Properties

Label 43.7.b.b.42.20
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 42.20
Root \(15.3591i\) 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.42.1

$q$-expansion

\(f(q)\) \(=\) \(q+15.3591i q^{2} +12.8491i q^{3} -171.901 q^{4} +213.900i q^{5} -197.350 q^{6} +274.602i q^{7} -1657.26i q^{8} +563.902 q^{9} +O(q^{10})\) \(q+15.3591i q^{2} +12.8491i q^{3} -171.901 q^{4} +213.900i q^{5} -197.350 q^{6} +274.602i q^{7} -1657.26i q^{8} +563.902 q^{9} -3285.30 q^{10} +1533.32 q^{11} -2208.77i q^{12} -2261.41 q^{13} -4217.62 q^{14} -2748.41 q^{15} +14452.3 q^{16} +8925.29 q^{17} +8661.00i q^{18} -851.013i q^{19} -36769.6i q^{20} -3528.37 q^{21} +23550.3i q^{22} +1902.42 q^{23} +21294.2 q^{24} -30128.1 q^{25} -34733.1i q^{26} +16612.6i q^{27} -47204.3i q^{28} +8479.42i q^{29} -42213.0i q^{30} -14740.7 q^{31} +115909. i q^{32} +19701.7i q^{33} +137084. i q^{34} -58737.2 q^{35} -96935.3 q^{36} -39610.5i q^{37} +13070.8 q^{38} -29057.0i q^{39} +354487. q^{40} -72090.6 q^{41} -54192.5i q^{42} +(4441.34 - 79382.9i) q^{43} -263579. q^{44} +120618. i q^{45} +29219.4i q^{46} +84141.9 q^{47} +185698. i q^{48} +42243.0 q^{49} -462740. i q^{50} +114682. i q^{51} +388738. q^{52} -139864. q^{53} -255154. q^{54} +327976. i q^{55} +455086. q^{56} +10934.7 q^{57} -130236. q^{58} +106075. q^{59} +472455. q^{60} +89596.6i q^{61} -226403. i q^{62} +154848. i q^{63} -855310. q^{64} -483715. i q^{65} -302599. q^{66} +221025. q^{67} -1.53427e6 q^{68} +24444.3i q^{69} -902149. i q^{70} +238817. i q^{71} -934531. i q^{72} -259632. i q^{73} +608380. q^{74} -387118. i q^{75} +146290. i q^{76} +421051. i q^{77} +446288. q^{78} +232291. q^{79} +3.09134e6i q^{80} +197628. q^{81} -1.10724e6i q^{82} +373116. q^{83} +606531. q^{84} +1.90912e6i q^{85} +(1.21925e6 + 68214.8i) q^{86} -108953. q^{87} -2.54110e6i q^{88} +277468. i q^{89} -1.85259e6 q^{90} -620986. i q^{91} -327027. q^{92} -189404. i q^{93} +1.29234e6i q^{94} +182032. q^{95} -1.48932e6 q^{96} +810136. q^{97} +648813. i q^{98} +864639. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} + O(q^{10}) \) \( 20q - 796q^{4} - 258q^{6} - 2736q^{9} - 1962q^{10} + 2616q^{11} - 5612q^{13} - 3876q^{14} + 4048q^{15} + 14900q^{16} + 3328q^{17} + 10544q^{21} - 836q^{23} + 26966q^{24} - 57904q^{25} + 17116q^{31} - 150472q^{35} - 132110q^{36} + 2266q^{38} + 401286q^{40} - 141936q^{41} + 58160q^{43} + 88544q^{44} + 48452q^{47} - 20644q^{49} + 12292q^{52} + 425212q^{53} + 173740q^{54} + 447864q^{56} - 92904q^{57} + 86502q^{58} - 918856q^{59} + 429848q^{60} - 156892q^{64} - 1246176q^{66} + 1098496q^{67} - 2589854q^{68} - 1224106q^{74} + 855716q^{78} - 401492q^{79} + 470644q^{81} + 1354360q^{83} - 637268q^{84} + 3046356q^{86} + 2116740q^{87} - 683716q^{90} - 485998q^{92} - 2711660q^{95} - 2480062q^{96} + 7814560q^{97} + 3744560q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.3591i 1.91988i 0.280199 + 0.959942i \(0.409599\pi\)
−0.280199 + 0.959942i \(0.590401\pi\)
\(3\) 12.8491i 0.475891i 0.971278 + 0.237946i \(0.0764740\pi\)
−0.971278 + 0.237946i \(0.923526\pi\)
\(4\) −171.901 −2.68595
\(5\) 213.900i 1.71120i 0.517639 + 0.855599i \(0.326811\pi\)
−0.517639 + 0.855599i \(0.673189\pi\)
\(6\) −197.350 −0.913656
\(7\) 274.602i 0.800588i 0.916387 + 0.400294i \(0.131092\pi\)
−0.916387 + 0.400294i \(0.868908\pi\)
\(8\) 1657.26i 3.23683i
\(9\) 563.902 0.773528
\(10\) −3285.30 −3.28530
\(11\) 1533.32 1.15200 0.576001 0.817449i \(-0.304612\pi\)
0.576001 + 0.817449i \(0.304612\pi\)
\(12\) 2208.77i 1.27822i
\(13\) −2261.41 −1.02932 −0.514658 0.857395i \(-0.672081\pi\)
−0.514658 + 0.857395i \(0.672081\pi\)
\(14\) −4217.62 −1.53704
\(15\) −2748.41 −0.814344
\(16\) 14452.3 3.52839
\(17\) 8925.29 1.81667 0.908334 0.418245i \(-0.137355\pi\)
0.908334 + 0.418245i \(0.137355\pi\)
\(18\) 8661.00i 1.48508i
\(19\) 851.013i 0.124073i −0.998074 0.0620363i \(-0.980241\pi\)
0.998074 0.0620363i \(-0.0197594\pi\)
\(20\) 36769.6i 4.59620i
\(21\) −3528.37 −0.380993
\(22\) 23550.3i 2.21171i
\(23\) 1902.42 0.156359 0.0781794 0.996939i \(-0.475089\pi\)
0.0781794 + 0.996939i \(0.475089\pi\)
\(24\) 21294.2 1.54038
\(25\) −30128.1 −1.92820
\(26\) 34733.1i 1.97617i
\(27\) 16612.6i 0.844006i
\(28\) 47204.3i 2.15034i
\(29\) 8479.42i 0.347674i 0.984774 + 0.173837i \(0.0556166\pi\)
−0.984774 + 0.173837i \(0.944383\pi\)
\(30\) 42213.0i 1.56345i
\(31\) −14740.7 −0.494803 −0.247402 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(32\) 115909.i 3.53727i
\(33\) 19701.7i 0.548228i
\(34\) 137084.i 3.48779i
\(35\) −58737.2 −1.36996
\(36\) −96935.3 −2.07766
\(37\) 39610.5i 0.781997i −0.920391 0.390998i \(-0.872130\pi\)
0.920391 0.390998i \(-0.127870\pi\)
\(38\) 13070.8 0.238205
\(39\) 29057.0i 0.489842i
\(40\) 354487. 5.53887
\(41\) −72090.6 −1.04599 −0.522995 0.852336i \(-0.675185\pi\)
−0.522995 + 0.852336i \(0.675185\pi\)
\(42\) 54192.5i 0.731461i
\(43\) 4441.34 79382.9i 0.0558610 0.998439i
\(44\) −263579. −3.09423
\(45\) 120618.i 1.32366i
\(46\) 29219.4i 0.300191i
\(47\) 84141.9 0.810436 0.405218 0.914220i \(-0.367196\pi\)
0.405218 + 0.914220i \(0.367196\pi\)
\(48\) 185698.i 1.67913i
\(49\) 42243.0 0.359059
\(50\) 462740.i 3.70192i
\(51\) 114682.i 0.864536i
\(52\) 388738. 2.76470
\(53\) −139864. −0.939457 −0.469729 0.882811i \(-0.655648\pi\)
−0.469729 + 0.882811i \(0.655648\pi\)
\(54\) −255154. −1.62039
\(55\) 327976.i 1.97131i
\(56\) 455086. 2.59137
\(57\) 10934.7 0.0590450
\(58\) −130236. −0.667494
\(59\) 106075. 0.516485 0.258243 0.966080i \(-0.416857\pi\)
0.258243 + 0.966080i \(0.416857\pi\)
\(60\) 472455. 2.18729
\(61\) 89596.6i 0.394732i 0.980330 + 0.197366i \(0.0632387\pi\)
−0.980330 + 0.197366i \(0.936761\pi\)
\(62\) 226403.i 0.949965i
\(63\) 154848.i 0.619277i
\(64\) −855310. −3.26275
\(65\) 483715.i 1.76136i
\(66\) −302599. −1.05253
\(67\) 221025. 0.734881 0.367441 0.930047i \(-0.380234\pi\)
0.367441 + 0.930047i \(0.380234\pi\)
\(68\) −1.53427e6 −4.87949
\(69\) 24444.3i 0.0744098i
\(70\) 902149.i 2.63017i
\(71\) 238817.i 0.667252i 0.942705 + 0.333626i \(0.108272\pi\)
−0.942705 + 0.333626i \(0.891728\pi\)
\(72\) 934531.i 2.50378i
\(73\) 259632.i 0.667406i −0.942678 0.333703i \(-0.891702\pi\)
0.942678 0.333703i \(-0.108298\pi\)
\(74\) 608380. 1.50134
\(75\) 387118.i 0.917613i
\(76\) 146290.i 0.333253i
\(77\) 421051.i 0.922279i
\(78\) 446288. 0.940441
\(79\) 232291. 0.471141 0.235571 0.971857i \(-0.424304\pi\)
0.235571 + 0.971857i \(0.424304\pi\)
\(80\) 3.09134e6i 6.03778i
\(81\) 197628. 0.371873
\(82\) 1.10724e6i 2.00818i
\(83\) 373116. 0.652544 0.326272 0.945276i \(-0.394207\pi\)
0.326272 + 0.945276i \(0.394207\pi\)
\(84\) 606531. 1.02333
\(85\) 1.90912e6i 3.10868i
\(86\) 1.21925e6 + 68214.8i 1.91689 + 0.107247i
\(87\) −108953. −0.165455
\(88\) 2.54110e6i 3.72884i
\(89\) 277468.i 0.393589i 0.980445 + 0.196794i \(0.0630531\pi\)
−0.980445 + 0.196794i \(0.936947\pi\)
\(90\) −1.85259e6 −2.54127
\(91\) 620986.i 0.824058i
\(92\) −327027. −0.419972
\(93\) 189404.i 0.235472i
\(94\) 1.29234e6i 1.55594i
\(95\) 182032. 0.212313
\(96\) −1.48932e6 −1.68335
\(97\) 810136. 0.887652 0.443826 0.896113i \(-0.353621\pi\)
0.443826 + 0.896113i \(0.353621\pi\)
\(98\) 648813.i 0.689352i
\(99\) 864639. 0.891106
\(100\) 5.17906e6 5.17906
\(101\) 980348. 0.951516 0.475758 0.879576i \(-0.342174\pi\)
0.475758 + 0.879576i \(0.342174\pi\)
\(102\) −1.76140e6 −1.65981
\(103\) −1.38382e6 −1.26639 −0.633197 0.773991i \(-0.718258\pi\)
−0.633197 + 0.773991i \(0.718258\pi\)
\(104\) 3.74774e6i 3.33173i
\(105\) 754718.i 0.651954i
\(106\) 2.14817e6i 1.80365i
\(107\) −1.50507e6 −1.22859 −0.614294 0.789077i \(-0.710559\pi\)
−0.614294 + 0.789077i \(0.710559\pi\)
\(108\) 2.85572e6i 2.26696i
\(109\) −357123. −0.275765 −0.137882 0.990449i \(-0.544030\pi\)
−0.137882 + 0.990449i \(0.544030\pi\)
\(110\) −5.03741e6 −3.78468
\(111\) 508958. 0.372145
\(112\) 3.96862e6i 2.82479i
\(113\) 2.14958e6i 1.48977i −0.667194 0.744884i \(-0.732505\pi\)
0.667194 0.744884i \(-0.267495\pi\)
\(114\) 167947.i 0.113360i
\(115\) 406927.i 0.267561i
\(116\) 1.45762e6i 0.933836i
\(117\) −1.27521e6 −0.796205
\(118\) 1.62922e6i 0.991592i
\(119\) 2.45090e6i 1.45440i
\(120\) 4.55483e6i 2.63590i
\(121\) 579496. 0.327111
\(122\) −1.37612e6 −0.757839
\(123\) 926297.i 0.497777i
\(124\) 2.53394e6 1.32902
\(125\) 3.10222e6i 1.58833i
\(126\) −2.37833e6 −1.18894
\(127\) −500467. −0.244323 −0.122161 0.992510i \(-0.538983\pi\)
−0.122161 + 0.992510i \(0.538983\pi\)
\(128\) 5.71858e6i 2.72683i
\(129\) 1.02000e6 + 57067.0i 0.475148 + 0.0265837i
\(130\) 7.42941e6 3.38161
\(131\) 3.30633e6i 1.47073i 0.677672 + 0.735364i \(0.262989\pi\)
−0.677672 + 0.735364i \(0.737011\pi\)
\(132\) 3.38674e6i 1.47251i
\(133\) 233690. 0.0993309
\(134\) 3.39474e6i 1.41089i
\(135\) −3.55343e6 −1.44426
\(136\) 1.47915e7i 5.88025i
\(137\) 59153.5i 0.0230048i −0.999934 0.0115024i \(-0.996339\pi\)
0.999934 0.0115024i \(-0.00366141\pi\)
\(138\) −375441. −0.142858
\(139\) −3.92748e6 −1.46241 −0.731206 0.682156i \(-0.761042\pi\)
−0.731206 + 0.682156i \(0.761042\pi\)
\(140\) 1.00970e7 3.67966
\(141\) 1.08114e6i 0.385679i
\(142\) −3.66801e6 −1.28105
\(143\) −3.46745e6 −1.18578
\(144\) 8.14967e6 2.72931
\(145\) −1.81375e6 −0.594939
\(146\) 3.98771e6 1.28134
\(147\) 542783.i 0.170873i
\(148\) 6.80908e6i 2.10041i
\(149\) 2.29558e6i 0.693958i −0.937873 0.346979i \(-0.887207\pi\)
0.937873 0.346979i \(-0.112793\pi\)
\(150\) 5.94577e6 1.76171
\(151\) 3.65749e6i 1.06231i 0.847274 + 0.531157i \(0.178242\pi\)
−0.847274 + 0.531157i \(0.821758\pi\)
\(152\) −1.41035e6 −0.401602
\(153\) 5.03299e6 1.40524
\(154\) −6.46695e6 −1.77067
\(155\) 3.15303e6i 0.846706i
\(156\) 4.99492e6i 1.31569i
\(157\) 4.30465e6i 1.11234i −0.831068 0.556171i \(-0.812270\pi\)
0.831068 0.556171i \(-0.187730\pi\)
\(158\) 3.56777e6i 0.904537i
\(159\) 1.79712e6i 0.447079i
\(160\) −2.47929e7 −6.05297
\(161\) 522407.i 0.125179i
\(162\) 3.03539e6i 0.713952i
\(163\) 4.48968e6i 1.03670i −0.855169 0.518349i \(-0.826547\pi\)
0.855169 0.518349i \(-0.173453\pi\)
\(164\) 1.23925e7 2.80948
\(165\) −4.21418e6 −0.938127
\(166\) 5.73072e6i 1.25281i
\(167\) 7.58942e6 1.62952 0.814760 0.579799i \(-0.196869\pi\)
0.814760 + 0.579799i \(0.196869\pi\)
\(168\) 5.84743e6i 1.23321i
\(169\) 287156. 0.0594920
\(170\) −2.93223e7 −5.96830
\(171\) 479888.i 0.0959735i
\(172\) −763471. + 1.36460e7i −0.150040 + 2.68176i
\(173\) −4.30786e6 −0.832001 −0.416000 0.909364i \(-0.636569\pi\)
−0.416000 + 0.909364i \(0.636569\pi\)
\(174\) 1.67341e6i 0.317654i
\(175\) 8.27323e6i 1.54369i
\(176\) 2.21599e7 4.06472
\(177\) 1.36297e6i 0.245791i
\(178\) −4.26165e6 −0.755645
\(179\) 9.22540e6i 1.60852i 0.594278 + 0.804260i \(0.297438\pi\)
−0.594278 + 0.804260i \(0.702562\pi\)
\(180\) 2.07344e7i 3.55529i
\(181\) 2.31947e6 0.391159 0.195580 0.980688i \(-0.437341\pi\)
0.195580 + 0.980688i \(0.437341\pi\)
\(182\) 9.53777e6 1.58210
\(183\) −1.15123e6 −0.187849
\(184\) 3.15280e6i 0.506107i
\(185\) 8.47268e6 1.33815
\(186\) 2.90907e6 0.452080
\(187\) 1.36853e7 2.09281
\(188\) −1.44641e7 −2.17679
\(189\) −4.56184e6 −0.675701
\(190\) 2.79584e6i 0.407616i
\(191\) 1.07589e7i 1.54408i −0.635575 0.772039i \(-0.719237\pi\)
0.635575 0.772039i \(-0.280763\pi\)
\(192\) 1.09899e7i 1.55271i
\(193\) 8.52106e6 1.18528 0.592641 0.805467i \(-0.298085\pi\)
0.592641 + 0.805467i \(0.298085\pi\)
\(194\) 1.24429e7i 1.70419i
\(195\) 6.21528e6 0.838218
\(196\) −7.26161e6 −0.964417
\(197\) −3.31316e6 −0.433354 −0.216677 0.976243i \(-0.569522\pi\)
−0.216677 + 0.976243i \(0.569522\pi\)
\(198\) 1.32801e7i 1.71082i
\(199\) 9.97517e6i 1.26579i 0.774238 + 0.632894i \(0.218133\pi\)
−0.774238 + 0.632894i \(0.781867\pi\)
\(200\) 4.99301e7i 6.24126i
\(201\) 2.83996e6i 0.349723i
\(202\) 1.50572e7i 1.82680i
\(203\) −2.32846e6 −0.278343
\(204\) 1.97139e7i 2.32210i
\(205\) 1.54202e7i 1.78990i
\(206\) 2.12542e7i 2.43133i
\(207\) 1.07278e6 0.120948
\(208\) −3.26825e7 −3.63183
\(209\) 1.30487e6i 0.142932i
\(210\) 1.15918e7 1.25168
\(211\) 6.67494e6i 0.710558i 0.934760 + 0.355279i \(0.115614\pi\)
−0.934760 + 0.355279i \(0.884386\pi\)
\(212\) 2.40427e7 2.52334
\(213\) −3.06857e6 −0.317539
\(214\) 2.31165e7i 2.35875i
\(215\) 1.69800e7 + 950002.i 1.70853 + 0.0955892i
\(216\) 2.75313e7 2.73191
\(217\) 4.04781e6i 0.396133i
\(218\) 5.48508e6i 0.529436i
\(219\) 3.33603e6 0.317613
\(220\) 5.63794e7i 5.29483i
\(221\) −2.01837e7 −1.86993
\(222\) 7.81711e6i 0.714476i
\(223\) 1.44149e7i 1.29986i 0.759993 + 0.649931i \(0.225202\pi\)
−0.759993 + 0.649931i \(0.774798\pi\)
\(224\) −3.18288e7 −2.83189
\(225\) −1.69893e7 −1.49152
\(226\) 3.30156e7 2.86018
\(227\) 3.62378e6i 0.309802i 0.987930 + 0.154901i \(0.0495059\pi\)
−0.987930 + 0.154901i \(0.950494\pi\)
\(228\) −1.87969e6 −0.158592
\(229\) −6.20931e6 −0.517055 −0.258528 0.966004i \(-0.583237\pi\)
−0.258528 + 0.966004i \(0.583237\pi\)
\(230\) −6.25001e6 −0.513686
\(231\) −5.41011e6 −0.438905
\(232\) 1.40526e7 1.12536
\(233\) 1.98080e7i 1.56593i −0.622066 0.782965i \(-0.713706\pi\)
0.622066 0.782965i \(-0.286294\pi\)
\(234\) 1.95861e7i 1.52862i
\(235\) 1.79979e7i 1.38682i
\(236\) −1.82344e7 −1.38726
\(237\) 2.98472e6i 0.224212i
\(238\) −3.76435e7 −2.79228
\(239\) 3.26633e6 0.239258 0.119629 0.992819i \(-0.461829\pi\)
0.119629 + 0.992819i \(0.461829\pi\)
\(240\) −3.97208e7 −2.87332
\(241\) 1.10191e7i 0.787218i 0.919278 + 0.393609i \(0.128774\pi\)
−0.919278 + 0.393609i \(0.871226\pi\)
\(242\) 8.90053e6i 0.628014i
\(243\) 1.46499e7i 1.02098i
\(244\) 1.54018e7i 1.06023i
\(245\) 9.03577e6i 0.614422i
\(246\) 1.42271e7 0.955674
\(247\) 1.92449e6i 0.127710i
\(248\) 2.44291e7i 1.60160i
\(249\) 4.79420e6i 0.310540i
\(250\) 4.76472e7 3.04942
\(251\) 1.04228e7 0.659117 0.329558 0.944135i \(-0.393100\pi\)
0.329558 + 0.944135i \(0.393100\pi\)
\(252\) 2.66186e7i 1.66335i
\(253\) 2.91701e6 0.180126
\(254\) 7.68670e6i 0.469071i
\(255\) −2.45304e7 −1.47939
\(256\) 3.30922e7 1.97245
\(257\) 2.59317e7i 1.52768i −0.645407 0.763839i \(-0.723312\pi\)
0.645407 0.763839i \(-0.276688\pi\)
\(258\) −876497. + 1.56662e7i −0.0510377 + 0.912229i
\(259\) 1.08771e7 0.626057
\(260\) 8.31510e7i 4.73094i
\(261\) 4.78156e6i 0.268935i
\(262\) −5.07822e7 −2.82363
\(263\) 1.65481e7i 0.909666i 0.890577 + 0.454833i \(0.150301\pi\)
−0.890577 + 0.454833i \(0.849699\pi\)
\(264\) 3.26508e7 1.77452
\(265\) 2.99168e7i 1.60760i
\(266\) 3.58925e6i 0.190704i
\(267\) −3.56520e6 −0.187305
\(268\) −3.79944e7 −1.97386
\(269\) −1.71681e7 −0.881996 −0.440998 0.897508i \(-0.645375\pi\)
−0.440998 + 0.897508i \(0.645375\pi\)
\(270\) 5.45773e7i 2.77281i
\(271\) 3.10767e7 1.56145 0.780723 0.624878i \(-0.214851\pi\)
0.780723 + 0.624878i \(0.214851\pi\)
\(272\) 1.28991e8 6.40992
\(273\) 7.97909e6 0.392162
\(274\) 908543. 0.0441666
\(275\) −4.61959e7 −2.22129
\(276\) 4.20200e6i 0.199861i
\(277\) 1.00741e7i 0.473986i 0.971511 + 0.236993i \(0.0761618\pi\)
−0.971511 + 0.236993i \(0.923838\pi\)
\(278\) 6.03225e7i 2.80766i
\(279\) −8.31229e6 −0.382744
\(280\) 9.73428e7i 4.43435i
\(281\) 1.56495e6 0.0705311 0.0352655 0.999378i \(-0.488772\pi\)
0.0352655 + 0.999378i \(0.488772\pi\)
\(282\) −1.66054e7 −0.740459
\(283\) −2.45515e6 −0.108323 −0.0541613 0.998532i \(-0.517249\pi\)
−0.0541613 + 0.998532i \(0.517249\pi\)
\(284\) 4.10529e7i 1.79221i
\(285\) 2.33894e6i 0.101038i
\(286\) 5.32568e7i 2.27655i
\(287\) 1.97962e7i 0.837406i
\(288\) 6.53614e7i 2.73617i
\(289\) 5.55232e7 2.30028
\(290\) 2.78575e7i 1.14221i
\(291\) 1.04095e7i 0.422426i
\(292\) 4.46311e7i 1.79262i
\(293\) −6.96069e6 −0.276726 −0.138363 0.990382i \(-0.544184\pi\)
−0.138363 + 0.990382i \(0.544184\pi\)
\(294\) −8.33664e6 −0.328057
\(295\) 2.26895e7i 0.883809i
\(296\) −6.56448e7 −2.53119
\(297\) 2.54723e7i 0.972297i
\(298\) 3.52580e7 1.33232
\(299\) −4.30214e6 −0.160943
\(300\) 6.65460e7i 2.46467i
\(301\) 2.17987e7 + 1.21960e6i 0.799338 + 0.0447216i
\(302\) −5.61757e7 −2.03952
\(303\) 1.25965e7i 0.452818i
\(304\) 1.22991e7i 0.437776i
\(305\) −1.91647e7 −0.675465
\(306\) 7.73020e7i 2.69790i
\(307\) −3.61363e7 −1.24890 −0.624451 0.781064i \(-0.714677\pi\)
−0.624451 + 0.781064i \(0.714677\pi\)
\(308\) 7.23791e7i 2.47720i
\(309\) 1.77808e7i 0.602665i
\(310\) 4.84276e7 1.62558
\(311\) −6.46269e6 −0.214849 −0.107424 0.994213i \(-0.534260\pi\)
−0.107424 + 0.994213i \(0.534260\pi\)
\(312\) −4.81549e7 −1.58554
\(313\) 3.01930e6i 0.0984629i −0.998787 0.0492315i \(-0.984323\pi\)
0.998787 0.0492315i \(-0.0156772\pi\)
\(314\) 6.61154e7 2.13557
\(315\) −3.31220e7 −1.05971
\(316\) −3.99311e7 −1.26546
\(317\) −5.16124e7 −1.62023 −0.810115 0.586271i \(-0.800595\pi\)
−0.810115 + 0.586271i \(0.800595\pi\)
\(318\) 2.76020e7 0.858340
\(319\) 1.30016e7i 0.400521i
\(320\) 1.82951e8i 5.58321i
\(321\) 1.93388e7i 0.584675i
\(322\) −8.02368e6 −0.240329
\(323\) 7.59554e6i 0.225399i
\(324\) −3.39725e7 −0.998832
\(325\) 6.81320e7 1.98473
\(326\) 6.89572e7 1.99034
\(327\) 4.58870e6i 0.131234i
\(328\) 1.19473e8i 3.38569i
\(329\) 2.31055e7i 0.648825i
\(330\) 6.47259e7i 1.80109i
\(331\) 2.44942e7i 0.675428i −0.941249 0.337714i \(-0.890346\pi\)
0.941249 0.337714i \(-0.109654\pi\)
\(332\) −6.41391e7 −1.75270
\(333\) 2.23364e7i 0.604896i
\(334\) 1.16566e8i 3.12849i
\(335\) 4.72772e7i 1.25753i
\(336\) −5.09931e7 −1.34429
\(337\) 6.86964e7 1.79492 0.897458 0.441100i \(-0.145412\pi\)
0.897458 + 0.441100i \(0.145412\pi\)
\(338\) 4.41045e6i 0.114218i
\(339\) 2.76201e7 0.708967
\(340\) 3.28179e8i 8.34977i
\(341\) −2.26021e7 −0.570015
\(342\) 7.37063e6 0.184258
\(343\) 4.39066e7i 1.08805i
\(344\) −1.31558e8 7.36045e6i −3.23178 0.180813i
\(345\) −5.22863e6 −0.127330
\(346\) 6.61648e7i 1.59734i
\(347\) 5.05288e7i 1.20935i 0.796474 + 0.604673i \(0.206696\pi\)
−0.796474 + 0.604673i \(0.793304\pi\)
\(348\) 1.87291e7 0.444404
\(349\) 7.43877e7i 1.74995i −0.484172 0.874973i \(-0.660879\pi\)
0.484172 0.874973i \(-0.339121\pi\)
\(350\) 1.27069e8 2.96371
\(351\) 3.75678e7i 0.868749i
\(352\) 1.77725e8i 4.07494i
\(353\) 6.81991e7 1.55044 0.775219 0.631692i \(-0.217639\pi\)
0.775219 + 0.631692i \(0.217639\pi\)
\(354\) −2.09339e7 −0.471890
\(355\) −5.10829e7 −1.14180
\(356\) 4.76970e7i 1.05716i
\(357\) −3.14917e7 −0.692137
\(358\) −1.41694e8 −3.08817
\(359\) 4.74093e7 1.02466 0.512331 0.858788i \(-0.328782\pi\)
0.512331 + 0.858788i \(0.328782\pi\)
\(360\) 1.99896e8 4.28447
\(361\) 4.63217e7 0.984606
\(362\) 3.56249e7i 0.750980i
\(363\) 7.44598e6i 0.155669i
\(364\) 1.06748e8i 2.21338i
\(365\) 5.55353e7 1.14206
\(366\) 1.76819e7i 0.360649i
\(367\) 1.93390e7 0.391233 0.195617 0.980680i \(-0.437329\pi\)
0.195617 + 0.980680i \(0.437329\pi\)
\(368\) 2.74943e7 0.551695
\(369\) −4.06520e7 −0.809102
\(370\) 1.30132e8i 2.56910i
\(371\) 3.84068e7i 0.752118i
\(372\) 3.25587e7i 0.632468i
\(373\) 9.21753e7i 1.77618i −0.459665 0.888092i \(-0.652031\pi\)
0.459665 0.888092i \(-0.347969\pi\)
\(374\) 2.10193e8i 4.01795i
\(375\) 3.98606e7 0.755874
\(376\) 1.39445e8i 2.62325i
\(377\) 1.91754e7i 0.357866i
\(378\) 7.00656e7i 1.29727i
\(379\) 2.95380e6 0.0542579 0.0271290 0.999632i \(-0.491364\pi\)
0.0271290 + 0.999632i \(0.491364\pi\)
\(380\) −3.12914e7 −0.570262
\(381\) 6.43053e6i 0.116271i
\(382\) 1.65247e8 2.96445
\(383\) 3.91227e7i 0.696358i −0.937428 0.348179i \(-0.886800\pi\)
0.937428 0.348179i \(-0.113200\pi\)
\(384\) 7.34784e7 1.29768
\(385\) −9.00627e7 −1.57820
\(386\) 1.30876e8i 2.27560i
\(387\) 2.50448e6 4.47641e7i 0.0432100 0.772320i
\(388\) −1.39263e8 −2.38419
\(389\) 1.61920e7i 0.275076i 0.990496 + 0.137538i \(0.0439189\pi\)
−0.990496 + 0.137538i \(0.956081\pi\)
\(390\) 9.54609e7i 1.60928i
\(391\) 1.69796e7 0.284052
\(392\) 7.00076e7i 1.16222i
\(393\) −4.24833e7 −0.699907
\(394\) 5.08870e7i 0.831990i
\(395\) 4.96870e7i 0.806216i
\(396\) −1.48632e8 −2.39347
\(397\) 8.82551e7 1.41048 0.705242 0.708967i \(-0.250838\pi\)
0.705242 + 0.708967i \(0.250838\pi\)
\(398\) −1.53209e8 −2.43017
\(399\) 3.00269e6i 0.0472707i
\(400\) −4.35420e8 −6.80344
\(401\) −3.91351e7 −0.606923 −0.303461 0.952844i \(-0.598142\pi\)
−0.303461 + 0.952844i \(0.598142\pi\)
\(402\) −4.36192e7 −0.671428
\(403\) 3.33347e7 0.509309
\(404\) −1.68523e8 −2.55573
\(405\) 4.22727e7i 0.636348i
\(406\) 3.57630e7i 0.534387i
\(407\) 6.07354e7i 0.900863i
\(408\) 1.90057e8 2.79836
\(409\) 1.45715e7i 0.212978i −0.994314 0.106489i \(-0.966039\pi\)
0.994314 0.106489i \(-0.0339609\pi\)
\(410\) 2.36839e8 3.43639
\(411\) 760067. 0.0109478
\(412\) 2.37880e8 3.40147
\(413\) 2.91284e7i 0.413492i
\(414\) 1.64768e7i 0.232206i
\(415\) 7.98095e7i 1.11663i
\(416\) 2.62118e8i 3.64097i
\(417\) 5.04645e7i 0.695949i
\(418\) 2.00416e7 0.274413
\(419\) 1.23103e7i 0.167350i 0.996493 + 0.0836750i \(0.0266658\pi\)
−0.996493 + 0.0836750i \(0.973334\pi\)
\(420\) 1.29737e8i 1.75112i
\(421\) 9.02713e7i 1.20977i 0.796312 + 0.604886i \(0.206781\pi\)
−0.796312 + 0.604886i \(0.793219\pi\)
\(422\) −1.02521e8 −1.36419
\(423\) 4.74477e7 0.626894
\(424\) 2.31790e8i 3.04087i
\(425\) −2.68902e8 −3.50290
\(426\) 4.71304e7i 0.609639i
\(427\) −2.46034e7 −0.316017
\(428\) 2.58724e8 3.29993
\(429\) 4.45535e7i 0.564300i
\(430\) −1.45911e7 + 2.60797e8i −0.183520 + 3.28017i
\(431\) −6.09927e7 −0.761809 −0.380905 0.924614i \(-0.624387\pi\)
−0.380905 + 0.924614i \(0.624387\pi\)
\(432\) 2.40090e8i 2.97798i
\(433\) 9.68502e7i 1.19299i −0.802617 0.596495i \(-0.796560\pi\)
0.802617 0.596495i \(-0.203440\pi\)
\(434\) 6.21707e7 0.760530
\(435\) 2.33049e7i 0.283126i
\(436\) 6.13899e7 0.740691
\(437\) 1.61898e6i 0.0193998i
\(438\) 5.12383e7i 0.609779i
\(439\) −4.73443e7 −0.559596 −0.279798 0.960059i \(-0.590267\pi\)
−0.279798 + 0.960059i \(0.590267\pi\)
\(440\) 5.43541e8 6.38079
\(441\) 2.38209e7 0.277742
\(442\) 3.10003e8i 3.59004i
\(443\) 6.31480e7 0.726354 0.363177 0.931720i \(-0.381692\pi\)
0.363177 + 0.931720i \(0.381692\pi\)
\(444\) −8.74903e7 −0.999565
\(445\) −5.93503e7 −0.673508
\(446\) −2.21400e8 −2.49558
\(447\) 2.94960e7 0.330249
\(448\) 2.34870e8i 2.61212i
\(449\) 1.36056e8i 1.50307i −0.659694 0.751535i \(-0.729314\pi\)
0.659694 0.751535i \(-0.270686\pi\)
\(450\) 2.60940e8i 2.86354i
\(451\) −1.10538e8 −1.20498
\(452\) 3.69515e8i 4.00145i
\(453\) −4.69954e7 −0.505546
\(454\) −5.56579e7 −0.594784
\(455\) 1.32829e8 1.41013
\(456\) 1.81217e7i 0.191119i
\(457\) 7.83614e7i 0.821020i 0.911856 + 0.410510i \(0.134649\pi\)
−0.911856 + 0.410510i \(0.865351\pi\)
\(458\) 9.53692e7i 0.992686i
\(459\) 1.48272e8i 1.53328i
\(460\) 6.99511e7i 0.718656i
\(461\) 7.38666e6 0.0753955 0.0376977 0.999289i \(-0.487998\pi\)
0.0376977 + 0.999289i \(0.487998\pi\)
\(462\) 8.30942e7i 0.842646i
\(463\) 1.21692e8i 1.22608i −0.790053 0.613038i \(-0.789947\pi\)
0.790053 0.613038i \(-0.210053\pi\)
\(464\) 1.22547e8i 1.22673i
\(465\) 4.05135e7 0.402940
\(466\) 3.04232e8 3.00640
\(467\) 4.52041e7i 0.443840i −0.975065 0.221920i \(-0.928768\pi\)
0.975065 0.221920i \(-0.0712325\pi\)
\(468\) 2.19210e8 2.13857
\(469\) 6.06938e7i 0.588337i
\(470\) −2.76431e8 −2.66253
\(471\) 5.53107e7 0.529354
\(472\) 1.75794e8i 1.67178i
\(473\) 6.80998e6 1.21719e8i 0.0643520 1.15020i
\(474\) −4.58426e7 −0.430461
\(475\) 2.56394e7i 0.239237i
\(476\) 4.21312e8i 3.90646i
\(477\) −7.88693e7 −0.726696
\(478\) 5.01678e7i 0.459348i
\(479\) 1.31849e7 0.119970 0.0599848 0.998199i \(-0.480895\pi\)
0.0599848 + 0.998199i \(0.480895\pi\)
\(480\) 3.18566e8i 2.88055i
\(481\) 8.95755e7i 0.804922i
\(482\) −1.69243e8 −1.51137
\(483\) −6.71244e6 −0.0595715
\(484\) −9.96160e7 −0.878604
\(485\) 1.73288e8i 1.51895i
\(486\) −2.25009e8 −1.96016
\(487\) −1.42982e8 −1.23793 −0.618964 0.785420i \(-0.712447\pi\)
−0.618964 + 0.785420i \(0.712447\pi\)
\(488\) 1.48485e8 1.27768
\(489\) 5.76881e7 0.493355
\(490\) −1.38781e8 −1.17962
\(491\) 1.24890e8i 1.05507i −0.849532 0.527537i \(-0.823115\pi\)
0.849532 0.527537i \(-0.176885\pi\)
\(492\) 1.59231e8i 1.33701i
\(493\) 7.56813e7i 0.631608i
\(494\) −2.95583e7 −0.245188
\(495\) 1.84946e8i 1.52486i
\(496\) −2.13037e8 −1.74586
\(497\) −6.55795e7 −0.534194
\(498\) −7.36344e7 −0.596201
\(499\) 8.63178e7i 0.694703i −0.937735 0.347351i \(-0.887081\pi\)
0.937735 0.347351i \(-0.112919\pi\)
\(500\) 5.33274e8i 4.26619i
\(501\) 9.75170e7i 0.775474i
\(502\) 1.60084e8i 1.26543i
\(503\) 2.41745e7i 0.189956i 0.995479 + 0.0949782i \(0.0302781\pi\)
−0.995479 + 0.0949782i \(0.969722\pi\)
\(504\) 2.56624e8 2.00450
\(505\) 2.09696e8i 1.62823i
\(506\) 4.48025e7i 0.345820i
\(507\) 3.68969e6i 0.0283117i
\(508\) 8.60307e7 0.656240
\(509\) 1.75528e8 1.33105 0.665524 0.746376i \(-0.268208\pi\)
0.665524 + 0.746376i \(0.268208\pi\)
\(510\) 3.76764e8i 2.84026i
\(511\) 7.12954e7 0.534317
\(512\) 1.42277e8i 1.06004i
\(513\) 1.41375e7 0.104718
\(514\) 3.98287e8 2.93296
\(515\) 2.95999e8i 2.16705i
\(516\) −1.75338e8 9.80988e6i −1.27623 0.0714027i
\(517\) 1.29016e8 0.933624
\(518\) 1.67062e8i 1.20196i
\(519\) 5.53520e7i 0.395942i
\(520\) −8.01641e8 −5.70124
\(521\) 6.01580e7i 0.425383i −0.977119 0.212691i \(-0.931777\pi\)
0.977119 0.212691i \(-0.0682229\pi\)
\(522\) −7.34403e7 −0.516325
\(523\) 2.27924e8i 1.59326i 0.604470 + 0.796628i \(0.293385\pi\)
−0.604470 + 0.796628i \(0.706615\pi\)
\(524\) 5.68362e8i 3.95031i
\(525\) 1.06303e8 0.734630
\(526\) −2.54164e8 −1.74645
\(527\) −1.31565e8 −0.898893
\(528\) 2.84734e8i 1.93436i
\(529\) −1.44417e8 −0.975552
\(530\) 4.59494e8 3.08640
\(531\) 5.98160e7 0.399516
\(532\) −4.01715e7 −0.266798
\(533\) 1.63026e8 1.07665
\(534\) 5.47582e7i 0.359605i
\(535\) 3.21935e8i 2.10236i
\(536\) 3.66296e8i 2.37869i
\(537\) −1.18538e8 −0.765480
\(538\) 2.63687e8i 1.69333i
\(539\) 6.47718e7 0.413638
\(540\) 6.10837e8 3.87922
\(541\) −8.34449e7 −0.526997 −0.263499 0.964660i \(-0.584876\pi\)
−0.263499 + 0.964660i \(0.584876\pi\)
\(542\) 4.77309e8i 2.99779i
\(543\) 2.98030e7i 0.186149i
\(544\) 1.03452e9i 6.42604i
\(545\) 7.63886e7i 0.471888i
\(546\) 1.22551e8i 0.752905i
\(547\) −1.02571e8 −0.626701 −0.313351 0.949638i \(-0.601451\pi\)
−0.313351 + 0.949638i \(0.601451\pi\)
\(548\) 1.01686e7i 0.0617899i
\(549\) 5.05237e7i 0.305336i
\(550\) 7.09527e8i 4.26462i
\(551\) 7.21610e6 0.0431368
\(552\) 4.05105e7 0.240852
\(553\) 6.37875e7i 0.377190i
\(554\) −1.54728e8 −0.909998
\(555\) 1.08866e8i 0.636815i
\(556\) 6.75138e8 3.92797
\(557\) −1.75878e8 −1.01776 −0.508880 0.860837i \(-0.669940\pi\)
−0.508880 + 0.860837i \(0.669940\pi\)
\(558\) 1.27669e8i 0.734824i
\(559\) −1.00437e7 + 1.79517e8i −0.0574986 + 1.02771i
\(560\) −8.48887e8 −4.83377
\(561\) 1.75843e8i 0.995948i
\(562\) 2.40361e7i 0.135411i
\(563\) 2.10250e8 1.17818 0.589088 0.808069i \(-0.299487\pi\)
0.589088 + 0.808069i \(0.299487\pi\)
\(564\) 1.85850e8i 1.03592i
\(565\) 4.59795e8 2.54929
\(566\) 3.77088e7i 0.207967i
\(567\) 5.42691e7i 0.297717i
\(568\) 3.95782e8 2.15978
\(569\) 1.85858e8 1.00889 0.504445 0.863444i \(-0.331697\pi\)
0.504445 + 0.863444i \(0.331697\pi\)
\(570\) −3.59239e7 −0.193981
\(571\) 6.24130e7i 0.335248i 0.985851 + 0.167624i \(0.0536095\pi\)
−0.985851 + 0.167624i \(0.946391\pi\)
\(572\) 5.96059e8 3.18494
\(573\) 1.38242e8 0.734813
\(574\) 3.04051e8 1.60772
\(575\) −5.73163e7 −0.301491
\(576\) −4.82311e8 −2.52383
\(577\) 5.34888e7i 0.278442i 0.990261 + 0.139221i \(0.0444599\pi\)
−0.990261 + 0.139221i \(0.955540\pi\)
\(578\) 8.52785e8i 4.41628i
\(579\) 1.09488e8i 0.564065i
\(580\) 3.11785e8 1.59798
\(581\) 1.02458e8i 0.522419i
\(582\) −1.59880e8 −0.811008
\(583\) −2.14455e8 −1.08226
\(584\) −4.30278e8 −2.16028
\(585\) 2.72768e8i 1.36246i
\(586\) 1.06910e8i 0.531281i
\(587\) 6.51087e7i 0.321903i −0.986962 0.160951i \(-0.948544\pi\)
0.986962 0.160951i \(-0.0514563\pi\)
\(588\) 9.33049e7i 0.458957i
\(589\) 1.25445e7i 0.0613915i
\(590\) −3.48489e8 −1.69681
\(591\) 4.25709e7i 0.206229i
\(592\) 5.72462e8i 2.75919i
\(593\) 1.65528e8i 0.793796i −0.917863 0.396898i \(-0.870087\pi\)
0.917863 0.396898i \(-0.129913\pi\)
\(594\) −3.91231e8 −1.86670
\(595\) −5.24247e8 −2.48877
\(596\) 3.94612e8i 1.86394i
\(597\) −1.28172e8 −0.602378
\(598\) 6.60769e7i 0.308991i
\(599\) 3.37403e8 1.56989 0.784944 0.619566i \(-0.212691\pi\)
0.784944 + 0.619566i \(0.212691\pi\)
\(600\) −6.41555e8 −2.97016
\(601\) 3.47057e8i 1.59874i 0.600842 + 0.799368i \(0.294832\pi\)
−0.600842 + 0.799368i \(0.705168\pi\)
\(602\) −1.87319e7 + 3.34807e8i −0.0858603 + 1.53464i
\(603\) 1.24636e8 0.568451
\(604\) 6.28727e8i 2.85332i
\(605\) 1.23954e8i 0.559751i
\(606\) −1.93471e8 −0.869358
\(607\) 2.68929e8i 1.20246i −0.799074 0.601232i \(-0.794677\pi\)
0.799074 0.601232i \(-0.205323\pi\)
\(608\) 9.86402e7 0.438878
\(609\) 2.99185e7i 0.132461i
\(610\) 2.94352e8i 1.29681i
\(611\) −1.90279e8 −0.834195
\(612\) −8.65175e8 −3.77442
\(613\) 1.60012e8 0.694658 0.347329 0.937743i \(-0.387089\pi\)
0.347329 + 0.937743i \(0.387089\pi\)
\(614\) 5.55019e8i 2.39775i
\(615\) 1.98135e8 0.851795
\(616\) 6.97790e8 2.98526
\(617\) −3.99697e8 −1.70167 −0.850835 0.525433i \(-0.823903\pi\)
−0.850835 + 0.525433i \(0.823903\pi\)
\(618\) 2.73097e8 1.15705
\(619\) 2.89266e8 1.21962 0.609812 0.792546i \(-0.291245\pi\)
0.609812 + 0.792546i \(0.291245\pi\)
\(620\) 5.42009e8i 2.27421i
\(621\) 3.16040e7i 0.131968i
\(622\) 9.92610e7i 0.412484i
\(623\) −7.61931e7 −0.315102
\(624\) 4.19940e8i 1.72836i
\(625\) 1.92811e8 0.789756
\(626\) 4.63736e7 0.189037
\(627\) 1.67664e7 0.0680200
\(628\) 7.39973e8i 2.98770i
\(629\) 3.53535e8i 1.42063i
\(630\) 5.08723e8i 2.03451i
\(631\) 4.58916e8i 1.82661i −0.407280 0.913303i \(-0.633523\pi\)
0.407280 0.913303i \(-0.366477\pi\)
\(632\) 3.84966e8i 1.52501i
\(633\) −8.57667e7 −0.338148
\(634\) 7.92719e8i 3.11065i
\(635\) 1.07050e8i 0.418085i
\(636\) 3.08926e8i 1.20083i
\(637\) −9.55286e7 −0.369586
\(638\) −1.99693e8 −0.768955
\(639\) 1.34669e8i 0.516138i
\(640\) 1.22320e9 4.66615
\(641\) 1.71310e8i 0.650444i 0.945638 + 0.325222i \(0.105439\pi\)
−0.945638 + 0.325222i \(0.894561\pi\)
\(642\) 2.97026e8 1.12251
\(643\) 2.81858e8 1.06023 0.530113 0.847927i \(-0.322150\pi\)
0.530113 + 0.847927i \(0.322150\pi\)
\(644\) 8.98022e7i 0.336225i
\(645\) −1.22066e7 + 2.18177e8i −0.0454901 + 0.813073i
\(646\) 1.16660e8 0.432739
\(647\) 2.11105e8i 0.779447i 0.920932 + 0.389724i \(0.127429\pi\)
−0.920932 + 0.389724i \(0.872571\pi\)
\(648\) 3.27521e8i 1.20369i
\(649\) 1.62647e8 0.594993
\(650\) 1.04644e9i 3.81045i
\(651\) 5.20106e7 0.188516
\(652\) 7.71780e8i 2.78452i
\(653\) 4.34044e8i 1.55881i 0.626519 + 0.779406i \(0.284479\pi\)
−0.626519 + 0.779406i \(0.715521\pi\)
\(654\) 7.04781e7 0.251954
\(655\) −7.07224e8 −2.51671
\(656\) −1.04187e9 −3.69066
\(657\) 1.46407e8i 0.516257i
\(658\) −3.54879e8 −1.24567
\(659\) −4.74544e7 −0.165814 −0.0829068 0.996557i \(-0.526420\pi\)
−0.0829068 + 0.996557i \(0.526420\pi\)
\(660\) 7.24422e8 2.51976
\(661\) −7.15485e7 −0.247740 −0.123870 0.992298i \(-0.539531\pi\)
−0.123870 + 0.992298i \(0.539531\pi\)
\(662\) 3.76208e8 1.29674
\(663\) 2.59342e8i 0.889881i
\(664\) 6.18351e8i 2.11218i
\(665\) 4.99862e7i 0.169975i
\(666\) 3.43067e8 1.16133
\(667\) 1.61314e7i 0.0543619i
\(668\) −1.30463e9 −4.37681
\(669\) −1.85218e8 −0.618593
\(670\) −7.26134e8 −2.41431
\(671\) 1.37380e8i 0.454732i
\(672\) 4.08971e8i 1.34767i
\(673\) 2.15921e7i 0.0708352i −0.999373 0.0354176i \(-0.988724\pi\)
0.999373 0.0354176i \(-0.0112761\pi\)
\(674\) 1.05511e9i 3.44603i
\(675\) 5.00506e8i 1.62741i
\(676\) −4.93625e7 −0.159793
\(677\) 1.59757e8i 0.514864i 0.966296 + 0.257432i \(0.0828764\pi\)
−0.966296 + 0.257432i \(0.917124\pi\)
\(678\) 4.24219e8i 1.36113i
\(679\) 2.22465e8i 0.710643i
\(680\) 3.16390e9 10.0623
\(681\) −4.65622e7 −0.147432
\(682\) 3.47148e8i 1.09436i
\(683\) 2.73296e8 0.857771 0.428886 0.903359i \(-0.358906\pi\)
0.428886 + 0.903359i \(0.358906\pi\)
\(684\) 8.24932e7i 0.257780i
\(685\) 1.26529e7 0.0393658
\(686\) −6.74364e8 −2.08892
\(687\) 7.97838e7i 0.246062i
\(688\) 6.41875e7 1.14726e9i 0.197099 3.52288i
\(689\) 3.16289e8 0.966999
\(690\) 8.03068e7i 0.244459i
\(691\) 2.18660e8i 0.662729i 0.943503 + 0.331364i \(0.107509\pi\)
−0.943503 + 0.331364i \(0.892491\pi\)
\(692\) 7.40526e8 2.23472
\(693\) 2.37431e8i 0.713408i
\(694\) −7.76075e8 −2.32180
\(695\) 8.40088e8i 2.50248i
\(696\) 1.80563e8i 0.535550i
\(697\) −6.43430e8 −1.90022
\(698\) 1.14253e9 3.35969
\(699\) 2.54514e8 0.745212
\(700\) 1.42218e9i 4.14629i
\(701\) −4.06383e8 −1.17973 −0.589863 0.807503i \(-0.700818\pi\)
−0.589863 + 0.807503i \(0.700818\pi\)
\(702\) 5.77006e8 1.66790
\(703\) −3.37091e7 −0.0970243
\(704\) −1.31146e9 −3.75870
\(705\) −2.31256e8 −0.659974
\(706\) 1.04747e9i 2.97666i
\(707\) 2.69205e8i 0.761772i
\(708\) 2.34295e8i 0.660183i
\(709\) −2.66283e8 −0.747145 −0.373573 0.927601i \(-0.621867\pi\)
−0.373573 + 0.927601i \(0.621867\pi\)
\(710\) 7.84586e8i 2.19213i
\(711\) 1.30989e8 0.364441
\(712\) 4.59836e8 1.27398
\(713\) −2.80429e7 −0.0773668
\(714\) 4.83684e8i 1.32882i
\(715\) 7.41687e8i 2.02910i
\(716\) 1.58586e9i 4.32041i
\(717\) 4.19693e7i 0.113861i
\(718\) 7.28163e8i 1.96723i
\(719\) −4.99086e8 −1.34273 −0.671366 0.741126i \(-0.734292\pi\)
−0.671366 + 0.741126i \(0.734292\pi\)
\(720\) 1.74321e9i 4.67039i
\(721\) 3.80000e8i 1.01386i
\(722\) 7.11458e8i 1.89033i
\(723\) −1.41585e8 −0.374630
\(724\) −3.98720e8 −1.05064
\(725\) 2.55469e8i 0.670385i
\(726\) −1.14363e8 −0.298866
\(727\) 2.89743e8i 0.754066i 0.926200 + 0.377033i \(0.123056\pi\)
−0.926200 + 0.377033i \(0.876944\pi\)
\(728\) −1.02913e9 −2.66734
\(729\) −4.41664e7 −0.114001
\(730\) 8.52971e8i 2.19263i
\(731\) 3.96402e7 7.08515e8i 0.101481 1.81383i
\(732\) 1.97898e8 0.504555
\(733\) 1.87282e8i 0.475536i 0.971322 + 0.237768i \(0.0764159\pi\)
−0.971322 + 0.237768i \(0.923584\pi\)
\(734\) 2.97029e8i 0.751122i
\(735\) −1.16101e8 −0.292398
\(736\) 2.20508e8i 0.553083i
\(737\) 3.38901e8 0.846585
\(738\) 6.24377e8i 1.55338i
\(739\) 8.30923e6i 0.0205886i 0.999947 + 0.0102943i \(0.00327684\pi\)
−0.999947 + 0.0102943i \(0.996723\pi\)
\(740\) −1.45646e9 −3.59421
\(741\) −2.47279e7 −0.0607760
\(742\) 5.89892e8 1.44398
\(743\) 1.16504e8i 0.284037i 0.989864 + 0.142019i \(0.0453593\pi\)
−0.989864 + 0.142019i \(0.954641\pi\)
\(744\) −3.13891e8 −0.762185
\(745\) 4.91024e8 1.18750
\(746\) 1.41573e9 3.41007
\(747\) 2.10401e8 0.504761
\(748\) −2.35251e9 −5.62118
\(749\) 4.13296e8i 0.983593i
\(750\) 6.12221e8i 1.45119i
\(751\) 1.60100e8i 0.377982i 0.981979 + 0.188991i \(0.0605216\pi\)
−0.981979 + 0.188991i \(0.939478\pi\)
\(752\) 1.21604e9 2.85953
\(753\) 1.33923e8i 0.313668i
\(754\) 2.94517e8 0.687062
\(755\) −7.82337e8 −1.81783
\(756\) 7.84185e8 1.81490
\(757\) 6.51063e7i 0.150084i 0.997180 + 0.0750422i \(0.0239092\pi\)
−0.997180 + 0.0750422i \(0.976091\pi\)
\(758\) 4.53676e7i 0.104169i
\(759\) 3.74808e7i 0.0857203i
\(760\) 3.01674e8i 0.687221i
\(761\) 6.42727e8i 1.45839i −0.684308 0.729193i \(-0.739896\pi\)
0.684308 0.729193i \(-0.260104\pi\)
\(762\) 9.87669e7 0.223227
\(763\) 9.80666e7i 0.220774i
\(764\) 1.84947e9i 4.14732i
\(765\) 1.07655e9i 2.40465i
\(766\) 6.00888e8 1.33693
\(767\) −2.39879e8 −0.531627
\(768\) 4.25204e8i 0.938672i
\(769\) −7.77041e7 −0.170870 −0.0854349 0.996344i \(-0.527228\pi\)
−0.0854349 + 0.996344i \(0.527228\pi\)
\(770\) 1.38328e9i 3.02997i
\(771\) 3.33198e8 0.727008
\(772\) −1.46478e9 −3.18361
\(773\) 2.33836e8i 0.506260i −0.967432 0.253130i \(-0.918540\pi\)
0.967432 0.253130i \(-0.0814600\pi\)
\(774\) 6.87535e8 + 3.84665e7i 1.48276 + 0.0829582i
\(775\) 4.44109e8 0.954080
\(776\) 1.34260e9i 2.87318i
\(777\) 1.39761e8i 0.297935i
\(778\) −2.48695e8 −0.528114
\(779\) 6.13501e7i 0.129779i
\(780\) −1.06841e9 −2.25141
\(781\) 3.66182e8i 0.768677i
\(782\) 2.60791e8i 0.545347i
\(783\) −1.40865e8 −0.293439