Properties

Label 105.4.g.b.104.28
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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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(104,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.104");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
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 104.28
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.27

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(8.51335 + 7.24727i) q^{5} +(2.39479 + 11.4136i) q^{6} +(-12.2768 + 13.8665i) q^{7} -24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +O(q^{10})\) \(q+2.24438 q^{2} +(1.06702 + 5.08542i) q^{3} -2.96275 q^{4} +(8.51335 + 7.24727i) q^{5} +(2.39479 + 11.4136i) q^{6} +(-12.2768 + 13.8665i) q^{7} -24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +(19.1072 + 16.2656i) q^{10} -25.7488i q^{11} +(-3.16130 - 15.0668i) q^{12} +68.2910 q^{13} +(-27.5539 + 31.1217i) q^{14} +(-27.7715 + 51.0269i) q^{15} -31.5201 q^{16} +30.6502i q^{17} +(-55.4878 + 24.3570i) q^{18} +109.632i q^{19} +(-25.2229 - 21.4718i) q^{20} +(-83.6165 - 47.6370i) q^{21} -57.7902i q^{22} +152.265 q^{23} +(-26.2535 - 125.125i) q^{24} +(19.9543 + 123.397i) q^{25} +153.271 q^{26} +(-81.5690 - 114.147i) q^{27} +(36.3731 - 41.0829i) q^{28} -191.763i q^{29} +(-62.3299 + 114.524i) q^{30} +16.4683i q^{31} +126.094 q^{32} +(130.944 - 27.4744i) q^{33} +68.7908i q^{34} +(-205.011 + 29.0770i) q^{35} +(73.2479 - 32.1531i) q^{36} -81.9337i q^{37} +246.055i q^{38} +(72.8676 + 347.288i) q^{39} +(-209.468 - 178.316i) q^{40} +372.656 q^{41} +(-187.667 - 106.916i) q^{42} -192.593i q^{43} +76.2873i q^{44} +(-289.126 - 86.7831i) q^{45} +341.741 q^{46} -0.366739i q^{47} +(-33.6325 - 160.293i) q^{48} +(-41.5595 - 340.473i) q^{49} +(44.7850 + 276.950i) q^{50} +(-155.869 + 32.7043i) q^{51} -202.329 q^{52} -5.95065 q^{53} +(-183.072 - 256.189i) q^{54} +(186.609 - 219.209i) q^{55} +(302.066 - 341.180i) q^{56} +(-557.523 + 116.979i) q^{57} -430.389i q^{58} -198.813 q^{59} +(82.2800 - 151.180i) q^{60} +83.5752i q^{61} +36.9613i q^{62} +(153.034 - 476.054i) q^{63} +535.163 q^{64} +(581.385 + 494.923i) q^{65} +(293.887 - 61.6631i) q^{66} +1080.15i q^{67} -90.8089i q^{68} +(162.469 + 774.332i) q^{69} +(-460.123 + 65.2599i) q^{70} -773.288i q^{71} +(608.298 - 267.020i) q^{72} -448.111 q^{73} -183.891i q^{74} +(-606.234 + 233.142i) q^{75} -324.811i q^{76} +(357.046 + 316.114i) q^{77} +(163.543 + 779.447i) q^{78} -1270.27 q^{79} +(-268.342 - 228.435i) q^{80} +(493.449 - 536.609i) q^{81} +836.382 q^{82} +429.749i q^{83} +(247.735 + 141.136i) q^{84} +(-222.130 + 260.936i) q^{85} -432.253i q^{86} +(975.193 - 204.614i) q^{87} +633.540i q^{88} +5.29611 q^{89} +(-648.909 - 194.775i) q^{90} +(-838.395 + 946.956i) q^{91} -451.123 q^{92} +(-83.7484 + 17.5720i) q^{93} -0.823102i q^{94} +(-794.530 + 933.333i) q^{95} +(134.544 + 641.238i) q^{96} +435.169 q^{97} +(-93.2755 - 764.151i) q^{98} +(279.438 + 636.587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 184 q^{4} + 4 q^{9} - 188 q^{15} + 184 q^{16} + 148 q^{21} + 712 q^{25} - 336 q^{30} - 1520 q^{36} + 644 q^{39} - 1488 q^{46} - 1496 q^{49} - 220 q^{51} + 1984 q^{60} + 40 q^{64} - 3000 q^{70} - 1192 q^{79} + 4636 q^{81} - 2192 q^{84} + 4808 q^{85} - 4408 q^{91} + 5276 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.24438 0.793509 0.396754 0.917925i \(-0.370136\pi\)
0.396754 + 0.917925i \(0.370136\pi\)
\(3\) 1.06702 + 5.08542i 0.205347 + 0.978689i
\(4\) −2.96275 −0.370344
\(5\) 8.51335 + 7.24727i 0.761457 + 0.648215i
\(6\) 2.39479 + 11.4136i 0.162945 + 0.776599i
\(7\) −12.2768 + 13.8665i −0.662886 + 0.748721i
\(8\) −24.6046 −1.08738
\(9\) −24.7230 + 10.8524i −0.915665 + 0.401943i
\(10\) 19.1072 + 16.2656i 0.604223 + 0.514365i
\(11\) 25.7488i 0.705779i −0.935665 0.352889i \(-0.885199\pi\)
0.935665 0.352889i \(-0.114801\pi\)
\(12\) −3.16130 15.0668i −0.0760491 0.362451i
\(13\) 68.2910 1.45696 0.728481 0.685066i \(-0.240227\pi\)
0.728481 + 0.685066i \(0.240227\pi\)
\(14\) −27.5539 + 31.1217i −0.526006 + 0.594116i
\(15\) −27.7715 + 51.0269i −0.478038 + 0.878339i
\(16\) −31.5201 −0.492502
\(17\) 30.6502i 0.437281i 0.975806 + 0.218640i \(0.0701621\pi\)
−0.975806 + 0.218640i \(0.929838\pi\)
\(18\) −55.4878 + 24.3570i −0.726588 + 0.318945i
\(19\) 109.632i 1.32375i 0.749615 + 0.661874i \(0.230239\pi\)
−0.749615 + 0.661874i \(0.769761\pi\)
\(20\) −25.2229 21.4718i −0.282001 0.240062i
\(21\) −83.6165 47.6370i −0.868887 0.495011i
\(22\) 57.7902i 0.560042i
\(23\) 152.265 1.38041 0.690206 0.723613i \(-0.257520\pi\)
0.690206 + 0.723613i \(0.257520\pi\)
\(24\) −26.2535 125.125i −0.223291 1.06421i
\(25\) 19.9543 + 123.397i 0.159634 + 0.987176i
\(26\) 153.271 1.15611
\(27\) −81.5690 114.147i −0.581406 0.813613i
\(28\) 36.3731 41.0829i 0.245495 0.277284i
\(29\) 191.763i 1.22791i −0.789340 0.613956i \(-0.789577\pi\)
0.789340 0.613956i \(-0.210423\pi\)
\(30\) −62.3299 + 114.524i −0.379327 + 0.696970i
\(31\) 16.4683i 0.0954130i 0.998861 + 0.0477065i \(0.0151912\pi\)
−0.998861 + 0.0477065i \(0.984809\pi\)
\(32\) 126.094 0.696575
\(33\) 130.944 27.4744i 0.690738 0.144930i
\(34\) 68.7908i 0.346986i
\(35\) −205.011 + 29.0770i −0.990091 + 0.140426i
\(36\) 73.2479 32.1531i 0.339111 0.148857i
\(37\) 81.9337i 0.364049i −0.983294 0.182025i \(-0.941735\pi\)
0.983294 0.182025i \(-0.0582651\pi\)
\(38\) 246.055i 1.05041i
\(39\) 72.8676 + 347.288i 0.299183 + 1.42591i
\(40\) −209.468 178.316i −0.827993 0.704856i
\(41\) 372.656 1.41949 0.709745 0.704459i \(-0.248810\pi\)
0.709745 + 0.704459i \(0.248810\pi\)
\(42\) −187.667 106.916i −0.689469 0.392796i
\(43\) 192.593i 0.683028i −0.939877 0.341514i \(-0.889060\pi\)
0.939877 0.341514i \(-0.110940\pi\)
\(44\) 76.2873i 0.261381i
\(45\) −289.126 86.7831i −0.957785 0.287486i
\(46\) 341.741 1.09537
\(47\) 0.366739i 0.00113818i −1.00000 0.000569089i \(-0.999819\pi\)
1.00000 0.000569089i \(-0.000181147\pi\)
\(48\) −33.6325 160.293i −0.101134 0.482006i
\(49\) −41.5595 340.473i −0.121165 0.992632i
\(50\) 44.7850 + 276.950i 0.126671 + 0.783333i
\(51\) −155.869 + 32.7043i −0.427962 + 0.0897944i
\(52\) −202.329 −0.539576
\(53\) −5.95065 −0.0154223 −0.00771117 0.999970i \(-0.502455\pi\)
−0.00771117 + 0.999970i \(0.502455\pi\)
\(54\) −183.072 256.189i −0.461351 0.645610i
\(55\) 186.609 219.209i 0.457497 0.537420i
\(56\) 302.066 341.180i 0.720809 0.814144i
\(57\) −557.523 + 116.979i −1.29554 + 0.271828i
\(58\) 430.389i 0.974359i
\(59\) −198.813 −0.438699 −0.219349 0.975646i \(-0.570393\pi\)
−0.219349 + 0.975646i \(0.570393\pi\)
\(60\) 82.2800 151.180i 0.177038 0.325287i
\(61\) 83.5752i 0.175421i 0.996146 + 0.0877107i \(0.0279551\pi\)
−0.996146 + 0.0877107i \(0.972045\pi\)
\(62\) 36.9613i 0.0757110i
\(63\) 153.034 476.054i 0.306039 0.952019i
\(64\) 535.163 1.04524
\(65\) 581.385 + 494.923i 1.10941 + 0.944425i
\(66\) 293.887 61.6631i 0.548107 0.115003i
\(67\) 1080.15i 1.96958i 0.173757 + 0.984789i \(0.444409\pi\)
−0.173757 + 0.984789i \(0.555591\pi\)
\(68\) 90.8089i 0.161944i
\(69\) 162.469 + 774.332i 0.283464 + 1.35099i
\(70\) −460.123 + 65.2599i −0.785646 + 0.111429i
\(71\) 773.288i 1.29257i −0.763097 0.646284i \(-0.776322\pi\)
0.763097 0.646284i \(-0.223678\pi\)
\(72\) 608.298 267.020i 0.995676 0.437064i
\(73\) −448.111 −0.718459 −0.359229 0.933249i \(-0.616960\pi\)
−0.359229 + 0.933249i \(0.616960\pi\)
\(74\) 183.891i 0.288876i
\(75\) −606.234 + 233.142i −0.933358 + 0.358946i
\(76\) 324.811i 0.490242i
\(77\) 357.046 + 316.114i 0.528431 + 0.467851i
\(78\) 163.543 + 779.447i 0.237405 + 1.13147i
\(79\) −1270.27 −1.80908 −0.904538 0.426393i \(-0.859784\pi\)
−0.904538 + 0.426393i \(0.859784\pi\)
\(80\) −268.342 228.435i −0.375019 0.319247i
\(81\) 493.449 536.609i 0.676884 0.736089i
\(82\) 836.382 1.12638
\(83\) 429.749i 0.568327i 0.958776 + 0.284163i \(0.0917158\pi\)
−0.958776 + 0.284163i \(0.908284\pi\)
\(84\) 247.735 + 141.136i 0.321787 + 0.183324i
\(85\) −222.130 + 260.936i −0.283452 + 0.332971i
\(86\) 432.253i 0.541989i
\(87\) 975.193 204.614i 1.20174 0.252148i
\(88\) 633.540i 0.767450i
\(89\) 5.29611 0.00630772 0.00315386 0.999995i \(-0.498996\pi\)
0.00315386 + 0.999995i \(0.498996\pi\)
\(90\) −648.909 194.775i −0.760011 0.228123i
\(91\) −838.395 + 946.956i −0.965799 + 1.09086i
\(92\) −451.123 −0.511227
\(93\) −83.7484 + 17.5720i −0.0933796 + 0.0195928i
\(94\) 0.823102i 0.000903154i
\(95\) −794.530 + 933.333i −0.858074 + 1.00798i
\(96\) 134.544 + 641.238i 0.143040 + 0.681730i
\(97\) 435.169 0.455513 0.227757 0.973718i \(-0.426861\pi\)
0.227757 + 0.973718i \(0.426861\pi\)
\(98\) −93.2755 764.151i −0.0961454 0.787663i
\(99\) 279.438 + 636.587i 0.283682 + 0.646257i
\(100\) −59.1194 365.594i −0.0591194 0.365594i
\(101\) 1122.41 1.10578 0.552891 0.833254i \(-0.313525\pi\)
0.552891 + 0.833254i \(0.313525\pi\)
\(102\) −349.830 + 73.4009i −0.339592 + 0.0712527i
\(103\) −625.230 −0.598114 −0.299057 0.954235i \(-0.596672\pi\)
−0.299057 + 0.954235i \(0.596672\pi\)
\(104\) −1680.27 −1.58427
\(105\) −366.619 1011.54i −0.340746 0.940155i
\(106\) −13.3555 −0.0122378
\(107\) −988.994 −0.893548 −0.446774 0.894647i \(-0.647427\pi\)
−0.446774 + 0.894647i \(0.647427\pi\)
\(108\) 241.669 + 338.188i 0.215320 + 0.301317i
\(109\) 810.973 0.712634 0.356317 0.934365i \(-0.384032\pi\)
0.356317 + 0.934365i \(0.384032\pi\)
\(110\) 418.821 491.988i 0.363028 0.426448i
\(111\) 416.667 87.4246i 0.356291 0.0747566i
\(112\) 386.967 437.074i 0.326473 0.368746i
\(113\) 107.711 0.0896687 0.0448343 0.998994i \(-0.485724\pi\)
0.0448343 + 0.998994i \(0.485724\pi\)
\(114\) −1251.29 + 262.545i −1.02802 + 0.215698i
\(115\) 1296.29 + 1103.51i 1.05112 + 0.894804i
\(116\) 568.145i 0.454749i
\(117\) −1688.35 + 741.124i −1.33409 + 0.585615i
\(118\) −446.212 −0.348111
\(119\) −425.011 376.287i −0.327401 0.289867i
\(120\) 683.307 1255.50i 0.519809 0.955088i
\(121\) 667.997 0.501876
\(122\) 187.575i 0.139199i
\(123\) 397.630 + 1895.11i 0.291488 + 1.38924i
\(124\) 48.7916i 0.0353356i
\(125\) −724.414 + 1195.14i −0.518348 + 0.855170i
\(126\) 343.466 1068.45i 0.242844 0.755436i
\(127\) 33.0601i 0.0230993i 0.999933 + 0.0115496i \(0.00367645\pi\)
−0.999933 + 0.0115496i \(0.996324\pi\)
\(128\) 192.362 0.132833
\(129\) 979.418 205.500i 0.668472 0.140258i
\(130\) 1304.85 + 1110.80i 0.880330 + 0.749409i
\(131\) 997.301 0.665150 0.332575 0.943077i \(-0.392083\pi\)
0.332575 + 0.943077i \(0.392083\pi\)
\(132\) −387.953 + 81.3998i −0.255810 + 0.0536738i
\(133\) −1520.21 1345.93i −0.991118 0.877494i
\(134\) 2424.28i 1.56288i
\(135\) 132.827 1562.92i 0.0846808 0.996408i
\(136\) 754.136i 0.475490i
\(137\) 1373.30 0.856418 0.428209 0.903680i \(-0.359145\pi\)
0.428209 + 0.903680i \(0.359145\pi\)
\(138\) 364.643 + 1737.90i 0.224931 + 1.07203i
\(139\) 1361.65i 0.830891i −0.909618 0.415446i \(-0.863626\pi\)
0.909618 0.415446i \(-0.136374\pi\)
\(140\) 607.396 86.1478i 0.366674 0.0520058i
\(141\) 1.86502 0.391316i 0.00111392 0.000233722i
\(142\) 1735.55i 1.02567i
\(143\) 1758.41i 1.02829i
\(144\) 779.271 342.071i 0.450967 0.197958i
\(145\) 1389.76 1632.54i 0.795951 0.935002i
\(146\) −1005.73 −0.570103
\(147\) 1687.10 574.638i 0.946598 0.322417i
\(148\) 242.749i 0.134823i
\(149\) 2971.73i 1.63392i −0.576697 0.816958i \(-0.695659\pi\)
0.576697 0.816958i \(-0.304341\pi\)
\(150\) −1360.62 + 523.261i −0.740628 + 0.284827i
\(151\) 1456.31 0.784851 0.392425 0.919784i \(-0.371636\pi\)
0.392425 + 0.919784i \(0.371636\pi\)
\(152\) 2697.44i 1.43942i
\(153\) −332.630 757.764i −0.175762 0.400403i
\(154\) 801.348 + 709.480i 0.419315 + 0.371244i
\(155\) −119.350 + 140.201i −0.0618481 + 0.0726529i
\(156\) −215.888 1028.93i −0.110801 0.528078i
\(157\) −2903.14 −1.47577 −0.737885 0.674927i \(-0.764175\pi\)
−0.737885 + 0.674927i \(0.764175\pi\)
\(158\) −2850.98 −1.43552
\(159\) −6.34944 30.2615i −0.00316694 0.0150937i
\(160\) 1073.48 + 913.834i 0.530412 + 0.451531i
\(161\) −1869.33 + 2111.38i −0.915056 + 1.03354i
\(162\) 1107.49 1204.36i 0.537114 0.584093i
\(163\) 1666.60i 0.800850i −0.916330 0.400425i \(-0.868863\pi\)
0.916330 0.400425i \(-0.131137\pi\)
\(164\) −1104.09 −0.525699
\(165\) 1313.88 + 715.084i 0.619913 + 0.337389i
\(166\) 964.522i 0.450972i
\(167\) 1688.52i 0.782403i −0.920305 0.391201i \(-0.872060\pi\)
0.920305 0.391201i \(-0.127940\pi\)
\(168\) 2057.35 + 1172.09i 0.944810 + 0.538265i
\(169\) 2466.65 1.12274
\(170\) −498.545 + 585.640i −0.224922 + 0.264215i
\(171\) −1189.77 2710.42i −0.532071 1.21211i
\(172\) 570.606i 0.252955i
\(173\) 719.668i 0.316274i 0.987417 + 0.158137i \(0.0505487\pi\)
−0.987417 + 0.158137i \(0.949451\pi\)
\(174\) 2188.71 459.232i 0.953594 0.200082i
\(175\) −1956.06 1238.23i −0.844938 0.534864i
\(176\) 811.607i 0.347598i
\(177\) −212.136 1011.05i −0.0900856 0.429350i
\(178\) 11.8865 0.00500523
\(179\) 1130.92i 0.472231i −0.971725 0.236115i \(-0.924126\pi\)
0.971725 0.236115i \(-0.0758743\pi\)
\(180\) 856.607 + 257.117i 0.354709 + 0.106469i
\(181\) 1072.04i 0.440243i −0.975472 0.220121i \(-0.929355\pi\)
0.975472 0.220121i \(-0.0706453\pi\)
\(182\) −1881.68 + 2125.33i −0.766370 + 0.865605i
\(183\) −425.015 + 89.1761i −0.171683 + 0.0360223i
\(184\) −3746.42 −1.50103
\(185\) 593.796 697.530i 0.235982 0.277208i
\(186\) −187.963 + 39.4383i −0.0740976 + 0.0155471i
\(187\) 789.208 0.308623
\(188\) 1.08655i 0.000421517i
\(189\) 2584.22 + 270.283i 0.994575 + 0.104022i
\(190\) −1783.23 + 2094.75i −0.680889 + 0.799839i
\(191\) 1611.22i 0.610386i 0.952291 + 0.305193i \(0.0987209\pi\)
−0.952291 + 0.305193i \(0.901279\pi\)
\(192\) 571.028 + 2721.53i 0.214637 + 1.02297i
\(193\) 1961.99i 0.731747i −0.930665 0.365874i \(-0.880770\pi\)
0.930665 0.365874i \(-0.119230\pi\)
\(194\) 976.687 0.361454
\(195\) −1896.54 + 3484.68i −0.696483 + 1.27971i
\(196\) 123.130 + 1008.74i 0.0448726 + 0.367615i
\(197\) 658.980 0.238327 0.119163 0.992875i \(-0.461979\pi\)
0.119163 + 0.992875i \(0.461979\pi\)
\(198\) 627.165 + 1428.75i 0.225105 + 0.512811i
\(199\) 5062.64i 1.80342i 0.432338 + 0.901712i \(0.357689\pi\)
−0.432338 + 0.901712i \(0.642311\pi\)
\(200\) −490.966 3036.13i −0.173583 1.07344i
\(201\) −5493.03 + 1152.54i −1.92760 + 0.404447i
\(202\) 2519.12 0.877447
\(203\) 2659.08 + 2354.23i 0.919362 + 0.813965i
\(204\) 461.801 96.8946i 0.158493 0.0332548i
\(205\) 3172.55 + 2700.74i 1.08088 + 0.920135i
\(206\) −1403.26 −0.474609
\(207\) −3764.44 + 1652.45i −1.26399 + 0.554846i
\(208\) −2152.54 −0.717557
\(209\) 2822.89 0.934274
\(210\) −822.833 2270.29i −0.270385 0.746022i
\(211\) −3467.27 −1.13126 −0.565631 0.824658i \(-0.691368\pi\)
−0.565631 + 0.824658i \(0.691368\pi\)
\(212\) 17.6303 0.00571157
\(213\) 3932.49 825.111i 1.26502 0.265426i
\(214\) −2219.68 −0.709038
\(215\) 1395.78 1639.61i 0.442749 0.520097i
\(216\) 2006.97 + 2808.54i 0.632209 + 0.884707i
\(217\) −228.358 202.179i −0.0714376 0.0632479i
\(218\) 1820.13 0.565481
\(219\) −478.142 2278.83i −0.147534 0.703148i
\(220\) −552.875 + 649.461i −0.169431 + 0.199030i
\(221\) 2093.13i 0.637101i
\(222\) 935.161 196.214i 0.282720 0.0593200i
\(223\) 2047.08 0.614720 0.307360 0.951593i \(-0.400555\pi\)
0.307360 + 0.951593i \(0.400555\pi\)
\(224\) −1548.03 + 1748.48i −0.461750 + 0.521540i
\(225\) −1832.49 2834.19i −0.542959 0.839759i
\(226\) 241.744 0.0711529
\(227\) 3998.46i 1.16911i 0.811355 + 0.584553i \(0.198730\pi\)
−0.811355 + 0.584553i \(0.801270\pi\)
\(228\) 1651.80 346.579i 0.479794 0.100670i
\(229\) 3325.60i 0.959659i −0.877362 0.479829i \(-0.840699\pi\)
0.877362 0.479829i \(-0.159301\pi\)
\(230\) 2909.36 + 2476.69i 0.834077 + 0.710035i
\(231\) −1226.60 + 2153.03i −0.349368 + 0.613242i
\(232\) 4718.24i 1.33521i
\(233\) −3464.53 −0.974116 −0.487058 0.873370i \(-0.661930\pi\)
−0.487058 + 0.873370i \(0.661930\pi\)
\(234\) −3789.31 + 1663.37i −1.05861 + 0.464691i
\(235\) 2.65785 3.12217i 0.000737784 0.000866673i
\(236\) 589.032 0.162469
\(237\) −1355.40 6459.88i −0.371489 1.77052i
\(238\) −953.888 844.532i −0.259796 0.230012i
\(239\) 4519.56i 1.22321i −0.791165 0.611603i \(-0.790525\pi\)
0.791165 0.611603i \(-0.209475\pi\)
\(240\) 875.361 1608.37i 0.235435 0.432584i
\(241\) 7087.15i 1.89429i −0.320810 0.947143i \(-0.603955\pi\)
0.320810 0.947143i \(-0.396045\pi\)
\(242\) 1499.24 0.398243
\(243\) 3255.40 + 1936.82i 0.859399 + 0.511305i
\(244\) 247.612i 0.0649662i
\(245\) 2113.69 3199.76i 0.551178 0.834388i
\(246\) 892.433 + 4253.35i 0.231299 + 1.10237i
\(247\) 7486.85i 1.92865i
\(248\) 405.197i 0.103750i
\(249\) −2185.46 + 458.550i −0.556215 + 0.116704i
\(250\) −1625.86 + 2682.34i −0.411314 + 0.678585i
\(251\) −4749.21 −1.19429 −0.597146 0.802132i \(-0.703699\pi\)
−0.597146 + 0.802132i \(0.703699\pi\)
\(252\) −453.400 + 1410.43i −0.113339 + 0.352574i
\(253\) 3920.65i 0.974266i
\(254\) 74.1995i 0.0183295i
\(255\) −1563.99 851.203i −0.384081 0.209037i
\(256\) −3849.57 −0.939837
\(257\) 1571.33i 0.381389i −0.981649 0.190695i \(-0.938926\pi\)
0.981649 0.190695i \(-0.0610740\pi\)
\(258\) 2198.19 461.221i 0.530439 0.111296i
\(259\) 1136.13 + 1005.89i 0.272571 + 0.241323i
\(260\) −1722.50 1466.33i −0.410864 0.349762i
\(261\) 2081.09 + 4740.94i 0.493550 + 1.12436i
\(262\) 2238.33 0.527802
\(263\) 5430.48 1.27322 0.636612 0.771184i \(-0.280335\pi\)
0.636612 + 0.771184i \(0.280335\pi\)
\(264\) −3221.81 + 675.997i −0.751095 + 0.157594i
\(265\) −50.6599 43.1259i −0.0117435 0.00999700i
\(266\) −3411.93 3020.78i −0.786461 0.696299i
\(267\) 5.65104 + 26.9330i 0.00129527 + 0.00617330i
\(268\) 3200.22i 0.729420i
\(269\) 5118.42 1.16013 0.580066 0.814570i \(-0.303027\pi\)
0.580066 + 0.814570i \(0.303027\pi\)
\(270\) 298.114 3507.80i 0.0671950 0.790659i
\(271\) 6280.28i 1.40775i 0.710324 + 0.703875i \(0.248548\pi\)
−0.710324 + 0.703875i \(0.751452\pi\)
\(272\) 966.099i 0.215362i
\(273\) −5710.25 3253.17i −1.26593 0.721213i
\(274\) 3082.22 0.679575
\(275\) 3177.33 513.799i 0.696728 0.112666i
\(276\) −481.356 2294.15i −0.104979 0.500332i
\(277\) 5807.51i 1.25971i −0.776713 0.629854i \(-0.783115\pi\)
0.776713 0.629854i \(-0.216885\pi\)
\(278\) 3056.07i 0.659320i
\(279\) −178.722 407.146i −0.0383505 0.0873663i
\(280\) 5044.21 715.428i 1.07661 0.152696i
\(281\) 201.056i 0.0426833i 0.999772 + 0.0213416i \(0.00679377\pi\)
−0.999772 + 0.0213416i \(0.993206\pi\)
\(282\) 4.18582 0.878263i 0.000883907 0.000185460i
\(283\) −4808.75 −1.01007 −0.505036 0.863098i \(-0.668521\pi\)
−0.505036 + 0.863098i \(0.668521\pi\)
\(284\) 2291.06i 0.478695i
\(285\) −5594.16 3044.63i −1.16270 0.632802i
\(286\) 3946.55i 0.815959i
\(287\) −4575.03 + 5167.43i −0.940959 + 1.06280i
\(288\) −3117.40 + 1368.42i −0.637829 + 0.279983i
\(289\) 3973.56 0.808786
\(290\) 3119.14 3664.05i 0.631594 0.741932i
\(291\) 464.333 + 2213.02i 0.0935384 + 0.445806i
\(292\) 1327.64 0.266076
\(293\) 6701.42i 1.33618i 0.744080 + 0.668091i \(0.232888\pi\)
−0.744080 + 0.668091i \(0.767112\pi\)
\(294\) 3786.50 1289.71i 0.751134 0.255841i
\(295\) −1692.56 1440.85i −0.334050 0.284371i
\(296\) 2015.95i 0.395860i
\(297\) −2939.15 + 2100.31i −0.574231 + 0.410344i
\(298\) 6669.69i 1.29653i
\(299\) 10398.3 2.01121
\(300\) 1796.12 690.742i 0.345663 0.132933i
\(301\) 2670.60 + 2364.43i 0.511397 + 0.452770i
\(302\) 3268.51 0.622786
\(303\) 1197.63 + 5707.92i 0.227069 + 1.08222i
\(304\) 3455.60i 0.651949i
\(305\) −605.692 + 711.505i −0.113711 + 0.133576i
\(306\) −746.549 1700.71i −0.139468 0.317723i
\(307\) 1476.12 0.274419 0.137209 0.990542i \(-0.456187\pi\)
0.137209 + 0.990542i \(0.456187\pi\)
\(308\) −1057.84 936.566i −0.195701 0.173266i
\(309\) −667.131 3179.56i −0.122821 0.585368i
\(310\) −267.868 + 314.664i −0.0490771 + 0.0576507i
\(311\) 2162.00 0.394199 0.197100 0.980383i \(-0.436848\pi\)
0.197100 + 0.980383i \(0.436848\pi\)
\(312\) −1792.88 8544.88i −0.325326 1.55051i
\(313\) −1187.83 −0.214505 −0.107253 0.994232i \(-0.534205\pi\)
−0.107253 + 0.994232i \(0.534205\pi\)
\(314\) −6515.75 −1.17104
\(315\) 4752.92 2943.74i 0.850149 0.526543i
\(316\) 3763.50 0.669980
\(317\) 4280.71 0.758450 0.379225 0.925305i \(-0.376191\pi\)
0.379225 + 0.925305i \(0.376191\pi\)
\(318\) −14.2506 67.9184i −0.00251299 0.0119770i
\(319\) −4937.67 −0.866634
\(320\) 4556.03 + 3878.47i 0.795906 + 0.677541i
\(321\) −1055.27 5029.45i −0.183488 0.874506i
\(322\) −4195.49 + 4738.75i −0.726105 + 0.820125i
\(323\) −3360.23 −0.578850
\(324\) −1461.96 + 1589.84i −0.250680 + 0.272606i
\(325\) 1362.69 + 8426.90i 0.232581 + 1.43828i
\(326\) 3740.50i 0.635481i
\(327\) 865.321 + 4124.13i 0.146337 + 0.697447i
\(328\) −9169.05 −1.54352
\(329\) 5.08538 + 4.50238i 0.000852177 + 0.000754481i
\(330\) 2948.86 + 1604.92i 0.491907 + 0.267721i
\(331\) 4975.22 0.826172 0.413086 0.910692i \(-0.364451\pi\)
0.413086 + 0.910692i \(0.364451\pi\)
\(332\) 1273.24i 0.210476i
\(333\) 889.181 + 2025.64i 0.146327 + 0.333347i
\(334\) 3789.67i 0.620843i
\(335\) −7828.16 + 9195.72i −1.27671 + 1.49975i
\(336\) 2635.60 + 1501.52i 0.427928 + 0.243794i
\(337\) 8230.66i 1.33042i −0.746655 0.665212i \(-0.768341\pi\)
0.746655 0.665212i \(-0.231659\pi\)
\(338\) 5536.11 0.890902
\(339\) 114.929 + 547.754i 0.0184132 + 0.0877578i
\(340\) 658.116 773.088i 0.104975 0.123313i
\(341\) 424.041 0.0673404
\(342\) −2670.30 6083.21i −0.422203 0.961820i
\(343\) 5231.39 + 3603.64i 0.823523 + 0.567283i
\(344\) 4738.68i 0.742711i
\(345\) −4228.63 + 7769.62i −0.659889 + 1.21247i
\(346\) 1615.21i 0.250966i
\(347\) 864.297 0.133712 0.0668558 0.997763i \(-0.478703\pi\)
0.0668558 + 0.997763i \(0.478703\pi\)
\(348\) −2889.25 + 606.219i −0.445058 + 0.0933815i
\(349\) 4811.80i 0.738022i 0.929425 + 0.369011i \(0.120304\pi\)
−0.929425 + 0.369011i \(0.879696\pi\)
\(350\) −4390.14 2779.06i −0.670466 0.424419i
\(351\) −5570.43 7795.19i −0.847086 1.18540i
\(352\) 3246.76i 0.491628i
\(353\) 1206.50i 0.181913i −0.995855 0.0909565i \(-0.971008\pi\)
0.995855 0.0909565i \(-0.0289924\pi\)
\(354\) −476.115 2269.17i −0.0714837 0.340693i
\(355\) 5604.22 6583.27i 0.837863 0.984236i
\(356\) −15.6911 −0.00233602
\(357\) 1460.08 2562.86i 0.216459 0.379947i
\(358\) 2538.23i 0.374719i
\(359\) 7589.54i 1.11577i 0.829919 + 0.557884i \(0.188387\pi\)
−0.829919 + 0.557884i \(0.811613\pi\)
\(360\) 7113.82 + 2135.26i 1.04148 + 0.312606i
\(361\) −5160.10 −0.752310
\(362\) 2406.06i 0.349337i
\(363\) 712.764 + 3397.05i 0.103059 + 0.491181i
\(364\) 2483.95 2805.59i 0.357678 0.403992i
\(365\) −3814.93 3247.58i −0.547075 0.465716i
\(366\) −953.896 + 200.145i −0.136232 + 0.0285840i
\(367\) 6905.34 0.982168 0.491084 0.871112i \(-0.336601\pi\)
0.491084 + 0.871112i \(0.336601\pi\)
\(368\) −4799.42 −0.679856
\(369\) −9213.15 + 4044.23i −1.29978 + 0.570553i
\(370\) 1332.70 1565.52i 0.187254 0.219967i
\(371\) 73.0550 82.5146i 0.0102233 0.0115470i
\(372\) 248.126 52.0614i 0.0345825 0.00725607i
\(373\) 11871.0i 1.64788i 0.566678 + 0.823939i \(0.308228\pi\)
−0.566678 + 0.823939i \(0.691772\pi\)
\(374\) 1771.28 0.244895
\(375\) −6850.73 2408.72i −0.943387 0.331695i
\(376\) 9.02346i 0.00123763i
\(377\) 13095.7i 1.78902i
\(378\) 5799.99 + 606.618i 0.789204 + 0.0825425i
\(379\) −4071.94 −0.551877 −0.275938 0.961175i \(-0.588989\pi\)
−0.275938 + 0.961175i \(0.588989\pi\)
\(380\) 2353.99 2765.23i 0.317782 0.373298i
\(381\) −168.124 + 35.2757i −0.0226070 + 0.00474338i
\(382\) 3616.19i 0.484346i
\(383\) 9559.09i 1.27532i −0.770319 0.637659i \(-0.779903\pi\)
0.770319 0.637659i \(-0.220097\pi\)
\(384\) 205.254 + 978.243i 0.0272768 + 0.130002i
\(385\) 748.699 + 5278.80i 0.0991096 + 0.698785i
\(386\) 4403.46i 0.580648i
\(387\) 2090.11 + 4761.48i 0.274538 + 0.625425i
\(388\) −1289.30 −0.168696
\(389\) 6559.03i 0.854899i −0.904039 0.427450i \(-0.859412\pi\)
0.904039 0.427450i \(-0.140588\pi\)
\(390\) −4256.57 + 7820.94i −0.552666 + 1.01546i
\(391\) 4666.96i 0.603628i
\(392\) 1022.56 + 8377.20i 0.131752 + 1.07937i
\(393\) 1064.14 + 5071.69i 0.136587 + 0.650975i
\(394\) 1479.00 0.189115
\(395\) −10814.3 9206.02i −1.37753 1.17267i
\(396\) −827.904 1886.05i −0.105060 0.239337i
\(397\) −3903.80 −0.493516 −0.246758 0.969077i \(-0.579365\pi\)
−0.246758 + 0.969077i \(0.579365\pi\)
\(398\) 11362.5i 1.43103i
\(399\) 5222.52 9167.01i 0.655271 1.15019i
\(400\) −628.961 3889.49i −0.0786201 0.486186i
\(401\) 3085.45i 0.384239i −0.981372 0.192120i \(-0.938464\pi\)
0.981372 0.192120i \(-0.0615362\pi\)
\(402\) −12328.5 + 2586.74i −1.52957 + 0.320933i
\(403\) 1124.64i 0.139013i
\(404\) −3325.42 −0.409519
\(405\) 8089.85 992.186i 0.992563 0.121734i
\(406\) 5967.98 + 5283.80i 0.729522 + 0.645889i
\(407\) −2109.70 −0.256938
\(408\) 3835.10 804.676i 0.465357 0.0976407i
\(409\) 254.304i 0.0307446i 0.999882 + 0.0153723i \(0.00489335\pi\)
−0.999882 + 0.0153723i \(0.995107\pi\)
\(410\) 7120.41 + 6061.48i 0.857688 + 0.730135i
\(411\) 1465.34 + 6983.82i 0.175863 + 0.838167i
\(412\) 1852.40 0.221508
\(413\) 2440.79 2756.84i 0.290807 0.328463i
\(414\) −8448.85 + 3708.73i −1.00299 + 0.440275i
\(415\) −3114.51 + 3658.61i −0.368398 + 0.432756i
\(416\) 8611.05 1.01488
\(417\) 6924.57 1452.91i 0.813184 0.170621i
\(418\) 6335.64 0.741355
\(419\) −1777.00 −0.207189 −0.103594 0.994620i \(-0.533034\pi\)
−0.103594 + 0.994620i \(0.533034\pi\)
\(420\) 1086.20 + 2996.94i 0.126193 + 0.348181i
\(421\) −6856.09 −0.793695 −0.396847 0.917885i \(-0.629896\pi\)
−0.396847 + 0.917885i \(0.629896\pi\)
\(422\) −7781.87 −0.897667
\(423\) 3.98001 + 9.06686i 0.000457482 + 0.00104219i
\(424\) 146.413 0.0167699
\(425\) −3782.15 + 611.602i −0.431673 + 0.0698049i
\(426\) 8826.02 1851.86i 1.00381 0.210618i
\(427\) −1158.90 1026.04i −0.131342 0.116284i
\(428\) 2930.14 0.330920
\(429\) 8942.26 1876.25i 1.00638 0.211157i
\(430\) 3132.65 3679.92i 0.351325 0.412701i
\(431\) 1425.61i 0.159325i 0.996822 + 0.0796625i \(0.0253842\pi\)
−0.996822 + 0.0796625i \(0.974616\pi\)
\(432\) 2571.07 + 3597.92i 0.286344 + 0.400706i
\(433\) −5863.42 −0.650757 −0.325379 0.945584i \(-0.605492\pi\)
−0.325379 + 0.945584i \(0.605492\pi\)
\(434\) −512.523 453.767i −0.0566864 0.0501878i
\(435\) 9785.05 + 5325.54i 1.07852 + 0.586988i
\(436\) −2402.71 −0.263919
\(437\) 16693.1i 1.82732i
\(438\) −1073.13 5114.57i −0.117069 0.557954i
\(439\) 9688.48i 1.05332i 0.850077 + 0.526658i \(0.176555\pi\)
−0.850077 + 0.526658i \(0.823445\pi\)
\(440\) −4591.43 + 5393.55i −0.497473 + 0.584380i
\(441\) 4722.44 + 7966.47i 0.509928 + 0.860217i
\(442\) 4697.79i 0.505546i
\(443\) −17681.9 −1.89637 −0.948185 0.317719i \(-0.897083\pi\)
−0.948185 + 0.317719i \(0.897083\pi\)
\(444\) −1234.48 + 259.017i −0.131950 + 0.0276856i
\(445\) 45.0877 + 38.3824i 0.00480306 + 0.00408876i
\(446\) 4594.42 0.487785
\(447\) 15112.5 3170.88i 1.59910 0.335520i
\(448\) −6570.10 + 7420.84i −0.692875 + 0.782593i
\(449\) 5275.90i 0.554533i 0.960793 + 0.277266i \(0.0894285\pi\)
−0.960793 + 0.277266i \(0.910572\pi\)
\(450\) −4112.80 6361.00i −0.430843 0.666356i
\(451\) 9595.45i 1.00185i
\(452\) −319.119 −0.0332082
\(453\) 1553.90 + 7405.92i 0.161167 + 0.768125i
\(454\) 8974.08i 0.927697i
\(455\) −14000.4 + 1985.69i −1.44252 + 0.204595i
\(456\) 13717.6 2878.22i 1.40874 0.295581i
\(457\) 696.329i 0.0712755i 0.999365 + 0.0356378i \(0.0113463\pi\)
−0.999365 + 0.0356378i \(0.988654\pi\)
\(458\) 7463.92i 0.761498i
\(459\) 3498.63 2500.11i 0.355777 0.254238i
\(460\) −3840.57 3269.41i −0.389277 0.331385i
\(461\) 7690.68 0.776986 0.388493 0.921452i \(-0.372996\pi\)
0.388493 + 0.921452i \(0.372996\pi\)
\(462\) −2752.95 + 4832.22i −0.277227 + 0.486613i
\(463\) 4517.49i 0.453446i −0.973959 0.226723i \(-0.927199\pi\)
0.973959 0.226723i \(-0.0728012\pi\)
\(464\) 6044.38i 0.604749i
\(465\) −840.328 457.351i −0.0838049 0.0456110i
\(466\) −7775.73 −0.772970
\(467\) 17707.4i 1.75461i −0.479934 0.877304i \(-0.659339\pi\)
0.479934 0.877304i \(-0.340661\pi\)
\(468\) 5002.17 2195.76i 0.494071 0.216879i
\(469\) −14977.9 13260.8i −1.47466 1.30560i
\(470\) 5.96524 7.00735i 0.000585438 0.000687713i
\(471\) −3097.70 14763.7i −0.303045 1.44432i
\(472\) 4891.71 0.477032
\(473\) −4959.05 −0.482067
\(474\) −3042.04 14498.4i −0.294780 1.40493i
\(475\) −13528.2 + 2187.62i −1.30677 + 0.211315i
\(476\) 1259.20 + 1114.84i 0.121251 + 0.107350i
\(477\) 147.118 64.5791i 0.0141217 0.00619890i
\(478\) 10143.6i 0.970624i
\(479\) −12707.4 −1.21214 −0.606072 0.795410i \(-0.707256\pi\)
−0.606072 + 0.795410i \(0.707256\pi\)
\(480\) −3501.81 + 6434.16i −0.332989 + 0.611829i
\(481\) 5595.33i 0.530406i
\(482\) 15906.3i 1.50313i
\(483\) −12731.9 7253.45i −1.19942 0.683320i
\(484\) −1979.11 −0.185867
\(485\) 3704.75 + 3153.79i 0.346854 + 0.295271i
\(486\) 7306.36 + 4346.97i 0.681941 + 0.405725i
\(487\) 224.275i 0.0208684i 0.999946 + 0.0104342i \(0.00332136\pi\)
−0.999946 + 0.0104342i \(0.996679\pi\)
\(488\) 2056.33i 0.190750i
\(489\) 8475.38 1778.29i 0.783783 0.164452i
\(490\) 4743.92 7181.48i 0.437364 0.662094i
\(491\) 6605.29i 0.607113i 0.952813 + 0.303557i \(0.0981742\pi\)
−0.952813 + 0.303557i \(0.901826\pi\)
\(492\) −1178.08 5614.74i −0.107951 0.514496i
\(493\) 5877.57 0.536942
\(494\) 16803.4i 1.53040i
\(495\) −2234.57 + 7444.65i −0.202901 + 0.675984i
\(496\) 519.084i 0.0469911i
\(497\) 10722.8 + 9493.51i 0.967773 + 0.856826i
\(498\) −4905.00 + 1029.16i −0.441362 + 0.0926060i
\(499\) 14083.4 1.26344 0.631722 0.775195i \(-0.282349\pi\)
0.631722 + 0.775195i \(0.282349\pi\)
\(500\) 2146.26 3540.89i 0.191967 0.316707i
\(501\) 8586.81 1801.67i 0.765729 0.160664i
\(502\) −10659.0 −0.947682
\(503\) 23.1056i 0.00204816i 0.999999 + 0.00102408i \(0.000325975\pi\)
−0.999999 + 0.00102408i \(0.999674\pi\)
\(504\) −3765.33 + 11713.1i −0.332780 + 1.03521i
\(505\) 9555.46 + 8134.40i 0.842005 + 0.716784i
\(506\) 8799.44i 0.773088i
\(507\) 2631.96 + 12544.0i 0.230551 + 1.09881i
\(508\) 97.9487i 0.00855467i
\(509\) 3934.85 0.342650 0.171325 0.985215i \(-0.445195\pi\)
0.171325 + 0.985215i \(0.445195\pi\)
\(510\) −3510.18 1910.42i −0.304772 0.165873i
\(511\) 5501.38 6213.74i 0.476256 0.537925i
\(512\) −10178.8 −0.878602
\(513\) 12514.1 8942.55i 1.07702 0.769636i
\(514\) 3526.67i 0.302636i
\(515\) −5322.81 4531.21i −0.455438 0.387707i
\(516\) −2901.77 + 608.845i −0.247564 + 0.0519437i
\(517\) −9.44309 −0.000803301
\(518\) 2549.92 + 2257.59i 0.216288 + 0.191492i
\(519\) −3659.81 + 767.897i −0.309533 + 0.0649459i
\(520\) −14304.7 12177.4i −1.20635 1.02695i
\(521\) −8113.65 −0.682275 −0.341138 0.940013i \(-0.610812\pi\)
−0.341138 + 0.940013i \(0.610812\pi\)
\(522\) 4670.77 + 10640.5i 0.391636 + 0.892186i
\(523\) −5518.74 −0.461410 −0.230705 0.973024i \(-0.574103\pi\)
−0.230705 + 0.973024i \(0.574103\pi\)
\(524\) −2954.75 −0.246334
\(525\) 4209.76 11268.6i 0.349960 0.936765i
\(526\) 12188.1 1.01031
\(527\) −504.759 −0.0417223
\(528\) −4127.36 + 865.998i −0.340190 + 0.0713782i
\(529\) 11017.7 0.905537
\(530\) −113.700 96.7911i −0.00931854 0.00793271i
\(531\) 4915.24 2157.61i 0.401701 0.176332i
\(532\) 4503.99 + 3987.64i 0.367054 + 0.324974i
\(533\) 25449.0 2.06814
\(534\) 12.6831 + 60.4478i 0.00102781 + 0.00489857i
\(535\) −8419.65 7167.50i −0.680398 0.579211i
\(536\) 26576.7i 2.14168i
\(537\) 5751.22 1206.72i 0.462167 0.0969713i
\(538\) 11487.7 0.920575
\(539\) −8766.78 + 1070.11i −0.700579 + 0.0855156i
\(540\) −393.532 + 4630.55i −0.0313610 + 0.369013i
\(541\) 3915.43 0.311160 0.155580 0.987823i \(-0.450275\pi\)
0.155580 + 0.987823i \(0.450275\pi\)
\(542\) 14095.4i 1.11706i
\(543\) 5451.76 1143.88i 0.430861 0.0904027i
\(544\) 3864.80i 0.304599i
\(545\) 6904.09 + 5877.33i 0.542640 + 0.461940i
\(546\) −12816.0 7301.36i −1.00453 0.572289i
\(547\) 5022.18i 0.392564i −0.980547 0.196282i \(-0.937113\pi\)
0.980547 0.196282i \(-0.0628869\pi\)
\(548\) −4068.75 −0.317169
\(549\) −906.996 2066.23i −0.0705093 0.160627i
\(550\) 7131.14 1153.16i 0.552860 0.0894017i
\(551\) 21023.3 1.62545
\(552\) −3997.49 19052.1i −0.308233 1.46904i
\(553\) 15594.9 17614.3i 1.19921 1.35449i
\(554\) 13034.3i 0.999590i
\(555\) 4180.82 + 2275.42i 0.319759 + 0.174029i
\(556\) 4034.23i 0.307715i
\(557\) −13585.5 −1.03346 −0.516729 0.856149i \(-0.672851\pi\)
−0.516729 + 0.856149i \(0.672851\pi\)
\(558\) −401.120 913.791i −0.0304315 0.0693259i
\(559\) 13152.4i 0.995146i
\(560\) 6461.98 916.510i 0.487622 0.0691601i
\(561\) 842.097 + 4013.45i 0.0633750 + 0.302046i
\(562\) 451.247i 0.0338696i
\(563\) 12293.5i 0.920267i −0.887850 0.460133i \(-0.847802\pi\)
0.887850 0.460133i \(-0.152198\pi\)
\(564\) −5.52558 + 1.15937i −0.000412534 + 8.65573e-5i
\(565\) 916.978 + 780.608i 0.0682789 + 0.0581246i
\(566\) −10792.7 −0.801502
\(567\) 1382.91 + 13430.3i 0.102428 + 0.994740i
\(568\) 19026.4i 1.40551i
\(569\) 10764.9i 0.793123i −0.918008 0.396562i \(-0.870203\pi\)
0.918008 0.396562i \(-0.129797\pi\)
\(570\) −12555.4 6833.32i −0.922613 0.502134i
\(571\) 14290.9 1.04738 0.523690 0.851909i \(-0.324555\pi\)
0.523690 + 0.851909i \(0.324555\pi\)
\(572\) 5209.73i 0.380822i
\(573\) −8193.72 + 1719.20i −0.597378 + 0.125341i
\(574\) −10268.1 + 11597.7i −0.746660 + 0.843342i
\(575\) 3038.34 + 18789.1i 0.220361 + 1.36271i
\(576\) −13230.8 + 5807.83i −0.957090 + 0.420127i
\(577\) −25946.6 −1.87205 −0.936024 0.351937i \(-0.885523\pi\)
−0.936024 + 0.351937i \(0.885523\pi\)
\(578\) 8918.20 0.641779
\(579\) 9977.55 2093.48i 0.716153 0.150262i
\(580\) −4117.49 + 4836.81i −0.294775 + 0.346272i
\(581\) −5959.12 5275.95i −0.425518 0.376736i
\(582\) 1042.14 + 4966.86i 0.0742236 + 0.353751i
\(583\) 153.222i 0.0108848i
\(584\) 11025.6 0.781237
\(585\) −19744.7 5926.50i −1.39546 0.418856i
\(586\) 15040.6i 1.06027i
\(587\) 18044.2i 1.26876i −0.773020 0.634382i \(-0.781255\pi\)
0.773020 0.634382i \(-0.218745\pi\)
\(588\) −4998.46 + 1702.51i −0.350566 + 0.119405i
\(589\) −1805.45 −0.126303
\(590\) −3798.76 3233.82i −0.265072 0.225651i
\(591\) 703.143 + 3351.19i 0.0489398 + 0.233248i
\(592\) 2582.56i 0.179295i
\(593\) 14485.3i 1.00310i 0.865129 + 0.501550i \(0.167237\pi\)
−0.865129 + 0.501550i \(0.832763\pi\)
\(594\) −6596.57 + 4713.89i −0.455658 + 0.325612i
\(595\) −891.216 6283.64i −0.0614056 0.432948i
\(596\) 8804.48i 0.605110i
\(597\) −25745.7 + 5401.92i −1.76499 + 0.370328i
\(598\) 23337.8 1.59591
\(599\) 2982.21i 0.203422i 0.994814 + 0.101711i \(0.0324317\pi\)
−0.994814 + 0.101711i \(0.967568\pi\)
\(600\) 14916.1 5736.37i 1.01492 0.390311i
\(601\) 15274.2i 1.03668i 0.855174 + 0.518341i \(0.173450\pi\)
−0.855174 + 0.518341i \(0.826550\pi\)
\(602\) 5993.84 + 5306.69i 0.405798 + 0.359277i
\(603\) −11722.3 26704.6i −0.791657 1.80347i
\(604\) −4314.67 −0.290664
\(605\) 5686.90 + 4841.16i 0.382157 + 0.325324i
\(606\) 2687.94 + 12810.8i 0.180182 + 0.858748i
\(607\) 14554.3 0.973214 0.486607 0.873621i \(-0.338234\pi\)
0.486607 + 0.873621i \(0.338234\pi\)
\(608\) 13823.8i 0.922090i
\(609\) −9134.99 + 16034.5i −0.607830 + 1.06692i
\(610\) −1359.40 + 1596.89i −0.0902306 + 0.105994i
\(611\) 25.0449i 0.00165828i
\(612\) 985.499 + 2245.06i 0.0650922 + 0.148287i
\(613\) 18176.4i 1.19761i 0.800893 + 0.598807i \(0.204358\pi\)
−0.800893 + 0.598807i \(0.795642\pi\)
\(614\) 3312.98 0.217754
\(615\) −10349.2 + 19015.5i −0.678570 + 1.24679i
\(616\) −8784.98 7777.85i −0.574605 0.508731i
\(617\) −7001.54 −0.456842 −0.228421 0.973562i \(-0.573356\pi\)
−0.228421 + 0.973562i \(0.573356\pi\)
\(618\) −1497.30 7136.14i −0.0974597 0.464495i
\(619\) 382.714i 0.0248507i −0.999923 0.0124253i \(-0.996045\pi\)
0.999923 0.0124253i \(-0.00395521\pi\)
\(620\) 353.605 415.380i 0.0229051 0.0269065i
\(621\) −12420.1 17380.6i −0.802580 1.12312i
\(622\) 4852.36 0.312801
\(623\) −65.0194 + 73.4386i −0.00418130 + 0.00472272i
\(624\) −2296.80 10946.6i −0.147348 0.702265i
\(625\) −14828.7 + 4924.59i −0.949034 + 0.315174i
\(626\) −2665.95 −0.170212
\(627\) 3012.07 + 14355.6i 0.191851 + 0.914364i
\(628\) 8601.27 0.546542
\(629\) 2511.29 0.159192
\(630\) 10667.4 6606.88i 0.674601 0.417816i
\(631\) −20481.5 −1.29217 −0.646083 0.763267i \(-0.723594\pi\)
−0.646083 + 0.763267i \(0.723594\pi\)
\(632\) 31254.6 1.96715
\(633\) −3699.63 17632.5i −0.232302 1.10715i
\(634\) 9607.55 0.601837
\(635\) −239.595 + 281.452i −0.0149733 + 0.0175891i
\(636\) 18.8118 + 89.6573i 0.00117286 + 0.00558985i
\(637\) −2838.14 23251.2i −0.176533 1.44623i
\(638\) −11082.0 −0.687682
\(639\) 8392.07 + 19118.0i 0.519538 + 1.18356i
\(640\) 1637.65 + 1394.10i 0.101146 + 0.0861042i
\(641\) 28510.2i 1.75676i 0.477962 + 0.878380i \(0.341376\pi\)
−0.477962 + 0.878380i \(0.658624\pi\)
\(642\) −2368.43 11288.0i −0.145599 0.693928i
\(643\) −1013.84 −0.0621802 −0.0310901 0.999517i \(-0.509898\pi\)
−0.0310901 + 0.999517i \(0.509898\pi\)
\(644\) 5538.36 6255.50i 0.338885 0.382766i
\(645\) 9827.44 + 5348.61i 0.599930 + 0.326513i
\(646\) −7541.65 −0.459322
\(647\) 9793.59i 0.595094i 0.954707 + 0.297547i \(0.0961685\pi\)
−0.954707 + 0.297547i \(0.903832\pi\)
\(648\) −12141.1 + 13203.1i −0.736031 + 0.800409i
\(649\) 5119.20i 0.309624i
\(650\) 3058.41 + 18913.2i 0.184555 + 1.14129i
\(651\) 784.502 1377.03i 0.0472305 0.0829030i
\(652\) 4937.73i 0.296590i
\(653\) −9713.50 −0.582111 −0.291056 0.956706i \(-0.594006\pi\)
−0.291056 + 0.956706i \(0.594006\pi\)
\(654\) 1942.11 + 9256.13i 0.116120 + 0.553430i
\(655\) 8490.38 + 7227.71i 0.506483 + 0.431160i
\(656\) −11746.2 −0.699101
\(657\) 11078.6 4863.11i 0.657867 0.288779i
\(658\) 11.4135 + 10.1051i 0.000676210 + 0.000598688i
\(659\) 14730.6i 0.870745i −0.900250 0.435373i \(-0.856617\pi\)
0.900250 0.435373i \(-0.143383\pi\)
\(660\) −3892.71 2118.61i −0.229581 0.124950i
\(661\) 23656.2i 1.39201i 0.718036 + 0.696006i \(0.245041\pi\)
−0.718036 + 0.696006i \(0.754959\pi\)
\(662\) 11166.3 0.655575
\(663\) −10644.5 + 2233.41i −0.623524 + 0.130827i
\(664\) 10573.8i 0.617987i
\(665\) −3187.76 22475.7i −0.185889 1.31063i
\(666\) 1995.66 + 4546.32i 0.116112 + 0.264514i
\(667\) 29198.8i 1.69502i
\(668\) 5002.65i 0.289758i
\(669\) 2184.27 + 10410.2i 0.126231 + 0.601619i
\(670\) −17569.4 + 20638.7i −1.01308 + 1.19006i
\(671\) 2151.96 0.123809
\(672\) −10543.5 6006.71i −0.605245 0.344813i
\(673\) 23206.9i 1.32921i 0.747194 + 0.664606i \(0.231400\pi\)
−0.747194 + 0.664606i \(0.768600\pi\)
\(674\) 18472.7i 1.05570i
\(675\) 12457.7 12343.1i 0.710368 0.703831i
\(676\) −7308.08 −0.415799
\(677\) 2008.10i 0.113999i −0.998374 0.0569997i \(-0.981847\pi\)
0.998374 0.0569997i \(-0.0181534\pi\)
\(678\) 257.945 + 1229.37i 0.0146111 + 0.0696366i
\(679\) −5342.50 + 6034.28i −0.301953 + 0.341052i
\(680\) 5465.43 6420.23i 0.308220 0.362065i
\(681\) −20333.8 + 4266.42i −1.14419 + 0.240073i
\(682\) 951.709 0.0534352
\(683\) −9344.15 −0.523491 −0.261745 0.965137i \(-0.584298\pi\)
−0.261745 + 0.965137i \(0.584298\pi\)
\(684\) 3524.99 + 8030.29i 0.197049 + 0.448897i
\(685\) 11691.4 + 9952.70i 0.652125 + 0.555143i
\(686\) 11741.2 + 8087.94i 0.653473 + 0.450144i
\(687\) 16912.1 3548.47i 0.939208 0.197063i
\(688\) 6070.57i 0.336393i
\(689\) −406.375 −0.0224698
\(690\) −9490.66 + 17438.0i −0.523628 + 0.962106i
\(691\) 28869.6i 1.58937i −0.607025 0.794683i \(-0.707637\pi\)
0.607025 0.794683i \(-0.292363\pi\)
\(692\) 2132.19i 0.117130i
\(693\) −12257.8 3940.44i −0.671915 0.215996i
\(694\) 1939.81 0.106101
\(695\) 9868.26 11592.2i 0.538596 0.632688i
\(696\) −23994.2 + 5034.44i −1.30675 + 0.274181i
\(697\) 11422.0i 0.620715i
\(698\) 10799.5i 0.585627i
\(699\) −3696.71 17618.6i −0.200032 0.953357i
\(700\) 5795.31 + 3668.56i 0.312917 + 0.198083i
\(701\) 3198.20i 0.172317i −0.996281 0.0861585i \(-0.972541\pi\)
0.996281 0.0861585i \(-0.0274592\pi\)
\(702\) −12502.2 17495.4i −0.672171 0.940628i
\(703\) 8982.53 0.481910
\(704\) 13779.8i 0.737709i
\(705\) 18.7135 + 10.1849i 0.000999706 + 0.000544092i
\(706\) 2707.84i 0.144350i
\(707\) −13779.6 + 15563.9i −0.733007 + 0.827921i
\(708\) 628.507 + 2995.48i 0.0333626 + 0.159007i
\(709\) −5643.25 −0.298923 −0.149462 0.988768i \(-0.547754\pi\)
−0.149462 + 0.988768i \(0.547754\pi\)
\(710\) 12578.0 14775.4i 0.664852 0.781000i
\(711\) 31404.9 13785.6i 1.65651 0.727145i
\(712\) −130.309 −0.00685889
\(713\) 2507.55i 0.131709i
\(714\) 3276.99 5752.05i 0.171762 0.301492i
\(715\) 12743.7 14970.0i 0.666555 0.783001i
\(716\) 3350.65i 0.174888i
\(717\) 22983.9 4822.44i 1.19714 0.251182i
\(718\) 17033.8i 0.885372i
\(719\) −31212.4 −1.61895 −0.809475 0.587154i \(-0.800248\pi\)
−0.809475 + 0.587154i \(0.800248\pi\)
\(720\) 9113.28 + 2735.42i 0.471711 + 0.141587i
\(721\) 7675.84 8669.76i 0.396482 0.447821i
\(722\) −11581.2 −0.596965
\(723\) 36041.1 7562.10i 1.85392 0.388987i
\(724\) 3176.18i 0.163041i
\(725\) 23662.9 3826.48i 1.21217 0.196016i
\(726\) 1599.71 + 7624.27i 0.0817782 + 0.389756i
\(727\) −34019.5 −1.73551 −0.867753 0.496995i \(-0.834437\pi\)
−0.867753 + 0.496995i \(0.834437\pi\)
\(728\) 20628.4 23299.5i 1.05019 1.18618i
\(729\) −6375.99 + 18621.7i −0.323934 + 0.946080i
\(730\) −8562.16 7288.82i −0.434109 0.369550i
\(731\) 5903.03 0.298675
\(732\) 1259.21 264.206i 0.0635817 0.0133406i
\(733\) −7823.52 −0.394227 −0.197113 0.980381i \(-0.563157\pi\)
−0.197113 + 0.980381i \(0.563157\pi\)
\(734\) 15498.2 0.779359
\(735\) 18527.4 + 7334.79i 0.929789 + 0.368092i
\(736\) 19199.7 0.961561
\(737\) 27812.7 1.39009
\(738\) −20677.8 + 9076.79i −1.03138 + 0.452739i
\(739\) 14767.9 0.735107 0.367554 0.930002i \(-0.380195\pi\)
0.367554 + 0.930002i \(0.380195\pi\)
\(740\) −1759.27 + 2066.61i −0.0873945 + 0.102662i
\(741\) −38073.8 + 7988.59i −1.88755 + 0.396043i
\(742\) 163.963 185.194i 0.00811224 0.00916267i
\(743\) 13145.6 0.649077 0.324539 0.945872i \(-0.394791\pi\)
0.324539 + 0.945872i \(0.394791\pi\)
\(744\) 2060.60 432.352i 0.101539 0.0213048i
\(745\) 21536.9 25299.4i 1.05913 1.24416i
\(746\) 26643.1i 1.30761i
\(747\) −4663.83 10624.7i −0.228435 0.520397i
\(748\) −2338.22 −0.114297
\(749\) 12141.7 13713.9i 0.592320 0.669018i
\(750\) −15375.6 5406.08i −0.748586 0.263203i
\(751\) 326.336 0.0158564 0.00792821 0.999969i \(-0.497476\pi\)
0.00792821 + 0.999969i \(0.497476\pi\)
\(752\) 11.5596i 0.000560555i
\(753\) −5067.48 24151.7i −0.245245 1.16884i
\(754\) 29391.7i 1.41960i
\(755\) 12398.0 + 10554.2i 0.597630 + 0.508752i
\(756\) −7656.41 800.780i −0.368334 0.0385239i
\(757\) 361.891i 0.0173754i −0.999962 0.00868769i \(-0.997235\pi\)
0.999962 0.00868769i \(-0.00276541\pi\)
\(758\) −9138.98 −0.437919
\(759\) 19938.1 4183.40i 0.953503 0.200063i
\(760\) 19549.1 22964.3i 0.933052 1.09605i
\(761\) −31708.0 −1.51040 −0.755199 0.655495i \(-0.772460\pi\)
−0.755199 + 0.655495i \(0.772460\pi\)
\(762\) −377.335 + 79.1721i −0.0179389 + 0.00376391i
\(763\) −9956.16 + 11245.4i −0.472395 + 0.533564i
\(764\) 4773.63i 0.226052i
\(765\) 2659.92 8861.77i 0.125712 0.418821i
\(766\) 21454.3i 1.01198i
\(767\) −13577.1 −0.639167
\(768\) −4107.55 19576.7i −0.192993 0.919808i
\(769\) 4392.75i 0.205990i −0.994682 0.102995i \(-0.967157\pi\)
0.994682 0.102995i \(-0.0328426\pi\)
\(770\) 1680.37 + 11847.6i 0.0786444 + 0.554492i
\(771\) 7990.89 1676.64i 0.373262 0.0783173i
\(772\) 5812.89i 0.270998i
\(773\) 11252.2i 0.523563i −0.965127 0.261782i \(-0.915690\pi\)
0.965127 0.261782i \(-0.0843100\pi\)
\(774\) 4691.00 + 10686.6i 0.217848 + 0.496280i
\(775\) −2032.14 + 328.613i −0.0941894 + 0.0152312i
\(776\) −10707.2 −0.495316
\(777\) −3903.07 + 6851.01i −0.180208 + 0.316317i
\(778\) 14721.0i 0.678370i
\(779\) 40854.9i 1.87905i
\(780\) 5618.98 10324.2i 0.257938 0.473931i
\(781\) −19911.3 −0.912268
\(782\) 10474.4i 0.478984i
\(783\) −21889.1 + 15641.9i −0.999045 + 0.713915i
\(784\) 1309.96 + 10731.8i 0.0596739 + 0.488874i
\(785\) −24715.4 21039.8i −1.12373 0.956616i
\(786\) 2388.33 + 11382.8i 0.108383 + 0.516554i
\(787\) −10540.6 −0.477421 −0.238711 0.971091i \(-0.576725\pi\)
−0.238711 + 0.971091i \(0.576725\pi\)
\(788\) −1952.39 −0.0882628
\(789\) 5794.41 + 27616.3i 0.261453 + 1.24609i
\(790\) −24271.4 20661.8i −1.09309 0.930525i
\(791\) −1322.34 + 1493.57i −0.0594401 + 0.0671368i
\(792\) −6875.46 15663.0i −0.308471 0.702727i
\(793\) 5707.43i 0.255582i
\(794\) −8761.61 −0.391609
\(795\) 165.258 303.643i 0.00737247 0.0135460i
\(796\) 14999.3i 0.667886i
\(797\) 34322.0i 1.52540i −0.646750 0.762702i \(-0.723872\pi\)
0.646750 0.762702i \(-0.276128\pi\)
\(798\) 11721.3 20574.3i 0.519963 0.912684i
\(799\) 11.2406 0.000497703
\(800\) 2516.10 + 15559.6i 0.111197 + 0.687642i
\(801\) −130.936 + 57.4758i −0.00577576 + 0.00253534i
\(802\) 6924.93i 0.304897i
\(803\) 11538.3i 0.507073i
\(804\) 16274.5 3414.69i 0.713876 0.149785i
\(805\) −31216.0 + 4427.41i −1.36673 + 0.193846i
\(806\) 2524.12i 0.110308i
\(807\) 5461.43 + 26029.3i 0.238230 + 1.13541i
\(808\) −27616.4 −1.20240
\(809\) 32097.4i 1.39491i −0.716627 0.697457i \(-0.754315\pi\)
0.716627 0.697457i \(-0.245685\pi\)
\(810\) 18156.7 2226.84i 0.787607 0.0965967i
\(811\) 15356.6i 0.664910i −0.943119 0.332455i \(-0.892123\pi\)
0.943119 0.332455i \(-0.107877\pi\)
\(812\) −7878.18 6975.01i −0.340480 0.301447i
\(813\) −31937.9 + 6701.16i −1.37775 + 0.289078i
\(814\) −4734.97 −0.203883
\(815\) 12078.3 14188.4i 0.519123 0.609813i
\(816\) 4913.02 1030.84i 0.210772 0.0442240i
\(817\) 21114.3 0.904158
\(818\) 570.756i 0.0243961i
\(819\) 10450.8 32510.2i 0.445887 1.38706i
\(820\) −9399.47 8001.60i −0.400297 0.340766i
\(821\) 38785.8i 1.64876i 0.566035 + 0.824381i \(0.308477\pi\)
−0.566035 + 0.824381i \(0.691523\pi\)
\(822\) 3288.78 + 15674.4i 0.139549 + 0.665093i
\(823\) 21905.2i 0.927787i 0.885891 + 0.463894i \(0.153548\pi\)
−0.885891 + 0.463894i \(0.846452\pi\)
\(824\) 15383.5 0.650378
\(825\) 6003.14 + 15609.8i 0.253337 + 0.658744i
\(826\) 5478.06 6187.40i 0.230758 0.260638i
\(827\) 14660.5 0.616438 0.308219 0.951315i \(-0.400267\pi\)
0.308219 + 0.951315i \(0.400267\pi\)
\(828\) 11153.1 4895.79i 0.468112 0.205484i
\(829\) 6485.45i 0.271712i 0.990729 + 0.135856i \(0.0433784\pi\)
−0.990729 + 0.135856i \(0.956622\pi\)
\(830\) −6990.15 + 8211.31i −0.292327 + 0.343396i
\(831\) 29533.6 6196.71i 1.23286 0.258678i
\(832\) 36546.8 1.52288
\(833\) 10435.6 1273.81i 0.434059 0.0529831i
\(834\) 15541.4 3260.88i 0.645269 0.135390i
\(835\) 12237.1 14374.9i 0.507165 0.595766i
\(836\) −8363.51 −0.346002
\(837\) 1879.81 1343.31i 0.0776293 0.0554737i
\(838\) −3988.27 −0.164406
\(839\) −10919.1 −0.449306 −0.224653 0.974439i \(-0.572125\pi\)
−0.224653 + 0.974439i \(0.572125\pi\)
\(840\) 9020.51 + 24888.6i 0.370520 + 1.02231i
\(841\) −12383.9 −0.507766
\(842\) −15387.7 −0.629804
\(843\) −1022.45 + 214.530i −0.0417736 + 0.00876490i
\(844\) 10272.6 0.418956
\(845\) 20999.5 + 17876.5i 0.854916 + 0.727775i
\(846\) 8.93267 + 20.3495i 0.000363016 + 0.000826986i
\(847\) −8200.88 + 9262.78i −0.332687 + 0.375765i
\(848\) 187.565 0.00759554
\(849\) −5131.01 24454.5i −0.207416 0.988547i
\(850\) −8488.58 + 1372.67i −0.342536 + 0.0553908i
\(851\) 12475.7i 0.502538i
\(852\) −11651.0 + 2444.60i −0.468493 + 0.0982987i
\(853\) 33026.1 1.32567 0.662833 0.748768i \(-0.269354\pi\)
0.662833 + 0.748768i \(0.269354\pi\)
\(854\) −2601.00 2302.82i −0.104221 0.0922727i
\(855\) 9514.18 31697.3i 0.380559 1.26787i
\(856\) 24333.8 0.971626
\(857\) 25463.0i 1.01494i 0.861671 + 0.507468i \(0.169418\pi\)
−0.861671 + 0.507468i \(0.830582\pi\)
\(858\) 20069.9 4211.03i 0.798571 0.167555i
\(859\) 16073.2i 0.638429i 0.947682 + 0.319215i \(0.103419\pi\)
−0.947682 + 0.319215i \(0.896581\pi\)
\(860\) −4135.33 + 4857.77i −0.163969 + 0.192614i
\(861\) −31160.2 17752.2i −1.23338 0.702663i
\(862\) 3199.61i 0.126426i
\(863\) −17723.7 −0.699099 −0.349549 0.936918i \(-0.613665\pi\)
−0.349549 + 0.936918i \(0.613665\pi\)
\(864\) −10285.3 14393.2i −0.404993 0.566743i
\(865\) −5215.62 + 6126.78i −0.205013 + 0.240829i
\(866\) −13159.8 −0.516382
\(867\) 4239.86 + 20207.2i 0.166082 + 0.791550i
\(868\) 676.568 + 599.005i 0.0264565 + 0.0234235i
\(869\) 32708.1i 1.27681i
\(870\) 21961.4 + 11952.5i 0.855817 + 0.465780i
\(871\) 73764.7i 2.86960i
\(872\) −19953.7 −0.774904
\(873\) −10758.7 + 4722.65i −0.417097 + 0.183090i
\(874\) 37465.6i 1.44999i
\(875\) −7678.86 24717.5i −0.296677 0.954978i
\(876\) 1416.61 + 6751.61i 0.0546381 + 0.260406i
\(877\) 24096.5i 0.927802i 0.885887 + 0.463901i \(0.153551\pi\)
−0.885887 + 0.463901i \(0.846449\pi\)
\(878\) 21744.6i 0.835816i
\(879\) −34079.5 + 7150.53i −1.30771 + 0.274381i
\(880\) −5881.93 + 6909.49i −0.225318 + 0.264681i
\(881\) 22774.5 0.870934 0.435467 0.900205i \(-0.356583\pi\)
0.435467 + 0.900205i \(0.356583\pi\)
\(882\) 10599.0 + 17879.8i 0.404632 + 0.682590i
\(883\) 739.337i 0.0281774i −0.999901 0.0140887i \(-0.995515\pi\)
0.999901 0.0140887i \(-0.00448472\pi\)
\(884\) 6201.43i 0.235946i
\(885\) 5521.33 10144.8i 0.209715 0.385326i
\(886\) −39684.9 −1.50479
\(887\) 2411.83i 0.0912979i −0.998958 0.0456490i \(-0.985464\pi\)
0.998958 0.0456490i \(-0.0145356\pi\)
\(888\) −10251.9 + 2151.05i −0.387424 + 0.0812888i
\(889\) −458.428 405.873i −0.0172949 0.0153122i
\(890\) 101.194 + 86.1447i 0.00381127 + 0.00324447i
\(891\) −13817.1 12705.7i −0.519516 0.477731i
\(892\) −6064.98 −0.227657
\(893\) 40.2062 0.00150666
\(894\) 33918.2 7116.67i 1.26890 0.266238i
\(895\) 8196.11 9627.96i 0.306107 0.359583i
\(896\) −2361.60 + 2667.39i −0.0880529 + 0.0994546i
\(897\) 11095.2 + 52879.9i 0.412996 + 1.96835i
\(898\) 11841.1i 0.440027i
\(899\) 3158.01 0.117159
\(900\) 5429.20 + 8396.98i 0.201082 + 0.310999i
\(901\) 182.389i 0.00674389i
\(902\) 21535.9i 0.794973i
\(903\) −9174.56 + 16104.0i −0.338107 + 0.593474i
\(904\) −2650.18 −0.0975039
\(905\) 7769.34 9126.63i 0.285372 0.335226i
\(906\) 3487.55 + 16621.7i 0.127888 + 0.609514i
\(907\) 21835.5i 0.799379i −0.916651 0.399690i \(-0.869118\pi\)
0.916651 0.399690i \(-0.130882\pi\)
\(908\) 11846.4i 0.432971i
\(909\) −27749.3 + 12180.9i −1.01253 + 0.444461i
\(910\) −31422.2 + 4456.66i −1.14466 + 0.162348i
\(911\) 25167.1i 0.915282i −0.889137 0.457641i \(-0.848694\pi\)
0.889137 0.457641i \(-0.151306\pi\)
\(912\) 17573.2 3687.19i 0.638055 0.133876i
\(913\) 11065.5 0.401113
\(914\) 1562.83i 0.0565577i
\(915\) −4264.58 2321.01i −0.154080 0.0838581i
\(916\) 9852.92i 0.355403i
\(917\) −12243.7 + 13829.1i −0.440918 + 0.498011i
\(918\) 7852.25 5611.20i 0.282313 0.201740i
\(919\) −30919.9 −1.10985 −0.554925 0.831900i \(-0.687253\pi\)
−0.554925 + 0.831900i \(0.687253\pi\)
\(920\) −31894.6 27151.3i −1.14297 0.972992i
\(921\) 1575.04 + 7506.68i 0.0563512 + 0.268571i
\(922\) 17260.8 0.616546
\(923\) 52808.6i 1.88322i
\(924\) 3634.10 6378.88i 0.129386 0.227110i
\(925\) 10110.4 1634.93i 0.359381 0.0581146i
\(926\) 10139.0i 0.359813i
\(927\) 15457.5 6785.28i 0.547672 0.240408i
\(928\) 24180.0i 0.855332i
\(929\) −27897.3 −0.985230 −0.492615 0.870247i \(-0.663959\pi\)
−0.492615 + 0.870247i \(0.663959\pi\)
\(930\) −1886.02 1026.47i −0.0665000 0.0361928i
\(931\) 37326.6 4556.24i 1.31400 0.160392i
\(932\) 10264.5 0.360758
\(933\) 2306.89 + 10994.7i 0.0809478 + 0.385798i
\(934\) 39742.3i 1.39230i
\(935\) 6718.80 + 5719.60i 0.235004 + 0.200054i
\(936\) 41541.3 18235.1i 1.45066 0.636786i
\(937\) 28956.4 1.00957 0.504784 0.863246i \(-0.331572\pi\)
0.504784 + 0.863246i \(0.331572\pi\)
\(938\) −33616.2 29762.4i −1.17016 1.03601i
\(939\) −1267.43 6040.61i −0.0440481 0.209934i
\(940\) −7.87455 + 9.25022i −0.000273233 + 0.000320967i
\(941\) −38808.0 −1.34442 −0.672212 0.740358i \(-0.734656\pi\)
−0.672212 + 0.740358i \(0.734656\pi\)
\(942\) −6952.42 33135.3i −0.240469 1.14608i
\(943\) 56742.5 1.95948
\(944\) 6266.61 0.216060
\(945\) 20041.6 + 21029.6i 0.689898 + 0.723907i
\(946\) −11130.0 −0.382524
\(947\) −19164.9 −0.657629 −0.328814 0.944395i \(-0.606649\pi\)
−0.328814 + 0.944395i \(0.606649\pi\)
\(948\) 4015.72 + 19139.0i 0.137579 + 0.655702i
\(949\) −30602.0 −1.04677
\(950\) −30362.5 + 4909.85i −1.03694 + 0.167681i
\(951\) 4567.59 + 21769.2i 0.155746 + 0.742287i
\(952\) 10457.2 + 9258.40i 0.356009 + 0.315196i
\(953\) −3621.39 −0.123094 −0.0615469 0.998104i \(-0.519603\pi\)
−0.0615469 + 0.998104i \(0.519603\pi\)
\(954\) 330.188 144.940i 0.0112057 0.00491888i
\(955\) −11676.9 + 13716.9i −0.395661 + 0.464782i
\(956\) 13390.3i 0.453006i
\(957\) −5268.57 25110.1i −0.177961 0.848165i
\(958\) −28520.3 −0.961848
\(959\) −16859.8 + 19042.9i −0.567707 + 0.641217i
\(960\) −14862.3 + 27307.7i −0.499665 + 0.918076i
\(961\) 29519.8 0.990896
\(962\) 12558.1i 0.420882i
\(963\) 24450.8 10733.0i 0.818190 0.359155i
\(964\) 20997.4i 0.701537i
\(965\) 14219.1 16703.1i 0.474330 0.557194i
\(966\) −28575.2 16279.5i −0.951752 0.542220i
\(967\) 9516.35i 0.316469i −0.987402 0.158234i \(-0.949420\pi\)
0.987402 0.158234i \(-0.0505801\pi\)
\(968\) −16435.8 −0.545730
\(969\) −3585.43 17088.2i −0.118865 0.566514i
\(970\) 8314.88 + 7078.31i 0.275231 + 0.234300i
\(971\) 1539.07 0.0508661 0.0254331 0.999677i \(-0.491904\pi\)
0.0254331 + 0.999677i \(0.491904\pi\)
\(972\) −9644.93 5738.32i −0.318273 0.189359i
\(973\) 18881.4 + 16716.8i 0.622105 + 0.550786i
\(974\) 503.360i 0.0165592i
\(975\) −41400.3 + 15921.5i −1.35987 + 0.522971i
\(976\) 2634.30i 0.0863954i
\(977\) 20070.0 0.657213 0.328607 0.944467i \(-0.393421\pi\)
0.328607 + 0.944467i \(0.393421\pi\)
\(978\) 19022.0 3991.17i 0.621939 0.130494i
\(979\) 136.369i 0.00445185i
\(980\) −6262.32 + 9480.08i −0.204125 + 0.309010i
\(981\) −20049.6 + 8801.04i −0.652534 + 0.286438i
\(982\) 14824.8i 0.481750i
\(983\) 7463.49i 0.242165i 0.992642 + 0.121083i \(0.0386366\pi\)
−0.992642 + 0.121083i \(0.961363\pi\)
\(984\) −9783.52 46628.4i −0.316959 1.51063i
\(985\) 5610.13 + 4775.81i 0.181476 + 0.154487i
\(986\) 13191.5 0.426068
\(987\) −17.4703 + 30.6654i −0.000563411 + 0.000988947i
\(988\) 22181.7i 0.714263i
\(989\) 29325.3i 0.942860i
\(990\) −5015.22 + 16708.6i −0.161004 + 0.536400i
\(991\) −21807.0 −0.699014 −0.349507 0.936934i \(-0.613651\pi\)
−0.349507 + 0.936934i \(0.613651\pi\)
\(992\) 2076.55i 0.0664623i
\(993\) 5308.64 + 25301.1i 0.169652 + 0.808566i
\(994\) 24066.1 + 21307.1i 0.767936 + 0.679899i
\(995\) −36690.3 + 43100.1i −1.16901 + 1.37323i
\(996\) 6474.95 1358.57i 0.205991 0.0432207i
\(997\) −34022.7 −1.08075 −0.540377 0.841423i \(-0.681718\pi\)
−0.540377 + 0.841423i \(0.681718\pi\)
\(998\) 31608.5 1.00255
\(999\) −9352.47 + 6683.25i −0.296195 + 0.211660i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 105.4.g.b.104.28 yes 40
3.2 odd 2 inner 105.4.g.b.104.15 yes 40
5.4 even 2 inner 105.4.g.b.104.13 40
7.6 odd 2 inner 105.4.g.b.104.25 yes 40
15.14 odd 2 inner 105.4.g.b.104.26 yes 40
21.20 even 2 inner 105.4.g.b.104.14 yes 40
35.34 odd 2 inner 105.4.g.b.104.16 yes 40
105.104 even 2 inner 105.4.g.b.104.27 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.g.b.104.13 40 5.4 even 2 inner
105.4.g.b.104.14 yes 40 21.20 even 2 inner
105.4.g.b.104.15 yes 40 3.2 odd 2 inner
105.4.g.b.104.16 yes 40 35.34 odd 2 inner
105.4.g.b.104.25 yes 40 7.6 odd 2 inner
105.4.g.b.104.26 yes 40 15.14 odd 2 inner
105.4.g.b.104.27 yes 40 105.104 even 2 inner
105.4.g.b.104.28 yes 40 1.1 even 1 trivial