Properties

Label 105.4.g.b.104.35
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

Related objects

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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 104.35
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.36

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+4.45958 q^{2} +(5.00290 - 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 - 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(-12.5955 + 13.5777i) q^{7} +17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +O(q^{10})\) \(q+4.45958 q^{2} +(5.00290 - 1.40393i) q^{3} +11.8879 q^{4} +(-0.892950 - 11.1446i) q^{5} +(22.3108 - 6.26096i) q^{6} +(-12.5955 + 13.5777i) q^{7} +17.3382 q^{8} +(23.0579 - 14.0475i) q^{9} +(-3.98218 - 49.7003i) q^{10} +30.2834i q^{11} +(59.4737 - 16.6898i) q^{12} -18.9551 q^{13} +(-56.1708 + 60.5506i) q^{14} +(-20.1137 - 54.5018i) q^{15} -17.7818 q^{16} -4.59392i q^{17} +(102.829 - 62.6458i) q^{18} +119.595i q^{19} +(-10.6153 - 132.486i) q^{20} +(-43.9520 + 85.6109i) q^{21} +135.051i q^{22} +134.577 q^{23} +(86.7411 - 24.3417i) q^{24} +(-123.405 + 19.9032i) q^{25} -84.5318 q^{26} +(95.6347 - 102.650i) q^{27} +(-149.734 + 161.409i) q^{28} -203.146i q^{29} +(-89.6985 - 243.055i) q^{30} +61.4983i q^{31} -218.005 q^{32} +(42.5159 + 151.505i) q^{33} -20.4870i q^{34} +(162.565 + 128.248i) q^{35} +(274.109 - 166.994i) q^{36} -337.592i q^{37} +533.342i q^{38} +(-94.8304 + 26.6117i) q^{39} +(-15.4821 - 193.227i) q^{40} -135.603 q^{41} +(-196.007 + 381.789i) q^{42} +270.630i q^{43} +360.004i q^{44} +(-177.143 - 244.428i) q^{45} +600.156 q^{46} -273.318i q^{47} +(-88.9606 + 24.9645i) q^{48} +(-25.7052 - 342.035i) q^{49} +(-550.336 + 88.7598i) q^{50} +(-6.44957 - 22.9829i) q^{51} -225.335 q^{52} +222.861 q^{53} +(426.491 - 457.775i) q^{54} +(337.497 - 27.0415i) q^{55} +(-218.384 + 235.412i) q^{56} +(167.903 + 598.319i) q^{57} -905.947i q^{58} -735.026 q^{59} +(-239.108 - 647.909i) q^{60} +312.240i q^{61} +274.257i q^{62} +(-99.6952 + 490.008i) q^{63} -829.955 q^{64} +(16.9260 + 211.247i) q^{65} +(189.603 + 675.646i) q^{66} -751.739i q^{67} -54.6119i q^{68} +(673.274 - 188.937i) q^{69} +(724.972 + 571.933i) q^{70} +640.823i q^{71} +(399.783 - 243.558i) q^{72} +469.117 q^{73} -1505.52i q^{74} +(-589.441 + 272.826i) q^{75} +1421.72i q^{76} +(-411.177 - 381.435i) q^{77} +(-422.904 + 118.677i) q^{78} +126.493 q^{79} +(15.8783 + 198.172i) q^{80} +(334.337 - 647.812i) q^{81} -604.734 q^{82} -299.265i q^{83} +(-522.495 + 1017.73i) q^{84} +(-51.1976 + 4.10215i) q^{85} +1206.90i q^{86} +(-285.204 - 1016.32i) q^{87} +525.058i q^{88} -425.893 q^{89} +(-789.985 - 1090.05i) q^{90} +(238.750 - 257.366i) q^{91} +1599.83 q^{92} +(86.3396 + 307.670i) q^{93} -1218.88i q^{94} +(1332.84 - 106.792i) q^{95} +(-1090.66 + 306.064i) q^{96} +561.656 q^{97} +(-114.635 - 1525.33i) q^{98} +(425.405 + 698.272i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 184 q^{4} + 4 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.45958 1.57670 0.788350 0.615227i \(-0.210936\pi\)
0.788350 + 0.615227i \(0.210936\pi\)
\(3\) 5.00290 1.40393i 0.962808 0.270187i
\(4\) 11.8879 1.48598
\(5\) −0.892950 11.1446i −0.0798679 0.996805i
\(6\) 22.3108 6.26096i 1.51806 0.426004i
\(7\) −12.5955 + 13.5777i −0.680095 + 0.733124i
\(8\) 17.3382 0.766247
\(9\) 23.0579 14.0475i 0.853998 0.520277i
\(10\) −3.98218 49.7003i −0.125928 1.57166i
\(11\) 30.2834i 0.830071i 0.909805 + 0.415035i \(0.136231\pi\)
−0.909805 + 0.415035i \(0.863769\pi\)
\(12\) 59.4737 16.6898i 1.43071 0.401493i
\(13\) −18.9551 −0.404400 −0.202200 0.979344i \(-0.564809\pi\)
−0.202200 + 0.979344i \(0.564809\pi\)
\(14\) −56.1708 + 60.5506i −1.07230 + 1.15592i
\(15\) −20.1137 54.5018i −0.346222 0.938153i
\(16\) −17.7818 −0.277841
\(17\) 4.59392i 0.0655406i −0.999463 0.0327703i \(-0.989567\pi\)
0.999463 0.0327703i \(-0.0104330\pi\)
\(18\) 102.829 62.6458i 1.34650 0.820320i
\(19\) 119.595i 1.44405i 0.691869 + 0.722023i \(0.256788\pi\)
−0.691869 + 0.722023i \(0.743212\pi\)
\(20\) −10.6153 132.486i −0.118682 1.48123i
\(21\) −43.9520 + 85.6109i −0.456720 + 0.889611i
\(22\) 135.051i 1.30877i
\(23\) 134.577 1.22005 0.610026 0.792381i \(-0.291159\pi\)
0.610026 + 0.792381i \(0.291159\pi\)
\(24\) 86.7411 24.3417i 0.737748 0.207030i
\(25\) −123.405 + 19.9032i −0.987242 + 0.159225i
\(26\) −84.5318 −0.637617
\(27\) 95.6347 102.650i 0.681663 0.731666i
\(28\) −149.734 + 161.409i −1.01061 + 1.08941i
\(29\) 203.146i 1.30080i −0.759590 0.650402i \(-0.774600\pi\)
0.759590 0.650402i \(-0.225400\pi\)
\(30\) −89.6985 243.055i −0.545887 1.47919i
\(31\) 61.4983i 0.356304i 0.984003 + 0.178152i \(0.0570119\pi\)
−0.984003 + 0.178152i \(0.942988\pi\)
\(32\) −218.005 −1.20432
\(33\) 42.5159 + 151.505i 0.224275 + 0.799198i
\(34\) 20.4870i 0.103338i
\(35\) 162.565 + 128.248i 0.785100 + 0.619369i
\(36\) 274.109 166.994i 1.26902 0.773122i
\(37\) 337.592i 1.49999i −0.661441 0.749997i \(-0.730055\pi\)
0.661441 0.749997i \(-0.269945\pi\)
\(38\) 533.342i 2.27683i
\(39\) −94.8304 + 26.6117i −0.389359 + 0.109264i
\(40\) −15.4821 193.227i −0.0611985 0.763799i
\(41\) −135.603 −0.516529 −0.258264 0.966074i \(-0.583151\pi\)
−0.258264 + 0.966074i \(0.583151\pi\)
\(42\) −196.007 + 381.789i −0.720110 + 1.40265i
\(43\) 270.630i 0.959785i 0.877327 + 0.479893i \(0.159324\pi\)
−0.877327 + 0.479893i \(0.840676\pi\)
\(44\) 360.004i 1.23347i
\(45\) −177.143 244.428i −0.586822 0.809716i
\(46\) 600.156 1.92366
\(47\) 273.318i 0.848245i −0.905605 0.424123i \(-0.860583\pi\)
0.905605 0.424123i \(-0.139417\pi\)
\(48\) −88.9606 + 24.9645i −0.267507 + 0.0750691i
\(49\) −25.7052 342.035i −0.0749424 0.997188i
\(50\) −550.336 + 88.7598i −1.55658 + 0.251051i
\(51\) −6.44957 22.9829i −0.0177082 0.0631030i
\(52\) −225.335 −0.600931
\(53\) 222.861 0.577591 0.288796 0.957391i \(-0.406745\pi\)
0.288796 + 0.957391i \(0.406745\pi\)
\(54\) 426.491 457.775i 1.07478 1.15362i
\(55\) 337.497 27.0415i 0.827419 0.0662960i
\(56\) −218.384 + 235.412i −0.521120 + 0.561754i
\(57\) 167.903 + 598.319i 0.390163 + 1.39034i
\(58\) 905.947i 2.05098i
\(59\) −735.026 −1.62190 −0.810951 0.585114i \(-0.801050\pi\)
−0.810951 + 0.585114i \(0.801050\pi\)
\(60\) −239.108 647.909i −0.514479 1.39408i
\(61\) 312.240i 0.655381i 0.944785 + 0.327691i \(0.106270\pi\)
−0.944785 + 0.327691i \(0.893730\pi\)
\(62\) 274.257i 0.561784i
\(63\) −99.6952 + 490.008i −0.199372 + 0.979924i
\(64\) −829.955 −1.62101
\(65\) 16.9260 + 211.247i 0.0322986 + 0.403108i
\(66\) 189.603 + 675.646i 0.353614 + 1.26010i
\(67\) 751.739i 1.37074i −0.728195 0.685370i \(-0.759641\pi\)
0.728195 0.685370i \(-0.240359\pi\)
\(68\) 54.6119i 0.0973921i
\(69\) 673.274 188.937i 1.17468 0.329643i
\(70\) 724.972 + 571.933i 1.23787 + 0.976559i
\(71\) 640.823i 1.07115i 0.844487 + 0.535576i \(0.179905\pi\)
−0.844487 + 0.535576i \(0.820095\pi\)
\(72\) 399.783 243.558i 0.654373 0.398660i
\(73\) 469.117 0.752137 0.376069 0.926592i \(-0.377276\pi\)
0.376069 + 0.926592i \(0.377276\pi\)
\(74\) 1505.52i 2.36504i
\(75\) −589.441 + 272.826i −0.907504 + 0.420044i
\(76\) 1421.72i 2.14583i
\(77\) −411.177 381.435i −0.608545 0.564527i
\(78\) −422.904 + 118.677i −0.613903 + 0.172276i
\(79\) 126.493 0.180147 0.0900733 0.995935i \(-0.471290\pi\)
0.0900733 + 0.995935i \(0.471290\pi\)
\(80\) 15.8783 + 198.172i 0.0221906 + 0.276953i
\(81\) 334.337 647.812i 0.458624 0.888630i
\(82\) −604.734 −0.814411
\(83\) 299.265i 0.395766i −0.980226 0.197883i \(-0.936593\pi\)
0.980226 0.197883i \(-0.0634066\pi\)
\(84\) −522.495 + 1017.73i −0.678677 + 1.32194i
\(85\) −51.1976 + 4.10215i −0.0653312 + 0.00523459i
\(86\) 1206.90i 1.51329i
\(87\) −285.204 1016.32i −0.351461 1.25242i
\(88\) 525.058i 0.636039i
\(89\) −425.893 −0.507242 −0.253621 0.967304i \(-0.581622\pi\)
−0.253621 + 0.967304i \(0.581622\pi\)
\(90\) −789.985 1090.05i −0.925242 1.27668i
\(91\) 238.750 257.366i 0.275030 0.296475i
\(92\) 1599.83 1.81297
\(93\) 86.3396 + 307.670i 0.0962688 + 0.343052i
\(94\) 1218.88i 1.33743i
\(95\) 1332.84 106.792i 1.43943 0.115333i
\(96\) −1090.66 + 306.064i −1.15953 + 0.325391i
\(97\) 561.656 0.587913 0.293957 0.955819i \(-0.405028\pi\)
0.293957 + 0.955819i \(0.405028\pi\)
\(98\) −114.635 1525.33i −0.118162 1.57227i
\(99\) 425.405 + 698.272i 0.431867 + 0.708878i
\(100\) −1467.02 + 236.606i −1.46702 + 0.236606i
\(101\) 1733.15 1.70747 0.853736 0.520706i \(-0.174331\pi\)
0.853736 + 0.520706i \(0.174331\pi\)
\(102\) −28.7624 102.494i −0.0279206 0.0994945i
\(103\) 1704.95 1.63101 0.815504 0.578751i \(-0.196460\pi\)
0.815504 + 0.578751i \(0.196460\pi\)
\(104\) −328.647 −0.309870
\(105\) 993.348 + 413.382i 0.923246 + 0.384209i
\(106\) 993.867 0.910688
\(107\) 397.788 0.359399 0.179699 0.983722i \(-0.442488\pi\)
0.179699 + 0.983722i \(0.442488\pi\)
\(108\) 1136.89 1220.29i 1.01294 1.08724i
\(109\) 1382.72 1.21505 0.607526 0.794300i \(-0.292162\pi\)
0.607526 + 0.794300i \(0.292162\pi\)
\(110\) 1505.09 120.594i 1.30459 0.104529i
\(111\) −473.957 1688.94i −0.405280 1.44421i
\(112\) 223.971 241.435i 0.188958 0.203692i
\(113\) −1029.11 −0.856728 −0.428364 0.903606i \(-0.640910\pi\)
−0.428364 + 0.903606i \(0.640910\pi\)
\(114\) 748.777 + 2668.25i 0.615170 + 2.19215i
\(115\) −120.170 1499.81i −0.0974430 1.21615i
\(116\) 2414.97i 1.93297i
\(117\) −437.066 + 266.271i −0.345357 + 0.210400i
\(118\) −3277.91 −2.55725
\(119\) 62.3747 + 57.8629i 0.0480494 + 0.0445738i
\(120\) −348.734 944.961i −0.265291 0.718856i
\(121\) 413.918 0.310983
\(122\) 1392.46i 1.03334i
\(123\) −678.409 + 190.378i −0.497318 + 0.139559i
\(124\) 731.083i 0.529461i
\(125\) 332.008 + 1357.53i 0.237566 + 0.971371i
\(126\) −444.599 + 2185.23i −0.314349 + 1.54505i
\(127\) 1251.75i 0.874602i 0.899315 + 0.437301i \(0.144066\pi\)
−0.899315 + 0.437301i \(0.855934\pi\)
\(128\) −1957.21 −1.35152
\(129\) 379.947 + 1353.94i 0.259322 + 0.924089i
\(130\) 75.4827 + 942.075i 0.0509251 + 0.635580i
\(131\) −1225.39 −0.817274 −0.408637 0.912697i \(-0.633996\pi\)
−0.408637 + 0.912697i \(0.633996\pi\)
\(132\) 505.422 + 1801.06i 0.333268 + 1.18759i
\(133\) −1623.81 1506.36i −1.05867 0.982088i
\(134\) 3352.44i 2.16124i
\(135\) −1229.39 974.152i −0.783772 0.621049i
\(136\) 79.6503i 0.0502203i
\(137\) −1748.45 −1.09037 −0.545183 0.838317i \(-0.683540\pi\)
−0.545183 + 0.838317i \(0.683540\pi\)
\(138\) 3002.52 842.579i 1.85211 0.519747i
\(139\) 2075.28i 1.26635i 0.774007 + 0.633177i \(0.218250\pi\)
−0.774007 + 0.633177i \(0.781750\pi\)
\(140\) 1932.55 + 1524.60i 1.16664 + 0.920371i
\(141\) −383.720 1367.38i −0.229185 0.816697i
\(142\) 2857.80i 1.68888i
\(143\) 574.024i 0.335681i
\(144\) −410.012 + 249.790i −0.237275 + 0.144554i
\(145\) −2263.99 + 181.399i −1.29665 + 0.103892i
\(146\) 2092.07 1.18589
\(147\) −608.796 1675.08i −0.341583 0.939852i
\(148\) 4013.25i 2.22896i
\(149\) 192.111i 0.105627i −0.998604 0.0528133i \(-0.983181\pi\)
0.998604 0.0528133i \(-0.0168188\pi\)
\(150\) −2628.66 + 1216.69i −1.43086 + 0.662283i
\(151\) −2157.41 −1.16270 −0.581350 0.813654i \(-0.697475\pi\)
−0.581350 + 0.813654i \(0.697475\pi\)
\(152\) 2073.55i 1.10650i
\(153\) −64.5330 105.926i −0.0340993 0.0559715i
\(154\) −1833.68 1701.04i −0.959493 0.890089i
\(155\) 685.376 54.9149i 0.355166 0.0284572i
\(156\) −1127.33 + 316.356i −0.578581 + 0.162364i
\(157\) 1016.31 0.516625 0.258312 0.966061i \(-0.416834\pi\)
0.258312 + 0.966061i \(0.416834\pi\)
\(158\) 564.106 0.284037
\(159\) 1114.95 312.882i 0.556109 0.156058i
\(160\) 194.667 + 2429.58i 0.0961863 + 1.20047i
\(161\) −1695.07 + 1827.24i −0.829751 + 0.894450i
\(162\) 1491.00 2888.97i 0.723112 1.40110i
\(163\) 2851.10i 1.37003i 0.728527 + 0.685017i \(0.240205\pi\)
−0.728527 + 0.685017i \(0.759795\pi\)
\(164\) −1612.03 −0.767552
\(165\) 1650.50 609.109i 0.778733 0.287388i
\(166\) 1334.59i 0.624004i
\(167\) 1887.62i 0.874662i −0.899301 0.437331i \(-0.855924\pi\)
0.899301 0.437331i \(-0.144076\pi\)
\(168\) −762.048 + 1484.34i −0.349960 + 0.681661i
\(169\) −1837.70 −0.836461
\(170\) −228.320 + 18.2938i −0.103008 + 0.00825338i
\(171\) 1680.00 + 2757.60i 0.751304 + 1.23321i
\(172\) 3217.21i 1.42622i
\(173\) 3491.67i 1.53449i 0.641353 + 0.767246i \(0.278373\pi\)
−0.641353 + 0.767246i \(0.721627\pi\)
\(174\) −1271.89 4532.36i −0.554148 1.97470i
\(175\) 1284.12 1926.25i 0.554686 0.832060i
\(176\) 538.493i 0.230628i
\(177\) −3677.26 + 1031.93i −1.56158 + 0.438217i
\(178\) −1899.30 −0.799769
\(179\) 172.498i 0.0720286i 0.999351 + 0.0360143i \(0.0114662\pi\)
−0.999351 + 0.0360143i \(0.988534\pi\)
\(180\) −2105.85 2905.73i −0.872006 1.20322i
\(181\) 2106.81i 0.865182i 0.901590 + 0.432591i \(0.142401\pi\)
−0.901590 + 0.432591i \(0.857599\pi\)
\(182\) 1064.72 1147.74i 0.433640 0.467453i
\(183\) 438.365 + 1562.10i 0.177076 + 0.631006i
\(184\) 2333.32 0.934861
\(185\) −3762.34 + 301.453i −1.49520 + 0.119801i
\(186\) 385.038 + 1372.08i 0.151787 + 0.540890i
\(187\) 139.119 0.0544033
\(188\) 3249.16i 1.26048i
\(189\) 189.174 + 2591.42i 0.0728063 + 0.997346i
\(190\) 5943.89 476.247i 2.26955 0.181845i
\(191\) 633.737i 0.240082i −0.992769 0.120041i \(-0.961697\pi\)
0.992769 0.120041i \(-0.0383026\pi\)
\(192\) −4152.18 + 1165.20i −1.56072 + 0.437975i
\(193\) 4520.88i 1.68611i −0.537824 0.843057i \(-0.680754\pi\)
0.537824 0.843057i \(-0.319246\pi\)
\(194\) 2504.75 0.926962
\(195\) 381.256 + 1033.09i 0.140012 + 0.379389i
\(196\) −305.580 4066.07i −0.111363 1.48180i
\(197\) −3816.25 −1.38018 −0.690092 0.723722i \(-0.742430\pi\)
−0.690092 + 0.723722i \(0.742430\pi\)
\(198\) 1897.13 + 3114.00i 0.680924 + 1.11769i
\(199\) 1340.01i 0.477341i −0.971101 0.238670i \(-0.923288\pi\)
0.971101 0.238670i \(-0.0767115\pi\)
\(200\) −2139.62 + 345.085i −0.756471 + 0.122006i
\(201\) −1055.39 3760.87i −0.370356 1.31976i
\(202\) 7729.11 2.69217
\(203\) 2758.25 + 2558.73i 0.953651 + 0.884670i
\(204\) −76.6715 273.218i −0.0263141 0.0937699i
\(205\) 121.087 + 1511.25i 0.0412541 + 0.514879i
\(206\) 7603.37 2.57161
\(207\) 3103.06 1890.46i 1.04192 0.634765i
\(208\) 337.056 0.112359
\(209\) −3621.73 −1.19866
\(210\) 4429.91 + 1843.51i 1.45568 + 0.605783i
\(211\) 729.169 0.237905 0.118953 0.992900i \(-0.462046\pi\)
0.118953 + 0.992900i \(0.462046\pi\)
\(212\) 2649.34 0.858290
\(213\) 899.674 + 3205.97i 0.289411 + 1.03131i
\(214\) 1773.97 0.566664
\(215\) 3016.07 241.660i 0.956719 0.0766560i
\(216\) 1658.13 1779.76i 0.522322 0.560636i
\(217\) −835.003 774.604i −0.261215 0.242320i
\(218\) 6166.36 1.91577
\(219\) 2346.95 658.610i 0.724164 0.203218i
\(220\) 4012.11 321.466i 1.22953 0.0985146i
\(221\) 87.0783i 0.0265046i
\(222\) −2113.65 7531.96i −0.639004 2.27708i
\(223\) −3259.48 −0.978793 −0.489396 0.872061i \(-0.662783\pi\)
−0.489396 + 0.872061i \(0.662783\pi\)
\(224\) 2745.89 2959.99i 0.819050 0.882915i
\(225\) −2565.88 + 2192.46i −0.760261 + 0.649617i
\(226\) −4589.39 −1.35080
\(227\) 4188.94i 1.22480i −0.790548 0.612401i \(-0.790204\pi\)
0.790548 0.612401i \(-0.209796\pi\)
\(228\) 1996.01 + 7112.73i 0.579775 + 2.06602i
\(229\) 1996.90i 0.576240i 0.957594 + 0.288120i \(0.0930302\pi\)
−0.957594 + 0.288120i \(0.906970\pi\)
\(230\) −535.909 6688.51i −0.153638 1.91751i
\(231\) −2592.59 1331.01i −0.738440 0.379110i
\(232\) 3522.19i 0.996736i
\(233\) 141.704 0.0398425 0.0199213 0.999802i \(-0.493658\pi\)
0.0199213 + 0.999802i \(0.493658\pi\)
\(234\) −1949.13 + 1187.46i −0.544524 + 0.331737i
\(235\) −3046.03 + 244.059i −0.845535 + 0.0677476i
\(236\) −8737.88 −2.41012
\(237\) 632.832 177.588i 0.173447 0.0486733i
\(238\) 278.165 + 258.044i 0.0757595 + 0.0702795i
\(239\) 2702.30i 0.731369i 0.930739 + 0.365684i \(0.119165\pi\)
−0.930739 + 0.365684i \(0.880835\pi\)
\(240\) 357.657 + 969.140i 0.0961945 + 0.260657i
\(241\) 4299.54i 1.14920i −0.818434 0.574601i \(-0.805157\pi\)
0.818434 0.574601i \(-0.194843\pi\)
\(242\) 1845.90 0.490326
\(243\) 763.168 3710.32i 0.201470 0.979495i
\(244\) 3711.86i 0.973884i
\(245\) −3788.90 + 591.896i −0.988017 + 0.154346i
\(246\) −3025.42 + 849.006i −0.784121 + 0.220043i
\(247\) 2266.93i 0.583972i
\(248\) 1066.27i 0.273017i
\(249\) −420.148 1497.19i −0.106931 0.381047i
\(250\) 1480.62 + 6054.03i 0.374570 + 1.53156i
\(251\) 3307.05 0.831630 0.415815 0.909449i \(-0.363496\pi\)
0.415815 + 0.909449i \(0.363496\pi\)
\(252\) −1185.16 + 5825.14i −0.296263 + 1.45615i
\(253\) 4075.44i 1.01273i
\(254\) 5582.26i 1.37898i
\(255\) −250.377 + 92.4006i −0.0614871 + 0.0226916i
\(256\) −2088.71 −0.509938
\(257\) 3931.01i 0.954123i 0.878870 + 0.477061i \(0.158298\pi\)
−0.878870 + 0.477061i \(0.841702\pi\)
\(258\) 1694.41 + 6037.99i 0.408872 + 1.45701i
\(259\) 4583.71 + 4252.15i 1.09968 + 1.02014i
\(260\) 201.213 + 2511.28i 0.0479951 + 0.599011i
\(261\) −2853.69 4684.13i −0.676778 1.11088i
\(262\) −5464.73 −1.28860
\(263\) −2083.22 −0.488430 −0.244215 0.969721i \(-0.578530\pi\)
−0.244215 + 0.969721i \(0.578530\pi\)
\(264\) 737.147 + 2626.81i 0.171850 + 0.612383i
\(265\) −199.004 2483.70i −0.0461310 0.575746i
\(266\) −7241.53 6717.72i −1.66920 1.54846i
\(267\) −2130.70 + 597.926i −0.488377 + 0.137050i
\(268\) 8936.56i 2.03689i
\(269\) −2905.93 −0.658653 −0.329326 0.944216i \(-0.606822\pi\)
−0.329326 + 0.944216i \(0.606822\pi\)
\(270\) −5482.57 4344.31i −1.23577 0.979208i
\(271\) 716.004i 0.160495i −0.996775 0.0802475i \(-0.974429\pi\)
0.996775 0.0802475i \(-0.0255711\pi\)
\(272\) 81.6883i 0.0182099i
\(273\) 833.115 1622.76i 0.184697 0.359759i
\(274\) −7797.36 −1.71918
\(275\) −602.735 3737.13i −0.132168 0.819481i
\(276\) 8003.78 2246.05i 1.74555 0.489843i
\(277\) 101.240i 0.0219601i 0.999940 + 0.0109801i \(0.00349513\pi\)
−0.999940 + 0.0109801i \(0.996505\pi\)
\(278\) 9254.89i 1.99666i
\(279\) 863.896 + 1418.02i 0.185377 + 0.304283i
\(280\) 2818.58 + 2223.59i 0.601580 + 0.474589i
\(281\) 7745.33i 1.64430i 0.569272 + 0.822149i \(0.307225\pi\)
−0.569272 + 0.822149i \(0.692775\pi\)
\(282\) −1711.23 6097.95i −0.361356 1.28769i
\(283\) 381.119 0.0800536 0.0400268 0.999199i \(-0.487256\pi\)
0.0400268 + 0.999199i \(0.487256\pi\)
\(284\) 7618.01i 1.59171i
\(285\) 6518.11 2405.48i 1.35474 0.499960i
\(286\) 2559.91i 0.529267i
\(287\) 1708.00 1841.17i 0.351288 0.378680i
\(288\) −5026.74 + 3062.42i −1.02848 + 0.626579i
\(289\) 4891.90 0.995704
\(290\) −10096.4 + 808.965i −2.04442 + 0.163807i
\(291\) 2809.91 788.529i 0.566047 0.158847i
\(292\) 5576.80 1.11766
\(293\) 2325.30i 0.463637i −0.972759 0.231818i \(-0.925532\pi\)
0.972759 0.231818i \(-0.0744675\pi\)
\(294\) −2714.97 7470.15i −0.538573 1.48186i
\(295\) 656.342 + 8191.59i 0.129538 + 1.61672i
\(296\) 5853.23i 1.14937i
\(297\) 3108.58 + 2896.14i 0.607334 + 0.565829i
\(298\) 856.735i 0.166541i
\(299\) −2550.92 −0.493389
\(300\) −7007.19 + 3243.32i −1.34853 + 0.624177i
\(301\) −3674.53 3408.73i −0.703642 0.652745i
\(302\) −9621.14 −1.83323
\(303\) 8670.76 2433.23i 1.64397 0.461337i
\(304\) 2126.61i 0.401215i
\(305\) 3479.80 278.815i 0.653287 0.0523439i
\(306\) −287.790 472.387i −0.0537643 0.0882503i
\(307\) −3447.89 −0.640981 −0.320491 0.947252i \(-0.603848\pi\)
−0.320491 + 0.947252i \(0.603848\pi\)
\(308\) −4888.01 4534.44i −0.904286 0.838876i
\(309\) 8529.70 2393.64i 1.57035 0.440678i
\(310\) 3056.49 244.897i 0.559990 0.0448685i
\(311\) 7675.73 1.39952 0.699760 0.714378i \(-0.253290\pi\)
0.699760 + 0.714378i \(0.253290\pi\)
\(312\) −1644.19 + 461.399i −0.298345 + 0.0837230i
\(313\) −9734.46 −1.75790 −0.878952 0.476910i \(-0.841757\pi\)
−0.878952 + 0.476910i \(0.841757\pi\)
\(314\) 4532.30 0.814562
\(315\) 5549.98 + 673.513i 0.992717 + 0.120470i
\(316\) 1503.73 0.267694
\(317\) 688.561 0.121998 0.0609991 0.998138i \(-0.480571\pi\)
0.0609991 + 0.998138i \(0.480571\pi\)
\(318\) 4972.21 1395.32i 0.876817 0.246056i
\(319\) 6151.95 1.07976
\(320\) 741.109 + 9249.54i 0.129466 + 1.61583i
\(321\) 1990.09 558.469i 0.346032 0.0971050i
\(322\) −7559.28 + 8148.71i −1.30827 + 1.41028i
\(323\) 549.409 0.0946437
\(324\) 3974.55 7701.09i 0.681507 1.32049i
\(325\) 2339.16 377.267i 0.399241 0.0643908i
\(326\) 12714.7i 2.16013i
\(327\) 6917.61 1941.25i 1.16986 0.328292i
\(328\) −2351.11 −0.395788
\(329\) 3711.02 + 3442.58i 0.621869 + 0.576887i
\(330\) 7360.52 2716.37i 1.22783 0.453125i
\(331\) 4447.67 0.738568 0.369284 0.929317i \(-0.379603\pi\)
0.369284 + 0.929317i \(0.379603\pi\)
\(332\) 3557.61i 0.588101i
\(333\) −4742.32 7784.18i −0.780413 1.28099i
\(334\) 8418.00i 1.37908i
\(335\) −8377.85 + 671.265i −1.36636 + 0.109478i
\(336\) 781.546 1522.32i 0.126895 0.247170i
\(337\) 4087.57i 0.660724i 0.943854 + 0.330362i \(0.107171\pi\)
−0.943854 + 0.330362i \(0.892829\pi\)
\(338\) −8195.39 −1.31885
\(339\) −5148.52 + 1444.80i −0.824864 + 0.231477i
\(340\) −608.629 + 48.7657i −0.0970810 + 0.00777850i
\(341\) −1862.38 −0.295757
\(342\) 7492.10 + 12297.8i 1.18458 + 1.94441i
\(343\) 4967.81 + 3959.10i 0.782031 + 0.623240i
\(344\) 4692.24i 0.735432i
\(345\) −2706.83 7334.67i −0.422408 1.14460i
\(346\) 15571.4i 2.41943i
\(347\) 5812.08 0.899161 0.449580 0.893240i \(-0.351573\pi\)
0.449580 + 0.893240i \(0.351573\pi\)
\(348\) −3390.46 12081.9i −0.522264 1.86108i
\(349\) 2804.01i 0.430073i −0.976606 0.215036i \(-0.931013\pi\)
0.976606 0.215036i \(-0.0689870\pi\)
\(350\) 5726.62 8590.24i 0.874573 1.31191i
\(351\) −1812.77 + 1945.74i −0.275665 + 0.295886i
\(352\) 6601.92i 0.999669i
\(353\) 1183.07i 0.178381i −0.996015 0.0891907i \(-0.971572\pi\)
0.996015 0.0891907i \(-0.0284281\pi\)
\(354\) −16399.0 + 4601.97i −2.46214 + 0.690937i
\(355\) 7141.74 572.223i 1.06773 0.0855506i
\(356\) −5062.95 −0.753753
\(357\) 393.290 + 201.912i 0.0583056 + 0.0299337i
\(358\) 769.269i 0.113567i
\(359\) 8708.99i 1.28034i −0.768232 0.640171i \(-0.778863\pi\)
0.768232 0.640171i \(-0.221137\pi\)
\(360\) −3071.34 4237.94i −0.449650 0.620442i
\(361\) −7443.86 −1.08527
\(362\) 9395.49i 1.36413i
\(363\) 2070.79 581.114i 0.299417 0.0840236i
\(364\) 2838.22 3059.53i 0.408690 0.440557i
\(365\) −418.898 5228.14i −0.0600716 0.749735i
\(366\) 1954.92 + 6966.33i 0.279195 + 0.994907i
\(367\) −7352.20 −1.04573 −0.522864 0.852416i \(-0.675136\pi\)
−0.522864 + 0.852416i \(0.675136\pi\)
\(368\) −2393.02 −0.338980
\(369\) −3126.73 + 1904.88i −0.441114 + 0.268738i
\(370\) −16778.4 + 1344.35i −2.35749 + 0.188891i
\(371\) −2807.05 + 3025.93i −0.392817 + 0.423446i
\(372\) 1026.39 + 3657.53i 0.143054 + 0.509769i
\(373\) 1319.56i 0.183174i −0.995797 0.0915872i \(-0.970806\pi\)
0.995797 0.0915872i \(-0.0291940\pi\)
\(374\) 620.414 0.0857777
\(375\) 3566.89 + 6325.48i 0.491182 + 0.871057i
\(376\) 4738.84i 0.649965i
\(377\) 3850.66i 0.526045i
\(378\) 843.637 + 11556.7i 0.114794 + 1.57252i
\(379\) −10334.2 −1.40062 −0.700309 0.713839i \(-0.746955\pi\)
−0.700309 + 0.713839i \(0.746955\pi\)
\(380\) 15844.6 1269.53i 2.13897 0.171383i
\(381\) 1757.37 + 6262.35i 0.236306 + 0.842074i
\(382\) 2826.20i 0.378537i
\(383\) 13328.0i 1.77815i −0.457763 0.889074i \(-0.651349\pi\)
0.457763 0.889074i \(-0.348651\pi\)
\(384\) −9791.74 + 2747.80i −1.30126 + 0.365164i
\(385\) −3883.79 + 4923.01i −0.514120 + 0.651688i
\(386\) 20161.2i 2.65850i
\(387\) 3801.67 + 6240.18i 0.499354 + 0.819654i
\(388\) 6676.89 0.873628
\(389\) 6183.45i 0.805947i 0.915212 + 0.402973i \(0.132023\pi\)
−0.915212 + 0.402973i \(0.867977\pi\)
\(390\) 1700.24 + 4607.13i 0.220757 + 0.598182i
\(391\) 618.236i 0.0799630i
\(392\) −445.682 5930.27i −0.0574243 0.764092i
\(393\) −6130.50 + 1720.37i −0.786878 + 0.220817i
\(394\) −17018.8 −2.17614
\(395\) −112.952 1409.72i −0.0143879 0.179571i
\(396\) 5057.15 + 8300.95i 0.641746 + 1.05338i
\(397\) 2722.53 0.344181 0.172091 0.985081i \(-0.444948\pi\)
0.172091 + 0.985081i \(0.444948\pi\)
\(398\) 5975.88i 0.752623i
\(399\) −10238.6 5256.42i −1.28464 0.659524i
\(400\) 2194.37 353.915i 0.274296 0.0442393i
\(401\) 6359.86i 0.792011i −0.918248 0.396005i \(-0.870396\pi\)
0.918248 0.396005i \(-0.129604\pi\)
\(402\) −4706.60 16771.9i −0.583941 2.08086i
\(403\) 1165.71i 0.144089i
\(404\) 20603.4 2.53727
\(405\) −7518.16 3147.60i −0.922421 0.386186i
\(406\) 12300.6 + 11410.9i 1.50362 + 1.39486i
\(407\) 10223.4 1.24510
\(408\) −111.824 398.482i −0.0135689 0.0483525i
\(409\) 2243.08i 0.271181i 0.990765 + 0.135591i \(0.0432932\pi\)
−0.990765 + 0.135591i \(0.956707\pi\)
\(410\) 539.997 + 6739.53i 0.0650453 + 0.811809i
\(411\) −8747.32 + 2454.71i −1.04981 + 0.294603i
\(412\) 20268.2 2.42365
\(413\) 9258.04 9979.93i 1.10305 1.18906i
\(414\) 13838.4 8430.67i 1.64280 1.00083i
\(415\) −3335.19 + 267.229i −0.394502 + 0.0316090i
\(416\) 4132.30 0.487026
\(417\) 2913.56 + 10382.4i 0.342153 + 1.21926i
\(418\) −16151.4 −1.88993
\(419\) 12565.4 1.46505 0.732527 0.680738i \(-0.238341\pi\)
0.732527 + 0.680738i \(0.238341\pi\)
\(420\) 11808.8 + 4914.23i 1.37193 + 0.570928i
\(421\) 3903.57 0.451896 0.225948 0.974139i \(-0.427452\pi\)
0.225948 + 0.974139i \(0.427452\pi\)
\(422\) 3251.79 0.375105
\(423\) −3839.43 6302.15i −0.441322 0.724399i
\(424\) 3864.01 0.442577
\(425\) 91.4337 + 566.915i 0.0104357 + 0.0647045i
\(426\) 4012.17 + 14297.3i 0.456315 + 1.62607i
\(427\) −4239.49 3932.83i −0.480476 0.445721i
\(428\) 4728.85 0.534060
\(429\) −805.892 2871.78i −0.0906966 0.323196i
\(430\) 13450.4 1077.70i 1.50846 0.120864i
\(431\) 5029.93i 0.562142i −0.959687 0.281071i \(-0.909310\pi\)
0.959687 0.281071i \(-0.0906897\pi\)
\(432\) −1700.56 + 1825.30i −0.189394 + 0.203287i
\(433\) 14864.3 1.64972 0.824862 0.565334i \(-0.191253\pi\)
0.824862 + 0.565334i \(0.191253\pi\)
\(434\) −3723.76 3454.41i −0.411858 0.382066i
\(435\) −11071.8 + 4086.01i −1.22035 + 0.450366i
\(436\) 16437.6 1.80555
\(437\) 16094.7i 1.76181i
\(438\) 10466.4 2937.12i 1.14179 0.320414i
\(439\) 11284.2i 1.22680i 0.789771 + 0.613402i \(0.210199\pi\)
−0.789771 + 0.613402i \(0.789801\pi\)
\(440\) 5851.58 468.851i 0.634007 0.0507991i
\(441\) −5397.44 7525.54i −0.582814 0.812605i
\(442\) 388.333i 0.0417898i
\(443\) −6406.23 −0.687064 −0.343532 0.939141i \(-0.611623\pi\)
−0.343532 + 0.939141i \(0.611623\pi\)
\(444\) −5634.33 20077.8i −0.602238 2.14606i
\(445\) 380.301 + 4746.42i 0.0405124 + 0.505622i
\(446\) −14535.9 −1.54326
\(447\) −269.712 961.113i −0.0285390 0.101698i
\(448\) 10453.7 11268.8i 1.10244 1.18840i
\(449\) 5647.45i 0.593585i 0.954942 + 0.296792i \(0.0959169\pi\)
−0.954942 + 0.296792i \(0.904083\pi\)
\(450\) −11442.8 + 9777.45i −1.19870 + 1.02425i
\(451\) 4106.52i 0.428755i
\(452\) −12233.9 −1.27308
\(453\) −10793.3 + 3028.86i −1.11946 + 0.314147i
\(454\) 18680.9i 1.93114i
\(455\) −3081.44 2430.96i −0.317494 0.250473i
\(456\) 2911.13 + 10373.8i 0.298961 + 1.06534i
\(457\) 4027.42i 0.412243i 0.978526 + 0.206121i \(0.0660842\pi\)
−0.978526 + 0.206121i \(0.933916\pi\)
\(458\) 8905.34i 0.908558i
\(459\) −471.566 439.339i −0.0479538 0.0446766i
\(460\) −1428.57 17829.5i −0.144798 1.80718i
\(461\) 4322.13 0.436663 0.218332 0.975875i \(-0.429939\pi\)
0.218332 + 0.975875i \(0.429939\pi\)
\(462\) −11561.8 5935.76i −1.16430 0.597742i
\(463\) 13087.8i 1.31370i −0.754021 0.656850i \(-0.771889\pi\)
0.754021 0.656850i \(-0.228111\pi\)
\(464\) 3612.31i 0.361416i
\(465\) 3351.77 1236.96i 0.334268 0.123360i
\(466\) 631.938 0.0628197
\(467\) 2525.04i 0.250203i 0.992144 + 0.125102i \(0.0399257\pi\)
−0.992144 + 0.125102i \(0.960074\pi\)
\(468\) −5195.77 + 3165.39i −0.513193 + 0.312650i
\(469\) 10206.8 + 9468.55i 1.00492 + 0.932232i
\(470\) −13584.0 + 1088.40i −1.33316 + 0.106818i
\(471\) 5084.47 1426.83i 0.497410 0.139585i
\(472\) −12744.0 −1.24278
\(473\) −8195.60 −0.796689
\(474\) 2822.16 791.968i 0.273473 0.0767432i
\(475\) −2380.31 14758.6i −0.229929 1.42562i
\(476\) 741.501 + 687.866i 0.0714005 + 0.0662359i
\(477\) 5138.72 3130.64i 0.493262 0.300507i
\(478\) 12051.1i 1.15315i
\(479\) −3175.55 −0.302911 −0.151456 0.988464i \(-0.548396\pi\)
−0.151456 + 0.988464i \(0.548396\pi\)
\(480\) 4384.87 + 11881.6i 0.416961 + 1.12983i
\(481\) 6399.09i 0.606598i
\(482\) 19174.1i 1.81195i
\(483\) −5914.92 + 11521.2i −0.557222 + 1.08537i
\(484\) 4920.59 0.462114
\(485\) −501.531 6259.45i −0.0469554 0.586035i
\(486\) 3403.41 16546.5i 0.317658 1.54437i
\(487\) 3971.81i 0.369569i −0.982779 0.184785i \(-0.940841\pi\)
0.982779 0.184785i \(-0.0591587\pi\)
\(488\) 5413.67i 0.502183i
\(489\) 4002.76 + 14263.8i 0.370166 + 1.31908i
\(490\) −16896.9 + 2639.61i −1.55781 + 0.243358i
\(491\) 10854.4i 0.997665i 0.866698 + 0.498833i \(0.166238\pi\)
−0.866698 + 0.498833i \(0.833762\pi\)
\(492\) −8064.83 + 2263.19i −0.739005 + 0.207383i
\(493\) −933.239 −0.0852555
\(494\) 10109.5i 0.920749i
\(495\) 7402.11 5364.50i 0.672122 0.487104i
\(496\) 1093.55i 0.0989958i
\(497\) −8700.88 8071.51i −0.785287 0.728484i
\(498\) −1873.68 6676.84i −0.168598 0.600796i
\(499\) −4802.55 −0.430845 −0.215423 0.976521i \(-0.569113\pi\)
−0.215423 + 0.976521i \(0.569113\pi\)
\(500\) 3946.87 + 16138.1i 0.353018 + 1.44344i
\(501\) −2650.10 9443.57i −0.236323 0.842131i
\(502\) 14748.1 1.31123
\(503\) 13959.0i 1.23738i 0.785636 + 0.618689i \(0.212336\pi\)
−0.785636 + 0.618689i \(0.787664\pi\)
\(504\) −1728.53 + 8495.85i −0.152768 + 0.750863i
\(505\) −1547.61 19315.3i −0.136372 1.70202i
\(506\) 18174.7i 1.59677i
\(507\) −9193.84 + 2580.02i −0.805351 + 0.226001i
\(508\) 14880.6i 1.29964i
\(509\) −13117.5 −1.14228 −0.571141 0.820852i \(-0.693499\pi\)
−0.571141 + 0.820852i \(0.693499\pi\)
\(510\) −1116.58 + 412.068i −0.0969467 + 0.0357778i
\(511\) −5908.78 + 6369.51i −0.511525 + 0.551410i
\(512\) 6342.96 0.547503
\(513\) 12276.4 + 11437.4i 1.05656 + 0.984354i
\(514\) 17530.6i 1.50436i
\(515\) −1522.44 19001.0i −0.130265 1.62580i
\(516\) 4516.76 + 16095.4i 0.385347 + 1.37318i
\(517\) 8276.99 0.704103
\(518\) 20441.4 + 18962.8i 1.73387 + 1.60845i
\(519\) 4902.08 + 17468.5i 0.414600 + 1.47742i
\(520\) 293.465 + 3662.65i 0.0247487 + 0.308880i
\(521\) 3567.96 0.300029 0.150015 0.988684i \(-0.452068\pi\)
0.150015 + 0.988684i \(0.452068\pi\)
\(522\) −12726.3 20889.3i −1.06708 1.75153i
\(523\) 6801.37 0.568648 0.284324 0.958728i \(-0.408231\pi\)
0.284324 + 0.958728i \(0.408231\pi\)
\(524\) −14567.3 −1.21445
\(525\) 3719.98 11439.6i 0.309244 0.950983i
\(526\) −9290.30 −0.770107
\(527\) 282.519 0.0233524
\(528\) −756.009 2694.02i −0.0623126 0.222050i
\(529\) 5943.91 0.488527
\(530\) −887.474 11076.3i −0.0727347 0.907779i
\(531\) −16948.2 + 10325.3i −1.38510 + 0.843838i
\(532\) −19303.7 17907.3i −1.57316 1.45936i
\(533\) 2570.37 0.208884
\(534\) −9502.02 + 2666.50i −0.770024 + 0.216087i
\(535\) −355.205 4433.20i −0.0287044 0.358251i
\(536\) 13033.8i 1.05032i
\(537\) 242.176 + 862.991i 0.0194612 + 0.0693497i
\(538\) −12959.2 −1.03850
\(539\) 10358.0 778.441i 0.827736 0.0622075i
\(540\) −14614.8 11580.6i −1.16467 0.922868i
\(541\) 2446.78 0.194446 0.0972229 0.995263i \(-0.469004\pi\)
0.0972229 + 0.995263i \(0.469004\pi\)
\(542\) 3193.07i 0.253052i
\(543\) 2957.82 + 10540.2i 0.233761 + 0.833004i
\(544\) 1001.50i 0.0789317i
\(545\) −1234.70 15409.9i −0.0970437 1.21117i
\(546\) 3715.34 7236.84i 0.291212 0.567231i
\(547\) 11784.9i 0.921179i −0.887613 0.460590i \(-0.847638\pi\)
0.887613 0.460590i \(-0.152362\pi\)
\(548\) −20785.3 −1.62026
\(549\) 4386.18 + 7199.61i 0.340980 + 0.559694i
\(550\) −2687.95 16666.0i −0.208390 1.29208i
\(551\) 24295.2 1.87842
\(552\) 11673.3 3275.82i 0.900091 0.252587i
\(553\) −1593.25 + 1717.48i −0.122517 + 0.132070i
\(554\) 451.490i 0.0346245i
\(555\) −18399.4 + 6790.21i −1.40722 + 0.519331i
\(556\) 24670.7i 1.88178i
\(557\) 1115.57 0.0848618 0.0424309 0.999099i \(-0.486490\pi\)
0.0424309 + 0.999099i \(0.486490\pi\)
\(558\) 3852.61 + 6323.79i 0.292283 + 0.479762i
\(559\) 5129.83i 0.388137i
\(560\) −2890.70 2280.49i −0.218133 0.172086i
\(561\) 696.000 195.315i 0.0523800 0.0146991i
\(562\) 34540.9i 2.59256i
\(563\) 16595.3i 1.24229i 0.783696 + 0.621145i \(0.213332\pi\)
−0.783696 + 0.621145i \(0.786668\pi\)
\(564\) −4561.61 16255.2i −0.340565 1.21360i
\(565\) 918.941 + 11469.0i 0.0684251 + 0.853991i
\(566\) 1699.63 0.126220
\(567\) 4584.61 + 12699.0i 0.339569 + 0.940581i
\(568\) 11110.7i 0.820766i
\(569\) 15891.3i 1.17082i −0.810736 0.585412i \(-0.800933\pi\)
0.810736 0.585412i \(-0.199067\pi\)
\(570\) 29068.0 10727.4i 2.13601 0.788287i
\(571\) 1303.38 0.0955252 0.0477626 0.998859i \(-0.484791\pi\)
0.0477626 + 0.998859i \(0.484791\pi\)
\(572\) 6823.91i 0.498815i
\(573\) −889.725 3170.52i −0.0648670 0.231153i
\(574\) 7616.94 8210.86i 0.553876 0.597064i
\(575\) −16607.5 + 2678.51i −1.20449 + 0.194263i
\(576\) −19137.1 + 11658.8i −1.38434 + 0.843372i
\(577\) −8256.36 −0.595696 −0.297848 0.954613i \(-0.596269\pi\)
−0.297848 + 0.954613i \(0.596269\pi\)
\(578\) 21815.8 1.56993
\(579\) −6347.02 22617.5i −0.455567 1.62340i
\(580\) −26914.0 + 2156.45i −1.92680 + 0.154382i
\(581\) 4063.31 + 3769.40i 0.290146 + 0.269158i
\(582\) 12531.0 3516.51i 0.892487 0.250453i
\(583\) 6748.99i 0.479442i
\(584\) 8133.64 0.576323
\(585\) 3357.77 + 4633.16i 0.237311 + 0.327449i
\(586\) 10369.9i 0.731016i
\(587\) 22031.8i 1.54915i 0.632484 + 0.774573i \(0.282035\pi\)
−0.632484 + 0.774573i \(0.717965\pi\)
\(588\) −7237.27 19913.1i −0.507585 1.39660i
\(589\) −7354.86 −0.514519
\(590\) 2927.01 + 36531.0i 0.204242 + 2.54908i
\(591\) −19092.3 + 5357.76i −1.32885 + 0.372908i
\(592\) 6003.00i 0.416760i
\(593\) 11710.2i 0.810929i 0.914111 + 0.405465i \(0.132890\pi\)
−0.914111 + 0.405465i \(0.867110\pi\)
\(594\) 13863.0 + 12915.6i 0.957584 + 0.892142i
\(595\) 589.163 746.811i 0.0405938 0.0514559i
\(596\) 2283.79i 0.156959i
\(597\) −1881.29 6703.93i −0.128971 0.459587i
\(598\) −11376.0 −0.777926
\(599\) 14539.0i 0.991729i −0.868400 0.495865i \(-0.834851\pi\)
0.868400 0.495865i \(-0.165149\pi\)
\(600\) −10219.8 + 4730.31i −0.695372 + 0.321857i
\(601\) 20293.0i 1.37732i −0.725083 0.688661i \(-0.758199\pi\)
0.725083 0.688661i \(-0.241801\pi\)
\(602\) −16386.8 15201.5i −1.10943 1.02918i
\(603\) −10560.0 17333.5i −0.713164 1.17061i
\(604\) −25647.0 −1.72775
\(605\) −369.608 4612.96i −0.0248375 0.309989i
\(606\) 38667.9 10851.2i 2.59204 0.727390i
\(607\) −4143.51 −0.277068 −0.138534 0.990358i \(-0.544239\pi\)
−0.138534 + 0.990358i \(0.544239\pi\)
\(608\) 26072.2i 1.73909i
\(609\) 17391.5 + 8928.68i 1.15721 + 0.594103i
\(610\) 15518.4 1243.40i 1.03004 0.0825306i
\(611\) 5180.77i 0.343030i
\(612\) −767.159 1259.24i −0.0506709 0.0831727i
\(613\) 13166.7i 0.867534i 0.901025 + 0.433767i \(0.142816\pi\)
−0.901025 + 0.433767i \(0.857184\pi\)
\(614\) −15376.1 −1.01063
\(615\) 2727.48 + 7390.62i 0.178833 + 0.484583i
\(616\) −7129.06 6613.39i −0.466295 0.432567i
\(617\) 8241.67 0.537759 0.268880 0.963174i \(-0.413347\pi\)
0.268880 + 0.963174i \(0.413347\pi\)
\(618\) 38038.9 10674.6i 2.47597 0.694816i
\(619\) 12892.7i 0.837162i −0.908180 0.418581i \(-0.862528\pi\)
0.908180 0.418581i \(-0.137472\pi\)
\(620\) 8147.64 652.820i 0.527770 0.0422869i
\(621\) 12870.2 13814.3i 0.831665 0.892671i
\(622\) 34230.5 2.20662
\(623\) 5364.35 5782.63i 0.344973 0.371872i
\(624\) 1686.26 473.205i 0.108180 0.0303579i
\(625\) 14832.7 4912.32i 0.949294 0.314388i
\(626\) −43411.6 −2.77169
\(627\) −18119.1 + 5084.67i −1.15408 + 0.323863i
\(628\) 12081.7 0.767695
\(629\) −1550.87 −0.0983106
\(630\) 24750.6 + 3003.59i 1.56522 + 0.189946i
\(631\) 26758.6 1.68818 0.844092 0.536198i \(-0.180140\pi\)
0.844092 + 0.536198i \(0.180140\pi\)
\(632\) 2193.16 0.138037
\(633\) 3647.95 1023.70i 0.229057 0.0642790i
\(634\) 3070.69 0.192355
\(635\) 13950.2 1117.75i 0.871808 0.0698526i
\(636\) 13254.4 3719.50i 0.826368 0.231899i
\(637\) 487.245 + 6483.32i 0.0303067 + 0.403263i
\(638\) 27435.1 1.70246
\(639\) 9001.95 + 14776.1i 0.557295 + 0.914761i
\(640\) 1747.69 + 21812.4i 0.107943 + 1.34721i
\(641\) 12483.3i 0.769204i 0.923082 + 0.384602i \(0.125661\pi\)
−0.923082 + 0.384602i \(0.874339\pi\)
\(642\) 8874.98 2490.54i 0.545588 0.153105i
\(643\) −15859.5 −0.972689 −0.486345 0.873767i \(-0.661670\pi\)
−0.486345 + 0.873767i \(0.661670\pi\)
\(644\) −20150.7 + 21721.9i −1.23299 + 1.32914i
\(645\) 14749.8 5443.37i 0.900425 0.332298i
\(646\) 2450.13 0.149225
\(647\) 26235.0i 1.59413i −0.603893 0.797066i \(-0.706384\pi\)
0.603893 0.797066i \(-0.293616\pi\)
\(648\) 5796.79 11231.9i 0.351419 0.680910i
\(649\) 22259.1i 1.34629i
\(650\) 10431.7 1682.45i 0.629483 0.101525i
\(651\) −5264.92 2702.97i −0.316972 0.162731i
\(652\) 33893.5i 2.03584i
\(653\) −11488.0 −0.688451 −0.344226 0.938887i \(-0.611858\pi\)
−0.344226 + 0.938887i \(0.611858\pi\)
\(654\) 30849.6 8657.16i 1.84452 0.517617i
\(655\) 1094.21 + 13656.5i 0.0652740 + 0.814663i
\(656\) 2411.27 0.143513
\(657\) 10816.9 6589.91i 0.642324 0.391320i
\(658\) 16549.6 + 15352.5i 0.980501 + 0.909578i
\(659\) 13746.7i 0.812588i −0.913743 0.406294i \(-0.866821\pi\)
0.913743 0.406294i \(-0.133179\pi\)
\(660\) 19620.9 7241.00i 1.15718 0.427054i
\(661\) 18205.0i 1.07124i −0.844458 0.535621i \(-0.820077\pi\)
0.844458 0.535621i \(-0.179923\pi\)
\(662\) 19834.7 1.16450
\(663\) 122.252 + 435.644i 0.00716121 + 0.0255189i
\(664\) 5188.71i 0.303254i
\(665\) −15337.8 + 19441.9i −0.894398 + 1.13372i
\(666\) −21148.7 34714.2i −1.23048 2.01974i
\(667\) 27338.8i 1.58705i
\(668\) 22439.8i 1.29973i
\(669\) −16306.8 + 4576.09i −0.942389 + 0.264457i
\(670\) −37361.7 + 2993.56i −2.15434 + 0.172614i
\(671\) −9455.68 −0.544013
\(672\) 9581.75 18663.6i 0.550036 1.07137i
\(673\) 2132.80i 0.122160i 0.998133 + 0.0610799i \(0.0194544\pi\)
−0.998133 + 0.0610799i \(0.980546\pi\)
\(674\) 18228.8i 1.04176i
\(675\) −9758.77 + 14571.0i −0.556467 + 0.830870i
\(676\) −21846.4 −1.24296
\(677\) 995.751i 0.0565285i −0.999600 0.0282643i \(-0.991002\pi\)
0.999600 0.0282643i \(-0.00899799\pi\)
\(678\) −22960.2 + 6443.20i −1.30056 + 0.364970i
\(679\) −7074.36 + 7625.98i −0.399837 + 0.431013i
\(680\) −887.673 + 71.1237i −0.0500598 + 0.00401099i
\(681\) −5881.00 20956.8i −0.330926 1.17925i
\(682\) −8305.41 −0.466321
\(683\) −24097.2 −1.35000 −0.675002 0.737816i \(-0.735857\pi\)
−0.675002 + 0.737816i \(0.735857\pi\)
\(684\) 19971.6 + 32782.0i 1.11642 + 1.83253i
\(685\) 1561.28 + 19485.8i 0.0870853 + 1.08688i
\(686\) 22154.3 + 17655.9i 1.23303 + 0.982662i
\(687\) 2803.52 + 9990.29i 0.155693 + 0.554809i
\(688\) 4812.30i 0.266667i
\(689\) −4224.36 −0.233578
\(690\) −12071.3 32709.5i −0.666011 1.80468i
\(691\) 18883.3i 1.03959i 0.854291 + 0.519794i \(0.173991\pi\)
−0.854291 + 0.519794i \(0.826009\pi\)
\(692\) 41508.5i 2.28023i
\(693\) −14839.1 3019.11i −0.813406 0.165493i
\(694\) 25919.4 1.41771
\(695\) 23128.3 1853.12i 1.26231 0.101141i
\(696\) −4944.92 17621.1i −0.269306 0.959666i
\(697\) 622.951i 0.0338536i
\(698\) 12504.7i 0.678095i
\(699\) 708.928 198.942i 0.0383607 0.0107649i
\(700\) 15265.4 22898.9i 0.824253 1.23643i
\(701\) 6421.10i 0.345965i −0.984925 0.172983i \(-0.944660\pi\)
0.984925 0.172983i \(-0.0553404\pi\)
\(702\) −8084.17 + 8677.18i −0.434640 + 0.466523i
\(703\) 40374.2 2.16606
\(704\) 25133.8i 1.34555i
\(705\) −14896.3 + 5497.42i −0.795784 + 0.293681i
\(706\) 5276.01i 0.281254i
\(707\) −21829.9 + 23532.1i −1.16124 + 1.25179i
\(708\) −43714.7 + 12267.4i −2.32048 + 0.651183i
\(709\) −5206.72 −0.275800 −0.137900 0.990446i \(-0.544035\pi\)
−0.137900 + 0.990446i \(0.544035\pi\)
\(710\) 31849.1 2551.88i 1.68349 0.134888i
\(711\) 2916.67 1776.91i 0.153845 0.0937261i
\(712\) −7384.21 −0.388673
\(713\) 8276.24i 0.434709i
\(714\) 1753.91 + 900.443i 0.0919305 + 0.0471964i
\(715\) −6397.28 + 512.575i −0.334608 + 0.0268101i
\(716\) 2050.63i 0.107033i
\(717\) 3793.85 + 13519.3i 0.197607 + 0.704168i
\(718\) 38838.4i 2.01872i
\(719\) −26323.4 −1.36537 −0.682683 0.730715i \(-0.739187\pi\)
−0.682683 + 0.730715i \(0.739187\pi\)
\(720\) 3149.93 + 4346.38i 0.163043 + 0.224972i
\(721\) −21474.8 + 23149.2i −1.10924 + 1.19573i
\(722\) −33196.5 −1.71114
\(723\) −6036.27 21510.2i −0.310500 1.10646i
\(724\) 25045.5i 1.28565i
\(725\) 4043.26 + 25069.3i 0.207121 + 1.28421i
\(726\) 9234.85 2591.52i 0.472090 0.132480i
\(727\) −653.079 −0.0333169 −0.0166584 0.999861i \(-0.505303\pi\)
−0.0166584 + 0.999861i \(0.505303\pi\)
\(728\) 4139.48 4462.25i 0.210741 0.227173i
\(729\) −1391.00 19633.8i −0.0706700 0.997500i
\(730\) −1868.11 23315.3i −0.0947149 1.18211i
\(731\) 1243.26 0.0629049
\(732\) 5211.21 + 18570.1i 0.263131 + 0.937663i
\(733\) 19283.5 0.971696 0.485848 0.874043i \(-0.338511\pi\)
0.485848 + 0.874043i \(0.338511\pi\)
\(734\) −32787.7 −1.64880
\(735\) −18124.5 + 8280.56i −0.909568 + 0.415555i
\(736\) −29338.4 −1.46933
\(737\) 22765.2 1.13781
\(738\) −13943.9 + 8494.98i −0.695505 + 0.423719i
\(739\) 11829.3 0.588832 0.294416 0.955677i \(-0.404875\pi\)
0.294416 + 0.955677i \(0.404875\pi\)
\(740\) −44726.1 + 3583.63i −2.22184 + 0.178023i
\(741\) −3182.62 11341.2i −0.157782 0.562253i
\(742\) −12518.3 + 13494.4i −0.619354 + 0.667647i
\(743\) 15784.6 0.779380 0.389690 0.920946i \(-0.372582\pi\)
0.389690 + 0.920946i \(0.372582\pi\)
\(744\) 1496.97 + 5334.43i 0.0737656 + 0.262863i
\(745\) −2141.01 + 171.546i −0.105289 + 0.00843618i
\(746\) 5884.67i 0.288811i
\(747\) −4203.91 6900.43i −0.205908 0.337983i
\(748\) 1653.83 0.0808423
\(749\) −5010.36 + 5401.03i −0.244425 + 0.263484i
\(750\) 15906.8 + 28209.0i 0.774447 + 1.37339i
\(751\) −719.429 −0.0349565 −0.0174782 0.999847i \(-0.505564\pi\)
−0.0174782 + 0.999847i \(0.505564\pi\)
\(752\) 4860.09i 0.235677i
\(753\) 16544.8 4642.88i 0.800700 0.224696i
\(754\) 17172.3i 0.829415i
\(755\) 1926.46 + 24043.5i 0.0928623 + 1.15899i
\(756\) 2248.87 + 30806.5i 0.108189 + 1.48204i
\(757\) 23060.3i 1.10719i −0.832787 0.553593i \(-0.813256\pi\)
0.832787 0.553593i \(-0.186744\pi\)
\(758\) −46086.4 −2.20835
\(759\) 5721.65 + 20389.0i 0.273627 + 0.975064i
\(760\) 23109.0 1851.58i 1.10296 0.0883735i
\(761\) 19804.3 0.943371 0.471686 0.881767i \(-0.343646\pi\)
0.471686 + 0.881767i \(0.343646\pi\)
\(762\) 7837.13 + 27927.5i 0.372584 + 1.32770i
\(763\) −17416.1 + 18774.1i −0.826351 + 0.890784i
\(764\) 7533.77i 0.356757i
\(765\) −1122.89 + 813.784i −0.0530693 + 0.0384607i
\(766\) 59437.4i 2.80361i
\(767\) 13932.5 0.655897
\(768\) −10449.6 + 2932.41i −0.490972 + 0.137779i
\(769\) 14623.5i 0.685746i 0.939382 + 0.342873i \(0.111400\pi\)
−0.939382 + 0.342873i \(0.888600\pi\)
\(770\) −17320.1 + 21954.6i −0.810613 + 1.02752i
\(771\) 5518.88 + 19666.4i 0.257792 + 0.918637i
\(772\) 53743.5i 2.50553i
\(773\) 40353.9i 1.87766i −0.344384 0.938829i \(-0.611912\pi\)
0.344384 0.938829i \(-0.388088\pi\)
\(774\) 16953.9 + 27828.6i 0.787331 + 1.29235i
\(775\) −1224.01 7589.22i −0.0567327 0.351758i
\(776\) 9738.10 0.450486
\(777\) 28901.6 + 14837.8i 1.33441 + 0.685077i
\(778\) 27575.6i 1.27074i
\(779\) 16217.4i 0.745891i
\(780\) 4532.32 + 12281.2i 0.208055 + 0.563765i
\(781\) −19406.3 −0.889131
\(782\) 2757.07i 0.126078i
\(783\) −20852.9 19427.8i −0.951754 0.886710i
\(784\) 457.086 + 6082.01i 0.0208220 + 0.277059i
\(785\) −907.511 11326.4i −0.0412617 0.514974i
\(786\) −27339.5 + 7672.12i −1.24067 + 0.348162i
\(787\) −9011.80 −0.408178 −0.204089 0.978952i \(-0.565423\pi\)
−0.204089 + 0.978952i \(0.565423\pi\)
\(788\) −45367.0 −2.05093
\(789\) −10422.1 + 2924.71i −0.470264 + 0.131968i
\(790\) −503.718 6286.75i −0.0226854 0.283130i
\(791\) 12962.2 13972.9i 0.582656 0.628088i
\(792\) 7375.74 + 12106.8i 0.330916 + 0.543176i
\(793\) 5918.54i 0.265036i
\(794\) 12141.3 0.542670
\(795\) −4482.55 12146.3i −0.199975 0.541869i
\(796\) 15929.8i 0.709319i
\(797\) 23157.4i 1.02921i −0.857428 0.514604i \(-0.827939\pi\)
0.857428 0.514604i \(-0.172061\pi\)
\(798\) −45659.8 23441.4i −2.02549 1.03987i
\(799\) −1255.60 −0.0555945
\(800\) 26902.9 4338.99i 1.18895 0.191758i
\(801\) −9820.22 + 5982.72i −0.433184 + 0.263907i
\(802\) 28362.3i 1.24876i
\(803\) 14206.4i 0.624327i
\(804\) −12546.3 44708.7i −0.550342 1.96114i
\(805\) 21877.5 + 17259.2i 0.957863 + 0.755663i
\(806\) 5198.56i 0.227186i
\(807\) −14538.1 + 4079.73i −0.634156 + 0.177960i
\(808\) 30049.6 1.30834
\(809\) 612.672i 0.0266259i −0.999911 0.0133130i \(-0.995762\pi\)
0.999911 0.0133130i \(-0.00423778\pi\)
\(810\) −33527.8 14037.0i −1.45438 0.608899i
\(811\) 20636.7i 0.893529i 0.894652 + 0.446764i \(0.147424\pi\)
−0.894652 + 0.446764i \(0.852576\pi\)
\(812\) 32789.7 + 30417.9i 1.41711 + 1.31460i
\(813\) −1005.22 3582.09i −0.0433637 0.154526i
\(814\) 45592.2 1.96315
\(815\) 31774.4 2545.89i 1.36566 0.109422i
\(816\) 114.685 + 408.678i 0.00492007 + 0.0175326i
\(817\) −32365.9 −1.38597
\(818\) 10003.2i 0.427571i
\(819\) 1889.73 9288.15i 0.0806259 0.396281i
\(820\) 1439.46 + 17965.5i 0.0613028 + 0.765100i
\(821\) 29514.0i 1.25462i 0.778768 + 0.627312i \(0.215845\pi\)
−0.778768 + 0.627312i \(0.784155\pi\)
\(822\) −39009.4 + 10947.0i −1.65524 + 0.464501i
\(823\) 8964.57i 0.379690i 0.981814 + 0.189845i \(0.0607986\pi\)
−0.981814 + 0.189845i \(0.939201\pi\)
\(824\) 29560.8 1.24975
\(825\) −8262.10 17850.3i −0.348666 0.753292i
\(826\) 41287.0 44506.3i 1.73917 1.87478i
\(827\) −36886.7 −1.55100 −0.775500 0.631348i \(-0.782502\pi\)
−0.775500 + 0.631348i \(0.782502\pi\)
\(828\) 36888.7 22473.6i 1.54828 0.943249i
\(829\) 29077.8i 1.21823i −0.793081 0.609116i \(-0.791525\pi\)
0.793081 0.609116i \(-0.208475\pi\)
\(830\) −14873.6 + 1191.73i −0.622011 + 0.0498379i
\(831\) 142.135 + 506.495i 0.00593334 + 0.0211434i
\(832\) 15731.9 0.655535
\(833\) −1571.29 + 118.088i −0.0653563 + 0.00491177i
\(834\) 12993.3 + 46301.3i 0.539472 + 1.92240i
\(835\) −21036.8 + 1685.55i −0.871868 + 0.0698574i
\(836\) −43054.5 −1.78119
\(837\) 6312.79 + 5881.37i 0.260695 + 0.242879i
\(838\) 56036.2 2.30995
\(839\) 32262.6 1.32757 0.663784 0.747924i \(-0.268949\pi\)
0.663784 + 0.747924i \(0.268949\pi\)
\(840\) 17222.8 + 7167.30i 0.707434 + 0.294399i
\(841\) −16879.4 −0.692091
\(842\) 17408.3 0.712505
\(843\) 10873.9 + 38749.1i 0.444268 + 1.58314i
\(844\) 8668.25 0.353523
\(845\) 1640.98 + 20480.5i 0.0668063 + 0.833789i
\(846\) −17122.2 28104.9i −0.695833 1.14216i
\(847\) −5213.52 + 5620.03i −0.211498 + 0.227989i
\(848\) −3962.88 −0.160478
\(849\) 1906.70 535.066i 0.0770762 0.0216295i
\(850\) 407.756 + 2528.20i 0.0164540 + 0.102019i
\(851\) 45432.1i 1.83007i
\(852\) 10695.2 + 38112.1i 0.430060 + 1.53251i
\(853\) −14995.9 −0.601935 −0.300968 0.953634i \(-0.597310\pi\)
−0.300968 + 0.953634i \(0.597310\pi\)
\(854\) −18906.3 17538.8i −0.757566 0.702768i
\(855\) 29232.3 21185.4i 1.16927 0.847398i
\(856\) 6896.93 0.275388
\(857\) 36795.5i 1.46664i −0.679884 0.733319i \(-0.737970\pi\)
0.679884 0.733319i \(-0.262030\pi\)
\(858\) −3593.94 12806.9i −0.143001 0.509583i
\(859\) 6908.88i 0.274421i 0.990542 + 0.137211i \(0.0438137\pi\)
−0.990542 + 0.137211i \(0.956186\pi\)
\(860\) 35854.6 2872.81i 1.42167 0.113909i
\(861\) 5960.04 11609.1i 0.235909 0.459509i
\(862\) 22431.4i 0.886330i
\(863\) −4307.42 −0.169903 −0.0849515 0.996385i \(-0.527074\pi\)
−0.0849515 + 0.996385i \(0.527074\pi\)
\(864\) −20848.8 + 22378.2i −0.820940 + 0.881158i
\(865\) 38913.4 3117.89i 1.52959 0.122557i
\(866\) 66288.3 2.60112
\(867\) 24473.6 6867.90i 0.958672 0.269027i
\(868\) −9926.39 9208.37i −0.388161 0.360084i
\(869\) 3830.64i 0.149534i
\(870\) −49375.7 + 18221.9i −1.92413 + 0.710092i
\(871\) 14249.3i 0.554327i
\(872\) 23973.9 0.931030
\(873\) 12950.6 7889.85i 0.502076 0.305878i
\(874\) 71775.4i 2.77785i
\(875\) −22613.9 12591.0i −0.873703 0.486459i
\(876\) 27900.1 7829.46i 1.07609 0.301978i
\(877\) 1580.51i 0.0608552i 0.999537 + 0.0304276i \(0.00968690\pi\)
−0.999537 + 0.0304276i \(0.990313\pi\)
\(878\) 50322.9i 1.93430i
\(879\) −3264.57 11633.2i −0.125269 0.446393i
\(880\) −6001.30 + 480.847i −0.229891 + 0.0184197i
\(881\) −29644.9 −1.13367 −0.566834 0.823832i \(-0.691832\pi\)
−0.566834 + 0.823832i \(0.691832\pi\)
\(882\) −24070.3 33560.7i −0.918923 1.28123i
\(883\) 16316.4i 0.621847i 0.950435 + 0.310923i \(0.100638\pi\)
−0.950435 + 0.310923i \(0.899362\pi\)
\(884\) 1035.17i 0.0393854i
\(885\) 14784.1 + 40060.2i 0.561538 + 1.52159i
\(886\) −28569.1 −1.08329
\(887\) 16452.1i 0.622783i −0.950282 0.311392i \(-0.899205\pi\)
0.950282 0.311392i \(-0.100795\pi\)
\(888\) −8217.56 29283.1i −0.310544 1.10662i
\(889\) −16995.8 15766.4i −0.641192 0.594812i
\(890\) 1695.98 + 21167.0i 0.0638759 + 0.797214i
\(891\) 19617.9 + 10124.8i 0.737626 + 0.380690i
\(892\) −38748.2 −1.45447
\(893\) 32687.4 1.22491
\(894\) −1202.80 4286.16i −0.0449974 0.160347i
\(895\) 1922.43 154.032i 0.0717985 0.00575277i
\(896\) 24652.1 26574.4i 0.919163 0.990834i
\(897\) −12762.0 + 3581.32i −0.475039 + 0.133307i
\(898\) 25185.2i 0.935905i
\(899\) 12493.2 0.463482
\(900\) −30502.8 + 26063.6i −1.12973 + 0.965319i
\(901\) 1023.81i 0.0378557i
\(902\) 18313.4i 0.676018i
\(903\) −23168.9 11894.8i −0.853835 0.438353i
\(904\) −17842.8 −0.656465
\(905\) 23479.6 1881.28i 0.862419 0.0691003i
\(906\) −48133.6 + 13507.5i −1.76505 + 0.495315i
\(907\) 15972.5i 0.584737i 0.956306 + 0.292369i \(0.0944434\pi\)
−0.956306 + 0.292369i \(0.905557\pi\)
\(908\) 49797.5i 1.82003i
\(909\) 39962.8 24346.3i 1.45818 0.888358i
\(910\) −13741.9 10841.1i −0.500593 0.394920i
\(911\) 47647.5i 1.73285i 0.499303 + 0.866427i \(0.333589\pi\)
−0.499303 + 0.866427i \(0.666411\pi\)
\(912\) −2985.62 10639.2i −0.108403 0.386293i
\(913\) 9062.74 0.328514
\(914\) 17960.6i 0.649983i
\(915\) 17017.6 6280.29i 0.614848 0.226907i
\(916\) 23738.9i 0.856282i
\(917\) 15434.4 16637.9i 0.555824 0.599163i
\(918\) −2102.99 1959.27i −0.0756088 0.0704416i
\(919\) −40628.7 −1.45834 −0.729171 0.684331i \(-0.760094\pi\)
−0.729171 + 0.684331i \(0.760094\pi\)
\(920\) −2083.54 26003.9i −0.0746654 0.931874i
\(921\) −17249.4 + 4840.60i −0.617142 + 0.173185i
\(922\) 19274.9 0.688487
\(923\) 12146.9i 0.433174i
\(924\) −30820.3 15822.9i −1.09731 0.563350i
\(925\) 6719.16 + 41660.7i 0.238837 + 1.48086i
\(926\) 58366.2i 2.07131i
\(927\) 39312.7 23950.3i 1.39288 0.848576i
\(928\) 44286.9i 1.56658i
\(929\) −42333.4 −1.49506 −0.747532 0.664226i \(-0.768761\pi\)
−0.747532 + 0.664226i \(0.768761\pi\)
\(930\) 14947.5 5516.30i 0.527039 0.194502i
\(931\) 40905.6 3074.21i 1.43999 0.108220i
\(932\) 1684.55 0.0592052
\(933\) 38400.9 10776.2i 1.34747 0.378132i
\(934\) 11260.6i 0.394495i
\(935\) −124.227 1550.43i −0.00434508 0.0542295i
\(936\) −7577.92 + 4616.66i −0.264628 + 0.161218i
\(937\) −14777.6 −0.515224 −0.257612 0.966248i \(-0.582936\pi\)
−0.257612 + 0.966248i \(0.582936\pi\)
\(938\) 45518.3 + 42225.8i 1.58446 + 1.46985i
\(939\) −48700.5 + 13666.5i −1.69252 + 0.474963i
\(940\) −36210.7 + 2901.34i −1.25645 + 0.100672i
\(941\) −37729.8 −1.30707 −0.653537 0.756894i \(-0.726716\pi\)
−0.653537 + 0.756894i \(0.726716\pi\)
\(942\) 22674.6 6363.05i 0.784266 0.220084i
\(943\) −18249.1 −0.630192
\(944\) 13070.1 0.450631
\(945\) 28711.5 4422.29i 0.988345 0.152230i
\(946\) −36548.9 −1.25614
\(947\) −13860.2 −0.475602 −0.237801 0.971314i \(-0.576427\pi\)
−0.237801 + 0.971314i \(0.576427\pi\)
\(948\) 7523.01 2111.14i 0.257738 0.0723276i
\(949\) −8892.17 −0.304164
\(950\) −10615.2 65817.2i −0.362529 2.24778i
\(951\) 3444.80 966.695i 0.117461 0.0329624i
\(952\) 1081.46 + 1003.24i 0.0368177 + 0.0341545i
\(953\) 54882.6 1.86550 0.932750 0.360523i \(-0.117402\pi\)
0.932750 + 0.360523i \(0.117402\pi\)
\(954\) 22916.5 13961.3i 0.777725 0.473810i
\(955\) −7062.76 + 565.896i −0.239315 + 0.0191748i
\(956\) 32124.5i 1.08680i
\(957\) 30777.6 8636.94i 1.03960 0.291737i
\(958\) −14161.6 −0.477600
\(959\) 22022.7 23739.9i 0.741553 0.799374i
\(960\) 16693.4 + 45234.0i 0.561228 + 1.52075i
\(961\) 26009.0 0.873048
\(962\) 28537.3i 0.956423i
\(963\) 9172.18 5587.92i 0.306926 0.186987i
\(964\) 51112.3i 1.70769i
\(965\) −50383.5 + 4036.92i −1.68073 + 0.134666i
\(966\) −26378.1 + 51379.9i −0.878571 + 1.71130i
\(967\) 21656.2i 0.720183i −0.932917 0.360092i \(-0.882745\pi\)
0.932917 0.360092i \(-0.117255\pi\)
\(968\) 7176.58 0.238289
\(969\) 2748.63 771.333i 0.0911237 0.0255715i
\(970\) −2236.62 27914.5i −0.0740345 0.924001i
\(971\) 4409.47 0.145733 0.0728664 0.997342i \(-0.476785\pi\)
0.0728664 + 0.997342i \(0.476785\pi\)
\(972\) 9072.43 44107.7i 0.299381 1.45551i
\(973\) −28177.5 26139.3i −0.928395 0.861241i
\(974\) 17712.6i 0.582699i
\(975\) 11172.9 5171.45i 0.366995 0.169866i
\(976\) 5552.19i 0.182092i
\(977\) −36452.4 −1.19367 −0.596834 0.802364i \(-0.703575\pi\)
−0.596834 + 0.802364i \(0.703575\pi\)
\(978\) 17850.6 + 63610.4i 0.583640 + 2.07979i
\(979\) 12897.5i 0.421047i
\(980\) −45041.9 + 7036.37i −1.46817 + 0.229356i
\(981\) 31882.7 19423.7i 1.03765 0.632164i
\(982\) 48406.2i 1.57302i
\(983\) 2111.09i 0.0684979i −0.999413 0.0342489i \(-0.989096\pi\)
0.999413 0.0342489i \(-0.0109039\pi\)
\(984\) −11762.4 + 3300.81i −0.381068 + 0.106937i
\(985\) 3407.72 + 42530.6i 0.110232 + 1.37577i
\(986\) −4161.85 −0.134422
\(987\) 23399.0 + 12012.9i 0.754608 + 0.387410i
\(988\) 26948.9i 0.867772i
\(989\) 36420.6i 1.17099i
\(990\) 33010.3 23923.4i 1.05973 0.768016i
\(991\) 5791.29 0.185637 0.0928186 0.995683i \(-0.470412\pi\)
0.0928186 + 0.995683i \(0.470412\pi\)
\(992\) 13406.9i 0.429103i
\(993\) 22251.2 6244.24i 0.711099 0.199552i
\(994\) −38802.3 35995.5i −1.23816 1.14860i
\(995\) −14933.9 + 1196.56i −0.475816 + 0.0381242i
\(996\) −4994.66 17798.4i −0.158897 0.566228i
\(997\) −15024.7 −0.477269 −0.238635 0.971109i \(-0.576700\pi\)
−0.238635 + 0.971109i \(0.576700\pi\)
\(998\) −21417.4 −0.679314
\(999\) −34653.8 32285.5i −1.09750 1.02249i
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.104.35 yes 40
3.2 odd 2 inner 105.4.g.b.104.8 yes 40
5.4 even 2 inner 105.4.g.b.104.6 yes 40
7.6 odd 2 inner 105.4.g.b.104.34 yes 40
15.14 odd 2 inner 105.4.g.b.104.33 yes 40
21.20 even 2 inner 105.4.g.b.104.5 40
35.34 odd 2 inner 105.4.g.b.104.7 yes 40
105.104 even 2 inner 105.4.g.b.104.36 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.g.b.104.5 40 21.20 even 2 inner
105.4.g.b.104.6 yes 40 5.4 even 2 inner
105.4.g.b.104.7 yes 40 35.34 odd 2 inner
105.4.g.b.104.8 yes 40 3.2 odd 2 inner
105.4.g.b.104.33 yes 40 15.14 odd 2 inner
105.4.g.b.104.34 yes 40 7.6 odd 2 inner
105.4.g.b.104.35 yes 40 1.1 even 1 trivial
105.4.g.b.104.36 yes 40 105.104 even 2 inner