Properties

Label 105.4.s.a.101.11
Level $105$
Weight $4$
Character 105.101
Analytic conductor $6.195$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,4,Mod(26,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.26");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.s (of order \(6\), degree \(2\), 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: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.11
Character \(\chi\) \(=\) 105.101
Dual form 105.4.s.a.26.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.48940 - 0.859905i) q^{2} +(-4.11977 - 3.16663i) q^{3} +(-2.52113 + 4.36672i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.85898 - 1.17376i) q^{6} +(2.28179 + 18.3792i) q^{7} +22.4302i q^{8} +(6.94494 + 26.0915i) q^{9} +O(q^{10})\) \(q+(1.48940 - 0.859905i) q^{2} +(-4.11977 - 3.16663i) q^{3} +(-2.52113 + 4.36672i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(-8.85898 - 1.17376i) q^{6} +(2.28179 + 18.3792i) q^{7} +22.4302i q^{8} +(6.94494 + 26.0915i) q^{9} +(-7.44700 - 4.29953i) q^{10} +(49.7733 + 28.7366i) q^{11} +(24.2142 - 10.0064i) q^{12} -44.6643i q^{13} +(19.2028 + 25.4118i) q^{14} +(-3.41248 + 25.7557i) q^{15} +(-0.881158 - 1.52621i) q^{16} +(-54.8920 + 95.0758i) q^{17} +(32.7800 + 32.8887i) q^{18} +(-79.5306 + 45.9170i) q^{19} +25.2113 q^{20} +(48.7995 - 82.9434i) q^{21} +98.8431 q^{22} +(-27.1329 + 15.6652i) q^{23} +(71.0281 - 92.4072i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-38.4071 - 66.5230i) q^{26} +(54.0106 - 129.483i) q^{27} +(-86.0093 - 36.3722i) q^{28} +183.561i q^{29} +(17.0649 + 41.2949i) q^{30} +(123.493 + 71.2990i) q^{31} +(-158.026 - 91.2362i) q^{32} +(-114.056 - 276.002i) q^{33} +188.808i q^{34} +(73.8796 - 55.8283i) q^{35} +(-131.443 - 35.4534i) q^{36} +(-114.912 - 199.033i) q^{37} +(-78.9686 + 136.778i) q^{38} +(-141.435 + 184.006i) q^{39} +(97.1256 - 56.0755i) q^{40} +185.753 q^{41} +(1.35845 - 165.499i) q^{42} -22.3617 q^{43} +(-250.969 + 144.897i) q^{44} +(95.6173 - 95.3013i) q^{45} +(-26.9412 + 46.6635i) q^{46} +(-116.516 - 201.811i) q^{47} +(-1.20277 + 9.07793i) q^{48} +(-332.587 + 83.8749i) q^{49} +42.9953i q^{50} +(527.212 - 217.867i) q^{51} +(195.036 + 112.604i) q^{52} +(400.091 + 230.993i) q^{53} +(-30.8998 - 239.296i) q^{54} -287.366i q^{55} +(-412.248 + 51.1811i) q^{56} +(473.050 + 62.6764i) q^{57} +(157.845 + 273.395i) q^{58} +(229.693 - 397.840i) q^{59} +(-103.864 - 79.8347i) q^{60} +(-248.601 + 143.530i) q^{61} +245.241 q^{62} +(-463.693 + 187.178i) q^{63} -299.720 q^{64} +(-193.402 + 111.661i) q^{65} +(-407.210 - 312.999i) q^{66} +(416.027 - 720.580i) q^{67} +(-276.779 - 479.396i) q^{68} +(161.387 + 21.3829i) q^{69} +(62.0292 - 146.680i) q^{70} +471.261i q^{71} +(-585.238 + 155.776i) q^{72} +(469.038 + 270.799i) q^{73} +(-342.300 - 197.627i) q^{74} +(120.057 - 49.6127i) q^{75} -463.050i q^{76} +(-414.583 + 980.362i) q^{77} +(-52.4254 + 395.680i) q^{78} +(-175.522 - 304.014i) q^{79} +(-4.40579 + 7.63105i) q^{80} +(-632.536 + 362.408i) q^{81} +(276.661 - 159.730i) q^{82} +866.597 q^{83} +(239.161 + 422.204i) q^{84} +548.920 q^{85} +(-33.3055 + 19.2290i) q^{86} +(581.269 - 756.228i) q^{87} +(-644.568 + 1116.43i) q^{88} +(519.613 + 899.995i) q^{89} +(60.4622 - 224.164i) q^{90} +(820.892 - 101.915i) q^{91} -157.976i q^{92} +(-282.987 - 684.793i) q^{93} +(-347.077 - 200.385i) q^{94} +(397.653 + 229.585i) q^{95} +(362.118 + 876.281i) q^{96} -323.548i q^{97} +(-423.230 + 410.916i) q^{98} +(-404.110 + 1498.24i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48940 0.859905i 0.526582 0.304022i −0.213041 0.977043i \(-0.568337\pi\)
0.739624 + 0.673021i \(0.235004\pi\)
\(3\) −4.11977 3.16663i −0.792849 0.609418i
\(4\) −2.52113 + 4.36672i −0.315141 + 0.545840i
\(5\) −2.50000 4.33013i −0.223607 0.387298i
\(6\) −8.85898 1.17376i −0.602777 0.0798646i
\(7\) 2.28179 + 18.3792i 0.123205 + 0.992381i
\(8\) 22.4302i 0.991284i
\(9\) 6.94494 + 26.0915i 0.257220 + 0.966353i
\(10\) −7.44700 4.29953i −0.235495 0.135963i
\(11\) 49.7733 + 28.7366i 1.36429 + 0.787674i 0.990192 0.139714i \(-0.0446183\pi\)
0.374100 + 0.927388i \(0.377952\pi\)
\(12\) 24.2142 10.0064i 0.582504 0.240716i
\(13\) 44.6643i 0.952896i −0.879203 0.476448i \(-0.841924\pi\)
0.879203 0.476448i \(-0.158076\pi\)
\(14\) 19.2028 + 25.4118i 0.366584 + 0.485113i
\(15\) −3.41248 + 25.7557i −0.0587400 + 0.443339i
\(16\) −0.881158 1.52621i −0.0137681 0.0238470i
\(17\) −54.8920 + 95.0758i −0.783134 + 1.35643i 0.146974 + 0.989140i \(0.453047\pi\)
−0.930108 + 0.367287i \(0.880287\pi\)
\(18\) 32.7800 + 32.8887i 0.429241 + 0.430664i
\(19\) −79.5306 + 45.9170i −0.960293 + 0.554426i −0.896263 0.443522i \(-0.853729\pi\)
−0.0640300 + 0.997948i \(0.520395\pi\)
\(20\) 25.2113 0.281870
\(21\) 48.7995 82.9434i 0.507091 0.861892i
\(22\) 98.8431 0.957883
\(23\) −27.1329 + 15.6652i −0.245983 + 0.142018i −0.617923 0.786238i \(-0.712026\pi\)
0.371941 + 0.928257i \(0.378693\pi\)
\(24\) 71.0281 92.4072i 0.604106 0.785939i
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −38.4071 66.5230i −0.289702 0.501778i
\(27\) 54.0106 129.483i 0.384976 0.922927i
\(28\) −86.0093 36.3722i −0.580508 0.245489i
\(29\) 183.561i 1.17539i 0.809082 + 0.587696i \(0.199965\pi\)
−0.809082 + 0.587696i \(0.800035\pi\)
\(30\) 17.0649 + 41.2949i 0.103854 + 0.251313i
\(31\) 123.493 + 71.2990i 0.715486 + 0.413086i 0.813089 0.582139i \(-0.197784\pi\)
−0.0976027 + 0.995225i \(0.531117\pi\)
\(32\) −158.026 91.2362i −0.872977 0.504014i
\(33\) −114.056 276.002i −0.601655 1.45593i
\(34\) 188.808i 0.952361i
\(35\) 73.8796 55.8283i 0.356798 0.269620i
\(36\) −131.443 35.4534i −0.608534 0.164136i
\(37\) −114.912 199.033i −0.510579 0.884349i −0.999925 0.0122589i \(-0.996098\pi\)
0.489346 0.872090i \(-0.337236\pi\)
\(38\) −78.9686 + 136.778i −0.337116 + 0.583901i
\(39\) −141.435 + 184.006i −0.580711 + 0.755503i
\(40\) 97.1256 56.0755i 0.383923 0.221658i
\(41\) 185.753 0.707555 0.353778 0.935330i \(-0.384897\pi\)
0.353778 + 0.935330i \(0.384897\pi\)
\(42\) 1.35845 165.499i 0.00499080 0.608024i
\(43\) −22.3617 −0.0793054 −0.0396527 0.999214i \(-0.512625\pi\)
−0.0396527 + 0.999214i \(0.512625\pi\)
\(44\) −250.969 + 144.897i −0.859888 + 0.496457i
\(45\) 95.6173 95.3013i 0.316751 0.315704i
\(46\) −26.9412 + 46.6635i −0.0863535 + 0.149569i
\(47\) −116.516 201.811i −0.361608 0.626323i 0.626618 0.779326i \(-0.284439\pi\)
−0.988226 + 0.153004i \(0.951105\pi\)
\(48\) −1.20277 + 9.07793i −0.00361678 + 0.0272976i
\(49\) −332.587 + 83.8749i −0.969641 + 0.244533i
\(50\) 42.9953i 0.121609i
\(51\) 527.212 217.867i 1.44754 0.598187i
\(52\) 195.036 + 112.604i 0.520128 + 0.300296i
\(53\) 400.091 + 230.993i 1.03692 + 0.598666i 0.918959 0.394352i \(-0.129031\pi\)
0.117961 + 0.993018i \(0.462364\pi\)
\(54\) −30.8998 239.296i −0.0778690 0.603038i
\(55\) 287.366i 0.704517i
\(56\) −412.248 + 51.1811i −0.983732 + 0.122131i
\(57\) 473.050 + 62.6764i 1.09924 + 0.145644i
\(58\) 157.845 + 273.395i 0.357346 + 0.618941i
\(59\) 229.693 397.840i 0.506839 0.877872i −0.493129 0.869956i \(-0.664147\pi\)
0.999969 0.00791551i \(-0.00251961\pi\)
\(60\) −103.864 79.8347i −0.223481 0.171777i
\(61\) −248.601 + 143.530i −0.521804 + 0.301264i −0.737673 0.675159i \(-0.764075\pi\)
0.215868 + 0.976423i \(0.430742\pi\)
\(62\) 245.241 0.502350
\(63\) −463.693 + 187.178i −0.927300 + 0.374320i
\(64\) −299.720 −0.585390
\(65\) −193.402 + 111.661i −0.369055 + 0.213074i
\(66\) −407.210 312.999i −0.759457 0.583751i
\(67\) 416.027 720.580i 0.758594 1.31392i −0.184973 0.982744i \(-0.559220\pi\)
0.943568 0.331180i \(-0.107447\pi\)
\(68\) −276.779 479.396i −0.493595 0.854931i
\(69\) 161.387 + 21.3829i 0.281576 + 0.0373072i
\(70\) 62.0292 146.680i 0.105913 0.250452i
\(71\) 471.261i 0.787723i 0.919170 + 0.393862i \(0.128861\pi\)
−0.919170 + 0.393862i \(0.871139\pi\)
\(72\) −585.238 + 155.776i −0.957930 + 0.254978i
\(73\) 469.038 + 270.799i 0.752010 + 0.434173i 0.826420 0.563054i \(-0.190374\pi\)
−0.0744096 + 0.997228i \(0.523707\pi\)
\(74\) −342.300 197.627i −0.537724 0.310455i
\(75\) 120.057 49.6127i 0.184839 0.0763838i
\(76\) 463.050i 0.698888i
\(77\) −414.583 + 980.362i −0.613585 + 1.45094i
\(78\) −52.4254 + 395.680i −0.0761026 + 0.574384i
\(79\) −175.522 304.014i −0.249972 0.432965i 0.713546 0.700609i \(-0.247088\pi\)
−0.963518 + 0.267644i \(0.913755\pi\)
\(80\) −4.40579 + 7.63105i −0.00615728 + 0.0106647i
\(81\) −632.536 + 362.408i −0.867676 + 0.497131i
\(82\) 276.661 159.730i 0.372586 0.215113i
\(83\) 866.597 1.14604 0.573020 0.819541i \(-0.305772\pi\)
0.573020 + 0.819541i \(0.305772\pi\)
\(84\) 239.161 + 422.204i 0.310650 + 0.548408i
\(85\) 548.920 0.700456
\(86\) −33.3055 + 19.2290i −0.0417608 + 0.0241106i
\(87\) 581.269 756.228i 0.716305 0.931909i
\(88\) −644.568 + 1116.43i −0.780809 + 1.35240i
\(89\) 519.613 + 899.995i 0.618863 + 1.07190i 0.989694 + 0.143202i \(0.0457398\pi\)
−0.370830 + 0.928701i \(0.620927\pi\)
\(90\) 60.4622 224.164i 0.0708142 0.262543i
\(91\) 820.892 101.915i 0.945636 0.117402i
\(92\) 157.976i 0.179023i
\(93\) −282.987 684.793i −0.315531 0.763545i
\(94\) −347.077 200.385i −0.380832 0.219874i
\(95\) 397.653 + 229.585i 0.429456 + 0.247947i
\(96\) 362.118 + 876.281i 0.384985 + 0.931615i
\(97\) 323.548i 0.338674i −0.985558 0.169337i \(-0.945837\pi\)
0.985558 0.169337i \(-0.0541626\pi\)
\(98\) −423.230 + 410.916i −0.436252 + 0.423559i
\(99\) −404.110 + 1498.24i −0.410248 + 1.52099i
\(100\) −63.0281 109.168i −0.0630281 0.109168i
\(101\) −87.3093 + 151.224i −0.0860158 + 0.148984i −0.905824 0.423655i \(-0.860747\pi\)
0.819808 + 0.572639i \(0.194080\pi\)
\(102\) 597.884 777.844i 0.580385 0.755079i
\(103\) −907.603 + 524.005i −0.868241 + 0.501279i −0.866763 0.498720i \(-0.833804\pi\)
−0.00147739 + 0.999999i \(0.500470\pi\)
\(104\) 1001.83 0.944590
\(105\) −481.154 3.94942i −0.447199 0.00367071i
\(106\) 794.528 0.728032
\(107\) 1345.17 776.636i 1.21535 0.701684i 0.251432 0.967875i \(-0.419098\pi\)
0.963920 + 0.266190i \(0.0857650\pi\)
\(108\) 429.248 + 562.292i 0.382449 + 0.500987i
\(109\) −274.721 + 475.830i −0.241408 + 0.418131i −0.961116 0.276146i \(-0.910943\pi\)
0.719708 + 0.694277i \(0.244276\pi\)
\(110\) −247.108 428.003i −0.214189 0.370986i
\(111\) −156.854 + 1183.85i −0.134126 + 1.01231i
\(112\) 26.0398 19.6774i 0.0219690 0.0166013i
\(113\) 1141.04i 0.949913i 0.880009 + 0.474957i \(0.157536\pi\)
−0.880009 + 0.474957i \(0.842464\pi\)
\(114\) 758.456 313.428i 0.623122 0.257502i
\(115\) 135.665 + 78.3260i 0.110007 + 0.0635125i
\(116\) −801.558 462.780i −0.641576 0.370414i
\(117\) 1165.36 310.191i 0.920833 0.245104i
\(118\) 790.058i 0.616362i
\(119\) −1872.66 791.926i −1.44258 0.610048i
\(120\) −577.705 76.5427i −0.439475 0.0582280i
\(121\) 986.087 + 1707.95i 0.740862 + 1.28321i
\(122\) −246.844 + 427.546i −0.183182 + 0.317280i
\(123\) −765.259 588.211i −0.560985 0.431197i
\(124\) −622.685 + 359.507i −0.450958 + 0.260361i
\(125\) 125.000 0.0894427
\(126\) −529.670 + 677.515i −0.374498 + 0.479030i
\(127\) −1279.98 −0.894329 −0.447165 0.894452i \(-0.647566\pi\)
−0.447165 + 0.894452i \(0.647566\pi\)
\(128\) 817.804 472.159i 0.564722 0.326042i
\(129\) 92.1251 + 70.8112i 0.0628772 + 0.0483301i
\(130\) −192.035 + 332.615i −0.129559 + 0.224402i
\(131\) −1165.86 2019.33i −0.777569 1.34679i −0.933339 0.358995i \(-0.883119\pi\)
0.155771 0.987793i \(-0.450214\pi\)
\(132\) 1492.77 + 197.784i 0.984311 + 0.130416i
\(133\) −1025.39 1356.93i −0.668515 0.884669i
\(134\) 1430.98i 0.922519i
\(135\) −695.704 + 89.8349i −0.443531 + 0.0572722i
\(136\) −2132.57 1231.24i −1.34460 0.776308i
\(137\) −1548.79 894.195i −0.965855 0.557637i −0.0678852 0.997693i \(-0.521625\pi\)
−0.897970 + 0.440056i \(0.854959\pi\)
\(138\) 258.757 106.930i 0.159615 0.0659600i
\(139\) 1312.40i 0.800839i 0.916332 + 0.400419i \(0.131136\pi\)
−0.916332 + 0.400419i \(0.868864\pi\)
\(140\) 57.5269 + 463.362i 0.0347279 + 0.279723i
\(141\) −159.043 + 1200.38i −0.0949918 + 0.716949i
\(142\) 405.239 + 701.895i 0.239485 + 0.414801i
\(143\) 1283.50 2223.09i 0.750571 1.30003i
\(144\) 33.7016 33.5902i 0.0195032 0.0194388i
\(145\) 794.842 458.902i 0.455228 0.262826i
\(146\) 931.447 0.527994
\(147\) 1635.78 + 707.634i 0.917802 + 0.397038i
\(148\) 1158.83 0.643617
\(149\) 745.637 430.494i 0.409966 0.236694i −0.280809 0.959764i \(-0.590603\pi\)
0.690775 + 0.723070i \(0.257269\pi\)
\(150\) 136.150 177.130i 0.0741107 0.0964176i
\(151\) 1587.96 2750.43i 0.855805 1.48230i −0.0200921 0.999798i \(-0.506396\pi\)
0.875897 0.482499i \(-0.160271\pi\)
\(152\) −1029.93 1783.89i −0.549593 0.951924i
\(153\) −2861.89 771.921i −1.51222 0.407883i
\(154\) 225.540 + 1816.65i 0.118016 + 0.950585i
\(155\) 712.990i 0.369476i
\(156\) −446.928 1081.51i −0.229378 0.555065i
\(157\) −1015.83 586.490i −0.516382 0.298134i 0.219071 0.975709i \(-0.429697\pi\)
−0.735453 + 0.677575i \(0.763031\pi\)
\(158\) −522.846 301.865i −0.263262 0.151994i
\(159\) −916.814 2218.58i −0.457284 1.10657i
\(160\) 912.362i 0.450804i
\(161\) −349.825 462.936i −0.171243 0.226611i
\(162\) −630.461 + 1083.69i −0.305764 + 0.525573i
\(163\) −425.656 737.258i −0.204540 0.354273i 0.745446 0.666566i \(-0.232236\pi\)
−0.949986 + 0.312293i \(0.898903\pi\)
\(164\) −468.307 + 811.132i −0.222979 + 0.386212i
\(165\) −909.982 + 1183.88i −0.429345 + 0.558576i
\(166\) 1290.71 745.191i 0.603485 0.348422i
\(167\) 1963.71 0.909921 0.454960 0.890512i \(-0.349653\pi\)
0.454960 + 0.890512i \(0.349653\pi\)
\(168\) 1860.44 + 1094.58i 0.854380 + 0.502672i
\(169\) 202.102 0.0919899
\(170\) 817.562 472.019i 0.368848 0.212954i
\(171\) −1750.38 1756.18i −0.782778 0.785373i
\(172\) 56.3767 97.6473i 0.0249923 0.0432880i
\(173\) 97.2325 + 168.412i 0.0427309 + 0.0740121i 0.886600 0.462537i \(-0.153061\pi\)
−0.843869 + 0.536549i \(0.819728\pi\)
\(174\) 215.457 1626.16i 0.0938723 0.708500i
\(175\) −426.443 180.337i −0.184206 0.0778983i
\(176\) 101.286i 0.0433791i
\(177\) −2206.10 + 911.657i −0.936838 + 0.387143i
\(178\) 1547.82 + 893.635i 0.651765 + 0.376297i
\(179\) 4101.34 + 2367.91i 1.71256 + 0.988749i 0.931075 + 0.364828i \(0.118872\pi\)
0.781488 + 0.623921i \(0.214461\pi\)
\(180\) 175.091 + 657.800i 0.0725028 + 0.272386i
\(181\) 2963.89i 1.21715i 0.793497 + 0.608575i \(0.208258\pi\)
−0.793497 + 0.608575i \(0.791742\pi\)
\(182\) 1135.00 857.681i 0.462262 0.349316i
\(183\) 1478.68 + 195.917i 0.597308 + 0.0791399i
\(184\) −351.374 608.597i −0.140780 0.243839i
\(185\) −574.560 + 995.167i −0.228338 + 0.395493i
\(186\) −1010.34 776.588i −0.398288 0.306141i
\(187\) −5464.31 + 3154.82i −2.13685 + 1.23371i
\(188\) 1175.00 0.455829
\(189\) 2503.03 + 697.216i 0.963326 + 0.268333i
\(190\) 789.686 0.301525
\(191\) −553.249 + 319.418i −0.209590 + 0.121007i −0.601121 0.799158i \(-0.705279\pi\)
0.391531 + 0.920165i \(0.371946\pi\)
\(192\) 1234.77 + 949.100i 0.464126 + 0.356747i
\(193\) 787.552 1364.08i 0.293727 0.508749i −0.680961 0.732319i \(-0.738438\pi\)
0.974688 + 0.223570i \(0.0717712\pi\)
\(194\) −278.221 481.893i −0.102964 0.178340i
\(195\) 1150.36 + 152.416i 0.422456 + 0.0559730i
\(196\) 472.235 1663.77i 0.172097 0.606331i
\(197\) 325.944i 0.117881i −0.998261 0.0589405i \(-0.981228\pi\)
0.998261 0.0589405i \(-0.0187722\pi\)
\(198\) 686.460 + 2578.97i 0.246387 + 0.925653i
\(199\) −526.526 303.990i −0.187560 0.108288i 0.403280 0.915077i \(-0.367870\pi\)
−0.590840 + 0.806789i \(0.701203\pi\)
\(200\) −485.628 280.378i −0.171695 0.0991284i
\(201\) −3995.74 + 1651.22i −1.40218 + 0.579443i
\(202\) 300.311i 0.104603i
\(203\) −3373.69 + 418.848i −1.16644 + 0.144815i
\(204\) −377.802 + 2851.46i −0.129664 + 0.978637i
\(205\) −464.383 804.335i −0.158214 0.274035i
\(206\) −901.189 + 1560.91i −0.304800 + 0.527929i
\(207\) −597.166 599.145i −0.200512 0.201176i
\(208\) −68.1671 + 39.3563i −0.0227237 + 0.0131196i
\(209\) −5278.00 −1.74683
\(210\) −720.027 + 407.865i −0.236603 + 0.134025i
\(211\) 3315.33 1.08169 0.540846 0.841122i \(-0.318104\pi\)
0.540846 + 0.841122i \(0.318104\pi\)
\(212\) −2017.36 + 1164.72i −0.653551 + 0.377328i
\(213\) 1492.31 1941.48i 0.480052 0.624546i
\(214\) 1335.67 2313.44i 0.426656 0.738989i
\(215\) 55.9043 + 96.8291i 0.0177332 + 0.0307148i
\(216\) 2904.33 + 1211.47i 0.914883 + 0.381620i
\(217\) −1028.63 + 2432.40i −0.321787 + 0.760930i
\(218\) 944.935i 0.293574i
\(219\) −1074.81 2600.90i −0.331638 0.802522i
\(220\) 1254.85 + 724.486i 0.384554 + 0.222022i
\(221\) 4246.49 + 2451.71i 1.29253 + 0.746245i
\(222\) 784.385 + 1898.11i 0.237137 + 0.573842i
\(223\) 4592.55i 1.37910i −0.724236 0.689552i \(-0.757808\pi\)
0.724236 0.689552i \(-0.242192\pi\)
\(224\) 1316.26 3112.56i 0.392618 0.928424i
\(225\) −651.710 175.782i −0.193099 0.0520834i
\(226\) 981.188 + 1699.47i 0.288795 + 0.500207i
\(227\) −2428.78 + 4206.77i −0.710149 + 1.23001i 0.254652 + 0.967033i \(0.418039\pi\)
−0.964801 + 0.262982i \(0.915294\pi\)
\(228\) −1466.31 + 1907.66i −0.425915 + 0.554113i
\(229\) 4633.45 2675.12i 1.33706 0.771953i 0.350691 0.936491i \(-0.385947\pi\)
0.986371 + 0.164539i \(0.0526135\pi\)
\(230\) 269.412 0.0772369
\(231\) 4812.42 2726.03i 1.37071 0.776450i
\(232\) −4117.31 −1.16515
\(233\) 1126.35 650.300i 0.316694 0.182844i −0.333224 0.942848i \(-0.608136\pi\)
0.649918 + 0.760004i \(0.274803\pi\)
\(234\) 1468.95 1464.10i 0.410377 0.409021i
\(235\) −582.578 + 1009.06i −0.161716 + 0.280100i
\(236\) 1158.17 + 2006.01i 0.319451 + 0.553306i
\(237\) −239.587 + 1808.28i −0.0656660 + 0.495613i
\(238\) −3470.13 + 430.820i −0.945105 + 0.117336i
\(239\) 1750.92i 0.473882i 0.971524 + 0.236941i \(0.0761448\pi\)
−0.971524 + 0.236941i \(0.923855\pi\)
\(240\) 42.3155 17.4867i 0.0113811 0.00470316i
\(241\) 1844.54 + 1064.95i 0.493018 + 0.284644i 0.725825 0.687879i \(-0.241458\pi\)
−0.232808 + 0.972523i \(0.574791\pi\)
\(242\) 2937.36 + 1695.88i 0.780249 + 0.450477i
\(243\) 3753.51 + 509.966i 0.990896 + 0.134627i
\(244\) 1447.43i 0.379762i
\(245\) 1194.66 + 1230.46i 0.311526 + 0.320861i
\(246\) −1645.58 218.031i −0.426498 0.0565086i
\(247\) 2050.85 + 3552.18i 0.528310 + 0.915059i
\(248\) −1599.25 + 2769.98i −0.409486 + 0.709250i
\(249\) −3570.18 2744.19i −0.908638 0.698418i
\(250\) 186.175 107.488i 0.0470990 0.0271926i
\(251\) −414.788 −0.104308 −0.0521538 0.998639i \(-0.516609\pi\)
−0.0521538 + 0.998639i \(0.516609\pi\)
\(252\) 351.677 2496.72i 0.0879110 0.624120i
\(253\) −1800.66 −0.447457
\(254\) −1906.40 + 1100.66i −0.470938 + 0.271896i
\(255\) −2261.42 1738.23i −0.555356 0.426870i
\(256\) 2010.90 3482.99i 0.490943 0.850338i
\(257\) −221.421 383.512i −0.0537426 0.0930848i 0.837903 0.545820i \(-0.183782\pi\)
−0.891645 + 0.452735i \(0.850448\pi\)
\(258\) 198.102 + 26.2474i 0.0478034 + 0.00633369i
\(259\) 3395.86 2566.14i 0.814705 0.615645i
\(260\) 1126.04i 0.268593i
\(261\) −4789.38 + 1274.82i −1.13584 + 0.302335i
\(262\) −3472.86 2005.06i −0.818908 0.472797i
\(263\) 4312.97 + 2490.09i 1.01121 + 0.583824i 0.911546 0.411197i \(-0.134889\pi\)
0.0996661 + 0.995021i \(0.468223\pi\)
\(264\) 6190.77 2558.30i 1.44324 0.596411i
\(265\) 2309.93i 0.535463i
\(266\) −2694.05 1139.28i −0.620987 0.262607i
\(267\) 709.268 5353.19i 0.162571 1.22700i
\(268\) 2097.71 + 3633.35i 0.478128 + 0.828142i
\(269\) −693.992 + 1202.03i −0.157299 + 0.272450i −0.933894 0.357551i \(-0.883612\pi\)
0.776595 + 0.630000i \(0.216945\pi\)
\(270\) −958.932 + 732.040i −0.216144 + 0.165002i
\(271\) 571.186 329.774i 0.128033 0.0739201i −0.434615 0.900616i \(-0.643116\pi\)
0.562649 + 0.826696i \(0.309782\pi\)
\(272\) 193.474 0.0431290
\(273\) −3704.61 2179.59i −0.821293 0.483205i
\(274\) −3075.69 −0.678136
\(275\) −1244.33 + 718.416i −0.272858 + 0.157535i
\(276\) −500.250 + 650.823i −0.109100 + 0.141938i
\(277\) −2718.43 + 4708.45i −0.589655 + 1.02131i 0.404622 + 0.914484i \(0.367403\pi\)
−0.994277 + 0.106829i \(0.965930\pi\)
\(278\) 1128.54 + 1954.69i 0.243473 + 0.421707i
\(279\) −1002.64 + 3717.30i −0.215150 + 0.797666i
\(280\) 1252.24 + 1657.13i 0.267270 + 0.353688i
\(281\) 3329.00i 0.706732i −0.935485 0.353366i \(-0.885037\pi\)
0.935485 0.353366i \(-0.114963\pi\)
\(282\) 795.331 + 1924.60i 0.167948 + 0.406413i
\(283\) 5532.85 + 3194.39i 1.16217 + 0.670979i 0.951823 0.306648i \(-0.0992075\pi\)
0.210346 + 0.977627i \(0.432541\pi\)
\(284\) −2057.86 1188.11i −0.429971 0.248244i
\(285\) −911.227 2205.06i −0.189391 0.458303i
\(286\) 4414.76i 0.912762i
\(287\) 423.850 + 3413.99i 0.0871745 + 0.702165i
\(288\) 1283.01 4756.76i 0.262508 0.973247i
\(289\) −3569.77 6183.02i −0.726596 1.25850i
\(290\) 789.225 1366.98i 0.159810 0.276799i
\(291\) −1024.56 + 1332.94i −0.206394 + 0.268517i
\(292\) −2365.01 + 1365.44i −0.473978 + 0.273651i
\(293\) −6510.06 −1.29803 −0.649013 0.760777i \(-0.724818\pi\)
−0.649013 + 0.760777i \(0.724818\pi\)
\(294\) 3044.83 352.667i 0.604007 0.0699590i
\(295\) −2296.93 −0.453331
\(296\) 4464.36 2577.50i 0.876641 0.506129i
\(297\) 6409.19 4892.71i 1.25219 0.955906i
\(298\) 740.368 1282.35i 0.143921 0.249278i
\(299\) 699.675 + 1211.87i 0.135329 + 0.234396i
\(300\) −86.0330 + 649.333i −0.0165571 + 0.124964i
\(301\) −51.0248 410.990i −0.00977084 0.0787011i
\(302\) 5461.99i 1.04074i
\(303\) 838.564 346.532i 0.158991 0.0657021i
\(304\) 140.158 + 80.9203i 0.0264428 + 0.0152668i
\(305\) 1243.00 + 717.649i 0.233358 + 0.134729i
\(306\) −4926.28 + 1311.26i −0.920316 + 0.244966i
\(307\) 2643.43i 0.491428i 0.969342 + 0.245714i \(0.0790225\pi\)
−0.969342 + 0.245714i \(0.920978\pi\)
\(308\) −3235.75 4281.98i −0.598617 0.792171i
\(309\) 5398.44 + 715.263i 0.993872 + 0.131682i
\(310\) −613.104 1061.93i −0.112329 0.194559i
\(311\) 1396.85 2419.42i 0.254688 0.441133i −0.710122 0.704078i \(-0.751360\pi\)
0.964811 + 0.262945i \(0.0846937\pi\)
\(312\) −4127.30 3172.42i −0.748918 0.575650i
\(313\) −5645.67 + 3259.53i −1.01953 + 0.588625i −0.913967 0.405788i \(-0.866997\pi\)
−0.105561 + 0.994413i \(0.533664\pi\)
\(314\) −2017.30 −0.362557
\(315\) 1969.74 + 1539.91i 0.352324 + 0.275441i
\(316\) 1770.06 0.315106
\(317\) −2657.94 + 1534.56i −0.470929 + 0.271891i −0.716629 0.697455i \(-0.754316\pi\)
0.245699 + 0.969346i \(0.420982\pi\)
\(318\) −3273.27 2515.97i −0.577219 0.443675i
\(319\) −5274.92 + 9136.43i −0.925827 + 1.60358i
\(320\) 749.299 + 1297.82i 0.130897 + 0.226720i
\(321\) −8001.11 1060.10i −1.39121 0.184328i
\(322\) −919.110 388.680i −0.159068 0.0672679i
\(323\) 10081.9i 1.73676i
\(324\) 12.1664 3675.78i 0.00208614 0.630278i
\(325\) 967.010 + 558.304i 0.165046 + 0.0952896i
\(326\) −1267.94 732.048i −0.215414 0.124369i
\(327\) 2638.56 1090.37i 0.446216 0.184396i
\(328\) 4166.48i 0.701388i
\(329\) 3443.25 2601.95i 0.576999 0.436019i
\(330\) −337.300 + 2545.77i −0.0562660 + 0.424667i
\(331\) 3072.11 + 5321.04i 0.510146 + 0.883598i 0.999931 + 0.0117549i \(0.00374179\pi\)
−0.489785 + 0.871843i \(0.662925\pi\)
\(332\) −2184.80 + 3784.19i −0.361164 + 0.625555i
\(333\) 4395.03 4380.51i 0.723262 0.720872i
\(334\) 2924.75 1688.61i 0.479148 0.276636i
\(335\) −4160.27 −0.678507
\(336\) −169.589 1.39203i −0.0275353 0.000226016i
\(337\) 4494.84 0.726556 0.363278 0.931681i \(-0.381658\pi\)
0.363278 + 0.931681i \(0.381658\pi\)
\(338\) 301.010 173.788i 0.0484403 0.0279670i
\(339\) 3613.25 4700.83i 0.578894 0.753138i
\(340\) −1383.90 + 2396.98i −0.220742 + 0.382337i
\(341\) 4097.78 + 7097.57i 0.650755 + 1.12714i
\(342\) −4117.17 1110.50i −0.650968 0.175581i
\(343\) −2300.44 5921.28i −0.362135 0.932126i
\(344\) 501.578i 0.0786142i
\(345\) −310.877 752.284i −0.0485132 0.117396i
\(346\) 289.636 + 167.221i 0.0450027 + 0.0259823i
\(347\) 3001.05 + 1732.66i 0.464279 + 0.268051i 0.713842 0.700307i \(-0.246954\pi\)
−0.249563 + 0.968359i \(0.580287\pi\)
\(348\) 1836.78 + 4444.78i 0.282936 + 0.684670i
\(349\) 4800.19i 0.736241i 0.929778 + 0.368121i \(0.119999\pi\)
−0.929778 + 0.368121i \(0.880001\pi\)
\(350\) −790.217 + 98.1063i −0.120682 + 0.0149829i
\(351\) −5783.27 2412.34i −0.879453 0.366842i
\(352\) −5243.64 9082.26i −0.793997 1.37524i
\(353\) −3971.17 + 6878.27i −0.598765 + 1.03709i 0.394238 + 0.919008i \(0.371009\pi\)
−0.993004 + 0.118084i \(0.962325\pi\)
\(354\) −2501.82 + 3254.85i −0.375622 + 0.488682i
\(355\) 2040.62 1178.15i 0.305084 0.176140i
\(356\) −5240.03 −0.780116
\(357\) 5207.21 + 9192.58i 0.771974 + 1.36281i
\(358\) 8144.72 1.20241
\(359\) 9607.02 5546.61i 1.41236 0.815429i 0.416754 0.909019i \(-0.363168\pi\)
0.995611 + 0.0935901i \(0.0298343\pi\)
\(360\) 2137.63 + 2144.71i 0.312952 + 0.313990i
\(361\) 787.245 1363.55i 0.114776 0.198797i
\(362\) 2548.66 + 4414.41i 0.370041 + 0.640929i
\(363\) 1346.00 10158.9i 0.194619 1.46889i
\(364\) −1624.54 + 3841.54i −0.233926 + 0.553164i
\(365\) 2707.99i 0.388336i
\(366\) 2370.82 979.728i 0.338592 0.139921i
\(367\) −3691.36 2131.21i −0.525034 0.303128i 0.213958 0.976843i \(-0.431364\pi\)
−0.738992 + 0.673715i \(0.764698\pi\)
\(368\) 47.8168 + 27.6070i 0.00677343 + 0.00391064i
\(369\) 1290.05 + 4846.58i 0.181997 + 0.683748i
\(370\) 1976.27i 0.277679i
\(371\) −3332.53 + 7880.42i −0.466351 + 1.10278i
\(372\) 3703.74 + 490.725i 0.516210 + 0.0683949i
\(373\) −1046.28 1812.22i −0.145240 0.251563i 0.784223 0.620480i \(-0.213062\pi\)
−0.929462 + 0.368917i \(0.879729\pi\)
\(374\) −5425.70 + 9397.58i −0.750150 + 1.29930i
\(375\) −514.971 395.828i −0.0709146 0.0545080i
\(376\) 4526.66 2613.47i 0.620864 0.358456i
\(377\) 8198.61 1.12003
\(378\) 4327.55 1113.94i 0.588850 0.151573i
\(379\) −7320.18 −0.992117 −0.496059 0.868289i \(-0.665220\pi\)
−0.496059 + 0.868289i \(0.665220\pi\)
\(380\) −2005.07 + 1157.63i −0.270678 + 0.156276i
\(381\) 5273.22 + 4053.22i 0.709068 + 0.545020i
\(382\) −549.339 + 951.483i −0.0735776 + 0.127440i
\(383\) −1594.48 2761.73i −0.212727 0.368453i 0.739840 0.672783i \(-0.234901\pi\)
−0.952567 + 0.304329i \(0.901568\pi\)
\(384\) −4864.31 644.494i −0.646435 0.0856490i
\(385\) 5281.55 655.710i 0.699150 0.0868003i
\(386\) 2708.88i 0.357198i
\(387\) −155.301 583.451i −0.0203989 0.0766370i
\(388\) 1412.84 + 815.706i 0.184862 + 0.106730i
\(389\) 5822.56 + 3361.65i 0.758908 + 0.438156i 0.828904 0.559391i \(-0.188965\pi\)
−0.0699955 + 0.997547i \(0.522298\pi\)
\(390\) 1844.41 762.191i 0.239475 0.0989617i
\(391\) 3439.58i 0.444877i
\(392\) −1881.33 7459.99i −0.242402 0.961190i
\(393\) −1591.39 + 12011.0i −0.204262 + 1.54166i
\(394\) −280.281 485.461i −0.0358385 0.0620740i
\(395\) −877.612 + 1520.07i −0.111791 + 0.193628i
\(396\) −5523.56 5541.87i −0.700933 0.703257i
\(397\) 10725.6 6192.45i 1.35593 0.782847i 0.366858 0.930277i \(-0.380434\pi\)
0.989072 + 0.147430i \(0.0471002\pi\)
\(398\) −1045.61 −0.131688
\(399\) −72.5383 + 8837.27i −0.00910140 + 1.10881i
\(400\) 44.0579 0.00550724
\(401\) 2395.94 1383.30i 0.298373 0.172266i −0.343339 0.939212i \(-0.611558\pi\)
0.641712 + 0.766946i \(0.278224\pi\)
\(402\) −4531.37 + 5895.29i −0.562199 + 0.731418i
\(403\) 3184.52 5515.75i 0.393628 0.681784i
\(404\) −440.235 762.510i −0.0542142 0.0939017i
\(405\) 3150.61 + 1832.94i 0.386556 + 0.224887i
\(406\) −4664.61 + 3524.89i −0.570199 + 0.430880i
\(407\) 13208.7i 1.60868i
\(408\) 4886.81 + 11825.5i 0.592973 + 1.43492i
\(409\) −5568.92 3215.22i −0.673265 0.388710i 0.124048 0.992276i \(-0.460412\pi\)
−0.797313 + 0.603567i \(0.793746\pi\)
\(410\) −1383.30 798.651i −0.166626 0.0962013i
\(411\) 3549.08 + 8588.32i 0.425944 + 1.03073i
\(412\) 5284.33i 0.631894i
\(413\) 7836.09 + 3313.78i 0.933628 + 0.394819i
\(414\) −1404.63 378.861i −0.166748 0.0449759i
\(415\) −2166.49 3752.48i −0.256263 0.443860i
\(416\) −4075.00 + 7058.11i −0.480272 + 0.831856i
\(417\) 4155.89 5406.79i 0.488045 0.634944i
\(418\) −7861.05 + 4538.58i −0.919848 + 0.531075i
\(419\) −2189.52 −0.255287 −0.127643 0.991820i \(-0.540741\pi\)
−0.127643 + 0.991820i \(0.540741\pi\)
\(420\) 1230.30 2091.11i 0.142934 0.242942i
\(421\) −8738.82 −1.01165 −0.505825 0.862636i \(-0.668812\pi\)
−0.505825 + 0.862636i \(0.668812\pi\)
\(422\) 4937.85 2850.87i 0.569600 0.328858i
\(423\) 4456.36 4441.64i 0.512236 0.510543i
\(424\) −5181.22 + 8974.13i −0.593448 + 1.02788i
\(425\) −1372.30 2376.89i −0.156627 0.271285i
\(426\) 553.149 4174.89i 0.0629112 0.474821i
\(427\) −3205.21 4241.57i −0.363258 0.480712i
\(428\) 7831.99i 0.884517i
\(429\) −12327.4 + 5094.24i −1.38735 + 0.573315i
\(430\) 166.528 + 96.1448i 0.0186760 + 0.0107826i
\(431\) 3823.61 + 2207.56i 0.427324 + 0.246716i 0.698206 0.715897i \(-0.253982\pi\)
−0.270882 + 0.962613i \(0.587315\pi\)
\(432\) −245.210 + 31.6635i −0.0273094 + 0.00352641i
\(433\) 10561.3i 1.17215i 0.810255 + 0.586077i \(0.199329\pi\)
−0.810255 + 0.586077i \(0.800671\pi\)
\(434\) 559.590 + 4507.33i 0.0618922 + 0.498523i
\(435\) −4727.73 626.398i −0.521098 0.0690425i
\(436\) −1385.21 2399.26i −0.152155 0.263540i
\(437\) 1438.60 2491.73i 0.157477 0.272758i
\(438\) −3837.34 2949.54i −0.418619 0.321769i
\(439\) 7929.27 4577.96i 0.862057 0.497709i −0.00264332 0.999997i \(-0.500841\pi\)
0.864701 + 0.502287i \(0.167508\pi\)
\(440\) 6445.68 0.698377
\(441\) −4498.22 8095.19i −0.485717 0.874116i
\(442\) 8432.96 0.907500
\(443\) −2931.50 + 1692.50i −0.314402 + 0.181520i −0.648894 0.760878i \(-0.724768\pi\)
0.334493 + 0.942398i \(0.391435\pi\)
\(444\) −4774.11 3669.59i −0.510291 0.392232i
\(445\) 2598.06 4499.98i 0.276764 0.479369i
\(446\) −3949.16 6840.15i −0.419278 0.726212i
\(447\) −4435.06 587.621i −0.469287 0.0621779i
\(448\) −683.898 5508.59i −0.0721231 0.580930i
\(449\) 8544.40i 0.898074i −0.893513 0.449037i \(-0.851767\pi\)
0.893513 0.449037i \(-0.148233\pi\)
\(450\) −1121.81 + 298.600i −0.117517 + 0.0312803i
\(451\) 9245.55 + 5337.92i 0.965312 + 0.557323i
\(452\) −4982.61 2876.71i −0.518500 0.299356i
\(453\) −15251.6 + 6302.65i −1.58186 + 0.653696i
\(454\) 8354.09i 0.863605i
\(455\) −2493.53 3299.78i −0.256920 0.339991i
\(456\) −1405.84 + 10610.6i −0.144374 + 1.08966i
\(457\) 7508.15 + 13004.5i 0.768526 + 1.33113i 0.938362 + 0.345654i \(0.112343\pi\)
−0.169836 + 0.985472i \(0.554324\pi\)
\(458\) 4600.71 7968.66i 0.469382 0.812993i
\(459\) 9345.95 + 12242.7i 0.950395 + 1.24497i
\(460\) −684.055 + 394.939i −0.0693353 + 0.0400308i
\(461\) −5195.83 −0.524932 −0.262466 0.964941i \(-0.584536\pi\)
−0.262466 + 0.964941i \(0.584536\pi\)
\(462\) 4823.49 8198.38i 0.485734 0.825592i
\(463\) 5865.44 0.588748 0.294374 0.955690i \(-0.404889\pi\)
0.294374 + 0.955690i \(0.404889\pi\)
\(464\) 280.152 161.746i 0.0280296 0.0161829i
\(465\) −2257.77 + 2937.35i −0.225165 + 0.292938i
\(466\) 1118.39 1937.11i 0.111177 0.192564i
\(467\) 1055.99 + 1829.02i 0.104637 + 0.181236i 0.913590 0.406637i \(-0.133299\pi\)
−0.808953 + 0.587873i \(0.799965\pi\)
\(468\) −1583.50 + 5870.83i −0.156405 + 0.579870i
\(469\) 14192.9 + 6002.01i 1.39738 + 0.590932i
\(470\) 2003.85i 0.196661i
\(471\) 2327.79 + 5632.95i 0.227726 + 0.551068i
\(472\) 8923.64 + 5152.07i 0.870220 + 0.502422i
\(473\) −1113.02 642.600i −0.108196 0.0624668i
\(474\) 1198.11 + 2899.27i 0.116099 + 0.280945i
\(475\) 2295.85i 0.221770i
\(476\) 8179.34 6180.85i 0.787604 0.595166i
\(477\) −3248.34 + 12043.2i −0.311806 + 1.15602i
\(478\) 1505.63 + 2607.82i 0.144071 + 0.249538i
\(479\) 2712.63 4698.41i 0.258754 0.448175i −0.707155 0.707059i \(-0.750022\pi\)
0.965908 + 0.258884i \(0.0833549\pi\)
\(480\) 2889.11 3758.72i 0.274728 0.357419i
\(481\) −8889.69 + 5132.46i −0.842692 + 0.486528i
\(482\) 3663.01 0.346152
\(483\) −24.7474 + 3014.95i −0.00233136 + 0.284027i
\(484\) −9944.20 −0.933903
\(485\) −1401.01 + 808.871i −0.131168 + 0.0757298i
\(486\) 6029.00 2468.12i 0.562718 0.230363i
\(487\) 5094.94 8824.69i 0.474073 0.821119i −0.525486 0.850802i \(-0.676116\pi\)
0.999559 + 0.0296831i \(0.00944980\pi\)
\(488\) −3219.40 5576.17i −0.298638 0.517256i
\(489\) −581.017 + 4385.22i −0.0537311 + 0.405535i
\(490\) 2837.40 + 805.350i 0.261593 + 0.0742490i
\(491\) 5998.74i 0.551364i −0.961249 0.275682i \(-0.911096\pi\)
0.961249 0.275682i \(-0.0889036\pi\)
\(492\) 4497.87 1858.72i 0.412153 0.170320i
\(493\) −17452.2 10076.0i −1.59433 0.920490i
\(494\) 6109.07 + 3527.07i 0.556397 + 0.321236i
\(495\) 7497.82 1995.74i 0.680812 0.181216i
\(496\) 251.303i 0.0227496i
\(497\) −8661.37 + 1075.32i −0.781722 + 0.0970516i
\(498\) −7677.16 1017.18i −0.690807 0.0915281i
\(499\) −10781.9 18674.7i −0.967259 1.67534i −0.703418 0.710776i \(-0.748344\pi\)
−0.263841 0.964566i \(-0.584989\pi\)
\(500\) −315.141 + 545.840i −0.0281870 + 0.0488214i
\(501\) −8090.04 6218.35i −0.721430 0.554522i
\(502\) −617.785 + 356.679i −0.0549265 + 0.0317118i
\(503\) 518.980 0.0460043 0.0230021 0.999735i \(-0.492678\pi\)
0.0230021 + 0.999735i \(0.492678\pi\)
\(504\) −4198.43 10400.7i −0.371058 0.919217i
\(505\) 873.093 0.0769349
\(506\) −2681.90 + 1548.40i −0.235623 + 0.136037i
\(507\) −832.612 639.981i −0.0729341 0.0560603i
\(508\) 3226.99 5589.31i 0.281840 0.488160i
\(509\) −7798.66 13507.7i −0.679115 1.17626i −0.975248 0.221115i \(-0.929030\pi\)
0.296133 0.955147i \(-0.404303\pi\)
\(510\) −4862.87 644.303i −0.422219 0.0559416i
\(511\) −3906.81 + 9238.43i −0.338214 + 0.799773i
\(512\) 637.807i 0.0550534i
\(513\) 1649.98 + 12777.9i 0.142005 + 1.09972i
\(514\) −659.567 380.801i −0.0565998 0.0326779i
\(515\) 4538.01 + 2620.02i 0.388289 + 0.224179i
\(516\) −541.472 + 223.760i −0.0461956 + 0.0190901i
\(517\) 13393.1i 1.13932i
\(518\) 2851.16 6742.13i 0.241839 0.571877i
\(519\) 132.722 1001.72i 0.0112251 0.0847214i
\(520\) −2504.57 4338.05i −0.211217 0.365838i
\(521\) 10040.4 17390.5i 0.844298 1.46237i −0.0419318 0.999120i \(-0.513351\pi\)
0.886230 0.463246i \(-0.153315\pi\)
\(522\) −6037.08 + 6017.13i −0.506199 + 0.504526i
\(523\) −17771.4 + 10260.3i −1.48583 + 0.857844i −0.999870 0.0161368i \(-0.994863\pi\)
−0.485960 + 0.873981i \(0.661530\pi\)
\(524\) 11757.1 0.980174
\(525\) 1185.78 + 2093.33i 0.0985750 + 0.174020i
\(526\) 8564.97 0.709982
\(527\) −13557.6 + 7827.49i −1.12064 + 0.647003i
\(528\) −320.735 + 417.275i −0.0264360 + 0.0343931i
\(529\) −5592.70 + 9686.85i −0.459662 + 0.796157i
\(530\) −1986.32 3440.41i −0.162793 0.281965i
\(531\) 11975.5 + 3230.07i 0.978703 + 0.263979i
\(532\) 8510.47 1056.59i 0.693564 0.0861067i
\(533\) 8296.53i 0.674226i
\(534\) −3546.85 8582.94i −0.287429 0.695543i
\(535\) −6725.86 3883.18i −0.543522 0.313803i
\(536\) 16162.8 + 9331.57i 1.30247 + 0.751983i
\(537\) −9398.28 22742.7i −0.755243 1.82759i
\(538\) 2387.07i 0.191290i
\(539\) −18964.2 5382.69i −1.51549 0.430147i
\(540\) 1361.68 3264.43i 0.108513 0.260146i
\(541\) 2325.89 + 4028.56i 0.184839 + 0.320150i 0.943522 0.331309i \(-0.107490\pi\)
−0.758683 + 0.651460i \(0.774157\pi\)
\(542\) 567.149 982.331i 0.0449468 0.0778501i
\(543\) 9385.52 12210.5i 0.741752 0.965016i
\(544\) 17348.7 10016.3i 1.36732 0.789420i
\(545\) 2747.21 0.215922
\(546\) −7391.89 60.6743i −0.579384 0.00475571i
\(547\) 2762.10 0.215903 0.107951 0.994156i \(-0.465571\pi\)
0.107951 + 0.994156i \(0.465571\pi\)
\(548\) 7809.40 4508.76i 0.608761 0.351468i
\(549\) −5471.43 5489.57i −0.425346 0.426756i
\(550\) −1235.54 + 2140.02i −0.0957883 + 0.165910i
\(551\) −8428.57 14598.7i −0.651668 1.12872i
\(552\) −479.623 + 3619.95i −0.0369821 + 0.279122i
\(553\) 5187.01 3919.65i 0.398868 0.301411i
\(554\) 9350.36i 0.717074i
\(555\) 5518.38 2280.44i 0.422058 0.174413i
\(556\) −5730.89 3308.73i −0.437130 0.252377i
\(557\) −7775.02 4488.91i −0.591451 0.341474i 0.174220 0.984707i \(-0.444260\pi\)
−0.765671 + 0.643233i \(0.777593\pi\)
\(558\) 1703.19 + 6398.72i 0.129215 + 0.485447i
\(559\) 998.770i 0.0755697i
\(560\) −150.305 63.5622i −0.0113421 0.00479642i
\(561\) 32501.8 + 4306.31i 2.44604 + 0.324087i
\(562\) −2862.63 4958.22i −0.214862 0.372153i
\(563\) −8779.23 + 15206.1i −0.657194 + 1.13829i 0.324145 + 0.946007i \(0.394923\pi\)
−0.981339 + 0.192286i \(0.938410\pi\)
\(564\) −4840.73 3720.79i −0.361404 0.277790i
\(565\) 4940.86 2852.60i 0.367900 0.212407i
\(566\) 10987.5 0.815970
\(567\) −8104.08 10798.5i −0.600246 0.799816i
\(568\) −10570.5 −0.780857
\(569\) −9424.90 + 5441.47i −0.694398 + 0.400911i −0.805257 0.592925i \(-0.797973\pi\)
0.110860 + 0.993836i \(0.464640\pi\)
\(570\) −3253.32 2500.64i −0.239064 0.183755i
\(571\) −3875.05 + 6711.78i −0.284003 + 0.491907i −0.972367 0.233458i \(-0.924996\pi\)
0.688364 + 0.725365i \(0.258329\pi\)
\(572\) 6471.73 + 11209.4i 0.473071 + 0.819384i
\(573\) 3290.73 + 436.004i 0.239917 + 0.0317876i
\(574\) 3566.99 + 4720.32i 0.259378 + 0.343244i
\(575\) 783.260i 0.0568073i
\(576\) −2081.54 7820.14i −0.150574 0.565693i
\(577\) −5455.78 3149.90i −0.393635 0.227265i 0.290099 0.956997i \(-0.406312\pi\)
−0.683734 + 0.729731i \(0.739645\pi\)
\(578\) −10633.6 6139.32i −0.765226 0.441803i
\(579\) −7564.06 + 3125.81i −0.542922 + 0.224359i
\(580\) 4627.80i 0.331308i
\(581\) 1977.40 + 15927.3i 0.141198 + 1.13731i
\(582\) −379.770 + 2866.31i −0.0270480 + 0.204145i
\(583\) 13275.9 + 22994.5i 0.943108 + 1.63351i
\(584\) −6074.08 + 10520.6i −0.430389 + 0.745456i
\(585\) −4256.56 4270.68i −0.300833 0.301830i
\(586\) −9696.08 + 5598.03i −0.683518 + 0.394629i
\(587\) −5755.97 −0.404727 −0.202363 0.979311i \(-0.564862\pi\)
−0.202363 + 0.979311i \(0.564862\pi\)
\(588\) −7214.04 + 5358.96i −0.505956 + 0.375850i
\(589\) −13095.3 −0.916102
\(590\) −3421.05 + 1975.14i −0.238716 + 0.137823i
\(591\) −1032.14 + 1342.81i −0.0718388 + 0.0934619i
\(592\) −202.511 + 350.760i −0.0140594 + 0.0243516i
\(593\) 4828.15 + 8362.60i 0.334348 + 0.579108i 0.983359 0.181671i \(-0.0581506\pi\)
−0.649011 + 0.760779i \(0.724817\pi\)
\(594\) 5338.57 12798.5i 0.368762 0.884056i
\(595\) 1252.52 + 10088.7i 0.0862999 + 0.695119i
\(596\) 4341.32i 0.298368i
\(597\) 1206.54 + 2919.68i 0.0827144 + 0.200158i
\(598\) 2084.19 + 1203.31i 0.142523 + 0.0822859i
\(599\) −13639.2 7874.61i −0.930356 0.537141i −0.0434321 0.999056i \(-0.513829\pi\)
−0.886924 + 0.461915i \(0.847163\pi\)
\(600\) 1112.82 + 2692.89i 0.0757180 + 0.183228i
\(601\) 11309.8i 0.767612i −0.923414 0.383806i \(-0.874613\pi\)
0.923414 0.383806i \(-0.125387\pi\)
\(602\) −429.408 568.251i −0.0290721 0.0384721i
\(603\) 21690.3 + 5850.40i 1.46484 + 0.395102i
\(604\) 8006.90 + 13868.4i 0.539398 + 0.934264i
\(605\) 4930.44 8539.77i 0.331324 0.573869i
\(606\) 950.972 1237.21i 0.0637469 0.0829344i
\(607\) 3.66243 2.11451i 0.000244899 0.000141392i −0.499878 0.866096i \(-0.666622\pi\)
0.500122 + 0.865955i \(0.333288\pi\)
\(608\) 16757.2 1.11775
\(609\) 15225.2 + 8957.67i 1.01306 + 0.596032i
\(610\) 2468.44 0.163843
\(611\) −9013.74 + 5204.09i −0.596820 + 0.344574i
\(612\) 10586.0 10551.0i 0.699202 0.696892i
\(613\) 10682.8 18503.2i 0.703876 1.21915i −0.263220 0.964736i \(-0.584784\pi\)
0.967096 0.254413i \(-0.0818822\pi\)
\(614\) 2273.10 + 3937.12i 0.149405 + 0.258777i
\(615\) −633.879 + 4784.20i −0.0415618 + 0.313687i
\(616\) −21989.7 9299.17i −1.43830 0.608237i
\(617\) 28128.0i 1.83532i 0.397369 + 0.917659i \(0.369923\pi\)
−0.397369 + 0.917659i \(0.630077\pi\)
\(618\) 8655.49 3576.83i 0.563390 0.232818i
\(619\) 13355.4 + 7710.75i 0.867204 + 0.500681i 0.866418 0.499319i \(-0.166416\pi\)
0.000786155 1.00000i \(0.499750\pi\)
\(620\) 3113.43 + 1797.54i 0.201674 + 0.116437i
\(621\) 562.912 + 4359.34i 0.0363750 + 0.281698i
\(622\) 4804.64i 0.309724i
\(623\) −15355.5 + 11603.6i −0.987489 + 0.746212i
\(624\) 405.459 + 53.7211i 0.0260118 + 0.00344642i
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) −5605.77 + 9709.49i −0.357910 + 0.619919i
\(627\) 21744.1 + 16713.5i 1.38497 + 1.06455i
\(628\) 5122.07 2957.23i 0.325466 0.187908i
\(629\) 25231.0 1.59941
\(630\) 4257.90 + 599.750i 0.269268 + 0.0379279i
\(631\) −15008.7 −0.946886 −0.473443 0.880824i \(-0.656989\pi\)
−0.473443 + 0.880824i \(0.656989\pi\)
\(632\) 6819.09 3937.00i 0.429191 0.247794i
\(633\) −13658.4 10498.4i −0.857618 0.659202i
\(634\) −2639.15 + 4571.15i −0.165322 + 0.286346i
\(635\) 3199.95 + 5542.47i 0.199978 + 0.346372i
\(636\) 11999.3 + 1589.84i 0.748118 + 0.0991215i
\(637\) 3746.21 + 14854.8i 0.233015 + 0.923967i
\(638\) 18143.7i 1.12589i
\(639\) −12295.9 + 3272.88i −0.761218 + 0.202618i
\(640\) −4089.02 2360.80i −0.252551 0.145810i
\(641\) −5560.90 3210.59i −0.342656 0.197832i 0.318790 0.947825i \(-0.396723\pi\)
−0.661446 + 0.749993i \(0.730057\pi\)
\(642\) −12828.4 + 5301.28i −0.788627 + 0.325896i
\(643\) 1853.26i 0.113663i 0.998384 + 0.0568316i \(0.0180998\pi\)
−0.998384 + 0.0568316i \(0.981900\pi\)
\(644\) 2903.46 360.468i 0.177659 0.0220566i
\(645\) 76.3090 575.941i 0.00465839 0.0351592i
\(646\) −8669.49 15016.0i −0.528013 0.914546i
\(647\) −807.258 + 1398.21i −0.0490519 + 0.0849604i −0.889509 0.456918i \(-0.848953\pi\)
0.840457 + 0.541878i \(0.182287\pi\)
\(648\) −8128.89 14187.9i −0.492798 0.860113i
\(649\) 22865.2 13201.2i 1.38295 0.798449i
\(650\) 1920.35 0.115881
\(651\) 11940.2 6763.62i 0.718853 0.407200i
\(652\) 4292.53 0.257835
\(653\) 23827.4 13756.8i 1.42793 0.824416i 0.430973 0.902365i \(-0.358171\pi\)
0.996957 + 0.0779494i \(0.0248373\pi\)
\(654\) 2992.26 3892.91i 0.178909 0.232760i
\(655\) −5829.29 + 10096.6i −0.347739 + 0.602302i
\(656\) −163.678 283.498i −0.00974169 0.0168731i
\(657\) −3808.12 + 14118.6i −0.226132 + 0.838385i
\(658\) 2890.95 6836.21i 0.171278 0.405020i
\(659\) 26973.3i 1.59443i 0.603694 + 0.797216i \(0.293695\pi\)
−0.603694 + 0.797216i \(0.706305\pi\)
\(660\) −2875.50 6958.35i −0.169589 0.410384i
\(661\) 2260.12 + 1304.88i 0.132993 + 0.0767837i 0.565021 0.825077i \(-0.308868\pi\)
−0.432027 + 0.901861i \(0.642202\pi\)
\(662\) 9151.18 + 5283.44i 0.537267 + 0.310191i
\(663\) −9730.89 23547.5i −0.570010 1.37935i
\(664\) 19437.9i 1.13605i
\(665\) −3312.22 + 7832.39i −0.193146 + 0.456733i
\(666\) 2779.13 10303.6i 0.161696 0.599486i
\(667\) −2875.52 4980.54i −0.166927 0.289126i
\(668\) −4950.77 + 8574.98i −0.286753 + 0.496671i
\(669\) −14542.9 + 18920.2i −0.840450 + 1.09342i
\(670\) −6196.31 + 3577.44i −0.357290 + 0.206281i
\(671\) −16498.2 −0.949191
\(672\) −15279.0 + 8654.92i −0.877085 + 0.496831i
\(673\) −1477.40 −0.0846206 −0.0423103 0.999105i \(-0.513472\pi\)
−0.0423103 + 0.999105i \(0.513472\pi\)
\(674\) 6694.61 3865.13i 0.382592 0.220889i
\(675\) 2128.26 + 2787.90i 0.121358 + 0.158972i
\(676\) −509.524 + 882.522i −0.0289898 + 0.0502117i
\(677\) −8237.90 14268.5i −0.467664 0.810017i 0.531654 0.846962i \(-0.321571\pi\)
−0.999317 + 0.0369447i \(0.988237\pi\)
\(678\) 1339.31 10108.5i 0.0758644 0.572586i
\(679\) 5946.55 738.270i 0.336093 0.0417264i
\(680\) 12312.4i 0.694351i
\(681\) 23327.3 9639.87i 1.31263 0.542439i
\(682\) 12206.5 + 7047.41i 0.685352 + 0.395688i
\(683\) −372.803 215.238i −0.0208857 0.0120583i 0.489521 0.871992i \(-0.337172\pi\)
−0.510406 + 0.859933i \(0.670505\pi\)
\(684\) 12081.7 3215.86i 0.675373 0.179768i
\(685\) 8941.95i 0.498766i
\(686\) −8518.02 6840.99i −0.474081 0.380744i
\(687\) −27559.9 3651.53i −1.53053 0.202787i
\(688\) 19.7042 + 34.1287i 0.00109188 + 0.00189120i
\(689\) 10317.1 17869.8i 0.570466 0.988077i
\(690\) −1109.91 853.127i −0.0612372 0.0470695i
\(691\) 7713.33 4453.29i 0.424644 0.245168i −0.272418 0.962179i \(-0.587823\pi\)
0.697062 + 0.717011i \(0.254490\pi\)
\(692\) −980.541 −0.0538650
\(693\) −28458.4 4008.53i −1.55995 0.219728i
\(694\) 5959.68 0.325974
\(695\) 5682.87 3281.01i 0.310163 0.179073i
\(696\) 16962.3 + 13038.0i 0.923787 + 0.710062i
\(697\) −10196.4 + 17660.6i −0.554110 + 0.959747i
\(698\) 4127.71 + 7149.40i 0.223834 + 0.387692i
\(699\) −6699.57 887.655i −0.362519 0.0480318i
\(700\) 1862.60 1407.50i 0.100571 0.0759980i
\(701\) 17716.9i 0.954579i 0.878746 + 0.477289i \(0.158381\pi\)
−0.878746 + 0.477289i \(0.841619\pi\)
\(702\) −10688.0 + 1380.12i −0.574632 + 0.0742011i
\(703\) 18278.0 + 10552.8i 0.980611 + 0.566156i
\(704\) −14918.0 8612.93i −0.798643 0.461097i
\(705\) 5595.39 2312.26i 0.298914 0.123525i
\(706\) 13659.3i 0.728153i
\(707\) −2978.59 1259.61i −0.158446 0.0670049i
\(708\) 1580.90 11931.8i 0.0839177 0.633368i
\(709\) −17844.9 30908.2i −0.945245 1.63721i −0.755261 0.655425i \(-0.772490\pi\)
−0.189984 0.981787i \(-0.560844\pi\)
\(710\) 2026.20 3509.48i 0.107101 0.185505i
\(711\) 6713.19 6691.00i 0.354099 0.352929i
\(712\) −20187.1 + 11655.0i −1.06256 + 0.613469i
\(713\) −4467.65 −0.234663
\(714\) 15660.4 + 9213.72i 0.820832 + 0.482934i
\(715\) −12835.0 −0.671332
\(716\) −20680.0 + 11939.6i −1.07940 + 0.623190i
\(717\) 5544.52 7213.39i 0.288792 0.375717i
\(718\) 9539.13 16522.2i 0.495818 0.858781i
\(719\) 182.576 + 316.231i 0.00947001 + 0.0164025i 0.870722 0.491776i \(-0.163652\pi\)
−0.861252 + 0.508179i \(0.830319\pi\)
\(720\) −229.704 61.9565i −0.0118897 0.00320692i
\(721\) −11701.7 15485.3i −0.604432 0.799865i
\(722\) 2707.83i 0.139577i
\(723\) −4226.79 10228.3i −0.217422 0.526133i
\(724\) −12942.5 7472.33i −0.664368 0.383573i
\(725\) −3974.21 2294.51i −0.203584 0.117539i
\(726\) −6730.99 16288.2i −0.344091 0.832658i
\(727\) 20316.5i 1.03645i −0.855245 0.518225i \(-0.826593\pi\)
0.855245 0.518225i \(-0.173407\pi\)
\(728\) 2285.97 + 18412.8i 0.116379 + 0.937394i
\(729\) −13848.7 13986.9i −0.703587 0.710609i
\(730\) −2328.62 4033.28i −0.118063 0.204491i
\(731\) 1227.48 2126.06i 0.0621067 0.107572i
\(732\) −4583.46 + 5963.06i −0.231434 + 0.301094i
\(733\) −8355.35 + 4823.97i −0.421026 + 0.243079i −0.695516 0.718510i \(-0.744824\pi\)
0.274490 + 0.961590i \(0.411491\pi\)
\(734\) −7330.54 −0.368631
\(735\) −1025.31 8852.22i −0.0514545 0.444244i
\(736\) 5716.94 0.286317
\(737\) 41414.1 23910.4i 2.06989 1.19505i
\(738\) 6089.00 + 6109.18i 0.303711 + 0.304718i
\(739\) 13850.5 23989.8i 0.689446 1.19416i −0.282572 0.959246i \(-0.591187\pi\)
0.972017 0.234909i \(-0.0754792\pi\)
\(740\) −2897.08 5017.88i −0.143917 0.249272i
\(741\) 2799.40 21128.4i 0.138783 1.04747i
\(742\) 1812.95 + 14602.7i 0.0896973 + 0.722485i
\(743\) 28617.3i 1.41301i −0.707709 0.706504i \(-0.750271\pi\)
0.707709 0.706504i \(-0.249729\pi\)
\(744\) 15360.0 6347.45i 0.756890 0.312781i
\(745\) −3728.19 2152.47i −0.183343 0.105853i
\(746\) −3116.67 1799.41i −0.152962 0.0883124i
\(747\) 6018.47 + 22610.8i 0.294785 + 1.10748i
\(748\) 31814.8i 1.55517i
\(749\) 17343.3 + 22951.0i 0.846076 + 1.11964i
\(750\) −1107.37 146.721i −0.0539140 0.00714331i
\(751\) 13096.8 + 22684.3i 0.636362 + 1.10221i 0.986225 + 0.165411i \(0.0528950\pi\)
−0.349862 + 0.936801i \(0.613772\pi\)
\(752\) −205.337 + 355.655i −0.00995729 + 0.0172465i
\(753\) 1708.83 + 1313.48i 0.0827002 + 0.0635669i
\(754\) 12211.0 7050.03i 0.589786 0.340513i
\(755\) −15879.6 −0.765455
\(756\) −9355.00 + 9172.26i −0.450050 + 0.441259i
\(757\) 31415.1 1.50832 0.754162 0.656689i \(-0.228044\pi\)
0.754162 + 0.656689i \(0.228044\pi\)
\(758\) −10902.7 + 6294.66i −0.522431 + 0.301626i
\(759\) 7418.30 + 5702.02i 0.354766 + 0.272688i
\(760\) −5149.64 + 8919.44i −0.245786 + 0.425713i
\(761\) −5159.76 8936.96i −0.245783 0.425709i 0.716568 0.697517i \(-0.245712\pi\)
−0.962352 + 0.271808i \(0.912378\pi\)
\(762\) 11339.3 + 1502.40i 0.539081 + 0.0714252i
\(763\) −9372.21 3963.39i −0.444688 0.188053i
\(764\) 3221.18i 0.152537i
\(765\) 3812.22 + 14322.2i 0.180171 + 0.676888i
\(766\) −4749.65 2742.21i −0.224036 0.129347i
\(767\) −17769.3 10259.1i −0.836520 0.482965i
\(768\) −19313.8 + 7981.31i −0.907455 + 0.375001i
\(769\) 13235.4i 0.620652i −0.950630 0.310326i \(-0.899562\pi\)
0.950630 0.310326i \(-0.100438\pi\)
\(770\) 7302.49 5518.25i 0.341771 0.258265i
\(771\) −302.238 + 2281.13i −0.0141178 + 0.106554i
\(772\) 3971.03 + 6878.03i 0.185130 + 0.320655i
\(773\) 15411.2 26693.0i 0.717080 1.24202i −0.245072 0.969505i \(-0.578812\pi\)
0.962152 0.272514i \(-0.0878550\pi\)
\(774\) −733.018 735.448i −0.0340411 0.0341539i
\(775\) −3087.34 + 1782.47i −0.143097 + 0.0826173i
\(776\) 7257.25 0.335722
\(777\) −22116.2 181.535i −1.02112 0.00838161i
\(778\) 11562.8 0.532837
\(779\) −14773.1 + 8529.23i −0.679461 + 0.392287i
\(780\) −3565.76 + 4639.03i −0.163685 + 0.212954i
\(781\) −13542.4 + 23456.2i −0.620469 + 1.07468i
\(782\) −2957.71 5122.91i −0.135253 0.234264i
\(783\) 23768.0 + 9914.23i 1.08480 + 0.452498i
\(784\) 421.072 + 433.690i 0.0191815 + 0.0197563i
\(785\) 5864.90i 0.266659i
\(786\) 7958.10 + 19257.6i 0.361140 + 0.873913i
\(787\) −17768.5 10258.6i −0.804800 0.464651i 0.0403468 0.999186i \(-0.487154\pi\)
−0.845147 + 0.534534i \(0.820487\pi\)
\(788\) 1423.31 + 821.746i 0.0643441 + 0.0371491i
\(789\) −9883.22 23916.2i −0.445947 1.07914i
\(790\) 3018.65i 0.135948i
\(791\) −20971.4 + 2603.62i −0.942676 + 0.117034i
\(792\) −33605.7 9064.26i −1.50774 0.406672i
\(793\) 6410.65 + 11103.6i 0.287073 + 0.497225i
\(794\) 10649.8 18446.1i 0.476006 0.824466i
\(795\) −7314.68 + 9516.36i −0.326321 + 0.424542i
\(796\) 2654.88 1532.79i 0.118216 0.0682518i
\(797\) −12338.0 −0.548349 −0.274175 0.961680i \(-0.588405\pi\)
−0.274175 + 0.961680i \(0.588405\pi\)
\(798\) 7491.17 + 13224.6i 0.332312 + 0.586649i
\(799\) 25583.1 1.13275
\(800\) 3950.64 2280.91i 0.174595 0.100803i
\(801\) −19873.6 + 19807.9i −0.876652 + 0.873755i
\(802\) 2379.01 4120.57i 0.104745 0.181424i
\(803\) 15563.7 + 26957.1i 0.683974 + 1.18468i
\(804\) 2863.37 21611.2i 0.125601 0.947971i
\(805\) −1130.01 + 2672.13i −0.0494752 + 0.116994i
\(806\) 10953.5i 0.478687i
\(807\) 6665.46 2754.47i 0.290750 0.120151i
\(808\) −3391.99 1958.36i −0.147685 0.0852661i
\(809\) −9637.68 5564.32i −0.418841 0.241818i 0.275740 0.961232i \(-0.411077\pi\)
−0.694581 + 0.719414i \(0.744410\pi\)
\(810\) 6268.68 + 20.7485i 0.271924 + 0.000900036i
\(811\) 10747.8i 0.465357i −0.972554 0.232679i \(-0.925251\pi\)
0.972554 0.232679i \(-0.0747490\pi\)
\(812\) 6676.52 15787.9i 0.288546 0.682325i
\(813\) −3397.42 450.139i −0.146559 0.0194183i
\(814\) −11358.3 19673.1i −0.489075 0.847102i
\(815\) −2128.28 + 3686.29i −0.0914729 + 0.158436i
\(816\) −797.068 612.660i −0.0341948 0.0262836i
\(817\) 1778.44 1026.78i 0.0761564 0.0439689i
\(818\) −11059.1 −0.472706
\(819\) 8360.16 + 20710.5i 0.356688 + 0.883620i
\(820\) 4683.07 0.199439
\(821\) 20479.9 11824.1i 0.870587 0.502634i 0.00304382 0.999995i \(-0.499031\pi\)
0.867543 + 0.497362i \(0.165698\pi\)
\(822\) 12671.1 + 9739.57i 0.537660 + 0.413268i
\(823\) −11311.0 + 19591.2i −0.479073 + 0.829779i −0.999712 0.0239982i \(-0.992360\pi\)
0.520639 + 0.853777i \(0.325694\pi\)
\(824\) −11753.5 20357.7i −0.496910 0.860673i
\(825\) 7401.31 + 980.632i 0.312340 + 0.0413833i
\(826\) 14520.6 1802.75i 0.611666 0.0759391i
\(827\) 39892.0i 1.67736i 0.544621 + 0.838682i \(0.316673\pi\)
−0.544621 + 0.838682i \(0.683327\pi\)
\(828\) 4121.83 1097.13i 0.172999 0.0460483i
\(829\) 17056.9 + 9847.79i 0.714608 + 0.412579i 0.812765 0.582592i \(-0.197961\pi\)
−0.0981571 + 0.995171i \(0.531295\pi\)
\(830\) −6453.55 3725.96i −0.269887 0.155819i
\(831\) 26109.2 10789.5i 1.08991 0.450401i
\(832\) 13386.8i 0.557815i
\(833\) 10281.9 36225.0i 0.427667 1.50675i
\(834\) 1540.45 11626.5i 0.0639586 0.482727i
\(835\) −4909.28 8503.13i −0.203464 0.352411i
\(836\) 13306.5 23047.5i 0.550496 0.953488i
\(837\) 15902.0 12139.4i 0.656693 0.501313i
\(838\) −3261.07 + 1882.78i −0.134429 + 0.0776128i
\(839\) 14471.2 0.595473 0.297736 0.954648i \(-0.403768\pi\)
0.297736 + 0.954648i \(0.403768\pi\)
\(840\) 88.5864 10792.4i 0.00363871 0.443301i
\(841\) −9305.58 −0.381548
\(842\) −13015.6 + 7514.56i −0.532716 + 0.307564i
\(843\) −10541.7 + 13714.7i −0.430695 + 0.560332i
\(844\) −8358.37 + 14477.1i −0.340885 + 0.590430i
\(845\) −505.255 875.127i −0.0205696 0.0356275i
\(846\) 2817.92 10447.4i 0.114518 0.424574i
\(847\) −29140.7 + 22020.6i −1.18216 + 0.893316i
\(848\) 814.164i 0.0329700i
\(849\) −12678.6 30680.6i −0.512519 1.24023i
\(850\) −4087.81 2360.10i −0.164954 0.0952361i
\(851\) 6235.80 + 3600.24i 0.251187 + 0.145023i
\(852\) 4715.62 + 11411.2i 0.189618 + 0.458851i
\(853\) 19866.7i 0.797446i 0.917071 + 0.398723i \(0.130547\pi\)
−0.917071 + 0.398723i \(0.869453\pi\)
\(854\) −8421.19 3561.21i −0.337432 0.142696i
\(855\) −3228.55 + 11969.8i −0.129139 + 0.478783i
\(856\) 17420.1 + 30172.5i 0.695569 + 1.20476i
\(857\) −3508.78 + 6077.39i −0.139857 + 0.242240i −0.927442 0.373966i \(-0.877998\pi\)
0.787585 + 0.616206i \(0.211331\pi\)
\(858\) −13979.9 + 18187.8i −0.556253 + 0.723683i
\(859\) 25313.0 14614.5i 1.00543 0.580487i 0.0955821 0.995422i \(-0.469529\pi\)
0.909851 + 0.414934i \(0.136195\pi\)
\(860\) −563.767 −0.0223538
\(861\) 9064.66 15407.0i 0.358795 0.609836i
\(862\) 7593.17 0.300028
\(863\) −37613.6 + 21716.2i −1.48364 + 0.856580i −0.999827 0.0185910i \(-0.994082\pi\)
−0.483813 + 0.875171i \(0.660749\pi\)
\(864\) −20348.6 + 15533.9i −0.801243 + 0.611661i
\(865\) 486.162 842.058i 0.0191098 0.0330992i
\(866\) 9081.70 + 15730.0i 0.356361 + 0.617236i
\(867\) −4872.71 + 36776.7i −0.190872 + 1.44060i
\(868\) −8028.28 10624.1i −0.313937 0.415444i
\(869\) 20175.7i 0.787587i
\(870\) −7580.13 + 3132.45i −0.295391 + 0.122069i
\(871\) −32184.2 18581.6i −1.25203 0.722861i
\(872\) −10673.0 6162.04i −0.414486 0.239304i
\(873\) 8441.87 2247.02i 0.327278 0.0871137i
\(874\) 4948.23i 0.191506i
\(875\) 285.224 + 2297.39i 0.0110198 + 0.0887613i
\(876\) 14067.1 + 1863.81i 0.542561 + 0.0718863i
\(877\) 1134.15 + 1964.40i 0.0436687 + 0.0756364i 0.887034 0.461705i \(-0.152762\pi\)
−0.843365 + 0.537341i \(0.819429\pi\)
\(878\) 7873.23 13636.8i 0.302629 0.524170i
\(879\) 26819.9 + 20614.9i 1.02914 + 0.791040i
\(880\) −438.581 + 253.215i −0.0168007 + 0.00969986i
\(881\) −23261.7 −0.889566 −0.444783 0.895638i \(-0.646719\pi\)
−0.444783 + 0.895638i \(0.646719\pi\)
\(882\) −13660.7 8188.93i −0.521521 0.312625i
\(883\) 1480.02 0.0564062 0.0282031 0.999602i \(-0.491021\pi\)
0.0282031 + 0.999602i \(0.491021\pi\)
\(884\) −21411.9 + 12362.2i −0.814660 + 0.470344i
\(885\) 9462.83 + 7273.53i 0.359423 + 0.276268i
\(886\) −2910.79 + 5041.63i −0.110372 + 0.191170i
\(887\) 6182.71 + 10708.8i 0.234042 + 0.405372i 0.958994 0.283427i \(-0.0914714\pi\)
−0.724952 + 0.688799i \(0.758138\pi\)
\(888\) −26554.1 3518.27i −1.00349 0.132957i
\(889\) −2920.65 23524.9i −0.110186 0.887516i
\(890\) 8936.35i 0.336570i
\(891\) −41897.8 138.676i −1.57534 0.00521418i
\(892\) 20054.4 + 11578.4i 0.752770 + 0.434612i
\(893\) 18533.1 + 10700.1i 0.694499 + 0.400969i
\(894\) −7110.88 + 2938.53i −0.266022 + 0.109932i
\(895\) 23679.1i 0.884364i
\(896\) 10544.0 + 13953.2i 0.393135 + 0.520249i
\(897\) 955.052 7208.24i 0.0355499 0.268312i
\(898\) −7347.37 12726.0i −0.273034 0.472910i
\(899\) −13087.7 + 22668.6i −0.485539 + 0.840978i
\(900\) 2410.63 2402.67i 0.0892826 0.0889876i
\(901\) −43923.6 + 25359.3i −1.62409 + 0.937671i
\(902\) 18360.4 0.677755
\(903\) −1091.24 + 1854.76i −0.0402151 + 0.0683527i
\(904\) −25593.8 −0.941634
\(905\) 12834.0 7409.72i 0.471400 0.272163i
\(906\) −17296.1 + 22502.1i −0.634242 + 0.825146i
\(907\) 10238.6 17733.8i 0.374827 0.649220i −0.615474 0.788157i \(-0.711035\pi\)
0.990301 + 0.138937i \(0.0443686\pi\)
\(908\) −12246.5 21211.6i −0.447594 0.775255i
\(909\) −4552.03 1227.79i −0.166096 0.0448000i
\(910\) −6551.37 2770.49i −0.238655 0.100924i
\(911\) 5201.00i 0.189151i −0.995518 0.0945756i \(-0.969851\pi\)
0.995518 0.0945756i \(-0.0301494\pi\)
\(912\) −321.174 777.201i −0.0116613 0.0282190i
\(913\) 43133.4 + 24903.1i 1.56353 + 0.902707i
\(914\) 22365.3 + 12912.6i 0.809384 + 0.467298i
\(915\) −2848.36 6892.67i −0.102911 0.249033i
\(916\) 26977.3i 0.973095i
\(917\) 34453.3 26035.2i 1.24073 0.937576i
\(918\) 24447.4 + 10197.6i 0.878959 + 0.366636i
\(919\) 7336.39 + 12707.0i 0.263336 + 0.456110i 0.967126 0.254297i \(-0.0818440\pi\)
−0.703791 + 0.710407i \(0.748511\pi\)
\(920\) −1756.87 + 3042.98i −0.0629589 + 0.109048i
\(921\) 8370.76 10890.3i 0.299485 0.389629i
\(922\) −7738.67 + 4467.92i −0.276420 + 0.159591i
\(923\) 21048.5 0.750618
\(924\) −228.904 + 27887.2i −0.00814978 + 0.992880i
\(925\) 5745.60 0.204232
\(926\) 8735.99 5043.72i 0.310024 0.178992i
\(927\) −19975.3 20041.6i −0.707741 0.710088i
\(928\) 16747.4 29007.3i 0.592414 1.02609i
\(929\) 19941.3 + 34539.4i 0.704256 + 1.21981i 0.966959 + 0.254930i \(0.0820525\pi\)
−0.262704 + 0.964877i \(0.584614\pi\)
\(930\) −836.882 + 6316.36i −0.0295080 + 0.222711i
\(931\) 22599.5 21942.0i 0.795564 0.772417i
\(932\) 6557.95i 0.230486i
\(933\) −13416.1 + 5544.12i −0.470764 + 0.194541i
\(934\) 3145.58 + 1816.10i 0.110200 + 0.0636237i
\(935\) 27321.6 + 15774.1i 0.955627 + 0.551731i
\(936\) 6957.65 + 26139.2i 0.242968 + 0.912808i
\(937\) 7011.20i 0.244446i 0.992503 + 0.122223i \(0.0390023\pi\)
−0.992503 + 0.122223i \(0.960998\pi\)
\(938\) 26300.1 3265.19i 0.915490 0.113659i
\(939\) 33580.6 + 4449.24i 1.16705 + 0.154628i
\(940\) −2937.51 5087.91i −0.101926 0.176542i
\(941\) 28387.5 49168.6i 0.983428 1.70335i 0.334704 0.942323i \(-0.391364\pi\)
0.648724 0.761024i \(-0.275303\pi\)
\(942\) 8310.81 + 6388.04i 0.287453 + 0.220949i
\(943\) −5040.03 + 2909.86i −0.174046 + 0.100486i
\(944\) −809.584 −0.0279128
\(945\) −3238.54 12581.5i −0.111481 0.433096i
\(946\) −2210.30 −0.0759652
\(947\) 507.141 292.798i 0.0174022 0.0100472i −0.491274 0.871005i \(-0.663469\pi\)
0.508676 + 0.860958i \(0.330135\pi\)
\(948\) −7292.22 5605.11i −0.249831 0.192031i
\(949\) 12095.1 20949.2i 0.413722 0.716587i
\(950\) −1974.21 3419.44i −0.0674231 0.116780i
\(951\) 15809.5 + 2094.66i 0.539071 + 0.0714239i
\(952\) 17763.1 42004.2i 0.604731 1.43001i
\(953\) 19659.9i 0.668256i 0.942528 + 0.334128i \(0.108442\pi\)
−0.942528 + 0.334128i \(0.891558\pi\)
\(954\) 5517.95 + 20730.4i 0.187264 + 0.703535i
\(955\) 2766.24 + 1597.09i 0.0937315 + 0.0541159i
\(956\) −7645.79 4414.30i −0.258664 0.149339i
\(957\) 50663.1 20936.2i 1.71129 0.707181i
\(958\) 9330.40i 0.314668i
\(959\) 12900.5 30505.9i 0.434390 1.02720i
\(960\) 1022.79 7719.48i 0.0343858 0.259526i
\(961\) −4728.41 8189.85i −0.158719 0.274910i
\(962\) −8826.87 + 15288.6i −0.295831 + 0.512395i
\(963\) 29605.8 + 29703.9i 0.990688 + 0.993972i
\(964\) −9300.63 + 5369.72i −0.310740 + 0.179406i
\(965\) −7875.52 −0.262717
\(966\) 2555.71 + 4511.75i 0.0851229 + 0.150272i
\(967\) 3382.88 0.112498 0.0562492 0.998417i \(-0.482086\pi\)
0.0562492 + 0.998417i \(0.482086\pi\)
\(968\) −38309.7 + 22118.1i −1.27203 + 0.734405i
\(969\) −31925.7 + 41535.1i −1.05841 + 1.37699i
\(970\) −1391.10 + 2409.46i −0.0460471 + 0.0797559i
\(971\) 23213.3 + 40206.6i 0.767199 + 1.32883i 0.939076 + 0.343709i \(0.111683\pi\)
−0.171877 + 0.985118i \(0.554983\pi\)
\(972\) −11690.0 + 15104.8i −0.385757 + 0.498444i
\(973\) −24120.9 + 2994.63i −0.794737 + 0.0986675i
\(974\) 17524.7i 0.576516i
\(975\) −2215.92 5362.24i −0.0727858 0.176132i
\(976\) 438.113 + 252.945i 0.0143685 + 0.00829566i
\(977\) 6254.69 + 3611.14i 0.204816 + 0.118251i 0.598900 0.800824i \(-0.295605\pi\)
−0.394084 + 0.919074i \(0.628938\pi\)
\(978\) 2905.51 + 7030.97i 0.0949979 + 0.229883i
\(979\) 59727.6i 1.94985i
\(980\) −8384.93 + 2114.59i −0.273313 + 0.0689267i
\(981\) −14323.1 3863.27i −0.466157 0.125734i
\(982\) −5158.35 8934.53i −0.167627 0.290338i
\(983\) 2487.41 4308.32i 0.0807080 0.139790i −0.822846 0.568264i \(-0.807615\pi\)
0.903554 + 0.428474i \(0.140949\pi\)
\(984\) 13193.7 17164.9i 0.427439 0.556095i
\(985\) −1411.38 + 814.860i −0.0456551 + 0.0263590i
\(986\) −34657.7 −1.11940
\(987\) −22424.8 184.068i −0.723191 0.00593611i
\(988\) −20681.8 −0.665968
\(989\) 606.739 350.301i 0.0195078 0.0112628i
\(990\) 9451.11 9419.88i 0.303410 0.302407i
\(991\) 14642.5 25361.6i 0.469359 0.812954i −0.530027 0.847981i \(-0.677818\pi\)
0.999386 + 0.0350269i \(0.0111517\pi\)
\(992\) −13010.1 22534.2i −0.416402 0.721230i
\(993\) 4193.40 31649.7i 0.134012 1.01145i
\(994\) −11975.6 + 9049.54i −0.382135 + 0.288767i
\(995\) 3039.90i 0.0968556i
\(996\) 20984.0 8671.51i 0.667573 0.275871i
\(997\) −655.300 378.338i −0.0208160 0.0120181i 0.489556 0.871972i \(-0.337159\pi\)
−0.510372 + 0.859954i \(0.670492\pi\)
\(998\) −32117.0 18542.8i −1.01868 0.588137i
\(999\) −31977.9 + 4129.24i −1.01275 + 0.130774i
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.s.a.101.11 yes 32
3.2 odd 2 105.4.s.b.101.6 yes 32
7.5 odd 6 105.4.s.b.26.6 yes 32
21.5 even 6 inner 105.4.s.a.26.11 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.s.a.26.11 32 21.5 even 6 inner
105.4.s.a.101.11 yes 32 1.1 even 1 trivial
105.4.s.b.26.6 yes 32 7.5 odd 6
105.4.s.b.101.6 yes 32 3.2 odd 2