Properties

Label 1950.2.y.i.49.4
Level $1950$
Weight $2$
Character 1950.49
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
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] = [1950,2,Mod(49,1950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1950.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not 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: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1950.49
Dual form 1950.2.y.i.199.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.465926 - 0.807007i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(0.465926 - 0.807007i) q^{7} +1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(1.45680 - 0.841081i) q^{11} +1.00000i q^{12} +(-3.08725 + 1.86250i) q^{13} -0.931852 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.21089 - 1.27646i) q^{17} -1.00000 q^{18} +(-2.27646 - 1.31431i) q^{19} -0.931852i q^{21} +(-1.45680 - 0.841081i) q^{22} +(-5.59197 + 3.22853i) q^{23} +(0.866025 - 0.500000i) q^{24} +(3.15660 + 1.74238i) q^{26} -1.00000i q^{27} +(0.465926 + 0.807007i) q^{28} +(-1.69419 - 2.93443i) q^{29} -9.29493i q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.841081 - 1.45680i) q^{33} +2.55291i q^{34} +(0.500000 + 0.866025i) q^{36} +(-4.57994 - 7.93269i) q^{37} +2.62863i q^{38} +(-1.74238 + 3.15660i) q^{39} +(1.01714 - 0.587246i) q^{41} +(-0.807007 + 0.465926i) q^{42} +(-2.55695 - 1.47626i) q^{43} +1.68216i q^{44} +(5.59197 + 3.22853i) q^{46} +3.97934 q^{47} +(-0.866025 - 0.500000i) q^{48} +(3.06583 + 5.31017i) q^{49} -2.55291 q^{51} +(-0.0693504 - 3.60488i) q^{52} -5.36068i q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.465926 - 0.807007i) q^{56} -2.62863 q^{57} +(-1.69419 + 2.93443i) q^{58} +(3.44174 + 1.98709i) q^{59} +(4.36188 - 7.55500i) q^{61} +(-8.04965 + 4.64747i) q^{62} +(-0.465926 - 0.807007i) q^{63} +1.00000 q^{64} -1.68216 q^{66} +(-2.59575 - 4.49598i) q^{67} +(2.21089 - 1.27646i) q^{68} +(-3.22853 + 5.59197i) q^{69} +(3.40803 + 1.96763i) q^{71} +(0.500000 - 0.866025i) q^{72} -7.26330 q^{73} +(-4.57994 + 7.93269i) q^{74} +(2.27646 - 1.31431i) q^{76} -1.56753i q^{77} +(3.60488 - 0.0693504i) q^{78} +3.68973 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.01714 - 0.587246i) q^{82} -3.84909 q^{83} +(0.807007 + 0.465926i) q^{84} +2.95252i q^{86} +(-2.93443 - 1.69419i) q^{87} +(1.45680 - 0.841081i) q^{88} +(-11.6628 + 6.73351i) q^{89} +(0.0646242 + 3.35922i) q^{91} -6.45705i q^{92} +(-4.64747 - 8.04965i) q^{93} +(-1.98967 - 3.44621i) q^{94} +1.00000i q^{96} +(7.04052 - 12.1945i) q^{97} +(3.06583 - 5.31017i) q^{98} -1.68216i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} - 4 q^{7} + 8 q^{8} + 4 q^{9} - 12 q^{11} + 8 q^{14} - 4 q^{16} - 8 q^{18} - 12 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{28} - 4 q^{29} - 4 q^{32} + 8 q^{33} + 4 q^{36} - 16 q^{37} + 24 q^{43} + 12 q^{46} + 32 q^{47} + 16 q^{49} - 8 q^{51} - 4 q^{56} - 4 q^{58} + 12 q^{59} - 16 q^{61} - 24 q^{62} + 4 q^{63} + 8 q^{64} - 16 q^{66} + 24 q^{67} - 4 q^{69} + 60 q^{71} + 4 q^{72} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 8 q^{79} - 4 q^{81} - 8 q^{83} - 12 q^{87} - 12 q^{88} - 24 q^{89} + 8 q^{91} + 4 q^{93} - 16 q^{94} + 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 0.465926 0.807007i 0.176103 0.305020i −0.764439 0.644696i \(-0.776984\pi\)
0.940543 + 0.339676i \(0.110317\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) 1.45680 0.841081i 0.439240 0.253596i −0.264035 0.964513i \(-0.585053\pi\)
0.703275 + 0.710918i \(0.251720\pi\)
\(12\) 1.00000i 0.288675i
\(13\) −3.08725 + 1.86250i −0.856248 + 0.516565i
\(14\) −0.931852 −0.249048
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.21089 1.27646i −0.536219 0.309586i 0.207326 0.978272i \(-0.433524\pi\)
−0.743545 + 0.668686i \(0.766857\pi\)
\(18\) −1.00000 −0.235702
\(19\) −2.27646 1.31431i −0.522255 0.301524i 0.215602 0.976481i \(-0.430829\pi\)
−0.737857 + 0.674957i \(0.764162\pi\)
\(20\) 0 0
\(21\) 0.931852i 0.203347i
\(22\) −1.45680 0.841081i −0.310590 0.179319i
\(23\) −5.59197 + 3.22853i −1.16601 + 0.673194i −0.952736 0.303799i \(-0.901745\pi\)
−0.213271 + 0.976993i \(0.568412\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) 3.15660 + 1.74238i 0.619060 + 0.341709i
\(27\) 1.00000i 0.192450i
\(28\) 0.465926 + 0.807007i 0.0880517 + 0.152510i
\(29\) −1.69419 2.93443i −0.314604 0.544910i 0.664749 0.747067i \(-0.268538\pi\)
−0.979353 + 0.202156i \(0.935205\pi\)
\(30\) 0 0
\(31\) 9.29493i 1.66942i −0.550690 0.834710i \(-0.685635\pi\)
0.550690 0.834710i \(-0.314365\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0.841081 1.45680i 0.146413 0.253596i
\(34\) 2.55291i 0.437821i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −4.57994 7.93269i −0.752938 1.30413i −0.946393 0.323017i \(-0.895303\pi\)
0.193456 0.981109i \(-0.438030\pi\)
\(38\) 2.62863i 0.426419i
\(39\) −1.74238 + 3.15660i −0.279005 + 0.505460i
\(40\) 0 0
\(41\) 1.01714 0.587246i 0.158851 0.0917124i −0.418467 0.908232i \(-0.637433\pi\)
0.577318 + 0.816519i \(0.304099\pi\)
\(42\) −0.807007 + 0.465926i −0.124524 + 0.0718939i
\(43\) −2.55695 1.47626i −0.389932 0.225127i 0.292199 0.956358i \(-0.405613\pi\)
−0.682131 + 0.731230i \(0.738946\pi\)
\(44\) 1.68216i 0.253596i
\(45\) 0 0
\(46\) 5.59197 + 3.22853i 0.824491 + 0.476020i
\(47\) 3.97934 0.580446 0.290223 0.956959i \(-0.406271\pi\)
0.290223 + 0.956959i \(0.406271\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 3.06583 + 5.31017i 0.437975 + 0.758595i
\(50\) 0 0
\(51\) −2.55291 −0.357480
\(52\) −0.0693504 3.60488i −0.00961716 0.499908i
\(53\) 5.36068i 0.736346i −0.929757 0.368173i \(-0.879983\pi\)
0.929757 0.368173i \(-0.120017\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) 0.465926 0.807007i 0.0622620 0.107841i
\(57\) −2.62863 −0.348170
\(58\) −1.69419 + 2.93443i −0.222459 + 0.385310i
\(59\) 3.44174 + 1.98709i 0.448076 + 0.258697i 0.707017 0.707196i \(-0.250040\pi\)
−0.258941 + 0.965893i \(0.583374\pi\)
\(60\) 0 0
\(61\) 4.36188 7.55500i 0.558481 0.967318i −0.439142 0.898418i \(-0.644718\pi\)
0.997624 0.0689005i \(-0.0219491\pi\)
\(62\) −8.04965 + 4.64747i −1.02231 + 0.590229i
\(63\) −0.465926 0.807007i −0.0587011 0.101673i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.68216 −0.207060
\(67\) −2.59575 4.49598i −0.317122 0.549271i 0.662764 0.748828i \(-0.269383\pi\)
−0.979886 + 0.199557i \(0.936050\pi\)
\(68\) 2.21089 1.27646i 0.268110 0.154793i
\(69\) −3.22853 + 5.59197i −0.388669 + 0.673194i
\(70\) 0 0
\(71\) 3.40803 + 1.96763i 0.404458 + 0.233514i 0.688406 0.725326i \(-0.258311\pi\)
−0.283947 + 0.958840i \(0.591644\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −7.26330 −0.850106 −0.425053 0.905169i \(-0.639744\pi\)
−0.425053 + 0.905169i \(0.639744\pi\)
\(74\) −4.57994 + 7.93269i −0.532407 + 0.922156i
\(75\) 0 0
\(76\) 2.27646 1.31431i 0.261128 0.150762i
\(77\) 1.56753i 0.178636i
\(78\) 3.60488 0.0693504i 0.408173 0.00785238i
\(79\) 3.68973 0.415127 0.207563 0.978222i \(-0.433447\pi\)
0.207563 + 0.978222i \(0.433447\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.01714 0.587246i −0.112324 0.0648505i
\(83\) −3.84909 −0.422493 −0.211246 0.977433i \(-0.567752\pi\)
−0.211246 + 0.977433i \(0.567752\pi\)
\(84\) 0.807007 + 0.465926i 0.0880517 + 0.0508367i
\(85\) 0 0
\(86\) 2.95252i 0.318378i
\(87\) −2.93443 1.69419i −0.314604 0.181637i
\(88\) 1.45680 0.841081i 0.155295 0.0896596i
\(89\) −11.6628 + 6.73351i −1.23625 + 0.713751i −0.968326 0.249689i \(-0.919672\pi\)
−0.267926 + 0.963439i \(0.586338\pi\)
\(90\) 0 0
\(91\) 0.0646242 + 3.35922i 0.00677446 + 0.352142i
\(92\) 6.45705i 0.673194i
\(93\) −4.64747 8.04965i −0.481920 0.834710i
\(94\) −1.98967 3.44621i −0.205219 0.355449i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 7.04052 12.1945i 0.714856 1.23817i −0.248159 0.968719i \(-0.579825\pi\)
0.963015 0.269448i \(-0.0868412\pi\)
\(98\) 3.06583 5.31017i 0.309695 0.536408i
\(99\) 1.68216i 0.169064i
\(100\) 0 0
\(101\) −5.65892 9.80153i −0.563083 0.975289i −0.997225 0.0744445i \(-0.976282\pi\)
0.434142 0.900845i \(-0.357052\pi\)
\(102\) 1.27646 + 2.21089i 0.126388 + 0.218911i
\(103\) 0.725003i 0.0714366i −0.999362 0.0357183i \(-0.988628\pi\)
0.999362 0.0357183i \(-0.0113719\pi\)
\(104\) −3.08725 + 1.86250i −0.302729 + 0.182633i
\(105\) 0 0
\(106\) −4.64248 + 2.68034i −0.450918 + 0.260337i
\(107\) −14.9106 + 8.60867i −1.44147 + 0.832231i −0.997948 0.0640338i \(-0.979603\pi\)
−0.443519 + 0.896265i \(0.646270\pi\)
\(108\) 0.866025 + 0.500000i 0.0833333 + 0.0481125i
\(109\) 10.2816i 0.984795i 0.870370 + 0.492398i \(0.163879\pi\)
−0.870370 + 0.492398i \(0.836121\pi\)
\(110\) 0 0
\(111\) −7.93269 4.57994i −0.752938 0.434709i
\(112\) −0.931852 −0.0880517
\(113\) −8.36308 4.82843i −0.786732 0.454220i 0.0520785 0.998643i \(-0.483415\pi\)
−0.838811 + 0.544423i \(0.816749\pi\)
\(114\) 1.31431 + 2.27646i 0.123097 + 0.213210i
\(115\) 0 0
\(116\) 3.38839 0.314604
\(117\) 0.0693504 + 3.60488i 0.00641144 + 0.333272i
\(118\) 3.97418i 0.365853i
\(119\) −2.06022 + 1.18947i −0.188860 + 0.109038i
\(120\) 0 0
\(121\) −4.08516 + 7.07571i −0.371379 + 0.643247i
\(122\) −8.72376 −0.789812
\(123\) 0.587246 1.01714i 0.0529502 0.0917124i
\(124\) 8.04965 + 4.64747i 0.722880 + 0.417355i
\(125\) 0 0
\(126\) −0.465926 + 0.807007i −0.0415080 + 0.0718939i
\(127\) 0.586302 0.338502i 0.0520259 0.0300372i −0.473761 0.880653i \(-0.657104\pi\)
0.525787 + 0.850616i \(0.323771\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.95252 −0.259955
\(130\) 0 0
\(131\) 1.86710 0.163130 0.0815648 0.996668i \(-0.474008\pi\)
0.0815648 + 0.996668i \(0.474008\pi\)
\(132\) 0.841081 + 1.45680i 0.0732067 + 0.126798i
\(133\) −2.12132 + 1.22474i −0.183942 + 0.106199i
\(134\) −2.59575 + 4.49598i −0.224239 + 0.388393i
\(135\) 0 0
\(136\) −2.21089 1.27646i −0.189582 0.109455i
\(137\) −3.64431 + 6.31212i −0.311354 + 0.539281i −0.978656 0.205506i \(-0.934116\pi\)
0.667302 + 0.744788i \(0.267449\pi\)
\(138\) 6.45705 0.549661
\(139\) 2.35569 4.08018i 0.199807 0.346076i −0.748659 0.662956i \(-0.769302\pi\)
0.948466 + 0.316879i \(0.102635\pi\)
\(140\) 0 0
\(141\) 3.44621 1.98967i 0.290223 0.167560i
\(142\) 3.93525i 0.330239i
\(143\) −2.93097 + 5.30991i −0.245100 + 0.444037i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 3.63165 + 6.29021i 0.300558 + 0.520581i
\(147\) 5.31017 + 3.06583i 0.437975 + 0.252865i
\(148\) 9.15988 0.752938
\(149\) 2.60016 + 1.50120i 0.213013 + 0.122983i 0.602711 0.797960i \(-0.294087\pi\)
−0.389698 + 0.920943i \(0.627421\pi\)
\(150\) 0 0
\(151\) 12.4200i 1.01073i −0.862907 0.505363i \(-0.831358\pi\)
0.862907 0.505363i \(-0.168642\pi\)
\(152\) −2.27646 1.31431i −0.184645 0.106605i
\(153\) −2.21089 + 1.27646i −0.178740 + 0.103195i
\(154\) −1.35752 + 0.783763i −0.109392 + 0.0631574i
\(155\) 0 0
\(156\) −1.86250 3.08725i −0.149119 0.247178i
\(157\) 22.5217i 1.79743i −0.438535 0.898714i \(-0.644502\pi\)
0.438535 0.898714i \(-0.355498\pi\)
\(158\) −1.84486 3.19540i −0.146769 0.254212i
\(159\) −2.68034 4.64248i −0.212565 0.368173i
\(160\) 0 0
\(161\) 6.01702i 0.474207i
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) −1.38745 + 2.40313i −0.108673 + 0.188227i −0.915233 0.402925i \(-0.867994\pi\)
0.806560 + 0.591152i \(0.201327\pi\)
\(164\) 1.17449i 0.0917124i
\(165\) 0 0
\(166\) 1.92455 + 3.33341i 0.149374 + 0.258723i
\(167\) 11.1022 + 19.2296i 0.859114 + 1.48803i 0.872775 + 0.488122i \(0.162318\pi\)
−0.0136615 + 0.999907i \(0.504349\pi\)
\(168\) 0.931852i 0.0718939i
\(169\) 6.06218 11.5000i 0.466321 0.884615i
\(170\) 0 0
\(171\) −2.27646 + 1.31431i −0.174085 + 0.100508i
\(172\) 2.55695 1.47626i 0.194966 0.112564i
\(173\) −0.823267 0.475314i −0.0625919 0.0361374i 0.468377 0.883528i \(-0.344839\pi\)
−0.530969 + 0.847391i \(0.678172\pi\)
\(174\) 3.38839i 0.256873i
\(175\) 0 0
\(176\) −1.45680 0.841081i −0.109810 0.0633989i
\(177\) 3.97418 0.298717
\(178\) 11.6628 + 6.73351i 0.874162 + 0.504698i
\(179\) −4.94156 8.55904i −0.369350 0.639732i 0.620114 0.784511i \(-0.287086\pi\)
−0.989464 + 0.144779i \(0.953753\pi\)
\(180\) 0 0
\(181\) 14.3015 1.06302 0.531511 0.847051i \(-0.321624\pi\)
0.531511 + 0.847051i \(0.321624\pi\)
\(182\) 2.87686 1.73557i 0.213247 0.128649i
\(183\) 8.72376i 0.644879i
\(184\) −5.59197 + 3.22853i −0.412246 + 0.238010i
\(185\) 0 0
\(186\) −4.64747 + 8.04965i −0.340769 + 0.590229i
\(187\) −4.29442 −0.314039
\(188\) −1.98967 + 3.44621i −0.145111 + 0.251340i
\(189\) −0.807007 0.465926i −0.0587011 0.0338911i
\(190\) 0 0
\(191\) 0.0573183 0.0992782i 0.00414741 0.00718352i −0.863944 0.503587i \(-0.832013\pi\)
0.868092 + 0.496404i \(0.165347\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −4.32843 7.49706i −0.311567 0.539650i 0.667135 0.744937i \(-0.267521\pi\)
−0.978702 + 0.205287i \(0.934187\pi\)
\(194\) −14.0810 −1.01096
\(195\) 0 0
\(196\) −6.13165 −0.437975
\(197\) 10.2401 + 17.7363i 0.729574 + 1.26366i 0.957063 + 0.289879i \(0.0936150\pi\)
−0.227489 + 0.973781i \(0.573052\pi\)
\(198\) −1.45680 + 0.841081i −0.103530 + 0.0597731i
\(199\) −0.955336 + 1.65469i −0.0677220 + 0.117298i −0.897898 0.440203i \(-0.854906\pi\)
0.830176 + 0.557501i \(0.188240\pi\)
\(200\) 0 0
\(201\) −4.49598 2.59575i −0.317122 0.183090i
\(202\) −5.65892 + 9.80153i −0.398160 + 0.689634i
\(203\) −3.15748 −0.221611
\(204\) 1.27646 2.21089i 0.0893699 0.154793i
\(205\) 0 0
\(206\) −0.627871 + 0.362501i −0.0437458 + 0.0252567i
\(207\) 6.45705i 0.448796i
\(208\) 3.15660 + 1.74238i 0.218871 + 0.120813i
\(209\) −4.42178 −0.305861
\(210\) 0 0
\(211\) −0.620118 1.07408i −0.0426907 0.0739425i 0.843891 0.536515i \(-0.180260\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(212\) 4.64248 + 2.68034i 0.318847 + 0.184086i
\(213\) 3.93525 0.269639
\(214\) 14.9106 + 8.60867i 1.01927 + 0.588476i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −7.50108 4.33075i −0.509206 0.293990i
\(218\) 8.90410 5.14078i 0.603062 0.348178i
\(219\) −6.29021 + 3.63165i −0.425053 + 0.245404i
\(220\) 0 0
\(221\) 9.20296 0.177046i 0.619058 0.0119094i
\(222\) 9.15988i 0.614771i
\(223\) −7.38915 12.7984i −0.494814 0.857043i 0.505168 0.863021i \(-0.331430\pi\)
−0.999982 + 0.00597823i \(0.998097\pi\)
\(224\) 0.465926 + 0.807007i 0.0311310 + 0.0539204i
\(225\) 0 0
\(226\) 9.65685i 0.642364i
\(227\) −4.78290 + 8.28423i −0.317452 + 0.549843i −0.979956 0.199215i \(-0.936161\pi\)
0.662503 + 0.749059i \(0.269494\pi\)
\(228\) 1.31431 2.27646i 0.0870425 0.150762i
\(229\) 15.1478i 1.00099i 0.865739 + 0.500497i \(0.166849\pi\)
−0.865739 + 0.500497i \(0.833151\pi\)
\(230\) 0 0
\(231\) −0.783763 1.35752i −0.0515678 0.0893181i
\(232\) −1.69419 2.93443i −0.111229 0.192655i
\(233\) 18.7413i 1.22778i 0.789391 + 0.613891i \(0.210397\pi\)
−0.789391 + 0.613891i \(0.789603\pi\)
\(234\) 3.08725 1.86250i 0.201820 0.121756i
\(235\) 0 0
\(236\) −3.44174 + 1.98709i −0.224038 + 0.129348i
\(237\) 3.19540 1.84486i 0.207563 0.119837i
\(238\) 2.06022 + 1.18947i 0.133544 + 0.0771018i
\(239\) 4.62330i 0.299057i 0.988757 + 0.149528i \(0.0477755\pi\)
−0.988757 + 0.149528i \(0.952224\pi\)
\(240\) 0 0
\(241\) 15.2373 + 8.79725i 0.981520 + 0.566681i 0.902729 0.430210i \(-0.141561\pi\)
0.0787915 + 0.996891i \(0.474894\pi\)
\(242\) 8.17033 0.525209
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) 4.36188 + 7.55500i 0.279241 + 0.483659i
\(245\) 0 0
\(246\) −1.17449 −0.0748829
\(247\) 9.47589 0.182296i 0.602937 0.0115992i
\(248\) 9.29493i 0.590229i
\(249\) −3.33341 + 1.92455i −0.211246 + 0.121963i
\(250\) 0 0
\(251\) −13.2599 + 22.9668i −0.836958 + 1.44965i 0.0554676 + 0.998460i \(0.482335\pi\)
−0.892426 + 0.451194i \(0.850998\pi\)
\(252\) 0.931852 0.0587011
\(253\) −5.43091 + 9.40661i −0.341438 + 0.591388i
\(254\) −0.586302 0.338502i −0.0367879 0.0212395i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −1.57986 + 0.912132i −0.0985489 + 0.0568972i −0.548464 0.836174i \(-0.684787\pi\)
0.449916 + 0.893071i \(0.351454\pi\)
\(258\) 1.47626 + 2.55695i 0.0919078 + 0.159189i
\(259\) −8.53565 −0.530379
\(260\) 0 0
\(261\) −3.38839 −0.209736
\(262\) −0.933552 1.61696i −0.0576750 0.0998960i
\(263\) 10.5106 6.06828i 0.648110 0.374186i −0.139622 0.990205i \(-0.544589\pi\)
0.787732 + 0.616019i \(0.211255\pi\)
\(264\) 0.841081 1.45680i 0.0517650 0.0896596i
\(265\) 0 0
\(266\) 2.12132 + 1.22474i 0.130066 + 0.0750939i
\(267\) −6.73351 + 11.6628i −0.412084 + 0.713751i
\(268\) 5.19151 0.317122
\(269\) 11.7655 20.3784i 0.717355 1.24250i −0.244689 0.969602i \(-0.578686\pi\)
0.962044 0.272894i \(-0.0879809\pi\)
\(270\) 0 0
\(271\) 10.9872 6.34349i 0.667427 0.385339i −0.127674 0.991816i \(-0.540751\pi\)
0.795101 + 0.606477i \(0.207418\pi\)
\(272\) 2.55291i 0.154793i
\(273\) 1.73557 + 2.87686i 0.105042 + 0.174115i
\(274\) 7.28861 0.440321
\(275\) 0 0
\(276\) −3.22853 5.59197i −0.194334 0.336597i
\(277\) 11.1055 + 6.41177i 0.667265 + 0.385246i 0.795040 0.606558i \(-0.207450\pi\)
−0.127774 + 0.991803i \(0.540783\pi\)
\(278\) −4.71139 −0.282570
\(279\) −8.04965 4.64747i −0.481920 0.278237i
\(280\) 0 0
\(281\) 5.16720i 0.308249i −0.988051 0.154125i \(-0.950744\pi\)
0.988051 0.154125i \(-0.0492557\pi\)
\(282\) −3.44621 1.98967i −0.205219 0.118483i
\(283\) −11.2258 + 6.48124i −0.667307 + 0.385270i −0.795055 0.606537i \(-0.792558\pi\)
0.127749 + 0.991807i \(0.459225\pi\)
\(284\) −3.40803 + 1.96763i −0.202229 + 0.116757i
\(285\) 0 0
\(286\) 6.06400 0.116659i 0.358572 0.00689817i
\(287\) 1.09445i 0.0646035i
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −5.24131 9.07822i −0.308313 0.534013i
\(290\) 0 0
\(291\) 14.0810i 0.825445i
\(292\) 3.63165 6.29021i 0.212526 0.368107i
\(293\) −6.73521 + 11.6657i −0.393475 + 0.681519i −0.992905 0.118908i \(-0.962061\pi\)
0.599430 + 0.800427i \(0.295394\pi\)
\(294\) 6.13165i 0.357605i
\(295\) 0 0
\(296\) −4.57994 7.93269i −0.266204 0.461078i
\(297\) −0.841081 1.45680i −0.0488045 0.0845319i
\(298\) 3.00240i 0.173925i
\(299\) 11.2507 20.3823i 0.650642 1.17874i
\(300\) 0 0
\(301\) −2.38270 + 1.37565i −0.137337 + 0.0792913i
\(302\) −10.7561 + 6.21001i −0.618941 + 0.357346i
\(303\) −9.80153 5.65892i −0.563083 0.325096i
\(304\) 2.62863i 0.150762i
\(305\) 0 0
\(306\) 2.21089 + 1.27646i 0.126388 + 0.0729702i
\(307\) 21.4620 1.22490 0.612450 0.790510i \(-0.290184\pi\)
0.612450 + 0.790510i \(0.290184\pi\)
\(308\) 1.35752 + 0.783763i 0.0773517 + 0.0446590i
\(309\) −0.362501 0.627871i −0.0206220 0.0357183i
\(310\) 0 0
\(311\) −14.7562 −0.836745 −0.418372 0.908276i \(-0.637399\pi\)
−0.418372 + 0.908276i \(0.637399\pi\)
\(312\) −1.74238 + 3.15660i −0.0986430 + 0.178707i
\(313\) 1.40441i 0.0793819i 0.999212 + 0.0396910i \(0.0126373\pi\)
−0.999212 + 0.0396910i \(0.987363\pi\)
\(314\) −19.5044 + 11.2609i −1.10070 + 0.635487i
\(315\) 0 0
\(316\) −1.84486 + 3.19540i −0.103782 + 0.179755i
\(317\) 33.1421 1.86144 0.930722 0.365729i \(-0.119180\pi\)
0.930722 + 0.365729i \(0.119180\pi\)
\(318\) −2.68034 + 4.64248i −0.150306 + 0.260337i
\(319\) −4.93619 2.84991i −0.276374 0.159564i
\(320\) 0 0
\(321\) −8.60867 + 14.9106i −0.480489 + 0.832231i
\(322\) 5.21089 3.00851i 0.290391 0.167658i
\(323\) 3.35533 + 5.81160i 0.186695 + 0.323366i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 2.77489 0.153687
\(327\) 5.14078 + 8.90410i 0.284286 + 0.492398i
\(328\) 1.01714 0.587246i 0.0561622 0.0324252i
\(329\) 1.85408 3.21135i 0.102218 0.177048i
\(330\) 0 0
\(331\) −6.05268 3.49452i −0.332686 0.192076i 0.324347 0.945938i \(-0.394855\pi\)
−0.657033 + 0.753862i \(0.728189\pi\)
\(332\) 1.92455 3.33341i 0.105623 0.182945i
\(333\) −9.15988 −0.501958
\(334\) 11.1022 19.2296i 0.607485 1.05220i
\(335\) 0 0
\(336\) −0.807007 + 0.465926i −0.0440259 + 0.0254183i
\(337\) 35.3229i 1.92416i −0.272761 0.962082i \(-0.587937\pi\)
0.272761 0.962082i \(-0.412063\pi\)
\(338\) −12.9904 + 0.500000i −0.706584 + 0.0271964i
\(339\) −9.65685 −0.524488
\(340\) 0 0
\(341\) −7.81779 13.5408i −0.423357 0.733276i
\(342\) 2.27646 + 1.31431i 0.123097 + 0.0710699i
\(343\) 12.2368 0.660723
\(344\) −2.55695 1.47626i −0.137862 0.0795945i
\(345\) 0 0
\(346\) 0.950627i 0.0511060i
\(347\) −3.13363 1.80920i −0.168222 0.0971232i 0.413525 0.910493i \(-0.364297\pi\)
−0.581747 + 0.813370i \(0.697631\pi\)
\(348\) 2.93443 1.69419i 0.157302 0.0908184i
\(349\) 25.1956 14.5467i 1.34869 0.778667i 0.360627 0.932710i \(-0.382563\pi\)
0.988064 + 0.154043i \(0.0492294\pi\)
\(350\) 0 0
\(351\) 1.86250 + 3.08725i 0.0994130 + 0.164785i
\(352\) 1.68216i 0.0896596i
\(353\) 4.79701 + 8.30867i 0.255319 + 0.442226i 0.964982 0.262315i \(-0.0844861\pi\)
−0.709663 + 0.704541i \(0.751153\pi\)
\(354\) −1.98709 3.44174i −0.105613 0.182926i
\(355\) 0 0
\(356\) 13.4670i 0.713751i
\(357\) −1.18947 + 2.06022i −0.0629534 + 0.109038i
\(358\) −4.94156 + 8.55904i −0.261170 + 0.452359i
\(359\) 6.31495i 0.333290i −0.986017 0.166645i \(-0.946707\pi\)
0.986017 0.166645i \(-0.0532935\pi\)
\(360\) 0 0
\(361\) −6.04516 10.4705i −0.318166 0.551080i
\(362\) −7.15075 12.3855i −0.375835 0.650965i
\(363\) 8.17033i 0.428831i
\(364\) −2.94148 1.62364i −0.154175 0.0851020i
\(365\) 0 0
\(366\) −7.55500 + 4.36188i −0.394906 + 0.227999i
\(367\) −30.2194 + 17.4472i −1.57744 + 0.910735i −0.582224 + 0.813028i \(0.697818\pi\)
−0.995215 + 0.0977071i \(0.968849\pi\)
\(368\) 5.59197 + 3.22853i 0.291502 + 0.168299i
\(369\) 1.17449i 0.0611416i
\(370\) 0 0
\(371\) −4.32611 2.49768i −0.224600 0.129673i
\(372\) 9.29493 0.481920
\(373\) 4.16745 + 2.40608i 0.215782 + 0.124582i 0.603996 0.796987i \(-0.293574\pi\)
−0.388213 + 0.921569i \(0.626908\pi\)
\(374\) 2.14721 + 3.71907i 0.111030 + 0.192309i
\(375\) 0 0
\(376\) 3.97934 0.205219
\(377\) 10.6958 + 5.90387i 0.550861 + 0.304065i
\(378\) 0.931852i 0.0479293i
\(379\) 24.0847 13.9053i 1.23715 0.714267i 0.268637 0.963241i \(-0.413427\pi\)
0.968510 + 0.248974i \(0.0800935\pi\)
\(380\) 0 0
\(381\) 0.338502 0.586302i 0.0173420 0.0300372i
\(382\) −0.114637 −0.00586532
\(383\) −0.402868 + 0.697788i −0.0205856 + 0.0356553i −0.876135 0.482066i \(-0.839886\pi\)
0.855549 + 0.517722i \(0.173220\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) −4.32843 + 7.49706i −0.220311 + 0.381590i
\(387\) −2.55695 + 1.47626i −0.129977 + 0.0750424i
\(388\) 7.04052 + 12.1945i 0.357428 + 0.619084i
\(389\) 27.5013 1.39437 0.697186 0.716891i \(-0.254435\pi\)
0.697186 + 0.716891i \(0.254435\pi\)
\(390\) 0 0
\(391\) 16.4843 0.833647
\(392\) 3.06583 + 5.31017i 0.154848 + 0.268204i
\(393\) 1.61696 0.933552i 0.0815648 0.0470914i
\(394\) 10.2401 17.7363i 0.515887 0.893542i
\(395\) 0 0
\(396\) 1.45680 + 0.841081i 0.0732067 + 0.0422659i
\(397\) 0.574094 0.994360i 0.0288130 0.0499055i −0.851259 0.524745i \(-0.824161\pi\)
0.880072 + 0.474840i \(0.157494\pi\)
\(398\) 1.91067 0.0957733
\(399\) −1.22474 + 2.12132i −0.0613139 + 0.106199i
\(400\) 0 0
\(401\) 11.8647 6.85009i 0.592495 0.342077i −0.173589 0.984818i \(-0.555536\pi\)
0.766083 + 0.642741i \(0.222203\pi\)
\(402\) 5.19151i 0.258929i
\(403\) 17.3118 + 28.6957i 0.862363 + 1.42944i
\(404\) 11.3178 0.563083
\(405\) 0 0
\(406\) 1.57874 + 2.73445i 0.0783515 + 0.135709i
\(407\) −13.3441 7.70420i −0.661441 0.381883i
\(408\) −2.55291 −0.126388
\(409\) 6.63613 + 3.83137i 0.328136 + 0.189449i 0.655013 0.755618i \(-0.272663\pi\)
−0.326878 + 0.945067i \(0.605996\pi\)
\(410\) 0 0
\(411\) 7.28861i 0.359521i
\(412\) 0.627871 + 0.362501i 0.0309330 + 0.0178592i
\(413\) 3.20719 1.85167i 0.157815 0.0911148i
\(414\) 5.59197 3.22853i 0.274830 0.158673i
\(415\) 0 0
\(416\) −0.0693504 3.60488i −0.00340018 0.176744i
\(417\) 4.71139i 0.230718i
\(418\) 2.21089 + 3.82937i 0.108138 + 0.187301i
\(419\) −19.5013 33.7773i −0.952701 1.65013i −0.739543 0.673110i \(-0.764958\pi\)
−0.213159 0.977018i \(-0.568375\pi\)
\(420\) 0 0
\(421\) 32.7923i 1.59820i 0.601198 + 0.799100i \(0.294690\pi\)
−0.601198 + 0.799100i \(0.705310\pi\)
\(422\) −0.620118 + 1.07408i −0.0301869 + 0.0522852i
\(423\) 1.98967 3.44621i 0.0967410 0.167560i
\(424\) 5.36068i 0.260337i
\(425\) 0 0
\(426\) −1.96763 3.40803i −0.0953318 0.165119i
\(427\) −4.06462 7.04014i −0.196701 0.340696i
\(428\) 17.2173i 0.832231i
\(429\) 0.116659 + 6.06400i 0.00563233 + 0.292773i
\(430\) 0 0
\(431\) −28.6031 + 16.5140i −1.37776 + 0.795452i −0.991890 0.127100i \(-0.959433\pi\)
−0.385873 + 0.922552i \(0.626100\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 7.78913 + 4.49706i 0.374322 + 0.216115i 0.675345 0.737502i \(-0.263995\pi\)
−0.301023 + 0.953617i \(0.597328\pi\)
\(434\) 8.66150i 0.415765i
\(435\) 0 0
\(436\) −8.90410 5.14078i −0.426429 0.246199i
\(437\) 16.9732 0.811937
\(438\) 6.29021 + 3.63165i 0.300558 + 0.173527i
\(439\) −3.65685 6.33386i −0.174532 0.302299i 0.765467 0.643475i \(-0.222508\pi\)
−0.939999 + 0.341176i \(0.889175\pi\)
\(440\) 0 0
\(441\) 6.13165 0.291983
\(442\) −4.75481 7.88147i −0.226163 0.374884i
\(443\) 27.5200i 1.30752i −0.756703 0.653758i \(-0.773191\pi\)
0.756703 0.653758i \(-0.226809\pi\)
\(444\) 7.93269 4.57994i 0.376469 0.217354i
\(445\) 0 0
\(446\) −7.38915 + 12.7984i −0.349886 + 0.606021i
\(447\) 3.00240 0.142009
\(448\) 0.465926 0.807007i 0.0220129 0.0381275i
\(449\) −8.88390 5.12912i −0.419257 0.242058i 0.275502 0.961300i \(-0.411156\pi\)
−0.694760 + 0.719242i \(0.744489\pi\)
\(450\) 0 0
\(451\) 0.987844 1.71100i 0.0465157 0.0805676i
\(452\) 8.36308 4.82843i 0.393366 0.227110i
\(453\) −6.21001 10.7561i −0.291772 0.505363i
\(454\) 9.56580 0.448945
\(455\) 0 0
\(456\) −2.62863 −0.123097
\(457\) 7.37005 + 12.7653i 0.344756 + 0.597135i 0.985309 0.170778i \(-0.0546282\pi\)
−0.640553 + 0.767914i \(0.721295\pi\)
\(458\) 13.1184 7.57389i 0.612981 0.353905i
\(459\) −1.27646 + 2.21089i −0.0595799 + 0.103195i
\(460\) 0 0
\(461\) 17.1993 + 9.93003i 0.801052 + 0.462487i 0.843839 0.536597i \(-0.180290\pi\)
−0.0427870 + 0.999084i \(0.513624\pi\)
\(462\) −0.783763 + 1.35752i −0.0364640 + 0.0631574i
\(463\) 32.1533 1.49429 0.747144 0.664662i \(-0.231424\pi\)
0.747144 + 0.664662i \(0.231424\pi\)
\(464\) −1.69419 + 2.93443i −0.0786510 + 0.136228i
\(465\) 0 0
\(466\) 16.2304 9.37064i 0.751860 0.434087i
\(467\) 22.2754i 1.03078i 0.856955 + 0.515392i \(0.172354\pi\)
−0.856955 + 0.515392i \(0.827646\pi\)
\(468\) −3.15660 1.74238i −0.145914 0.0805417i
\(469\) −4.83772 −0.223385
\(470\) 0 0
\(471\) −11.2609 19.5044i −0.518873 0.898714i
\(472\) 3.44174 + 1.98709i 0.158419 + 0.0914631i
\(473\) −4.96661 −0.228365
\(474\) −3.19540 1.84486i −0.146769 0.0847374i
\(475\) 0 0
\(476\) 2.37894i 0.109038i
\(477\) −4.64248 2.68034i −0.212565 0.122724i
\(478\) 4.00390 2.31165i 0.183134 0.105732i
\(479\) 19.0007 10.9700i 0.868163 0.501234i 0.00142578 0.999999i \(-0.499546\pi\)
0.866737 + 0.498765i \(0.166213\pi\)
\(480\) 0 0
\(481\) 28.9140 + 15.9600i 1.31837 + 0.727714i
\(482\) 17.5945i 0.801408i
\(483\) 3.00851 + 5.21089i 0.136892 + 0.237104i
\(484\) −4.08516 7.07571i −0.185689 0.321623i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 4.52651 7.84015i 0.205116 0.355271i −0.745054 0.667004i \(-0.767576\pi\)
0.950170 + 0.311733i \(0.100910\pi\)
\(488\) 4.36188 7.55500i 0.197453 0.341999i
\(489\) 2.77489i 0.125485i
\(490\) 0 0
\(491\) −15.1000 26.1540i −0.681455 1.18031i −0.974537 0.224227i \(-0.928014\pi\)
0.293082 0.956087i \(-0.405319\pi\)
\(492\) 0.587246 + 1.01714i 0.0264751 + 0.0458562i
\(493\) 8.65027i 0.389588i
\(494\) −4.89582 8.11522i −0.220273 0.365121i
\(495\) 0 0
\(496\) −8.04965 + 4.64747i −0.361440 + 0.208677i
\(497\) 3.17578 1.83354i 0.142453 0.0822453i
\(498\) 3.33341 + 1.92455i 0.149374 + 0.0862410i
\(499\) 9.04336i 0.404836i 0.979299 + 0.202418i \(0.0648800\pi\)
−0.979299 + 0.202418i \(0.935120\pi\)
\(500\) 0 0
\(501\) 19.2296 + 11.1022i 0.859114 + 0.496010i
\(502\) 26.5198 1.18364
\(503\) 26.9241 + 15.5446i 1.20049 + 0.693101i 0.960663 0.277715i \(-0.0895772\pi\)
0.239823 + 0.970817i \(0.422911\pi\)
\(504\) −0.465926 0.807007i −0.0207540 0.0359470i
\(505\) 0 0
\(506\) 10.8618 0.482867
\(507\) −0.500000 12.9904i −0.0222058 0.576923i
\(508\) 0.677003i 0.0300372i
\(509\) 22.5466 13.0173i 0.999361 0.576981i 0.0913018 0.995823i \(-0.470897\pi\)
0.908059 + 0.418842i \(0.137564\pi\)
\(510\) 0 0
\(511\) −3.38416 + 5.86154i −0.149706 + 0.259299i
\(512\) 1.00000 0.0441942
\(513\) −1.31431 + 2.27646i −0.0580283 + 0.100508i
\(514\) 1.57986 + 0.912132i 0.0696846 + 0.0402324i
\(515\) 0 0
\(516\) 1.47626 2.55695i 0.0649886 0.112564i
\(517\) 5.79708 3.34695i 0.254955 0.147198i
\(518\) 4.26782 + 7.39209i 0.187517 + 0.324790i
\(519\) −0.950627 −0.0417279
\(520\) 0 0
\(521\) −24.8332 −1.08796 −0.543982 0.839097i \(-0.683084\pi\)
−0.543982 + 0.839097i \(0.683084\pi\)
\(522\) 1.69419 + 2.93443i 0.0741529 + 0.128437i
\(523\) −7.28231 + 4.20445i −0.318433 + 0.183848i −0.650694 0.759340i \(-0.725522\pi\)
0.332261 + 0.943188i \(0.392189\pi\)
\(524\) −0.933552 + 1.61696i −0.0407824 + 0.0706372i
\(525\) 0 0
\(526\) −10.5106 6.06828i −0.458283 0.264590i
\(527\) −11.8646 + 20.5501i −0.516829 + 0.895175i
\(528\) −1.68216 −0.0732067
\(529\) 9.34677 16.1891i 0.406381 0.703873i
\(530\) 0 0
\(531\) 3.44174 1.98709i 0.149359 0.0862323i
\(532\) 2.44949i 0.106199i
\(533\) −2.04642 + 3.70740i −0.0886401 + 0.160585i
\(534\) 13.4670 0.582775
\(535\) 0 0
\(536\) −2.59575 4.49598i −0.112120 0.194197i
\(537\) −8.55904 4.94156i −0.369350 0.213244i
\(538\) −23.5310 −1.01449
\(539\) 8.93256 + 5.15722i 0.384753 + 0.222137i
\(540\) 0 0
\(541\) 15.7195i 0.675833i −0.941176 0.337916i \(-0.890278\pi\)
0.941176 0.337916i \(-0.109722\pi\)
\(542\) −10.9872 6.34349i −0.471942 0.272476i
\(543\) 12.3855 7.15075i 0.531511 0.306868i
\(544\) 2.21089 1.27646i 0.0947911 0.0547276i
\(545\) 0 0
\(546\) 1.62364 2.94148i 0.0694855 0.125884i
\(547\) 23.0313i 0.984745i −0.870385 0.492373i \(-0.836130\pi\)
0.870385 0.492373i \(-0.163870\pi\)
\(548\) −3.64431 6.31212i −0.155677 0.269641i
\(549\) −4.36188 7.55500i −0.186160 0.322439i
\(550\) 0 0
\(551\) 8.90681i 0.379443i
\(552\) −3.22853 + 5.59197i −0.137415 + 0.238010i
\(553\) 1.71914 2.97764i 0.0731052 0.126622i
\(554\) 12.8235i 0.544820i
\(555\) 0 0
\(556\) 2.35569 + 4.08018i 0.0999036 + 0.173038i
\(557\) −20.3283 35.2097i −0.861339 1.49188i −0.870637 0.491925i \(-0.836293\pi\)
0.00929877 0.999957i \(-0.497040\pi\)
\(558\) 9.29493i 0.393486i
\(559\) 10.6435 0.204758i 0.450171 0.00866034i
\(560\) 0 0
\(561\) −3.71907 + 2.14721i −0.157019 + 0.0906552i
\(562\) −4.47492 + 2.58360i −0.188763 + 0.108982i
\(563\) 2.97514 + 1.71770i 0.125387 + 0.0723923i 0.561382 0.827557i \(-0.310270\pi\)
−0.435995 + 0.899949i \(0.643603\pi\)
\(564\) 3.97934i 0.167560i
\(565\) 0 0
\(566\) 11.2258 + 6.48124i 0.471857 + 0.272427i
\(567\) −0.931852 −0.0391341
\(568\) 3.40803 + 1.96763i 0.142998 + 0.0825597i
\(569\) 11.0320 + 19.1079i 0.462484 + 0.801046i 0.999084 0.0427908i \(-0.0136249\pi\)
−0.536600 + 0.843837i \(0.680292\pi\)
\(570\) 0 0
\(571\) 4.56829 0.191177 0.0955885 0.995421i \(-0.469527\pi\)
0.0955885 + 0.995421i \(0.469527\pi\)
\(572\) −3.13303 5.19325i −0.130999 0.217141i
\(573\) 0.114637i 0.00478901i
\(574\) −0.947824 + 0.547226i −0.0395614 + 0.0228408i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 4.42655 0.184280 0.0921398 0.995746i \(-0.470629\pi\)
0.0921398 + 0.995746i \(0.470629\pi\)
\(578\) −5.24131 + 9.07822i −0.218010 + 0.377604i
\(579\) −7.49706 4.32843i −0.311567 0.179883i
\(580\) 0 0
\(581\) −1.79339 + 3.10624i −0.0744024 + 0.128869i
\(582\) −12.1945 + 7.04052i −0.505480 + 0.291839i
\(583\) −4.50877 7.80941i −0.186734 0.323433i
\(584\) −7.26330 −0.300558
\(585\) 0 0
\(586\) 13.4704 0.556458
\(587\) 21.5770 + 37.3725i 0.890580 + 1.54253i 0.839181 + 0.543852i \(0.183035\pi\)
0.0513987 + 0.998678i \(0.483632\pi\)
\(588\) −5.31017 + 3.06583i −0.218988 + 0.126433i
\(589\) −12.2165 + 21.1595i −0.503370 + 0.871863i
\(590\) 0 0
\(591\) 17.7363 + 10.2401i 0.729574 + 0.421220i
\(592\) −4.57994 + 7.93269i −0.188234 + 0.326032i
\(593\) 28.8372 1.18420 0.592101 0.805864i \(-0.298299\pi\)
0.592101 + 0.805864i \(0.298299\pi\)
\(594\) −0.841081 + 1.45680i −0.0345100 + 0.0597731i
\(595\) 0 0
\(596\) −2.60016 + 1.50120i −0.106507 + 0.0614916i
\(597\) 1.91067i 0.0781986i
\(598\) −23.2769 + 0.447799i −0.951864 + 0.0183119i
\(599\) 28.1704 1.15101 0.575505 0.817798i \(-0.304806\pi\)
0.575505 + 0.817798i \(0.304806\pi\)
\(600\) 0 0
\(601\) 7.31925 + 12.6773i 0.298558 + 0.517118i 0.975806 0.218637i \(-0.0701610\pi\)
−0.677248 + 0.735755i \(0.736828\pi\)
\(602\) 2.38270 + 1.37565i 0.0971117 + 0.0560674i
\(603\) −5.19151 −0.211415
\(604\) 10.7561 + 6.21001i 0.437657 + 0.252682i
\(605\) 0 0
\(606\) 11.3178i 0.459756i
\(607\) −11.2731 6.50853i −0.457561 0.264173i 0.253457 0.967347i \(-0.418432\pi\)
−0.711018 + 0.703174i \(0.751766\pi\)
\(608\) 2.27646 1.31431i 0.0923225 0.0533024i
\(609\) −2.73445 + 1.57874i −0.110806 + 0.0639737i
\(610\) 0 0
\(611\) −12.2852 + 7.41152i −0.497006 + 0.299838i
\(612\) 2.55291i 0.103195i
\(613\) −13.6146 23.5813i −0.549890 0.952438i −0.998282 0.0586006i \(-0.981336\pi\)
0.448391 0.893837i \(-0.351997\pi\)
\(614\) −10.7310 18.5866i −0.433067 0.750094i
\(615\) 0 0
\(616\) 1.56753i 0.0631574i
\(617\) 11.7678 20.3825i 0.473755 0.820569i −0.525793 0.850613i \(-0.676231\pi\)
0.999549 + 0.0300439i \(0.00956471\pi\)
\(618\) −0.362501 + 0.627871i −0.0145819 + 0.0252567i
\(619\) 23.0280i 0.925573i 0.886470 + 0.462786i \(0.153150\pi\)
−0.886470 + 0.462786i \(0.846850\pi\)
\(620\) 0 0
\(621\) 3.22853 + 5.59197i 0.129556 + 0.224398i
\(622\) 7.37808 + 12.7792i 0.295834 + 0.512399i
\(623\) 12.5493i 0.502776i
\(624\) 3.60488 0.0693504i 0.144311 0.00277624i
\(625\) 0 0
\(626\) 1.21625 0.702205i 0.0486113 0.0280658i
\(627\) −3.82937 + 2.21089i −0.152930 + 0.0882944i
\(628\) 19.5044 + 11.2609i 0.778309 + 0.449357i
\(629\) 23.3844i 0.932397i
\(630\) 0 0
\(631\) −14.3378 8.27792i −0.570778 0.329539i 0.186682 0.982420i \(-0.440227\pi\)
−0.757460 + 0.652882i \(0.773560\pi\)
\(632\) 3.68973 0.146769
\(633\) −1.07408 0.620118i −0.0426907 0.0246475i
\(634\) −16.5710 28.7019i −0.658119 1.13990i
\(635\) 0 0
\(636\) 5.36068 0.212565
\(637\) −19.3552 10.6837i −0.766879 0.423303i
\(638\) 5.69982i 0.225658i
\(639\) 3.40803 1.96763i 0.134819 0.0778381i
\(640\) 0 0
\(641\) −0.390454 + 0.676286i −0.0154220 + 0.0267117i −0.873633 0.486585i \(-0.838243\pi\)
0.858211 + 0.513296i \(0.171576\pi\)
\(642\) 17.2173 0.679514
\(643\) 12.2743 21.2597i 0.484050 0.838399i −0.515782 0.856720i \(-0.672499\pi\)
0.999832 + 0.0183207i \(0.00583198\pi\)
\(644\) −5.21089 3.00851i −0.205338 0.118552i
\(645\) 0 0
\(646\) 3.35533 5.81160i 0.132014 0.228654i
\(647\) 2.74011 1.58200i 0.107725 0.0621950i −0.445170 0.895446i \(-0.646857\pi\)
0.552894 + 0.833251i \(0.313523\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 6.68521 0.262417
\(650\) 0 0
\(651\) −8.66150 −0.339471
\(652\) −1.38745 2.40313i −0.0543366 0.0941137i
\(653\) 27.9627 16.1443i 1.09426 0.631774i 0.159556 0.987189i \(-0.448994\pi\)
0.934709 + 0.355415i \(0.115660\pi\)
\(654\) 5.14078 8.90410i 0.201021 0.348178i
\(655\) 0 0
\(656\) −1.01714 0.587246i −0.0397127 0.0229281i
\(657\) −3.63165 + 6.29021i −0.141684 + 0.245404i
\(658\) −3.70815 −0.144559
\(659\) 17.6775 30.6184i 0.688619 1.19272i −0.283666 0.958923i \(-0.591551\pi\)
0.972285 0.233799i \(-0.0751159\pi\)
\(660\) 0 0
\(661\) 16.9243 9.77124i 0.658279 0.380057i −0.133342 0.991070i \(-0.542571\pi\)
0.791621 + 0.611013i \(0.209238\pi\)
\(662\) 6.98904i 0.271637i
\(663\) 7.88147 4.75481i 0.306091 0.184661i
\(664\) −3.84909 −0.149374
\(665\) 0 0
\(666\) 4.57994 + 7.93269i 0.177469 + 0.307385i
\(667\) 18.9478 + 10.9395i 0.733661 + 0.423579i
\(668\) −22.2044 −0.859114
\(669\) −12.7984 7.38915i −0.494814 0.285681i
\(670\) 0 0
\(671\) 14.6748i 0.566514i
\(672\) 0.807007 + 0.465926i 0.0311310 + 0.0179735i
\(673\) 2.17903 1.25806i 0.0839954 0.0484948i −0.457414 0.889254i \(-0.651224\pi\)
0.541409 + 0.840759i \(0.317891\pi\)
\(674\) −30.5906 + 17.6615i −1.17830 + 0.680295i
\(675\) 0 0
\(676\) 6.92820 + 11.0000i 0.266469 + 0.423077i
\(677\) 41.0114i 1.57620i −0.615550 0.788098i \(-0.711066\pi\)
0.615550 0.788098i \(-0.288934\pi\)
\(678\) 4.82843 + 8.36308i 0.185435 + 0.321182i
\(679\) −6.56072 11.3635i −0.251777 0.436091i
\(680\) 0 0
\(681\) 9.56580i 0.366562i
\(682\) −7.81779 + 13.5408i −0.299359 + 0.518505i
\(683\) 12.0769 20.9177i 0.462108 0.800395i −0.536958 0.843609i \(-0.680426\pi\)
0.999066 + 0.0432142i \(0.0137598\pi\)
\(684\) 2.62863i 0.100508i
\(685\) 0 0
\(686\) −6.11838 10.5973i −0.233601 0.404608i
\(687\) 7.57389 + 13.1184i 0.288962 + 0.500497i
\(688\) 2.95252i 0.112564i
\(689\) 9.98427 + 16.5497i 0.380370 + 0.630494i
\(690\) 0 0
\(691\) −35.7340 + 20.6310i −1.35939 + 0.784841i −0.989541 0.144252i \(-0.953922\pi\)
−0.369844 + 0.929094i \(0.620589\pi\)
\(692\) 0.823267 0.475314i 0.0312959 0.0180687i
\(693\) −1.35752 0.783763i −0.0515678 0.0297727i
\(694\) 3.61841i 0.137353i
\(695\) 0 0
\(696\) −2.93443 1.69419i −0.111229 0.0642183i
\(697\) −2.99838 −0.113572
\(698\) −25.1956 14.5467i −0.953669 0.550601i
\(699\) 9.37064 + 16.2304i 0.354430 + 0.613891i
\(700\) 0 0
\(701\) 27.2880 1.03065 0.515327 0.856994i \(-0.327671\pi\)
0.515327 + 0.856994i \(0.327671\pi\)
\(702\) 1.74238 3.15660i 0.0657620 0.119138i
\(703\) 24.0779i 0.908115i
\(704\) 1.45680 0.841081i 0.0549051 0.0316994i
\(705\) 0 0
\(706\) 4.79701 8.30867i 0.180538 0.312701i
\(707\) −10.5465 −0.396644
\(708\) −1.98709 + 3.44174i −0.0746793 + 0.129348i
\(709\) −2.18928 1.26398i −0.0822200 0.0474697i 0.458326 0.888784i \(-0.348449\pi\)
−0.540546 + 0.841314i \(0.681782\pi\)
\(710\) 0 0
\(711\) 1.84486 3.19540i 0.0691878 0.119837i
\(712\) −11.6628 + 6.73351i −0.437081 + 0.252349i
\(713\) 30.0089 + 51.9770i 1.12384 + 1.94655i
\(714\) 2.37894 0.0890295
\(715\) 0 0
\(716\) 9.88312 0.369350
\(717\) 2.31165 + 4.00390i 0.0863302 + 0.149528i
\(718\) −5.46891 + 3.15748i −0.204098 + 0.117836i
\(719\) −26.6943 + 46.2359i −0.995530 + 1.72431i −0.415968 + 0.909379i \(0.636557\pi\)
−0.579562 + 0.814928i \(0.696776\pi\)
\(720\) 0 0
\(721\) −0.585082 0.337797i −0.0217896 0.0125802i
\(722\) −6.04516 + 10.4705i −0.224978 + 0.389673i
\(723\) 17.5945 0.654347
\(724\) −7.15075 + 12.3855i −0.265756 + 0.460302i
\(725\) 0 0
\(726\) 7.07571 4.08516i 0.262604 0.151615i
\(727\) 2.09614i 0.0777417i 0.999244 + 0.0388709i \(0.0123761\pi\)
−0.999244 + 0.0388709i \(0.987624\pi\)
\(728\) 0.0646242 + 3.35922i 0.00239513 + 0.124501i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 3.76876 + 6.52768i 0.139393 + 0.241435i
\(732\) 7.55500 + 4.36188i 0.279241 + 0.161220i
\(733\) −16.7827 −0.619883 −0.309942 0.950756i \(-0.600310\pi\)
−0.309942 + 0.950756i \(0.600310\pi\)
\(734\) 30.2194 + 17.4472i 1.11542 + 0.643987i
\(735\) 0 0
\(736\) 6.45705i 0.238010i
\(737\) −7.56297 4.36648i −0.278585 0.160841i
\(738\) −1.01714 + 0.587246i −0.0374414 + 0.0216168i
\(739\) −8.24563 + 4.76062i −0.303321 + 0.175122i −0.643934 0.765081i \(-0.722699\pi\)
0.340613 + 0.940204i \(0.389365\pi\)
\(740\) 0 0
\(741\) 8.11522 4.89582i 0.298120 0.179852i
\(742\) 4.99536i 0.183385i
\(743\) −16.2832 28.2034i −0.597374 1.03468i −0.993207 0.116360i \(-0.962877\pi\)
0.395833 0.918323i \(-0.370456\pi\)
\(744\) −4.64747 8.04965i −0.170384 0.295114i
\(745\) 0 0
\(746\) 4.81216i 0.176186i
\(747\) −1.92455 + 3.33341i −0.0704154 + 0.121963i
\(748\) 2.14721 3.71907i 0.0785097 0.135983i
\(749\) 16.0440i 0.586235i
\(750\) 0 0
\(751\) −7.38117 12.7846i −0.269343 0.466515i 0.699350 0.714780i \(-0.253473\pi\)
−0.968692 + 0.248265i \(0.920140\pi\)
\(752\) −1.98967 3.44621i −0.0725557 0.125670i
\(753\) 26.5198i 0.966436i
\(754\) −0.234986 12.2148i −0.00855769 0.444835i
\(755\) 0 0
\(756\) 0.807007 0.465926i 0.0293506 0.0169456i
\(757\) −30.4462 + 17.5781i −1.10659 + 0.638888i −0.937943 0.346789i \(-0.887272\pi\)
−0.168643 + 0.985677i \(0.553939\pi\)
\(758\) −24.0847 13.9053i −0.874795 0.505063i
\(759\) 10.8618i 0.394259i
\(760\) 0 0
\(761\) −36.2215 20.9125i −1.31303 0.758076i −0.330431 0.943830i \(-0.607194\pi\)
−0.982596 + 0.185754i \(0.940527\pi\)
\(762\) −0.677003 −0.0245252
\(763\) 8.29730 + 4.79045i 0.300382 + 0.173426i
\(764\) 0.0573183 + 0.0992782i 0.00207370 + 0.00359176i
\(765\) 0 0
\(766\) 0.805736 0.0291124
\(767\) −14.3264 + 0.275611i −0.517298 + 0.00995172i
\(768\) 1.00000i 0.0360844i
\(769\) −39.4957 + 22.8028i −1.42425 + 0.822291i −0.996659 0.0816812i \(-0.973971\pi\)
−0.427591 + 0.903972i \(0.640638\pi\)
\(770\) 0 0
\(771\) −0.912132 + 1.57986i −0.0328496 + 0.0568972i
\(772\) 8.65685 0.311567
\(773\) 6.31759 10.9424i 0.227228 0.393570i −0.729758 0.683706i \(-0.760367\pi\)
0.956986 + 0.290136i \(0.0937004\pi\)
\(774\) 2.55695 + 1.47626i 0.0919078 + 0.0530630i
\(775\) 0 0
\(776\) 7.04052 12.1945i 0.252740 0.437758i
\(777\) −7.39209 + 4.26782i −0.265190 + 0.153107i
\(778\) −13.7507 23.8168i −0.492985 0.853875i
\(779\) −3.08730 −0.110614
\(780\) 0 0
\(781\) 6.61973 0.236873
\(782\) −8.24215 14.2758i −0.294739 0.510502i
\(783\) −2.93443 + 1.69419i −0.104868 + 0.0605456i
\(784\) 3.06583 5.31017i 0.109494 0.189649i
\(785\) 0 0
\(786\) −1.61696 0.933552i −0.0576750 0.0332987i
\(787\) −26.0708 + 45.1559i −0.929323 + 1.60963i −0.144865 + 0.989451i \(0.546275\pi\)
−0.784458 + 0.620182i \(0.787059\pi\)
\(788\) −20.4801 −0.729574
\(789\) 6.06828 10.5106i 0.216037 0.374186i
\(790\) 0 0
\(791\) −7.79315 + 4.49938i −0.277093 + 0.159979i
\(792\) 1.68216i 0.0597731i
\(793\) 0.604996 + 31.4481i 0.0214840 + 1.11676i
\(794\) −1.14819 −0.0407477
\(795\) 0 0
\(796\) −0.955336 1.65469i −0.0338610 0.0586489i
\(797\) 37.0582 + 21.3956i 1.31267 + 0.757870i 0.982537 0.186065i \(-0.0595736\pi\)
0.330132 + 0.943935i \(0.392907\pi\)
\(798\) 2.44949 0.0867110
\(799\) −8.79787 5.07945i −0.311246 0.179698i
\(800\) 0 0
\(801\) 13.4670i 0.475834i
\(802\) −11.8647 6.85009i −0.418957 0.241885i
\(803\) −10.5812 + 6.10903i −0.373401 + 0.215583i
\(804\) 4.49598 2.59575i 0.158561 0.0915452i
\(805\) 0 0
\(806\) 16.1953 29.3404i 0.570456 1.03347i
\(807\) 23.5310i 0.828331i
\(808\) −5.65892 9.80153i −0.199080 0.344817i
\(809\) 24.3918 + 42.2478i 0.857569 + 1.48535i 0.874241 + 0.485492i \(0.161360\pi\)
−0.0166719 + 0.999861i \(0.505307\pi\)
\(810\) 0 0
\(811\) 7.87402i 0.276494i 0.990398 + 0.138247i \(0.0441468\pi\)
−0.990398 + 0.138247i \(0.955853\pi\)
\(812\) 1.57874 2.73445i 0.0554029 0.0959606i
\(813\) 6.34349 10.9872i 0.222476 0.385339i
\(814\) 15.4084i 0.540064i
\(815\) 0 0
\(816\) 1.27646 + 2.21089i 0.0446849 + 0.0773966i
\(817\) 3.88053 + 6.72128i 0.135763 + 0.235148i
\(818\) 7.66274i 0.267922i
\(819\) 2.94148 + 1.62364i 0.102784 + 0.0567347i
\(820\) 0 0
\(821\) −24.6790 + 14.2484i −0.861304 + 0.497274i −0.864449 0.502721i \(-0.832332\pi\)
0.00314470 + 0.999995i \(0.498999\pi\)
\(822\) 6.31212 3.64431i 0.220161 0.127110i
\(823\) −40.0387 23.1164i −1.39566 0.805786i −0.401728 0.915759i \(-0.631590\pi\)
−0.993935 + 0.109973i \(0.964924\pi\)
\(824\) 0.725003i 0.0252567i
\(825\) 0 0
\(826\) −3.20719 1.85167i −0.111592 0.0644279i
\(827\) 9.53716 0.331640 0.165820 0.986156i \(-0.446973\pi\)
0.165820 + 0.986156i \(0.446973\pi\)
\(828\) −5.59197 3.22853i −0.194334 0.112199i
\(829\) −6.64904 11.5165i −0.230931 0.399984i 0.727152 0.686477i \(-0.240844\pi\)
−0.958082 + 0.286493i \(0.907510\pi\)
\(830\) 0 0
\(831\) 12.8235 0.444843
\(832\) −3.08725 + 1.86250i −0.107031 + 0.0645706i
\(833\) 15.6536i 0.542365i
\(834\) −4.08018 + 2.35569i −0.141285 + 0.0815710i
\(835\) 0 0
\(836\) 2.21089 3.82937i 0.0764652 0.132442i
\(837\) −9.29493 −0.321280
\(838\) −19.5013 + 33.7773i −0.673662 + 1.16682i
\(839\) −42.8848 24.7595i −1.48055 0.854794i −0.480790 0.876836i \(-0.659650\pi\)
−0.999757 + 0.0220420i \(0.992983\pi\)
\(840\) 0 0
\(841\) 8.75941 15.1717i 0.302049 0.523163i
\(842\) 28.3990 16.3962i 0.978694 0.565049i
\(843\) −2.58360 4.47492i −0.0889838 0.154125i
\(844\) 1.24024 0.0426907
\(845\) 0 0
\(846\) −3.97934 −0.136812
\(847\) 3.80677 + 6.59351i 0.130802 + 0.226556i
\(848\) −4.64248 + 2.68034i −0.159424 + 0.0920432i
\(849\) −6.48124 + 11.2258i −0.222436 + 0.385270i
\(850\) 0 0
\(851\) 51.2218 + 29.5729i 1.75586 + 1.01375i
\(852\) −1.96763 + 3.40803i −0.0674097 + 0.116757i
\(853\) 6.87904 0.235534 0.117767 0.993041i \(-0.462426\pi\)
0.117767 + 0.993041i \(0.462426\pi\)
\(854\) −4.06462 + 7.04014i −0.139089 + 0.240908i
\(855\) 0 0
\(856\) −14.9106 + 8.60867i −0.509635 + 0.294238i
\(857\) 25.1526i 0.859198i −0.903020 0.429599i \(-0.858655\pi\)
0.903020 0.429599i \(-0.141345\pi\)
\(858\) 5.19325 3.13303i 0.177295 0.106960i
\(859\) −52.3171 −1.78504 −0.892518 0.451012i \(-0.851063\pi\)
−0.892518 + 0.451012i \(0.851063\pi\)
\(860\) 0 0
\(861\) −0.547226 0.947824i −0.0186494 0.0323017i
\(862\) 28.6031 + 16.5140i 0.974225 + 0.562469i
\(863\) 29.9308 1.01886 0.509428 0.860513i \(-0.329857\pi\)
0.509428 + 0.860513i \(0.329857\pi\)
\(864\) 0.866025 + 0.500000i 0.0294628 + 0.0170103i
\(865\) 0 0
\(866\) 8.99411i 0.305632i
\(867\) −9.07822 5.24131i −0.308313 0.178004i
\(868\) 7.50108 4.33075i 0.254603 0.146995i
\(869\) 5.37518 3.10336i 0.182340 0.105274i
\(870\) 0 0
\(871\) 16.3875 + 9.04560i 0.555269 + 0.306498i
\(872\) 10.2816i 0.348178i
\(873\) −7.04052 12.1945i −0.238285 0.412722i
\(874\) −8.48659 14.6992i −0.287063 0.497208i
\(875\) 0 0
\(876\) 7.26330i 0.245404i
\(877\) 7.87295 13.6363i 0.265851 0.460467i −0.701936 0.712240i \(-0.747681\pi\)
0.967786 + 0.251774i \(0.0810139\pi\)
\(878\) −3.65685 + 6.33386i −0.123413 + 0.213757i
\(879\) 13.4704i 0.454346i
\(880\) 0 0
\(881\) 7.56434 + 13.1018i 0.254849 + 0.441412i 0.964855 0.262785i \(-0.0846409\pi\)
−0.710005 + 0.704196i \(0.751308\pi\)
\(882\) −3.06583 5.31017i −0.103232 0.178803i
\(883\) 54.8263i 1.84505i −0.385936 0.922525i \(-0.626122\pi\)
0.385936 0.922525i \(-0.373878\pi\)
\(884\) −4.44815 + 8.05852i −0.149608 + 0.271037i
\(885\) 0 0
\(886\) −23.8331 + 13.7600i −0.800687 + 0.462277i
\(887\) −40.5176 + 23.3928i −1.36045 + 0.785454i −0.989683 0.143273i \(-0.954237\pi\)
−0.370763 + 0.928727i \(0.620904\pi\)
\(888\) −7.93269 4.57994i −0.266204 0.153693i
\(889\) 0.630866i 0.0211586i
\(890\) 0 0
\(891\) −1.45680 0.841081i −0.0488045 0.0281773i
\(892\) 14.7783 0.494814
\(893\) −9.05879 5.23009i −0.303141 0.175018i
\(894\) −1.50120 2.60016i −0.0502077 0.0869623i
\(895\) 0 0
\(896\) −0.931852 −0.0311310
\(897\) −0.447799 23.2769i −0.0149516 0.777194i
\(898\) 10.2582i 0.342322i
\(899\) −27.2753 + 15.7474i −0.909684 + 0.525206i
\(900\) 0 0
\(901\) −6.84267 + 11.8519i −0.227963 + 0.394843i
\(902\) −1.97569 −0.0657832
\(903\) −1.37565 + 2.38270i −0.0457789 + 0.0792913i
\(904\) −8.36308 4.82843i −0.278152 0.160591i
\(905\) 0 0
\(906\) −6.21001 + 10.7561i −0.206314 + 0.357346i
\(907\) −25.2077 + 14.5536i −0.837006 + 0.483246i −0.856246 0.516569i \(-0.827209\pi\)
0.0192392 + 0.999815i \(0.493876\pi\)
\(908\) −4.78290 8.28423i −0.158726 0.274922i
\(909\) −11.3178 −0.375389
\(910\) 0 0
\(911\) −6.59919 −0.218641 −0.109320 0.994007i \(-0.534867\pi\)
−0.109320 + 0.994007i \(0.534867\pi\)
\(912\) 1.31431 + 2.27646i 0.0435213 + 0.0753810i
\(913\) −5.60734 + 3.23740i −0.185576 + 0.107142i
\(914\) 7.37005 12.7653i 0.243780 0.422238i
\(915\) 0 0
\(916\) −13.1184 7.57389i −0.433443 0.250248i
\(917\) 0.869932 1.50677i 0.0287277 0.0497578i
\(918\) 2.55291 0.0842587
\(919\) −16.9793 + 29.4089i −0.560094 + 0.970111i 0.437394 + 0.899270i \(0.355902\pi\)
−0.997488 + 0.0708412i \(0.977432\pi\)
\(920\) 0 0
\(921\) 18.5866 10.7310i 0.612450 0.353598i
\(922\) 19.8601i 0.654056i
\(923\) −14.1861 + 0.272911i −0.466942 + 0.00898298i
\(924\) 1.56753 0.0515678
\(925\) 0 0
\(926\) −16.0766 27.8455i −0.528311 0.915061i
\(927\) −0.627871 0.362501i −0.0206220 0.0119061i
\(928\) 3.38839 0.111229
\(929\) −0.599403 0.346065i −0.0196658 0.0113540i 0.490135 0.871647i \(-0.336948\pi\)
−0.509801 + 0.860293i \(0.670281\pi\)
\(930\) 0 0
\(931\) 16.1178i 0.528240i
\(932\) −16.2304 9.37064i −0.531646 0.306946i
\(933\) −12.7792 + 7.37808i −0.418372 + 0.241547i
\(934\) 19.2911 11.1377i 0.631224 0.364437i
\(935\) 0 0
\(936\) 0.0693504 + 3.60488i 0.00226679 + 0.117829i
\(937\) 22.0269i 0.719589i −0.933032 0.359795i \(-0.882847\pi\)
0.933032 0.359795i \(-0.117153\pi\)
\(938\) 2.41886 + 4.18958i 0.0789785 + 0.136795i
\(939\) 0.702205 + 1.21625i 0.0229156 + 0.0396910i
\(940\) 0 0
\(941\) 15.7015i 0.511855i −0.966696 0.255928i \(-0.917619\pi\)
0.966696 0.255928i \(-0.0823809\pi\)
\(942\) −11.2609 + 19.5044i −0.366899 + 0.635487i
\(943\) −3.79188 + 6.56773i −0.123481 + 0.213875i
\(944\) 3.97418i 0.129348i
\(945\) 0 0
\(946\) 2.48331 + 4.30121i 0.0807392 + 0.139844i
\(947\) −13.0966 22.6839i −0.425581 0.737129i 0.570893 0.821024i \(-0.306597\pi\)
−0.996475 + 0.0838957i \(0.973264\pi\)
\(948\) 3.68973i 0.119837i
\(949\) 22.4236 13.5279i 0.727901 0.439135i
\(950\) 0 0
\(951\) 28.7019 16.5710i 0.930722 0.537352i
\(952\) −2.06022 + 1.18947i −0.0667721 + 0.0385509i
\(953\) 19.4420 + 11.2248i 0.629788 + 0.363608i 0.780670 0.624943i \(-0.214878\pi\)
−0.150882 + 0.988552i \(0.548211\pi\)
\(954\) 5.36068i 0.173558i
\(955\) 0 0
\(956\) −4.00390 2.31165i −0.129495 0.0747641i
\(957\) −5.69982 −0.184249
\(958\) −19.0007 10.9700i −0.613884 0.354426i
\(959\) 3.39595 + 5.88196i 0.109661 + 0.189939i
\(960\) 0 0
\(961\) −55.3958 −1.78696
\(962\) −0.635241 33.0203i −0.0204810 1.06462i
\(963\) 17.2173i 0.554821i
\(964\) −15.2373 + 8.79725i −0.490760 + 0.283341i
\(965\) 0 0
\(966\) 3.00851 5.21089i 0.0967972 0.167658i
\(967\) 36.7073 1.18043 0.590213 0.807248i \(-0.299044\pi\)
0.590213 + 0.807248i \(0.299044\pi\)
\(968\) −4.08516 + 7.07571i −0.131302 + 0.227422i
\(969\) 5.81160 + 3.35533i 0.186695 + 0.107789i
\(970\) 0 0
\(971\) −12.8673 + 22.2869i −0.412932 + 0.715219i −0.995209 0.0977711i \(-0.968829\pi\)
0.582277 + 0.812991i \(0.302162\pi\)
\(972\) 0.866025 0.500000i 0.0277778 0.0160375i
\(973\) −2.19516 3.80212i −0.0703735 0.121890i
\(974\) −9.05302 −0.290078
\(975\) 0 0
\(976\) −8.72376 −0.279241
\(977\) 15.3079 + 26.5140i 0.489742 + 0.848258i 0.999930 0.0118045i \(-0.00375759\pi\)
−0.510188 + 0.860063i \(0.670424\pi\)
\(978\) 2.40313 1.38745i 0.0768435 0.0443656i
\(979\) −11.3269 + 19.6187i −0.362008 + 0.627016i
\(980\) 0 0
\(981\) 8.90410 + 5.14078i 0.284286 + 0.164133i
\(982\) −15.1000 + 26.1540i −0.481861 + 0.834609i
\(983\) −61.1797 −1.95133 −0.975665 0.219266i \(-0.929634\pi\)
−0.975665 + 0.219266i \(0.929634\pi\)
\(984\) 0.587246 1.01714i 0.0187207 0.0324252i
\(985\) 0 0
\(986\) 7.49135 4.32513i 0.238573 0.137740i
\(987\) 3.70815i 0.118032i
\(988\) −4.58007 + 8.29751i −0.145712 + 0.263979i
\(989\) 19.0646 0.606218
\(990\) 0 0
\(991\) −25.3797 43.9589i −0.806212 1.39640i −0.915470 0.402387i \(-0.868181\pi\)
0.109258 0.994013i \(-0.465153\pi\)
\(992\) 8.04965 + 4.64747i 0.255577 + 0.147557i
\(993\) −6.98904 −0.221790
\(994\) −3.17578 1.83354i −0.100730 0.0581562i
\(995\) 0 0
\(996\) 3.84909i 0.121963i
\(997\) 42.6273 + 24.6109i 1.35002 + 0.779434i 0.988252 0.152834i \(-0.0488399\pi\)
0.361768 + 0.932268i \(0.382173\pi\)
\(998\) 7.83178 4.52168i 0.247911 0.143131i
\(999\) −7.93269 + 4.57994i −0.250979 + 0.144903i
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 1950.2.y.i.49.4 8
5.2 odd 4 1950.2.bc.e.751.4 8
5.3 odd 4 1950.2.bc.f.751.1 yes 8
5.4 even 2 1950.2.y.l.49.1 8
13.4 even 6 1950.2.y.l.199.1 8
65.4 even 6 inner 1950.2.y.i.199.4 8
65.17 odd 12 1950.2.bc.e.901.4 yes 8
65.43 odd 12 1950.2.bc.f.901.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1950.2.y.i.49.4 8 1.1 even 1 trivial
1950.2.y.i.199.4 8 65.4 even 6 inner
1950.2.y.l.49.1 8 5.4 even 2
1950.2.y.l.199.1 8 13.4 even 6
1950.2.bc.e.751.4 8 5.2 odd 4
1950.2.bc.e.901.4 yes 8 65.17 odd 12
1950.2.bc.f.751.1 yes 8 5.3 odd 4
1950.2.bc.f.901.1 yes 8 65.43 odd 12