Properties

Label 722.2.e.r.245.4
Level $722$
Weight $2$
Character 722.245
Analytic conductor $5.765$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $6$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [722,2,Mod(99,722)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(722, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("722.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 722.e (of order \(9\), degree \(6\), 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: \(5.76519902594\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 245.4
Character \(\chi\) \(=\) 722.245
Dual form 722.2.e.r.389.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 - 0.984808i) q^{2} +(2.14003 + 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +O(q^{10})\) \(q+(0.173648 - 0.984808i) q^{2} +(2.14003 + 1.79569i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(2.20318 - 0.801892i) q^{5} +(2.14003 - 1.79569i) q^{6} +(0.642040 + 1.11205i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.834245 + 4.73124i) q^{9} +(-0.407131 - 2.30896i) q^{10} +(-2.87811 + 4.98503i) q^{11} +(-1.39680 - 2.41933i) q^{12} +(0.233094 - 0.195589i) q^{13} +(1.20664 - 0.439181i) q^{14} +(6.15482 + 2.24017i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.726925 - 4.12259i) q^{17} +4.80423 q^{18} -2.34458 q^{20} +(-0.622912 + 3.53271i) q^{21} +(4.40952 + 3.70002i) q^{22} +(6.08623 + 2.21521i) q^{23} +(-2.62513 + 0.955469i) q^{24} +(0.380754 - 0.319491i) q^{25} +(-0.152141 - 0.263516i) q^{26} +(-2.52015 + 4.36502i) q^{27} +(-0.222978 - 1.26457i) q^{28} +(-0.543095 - 3.08004i) q^{29} +(3.27491 - 5.67231i) q^{30} +(-3.22123 - 5.57934i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-15.1108 + 5.49989i) q^{33} +(-3.93373 - 1.43176i) q^{34} +(2.30627 + 1.93519i) q^{35} +(0.834245 - 4.73124i) q^{36} -3.97980 q^{37} +0.850045 q^{39} +(-0.407131 + 2.30896i) q^{40} +(-3.84339 - 3.22499i) q^{41} +(3.37087 + 1.22690i) q^{42} +(0.929712 - 0.338387i) q^{43} +(4.40952 - 3.70002i) q^{44} +(5.63194 + 9.75480i) q^{45} +(3.23842 - 5.60910i) q^{46} +(-0.763089 - 4.32769i) q^{47} +(0.485104 + 2.75116i) q^{48} +(2.67557 - 4.63422i) q^{49} +(-0.248520 - 0.430448i) q^{50} +(8.95856 - 7.51712i) q^{51} +(-0.285932 + 0.104071i) q^{52} +(-3.09219 - 1.12547i) q^{53} +(3.86109 + 3.23984i) q^{54} +(-2.34354 + 13.2909i) q^{55} -1.28408 q^{56} -3.12756 q^{58} +(0.575427 - 3.26341i) q^{59} +(-5.01745 - 4.21014i) q^{60} +(10.3004 + 3.74904i) q^{61} +(-6.05394 + 2.20345i) q^{62} +(-4.72573 + 3.96536i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.356707 - 0.617834i) q^{65} +(2.79236 + 15.8363i) q^{66} +(-0.760720 - 4.31426i) q^{67} +(-2.09310 + 3.62535i) q^{68} +(9.04686 + 15.6696i) q^{69} +(2.30627 - 1.93519i) q^{70} +(4.14940 - 1.51026i) q^{71} +(-4.51450 - 1.64314i) q^{72} +(-1.73654 - 1.45713i) q^{73} +(-0.691084 + 3.91933i) q^{74} +1.38853 q^{75} -7.39144 q^{77} +(0.147609 - 0.837131i) q^{78} +(6.57005 + 5.51292i) q^{79} +(2.20318 + 0.801892i) q^{80} +(0.312063 - 0.113582i) q^{81} +(-3.84339 + 3.22499i) q^{82} +(4.88232 + 8.45643i) q^{83} +(1.79360 - 3.10661i) q^{84} +(-1.70433 - 9.66574i) q^{85} +(-0.171804 - 0.974348i) q^{86} +(4.36858 - 7.56661i) q^{87} +(-2.87811 - 4.98503i) q^{88} +(-11.5493 + 9.69101i) q^{89} +(10.5846 - 3.85247i) q^{90} +(0.367159 + 0.133635i) q^{91} +(-4.96154 - 4.16323i) q^{92} +(3.12527 - 17.7243i) q^{93} -4.39445 q^{94} +2.79360 q^{96} +(3.01317 - 17.0886i) q^{97} +(-4.09921 - 3.43965i) q^{98} +(-25.9864 - 9.45828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/722\mathbb{Z}\right)^\times\).

\(n\) \(363\)
\(\chi(n)\) \(e\left(\frac{5}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 0.984808i 0.122788 0.696364i
\(3\) 2.14003 + 1.79569i 1.23554 + 1.03674i 0.997859 + 0.0654024i \(0.0208331\pi\)
0.237685 + 0.971342i \(0.423611\pi\)
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) 2.20318 0.801892i 0.985293 0.358617i 0.201397 0.979510i \(-0.435452\pi\)
0.783896 + 0.620893i \(0.213230\pi\)
\(6\) 2.14003 1.79569i 0.873662 0.733089i
\(7\) 0.642040 + 1.11205i 0.242668 + 0.420314i 0.961473 0.274898i \(-0.0886441\pi\)
−0.718805 + 0.695211i \(0.755311\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 0.834245 + 4.73124i 0.278082 + 1.57708i
\(10\) −0.407131 2.30896i −0.128746 0.730156i
\(11\) −2.87811 + 4.98503i −0.867782 + 1.50304i −0.00352407 + 0.999994i \(0.501122\pi\)
−0.864258 + 0.503049i \(0.832212\pi\)
\(12\) −1.39680 2.41933i −0.403222 0.698401i
\(13\) 0.233094 0.195589i 0.0646486 0.0542466i −0.609891 0.792485i \(-0.708787\pi\)
0.674539 + 0.738239i \(0.264342\pi\)
\(14\) 1.20664 0.439181i 0.322488 0.117376i
\(15\) 6.15482 + 2.24017i 1.58917 + 0.578409i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 0.726925 4.12259i 0.176305 0.999876i −0.760322 0.649547i \(-0.774959\pi\)
0.936627 0.350329i \(-0.113930\pi\)
\(18\) 4.80423 1.13237
\(19\) 0 0
\(20\) −2.34458 −0.524263
\(21\) −0.622912 + 3.53271i −0.135931 + 0.770901i
\(22\) 4.40952 + 3.70002i 0.940112 + 0.788848i
\(23\) 6.08623 + 2.21521i 1.26907 + 0.461903i 0.886802 0.462150i \(-0.152922\pi\)
0.382266 + 0.924052i \(0.375144\pi\)
\(24\) −2.62513 + 0.955469i −0.535852 + 0.195034i
\(25\) 0.380754 0.319491i 0.0761508 0.0638981i
\(26\) −0.152141 0.263516i −0.0298374 0.0516798i
\(27\) −2.52015 + 4.36502i −0.485003 + 0.840049i
\(28\) −0.222978 1.26457i −0.0421389 0.238981i
\(29\) −0.543095 3.08004i −0.100850 0.571950i −0.992797 0.119809i \(-0.961772\pi\)
0.891947 0.452141i \(-0.149339\pi\)
\(30\) 3.27491 5.67231i 0.597914 1.03562i
\(31\) −3.22123 5.57934i −0.578550 1.00208i −0.995646 0.0932159i \(-0.970285\pi\)
0.417096 0.908863i \(-0.363048\pi\)
\(32\) 0.766044 0.642788i 0.135419 0.113630i
\(33\) −15.1108 + 5.49989i −2.63045 + 0.957407i
\(34\) −3.93373 1.43176i −0.674630 0.245545i
\(35\) 2.30627 + 1.93519i 0.389831 + 0.327107i
\(36\) 0.834245 4.73124i 0.139041 0.788540i
\(37\) −3.97980 −0.654275 −0.327137 0.944977i \(-0.606084\pi\)
−0.327137 + 0.944977i \(0.606084\pi\)
\(38\) 0 0
\(39\) 0.850045 0.136116
\(40\) −0.407131 + 2.30896i −0.0643731 + 0.365078i
\(41\) −3.84339 3.22499i −0.600236 0.503658i 0.291285 0.956636i \(-0.405917\pi\)
−0.891522 + 0.452978i \(0.850362\pi\)
\(42\) 3.37087 + 1.22690i 0.520137 + 0.189314i
\(43\) 0.929712 0.338387i 0.141780 0.0516036i −0.270156 0.962817i \(-0.587075\pi\)
0.411935 + 0.911213i \(0.364853\pi\)
\(44\) 4.40952 3.70002i 0.664760 0.557800i
\(45\) 5.63194 + 9.75480i 0.839560 + 1.45416i
\(46\) 3.23842 5.60910i 0.477479 0.827017i
\(47\) −0.763089 4.32769i −0.111308 0.631259i −0.988512 0.151141i \(-0.951705\pi\)
0.877204 0.480117i \(-0.159406\pi\)
\(48\) 0.485104 + 2.75116i 0.0700188 + 0.397096i
\(49\) 2.67557 4.63422i 0.382224 0.662032i
\(50\) −0.248520 0.430448i −0.0351460 0.0608746i
\(51\) 8.95856 7.51712i 1.25445 1.05261i
\(52\) −0.285932 + 0.104071i −0.0396516 + 0.0144320i
\(53\) −3.09219 1.12547i −0.424745 0.154595i 0.120798 0.992677i \(-0.461455\pi\)
−0.545544 + 0.838082i \(0.683677\pi\)
\(54\) 3.86109 + 3.23984i 0.525428 + 0.440886i
\(55\) −2.34354 + 13.2909i −0.316002 + 1.79214i
\(56\) −1.28408 −0.171592
\(57\) 0 0
\(58\) −3.12756 −0.410669
\(59\) 0.575427 3.26341i 0.0749142 0.424860i −0.924166 0.381990i \(-0.875239\pi\)
0.999081 0.0428696i \(-0.0136500\pi\)
\(60\) −5.01745 4.21014i −0.647750 0.543527i
\(61\) 10.3004 + 3.74904i 1.31883 + 0.480015i 0.903084 0.429465i \(-0.141298\pi\)
0.415748 + 0.909480i \(0.363520\pi\)
\(62\) −6.05394 + 2.20345i −0.768851 + 0.279839i
\(63\) −4.72573 + 3.96536i −0.595386 + 0.499588i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) 0.356707 0.617834i 0.0442440 0.0766329i
\(66\) 2.79236 + 15.8363i 0.343716 + 1.94931i
\(67\) −0.760720 4.31426i −0.0929368 0.527071i −0.995360 0.0962201i \(-0.969325\pi\)
0.902423 0.430851i \(-0.141786\pi\)
\(68\) −2.09310 + 3.62535i −0.253825 + 0.439638i
\(69\) 9.04686 + 15.6696i 1.08911 + 1.88640i
\(70\) 2.30627 1.93519i 0.275652 0.231299i
\(71\) 4.14940 1.51026i 0.492443 0.179235i −0.0838491 0.996478i \(-0.526721\pi\)
0.576292 + 0.817244i \(0.304499\pi\)
\(72\) −4.51450 1.64314i −0.532038 0.193646i
\(73\) −1.73654 1.45713i −0.203247 0.170544i 0.535483 0.844546i \(-0.320130\pi\)
−0.738730 + 0.674002i \(0.764574\pi\)
\(74\) −0.691084 + 3.91933i −0.0803369 + 0.455613i
\(75\) 1.38853 0.160334
\(76\) 0 0
\(77\) −7.39144 −0.842332
\(78\) 0.147609 0.837131i 0.0167134 0.0947864i
\(79\) 6.57005 + 5.51292i 0.739188 + 0.620252i 0.932619 0.360861i \(-0.117517\pi\)
−0.193431 + 0.981114i \(0.561962\pi\)
\(80\) 2.20318 + 0.801892i 0.246323 + 0.0896543i
\(81\) 0.312063 0.113582i 0.0346736 0.0126202i
\(82\) −3.84339 + 3.22499i −0.424431 + 0.356140i
\(83\) 4.88232 + 8.45643i 0.535904 + 0.928214i 0.999119 + 0.0419676i \(0.0133626\pi\)
−0.463214 + 0.886246i \(0.653304\pi\)
\(84\) 1.79360 3.10661i 0.195698 0.338959i
\(85\) −1.70433 9.66574i −0.184861 1.04840i
\(86\) −0.171804 0.974348i −0.0185261 0.105067i
\(87\) 4.36858 7.56661i 0.468361 0.811225i
\(88\) −2.87811 4.98503i −0.306807 0.531406i
\(89\) −11.5493 + 9.69101i −1.22422 + 1.02724i −0.225630 + 0.974213i \(0.572444\pi\)
−0.998593 + 0.0530316i \(0.983112\pi\)
\(90\) 10.5846 3.85247i 1.11571 0.406086i
\(91\) 0.367159 + 0.133635i 0.0384888 + 0.0140088i
\(92\) −4.96154 4.16323i −0.517277 0.434047i
\(93\) 3.12527 17.7243i 0.324075 1.83792i
\(94\) −4.39445 −0.453253
\(95\) 0 0
\(96\) 2.79360 0.285121
\(97\) 3.01317 17.0886i 0.305942 1.73508i −0.313098 0.949721i \(-0.601367\pi\)
0.619040 0.785360i \(-0.287522\pi\)
\(98\) −4.09921 3.43965i −0.414083 0.347457i
\(99\) −25.9864 9.45828i −2.61173 0.950593i
\(100\) −0.467064 + 0.169997i −0.0467064 + 0.0169997i
\(101\) 2.81649 2.36332i 0.280251 0.235159i −0.491817 0.870699i \(-0.663667\pi\)
0.772068 + 0.635540i \(0.219223\pi\)
\(102\) −5.84728 10.1278i −0.578967 1.00280i
\(103\) −9.50676 + 16.4662i −0.936729 + 1.62246i −0.165208 + 0.986259i \(0.552830\pi\)
−0.771521 + 0.636204i \(0.780504\pi\)
\(104\) 0.0528381 + 0.299660i 0.00518120 + 0.0293841i
\(105\) 1.46047 + 8.28271i 0.142527 + 0.808310i
\(106\) −1.64532 + 2.84978i −0.159808 + 0.276795i
\(107\) −5.01864 8.69254i −0.485170 0.840339i 0.514685 0.857380i \(-0.327909\pi\)
−0.999855 + 0.0170403i \(0.994576\pi\)
\(108\) 3.86109 3.23984i 0.371533 0.311754i
\(109\) 8.31015 3.02465i 0.795968 0.289709i 0.0881536 0.996107i \(-0.471903\pi\)
0.707815 + 0.706398i \(0.249681\pi\)
\(110\) 12.6820 + 4.61587i 1.20918 + 0.440105i
\(111\) −8.51686 7.14650i −0.808385 0.678316i
\(112\) −0.222978 + 1.26457i −0.0210694 + 0.119491i
\(113\) −14.2502 −1.34055 −0.670275 0.742113i \(-0.733824\pi\)
−0.670275 + 0.742113i \(0.733824\pi\)
\(114\) 0 0
\(115\) 15.1854 1.41605
\(116\) −0.543095 + 3.08004i −0.0504251 + 0.285975i
\(117\) 1.11984 + 0.939654i 0.103529 + 0.0868710i
\(118\) −3.11391 1.13337i −0.286658 0.104335i
\(119\) 5.05123 1.83850i 0.463045 0.168535i
\(120\) −5.01745 + 4.21014i −0.458029 + 0.384332i
\(121\) −11.0670 19.1686i −1.00609 1.74260i
\(122\) 5.48073 9.49290i 0.496202 0.859447i
\(123\) −2.43386 13.8031i −0.219454 1.24458i
\(124\) 1.11872 + 6.34459i 0.100464 + 0.569761i
\(125\) −5.27877 + 9.14309i −0.472147 + 0.817783i
\(126\) 3.08450 + 5.34252i 0.274789 + 0.475949i
\(127\) 1.70839 1.43351i 0.151595 0.127203i −0.563836 0.825887i \(-0.690675\pi\)
0.715431 + 0.698684i \(0.246230\pi\)
\(128\) −0.939693 + 0.342020i −0.0830579 + 0.0302306i
\(129\) 2.59725 + 0.945320i 0.228675 + 0.0832308i
\(130\) −0.546506 0.458573i −0.0479318 0.0402195i
\(131\) 0.264406 1.49952i 0.0231013 0.131014i −0.971076 0.238771i \(-0.923256\pi\)
0.994177 + 0.107757i \(0.0343667\pi\)
\(132\) 16.0806 1.39964
\(133\) 0 0
\(134\) −4.38081 −0.378445
\(135\) −2.05206 + 11.6378i −0.176613 + 1.00162i
\(136\) 3.20681 + 2.69083i 0.274982 + 0.230737i
\(137\) −10.0658 3.66363i −0.859975 0.313005i −0.125875 0.992046i \(-0.540174\pi\)
−0.734101 + 0.679041i \(0.762396\pi\)
\(138\) 17.0025 6.18842i 1.44735 0.526793i
\(139\) −8.28426 + 6.95132i −0.702662 + 0.589603i −0.922530 0.385926i \(-0.873882\pi\)
0.219868 + 0.975530i \(0.429437\pi\)
\(140\) −1.50531 2.60727i −0.127222 0.220355i
\(141\) 6.13818 10.6316i 0.516928 0.895346i
\(142\) −0.766777 4.34861i −0.0643465 0.364927i
\(143\) 0.304147 + 1.72491i 0.0254341 + 0.144244i
\(144\) −2.40211 + 4.16058i −0.200176 + 0.346715i
\(145\) −3.66640 6.35039i −0.304478 0.527371i
\(146\) −1.73654 + 1.45713i −0.143717 + 0.120593i
\(147\) 14.0474 5.11285i 1.15861 0.421701i
\(148\) 3.73979 + 1.36117i 0.307408 + 0.111888i
\(149\) −7.15014 5.99968i −0.585762 0.491513i 0.301072 0.953602i \(-0.402656\pi\)
−0.886834 + 0.462089i \(0.847100\pi\)
\(150\) 0.241116 1.36744i 0.0196870 0.111651i
\(151\) 19.8232 1.61319 0.806593 0.591107i \(-0.201309\pi\)
0.806593 + 0.591107i \(0.201309\pi\)
\(152\) 0 0
\(153\) 20.1114 1.62591
\(154\) −1.28351 + 7.27914i −0.103428 + 0.586570i
\(155\) −11.5710 9.70921i −0.929404 0.779862i
\(156\) −0.798781 0.290732i −0.0639537 0.0232772i
\(157\) −13.0313 + 4.74301i −1.04001 + 0.378533i −0.804885 0.593431i \(-0.797773\pi\)
−0.235127 + 0.971965i \(0.575551\pi\)
\(158\) 6.57005 5.51292i 0.522685 0.438585i
\(159\) −4.59638 7.96116i −0.364517 0.631361i
\(160\) 1.17229 2.03046i 0.0926775 0.160522i
\(161\) 1.44419 + 8.19042i 0.113818 + 0.645495i
\(162\) −0.0576668 0.327045i −0.00453074 0.0256951i
\(163\) −7.12480 + 12.3405i −0.558057 + 0.966583i 0.439601 + 0.898193i \(0.355120\pi\)
−0.997659 + 0.0683904i \(0.978214\pi\)
\(164\) 2.50859 + 4.34501i 0.195888 + 0.339288i
\(165\) −28.8815 + 24.2345i −2.24842 + 1.88665i
\(166\) 9.17576 3.33971i 0.712177 0.259211i
\(167\) −10.8911 3.96405i −0.842782 0.306748i −0.115688 0.993286i \(-0.536907\pi\)
−0.727094 + 0.686538i \(0.759130\pi\)
\(168\) −2.74796 2.30581i −0.212010 0.177897i
\(169\) −2.24135 + 12.7113i −0.172411 + 0.977794i
\(170\) −9.81485 −0.752764
\(171\) 0 0
\(172\) −0.989378 −0.0754394
\(173\) 0.691732 3.92301i 0.0525914 0.298261i −0.947155 0.320776i \(-0.896056\pi\)
0.999746 + 0.0225153i \(0.00716744\pi\)
\(174\) −6.69306 5.61614i −0.507399 0.425759i
\(175\) 0.599747 + 0.218290i 0.0453366 + 0.0165012i
\(176\) −5.40907 + 1.96874i −0.407724 + 0.148399i
\(177\) 7.09151 5.95048i 0.533031 0.447266i
\(178\) 7.53827 + 13.0567i 0.565017 + 0.978638i
\(179\) 4.22545 7.31869i 0.315825 0.547024i −0.663788 0.747921i \(-0.731052\pi\)
0.979612 + 0.200897i \(0.0643855\pi\)
\(180\) −1.95595 11.0928i −0.145788 0.826805i
\(181\) 1.47345 + 8.35635i 0.109521 + 0.621123i 0.989318 + 0.145774i \(0.0465672\pi\)
−0.879797 + 0.475349i \(0.842322\pi\)
\(182\) 0.195361 0.338376i 0.0144811 0.0250821i
\(183\) 15.3110 + 26.5194i 1.13182 + 1.96037i
\(184\) −4.96154 + 4.16323i −0.365770 + 0.306917i
\(185\) −8.76821 + 3.19137i −0.644652 + 0.234634i
\(186\) −16.9123 6.15557i −1.24007 0.451349i
\(187\) 18.4591 + 15.4890i 1.34986 + 1.13267i
\(188\) −0.763089 + 4.32769i −0.0556540 + 0.315629i
\(189\) −6.47214 −0.470779
\(190\) 0 0
\(191\) −22.3790 −1.61929 −0.809644 0.586921i \(-0.800340\pi\)
−0.809644 + 0.586921i \(0.800340\pi\)
\(192\) 0.485104 2.75116i 0.0350094 0.198548i
\(193\) 5.69026 + 4.77470i 0.409594 + 0.343690i 0.824188 0.566316i \(-0.191632\pi\)
−0.414594 + 0.910007i \(0.636076\pi\)
\(194\) −16.3057 5.93480i −1.17068 0.426093i
\(195\) 1.87280 0.681645i 0.134114 0.0488136i
\(196\) −4.09921 + 3.43965i −0.292801 + 0.245689i
\(197\) −4.26777 7.39199i −0.304066 0.526658i 0.672987 0.739654i \(-0.265011\pi\)
−0.977053 + 0.212997i \(0.931678\pi\)
\(198\) −13.8271 + 23.9492i −0.982648 + 1.70200i
\(199\) −1.10427 6.26264i −0.0782798 0.443947i −0.998605 0.0527939i \(-0.983187\pi\)
0.920326 0.391153i \(-0.127924\pi\)
\(200\) 0.0863099 + 0.489488i 0.00610303 + 0.0346120i
\(201\) 6.11913 10.5986i 0.431610 0.747571i
\(202\) −1.83833 3.18409i −0.129345 0.224032i
\(203\) 3.07646 2.58146i 0.215925 0.181183i
\(204\) −10.9893 + 3.99978i −0.769405 + 0.280040i
\(205\) −11.0538 4.02324i −0.772029 0.280996i
\(206\) 14.5652 + 12.2217i 1.01481 + 0.851523i
\(207\) −5.40327 + 30.6435i −0.375553 + 2.12987i
\(208\) 0.304282 0.0210982
\(209\) 0 0
\(210\) 8.41049 0.580379
\(211\) −2.42375 + 13.7457i −0.166858 + 0.946296i 0.780271 + 0.625442i \(0.215081\pi\)
−0.947128 + 0.320855i \(0.896030\pi\)
\(212\) 2.52078 + 2.11518i 0.173128 + 0.145271i
\(213\) 11.5918 + 4.21906i 0.794255 + 0.289085i
\(214\) −9.43195 + 3.43295i −0.644755 + 0.234672i
\(215\) 1.77697 1.49106i 0.121189 0.101689i
\(216\) −2.52015 4.36502i −0.171474 0.297002i
\(217\) 4.13632 7.16431i 0.280791 0.486345i
\(218\) −1.53565 8.70913i −0.104008 0.589857i
\(219\) −1.09968 6.23659i −0.0743095 0.421430i
\(220\) 6.74794 11.6878i 0.454946 0.787990i
\(221\) −0.636892 1.10313i −0.0428420 0.0742046i
\(222\) −8.51686 + 7.14650i −0.571615 + 0.479642i
\(223\) −8.38582 + 3.05219i −0.561556 + 0.204390i −0.607173 0.794569i \(-0.707697\pi\)
0.0456176 + 0.998959i \(0.485474\pi\)
\(224\) 1.20664 + 0.439181i 0.0806220 + 0.0293440i
\(225\) 1.82923 + 1.53490i 0.121949 + 0.102327i
\(226\) −2.47453 + 14.0337i −0.164603 + 0.933511i
\(227\) −0.659796 −0.0437922 −0.0218961 0.999760i \(-0.506970\pi\)
−0.0218961 + 0.999760i \(0.506970\pi\)
\(228\) 0 0
\(229\) −6.97208 −0.460728 −0.230364 0.973105i \(-0.573992\pi\)
−0.230364 + 0.973105i \(0.573992\pi\)
\(230\) 2.63692 14.9547i 0.173874 0.986086i
\(231\) −15.8179 13.2728i −1.04074 0.873283i
\(232\) 2.93894 + 1.06969i 0.192951 + 0.0702285i
\(233\) 27.8240 10.1271i 1.82281 0.663449i 0.828120 0.560551i \(-0.189411\pi\)
0.994692 0.102898i \(-0.0328115\pi\)
\(234\) 1.11984 0.939654i 0.0732060 0.0614271i
\(235\) −5.15156 8.92277i −0.336051 0.582057i
\(236\) −1.65688 + 2.86979i −0.107853 + 0.186808i
\(237\) 4.16054 + 23.5956i 0.270256 + 1.53270i
\(238\) −0.933429 5.29374i −0.0605052 0.343142i
\(239\) 12.3517 21.3938i 0.798965 1.38385i −0.121326 0.992613i \(-0.538715\pi\)
0.920291 0.391235i \(-0.127952\pi\)
\(240\) 3.27491 + 5.67231i 0.211395 + 0.366146i
\(241\) 21.1111 17.7144i 1.35989 1.14108i 0.383872 0.923386i \(-0.374590\pi\)
0.976017 0.217696i \(-0.0698540\pi\)
\(242\) −20.7992 + 7.57028i −1.33702 + 0.486636i
\(243\) 15.0808 + 5.48895i 0.967431 + 0.352116i
\(244\) −8.39696 7.04589i −0.537561 0.451067i
\(245\) 2.17862 12.3556i 0.139187 0.789367i
\(246\) −14.0160 −0.893630
\(247\) 0 0
\(248\) 6.44246 0.409097
\(249\) −4.73687 + 26.8641i −0.300187 + 1.70245i
\(250\) 8.08754 + 6.78625i 0.511501 + 0.429200i
\(251\) 2.80832 + 1.02215i 0.177260 + 0.0645172i 0.429125 0.903245i \(-0.358822\pi\)
−0.251866 + 0.967762i \(0.581044\pi\)
\(252\) 5.79697 2.10992i 0.365175 0.132913i
\(253\) −28.5597 + 23.9644i −1.79553 + 1.50663i
\(254\) −1.11507 1.93136i −0.0699659 0.121185i
\(255\) 13.7094 23.7454i 0.858516 1.48699i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) 2.45404 + 13.9176i 0.153079 + 0.868153i 0.960521 + 0.278207i \(0.0897401\pi\)
−0.807442 + 0.589947i \(0.799149\pi\)
\(258\) 1.38197 2.39364i 0.0860374 0.149021i
\(259\) −2.55519 4.42571i −0.158772 0.275000i
\(260\) −0.546506 + 0.458573i −0.0338929 + 0.0284395i
\(261\) 14.1194 5.13902i 0.873966 0.318098i
\(262\) −1.43083 0.520778i −0.0883968 0.0321738i
\(263\) 5.79809 + 4.86518i 0.357526 + 0.300000i 0.803804 0.594895i \(-0.202806\pi\)
−0.446278 + 0.894894i \(0.647251\pi\)
\(264\) 2.79236 15.8363i 0.171858 0.974656i
\(265\) −7.71517 −0.473939
\(266\) 0 0
\(267\) −42.1179 −2.57757
\(268\) −0.760720 + 4.31426i −0.0464684 + 0.263535i
\(269\) −5.87613 4.93066i −0.358274 0.300628i 0.445828 0.895118i \(-0.352909\pi\)
−0.804102 + 0.594491i \(0.797354\pi\)
\(270\) 11.1047 + 4.04177i 0.675809 + 0.245975i
\(271\) −10.9614 + 3.98963i −0.665858 + 0.242353i −0.652764 0.757562i \(-0.726391\pi\)
−0.0130948 + 0.999914i \(0.504168\pi\)
\(272\) 3.20681 2.69083i 0.194441 0.163156i
\(273\) 0.545762 + 0.945288i 0.0330310 + 0.0572114i
\(274\) −5.35588 + 9.27665i −0.323560 + 0.560423i
\(275\) 0.496818 + 2.81760i 0.0299593 + 0.169908i
\(276\) −3.14194 17.8188i −0.189123 1.07257i
\(277\) −13.7202 + 23.7642i −0.824370 + 1.42785i 0.0780307 + 0.996951i \(0.475137\pi\)
−0.902400 + 0.430899i \(0.858197\pi\)
\(278\) 5.40717 + 9.36549i 0.324300 + 0.561705i
\(279\) 23.7099 19.8950i 1.41947 1.19108i
\(280\) −2.82906 + 1.02969i −0.169069 + 0.0615359i
\(281\) −15.2902 5.56517i −0.912136 0.331990i −0.157031 0.987594i \(-0.550192\pi\)
−0.755106 + 0.655603i \(0.772414\pi\)
\(282\) −9.40424 7.89109i −0.560014 0.469908i
\(283\) 0.589317 3.34218i 0.0350312 0.198672i −0.962269 0.272099i \(-0.912282\pi\)
0.997301 + 0.0734265i \(0.0233934\pi\)
\(284\) −4.41570 −0.262023
\(285\) 0 0
\(286\) 1.75152 0.103569
\(287\) 1.11872 6.34459i 0.0660361 0.374509i
\(288\) 3.68025 + 3.08810i 0.216861 + 0.181968i
\(289\) −0.492591 0.179288i −0.0289759 0.0105464i
\(290\) −6.89058 + 2.50797i −0.404629 + 0.147273i
\(291\) 37.1341 31.1592i 2.17684 1.82659i
\(292\) 1.13345 + 1.96319i 0.0663299 + 0.114887i
\(293\) −11.6892 + 20.2462i −0.682888 + 1.18280i 0.291208 + 0.956660i \(0.405943\pi\)
−0.974096 + 0.226136i \(0.927391\pi\)
\(294\) −2.59586 14.7219i −0.151394 0.858596i
\(295\) −1.34913 7.65131i −0.0785495 0.445477i
\(296\) 1.98990 3.44660i 0.115660 0.200330i
\(297\) −14.5065 25.1260i −0.841753 1.45796i
\(298\) −7.15014 + 5.99968i −0.414196 + 0.347552i
\(299\) 1.85193 0.674049i 0.107100 0.0389813i
\(300\) −1.30479 0.474905i −0.0753322 0.0274187i
\(301\) 0.973214 + 0.816623i 0.0560951 + 0.0470694i
\(302\) 3.44226 19.5220i 0.198080 1.12337i
\(303\) 10.2712 0.590062
\(304\) 0 0
\(305\) 25.7000 1.47158
\(306\) 3.49231 19.8059i 0.199642 1.13223i
\(307\) −1.06329 0.892202i −0.0606849 0.0509207i 0.611941 0.790904i \(-0.290389\pi\)
−0.672626 + 0.739983i \(0.734834\pi\)
\(308\) 6.94568 + 2.52802i 0.395767 + 0.144047i
\(309\) −49.9130 + 18.1668i −2.83945 + 1.03348i
\(310\) −11.5710 + 9.70921i −0.657188 + 0.551446i
\(311\) 6.09512 + 10.5571i 0.345623 + 0.598636i 0.985467 0.169869i \(-0.0543343\pi\)
−0.639844 + 0.768505i \(0.721001\pi\)
\(312\) −0.425022 + 0.736160i −0.0240622 + 0.0416769i
\(313\) 2.87065 + 16.2803i 0.162259 + 0.920215i 0.951846 + 0.306577i \(0.0991836\pi\)
−0.789587 + 0.613638i \(0.789705\pi\)
\(314\) 2.40809 + 13.6569i 0.135896 + 0.770706i
\(315\) −7.23185 + 12.5259i −0.407469 + 0.705757i
\(316\) −4.28829 7.42754i −0.241235 0.417832i
\(317\) 2.05921 1.72789i 0.115657 0.0970477i −0.583125 0.812382i \(-0.698170\pi\)
0.698782 + 0.715335i \(0.253726\pi\)
\(318\) −8.63837 + 3.14411i −0.484415 + 0.176313i
\(319\) 16.9172 + 6.15736i 0.947181 + 0.344746i
\(320\) −1.79605 1.50706i −0.100402 0.0842475i
\(321\) 4.86913 27.6142i 0.271768 1.54127i
\(322\) 8.31677 0.463475
\(323\) 0 0
\(324\) −0.332090 −0.0184495
\(325\) 0.0262626 0.148943i 0.00145679 0.00826185i
\(326\) 10.9158 + 9.15946i 0.604571 + 0.507296i
\(327\) 23.2153 + 8.44967i 1.28381 + 0.467268i
\(328\) 4.71461 1.71598i 0.260321 0.0947491i
\(329\) 4.32265 3.62714i 0.238316 0.199971i
\(330\) 18.8511 + 32.6510i 1.03772 + 1.79738i
\(331\) −2.60651 + 4.51462i −0.143267 + 0.248146i −0.928725 0.370769i \(-0.879094\pi\)
0.785458 + 0.618915i \(0.212427\pi\)
\(332\) −1.69561 9.61630i −0.0930588 0.527763i
\(333\) −3.32013 18.8294i −0.181942 1.03184i
\(334\) −5.79506 + 10.0373i −0.317091 + 0.549218i
\(335\) −5.13558 8.89508i −0.280587 0.485990i
\(336\) −2.74796 + 2.30581i −0.149914 + 0.125792i
\(337\) 25.1156 9.14133i 1.36813 0.497960i 0.449575 0.893243i \(-0.351576\pi\)
0.918560 + 0.395283i \(0.129353\pi\)
\(338\) 12.1290 + 4.41459i 0.659731 + 0.240122i
\(339\) −30.4959 25.5891i −1.65631 1.38981i
\(340\) −1.70433 + 9.66574i −0.0924303 + 0.524198i
\(341\) 37.0842 2.00822
\(342\) 0 0
\(343\) 15.8598 0.856351
\(344\) −0.171804 + 0.974348i −0.00926304 + 0.0525333i
\(345\) 32.4972 + 27.2684i 1.74959 + 1.46808i
\(346\) −3.74329 1.36245i −0.201241 0.0732456i
\(347\) 30.6981 11.1732i 1.64796 0.599808i 0.659555 0.751657i \(-0.270745\pi\)
0.988404 + 0.151849i \(0.0485227\pi\)
\(348\) −6.69306 + 5.61614i −0.358785 + 0.301057i
\(349\) 14.5529 + 25.2063i 0.778998 + 1.34926i 0.932520 + 0.361119i \(0.117605\pi\)
−0.153521 + 0.988145i \(0.549061\pi\)
\(350\) 0.319119 0.552730i 0.0170576 0.0295447i
\(351\) 0.266320 + 1.51037i 0.0142151 + 0.0806178i
\(352\) 0.999556 + 5.66877i 0.0532765 + 0.302146i
\(353\) 7.15244 12.3884i 0.380686 0.659368i −0.610474 0.792036i \(-0.709021\pi\)
0.991160 + 0.132668i \(0.0423545\pi\)
\(354\) −4.62866 8.01707i −0.246010 0.426102i
\(355\) 7.93081 6.65474i 0.420924 0.353197i
\(356\) 14.1673 5.15648i 0.750866 0.273293i
\(357\) 14.1111 + 5.13603i 0.746840 + 0.271828i
\(358\) −6.47376 5.43213i −0.342149 0.287097i
\(359\) 3.41578 19.3719i 0.180278 1.02241i −0.751595 0.659624i \(-0.770715\pi\)
0.931874 0.362783i \(-0.118173\pi\)
\(360\) −11.2639 −0.593658
\(361\) 0 0
\(362\) 8.48526 0.445976
\(363\) 10.7373 60.8943i 0.563562 3.19612i
\(364\) −0.299311 0.251152i −0.0156882 0.0131639i
\(365\) −4.99438 1.81780i −0.261418 0.0951482i
\(366\) 28.7752 10.4733i 1.50411 0.547450i
\(367\) 7.31613 6.13896i 0.381899 0.320451i −0.431548 0.902090i \(-0.642033\pi\)
0.813447 + 0.581638i \(0.197588\pi\)
\(368\) 3.23842 + 5.60910i 0.168814 + 0.292395i
\(369\) 12.0518 20.8744i 0.627394 1.08668i
\(370\) 1.62030 + 9.18918i 0.0842354 + 0.477723i
\(371\) −0.733741 4.16125i −0.0380939 0.216041i
\(372\) −8.99885 + 15.5865i −0.466569 + 0.808120i
\(373\) −1.82005 3.15242i −0.0942387 0.163226i 0.815052 0.579388i \(-0.196708\pi\)
−0.909291 + 0.416162i \(0.863375\pi\)
\(374\) 18.4591 15.4890i 0.954496 0.800918i
\(375\) −27.7149 + 10.0874i −1.43119 + 0.520911i
\(376\) 4.12943 + 1.50299i 0.212959 + 0.0775109i
\(377\) −0.729015 0.611716i −0.0375462 0.0315050i
\(378\) −1.12387 + 6.37381i −0.0578059 + 0.327833i
\(379\) 8.34741 0.428778 0.214389 0.976748i \(-0.431224\pi\)
0.214389 + 0.976748i \(0.431224\pi\)
\(380\) 0 0
\(381\) 6.23015 0.319180
\(382\) −3.88608 + 22.0390i −0.198829 + 1.12761i
\(383\) −7.26644 6.09727i −0.371298 0.311556i 0.437977 0.898986i \(-0.355695\pi\)
−0.809275 + 0.587430i \(0.800140\pi\)
\(384\) −2.62513 0.955469i −0.133963 0.0487586i
\(385\) −16.2847 + 5.92714i −0.829944 + 0.302075i
\(386\) 5.69026 4.77470i 0.289627 0.243026i
\(387\) 2.37660 + 4.11639i 0.120809 + 0.209248i
\(388\) −8.67609 + 15.0274i −0.440462 + 0.762902i
\(389\) 6.25966 + 35.5003i 0.317378 + 1.79994i 0.558567 + 0.829460i \(0.311351\pi\)
−0.241189 + 0.970478i \(0.577537\pi\)
\(390\) −0.346080 1.96272i −0.0175244 0.0993860i
\(391\) 13.5566 23.4808i 0.685589 1.18747i
\(392\) 2.67557 + 4.63422i 0.135137 + 0.234064i
\(393\) 3.25852 2.73422i 0.164371 0.137923i
\(394\) −8.02078 + 2.91933i −0.404081 + 0.147074i
\(395\) 18.8958 + 6.87750i 0.950750 + 0.346045i
\(396\) 21.1843 + 17.7758i 1.06455 + 0.893265i
\(397\) −1.11292 + 6.31169i −0.0558559 + 0.316775i −0.999915 0.0130002i \(-0.995862\pi\)
0.944060 + 0.329775i \(0.106973\pi\)
\(398\) −6.35926 −0.318761
\(399\) 0 0
\(400\) 0.497039 0.0248520
\(401\) 0.0325868 0.184809i 0.00162731 0.00922891i −0.983983 0.178261i \(-0.942953\pi\)
0.985611 + 0.169032i \(0.0540641\pi\)
\(402\) −9.37505 7.86660i −0.467585 0.392350i
\(403\) −1.84211 0.670472i −0.0917619 0.0333986i
\(404\) −3.45494 + 1.25749i −0.171890 + 0.0625627i
\(405\) 0.596450 0.500481i 0.0296379 0.0248691i
\(406\) −2.00802 3.47799i −0.0996562 0.172610i
\(407\) 11.4543 19.8394i 0.567768 0.983402i
\(408\) 2.03074 + 11.5169i 0.100537 + 0.570171i
\(409\) 2.99826 + 17.0040i 0.148254 + 0.840792i 0.964696 + 0.263364i \(0.0848321\pi\)
−0.816442 + 0.577427i \(0.804057\pi\)
\(410\) −5.88159 + 10.1872i −0.290471 + 0.503110i
\(411\) −14.9622 25.9153i −0.738031 1.27831i
\(412\) 14.5652 12.2217i 0.717576 0.602118i
\(413\) 3.99850 1.45534i 0.196754 0.0716124i
\(414\) 29.2396 + 10.6424i 1.43705 + 0.523044i
\(415\) 17.5378 + 14.7160i 0.860896 + 0.722378i
\(416\) 0.0528381 0.299660i 0.00259060 0.0146920i
\(417\) −30.2110 −1.47944
\(418\) 0 0
\(419\) −1.72572 −0.0843068 −0.0421534 0.999111i \(-0.513422\pi\)
−0.0421534 + 0.999111i \(0.513422\pi\)
\(420\) 1.46047 8.28271i 0.0712634 0.404155i
\(421\) 25.0914 + 21.0542i 1.22288 + 1.02612i 0.998669 + 0.0515798i \(0.0164257\pi\)
0.224213 + 0.974540i \(0.428019\pi\)
\(422\) 13.1160 + 4.77385i 0.638479 + 0.232387i
\(423\) 19.8387 7.22071i 0.964592 0.351083i
\(424\) 2.52078 2.11518i 0.122420 0.102722i
\(425\) −1.04035 1.80194i −0.0504644 0.0874069i
\(426\) 6.16785 10.6830i 0.298833 0.517595i
\(427\) 2.44416 + 13.8615i 0.118281 + 0.670807i
\(428\) 1.74295 + 9.88479i 0.0842489 + 0.477799i
\(429\) −2.44652 + 4.23750i −0.118119 + 0.204588i
\(430\) −1.15984 2.00890i −0.0559323 0.0968776i
\(431\) −19.5433 + 16.3987i −0.941366 + 0.789900i −0.977822 0.209435i \(-0.932837\pi\)
0.0364565 + 0.999335i \(0.488393\pi\)
\(432\) −4.73633 + 1.72388i −0.227877 + 0.0829403i
\(433\) −23.0069 8.37382i −1.10564 0.402420i −0.276247 0.961087i \(-0.589091\pi\)
−0.829392 + 0.558667i \(0.811313\pi\)
\(434\) −6.33720 5.31755i −0.304196 0.255250i
\(435\) 3.55717 20.1737i 0.170553 0.967257i
\(436\) −8.84348 −0.423526
\(437\) 0 0
\(438\) −6.33280 −0.302593
\(439\) −5.35510 + 30.3703i −0.255585 + 1.44949i 0.538981 + 0.842318i \(0.318809\pi\)
−0.794566 + 0.607177i \(0.792302\pi\)
\(440\) −10.3384 8.67499i −0.492866 0.413564i
\(441\) 24.1577 + 8.79269i 1.15037 + 0.418699i
\(442\) −1.19697 + 0.435660i −0.0569339 + 0.0207222i
\(443\) 8.20026 6.88083i 0.389606 0.326918i −0.426854 0.904321i \(-0.640378\pi\)
0.816460 + 0.577402i \(0.195934\pi\)
\(444\) 5.55899 + 9.62845i 0.263818 + 0.456946i
\(445\) −17.6740 + 30.6123i −0.837830 + 1.45116i
\(446\) 1.54964 + 8.78842i 0.0733774 + 0.416144i
\(447\) −4.52789 25.6789i −0.214162 1.21457i
\(448\) 0.642040 1.11205i 0.0303335 0.0525392i
\(449\) −1.15781 2.00538i −0.0546403 0.0946399i 0.837411 0.546573i \(-0.184068\pi\)
−0.892052 + 0.451933i \(0.850735\pi\)
\(450\) 1.82923 1.53490i 0.0862306 0.0723561i
\(451\) 27.1383 9.87754i 1.27789 0.465115i
\(452\) 13.3908 + 4.87387i 0.629852 + 0.229247i
\(453\) 42.4221 + 35.5963i 1.99316 + 1.67246i
\(454\) −0.114572 + 0.649772i −0.00537715 + 0.0304953i
\(455\) 0.916079 0.0429465
\(456\) 0 0
\(457\) −0.0521810 −0.00244092 −0.00122046 0.999999i \(-0.500388\pi\)
−0.00122046 + 0.999999i \(0.500388\pi\)
\(458\) −1.21069 + 6.86616i −0.0565718 + 0.320834i
\(459\) 16.1633 + 13.5626i 0.754436 + 0.633047i
\(460\) −14.2696 5.19373i −0.665326 0.242159i
\(461\) −37.0916 + 13.5002i −1.72753 + 0.628768i −0.998450 0.0556634i \(-0.982273\pi\)
−0.729077 + 0.684432i \(0.760050\pi\)
\(462\) −15.8179 + 13.2728i −0.735913 + 0.617505i
\(463\) 3.09528 + 5.36119i 0.143850 + 0.249155i 0.928943 0.370222i \(-0.120718\pi\)
−0.785093 + 0.619377i \(0.787385\pi\)
\(464\) 1.56378 2.70855i 0.0725967 0.125741i
\(465\) −7.32743 41.5559i −0.339801 1.92711i
\(466\) −5.14167 29.1599i −0.238183 1.35080i
\(467\) 10.4981 18.1832i 0.485793 0.841418i −0.514074 0.857746i \(-0.671864\pi\)
0.999867 + 0.0163277i \(0.00519750\pi\)
\(468\) −0.730921 1.26599i −0.0337868 0.0585205i
\(469\) 4.30924 3.61588i 0.198982 0.166966i
\(470\) −9.68178 + 3.52388i −0.446587 + 0.162544i
\(471\) −36.4043 13.2501i −1.67742 0.610532i
\(472\) 2.53848 + 2.13004i 0.116843 + 0.0980430i
\(473\) −0.988939 + 5.60855i −0.0454715 + 0.257882i
\(474\) 23.9596 1.10050
\(475\) 0 0
\(476\) −5.37540 −0.246381
\(477\) 2.74520 15.5688i 0.125694 0.712847i
\(478\) −18.9239 15.8790i −0.865559 0.726290i
\(479\) −14.5868 5.30916i −0.666487 0.242582i −0.0134527 0.999910i \(-0.504282\pi\)
−0.653035 + 0.757328i \(0.726504\pi\)
\(480\) 6.15482 2.24017i 0.280928 0.102249i
\(481\) −0.927666 + 0.778404i −0.0422979 + 0.0354922i
\(482\) −13.7793 23.8665i −0.627631 1.08709i
\(483\) −11.6169 + 20.1210i −0.528586 + 0.915539i
\(484\) 3.84353 + 21.7977i 0.174706 + 0.990807i
\(485\) −7.06462 40.0654i −0.320788 1.81928i
\(486\) 8.02431 13.8985i 0.363990 0.630449i
\(487\) 14.3033 + 24.7740i 0.648143 + 1.12262i 0.983566 + 0.180549i \(0.0577875\pi\)
−0.335423 + 0.942068i \(0.608879\pi\)
\(488\) −8.39696 + 7.04589i −0.380113 + 0.318952i
\(489\) −37.4070 + 13.6150i −1.69160 + 0.615694i
\(490\) −11.7895 4.29104i −0.532597 0.193849i
\(491\) −23.2486 19.5079i −1.04919 0.880377i −0.0561842 0.998420i \(-0.517893\pi\)
−0.993008 + 0.118043i \(0.962338\pi\)
\(492\) −2.43386 + 13.8031i −0.109727 + 0.622292i
\(493\) −13.0926 −0.589659
\(494\) 0 0
\(495\) −64.8373 −2.91422
\(496\) 1.11872 6.34459i 0.0502321 0.284880i
\(497\) 4.34355 + 3.64467i 0.194835 + 0.163486i
\(498\) 25.6335 + 9.32982i 1.14866 + 0.418079i
\(499\) −8.24696 + 3.00165i −0.369185 + 0.134372i −0.519949 0.854198i \(-0.674049\pi\)
0.150764 + 0.988570i \(0.451827\pi\)
\(500\) 8.08754 6.78625i 0.361686 0.303490i
\(501\) −16.1891 28.0403i −0.723275 1.25275i
\(502\) 1.49428 2.58816i 0.0666928 0.115515i
\(503\) −3.66473 20.7837i −0.163402 0.926700i −0.950697 0.310123i \(-0.899630\pi\)
0.787294 0.616577i \(-0.211481\pi\)
\(504\) −1.07124 6.07528i −0.0477167 0.270615i
\(505\) 4.31011 7.46533i 0.191798 0.332203i
\(506\) 18.6410 + 32.2872i 0.828695 + 1.43534i
\(507\) −27.6222 + 23.1778i −1.22674 + 1.02936i
\(508\) −2.09565 + 0.762755i −0.0929795 + 0.0338418i
\(509\) −20.8811 7.60009i −0.925537 0.336868i −0.165098 0.986277i \(-0.552794\pi\)
−0.760439 + 0.649409i \(0.775016\pi\)
\(510\) −21.0040 17.6245i −0.930074 0.780424i
\(511\) 0.505467 2.86665i 0.0223606 0.126813i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 14.1323 0.623347
\(515\) −7.74100 + 43.9014i −0.341109 + 1.93453i
\(516\) −2.11729 1.77662i −0.0932087 0.0782114i
\(517\) 23.7699 + 8.65154i 1.04540 + 0.380494i
\(518\) −4.80218 + 1.74785i −0.210996 + 0.0767961i
\(519\) 8.52485 7.15320i 0.374199 0.313990i
\(520\) 0.356707 + 0.617834i 0.0156426 + 0.0270938i
\(521\) −5.01661 + 8.68902i −0.219782 + 0.380673i −0.954741 0.297438i \(-0.903868\pi\)
0.734959 + 0.678111i \(0.237201\pi\)
\(522\) −2.60915 14.7972i −0.114199 0.647657i
\(523\) 5.08482 + 28.8374i 0.222343 + 1.26097i 0.867699 + 0.497090i \(0.165598\pi\)
−0.645356 + 0.763882i \(0.723291\pi\)
\(524\) −0.761327 + 1.31866i −0.0332587 + 0.0576058i
\(525\) 0.891491 + 1.54411i 0.0389079 + 0.0673904i
\(526\) 5.79809 4.86518i 0.252809 0.212132i
\(527\) −25.3429 + 9.22407i −1.10396 + 0.401807i
\(528\) −15.1108 5.49989i −0.657614 0.239352i
\(529\) 14.5161 + 12.1804i 0.631134 + 0.529584i
\(530\) −1.33972 + 7.59795i −0.0581939 + 0.330034i
\(531\) 15.9200 0.690870
\(532\) 0 0
\(533\) −1.52664 −0.0661262
\(534\) −7.31369 + 41.4780i −0.316494 + 1.79493i
\(535\) −18.0274 15.1268i −0.779395 0.653990i
\(536\) 4.11662 + 1.49833i 0.177811 + 0.0647178i
\(537\) 22.1847 8.07457i 0.957340 0.348443i
\(538\) −5.87613 + 4.93066i −0.253338 + 0.212576i
\(539\) 15.4012 + 26.6756i 0.663375 + 1.14900i
\(540\) 5.90868 10.2341i 0.254269 0.440407i
\(541\) −6.57091 37.2655i −0.282505 1.60217i −0.714062 0.700082i \(-0.753147\pi\)
0.431557 0.902086i \(-0.357964\pi\)
\(542\) 2.02559 + 11.4877i 0.0870064 + 0.493438i
\(543\) −11.8522 + 20.5287i −0.508628 + 0.880970i
\(544\) −2.09310 3.62535i −0.0897408 0.155436i
\(545\) 15.8833 13.3277i 0.680367 0.570896i
\(546\) 1.02570 0.373323i 0.0438958 0.0159768i
\(547\) 13.6233 + 4.95846i 0.582488 + 0.212008i 0.616422 0.787416i \(-0.288581\pi\)
−0.0339340 + 0.999424i \(0.510804\pi\)
\(548\) 8.20568 + 6.88538i 0.350529 + 0.294129i
\(549\) −9.14454 + 51.8613i −0.390280 + 2.21339i
\(550\) 2.86106 0.121996
\(551\) 0 0
\(552\) −18.0937 −0.770120
\(553\) −1.91239 + 10.8457i −0.0813231 + 0.461206i
\(554\) 21.0206 + 17.6384i 0.893081 + 0.749384i
\(555\) −24.4949 8.91542i −1.03975 0.378439i
\(556\) 10.1622 3.69872i 0.430971 0.156861i
\(557\) −3.32311 + 2.78842i −0.140805 + 0.118149i −0.710470 0.703728i \(-0.751517\pi\)
0.569665 + 0.821877i \(0.307073\pi\)
\(558\) −15.4755 26.8044i −0.655131 1.13472i
\(559\) 0.150525 0.260717i 0.00636654 0.0110272i
\(560\) 0.522789 + 2.96488i 0.0220919 + 0.125289i
\(561\) 11.6894 + 66.2937i 0.493526 + 2.79892i
\(562\) −8.13574 + 14.0915i −0.343185 + 0.594415i
\(563\) 13.6468 + 23.6370i 0.575144 + 0.996179i 0.996026 + 0.0890637i \(0.0283875\pi\)
−0.420882 + 0.907116i \(0.638279\pi\)
\(564\) −9.40424 + 7.89109i −0.395990 + 0.332275i
\(565\) −31.3959 + 11.4272i −1.32083 + 0.480744i
\(566\) −3.18907 1.16073i −0.134047 0.0487890i
\(567\) 0.326664 + 0.274104i 0.0137186 + 0.0115113i
\(568\) −0.766777 + 4.34861i −0.0321733 + 0.182464i
\(569\) −7.19043 −0.301439 −0.150719 0.988577i \(-0.548159\pi\)
−0.150719 + 0.988577i \(0.548159\pi\)
\(570\) 0 0
\(571\) 42.0134 1.75821 0.879103 0.476631i \(-0.158142\pi\)
0.879103 + 0.476631i \(0.158142\pi\)
\(572\) 0.304147 1.72491i 0.0127170 0.0721219i
\(573\) −47.8917 40.1859i −2.00070 1.67879i
\(574\) −6.05394 2.20345i −0.252686 0.0919703i
\(575\) 3.02510 1.10104i 0.126155 0.0459168i
\(576\) 3.68025 3.08810i 0.153344 0.128671i
\(577\) −10.8357 18.7679i −0.451095 0.781319i 0.547359 0.836898i \(-0.315633\pi\)
−0.998454 + 0.0555783i \(0.982300\pi\)
\(578\) −0.262102 + 0.453974i −0.0109020 + 0.0188828i
\(579\) 3.60341 + 20.4360i 0.149753 + 0.849289i
\(580\) 1.27333 + 7.22140i 0.0528721 + 0.299852i
\(581\) −6.26929 + 10.8587i −0.260094 + 0.450496i
\(582\) −24.2376 41.9807i −1.00468 1.74016i
\(583\) 14.5101 12.1755i 0.600949 0.504256i
\(584\) 2.13018 0.775323i 0.0881476 0.0320831i
\(585\) 3.22070 + 1.17224i 0.133160 + 0.0484662i
\(586\) 17.9088 + 15.0273i 0.739807 + 0.620771i
\(587\) −0.220298 + 1.24937i −0.00909267 + 0.0515671i −0.989017 0.147805i \(-0.952779\pi\)
0.979924 + 0.199372i \(0.0638903\pi\)
\(588\) −14.9490 −0.616485
\(589\) 0 0
\(590\) −7.76934 −0.319859
\(591\) 4.14063 23.4827i 0.170323 0.965948i
\(592\) −3.04870 2.55816i −0.125301 0.105140i
\(593\) −20.2598 7.37395i −0.831969 0.302812i −0.109302 0.994009i \(-0.534862\pi\)
−0.722667 + 0.691197i \(0.757084\pi\)
\(594\) −27.2633 + 9.92304i −1.11863 + 0.407147i
\(595\) 9.65449 8.10108i 0.395795 0.332112i
\(596\) 4.66692 + 8.08334i 0.191165 + 0.331107i
\(597\) 8.88262 15.3852i 0.363542 0.629672i
\(598\) −0.342224 1.94085i −0.0139946 0.0793671i
\(599\) −4.97359 28.2066i −0.203215 1.15249i −0.900224 0.435428i \(-0.856597\pi\)
0.697008 0.717063i \(-0.254514\pi\)
\(600\) −0.694265 + 1.20250i −0.0283433 + 0.0490920i
\(601\) −3.77932 6.54598i −0.154162 0.267016i 0.778592 0.627531i \(-0.215934\pi\)
−0.932754 + 0.360515i \(0.882601\pi\)
\(602\) 0.973214 0.816623i 0.0396652 0.0332831i
\(603\) 19.7772 7.19830i 0.805388 0.293137i
\(604\) −18.6277 6.77992i −0.757950 0.275871i
\(605\) −39.7538 33.3574i −1.61622 1.35617i
\(606\) 1.78357 10.1151i 0.0724525 0.410898i
\(607\) 1.72737 0.0701117 0.0350558 0.999385i \(-0.488839\pi\)
0.0350558 + 0.999385i \(0.488839\pi\)
\(608\) 0 0
\(609\) 11.2192 0.454625
\(610\) 4.46275 25.3095i 0.180692 1.02475i
\(611\) −1.02432 0.859507i −0.0414396 0.0347719i
\(612\) −18.8985 6.87851i −0.763928 0.278047i
\(613\) 25.7635 9.37714i 1.04058 0.378739i 0.235479 0.971880i \(-0.424334\pi\)
0.805099 + 0.593140i \(0.202112\pi\)
\(614\) −1.06329 + 0.892202i −0.0429107 + 0.0360064i
\(615\) −16.4308 28.4590i −0.662555 1.14758i
\(616\) 3.69572 6.40117i 0.148905 0.257911i
\(617\) 1.84545 + 10.4660i 0.0742949 + 0.421347i 0.999157 + 0.0410453i \(0.0130688\pi\)
−0.924862 + 0.380302i \(0.875820\pi\)
\(618\) 9.22354 + 52.3093i 0.371025 + 2.10419i
\(619\) −4.18004 + 7.24004i −0.168010 + 0.291002i −0.937720 0.347392i \(-0.887067\pi\)
0.769710 + 0.638394i \(0.220401\pi\)
\(620\) 7.55242 + 13.0812i 0.303313 + 0.525353i
\(621\) −25.0076 + 20.9839i −1.00352 + 0.842055i
\(622\) 11.4551 4.16931i 0.459307 0.167174i
\(623\) −18.1919 6.62132i −0.728845 0.265278i
\(624\) 0.651172 + 0.546398i 0.0260677 + 0.0218734i
\(625\) −4.72985 + 26.8243i −0.189194 + 1.07297i
\(626\) 16.5314 0.660728
\(627\) 0 0
\(628\) 13.8676 0.553379
\(629\) −2.89301 + 16.4071i −0.115352 + 0.654193i
\(630\) 11.0798 + 9.29709i 0.441431 + 0.370405i
\(631\) −23.0508 8.38980i −0.917638 0.333993i −0.160339 0.987062i \(-0.551259\pi\)
−0.757298 + 0.653069i \(0.773481\pi\)
\(632\) −8.05936 + 2.93337i −0.320584 + 0.116683i
\(633\) −29.8700 + 25.0639i −1.18723 + 0.996202i
\(634\) −1.34406 2.32797i −0.0533793 0.0924557i
\(635\) 2.61437 4.52823i 0.103748 0.179697i
\(636\) 1.59631 + 9.05310i 0.0632976 + 0.358979i
\(637\) −0.282744 1.60352i −0.0112027 0.0635338i
\(638\) 9.00145 15.5910i 0.356371 0.617253i
\(639\) 10.6070 + 18.3719i 0.419606 + 0.726780i
\(640\) −1.79605 + 1.50706i −0.0709951 + 0.0595720i
\(641\) 6.55220 2.38480i 0.258796 0.0941941i −0.209364 0.977838i \(-0.567139\pi\)
0.468160 + 0.883644i \(0.344917\pi\)
\(642\) −26.3492 9.59031i −1.03992 0.378499i
\(643\) −6.96353 5.84309i −0.274615 0.230429i 0.495070 0.868853i \(-0.335142\pi\)
−0.769685 + 0.638424i \(0.779587\pi\)
\(644\) 1.44419 8.19042i 0.0569091 0.322748i
\(645\) 6.48025 0.255160
\(646\) 0 0
\(647\) 30.0074 1.17971 0.589856 0.807509i \(-0.299185\pi\)
0.589856 + 0.807509i \(0.299185\pi\)
\(648\) −0.0576668 + 0.327045i −0.00226537 + 0.0128475i
\(649\) 14.6120 + 12.2610i 0.573573 + 0.481285i
\(650\) −0.142119 0.0517272i −0.00557438 0.00202891i
\(651\) 21.7167 7.90424i 0.851146 0.309792i
\(652\) 10.9158 9.15946i 0.427497 0.358712i
\(653\) −5.20956 9.02323i −0.203866 0.353106i 0.745905 0.666053i \(-0.232017\pi\)
−0.949771 + 0.312946i \(0.898684\pi\)
\(654\) 12.3526 21.3953i 0.483025 0.836623i
\(655\) −0.619920 3.51574i −0.0242223 0.137371i
\(656\) −0.871225 4.94096i −0.0340156 0.192912i
\(657\) 5.44533 9.43159i 0.212443 0.367962i
\(658\) −2.82141 4.88683i −0.109990 0.190508i
\(659\) −20.2049 + 16.9539i −0.787071 + 0.660431i −0.945019 0.327017i \(-0.893957\pi\)
0.157948 + 0.987447i \(0.449512\pi\)
\(660\) 35.4285 12.8949i 1.37905 0.501933i
\(661\) 23.2047 + 8.44583i 0.902559 + 0.328505i 0.751278 0.659986i \(-0.229438\pi\)
0.151281 + 0.988491i \(0.451660\pi\)
\(662\) 3.99341 + 3.35087i 0.155208 + 0.130235i
\(663\) 0.617919 3.50439i 0.0239980 0.136099i
\(664\) −9.76464 −0.378942
\(665\) 0 0
\(666\) −19.1198 −0.740879
\(667\) 3.51754 19.9489i 0.136200 0.772426i
\(668\) 8.87854 + 7.44998i 0.343521 + 0.288248i
\(669\) −23.4267 8.52660i −0.905727 0.329658i
\(670\) −9.65173 + 3.51294i −0.372879 + 0.135717i
\(671\) −48.3347 + 40.5577i −1.86594 + 1.56571i
\(672\) 1.79360 + 3.10661i 0.0691898 + 0.119840i
\(673\) 4.88690 8.46436i 0.188376 0.326277i −0.756333 0.654187i \(-0.773011\pi\)
0.944709 + 0.327910i \(0.106344\pi\)
\(674\) −4.64118 26.3214i −0.178771 1.01386i
\(675\) 0.435027 + 2.46716i 0.0167442 + 0.0949611i
\(676\) 6.45371 11.1781i 0.248219 0.429929i
\(677\) 10.7874 + 18.6843i 0.414592 + 0.718094i 0.995386 0.0959565i \(-0.0305910\pi\)
−0.580794 + 0.814051i \(0.697258\pi\)
\(678\) −30.4959 + 25.5891i −1.17119 + 0.982742i
\(679\) 20.9378 7.62075i 0.803520 0.292457i
\(680\) 9.22294 + 3.35688i 0.353684 + 0.128730i
\(681\) −1.41198 1.18479i −0.0541072 0.0454013i
\(682\) 6.43960 36.5208i 0.246585 1.39845i
\(683\) 33.2509 1.27231 0.636155 0.771561i \(-0.280524\pi\)
0.636155 + 0.771561i \(0.280524\pi\)
\(684\) 0 0
\(685\) −25.1145 −0.959576
\(686\) 2.75403 15.6189i 0.105149 0.596332i
\(687\) −14.9204 12.5197i −0.569250 0.477657i
\(688\) 0.929712 + 0.338387i 0.0354449 + 0.0129009i
\(689\) −0.940900 + 0.342460i −0.0358454 + 0.0130467i
\(690\) 32.4972 27.2684i 1.23715 1.03809i
\(691\) −2.40466 4.16500i −0.0914776 0.158444i 0.816655 0.577126i \(-0.195826\pi\)
−0.908133 + 0.418682i \(0.862492\pi\)
\(692\) −1.99176 + 3.44983i −0.0757155 + 0.131143i
\(693\) −6.16627 34.9706i −0.234237 1.32843i
\(694\) −5.67277 32.1719i −0.215335 1.22123i
\(695\) −12.6775 + 21.9581i −0.480886 + 0.832919i
\(696\) 4.36858 + 7.56661i 0.165591 + 0.286811i
\(697\) −16.0892 + 13.5004i −0.609420 + 0.511364i
\(698\) 27.3505 9.95476i 1.03523 0.376793i
\(699\) 77.7293 + 28.2911i 2.93999 + 1.07007i
\(700\) −0.488918 0.410251i −0.0184794 0.0155060i
\(701\) 0.601633 3.41203i 0.0227234 0.128871i −0.971336 0.237711i \(-0.923603\pi\)
0.994059 + 0.108841i \(0.0347139\pi\)
\(702\) 1.53367 0.0578848
\(703\) 0 0
\(704\) 5.75621 0.216946
\(705\) 4.99809 28.3456i 0.188239 1.06756i
\(706\) −10.9582 9.19500i −0.412416 0.346058i
\(707\) 4.43641 + 1.61472i 0.166848 + 0.0607279i
\(708\) −8.69903 + 3.16619i −0.326929 + 0.118993i
\(709\) 15.7608 13.2249i 0.591910 0.496672i −0.296924 0.954901i \(-0.595961\pi\)
0.888834 + 0.458230i \(0.151516\pi\)
\(710\) −5.17647 8.96591i −0.194269 0.336484i
\(711\) −20.6019 + 35.6836i −0.772633 + 1.33824i
\(712\) −2.61801 14.8475i −0.0981142 0.556433i
\(713\) −7.24578 41.0929i −0.271357 1.53894i
\(714\) 7.50837 13.0049i 0.280994 0.486696i
\(715\) 2.05328 + 3.55639i 0.0767884 + 0.133001i
\(716\) −6.47376 + 5.43213i −0.241936 + 0.203008i
\(717\) 64.8496 23.6033i 2.42185 0.881482i
\(718\) −18.4844 6.72778i −0.689832 0.251078i
\(719\) 18.5295 + 15.5481i 0.691034 + 0.579846i 0.919207 0.393774i \(-0.128831\pi\)
−0.228173 + 0.973621i \(0.573275\pi\)
\(720\) −1.95595 + 11.0928i −0.0728940 + 0.413402i
\(721\) −24.4149 −0.909257
\(722\) 0 0
\(723\) 76.9880 2.86321
\(724\) 1.47345 8.35635i 0.0547604 0.310561i
\(725\) −1.19083 0.999226i −0.0442263 0.0371103i
\(726\) −58.1046 21.1484i −2.15647 0.784889i
\(727\) −17.0344 + 6.20001i −0.631771 + 0.229946i −0.638002 0.770035i \(-0.720239\pi\)
0.00623100 + 0.999981i \(0.498017\pi\)
\(728\) −0.299311 + 0.251152i −0.0110932 + 0.00930830i
\(729\) 21.9186 + 37.9641i 0.811800 + 1.40608i
\(730\) −2.65745 + 4.60284i −0.0983567 + 0.170359i
\(731\) −0.719204 4.07881i −0.0266007 0.150860i
\(732\) −5.31745 30.1568i −0.196539 1.11463i
\(733\) −11.3682 + 19.6902i −0.419893 + 0.727275i −0.995928 0.0901491i \(-0.971266\pi\)
0.576036 + 0.817425i \(0.304599\pi\)
\(734\) −4.77527 8.27100i −0.176258 0.305288i
\(735\) 26.8491 22.5291i 0.990344 0.830997i
\(736\) 6.08623 2.21521i 0.224342 0.0816537i
\(737\) 23.6961 + 8.62469i 0.872858 + 0.317695i
\(738\) −18.4645 15.4936i −0.679688 0.570326i
\(739\) 2.63575 14.9481i 0.0969575 0.549873i −0.897172 0.441680i \(-0.854383\pi\)
0.994130 0.108193i \(-0.0345064\pi\)
\(740\) 9.33094 0.343012
\(741\) 0 0
\(742\) −4.22545 −0.155121
\(743\) −0.568915 + 3.22648i −0.0208715 + 0.118368i −0.993463 0.114150i \(-0.963585\pi\)
0.972592 + 0.232518i \(0.0746965\pi\)
\(744\) 13.7870 + 11.5687i 0.505457 + 0.424129i
\(745\) −20.5641 7.48474i −0.753412 0.274220i
\(746\) −3.42058 + 1.24499i −0.125236 + 0.0455823i
\(747\) −35.9363 + 30.1542i −1.31484 + 1.10328i
\(748\) −12.0483 20.8683i −0.440530 0.763020i
\(749\) 6.44433 11.1619i 0.235471 0.407847i
\(750\) 5.12151 + 29.0455i 0.187011 + 1.06059i
\(751\) 9.07005 + 51.4388i 0.330971 + 1.87703i 0.463877 + 0.885899i \(0.346458\pi\)
−0.132907 + 0.991129i \(0.542431\pi\)
\(752\) 2.19723 3.80571i 0.0801246 0.138780i
\(753\) 4.17442 + 7.23030i 0.152124 + 0.263487i
\(754\) −0.729015 + 0.611716i −0.0265492 + 0.0222774i
\(755\) 43.6740 15.8960i 1.58946 0.578516i
\(756\) 6.08182 + 2.21360i 0.221194 + 0.0805079i
\(757\) −18.5645 15.5774i −0.674737 0.566172i 0.239726 0.970841i \(-0.422942\pi\)
−0.914463 + 0.404669i \(0.867387\pi\)
\(758\) 1.44951 8.22060i 0.0526487 0.298585i
\(759\) −104.151 −3.78045
\(760\) 0 0
\(761\) −24.8054 −0.899195 −0.449597 0.893231i \(-0.648433\pi\)
−0.449597 + 0.893231i \(0.648433\pi\)
\(762\) 1.08185 6.13550i 0.0391914 0.222266i
\(763\) 8.69899 + 7.29932i 0.314925 + 0.264253i
\(764\) 21.0294 + 7.65408i 0.760817 + 0.276915i
\(765\) 44.3091 16.1272i 1.60200 0.583080i
\(766\) −7.26644 + 6.09727i −0.262547 + 0.220303i
\(767\) −0.504158 0.873228i −0.0182041 0.0315304i
\(768\) −1.39680 + 2.41933i −0.0504028 + 0.0873001i
\(769\) 1.67447 + 9.49640i 0.0603830 + 0.342449i 1.00000 0.000221010i \(7.03495e-5\pi\)
−0.939617 + 0.342228i \(0.888819\pi\)
\(770\) 3.00929 + 17.0665i 0.108447 + 0.615034i
\(771\) −19.7400 + 34.1906i −0.710918 + 1.23135i
\(772\) −3.71406 6.43293i −0.133672 0.231526i
\(773\) 0.986137 0.827468i 0.0354689 0.0297619i −0.624881 0.780720i \(-0.714852\pi\)
0.660350 + 0.750958i \(0.270408\pi\)
\(774\) 4.46654 1.62569i 0.160547 0.0584342i
\(775\) −3.00904 1.09520i −0.108088 0.0393408i
\(776\) 13.2925 + 11.1538i 0.477174 + 0.400397i
\(777\) 2.47906 14.0595i 0.0889359 0.504381i
\(778\) 36.0480 1.29238
\(779\) 0 0
\(780\) −1.99300 −0.0713607
\(781\) −4.41374 + 25.0315i −0.157936 + 0.895699i
\(782\) −20.7700 17.4281i −0.742733 0.623227i
\(783\) 14.8131 + 5.39154i 0.529379 + 0.192678i
\(784\) 5.02843 1.83020i 0.179587 0.0653642i
\(785\) −24.9070 + 20.8994i −0.888967 + 0.745932i
\(786\) −2.12685 3.68381i −0.0758621 0.131397i
\(787\) 8.17232 14.1549i 0.291312 0.504567i −0.682808 0.730598i \(-0.739242\pi\)
0.974120 + 0.226031i \(0.0725749\pi\)
\(788\) 1.48218 + 8.40586i 0.0528005 + 0.299447i
\(789\) 3.67169 + 20.8232i 0.130716 + 0.741326i
\(790\) 10.0542 17.4144i 0.357714 0.619578i
\(791\) −9.14922 15.8469i −0.325309 0.563451i
\(792\) 21.1843 17.7758i 0.752752 0.631634i
\(793\) 3.13423 1.14077i 0.111300 0.0405098i
\(794\) 6.02255 + 2.19203i 0.213732 + 0.0777922i
\(795\) −16.5106 13.8541i −0.585572 0.491354i
\(796\) −1.10427 + 6.26264i −0.0391399 + 0.221974i
\(797\) −15.6884 −0.555712 −0.277856 0.960623i \(-0.589624\pi\)
−0.277856 + 0.960623i \(0.589624\pi\)
\(798\) 0 0
\(799\) −18.3960 −0.650804
\(800\) 0.0863099 0.489488i 0.00305152 0.0173060i
\(801\) −55.4854 46.5578i −1.96048 1.64504i
\(802\) −0.176343 0.0641834i −0.00622687 0.00226640i
\(803\) 12.2618 4.46293i 0.432709 0.157493i
\(804\) −9.37505 + 7.86660i −0.330633 + 0.277434i
\(805\) 9.74965 + 16.8869i 0.343630 + 0.595185i
\(806\) −0.980164 + 1.69769i −0.0345248 + 0.0597987i
\(807\) −3.72111 21.1035i −0.130989 0.742877i
\(808\) 0.638446 + 3.62081i 0.0224605 + 0.127380i
\(809\) 5.76242 9.98080i 0.202596 0.350906i −0.746768 0.665084i \(-0.768396\pi\)
0.949364 + 0.314178i \(0.101729\pi\)
\(810\) −0.389305 0.674297i −0.0136788 0.0236924i
\(811\) −6.35895 + 5.33579i −0.223293 + 0.187365i −0.747571 0.664182i \(-0.768780\pi\)
0.524278 + 0.851547i \(0.324335\pi\)
\(812\) −3.77384 + 1.37356i −0.132436 + 0.0482027i
\(813\) −30.6219 11.1454i −1.07396 0.390888i
\(814\) −17.5490 14.7253i −0.615091 0.516123i
\(815\) −5.80146 + 32.9017i −0.203216 + 1.15250i
\(816\) 11.6946 0.409392
\(817\) 0 0
\(818\) 17.2663 0.603701
\(819\) −0.325959 + 1.84860i −0.0113899 + 0.0645954i
\(820\) 9.01112 + 7.56122i 0.314682 + 0.264049i
\(821\) 31.6782 + 11.5299i 1.10558 + 0.402397i 0.829369 0.558701i \(-0.188700\pi\)
0.276208 + 0.961098i \(0.410922\pi\)
\(822\) −28.1197 + 10.2347i −0.980788 + 0.356978i
\(823\) 16.7517 14.0563i 0.583927 0.489973i −0.302307 0.953211i \(-0.597757\pi\)
0.886234 + 0.463238i \(0.153312\pi\)
\(824\) −9.50676 16.4662i −0.331184 0.573627i
\(825\) −3.99634 + 6.92186i −0.139135 + 0.240988i
\(826\) −0.738894 4.19047i −0.0257094 0.145805i
\(827\) 6.80171 + 38.5744i 0.236519 + 1.34136i 0.839392 + 0.543527i \(0.182911\pi\)
−0.602873 + 0.797837i \(0.705977\pi\)
\(828\) 15.5581 26.9474i 0.540681 0.936487i
\(829\) 7.20878 + 12.4860i 0.250371 + 0.433656i 0.963628 0.267247i \(-0.0861140\pi\)
−0.713257 + 0.700903i \(0.752781\pi\)
\(830\) 17.5378 14.7160i 0.608745 0.510798i
\(831\) −72.0348 + 26.2185i −2.49886 + 0.909511i
\(832\) −0.285932 0.104071i −0.00991291 0.00360800i
\(833\) −17.1601 14.3990i −0.594562 0.498897i
\(834\) −5.24608 + 29.7520i −0.181657 + 1.03023i
\(835\) −27.1739 −0.940392
\(836\) 0 0
\(837\) 32.4719 1.12239
\(838\) −0.299668 + 1.69950i −0.0103518 + 0.0587082i
\(839\) 16.0511 + 13.4685i 0.554145 + 0.464983i 0.876342 0.481690i \(-0.159977\pi\)
−0.322197 + 0.946673i \(0.604421\pi\)
\(840\) −7.90327 2.87656i −0.272689 0.0992506i
\(841\) 18.0594 6.57307i 0.622737 0.226658i
\(842\) 25.0914 21.0542i 0.864708 0.725576i
\(843\) −22.7280 39.3661i −0.782795 1.35584i
\(844\) 6.97890 12.0878i 0.240224 0.416079i
\(845\) 5.25501 + 29.8027i 0.180778 + 1.02524i
\(846\) −3.66605 20.7912i −0.126041 0.714816i
\(847\) 14.2109 24.6140i 0.488293 0.845748i
\(848\) −1.64532 2.84978i −0.0565006 0.0978619i
\(849\) 7.26269 6.09412i 0.249255 0.209150i
\(850\) −1.95522 + 0.711642i −0.0670635 + 0.0244091i
\(851\) −24.2220 8.81608i −0.830319 0.302211i
\(852\) −9.44970 7.92924i −0.323741 0.271651i
\(853\) 9.02194 51.1660i 0.308906 1.75189i −0.295621 0.955305i \(-0.595527\pi\)
0.604527 0.796585i \(-0.293362\pi\)
\(854\) 14.0754 0.481650
\(855\) 0 0
\(856\) 10.0373 0.343067
\(857\) 5.06765 28.7401i 0.173108 0.981743i −0.767198 0.641411i \(-0.778349\pi\)
0.940305 0.340332i \(-0.110539\pi\)
\(858\) 3.74829 + 3.14519i 0.127964 + 0.107375i
\(859\) −20.6651 7.52148i −0.705084 0.256630i −0.0355042 0.999370i \(-0.511304\pi\)
−0.669580 + 0.742740i \(0.733526\pi\)
\(860\) −2.17978 + 0.793375i −0.0743299 + 0.0270539i
\(861\) 13.7870 11.5687i 0.469861 0.394260i
\(862\) 12.7560 + 22.0940i 0.434470 + 0.752524i
\(863\) 17.9079 31.0173i 0.609590 1.05584i −0.381717 0.924279i \(-0.624667\pi\)
0.991308 0.131562i \(-0.0419994\pi\)
\(864\) 0.875238 + 4.96372i 0.0297762 + 0.168869i
\(865\) −1.62182 9.19779i −0.0551435 0.312734i
\(866\) −12.2417 + 21.2032i −0.415990 + 0.720516i
\(867\) −0.732209 1.26822i −0.0248671 0.0430711i
\(868\) −6.33720 + 5.31755i −0.215099 + 0.180489i
\(869\) −46.3914 + 16.8851i −1.57372 + 0.572787i
\(870\) −19.2496 7.00627i −0.652621 0.237535i
\(871\) −1.02114 0.856839i −0.0346000 0.0290329i
\(872\) −1.53565 + 8.70913i −0.0520038 + 0.294928i
\(873\) 83.3638 2.82144
\(874\) 0 0
\(875\) −13.5567 −0.458300
\(876\) −1.09968 + 6.23659i −0.0371547 + 0.210715i
\(877\) 5.99416 + 5.02970i 0.202409 + 0.169841i 0.738358 0.674409i \(-0.235602\pi\)
−0.535949 + 0.844250i \(0.680046\pi\)
\(878\) 28.9790 + 10.5475i 0.977994 + 0.355961i
\(879\) −61.3711 + 22.3372i −2.07000 + 0.753417i
\(880\) −10.3384 + 8.67499i −0.348509 + 0.292434i
\(881\) 7.24145 + 12.5426i 0.243970 + 0.422569i 0.961842 0.273607i \(-0.0882167\pi\)
−0.717871 + 0.696176i \(0.754883\pi\)
\(882\) 12.8540 22.2639i 0.432818 0.749663i
\(883\) −4.08992 23.1951i −0.137637 0.780577i −0.972987 0.230859i \(-0.925846\pi\)
0.835350 0.549718i \(-0.185265\pi\)
\(884\) 0.221190 + 1.25443i 0.00743944 + 0.0421912i
\(885\) 10.8522 18.7966i 0.364794 0.631842i
\(886\) −5.35234 9.27052i −0.179815 0.311449i
\(887\) −12.1599 + 10.2033i −0.408288 + 0.342594i −0.823687 0.567045i \(-0.808087\pi\)
0.415399 + 0.909639i \(0.363642\pi\)
\(888\) 10.4475 3.80257i 0.350595 0.127606i
\(889\) 2.69098 + 0.979438i 0.0902527 + 0.0328493i
\(890\) 27.0782 + 22.7213i 0.907663 + 0.761620i
\(891\) −0.331943 + 1.88254i −0.0111205 + 0.0630675i
\(892\) 8.92400 0.298798
\(893\) 0 0
\(894\) −26.0751 −0.872081
\(895\) 3.44062 19.5127i 0.115007 0.652239i
\(896\) −0.983662 0.825390i −0.0328618 0.0275743i
\(897\) 5.17357 + 1.88303i 0.172741 + 0.0628724i
\(898\) −2.17597 + 0.791987i −0.0726130 + 0.0264290i
\(899\) −15.4352 + 12.9516i −0.514792 + 0.431962i
\(900\) −1.19394 2.06797i −0.0397981 0.0689324i
\(901\) −6.88763 + 11.9297i −0.229460 + 0.397437i
\(902\) −5.01496 28.4412i −0.166980 0.946990i
\(903\) 0.616296 + 3.49519i 0.0205090 + 0.116313i
\(904\) 7.12512 12.3411i 0.236978 0.410458i
\(905\) 9.94718 + 17.2290i 0.330655 + 0.572712i
\(906\) 42.4221 35.5963i 1.40938 1.18261i
\(907\) −42.2981 + 15.3953i −1.40449 + 0.511191i −0.929506 0.368806i \(-0.879767\pi\)
−0.474979 + 0.879997i \(0.657544\pi\)
\(908\) 0.620005 + 0.225663i 0.0205756 + 0.00748890i
\(909\) 13.5311 + 11.3539i 0.448797 + 0.376585i
\(910\) 0.159076 0.902162i 0.00527330 0.0299064i
\(911\) −2.75901 −0.0914100 −0.0457050 0.998955i \(-0.514553\pi\)
−0.0457050 + 0.998955i \(0.514553\pi\)
\(912\) 0 0
\(913\) −56.2074 −1.86019
\(914\) −0.00906113 + 0.0513882i −0.000299716 + 0.00169977i
\(915\) 54.9986 + 46.1493i 1.81820 + 1.52565i
\(916\) 6.55161 + 2.38459i 0.216471 + 0.0787891i
\(917\) 1.83730 0.668721i 0.0606728 0.0220831i
\(918\) 16.1633 13.5626i 0.533467 0.447632i
\(919\) 19.6542 + 34.0420i 0.648331 + 1.12294i 0.983521 + 0.180792i \(0.0578660\pi\)
−0.335191 + 0.942150i \(0.608801\pi\)
\(920\) −7.59272 + 13.1510i −0.250325 + 0.433575i
\(921\) −0.673335 3.81867i −0.0221871 0.125829i
\(922\) 6.85424 + 38.8724i 0.225733 + 1.28019i
\(923\) 0.671809 1.16361i 0.0221129 0.0383006i
\(924\) 10.3244 + 17.8823i 0.339647 + 0.588286i
\(925\) −1.51532 + 1.27151i −0.0498235 + 0.0418069i
\(926\) 5.81723 2.11730i 0.191166 0.0695787i
\(927\) −85.8365 31.2419i −2.81924 1.02612i
\(928\) −2.39585 2.01036i −0.0786476 0.0659932i
\(929\) −5.16460 + 29.2899i −0.169445 + 0.960970i 0.774917 + 0.632063i \(0.217792\pi\)
−0.944362 + 0.328907i \(0.893320\pi\)
\(930\) −42.1970 −1.38369
\(931\) 0 0
\(932\) −29.6097 −0.969898
\(933\) −5.91354 + 33.5374i −0.193601 + 1.09796i
\(934\) −16.0840 13.4961i −0.526284 0.441605i
\(935\) 53.0892 + 19.3229i 1.73620 + 0.631926i
\(936\) −1.37368 + 0.499979i −0.0449002 + 0.0163423i
\(937\) 28.8960 24.2467i 0.943993 0.792104i −0.0342830 0.999412i \(-0.510915\pi\)
0.978276 + 0.207308i \(0.0664703\pi\)
\(938\) −2.81266 4.87166i −0.0918365 0.159065i
\(939\) −23.0911 + 39.9950i −0.753550 + 1.30519i
\(940\) 1.78912 + 10.1466i 0.0583547 + 0.330946i
\(941\) −1.12464 6.37813i −0.0366621 0.207921i 0.960974 0.276638i \(-0.0892204\pi\)
−0.997636 + 0.0687174i \(0.978109\pi\)
\(942\) −19.3703 + 33.5504i −0.631120 + 1.09313i
\(943\) −16.2477 28.1419i −0.529099 0.916427i
\(944\) 2.53848 2.13004i 0.0826205 0.0693268i
\(945\) −14.2593 + 5.18996i −0.463855 + 0.168829i
\(946\) 5.35162 + 1.94783i 0.173996 + 0.0633294i
\(947\) 12.4798 + 10.4718i 0.405541 + 0.340289i 0.822631 0.568576i \(-0.192506\pi\)
−0.417090 + 0.908865i \(0.636950\pi\)
\(948\) 4.16054 23.5956i 0.135128 0.766349i
\(949\) −0.689776 −0.0223911
\(950\) 0 0
\(951\) 7.50953 0.243513
\(952\) −0.933429 + 5.29374i −0.0302526 + 0.171571i
\(953\) −26.5215 22.2542i −0.859115 0.720883i 0.102662 0.994716i \(-0.467264\pi\)
−0.961777 + 0.273833i \(0.911708\pi\)
\(954\) −14.8556 5.40699i −0.480968 0.175058i
\(955\) −49.3050 + 17.9456i −1.59547 + 0.580705i
\(956\) −18.9239 + 15.8790i −0.612043 + 0.513565i
\(957\) 25.1465 + 43.5550i 0.812871 + 1.40793i
\(958\) −7.76147 + 13.4433i −0.250762 + 0.434332i
\(959\) −2.38848 13.5458i −0.0771282 0.437416i
\(960\) −1.13736 6.45031i −0.0367083 0.208183i
\(961\) −5.25267 + 9.09789i −0.169441 + 0.293480i
\(962\) 0.605491 + 1.04874i 0.0195218 + 0.0338128i
\(963\) 36.9397 30.9961i 1.19037 0.998835i
\(964\) −25.8967 + 9.42561i −0.834075 + 0.303579i
\(965\) 16.3655 + 5.95655i 0.526823 + 0.191748i
\(966\) 17.7981 + 14.9344i 0.572644 + 0.480506i
\(967\) −8.49322 + 48.1674i −0.273124 + 1.54896i 0.471736 + 0.881740i \(0.343627\pi\)
−0.744860 + 0.667221i \(0.767484\pi\)
\(968\) 22.1340 0.711414
\(969\) 0 0
\(970\) −40.6835 −1.30627
\(971\) 1.05507 5.98361i 0.0338589 0.192023i −0.963187 0.268833i \(-0.913362\pi\)
0.997046 + 0.0768093i \(0.0244733\pi\)
\(972\) −12.2939 10.3158i −0.394329 0.330881i
\(973\) −13.0490 4.74945i −0.418332 0.152260i
\(974\) 26.8814 9.78401i 0.861334 0.313500i
\(975\) 0.323658 0.271581i 0.0103654 0.00869756i
\(976\) 5.48073 + 9.49290i 0.175434 + 0.303860i
\(977\) −28.5239 + 49.4048i −0.912559 + 1.58060i −0.102124 + 0.994772i \(0.532564\pi\)
−0.810436 + 0.585828i \(0.800770\pi\)
\(978\) 6.91254 + 39.2030i 0.221039 + 1.25357i
\(979\) −15.0698 85.4653i −0.481634 2.73148i
\(980\) −6.27308 + 10.8653i −0.200386 + 0.347079i
\(981\) 21.2430 + 36.7940i 0.678238 + 1.17474i
\(982\) −23.2486 + 19.5079i −0.741891 + 0.622521i
\(983\) −0.175271 + 0.0637934i −0.00559028 + 0.00203469i −0.344814 0.938671i \(-0.612058\pi\)
0.339223 + 0.940706i \(0.389836\pi\)
\(984\) 13.1708 + 4.79377i 0.419869 + 0.152820i
\(985\) −15.3303 12.8636i −0.488462 0.409869i
\(986\) −2.27350 + 12.8937i −0.0724030 + 0.410618i
\(987\) 15.7638 0.501768
\(988\) 0 0
\(989\) 6.40804 0.203764
\(990\) −11.2589 + 63.8523i −0.357831 + 2.02936i
\(991\) −35.4218 29.7224i −1.12521 0.944163i −0.126354 0.991985i \(-0.540327\pi\)
−0.998856 + 0.0478224i \(0.984772\pi\)
\(992\) −6.05394 2.20345i −0.192213 0.0699597i
\(993\) −13.6849 + 4.98089i −0.434276 + 0.158064i
\(994\) 4.34355 3.64467i 0.137769 0.115602i
\(995\) −7.45488 12.9122i −0.236336 0.409345i
\(996\) 13.6393 23.6239i 0.432177 0.748553i
\(997\) −3.62039 20.5323i −0.114659 0.650263i −0.986918 0.161220i \(-0.948457\pi\)
0.872260 0.489043i \(-0.162654\pi\)
\(998\) 1.52398 + 8.64291i 0.0482407 + 0.273586i
\(999\) 10.0297 17.3719i 0.317325 0.549623i
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 722.2.e.r.245.4 24
19.2 odd 18 722.2.c.n.429.4 8
19.3 odd 18 722.2.a.m.1.1 4
19.4 even 9 inner 722.2.e.r.595.1 24
19.5 even 9 722.2.c.m.653.1 8
19.6 even 9 inner 722.2.e.r.99.4 24
19.7 even 3 inner 722.2.e.r.415.1 24
19.8 odd 6 722.2.e.s.423.1 24
19.9 even 9 inner 722.2.e.r.389.4 24
19.10 odd 18 722.2.e.s.389.1 24
19.11 even 3 inner 722.2.e.r.423.4 24
19.12 odd 6 722.2.e.s.415.4 24
19.13 odd 18 722.2.e.s.99.1 24
19.14 odd 18 722.2.c.n.653.4 8
19.15 odd 18 722.2.e.s.595.4 24
19.16 even 9 722.2.a.n.1.4 yes 4
19.17 even 9 722.2.c.m.429.1 8
19.18 odd 2 722.2.e.s.245.1 24
57.35 odd 18 6498.2.a.bx.1.3 4
57.41 even 18 6498.2.a.ca.1.3 4
76.3 even 18 5776.2.a.bv.1.4 4
76.35 odd 18 5776.2.a.bt.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
722.2.a.m.1.1 4 19.3 odd 18
722.2.a.n.1.4 yes 4 19.16 even 9
722.2.c.m.429.1 8 19.17 even 9
722.2.c.m.653.1 8 19.5 even 9
722.2.c.n.429.4 8 19.2 odd 18
722.2.c.n.653.4 8 19.14 odd 18
722.2.e.r.99.4 24 19.6 even 9 inner
722.2.e.r.245.4 24 1.1 even 1 trivial
722.2.e.r.389.4 24 19.9 even 9 inner
722.2.e.r.415.1 24 19.7 even 3 inner
722.2.e.r.423.4 24 19.11 even 3 inner
722.2.e.r.595.1 24 19.4 even 9 inner
722.2.e.s.99.1 24 19.13 odd 18
722.2.e.s.245.1 24 19.18 odd 2
722.2.e.s.389.1 24 19.10 odd 18
722.2.e.s.415.4 24 19.12 odd 6
722.2.e.s.423.1 24 19.8 odd 6
722.2.e.s.595.4 24 19.15 odd 18
5776.2.a.bt.1.1 4 76.35 odd 18
5776.2.a.bv.1.4 4 76.3 even 18
6498.2.a.bx.1.3 4 57.35 odd 18
6498.2.a.ca.1.3 4 57.41 even 18