)
−0.983294 + 0.182026i \(0.941735\pi\)
\(602\) −4.50061e8 2.80606e8i −2.06292 1.28620i
\(603\) 3.03912e7 0.138610
\(604\) 7.97007e8i 3.61702i
\(605\) 3.82493e8i 1.72726i
\(606\) −1.34818e8 −0.605803
\(607\) 1.34486e8i 0.601326i 0.953730 + 0.300663i \(0.0972080\pi\)
−0.953730 + 0.300663i \(0.902792\pi\)
\(608\) −4.16634e6 −0.0185372
\(609\) 2.82579e8i 1.25109i
\(610\) 7.84910e7i 0.345804i
\(611\) −2.42120e8 −1.06147
\(612\) 2.06379e8 0.900352
\(613\) −2.33648e8 −1.01433 −0.507167 0.861848i \(-0.669307\pi\)
−0.507167 + 0.861848i \(0.669307\pi\)
\(614\) 4.05007e8i 1.74967i
\(615\) 2.88570e7 0.124058
\(616\) 8.94341e8 3.82614
\(617\) 3.91319e8 1.66600 0.833001 0.553272i \(-0.186621\pi\)
0.833001 + 0.553272i \(0.186621\pi\)
\(618\) −1.91191e8 −0.810034
\(619\) −5.31148e7 −0.223946 −0.111973 0.993711i \(-0.535717\pi\)
−0.111973 + 0.993711i \(0.535717\pi\)
\(620\) 6.54184e8i 2.74489i
\(621\) 2.18066e8i 0.910569i
\(622\) 3.18549e8i 1.32375i
\(623\) 3.30362e8 1.36624
\(624\) 1.29455e8i 0.532802i
\(625\) −2.46178e8 −1.00835
\(626\) 2.70488e8 1.10262
\(627\) −2.67065e7 −0.108346
\(628\) 5.16395e7i 0.208499i
\(629\) 2.18599e8i 0.878407i
\(630\) 4.29723e8i 1.71857i
\(631\) 1.17430e7i 0.0467403i −0.999727 0.0233702i \(-0.992560\pi\)
0.999727 0.0233702i \(-0.00743963\pi\)
\(632\) 2.23502e6i 0.00885380i
\(633\) −1.38389e8 −0.545622
\(634\) 2.58877e8i 1.01584i
\(635\) 2.42454e8i 0.946910i
\(636\) 1.36378e8i 0.530119i
\(637\) 2.92761e8 1.13265
\(638\) −1.19683e9 −4.60863
\(639\) 2.31449e8i 0.887059i
\(640\) 4.70355e8 1.79426
\(641\) 2.37189e8i 0.900575i 0.892884 + 0.450287i \(0.148678\pi\)
−0.892884 + 0.450287i \(0.851322\pi\)
\(642\) 3.75277e8 1.41823
\(643\) −2.27808e8 −0.856913 −0.428456 0.903562i \(-0.640942\pi\)
−0.428456 + 0.903562i \(0.640942\pi\)
\(644\) 7.25097e8i 2.71480i
\(645\) −1.24410e8 7.75679e7i −0.463635 0.289070i
\(646\) −3.66144e7 −0.135817
\(647\) 1.03798e8i 0.383243i −0.981469 0.191621i \(-0.938625\pi\)
0.981469 0.191621i \(-0.0613746\pi\)
\(648\) 8.90603e7i 0.327310i
\(649\) 3.51173e8 1.28466
\(650\) 4.49745e6i 0.0163767i
\(651\) −2.96954e8 −1.07633
\(652\) 3.91367e8i 1.41202i
\(653\) 1.89194e8i 0.679466i 0.940522 + 0.339733i \(0.110337\pi\)
−0.940522 + 0.339733i \(0.889663\pi\)
\(654\) 1.88525e8 0.673962
\(655\) −4.43901e8 −1.57965
\(656\) 5.54439e7 0.196400
\(657\) 5.27138e7i 0.185878i
\(658\) 6.49350e8 2.27930
\(659\) 2.37555e8 0.830056 0.415028 0.909809i \(-0.363772\pi\)
0.415028 + 0.909809i \(0.363772\pi\)
\(660\) 5.06285e8 1.76102
\(661\) −2.01381e8 −0.697292 −0.348646 0.937254i \(-0.613358\pi\)
−0.348646 + 0.937254i \(0.613358\pi\)
\(662\) −2.94594e8 −1.01543
\(663\) 1.17482e8i 0.403116i
\(664\) 5.52272e8i 1.88647i
\(665\) 5.04324e7i 0.171492i
\(666\) −4.79772e8 −1.62410
\(667\) 4.73826e8i 1.59677i
\(668\) 3.26485e8 1.09530
\(669\) −8.03533e7 −0.268365
\(670\) 1.02214e8 0.339850
\(671\) 9.98248e7i 0.330424i
\(672\) 3.58527e7i 0.118145i
\(673\) 2.44156e8i 0.800980i −0.916301 0.400490i \(-0.868840\pi\)
0.916301 0.400490i \(-0.131160\pi\)
\(674\) 1.10511e8i 0.360932i
\(675\) 2.39962e6i 0.00780245i
\(676\) −1.70079e8 −0.550566
\(677\) 1.87157e8i 0.603170i 0.953439 + 0.301585i \(0.0975157\pi\)
−0.953439 + 0.301585i \(0.902484\pi\)
\(678\) 1.24904e8i 0.400763i
\(679\) 6.09608e8i 1.94734i
\(680\) 3.38940e8 1.07794
\(681\) 2.98683e8 0.945733
\(682\) 1.25772e9i 3.96487i
\(683\) 1.98182e8 0.622016 0.311008 0.950407i \(-0.399333\pi\)
0.311008 + 0.950407i \(0.399333\pi\)
\(684\) 5.31587e7i 0.166114i
\(685\) −5.27608e8 −1.64149
\(686\) −357914. −0.00110868
\(687\) 2.67331e8i 0.824479i
\(688\) −2.39033e8 1.49034e8i −0.733995 0.457635i
\(689\) 1.84617e8 0.564435
\(690\) 3.03001e8i 0.922352i
\(691\) 1.03318e8i 0.313144i −0.987667 0.156572i \(-0.949956\pi\)
0.987667 0.156572i \(-0.0500443\pi\)
\(692\) −1.25411e9 −3.78457
\(693\) 5.46521e8i 1.64213i
\(694\) −1.21194e8 −0.362578
\(695\) 1.02801e8i 0.306228i
\(696\) 4.89171e8i 1.45089i
\(697\) −5.03158e7 −0.148596
\(698\) −4.24328e8 −1.24777
\(699\) 2.97006e8 0.869627
\(700\) 7.97905e6i 0.0232625i
\(701\) 5.94012e8 1.72441 0.862207 0.506556i \(-0.169082\pi\)
0.862207 + 0.506556i \(0.169082\pi\)
\(702\) 6.24114e8 1.80407
\(703\) 5.63062e7 0.162065
\(704\) −6.49596e8 −1.86177
\(705\) 1.79499e8 0.512266
\(706\) 1.82729e8i 0.519270i
\(707\) 3.23788e8i 0.916226i
\(708\) 2.93938e8i 0.828240i
\(709\) −7.07249e7 −0.198442 −0.0992210 0.995065i \(-0.531635\pi\)
−0.0992210 + 0.995065i \(0.531635\pi\)
\(710\) 7.78429e8i 2.17492i
\(711\) 1.36579e6 0.00379993
\(712\) 5.71888e8 1.58442
\(713\) −4.97929e8 −1.37372
\(714\) 3.15079e8i 0.865614i
\(715\) 6.85365e8i 1.87501i
\(716\) 4.28335e8i 1.16693i
\(717\) 9.36875e7i 0.254170i
\(718\) 2.67816e8i 0.723542i
\(719\) 3.82388e7 0.102877 0.0514385 0.998676i \(-0.483619\pi\)
0.0514385 + 0.998676i \(0.483619\pi\)
\(720\) 2.28231e8i 0.611474i
\(721\) 4.59177e8i 1.22511i
\(722\) 6.37471e8i 1.69375i
\(723\) 9.36129e7 0.247697
\(724\) −7.89486e8 −2.08031
\(725\) 5.21403e6i 0.0136823i
\(726\) −6.15517e8 −1.60853
\(727\) 6.69439e8i 1.74224i −0.491071 0.871119i \(-0.663395\pi\)
0.491071 0.871119i \(-0.336605\pi\)
\(728\) 1.01336e9 2.62646
\(729\) −1.41000e8 −0.363946
\(730\) 1.77292e8i 0.455743i
\(731\) 2.16925e8 + 1.35249e8i 0.555338 + 0.346245i
\(732\) 8.35552e7 0.213030
\(733\) 1.78625e8i 0.453555i −0.973947 0.226778i \(-0.927181\pi\)
0.973947 0.226778i \(-0.0728191\pi\)
\(734\) 9.28538e8i 2.34807i
\(735\) −2.17043e8 −0.546618
\(736\) 6.01174e7i 0.150788i
\(737\) −1.29996e8 −0.324734
\(738\) 1.10431e8i 0.274740i
\(739\) 6.78462e8i 1.68109i 0.541739 + 0.840547i \(0.317766\pi\)
−0.541739 + 0.840547i \(0.682234\pi\)
\(740\) −1.06742e9 −2.63414
\(741\) −3.02607e7 −0.0743744
\(742\) −4.95131e8 −1.21202
\(743\) 2.72990e7i 0.0665550i 0.999446 + 0.0332775i \(0.0105945\pi\)
−0.999446 + 0.0332775i \(0.989405\pi\)
\(744\) −5.14055e8 −1.24822
\(745\) 3.70988e8 0.897204
\(746\) 1.22456e9 2.94960
\(747\) −3.37487e8 −0.809646
\(748\) −8.82772e8 −2.10933
\(749\) 9.01287e8i 2.14495i
\(750\) 3.92850e8i 0.931199i
\(751\) 6.37092e8i 1.50412i 0.659095 + 0.752060i \(0.270940\pi\)
−0.659095 + 0.752060i \(0.729060\pi\)
\(752\) 3.44878e8 0.810984
\(753\) 3.94801e8i 0.924683i
\(754\) −1.35611e9 −3.16360
\(755\) 7.99875e8 1.85858
\(756\) −1.10726e9 −2.56261
\(757\) 1.20716e8i 0.278277i 0.990273 + 0.139139i \(0.0444334\pi\)
−0.990273 + 0.139139i \(0.955567\pi\)
\(758\) 1.45116e9i 3.33202i
\(759\) 3.85356e8i 0.881328i
\(760\) 8.73033e7i 0.198879i
\(761\) 4.57356e8i 1.03777i −0.854844 0.518885i \(-0.826347\pi\)
0.854844 0.518885i \(-0.173653\pi\)
\(762\) 3.90164e8 0.881824
\(763\) 4.52773e8i 1.01931i
\(764\) 1.03872e9i 2.32927i
\(765\) 2.07122e8i 0.462639i
\(766\) 1.41679e9 3.15224
\(767\) 3.97908e8 0.881854
\(768\) 4.78687e8i 1.05674i
\(769\) −3.76239e8 −0.827341 −0.413671 0.910427i \(-0.635754\pi\)
−0.413671 + 0.910427i \(0.635754\pi\)
\(770\) 1.83811e9i 4.02623i
\(771\) −1.02121e8 −0.222819
\(772\) 6.04232e8 1.31326
\(773\) 6.60610e8i 1.43023i −0.699006 0.715116i \(-0.746374\pi\)
0.699006 0.715116i \(-0.253626\pi\)
\(774\) 2.96840e8 4.76097e8i 0.640175 1.02677i
\(775\) 5.47927e6 0.0117711
\(776\) 1.05529e9i 2.25832i
\(777\) 4.84533e8i 1.03290i
\(778\) 2.15923e8 0.458522
\(779\) 1.29602e7i 0.0274158i
\(780\) 5.73663e8 1.20885
\(781\) 9.90005e8i 2.07819i
\(782\) 5.28321e8i 1.10478i
\(783\) 7.23555e8