Properties

Label 950.2.n.b.39.13
Level $950$
Weight $2$
Character 950.39
Analytic conductor $7.586$
Analytic rank $0$
Dimension $96$
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] = [950,2,Mod(39,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.39");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.n (of order \(10\), degree \(4\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 39.13
Character \(\chi\) \(=\) 950.39
Dual form 950.2.n.b.609.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.587785 + 0.809017i) q^{2} +(-3.02842 - 0.983992i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.06990 + 1.96349i) q^{5} +(-0.983992 - 3.02842i) q^{6} -2.61307i q^{7} +(-0.951057 + 0.309017i) q^{8} +(5.77601 + 4.19652i) q^{9} +O(q^{10})\) \(q+(0.587785 + 0.809017i) q^{2} +(-3.02842 - 0.983992i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(1.06990 + 1.96349i) q^{5} +(-0.983992 - 3.02842i) q^{6} -2.61307i q^{7} +(-0.951057 + 0.309017i) q^{8} +(5.77601 + 4.19652i) q^{9} +(-0.959627 + 2.01968i) q^{10} +(-3.99793 + 2.90467i) q^{11} +(1.87166 - 2.57612i) q^{12} +(4.02848 - 5.54473i) q^{13} +(2.11402 - 1.53592i) q^{14} +(-1.30805 - 6.99905i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(0.979111 - 0.318132i) q^{17} +7.13954i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-2.19801 + 0.410785i) q^{20} +(-2.57124 + 7.91346i) q^{21} +(-4.69985 - 1.52707i) q^{22} +(3.77282 + 5.19284i) q^{23} +3.18427 q^{24} +(-2.71062 + 4.20149i) q^{25} +6.85367 q^{26} +(-7.74784 - 10.6640i) q^{27} +(2.48518 + 0.807483i) q^{28} +(0.0633261 - 0.194898i) q^{29} +(4.89350 - 5.17217i) q^{30} +(-0.453143 - 1.39463i) q^{31} -1.00000i q^{32} +(14.9656 - 4.86260i) q^{33} +(0.832882 + 0.605124i) q^{34} +(5.13075 - 2.79573i) q^{35} +(-5.77601 + 4.19652i) q^{36} +(-4.32899 + 5.95834i) q^{37} +(0.587785 - 0.809017i) q^{38} +(-17.6559 + 12.8278i) q^{39} +(-1.62429 - 1.53678i) q^{40} +(6.78402 + 4.92888i) q^{41} +(-7.91346 + 2.57124i) q^{42} +10.3569i q^{43} +(-1.52707 - 4.69985i) q^{44} +(-2.06007 + 15.8310i) q^{45} +(-1.98349 + 6.10455i) q^{46} +(3.27161 + 1.06301i) q^{47} +(1.87166 + 2.57612i) q^{48} +0.171866 q^{49} +(-4.99234 + 0.276641i) q^{50} -3.27820 q^{51} +(4.02848 + 5.54473i) q^{52} +(9.72507 + 3.15987i) q^{53} +(4.07328 - 12.5363i) q^{54} +(-9.98069 - 4.74220i) q^{55} +(0.807483 + 2.48518i) q^{56} +3.18427i q^{57} +(0.194898 - 0.0633261i) q^{58} +(8.94530 + 6.49914i) q^{59} +(7.06070 + 0.918799i) q^{60} +(-4.00965 + 2.91318i) q^{61} +(0.861929 - 1.18634i) q^{62} +(10.9658 - 15.0931i) q^{63} +(0.809017 - 0.587785i) q^{64} +(15.1971 + 1.97758i) q^{65} +(12.7305 + 9.24922i) q^{66} +(-1.72989 + 0.562077i) q^{67} +1.02950i q^{68} +(-6.31595 - 19.4385i) q^{69} +(5.27757 + 2.50757i) q^{70} +(-1.68685 + 5.19158i) q^{71} +(-6.79011 - 2.20624i) q^{72} +(-0.796674 - 1.09653i) q^{73} -7.36491 q^{74} +(12.3431 - 10.0566i) q^{75} +1.00000 q^{76} +(7.59009 + 10.4469i) q^{77} +(-20.7558 - 6.74395i) q^{78} +(-0.267074 + 0.821970i) q^{79} +(0.288543 - 2.21737i) q^{80} +(6.35168 + 19.5485i) q^{81} +8.38551i q^{82} +(-6.89062 + 2.23890i) q^{83} +(-6.73159 - 4.89079i) q^{84} +(1.67220 + 1.58211i) q^{85} +(-8.37894 + 6.08765i) q^{86} +(-0.383555 + 0.527919i) q^{87} +(2.90467 - 3.99793i) q^{88} +(-12.1055 + 8.79515i) q^{89} +(-14.0185 + 7.63862i) q^{90} +(-14.4888 - 10.5267i) q^{91} +(-6.10455 + 1.98349i) q^{92} +4.66941i q^{93} +(1.06301 + 3.27161i) q^{94} +(1.53678 - 1.62429i) q^{95} +(-0.983992 + 3.02842i) q^{96} +(8.78055 + 2.85297i) q^{97} +(0.101020 + 0.139043i) q^{98} -35.2816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 96 q + 24 q^{4} + 8 q^{5} - 6 q^{6} + 34 q^{9} - 24 q^{11} + 10 q^{12} + 10 q^{14} - 8 q^{15} - 24 q^{16} + 30 q^{17} + 24 q^{19} + 2 q^{20} - 24 q^{24} - 60 q^{25} + 84 q^{26} - 30 q^{27} - 10 q^{28} - 4 q^{29} + 16 q^{30} - 14 q^{31} + 100 q^{33} + 8 q^{34} + 42 q^{35} - 34 q^{36} - 30 q^{37} + 32 q^{39} + 12 q^{41} + 10 q^{42} + 4 q^{44} - 18 q^{45} - 10 q^{46} + 10 q^{48} - 132 q^{49} - 36 q^{50} + 36 q^{51} + 30 q^{53} + 24 q^{54} - 4 q^{55} - 10 q^{56} + 60 q^{58} + 16 q^{59} + 8 q^{60} + 42 q^{61} - 110 q^{63} + 24 q^{64} + 12 q^{65} - 20 q^{66} + 130 q^{67} - 8 q^{69} + 20 q^{70} - 8 q^{71} - 120 q^{73} - 124 q^{74} - 24 q^{75} + 96 q^{76} - 50 q^{78} + 4 q^{79} - 2 q^{80} - 10 q^{81} - 70 q^{83} + 52 q^{85} - 44 q^{86} - 70 q^{87} + 10 q^{88} - 26 q^{89} + 32 q^{90} - 4 q^{91} - 10 q^{92} + 10 q^{94} + 2 q^{95} - 6 q^{96} - 10 q^{97} - 60 q^{98} - 184 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(e\left(\frac{3}{10}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.587785 + 0.809017i 0.415627 + 0.572061i
\(3\) −3.02842 0.983992i −1.74846 0.568108i −0.752553 0.658531i \(-0.771178\pi\)
−0.995903 + 0.0904232i \(0.971178\pi\)
\(4\) −0.309017 + 0.951057i −0.154508 + 0.475528i
\(5\) 1.06990 + 1.96349i 0.478475 + 0.878101i
\(6\) −0.983992 3.02842i −0.401713 1.23635i
\(7\) 2.61307i 0.987648i −0.869562 0.493824i \(-0.835599\pi\)
0.869562 0.493824i \(-0.164401\pi\)
\(8\) −0.951057 + 0.309017i −0.336249 + 0.109254i
\(9\) 5.77601 + 4.19652i 1.92534 + 1.39884i
\(10\) −0.959627 + 2.01968i −0.303461 + 0.638680i
\(11\) −3.99793 + 2.90467i −1.20542 + 0.875790i −0.994807 0.101780i \(-0.967546\pi\)
−0.210614 + 0.977569i \(0.567546\pi\)
\(12\) 1.87166 2.57612i 0.540303 0.743663i
\(13\) 4.02848 5.54473i 1.11730 1.53783i 0.307103 0.951676i \(-0.400641\pi\)
0.810198 0.586156i \(-0.199359\pi\)
\(14\) 2.11402 1.53592i 0.564995 0.410493i
\(15\) −1.30805 6.99905i −0.337736 1.80715i
\(16\) −0.809017 0.587785i −0.202254 0.146946i
\(17\) 0.979111 0.318132i 0.237469 0.0771585i −0.187865 0.982195i \(-0.560157\pi\)
0.425334 + 0.905036i \(0.360157\pi\)
\(18\) 7.13954i 1.68281i
\(19\) −0.309017 0.951057i −0.0708934 0.218187i
\(20\) −2.19801 + 0.410785i −0.491490 + 0.0918543i
\(21\) −2.57124 + 7.91346i −0.561091 + 1.72686i
\(22\) −4.69985 1.52707i −1.00201 0.325573i
\(23\) 3.77282 + 5.19284i 0.786687 + 1.08278i 0.994513 + 0.104616i \(0.0333615\pi\)
−0.207825 + 0.978166i \(0.566639\pi\)
\(24\) 3.18427 0.649985
\(25\) −2.71062 + 4.20149i −0.542123 + 0.840299i
\(26\) 6.85367 1.34411
\(27\) −7.74784 10.6640i −1.49107 2.05228i
\(28\) 2.48518 + 0.807483i 0.469654 + 0.152600i
\(29\) 0.0633261 0.194898i 0.0117594 0.0361916i −0.945005 0.327057i \(-0.893943\pi\)
0.956764 + 0.290865i \(0.0939431\pi\)
\(30\) 4.89350 5.17217i 0.893427 0.944305i
\(31\) −0.453143 1.39463i −0.0813868 0.250483i 0.902081 0.431567i \(-0.142039\pi\)
−0.983468 + 0.181084i \(0.942039\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 14.9656 4.86260i 2.60517 0.846471i
\(34\) 0.832882 + 0.605124i 0.142838 + 0.103778i
\(35\) 5.13075 2.79573i 0.867254 0.472565i
\(36\) −5.77601 + 4.19652i −0.962669 + 0.699420i
\(37\) −4.32899 + 5.95834i −0.711681 + 0.979545i 0.288078 + 0.957607i \(0.406984\pi\)
−0.999759 + 0.0219379i \(0.993016\pi\)
\(38\) 0.587785 0.809017i 0.0953514 0.131240i
\(39\) −17.6559 + 12.8278i −2.82721 + 2.05409i
\(40\) −1.62429 1.53678i −0.256823 0.242986i
\(41\) 6.78402 + 4.92888i 1.05949 + 0.769762i 0.973993 0.226577i \(-0.0727535\pi\)
0.0854930 + 0.996339i \(0.472753\pi\)
\(42\) −7.91346 + 2.57124i −1.22107 + 0.396751i
\(43\) 10.3569i 1.57942i 0.613482 + 0.789709i \(0.289768\pi\)
−0.613482 + 0.789709i \(0.710232\pi\)
\(44\) −1.52707 4.69985i −0.230215 0.708529i
\(45\) −2.06007 + 15.8310i −0.307097 + 2.35995i
\(46\) −1.98349 + 6.10455i −0.292450 + 0.900067i
\(47\) 3.27161 + 1.06301i 0.477214 + 0.155056i 0.537741 0.843110i \(-0.319278\pi\)
−0.0605266 + 0.998167i \(0.519278\pi\)
\(48\) 1.87166 + 2.57612i 0.270151 + 0.371832i
\(49\) 0.171866 0.0245523
\(50\) −4.99234 + 0.276641i −0.706024 + 0.0391230i
\(51\) −3.27820 −0.459039
\(52\) 4.02848 + 5.54473i 0.558650 + 0.768916i
\(53\) 9.72507 + 3.15987i 1.33584 + 0.434041i 0.887906 0.460025i \(-0.152159\pi\)
0.447935 + 0.894066i \(0.352159\pi\)
\(54\) 4.07328 12.5363i 0.554303 1.70597i
\(55\) −9.98069 4.74220i −1.34580 0.639438i
\(56\) 0.807483 + 2.48518i 0.107904 + 0.332096i
\(57\) 3.18427i 0.421766i
\(58\) 0.194898 0.0633261i 0.0255913 0.00831512i
\(59\) 8.94530 + 6.49914i 1.16458 + 0.846116i 0.990350 0.138589i \(-0.0442566\pi\)
0.174229 + 0.984705i \(0.444257\pi\)
\(60\) 7.06070 + 0.918799i 0.911533 + 0.118616i
\(61\) −4.00965 + 2.91318i −0.513383 + 0.372995i −0.814106 0.580717i \(-0.802772\pi\)
0.300722 + 0.953712i \(0.402772\pi\)
\(62\) 0.861929 1.18634i 0.109465 0.150666i
\(63\) 10.9658 15.0931i 1.38156 1.90155i
\(64\) 0.809017 0.587785i 0.101127 0.0734732i
\(65\) 15.1971 + 1.97758i 1.88497 + 0.245289i
\(66\) 12.7305 + 9.24922i 1.56701 + 1.13850i
\(67\) −1.72989 + 0.562077i −0.211340 + 0.0686686i −0.412774 0.910834i \(-0.635440\pi\)
0.201434 + 0.979502i \(0.435440\pi\)
\(68\) 1.02950i 0.124845i
\(69\) −6.31595 19.4385i −0.760352 2.34012i
\(70\) 5.27757 + 2.50757i 0.630790 + 0.299712i
\(71\) −1.68685 + 5.19158i −0.200192 + 0.616128i 0.799685 + 0.600420i \(0.205000\pi\)
−0.999877 + 0.0157074i \(0.995000\pi\)
\(72\) −6.79011 2.20624i −0.800222 0.260008i
\(73\) −0.796674 1.09653i −0.0932436 0.128339i 0.759846 0.650103i \(-0.225274\pi\)
−0.853090 + 0.521764i \(0.825274\pi\)
\(74\) −7.36491 −0.856154
\(75\) 12.3431 10.0566i 1.42526 1.16124i
\(76\) 1.00000 0.114708
\(77\) 7.59009 + 10.4469i 0.864971 + 1.19053i
\(78\) −20.7558 6.74395i −2.35013 0.763602i
\(79\) −0.267074 + 0.821970i −0.0300482 + 0.0924788i −0.964956 0.262412i \(-0.915482\pi\)
0.934908 + 0.354891i \(0.115482\pi\)
\(80\) 0.288543 2.21737i 0.0322601 0.247910i
\(81\) 6.35168 + 19.5485i 0.705742 + 2.17205i
\(82\) 8.38551i 0.926025i
\(83\) −6.89062 + 2.23890i −0.756343 + 0.245751i −0.661708 0.749761i \(-0.730168\pi\)
−0.0946348 + 0.995512i \(0.530168\pi\)
\(84\) −6.73159 4.89079i −0.734477 0.533629i
\(85\) 1.67220 + 1.58211i 0.181376 + 0.171604i
\(86\) −8.37894 + 6.08765i −0.903524 + 0.656449i
\(87\) −0.383555 + 0.527919i −0.0411214 + 0.0565988i
\(88\) 2.90467 3.99793i 0.309638 0.426181i
\(89\) −12.1055 + 8.79515i −1.28318 + 0.932284i −0.999644 0.0266777i \(-0.991507\pi\)
−0.283535 + 0.958962i \(0.591507\pi\)
\(90\) −14.0185 + 7.63862i −1.47767 + 0.805181i
\(91\) −14.4888 10.5267i −1.51884 1.10350i
\(92\) −6.10455 + 1.98349i −0.636444 + 0.206793i
\(93\) 4.66941i 0.484195i
\(94\) 1.06301 + 3.27161i 0.109641 + 0.337441i
\(95\) 1.53678 1.62429i 0.157670 0.166649i
\(96\) −0.983992 + 3.02842i −0.100428 + 0.309086i
\(97\) 8.78055 + 2.85297i 0.891530 + 0.289676i 0.718737 0.695282i \(-0.244721\pi\)
0.172793 + 0.984958i \(0.444721\pi\)
\(98\) 0.101020 + 0.139043i 0.0102046 + 0.0140454i
\(99\) −35.2816 −3.54593
\(100\) −3.15823 3.87628i −0.315823 0.387628i
\(101\) −6.86878 −0.683469 −0.341735 0.939796i \(-0.611014\pi\)
−0.341735 + 0.939796i \(0.611014\pi\)
\(102\) −1.92687 2.65212i −0.190789 0.262599i
\(103\) 14.8654 + 4.83008i 1.46474 + 0.475922i 0.929513 0.368789i \(-0.120228\pi\)
0.535223 + 0.844711i \(0.320228\pi\)
\(104\) −2.11790 + 6.51823i −0.207677 + 0.639165i
\(105\) −18.2890 + 3.41802i −1.78482 + 0.333565i
\(106\) 3.15987 + 9.72507i 0.306913 + 0.944583i
\(107\) 17.8003i 1.72082i −0.509604 0.860409i \(-0.670208\pi\)
0.509604 0.860409i \(-0.329792\pi\)
\(108\) 12.5363 4.07328i 1.20630 0.391951i
\(109\) −6.38975 4.64242i −0.612027 0.444664i 0.238101 0.971241i \(-0.423475\pi\)
−0.850127 + 0.526577i \(0.823475\pi\)
\(110\) −2.02998 10.8619i −0.193551 1.03565i
\(111\) 18.9729 13.7846i 1.80083 1.30838i
\(112\) −1.53592 + 2.11402i −0.145131 + 0.199756i
\(113\) −0.241792 + 0.332798i −0.0227459 + 0.0313070i −0.820238 0.572022i \(-0.806159\pi\)
0.797493 + 0.603329i \(0.206159\pi\)
\(114\) −2.57612 + 1.87166i −0.241276 + 0.175297i
\(115\) −6.15956 + 12.9637i −0.574382 + 1.20888i
\(116\) 0.165790 + 0.120453i 0.0153932 + 0.0111838i
\(117\) 46.5372 15.1208i 4.30236 1.39792i
\(118\) 11.0570i 1.01788i
\(119\) −0.831302 2.55849i −0.0762054 0.234536i
\(120\) 3.40685 + 6.25229i 0.311002 + 0.570753i
\(121\) 4.14717 12.7637i 0.377015 1.16033i
\(122\) −4.71363 1.53155i −0.426752 0.138660i
\(123\) −15.6949 21.6021i −1.41516 1.94780i
\(124\) 1.46640 0.131687
\(125\) −11.1497 0.827090i −0.997260 0.0739772i
\(126\) 18.6561 1.66202
\(127\) −3.51955 4.84424i −0.312309 0.429857i 0.623790 0.781592i \(-0.285592\pi\)
−0.936100 + 0.351735i \(0.885592\pi\)
\(128\) 0.951057 + 0.309017i 0.0840623 + 0.0273135i
\(129\) 10.1911 31.3651i 0.897280 2.76154i
\(130\) 7.33276 + 13.4571i 0.643125 + 1.18027i
\(131\) 0.900063 + 2.77011i 0.0786388 + 0.242025i 0.982646 0.185493i \(-0.0593881\pi\)
−0.904007 + 0.427518i \(0.859388\pi\)
\(132\) 15.7357i 1.36962i
\(133\) −2.48518 + 0.807483i −0.215492 + 0.0700177i
\(134\) −1.47154 1.06913i −0.127121 0.0923591i
\(135\) 12.6492 26.6223i 1.08867 2.29128i
\(136\) −0.832882 + 0.605124i −0.0714190 + 0.0518889i
\(137\) 7.72206 10.6285i 0.659740 0.908054i −0.339733 0.940522i \(-0.610337\pi\)
0.999473 + 0.0324679i \(0.0103367\pi\)
\(138\) 12.0137 16.5354i 1.02267 1.40759i
\(139\) 5.03123 3.65540i 0.426743 0.310047i −0.353602 0.935396i \(-0.615043\pi\)
0.780345 + 0.625349i \(0.215043\pi\)
\(140\) 1.07341 + 5.74356i 0.0907197 + 0.485419i
\(141\) −8.86181 6.43848i −0.746299 0.542218i
\(142\) −5.19158 + 1.68685i −0.435668 + 0.141557i
\(143\) 33.8689i 2.83226i
\(144\) −2.20624 6.79011i −0.183853 0.565842i
\(145\) 0.450433 0.0841811i 0.0374064 0.00699086i
\(146\) 0.418836 1.28905i 0.0346631 0.106682i
\(147\) −0.520483 0.169115i −0.0429287 0.0139484i
\(148\) −4.32899 5.95834i −0.355840 0.489772i
\(149\) 9.08826 0.744540 0.372270 0.928125i \(-0.378580\pi\)
0.372270 + 0.928125i \(0.378580\pi\)
\(150\) 15.3911 + 4.07464i 1.25668 + 0.332693i
\(151\) 22.0158 1.79162 0.895808 0.444440i \(-0.146597\pi\)
0.895808 + 0.444440i \(0.146597\pi\)
\(152\) 0.587785 + 0.809017i 0.0476757 + 0.0656199i
\(153\) 6.99041 + 2.27132i 0.565141 + 0.183625i
\(154\) −3.99035 + 12.2810i −0.321551 + 0.989633i
\(155\) 2.25353 2.38186i 0.181008 0.191316i
\(156\) −6.74395 20.7558i −0.539949 1.66179i
\(157\) 4.18116i 0.333693i 0.985983 + 0.166846i \(0.0533584\pi\)
−0.985983 + 0.166846i \(0.946642\pi\)
\(158\) −0.821970 + 0.267074i −0.0653924 + 0.0212473i
\(159\) −26.3423 19.1388i −2.08908 1.51780i
\(160\) 1.96349 1.06990i 0.155228 0.0845832i
\(161\) 13.5693 9.85864i 1.06941 0.776970i
\(162\) −12.0816 + 16.6289i −0.949221 + 1.30649i
\(163\) 7.91066 10.8881i 0.619611 0.852821i −0.377714 0.925922i \(-0.623290\pi\)
0.997325 + 0.0731013i \(0.0232897\pi\)
\(164\) −6.78402 + 4.92888i −0.529743 + 0.384881i
\(165\) 25.5594 + 24.1823i 1.98980 + 1.88259i
\(166\) −5.86151 4.25863i −0.454941 0.330534i
\(167\) 6.64274 2.15836i 0.514031 0.167019i −0.0405038 0.999179i \(-0.512896\pi\)
0.554535 + 0.832161i \(0.312896\pi\)
\(168\) 8.32071i 0.641956i
\(169\) −10.4982 32.3100i −0.807551 2.48539i
\(170\) −0.297055 + 2.28278i −0.0227831 + 0.175081i
\(171\) 2.20624 6.79011i 0.168715 0.519253i
\(172\) −9.85003 3.20047i −0.751058 0.244033i
\(173\) −4.21906 5.80704i −0.320769 0.441501i 0.617933 0.786231i \(-0.287970\pi\)
−0.938702 + 0.344730i \(0.887970\pi\)
\(174\) −0.652543 −0.0494692
\(175\) 10.9788 + 7.08303i 0.829919 + 0.535427i
\(176\) 4.94171 0.372496
\(177\) −20.6950 28.4842i −1.55553 2.14100i
\(178\) −14.2309 4.62388i −1.06665 0.346575i
\(179\) −5.20794 + 16.0284i −0.389260 + 1.19802i 0.544082 + 0.839032i \(0.316878\pi\)
−0.933342 + 0.358987i \(0.883122\pi\)
\(180\) −14.4196 6.85130i −1.07477 0.510666i
\(181\) 0.817864 + 2.51713i 0.0607913 + 0.187097i 0.976840 0.213970i \(-0.0686395\pi\)
−0.916049 + 0.401067i \(0.868640\pi\)
\(182\) 17.9091i 1.32751i
\(183\) 15.0094 4.87686i 1.10953 0.360508i
\(184\) −5.19284 3.77282i −0.382821 0.278136i
\(185\) −16.3308 2.12510i −1.20066 0.156240i
\(186\) −3.77763 + 2.74461i −0.276989 + 0.201245i
\(187\) −2.99035 + 4.11586i −0.218676 + 0.300982i
\(188\) −2.02197 + 2.78300i −0.147467 + 0.202971i
\(189\) −27.8657 + 20.2456i −2.02693 + 1.47265i
\(190\) 2.21737 + 0.288543i 0.160865 + 0.0209331i
\(191\) 16.5634 + 12.0340i 1.19849 + 0.870751i 0.994135 0.108147i \(-0.0344916\pi\)
0.204351 + 0.978898i \(0.434492\pi\)
\(192\) −3.02842 + 0.983992i −0.218557 + 0.0710135i
\(193\) 4.95542i 0.356699i 0.983967 + 0.178349i \(0.0570757\pi\)
−0.983967 + 0.178349i \(0.942924\pi\)
\(194\) 2.85297 + 8.78055i 0.204832 + 0.630407i
\(195\) −44.0773 20.9428i −3.15644 1.49975i
\(196\) −0.0531096 + 0.163455i −0.00379354 + 0.0116753i
\(197\) −3.96584 1.28858i −0.282554 0.0918075i 0.164311 0.986409i \(-0.447460\pi\)
−0.446866 + 0.894601i \(0.647460\pi\)
\(198\) −20.7380 28.5434i −1.47378 2.02849i
\(199\) 14.1230 1.00115 0.500577 0.865692i \(-0.333121\pi\)
0.500577 + 0.865692i \(0.333121\pi\)
\(200\) 1.27962 4.83349i 0.0904826 0.341779i
\(201\) 5.79192 0.408530
\(202\) −4.03737 5.55696i −0.284068 0.390986i
\(203\) −0.509281 0.165475i −0.0357445 0.0116141i
\(204\) 1.01302 3.11775i 0.0709255 0.218286i
\(205\) −2.41958 + 18.5938i −0.168991 + 1.29865i
\(206\) 4.83008 + 14.8654i 0.336527 + 1.03572i
\(207\) 45.8266i 3.18517i
\(208\) −6.51823 + 2.11790i −0.451958 + 0.146850i
\(209\) 3.99793 + 2.90467i 0.276543 + 0.200920i
\(210\) −13.5152 12.7871i −0.932641 0.882391i
\(211\) −8.68983 + 6.31353i −0.598233 + 0.434641i −0.845251 0.534369i \(-0.820549\pi\)
0.247018 + 0.969011i \(0.420549\pi\)
\(212\) −6.01043 + 8.27264i −0.412798 + 0.568167i
\(213\) 10.2170 14.0624i 0.700054 0.963542i
\(214\) 14.4007 10.4627i 0.984414 0.715219i
\(215\) −20.3358 + 11.0809i −1.38689 + 0.755712i
\(216\) 10.6640 + 7.74784i 0.725592 + 0.527173i
\(217\) −3.64426 + 1.18409i −0.247389 + 0.0803815i
\(218\) 7.89816i 0.534931i
\(219\) 1.33369 + 4.10466i 0.0901221 + 0.277367i
\(220\) 7.59430 8.02678i 0.512008 0.541165i
\(221\) 2.18037 6.71050i 0.146668 0.451397i
\(222\) 22.3040 + 7.24701i 1.49695 + 0.486388i
\(223\) −2.53109 3.48375i −0.169494 0.233289i 0.715817 0.698288i \(-0.246055\pi\)
−0.885311 + 0.464999i \(0.846055\pi\)
\(224\) −2.61307 −0.174593
\(225\) −33.2882 + 12.8927i −2.21921 + 0.859515i
\(226\) −0.411361 −0.0273633
\(227\) −15.7029 21.6132i −1.04224 1.43452i −0.895347 0.445369i \(-0.853072\pi\)
−0.146894 0.989152i \(-0.546928\pi\)
\(228\) −3.02842 0.983992i −0.200562 0.0651665i
\(229\) 0.293786 0.904181i 0.0194139 0.0597499i −0.940880 0.338739i \(-0.889999\pi\)
0.960294 + 0.278990i \(0.0899995\pi\)
\(230\) −14.1084 + 2.63671i −0.930280 + 0.173859i
\(231\) −12.7063 39.1061i −0.836015 2.57299i
\(232\) 0.204927i 0.0134541i
\(233\) −9.68361 + 3.14640i −0.634394 + 0.206127i −0.608521 0.793538i \(-0.708237\pi\)
−0.0258737 + 0.999665i \(0.508237\pi\)
\(234\) 39.5869 + 28.7615i 2.58787 + 1.88020i
\(235\) 1.41309 + 7.56111i 0.0921799 + 0.493233i
\(236\) −8.94530 + 6.49914i −0.582290 + 0.423058i
\(237\) 1.61762 2.22647i 0.105076 0.144625i
\(238\) 1.58123 2.17638i 0.102496 0.141074i
\(239\) 2.54946 1.85229i 0.164911 0.119815i −0.502269 0.864711i \(-0.667501\pi\)
0.667180 + 0.744897i \(0.267501\pi\)
\(240\) −3.05571 + 6.43120i −0.197245 + 0.415132i
\(241\) −10.3041 7.48635i −0.663744 0.482238i 0.204181 0.978933i \(-0.434547\pi\)
−0.867925 + 0.496695i \(0.834547\pi\)
\(242\) 12.7637 4.14717i 0.820480 0.266590i
\(243\) 25.9066i 1.66191i
\(244\) −1.53155 4.71363i −0.0980475 0.301759i
\(245\) 0.183880 + 0.337458i 0.0117477 + 0.0215594i
\(246\) 8.25128 25.3948i 0.526082 1.61911i
\(247\) −6.51823 2.11790i −0.414745 0.134759i
\(248\) 0.861929 + 1.18634i 0.0547325 + 0.0753329i
\(249\) 23.0707 1.46205
\(250\) −5.88450 9.50645i −0.372169 0.601241i
\(251\) −3.85340 −0.243224 −0.121612 0.992578i \(-0.538806\pi\)
−0.121612 + 0.992578i \(0.538806\pi\)
\(252\) 10.9658 + 15.0931i 0.690780 + 0.950777i
\(253\) −30.1669 9.80183i −1.89658 0.616236i
\(254\) 1.85034 5.69475i 0.116100 0.357320i
\(255\) −3.50735 6.43672i −0.219639 0.403083i
\(256\) 0.309017 + 0.951057i 0.0193136 + 0.0594410i
\(257\) 26.8827i 1.67690i −0.544979 0.838450i \(-0.683462\pi\)
0.544979 0.838450i \(-0.316538\pi\)
\(258\) 31.3651 10.1911i 1.95271 0.634473i
\(259\) 15.5696 + 11.3119i 0.967445 + 0.702890i
\(260\) −6.57696 + 13.8422i −0.407886 + 0.858459i
\(261\) 1.18366 0.859982i 0.0732669 0.0532315i
\(262\) −1.71202 + 2.35639i −0.105769 + 0.145579i
\(263\) 2.92229 4.02218i 0.180196 0.248018i −0.709358 0.704848i \(-0.751015\pi\)
0.889554 + 0.456830i \(0.151015\pi\)
\(264\) −12.7305 + 9.24922i −0.783506 + 0.569250i
\(265\) 4.20050 + 22.4759i 0.258035 + 1.38068i
\(266\) −2.11402 1.53592i −0.129619 0.0941735i
\(267\) 45.3148 14.7237i 2.77322 0.901074i
\(268\) 1.81892i 0.111108i
\(269\) 6.77914 + 20.8641i 0.413332 + 1.27210i 0.913735 + 0.406312i \(0.133185\pi\)
−0.500403 + 0.865793i \(0.666815\pi\)
\(270\) 28.9729 5.41472i 1.76323 0.329529i
\(271\) −8.58516 + 26.4224i −0.521511 + 1.60505i 0.249602 + 0.968349i \(0.419700\pi\)
−0.771113 + 0.636698i \(0.780300\pi\)
\(272\) −0.979111 0.318132i −0.0593673 0.0192896i
\(273\) 33.5198 + 46.1361i 2.02871 + 2.79228i
\(274\) 13.1375 0.793668
\(275\) −1.36708 24.6707i −0.0824381 1.48770i
\(276\) 20.4389 1.23027
\(277\) −4.78212 6.58202i −0.287329 0.395475i 0.640815 0.767695i \(-0.278597\pi\)
−0.928144 + 0.372220i \(0.878597\pi\)
\(278\) 5.91457 + 1.92176i 0.354732 + 0.115259i
\(279\) 3.23523 9.95702i 0.193688 0.596111i
\(280\) −4.01570 + 4.24439i −0.239984 + 0.253651i
\(281\) 4.51374 + 13.8919i 0.269267 + 0.828720i 0.990679 + 0.136214i \(0.0434933\pi\)
−0.721412 + 0.692506i \(0.756507\pi\)
\(282\) 10.9538i 0.652290i
\(283\) −1.73599 + 0.564056i −0.103194 + 0.0335297i −0.360159 0.932891i \(-0.617277\pi\)
0.256965 + 0.966421i \(0.417277\pi\)
\(284\) −4.41623 3.20858i −0.262055 0.190394i
\(285\) −6.25229 + 3.40685i −0.370353 + 0.201805i
\(286\) −27.4005 + 19.9076i −1.62022 + 1.17716i
\(287\) 12.8795 17.7271i 0.760253 1.04640i
\(288\) 4.19652 5.77601i 0.247282 0.340355i
\(289\) −12.8958 + 9.36938i −0.758579 + 0.551140i
\(290\) 0.332862 + 0.314927i 0.0195463 + 0.0184932i
\(291\) −23.7839 17.2800i −1.39423 1.01297i
\(292\) 1.28905 0.418836i 0.0754357 0.0245105i
\(293\) 16.3821i 0.957054i 0.878073 + 0.478527i \(0.158829\pi\)
−0.878073 + 0.478527i \(0.841171\pi\)
\(294\) −0.169115 0.520483i −0.00986299 0.0303552i
\(295\) −3.19043 + 24.5175i −0.185754 + 1.42746i
\(296\) 2.27588 7.00445i 0.132283 0.407125i
\(297\) 61.9506 + 20.1290i 3.59474 + 1.16800i
\(298\) 5.34195 + 7.35256i 0.309451 + 0.425922i
\(299\) 43.9917 2.54410
\(300\) 5.75021 + 14.8467i 0.331988 + 0.857173i
\(301\) 27.0634 1.55991
\(302\) 12.9405 + 17.8111i 0.744644 + 1.02491i
\(303\) 20.8015 + 6.75883i 1.19502 + 0.388285i
\(304\) −0.309017 + 0.951057i −0.0177233 + 0.0545468i
\(305\) −10.0100 4.75611i −0.573168 0.272334i
\(306\) 2.27132 + 6.99041i 0.129843 + 0.399615i
\(307\) 8.96379i 0.511591i −0.966731 0.255795i \(-0.917663\pi\)
0.966731 0.255795i \(-0.0823373\pi\)
\(308\) −12.2810 + 3.99035i −0.699777 + 0.227371i
\(309\) −40.2660 29.2550i −2.29065 1.66426i
\(310\) 3.25156 + 0.423120i 0.184676 + 0.0240316i
\(311\) 1.17615 0.854526i 0.0666936 0.0484557i −0.553939 0.832557i \(-0.686876\pi\)
0.620633 + 0.784102i \(0.286876\pi\)
\(312\) 12.8278 17.6559i 0.726229 0.999569i
\(313\) −17.4754 + 24.0528i −0.987765 + 1.35954i −0.0552259 + 0.998474i \(0.517588\pi\)
−0.932539 + 0.361068i \(0.882412\pi\)
\(314\) −3.38263 + 2.45762i −0.190893 + 0.138692i
\(315\) 41.3676 + 5.38310i 2.33080 + 0.303303i
\(316\) −0.699209 0.508005i −0.0393336 0.0285775i
\(317\) −20.5818 + 6.68744i −1.15599 + 0.375604i −0.823397 0.567466i \(-0.807924\pi\)
−0.332594 + 0.943070i \(0.607924\pi\)
\(318\) 32.5608i 1.82592i
\(319\) 0.312939 + 0.963127i 0.0175212 + 0.0539248i
\(320\) 2.01968 + 0.959627i 0.112904 + 0.0536448i
\(321\) −17.5153 + 53.9067i −0.977611 + 3.00878i
\(322\) 15.9516 + 5.18300i 0.888949 + 0.288837i
\(323\) −0.605124 0.832882i −0.0336700 0.0463428i
\(324\) −20.5545 −1.14191
\(325\) 12.3765 + 31.9553i 0.686524 + 1.77256i
\(326\) 13.4584 0.745393
\(327\) 14.7827 + 20.3467i 0.817486 + 1.12517i
\(328\) −7.97510 2.59127i −0.440351 0.143079i
\(329\) 2.77772 8.54896i 0.153141 0.471319i
\(330\) −4.54044 + 34.8920i −0.249943 + 1.92074i
\(331\) 2.76812 + 8.51940i 0.152150 + 0.468269i 0.997861 0.0653721i \(-0.0208234\pi\)
−0.845711 + 0.533641i \(0.820823\pi\)
\(332\) 7.24522i 0.397633i
\(333\) −50.0086 + 16.2488i −2.74045 + 0.890427i
\(334\) 5.65065 + 4.10544i 0.309190 + 0.224640i
\(335\) −2.95445 2.79527i −0.161419 0.152722i
\(336\) 6.73159 4.89079i 0.367239 0.266814i
\(337\) −2.22602 + 3.06385i −0.121259 + 0.166898i −0.865331 0.501201i \(-0.832892\pi\)
0.744072 + 0.668099i \(0.232892\pi\)
\(338\) 19.9687 27.4845i 1.08615 1.49496i
\(339\) 1.05972 0.769929i 0.0575559 0.0418168i
\(340\) −2.02141 + 1.10146i −0.109627 + 0.0597352i
\(341\) 5.86256 + 4.25940i 0.317476 + 0.230660i
\(342\) 6.79011 2.20624i 0.367167 0.119300i
\(343\) 18.7406i 1.01190i
\(344\) −3.20047 9.85003i −0.172558 0.531078i
\(345\) 31.4099 33.1987i 1.69105 1.78736i
\(346\) 2.21809 6.82658i 0.119245 0.366999i
\(347\) 13.7457 + 4.46624i 0.737907 + 0.239761i 0.653770 0.756694i \(-0.273187\pi\)
0.0841374 + 0.996454i \(0.473187\pi\)
\(348\) −0.383555 0.527919i −0.0205607 0.0282994i
\(349\) 16.6211 0.889707 0.444853 0.895603i \(-0.353256\pi\)
0.444853 + 0.895603i \(0.353256\pi\)
\(350\) 0.722883 + 13.0453i 0.0386397 + 0.697303i
\(351\) −90.3410 −4.82204
\(352\) 2.90467 + 3.99793i 0.154819 + 0.213090i
\(353\) −14.1495 4.59744i −0.753100 0.244697i −0.0927853 0.995686i \(-0.529577\pi\)
−0.660314 + 0.750989i \(0.729577\pi\)
\(354\) 10.8800 33.4852i 0.578266 1.77972i
\(355\) −11.9984 + 2.24237i −0.636809 + 0.119013i
\(356\) −4.62388 14.2309i −0.245065 0.754234i
\(357\) 8.56615i 0.453369i
\(358\) −16.0284 + 5.20794i −0.847128 + 0.275248i
\(359\) −7.07206 5.13816i −0.373249 0.271181i 0.385308 0.922788i \(-0.374095\pi\)
−0.758557 + 0.651607i \(0.774095\pi\)
\(360\) −2.93282 15.6928i −0.154573 0.827083i
\(361\) −0.809017 + 0.587785i −0.0425798 + 0.0309361i
\(362\) −1.55567 + 2.14120i −0.0817642 + 0.112539i
\(363\) −25.1187 + 34.5729i −1.31839 + 1.81461i
\(364\) 14.4888 10.5267i 0.759418 0.551750i
\(365\) 1.30066 2.73744i 0.0680798 0.143284i
\(366\) 12.7678 + 9.27635i 0.667383 + 0.484882i
\(367\) 7.08378 2.30166i 0.369770 0.120146i −0.118237 0.992985i \(-0.537724\pi\)
0.488007 + 0.872840i \(0.337724\pi\)
\(368\) 6.41871i 0.334598i
\(369\) 18.5005 + 56.9386i 0.963095 + 2.96410i
\(370\) −7.87974 14.4610i −0.409648 0.751789i
\(371\) 8.25695 25.4123i 0.428680 1.31934i
\(372\) −4.44087 1.44293i −0.230248 0.0748122i
\(373\) 4.17340 + 5.74419i 0.216090 + 0.297423i 0.903277 0.429058i \(-0.141154\pi\)
−0.687186 + 0.726481i \(0.741154\pi\)
\(374\) −5.08748 −0.263068
\(375\) 32.9521 + 13.4760i 1.70164 + 0.695897i
\(376\) −3.43998 −0.177403
\(377\) −0.825547 1.13627i −0.0425178 0.0585208i
\(378\) −32.7581 10.6438i −1.68490 0.547456i
\(379\) 8.56862 26.3715i 0.440141 1.35461i −0.447585 0.894241i \(-0.647716\pi\)
0.887726 0.460372i \(-0.152284\pi\)
\(380\) 1.06990 + 1.96349i 0.0548848 + 0.100725i
\(381\) 5.89196 + 18.1336i 0.301854 + 0.929012i
\(382\) 20.4735i 1.04752i
\(383\) 29.0872 9.45100i 1.48629 0.482924i 0.550302 0.834966i \(-0.314513\pi\)
0.935984 + 0.352042i \(0.114513\pi\)
\(384\) −2.57612 1.87166i −0.131462 0.0955130i
\(385\) −12.3917 + 26.0802i −0.631539 + 1.32917i
\(386\) −4.00902 + 2.91272i −0.204054 + 0.148254i
\(387\) −43.4631 + 59.8218i −2.20935 + 3.04091i
\(388\) −5.42668 + 7.46918i −0.275498 + 0.379190i
\(389\) −15.7258 + 11.4254i −0.797328 + 0.579292i −0.910129 0.414325i \(-0.864018\pi\)
0.112801 + 0.993618i \(0.464018\pi\)
\(390\) −8.96493 47.9692i −0.453957 2.42901i
\(391\) 5.34602 + 3.88411i 0.270360 + 0.196428i
\(392\) −0.163455 + 0.0531096i −0.00825570 + 0.00268244i
\(393\) 9.27469i 0.467846i
\(394\) −1.28858 3.96584i −0.0649177 0.199796i
\(395\) −1.89968 + 0.355029i −0.0955831 + 0.0178635i
\(396\) 10.9026 33.5548i 0.547876 1.68619i
\(397\) 5.69498 + 1.85041i 0.285823 + 0.0928694i 0.448420 0.893823i \(-0.351987\pi\)
−0.162597 + 0.986693i \(0.551987\pi\)
\(398\) 8.30131 + 11.4258i 0.416107 + 0.572722i
\(399\) 8.32071 0.416556
\(400\) 4.66251 1.80582i 0.233126 0.0902910i
\(401\) −8.48337 −0.423639 −0.211820 0.977309i \(-0.567939\pi\)
−0.211820 + 0.977309i \(0.567939\pi\)
\(402\) 3.40440 + 4.68576i 0.169796 + 0.233705i
\(403\) −9.55833 3.10569i −0.476134 0.154705i
\(404\) 2.12257 6.53260i 0.105602 0.325009i
\(405\) −31.5876 + 33.3864i −1.56960 + 1.65898i
\(406\) −0.165475 0.509281i −0.00821241 0.0252752i
\(407\) 36.3953i 1.80405i
\(408\) 3.11775 1.01302i 0.154352 0.0501519i
\(409\) −5.75457 4.18094i −0.284545 0.206734i 0.436352 0.899776i \(-0.356270\pi\)
−0.720897 + 0.693042i \(0.756270\pi\)
\(410\) −16.4649 + 8.97168i −0.813144 + 0.443080i
\(411\) −33.8440 + 24.5891i −1.66940 + 1.21289i
\(412\) −9.18735 + 12.6453i −0.452628 + 0.622989i
\(413\) 16.9827 23.3747i 0.835665 1.15019i
\(414\) −37.0745 + 26.9362i −1.82211 + 1.32384i
\(415\) −11.7683 11.1343i −0.577685 0.546560i
\(416\) −5.54473 4.02848i −0.271853 0.197513i
\(417\) −18.8335 + 6.11939i −0.922283 + 0.299668i
\(418\) 4.94171i 0.241707i
\(419\) −1.45338 4.47304i −0.0710021 0.218522i 0.909258 0.416232i \(-0.136650\pi\)
−0.980261 + 0.197710i \(0.936650\pi\)
\(420\) 2.40089 18.4501i 0.117151 0.900273i
\(421\) 9.66798 29.7550i 0.471188 1.45017i −0.379842 0.925052i \(-0.624022\pi\)
0.851030 0.525117i \(-0.175978\pi\)
\(422\) −10.2155 3.31922i −0.497283 0.161577i
\(423\) 14.4359 + 19.8694i 0.701899 + 0.966081i
\(424\) −10.2255 −0.496596
\(425\) −1.31736 + 4.97606i −0.0639015 + 0.241375i
\(426\) 17.3821 0.842167
\(427\) 7.61235 + 10.4775i 0.368387 + 0.507042i
\(428\) 16.9291 + 5.50059i 0.818298 + 0.265881i
\(429\) 33.3267 102.569i 1.60903 4.95208i
\(430\) −20.9177 9.93879i −1.00874 0.479291i
\(431\) −5.31332 16.3527i −0.255934 0.787683i −0.993644 0.112566i \(-0.964093\pi\)
0.737711 0.675117i \(-0.235907\pi\)
\(432\) 13.1814i 0.634191i
\(433\) 25.3469 8.23570i 1.21809 0.395783i 0.371706 0.928350i \(-0.378773\pi\)
0.846387 + 0.532568i \(0.178773\pi\)
\(434\) −3.10000 2.25228i −0.148805 0.108113i
\(435\) −1.44693 0.188287i −0.0693751 0.00902767i
\(436\) 6.38975 4.64242i 0.306013 0.222332i
\(437\) 3.77282 5.19284i 0.180478 0.248407i
\(438\) −2.53682 + 3.49163i −0.121214 + 0.166837i
\(439\) 6.74163 4.89808i 0.321761 0.233773i −0.415166 0.909746i \(-0.636276\pi\)
0.736926 + 0.675973i \(0.236276\pi\)
\(440\) 10.9576 + 1.42590i 0.522384 + 0.0679770i
\(441\) 0.992702 + 0.721240i 0.0472715 + 0.0343448i
\(442\) 6.71050 2.18037i 0.319186 0.103710i
\(443\) 15.9290i 0.756808i 0.925641 + 0.378404i \(0.123527\pi\)
−0.925641 + 0.378404i \(0.876473\pi\)
\(444\) 7.24701 + 22.3040i 0.343928 + 1.05850i
\(445\) −30.2209 14.3591i −1.43261 0.680686i
\(446\) 1.33067 4.09539i 0.0630092 0.193923i
\(447\) −27.5230 8.94278i −1.30180 0.422979i
\(448\) −1.53592 2.11402i −0.0725656 0.0998780i
\(449\) 41.7187 1.96883 0.984414 0.175868i \(-0.0562733\pi\)
0.984414 + 0.175868i \(0.0562733\pi\)
\(450\) −29.9968 19.3526i −1.41406 0.912289i
\(451\) −41.4388 −1.95128
\(452\) −0.241792 0.332798i −0.0113729 0.0156535i
\(453\) −66.6729 21.6633i −3.13256 1.01783i
\(454\) 8.25552 25.4079i 0.387451 1.19245i
\(455\) 5.16756 39.7112i 0.242259 1.86169i
\(456\) −0.983992 3.02842i −0.0460796 0.141819i
\(457\) 9.21965i 0.431277i −0.976473 0.215638i \(-0.930817\pi\)
0.976473 0.215638i \(-0.0691833\pi\)
\(458\) 0.904181 0.293786i 0.0422496 0.0137277i
\(459\) −10.9786 7.97638i −0.512435 0.372306i
\(460\) −10.4258 9.86411i −0.486108 0.459917i
\(461\) 2.78450 2.02306i 0.129687 0.0942233i −0.521051 0.853526i \(-0.674460\pi\)
0.650738 + 0.759303i \(0.274460\pi\)
\(462\) 24.1689 33.2656i 1.12444 1.54766i
\(463\) 9.20988 12.6763i 0.428019 0.589118i −0.539478 0.842000i \(-0.681378\pi\)
0.967497 + 0.252882i \(0.0813784\pi\)
\(464\) −0.165790 + 0.120453i −0.00769660 + 0.00559190i
\(465\) −9.16835 + 4.99581i −0.425172 + 0.231675i
\(466\) −8.23737 5.98480i −0.381589 0.277241i
\(467\) 4.01867 1.30575i 0.185962 0.0604227i −0.214556 0.976712i \(-0.568830\pi\)
0.400518 + 0.916289i \(0.368830\pi\)
\(468\) 48.9321i 2.26189i
\(469\) 1.46875 + 4.52033i 0.0678204 + 0.208730i
\(470\) −5.28648 + 5.58753i −0.243847 + 0.257733i
\(471\) 4.11423 12.6623i 0.189574 0.583447i
\(472\) −10.5158 3.41680i −0.484031 0.157271i
\(473\) −30.0834 41.4063i −1.38324 1.90386i
\(474\) 2.75207 0.126407
\(475\) 4.83349 + 1.27962i 0.221776 + 0.0587128i
\(476\) 2.69015 0.123303
\(477\) 42.9117 + 59.0629i 1.96479 + 2.70430i
\(478\) 2.99707 + 0.973806i 0.137083 + 0.0445409i
\(479\) −5.10634 + 15.7157i −0.233315 + 0.718069i 0.764026 + 0.645186i \(0.223220\pi\)
−0.997340 + 0.0728830i \(0.976780\pi\)
\(480\) −6.99905 + 1.30805i −0.319462 + 0.0597039i
\(481\) 15.5981 + 48.0062i 0.711214 + 2.18889i
\(482\) 12.7365i 0.580133i
\(483\) −50.7942 + 16.5040i −2.31122 + 0.750959i
\(484\) 10.8574 + 7.88838i 0.493519 + 0.358563i
\(485\) 3.79254 + 20.2930i 0.172210 + 0.921456i
\(486\) 20.9589 15.2275i 0.950715 0.690735i
\(487\) −9.71323 + 13.3691i −0.440148 + 0.605812i −0.970245 0.242125i \(-0.922156\pi\)
0.530097 + 0.847937i \(0.322156\pi\)
\(488\) 2.91318 4.00965i 0.131874 0.181508i
\(489\) −34.6706 + 25.1896i −1.56786 + 1.13911i
\(490\) −0.164928 + 0.347115i −0.00745067 + 0.0156811i
\(491\) 14.3637 + 10.4359i 0.648226 + 0.470964i 0.862667 0.505773i \(-0.168793\pi\)
−0.214440 + 0.976737i \(0.568793\pi\)
\(492\) 25.3948 8.25128i 1.14489 0.371996i
\(493\) 0.210972i 0.00950172i
\(494\) −2.11790 6.51823i −0.0952888 0.293269i
\(495\) −37.7478 69.2751i −1.69664 3.11369i
\(496\) −0.453143 + 1.39463i −0.0203467 + 0.0626207i
\(497\) 13.5660 + 4.40785i 0.608517 + 0.197719i
\(498\) 13.5606 + 18.6646i 0.607666 + 0.836380i
\(499\) −35.6431 −1.59560 −0.797801 0.602920i \(-0.794004\pi\)
−0.797801 + 0.602920i \(0.794004\pi\)
\(500\) 4.23206 10.3484i 0.189263 0.462795i
\(501\) −22.2408 −0.993645
\(502\) −2.26497 3.11746i −0.101091 0.139139i
\(503\) 11.9456 + 3.88136i 0.532628 + 0.173061i 0.562969 0.826478i \(-0.309659\pi\)
−0.0303407 + 0.999540i \(0.509659\pi\)
\(504\) −5.76506 + 17.7430i −0.256796 + 0.790337i
\(505\) −7.34893 13.4868i −0.327023 0.600155i
\(506\) −9.80183 30.1669i −0.435745 1.34108i
\(507\) 108.178i 4.80437i
\(508\) 5.69475 1.85034i 0.252664 0.0820954i
\(509\) −14.1970 10.3148i −0.629273 0.457193i 0.226876 0.973924i \(-0.427149\pi\)
−0.856148 + 0.516730i \(0.827149\pi\)
\(510\) 3.14584 6.62091i 0.139300 0.293179i
\(511\) −2.86530 + 2.08176i −0.126754 + 0.0920919i
\(512\) −0.587785 + 0.809017i −0.0259767 + 0.0357538i
\(513\) −7.74784 + 10.6640i −0.342075 + 0.470826i
\(514\) 21.7486 15.8013i 0.959290 0.696965i
\(515\) 6.42075 + 34.3559i 0.282932 + 1.51390i
\(516\) 26.6808 + 19.3847i 1.17455 + 0.853364i
\(517\) −16.1674 + 5.25310i −0.711040 + 0.231031i
\(518\) 19.2450i 0.845578i
\(519\) 7.06299 + 21.7376i 0.310031 + 0.954177i
\(520\) −15.0644 + 2.81538i −0.660620 + 0.123463i
\(521\) 5.55474 17.0957i 0.243358 0.748978i −0.752545 0.658541i \(-0.771174\pi\)
0.995902 0.0904365i \(-0.0288262\pi\)
\(522\) 1.39148 + 0.452119i 0.0609034 + 0.0197887i
\(523\) −1.69580 2.33407i −0.0741521 0.102062i 0.770330 0.637646i \(-0.220092\pi\)
−0.844482 + 0.535584i \(0.820092\pi\)
\(524\) −2.91266 −0.127240
\(525\) −26.2787 32.2534i −1.14690 1.40765i
\(526\) 4.97169 0.216776
\(527\) −0.887354 1.22134i −0.0386537 0.0532023i
\(528\) −14.9656 4.86260i −0.651292 0.211618i
\(529\) −5.62404 + 17.3090i −0.244524 + 0.752566i
\(530\) −15.7144 + 16.6093i −0.682589 + 0.721460i
\(531\) 24.3944 + 75.0783i 1.05863 + 3.25812i
\(532\) 2.61307i 0.113291i
\(533\) 54.6587 17.7597i 2.36753 0.769257i
\(534\) 38.5471 + 28.0061i 1.66810 + 1.21194i
\(535\) 34.9508 19.0446i 1.51105 0.823369i
\(536\) 1.47154 1.06913i 0.0635607 0.0461795i
\(537\) 31.5436 43.4161i 1.36121 1.87354i
\(538\) −12.8947 + 17.7480i −0.555930 + 0.765172i
\(539\) −0.687109 + 0.499214i −0.0295959 + 0.0215027i
\(540\) 21.4104 + 20.2569i 0.921358 + 0.871717i
\(541\) −1.45101 1.05422i −0.0623837 0.0453244i 0.556156 0.831078i \(-0.312276\pi\)
−0.618540 + 0.785753i \(0.712276\pi\)
\(542\) −26.4224 + 8.58516i −1.13494 + 0.368764i
\(543\) 8.42768i 0.361666i
\(544\) −0.318132 0.979111i −0.0136398 0.0419790i
\(545\) 2.27896 17.5132i 0.0976201 0.750182i
\(546\) −17.6224 + 54.2362i −0.754170 + 2.32110i
\(547\) −3.02075 0.981502i −0.129158 0.0419660i 0.243725 0.969844i \(-0.421631\pi\)
−0.372883 + 0.927878i \(0.621631\pi\)
\(548\) 7.72206 + 10.6285i 0.329870 + 0.454027i
\(549\) −35.3850 −1.51020
\(550\) 19.1555 15.6071i 0.816792 0.665488i
\(551\) −0.204927 −0.00873020
\(552\) 12.0137 + 16.5354i 0.511335 + 0.703793i
\(553\) 2.14786 + 0.697884i 0.0913365 + 0.0296770i
\(554\) 2.51411 7.73763i 0.106814 0.328740i
\(555\) 47.3652 + 22.5050i 2.01054 + 0.955284i
\(556\) 1.92176 + 5.91457i 0.0815007 + 0.250833i
\(557\) 30.2127i 1.28015i 0.768312 + 0.640076i \(0.221097\pi\)
−0.768312 + 0.640076i \(0.778903\pi\)
\(558\) 9.95702 3.23523i 0.421514 0.136958i
\(559\) 57.4264 + 41.7228i 2.42888 + 1.76468i
\(560\) −5.79415 0.753984i −0.244848 0.0318616i
\(561\) 13.1060 9.52206i 0.553335 0.402022i
\(562\) −8.58565 + 11.8171i −0.362164 + 0.498476i
\(563\) 14.8452 20.4326i 0.625650 0.861133i −0.372099 0.928193i \(-0.621362\pi\)
0.997749 + 0.0670598i \(0.0213618\pi\)
\(564\) 8.86181 6.43848i 0.373150 0.271109i
\(565\) −0.912140 0.118695i −0.0383740 0.00499355i
\(566\) −1.47672 1.07290i −0.0620711 0.0450973i
\(567\) 51.0815 16.5974i 2.14522 0.697024i
\(568\) 5.45875i 0.229044i
\(569\) −9.48544 29.1932i −0.397650 1.22384i −0.926878 0.375362i \(-0.877518\pi\)
0.529228 0.848480i \(-0.322482\pi\)
\(570\) −6.43120 3.05571i −0.269373 0.127989i
\(571\) −4.89118 + 15.0535i −0.204690 + 0.629970i 0.795036 + 0.606562i \(0.207452\pi\)
−0.999726 + 0.0234081i \(0.992548\pi\)
\(572\) −32.2112 10.4661i −1.34682 0.437608i
\(573\) −38.3195 52.7423i −1.60082 2.20334i
\(574\) 21.9119 0.914586
\(575\) −32.0444 + 1.77568i −1.33634 + 0.0740509i
\(576\) 7.13954 0.297481
\(577\) −10.2686 14.1335i −0.427488 0.588386i 0.539887 0.841738i \(-0.318467\pi\)
−0.967374 + 0.253351i \(0.918467\pi\)
\(578\) −15.1600 4.92577i −0.630572 0.204885i
\(579\) 4.87609 15.0071i 0.202643 0.623672i
\(580\) −0.0591305 + 0.454400i −0.00245526 + 0.0188680i
\(581\) 5.85039 + 18.0057i 0.242715 + 0.747001i
\(582\) 29.3985i 1.21861i
\(583\) −48.0585 + 15.6152i −1.99038 + 0.646714i
\(584\) 1.09653 + 0.796674i 0.0453746 + 0.0329666i
\(585\) 79.4799 + 75.1976i 3.28609 + 3.10904i
\(586\) −13.2534 + 9.62917i −0.547494 + 0.397778i
\(587\) 8.64704 11.9016i 0.356901 0.491233i −0.592381 0.805658i \(-0.701812\pi\)
0.949282 + 0.314425i \(0.101812\pi\)
\(588\) 0.321676 0.442749i 0.0132657 0.0182587i
\(589\) −1.18634 + 0.861929i −0.0488824 + 0.0355151i
\(590\) −21.7104 + 11.8299i −0.893801 + 0.487030i
\(591\) 10.7423 + 7.80471i 0.441877 + 0.321043i
\(592\) 7.00445 2.27588i 0.287881 0.0935382i
\(593\) 10.5122i 0.431685i −0.976428 0.215843i \(-0.930750\pi\)
0.976428 0.215843i \(-0.0692498\pi\)
\(594\) 20.1290 + 61.9506i 0.825902 + 2.54186i
\(595\) 4.13416 4.36959i 0.169484 0.179136i
\(596\) −2.80843 + 8.64345i −0.115038 + 0.354050i
\(597\) −42.7704 13.8969i −1.75048 0.568764i
\(598\) 25.8577 + 35.5900i 1.05740 + 1.45538i
\(599\) −36.3642 −1.48580 −0.742900 0.669402i \(-0.766550\pi\)
−0.742900 + 0.669402i \(0.766550\pi\)
\(600\) −8.63132 + 13.3787i −0.352372 + 0.546182i
\(601\) 16.6875 0.680696 0.340348 0.940300i \(-0.389455\pi\)
0.340348 + 0.940300i \(0.389455\pi\)
\(602\) 15.9075 + 21.8947i 0.648340 + 0.892363i
\(603\) −12.3507 4.01297i −0.502958 0.163421i
\(604\) −6.80324 + 20.9382i −0.276820 + 0.851964i
\(605\) 29.4984 5.51294i 1.19928 0.224133i
\(606\) 6.75883 + 20.8015i 0.274559 + 0.845004i
\(607\) 40.4562i 1.64207i −0.570879 0.821034i \(-0.693397\pi\)
0.570879 0.821034i \(-0.306603\pi\)
\(608\) −0.951057 + 0.309017i −0.0385704 + 0.0125323i
\(609\) 1.37949 + 1.00226i 0.0558997 + 0.0406135i
\(610\) −2.03593 10.8938i −0.0824325 0.441077i
\(611\) 19.0738 13.8579i 0.771642 0.560631i
\(612\) −4.32031 + 5.94639i −0.174638 + 0.240369i
\(613\) 4.30913 5.93101i 0.174044 0.239551i −0.713079 0.701083i \(-0.752700\pi\)
0.887124 + 0.461532i \(0.152700\pi\)
\(614\) 7.25186 5.26879i 0.292661 0.212631i
\(615\) 25.6237 53.9289i 1.03325 2.17462i
\(616\) −10.4469 7.59009i −0.420916 0.305814i
\(617\) −33.1253 + 10.7631i −1.33358 + 0.433305i −0.887136 0.461509i \(-0.847308\pi\)
−0.446440 + 0.894814i \(0.647308\pi\)
\(618\) 49.7715i 2.00210i
\(619\) 6.67548 + 20.5450i 0.268310 + 0.825774i 0.990912 + 0.134510i \(0.0429459\pi\)
−0.722602 + 0.691264i \(0.757054\pi\)
\(620\) 1.56891 + 2.87927i 0.0630088 + 0.115634i
\(621\) 26.1452 80.4666i 1.04917 3.22901i
\(622\) 1.38265 + 0.449251i 0.0554393 + 0.0180133i
\(623\) 22.9823 + 31.6325i 0.920768 + 1.26733i
\(624\) 21.8239 0.873655
\(625\) −10.3051 22.7773i −0.412204 0.911091i
\(626\) −29.7308 −1.18828
\(627\) −9.24922 12.7305i −0.369378 0.508406i
\(628\) −3.97652 1.29205i −0.158680 0.0515584i
\(629\) −2.34302 + 7.21107i −0.0934222 + 0.287524i
\(630\) 19.9602 + 36.6312i 0.795235 + 1.45942i
\(631\) −11.9492 36.7759i −0.475690 1.46402i −0.845025 0.534727i \(-0.820414\pi\)
0.369334 0.929297i \(-0.379586\pi\)
\(632\) 0.864270i 0.0343788i
\(633\) 32.5289 10.5693i 1.29291 0.420091i
\(634\) −17.5080 12.7203i −0.695330 0.505186i
\(635\) 5.74606 12.0935i 0.228026 0.479915i
\(636\) 26.3423 19.1388i 1.04454 0.758902i
\(637\) 0.692361 0.952953i 0.0274323 0.0377574i
\(638\) −0.595246 + 0.819285i −0.0235660 + 0.0324358i
\(639\) −31.5298 + 22.9078i −1.24730 + 0.906217i
\(640\) 0.410785 + 2.19801i 0.0162377 + 0.0868840i
\(641\) 18.3972 + 13.3664i 0.726647 + 0.527940i 0.888501 0.458875i \(-0.151747\pi\)
−0.161854 + 0.986815i \(0.551747\pi\)
\(642\) −53.9067 + 17.5153i −2.12753 + 0.691275i
\(643\) 0.656809i 0.0259020i 0.999916 + 0.0129510i \(0.00412255\pi\)
−0.999916 + 0.0129510i \(0.995877\pi\)
\(644\) 5.18300 + 15.9516i 0.204239 + 0.628582i
\(645\) 72.4887 13.5474i 2.85424 0.533427i
\(646\) 0.318132 0.979111i 0.0125168 0.0385226i
\(647\) −24.6218 8.00011i −0.967983 0.314517i −0.217981 0.975953i \(-0.569947\pi\)
−0.750001 + 0.661436i \(0.769947\pi\)
\(648\) −12.0816 16.6289i −0.474610 0.653245i
\(649\) −54.6405 −2.14483
\(650\) −18.5777 + 28.7956i −0.728676 + 1.12946i
\(651\) 12.2015 0.478214
\(652\) 7.91066 + 10.8881i 0.309805 + 0.426411i
\(653\) 8.00173 + 2.59992i 0.313132 + 0.101743i 0.461367 0.887209i \(-0.347359\pi\)
−0.148235 + 0.988952i \(0.547359\pi\)
\(654\) −7.77173 + 23.9189i −0.303899 + 0.935304i
\(655\) −4.47611 + 4.73101i −0.174896 + 0.184856i
\(656\) −2.59127 7.97510i −0.101172 0.311375i
\(657\) 9.67682i 0.377529i
\(658\) 8.54896 2.77772i 0.333273 0.108287i
\(659\) −16.3359 11.8687i −0.636354 0.462339i 0.222241 0.974992i \(-0.428663\pi\)
−0.858596 + 0.512653i \(0.828663\pi\)
\(660\) −30.8970 + 16.8357i −1.20266 + 0.655328i
\(661\) −20.8028 + 15.1141i −0.809135 + 0.587871i −0.913580 0.406660i \(-0.866693\pi\)
0.104445 + 0.994531i \(0.466693\pi\)
\(662\) −5.26528 + 7.24704i −0.204641 + 0.281664i
\(663\) −13.2062 + 18.1767i −0.512885 + 0.705925i
\(664\) 5.86151 4.25863i 0.227471 0.165267i
\(665\) −4.24439 4.01570i −0.164590 0.155722i
\(666\) −42.5398 30.9070i −1.64838 1.19762i
\(667\) 1.25099 0.406471i 0.0484385 0.0157386i
\(668\) 6.98459i 0.270242i
\(669\) 4.23722 + 13.0408i 0.163820 + 0.504187i
\(670\) 0.524837 4.03322i 0.0202762 0.155817i
\(671\) 7.56848 23.2934i 0.292178 0.899231i
\(672\) 7.91346 + 2.57124i 0.305268 + 0.0991877i
\(673\) −21.3995 29.4538i −0.824888 1.13536i −0.988853 0.148895i \(-0.952428\pi\)
0.163964 0.986466i \(-0.447572\pi\)
\(674\) −3.78712 −0.145875
\(675\) 65.8061 3.64652i 2.53288 0.140355i
\(676\) 33.9728 1.30664
\(677\) −23.8102 32.7719i −0.915100 1.25953i −0.965395 0.260793i \(-0.916016\pi\)
0.0502944 0.998734i \(-0.483984\pi\)
\(678\) 1.24577 + 0.404776i 0.0478436 + 0.0155453i
\(679\) 7.45502 22.9442i 0.286097 0.880517i
\(680\) −2.07926 0.987934i −0.0797360 0.0378856i
\(681\) 26.2878 + 80.9055i 1.00735 + 3.10030i
\(682\) 7.24653i 0.277484i
\(683\) −36.2305 + 11.7720i −1.38632 + 0.450443i −0.904742 0.425959i \(-0.859937\pi\)
−0.481580 + 0.876402i \(0.659937\pi\)
\(684\) 5.77601 + 4.19652i 0.220851 + 0.160458i
\(685\) 29.1308 + 3.79075i 1.11303 + 0.144837i
\(686\) 15.1615 11.0154i 0.578867 0.420571i
\(687\) −1.77941 + 2.44915i −0.0678888 + 0.0934410i
\(688\) 6.08765 8.37894i 0.232090 0.319444i
\(689\) 56.6979 41.1935i 2.16002 1.56935i
\(690\) 45.3206 + 5.89750i 1.72532 + 0.224514i
\(691\) −28.3519 20.5989i −1.07856 0.783619i −0.101128 0.994873i \(-0.532245\pi\)
−0.977431 + 0.211255i \(0.932245\pi\)
\(692\) 6.82658 2.21809i 0.259508 0.0843192i
\(693\) 92.1932i 3.50213i
\(694\) 4.46624 + 13.7457i 0.169536 + 0.521779i
\(695\) 12.5603 + 5.96787i 0.476439 + 0.226374i
\(696\) 0.201647 0.620605i 0.00764341 0.0235240i
\(697\) 8.21035 + 2.66770i 0.310989 + 0.101046i
\(698\) 9.76963 + 13.4467i 0.369786 + 0.508967i
\(699\) 32.4220 1.22631
\(700\) −10.1290 + 8.25268i −0.382840 + 0.311922i
\(701\) 12.8187 0.484155 0.242078 0.970257i \(-0.422171\pi\)
0.242078 + 0.970257i \(0.422171\pi\)
\(702\) −53.1011 73.0874i −2.00417 2.75851i
\(703\) 7.00445 + 2.27588i 0.264178 + 0.0858365i
\(704\) −1.52707 + 4.69985i −0.0575537 + 0.177132i
\(705\) 3.16065 24.2887i 0.119037 0.914764i
\(706\) −4.59744 14.1495i −0.173027 0.532522i
\(707\) 17.9486i 0.675027i
\(708\) 33.4852 10.8800i 1.25845 0.408896i
\(709\) 1.94611 + 1.41393i 0.0730875 + 0.0531012i 0.623729 0.781641i \(-0.285617\pi\)
−0.550642 + 0.834742i \(0.685617\pi\)
\(710\) −8.86660 8.38888i −0.332758 0.314829i
\(711\) −4.99204 + 3.62693i −0.187216 + 0.136020i
\(712\) 8.79515 12.1055i 0.329612 0.453672i
\(713\) 5.53247 7.61479i 0.207192 0.285176i
\(714\) −6.93016 + 5.03506i −0.259355 + 0.188432i
\(715\) −66.5013 + 36.2364i −2.48701 + 1.35516i
\(716\) −13.6346 9.90610i −0.509548 0.370208i
\(717\) −9.54346 + 3.10086i −0.356407 + 0.115804i
\(718\) 8.74155i 0.326232i
\(719\) 6.71315 + 20.6609i 0.250358 + 0.770523i 0.994709 + 0.102734i \(0.0327591\pi\)
−0.744351 + 0.667789i \(0.767241\pi\)
\(720\) 10.9719 11.5967i 0.408898 0.432183i
\(721\) 12.6213 38.8445i 0.470043 1.44664i
\(722\) −0.951057 0.309017i −0.0353947 0.0115004i
\(723\) 23.8385 + 32.8109i 0.886564 + 1.22025i
\(724\) −2.64666 −0.0983625
\(725\) 0.647208 + 0.794357i 0.0240367 + 0.0295017i
\(726\) −42.7345 −1.58603
\(727\) 10.9156 + 15.0240i 0.404837 + 0.557210i 0.961950 0.273227i \(-0.0880910\pi\)
−0.557113 + 0.830437i \(0.688091\pi\)
\(728\) 17.0326 + 5.53422i 0.631269 + 0.205112i
\(729\) −6.43688 + 19.8107i −0.238403 + 0.733729i
\(730\) 2.97915 0.556771i 0.110263 0.0206070i
\(731\) 3.29488 + 10.1406i 0.121865 + 0.375063i
\(732\) 15.7819i 0.583314i
\(733\) 4.60705 1.49692i 0.170165 0.0552900i −0.222695 0.974888i \(-0.571486\pi\)
0.392861 + 0.919598i \(0.371486\pi\)
\(734\) 6.02582 + 4.37801i 0.222417 + 0.161595i
\(735\) −0.224809 1.20290i −0.00829222 0.0443697i
\(736\) 5.19284 3.77282i 0.191411 0.139068i
\(737\) 5.28335 7.27191i 0.194615 0.267864i
\(738\) −35.1900 + 48.4348i −1.29536 + 1.78291i
\(739\) 3.89494 2.82984i 0.143278 0.104097i −0.513837 0.857888i \(-0.671777\pi\)
0.657115 + 0.753790i \(0.271777\pi\)
\(740\) 7.06757 14.8748i 0.259809 0.546808i
\(741\) 17.6559 + 12.8278i 0.648606 + 0.471240i
\(742\) 25.4123 8.25695i 0.932915 0.303122i
\(743\) 16.9199i 0.620732i 0.950617 + 0.310366i \(0.100452\pi\)
−0.950617 + 0.310366i \(0.899548\pi\)
\(744\) −1.44293 4.44087i −0.0529002 0.162810i
\(745\) 9.72356 + 17.8447i 0.356244 + 0.653781i
\(746\) −2.19409 + 6.75270i −0.0803312 + 0.247234i
\(747\) −49.1959 15.9847i −1.79998 0.584850i
\(748\) −2.99035 4.11586i −0.109338 0.150491i
\(749\) −46.5134 −1.69956
\(750\) 8.46645 + 34.5798i 0.309151 + 1.26268i
\(751\) 4.58647 0.167363 0.0836813 0.996493i \(-0.473332\pi\)
0.0836813 + 0.996493i \(0.473332\pi\)
\(752\) −2.02197 2.78300i −0.0737336 0.101486i
\(753\) 11.6697 + 3.79171i 0.425267 + 0.138178i
\(754\) 0.434016 1.33576i 0.0158059 0.0486456i
\(755\) 23.5547 + 43.2278i 0.857244 + 1.57322i
\(756\) −10.6438 32.7581i −0.387110 1.19140i
\(757\) 40.1226i 1.45828i −0.684364 0.729140i \(-0.739920\pi\)
0.684364 0.729140i \(-0.260080\pi\)
\(758\) 26.3715 8.56862i 0.957857 0.311226i
\(759\) 81.7131 + 59.3680i 2.96600 + 2.15492i
\(760\) −0.959627 + 2.01968i −0.0348093 + 0.0732616i
\(761\) −7.93170 + 5.76272i −0.287524 + 0.208898i −0.722192 0.691692i \(-0.756866\pi\)
0.434669 + 0.900590i \(0.356866\pi\)
\(762\) −11.2072 + 15.4253i −0.405993 + 0.558801i
\(763\) −12.1310 + 16.6969i −0.439171 + 0.604467i
\(764\) −16.5634 + 12.0340i −0.599243 + 0.435376i
\(765\) 3.01933 + 16.1557i 0.109164 + 0.584111i
\(766\) 24.7430 + 17.9769i 0.894002 + 0.649531i
\(767\) 72.0720 23.4176i 2.60237 0.845561i
\(768\) 3.18427i 0.114902i
\(769\) 9.51453 + 29.2827i 0.343103 + 1.05596i 0.962592 + 0.270957i \(0.0873400\pi\)
−0.619489 + 0.785006i \(0.712660\pi\)
\(770\) −28.3830 + 5.30448i −1.02285 + 0.191160i
\(771\) −26.4524 + 81.4121i −0.952660 + 2.93199i
\(772\) −4.71288 1.53131i −0.169620 0.0551130i
\(773\) −6.94380 9.55732i −0.249751 0.343753i 0.665673 0.746244i \(-0.268145\pi\)
−0.915424 + 0.402491i \(0.868145\pi\)
\(774\) −73.9438 −2.65785
\(775\) 7.08783 + 1.87643i 0.254602 + 0.0674034i
\(776\) −9.23242 −0.331425
\(777\) −36.0202 49.5776i −1.29222 1.77859i
\(778\) −18.4867 6.00671i −0.662782 0.215351i
\(779\) 2.59127 7.97510i 0.0928417 0.285737i
\(780\) 33.5384 35.4484i 1.20087 1.26925i
\(781\) −8.33592 25.6553i −0.298283 0.918019i
\(782\) 6.60805i 0.236303i
\(783\) −2.56902 + 0.834726i −0.0918094 + 0.0298307i
\(784\) −0.139043 0.101020i −0.00496581 0.00360787i
\(785\) −8.20968 + 4.47343i −0.293016 + 0.159664i
\(786\) 7.50338 5.45153i 0.267637 0.194450i
\(787\) −31.6875 + 43.6140i −1.12954 + 1.55467i −0.340588 + 0.940213i \(0.610626\pi\)
−0.788948 + 0.614460i \(0.789374\pi\)
\(788\) 2.45102 3.37354i 0.0873141 0.120178i
\(789\) −12.8077 + 9.30533i −0.455966 + 0.331279i
\(790\) −1.40383 1.32819i −0.0499459 0.0472549i
\(791\) 0.869624 + 0.631819i 0.0309203 + 0.0224649i
\(792\) 33.5548 10.9026i 1.19232 0.387407i
\(793\) 33.9682i 1.20624i
\(794\) 1.85041 + 5.69498i 0.0656686 + 0.202107i
\(795\) 9.39522 72.1995i 0.333214 2.56065i
\(796\) −4.36425 + 13.4318i −0.154687 + 0.476077i
\(797\) 5.50589 + 1.78897i 0.195029 + 0.0633687i 0.404903 0.914360i \(-0.367305\pi\)
−0.209874 + 0.977728i \(0.567305\pi\)
\(798\) 4.89079 + 6.73159i 0.173132 + 0.238296i
\(799\) 3.54145 0.125288
\(800\) 4.20149 + 2.71062i 0.148545 + 0.0958348i
\(801\) −106.830 −3.77467
\(802\) −4.98640 6.86319i −0.176076 0.242348i
\(803\) 6.37009 + 2.06977i 0.224796 + 0.0730405i
\(804\) −1.78980 + 5.50844i −0.0631214 + 0.194268i
\(805\) 33.8752 + 16.0954i 1.19394 + 0.567287i
\(806\) −3.10569 9.55833i −0.109393 0.336678i
\(807\) 69.8557i 2.45904i
\(808\) 6.53260 2.12257i 0.229816 0.0746718i
\(809\) 1.66458 + 1.20939i 0.0585236 + 0.0425199i 0.616662 0.787228i \(-0.288484\pi\)
−0.558139 + 0.829748i \(0.688484\pi\)
\(810\) −45.5769 5.93085i −1.60141 0.208389i
\(811\) 28.7211 20.8671i 1.00853 0.732742i 0.0446325 0.999003i \(-0.485788\pi\)
0.963901 + 0.266261i \(0.0857883\pi\)
\(812\) 0.314753 0.433220i 0.0110457 0.0152030i
\(813\) 51.9989 71.5703i 1.82368 2.51008i
\(814\) 29.4444 21.3926i 1.03203 0.749810i
\(815\) 29.8423 + 3.88334i 1.04533 + 0.136027i
\(816\) 2.65212 + 1.92687i 0.0928426 + 0.0674541i
\(817\) 9.85003 3.20047i 0.344609 0.111970i
\(818\) 7.11303i 0.248701i
\(819\) −39.5118 121.605i −1.38065 4.24922i
\(820\) −16.9361 8.04696i −0.591433 0.281012i
\(821\) −6.55842 + 20.1847i −0.228890 + 0.704452i 0.768983 + 0.639269i \(0.220763\pi\)
−0.997873 + 0.0651828i \(0.979237\pi\)
\(822\) −39.7860 12.9272i −1.38769 0.450889i
\(823\) 13.7089 + 18.8686i 0.477861 + 0.657719i 0.978092 0.208173i \(-0.0667517\pi\)
−0.500231 + 0.865892i \(0.666752\pi\)
\(824\) −15.6305 −0.544513
\(825\) −20.1357 + 76.0584i −0.701035 + 2.64801i
\(826\) 28.8927 1.00531
\(827\) −5.59729 7.70401i −0.194637 0.267895i 0.700533 0.713620i \(-0.252946\pi\)
−0.895170 + 0.445725i \(0.852946\pi\)
\(828\) −43.5837 14.1612i −1.51464 0.492136i
\(829\) −10.5117 + 32.3518i −0.365088 + 1.12362i 0.584838 + 0.811150i \(0.301158\pi\)
−0.949926 + 0.312475i \(0.898842\pi\)
\(830\) 2.09056 16.0654i 0.0725644 0.557637i
\(831\) 8.00558 + 24.6386i 0.277711 + 0.854705i
\(832\) 6.85367i 0.237608i
\(833\) 0.168276 0.0546763i 0.00583042 0.00189442i
\(834\) −16.0208 11.6398i −0.554754 0.403052i
\(835\) 11.3450 + 10.7338i 0.392610 + 0.371457i
\(836\) −3.99793 + 2.90467i −0.138271 + 0.100460i
\(837\) −11.3614 + 15.6377i −0.392708 + 0.540517i
\(838\) 2.76449 3.80499i 0.0954977 0.131441i
\(839\) −13.5974 + 9.87911i −0.469435 + 0.341065i −0.797221 0.603687i \(-0.793698\pi\)
0.327786 + 0.944752i \(0.393698\pi\)
\(840\) 16.3377 8.90235i 0.563703 0.307160i
\(841\) 23.4275 + 17.0211i 0.807845 + 0.586934i
\(842\) 29.7550 9.66798i 1.02542 0.333180i
\(843\) 46.5119i 1.60195i
\(844\) −3.31922 10.2155i −0.114252 0.351632i
\(845\) 52.2085 55.1816i 1.79603 1.89831i
\(846\) −7.58942 + 23.3578i −0.260930 + 0.803059i
\(847\) −33.3524 10.8368i −1.14600 0.372358i
\(848\) −6.01043 8.27264i −0.206399 0.284084i
\(849\) 5.81231 0.199478
\(850\) −4.80005 + 1.85909i −0.164640 + 0.0637662i
\(851\) −47.2732 −1.62050
\(852\) 10.2170 + 14.0624i 0.350027 + 0.481771i
\(853\) 9.03505 + 2.93567i 0.309354 + 0.100515i 0.459580 0.888136i \(-0.348000\pi\)
−0.150226 + 0.988652i \(0.548000\pi\)
\(854\) −4.00205 + 12.3170i −0.136947 + 0.421480i
\(855\) 15.6928 2.93282i 0.536683 0.100300i
\(856\) 5.50059 + 16.9291i 0.188006 + 0.578624i
\(857\) 48.0386i 1.64097i −0.571671 0.820483i \(-0.693705\pi\)
0.571671 0.820483i \(-0.306295\pi\)
\(858\) 102.569 33.3267i 3.50165 1.13775i
\(859\) −30.2760 21.9968i −1.03300 0.750520i −0.0640949 0.997944i \(-0.520416\pi\)
−0.968907 + 0.247424i \(0.920416\pi\)
\(860\) −4.25447 22.7647i −0.145076 0.776269i
\(861\) −56.4479 + 41.0118i −1.92374 + 1.39768i
\(862\) 10.1065 13.9104i 0.344230 0.473792i
\(863\) −5.86473 + 8.07211i −0.199638 + 0.274778i −0.897085 0.441859i \(-0.854319\pi\)
0.697447 + 0.716636i \(0.254319\pi\)
\(864\) −10.6640 + 7.74784i −0.362796 + 0.263587i
\(865\) 6.88810 14.4971i 0.234202 0.492915i
\(866\) 21.5613 + 15.6652i 0.732684 + 0.532326i
\(867\) 48.2734 15.6850i 1.63945 0.532689i
\(868\) 3.83181i 0.130060i
\(869\) −1.31980 4.06194i −0.0447713 0.137792i
\(870\) −0.698158 1.28126i −0.0236698 0.0434389i
\(871\) −3.85229 + 11.8561i −0.130530 + 0.401729i
\(872\) 7.51160 + 2.44067i 0.254375 + 0.0826514i
\(873\) 38.7440 + 53.3266i 1.31129 + 1.80483i
\(874\) 6.41871 0.217116
\(875\) −2.16124 + 29.1350i −0.0730634 + 0.984941i
\(876\) −4.31590 −0.145821
\(877\) −4.53484 6.24168i −0.153131 0.210766i 0.725559 0.688160i \(-0.241581\pi\)
−0.878689 + 0.477394i \(0.841581\pi\)
\(878\) 7.92526 + 2.57507i 0.267465 + 0.0869045i
\(879\) 16.1199 49.6119i 0.543710 1.67337i
\(880\) 5.28715 + 9.70302i 0.178230 + 0.327089i
\(881\) 3.45729 + 10.6404i 0.116479 + 0.358486i 0.992253 0.124236i \(-0.0396481\pi\)
−0.875774 + 0.482722i \(0.839648\pi\)
\(882\) 1.22705i 0.0413168i
\(883\) −32.7100 + 10.6281i −1.10078 + 0.357665i −0.802402 0.596783i \(-0.796445\pi\)
−0.298377 + 0.954448i \(0.596445\pi\)
\(884\) 5.70829 + 4.14732i 0.191991 + 0.139489i
\(885\) 33.7870 71.1098i 1.13574 2.39033i
\(886\) −12.8868 + 9.36281i −0.432941 + 0.314550i
\(887\) 18.7409 25.7946i 0.629256 0.866097i −0.368729 0.929537i \(-0.620207\pi\)
0.997986 + 0.0634399i \(0.0202071\pi\)
\(888\) −13.7846 + 18.9729i −0.462582 + 0.636690i
\(889\) −12.6583 + 9.19682i −0.424547 + 0.308451i
\(890\) −6.14666 32.8893i −0.206036 1.10245i
\(891\) −82.1753 59.7038i −2.75297 2.00015i
\(892\) 4.09539 1.33067i 0.137124 0.0445543i
\(893\) 3.43998i 0.115115i
\(894\) −8.94278 27.5230i −0.299091 0.920508i
\(895\) −37.0437 + 6.92306i −1.23823 + 0.231413i
\(896\) 0.807483 2.48518i 0.0269761 0.0830239i
\(897\) −133.225 43.2875i −4.44826 1.44533i
\(898\) 24.5216 + 33.7511i 0.818298 + 1.12629i
\(899\) −0.300506 −0.0100224
\(900\) −1.97509 35.6430i −0.0658364 1.18810i
\(901\) 10.5272 0.350711
\(902\) −24.3571 33.5247i −0.811003 1.11625i
\(903\) −81.9592 26.6302i −2.72743 0.886196i
\(904\) 0.127117 0.391227i 0.00422786 0.0130120i
\(905\) −4.06733 + 4.29895i −0.135203 + 0.142902i
\(906\) −21.6633 66.6729i −0.719716 2.21506i
\(907\) 27.5721i 0.915516i 0.889077 + 0.457758i \(0.151347\pi\)
−0.889077 + 0.457758i \(0.848653\pi\)
\(908\) 25.4079 8.25552i 0.843191 0.273969i
\(909\) −39.6742 28.8250i −1.31591 0.956064i
\(910\) 35.1644 19.1610i 1.16569 0.635181i
\(911\) −21.3795 + 15.5331i −0.708334 + 0.514635i −0.882636 0.470058i \(-0.844233\pi\)
0.174302 + 0.984692i \(0.444233\pi\)
\(912\) 1.87166 2.57612i 0.0619770 0.0853040i
\(913\) 21.0449 28.9659i 0.696486 0.958631i
\(914\) 7.45885 5.41917i 0.246717 0.179250i
\(915\) 25.6343 + 24.2532i 0.847445 + 0.801785i
\(916\) 0.769142 + 0.558814i 0.0254132 + 0.0184637i
\(917\) 7.23848 2.35193i 0.239036 0.0776674i
\(918\) 13.5702i 0.447884i
\(919\) −6.21623 19.1316i −0.205055 0.631093i −0.999711 0.0240340i \(-0.992349\pi\)
0.794656 0.607059i \(-0.207651\pi\)
\(920\) 1.85208 14.2327i 0.0610611 0.469237i
\(921\) −8.82030 + 27.1461i −0.290639 + 0.894494i
\(922\) 3.27338 + 1.06359i 0.107803 + 0.0350273i
\(923\) 21.9905 + 30.2673i 0.723826 + 0.996262i
\(924\) 41.1185 1.35270
\(925\) −13.2997 34.3390i −0.437292 1.12906i
\(926\) 15.6688 0.514908
\(927\) 65.5935 + 90.2817i 2.15437 + 2.96524i
\(928\) −0.194898 0.0633261i −0.00639783 0.00207878i
\(929\) −8.68209 + 26.7207i −0.284850 + 0.876678i 0.701594 + 0.712577i \(0.252472\pi\)
−0.986444 + 0.164101i \(0.947528\pi\)
\(930\) −9.43072 4.48089i −0.309245 0.146934i
\(931\) −0.0531096 0.163455i −0.00174060 0.00535701i
\(932\) 10.1819i 0.333521i
\(933\) −4.40273 + 1.43053i −0.144139 + 0.0468336i
\(934\) 3.41849 + 2.48368i 0.111856 + 0.0812684i
\(935\) −11.2808 1.46796i −0.368923 0.0480074i
\(936\) −39.5869 + 28.7615i −1.29394 + 0.940101i
\(937\) 13.4516 18.5145i 0.439445 0.604844i −0.530644 0.847595i \(-0.678050\pi\)
0.970089 + 0.242751i \(0.0780498\pi\)
\(938\) −2.79372 + 3.84523i −0.0912182 + 0.125551i
\(939\) 76.5904 55.6461i 2.49943 1.81594i
\(940\) −7.62772 0.992583i −0.248789 0.0323745i
\(941\) 19.8737 + 14.4391i 0.647864 + 0.470701i 0.862543 0.505984i \(-0.168871\pi\)
−0.214679 + 0.976685i \(0.568871\pi\)
\(942\) 12.6623 4.11423i 0.412560 0.134049i
\(943\) 53.8241i 1.75276i
\(944\) −3.41680 10.5158i −0.111207 0.342261i
\(945\) −69.5658 33.0533i −2.26298 1.07522i
\(946\) 15.8158 48.6760i 0.514216 1.58259i
\(947\) 1.53044 + 0.497269i 0.0497325 + 0.0161591i 0.333778 0.942652i \(-0.391677\pi\)
−0.284045 + 0.958811i \(0.591677\pi\)
\(948\) 1.61762 + 2.22647i 0.0525380 + 0.0723123i
\(949\) −9.28934 −0.301545
\(950\) 1.80582 + 4.66251i 0.0585885 + 0.151272i
\(951\) 68.9107 2.23458
\(952\) 1.58123 + 2.17638i 0.0512480 + 0.0705368i
\(953\) 29.0812 + 9.44907i 0.942034 + 0.306085i 0.739474 0.673185i \(-0.235074\pi\)
0.202559 + 0.979270i \(0.435074\pi\)
\(954\) −22.5600 + 69.4326i −0.730407 + 2.24796i
\(955\) −5.90749 + 45.3974i −0.191162 + 1.46902i
\(956\) 0.973806 + 2.99707i 0.0314951 + 0.0969321i
\(957\) 3.22468i 0.104239i
\(958\) −15.7157 + 5.10634i −0.507751 + 0.164978i
\(959\) −27.7730 20.1783i −0.896837 0.651590i
\(960\) −5.17217 4.89350i −0.166931 0.157937i
\(961\) 23.3399 16.9574i 0.752899 0.547013i
\(962\) −29.6694 + 40.8365i −0.956581 + 1.31662i
\(963\) 74.6992 102.815i 2.40715 3.31316i
\(964\) 10.3041 7.48635i 0.331872 0.241119i
\(965\) −9.72993 + 5.30181i −0.313217 + 0.170671i
\(966\) −43.2081 31.3925i −1.39020 1.01004i
\(967\) −54.5523 + 17.7251i −1.75429 + 0.570002i −0.996583 0.0825985i \(-0.973678\pi\)
−0.757702 + 0.652600i \(0.773678\pi\)
\(968\) 13.4205i 0.431352i
\(969\) 1.01302 + 3.11775i 0.0325428 + 0.100157i
\(970\) −14.1882 + 14.9961i −0.455554 + 0.481497i
\(971\) 15.8040 48.6398i 0.507175 1.56092i −0.289908 0.957055i \(-0.593625\pi\)
0.797083 0.603870i \(-0.206375\pi\)
\(972\) 24.6387 + 8.00559i 0.790286 + 0.256779i
\(973\) −9.55182 13.1470i −0.306217 0.421472i
\(974\) −16.5251 −0.529499
\(975\) −6.03739 108.952i −0.193351 3.48927i
\(976\) 4.95620 0.158644
\(977\) −9.18611 12.6436i −0.293890 0.404504i 0.636383 0.771373i \(-0.280430\pi\)
−0.930273 + 0.366869i \(0.880430\pi\)
\(978\) −40.7577 13.2430i −1.30329 0.423464i
\(979\) 22.8499 70.3248i 0.730286 2.24759i
\(980\) −0.377764 + 0.0706001i −0.0120672 + 0.00225524i
\(981\) −17.4252 53.6294i −0.556345 1.71225i
\(982\) 17.7546i 0.566571i
\(983\) −25.6625 + 8.33824i −0.818505 + 0.265948i −0.688196 0.725525i \(-0.741597\pi\)
−0.130309 + 0.991473i \(0.541597\pi\)
\(984\) 21.6021 + 15.6949i 0.688651 + 0.500334i
\(985\) −1.71294 9.16555i −0.0545789 0.292039i
\(986\) 0.170680 0.124006i 0.00543557 0.00394917i
\(987\) −16.8242 + 23.1565i −0.535521 + 0.737081i
\(988\) 4.02848 5.54473i 0.128163 0.176401i
\(989\) −53.7819 + 39.0749i −1.71017 + 1.24251i
\(990\) 33.8571 71.2576i 1.07605 2.26471i
\(991\) 19.9955 + 14.5276i 0.635179 + 0.461485i 0.858191 0.513331i \(-0.171589\pi\)
−0.223012 + 0.974816i \(0.571589\pi\)
\(992\) −1.39463 + 0.453143i −0.0442795 + 0.0143873i
\(993\) 28.5241i 0.905185i
\(994\) 4.40785 + 13.5660i 0.139809 + 0.430286i
\(995\) 15.1103 + 27.7305i 0.479027 + 0.879115i
\(996\) −7.12924 + 21.9415i −0.225899 + 0.695245i
\(997\) 6.04515 + 1.96419i 0.191452 + 0.0622065i 0.403174 0.915124i \(-0.367907\pi\)
−0.211722 + 0.977330i \(0.567907\pi\)
\(998\) −20.9505 28.8358i −0.663175 0.912783i
\(999\) 97.0799 3.07147
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 950.2.n.b.39.13 96
25.9 even 10 inner 950.2.n.b.609.13 yes 96
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.n.b.39.13 96 1.1 even 1 trivial
950.2.n.b.609.13 yes 96 25.9 even 10 inner