Properties

Label 177.3.b.a.119.2
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

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 119.2
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.37

$q$-expansion

\(f(q)\) \(=\) \(q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +O(q^{10})\) \(q-3.62092i q^{2} +(-1.98632 + 2.24823i) q^{3} -9.11103 q^{4} +2.81281i q^{5} +(8.14066 + 7.19229i) q^{6} +8.99888 q^{7} +18.5066i q^{8} +(-1.10909 - 8.93140i) q^{9} +10.1850 q^{10} +19.0108i q^{11} +(18.0974 - 20.4837i) q^{12} +8.47140 q^{13} -32.5842i q^{14} +(-6.32386 - 5.58714i) q^{15} +30.5668 q^{16} -19.9551i q^{17} +(-32.3399 + 4.01593i) q^{18} +16.3132 q^{19} -25.6276i q^{20} +(-17.8746 + 20.2316i) q^{21} +68.8365 q^{22} +10.3343i q^{23} +(-41.6072 - 36.7600i) q^{24} +17.0881 q^{25} -30.6742i q^{26} +(22.2829 + 15.2471i) q^{27} -81.9891 q^{28} +47.7591i q^{29} +(-20.2306 + 22.8982i) q^{30} +4.05578 q^{31} -36.6533i q^{32} +(-42.7407 - 37.7615i) q^{33} -72.2559 q^{34} +25.3122i q^{35} +(10.1050 + 81.3743i) q^{36} -13.8783 q^{37} -59.0688i q^{38} +(-16.8269 + 19.0457i) q^{39} -52.0557 q^{40} +55.0214i q^{41} +(73.2568 + 64.7226i) q^{42} +44.9435 q^{43} -173.208i q^{44} +(25.1224 - 3.11967i) q^{45} +37.4197 q^{46} +2.46701i q^{47} +(-60.7153 + 68.7212i) q^{48} +31.9799 q^{49} -61.8745i q^{50} +(44.8638 + 39.6372i) q^{51} -77.1832 q^{52} -74.2215i q^{53} +(55.2084 - 80.6844i) q^{54} -53.4739 q^{55} +166.539i q^{56} +(-32.4032 + 36.6759i) q^{57} +172.932 q^{58} +7.68115i q^{59} +(57.6169 + 50.9046i) q^{60} +32.9933 q^{61} -14.6856i q^{62} +(-9.98059 - 80.3726i) q^{63} -10.4513 q^{64} +23.8285i q^{65} +(-136.731 + 154.760i) q^{66} -51.8358 q^{67} +181.812i q^{68} +(-23.2340 - 20.5273i) q^{69} +91.6533 q^{70} -95.1596i q^{71} +(165.290 - 20.5256i) q^{72} -123.796 q^{73} +50.2521i q^{74} +(-33.9423 + 38.4179i) q^{75} -148.630 q^{76} +171.076i q^{77} +(68.9627 + 60.9287i) q^{78} -138.482 q^{79} +85.9787i q^{80} +(-78.5398 + 19.8115i) q^{81} +199.228 q^{82} +27.4328i q^{83} +(162.856 - 184.331i) q^{84} +56.1301 q^{85} -162.737i q^{86} +(-107.374 - 94.8648i) q^{87} -351.826 q^{88} -89.1780i q^{89} +(-11.2961 - 90.9660i) q^{90} +76.2331 q^{91} -94.1564i q^{92} +(-8.05606 + 9.11833i) q^{93} +8.93283 q^{94} +45.8861i q^{95} +(82.4051 + 72.8050i) q^{96} +17.0787 q^{97} -115.797i q^{98} +(169.793 - 21.0847i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.62092i 1.81046i −0.424924 0.905229i \(-0.639699\pi\)
0.424924 0.905229i \(-0.360301\pi\)
\(3\) −1.98632 + 2.24823i −0.662106 + 0.749411i
\(4\) −9.11103 −2.27776
\(5\) 2.81281i 0.562563i 0.959625 + 0.281281i \(0.0907595\pi\)
−0.959625 + 0.281281i \(0.909241\pi\)
\(6\) 8.14066 + 7.19229i 1.35678 + 1.19871i
\(7\) 8.99888 1.28555 0.642777 0.766053i \(-0.277782\pi\)
0.642777 + 0.766053i \(0.277782\pi\)
\(8\) 18.5066i 2.31333i
\(9\) −1.10909 8.93140i −0.123232 0.992378i
\(10\) 10.1850 1.01850
\(11\) 19.0108i 1.72825i 0.503273 + 0.864127i \(0.332129\pi\)
−0.503273 + 0.864127i \(0.667871\pi\)
\(12\) 18.0974 20.4837i 1.50812 1.70698i
\(13\) 8.47140 0.651646 0.325823 0.945431i \(-0.394359\pi\)
0.325823 + 0.945431i \(0.394359\pi\)
\(14\) 32.5842i 2.32744i
\(15\) −6.32386 5.58714i −0.421591 0.372476i
\(16\) 30.5668 1.91042
\(17\) 19.9551i 1.17383i −0.809648 0.586916i \(-0.800342\pi\)
0.809648 0.586916i \(-0.199658\pi\)
\(18\) −32.3399 + 4.01593i −1.79666 + 0.223107i
\(19\) 16.3132 0.858591 0.429295 0.903164i \(-0.358762\pi\)
0.429295 + 0.903164i \(0.358762\pi\)
\(20\) 25.6276i 1.28138i
\(21\) −17.8746 + 20.2316i −0.851173 + 0.963409i
\(22\) 68.8365 3.12893
\(23\) 10.3343i 0.449319i 0.974437 + 0.224659i \(0.0721269\pi\)
−0.974437 + 0.224659i \(0.927873\pi\)
\(24\) −41.6072 36.7600i −1.73363 1.53167i
\(25\) 17.0881 0.683523
\(26\) 30.6742i 1.17978i
\(27\) 22.2829 + 15.2471i 0.825291 + 0.564707i
\(28\) −81.9891 −2.92818
\(29\) 47.7591i 1.64687i 0.567413 + 0.823434i \(0.307944\pi\)
−0.567413 + 0.823434i \(0.692056\pi\)
\(30\) −20.2306 + 22.8982i −0.674352 + 0.763272i
\(31\) 4.05578 0.130832 0.0654158 0.997858i \(-0.479163\pi\)
0.0654158 + 0.997858i \(0.479163\pi\)
\(32\) 36.6533i 1.14542i
\(33\) −42.7407 37.7615i −1.29517 1.14429i
\(34\) −72.2559 −2.12517
\(35\) 25.3122i 0.723206i
\(36\) 10.1050 + 81.3743i 0.280694 + 2.26040i
\(37\) −13.8783 −0.375088 −0.187544 0.982256i \(-0.560053\pi\)
−0.187544 + 0.982256i \(0.560053\pi\)
\(38\) 59.0688i 1.55444i
\(39\) −16.8269 + 19.0457i −0.431458 + 0.488350i
\(40\) −52.0557 −1.30139
\(41\) 55.0214i 1.34199i 0.741464 + 0.670993i \(0.234132\pi\)
−0.741464 + 0.670993i \(0.765868\pi\)
\(42\) 73.2568 + 64.7226i 1.74421 + 1.54101i
\(43\) 44.9435 1.04520 0.522599 0.852579i \(-0.324963\pi\)
0.522599 + 0.852579i \(0.324963\pi\)
\(44\) 173.208i 3.93655i
\(45\) 25.1224 3.11967i 0.558275 0.0693260i
\(46\) 37.4197 0.813473
\(47\) 2.46701i 0.0524895i 0.999656 + 0.0262448i \(0.00835493\pi\)
−0.999656 + 0.0262448i \(0.991645\pi\)
\(48\) −60.7153 + 68.7212i −1.26490 + 1.43169i
\(49\) 31.9799 0.652652
\(50\) 61.8745i 1.23749i
\(51\) 44.8638 + 39.6372i 0.879682 + 0.777200i
\(52\) −77.1832 −1.48429
\(53\) 74.2215i 1.40040i −0.713944 0.700202i \(-0.753093\pi\)
0.713944 0.700202i \(-0.246907\pi\)
\(54\) 55.2084 80.6844i 1.02238 1.49416i
\(55\) −53.4739 −0.972252
\(56\) 166.539i 2.97391i
\(57\) −32.4032 + 36.6759i −0.568478 + 0.643437i
\(58\) 172.932 2.98158
\(59\) 7.68115i 0.130189i
\(60\) 57.6169 + 50.9046i 0.960282 + 0.848410i
\(61\) 32.9933 0.540873 0.270437 0.962738i \(-0.412832\pi\)
0.270437 + 0.962738i \(0.412832\pi\)
\(62\) 14.6856i 0.236865i
\(63\) −9.98059 80.3726i −0.158422 1.27576i
\(64\) −10.4513 −0.163302
\(65\) 23.8285i 0.366592i
\(66\) −136.731 + 154.760i −2.07168 + 2.34486i
\(67\) −51.8358 −0.773669 −0.386834 0.922149i \(-0.626431\pi\)
−0.386834 + 0.922149i \(0.626431\pi\)
\(68\) 181.812i 2.67370i
\(69\) −23.2340 20.5273i −0.336724 0.297496i
\(70\) 91.6533 1.30933
\(71\) 95.1596i 1.34028i −0.742236 0.670138i \(-0.766235\pi\)
0.742236 0.670138i \(-0.233765\pi\)
\(72\) 165.290 20.5256i 2.29569 0.285077i
\(73\) −123.796 −1.69583 −0.847915 0.530131i \(-0.822143\pi\)
−0.847915 + 0.530131i \(0.822143\pi\)
\(74\) 50.2521i 0.679082i
\(75\) −33.9423 + 38.4179i −0.452564 + 0.512239i
\(76\) −148.630 −1.95566
\(77\) 171.076i 2.22177i
\(78\) 68.9627 + 60.9287i 0.884138 + 0.781137i
\(79\) −138.482 −1.75293 −0.876466 0.481463i \(-0.840106\pi\)
−0.876466 + 0.481463i \(0.840106\pi\)
\(80\) 85.9787i 1.07473i
\(81\) −78.5398 + 19.8115i −0.969628 + 0.244586i
\(82\) 199.228 2.42961
\(83\) 27.4328i 0.330516i 0.986250 + 0.165258i \(0.0528457\pi\)
−0.986250 + 0.165258i \(0.947154\pi\)
\(84\) 162.856 184.331i 1.93877 2.19441i
\(85\) 56.1301 0.660354
\(86\) 162.737i 1.89229i
\(87\) −107.374 94.8648i −1.23418 1.09040i
\(88\) −351.826 −3.99802
\(89\) 89.1780i 1.00200i −0.865447 0.501000i \(-0.832966\pi\)
0.865447 0.501000i \(-0.167034\pi\)
\(90\) −11.2961 90.9660i −0.125512 1.01073i
\(91\) 76.2331 0.837727
\(92\) 94.1564i 1.02344i
\(93\) −8.05606 + 9.11833i −0.0866244 + 0.0980466i
\(94\) 8.93283 0.0950301
\(95\) 45.8861i 0.483011i
\(96\) 82.4051 + 72.8050i 0.858386 + 0.758386i
\(97\) 17.0787 0.176069 0.0880345 0.996117i \(-0.471941\pi\)
0.0880345 + 0.996117i \(0.471941\pi\)
\(98\) 115.797i 1.18160i
\(99\) 169.793 21.0847i 1.71508 0.212977i
\(100\) −155.690 −1.55690
\(101\) 67.1513i 0.664865i 0.943127 + 0.332432i \(0.107869\pi\)
−0.943127 + 0.332432i \(0.892131\pi\)
\(102\) 143.523 162.448i 1.40709 1.59263i
\(103\) 167.112 1.62245 0.811225 0.584734i \(-0.198801\pi\)
0.811225 + 0.584734i \(0.198801\pi\)
\(104\) 156.777i 1.50747i
\(105\) −56.9077 50.2780i −0.541978 0.478838i
\(106\) −268.750 −2.53537
\(107\) 41.9211i 0.391786i −0.980625 0.195893i \(-0.937239\pi\)
0.980625 0.195893i \(-0.0627605\pi\)
\(108\) −203.020 138.917i −1.87981 1.28627i
\(109\) −14.5692 −0.133662 −0.0668311 0.997764i \(-0.521289\pi\)
−0.0668311 + 0.997764i \(0.521289\pi\)
\(110\) 193.624i 1.76022i
\(111\) 27.5666 31.2016i 0.248348 0.281095i
\(112\) 275.067 2.45596
\(113\) 0.786761i 0.00696249i 0.999994 + 0.00348124i \(0.00110812\pi\)
−0.999994 + 0.00348124i \(0.998892\pi\)
\(114\) 132.800 + 117.329i 1.16492 + 1.02921i
\(115\) −29.0686 −0.252770
\(116\) 435.135i 3.75117i
\(117\) −9.39556 75.6614i −0.0803039 0.646679i
\(118\) 27.8128 0.235702
\(119\) 179.574i 1.50902i
\(120\) 103.399 117.033i 0.861659 0.975277i
\(121\) −240.411 −1.98686
\(122\) 119.466i 0.979228i
\(123\) −123.701 109.290i −1.00570 0.888536i
\(124\) −36.9524 −0.298003
\(125\) 118.386i 0.947088i
\(126\) −291.023 + 36.1389i −2.30970 + 0.286817i
\(127\) 189.829 1.49472 0.747358 0.664421i \(-0.231322\pi\)
0.747358 + 0.664421i \(0.231322\pi\)
\(128\) 108.770i 0.849764i
\(129\) −89.2720 + 101.043i −0.692031 + 0.783282i
\(130\) 86.2809 0.663699
\(131\) 126.252i 0.963753i −0.876239 0.481876i \(-0.839955\pi\)
0.876239 0.481876i \(-0.160045\pi\)
\(132\) 389.412 + 344.046i 2.95009 + 2.60641i
\(133\) 146.801 1.10377
\(134\) 187.693i 1.40069i
\(135\) −42.8872 + 62.6776i −0.317683 + 0.464278i
\(136\) 369.302 2.71546
\(137\) 74.7474i 0.545601i 0.962071 + 0.272801i \(0.0879500\pi\)
−0.962071 + 0.272801i \(0.912050\pi\)
\(138\) −74.3275 + 84.1283i −0.538605 + 0.609625i
\(139\) −80.8582 −0.581714 −0.290857 0.956767i \(-0.593940\pi\)
−0.290857 + 0.956767i \(0.593940\pi\)
\(140\) 230.620i 1.64729i
\(141\) −5.54641 4.90026i −0.0393362 0.0347536i
\(142\) −344.565 −2.42651
\(143\) 161.048i 1.12621i
\(144\) −33.9014 273.004i −0.235426 1.89586i
\(145\) −134.338 −0.926466
\(146\) 448.254i 3.07023i
\(147\) −63.5223 + 71.8983i −0.432124 + 0.489104i
\(148\) 126.445 0.854361
\(149\) 175.759i 1.17959i −0.807552 0.589797i \(-0.799208\pi\)
0.807552 0.589797i \(-0.200792\pi\)
\(150\) 139.108 + 122.902i 0.927388 + 0.819349i
\(151\) 195.888 1.29727 0.648635 0.761100i \(-0.275340\pi\)
0.648635 + 0.761100i \(0.275340\pi\)
\(152\) 301.903i 1.98620i
\(153\) −178.227 + 22.1321i −1.16488 + 0.144654i
\(154\) 619.452 4.02241
\(155\) 11.4082i 0.0736010i
\(156\) 153.310 173.526i 0.982758 1.11234i
\(157\) −137.817 −0.877813 −0.438907 0.898533i \(-0.644634\pi\)
−0.438907 + 0.898533i \(0.644634\pi\)
\(158\) 501.431i 3.17361i
\(159\) 166.867 + 147.427i 1.04948 + 0.927216i
\(160\) 103.099 0.644368
\(161\) 92.9975i 0.577624i
\(162\) 71.7358 + 284.386i 0.442813 + 1.75547i
\(163\) 265.663 1.62984 0.814919 0.579576i \(-0.196782\pi\)
0.814919 + 0.579576i \(0.196782\pi\)
\(164\) 501.302i 3.05672i
\(165\) 106.216 120.222i 0.643734 0.728616i
\(166\) 99.3320 0.598386
\(167\) 114.909i 0.688078i −0.938955 0.344039i \(-0.888205\pi\)
0.938955 0.344039i \(-0.111795\pi\)
\(168\) −374.418 330.799i −2.22868 1.96904i
\(169\) −97.2355 −0.575358
\(170\) 203.242i 1.19554i
\(171\) −18.0929 145.700i −0.105806 0.852047i
\(172\) −409.482 −2.38071
\(173\) 67.7045i 0.391356i 0.980668 + 0.195678i \(0.0626907\pi\)
−0.980668 + 0.195678i \(0.937309\pi\)
\(174\) −343.497 + 388.791i −1.97412 + 2.23443i
\(175\) 153.774 0.878706
\(176\) 581.099i 3.30170i
\(177\) −17.2690 15.2572i −0.0975649 0.0861988i
\(178\) −322.906 −1.81408
\(179\) 210.640i 1.17676i −0.808585 0.588380i \(-0.799766\pi\)
0.808585 0.588380i \(-0.200234\pi\)
\(180\) −228.891 + 28.4234i −1.27162 + 0.157908i
\(181\) −91.8129 −0.507254 −0.253627 0.967302i \(-0.581624\pi\)
−0.253627 + 0.967302i \(0.581624\pi\)
\(182\) 276.034i 1.51667i
\(183\) −65.5351 + 74.1765i −0.358115 + 0.405336i
\(184\) −191.254 −1.03942
\(185\) 39.0370i 0.211011i
\(186\) 33.0167 + 29.1703i 0.177509 + 0.156830i
\(187\) 379.363 2.02868
\(188\) 22.4770i 0.119558i
\(189\) 200.521 + 137.207i 1.06096 + 0.725962i
\(190\) 166.150 0.874472
\(191\) 59.8897i 0.313559i −0.987634 0.156779i \(-0.949889\pi\)
0.987634 0.156779i \(-0.0501111\pi\)
\(192\) 20.7596 23.4970i 0.108123 0.122380i
\(193\) −29.7862 −0.154333 −0.0771664 0.997018i \(-0.524587\pi\)
−0.0771664 + 0.997018i \(0.524587\pi\)
\(194\) 61.8405i 0.318765i
\(195\) −53.5719 47.3309i −0.274728 0.242722i
\(196\) −291.370 −1.48658
\(197\) 179.374i 0.910528i −0.890357 0.455264i \(-0.849545\pi\)
0.890357 0.455264i \(-0.150455\pi\)
\(198\) −76.3461 614.807i −0.385586 3.10508i
\(199\) 63.2008 0.317592 0.158796 0.987311i \(-0.449239\pi\)
0.158796 + 0.987311i \(0.449239\pi\)
\(200\) 316.242i 1.58121i
\(201\) 102.962 116.539i 0.512250 0.579796i
\(202\) 243.149 1.20371
\(203\) 429.779i 2.11714i
\(204\) −408.755 361.136i −2.00370 1.77027i
\(205\) −154.765 −0.754952
\(206\) 605.100i 2.93738i
\(207\) 92.3001 11.4617i 0.445894 0.0553707i
\(208\) 258.943 1.24492
\(209\) 310.128i 1.48386i
\(210\) −182.053 + 206.058i −0.866917 + 0.981228i
\(211\) −100.345 −0.475567 −0.237783 0.971318i \(-0.576421\pi\)
−0.237783 + 0.971318i \(0.576421\pi\)
\(212\) 676.234i 3.18978i
\(213\) 213.941 + 189.017i 1.00442 + 0.887405i
\(214\) −151.793 −0.709312
\(215\) 126.418i 0.587990i
\(216\) −282.172 + 412.381i −1.30635 + 1.90917i
\(217\) 36.4975 0.168191
\(218\) 52.7538i 0.241990i
\(219\) 245.897 278.321i 1.12282 1.27087i
\(220\) 487.202 2.21456
\(221\) 169.048i 0.764922i
\(222\) −112.978 99.8165i −0.508911 0.449624i
\(223\) −207.548 −0.930710 −0.465355 0.885124i \(-0.654073\pi\)
−0.465355 + 0.885124i \(0.654073\pi\)
\(224\) 329.839i 1.47249i
\(225\) −18.9523 152.620i −0.0842322 0.678313i
\(226\) 2.84880 0.0126053
\(227\) 405.735i 1.78738i 0.448687 + 0.893689i \(0.351892\pi\)
−0.448687 + 0.893689i \(0.648108\pi\)
\(228\) 295.227 334.155i 1.29486 1.46559i
\(229\) −178.686 −0.780288 −0.390144 0.920754i \(-0.627575\pi\)
−0.390144 + 0.920754i \(0.627575\pi\)
\(230\) 105.255i 0.457630i
\(231\) −384.619 339.811i −1.66502 1.47104i
\(232\) −883.860 −3.80974
\(233\) 88.5617i 0.380093i 0.981775 + 0.190046i \(0.0608639\pi\)
−0.981775 + 0.190046i \(0.939136\pi\)
\(234\) −273.964 + 34.0205i −1.17078 + 0.145387i
\(235\) −6.93924 −0.0295287
\(236\) 69.9832i 0.296539i
\(237\) 275.068 311.339i 1.16063 1.31367i
\(238\) −650.222 −2.73203
\(239\) 204.857i 0.857144i −0.903508 0.428572i \(-0.859017\pi\)
0.903508 0.428572i \(-0.140983\pi\)
\(240\) −193.300 170.781i −0.805417 0.711587i
\(241\) 255.665 1.06085 0.530425 0.847732i \(-0.322032\pi\)
0.530425 + 0.847732i \(0.322032\pi\)
\(242\) 870.507i 3.59713i
\(243\) 111.464 215.928i 0.458700 0.888591i
\(244\) −300.603 −1.23198
\(245\) 89.9536i 0.367158i
\(246\) −395.730 + 447.911i −1.60866 + 1.82078i
\(247\) 138.196 0.559497
\(248\) 75.0588i 0.302656i
\(249\) −61.6754 54.4903i −0.247692 0.218837i
\(250\) 428.666 1.71466
\(251\) 208.746i 0.831659i −0.909443 0.415830i \(-0.863491\pi\)
0.909443 0.415830i \(-0.136509\pi\)
\(252\) 90.9335 + 732.278i 0.360847 + 2.90586i
\(253\) −196.464 −0.776537
\(254\) 687.355i 2.70612i
\(255\) −111.492 + 126.193i −0.437224 + 0.494876i
\(256\) −435.652 −1.70176
\(257\) 111.276i 0.432981i −0.976285 0.216491i \(-0.930539\pi\)
0.976285 0.216491i \(-0.0694611\pi\)
\(258\) 365.870 + 323.247i 1.41810 + 1.25289i
\(259\) −124.889 −0.482197
\(260\) 217.102i 0.835007i
\(261\) 426.556 52.9693i 1.63431 0.202948i
\(262\) −457.146 −1.74483
\(263\) 58.7836i 0.223512i −0.993736 0.111756i \(-0.964353\pi\)
0.993736 0.111756i \(-0.0356475\pi\)
\(264\) 698.837 790.986i 2.64711 2.99616i
\(265\) 208.771 0.787816
\(266\) 531.554i 1.99832i
\(267\) 200.493 + 177.136i 0.750910 + 0.663430i
\(268\) 472.278 1.76223
\(269\) 68.0727i 0.253058i 0.991963 + 0.126529i \(0.0403837\pi\)
−0.991963 + 0.126529i \(0.959616\pi\)
\(270\) 226.950 + 155.291i 0.840556 + 0.575152i
\(271\) 154.616 0.570540 0.285270 0.958447i \(-0.407917\pi\)
0.285270 + 0.958447i \(0.407917\pi\)
\(272\) 609.964i 2.24252i
\(273\) −151.423 + 171.390i −0.554663 + 0.627801i
\(274\) 270.654 0.987788
\(275\) 324.858i 1.18130i
\(276\) 211.686 + 187.025i 0.766976 + 0.677625i
\(277\) 482.276 1.74107 0.870534 0.492109i \(-0.163774\pi\)
0.870534 + 0.492109i \(0.163774\pi\)
\(278\) 292.781i 1.05317i
\(279\) −4.49824 36.2238i −0.0161227 0.129834i
\(280\) −468.443 −1.67301
\(281\) 7.90211i 0.0281214i −0.999901 0.0140607i \(-0.995524\pi\)
0.999901 0.0140607i \(-0.00447581\pi\)
\(282\) −17.7434 + 20.0831i −0.0629200 + 0.0712166i
\(283\) 342.096 1.20882 0.604410 0.796673i \(-0.293409\pi\)
0.604410 + 0.796673i \(0.293409\pi\)
\(284\) 867.003i 3.05283i
\(285\) −103.163 91.1443i −0.361974 0.319805i
\(286\) 583.141 2.03896
\(287\) 495.132i 1.72520i
\(288\) −327.365 + 40.6519i −1.13668 + 0.141152i
\(289\) −109.207 −0.377880
\(290\) 486.425i 1.67733i
\(291\) −33.9237 + 38.3969i −0.116576 + 0.131948i
\(292\) 1127.91 3.86269
\(293\) 58.8955i 0.201009i 0.994937 + 0.100504i \(0.0320456\pi\)
−0.994937 + 0.100504i \(0.967954\pi\)
\(294\) 260.338 + 230.009i 0.885502 + 0.782343i
\(295\) −21.6056 −0.0732395
\(296\) 256.840i 0.867702i
\(297\) −289.859 + 423.615i −0.975958 + 1.42631i
\(298\) −636.410 −2.13560
\(299\) 87.5462i 0.292797i
\(300\) 309.250 350.027i 1.03083 1.16676i
\(301\) 404.441 1.34366
\(302\) 709.293i 2.34865i
\(303\) −150.972 133.384i −0.498257 0.440211i
\(304\) 498.643 1.64027
\(305\) 92.8039i 0.304275i
\(306\) 80.1384 + 645.346i 0.261890 + 2.10897i
\(307\) −597.151 −1.94512 −0.972559 0.232656i \(-0.925258\pi\)
−0.972559 + 0.232656i \(0.925258\pi\)
\(308\) 1558.68i 5.06065i
\(309\) −331.938 + 375.707i −1.07423 + 1.21588i
\(310\) 41.3080 0.133252
\(311\) 29.6874i 0.0954578i −0.998860 0.0477289i \(-0.984802\pi\)
0.998860 0.0477289i \(-0.0151983\pi\)
\(312\) −352.471 311.409i −1.12971 0.998104i
\(313\) −167.252 −0.534351 −0.267176 0.963648i \(-0.586090\pi\)
−0.267176 + 0.963648i \(0.586090\pi\)
\(314\) 499.023i 1.58924i
\(315\) 226.073 28.0736i 0.717693 0.0891224i
\(316\) 1261.71 3.99276
\(317\) 395.131i 1.24647i −0.782035 0.623234i \(-0.785818\pi\)
0.782035 0.623234i \(-0.214182\pi\)
\(318\) 533.822 604.212i 1.67869 1.90004i
\(319\) −907.940 −2.84621
\(320\) 29.3976i 0.0918676i
\(321\) 94.2484 + 83.2686i 0.293609 + 0.259404i
\(322\) 336.736 1.04576
\(323\) 325.533i 1.00784i
\(324\) 715.579 180.503i 2.20858 0.557109i
\(325\) 144.760 0.445415
\(326\) 961.945i 2.95075i
\(327\) 28.9390 32.7549i 0.0884985 0.100168i
\(328\) −1018.26 −3.10445
\(329\) 22.2003i 0.0674782i
\(330\) −435.312 384.599i −1.31913 1.16545i
\(331\) −260.174 −0.786025 −0.393013 0.919533i \(-0.628567\pi\)
−0.393013 + 0.919533i \(0.628567\pi\)
\(332\) 249.942i 0.752836i
\(333\) 15.3923 + 123.952i 0.0462231 + 0.372229i
\(334\) −416.076 −1.24574
\(335\) 145.805i 0.435237i
\(336\) −546.370 + 618.414i −1.62610 + 1.84052i
\(337\) 98.0518 0.290955 0.145477 0.989362i \(-0.453528\pi\)
0.145477 + 0.989362i \(0.453528\pi\)
\(338\) 352.081i 1.04166i
\(339\) −1.76882 1.56276i −0.00521776 0.00460990i
\(340\) −511.403 −1.50413
\(341\) 77.1036i 0.226110i
\(342\) −527.567 + 65.5128i −1.54259 + 0.191558i
\(343\) −153.162 −0.446535
\(344\) 831.752i 2.41789i
\(345\) 57.7394 65.3529i 0.167360 0.189429i
\(346\) 245.152 0.708533
\(347\) 386.618i 1.11417i −0.830454 0.557087i \(-0.811919\pi\)
0.830454 0.557087i \(-0.188081\pi\)
\(348\) 978.285 + 864.316i 2.81116 + 2.48367i
\(349\) −447.308 −1.28168 −0.640842 0.767673i \(-0.721415\pi\)
−0.640842 + 0.767673i \(0.721415\pi\)
\(350\) 556.801i 1.59086i
\(351\) 188.767 + 129.164i 0.537798 + 0.367989i
\(352\) 696.808 1.97957
\(353\) 468.936i 1.32843i 0.747541 + 0.664216i \(0.231234\pi\)
−0.747541 + 0.664216i \(0.768766\pi\)
\(354\) −55.2450 + 62.5296i −0.156059 + 0.176637i
\(355\) 267.666 0.753990
\(356\) 812.504i 2.28231i
\(357\) 403.724 + 356.691i 1.13088 + 0.999134i
\(358\) −762.710 −2.13047
\(359\) 59.9848i 0.167088i −0.996504 0.0835442i \(-0.973376\pi\)
0.996504 0.0835442i \(-0.0266240\pi\)
\(360\) 57.7346 + 464.930i 0.160374 + 1.29147i
\(361\) −94.8786 −0.262822
\(362\) 332.447i 0.918361i
\(363\) 477.532 540.499i 1.31551 1.48898i
\(364\) −694.562 −1.90814
\(365\) 348.214i 0.954012i
\(366\) 268.587 + 237.297i 0.733844 + 0.648352i
\(367\) 42.3632 0.115431 0.0577155 0.998333i \(-0.481618\pi\)
0.0577155 + 0.998333i \(0.481618\pi\)
\(368\) 315.887i 0.858390i
\(369\) 491.418 61.0238i 1.33176 0.165376i
\(370\) −141.350 −0.382026
\(371\) 667.910i 1.80030i
\(372\) 73.3991 83.0774i 0.197309 0.223326i
\(373\) −210.832 −0.565232 −0.282616 0.959233i \(-0.591202\pi\)
−0.282616 + 0.959233i \(0.591202\pi\)
\(374\) 1373.64i 3.67284i
\(375\) −266.159 235.152i −0.709758 0.627072i
\(376\) −45.6560 −0.121425
\(377\) 404.587i 1.07317i
\(378\) 496.814 726.070i 1.31432 1.92082i
\(379\) 142.841 0.376890 0.188445 0.982084i \(-0.439655\pi\)
0.188445 + 0.982084i \(0.439655\pi\)
\(380\) 418.070i 1.10018i
\(381\) −377.060 + 426.780i −0.989660 + 1.12016i
\(382\) −216.856 −0.567685
\(383\) 215.564i 0.562830i 0.959586 + 0.281415i \(0.0908038\pi\)
−0.959586 + 0.281415i \(0.909196\pi\)
\(384\) 244.540 + 216.051i 0.636822 + 0.562633i
\(385\) −481.205 −1.24988
\(386\) 107.853i 0.279413i
\(387\) −49.8465 401.408i −0.128802 1.03723i
\(388\) −155.605 −0.401043
\(389\) 377.794i 0.971193i 0.874183 + 0.485596i \(0.161398\pi\)
−0.874183 + 0.485596i \(0.838602\pi\)
\(390\) −171.381 + 193.979i −0.439439 + 0.497383i
\(391\) 206.223 0.527425
\(392\) 591.840i 1.50980i
\(393\) 283.843 + 250.776i 0.722246 + 0.638106i
\(394\) −649.498 −1.64847
\(395\) 389.523i 0.986135i
\(396\) −1546.99 + 192.104i −3.90654 + 0.485110i
\(397\) −420.666 −1.05961 −0.529806 0.848119i \(-0.677735\pi\)
−0.529806 + 0.848119i \(0.677735\pi\)
\(398\) 228.845i 0.574987i
\(399\) −291.593 + 330.042i −0.730810 + 0.827174i
\(400\) 522.327 1.30582
\(401\) 762.529i 1.90157i −0.309854 0.950784i \(-0.600280\pi\)
0.309854 0.950784i \(-0.399720\pi\)
\(402\) −421.978 372.818i −1.04970 0.927408i
\(403\) 34.3581 0.0852559
\(404\) 611.818i 1.51440i
\(405\) −55.7261 220.918i −0.137595 0.545477i
\(406\) 1556.19 3.83299
\(407\) 263.837i 0.648248i
\(408\) −733.551 + 830.277i −1.79792 + 2.03499i
\(409\) 389.355 0.951968 0.475984 0.879454i \(-0.342092\pi\)
0.475984 + 0.879454i \(0.342092\pi\)
\(410\) 560.391i 1.36681i
\(411\) −168.049 148.472i −0.408879 0.361246i
\(412\) −1522.57 −3.69555
\(413\) 69.1217i 0.167365i
\(414\) −41.5020 334.211i −0.100246 0.807272i
\(415\) −77.1635 −0.185936
\(416\) 310.504i 0.746405i
\(417\) 160.610 181.788i 0.385156 0.435942i
\(418\) 1122.95 2.68647
\(419\) 170.383i 0.406641i −0.979112 0.203320i \(-0.934827\pi\)
0.979112 0.203320i \(-0.0651733\pi\)
\(420\) 518.488 + 458.085i 1.23449 + 1.09068i
\(421\) −211.619 −0.502657 −0.251329 0.967902i \(-0.580867\pi\)
−0.251329 + 0.967902i \(0.580867\pi\)
\(422\) 363.339i 0.860994i
\(423\) 22.0338 2.73614i 0.0520894 0.00646842i
\(424\) 1373.59 3.23960
\(425\) 340.995i 0.802341i
\(426\) 684.415 774.662i 1.60661 1.81846i
\(427\) 296.903 0.695322
\(428\) 381.945i 0.892394i
\(429\) −362.073 319.892i −0.843994 0.745670i
\(430\) 457.748 1.06453
\(431\) 319.026i 0.740199i 0.928992 + 0.370100i \(0.120676\pi\)
−0.928992 + 0.370100i \(0.879324\pi\)
\(432\) 681.116 + 466.055i 1.57666 + 1.07883i
\(433\) −86.0871 −0.198815 −0.0994077 0.995047i \(-0.531695\pi\)
−0.0994077 + 0.995047i \(0.531695\pi\)
\(434\) 132.154i 0.304503i
\(435\) 266.837 302.022i 0.613419 0.694304i
\(436\) 132.740 0.304450
\(437\) 168.586i 0.385781i
\(438\) −1007.78 890.374i −2.30086 2.03282i
\(439\) −334.000 −0.760821 −0.380410 0.924818i \(-0.624217\pi\)
−0.380410 + 0.924818i \(0.624217\pi\)
\(440\) 989.621i 2.24914i
\(441\) −35.4687 285.626i −0.0804279 0.647677i
\(442\) −612.108 −1.38486
\(443\) 503.833i 1.13732i 0.822573 + 0.568660i \(0.192538\pi\)
−0.822573 + 0.568660i \(0.807462\pi\)
\(444\) −251.161 + 284.279i −0.565677 + 0.640267i
\(445\) 250.841 0.563688
\(446\) 751.515i 1.68501i
\(447\) 395.148 + 349.114i 0.884000 + 0.781015i
\(448\) −94.0503 −0.209934
\(449\) 532.639i 1.18628i −0.805100 0.593139i \(-0.797888\pi\)
0.805100 0.593139i \(-0.202112\pi\)
\(450\) −552.626 + 68.6245i −1.22806 + 0.152499i
\(451\) −1046.00 −2.31929
\(452\) 7.16821i 0.0158589i
\(453\) −389.095 + 440.401i −0.858930 + 0.972188i
\(454\) 1469.13 3.23597
\(455\) 214.430i 0.471274i
\(456\) −678.747 599.674i −1.48848 1.31508i
\(457\) −52.1223 −0.114053 −0.0570266 0.998373i \(-0.518162\pi\)
−0.0570266 + 0.998373i \(0.518162\pi\)
\(458\) 647.007i 1.41268i
\(459\) 304.258 444.658i 0.662871 0.968753i
\(460\) 264.845 0.575749
\(461\) 830.105i 1.80066i −0.435207 0.900330i \(-0.643325\pi\)
0.435207 0.900330i \(-0.356675\pi\)
\(462\) −1230.43 + 1392.67i −2.66326 + 3.01444i
\(463\) 185.779 0.401250 0.200625 0.979668i \(-0.435703\pi\)
0.200625 + 0.979668i \(0.435703\pi\)
\(464\) 1459.84i 3.14621i
\(465\) −25.6482 22.6602i −0.0551574 0.0487317i
\(466\) 320.674 0.688142
\(467\) 834.915i 1.78783i 0.448239 + 0.893914i \(0.352051\pi\)
−0.448239 + 0.893914i \(0.647949\pi\)
\(468\) 85.6032 + 689.354i 0.182913 + 1.47298i
\(469\) −466.464 −0.994594
\(470\) 25.1264i 0.0534604i
\(471\) 273.748 309.844i 0.581205 0.657843i
\(472\) −142.152 −0.301170
\(473\) 854.412i 1.80637i
\(474\) −1127.33 996.000i −2.37834 2.10127i
\(475\) 278.762 0.586867
\(476\) 1636.10i 3.43719i
\(477\) −662.902 + 82.3185i −1.38973 + 0.172575i
\(478\) −741.771 −1.55182
\(479\) 3.76008i 0.00784985i 0.999992 + 0.00392492i \(0.00124935\pi\)
−0.999992 + 0.00392492i \(0.998751\pi\)
\(480\) −204.787 + 231.790i −0.426640 + 0.482896i
\(481\) −117.568 −0.244425
\(482\) 925.741i 1.92063i
\(483\) −209.080 184.722i −0.432878 0.382448i
\(484\) 2190.39 4.52560
\(485\) 48.0392i 0.0990499i
\(486\) −781.856 403.602i −1.60876 0.830457i
\(487\) 532.953 1.09436 0.547180 0.837015i \(-0.315701\pi\)
0.547180 + 0.837015i \(0.315701\pi\)
\(488\) 610.594i 1.25122i
\(489\) −527.692 + 597.273i −1.07912 + 1.22142i
\(490\) 325.715 0.664723
\(491\) 457.567i 0.931907i 0.884809 + 0.465954i \(0.154289\pi\)
−0.884809 + 0.465954i \(0.845711\pi\)
\(492\) 1127.04 + 995.745i 2.29074 + 2.02387i
\(493\) 953.040 1.93314
\(494\) 500.395i 1.01295i
\(495\) 59.3075 + 477.596i 0.119813 + 0.964841i
\(496\) 123.972 0.249944
\(497\) 856.331i 1.72300i
\(498\) −197.305 + 223.321i −0.396195 + 0.448437i
\(499\) 838.159 1.67968 0.839839 0.542836i \(-0.182649\pi\)
0.839839 + 0.542836i \(0.182649\pi\)
\(500\) 1078.62i 2.15724i
\(501\) 258.342 + 228.246i 0.515653 + 0.455580i
\(502\) −755.853 −1.50568
\(503\) 85.9693i 0.170913i 0.996342 + 0.0854566i \(0.0272349\pi\)
−0.996342 + 0.0854566i \(0.972765\pi\)
\(504\) 1487.43 184.707i 2.95124 0.366482i
\(505\) −188.884 −0.374028
\(506\) 711.379i 1.40589i
\(507\) 193.140 218.608i 0.380948 0.431179i
\(508\) −1729.54 −3.40460
\(509\) 788.265i 1.54865i 0.632786 + 0.774327i \(0.281911\pi\)
−0.632786 + 0.774327i \(0.718089\pi\)
\(510\) 456.936 + 403.704i 0.895953 + 0.791576i
\(511\) −1114.02 −2.18008
\(512\) 1142.38i 2.23121i
\(513\) 363.505 + 248.729i 0.708588 + 0.484852i
\(514\) −402.922 −0.783894
\(515\) 470.056i 0.912731i
\(516\) 813.360 920.610i 1.57628 1.78413i
\(517\) −46.8998 −0.0907153
\(518\) 452.212i 0.872997i
\(519\) −152.216 134.483i −0.293286 0.259119i
\(520\) −440.984 −0.848047
\(521\) 764.944i 1.46822i −0.679029 0.734111i \(-0.737599\pi\)
0.679029 0.734111i \(-0.262401\pi\)
\(522\) −191.797 1544.52i −0.367428 2.95886i
\(523\) −901.245 −1.72322 −0.861611 0.507569i \(-0.830544\pi\)
−0.861611 + 0.507569i \(0.830544\pi\)
\(524\) 1150.28i 2.19520i
\(525\) −305.443 + 345.719i −0.581796 + 0.658512i
\(526\) −212.851 −0.404659
\(527\) 80.9337i 0.153574i
\(528\) −1306.45 1154.25i −2.47433 2.18607i
\(529\) 422.202 0.798113
\(530\) 755.943i 1.42631i
\(531\) 68.6034 8.51910i 0.129197 0.0160435i
\(532\) −1337.51 −2.51411
\(533\) 466.108i 0.874500i
\(534\) 641.394 725.968i 1.20111 1.35949i
\(535\) 117.916 0.220404
\(536\) 959.306i 1.78975i
\(537\) 473.567 + 418.398i 0.881876 + 0.779139i
\(538\) 246.486 0.458152
\(539\) 607.964i 1.12795i
\(540\) 390.747 571.057i 0.723606 1.05751i
\(541\) 660.541 1.22096 0.610482 0.792030i \(-0.290976\pi\)
0.610482 + 0.792030i \(0.290976\pi\)
\(542\) 559.852i 1.03294i
\(543\) 182.370 206.417i 0.335855 0.380141i
\(544\) −731.421 −1.34452
\(545\) 40.9804i 0.0751934i
\(546\) 620.588 + 548.290i 1.13661 + 1.00419i
\(547\) −446.351 −0.815998 −0.407999 0.912982i \(-0.633773\pi\)
−0.407999 + 0.912982i \(0.633773\pi\)
\(548\) 681.026i 1.24275i
\(549\) −36.5926 294.676i −0.0666531 0.536750i
\(550\) 1176.28 2.13870
\(551\) 779.106i 1.41399i
\(552\) 379.890 429.982i 0.688207 0.778954i
\(553\) −1246.18 −2.25349
\(554\) 1746.28i 3.15213i
\(555\) 87.7642 + 77.5399i 0.158134 + 0.139711i
\(556\) 736.702 1.32500
\(557\) 426.163i 0.765104i −0.923934 0.382552i \(-0.875045\pi\)
0.923934 0.382552i \(-0.124955\pi\)
\(558\) −131.163 + 16.2877i −0.235060 + 0.0291895i
\(559\) 380.734 0.681099
\(560\) 773.713i 1.38163i
\(561\) −753.535 + 852.896i −1.34320 + 1.52031i
\(562\) −28.6129 −0.0509126
\(563\) 128.538i 0.228309i 0.993463 + 0.114155i \(0.0364160\pi\)
−0.993463 + 0.114155i \(0.963584\pi\)
\(564\) 50.5335 + 44.6464i 0.0895984 + 0.0791603i
\(565\) −2.21301 −0.00391684
\(566\) 1238.70i 2.18852i
\(567\) −706.771 + 178.281i −1.24651 + 0.314429i
\(568\) 1761.08 3.10050
\(569\) 276.291i 0.485572i −0.970080 0.242786i \(-0.921939\pi\)
0.970080 0.242786i \(-0.0780613\pi\)
\(570\) −330.026 + 373.543i −0.578993 + 0.655339i
\(571\) −148.282 −0.259689 −0.129844 0.991534i \(-0.541448\pi\)
−0.129844 + 0.991534i \(0.541448\pi\)
\(572\) 1467.31i 2.56523i
\(573\) 134.646 + 118.960i 0.234984 + 0.207609i
\(574\) 1792.83 3.12340
\(575\) 176.594i 0.307120i
\(576\) 11.5915 + 93.3450i 0.0201241 + 0.162057i
\(577\) −186.092 −0.322516 −0.161258 0.986912i \(-0.551555\pi\)
−0.161258 + 0.986912i \(0.551555\pi\)
\(578\) 395.431i 0.684137i
\(579\) 59.1649 66.9664i 0.102185 0.115659i
\(580\) 1223.95 2.11027
\(581\) 246.865i 0.424897i
\(582\) 139.032 + 122.835i 0.238886 + 0.211056i
\(583\) 1411.01 2.42026
\(584\) 2291.04i 3.92301i
\(585\) 212.822 26.4280i 0.363798 0.0451760i
\(586\) 213.256 0.363918
\(587\) 985.876i 1.67952i −0.542960 0.839758i \(-0.682697\pi\)
0.542960 0.839758i \(-0.317303\pi\)
\(588\) 578.753 655.068i 0.984275 1.11406i
\(589\) 66.1629 0.112331
\(590\) 78.2322i 0.132597i
\(591\) 403.274 + 356.293i 0.682359 + 0.602865i
\(592\) −424.214 −0.716578
\(593\) 366.566i 0.618155i −0.951037 0.309078i \(-0.899980\pi\)
0.951037 0.309078i \(-0.100020\pi\)
\(594\) 1533.87 + 1049.56i 2.58228 + 1.76693i
\(595\) 505.108 0.848922
\(596\) 1601.35i 2.68683i
\(597\) −125.537 + 142.090i −0.210279 + 0.238007i
\(598\) 316.997 0.530096
\(599\) 544.283i 0.908653i 0.890835 + 0.454327i \(0.150120\pi\)
−0.890835 + 0.454327i \(0.849880\pi\)
\(600\) −710.986 628.158i −1.18498 1.04693i
\(601\) −648.078 −1.07833 −0.539166 0.842199i \(-0.681261\pi\)
−0.539166 + 0.842199i \(0.681261\pi\)
\(602\) 1464.45i 2.43264i
\(603\) 57.4907 + 462.966i 0.0953411 + 0.767772i
\(604\) −1784.74 −2.95487
\(605\) 676.230i 1.11774i
\(606\) −482.972 + 546.656i −0.796983 + 0.902073i
\(607\) −288.308 −0.474972 −0.237486 0.971391i \(-0.576323\pi\)
−0.237486 + 0.971391i \(0.576323\pi\)
\(608\) 597.933i 0.983443i
\(609\) −966.243 853.677i −1.58661 1.40177i
\(610\) 336.035 0.550877
\(611\) 20.8990i 0.0342046i
\(612\) 1623.83 201.646i 2.65332 0.329487i
\(613\) 259.679 0.423620 0.211810 0.977311i \(-0.432064\pi\)
0.211810 + 0.977311i \(0.432064\pi\)
\(614\) 2162.23i 3.52156i
\(615\) 307.412 347.948i 0.499858 0.565769i
\(616\) −3166.04 −5.13967
\(617\) 622.301i 1.00859i −0.863531 0.504296i \(-0.831752\pi\)
0.863531 0.504296i \(-0.168248\pi\)
\(618\) 1360.41 + 1201.92i 2.20130 + 1.94485i
\(619\) 605.489 0.978172 0.489086 0.872236i \(-0.337330\pi\)
0.489086 + 0.872236i \(0.337330\pi\)
\(620\) 103.940i 0.167645i
\(621\) −157.569 + 230.279i −0.253734 + 0.370819i
\(622\) −107.495 −0.172822
\(623\) 802.503i 1.28813i
\(624\) −514.343 + 582.165i −0.824268 + 0.932956i
\(625\) 94.2041 0.150727
\(626\) 605.605i 0.967421i
\(627\) −697.239 616.012i −1.11202 0.982475i
\(628\) 1255.65 1.99945
\(629\) 276.943i 0.440291i
\(630\) −101.652 818.593i −0.161352 1.29935i
\(631\) −941.970 −1.49282 −0.746411 0.665486i \(-0.768224\pi\)
−0.746411 + 0.665486i \(0.768224\pi\)
\(632\) 2562.83i 4.05511i
\(633\) 199.316 225.598i 0.314875 0.356395i
\(634\) −1430.73 −2.25668
\(635\) 533.954i 0.840872i
\(636\) −1520.33 1343.22i −2.39046 2.11197i
\(637\) 270.915 0.425298
\(638\) 3287.57i 5.15294i
\(639\) −849.909 + 105.541i −1.33006 + 0.165166i
\(640\) 305.949 0.478046
\(641\) 401.011i 0.625602i −0.949819 0.312801i \(-0.898733\pi\)
0.949819 0.312801i \(-0.101267\pi\)
\(642\) 301.509 341.265i 0.469640 0.531566i
\(643\) 851.435 1.32416 0.662080 0.749433i \(-0.269674\pi\)
0.662080 + 0.749433i \(0.269674\pi\)
\(644\) 847.303i 1.31569i
\(645\) −284.216 251.106i −0.440646 0.389311i
\(646\) −1178.73 −1.82465
\(647\) 221.121i 0.341764i −0.985292 0.170882i \(-0.945338\pi\)
0.985292 0.170882i \(-0.0546617\pi\)
\(648\) −366.644 1453.51i −0.565808 2.24307i
\(649\) −146.025 −0.225000
\(650\) 524.163i 0.806405i
\(651\) −72.4956 + 82.0548i −0.111360 + 0.126044i
\(652\) −2420.47 −3.71237
\(653\) 512.798i 0.785296i −0.919689 0.392648i \(-0.871559\pi\)
0.919689 0.392648i \(-0.128441\pi\)
\(654\) −118.603 104.786i −0.181350 0.160223i
\(655\) 355.122 0.542172
\(656\) 1681.83i 2.56376i
\(657\) 137.301 + 1105.67i 0.208981 + 1.68291i
\(658\) 80.3855 0.122166
\(659\) 241.786i 0.366898i 0.983029 + 0.183449i \(0.0587262\pi\)
−0.983029 + 0.183449i \(0.941274\pi\)
\(660\) −967.738 + 1095.34i −1.46627 + 1.65961i
\(661\) −1100.95 −1.66558 −0.832790 0.553590i \(-0.813258\pi\)
−0.832790 + 0.553590i \(0.813258\pi\)
\(662\) 942.070i 1.42307i
\(663\) 380.059 + 335.783i 0.573241 + 0.506459i
\(664\) −507.689 −0.764592
\(665\) 412.924i 0.620938i
\(666\) 448.821 55.7342i 0.673906 0.0836849i
\(667\) −493.559 −0.739968
\(668\) 1046.94i 1.56728i
\(669\) 412.257 466.617i 0.616228 0.697484i
\(670\) −527.946 −0.787979
\(671\) 627.228i 0.934767i
\(672\) 741.554 + 655.164i 1.10350 + 0.974947i
\(673\) 820.295 1.21886 0.609431 0.792839i \(-0.291398\pi\)
0.609431 + 0.792839i \(0.291398\pi\)
\(674\) 355.037i 0.526762i
\(675\) 380.771 + 260.543i 0.564106 + 0.385990i
\(676\) 885.915 1.31053
\(677\) 863.866i 1.27602i 0.770028 + 0.638010i \(0.220242\pi\)
−0.770028 + 0.638010i \(0.779758\pi\)
\(678\) −5.65861 + 6.40475i −0.00834603 + 0.00944654i
\(679\) 153.689 0.226346
\(680\) 1038.78i 1.52762i
\(681\) −912.186 805.918i −1.33948 1.18343i
\(682\) 279.186 0.409363
\(683\) 1009.66i 1.47828i −0.673554 0.739138i \(-0.735233\pi\)
0.673554 0.739138i \(-0.264767\pi\)
\(684\) 164.845 + 1327.48i 0.241001 + 1.94076i
\(685\) −210.251 −0.306935
\(686\) 554.585i 0.808434i
\(687\) 354.927 401.727i 0.516633 0.584756i
\(688\) 1373.78 1.99677
\(689\) 628.759i 0.912568i
\(690\) −236.637 209.069i −0.342953 0.302999i
\(691\) 584.388 0.845714 0.422857 0.906196i \(-0.361027\pi\)
0.422857 + 0.906196i \(0.361027\pi\)
\(692\) 616.858i 0.891414i
\(693\) 1527.95 189.739i 2.20483 0.273794i
\(694\) −1399.91 −2.01716
\(695\) 227.439i 0.327251i
\(696\) 1755.63 1987.12i 2.52245 2.85506i
\(697\) 1097.96 1.57527
\(698\) 1619.66i 2.32043i
\(699\) −199.107 175.911i −0.284846 0.251662i
\(700\) −1401.04 −2.00148
\(701\) 813.924i 1.16109i 0.814228 + 0.580545i \(0.197160\pi\)
−0.814228 + 0.580545i \(0.802840\pi\)
\(702\) 467.693 683.509i 0.666229 0.973660i
\(703\) −226.399 −0.322048
\(704\) 198.688i 0.282227i
\(705\) 13.7835 15.6010i 0.0195511 0.0221291i
\(706\) 1697.98 2.40507
\(707\) 604.287i 0.854720i
\(708\) 157.338 + 139.009i 0.222229 + 0.196340i
\(709\) 275.826 0.389035 0.194518 0.980899i \(-0.437686\pi\)
0.194518 + 0.980899i \(0.437686\pi\)
\(710\) 969.198i 1.36507i
\(711\) 153.589 + 1236.84i 0.216018 + 1.73957i
\(712\) 1650.38 2.31796
\(713\) 41.9138i 0.0587851i
\(714\) 1291.55 1461.85i 1.80889 2.04741i
\(715\) −452.998 −0.633564
\(716\) 1919.15i 2.68037i
\(717\) 460.567 + 406.912i 0.642353 + 0.567520i
\(718\) −217.200 −0.302507
\(719\) 79.3016i 0.110294i 0.998478 + 0.0551471i \(0.0175628\pi\)
−0.998478 + 0.0551471i \(0.982437\pi\)
\(720\) 767.910 95.3583i 1.06654 0.132442i
\(721\) 1503.83 2.08575
\(722\) 343.547i 0.475827i
\(723\) −507.832 + 574.794i −0.702395 + 0.795013i
\(724\) 836.510 1.15540
\(725\) 816.112i 1.12567i
\(726\) −1957.10 1729.10i −2.69573 2.38168i
\(727\) −432.390 −0.594759 −0.297380 0.954759i \(-0.596113\pi\)
−0.297380 + 0.954759i \(0.596113\pi\)
\(728\) 1410.82i 1.93794i
\(729\) 264.052 + 679.498i 0.362212 + 0.932096i
\(730\) −1260.85 −1.72720
\(731\) 896.854i 1.22689i
\(732\) 597.092 675.824i 0.815700 0.923257i
\(733\) −700.451 −0.955595 −0.477797 0.878470i \(-0.658565\pi\)
−0.477797 + 0.878470i \(0.658565\pi\)
\(734\) 153.393i 0.208983i
\(735\) −202.237 178.676i −0.275152 0.243097i
\(736\) 378.787 0.514657
\(737\) 985.440i 1.33710i
\(738\) −220.962 1779.38i −0.299407 2.41109i
\(739\) 906.590 1.22678 0.613389 0.789781i \(-0.289806\pi\)
0.613389 + 0.789781i \(0.289806\pi\)
\(740\) 355.667i 0.480632i
\(741\) −274.501 + 310.696i −0.370446 + 0.419293i
\(742\) −2418.45 −3.25936
\(743\) 350.702i 0.472008i −0.971752 0.236004i \(-0.924162\pi\)
0.971752 0.236004i \(-0.0758378\pi\)
\(744\) −168.750 149.091i −0.226814 0.200390i
\(745\) 494.379 0.663595
\(746\) 763.404i 1.02333i
\(747\) 245.014 30.4256i 0.327997 0.0407303i
\(748\) −3456.39 −4.62084
\(749\) 377.243i 0.503663i
\(750\) −851.466 + 963.740i −1.13529 + 1.28499i
\(751\) −688.234 −0.916423 −0.458212 0.888843i \(-0.651510\pi\)
−0.458212 + 0.888843i \(0.651510\pi\)
\(752\) 75.4085i 0.100277i
\(753\) 469.310 + 414.637i 0.623254 + 0.550646i
\(754\) 1464.97 1.94294
\(755\) 550.996i 0.729796i
\(756\) −1826.95 1250.10i −2.41660 1.65357i
\(757\) 1336.84 1.76597 0.882983 0.469406i \(-0.155532\pi\)
0.882983 + 0.469406i \(0.155532\pi\)
\(758\) 517.217i 0.682344i
\(759\) 390.240 441.696i 0.514150 0.581945i
\(760\) −849.196 −1.11736
\(761\) 882.165i 1.15922i −0.814895 0.579609i \(-0.803205\pi\)
0.814895 0.579609i \(-0.196795\pi\)
\(762\) 1545.33 + 1365.30i 2.02800 + 1.79174i
\(763\) −131.106 −0.171830
\(764\) 545.657i 0.714211i
\(765\) −62.2535 501.320i −0.0813771 0.655321i
\(766\) 780.539 1.01898
\(767\) 65.0700i 0.0848371i
\(768\) 865.342 979.446i 1.12675 1.27532i
\(769\) −142.803 −0.185700 −0.0928500 0.995680i \(-0.529598\pi\)
−0.0928500 + 0.995680i \(0.529598\pi\)
\(770\) 1742.40i 2.26286i
\(771\) 250.175 + 221.030i 0.324481 + 0.286679i
\(772\) 271.383 0.351533
\(773\) 43.6724i 0.0564973i −0.999601 0.0282486i \(-0.991007\pi\)
0.999601 0.0282486i \(-0.00899302\pi\)
\(774\) −1453.47 + 180.490i −1.87786 + 0.233191i
\(775\) 69.3055 0.0894264
\(776\) 316.069i 0.407305i
\(777\) 248.069 280.779i 0.319265 0.361363i
\(778\) 1367.96 1.75830
\(779\) 897.577i 1.15222i
\(780\) 488.095 + 431.233i 0.625763 + 0.552863i
\(781\) 1809.06 2.31634
\(782\) 746.716i 0.954880i
\(783\) −728.188 + 1064.21i −0.929998 + 1.35915i
\(784\) 977.524 1.24684
\(785\) 387.653i 0.493825i
\(786\) 908.038 1027.77i 1.15526 1.30760i