Properties

Label 1386.2.r.d.1277.2
Level $1386$
Weight $2$
Character 1386.1277
Analytic conductor $11.067$
Analytic rank $0$
Dimension $24$
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] = [1386,2,Mod(89,1386)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1386.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.r (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1277.2
Character \(\chi\) \(=\) 1386.1277
Dual form 1386.2.r.d.89.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.651304 + 1.12809i) q^{5} +(-0.212626 + 2.63719i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.651304 + 1.12809i) q^{5} +(-0.212626 + 2.63719i) q^{7} +1.00000i q^{8} +(-1.12809 - 0.651304i) q^{10} +(0.866025 + 0.500000i) q^{11} -1.37037i q^{13} +(-1.13446 - 2.39019i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.86353 + 4.95978i) q^{17} +(-0.481496 + 0.277992i) q^{19} +1.30261 q^{20} -1.00000 q^{22} +(-5.02204 + 2.89948i) q^{23} +(1.65161 - 2.86067i) q^{25} +(0.685187 + 1.18678i) q^{26} +(2.17756 + 1.50274i) q^{28} +6.53981i q^{29} +(0.660821 + 0.381525i) q^{31} +(0.866025 + 0.500000i) q^{32} -5.72706i q^{34} +(-3.11348 + 1.47775i) q^{35} +(-3.34141 - 5.78749i) q^{37} +(0.277992 - 0.481496i) q^{38} +(-1.12809 + 0.651304i) q^{40} +2.25518 q^{41} +3.91214 q^{43} +(0.866025 - 0.500000i) q^{44} +(2.89948 - 5.02204i) q^{46} +(0.483428 + 0.837321i) q^{47} +(-6.90958 - 1.12147i) q^{49} +3.30321i q^{50} +(-1.18678 - 0.685187i) q^{52} +(-7.40860 - 4.27736i) q^{53} +1.30261i q^{55} +(-2.63719 - 0.212626i) q^{56} +(-3.26990 - 5.66364i) q^{58} +(-0.499578 + 0.865295i) q^{59} +(0.127371 - 0.0735377i) q^{61} -0.763050 q^{62} -1.00000 q^{64} +(1.54591 - 0.892530i) q^{65} +(-3.60430 + 6.24283i) q^{67} +(2.86353 + 4.95978i) q^{68} +(1.95748 - 2.83651i) q^{70} +1.17582i q^{71} +(-1.44038 - 0.831605i) q^{73} +(5.78749 + 3.34141i) q^{74} +0.555984i q^{76} +(-1.50274 + 2.17756i) q^{77} +(0.361898 + 0.626826i) q^{79} +(0.651304 - 1.12809i) q^{80} +(-1.95305 + 1.12759i) q^{82} -5.54322 q^{83} -7.46011 q^{85} +(-3.38801 + 1.95607i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(4.25940 + 7.37750i) q^{89} +(3.61394 + 0.291378i) q^{91} +5.79896i q^{92} +(-0.837321 - 0.483428i) q^{94} +(-0.627201 - 0.362114i) q^{95} +12.9667i q^{97} +(6.54461 - 2.48356i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 12 q^{4} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{4} + 8 q^{7} - 12 q^{16} + 12 q^{19} - 24 q^{22} + 4 q^{25} + 4 q^{28} + 20 q^{37} + 24 q^{43} + 12 q^{46} + 40 q^{49} - 28 q^{58} - 120 q^{61} - 24 q^{64} - 32 q^{67} + 48 q^{70} - 48 q^{73} - 64 q^{79} - 48 q^{82} + 32 q^{85} - 12 q^{88} + 56 q^{91} + 60 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0.651304 + 1.12809i 0.291272 + 0.504498i 0.974111 0.226071i \(-0.0725882\pi\)
−0.682839 + 0.730569i \(0.739255\pi\)
\(6\) 0 0
\(7\) −0.212626 + 2.63719i −0.0803652 + 0.996765i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) −1.12809 0.651304i −0.356734 0.205960i
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i
\(12\) 0 0
\(13\) 1.37037i 0.380073i −0.981777 0.190037i \(-0.939139\pi\)
0.981777 0.190037i \(-0.0608607\pi\)
\(14\) −1.13446 2.39019i −0.303196 0.638805i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.86353 + 4.95978i −0.694508 + 1.20292i 0.275838 + 0.961204i \(0.411045\pi\)
−0.970346 + 0.241719i \(0.922289\pi\)
\(18\) 0 0
\(19\) −0.481496 + 0.277992i −0.110463 + 0.0637757i −0.554214 0.832375i \(-0.686981\pi\)
0.443751 + 0.896150i \(0.353648\pi\)
\(20\) 1.30261 0.291272
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −5.02204 + 2.89948i −1.04717 + 0.604583i −0.921855 0.387534i \(-0.873327\pi\)
−0.125313 + 0.992117i \(0.539994\pi\)
\(24\) 0 0
\(25\) 1.65161 2.86067i 0.330321 0.572133i
\(26\) 0.685187 + 1.18678i 0.134376 + 0.232746i
\(27\) 0 0
\(28\) 2.17756 + 1.50274i 0.411521 + 0.283991i
\(29\) 6.53981i 1.21441i 0.794545 + 0.607206i \(0.207710\pi\)
−0.794545 + 0.607206i \(0.792290\pi\)
\(30\) 0 0
\(31\) 0.660821 + 0.381525i 0.118687 + 0.0685239i 0.558168 0.829728i \(-0.311504\pi\)
−0.439481 + 0.898252i \(0.644838\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 5.72706i 0.982183i
\(35\) −3.11348 + 1.47775i −0.526274 + 0.249786i
\(36\) 0 0
\(37\) −3.34141 5.78749i −0.549324 0.951457i −0.998321 0.0579236i \(-0.981552\pi\)
0.448997 0.893533i \(-0.351781\pi\)
\(38\) 0.277992 0.481496i 0.0450962 0.0781090i
\(39\) 0 0
\(40\) −1.12809 + 0.651304i −0.178367 + 0.102980i
\(41\) 2.25518 0.352200 0.176100 0.984372i \(-0.443652\pi\)
0.176100 + 0.984372i \(0.443652\pi\)
\(42\) 0 0
\(43\) 3.91214 0.596595 0.298298 0.954473i \(-0.403581\pi\)
0.298298 + 0.954473i \(0.403581\pi\)
\(44\) 0.866025 0.500000i 0.130558 0.0753778i
\(45\) 0 0
\(46\) 2.89948 5.02204i 0.427505 0.740460i
\(47\) 0.483428 + 0.837321i 0.0705152 + 0.122136i 0.899127 0.437687i \(-0.144202\pi\)
−0.828612 + 0.559823i \(0.810869\pi\)
\(48\) 0 0
\(49\) −6.90958 1.12147i −0.987083 0.160211i
\(50\) 3.30321i 0.467145i
\(51\) 0 0
\(52\) −1.18678 0.685187i −0.164577 0.0950183i
\(53\) −7.40860 4.27736i −1.01765 0.587540i −0.104227 0.994554i \(-0.533237\pi\)
−0.913422 + 0.407013i \(0.866570\pi\)
\(54\) 0 0
\(55\) 1.30261i 0.175644i
\(56\) −2.63719 0.212626i −0.352410 0.0284134i
\(57\) 0 0
\(58\) −3.26990 5.66364i −0.429359 0.743672i
\(59\) −0.499578 + 0.865295i −0.0650396 + 0.112652i −0.896712 0.442615i \(-0.854051\pi\)
0.831672 + 0.555267i \(0.187384\pi\)
\(60\) 0 0
\(61\) 0.127371 0.0735377i 0.0163082 0.00941554i −0.491824 0.870695i \(-0.663670\pi\)
0.508132 + 0.861279i \(0.330336\pi\)
\(62\) −0.763050 −0.0969075
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.54591 0.892530i 0.191746 0.110705i
\(66\) 0 0
\(67\) −3.60430 + 6.24283i −0.440335 + 0.762683i −0.997714 0.0675752i \(-0.978474\pi\)
0.557379 + 0.830258i \(0.311807\pi\)
\(68\) 2.86353 + 4.95978i 0.347254 + 0.601462i
\(69\) 0 0
\(70\) 1.95748 2.83651i 0.233963 0.339028i
\(71\) 1.17582i 0.139544i 0.997563 + 0.0697720i \(0.0222272\pi\)
−0.997563 + 0.0697720i \(0.977773\pi\)
\(72\) 0 0
\(73\) −1.44038 0.831605i −0.168584 0.0973320i 0.413334 0.910579i \(-0.364364\pi\)
−0.581918 + 0.813247i \(0.697698\pi\)
\(74\) 5.78749 + 3.34141i 0.672782 + 0.388431i
\(75\) 0 0
\(76\) 0.555984i 0.0637757i
\(77\) −1.50274 + 2.17756i −0.171253 + 0.248156i
\(78\) 0 0
\(79\) 0.361898 + 0.626826i 0.0407167 + 0.0705235i 0.885666 0.464324i \(-0.153703\pi\)
−0.844949 + 0.534847i \(0.820369\pi\)
\(80\) 0.651304 1.12809i 0.0728180 0.126125i
\(81\) 0 0
\(82\) −1.95305 + 1.12759i −0.215678 + 0.124522i
\(83\) −5.54322 −0.608448 −0.304224 0.952601i \(-0.598397\pi\)
−0.304224 + 0.952601i \(0.598397\pi\)
\(84\) 0 0
\(85\) −7.46011 −0.809163
\(86\) −3.38801 + 1.95607i −0.365338 + 0.210928i
\(87\) 0 0
\(88\) −0.500000 + 0.866025i −0.0533002 + 0.0923186i
\(89\) 4.25940 + 7.37750i 0.451496 + 0.782014i 0.998479 0.0551297i \(-0.0175572\pi\)
−0.546983 + 0.837144i \(0.684224\pi\)
\(90\) 0 0
\(91\) 3.61394 + 0.291378i 0.378844 + 0.0305447i
\(92\) 5.79896i 0.604583i
\(93\) 0 0
\(94\) −0.837321 0.483428i −0.0863631 0.0498618i
\(95\) −0.627201 0.362114i −0.0643494 0.0371522i
\(96\) 0 0
\(97\) 12.9667i 1.31657i 0.752769 + 0.658285i \(0.228718\pi\)
−0.752769 + 0.658285i \(0.771282\pi\)
\(98\) 6.54461 2.48356i 0.661105 0.250878i
\(99\) 0 0
\(100\) −1.65161 2.86067i −0.165161 0.286067i
\(101\) 3.67391 6.36340i 0.365568 0.633182i −0.623299 0.781983i \(-0.714208\pi\)
0.988867 + 0.148801i \(0.0475415\pi\)
\(102\) 0 0
\(103\) −15.4637 + 8.92798i −1.52369 + 0.879700i −0.524079 + 0.851670i \(0.675590\pi\)
−0.999607 + 0.0280307i \(0.991076\pi\)
\(104\) 1.37037 0.134376
\(105\) 0 0
\(106\) 8.55471 0.830907
\(107\) −8.72859 + 5.03946i −0.843825 + 0.487183i −0.858563 0.512709i \(-0.828642\pi\)
0.0147376 + 0.999891i \(0.495309\pi\)
\(108\) 0 0
\(109\) 0.368886 0.638929i 0.0353329 0.0611983i −0.847818 0.530287i \(-0.822084\pi\)
0.883151 + 0.469089i \(0.155418\pi\)
\(110\) −0.651304 1.12809i −0.0620994 0.107559i
\(111\) 0 0
\(112\) 2.39019 1.13446i 0.225852 0.107196i
\(113\) 4.81235i 0.452708i 0.974045 + 0.226354i \(0.0726806\pi\)
−0.974045 + 0.226354i \(0.927319\pi\)
\(114\) 0 0
\(115\) −6.54176 3.77689i −0.610022 0.352196i
\(116\) 5.66364 + 3.26990i 0.525856 + 0.303603i
\(117\) 0 0
\(118\) 0.999157i 0.0919798i
\(119\) −12.4710 8.60626i −1.14322 0.788935i
\(120\) 0 0
\(121\) 0.500000 + 0.866025i 0.0454545 + 0.0787296i
\(122\) −0.0735377 + 0.127371i −0.00665779 + 0.0115316i
\(123\) 0 0
\(124\) 0.660821 0.381525i 0.0593435 0.0342620i
\(125\) 10.8158 0.967397
\(126\) 0 0
\(127\) 12.5158 1.11060 0.555299 0.831651i \(-0.312604\pi\)
0.555299 + 0.831651i \(0.312604\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) −0.892530 + 1.54591i −0.0782801 + 0.135585i
\(131\) 7.42443 + 12.8595i 0.648675 + 1.12354i 0.983440 + 0.181237i \(0.0580100\pi\)
−0.334764 + 0.942302i \(0.608657\pi\)
\(132\) 0 0
\(133\) −0.630739 1.32891i −0.0546920 0.115231i
\(134\) 7.20860i 0.622728i
\(135\) 0 0
\(136\) −4.95978 2.86353i −0.425298 0.245546i
\(137\) −18.1030 10.4518i −1.54664 0.892953i −0.998395 0.0566359i \(-0.981963\pi\)
−0.548246 0.836317i \(-0.684704\pi\)
\(138\) 0 0
\(139\) 3.21195i 0.272434i 0.990679 + 0.136217i \(0.0434944\pi\)
−0.990679 + 0.136217i \(0.956506\pi\)
\(140\) −0.276969 + 3.43523i −0.0234081 + 0.290330i
\(141\) 0 0
\(142\) −0.587909 1.01829i −0.0493363 0.0854529i
\(143\) 0.685187 1.18678i 0.0572982 0.0992434i
\(144\) 0 0
\(145\) −7.37750 + 4.25940i −0.612668 + 0.353724i
\(146\) 1.66321 0.137648
\(147\) 0 0
\(148\) −6.68281 −0.549324
\(149\) −17.7299 + 10.2363i −1.45249 + 0.838594i −0.998622 0.0524768i \(-0.983288\pi\)
−0.453865 + 0.891071i \(0.649955\pi\)
\(150\) 0 0
\(151\) −7.80068 + 13.5112i −0.634810 + 1.09952i 0.351745 + 0.936096i \(0.385588\pi\)
−0.986555 + 0.163428i \(0.947745\pi\)
\(152\) −0.277992 0.481496i −0.0225481 0.0390545i
\(153\) 0 0
\(154\) 0.212626 2.63719i 0.0171339 0.212511i
\(155\) 0.993956i 0.0798364i
\(156\) 0 0
\(157\) −6.72012 3.87986i −0.536324 0.309647i 0.207264 0.978285i \(-0.433544\pi\)
−0.743588 + 0.668638i \(0.766877\pi\)
\(158\) −0.626826 0.361898i −0.0498676 0.0287911i
\(159\) 0 0
\(160\) 1.30261i 0.102980i
\(161\) −6.57867 13.8606i −0.518472 1.09237i
\(162\) 0 0
\(163\) −2.36269 4.09229i −0.185060 0.320533i 0.758537 0.651630i \(-0.225915\pi\)
−0.943597 + 0.331097i \(0.892581\pi\)
\(164\) 1.12759 1.95305i 0.0880501 0.152507i
\(165\) 0 0
\(166\) 4.80057 2.77161i 0.372597 0.215119i
\(167\) 2.49753 0.193264 0.0966322 0.995320i \(-0.469193\pi\)
0.0966322 + 0.995320i \(0.469193\pi\)
\(168\) 0 0
\(169\) 11.1221 0.855544
\(170\) 6.46065 3.73006i 0.495509 0.286082i
\(171\) 0 0
\(172\) 1.95607 3.38801i 0.149149 0.258333i
\(173\) −7.76337 13.4466i −0.590238 1.02232i −0.994200 0.107547i \(-0.965701\pi\)
0.403962 0.914776i \(-0.367633\pi\)
\(174\) 0 0
\(175\) 7.19295 + 4.96386i 0.543736 + 0.375232i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) −7.37750 4.25940i −0.552967 0.319256i
\(179\) −7.40921 4.27771i −0.553790 0.319731i 0.196859 0.980432i \(-0.436926\pi\)
−0.750649 + 0.660701i \(0.770259\pi\)
\(180\) 0 0
\(181\) 22.8485i 1.69832i −0.528140 0.849158i \(-0.677110\pi\)
0.528140 0.849158i \(-0.322890\pi\)
\(182\) −3.27545 + 1.55463i −0.242793 + 0.115237i
\(183\) 0 0
\(184\) −2.89948 5.02204i −0.213752 0.370230i
\(185\) 4.35254 7.53883i 0.320005 0.554266i
\(186\) 0 0
\(187\) −4.95978 + 2.86353i −0.362695 + 0.209402i
\(188\) 0.966856 0.0705152
\(189\) 0 0
\(190\) 0.724229 0.0525411
\(191\) 14.0830 8.13084i 1.01901 0.588327i 0.105195 0.994452i \(-0.466453\pi\)
0.913818 + 0.406125i \(0.133120\pi\)
\(192\) 0 0
\(193\) −2.83770 + 4.91503i −0.204262 + 0.353792i −0.949897 0.312562i \(-0.898813\pi\)
0.745635 + 0.666354i \(0.232146\pi\)
\(194\) −6.48336 11.2295i −0.465478 0.806231i
\(195\) 0 0
\(196\) −4.42602 + 5.42313i −0.316144 + 0.387367i
\(197\) 2.08781i 0.148750i −0.997230 0.0743750i \(-0.976304\pi\)
0.997230 0.0743750i \(-0.0236962\pi\)
\(198\) 0 0
\(199\) 15.0881 + 8.71113i 1.06957 + 0.617516i 0.928064 0.372422i \(-0.121472\pi\)
0.141505 + 0.989937i \(0.454806\pi\)
\(200\) 2.86067 + 1.65161i 0.202280 + 0.116786i
\(201\) 0 0
\(202\) 7.34782i 0.516991i
\(203\) −17.2467 1.39054i −1.21048 0.0975965i
\(204\) 0 0
\(205\) 1.46881 + 2.54405i 0.102586 + 0.177684i
\(206\) 8.92798 15.4637i 0.622042 1.07741i
\(207\) 0 0
\(208\) −1.18678 + 0.685187i −0.0822883 + 0.0475092i
\(209\) −0.555984 −0.0384582
\(210\) 0 0
\(211\) 25.5583 1.75951 0.879753 0.475431i \(-0.157708\pi\)
0.879753 + 0.475431i \(0.157708\pi\)
\(212\) −7.40860 + 4.27736i −0.508825 + 0.293770i
\(213\) 0 0
\(214\) 5.03946 8.72859i 0.344490 0.596674i
\(215\) 2.54799 + 4.41325i 0.173772 + 0.300981i
\(216\) 0 0
\(217\) −1.14666 + 1.66159i −0.0778406 + 0.112796i
\(218\) 0.737772i 0.0499682i
\(219\) 0 0
\(220\) 1.12809 + 0.651304i 0.0760559 + 0.0439109i
\(221\) 6.79675 + 3.92411i 0.457199 + 0.263964i
\(222\) 0 0
\(223\) 9.64025i 0.645559i 0.946474 + 0.322779i \(0.104617\pi\)
−0.946474 + 0.322779i \(0.895383\pi\)
\(224\) −1.50274 + 2.17756i −0.100406 + 0.145495i
\(225\) 0 0
\(226\) −2.40618 4.16762i −0.160056 0.277226i
\(227\) −3.53947 + 6.13055i −0.234923 + 0.406899i −0.959250 0.282558i \(-0.908817\pi\)
0.724327 + 0.689456i \(0.242150\pi\)
\(228\) 0 0
\(229\) −16.3612 + 9.44614i −1.08118 + 0.624219i −0.931214 0.364473i \(-0.881249\pi\)
−0.149965 + 0.988691i \(0.547916\pi\)
\(230\) 7.55377 0.498081
\(231\) 0 0
\(232\) −6.53981 −0.429359
\(233\) 8.01488 4.62739i 0.525072 0.303151i −0.213935 0.976848i \(-0.568628\pi\)
0.739007 + 0.673697i \(0.235295\pi\)
\(234\) 0 0
\(235\) −0.629717 + 1.09070i −0.0410782 + 0.0711495i
\(236\) 0.499578 + 0.865295i 0.0325198 + 0.0563259i
\(237\) 0 0
\(238\) 15.1034 + 1.21772i 0.979006 + 0.0789333i
\(239\) 4.86932i 0.314970i −0.987521 0.157485i \(-0.949661\pi\)
0.987521 0.157485i \(-0.0503386\pi\)
\(240\) 0 0
\(241\) 18.4869 + 10.6734i 1.19085 + 0.687535i 0.958498 0.285098i \(-0.0920262\pi\)
0.232347 + 0.972633i \(0.425360\pi\)
\(242\) −0.866025 0.500000i −0.0556702 0.0321412i
\(243\) 0 0
\(244\) 0.147075i 0.00941554i
\(245\) −3.23511 8.52506i −0.206684 0.544646i
\(246\) 0 0
\(247\) 0.380953 + 0.659829i 0.0242394 + 0.0419839i
\(248\) −0.381525 + 0.660821i −0.0242269 + 0.0419622i
\(249\) 0 0
\(250\) −9.36679 + 5.40792i −0.592408 + 0.342027i
\(251\) 21.2321 1.34016 0.670078 0.742291i \(-0.266261\pi\)
0.670078 + 0.742291i \(0.266261\pi\)
\(252\) 0 0
\(253\) −5.79896 −0.364577
\(254\) −10.8390 + 6.25791i −0.680100 + 0.392656i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.21276 + 12.4929i 0.449920 + 0.779284i 0.998380 0.0568927i \(-0.0181193\pi\)
−0.548461 + 0.836176i \(0.684786\pi\)
\(258\) 0 0
\(259\) 15.9732 7.58136i 0.992526 0.471083i
\(260\) 1.78506i 0.110705i
\(261\) 0 0
\(262\) −12.8595 7.42443i −0.794462 0.458683i
\(263\) 14.7636 + 8.52378i 0.910364 + 0.525599i 0.880548 0.473956i \(-0.157175\pi\)
0.0298158 + 0.999555i \(0.490508\pi\)
\(264\) 0 0
\(265\) 11.1434i 0.684536i
\(266\) 1.21069 + 0.835497i 0.0742321 + 0.0512276i
\(267\) 0 0
\(268\) 3.60430 + 6.24283i 0.220168 + 0.381342i
\(269\) 11.1844 19.3720i 0.681927 1.18113i −0.292464 0.956276i \(-0.594475\pi\)
0.974392 0.224857i \(-0.0721914\pi\)
\(270\) 0 0
\(271\) −1.99443 + 1.15148i −0.121153 + 0.0699476i −0.559352 0.828930i \(-0.688950\pi\)
0.438199 + 0.898878i \(0.355617\pi\)
\(272\) 5.72706 0.347254
\(273\) 0 0
\(274\) 20.9035 1.26283
\(275\) 2.86067 1.65161i 0.172505 0.0995956i
\(276\) 0 0
\(277\) 3.66323 6.34490i 0.220102 0.381228i −0.734737 0.678352i \(-0.762694\pi\)
0.954839 + 0.297124i \(0.0960276\pi\)
\(278\) −1.60597 2.78163i −0.0963199 0.166831i
\(279\) 0 0
\(280\) −1.47775 3.11348i −0.0883126 0.186066i
\(281\) 11.0454i 0.658911i −0.944171 0.329456i \(-0.893135\pi\)
0.944171 0.329456i \(-0.106865\pi\)
\(282\) 0 0
\(283\) 25.8803 + 14.9420i 1.53842 + 0.888209i 0.998931 + 0.0462173i \(0.0147167\pi\)
0.539491 + 0.841991i \(0.318617\pi\)
\(284\) 1.01829 + 0.587909i 0.0604243 + 0.0348860i
\(285\) 0 0
\(286\) 1.37037i 0.0810319i
\(287\) −0.479512 + 5.94735i −0.0283047 + 0.351061i
\(288\) 0 0
\(289\) −7.89960 13.6825i −0.464683 0.804854i
\(290\) 4.25940 7.37750i 0.250121 0.433222i
\(291\) 0 0
\(292\) −1.44038 + 0.831605i −0.0842920 + 0.0486660i
\(293\) 24.4813 1.43021 0.715106 0.699016i \(-0.246379\pi\)
0.715106 + 0.699016i \(0.246379\pi\)
\(294\) 0 0
\(295\) −1.30151 −0.0757768
\(296\) 5.78749 3.34141i 0.336391 0.194215i
\(297\) 0 0
\(298\) 10.2363 17.7299i 0.592975 1.02706i
\(299\) 3.97337 + 6.88208i 0.229786 + 0.398001i
\(300\) 0 0
\(301\) −0.831824 + 10.3171i −0.0479455 + 0.594665i
\(302\) 15.6014i 0.897757i
\(303\) 0 0
\(304\) 0.481496 + 0.277992i 0.0276157 + 0.0159439i
\(305\) 0.165915 + 0.0957908i 0.00950024 + 0.00548497i
\(306\) 0 0
\(307\) 8.72480i 0.497951i −0.968510 0.248975i \(-0.919906\pi\)
0.968510 0.248975i \(-0.0800939\pi\)
\(308\) 1.13446 + 2.39019i 0.0646417 + 0.136194i
\(309\) 0 0
\(310\) −0.496978 0.860791i −0.0282264 0.0488896i
\(311\) 1.31098 2.27069i 0.0743390 0.128759i −0.826460 0.562996i \(-0.809649\pi\)
0.900799 + 0.434237i \(0.142982\pi\)
\(312\) 0 0
\(313\) −20.4146 + 11.7864i −1.15390 + 0.666205i −0.949835 0.312752i \(-0.898749\pi\)
−0.204066 + 0.978957i \(0.565416\pi\)
\(314\) 7.75972 0.437906
\(315\) 0 0
\(316\) 0.723797 0.0407167
\(317\) 16.3099 9.41654i 0.916057 0.528886i 0.0336819 0.999433i \(-0.489277\pi\)
0.882375 + 0.470547i \(0.155943\pi\)
\(318\) 0 0
\(319\) −3.26990 + 5.66364i −0.183079 + 0.317103i
\(320\) −0.651304 1.12809i −0.0364090 0.0630623i
\(321\) 0 0
\(322\) 12.6276 + 8.71431i 0.703709 + 0.485629i
\(323\) 3.18415i 0.177171i
\(324\) 0 0
\(325\) −3.92018 2.26332i −0.217452 0.125546i
\(326\) 4.09229 + 2.36269i 0.226651 + 0.130857i
\(327\) 0 0
\(328\) 2.25518i 0.124522i
\(329\) −2.31097 + 1.09686i −0.127408 + 0.0604716i
\(330\) 0 0
\(331\) −1.00063 1.73314i −0.0549997 0.0952622i 0.837215 0.546874i \(-0.184182\pi\)
−0.892214 + 0.451612i \(0.850849\pi\)
\(332\) −2.77161 + 4.80057i −0.152112 + 0.263466i
\(333\) 0 0
\(334\) −2.16292 + 1.24876i −0.118350 + 0.0683293i
\(335\) −9.38998 −0.513029
\(336\) 0 0
\(337\) −2.24786 −0.122449 −0.0612243 0.998124i \(-0.519500\pi\)
−0.0612243 + 0.998124i \(0.519500\pi\)
\(338\) −9.63200 + 5.56104i −0.523912 + 0.302481i
\(339\) 0 0
\(340\) −3.73006 + 6.46065i −0.202291 + 0.350378i
\(341\) 0.381525 + 0.660821i 0.0206607 + 0.0357855i
\(342\) 0 0
\(343\) 4.42670 17.9834i 0.239020 0.971015i
\(344\) 3.91214i 0.210928i
\(345\) 0 0
\(346\) 13.4466 + 7.76337i 0.722891 + 0.417361i
\(347\) 15.0915 + 8.71306i 0.810152 + 0.467741i 0.847009 0.531579i \(-0.178401\pi\)
−0.0368567 + 0.999321i \(0.511735\pi\)
\(348\) 0 0
\(349\) 24.6300i 1.31841i 0.751962 + 0.659206i \(0.229108\pi\)
−0.751962 + 0.659206i \(0.770892\pi\)
\(350\) −8.71121 0.702350i −0.465634 0.0375422i
\(351\) 0 0
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 7.91758 13.7137i 0.421410 0.729904i −0.574667 0.818387i \(-0.694869\pi\)
0.996078 + 0.0884828i \(0.0282018\pi\)
\(354\) 0 0
\(355\) −1.32643 + 0.765815i −0.0703997 + 0.0406453i
\(356\) 8.51881 0.451496
\(357\) 0 0
\(358\) 8.55542 0.452168
\(359\) −11.6373 + 6.71878i −0.614192 + 0.354604i −0.774604 0.632446i \(-0.782051\pi\)
0.160413 + 0.987050i \(0.448718\pi\)
\(360\) 0 0
\(361\) −9.34544 + 16.1868i −0.491865 + 0.851936i
\(362\) 11.4242 + 19.7874i 0.600445 + 1.04000i
\(363\) 0 0
\(364\) 2.05931 2.98408i 0.107937 0.156408i
\(365\) 2.16651i 0.113400i
\(366\) 0 0
\(367\) 29.7226 + 17.1603i 1.55151 + 0.895763i 0.998020 + 0.0629050i \(0.0200365\pi\)
0.553487 + 0.832858i \(0.313297\pi\)
\(368\) 5.02204 + 2.89948i 0.261792 + 0.151146i
\(369\) 0 0
\(370\) 8.70509i 0.452556i
\(371\) 12.8555 18.6284i 0.667423 0.967140i
\(372\) 0 0
\(373\) −5.02865 8.70988i −0.260374 0.450980i 0.705968 0.708244i \(-0.250512\pi\)
−0.966341 + 0.257264i \(0.917179\pi\)
\(374\) 2.86353 4.95978i 0.148070 0.256464i
\(375\) 0 0
\(376\) −0.837321 + 0.483428i −0.0431816 + 0.0249309i
\(377\) 8.96198 0.461566
\(378\) 0 0
\(379\) 4.33975 0.222918 0.111459 0.993769i \(-0.464448\pi\)
0.111459 + 0.993769i \(0.464448\pi\)
\(380\) −0.627201 + 0.362114i −0.0321747 + 0.0185761i
\(381\) 0 0
\(382\) −8.13084 + 14.0830i −0.416010 + 0.720551i
\(383\) −8.82958 15.2933i −0.451170 0.781450i 0.547289 0.836944i \(-0.315660\pi\)
−0.998459 + 0.0554940i \(0.982327\pi\)
\(384\) 0 0
\(385\) −3.43523 0.276969i −0.175076 0.0141156i
\(386\) 5.67539i 0.288870i
\(387\) 0 0
\(388\) 11.2295 + 6.48336i 0.570092 + 0.329143i
\(389\) 1.71694 + 0.991276i 0.0870523 + 0.0502597i 0.542894 0.839801i \(-0.317328\pi\)
−0.455842 + 0.890061i \(0.650662\pi\)
\(390\) 0 0
\(391\) 33.2110i 1.67955i
\(392\) 1.12147 6.90958i 0.0566430 0.348986i
\(393\) 0 0
\(394\) 1.04390 + 1.80809i 0.0525911 + 0.0910905i
\(395\) −0.471412 + 0.816509i −0.0237193 + 0.0410830i
\(396\) 0 0
\(397\) 32.6030 18.8234i 1.63630 0.944717i 0.654206 0.756316i \(-0.273003\pi\)
0.982092 0.188401i \(-0.0603305\pi\)
\(398\) −17.4223 −0.873299
\(399\) 0 0
\(400\) −3.30321 −0.165161
\(401\) −28.2285 + 16.2978i −1.40967 + 0.813871i −0.995356 0.0962648i \(-0.969310\pi\)
−0.414310 + 0.910136i \(0.635977\pi\)
\(402\) 0 0
\(403\) 0.522832 0.905572i 0.0260441 0.0451097i
\(404\) −3.67391 6.36340i −0.182784 0.316591i
\(405\) 0 0
\(406\) 15.6314 7.41913i 0.775772 0.368205i
\(407\) 6.68281i 0.331255i
\(408\) 0 0
\(409\) 30.7939 + 17.7789i 1.52266 + 0.879110i 0.999641 + 0.0267904i \(0.00852867\pi\)
0.523022 + 0.852319i \(0.324805\pi\)
\(410\) −2.54405 1.46881i −0.125642 0.0725394i
\(411\) 0 0
\(412\) 17.8560i 0.879700i
\(413\) −2.17573 1.50147i −0.107061 0.0738825i
\(414\) 0 0
\(415\) −3.61032 6.25326i −0.177224 0.306961i
\(416\) 0.685187 1.18678i 0.0335940 0.0581866i
\(417\) 0 0
\(418\) 0.481496 0.277992i 0.0235507 0.0135970i
\(419\) −4.47363 −0.218551 −0.109275 0.994012i \(-0.534853\pi\)
−0.109275 + 0.994012i \(0.534853\pi\)
\(420\) 0 0
\(421\) 0.772473 0.0376480 0.0188240 0.999823i \(-0.494008\pi\)
0.0188240 + 0.999823i \(0.494008\pi\)
\(422\) −22.1341 + 12.7791i −1.07747 + 0.622079i
\(423\) 0 0
\(424\) 4.27736 7.40860i 0.207727 0.359793i
\(425\) 9.45884 + 16.3832i 0.458821 + 0.794702i
\(426\) 0 0
\(427\) 0.166851 + 0.351538i 0.00807447 + 0.0170121i
\(428\) 10.0789i 0.487183i
\(429\) 0 0
\(430\) −4.41325 2.54799i −0.212826 0.122875i
\(431\) −7.03670 4.06264i −0.338946 0.195690i 0.320860 0.947127i \(-0.396028\pi\)
−0.659806 + 0.751436i \(0.729361\pi\)
\(432\) 0 0
\(433\) 34.5052i 1.65822i −0.559088 0.829108i \(-0.688849\pi\)
0.559088 0.829108i \(-0.311151\pi\)
\(434\) 0.162245 2.01231i 0.00778799 0.0965940i
\(435\) 0 0
\(436\) −0.368886 0.638929i −0.0176664 0.0305992i
\(437\) 1.61206 2.79217i 0.0771154 0.133568i
\(438\) 0 0
\(439\) 12.2137 7.05159i 0.582929 0.336554i −0.179368 0.983782i \(-0.557405\pi\)
0.762296 + 0.647228i \(0.224072\pi\)
\(440\) −1.30261 −0.0620994
\(441\) 0 0
\(442\) −7.84821 −0.373301
\(443\) −13.6938 + 7.90614i −0.650614 + 0.375632i −0.788691 0.614789i \(-0.789241\pi\)
0.138077 + 0.990421i \(0.455908\pi\)
\(444\) 0 0
\(445\) −5.54833 + 9.61000i −0.263016 + 0.455558i
\(446\) −4.82012 8.34870i −0.228240 0.395322i
\(447\) 0 0
\(448\) 0.212626 2.63719i 0.0100457 0.124596i
\(449\) 33.1895i 1.56631i −0.621828 0.783154i \(-0.713610\pi\)
0.621828 0.783154i \(-0.286390\pi\)
\(450\) 0 0
\(451\) 1.95305 + 1.12759i 0.0919653 + 0.0530962i
\(452\) 4.16762 + 2.40618i 0.196028 + 0.113177i
\(453\) 0 0
\(454\) 7.07894i 0.332231i
\(455\) 2.02507 + 4.26663i 0.0949369 + 0.200023i
\(456\) 0 0
\(457\) −8.53304 14.7797i −0.399159 0.691363i 0.594463 0.804123i \(-0.297364\pi\)
−0.993622 + 0.112759i \(0.964031\pi\)
\(458\) 9.44614 16.3612i 0.441389 0.764509i
\(459\) 0 0
\(460\) −6.54176 + 3.77689i −0.305011 + 0.176098i
\(461\) 32.1100 1.49551 0.747755 0.663974i \(-0.231132\pi\)
0.747755 + 0.663974i \(0.231132\pi\)
\(462\) 0 0
\(463\) 21.5146 0.999867 0.499933 0.866064i \(-0.333358\pi\)
0.499933 + 0.866064i \(0.333358\pi\)
\(464\) 5.66364 3.26990i 0.262928 0.151801i
\(465\) 0 0
\(466\) −4.62739 + 8.01488i −0.214360 + 0.371282i
\(467\) 19.8774 + 34.4287i 0.919817 + 1.59317i 0.799691 + 0.600411i \(0.204996\pi\)
0.120126 + 0.992759i \(0.461670\pi\)
\(468\) 0 0
\(469\) −15.6972 10.8326i −0.724828 0.500204i
\(470\) 1.25943i 0.0580934i
\(471\) 0 0
\(472\) −0.865295 0.499578i −0.0398284 0.0229950i
\(473\) 3.38801 + 1.95607i 0.155781 + 0.0899401i
\(474\) 0 0
\(475\) 1.83653i 0.0842659i
\(476\) −13.6888 + 6.49710i −0.627423 + 0.297794i
\(477\) 0 0
\(478\) 2.43466 + 4.21695i 0.111359 + 0.192879i
\(479\) 5.58073 9.66610i 0.254990 0.441655i −0.709903 0.704300i \(-0.751261\pi\)
0.964893 + 0.262644i \(0.0845945\pi\)
\(480\) 0 0
\(481\) −7.93102 + 4.57898i −0.361623 + 0.208783i
\(482\) −21.3468 −0.972321
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) −14.6276 + 8.44528i −0.664207 + 0.383480i
\(486\) 0 0
\(487\) −13.5154 + 23.4094i −0.612442 + 1.06078i 0.378385 + 0.925648i \(0.376479\pi\)
−0.990828 + 0.135133i \(0.956854\pi\)
\(488\) 0.0735377 + 0.127371i 0.00332890 + 0.00576582i
\(489\) 0 0
\(490\) 7.06422 + 5.76536i 0.319129 + 0.260453i
\(491\) 21.7459i 0.981380i 0.871334 + 0.490690i \(0.163255\pi\)
−0.871334 + 0.490690i \(0.836745\pi\)
\(492\) 0 0
\(493\) −32.4360 18.7269i −1.46084 0.843419i
\(494\) −0.659829 0.380953i −0.0296871 0.0171399i
\(495\) 0 0
\(496\) 0.763050i 0.0342620i
\(497\) −3.10086 0.250010i −0.139093 0.0112145i
\(498\) 0 0
\(499\) 8.55069 + 14.8102i 0.382782 + 0.662997i 0.991459 0.130421i \(-0.0416328\pi\)
−0.608677 + 0.793418i \(0.708300\pi\)
\(500\) 5.40792 9.36679i 0.241849 0.418895i
\(501\) 0 0
\(502\) −18.3875 + 10.6160i −0.820675 + 0.473817i
\(503\) −20.0922 −0.895867 −0.447933 0.894067i \(-0.647840\pi\)
−0.447933 + 0.894067i \(0.647840\pi\)
\(504\) 0 0
\(505\) 9.57133 0.425919
\(506\) 5.02204 2.89948i 0.223257 0.128898i
\(507\) 0 0
\(508\) 6.25791 10.8390i 0.277650 0.480903i
\(509\) −5.05011 8.74704i −0.223842 0.387706i 0.732129 0.681166i \(-0.238527\pi\)
−0.955971 + 0.293460i \(0.905193\pi\)
\(510\) 0 0
\(511\) 2.49937 3.62175i 0.110565 0.160217i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −12.4929 7.21276i −0.551037 0.318141i
\(515\) −20.1432 11.6297i −0.887614 0.512464i
\(516\) 0 0
\(517\) 0.966856i 0.0425223i
\(518\) −10.0425 + 14.5522i −0.441242 + 0.639389i
\(519\) 0 0
\(520\) 0.892530 + 1.54591i 0.0391400 + 0.0677925i
\(521\) 16.2935 28.2211i 0.713829 1.23639i −0.249580 0.968354i \(-0.580293\pi\)
0.963409 0.268035i \(-0.0863741\pi\)
\(522\) 0 0
\(523\) 25.5548 14.7541i 1.11743 0.645150i 0.176689 0.984267i \(-0.443461\pi\)
0.940744 + 0.339116i \(0.110128\pi\)
\(524\) 14.8489 0.648675
\(525\) 0 0
\(526\) −17.0476 −0.743309
\(527\) −3.78456 + 2.18502i −0.164858 + 0.0951808i
\(528\) 0 0
\(529\) 5.31396 9.20404i 0.231042 0.400176i
\(530\) 5.57172 + 9.65050i 0.242020 + 0.419191i
\(531\) 0 0
\(532\) −1.46624 0.118217i −0.0635694 0.00512535i
\(533\) 3.09044i 0.133862i
\(534\) 0 0
\(535\) −11.3699 6.56444i −0.491565 0.283805i
\(536\) −6.24283 3.60430i −0.269649 0.155682i
\(537\) 0 0
\(538\) 22.3689i 0.964391i
\(539\) −5.42313 4.42602i −0.233591 0.190642i
\(540\) 0 0
\(541\) −11.9017 20.6144i −0.511694 0.886281i −0.999908 0.0135565i \(-0.995685\pi\)
0.488214 0.872724i \(-0.337649\pi\)
\(542\) 1.15148 1.99443i 0.0494604 0.0856679i
\(543\) 0 0
\(544\) −4.95978 + 2.86353i −0.212649 + 0.122773i
\(545\) 0.961028 0.0411659
\(546\) 0 0
\(547\) −43.4345 −1.85713 −0.928563 0.371174i \(-0.878955\pi\)
−0.928563 + 0.371174i \(0.878955\pi\)
\(548\) −18.1030 + 10.4518i −0.773320 + 0.446477i
\(549\) 0 0
\(550\) −1.65161 + 2.86067i −0.0704247 + 0.121979i
\(551\) −1.81801 3.14889i −0.0774500 0.134147i
\(552\) 0 0
\(553\) −1.73001 + 0.821116i −0.0735676 + 0.0349174i
\(554\) 7.32646i 0.311271i
\(555\) 0 0
\(556\) 2.78163 + 1.60597i 0.117967 + 0.0681085i
\(557\) 13.5945 + 7.84877i 0.576016 + 0.332563i 0.759549 0.650451i \(-0.225420\pi\)
−0.183532 + 0.983014i \(0.558753\pi\)
\(558\) 0 0
\(559\) 5.36109i 0.226750i
\(560\) 2.83651 + 1.95748i 0.119865 + 0.0827185i
\(561\) 0 0
\(562\) 5.52268 + 9.56557i 0.232960 + 0.403499i
\(563\) −16.4468 + 28.4867i −0.693151 + 1.20057i 0.277649 + 0.960683i \(0.410445\pi\)
−0.970800 + 0.239890i \(0.922889\pi\)
\(564\) 0 0
\(565\) −5.42878 + 3.13431i −0.228390 + 0.131861i
\(566\) −29.8840 −1.25612
\(567\) 0 0
\(568\) −1.17582 −0.0493363
\(569\) −9.79385 + 5.65448i −0.410580 + 0.237048i −0.691039 0.722818i \(-0.742847\pi\)
0.280459 + 0.959866i \(0.409513\pi\)
\(570\) 0 0
\(571\) 10.1162 17.5218i 0.423350 0.733264i −0.572915 0.819615i \(-0.694187\pi\)
0.996265 + 0.0863510i \(0.0275207\pi\)
\(572\) −0.685187 1.18678i −0.0286491 0.0496217i
\(573\) 0 0
\(574\) −2.55841 5.39032i −0.106786 0.224987i
\(575\) 19.1552i 0.798826i
\(576\) 0 0
\(577\) −17.8277 10.2928i −0.742178 0.428497i 0.0806827 0.996740i \(-0.474290\pi\)
−0.822861 + 0.568243i \(0.807623\pi\)
\(578\) 13.6825 + 7.89960i 0.569118 + 0.328580i
\(579\) 0 0
\(580\) 8.51881i 0.353724i
\(581\) 1.17864 14.6185i 0.0488980 0.606480i
\(582\) 0 0
\(583\) −4.27736 7.40860i −0.177150 0.306833i
\(584\) 0.831605 1.44038i 0.0344121 0.0596034i
\(585\) 0 0
\(586\) −21.2014 + 12.2406i −0.875822 + 0.505656i
\(587\) 26.7987 1.10610 0.553050 0.833148i \(-0.313464\pi\)
0.553050 + 0.833148i \(0.313464\pi\)
\(588\) 0 0
\(589\) −0.424243 −0.0174806
\(590\) 1.12714 0.650755i 0.0464036 0.0267912i
\(591\) 0 0
\(592\) −3.34141 + 5.78749i −0.137331 + 0.237864i
\(593\) 19.4485 + 33.6858i 0.798653 + 1.38331i 0.920493 + 0.390759i \(0.127787\pi\)
−0.121840 + 0.992550i \(0.538879\pi\)
\(594\) 0 0
\(595\) 1.58622 19.6738i 0.0650286 0.806546i
\(596\) 20.4727i 0.838594i
\(597\) 0 0
\(598\) −6.88208 3.97337i −0.281429 0.162483i
\(599\) −24.0811 13.9032i −0.983926 0.568070i −0.0804730 0.996757i \(-0.525643\pi\)
−0.903453 + 0.428687i \(0.858976\pi\)
\(600\) 0 0
\(601\) 7.32197i 0.298669i −0.988787 0.149335i \(-0.952287\pi\)
0.988787 0.149335i \(-0.0477132\pi\)
\(602\) −4.43815 9.35075i −0.180885 0.381108i
\(603\) 0 0
\(604\) 7.80068 + 13.5112i 0.317405 + 0.549762i
\(605\) −0.651304 + 1.12809i −0.0264793 + 0.0458635i
\(606\) 0 0
\(607\) −5.43361 + 3.13710i −0.220543 + 0.127331i −0.606202 0.795311i \(-0.707308\pi\)
0.385658 + 0.922642i \(0.373974\pi\)
\(608\) −0.555984 −0.0225481
\(609\) 0 0
\(610\) −0.191582 −0.00775691
\(611\) 1.14744 0.662477i 0.0464206 0.0268009i
\(612\) 0 0
\(613\) −3.08473 + 5.34292i −0.124591 + 0.215798i −0.921573 0.388205i \(-0.873095\pi\)
0.796982 + 0.604003i \(0.206429\pi\)
\(614\) 4.36240 + 7.55590i 0.176052 + 0.304931i
\(615\) 0 0
\(616\) −2.17756 1.50274i −0.0877365 0.0605470i
\(617\) 3.03336i 0.122119i 0.998134 + 0.0610593i \(0.0194479\pi\)
−0.998134 + 0.0610593i \(0.980552\pi\)
\(618\) 0 0
\(619\) 30.9228 + 17.8533i 1.24289 + 0.717583i 0.969682 0.244371i \(-0.0785816\pi\)
0.273209 + 0.961955i \(0.411915\pi\)
\(620\) 0.860791 + 0.496978i 0.0345702 + 0.0199591i
\(621\) 0 0
\(622\) 2.62196i 0.105131i
\(623\) −20.3616 + 9.66422i −0.815769 + 0.387189i
\(624\) 0 0
\(625\) −1.21363 2.10207i −0.0485453 0.0840830i
\(626\) 11.7864 20.4146i 0.471078 0.815931i
\(627\) 0 0
\(628\) −6.72012 + 3.87986i −0.268162 + 0.154823i
\(629\) 38.2729 1.52604
\(630\) 0 0
\(631\) 5.45597 0.217199 0.108599 0.994086i \(-0.465363\pi\)
0.108599 + 0.994086i \(0.465363\pi\)
\(632\) −0.626826 + 0.361898i −0.0249338 + 0.0143955i
\(633\) 0 0
\(634\) −9.41654 + 16.3099i −0.373979 + 0.647750i
\(635\) 8.15160 + 14.1190i 0.323486 + 0.560295i
\(636\) 0 0
\(637\) −1.53684 + 9.46871i −0.0608918 + 0.375164i
\(638\) 6.53981i 0.258913i
\(639\) 0 0
\(640\) 1.12809 + 0.651304i 0.0445917 + 0.0257451i
\(641\) −32.8636 18.9738i −1.29804 0.749421i −0.317971 0.948101i \(-0.603001\pi\)
−0.980064 + 0.198680i \(0.936335\pi\)
\(642\) 0 0
\(643\) 2.15376i 0.0849360i −0.999098 0.0424680i \(-0.986478\pi\)
0.999098 0.0424680i \(-0.0135221\pi\)
\(644\) −15.2930 1.23301i −0.602628 0.0485875i
\(645\) 0 0
\(646\) 1.59208 + 2.75756i 0.0626394 + 0.108495i
\(647\) 2.88258 4.99277i 0.113326 0.196286i −0.803783 0.594922i \(-0.797183\pi\)
0.917109 + 0.398636i \(0.130516\pi\)
\(648\) 0 0
\(649\) −0.865295 + 0.499578i −0.0339658 + 0.0196102i
\(650\) 4.52663 0.177549
\(651\) 0 0
\(652\) −4.72537 −0.185060
\(653\) −18.1451 + 10.4761i −0.710071 + 0.409960i −0.811087 0.584925i \(-0.801124\pi\)
0.101016 + 0.994885i \(0.467791\pi\)
\(654\) 0 0
\(655\) −9.67112 + 16.7509i −0.377882 + 0.654511i
\(656\) −1.12759 1.95305i −0.0440251 0.0762536i
\(657\) 0 0
\(658\) 1.45293 2.10539i 0.0566411 0.0820766i
\(659\) 29.5567i 1.15137i 0.817673 + 0.575683i \(0.195264\pi\)
−0.817673 + 0.575683i \(0.804736\pi\)
\(660\) 0 0
\(661\) −3.57741 2.06542i −0.139145 0.0803356i 0.428811 0.903394i \(-0.358933\pi\)
−0.567957 + 0.823059i \(0.692266\pi\)
\(662\) 1.73314 + 1.00063i 0.0673605 + 0.0388906i
\(663\) 0 0
\(664\) 5.54322i 0.215119i
\(665\) 1.08833 1.57705i 0.0422034 0.0611555i
\(666\) 0 0
\(667\) −18.9620 32.8432i −0.734213 1.27169i
\(668\) 1.24876 2.16292i 0.0483161 0.0836860i
\(669\) 0 0
\(670\) 8.13196 4.69499i 0.314165 0.181383i
\(671\) 0.147075 0.00567778
\(672\) 0 0
\(673\) 14.0120 0.540123 0.270061 0.962843i \(-0.412956\pi\)
0.270061 + 0.962843i \(0.412956\pi\)
\(674\) 1.94670 1.12393i 0.0749841 0.0432921i
\(675\) 0 0
\(676\) 5.56104 9.63200i 0.213886 0.370462i
\(677\) 3.80304 + 6.58706i 0.146163 + 0.253161i 0.929806 0.368050i \(-0.119974\pi\)
−0.783643 + 0.621211i \(0.786641\pi\)
\(678\) 0 0
\(679\) −34.1957 2.75707i −1.31231 0.105807i
\(680\) 7.46011i 0.286082i
\(681\) 0 0
\(682\) −0.660821 0.381525i −0.0253041 0.0146094i
\(683\) 15.2464 + 8.80252i 0.583388 + 0.336819i 0.762479 0.647013i \(-0.223982\pi\)
−0.179091 + 0.983833i \(0.557316\pi\)
\(684\) 0 0
\(685\) 27.2291i 1.04037i
\(686\) 5.15808 + 17.7875i 0.196937 + 0.679129i
\(687\) 0 0
\(688\) −1.95607 3.38801i −0.0745744 0.129167i
\(689\) −5.86158 + 10.1526i −0.223308 + 0.386781i
\(690\) 0 0
\(691\) −41.2387 + 23.8092i −1.56879 + 0.905744i −0.572485 + 0.819915i \(0.694020\pi\)
−0.996310 + 0.0858285i \(0.972646\pi\)
\(692\) −15.5267 −0.590238
\(693\) 0 0
\(694\) −17.4261 −0.661486
\(695\) −3.62337 + 2.09196i −0.137442 + 0.0793524i
\(696\) 0 0
\(697\) −6.45778 + 11.1852i −0.244606 + 0.423670i
\(698\) −12.3150 21.3302i −0.466129 0.807360i
\(699\) 0 0
\(700\) 7.89530 3.74735i 0.298414 0.141637i
\(701\) 40.9069i 1.54503i −0.634994 0.772517i \(-0.718998\pi\)
0.634994 0.772517i \(-0.281002\pi\)
\(702\) 0 0
\(703\) 3.21775 + 1.85777i 0.121360 + 0.0700670i
\(704\) −0.866025 0.500000i −0.0326396 0.0188445i
\(705\) 0 0
\(706\) 15.8352i 0.595964i
\(707\) 16.0003 + 11.0418i 0.601755 + 0.415271i
\(708\) 0 0
\(709\) −3.08240 5.33888i −0.115762 0.200506i 0.802322 0.596891i \(-0.203598\pi\)
−0.918084 + 0.396386i \(0.870264\pi\)
\(710\) 0.765815 1.32643i 0.0287405 0.0497801i
\(711\) 0 0
\(712\) −7.37750 + 4.25940i −0.276484 + 0.159628i
\(713\) −4.42490 −0.165714
\(714\) 0 0
\(715\) 1.78506 0.0667575
\(716\) −7.40921 + 4.27771i −0.276895 + 0.159866i
\(717\) 0 0
\(718\) 6.71878 11.6373i 0.250743 0.434299i
\(719\) −9.93587 17.2094i −0.370545 0.641804i 0.619104 0.785309i \(-0.287496\pi\)
−0.989650 + 0.143505i \(0.954163\pi\)
\(720\) 0 0
\(721\) −20.2568 42.6792i −0.754404 1.58945i
\(722\) 18.6909i 0.695603i
\(723\) 0 0
\(724\) −19.7874 11.4242i −0.735392 0.424579i
\(725\) 18.7082 + 10.8012i 0.694805 + 0.401146i
\(726\) 0 0
\(727\) 42.4001i 1.57253i 0.617888 + 0.786266i \(0.287989\pi\)
−0.617888 + 0.786266i \(0.712011\pi\)
\(728\) −0.291378 + 3.61394i −0.0107992 + 0.133942i
\(729\) 0 0
\(730\) 1.08326 + 1.87625i 0.0400931 + 0.0694433i
\(731\) −11.2025 + 19.4033i −0.414340 + 0.717658i
\(732\) 0 0
\(733\) −14.9313 + 8.62060i −0.551501 + 0.318409i −0.749727 0.661747i \(-0.769815\pi\)
0.198226 + 0.980156i \(0.436482\pi\)
\(734\) −34.3207 −1.26680
\(735\) 0 0
\(736\) −5.79896 −0.213752
\(737\) −6.24283 + 3.60430i −0.229958 + 0.132766i
\(738\) 0 0
\(739\) 9.99251 17.3075i 0.367581 0.636668i −0.621606 0.783330i \(-0.713520\pi\)
0.989187 + 0.146662i \(0.0468529\pi\)
\(740\) −4.35254 7.53883i −0.160003 0.277133i
\(741\) 0 0
\(742\) −1.81896 + 22.5604i −0.0667761 + 0.828220i
\(743\) 5.37602i 0.197227i −0.995126 0.0986136i \(-0.968559\pi\)
0.995126 0.0986136i \(-0.0314408\pi\)
\(744\) 0 0
\(745\) −23.0951 13.3339i −0.846138 0.488518i
\(746\) 8.70988 + 5.02865i 0.318891 + 0.184112i
\(747\) 0 0
\(748\) 5.72706i 0.209402i
\(749\) −11.4341 24.0905i −0.417793 0.880248i
\(750\) 0 0
\(751\) −22.6527 39.2356i −0.826607 1.43173i −0.900685 0.434473i \(-0.856935\pi\)
0.0740775 0.997252i \(-0.476399\pi\)
\(752\) 0.483428 0.837321i 0.0176288 0.0305340i
\(753\) 0 0
\(754\) −7.76130 + 4.48099i −0.282650 + 0.163188i
\(755\) −20.3225 −0.739610
\(756\) 0 0
\(757\) −13.5594 −0.492823 −0.246412 0.969165i \(-0.579251\pi\)
−0.246412 + 0.969165i \(0.579251\pi\)
\(758\) −3.75833 + 2.16987i −0.136509 + 0.0788133i
\(759\) 0 0
\(760\) 0.362114 0.627201i 0.0131353 0.0227510i
\(761\) 15.4116 + 26.6938i 0.558672 + 0.967648i 0.997608 + 0.0691296i \(0.0220222\pi\)
−0.438936 + 0.898518i \(0.644644\pi\)
\(762\) 0 0
\(763\) 1.60655 + 1.10868i 0.0581608 + 0.0401368i
\(764\) 16.2617i 0.588327i
\(765\) 0 0
\(766\) 15.2933 + 8.82958i 0.552569 + 0.319026i
\(767\) 1.18578 + 0.684609i 0.0428160 + 0.0247198i
\(768\) 0 0
\(769\) 17.6776i 0.637470i −0.947844 0.318735i \(-0.896742\pi\)
0.947844 0.318735i \(-0.103258\pi\)
\(770\) 3.11348 1.47775i 0.112202 0.0532545i
\(771\) 0 0
\(772\) 2.83770 + 4.91503i 0.102131 + 0.176896i
\(773\) 6.74571 11.6839i 0.242626 0.420241i −0.718835 0.695180i \(-0.755324\pi\)
0.961462 + 0.274939i \(0.0886578\pi\)
\(774\) 0 0
\(775\) 2.18283 1.26026i 0.0784096 0.0452698i
\(776\) −12.9667 −0.465478
\(777\) 0 0
\(778\) −1.98255 −0.0710779
\(779\) −1.08586 + 0.626922i −0.0389050 + 0.0224618i
\(780\) 0 0
\(781\) −0.587909 + 1.01829i −0.0210370 + 0.0364372i
\(782\) 16.6055 + 28.7615i 0.593811 + 1.02851i
\(783\) 0 0
\(784\) 2.48356 + 6.54461i 0.0886987 + 0.233736i
\(785\) 10.1079i 0.360766i
\(786\) 0 0
\(787\) 30.1209 + 17.3903i 1.07370 + 0.619898i 0.929189 0.369606i \(-0.120507\pi\)
0.144507 + 0.989504i \(0.453841\pi\)
\(788\) −1.80809 1.04390i −0.0644107 0.0371875i
\(789\) 0 0
\(790\) 0.942824i 0.0335442i
\(791\) −12.6911 1.02323i −0.451244 0.0363820i
\(792\) 0 0
\(793\) −0.100774 0.174546i −0.00357859 0.00619831i
\(794\) −18.8234 + 32.6030i −0.668016 + 1.15704i
\(795\) 0 0
\(796\) 15.0881 8.71113i 0.534785 0.308758i
\(797\) −11.4732 −0.406401 −0.203201 0.979137i \(-0.565134\pi\)
−0.203201 + 0.979137i \(0.565134\pi\)
\(798\) 0 0
\(799\) −5.53724 −0.195893
\(800\) 2.86067 1.65161i 0.101140 0.0583931i
\(801\) 0 0
\(802\) 16.2978 28.2285i 0.575494 0.996784i
\(803\) −0.831605 1.44038i −0.0293467 0.0508300i
\(804\) 0 0
\(805\) 11.3513 16.4488i 0.400082 0.579745i
\(806\) 1.04566i 0.0368319i
\(807\) 0 0
\(808\) 6.36340 + 3.67391i 0.223864 + 0.129248i
\(809\) 22.0848 + 12.7507i 0.776460 + 0.448289i 0.835174 0.549985i \(-0.185367\pi\)
−0.0587142 + 0.998275i \(0.518700\pi\)
\(810\) 0 0
\(811\) 18.6249i 0.654008i 0.945023 + 0.327004i \(0.106039\pi\)
−0.945023 + 0.327004i \(0.893961\pi\)
\(812\) −9.82761 + 14.2408i −0.344881 + 0.499756i
\(813\) 0 0
\(814\) 3.34141 + 5.78749i 0.117116 + 0.202851i
\(815\) 3.07766 5.33066i 0.107806 0.186725i
\(816\) 0 0
\(817\) −1.88368 + 1.08754i −0.0659015 + 0.0380483i
\(818\) −35.5578 −1.24325
\(819\) 0 0
\(820\) 2.93762 0.102586
\(821\) −19.2122 + 11.0922i −0.670512 + 0.387120i −0.796270 0.604941i \(-0.793197\pi\)
0.125759 + 0.992061i \(0.459863\pi\)
\(822\) 0 0
\(823\) −21.8996 + 37.9312i −0.763371 + 1.32220i 0.177732 + 0.984079i \(0.443124\pi\)
−0.941103 + 0.338119i \(0.890209\pi\)
\(824\) −8.92798 15.4637i −0.311021 0.538704i
\(825\) 0 0
\(826\) 2.63497 + 0.212447i 0.0916823 + 0.00739198i
\(827\) 36.7143i 1.27668i 0.769754 + 0.638341i \(0.220379\pi\)
−0.769754 + 0.638341i \(0.779621\pi\)
\(828\) 0 0
\(829\) 32.1439 + 18.5583i 1.11640 + 0.644555i 0.940480 0.339849i \(-0.110376\pi\)
0.175922 + 0.984404i \(0.443709\pi\)
\(830\) 6.25326 + 3.61032i 0.217054 + 0.125316i
\(831\) 0 0
\(832\) 1.37037i 0.0475092i
\(833\) 25.3480 31.0586i 0.878258 1.07612i
\(834\) 0 0
\(835\) 1.62665 + 2.81744i 0.0562925 + 0.0975015i
\(836\) −0.277992 + 0.481496i −0.00961455 + 0.0166529i
\(837\) 0 0
\(838\) 3.87427 2.23681i 0.133835 0.0772694i
\(839\) −11.7171 −0.404517 −0.202259 0.979332i \(-0.564828\pi\)
−0.202259 + 0.979332i \(0.564828\pi\)
\(840\) 0 0
\(841\) −13.7691 −0.474796
\(842\) −0.668981 + 0.386236i −0.0230546 + 0.0133106i
\(843\) 0 0
\(844\) 12.7791 22.1341i 0.439876 0.761888i
\(845\) 7.24385 + 12.5467i 0.249196 + 0.431620i
\(846\) 0 0
\(847\) −2.39019 + 1.13446i −0.0821279 + 0.0389804i
\(848\) 8.55471i 0.293770i
\(849\) 0 0
\(850\) −16.3832 9.45884i −0.561939 0.324436i
\(851\) 33.5614 + 19.3767i 1.15047 + 0.664224i
\(852\) 0 0
\(853\) 5.99115i 0.205133i −0.994726 0.102567i \(-0.967295\pi\)
0.994726 0.102567i \(-0.0327055\pi\)
\(854\) −0.320266 0.221016i −0.0109593 0.00756300i
\(855\) 0 0
\(856\) −5.03946 8.72859i −0.172245 0.298337i
\(857\) −24.0477 + 41.6518i −0.821453 + 1.42280i 0.0831470 + 0.996537i \(0.473503\pi\)
−0.904600 + 0.426261i \(0.859830\pi\)
\(858\) 0 0
\(859\) 41.0197 23.6827i 1.39957 0.808045i 0.405226 0.914216i \(-0.367193\pi\)
0.994348 + 0.106172i \(0.0338594\pi\)
\(860\) 5.09598 0.173772
\(861\) 0 0
\(862\) 8.12528 0.276748
\(863\) −25.1635 + 14.5281i −0.856574 + 0.494543i −0.862864 0.505437i \(-0.831331\pi\)
0.00628929 + 0.999980i \(0.497998\pi\)
\(864\) 0 0
\(865\) 10.1126 17.5156i 0.343840 0.595548i
\(866\) 17.2526 + 29.8824i 0.586268 + 1.01545i
\(867\) 0 0
\(868\) 0.865648 + 1.82383i 0.0293820 + 0.0619050i
\(869\) 0.723797i 0.0245531i
\(870\) 0 0
\(871\) 8.55501 + 4.93924i 0.289875 + 0.167360i
\(872\) 0.638929 + 0.368886i 0.0216369 + 0.0124921i
\(873\) 0 0
\(874\) 3.22413i 0.109058i
\(875\) −2.29973 + 28.5234i −0.0777451 + 0.964268i
\(876\) 0 0
\(877\) −1.48397 2.57031i −0.0501100 0.0867931i 0.839882 0.542768i \(-0.182624\pi\)
−0.889992 + 0.455975i \(0.849291\pi\)
\(878\) −7.05159 + 12.2137i −0.237980 + 0.412193i
\(879\) 0 0
\(880\) 1.12809 0.651304i 0.0380280 0.0219555i
\(881\) 7.81186 0.263188 0.131594 0.991304i \(-0.457990\pi\)
0.131594 + 0.991304i \(0.457990\pi\)
\(882\) 0 0
\(883\) 3.07807 0.103585 0.0517927 0.998658i \(-0.483507\pi\)
0.0517927 + 0.998658i \(0.483507\pi\)
\(884\) 6.79675 3.92411i 0.228599 0.131982i
\(885\) 0 0
\(886\) 7.90614 13.6938i 0.265612 0.460054i
\(887\) −10.5062 18.1974i −0.352765 0.611007i 0.633968 0.773360i \(-0.281425\pi\)
−0.986733 + 0.162352i \(0.948092\pi\)
\(888\) 0 0
\(889\) −2.66119 + 33.0066i −0.0892535 + 1.10701i
\(890\) 11.0967i 0.371961i
\(891\) 0 0
\(892\) 8.34870 + 4.82012i 0.279535 + 0.161390i
\(893\) −0.465537 0.268778i −0.0155786 0.00899431i
\(894\) 0 0
\(895\) 11.1444i 0.372515i
\(896\) 1.13446 + 2.39019i 0.0378995 + 0.0798506i
\(897\) 0 0
\(898\) 16.5947 + 28.7429i 0.553773 + 0.959163i
\(899\) −2.49510 + 4.32164i −0.0832163 + 0.144135i
\(900\) 0 0
\(901\) 42.4295 24.4967i 1.41353 0.816103i
\(902\) −2.25518 −0.0750894
\(903\) 0 0
\(904\) −4.81235 −0.160056
\(905\) 25.7752 14.8813i 0.856797 0.494672i
\(906\) 0 0
\(907\) −16.8569 + 29.1970i −0.559724 + 0.969470i 0.437796 + 0.899075i \(0.355759\pi\)
−0.997519 + 0.0703952i \(0.977574\pi\)
\(908\) 3.53947 + 6.13055i 0.117462 + 0.203449i
\(909\) 0 0
\(910\) −3.88708 2.68248i −0.128856 0.0889232i
\(911\) 22.8272i 0.756298i −0.925745 0.378149i \(-0.876561\pi\)
0.925745 0.378149i \(-0.123439\pi\)
\(912\) 0 0
\(913\) −4.80057 2.77161i −0.158876 0.0917269i
\(914\) 14.7797 + 8.53304i 0.488868 + 0.282248i
\(915\) 0 0
\(916\) 18.8923i 0.624219i
\(917\) −35.4916 + 16.8454i −1.17204 + 0.556284i
\(918\) 0 0
\(919\) 8.07735 + 13.9904i 0.266447 + 0.461500i 0.967942 0.251175i \(-0.0808169\pi\)
−0.701495 + 0.712675i \(0.747484\pi\)
\(920\) 3.77689 6.54176i 0.124520 0.215675i
\(921\) 0 0
\(922\) −27.8081 + 16.0550i −0.915810 + 0.528743i
\(923\) 1.61131 0.0530369
\(924\) 0 0
\(925\) −22.0747 −0.725813
\(926\) −18.6322 + 10.7573i −0.612291 + 0.353506i
\(927\) 0 0
\(928\) −3.26990 + 5.66364i −0.107340 + 0.185918i
\(929\) −12.8229 22.2099i −0.420706 0.728685i 0.575302 0.817941i \(-0.304884\pi\)
−0.996009 + 0.0892562i \(0.971551\pi\)
\(930\) 0 0
\(931\) 3.63870 1.38082i 0.119253 0.0452546i
\(932\) 9.25479i 0.303151i
\(933\) 0 0
\(934\) −34.4287 19.8774i −1.12654 0.650409i
\(935\) −6.46065 3.73006i −0.211286 0.121986i
\(936\) 0 0
\(937\) 43.9317i 1.43518i 0.696463 + 0.717592i \(0.254756\pi\)
−0.696463 + 0.717592i \(0.745244\pi\)
\(938\) 19.0105 + 1.53274i 0.620714 + 0.0500457i
\(939\) 0 0
\(940\) 0.629717 + 1.09070i 0.0205391 + 0.0355748i
\(941\) −21.9166 + 37.9607i −0.714460 + 1.23748i 0.248707 + 0.968579i \(0.419994\pi\)
−0.963167 + 0.268903i \(0.913339\pi\)
\(942\) 0 0
\(943\) −11.3256 + 6.53886i −0.368813 + 0.212934i
\(944\) 0.999157 0.0325198
\(945\) 0 0
\(946\) −3.91214 −0.127195
\(947\) 15.4512 8.92077i 0.502097 0.289886i −0.227482 0.973782i \(-0.573049\pi\)
0.729579 + 0.683896i \(0.239716\pi\)
\(948\) 0 0
\(949\) −1.13961 + 1.97386i −0.0369933 + 0.0640743i
\(950\) −0.918266 1.59048i −0.0297925 0.0516021i
\(951\) 0 0
\(952\) 8.60626 12.4710i 0.278931 0.404189i
\(953\) 5.09951i 0.165189i −0.996583 0.0825946i \(-0.973679\pi\)
0.996583 0.0825946i \(-0.0263207\pi\)
\(954\) 0 0
\(955\) 18.3447 + 10.5913i 0.593620 + 0.342726i
\(956\) −4.21695 2.43466i −0.136386 0.0787425i
\(957\) 0 0
\(958\) 11.1615i 0.360610i
\(959\) 31.4125 45.5187i 1.01436 1.46988i
\(960\) 0 0
\(961\) −15.2089 26.3425i −0.490609 0.849760i
\(962\) 4.57898 7.93102i 0.147632 0.255706i
\(963\) 0 0
\(964\) 18.4869 10.6734i 0.595423 0.343767i
\(965\) −7.39281 −0.237983
\(966\) 0 0
\(967\) −36.1081 −1.16116 −0.580578 0.814204i \(-0.697174\pi\)
−0.580578 + 0.814204i \(0.697174\pi\)
\(968\) −0.866025 + 0.500000i −0.0278351 + 0.0160706i
\(969\) 0 0
\(970\) 8.44528 14.6276i 0.271161 0.469665i
\(971\) 15.1490 + 26.2388i 0.486153 + 0.842042i 0.999873 0.0159157i \(-0.00506633\pi\)
−0.513720 + 0.857958i \(0.671733\pi\)
\(972\) 0 0
\(973\) −8.47053 0.682945i −0.271553 0.0218942i
\(974\) 27.0308i 0.866124i
\(975\) 0 0
\(976\) −0.127371 0.0735377i −0.00407705 0.00235388i
\(977\) 21.0168 + 12.1341i 0.672388 + 0.388203i 0.796981 0.604005i \(-0.206429\pi\)
−0.124593 + 0.992208i \(0.539763\pi\)
\(978\) 0 0
\(979\) 8.51881i 0.272262i
\(980\) −9.00048 1.46084i −0.287510 0.0466649i
\(981\) 0 0
\(982\) −10.8730 18.8325i −0.346970 0.600970i
\(983\) 29.2363 50.6388i 0.932493 1.61513i 0.153449 0.988157i \(-0.450962\pi\)
0.779044 0.626969i \(-0.215705\pi\)
\(984\) 0 0
\(985\) 2.35524 1.35980i 0.0750441 0.0433267i
\(986\) 37.4539 1.19277
\(987\) 0 0
\(988\) 0.761905 0.0242394
\(989\) −19.6469 + 11.3432i −0.624736 + 0.360691i
\(990\) 0 0
\(991\) 22.1078 38.2918i 0.702277 1.21638i −0.265388 0.964142i \(-0.585500\pi\)
0.967665 0.252238i \(-0.0811665\pi\)
\(992\) 0.381525 + 0.660821i 0.0121134 + 0.0209811i
\(993\) 0 0
\(994\) 2.81043 1.33392i 0.0891414 0.0423092i
\(995\) 22.6944i 0.719461i
\(996\) 0 0
\(997\) −33.7758 19.5005i −1.06969 0.617586i −0.141593 0.989925i \(-0.545223\pi\)
−0.928097 + 0.372339i \(0.878556\pi\)
\(998\) −14.8102 8.55069i −0.468810 0.270667i
\(999\) 0 0
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 1386.2.r.d.1277.2 yes 24
3.2 odd 2 inner 1386.2.r.d.1277.11 yes 24
7.5 odd 6 inner 1386.2.r.d.89.11 yes 24
21.5 even 6 inner 1386.2.r.d.89.2 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1386.2.r.d.89.2 24 21.5 even 6 inner
1386.2.r.d.89.11 yes 24 7.5 odd 6 inner
1386.2.r.d.1277.2 yes 24 1.1 even 1 trivial
1386.2.r.d.1277.11 yes 24 3.2 odd 2 inner