Properties

Label 43.5.b.b.42.11
Level 43
Weight 5
Character 43.42
Analytic conductor 4.445
Analytic rank 0
Dimension 12
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.44490841261\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.11
Root \(6.72223i\) of \(x^{12} + 142 x^{10} + 7173 x^{8} + 157368 x^{6} + 1510016 x^{4} + 5098688 x^{2} + 90352\)
Character \(\chi\) \(=\) 43.42
Dual form 43.5.b.b.42.2

$q$-expansion

\(f(q)\) \(=\) \(q+6.72223i q^{2} +8.31879i q^{3} -29.1884 q^{4} -1.48242i q^{5} -55.9208 q^{6} +13.7963i q^{7} -88.6554i q^{8} +11.7977 q^{9} +O(q^{10})\) \(q+6.72223i q^{2} +8.31879i q^{3} -29.1884 q^{4} -1.48242i q^{5} -55.9208 q^{6} +13.7963i q^{7} -88.6554i q^{8} +11.7977 q^{9} +9.96518 q^{10} -10.2025 q^{11} -242.812i q^{12} +98.4183 q^{13} -92.7416 q^{14} +12.3320 q^{15} +128.948 q^{16} -286.515 q^{17} +79.3069i q^{18} +367.004i q^{19} +43.2695i q^{20} -114.768 q^{21} -68.5838i q^{22} -242.039 q^{23} +737.506 q^{24} +622.802 q^{25} +661.591i q^{26} +771.965i q^{27} -402.691i q^{28} +1147.40i q^{29} +82.8983i q^{30} +895.225 q^{31} -551.669i q^{32} -84.8728i q^{33} -1926.02i q^{34} +20.4519 q^{35} -344.356 q^{36} -2295.69i q^{37} -2467.09 q^{38} +818.722i q^{39} -131.425 q^{40} +1692.26 q^{41} -771.498i q^{42} +(-1546.34 + 1013.73i) q^{43} +297.796 q^{44} -17.4892i q^{45} -1627.04i q^{46} +743.419 q^{47} +1072.69i q^{48} +2210.66 q^{49} +4186.62i q^{50} -2383.46i q^{51} -2872.67 q^{52} +99.3399 q^{53} -5189.33 q^{54} +15.1245i q^{55} +1223.11 q^{56} -3053.03 q^{57} -7713.09 q^{58} +3286.35 q^{59} -359.950 q^{60} -3223.22i q^{61} +6017.91i q^{62} +162.764i q^{63} +5771.61 q^{64} -145.898i q^{65} +570.534 q^{66} +5556.36 q^{67} +8362.90 q^{68} -2013.47i q^{69} +137.482i q^{70} +2953.33i q^{71} -1045.93i q^{72} -3618.34i q^{73} +15432.2 q^{74} +5180.96i q^{75} -10712.3i q^{76} -140.757i q^{77} -5503.64 q^{78} +2380.74 q^{79} -191.155i q^{80} -5466.20 q^{81} +11375.7i q^{82} -6427.91 q^{83} +3349.90 q^{84} +424.736i q^{85} +(-6814.51 - 10394.8i) q^{86} -9544.98 q^{87} +904.510i q^{88} +3293.36i q^{89} +117.566 q^{90} +1357.80i q^{91} +7064.72 q^{92} +7447.19i q^{93} +4997.44i q^{94} +544.055 q^{95} +4589.22 q^{96} -9329.95 q^{97} +14860.6i q^{98} -120.367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + O(q^{10}) \) \( 12q - 92q^{4} + 126q^{6} - 462q^{9} + 182q^{10} - 180q^{11} - 216q^{13} + 732q^{14} - 92q^{15} + 1076q^{16} + 678q^{17} - 2392q^{21} + 1566q^{23} - 4234q^{24} - 174q^{25} + 5710q^{31} + 936q^{35} + 4210q^{36} + 1242q^{38} - 2618q^{40} + 4878q^{41} - 1108q^{43} - 15168q^{44} - 5526q^{47} - 8544q^{49} + 24084q^{52} + 1212q^{53} - 10004q^{54} - 10152q^{56} - 7692q^{57} - 4666q^{58} + 14016q^{59} + 15848q^{60} - 15580q^{64} + 29808q^{66} - 1088q^{67} + 15186q^{68} - 7674q^{74} - 67708q^{78} + 24302q^{79} - 23660q^{81} - 7032q^{83} + 37180q^{84} - 14412q^{86} + 17850q^{87} + 4268q^{90} + 48354q^{92} + 606q^{95} + 50546q^{96} - 5842q^{97} - 25924q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.72223i 1.68056i 0.542154 + 0.840279i \(0.317609\pi\)
−0.542154 + 0.840279i \(0.682391\pi\)
\(3\) 8.31879i 0.924310i 0.886799 + 0.462155i \(0.152924\pi\)
−0.886799 + 0.462155i \(0.847076\pi\)
\(4\) −29.1884 −1.82427
\(5\) 1.48242i 0.0592969i −0.999560 0.0296484i \(-0.990561\pi\)
0.999560 0.0296484i \(-0.00943877\pi\)
\(6\) −55.9208 −1.55336
\(7\) 13.7963i 0.281556i 0.990041 + 0.140778i \(0.0449604\pi\)
−0.990041 + 0.140778i \(0.955040\pi\)
\(8\) 88.6554i 1.38524i
\(9\) 11.7977 0.145651
\(10\) 9.96518 0.0996518
\(11\) −10.2025 −0.0843185 −0.0421592 0.999111i \(-0.513424\pi\)
−0.0421592 + 0.999111i \(0.513424\pi\)
\(12\) 242.812i 1.68620i
\(13\) 98.4183 0.582357 0.291179 0.956669i \(-0.405953\pi\)
0.291179 + 0.956669i \(0.405953\pi\)
\(14\) −92.7416 −0.473172
\(15\) 12.3320 0.0548087
\(16\) 128.948 0.503703
\(17\) −286.515 −0.991400 −0.495700 0.868494i \(-0.665089\pi\)
−0.495700 + 0.868494i \(0.665089\pi\)
\(18\) 79.3069i 0.244775i
\(19\) 367.004i 1.01663i 0.861171 + 0.508316i \(0.169732\pi\)
−0.861171 + 0.508316i \(0.830268\pi\)
\(20\) 43.2695i 0.108174i
\(21\) −114.768 −0.260245
\(22\) 68.5838i 0.141702i
\(23\) −242.039 −0.457540 −0.228770 0.973480i \(-0.573470\pi\)
−0.228770 + 0.973480i \(0.573470\pi\)
\(24\) 737.506 1.28039
\(25\) 622.802 0.996484
\(26\) 661.591i 0.978685i
\(27\) 771.965i 1.05894i
\(28\) 402.691i 0.513636i
\(29\) 1147.40i 1.36433i 0.731199 + 0.682164i \(0.238961\pi\)
−0.731199 + 0.682164i \(0.761039\pi\)
\(30\) 82.8983i 0.0921092i
\(31\) 895.225 0.931556 0.465778 0.884902i \(-0.345775\pi\)
0.465778 + 0.884902i \(0.345775\pi\)
\(32\) 551.669i 0.538739i
\(33\) 84.8728i 0.0779364i
\(34\) 1926.02i 1.66611i
\(35\) 20.4519 0.0166954
\(36\) −344.356 −0.265707
\(37\) 2295.69i 1.67691i −0.544969 0.838456i \(-0.683459\pi\)
0.544969 0.838456i \(-0.316541\pi\)
\(38\) −2467.09 −1.70851
\(39\) 818.722i 0.538279i
\(40\) −131.425 −0.0821405
\(41\) 1692.26 1.00670 0.503348 0.864084i \(-0.332101\pi\)
0.503348 + 0.864084i \(0.332101\pi\)
\(42\) 771.498i 0.437357i
\(43\) −1546.34 + 1013.73i −0.836310 + 0.548257i
\(44\) 297.796 0.153820
\(45\) 17.4892i 0.00863663i
\(46\) 1627.04i 0.768923i
\(47\) 743.419 0.336541 0.168271 0.985741i \(-0.446182\pi\)
0.168271 + 0.985741i \(0.446182\pi\)
\(48\) 1072.69i 0.465578i
\(49\) 2210.66 0.920726
\(50\) 4186.62i 1.67465i
\(51\) 2383.46i 0.916361i
\(52\) −2872.67 −1.06238
\(53\) 99.3399 0.0353649 0.0176824 0.999844i \(-0.494371\pi\)
0.0176824 + 0.999844i \(0.494371\pi\)
\(54\) −5189.33 −1.77960
\(55\) 15.1245i 0.00499982i
\(56\) 1223.11 0.390023
\(57\) −3053.03 −0.939683
\(58\) −7713.09 −2.29283
\(59\) 3286.35 0.944082 0.472041 0.881577i \(-0.343517\pi\)
0.472041 + 0.881577i \(0.343517\pi\)
\(60\) −359.950 −0.0999861
\(61\) 3223.22i 0.866225i −0.901340 0.433112i \(-0.857415\pi\)
0.901340 0.433112i \(-0.142585\pi\)
\(62\) 6017.91i 1.56553i
\(63\) 162.764i 0.0410089i
\(64\) 5771.61 1.40908
\(65\) 145.898i 0.0345320i
\(66\) 570.534 0.130977
\(67\) 5556.36 1.23777 0.618886 0.785481i \(-0.287584\pi\)
0.618886 + 0.785481i \(0.287584\pi\)
\(68\) 8362.90 1.80859
\(69\) 2013.47i 0.422909i
\(70\) 137.482i 0.0280576i
\(71\) 2953.33i 0.585861i 0.956134 + 0.292930i \(0.0946305\pi\)
−0.956134 + 0.292930i \(0.905370\pi\)
\(72\) 1045.93i 0.201761i
\(73\) 3618.34i 0.678991i −0.940608 0.339496i \(-0.889744\pi\)
0.940608 0.339496i \(-0.110256\pi\)
\(74\) 15432.2 2.81815
\(75\) 5180.96i 0.921060i
\(76\) 10712.3i 1.85461i
\(77\) 140.757i 0.0237404i
\(78\) −5503.64 −0.904608
\(79\) 2380.74 0.381468 0.190734 0.981642i \(-0.438913\pi\)
0.190734 + 0.981642i \(0.438913\pi\)
\(80\) 191.155i 0.0298680i
\(81\) −5466.20 −0.833135
\(82\) 11375.7i 1.69181i
\(83\) −6427.91 −0.933069 −0.466535 0.884503i \(-0.654498\pi\)
−0.466535 + 0.884503i \(0.654498\pi\)
\(84\) 3349.90 0.474759
\(85\) 424.736i 0.0587869i
\(86\) −6814.51 10394.8i −0.921377 1.40547i
\(87\) −9544.98 −1.26106
\(88\) 904.510i 0.116801i
\(89\) 3293.36i 0.415776i 0.978153 + 0.207888i \(0.0666590\pi\)
−0.978153 + 0.207888i \(0.933341\pi\)
\(90\) 117.566 0.0145144
\(91\) 1357.80i 0.163966i
\(92\) 7064.72 0.834679
\(93\) 7447.19i 0.861046i
\(94\) 4997.44i 0.565577i
\(95\) 544.055 0.0602831
\(96\) 4589.22 0.497962
\(97\) −9329.95 −0.991599 −0.495799 0.868437i \(-0.665125\pi\)
−0.495799 + 0.868437i \(0.665125\pi\)
\(98\) 14860.6i 1.54733i
\(99\) −120.367 −0.0122811
\(100\) −18178.6 −1.81786
\(101\) −13572.8 −1.33054 −0.665270 0.746603i \(-0.731683\pi\)
−0.665270 + 0.746603i \(0.731683\pi\)
\(102\) 16022.1 1.54000
\(103\) −5527.90 −0.521057 −0.260529 0.965466i \(-0.583897\pi\)
−0.260529 + 0.965466i \(0.583897\pi\)
\(104\) 8725.32i 0.806705i
\(105\) 170.135i 0.0154317i
\(106\) 667.786i 0.0594327i
\(107\) −2435.69 −0.212742 −0.106371 0.994326i \(-0.533923\pi\)
−0.106371 + 0.994326i \(0.533923\pi\)
\(108\) 22532.4i 1.93179i
\(109\) 3235.93 0.272362 0.136181 0.990684i \(-0.456517\pi\)
0.136181 + 0.990684i \(0.456517\pi\)
\(110\) −101.670 −0.00840249
\(111\) 19097.4 1.54999
\(112\) 1779.00i 0.141821i
\(113\) 14680.9i 1.14973i −0.818247 0.574867i \(-0.805054\pi\)
0.818247 0.574867i \(-0.194946\pi\)
\(114\) 20523.2i 1.57919i
\(115\) 358.803i 0.0271307i
\(116\) 33490.7i 2.48891i
\(117\) 1161.11 0.0848207
\(118\) 22091.6i 1.58658i
\(119\) 3952.83i 0.279135i
\(120\) 1093.29i 0.0759233i
\(121\) −14536.9 −0.992890
\(122\) 21667.2 1.45574
\(123\) 14077.5i 0.930499i
\(124\) −26130.2 −1.69941
\(125\) 1849.77i 0.118385i
\(126\) −1094.14 −0.0689178
\(127\) 27000.0 1.67400 0.837001 0.547201i \(-0.184307\pi\)
0.837001 + 0.547201i \(0.184307\pi\)
\(128\) 29971.4i 1.82931i
\(129\) −8432.98 12863.7i −0.506759 0.773010i
\(130\) 980.757 0.0580329
\(131\) 17222.3i 1.00357i −0.864991 0.501787i \(-0.832676\pi\)
0.864991 0.501787i \(-0.167324\pi\)
\(132\) 2477.30i 0.142177i
\(133\) −5063.28 −0.286239
\(134\) 37351.1i 2.08015i
\(135\) 1144.38 0.0627916
\(136\) 25401.1i 1.37333i
\(137\) 1880.48i 0.100191i 0.998744 + 0.0500955i \(0.0159526\pi\)
−0.998744 + 0.0500955i \(0.984047\pi\)
\(138\) 13535.0 0.710723
\(139\) 20668.9 1.06977 0.534883 0.844926i \(-0.320356\pi\)
0.534883 + 0.844926i \(0.320356\pi\)
\(140\) −596.957 −0.0304570
\(141\) 6184.35i 0.311068i
\(142\) −19852.9 −0.984573
\(143\) −1004.12 −0.0491035
\(144\) 1521.29 0.0733647
\(145\) 1700.93 0.0809004
\(146\) 24323.3 1.14108
\(147\) 18390.0i 0.851036i
\(148\) 67007.6i 3.05915i
\(149\) 13651.5i 0.614904i 0.951564 + 0.307452i \(0.0994763\pi\)
−0.951564 + 0.307452i \(0.900524\pi\)
\(150\) −34827.6 −1.54789
\(151\) 41870.6i 1.83635i −0.396175 0.918175i \(-0.629662\pi\)
0.396175 0.918175i \(-0.370338\pi\)
\(152\) 32536.9 1.40828
\(153\) −3380.22 −0.144398
\(154\) 946.200 0.0398971
\(155\) 1327.10i 0.0552383i
\(156\) 23897.2i 0.981968i
\(157\) 41348.7i 1.67750i −0.544517 0.838750i \(-0.683287\pi\)
0.544517 0.838750i \(-0.316713\pi\)
\(158\) 16003.9i 0.641079i
\(159\) 826.388i 0.0326881i
\(160\) −817.806 −0.0319455
\(161\) 3339.23i 0.128823i
\(162\) 36745.1i 1.40013i
\(163\) 6111.31i 0.230017i 0.993365 + 0.115008i \(0.0366895\pi\)
−0.993365 + 0.115008i \(0.963311\pi\)
\(164\) −49394.2 −1.83649
\(165\) −125.817 −0.00462139
\(166\) 43209.9i 1.56808i
\(167\) 34991.0 1.25465 0.627326 0.778757i \(-0.284149\pi\)
0.627326 + 0.778757i \(0.284149\pi\)
\(168\) 10174.8i 0.360503i
\(169\) −18874.8 −0.660860
\(170\) −2855.17 −0.0987949
\(171\) 4329.81i 0.148073i
\(172\) 45135.1 29589.1i 1.52566 1.00017i
\(173\) −4597.15 −0.153602 −0.0768009 0.997046i \(-0.524471\pi\)
−0.0768009 + 0.997046i \(0.524471\pi\)
\(174\) 64163.5i 2.11929i
\(175\) 8592.34i 0.280566i
\(176\) −1315.60 −0.0424715
\(177\) 27338.5i 0.872624i
\(178\) −22138.7 −0.698736
\(179\) 26315.3i 0.821301i 0.911793 + 0.410650i \(0.134698\pi\)
−0.911793 + 0.410650i \(0.865302\pi\)
\(180\) 510.481i 0.0157556i
\(181\) 48133.4 1.46923 0.734614 0.678485i \(-0.237363\pi\)
0.734614 + 0.678485i \(0.237363\pi\)
\(182\) −9127.48 −0.275555
\(183\) 26813.3 0.800660
\(184\) 21458.0i 0.633803i
\(185\) −3403.19 −0.0994357
\(186\) −50061.7 −1.44704
\(187\) 2923.18 0.0835934
\(188\) −21699.2 −0.613943
\(189\) −10650.2 −0.298150
\(190\) 3657.26i 0.101309i
\(191\) 46954.1i 1.28708i 0.765411 + 0.643542i \(0.222536\pi\)
−0.765411 + 0.643542i \(0.777464\pi\)
\(192\) 48012.8i 1.30243i
\(193\) 18967.8 0.509215 0.254608 0.967044i \(-0.418054\pi\)
0.254608 + 0.967044i \(0.418054\pi\)
\(194\) 62718.1i 1.66644i
\(195\) 1213.69 0.0319182
\(196\) −64525.7 −1.67966
\(197\) −77177.1 −1.98864 −0.994320 0.106435i \(-0.966056\pi\)
−0.994320 + 0.106435i \(0.966056\pi\)
\(198\) 809.132i 0.0206390i
\(199\) 2250.86i 0.0568385i −0.999596 0.0284192i \(-0.990953\pi\)
0.999596 0.0284192i \(-0.00904734\pi\)
\(200\) 55214.8i 1.38037i
\(201\) 46222.2i 1.14409i
\(202\) 91239.7i 2.23605i
\(203\) −15829.8 −0.384135
\(204\) 69569.3i 1.67169i
\(205\) 2508.64i 0.0596939i
\(206\) 37159.8i 0.875667i
\(207\) −2855.50 −0.0666411
\(208\) 12690.8 0.293335
\(209\) 3744.37i 0.0857208i
\(210\) −1143.69 −0.0259339
\(211\) 64198.9i 1.44199i 0.692939 + 0.720996i \(0.256315\pi\)
−0.692939 + 0.720996i \(0.743685\pi\)
\(212\) −2899.57 −0.0645152
\(213\) −24568.1 −0.541517
\(214\) 16373.2i 0.357526i
\(215\) 1502.77 + 2292.32i 0.0325099 + 0.0495906i
\(216\) 68438.9 1.46688
\(217\) 12350.8i 0.262285i
\(218\) 21752.7i 0.457720i
\(219\) 30100.2 0.627598
\(220\) 441.459i 0.00912105i
\(221\) −28198.3 −0.577349
\(222\) 128377.i 2.60484i
\(223\) 53407.6i 1.07397i −0.843591 0.536987i \(-0.819563\pi\)
0.843591 0.536987i \(-0.180437\pi\)
\(224\) 7610.96 0.151685
\(225\) 7347.64 0.145139
\(226\) 98688.7 1.93219
\(227\) 43494.8i 0.844084i 0.906576 + 0.422042i \(0.138687\pi\)
−0.906576 + 0.422042i \(0.861313\pi\)
\(228\) 89113.0 1.71424
\(229\) 67145.4 1.28040 0.640199 0.768209i \(-0.278852\pi\)
0.640199 + 0.768209i \(0.278852\pi\)
\(230\) −2411.96 −0.0455947
\(231\) 1170.93 0.0219435
\(232\) 101723. 1.88992
\(233\) 76734.0i 1.41344i −0.707496 0.706718i \(-0.750175\pi\)
0.707496 0.706718i \(-0.249825\pi\)
\(234\) 7805.26i 0.142546i
\(235\) 1102.06i 0.0199558i
\(236\) −95923.2 −1.72226
\(237\) 19804.9i 0.352595i
\(238\) 26571.8 0.469103
\(239\) −26767.6 −0.468613 −0.234307 0.972163i \(-0.575282\pi\)
−0.234307 + 0.972163i \(0.575282\pi\)
\(240\) 1590.18 0.0276073
\(241\) 100445.i 1.72939i −0.502297 0.864695i \(-0.667512\pi\)
0.502297 0.864695i \(-0.332488\pi\)
\(242\) 97720.5i 1.66861i
\(243\) 17057.0i 0.288861i
\(244\) 94080.7i 1.58023i
\(245\) 3277.14i 0.0545962i
\(246\) −94632.4 −1.56376
\(247\) 36119.9i 0.592043i
\(248\) 79366.5i 1.29043i
\(249\) 53472.5i 0.862445i
\(250\) 12434.6 0.198953
\(251\) −71737.6 −1.13867 −0.569337 0.822104i \(-0.692800\pi\)
−0.569337 + 0.822104i \(0.692800\pi\)
\(252\) 4750.83i 0.0748115i
\(253\) 2469.41 0.0385791
\(254\) 181500.i 2.81326i
\(255\) −3533.29 −0.0543374
\(256\) −109129. −1.66518
\(257\) 7267.88i 0.110038i 0.998485 + 0.0550189i \(0.0175219\pi\)
−0.998485 + 0.0550189i \(0.982478\pi\)
\(258\) 86472.5 56688.5i 1.29909 0.851638i
\(259\) 31672.0 0.472145
\(260\) 4258.51i 0.0629958i
\(261\) 13536.7i 0.198715i
\(262\) 115773. 1.68656
\(263\) 73838.4i 1.06751i −0.845640 0.533754i \(-0.820781\pi\)
0.845640 0.533754i \(-0.179219\pi\)
\(264\) −7524.43 −0.107961
\(265\) 147.264i 0.00209703i
\(266\) 34036.6i 0.481041i
\(267\) −27396.8 −0.384306
\(268\) −162181. −2.25804
\(269\) 127266. 1.75877 0.879384 0.476113i \(-0.157955\pi\)
0.879384 + 0.476113i \(0.157955\pi\)
\(270\) 7692.77i 0.105525i
\(271\) 44182.9 0.601610 0.300805 0.953686i \(-0.402745\pi\)
0.300805 + 0.953686i \(0.402745\pi\)
\(272\) −36945.5 −0.499371
\(273\) −11295.3 −0.151556
\(274\) −12641.0 −0.168377
\(275\) −6354.17 −0.0840220
\(276\) 58769.9i 0.771502i
\(277\) 31197.7i 0.406596i 0.979117 + 0.203298i \(0.0651660\pi\)
−0.979117 + 0.203298i \(0.934834\pi\)
\(278\) 138941.i 1.79780i
\(279\) 10561.6 0.135682
\(280\) 1813.17i 0.0231272i
\(281\) −140212. −1.77572 −0.887859 0.460116i \(-0.847808\pi\)
−0.887859 + 0.460116i \(0.847808\pi\)
\(282\) −41572.6 −0.522768
\(283\) 2024.17 0.0252740 0.0126370 0.999920i \(-0.495977\pi\)
0.0126370 + 0.999920i \(0.495977\pi\)
\(284\) 86202.8i 1.06877i
\(285\) 4525.88i 0.0557203i
\(286\) 6749.91i 0.0825212i
\(287\) 23346.8i 0.283442i
\(288\) 6508.43i 0.0784677i
\(289\) −1430.31 −0.0171252
\(290\) 11434.0i 0.135958i
\(291\) 77613.9i 0.916545i
\(292\) 105614.i 1.23867i
\(293\) 75732.9 0.882164 0.441082 0.897467i \(-0.354595\pi\)
0.441082 + 0.897467i \(0.354595\pi\)
\(294\) −123622. −1.43022
\(295\) 4871.76i 0.0559811i
\(296\) −203526. −2.32293
\(297\) 7876.00i 0.0892879i
\(298\) −91768.4 −1.03338
\(299\) −23821.0 −0.266452
\(300\) 151224.i 1.68027i
\(301\) −13985.6 21333.7i −0.154365 0.235468i
\(302\) 281464. 3.08609
\(303\) 112910.i 1.22983i
\(304\) 47324.4i 0.512080i
\(305\) −4778.18 −0.0513644
\(306\) 22722.6i 0.242670i
\(307\) −158838. −1.68530 −0.842652 0.538458i \(-0.819007\pi\)
−0.842652 + 0.538458i \(0.819007\pi\)
\(308\) 4108.47i 0.0433090i
\(309\) 45985.4i 0.481619i
\(310\) 8921.08 0.0928312
\(311\) −49344.1 −0.510169 −0.255085 0.966919i \(-0.582103\pi\)
−0.255085 + 0.966919i \(0.582103\pi\)
\(312\) 72584.1 0.745645
\(313\) 66350.6i 0.677261i 0.940919 + 0.338631i \(0.109964\pi\)
−0.940919 + 0.338631i \(0.890036\pi\)
\(314\) 277955. 2.81914
\(315\) 241.285 0.00243170
\(316\) −69490.0 −0.695903
\(317\) 15717.4 0.156409 0.0782046 0.996937i \(-0.475081\pi\)
0.0782046 + 0.996937i \(0.475081\pi\)
\(318\) −5555.17 −0.0549342
\(319\) 11706.4i 0.115038i
\(320\) 8555.96i 0.0835543i
\(321\) 20262.0i 0.196640i
\(322\) 22447.1 0.216495
\(323\) 105152.i 1.00789i
\(324\) 159550. 1.51987
\(325\) 61295.2 0.580309
\(326\) −41081.6 −0.386556
\(327\) 26919.1i 0.251747i
\(328\) 150028.i 1.39452i
\(329\) 10256.4i 0.0947553i
\(330\) 845.773i 0.00776651i
\(331\) 85452.6i 0.779954i 0.920825 + 0.389977i \(0.127517\pi\)
−0.920825 + 0.389977i \(0.872483\pi\)
\(332\) 187620. 1.70217
\(333\) 27083.9i 0.244244i
\(334\) 235218.i 2.10852i
\(335\) 8236.87i 0.0733960i
\(336\) −14799.1 −0.131086
\(337\) −146925. −1.29371 −0.646855 0.762613i \(-0.723916\pi\)
−0.646855 + 0.762613i \(0.723916\pi\)
\(338\) 126881.i 1.11061i
\(339\) 122128. 1.06271
\(340\) 12397.4i 0.107244i
\(341\) −9133.57 −0.0785474
\(342\) −29106.0 −0.248845
\(343\) 63623.7i 0.540793i
\(344\) 89872.4 + 137091.i 0.759468 + 1.15849i
\(345\) −2984.81 −0.0250772
\(346\) 30903.1i 0.258137i
\(347\) 78623.4i 0.652969i 0.945203 + 0.326485i \(0.105864\pi\)
−0.945203 + 0.326485i \(0.894136\pi\)
\(348\) 278603. 2.30052
\(349\) 165981.i 1.36273i 0.731945 + 0.681363i \(0.238613\pi\)
−0.731945 + 0.681363i \(0.761387\pi\)
\(350\) −57759.7 −0.471508
\(351\) 75975.5i 0.616679i
\(352\) 5628.42i 0.0454257i
\(353\) 53106.9 0.426188 0.213094 0.977032i \(-0.431646\pi\)
0.213094 + 0.977032i \(0.431646\pi\)
\(354\) −183775. −1.46650
\(355\) 4378.07 0.0347397
\(356\) 96127.9i 0.758490i
\(357\) 32882.8 0.258007
\(358\) −176897. −1.38024
\(359\) −120101. −0.931879 −0.465939 0.884817i \(-0.654284\pi\)
−0.465939 + 0.884817i \(0.654284\pi\)
\(360\) −1550.51 −0.0119638
\(361\) −4370.92 −0.0335396
\(362\) 323564.i 2.46912i
\(363\) 120930.i 0.917739i
\(364\) 39632.1i 0.299120i
\(365\) −5363.91 −0.0402620
\(366\) 180245.i 1.34556i
\(367\) −37702.0 −0.279919 −0.139959 0.990157i \(-0.544697\pi\)
−0.139959 + 0.990157i \(0.544697\pi\)
\(368\) −31210.4 −0.230464
\(369\) 19964.7 0.146626
\(370\) 22877.0i 0.167107i
\(371\) 1370.52i 0.00995720i
\(372\) 217371.i 1.57078i
\(373\) 139388.i 1.00186i 0.865488 + 0.500930i \(0.167009\pi\)
−0.865488 + 0.500930i \(0.832991\pi\)
\(374\) 19650.3i 0.140484i
\(375\) 15387.8 0.109425
\(376\) 65908.1i 0.466190i
\(377\) 112925.i 0.794526i
\(378\) 71593.3i 0.501059i
\(379\) −88126.5 −0.613519 −0.306759 0.951787i \(-0.599245\pi\)
−0.306759 + 0.951787i \(0.599245\pi\)
\(380\) −15880.1 −0.109973
\(381\) 224607.i 1.54730i
\(382\) −315636. −2.16302
\(383\) 250818.i 1.70986i −0.518743 0.854930i \(-0.673600\pi\)
0.518743 0.854930i \(-0.326400\pi\)
\(384\) −249326. −1.69085
\(385\) −208.661 −0.00140773
\(386\) 127506.i 0.855766i
\(387\) −18243.2 + 11959.7i −0.121809 + 0.0798540i
\(388\) 272326. 1.80895
\(389\) 34015.7i 0.224792i −0.993664 0.112396i \(-0.964148\pi\)
0.993664 0.112396i \(-0.0358524\pi\)
\(390\) 8158.71i 0.0536404i
\(391\) 69347.7 0.453605
\(392\) 195987.i 1.27543i
\(393\) 143269. 0.927614
\(394\) 518802.i 3.34202i
\(395\) 3529.26i 0.0226199i
\(396\) 3513.31 0.0224040
\(397\) 206559. 1.31058 0.655291 0.755377i \(-0.272546\pi\)
0.655291 + 0.755377i \(0.272546\pi\)
\(398\) 15130.8 0.0955203
\(399\) 42120.4i 0.264574i
\(400\) 80309.1 0.501932
\(401\) 85162.0 0.529611 0.264806 0.964302i \(-0.414692\pi\)
0.264806 + 0.964302i \(0.414692\pi\)
\(402\) −310716. −1.92270
\(403\) 88106.5 0.542498
\(404\) 396169. 2.42727
\(405\) 8103.21i 0.0494023i
\(406\) 106412.i 0.645561i
\(407\) 23421.9i 0.141395i
\(408\) −211306. −1.26938
\(409\) 216421.i 1.29375i −0.762594 0.646877i \(-0.776075\pi\)
0.762594 0.646877i \(-0.223925\pi\)
\(410\) 16863.6 0.100319
\(411\) −15643.3 −0.0926075
\(412\) 161350. 0.950552
\(413\) 45339.3i 0.265812i
\(414\) 19195.3i 0.111994i
\(415\) 9528.88i 0.0553281i
\(416\) 54294.3i 0.313738i
\(417\) 171941.i 0.988795i
\(418\) 25170.5 0.144059
\(419\) 195727.i 1.11487i −0.830222 0.557433i \(-0.811786\pi\)
0.830222 0.557433i \(-0.188214\pi\)
\(420\) 4965.96i 0.0281517i
\(421\) 216454.i 1.22124i 0.791924 + 0.610620i \(0.209080\pi\)
−0.791924 + 0.610620i \(0.790920\pi\)
\(422\) −431560. −2.42335
\(423\) 8770.65 0.0490175
\(424\) 8807.02i 0.0489889i
\(425\) −178442. −0.987915
\(426\) 165152.i 0.910051i
\(427\) 44468.4 0.243891
\(428\) 71093.8 0.388100
\(429\) 8353.04i 0.0453868i
\(430\) −15409.5 + 10102.0i −0.0833398 + 0.0546348i
\(431\) −219971. −1.18416 −0.592082 0.805878i \(-0.701694\pi\)
−0.592082 + 0.805878i \(0.701694\pi\)
\(432\) 99543.3i 0.533390i
\(433\) 141123.i 0.752699i −0.926478 0.376349i \(-0.877179\pi\)
0.926478 0.376349i \(-0.122821\pi\)
\(434\) −83024.6 −0.440786
\(435\) 14149.7i 0.0747770i
\(436\) −94451.7 −0.496863
\(437\) 88829.2i 0.465150i
\(438\) 202341.i 1.05472i
\(439\) −18660.8 −0.0968279 −0.0484139 0.998827i \(-0.515417\pi\)
−0.0484139 + 0.998827i \(0.515417\pi\)
\(440\) 1340.87 0.00692596
\(441\) 26080.8 0.134104
\(442\) 189556.i 0.970268i
\(443\) 21366.2 0.108873 0.0544366 0.998517i \(-0.482664\pi\)
0.0544366 + 0.998517i \(0.482664\pi\)
\(444\) −557422. −2.82760
\(445\) 4882.15 0.0246542
\(446\) 359018. 1.80487
\(447\) −113564. −0.568362
\(448\) 79626.7i 0.396737i
\(449\) 101517.i 0.503553i −0.967785 0.251777i \(-0.918985\pi\)
0.967785 0.251777i \(-0.0810148\pi\)
\(450\) 49392.6i 0.243914i
\(451\) −17265.3 −0.0848831
\(452\) 428513.i 2.09743i
\(453\) 348313. 1.69736
\(454\) −292382. −1.41853
\(455\) 2012.84 0.00972269
\(456\) 270668.i 1.30169i
\(457\) 308003.i 1.47477i 0.675475 + 0.737383i \(0.263939\pi\)
−0.675475 + 0.737383i \(0.736061\pi\)
\(458\) 451367.i 2.15178i
\(459\) 221179.i 1.04983i
\(460\) 10472.9i 0.0494938i
\(461\) 156343. 0.735660 0.367830 0.929893i \(-0.380101\pi\)
0.367830 + 0.929893i \(0.380101\pi\)
\(462\) 7871.24i 0.0368773i
\(463\) 203393.i 0.948800i 0.880309 + 0.474400i \(0.157335\pi\)
−0.880309 + 0.474400i \(0.842665\pi\)
\(464\) 147955.i 0.687216i
\(465\) 11039.9 0.0510573
\(466\) 515824. 2.37536
\(467\) 208975.i 0.958209i 0.877758 + 0.479104i \(0.159038\pi\)
−0.877758 + 0.479104i \(0.840962\pi\)
\(468\) −33891.0 −0.154736
\(469\) 76657.0i 0.348503i
\(470\) 7408.31 0.0335369
\(471\) 343971. 1.55053
\(472\) 291353.i 1.30778i
\(473\) 15776.6 10342.6i 0.0705164 0.0462282i
\(474\) −133133. −0.592556
\(475\) 228571.i 1.01306i
\(476\) 115377.i 0.509219i
\(477\) 1171.98 0.00515092
\(478\) 179938.i 0.787531i
\(479\) 98547.6 0.429512 0.214756 0.976668i \(-0.431104\pi\)
0.214756 + 0.976668i \(0.431104\pi\)
\(480\) 6803.16i 0.0295276i
\(481\) 225938.i 0.976562i
\(482\) 675212. 2.90634
\(483\) 27778.3 0.119073
\(484\) 424309. 1.81130
\(485\) 13830.9i 0.0587987i
\(486\) −114661. −0.485448
\(487\) −319902. −1.34884 −0.674418 0.738350i \(-0.735605\pi\)
−0.674418 + 0.738350i \(0.735605\pi\)
\(488\) −285756. −1.19993
\(489\) −50838.7 −0.212607
\(490\) 22029.7 0.0917520
\(491\) 454263.i 1.88428i −0.335226 0.942138i \(-0.608813\pi\)
0.335226 0.942138i \(-0.391187\pi\)
\(492\) 410900.i 1.69749i
\(493\) 328747.i 1.35260i
\(494\) −242806. −0.994962
\(495\) 178.434i 0.000728228i
\(496\) 115437. 0.469227
\(497\) −40744.8 −0.164953
\(498\) 359454. 1.44939
\(499\) 336510.i 1.35144i −0.737158 0.675720i \(-0.763833\pi\)
0.737158 0.675720i \(-0.236167\pi\)
\(500\) 53991.8i 0.215967i
\(501\) 291083.i 1.15969i
\(502\) 482237.i 1.91361i
\(503\) 313054.i 1.23732i 0.785658 + 0.618661i \(0.212325\pi\)
−0.785658 + 0.618661i \(0.787675\pi\)
\(504\) 14429.9 0.0568072
\(505\) 20120.7i 0.0788968i
\(506\) 16599.9i 0.0648344i
\(507\) 157016.i 0.610840i
\(508\) −788086. −3.05384
\(509\) 406043. 1.56724 0.783621 0.621239i \(-0.213370\pi\)
0.783621 + 0.621239i \(0.213370\pi\)
\(510\) 23751.6i 0.0913171i
\(511\) 49919.6 0.191174
\(512\) 254048.i 0.969114i
\(513\) −283314. −1.07655
\(514\) −48856.4 −0.184925
\(515\) 8194.68i 0.0308971i
\(516\) 246145. + 375469.i 0.924468 + 1.41018i
\(517\) −7584.76 −0.0283766
\(518\) 212906.i 0.793467i
\(519\) 38242.7i 0.141976i
\(520\) −12934.6 −0.0478351
\(521\) 221529.i 0.816122i −0.912955 0.408061i \(-0.866205\pi\)
0.912955 0.408061i \(-0.133795\pi\)
\(522\) −90996.8 −0.333953
\(523\) 146666.i 0.536199i −0.963391 0.268099i \(-0.913604\pi\)
0.963391 0.268099i \(-0.0863955\pi\)
\(524\) 502692.i 1.83080i
\(525\) −71477.9 −0.259330
\(526\) 496359. 1.79401
\(527\) −256495. −0.923545
\(528\) 10944.2i 0.0392568i
\(529\) −221258. −0.790657
\(530\) 989.940 0.00352417
\(531\) 38771.4 0.137506
\(532\) 147789. 0.522179
\(533\) 166549. 0.586257
\(534\) 184168.i 0.645848i
\(535\) 3610.71i 0.0126150i
\(536\) 492601.i 1.71461i
\(537\) −218911. −0.759137
\(538\) 855513.i 2.95571i
\(539\) −22554.4 −0.0776342
\(540\) −33402.5 −0.114549
\(541\) 38164.1 0.130395 0.0651974 0.997872i \(-0.479232\pi\)
0.0651974 + 0.997872i \(0.479232\pi\)
\(542\) 297007.i 1.01104i
\(543\) 400411.i 1.35802i
\(544\) 158061.i 0.534106i
\(545\) 4797.02i 0.0161502i
\(546\) 75929.6i 0.254698i
\(547\) 105758. 0.353459 0.176730 0.984259i \(-0.443448\pi\)
0.176730 + 0.984259i \(0.443448\pi\)
\(548\) 54888.3i 0.182776i
\(549\) 38026.6i 0.126166i
\(550\) 42714.2i 0.141204i
\(551\) −421100. −1.38702
\(552\) −178505. −0.585831
\(553\) 32845.3i 0.107405i
\(554\) −209718. −0.683308
\(555\) 28310.4i 0.0919094i
\(556\) −603293. −1.95155
\(557\) 280135. 0.902936 0.451468 0.892287i \(-0.350900\pi\)
0.451468 + 0.892287i \(0.350900\pi\)
\(558\) 70997.5i 0.228021i
\(559\) −152188. + 99769.3i −0.487031 + 0.319281i
\(560\) 2637.23 0.00840953
\(561\) 24317.3i 0.0772662i
\(562\) 942541.i 2.98420i
\(563\) −403332. −1.27247 −0.636233 0.771497i \(-0.719508\pi\)
−0.636233 + 0.771497i \(0.719508\pi\)
\(564\) 180511.i 0.567474i
\(565\) −21763.3 −0.0681756
\(566\) 13606.9i 0.0424744i
\(567\) 75413.1i 0.234574i
\(568\) 261828. 0.811559
\(569\) −72865.2 −0.225059 −0.112529 0.993648i \(-0.535895\pi\)
−0.112529 + 0.993648i \(0.535895\pi\)
\(570\) −30424.0 −0.0936411
\(571\) 280074.i 0.859015i 0.903063 + 0.429507i \(0.141313\pi\)
−0.903063 + 0.429507i \(0.858687\pi\)
\(572\) 29308.6 0.0895782
\(573\) −390601. −1.18966
\(574\) −156943. −0.476340
\(575\) −150742. −0.455931
\(576\) 68091.8 0.205234
\(577\) 205999.i 0.618748i −0.950940 0.309374i \(-0.899881\pi\)
0.950940 0.309374i \(-0.100119\pi\)
\(578\) 9614.89i 0.0287799i
\(579\) 157789.i 0.470673i
\(580\) −49647.4 −0.147584
\(581\) 88681.2i 0.262712i
\(582\) 521739. 1.54031
\(583\) −1013.52 −0.00298191
\(584\) −320786. −0.940566
\(585\) 1721.26i 0.00502960i
\(586\) 509094.i 1.48253i
\(587\) 466185.i 1.35295i 0.736464 + 0.676476i \(0.236494\pi\)
−0.736464 + 0.676476i \(0.763506\pi\)
\(588\) 536776.i 1.55252i
\(589\) 328551.i 0.947049i
\(590\) 32749.1 0.0940795
\(591\) 642020.i 1.83812i
\(592\) 296025.i 0.844666i
\(593\) 284311.i 0.808507i −0.914647 0.404253i \(-0.867531\pi\)
0.914647 0.404253i \(-0.132469\pi\)
\(594\) 52944.3 0.150054
\(595\) −5859.76 −0.0165518
\(596\) 398465.i 1.12175i
\(597\) 18724.4 0.0525364
\(598\) 160131.i 0.447787i
\(599\) 438880. 1.22318 0.611592 0.791173i \(-0.290529\pi\)
0.611592 + 0.791173i \(0.290529\pi\)
\(600\) 459320. 1.27589
\(601\) 52157.2i 0.144399i −0.997390 0.0721997i \(-0.976998\pi\)
0.997390 0.0721997i \(-0.0230019\pi\)
\(602\) 143410. 94014.7i 0.395718 0.259420i
\(603\) 65552.3 0.180282
\(604\) 1.22214e6i 3.35001i
\(605\) 21549.8i 0.0588753i
\(606\) 759004. 2.06680
\(607\) 328500.i 0.891575i 0.895139 + 0.445788i \(0.147076\pi\)
−0.895139 + 0.445788i \(0.852924\pi\)
\(608\) 202465. 0.547699
\(609\) 131685.i 0.355060i
\(610\) 32120.0i 0.0863209i
\(611\) 73166.1 0.195987
\(612\) 98663.1 0.263422
\(613\) −194249. −0.516937 −0.258468 0.966020i \(-0.583218\pi\)
−0.258468 + 0.966020i \(0.583218\pi\)
\(614\) 1.06775e6i 2.83225i
\(615\) 20868.8 0.0551757
\(616\) −12478.9 −0.0328862
\(617\) −203384. −0.534253 −0.267126 0.963662i \(-0.586074\pi\)
−0.267126 + 0.963662i \(0.586074\pi\)
\(618\) 309125. 0.809388
\(619\) 504248. 1.31602 0.658011 0.753008i \(-0.271398\pi\)
0.658011 + 0.753008i \(0.271398\pi\)
\(620\) 38735.9i 0.100770i
\(621\) 186845.i 0.484506i
\(622\) 331702.i 0.857369i
\(623\) −45436.1 −0.117064
\(624\) 105572.i 0.271133i
\(625\) 386509. 0.989464
\(626\) −446024. −1.13818
\(627\) 31148.6 0.0792326
\(628\) 1.20690e6i 3.06022i
\(629\) 657750.i 1.66249i
\(630\) 1621.98i 0.00408661i
\(631\) 612948.i 1.53945i 0.638376 + 0.769724i \(0.279606\pi\)
−0.638376 + 0.769724i \(0.720394\pi\)
\(632\) 211066.i 0.528425i
\(633\) −534057. −1.33285
\(634\) 105656.i 0.262855i
\(635\) 40025.4i 0.0992631i
\(636\) 24120.9i 0.0596321i
\(637\) 217570. 0.536191
\(638\) 78693.0 0.193328
\(639\) 34842.5i 0.0853311i
\(640\) 44430.3 0.108472
\(641\) 571747.i 1.39151i −0.718277 0.695757i \(-0.755069\pi\)
0.718277 0.695757i \(-0.244931\pi\)
\(642\) 136206. 0.330465
\(643\) −530650. −1.28347 −0.641736 0.766926i \(-0.721785\pi\)
−0.641736 + 0.766926i \(0.721785\pi\)
\(644\) 97466.7i 0.235009i
\(645\) −19069.4 + 12501.2i −0.0458371 + 0.0300492i
\(646\) 706856. 1.69382
\(647\) 481379.i 1.14995i −0.818171 0.574975i \(-0.805012\pi\)
0.818171 0.574975i \(-0.194988\pi\)
\(648\) 484608.i 1.15409i
\(649\) −33529.1 −0.0796036
\(650\) 412040.i 0.975244i
\(651\) −102743. −0.242433
\(652\) 178379.i 0.419613i
\(653\) 293363.i 0.687984i −0.938973 0.343992i \(-0.888221\pi\)
0.938973 0.343992i \(-0.111779\pi\)
\(654\) −180956. −0.423076
\(655\) −25530.8 −0.0595088
\(656\) 218213. 0.507076
\(657\) 42688.2i 0.0988956i
\(658\) −68945.9 −0.159242
\(659\) 657906. 1.51493 0.757466 0.652875i \(-0.226437\pi\)
0.757466 + 0.652875i \(0.226437\pi\)
\(660\) 3672.40 0.00843068
\(661\) −267844. −0.613026 −0.306513 0.951866i \(-0.599162\pi\)
−0.306513 + 0.951866i \(0.599162\pi\)
\(662\) −574432. −1.31076
\(663\) 234576.i 0.533650i
\(664\) 569869.i 1.29253i
\(665\) 7505.92i 0.0169731i
\(666\) 182064. 0.410465
\(667\) 277715.i 0.624235i
\(668\) −1.02133e6 −2.28883
\(669\) 444287. 0.992685
\(670\) 55370.1 0.123346
\(671\) 32885.0i 0.0730388i
\(672\) 63314.0i 0.140204i
\(673\) 48089.2i 0.106174i 0.998590 + 0.0530869i \(0.0169060\pi\)
−0.998590 + 0.0530869i \(0.983094\pi\)
\(674\) 987667.i 2.17416i
\(675\) 480782.i 1.05521i
\(676\) 550926. 1.20559
\(677\) 84879.3i 0.185193i −0.995704 0.0925964i \(-0.970483\pi\)
0.995704 0.0925964i \(-0.0295166\pi\)
\(678\) 820971.i 1.78595i
\(679\) 128718.i 0.279191i
\(680\) 37655.1 0.0814341
\(681\) −361824. −0.780195
\(682\) 61397.9i 0.132003i
\(683\) −707010. −1.51560 −0.757799 0.652488i \(-0.773725\pi\)
−0.757799 + 0.652488i \(0.773725\pi\)
\(684\) 126380.i 0.270126i
\(685\) 2787.67 0.00594101
\(686\) −427693. −0.908833
\(687\) 558568.i 1.18348i
\(688\) −199397. + 130718.i −0.421252 + 0.276159i
\(689\) 9776.87 0.0205950
\(690\) 20064.6i 0.0421436i
\(691\) 316021.i 0.661851i −0.943657 0.330925i \(-0.892639\pi\)
0.943657 0.330925i \(-0.107361\pi\)
\(692\) 134183. 0.280212
\(693\) 1660.61i 0.00345781i
\(694\) −528525. −1.09735
\(695\) 30640.1i 0.0634338i
\(696\) 846214.i 1.74687i
\(697\) −484856. −0.998039
\(698\) −1.11577e6 −2.29014
\(699\) 638334. 1.30645
\(700\) 250797.i 0.511830i
\(701\) 790342. 1.60835 0.804173 0.594396i \(-0.202609\pi\)
0.804173 + 0.594396i \(0.202609\pi\)
\(702\) −510725. −1.03637
\(703\) 842529. 1.70480
\(704\) −58885.1 −0.118812
\(705\) 9167.81 0.0184454
\(706\) 356997.i 0.716234i
\(707\) 187254.i 0.374622i
\(708\) 797965.i 1.59191i
\(709\) 218246. 0.434165 0.217082 0.976153i \(-0.430346\pi\)
0.217082 + 0.976153i \(0.430346\pi\)
\(710\) 29430.4i 0.0583821i
\(711\) 28087.3 0.0555611
\(712\) 291974. 0.575950
\(713\) −216679. −0.426224
\(714\) 221046.i 0.433596i
\(715\) 1488.52i 0.00291168i
\(716\) 768101.i 1.49828i
\(717\) 222674.i 0.433144i
\(718\) 807350.i 1.56608i
\(719\) 733807. 1.41946 0.709732 0.704472i \(-0.248816\pi\)
0.709732 + 0.704472i \(0.248816\pi\)
\(720\) 2255.19i 0.00435030i
\(721\) 76264.3i 0.146707i
\(722\) 29382.3i 0.0563653i
\(723\) 835578. 1.59849
\(724\) −1.40494e6 −2.68027
\(725\) 714603.i 1.35953i
\(726\) 812916. 1.54231
\(727\) 250259.i 0.473501i −0.971570 0.236750i \(-0.923918\pi\)
0.971570 0.236750i \(-0.0760824\pi\)
\(728\) 120377. 0.227133
\(729\) −584656. −1.10013
\(730\) 36057.5i 0.0676627i
\(731\) 443048. 290448.i 0.829118 0.543542i
\(732\) −782638. −1.46062
\(733\) 610120.i 1.13555i −0.823183 0.567776i \(-0.807804\pi\)
0.823183 0.567776i \(-0.192196\pi\)
\(734\) 253441.i 0.470419i
\(735\) 27261.8 0.0504638
\(736\) 133525.i 0.246495i
\(737\) −56689.0 −0.104367
\(738\) 134208.i 0.246414i
\(739\) 67964.4i 0.124449i −0.998062 0.0622246i \(-0.980180\pi\)
0.998062 0.0622246i \(-0.0198195\pi\)
\(740\) 99333.5 0.181398
\(741\) −300474. −0.547231
\(742\) −9212.95 −0.0167337
\(743\) 707585.i 1.28174i 0.767648 + 0.640871i \(0.221427\pi\)
−0.767648 + 0.640871i \(0.778573\pi\)
\(744\) 660234. 1.19276
\(745\) 20237.3 0.0364619
\(746\) −936998. −1.68368
\(747\) −75834.7 −0.135902
\(748\) −85322.8 −0.152497
\(749\) 33603.4i 0.0598989i
\(750\) 103441.i 0.183895i
\(751\) 613506.i 1.08778i −0.839158 0.543888i \(-0.816952\pi\)
0.839158 0.543888i \(-0.183048\pi\)
\(752\) 95862.4 0.169517
\(753\) 596770.i 1.05249i
\(754\) −759109. −1.33525
\(755\) −62069.9 −0.108890
\(756\) 310863. 0.543908
\(757\) 132879.i 0.231880i −0.993256 0.115940i \(-0.963012\pi\)
0.993256 0.115940i \(-0.0369881\pi\)
\(758\) 592406.i 1.03105i
\(759\) 20542.5i 0.0356590i
\(760\) 48233.4i 0.0835066i
\(761\) 790123.i 1.36435i 0.731190 + 0.682174i \(0.238965\pi\)
−0.731190 + 0.682174i \(0.761035\pi\)
\(762\) −1.50986e6 −2.60032
\(763\) 44643.8i 0.0766853i
\(764\) 1.37051e6i 2.34799i
\(765\) 5010.91i 0.00856236i
\(766\) 1.68605e6 2.87352
\(767\) 323437. 0.549793
\(768\) 907821.i 1.53914i
\(769\) −204245. −0.345382 −0.172691 0.984976i \(-0.555246\pi\)
−0.172691 + 0.984976i \(0.555246\pi\)
\(770\) 1402.67i 0.00236577i
\(771\) −60460.0 −0.101709
\(772\) −553638. −0.928948
\(773\) 824077.i 1.37914i 0.724218 + 0.689571i \(0.242201\pi\)
−0.724218 + 0.689571i \(0.757799\pi\)
\(774\) −80395.6 122635.i −0.134199 0.204707i
\(775\) 557548. 0.928280
\(776\) 827151.i 1.37360i
\(777\) 263473.i 0.436409i
\(778\) 228661. 0.377775
\(779\) 621065.i 1.02344i
\(780\) −35425.7 −0.0582276
\(781\) 30131.4i 0.0493989i
\(782\) 466171.i 0.762310i
\(783\) −885752. −1.44474
\(784\) 285061. 0.463772
\(785\) −61296.2 −0.0994705
\(786\) 963088.i 1.55891i
\(787\) 347326. 0.560774 0.280387 0.959887i \(-0.409537\pi\)
0.280387 + 0.959887i \(0.409537\pi\)
\(788\) 2.25268e6 3.62782