Properties

Label 43.7.b.b.42.18
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 42.18
Root \(13.1339i\) 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.42.3

$q$-expansion

\(f(q)\) \(=\) \(q+13.1339i q^{2} -22.6278i q^{3} -108.500 q^{4} -138.961i q^{5} +297.193 q^{6} +295.441i q^{7} -584.463i q^{8} +216.980 q^{9} +O(q^{10})\) \(q+13.1339i q^{2} -22.6278i q^{3} -108.500 q^{4} -138.961i q^{5} +297.193 q^{6} +295.441i q^{7} -584.463i q^{8} +216.980 q^{9} +1825.10 q^{10} +1638.85 q^{11} +2455.13i q^{12} +3924.21 q^{13} -3880.31 q^{14} -3144.38 q^{15} +732.289 q^{16} -3266.76 q^{17} +2849.81i q^{18} -8538.82i q^{19} +15077.3i q^{20} +6685.20 q^{21} +21524.6i q^{22} +9920.10 q^{23} -13225.2 q^{24} -3685.02 q^{25} +51540.4i q^{26} -21405.5i q^{27} -32055.5i q^{28} +10554.6i q^{29} -41298.0i q^{30} +18861.5 q^{31} -27787.8i q^{32} -37083.7i q^{33} -42905.5i q^{34} +41054.7 q^{35} -23542.4 q^{36} +9016.52i q^{37} +112148. q^{38} -88796.5i q^{39} -81217.3 q^{40} -83955.2 q^{41} +87803.0i q^{42} +(-49574.1 + 62159.2i) q^{43} -177816. q^{44} -30151.7i q^{45} +130290. i q^{46} +98965.6 q^{47} -16570.1i q^{48} +30363.5 q^{49} -48398.9i q^{50} +73919.9i q^{51} -425778. q^{52} +49401.5 q^{53} +281138. q^{54} -227736. i q^{55} +172675. q^{56} -193215. q^{57} -138623. q^{58} -32952.4 q^{59} +341166. q^{60} +294417. i q^{61} +247726. i q^{62} +64105.0i q^{63} +411830. q^{64} -545311. i q^{65} +487054. q^{66} -352200. q^{67} +354445. q^{68} -224470. i q^{69} +539209. i q^{70} -412839. i q^{71} -126817. i q^{72} +380514. i q^{73} -118422. q^{74} +83384.2i q^{75} +926464. i q^{76} +484184. i q^{77} +1.16625e6 q^{78} -752994. q^{79} -101759. i q^{80} -326182. q^{81} -1.10266e6i q^{82} -164914. q^{83} -725346. q^{84} +453951. i q^{85} +(-816395. - 651103. i) q^{86} +238827. q^{87} -957848. i q^{88} -904693. i q^{89} +396011. q^{90} +1.15937e6i q^{91} -1.07633e6 q^{92} -426795. i q^{93} +1.29981e6i q^{94} -1.18656e6 q^{95} -628779. q^{96} +977097. q^{97} +398792. i q^{98} +355599. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 13.1339i 1.64174i 0.571114 + 0.820871i \(0.306512\pi\)
−0.571114 + 0.820871i \(0.693488\pi\)
\(3\) 22.6278i 0.838068i −0.907970 0.419034i \(-0.862369\pi\)
0.907970 0.419034i \(-0.137631\pi\)
\(4\) −108.500 −1.69532
\(5\) 138.961i 1.11168i −0.831288 0.555842i \(-0.812396\pi\)
0.831288 0.555842i \(-0.187604\pi\)
\(6\) 297.193 1.37589
\(7\) 295.441i 0.861345i 0.902508 + 0.430672i \(0.141724\pi\)
−0.902508 + 0.430672i \(0.858276\pi\)
\(8\) 584.463i 1.14153i
\(9\) 216.980 0.297641
\(10\) 1825.10 1.82510
\(11\) 1638.85 1.23129 0.615646 0.788023i \(-0.288895\pi\)
0.615646 + 0.788023i \(0.288895\pi\)
\(12\) 2455.13i 1.42079i
\(13\) 3924.21 1.78617 0.893084 0.449889i \(-0.148536\pi\)
0.893084 + 0.449889i \(0.148536\pi\)
\(14\) −3880.31 −1.41411
\(15\) −3144.38 −0.931667
\(16\) 732.289 0.178782
\(17\) −3266.76 −0.664923 −0.332461 0.943117i \(-0.607879\pi\)
−0.332461 + 0.943117i \(0.607879\pi\)
\(18\) 2849.81i 0.488650i
\(19\) 8538.82i 1.24491i −0.782657 0.622454i \(-0.786136\pi\)
0.782657 0.622454i \(-0.213864\pi\)
\(20\) 15077.3i 1.88466i
\(21\) 6685.20 0.721866
\(22\) 21524.6i 2.02146i
\(23\) 9920.10 0.815328 0.407664 0.913132i \(-0.366343\pi\)
0.407664 + 0.913132i \(0.366343\pi\)
\(24\) −13225.2 −0.956680
\(25\) −3685.02 −0.235842
\(26\) 51540.4i 2.93243i
\(27\) 21405.5i 1.08751i
\(28\) 32055.5i 1.46025i
\(29\) 10554.6i 0.432759i 0.976309 + 0.216380i \(0.0694249\pi\)
−0.976309 + 0.216380i \(0.930575\pi\)
\(30\) 41298.0i 1.52956i
\(31\) 18861.5 0.633128 0.316564 0.948571i \(-0.397471\pi\)
0.316564 + 0.948571i \(0.397471\pi\)
\(32\) 27787.8i 0.848017i
\(33\) 37083.7i 1.03191i
\(34\) 42905.5i 1.09163i
\(35\) 41054.7 0.957543
\(36\) −23542.4 −0.504596
\(37\) 9016.52i 0.178006i 0.996031 + 0.0890029i \(0.0283680\pi\)
−0.996031 + 0.0890029i \(0.971632\pi\)
\(38\) 112148. 2.04382
\(39\) 88796.5i 1.49693i
\(40\) −81217.3 −1.26902
\(41\) −83955.2 −1.21814 −0.609068 0.793118i \(-0.708457\pi\)
−0.609068 + 0.793118i \(0.708457\pi\)
\(42\) 87803.0i 1.18512i
\(43\) −49574.1 + 62159.2i −0.623519 + 0.781808i
\(44\) −177816. −2.08743
\(45\) 30151.7i 0.330883i
\(46\) 130290.i 1.33856i
\(47\) 98965.6 0.953215 0.476607 0.879116i \(-0.341866\pi\)
0.476607 + 0.879116i \(0.341866\pi\)
\(48\) 16570.1i 0.149831i
\(49\) 30363.5 0.258085
\(50\) 48398.9i 0.387191i
\(51\) 73919.9i 0.557251i
\(52\) −425778. −3.02812
\(53\) 49401.5 0.331828 0.165914 0.986140i \(-0.446943\pi\)
0.165914 + 0.986140i \(0.446943\pi\)
\(54\) 281138. 1.78541
\(55\) 227736.i 1.36881i
\(56\) 172675. 0.983251
\(57\) −193215. −1.04332
\(58\) −138623. −0.710479
\(59\) −32952.4 −0.160447 −0.0802234 0.996777i \(-0.525563\pi\)
−0.0802234 + 0.996777i \(0.525563\pi\)
\(60\) 341166. 1.57947
\(61\) 294417.i 1.29710i 0.761172 + 0.648550i \(0.224624\pi\)
−0.761172 + 0.648550i \(0.775376\pi\)
\(62\) 247726.i 1.03943i
\(63\) 64105.0i 0.256372i
\(64\) 411830. 1.57101
\(65\) 545311.i 1.98566i
\(66\) 487054. 1.69413
\(67\) −352200. −1.17102 −0.585510 0.810665i \(-0.699106\pi\)
−0.585510 + 0.810665i \(0.699106\pi\)
\(68\) 354445. 1.12725
\(69\) 224470.i 0.683301i
\(70\) 539209.i 1.57204i
\(71\) 412839.i 1.15347i −0.816932 0.576735i \(-0.804327\pi\)
0.816932 0.576735i \(-0.195673\pi\)
\(72\) 126817.i 0.339766i
\(73\) 380514.i 0.978141i 0.872244 + 0.489071i \(0.162664\pi\)
−0.872244 + 0.489071i \(0.837336\pi\)
\(74\) −118422. −0.292239
\(75\) 83384.2i 0.197651i
\(76\) 926464.i 2.11051i
\(77\) 484184.i 1.06057i
\(78\) 1.16625e6 2.45758
\(79\) −752994. −1.52725 −0.763625 0.645660i \(-0.776582\pi\)
−0.763625 + 0.645660i \(0.776582\pi\)
\(80\) 101759.i 0.198749i
\(81\) −326182. −0.613768
\(82\) 1.10266e6i 1.99987i
\(83\) −164914. −0.288418 −0.144209 0.989547i \(-0.546064\pi\)
−0.144209 + 0.989547i \(0.546064\pi\)
\(84\) −725346. −1.22379
\(85\) 453951.i 0.739184i
\(86\) −816395. 651103.i −1.28353 1.02366i
\(87\) 238827. 0.362682
\(88\) 957848.i 1.40556i
\(89\) 904693.i 1.28331i −0.766994 0.641655i \(-0.778248\pi\)
0.766994 0.641655i \(-0.221752\pi\)
\(90\) 396011. 0.543225
\(91\) 1.15937e6i 1.53851i
\(92\) −1.07633e6 −1.38224
\(93\) 426795.i 0.530604i
\(94\) 1.29981e6i 1.56493i
\(95\) −1.18656e6 −1.38394
\(96\) −628779. −0.710696
\(97\) 977097. 1.07059 0.535294 0.844666i \(-0.320201\pi\)
0.535294 + 0.844666i \(0.320201\pi\)
\(98\) 398792.i 0.423709i
\(99\) 355599. 0.366484
\(100\) 399826. 0.399826
\(101\) 1.36505e6 1.32490 0.662450 0.749106i \(-0.269517\pi\)
0.662450 + 0.749106i \(0.269517\pi\)
\(102\) −970859. −0.914862
\(103\) −481251. −0.440413 −0.220207 0.975453i \(-0.570673\pi\)
−0.220207 + 0.975453i \(0.570673\pi\)
\(104\) 2.29356e6i 2.03897i
\(105\) 928979.i 0.802487i
\(106\) 648837.i 0.544776i
\(107\) 839996. 0.685687 0.342843 0.939393i \(-0.388610\pi\)
0.342843 + 0.939393i \(0.388610\pi\)
\(108\) 2.32250e6i 1.84368i
\(109\) −1.81764e6 −1.40355 −0.701776 0.712398i \(-0.747609\pi\)
−0.701776 + 0.712398i \(0.747609\pi\)
\(110\) 2.99106e6 2.24723
\(111\) 204025. 0.149181
\(112\) 216348.i 0.153993i
\(113\) 1.55685e6i 1.07897i −0.841994 0.539486i \(-0.818618\pi\)
0.841994 0.539486i \(-0.181382\pi\)
\(114\) 2.53767e6i 1.71286i
\(115\) 1.37850e6i 0.906387i
\(116\) 1.14517e6i 0.733664i
\(117\) 851478. 0.531638
\(118\) 432795.i 0.263412i
\(119\) 965137.i 0.572728i
\(120\) 1.83777e6i 1.06353i
\(121\) 914270. 0.516082
\(122\) −3.86686e6 −2.12950
\(123\) 1.89973e6i 1.02088i
\(124\) −2.04648e6 −1.07335
\(125\) 1.65919e6i 0.849503i
\(126\) −841951. −0.420896
\(127\) −960451. −0.468882 −0.234441 0.972130i \(-0.575326\pi\)
−0.234441 + 0.972130i \(0.575326\pi\)
\(128\) 3.63053e6i 1.73117i
\(129\) 1.40653e6 + 1.12176e6i 0.655209 + 0.522551i
\(130\) 7.16207e6 3.25993
\(131\) 3.57250e6i 1.58913i 0.607182 + 0.794563i \(0.292300\pi\)
−0.607182 + 0.794563i \(0.707700\pi\)
\(132\) 4.02359e6i 1.74941i
\(133\) 2.52272e6 1.07229
\(134\) 4.62577e6i 1.92251i
\(135\) −2.97452e6 −1.20897
\(136\) 1.90930e6i 0.759029i
\(137\) 4.56853e6i 1.77670i 0.459164 + 0.888351i \(0.348149\pi\)
−0.459164 + 0.888351i \(0.651851\pi\)
\(138\) 2.94818e6 1.12180
\(139\) −3.61640e6 −1.34658 −0.673290 0.739378i \(-0.735120\pi\)
−0.673290 + 0.739378i \(0.735120\pi\)
\(140\) −4.45444e6 −1.62334
\(141\) 2.23938e6i 0.798859i
\(142\) 5.42220e6 1.89370
\(143\) 6.43120e6 2.19930
\(144\) 158892. 0.0532128
\(145\) 1.46667e6 0.481092
\(146\) −4.99764e6 −1.60586
\(147\) 687060.i 0.216293i
\(148\) 978295.i 0.301776i
\(149\) 2.60224e6i 0.786663i 0.919397 + 0.393331i \(0.128677\pi\)
−0.919397 + 0.393331i \(0.871323\pi\)
\(150\) −1.09516e6 −0.324492
\(151\) 2.66549e6i 0.774188i −0.922040 0.387094i \(-0.873479\pi\)
0.922040 0.387094i \(-0.126521\pi\)
\(152\) −4.99063e6 −1.42110
\(153\) −708824. −0.197908
\(154\) −6.35924e6 −1.74118
\(155\) 2.62100e6i 0.703838i
\(156\) 9.63444e6i 2.53777i
\(157\) 5.69323e6i 1.47116i 0.677438 + 0.735580i \(0.263090\pi\)
−0.677438 + 0.735580i \(0.736910\pi\)
\(158\) 9.88977e6i 2.50735i
\(159\) 1.11785e6i 0.278095i
\(160\) −3.86141e6 −0.942727
\(161\) 2.93081e6i 0.702279i
\(162\) 4.28405e6i 1.00765i
\(163\) 3.64901e6i 0.842582i −0.906926 0.421291i \(-0.861577\pi\)
0.906926 0.421291i \(-0.138423\pi\)
\(164\) 9.10916e6 2.06513
\(165\) −5.15316e6 −1.14716
\(166\) 2.16596e6i 0.473508i
\(167\) 3.21802e6 0.690938 0.345469 0.938430i \(-0.387720\pi\)
0.345469 + 0.938430i \(0.387720\pi\)
\(168\) 3.90726e6i 0.824032i
\(169\) 1.05726e7 2.19040
\(170\) −5.96217e6 −1.21355
\(171\) 1.85276e6i 0.370536i
\(172\) 5.37880e6 6.74429e6i 1.05706 1.32541i
\(173\) 3.00030e6 0.579464 0.289732 0.957108i \(-0.406434\pi\)
0.289732 + 0.957108i \(0.406434\pi\)
\(174\) 3.13674e6i 0.595430i
\(175\) 1.08871e6i 0.203141i
\(176\) 1.20011e6 0.220132
\(177\) 745642.i 0.134465i
\(178\) 1.18822e7 2.10686
\(179\) 2.48400e6i 0.433104i 0.976271 + 0.216552i \(0.0694811\pi\)
−0.976271 + 0.216552i \(0.930519\pi\)
\(180\) 3.27147e6i 0.560951i
\(181\) −9.37063e6 −1.58028 −0.790138 0.612929i \(-0.789991\pi\)
−0.790138 + 0.612929i \(0.789991\pi\)
\(182\) −1.52272e7 −2.52583
\(183\) 6.66203e6 1.08706
\(184\) 5.79793e6i 0.930722i
\(185\) 1.25294e6 0.197886
\(186\) 5.60550e6 0.871115
\(187\) −5.35374e6 −0.818714
\(188\) −1.07378e7 −1.61600
\(189\) 6.32407e6 0.936723
\(190\) 1.55842e7i 2.27208i
\(191\) 5.54978e6i 0.796482i −0.917281 0.398241i \(-0.869621\pi\)
0.917281 0.398241i \(-0.130379\pi\)
\(192\) 9.31883e6i 1.31661i
\(193\) −86852.8 −0.0120812 −0.00604062 0.999982i \(-0.501923\pi\)
−0.00604062 + 0.999982i \(0.501923\pi\)
\(194\) 1.28331e7i 1.75763i
\(195\) −1.23392e7 −1.66412
\(196\) −3.29444e6 −0.437536
\(197\) −9.72532e6 −1.27205 −0.636026 0.771667i \(-0.719423\pi\)
−0.636026 + 0.771667i \(0.719423\pi\)
\(198\) 4.67041e6i 0.601671i
\(199\) 1.24242e7i 1.57656i 0.615318 + 0.788279i \(0.289028\pi\)
−0.615318 + 0.788279i \(0.710972\pi\)
\(200\) 2.15376e6i 0.269220i
\(201\) 7.96952e6i 0.981395i
\(202\) 1.79284e7i 2.17514i
\(203\) −3.11826e6 −0.372755
\(204\) 8.02032e6i 0.944716i
\(205\) 1.16665e7i 1.35418i
\(206\) 6.32072e6i 0.723045i
\(207\) 2.15247e6 0.242675
\(208\) 2.87366e6 0.319334
\(209\) 1.39938e7i 1.53285i
\(210\) 1.22011e7 1.31748
\(211\) 1.09760e6i 0.116842i −0.998292 0.0584209i \(-0.981393\pi\)
0.998292 0.0584209i \(-0.0186065\pi\)
\(212\) −5.36008e6 −0.562553
\(213\) −9.34166e6 −0.966686
\(214\) 1.10325e7i 1.12572i
\(215\) 8.63768e6 + 6.88884e6i 0.869124 + 0.693156i
\(216\) −1.25107e7 −1.24143
\(217\) 5.57247e6i 0.545341i
\(218\) 2.38728e7i 2.30427i
\(219\) 8.61021e6 0.819750
\(220\) 2.47094e7i 2.32056i
\(221\) −1.28195e7 −1.18766
\(222\) 2.67964e6i 0.244917i
\(223\) 1.37225e7i 1.23743i −0.785616 0.618714i \(-0.787654\pi\)
0.785616 0.618714i \(-0.212346\pi\)
\(224\) 8.20967e6 0.730435
\(225\) −799578. −0.0701962
\(226\) 2.04475e7 1.77140
\(227\) 3.65964e6i 0.312868i 0.987688 + 0.156434i \(0.0499998\pi\)
−0.987688 + 0.156434i \(0.950000\pi\)
\(228\) 2.09639e7 1.76875
\(229\) 8.39728e6 0.699250 0.349625 0.936890i \(-0.386309\pi\)
0.349625 + 0.936890i \(0.386309\pi\)
\(230\) 1.81052e7 1.48805
\(231\) 1.09560e7 0.888828
\(232\) 6.16876e6 0.494008
\(233\) 8.63710e6i 0.682811i −0.939916 0.341405i \(-0.889097\pi\)
0.939916 0.341405i \(-0.110903\pi\)
\(234\) 1.11833e7i 0.872812i
\(235\) 1.37523e7i 1.05967i
\(236\) 3.57534e6 0.272008
\(237\) 1.70386e7i 1.27994i
\(238\) 1.26760e7 0.940271
\(239\) −2.41978e7 −1.77248 −0.886240 0.463226i \(-0.846692\pi\)
−0.886240 + 0.463226i \(0.846692\pi\)
\(240\) −2.30259e6 −0.166565
\(241\) 2.77131e7i 1.97985i 0.141576 + 0.989927i \(0.454783\pi\)
−0.141576 + 0.989927i \(0.545217\pi\)
\(242\) 1.20080e7i 0.847273i
\(243\) 8.22382e6i 0.573132i
\(244\) 3.19443e7i 2.19900i
\(245\) 4.21932e6i 0.286909i
\(246\) −2.49509e7 −1.67602
\(247\) 3.35081e7i 2.22361i
\(248\) 1.10239e7i 0.722734i
\(249\) 3.73164e6i 0.241714i
\(250\) 2.17916e7 1.39466
\(251\) −7.61274e6 −0.481415 −0.240708 0.970598i \(-0.577379\pi\)
−0.240708 + 0.970598i \(0.577379\pi\)
\(252\) 6.95541e6i 0.434631i
\(253\) 1.62576e7 1.00391
\(254\) 1.26145e7i 0.769784i
\(255\) 1.02719e7 0.619487
\(256\) −2.13260e7 −1.27113
\(257\) 6.67289e6i 0.393111i −0.980493 0.196555i \(-0.937024\pi\)
0.980493 0.196555i \(-0.0629755\pi\)
\(258\) −1.47331e7 + 1.84733e7i −0.857894 + 1.07568i
\(259\) −2.66385e6 −0.153324
\(260\) 5.91663e7i 3.36631i
\(261\) 2.29014e6i 0.128807i
\(262\) −4.69210e7 −2.60894
\(263\) 1.90916e7i 1.04948i −0.851262 0.524741i \(-0.824162\pi\)
0.851262 0.524741i \(-0.175838\pi\)
\(264\) −2.16740e7 −1.17795
\(265\) 6.86486e6i 0.368888i
\(266\) 3.31332e7i 1.76043i
\(267\) −2.04713e7 −1.07550
\(268\) 3.82137e7 1.98525
\(269\) 3.35363e7 1.72289 0.861446 0.507849i \(-0.169559\pi\)
0.861446 + 0.507849i \(0.169559\pi\)
\(270\) 3.90671e7i 1.98482i
\(271\) −3.07340e7 −1.54423 −0.772114 0.635484i \(-0.780800\pi\)
−0.772114 + 0.635484i \(0.780800\pi\)
\(272\) −2.39222e6 −0.118876
\(273\) 2.62342e7 1.28937
\(274\) −6.00028e7 −2.91689
\(275\) −6.03920e6 −0.290390
\(276\) 2.43551e7i 1.15841i
\(277\) 5.66158e6i 0.266378i −0.991091 0.133189i \(-0.957478\pi\)
0.991091 0.133189i \(-0.0425217\pi\)
\(278\) 4.74976e7i 2.21074i
\(279\) 4.09258e6 0.188445
\(280\) 2.39950e7i 1.09306i
\(281\) 1.65801e7 0.747253 0.373627 0.927579i \(-0.378114\pi\)
0.373627 + 0.927579i \(0.378114\pi\)
\(282\) 2.94119e7 1.31152
\(283\) −2.42978e7 −1.07203 −0.536016 0.844208i \(-0.680071\pi\)
−0.536016 + 0.844208i \(0.680071\pi\)
\(284\) 4.47932e7i 1.95550i
\(285\) 2.68493e7i 1.15984i
\(286\) 8.44670e7i 3.61068i
\(287\) 2.48038e7i 1.04924i
\(288\) 6.02942e6i 0.252405i
\(289\) −1.34658e7 −0.557878
\(290\) 1.92631e7i 0.789829i
\(291\) 2.21096e7i 0.897226i
\(292\) 4.12858e7i 1.65826i
\(293\) −3.69429e7 −1.46868 −0.734342 0.678779i \(-0.762509\pi\)
−0.734342 + 0.678779i \(0.762509\pi\)
\(294\) 9.02380e6 0.355097
\(295\) 4.57908e6i 0.178366i
\(296\) 5.26983e6 0.203199
\(297\) 3.50804e7i 1.33905i
\(298\) −3.41777e7 −1.29150
\(299\) 3.89286e7 1.45631
\(300\) 9.04720e6i 0.335082i
\(301\) −1.83644e7 1.46462e7i −0.673407 0.537065i
\(302\) 3.50084e7 1.27102
\(303\) 3.08880e7i 1.11036i
\(304\) 6.25288e6i 0.222566i
\(305\) 4.09124e7 1.44197
\(306\) 9.30965e6i 0.324915i
\(307\) −1.07968e7 −0.373148 −0.186574 0.982441i \(-0.559738\pi\)
−0.186574 + 0.982441i \(0.559738\pi\)
\(308\) 5.25341e7i 1.79800i
\(309\) 1.08897e7i 0.369096i
\(310\) 3.44241e7 1.15552
\(311\) 1.93935e7 0.644727 0.322363 0.946616i \(-0.395523\pi\)
0.322363 + 0.946616i \(0.395523\pi\)
\(312\) −5.18983e7 −1.70879
\(313\) 1.28612e6i 0.0419420i −0.999780 0.0209710i \(-0.993324\pi\)
0.999780 0.0209710i \(-0.00667576\pi\)
\(314\) −7.47745e7 −2.41526
\(315\) 8.90806e6 0.285004
\(316\) 8.17000e7 2.58917
\(317\) 4.25006e7 1.33419 0.667094 0.744974i \(-0.267538\pi\)
0.667094 + 0.744974i \(0.267538\pi\)
\(318\) 1.46818e7 0.456559
\(319\) 1.72974e7i 0.532854i
\(320\) 5.72281e7i 1.74646i
\(321\) 1.90073e7i 0.574653i
\(322\) −3.84930e7 −1.15296
\(323\) 2.78943e7i 0.827767i
\(324\) 3.53908e7 1.04053
\(325\) −1.44608e7 −0.421253
\(326\) 4.79259e7 1.38330
\(327\) 4.11293e7i 1.17627i
\(328\) 4.90688e7i 1.39054i
\(329\) 2.92385e7i 0.821046i
\(330\) 6.76813e7i 1.88333i
\(331\) 4.77276e7i 1.31609i 0.752979 + 0.658045i \(0.228616\pi\)
−0.752979 + 0.658045i \(0.771384\pi\)
\(332\) 1.78932e7 0.488960
\(333\) 1.95641e6i 0.0529818i
\(334\) 4.22652e7i 1.13434i
\(335\) 4.89418e7i 1.30180i
\(336\) 4.89550e6 0.129056
\(337\) −2.31815e7 −0.605692 −0.302846 0.953040i \(-0.597937\pi\)
−0.302846 + 0.953040i \(0.597937\pi\)
\(338\) 1.38860e8i 3.59607i
\(339\) −3.52281e7 −0.904253
\(340\) 4.92538e7i 1.25315i
\(341\) 3.09112e7 0.779566
\(342\) 2.43340e7 0.608324
\(343\) 4.37290e7i 1.08365i
\(344\) 3.63298e7 + 2.89743e7i 0.892458 + 0.711765i
\(345\) −3.11925e7 −0.759615
\(346\) 3.94058e7i 0.951330i
\(347\) 4.51753e7i 1.08122i −0.841275 0.540608i \(-0.818194\pi\)
0.841275 0.540608i \(-0.181806\pi\)
\(348\) −2.59128e7 −0.614861
\(349\) 3.63458e7i 0.855024i 0.904010 + 0.427512i \(0.140610\pi\)
−0.904010 + 0.427512i \(0.859390\pi\)
\(350\) 1.42990e7 0.333505
\(351\) 8.39998e7i 1.94248i
\(352\) 4.55401e7i 1.04416i
\(353\) 6.26609e6 0.142453 0.0712266 0.997460i \(-0.477309\pi\)
0.0712266 + 0.997460i \(0.477309\pi\)
\(354\) −9.79322e6 −0.220758
\(355\) −5.73684e7 −1.28229
\(356\) 9.81594e7i 2.17562i
\(357\) −2.18390e7 −0.479985
\(358\) −3.26247e7 −0.711045
\(359\) −7.60423e7 −1.64351 −0.821754 0.569843i \(-0.807004\pi\)
−0.821754 + 0.569843i \(0.807004\pi\)
\(360\) −1.76226e7 −0.377713
\(361\) −2.58655e7 −0.549794
\(362\) 1.23073e8i 2.59440i
\(363\) 2.06880e7i 0.432512i
\(364\) 1.25792e8i 2.60826i
\(365\) 5.28764e7 1.08738
\(366\) 8.74987e7i 1.78467i
\(367\) 1.84223e6 0.0372688 0.0186344 0.999826i \(-0.494068\pi\)
0.0186344 + 0.999826i \(0.494068\pi\)
\(368\) 7.26438e6 0.145766
\(369\) −1.82166e7 −0.362568
\(370\) 1.64560e7i 0.324878i
\(371\) 1.45953e7i 0.285818i
\(372\) 4.63074e7i 0.899542i
\(373\) 3.24275e7i 0.624865i −0.949940 0.312433i \(-0.898856\pi\)
0.949940 0.312433i \(-0.101144\pi\)
\(374\) 7.03157e7i 1.34412i
\(375\) −3.75438e7 −0.711942
\(376\) 5.78418e7i 1.08812i
\(377\) 4.14184e7i 0.772981i
\(378\) 8.30599e7i 1.53786i
\(379\) 5.84087e6 0.107290 0.0536451 0.998560i \(-0.482916\pi\)
0.0536451 + 0.998560i \(0.482916\pi\)
\(380\) 1.28742e8 2.34622
\(381\) 2.17329e7i 0.392956i
\(382\) 7.28905e7 1.30762
\(383\) 3.08598e7i 0.549284i −0.961547 0.274642i \(-0.911441\pi\)
0.961547 0.274642i \(-0.0885593\pi\)
\(384\) 8.21510e7 1.45084
\(385\) 6.72825e7 1.17902
\(386\) 1.14072e6i 0.0198343i
\(387\) −1.07566e7 + 1.34873e7i −0.185585 + 0.232698i
\(388\) −1.06015e8 −1.81499
\(389\) 8.63120e7i 1.46630i 0.680068 + 0.733149i \(0.261950\pi\)
−0.680068 + 0.733149i \(0.738050\pi\)
\(390\) 1.62062e8i 2.73205i
\(391\) −3.24066e7 −0.542130
\(392\) 1.77463e7i 0.294612i
\(393\) 8.08380e7 1.33180
\(394\) 1.27732e8i 2.08838i
\(395\) 1.04636e8i 1.69782i
\(396\) −3.85825e7 −0.621306
\(397\) 6.88256e7 1.09996 0.549982 0.835176i \(-0.314634\pi\)
0.549982 + 0.835176i \(0.314634\pi\)
\(398\) −1.63179e8 −2.58830
\(399\) 5.70837e7i 0.898656i
\(400\) −2.69850e6 −0.0421641
\(401\) 2.18197e7 0.338389 0.169194 0.985583i \(-0.445883\pi\)
0.169194 + 0.985583i \(0.445883\pi\)
\(402\) −1.04671e8 −1.61120
\(403\) 7.40166e7 1.13087
\(404\) −1.48108e8 −2.24612
\(405\) 4.53264e7i 0.682317i
\(406\) 4.09550e7i 0.611968i
\(407\) 1.47767e7i 0.219177i
\(408\) 4.32035e7 0.636119
\(409\) 3.33427e7i 0.487339i −0.969858 0.243669i \(-0.921649\pi\)
0.969858 0.243669i \(-0.0783512\pi\)
\(410\) −1.53227e8 −2.22322
\(411\) 1.03376e8 1.48900
\(412\) 5.22159e7 0.746639
\(413\) 9.73550e6i 0.138200i
\(414\) 2.82704e7i 0.398410i
\(415\) 2.29165e7i 0.320630i
\(416\) 1.09045e8i 1.51470i
\(417\) 8.18314e7i 1.12853i
\(418\) 1.83794e8 2.51654
\(419\) 9.15691e7i 1.24482i −0.782691 0.622411i \(-0.786153\pi\)
0.782691 0.622411i \(-0.213847\pi\)
\(420\) 1.00794e8i 1.36047i
\(421\) 9.23221e6i 0.123726i 0.998085 + 0.0618628i \(0.0197041\pi\)
−0.998085 + 0.0618628i \(0.980296\pi\)
\(422\) 1.44159e7 0.191824
\(423\) 2.14736e7 0.283716
\(424\) 2.88734e7i 0.378792i
\(425\) 1.20381e7 0.156816
\(426\) 1.22693e8i 1.58705i
\(427\) −8.69830e7 −1.11725
\(428\) −9.11398e7 −1.16246
\(429\) 1.45524e8i 1.84316i
\(430\) −9.04776e7 + 1.13447e8i −1.13798 + 1.42688i
\(431\) −1.01039e8 −1.26199 −0.630996 0.775786i \(-0.717354\pi\)
−0.630996 + 0.775786i \(0.717354\pi\)
\(432\) 1.56750e7i 0.194427i
\(433\) 5.06133e7i 0.623449i 0.950173 + 0.311724i \(0.100907\pi\)
−0.950173 + 0.311724i \(0.899093\pi\)
\(434\) −7.31884e7 −0.895310
\(435\) 3.31875e7i 0.403188i
\(436\) 1.97214e8 2.37946
\(437\) 8.47059e7i 1.01501i
\(438\) 1.13086e8i 1.34582i
\(439\) 1.13037e8 1.33606 0.668031 0.744133i \(-0.267137\pi\)
0.668031 + 0.744133i \(0.267137\pi\)
\(440\) −1.33103e8 −1.56254
\(441\) 6.58828e6 0.0768168
\(442\) 1.68370e8i 1.94984i
\(443\) 2.36191e6 0.0271677 0.0135838 0.999908i \(-0.495676\pi\)
0.0135838 + 0.999908i \(0.495676\pi\)
\(444\) −2.21367e7 −0.252909
\(445\) −1.25717e8 −1.42663
\(446\) 1.80231e8 2.03154
\(447\) 5.88831e7 0.659277
\(448\) 1.21672e8i 1.35318i
\(449\) 4.84461e7i 0.535204i 0.963529 + 0.267602i \(0.0862313\pi\)
−0.963529 + 0.267602i \(0.913769\pi\)
\(450\) 1.05016e7i 0.115244i
\(451\) −1.37590e8 −1.49988
\(452\) 1.68918e8i 1.82920i
\(453\) −6.03144e7 −0.648823
\(454\) −4.80655e7 −0.513648
\(455\) 1.61107e8 1.71033
\(456\) 1.12927e8i 1.19098i
\(457\) 8.69144e7i 0.910632i 0.890330 + 0.455316i \(0.150474\pi\)
−0.890330 + 0.455316i \(0.849526\pi\)
\(458\) 1.10289e8i 1.14799i
\(459\) 6.99267e7i 0.723111i
\(460\) 1.49568e8i 1.53661i
\(461\) 8.68002e7 0.885968 0.442984 0.896530i \(-0.353920\pi\)
0.442984 + 0.896530i \(0.353920\pi\)
\(462\) 1.43896e8i 1.45923i
\(463\) 1.01559e8i 1.02324i −0.859212 0.511619i \(-0.829046\pi\)
0.859212 0.511619i \(-0.170954\pi\)
\(464\) 7.72900e6i 0.0773694i
\(465\) −5.93077e7 −0.589864
\(466\) 1.13439e8 1.12100
\(467\) 7.61686e7i 0.747869i −0.927455 0.373934i \(-0.878009\pi\)
0.927455 0.373934i \(-0.121991\pi\)
\(468\) −9.23855e7 −0.901294
\(469\) 1.04054e8i 1.00865i
\(470\) 1.80622e8 1.73971
\(471\) 1.28826e8 1.23293
\(472\) 1.92595e7i 0.183155i
\(473\) −8.12445e7 + 1.01870e8i −0.767734 + 0.962635i
\(474\) −2.23784e8 −2.10133
\(475\) 3.14657e7i 0.293601i
\(476\) 1.04718e8i 0.970955i
\(477\) 1.07192e7 0.0987657
\(478\) 3.17812e8i 2.90995i
\(479\) 6.83393e7 0.621819 0.310910 0.950439i \(-0.399366\pi\)
0.310910 + 0.950439i \(0.399366\pi\)
\(480\) 8.73754e7i 0.790070i
\(481\) 3.53828e7i 0.317948i
\(482\) −3.63982e8 −3.25041
\(483\) 6.63178e7 0.588558
\(484\) −9.91986e7 −0.874922
\(485\) 1.35778e8i 1.19016i
\(486\) 1.08011e8 0.940935
\(487\) 1.15513e8 1.00010 0.500050 0.865997i \(-0.333315\pi\)
0.500050 + 0.865997i \(0.333315\pi\)
\(488\) 1.72076e8 1.48068
\(489\) −8.25692e7 −0.706141
\(490\) 5.54163e7 0.471031
\(491\) 4.76707e7i 0.402724i 0.979517 + 0.201362i \(0.0645367\pi\)
−0.979517 + 0.201362i \(0.935463\pi\)
\(492\) 2.06121e8i 1.73072i
\(493\) 3.44793e7i 0.287752i
\(494\) 4.40094e8 3.65060
\(495\) 4.94142e7i 0.407414i
\(496\) 1.38121e7 0.113192
\(497\) 1.21970e8 0.993535
\(498\) −4.90111e7 −0.396832
\(499\) 1.77336e8i 1.42723i 0.700537 + 0.713616i \(0.252944\pi\)
−0.700537 + 0.713616i \(0.747056\pi\)
\(500\) 1.80022e8i 1.44018i
\(501\) 7.28168e7i 0.579053i
\(502\) 9.99852e7i 0.790359i
\(503\) 2.49388e6i 0.0195962i −0.999952 0.00979809i \(-0.996881\pi\)
0.999952 0.00979809i \(-0.00311888\pi\)
\(504\) 3.74670e7 0.292656
\(505\) 1.89687e8i 1.47287i
\(506\) 2.13526e8i 1.64816i
\(507\) 2.39236e8i 1.83570i
\(508\) 1.04209e8 0.794904
\(509\) −7.63361e7 −0.578864 −0.289432 0.957199i \(-0.593466\pi\)
−0.289432 + 0.957199i \(0.593466\pi\)
\(510\) 1.34911e8i 1.01704i
\(511\) −1.12419e8 −0.842517
\(512\) 4.77405e7i 0.355694i
\(513\) −1.82778e8 −1.35385
\(514\) 8.76413e7 0.645386
\(515\) 6.68749e7i 0.489600i
\(516\) −1.52609e8 1.21711e8i −1.11079 0.885890i
\(517\) 1.62190e8 1.17369
\(518\) 3.49869e7i 0.251719i
\(519\) 6.78904e7i 0.485631i
\(520\) −3.18714e8 −2.26669
\(521\) 5.85908e7i 0.414301i 0.978309 + 0.207151i \(0.0664190\pi\)
−0.978309 + 0.207151i \(0.933581\pi\)
\(522\) −3.00785e7 −0.211468
\(523\) 1.14240e8i 0.798568i 0.916827 + 0.399284i \(0.130741\pi\)
−0.916827 + 0.399284i \(0.869259\pi\)
\(524\) 3.87617e8i 2.69407i
\(525\) −2.46351e7 −0.170246
\(526\) 2.50748e8 1.72298
\(527\) −6.16161e7 −0.420981
\(528\) 2.71560e7i 0.184486i
\(529\) −4.96275e7 −0.335240
\(530\) 9.01627e7 0.605619
\(531\) −7.15003e6 −0.0477556
\(532\) −2.73716e8 −1.81788
\(533\) −3.29458e8 −2.17580
\(534\) 2.68868e8i 1.76569i
\(535\) 1.16726e8i 0.762267i
\(536\) 2.05848e8i 1.33676i
\(537\) 5.62076e7 0.362971
\(538\) 4.40463e8i 2.82854i
\(539\) 4.97612e7 0.317778
\(540\) 3.22736e8 2.04959
\(541\) −6.24119e6 −0.0394163 −0.0197081 0.999806i \(-0.506274\pi\)
−0.0197081 + 0.999806i \(0.506274\pi\)
\(542\) 4.03658e8i 2.53522i
\(543\) 2.12037e8i 1.32438i
\(544\) 9.07763e7i 0.563866i
\(545\) 2.52580e8i 1.56031i
\(546\) 3.44558e8i 2.11682i
\(547\) −9.45969e7 −0.577983 −0.288991 0.957332i \(-0.593320\pi\)
−0.288991 + 0.957332i \(0.593320\pi\)
\(548\) 4.95687e8i 3.01207i
\(549\) 6.38828e7i 0.386071i
\(550\) 7.93185e7i 0.476745i
\(551\) 9.01236e7 0.538745
\(552\) −1.31195e8 −0.780009
\(553\) 2.22465e8i 1.31549i
\(554\) 7.43588e7 0.437324
\(555\) 2.83514e7i 0.165842i
\(556\) 3.92381e8 2.28288
\(557\) −3.64924e7 −0.211172 −0.105586 0.994410i \(-0.533672\pi\)
−0.105586 + 0.994410i \(0.533672\pi\)
\(558\) 5.37517e7i 0.309378i
\(559\) −1.94539e8 + 2.43926e8i −1.11371 + 1.39644i
\(560\) 3.00639e7 0.171191
\(561\) 1.21144e8i 0.686139i
\(562\) 2.17762e8i 1.22680i
\(563\) −8.39838e7 −0.470620 −0.235310 0.971920i \(-0.575611\pi\)
−0.235310 + 0.971920i \(0.575611\pi\)
\(564\) 2.42973e8i 1.35432i
\(565\) −2.16340e8 −1.19948
\(566\) 3.19126e8i 1.76000i
\(567\) 9.63675e7i 0.528666i
\(568\) −2.41289e8 −1.31672
\(569\) −1.07209e8 −0.581963 −0.290981 0.956729i \(-0.593982\pi\)
−0.290981 + 0.956729i \(0.593982\pi\)
\(570\) −3.52637e8 −1.90416
\(571\) 1.05706e8i 0.567797i 0.958854 + 0.283899i \(0.0916279\pi\)
−0.958854 + 0.283899i \(0.908372\pi\)
\(572\) −6.97787e8 −3.72850
\(573\) −1.25580e8 −0.667506
\(574\) 3.25772e8 1.72257
\(575\) −3.65558e7 −0.192288
\(576\) 8.93591e7 0.467596
\(577\) 1.36661e8i 0.711403i −0.934600 0.355702i \(-0.884242\pi\)
0.934600 0.355702i \(-0.115758\pi\)
\(578\) 1.76859e8i 0.915891i
\(579\) 1.96529e6i 0.0101249i
\(580\) −1.59134e8 −0.815603
\(581\) 4.87223e7i 0.248427i
\(582\) 2.90386e8 1.47301
\(583\) 8.09618e7 0.408577
\(584\) 2.22396e8 1.11658
\(585\) 1.18322e8i 0.591013i
\(586\) 4.85206e8i 2.41120i
\(587\) 1.16599e8i 0.576475i −0.957559 0.288238i \(-0.906931\pi\)
0.957559 0.288238i \(-0.0930693\pi\)
\(588\) 7.45461e7i 0.366685i
\(589\) 1.61055e8i 0.788185i
\(590\) −6.01414e7 −0.292831
\(591\) 2.20063e8i 1.06607i
\(592\) 6.60270e6i 0.0318241i
\(593\) 3.03405e8i 1.45499i 0.686115 + 0.727493i \(0.259315\pi\)
−0.686115 + 0.727493i \(0.740685\pi\)
\(594\) 4.60744e8 2.19837
\(595\) −1.34116e8 −0.636692
\(596\) 2.82344e8i 1.33364i
\(597\) 2.81133e8 1.32126
\(598\) 5.11285e8i 2.39089i
\(599\) −3.82574e8 −1.78006 −0.890030 0.455901i \(-0.849317\pi\)
−0.890030 + 0.455901i \(0.849317\pi\)
\(600\) 4.87350e7 0.225625
\(601\) 4.50470e7i 0.207512i −0.994603 0.103756i \(-0.966914\pi\)
0.994603 0.103756i \(-0.0330861\pi\)
\(602\) 1.92363e8 2.41197e8i 0.881721 1.10556i
\(603\) −7.64204e7 −0.348544
\(604\) 2.89207e8i 1.31249i
\(605\) 1.27047e8i 0.573720i
\(606\) 4.05682e8 1.82292
\(607\) 1.78401e8i 0.797685i −0.917020 0.398842i \(-0.869412\pi\)
0.917020 0.398842i \(-0.130588\pi\)
\(608\) −2.37275e8 −1.05570
\(609\) 7.05594e7i 0.312394i
\(610\) 5.37340e8i 2.36734i
\(611\) 3.88362e8 1.70260
\(612\) 7.69076e7 0.335517
\(613\) 2.81992e8 1.22421 0.612104 0.790777i \(-0.290323\pi\)
0.612104 + 0.790777i \(0.290323\pi\)
\(614\) 1.41805e8i 0.612612i
\(615\) 2.63987e8 1.13490
\(616\) 2.82988e8 1.21067
\(617\) 3.33667e8 1.42055 0.710277 0.703923i \(-0.248570\pi\)
0.710277 + 0.703923i \(0.248570\pi\)
\(618\) −1.43024e8 −0.605961
\(619\) 9.98403e7 0.420953 0.210477 0.977599i \(-0.432498\pi\)
0.210477 + 0.977599i \(0.432498\pi\)
\(620\) 2.84380e8i 1.19323i
\(621\) 2.12345e8i 0.886679i
\(622\) 2.54713e8i 1.05847i
\(623\) 2.67284e8 1.10537
\(624\) 6.50247e7i 0.267624i
\(625\) −2.88140e8 −1.18022
\(626\) 1.68918e7 0.0688579
\(627\) −3.16651e8 −1.28463
\(628\) 6.17717e8i 2.49408i
\(629\) 2.94549e7i 0.118360i
\(630\) 1.16998e8i 0.467904i
\(631\) 2.37989e8i 0.947257i −0.880725 0.473629i \(-0.842944\pi\)
0.880725 0.473629i \(-0.157056\pi\)
\(632\) 4.40097e8i 1.74340i
\(633\) −2.48364e7 −0.0979214
\(634\) 5.58200e8i 2.19039i
\(635\) 1.33465e8i 0.521249i
\(636\) 1.21287e8i 0.471458i
\(637\) 1.19153e8 0.460984
\(638\) −2.27182e8 −0.874808
\(639\) 8.95781e7i 0.343320i
\(640\) 5.04500e8 1.92451
\(641\) 9.09313e7i 0.345254i −0.984987 0.172627i \(-0.944774\pi\)
0.984987 0.172627i \(-0.0552256\pi\)
\(642\) 2.49641e8 0.943431
\(643\) −9.69805e7 −0.364797 −0.182399 0.983225i \(-0.558386\pi\)
−0.182399 + 0.983225i \(0.558386\pi\)
\(644\) 3.17993e8i 1.19058i
\(645\) 1.55880e8 1.95452e8i 0.580912 0.728385i
\(646\) −3.66362e8 −1.35898
\(647\) 909696.i 0.00335880i 0.999999 + 0.00167940i \(0.000534569\pi\)
−0.999999 + 0.00167940i \(0.999465\pi\)
\(648\) 1.90641e8i 0.700635i
\(649\) −5.40041e7 −0.197557
\(650\) 1.89927e8i 0.691588i
\(651\) 1.26093e8 0.457033
\(652\) 3.95918e8i 1.42844i
\(653\) 1.20112e8i 0.431367i −0.976463 0.215683i \(-0.930802\pi\)
0.976463 0.215683i \(-0.0691979\pi\)
\(654\) −5.40189e8 −1.93113
\(655\) 4.96436e8 1.76661
\(656\) −6.14795e7 −0.217780
\(657\) 8.25640e7i 0.291135i
\(658\) −3.84017e8 −1.34795
\(659\) 2.23855e7 0.0782187 0.0391093 0.999235i \(-0.487548\pi\)
0.0391093 + 0.999235i \(0.487548\pi\)
\(660\) 5.59120e8 1.94479
\(661\) −4.33191e8 −1.49994 −0.749972 0.661469i \(-0.769933\pi\)
−0.749972 + 0.661469i \(0.769933\pi\)
\(662\) −6.26851e8 −2.16068
\(663\) 2.90077e8i 0.995344i
\(664\) 9.63860e7i 0.329238i
\(665\) 3.50558e8i 1.19205i
\(666\) −2.56954e7 −0.0869825
\(667\) 1.04702e8i 0.352841i
\(668\) −3.49156e8 −1.17136
\(669\) −3.10512e8 −1.03705
\(670\) −6.42799e8 −2.13723
\(671\) 4.82506e8i 1.59711i
\(672\) 1.85767e8i 0.612155i
\(673\) 2.73875e8i 0.898477i −0.893412 0.449239i \(-0.851695\pi\)
0.893412 0.449239i \(-0.148305\pi\)
\(674\) 3.04464e8i 0.994390i
\(675\) 7.88798e7i 0.256481i
\(676\) −1.14713e9 −3.71342
\(677\) 5.41280e7i 0.174444i −0.996189 0.0872219i \(-0.972201\pi\)
0.996189 0.0872219i \(-0.0277989\pi\)
\(678\) 4.62684e8i 1.48455i
\(679\) 2.88675e8i 0.922146i
\(680\) 2.65318e8 0.843801
\(681\) 8.28098e7 0.262205
\(682\) 4.05986e8i 1.27985i
\(683\) 5.00593e8 1.57117 0.785583 0.618756i \(-0.212363\pi\)
0.785583 + 0.618756i \(0.212363\pi\)
\(684\) 2.01025e8i 0.628175i
\(685\) 6.34845e8 1.97513
\(686\) −5.74334e8 −1.77907
\(687\) 1.90012e8i 0.586019i
\(688\) −3.63026e7 + 4.55185e7i −0.111474 + 0.139773i
\(689\) 1.93862e8 0.592701
\(690\) 4.09681e8i 1.24709i
\(691\) 6.59368e8i 1.99845i 0.0393546 + 0.999225i \(0.487470\pi\)
−0.0393546 + 0.999225i \(0.512530\pi\)
\(692\) −3.25533e8 −0.982375
\(693\) 1.05058e8i 0.315669i
\(694\) 5.93329e8 1.77508
\(695\) 5.02537e8i 1.49697i
\(696\) 1.39586e8i 0.414012i
\(697\) 2.74262e8 0.809967
\(698\) −4.77364e8 −1.40373
\(699\) −1.95439e8 −0.572242
\(700\) 1.18125e8i 0.344388i
\(701\) −1.34774e8 −0.391248 −0.195624 0.980679i \(-0.562673\pi\)
−0.195624 + 0.980679i \(0.562673\pi\)
\(702\) 1.10325e9 3.18905
\(703\) 7.69905e7 0.221601
\(704\) 6.74928e8 1.93437
\(705\) −3.11185e8 −0.888079
\(706\) 8.22984e7i 0.233872i
\(707\) 4.03291e8i 1.14120i
\(708\) 8.09024e7i 0.227961i
\(709\) −1.73069e8 −0.485601 −0.242801 0.970076i \(-0.578066\pi\)
−0.242801 + 0.970076i \(0.578066\pi\)
\(710\) 7.53472e8i 2.10519i
\(711\) −1.63385e8 −0.454573
\(712\) −5.28760e8 −1.46494
\(713\) 1.87108e8 0.516207
\(714\) 2.86832e8i 0.788011i
\(715\) 8.93683e8i 2.44492i
\(716\) 2.69515e8i 0.734249i
\(717\) 5.47543e8i 1.48546i
\(718\) 9.98734e8i 2.69821i
\(719\) −5.58345e7 −0.150216 −0.0751079 0.997175i \(-0.523930\pi\)
−0.0751079 + 0.997175i \(0.523930\pi\)
\(720\) 2.20798e7i 0.0591558i
\(721\) 1.42181e8i 0.379347i
\(722\) 3.39716e8i 0.902620i
\(723\) 6.27087e8 1.65925
\(724\) 1.01672e9 2.67907
\(725\) 3.88938e7i 0.102063i
\(726\) 2.71714e8 0.710073
\(727\) 6.04466e8i 1.57314i −0.617499 0.786572i \(-0.711854\pi\)
0.617499 0.786572i \(-0.288146\pi\)
\(728\) 6.77612e8 1.75625
\(729\) −4.23874e8 −1.09409
\(730\) 6.94475e8i 1.78520i
\(731\) 1.61947e8 2.03060e8i 0.414592 0.519842i
\(732\) −7.22832e8 −1.84291
\(733\) 7.18216e8i 1.82366i −0.410572 0.911828i \(-0.634671\pi\)
0.410572 0.911828i \(-0.365329\pi\)
\(734\) 2.41957e7i 0.0611858i
\(735\) −9.54742e7 −0.240449
\(736\) 2.75658e8i 0.691412i
\(737\) −5.77203e8 −1.44187
\(738\) 2.39256e8i 0.595243i
\(739\) 1.73211e8i 0.429182i −0.976704 0.214591i \(-0.931158\pi\)
0.976704 0.214591i \(-0.0688418\pi\)
\(740\) −1.35944e8 −0.335480
\(741\) −7.58217e8 −1.86354
\(742\) −1.91693e8 −0.469240
\(743\) 1.73962e8i 0.424119i 0.977257 + 0.212060i \(0.0680171\pi\)
−0.977257 + 0.212060i \(0.931983\pi\)
\(744\) −2.49446e8 −0.605701
\(745\) 3.61609e8 0.874521
\(746\) 4.25900e8 1.02587
\(747\) −3.57830e7 −0.0858451
\(748\) 5.80882e8 1.38798
\(749\) 2.48169e8i 0.590613i
\(750\) 4.93098e8i 1.16882i
\(751\) 8.34005e8i 1.96901i 0.175345 + 0.984507i \(0.443896\pi\)
−0.175345 + 0.984507i \(0.556104\pi\)
\(752\) 7.24714e7 0.170417
\(753\) 1.72260e8i 0.403459i
\(754\) −5.43986e8 −1.26904
\(755\) −3.70398e8 −0.860653
\(756\) −6.86163e8 −1.58804
\(757\) 3.17760e8i 0.732508i 0.930515 + 0.366254i \(0.119360\pi\)
−0.930515 + 0.366254i \(0.880640\pi\)
\(758\) 7.67136e7i 0.176143i
\(759\) 3.67874e8i 0.841343i
\(760\) 6.93500e8i 1.57981i
\(761\) 1.38371e8i 0.313972i −0.987601 0.156986i \(-0.949822\pi\)
0.987601 0.156986i \(-0.0501777\pi\)
\(762\) −2.85439e8 −0.645132
\(763\) 5.37006e8i 1.20894i
\(764\) 6.02153e8i 1.35029i
\(765\) 9.84986e7i 0.220012i
\(766\) 4.05311e8 0.901782
\(767\) −1.29312e8 −0.286585
\(768\) 4.82561e8i 1.06529i
\(769\) 6.44915e8 1.41815 0.709077 0.705131i \(-0.249112\pi\)
0.709077 + 0.705131i \(0.249112\pi\)
\(770\) 8.83684e8i 1.93564i
\(771\) −1.50993e8 −0.329454
\(772\) 9.42355e6 0.0204815
\(773\) 5.45053e8i 1.18005i 0.807385 + 0.590025i \(0.200882\pi\)
−0.807385 + 0.590025i \(0.799118\pi\)
\(774\) −1.77142e8 1.41277e8i −0.382031 0.304682i
\(775\) −6.95051e7 −0.149318
\(776\) 5.71078e8i 1.22211i
\(777\) 6.02773e7i 0.128496i
\(778\) −1.13362e9 −2.40728
\(779\) 7.16878e8i 1.51647i
\(780\) 1.33881e9 2.82120
\(781\) 6.76582e8i 1.42026i
\(782\) 4.25627e8i 0.890038i
\(783\) 2.25926e8