Properties

Label 177.5.b.a.119.12
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.12
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.67

$q$-expansion

\(f(q)\) \(=\) \(q-5.88235i q^{2} +(-8.00524 + 4.11293i) q^{3} -18.6020 q^{4} -15.2405i q^{5} +(24.1937 + 47.0896i) q^{6} +49.3247 q^{7} +15.3061i q^{8} +(47.1676 - 65.8500i) q^{9} +O(q^{10})\) \(q-5.88235i q^{2} +(-8.00524 + 4.11293i) q^{3} -18.6020 q^{4} -15.2405i q^{5} +(24.1937 + 47.0896i) q^{6} +49.3247 q^{7} +15.3061i q^{8} +(47.1676 - 65.8500i) q^{9} -89.6502 q^{10} -123.986i q^{11} +(148.914 - 76.5089i) q^{12} -224.934 q^{13} -290.145i q^{14} +(62.6833 + 122.004i) q^{15} -207.597 q^{16} -169.629i q^{17} +(-387.353 - 277.456i) q^{18} +279.664 q^{19} +283.505i q^{20} +(-394.856 + 202.869i) q^{21} -729.327 q^{22} -54.0419i q^{23} +(-62.9529 - 122.529i) q^{24} +392.726 q^{25} +1323.14i q^{26} +(-106.751 + 721.142i) q^{27} -917.541 q^{28} +809.583i q^{29} +(717.671 - 368.725i) q^{30} -1470.77 q^{31} +1466.05i q^{32} +(509.944 + 992.534i) q^{33} -997.814 q^{34} -751.736i q^{35} +(-877.413 + 1224.94i) q^{36} -139.391 q^{37} -1645.08i q^{38} +(1800.65 - 925.138i) q^{39} +233.273 q^{40} +769.777i q^{41} +(1193.35 + 2322.68i) q^{42} -2761.82 q^{43} +2306.38i q^{44} +(-1003.59 - 718.860i) q^{45} -317.893 q^{46} -3561.82i q^{47} +(1661.86 - 853.832i) q^{48} +31.9294 q^{49} -2310.15i q^{50} +(697.671 + 1357.92i) q^{51} +4184.23 q^{52} +2805.15i q^{53} +(4242.01 + 627.947i) q^{54} -1889.61 q^{55} +754.969i q^{56} +(-2238.78 + 1150.24i) q^{57} +4762.25 q^{58} +453.188i q^{59} +(-1166.04 - 2269.53i) q^{60} -5104.03 q^{61} +8651.55i q^{62} +(2326.53 - 3248.03i) q^{63} +5302.30 q^{64} +3428.12i q^{65} +(5838.43 - 2999.67i) q^{66} -2153.50 q^{67} +3155.44i q^{68} +(222.271 + 432.618i) q^{69} -4421.97 q^{70} +2285.42i q^{71} +(1007.91 + 721.951i) q^{72} +7254.81 q^{73} +819.947i q^{74} +(-3143.86 + 1615.25i) q^{75} -5202.32 q^{76} -6115.56i q^{77} +(-5441.99 - 10592.0i) q^{78} +1082.58 q^{79} +3163.89i q^{80} +(-2111.44 - 6211.97i) q^{81} +4528.10 q^{82} -1104.74i q^{83} +(7345.13 - 3773.78i) q^{84} -2585.23 q^{85} +16246.0i q^{86} +(-3329.76 - 6480.90i) q^{87} +1897.73 q^{88} -9270.57i q^{89} +(-4228.58 + 5903.47i) q^{90} -11094.8 q^{91} +1005.29i q^{92} +(11773.8 - 6049.16i) q^{93} -20951.8 q^{94} -4262.24i q^{95} +(-6029.78 - 11736.1i) q^{96} -16911.4 q^{97} -187.820i q^{98} +(-8164.45 - 5848.10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.88235i 1.47059i −0.677749 0.735294i \(-0.737044\pi\)
0.677749 0.735294i \(-0.262956\pi\)
\(3\) −8.00524 + 4.11293i −0.889471 + 0.456992i
\(4\) −18.6020 −1.16263
\(5\) 15.2405i 0.609622i −0.952413 0.304811i \(-0.901407\pi\)
0.952413 0.304811i \(-0.0985933\pi\)
\(6\) 24.1937 + 47.0896i 0.672047 + 1.30804i
\(7\) 49.3247 1.00663 0.503314 0.864104i \(-0.332114\pi\)
0.503314 + 0.864104i \(0.332114\pi\)
\(8\) 15.3061i 0.239158i
\(9\) 47.1676 65.8500i 0.582316 0.812963i
\(10\) −89.6502 −0.896502
\(11\) 123.986i 1.02467i −0.858784 0.512337i \(-0.828780\pi\)
0.858784 0.512337i \(-0.171220\pi\)
\(12\) 148.914 76.5089i 1.03412 0.531312i
\(13\) −224.934 −1.33097 −0.665485 0.746411i \(-0.731775\pi\)
−0.665485 + 0.746411i \(0.731775\pi\)
\(14\) 290.145i 1.48033i
\(15\) 62.6833 + 122.004i 0.278593 + 0.542241i
\(16\) −207.597 −0.810925
\(17\) 169.629i 0.586950i −0.955967 0.293475i \(-0.905188\pi\)
0.955967 0.293475i \(-0.0948117\pi\)
\(18\) −387.353 277.456i −1.19553 0.856346i
\(19\) 279.664 0.774693 0.387347 0.921934i \(-0.373392\pi\)
0.387347 + 0.921934i \(0.373392\pi\)
\(20\) 283.505i 0.708763i
\(21\) −394.856 + 202.869i −0.895365 + 0.460021i
\(22\) −729.327 −1.50687
\(23\) 54.0419i 0.102159i −0.998695 0.0510793i \(-0.983734\pi\)
0.998695 0.0510793i \(-0.0162661\pi\)
\(24\) −62.9529 122.529i −0.109293 0.212724i
\(25\) 392.726 0.628361
\(26\) 1323.14i 1.95731i
\(27\) −106.751 + 721.142i −0.146435 + 0.989220i
\(28\) −917.541 −1.17033
\(29\) 809.583i 0.962643i 0.876544 + 0.481322i \(0.159843\pi\)
−0.876544 + 0.481322i \(0.840157\pi\)
\(30\) 717.671 368.725i 0.797412 0.409695i
\(31\) −1470.77 −1.53045 −0.765226 0.643761i \(-0.777373\pi\)
−0.765226 + 0.643761i \(0.777373\pi\)
\(32\) 1466.05i 1.43169i
\(33\) 509.944 + 992.534i 0.468268 + 0.911418i
\(34\) −997.814 −0.863161
\(35\) 751.736i 0.613662i
\(36\) −877.413 + 1224.94i −0.677016 + 0.945173i
\(37\) −139.391 −0.101820 −0.0509098 0.998703i \(-0.516212\pi\)
−0.0509098 + 0.998703i \(0.516212\pi\)
\(38\) 1645.08i 1.13925i
\(39\) 1800.65 925.138i 1.18386 0.608243i
\(40\) 233.273 0.145796
\(41\) 769.777i 0.457928i 0.973435 + 0.228964i \(0.0735338\pi\)
−0.973435 + 0.228964i \(0.926466\pi\)
\(42\) 1193.35 + 2322.68i 0.676501 + 1.31671i
\(43\) −2761.82 −1.49368 −0.746841 0.665003i \(-0.768430\pi\)
−0.746841 + 0.665003i \(0.768430\pi\)
\(44\) 2306.38i 1.19131i
\(45\) −1003.59 718.860i −0.495600 0.354992i
\(46\) −317.893 −0.150233
\(47\) 3561.82i 1.61241i −0.591635 0.806206i \(-0.701518\pi\)
0.591635 0.806206i \(-0.298482\pi\)
\(48\) 1661.86 853.832i 0.721294 0.370587i
\(49\) 31.9294 0.0132984
\(50\) 2310.15i 0.924060i
\(51\) 697.671 + 1357.92i 0.268232 + 0.522075i
\(52\) 4184.23 1.54742
\(53\) 2805.15i 0.998629i 0.866421 + 0.499314i \(0.166415\pi\)
−0.866421 + 0.499314i \(0.833585\pi\)
\(54\) 4242.01 + 627.947i 1.45473 + 0.215345i
\(55\) −1889.61 −0.624664
\(56\) 754.969i 0.240743i
\(57\) −2238.78 + 1150.24i −0.689067 + 0.354029i
\(58\) 4762.25 1.41565
\(59\) 453.188i 0.130189i
\(60\) −1166.04 2269.53i −0.323899 0.630424i
\(61\) −5104.03 −1.37168 −0.685841 0.727752i \(-0.740565\pi\)
−0.685841 + 0.727752i \(0.740565\pi\)
\(62\) 8651.55i 2.25066i
\(63\) 2326.53 3248.03i 0.586175 0.818350i
\(64\) 5302.30 1.29451
\(65\) 3428.12i 0.811389i
\(66\) 5838.43 2999.67i 1.34032 0.688630i
\(67\) −2153.50 −0.479728 −0.239864 0.970806i \(-0.577103\pi\)
−0.239864 + 0.970806i \(0.577103\pi\)
\(68\) 3155.44i 0.682404i
\(69\) 222.271 + 432.618i 0.0466857 + 0.0908670i
\(70\) −4421.97 −0.902444
\(71\) 2285.42i 0.453366i 0.973969 + 0.226683i \(0.0727881\pi\)
−0.973969 + 0.226683i \(0.927212\pi\)
\(72\) 1007.91 + 721.951i 0.194426 + 0.139265i
\(73\) 7254.81 1.36138 0.680691 0.732570i \(-0.261680\pi\)
0.680691 + 0.732570i \(0.261680\pi\)
\(74\) 819.947i 0.149735i
\(75\) −3143.86 + 1615.25i −0.558909 + 0.287156i
\(76\) −5202.32 −0.900679
\(77\) 6115.56i 1.03146i
\(78\) −5441.99 10592.0i −0.894475 1.74097i
\(79\) 1082.58 0.173462 0.0867311 0.996232i \(-0.472358\pi\)
0.0867311 + 0.996232i \(0.472358\pi\)
\(80\) 3163.89i 0.494358i
\(81\) −2111.44 6211.97i −0.321817 0.946802i
\(82\) 4528.10 0.673423
\(83\) 1104.74i 0.160363i −0.996780 0.0801815i \(-0.974450\pi\)
0.996780 0.0801815i \(-0.0255500\pi\)
\(84\) 7345.13 3773.78i 1.04098 0.534833i
\(85\) −2585.23 −0.357818
\(86\) 16246.0i 2.19659i
\(87\) −3329.76 6480.90i −0.439921 0.856243i
\(88\) 1897.73 0.245059
\(89\) 9270.57i 1.17038i −0.810897 0.585189i \(-0.801020\pi\)
0.810897 0.585189i \(-0.198980\pi\)
\(90\) −4228.58 + 5903.47i −0.522047 + 0.728823i
\(91\) −11094.8 −1.33979
\(92\) 1005.29i 0.118772i
\(93\) 11773.8 6049.16i 1.36129 0.699405i
\(94\) −20951.8 −2.37119
\(95\) 4262.24i 0.472270i
\(96\) −6029.78 11736.1i −0.654273 1.27345i
\(97\) −16911.4 −1.79736 −0.898682 0.438601i \(-0.855474\pi\)
−0.898682 + 0.438601i \(0.855474\pi\)
\(98\) 187.820i 0.0195564i
\(99\) −8164.45 5848.10i −0.833022 0.596684i
\(100\) −7305.50 −0.730550
\(101\) 17354.8i 1.70128i −0.525746 0.850642i \(-0.676214\pi\)
0.525746 0.850642i \(-0.323786\pi\)
\(102\) 7987.74 4103.94i 0.767757 0.394458i
\(103\) 7492.43 0.706233 0.353117 0.935579i \(-0.385122\pi\)
0.353117 + 0.935579i \(0.385122\pi\)
\(104\) 3442.86i 0.318312i
\(105\) 3091.84 + 6017.82i 0.280439 + 0.545834i
\(106\) 16500.9 1.46857
\(107\) 9844.86i 0.859888i 0.902856 + 0.429944i \(0.141467\pi\)
−0.902856 + 0.429944i \(0.858533\pi\)
\(108\) 1985.79 13414.7i 0.170249 1.15009i
\(109\) 16924.3 1.42448 0.712240 0.701936i \(-0.247681\pi\)
0.712240 + 0.701936i \(0.247681\pi\)
\(110\) 11115.3i 0.918623i
\(111\) 1115.86 573.306i 0.0905656 0.0465308i
\(112\) −10239.7 −0.816299
\(113\) 11770.3i 0.921790i −0.887455 0.460895i \(-0.847528\pi\)
0.887455 0.460895i \(-0.152472\pi\)
\(114\) 6766.11 + 13169.3i 0.520630 + 1.01333i
\(115\) −823.628 −0.0622781
\(116\) 15059.9i 1.11920i
\(117\) −10609.6 + 14811.9i −0.775045 + 1.08203i
\(118\) 2665.81 0.191454
\(119\) 8366.88i 0.590840i
\(120\) −1867.41 + 959.437i −0.129681 + 0.0666276i
\(121\) −731.424 −0.0499572
\(122\) 30023.7i 2.01718i
\(123\) −3166.04 6162.25i −0.209270 0.407314i
\(124\) 27359.2 1.77935
\(125\) 15510.7i 0.992685i
\(126\) −19106.1 13685.5i −1.20346 0.862021i
\(127\) −7280.12 −0.451369 −0.225684 0.974200i \(-0.572462\pi\)
−0.225684 + 0.974200i \(0.572462\pi\)
\(128\) 7733.09i 0.471990i
\(129\) 22109.0 11359.2i 1.32859 0.682601i
\(130\) 20165.4 1.19322
\(131\) 2963.72i 0.172701i −0.996265 0.0863504i \(-0.972480\pi\)
0.996265 0.0863504i \(-0.0275205\pi\)
\(132\) −9486.00 18463.1i −0.544422 1.05964i
\(133\) 13794.4 0.779827
\(134\) 12667.6i 0.705483i
\(135\) 10990.6 + 1626.94i 0.603050 + 0.0892699i
\(136\) 2596.35 0.140374
\(137\) 10193.5i 0.543103i 0.962424 + 0.271552i \(0.0875368\pi\)
−0.962424 + 0.271552i \(0.912463\pi\)
\(138\) 2544.81 1307.47i 0.133628 0.0686554i
\(139\) −3129.37 −0.161967 −0.0809836 0.996715i \(-0.525806\pi\)
−0.0809836 + 0.996715i \(0.525806\pi\)
\(140\) 13983.8i 0.713460i
\(141\) 14649.5 + 28513.2i 0.736860 + 1.43419i
\(142\) 13443.6 0.666714
\(143\) 27888.6i 1.36381i
\(144\) −9791.84 + 13670.2i −0.472214 + 0.659252i
\(145\) 12338.5 0.586848
\(146\) 42675.3i 2.00203i
\(147\) −255.603 + 131.324i −0.0118285 + 0.00607726i
\(148\) 2592.96 0.118378
\(149\) 14798.2i 0.666555i 0.942829 + 0.333278i \(0.108155\pi\)
−0.942829 + 0.333278i \(0.891845\pi\)
\(150\) 9501.49 + 18493.3i 0.422288 + 0.821924i
\(151\) 17621.0 0.772819 0.386409 0.922327i \(-0.373715\pi\)
0.386409 + 0.922327i \(0.373715\pi\)
\(152\) 4280.57i 0.185274i
\(153\) −11170.0 8000.97i −0.477168 0.341790i
\(154\) −35973.8 −1.51686
\(155\) 22415.3i 0.932998i
\(156\) −33495.7 + 17209.5i −1.37639 + 0.707160i
\(157\) 25777.4 1.04578 0.522889 0.852401i \(-0.324854\pi\)
0.522889 + 0.852401i \(0.324854\pi\)
\(158\) 6368.10i 0.255091i
\(159\) −11537.4 22455.9i −0.456366 0.888251i
\(160\) 22343.5 0.872792
\(161\) 2665.60i 0.102836i
\(162\) −36541.0 + 12420.2i −1.39236 + 0.473260i
\(163\) −17420.6 −0.655675 −0.327837 0.944734i \(-0.606320\pi\)
−0.327837 + 0.944734i \(0.606320\pi\)
\(164\) 14319.4i 0.532400i
\(165\) 15126.8 7771.83i 0.555620 0.285467i
\(166\) −6498.47 −0.235828
\(167\) 35985.0i 1.29029i −0.764058 0.645147i \(-0.776796\pi\)
0.764058 0.645147i \(-0.223204\pi\)
\(168\) −3105.14 6043.70i −0.110018 0.214134i
\(169\) 22034.3 0.771481
\(170\) 15207.2i 0.526202i
\(171\) 13191.1 18415.9i 0.451116 0.629797i
\(172\) 51375.4 1.73660
\(173\) 26606.6i 0.888991i −0.895781 0.444495i \(-0.853383\pi\)
0.895781 0.444495i \(-0.146617\pi\)
\(174\) −38122.9 + 19586.8i −1.25918 + 0.646942i
\(175\) 19371.1 0.632525
\(176\) 25739.0i 0.830934i
\(177\) −1863.93 3627.87i −0.0594954 0.115799i
\(178\) −54532.7 −1.72114
\(179\) 40762.9i 1.27221i 0.771602 + 0.636106i \(0.219456\pi\)
−0.771602 + 0.636106i \(0.780544\pi\)
\(180\) 18668.8 + 13372.3i 0.576198 + 0.412724i
\(181\) 33129.4 1.01124 0.505622 0.862755i \(-0.331263\pi\)
0.505622 + 0.862755i \(0.331263\pi\)
\(182\) 65263.5i 1.97028i
\(183\) 40858.9 20992.5i 1.22007 0.626848i
\(184\) 827.170 0.0244320
\(185\) 2124.40i 0.0620715i
\(186\) −35583.3 69257.7i −1.02854 2.00190i
\(187\) −21031.5 −0.601433
\(188\) 66257.0i 1.87463i
\(189\) −5265.47 + 35570.1i −0.147405 + 0.995776i
\(190\) −25072.0 −0.694514
\(191\) 14106.1i 0.386671i −0.981133 0.193335i \(-0.938069\pi\)
0.981133 0.193335i \(-0.0619306\pi\)
\(192\) −42446.1 + 21808.0i −1.15142 + 0.591579i
\(193\) −22117.2 −0.593766 −0.296883 0.954914i \(-0.595947\pi\)
−0.296883 + 0.954914i \(0.595947\pi\)
\(194\) 99478.7i 2.64318i
\(195\) −14099.6 27442.9i −0.370798 0.721706i
\(196\) −593.952 −0.0154611
\(197\) 32991.9i 0.850109i −0.905168 0.425055i \(-0.860255\pi\)
0.905168 0.425055i \(-0.139745\pi\)
\(198\) −34400.6 + 48026.1i −0.877476 + 1.22503i
\(199\) 43534.9 1.09934 0.549669 0.835383i \(-0.314754\pi\)
0.549669 + 0.835383i \(0.314754\pi\)
\(200\) 6011.10i 0.150277i
\(201\) 17239.3 8857.20i 0.426704 0.219232i
\(202\) −102087. −2.50189
\(203\) 39932.5i 0.969023i
\(204\) −12978.1 25260.0i −0.311854 0.606978i
\(205\) 11731.8 0.279163
\(206\) 44073.1i 1.03858i
\(207\) −3558.66 2549.02i −0.0830511 0.0594885i
\(208\) 46695.6 1.07932
\(209\) 34674.3i 0.793808i
\(210\) 35398.9 18187.3i 0.802697 0.412410i
\(211\) −28026.5 −0.629511 −0.314756 0.949173i \(-0.601923\pi\)
−0.314756 + 0.949173i \(0.601923\pi\)
\(212\) 52181.5i 1.16103i
\(213\) −9399.76 18295.3i −0.207185 0.403255i
\(214\) 57910.9 1.26454
\(215\) 42091.6i 0.910581i
\(216\) −11037.9 1633.94i −0.236580 0.0350210i
\(217\) −72545.1 −1.54060
\(218\) 99554.4i 2.09482i
\(219\) −58076.4 + 29838.5i −1.21091 + 0.622142i
\(220\) 35150.6 0.726251
\(221\) 38155.2i 0.781213i
\(222\) −3372.39 6563.87i −0.0684276 0.133185i
\(223\) −87492.3 −1.75938 −0.879691 0.475547i \(-0.842250\pi\)
−0.879691 + 0.475547i \(0.842250\pi\)
\(224\) 72312.7i 1.44118i
\(225\) 18523.9 25861.0i 0.365905 0.510834i
\(226\) −69237.3 −1.35557
\(227\) 49341.9i 0.957556i −0.877936 0.478778i \(-0.841080\pi\)
0.877936 0.478778i \(-0.158920\pi\)
\(228\) 41645.8 21396.8i 0.801128 0.411604i
\(229\) −17223.7 −0.328440 −0.164220 0.986424i \(-0.552511\pi\)
−0.164220 + 0.986424i \(0.552511\pi\)
\(230\) 4844.87i 0.0915854i
\(231\) 25152.9 + 48956.5i 0.471372 + 0.917458i
\(232\) −12391.6 −0.230224
\(233\) 64426.6i 1.18673i −0.804932 0.593367i \(-0.797798\pi\)
0.804932 0.593367i \(-0.202202\pi\)
\(234\) 87128.7 + 62409.3i 1.59122 + 1.13977i
\(235\) −54284.0 −0.982961
\(236\) 8430.21i 0.151361i
\(237\) −8666.28 + 4452.57i −0.154289 + 0.0792709i
\(238\) −49216.9 −0.868882
\(239\) 39148.1i 0.685353i −0.939453 0.342677i \(-0.888666\pi\)
0.939453 0.342677i \(-0.111334\pi\)
\(240\) −13012.9 25327.7i −0.225918 0.439717i
\(241\) 48214.2 0.830120 0.415060 0.909794i \(-0.363761\pi\)
0.415060 + 0.909794i \(0.363761\pi\)
\(242\) 4302.49i 0.0734665i
\(243\) 42452.0 + 41044.1i 0.718928 + 0.695085i
\(244\) 94945.3 1.59475
\(245\) 486.622i 0.00810699i
\(246\) −36248.5 + 18623.8i −0.598990 + 0.307749i
\(247\) −62906.0 −1.03109
\(248\) 22511.7i 0.366020i
\(249\) 4543.72 + 8843.71i 0.0732847 + 0.142638i
\(250\) −91239.3 −1.45983
\(251\) 116271.i 1.84553i 0.385358 + 0.922767i \(0.374078\pi\)
−0.385358 + 0.922767i \(0.625922\pi\)
\(252\) −43278.2 + 60420.0i −0.681503 + 0.951437i
\(253\) −6700.41 −0.104679
\(254\) 42824.2i 0.663777i
\(255\) 20695.4 10632.9i 0.318268 0.163520i
\(256\) 39348.0 0.600403
\(257\) 94140.4i 1.42531i −0.701514 0.712656i \(-0.747492\pi\)
0.701514 0.712656i \(-0.252508\pi\)
\(258\) −66818.6 130053.i −1.00383 1.95380i
\(259\) −6875.43 −0.102494
\(260\) 63769.9i 0.943342i
\(261\) 53311.0 + 38186.1i 0.782593 + 0.560562i
\(262\) −17433.6 −0.253972
\(263\) 28118.8i 0.406524i 0.979124 + 0.203262i \(0.0651543\pi\)
−0.979124 + 0.203262i \(0.934846\pi\)
\(264\) −15191.8 + 7805.25i −0.217973 + 0.111990i
\(265\) 42752.0 0.608786
\(266\) 81143.3i 1.14680i
\(267\) 38129.2 + 74213.1i 0.534854 + 1.04102i
\(268\) 40059.5 0.557745
\(269\) 34585.5i 0.477958i 0.971025 + 0.238979i \(0.0768128\pi\)
−0.971025 + 0.238979i \(0.923187\pi\)
\(270\) 9570.26 64650.5i 0.131279 0.886838i
\(271\) 11725.0 0.159651 0.0798257 0.996809i \(-0.474564\pi\)
0.0798257 + 0.996809i \(0.474564\pi\)
\(272\) 35214.3i 0.475972i
\(273\) 88816.5 45632.2i 1.19170 0.612274i
\(274\) 59961.8 0.798681
\(275\) 48692.3i 0.643865i
\(276\) −4134.69 8047.58i −0.0542781 0.105644i
\(277\) 33960.1 0.442599 0.221299 0.975206i \(-0.428970\pi\)
0.221299 + 0.975206i \(0.428970\pi\)
\(278\) 18408.0i 0.238187i
\(279\) −69372.4 + 96849.8i −0.891207 + 1.24420i
\(280\) 11506.1 0.146762
\(281\) 62954.1i 0.797280i −0.917107 0.398640i \(-0.869482\pi\)
0.917107 0.398640i \(-0.130518\pi\)
\(282\) 167724. 86173.5i 2.10911 1.08362i
\(283\) 128582. 1.60549 0.802743 0.596325i \(-0.203373\pi\)
0.802743 + 0.596325i \(0.203373\pi\)
\(284\) 42513.4i 0.527095i
\(285\) 17530.3 + 34120.2i 0.215824 + 0.420070i
\(286\) 164050. 2.00560
\(287\) 37969.1i 0.460963i
\(288\) 96539.7 + 69150.2i 1.16391 + 0.833698i
\(289\) 54747.2 0.655490
\(290\) 72579.3i 0.863012i
\(291\) 135380. 69555.4i 1.59870 0.821382i
\(292\) −134954. −1.58278
\(293\) 138140.i 1.60911i −0.593881 0.804553i \(-0.702405\pi\)
0.593881 0.804553i \(-0.297595\pi\)
\(294\) 772.491 + 1503.54i 0.00893715 + 0.0173949i
\(295\) 6906.83 0.0793660
\(296\) 2133.53i 0.0243510i
\(297\) 89411.2 + 13235.6i 1.01363 + 0.150048i
\(298\) 87048.1 0.980227
\(299\) 12155.9i 0.135970i
\(300\) 58482.2 30047.0i 0.649803 0.333856i
\(301\) −136226. −1.50358
\(302\) 103653.i 1.13650i
\(303\) 71379.1 + 138929.i 0.777474 + 1.51324i
\(304\) −58057.4 −0.628218
\(305\) 77788.1i 0.836207i
\(306\) −47064.5 + 65706.1i −0.502632 + 0.701718i
\(307\) −77433.6 −0.821586 −0.410793 0.911729i \(-0.634748\pi\)
−0.410793 + 0.911729i \(0.634748\pi\)
\(308\) 113762.i 1.19921i
\(309\) −59978.6 + 30815.8i −0.628174 + 0.322743i
\(310\) 131854. 1.37205
\(311\) 139256.i 1.43977i −0.694095 0.719884i \(-0.744195\pi\)
0.694095 0.719884i \(-0.255805\pi\)
\(312\) 14160.2 + 27560.9i 0.145466 + 0.283129i
\(313\) −66882.1 −0.682687 −0.341343 0.939939i \(-0.610882\pi\)
−0.341343 + 0.939939i \(0.610882\pi\)
\(314\) 151632.i 1.53791i
\(315\) −49501.8 35457.6i −0.498884 0.357345i
\(316\) −20138.1 −0.201672
\(317\) 111320.i 1.10779i 0.832588 + 0.553893i \(0.186858\pi\)
−0.832588 + 0.553893i \(0.813142\pi\)
\(318\) −132093. + 67866.9i −1.30625 + 0.671126i
\(319\) 100377. 0.986396
\(320\) 80809.9i 0.789159i
\(321\) −40491.2 78810.4i −0.392962 0.764845i
\(322\) −15680.0 −0.151229
\(323\) 47439.0i 0.454706i
\(324\) 39277.1 + 115555.i 0.374153 + 1.10078i
\(325\) −88337.3 −0.836330
\(326\) 102474.i 0.964227i
\(327\) −135483. + 69608.3i −1.26703 + 0.650977i
\(328\) −11782.3 −0.109517
\(329\) 175686.i 1.62310i
\(330\) −45716.6 88980.9i −0.419804 0.817088i
\(331\) −139163. −1.27019 −0.635093 0.772436i \(-0.719038\pi\)
−0.635093 + 0.772436i \(0.719038\pi\)
\(332\) 20550.4i 0.186442i
\(333\) −6574.74 + 9178.90i −0.0592912 + 0.0827756i
\(334\) −211676. −1.89749
\(335\) 32820.5i 0.292453i
\(336\) 81970.9 42115.0i 0.726074 0.373043i
\(337\) −138854. −1.22264 −0.611318 0.791385i \(-0.709360\pi\)
−0.611318 + 0.791385i \(0.709360\pi\)
\(338\) 129613.i 1.13453i
\(339\) 48410.6 + 94224.3i 0.421251 + 0.819905i
\(340\) 48090.6 0.416009
\(341\) 182354.i 1.56822i
\(342\) −108329. 77594.6i −0.926171 0.663406i
\(343\) −116854. −0.993241
\(344\) 42272.6i 0.357226i
\(345\) 6593.33 3387.53i 0.0553945 0.0284606i
\(346\) −156509. −1.30734
\(347\) 149932.i 1.24519i 0.782543 + 0.622596i \(0.213922\pi\)
−0.782543 + 0.622596i \(0.786078\pi\)
\(348\) 61940.3 + 120558.i 0.511464 + 0.995491i
\(349\) 138433. 1.13655 0.568275 0.822839i \(-0.307611\pi\)
0.568275 + 0.822839i \(0.307611\pi\)
\(350\) 113948.i 0.930184i
\(351\) 24011.9 162209.i 0.194900 1.31662i
\(352\) 181770. 1.46702
\(353\) 122883.i 0.986152i −0.869986 0.493076i \(-0.835872\pi\)
0.869986 0.493076i \(-0.164128\pi\)
\(354\) −21340.4 + 10964.3i −0.170293 + 0.0874931i
\(355\) 34831.0 0.276382
\(356\) 172451.i 1.36071i
\(357\) 34412.4 + 66978.9i 0.270009 + 0.525535i
\(358\) 239782. 1.87090
\(359\) 56279.8i 0.436681i −0.975873 0.218340i \(-0.929936\pi\)
0.975873 0.218340i \(-0.0700643\pi\)
\(360\) 11002.9 15361.0i 0.0848992 0.118527i
\(361\) −52108.9 −0.399851
\(362\) 194879.i 1.48712i
\(363\) 5855.22 3008.30i 0.0444355 0.0228301i
\(364\) 206386. 1.55768
\(365\) 110567.i 0.829929i
\(366\) −123485. 240346.i −0.921835 1.79422i
\(367\) −116381. −0.864070 −0.432035 0.901857i \(-0.642204\pi\)
−0.432035 + 0.901857i \(0.642204\pi\)
\(368\) 11218.9i 0.0828429i
\(369\) 50689.8 + 36308.5i 0.372279 + 0.266659i
\(370\) 12496.4 0.0912815
\(371\) 138363.i 1.00525i
\(372\) −219017. + 112527.i −1.58268 + 0.813148i
\(373\) 57582.7 0.413880 0.206940 0.978354i \(-0.433650\pi\)
0.206940 + 0.978354i \(0.433650\pi\)
\(374\) 123715.i 0.884459i
\(375\) 63794.4 + 124167.i 0.453649 + 0.882964i
\(376\) 54517.5 0.385621
\(377\) 182103.i 1.28125i
\(378\) 209236. + 30973.3i 1.46438 + 0.216772i
\(379\) −225636. −1.57083 −0.785417 0.618967i \(-0.787552\pi\)
−0.785417 + 0.618967i \(0.787552\pi\)
\(380\) 79286.3i 0.549074i
\(381\) 58279.1 29942.7i 0.401479 0.206272i
\(382\) −82977.3 −0.568633
\(383\) 37591.3i 0.256265i −0.991757 0.128133i \(-0.959102\pi\)
0.991757 0.128133i \(-0.0408983\pi\)
\(384\) 31805.7 + 61905.2i 0.215696 + 0.419821i
\(385\) −93204.4 −0.628804
\(386\) 130101.i 0.873184i
\(387\) −130268. + 181866.i −0.869795 + 1.21431i
\(388\) 314586. 2.08966
\(389\) 151832.i 1.00338i −0.865048 0.501689i \(-0.832712\pi\)
0.865048 0.501689i \(-0.167288\pi\)
\(390\) −161429. + 82938.8i −1.06133 + 0.545292i
\(391\) −9167.05 −0.0599620
\(392\) 488.715i 0.00318041i
\(393\) 12189.6 + 23725.3i 0.0789229 + 0.153612i
\(394\) −194070. −1.25016
\(395\) 16499.1i 0.105746i
\(396\) 151875. + 108787.i 0.968494 + 0.693721i
\(397\) −283068. −1.79601 −0.898007 0.439980i \(-0.854985\pi\)
−0.898007 + 0.439980i \(0.854985\pi\)
\(398\) 256087.i 1.61667i
\(399\) −110427. + 56735.3i −0.693633 + 0.356375i
\(400\) −81528.6 −0.509554
\(401\) 50608.6i 0.314728i 0.987541 + 0.157364i \(0.0502996\pi\)
−0.987541 + 0.157364i \(0.949700\pi\)
\(402\) −52101.2 101407.i −0.322400 0.627506i
\(403\) 330825. 2.03699
\(404\) 322835.i 1.97796i
\(405\) −94673.8 + 32179.5i −0.577191 + 0.196187i
\(406\) 234897. 1.42503
\(407\) 17282.5i 0.104332i
\(408\) −20784.4 + 10678.6i −0.124858 + 0.0641497i
\(409\) 64475.9 0.385434 0.192717 0.981254i \(-0.438270\pi\)
0.192717 + 0.981254i \(0.438270\pi\)
\(410\) 69010.7i 0.410534i
\(411\) −41925.2 81601.4i −0.248194 0.483074i
\(412\) −139374. −0.821086
\(413\) 22353.4i 0.131052i
\(414\) −14994.3 + 20933.3i −0.0874831 + 0.122134i
\(415\) −16836.9 −0.0977608
\(416\) 329765.i 1.90554i
\(417\) 25051.3 12870.9i 0.144065 0.0740178i
\(418\) −203967. −1.16736
\(419\) 119804.i 0.682405i −0.939990 0.341202i \(-0.889166\pi\)
0.939990 0.341202i \(-0.110834\pi\)
\(420\) −57514.5 111944.i −0.326046 0.634602i
\(421\) 215727. 1.21714 0.608568 0.793501i \(-0.291744\pi\)
0.608568 + 0.793501i \(0.291744\pi\)
\(422\) 164861.i 0.925751i
\(423\) −234546. 168002.i −1.31083 0.938932i
\(424\) −42935.9 −0.238830
\(425\) 66617.5i 0.368817i
\(426\) −107619. + 55292.7i −0.593022 + 0.304683i
\(427\) −251755. −1.38077
\(428\) 183134.i 0.999729i
\(429\) −114704. 223255.i −0.623251 1.21307i
\(430\) 247598. 1.33909
\(431\) 113110.i 0.608899i −0.952529 0.304449i \(-0.901528\pi\)
0.952529 0.304449i \(-0.0984724\pi\)
\(432\) 22161.2 149707.i 0.118748 0.802183i
\(433\) 292137. 1.55816 0.779079 0.626926i \(-0.215687\pi\)
0.779079 + 0.626926i \(0.215687\pi\)
\(434\) 426736.i 2.26558i
\(435\) −98772.5 + 50747.4i −0.521984 + 0.268185i
\(436\) −314826. −1.65614
\(437\) 15113.6i 0.0791415i
\(438\) 175521. + 341626.i 0.914913 + 1.78075i
\(439\) 307872. 1.59750 0.798752 0.601661i \(-0.205494\pi\)
0.798752 + 0.601661i \(0.205494\pi\)
\(440\) 28922.5i 0.149393i
\(441\) 1506.03 2102.55i 0.00774386 0.0108111i
\(442\) 224442. 1.14884
\(443\) 173339.i 0.883259i 0.897198 + 0.441629i \(0.145599\pi\)
−0.897198 + 0.441629i \(0.854401\pi\)
\(444\) −20757.2 + 10664.7i −0.105294 + 0.0540980i
\(445\) −141289. −0.713488
\(446\) 514660.i 2.58732i
\(447\) −60863.9 118463.i −0.304611 0.592881i
\(448\) 261534. 1.30308
\(449\) 339199.i 1.68252i 0.540627 + 0.841262i \(0.318187\pi\)
−0.540627 + 0.841262i \(0.681813\pi\)
\(450\) −152123. 108964.i −0.751226 0.538095i
\(451\) 95441.3 0.469227
\(452\) 218952.i 1.07170i
\(453\) −141061. + 72474.2i −0.687400 + 0.353172i
\(454\) −290246. −1.40817
\(455\) 169091.i 0.816766i
\(456\) −17605.7 34266.9i −0.0846687 0.164796i
\(457\) 242846. 1.16278 0.581392 0.813624i \(-0.302508\pi\)
0.581392 + 0.813624i \(0.302508\pi\)
\(458\) 101316.i 0.482999i
\(459\) 122326. + 18108.0i 0.580623 + 0.0859500i
\(460\) 15321.2 0.0724062
\(461\) 51850.3i 0.243977i 0.992532 + 0.121989i \(0.0389271\pi\)
−0.992532 + 0.121989i \(0.961073\pi\)
\(462\) 287979. 147958.i 1.34920 0.693193i
\(463\) −95951.7 −0.447600 −0.223800 0.974635i \(-0.571846\pi\)
−0.223800 + 0.974635i \(0.571846\pi\)
\(464\) 168067.i 0.780631i
\(465\) −92192.5 179439.i −0.426373 0.829874i
\(466\) −378980. −1.74520
\(467\) 392363.i 1.79910i −0.436822 0.899548i \(-0.643896\pi\)
0.436822 0.899548i \(-0.356104\pi\)
\(468\) 197360. 275531.i 0.901088 1.25800i
\(469\) −106221. −0.482908
\(470\) 319318.i 1.44553i
\(471\) −206354. + 106021.i −0.930189 + 0.477913i
\(472\) −6936.53 −0.0311357
\(473\) 342426.i 1.53054i
\(474\) 26191.6 + 50978.1i 0.116575 + 0.226896i
\(475\) 109831. 0.486787
\(476\) 155641.i 0.686927i
\(477\) 184719. + 132312.i 0.811848 + 0.581517i
\(478\) −230283. −1.00787
\(479\) 66939.6i 0.291751i 0.989303 + 0.145875i \(0.0465998\pi\)
−0.989303 + 0.145875i \(0.953400\pi\)
\(480\) −178865. + 91897.2i −0.776323 + 0.398859i
\(481\) 31353.8 0.135519
\(482\) 283613.i 1.22076i
\(483\) 10963.4 + 21338.8i 0.0469951 + 0.0914692i
\(484\) 13606.0 0.0580816
\(485\) 257739.i 1.09571i
\(486\) 241435. 249717.i 1.02218 1.05725i
\(487\) −217260. −0.916056 −0.458028 0.888938i \(-0.651444\pi\)
−0.458028 + 0.888938i \(0.651444\pi\)
\(488\) 78122.7i 0.328048i
\(489\) 139456. 71649.8i 0.583203 0.299638i
\(490\) −2862.48 −0.0119220
\(491\) 87207.2i 0.361734i 0.983508 + 0.180867i \(0.0578903\pi\)
−0.983508 + 0.180867i \(0.942110\pi\)
\(492\) 58894.8 + 114630.i 0.243303 + 0.473554i
\(493\) 137328. 0.565023
\(494\) 370035.i 1.51631i
\(495\) −89128.2 + 124431.i −0.363752 + 0.507828i
\(496\) 305326. 1.24108
\(497\) 112728.i 0.456370i
\(498\) 52021.8 26727.8i 0.209762 0.107772i
\(499\) 227429. 0.913367 0.456683 0.889629i \(-0.349037\pi\)
0.456683 + 0.889629i \(0.349037\pi\)
\(500\) 288531.i 1.15412i
\(501\) 148004. + 288068.i 0.589655 + 1.14768i
\(502\) 683944. 2.71402
\(503\) 13528.5i 0.0534705i −0.999643 0.0267352i \(-0.991489\pi\)
0.999643 0.0267352i \(-0.00851111\pi\)
\(504\) 49714.7 + 35610.1i 0.195715 + 0.140188i
\(505\) −264497. −1.03714
\(506\) 39414.2i 0.153940i
\(507\) −176390. + 90625.5i −0.686210 + 0.352561i
\(508\) 135425. 0.524773
\(509\) 429673.i 1.65845i −0.558915 0.829225i \(-0.688782\pi\)
0.558915 0.829225i \(-0.311218\pi\)
\(510\) −62546.3 121738.i −0.240470 0.468041i
\(511\) 357841. 1.37040
\(512\) 355188.i 1.35494i
\(513\) −29854.4 + 201677.i −0.113442 + 0.766342i
\(514\) −553767. −2.09605
\(515\) 114189.i 0.430535i
\(516\) −411273. + 211304.i −1.54465 + 0.793611i
\(517\) −441614. −1.65220
\(518\) 40443.7i 0.150727i
\(519\) 109431. + 212992.i 0.406262 + 0.790731i
\(520\) −52471.1 −0.194050
\(521\) 263423.i 0.970460i 0.874387 + 0.485230i \(0.161264\pi\)
−0.874387 + 0.485230i \(0.838736\pi\)
\(522\) 224624. 313594.i 0.824356 1.15087i
\(523\) 141318. 0.516647 0.258324 0.966058i \(-0.416830\pi\)
0.258324 + 0.966058i \(0.416830\pi\)
\(524\) 55131.2i 0.200787i
\(525\) −155070. + 79672.0i −0.562613 + 0.289059i
\(526\) 165405. 0.597829
\(527\) 249484.i 0.898299i
\(528\) −105863. 206047.i −0.379731 0.739091i
\(529\) 276920. 0.989564
\(530\) 251482.i 0.895273i
\(531\) 29842.4 + 21375.8i 0.105839 + 0.0758111i
\(532\) −256603. −0.906648
\(533\) 173149.i 0.609489i
\(534\) 436547. 224289.i 1.53091 0.786550i
\(535\) 150041. 0.524206
\(536\) 32961.7i 0.114731i
\(537\) −167655. 326317.i −0.581391 1.13159i
\(538\) 203444. 0.702880
\(539\) 3958.79i 0.0136265i
\(540\) −204447. 30264.5i −0.701123 0.103788i
\(541\) −142028. −0.485267 −0.242633 0.970118i \(-0.578011\pi\)
−0.242633 + 0.970118i \(0.578011\pi\)
\(542\) 68970.3i 0.234781i
\(543\) −265208. + 136259.i −0.899472 + 0.462131i
\(544\) 248685. 0.840333
\(545\) 257935.i 0.868394i
\(546\) −268424. 522450.i −0.900403 1.75251i
\(547\) 53779.5 0.179739 0.0898694 0.995954i \(-0.471355\pi\)
0.0898694 + 0.995954i \(0.471355\pi\)
\(548\) 189620.i 0.631427i
\(549\) −240745. + 336100.i −0.798752 + 1.11513i
\(550\) −286425. −0.946860
\(551\) 226411.i 0.745753i
\(552\) −6621.69 + 3402.09i −0.0217316 + 0.0111652i
\(553\) 53397.8 0.174612
\(554\) 199765.i 0.650880i
\(555\) −8737.50 17006.3i −0.0283662 0.0552108i
\(556\) 58212.7 0.188308
\(557\) 450810.i 1.45306i −0.687135 0.726530i \(-0.741132\pi\)
0.687135 0.726530i \(-0.258868\pi\)
\(558\) 569705. + 408073.i 1.82971 + 1.31060i
\(559\) 621227. 1.98805
\(560\) 156058.i 0.497634i
\(561\) 168362. 86501.1i 0.534957 0.274850i
\(562\) −370318. −1.17247
\(563\) 104734.i 0.330425i −0.986258 0.165212i \(-0.947169\pi\)
0.986258 0.165212i \(-0.0528309\pi\)
\(564\) −272511. 530403.i −0.856693 1.66743i
\(565\) −179386. −0.561944
\(566\) 756363.i 2.36101i
\(567\) −104146. 306404.i −0.323949 0.953077i
\(568\) −34980.8 −0.108426
\(569\) 226042.i 0.698174i 0.937090 + 0.349087i \(0.113508\pi\)
−0.937090 + 0.349087i \(0.886492\pi\)
\(570\) 200707. 103119.i 0.617750 0.317388i
\(571\) 234488. 0.719199 0.359599 0.933107i \(-0.382913\pi\)
0.359599 + 0.933107i \(0.382913\pi\)
\(572\) 518784.i 1.58560i
\(573\) 58017.6 + 112923.i 0.176706 + 0.343932i
\(574\) 223347. 0.677886
\(575\) 21223.6i 0.0641925i
\(576\) 250096. 349156.i 0.753811 1.05239i
\(577\) 511742. 1.53709 0.768545 0.639795i \(-0.220981\pi\)
0.768545 + 0.639795i \(0.220981\pi\)
\(578\) 322042.i 0.963955i
\(579\) 177053. 90966.5i 0.528137 0.271346i
\(580\) −229521. −0.682286
\(581\) 54491.0i 0.161426i
\(582\) −409149. 796351.i −1.20791 2.35103i
\(583\) 347798. 1.02327
\(584\) 111043.i 0.325585i
\(585\) 225741. + 161696.i 0.659629 + 0.472484i
\(586\) −812588. −2.36633
\(587\) 280845.i 0.815061i −0.913192 0.407530i \(-0.866390\pi\)
0.913192 0.407530i \(-0.133610\pi\)
\(588\) 4754.73 2442.89i 0.0137522 0.00706559i
\(589\) −411320. −1.18563
\(590\) 40628.4i 0.116715i
\(591\) 135693. + 264108.i 0.388494 + 0.756147i
\(592\) 28937.1 0.0825681
\(593\) 20164.1i 0.0573415i 0.999589 + 0.0286708i \(0.00912743\pi\)
−0.999589 + 0.0286708i \(0.990873\pi\)
\(594\) 77856.4 525948.i 0.220659 1.49063i
\(595\) −127516. −0.360189
\(596\) 275276.i 0.774955i
\(597\) −348507. + 179056.i −0.977828 + 0.502389i
\(598\) 71505.0 0.199956
\(599\) 303956.i 0.847145i −0.905862 0.423572i \(-0.860776\pi\)
0.905862 0.423572i \(-0.139224\pi\)
\(600\) −24723.2 48120.2i −0.0686756 0.133667i
\(601\) −388960. −1.07685 −0.538426 0.842673i \(-0.680981\pi\)
−0.538426 + 0.842673i \(0.680981\pi\)
\(602\) 801329.i 2.21115i
\(603\) −101575. + 141808.i −0.279353 + 0.390001i
\(604\) −327787. −0.898500
\(605\) 11147.3i 0.0304550i
\(606\) 817230. 419877.i 2.22535 1.14334i
\(607\) −166195. −0.451068 −0.225534 0.974235i \(-0.572413\pi\)
−0.225534 + 0.974235i \(0.572413\pi\)
\(608\) 410003.i 1.10912i
\(609\) −164239. 319669.i −0.442836 0.861917i
\(610\) 457577. 1.22972
\(611\) 801173.i 2.14607i
\(612\) 207785. + 148834.i 0.554769 + 0.397375i
\(613\) 53157.1 0.141462 0.0707311 0.997495i \(-0.477467\pi\)
0.0707311 + 0.997495i \(0.477467\pi\)
\(614\) 455492.i 1.20821i
\(615\) −93916.0 + 48252.2i −0.248307 + 0.127575i
\(616\) 93605.3 0.246683
\(617\) 235218.i 0.617875i −0.951082 0.308937i \(-0.900027\pi\)
0.951082 0.308937i \(-0.0999734\pi\)
\(618\) 181270. + 352815.i 0.474622 + 0.923784i
\(619\) −296875. −0.774806 −0.387403 0.921911i \(-0.626628\pi\)
−0.387403 + 0.921911i \(0.626628\pi\)
\(620\) 416970.i 1.08473i
\(621\) 38971.8 + 5769.03i 0.101057 + 0.0149596i
\(622\) −819151. −2.11730
\(623\) 457268.i 1.17813i
\(624\) −373809. + 192056.i −0.960021 + 0.493240i
\(625\) 9062.03 0.0231988
\(626\) 393424.i 1.00395i
\(627\) 142613. + 277576.i 0.362764 + 0.706069i
\(628\) −479512. −1.21585
\(629\) 23644.7i 0.0597630i
\(630\) −208574. + 291187.i −0.525507 + 0.733653i
\(631\) −389074. −0.977178 −0.488589 0.872514i \(-0.662488\pi\)
−0.488589 + 0.872514i \(0.662488\pi\)
\(632\) 16570.0i 0.0414848i
\(633\) 224358. 115271.i 0.559932 0.287682i
\(634\) 654825. 1.62910
\(635\) 110953.i 0.275164i
\(636\) 214619. + 417725.i 0.530583 + 1.03270i
\(637\) −7182.01 −0.0176998
\(638\) 590450.i 1.45058i
\(639\) 150495. + 107798.i 0.368569 + 0.264002i
\(640\) −117857. −0.287736
\(641\) 313702.i 0.763487i −0.924268 0.381743i \(-0.875324\pi\)
0.924268 0.381743i \(-0.124676\pi\)
\(642\) −463590. + 238184.i −1.12477 + 0.577885i
\(643\) −225264. −0.544840 −0.272420 0.962178i \(-0.587824\pi\)
−0.272420 + 0.962178i \(0.587824\pi\)
\(644\) 49585.6i 0.119559i
\(645\) −173120. 336953.i −0.416129 0.809935i
\(646\) −279053. −0.668685
\(647\) 99693.7i 0.238155i −0.992885 0.119077i \(-0.962006\pi\)
0.992885 0.119077i \(-0.0379936\pi\)
\(648\) 95081.0 32317.9i 0.226435 0.0769649i
\(649\) 56188.7 0.133401
\(650\) 519631.i 1.22990i
\(651\) 580741. 298373.i 1.37031 0.704040i
\(652\) 324059. 0.762305
\(653\) 345044.i 0.809185i −0.914497 0.404592i \(-0.867413\pi\)
0.914497 0.404592i \(-0.132587\pi\)
\(654\) 409460. + 796956.i 0.957318 + 1.86328i
\(655\) −45168.7 −0.105282
\(656\) 159803.i 0.371345i
\(657\) 342192. 477729.i 0.792754 1.10675i
\(658\) −1.03344e6 −2.38691
\(659\) 813114.i 1.87232i 0.351571 + 0.936161i \(0.385648\pi\)
−0.351571 + 0.936161i \(0.614352\pi\)
\(660\) −281389. + 144572.i −0.645979 + 0.331891i
\(661\) 7039.51 0.0161116 0.00805581 0.999968i \(-0.497436\pi\)
0.00805581 + 0.999968i \(0.497436\pi\)
\(662\) 818604.i 1.86792i
\(663\) −156930. 305441.i −0.357008 0.694866i
\(664\) 16909.3 0.0383520
\(665\) 210234.i 0.475400i
\(666\) 53993.5 + 38674.9i 0.121729 + 0.0871929i
\(667\) 43751.4 0.0983422
\(668\) 669395.i 1.50013i
\(669\) 700396. 359850.i 1.56492 0.804024i
\(670\) 193062. 0.430078
\(671\) 632826.i 1.40553i
\(672\) −297417. 578881.i −0.658609 1.28189i
\(673\) 597227. 1.31859 0.659294 0.751885i \(-0.270855\pi\)
0.659294 + 0.751885i \(0.270855\pi\)
\(674\) 816785.i 1.79799i
\(675\) −41923.9 + 283211.i −0.0920140 + 0.621588i
\(676\) −409882. −0.896945
\(677\) 29338.0i 0.0640108i 0.999488 + 0.0320054i \(0.0101894\pi\)
−0.999488 + 0.0320054i \(0.989811\pi\)
\(678\) 554261. 284768.i 1.20574 0.619487i
\(679\) −834150. −1.80928
\(680\) 39569.8i 0.0855748i
\(681\) 202940. + 394993.i 0.437596 + 0.851718i
\(682\) 1.07267e6 2.30620
\(683\) 689749.i 1.47860i −0.673378 0.739299i \(-0.735157\pi\)
0.673378 0.739299i \(-0.264843\pi\)
\(684\) −245381. + 342573.i −0.524480 + 0.732219i
\(685\) 155355. 0.331088
\(686\) 687375.i 1.46065i
\(687\) 137880. 70839.9i 0.292137 0.150094i
\(688\) 573345. 1.21126
\(689\) 630973.i 1.32914i
\(690\) −19926.6 38784.3i −0.0418538 0.0814625i
\(691\) −489418. −1.02500 −0.512500 0.858687i \(-0.671281\pi\)
−0.512500 + 0.858687i \(0.671281\pi\)
\(692\) 494937.i 1.03357i
\(693\) −402709. 288456.i −0.838543 0.600638i
\(694\) 881955. 1.83116
\(695\) 47693.3i 0.0987388i
\(696\) 99197.3 50965.6i 0.204777 0.105210i
\(697\) 130576. 0.268781
\(698\) 814310.i 1.67139i
\(699\) 264982. + 515750.i 0.542329 + 1.05557i
\(700\) −360342. −0.735391
\(701\) 850602.i 1.73097i 0.500933 + 0.865486i \(0.332990\pi\)
−0.500933 + 0.865486i \(0.667010\pi\)
\(702\) −954171. 141247.i −1.93621 0.286618i
\(703\) −38982.7 −0.0788790
\(704\) 657408.i 1.32645i
\(705\) 434556. 223267.i 0.874315 0.449206i
\(706\) −722843. −1.45022
\(707\) 856021.i 1.71256i
\(708\) 34672.9 + 67485.8i 0.0691709 + 0.134631i
\(709\) 606237. 1.20601 0.603003 0.797739i \(-0.293971\pi\)
0.603003 + 0.797739i \(0.293971\pi\)
\(710\) 204888.i 0.406443i
\(711\) 51062.5 71287.7i 0.101010 0.141018i
\(712\) 141896. 0.279905
\(713\) 79482.9i 0.156349i
\(714\) 393993. 202426.i 0.772845 0.397072i
\(715\) 425037. 0.831409
\(716\) 758273.i 1.47911i
\(717\) 161013. + 313389.i 0.313201 + 0.609602i
\(718\) −331058. −0.642177
\(719\) 226372.i 0.437890i 0.975737 + 0.218945i \(0.0702615\pi\)
−0.975737 + 0.218945i \(0.929738\pi\)
\(720\) 208342. + 149233.i 0.401894 + 0.287872i
\(721\) 369562. 0.710913
\(722\) 306523.i 0.588015i
\(723\) −385966. + 198302.i −0.738367 + 0.379359i
\(724\) −616274. −1.17570
\(725\) 317944.i 0.604887i
\(726\) −17695.8 34442.4i −0.0335736 0.0653463i
\(727\) −24127.5 −0.0456504 −0.0228252 0.999739i \(-0.507266\pi\)
−0.0228252 + 0.999739i \(0.507266\pi\)
\(728\) 169818.i 0.320421i
\(729\) −508649. 153965.i −0.957114 0.289713i
\(730\) −650395. −1.22048
\(731\) 468483.i 0.876717i
\(732\) −760059. + 390503.i −1.41849 + 0.728791i
\(733\) −890358. −1.65713 −0.828565 0.559892i \(-0.810842\pi\)
−0.828565 + 0.559892i \(0.810842\pi\)
\(734\) 684592.i 1.27069i
\(735\) 2001.44 + 3895.52i 0.00370483 + 0.00721093i
\(736\) 79228.3 0.146260
\(737\) 267003.i 0.491565i
\(738\) 213579. 298175.i 0.392145 0.547468i
\(739\) 782946. 1.43365 0.716825 0.697253i \(-0.245595\pi\)
0.716825 + 0.697253i \(0.245595\pi\)
\(740\) 39518.1i 0.0721660i
\(741\) 503577. 258728.i 0.917127 0.471202i
\(742\) 813901. 1.47830
\(743\) 124363.i 0.225276i 0.993636 + 0.112638i \(0.0359301\pi\)
−0.993636 + 0.112638i \(0.964070\pi\)
\(744\) 92589.0 + 180211.i 0.167268 + 0.325564i
\(745\) 225532. 0.406347
\(746\) 338722.i 0.608647i
\(747\) −72747.1 52107.9i −0.130369 0.0933819i
\(748\) 391229. 0.699242
\(749\) 485595.i 0.865586i
\(750\) 730392. 375261.i 1.29848 0.667131i
\(751\) −161211. −0.285835 −0.142918 0.989735i \(-0.545648\pi\)
−0.142918 + 0.989735i \(0.545648\pi\)
\(752\) 739422.i 1.30754i
\(753\) −478213. 930773.i −0.843395 1.64155i
\(754\) −1.07119e6 −1.88419
\(755\) 268554.i 0.471127i
\(756\) 97948.4 661677.i 0.171378 1.15772i
\(757\) 959401. 1.67420 0.837102 0.547047i \(-0.184248\pi\)
0.837102 + 0.547047i \(0.184248\pi\)
\(758\) 1.32727e6i 2.31005i
\(759\) 53638.4 27558.3i 0.0931091 0.0478376i
\(760\) 65238.2 0.112947
\(761\) 265448.i 0.458363i −0.973384 0.229181i \(-0.926395\pi\)
0.973384 0.229181i \(-0.0736049\pi\)
\(762\) −176133. 342818.i −0.303341 0.590410i
\(763\) 834784. 1.43392
\(764\) 262403.i 0.449554i
\(765\) −121939. + 170237.i −0.208363 + 0.290892i
\(766\) −221125. −0.376861
\(767\) 101937.i 0.173278i
\(768\) −314990. + 161836.i −0.534041 + 0.274380i
\(769\) 953553. 1.61247 0.806236 0.591594i \(-0.201501\pi\)
0.806236 + 0.591594i \(0.201501\pi\)
\(770\) 548261.i 0.924711i
\(771\) 387193. + 753616.i 0.651357 + 1.26777i
\(772\) 411425. 0.690328
\(773\) 927815.i 1.55275i −0.630269 0.776377i \(-0.717055\pi\)
0.630269 0.776377i \(-0.282945\pi\)
\(774\) 1.06980e6 + 766284.i 1.78575 + 1.27911i
\(775\) −577607. −0.961677
\(776\) 258847.i 0.429853i
\(777\) 55039.4 28278.2i 0.0911658 0.0468392i
\(778\) −893130. −1.47556
\(779\) 215279.i 0.354754i
\(780\) 262281. + 510493.i 0.431100 + 0.839075i
\(781\) 283359. 0.464552
\(782\) 53923.8i 0.0881793i