Properties

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

$q$-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 \(-0.863769\pi\)
0.909805 0.415035i \(-0.136231\pi\)
\(12\) −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 \(-0.989567\pi\)
0.999463 0.0327703i \(-0.0104330\pi\)
\(18\) −102.829 62.6458i −1.34650 0.820320i
\(19\) 119.595i 1.44405i −0.691869 0.722023i \(-0.743212\pi\)
0.691869 0.722023i \(-0.256788\pi\)
\(20\) −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 \(0.225400\pi\)
−0.759590 + 0.650402i \(0.774600\pi\)
\(30\) 49.8536 254.236i 0.303399 1.54723i
\(31\) 61.4983i 0.356304i −0.984003 0.178152i \(-0.942988\pi\)
0.984003 0.178152i \(-0.0570119\pi\)
\(32\) 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 \(-0.730055\pi\)
0.661441 0.749997i \(-0.269945\pi\)
\(38\) 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 \(0.159324\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(44\) 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 \(-0.860583\pi\)
0.905605 0.424123i \(-0.139417\pi\)
\(48\) 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 \(-0.893730\pi\)
0.944785 0.327691i \(-0.106270\pi\)
\(62\) 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 \(-0.759641\pi\)
0.728195 0.685370i \(-0.240359\pi\)
\(68\) 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 \(-0.820095\pi\)
0.844487 0.535576i \(-0.179905\pi\)
\(72\) −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 \(-0.936593\pi\)
0.980226 0.197883i \(-0.0634066\pi\)
\(84\) −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 \(0.144066\pi\)
−0.899315 + 0.437301i \(0.855934\pi\)
\(128\) 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 \(-0.781750\pi\)
0.774007 0.633177i \(-0.218250\pi\)
\(140\) 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 \(0.0168188\pi\)
−0.998604 + 0.0528133i \(0.983181\pi\)
\(150\) −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 \(0.240205\pi\)
−0.728527 + 0.685017i \(0.759795\pi\)
\(164\) −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 \(-0.855924\pi\)
0.899301 0.437331i \(-0.144076\pi\)
\(168\) 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 \(0.278373\pi\)
−0.641353 + 0.767246i \(0.721627\pi\)
\(174\) −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 \(-0.988534\pi\)
0.999351 0.0360143i \(-0.0114662\pi\)
\(180\) 1616.32 3203.96i 0.669298 1.32672i
\(181\) 2106.81i 0.865182i −0.901590 0.432591i \(-0.857599\pi\)
0.901590 0.432591i \(-0.142401\pi\)
\(182\) −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 \(0.0383026\pi\)
−0.992769 + 0.120041i \(0.961697\pi\)
\(192\) 4152.18 + 1165.20i 1.56072 + 0.437975i
\(193\) 4520.88i 1.68611i −0.537824 0.843057i \(-0.680754\pi\)
0.537824 0.843057i \(-0.319246\pi\)
\(194\) 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 \(0.0767115\pi\)
−0.971101 + 0.238670i \(0.923288\pi\)
\(200\) 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 \(-0.790204\pi\)
0.790548 0.612401i \(-0.209796\pi\)
\(228\) −1996.01 + 7112.73i −0.579775 + 2.06602i
\(229\) 1996.90i 0.576240i −0.957594 0.288120i \(-0.906970\pi\)
0.957594 0.288120i \(-0.0930302\pi\)
\(230\) −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 \(-0.880835\pi\)
0.930739 0.365684i \(-0.119165\pi\)
\(240\) 198.783 1013.72i 0.0534640 0.272648i
\(241\) 4299.54i 1.14920i 0.818434 + 0.574601i \(0.194843\pi\)
−0.818434 + 0.574601i \(0.805157\pi\)
\(242\) −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 \(0.158298\pi\)
−0.878870 + 0.477061i \(0.841702\pi\)
\(258\) −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 \(0.0255711\pi\)
−0.996775 + 0.0802475i \(0.974429\pi\)
\(272\) 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 \(0.00349513\pi\)
−0.999940 + 0.0109801i \(0.996505\pi\)
\(278\) 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 \(-0.692775\pi\)
0.569272 0.822149i \(-0.307225\pi\)
\(282\) 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 \(-0.925532\pi\)
0.972759 0.231818i \(-0.0744675\pi\)
\(294\) −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 \(0.107171\pi\)
−0.943854 + 0.330362i \(0.892829\pi\)
\(338\) 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 \(0.0689870\pi\)
−0.976606 + 0.215036i \(0.931013\pi\)
\(350\) 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 \(-0.971572\pi\)
0.996015 0.0891907i \(-0.0284281\pi\)
\(354\) −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 \(0.221137\pi\)
−0.768232 + 0.640171i \(0.778863\pi\)
\(360\) −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 \(-0.970806\pi\)
0.995797 0.0915872i \(-0.0291940\pi\)
\(374\) 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 \(-0.651349\pi\)
0.457763 0.889074i \(-0.348651\pi\)
\(384\) −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 \(-0.867977\pi\)
0.915212 0.402973i \(-0.132023\pi\)
\(390\) 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 \(0.129604\pi\)
−0.918248 + 0.396005i \(0.870396\pi\)
\(402\) 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 \(-0.956707\pi\)
0.990765 0.135591i \(-0.0432932\pi\)
\(410\) −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 \(0.0906897\pi\)
−0.959687 + 0.281071i \(0.909310\pi\)
\(432\) 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 \(-0.789801\pi\)
0.789771 0.613402i \(-0.210199\pi\)
\(440\) 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 \(-0.904083\pi\)
0.954942 0.296792i \(-0.0959169\pi\)
\(450\) 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 \(0.0660842\pi\)
−0.978526 + 0.206121i \(0.933916\pi\)
\(458\) 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 \(-0.771889\pi\)
0.754021 0.656850i \(-0.228111\pi\)
\(464\) 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 \(0.0399257\pi\)
−0.992144 + 0.125102i \(0.960074\pi\)
\(468\) 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 \(-0.940841\pi\)
0.982779 0.184785i \(-0.0591587\pi\)
\(488\) 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 \(-0.833762\pi\)
0.866698 0.498833i \(-0.166238\pi\)
\(492\) 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 \(0.212336\pi\)
−0.785636 + 0.618689i \(0.787664\pi\)
\(504\) −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 \(-0.847638\pi\)
0.887613 0.460590i \(-0.152362\pi\)
\(548\) 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 \(0.213332\pi\)
−0.783696 + 0.621145i \(0.786668\pi\)
\(564\) −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 \(0.199067\pi\)
−0.810736 + 0.585412i \(0.800933\pi\)
\(570\) −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 \(0.282035\pi\)
−0.632484 + 0.774573i \(0.717965\pi\)
\(588\) 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 \(0.132890\pi\)
−0.914111 + 0.405465i \(0.867110\pi\)
\(594\) 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 \(0.165149\pi\)
−0.868400 + 0.495865i \(0.834851\pi\)
\(600\) −11188.8 1277.47i −0.761301 0.0869205i
\(601\) 20293.0i 1.37732i 0.725083 + 0.688661i \(0.241801\pi\)
−0.725083 + 0.688661i \(0.758199\pi\)
\(602\) 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 \(0.142816\pi\)
−0.901025 + 0.433767i \(0.857184\pi\)
\(614\) −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 \(0.137472\pi\)
−0.908180 + 0.418581i \(0.862528\pi\)
\(620\) −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 \(-0.874339\pi\)
0.923082 0.384602i \(-0.125661\pi\)
\(642\) −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 \(-0.706384\pi\)
0.603893 0.797066i \(-0.293616\pi\)
\(648\) −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 \(0.133179\pi\)
−0.913743 + 0.406294i \(0.866821\pi\)
\(660\) 20523.5 + 4024.48i 1.21042 + 0.237353i
\(661\) 18205.0i 1.07124i 0.844458 + 0.535621i \(0.179923\pi\)
−0.844458 + 0.535621i \(0.820077\pi\)
\(662\) −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 \(0.0194544\pi\)
−0.998133 + 0.0610799i \(0.980546\pi\)
\(674\) 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 \(-0.991002\pi\)
0.999600 0.0282643i \(-0.00899799\pi\)
\(678\) 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 \(-0.826009\pi\)
0.854291 0.519794i \(-0.173991\pi\)
\(692\) 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 \(0.0553404\pi\)
−0.984925 + 0.172983i \(0.944660\pi\)
\(702\) 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 \(-0.813256\pi\)
0.832787 0.553593i \(-0.186744\pi\)
\(758\) 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 \(-0.888600\pi\)
0.939382 0.342873i \(-0.111400\pi\)
\(770\) 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 \(-0.611912\pi\)
0.344384 0.938829i \(-0.388088\pi\)
\(774\) 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