Properties

Label 43.7.b.b.42.9
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 42.9
Root \(-2.98785i\) 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.42.12

$q$-expansion

\(f(q)\) \(=\) \(q-2.98785i q^{2} +41.6692i q^{3} +55.0727 q^{4} +126.319i q^{5} +124.502 q^{6} +69.5744i q^{7} -355.772i q^{8} -1007.32 q^{9} +O(q^{10})\) \(q-2.98785i q^{2} +41.6692i q^{3} +55.0727 q^{4} +126.319i q^{5} +124.502 q^{6} +69.5744i q^{7} -355.772i q^{8} -1007.32 q^{9} +377.422 q^{10} -100.569 q^{11} +2294.84i q^{12} -1723.32 q^{13} +207.878 q^{14} -5263.61 q^{15} +2461.66 q^{16} -115.904 q^{17} +3009.74i q^{18} +9219.04i q^{19} +6956.72i q^{20} -2899.11 q^{21} +300.485i q^{22} +6392.18 q^{23} +14824.7 q^{24} -331.444 q^{25} +5149.02i q^{26} -11597.6i q^{27} +3831.65i q^{28} -15483.4i q^{29} +15726.9i q^{30} -42010.7 q^{31} -30124.5i q^{32} -4190.63i q^{33} +346.304i q^{34} -8788.56 q^{35} -55476.1 q^{36} -38260.7i q^{37} +27545.1 q^{38} -71809.3i q^{39} +44940.7 q^{40} +78659.7 q^{41} +8662.12i q^{42} +(35141.8 + 71319.1i) q^{43} -5538.60 q^{44} -127244. i q^{45} -19098.9i q^{46} +138058. q^{47} +102576. i q^{48} +112808. q^{49} +990.307i q^{50} -4829.62i q^{51} -94907.8 q^{52} +54847.1 q^{53} -34651.8 q^{54} -12703.7i q^{55} +24752.6 q^{56} -384150. q^{57} -46262.1 q^{58} -177043. q^{59} -289881. q^{60} +372244. i q^{61} +125522. i q^{62} -70084.0i q^{63} +67538.8 q^{64} -217687. i q^{65} -12521.0 q^{66} +575276. q^{67} -6383.14 q^{68} +266357. i q^{69} +26258.9i q^{70} -367418. i q^{71} +358378. i q^{72} -47584.3i q^{73} -114317. q^{74} -13811.0i q^{75} +507718. i q^{76} -6997.02i q^{77} -214556. q^{78} +234069. q^{79} +310954. i q^{80} -251078. q^{81} -235023. i q^{82} -68786.3 q^{83} -159662. q^{84} -14640.8i q^{85} +(213091. - 104998. i) q^{86} +645181. q^{87} +35779.6i q^{88} -33503.7i q^{89} -380187. q^{90} -119899. i q^{91} +352035. q^{92} -1.75055e6i q^{93} -412497. i q^{94} -1.16454e6 q^{95} +1.25526e6 q^{96} +341432. q^{97} -337055. i q^{98} +101306. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.98785i 0.373482i −0.982409 0.186741i \(-0.940208\pi\)
0.982409 0.186741i \(-0.0597925\pi\)
\(3\) 41.6692i 1.54330i 0.636044 + 0.771652i \(0.280569\pi\)
−0.636044 + 0.771652i \(0.719431\pi\)
\(4\) 55.0727 0.860511
\(5\) 126.319i 1.01055i 0.862958 + 0.505275i \(0.168609\pi\)
−0.862958 + 0.505275i \(0.831391\pi\)
\(6\) 124.502 0.576396
\(7\) 69.5744i 0.202841i 0.994844 + 0.101420i \(0.0323387\pi\)
−0.994844 + 0.101420i \(0.967661\pi\)
\(8\) 355.772i 0.694867i
\(9\) −1007.32 −1.38179
\(10\) 377.422 0.377422
\(11\) −100.569 −0.0755589 −0.0377795 0.999286i \(-0.512028\pi\)
−0.0377795 + 0.999286i \(0.512028\pi\)
\(12\) 2294.84i 1.32803i
\(13\) −1723.32 −0.784396 −0.392198 0.919881i \(-0.628285\pi\)
−0.392198 + 0.919881i \(0.628285\pi\)
\(14\) 207.878 0.0757573
\(15\) −5263.61 −1.55959
\(16\) 2461.66 0.600991
\(17\) −115.904 −0.0235912 −0.0117956 0.999930i \(-0.503755\pi\)
−0.0117956 + 0.999930i \(0.503755\pi\)
\(18\) 3009.74i 0.516073i
\(19\) 9219.04i 1.34408i 0.740515 + 0.672039i \(0.234581\pi\)
−0.740515 + 0.672039i \(0.765419\pi\)
\(20\) 6956.72i 0.869590i
\(21\) −2899.11 −0.313045
\(22\) 300.485i 0.0282199i
\(23\) 6392.18 0.525370 0.262685 0.964882i \(-0.415392\pi\)
0.262685 + 0.964882i \(0.415392\pi\)
\(24\) 14824.7 1.07239
\(25\) −331.444 −0.0212124
\(26\) 5149.02i 0.292957i
\(27\) 11597.6i 0.589218i
\(28\) 3831.65i 0.174547i
\(29\) 15483.4i 0.634851i −0.948283 0.317426i \(-0.897182\pi\)
0.948283 0.317426i \(-0.102818\pi\)
\(30\) 15726.9i 0.582477i
\(31\) −42010.7 −1.41018 −0.705091 0.709117i \(-0.749094\pi\)
−0.705091 + 0.709117i \(0.749094\pi\)
\(32\) 30124.5i 0.919326i
\(33\) 4190.63i 0.116610i
\(34\) 346.304i 0.00881090i
\(35\) −8788.56 −0.204981
\(36\) −55476.1 −1.18905
\(37\) 38260.7i 0.755350i −0.925938 0.377675i \(-0.876724\pi\)
0.925938 0.377675i \(-0.123276\pi\)
\(38\) 27545.1 0.501989
\(39\) 71809.3i 1.21056i
\(40\) 44940.7 0.702198
\(41\) 78659.7 1.14130 0.570651 0.821193i \(-0.306691\pi\)
0.570651 + 0.821193i \(0.306691\pi\)
\(42\) 8662.12i 0.116917i
\(43\) 35141.8 + 71319.1i 0.441996 + 0.897017i
\(44\) −5538.60 −0.0650193
\(45\) 127244.i 1.39637i
\(46\) 19098.9i 0.196216i
\(47\) 138058. 1.32974 0.664871 0.746958i \(-0.268486\pi\)
0.664871 + 0.746958i \(0.268486\pi\)
\(48\) 102576.i 0.927513i
\(49\) 112808. 0.958856
\(50\) 990.307i 0.00792245i
\(51\) 4829.62i 0.0364085i
\(52\) −94907.8 −0.674981
\(53\) 54847.1 0.368406 0.184203 0.982888i \(-0.441030\pi\)
0.184203 + 0.982888i \(0.441030\pi\)
\(54\) −34651.8 −0.220062
\(55\) 12703.7i 0.0763561i
\(56\) 24752.6 0.140947
\(57\) −384150. −2.07432
\(58\) −46262.1 −0.237105
\(59\) −177043. −0.862029 −0.431015 0.902345i \(-0.641844\pi\)
−0.431015 + 0.902345i \(0.641844\pi\)
\(60\) −289881. −1.34204
\(61\) 372244.i 1.63998i 0.572377 + 0.819990i \(0.306021\pi\)
−0.572377 + 0.819990i \(0.693979\pi\)
\(62\) 125522.i 0.526677i
\(63\) 70084.0i 0.280283i
\(64\) 67538.8 0.257640
\(65\) 217687.i 0.792671i
\(66\) −12521.0 −0.0435519
\(67\) 575276. 1.91272 0.956361 0.292189i \(-0.0943836\pi\)
0.956361 + 0.292189i \(0.0943836\pi\)
\(68\) −6383.14 −0.0203005
\(69\) 266357.i 0.810806i
\(70\) 26258.9i 0.0765566i
\(71\) 367418.i 1.02656i −0.858220 0.513282i \(-0.828430\pi\)
0.858220 0.513282i \(-0.171570\pi\)
\(72\) 358378.i 0.960160i
\(73\) 47584.3i 0.122319i −0.998128 0.0611597i \(-0.980520\pi\)
0.998128 0.0611597i \(-0.0194799\pi\)
\(74\) −114317. −0.282109
\(75\) 13811.0i 0.0327373i
\(76\) 507718.i 1.15660i
\(77\) 6997.02i 0.0153264i
\(78\) −214556. −0.452123
\(79\) 234069. 0.474748 0.237374 0.971418i \(-0.423713\pi\)
0.237374 + 0.971418i \(0.423713\pi\)
\(80\) 310954.i 0.607332i
\(81\) −251078. −0.472447
\(82\) 235023.i 0.426255i
\(83\) −68786.3 −0.120301 −0.0601503 0.998189i \(-0.519158\pi\)
−0.0601503 + 0.998189i \(0.519158\pi\)
\(84\) −159662. −0.269379
\(85\) 14640.8i 0.0238401i
\(86\) 213091. 104998.i 0.335019 0.165077i
\(87\) 645181. 0.979769
\(88\) 35779.6i 0.0525034i
\(89\) 33503.7i 0.0475251i −0.999718 0.0237625i \(-0.992435\pi\)
0.999718 0.0237625i \(-0.00756456\pi\)
\(90\) −380187. −0.521518
\(91\) 119899.i 0.159107i
\(92\) 352035. 0.452087
\(93\) 1.75055e6i 2.17634i
\(94\) 412497.i 0.496634i
\(95\) −1.16454e6 −1.35826
\(96\) 1.25526e6 1.41880
\(97\) 341432. 0.374101 0.187051 0.982350i \(-0.440107\pi\)
0.187051 + 0.982350i \(0.440107\pi\)
\(98\) 337055.i 0.358115i
\(99\) 101306. 0.104407
\(100\) −18253.5 −0.0182535
\(101\) −785657. −0.762551 −0.381275 0.924462i \(-0.624515\pi\)
−0.381275 + 0.924462i \(0.624515\pi\)
\(102\) −14430.2 −0.0135979
\(103\) 51634.9 0.0472532 0.0236266 0.999721i \(-0.492479\pi\)
0.0236266 + 0.999721i \(0.492479\pi\)
\(104\) 613108.i 0.545051i
\(105\) 366212.i 0.316348i
\(106\) 163875.i 0.137593i
\(107\) 1.82956e6 1.49347 0.746733 0.665124i \(-0.231621\pi\)
0.746733 + 0.665124i \(0.231621\pi\)
\(108\) 638710.i 0.507029i
\(109\) −2.10066e6 −1.62209 −0.811046 0.584982i \(-0.801102\pi\)
−0.811046 + 0.584982i \(0.801102\pi\)
\(110\) −37956.9 −0.0285176
\(111\) 1.59430e6 1.16574
\(112\) 171269.i 0.121906i
\(113\) 2.18163e6i 1.51198i −0.654583 0.755990i \(-0.727156\pi\)
0.654583 0.755990i \(-0.272844\pi\)
\(114\) 1.14778e6i 0.774722i
\(115\) 807452.i 0.530913i
\(116\) 852712.i 0.546297i
\(117\) 1.73594e6 1.08387
\(118\) 528978.i 0.321952i
\(119\) 8063.94i 0.00478527i
\(120\) 1.87264e6i 1.08371i
\(121\) −1.76145e6 −0.994291
\(122\) 1.11221e6 0.612503
\(123\) 3.27769e6i 1.76138i
\(124\) −2.31365e6 −1.21348
\(125\) 1.93186e6i 0.989114i
\(126\) −209401. −0.104681
\(127\) 1.20370e6 0.587636 0.293818 0.955861i \(-0.405074\pi\)
0.293818 + 0.955861i \(0.405074\pi\)
\(128\) 2.12976e6i 1.01555i
\(129\) −2.97181e6 + 1.46433e6i −1.38437 + 0.682134i
\(130\) −650418. −0.296048
\(131\) 2.57371e6i 1.14484i −0.819960 0.572421i \(-0.806004\pi\)
0.819960 0.572421i \(-0.193996\pi\)
\(132\) 230789.i 0.100345i
\(133\) −641409. −0.272634
\(134\) 1.71884e6i 0.714366i
\(135\) 1.46499e6 0.595434
\(136\) 41235.3i 0.0163928i
\(137\) 996805.i 0.387658i −0.981035 0.193829i \(-0.937909\pi\)
0.981035 0.193829i \(-0.0620906\pi\)
\(138\) 795836. 0.302821
\(139\) −1.90604e6 −0.709720 −0.354860 0.934920i \(-0.615471\pi\)
−0.354860 + 0.934920i \(0.615471\pi\)
\(140\) −484010. −0.176388
\(141\) 5.75276e6i 2.05220i
\(142\) −1.09779e6 −0.383403
\(143\) 173312. 0.0592681
\(144\) −2.47969e6 −0.830444
\(145\) 1.95584e6 0.641549
\(146\) −142175. −0.0456841
\(147\) 4.70064e6i 1.47981i
\(148\) 2.10712e6i 0.649987i
\(149\) 192908.i 0.0583165i 0.999575 + 0.0291582i \(0.00928267\pi\)
−0.999575 + 0.0291582i \(0.990717\pi\)
\(150\) −41265.3 −0.0122268
\(151\) 2.12036e6i 0.615856i 0.951410 + 0.307928i \(0.0996356\pi\)
−0.951410 + 0.307928i \(0.900364\pi\)
\(152\) 3.27987e6 0.933956
\(153\) 116753. 0.0325981
\(154\) −20906.1 −0.00572414
\(155\) 5.30675e6i 1.42506i
\(156\) 3.95473e6i 1.04170i
\(157\) 4.75453e6i 1.22860i 0.789074 + 0.614298i \(0.210561\pi\)
−0.789074 + 0.614298i \(0.789439\pi\)
\(158\) 699364.i 0.177309i
\(159\) 2.28544e6i 0.568562i
\(160\) 3.80529e6 0.929026
\(161\) 444732.i 0.106567i
\(162\) 750183.i 0.176450i
\(163\) 663761.i 0.153267i 0.997059 + 0.0766335i \(0.0244172\pi\)
−0.997059 + 0.0766335i \(0.975583\pi\)
\(164\) 4.33200e6 0.982103
\(165\) 529355. 0.117841
\(166\) 205523.i 0.0449301i
\(167\) 2.20047e6 0.472460 0.236230 0.971697i \(-0.424088\pi\)
0.236230 + 0.971697i \(0.424088\pi\)
\(168\) 1.03142e6i 0.217525i
\(169\) −1.85699e6 −0.384723
\(170\) −43744.7 −0.00890386
\(171\) 9.28656e6i 1.85723i
\(172\) 1.93535e6 + 3.92774e6i 0.380343 + 0.771893i
\(173\) −8.81032e6 −1.70158 −0.850792 0.525502i \(-0.823878\pi\)
−0.850792 + 0.525502i \(0.823878\pi\)
\(174\) 1.92770e6i 0.365926i
\(175\) 23060.0i 0.00430275i
\(176\) −247567. −0.0454103
\(177\) 7.37723e6i 1.33037i
\(178\) −100104. −0.0177497
\(179\) 8.87459e6i 1.54735i −0.633582 0.773676i \(-0.718416\pi\)
0.633582 0.773676i \(-0.281584\pi\)
\(180\) 7.00768e6i 1.20159i
\(181\) 3.01860e6 0.509060 0.254530 0.967065i \(-0.418079\pi\)
0.254530 + 0.967065i \(0.418079\pi\)
\(182\) −358240. −0.0594237
\(183\) −1.55111e7 −2.53099
\(184\) 2.27416e6i 0.365062i
\(185\) 4.83305e6 0.763319
\(186\) −5.23040e6 −0.812823
\(187\) 11656.3 0.00178253
\(188\) 7.60322e6 1.14426
\(189\) 806894. 0.119517
\(190\) 3.47947e6i 0.507285i
\(191\) 1.43958e6i 0.206602i −0.994650 0.103301i \(-0.967060\pi\)
0.994650 0.103301i \(-0.0329405\pi\)
\(192\) 2.81429e6i 0.397617i
\(193\) −7.10710e6 −0.988599 −0.494300 0.869292i \(-0.664575\pi\)
−0.494300 + 0.869292i \(0.664575\pi\)
\(194\) 1.02015e6i 0.139720i
\(195\) 9.07087e6 1.22333
\(196\) 6.21267e6 0.825106
\(197\) 1.16308e7 1.52128 0.760640 0.649173i \(-0.224885\pi\)
0.760640 + 0.649173i \(0.224885\pi\)
\(198\) 302686.i 0.0389939i
\(199\) 9.37093e6i 1.18911i −0.804054 0.594557i \(-0.797328\pi\)
0.804054 0.594557i \(-0.202672\pi\)
\(200\) 117919.i 0.0147398i
\(201\) 2.39713e7i 2.95191i
\(202\) 2.34743e6i 0.284799i
\(203\) 1.07725e6 0.128774
\(204\) 265980.i 0.0313299i
\(205\) 9.93619e6i 1.15334i
\(206\) 154277.i 0.0176482i
\(207\) −6.43900e6 −0.725951
\(208\) −4.24222e6 −0.471415
\(209\) 927148.i 0.101557i
\(210\) −1.09419e6 −0.118150
\(211\) 1.53230e7i 1.63116i 0.578644 + 0.815580i \(0.303582\pi\)
−0.578644 + 0.815580i \(0.696418\pi\)
\(212\) 3.02058e6 0.317017
\(213\) 1.53100e7 1.58430
\(214\) 5.46645e6i 0.557782i
\(215\) −9.00895e6 + 4.43907e6i −0.906481 + 0.446659i
\(216\) −4.12609e6 −0.409428
\(217\) 2.92287e6i 0.286043i
\(218\) 6.27646e6i 0.605822i
\(219\) 1.98280e6 0.188776
\(220\) 699630.i 0.0657053i
\(221\) 199739. 0.0185049
\(222\) 4.76352e6i 0.435381i
\(223\) 1.92740e7i 1.73803i −0.494789 0.869013i \(-0.664755\pi\)
0.494789 0.869013i \(-0.335245\pi\)
\(224\) 2.09589e6 0.186477
\(225\) 333872. 0.0293111
\(226\) −6.51839e6 −0.564697
\(227\) 1.18617e7i 1.01407i −0.861924 0.507037i \(-0.830741\pi\)
0.861924 0.507037i \(-0.169259\pi\)
\(228\) −2.11562e7 −1.78498
\(229\) 4.46227e6 0.371577 0.185789 0.982590i \(-0.440516\pi\)
0.185789 + 0.982590i \(0.440516\pi\)
\(230\) 2.41255e6 0.198286
\(231\) 291561. 0.0236534
\(232\) −5.50855e6 −0.441137
\(233\) 2.31494e7i 1.83009i 0.403351 + 0.915045i \(0.367845\pi\)
−0.403351 + 0.915045i \(0.632155\pi\)
\(234\) 5.18673e6i 0.404805i
\(235\) 1.74393e7i 1.34377i
\(236\) −9.75023e6 −0.741786
\(237\) 9.75348e6i 0.732680i
\(238\) −24093.9 −0.00178721
\(239\) −1.52813e7 −1.11935 −0.559674 0.828713i \(-0.689074\pi\)
−0.559674 + 0.828713i \(0.689074\pi\)
\(240\) −1.29572e7 −0.937299
\(241\) 1.36802e7i 0.977330i −0.872472 0.488665i \(-0.837484\pi\)
0.872472 0.488665i \(-0.162516\pi\)
\(242\) 5.26294e6i 0.371349i
\(243\) 1.89168e7i 1.31835i
\(244\) 2.05005e7i 1.41122i
\(245\) 1.42498e7i 0.968972i
\(246\) 9.79325e6 0.657842
\(247\) 1.58873e7i 1.05429i
\(248\) 1.49462e7i 0.979889i
\(249\) 2.86627e6i 0.185661i
\(250\) 5.77213e6 0.369416
\(251\) 1.66557e7 1.05328 0.526638 0.850089i \(-0.323452\pi\)
0.526638 + 0.850089i \(0.323452\pi\)
\(252\) 3.85972e6i 0.241187i
\(253\) −642854. −0.0396964
\(254\) 3.59649e6i 0.219471i
\(255\) 610072. 0.0367926
\(256\) −2.04094e6 −0.121649
\(257\) 1.62803e7i 0.959101i −0.877514 0.479550i \(-0.840800\pi\)
0.877514 0.479550i \(-0.159200\pi\)
\(258\) 4.37520e6 + 8.87934e6i 0.254765 + 0.517037i
\(259\) 2.66197e6 0.153216
\(260\) 1.19886e7i 0.682103i
\(261\) 1.55968e7i 0.877231i
\(262\) −7.68987e6 −0.427578
\(263\) 2.85794e7i 1.57104i −0.618839 0.785518i \(-0.712397\pi\)
0.618839 0.785518i \(-0.287603\pi\)
\(264\) −1.49091e6 −0.0810287
\(265\) 6.92822e6i 0.372292i
\(266\) 1.91644e6i 0.101824i
\(267\) 1.39607e6 0.0733457
\(268\) 3.16820e7 1.64592
\(269\) 2.80627e7 1.44169 0.720846 0.693095i \(-0.243753\pi\)
0.720846 + 0.693095i \(0.243753\pi\)
\(270\) 4.37718e6i 0.222384i
\(271\) −1.61533e7 −0.811622 −0.405811 0.913957i \(-0.633011\pi\)
−0.405811 + 0.913957i \(0.633011\pi\)
\(272\) −285316. −0.0141781
\(273\) 4.99609e6 0.245551
\(274\) −2.97831e6 −0.144783
\(275\) 33333.0 0.00160279
\(276\) 1.46690e7i 0.697708i
\(277\) 3.22384e7i 1.51682i −0.651777 0.758410i \(-0.725976\pi\)
0.651777 0.758410i \(-0.274024\pi\)
\(278\) 5.69496e6i 0.265067i
\(279\) 4.23184e7 1.94858
\(280\) 3.12672e6i 0.142434i
\(281\) −2.09764e7 −0.945393 −0.472697 0.881225i \(-0.656719\pi\)
−0.472697 + 0.881225i \(0.656719\pi\)
\(282\) 1.71884e7 0.766458
\(283\) 1.16336e7 0.513282 0.256641 0.966507i \(-0.417384\pi\)
0.256641 + 0.966507i \(0.417384\pi\)
\(284\) 2.02347e7i 0.883370i
\(285\) 4.85254e7i 2.09621i
\(286\) 517831.i 0.0221355i
\(287\) 5.47270e6i 0.231503i
\(288\) 3.03451e7i 1.27032i
\(289\) −2.41241e7 −0.999443
\(290\) 5.84377e6i 0.239607i
\(291\) 1.42272e7i 0.577352i
\(292\) 2.62060e6i 0.105257i
\(293\) −2.45473e7 −0.975888 −0.487944 0.872875i \(-0.662253\pi\)
−0.487944 + 0.872875i \(0.662253\pi\)
\(294\) 1.40448e7 0.552681
\(295\) 2.23638e7i 0.871124i
\(296\) −1.36121e7 −0.524868
\(297\) 1.16636e6i 0.0445206i
\(298\) 576381. 0.0217801
\(299\) −1.10157e7 −0.412098
\(300\) 760611.i 0.0281708i
\(301\) −4.96199e6 + 2.44497e6i −0.181952 + 0.0896548i
\(302\) 6.33533e6 0.230011
\(303\) 3.27377e7i 1.17685i
\(304\) 2.26941e7i 0.807780i
\(305\) −4.70215e7 −1.65728
\(306\) 348840.i 0.0121748i
\(307\) 1.50700e7 0.520831 0.260416 0.965497i \(-0.416140\pi\)
0.260416 + 0.965497i \(0.416140\pi\)
\(308\) 385345.i 0.0131886i
\(309\) 2.15159e6i 0.0729262i
\(310\) −1.58558e7 −0.532234
\(311\) 1.25190e7 0.416186 0.208093 0.978109i \(-0.433274\pi\)
0.208093 + 0.978109i \(0.433274\pi\)
\(312\) −2.55477e7 −0.841179
\(313\) 2.09806e7i 0.684201i 0.939663 + 0.342101i \(0.111138\pi\)
−0.939663 + 0.342101i \(0.888862\pi\)
\(314\) 1.42058e7 0.458858
\(315\) 8.85293e6 0.283241
\(316\) 1.28908e7 0.408526
\(317\) −3.56390e7 −1.11879 −0.559394 0.828902i \(-0.688966\pi\)
−0.559394 + 0.828902i \(0.688966\pi\)
\(318\) 6.82855e6 0.212347
\(319\) 1.55715e6i 0.0479687i
\(320\) 8.53142e6i 0.260358i
\(321\) 7.62363e7i 2.30487i
\(322\) 1.32879e6 0.0398006
\(323\) 1.06852e6i 0.0317085i
\(324\) −1.38275e7 −0.406546
\(325\) 571184. 0.0166389
\(326\) 1.98322e6 0.0572424
\(327\) 8.75328e7i 2.50338i
\(328\) 2.79849e7i 0.793053i
\(329\) 9.60529e6i 0.269726i
\(330\) 1.58164e6i 0.0440113i
\(331\) 4.51562e6i 0.124518i 0.998060 + 0.0622592i \(0.0198306\pi\)
−0.998060 + 0.0622592i \(0.980169\pi\)
\(332\) −3.78825e6 −0.103520
\(333\) 3.85410e7i 1.04373i
\(334\) 6.57467e6i 0.176455i
\(335\) 7.26682e7i 1.93290i
\(336\) −7.13663e6 −0.188138
\(337\) 3.54358e7 0.925876 0.462938 0.886391i \(-0.346795\pi\)
0.462938 + 0.886391i \(0.346795\pi\)
\(338\) 5.54840e6i 0.143687i
\(339\) 9.09069e7 2.33345
\(340\) 806311.i 0.0205147i
\(341\) 4.22497e6 0.106552
\(342\) −2.77469e7 −0.693643
\(343\) 1.60339e7i 0.397336i
\(344\) 2.53733e7 1.25025e7i 0.623307 0.307128i
\(345\) −3.36459e7 −0.819361
\(346\) 2.63240e7i 0.635511i
\(347\) 7.07630e7i 1.69363i 0.531889 + 0.846814i \(0.321482\pi\)
−0.531889 + 0.846814i \(0.678518\pi\)
\(348\) 3.55319e7 0.843102
\(349\) 5.72662e6i 0.134717i −0.997729 0.0673585i \(-0.978543\pi\)
0.997729 0.0673585i \(-0.0214571\pi\)
\(350\) −68900.0 −0.00160700
\(351\) 1.99863e7i 0.462180i
\(352\) 3.02959e6i 0.0694633i
\(353\) −3.74887e7 −0.852268 −0.426134 0.904660i \(-0.640125\pi\)
−0.426134 + 0.904660i \(0.640125\pi\)
\(354\) −2.20421e7 −0.496870
\(355\) 4.64119e7 1.03739
\(356\) 1.84514e6i 0.0408959i
\(357\) 336018. 0.00738513
\(358\) −2.65160e7 −0.577907
\(359\) 6.27195e6 0.135556 0.0677781 0.997700i \(-0.478409\pi\)
0.0677781 + 0.997700i \(0.478409\pi\)
\(360\) −4.52699e7 −0.970290
\(361\) −3.79448e7 −0.806548
\(362\) 9.01912e6i 0.190125i
\(363\) 7.33981e7i 1.53449i
\(364\) 6.60315e6i 0.136914i
\(365\) 6.01080e6 0.123610
\(366\) 4.63450e7i 0.945278i
\(367\) −6.87779e6 −0.139140 −0.0695698 0.997577i \(-0.522163\pi\)
−0.0695698 + 0.997577i \(0.522163\pi\)
\(368\) 1.57354e7 0.315743
\(369\) −7.92358e7 −1.57704
\(370\) 1.44404e7i 0.285086i
\(371\) 3.81596e6i 0.0747277i
\(372\) 9.64078e7i 1.87277i
\(373\) 9.99739e6i 0.192646i −0.995350 0.0963231i \(-0.969292\pi\)
0.995350 0.0963231i \(-0.0307082\pi\)
\(374\) 34827.4i 0.000665742i
\(375\) −8.04993e7 −1.52650
\(376\) 4.91171e7i 0.923994i
\(377\) 2.66828e7i 0.497974i
\(378\) 2.41088e6i 0.0446376i
\(379\) 9.50197e7 1.74540 0.872702 0.488253i \(-0.162366\pi\)
0.872702 + 0.488253i \(0.162366\pi\)
\(380\) −6.41343e7 −1.16880
\(381\) 5.01574e7i 0.906902i
\(382\) −4.30124e6 −0.0771620
\(383\) 4.30196e7i 0.765720i 0.923806 + 0.382860i \(0.125061\pi\)
−0.923806 + 0.382860i \(0.874939\pi\)
\(384\) 8.87456e7 1.56730
\(385\) 883856. 0.0154881
\(386\) 2.12350e7i 0.369224i
\(387\) −3.53992e7 7.18415e7i −0.610745 1.23949i
\(388\) 1.88036e7 0.321919
\(389\) 3.21983e6i 0.0546996i −0.999626 0.0273498i \(-0.991293\pi\)
0.999626 0.0273498i \(-0.00870680\pi\)
\(390\) 2.71024e7i 0.456893i
\(391\) −740878. −0.0123941
\(392\) 4.01341e7i 0.666277i
\(393\) 1.07244e8 1.76684
\(394\) 3.47510e7i 0.568170i
\(395\) 2.95673e7i 0.479756i
\(396\) 5.57917e6 0.0898430
\(397\) −5.56628e7 −0.889597 −0.444799 0.895631i \(-0.646725\pi\)
−0.444799 + 0.895631i \(0.646725\pi\)
\(398\) −2.79990e7 −0.444112
\(399\) 2.67270e7i 0.420758i
\(400\) −815903. −0.0127485
\(401\) 1.03598e8 1.60664 0.803319 0.595549i \(-0.203065\pi\)
0.803319 + 0.595549i \(0.203065\pi\)
\(402\) 7.16227e7 1.10248
\(403\) 7.23978e7 1.10614
\(404\) −4.32683e7 −0.656184
\(405\) 3.17158e7i 0.477432i
\(406\) 3.21866e6i 0.0480946i
\(407\) 3.84784e6i 0.0570734i
\(408\) −1.71824e6 −0.0252990
\(409\) 4.89797e7i 0.715890i −0.933743 0.357945i \(-0.883478\pi\)
0.933743 0.357945i \(-0.116522\pi\)
\(410\) 2.96879e7 0.430752
\(411\) 4.15361e7 0.598274
\(412\) 2.84367e6 0.0406620
\(413\) 1.23176e7i 0.174855i
\(414\) 1.92388e7i 0.271129i
\(415\) 8.68901e6i 0.121570i
\(416\) 5.19140e7i 0.721115i
\(417\) 7.94231e7i 1.09531i
\(418\) −2.77018e6 −0.0379297
\(419\) 1.02750e8i 1.39682i 0.715699 + 0.698408i \(0.246108\pi\)
−0.715699 + 0.698408i \(0.753892\pi\)
\(420\) 2.01683e7i 0.272221i
\(421\) 5.62844e7i 0.754296i −0.926153 0.377148i \(-0.876905\pi\)
0.926153 0.377148i \(-0.123095\pi\)
\(422\) 4.57829e7 0.609208
\(423\) −1.39069e8 −1.83742
\(424\) 1.95131e7i 0.255993i
\(425\) 38415.6 0.000500428
\(426\) 4.57442e7i 0.591707i
\(427\) −2.58987e7 −0.332655
\(428\) 1.00759e8 1.28514
\(429\) 7.22178e6i 0.0914687i
\(430\) 1.32633e7 + 2.69174e7i 0.166819 + 0.338554i
\(431\) −7.60304e7 −0.949632 −0.474816 0.880085i \(-0.657485\pi\)
−0.474816 + 0.880085i \(0.657485\pi\)
\(432\) 2.85493e7i 0.354115i
\(433\) 1.14226e7i 0.140702i 0.997522 + 0.0703511i \(0.0224120\pi\)
−0.997522 + 0.0703511i \(0.977588\pi\)
\(434\) −8.73311e6 −0.106832
\(435\) 8.14985e7i 0.990106i
\(436\) −1.15689e8 −1.39583
\(437\) 5.89297e7i 0.706139i
\(438\) 5.92432e6i 0.0705044i
\(439\) −2.07515e7 −0.245277 −0.122638 0.992451i \(-0.539136\pi\)
−0.122638 + 0.992451i \(0.539136\pi\)
\(440\) −4.51963e6 −0.0530573
\(441\) −1.13635e8 −1.32494
\(442\) 596791.i 0.00691123i
\(443\) −1.36002e7 −0.156435 −0.0782175 0.996936i \(-0.524923\pi\)
−0.0782175 + 0.996936i \(0.524923\pi\)
\(444\) 8.78022e7 1.00313
\(445\) 4.23215e6 0.0480265
\(446\) −5.75878e7 −0.649121
\(447\) −8.03832e6 −0.0900001
\(448\) 4.69897e6i 0.0522599i
\(449\) 1.38176e8i 1.52649i 0.646107 + 0.763246i \(0.276396\pi\)
−0.646107 + 0.763246i \(0.723604\pi\)
\(450\) 997560.i 0.0109472i
\(451\) −7.91072e6 −0.0862355
\(452\) 1.20148e8i 1.30108i
\(453\) −8.83538e7 −0.950453
\(454\) −3.54410e7 −0.378738
\(455\) 1.51455e7 0.160786
\(456\) 1.36670e8i 1.44138i
\(457\) 1.58547e7i 0.166116i −0.996545 0.0830578i \(-0.973531\pi\)
0.996545 0.0830578i \(-0.0264686\pi\)
\(458\) 1.33326e7i 0.138777i
\(459\) 1.34420e6i 0.0139004i
\(460\) 4.44686e7i 0.456857i
\(461\) 1.06966e8 1.09180 0.545901 0.837849i \(-0.316187\pi\)
0.545901 + 0.837849i \(0.316187\pi\)
\(462\) 871140.i 0.00883409i
\(463\) 6.74339e7i 0.679415i −0.940531 0.339707i \(-0.889672\pi\)
0.940531 0.339707i \(-0.110328\pi\)
\(464\) 3.81148e7i 0.381540i
\(465\) 2.21128e8 2.19930
\(466\) 6.91671e7 0.683505
\(467\) 1.09689e8i 1.07699i −0.842627 0.538497i \(-0.818992\pi\)
0.842627 0.538497i \(-0.181008\pi\)
\(468\) 9.56030e7 0.932682
\(469\) 4.00245e7i 0.387978i
\(470\) 5.21061e7 0.501874
\(471\) −1.98118e8 −1.89610
\(472\) 6.29868e7i 0.598996i
\(473\) −3.53417e6 7.17249e6i −0.0333967 0.0677776i
\(474\) 2.91420e7 0.273643
\(475\) 3.05560e6i 0.0285112i
\(476\) 444103.i 0.00411778i
\(477\) −5.52488e7 −0.509059
\(478\) 4.56582e7i 0.418056i
\(479\) −1.79146e8 −1.63005 −0.815026 0.579425i \(-0.803277\pi\)
−0.815026 + 0.579425i \(0.803277\pi\)
\(480\) 1.58563e8i 1.43377i
\(481\) 6.59354e7i 0.592493i
\(482\) −4.08744e7 −0.365015
\(483\) −1.85316e7 −0.164465
\(484\) −9.70077e7 −0.855599
\(485\) 4.31293e7i 0.378048i
\(486\) −5.65208e7 −0.492379
\(487\) 2.19363e8 1.89922 0.949612 0.313428i \(-0.101477\pi\)
0.949612 + 0.313428i \(0.101477\pi\)
\(488\) 1.32434e8 1.13957
\(489\) −2.76584e7 −0.236538
\(490\) 4.25764e7 0.361893
\(491\) 4.75542e7i 0.401740i −0.979618 0.200870i \(-0.935623\pi\)
0.979618 0.200870i \(-0.0643768\pi\)
\(492\) 1.80511e8i 1.51568i
\(493\) 1.79458e6i 0.0149769i
\(494\) −4.74690e7 −0.393758
\(495\) 1.27968e7i 0.105508i
\(496\) −1.03416e8 −0.847507
\(497\) 2.55629e7 0.208229
\(498\) −8.56401e6 −0.0693408
\(499\) 1.26074e8i 1.01467i 0.861750 + 0.507333i \(0.169368\pi\)
−0.861750 + 0.507333i \(0.830632\pi\)
\(500\) 1.06393e8i 0.851144i
\(501\) 9.16917e7i 0.729150i
\(502\) 4.97649e7i 0.393380i
\(503\) 1.56016e8i 1.22593i −0.790110 0.612965i \(-0.789977\pi\)
0.790110 0.612965i \(-0.210023\pi\)
\(504\) −2.49339e7 −0.194760
\(505\) 9.92432e7i 0.770596i
\(506\) 1.92075e6i 0.0148259i
\(507\) 7.73792e7i 0.593746i
\(508\) 6.62913e7 0.505668
\(509\) −3.00795e7 −0.228096 −0.114048 0.993475i \(-0.536382\pi\)
−0.114048 + 0.993475i \(0.536382\pi\)
\(510\) 1.82281e6i 0.0137414i
\(511\) 3.31065e6 0.0248114
\(512\) 1.30207e8i 0.970116i
\(513\) 1.06918e8 0.791955
\(514\) −4.86433e7 −0.358206
\(515\) 6.52246e6i 0.0477518i
\(516\) −1.63666e8 + 8.06447e7i −1.19127 + 0.586984i
\(517\) −1.38843e7 −0.100474
\(518\) 7.95357e6i 0.0572233i
\(519\) 3.67119e8i 2.62606i
\(520\) −7.74470e7 −0.550801
\(521\) 7.50174e7i 0.530455i 0.964186 + 0.265228i \(0.0854471\pi\)
−0.964186 + 0.265228i \(0.914553\pi\)
\(522\) 4.66009e7 0.327630
\(523\) 7.31971e6i 0.0511668i 0.999673 + 0.0255834i \(0.00814435\pi\)
−0.999673 + 0.0255834i \(0.991856\pi\)
\(524\) 1.41741e8i 0.985150i
\(525\) 960894. 0.00664045
\(526\) −8.53911e7 −0.586753
\(527\) 4.86920e6 0.0332680
\(528\) 1.03159e7i 0.0700819i
\(529\) −1.07176e8 −0.723986
\(530\) 2.07005e7 0.139044
\(531\) 1.78339e8 1.19114
\(532\) −3.53242e7 −0.234605
\(533\) −1.35556e8 −0.895232
\(534\) 4.17126e6i 0.0273933i
\(535\) 2.31108e8i 1.50922i
\(536\) 2.04667e8i 1.32909i
\(537\) 3.69797e8 2.38804
\(538\) 8.38472e7i 0.538446i
\(539\) −1.13450e7 −0.0724501
\(540\) 8.06811e7 0.512378
\(541\) −1.94691e7 −0.122957 −0.0614785 0.998108i \(-0.519582\pi\)
−0.0614785 + 0.998108i \(0.519582\pi\)
\(542\) 4.82638e7i 0.303126i
\(543\) 1.25783e8i 0.785635i
\(544\) 3.49154e6i 0.0216880i
\(545\) 2.65353e8i 1.63921i
\(546\) 1.49276e7i 0.0917089i
\(547\) 9.15424e7 0.559320 0.279660 0.960099i \(-0.409778\pi\)
0.279660 + 0.960099i \(0.409778\pi\)
\(548\) 5.48968e7i 0.333584i
\(549\) 3.74971e8i 2.26611i
\(550\) 99594.1i 0.000598612i
\(551\) 1.42742e8 0.853290
\(552\) 9.47624e7 0.563402
\(553\) 1.62852e7i 0.0962982i
\(554\) −9.63236e7 −0.566505
\(555\) 2.01390e8i 1.17803i
\(556\) −1.04971e8 −0.610722
\(557\) 2.38280e7 0.137886 0.0689432 0.997621i \(-0.478037\pi\)
0.0689432 + 0.997621i \(0.478037\pi\)
\(558\) 1.26441e8i 0.727757i
\(559\) −6.05604e7 1.22905e8i −0.346700 0.703616i
\(560\) −2.16344e7 −0.123192
\(561\) 485710.i 0.00275099i
\(562\) 6.26745e7i 0.353087i
\(563\) −1.26545e8 −0.709123 −0.354561 0.935033i \(-0.615370\pi\)
−0.354561 + 0.935033i \(0.615370\pi\)
\(564\) 3.16820e8i 1.76594i
\(565\) 2.75581e8 1.52793
\(566\) 3.47596e7i 0.191701i
\(567\) 1.74686e7i 0.0958316i
\(568\) −1.30717e8 −0.713325
\(569\) 2.44261e8 1.32592 0.662959 0.748656i \(-0.269300\pi\)
0.662959 + 0.748656i \(0.269300\pi\)
\(570\) −1.44987e8 −0.782895
\(571\) 2.69338e8i 1.44674i 0.690462 + 0.723368i \(0.257407\pi\)
−0.690462 + 0.723368i \(0.742593\pi\)
\(572\) 9.54477e6 0.0510009
\(573\) 5.99860e7 0.318850
\(574\) 1.63516e7 0.0864620
\(575\) −2.11865e6 −0.0111444
\(576\) −6.80335e7 −0.356004
\(577\) 1.55241e8i 0.808126i −0.914731 0.404063i \(-0.867598\pi\)
0.914731 0.404063i \(-0.132402\pi\)
\(578\) 7.20794e7i 0.373274i
\(579\) 2.96147e8i 1.52571i
\(580\) 1.07714e8 0.552060
\(581\) 4.78577e6i 0.0244019i
\(582\) 4.25088e7 0.215631
\(583\) −5.51591e6 −0.0278363
\(584\) −1.69292e7 −0.0849957
\(585\) 2.19282e8i 1.09531i
\(586\) 7.33436e7i 0.364476i
\(587\) 1.52542e8i 0.754179i 0.926177 + 0.377090i \(0.123075\pi\)
−0.926177 + 0.377090i \(0.876925\pi\)
\(588\) 2.58877e8i 1.27339i
\(589\) 3.87299e8i 1.89540i
\(590\) −6.68198e7 −0.325349
\(591\) 4.84645e8i 2.34780i
\(592\) 9.41850e7i 0.453959i
\(593\) 2.05477e8i 0.985369i −0.870208 0.492685i \(-0.836016\pi\)
0.870208 0.492685i \(-0.163984\pi\)
\(594\) 3.48490e6 0.0166276
\(595\) 1.01863e6 0.00483576
\(596\) 1.06240e7i 0.0501820i
\(597\) 3.90479e8 1.83516
\(598\) 3.29134e7i 0.153911i
\(599\) 2.54531e8 1.18430 0.592149 0.805829i \(-0.298280\pi\)
0.592149 + 0.805829i \(0.298280\pi\)
\(600\) −4.91357e6 −0.0227480
\(601\) 1.86617e8i 0.859661i 0.902910 + 0.429831i \(0.141427\pi\)
−0.902910 + 0.429831i \(0.858573\pi\)
\(602\) 7.30520e6 + 1.48257e7i 0.0334844 + 0.0679556i
\(603\) −5.79489e8 −2.64298
\(604\) 1.16774e8i 0.529951i
\(605\) 2.22504e8i 1.00478i
\(606\) −9.78155e7 −0.439531
\(607\) 5.73996e7i 0.256651i −0.991732 0.128325i \(-0.959040\pi\)
0.991732 0.128325i \(-0.0409602\pi\)
\(608\) 2.77719e8 1.23565
\(609\) 4.48881e7i 0.198737i
\(610\) 1.40493e8i 0.618965i
\(611\) −2.37917e8 −1.04304
\(612\) 6.42989e6 0.0280511
\(613\) −1.23866e8 −0.537739 −0.268869 0.963177i \(-0.586650\pi\)
−0.268869 + 0.963177i \(0.586650\pi\)
\(614\) 4.50268e7i 0.194521i
\(615\) −4.14034e8 −1.77996
\(616\) −2.48934e6 −0.0106498
\(617\) −2.71924e7 −0.115769 −0.0578845 0.998323i \(-0.518436\pi\)
−0.0578845 + 0.998323i \(0.518436\pi\)
\(618\) 6.42862e6 0.0272366
\(619\) −2.18698e8 −0.922091 −0.461045 0.887377i \(-0.652525\pi\)
−0.461045 + 0.887377i \(0.652525\pi\)
\(620\) 2.92257e8i 1.22628i
\(621\) 7.41337e7i 0.309557i
\(622\) 3.74049e7i 0.155438i
\(623\) 2.33100e6 0.00964003
\(624\) 1.76770e8i 0.727537i
\(625\) −2.49210e8 −1.02076
\(626\) 6.26868e7 0.255537
\(627\) 3.86336e7 0.156734
\(628\) 2.61845e8i 1.05722i
\(629\) 4.43456e6i 0.0178196i
\(630\) 2.64513e7i 0.105785i
\(631\) 3.08632e8i 1.22844i −0.789135 0.614219i \(-0.789471\pi\)
0.789135 0.614219i \(-0.210529\pi\)
\(632\) 8.32752e7i 0.329886i
\(633\) −6.38498e8 −2.51738
\(634\) 1.06484e8i 0.417847i
\(635\) 1.52051e8i 0.593836i
\(636\) 1.25865e8i 0.489254i
\(637\) −1.94405e8 −0.752122
\(638\) 4.65253e6 0.0179154
\(639\) 3.70110e8i 1.41849i
\(640\) 2.69029e8 1.02626
\(641\) 2.78366e8i 1.05692i 0.848958 + 0.528460i \(0.177230\pi\)
−0.848958 + 0.528460i \(0.822770\pi\)
\(642\) 2.27783e8 0.860827
\(643\) 3.11174e8 1.17050 0.585248 0.810855i \(-0.300997\pi\)
0.585248 + 0.810855i \(0.300997\pi\)
\(644\) 2.44926e7i 0.0917017i
\(645\) −1.84972e8 3.75396e8i −0.689331 1.39898i
\(646\) −3.19258e6 −0.0118425
\(647\) 4.55247e8i 1.68087i 0.541913 + 0.840435i \(0.317700\pi\)
−0.541913 + 0.840435i \(0.682300\pi\)
\(648\) 8.93264e7i 0.328288i
\(649\) 1.78050e7 0.0651340
\(650\) 1.70661e6i 0.00621434i
\(651\) 1.21794e8 0.441451
\(652\) 3.65551e7i 0.131888i
\(653\) 1.72465e8i 0.619386i 0.950837 + 0.309693i \(0.100226\pi\)
−0.950837 + 0.309693i \(0.899774\pi\)
\(654\) −2.61535e8 −0.934968
\(655\) 3.25108e8 1.15692
\(656\) 1.93633e8 0.685913
\(657\) 4.79329e7i 0.169020i
\(658\) 2.86992e7 0.100738
\(659\) −3.61115e7 −0.126180 −0.0630898 0.998008i \(-0.520095\pi\)
−0.0630898 + 0.998008i \(0.520095\pi\)
\(660\) 2.91530e7 0.101403
\(661\) −4.17097e8 −1.44422 −0.722109 0.691779i \(-0.756827\pi\)
−0.722109 + 0.691779i \(0.756827\pi\)
\(662\) 1.34920e7 0.0465054
\(663\) 8.32297e6i 0.0285587i
\(664\) 2.44722e7i 0.0835929i
\(665\) 8.10220e7i 0.275511i
\(666\) 1.15155e8 0.389816
\(667\) 9.89725e7i 0.333532i
\(668\) 1.21186e8 0.406557
\(669\) 8.03131e8 2.68230
\(670\) 2.17122e8 0.721903
\(671\) 3.74362e7i 0.123915i
\(672\) 8.73342e7i 0.287791i
\(673\) 5.11802e8i 1.67902i 0.543341 + 0.839512i \(0.317159\pi\)
−0.543341 + 0.839512i \(0.682841\pi\)
\(674\) 1.05877e8i 0.345798i
\(675\) 3.84395e6i 0.0124987i
\(676\) −1.02269e8 −0.331059
\(677\) 1.81913e8i 0.586269i −0.956071 0.293134i \(-0.905302\pi\)
0.956071 0.293134i \(-0.0946984\pi\)
\(678\) 2.71616e8i 0.871499i
\(679\) 2.37549e7i 0.0758830i
\(680\) −5.20880e6 −0.0165657
\(681\) 4.94268e8 1.56502
\(682\) 1.26236e7i 0.0397951i
\(683\) 4.25041e8 1.33404 0.667020 0.745040i \(-0.267569\pi\)
0.667020 + 0.745040i \(0.267569\pi\)
\(684\) 5.11436e8i 1.59817i
\(685\) 1.25915e8 0.391748
\(686\) 4.79071e7 0.148398
\(687\) 1.85939e8i 0.573457i
\(688\) 8.65071e7 + 1.75564e8i 0.265636 + 0.539100i
\(689\) −9.45190e7 −0.288976
\(690\) 1.00529e8i 0.306016i
\(691\) 1.14153e8i 0.345982i −0.984923 0.172991i \(-0.944657\pi\)
0.984923 0.172991i \(-0.0553432\pi\)
\(692\) −4.85209e8 −1.46423
\(693\) 7.04827e6i 0.0211779i
\(694\) 2.11430e8 0.632539
\(695\) 2.40768e8i 0.717208i
\(696\) 2.29537e8i 0.680809i
\(697\) −9.11695e6 −0.0269247
\(698\) −1.71103e7 −0.0503143
\(699\) −9.64619e8 −2.82439
\(700\) 1.26998e6i 0.00370256i
\(701\) −2.36723e8 −0.687204 −0.343602 0.939115i \(-0.611647\pi\)
−0.343602 + 0.939115i \(0.611647\pi\)
\(702\) 5.97161e7 0.172616
\(703\) 3.52727e8 1.01525
\(704\) −6.79230e6 −0.0194670
\(705\) −7.26682e8 −2.07385
\(706\) 1.12011e8i 0.318306i
\(707\) 5.46616e7i 0.154676i
\(708\) 4.06284e8i 1.14480i
\(709\) 4.51159e7 0.126588 0.0632938 0.997995i \(-0.479839\pi\)
0.0632938 + 0.997995i \(0.479839\pi\)
\(710\) 1.38672e8i 0.387448i
\(711\) −2.35784e8 −0.656001
\(712\) −1.19197e7 −0.0330236
\(713\) −2.68540e8 −0.740867
\(714\) 1.00397e6i 0.00275821i
\(715\) 2.18926e7i 0.0598934i
\(716\) 4.88748e8i 1.33151i
\(717\) 6.36758e8i 1.72750i
\(718\) 1.87397e7i 0.0506277i
\(719\) 6.75759e8 1.81805 0.909024 0.416744i \(-0.136829\pi\)
0.909024 + 0.416744i \(0.136829\pi\)
\(720\) 3.13232e8i 0.839205i
\(721\) 3.59247e6i 0.00958489i
\(722\) 1.13373e8i 0.301231i
\(723\) 5.70043e8 1.50832
\(724\) 1.66242e8 0.438052
\(725\) 5.13188e6i 0.0134667i
\(726\) −2.19303e8 −0.573105
\(727\) 1.12489e8i 0.292758i −0.989229 0.146379i \(-0.953238\pi\)
0.989229 0.146379i \(-0.0467618\pi\)
\(728\) −4.26566e7 −0.110559
\(729\) 6.05215e8 1.56216
\(730\) 1.79594e7i 0.0461660i
\(731\) −4.07306e6 8.26616e6i −0.0104272 0.0211618i
\(732\) −8.54241e8 −2.17795
\(733\) 6.77003e8i 1.71901i −0.511126 0.859506i \(-0.670771\pi\)
0.511126 0.859506i \(-0.329229\pi\)
\(734\) 2.05498e7i 0.0519661i
\(735\) −5.93779e8 −1.49542
\(736\) 1.92561e8i 0.482986i
\(737\) −5.78549e7 −0.144523
\(738\) 2.36745e8i 0.588995i
\(739\) 5.36084e8i 1.32831i 0.747595 + 0.664155i \(0.231209\pi\)
−0.747595 + 0.664155i \(0.768791\pi\)
\(740\) 2.66169e8 0.656845
\(741\) 6.62013e8 1.62709
\(742\) 1.14015e7 0.0279094
\(743\) 2.50988e7i 0.0611909i 0.999532 + 0.0305955i \(0.00974036\pi\)
−0.999532 + 0.0305955i \(0.990260\pi\)
\(744\) −6.22798e8 −1.51227
\(745\) −2.43679e7 −0.0589318
\(746\) −2.98707e7 −0.0719498
\(747\) 6.92902e7 0.166230
\(748\) 641945. 0.00153389
\(749\) 1.27291e8i 0.302936i
\(750\) 2.40520e8i 0.570122i
\(751\) 6.06389e8i 1.43163i 0.698289 + 0.715816i \(0.253945\pi\)
−0.698289 + 0.715816i \(0.746055\pi\)
\(752\) 3.39852e8 0.799164
\(753\) 6.94031e8i 1.62553i
\(754\) 7.97242e7 0.185984
\(755\) −2.67842e8 −0.622354
\(756\) 4.44379e7 0.102846
\(757\) 4.02328e7i 0.0927454i −0.998924 0.0463727i \(-0.985234\pi\)
0.998924 0.0463727i \(-0.0147662\pi\)
\(758\) 2.83905e8i 0.651876i
\(759\) 2.67872e7i 0.0612636i
\(760\) 4.14310e8i 0.943810i
\(761\) 1.17921e8i 0.267571i 0.991010 + 0.133785i \(0.0427133\pi\)
−0.991010 + 0.133785i \(0.957287\pi\)
\(762\) 1.49863e8 0.338711
\(763\) 1.46152e8i 0.329027i
\(764\) 7.92813e7i 0.177783i
\(765\) 1.47481e7i 0.0329421i
\(766\) 1.28536e8 0.285983
\(767\) 3.05101e8 0.676172
\(768\) 8.50442e7i 0.187742i
\(769\) −2.78052e8 −0.611430 −0.305715 0.952123i \(-0.598895\pi\)
−0.305715 + 0.952123i \(0.598895\pi\)
\(770\) 2.64083e6i 0.00578453i
\(771\) 6.78389e8 1.48018
\(772\) −3.91407e8 −0.850701
\(773\) 3.45546e8i 0.748114i 0.927406 + 0.374057i \(0.122034\pi\)
−0.927406 + 0.374057i \(0.877966\pi\)
\(774\) −2.14652e8 + 1.05768e8i −0.462926 + 0.228102i
\(775\) 1.39242e7 0.0299134
\(776\) 1.21472e8i 0.259951i
\(777\) 1.10922e8i 0.236459i
\(778\) −9.62038e6 −0.0204293
\(779\) 7.25166e8i 1.53400i
\(780\) 4.99557e8 1.05269
\(781\) 3.69509e7i 0.0775660i
\(782\) 2.21363e6i 0.00462898i
\(783\) −1.79570e8