Properties

Label 105.4.g.b.104.6
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 104.6
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.5

$q$-expansion

\(f(q)\) \(=\) \(q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +O(q^{10})\) \(q-4.45958 q^{2} +(-5.00290 + 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 + 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(12.5955 - 13.5777i) q^{7} -17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +(3.98218 - 49.7003i) q^{10} +30.2834i q^{11} +(-59.4737 + 16.6898i) q^{12} +18.9551 q^{13} +(-56.1708 + 60.5506i) q^{14} +(-11.1790 - 57.0090i) q^{15} -17.7818 q^{16} +4.59392i q^{17} +(-102.829 + 62.6458i) q^{18} +119.595i q^{19} +(-10.6153 + 132.486i) q^{20} +(-43.9520 + 85.6109i) q^{21} -135.051i q^{22} -134.577 q^{23} +(86.7411 - 24.3417i) q^{24} +(-123.405 - 19.9032i) q^{25} -84.5318 q^{26} +(-95.6347 + 102.650i) q^{27} +(149.734 - 161.409i) q^{28} -203.146i q^{29} +(49.8536 + 254.236i) q^{30} +61.4983i q^{31} +218.005 q^{32} +(-42.5159 - 151.505i) q^{33} -20.4870i q^{34} +(140.071 + 152.497i) q^{35} +(274.109 - 166.994i) q^{36} +337.592i q^{37} -533.342i q^{38} +(-94.8304 + 26.6117i) q^{39} +(15.4821 - 193.227i) q^{40} -135.603 q^{41} +(196.007 - 381.789i) q^{42} -270.630i q^{43} +360.004i q^{44} +(135.964 + 269.516i) q^{45} +600.156 q^{46} +273.318i q^{47} +(88.9606 - 24.9645i) q^{48} +(-25.7052 - 342.035i) q^{49} +(550.336 + 88.7598i) q^{50} +(-6.44957 - 22.9829i) q^{51} +225.335 q^{52} -222.861 q^{53} +(426.491 - 457.775i) q^{54} +(-337.497 - 27.0415i) q^{55} +(-218.384 + 235.412i) q^{56} +(-167.903 - 598.319i) q^{57} +905.947i q^{58} -735.026 q^{59} +(-132.894 - 677.715i) q^{60} +312.240i q^{61} -274.257i q^{62} +(99.6952 - 490.008i) q^{63} -829.955 q^{64} +(-16.9260 + 211.247i) q^{65} +(189.603 + 675.646i) q^{66} +751.739i q^{67} +54.6119i q^{68} +(673.274 - 188.937i) q^{69} +(-624.656 - 680.071i) q^{70} +640.823i q^{71} +(-399.783 + 243.558i) q^{72} -469.117 q^{73} -1505.52i q^{74} +(645.327 - 73.6793i) q^{75} +1421.72i q^{76} +(411.177 + 381.435i) q^{77} +(422.904 - 118.677i) q^{78} +126.493 q^{79} +(15.8783 - 198.172i) q^{80} +(334.337 - 647.812i) q^{81} +604.734 q^{82} +299.265i q^{83} +(-522.495 + 1017.73i) q^{84} +(-51.1976 - 4.10215i) q^{85} +1206.90i q^{86} +(285.204 + 1016.32i) q^{87} -525.058i q^{88} -425.893 q^{89} +(-606.343 - 1201.93i) q^{90} +(238.750 - 257.366i) q^{91} -1599.83 q^{92} +(-86.3396 - 307.670i) q^{93} -1218.88i q^{94} +(-1332.84 - 106.792i) q^{95} +(-1090.66 + 306.064i) q^{96} -561.656 q^{97} +(114.635 + 1525.33i) q^{98} +(425.405 + 698.272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 184q^{4} + 4q^{9} + O(q^{10}) \) \( 40q + 184q^{4} + 4q^{9} - 188q^{15} + 184q^{16} + 148q^{21} + 712q^{25} - 336q^{30} - 1520q^{36} + 644q^{39} - 1488q^{46} - 1496q^{49} - 220q^{51} + 1984q^{60} + 40q^{64} - 3000q^{70} - 1192q^{79} + 4636q^{81} - 2192q^{84} + 4808q^{85} - 4408q^{91} + 5276q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.45958 −1.57670 −0.788350 0.615227i \(-0.789064\pi\)
−0.788350 + 0.615227i \(0.789064\pi\)
\(3\) −5.00290 + 1.40393i −0.962808 + 0.270187i
\(4\) 11.8879 1.48598
\(5\) −0.892950 + 11.1446i −0.0798679 + 0.996805i
\(6\) 22.3108 6.26096i 1.51806 0.426004i
\(7\) 12.5955 13.5777i 0.680095 0.733124i
\(8\) −17.3382 −0.766247
\(9\) 23.0579 14.0475i 0.853998 0.520277i
\(10\) 3.98218 49.7003i 0.125928 1.57166i
\(11\) 30.2834i 0.830071i 0.909805 + 0.415035i \(0.136231\pi\)
−0.909805 + 0.415035i \(0.863769\pi\)
\(12\) −59.4737 + 16.6898i −1.43071 + 0.401493i
\(13\) 18.9551 0.404400 0.202200 0.979344i \(-0.435191\pi\)
0.202200 + 0.979344i \(0.435191\pi\)
\(14\) −56.1708 + 60.5506i −1.07230 + 1.15592i
\(15\) −11.1790 57.0090i −0.192427 0.981311i
\(16\) −17.7818 −0.277841
\(17\) 4.59392i 0.0655406i 0.999463 + 0.0327703i \(0.0104330\pi\)
−0.999463 + 0.0327703i \(0.989567\pi\)
\(18\) −102.829 + 62.6458i −1.34650 + 0.820320i
\(19\) 119.595i 1.44405i 0.691869 + 0.722023i \(0.256788\pi\)
−0.691869 + 0.722023i \(0.743212\pi\)
\(20\) −10.6153 + 132.486i −0.118682 + 1.48123i
\(21\) −43.9520 + 85.6109i −0.456720 + 0.889611i
\(22\) 135.051i 1.30877i
\(23\) −134.577 −1.22005 −0.610026 0.792381i \(-0.708841\pi\)
−0.610026 + 0.792381i \(0.708841\pi\)
\(24\) 86.7411 24.3417i 0.737748 0.207030i
\(25\) −123.405 19.9032i −0.987242 0.159225i
\(26\) −84.5318 −0.637617
\(27\) −95.6347 + 102.650i −0.681663 + 0.731666i
\(28\) 149.734 161.409i 1.01061 1.08941i
\(29\) 203.146i 1.30080i −0.759590 0.650402i \(-0.774600\pi\)
0.759590 0.650402i \(-0.225400\pi\)
\(30\) 49.8536 + 254.236i 0.303399 + 1.54723i
\(31\) 61.4983i 0.356304i 0.984003 + 0.178152i \(0.0570119\pi\)
−0.984003 + 0.178152i \(0.942988\pi\)
\(32\) 218.005 1.20432
\(33\) −42.5159 151.505i −0.224275 0.799198i
\(34\) 20.4870i 0.103338i
\(35\) 140.071 + 152.497i 0.676465 + 0.736475i
\(36\) 274.109 166.994i 1.26902 0.773122i
\(37\) 337.592i 1.49999i 0.661441 + 0.749997i \(0.269945\pi\)
−0.661441 + 0.749997i \(0.730055\pi\)
\(38\) 533.342i 2.27683i
\(39\) −94.8304 + 26.6117i −0.389359 + 0.109264i
\(40\) 15.4821 193.227i 0.0611985 0.763799i
\(41\) −135.603 −0.516529 −0.258264 0.966074i \(-0.583151\pi\)
−0.258264 + 0.966074i \(0.583151\pi\)
\(42\) 196.007 381.789i 0.720110 1.40265i
\(43\) 270.630i 0.959785i −0.877327 0.479893i \(-0.840676\pi\)
0.877327 0.479893i \(-0.159324\pi\)
\(44\) 360.004i 1.23347i
\(45\) 135.964 + 269.516i 0.450408 + 0.892823i
\(46\) 600.156 1.92366
\(47\) 273.318i 0.848245i 0.905605 + 0.424123i \(0.139417\pi\)
−0.905605 + 0.424123i \(0.860583\pi\)
\(48\) 88.9606 24.9645i 0.267507 0.0750691i
\(49\) −25.7052 342.035i −0.0749424 0.997188i
\(50\) 550.336 + 88.7598i 1.55658 + 0.251051i
\(51\) −6.44957 22.9829i −0.0177082 0.0631030i
\(52\) 225.335 0.600931
\(53\) −222.861 −0.577591 −0.288796 0.957391i \(-0.593255\pi\)
−0.288796 + 0.957391i \(0.593255\pi\)
\(54\) 426.491 457.775i 1.07478 1.15362i
\(55\) −337.497 27.0415i −0.827419 0.0662960i
\(56\) −218.384 + 235.412i −0.521120 + 0.561754i
\(57\) −167.903 598.319i −0.390163 1.39034i
\(58\) 905.947i 2.05098i
\(59\) −735.026 −1.62190 −0.810951 0.585114i \(-0.801050\pi\)
−0.810951 + 0.585114i \(0.801050\pi\)
\(60\) −132.894 677.715i −0.285943 1.45821i
\(61\) 312.240i 0.655381i 0.944785 + 0.327691i \(0.106270\pi\)
−0.944785 + 0.327691i \(0.893730\pi\)
\(62\) 274.257i 0.561784i
\(63\) 99.6952 490.008i 0.199372 0.979924i
\(64\) −829.955 −1.62101
\(65\) −16.9260 + 211.247i −0.0322986 + 0.403108i
\(66\) 189.603 + 675.646i 0.353614 + 1.26010i
\(67\) 751.739i 1.37074i 0.728195 + 0.685370i \(0.240359\pi\)
−0.728195 + 0.685370i \(0.759641\pi\)
\(68\) 54.6119i 0.0973921i
\(69\) 673.274 188.937i 1.17468 0.329643i
\(70\) −624.656 680.071i −1.06658 1.16120i
\(71\) 640.823i 1.07115i 0.844487 + 0.535576i \(0.179905\pi\)
−0.844487 + 0.535576i \(0.820095\pi\)
\(72\) −399.783 + 243.558i −0.654373 + 0.398660i
\(73\) −469.117 −0.752137 −0.376069 0.926592i \(-0.622724\pi\)
−0.376069 + 0.926592i \(0.622724\pi\)
\(74\) 1505.52i 2.36504i
\(75\) 645.327 73.6793i 0.993545 0.113437i
\(76\) 1421.72i 2.14583i
\(77\) 411.177 + 381.435i 0.608545 + 0.564527i
\(78\) 422.904 118.677i 0.613903 0.172276i
\(79\) 126.493 0.180147 0.0900733 0.995935i \(-0.471290\pi\)
0.0900733 + 0.995935i \(0.471290\pi\)
\(80\) 15.8783 198.172i 0.0221906 0.276953i
\(81\) 334.337 647.812i 0.458624 0.888630i
\(82\) 604.734 0.814411
\(83\) 299.265i 0.395766i 0.980226 + 0.197883i \(0.0634066\pi\)
−0.980226 + 0.197883i \(0.936593\pi\)
\(84\) −522.495 + 1017.73i −0.678677 + 1.32194i
\(85\) −51.1976 4.10215i −0.0653312 0.00523459i
\(86\) 1206.90i 1.51329i
\(87\) 285.204 + 1016.32i 0.351461 + 1.25242i
\(88\) 525.058i 0.636039i
\(89\) −425.893 −0.507242 −0.253621 0.967304i \(-0.581622\pi\)
−0.253621 + 0.967304i \(0.581622\pi\)
\(90\) −606.343 1201.93i −0.710158 1.40771i
\(91\) 238.750 257.366i 0.275030 0.296475i
\(92\) −1599.83 −1.81297
\(93\) −86.3396 307.670i −0.0962688 0.343052i
\(94\) 1218.88i 1.33743i
\(95\) −1332.84 106.792i −1.43943 0.115333i
\(96\) −1090.66 + 306.064i −1.15953 + 0.325391i
\(97\) −561.656 −0.587913 −0.293957 0.955819i \(-0.594972\pi\)
−0.293957 + 0.955819i \(0.594972\pi\)
\(98\) 114.635 + 1525.33i 0.118162 + 1.57227i
\(99\) 425.405 + 698.272i 0.431867 + 0.708878i
\(100\) −1467.02 236.606i −1.46702 0.236606i
\(101\) 1733.15 1.70747 0.853736 0.520706i \(-0.174331\pi\)
0.853736 + 0.520706i \(0.174331\pi\)
\(102\) 28.7624 + 102.494i 0.0279206 + 0.0994945i
\(103\) −1704.95 −1.63101 −0.815504 0.578751i \(-0.803540\pi\)
−0.815504 + 0.578751i \(0.803540\pi\)
\(104\) −328.647 −0.309870
\(105\) −914.854 566.275i −0.850292 0.526312i
\(106\) 993.867 0.910688
\(107\) −397.788 −0.359399 −0.179699 0.983722i \(-0.557512\pi\)
−0.179699 + 0.983722i \(0.557512\pi\)
\(108\) −1136.89 + 1220.29i −1.01294 + 1.08724i
\(109\) 1382.72 1.21505 0.607526 0.794300i \(-0.292162\pi\)
0.607526 + 0.794300i \(0.292162\pi\)
\(110\) 1505.09 + 120.594i 1.30459 + 0.104529i
\(111\) −473.957 1688.94i −0.405280 1.44421i
\(112\) −223.971 + 241.435i −0.188958 + 0.203692i
\(113\) 1029.11 0.856728 0.428364 0.903606i \(-0.359090\pi\)
0.428364 + 0.903606i \(0.359090\pi\)
\(114\) 748.777 + 2668.25i 0.615170 + 2.19215i
\(115\) 120.170 1499.81i 0.0974430 1.21615i
\(116\) 2414.97i 1.93297i
\(117\) 437.066 266.271i 0.345357 0.210400i
\(118\) 3277.91 2.55725
\(119\) 62.3747 + 57.8629i 0.0480494 + 0.0445738i
\(120\) 193.823 + 988.433i 0.147446 + 0.751926i
\(121\) 413.918 0.310983
\(122\) 1392.46i 1.03334i
\(123\) 678.409 190.378i 0.497318 0.139559i
\(124\) 731.083i 0.529461i
\(125\) 332.008 1357.53i 0.237566 0.971371i
\(126\) −444.599 + 2185.23i −0.314349 + 1.54505i
\(127\) 1251.75i 0.874602i −0.899315 0.437301i \(-0.855934\pi\)
0.899315 0.437301i \(-0.144066\pi\)
\(128\) 1957.21 1.35152
\(129\) 379.947 + 1353.94i 0.259322 + 0.924089i
\(130\) 75.4827 942.075i 0.0509251 0.635580i
\(131\) −1225.39 −0.817274 −0.408637 0.912697i \(-0.633996\pi\)
−0.408637 + 0.912697i \(0.633996\pi\)
\(132\) −505.422 1801.06i −0.333268 1.18759i
\(133\) 1623.81 + 1506.36i 1.05867 + 0.982088i
\(134\) 3352.44i 2.16124i
\(135\) −1058.60 1157.47i −0.674886 0.737922i
\(136\) 79.6503i 0.0502203i
\(137\) 1748.45 1.09037 0.545183 0.838317i \(-0.316460\pi\)
0.545183 + 0.838317i \(0.316460\pi\)
\(138\) −3002.52 + 842.579i −1.85211 + 0.519747i
\(139\) 2075.28i 1.26635i 0.774007 + 0.633177i \(0.218250\pi\)
−0.774007 + 0.633177i \(0.781750\pi\)
\(140\) 1665.14 + 1812.86i 1.00521 + 1.09439i
\(141\) −383.720 1367.38i −0.229185 0.816697i
\(142\) 2857.80i 1.68888i
\(143\) 574.024i 0.335681i
\(144\) −410.012 + 249.790i −0.237275 + 0.144554i
\(145\) 2263.99 + 181.399i 1.29665 + 0.103892i
\(146\) 2092.07 1.18589
\(147\) 608.796 + 1675.08i 0.341583 + 0.939852i
\(148\) 4013.25i 2.22896i
\(149\) 192.111i 0.105627i −0.998604 0.0528133i \(-0.983181\pi\)
0.998604 0.0528133i \(-0.0168188\pi\)
\(150\) −2877.89 + 328.579i −1.56652 + 0.178856i
\(151\) −2157.41 −1.16270 −0.581350 0.813654i \(-0.697475\pi\)
−0.581350 + 0.813654i \(0.697475\pi\)
\(152\) 2073.55i 1.10650i
\(153\) 64.5330 + 105.926i 0.0340993 + 0.0559715i
\(154\) −1833.68 1701.04i −0.959493 0.890089i
\(155\) −685.376 54.9149i −0.355166 0.0284572i
\(156\) −1127.33 + 316.356i −0.578581 + 0.162364i
\(157\) −1016.31 −0.516625 −0.258312 0.966061i \(-0.583166\pi\)
−0.258312 + 0.966061i \(0.583166\pi\)
\(158\) −564.106 −0.284037
\(159\) 1114.95 312.882i 0.556109 0.156058i
\(160\) −194.667 + 2429.58i −0.0961863 + 1.20047i
\(161\) −1695.07 + 1827.24i −0.829751 + 0.894450i
\(162\) −1491.00 + 2888.97i −0.723112 + 1.40110i
\(163\) 2851.10i 1.37003i −0.728527 0.685017i \(-0.759795\pi\)
0.728527 0.685017i \(-0.240205\pi\)
\(164\) −1612.03 −0.767552
\(165\) 1726.43 338.537i 0.814558 0.159728i
\(166\) 1334.59i 0.624004i
\(167\) 1887.62i 0.874662i 0.899301 + 0.437331i \(0.144076\pi\)
−0.899301 + 0.437331i \(0.855924\pi\)
\(168\) 762.048 1484.34i 0.349960 0.681661i
\(169\) −1837.70 −0.836461
\(170\) 228.320 + 18.2938i 0.103008 + 0.00825338i
\(171\) 1680.00 + 2757.60i 0.751304 + 1.23321i
\(172\) 3217.21i 1.42622i
\(173\) 3491.67i 1.53449i −0.641353 0.767246i \(-0.721627\pi\)
0.641353 0.767246i \(-0.278373\pi\)
\(174\) −1271.89 4532.36i −0.554148 1.97470i
\(175\) −1824.59 + 1424.86i −0.788150 + 0.615483i
\(176\) 538.493i 0.230628i
\(177\) 3677.26 1031.93i 1.56158 0.438217i
\(178\) 1899.30 0.799769
\(179\) 172.498i 0.0720286i 0.999351 + 0.0360143i \(0.0114662\pi\)
−0.999351 + 0.0360143i \(0.988534\pi\)
\(180\) 1616.32 + 3203.96i 0.669298 + 1.32672i
\(181\) 2106.81i 0.865182i 0.901590 + 0.432591i \(0.142401\pi\)
−0.901590 + 0.432591i \(0.857599\pi\)
\(182\) −1064.72 + 1147.74i −0.433640 + 0.467453i
\(183\) −438.365 1562.10i −0.177076 0.631006i
\(184\) 2333.32 0.934861
\(185\) −3762.34 301.453i −1.49520 0.119801i
\(186\) 385.038 + 1372.08i 0.151787 + 0.540890i
\(187\) −139.119 −0.0544033
\(188\) 3249.16i 1.26048i
\(189\) 189.174 + 2591.42i 0.0728063 + 0.997346i
\(190\) 5943.89 + 476.247i 2.26955 + 0.181845i
\(191\) 633.737i 0.240082i −0.992769 0.120041i \(-0.961697\pi\)
0.992769 0.120041i \(-0.0383026\pi\)
\(192\) 4152.18 1165.20i 1.56072 0.437975i
\(193\) 4520.88i 1.68611i 0.537824 + 0.843057i \(0.319246\pi\)
−0.537824 + 0.843057i \(0.680754\pi\)
\(194\) 2504.75 0.926962
\(195\) −211.899 1080.61i −0.0778174 0.396842i
\(196\) −305.580 4066.07i −0.111363 1.48180i
\(197\) 3816.25 1.38018 0.690092 0.723722i \(-0.257570\pi\)
0.690092 + 0.723722i \(0.257570\pi\)
\(198\) −1897.13 3114.00i −0.680924 1.11769i
\(199\) 1340.01i 0.477341i −0.971101 0.238670i \(-0.923288\pi\)
0.971101 0.238670i \(-0.0767115\pi\)
\(200\) 2139.62 + 345.085i 0.756471 + 0.122006i
\(201\) −1055.39 3760.87i −0.370356 1.31976i
\(202\) −7729.11 −2.69217
\(203\) −2758.25 2558.73i −0.953651 0.884670i
\(204\) −76.6715 273.218i −0.0263141 0.0937699i
\(205\) 121.087 1511.25i 0.0412541 0.514879i
\(206\) 7603.37 2.57161
\(207\) −3103.06 + 1890.46i −1.04192 + 0.634765i
\(208\) −337.056 −0.112359
\(209\) −3621.73 −1.19866
\(210\) 4079.86 + 2525.35i 1.34065 + 0.829836i
\(211\) 729.169 0.237905 0.118953 0.992900i \(-0.462046\pi\)
0.118953 + 0.992900i \(0.462046\pi\)
\(212\) −2649.34 −0.858290
\(213\) −899.674 3205.97i −0.289411 1.03131i
\(214\) 1773.97 0.566664
\(215\) 3016.07 + 241.660i 0.956719 + 0.0766560i
\(216\) 1658.13 1779.76i 0.522322 0.560636i
\(217\) 835.003 + 774.604i 0.261215 + 0.242320i
\(218\) −6166.36 −1.91577
\(219\) 2346.95 658.610i 0.724164 0.203218i
\(220\) −4012.11 321.466i −1.22953 0.0985146i
\(221\) 87.0783i 0.0265046i
\(222\) 2113.65 + 7531.96i 0.639004 + 2.27708i
\(223\) 3259.48 0.978793 0.489396 0.872061i \(-0.337217\pi\)
0.489396 + 0.872061i \(0.337217\pi\)
\(224\) 2745.89 2959.99i 0.819050 0.882915i
\(225\) −3125.06 + 1274.61i −0.925944 + 0.377661i
\(226\) −4589.39 −1.35080
\(227\) 4188.94i 1.22480i 0.790548 + 0.612401i \(0.209796\pi\)
−0.790548 + 0.612401i \(0.790204\pi\)
\(228\) −1996.01 7112.73i −0.579775 2.06602i
\(229\) 1996.90i 0.576240i 0.957594 + 0.288120i \(0.0930302\pi\)
−0.957594 + 0.288120i \(0.906970\pi\)
\(230\) −535.909 + 6688.51i −0.153638 + 1.91751i
\(231\) −2592.59 1331.01i −0.738440 0.379110i
\(232\) 3522.19i 0.996736i
\(233\) −141.704 −0.0398425 −0.0199213 0.999802i \(-0.506342\pi\)
−0.0199213 + 0.999802i \(0.506342\pi\)
\(234\) −1949.13 + 1187.46i −0.544524 + 0.331737i
\(235\) −3046.03 244.059i −0.845535 0.0677476i
\(236\) −8737.88 −2.41012
\(237\) −632.832 + 177.588i −0.173447 + 0.0486733i
\(238\) −278.165 258.044i −0.0757595 0.0702795i
\(239\) 2702.30i 0.731369i 0.930739 + 0.365684i \(0.119165\pi\)
−0.930739 + 0.365684i \(0.880835\pi\)
\(240\) 198.783 + 1013.72i 0.0534640 + 0.272648i
\(241\) 4299.54i 1.14920i −0.818434 0.574601i \(-0.805157\pi\)
0.818434 0.574601i \(-0.194843\pi\)
\(242\) −1845.90 −0.490326
\(243\) −763.168 + 3710.32i −0.201470 + 0.979495i
\(244\) 3711.86i 0.973884i
\(245\) 3834.81 + 18.9455i 0.999988 + 0.00494033i
\(246\) −3025.42 + 849.006i −0.784121 + 0.220043i
\(247\) 2266.93i 0.583972i
\(248\) 1066.27i 0.273017i
\(249\) −420.148 1497.19i −0.106931 0.381047i
\(250\) −1480.62 + 6054.03i −0.374570 + 1.53156i
\(251\) 3307.05 0.831630 0.415815 0.909449i \(-0.363496\pi\)
0.415815 + 0.909449i \(0.363496\pi\)
\(252\) 1185.16 5825.14i 0.296263 1.45615i
\(253\) 4075.44i 1.01273i
\(254\) 5582.26i 1.37898i
\(255\) 261.895 51.3554i 0.0643157 0.0126118i
\(256\) −2088.71 −0.509938
\(257\) 3931.01i 0.954123i −0.878870 0.477061i \(-0.841702\pi\)
0.878870 0.477061i \(-0.158298\pi\)
\(258\) −1694.41 6037.99i −0.408872 1.45701i
\(259\) 4583.71 + 4252.15i 1.09968 + 1.02014i
\(260\) −201.213 + 2511.28i −0.0479951 + 0.599011i
\(261\) −2853.69 4684.13i −0.676778 1.11088i
\(262\) 5464.73 1.28860
\(263\) 2083.22 0.488430 0.244215 0.969721i \(-0.421470\pi\)
0.244215 + 0.969721i \(0.421470\pi\)
\(264\) 737.147 + 2626.81i 0.171850 + 0.612383i
\(265\) 199.004 2483.70i 0.0461310 0.575746i
\(266\) −7241.53 6717.72i −1.66920 1.54846i
\(267\) 2130.70 597.926i 0.488377 0.137050i
\(268\) 8936.56i 2.03689i
\(269\) −2905.93 −0.658653 −0.329326 0.944216i \(-0.606822\pi\)
−0.329326 + 0.944216i \(0.606822\pi\)
\(270\) 4720.90 + 5161.85i 1.06409 + 1.16348i
\(271\) 716.004i 0.160495i −0.996775 0.0802475i \(-0.974429\pi\)
0.996775 0.0802475i \(-0.0255711\pi\)
\(272\) 81.6883i 0.0182099i
\(273\) −833.115 + 1622.76i −0.184697 + 0.359759i
\(274\) −7797.36 −1.71918
\(275\) 602.735 3737.13i 0.132168 0.819481i
\(276\) 8003.78 2246.05i 1.74555 0.489843i
\(277\) 101.240i 0.0219601i −0.999940 0.0109801i \(-0.996505\pi\)
0.999940 0.0109801i \(-0.00349513\pi\)
\(278\) 9254.89i 1.99666i
\(279\) 863.896 + 1418.02i 0.185377 + 0.304283i
\(280\) −2428.57 2644.01i −0.518339 0.564322i
\(281\) 7745.33i 1.64430i 0.569272 + 0.822149i \(0.307225\pi\)
−0.569272 + 0.822149i \(0.692775\pi\)
\(282\) 1711.23 + 6097.95i 0.361356 + 1.28769i
\(283\) −381.119 −0.0800536 −0.0400268 0.999199i \(-0.512744\pi\)
−0.0400268 + 0.999199i \(0.512744\pi\)
\(284\) 7618.01i 1.59171i
\(285\) 6817.97 1336.95i 1.41706 0.277873i
\(286\) 2559.91i 0.529267i
\(287\) −1708.00 + 1841.17i −0.351288 + 0.378680i
\(288\) 5026.74 3062.42i 1.02848 0.626579i
\(289\) 4891.90 0.995704
\(290\) −10096.4 808.965i −2.04442 0.163807i
\(291\) 2809.91 788.529i 0.566047 0.158847i
\(292\) −5576.80 −1.11766
\(293\) 2325.30i 0.463637i 0.972759 + 0.231818i \(0.0744675\pi\)
−0.972759 + 0.231818i \(0.925532\pi\)
\(294\) −2714.97 7470.15i −0.538573 1.48186i
\(295\) 656.342 8191.59i 0.129538 1.61672i
\(296\) 5853.23i 1.14937i
\(297\) −3108.58 2896.14i −0.607334 0.565829i
\(298\) 856.735i 0.166541i
\(299\) −2550.92 −0.493389
\(300\) 7671.55 875.889i 1.47639 0.168565i
\(301\) −3674.53 3408.73i −0.703642 0.652745i
\(302\) 9621.14 1.83323
\(303\) −8670.76 + 2433.23i −1.64397 + 0.461337i
\(304\) 2126.61i 0.401215i
\(305\) −3479.80 278.815i −0.653287 0.0523439i
\(306\) −287.790 472.387i −0.0537643 0.0882503i
\(307\) 3447.89 0.640981 0.320491 0.947252i \(-0.396152\pi\)
0.320491 + 0.947252i \(0.396152\pi\)
\(308\) 4888.01 + 4534.44i 0.904286 + 0.838876i
\(309\) 8529.70 2393.64i 1.57035 0.440678i
\(310\) 3056.49 + 244.897i 0.559990 + 0.0448685i
\(311\) 7675.73 1.39952 0.699760 0.714378i \(-0.253290\pi\)
0.699760 + 0.714378i \(0.253290\pi\)
\(312\) 1644.19 461.399i 0.298345 0.0837230i
\(313\) 9734.46 1.75790 0.878952 0.476910i \(-0.158243\pi\)
0.878952 + 0.476910i \(0.158243\pi\)
\(314\) 4532.30 0.814562
\(315\) 5371.93 + 1548.62i 0.960870 + 0.276999i
\(316\) 1503.73 0.267694
\(317\) −688.561 −0.121998 −0.0609991 0.998138i \(-0.519429\pi\)
−0.0609991 + 0.998138i \(0.519429\pi\)
\(318\) −4972.21 + 1395.32i −0.876817 + 0.246056i
\(319\) 6151.95 1.07976
\(320\) 741.109 9249.54i 0.129466 1.61583i
\(321\) 1990.09 558.469i 0.346032 0.0971050i
\(322\) 7559.28 8148.71i 1.30827 1.41028i
\(323\) −549.409 −0.0946437
\(324\) 3974.55 7701.09i 0.681507 1.32049i
\(325\) −2339.16 377.267i −0.399241 0.0643908i
\(326\) 12714.7i 2.16013i
\(327\) −6917.61 + 1941.25i −1.16986 + 0.328292i
\(328\) 2351.11 0.395788
\(329\) 3711.02 + 3442.58i 0.621869 + 0.576887i
\(330\) −7699.13 + 1509.73i −1.28431 + 0.251843i
\(331\) 4447.67 0.738568 0.369284 0.929317i \(-0.379603\pi\)
0.369284 + 0.929317i \(0.379603\pi\)
\(332\) 3557.61i 0.588101i
\(333\) 4742.32 + 7784.18i 0.780413 + 1.28099i
\(334\) 8418.00i 1.37908i
\(335\) −8377.85 671.265i −1.36636 0.109478i
\(336\) 781.546 1522.32i 0.126895 0.247170i
\(337\) 4087.57i 0.660724i −0.943854 0.330362i \(-0.892829\pi\)
0.943854 0.330362i \(-0.107171\pi\)
\(338\) 8195.39 1.31885
\(339\) −5148.52 + 1444.80i −0.824864 + 0.231477i
\(340\) −608.629 48.7657i −0.0970810 0.00777850i
\(341\) −1862.38 −0.295757
\(342\) −7492.10 12297.8i −1.18458 1.94441i
\(343\) −4967.81 3959.10i −0.782031 0.623240i
\(344\) 4692.24i 0.735432i
\(345\) 1504.43 + 7672.09i 0.234771 + 1.19725i
\(346\) 15571.4i 2.41943i
\(347\) −5812.08 −0.899161 −0.449580 0.893240i \(-0.648427\pi\)
−0.449580 + 0.893240i \(0.648427\pi\)
\(348\) 3390.46 + 12081.9i 0.522264 + 1.86108i
\(349\) 2804.01i 0.430073i −0.976606 0.215036i \(-0.931013\pi\)
0.976606 0.215036i \(-0.0689870\pi\)
\(350\) 8136.92 6354.29i 1.24268 0.970431i
\(351\) −1812.77 + 1945.74i −0.275665 + 0.295886i
\(352\) 6601.92i 0.999669i
\(353\) 1183.07i 0.178381i 0.996015 + 0.0891907i \(0.0284281\pi\)
−0.996015 + 0.0891907i \(0.971572\pi\)
\(354\) −16399.0 + 4601.97i −2.46214 + 0.690937i
\(355\) −7141.74 572.223i −1.06773 0.0855506i
\(356\) −5062.95 −0.753753
\(357\) −393.290 201.912i −0.0583056 0.0299337i
\(358\) 769.269i 0.113567i
\(359\) 8708.99i 1.28034i −0.768232 0.640171i \(-0.778863\pi\)
0.768232 0.640171i \(-0.221137\pi\)
\(360\) −2357.37 4672.91i −0.345123 0.684122i
\(361\) −7443.86 −1.08527
\(362\) 9395.49i 1.36413i
\(363\) −2070.79 + 581.114i −0.299417 + 0.0840236i
\(364\) 2838.22 3059.53i 0.408690 0.440557i
\(365\) 418.898 5228.14i 0.0600716 0.749735i
\(366\) 1954.92 + 6966.33i 0.279195 + 0.994907i
\(367\) 7352.20 1.04573 0.522864 0.852416i \(-0.324864\pi\)
0.522864 + 0.852416i \(0.324864\pi\)
\(368\) 2393.02 0.338980
\(369\) −3126.73 + 1904.88i −0.441114 + 0.268738i
\(370\) 16778.4 + 1344.35i 2.35749 + 0.188891i
\(371\) −2807.05 + 3025.93i −0.392817 + 0.423446i
\(372\) −1026.39 3657.53i −0.143054 0.509769i
\(373\) 1319.56i 0.183174i 0.995797 + 0.0915872i \(0.0291940\pi\)
−0.995797 + 0.0915872i \(0.970806\pi\)
\(374\) 620.414 0.0857777
\(375\) 244.884 + 7257.71i 0.0337220 + 0.999431i
\(376\) 4738.84i 0.649965i
\(377\) 3850.66i 0.526045i
\(378\) −843.637 11556.7i −0.114794 1.57252i
\(379\) −10334.2 −1.40062 −0.700309 0.713839i \(-0.746955\pi\)
−0.700309 + 0.713839i \(0.746955\pi\)
\(380\) −15844.6 1269.53i −2.13897 0.171383i
\(381\) 1757.37 + 6262.35i 0.236306 + 0.842074i
\(382\) 2826.20i 0.378537i
\(383\) 13328.0i 1.77815i 0.457763 + 0.889074i \(0.348651\pi\)
−0.457763 + 0.889074i \(0.651349\pi\)
\(384\) −9791.74 + 2747.80i −1.30126 + 0.365164i
\(385\) −4618.11 + 4241.81i −0.611326 + 0.561513i
\(386\) 20161.2i 2.65850i
\(387\) −3801.67 6240.18i −0.499354 0.819654i
\(388\) −6676.89 −0.873628
\(389\) 6183.45i 0.805947i 0.915212 + 0.402973i \(0.132023\pi\)
−0.915212 + 0.402973i \(0.867977\pi\)
\(390\) 944.979 + 4819.08i 0.122695 + 0.625701i
\(391\) 618.236i 0.0799630i
\(392\) 445.682 + 5930.27i 0.0574243 + 0.764092i
\(393\) 6130.50 1720.37i 0.786878 0.220817i
\(394\) −17018.8 −2.17614
\(395\) −112.952 + 1409.72i −0.0143879 + 0.179571i
\(396\) 5057.15 + 8300.95i 0.641746 + 1.05338i
\(397\) −2722.53 −0.344181 −0.172091 0.985081i \(-0.555052\pi\)
−0.172091 + 0.985081i \(0.555052\pi\)
\(398\) 5975.88i 0.752623i
\(399\) −10238.6 5256.42i −1.28464 0.659524i
\(400\) 2194.37 + 353.915i 0.274296 + 0.0442393i
\(401\) 6359.86i 0.792011i −0.918248 0.396005i \(-0.870396\pi\)
0.918248 0.396005i \(-0.129604\pi\)
\(402\) 4706.60 + 16771.9i 0.583941 + 2.08086i
\(403\) 1165.71i 0.144089i
\(404\) 20603.4 2.53727
\(405\) 6921.07 + 4304.52i 0.849162 + 0.528132i
\(406\) 12300.6 + 11410.9i 1.50362 + 1.39486i
\(407\) −10223.4 −1.24510
\(408\) 111.824 + 398.482i 0.0135689 + 0.0483525i
\(409\) 2243.08i 0.271181i 0.990765 + 0.135591i \(0.0432932\pi\)
−0.990765 + 0.135591i \(0.956707\pi\)
\(410\) −539.997 + 6739.53i −0.0650453 + 0.811809i
\(411\) −8747.32 + 2454.71i −1.04981 + 0.294603i
\(412\) −20268.2 −2.42365
\(413\) −9258.04 + 9979.93i −1.10305 + 1.18906i
\(414\) 13838.4 8430.67i 1.64280 1.00083i
\(415\) −3335.19 267.229i −0.394502 0.0316090i
\(416\) 4132.30 0.487026
\(417\) −2913.56 10382.4i −0.342153 1.21926i
\(418\) 16151.4 1.88993
\(419\) 12565.4 1.46505 0.732527 0.680738i \(-0.238341\pi\)
0.732527 + 0.680738i \(0.238341\pi\)
\(420\) −10875.6 6731.79i −1.26352 0.782090i
\(421\) 3903.57 0.451896 0.225948 0.974139i \(-0.427452\pi\)
0.225948 + 0.974139i \(0.427452\pi\)
\(422\) −3251.79 −0.375105
\(423\) 3839.43 + 6302.15i 0.441322 + 0.724399i
\(424\) 3864.01 0.442577
\(425\) 91.4337 566.915i 0.0104357 0.0647045i
\(426\) 4012.17 + 14297.3i 0.456315 + 1.62607i
\(427\) 4239.49 + 3932.83i 0.480476 + 0.445721i
\(428\) −4728.85 −0.534060
\(429\) −805.892 2871.78i −0.0906966 0.323196i
\(430\) −13450.4 1077.70i −1.50846 0.120864i
\(431\) 5029.93i 0.562142i −0.959687 0.281071i \(-0.909310\pi\)
0.959687 0.281071i \(-0.0906897\pi\)
\(432\) 1700.56 1825.30i 0.189394 0.203287i
\(433\) −14864.3 −1.64972 −0.824862 0.565334i \(-0.808747\pi\)
−0.824862 + 0.565334i \(0.808747\pi\)
\(434\) −3723.76 3454.41i −0.411858 0.382066i
\(435\) −11581.2 + 2270.97i −1.27649 + 0.250309i
\(436\) 16437.6 1.80555
\(437\) 16094.7i 1.76181i
\(438\) −10466.4 + 2937.12i −1.14179 + 0.320414i
\(439\) 11284.2i 1.22680i 0.789771 + 0.613402i \(0.210199\pi\)
−0.789771 + 0.613402i \(0.789801\pi\)
\(440\) 5851.58 + 468.851i 0.634007 + 0.0507991i
\(441\) −5397.44 7525.54i −0.582814 0.812605i
\(442\) 388.333i 0.0417898i
\(443\) 6406.23 0.687064 0.343532 0.939141i \(-0.388377\pi\)
0.343532 + 0.939141i \(0.388377\pi\)
\(444\) −5634.33 20077.8i −0.602238 2.14606i
\(445\) 380.301 4746.42i 0.0405124 0.505622i
\(446\) −14535.9 −1.54326
\(447\) 269.712 + 961.113i 0.0285390 + 0.101698i
\(448\) −10453.7 + 11268.8i −1.10244 + 1.18840i
\(449\) 5647.45i 0.593585i 0.954942 + 0.296792i \(0.0959169\pi\)
−0.954942 + 0.296792i \(0.904083\pi\)
\(450\) 13936.5 5684.21i 1.45994 0.595458i
\(451\) 4106.52i 0.428755i
\(452\) 12233.9 1.27308
\(453\) 10793.3 3028.86i 1.11946 0.314147i
\(454\) 18680.9i 1.93114i
\(455\) 2655.05 + 2890.59i 0.273562 + 0.297831i
\(456\) 2911.13 + 10373.8i 0.298961 + 1.06534i
\(457\) 4027.42i 0.412243i −0.978526 0.206121i \(-0.933916\pi\)
0.978526 0.206121i \(-0.0660842\pi\)
\(458\) 8905.34i 0.908558i
\(459\) −471.566 439.339i −0.0479538 0.0446766i
\(460\) 1428.57 17829.5i 0.144798 1.80718i
\(461\) 4322.13 0.436663 0.218332 0.975875i \(-0.429939\pi\)
0.218332 + 0.975875i \(0.429939\pi\)
\(462\) 11561.8 + 5935.76i 1.16430 + 0.597742i
\(463\) 13087.8i 1.31370i 0.754021 + 0.656850i \(0.228111\pi\)
−0.754021 + 0.656850i \(0.771889\pi\)
\(464\) 3612.31i 0.361416i
\(465\) 3505.96 687.489i 0.349645 0.0685624i
\(466\) 631.938 0.0628197
\(467\) 2525.04i 0.250203i −0.992144 0.125102i \(-0.960074\pi\)
0.992144 0.125102i \(-0.0399257\pi\)
\(468\) 5195.77 3165.39i 0.513193 0.312650i
\(469\) 10206.8 + 9468.55i 1.00492 + 0.932232i
\(470\) 13584.0 + 1088.40i 1.33316 + 0.106818i
\(471\) 5084.47 1426.83i 0.497410 0.139585i
\(472\) 12744.0 1.24278
\(473\) 8195.60 0.796689
\(474\) 2822.16 791.968i 0.273473 0.0767432i
\(475\) 2380.31 14758.6i 0.229929 1.42562i
\(476\) 741.501 + 687.866i 0.0714005 + 0.0662359i
\(477\) −5138.72 + 3130.64i −0.493262 + 0.300507i
\(478\) 12051.1i 1.15315i
\(479\) −3175.55 −0.302911 −0.151456 0.988464i \(-0.548396\pi\)
−0.151456 + 0.988464i \(0.548396\pi\)
\(480\) −2437.07 12428.2i −0.231743 1.18181i
\(481\) 6399.09i 0.606598i
\(482\) 19174.1i 1.81195i
\(483\) 5914.92 11521.2i 0.557222 1.08537i
\(484\) 4920.59 0.462114
\(485\) 501.531 6259.45i 0.0469554 0.586035i
\(486\) 3403.41 16546.5i 0.317658 1.54437i
\(487\) 3971.81i 0.369569i 0.982779 + 0.184785i \(0.0591587\pi\)
−0.982779 + 0.184785i \(0.940841\pi\)
\(488\) 5413.67i 0.502183i
\(489\) 4002.76 + 14263.8i 0.370166 + 1.31908i
\(490\) −17101.6 84.4888i −1.57668 0.00778941i
\(491\) 10854.4i 0.997665i 0.866698 + 0.498833i \(0.166238\pi\)
−0.866698 + 0.498833i \(0.833762\pi\)
\(492\) 8064.83 2263.19i 0.739005 0.207383i
\(493\) 933.239 0.0852555
\(494\) 10109.5i 0.920749i
\(495\) −8161.84 + 4117.45i −0.741106 + 0.373870i
\(496\) 1093.55i 0.0989958i
\(497\) 8700.88 + 8071.51i 0.785287 + 0.728484i
\(498\) 1873.68 + 6676.84i 0.168598 + 0.600796i
\(499\) −4802.55 −0.430845 −0.215423 0.976521i \(-0.569113\pi\)
−0.215423 + 0.976521i \(0.569113\pi\)
\(500\) 3946.87 16138.1i 0.353018 1.44344i
\(501\) −2650.10 9443.57i −0.236323 0.842131i
\(502\) −14748.1 −1.31123
\(503\) 13959.0i 1.23738i −0.785636 0.618689i \(-0.787664\pi\)
0.785636 0.618689i \(-0.212336\pi\)
\(504\) −1728.53 + 8495.85i −0.152768 + 0.750863i
\(505\) −1547.61 + 19315.3i −0.136372 + 1.70202i
\(506\) 18174.7i 1.59677i
\(507\) 9193.84 2580.02i 0.805351 0.226001i
\(508\) 14880.6i 1.29964i
\(509\) −13117.5 −1.14228 −0.571141 0.820852i \(-0.693499\pi\)
−0.571141 + 0.820852i \(0.693499\pi\)
\(510\) −1167.94 + 229.024i −0.101407 + 0.0198850i
\(511\) −5908.78 + 6369.51i −0.511525 + 0.551410i
\(512\) −6342.96 −0.547503
\(513\) −12276.4 11437.4i −1.05656 0.984354i
\(514\) 17530.6i 1.50436i
\(515\) 1522.44 19001.0i 0.130265 1.62580i
\(516\) 4516.76 + 16095.4i 0.385347 + 1.37318i
\(517\) −8276.99 −0.704103
\(518\) −20441.4 18962.8i −1.73387 1.60845i
\(519\) 4902.08 + 17468.5i 0.414600 + 1.47742i
\(520\) 293.465 3662.65i 0.0247487 0.308880i
\(521\) 3567.96 0.300029 0.150015 0.988684i \(-0.452068\pi\)
0.150015 + 0.988684i \(0.452068\pi\)
\(522\) 12726.3 + 20889.3i 1.06708 + 1.75153i
\(523\) −6801.37 −0.568648 −0.284324 0.958728i \(-0.591769\pi\)
−0.284324 + 0.958728i \(0.591769\pi\)
\(524\) −14567.3 −1.21445
\(525\) 7127.84 9690.05i 0.592542 0.805540i
\(526\) −9290.30 −0.770107
\(527\) −282.519 −0.0233524
\(528\) 756.009 + 2694.02i 0.0623126 + 0.222050i
\(529\) 5943.91 0.488527
\(530\) −887.474 + 11076.3i −0.0727347 + 0.907779i
\(531\) −16948.2 + 10325.3i −1.38510 + 0.843838i
\(532\) 19303.7 + 17907.3i 1.57316 + 1.45936i
\(533\) −2570.37 −0.208884
\(534\) −9502.02 + 2666.50i −0.770024 + 0.216087i
\(535\) 355.205 4433.20i 0.0287044 0.358251i
\(536\) 13033.8i 1.05032i
\(537\) −242.176 862.991i −0.0194612 0.0693497i
\(538\) 12959.2 1.03850
\(539\) 10358.0 778.441i 0.827736 0.0622075i
\(540\) −12584.4 13759.9i −1.00287 1.09654i
\(541\) 2446.78 0.194446 0.0972229 0.995263i \(-0.469004\pi\)
0.0972229 + 0.995263i \(0.469004\pi\)
\(542\) 3193.07i 0.253052i
\(543\) −2957.82 10540.2i −0.233761 0.833004i
\(544\) 1001.50i 0.0789317i
\(545\) −1234.70 + 15409.9i −0.0970437 + 1.21117i
\(546\) 3715.34 7236.84i 0.291212 0.567231i
\(547\) 11784.9i 0.921179i 0.887613 + 0.460590i \(0.152362\pi\)
−0.887613 + 0.460590i \(0.847638\pi\)
\(548\) 20785.3 1.62026
\(549\) 4386.18 + 7199.61i 0.340980 + 0.559694i
\(550\) −2687.95 + 16666.0i −0.208390 + 1.29208i
\(551\) 24295.2 1.87842
\(552\) −11673.3 + 3275.82i −0.900091 + 0.252587i
\(553\) 1593.25 1717.48i 0.122517 0.132070i
\(554\) 451.490i 0.0346245i
\(555\) 19245.8 3773.94i 1.47196 0.288639i
\(556\) 24670.7i 1.88178i
\(557\) −1115.57 −0.0848618 −0.0424309 0.999099i \(-0.513510\pi\)
−0.0424309 + 0.999099i \(0.513510\pi\)
\(558\) −3852.61 6323.79i −0.292283 0.479762i
\(559\) 5129.83i 0.388137i
\(560\) −2490.71 2711.67i −0.187949 0.204623i
\(561\) 696.000 195.315i 0.0523800 0.0146991i
\(562\) 34540.9i 2.59256i
\(563\) 16595.3i 1.24229i −0.783696 0.621145i \(-0.786668\pi\)
0.783696 0.621145i \(-0.213332\pi\)
\(564\) −4561.61 16255.2i −0.340565 1.21360i
\(565\) −918.941 + 11469.0i −0.0684251 + 0.853991i
\(566\) 1699.63 0.126220
\(567\) −4584.61 12699.0i −0.339569 0.940581i
\(568\) 11110.7i 0.820766i
\(569\) 15891.3i 1.17082i −0.810736 0.585412i \(-0.800933\pi\)
0.810736 0.585412i \(-0.199067\pi\)
\(570\) −30405.3 + 5962.22i −2.23428 + 0.438122i
\(571\) 1303.38 0.0955252 0.0477626 0.998859i \(-0.484791\pi\)
0.0477626 + 0.998859i \(0.484791\pi\)
\(572\) 6823.91i 0.498815i
\(573\) 889.725 + 3170.52i 0.0648670 + 0.231153i
\(574\) 7616.94 8210.86i 0.553876 0.597064i
\(575\) 16607.5 + 2678.51i 1.20449 + 0.194263i
\(576\) −19137.1 + 11658.8i −1.38434 + 0.843372i
\(577\) 8256.36 0.595696 0.297848 0.954613i \(-0.403731\pi\)
0.297848 + 0.954613i \(0.403731\pi\)
\(578\) −21815.8 −1.56993
\(579\) −6347.02 22617.5i −0.455567 1.62340i
\(580\) 26914.0 + 2156.45i 1.92680 + 0.154382i
\(581\) 4063.31 + 3769.40i 0.290146 + 0.269158i
\(582\) −12531.0 + 3516.51i −0.892487 + 0.250453i
\(583\) 6748.99i 0.479442i
\(584\) 8133.64 0.576323
\(585\) 2577.22 + 5108.70i 0.182145 + 0.361058i
\(586\) 10369.9i 0.731016i
\(587\) 22031.8i 1.54915i −0.632484 0.774573i \(-0.717965\pi\)
0.632484 0.774573i \(-0.282035\pi\)
\(588\) 7237.27 + 19913.1i 0.507585 + 1.39660i
\(589\) −7354.86 −0.514519
\(590\) −2927.01 + 36531.0i −0.204242 + 2.54908i
\(591\) −19092.3 + 5357.76i −1.32885 + 0.372908i
\(592\) 6003.00i 0.416760i
\(593\) 11710.2i 0.810929i −0.914111 0.405465i \(-0.867110\pi\)
0.914111 0.405465i \(-0.132890\pi\)
\(594\) 13863.0 + 12915.6i 0.957584 + 0.892142i
\(595\) −700.558 + 643.474i −0.0482690 + 0.0443359i
\(596\) 2283.79i 0.156959i
\(597\) 1881.29 + 6703.93i 0.128971 + 0.459587i
\(598\) 11376.0 0.777926
\(599\) 14539.0i 0.991729i −0.868400 0.495865i \(-0.834851\pi\)
0.868400 0.495865i \(-0.165149\pi\)
\(600\) −11188.8 + 1277.47i −0.761301 + 0.0869205i
\(601\) 20293.0i 1.37732i −0.725083 0.688661i \(-0.758199\pi\)
0.725083 0.688661i \(-0.241801\pi\)
\(602\) 16386.8 + 15201.5i 1.10943 + 1.02918i
\(603\) 10560.0 + 17333.5i 0.713164 + 1.17061i
\(604\) −25647.0 −1.72775
\(605\) −369.608 + 4612.96i −0.0248375 + 0.309989i
\(606\) 38667.9 10851.2i 2.59204 0.727390i
\(607\) 4143.51 0.277068 0.138534 0.990358i \(-0.455761\pi\)
0.138534 + 0.990358i \(0.455761\pi\)
\(608\) 26072.2i 1.73909i
\(609\) 17391.5 + 8928.68i 1.15721 + 0.594103i
\(610\) 15518.4 + 1243.40i 1.03004 + 0.0825306i
\(611\) 5180.77i 0.343030i
\(612\) 767.159 + 1259.24i 0.0506709 + 0.0831727i
\(613\) 13166.7i 0.867534i −0.901025 0.433767i \(-0.857184\pi\)
0.901025 0.433767i \(-0.142816\pi\)
\(614\) −15376.1 −1.01063
\(615\) 1515.91 + 7730.61i 0.0993939 + 0.506875i
\(616\) −7129.06 6613.39i −0.466295 0.432567i
\(617\) −8241.67 −0.537759 −0.268880 0.963174i \(-0.586653\pi\)
−0.268880 + 0.963174i \(0.586653\pi\)
\(618\) −38038.9 + 10674.6i −2.47597 + 0.694816i
\(619\) 12892.7i 0.837162i −0.908180 0.418581i \(-0.862528\pi\)
0.908180 0.418581i \(-0.137472\pi\)
\(620\) −8147.64 652.820i −0.527770 0.0422869i
\(621\) 12870.2 13814.3i 0.831665 0.892671i
\(622\) −34230.5 −2.20662
\(623\) −5364.35 + 5782.63i −0.344973 + 0.371872i
\(624\) 1686.26 473.205i 0.108180 0.0303579i
\(625\) 14832.7 + 4912.32i 0.949294 + 0.314388i
\(626\) −43411.6 −2.77169
\(627\) 18119.1 5084.67i 1.15408 0.323863i
\(628\) −12081.7 −0.767695
\(629\) −1550.87 −0.0983106
\(630\) −23956.6 6906.19i −1.51500 0.436745i
\(631\) 26758.6 1.68818 0.844092 0.536198i \(-0.180140\pi\)
0.844092 + 0.536198i \(0.180140\pi\)
\(632\) −2193.16 −0.138037
\(633\) −3647.95 + 1023.70i −0.229057 + 0.0642790i
\(634\) 3070.69 0.192355
\(635\) 13950.2 + 1117.75i 0.871808 + 0.0698526i
\(636\) 13254.4 3719.50i 0.826368 0.231899i
\(637\) −487.245 6483.32i −0.0303067 0.403263i
\(638\) −27435.1 −1.70246
\(639\) 9001.95 + 14776.1i 0.557295 + 0.914761i
\(640\) −1747.69 + 21812.4i −0.107943 + 1.34721i
\(641\) 12483.3i 0.769204i 0.923082 + 0.384602i \(0.125661\pi\)
−0.923082 + 0.384602i \(0.874339\pi\)
\(642\) −8874.98 + 2490.54i −0.545588 + 0.153105i
\(643\) 15859.5 0.972689 0.486345 0.873767i \(-0.338330\pi\)
0.486345 + 0.873767i \(0.338330\pi\)
\(644\) −20150.7 + 21721.9i −1.23299 + 1.32914i
\(645\) −15428.4 + 3025.37i −0.941848 + 0.184688i
\(646\) 2450.13 0.149225
\(647\) 26235.0i 1.59413i 0.603893 + 0.797066i \(0.293616\pi\)
−0.603893 + 0.797066i \(0.706384\pi\)
\(648\) −5796.79 + 11231.9i −0.351419 + 0.680910i
\(649\) 22259.1i 1.34629i
\(650\) 10431.7 + 1682.45i 0.629483 + 0.101525i
\(651\) −5264.92 2702.97i −0.316972 0.162731i
\(652\) 33893.5i 2.03584i
\(653\) 11488.0 0.688451 0.344226 0.938887i \(-0.388142\pi\)
0.344226 + 0.938887i \(0.388142\pi\)
\(654\) 30849.6 8657.16i 1.84452 0.517617i
\(655\) 1094.21 13656.5i 0.0652740 0.814663i
\(656\) 2411.27 0.143513
\(657\) −10816.9 + 6589.91i −0.642324 + 0.391320i
\(658\) −16549.6 15352.5i −0.980501 0.909578i
\(659\) 13746.7i 0.812588i −0.913743 0.406294i \(-0.866821\pi\)
0.913743 0.406294i \(-0.133179\pi\)
\(660\) 20523.5 4024.48i 1.21042 0.237353i
\(661\) 18205.0i 1.07124i −0.844458 0.535621i \(-0.820077\pi\)
0.844458 0.535621i \(-0.179923\pi\)
\(662\) −19834.7 −1.16450
\(663\) −122.252 435.644i −0.00716121 0.0255189i
\(664\) 5188.71i 0.303254i
\(665\) −18237.8 + 16751.7i −1.06350 + 0.976846i
\(666\) −21148.7 34714.2i −1.23048 2.01974i
\(667\) 27338.8i 1.58705i
\(668\) 22439.8i 1.29973i
\(669\) −16306.8 + 4576.09i −0.942389 + 0.264457i
\(670\) 37361.7 + 2993.56i 2.15434 + 0.172614i
\(671\) −9455.68 −0.544013
\(672\) −9581.75 + 18663.6i −0.550036 + 1.07137i
\(673\) 2132.80i 0.122160i −0.998133 0.0610799i \(-0.980546\pi\)
0.998133 0.0610799i \(-0.0194544\pi\)
\(674\) 18228.8i 1.04176i
\(675\) 13844.9 10764.1i 0.789467 0.613793i
\(676\) −21846.4 −1.24296
\(677\) 995.751i 0.0565285i 0.999600 + 0.0282643i \(0.00899799\pi\)
−0.999600 + 0.0282643i \(0.991002\pi\)
\(678\) 22960.2 6443.20i 1.30056 0.364970i
\(679\) −7074.36 + 7625.98i −0.399837 + 0.431013i
\(680\) 887.673 + 71.1237i 0.0500598 + 0.00401099i
\(681\) −5881.00 20956.8i −0.330926 1.17925i
\(682\) 8305.41 0.466321
\(683\) 24097.2 1.35000 0.675002 0.737816i \(-0.264143\pi\)
0.675002 + 0.737816i \(0.264143\pi\)
\(684\) 19971.6 + 32782.0i 1.11642 + 1.83253i
\(685\) −1561.28 + 19485.8i −0.0870853 + 1.08688i
\(686\) 22154.3 + 17655.9i 1.23303 + 0.982662i
\(687\) −2803.52 9990.29i −0.155693 0.554809i
\(688\) 4812.30i 0.266667i
\(689\) −4224.36 −0.233578
\(690\) −6709.13 34214.3i −0.370163 1.88771i
\(691\) 18883.3i 1.03959i 0.854291 + 0.519794i \(0.173991\pi\)
−0.854291 + 0.519794i \(0.826009\pi\)
\(692\) 41508.5i 2.28023i
\(693\) 14839.1 + 3019.11i 0.813406 + 0.165493i
\(694\) 25919.4 1.41771
\(695\) −23128.3 1853.12i −1.26231 0.101141i
\(696\) −4944.92 17621.1i −0.269306 0.959666i
\(697\) 622.951i 0.0338536i
\(698\) 12504.7i 0.678095i
\(699\) 708.928 198.942i 0.0383607 0.0107649i
\(700\) −21690.5 + 16938.6i −1.17118 + 0.914596i
\(701\) 6421.10i 0.345965i −0.984925 0.172983i \(-0.944660\pi\)
0.984925 0.172983i \(-0.0553404\pi\)
\(702\) 8084.17 8677.18i 0.434640 0.466523i
\(703\) −40374.2 −2.16606
\(704\) 25133.8i 1.34555i
\(705\) 15581.6 3055.42i 0.832393 0.163225i
\(706\) 5276.01i 0.281254i
\(707\) 21829.9 23532.1i 1.16124 1.25179i
\(708\) 43714.7 12267.4i 2.32048 0.651183i
\(709\) −5206.72 −0.275800 −0.137900 0.990446i \(-0.544035\pi\)
−0.137900 + 0.990446i \(0.544035\pi\)
\(710\) 31849.1 + 2551.88i 1.68349 + 0.134888i
\(711\) 2916.67 1776.91i 0.153845 0.0937261i
\(712\) 7384.21 0.388673
\(713\) 8276.24i 0.434709i
\(714\) 1753.91 + 900.443i 0.0919305 + 0.0471964i
\(715\) −6397.28 512.575i −0.334608 0.0268101i
\(716\) 2050.63i 0.107033i
\(717\) −3793.85 13519.3i −0.197607 0.704168i
\(718\) 38838.4i 2.01872i
\(719\) −26323.4 −1.36537 −0.682683 0.730715i \(-0.739187\pi\)
−0.682683 + 0.730715i \(0.739187\pi\)
\(720\) −2417.69 4792.48i −0.125142 0.248063i
\(721\) −21474.8 + 23149.2i −1.10924 + 1.19573i
\(722\) 33196.5 1.71114
\(723\) 6036.27 + 21510.2i 0.310500 + 1.10646i
\(724\) 25045.5i 1.28565i
\(725\) −4043.26 + 25069.3i −0.207121 + 1.28421i
\(726\) 9234.85 2591.52i 0.472090 0.132480i
\(727\) 653.079 0.0333169 0.0166584 0.999861i \(-0.494697\pi\)
0.0166584 + 0.999861i \(0.494697\pi\)
\(728\) −4139.48 + 4462.25i −0.210741 + 0.227173i
\(729\) −1391.00 19633.8i −0.0706700 0.997500i
\(730\) −1868.11 + 23315.3i −0.0947149 + 1.18211i
\(731\) 1243.26 0.0629049
\(732\) −5211.21 18570.1i −0.263131 0.937663i
\(733\) −19283.5 −0.971696 −0.485848 0.874043i \(-0.661489\pi\)
−0.485848 + 0.874043i \(0.661489\pi\)
\(734\) −32787.7 −1.64880
\(735\) −19211.8 + 5289.04i −0.964131 + 0.265427i
\(736\) −29338.4 −1.46933
\(737\) −22765.2 −1.13781
\(738\) 13943.9 8494.98i 0.695505 0.423719i
\(739\) 11829.3 0.588832 0.294416 0.955677i \(-0.404875\pi\)
0.294416 + 0.955677i \(0.404875\pi\)
\(740\) −44726.1 3583.63i −2.22184 0.178023i
\(741\) −3182.62 11341.2i −0.157782 0.562253i
\(742\) 12518.3 13494.4i 0.619354 0.667647i
\(743\) −15784.6 −0.779380 −0.389690 0.920946i \(-0.627418\pi\)
−0.389690 + 0.920946i \(0.627418\pi\)
\(744\) 1496.97 + 5334.43i 0.0737656 + 0.262863i
\(745\) 2141.01 + 171.546i 0.105289 + 0.00843618i
\(746\) 5884.67i 0.288811i
\(747\) 4203.91 + 6900.43i 0.205908 + 0.337983i
\(748\) −1653.83 −0.0808423
\(749\) −5010.36 + 5401.03i −0.244425 + 0.263484i
\(750\) −1092.08 32366.4i −0.0531695 1.57580i
\(751\) −719.429 −0.0349565 −0.0174782 0.999847i \(-0.505564\pi\)
−0.0174782 + 0.999847i \(0.505564\pi\)
\(752\) 4860.09i 0.235677i
\(753\) −16544.8 + 4642.88i −0.800700 + 0.224696i
\(754\) 17172.3i 0.829415i
\(755\) 1926.46 24043.5i 0.0928623 1.15899i
\(756\) 2248.87 + 30806.5i 0.108189 + 1.48204i
\(757\) 23060.3i 1.10719i 0.832787 + 0.553593i \(0.186744\pi\)
−0.832787 + 0.553593i \(0.813256\pi\)
\(758\) 46086.4 2.20835
\(759\) 5721.65 + 20389.0i 0.273627 + 0.975064i
\(760\) 23109.0 + 1851.58i 1.10296 + 0.0883735i
\(761\) 19804.3 0.943371 0.471686 0.881767i \(-0.343646\pi\)
0.471686 + 0.881767i \(0.343646\pi\)
\(762\) −7837.13 27927.5i −0.372584 1.32770i
\(763\) 17416.1 18774.1i 0.826351 0.890784i
\(764\) 7533.77i 0.356757i
\(765\) −1238.14 + 624.609i −0.0585162 + 0.0295200i
\(766\) 59437.4i 2.80361i
\(767\) −13932.5 −0.655897
\(768\) 10449.6 2932.41i 0.490972 0.137779i
\(769\) 14623.5i 0.685746i 0.939382 + 0.342873i \(0.111400\pi\)
−0.939382 + 0.342873i \(0.888600\pi\)
\(770\) 20594.8 18916.7i 0.963878 0.885338i
\(771\) 5518.88 + 19666.4i 0.257792 + 0.918637i
\(772\) 53743.5i 2.50553i
\(773\) 40353.9i 1.87766i 0.344384 + 0.938829i \(0.388088\pi\)
−0.344384 + 0.938829i \(0.611912\pi\)
\(774\) 16953.9 + 27828.6i 0.787331 + 1.29235i
\(775\) 1224.01 7589.22i 0.0567327 0.351758i
\(776\) 9738.10 0.450486
\(777\) −28901.6 14837.8i −1.33441 0.685077i
\(778\) 27575.6i 1.27074i
\(779\) 16217.4i