Properties

Label 105.4.g.b.104.7
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 104.7
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.8

$q$-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} +(-82.0763 - 50.2443i) 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} +(-162.565 + 128.248i) 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} +(366.026 + 224.068i) 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} +(-481.159 - 136.137i) 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} +(724.972 - 571.933i) 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} +(-975.710 - 597.297i) 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 \(-0.564809\pi\)
−0.202200 + 0.979344i \(0.564809\pi\)
\(14\) 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
\(21\) −82.0763 50.2443i −0.852881 0.522105i
\(22\) 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 \(-0.942988\pi\)
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
\(35\) −162.565 + 128.248i −0.785100 + 0.619369i
\(36\) 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 \(-0.416849\pi\)
0.258264 + 0.966074i \(0.416849\pi\)
\(42\) 366.026 + 224.068i 1.34474 + 0.823202i
\(43\) 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 \(-0.860583\pi\)
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 \(-0.198950\pi\)
0.810951 + 0.585114i \(0.198950\pi\)
\(60\) −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
\(63\) −481.159 136.137i −0.962227 0.272249i
\(64\) −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
\(70\) 724.972 571.933i 1.23787 0.976559i
\(71\) 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 \(-0.377276\pi\)
0.376069 + 0.926592i \(0.377276\pi\)
\(74\) 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 \(-0.0634066\pi\)
\(84\) −975.710 597.297i −1.26737 0.775838i
\(85\) −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 \(-0.418378\pi\)
0.253621 + 0.967304i \(0.418378\pi\)
\(90\) 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 \(-0.405028\pi\)
0.293957 + 0.955819i \(0.405028\pi\)
\(98\) 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 \(-0.825669\pi\)
−0.853736 + 0.520706i \(0.825669\pi\)
\(102\) 28.7624 + 102.494i 0.0279206 + 0.0994945i
\(103\) 1704.95 1.63101 0.815504 0.578751i \(-0.196460\pi\)
0.815504 + 0.578751i \(0.196460\pi\)
\(104\) 328.647 0.309870
\(105\) −633.244 + 869.843i −0.588555 + 0.808457i
\(106\) 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
\(126\) 2145.77 + 607.115i 1.51714 + 0.429255i
\(127\) 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 \(-0.366004\pi\)
0.408637 + 0.912697i \(0.366004\pi\)
\(132\) 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 \(-0.218250\pi\)
\(140\) −1932.55 + 1524.60i −1.16664 + 0.920371i
\(141\) −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
\(147\) 351.595 + 1747.26i 0.197272 + 0.980349i
\(148\) 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 \(-0.416834\pi\)
0.258312 + 0.966061i \(0.416834\pi\)
\(158\) −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 \(-0.855924\pi\)
0.899301 0.437331i \(-0.144076\pi\)
\(168\) 1423.05 + 871.144i 0.653517 + 0.400061i
\(169\) −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
\(175\) 1284.12 + 1926.25i 0.554686 + 0.832060i
\(176\) 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 \(-0.857599\pi\)
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
\(189\) −2598.31 5.56529i −0.999998 0.00214188i
\(190\) 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 \(0.0767115\pi\)
−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
\(210\) 2824.00 3879.14i 0.927974 1.27469i
\(211\) 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 \(-0.662783\pi\)
−0.489396 + 0.872061i \(0.662783\pi\)
\(224\) −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
\(231\) 1521.57 2485.55i 0.433384 0.707952i
\(232\) 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 \(0.194843\pi\)
−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
\(245\) 3788.90 + 591.896i 0.988017 + 0.154346i
\(246\) −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 \(-0.636504\pi\)
−0.415815 + 0.909449i \(0.636504\pi\)
\(252\) −5719.94 1618.38i −1.42985 0.404557i
\(253\) 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 \(-0.393178\pi\)
0.329326 + 0.944216i \(0.393178\pi\)
\(270\) 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
\(273\) 1555.76 + 952.385i 0.344905 + 0.211139i
\(274\) −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
\(280\) 2818.58 2223.59i 0.601580 0.474589i
\(281\) 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 \(-0.487256\pi\)
0.0400268 + 0.999199i \(0.487256\pi\)
\(284\) 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 \(-0.0744675\pi\)
\(294\) −1567.96 7792.03i −0.311039 1.54572i
\(295\) 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 \(-0.603848\pi\)
−0.320491 + 0.947252i \(0.603848\pi\)
\(308\) 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 \(-0.746710\pi\)
−0.699760 + 0.714378i \(0.746710\pi\)
\(312\) 1644.19 461.399i 0.298345 0.0837230i
\(313\) −9734.46 −1.75790 −0.878952 0.476910i \(-0.841757\pi\)
−0.878952 + 0.476910i \(0.841757\pi\)
\(314\) −4532.30 −0.814562
\(315\) −1946.85 + 5240.77i −0.348230 + 0.937409i
\(316\) 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
\(336\) 1459.46 + 893.434i 0.236965 + 0.145062i
\(337\) 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 \(0.0689870\pi\)
−0.976606 + 0.215036i \(0.931013\pi\)
\(350\) −5726.62 8590.24i −0.874573 1.31191i
\(351\) −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
\(357\) −230.818 + 377.052i −0.0342191 + 0.0558984i
\(358\) 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 \(-0.675136\pi\)
−0.522864 + 0.852416i \(0.675136\pi\)
\(368\) 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
\(378\) 11587.4 + 24.8188i 1.57670 + 0.00337710i
\(379\) −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
\(385\) −3883.79 4923.01i −0.514120 0.651688i
\(386\) 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 \(-0.444948\pi\)
0.172091 + 0.985081i \(0.444948\pi\)
\(398\) 5975.88i 0.752623i
\(399\) −6008.94 + 9815.88i −0.753944 + 1.23160i
\(400\) 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 \(-0.956707\pi\)
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 \(-0.761659\pi\)
−0.732527 + 0.680738i \(0.761659\pi\)
\(420\) −7527.91 + 10340.6i −0.874581 + 1.20135i
\(421\) 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 \(-0.191253\pi\)
0.824862 + 0.565334i \(0.191253\pi\)
\(434\) 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
\(441\) 4212.02 + 8247.73i 0.454813 + 0.890587i
\(442\) 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
\(455\) 3081.44 2430.96i 0.317494 0.250473i
\(456\) 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 \(-0.570061\pi\)
−0.218332 + 0.975875i \(0.570061\pi\)
\(462\) −6785.54 + 11084.5i −0.683316 + 1.11623i
\(463\) 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 \(0.0399257\pi\)
−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 \(-0.451604\pi\)
0.151456 + 0.988464i \(0.451604\pi\)
\(480\) −2437.07 12428.2i −0.231743 1.18181i
\(481\) 6399.09i 0.606598i
\(482\) 19174.1i 1.81195i
\(483\) 11045.6 + 6761.71i 1.04056 + 0.636995i
\(484\) 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
\(490\) −16896.9 2639.61i −1.55781 0.243358i
\(491\) 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 \(0.212336\pi\)
−0.785636 + 0.618689i \(0.787664\pi\)
\(504\) 8342.42 + 2360.37i 0.737303 + 0.208610i
\(505\) −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 \(-0.306501\pi\)
0.571141 + 0.820852i \(0.306501\pi\)
\(510\) 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 \(-0.547932\pi\)
−0.150015 + 0.988684i \(0.547932\pi\)
\(522\) 12726.3 + 20889.3i 1.06708 + 1.75153i
\(523\) 6801.37 0.568648 0.284324 0.958728i \(-0.408231\pi\)
0.284324 + 0.958728i \(0.408231\pi\)
\(524\) 14567.3 1.21445
\(525\) 9128.62 + 7833.99i 0.758868 + 0.651244i
\(526\) −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
\(546\) −6938.05 4247.24i −0.543812 0.332903i
\(547\) 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
\(560\) 2890.70 2280.49i 0.218133 0.172086i
\(561\) 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
\(567\) −13006.9 + 3620.02i −0.963384 + 0.268124i
\(568\) 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 \(-0.596269\pi\)
−0.297848 + 0.954613i \(0.596269\pi\)
\(578\) −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 \(0.717965\pi\)
\(588\) 4179.71 + 20771.1i 0.293143 + 1.45678i
\(589\) −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
\(595\) 589.163 + 746.811i 0.0405938 + 0.0514559i
\(596\) 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 \(0.241801\pi\)
−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 \(-0.544239\pi\)
−0.138534 + 0.990358i \(0.544239\pi\)
\(608\) 26072.2i 1.73909i
\(609\) −10206.9 + 16673.5i −0.679156 + 1.10943i
\(610\) 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 \(0.137472\pi\)
−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
\(630\) 8682.13 23371.6i 0.549054 1.47801i
\(631\) 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 \(-0.661670\pi\)
−0.486345 + 0.873767i \(0.661670\pi\)
\(644\) 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
\(651\) −3089.94 + 5047.55i −0.186028 + 0.303885i
\(652\) 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 \(0.179923\pi\)
−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
\(665\) 15337.8 + 19441.9i 0.894398 + 1.13372i
\(666\) −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
\(672\) −17893.0 10953.5i −1.02714 0.628780i
\(673\) 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 \(-0.991002\pi\)
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
\(693\) 4122.69 14571.1i 0.225986 0.798716i
\(694\) 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
\(700\) 15265.4 + 22898.9i 0.824253 + 1.23643i
\(701\) 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
\(714\) 1029.35 1681.49i 0.0539532 0.0881349i
\(715\) −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 \(-0.260813\pi\)
0.682683 + 0.730715i \(0.260813\pi\)
\(720\) 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 \(-0.505303\pi\)
−0.0166584 + 0.999861i \(0.505303\pi\)
\(728\) −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 \(-0.338511\pi\)
0.485848 + 0.874043i \(0.338511\pi\)
\(734\) 32787.7 1.64880
\(735\) 19786.5 2358.18i 0.992973 0.118344i
\(736\) −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
\(756\) −30888.4 66.1593i −1.48598 0.00318279i
\(757\) 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 \(-0.656354\pi\)
−0.471686 + 0.881767i \(0.656354\pi\)
\(762\) 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 \(-0.111400\pi\)
\(770\) 17320.1 + 21954.6i 0.810613 + 1.02752i
\(771\) 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
\(777\) 16962.1 27708.3i 0.783155 1.27932i
\(778\) 27575.6i 1.27074i
\(779\)