Properties

Label 105.4.g.b.104.19
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 104.19
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.20

$q$-expansion

\(f(q)\) \(=\) \(q-1.22256 q^{2} +(4.91936 - 1.67328i) q^{3} -6.50535 q^{4} +(9.89077 - 5.21274i) q^{5} +(-6.01420 + 2.04568i) q^{6} +(1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +O(q^{10})\) \(q-1.22256 q^{2} +(4.91936 - 1.67328i) q^{3} -6.50535 q^{4} +(9.89077 - 5.21274i) q^{5} +(-6.01420 + 2.04568i) q^{6} +(1.55936 + 18.4545i) q^{7} +17.7336 q^{8} +(21.4003 - 16.4630i) q^{9} +(-12.0920 + 6.37288i) q^{10} -54.5342i q^{11} +(-32.0022 + 10.8853i) q^{12} +24.4972 q^{13} +(-1.90640 - 22.5617i) q^{14} +(39.9339 - 42.1934i) q^{15} +30.3625 q^{16} +36.0147i q^{17} +(-26.1630 + 20.1269i) q^{18} -99.5921i q^{19} +(-64.3430 + 33.9107i) q^{20} +(38.5506 + 88.1751i) q^{21} +66.6712i q^{22} +97.3866 q^{23} +(87.2381 - 29.6733i) q^{24} +(70.6546 - 103.116i) q^{25} -29.9492 q^{26} +(77.7285 - 116.796i) q^{27} +(-10.1442 - 120.053i) q^{28} -14.1008i q^{29} +(-48.8215 + 51.5839i) q^{30} +186.132i q^{31} -178.989 q^{32} +(-91.2510 - 268.273i) q^{33} -44.0300i q^{34} +(111.622 + 174.401i) q^{35} +(-139.216 + 107.097i) q^{36} +199.381i q^{37} +121.757i q^{38} +(120.510 - 40.9906i) q^{39} +(175.399 - 92.4408i) q^{40} -313.963 q^{41} +(-47.1303 - 107.799i) q^{42} -30.0581i q^{43} +354.764i q^{44} +(125.848 - 274.385i) q^{45} -119.061 q^{46} +514.304i q^{47} +(149.364 - 50.8049i) q^{48} +(-338.137 + 57.5542i) q^{49} +(-86.3794 + 126.065i) q^{50} +(60.2627 + 177.169i) q^{51} -159.363 q^{52} -451.022 q^{53} +(-95.0275 + 142.790i) q^{54} +(-284.273 - 539.385i) q^{55} +(27.6530 + 327.265i) q^{56} +(-166.646 - 489.930i) q^{57} +17.2390i q^{58} -355.610 q^{59} +(-259.784 + 274.483i) q^{60} +656.101i q^{61} -227.557i q^{62} +(337.186 + 369.259i) q^{63} -24.0755 q^{64} +(242.296 - 127.697i) q^{65} +(111.560 + 327.980i) q^{66} -73.7273i q^{67} -234.288i q^{68} +(479.080 - 162.955i) q^{69} +(-136.464 - 213.215i) q^{70} -611.294i q^{71} +(379.504 - 291.948i) q^{72} +424.158 q^{73} -243.755i q^{74} +(175.034 - 625.490i) q^{75} +647.882i q^{76} +(1006.40 - 85.0382i) q^{77} +(-147.331 + 50.1134i) q^{78} +814.120 q^{79} +(300.308 - 158.272i) q^{80} +(186.942 - 704.623i) q^{81} +383.838 q^{82} +585.698i q^{83} +(-250.785 - 573.610i) q^{84} +(187.735 + 356.213i) q^{85} +36.7477i q^{86} +(-23.5946 - 69.3670i) q^{87} -967.089i q^{88} +732.894 q^{89} +(-153.856 + 335.452i) q^{90} +(38.1998 + 452.083i) q^{91} -633.535 q^{92} +(311.451 + 915.650i) q^{93} -628.766i q^{94} +(-519.148 - 985.043i) q^{95} +(-880.511 + 299.499i) q^{96} -272.613 q^{97} +(413.392 - 70.3633i) q^{98} +(-897.794 - 1167.05i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22256 −0.432239 −0.216120 0.976367i \(-0.569340\pi\)
−0.216120 + 0.976367i \(0.569340\pi\)
\(3\) 4.91936 1.67328i 0.946732 0.322023i
\(4\) −6.50535 −0.813169
\(5\) 9.89077 5.21274i 0.884657 0.466242i
\(6\) −6.01420 + 2.04568i −0.409215 + 0.139191i
\(7\) 1.55936 + 18.4545i 0.0841973 + 0.996449i
\(8\) 17.7336 0.783723
\(9\) 21.4003 16.4630i 0.792602 0.609739i
\(10\) −12.0920 + 6.37288i −0.382384 + 0.201528i
\(11\) 54.5342i 1.49479i −0.664381 0.747394i \(-0.731305\pi\)
0.664381 0.747394i \(-0.268695\pi\)
\(12\) −32.0022 + 10.8853i −0.769853 + 0.261859i
\(13\) 24.4972 0.522637 0.261319 0.965253i \(-0.415843\pi\)
0.261319 + 0.965253i \(0.415843\pi\)
\(14\) −1.90640 22.5617i −0.0363934 0.430704i
\(15\) 39.9339 42.1934i 0.687393 0.726286i
\(16\) 30.3625 0.474413
\(17\) 36.0147i 0.513815i 0.966436 + 0.256907i \(0.0827035\pi\)
−0.966436 + 0.256907i \(0.917296\pi\)
\(18\) −26.1630 + 20.1269i −0.342594 + 0.263553i
\(19\) 99.5921i 1.20253i −0.799051 0.601263i \(-0.794664\pi\)
0.799051 0.601263i \(-0.205336\pi\)
\(20\) −64.3430 + 33.9107i −0.719376 + 0.379133i
\(21\) 38.5506 + 88.1751i 0.400592 + 0.916257i
\(22\) 66.6712i 0.646106i
\(23\) 97.3866 0.882892 0.441446 0.897288i \(-0.354466\pi\)
0.441446 + 0.897288i \(0.354466\pi\)
\(24\) 87.2381 29.6733i 0.741975 0.252377i
\(25\) 70.6546 103.116i 0.565237 0.824928i
\(26\) −29.9492 −0.225904
\(27\) 77.7285 116.796i 0.554032 0.832496i
\(28\) −10.1442 120.053i −0.0684666 0.810282i
\(29\) 14.1008i 0.0902915i −0.998980 0.0451457i \(-0.985625\pi\)
0.998980 0.0451457i \(-0.0143752\pi\)
\(30\) −48.8215 + 51.5839i −0.297118 + 0.313929i
\(31\) 186.132i 1.07840i 0.842179 + 0.539198i \(0.181272\pi\)
−0.842179 + 0.539198i \(0.818728\pi\)
\(32\) −178.989 −0.988783
\(33\) −91.2510 268.273i −0.481356 1.41516i
\(34\) 44.0300i 0.222091i
\(35\) 111.622 + 174.401i 0.539072 + 0.842260i
\(36\) −139.216 + 107.097i −0.644520 + 0.495821i
\(37\) 199.381i 0.885894i 0.896548 + 0.442947i \(0.146067\pi\)
−0.896548 + 0.442947i \(0.853933\pi\)
\(38\) 121.757i 0.519779i
\(39\) 120.510 40.9906i 0.494798 0.168301i
\(40\) 175.399 92.4408i 0.693326 0.365404i
\(41\) −313.963 −1.19592 −0.597961 0.801525i \(-0.704022\pi\)
−0.597961 + 0.801525i \(0.704022\pi\)
\(42\) −47.1303 107.799i −0.173152 0.396042i
\(43\) 30.0581i 0.106600i −0.998579 0.0533002i \(-0.983026\pi\)
0.998579 0.0533002i \(-0.0169740\pi\)
\(44\) 354.764i 1.21552i
\(45\) 125.848 274.385i 0.416896 0.908954i
\(46\) −119.061 −0.381621
\(47\) 514.304i 1.59615i 0.602559 + 0.798074i \(0.294148\pi\)
−0.602559 + 0.798074i \(0.705852\pi\)
\(48\) 149.364 50.8049i 0.449142 0.152772i
\(49\) −338.137 + 57.5542i −0.985822 + 0.167797i
\(50\) −86.3794 + 126.065i −0.244318 + 0.356567i
\(51\) 60.2627 + 177.169i 0.165460 + 0.486445i
\(52\) −159.363 −0.424993
\(53\) −451.022 −1.16892 −0.584458 0.811424i \(-0.698693\pi\)
−0.584458 + 0.811424i \(0.698693\pi\)
\(54\) −95.0275 + 142.790i −0.239474 + 0.359837i
\(55\) −284.273 539.385i −0.696933 1.32238i
\(56\) 27.6530 + 327.265i 0.0659873 + 0.780940i
\(57\) −166.646 489.930i −0.387241 1.13847i
\(58\) 17.2390i 0.0390275i
\(59\) −355.610 −0.784686 −0.392343 0.919819i \(-0.628335\pi\)
−0.392343 + 0.919819i \(0.628335\pi\)
\(60\) −259.784 + 274.483i −0.558966 + 0.590593i
\(61\) 656.101i 1.37713i 0.725173 + 0.688566i \(0.241760\pi\)
−0.725173 + 0.688566i \(0.758240\pi\)
\(62\) 227.557i 0.466125i
\(63\) 337.186 + 369.259i 0.674309 + 0.738449i
\(64\) −24.0755 −0.0470224
\(65\) 242.296 127.697i 0.462355 0.243675i
\(66\) 111.560 + 327.980i 0.208061 + 0.611689i
\(67\) 73.7273i 0.134436i −0.997738 0.0672181i \(-0.978588\pi\)
0.997738 0.0672181i \(-0.0214123\pi\)
\(68\) 234.288i 0.417818i
\(69\) 479.080 162.955i 0.835862 0.284312i
\(70\) −136.464 213.215i −0.233008 0.364058i
\(71\) 611.294i 1.02179i −0.859643 0.510896i \(-0.829314\pi\)
0.859643 0.510896i \(-0.170686\pi\)
\(72\) 379.504 291.948i 0.621181 0.477866i
\(73\) 424.158 0.680053 0.340027 0.940416i \(-0.389564\pi\)
0.340027 + 0.940416i \(0.389564\pi\)
\(74\) 243.755i 0.382918i
\(75\) 175.034 625.490i 0.269482 0.963005i
\(76\) 647.882i 0.977858i
\(77\) 1006.40 85.0382i 1.48948 0.125857i
\(78\) −147.331 + 50.1134i −0.213871 + 0.0727465i
\(79\) 814.120 1.15944 0.579719 0.814816i \(-0.303162\pi\)
0.579719 + 0.814816i \(0.303162\pi\)
\(80\) 300.308 158.272i 0.419693 0.221191i
\(81\) 186.942 704.623i 0.256437 0.966561i
\(82\) 383.838 0.516925
\(83\) 585.698i 0.774562i 0.921962 + 0.387281i \(0.126586\pi\)
−0.921962 + 0.387281i \(0.873414\pi\)
\(84\) −250.785 573.610i −0.325749 0.745072i
\(85\) 187.735 + 356.213i 0.239562 + 0.454550i
\(86\) 36.7477i 0.0460769i
\(87\) −23.5946 69.3670i −0.0290759 0.0854818i
\(88\) 967.089i 1.17150i
\(89\) 732.894 0.872883 0.436442 0.899733i \(-0.356239\pi\)
0.436442 + 0.899733i \(0.356239\pi\)
\(90\) −153.856 + 335.452i −0.180199 + 0.392886i
\(91\) 38.1998 + 452.083i 0.0440047 + 0.520782i
\(92\) −633.535 −0.717941
\(93\) 311.451 + 915.650i 0.347268 + 1.02095i
\(94\) 628.766i 0.689918i
\(95\) −519.148 985.043i −0.560668 1.06382i
\(96\) −880.511 + 299.499i −0.936112 + 0.318411i
\(97\) −272.613 −0.285357 −0.142678 0.989769i \(-0.545571\pi\)
−0.142678 + 0.989769i \(0.545571\pi\)
\(98\) 413.392 70.3633i 0.426111 0.0725283i
\(99\) −897.794 1167.05i −0.911431 1.18477i
\(100\) −459.633 + 670.806i −0.459633 + 0.670806i
\(101\) −1204.16 −1.18632 −0.593161 0.805084i \(-0.702120\pi\)
−0.593161 + 0.805084i \(0.702120\pi\)
\(102\) −73.6746 216.600i −0.0715184 0.210260i
\(103\) −1737.25 −1.66190 −0.830952 0.556344i \(-0.812204\pi\)
−0.830952 + 0.556344i \(0.812204\pi\)
\(104\) 434.423 0.409603
\(105\) 840.929 + 671.165i 0.781584 + 0.623800i
\(106\) 551.400 0.505252
\(107\) 939.557 0.848882 0.424441 0.905456i \(-0.360471\pi\)
0.424441 + 0.905456i \(0.360471\pi\)
\(108\) −505.651 + 759.799i −0.450522 + 0.676960i
\(109\) 515.039 0.452585 0.226293 0.974059i \(-0.427339\pi\)
0.226293 + 0.974059i \(0.427339\pi\)
\(110\) 347.540 + 659.429i 0.301242 + 0.571583i
\(111\) 333.621 + 980.829i 0.285278 + 0.838704i
\(112\) 47.3459 + 560.324i 0.0399443 + 0.472729i
\(113\) −371.631 −0.309381 −0.154691 0.987963i \(-0.549438\pi\)
−0.154691 + 0.987963i \(0.549438\pi\)
\(114\) 203.734 + 598.967i 0.167381 + 0.492092i
\(115\) 963.229 507.651i 0.781057 0.411641i
\(116\) 91.7307i 0.0734223i
\(117\) 524.245 403.295i 0.414244 0.318672i
\(118\) 434.753 0.339172
\(119\) −664.633 + 56.1597i −0.511990 + 0.0432618i
\(120\) 708.173 748.242i 0.538725 0.569207i
\(121\) −1642.98 −1.23439
\(122\) 802.121i 0.595251i
\(123\) −1544.50 + 525.349i −1.13222 + 0.385115i
\(124\) 1210.85i 0.876918i
\(125\) 161.311 1388.20i 0.115425 0.993316i
\(126\) −412.229 451.441i −0.291463 0.319187i
\(127\) 56.0497i 0.0391623i −0.999808 0.0195811i \(-0.993767\pi\)
0.999808 0.0195811i \(-0.00623327\pi\)
\(128\) 1461.34 1.00911
\(129\) −50.2956 147.867i −0.0343278 0.100922i
\(130\) −296.220 + 156.117i −0.199848 + 0.105326i
\(131\) 2147.48 1.43226 0.716132 0.697965i \(-0.245911\pi\)
0.716132 + 0.697965i \(0.245911\pi\)
\(132\) 593.620 + 1745.21i 0.391424 + 1.15077i
\(133\) 1837.92 155.300i 1.19826 0.101249i
\(134\) 90.1358i 0.0581086i
\(135\) 159.968 1560.38i 0.101984 0.994786i
\(136\) 638.671i 0.402688i
\(137\) −2872.66 −1.79145 −0.895724 0.444611i \(-0.853342\pi\)
−0.895724 + 0.444611i \(0.853342\pi\)
\(138\) −585.703 + 199.222i −0.361292 + 0.122891i
\(139\) 651.443i 0.397516i 0.980049 + 0.198758i \(0.0636907\pi\)
−0.980049 + 0.198758i \(0.936309\pi\)
\(140\) −726.139 1134.54i −0.438357 0.684900i
\(141\) 860.576 + 2530.05i 0.513997 + 1.51112i
\(142\) 747.342i 0.441659i
\(143\) 1335.93i 0.781233i
\(144\) 649.764 499.856i 0.376021 0.289268i
\(145\) −73.5038 139.468i −0.0420977 0.0798770i
\(146\) −518.557 −0.293946
\(147\) −1567.11 + 848.928i −0.879274 + 0.476316i
\(148\) 1297.05i 0.720382i
\(149\) 2941.51i 1.61730i 0.588288 + 0.808652i \(0.299802\pi\)
−0.588288 + 0.808652i \(0.700198\pi\)
\(150\) −213.989 + 764.698i −0.116481 + 0.416249i
\(151\) 717.383 0.386621 0.193311 0.981138i \(-0.438077\pi\)
0.193311 + 0.981138i \(0.438077\pi\)
\(152\) 1766.13i 0.942448i
\(153\) 592.908 + 770.724i 0.313293 + 0.407251i
\(154\) −1230.38 + 103.964i −0.643812 + 0.0544004i
\(155\) 970.257 + 1840.99i 0.502793 + 0.954010i
\(156\) −783.963 + 266.658i −0.402354 + 0.136857i
\(157\) −725.468 −0.368781 −0.184391 0.982853i \(-0.559031\pi\)
−0.184391 + 0.982853i \(0.559031\pi\)
\(158\) −995.308 −0.501155
\(159\) −2218.74 + 754.686i −1.10665 + 0.376418i
\(160\) −1770.34 + 933.023i −0.874734 + 0.461012i
\(161\) 151.860 + 1797.22i 0.0743371 + 0.879757i
\(162\) −228.548 + 861.442i −0.110842 + 0.417786i
\(163\) 2478.01i 1.19076i −0.803446 0.595378i \(-0.797002\pi\)
0.803446 0.595378i \(-0.202998\pi\)
\(164\) 2042.44 0.972487
\(165\) −2300.98 2177.76i −1.08564 1.02751i
\(166\) 716.049i 0.334796i
\(167\) 392.827i 0.182023i 0.995850 + 0.0910117i \(0.0290101\pi\)
−0.995850 + 0.0910117i \(0.970990\pi\)
\(168\) 683.642 + 1563.66i 0.313953 + 0.718091i
\(169\) −1596.89 −0.726850
\(170\) −229.517 435.491i −0.103548 0.196474i
\(171\) −1639.58 2131.30i −0.733227 0.953125i
\(172\) 195.538i 0.0866841i
\(173\) 1758.06i 0.772615i 0.922370 + 0.386308i \(0.126250\pi\)
−0.922370 + 0.386308i \(0.873750\pi\)
\(174\) 28.8458 + 84.8051i 0.0125678 + 0.0369486i
\(175\) 2013.13 + 1143.10i 0.869591 + 0.493773i
\(176\) 1655.79i 0.709148i
\(177\) −1749.37 + 595.035i −0.742887 + 0.252687i
\(178\) −896.005 −0.377294
\(179\) 561.038i 0.234268i −0.993116 0.117134i \(-0.962629\pi\)
0.993116 0.117134i \(-0.0373707\pi\)
\(180\) −818.685 + 1784.97i −0.339007 + 0.739134i
\(181\) 3519.60i 1.44536i −0.691183 0.722680i \(-0.742910\pi\)
0.691183 0.722680i \(-0.257090\pi\)
\(182\) −46.7014 552.697i −0.0190205 0.225102i
\(183\) 1097.84 + 3227.60i 0.443469 + 1.30378i
\(184\) 1727.02 0.691943
\(185\) 1039.32 + 1972.03i 0.413041 + 0.783712i
\(186\) −380.766 1119.43i −0.150103 0.441295i
\(187\) 1964.03 0.768044
\(188\) 3345.73i 1.29794i
\(189\) 2276.62 + 1252.31i 0.876187 + 0.481971i
\(190\) 634.688 + 1204.27i 0.242343 + 0.459826i
\(191\) 2737.21i 1.03695i −0.855093 0.518475i \(-0.826500\pi\)
0.855093 0.518475i \(-0.173500\pi\)
\(192\) −118.436 + 40.2851i −0.0445176 + 0.0151423i
\(193\) 1381.34i 0.515186i −0.966253 0.257593i \(-0.917071\pi\)
0.966253 0.257593i \(-0.0829294\pi\)
\(194\) 333.284 0.123342
\(195\) 978.267 1033.62i 0.359257 0.379584i
\(196\) 2199.70 374.411i 0.801640 0.136447i
\(197\) 474.652 0.171663 0.0858314 0.996310i \(-0.472645\pi\)
0.0858314 + 0.996310i \(0.472645\pi\)
\(198\) 1097.60 + 1426.78i 0.393956 + 0.512105i
\(199\) 3657.03i 1.30271i 0.758772 + 0.651357i \(0.225800\pi\)
−0.758772 + 0.651357i \(0.774200\pi\)
\(200\) 1252.96 1828.62i 0.442989 0.646515i
\(201\) −123.366 362.691i −0.0432915 0.127275i
\(202\) 1472.16 0.512775
\(203\) 260.223 21.9882i 0.0899709 0.00760230i
\(204\) −392.030 1152.55i −0.134547 0.395562i
\(205\) −3105.34 + 1636.61i −1.05798 + 0.557589i
\(206\) 2123.88 0.718340
\(207\) 2084.10 1603.27i 0.699782 0.538334i
\(208\) 743.794 0.247946
\(209\) −5431.18 −1.79752
\(210\) −1028.08 820.538i −0.337831 0.269631i
\(211\) −266.470 −0.0869410 −0.0434705 0.999055i \(-0.513841\pi\)
−0.0434705 + 0.999055i \(0.513841\pi\)
\(212\) 2934.05 0.950527
\(213\) −1022.87 3007.18i −0.329041 0.967363i
\(214\) −1148.66 −0.366920
\(215\) −156.685 297.298i −0.0497015 0.0943048i
\(216\) 1378.41 2071.21i 0.434207 0.652446i
\(217\) −3434.97 + 290.246i −1.07457 + 0.0907979i
\(218\) −629.665 −0.195625
\(219\) 2086.58 709.735i 0.643828 0.218993i
\(220\) 1849.29 + 3508.89i 0.566724 + 1.07532i
\(221\) 882.258i 0.268539i
\(222\) −407.871 1199.12i −0.123308 0.362521i
\(223\) −1634.62 −0.490863 −0.245431 0.969414i \(-0.578930\pi\)
−0.245431 + 0.969414i \(0.578930\pi\)
\(224\) −279.107 3303.15i −0.0832528 0.985272i
\(225\) −185.567 3369.89i −0.0549829 0.998487i
\(226\) 454.340 0.133727
\(227\) 2561.56i 0.748972i 0.927232 + 0.374486i \(0.122181\pi\)
−0.927232 + 0.374486i \(0.877819\pi\)
\(228\) 1084.09 + 3187.17i 0.314893 + 0.925769i
\(229\) 4252.03i 1.22699i 0.789697 + 0.613497i \(0.210238\pi\)
−0.789697 + 0.613497i \(0.789762\pi\)
\(230\) −1177.60 + 620.633i −0.337604 + 0.177928i
\(231\) 4808.56 2102.33i 1.36961 0.598800i
\(232\) 250.058i 0.0707635i
\(233\) −3657.28 −1.02831 −0.514156 0.857697i \(-0.671895\pi\)
−0.514156 + 0.857697i \(0.671895\pi\)
\(234\) −640.920 + 493.052i −0.179052 + 0.137743i
\(235\) 2680.94 + 5086.86i 0.744191 + 1.41204i
\(236\) 2313.37 0.638082
\(237\) 4004.95 1362.25i 1.09768 0.373366i
\(238\) 812.552 68.6585i 0.221302 0.0186994i
\(239\) 1938.73i 0.524710i −0.964971 0.262355i \(-0.915501\pi\)
0.964971 0.262355i \(-0.0844992\pi\)
\(240\) 1212.49 1281.10i 0.326108 0.344560i
\(241\) 5100.72i 1.36334i −0.731658 0.681672i \(-0.761253\pi\)
0.731658 0.681672i \(-0.238747\pi\)
\(242\) 2008.63 0.533553
\(243\) −259.395 3779.10i −0.0684782 0.997653i
\(244\) 4268.17i 1.11984i
\(245\) −3044.42 + 2331.88i −0.793881 + 0.608074i
\(246\) 1888.24 642.269i 0.489389 0.166462i
\(247\) 2439.72i 0.628485i
\(248\) 3300.79i 0.845163i
\(249\) 980.037 + 2881.26i 0.249427 + 0.733303i
\(250\) −197.212 + 1697.16i −0.0498912 + 0.429350i
\(251\) −1834.02 −0.461205 −0.230603 0.973048i \(-0.574070\pi\)
−0.230603 + 0.973048i \(0.574070\pi\)
\(252\) −2193.51 2402.16i −0.548327 0.600484i
\(253\) 5310.90i 1.31974i
\(254\) 68.5240i 0.0169275i
\(255\) 1519.58 + 1438.21i 0.373176 + 0.353192i
\(256\) −1593.97 −0.389154
\(257\) 7667.08i 1.86093i 0.366380 + 0.930465i \(0.380597\pi\)
−0.366380 + 0.930465i \(0.619403\pi\)
\(258\) 61.4893 + 180.775i 0.0148378 + 0.0436224i
\(259\) −3679.48 + 310.906i −0.882748 + 0.0745898i
\(260\) −1576.22 + 830.716i −0.375973 + 0.198149i
\(261\) −232.141 301.761i −0.0550542 0.0715652i
\(262\) −2625.42 −0.619081
\(263\) 6022.49 1.41203 0.706013 0.708199i \(-0.250492\pi\)
0.706013 + 0.708199i \(0.250492\pi\)
\(264\) −1618.21 4757.46i −0.377250 1.10910i
\(265\) −4460.95 + 2351.06i −1.03409 + 0.544998i
\(266\) −2246.97 + 189.863i −0.517934 + 0.0437640i
\(267\) 3605.37 1226.34i 0.826386 0.281089i
\(268\) 479.622i 0.109319i
\(269\) 3060.15 0.693609 0.346805 0.937937i \(-0.387267\pi\)
0.346805 + 0.937937i \(0.387267\pi\)
\(270\) −195.570 + 1907.65i −0.0440815 + 0.429986i
\(271\) 4427.98i 0.992547i −0.868166 0.496274i \(-0.834701\pi\)
0.868166 0.496274i \(-0.165299\pi\)
\(272\) 1093.49i 0.243760i
\(273\) 944.380 + 2160.04i 0.209364 + 0.478870i
\(274\) 3512.00 0.774334
\(275\) −5623.35 3853.09i −1.23309 0.844910i
\(276\) −3116.59 + 1060.08i −0.679697 + 0.231193i
\(277\) 2979.18i 0.646216i 0.946362 + 0.323108i \(0.104728\pi\)
−0.946362 + 0.323108i \(0.895272\pi\)
\(278\) 796.426i 0.171822i
\(279\) 3064.28 + 3983.27i 0.657540 + 0.854738i
\(280\) 1979.46 + 3092.76i 0.422483 + 0.660098i
\(281\) 2966.90i 0.629859i 0.949115 + 0.314930i \(0.101981\pi\)
−0.949115 + 0.314930i \(0.898019\pi\)
\(282\) −1052.10 3093.13i −0.222170 0.653167i
\(283\) 5731.24 1.20384 0.601920 0.798556i \(-0.294402\pi\)
0.601920 + 0.798556i \(0.294402\pi\)
\(284\) 3976.68i 0.830890i
\(285\) −4202.13 3977.10i −0.873378 0.826608i
\(286\) 1633.25i 0.337679i
\(287\) −489.580 5794.03i −0.100693 1.19168i
\(288\) −3830.41 + 2946.69i −0.783712 + 0.602900i
\(289\) 3615.94 0.735995
\(290\) 89.8627 + 170.507i 0.0181963 + 0.0345260i
\(291\) −1341.08 + 456.157i −0.270156 + 0.0918915i
\(292\) −2759.29 −0.552998
\(293\) 1743.02i 0.347537i 0.984787 + 0.173768i \(0.0555944\pi\)
−0.984787 + 0.173768i \(0.944406\pi\)
\(294\) 1915.89 1037.86i 0.380057 0.205882i
\(295\) −3517.25 + 1853.70i −0.694178 + 0.365853i
\(296\) 3535.75i 0.694295i
\(297\) −6369.37 4238.86i −1.24440 0.828160i
\(298\) 3596.17i 0.699062i
\(299\) 2385.70 0.461432
\(300\) −1138.66 + 4069.04i −0.219134 + 0.783086i
\(301\) 554.707 46.8712i 0.106222 0.00897546i
\(302\) −877.042 −0.167113
\(303\) −5923.71 + 2014.90i −1.12313 + 0.382023i
\(304\) 3023.86i 0.570495i
\(305\) 3420.08 + 6489.34i 0.642077 + 1.21829i
\(306\) −724.864 942.254i −0.135417 0.176030i
\(307\) 10595.5 1.96976 0.984878 0.173247i \(-0.0554260\pi\)
0.984878 + 0.173247i \(0.0554260\pi\)
\(308\) −6546.99 + 553.203i −1.21120 + 0.102343i
\(309\) −8546.15 + 2906.90i −1.57338 + 0.535171i
\(310\) −1186.19 2250.71i −0.217327 0.412361i
\(311\) −3683.11 −0.671543 −0.335772 0.941943i \(-0.608997\pi\)
−0.335772 + 0.941943i \(0.608997\pi\)
\(312\) 2137.09 726.912i 0.387784 0.131902i
\(313\) −82.6926 −0.0149331 −0.00746655 0.999972i \(-0.502377\pi\)
−0.00746655 + 0.999972i \(0.502377\pi\)
\(314\) 886.926 0.159402
\(315\) 5259.88 + 1894.60i 0.940828 + 0.338884i
\(316\) −5296.14 −0.942820
\(317\) −8772.72 −1.55434 −0.777168 0.629293i \(-0.783345\pi\)
−0.777168 + 0.629293i \(0.783345\pi\)
\(318\) 2712.53 922.647i 0.478338 0.162703i
\(319\) −768.976 −0.134967
\(320\) −238.125 + 125.499i −0.0415987 + 0.0219238i
\(321\) 4622.02 1572.14i 0.803664 0.273360i
\(322\) −185.658 2197.21i −0.0321314 0.380266i
\(323\) 3586.78 0.617876
\(324\) −1216.13 + 4583.82i −0.208526 + 0.785978i
\(325\) 1730.84 2526.05i 0.295414 0.431139i
\(326\) 3029.51i 0.514691i
\(327\) 2533.66 861.805i 0.428477 0.145743i
\(328\) −5567.71 −0.937272
\(329\) −9491.22 + 801.983i −1.59048 + 0.134391i
\(330\) 2813.08 + 2662.44i 0.469258 + 0.444129i
\(331\) 6259.67 1.03946 0.519732 0.854329i \(-0.326032\pi\)
0.519732 + 0.854329i \(0.326032\pi\)
\(332\) 3810.17i 0.629850i
\(333\) 3282.40 + 4266.81i 0.540164 + 0.702161i
\(334\) 480.254i 0.0786776i
\(335\) −384.321 729.220i −0.0626797 0.118930i
\(336\) 1170.49 + 2677.21i 0.190046 + 0.434684i
\(337\) 8203.39i 1.32602i 0.748612 + 0.663008i \(0.230720\pi\)
−0.748612 + 0.663008i \(0.769280\pi\)
\(338\) 1952.29 0.314173
\(339\) −1828.19 + 621.843i −0.292901 + 0.0996279i
\(340\) −1221.28 2317.29i −0.194804 0.369626i
\(341\) 10150.5 1.61197
\(342\) 2004.48 + 2605.63i 0.316930 + 0.411978i
\(343\) −1589.41 6150.40i −0.250204 0.968193i
\(344\) 533.039i 0.0835451i
\(345\) 3889.03 4109.07i 0.606893 0.641232i
\(346\) 2149.32i 0.333955i
\(347\) 2993.06 0.463043 0.231521 0.972830i \(-0.425630\pi\)
0.231521 + 0.972830i \(0.425630\pi\)
\(348\) 153.491 + 451.257i 0.0236437 + 0.0695112i
\(349\) 7305.70i 1.12053i 0.828313 + 0.560265i \(0.189301\pi\)
−0.828313 + 0.560265i \(0.810699\pi\)
\(350\) −2461.17 1397.51i −0.375871 0.213428i
\(351\) 1904.13 2861.17i 0.289558 0.435093i
\(352\) 9761.01i 1.47802i
\(353\) 6126.46i 0.923735i 0.886949 + 0.461867i \(0.152820\pi\)
−0.886949 + 0.461867i \(0.847180\pi\)
\(354\) 2138.71 727.465i 0.321105 0.109221i
\(355\) −3186.52 6046.17i −0.476402 0.903936i
\(356\) −4767.74 −0.709802
\(357\) −3175.60 + 1388.39i −0.470786 + 0.205830i
\(358\) 685.901i 0.101260i
\(359\) 8351.09i 1.22773i −0.789413 0.613863i \(-0.789615\pi\)
0.789413 0.613863i \(-0.210385\pi\)
\(360\) 2231.74 4865.85i 0.326731 0.712368i
\(361\) −3059.59 −0.446070
\(362\) 4302.92i 0.624741i
\(363\) −8082.40 + 2749.16i −1.16864 + 0.397503i
\(364\) −248.503 2940.96i −0.0357832 0.423484i
\(365\) 4195.24 2211.02i 0.601614 0.317069i
\(366\) −1342.17 3945.92i −0.191685 0.563543i
\(367\) −10233.1 −1.45549 −0.727745 0.685848i \(-0.759432\pi\)
−0.727745 + 0.685848i \(0.759432\pi\)
\(368\) 2956.90 0.418856
\(369\) −6718.90 + 5168.76i −0.947891 + 0.729201i
\(370\) −1270.63 2410.92i −0.178532 0.338751i
\(371\) −703.303 8323.37i −0.0984196 1.16477i
\(372\) −2026.10 5956.62i −0.282388 0.830206i
\(373\) 9039.05i 1.25476i −0.778715 0.627378i \(-0.784128\pi\)
0.778715 0.627378i \(-0.215872\pi\)
\(374\) −2401.14 −0.331979
\(375\) −1529.30 7098.99i −0.210594 0.977574i
\(376\) 9120.48i 1.25094i
\(377\) 345.429i 0.0471897i
\(378\) −2783.29 1531.03i −0.378723 0.208327i
\(379\) 5342.32 0.724054 0.362027 0.932168i \(-0.382085\pi\)
0.362027 + 0.932168i \(0.382085\pi\)
\(380\) 3377.24 + 6408.05i 0.455918 + 0.865069i
\(381\) −93.7869 275.729i −0.0126112 0.0370762i
\(382\) 3346.40i 0.448211i
\(383\) 2265.22i 0.302213i 0.988518 + 0.151106i \(0.0482836\pi\)
−0.988518 + 0.151106i \(0.951716\pi\)
\(384\) 7188.88 2445.24i 0.955355 0.324956i
\(385\) 9510.80 6087.20i 1.25900 0.805799i
\(386\) 1688.77i 0.222684i
\(387\) −494.845 643.251i −0.0649984 0.0844917i
\(388\) 1773.44 0.232043
\(389\) 2359.74i 0.307567i −0.988105 0.153783i \(-0.950854\pi\)
0.988105 0.153783i \(-0.0491458\pi\)
\(390\) −1195.99 + 1263.66i −0.155285 + 0.164071i
\(391\) 3507.35i 0.453643i
\(392\) −5996.39 + 1020.65i −0.772611 + 0.131506i
\(393\) 10564.3 3593.35i 1.35597 0.461222i
\(394\) −580.289 −0.0741994
\(395\) 8052.27 4243.80i 1.02571 0.540579i
\(396\) 5840.47 + 7592.05i 0.741148 + 0.963421i
\(397\) 3203.32 0.404962 0.202481 0.979286i \(-0.435100\pi\)
0.202481 + 0.979286i \(0.435100\pi\)
\(398\) 4470.93i 0.563084i
\(399\) 8781.55 3839.34i 1.10182 0.481722i
\(400\) 2145.25 3130.86i 0.268156 0.391357i
\(401\) 4753.14i 0.591921i −0.955200 0.295961i \(-0.904360\pi\)
0.955200 0.295961i \(-0.0956397\pi\)
\(402\) 150.823 + 443.411i 0.0187123 + 0.0550132i
\(403\) 4559.70i 0.563610i
\(404\) 7833.50 0.964681
\(405\) −1824.01 7943.75i −0.223793 0.974637i
\(406\) −318.138 + 26.8818i −0.0388889 + 0.00328601i
\(407\) 10873.1 1.32422
\(408\) 1068.68 + 3141.86i 0.129675 + 0.381238i
\(409\) 1599.93i 0.193427i 0.995312 + 0.0967134i \(0.0308330\pi\)
−0.995312 + 0.0967134i \(0.969167\pi\)
\(410\) 3796.45 2000.85i 0.457301 0.241012i
\(411\) −14131.7 + 4806.78i −1.69602 + 0.576887i
\(412\) 11301.4 1.35141
\(413\) −554.522 6562.60i −0.0660684 0.781899i
\(414\) −2547.93 + 1960.09i −0.302473 + 0.232689i
\(415\) 3053.09 + 5793.00i 0.361133 + 0.685222i
\(416\) −4384.72 −0.516775
\(417\) 1090.05 + 3204.68i 0.128009 + 0.376341i
\(418\) 6639.92 0.776960
\(419\) 6140.88 0.715995 0.357997 0.933723i \(-0.383460\pi\)
0.357997 + 0.933723i \(0.383460\pi\)
\(420\) −5470.54 4366.17i −0.635560 0.507255i
\(421\) 2459.78 0.284757 0.142378 0.989812i \(-0.454525\pi\)
0.142378 + 0.989812i \(0.454525\pi\)
\(422\) 325.775 0.0375793
\(423\) 8466.97 + 11006.2i 0.973234 + 1.26511i
\(424\) −7998.25 −0.916107
\(425\) 3713.69 + 2544.61i 0.423860 + 0.290427i
\(426\) 1250.51 + 3676.45i 0.142224 + 0.418132i
\(427\) −12108.0 + 1023.09i −1.37224 + 0.115951i
\(428\) −6112.15 −0.690285
\(429\) −2235.39 6571.93i −0.251575 0.739618i
\(430\) 191.556 + 363.463i 0.0214830 + 0.0407622i
\(431\) 5814.41i 0.649815i −0.945746 0.324907i \(-0.894667\pi\)
0.945746 0.324907i \(-0.105333\pi\)
\(432\) 2360.03 3546.21i 0.262840 0.394947i
\(433\) −6273.51 −0.696272 −0.348136 0.937444i \(-0.613185\pi\)
−0.348136 + 0.937444i \(0.613185\pi\)
\(434\) 4199.44 354.842i 0.464470 0.0392464i
\(435\) −594.961 563.100i −0.0655775 0.0620657i
\(436\) −3350.51 −0.368028
\(437\) 9698.94i 1.06170i
\(438\) −2550.97 + 867.691i −0.278288 + 0.0946573i
\(439\) 8309.95i 0.903445i −0.892158 0.451723i \(-0.850810\pi\)
0.892158 0.451723i \(-0.149190\pi\)
\(440\) −5041.18 9565.25i −0.546202 1.03638i
\(441\) −6288.70 + 6798.41i −0.679052 + 0.734090i
\(442\) 1078.61i 0.116073i
\(443\) −2263.02 −0.242707 −0.121354 0.992609i \(-0.538724\pi\)
−0.121354 + 0.992609i \(0.538724\pi\)
\(444\) −2170.32 6380.64i −0.231979 0.682008i
\(445\) 7248.89 3820.39i 0.772203 0.406975i
\(446\) 1998.42 0.212170
\(447\) 4921.98 + 14470.4i 0.520809 + 1.53115i
\(448\) −37.5422 444.301i −0.00395916 0.0468555i
\(449\) 1895.08i 0.199186i 0.995028 + 0.0995928i \(0.0317540\pi\)
−0.995028 + 0.0995928i \(0.968246\pi\)
\(450\) 226.866 + 4119.89i 0.0237658 + 0.431585i
\(451\) 17121.7i 1.78765i
\(452\) 2417.59 0.251579
\(453\) 3529.07 1200.38i 0.366027 0.124501i
\(454\) 3131.65i 0.323735i
\(455\) 2734.41 + 4272.32i 0.281739 + 0.440196i
\(456\) −2955.23 8688.23i −0.303490 0.892245i
\(457\) 10430.5i 1.06766i −0.845592 0.533829i \(-0.820752\pi\)
0.845592 0.533829i \(-0.179248\pi\)
\(458\) 5198.35i 0.530355i
\(459\) 4206.37 + 2799.37i 0.427748 + 0.284670i
\(460\) −6266.14 + 3302.45i −0.635131 + 0.334734i
\(461\) −7025.94 −0.709828 −0.354914 0.934899i \(-0.615490\pi\)
−0.354914 + 0.934899i \(0.615490\pi\)
\(462\) −5878.74 + 2570.21i −0.591999 + 0.258825i
\(463\) 12799.1i 1.28472i 0.766405 + 0.642358i \(0.222044\pi\)
−0.766405 + 0.642358i \(0.777956\pi\)
\(464\) 428.135i 0.0428355i
\(465\) 7853.53 + 7432.97i 0.783223 + 0.741281i
\(466\) 4471.24 0.444476
\(467\) 14926.4i 1.47904i −0.673134 0.739520i \(-0.735052\pi\)
0.673134 0.739520i \(-0.264948\pi\)
\(468\) −3410.40 + 2623.58i −0.336850 + 0.259135i
\(469\) 1360.60 114.967i 0.133959 0.0113192i
\(470\) −3277.60 6218.98i −0.321669 0.610341i
\(471\) −3568.84 + 1213.91i −0.349137 + 0.118756i
\(472\) −6306.25 −0.614976
\(473\) −1639.19 −0.159345
\(474\) −4896.28 + 1665.43i −0.474459 + 0.161383i
\(475\) −10269.5 7036.65i −0.991998 0.679713i
\(476\) 4323.67 365.339i 0.416335 0.0351792i
\(477\) −9651.98 + 7425.15i −0.926486 + 0.712734i
\(478\) 2370.20i 0.226800i
\(479\) −1243.12 −0.118579 −0.0592897 0.998241i \(-0.518884\pi\)
−0.0592897 + 0.998241i \(0.518884\pi\)
\(480\) −7147.72 + 7552.15i −0.679682 + 0.718139i
\(481\) 4884.27i 0.463001i
\(482\) 6235.92i 0.589291i
\(483\) 3754.31 + 8587.08i 0.353679 + 0.808956i
\(484\) 10688.1 1.00377
\(485\) −2696.35 + 1421.06i −0.252443 + 0.133045i
\(486\) 317.126 + 4620.17i 0.0295990 + 0.431225i
\(487\) 11664.2i 1.08533i −0.839949 0.542665i \(-0.817415\pi\)
0.839949 0.542665i \(-0.182585\pi\)
\(488\) 11635.0i 1.07929i
\(489\) −4146.41 12190.3i −0.383451 1.12733i
\(490\) 3721.98 2850.85i 0.343146 0.262833i
\(491\) 15943.8i 1.46544i 0.680530 + 0.732721i \(0.261750\pi\)
−0.680530 + 0.732721i \(0.738250\pi\)
\(492\) 10047.5 3417.58i 0.920685 0.313163i
\(493\) 507.836 0.0463931
\(494\) 2982.70i 0.271656i
\(495\) −14963.4 6863.01i −1.35869 0.623171i
\(496\) 5651.42i 0.511605i
\(497\) 11281.1 953.224i 1.01816 0.0860321i
\(498\) −1198.15 3522.50i −0.107812 0.316962i
\(499\) −20046.9 −1.79844 −0.899221 0.437494i \(-0.855866\pi\)
−0.899221 + 0.437494i \(0.855866\pi\)
\(500\) −1049.39 + 9030.74i −0.0938601 + 0.807734i
\(501\) 657.311 + 1932.46i 0.0586157 + 0.172327i
\(502\) 2242.20 0.199351
\(503\) 20523.9i 1.81931i −0.415361 0.909657i \(-0.636345\pi\)
0.415361 0.909657i \(-0.363655\pi\)
\(504\) 5979.53 + 6548.31i 0.528471 + 0.578740i
\(505\) −11910.1 + 6276.99i −1.04949 + 0.553113i
\(506\) 6492.88i 0.570442i
\(507\) −7855.68 + 2672.05i −0.688132 + 0.234063i
\(508\) 364.623i 0.0318455i
\(509\) 9493.01 0.826661 0.413330 0.910581i \(-0.364365\pi\)
0.413330 + 0.910581i \(0.364365\pi\)
\(510\) −1857.78 1758.29i −0.161301 0.152664i
\(511\) 661.412 + 7827.61i 0.0572586 + 0.677638i
\(512\) −9742.03 −0.840900
\(513\) −11632.0 7741.15i −1.00110 0.666238i
\(514\) 9373.44i 0.804367i
\(515\) −17182.7 + 9055.82i −1.47022 + 0.774849i
\(516\) 327.191 + 961.925i 0.0279143 + 0.0820666i
\(517\) 28047.2 2.38590
\(518\) 4498.37 380.101i 0.381558 0.0322407i
\(519\) 2941.72 + 8648.51i 0.248800 + 0.731460i
\(520\) 4296.78 2264.54i 0.362358 0.190974i
\(521\) 6019.18 0.506152 0.253076 0.967446i \(-0.418558\pi\)
0.253076 + 0.967446i \(0.418558\pi\)
\(522\) 283.806 + 368.920i 0.0237966 + 0.0309333i
\(523\) 464.284 0.0388178 0.0194089 0.999812i \(-0.493822\pi\)
0.0194089 + 0.999812i \(0.493822\pi\)
\(524\) −13970.1 −1.16467
\(525\) 11816.0 + 2254.80i 0.982276 + 0.187443i
\(526\) −7362.84 −0.610333
\(527\) −6703.48 −0.554095
\(528\) −2770.60 8145.44i −0.228362 0.671373i
\(529\) −2682.84 −0.220502
\(530\) 5453.77 2874.30i 0.446975 0.235569i
\(531\) −7610.14 + 5854.39i −0.621944 + 0.478453i
\(532\) −11956.3 + 1010.28i −0.974385 + 0.0823329i
\(533\) −7691.21 −0.625034
\(534\) −4407.77 + 1499.27i −0.357197 + 0.121498i
\(535\) 9292.94 4897.67i 0.750970 0.395784i
\(536\) 1307.45i 0.105361i
\(537\) −938.774 2759.95i −0.0754396 0.221789i
\(538\) −3741.21 −0.299805
\(539\) 3138.67 + 18440.0i 0.250820 + 1.47359i
\(540\) −1040.65 + 10150.8i −0.0829302 + 0.808929i
\(541\) 9639.52 0.766054 0.383027 0.923737i \(-0.374882\pi\)
0.383027 + 0.923737i \(0.374882\pi\)
\(542\) 5413.45i 0.429018i
\(543\) −5889.28 17314.2i −0.465439 1.36837i
\(544\) 6446.23i 0.508051i
\(545\) 5094.13 2684.77i 0.400383 0.211014i
\(546\) −1154.56 2640.77i −0.0904955 0.206986i
\(547\) 24026.4i 1.87806i −0.343842 0.939028i \(-0.611728\pi\)
0.343842 0.939028i \(-0.388272\pi\)
\(548\) 18687.7 1.45675
\(549\) 10801.4 + 14040.7i 0.839691 + 1.09152i
\(550\) 6874.87 + 4710.63i 0.532992 + 0.365203i
\(551\) −1404.33 −0.108578
\(552\) 8495.83 2889.79i 0.655084 0.222822i
\(553\) 1269.50 + 15024.2i 0.0976215 + 1.15532i
\(554\) 3642.22i 0.279320i
\(555\) 8412.57 + 7962.07i 0.643412 + 0.608957i
\(556\) 4237.87i 0.323247i
\(557\) −266.067 −0.0202399 −0.0101199 0.999949i \(-0.503221\pi\)
−0.0101199 + 0.999949i \(0.503221\pi\)
\(558\) −3746.26 4869.77i −0.284214 0.369452i
\(559\) 736.337i 0.0557133i
\(560\) 3389.11 + 5295.23i 0.255743 + 0.399579i
\(561\) 9661.79 3286.38i 0.727132 0.247328i
\(562\) 3627.21i 0.272250i
\(563\) 5312.19i 0.397659i −0.980034 0.198829i \(-0.936286\pi\)
0.980034 0.198829i \(-0.0637140\pi\)
\(564\) −5598.35 16458.9i −0.417966 1.22880i
\(565\) −3675.71 + 1937.21i −0.273696 + 0.144246i
\(566\) −7006.77 −0.520347
\(567\) 13295.0 + 2351.17i 0.984720 + 0.174144i
\(568\) 10840.5i 0.800802i
\(569\) 3367.91i 0.248137i −0.992274 0.124069i \(-0.960406\pi\)
0.992274 0.124069i \(-0.0395943\pi\)
\(570\) 5137.35 + 4862.24i 0.377508 + 0.357292i
\(571\) −17311.2 −1.26874 −0.634371 0.773029i \(-0.718741\pi\)
−0.634371 + 0.773029i \(0.718741\pi\)
\(572\) 8690.71i 0.635274i
\(573\) −4580.12 13465.3i −0.333922 0.981714i
\(574\) 598.540 + 7083.54i 0.0435236 + 0.515089i
\(575\) 6880.82 10042.1i 0.499043 0.728323i
\(576\) −515.222 + 396.354i −0.0372701 + 0.0286714i
\(577\) −14972.0 −1.08023 −0.540114 0.841592i \(-0.681619\pi\)
−0.540114 + 0.841592i \(0.681619\pi\)
\(578\) −4420.70 −0.318126
\(579\) −2311.37 6795.31i −0.165902 0.487743i
\(580\) 478.168 + 907.287i 0.0342325 + 0.0649535i
\(581\) −10808.8 + 913.311i −0.771812 + 0.0652160i
\(582\) 1639.55 557.679i 0.116772 0.0397191i
\(583\) 24596.1i 1.74728i
\(584\) 7521.85 0.532973
\(585\) 3082.92 6721.66i 0.217885 0.475054i
\(586\) 2130.94i 0.150219i
\(587\) 13991.7i 0.983812i 0.870648 + 0.491906i \(0.163700\pi\)
−0.870648 + 0.491906i \(0.836300\pi\)
\(588\) 10194.6 5522.58i 0.714999 0.387325i
\(589\) 18537.3 1.29680
\(590\) 4300.05 2266.26i 0.300051 0.158136i
\(591\) 2334.99 794.226i 0.162519 0.0552794i
\(592\) 6053.70i 0.420280i
\(593\) 2682.43i 0.185758i −0.995677 0.0928788i \(-0.970393\pi\)
0.995677 0.0928788i \(-0.0296069\pi\)
\(594\) 7786.92 + 5182.25i 0.537881 + 0.357963i
\(595\) −6280.99 + 4020.02i −0.432765 + 0.276983i
\(596\) 19135.6i 1.31514i
\(597\) 6119.24 + 17990.3i 0.419504 + 1.23332i
\(598\) −2916.65 −0.199449
\(599\) 10409.6i 0.710060i −0.934855 0.355030i \(-0.884471\pi\)
0.934855 0.355030i \(-0.115529\pi\)
\(600\) 3103.98 11092.2i 0.211199 0.754729i
\(601\) 9004.50i 0.611150i −0.952168 0.305575i \(-0.901151\pi\)
0.952168 0.305575i \(-0.0988487\pi\)
\(602\) −678.161 + 57.3028i −0.0459132 + 0.00387955i
\(603\) −1213.77 1577.78i −0.0819710 0.106554i
\(604\) −4666.83 −0.314388
\(605\) −16250.3 + 8564.42i −1.09201 + 0.575526i
\(606\) 7242.08 2463.33i 0.485461 0.165125i
\(607\) 7532.63 0.503690 0.251845 0.967768i \(-0.418963\pi\)
0.251845 + 0.967768i \(0.418963\pi\)
\(608\) 17825.9i 1.18904i
\(609\) 1243.34 543.594i 0.0827302 0.0361700i
\(610\) −4181.25 7933.59i −0.277531 0.526593i
\(611\) 12599.0i 0.834207i
\(612\) −3857.08 5013.83i −0.254760 0.331164i
\(613\) 5607.50i 0.369469i 0.982788 + 0.184735i \(0.0591426\pi\)
−0.982788 + 0.184735i \(0.940857\pi\)
\(614\) −12953.6 −0.851406
\(615\) −12537.8 + 13247.2i −0.822068 + 0.868582i
\(616\) 17847.1 1508.04i 1.16734 0.0986371i
\(617\) −6623.55 −0.432178 −0.216089 0.976374i \(-0.569330\pi\)
−0.216089 + 0.976374i \(0.569330\pi\)
\(618\) 10448.2 3553.86i 0.680075 0.231322i
\(619\) 89.5674i 0.00581586i −0.999996 0.00290793i \(-0.999074\pi\)
0.999996 0.00290793i \(-0.000925625\pi\)
\(620\) −6311.86 11976.3i −0.408856 0.775772i
\(621\) 7569.72 11374.4i 0.489150 0.735004i
\(622\) 4502.81 0.290267
\(623\) 1142.84 + 13525.2i 0.0734944 + 0.869784i
\(624\) 3658.99 1244.58i 0.234739 0.0798444i
\(625\) −5640.84 14571.3i −0.361014 0.932560i
\(626\) 101.096 0.00645468
\(627\) −26717.9 + 9087.88i −1.70177 + 0.578844i
\(628\) 4719.42 0.299881
\(629\) −7180.65 −0.455185
\(630\) −6430.51 2316.25i −0.406663 0.146479i
\(631\) −4797.64 −0.302680 −0.151340 0.988482i \(-0.548359\pi\)
−0.151340 + 0.988482i \(0.548359\pi\)
\(632\) 14437.3 0.908678
\(633\) −1310.86 + 445.879i −0.0823099 + 0.0279970i
\(634\) 10725.1 0.671845
\(635\) −292.173 554.375i −0.0182591 0.0346452i
\(636\) 14433.7 4909.50i 0.899894 0.306092i
\(637\) −8283.39 + 1409.91i −0.515227 + 0.0876968i
\(638\) 940.117 0.0583379
\(639\) −10063.7 13081.8i −0.623026 0.809875i
\(640\) 14453.8 7617.61i 0.892715 0.470488i
\(641\) 17890.0i 1.10236i −0.834387 0.551179i \(-0.814178\pi\)
0.834387 0.551179i \(-0.185822\pi\)
\(642\) −5650.69 + 1922.04i −0.347375 + 0.118157i
\(643\) −4734.63 −0.290382 −0.145191 0.989404i \(-0.546380\pi\)
−0.145191 + 0.989404i \(0.546380\pi\)
\(644\) −987.905 11691.6i −0.0604486 0.715391i
\(645\) −1268.25 1200.34i −0.0774223 0.0732763i
\(646\) −4385.05 −0.267070
\(647\) 6925.33i 0.420808i −0.977615 0.210404i \(-0.932522\pi\)
0.977615 0.210404i \(-0.0674779\pi\)
\(648\) 3315.17 12495.5i 0.200975 0.757516i
\(649\) 19392.9i 1.17294i
\(650\) −2116.05 + 3088.24i −0.127690 + 0.186355i
\(651\) −16412.2 + 7175.49i −0.988087 + 0.431996i
\(652\) 16120.4i 0.968285i
\(653\) 16122.5 0.966192 0.483096 0.875567i \(-0.339512\pi\)
0.483096 + 0.875567i \(0.339512\pi\)
\(654\) −3097.55 + 1053.61i −0.185205 + 0.0629958i
\(655\) 21240.3 11194.3i 1.26706 0.667781i
\(656\) −9532.69 −0.567362
\(657\) 9077.08 6982.89i 0.539012 0.414655i
\(658\) 11603.6 980.470i 0.687468 0.0580892i
\(659\) 17386.0i 1.02771i 0.857877 + 0.513855i \(0.171783\pi\)
−0.857877 + 0.513855i \(0.828217\pi\)
\(660\) 14968.7 + 14167.1i 0.882812 + 0.835537i
\(661\) 16253.3i 0.956401i −0.878251 0.478201i \(-0.841289\pi\)
0.878251 0.478201i \(-0.158711\pi\)
\(662\) −7652.81 −0.449297
\(663\) 1476.26 + 4340.15i 0.0864757 + 0.254234i
\(664\) 10386.5i 0.607042i
\(665\) 17368.9 11116.6i 1.01284 0.648248i
\(666\) −4012.93 5216.42i −0.233480 0.303502i
\(667\) 1373.23i 0.0797176i
\(668\) 2555.48i 0.148016i
\(669\) −8041.30 + 2735.18i −0.464715 + 0.158069i
\(670\) 469.855 + 891.513i 0.0270926 + 0.0514062i
\(671\) 35779.9 2.05852
\(672\) −6900.13 15782.4i −0.396098 0.905979i
\(673\) 14216.2i 0.814255i 0.913371 + 0.407128i \(0.133470\pi\)
−0.913371 + 0.407128i \(0.866530\pi\)
\(674\) 10029.1i 0.573156i
\(675\) −6551.65 16267.2i −0.373590 0.927594i
\(676\) 10388.3 0.591052
\(677\) 24424.5i 1.38657i 0.720663 + 0.693286i \(0.243838\pi\)
−0.720663 + 0.693286i \(0.756162\pi\)
\(678\) 2235.06 760.238i 0.126603 0.0430631i
\(679\) −425.100 5030.93i −0.0240263 0.284344i
\(680\) 3329.23 + 6316.95i 0.187750 + 0.356241i
\(681\) 4286.21 + 12601.2i 0.241186 + 0.709076i
\(682\) −12409.6 −0.696758
\(683\) −31372.1 −1.75757 −0.878785 0.477217i \(-0.841646\pi\)
−0.878785 + 0.477217i \(0.841646\pi\)
\(684\) 10666.1 + 13864.8i 0.596238 + 0.775052i
\(685\) −28412.9 + 14974.5i −1.58482 + 0.835248i
\(686\) 1943.14 + 7519.21i 0.108148 + 0.418491i
\(687\) 7114.83 + 20917.3i 0.395121 + 1.16163i
\(688\) 912.637i 0.0505726i
\(689\) −11048.7 −0.610920
\(690\) −4754.56 + 5023.58i −0.262323 + 0.277166i
\(691\) 7582.28i 0.417429i −0.977977 0.208715i \(-0.933072\pi\)
0.977977 0.208715i \(-0.0669280\pi\)
\(692\) 11436.8i 0.628267i
\(693\) 20137.3 18388.2i 1.10383 1.00795i
\(694\) −3659.19 −0.200145
\(695\) 3395.80 + 6443.27i 0.185338 + 0.351665i
\(696\) −418.418 1230.13i −0.0227875 0.0669941i
\(697\) 11307.3i 0.614482i
\(698\) 8931.64i 0.484337i
\(699\) −17991.5 + 6119.66i −0.973535 + 0.331140i
\(700\) −13096.1 7436.28i −0.707124 0.401521i
\(701\) 6851.81i 0.369172i −0.982816 0.184586i \(-0.940906\pi\)
0.982816 0.184586i \(-0.0590944\pi\)
\(702\) −2327.90 + 3497.94i −0.125158 + 0.188064i
\(703\) 19856.8 1.06531
\(704\) 1312.94i 0.0702886i
\(705\) 21700.2 + 20538.2i 1.15926 + 1.09718i
\(706\) 7489.95i 0.399275i
\(707\) −1877.72 22222.2i −0.0998851 1.18211i
\(708\) 11380.3 3870.91i 0.604093 0.205477i
\(709\) 2516.36 0.133292 0.0666459 0.997777i \(-0.478770\pi\)
0.0666459 + 0.997777i \(0.478770\pi\)
\(710\) 3895.70 + 7391.79i 0.205920 + 0.390717i
\(711\) 17422.4 13402.8i 0.918973 0.706955i
\(712\) 12996.9 0.684099
\(713\) 18126.7i 0.952106i
\(714\) 3882.35 1697.38i 0.203492 0.0889678i
\(715\) −6963.87 13213.4i −0.364243 0.691123i
\(716\) 3649.75i 0.190499i
\(717\) −3244.03 9537.30i −0.168969 0.496760i
\(718\) 10209.7i 0.530671i
\(719\) −4061.37 −0.210658 −0.105329 0.994437i \(-0.533590\pi\)
−0.105329 + 0.994437i \(0.533590\pi\)
\(720\) 3821.05 8331.01i 0.197781 0.431220i
\(721\) −2708.99 32060.0i −0.139928 1.65600i
\(722\) 3740.53 0.192809
\(723\) −8534.93 25092.3i −0.439028 1.29072i
\(724\) 22896.3i 1.17532i
\(725\) −1454.02 996.287i −0.0744840 0.0510361i
\(726\) 9881.20 3361.01i 0.505132 0.171816i
\(727\) 22093.5 1.12710 0.563551 0.826081i \(-0.309435\pi\)
0.563551 + 0.826081i \(0.309435\pi\)
\(728\) 677.420 + 8017.06i 0.0344875 + 0.408149i
\(729\) −7599.56 18156.7i −0.386098 0.922458i
\(730\) −5128.93 + 2703.10i −0.260041 + 0.137050i
\(731\) 1082.53 0.0547728
\(732\) −7141.84 20996.7i −0.360615 1.06019i
\(733\) −35895.7 −1.80878 −0.904391 0.426705i \(-0.859674\pi\)
−0.904391 + 0.426705i \(0.859674\pi\)
\(734\) 12510.6 0.629120
\(735\) −11074.7 + 16565.5i −0.555778 + 0.831331i
\(736\) −17431.1 −0.872989
\(737\) −4020.66 −0.200954
\(738\) 8214.24 6319.11i 0.409716 0.315189i
\(739\) 8613.60 0.428764 0.214382 0.976750i \(-0.431226\pi\)
0.214382 + 0.976750i \(0.431226\pi\)
\(740\) −6761.16 12828.8i −0.335872 0.637291i
\(741\) −4082.34 12001.9i −0.202387 0.595007i
\(742\) 859.828 + 10175.8i 0.0425408 + 0.503458i
\(743\) 636.669 0.0314362 0.0157181 0.999876i \(-0.494997\pi\)
0.0157181 + 0.999876i \(0.494997\pi\)
\(744\) 5523.15 + 16237.8i 0.272162 + 0.800143i
\(745\) 15333.3 + 29093.8i 0.754054 + 1.43076i
\(746\) 11050.8i 0.542355i
\(747\) 9642.31 + 12534.1i 0.472281 + 0.613920i
\(748\) −12776.7 −0.624550
\(749\) 1465.10 + 17339.1i 0.0714736 + 0.845868i
\(750\) 1869.66 + 8678.92i 0.0910271 + 0.422546i
\(751\) 26006.9 1.26366 0.631828 0.775109i \(-0.282305\pi\)
0.631828 + 0.775109i \(0.282305\pi\)
\(752\) 15615.5i 0.757234i
\(753\) −9022.23 + 3068.84i −0.436638 + 0.148519i
\(754\) 422.307i 0.0203973i
\(755\) 7095.47 3739.53i 0.342027 0.180259i
\(756\) −14810.2 8146.74i −0.712489 0.391924i
\(757\) 17235.8i 0.827537i −0.910382 0.413769i \(-0.864212\pi\)
0.910382 0.413769i \(-0.135788\pi\)
\(758\) −6531.29 −0.312965
\(759\) −8886.63 26126.2i −0.424986 1.24944i
\(760\) −9206.38 17468.4i −0.439409 0.833743i
\(761\) −18532.2 −0.882775 −0.441388 0.897317i \(-0.645514\pi\)
−0.441388 + 0.897317i \(0.645514\pi\)
\(762\) 114.660 + 337.094i 0.00545104 + 0.0160258i
\(763\) 803.129 + 9504.79i 0.0381065 + 0.450978i
\(764\) 17806.5i 0.843216i
\(765\) 9881.90 + 4532.38i 0.467034 + 0.214207i
\(766\) 2769.36i 0.130628i
\(767\) −8711.43 −0.410106
\(768\) −7841.33 + 2667.17i −0.368424 + 0.125316i
\(769\) 14838.4i 0.695822i −0.937528 0.347911i \(-0.886891\pi\)
0.937528 0.347911i \(-0.113109\pi\)
\(770\) −11627.5 + 7441.95i −0.544189 + 0.348298i
\(771\) 12829.2 + 37717.1i 0.599263 + 1.76180i
\(772\) 8986.10i 0.418933i
\(773\) 21416.9i 0.996525i 0.867026 + 0.498262i \(0.166028\pi\)
−0.867026 + 0.498262i \(0.833972\pi\)
\(774\) 604.976 + 786.411i 0.0280949 + 0.0365206i
\(775\) 19193.2 + 13151.1i 0.889599 + 0.609549i
\(776\) −4834.41 −0.223641
\(777\) −17580.5 + 7686.26i −0.811706 + 0.354882i
\(778\) 2884.91i 0.132942i
\(779\)