Properties

Label 177.3.b.a.119.9
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.9
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.30

$q$-expansion

\(f(q)\) \(=\) \(q-2.36527i q^{2} +(2.69227 + 1.32352i) q^{3} -1.59452 q^{4} -8.24482i q^{5} +(3.13049 - 6.36794i) q^{6} -0.755379 q^{7} -5.68962i q^{8} +(5.49658 + 7.12654i) q^{9} +O(q^{10})\) \(q-2.36527i q^{2} +(2.69227 + 1.32352i) q^{3} -1.59452 q^{4} -8.24482i q^{5} +(3.13049 - 6.36794i) q^{6} -0.755379 q^{7} -5.68962i q^{8} +(5.49658 + 7.12654i) q^{9} -19.5013 q^{10} +12.7075i q^{11} +(-4.29288 - 2.11038i) q^{12} -1.31367 q^{13} +1.78668i q^{14} +(10.9122 - 22.1972i) q^{15} -19.8356 q^{16} -16.7462i q^{17} +(16.8562 - 13.0009i) q^{18} +11.8048 q^{19} +13.1465i q^{20} +(-2.03368 - 0.999760i) q^{21} +30.0566 q^{22} -13.6222i q^{23} +(7.53033 - 15.3180i) q^{24} -42.9771 q^{25} +3.10719i q^{26} +(5.36613 + 26.4614i) q^{27} +1.20447 q^{28} +36.0473i q^{29} +(-52.5026 - 25.8103i) q^{30} +8.07287 q^{31} +24.1581i q^{32} +(-16.8186 + 34.2119i) q^{33} -39.6093 q^{34} +6.22797i q^{35} +(-8.76442 - 11.3634i) q^{36} +50.0853 q^{37} -27.9216i q^{38} +(-3.53675 - 1.73867i) q^{39} -46.9099 q^{40} +47.7769i q^{41} +(-2.36471 + 4.81021i) q^{42} +24.6656 q^{43} -20.2623i q^{44} +(58.7571 - 45.3183i) q^{45} -32.2203 q^{46} -18.1017i q^{47} +(-53.4027 - 26.2528i) q^{48} -48.4294 q^{49} +101.653i q^{50} +(22.1639 - 45.0851i) q^{51} +2.09468 q^{52} +47.1050i q^{53} +(62.5884 - 12.6924i) q^{54} +104.771 q^{55} +4.29782i q^{56} +(31.7816 + 15.6239i) q^{57} +85.2616 q^{58} -7.68115i q^{59} +(-17.3997 + 35.3940i) q^{60} +41.9771 q^{61} -19.0945i q^{62} +(-4.15200 - 5.38324i) q^{63} -22.2017 q^{64} +10.8310i q^{65} +(80.9205 + 39.7806i) q^{66} +84.5251 q^{67} +26.7021i q^{68} +(18.0293 - 36.6747i) q^{69} +14.7308 q^{70} +117.846i q^{71} +(40.5473 - 31.2734i) q^{72} -106.420 q^{73} -118.466i q^{74} +(-115.706 - 56.8811i) q^{75} -18.8230 q^{76} -9.59896i q^{77} +(-4.11244 + 8.36538i) q^{78} +100.619 q^{79} +163.541i q^{80} +(-20.5752 + 78.3432i) q^{81} +113.006 q^{82} +60.9531i q^{83} +(3.24275 + 1.59414i) q^{84} -138.069 q^{85} -58.3409i q^{86} +(-47.7093 + 97.0488i) q^{87} +72.3006 q^{88} -72.2494i q^{89} +(-107.190 - 138.977i) q^{90} +0.992320 q^{91} +21.7210i q^{92} +(21.7343 + 10.6846i) q^{93} -42.8155 q^{94} -97.3284i q^{95} +(-31.9738 + 65.0401i) q^{96} -171.901 q^{97} +114.549i q^{98} +(-90.5603 + 69.8476i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.36527i 1.18264i −0.806438 0.591319i \(-0.798608\pi\)
0.806438 0.591319i \(-0.201392\pi\)
\(3\) 2.69227 + 1.32352i 0.897422 + 0.441174i
\(4\) −1.59452 −0.398630
\(5\) 8.24482i 1.64896i −0.565888 0.824482i \(-0.691467\pi\)
0.565888 0.824482i \(-0.308533\pi\)
\(6\) 3.13049 6.36794i 0.521749 1.06132i
\(7\) −0.755379 −0.107911 −0.0539556 0.998543i \(-0.517183\pi\)
−0.0539556 + 0.998543i \(0.517183\pi\)
\(8\) 5.68962i 0.711202i
\(9\) 5.49658 + 7.12654i 0.610731 + 0.791838i
\(10\) −19.5013 −1.95013
\(11\) 12.7075i 1.15522i 0.816311 + 0.577612i \(0.196015\pi\)
−0.816311 + 0.577612i \(0.803985\pi\)
\(12\) −4.29288 2.11038i −0.357740 0.175865i
\(13\) −1.31367 −0.101052 −0.0505258 0.998723i \(-0.516090\pi\)
−0.0505258 + 0.998723i \(0.516090\pi\)
\(14\) 1.78668i 0.127620i
\(15\) 10.9122 22.1972i 0.727480 1.47982i
\(16\) −19.8356 −1.23972
\(17\) 16.7462i 0.985068i −0.870293 0.492534i \(-0.836071\pi\)
0.870293 0.492534i \(-0.163929\pi\)
\(18\) 16.8562 13.0009i 0.936457 0.722274i
\(19\) 11.8048 0.621305 0.310652 0.950524i \(-0.399453\pi\)
0.310652 + 0.950524i \(0.399453\pi\)
\(20\) 13.1465i 0.657327i
\(21\) −2.03368 0.999760i −0.0968419 0.0476076i
\(22\) 30.0566 1.36621
\(23\) 13.6222i 0.592272i −0.955146 0.296136i \(-0.904302\pi\)
0.955146 0.296136i \(-0.0956981\pi\)
\(24\) 7.53033 15.3180i 0.313764 0.638248i
\(25\) −42.9771 −1.71908
\(26\) 3.10719i 0.119507i
\(27\) 5.36613 + 26.4614i 0.198745 + 0.980051i
\(28\) 1.20447 0.0430167
\(29\) 36.0473i 1.24301i 0.783411 + 0.621504i \(0.213478\pi\)
−0.783411 + 0.621504i \(0.786522\pi\)
\(30\) −52.5026 25.8103i −1.75009 0.860345i
\(31\) 8.07287 0.260415 0.130208 0.991487i \(-0.458436\pi\)
0.130208 + 0.991487i \(0.458436\pi\)
\(32\) 24.1581i 0.754942i
\(33\) −16.8186 + 34.2119i −0.509655 + 1.03672i
\(34\) −39.6093 −1.16498
\(35\) 6.22797i 0.177942i
\(36\) −8.76442 11.3634i −0.243456 0.315651i
\(37\) 50.0853 1.35366 0.676829 0.736141i \(-0.263354\pi\)
0.676829 + 0.736141i \(0.263354\pi\)
\(38\) 27.9216i 0.734778i
\(39\) −3.53675 1.73867i −0.0906859 0.0445813i
\(40\) −46.9099 −1.17275
\(41\) 47.7769i 1.16529i 0.812726 + 0.582645i \(0.197982\pi\)
−0.812726 + 0.582645i \(0.802018\pi\)
\(42\) −2.36471 + 4.81021i −0.0563026 + 0.114529i
\(43\) 24.6656 0.573619 0.286809 0.957988i \(-0.407405\pi\)
0.286809 + 0.957988i \(0.407405\pi\)
\(44\) 20.2623i 0.460508i
\(45\) 58.7571 45.3183i 1.30571 1.00707i
\(46\) −32.2203 −0.700442
\(47\) 18.1017i 0.385143i −0.981283 0.192572i \(-0.938317\pi\)
0.981283 0.192572i \(-0.0616827\pi\)
\(48\) −53.4027 26.2528i −1.11256 0.546934i
\(49\) −48.4294 −0.988355
\(50\) 101.653i 2.03305i
\(51\) 22.1639 45.0851i 0.434586 0.884022i
\(52\) 2.09468 0.0402823
\(53\) 47.1050i 0.888774i 0.895835 + 0.444387i \(0.146578\pi\)
−0.895835 + 0.444387i \(0.853422\pi\)
\(54\) 62.5884 12.6924i 1.15904 0.235044i
\(55\) 104.771 1.90492
\(56\) 4.29782i 0.0767467i
\(57\) 31.7816 + 15.6239i 0.557572 + 0.274103i
\(58\) 85.2616 1.47003
\(59\) 7.68115i 0.130189i
\(60\) −17.3997 + 35.3940i −0.289996 + 0.589900i
\(61\) 41.9771 0.688149 0.344074 0.938942i \(-0.388193\pi\)
0.344074 + 0.938942i \(0.388193\pi\)
\(62\) 19.0945i 0.307977i
\(63\) −4.15200 5.38324i −0.0659048 0.0854482i
\(64\) −22.2017 −0.346902
\(65\) 10.8310i 0.166631i
\(66\) 80.9205 + 39.7806i 1.22607 + 0.602737i
\(67\) 84.5251 1.26157 0.630784 0.775958i \(-0.282733\pi\)
0.630784 + 0.775958i \(0.282733\pi\)
\(68\) 26.7021i 0.392678i
\(69\) 18.0293 36.6747i 0.261295 0.531517i
\(70\) 14.7308 0.210441
\(71\) 117.846i 1.65980i 0.557909 + 0.829902i \(0.311604\pi\)
−0.557909 + 0.829902i \(0.688396\pi\)
\(72\) 40.5473 31.2734i 0.563157 0.434353i
\(73\) −106.420 −1.45781 −0.728905 0.684615i \(-0.759970\pi\)
−0.728905 + 0.684615i \(0.759970\pi\)
\(74\) 118.466i 1.60089i
\(75\) −115.706 56.8811i −1.54274 0.758414i
\(76\) −18.8230 −0.247671
\(77\) 9.59896i 0.124662i
\(78\) −4.11244 + 8.36538i −0.0527235 + 0.107249i
\(79\) 100.619 1.27365 0.636827 0.771007i \(-0.280247\pi\)
0.636827 + 0.771007i \(0.280247\pi\)
\(80\) 163.541i 2.04426i
\(81\) −20.5752 + 78.3432i −0.254014 + 0.967200i
\(82\) 113.006 1.37812
\(83\) 60.9531i 0.734375i 0.930147 + 0.367187i \(0.119679\pi\)
−0.930147 + 0.367187i \(0.880321\pi\)
\(84\) 3.24275 + 1.59414i 0.0386041 + 0.0189779i
\(85\) −138.069 −1.62434
\(86\) 58.3409i 0.678383i
\(87\) −47.7093 + 97.0488i −0.548383 + 1.11550i
\(88\) 72.3006 0.821598
\(89\) 72.2494i 0.811791i −0.913920 0.405895i \(-0.866960\pi\)
0.913920 0.405895i \(-0.133040\pi\)
\(90\) −107.190 138.977i −1.19100 1.54418i
\(91\) 0.992320 0.0109046
\(92\) 21.7210i 0.236098i
\(93\) 21.7343 + 10.6846i 0.233702 + 0.114888i
\(94\) −42.8155 −0.455485
\(95\) 97.3284i 1.02451i
\(96\) −31.9738 + 65.0401i −0.333061 + 0.677501i
\(97\) −171.901 −1.77218 −0.886089 0.463516i \(-0.846588\pi\)
−0.886089 + 0.463516i \(0.846588\pi\)
\(98\) 114.549i 1.16887i
\(99\) −90.5603 + 69.8476i −0.914751 + 0.705532i
\(100\) 68.5279 0.685279
\(101\) 15.1618i 0.150117i −0.997179 0.0750583i \(-0.976086\pi\)
0.997179 0.0750583i \(-0.0239143\pi\)
\(102\) −106.639 52.4237i −1.04548 0.513958i
\(103\) −173.109 −1.68067 −0.840335 0.542067i \(-0.817642\pi\)
−0.840335 + 0.542067i \(0.817642\pi\)
\(104\) 7.47428i 0.0718681i
\(105\) −8.24285 + 16.7673i −0.0785033 + 0.159689i
\(106\) 111.416 1.05110
\(107\) 191.084i 1.78583i −0.450224 0.892916i \(-0.648656\pi\)
0.450224 0.892916i \(-0.351344\pi\)
\(108\) −8.55641 42.1933i −0.0792260 0.390678i
\(109\) 12.3513 0.113314 0.0566572 0.998394i \(-0.481956\pi\)
0.0566572 + 0.998394i \(0.481956\pi\)
\(110\) 247.812i 2.25283i
\(111\) 134.843 + 66.2890i 1.21480 + 0.597198i
\(112\) 14.9834 0.133780
\(113\) 140.835i 1.24632i −0.782093 0.623162i \(-0.785848\pi\)
0.782093 0.623162i \(-0.214152\pi\)
\(114\) 36.9548 75.1722i 0.324165 0.659406i
\(115\) −112.313 −0.976635
\(116\) 57.4781i 0.495501i
\(117\) −7.22070 9.36193i −0.0617154 0.0800165i
\(118\) −18.1680 −0.153966
\(119\) 12.6497i 0.106300i
\(120\) −126.294 62.0862i −1.05245 0.517385i
\(121\) −40.4798 −0.334544
\(122\) 99.2873i 0.813831i
\(123\) −63.2338 + 128.628i −0.514096 + 1.04576i
\(124\) −12.8724 −0.103809
\(125\) 148.218i 1.18574i
\(126\) −12.7328 + 9.82063i −0.101054 + 0.0779415i
\(127\) 147.769 1.16354 0.581768 0.813355i \(-0.302361\pi\)
0.581768 + 0.813355i \(0.302361\pi\)
\(128\) 149.146i 1.16520i
\(129\) 66.4064 + 32.6455i 0.514778 + 0.253066i
\(130\) 25.6182 0.197063
\(131\) 47.5616i 0.363066i −0.983385 0.181533i \(-0.941894\pi\)
0.983385 0.181533i \(-0.0581059\pi\)
\(132\) 26.8176 54.5516i 0.203164 0.413270i
\(133\) −8.91709 −0.0670458
\(134\) 199.925i 1.49198i
\(135\) 218.169 44.2427i 1.61607 0.327724i
\(136\) −95.2792 −0.700582
\(137\) 261.817i 1.91107i 0.294874 + 0.955536i \(0.404722\pi\)
−0.294874 + 0.955536i \(0.595278\pi\)
\(138\) −86.7457 42.6443i −0.628592 0.309017i
\(139\) −138.939 −0.999560 −0.499780 0.866153i \(-0.666586\pi\)
−0.499780 + 0.866153i \(0.666586\pi\)
\(140\) 9.93063i 0.0709331i
\(141\) 23.9580 48.7346i 0.169915 0.345636i
\(142\) 278.738 1.96295
\(143\) 16.6934i 0.116737i
\(144\) −109.028 141.359i −0.757138 0.981661i
\(145\) 297.203 2.04968
\(146\) 251.713i 1.72406i
\(147\) −130.385 64.0974i −0.886971 0.436036i
\(148\) −79.8622 −0.539609
\(149\) 57.3808i 0.385106i 0.981287 + 0.192553i \(0.0616767\pi\)
−0.981287 + 0.192553i \(0.938323\pi\)
\(150\) −134.539 + 273.676i −0.896929 + 1.82450i
\(151\) 45.3936 0.300620 0.150310 0.988639i \(-0.451973\pi\)
0.150310 + 0.988639i \(0.451973\pi\)
\(152\) 67.1647i 0.441873i
\(153\) 119.342 92.0466i 0.780014 0.601612i
\(154\) −22.7042 −0.147430
\(155\) 66.5594i 0.429415i
\(156\) 5.63943 + 2.77235i 0.0361502 + 0.0177715i
\(157\) −74.9347 −0.477291 −0.238645 0.971107i \(-0.576703\pi\)
−0.238645 + 0.971107i \(0.576703\pi\)
\(158\) 237.991i 1.50627i
\(159\) −62.3445 + 126.819i −0.392104 + 0.797605i
\(160\) 199.180 1.24487
\(161\) 10.2900i 0.0639128i
\(162\) 185.303 + 48.6659i 1.14385 + 0.300407i
\(163\) −313.263 −1.92186 −0.960930 0.276791i \(-0.910729\pi\)
−0.960930 + 0.276791i \(0.910729\pi\)
\(164\) 76.1814i 0.464520i
\(165\) 282.071 + 138.666i 1.70952 + 0.840403i
\(166\) 144.171 0.868499
\(167\) 239.568i 1.43454i −0.696795 0.717270i \(-0.745391\pi\)
0.696795 0.717270i \(-0.254609\pi\)
\(168\) −5.68825 + 11.5709i −0.0338586 + 0.0688742i
\(169\) −167.274 −0.989789
\(170\) 326.571i 1.92101i
\(171\) 64.8860 + 84.1273i 0.379450 + 0.491973i
\(172\) −39.3299 −0.228662
\(173\) 277.582i 1.60452i −0.596977 0.802259i \(-0.703631\pi\)
0.596977 0.802259i \(-0.296369\pi\)
\(174\) 229.547 + 112.846i 1.31924 + 0.648538i
\(175\) 32.4640 0.185508
\(176\) 252.060i 1.43216i
\(177\) 10.1662 20.6797i 0.0574359 0.116834i
\(178\) −170.890 −0.960054
\(179\) 65.6583i 0.366806i 0.983038 + 0.183403i \(0.0587114\pi\)
−0.983038 + 0.183403i \(0.941289\pi\)
\(180\) −93.6894 + 72.2611i −0.520497 + 0.401450i
\(181\) 79.2983 0.438112 0.219056 0.975712i \(-0.429702\pi\)
0.219056 + 0.975712i \(0.429702\pi\)
\(182\) 2.34711i 0.0128962i
\(183\) 113.013 + 55.5576i 0.617560 + 0.303593i
\(184\) −77.5053 −0.421225
\(185\) 412.945i 2.23213i
\(186\) 25.2720 51.4076i 0.135871 0.276385i
\(187\) 212.801 1.13797
\(188\) 28.8636i 0.153530i
\(189\) −4.05346 19.9884i −0.0214469 0.105759i
\(190\) −230.208 −1.21162
\(191\) 233.915i 1.22469i −0.790592 0.612343i \(-0.790227\pi\)
0.790592 0.612343i \(-0.209773\pi\)
\(192\) −59.7729 29.3844i −0.311317 0.153044i
\(193\) −64.8763 −0.336147 −0.168073 0.985774i \(-0.553755\pi\)
−0.168073 + 0.985774i \(0.553755\pi\)
\(194\) 406.593i 2.09584i
\(195\) −14.3350 + 29.1599i −0.0735130 + 0.149538i
\(196\) 77.2217 0.393989
\(197\) 197.217i 1.00110i 0.865707 + 0.500551i \(0.166869\pi\)
−0.865707 + 0.500551i \(0.833131\pi\)
\(198\) 165.209 + 214.200i 0.834388 + 1.08182i
\(199\) −240.503 −1.20856 −0.604280 0.796772i \(-0.706539\pi\)
−0.604280 + 0.796772i \(0.706539\pi\)
\(200\) 244.523i 1.22262i
\(201\) 227.564 + 111.871i 1.13216 + 0.556571i
\(202\) −35.8618 −0.177534
\(203\) 27.2293i 0.134135i
\(204\) −35.3408 + 71.8892i −0.173239 + 0.352398i
\(205\) 393.912 1.92152
\(206\) 409.450i 1.98762i
\(207\) 97.0795 74.8758i 0.468983 0.361719i
\(208\) 26.0574 0.125276
\(209\) 150.009i 0.717746i
\(210\) 39.6593 + 19.4966i 0.188854 + 0.0928409i
\(211\) −347.814 −1.64841 −0.824205 0.566292i \(-0.808377\pi\)
−0.824205 + 0.566292i \(0.808377\pi\)
\(212\) 75.1100i 0.354292i
\(213\) −155.972 + 317.273i −0.732262 + 1.48954i
\(214\) −451.966 −2.11199
\(215\) 203.364i 0.945877i
\(216\) 150.555 30.5312i 0.697014 0.141348i
\(217\) −6.09808 −0.0281017
\(218\) 29.2141i 0.134010i
\(219\) −286.511 140.849i −1.30827 0.643148i
\(220\) −167.059 −0.759361
\(221\) 21.9989i 0.0995427i
\(222\) 156.792 318.941i 0.706269 1.43667i
\(223\) 297.512 1.33413 0.667066 0.744998i \(-0.267550\pi\)
0.667066 + 0.744998i \(0.267550\pi\)
\(224\) 18.2486i 0.0814668i
\(225\) −236.227 306.278i −1.04990 1.36124i
\(226\) −333.112 −1.47395
\(227\) 54.2423i 0.238953i −0.992837 0.119476i \(-0.961878\pi\)
0.992837 0.119476i \(-0.0381216\pi\)
\(228\) −50.6765 24.9126i −0.222265 0.109266i
\(229\) −225.479 −0.984624 −0.492312 0.870419i \(-0.663848\pi\)
−0.492312 + 0.870419i \(0.663848\pi\)
\(230\) 265.651i 1.15500i
\(231\) 12.7044 25.8429i 0.0549975 0.111874i
\(232\) 205.095 0.884030
\(233\) 73.7226i 0.316406i −0.987407 0.158203i \(-0.949430\pi\)
0.987407 0.158203i \(-0.0505700\pi\)
\(234\) −22.1435 + 17.0789i −0.0946305 + 0.0729869i
\(235\) −149.245 −0.635087
\(236\) 12.2478i 0.0518973i
\(237\) 270.892 + 133.171i 1.14300 + 0.561903i
\(238\) 29.9200 0.125714
\(239\) 338.302i 1.41549i −0.706468 0.707745i \(-0.749713\pi\)
0.706468 0.707745i \(-0.250287\pi\)
\(240\) −216.450 + 440.295i −0.901874 + 1.83456i
\(241\) 238.213 0.988435 0.494218 0.869338i \(-0.335455\pi\)
0.494218 + 0.869338i \(0.335455\pi\)
\(242\) 95.7458i 0.395644i
\(243\) −159.083 + 183.689i −0.654662 + 0.755922i
\(244\) −66.9334 −0.274317
\(245\) 399.292i 1.62976i
\(246\) 304.241 + 149.565i 1.23675 + 0.607989i
\(247\) −15.5076 −0.0627838
\(248\) 45.9315i 0.185208i
\(249\) −80.6727 + 164.102i −0.323987 + 0.659044i
\(250\) 350.576 1.40230
\(251\) 151.843i 0.604953i 0.953157 + 0.302477i \(0.0978134\pi\)
−0.953157 + 0.302477i \(0.902187\pi\)
\(252\) 6.62046 + 8.58369i 0.0262717 + 0.0340623i
\(253\) 173.104 0.684207
\(254\) 349.515i 1.37604i
\(255\) −371.719 182.737i −1.45772 0.716617i
\(256\) 263.964 1.03111
\(257\) 370.120i 1.44016i 0.693893 + 0.720078i \(0.255894\pi\)
−0.693893 + 0.720078i \(0.744106\pi\)
\(258\) 77.2155 157.069i 0.299285 0.608796i
\(259\) −37.8334 −0.146075
\(260\) 17.2702i 0.0664240i
\(261\) −256.892 + 198.137i −0.984261 + 0.759144i
\(262\) −112.496 −0.429375
\(263\) 280.769i 1.06756i 0.845622 + 0.533782i \(0.179230\pi\)
−0.845622 + 0.533782i \(0.820770\pi\)
\(264\) 194.652 + 95.6914i 0.737320 + 0.362467i
\(265\) 388.372 1.46556
\(266\) 21.0914i 0.0792908i
\(267\) 95.6236 194.514i 0.358141 0.728518i
\(268\) −134.777 −0.502900
\(269\) 259.946i 0.966342i −0.875526 0.483171i \(-0.839485\pi\)
0.875526 0.483171i \(-0.160515\pi\)
\(270\) −104.646 516.030i −0.387579 1.91122i
\(271\) 142.113 0.524402 0.262201 0.965013i \(-0.415552\pi\)
0.262201 + 0.965013i \(0.415552\pi\)
\(272\) 332.170i 1.22121i
\(273\) 2.67159 + 1.31336i 0.00978603 + 0.00481083i
\(274\) 619.269 2.26011
\(275\) 546.130i 1.98593i
\(276\) −28.7482 + 58.4786i −0.104160 + 0.211879i
\(277\) 246.675 0.890523 0.445262 0.895400i \(-0.353111\pi\)
0.445262 + 0.895400i \(0.353111\pi\)
\(278\) 328.628i 1.18212i
\(279\) 44.3732 + 57.5316i 0.159044 + 0.206207i
\(280\) 35.4347 0.126553
\(281\) 68.3398i 0.243202i −0.992579 0.121601i \(-0.961197\pi\)
0.992579 0.121601i \(-0.0388028\pi\)
\(282\) −115.271 56.6673i −0.408762 0.200948i
\(283\) −104.955 −0.370866 −0.185433 0.982657i \(-0.559369\pi\)
−0.185433 + 0.982657i \(0.559369\pi\)
\(284\) 187.908i 0.661649i
\(285\) 128.816 262.034i 0.451987 0.919417i
\(286\) −39.4845 −0.138058
\(287\) 36.0897i 0.125748i
\(288\) −172.164 + 132.787i −0.597792 + 0.461067i
\(289\) 8.56615 0.0296406
\(290\) 702.967i 2.42402i
\(291\) −462.804 227.515i −1.59039 0.781838i
\(292\) 169.689 0.581128
\(293\) 9.70650i 0.0331280i −0.999863 0.0165640i \(-0.994727\pi\)
0.999863 0.0165640i \(-0.00527273\pi\)
\(294\) −151.608 + 308.396i −0.515673 + 1.04897i
\(295\) −63.3297 −0.214677
\(296\) 284.966i 0.962724i
\(297\) −336.257 + 68.1899i −1.13218 + 0.229596i
\(298\) 135.721 0.455441
\(299\) 17.8951i 0.0598500i
\(300\) 184.495 + 90.6981i 0.614984 + 0.302327i
\(301\) −18.6319 −0.0619000
\(302\) 107.368i 0.355524i
\(303\) 20.0669 40.8195i 0.0662275 0.134718i
\(304\) −234.155 −0.770246
\(305\) 346.094i 1.13473i
\(306\) −217.716 282.277i −0.711489 0.922474i
\(307\) 266.280 0.867363 0.433682 0.901066i \(-0.357214\pi\)
0.433682 + 0.901066i \(0.357214\pi\)
\(308\) 15.3057i 0.0496940i
\(309\) −466.056 229.114i −1.50827 0.741468i
\(310\) −157.431 −0.507842
\(311\) 186.416i 0.599408i −0.954032 0.299704i \(-0.903112\pi\)
0.954032 0.299704i \(-0.0968879\pi\)
\(312\) −9.89237 + 20.1227i −0.0317063 + 0.0644960i
\(313\) 564.581 1.80377 0.901887 0.431972i \(-0.142182\pi\)
0.901887 + 0.431972i \(0.142182\pi\)
\(314\) 177.241i 0.564462i
\(315\) −44.3838 + 34.2325i −0.140901 + 0.108675i
\(316\) −160.439 −0.507717
\(317\) 66.4847i 0.209731i 0.994486 + 0.104866i \(0.0334412\pi\)
−0.994486 + 0.104866i \(0.966559\pi\)
\(318\) 299.962 + 147.462i 0.943277 + 0.463716i
\(319\) −458.069 −1.43595
\(320\) 183.049i 0.572029i
\(321\) 252.904 514.449i 0.787862 1.60264i
\(322\) 24.3386 0.0755856
\(323\) 197.685i 0.612027i
\(324\) 32.8076 124.920i 0.101258 0.385556i
\(325\) 56.4577 0.173716
\(326\) 740.954i 2.27286i
\(327\) 33.2529 + 16.3472i 0.101691 + 0.0499913i
\(328\) 271.832 0.828757
\(329\) 13.6737i 0.0415613i
\(330\) 327.984 667.175i 0.993891 2.02174i
\(331\) −112.836 −0.340893 −0.170446 0.985367i \(-0.554521\pi\)
−0.170446 + 0.985367i \(0.554521\pi\)
\(332\) 97.1911i 0.292744i
\(333\) 275.298 + 356.935i 0.826721 + 1.07188i
\(334\) −566.645 −1.69654
\(335\) 696.895i 2.08028i
\(336\) 40.3392 + 19.8308i 0.120057 + 0.0590203i
\(337\) −419.505 −1.24482 −0.622411 0.782690i \(-0.713847\pi\)
−0.622411 + 0.782690i \(0.713847\pi\)
\(338\) 395.650i 1.17056i
\(339\) 186.398 379.164i 0.549845 1.11848i
\(340\) 220.154 0.647512
\(341\) 102.586i 0.300838i
\(342\) 198.984 153.473i 0.581825 0.448752i
\(343\) 73.5961 0.214566
\(344\) 140.338i 0.407959i
\(345\) −302.376 148.649i −0.876453 0.430866i
\(346\) −656.556 −1.89756
\(347\) 399.509i 1.15132i 0.817688 + 0.575662i \(0.195256\pi\)
−0.817688 + 0.575662i \(0.804744\pi\)
\(348\) 76.0736 154.746i 0.218602 0.444674i
\(349\) −139.763 −0.400466 −0.200233 0.979748i \(-0.564170\pi\)
−0.200233 + 0.979748i \(0.564170\pi\)
\(350\) 76.7862i 0.219389i
\(351\) −7.04932 34.7615i −0.0200835 0.0990358i
\(352\) −306.989 −0.872127
\(353\) 257.040i 0.728158i 0.931368 + 0.364079i \(0.118616\pi\)
−0.931368 + 0.364079i \(0.881384\pi\)
\(354\) −48.9131 24.0458i −0.138173 0.0679259i
\(355\) 971.620 2.73696
\(356\) 115.203i 0.323604i
\(357\) −16.7421 + 34.0563i −0.0468968 + 0.0953959i
\(358\) 155.300 0.433799
\(359\) 619.504i 1.72564i 0.505514 + 0.862818i \(0.331303\pi\)
−0.505514 + 0.862818i \(0.668697\pi\)
\(360\) −257.844 334.305i −0.716233 0.928625i
\(361\) −221.647 −0.613981
\(362\) 187.562i 0.518128i
\(363\) −108.982 53.5758i −0.300227 0.147592i
\(364\) −1.58228 −0.00434691
\(365\) 877.415i 2.40388i
\(366\) 131.409 267.308i 0.359041 0.730349i
\(367\) −102.428 −0.279095 −0.139548 0.990215i \(-0.544565\pi\)
−0.139548 + 0.990215i \(0.544565\pi\)
\(368\) 270.205i 0.734253i
\(369\) −340.484 + 262.610i −0.922721 + 0.711680i
\(370\) −976.727 −2.63980
\(371\) 35.5821i 0.0959087i
\(372\) −34.6558 17.0369i −0.0931608 0.0457980i
\(373\) −293.963 −0.788105 −0.394052 0.919088i \(-0.628927\pi\)
−0.394052 + 0.919088i \(0.628927\pi\)
\(374\) 503.333i 1.34581i
\(375\) −196.169 + 399.042i −0.523118 + 1.06411i
\(376\) −102.992 −0.273914
\(377\) 47.3542i 0.125608i
\(378\) −47.2780 + 9.58754i −0.125074 + 0.0253639i
\(379\) −0.946681 −0.00249784 −0.00124892 0.999999i \(-0.500398\pi\)
−0.00124892 + 0.999999i \(0.500398\pi\)
\(380\) 155.192i 0.408401i
\(381\) 397.834 + 195.576i 1.04418 + 0.513322i
\(382\) −553.273 −1.44836
\(383\) 136.045i 0.355210i −0.984102 0.177605i \(-0.943165\pi\)
0.984102 0.177605i \(-0.0568349\pi\)
\(384\) −197.398 + 401.540i −0.514056 + 1.04568i
\(385\) −79.1417 −0.205563
\(386\) 153.450i 0.397539i
\(387\) 135.577 + 175.781i 0.350327 + 0.454213i
\(388\) 274.100 0.706444
\(389\) 152.657i 0.392433i −0.980561 0.196217i \(-0.937134\pi\)
0.980561 0.196217i \(-0.0628656\pi\)
\(390\) 68.9711 + 33.9063i 0.176849 + 0.0869392i
\(391\) −228.120 −0.583428
\(392\) 275.545i 0.702920i
\(393\) 62.9488 128.049i 0.160175 0.325823i
\(394\) 466.472 1.18394
\(395\) 829.582i 2.10021i
\(396\) 144.400 111.374i 0.364647 0.281246i
\(397\) 350.842 0.883733 0.441867 0.897081i \(-0.354316\pi\)
0.441867 + 0.897081i \(0.354316\pi\)
\(398\) 568.856i 1.42929i
\(399\) −24.0072 11.8020i −0.0601683 0.0295788i
\(400\) 852.476 2.13119
\(401\) 522.970i 1.30417i 0.758148 + 0.652083i \(0.226105\pi\)
−0.758148 + 0.652083i \(0.773895\pi\)
\(402\) 264.605 538.251i 0.658222 1.33893i
\(403\) −10.6051 −0.0263154
\(404\) 24.1758i 0.0598411i
\(405\) 645.926 + 169.639i 1.59488 + 0.418861i
\(406\) −64.4049 −0.158633
\(407\) 636.458i 1.56378i
\(408\) −256.517 126.104i −0.628718 0.309079i
\(409\) 639.029 1.56242 0.781209 0.624270i \(-0.214603\pi\)
0.781209 + 0.624270i \(0.214603\pi\)
\(410\) 931.710i 2.27246i
\(411\) −346.520 + 704.881i −0.843115 + 1.71504i
\(412\) 276.026 0.669967
\(413\) 5.80218i 0.0140489i
\(414\) −177.102 229.620i −0.427782 0.554637i
\(415\) 502.547 1.21096
\(416\) 31.7359i 0.0762881i
\(417\) −374.060 183.888i −0.897026 0.440979i
\(418\) 354.812 0.848833
\(419\) 378.805i 0.904069i −0.892000 0.452035i \(-0.850698\pi\)
0.892000 0.452035i \(-0.149302\pi\)
\(420\) 13.1434 26.7359i 0.0312938 0.0636569i
\(421\) −672.352 −1.59704 −0.798518 0.601971i \(-0.794382\pi\)
−0.798518 + 0.601971i \(0.794382\pi\)
\(422\) 822.676i 1.94947i
\(423\) 129.003 99.4976i 0.304971 0.235219i
\(424\) 268.009 0.632098
\(425\) 719.701i 1.69341i
\(426\) 750.437 + 368.916i 1.76159 + 0.866000i
\(427\) −31.7086 −0.0742590
\(428\) 304.688i 0.711887i
\(429\) 22.0941 44.9431i 0.0515014 0.104763i
\(430\) −481.011 −1.11863
\(431\) 152.719i 0.354337i 0.984180 + 0.177169i \(0.0566938\pi\)
−0.984180 + 0.177169i \(0.943306\pi\)
\(432\) −106.440 524.877i −0.246389 1.21499i
\(433\) −72.8581 −0.168264 −0.0841318 0.996455i \(-0.526812\pi\)
−0.0841318 + 0.996455i \(0.526812\pi\)
\(434\) 14.4236i 0.0332341i
\(435\) 800.150 + 393.355i 1.83942 + 0.904264i
\(436\) −19.6944 −0.0451706
\(437\) 160.808i 0.367981i
\(438\) −333.147 + 677.678i −0.760610 + 1.54721i
\(439\) 527.988 1.20271 0.601353 0.798984i \(-0.294629\pi\)
0.601353 + 0.798984i \(0.294629\pi\)
\(440\) 596.106i 1.35479i
\(441\) −266.196 345.134i −0.603619 0.782617i
\(442\) 52.0335 0.117723
\(443\) 445.420i 1.00546i −0.864443 0.502731i \(-0.832328\pi\)
0.864443 0.502731i \(-0.167672\pi\)
\(444\) −215.010 105.699i −0.484257 0.238061i
\(445\) −595.683 −1.33861
\(446\) 703.696i 1.57779i
\(447\) −75.9447 + 154.484i −0.169899 + 0.345602i
\(448\) 16.7707 0.0374346
\(449\) 405.943i 0.904104i 0.891992 + 0.452052i \(0.149308\pi\)
−0.891992 + 0.452052i \(0.850692\pi\)
\(450\) −724.431 + 558.742i −1.60985 + 1.24165i
\(451\) −607.124 −1.34617
\(452\) 224.564i 0.496823i
\(453\) 122.212 + 60.0794i 0.269783 + 0.132626i
\(454\) −128.298 −0.282594
\(455\) 8.18150i 0.0179813i
\(456\) 88.8939 180.825i 0.194943 0.396546i
\(457\) 4.27855 0.00936226 0.00468113 0.999989i \(-0.498510\pi\)
0.00468113 + 0.999989i \(0.498510\pi\)
\(458\) 533.319i 1.16445i
\(459\) 443.127 89.8620i 0.965417 0.195778i
\(460\) 179.086 0.389316
\(461\) 87.0024i 0.188725i 0.995538 + 0.0943627i \(0.0300813\pi\)
−0.995538 + 0.0943627i \(0.969919\pi\)
\(462\) −61.1256 30.0494i −0.132307 0.0650421i
\(463\) −144.683 −0.312491 −0.156245 0.987718i \(-0.549939\pi\)
−0.156245 + 0.987718i \(0.549939\pi\)
\(464\) 715.018i 1.54099i
\(465\) 88.0927 179.195i 0.189447 0.385367i
\(466\) −174.374 −0.374194
\(467\) 322.080i 0.689678i −0.938662 0.344839i \(-0.887934\pi\)
0.938662 0.344839i \(-0.112066\pi\)
\(468\) 11.5136 + 14.9278i 0.0246016 + 0.0318970i
\(469\) −63.8485 −0.136138
\(470\) 353.007i 0.751078i
\(471\) −201.744 99.1776i −0.428331 0.210568i
\(472\) −43.7028 −0.0925906
\(473\) 313.438i 0.662659i
\(474\) 314.986 640.734i 0.664527 1.35176i
\(475\) −507.335 −1.06807
\(476\) 20.1702i 0.0423744i
\(477\) −335.696 + 258.917i −0.703765 + 0.542802i
\(478\) −800.177 −1.67401
\(479\) 174.177i 0.363625i −0.983333 0.181813i \(-0.941804\pi\)
0.983333 0.181813i \(-0.0581965\pi\)
\(480\) 536.244 + 263.618i 1.11718 + 0.549205i
\(481\) −65.7956 −0.136789
\(482\) 563.439i 1.16896i
\(483\) −13.6190 + 27.7033i −0.0281966 + 0.0573567i
\(484\) 64.5459 0.133359
\(485\) 1417.29i 2.92226i
\(486\) 434.475 + 376.274i 0.893981 + 0.774227i
\(487\) 312.915 0.642537 0.321268 0.946988i \(-0.395891\pi\)
0.321268 + 0.946988i \(0.395891\pi\)
\(488\) 238.833i 0.489413i
\(489\) −843.388 414.611i −1.72472 0.847875i
\(490\) 944.435 1.92742
\(491\) 308.713i 0.628744i −0.949300 0.314372i \(-0.898206\pi\)
0.949300 0.314372i \(-0.101794\pi\)
\(492\) 100.828 205.100i 0.204934 0.416871i
\(493\) 603.653 1.22445
\(494\) 36.6797i 0.0742505i
\(495\) 575.881 + 746.653i 1.16340 + 1.50839i
\(496\) −160.130 −0.322843
\(497\) 89.0185i 0.179112i
\(498\) 388.146 + 190.813i 0.779410 + 0.383159i
\(499\) 221.514 0.443915 0.221957 0.975056i \(-0.428755\pi\)
0.221957 + 0.975056i \(0.428755\pi\)
\(500\) 236.337i 0.472673i
\(501\) 317.074 644.981i 0.632882 1.28739i
\(502\) 359.151 0.715440
\(503\) 444.545i 0.883786i 0.897068 + 0.441893i \(0.145693\pi\)
−0.897068 + 0.441893i \(0.854307\pi\)
\(504\) −30.6286 + 23.6233i −0.0607710 + 0.0468716i
\(505\) −125.006 −0.247537
\(506\) 409.439i 0.809168i
\(507\) −450.347 221.391i −0.888258 0.436669i
\(508\) −235.621 −0.463821
\(509\) 675.982i 1.32806i −0.747707 0.664029i \(-0.768845\pi\)
0.747707 0.664029i \(-0.231155\pi\)
\(510\) −432.224 + 879.216i −0.847498 + 1.72395i
\(511\) 80.3875 0.157314
\(512\) 27.7635i 0.0542257i
\(513\) 63.3460 + 312.371i 0.123481 + 0.608910i
\(514\) 875.435 1.70318
\(515\) 1427.25i 2.77137i
\(516\) −105.886 52.0539i −0.205206 0.100880i
\(517\) 230.027 0.444927
\(518\) 89.4864i 0.172754i
\(519\) 367.385 747.323i 0.707871 1.43993i
\(520\) 61.6241 0.118508
\(521\) 600.786i 1.15314i 0.817048 + 0.576570i \(0.195609\pi\)
−0.817048 + 0.576570i \(0.804391\pi\)
\(522\) 468.648 + 607.621i 0.897792 + 1.16402i
\(523\) 690.414 1.32010 0.660052 0.751220i \(-0.270534\pi\)
0.660052 + 0.751220i \(0.270534\pi\)
\(524\) 75.8381i 0.144729i
\(525\) 87.4016 + 42.9668i 0.166479 + 0.0818415i
\(526\) 664.097 1.26254
\(527\) 135.190i 0.256527i
\(528\) 333.607 678.613i 0.631831 1.28525i
\(529\) 343.434 0.649214
\(530\) 918.607i 1.73322i
\(531\) 54.7400 42.2200i 0.103089 0.0795104i
\(532\) 14.2185 0.0267265
\(533\) 62.7632i 0.117755i
\(534\) −460.080 226.176i −0.861573 0.423551i
\(535\) −1575.45 −2.94477
\(536\) 480.915i 0.897230i
\(537\) −86.9002 + 176.770i −0.161825 + 0.329180i
\(538\) −614.844 −1.14283
\(539\) 615.415i 1.14177i
\(540\) −347.876 + 70.5460i −0.644215 + 0.130641i
\(541\) 2.37133 0.00438324 0.00219162 0.999998i \(-0.499302\pi\)
0.00219162 + 0.999998i \(0.499302\pi\)
\(542\) 336.136i 0.620177i
\(543\) 213.492 + 104.953i 0.393172 + 0.193284i
\(544\) 404.556 0.743669
\(545\) 101.834i 0.186851i
\(546\) 3.10645 6.31904i 0.00568946 0.0115733i
\(547\) −78.2775 −0.143103 −0.0715517 0.997437i \(-0.522795\pi\)
−0.0715517 + 0.997437i \(0.522795\pi\)
\(548\) 417.473i 0.761812i
\(549\) 230.731 + 299.151i 0.420274 + 0.544902i
\(550\) −1291.75 −2.34863
\(551\) 425.530i 0.772287i
\(552\) −208.665 102.580i −0.378016 0.185833i
\(553\) −76.0052 −0.137442
\(554\) 583.454i 1.05317i
\(555\) 546.541 1111.76i 0.984759 2.00316i
\(556\) 221.541 0.398455
\(557\) 116.140i 0.208509i −0.994551 0.104255i \(-0.966754\pi\)
0.994551 0.104255i \(-0.0332457\pi\)
\(558\) 136.078 104.955i 0.243868 0.188091i
\(559\) −32.4025 −0.0579651
\(560\) 123.535i 0.220599i
\(561\) 572.918 + 281.647i 1.02124 + 0.502045i
\(562\) −161.642 −0.287620
\(563\) 509.696i 0.905321i 0.891683 + 0.452661i \(0.149525\pi\)
−0.891683 + 0.452661i \(0.850475\pi\)
\(564\) −38.2016 + 77.7085i −0.0677333 + 0.137781i
\(565\) −1161.16 −2.05514
\(566\) 248.247i 0.438600i
\(567\) 15.5421 59.1788i 0.0274110 0.104372i
\(568\) 670.499 1.18046
\(569\) 795.747i 1.39850i −0.714877 0.699250i \(-0.753517\pi\)
0.714877 0.699250i \(-0.246483\pi\)
\(570\) −619.782 304.686i −1.08734 0.534536i
\(571\) −324.633 −0.568534 −0.284267 0.958745i \(-0.591750\pi\)
−0.284267 + 0.958745i \(0.591750\pi\)
\(572\) 26.6180i 0.0465350i
\(573\) 309.591 629.761i 0.540299 1.09906i
\(574\) −85.3620 −0.148714
\(575\) 585.444i 1.01816i
\(576\) −122.034 158.221i −0.211864 0.274690i
\(577\) −209.324 −0.362780 −0.181390 0.983411i \(-0.558060\pi\)
−0.181390 + 0.983411i \(0.558060\pi\)
\(578\) 20.2613i 0.0350541i
\(579\) −174.664 85.8652i −0.301665 0.148299i
\(580\) −473.897 −0.817064
\(581\) 46.0427i 0.0792473i
\(582\) −538.135 + 1094.66i −0.924631 + 1.88085i
\(583\) −598.586 −1.02673
\(584\) 605.490i 1.03680i
\(585\) −77.1874 + 59.5334i −0.131944 + 0.101766i
\(586\) −22.9585 −0.0391784
\(587\) 84.7067i 0.144304i 0.997394 + 0.0721522i \(0.0229867\pi\)
−0.997394 + 0.0721522i \(0.977013\pi\)
\(588\) 207.901 + 102.205i 0.353574 + 0.173817i
\(589\) 95.2985 0.161797
\(590\) 149.792i 0.253885i
\(591\) −261.021 + 530.960i −0.441660 + 0.898410i
\(592\) −993.472 −1.67816
\(593\) 1039.81i 1.75347i −0.480971 0.876737i \(-0.659716\pi\)
0.480971 0.876737i \(-0.340284\pi\)
\(594\) 161.288 + 795.340i 0.271528 + 1.33896i
\(595\) 104.294 0.175285
\(596\) 91.4949i 0.153515i
\(597\) −647.499 318.311i −1.08459 0.533185i
\(598\) 42.3269 0.0707808
\(599\) 331.588i 0.553569i −0.960932 0.276784i \(-0.910731\pi\)
0.960932 0.276784i \(-0.0892688\pi\)
\(600\) −323.631 + 658.321i −0.539386 + 1.09720i
\(601\) 471.745 0.784933 0.392467 0.919766i \(-0.371622\pi\)
0.392467 + 0.919766i \(0.371622\pi\)
\(602\) 44.0695i 0.0732052i
\(603\) 464.599 + 602.372i 0.770480 + 0.998958i
\(604\) −72.3811 −0.119836
\(605\) 333.749i 0.551650i
\(606\) −96.5494 47.4638i −0.159322 0.0783232i
\(607\) 631.905 1.04103 0.520515 0.853852i \(-0.325740\pi\)
0.520515 + 0.853852i \(0.325740\pi\)
\(608\) 285.182i 0.469049i
\(609\) 36.0386 73.3086i 0.0591767 0.120375i
\(610\) −818.606 −1.34198
\(611\) 23.7797i 0.0389193i
\(612\) −190.294 + 146.770i −0.310937 + 0.239821i
\(613\) 727.960 1.18754 0.593768 0.804636i \(-0.297640\pi\)
0.593768 + 0.804636i \(0.297640\pi\)
\(614\) 629.826i 1.02578i
\(615\) 1060.52 + 521.351i 1.72442 + 0.847726i
\(616\) −54.6144 −0.0886597
\(617\) 342.421i 0.554977i −0.960729 0.277489i \(-0.910498\pi\)
0.960729 0.277489i \(-0.0895021\pi\)
\(618\) −541.916 + 1102.35i −0.876888 + 1.78374i
\(619\) −882.209 −1.42522 −0.712608 0.701562i \(-0.752486\pi\)
−0.712608 + 0.701562i \(0.752486\pi\)
\(620\) 106.130i 0.171178i
\(621\) 360.463 73.0987i 0.580456 0.117711i
\(622\) −440.925 −0.708882
\(623\) 54.5757i 0.0876014i
\(624\) 70.1535 + 34.4876i 0.112426 + 0.0552686i
\(625\) 147.602 0.236164
\(626\) 1335.39i 2.13321i
\(627\) −198.540 + 403.864i −0.316651 + 0.644121i
\(628\) 119.485 0.190263
\(629\) 838.737i 1.33344i
\(630\) 80.9693 + 104.980i 0.128523 + 0.166635i
\(631\) −145.624 −0.230783 −0.115392 0.993320i \(-0.536812\pi\)
−0.115392 + 0.993320i \(0.536812\pi\)
\(632\) 572.481i 0.905825i
\(633\) −936.408 460.340i −1.47932 0.727235i
\(634\) 157.255 0.248036
\(635\) 1218.33i 1.91863i
\(636\) 99.4097 202.216i 0.156305 0.317950i
\(637\) 63.6203 0.0998749
\(638\) 1083.46i 1.69821i
\(639\) −839.835 + 647.751i −1.31430 + 1.01369i
\(640\) 1229.68 1.92137
\(641\) 588.864i 0.918665i 0.888264 + 0.459332i \(0.151911\pi\)
−0.888264 + 0.459332i \(0.848089\pi\)
\(642\) −1216.81 598.187i −1.89535 0.931755i
\(643\) 86.5512 0.134605 0.0673027 0.997733i \(-0.478561\pi\)
0.0673027 + 0.997733i \(0.478561\pi\)
\(644\) 16.4076i 0.0254776i
\(645\) 269.156 547.509i 0.417296 0.848851i
\(646\) −467.579 −0.723806
\(647\) 607.286i 0.938618i 0.883034 + 0.469309i \(0.155497\pi\)
−0.883034 + 0.469309i \(0.844503\pi\)
\(648\) 445.743 + 117.065i 0.687875 + 0.180656i
\(649\) 97.6079 0.150397
\(650\) 133.538i 0.205443i
\(651\) −16.4176 8.07093i −0.0252191 0.0123977i
\(652\) 499.505 0.766112
\(653\) 1115.22i 1.70783i −0.520410 0.853917i \(-0.674221\pi\)
0.520410 0.853917i \(-0.325779\pi\)
\(654\) 38.6655 78.6522i 0.0591216 0.120263i
\(655\) −392.137 −0.598683
\(656\) 947.683i 1.44464i
\(657\) −584.947 758.407i −0.890330 1.15435i
\(658\) 32.3420 0.0491519
\(659\) 974.698i 1.47906i −0.673126 0.739528i \(-0.735049\pi\)
0.673126 0.739528i \(-0.264951\pi\)
\(660\) −449.768 221.107i −0.681467 0.335010i
\(661\) −24.7297 −0.0374126 −0.0187063 0.999825i \(-0.505955\pi\)
−0.0187063 + 0.999825i \(0.505955\pi\)
\(662\) 266.887i 0.403153i
\(663\) −29.1161 + 59.2270i −0.0439156 + 0.0893318i
\(664\) 346.800 0.522289
\(665\) 73.5198i 0.110556i
\(666\) 844.249 651.156i 1.26764 0.977711i
\(667\) 491.045 0.736199
\(668\) 381.997i 0.571852i
\(669\) 800.980 + 393.763i 1.19728 + 0.588584i
\(670\) −1648.35 −2.46022
\(671\) 533.423i 0.794967i
\(672\) 24.1524 49.1299i 0.0359410 0.0731100i
\(673\) 509.624 0.757243 0.378621 0.925552i \(-0.376398\pi\)
0.378621 + 0.925552i \(0.376398\pi\)
\(674\) 992.245i 1.47217i
\(675\) −230.620 1137.23i −0.341660 1.68479i
\(676\) 266.723 0.394560
\(677\) 344.692i 0.509146i −0.967054 0.254573i \(-0.918065\pi\)
0.967054 0.254573i \(-0.0819349\pi\)
\(678\) −896.827 440.881i −1.32275 0.650268i
\(679\) 129.851 0.191238
\(680\) 785.560i 1.15524i
\(681\) 71.7908 146.035i 0.105420 0.214441i
\(682\) 242.643 0.355782
\(683\) 494.770i 0.724407i 0.932099 + 0.362204i \(0.117976\pi\)
−0.932099 + 0.362204i \(0.882024\pi\)
\(684\) −103.462 134.143i −0.151260 0.196115i
\(685\) 2158.63 3.15129
\(686\) 174.075i 0.253754i
\(687\) −607.049 298.426i −0.883623 0.434390i
\(688\) −489.257 −0.711129
\(689\) 61.8805i 0.0898120i
\(690\) −351.595 + 715.203i −0.509558 + 1.03653i
\(691\) 399.559 0.578234 0.289117 0.957294i \(-0.406638\pi\)
0.289117 + 0.957294i \(0.406638\pi\)
\(692\) 442.610i 0.639610i
\(693\) 68.4074 52.7614i 0.0987119 0.0761348i
\(694\) 944.949 1.36160
\(695\) 1145.53i 1.64824i
\(696\) 552.170 + 271.448i 0.793348 + 0.390011i
\(697\) 800.080 1.14789
\(698\) 330.577i 0.473606i
\(699\) 97.5735 198.481i 0.139590 0.283950i
\(700\) −51.7645 −0.0739493
\(701\) 372.029i 0.530711i 0.964151 + 0.265356i \(0.0854893\pi\)
−0.964151 + 0.265356i \(0.914511\pi\)
\(702\) −82.2206 + 16.6736i −0.117123 + 0.0237515i
\(703\) 591.247 0.841034
\(704\) 282.128i 0.400749i
\(705\) −401.808 197.530i −0.569941 0.280184i
\(706\) 607.970 0.861147
\(707\) 11.4529i 0.0161993i
\(708\) −16.2102 + 32.9742i −0.0228957 + 0.0465737i
\(709\) −848.826 −1.19722 −0.598608 0.801042i \(-0.704279\pi\)
−0.598608 + 0.801042i \(0.704279\pi\)
\(710\) 2298.15i 3.23683i
\(711\) 553.058 + 717.063i 0.777860 + 1.00853i
\(712\) −411.071 −0.577347
\(713\) 109.971i 0.154236i
\(714\) 80.5526 + 39.5998i 0.112819 + 0.0554619i
\(715\) −137.634 −0.192496
\(716\) 104.694i 0.146220i
\(717\) 447.750 910.799i 0.624477 1.27029i
\(718\) 1465.30 2.04080
\(719\) 735.217i 1.02256i −0.859416 0.511278i \(-0.829172\pi\)
0.859416 0.511278i \(-0.170828\pi\)
\(720\) −1165.48 + 898.916i −1.61872 + 1.24849i
\(721\) 130.763 0.181363
\(722\) 524.256i 0.726116i
\(723\) 641.332 + 315.280i 0.887043 + 0.436072i
\(724\) −126.443 −0.174645
\(725\) 1549.21i 2.13684i
\(726\) −126.722 + 257.773i −0.174548 + 0.355059i
\(727\) −760.051 −1.04546 −0.522731 0.852497i \(-0.675087\pi\)
−0.522731 + 0.852497i \(0.675087\pi\)
\(728\) 5.64592i 0.00775538i
\(729\) −671.409 + 283.990i −0.921001 + 0.389561i
\(730\) 2075.33 2.84291
\(731\) 413.054i 0.565054i
\(732\) −180.202 88.5878i −0.246178 0.121022i
\(733\) 183.791 0.250738 0.125369 0.992110i \(-0.459988\pi\)
0.125369 + 0.992110i \(0.459988\pi\)
\(734\) 242.270i 0.330069i
\(735\) −528.471 + 1075.00i −0.719008 + 1.46258i
\(736\) 329.088 0.447131
\(737\) 1074.10i 1.45740i
\(738\) 621.144 + 805.339i 0.841659 + 1.09124i
\(739\) 413.355 0.559344 0.279672 0.960096i \(-0.409774\pi\)
0.279672 + 0.960096i \(0.409774\pi\)
\(740\) 658.449i 0.889796i
\(741\) −41.7506 20.5247i −0.0563436 0.0276986i
\(742\) −84.1615 −0.113425
\(743\) 39.2804i 0.0528673i −0.999651 0.0264337i \(-0.991585\pi\)
0.999651 0.0264337i \(-0.00841508\pi\)
\(744\) 60.7913 123.660i 0.0817088 0.166209i
\(745\) 473.094 0.635026
\(746\) 695.303i 0.932042i
\(747\) −434.385 + 335.034i −0.581506 + 0.448506i
\(748\) −339.316 −0.453632
\(749\) 144.341i 0.192711i
\(750\) 943.843 + 463.994i 1.25846 + 0.618659i
\(751\) 471.380 0.627670 0.313835 0.949478i \(-0.398386\pi\)
0.313835 + 0.949478i \(0.398386\pi\)
\(752\) 359.058i 0.477471i
\(753\) −200.968 + 408.802i −0.266890 + 0.542898i
\(754\) −112.006 −0.148549
\(755\) 374.262i 0.495711i
\(756\) 6.46333 + 31.8719i 0.00854938 + 0.0421586i
\(757\) −1070.90 −1.41466 −0.707331 0.706883i \(-0.750101\pi\)
−0.707331 + 0.706883i \(0.750101\pi\)
\(758\) 2.23916i 0.00295404i
\(759\) 466.043 + 229.107i 0.614022 + 0.301854i
\(760\) −553.761 −0.728633
\(761\) 144.426i 0.189784i 0.995488 + 0.0948922i \(0.0302506\pi\)
−0.995488 + 0.0948922i \(0.969749\pi\)
\(762\) 462.590 940.986i 0.607074 1.23489i
\(763\) −9.32989 −0.0122279
\(764\) 372.983i 0.488197i
\(765\) −758.908 983.955i −0.992037 1.28622i
\(766\) −321.784 −0.420084
\(767\) 10.0905i 0.0131558i
\(768\) 710.660 + 349.362i 0.925339 + 0.454898i
\(769\) −362.767 −0.471738 −0.235869 0.971785i \(-0.575794\pi\)
−0.235869 + 0.971785i \(0.575794\pi\)
\(770\) 187.192i 0.243106i
\(771\) −489.862 + 996.461i −0.635359 + 1.29243i
\(772\) 103.447 0.133998
\(773\) 221.150i 0.286094i −0.989716 0.143047i \(-0.954310\pi\)
0.989716 0.143047i \(-0.0456899\pi\)
\(774\) 415.769 320.676i 0.537169 0.414310i
\(775\) −346.948 −0.447675
\(776\) 978.052i 1.26038i
\(777\) −101.858 50.0733i −0.131091 0.0644444i
\(778\) −361.075 −0.464106
\(779\) 563.997i 0.724001i
\(780\) 22.8575 46.4961i 0.0293045 0.0596103i
\(781\) −1497.53 −1.91745
\(782\) 539.567i 0.689983i
\(783\) −953.860 + 193.434i −1.21821 + 0.247042i
\(784\) 960.626 1.22529
\(785\) 617.823i 0.787035i
\(786\) −302.870 148.891i −0.385331