Properties

Label 273.2.e.a.209.2
Level $273$
Weight $2$
Character 273.209
Analytic conductor $2.180$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [273,2,Mod(209,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.209");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.e (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 209.2
Character \(\chi\) \(=\) 273.209
Dual form 273.2.e.a.209.32

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62996i q^{2} +(0.518189 - 1.65272i) q^{3} -4.91669 q^{4} -2.48925 q^{5} +(-4.34658 - 1.36282i) q^{6} +(1.33971 + 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} +O(q^{10})\) \(q-2.62996i q^{2} +(0.518189 - 1.65272i) q^{3} -4.91669 q^{4} -2.48925 q^{5} +(-4.34658 - 1.36282i) q^{6} +(1.33971 + 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} +6.54663i q^{10} -5.20518i q^{11} +(-2.54777 + 8.12590i) q^{12} +1.00000i q^{13} +(6.00022 - 3.52338i) q^{14} +(-1.28990 + 4.11403i) q^{15} +10.3404 q^{16} -2.44427 q^{17} +(-4.50471 + 6.47748i) q^{18} -2.29598i q^{19} +12.2389 q^{20} +(4.46488 - 1.03192i) q^{21} -13.6894 q^{22} -5.95242i q^{23} +(12.6776 + 3.97491i) q^{24} +1.19637 q^{25} +2.62996 q^{26} +(-4.10713 + 3.18300i) q^{27} +(-6.58692 - 11.2174i) q^{28} +2.80952i q^{29} +(10.8197 + 3.39239i) q^{30} -6.81176i q^{31} -11.8534i q^{32} +(-8.60270 - 2.69727i) q^{33} +6.42832i q^{34} +(-3.33487 - 5.67919i) q^{35} +(12.1096 + 8.42151i) q^{36} +3.17079 q^{37} -6.03833 q^{38} +(1.65272 + 0.518189i) q^{39} -19.0945i q^{40} -0.133822 q^{41} +(-2.71391 - 11.7424i) q^{42} +6.61311 q^{43} +25.5922i q^{44} +(6.13092 + 4.26369i) q^{45} -15.6546 q^{46} +4.15911 q^{47} +(5.35830 - 17.0898i) q^{48} +(-3.41036 + 6.11305i) q^{49} -3.14640i q^{50} +(-1.26659 + 4.03969i) q^{51} -4.91669i q^{52} +7.32479i q^{53} +(8.37117 + 10.8016i) q^{54} +12.9570i q^{55} +(-17.5007 + 10.2766i) q^{56} +(-3.79461 - 1.18975i) q^{57} +7.38893 q^{58} +0.723671 q^{59} +(6.34205 - 20.2274i) q^{60} -8.23191i q^{61} -17.9147 q^{62} +(0.608179 - 7.91392i) q^{63} -10.4930 q^{64} -2.48925i q^{65} +(-7.09370 + 22.6247i) q^{66} -1.52087 q^{67} +12.0177 q^{68} +(-9.83767 - 3.08448i) q^{69} +(-14.9360 + 8.77057i) q^{70} -7.17852i q^{71} +(13.1388 - 18.8928i) q^{72} -16.4534i q^{73} -8.33904i q^{74} +(0.619945 - 1.97726i) q^{75} +11.2886i q^{76} +(11.8755 - 6.97342i) q^{77} +(1.36282 - 4.34658i) q^{78} -0.0675159 q^{79} -25.7399 q^{80} +(3.13234 + 8.43732i) q^{81} +0.351945i q^{82} +6.38210 q^{83} +(-21.9524 + 5.07362i) q^{84} +6.08439 q^{85} -17.3922i q^{86} +(4.64335 + 1.45586i) q^{87} +39.9277 q^{88} -14.3874 q^{89} +(11.2133 - 16.1241i) q^{90} +(-2.28149 + 1.33971i) q^{91} +29.2662i q^{92} +(-11.2579 - 3.52978i) q^{93} -10.9383i q^{94} +5.71527i q^{95} +(-19.5903 - 6.14229i) q^{96} -16.7297i q^{97} +(16.0771 + 8.96912i) q^{98} +(-8.91565 + 12.8201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.62996i 1.85966i −0.367987 0.929831i \(-0.619953\pi\)
0.367987 0.929831i \(-0.380047\pi\)
\(3\) 0.518189 1.65272i 0.299177 0.954198i
\(4\) −4.91669 −2.45834
\(5\) −2.48925 −1.11323 −0.556613 0.830772i \(-0.687899\pi\)
−0.556613 + 0.830772i \(0.687899\pi\)
\(6\) −4.34658 1.36282i −1.77449 0.556367i
\(7\) 1.33971 + 2.28149i 0.506362 + 0.862321i
\(8\) 7.67077i 2.71203i
\(9\) −2.46296 1.71284i −0.820987 0.570947i
\(10\) 6.54663i 2.07023i
\(11\) 5.20518i 1.56942i −0.619863 0.784710i \(-0.712812\pi\)
0.619863 0.784710i \(-0.287188\pi\)
\(12\) −2.54777 + 8.12590i −0.735479 + 2.34575i
\(13\) 1.00000i 0.277350i
\(14\) 6.00022 3.52338i 1.60363 0.941662i
\(15\) −1.28990 + 4.11403i −0.333051 + 1.06224i
\(16\) 10.3404 2.58511
\(17\) −2.44427 −0.592822 −0.296411 0.955061i \(-0.595790\pi\)
−0.296411 + 0.955061i \(0.595790\pi\)
\(18\) −4.50471 + 6.47748i −1.06177 + 1.52676i
\(19\) 2.29598i 0.526734i −0.964696 0.263367i \(-0.915167\pi\)
0.964696 0.263367i \(-0.0848330\pi\)
\(20\) 12.2389 2.73669
\(21\) 4.46488 1.03192i 0.974316 0.225183i
\(22\) −13.6894 −2.91859
\(23\) 5.95242i 1.24116i −0.784141 0.620582i \(-0.786896\pi\)
0.784141 0.620582i \(-0.213104\pi\)
\(24\) 12.6776 + 3.97491i 2.58781 + 0.811375i
\(25\) 1.19637 0.239273
\(26\) 2.62996 0.515777
\(27\) −4.10713 + 3.18300i −0.790417 + 0.612569i
\(28\) −6.58692 11.2174i −1.24481 2.11988i
\(29\) 2.80952i 0.521715i 0.965377 + 0.260858i \(0.0840053\pi\)
−0.965377 + 0.260858i \(0.915995\pi\)
\(30\) 10.8197 + 3.39239i 1.97540 + 0.619363i
\(31\) 6.81176i 1.22343i −0.791079 0.611714i \(-0.790480\pi\)
0.791079 0.611714i \(-0.209520\pi\)
\(32\) 11.8534i 2.09540i
\(33\) −8.60270 2.69727i −1.49754 0.469534i
\(34\) 6.42832i 1.10245i
\(35\) −3.33487 5.67919i −0.563696 0.959959i
\(36\) 12.1096 + 8.42151i 2.01827 + 1.40358i
\(37\) 3.17079 0.521274 0.260637 0.965437i \(-0.416067\pi\)
0.260637 + 0.965437i \(0.416067\pi\)
\(38\) −6.03833 −0.979547
\(39\) 1.65272 + 0.518189i 0.264647 + 0.0829767i
\(40\) 19.0945i 3.01910i
\(41\) −0.133822 −0.0208994 −0.0104497 0.999945i \(-0.503326\pi\)
−0.0104497 + 0.999945i \(0.503326\pi\)
\(42\) −2.71391 11.7424i −0.418765 1.81190i
\(43\) 6.61311 1.00849 0.504245 0.863561i \(-0.331771\pi\)
0.504245 + 0.863561i \(0.331771\pi\)
\(44\) 25.5922i 3.85817i
\(45\) 6.13092 + 4.26369i 0.913944 + 0.635594i
\(46\) −15.6546 −2.30815
\(47\) 4.15911 0.606669 0.303334 0.952884i \(-0.401900\pi\)
0.303334 + 0.952884i \(0.401900\pi\)
\(48\) 5.35830 17.0898i 0.773404 2.46670i
\(49\) −3.41036 + 6.11305i −0.487195 + 0.873293i
\(50\) 3.14640i 0.444968i
\(51\) −1.26659 + 4.03969i −0.177358 + 0.565669i
\(52\) 4.91669i 0.681822i
\(53\) 7.32479i 1.00614i 0.864247 + 0.503069i \(0.167796\pi\)
−0.864247 + 0.503069i \(0.832204\pi\)
\(54\) 8.37117 + 10.8016i 1.13917 + 1.46991i
\(55\) 12.9570i 1.74712i
\(56\) −17.5007 + 10.2766i −2.33864 + 1.37327i
\(57\) −3.79461 1.18975i −0.502608 0.157586i
\(58\) 7.38893 0.970214
\(59\) 0.723671 0.0942140 0.0471070 0.998890i \(-0.485000\pi\)
0.0471070 + 0.998890i \(0.485000\pi\)
\(60\) 6.34205 20.2274i 0.818755 2.61135i
\(61\) 8.23191i 1.05399i −0.849869 0.526994i \(-0.823319\pi\)
0.849869 0.526994i \(-0.176681\pi\)
\(62\) −17.9147 −2.27516
\(63\) 0.608179 7.91392i 0.0766233 0.997060i
\(64\) −10.4930 −1.31163
\(65\) 2.48925i 0.308754i
\(66\) −7.09370 + 22.6247i −0.873174 + 2.78491i
\(67\) −1.52087 −0.185804 −0.0929020 0.995675i \(-0.529614\pi\)
−0.0929020 + 0.995675i \(0.529614\pi\)
\(68\) 12.0177 1.45736
\(69\) −9.83767 3.08448i −1.18432 0.371328i
\(70\) −14.9360 + 8.77057i −1.78520 + 1.04828i
\(71\) 7.17852i 0.851933i −0.904739 0.425967i \(-0.859934\pi\)
0.904739 0.425967i \(-0.140066\pi\)
\(72\) 13.1388 18.8928i 1.54842 2.22654i
\(73\) 16.4534i 1.92573i −0.269989 0.962864i \(-0.587020\pi\)
0.269989 0.962864i \(-0.412980\pi\)
\(74\) 8.33904i 0.969394i
\(75\) 0.619945 1.97726i 0.0715850 0.228314i
\(76\) 11.2886i 1.29489i
\(77\) 11.8755 6.97342i 1.35334 0.794695i
\(78\) 1.36282 4.34658i 0.154309 0.492154i
\(79\) −0.0675159 −0.00759613 −0.00379806 0.999993i \(-0.501209\pi\)
−0.00379806 + 0.999993i \(0.501209\pi\)
\(80\) −25.7399 −2.87781
\(81\) 3.13234 + 8.43732i 0.348038 + 0.937480i
\(82\) 0.351945i 0.0388659i
\(83\) 6.38210 0.700526 0.350263 0.936651i \(-0.386092\pi\)
0.350263 + 0.936651i \(0.386092\pi\)
\(84\) −21.9524 + 5.07362i −2.39520 + 0.553578i
\(85\) 6.08439 0.659945
\(86\) 17.3922i 1.87545i
\(87\) 4.64335 + 1.45586i 0.497819 + 0.156085i
\(88\) 39.9277 4.25631
\(89\) −14.3874 −1.52506 −0.762531 0.646952i \(-0.776043\pi\)
−0.762531 + 0.646952i \(0.776043\pi\)
\(90\) 11.2133 16.1241i 1.18199 1.69963i
\(91\) −2.28149 + 1.33971i −0.239165 + 0.140440i
\(92\) 29.2662i 3.05121i
\(93\) −11.2579 3.52978i −1.16739 0.366021i
\(94\) 10.9383i 1.12820i
\(95\) 5.71527i 0.586374i
\(96\) −19.5903 6.14229i −1.99943 0.626895i
\(97\) 16.7297i 1.69864i −0.527875 0.849322i \(-0.677011\pi\)
0.527875 0.849322i \(-0.322989\pi\)
\(98\) 16.0771 + 8.96912i 1.62403 + 0.906018i
\(99\) −8.91565 + 12.8201i −0.896056 + 1.28847i
\(100\) −5.88216 −0.588216
\(101\) 7.10159 0.706634 0.353317 0.935504i \(-0.385054\pi\)
0.353317 + 0.935504i \(0.385054\pi\)
\(102\) 10.6242 + 3.33109i 1.05195 + 0.329827i
\(103\) 6.92654i 0.682492i 0.939974 + 0.341246i \(0.110849\pi\)
−0.939974 + 0.341246i \(0.889151\pi\)
\(104\) −7.67077 −0.752180
\(105\) −11.1142 + 2.56871i −1.08463 + 0.250680i
\(106\) 19.2639 1.87108
\(107\) 5.50532i 0.532219i 0.963943 + 0.266110i \(0.0857383\pi\)
−0.963943 + 0.266110i \(0.914262\pi\)
\(108\) 20.1934 15.6498i 1.94312 1.50591i
\(109\) 19.7025 1.88716 0.943579 0.331146i \(-0.107435\pi\)
0.943579 + 0.331146i \(0.107435\pi\)
\(110\) 34.0764 3.24905
\(111\) 1.64307 5.24042i 0.155953 0.497399i
\(112\) 13.8532 + 23.5916i 1.30900 + 2.22919i
\(113\) 1.15948i 0.109075i −0.998512 0.0545375i \(-0.982632\pi\)
0.998512 0.0545375i \(-0.0173684\pi\)
\(114\) −3.12900 + 9.97966i −0.293057 + 0.934681i
\(115\) 14.8171i 1.38170i
\(116\) 13.8135i 1.28255i
\(117\) 1.71284 2.46296i 0.158352 0.227701i
\(118\) 1.90323i 0.175206i
\(119\) −3.27460 5.57656i −0.300183 0.511203i
\(120\) −31.5578 9.89454i −2.88082 0.903244i
\(121\) −16.0939 −1.46308
\(122\) −21.6496 −1.96006
\(123\) −0.0693449 + 0.221169i −0.00625262 + 0.0199422i
\(124\) 33.4913i 3.00761i
\(125\) 9.46819 0.846861
\(126\) −20.8133 1.59949i −1.85419 0.142493i
\(127\) −9.96125 −0.883918 −0.441959 0.897035i \(-0.645716\pi\)
−0.441959 + 0.897035i \(0.645716\pi\)
\(128\) 3.88951i 0.343788i
\(129\) 3.42684 10.9296i 0.301717 0.962299i
\(130\) −6.54663 −0.574177
\(131\) 0.482982 0.0421983 0.0210991 0.999777i \(-0.493283\pi\)
0.0210991 + 0.999777i \(0.493283\pi\)
\(132\) 42.2968 + 13.2616i 3.68146 + 1.15428i
\(133\) 5.23825 3.07594i 0.454213 0.266718i
\(134\) 3.99983i 0.345533i
\(135\) 10.2237 7.92329i 0.879913 0.681929i
\(136\) 18.7494i 1.60775i
\(137\) 14.2883i 1.22073i 0.792119 + 0.610366i \(0.208978\pi\)
−0.792119 + 0.610366i \(0.791022\pi\)
\(138\) −8.11205 + 25.8727i −0.690544 + 2.20243i
\(139\) 15.6954i 1.33127i 0.746280 + 0.665633i \(0.231838\pi\)
−0.746280 + 0.665633i \(0.768162\pi\)
\(140\) 16.3965 + 27.9228i 1.38576 + 2.35991i
\(141\) 2.15521 6.87384i 0.181501 0.578882i
\(142\) −18.8792 −1.58431
\(143\) 5.20518 0.435279
\(144\) −25.4681 17.7115i −2.12234 1.47596i
\(145\) 6.99360i 0.580787i
\(146\) −43.2718 −3.58120
\(147\) 8.33595 + 8.80409i 0.687537 + 0.726149i
\(148\) −15.5898 −1.28147
\(149\) 2.86126i 0.234403i 0.993108 + 0.117202i \(0.0373924\pi\)
−0.993108 + 0.117202i \(0.962608\pi\)
\(150\) −5.20011 1.63043i −0.424587 0.133124i
\(151\) 7.22458 0.587928 0.293964 0.955816i \(-0.405025\pi\)
0.293964 + 0.955816i \(0.405025\pi\)
\(152\) 17.6119 1.42851
\(153\) 6.02013 + 4.18664i 0.486699 + 0.338470i
\(154\) −18.3398 31.2322i −1.47786 2.51676i
\(155\) 16.9562i 1.36195i
\(156\) −8.12590 2.54777i −0.650593 0.203985i
\(157\) 5.09913i 0.406955i 0.979080 + 0.203477i \(0.0652243\pi\)
−0.979080 + 0.203477i \(0.934776\pi\)
\(158\) 0.177564i 0.0141262i
\(159\) 12.1058 + 3.79563i 0.960054 + 0.301013i
\(160\) 29.5060i 2.33266i
\(161\) 13.5804 7.97450i 1.07028 0.628479i
\(162\) 22.1898 8.23794i 1.74340 0.647233i
\(163\) 13.2180 1.03531 0.517657 0.855588i \(-0.326804\pi\)
0.517657 + 0.855588i \(0.326804\pi\)
\(164\) 0.657959 0.0513779
\(165\) 21.4143 + 6.71417i 1.66710 + 0.522698i
\(166\) 16.7847i 1.30274i
\(167\) 14.8090 1.14596 0.572979 0.819570i \(-0.305788\pi\)
0.572979 + 0.819570i \(0.305788\pi\)
\(168\) 7.91561 + 34.2490i 0.610703 + 2.64237i
\(169\) −1.00000 −0.0769231
\(170\) 16.0017i 1.22727i
\(171\) −3.93265 + 5.65490i −0.300737 + 0.432441i
\(172\) −32.5146 −2.47921
\(173\) 5.26717 0.400455 0.200228 0.979749i \(-0.435832\pi\)
0.200228 + 0.979749i \(0.435832\pi\)
\(174\) 3.82886 12.2118i 0.290265 0.925776i
\(175\) 1.60278 + 2.72950i 0.121159 + 0.206331i
\(176\) 53.8238i 4.05712i
\(177\) 0.374999 1.19603i 0.0281866 0.0898988i
\(178\) 37.8383i 2.83610i
\(179\) 1.62411i 0.121391i 0.998156 + 0.0606957i \(0.0193319\pi\)
−0.998156 + 0.0606957i \(0.980668\pi\)
\(180\) −30.1438 20.9632i −2.24679 1.56251i
\(181\) 2.03409i 0.151193i 0.997139 + 0.0755963i \(0.0240860\pi\)
−0.997139 + 0.0755963i \(0.975914\pi\)
\(182\) 3.52338 + 6.00022i 0.261170 + 0.444766i
\(183\) −13.6050 4.26568i −1.00571 0.315328i
\(184\) 45.6596 3.36607
\(185\) −7.89288 −0.580296
\(186\) −9.28318 + 29.6079i −0.680676 + 2.17096i
\(187\) 12.7228i 0.930386i
\(188\) −20.4491 −1.49140
\(189\) −12.7643 5.10606i −0.928469 0.371411i
\(190\) 15.0309 1.09046
\(191\) 3.53954i 0.256112i −0.991767 0.128056i \(-0.959126\pi\)
0.991767 0.128056i \(-0.0408738\pi\)
\(192\) −5.43738 + 17.3420i −0.392409 + 1.25155i
\(193\) −12.8190 −0.922732 −0.461366 0.887210i \(-0.652640\pi\)
−0.461366 + 0.887210i \(0.652640\pi\)
\(194\) −43.9985 −3.15891
\(195\) −4.11403 1.28990i −0.294612 0.0923718i
\(196\) 16.7677 30.0560i 1.19769 2.14685i
\(197\) 15.2887i 1.08927i −0.838673 0.544636i \(-0.816668\pi\)
0.838673 0.544636i \(-0.183332\pi\)
\(198\) 33.7165 + 23.4478i 2.39612 + 1.66636i
\(199\) 9.65388i 0.684345i 0.939637 + 0.342173i \(0.111163\pi\)
−0.939637 + 0.342173i \(0.888837\pi\)
\(200\) 9.17705i 0.648916i
\(201\) −0.788099 + 2.51357i −0.0555882 + 0.177294i
\(202\) 18.6769i 1.31410i
\(203\) −6.40989 + 3.76394i −0.449886 + 0.264177i
\(204\) 6.22744 19.8619i 0.436008 1.39061i
\(205\) 0.333115 0.0232658
\(206\) 18.2165 1.26921
\(207\) −10.1956 + 14.6606i −0.708640 + 1.01898i
\(208\) 10.3404i 0.716980i
\(209\) −11.9510 −0.826666
\(210\) 6.75559 + 29.2299i 0.466180 + 2.01705i
\(211\) −1.99971 −0.137666 −0.0688328 0.997628i \(-0.521928\pi\)
−0.0688328 + 0.997628i \(0.521928\pi\)
\(212\) 36.0137i 2.47343i
\(213\) −11.8641 3.71983i −0.812913 0.254879i
\(214\) 14.4788 0.989748
\(215\) −16.4617 −1.12268
\(216\) −24.4161 31.5048i −1.66130 2.14363i
\(217\) 15.5409 9.12577i 1.05499 0.619498i
\(218\) 51.8168i 3.50948i
\(219\) −27.1929 8.52598i −1.83752 0.576133i
\(220\) 63.7055i 4.29502i
\(221\) 2.44427i 0.164419i
\(222\) −13.7821 4.32120i −0.924993 0.290020i
\(223\) 13.5978i 0.910579i −0.890343 0.455290i \(-0.849536\pi\)
0.890343 0.455290i \(-0.150464\pi\)
\(224\) 27.0433 15.8801i 1.80691 1.06103i
\(225\) −2.94660 2.04919i −0.196440 0.136613i
\(226\) −3.04939 −0.202843
\(227\) −3.90471 −0.259165 −0.129582 0.991569i \(-0.541364\pi\)
−0.129582 + 0.991569i \(0.541364\pi\)
\(228\) 18.6569 + 5.84963i 1.23558 + 0.387401i
\(229\) 17.1919i 1.13608i 0.823002 + 0.568038i \(0.192297\pi\)
−0.823002 + 0.568038i \(0.807703\pi\)
\(230\) 38.9683 2.56949
\(231\) −5.37132 23.2405i −0.353407 1.52911i
\(232\) −21.5512 −1.41490
\(233\) 7.00005i 0.458589i −0.973357 0.229294i \(-0.926358\pi\)
0.973357 0.229294i \(-0.0736418\pi\)
\(234\) −6.47748 4.50471i −0.423446 0.294482i
\(235\) −10.3531 −0.675360
\(236\) −3.55806 −0.231610
\(237\) −0.0349860 + 0.111585i −0.00227258 + 0.00724821i
\(238\) −14.6661 + 8.61208i −0.950664 + 0.558238i
\(239\) 11.5946i 0.749991i 0.927027 + 0.374995i \(0.122356\pi\)
−0.927027 + 0.374995i \(0.877644\pi\)
\(240\) −13.3381 + 42.5408i −0.860974 + 2.74600i
\(241\) 21.0706i 1.35727i 0.734473 + 0.678637i \(0.237429\pi\)
−0.734473 + 0.678637i \(0.762571\pi\)
\(242\) 42.3262i 2.72083i
\(243\) 15.5677 0.804754i 0.998667 0.0516250i
\(244\) 40.4737i 2.59106i
\(245\) 8.48925 15.2169i 0.542358 0.972173i
\(246\) 0.581667 + 0.182374i 0.0370857 + 0.0116278i
\(247\) 2.29598 0.146090
\(248\) 52.2514 3.31797
\(249\) 3.30713 10.5478i 0.209581 0.668441i
\(250\) 24.9010i 1.57488i
\(251\) 2.45633 0.155042 0.0775212 0.996991i \(-0.475299\pi\)
0.0775212 + 0.996991i \(0.475299\pi\)
\(252\) −2.99022 + 38.9103i −0.188366 + 2.45112i
\(253\) −30.9834 −1.94791
\(254\) 26.1977i 1.64379i
\(255\) 3.15287 10.0558i 0.197440 0.629718i
\(256\) −10.7568 −0.672301
\(257\) 9.21648 0.574908 0.287454 0.957794i \(-0.407191\pi\)
0.287454 + 0.957794i \(0.407191\pi\)
\(258\) −28.7444 9.01245i −1.78955 0.561091i
\(259\) 4.24793 + 7.23411i 0.263953 + 0.449506i
\(260\) 12.2389i 0.759022i
\(261\) 4.81227 6.91974i 0.297872 0.428321i
\(262\) 1.27022i 0.0784746i
\(263\) 20.7018i 1.27653i 0.769817 + 0.638265i \(0.220348\pi\)
−0.769817 + 0.638265i \(0.779652\pi\)
\(264\) 20.6901 65.9893i 1.27339 4.06136i
\(265\) 18.2332i 1.12006i
\(266\) −8.08960 13.7764i −0.496005 0.844684i
\(267\) −7.45539 + 23.7783i −0.456263 + 1.45521i
\(268\) 7.47764 0.456770
\(269\) −29.7555 −1.81422 −0.907111 0.420891i \(-0.861718\pi\)
−0.907111 + 0.420891i \(0.861718\pi\)
\(270\) −20.8379 26.8878i −1.26816 1.63634i
\(271\) 2.24336i 0.136274i −0.997676 0.0681372i \(-0.978294\pi\)
0.997676 0.0681372i \(-0.0217056\pi\)
\(272\) −25.2748 −1.53251
\(273\) 1.03192 + 4.46488i 0.0624546 + 0.270227i
\(274\) 37.5777 2.27015
\(275\) 6.22730i 0.375521i
\(276\) 48.3687 + 15.1654i 2.91146 + 0.912850i
\(277\) 11.1835 0.671949 0.335974 0.941871i \(-0.390934\pi\)
0.335974 + 0.941871i \(0.390934\pi\)
\(278\) 41.2782 2.47570
\(279\) −11.6675 + 16.7771i −0.698513 + 1.00442i
\(280\) 43.5637 25.5810i 2.60343 1.52876i
\(281\) 20.1280i 1.20074i −0.799724 0.600368i \(-0.795021\pi\)
0.799724 0.600368i \(-0.204979\pi\)
\(282\) −18.0779 5.66811i −1.07653 0.337531i
\(283\) 1.71130i 0.101726i −0.998706 0.0508632i \(-0.983803\pi\)
0.998706 0.0508632i \(-0.0161972\pi\)
\(284\) 35.2945i 2.09434i
\(285\) 9.44573 + 2.96159i 0.559517 + 0.175429i
\(286\) 13.6894i 0.809472i
\(287\) −0.179282 0.305312i −0.0105827 0.0180220i
\(288\) −20.3030 + 29.1944i −1.19636 + 1.72030i
\(289\) −11.0256 −0.648562
\(290\) −18.3929 −1.08007
\(291\) −27.6495 8.66915i −1.62084 0.508195i
\(292\) 80.8963i 4.73410i
\(293\) 10.3117 0.602414 0.301207 0.953559i \(-0.402610\pi\)
0.301207 + 0.953559i \(0.402610\pi\)
\(294\) 23.1544 21.9232i 1.35039 1.27859i
\(295\) −1.80140 −0.104881
\(296\) 24.3224i 1.41371i
\(297\) 16.5681 + 21.3783i 0.961379 + 1.24050i
\(298\) 7.52499 0.435911
\(299\) 5.95242 0.344237
\(300\) −3.04807 + 9.72156i −0.175981 + 0.561275i
\(301\) 8.85964 + 15.0877i 0.510661 + 0.869642i
\(302\) 19.0004i 1.09335i
\(303\) 3.67997 11.7369i 0.211409 0.674269i
\(304\) 23.7414i 1.36166i
\(305\) 20.4913i 1.17333i
\(306\) 11.0107 15.8327i 0.629440 0.905095i
\(307\) 5.34432i 0.305017i 0.988302 + 0.152508i \(0.0487351\pi\)
−0.988302 + 0.152508i \(0.951265\pi\)
\(308\) −58.3883 + 34.2861i −3.32698 + 1.95363i
\(309\) 11.4476 + 3.58926i 0.651233 + 0.204186i
\(310\) 44.5941 2.53277
\(311\) −27.6338 −1.56697 −0.783483 0.621413i \(-0.786559\pi\)
−0.783483 + 0.621413i \(0.786559\pi\)
\(312\) −3.97491 + 12.6776i −0.225035 + 0.717729i
\(313\) 16.7987i 0.949516i −0.880116 0.474758i \(-0.842536\pi\)
0.880116 0.474758i \(-0.157464\pi\)
\(314\) 13.4105 0.756798
\(315\) −1.51391 + 19.6997i −0.0852991 + 1.10995i
\(316\) 0.331954 0.0186739
\(317\) 13.4327i 0.754457i −0.926120 0.377228i \(-0.876877\pi\)
0.926120 0.377228i \(-0.123123\pi\)
\(318\) 9.98234 31.8378i 0.559782 1.78538i
\(319\) 14.6241 0.818790
\(320\) 26.1198 1.46014
\(321\) 9.09874 + 2.85280i 0.507842 + 0.159228i
\(322\) −20.9726 35.7158i −1.16876 1.99036i
\(323\) 5.61198i 0.312259i
\(324\) −15.4008 41.4837i −0.855597 2.30465i
\(325\) 1.19637i 0.0663625i
\(326\) 34.7628i 1.92534i
\(327\) 10.2096 32.5627i 0.564594 1.80072i
\(328\) 1.02651i 0.0566798i
\(329\) 5.57200 + 9.48896i 0.307194 + 0.523143i
\(330\) 17.6580 56.3186i 0.972041 3.10024i
\(331\) −5.47069 −0.300696 −0.150348 0.988633i \(-0.548039\pi\)
−0.150348 + 0.988633i \(0.548039\pi\)
\(332\) −31.3788 −1.72213
\(333\) −7.80952 5.43106i −0.427959 0.297620i
\(334\) 38.9472i 2.13110i
\(335\) 3.78583 0.206842
\(336\) 46.1688 10.6705i 2.51871 0.582123i
\(337\) 26.4845 1.44270 0.721351 0.692570i \(-0.243521\pi\)
0.721351 + 0.692570i \(0.243521\pi\)
\(338\) 2.62996i 0.143051i
\(339\) −1.91630 0.600832i −0.104079 0.0326327i
\(340\) −29.9150 −1.62237
\(341\) −35.4564 −1.92007
\(342\) 14.8722 + 10.3427i 0.804195 + 0.559270i
\(343\) −18.5157 + 0.409009i −0.999756 + 0.0220844i
\(344\) 50.7276i 2.73505i
\(345\) 24.4884 + 7.67804i 1.31841 + 0.413372i
\(346\) 13.8524i 0.744712i
\(347\) 2.33454i 0.125325i −0.998035 0.0626625i \(-0.980041\pi\)
0.998035 0.0626625i \(-0.0199592\pi\)
\(348\) −22.8299 7.15802i −1.22381 0.383710i
\(349\) 6.44496i 0.344991i −0.985010 0.172495i \(-0.944817\pi\)
0.985010 0.172495i \(-0.0551830\pi\)
\(350\) 7.17846 4.21525i 0.383705 0.225315i
\(351\) −3.18300 4.10713i −0.169896 0.219222i
\(352\) −61.6989 −3.28856
\(353\) 4.66374 0.248226 0.124113 0.992268i \(-0.460392\pi\)
0.124113 + 0.992268i \(0.460392\pi\)
\(354\) −3.14550 0.986231i −0.167181 0.0524176i
\(355\) 17.8691i 0.948395i
\(356\) 70.7383 3.74912
\(357\) −10.9134 + 2.52229i −0.577596 + 0.133494i
\(358\) 4.27133 0.225747
\(359\) 9.24058i 0.487699i −0.969813 0.243850i \(-0.921590\pi\)
0.969813 0.243850i \(-0.0784103\pi\)
\(360\) −32.7058 + 47.0289i −1.72375 + 2.47864i
\(361\) 13.7285 0.722552
\(362\) 5.34957 0.281167
\(363\) −8.33967 + 26.5987i −0.437719 + 1.39607i
\(364\) 11.2174 6.58692i 0.587949 0.345249i
\(365\) 40.9567i 2.14377i
\(366\) −11.2186 + 35.7807i −0.586404 + 1.87029i
\(367\) 22.3513i 1.16673i −0.812211 0.583363i \(-0.801736\pi\)
0.812211 0.583363i \(-0.198264\pi\)
\(368\) 61.5505i 3.20854i
\(369\) 0.329597 + 0.229215i 0.0171581 + 0.0119325i
\(370\) 20.7580i 1.07915i
\(371\) −16.7114 + 9.81308i −0.867613 + 0.509470i
\(372\) 55.3517 + 17.3548i 2.86985 + 0.899806i
\(373\) 9.69869 0.502179 0.251090 0.967964i \(-0.419211\pi\)
0.251090 + 0.967964i \(0.419211\pi\)
\(374\) 33.4606 1.73020
\(375\) 4.90632 15.6483i 0.253361 0.808073i
\(376\) 31.9036i 1.64530i
\(377\) −2.80952 −0.144698
\(378\) −13.4287 + 33.5697i −0.690699 + 1.72664i
\(379\) −4.26162 −0.218905 −0.109452 0.993992i \(-0.534910\pi\)
−0.109452 + 0.993992i \(0.534910\pi\)
\(380\) 28.1002i 1.44151i
\(381\) −5.16181 + 16.4631i −0.264448 + 0.843432i
\(382\) −9.30885 −0.476282
\(383\) −26.7904 −1.36893 −0.684463 0.729047i \(-0.739963\pi\)
−0.684463 + 0.729047i \(0.739963\pi\)
\(384\) 6.42827 + 2.01550i 0.328041 + 0.102853i
\(385\) −29.5612 + 17.3586i −1.50658 + 0.884676i
\(386\) 33.7135i 1.71597i
\(387\) −16.2878 11.3272i −0.827957 0.575795i
\(388\) 82.2547i 4.17585i
\(389\) 32.2579i 1.63554i −0.575543 0.817771i \(-0.695209\pi\)
0.575543 0.817771i \(-0.304791\pi\)
\(390\) −3.39239 + 10.8197i −0.171780 + 0.547879i
\(391\) 14.5493i 0.735790i
\(392\) −46.8918 26.1601i −2.36839 1.32128i
\(393\) 0.250276 0.798233i 0.0126247 0.0402655i
\(394\) −40.2086 −2.02568
\(395\) 0.168064 0.00845621
\(396\) 43.8354 63.0326i 2.20281 3.16751i
\(397\) 4.07733i 0.204635i 0.994752 + 0.102318i \(0.0326258\pi\)
−0.994752 + 0.102318i \(0.967374\pi\)
\(398\) 25.3893 1.27265
\(399\) −2.36927 10.2513i −0.118612 0.513205i
\(400\) 12.3710 0.618548
\(401\) 35.7637i 1.78595i 0.450103 + 0.892977i \(0.351387\pi\)
−0.450103 + 0.892977i \(0.648613\pi\)
\(402\) 6.61059 + 2.07267i 0.329706 + 0.103375i
\(403\) 6.81176 0.339318
\(404\) −34.9163 −1.73715
\(405\) −7.79719 21.0026i −0.387445 1.04363i
\(406\) 9.89901 + 16.8577i 0.491280 + 0.836636i
\(407\) 16.5045i 0.818098i
\(408\) −30.9875 9.71573i −1.53411 0.481001i
\(409\) 20.5606i 1.01665i −0.861164 0.508327i \(-0.830264\pi\)
0.861164 0.508327i \(-0.169736\pi\)
\(410\) 0.876080i 0.0432665i
\(411\) 23.6146 + 7.40405i 1.16482 + 0.365215i
\(412\) 34.0556i 1.67780i
\(413\) 0.969508 + 1.65105i 0.0477064 + 0.0812427i
\(414\) 38.5567 + 26.8139i 1.89496 + 1.31783i
\(415\) −15.8866 −0.779845
\(416\) 11.8534 0.581160
\(417\) 25.9401 + 8.13318i 1.27029 + 0.398283i
\(418\) 31.4306i 1.53732i
\(419\) −10.2990 −0.503139 −0.251570 0.967839i \(-0.580947\pi\)
−0.251570 + 0.967839i \(0.580947\pi\)
\(420\) 54.6450 12.6295i 2.66640 0.616258i
\(421\) −25.8012 −1.25747 −0.628737 0.777618i \(-0.716428\pi\)
−0.628737 + 0.777618i \(0.716428\pi\)
\(422\) 5.25915i 0.256012i
\(423\) −10.2437 7.12390i −0.498067 0.346376i
\(424\) −56.1867 −2.72867
\(425\) −2.92424 −0.141847
\(426\) −9.78300 + 31.2020i −0.473988 + 1.51174i
\(427\) 18.7810 11.0284i 0.908876 0.533699i
\(428\) 27.0679i 1.30838i
\(429\) 2.69727 8.60270i 0.130225 0.415342i
\(430\) 43.2936i 2.08780i
\(431\) 27.5266i 1.32591i 0.748660 + 0.662954i \(0.230697\pi\)
−0.748660 + 0.662954i \(0.769303\pi\)
\(432\) −42.4694 + 32.9136i −2.04331 + 1.58356i
\(433\) 10.7663i 0.517397i −0.965958 0.258698i \(-0.916706\pi\)
0.965958 0.258698i \(-0.0832936\pi\)
\(434\) −24.0004 40.8720i −1.15206 1.96192i
\(435\) −11.5585 3.62401i −0.554186 0.173758i
\(436\) −96.8711 −4.63928
\(437\) −13.6666 −0.653763
\(438\) −22.4230 + 71.5162i −1.07141 + 3.41717i
\(439\) 9.68084i 0.462041i −0.972949 0.231021i \(-0.925794\pi\)
0.972949 0.231021i \(-0.0742065\pi\)
\(440\) −99.3900 −4.73823
\(441\) 18.8703 9.21479i 0.898585 0.438800i
\(442\) −6.42832 −0.305764
\(443\) 11.8594i 0.563459i 0.959494 + 0.281729i \(0.0909080\pi\)
−0.959494 + 0.281729i \(0.909092\pi\)
\(444\) −8.07845 + 25.7655i −0.383386 + 1.22278i
\(445\) 35.8138 1.69774
\(446\) −35.7618 −1.69337
\(447\) 4.72885 + 1.48267i 0.223667 + 0.0701280i
\(448\) −14.0576 23.9397i −0.664160 1.13105i
\(449\) 34.4245i 1.62459i 0.583245 + 0.812296i \(0.301783\pi\)
−0.583245 + 0.812296i \(0.698217\pi\)
\(450\) −5.38928 + 7.74945i −0.254053 + 0.365313i
\(451\) 0.696565i 0.0328000i
\(452\) 5.70082i 0.268144i
\(453\) 3.74370 11.9402i 0.175894 0.561000i
\(454\) 10.2692i 0.481959i
\(455\) 5.67919 3.33487i 0.266245 0.156341i
\(456\) 9.12630 29.1075i 0.427378 1.36309i
\(457\) −39.3323 −1.83989 −0.919943 0.392053i \(-0.871765\pi\)
−0.919943 + 0.392053i \(0.871765\pi\)
\(458\) 45.2141 2.11272
\(459\) 10.0389 7.78011i 0.468576 0.363145i
\(460\) 72.8508i 3.39669i
\(461\) 34.8799 1.62452 0.812260 0.583295i \(-0.198237\pi\)
0.812260 + 0.583295i \(0.198237\pi\)
\(462\) −61.1215 + 14.1264i −2.84363 + 0.657218i
\(463\) −16.5025 −0.766936 −0.383468 0.923554i \(-0.625270\pi\)
−0.383468 + 0.923554i \(0.625270\pi\)
\(464\) 29.0517i 1.34869i
\(465\) 28.0238 + 8.78651i 1.29957 + 0.407465i
\(466\) −18.4099 −0.852820
\(467\) 31.5382 1.45941 0.729706 0.683761i \(-0.239657\pi\)
0.729706 + 0.683761i \(0.239657\pi\)
\(468\) −8.42151 + 12.1096i −0.389284 + 0.559766i
\(469\) −2.03752 3.46985i −0.0940841 0.160223i
\(470\) 27.2282i 1.25594i
\(471\) 8.42742 + 2.64231i 0.388315 + 0.121751i
\(472\) 5.55111i 0.255511i
\(473\) 34.4224i 1.58274i
\(474\) 0.293463 + 0.0920117i 0.0134792 + 0.00422624i
\(475\) 2.74683i 0.126033i
\(476\) 16.1002 + 27.4182i 0.737952 + 1.25671i
\(477\) 12.5462 18.0407i 0.574451 0.826025i
\(478\) 30.4933 1.39473
\(479\) 23.0063 1.05118 0.525592 0.850737i \(-0.323844\pi\)
0.525592 + 0.850737i \(0.323844\pi\)
\(480\) 48.7652 + 15.2897i 2.22581 + 0.697876i
\(481\) 3.17079i 0.144575i
\(482\) 55.4148 2.52407
\(483\) −6.14242 26.5768i −0.279490 1.20929i
\(484\) 79.1285 3.59675
\(485\) 41.6444i 1.89098i
\(486\) −2.11647 40.9423i −0.0960051 1.85718i
\(487\) 10.7586 0.487519 0.243759 0.969836i \(-0.421619\pi\)
0.243759 + 0.969836i \(0.421619\pi\)
\(488\) 63.1450 2.85844
\(489\) 6.84943 21.8457i 0.309742 0.987895i
\(490\) −40.0199 22.3264i −1.80791 1.00860i
\(491\) 19.7765i 0.892502i −0.894908 0.446251i \(-0.852759\pi\)
0.894908 0.446251i \(-0.147241\pi\)
\(492\) 0.340947 1.08742i 0.0153711 0.0490247i
\(493\) 6.86722i 0.309284i
\(494\) 6.03833i 0.271677i
\(495\) 22.1933 31.9125i 0.997514 1.43436i
\(496\) 70.4365i 3.16269i
\(497\) 16.3777 9.61712i 0.734640 0.431387i
\(498\) −27.7403 8.69763i −1.24307 0.389750i
\(499\) 25.7171 1.15126 0.575629 0.817711i \(-0.304757\pi\)
0.575629 + 0.817711i \(0.304757\pi\)
\(500\) −46.5521 −2.08187
\(501\) 7.67389 24.4752i 0.342844 1.09347i
\(502\) 6.46005i 0.288326i
\(503\) 0.0498348 0.00222202 0.00111101 0.999999i \(-0.499646\pi\)
0.00111101 + 0.999999i \(0.499646\pi\)
\(504\) 60.7058 + 4.66520i 2.70405 + 0.207804i
\(505\) −17.6776 −0.786644
\(506\) 81.4851i 3.62245i
\(507\) −0.518189 + 1.65272i −0.0230136 + 0.0733998i
\(508\) 48.9763 2.17297
\(509\) −5.38039 −0.238482 −0.119241 0.992865i \(-0.538046\pi\)
−0.119241 + 0.992865i \(0.538046\pi\)
\(510\) −26.4463 8.29191i −1.17106 0.367172i
\(511\) 37.5383 22.0428i 1.66059 0.975115i
\(512\) 36.0690i 1.59404i
\(513\) 7.30811 + 9.42987i 0.322661 + 0.416339i
\(514\) 24.2390i 1.06914i
\(515\) 17.2419i 0.759769i
\(516\) −16.8487 + 53.7375i −0.741723 + 2.36566i
\(517\) 21.6489i 0.952118i
\(518\) 19.0254 11.1719i 0.835929 0.490864i
\(519\) 2.72939 8.70515i 0.119807 0.382114i
\(520\) 19.0945 0.837347
\(521\) 0.957985 0.0419701 0.0209850 0.999780i \(-0.493320\pi\)
0.0209850 + 0.999780i \(0.493320\pi\)
\(522\) −18.1986 12.6561i −0.796533 0.553941i
\(523\) 21.4942i 0.939877i 0.882699 + 0.469939i \(0.155724\pi\)
−0.882699 + 0.469939i \(0.844276\pi\)
\(524\) −2.37467 −0.103738
\(525\) 5.34164 1.23455i 0.233128 0.0538804i
\(526\) 54.4450 2.37391
\(527\) 16.6498i 0.725275i
\(528\) −88.9556 27.8909i −3.87129 1.21380i
\(529\) −12.4313 −0.540490
\(530\) −47.9527 −2.08293
\(531\) −1.78237 1.23953i −0.0773484 0.0537912i
\(532\) −25.7548 + 15.1234i −1.11661 + 0.655684i
\(533\) 0.133822i 0.00579646i
\(534\) 62.5360 + 19.6074i 2.70620 + 0.848494i
\(535\) 13.7041i 0.592481i
\(536\) 11.6662i 0.503905i
\(537\) 2.68419 + 0.841594i 0.115831 + 0.0363175i
\(538\) 78.2557i 3.37384i
\(539\) 31.8195 + 17.7515i 1.37056 + 0.764613i
\(540\) −50.2665 + 38.9564i −2.16313 + 1.67641i
\(541\) 9.68496 0.416389 0.208195 0.978087i \(-0.433241\pi\)
0.208195 + 0.978087i \(0.433241\pi\)
\(542\) −5.89995 −0.253424
\(543\) 3.36178 + 1.05404i 0.144268 + 0.0452333i
\(544\) 28.9728i 1.24220i
\(545\) −49.0445 −2.10084
\(546\) 11.7424 2.71391i 0.502530 0.116144i
\(547\) −27.7026 −1.18448 −0.592238 0.805763i \(-0.701756\pi\)
−0.592238 + 0.805763i \(0.701756\pi\)
\(548\) 70.2511i 3.00098i
\(549\) −14.1000 + 20.2749i −0.601771 + 0.865310i
\(550\) −16.3776 −0.698341
\(551\) 6.45060 0.274805
\(552\) 23.6603 75.4625i 1.00705 3.21190i
\(553\) −0.0904516 0.154037i −0.00384639 0.00655030i
\(554\) 29.4120i 1.24960i
\(555\) −4.09001 + 13.0447i −0.173611 + 0.553717i
\(556\) 77.1693i 3.27271i
\(557\) 34.1530i 1.44711i −0.690266 0.723556i \(-0.742507\pi\)
0.690266 0.723556i \(-0.257493\pi\)
\(558\) 44.1231 + 30.6850i 1.86788 + 1.29900i
\(559\) 6.61311i 0.279705i
\(560\) −34.4840 58.7253i −1.45721 2.48160i
\(561\) 21.0273 + 6.59284i 0.887773 + 0.278350i
\(562\) −52.9358 −2.23296
\(563\) 30.0552 1.26668 0.633338 0.773875i \(-0.281684\pi\)
0.633338 + 0.773875i \(0.281684\pi\)
\(564\) −10.5965 + 33.7965i −0.446192 + 1.42309i
\(565\) 2.88624i 0.121425i
\(566\) −4.50065 −0.189177
\(567\) −15.0532 + 18.4500i −0.632176 + 0.774825i
\(568\) 55.0647 2.31046
\(569\) 38.1685i 1.60011i −0.599928 0.800054i \(-0.704804\pi\)
0.599928 0.800054i \(-0.295196\pi\)
\(570\) 7.78886 24.8419i 0.326239 1.04051i
\(571\) −18.7251 −0.783620 −0.391810 0.920046i \(-0.628151\pi\)
−0.391810 + 0.920046i \(0.628151\pi\)
\(572\) −25.5922 −1.07006
\(573\) −5.84987 1.83415i −0.244382 0.0766228i
\(574\) −0.802959 + 0.471504i −0.0335148 + 0.0196802i
\(575\) 7.12128i 0.296978i
\(576\) 25.8439 + 17.9729i 1.07683 + 0.748872i
\(577\) 12.3887i 0.515750i 0.966178 + 0.257875i \(0.0830223\pi\)
−0.966178 + 0.257875i \(0.916978\pi\)
\(578\) 28.9968i 1.20611i
\(579\) −6.64267 + 21.1862i −0.276060 + 0.880469i
\(580\) 34.3854i 1.42777i
\(581\) 8.55015 + 14.5607i 0.354720 + 0.604079i
\(582\) −22.7995 + 72.7171i −0.945071 + 3.01422i
\(583\) 38.1268 1.57905
\(584\) 126.210 5.22262
\(585\) −4.26369 + 6.13092i −0.176282 + 0.253483i
\(586\) 27.1193i 1.12029i
\(587\) 45.0894 1.86104 0.930520 0.366240i \(-0.119355\pi\)
0.930520 + 0.366240i \(0.119355\pi\)
\(588\) −40.9852 43.2869i −1.69020 1.78512i
\(589\) −15.6397 −0.644421
\(590\) 4.73761i 0.195044i
\(591\) −25.2679 7.92242i −1.03938 0.325885i
\(592\) 32.7873 1.34755
\(593\) −47.2250 −1.93930 −0.969649 0.244501i \(-0.921376\pi\)
−0.969649 + 0.244501i \(0.921376\pi\)
\(594\) 56.2241 43.5734i 2.30690 1.78784i
\(595\) 8.15131 + 13.8815i 0.334171 + 0.569084i
\(596\) 14.0679i 0.576244i
\(597\) 15.9552 + 5.00254i 0.653001 + 0.204740i
\(598\) 15.6546i 0.640165i
\(599\) 39.4389i 1.61143i 0.592303 + 0.805715i \(0.298219\pi\)
−0.592303 + 0.805715i \(0.701781\pi\)
\(600\) 15.1671 + 4.75545i 0.619194 + 0.194140i
\(601\) 14.6955i 0.599440i 0.954027 + 0.299720i \(0.0968933\pi\)
−0.954027 + 0.299720i \(0.903107\pi\)
\(602\) 39.6801 23.3005i 1.61724 0.949657i
\(603\) 3.74584 + 2.60501i 0.152543 + 0.106084i
\(604\) −35.5210 −1.44533
\(605\) 40.0617 1.62874
\(606\) −30.8676 9.67816i −1.25391 0.393148i
\(607\) 14.1329i 0.573637i 0.957985 + 0.286818i \(0.0925976\pi\)
−0.957985 + 0.286818i \(0.907402\pi\)
\(608\) −27.2151 −1.10372
\(609\) 2.89920 + 12.5442i 0.117482 + 0.508316i
\(610\) 53.8912 2.18199
\(611\) 4.15911i 0.168260i
\(612\) −29.5991 20.5844i −1.19647 0.832075i
\(613\) 0.855412 0.0345498 0.0172749 0.999851i \(-0.494501\pi\)
0.0172749 + 0.999851i \(0.494501\pi\)
\(614\) 14.0554 0.567228
\(615\) 0.172617 0.550546i 0.00696058 0.0222002i
\(616\) 53.4915 + 91.0945i 2.15523 + 3.67030i
\(617\) 0.301821i 0.0121509i 0.999982 + 0.00607543i \(0.00193388\pi\)
−0.999982 + 0.00607543i \(0.998066\pi\)
\(618\) 9.43960 30.1068i 0.379717 1.21107i
\(619\) 17.1645i 0.689899i −0.938621 0.344949i \(-0.887896\pi\)
0.938621 0.344949i \(-0.112104\pi\)
\(620\) 83.3682i 3.34815i
\(621\) 18.9466 + 24.4473i 0.760300 + 0.981037i
\(622\) 72.6757i 2.91403i
\(623\) −19.2749 32.8247i −0.772233 1.31509i
\(624\) 17.0898 + 5.35830i 0.684140 + 0.214504i
\(625\) −29.5505 −1.18202
\(626\) −44.1798 −1.76578
\(627\) −6.19287 + 19.7516i −0.247319 + 0.788803i
\(628\) 25.0708i 1.00043i
\(629\) −7.75025 −0.309023
\(630\) 51.8095 + 3.98152i 2.06414 + 0.158628i
\(631\) 36.1119 1.43759 0.718797 0.695220i \(-0.244693\pi\)
0.718797 + 0.695220i \(0.244693\pi\)
\(632\) 0.517898i 0.0206009i
\(633\) −1.03623 + 3.30496i −0.0411864 + 0.131360i
\(634\) −35.3275 −1.40303
\(635\) 24.7960 0.984001
\(636\) −59.5205 18.6619i −2.36014 0.739993i
\(637\) −6.11305 3.41036i −0.242208 0.135124i
\(638\) 38.4607i 1.52267i
\(639\) −12.2957 + 17.6804i −0.486409 + 0.699426i
\(640\) 9.68197i 0.382714i
\(641\) 17.5910i 0.694802i −0.937717 0.347401i \(-0.887064\pi\)
0.937717 0.347401i \(-0.112936\pi\)
\(642\) 7.50274 23.9293i 0.296109 0.944415i
\(643\) 16.4792i 0.649878i −0.945735 0.324939i \(-0.894656\pi\)
0.945735 0.324939i \(-0.105344\pi\)
\(644\) −66.7704 + 39.2081i −2.63112 + 1.54502i
\(645\) −8.53027 + 27.2065i −0.335879 + 1.07126i
\(646\) 14.7593 0.580697
\(647\) 38.1387 1.49939 0.749694 0.661785i \(-0.230201\pi\)
0.749694 + 0.661785i \(0.230201\pi\)
\(648\) −64.7207 + 24.0275i −2.54247 + 0.943888i
\(649\) 3.76684i 0.147861i
\(650\) 3.14640 0.123412
\(651\) −7.02919 30.4137i −0.275496 1.19201i
\(652\) −64.9888 −2.54516
\(653\) 9.85577i 0.385686i 0.981230 + 0.192843i \(0.0617708\pi\)
−0.981230 + 0.192843i \(0.938229\pi\)
\(654\) −85.6386 26.8509i −3.34874 1.04995i
\(655\) −1.20226 −0.0469763
\(656\) −1.38377 −0.0540272
\(657\) −28.1821 + 40.5241i −1.09949 + 1.58100i
\(658\) 24.9556 14.6541i 0.972870 0.571277i
\(659\) 40.0519i 1.56020i −0.625655 0.780100i \(-0.715168\pi\)
0.625655 0.780100i \(-0.284832\pi\)
\(660\) −105.287 33.0115i −4.09830 1.28497i
\(661\) 47.9693i 1.86579i −0.360147 0.932896i \(-0.617273\pi\)
0.360147 0.932896i \(-0.382727\pi\)
\(662\) 14.3877i 0.559193i
\(663\) −4.03969 1.26659i −0.156888 0.0491904i
\(664\) 48.9556i 1.89985i
\(665\) −13.0393 + 7.65679i −0.505642 + 0.296918i
\(666\) −14.2835 + 20.5387i −0.553473 + 0.795859i
\(667\) 16.7234 0.647534
\(668\) −72.8114 −2.81716
\(669\) −22.4734 7.04626i −0.868873 0.272424i
\(670\) 9.95657i 0.384656i
\(671\) −42.8485 −1.65415
\(672\) −12.2317 52.9239i −0.471849 2.04158i
\(673\) −8.51964 −0.328408 −0.164204 0.986426i \(-0.552506\pi\)
−0.164204 + 0.986426i \(0.552506\pi\)
\(674\) 69.6531i 2.68294i
\(675\) −4.91363 + 3.80804i −0.189126 + 0.146572i
\(676\) 4.91669 0.189103
\(677\) 4.89321 0.188061 0.0940307 0.995569i \(-0.470025\pi\)
0.0940307 + 0.995569i \(0.470025\pi\)
\(678\) −1.58016 + 5.03979i −0.0606858 + 0.193552i
\(679\) 38.1686 22.4129i 1.46478 0.860129i
\(680\) 46.6719i 1.78979i
\(681\) −2.02338 + 6.45339i −0.0775360 + 0.247294i
\(682\) 93.2490i 3.57069i
\(683\) 24.7729i 0.947910i −0.880549 0.473955i \(-0.842826\pi\)
0.880549 0.473955i \(-0.157174\pi\)
\(684\) 19.3356 27.8034i 0.739315 1.06309i
\(685\) 35.5672i 1.35895i
\(686\) 1.07568 + 48.6956i 0.0410695 + 1.85921i
\(687\) 28.4135 + 8.90868i 1.08404 + 0.339887i
\(688\) 68.3824 2.60705
\(689\) −7.32479 −0.279052
\(690\) 20.1929 64.4036i 0.768732 2.45180i
\(691\) 20.7376i 0.788895i 0.918919 + 0.394447i \(0.129064\pi\)
−0.918919 + 0.394447i \(0.870936\pi\)
\(692\) −25.8970 −0.984457
\(693\) −41.1934 3.16568i −1.56481 0.120254i
\(694\) −6.13976 −0.233062
\(695\) 39.0697i 1.48200i
\(696\) −11.1676 + 35.6180i −0.423306 + 1.35010i
\(697\) 0.327096 0.0123896
\(698\) −16.9500 −0.641566
\(699\) −11.5691 3.62735i −0.437584 0.137199i
\(700\) −7.88038 13.4201i −0.297850 0.507231i
\(701\) 50.4855i 1.90681i 0.301693 + 0.953405i \(0.402448\pi\)
−0.301693 + 0.953405i \(0.597552\pi\)
\(702\) −10.8016 + 8.37117i −0.407679 + 0.315950i
\(703\) 7.28006i 0.274573i
\(704\) 54.6181i 2.05850i
\(705\) −5.36485 + 17.1107i −0.202052 + 0.644427i
\(706\) 12.2654i 0.461616i
\(707\) 9.51406 + 16.2022i 0.357813 + 0.609346i
\(708\) −1.84375 + 5.88048i −0.0692924 + 0.221002i
\(709\) −22.2910 −0.837155 −0.418577 0.908181i \(-0.637471\pi\)
−0.418577 + 0.908181i \(0.637471\pi\)
\(710\) 46.9951 1.76369
\(711\) 0.166289 + 0.115644i 0.00623632 + 0.00433699i
\(712\) 110.362i 4.13600i
\(713\) −40.5464 −1.51848
\(714\) 6.63351 + 28.7017i 0.248253 + 1.07413i
\(715\) −12.9570 −0.484564
\(716\) 7.98522i 0.298422i
\(717\) 19.1626 + 6.00818i 0.715639 + 0.224380i
\(718\) −24.3023 −0.906956
\(719\) −31.8409 −1.18747 −0.593733 0.804662i \(-0.702346\pi\)
−0.593733 + 0.804662i \(0.702346\pi\)
\(720\) 63.3964 + 44.0884i 2.36264 + 1.64308i
\(721\) −15.8028 + 9.27955i −0.588528 + 0.345588i
\(722\) 36.1053i 1.34370i
\(723\) 34.8237 + 10.9185i 1.29511 + 0.406065i
\(724\) 10.0010i 0.371683i
\(725\) 3.36122i 0.124833i
\(726\) 69.9534 + 21.9330i 2.59621 + 0.814010i
\(727\) 26.1490i 0.969811i −0.874566 0.484906i \(-0.838854\pi\)
0.874566 0.484906i \(-0.161146\pi\)
\(728\) −10.2766 17.5007i −0.380876 0.648621i
\(729\) 6.73697 26.1460i 0.249517 0.968370i
\(730\) 107.714 3.98669
\(731\) −16.1642 −0.597855
\(732\) 66.8916 + 20.9730i 2.47239 + 0.775186i
\(733\) 15.7431i 0.581484i −0.956802 0.290742i \(-0.906098\pi\)
0.956802 0.290742i \(-0.0939021\pi\)
\(734\) −58.7829 −2.16972
\(735\) −20.7503 21.9156i −0.765385 0.808369i
\(736\) −70.5562 −2.60074
\(737\) 7.91640i 0.291604i
\(738\) 0.602827 0.866827i 0.0221904 0.0319084i
\(739\) −25.5426 −0.939600 −0.469800 0.882773i \(-0.655674\pi\)
−0.469800 + 0.882773i \(0.655674\pi\)
\(740\) 38.8068 1.42657
\(741\) 1.18975 3.79461i 0.0437066 0.139398i
\(742\) 25.8080 + 43.9503i 0.947442 + 1.61347i
\(743\) 10.3372i 0.379234i 0.981858 + 0.189617i \(0.0607246\pi\)
−0.981858 + 0.189617i \(0.939275\pi\)
\(744\) 27.0761 86.3569i 0.992659 3.16600i
\(745\) 7.12239i 0.260944i
\(746\) 25.5072i 0.933883i
\(747\) −15.7189 10.9315i −0.575123 0.399964i
\(748\) 62.5542i 2.28721i
\(749\) −12.5603 + 7.37552i −0.458944 + 0.269496i
\(750\) −41.1543 12.9034i −1.50274 0.471166i
\(751\) 38.9962 1.42299 0.711496 0.702691i \(-0.248018\pi\)
0.711496 + 0.702691i \(0.248018\pi\)
\(752\) 43.0070 1.56830
\(753\) 1.27284 4.05963i 0.0463850 0.147941i
\(754\) 7.38893i 0.269089i
\(755\) −17.9838 −0.654497
\(756\) 62.7582 + 25.1049i 2.28249 + 0.913055i
\(757\) 3.99142 0.145071 0.0725354 0.997366i \(-0.476891\pi\)
0.0725354 + 0.997366i \(0.476891\pi\)
\(758\) 11.2079i 0.407089i
\(759\) −16.0553 + 51.2068i −0.582769 + 1.85869i
\(760\) −43.8405 −1.59026
\(761\) 38.0670 1.37993 0.689964 0.723844i \(-0.257626\pi\)
0.689964 + 0.723844i \(0.257626\pi\)
\(762\) 43.2974 + 13.5754i 1.56850 + 0.491783i
\(763\) 26.3956 + 44.9510i 0.955586 + 1.62734i
\(764\) 17.4028i 0.629612i
\(765\) −14.9856 10.4216i −0.541806 0.376794i
\(766\) 70.4577i 2.54574i
\(767\) 0.723671i 0.0261303i
\(768\) −5.57407 + 17.7780i −0.201137 + 0.641508i
\(769\) 49.6363i 1.78993i 0.446135 + 0.894966i \(0.352800\pi\)
−0.446135 + 0.894966i \(0.647200\pi\)
\(770\) 45.6524 + 77.7448i 1.64520 + 2.80173i
\(771\) 4.77588 15.2323i 0.171999 0.548576i
\(772\) 63.0270 2.26839
\(773\) 25.7709 0.926916 0.463458 0.886119i \(-0.346609\pi\)
0.463458 + 0.886119i \(0.346609\pi\)
\(774\) −29.7901 + 42.8363i −1.07078 + 1.53972i
\(775\) 8.14937i 0.292734i
\(776\) 128.330 4.60677
\(777\) 14.1572 3.27200i 0.507886 0.117382i
\(778\) −84.8371 −3.04156
\(779\) 0.307252i 0.0110084i
\(780\) 20.2274 + 6.34205i 0.724257 + 0.227082i
\(781\) −37.3655 −1.33704
\(782\) 38.2641 1.36832
\(783\) −8.94272 11.5391i −0.319587 0.412372i
\(784\) −35.2646 + 63.2116i −1.25945 + 2.25756i
\(785\) 12.6930i 0.453033i
\(786\) −2.09932 0.658215i −0.0748803 0.0234778i
\(787\) 49.8715i 1.77773i −0.458171 0.888864i \(-0.651495\pi\)
0.458171 0.888864i \(-0.348505\pi\)
\(788\) 75.1695i 2.67780i
\(789\) 34.2143 + 10.7275i 1.21806 + 0.381908i
\(790\) 0.442001i 0.0157257i
\(791\) 2.64535 1.55337i 0.0940577 0.0552315i
\(792\) −98.3403 68.3898i −3.49437 2.43013i
\(793\) 8.23191 0.292324
\(794\) 10.7232 0.380552
\(795\) −30.1344 9.44826i −1.06876 0.335095i
\(796\) 47.4651i 1.68236i
\(797\) 31.5593 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(798\) −26.9604 + 6.23107i −0.954388 + 0.220578i
\(799\) −10.1660 −0.359647
\(800\) 14.1810i 0.501374i
\(801\) 35.4356 + 24.6433i 1.25205 + 0.870730i
\(802\) 94.0570 3.32127
\(803\) −85.6430 −3.02227
\(804\) 3.87483 12.3584i 0.136655 0.435849i
\(805\) −33.8049 + 19.8505i −1.19147 + 0.699639i
\(806\) 17.9147i 0.631017i
\(807\) −15.4190 + 49.1774i −0.542773 + 1.73113i
\(808\) 54.4746i 1.91641i
\(809\) 42.3362i 1.48846i −0.667923 0.744230i \(-0.732817\pi\)
0.667923 0.744230i \(-0.267183\pi\)
\(810\) −55.2360 + 20.5063i −1.94080 + 0.720517i
\(811\) 15.2751i 0.536380i −0.963366 0.268190i \(-0.913574\pi\)
0.963366 0.268190i \(-0.0864255\pi\)
\(812\) 31.5154 18.5061i 1.10597 0.649437i
\(813\) −3.70764 1.16249i −0.130033 0.0407701i
\(814\) −43.4062 −1.52139
\(815\) −32.9029 −1.15254
\(816\) −13.0971 + 41.7721i −0.458491 + 1.46232i
\(817\) 15.1836i 0.531205i
\(818\) −54.0734 −1.89063
\(819\) 7.91392 + 0.608179i 0.276535 + 0.0212515i
\(820\) −1.63782 −0.0571953
\(821\) 1.23687i 0.0431672i −0.999767 0.0215836i \(-0.993129\pi\)
0.999767 0.0215836i \(-0.00687081\pi\)
\(822\) 19.4723 62.1053i 0.679176 2.16617i
\(823\) −4.50870 −0.157164 −0.0785818 0.996908i \(-0.525039\pi\)
−0.0785818 + 0.996908i \(0.525039\pi\)
\(824\) −53.1319 −1.85094
\(825\) −10.2920 3.22692i −0.358321 0.112347i
\(826\) 4.34218 2.54977i 0.151084 0.0887178i
\(827\) 29.0856i 1.01140i −0.862708 0.505702i \(-0.831233\pi\)
0.862708 0.505702i \(-0.168767\pi\)
\(828\) 50.1283 72.0814i 1.74208 2.50500i
\(829\) 45.0204i 1.56362i 0.623514 + 0.781812i \(0.285704\pi\)
−0.623514 + 0.781812i \(0.714296\pi\)
\(830\) 41.7812i 1.45025i
\(831\) 5.79514 18.4831i 0.201031 0.641172i
\(832\) 10.4930i 0.363781i
\(833\) 8.33584 14.9419i 0.288820 0.517707i
\(834\) 21.3899 68.2213i 0.740673 2.36231i
\(835\) −36.8634 −1.27571
\(836\) 58.7592 2.03223
\(837\) 21.6819 + 27.9768i 0.749435 + 0.967018i
\(838\) 27.0860i 0.935669i
\(839\) 47.7484 1.64846 0.824229 0.566256i \(-0.191609\pi\)
0.824229 + 0.566256i \(0.191609\pi\)
\(840\) −19.7039 85.2544i −0.679851 2.94156i
\(841\) 21.1066 0.727813
\(842\) 67.8561i 2.33848i
\(843\) −33.2659 10.4301i −1.14574 0.359232i
\(844\) 9.83194 0.338429
\(845\) 2.48925 0.0856328
\(846\) −18.7356 + 26.9406i −0.644142 + 0.926237i
\(847\) −21.5611 36.7180i −0.740848 1.26164i
\(848\) 75.7415i 2.60097i
\(849\) −2.82830 0.886778i −0.0970671 0.0304341i
\(850\) 7.69064i 0.263787i
\(851\) 18.8738i 0.646987i
\(852\) 58.3319 + 18.2892i 1.99842 + 0.626579i
\(853\) 9.77198i 0.334586i 0.985907 + 0.167293i \(0.0535026\pi\)
−0.985907 + 0.167293i \(0.946497\pi\)
\(854\) −29.0041 49.3932i −0.992500 1.69020i
\(855\) 9.78935 14.0765i 0.334789 0.481405i
\(856\) −42.2300 −1.44339
\(857\) 6.35976 0.217245 0.108623 0.994083i \(-0.465356\pi\)
0.108623 + 0.994083i \(0.465356\pi\)
\(858\) −22.6247 7.09370i −0.772396 0.242175i
\(859\) 43.5034i 1.48432i 0.670225 + 0.742158i \(0.266197\pi\)
−0.670225 + 0.742158i \(0.733803\pi\)
\(860\) 80.9369 2.75993
\(861\) −0.597497 + 0.138093i −0.0203627 + 0.00470620i
\(862\) 72.3937 2.46574
\(863\) 3.75973i 0.127983i −0.997950 0.0639914i \(-0.979617\pi\)
0.997950 0.0639914i \(-0.0203830\pi\)
\(864\) 37.7293 + 48.6833i 1.28358 + 1.65624i
\(865\) −13.1113 −0.445798
\(866\) −28.3150 −0.962183
\(867\) −5.71333 + 18.2222i −0.194035 + 0.618857i
\(868\) −76.4099 + 44.8686i −2.59352 + 1.52294i
\(869\) 0.351432i 0.0119215i
\(870\) −9.53100 + 30.3983i −0.323131 + 1.03060i
\(871\) 1.52087i 0.0515327i
\(872\) 151.133i 5.11802i
\(873\) −28.6554 + 41.2046i −0.969837 + 1.39456i
\(874\) 35.9427i 1.21578i
\(875\) 12.6846 + 21.6016i 0.428818 + 0.730266i
\(876\) 133.699 + 41.9196i 4.51727 + 1.41633i
\(877\) −13.4380 −0.453769 −0.226885 0.973922i \(-0.572854\pi\)
−0.226885 + 0.973922i \(0.572854\pi\)
\(878\) −25.4602 −0.859240
\(879\) 5.34340 17.0423i 0.180228 0.574823i
\(880\) 133.981i 4.51649i
\(881\) 14.3019 0.481842 0.240921 0.970545i \(-0.422551\pi\)
0.240921 + 0.970545i \(0.422551\pi\)
\(882\) −24.2345 49.6281i −0.816019 1.67106i
\(883\) −25.8260 −0.869115 −0.434557 0.900644i \(-0.643095\pi\)
−0.434557 + 0.900644i \(0.643095\pi\)
\(884\) 12.0177i 0.404199i
\(885\) −0.933465 + 2.97721i −0.0313781 + 0.100078i
\(886\) 31.1898 1.04784
\(887\) −13.9430 −0.468160 −0.234080 0.972217i \(-0.575208\pi\)
−0.234080 + 0.972217i \(0.575208\pi\)
\(888\) 40.1980 + 12.6036i 1.34896 + 0.422949i
\(889\) −13.3452 22.7265i −0.447582 0.762221i
\(890\) 94.1889i 3.15722i
\(891\) 43.9178 16.3044i 1.47130 0.546218i
\(892\) 66.8564i 2.23852i
\(893\) 9.54923i 0.319553i
\(894\) 3.89937 12.4367i 0.130414 0.415945i
\(895\) 4.04281i 0.135136i
\(896\) −8.87387 + 5.21081i −0.296455 + 0.174081i
\(897\) 3.08448 9.83767i 0.102988 0.328470i
\(898\) 90.5350 3.02119
\(899\) 19.1378 0.638281
\(900\) 14.4875 + 10.0752i 0.482918 + 0.335841i
\(901\) 17.9037i 0.596460i
\(902\) 1.83194 0.0609969
\(903\) 29.5267 6.82420i 0.982588 0.227095i
\(904\) 8.89413 0.295814
\(905\) 5.06335i 0.168312i
\(906\) −31.4023 9.84578i −1.04327 0.327104i
\(907\) −35.4212 −1.17614 −0.588072 0.808809i \(-0.700113\pi\)
−0.588072 + 0.808809i \(0.700113\pi\)
\(908\) 19.1982 0.637116
\(909\) −17.4909 12.1639i −0.580137 0.403451i
\(910\) −8.77057 14.9360i −0.290742 0.495125i
\(911\) 14.6081i 0.483987i −0.970278 0.241994i \(-0.922199\pi\)
0.970278 0.241994i \(-0.0778013\pi\)
\(912\) −39.2379 12.3025i −1.29930 0.407378i
\(913\) 33.2200i 1.09942i
\(914\) 103.442i 3.42156i
\(915\) 33.8663 + 10.6184i 1.11959 + 0.351032i
\(916\) 84.5274i 2.79286i
\(917\) 0.647054 + 1.10192i 0.0213676 + 0.0363885i
\(918\) −20.4614 26.4019i −0.675326 0.871394i
\(919\) 1.38147 0.0455704 0.0227852 0.999740i \(-0.492747\pi\)
0.0227852 + 0.999740i \(0.492747\pi\)
\(920\) −113.658 −3.74720
\(921\) 8.83267 + 2.76937i 0.291046 + 0.0912539i
\(922\) 91.7328i 3.02106i
\(923\) 7.17852 0.236284
\(924\) 26.4091 + 114.266i 0.868796 + 3.75908i
\(925\) 3.79343 0.124727
\(926\) 43.4009i 1.42624i
\(927\) 11.8641 17.0598i 0.389667 0.560317i
\(928\) 33.3023 1.09320
\(929\) −0.336654 −0.0110453 −0.00552263 0.999985i \(-0.501758\pi\)
−0.00552263 + 0.999985i \(0.501758\pi\)
\(930\) 23.1082 73.7014i 0.757746 2.41677i
\(931\) 14.0354 + 7.83012i 0.459993 + 0.256622i
\(932\) 34.4171i 1.12737i
\(933\) −14.3195 + 45.6708i −0.468800 + 1.49520i
\(934\) 82.9441i 2.71401i
\(935\) 31.6703i 1.03573i
\(936\) 18.8928 + 13.1388i 0.617530 + 0.429455i
\(937\) 9.34072i 0.305148i −0.988292 0.152574i \(-0.951244\pi\)
0.988292 0.152574i \(-0.0487563\pi\)
\(938\) −9.12555 + 5.35860i −0.297960 + 0.174965i
\(939\) −27.7635 8.70488i −0.906026 0.284073i
\(940\) 50.9028 1.66027
\(941\) −37.7545 −1.23076 −0.615380 0.788230i \(-0.710998\pi\)
−0.615380 + 0.788230i \(0.710998\pi\)
\(942\) 6.94917 22.1638i 0.226416 0.722135i
\(943\) 0.796562i 0.0259396i
\(944\) 7.48307 0.243553
\(945\) 31.7736 + 12.7103i 1.03360 + 0.413465i
\(946\) −90.5295 −2.94337
\(947\) 29.5311i 0.959633i 0.877369 + 0.479816i \(0.159297\pi\)
−0.877369 + 0.479816i \(0.840703\pi\)
\(948\) 0.172015 0.548627i 0.00558679 0.0178186i
\(949\) 16.4534 0.534101
\(950\) −7.22406 −0.234380
\(951\) −22.2005 6.96069i −0.719901 0.225716i
\(952\) 42.7765 25.1187i 1.38639 0.814102i
\(953\) 31.3418i 1.01526i −0.861575 0.507630i \(-0.830522\pi\)
0.861575 0.507630i \(-0.169478\pi\)
\(954\) −47.4462 32.9960i −1.53613 1.06829i
\(955\) 8.81081i 0.285111i
\(956\) 57.0069i 1.84373i
\(957\) 7.57803 24.1695i 0.244963 0.781288i
\(958\) 60.5056i 1.95485i
\(959\) −32.5986 + 19.1422i −1.05266 + 0.618133i
\(960\) 13.5350 43.1687i 0.436840 1.39326i
\(961\) −15.4001 −0.496777
\(962\) 8.33904 0.268861
\(963\) 9.42974 13.5594i 0.303869 0.436945i
\(964\) 103.597i 3.33665i
\(965\) 31.9097 1.02721
\(966\) −69.8960 + 16.1543i −2.24887 + 0.519756i
\(967\) 20.2236 0.650347 0.325173 0.945654i \(-0.394577\pi\)
0.325173 + 0.945654i \(0.394577\pi\)
\(968\) 123.452i 3.96791i
\(969\) 9.27503 + 2.90807i 0.297957 + 0.0934207i
\(970\) 109.523 3.51658
\(971\) −7.96623 −0.255649 −0.127824 0.991797i \(-0.540799\pi\)
−0.127824 + 0.991797i \(0.540799\pi\)
\(972\) −76.5413 + 3.95673i −2.45506 + 0.126912i
\(973\) −35.8088 + 21.0272i −1.14798 + 0.674102i
\(974\) 28.2947i 0.906620i
\(975\) 1.97726 + 0.619945i 0.0633230 + 0.0198541i
\(976\) 85.1214i 2.72467i
\(977\) 25.2368i 0.807397i 0.914892 + 0.403698i \(0.132275\pi\)
−0.914892 + 0.403698i \(0.867725\pi\)
\(978\) −57.4532 18.0137i −1.83715 0.576015i
\(979\) 74.8890i 2.39346i
\(980\) −41.7390 + 74.8168i −1.33330 + 2.38994i
\(981\) −48.5265 33.7473i −1.54933 1.07747i
\(982\) −52.0115 −1.65975
\(983\) 17.8377 0.568933 0.284466 0.958686i \(-0.408184\pi\)
0.284466 + 0.958686i \(0.408184\pi\)
\(984\) −1.69654 0.531928i −0.0540837 0.0169573i
\(985\) 38.0573i 1.21261i
\(986\) −18.0605 −0.575164
\(987\) 18.5699 4.29187i 0.591088 0.136612i
\(988\) −11.2886 −0.359138
\(989\) 39.3640i 1.25170i
\(990\) −83.9287 58.3674i −2.66743 1.85504i
\(991\) −29.8604 −0.948547 −0.474273 0.880378i \(-0.657289\pi\)
−0.474273 + 0.880378i \(0.657289\pi\)
\(992\) −80.7424 −2.56357
\(993\) −2.83485 + 9.04151i −0.0899612 + 0.286924i
\(994\) −25.2926 43.0727i −0.802234 1.36618i
\(995\) 24.0309i 0.761832i
\(996\) −16.2601 + 51.8603i −0.515222 + 1.64326i
\(997\) 37.4471i 1.18596i 0.805216 + 0.592981i \(0.202049\pi\)
−0.805216 + 0.592981i \(0.797951\pi\)
\(998\) 67.6350i 2.14095i
\(999\) −13.0228 + 10.0926i −0.412024 + 0.319317i
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 273.2.e.a.209.2 yes 32
3.2 odd 2 inner 273.2.e.a.209.31 yes 32
7.6 odd 2 inner 273.2.e.a.209.1 32
21.20 even 2 inner 273.2.e.a.209.32 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.e.a.209.1 32 7.6 odd 2 inner
273.2.e.a.209.2 yes 32 1.1 even 1 trivial
273.2.e.a.209.31 yes 32 3.2 odd 2 inner
273.2.e.a.209.32 yes 32 21.20 even 2 inner