Properties

Label 38.5.b.a.37.8
Level $38$
Weight $5$
Character 38.37
Analytic conductor $3.928$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 38.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92805859719\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 450 x^{6} + 68229 x^{4} + 4001228 x^{2} + 77475204\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 37.8
Root \(13.9305i\) of defining polynomial
Character \(\chi\) \(=\) 38.37
Dual form 38.5.b.a.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.82843i q^{2} +15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} -22.6274i q^{8} -154.460 q^{9} +O(q^{10})\) \(q+2.82843i q^{2} +15.3447i q^{3} -8.00000 q^{4} +41.6240 q^{5} -43.4013 q^{6} -62.4342 q^{7} -22.6274i q^{8} -154.460 q^{9} +117.730i q^{10} +122.938 q^{11} -122.758i q^{12} -68.9610i q^{13} -176.591i q^{14} +638.707i q^{15} +64.0000 q^{16} +297.375 q^{17} -436.878i q^{18} +(-195.642 + 303.390i) q^{19} -332.992 q^{20} -958.034i q^{21} +347.721i q^{22} +268.685 q^{23} +347.211 q^{24} +1107.56 q^{25} +195.051 q^{26} -1127.21i q^{27} +499.474 q^{28} +561.405i q^{29} -1806.54 q^{30} +252.423i q^{31} +181.019i q^{32} +1886.44i q^{33} +841.104i q^{34} -2598.76 q^{35} +1235.68 q^{36} -2407.33i q^{37} +(-858.116 - 553.358i) q^{38} +1058.18 q^{39} -941.843i q^{40} +690.246i q^{41} +2709.73 q^{42} +218.905 q^{43} -983.502 q^{44} -6429.22 q^{45} +759.956i q^{46} -83.1049 q^{47} +982.060i q^{48} +1497.03 q^{49} +3132.64i q^{50} +4563.13i q^{51} +551.688i q^{52} -4389.68i q^{53} +3188.24 q^{54} +5117.16 q^{55} +1412.73i q^{56} +(-4655.42 - 3002.06i) q^{57} -1587.89 q^{58} +476.981i q^{59} -5109.66i q^{60} +3965.09 q^{61} -713.960 q^{62} +9643.57 q^{63} -512.000 q^{64} -2870.43i q^{65} -5335.66 q^{66} -5111.96i q^{67} -2379.00 q^{68} +4122.89i q^{69} -7350.41i q^{70} -8182.93i q^{71} +3495.02i q^{72} -7345.23 q^{73} +6808.95 q^{74} +16995.1i q^{75} +(1565.13 - 2427.12i) q^{76} -7675.53 q^{77} +2993.00i q^{78} +1485.61i q^{79} +2663.94 q^{80} +4785.54 q^{81} -1952.31 q^{82} +5347.30 q^{83} +7664.27i q^{84} +12377.9 q^{85} +619.156i q^{86} -8614.59 q^{87} -2781.76i q^{88} +11172.3i q^{89} -18184.6i q^{90} +4305.53i q^{91} -2149.48 q^{92} -3873.35 q^{93} -235.056i q^{94} +(-8143.39 + 12628.3i) q^{95} -2777.69 q^{96} -1078.13i q^{97} +4234.25i q^{98} -18988.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} + O(q^{10}) \) \( 8q - 64q^{4} + 18q^{5} - 32q^{6} - 162q^{7} - 268q^{9} - 6q^{11} + 512q^{16} + 510q^{17} - 12q^{19} - 144q^{20} - 396q^{23} + 256q^{24} + 3458q^{25} - 192q^{26} + 1296q^{28} - 2752q^{30} + 1002q^{35} + 2144q^{36} - 3216q^{38} - 6588q^{39} + 1376q^{42} - 8654q^{43} + 48q^{44} - 10334q^{45} + 3210q^{47} + 9222q^{49} + 9088q^{54} + 17146q^{55} - 14076q^{57} - 960q^{58} + 1314q^{61} - 15168q^{62} + 29938q^{63} - 4096q^{64} + 4928q^{66} - 4080q^{68} + 23398q^{73} + 13152q^{74} + 96q^{76} - 44622q^{77} + 1152q^{80} - 20368q^{81} + 16512q^{82} - 10440q^{83} + 21274q^{85} - 14316q^{87} + 3168q^{92} + 19416q^{93} - 34686q^{95} - 2048q^{96} - 56798q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82843i 0.707107i
\(3\) 15.3447i 1.70497i 0.522755 + 0.852483i \(0.324904\pi\)
−0.522755 + 0.852483i \(0.675096\pi\)
\(4\) −8.00000 −0.500000
\(5\) 41.6240 1.66496 0.832480 0.554055i \(-0.186920\pi\)
0.832480 + 0.554055i \(0.186920\pi\)
\(6\) −43.4013 −1.20559
\(7\) −62.4342 −1.27417 −0.637084 0.770794i \(-0.719860\pi\)
−0.637084 + 0.770794i \(0.719860\pi\)
\(8\) 22.6274i 0.353553i
\(9\) −154.460 −1.90691
\(10\) 117.730i 1.17730i
\(11\) 122.938 1.01601 0.508007 0.861353i \(-0.330382\pi\)
0.508007 + 0.861353i \(0.330382\pi\)
\(12\) 122.758i 0.852483i
\(13\) 68.9610i 0.408053i −0.978965 0.204027i \(-0.934597\pi\)
0.978965 0.204027i \(-0.0654029\pi\)
\(14\) 176.591i 0.900973i
\(15\) 638.707i 2.83870i
\(16\) 64.0000 0.250000
\(17\) 297.375 1.02898 0.514490 0.857496i \(-0.327981\pi\)
0.514490 + 0.857496i \(0.327981\pi\)
\(18\) 436.878i 1.34839i
\(19\) −195.642 + 303.390i −0.541944 + 0.840415i
\(20\) −332.992 −0.832480
\(21\) 958.034i 2.17241i
\(22\) 347.721i 0.718431i
\(23\) 268.685 0.507911 0.253956 0.967216i \(-0.418268\pi\)
0.253956 + 0.967216i \(0.418268\pi\)
\(24\) 347.211 0.602796
\(25\) 1107.56 1.77209
\(26\) 195.051 0.288537
\(27\) 1127.21i 1.54625i
\(28\) 499.474 0.637084
\(29\) 561.405i 0.667545i 0.942654 + 0.333772i \(0.108322\pi\)
−0.942654 + 0.333772i \(0.891678\pi\)
\(30\) −1806.54 −2.00726
\(31\) 252.423i 0.262667i 0.991338 + 0.131333i \(0.0419259\pi\)
−0.991338 + 0.131333i \(0.958074\pi\)
\(32\) 181.019i 0.176777i
\(33\) 1886.44i 1.73227i
\(34\) 841.104i 0.727599i
\(35\) −2598.76 −2.12144
\(36\) 1235.68 0.953454
\(37\) 2407.33i 1.75846i −0.476400 0.879228i \(-0.658059\pi\)
0.476400 0.879228i \(-0.341941\pi\)
\(38\) −858.116 553.358i −0.594263 0.383212i
\(39\) 1058.18 0.695717
\(40\) 941.843i 0.588652i
\(41\) 690.246i 0.410616i 0.978697 + 0.205308i \(0.0658197\pi\)
−0.978697 + 0.205308i \(0.934180\pi\)
\(42\) 2709.73 1.53613
\(43\) 218.905 0.118391 0.0591954 0.998246i \(-0.481146\pi\)
0.0591954 + 0.998246i \(0.481146\pi\)
\(44\) −983.502 −0.508007
\(45\) −6429.22 −3.17493
\(46\) 759.956i 0.359148i
\(47\) −83.1049 −0.0376211 −0.0188105 0.999823i \(-0.505988\pi\)
−0.0188105 + 0.999823i \(0.505988\pi\)
\(48\) 982.060i 0.426241i
\(49\) 1497.03 0.623505
\(50\) 3132.64i 1.25306i
\(51\) 4563.13i 1.75438i
\(52\) 551.688i 0.204027i
\(53\) 4389.68i 1.56272i −0.624080 0.781360i \(-0.714526\pi\)
0.624080 0.781360i \(-0.285474\pi\)
\(54\) 3188.24 1.09336
\(55\) 5117.16 1.69162
\(56\) 1412.73i 0.450486i
\(57\) −4655.42 3002.06i −1.43288 0.923996i
\(58\) −1587.89 −0.472025
\(59\) 476.981i 0.137024i 0.997650 + 0.0685120i \(0.0218252\pi\)
−0.997650 + 0.0685120i \(0.978175\pi\)
\(60\) 5109.66i 1.41935i
\(61\) 3965.09 1.06560 0.532799 0.846242i \(-0.321140\pi\)
0.532799 + 0.846242i \(0.321140\pi\)
\(62\) −713.960 −0.185734
\(63\) 9643.57 2.42972
\(64\) −512.000 −0.125000
\(65\) 2870.43i 0.679392i
\(66\) −5335.66 −1.22490
\(67\) 5111.96i 1.13878i −0.822069 0.569388i \(-0.807180\pi\)
0.822069 0.569388i \(-0.192820\pi\)
\(68\) −2379.00 −0.514490
\(69\) 4122.89i 0.865972i
\(70\) 7350.41i 1.50008i
\(71\) 8182.93i 1.62327i −0.584161 0.811637i \(-0.698577\pi\)
0.584161 0.811637i \(-0.301423\pi\)
\(72\) 3495.02i 0.674194i
\(73\) −7345.23 −1.37835 −0.689175 0.724595i \(-0.742027\pi\)
−0.689175 + 0.724595i \(0.742027\pi\)
\(74\) 6808.95 1.24342
\(75\) 16995.1i 3.02135i
\(76\) 1565.13 2427.12i 0.270972 0.420207i
\(77\) −7675.53 −1.29457
\(78\) 2993.00i 0.491946i
\(79\) 1485.61i 0.238041i 0.992892 + 0.119021i \(0.0379754\pi\)
−0.992892 + 0.119021i \(0.962025\pi\)
\(80\) 2663.94 0.416240
\(81\) 4785.54 0.729391
\(82\) −1952.31 −0.290350
\(83\) 5347.30 0.776209 0.388104 0.921615i \(-0.373130\pi\)
0.388104 + 0.921615i \(0.373130\pi\)
\(84\) 7664.27i 1.08621i
\(85\) 12377.9 1.71321
\(86\) 619.156i 0.0837150i
\(87\) −8614.59 −1.13814
\(88\) 2781.76i 0.359215i
\(89\) 11172.3i 1.41047i 0.708975 + 0.705234i \(0.249158\pi\)
−0.708975 + 0.705234i \(0.750842\pi\)
\(90\) 18184.6i 2.24501i
\(91\) 4305.53i 0.519928i
\(92\) −2149.48 −0.253956
\(93\) −3873.35 −0.447838
\(94\) 235.056i 0.0266021i
\(95\) −8143.39 + 12628.3i −0.902315 + 1.39926i
\(96\) −2777.69 −0.301398
\(97\) 1078.13i 0.114585i −0.998357 0.0572927i \(-0.981753\pi\)
0.998357 0.0572927i \(-0.0182468\pi\)
\(98\) 4234.25i 0.440884i
\(99\) −18988.9 −1.93745
\(100\) −8860.45 −0.886045
\(101\) 1393.71 0.136625 0.0683126 0.997664i \(-0.478238\pi\)
0.0683126 + 0.997664i \(0.478238\pi\)
\(102\) −12906.5 −1.24053
\(103\) 11163.2i 1.05224i −0.850411 0.526119i \(-0.823647\pi\)
0.850411 0.526119i \(-0.176353\pi\)
\(104\) −1560.41 −0.144269
\(105\) 39877.2i 3.61698i
\(106\) 12415.9 1.10501
\(107\) 502.078i 0.0438534i −0.999760 0.0219267i \(-0.993020\pi\)
0.999760 0.0219267i \(-0.00698005\pi\)
\(108\) 9017.72i 0.773124i
\(109\) 11387.7i 0.958477i 0.877685 + 0.479238i \(0.159087\pi\)
−0.877685 + 0.479238i \(0.840913\pi\)
\(110\) 14473.5i 1.19616i
\(111\) 36939.7 2.99811
\(112\) −3995.79 −0.318542
\(113\) 4779.02i 0.374267i −0.982334 0.187133i \(-0.940080\pi\)
0.982334 0.187133i \(-0.0599197\pi\)
\(114\) 8491.12 13167.5i 0.653364 1.01320i
\(115\) 11183.7 0.845652
\(116\) 4491.24i 0.333772i
\(117\) 10651.7i 0.778120i
\(118\) −1349.11 −0.0968906
\(119\) −18566.4 −1.31109
\(120\) 14452.3 1.00363
\(121\) 472.695 0.0322857
\(122\) 11215.0i 0.753491i
\(123\) −10591.6 −0.700087
\(124\) 2019.38i 0.131333i
\(125\) 20085.9 1.28550
\(126\) 27276.1i 1.71807i
\(127\) 17552.6i 1.08826i 0.839001 + 0.544130i \(0.183140\pi\)
−0.839001 + 0.544130i \(0.816860\pi\)
\(128\) 1448.15i 0.0883883i
\(129\) 3359.02i 0.201852i
\(130\) 8118.80 0.480403
\(131\) −7401.84 −0.431317 −0.215659 0.976469i \(-0.569190\pi\)
−0.215659 + 0.976469i \(0.569190\pi\)
\(132\) 15091.5i 0.866135i
\(133\) 12214.7 18941.9i 0.690528 1.07083i
\(134\) 14458.8 0.805236
\(135\) 46919.2i 2.57444i
\(136\) 6728.83i 0.363799i
\(137\) 1692.77 0.0901896 0.0450948 0.998983i \(-0.485641\pi\)
0.0450948 + 0.998983i \(0.485641\pi\)
\(138\) −11661.3 −0.612334
\(139\) −37366.7 −1.93399 −0.966996 0.254791i \(-0.917993\pi\)
−0.966996 + 0.254791i \(0.917993\pi\)
\(140\) 20790.1 1.06072
\(141\) 1275.22i 0.0641426i
\(142\) 23144.8 1.14783
\(143\) 8477.91i 0.414588i
\(144\) −9885.41 −0.476727
\(145\) 23367.9i 1.11143i
\(146\) 20775.4i 0.974641i
\(147\) 22971.5i 1.06305i
\(148\) 19258.6i 0.879228i
\(149\) −6037.22 −0.271935 −0.135967 0.990713i \(-0.543414\pi\)
−0.135967 + 0.990713i \(0.543414\pi\)
\(150\) −48069.4 −2.13642
\(151\) 20619.1i 0.904307i −0.891940 0.452153i \(-0.850656\pi\)
0.891940 0.452153i \(-0.149344\pi\)
\(152\) 6864.92 + 4426.87i 0.297131 + 0.191606i
\(153\) −45932.4 −1.96217
\(154\) 21709.7i 0.915402i
\(155\) 10506.8i 0.437330i
\(156\) −8465.48 −0.347858
\(157\) −1043.55 −0.0423362 −0.0211681 0.999776i \(-0.506739\pi\)
−0.0211681 + 0.999776i \(0.506739\pi\)
\(158\) −4201.95 −0.168321
\(159\) 67358.3 2.66439
\(160\) 7534.75i 0.294326i
\(161\) −16775.2 −0.647165
\(162\) 13535.5i 0.515757i
\(163\) 1587.92 0.0597658 0.0298829 0.999553i \(-0.490487\pi\)
0.0298829 + 0.999553i \(0.490487\pi\)
\(164\) 5521.97i 0.205308i
\(165\) 78521.3i 2.88416i
\(166\) 15124.5i 0.548862i
\(167\) 21277.9i 0.762948i 0.924380 + 0.381474i \(0.124583\pi\)
−0.924380 + 0.381474i \(0.875417\pi\)
\(168\) −21677.8 −0.768064
\(169\) 23805.4 0.833493
\(170\) 35010.1i 1.21142i
\(171\) 30218.7 46861.4i 1.03344 1.60259i
\(172\) −1751.24 −0.0591954
\(173\) 23629.3i 0.789513i −0.918786 0.394756i \(-0.870829\pi\)
0.918786 0.394756i \(-0.129171\pi\)
\(174\) 24365.7i 0.804787i
\(175\) −69149.5 −2.25794
\(176\) 7868.02 0.254004
\(177\) −7319.12 −0.233621
\(178\) −31600.1 −0.997351
\(179\) 54580.1i 1.70345i −0.523993 0.851723i \(-0.675558\pi\)
0.523993 0.851723i \(-0.324442\pi\)
\(180\) 51433.8 1.58746
\(181\) 48461.8i 1.47925i 0.673017 + 0.739627i \(0.264998\pi\)
−0.673017 + 0.739627i \(0.735002\pi\)
\(182\) −12177.9 −0.367645
\(183\) 60843.0i 1.81681i
\(184\) 6079.65i 0.179574i
\(185\) 100203.i 2.92776i
\(186\) 10955.5i 0.316669i
\(187\) 36558.6 1.04546
\(188\) 664.839 0.0188105
\(189\) 70376.8i 1.97018i
\(190\) −35718.2 23033.0i −0.989424 0.638033i
\(191\) 10718.8 0.293819 0.146909 0.989150i \(-0.453067\pi\)
0.146909 + 0.989150i \(0.453067\pi\)
\(192\) 7856.48i 0.213121i
\(193\) 25358.2i 0.680776i 0.940285 + 0.340388i \(0.110558\pi\)
−0.940285 + 0.340388i \(0.889442\pi\)
\(194\) 3049.42 0.0810241
\(195\) 44045.9 1.15834
\(196\) −11976.3 −0.311752
\(197\) −4536.94 −0.116904 −0.0584521 0.998290i \(-0.518617\pi\)
−0.0584521 + 0.998290i \(0.518617\pi\)
\(198\) 53708.8i 1.36998i
\(199\) −67698.1 −1.70951 −0.854753 0.519035i \(-0.826291\pi\)
−0.854753 + 0.519035i \(0.826291\pi\)
\(200\) 25061.1i 0.626529i
\(201\) 78441.5 1.94157
\(202\) 3942.01i 0.0966085i
\(203\) 35050.9i 0.850564i
\(204\) 36505.0i 0.877188i
\(205\) 28730.8i 0.683660i
\(206\) 31574.2 0.744044
\(207\) −41501.0 −0.968540
\(208\) 4413.50i 0.102013i
\(209\) −24051.8 + 37298.1i −0.550623 + 0.853874i
\(210\) 112790. 2.55759
\(211\) 2816.81i 0.0632691i 0.999500 + 0.0316346i \(0.0100713\pi\)
−0.999500 + 0.0316346i \(0.989929\pi\)
\(212\) 35117.5i 0.781360i
\(213\) 125565. 2.76763
\(214\) 1420.09 0.0310090
\(215\) 9111.68 0.197116
\(216\) −25506.0 −0.546681
\(217\) 15759.8i 0.334682i
\(218\) −32209.2 −0.677746
\(219\) 112710.i 2.35004i
\(220\) −40937.3 −0.845812
\(221\) 20507.3i 0.419878i
\(222\) 104481.i 2.11998i
\(223\) 36870.4i 0.741426i 0.928747 + 0.370713i \(0.120887\pi\)
−0.928747 + 0.370713i \(0.879113\pi\)
\(224\) 11301.8i 0.225243i
\(225\) −171073. −3.37921
\(226\) 13517.1 0.264647
\(227\) 56826.9i 1.10281i 0.834236 + 0.551407i \(0.185909\pi\)
−0.834236 + 0.551407i \(0.814091\pi\)
\(228\) 37243.4 + 24016.5i 0.716439 + 0.461998i
\(229\) 7632.64 0.145547 0.0727736 0.997348i \(-0.476815\pi\)
0.0727736 + 0.997348i \(0.476815\pi\)
\(230\) 31632.4i 0.597966i
\(231\) 117779.i 2.20720i
\(232\) 12703.1 0.236013
\(233\) 91249.2 1.68080 0.840402 0.541964i \(-0.182319\pi\)
0.840402 + 0.541964i \(0.182319\pi\)
\(234\) −30127.5 −0.550214
\(235\) −3459.16 −0.0626375
\(236\) 3815.85i 0.0685120i
\(237\) −22796.3 −0.405852
\(238\) 52513.7i 0.927083i
\(239\) −110161. −1.92856 −0.964280 0.264884i \(-0.914666\pi\)
−0.964280 + 0.264884i \(0.914666\pi\)
\(240\) 40877.3i 0.709675i
\(241\) 58423.0i 1.00589i −0.864319 0.502944i \(-0.832250\pi\)
0.864319 0.502944i \(-0.167750\pi\)
\(242\) 1336.98i 0.0228295i
\(243\) 17871.8i 0.302661i
\(244\) −31720.7 −0.532799
\(245\) 62312.6 1.03811
\(246\) 29957.6i 0.495036i
\(247\) 20922.0 + 13491.6i 0.342934 + 0.221142i
\(248\) 5711.68 0.0928668
\(249\) 82052.7i 1.32341i
\(250\) 56811.6i 0.908985i
\(251\) −17258.3 −0.273936 −0.136968 0.990575i \(-0.543736\pi\)
−0.136968 + 0.990575i \(0.543736\pi\)
\(252\) −77148.5 −1.21486
\(253\) 33031.5 0.516045
\(254\) −49646.1 −0.769517
\(255\) 189936.i 2.92096i
\(256\) 4096.00 0.0625000
\(257\) 41195.7i 0.623714i −0.950129 0.311857i \(-0.899049\pi\)
0.950129 0.311857i \(-0.100951\pi\)
\(258\) −9500.75 −0.142731
\(259\) 150300.i 2.24057i
\(260\) 22963.4i 0.339696i
\(261\) 86714.4i 1.27295i
\(262\) 20935.6i 0.304987i
\(263\) −41179.7 −0.595349 −0.297675 0.954667i \(-0.596211\pi\)
−0.297675 + 0.954667i \(0.596211\pi\)
\(264\) 42685.3 0.612450
\(265\) 182716.i 2.60187i
\(266\) 53575.8 + 34548.5i 0.757191 + 0.488277i
\(267\) −171436. −2.40480
\(268\) 40895.7i 0.569388i
\(269\) 19858.8i 0.274440i 0.990541 + 0.137220i \(0.0438168\pi\)
−0.990541 + 0.137220i \(0.956183\pi\)
\(270\) 132707. 1.82040
\(271\) 110976. 1.51110 0.755549 0.655093i \(-0.227370\pi\)
0.755549 + 0.655093i \(0.227370\pi\)
\(272\) 19032.0 0.257245
\(273\) −66067.0 −0.886460
\(274\) 4787.87i 0.0637737i
\(275\) 136161. 1.80047
\(276\) 32983.1i 0.432986i
\(277\) −87534.8 −1.14083 −0.570415 0.821357i \(-0.693218\pi\)
−0.570415 + 0.821357i \(0.693218\pi\)
\(278\) 105689.i 1.36754i
\(279\) 38989.1i 0.500882i
\(280\) 58803.3i 0.750042i
\(281\) 133298.i 1.68815i 0.536228 + 0.844073i \(0.319849\pi\)
−0.536228 + 0.844073i \(0.680151\pi\)
\(282\) 3606.86 0.0453557
\(283\) 29905.8 0.373407 0.186704 0.982416i \(-0.440220\pi\)
0.186704 + 0.982416i \(0.440220\pi\)
\(284\) 65463.4i 0.811637i
\(285\) −193777. 124958.i −2.38568 1.53842i
\(286\) 23979.1 0.293158
\(287\) 43095.0i 0.523194i
\(288\) 27960.2i 0.337097i
\(289\) 4910.99 0.0587994
\(290\) −66094.5 −0.785903
\(291\) 16543.6 0.195364
\(292\) 58761.8 0.689175
\(293\) 42625.4i 0.496516i 0.968694 + 0.248258i \(0.0798580\pi\)
−0.968694 + 0.248258i \(0.920142\pi\)
\(294\) −64973.3 −0.751693
\(295\) 19853.8i 0.228140i
\(296\) −54471.6 −0.621708
\(297\) 138577.i 1.57101i
\(298\) 17075.8i 0.192287i
\(299\) 18528.8i 0.207255i
\(300\) 135961.i 1.51068i
\(301\) −13667.1 −0.150850
\(302\) 58319.6 0.639441
\(303\) 21386.1i 0.232941i
\(304\) −12521.1 + 19416.9i −0.135486 + 0.210104i
\(305\) 165043. 1.77418
\(306\) 129917.i 1.38746i
\(307\) 39047.5i 0.414302i −0.978309 0.207151i \(-0.933581\pi\)
0.978309 0.207151i \(-0.0664191\pi\)
\(308\) 61404.2 0.647287
\(309\) 171296. 1.79403
\(310\) −29717.9 −0.309239
\(311\) 79232.0 0.819180 0.409590 0.912270i \(-0.365672\pi\)
0.409590 + 0.912270i \(0.365672\pi\)
\(312\) 23944.0i 0.245973i
\(313\) −107079. −1.09298 −0.546492 0.837464i \(-0.684037\pi\)
−0.546492 + 0.837464i \(0.684037\pi\)
\(314\) 2951.59i 0.0299362i
\(315\) 401404. 4.04539
\(316\) 11884.9i 0.119021i
\(317\) 132924.i 1.32277i 0.750046 + 0.661385i \(0.230031\pi\)
−0.750046 + 0.661385i \(0.769969\pi\)
\(318\) 190518.i 1.88401i
\(319\) 69017.9i 0.678235i
\(320\) −21311.5 −0.208120
\(321\) 7704.23 0.0747686
\(322\) 47447.3i 0.457614i
\(323\) −58179.0 + 90220.6i −0.557649 + 0.864770i
\(324\) −38284.3 −0.364696
\(325\) 76378.2i 0.723107i
\(326\) 4491.31i 0.0422608i
\(327\) −174740. −1.63417
\(328\) 15618.5 0.145175
\(329\) 5188.59 0.0479356
\(330\) −222092. −2.03941
\(331\) 44623.1i 0.407290i 0.979045 + 0.203645i \(0.0652788\pi\)
−0.979045 + 0.203645i \(0.934721\pi\)
\(332\) −42778.4 −0.388104
\(333\) 371835.i 3.35322i
\(334\) −60182.9 −0.539486
\(335\) 212780.i 1.89602i
\(336\) 61314.2i 0.543103i
\(337\) 5142.51i 0.0452810i −0.999744 0.0226405i \(-0.992793\pi\)
0.999744 0.0226405i \(-0.00720730\pi\)
\(338\) 67331.8i 0.589368i
\(339\) 73332.5 0.638112
\(340\) −99023.5 −0.856605
\(341\) 31032.3i 0.266873i
\(342\) 132544. + 85471.5i 1.13320 + 0.730751i
\(343\) 56438.4 0.479718
\(344\) 4953.25i 0.0418575i
\(345\) 171611.i 1.44181i
\(346\) 66833.8 0.558270
\(347\) −175661. −1.45887 −0.729436 0.684049i \(-0.760218\pi\)
−0.729436 + 0.684049i \(0.760218\pi\)
\(348\) 68916.7 0.569070
\(349\) 137125. 1.12581 0.562906 0.826521i \(-0.309683\pi\)
0.562906 + 0.826521i \(0.309683\pi\)
\(350\) 195584.i 1.59661i
\(351\) −77733.8 −0.630951
\(352\) 22254.1i 0.179608i
\(353\) −199391. −1.60013 −0.800065 0.599913i \(-0.795202\pi\)
−0.800065 + 0.599913i \(0.795202\pi\)
\(354\) 20701.6i 0.165195i
\(355\) 340606.i 2.70269i
\(356\) 89378.5i 0.705234i
\(357\) 284896.i 2.23537i
\(358\) 154376. 1.20452
\(359\) 6307.95 0.0489440 0.0244720 0.999701i \(-0.492210\pi\)
0.0244720 + 0.999701i \(0.492210\pi\)
\(360\) 145477.i 1.12251i
\(361\) −53769.6 118711.i −0.412594 0.910915i
\(362\) −137071. −1.04599
\(363\) 7253.36i 0.0550460i
\(364\) 34444.2i 0.259964i
\(365\) −305738. −2.29490
\(366\) −172090. −1.28468
\(367\) 52946.3 0.393100 0.196550 0.980494i \(-0.437026\pi\)
0.196550 + 0.980494i \(0.437026\pi\)
\(368\) 17195.8 0.126978
\(369\) 106615.i 0.783008i
\(370\) 283416. 2.07024
\(371\) 274067.i 1.99117i
\(372\) 30986.8 0.223919
\(373\) 9312.99i 0.0669378i 0.999440 + 0.0334689i \(0.0106555\pi\)
−0.999440 + 0.0334689i \(0.989345\pi\)
\(374\) 103403.i 0.739251i
\(375\) 308212.i 2.19173i
\(376\) 1880.45i 0.0133011i
\(377\) 38715.0 0.272394
\(378\) −199056. −1.39313
\(379\) 178291.i 1.24123i 0.784117 + 0.620613i \(0.213116\pi\)
−0.784117 + 0.620613i \(0.786884\pi\)
\(380\) 65147.1 101026.i 0.451157 0.699628i
\(381\) −269339. −1.85545
\(382\) 30317.3i 0.207761i
\(383\) 27764.8i 0.189276i −0.995512 0.0946382i \(-0.969831\pi\)
0.995512 0.0946382i \(-0.0301694\pi\)
\(384\) 22221.5 0.150699
\(385\) −319486. −2.15541
\(386\) −71723.9 −0.481381
\(387\) −33811.9 −0.225760
\(388\) 8625.07i 0.0572927i
\(389\) 241135. 1.59353 0.796765 0.604289i \(-0.206543\pi\)
0.796765 + 0.604289i \(0.206543\pi\)
\(390\) 124581.i 0.819070i
\(391\) 79900.3 0.522631
\(392\) 33874.0i 0.220442i
\(393\) 113579.i 0.735381i
\(394\) 12832.4i 0.0826638i
\(395\) 61837.2i 0.396329i
\(396\) 151911. 0.968723
\(397\) 234920. 1.49052 0.745261 0.666772i \(-0.232325\pi\)
0.745261 + 0.666772i \(0.232325\pi\)
\(398\) 191479.i 1.20880i
\(399\) 290658. + 187432.i 1.82573 + 1.17733i
\(400\) 70883.6 0.443023
\(401\) 311500.i 1.93718i 0.248667 + 0.968589i \(0.420007\pi\)
−0.248667 + 0.968589i \(0.579993\pi\)
\(402\) 221866.i 1.37290i
\(403\) 17407.3 0.107182
\(404\) −11149.7 −0.0683126
\(405\) 199193. 1.21441
\(406\) 99138.9 0.601440
\(407\) 295951.i 1.78662i
\(408\) 103252. 0.620265
\(409\) 243636.i 1.45645i −0.685338 0.728225i \(-0.740345\pi\)
0.685338 0.728225i \(-0.259655\pi\)
\(410\) −81263.0 −0.483420
\(411\) 25975.0i 0.153770i
\(412\) 89305.5i 0.526119i
\(413\) 29779.9i 0.174592i
\(414\) 117383.i 0.684862i
\(415\) 222576. 1.29236
\(416\) 12483.3 0.0721343
\(417\) 573380.i 3.29739i
\(418\) −105495. 68028.7i −0.603780 0.389349i
\(419\) −193805. −1.10392 −0.551960 0.833871i \(-0.686120\pi\)
−0.551960 + 0.833871i \(0.686120\pi\)
\(420\) 319018.i 1.80849i
\(421\) 136536.i 0.770339i −0.922846 0.385169i \(-0.874143\pi\)
0.922846 0.385169i \(-0.125857\pi\)
\(422\) −7967.13 −0.0447380
\(423\) 12836.3 0.0717399
\(424\) −99327.2 −0.552505
\(425\) 329360. 1.82345
\(426\) 355150.i 1.95701i
\(427\) −247557. −1.35775
\(428\) 4016.62i 0.0219267i
\(429\) 130091. 0.706858
\(430\) 25771.7i 0.139382i
\(431\) 323841.i 1.74332i −0.490113 0.871659i \(-0.663044\pi\)
0.490113 0.871659i \(-0.336956\pi\)
\(432\) 72141.7i 0.386562i
\(433\) 286129.i 1.52611i −0.646333 0.763056i \(-0.723698\pi\)
0.646333 0.763056i \(-0.276302\pi\)
\(434\) 44575.5 0.236656
\(435\) −358574. −1.89496
\(436\) 91101.3i 0.479238i
\(437\) −52566.0 + 81516.3i −0.275259 + 0.426856i
\(438\) 318793. 1.66173
\(439\) 26283.3i 0.136380i 0.997672 + 0.0681901i \(0.0217224\pi\)
−0.997672 + 0.0681901i \(0.978278\pi\)
\(440\) 115788.i 0.598079i
\(441\) −231231. −1.18897
\(442\) 58003.3 0.296899
\(443\) −317887. −1.61981 −0.809907 0.586558i \(-0.800482\pi\)
−0.809907 + 0.586558i \(0.800482\pi\)
\(444\) −295518. −1.49905
\(445\) 465036.i 2.34837i
\(446\) −104285. −0.524267
\(447\) 92639.3i 0.463639i
\(448\) 31966.3 0.159271
\(449\) 68728.7i 0.340915i 0.985365 + 0.170457i \(0.0545245\pi\)
−0.985365 + 0.170457i \(0.945476\pi\)
\(450\) 483867.i 2.38947i
\(451\) 84857.3i 0.417192i
\(452\) 38232.1i 0.187133i
\(453\) 316394. 1.54181
\(454\) −160731. −0.779808
\(455\) 179213.i 0.865660i
\(456\) −67928.9 + 105340.i −0.326682 + 0.506599i
\(457\) 182859. 0.875555 0.437778 0.899083i \(-0.355766\pi\)
0.437778 + 0.899083i \(0.355766\pi\)
\(458\) 21588.4i 0.102917i
\(459\) 335206.i 1.59106i
\(460\) −89470.0 −0.422826
\(461\) 142804. 0.671951 0.335976 0.941871i \(-0.390934\pi\)
0.335976 + 0.941871i \(0.390934\pi\)
\(462\) 333128. 1.56073
\(463\) 96212.9 0.448819 0.224409 0.974495i \(-0.427955\pi\)
0.224409 + 0.974495i \(0.427955\pi\)
\(464\) 35929.9i 0.166886i
\(465\) −161224. −0.745632
\(466\) 258092.i 1.18851i
\(467\) 287321. 1.31745 0.658724 0.752384i \(-0.271096\pi\)
0.658724 + 0.752384i \(0.271096\pi\)
\(468\) 85213.5i 0.389060i
\(469\) 319162.i 1.45099i
\(470\) 9783.98i 0.0442914i
\(471\) 16012.9i 0.0721818i
\(472\) 10792.8 0.0484453
\(473\) 26911.6 0.120287
\(474\) 64477.7i 0.286981i
\(475\) −216684. + 336021.i −0.960374 + 1.48929i
\(476\) 148531. 0.655547
\(477\) 678029.i 2.97997i
\(478\) 311583.i 1.36370i
\(479\) 101492. 0.442346 0.221173 0.975235i \(-0.429011\pi\)
0.221173 + 0.975235i \(0.429011\pi\)
\(480\) −115618. −0.501816
\(481\) −166012. −0.717544
\(482\) 165245. 0.711270
\(483\) 257410.i 1.10339i
\(484\) −3781.56 −0.0161429
\(485\) 44876.2i 0.190780i
\(486\) 50549.1 0.214014
\(487\) 203340.i 0.857363i −0.903456 0.428682i \(-0.858978\pi\)
0.903456 0.428682i \(-0.141022\pi\)
\(488\) 89719.7i 0.376745i
\(489\) 24366.1i 0.101899i
\(490\) 176247.i 0.734055i
\(491\) −227758. −0.944735 −0.472368 0.881402i \(-0.656601\pi\)
−0.472368 + 0.881402i \(0.656601\pi\)
\(492\) 84732.9 0.350043
\(493\) 166948.i 0.686890i
\(494\) −38160.1 + 59176.5i −0.156371 + 0.242491i
\(495\) −790394. −3.22577
\(496\) 16155.1i 0.0656667i
\(497\) 510895.i 2.06833i
\(498\) −232080. −0.935792
\(499\) −132829. −0.533447 −0.266724 0.963773i \(-0.585941\pi\)
−0.266724 + 0.963773i \(0.585941\pi\)
\(500\) −160687. −0.642750
\(501\) −326502. −1.30080
\(502\) 48813.8i 0.193702i
\(503\) 279294. 1.10389 0.551945 0.833880i \(-0.313886\pi\)
0.551945 + 0.833880i \(0.313886\pi\)
\(504\) 218209.i 0.859036i
\(505\) 58011.9 0.227475
\(506\) 93427.3i 0.364899i
\(507\) 365286.i 1.42108i
\(508\) 140420.i 0.544130i
\(509\) 304788.i 1.17642i −0.808709 0.588209i \(-0.799833\pi\)
0.808709 0.588209i \(-0.200167\pi\)
\(510\) −537219. −2.06543
\(511\) 458594. 1.75625
\(512\) 11585.2i 0.0441942i
\(513\) 341985. + 220530.i 1.29949 + 0.837980i
\(514\) 116519. 0.441032
\(515\) 464656.i 1.75193i
\(516\) 26872.2i 0.100926i
\(517\) −10216.7 −0.0382235
\(518\) −425112. −1.58432
\(519\) 362585. 1.34609
\(520\) −64950.4 −0.240201
\(521\) 181301.i 0.667919i 0.942587 + 0.333959i \(0.108385\pi\)
−0.942587 + 0.333959i \(0.891615\pi\)
\(522\) 245265. 0.900109
\(523\) 5966.86i 0.0218144i −0.999941 0.0109072i \(-0.996528\pi\)
0.999941 0.0109072i \(-0.00347193\pi\)
\(524\) 59214.7 0.215659
\(525\) 1.06108e6i 3.84971i
\(526\) 116474.i 0.420976i
\(527\) 75064.3i 0.270279i
\(528\) 120732.i 0.433068i
\(529\) −207649. −0.742026
\(530\) 516799. 1.83980
\(531\) 73674.2i 0.261292i
\(532\) −97718.0 + 151535.i −0.345264 + 0.535415i
\(533\) 47600.1 0.167553
\(534\) 484893.i 1.70045i
\(535\) 20898.5i 0.0730142i
\(536\) −115671. −0.402618
\(537\) 837515. 2.90432
\(538\) −56169.1 −0.194058
\(539\) 184042. 0.633490
\(540\) 375353.i 1.28722i
\(541\) −121383. −0.414727 −0.207364 0.978264i \(-0.566488\pi\)
−0.207364 + 0.978264i \(0.566488\pi\)
\(542\) 313889.i 1.06851i
\(543\) −743632. −2.52208
\(544\) 53830.7i 0.181900i
\(545\) 474000.i 1.59583i
\(546\) 186866.i 0.626822i
\(547\) 297533.i 0.994399i −0.867636 0.497200i \(-0.834362\pi\)
0.867636 0.497200i \(-0.165638\pi\)
\(548\) −13542.2 −0.0450948
\(549\) −612446. −2.03200
\(550\) 385120.i 1.27312i
\(551\) −170325. 109834.i −0.561014 0.361772i
\(552\) 93290.4 0.306167
\(553\) 92753.2i 0.303304i
\(554\) 247586.i 0.806689i
\(555\) 1.53758e6 4.99173
\(556\) 298933. 0.966996
\(557\) 192568. 0.620687 0.310344 0.950624i \(-0.399556\pi\)
0.310344 + 0.950624i \(0.399556\pi\)
\(558\) 110278. 0.354177
\(559\) 15095.9i 0.0483097i
\(560\) −166321. −0.530360
\(561\) 560981.i 1.78247i
\(562\) −377023. −1.19370
\(563\) 21470.7i 0.0677376i −0.999426 0.0338688i \(-0.989217\pi\)
0.999426 0.0338688i \(-0.0107828\pi\)
\(564\) 10201.8i 0.0320713i
\(565\) 198922.i 0.623139i
\(566\) 84586.4i 0.264039i
\(567\) −298781. −0.929367
\(568\) −185159. −0.573914
\(569\) 51249.7i 0.158295i −0.996863 0.0791474i \(-0.974780\pi\)
0.996863 0.0791474i \(-0.0252198\pi\)
\(570\) 353434. 548085.i 1.08782 1.68693i
\(571\) 515089. 1.57983 0.789914 0.613218i \(-0.210125\pi\)
0.789914 + 0.613218i \(0.210125\pi\)
\(572\) 67823.3i 0.207294i
\(573\) 164477.i 0.500951i
\(574\) 121891. 0.369954
\(575\) 297584. 0.900065
\(576\) 79083.3 0.238364
\(577\) −419849. −1.26108 −0.630538 0.776159i \(-0.717166\pi\)
−0.630538 + 0.776159i \(0.717166\pi\)
\(578\) 13890.4i 0.0415775i
\(579\) −389114. −1.16070
\(580\) 186943.i 0.555717i
\(581\) −333855. −0.989020
\(582\) 46792.5i 0.138143i
\(583\) 539658.i 1.58775i
\(584\) 166204.i 0.487320i
\(585\) 443366.i 1.29554i
\(586\) −120563. −0.351090
\(587\) 311469. 0.903939 0.451970 0.892033i \(-0.350722\pi\)
0.451970 + 0.892033i \(0.350722\pi\)
\(588\) 183772.i 0.531527i
\(589\) −76582.5 49384.5i −0.220749 0.142351i
\(590\) −56155.1 −0.161319
\(591\) 69617.9i 0.199318i
\(592\) 154069.i 0.439614i
\(593\) −131604. −0.374247 −0.187124 0.982336i \(-0.559917\pi\)
−0.187124 + 0.982336i \(0.559917\pi\)
\(594\) 391956. 1.11087
\(595\) −772807. −2.18292
\(596\) 48297.8 0.135967
\(597\) 1.03881e6i 2.91465i
\(598\) 52407.3 0.146551
\(599\) 199776.i 0.556788i −0.960467 0.278394i \(-0.910198\pi\)
0.960467 0.278394i \(-0.0898021\pi\)
\(600\) 384556. 1.06821
\(601\) 328476.i 0.909399i 0.890645 + 0.454700i \(0.150253\pi\)
−0.890645 + 0.454700i \(0.849747\pi\)
\(602\) 38656.5i 0.106667i
\(603\) 789592.i 2.17154i
\(604\) 164953.i 0.452153i
\(605\) 19675.5 0.0537544
\(606\) −60489.0 −0.164714
\(607\) 275312.i 0.747219i 0.927586 + 0.373610i \(0.121880\pi\)
−0.927586 + 0.373610i \(0.878120\pi\)
\(608\) −54919.4 35414.9i −0.148566 0.0958031i
\(609\) 537845. 1.45018
\(610\) 466811.i 1.25453i
\(611\) 5731.00i 0.0153514i
\(612\) 367460. 0.981085
\(613\) −473140. −1.25912 −0.629562 0.776950i \(-0.716766\pi\)
−0.629562 + 0.776950i \(0.716766\pi\)
\(614\) 110443. 0.292956
\(615\) −440865. −1.16562
\(616\) 173677.i 0.457701i
\(617\) 10864.2 0.0285382 0.0142691 0.999898i \(-0.495458\pi\)
0.0142691 + 0.999898i \(0.495458\pi\)
\(618\) 484497.i 1.26857i
\(619\) 8963.62 0.0233939 0.0116969 0.999932i \(-0.496277\pi\)
0.0116969 + 0.999932i \(0.496277\pi\)
\(620\) 84054.8i 0.218665i
\(621\) 302866.i 0.785357i
\(622\) 224102.i 0.579248i
\(623\) 697535.i 1.79717i
\(624\) 67723.8 0.173929
\(625\) 143834. 0.368214
\(626\) 302864.i 0.772857i
\(627\) −572327. 369067.i −1.45583 0.938793i
\(628\) 8348.36 0.0211681
\(629\) 715879.i 1.80942i
\(630\) 1.13534e6i 2.86052i
\(631\) −439268. −1.10324 −0.551621 0.834095i \(-0.685991\pi\)
−0.551621 + 0.834095i \(0.685991\pi\)
\(632\) 33615.6 0.0841603
\(633\) −43223.0 −0.107872
\(634\) −375966. −0.935340
\(635\) 730608.i 1.81191i
\(636\) −538867. −1.33219
\(637\) 103237.i 0.254423i
\(638\) −195212. −0.479585
\(639\) 1.26393e6i 3.09544i
\(640\) 60278.0i 0.147163i
\(641\) 351470.i 0.855406i 0.903919 + 0.427703i \(0.140677\pi\)
−0.903919 + 0.427703i \(0.859323\pi\)
\(642\) 21790.8i 0.0528694i
\(643\) −257336. −0.622412 −0.311206 0.950342i \(-0.600733\pi\)
−0.311206 + 0.950342i \(0.600733\pi\)
\(644\) 134201. 0.323582
\(645\) 139816.i 0.336076i
\(646\) −255182. 164555.i −0.611485 0.394318i
\(647\) 352433. 0.841915 0.420957 0.907080i \(-0.361694\pi\)
0.420957 + 0.907080i \(0.361694\pi\)
\(648\) 108284.i 0.257879i
\(649\) 58639.0i 0.139218i
\(650\) 216030. 0.511314
\(651\) 241830. 0.570621
\(652\) −12703.3 −0.0298829
\(653\) −51680.8 −0.121200 −0.0606001 0.998162i \(-0.519301\pi\)
−0.0606001 + 0.998162i \(0.519301\pi\)
\(654\) 494240.i 1.15553i
\(655\) −308094. −0.718126
\(656\) 44175.8i 0.102654i
\(657\) 1.13454e6 2.62839
\(658\) 14675.6i 0.0338956i
\(659\) 144227.i 0.332105i −0.986117 0.166053i \(-0.946898\pi\)
0.986117 0.166053i \(-0.0531021\pi\)
\(660\) 628170.i 1.44208i
\(661\) 615181.i 1.40799i 0.710205 + 0.703995i \(0.248602\pi\)
−0.710205 + 0.703995i \(0.751398\pi\)
\(662\) −126213. −0.287997
\(663\) 314678. 0.715878
\(664\) 120996.i 0.274431i
\(665\) 508426. 788438.i 1.14970 1.78289i
\(666\) −1.05171e6 −2.37108
\(667\) 150841.i 0.339054i
\(668\) 170223.i 0.381474i
\(669\) −565765. −1.26411
\(670\) 601834. 1.34069
\(671\) 487459. 1.08266
\(672\) 173423. 0.384032
\(673\) 334936.i 0.739489i −0.929133 0.369745i \(-0.879445\pi\)
0.929133 0.369745i \(-0.120555\pi\)
\(674\) 14545.2 0.0320185
\(675\) 1.24845e6i 2.74009i
\(676\) −190443. −0.416746
\(677\) 504808.i 1.10141i 0.834700 + 0.550705i \(0.185641\pi\)
−0.834700 + 0.550705i \(0.814359\pi\)
\(678\) 207416.i 0.451214i
\(679\) 67312.5i 0.146001i
\(680\) 280081.i 0.605711i
\(681\) −871992. −1.88026
\(682\) −87772.6 −0.188708
\(683\) 690506.i 1.48022i −0.672486 0.740110i \(-0.734773\pi\)
0.672486 0.740110i \(-0.265227\pi\)
\(684\) −241750. + 374892.i −0.516719 + 0.801297i
\(685\) 70459.8 0.150162
\(686\) 159632.i 0.339212i
\(687\) 117121.i 0.248153i
\(688\) 14009.9 0.0295977
\(689\) −302717. −0.637673
\(690\) −485390. −1.01951
\(691\) 461905. 0.967379 0.483690 0.875240i \(-0.339296\pi\)
0.483690 + 0.875240i \(0.339296\pi\)
\(692\) 189035.i 0.394756i
\(693\) 1.18556e6 2.46863
\(694\) 496846.i 1.03158i
\(695\) −1.55535e6 −3.22002
\(696\) 194926.i 0.402394i
\(697\) 205262.i 0.422516i
\(698\) 387848.i 0.796069i
\(699\) 1.40019e6i 2.86571i
\(700\) 553196. 1.12897
\(701\) −410170. −0.834694 −0.417347 0.908747i \(-0.637040\pi\)
−0.417347 + 0.908747i \(0.637040\pi\)
\(702\) 219864.i 0.446150i
\(703\) 730358. + 470974.i 1.47783 + 0.952985i
\(704\) −62944.1 −0.127002
\(705\) 53079.7i 0.106795i
\(706\) 563962.i 1.13146i
\(707\) −87015.4 −0.174083
\(708\) 58553.0 0.116811
\(709\) 368245. 0.732562 0.366281 0.930504i \(-0.380631\pi\)
0.366281 + 0.930504i \(0.380631\pi\)
\(710\) 963380. 1.91109
\(711\) 229467.i 0.453923i
\(712\) 252801. 0.498675
\(713\) 67822.3i 0.133411i
\(714\) 805806. 1.58064
\(715\) 352884.i 0.690272i
\(716\) 436641.i 0.851723i
\(717\) 1.69039e6i 3.28813i
\(718\) 17841.6i 0.0346086i
\(719\) −460066. −0.889943 −0.444971 0.895545i \(-0.646786\pi\)
−0.444971 + 0.895545i \(0.646786\pi\)
\(720\) −411470. −0.793731
\(721\) 696965.i 1.34073i
\(722\) 335766. 152083.i 0.644114 0.291748i
\(723\) 896482. 1.71500
\(724\) 387695.i 0.739627i
\(725\) 621788.i 1.18295i
\(726\) −20515.6 −0.0389234
\(727\) 196263. 0.371339 0.185670 0.982612i \(-0.440555\pi\)
0.185670 + 0.982612i \(0.440555\pi\)
\(728\) 97422.9 0.183822
\(729\) 661866. 1.24542
\(730\) 864757.i 1.62274i
\(731\) 65096.8 0.121822
\(732\) 486744.i 0.908403i
\(733\) 578892. 1.07743 0.538716 0.842487i \(-0.318910\pi\)
0.538716 + 0.842487i \(0.318910\pi\)
\(734\) 149755.i 0.277964i
\(735\) 956167.i 1.76994i
\(736\) 48637.2i 0.0897869i
\(737\) 628453.i 1.15701i
\(738\) 301553. 0.553670
\(739\) 721624. 1.32136 0.660681 0.750667i \(-0.270268\pi\)
0.660681 + 0.750667i \(0.270268\pi\)
\(740\) 801621.i 1.46388i
\(741\) −207025. + 321042.i −0.377039 + 0.584690i
\(742\) −775177. −1.40797
\(743\) 963975.i 1.74618i 0.487562 + 0.873088i \(0.337886\pi\)
−0.487562 + 0.873088i \(0.662114\pi\)
\(744\) 87643.9i 0.158335i
\(745\) −251293. −0.452760
\(746\) −26341.1 −0.0473322
\(747\) −825942. −1.48016
\(748\) −292469. −0.522729
\(749\) 31346.8i 0.0558766i
\(750\) −871756. −1.54979
\(751\) 632486.i 1.12143i 0.828010 + 0.560713i \(0.189473\pi\)
−0.828010 + 0.560713i \(0.810527\pi\)
\(752\) −5318.71 −0.00940526
\(753\) 264823.i 0.467052i
\(754\) 109503.i 0.192611i
\(755\) 858249.i 1.50563i
\(756\) 563014.i 0.985090i
\(757\) 684418. 1.19434 0.597172 0.802113i \(-0.296291\pi\)
0.597172 + 0.802113i \(0.296291\pi\)
\(758\) −504283. −0.877680
\(759\) 506859.i 0.879840i
\(760\) 285746. + 184264.i 0.494712 + 0.319016i
\(761\) −201444. −0.347845 −0.173923 0.984759i \(-0.555644\pi\)
−0.173923 + 0.984759i \(0.555644\pi\)
\(762\) 761805.i 1.31200i
\(763\) 710980.i 1.22126i
\(764\) −85750.4 −0.146909
\(765\) −1.91189e6 −3.26693
\(766\) 78530.6 0.133839
\(767\) 32893.1 0.0559131
\(768\) 62851.9i 0.106560i
\(769\) 343992. 0.581695 0.290847 0.956769i \(-0.406063\pi\)
0.290847 + 0.956769i \(0.406063\pi\)
\(770\) 903643.i 1.52411i
\(771\) 632135. 1.06341
\(772\) 202866.i 0.340388i
\(773\) 323326.i 0.541105i 0.962705 + 0.270553i \(0.0872064\pi\)
−0.962705 + 0.270553i \(0.912794\pi\)
\(774\) 95634.5i 0.159637i
\(775\) 279573.i 0.465469i
\(776\) −24395.4 −0.0405121
\(777\) −2.30630e6 −3.82010
\(778\) 682032.i 1.12680i
\(779\) −209414. 135041.i −0.345088 0.222531i
\(780\) −352367. −0.579170
\(781\) 1.00599e6i 1.64927i
\(782\) 225992.i 0.369556i
\(783\) 632824. 1.03219
\(784\) 95810.2 0.155876
\(785\) −43436.5 −0.0704881
\(786\) 321250. 0.519993
\(787\) 526771.i 0.850496i 0.905077 + 0.425248i