Properties

Label 177.5.b.a.119.8
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 119.8
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.71

$q$-expansion

\(f(q)\) \(=\) \(q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} +O(q^{10})\) \(q-6.80672i q^{2} +(7.51401 + 4.95376i) q^{3} -30.3314 q^{4} -9.67205i q^{5} +(33.7188 - 51.1457i) q^{6} -60.1761 q^{7} +97.5501i q^{8} +(31.9206 + 74.4451i) q^{9} -65.8349 q^{10} +66.8602i q^{11} +(-227.911 - 150.255i) q^{12} -79.5991 q^{13} +409.602i q^{14} +(47.9130 - 72.6758i) q^{15} +178.693 q^{16} -76.6480i q^{17} +(506.727 - 217.274i) q^{18} -369.199 q^{19} +293.367i q^{20} +(-452.163 - 298.098i) q^{21} +455.098 q^{22} +853.775i q^{23} +(-483.240 + 732.992i) q^{24} +531.452 q^{25} +541.809i q^{26} +(-128.932 + 717.508i) q^{27} +1825.23 q^{28} +694.927i q^{29} +(-494.684 - 326.130i) q^{30} -1164.96 q^{31} +344.487i q^{32} +(-331.209 + 502.388i) q^{33} -521.721 q^{34} +582.026i q^{35} +(-968.197 - 2258.03i) q^{36} -1061.64 q^{37} +2513.04i q^{38} +(-598.108 - 394.315i) q^{39} +943.509 q^{40} -738.368i q^{41} +(-2029.07 + 3077.75i) q^{42} +1783.16 q^{43} -2027.97i q^{44} +(720.037 - 308.737i) q^{45} +5811.40 q^{46} -1018.21i q^{47} +(1342.70 + 885.202i) q^{48} +1220.16 q^{49} -3617.44i q^{50} +(379.696 - 575.934i) q^{51} +2414.36 q^{52} -3786.72i q^{53} +(4883.88 + 877.603i) q^{54} +646.675 q^{55} -5870.18i q^{56} +(-2774.17 - 1828.92i) q^{57} +4730.17 q^{58} -453.188i q^{59} +(-1453.27 + 2204.36i) q^{60} -3105.94 q^{61} +7929.55i q^{62} +(-1920.85 - 4479.81i) q^{63} +5203.92 q^{64} +769.887i q^{65} +(3419.61 + 2254.45i) q^{66} -6621.39 q^{67} +2324.84i q^{68} +(-4229.39 + 6415.27i) q^{69} +3961.69 q^{70} -2089.76i q^{71} +(-7262.13 + 3113.85i) q^{72} +1724.26 q^{73} +7226.28i q^{74} +(3993.33 + 2632.68i) q^{75} +11198.3 q^{76} -4023.38i q^{77} +(-2683.99 + 4071.16i) q^{78} -4302.81 q^{79} -1728.33i q^{80} +(-4523.15 + 4752.66i) q^{81} -5025.86 q^{82} +5199.00i q^{83} +(13714.8 + 9041.73i) q^{84} -741.343 q^{85} -12137.5i q^{86} +(-3442.50 + 5221.68i) q^{87} -6522.22 q^{88} -3690.17i q^{89} +(-2101.49 - 4901.09i) q^{90} +4789.96 q^{91} -25896.2i q^{92} +(-8753.51 - 5770.93i) q^{93} -6930.68 q^{94} +3570.91i q^{95} +(-1706.51 + 2588.48i) q^{96} -12997.5 q^{97} -8305.27i q^{98} +(-4977.41 + 2134.21i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.80672i 1.70168i −0.525425 0.850840i \(-0.676094\pi\)
0.525425 0.850840i \(-0.323906\pi\)
\(3\) 7.51401 + 4.95376i 0.834890 + 0.550418i
\(4\) −30.3314 −1.89571
\(5\) 9.67205i 0.386882i −0.981112 0.193441i \(-0.938035\pi\)
0.981112 0.193441i \(-0.0619648\pi\)
\(6\) 33.7188 51.1457i 0.936635 1.42071i
\(7\) −60.1761 −1.22808 −0.614041 0.789274i \(-0.710457\pi\)
−0.614041 + 0.789274i \(0.710457\pi\)
\(8\) 97.5501i 1.52422i
\(9\) 31.9206 + 74.4451i 0.394081 + 0.919076i
\(10\) −65.8349 −0.658349
\(11\) 66.8602i 0.552563i 0.961077 + 0.276282i \(0.0891023\pi\)
−0.961077 + 0.276282i \(0.910898\pi\)
\(12\) −227.911 150.255i −1.58271 1.04343i
\(13\) −79.5991 −0.471001 −0.235500 0.971874i \(-0.575673\pi\)
−0.235500 + 0.971874i \(0.575673\pi\)
\(14\) 409.602i 2.08980i
\(15\) 47.9130 72.6758i 0.212947 0.323004i
\(16\) 178.693 0.698020
\(17\) 76.6480i 0.265218i −0.991168 0.132609i \(-0.957665\pi\)
0.991168 0.132609i \(-0.0423355\pi\)
\(18\) 506.727 217.274i 1.56397 0.670600i
\(19\) −369.199 −1.02271 −0.511356 0.859369i \(-0.670857\pi\)
−0.511356 + 0.859369i \(0.670857\pi\)
\(20\) 293.367i 0.733418i
\(21\) −452.163 298.098i −1.02531 0.675958i
\(22\) 455.098 0.940286
\(23\) 853.775i 1.61394i 0.590592 + 0.806970i \(0.298894\pi\)
−0.590592 + 0.806970i \(0.701106\pi\)
\(24\) −483.240 + 732.992i −0.838957 + 1.27256i
\(25\) 531.452 0.850322
\(26\) 541.809i 0.801493i
\(27\) −128.932 + 717.508i −0.176861 + 0.984236i
\(28\) 1825.23 2.32809
\(29\) 694.927i 0.826310i 0.910661 + 0.413155i \(0.135573\pi\)
−0.910661 + 0.413155i \(0.864427\pi\)
\(30\) −494.684 326.130i −0.549649 0.362367i
\(31\) −1164.96 −1.21224 −0.606118 0.795375i \(-0.707274\pi\)
−0.606118 + 0.795375i \(0.707274\pi\)
\(32\) 344.487i 0.336413i
\(33\) −331.209 + 502.388i −0.304141 + 0.461329i
\(34\) −521.721 −0.451316
\(35\) 582.026i 0.475123i
\(36\) −968.197 2258.03i −0.747065 1.74231i
\(37\) −1061.64 −0.775485 −0.387742 0.921768i \(-0.626745\pi\)
−0.387742 + 0.921768i \(0.626745\pi\)
\(38\) 2513.04i 1.74033i
\(39\) −598.108 394.315i −0.393234 0.259247i
\(40\) 943.509 0.589693
\(41\) 738.368i 0.439243i −0.975585 0.219622i \(-0.929518\pi\)
0.975585 0.219622i \(-0.0704822\pi\)
\(42\) −2029.07 + 3077.75i −1.15026 + 1.74476i
\(43\) 1783.16 0.964394 0.482197 0.876063i \(-0.339839\pi\)
0.482197 + 0.876063i \(0.339839\pi\)
\(44\) 2027.97i 1.04750i
\(45\) 720.037 308.737i 0.355574 0.152463i
\(46\) 5811.40 2.74641
\(47\) 1018.21i 0.460938i −0.973080 0.230469i \(-0.925974\pi\)
0.973080 0.230469i \(-0.0740260\pi\)
\(48\) 1342.70 + 885.202i 0.582770 + 0.384202i
\(49\) 1220.16 0.508187
\(50\) 3617.44i 1.44698i
\(51\) 379.696 575.934i 0.145981 0.221428i
\(52\) 2414.36 0.892883
\(53\) 3786.72i 1.34807i −0.738700 0.674034i \(-0.764560\pi\)
0.738700 0.674034i \(-0.235440\pi\)
\(54\) 4883.88 + 877.603i 1.67485 + 0.300961i
\(55\) 646.675 0.213777
\(56\) 5870.18i 1.87187i
\(57\) −2774.17 1828.92i −0.853852 0.562919i
\(58\) 4730.17 1.40611
\(59\) 453.188i 0.130189i
\(60\) −1453.27 + 2204.36i −0.403686 + 0.612323i
\(61\) −3105.94 −0.834706 −0.417353 0.908744i \(-0.637042\pi\)
−0.417353 + 0.908744i \(0.637042\pi\)
\(62\) 7929.55i 2.06284i
\(63\) −1920.85 4479.81i −0.483964 1.12870i
\(64\) 5203.92 1.27049
\(65\) 769.887i 0.182222i
\(66\) 3419.61 + 2254.45i 0.785035 + 0.517550i
\(67\) −6621.39 −1.47502 −0.737512 0.675334i \(-0.764000\pi\)
−0.737512 + 0.675334i \(0.764000\pi\)
\(68\) 2324.84i 0.502778i
\(69\) −4229.39 + 6415.27i −0.888341 + 1.34746i
\(70\) 3961.69 0.808507
\(71\) 2089.76i 0.414552i −0.978283 0.207276i \(-0.933540\pi\)
0.978283 0.207276i \(-0.0664598\pi\)
\(72\) −7262.13 + 3113.85i −1.40087 + 0.600666i
\(73\) 1724.26 0.323562 0.161781 0.986827i \(-0.448276\pi\)
0.161781 + 0.986827i \(0.448276\pi\)
\(74\) 7226.28i 1.31963i
\(75\) 3993.33 + 2632.68i 0.709925 + 0.468032i
\(76\) 11198.3 1.93877
\(77\) 4023.38i 0.678594i
\(78\) −2683.99 + 4071.16i −0.441156 + 0.669158i
\(79\) −4302.81 −0.689443 −0.344721 0.938705i \(-0.612027\pi\)
−0.344721 + 0.938705i \(0.612027\pi\)
\(80\) 1728.33i 0.270051i
\(81\) −4523.15 + 4752.66i −0.689400 + 0.724381i
\(82\) −5025.86 −0.747451
\(83\) 5199.00i 0.754681i 0.926075 + 0.377341i \(0.123161\pi\)
−0.926075 + 0.377341i \(0.876839\pi\)
\(84\) 13714.8 + 9041.73i 1.94370 + 1.28142i
\(85\) −741.343 −0.102608
\(86\) 12137.5i 1.64109i
\(87\) −3442.50 + 5221.68i −0.454815 + 0.689877i
\(88\) −6522.22 −0.842228
\(89\) 3690.17i 0.465872i −0.972492 0.232936i \(-0.925167\pi\)
0.972492 0.232936i \(-0.0748333\pi\)
\(90\) −2101.49 4901.09i −0.259443 0.605073i
\(91\) 4789.96 0.578428
\(92\) 25896.2i 3.05957i
\(93\) −8753.51 5770.93i −1.01208 0.667236i
\(94\) −6930.68 −0.784369
\(95\) 3570.91i 0.395669i
\(96\) −1706.51 + 2588.48i −0.185168 + 0.280868i
\(97\) −12997.5 −1.38139 −0.690695 0.723147i \(-0.742695\pi\)
−0.690695 + 0.723147i \(0.742695\pi\)
\(98\) 8305.27i 0.864772i
\(99\) −4977.41 + 2134.21i −0.507848 + 0.217755i
\(100\) −16119.7 −1.61197
\(101\) 7148.94i 0.700808i 0.936599 + 0.350404i \(0.113956\pi\)
−0.936599 + 0.350404i \(0.886044\pi\)
\(102\) −3920.22 2584.48i −0.376799 0.248412i
\(103\) 4725.85 0.445456 0.222728 0.974881i \(-0.428504\pi\)
0.222728 + 0.974881i \(0.428504\pi\)
\(104\) 7764.90i 0.717909i
\(105\) −2883.21 + 4373.34i −0.261516 + 0.396675i
\(106\) −25775.2 −2.29398
\(107\) 2061.82i 0.180088i −0.995938 0.0900439i \(-0.971299\pi\)
0.995938 0.0900439i \(-0.0287007\pi\)
\(108\) 3910.69 21763.0i 0.335278 1.86583i
\(109\) 1859.91 0.156545 0.0782725 0.996932i \(-0.475060\pi\)
0.0782725 + 0.996932i \(0.475060\pi\)
\(110\) 4401.73i 0.363780i
\(111\) −7977.16 5259.10i −0.647444 0.426840i
\(112\) −10753.0 −0.857226
\(113\) 15951.3i 1.24922i −0.780935 0.624612i \(-0.785257\pi\)
0.780935 0.624612i \(-0.214743\pi\)
\(114\) −12449.0 + 18883.0i −0.957908 + 1.45298i
\(115\) 8257.75 0.624404
\(116\) 21078.1i 1.56645i
\(117\) −2540.85 5925.77i −0.185613 0.432885i
\(118\) −3084.72 −0.221540
\(119\) 4612.37i 0.325710i
\(120\) 7089.53 + 4673.92i 0.492329 + 0.324577i
\(121\) 10170.7 0.694674
\(122\) 21141.3i 1.42040i
\(123\) 3657.69 5548.10i 0.241767 0.366719i
\(124\) 35334.9 2.29805
\(125\) 11185.3i 0.715856i
\(126\) −30492.8 + 13074.7i −1.92069 + 0.823552i
\(127\) −28137.9 −1.74455 −0.872276 0.489014i \(-0.837357\pi\)
−0.872276 + 0.489014i \(0.837357\pi\)
\(128\) 29909.8i 1.82555i
\(129\) 13398.7 + 8833.36i 0.805162 + 0.530819i
\(130\) 5240.40 0.310083
\(131\) 32488.0i 1.89313i 0.322512 + 0.946565i \(0.395473\pi\)
−0.322512 + 0.946565i \(0.604527\pi\)
\(132\) 10046.0 15238.1i 0.576564 0.874549i
\(133\) 22217.0 1.25598
\(134\) 45069.9i 2.51002i
\(135\) 6939.77 + 1247.03i 0.380783 + 0.0684244i
\(136\) 7477.02 0.404251
\(137\) 8126.87i 0.432994i 0.976283 + 0.216497i \(0.0694632\pi\)
−0.976283 + 0.216497i \(0.930537\pi\)
\(138\) 43666.9 + 28788.3i 2.29295 + 1.51167i
\(139\) −12474.3 −0.645633 −0.322816 0.946462i \(-0.604630\pi\)
−0.322816 + 0.946462i \(0.604630\pi\)
\(140\) 17653.7i 0.900698i
\(141\) 5043.98 7650.85i 0.253708 0.384832i
\(142\) −14224.4 −0.705434
\(143\) 5322.01i 0.260258i
\(144\) 5703.99 + 13302.8i 0.275076 + 0.641533i
\(145\) 6721.36 0.319684
\(146\) 11736.6i 0.550599i
\(147\) 9168.27 + 6044.37i 0.424280 + 0.279715i
\(148\) 32201.0 1.47010
\(149\) 3743.91i 0.168637i −0.996439 0.0843186i \(-0.973129\pi\)
0.996439 0.0843186i \(-0.0268713\pi\)
\(150\) 17919.9 27181.5i 0.796441 1.20807i
\(151\) −6575.64 −0.288393 −0.144196 0.989549i \(-0.546060\pi\)
−0.144196 + 0.989549i \(0.546060\pi\)
\(152\) 36015.4i 1.55884i
\(153\) 5706.07 2446.65i 0.243755 0.104517i
\(154\) −27386.0 −1.15475
\(155\) 11267.5i 0.468992i
\(156\) 18141.5 + 11960.1i 0.745459 + 0.491459i
\(157\) 41732.5 1.69307 0.846536 0.532331i \(-0.178684\pi\)
0.846536 + 0.532331i \(0.178684\pi\)
\(158\) 29288.0i 1.17321i
\(159\) 18758.5 28453.5i 0.742000 1.12549i
\(160\) 3331.90 0.130152
\(161\) 51376.8i 1.98205i
\(162\) 32350.0 + 30787.8i 1.23266 + 1.17314i
\(163\) −596.443 −0.0224488 −0.0112244 0.999937i \(-0.503573\pi\)
−0.0112244 + 0.999937i \(0.503573\pi\)
\(164\) 22395.8i 0.832680i
\(165\) 4859.12 + 3203.47i 0.178480 + 0.117666i
\(166\) 35388.1 1.28423
\(167\) 16614.0i 0.595719i 0.954610 + 0.297859i \(0.0962726\pi\)
−0.954610 + 0.297859i \(0.903727\pi\)
\(168\) 29079.4 44108.6i 1.03031 1.56280i
\(169\) −22225.0 −0.778158
\(170\) 5046.11i 0.174606i
\(171\) −11785.0 27485.1i −0.403032 0.939950i
\(172\) −54085.9 −1.82822
\(173\) 42859.0i 1.43202i 0.698088 + 0.716012i \(0.254034\pi\)
−0.698088 + 0.716012i \(0.745966\pi\)
\(174\) 35542.5 + 23432.1i 1.17395 + 0.773950i
\(175\) −31980.7 −1.04427
\(176\) 11947.5i 0.385700i
\(177\) 2244.98 3405.25i 0.0716583 0.108693i
\(178\) −25118.0 −0.792765
\(179\) 53772.0i 1.67822i −0.543959 0.839112i \(-0.683075\pi\)
0.543959 0.839112i \(-0.316925\pi\)
\(180\) −21839.8 + 9364.44i −0.674066 + 0.289026i
\(181\) −55039.5 −1.68003 −0.840015 0.542563i \(-0.817454\pi\)
−0.840015 + 0.542563i \(0.817454\pi\)
\(182\) 32603.9i 0.984299i
\(183\) −23338.1 15386.1i −0.696887 0.459437i
\(184\) −83285.8 −2.46000
\(185\) 10268.2i 0.300021i
\(186\) −39281.1 + 59582.7i −1.13542 + 1.72224i
\(187\) 5124.70 0.146550
\(188\) 30883.8i 0.873807i
\(189\) 7758.61 43176.8i 0.217200 1.20872i
\(190\) 24306.2 0.673302
\(191\) 64602.6i 1.77086i −0.464776 0.885428i \(-0.653865\pi\)
0.464776 0.885428i \(-0.346135\pi\)
\(192\) 39102.3 + 25779.0i 1.06072 + 0.699299i
\(193\) 64886.0 1.74195 0.870976 0.491326i \(-0.163488\pi\)
0.870976 + 0.491326i \(0.163488\pi\)
\(194\) 88470.3i 2.35068i
\(195\) −3813.83 + 5784.93i −0.100298 + 0.152135i
\(196\) −37009.1 −0.963378
\(197\) 40406.6i 1.04117i 0.853811 + 0.520583i \(0.174285\pi\)
−0.853811 + 0.520583i \(0.825715\pi\)
\(198\) 14527.0 + 33879.9i 0.370549 + 0.864194i
\(199\) 17926.2 0.452670 0.226335 0.974050i \(-0.427326\pi\)
0.226335 + 0.974050i \(0.427326\pi\)
\(200\) 51843.1i 1.29608i
\(201\) −49753.1 32800.7i −1.23148 0.811880i
\(202\) 48660.8 1.19255
\(203\) 41817.9i 1.01478i
\(204\) −11516.7 + 17468.9i −0.276738 + 0.419764i
\(205\) −7141.53 −0.169935
\(206\) 32167.5i 0.758024i
\(207\) −63559.4 + 27253.0i −1.48333 + 0.636023i
\(208\) −14223.8 −0.328768
\(209\) 24684.7i 0.565114i
\(210\) 29768.1 + 19625.2i 0.675014 + 0.445017i
\(211\) 64119.6 1.44021 0.720105 0.693865i \(-0.244094\pi\)
0.720105 + 0.693865i \(0.244094\pi\)
\(212\) 114857.i 2.55555i
\(213\) 10352.1 15702.4i 0.228177 0.346105i
\(214\) −14034.3 −0.306452
\(215\) 17246.8i 0.373106i
\(216\) −69993.0 12577.3i −1.50019 0.269575i
\(217\) 70102.7 1.48873
\(218\) 12659.9i 0.266390i
\(219\) 12956.1 + 8541.58i 0.270139 + 0.178094i
\(220\) −19614.6 −0.405260
\(221\) 6101.12i 0.124918i
\(222\) −35797.2 + 54298.3i −0.726346 + 1.10174i
\(223\) −39719.5 −0.798719 −0.399359 0.916794i \(-0.630767\pi\)
−0.399359 + 0.916794i \(0.630767\pi\)
\(224\) 20729.9i 0.413143i
\(225\) 16964.2 + 39564.0i 0.335096 + 0.781511i
\(226\) −108576. −2.12578
\(227\) 12769.2i 0.247807i −0.992294 0.123903i \(-0.960459\pi\)
0.992294 0.123903i \(-0.0395413\pi\)
\(228\) 84144.4 + 55473.9i 1.61866 + 1.06713i
\(229\) 79213.6 1.51053 0.755264 0.655421i \(-0.227509\pi\)
0.755264 + 0.655421i \(0.227509\pi\)
\(230\) 56208.2i 1.06254i
\(231\) 19930.9 30231.7i 0.373510 0.566551i
\(232\) −67790.1 −1.25948
\(233\) 23.2998i 0.000429182i 1.00000 0.000214591i \(6.83064e-5\pi\)
−1.00000 0.000214591i \(0.999932\pi\)
\(234\) −40335.1 + 17294.9i −0.736633 + 0.315853i
\(235\) −9848.20 −0.178329
\(236\) 13745.8i 0.246801i
\(237\) −32331.3 21315.1i −0.575608 0.379481i
\(238\) 31395.1 0.554254
\(239\) 66769.5i 1.16891i 0.811425 + 0.584457i \(0.198692\pi\)
−0.811425 + 0.584457i \(0.801308\pi\)
\(240\) 8561.72 12986.7i 0.148641 0.225463i
\(241\) 54046.8 0.930542 0.465271 0.885168i \(-0.345957\pi\)
0.465271 + 0.885168i \(0.345957\pi\)
\(242\) 69229.2i 1.18211i
\(243\) −57530.5 + 13304.9i −0.974285 + 0.225320i
\(244\) 94207.7 1.58236
\(245\) 11801.4i 0.196608i
\(246\) −37764.4 24896.9i −0.624039 0.411410i
\(247\) 29387.9 0.481699
\(248\) 113642.i 1.84772i
\(249\) −25754.6 + 39065.3i −0.415390 + 0.630075i
\(250\) −76134.9 −1.21816
\(251\) 6027.25i 0.0956691i 0.998855 + 0.0478345i \(0.0152320\pi\)
−0.998855 + 0.0478345i \(0.984768\pi\)
\(252\) 58262.3 + 135879.i 0.917458 + 2.13970i
\(253\) −57083.5 −0.891804
\(254\) 191527.i 2.96867i
\(255\) −5570.46 3672.43i −0.0856664 0.0564773i
\(256\) −120325. −1.83602
\(257\) 74332.0i 1.12541i 0.826659 + 0.562703i \(0.190239\pi\)
−0.826659 + 0.562703i \(0.809761\pi\)
\(258\) 60126.2 91201.2i 0.903284 1.37013i
\(259\) 63885.2 0.952360
\(260\) 23351.8i 0.345440i
\(261\) −51733.9 + 22182.4i −0.759441 + 0.325633i
\(262\) 221137. 3.22150
\(263\) 46448.8i 0.671527i 0.941946 + 0.335763i \(0.108994\pi\)
−0.941946 + 0.335763i \(0.891006\pi\)
\(264\) −49008.0 32309.5i −0.703168 0.463577i
\(265\) −36625.4 −0.521543
\(266\) 151225.i 2.13727i
\(267\) 18280.2 27728.0i 0.256424 0.388952i
\(268\) 200836. 2.79623
\(269\) 36243.2i 0.500867i −0.968134 0.250433i \(-0.919427\pi\)
0.968134 0.250433i \(-0.0805731\pi\)
\(270\) 8488.22 47237.1i 0.116436 0.647971i
\(271\) −8415.64 −0.114590 −0.0572952 0.998357i \(-0.518248\pi\)
−0.0572952 + 0.998357i \(0.518248\pi\)
\(272\) 13696.5i 0.185127i
\(273\) 35991.8 + 23728.3i 0.482924 + 0.318377i
\(274\) 55317.3 0.736818
\(275\) 35532.9i 0.469857i
\(276\) 128284. 194584.i 1.68404 2.55440i
\(277\) 52973.6 0.690399 0.345199 0.938529i \(-0.387811\pi\)
0.345199 + 0.938529i \(0.387811\pi\)
\(278\) 84908.8i 1.09866i
\(279\) −37186.2 86725.5i −0.477719 1.11414i
\(280\) −56776.7 −0.724192
\(281\) 38300.1i 0.485051i −0.970145 0.242526i \(-0.922024\pi\)
0.970145 0.242526i \(-0.0779759\pi\)
\(282\) −52077.2 34332.9i −0.654862 0.431730i
\(283\) −12441.2 −0.155342 −0.0776712 0.996979i \(-0.524748\pi\)
−0.0776712 + 0.996979i \(0.524748\pi\)
\(284\) 63385.3i 0.785872i
\(285\) −17689.4 + 26831.9i −0.217783 + 0.330340i
\(286\) −36225.4 −0.442876
\(287\) 44432.0i 0.539427i
\(288\) −25645.4 + 10996.2i −0.309189 + 0.132574i
\(289\) 77646.1 0.929659
\(290\) 45750.4i 0.544000i
\(291\) −97663.2 64386.4i −1.15331 0.760341i
\(292\) −52299.4 −0.613382
\(293\) 146740.i 1.70928i −0.519223 0.854639i \(-0.673779\pi\)
0.519223 0.854639i \(-0.326221\pi\)
\(294\) 41142.3 62405.9i 0.475986 0.721989i
\(295\) −4383.25 −0.0503677
\(296\) 103563.i 1.18201i
\(297\) −47972.7 8620.40i −0.543853 0.0977270i
\(298\) −25483.8 −0.286966
\(299\) 67959.7i 0.760167i
\(300\) −121123. 79853.0i −1.34582 0.887256i
\(301\) −107304. −1.18436
\(302\) 44758.5i 0.490752i
\(303\) −35414.1 + 53717.2i −0.385737 + 0.585097i
\(304\) −65973.4 −0.713874
\(305\) 30040.8i 0.322933i
\(306\) −16653.6 38839.6i −0.177855 0.414794i
\(307\) −38709.3 −0.410713 −0.205356 0.978687i \(-0.565835\pi\)
−0.205356 + 0.978687i \(0.565835\pi\)
\(308\) 122035.i 1.28642i
\(309\) 35510.0 + 23410.7i 0.371907 + 0.245187i
\(310\) 76695.0 0.798075
\(311\) 69420.6i 0.717741i 0.933387 + 0.358870i \(0.116838\pi\)
−0.933387 + 0.358870i \(0.883162\pi\)
\(312\) 38465.5 58345.5i 0.395150 0.599375i
\(313\) 90383.4 0.922572 0.461286 0.887252i \(-0.347388\pi\)
0.461286 + 0.887252i \(0.347388\pi\)
\(314\) 284062.i 2.88107i
\(315\) −43329.0 + 18578.6i −0.436674 + 0.187237i
\(316\) 130510. 1.30699
\(317\) 18279.9i 0.181910i 0.995855 + 0.0909549i \(0.0289919\pi\)
−0.995855 + 0.0909549i \(0.971008\pi\)
\(318\) −193675. 127684.i −1.91522 1.26265i
\(319\) −46462.9 −0.456589
\(320\) 50332.5i 0.491529i
\(321\) 10213.8 15492.6i 0.0991234 0.150353i
\(322\) −349707. −3.37282
\(323\) 28298.4i 0.271242i
\(324\) 137194. 144155.i 1.30691 1.37322i
\(325\) −42303.1 −0.400503
\(326\) 4059.82i 0.0382007i
\(327\) 13975.4 + 9213.55i 0.130698 + 0.0861651i
\(328\) 72027.8 0.669503
\(329\) 61272.0i 0.566070i
\(330\) 21805.1 33074.7i 0.200231 0.303716i
\(331\) 93312.0 0.851690 0.425845 0.904796i \(-0.359977\pi\)
0.425845 + 0.904796i \(0.359977\pi\)
\(332\) 157693.i 1.43066i
\(333\) −33888.1 79033.8i −0.305604 0.712729i
\(334\) 113087. 1.01372
\(335\) 64042.4i 0.570660i
\(336\) −80798.5 53268.0i −0.715689 0.471832i
\(337\) 153601. 1.35249 0.676247 0.736675i \(-0.263605\pi\)
0.676247 + 0.736675i \(0.263605\pi\)
\(338\) 151279.i 1.32418i
\(339\) 79019.1 119859.i 0.687595 1.04296i
\(340\) 22486.0 0.194516
\(341\) 77889.4i 0.669837i
\(342\) −187083. + 80217.5i −1.59949 + 0.685831i
\(343\) 71058.4 0.603987
\(344\) 173948.i 1.46995i
\(345\) 62048.8 + 40906.9i 0.521309 + 0.343683i
\(346\) 291730. 2.43685
\(347\) 45198.1i 0.375371i 0.982229 + 0.187686i \(0.0600986\pi\)
−0.982229 + 0.187686i \(0.939901\pi\)
\(348\) 104416. 158381.i 0.862200 1.30781i
\(349\) −226920. −1.86304 −0.931518 0.363695i \(-0.881515\pi\)
−0.931518 + 0.363695i \(0.881515\pi\)
\(350\) 217683.i 1.77701i
\(351\) 10262.9 57113.0i 0.0833018 0.463576i
\(352\) −23032.5 −0.185890
\(353\) 102234.i 0.820436i 0.911987 + 0.410218i \(0.134547\pi\)
−0.911987 + 0.410218i \(0.865453\pi\)
\(354\) −23178.6 15281.0i −0.184961 0.121939i
\(355\) −20212.2 −0.160383
\(356\) 111928.i 0.883161i
\(357\) −22848.6 + 34657.4i −0.179276 + 0.271932i
\(358\) −366011. −2.85580
\(359\) 149322.i 1.15860i 0.815114 + 0.579301i \(0.196675\pi\)
−0.815114 + 0.579301i \(0.803325\pi\)
\(360\) 30117.3 + 70239.7i 0.232387 + 0.541973i
\(361\) 5987.10 0.0459412
\(362\) 374638.i 2.85887i
\(363\) 76422.8 + 50383.3i 0.579976 + 0.382361i
\(364\) −145286. −1.09653
\(365\) 16677.2i 0.125180i
\(366\) −104729. + 158856.i −0.781814 + 1.18588i
\(367\) −126266. −0.937463 −0.468732 0.883341i \(-0.655289\pi\)
−0.468732 + 0.883341i \(0.655289\pi\)
\(368\) 152564.i 1.12656i
\(369\) 54967.9 23569.1i 0.403698 0.173097i
\(370\) 69892.9 0.510540
\(371\) 227870.i 1.65554i
\(372\) 265507. + 175040.i 1.91862 + 1.26489i
\(373\) −56999.8 −0.409690 −0.204845 0.978794i \(-0.565669\pi\)
−0.204845 + 0.978794i \(0.565669\pi\)
\(374\) 34882.4i 0.249381i
\(375\) 55409.0 84046.1i 0.394020 0.597661i
\(376\) 99326.7 0.702571
\(377\) 55315.6i 0.389193i
\(378\) −293892. 52810.7i −2.05686 0.369605i
\(379\) 198960. 1.38512 0.692561 0.721359i \(-0.256482\pi\)
0.692561 + 0.721359i \(0.256482\pi\)
\(380\) 108311.i 0.750076i
\(381\) −211428. 139388.i −1.45651 0.960232i
\(382\) −439732. −3.01343
\(383\) 173036.i 1.17961i 0.807544 + 0.589807i \(0.200796\pi\)
−0.807544 + 0.589807i \(0.799204\pi\)
\(384\) 148166. 224743.i 1.00482 1.52413i
\(385\) −38914.3 −0.262536
\(386\) 441661.i 2.96424i
\(387\) 56919.6 + 132748.i 0.380049 + 0.886351i
\(388\) 394233. 2.61872
\(389\) 13759.1i 0.0909265i −0.998966 0.0454632i \(-0.985524\pi\)
0.998966 0.0454632i \(-0.0144764\pi\)
\(390\) 39376.4 + 25959.7i 0.258885 + 0.170675i
\(391\) 65440.1 0.428046
\(392\) 119026.i 0.774589i
\(393\) −160938. + 244115.i −1.04201 + 1.58055i
\(394\) 275037. 1.77173
\(395\) 41617.0i 0.266733i
\(396\) 150972. 64733.8i 0.962734 0.412801i
\(397\) −308123. −1.95499 −0.977493 0.210969i \(-0.932338\pi\)
−0.977493 + 0.210969i \(0.932338\pi\)
\(398\) 122019.i 0.770300i
\(399\) 166938. + 110057.i 1.04860 + 0.691311i
\(400\) 94966.7 0.593542
\(401\) 92117.9i 0.572869i 0.958100 + 0.286435i \(0.0924701\pi\)
−0.958100 + 0.286435i \(0.907530\pi\)
\(402\) −223265. + 338656.i −1.38156 + 2.09559i
\(403\) 92729.8 0.570964
\(404\) 216838.i 1.32853i
\(405\) 45968.0 + 43748.2i 0.280250 + 0.266716i
\(406\) −284643. −1.72683
\(407\) 70981.4i 0.428505i
\(408\) 56182.4 + 37039.3i 0.337505 + 0.222507i
\(409\) 133670. 0.799072 0.399536 0.916717i \(-0.369171\pi\)
0.399536 + 0.916717i \(0.369171\pi\)
\(410\) 48610.4i 0.289175i
\(411\) −40258.6 + 61065.4i −0.238328 + 0.361503i
\(412\) −143342. −0.844458
\(413\) 27271.0i 0.159883i
\(414\) 185503. + 432631.i 1.08231 + 2.52416i
\(415\) 50285.0 0.291973
\(416\) 27420.9i 0.158451i
\(417\) −93731.7 61794.5i −0.539032 0.355367i
\(418\) −168022. −0.961642
\(419\) 17851.9i 0.101685i 0.998707 + 0.0508425i \(0.0161906\pi\)
−0.998707 + 0.0508425i \(0.983809\pi\)
\(420\) 87452.0 132650.i 0.495760 0.751983i
\(421\) −199234. −1.12408 −0.562042 0.827109i \(-0.689984\pi\)
−0.562042 + 0.827109i \(0.689984\pi\)
\(422\) 436444.i 2.45078i
\(423\) 75800.9 32501.9i 0.423637 0.181647i
\(424\) 369395. 2.05475
\(425\) 40734.7i 0.225521i
\(426\) −106882. 70464.1i −0.588960 0.388284i
\(427\) 186903. 1.02509
\(428\) 62538.1i 0.341395i
\(429\) 26364.0 39989.6i 0.143250 0.217287i
\(430\) −117394. −0.634908
\(431\) 42353.7i 0.228001i 0.993481 + 0.114001i \(0.0363666\pi\)
−0.993481 + 0.114001i \(0.963633\pi\)
\(432\) −23039.2 + 128214.i −0.123453 + 0.687016i
\(433\) −218337. −1.16453 −0.582267 0.812997i \(-0.697834\pi\)
−0.582267 + 0.812997i \(0.697834\pi\)
\(434\) 477169.i 2.53334i
\(435\) 50504.4 + 33296.0i 0.266901 + 0.175960i
\(436\) −56413.8 −0.296765
\(437\) 315213.i 1.65060i
\(438\) 58140.2 88188.7i 0.303060 0.459690i
\(439\) −77607.9 −0.402696 −0.201348 0.979520i \(-0.564532\pi\)
−0.201348 + 0.979520i \(0.564532\pi\)
\(440\) 63083.2i 0.325843i
\(441\) 38948.1 + 90834.8i 0.200267 + 0.467063i
\(442\) 41528.6 0.212570
\(443\) 106771.i 0.544057i 0.962289 + 0.272028i \(0.0876945\pi\)
−0.962289 + 0.272028i \(0.912306\pi\)
\(444\) 241959. + 159516.i 1.22737 + 0.809168i
\(445\) −35691.5 −0.180237
\(446\) 270359.i 1.35916i
\(447\) 18546.4 28131.8i 0.0928208 0.140793i
\(448\) −313151. −1.56026
\(449\) 373144.i 1.85090i −0.378866 0.925451i \(-0.623686\pi\)
0.378866 0.925451i \(-0.376314\pi\)
\(450\) 269301. 115471.i 1.32988 0.570226i
\(451\) 49367.4 0.242710
\(452\) 483827.i 2.36817i
\(453\) −49409.4 32574.1i −0.240776 0.158736i
\(454\) −86916.5 −0.421687
\(455\) 46328.7i 0.223783i
\(456\) 178412. 270620.i 0.858012 1.30146i
\(457\) −11487.8 −0.0550054 −0.0275027 0.999622i \(-0.508755\pi\)
−0.0275027 + 0.999622i \(0.508755\pi\)
\(458\) 539185.i 2.57043i
\(459\) 54995.5 + 9882.37i 0.261037 + 0.0469068i
\(460\) −250469. −1.18369
\(461\) 103362.i 0.486362i 0.969981 + 0.243181i \(0.0781908\pi\)
−0.969981 + 0.243181i \(0.921809\pi\)
\(462\) −205779. 135664.i −0.964088 0.635594i
\(463\) 228771. 1.06719 0.533593 0.845742i \(-0.320842\pi\)
0.533593 + 0.845742i \(0.320842\pi\)
\(464\) 124179.i 0.576781i
\(465\) −55816.7 + 84664.4i −0.258142 + 0.391557i
\(466\) 158.596 0.000730330
\(467\) 362034.i 1.66003i 0.557744 + 0.830013i \(0.311667\pi\)
−0.557744 + 0.830013i \(0.688333\pi\)
\(468\) 77067.6 + 179737.i 0.351868 + 0.820627i
\(469\) 398449. 1.81145
\(470\) 67033.9i 0.303458i
\(471\) 313579. + 206733.i 1.41353 + 0.931897i
\(472\) 44208.5 0.198437
\(473\) 119223.i 0.532889i
\(474\) −145086. + 220070.i −0.645756 + 0.979501i
\(475\) −196212. −0.869635
\(476\) 139900.i 0.617453i
\(477\) 281903. 120874.i 1.23898 0.531248i
\(478\) 454481. 1.98912
\(479\) 36289.9i 0.158166i −0.996868 0.0790832i \(-0.974801\pi\)
0.996868 0.0790832i \(-0.0251993\pi\)
\(480\) 25035.9 + 16505.4i 0.108663 + 0.0716381i
\(481\) 84505.5 0.365254
\(482\) 367882.i 1.58348i
\(483\) 254508. 386045.i 1.09096 1.65480i
\(484\) −308492. −1.31690
\(485\) 125712.i 0.534434i
\(486\) 90562.8 + 391594.i 0.383422 + 1.65792i
\(487\) −147016. −0.619880 −0.309940 0.950756i \(-0.600309\pi\)
−0.309940 + 0.950756i \(0.600309\pi\)
\(488\) 302985.i 1.27228i
\(489\) −4481.67 2954.63i −0.0187423 0.0123562i
\(490\) −80329.0 −0.334565
\(491\) 253813.i 1.05281i 0.850233 + 0.526406i \(0.176461\pi\)
−0.850233 + 0.526406i \(0.823539\pi\)
\(492\) −110943. + 168282.i −0.458321 + 0.695195i
\(493\) 53264.7 0.219152
\(494\) 200036.i 0.819697i
\(495\) 20642.2 + 48141.8i 0.0842454 + 0.196477i
\(496\) −208170. −0.846165
\(497\) 125753.i 0.509104i
\(498\) 265907. + 175304.i 1.07219 + 0.706861i
\(499\) −361497. −1.45179 −0.725895 0.687805i \(-0.758574\pi\)
−0.725895 + 0.687805i \(0.758574\pi\)
\(500\) 339265.i 1.35706i
\(501\) −82301.7 + 124838.i −0.327894 + 0.497359i
\(502\) 41025.8 0.162798
\(503\) 487472.i 1.92670i 0.268252 + 0.963349i \(0.413554\pi\)
−0.268252 + 0.963349i \(0.586446\pi\)
\(504\) 437006. 187379.i 1.72039 0.737668i
\(505\) 69144.9 0.271130
\(506\) 388551.i 1.51757i
\(507\) −166999. 110097.i −0.649676 0.428312i
\(508\) 853462. 3.30717
\(509\) 213583.i 0.824389i −0.911096 0.412194i \(-0.864762\pi\)
0.911096 0.412194i \(-0.135238\pi\)
\(510\) −24997.2 + 37916.5i −0.0961062 + 0.145777i
\(511\) −103759. −0.397361
\(512\) 340462.i 1.29876i
\(513\) 47601.5 264903.i 0.180878 1.00659i
\(514\) 505957. 1.91508
\(515\) 45708.6i 0.172339i
\(516\) −406402. 267929.i −1.52636 1.00628i
\(517\) 68077.8 0.254697
\(518\) 434849.i 1.62061i
\(519\) −212313. + 322043.i −0.788211 + 1.19558i
\(520\) −75102.5 −0.277746
\(521\) 464857.i 1.71255i 0.516517 + 0.856277i \(0.327228\pi\)
−0.516517 + 0.856277i \(0.672772\pi\)
\(522\) 150990. + 352138.i 0.554123 + 1.29233i
\(523\) 228186. 0.834230 0.417115 0.908854i \(-0.363041\pi\)
0.417115 + 0.908854i \(0.363041\pi\)
\(524\) 985408.i 3.58884i
\(525\) −240303. 158424.i −0.871847 0.574782i
\(526\) 316164. 1.14272
\(527\) 89291.8i 0.321507i
\(528\) −59184.8 + 89773.2i −0.212296 + 0.322017i
\(529\) −449090. −1.60480
\(530\) 249299.i 0.887499i
\(531\) 33737.6 14466.0i 0.119653 0.0513050i
\(532\) −673872. −2.38097
\(533\) 58773.4i 0.206884i
\(534\) −188737. 124428.i −0.661871 0.436352i
\(535\) −19942.1 −0.0696727
\(536\) 645917.i 2.24826i
\(537\) 266373. 404043.i 0.923724 1.40113i
\(538\) −246698. −0.852315
\(539\) 81580.0i 0.280806i
\(540\) −210493. 37824.4i −0.721856 0.129713i
\(541\) −397328. −1.35755 −0.678773 0.734348i \(-0.737488\pi\)
−0.678773 + 0.734348i \(0.737488\pi\)
\(542\) 57282.9i 0.194996i
\(543\) −413567. 272652.i −1.40264 0.924718i
\(544\) 26404.3 0.0892229
\(545\) 17989.2i 0.0605644i
\(546\) 161512. 244986.i 0.541776 0.821781i
\(547\) 193122. 0.645441 0.322720 0.946494i \(-0.395403\pi\)
0.322720 + 0.946494i \(0.395403\pi\)
\(548\) 246500.i 0.820834i
\(549\) −99143.4 231222.i −0.328942 0.767158i
\(550\) 241863. 0.799546
\(551\) 256566.i 0.845078i
\(552\) −625810. 412578.i −2.05383 1.35403i
\(553\) 258926. 0.846693
\(554\) 360576.i 1.17484i
\(555\) −50866.3 + 77155.5i −0.165137 + 0.250484i
\(556\) 378362. 1.22394
\(557\) 226827.i 0.731112i −0.930789 0.365556i \(-0.880879\pi\)
0.930789 0.365556i \(-0.119121\pi\)
\(558\) −590316. + 253116.i −1.89590 + 0.812926i
\(559\) −141938. −0.454230
\(560\) 104004.i 0.331645i
\(561\) 38507.0 + 25386.5i 0.122353 + 0.0806636i
\(562\) −260698. −0.825402
\(563\) 184337.i 0.581562i 0.956790 + 0.290781i \(0.0939151\pi\)
−0.956790 + 0.290781i \(0.906085\pi\)
\(564\) −152991. + 232061.i −0.480959 + 0.729532i
\(565\) −154282. −0.483302
\(566\) 84683.9i 0.264343i
\(567\) 272186. 285996.i 0.846641 0.889599i
\(568\) 203856. 0.631868
\(569\) 337265.i 1.04171i −0.853645 0.520856i \(-0.825613\pi\)
0.853645 0.520856i \(-0.174387\pi\)
\(570\) 182637. + 120407.i 0.562133 + 0.370597i
\(571\) 571586. 1.75311 0.876556 0.481300i \(-0.159835\pi\)
0.876556 + 0.481300i \(0.159835\pi\)
\(572\) 161424.i 0.493375i
\(573\) 320026. 485424.i 0.974710 1.47847i
\(574\) 302437. 0.917932
\(575\) 453740.i 1.37237i
\(576\) 166112. + 387406.i 0.500675 + 1.16767i
\(577\) −547922. −1.64576 −0.822882 0.568213i \(-0.807635\pi\)
−0.822882 + 0.568213i \(0.807635\pi\)
\(578\) 528515.i 1.58198i
\(579\) 487553. + 321429.i 1.45434 + 0.958801i
\(580\) −203869. −0.606030
\(581\) 312855.i 0.926811i
\(582\) −438260. + 664766.i −1.29386 + 1.96256i
\(583\) 253181. 0.744893
\(584\) 168202.i 0.493180i
\(585\) −57314.3 + 24575.2i −0.167476 + 0.0718101i
\(586\) −998816. −2.90864
\(587\) 547351.i 1.58851i −0.607585 0.794255i \(-0.707862\pi\)
0.607585 0.794255i \(-0.292138\pi\)
\(588\) −278087. 183334.i −0.804314 0.530260i
\(589\) 430102. 1.23977
\(590\) 29835.6i 0.0857098i
\(591\) −200165. + 303616.i −0.573076 + 0.869259i
\(592\) −189708. −0.541304
\(593\) 618108.i 1.75774i 0.477060 + 0.878871i \(0.341703\pi\)
−0.477060 + 0.878871i \(0.658297\pi\)
\(594\) −58676.7 + 326537.i −0.166300 + 0.925463i
\(595\) 44611.1 0.126011
\(596\) 113558.i 0.319688i
\(597\) 134698. + 88802.0i 0.377930 + 0.249158i
\(598\) −462583. −1.29356
\(599\) 466415.i 1.29993i −0.759966 0.649963i \(-0.774784\pi\)
0.759966 0.649963i \(-0.225216\pi\)
\(600\) −256818. + 389550.i −0.713384 + 1.08208i
\(601\) −572948. −1.58623 −0.793115 0.609072i \(-0.791542\pi\)
−0.793115 + 0.609072i \(0.791542\pi\)
\(602\) 730387.i 2.01539i
\(603\) −211358. 492930.i −0.581279 1.35566i
\(604\) 199449. 0.546710
\(605\) 98371.7i 0.268757i
\(606\) 365638. + 241054.i 0.995648 + 0.656401i
\(607\) −568966. −1.54422 −0.772110 0.635489i \(-0.780798\pi\)
−0.772110 + 0.635489i \(0.780798\pi\)
\(608\) 127184.i 0.344054i
\(609\) 207156. 314220.i 0.558551 0.847227i
\(610\) 204479. 0.549528
\(611\) 81048.8i 0.217102i
\(612\) −173073. + 74210.3i −0.462091 + 0.198135i
\(613\) 80594.2 0.214478 0.107239 0.994233i \(-0.465799\pi\)
0.107239 + 0.994233i \(0.465799\pi\)
\(614\) 263483.i 0.698902i
\(615\) −53661.5 35377.4i −0.141877 0.0935353i
\(616\) 392481. 1.03433
\(617\) 112761.i 0.296203i −0.988972 0.148101i \(-0.952684\pi\)
0.988972 0.148101i \(-0.0473162\pi\)
\(618\) 159350. 241707.i 0.417230 0.632867i
\(619\) −308341. −0.804729 −0.402364 0.915480i \(-0.631812\pi\)
−0.402364 + 0.915480i \(0.631812\pi\)
\(620\) 341761.i 0.889076i
\(621\) −612590. 110079.i −1.58850 0.285444i
\(622\) 472527. 1.22137
\(623\) 222060.i 0.572129i
\(624\) −106878. 70461.4i −0.274485 0.180960i
\(625\) 223973. 0.573371
\(626\) 615215.i 1.56992i
\(627\) 122282. 185481.i 0.311048 0.471807i
\(628\) −1.26581e6 −3.20958
\(629\) 81372.5i 0.205673i
\(630\) 126459. + 294928.i 0.318617 + 0.743079i
\(631\) 303140. 0.761351 0.380676 0.924709i \(-0.375691\pi\)
0.380676 + 0.924709i \(0.375691\pi\)
\(632\) 419740.i 1.05086i
\(633\) 481795. + 317633.i 1.20242 + 0.792717i
\(634\) 124426. 0.309552
\(635\) 272151.i 0.674936i
\(636\) −568973. + 863034.i −1.40662 + 2.13360i
\(637\) −97123.5 −0.239357
\(638\) 316260.i 0.776968i
\(639\) 155572. 66706.2i 0.381004 0.163367i
\(640\) −289289. −0.706272
\(641\) 579703.i 1.41088i −0.708770 0.705440i \(-0.750750\pi\)
0.708770 0.705440i \(-0.249250\pi\)
\(642\) −105454. 69522.3i −0.255853 0.168676i
\(643\) −193005. −0.466816 −0.233408 0.972379i \(-0.574988\pi\)
−0.233408 + 0.972379i \(0.574988\pi\)
\(644\) 1.55833e6i 3.75741i
\(645\) 85436.7 129593.i 0.205364 0.311503i
\(646\) 192619. 0.461567
\(647\) 426473.i 1.01879i −0.860534 0.509393i \(-0.829870\pi\)
0.860534 0.509393i \(-0.170130\pi\)
\(648\) −463623. 441234.i −1.10412 1.05080i
\(649\) 30300.2 0.0719376
\(650\) 287945.i 0.681527i
\(651\) 526752. + 347272.i 1.24292 + 0.819421i
\(652\) 18091.0 0.0425566
\(653\) 315858.i 0.740741i 0.928884 + 0.370370i \(0.120769\pi\)
−0.928884 + 0.370370i \(0.879231\pi\)
\(654\) 62714.1 95126.5i 0.146625 0.222406i
\(655\) 314226. 0.732418
\(656\) 131941.i 0.306600i
\(657\) 55039.5 + 128363.i 0.127510 + 0.297378i
\(658\) 417061. 0.963270
\(659\) 809211.i 1.86333i 0.363312 + 0.931667i \(0.381646\pi\)
−0.363312 + 0.931667i \(0.618354\pi\)
\(660\) −147384. 97165.9i −0.338347 0.223062i
\(661\) 440500. 1.00819 0.504096 0.863648i \(-0.331826\pi\)
0.504096 + 0.863648i \(0.331826\pi\)
\(662\) 635148.i 1.44930i
\(663\) −30223.4 + 45843.8i −0.0687570 + 0.104293i
\(664\) −507163. −1.15030
\(665\) 214883.i 0.485914i
\(666\) −537961. + 230667.i −1.21284 + 0.520040i
\(667\) −593311. −1.33361
\(668\) 503926.i 1.12931i
\(669\) −298452. 196761.i −0.666842 0.439629i
\(670\) 435918. 0.971081
\(671\) 207664.i 0.461228i
\(672\) 102691. 155764.i 0.227401 0.344929i
\(673\) 210294. 0.464297 0.232148 0.972680i \(-0.425424\pi\)
0.232148 + 0.972680i \(0.425424\pi\)
\(674\) 1.04552e6i 2.30151i
\(675\) −68521.0 + 381321.i −0.150389 + 0.836918i
\(676\) 674115. 1.47517
\(677\) 765156.i 1.66945i −0.550670 0.834723i \(-0.685628\pi\)
0.550670 0.834723i \(-0.314372\pi\)
\(678\) −815843. 537861.i −1.77479 1.17007i
\(679\) 782138. 1.69646
\(680\) 72318.1i 0.156397i
\(681\) 63255.6 95948.0i 0.136397 0.206891i
\(682\) −530171. −1.13985
\(683\) 490389.i 1.05123i −0.850721 0.525617i \(-0.823835\pi\)
0.850721 0.525617i \(-0.176165\pi\)
\(684\) 357458. + 833662.i 0.764033 + 1.78188i
\(685\) 78603.5 0.167518
\(686\) 483675.i 1.02779i
\(687\) 595211. + 392405.i 1.26112 + 0.831421i
\(688\) 318639. 0.673166
\(689\) 301420.i 0.634941i
\(690\) 278442. 422349.i 0.584839 0.887101i
\(691\) 616309. 1.29075 0.645375 0.763866i \(-0.276701\pi\)
0.645375 + 0.763866i \(0.276701\pi\)
\(692\) 1.29998e6i 2.71471i
\(693\) 299521. 128429.i 0.623679 0.267421i
\(694\) 307651. 0.638761
\(695\) 120652.i 0.249784i
\(696\) −509376. 335816.i −1.05153 0.693239i
\(697\) −56594.4 −0.116495
\(698\) 1.54458e6i 3.17029i
\(699\) −115.422 + 175.075i −0.000236229 + 0.000358319i
\(700\) 970019. 1.97963
\(701\) 264327.i 0.537905i −0.963153 0.268953i \(-0.913322\pi\)
0.963153 0.268953i \(-0.0866775\pi\)
\(702\) −388752. 69856.4i −0.788858 0.141753i
\(703\) 391956. 0.793098
\(704\) 347935.i 0.702025i
\(705\) −73999.4 48785.6i −0.148885 0.0981552i
\(706\) 695876. 1.39612
\(707\) 430195.i 0.860650i
\(708\) −68093.5 + 103286.i −0.135844 + 0.206052i
\(709\) −581894. −1.15758 −0.578791 0.815476i \(-0.696475\pi\)
−0.578791 + 0.815476i \(0.696475\pi\)
\(710\) 137579.i 0.272920i
\(711\) −137348. 320323.i −0.271696 0.633650i
\(712\) 359977. 0.710092
\(713\) 994613.i 1.95648i
\(714\) 235903. + 155524.i 0.462741 + 0.305071i
\(715\) −51474.8 −0.100689
\(716\) 1.63098e6i 3.18143i
\(717\) −330760. + 501706.i −0.643390 + 0.975913i
\(718\) 1.01639e6 1.97157
\(719\) 178512.i 0.345310i −0.984982 0.172655i \(-0.944765\pi\)
0.984982 0.172655i \(-0.0552346\pi\)
\(720\) 128666. 55169.2i 0.248198 0.106422i
\(721\) −284383. −0.547057
\(722\) 40752.5i 0.0781772i
\(723\) 406108. + 267735.i 0.776900 + 0.512187i
\(724\) 1.66943e6 3.18486
\(725\) 369320.i 0.702630i
\(726\) 342945. 520189.i 0.650655 0.986933i
\(727\) −211.589 −0.000400336 −0.000200168 1.00000i \(-0.500064\pi\)
−0.000200168 1.00000i \(0.500064\pi\)
\(728\) 467261.i 0.881652i
\(729\) −498194. 185019.i −0.937440 0.348146i
\(730\) −113517. −0.213017
\(731\) 136676.i 0.255775i
\(732\) 707877. + 466682.i 1.32110 + 0.870961i
\(733\) −534109. −0.994081 −0.497040 0.867727i \(-0.665580\pi\)
−0.497040 + 0.867727i \(0.665580\pi\)
\(734\) 859457.i 1.59526i
\(735\) 58461.4 88676.0i 0.108217 0.164146i
\(736\) −294114. −0.542951
\(737\) 442707.i 0.815045i
\(738\) −160428. 374151.i −0.294556 0.686964i
\(739\) −361404. −0.661765 −0.330882 0.943672i \(-0.607346\pi\)
−0.330882 + 0.943672i \(0.607346\pi\)
\(740\) 311450.i 0.568754i
\(741\) 220821. + 145581.i 0.402165 + 0.265135i
\(742\) 1.55105e6 2.81720
\(743\) 85738.0i 0.155309i 0.996980 + 0.0776543i \(0.0247430\pi\)
−0.996980 + 0.0776543i \(0.975257\pi\)
\(744\) 562954. 853906.i 1.01701 1.54264i
\(745\) −36211.3 −0.0652426
\(746\) 387982.i 0.697162i
\(747\) −387040. + 165955.i −0.693609 + 0.297406i
\(748\) −155439. −0.277817
\(749\) 124072.i 0.221163i
\(750\) −572078. 377154.i −1.01703 0.670496i
\(751\) 193039. 0.342267 0.171134 0.985248i \(-0.445257\pi\)
0.171134 + 0.985248i \(0.445257\pi\)
\(752\) 181948.i 0.321744i
\(753\) −29857.5 + 45288.8i −0.0526579 + 0.0798731i
\(754\) −376518. −0.662281
\(755\) 63599.9i 0.111574i
\(756\) −235330. + 1.30961e6i −0.411750 + 2.29139i
\(757\) −849700. −1.48277 −0.741385 0.671080i \(-0.765831\pi\)
−0.741385 + 0.671080i \(0.765831\pi\)
\(758\) 1.35427e6i 2.35704i
\(759\) −428926. 282778.i −0.744558 0.490865i
\(760\) −348343. −0.603087
\(761\) 515391.i 0.889954i −0.895542 0.444977i \(-0.853212\pi\)
0.895542 0.444977i \(-0.146788\pi\)
\(762\) −948777. + 1.43913e6i −1.63401 + 2.47851i
\(763\) −111922. −0.192250
\(764\) 1.95949e6i 3.35704i
\(765\) −23664.1 55189.4i −0.0404359 0.0943046i
\(766\) 1.17781e6 2.00732
\(767\) 36073.3i 0.0613191i
\(768\) −904123. 596061.i −1.53287 1.01057i
\(769\) −437007. −0.738985 −0.369493 0.929234i \(-0.620468\pi\)
−0.369493 + 0.929234i \(0.620468\pi\)
\(770\) 264879.i 0.446752i
\(771\) −368223. + 558531.i −0.619443 + 0.939590i
\(772\) −1.96808e6 −3.30224
\(773\) 490308.i 0.820559i 0.911960 + 0.410280i \(0.134569\pi\)
−0.911960 + 0.410280i \(0.865431\pi\)
\(774\) 903577. 387436.i 1.50829 0.646722i
\(775\) −619119. −1.03079
\(776\) 1.26791e6i 2.10554i
\(777\) 480034. + 316472.i 0.795115 + 0.524195i
\(778\) −93654.3 −0.154728
\(779\) 272605.i 0.449219i
\(780\) 115679. 175465.i 0.190136 0.288405i
\(781\) 139721. 0.229066
\(782\) 445433.i 0.728397i