Properties

Label 43.7.b.b.42.7
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 42.7
Root \(-7.14115i\) 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.42.14

$q$-expansion

\(f(q)\) \(=\) \(q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} +O(q^{10})\) \(q-7.14115i q^{2} -19.7617i q^{3} +13.0039 q^{4} -151.678i q^{5} -141.122 q^{6} +62.8896i q^{7} -549.897i q^{8} +338.474 q^{9} -1083.16 q^{10} -497.851 q^{11} -256.980i q^{12} +850.633 q^{13} +449.105 q^{14} -2997.43 q^{15} -3094.65 q^{16} -8046.00 q^{17} -2417.10i q^{18} +11446.3i q^{19} -1972.42i q^{20} +1242.81 q^{21} +3555.23i q^{22} +6206.07 q^{23} -10866.9 q^{24} -7381.34 q^{25} -6074.50i q^{26} -21095.1i q^{27} +817.813i q^{28} -23809.8i q^{29} +21405.1i q^{30} +26939.3 q^{31} -13094.1i q^{32} +9838.40i q^{33} +57457.7i q^{34} +9539.00 q^{35} +4401.49 q^{36} -23588.9i q^{37} +81740.0 q^{38} -16810.0i q^{39} -83407.5 q^{40} +87352.8 q^{41} -8875.08i q^{42} +(79070.1 - 8323.35i) q^{43} -6474.02 q^{44} -51339.2i q^{45} -44318.5i q^{46} -39004.6 q^{47} +61155.6i q^{48} +113694. q^{49} +52711.3i q^{50} +159003. i q^{51} +11061.6 q^{52} -178171. q^{53} -150644. q^{54} +75513.3i q^{55} +34582.8 q^{56} +226199. q^{57} -170030. q^{58} +19938.3 q^{59} -38978.3 q^{60} +34949.8i q^{61} -192377. i q^{62} +21286.5i q^{63} -291564. q^{64} -129023. i q^{65} +70257.5 q^{66} -299904. q^{67} -104630. q^{68} -122643. i q^{69} -68119.5i q^{70} -362351. i q^{71} -186126. i q^{72} -89951.1i q^{73} -168452. q^{74} +145868. i q^{75} +148847. i q^{76} -31309.7i q^{77} -120043. q^{78} +434327. q^{79} +469391. i q^{80} -170129. q^{81} -623800. i q^{82} +662276. q^{83} +16161.4 q^{84} +1.22041e6i q^{85} +(-59438.3 - 564652. i) q^{86} -470523. q^{87} +273767. i q^{88} +1.26108e6i q^{89} -366621. q^{90} +53496.0i q^{91} +80703.2 q^{92} -532366. i q^{93} +278538. i q^{94} +1.73616e6 q^{95} -258761. q^{96} +83771.3 q^{97} -811906. i q^{98} -168510. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.14115i 0.892644i −0.894872 0.446322i \(-0.852734\pi\)
0.894872 0.446322i \(-0.147266\pi\)
\(3\) 19.7617i 0.731916i −0.930631 0.365958i \(-0.880741\pi\)
0.930631 0.365958i \(-0.119259\pi\)
\(4\) 13.0039 0.203186
\(5\) 151.678i 1.21343i −0.794920 0.606714i \(-0.792487\pi\)
0.794920 0.606714i \(-0.207513\pi\)
\(6\) −141.122 −0.653340
\(7\) 62.8896i 0.183352i 0.995789 + 0.0916759i \(0.0292224\pi\)
−0.995789 + 0.0916759i \(0.970778\pi\)
\(8\) 549.897i 1.07402i
\(9\) 338.474 0.464299
\(10\) −1083.16 −1.08316
\(11\) −497.851 −0.374043 −0.187021 0.982356i \(-0.559883\pi\)
−0.187021 + 0.982356i \(0.559883\pi\)
\(12\) 256.980i 0.148715i
\(13\) 850.633 0.387179 0.193590 0.981083i \(-0.437987\pi\)
0.193590 + 0.981083i \(0.437987\pi\)
\(14\) 449.105 0.163668
\(15\) −2997.43 −0.888127
\(16\) −3094.65 −0.755529
\(17\) −8046.00 −1.63770 −0.818848 0.574010i \(-0.805387\pi\)
−0.818848 + 0.574010i \(0.805387\pi\)
\(18\) 2417.10i 0.414454i
\(19\) 11446.3i 1.66880i 0.551156 + 0.834402i \(0.314187\pi\)
−0.551156 + 0.834402i \(0.685813\pi\)
\(20\) 1972.42i 0.246552i
\(21\) 1242.81 0.134198
\(22\) 3555.23i 0.333887i
\(23\) 6206.07 0.510074 0.255037 0.966931i \(-0.417912\pi\)
0.255037 + 0.966931i \(0.417912\pi\)
\(24\) −10866.9 −0.786090
\(25\) −7381.34 −0.472406
\(26\) 6074.50i 0.345613i
\(27\) 21095.1i 1.07174i
\(28\) 817.813i 0.0372546i
\(29\) 23809.8i 0.976253i −0.872773 0.488126i \(-0.837680\pi\)
0.872773 0.488126i \(-0.162320\pi\)
\(30\) 21405.1i 0.792781i
\(31\) 26939.3 0.904275 0.452138 0.891948i \(-0.350662\pi\)
0.452138 + 0.891948i \(0.350662\pi\)
\(32\) 13094.1i 0.399599i
\(33\) 9838.40i 0.273768i
\(34\) 57457.7i 1.46188i
\(35\) 9539.00 0.222484
\(36\) 4401.49 0.0943393
\(37\) 23588.9i 0.465696i −0.972513 0.232848i \(-0.925196\pi\)
0.972513 0.232848i \(-0.0748044\pi\)
\(38\) 81740.0 1.48965
\(39\) 16810.0i 0.283383i
\(40\) −83407.5 −1.30324
\(41\) 87352.8 1.26743 0.633717 0.773565i \(-0.281528\pi\)
0.633717 + 0.773565i \(0.281528\pi\)
\(42\) 8875.08i 0.119791i
\(43\) 79070.1 8323.35i 0.994505 0.104687i
\(44\) −6474.02 −0.0760004
\(45\) 51339.2i 0.563393i
\(46\) 44318.5i 0.455314i
\(47\) −39004.6 −0.375684 −0.187842 0.982199i \(-0.560149\pi\)
−0.187842 + 0.982199i \(0.560149\pi\)
\(48\) 61155.6i 0.552984i
\(49\) 113694. 0.966382
\(50\) 52711.3i 0.421690i
\(51\) 159003.i 1.19866i
\(52\) 11061.6 0.0786696
\(53\) −178171. −1.19676 −0.598382 0.801211i \(-0.704190\pi\)
−0.598382 + 0.801211i \(0.704190\pi\)
\(54\) −150644. −0.956686
\(55\) 75513.3i 0.453874i
\(56\) 34582.8 0.196923
\(57\) 226199. 1.22142
\(58\) −170030. −0.871446
\(59\) 19938.3 0.0970806 0.0485403 0.998821i \(-0.484543\pi\)
0.0485403 + 0.998821i \(0.484543\pi\)
\(60\) −38978.3 −0.180455
\(61\) 34949.8i 0.153977i 0.997032 + 0.0769885i \(0.0245305\pi\)
−0.997032 + 0.0769885i \(0.975470\pi\)
\(62\) 192377.i 0.807196i
\(63\) 21286.5i 0.0851301i
\(64\) −291564. −1.11223
\(65\) 129023.i 0.469814i
\(66\) 70257.5 0.244377
\(67\) −299904. −0.997143 −0.498572 0.866849i \(-0.666142\pi\)
−0.498572 + 0.866849i \(0.666142\pi\)
\(68\) −104630. −0.332758
\(69\) 122643.i 0.373331i
\(70\) 68119.5i 0.198599i
\(71\) 362351.i 1.01241i −0.862414 0.506203i \(-0.831049\pi\)
0.862414 0.506203i \(-0.168951\pi\)
\(72\) 186126.i 0.498665i
\(73\) 89951.1i 0.231227i −0.993294 0.115613i \(-0.963117\pi\)
0.993294 0.115613i \(-0.0368833\pi\)
\(74\) −168452. −0.415701
\(75\) 145868.i 0.345761i
\(76\) 148847.i 0.339078i
\(77\) 31309.7i 0.0685814i
\(78\) −120043. −0.252960
\(79\) 434327. 0.880917 0.440459 0.897773i \(-0.354816\pi\)
0.440459 + 0.897773i \(0.354816\pi\)
\(80\) 469391.i 0.916779i
\(81\) −170129. −0.320127
\(82\) 623800.i 1.13137i
\(83\) 662276. 1.15826 0.579128 0.815236i \(-0.303393\pi\)
0.579128 + 0.815236i \(0.303393\pi\)
\(84\) 16161.4 0.0272672
\(85\) 1.22041e6i 1.98723i
\(86\) −59438.3 564652.i −0.0934483 0.887739i
\(87\) −470523. −0.714535
\(88\) 273767.i 0.401729i
\(89\) 1.26108e6i 1.78884i 0.447223 + 0.894422i \(0.352413\pi\)
−0.447223 + 0.894422i \(0.647587\pi\)
\(90\) −366621. −0.502910
\(91\) 53496.0i 0.0709900i
\(92\) 80703.2 0.103640
\(93\) 532366.i 0.661853i
\(94\) 278538.i 0.335352i
\(95\) 1.73616e6 2.02497
\(96\) −258761. −0.292473
\(97\) 83771.3 0.0917868 0.0458934 0.998946i \(-0.485387\pi\)
0.0458934 + 0.998946i \(0.485387\pi\)
\(98\) 811906.i 0.862635i
\(99\) −168510. −0.173668
\(100\) −95986.5 −0.0959865
\(101\) 1.19842e6 1.16318 0.581588 0.813483i \(-0.302432\pi\)
0.581588 + 0.813483i \(0.302432\pi\)
\(102\) 1.13546e6 1.06997
\(103\) 737144. 0.674592 0.337296 0.941399i \(-0.390488\pi\)
0.337296 + 0.941399i \(0.390488\pi\)
\(104\) 467760.i 0.415837i
\(105\) 188507.i 0.162840i
\(106\) 1.27234e6i 1.06829i
\(107\) −604874. −0.493758 −0.246879 0.969046i \(-0.579405\pi\)
−0.246879 + 0.969046i \(0.579405\pi\)
\(108\) 274320.i 0.217764i
\(109\) −1.09966e6 −0.849137 −0.424569 0.905396i \(-0.639574\pi\)
−0.424569 + 0.905396i \(0.639574\pi\)
\(110\) 539252. 0.405148
\(111\) −466157. −0.340850
\(112\) 194621.i 0.138528i
\(113\) 543549.i 0.376707i 0.982101 + 0.188354i \(0.0603151\pi\)
−0.982101 + 0.188354i \(0.939685\pi\)
\(114\) 1.61532e6i 1.09030i
\(115\) 941326.i 0.618937i
\(116\) 309621.i 0.198361i
\(117\) 287917. 0.179767
\(118\) 142383.i 0.0866585i
\(119\) 506010.i 0.300275i
\(120\) 1.64828e6i 0.953864i
\(121\) −1.52371e6 −0.860092
\(122\) 249582. 0.137447
\(123\) 1.72624e6i 0.927655i
\(124\) 350316. 0.183736
\(125\) 1.25038e6i 0.640197i
\(126\) 152010. 0.0759908
\(127\) −1.48723e6 −0.726050 −0.363025 0.931779i \(-0.618256\pi\)
−0.363025 + 0.931779i \(0.618256\pi\)
\(128\) 1.24408e6i 0.593225i
\(129\) −164484. 1.56256e6i −0.0766221 0.727894i
\(130\) −921370. −0.419377
\(131\) 1.22120e6i 0.543216i −0.962408 0.271608i \(-0.912445\pi\)
0.962408 0.271608i \(-0.0875554\pi\)
\(132\) 127938.i 0.0556259i
\(133\) −719856. −0.305978
\(134\) 2.14166e6i 0.890094i
\(135\) −3.19968e6 −1.30048
\(136\) 4.42447e6i 1.75891i
\(137\) 4.63396e6i 1.80215i 0.433663 + 0.901075i \(0.357221\pi\)
−0.433663 + 0.901075i \(0.642779\pi\)
\(138\) −875809. −0.333252
\(139\) 4.40785e6 1.64128 0.820640 0.571445i \(-0.193617\pi\)
0.820640 + 0.571445i \(0.193617\pi\)
\(140\) 124045. 0.0452057
\(141\) 770799.i 0.274969i
\(142\) −2.58761e6 −0.903718
\(143\) −423488. −0.144822
\(144\) −1.04746e6 −0.350791
\(145\) −3.61144e6 −1.18461
\(146\) −642355. −0.206403
\(147\) 2.24679e6i 0.707310i
\(148\) 306748.i 0.0946231i
\(149\) 285992.i 0.0864560i 0.999065 + 0.0432280i \(0.0137642\pi\)
−0.999065 + 0.0432280i \(0.986236\pi\)
\(150\) 1.04167e6 0.308642
\(151\) 663208.i 0.192628i 0.995351 + 0.0963139i \(0.0307053\pi\)
−0.995351 + 0.0963139i \(0.969295\pi\)
\(152\) 6.29430e6 1.79233
\(153\) −2.72336e6 −0.760381
\(154\) −223587. −0.0612188
\(155\) 4.08610e6i 1.09727i
\(156\) 218596.i 0.0575795i
\(157\) 5.29376e6i 1.36793i −0.729513 0.683967i \(-0.760253\pi\)
0.729513 0.683967i \(-0.239747\pi\)
\(158\) 3.10159e6i 0.786346i
\(159\) 3.52096e6i 0.875931i
\(160\) −1.98609e6 −0.484884
\(161\) 390297.i 0.0935229i
\(162\) 1.21492e6i 0.285760i
\(163\) 3.06833e6i 0.708499i −0.935151 0.354250i \(-0.884736\pi\)
0.935151 0.354250i \(-0.115264\pi\)
\(164\) 1.13593e6 0.257525
\(165\) 1.49227e6 0.332198
\(166\) 4.72942e6i 1.03391i
\(167\) 3.30726e6 0.710100 0.355050 0.934847i \(-0.384464\pi\)
0.355050 + 0.934847i \(0.384464\pi\)
\(168\) 683416.i 0.144131i
\(169\) −4.10323e6 −0.850092
\(170\) 8.71510e6 1.77389
\(171\) 3.87429e6i 0.774825i
\(172\) 1.02822e6 108236.i 0.202070 0.0212710i
\(173\) 4.04583e6 0.781393 0.390696 0.920520i \(-0.372234\pi\)
0.390696 + 0.920520i \(0.372234\pi\)
\(174\) 3.36008e6i 0.637825i
\(175\) 464210.i 0.0866165i
\(176\) 1.54067e6 0.282600
\(177\) 394016.i 0.0710549i
\(178\) 9.00557e6 1.59680
\(179\) 1.00806e7i 1.75763i 0.477160 + 0.878816i \(0.341666\pi\)
−0.477160 + 0.878816i \(0.658334\pi\)
\(180\) 667612.i 0.114474i
\(181\) −7.62117e6 −1.28524 −0.642622 0.766183i \(-0.722154\pi\)
−0.642622 + 0.766183i \(0.722154\pi\)
\(182\) 382023. 0.0633688
\(183\) 690669. 0.112698
\(184\) 3.41270e6i 0.547828i
\(185\) −3.57793e6 −0.565088
\(186\) −3.80171e6 −0.590800
\(187\) 4.00571e6 0.612569
\(188\) −507213. −0.0763339
\(189\) 1.32667e6 0.196506
\(190\) 1.23982e7i 1.80758i
\(191\) 9.84078e6i 1.41231i 0.708058 + 0.706154i \(0.249571\pi\)
−0.708058 + 0.706154i \(0.750429\pi\)
\(192\) 5.76181e6i 0.814058i
\(193\) 2.29302e6 0.318960 0.159480 0.987201i \(-0.449018\pi\)
0.159480 + 0.987201i \(0.449018\pi\)
\(194\) 598224.i 0.0819329i
\(195\) −2.54971e6 −0.343864
\(196\) 1.47847e6 0.196356
\(197\) 3.50465e6 0.458401 0.229201 0.973379i \(-0.426389\pi\)
0.229201 + 0.973379i \(0.426389\pi\)
\(198\) 1.20335e6i 0.155024i
\(199\) 7.63511e6i 0.968849i 0.874833 + 0.484425i \(0.160971\pi\)
−0.874833 + 0.484425i \(0.839029\pi\)
\(200\) 4.05898e6i 0.507372i
\(201\) 5.92662e6i 0.729825i
\(202\) 8.55811e6i 1.03830i
\(203\) 1.49739e6 0.178998
\(204\) 2.06766e6i 0.243551i
\(205\) 1.32495e7i 1.53794i
\(206\) 5.26406e6i 0.602170i
\(207\) 2.10059e6 0.236827
\(208\) −2.63241e6 −0.292525
\(209\) 5.69857e6i 0.624205i
\(210\) −1.34616e6 −0.145358
\(211\) 1.06028e7i 1.12869i 0.825540 + 0.564344i \(0.190871\pi\)
−0.825540 + 0.564344i \(0.809129\pi\)
\(212\) −2.31692e6 −0.243166
\(213\) −7.16069e6 −0.740996
\(214\) 4.31950e6i 0.440750i
\(215\) −1.26247e6 1.19932e7i −0.127030 1.20676i
\(216\) −1.16001e7 −1.15107
\(217\) 1.69420e6i 0.165800i
\(218\) 7.85282e6i 0.757978i
\(219\) −1.77759e6 −0.169238
\(220\) 981969.i 0.0922210i
\(221\) −6.84419e6 −0.634082
\(222\) 3.32890e6i 0.304258i
\(223\) 6.78272e6i 0.611631i −0.952091 0.305815i \(-0.901071\pi\)
0.952091 0.305815i \(-0.0989290\pi\)
\(224\) 823481. 0.0732671
\(225\) −2.49839e6 −0.219338
\(226\) 3.88157e6 0.336265
\(227\) 2.30718e6i 0.197244i −0.995125 0.0986220i \(-0.968557\pi\)
0.995125 0.0986220i \(-0.0314435\pi\)
\(228\) 2.94148e6 0.248177
\(229\) −3.28542e6 −0.273580 −0.136790 0.990600i \(-0.543679\pi\)
−0.136790 + 0.990600i \(0.543679\pi\)
\(230\) −6.72215e6 −0.552491
\(231\) −618733. −0.0501958
\(232\) −1.30930e7 −1.04851
\(233\) 1.01559e6i 0.0802878i −0.999194 0.0401439i \(-0.987218\pi\)
0.999194 0.0401439i \(-0.0127816\pi\)
\(234\) 2.05606e6i 0.160468i
\(235\) 5.91616e6i 0.455865i
\(236\) 259277. 0.0197255
\(237\) 8.58304e6i 0.644757i
\(238\) −3.61350e6 −0.268038
\(239\) 1.27984e7 0.937479 0.468740 0.883336i \(-0.344708\pi\)
0.468740 + 0.883336i \(0.344708\pi\)
\(240\) 9.27598e6 0.671005
\(241\) 7.77825e6i 0.555688i 0.960626 + 0.277844i \(0.0896198\pi\)
−0.960626 + 0.277844i \(0.910380\pi\)
\(242\) 1.08810e7i 0.767756i
\(243\) 1.20163e7i 0.837438i
\(244\) 454485.i 0.0312860i
\(245\) 1.72449e7i 1.17263i
\(246\) −1.23274e7 −0.828066
\(247\) 9.73662e6i 0.646127i
\(248\) 1.48138e7i 0.971207i
\(249\) 1.30877e7i 0.847746i
\(250\) −8.92919e6 −0.571468
\(251\) 1.19067e7 0.752956 0.376478 0.926425i \(-0.377135\pi\)
0.376478 + 0.926425i \(0.377135\pi\)
\(252\) 276808.i 0.0172973i
\(253\) −3.08970e6 −0.190789
\(254\) 1.06205e7i 0.648104i
\(255\) 2.41173e7 1.45448
\(256\) −9.77590e6 −0.582689
\(257\) 6.20650e6i 0.365635i −0.983147 0.182817i \(-0.941478\pi\)
0.983147 0.182817i \(-0.0585217\pi\)
\(258\) −1.11585e7 + 1.17460e6i −0.649750 + 0.0683963i
\(259\) 1.48350e6 0.0853861
\(260\) 1.67780e6i 0.0954598i
\(261\) 8.05901e6i 0.453273i
\(262\) −8.72076e6 −0.484898
\(263\) 1.56294e7i 0.859162i 0.903028 + 0.429581i \(0.141339\pi\)
−0.903028 + 0.429581i \(0.858661\pi\)
\(264\) 5.41010e6 0.294032
\(265\) 2.70247e7i 1.45219i
\(266\) 5.14060e6i 0.273130i
\(267\) 2.49211e7 1.30928
\(268\) −3.89993e6 −0.202606
\(269\) −2.69821e7 −1.38618 −0.693090 0.720851i \(-0.743751\pi\)
−0.693090 + 0.720851i \(0.743751\pi\)
\(270\) 2.28494e7i 1.16087i
\(271\) 2.23391e7 1.12243 0.561213 0.827672i \(-0.310335\pi\)
0.561213 + 0.827672i \(0.310335\pi\)
\(272\) 2.48995e7 1.23733
\(273\) 1.05717e6 0.0519587
\(274\) 3.30919e7 1.60868
\(275\) 3.67481e6 0.176700
\(276\) 1.59484e6i 0.0758558i
\(277\) 3.66692e7i 1.72529i 0.505812 + 0.862644i \(0.331193\pi\)
−0.505812 + 0.862644i \(0.668807\pi\)
\(278\) 3.14772e7i 1.46508i
\(279\) 9.11824e6 0.419854
\(280\) 5.24547e6i 0.238952i
\(281\) −3.37401e7 −1.52065 −0.760323 0.649546i \(-0.774959\pi\)
−0.760323 + 0.649546i \(0.774959\pi\)
\(282\) 5.50439e6 0.245449
\(283\) −1.38133e7 −0.609448 −0.304724 0.952441i \(-0.598564\pi\)
−0.304724 + 0.952441i \(0.598564\pi\)
\(284\) 4.71199e6i 0.205707i
\(285\) 3.43096e7i 1.48211i
\(286\) 3.02420e6i 0.129274i
\(287\) 5.49359e6i 0.232386i
\(288\) 4.43200e6i 0.185533i
\(289\) 4.06006e7 1.68205
\(290\) 2.57898e7i 1.05744i
\(291\) 1.65547e6i 0.0671802i
\(292\) 1.16972e6i 0.0469821i
\(293\) 3.07684e7 1.22321 0.611605 0.791163i \(-0.290524\pi\)
0.611605 + 0.791163i \(0.290524\pi\)
\(294\) −1.60447e7 −0.631377
\(295\) 3.02421e6i 0.117800i
\(296\) −1.29715e7 −0.500165
\(297\) 1.05022e7i 0.400878i
\(298\) 2.04231e6 0.0771744
\(299\) 5.27908e6 0.197490
\(300\) 1.89686e6i 0.0702540i
\(301\) 523453. + 4.97269e6i 0.0191946 + 0.182344i
\(302\) 4.73607e6 0.171948
\(303\) 2.36829e7i 0.851347i
\(304\) 3.54223e7i 1.26083i
\(305\) 5.30114e6 0.186840
\(306\) 1.94480e7i 0.678750i
\(307\) 1.70554e7 0.589450 0.294725 0.955582i \(-0.404772\pi\)
0.294725 + 0.955582i \(0.404772\pi\)
\(308\) 407149.i 0.0139348i
\(309\) 1.45672e7i 0.493744i
\(310\) −2.91795e7 −0.979474
\(311\) −1.62947e7 −0.541709 −0.270855 0.962620i \(-0.587306\pi\)
−0.270855 + 0.962620i \(0.587306\pi\)
\(312\) −9.24375e6 −0.304358
\(313\) 3.82726e7i 1.24811i 0.781379 + 0.624057i \(0.214517\pi\)
−0.781379 + 0.624057i \(0.785483\pi\)
\(314\) −3.78035e7 −1.22108
\(315\) 3.22870e6 0.103299
\(316\) 5.64795e6 0.178990
\(317\) −3.73589e7 −1.17278 −0.586390 0.810029i \(-0.699452\pi\)
−0.586390 + 0.810029i \(0.699452\pi\)
\(318\) 2.51437e7 0.781895
\(319\) 1.18538e7i 0.365160i
\(320\) 4.42240e7i 1.34961i
\(321\) 1.19534e7i 0.361389i
\(322\) 2.78717e6 0.0834826
\(323\) 9.20972e7i 2.73300i
\(324\) −2.21234e6 −0.0650455
\(325\) −6.27881e6 −0.182906
\(326\) −2.19114e7 −0.632438
\(327\) 2.17311e7i 0.621497i
\(328\) 4.80350e7i 1.36125i
\(329\) 2.45299e6i 0.0688823i
\(330\) 1.06565e7i 0.296534i
\(331\) 5.23966e7i 1.44484i −0.691455 0.722419i \(-0.743030\pi\)
0.691455 0.722419i \(-0.256970\pi\)
\(332\) 8.61219e6 0.235342
\(333\) 7.98423e6i 0.216222i
\(334\) 2.36177e7i 0.633866i
\(335\) 4.54889e7i 1.20996i
\(336\) −3.84605e6 −0.101390
\(337\) −1.79657e7 −0.469413 −0.234706 0.972066i \(-0.575413\pi\)
−0.234706 + 0.972066i \(0.575413\pi\)
\(338\) 2.93018e7i 0.758830i
\(339\) 1.07415e7 0.275718
\(340\) 1.58701e7i 0.403777i
\(341\) −1.34117e7 −0.338238
\(342\) 2.76669e7 0.691643
\(343\) 1.45491e7i 0.360540i
\(344\) −4.57699e6 4.34804e7i −0.112436 1.06812i
\(345\) −1.86022e7 −0.453010
\(346\) 2.88919e7i 0.697506i
\(347\) 1.42201e7i 0.340342i 0.985415 + 0.170171i \(0.0544319\pi\)
−0.985415 + 0.170171i \(0.945568\pi\)
\(348\) −6.11865e6 −0.145184
\(349\) 5.94543e7i 1.39864i 0.714807 + 0.699322i \(0.246515\pi\)
−0.714807 + 0.699322i \(0.753485\pi\)
\(350\) −3.31500e6 −0.0773177
\(351\) 1.79442e7i 0.414957i
\(352\) 6.51889e6i 0.149467i
\(353\) −4.22812e7 −0.961222 −0.480611 0.876934i \(-0.659585\pi\)
−0.480611 + 0.876934i \(0.659585\pi\)
\(354\) −2.81373e6 −0.0634267
\(355\) −5.49609e7 −1.22848
\(356\) 1.63990e7i 0.363469i
\(357\) −9.99964e6 −0.219776
\(358\) 7.19873e7 1.56894
\(359\) −4.65626e6 −0.100636 −0.0503181 0.998733i \(-0.516024\pi\)
−0.0503181 + 0.998733i \(0.516024\pi\)
\(360\) −2.82313e7 −0.605094
\(361\) −8.39726e7 −1.78491
\(362\) 5.44239e7i 1.14727i
\(363\) 3.01110e7i 0.629515i
\(364\) 695658.i 0.0144242i
\(365\) −1.36436e7 −0.280577
\(366\) 4.93218e6i 0.100599i
\(367\) 8.70497e7 1.76104 0.880519 0.474010i \(-0.157194\pi\)
0.880519 + 0.474010i \(0.157194\pi\)
\(368\) −1.92056e7 −0.385375
\(369\) 2.95667e7 0.588469
\(370\) 2.55505e7i 0.504423i
\(371\) 1.12051e7i 0.219429i
\(372\) 6.92285e6i 0.134480i
\(373\) 7.31787e7i 1.41013i 0.709144 + 0.705064i \(0.249082\pi\)
−0.709144 + 0.705064i \(0.750918\pi\)
\(374\) 2.86054e7i 0.546806i
\(375\) −2.47098e7 −0.468570
\(376\) 2.14485e7i 0.403491i
\(377\) 2.02534e7i 0.377985i
\(378\) 9.47392e6i 0.175410i
\(379\) 6.34098e7 1.16477 0.582383 0.812914i \(-0.302120\pi\)
0.582383 + 0.812914i \(0.302120\pi\)
\(380\) 2.25769e7 0.411447
\(381\) 2.93902e7i 0.531407i
\(382\) 7.02745e7 1.26069
\(383\) 3.12303e7i 0.555878i 0.960599 + 0.277939i \(0.0896514\pi\)
−0.960599 + 0.277939i \(0.910349\pi\)
\(384\) 2.45852e7 0.434191
\(385\) −4.74900e6 −0.0832186
\(386\) 1.63748e7i 0.284718i
\(387\) 2.67632e7 2.81724e6i 0.461748 0.0486061i
\(388\) 1.08936e6 0.0186498
\(389\) 8.33816e7i 1.41652i −0.705954 0.708258i \(-0.749481\pi\)
0.705954 0.708258i \(-0.250519\pi\)
\(390\) 1.82079e7i 0.306948i
\(391\) −4.99340e7 −0.835346
\(392\) 6.25199e7i 1.03791i
\(393\) −2.41330e7 −0.397588
\(394\) 2.50272e7i 0.409189i
\(395\) 6.58780e7i 1.06893i
\(396\) −2.19129e6 −0.0352869
\(397\) 5.18629e7 0.828868 0.414434 0.910079i \(-0.363980\pi\)
0.414434 + 0.910079i \(0.363980\pi\)
\(398\) 5.45235e7 0.864838
\(399\) 1.42256e7i 0.223950i
\(400\) 2.28426e7 0.356916
\(401\) −7.16633e7 −1.11138 −0.555692 0.831389i \(-0.687546\pi\)
−0.555692 + 0.831389i \(0.687546\pi\)
\(402\) 4.23229e7 0.651474
\(403\) 2.29154e7 0.350117
\(404\) 1.55842e7 0.236342
\(405\) 2.58049e7i 0.388451i
\(406\) 1.06931e7i 0.159781i
\(407\) 1.17438e7i 0.174190i
\(408\) 8.74352e7 1.28738
\(409\) 7.67014e7i 1.12107i −0.828130 0.560536i \(-0.810595\pi\)
0.828130 0.560536i \(-0.189405\pi\)
\(410\) −9.46170e7 −1.37283
\(411\) 9.15751e7 1.31902
\(412\) 9.58577e6 0.137068
\(413\) 1.25391e6i 0.0177999i
\(414\) 1.50007e7i 0.211402i
\(415\) 1.00453e8i 1.40546i
\(416\) 1.11382e7i 0.154716i
\(417\) 8.71068e7i 1.20128i
\(418\) −4.06944e7 −0.557193
\(419\) 1.21037e8i 1.64542i 0.568463 + 0.822709i \(0.307538\pi\)
−0.568463 + 0.822709i \(0.692462\pi\)
\(420\) 2.45133e6i 0.0330868i
\(421\) 9.79470e7i 1.31264i −0.754484 0.656319i \(-0.772113\pi\)
0.754484 0.656319i \(-0.227887\pi\)
\(422\) 7.57163e7 1.00752
\(423\) −1.32021e7 −0.174430
\(424\) 9.79755e7i 1.28535i
\(425\) 5.93903e7 0.773658
\(426\) 5.11356e7i 0.661446i
\(427\) −2.19798e6 −0.0282319
\(428\) −7.86574e6 −0.100325
\(429\) 8.36886e6i 0.105997i
\(430\) −8.56455e7 + 9.01551e6i −1.07721 + 0.113393i
\(431\) −1.07153e8 −1.33836 −0.669180 0.743100i \(-0.733355\pi\)
−0.669180 + 0.743100i \(0.733355\pi\)
\(432\) 6.52820e7i 0.809733i
\(433\) 6.76798e7i 0.833672i 0.908982 + 0.416836i \(0.136861\pi\)
−0.908982 + 0.416836i \(0.863139\pi\)
\(434\) 1.20985e7 0.148001
\(435\) 7.13683e7i 0.867036i
\(436\) −1.42999e7 −0.172533
\(437\) 7.10367e7i 0.851213i
\(438\) 1.26940e7i 0.151070i
\(439\) −4.94825e7 −0.584868 −0.292434 0.956286i \(-0.594465\pi\)
−0.292434 + 0.956286i \(0.594465\pi\)
\(440\) 4.15245e7 0.487468
\(441\) 3.84824e7 0.448690
\(442\) 4.88754e7i 0.566010i
\(443\) −1.18835e8 −1.36689 −0.683446 0.730001i \(-0.739520\pi\)
−0.683446 + 0.730001i \(0.739520\pi\)
\(444\) −6.06188e6 −0.0692561
\(445\) 1.91279e8 2.17063
\(446\) −4.84365e7 −0.545969
\(447\) 5.65170e6 0.0632785
\(448\) 1.83364e7i 0.203929i
\(449\) 4.56263e7i 0.504054i 0.967720 + 0.252027i \(0.0810971\pi\)
−0.967720 + 0.252027i \(0.918903\pi\)
\(450\) 1.78414e7i 0.195791i
\(451\) −4.34887e7 −0.474075
\(452\) 7.06828e6i 0.0765418i
\(453\) 1.31061e7 0.140987
\(454\) −1.64759e7 −0.176069
\(455\) 8.11419e6 0.0861412
\(456\) 1.24386e8i 1.31183i
\(457\) 1.21404e8i 1.27199i −0.771693 0.635996i \(-0.780590\pi\)
0.771693 0.635996i \(-0.219410\pi\)
\(458\) 2.34617e7i 0.244209i
\(459\) 1.69732e8i 1.75519i
\(460\) 1.22409e7i 0.125760i
\(461\) −1.90871e8 −1.94821 −0.974106 0.226093i \(-0.927405\pi\)
−0.974106 + 0.226093i \(0.927405\pi\)
\(462\) 4.41847e6i 0.0448070i
\(463\) 8.17525e6i 0.0823680i −0.999152 0.0411840i \(-0.986887\pi\)
0.999152 0.0411840i \(-0.0131130\pi\)
\(464\) 7.36830e7i 0.737587i
\(465\) −8.07485e7 −0.803111
\(466\) −7.25247e6 −0.0716684
\(467\) 1.86571e8i 1.83186i −0.401334 0.915932i \(-0.631453\pi\)
0.401334 0.915932i \(-0.368547\pi\)
\(468\) 3.74405e6 0.0365262
\(469\) 1.88608e7i 0.182828i
\(470\) 4.22482e7 0.406925
\(471\) −1.04614e8 −1.00121
\(472\) 1.09640e7i 0.104266i
\(473\) −3.93652e7 + 4.14379e6i −0.371988 + 0.0391574i
\(474\) −6.12928e7 −0.575539
\(475\) 8.44893e7i 0.788353i
\(476\) 6.58012e6i 0.0610117i
\(477\) −6.03062e7 −0.555657
\(478\) 9.13952e7i 0.836835i
\(479\) 1.51306e8 1.37673 0.688365 0.725364i \(-0.258329\pi\)
0.688365 + 0.725364i \(0.258329\pi\)
\(480\) 3.92485e7i 0.354894i
\(481\) 2.00655e7i 0.180308i
\(482\) 5.55457e7 0.496031
\(483\) 7.71295e6 0.0684509
\(484\) −1.98142e7 −0.174759
\(485\) 1.27063e7i 0.111377i
\(486\) −8.58103e7 −0.747534
\(487\) 1.17577e8 1.01797 0.508984 0.860776i \(-0.330021\pi\)
0.508984 + 0.860776i \(0.330021\pi\)
\(488\) 1.92188e7 0.165374
\(489\) −6.06355e7 −0.518562
\(490\) −1.23149e8 −1.04675
\(491\) 1.63911e7i 0.138472i 0.997600 + 0.0692362i \(0.0220562\pi\)
−0.997600 + 0.0692362i \(0.977944\pi\)
\(492\) 2.24479e7i 0.188487i
\(493\) 1.91574e8i 1.59881i
\(494\) 6.95307e7 0.576761
\(495\) 2.55593e7i 0.210733i
\(496\) −8.33675e7 −0.683206
\(497\) 2.27881e7 0.185626
\(498\) −9.34614e7 −0.756736
\(499\) 1.32763e8i 1.06850i −0.845325 0.534252i \(-0.820593\pi\)
0.845325 0.534252i \(-0.179407\pi\)
\(500\) 1.62599e7i 0.130079i
\(501\) 6.53572e7i 0.519733i
\(502\) 8.50275e7i 0.672122i
\(503\) 2.13319e8i 1.67620i 0.545518 + 0.838099i \(0.316333\pi\)
−0.545518 + 0.838099i \(0.683667\pi\)
\(504\) 1.17054e7 0.0914312
\(505\) 1.81775e8i 1.41143i
\(506\) 2.20640e7i 0.170307i
\(507\) 8.10870e7i 0.622196i
\(508\) −1.93398e7 −0.147523
\(509\) 2.22706e8 1.68880 0.844400 0.535713i \(-0.179957\pi\)
0.844400 + 0.535713i \(0.179957\pi\)
\(510\) 1.72225e8i 1.29834i
\(511\) 5.65699e6 0.0423958
\(512\) 1.49433e8i 1.11336i
\(513\) 2.41462e8 1.78853
\(514\) −4.43216e7 −0.326382
\(515\) 1.11809e8i 0.818568i
\(516\) −2.13894e6 2.03195e7i −0.0155686 0.147898i
\(517\) 1.94185e7 0.140522
\(518\) 1.05939e7i 0.0762194i
\(519\) 7.99526e7i 0.571914i
\(520\) −7.09491e7 −0.504588
\(521\) 8.01608e7i 0.566825i −0.958998 0.283412i \(-0.908533\pi\)
0.958998 0.283412i \(-0.0914665\pi\)
\(522\) −5.75506e7 −0.404612
\(523\) 1.76645e8i 1.23480i 0.786650 + 0.617400i \(0.211814\pi\)
−0.786650 + 0.617400i \(0.788186\pi\)
\(524\) 1.58804e7i 0.110374i
\(525\) −9.17359e6 −0.0633960
\(526\) 1.11612e8 0.766926
\(527\) −2.16753e8 −1.48093
\(528\) 3.04464e7i 0.206840i
\(529\) −1.09521e8 −0.739825
\(530\) 1.92987e8 1.29629
\(531\) 6.74861e6 0.0450745
\(532\) −9.36095e6 −0.0621706
\(533\) 7.43052e7 0.490724
\(534\) 1.77966e8i 1.16872i
\(535\) 9.17464e7i 0.599139i
\(536\) 1.64916e8i 1.07095i
\(537\) 1.99210e8 1.28644
\(538\) 1.92684e8i 1.23736i
\(539\) −5.66026e7 −0.361468
\(540\) −4.16084e7 −0.264241
\(541\) −6.68009e7 −0.421882 −0.210941 0.977499i \(-0.567653\pi\)
−0.210941 + 0.977499i \(0.567653\pi\)
\(542\) 1.59527e8i 1.00193i
\(543\) 1.50607e8i 0.940691i
\(544\) 1.05355e8i 0.654422i
\(545\) 1.66794e8i 1.03037i
\(546\) 7.54944e6i 0.0463806i
\(547\) 1.50528e8 0.919718 0.459859 0.887992i \(-0.347900\pi\)
0.459859 + 0.887992i \(0.347900\pi\)
\(548\) 6.02598e7i 0.366172i
\(549\) 1.18296e7i 0.0714914i
\(550\) 2.62424e7i 0.157730i
\(551\) 2.72535e8 1.62918
\(552\) −6.74408e7 −0.400964
\(553\) 2.73146e7i 0.161518i
\(554\) 2.61860e8 1.54007
\(555\) 7.07060e7i 0.413597i
\(556\) 5.73194e7 0.333486
\(557\) 2.12922e8 1.23213 0.616063 0.787697i \(-0.288727\pi\)
0.616063 + 0.787697i \(0.288727\pi\)
\(558\) 6.51148e7i 0.374780i
\(559\) 6.72596e7 7.08012e6i 0.385052 0.0405326i
\(560\) −2.95198e7 −0.168093
\(561\) 7.91598e7i 0.448349i
\(562\) 2.40943e8i 1.35739i
\(563\) −2.20517e8 −1.23571 −0.617854 0.786293i \(-0.711998\pi\)
−0.617854 + 0.786293i \(0.711998\pi\)
\(564\) 1.00234e7i 0.0558700i
\(565\) 8.24447e7 0.457107
\(566\) 9.86426e7i 0.544021i
\(567\) 1.06993e7i 0.0586959i
\(568\) −1.99256e8 −1.08734
\(569\) −7.04114e7 −0.382214 −0.191107 0.981569i \(-0.561208\pi\)
−0.191107 + 0.981569i \(0.561208\pi\)
\(570\) −2.45010e8 −1.32300
\(571\) 1.62010e8i 0.870230i −0.900375 0.435115i \(-0.856708\pi\)
0.900375 0.435115i \(-0.143292\pi\)
\(572\) −5.50701e6 −0.0294258
\(573\) 1.94471e8 1.03369
\(574\) 3.92306e7 0.207438
\(575\) −4.58091e7 −0.240962
\(576\) −9.86869e7 −0.516407
\(577\) 1.10893e8i 0.577267i 0.957440 + 0.288633i \(0.0932009\pi\)
−0.957440 + 0.288633i \(0.906799\pi\)
\(578\) 2.89935e8i 1.50147i
\(579\) 4.53140e7i 0.233452i
\(580\) −4.69629e7 −0.240697
\(581\) 4.16503e7i 0.212368i
\(582\) −1.18219e7 −0.0599680
\(583\) 8.87025e7 0.447641
\(584\) −4.94638e7 −0.248341
\(585\) 4.36708e7i 0.218134i
\(586\) 2.19722e8i 1.09189i
\(587\) 3.50946e8i 1.73510i −0.497346 0.867552i \(-0.665692\pi\)
0.497346 0.867552i \(-0.334308\pi\)
\(588\) 2.92171e7i 0.143716i
\(589\) 3.08356e8i 1.50906i
\(590\) −2.15964e7 −0.105154
\(591\) 6.92579e7i 0.335511i
\(592\) 7.29993e7i 0.351847i
\(593\) 2.22461e8i 1.06682i −0.845857 0.533409i \(-0.820911\pi\)
0.845857 0.533409i \(-0.179089\pi\)
\(594\) 7.49981e7 0.357842
\(595\) −7.67508e7 −0.364361
\(596\) 3.71902e6i 0.0175667i
\(597\) 1.50883e8 0.709116
\(598\) 3.76987e7i 0.176288i
\(599\) −1.33213e8 −0.619818 −0.309909 0.950766i \(-0.600299\pi\)
−0.309909 + 0.950766i \(0.600299\pi\)
\(600\) 8.02124e7 0.371354
\(601\) 2.01869e8i 0.929923i 0.885331 + 0.464961i \(0.153932\pi\)
−0.885331 + 0.464961i \(0.846068\pi\)
\(602\) 3.55108e7 3.73806e6i 0.162769 0.0171339i
\(603\) −1.01510e8 −0.462973
\(604\) 8.62432e6i 0.0391394i
\(605\) 2.31113e8i 1.04366i
\(606\) −1.69123e8 −0.759950
\(607\) 2.22303e8i 0.993984i −0.867755 0.496992i \(-0.834438\pi\)
0.867755 0.496992i \(-0.165562\pi\)
\(608\) 1.49879e8 0.666853
\(609\) 2.95911e7i 0.131011i
\(610\) 3.78562e7i 0.166782i
\(611\) −3.31786e7 −0.145457
\(612\) −3.54144e7 −0.154499
\(613\) −1.59462e8 −0.692272 −0.346136 0.938184i \(-0.612506\pi\)
−0.346136 + 0.938184i \(0.612506\pi\)
\(614\) 1.21795e8i 0.526169i
\(615\) −2.61834e8 −1.12564
\(616\) −1.72171e7 −0.0736576
\(617\) 2.02638e8 0.862710 0.431355 0.902182i \(-0.358036\pi\)
0.431355 + 0.902182i \(0.358036\pi\)
\(618\) −1.04027e8 −0.440738
\(619\) −3.11733e8 −1.31435 −0.657176 0.753737i \(-0.728249\pi\)
−0.657176 + 0.753737i \(0.728249\pi\)
\(620\) 5.31354e7i 0.222951i
\(621\) 1.30918e8i 0.546668i
\(622\) 1.16363e8i 0.483554i
\(623\) −7.93089e7 −0.327988
\(624\) 5.20209e7i 0.214104i
\(625\) −3.04990e8 −1.24924
\(626\) 2.73310e8 1.11412
\(627\) −1.12614e8 −0.456865
\(628\) 6.88397e7i 0.277946i
\(629\) 1.89796e8i 0.762668i
\(630\) 2.30567e7i 0.0922094i
\(631\) 5.37251e7i 0.213840i 0.994268 + 0.106920i \(0.0340989\pi\)
−0.994268 + 0.106920i \(0.965901\pi\)
\(632\) 2.38835e8i 0.946120i
\(633\) 2.09530e8 0.826105
\(634\) 2.66786e8i 1.04688i
\(635\) 2.25580e8i 0.881008i
\(636\) 4.57863e7i 0.177977i
\(637\) 9.67117e7 0.374163
\(638\) 8.46495e7 0.325958
\(639\) 1.22647e8i 0.470059i
\(640\) 1.88701e8 0.719836
\(641\) 2.85462e8i 1.08386i −0.840423 0.541932i \(-0.817693\pi\)
0.840423 0.541932i \(-0.182307\pi\)
\(642\) 8.53608e7 0.322592
\(643\) 1.02329e7 0.0384917 0.0192458 0.999815i \(-0.493873\pi\)
0.0192458 + 0.999815i \(0.493873\pi\)
\(644\) 5.07540e6i 0.0190026i
\(645\) −2.37007e8 + 2.49486e7i −0.883247 + 0.0929754i
\(646\) −6.57680e8 −2.43959
\(647\) 3.72540e8i 1.37550i 0.725948 + 0.687750i \(0.241401\pi\)
−0.725948 + 0.687750i \(0.758599\pi\)
\(648\) 9.35532e7i 0.343822i
\(649\) −9.92632e6 −0.0363123
\(650\) 4.48380e7i 0.163270i
\(651\) 3.34803e7 0.121352
\(652\) 3.99004e7i 0.143957i
\(653\) 4.26942e7i 0.153331i 0.997057 + 0.0766653i \(0.0244273\pi\)
−0.997057 + 0.0766653i \(0.975573\pi\)
\(654\) 1.55185e8 0.554776
\(655\) −1.85229e8 −0.659153
\(656\) −2.70326e8 −0.957583
\(657\) 3.04461e7i 0.107358i
\(658\) −1.75172e7 −0.0614874
\(659\) 5.08637e8 1.77726 0.888632 0.458621i \(-0.151656\pi\)
0.888632 + 0.458621i \(0.151656\pi\)
\(660\) 1.94054e7 0.0674980
\(661\) −2.03116e7 −0.0703299 −0.0351650 0.999382i \(-0.511196\pi\)
−0.0351650 + 0.999382i \(0.511196\pi\)
\(662\) −3.74172e8 −1.28973
\(663\) 1.35253e8i 0.464095i
\(664\) 3.64184e8i 1.24399i
\(665\) 1.09187e8i 0.371282i
\(666\) −5.70166e7 −0.193009
\(667\) 1.47765e8i 0.497961i
\(668\) 4.30074e7 0.144283
\(669\) −1.34038e8 −0.447662
\(670\) 3.24843e8 1.08006
\(671\) 1.73998e7i 0.0575940i
\(672\) 1.62734e7i 0.0536254i
\(673\) 1.75373e8i 0.575329i 0.957731 + 0.287665i \(0.0928789\pi\)
−0.957731 + 0.287665i \(0.907121\pi\)
\(674\) 1.28296e8i 0.419018i
\(675\) 1.55710e8i 0.506298i
\(676\) −5.33582e7 −0.172727
\(677\) 5.93350e8i 1.91225i −0.292956 0.956126i \(-0.594639\pi\)
0.292956 0.956126i \(-0.405361\pi\)
\(678\) 7.67065e7i 0.246118i
\(679\) 5.26835e6i 0.0168293i
\(680\) 6.71097e8 2.13432
\(681\) −4.55939e7 −0.144366
\(682\) 9.57753e7i 0.301926i
\(683\) −3.53734e8 −1.11024 −0.555118 0.831772i \(-0.687327\pi\)
−0.555118 + 0.831772i \(0.687327\pi\)
\(684\) 5.03810e7i 0.157434i
\(685\) 7.02872e8 2.18678
\(686\) 1.03897e8 0.321834
\(687\) 6.49255e7i 0.200237i
\(688\) −2.44694e8 + 2.57578e7i −0.751377 + 0.0790941i
\(689\) −1.51558e8 −0.463362
\(690\) 1.32841e8i 0.404377i
\(691\) 8.65200e7i 0.262230i 0.991367 + 0.131115i \(0.0418557\pi\)
−0.991367 + 0.131115i \(0.958144\pi\)
\(692\) 5.26117e7 0.158768
\(693\) 1.05975e7i 0.0318423i
\(694\) 1.01548e8 0.303804
\(695\) 6.68576e8i 1.99158i
\(696\) 2.58739e8i 0.767423i
\(697\) −7.02841e8 −2.07567
\(698\) 4.24573e8 1.24849
\(699\) −2.00698e7 −0.0587639
\(700\) 6.03656e6i 0.0175993i
\(701\) 1.50201e8 0.436032 0.218016 0.975945i \(-0.430042\pi\)
0.218016 + 0.975945i \(0.430042\pi\)
\(702\) −1.28142e8 −0.370409
\(703\) 2.70006e8 0.777155
\(704\) 1.45155e8 0.416021
\(705\) 1.16914e8 0.333655
\(706\) 3.01937e8i 0.858029i
\(707\) 7.53683e7i 0.213270i
\(708\) 5.12375e6i 0.0144374i
\(709\) 7.03450e8 1.97376 0.986880 0.161454i \(-0.0516184\pi\)
0.986880 + 0.161454i \(0.0516184\pi\)
\(710\) 3.92484e8i 1.09660i
\(711\) 1.47008e8 0.409009
\(712\) 6.93464e8 1.92125
\(713\) 1.67187e8 0.461247
\(714\) 7.14090e7i 0.196181i
\(715\) 6.42341e7i 0.175731i
\(716\) 1.31088e8i 0.357127i
\(717\) 2.52918e8i 0.686156i
\(718\) 3.32511e7i 0.0898323i
\(719\) −6.87823e8 −1.85050 −0.925252 0.379354i \(-0.876146\pi\)
−0.925252 + 0.379354i \(0.876146\pi\)
\(720\) 1.58877e8i 0.425660i
\(721\) 4.63587e7i 0.123688i
\(722\) 5.99661e8i 1.59329i
\(723\) 1.53712e8 0.406717
\(724\) −9.91052e7 −0.261144
\(725\) 1.75749e8i 0.461188i
\(726\) 2.15028e8 0.561933
\(727\) 4.47696e8i 1.16514i −0.812779 0.582572i \(-0.802046\pi\)
0.812779 0.582572i \(-0.197954\pi\)
\(728\) 2.94173e7 0.0762445
\(729\) −3.61487e8 −0.933061
\(730\) 9.74313e7i 0.250455i
\(731\) −6.36199e8 + 6.69697e7i −1.62870 + 0.171446i
\(732\) 8.98142e6 0.0228987
\(733\) 5.04366e8i 1.28066i −0.768100 0.640330i \(-0.778798\pi\)
0.768100 0.640330i \(-0.221202\pi\)
\(734\) 6.21635e8i 1.57198i
\(735\) −3.40789e8 −0.858270
\(736\) 8.12626e7i 0.203825i
\(737\) 1.49307e8 0.372974
\(738\) 2.11140e8i 0.525293i
\(739\) 2.26091e8i 0.560209i −0.959970 0.280104i \(-0.909631\pi\)
0.959970 0.280104i \(-0.0903691\pi\)
\(740\) −4.65271e7 −0.114818
\(741\) 1.92413e8 0.472910
\(742\) −8.00173e7 −0.195872
\(743\) 2.00268e8i 0.488252i 0.969743 + 0.244126i \(0.0785011\pi\)
−0.969743 + 0.244126i \(0.921499\pi\)
\(744\) −2.92747e8 −0.710842
\(745\) 4.33788e7 0.104908
\(746\) 5.22580e8 1.25874
\(747\) 2.24163e8 0.537778
\(748\) 5.20900e7 0.124466
\(749\) 3.80403e7i 0.0905313i
\(750\) 1.76456e8i 0.418267i
\(751\) 7.41639e8i 1.75095i −0.483267 0.875473i \(-0.660550\pi\)
0.483267 0.875473i \(-0.339450\pi\)
\(752\) 1.20706e8 0.283840
\(753\) 2.35297e8i 0.551101i
\(754\) −1.44633e8 −0.337406
\(755\) 1.00594e8 0.233740
\(756\) 1.72519e7 0.0399274
\(757\) 4.49947e8i 1.03723i 0.855009 + 0.518614i \(0.173552\pi\)
−0.855009 + 0.518614i \(0.826448\pi\)
\(758\) 4.52819e8i 1.03972i
\(759\) 6.10577e7i 0.139642i
\(760\) 9.54710e8i 2.17486i
\(761\) 3.06930e8i 0.696442i 0.937412 + 0.348221i \(0.113214\pi\)
−0.937412 + 0.348221i \(0.886786\pi\)
\(762\) 2.09880e8 0.474358
\(763\) 6.91571e7i 0.155691i
\(764\) 1.27969e8i 0.286962i
\(765\) 4.13076e8i 0.922667i
\(766\) 2.23020e8 0.496201
\(767\) 1.69602e7 0.0375876
\(768\) 1.93189e8i 0.426480i
\(769\) 5.68563e8 1.25026 0.625129 0.780522i \(-0.285046\pi\)
0.625129 + 0.780522i \(0.285046\pi\)
\(770\) 3.39134e7i 0.0742846i
\(771\) −1.22651e8 −0.267614
\(772\) 2.98183e7 0.0648083
\(773\) 1.80822e8i 0.391483i −0.980656 0.195741i \(-0.937289\pi\)
0.980656 0.195741i \(-0.0627113\pi\)
\(774\) −2.01183e7 1.91120e8i −0.0433880 0.412177i
\(775\) −1.98848e8 −0.427185
\(776\) 4.60656e7i 0.0985806i
\(777\) 2.93165e7i 0.0624955i
\(778\) −5.95441e8 −1.26444
\(779\) 9.99870e8i 2.11510i
\(780\) −3.31563e7 −0.0698685
\(781\) 1.80397e8i 0.378683i
\(782\) 3.56587e8i 0.745667i
\(783\) −5.02272e8