Properties

Label 177.5.b.a.119.14
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 119.14
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.65

$q$-expansion

\(f(q)\) \(=\) \(q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +O(q^{10})\) \(q-5.57893i q^{2} +(-6.24762 + 6.47821i) q^{3} -15.1244 q^{4} +38.3444i q^{5} +(36.1415 + 34.8550i) q^{6} +12.9947 q^{7} -4.88479i q^{8} +(-2.93443 - 80.9468i) q^{9} +213.920 q^{10} +6.78867i q^{11} +(94.4917 - 97.9792i) q^{12} +101.844 q^{13} -72.4966i q^{14} +(-248.403 - 239.561i) q^{15} -269.243 q^{16} +232.064i q^{17} +(-451.596 + 16.3710i) q^{18} -576.777 q^{19} -579.936i q^{20} +(-81.1861 + 84.1825i) q^{21} +37.8735 q^{22} -40.2549i q^{23} +(31.6447 + 30.5183i) q^{24} -845.289 q^{25} -568.182i q^{26} +(542.724 + 486.715i) q^{27} -196.538 q^{28} -784.639i q^{29} +(-1336.49 + 1385.82i) q^{30} -1041.73 q^{31} +1423.93i q^{32} +(-43.9784 - 42.4130i) q^{33} +1294.67 q^{34} +498.274i q^{35} +(44.3815 + 1224.27i) q^{36} -2432.59 q^{37} +3217.79i q^{38} +(-636.285 + 659.769i) q^{39} +187.304 q^{40} -2586.07i q^{41} +(469.648 + 452.931i) q^{42} +1128.10 q^{43} -102.675i q^{44} +(3103.85 - 112.519i) q^{45} -224.579 q^{46} +2146.95i q^{47} +(1682.13 - 1744.21i) q^{48} -2232.14 q^{49} +4715.81i q^{50} +(-1503.36 - 1449.85i) q^{51} -1540.34 q^{52} -2753.90i q^{53} +(2715.35 - 3027.82i) q^{54} -260.307 q^{55} -63.4765i q^{56} +(3603.48 - 3736.48i) q^{57} -4377.44 q^{58} +453.188i q^{59} +(3756.95 + 3623.22i) q^{60} +1249.49 q^{61} +5811.74i q^{62} +(-38.1320 - 1051.88i) q^{63} +3636.11 q^{64} +3905.16i q^{65} +(-236.619 + 245.352i) q^{66} -7317.61 q^{67} -3509.84i q^{68} +(260.780 + 251.497i) q^{69} +2779.83 q^{70} +4746.24i q^{71} +(-395.408 + 14.3341i) q^{72} -2510.30 q^{73} +13571.2i q^{74} +(5281.05 - 5475.96i) q^{75} +8723.41 q^{76} +88.2168i q^{77} +(3680.80 + 3549.79i) q^{78} -3075.09 q^{79} -10323.9i q^{80} +(-6543.78 + 475.065i) q^{81} -14427.5 q^{82} -5431.72i q^{83} +(1227.89 - 1273.21i) q^{84} -8898.35 q^{85} -6293.57i q^{86} +(5083.05 + 4902.13i) q^{87} +33.1612 q^{88} +10693.2i q^{89} +(-627.733 - 17316.2i) q^{90} +1323.44 q^{91} +608.832i q^{92} +(6508.34 - 6748.55i) q^{93} +11977.7 q^{94} -22116.1i q^{95} +(-9224.51 - 8896.17i) q^{96} +12979.5 q^{97} +12452.9i q^{98} +(549.521 - 19.9208i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.57893i 1.39473i −0.716715 0.697366i \(-0.754355\pi\)
0.716715 0.697366i \(-0.245645\pi\)
\(3\) −6.24762 + 6.47821i −0.694180 + 0.719801i
\(4\) −15.1244 −0.945276
\(5\) 38.3444i 1.53377i 0.641782 + 0.766887i \(0.278195\pi\)
−0.641782 + 0.766887i \(0.721805\pi\)
\(6\) 36.1415 + 34.8550i 1.00393 + 0.968195i
\(7\) 12.9947 0.265198 0.132599 0.991170i \(-0.457668\pi\)
0.132599 + 0.991170i \(0.457668\pi\)
\(8\) 4.88479i 0.0763248i
\(9\) −2.93443 80.9468i −0.0362275 0.999344i
\(10\) 213.920 2.13920
\(11\) 6.78867i 0.0561047i 0.999606 + 0.0280523i \(0.00893051\pi\)
−0.999606 + 0.0280523i \(0.991069\pi\)
\(12\) 94.4917 97.9792i 0.656192 0.680411i
\(13\) 101.844 0.602630 0.301315 0.953525i \(-0.402575\pi\)
0.301315 + 0.953525i \(0.402575\pi\)
\(14\) 72.4966i 0.369880i
\(15\) −248.403 239.561i −1.10401 1.06472i
\(16\) −269.243 −1.05173
\(17\) 232.064i 0.802990i 0.915861 + 0.401495i \(0.131509\pi\)
−0.915861 + 0.401495i \(0.868491\pi\)
\(18\) −451.596 + 16.3710i −1.39382 + 0.0505276i
\(19\) −576.777 −1.59772 −0.798860 0.601518i \(-0.794563\pi\)
−0.798860 + 0.601518i \(0.794563\pi\)
\(20\) 579.936i 1.44984i
\(21\) −81.1861 + 84.1825i −0.184095 + 0.190890i
\(22\) 37.8735 0.0782510
\(23\) 40.2549i 0.0760962i −0.999276 0.0380481i \(-0.987886\pi\)
0.999276 0.0380481i \(-0.0121140\pi\)
\(24\) 31.6447 + 30.5183i 0.0549387 + 0.0529832i
\(25\) −845.289 −1.35246
\(26\) 568.182i 0.840506i
\(27\) 542.724 + 486.715i 0.744477 + 0.667648i
\(28\) −196.538 −0.250686
\(29\) 784.639i 0.932983i −0.884526 0.466491i \(-0.845518\pi\)
0.884526 0.466491i \(-0.154482\pi\)
\(30\) −1336.49 + 1385.82i −1.48499 + 1.53980i
\(31\) −1041.73 −1.08401 −0.542003 0.840376i \(-0.682334\pi\)
−0.542003 + 0.840376i \(0.682334\pi\)
\(32\) 1423.93i 1.39055i
\(33\) −43.9784 42.4130i −0.0403842 0.0389468i
\(34\) 1294.67 1.11996
\(35\) 498.274i 0.406754i
\(36\) 44.3815 + 1224.27i 0.0342450 + 0.944656i
\(37\) −2432.59 −1.77691 −0.888455 0.458963i \(-0.848221\pi\)
−0.888455 + 0.458963i \(0.848221\pi\)
\(38\) 3217.79i 2.22839i
\(39\) −636.285 + 659.769i −0.418334 + 0.433773i
\(40\) 187.304 0.117065
\(41\) 2586.07i 1.53841i −0.639000 0.769206i \(-0.720652\pi\)
0.639000 0.769206i \(-0.279348\pi\)
\(42\) 469.648 + 452.931i 0.266240 + 0.256764i
\(43\) 1128.10 0.610112 0.305056 0.952334i \(-0.401325\pi\)
0.305056 + 0.952334i \(0.401325\pi\)
\(44\) 102.675i 0.0530344i
\(45\) 3103.85 112.519i 1.53277 0.0555648i
\(46\) −224.579 −0.106134
\(47\) 2146.95i 0.971909i 0.873984 + 0.485954i \(0.161528\pi\)
−0.873984 + 0.485954i \(0.838472\pi\)
\(48\) 1682.13 1744.21i 0.730090 0.757036i
\(49\) −2232.14 −0.929670
\(50\) 4715.81i 1.88632i
\(51\) −1503.36 1449.85i −0.577993 0.557420i
\(52\) −1540.34 −0.569651
\(53\) 2753.90i 0.980384i −0.871614 0.490192i \(-0.836927\pi\)
0.871614 0.490192i \(-0.163073\pi\)
\(54\) 2715.35 3027.82i 0.931190 1.03835i
\(55\) −260.307 −0.0860519
\(56\) 63.4765i 0.0202412i
\(57\) 3603.48 3736.48i 1.10911 1.15004i
\(58\) −4377.44 −1.30126
\(59\) 453.188i 0.130189i
\(60\) 3756.95 + 3623.22i 1.04360 + 1.00645i
\(61\) 1249.49 0.335794 0.167897 0.985805i \(-0.446302\pi\)
0.167897 + 0.985805i \(0.446302\pi\)
\(62\) 5811.74i 1.51190i
\(63\) −38.1320 1051.88i −0.00960747 0.265024i
\(64\) 3636.11 0.887722
\(65\) 3905.16i 0.924297i
\(66\) −236.619 + 245.352i −0.0543203 + 0.0563252i
\(67\) −7317.61 −1.63012 −0.815060 0.579376i \(-0.803296\pi\)
−0.815060 + 0.579376i \(0.803296\pi\)
\(68\) 3509.84i 0.759047i
\(69\) 260.780 + 251.497i 0.0547741 + 0.0528245i
\(70\) 2779.83 0.567313
\(71\) 4746.24i 0.941528i 0.882259 + 0.470764i \(0.156022\pi\)
−0.882259 + 0.470764i \(0.843978\pi\)
\(72\) −395.408 + 14.3341i −0.0762747 + 0.00276506i
\(73\) −2510.30 −0.471064 −0.235532 0.971867i \(-0.575683\pi\)
−0.235532 + 0.971867i \(0.575683\pi\)
\(74\) 13571.2i 2.47831i
\(75\) 5281.05 5475.96i 0.938853 0.973504i
\(76\) 8723.41 1.51029
\(77\) 88.2168i 0.0148789i
\(78\) 3680.80 + 3549.79i 0.604998 + 0.583463i
\(79\) −3075.09 −0.492724 −0.246362 0.969178i \(-0.579235\pi\)
−0.246362 + 0.969178i \(0.579235\pi\)
\(80\) 10323.9i 1.61311i
\(81\) −6543.78 + 475.065i −0.997375 + 0.0724074i
\(82\) −14427.5 −2.14567
\(83\) 5431.72i 0.788463i −0.919011 0.394231i \(-0.871011\pi\)
0.919011 0.394231i \(-0.128989\pi\)
\(84\) 1227.89 1273.21i 0.174021 0.180444i
\(85\) −8898.35 −1.23161
\(86\) 6293.57i 0.850943i
\(87\) 5083.05 + 4902.13i 0.671562 + 0.647658i
\(88\) 33.1612 0.00428218
\(89\) 10693.2i 1.34998i 0.737828 + 0.674989i \(0.235851\pi\)
−0.737828 + 0.674989i \(0.764149\pi\)
\(90\) −627.733 17316.2i −0.0774980 2.13780i
\(91\) 1323.44 0.159816
\(92\) 608.832i 0.0719319i
\(93\) 6508.34 6748.55i 0.752496 0.780269i
\(94\) 11977.7 1.35555
\(95\) 22116.1i 2.45054i
\(96\) −9224.51 8896.17i −1.00092 0.965296i
\(97\) 12979.5 1.37948 0.689740 0.724057i \(-0.257725\pi\)
0.689740 + 0.724057i \(0.257725\pi\)
\(98\) 12452.9i 1.29664i
\(99\) 549.521 19.9208i 0.0560679 0.00203253i
\(100\) 12784.5 1.27845
\(101\) 10719.9i 1.05087i −0.850835 0.525434i \(-0.823903\pi\)
0.850835 0.525434i \(-0.176097\pi\)
\(102\) −8088.60 + 8387.14i −0.777451 + 0.806145i
\(103\) −6184.26 −0.582926 −0.291463 0.956582i \(-0.594142\pi\)
−0.291463 + 0.956582i \(0.594142\pi\)
\(104\) 497.488i 0.0459956i
\(105\) −3227.92 3113.03i −0.292782 0.282361i
\(106\) −15363.8 −1.36737
\(107\) 8100.09i 0.707493i −0.935341 0.353747i \(-0.884908\pi\)
0.935341 0.353747i \(-0.115092\pi\)
\(108\) −8208.38 7361.29i −0.703737 0.631112i
\(109\) 163.281 0.0137430 0.00687151 0.999976i \(-0.497813\pi\)
0.00687151 + 0.999976i \(0.497813\pi\)
\(110\) 1452.23i 0.120019i
\(111\) 15197.9 15758.8i 1.23350 1.27902i
\(112\) −3498.73 −0.278917
\(113\) 4303.61i 0.337036i 0.985699 + 0.168518i \(0.0538981\pi\)
−0.985699 + 0.168518i \(0.946102\pi\)
\(114\) −20845.5 20103.6i −1.60400 1.54690i
\(115\) 1543.55 0.116714
\(116\) 11867.2i 0.881927i
\(117\) −298.855 8243.98i −0.0218318 0.602234i
\(118\) 2528.30 0.181579
\(119\) 3015.61i 0.212952i
\(120\) −1170.21 + 1213.40i −0.0812643 + 0.0842636i
\(121\) 14594.9 0.996852
\(122\) 6970.80i 0.468342i
\(123\) 16753.1 + 16156.8i 1.10735 + 1.06794i
\(124\) 15755.6 1.02469
\(125\) 8446.85i 0.540598i
\(126\) −5868.37 + 212.736i −0.369638 + 0.0133998i
\(127\) −9886.33 −0.612954 −0.306477 0.951878i \(-0.599150\pi\)
−0.306477 + 0.951878i \(0.599150\pi\)
\(128\) 2497.27i 0.152421i
\(129\) −7047.93 + 7308.06i −0.423528 + 0.439160i
\(130\) 21786.6 1.28915
\(131\) 4937.30i 0.287705i 0.989599 + 0.143852i \(0.0459491\pi\)
−0.989599 + 0.143852i \(0.954051\pi\)
\(132\) 665.148 + 641.473i 0.0381743 + 0.0368155i
\(133\) −7495.05 −0.423712
\(134\) 40824.4i 2.27358i
\(135\) −18662.8 + 20810.4i −1.02402 + 1.14186i
\(136\) 1133.58 0.0612881
\(137\) 6806.81i 0.362662i −0.983422 0.181331i \(-0.941959\pi\)
0.983422 0.181331i \(-0.0580406\pi\)
\(138\) 1403.09 1454.87i 0.0736760 0.0763952i
\(139\) 12888.9 0.667095 0.333548 0.942733i \(-0.391754\pi\)
0.333548 + 0.942733i \(0.391754\pi\)
\(140\) 7536.11i 0.384495i
\(141\) −13908.4 13413.3i −0.699581 0.674680i
\(142\) 26478.9 1.31318
\(143\) 691.388i 0.0338103i
\(144\) 790.073 + 21794.3i 0.0381015 + 1.05104i
\(145\) 30086.5 1.43098
\(146\) 14004.8i 0.657007i
\(147\) 13945.6 14460.3i 0.645358 0.669177i
\(148\) 36791.5 1.67967
\(149\) 26852.8i 1.20953i 0.796404 + 0.604765i \(0.206733\pi\)
−0.796404 + 0.604765i \(0.793267\pi\)
\(150\) −30550.0 29462.6i −1.35778 1.30945i
\(151\) 30292.0 1.32854 0.664269 0.747494i \(-0.268743\pi\)
0.664269 + 0.747494i \(0.268743\pi\)
\(152\) 2817.43i 0.121946i
\(153\) 18784.9 680.975i 0.802463 0.0290903i
\(154\) 492.155 0.0207520
\(155\) 39944.5i 1.66262i
\(156\) 9623.45 9978.63i 0.395441 0.410036i
\(157\) 11799.5 0.478703 0.239351 0.970933i \(-0.423065\pi\)
0.239351 + 0.970933i \(0.423065\pi\)
\(158\) 17155.7i 0.687218i
\(159\) 17840.3 + 17205.3i 0.705682 + 0.680564i
\(160\) −54599.6 −2.13280
\(161\) 523.101i 0.0201806i
\(162\) 2650.35 + 36507.3i 0.100989 + 1.39107i
\(163\) −17056.7 −0.641978 −0.320989 0.947083i \(-0.604015\pi\)
−0.320989 + 0.947083i \(0.604015\pi\)
\(164\) 39112.8i 1.45423i
\(165\) 1626.30 1686.32i 0.0597356 0.0619403i
\(166\) −30303.2 −1.09969
\(167\) 31563.1i 1.13174i 0.824494 + 0.565870i \(0.191460\pi\)
−0.824494 + 0.565870i \(0.808540\pi\)
\(168\) 411.214 + 396.577i 0.0145697 + 0.0140511i
\(169\) −18188.7 −0.636838
\(170\) 49643.2i 1.71776i
\(171\) 1692.51 + 46688.2i 0.0578814 + 1.59667i
\(172\) −17061.8 −0.576725
\(173\) 48967.2i 1.63611i −0.575139 0.818055i \(-0.695052\pi\)
0.575139 0.818055i \(-0.304948\pi\)
\(174\) 27348.6 28358.0i 0.903309 0.936649i
\(175\) −10984.3 −0.358671
\(176\) 1827.80i 0.0590069i
\(177\) −2935.84 2831.35i −0.0937101 0.0903746i
\(178\) 59656.4 1.88286
\(179\) 55542.2i 1.73347i 0.498766 + 0.866737i \(0.333787\pi\)
−0.498766 + 0.866737i \(0.666213\pi\)
\(180\) −46944.0 + 1701.78i −1.44889 + 0.0525241i
\(181\) −29763.3 −0.908499 −0.454249 0.890875i \(-0.650093\pi\)
−0.454249 + 0.890875i \(0.650093\pi\)
\(182\) 7383.37i 0.222901i
\(183\) −7806.33 + 8094.45i −0.233101 + 0.241705i
\(184\) −196.637 −0.00580803
\(185\) 93276.1i 2.72538i
\(186\) −37649.7 36309.5i −1.08827 1.04953i
\(187\) −1575.41 −0.0450515
\(188\) 32471.3i 0.918722i
\(189\) 7052.54 + 6324.73i 0.197434 + 0.177059i
\(190\) −123384. −3.41785
\(191\) 12576.4i 0.344739i 0.985032 + 0.172369i \(0.0551423\pi\)
−0.985032 + 0.172369i \(0.944858\pi\)
\(192\) −22717.0 + 23555.5i −0.616239 + 0.638983i
\(193\) 16944.0 0.454886 0.227443 0.973791i \(-0.426963\pi\)
0.227443 + 0.973791i \(0.426963\pi\)
\(194\) 72411.8i 1.92400i
\(195\) −25298.4 24397.9i −0.665310 0.641629i
\(196\) 33759.8 0.878795
\(197\) 37753.7i 0.972808i 0.873734 + 0.486404i \(0.161692\pi\)
−0.873734 + 0.486404i \(0.838308\pi\)
\(198\) −111.137 3065.74i −0.00283484 0.0781996i
\(199\) −41087.8 −1.03754 −0.518772 0.854913i \(-0.673611\pi\)
−0.518772 + 0.854913i \(0.673611\pi\)
\(200\) 4129.06i 0.103227i
\(201\) 45717.7 47405.0i 1.13160 1.17336i
\(202\) −59805.5 −1.46568
\(203\) 10196.2i 0.247425i
\(204\) 22737.5 + 21928.1i 0.546363 + 0.526916i
\(205\) 99161.3 2.35958
\(206\) 34501.5i 0.813025i
\(207\) −3258.51 + 118.125i −0.0760462 + 0.00275677i
\(208\) −27420.8 −0.633803
\(209\) 3915.54i 0.0896395i
\(210\) −17367.4 + 18008.4i −0.393818 + 0.408353i
\(211\) −16254.8 −0.365104 −0.182552 0.983196i \(-0.558436\pi\)
−0.182552 + 0.983196i \(0.558436\pi\)
\(212\) 41651.1i 0.926734i
\(213\) −30747.1 29652.7i −0.677713 0.653590i
\(214\) −45189.8 −0.986763
\(215\) 43256.2i 0.935775i
\(216\) 2377.50 2651.09i 0.0509581 0.0568221i
\(217\) −13537.0 −0.287477
\(218\) 910.931i 0.0191678i
\(219\) 15683.4 16262.2i 0.327003 0.339072i
\(220\) 3936.99 0.0813428
\(221\) 23634.4i 0.483905i
\(222\) −87917.4 84788.0i −1.78389 1.72040i
\(223\) 82199.1 1.65294 0.826471 0.562980i \(-0.190345\pi\)
0.826471 + 0.562980i \(0.190345\pi\)
\(224\) 18503.5i 0.368773i
\(225\) 2480.44 + 68423.5i 0.0489963 + 1.35157i
\(226\) 24009.5 0.470074
\(227\) 29189.5i 0.566468i 0.959051 + 0.283234i \(0.0914073\pi\)
−0.959051 + 0.283234i \(0.908593\pi\)
\(228\) −54500.6 + 56512.1i −1.04841 + 1.08711i
\(229\) −28329.3 −0.540212 −0.270106 0.962831i \(-0.587059\pi\)
−0.270106 + 0.962831i \(0.587059\pi\)
\(230\) 8611.34i 0.162785i
\(231\) −571.487 551.145i −0.0107098 0.0103286i
\(232\) −3832.79 −0.0712098
\(233\) 12095.0i 0.222790i −0.993776 0.111395i \(-0.964468\pi\)
0.993776 0.111395i \(-0.0355319\pi\)
\(234\) −45992.6 + 1667.29i −0.839955 + 0.0304494i
\(235\) −82323.3 −1.49069
\(236\) 6854.20i 0.123064i
\(237\) 19212.0 19921.1i 0.342039 0.354663i
\(238\) 16823.9 0.297010
\(239\) 96293.0i 1.68577i 0.538091 + 0.842886i \(0.319145\pi\)
−0.538091 + 0.842886i \(0.680855\pi\)
\(240\) 66880.6 + 64500.0i 1.16112 + 1.11979i
\(241\) 61200.7 1.05371 0.526856 0.849954i \(-0.323371\pi\)
0.526856 + 0.849954i \(0.323371\pi\)
\(242\) 81424.0i 1.39034i
\(243\) 37805.5 45360.0i 0.640239 0.768176i
\(244\) −18897.8 −0.317418
\(245\) 85589.9i 1.42590i
\(246\) 90137.6 93464.4i 1.48948 1.54446i
\(247\) −58741.5 −0.962833
\(248\) 5088.63i 0.0827366i
\(249\) 35187.8 + 33935.3i 0.567536 + 0.547335i
\(250\) −47124.3 −0.753990
\(251\) 101001.i 1.60317i −0.597879 0.801586i \(-0.703990\pi\)
0.597879 0.801586i \(-0.296010\pi\)
\(252\) 576.725 + 15909.1i 0.00908171 + 0.250521i
\(253\) 273.277 0.00426935
\(254\) 55155.1i 0.854906i
\(255\) 55593.5 57645.4i 0.854956 0.886511i
\(256\) 72109.8 1.10031
\(257\) 36299.1i 0.549578i 0.961505 + 0.274789i \(0.0886080\pi\)
−0.961505 + 0.274789i \(0.911392\pi\)
\(258\) 40771.1 + 39319.9i 0.612510 + 0.590708i
\(259\) −31610.8 −0.471234
\(260\) 59063.2i 0.873717i
\(261\) −63514.0 + 2302.46i −0.932370 + 0.0337996i
\(262\) 27544.9 0.401271
\(263\) 734.663i 0.0106213i 0.999986 + 0.00531064i \(0.00169044\pi\)
−0.999986 + 0.00531064i \(0.998310\pi\)
\(264\) −207.179 + 214.825i −0.00297261 + 0.00308232i
\(265\) 105597. 1.50369
\(266\) 41814.3i 0.590965i
\(267\) −69272.6 66806.9i −0.971715 0.937128i
\(268\) 110675. 1.54091
\(269\) 51411.5i 0.710487i 0.934774 + 0.355243i \(0.115602\pi\)
−0.934774 + 0.355243i \(0.884398\pi\)
\(270\) 116100. + 104118.i 1.59259 + 1.42823i
\(271\) −17169.8 −0.233791 −0.116895 0.993144i \(-0.537294\pi\)
−0.116895 + 0.993144i \(0.537294\pi\)
\(272\) 62481.6i 0.844528i
\(273\) −8268.35 + 8573.52i −0.110941 + 0.115036i
\(274\) −37974.7 −0.505816
\(275\) 5738.39i 0.0758795i
\(276\) −3944.14 3803.75i −0.0517767 0.0499337i
\(277\) 23472.2 0.305911 0.152955 0.988233i \(-0.451121\pi\)
0.152955 + 0.988233i \(0.451121\pi\)
\(278\) 71906.5i 0.930419i
\(279\) 3056.88 + 84324.8i 0.0392708 + 1.08330i
\(280\) 2433.96 0.0310455
\(281\) 11914.9i 0.150896i 0.997150 + 0.0754479i \(0.0240387\pi\)
−0.997150 + 0.0754479i \(0.975961\pi\)
\(282\) −74831.9 + 77593.8i −0.940997 + 0.975728i
\(283\) −44053.2 −0.550053 −0.275027 0.961437i \(-0.588687\pi\)
−0.275027 + 0.961437i \(0.588687\pi\)
\(284\) 71784.1i 0.890004i
\(285\) 143273. + 138173.i 1.76390 + 1.70112i
\(286\) 3857.20 0.0471564
\(287\) 33605.3i 0.407985i
\(288\) 115262. 4178.41i 1.38964 0.0503763i
\(289\) 29667.2 0.355207
\(290\) 167850.i 1.99584i
\(291\) −81091.1 + 84084.1i −0.957607 + 0.992951i
\(292\) 37966.8 0.445285
\(293\) 82313.8i 0.958820i 0.877591 + 0.479410i \(0.159149\pi\)
−0.877591 + 0.479410i \(0.840851\pi\)
\(294\) −80672.7 77801.2i −0.933323 0.900102i
\(295\) −17377.2 −0.199680
\(296\) 11882.7i 0.135622i
\(297\) −3304.15 + 3684.37i −0.0374582 + 0.0417687i
\(298\) 149810. 1.68697
\(299\) 4099.73i 0.0458578i
\(300\) −79872.8 + 82820.8i −0.887475 + 0.920231i
\(301\) 14659.3 0.161801
\(302\) 168997.i 1.85295i
\(303\) 69445.7 + 66973.9i 0.756415 + 0.729491i
\(304\) 155293. 1.68037
\(305\) 47910.8i 0.515031i
\(306\) −3799.11 104799.i −0.0405732 1.11922i
\(307\) −37488.0 −0.397755 −0.198878 0.980024i \(-0.563730\pi\)
−0.198878 + 0.980024i \(0.563730\pi\)
\(308\) 1334.23i 0.0140646i
\(309\) 38636.9 40062.9i 0.404656 0.419591i
\(310\) −222847. −2.31891
\(311\) 11774.6i 0.121738i −0.998146 0.0608688i \(-0.980613\pi\)
0.998146 0.0608688i \(-0.0193871\pi\)
\(312\) 3222.83 + 3108.12i 0.0331077 + 0.0319292i
\(313\) −114514. −1.16888 −0.584442 0.811435i \(-0.698687\pi\)
−0.584442 + 0.811435i \(0.698687\pi\)
\(314\) 65828.8i 0.667662i
\(315\) 40333.7 1462.15i 0.406487 0.0147357i
\(316\) 46509.0 0.465760
\(317\) 113216.i 1.12665i −0.826235 0.563325i \(-0.809522\pi\)
0.826235 0.563325i \(-0.190478\pi\)
\(318\) 95987.3 99530.0i 0.949204 0.984237i
\(319\) 5326.65 0.0523447
\(320\) 139424.i 1.36156i
\(321\) 52474.1 + 50606.3i 0.509254 + 0.491128i
\(322\) −2918.34 −0.0281465
\(323\) 133849.i 1.28295i
\(324\) 98970.9 7185.08i 0.942795 0.0684450i
\(325\) −86088.0 −0.815034
\(326\) 95158.2i 0.895388i
\(327\) −1020.12 + 1057.77i −0.00954013 + 0.00989224i
\(328\) −12632.4 −0.117419
\(329\) 27899.0i 0.257749i
\(330\) −9407.88 9073.01i −0.0863901 0.0833151i
\(331\) −188979. −1.72487 −0.862437 0.506164i \(-0.831063\pi\)
−0.862437 + 0.506164i \(0.831063\pi\)
\(332\) 82151.6i 0.745315i
\(333\) 7138.26 + 196911.i 0.0643730 + 1.77574i
\(334\) 176088. 1.57847
\(335\) 280589.i 2.50024i
\(336\) 21858.8 22665.5i 0.193619 0.200765i
\(337\) −137175. −1.20786 −0.603929 0.797038i \(-0.706399\pi\)
−0.603929 + 0.797038i \(0.706399\pi\)
\(338\) 101474.i 0.888218i
\(339\) −27879.7 26887.3i −0.242599 0.233964i
\(340\) 134582. 1.16421
\(341\) 7071.96i 0.0608179i
\(342\) 260470. 9442.38i 2.22693 0.0807290i
\(343\) −60206.3 −0.511745
\(344\) 5510.52i 0.0465667i
\(345\) −9643.50 + 9999.43i −0.0810208 + 0.0840111i
\(346\) −273184. −2.28194
\(347\) 123162.i 1.02286i −0.859325 0.511431i \(-0.829116\pi\)
0.859325 0.511431i \(-0.170884\pi\)
\(348\) −76878.2 74141.8i −0.634812 0.612216i
\(349\) 177581. 1.45796 0.728979 0.684536i \(-0.239995\pi\)
0.728979 + 0.684536i \(0.239995\pi\)
\(350\) 61280.6i 0.500250i
\(351\) 55273.4 + 49569.2i 0.448644 + 0.402344i
\(352\) −9666.58 −0.0780167
\(353\) 134012.i 1.07546i −0.843117 0.537731i \(-0.819282\pi\)
0.843117 0.537731i \(-0.180718\pi\)
\(354\) −15795.9 + 16378.9i −0.126048 + 0.130700i
\(355\) −181992. −1.44409
\(356\) 161728.i 1.27610i
\(357\) −19535.7 18840.4i −0.153283 0.147827i
\(358\) 309866. 2.41773
\(359\) 214315.i 1.66289i 0.555606 + 0.831446i \(0.312486\pi\)
−0.555606 + 0.831446i \(0.687514\pi\)
\(360\) −549.630 15161.7i −0.00424097 0.116988i
\(361\) 202350. 1.55271
\(362\) 166047.i 1.26711i
\(363\) −91183.5 + 94548.9i −0.691995 + 0.717535i
\(364\) −20016.2 −0.151071
\(365\) 96255.7i 0.722505i
\(366\) 45158.3 + 43550.9i 0.337113 + 0.325114i
\(367\) −160738. −1.19340 −0.596700 0.802465i \(-0.703522\pi\)
−0.596700 + 0.802465i \(0.703522\pi\)
\(368\) 10838.3i 0.0800326i
\(369\) −209334. + 7588.64i −1.53740 + 0.0557328i
\(370\) −520381. −3.80117
\(371\) 35786.2i 0.259996i
\(372\) −98434.9 + 102068.i −0.711317 + 0.737570i
\(373\) 165801. 1.19171 0.595854 0.803093i \(-0.296814\pi\)
0.595854 + 0.803093i \(0.296814\pi\)
\(374\) 8789.08i 0.0628348i
\(375\) 54720.5 + 52772.7i 0.389123 + 0.375273i
\(376\) 10487.4 0.0741808
\(377\) 79911.0i 0.562243i
\(378\) 35285.2 39345.6i 0.246950 0.275368i
\(379\) −200893. −1.39858 −0.699289 0.714839i \(-0.746500\pi\)
−0.699289 + 0.714839i \(0.746500\pi\)
\(380\) 334494.i 2.31644i
\(381\) 61766.1 64045.7i 0.425500 0.441205i
\(382\) 70162.9 0.480818
\(383\) 106868.i 0.728538i 0.931294 + 0.364269i \(0.118681\pi\)
−0.931294 + 0.364269i \(0.881319\pi\)
\(384\) −16177.8 15602.0i −0.109713 0.105808i
\(385\) −3382.62 −0.0228208
\(386\) 94529.6i 0.634444i
\(387\) −3310.32 91315.9i −0.0221028 0.609712i
\(388\) −196308. −1.30399
\(389\) 232911.i 1.53918i −0.638536 0.769592i \(-0.720459\pi\)
0.638536 0.769592i \(-0.279541\pi\)
\(390\) −136114. + 141138.i −0.894900 + 0.927929i
\(391\) 9341.72 0.0611045
\(392\) 10903.5i 0.0709569i
\(393\) −31984.9 30846.4i −0.207090 0.199719i
\(394\) 210625. 1.35681
\(395\) 117912.i 0.755727i
\(396\) −8311.19 + 301.291i −0.0529996 + 0.00192130i
\(397\) −212073. −1.34557 −0.672783 0.739840i \(-0.734901\pi\)
−0.672783 + 0.739840i \(0.734901\pi\)
\(398\) 229226.i 1.44710i
\(399\) 46826.2 48554.5i 0.294133 0.304989i
\(400\) 227588. 1.42242
\(401\) 11049.0i 0.0687121i 0.999410 + 0.0343560i \(0.0109380\pi\)
−0.999410 + 0.0343560i \(0.989062\pi\)
\(402\) −264469. 255056.i −1.63653 1.57827i
\(403\) −106094. −0.653254
\(404\) 162132.i 0.993360i
\(405\) −18216.1 250917.i −0.111057 1.52975i
\(406\) −56883.6 −0.345092
\(407\) 16514.1i 0.0996930i
\(408\) −7082.21 + 7343.60i −0.0425450 + 0.0441152i
\(409\) 261486. 1.56315 0.781577 0.623809i \(-0.214416\pi\)
0.781577 + 0.623809i \(0.214416\pi\)
\(410\) 553213.i 3.29098i
\(411\) 44095.9 + 42526.4i 0.261045 + 0.251753i
\(412\) 93533.4 0.551026
\(413\) 5889.05i 0.0345259i
\(414\) 659.011 + 18179.0i 0.00384496 + 0.106064i
\(415\) 208276. 1.20932
\(416\) 145019.i 0.837989i
\(417\) −80525.3 + 83497.3i −0.463084 + 0.480176i
\(418\) −21844.5 −0.125023
\(419\) 199009.i 1.13356i −0.823870 0.566779i \(-0.808189\pi\)
0.823870 0.566779i \(-0.191811\pi\)
\(420\) 48820.5 + 47082.7i 0.276760 + 0.266909i
\(421\) 137054. 0.773262 0.386631 0.922235i \(-0.373639\pi\)
0.386631 + 0.922235i \(0.373639\pi\)
\(422\) 90684.2i 0.509222i
\(423\) 173788. 6300.06i 0.971271 0.0352098i
\(424\) −13452.2 −0.0748277
\(425\) 196161.i 1.08601i
\(426\) −165430. + 171536.i −0.911583 + 0.945227i
\(427\) 16236.7 0.0890519
\(428\) 122509.i 0.668776i
\(429\) −4478.96 4319.53i −0.0243367 0.0234705i
\(430\) 241323. 1.30515
\(431\) 170227.i 0.916377i 0.888855 + 0.458188i \(0.151501\pi\)
−0.888855 + 0.458188i \(0.848499\pi\)
\(432\) −146124. 131045.i −0.782988 0.702185i
\(433\) 265080. 1.41384 0.706921 0.707293i \(-0.250084\pi\)
0.706921 + 0.707293i \(0.250084\pi\)
\(434\) 75521.9i 0.400953i
\(435\) −187969. + 194906.i −0.993361 + 1.03002i
\(436\) −2469.53 −0.0129909
\(437\) 23218.1i 0.121580i
\(438\) −90725.8 87496.5i −0.472915 0.456081i
\(439\) −291195. −1.51097 −0.755484 0.655167i \(-0.772598\pi\)
−0.755484 + 0.655167i \(0.772598\pi\)
\(440\) 1271.55i 0.00656790i
\(441\) 6550.04 + 180684.i 0.0336796 + 0.929060i
\(442\) 131855. 0.674918
\(443\) 207205.i 1.05583i 0.849299 + 0.527913i \(0.177025\pi\)
−0.849299 + 0.527913i \(0.822975\pi\)
\(444\) −229860. + 238343.i −1.16599 + 1.20903i
\(445\) −410023. −2.07056
\(446\) 458583.i 2.30541i
\(447\) −173958. 167766.i −0.870621 0.839632i
\(448\) 47250.2 0.235422
\(449\) 77382.6i 0.383840i −0.981411 0.191920i \(-0.938529\pi\)
0.981411 0.191920i \(-0.0614715\pi\)
\(450\) 381730. 13838.2i 1.88508 0.0683367i
\(451\) 17556.0 0.0863122
\(452\) 65089.6i 0.318592i
\(453\) −189253. + 196238.i −0.922244 + 0.956283i
\(454\) 162846. 0.790071
\(455\) 50746.4i 0.245122i
\(456\) −18251.9 17602.3i −0.0877766 0.0846523i
\(457\) −117220. −0.561268 −0.280634 0.959815i \(-0.590545\pi\)
−0.280634 + 0.959815i \(0.590545\pi\)
\(458\) 158047.i 0.753451i
\(459\) −112949. + 125947.i −0.536115 + 0.597808i
\(460\) −23345.3 −0.110327
\(461\) 295320.i 1.38960i 0.719202 + 0.694802i \(0.244508\pi\)
−0.719202 + 0.694802i \(0.755492\pi\)
\(462\) −3074.80 + 3188.29i −0.0144057 + 0.0149373i
\(463\) 54174.8 0.252718 0.126359 0.991985i \(-0.459671\pi\)
0.126359 + 0.991985i \(0.459671\pi\)
\(464\) 211258.i 0.981245i
\(465\) 258769. + 249558.i 1.19676 + 1.15416i
\(466\) −67477.4 −0.310732
\(467\) 335342.i 1.53764i 0.639467 + 0.768819i \(0.279155\pi\)
−0.639467 + 0.768819i \(0.720845\pi\)
\(468\) 4520.01 + 124685.i 0.0206370 + 0.569277i
\(469\) −95090.3 −0.432305
\(470\) 459275.i 2.07911i
\(471\) −73719.1 + 76440.0i −0.332306 + 0.344571i
\(472\) 2213.73 0.00993665
\(473\) 7658.28i 0.0342302i
\(474\) −111138. 107182.i −0.494660 0.477053i
\(475\) 487543. 2.16086
\(476\) 45609.3i 0.201298i
\(477\) −222919. + 8081.12i −0.979741 + 0.0355169i
\(478\) 537212. 2.35120
\(479\) 352835.i 1.53780i 0.639367 + 0.768902i \(0.279197\pi\)
−0.639367 + 0.768902i \(0.720803\pi\)
\(480\) 341118. 353708.i 1.48055 1.53519i
\(481\) −247746. −1.07082
\(482\) 341434.i 1.46965i
\(483\) 3388.76 + 3268.14i 0.0145260 + 0.0140090i
\(484\) −220740. −0.942301
\(485\) 497691.i 2.11581i
\(486\) −253060. 210914.i −1.07140 0.892962i
\(487\) 207837. 0.876324 0.438162 0.898896i \(-0.355630\pi\)
0.438162 + 0.898896i \(0.355630\pi\)
\(488\) 6103.49i 0.0256294i
\(489\) 106564. 110497.i 0.445649 0.462097i
\(490\) −477500. −1.98875
\(491\) 12389.1i 0.0513899i 0.999670 + 0.0256950i \(0.00817986\pi\)
−0.999670 + 0.0256950i \(0.991820\pi\)
\(492\) −253381. 244362.i −1.04675 1.00949i
\(493\) 182086. 0.749176
\(494\) 327714.i 1.34289i
\(495\) 763.852 + 21071.0i 0.00311745 + 0.0859954i
\(496\) 280478. 1.14008
\(497\) 61676.1i 0.249692i
\(498\) 189323. 196310.i 0.763386 0.791561i
\(499\) −50253.7 −0.201821 −0.100911 0.994895i \(-0.532176\pi\)
−0.100911 + 0.994895i \(0.532176\pi\)
\(500\) 127754.i 0.511015i
\(501\) −204472. 197194.i −0.814628 0.785632i
\(502\) −563480. −2.23600
\(503\) 362596.i 1.43314i 0.697517 + 0.716568i \(0.254288\pi\)
−0.697517 + 0.716568i \(0.745712\pi\)
\(504\) −5138.22 + 186.267i −0.0202279 + 0.000733289i
\(505\) 411047. 1.61179
\(506\) 1524.59i 0.00595460i
\(507\) 113636. 117830.i 0.442080 0.458397i
\(508\) 149525. 0.579411
\(509\) 169930.i 0.655896i 0.944696 + 0.327948i \(0.106357\pi\)
−0.944696 + 0.327948i \(0.893643\pi\)
\(510\) −321599. 310152.i −1.23644 1.19243i
\(511\) −32620.6 −0.124925
\(512\) 362339.i 1.38221i
\(513\) −313030. 280726.i −1.18947 1.06671i
\(514\) 202510. 0.766514
\(515\) 237131.i 0.894077i
\(516\) 106596. 110530.i 0.400351 0.415127i
\(517\) −14574.9 −0.0545286
\(518\) 176355.i 0.657245i
\(519\) 317220. + 305928.i 1.17767 + 1.13576i
\(520\) 19075.9 0.0705469
\(521\) 68945.7i 0.253999i 0.991903 + 0.126999i \(0.0405346\pi\)
−0.991903 + 0.126999i \(0.959465\pi\)
\(522\) 12845.3 + 354340.i 0.0471414 + 1.30041i
\(523\) −408744. −1.49434 −0.747168 0.664636i \(-0.768587\pi\)
−0.747168 + 0.664636i \(0.768587\pi\)
\(524\) 74673.9i 0.271961i
\(525\) 68625.7 71158.6i 0.248982 0.258172i
\(526\) 4098.63 0.0148138
\(527\) 241748.i 0.870447i
\(528\) 11840.9 + 11419.4i 0.0424733 + 0.0409615i
\(529\) 278221. 0.994209
\(530\) 589115.i 2.09724i
\(531\) 36684.1 1329.85i 0.130103 0.00471642i
\(532\) 113358. 0.400525
\(533\) 263377.i 0.927093i
\(534\) −372711. + 386467.i −1.30704 + 1.35528i
\(535\) 310593. 1.08513
\(536\) 35745.0i 0.124419i
\(537\) −359814. 347007.i −1.24776 1.20334i
\(538\) 286821. 0.990938
\(539\) 15153.2i 0.0521588i
\(540\) 282264. 314745.i 0.967983 1.07937i
\(541\) −362238. −1.23766 −0.618828 0.785527i \(-0.712392\pi\)
−0.618828 + 0.785527i \(0.712392\pi\)
\(542\) 95789.1i 0.326075i
\(543\) 185950. 192813.i 0.630662 0.653939i
\(544\) −330443. −1.11660
\(545\) 6260.89i 0.0210787i
\(546\) 47831.0 + 46128.5i 0.160444 + 0.154733i
\(547\) 179531. 0.600020 0.300010 0.953936i \(-0.403010\pi\)
0.300010 + 0.953936i \(0.403010\pi\)
\(548\) 102949.i 0.342816i
\(549\) −3666.53 101142.i −0.0121650 0.335573i
\(550\) −32014.0 −0.105832
\(551\) 452561.i 1.49064i
\(552\) 1228.51 1273.85i 0.00403182 0.00418063i
\(553\) −39959.9 −0.130670
\(554\) 130950.i 0.426663i
\(555\) 604262. + 582754.i 1.96173 + 1.89190i
\(556\) −194938. −0.630589
\(557\) 423794.i 1.36598i −0.730427 0.682991i \(-0.760679\pi\)
0.730427 0.682991i \(-0.239321\pi\)
\(558\) 470442. 17054.1i 1.51091 0.0547723i
\(559\) 114890. 0.367672
\(560\) 134157.i 0.427795i
\(561\) 9842.54 10205.8i 0.0312739 0.0324281i
\(562\) 66472.3 0.210459
\(563\) 554411.i 1.74910i −0.484933 0.874552i \(-0.661156\pi\)
0.484933 0.874552i \(-0.338844\pi\)
\(564\) 210356. + 202869.i 0.661297 + 0.637759i
\(565\) −165019. −0.516937
\(566\) 245770.i 0.767177i
\(567\) −85034.6 + 6173.34i −0.264502 + 0.0192023i
\(568\) 23184.4 0.0718620
\(569\) 490601.i 1.51532i −0.652651 0.757659i \(-0.726343\pi\)
0.652651 0.757659i \(-0.273657\pi\)
\(570\) 770858. 799309.i 2.37260 2.46017i
\(571\) −540936. −1.65910 −0.829552 0.558429i \(-0.811404\pi\)
−0.829552 + 0.558429i \(0.811404\pi\)
\(572\) 10456.8i 0.0319601i
\(573\) −81472.7 78572.7i −0.248143 0.239311i
\(574\) −187481. −0.569029
\(575\) 34027.0i 0.102917i
\(576\) −10669.9 294331.i −0.0321599 0.887139i
\(577\) −469761. −1.41100 −0.705498 0.708712i \(-0.749277\pi\)
−0.705498 + 0.708712i \(0.749277\pi\)
\(578\) 165511.i 0.495418i
\(579\) −105860. + 109767.i −0.315773 + 0.327427i
\(580\) −455040. −1.35268
\(581\) 70583.7i 0.209099i
\(582\) 469099. + 452402.i 1.38490 + 1.33561i
\(583\) 18695.3 0.0550042
\(584\) 12262.3i 0.0359539i
\(585\) 316110. 11459.4i 0.923691 0.0334850i
\(586\) 459222. 1.33730
\(587\) 215040.i 0.624083i −0.950068 0.312041i \(-0.898987\pi\)
0.950068 0.312041i \(-0.101013\pi\)
\(588\) −210918. + 218703.i −0.610042 + 0.632558i
\(589\) 600846. 1.73194
\(590\) 96946.0i 0.278501i
\(591\) −244576. 235871.i −0.700228 0.675304i
\(592\) 654957. 1.86883
\(593\) 573291.i 1.63029i −0.579254 0.815147i \(-0.696656\pi\)
0.579254 0.815147i \(-0.303344\pi\)
\(594\) 20554.8 + 18433.6i 0.0582561 + 0.0522441i
\(595\) −115632. −0.326620
\(596\) 406133.i 1.14334i
\(597\) 256701. 266175.i 0.720243 0.746825i
\(598\) −22872.1 −0.0639593
\(599\) 178694.i 0.498032i 0.968499 + 0.249016i \(0.0801071\pi\)
−0.968499 + 0.249016i \(0.919893\pi\)
\(600\) −26748.9 25796.8i −0.0743026 0.0716578i
\(601\) 668298. 1.85021 0.925106 0.379709i \(-0.123976\pi\)
0.925106 + 0.379709i \(0.123976\pi\)
\(602\) 81783.2i 0.225669i
\(603\) 21473.0 + 592337.i 0.0590552 + 1.62905i
\(604\) −458149. −1.25583
\(605\) 559633.i 1.52895i
\(606\) 373642. 387433.i 1.01744 1.05500i
\(607\) 109937. 0.298379 0.149189 0.988809i \(-0.452334\pi\)
0.149189 + 0.988809i \(0.452334\pi\)
\(608\) 821288.i 2.22172i
\(609\) 66052.8 + 63701.7i 0.178097 + 0.171758i
\(610\) 267291. 0.718331
\(611\) 218654.i 0.585701i
\(612\) −284110. + 10299.4i −0.758549 + 0.0274984i
\(613\) −205618. −0.547193 −0.273597 0.961845i \(-0.588213\pi\)
−0.273597 + 0.961845i \(0.588213\pi\)
\(614\) 209143.i 0.554762i
\(615\) −619522. + 642388.i −1.63797 + 1.69843i
\(616\) 430.921 0.00113563
\(617\) 83595.6i 0.219590i 0.993954 + 0.109795i \(0.0350195\pi\)
−0.993954 + 0.109795i \(0.964981\pi\)
\(618\) −223508. 215553.i −0.585216 0.564386i
\(619\) 280975. 0.733308 0.366654 0.930357i \(-0.380503\pi\)
0.366654 + 0.930357i \(0.380503\pi\)
\(620\) 604137.i 1.57164i
\(621\) 19592.7 21847.3i 0.0508055 0.0566519i
\(622\) −65689.5 −0.169791
\(623\) 138955.i 0.358012i
\(624\) 171315. 177638.i 0.439973 0.456212i
\(625\) −204417. −0.523307
\(626\) 638868.i 1.63028i
\(627\) 25365.7 + 24462.8i 0.0645226 + 0.0622260i
\(628\) −178461. −0.452507
\(629\) 564517.i 1.42684i
\(630\) −8157.22 225019.i −0.0205523 0.566941i
\(631\) −494877. −1.24291 −0.621454 0.783451i \(-0.713458\pi\)
−0.621454 + 0.783451i \(0.713458\pi\)
\(632\) 15021.2i 0.0376071i
\(633\) 101554. 105302.i 0.253448 0.262802i
\(634\) −631623. −1.57137
\(635\) 379085.i 0.940133i
\(636\) −269825. 260221.i −0.667064 0.643321i
\(637\) −227331. −0.560246
\(638\) 29717.0i 0.0730068i
\(639\) 384193. 13927.5i 0.940910 0.0341092i
\(640\) −95756.1 −0.233780
\(641\) 389193.i 0.947217i −0.880736 0.473608i \(-0.842951\pi\)
0.880736 0.473608i \(-0.157049\pi\)
\(642\) 282329. 292749.i 0.684991 0.710273i
\(643\) −527339. −1.27546 −0.637732 0.770259i \(-0.720127\pi\)
−0.637732 + 0.770259i \(0.720127\pi\)
\(644\) 7911.60i 0.0190762i
\(645\) −280223. 270248.i −0.673572 0.649596i
\(646\) −746735. −1.78937
\(647\) 36056.0i 0.0861328i 0.999072 + 0.0430664i \(0.0137127\pi\)
−0.999072 + 0.0430664i \(0.986287\pi\)
\(648\) 2320.59 + 31965.0i 0.00552649 + 0.0761245i
\(649\) −3076.54 −0.00730421
\(650\) 480278.i 1.13675i
\(651\) 84574.0 87695.5i 0.199561 0.206926i
\(652\) 257973. 0.606847
\(653\) 329386.i 0.772464i 0.922402 + 0.386232i \(0.126224\pi\)
−0.922402 + 0.386232i \(0.873776\pi\)
\(654\) 5901.20 + 5691.15i 0.0137970 + 0.0133059i
\(655\) −189318. −0.441274
\(656\) 696281.i 1.61799i
\(657\) 7366.29 + 203201.i 0.0170655 + 0.470754i
\(658\) 155646. 0.359490
\(659\) 34206.6i 0.0787660i −0.999224 0.0393830i \(-0.987461\pi\)
0.999224 0.0393830i \(-0.0125392\pi\)
\(660\) −24596.9 + 25504.7i −0.0564666 + 0.0585507i
\(661\) 16004.0 0.0366290 0.0183145 0.999832i \(-0.494170\pi\)
0.0183145 + 0.999832i \(0.494170\pi\)
\(662\) 1.05430e6i 2.40574i
\(663\) −153109. 147659.i −0.348316 0.335918i
\(664\) −26532.8 −0.0601793
\(665\) 287393.i 0.649879i
\(666\) 1.09855e6 39823.8i 2.47669 0.0897831i
\(667\) −31585.5 −0.0709964
\(668\) 477374.i 1.06981i
\(669\) −513549. + 532503.i −1.14744 + 1.18979i
\(670\) −1.56539e6 −3.48716
\(671\) 8482.36i 0.0188396i
\(672\) −119870. 115603.i −0.265443 0.255995i
\(673\) 599163. 1.32286 0.661432 0.750005i \(-0.269949\pi\)
0.661432 + 0.750005i \(0.269949\pi\)
\(674\) 765290.i 1.68464i
\(675\) −458759. 411415.i −1.00688 0.902969i
\(676\) 275094. 0.601988
\(677\) 349265.i 0.762040i 0.924567 + 0.381020i \(0.124427\pi\)
−0.924567 + 0.381020i \(0.875573\pi\)
\(678\) −150002. + 155539.i −0.326316 + 0.338360i
\(679\) 168665. 0.365836
\(680\) 43466.6i 0.0940021i
\(681\) −189096. 182365.i −0.407744 0.393231i
\(682\) −39454.0 −0.0848246
\(683\) 202624.i 0.434360i −0.976132 0.217180i \(-0.930314\pi\)
0.976132 0.217180i \(-0.0696858\pi\)
\(684\) −25598.2 706133.i −0.0547139 1.50929i
\(685\) 261003. 0.556242
\(686\) 335887.i 0.713747i
\(687\) 176991. 183523.i 0.375005 0.388845i
\(688\) −303732. −0.641673
\(689\) 280469.i 0.590809i
\(690\) 55786.1 + 53800.4i 0.117173 + 0.113002i
\(691\) 498749. 1.04454 0.522271 0.852779i \(-0.325085\pi\)
0.522271 + 0.852779i \(0.325085\pi\)
\(692\) 740600.i 1.54658i
\(693\) 7140.87 258.866i 0.0148691 0.000539024i
\(694\) −687110. −1.42662
\(695\) 494218.i 1.02317i
\(696\) 23945.9 24829.6i 0.0494324 0.0512569i
\(697\) 600135. 1.23533
\(698\) 990710.i 2.03346i
\(699\) 78354.2 + 75565.3i 0.160364 + 0.154656i
\(700\) 166131. 0.339043
\(701\) 295314.i 0.600963i 0.953788 + 0.300482i \(0.0971474\pi\)
−0.953788 + 0.300482i \(0.902853\pi\)
\(702\) 276543. 308366.i 0.561162 0.625738i
\(703\) 1.40306e6 2.83900
\(704\) 24684.3i 0.0498054i
\(705\) 514325. 533307.i 1.03481 1.07300i
\(706\) −747644. −1.49998
\(707\) 139302.i 0.278688i
\(708\) 44403.0 + 42822.5i 0.0885820 + 0.0854289i
\(709\) 288827. 0.574574 0.287287 0.957845i \(-0.407247\pi\)
0.287287 + 0.957845i \(0.407247\pi\)
\(710\) 1.01532e6i 2.01412i
\(711\) 9023.63 + 248919.i 0.0178502 + 0.492401i
\(712\) 52233.9 0.103037
\(713\) 41934.7i 0.0824888i
\(714\) −105109. + 108988.i −0.206179 + 0.213788i
\(715\) −26510.8 −0.0518574
\(716\) 840044.i 1.63861i
\(717\) −623807. 601603.i −1.21342 1.17023i
\(718\) 1.19565e6 2.31929
\(719\) 701167.i 1.35632i −0.734912 0.678162i \(-0.762777\pi\)
0.734912 0.678162i \(-0.237223\pi\)
\(720\) −835690. + 30294.8i −1.61206 + 0.0584391i
\(721\) −80362.7 −0.154591
\(722\) 1.12890e6i 2.16561i
\(723\) −382359. + 396471.i −0.731466 + 0.758463i
\(724\) 450153. 0.858783
\(725\) 663247.i 1.26182i
\(726\) 527482. + 508706.i 1.00077 + 0.965148i
\(727\) 742674. 1.40517 0.702586 0.711599i \(-0.252029\pi\)
0.702586 + 0.711599i \(0.252029\pi\)
\(728\) 6464.72i 0.0121980i
\(729\) 57657.2 + 528304.i 0.108492 + 0.994097i
\(730\) −537004. −1.00770
\(731\) 261791.i 0.489914i
\(732\) 118066. 122424.i 0.220345 0.228478i
\(733\) 628469. 1.16970 0.584852 0.811140i \(-0.301153\pi\)
0.584852 + 0.811140i \(0.301153\pi\)
\(734\) 896744.i 1.66447i
\(735\) 554469. + 534733.i 1.02637 + 0.989834i
\(736\) 57320.1 0.105816
\(737\) 49676.8i 0.0914574i
\(738\) 42336.5 + 1.16786e6i 0.0777324 + 2.14426i
\(739\) 317437. 0.581257 0.290628 0.956836i \(-0.406136\pi\)
0.290628 + 0.956836i \(0.406136\pi\)
\(740\) 1.41075e6i 2.57624i
\(741\) 366994. 380540.i 0.668379 0.693048i
\(742\) −199648. −0.362625
\(743\) 854010.i 1.54698i −0.633807 0.773492i \(-0.718509\pi\)
0.633807 0.773492i \(-0.281491\pi\)
\(744\) −32965.2 31791.9i −0.0595539 0.0574341i
\(745\) −1.02965e6 −1.85515
\(746\) 924992.i 1.66211i
\(747\) −439681. + 15939.0i −0.787945 + 0.0285640i
\(748\) 23827.1 0.0425861
\(749\) 105258.i 0.187626i
\(750\) 294415. 305281.i 0.523405 0.542723i
\(751\) −364327. −0.645969 −0.322985 0.946404i \(-0.604686\pi\)
−0.322985 + 0.946404i \(0.604686\pi\)
\(752\) 578049.i 1.02218i
\(753\) 654309. + 631019.i 1.15397 + 1.11289i
\(754\) −445818. −0.784178
\(755\) 1.16153e6i 2.03768i
\(756\) −106666. 95657.9i −0.186630 0.167370i
\(757\) −952412. −1.66201 −0.831004 0.556266i \(-0.812234\pi\)
−0.831004 + 0.556266i \(0.812234\pi\)
\(758\) 1.12077e6i 1.95064i
\(759\) −1707.33 + 1770.35i −0.00296370 + 0.00307309i
\(760\) −108033. −0.187037
\(761\) 814752.i 1.40688i 0.710756 + 0.703439i \(0.248353\pi\)
−0.710756 + 0.703439i \(0.751647\pi\)
\(762\) −357306. 344588.i −0.615362 0.593459i
\(763\) 2121.79 0.00364462
\(764\) 190211.i 0.325873i
\(765\) 26111.5 + 720293.i 0.0446180 + 1.23080i
\(766\) 596211. 1.01611
\(767\) 46154.6i 0.0784557i
\(768\) −450515. + 467143.i −0.763812 + 0.792003i
\(769\) 841756. 1.42342 0.711711 0.702473i \(-0.247921\pi\)
0.711711 + 0.702473i \(0.247921\pi\)
\(770\) 18871.4i 0.0318289i
\(771\) −235153. 226783.i −0.395587 0.381506i
\(772\) −256269. −0.429993
\(773\) 972648.i 1.62778i −0.581017 0.813892i \(-0.697345\pi\)
0.581017 0.813892i \(-0.302655\pi\)
\(774\) −509445. + 18468.0i −0.850384 + 0.0308275i
\(775\) 880564. 1.46608
\(776\) 63402.2i 0.105289i
\(777\) 197493. 204782.i 0.327121 0.339195i
\(778\) −1.29939e6 −2.14675
\(779\) 1.49159e6i 2.45795i
\(780\) 382624. + 369005.i 0.628902 + 0.606517i
\(781\) −32220.7 −0.0528241
\(782\) 52116.7i 0.0852244i