Properties

Label 177.5.b.a.119.16
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 119.16
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.63

$q$-expansion

\(f(q)\) \(=\) \(q-5.41049i q^{2} +(7.81854 - 4.45762i) q^{3} -13.2734 q^{4} +41.9044i q^{5} +(-24.1179 - 42.3021i) q^{6} -64.0047 q^{7} -14.7525i q^{8} +(41.2592 - 69.7042i) q^{9} +O(q^{10})\) \(q-5.41049i q^{2} +(7.81854 - 4.45762i) q^{3} -13.2734 q^{4} +41.9044i q^{5} +(-24.1179 - 42.3021i) q^{6} -64.0047 q^{7} -14.7525i q^{8} +(41.2592 - 69.7042i) q^{9} +226.723 q^{10} -161.993i q^{11} +(-103.778 + 59.1676i) q^{12} -266.705 q^{13} +346.297i q^{14} +(186.794 + 327.631i) q^{15} -292.192 q^{16} +98.3026i q^{17} +(-377.134 - 223.232i) q^{18} -447.364 q^{19} -556.211i q^{20} +(-500.424 + 285.309i) q^{21} -876.458 q^{22} +28.8687i q^{23} +(-65.7610 - 115.343i) q^{24} -1130.98 q^{25} +1443.00i q^{26} +(11.8714 - 728.903i) q^{27} +849.558 q^{28} +337.070i q^{29} +(1772.64 - 1010.65i) q^{30} +1735.49 q^{31} +1344.86i q^{32} +(-722.102 - 1266.55i) q^{33} +531.865 q^{34} -2682.08i q^{35} +(-547.648 + 925.209i) q^{36} -328.761 q^{37} +2420.46i q^{38} +(-2085.24 + 1188.87i) q^{39} +618.194 q^{40} -606.752i q^{41} +(1543.66 + 2707.54i) q^{42} -2506.79 q^{43} +2150.18i q^{44} +(2920.91 + 1728.94i) q^{45} +156.194 q^{46} -2517.63i q^{47} +(-2284.51 + 1302.48i) q^{48} +1695.61 q^{49} +6119.13i q^{50} +(438.196 + 768.583i) q^{51} +3540.06 q^{52} -1760.77i q^{53} +(-3943.72 - 64.2303i) q^{54} +6788.20 q^{55} +944.229i q^{56} +(-3497.73 + 1994.18i) q^{57} +1823.71 q^{58} -453.188i q^{59} +(-2479.38 - 4348.76i) q^{60} +1300.26 q^{61} -9389.82i q^{62} +(-2640.78 + 4461.40i) q^{63} +2601.27 q^{64} -11176.1i q^{65} +(-6852.63 + 3906.92i) q^{66} +5806.28 q^{67} -1304.80i q^{68} +(128.686 + 225.711i) q^{69} -14511.3 q^{70} +7039.96i q^{71} +(-1028.31 - 608.676i) q^{72} +3733.10 q^{73} +1778.75i q^{74} +(-8842.58 + 5041.47i) q^{75} +5938.02 q^{76} +10368.3i q^{77} +(6432.36 + 11282.2i) q^{78} -4184.54 q^{79} -12244.1i q^{80} +(-3156.36 - 5751.88i) q^{81} -3282.82 q^{82} +6012.45i q^{83} +(6642.30 - 3787.01i) q^{84} -4119.31 q^{85} +13562.9i q^{86} +(1502.53 + 2635.40i) q^{87} -2389.79 q^{88} -13337.9i q^{89} +(9354.41 - 15803.6i) q^{90} +17070.4 q^{91} -383.184i q^{92} +(13569.0 - 7736.14i) q^{93} -13621.6 q^{94} -18746.5i q^{95} +(5994.88 + 10514.8i) q^{96} -7745.75 q^{97} -9174.06i q^{98} +(-11291.6 - 6683.68i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.41049i 1.35262i −0.736617 0.676311i \(-0.763578\pi\)
0.736617 0.676311i \(-0.236422\pi\)
\(3\) 7.81854 4.45762i 0.868727 0.495291i
\(4\) −13.2734 −0.829584
\(5\) 41.9044i 1.67617i 0.545536 + 0.838087i \(0.316326\pi\)
−0.545536 + 0.838087i \(0.683674\pi\)
\(6\) −24.1179 42.3021i −0.669942 1.17506i
\(7\) −64.0047 −1.30622 −0.653110 0.757263i \(-0.726536\pi\)
−0.653110 + 0.757263i \(0.726536\pi\)
\(8\) 14.7525i 0.230508i
\(9\) 41.2592 69.7042i 0.509373 0.860546i
\(10\) 226.723 2.26723
\(11\) 161.993i 1.33878i −0.742911 0.669391i \(-0.766555\pi\)
0.742911 0.669391i \(-0.233445\pi\)
\(12\) −103.778 + 59.1676i −0.720682 + 0.410886i
\(13\) −266.705 −1.57813 −0.789067 0.614308i \(-0.789435\pi\)
−0.789067 + 0.614308i \(0.789435\pi\)
\(14\) 346.297i 1.76682i
\(15\) 186.794 + 327.631i 0.830195 + 1.45614i
\(16\) −292.192 −1.14137
\(17\) 98.3026i 0.340147i 0.985431 + 0.170074i \(0.0544006\pi\)
−0.985431 + 0.170074i \(0.945599\pi\)
\(18\) −377.134 223.232i −1.16399 0.688988i
\(19\) −447.364 −1.23924 −0.619618 0.784904i \(-0.712712\pi\)
−0.619618 + 0.784904i \(0.712712\pi\)
\(20\) 556.211i 1.39053i
\(21\) −500.424 + 285.309i −1.13475 + 0.646959i
\(22\) −876.458 −1.81086
\(23\) 28.8687i 0.0545722i 0.999628 + 0.0272861i \(0.00868651\pi\)
−0.999628 + 0.0272861i \(0.991313\pi\)
\(24\) −65.7610 115.343i −0.114168 0.200248i
\(25\) −1130.98 −1.80956
\(26\) 1443.00i 2.13462i
\(27\) 11.8714 728.903i 0.0162846 0.999867i
\(28\) 849.558 1.08362
\(29\) 337.070i 0.400797i 0.979715 + 0.200398i \(0.0642236\pi\)
−0.979715 + 0.200398i \(0.935776\pi\)
\(30\) 1772.64 1010.65i 1.96960 1.12294i
\(31\) 1735.49 1.80592 0.902958 0.429728i \(-0.141390\pi\)
0.902958 + 0.429728i \(0.141390\pi\)
\(32\) 1344.86i 1.31334i
\(33\) −722.102 1266.55i −0.663087 1.16304i
\(34\) 531.865 0.460090
\(35\) 2682.08i 2.18945i
\(36\) −547.648 + 925.209i −0.422568 + 0.713896i
\(37\) −328.761 −0.240146 −0.120073 0.992765i \(-0.538313\pi\)
−0.120073 + 0.992765i \(0.538313\pi\)
\(38\) 2420.46i 1.67622i
\(39\) −2085.24 + 1188.87i −1.37097 + 0.781636i
\(40\) 618.194 0.386371
\(41\) 606.752i 0.360947i −0.983580 0.180473i \(-0.942237\pi\)
0.983580 0.180473i \(-0.0577630\pi\)
\(42\) 1543.66 + 2707.54i 0.875091 + 1.53488i
\(43\) −2506.79 −1.35575 −0.677876 0.735176i \(-0.737099\pi\)
−0.677876 + 0.735176i \(0.737099\pi\)
\(44\) 2150.18i 1.11063i
\(45\) 2920.91 + 1728.94i 1.44243 + 0.853798i
\(46\) 156.194 0.0738155
\(47\) 2517.63i 1.13971i −0.821744 0.569857i \(-0.806999\pi\)
0.821744 0.569857i \(-0.193001\pi\)
\(48\) −2284.51 + 1302.48i −0.991542 + 0.565313i
\(49\) 1695.61 0.706209
\(50\) 6119.13i 2.44765i
\(51\) 438.196 + 768.583i 0.168472 + 0.295495i
\(52\) 3540.06 1.30919
\(53\) 1760.77i 0.626832i −0.949616 0.313416i \(-0.898527\pi\)
0.949616 0.313416i \(-0.101473\pi\)
\(54\) −3943.72 64.2303i −1.35244 0.0220269i
\(55\) 6788.20 2.24403
\(56\) 944.229i 0.301094i
\(57\) −3497.73 + 1994.18i −1.07656 + 0.613783i
\(58\) 1823.71 0.542126
\(59\) 453.188i 0.130189i
\(60\) −2479.38 4348.76i −0.688717 1.20799i
\(61\) 1300.26 0.349437 0.174719 0.984618i \(-0.444098\pi\)
0.174719 + 0.984618i \(0.444098\pi\)
\(62\) 9389.82i 2.44272i
\(63\) −2640.78 + 4461.40i −0.665352 + 1.12406i
\(64\) 2601.27 0.635077
\(65\) 11176.1i 2.64523i
\(66\) −6852.63 + 3906.92i −1.57315 + 0.896906i
\(67\) 5806.28 1.29345 0.646723 0.762725i \(-0.276139\pi\)
0.646723 + 0.762725i \(0.276139\pi\)
\(68\) 1304.80i 0.282181i
\(69\) 128.686 + 225.711i 0.0270291 + 0.0474083i
\(70\) −14511.3 −2.96150
\(71\) 7039.96i 1.39654i 0.715834 + 0.698270i \(0.246047\pi\)
−0.715834 + 0.698270i \(0.753953\pi\)
\(72\) −1028.31 608.676i −0.198362 0.117414i
\(73\) 3733.10 0.700526 0.350263 0.936651i \(-0.386092\pi\)
0.350263 + 0.936651i \(0.386092\pi\)
\(74\) 1778.75i 0.324827i
\(75\) −8842.58 + 5041.47i −1.57201 + 0.896261i
\(76\) 5938.02 1.02805
\(77\) 10368.3i 1.74874i
\(78\) 6432.36 + 11282.2i 1.05726 + 1.85440i
\(79\) −4184.54 −0.670493 −0.335246 0.942131i \(-0.608820\pi\)
−0.335246 + 0.942131i \(0.608820\pi\)
\(80\) 12244.1i 1.91314i
\(81\) −3156.36 5751.88i −0.481079 0.876677i
\(82\) −3282.82 −0.488225
\(83\) 6012.45i 0.872762i 0.899762 + 0.436381i \(0.143740\pi\)
−0.899762 + 0.436381i \(0.856260\pi\)
\(84\) 6642.30 3787.01i 0.941369 0.536707i
\(85\) −4119.31 −0.570146
\(86\) 13562.9i 1.83382i
\(87\) 1502.53 + 2635.40i 0.198511 + 0.348183i
\(88\) −2389.79 −0.308599
\(89\) 13337.9i 1.68387i −0.539579 0.841935i \(-0.681416\pi\)
0.539579 0.841935i \(-0.318584\pi\)
\(90\) 9354.41 15803.6i 1.15486 1.95106i
\(91\) 17070.4 2.06139
\(92\) 383.184i 0.0452722i
\(93\) 13569.0 7736.14i 1.56885 0.894455i
\(94\) −13621.6 −1.54160
\(95\) 18746.5i 2.07717i
\(96\) 5994.88 + 10514.8i 0.650486 + 1.14093i
\(97\) −7745.75 −0.823228 −0.411614 0.911358i \(-0.635035\pi\)
−0.411614 + 0.911358i \(0.635035\pi\)
\(98\) 9174.06i 0.955233i
\(99\) −11291.6 6683.68i −1.15208 0.681939i
\(100\) 15011.8 1.50118
\(101\) 1454.56i 0.142590i 0.997455 + 0.0712951i \(0.0227132\pi\)
−0.997455 + 0.0712951i \(0.977287\pi\)
\(102\) 4158.41 2370.85i 0.399693 0.227879i
\(103\) 11377.7 1.07245 0.536227 0.844074i \(-0.319849\pi\)
0.536227 + 0.844074i \(0.319849\pi\)
\(104\) 3934.56i 0.363772i
\(105\) −11955.7 20969.9i −1.08442 1.90204i
\(106\) −9526.63 −0.847867
\(107\) 6247.21i 0.545656i −0.962063 0.272828i \(-0.912041\pi\)
0.962063 0.272828i \(-0.0879590\pi\)
\(108\) −157.574 + 9674.99i −0.0135094 + 0.829474i
\(109\) −8355.95 −0.703304 −0.351652 0.936131i \(-0.614380\pi\)
−0.351652 + 0.936131i \(0.614380\pi\)
\(110\) 36727.4i 3.03533i
\(111\) −2570.43 + 1465.49i −0.208622 + 0.118943i
\(112\) 18701.7 1.49088
\(113\) 2933.39i 0.229727i 0.993381 + 0.114864i \(0.0366431\pi\)
−0.993381 + 0.114864i \(0.963357\pi\)
\(114\) 10789.5 + 18924.4i 0.830215 + 1.45617i
\(115\) −1209.72 −0.0914725
\(116\) 4474.05i 0.332495i
\(117\) −11004.0 + 18590.4i −0.803858 + 1.35806i
\(118\) −2451.96 −0.176096
\(119\) 6291.83i 0.444307i
\(120\) 4833.37 2755.68i 0.335651 0.191366i
\(121\) −11600.6 −0.792336
\(122\) 7035.02i 0.472656i
\(123\) −2704.67 4743.91i −0.178774 0.313564i
\(124\) −23035.7 −1.49816
\(125\) 21202.6i 1.35697i
\(126\) 24138.3 + 14287.9i 1.52043 + 0.899970i
\(127\) 17272.2 1.07088 0.535438 0.844575i \(-0.320147\pi\)
0.535438 + 0.844575i \(0.320147\pi\)
\(128\) 7443.60i 0.454321i
\(129\) −19599.4 + 11174.3i −1.17778 + 0.671493i
\(130\) −60468.0 −3.57799
\(131\) 8931.88i 0.520476i −0.965545 0.260238i \(-0.916199\pi\)
0.965545 0.260238i \(-0.0838009\pi\)
\(132\) 9584.71 + 16811.3i 0.550087 + 0.964836i
\(133\) 28633.4 1.61871
\(134\) 31414.8i 1.74954i
\(135\) 30544.2 + 497.466i 1.67595 + 0.0272958i
\(136\) 1450.21 0.0784066
\(137\) 27846.5i 1.48364i −0.670597 0.741822i \(-0.733962\pi\)
0.670597 0.741822i \(-0.266038\pi\)
\(138\) 1221.21 696.252i 0.0641255 0.0365602i
\(139\) −14087.1 −0.729111 −0.364555 0.931182i \(-0.618779\pi\)
−0.364555 + 0.931182i \(0.618779\pi\)
\(140\) 35600.2i 1.81634i
\(141\) −11222.6 19684.2i −0.564491 0.990100i
\(142\) 38089.6 1.88899
\(143\) 43204.2i 2.11278i
\(144\) −12055.6 + 20367.0i −0.581385 + 0.982205i
\(145\) −14124.7 −0.671805
\(146\) 20197.9i 0.947546i
\(147\) 13257.2 7558.38i 0.613503 0.349779i
\(148\) 4363.75 0.199222
\(149\) 21635.1i 0.974512i 0.873259 + 0.487256i \(0.162002\pi\)
−0.873259 + 0.487256i \(0.837998\pi\)
\(150\) 27276.8 + 47842.7i 1.21230 + 2.12634i
\(151\) −10716.1 −0.469985 −0.234992 0.971997i \(-0.575507\pi\)
−0.234992 + 0.971997i \(0.575507\pi\)
\(152\) 6599.73i 0.285653i
\(153\) 6852.10 + 4055.88i 0.292712 + 0.173262i
\(154\) 56097.5 2.36539
\(155\) 72724.5i 3.02703i
\(156\) 27678.1 15780.3i 1.13733 0.648433i
\(157\) −43733.5 −1.77425 −0.887125 0.461529i \(-0.847301\pi\)
−0.887125 + 0.461529i \(0.847301\pi\)
\(158\) 22640.4i 0.906923i
\(159\) −7848.86 13766.7i −0.310465 0.544546i
\(160\) −56355.5 −2.20139
\(161\) 1847.73i 0.0712833i
\(162\) −31120.5 + 17077.4i −1.18581 + 0.650718i
\(163\) −29538.5 −1.11176 −0.555882 0.831261i \(-0.687619\pi\)
−0.555882 + 0.831261i \(0.687619\pi\)
\(164\) 8053.63i 0.299436i
\(165\) 53073.8 30259.2i 1.94945 1.11145i
\(166\) 32530.3 1.18052
\(167\) 24433.8i 0.876108i −0.898949 0.438054i \(-0.855668\pi\)
0.898949 0.438054i \(-0.144332\pi\)
\(168\) 4209.02 + 7382.50i 0.149129 + 0.261568i
\(169\) 42570.3 1.49051
\(170\) 22287.4i 0.771192i
\(171\) −18457.9 + 31183.2i −0.631232 + 1.06642i
\(172\) 33273.5 1.12471
\(173\) 18199.7i 0.608097i −0.952656 0.304049i \(-0.901661\pi\)
0.952656 0.304049i \(-0.0983386\pi\)
\(174\) 14258.8 8129.42i 0.470959 0.268510i
\(175\) 72387.8 2.36368
\(176\) 47332.9i 1.52805i
\(177\) −2020.14 3543.27i −0.0644815 0.113099i
\(178\) −72164.7 −2.27764
\(179\) 36106.0i 1.12687i 0.826161 + 0.563435i \(0.190520\pi\)
−0.826161 + 0.563435i \(0.809480\pi\)
\(180\) −38770.3 22948.8i −1.19661 0.708297i
\(181\) 4609.61 0.140704 0.0703521 0.997522i \(-0.477588\pi\)
0.0703521 + 0.997522i \(0.477588\pi\)
\(182\) 92358.9i 2.78828i
\(183\) 10166.1 5796.05i 0.303566 0.173073i
\(184\) 425.885 0.0125793
\(185\) 13776.5i 0.402527i
\(186\) −41856.3 73414.7i −1.20986 2.12206i
\(187\) 15924.3 0.455383
\(188\) 33417.4i 0.945489i
\(189\) −759.829 + 46653.3i −0.0212712 + 1.30605i
\(190\) −101428. −2.80963
\(191\) 71978.1i 1.97303i −0.163671 0.986515i \(-0.552334\pi\)
0.163671 0.986515i \(-0.447666\pi\)
\(192\) 20338.2 11595.5i 0.551708 0.314548i
\(193\) −65292.5 −1.75287 −0.876433 0.481523i \(-0.840084\pi\)
−0.876433 + 0.481523i \(0.840084\pi\)
\(194\) 41908.3i 1.11352i
\(195\) −49818.8 87380.7i −1.31016 2.29798i
\(196\) −22506.4 −0.585860
\(197\) 20345.6i 0.524249i 0.965034 + 0.262124i \(0.0844231\pi\)
−0.965034 + 0.262124i \(0.915577\pi\)
\(198\) −36162.0 + 61092.9i −0.922405 + 1.55833i
\(199\) 40599.6 1.02522 0.512608 0.858623i \(-0.328679\pi\)
0.512608 + 0.858623i \(0.328679\pi\)
\(200\) 16684.7i 0.417118i
\(201\) 45396.6 25882.2i 1.12365 0.640633i
\(202\) 7869.89 0.192871
\(203\) 21574.1i 0.523528i
\(204\) −5816.33 10201.7i −0.139762 0.245138i
\(205\) 25425.6 0.605010
\(206\) 61558.6i 1.45062i
\(207\) 2012.27 + 1191.10i 0.0469619 + 0.0277976i
\(208\) 77928.9 1.80124
\(209\) 72469.6i 1.65906i
\(210\) −113458. + 64686.1i −2.57273 + 1.46681i
\(211\) 75004.1 1.68469 0.842345 0.538939i \(-0.181175\pi\)
0.842345 + 0.538939i \(0.181175\pi\)
\(212\) 23371.3i 0.520010i
\(213\) 31381.5 + 55042.2i 0.691695 + 1.21321i
\(214\) −33800.5 −0.738066
\(215\) 105045.i 2.27248i
\(216\) −10753.1 175.133i −0.230477 0.00375372i
\(217\) −111079. −2.35892
\(218\) 45209.7i 0.951304i
\(219\) 29187.4 16640.8i 0.608566 0.346965i
\(220\) −90102.1 −1.86161
\(221\) 26217.7i 0.536798i
\(222\) 7929.02 + 13907.3i 0.160884 + 0.282186i
\(223\) −38212.6 −0.768418 −0.384209 0.923246i \(-0.625526\pi\)
−0.384209 + 0.923246i \(0.625526\pi\)
\(224\) 86077.4i 1.71551i
\(225\) −46663.2 + 78833.8i −0.921741 + 1.55721i
\(226\) 15871.1 0.310734
\(227\) 57636.8i 1.11853i 0.828989 + 0.559265i \(0.188917\pi\)
−0.828989 + 0.559265i \(0.811083\pi\)
\(228\) 46426.6 26469.4i 0.893095 0.509185i
\(229\) 18933.1 0.361036 0.180518 0.983572i \(-0.442223\pi\)
0.180518 + 0.983572i \(0.442223\pi\)
\(230\) 6545.20i 0.123728i
\(231\) 46217.9 + 81064.9i 0.866137 + 1.51918i
\(232\) 4972.62 0.0923867
\(233\) 12366.1i 0.227783i −0.993493 0.113891i \(-0.963668\pi\)
0.993493 0.113891i \(-0.0363316\pi\)
\(234\) 100583. + 59537.0i 1.83694 + 1.08732i
\(235\) 105500. 1.91036
\(236\) 6015.32i 0.108003i
\(237\) −32717.0 + 18653.1i −0.582475 + 0.332089i
\(238\) −34041.9 −0.600979
\(239\) 11878.9i 0.207960i −0.994579 0.103980i \(-0.966842\pi\)
0.994579 0.103980i \(-0.0331578\pi\)
\(240\) −54579.6 95731.1i −0.947563 1.66200i
\(241\) −45059.9 −0.775811 −0.387905 0.921699i \(-0.626801\pi\)
−0.387905 + 0.921699i \(0.626801\pi\)
\(242\) 62764.8i 1.07173i
\(243\) −50317.8 30901.4i −0.852137 0.523319i
\(244\) −17258.8 −0.289888
\(245\) 71053.4i 1.18373i
\(246\) −25666.9 + 14633.6i −0.424134 + 0.241813i
\(247\) 119314. 1.95568
\(248\) 25602.7i 0.416278i
\(249\) 26801.3 + 47008.6i 0.432271 + 0.758191i
\(250\) −114716. −1.83546
\(251\) 10604.9i 0.168329i −0.996452 0.0841646i \(-0.973178\pi\)
0.996452 0.0841646i \(-0.0268221\pi\)
\(252\) 35052.1 59217.8i 0.551966 0.932504i
\(253\) 4676.51 0.0730602
\(254\) 93450.7i 1.44849i
\(255\) −32207.0 + 18362.3i −0.495301 + 0.282389i
\(256\) 81893.8 1.24960
\(257\) 11638.4i 0.176209i −0.996111 0.0881046i \(-0.971919\pi\)
0.996111 0.0881046i \(-0.0280810\pi\)
\(258\) 60458.4 + 106042.i 0.908275 + 1.59309i
\(259\) 21042.2 0.313684
\(260\) 148344.i 2.19444i
\(261\) 23495.2 + 13907.2i 0.344904 + 0.204155i
\(262\) −48325.8 −0.704006
\(263\) 3594.97i 0.0519737i −0.999662 0.0259869i \(-0.991727\pi\)
0.999662 0.0259869i \(-0.00827280\pi\)
\(264\) −18684.7 + 10652.8i −0.268089 + 0.152847i
\(265\) 73784.0 1.05068
\(266\) 154921.i 2.18951i
\(267\) −59455.5 104283.i −0.834007 1.46282i
\(268\) −77068.8 −1.07302
\(269\) 32803.0i 0.453325i −0.973973 0.226662i \(-0.927219\pi\)
0.973973 0.226662i \(-0.0727814\pi\)
\(270\) 2691.53 165259.i 0.0369209 2.26693i
\(271\) 28994.4 0.394798 0.197399 0.980323i \(-0.436751\pi\)
0.197399 + 0.980323i \(0.436751\pi\)
\(272\) 28723.2i 0.388235i
\(273\) 133465. 76093.2i 1.79078 1.02099i
\(274\) −150663. −2.00681
\(275\) 183210.i 2.42261i
\(276\) −1708.09 2995.94i −0.0224230 0.0393292i
\(277\) −88957.8 −1.15938 −0.579688 0.814838i \(-0.696826\pi\)
−0.579688 + 0.814838i \(0.696826\pi\)
\(278\) 76218.3i 0.986211i
\(279\) 71604.7 120971.i 0.919885 1.55407i
\(280\) −39567.3 −0.504685
\(281\) 62305.2i 0.789063i 0.918882 + 0.394532i \(0.129093\pi\)
−0.918882 + 0.394532i \(0.870907\pi\)
\(282\) −106501. + 60719.9i −1.33923 + 0.763542i
\(283\) −102769. −1.28318 −0.641592 0.767046i \(-0.721726\pi\)
−0.641592 + 0.767046i \(0.721726\pi\)
\(284\) 93443.9i 1.15855i
\(285\) −83564.8 146570.i −1.02881 1.80450i
\(286\) 233755. 2.85779
\(287\) 38835.0i 0.471476i
\(288\) 93742.4 + 55487.8i 1.13019 + 0.668979i
\(289\) 73857.6 0.884300
\(290\) 76421.5i 0.908698i
\(291\) −60560.5 + 34527.6i −0.715160 + 0.407738i
\(292\) −49550.8 −0.581145
\(293\) 124891.i 1.45478i −0.686225 0.727389i \(-0.740733\pi\)
0.686225 0.727389i \(-0.259267\pi\)
\(294\) −40894.5 71727.8i −0.473119 0.829837i
\(295\) 18990.5 0.218219
\(296\) 4850.04i 0.0553556i
\(297\) −118077. 1923.09i −1.33860 0.0218015i
\(298\) 117057. 1.31815
\(299\) 7699.41i 0.0861222i
\(300\) 117371. 66917.1i 1.30412 0.743524i
\(301\) 160446. 1.77091
\(302\) 57979.4i 0.635712i
\(303\) 6483.89 + 11372.6i 0.0706237 + 0.123872i
\(304\) 130716. 1.41443
\(305\) 54486.4i 0.585718i
\(306\) 21944.3 37073.2i 0.234358 0.395929i
\(307\) 82222.6 0.872398 0.436199 0.899850i \(-0.356324\pi\)
0.436199 + 0.899850i \(0.356324\pi\)
\(308\) 137622.i 1.45073i
\(309\) 88956.7 50717.3i 0.931669 0.531177i
\(310\) 393475. 4.09443
\(311\) 153255.i 1.58450i −0.610195 0.792251i \(-0.708909\pi\)
0.610195 0.792251i \(-0.291091\pi\)
\(312\) 17538.8 + 30762.5i 0.180173 + 0.316018i
\(313\) −146232. −1.49263 −0.746316 0.665591i \(-0.768179\pi\)
−0.746316 + 0.665591i \(0.768179\pi\)
\(314\) 236619.i 2.39989i
\(315\) −186952. 110660.i −1.88412 1.11525i
\(316\) 55542.9 0.556230
\(317\) 47521.9i 0.472907i 0.971643 + 0.236453i \(0.0759851\pi\)
−0.971643 + 0.236453i \(0.924015\pi\)
\(318\) −74484.4 + 42466.1i −0.736565 + 0.419941i
\(319\) 54602.8 0.536579
\(320\) 109005.i 1.06450i
\(321\) −27847.7 48844.1i −0.270259 0.474026i
\(322\) −9997.13 −0.0964193
\(323\) 43977.0i 0.421522i
\(324\) 41895.5 + 76346.7i 0.399096 + 0.727278i
\(325\) 301636. 2.85573
\(326\) 159817.i 1.50380i
\(327\) −65331.3 + 37247.7i −0.610979 + 0.348340i
\(328\) −8951.10 −0.0832010
\(329\) 161140.i 1.48872i
\(330\) −163717. 287155.i −1.50337 2.63687i
\(331\) 23464.2 0.214165 0.107083 0.994250i \(-0.465849\pi\)
0.107083 + 0.994250i \(0.465849\pi\)
\(332\) 79805.4i 0.724029i
\(333\) −13564.4 + 22916.0i −0.122324 + 0.206657i
\(334\) −132199. −1.18504
\(335\) 243308.i 2.16804i
\(336\) 146220. 83365.0i 1.29517 0.738423i
\(337\) −98655.4 −0.868682 −0.434341 0.900748i \(-0.643019\pi\)
−0.434341 + 0.900748i \(0.643019\pi\)
\(338\) 230326.i 2.01609i
\(339\) 13075.9 + 22934.8i 0.113782 + 0.199570i
\(340\) 54677.0 0.472985
\(341\) 281136.i 2.41773i
\(342\) 168716. + 99866.0i 1.44246 + 0.853819i
\(343\) 45148.4 0.383755
\(344\) 36981.3i 0.312511i
\(345\) −9458.28 + 5392.50i −0.0794646 + 0.0453056i
\(346\) −98469.5 −0.822525
\(347\) 166071.i 1.37923i −0.724178 0.689614i \(-0.757780\pi\)
0.724178 0.689614i \(-0.242220\pi\)
\(348\) −19943.6 34980.5i −0.164682 0.288847i
\(349\) −4808.67 −0.0394797 −0.0197399 0.999805i \(-0.506284\pi\)
−0.0197399 + 0.999805i \(0.506284\pi\)
\(350\) 391653.i 3.19717i
\(351\) −3166.17 + 194402.i −0.0256992 + 1.57792i
\(352\) 217857. 1.75827
\(353\) 75307.1i 0.604347i 0.953253 + 0.302174i \(0.0977122\pi\)
−0.953253 + 0.302174i \(0.902288\pi\)
\(354\) −19170.8 + 10929.9i −0.152980 + 0.0872190i
\(355\) −295005. −2.34085
\(356\) 177039.i 1.39691i
\(357\) −28046.6 49192.9i −0.220061 0.385981i
\(358\) 195351. 1.52423
\(359\) 198922.i 1.54346i 0.635953 + 0.771728i \(0.280607\pi\)
−0.635953 + 0.771728i \(0.719393\pi\)
\(360\) 25506.2 43090.7i 0.196807 0.332490i
\(361\) 69813.4 0.535704
\(362\) 24940.2i 0.190319i
\(363\) −90699.7 + 51711.1i −0.688323 + 0.392437i
\(364\) −226581. −1.71010
\(365\) 156433.i 1.17420i
\(366\) −31359.5 55003.6i −0.234103 0.410609i
\(367\) −152393. −1.13144 −0.565722 0.824596i \(-0.691402\pi\)
−0.565722 + 0.824596i \(0.691402\pi\)
\(368\) 8435.19i 0.0622873i
\(369\) −42293.2 25034.1i −0.310611 0.183857i
\(370\) −74537.6 −0.544467
\(371\) 112698.i 0.818780i
\(372\) −180106. + 102685.i −1.30149 + 0.742026i
\(373\) −116970. −0.840733 −0.420366 0.907354i \(-0.638098\pi\)
−0.420366 + 0.907354i \(0.638098\pi\)
\(374\) 86158.1i 0.615961i
\(375\) −94513.3 165773.i −0.672094 1.17883i
\(376\) −37141.3 −0.262713
\(377\) 89898.1i 0.632510i
\(378\) 252417. + 4111.04i 1.76659 + 0.0287719i
\(379\) −185149. −1.28897 −0.644487 0.764616i \(-0.722929\pi\)
−0.644487 + 0.764616i \(0.722929\pi\)
\(380\) 248829.i 1.72319i
\(381\) 135043. 76992.8i 0.930298 0.530396i
\(382\) −389436. −2.66876
\(383\) 219154.i 1.49401i 0.664821 + 0.747003i \(0.268508\pi\)
−0.664821 + 0.747003i \(0.731492\pi\)
\(384\) 33180.7 + 58198.1i 0.225021 + 0.394681i
\(385\) −434477. −2.93120
\(386\) 353264.i 2.37096i
\(387\) −103428. + 174734.i −0.690583 + 1.16669i
\(388\) 102812. 0.682937
\(389\) 177651.i 1.17400i −0.809586 0.587002i \(-0.800308\pi\)
0.809586 0.587002i \(-0.199692\pi\)
\(390\) −472772. + 269544.i −3.10830 + 1.77215i
\(391\) −2837.87 −0.0185626
\(392\) 25014.4i 0.162787i
\(393\) −39815.0 69834.3i −0.257787 0.452151i
\(394\) 110079. 0.709110
\(395\) 175351.i 1.12386i
\(396\) 149877. + 88714.8i 0.955750 + 0.565726i
\(397\) 202948. 1.28767 0.643834 0.765165i \(-0.277343\pi\)
0.643834 + 0.765165i \(0.277343\pi\)
\(398\) 219663.i 1.38673i
\(399\) 223872. 127637.i 1.40622 0.801735i
\(400\) 330462. 2.06539
\(401\) 71075.9i 0.442012i −0.975272 0.221006i \(-0.929066\pi\)
0.975272 0.221006i \(-0.0709340\pi\)
\(402\) −140035. 245618.i −0.866534 1.51987i
\(403\) −462862. −2.84998
\(404\) 19306.9i 0.118291i
\(405\) 241029. 132265.i 1.46946 0.806372i
\(406\) −116726. −0.708136
\(407\) 53256.8i 0.321504i
\(408\) 11338.5 6464.48i 0.0681139 0.0388341i
\(409\) 237140. 1.41762 0.708808 0.705402i \(-0.249233\pi\)
0.708808 + 0.705402i \(0.249233\pi\)
\(410\) 137565.i 0.818350i
\(411\) −124129. 217719.i −0.734836 1.28888i
\(412\) −151020. −0.889690
\(413\) 29006.2i 0.170055i
\(414\) 6444.42 10887.4i 0.0375996 0.0635216i
\(415\) −251948. −1.46290
\(416\) 358680.i 2.07262i
\(417\) −110141. + 62795.2i −0.633398 + 0.361122i
\(418\) 392096. 2.24409
\(419\) 148867.i 0.847950i 0.905674 + 0.423975i \(0.139366\pi\)
−0.905674 + 0.423975i \(0.860634\pi\)
\(420\) 158692. + 278341.i 0.899615 + 1.57790i
\(421\) −205091. −1.15713 −0.578565 0.815636i \(-0.696387\pi\)
−0.578565 + 0.815636i \(0.696387\pi\)
\(422\) 405808.i 2.27875i
\(423\) −175489. 103875.i −0.980776 0.580539i
\(424\) −25975.8 −0.144490
\(425\) 111178.i 0.615518i
\(426\) 297805. 169789.i 1.64102 0.935601i
\(427\) −83222.6 −0.456442
\(428\) 82921.5i 0.452668i
\(429\) 192588. + 337793.i 1.04644 + 1.83542i
\(430\) −568346. −3.07380
\(431\) 209347.i 1.12697i 0.826126 + 0.563485i \(0.190540\pi\)
−0.826126 + 0.563485i \(0.809460\pi\)
\(432\) −3468.74 + 212980.i −0.0185868 + 1.14122i
\(433\) 207554. 1.10702 0.553511 0.832842i \(-0.313288\pi\)
0.553511 + 0.832842i \(0.313288\pi\)
\(434\) 600993.i 3.19073i
\(435\) −110435. + 62962.6i −0.583615 + 0.332739i
\(436\) 110911. 0.583450
\(437\) 12914.8i 0.0676278i
\(438\) −90034.6 157918.i −0.469312 0.823159i
\(439\) 87515.8 0.454106 0.227053 0.973882i \(-0.427091\pi\)
0.227053 + 0.973882i \(0.427091\pi\)
\(440\) 100143.i 0.517266i
\(441\) 69959.4 118191.i 0.359724 0.607725i
\(442\) −141851. −0.726084
\(443\) 262305.i 1.33659i 0.743896 + 0.668296i \(0.232976\pi\)
−0.743896 + 0.668296i \(0.767024\pi\)
\(444\) 34118.2 19452.0i 0.173069 0.0986729i
\(445\) 558918. 2.82246
\(446\) 206749.i 1.03938i
\(447\) 96441.3 + 169155.i 0.482668 + 0.846585i
\(448\) −166494. −0.829549
\(449\) 171982.i 0.853080i 0.904469 + 0.426540i \(0.140268\pi\)
−0.904469 + 0.426540i \(0.859732\pi\)
\(450\) 426529. + 252470.i 2.10632 + 1.24677i
\(451\) −98289.3 −0.483229
\(452\) 38935.9i 0.190578i
\(453\) −83784.5 + 47768.4i −0.408288 + 0.232779i
\(454\) 311843. 1.51295
\(455\) 715323.i 3.45525i
\(456\) 29419.1 + 51600.3i 0.141482 + 0.248155i
\(457\) 3157.29 0.0151176 0.00755879 0.999971i \(-0.497594\pi\)
0.00755879 + 0.999971i \(0.497594\pi\)
\(458\) 102437.i 0.488345i
\(459\) 71653.1 + 1166.99i 0.340102 + 0.00553915i
\(460\) 16057.1 0.0758842
\(461\) 272235.i 1.28098i −0.767966 0.640490i \(-0.778731\pi\)
0.767966 0.640490i \(-0.221269\pi\)
\(462\) 438601. 250062.i 2.05487 1.17156i
\(463\) 249599. 1.16434 0.582171 0.813066i \(-0.302203\pi\)
0.582171 + 0.813066i \(0.302203\pi\)
\(464\) 98489.1i 0.457459i
\(465\) 324178. + 568599.i 1.49926 + 2.62966i
\(466\) −66906.6 −0.308104
\(467\) 159468.i 0.731207i −0.930771 0.365604i \(-0.880863\pi\)
0.930771 0.365604i \(-0.119137\pi\)
\(468\) 146060. 246757.i 0.666868 1.12662i
\(469\) −371629. −1.68952
\(470\) 570804.i 2.58399i
\(471\) −341932. + 194947.i −1.54134 + 0.878771i
\(472\) −6685.65 −0.0300095
\(473\) 406081.i 1.81506i
\(474\) 100922. + 177015.i 0.449191 + 0.787868i
\(475\) 505958. 2.24247
\(476\) 83513.7i 0.368590i
\(477\) −122733. 72648.0i −0.539418 0.319291i
\(478\) −64270.5 −0.281291
\(479\) 285627.i 1.24488i 0.782666 + 0.622441i \(0.213859\pi\)
−0.782666 + 0.622441i \(0.786141\pi\)
\(480\) −440618. + 251212.i −1.91240 + 1.09033i
\(481\) 87681.9 0.378983
\(482\) 243796.i 1.04938i
\(483\) −8236.50 14446.6i −0.0353060 0.0619257i
\(484\) 153979. 0.657309
\(485\) 324581.i 1.37987i
\(486\) −167192. + 272244.i −0.707852 + 1.15262i
\(487\) −325973. −1.37443 −0.687216 0.726453i \(-0.741167\pi\)
−0.687216 + 0.726453i \(0.741167\pi\)
\(488\) 19182.0i 0.0805480i
\(489\) −230948. + 131671.i −0.965820 + 0.550648i
\(490\) 384433. 1.60114
\(491\) 278762.i 1.15630i −0.815931 0.578149i \(-0.803775\pi\)
0.815931 0.578149i \(-0.196225\pi\)
\(492\) 35900.1 + 62967.6i 0.148308 + 0.260128i
\(493\) −33134.8 −0.136330
\(494\) 645547.i 2.64529i
\(495\) 280075. 473166.i 1.14305 1.93109i
\(496\) −507095. −2.06123
\(497\) 450591.i 1.82419i
\(498\) 254339. 145008.i 1.02555 0.584699i
\(499\) −204145. −0.819857 −0.409928 0.912118i \(-0.634446\pi\)
−0.409928 + 0.912118i \(0.634446\pi\)
\(500\) 281430.i 1.12572i
\(501\) −108917. 191037.i −0.433929 0.761099i
\(502\) −57377.7 −0.227686
\(503\) 27595.1i 0.109068i −0.998512 0.0545339i \(-0.982633\pi\)
0.998512 0.0545339i \(-0.0173673\pi\)
\(504\) 65816.8 + 38958.1i 0.259105 + 0.153369i
\(505\) −60952.5 −0.239006
\(506\) 25302.2i 0.0988228i
\(507\) 332838. 189762.i 1.29484 0.738234i
\(508\) −229259. −0.888382
\(509\) 84040.5i 0.324379i 0.986760 + 0.162190i \(0.0518556\pi\)
−0.986760 + 0.162190i \(0.948144\pi\)
\(510\) 99349.1 + 174255.i 0.381965 + 0.669955i
\(511\) −238936. −0.915041
\(512\) 323988.i 1.23592i
\(513\) −5310.86 + 326085.i −0.0201804 + 1.23907i
\(514\) −62969.6 −0.238344
\(515\) 476773.i 1.79762i
\(516\) 260150. 148321.i 0.977067 0.557060i
\(517\) −407837. −1.52583
\(518\) 113849.i 0.424296i
\(519\) −81127.6 142295.i −0.301185 0.528270i
\(520\) −164875. −0.609745
\(521\) 107436.i 0.395800i −0.980222 0.197900i \(-0.936588\pi\)
0.980222 0.197900i \(-0.0634121\pi\)
\(522\) 75244.9 127120.i 0.276144 0.466524i
\(523\) −102442. −0.374521 −0.187261 0.982310i \(-0.559961\pi\)
−0.187261 + 0.982310i \(0.559961\pi\)
\(524\) 118556.i 0.431778i
\(525\) 565967. 322678.i 2.05340 1.17071i
\(526\) −19450.5 −0.0703007
\(527\) 170603.i 0.614278i
\(528\) 210992. + 370074.i 0.756830 + 1.32746i
\(529\) 279008. 0.997022
\(530\) 399207.i 1.42117i
\(531\) −31589.1 18698.2i −0.112034 0.0663147i
\(532\) −380061. −1.34286
\(533\) 161823.i 0.569622i
\(534\) −564223. + 321683.i −1.97865 + 1.12810i
\(535\) 261786. 0.914615
\(536\) 85657.1i 0.298149i
\(537\) 160947. + 282296.i 0.558129 + 0.978942i
\(538\) −177480. −0.613177
\(539\) 274676.i 0.945460i
\(540\) −405424. 6603.04i −1.39034 0.0226442i
\(541\) −40329.8 −0.137794 −0.0688972 0.997624i \(-0.521948\pi\)
−0.0688972 + 0.997624i \(0.521948\pi\)
\(542\) 156874.i 0.534012i
\(543\) 36040.4 20547.9i 0.122233 0.0696896i
\(544\) −132203. −0.446729
\(545\) 350151.i 1.17886i
\(546\) −411701. 722112.i −1.38101 2.42225i
\(547\) 123440. 0.412556 0.206278 0.978493i \(-0.433865\pi\)
0.206278 + 0.978493i \(0.433865\pi\)
\(548\) 369616.i 1.23081i
\(549\) 53647.5 90633.4i 0.177994 0.300707i
\(550\) 991253. 3.27687
\(551\) 150793.i 0.496681i
\(552\) 3329.80 1898.44i 0.0109280 0.00623042i
\(553\) 267831. 0.875810
\(554\) 481305.i 1.56820i
\(555\) −61410.5 107712.i −0.199368 0.349686i
\(556\) 186984. 0.604859
\(557\) 309624.i 0.997987i 0.866606 + 0.498993i \(0.166297\pi\)
−0.866606 + 0.498993i \(0.833703\pi\)
\(558\) −654510. 387416.i −2.10207 1.24426i
\(559\) 668571. 2.13956
\(560\) 783681.i 2.49898i
\(561\) 124505. 70984.5i 0.395603 0.225547i
\(562\) 337102. 1.06730
\(563\) 501724.i 1.58288i −0.611247 0.791440i \(-0.709332\pi\)
0.611247 0.791440i \(-0.290668\pi\)
\(564\) 148962. + 261275.i 0.468293 + 0.821372i
\(565\) −122922. −0.385063
\(566\) 556030.i 1.73566i
\(567\) 202022. + 368148.i 0.628395 + 1.14513i
\(568\) 103857. 0.321913
\(569\) 187984.i 0.580627i −0.956932 0.290313i \(-0.906240\pi\)
0.956932 0.290313i \(-0.0937595\pi\)
\(570\) −793016. + 452126.i −2.44080 + 1.39159i
\(571\) 404837. 1.24167 0.620837 0.783939i \(-0.286793\pi\)
0.620837 + 0.783939i \(0.286793\pi\)
\(572\) 573464.i 1.75273i
\(573\) −320851. 562764.i −0.977225 1.71402i
\(574\) 210116. 0.637728
\(575\) 32649.8i 0.0987518i
\(576\) 107326. 181320.i 0.323491 0.546513i
\(577\) 285933. 0.858841 0.429421 0.903105i \(-0.358718\pi\)
0.429421 + 0.903105i \(0.358718\pi\)
\(578\) 399605.i 1.19612i
\(579\) −510492. + 291050.i −1.52276 + 0.868180i
\(580\) 187482. 0.557319
\(581\) 384826.i 1.14002i
\(582\) 186811. + 327661.i 0.551515 + 0.967341i
\(583\) −285232. −0.839191
\(584\) 55072.6i 0.161477i
\(585\) −779020. 461116.i −2.27634 1.34741i
\(586\) −675722. −1.96776
\(587\) 186645.i 0.541676i −0.962625 0.270838i \(-0.912699\pi\)
0.962625 0.270838i \(-0.0873008\pi\)
\(588\) −175967. + 100325.i −0.508952 + 0.290172i
\(589\) −776394. −2.23796
\(590\) 102748.i 0.295168i
\(591\) 90692.9 + 159073.i 0.259656 + 0.455429i
\(592\) 96061.1 0.274097
\(593\) 160449.i 0.456276i 0.973629 + 0.228138i \(0.0732637\pi\)
−0.973629 + 0.228138i \(0.926736\pi\)
\(594\) −10404.8 + 638853.i −0.0294891 + 1.81062i
\(595\) 263655. 0.744736
\(596\) 287171.i 0.808440i
\(597\) 317429. 180978.i 0.890632 0.507781i
\(598\) −41657.6 −0.116491
\(599\) 258334.i 0.719993i 0.932954 + 0.359996i \(0.117222\pi\)
−0.932954 + 0.359996i \(0.882778\pi\)
\(600\) 74374.2 + 130450.i 0.206595 + 0.362361i
\(601\) 173281. 0.479734 0.239867 0.970806i \(-0.422896\pi\)
0.239867 + 0.970806i \(0.422896\pi\)
\(602\) 868092.i 2.39537i
\(603\) 239562. 404722.i 0.658846 1.11307i
\(604\) 142239. 0.389892
\(605\) 486115.i 1.32809i
\(606\) 61531.1 35081.0i 0.167552 0.0955271i
\(607\) −592777. −1.60884 −0.804422 0.594058i \(-0.797525\pi\)
−0.804422 + 0.594058i \(0.797525\pi\)
\(608\) 601642.i 1.62754i
\(609\) −96169.1 168678.i −0.259299 0.454803i
\(610\) 294798. 0.792255
\(611\) 671463.i 1.79862i
\(612\) −90950.4 53835.2i −0.242830 0.143735i
\(613\) 144770. 0.385264 0.192632 0.981271i \(-0.438298\pi\)
0.192632 + 0.981271i \(0.438298\pi\)
\(614\) 444864.i 1.18002i
\(615\) 198791. 113338.i 0.525589 0.299656i
\(616\) 152958. 0.403098
\(617\) 57533.0i 0.151129i −0.997141 0.0755643i \(-0.975924\pi\)
0.997141 0.0755643i \(-0.0240758\pi\)
\(618\) −274405. 481299.i −0.718481 1.26020i
\(619\) 349680. 0.912618 0.456309 0.889821i \(-0.349171\pi\)
0.456309 + 0.889821i \(0.349171\pi\)
\(620\) 965297.i 2.51118i
\(621\) 21042.5 + 342.713i 0.0545650 + 0.000888685i
\(622\) −829182. −2.14323
\(623\) 853691.i 2.19950i
\(624\) 609290. 347378.i 1.56479 0.892139i
\(625\) 181622. 0.464952
\(626\) 791185.i 2.01897i
\(627\) 323042. + 566607.i 0.821721 + 1.44127i
\(628\) 580490. 1.47189
\(629\) 32318.0i 0.0816852i
\(630\) −598726. + 1.01150e6i −1.50851 + 2.54851i
\(631\) 152337. 0.382601 0.191300 0.981532i \(-0.438730\pi\)
0.191300 + 0.981532i \(0.438730\pi\)
\(632\) 61732.5i 0.154554i
\(633\) 586422. 334340.i 1.46354 0.834412i
\(634\) 257117. 0.639664
\(635\) 723779.i 1.79497i
\(636\) 104181. + 182730.i 0.257557 + 0.451747i
\(637\) −452226. −1.11449
\(638\) 295428.i 0.725788i
\(639\) 490715. + 290463.i 1.20179 + 0.711360i
\(640\) −311919. −0.761521
\(641\) 367955.i 0.895526i −0.894152 0.447763i \(-0.852221\pi\)
0.894152 0.447763i \(-0.147779\pi\)
\(642\) −264270. + 150670.i −0.641178 + 0.365558i
\(643\) −369504. −0.893711 −0.446856 0.894606i \(-0.647456\pi\)
−0.446856 + 0.894606i \(0.647456\pi\)
\(644\) 24525.6i 0.0591355i
\(645\) −468252. 821301.i −1.12554 1.97416i
\(646\) −237937. −0.570160
\(647\) 358923.i 0.857419i −0.903442 0.428709i \(-0.858968\pi\)
0.903442 0.428709i \(-0.141032\pi\)
\(648\) −84854.5 + 46564.2i −0.202081 + 0.110892i
\(649\) −73413.0 −0.174294
\(650\) 1.63200e6i 3.86272i
\(651\) −868479. + 495150.i −2.04926 + 1.16835i
\(652\) 392075. 0.922303
\(653\) 415428.i 0.974247i −0.873333 0.487123i \(-0.838046\pi\)
0.873333 0.487123i \(-0.161954\pi\)
\(654\) 201528. + 353474.i 0.471173 + 0.826423i
\(655\) 374285. 0.872408
\(656\) 177288.i 0.411976i
\(657\) 154025. 260213.i 0.356829 0.602835i
\(658\) 871846. 2.01367
\(659\) 689382.i 1.58741i −0.608303 0.793705i \(-0.708149\pi\)
0.608303 0.793705i \(-0.291851\pi\)
\(660\) −704467. + 401641.i −1.61723 + 0.922042i
\(661\) 213731. 0.489175 0.244587 0.969627i \(-0.421347\pi\)
0.244587 + 0.969627i \(0.421347\pi\)
\(662\) 126953.i 0.289685i
\(663\) −116869. 204984.i −0.265871 0.466331i
\(664\) 88698.7 0.201178
\(665\) 1.19987e6i 2.71325i
\(666\) 123987. + 73389.9i 0.279529 + 0.165458i
\(667\) −9730.77 −0.0218723
\(668\) 324318.i 0.726806i
\(669\) −298767. + 170338.i −0.667545 + 0.380591i
\(670\) 1.31642e6 2.93254
\(671\) 210632.i 0.467820i
\(672\) −383701. 673000.i −0.849677 1.49031i
\(673\) −807880. −1.78368 −0.891840 0.452352i \(-0.850585\pi\)
−0.891840 + 0.452352i \(0.850585\pi\)
\(674\) 533773.i 1.17500i
\(675\) −13426.3 + 824372.i −0.0294679 + 1.80932i
\(676\) −565051. −1.23650
\(677\) 189407.i 0.413256i 0.978420 + 0.206628i \(0.0662490\pi\)
−0.978420 + 0.206628i \(0.933751\pi\)
\(678\) 124089. 70747.2i 0.269943 0.153904i
\(679\) 495765. 1.07532
\(680\) 60770.0i 0.131423i
\(681\) 256923. + 450636.i 0.553999 + 0.971698i
\(682\) −1.52108e6 −3.27027
\(683\) 547508.i 1.17368i 0.809704 + 0.586839i \(0.199628\pi\)
−0.809704 + 0.586839i \(0.800372\pi\)
\(684\) 244998. 413905.i 0.523661 0.884685i
\(685\) 1.16689e6 2.48685
\(686\) 244275.i 0.519076i
\(687\) 148029. 84396.5i 0.313641 0.178818i
\(688\) 732462. 1.54742
\(689\) 469606.i 0.989225i
\(690\) 29176.0 + 51173.9i 0.0612813 + 0.107486i
\(691\) 442497. 0.926733 0.463366 0.886167i \(-0.346641\pi\)
0.463366 + 0.886167i \(0.346641\pi\)
\(692\) 241572.i 0.504468i
\(693\) 722714. + 427787.i 1.50487 + 0.890761i
\(694\) −898527. −1.86557
\(695\) 590313.i 1.22212i
\(696\) 38878.6 22166.1i 0.0802588 0.0457583i
\(697\) 59645.3 0.122775
\(698\) 26017.2i 0.0534011i
\(699\) −55123.4 96684.9i −0.112819 0.197881i
\(700\) −960829. −1.96088
\(701\) 468708.i 0.953820i 0.878952 + 0.476910i \(0.158243\pi\)
−0.878952 + 0.476910i \(0.841757\pi\)
\(702\) 1.05181e6 + 17130.5i 2.13433 + 0.0347613i
\(703\) 147076. 0.297598
\(704\) 421387.i 0.850229i
\(705\) 824853. 470278.i 1.65958 0.946185i
\(706\) 407448. 0.817453
\(707\) 93098.9i 0.186254i
\(708\) 26814.0 + 47031.0i 0.0534928 + 0.0938248i
\(709\) 532060. 1.05844 0.529222 0.848483i \(-0.322484\pi\)
0.529222 + 0.848483i \(0.322484\pi\)
\(710\) 1.59612e6i 3.16628i
\(711\) −172651. + 291680.i −0.341531 + 0.576990i
\(712\) −196768. −0.388145
\(713\) 50101.2i 0.0985529i
\(714\) −266158. + 151746.i −0.522087 + 0.297660i
\(715\) −1.81044e6 −3.54138
\(716\) 479248.i 0.934834i
\(717\) −52951.6 92875.5i −0.103001 0.180660i
\(718\) 1.07627e6 2.08771
\(719\) 408677.i 0.790537i 0.918566 + 0.395268i \(0.129348\pi\)
−0.918566 + 0.395268i \(0.870652\pi\)
\(720\) −853466. 505182.i −1.64635 0.974502i
\(721\) −728224. −1.40086
\(722\) 377725.i 0.724604i
\(723\) −352302. + 200860.i −0.673968 + 0.384252i
\(724\) −61184.9 −0.116726
\(725\) 381218.i 0.725266i
\(726\) 279782. + 490729.i 0.530819 + 0.931041i
\(727\) −235444. −0.445471 −0.222735 0.974879i \(-0.571499\pi\)
−0.222735 + 0.974879i \(0.571499\pi\)
\(728\) 251830.i 0.475166i
\(729\) −531159. 17306.3i −0.999470 0.0325648i
\(730\) 846380. 1.58825
\(731\) 246423.i 0.461155i
\(732\) −134938. + 76933.0i −0.251833 + 0.143579i
\(733\) 342720. 0.637869 0.318934 0.947777i \(-0.396675\pi\)
0.318934 + 0.947777i \(0.396675\pi\)
\(734\) 824520.i 1.53041i
\(735\) 316729. + 555534.i 0.586291 + 1.02834i
\(736\) −38824.3 −0.0716718
\(737\) 940574.i 1.73164i
\(738\) −135447. + 228827.i −0.248688 + 0.420140i
\(739\) 234714. 0.429784 0.214892 0.976638i \(-0.431060\pi\)
0.214892 + 0.976638i \(0.431060\pi\)
\(740\) 182860.i 0.333931i
\(741\) 932861. 531857.i 1.69895 0.968631i
\(742\) 609750. 1.10750
\(743\) 367771.i 0.666193i 0.942893 + 0.333096i \(0.108093\pi\)
−0.942893 + 0.333096i \(0.891907\pi\)
\(744\) −114127. 200176.i −0.206179 0.361632i
\(745\) −906607. −1.63345
\(746\) 632866.i 1.13719i
\(747\) 419094. + 248069.i 0.751052 + 0.444561i
\(748\) −211369. −0.377779
\(749\) 399851.i 0.712746i
\(750\) −896915. + 511363.i −1.59452 + 0.909089i
\(751\) 769434. 1.36424 0.682122 0.731239i \(-0.261057\pi\)
0.682122 + 0.731239i \(0.261057\pi\)
\(752\) 735630.i 1.30084i
\(753\) −47272.7 82914.9i −0.0833720 0.146232i
\(754\) −486392. −0.855547
\(755\) 449052.i 0.787777i
\(756\) 10085.5 619245.i 0.0176463 1.08348i
\(757\) −311650. −0.543845 −0.271923 0.962319i \(-0.587659\pi\)
−0.271923 + 0.962319i \(0.587659\pi\)
\(758\) 1.00175e6i 1.74349i
\(759\) 36563.5 20846.1i 0.0634694 0.0361861i
\(760\) −276558. −0.478805
\(761\) 825994.i 1.42629i −0.701017 0.713144i \(-0.747270\pi\)
0.701017 0.713144i \(-0.252730\pi\)
\(762\) −416568. 730648.i −0.717424 1.25834i
\(763\) 534821. 0.918669
\(764\) 955391.i 1.63679i
\(765\) −169959. + 287133.i −0.290417 + 0.490637i
\(766\) 1.18573e6 2.02082
\(767\) 120867.i 0.205455i
\(768\) 640290. 365052.i 1.08556 0.618917i
\(769\) −441175. −0.746033 −0.373016 0.927825i \(-0.621676\pi\)
−0.373016 + 0.927825i \(0.621676\pi\)
\(770\) 2.35073e6i 3.96480i
\(771\) −51879.8 90995.6i −0.0872749 0.153078i
\(772\) 866651. 1.45415
\(773\) 550891.i 0.921949i 0.887413 + 0.460975i \(0.152500\pi\)
−0.887413 + 0.460975i \(0.847500\pi\)
\(774\) 945393. + 559595.i 1.57809 + 0.934097i
\(775\) −1.96279e6 −3.26792
\(776\) 114269.i 0.189760i
\(777\) 164520. 93798.4i 0.272506 0.155365i
\(778\) −961180. −1.58798
\(779\) 271439.i 0.447298i
\(780\) 661262. + 1.15983e6i 1.08689 + 1.90637i
\(781\) 1.14042e6 1.86966
\(782\) 15354.2i 0.0251081i