Properties

Label 441.2.u.d.190.3
Level $441$
Weight $2$
Character 441.190
Analytic conductor $3.521$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [441,2,Mod(64,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([0, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.u (of order \(7\), degree \(6\), 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: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{7})\)
Twist minimal: no (minimal twist has level 147)
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 190.3
Character \(\chi\) \(=\) 441.190
Dual form 441.2.u.d.253.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.494936 + 0.620630i) q^{2} +(0.304822 + 1.33551i) q^{4} +(-1.66830 - 0.803409i) q^{5} +(0.814382 - 2.51730i) q^{7} +(-2.41013 - 1.16066i) q^{8} +O(q^{10})\) \(q+(-0.494936 + 0.620630i) q^{2} +(0.304822 + 1.33551i) q^{4} +(-1.66830 - 0.803409i) q^{5} +(0.814382 - 2.51730i) q^{7} +(-2.41013 - 1.16066i) q^{8} +(1.32432 - 0.637759i) q^{10} +(-2.05686 + 2.57922i) q^{11} +(-3.75557 + 4.70933i) q^{13} +(1.15924 + 1.75133i) q^{14} +(-0.555194 + 0.267367i) q^{16} +(-1.06962 + 4.68631i) q^{17} -3.59852 q^{19} +(0.564429 - 2.47293i) q^{20} +(-0.582729 - 2.55310i) q^{22} +(-0.399015 - 1.74820i) q^{23} +(-0.979701 - 1.22851i) q^{25} +(-1.06399 - 4.66164i) q^{26} +(3.61012 + 0.320290i) q^{28} +(1.56209 - 6.84396i) q^{29} -7.52567 q^{31} +(1.29936 - 5.69285i) q^{32} +(-2.37908 - 2.98327i) q^{34} +(-3.38105 + 3.54532i) q^{35} +(-0.545948 + 2.39196i) q^{37} +(1.78104 - 2.23335i) q^{38} +(3.08833 + 3.87265i) q^{40} +(5.35705 + 2.57982i) q^{41} +(6.85394 - 3.30068i) q^{43} +(-4.07156 - 1.96076i) q^{44} +(1.28247 + 0.617607i) q^{46} +(-5.03967 + 6.31955i) q^{47} +(-5.67356 - 4.10008i) q^{49} +1.24734 q^{50} +(-7.43415 - 3.58010i) q^{52} +(2.61082 + 11.4388i) q^{53} +(5.50363 - 2.65041i) q^{55} +(-4.88449 + 5.12180i) q^{56} +(3.47444 + 4.35681i) q^{58} +(0.864413 - 0.416279i) q^{59} +(-1.40853 + 6.17118i) q^{61} +(3.72473 - 4.67066i) q^{62} +(2.12165 + 2.66046i) q^{64} +(10.0489 - 4.83931i) q^{65} +7.63216 q^{67} -6.58467 q^{68} +(-0.526926 - 3.85309i) q^{70} +(-0.688296 - 3.01562i) q^{71} +(1.29619 + 1.62537i) q^{73} +(-1.21431 - 1.52270i) q^{74} +(-1.09691 - 4.80586i) q^{76} +(4.81760 + 7.27821i) q^{77} -7.73554 q^{79} +1.14103 q^{80} +(-4.25251 + 2.04790i) q^{82} +(-1.26408 - 1.58510i) q^{83} +(5.54947 - 6.95882i) q^{85} +(-1.34376 + 5.88739i) q^{86} +(7.95091 - 3.82896i) q^{88} +(-3.01589 - 3.78180i) q^{89} +(8.79632 + 13.2891i) q^{91} +(2.21311 - 1.06578i) q^{92} +(-1.42779 - 6.25555i) q^{94} +(6.00340 + 2.89108i) q^{95} +11.4584 q^{97} +(5.35269 - 1.49191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 36 q + q^{2} - 9 q^{4} + 4 q^{5} - 6 q^{7} + 15 q^{8} + 10 q^{10} + 7 q^{11} - 12 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} + 6 q^{19} - 25 q^{20} - 21 q^{22} + 20 q^{23} - 2 q^{25} - 6 q^{26} - q^{28} + 22 q^{29} + 16 q^{31} - 26 q^{32} + 6 q^{34} + 9 q^{35} + 32 q^{37} - 17 q^{38} - 21 q^{40} + 5 q^{41} - 34 q^{43} - 2 q^{44} - 32 q^{46} + 7 q^{47} + 20 q^{49} - 236 q^{50} + 20 q^{52} + 32 q^{53} - 17 q^{55} + 39 q^{56} - 53 q^{58} + q^{59} + 14 q^{61} + 60 q^{62} - 21 q^{64} + 39 q^{65} - 22 q^{67} + 110 q^{68} - 40 q^{70} - 36 q^{71} - 11 q^{73} + 46 q^{74} - 101 q^{76} + 17 q^{77} - 14 q^{79} + 112 q^{80} + 2 q^{82} - 12 q^{83} - 44 q^{85} - 184 q^{86} + 204 q^{88} - 12 q^{89} - 16 q^{91} + 105 q^{92} - 5 q^{94} - 18 q^{95} + 172 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{7}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.494936 + 0.620630i −0.349973 + 0.438852i −0.925395 0.379005i \(-0.876266\pi\)
0.575422 + 0.817857i \(0.304838\pi\)
\(3\) 0 0
\(4\) 0.304822 + 1.33551i 0.152411 + 0.667756i
\(5\) −1.66830 0.803409i −0.746085 0.359296i 0.0219027 0.999760i \(-0.493028\pi\)
−0.767988 + 0.640464i \(0.778742\pi\)
\(6\) 0 0
\(7\) 0.814382 2.51730i 0.307808 0.951449i
\(8\) −2.41013 1.16066i −0.852111 0.410355i
\(9\) 0 0
\(10\) 1.32432 0.637759i 0.418787 0.201677i
\(11\) −2.05686 + 2.57922i −0.620167 + 0.777665i −0.988368 0.152081i \(-0.951403\pi\)
0.368201 + 0.929746i \(0.379974\pi\)
\(12\) 0 0
\(13\) −3.75557 + 4.70933i −1.04161 + 1.30613i −0.0909619 + 0.995854i \(0.528994\pi\)
−0.950645 + 0.310280i \(0.899577\pi\)
\(14\) 1.15924 + 1.75133i 0.309821 + 0.468063i
\(15\) 0 0
\(16\) −0.555194 + 0.267367i −0.138798 + 0.0668418i
\(17\) −1.06962 + 4.68631i −0.259421 + 1.13660i 0.662451 + 0.749105i \(0.269516\pi\)
−0.921872 + 0.387493i \(0.873341\pi\)
\(18\) 0 0
\(19\) −3.59852 −0.825557 −0.412779 0.910831i \(-0.635442\pi\)
−0.412779 + 0.910831i \(0.635442\pi\)
\(20\) 0.564429 2.47293i 0.126210 0.552963i
\(21\) 0 0
\(22\) −0.582729 2.55310i −0.124238 0.544323i
\(23\) −0.399015 1.74820i −0.0832004 0.364525i 0.916139 0.400860i \(-0.131289\pi\)
−0.999340 + 0.0363353i \(0.988432\pi\)
\(24\) 0 0
\(25\) −0.979701 1.22851i −0.195940 0.245701i
\(26\) −1.06399 4.66164i −0.208665 0.914223i
\(27\) 0 0
\(28\) 3.61012 + 0.320290i 0.682248 + 0.0605291i
\(29\) 1.56209 6.84396i 0.290073 1.27089i −0.594350 0.804206i \(-0.702591\pi\)
0.884423 0.466686i \(-0.154552\pi\)
\(30\) 0 0
\(31\) −7.52567 −1.35165 −0.675825 0.737062i \(-0.736212\pi\)
−0.675825 + 0.737062i \(0.736212\pi\)
\(32\) 1.29936 5.69285i 0.229696 1.00636i
\(33\) 0 0
\(34\) −2.37908 2.98327i −0.408008 0.511626i
\(35\) −3.38105 + 3.54532i −0.571502 + 0.599268i
\(36\) 0 0
\(37\) −0.545948 + 2.39196i −0.0897534 + 0.393235i −0.999772 0.0213311i \(-0.993210\pi\)
0.910019 + 0.414566i \(0.136067\pi\)
\(38\) 1.78104 2.23335i 0.288922 0.362297i
\(39\) 0 0
\(40\) 3.08833 + 3.87265i 0.488308 + 0.612319i
\(41\) 5.35705 + 2.57982i 0.836631 + 0.402900i 0.802598 0.596520i \(-0.203451\pi\)
0.0340331 + 0.999421i \(0.489165\pi\)
\(42\) 0 0
\(43\) 6.85394 3.30068i 1.04522 0.503349i 0.169175 0.985586i \(-0.445890\pi\)
0.876041 + 0.482237i \(0.160176\pi\)
\(44\) −4.07156 1.96076i −0.613811 0.295596i
\(45\) 0 0
\(46\) 1.28247 + 0.617607i 0.189090 + 0.0910611i
\(47\) −5.03967 + 6.31955i −0.735112 + 0.921801i −0.999087 0.0427287i \(-0.986395\pi\)
0.263975 + 0.964529i \(0.414966\pi\)
\(48\) 0 0
\(49\) −5.67356 4.10008i −0.810509 0.585726i
\(50\) 1.24734 0.176400
\(51\) 0 0
\(52\) −7.43415 3.58010i −1.03093 0.496470i
\(53\) 2.61082 + 11.4388i 0.358624 + 1.57124i 0.756624 + 0.653850i \(0.226847\pi\)
−0.398000 + 0.917386i \(0.630296\pi\)
\(54\) 0 0
\(55\) 5.50363 2.65041i 0.742109 0.357381i
\(56\) −4.88449 + 5.12180i −0.652718 + 0.684429i
\(57\) 0 0
\(58\) 3.47444 + 4.35681i 0.456216 + 0.572077i
\(59\) 0.864413 0.416279i 0.112537 0.0541950i −0.376768 0.926308i \(-0.622965\pi\)
0.489305 + 0.872113i \(0.337250\pi\)
\(60\) 0 0
\(61\) −1.40853 + 6.17118i −0.180344 + 0.790138i 0.801122 + 0.598501i \(0.204237\pi\)
−0.981466 + 0.191637i \(0.938620\pi\)
\(62\) 3.72473 4.67066i 0.473041 0.593174i
\(63\) 0 0
\(64\) 2.12165 + 2.66046i 0.265206 + 0.332558i
\(65\) 10.0489 4.83931i 1.24642 0.600242i
\(66\) 0 0
\(67\) 7.63216 0.932417 0.466208 0.884675i \(-0.345620\pi\)
0.466208 + 0.884675i \(0.345620\pi\)
\(68\) −6.58467 −0.798508
\(69\) 0 0
\(70\) −0.526926 3.85309i −0.0629797 0.460532i
\(71\) −0.688296 3.01562i −0.0816857 0.357889i 0.917522 0.397685i \(-0.130186\pi\)
−0.999208 + 0.0397963i \(0.987329\pi\)
\(72\) 0 0
\(73\) 1.29619 + 1.62537i 0.151707 + 0.190235i 0.851878 0.523741i \(-0.175464\pi\)
−0.700170 + 0.713976i \(0.746893\pi\)
\(74\) −1.21431 1.52270i −0.141161 0.177010i
\(75\) 0 0
\(76\) −1.09691 4.80586i −0.125824 0.551270i
\(77\) 4.81760 + 7.27821i 0.549016 + 0.829429i
\(78\) 0 0
\(79\) −7.73554 −0.870317 −0.435158 0.900354i \(-0.643308\pi\)
−0.435158 + 0.900354i \(0.643308\pi\)
\(80\) 1.14103 0.127571
\(81\) 0 0
\(82\) −4.25251 + 2.04790i −0.469612 + 0.226153i
\(83\) −1.26408 1.58510i −0.138751 0.173988i 0.707601 0.706612i \(-0.249777\pi\)
−0.846352 + 0.532624i \(0.821206\pi\)
\(84\) 0 0
\(85\) 5.54947 6.95882i 0.601925 0.754790i
\(86\) −1.34376 + 5.88739i −0.144901 + 0.634853i
\(87\) 0 0
\(88\) 7.95091 3.82896i 0.847570 0.408168i
\(89\) −3.01589 3.78180i −0.319683 0.400870i 0.595861 0.803088i \(-0.296811\pi\)
−0.915544 + 0.402218i \(0.868240\pi\)
\(90\) 0 0
\(91\) 8.79632 + 13.2891i 0.922105 + 1.39307i
\(92\) 2.21311 1.06578i 0.230733 0.111115i
\(93\) 0 0
\(94\) −1.42779 6.25555i −0.147265 0.645210i
\(95\) 6.00340 + 2.89108i 0.615936 + 0.296619i
\(96\) 0 0
\(97\) 11.4584 1.16343 0.581715 0.813393i \(-0.302382\pi\)
0.581715 + 0.813393i \(0.302382\pi\)
\(98\) 5.35269 1.49191i 0.540703 0.150705i
\(99\) 0 0
\(100\) 1.34205 1.68288i 0.134205 0.168288i
\(101\) −15.6394 7.53154i −1.55618 0.749416i −0.559346 0.828935i \(-0.688948\pi\)
−0.996833 + 0.0795183i \(0.974662\pi\)
\(102\) 0 0
\(103\) 9.20924 + 4.43494i 0.907414 + 0.436987i 0.828561 0.559899i \(-0.189160\pi\)
0.0788526 + 0.996886i \(0.474874\pi\)
\(104\) 14.5173 6.99119i 1.42354 0.685542i
\(105\) 0 0
\(106\) −8.39144 4.04110i −0.815048 0.392507i
\(107\) 10.6528 + 13.3582i 1.02985 + 1.29138i 0.955765 + 0.294133i \(0.0950307\pi\)
0.0740805 + 0.997252i \(0.476398\pi\)
\(108\) 0 0
\(109\) −5.53636 + 6.94238i −0.530287 + 0.664959i −0.972758 0.231824i \(-0.925531\pi\)
0.442470 + 0.896783i \(0.354102\pi\)
\(110\) −1.07902 + 4.72750i −0.102881 + 0.450750i
\(111\) 0 0
\(112\) 0.220903 + 1.61533i 0.0208733 + 0.152634i
\(113\) −10.4119 13.0561i −0.979468 1.22821i −0.973607 0.228232i \(-0.926706\pi\)
−0.00586137 0.999983i \(-0.501866\pi\)
\(114\) 0 0
\(115\) −0.738845 + 3.23709i −0.0688976 + 0.301860i
\(116\) 9.61635 0.892856
\(117\) 0 0
\(118\) −0.169474 + 0.742513i −0.0156013 + 0.0683538i
\(119\) 10.9258 + 6.50900i 1.00156 + 0.596679i
\(120\) 0 0
\(121\) 0.0260169 + 0.113988i 0.00236518 + 0.0103625i
\(122\) −3.13289 3.92851i −0.283638 0.355671i
\(123\) 0 0
\(124\) −2.29399 10.0506i −0.206006 0.902572i
\(125\) 2.70762 + 11.8628i 0.242176 + 1.06104i
\(126\) 0 0
\(127\) −2.06099 + 9.02978i −0.182883 + 0.801263i 0.797366 + 0.603496i \(0.206226\pi\)
−0.980249 + 0.197767i \(0.936631\pi\)
\(128\) 8.97727 0.793486
\(129\) 0 0
\(130\) −1.97016 + 8.63182i −0.172794 + 0.757060i
\(131\) 5.30138 2.55301i 0.463184 0.223058i −0.187713 0.982224i \(-0.560107\pi\)
0.650897 + 0.759166i \(0.274393\pi\)
\(132\) 0 0
\(133\) −2.93057 + 9.05854i −0.254113 + 0.785475i
\(134\) −3.77743 + 4.73675i −0.326321 + 0.409193i
\(135\) 0 0
\(136\) 8.01714 10.0532i 0.687464 0.862053i
\(137\) 4.71367 2.26999i 0.402716 0.193938i −0.221551 0.975149i \(-0.571112\pi\)
0.624267 + 0.781211i \(0.285398\pi\)
\(138\) 0 0
\(139\) 7.42989 + 3.57804i 0.630195 + 0.303486i 0.721581 0.692330i \(-0.243416\pi\)
−0.0913866 + 0.995815i \(0.529130\pi\)
\(140\) −5.76543 3.43474i −0.487267 0.290289i
\(141\) 0 0
\(142\) 2.21225 + 1.06536i 0.185648 + 0.0894033i
\(143\) −4.42174 19.3729i −0.369764 1.62004i
\(144\) 0 0
\(145\) −8.10454 + 10.1628i −0.673045 + 0.843972i
\(146\) −1.65028 −0.136579
\(147\) 0 0
\(148\) −3.36090 −0.276264
\(149\) −7.03129 + 8.81696i −0.576025 + 0.722313i −0.981429 0.191825i \(-0.938560\pi\)
0.405404 + 0.914138i \(0.367131\pi\)
\(150\) 0 0
\(151\) −4.61340 20.2126i −0.375433 1.64488i −0.711239 0.702950i \(-0.751866\pi\)
0.335806 0.941931i \(-0.390991\pi\)
\(152\) 8.67291 + 4.17665i 0.703466 + 0.338771i
\(153\) 0 0
\(154\) −6.90148 0.612300i −0.556137 0.0493405i
\(155\) 12.5550 + 6.04619i 1.00845 + 0.485642i
\(156\) 0 0
\(157\) −6.77503 + 3.26268i −0.540706 + 0.260390i −0.684242 0.729255i \(-0.739867\pi\)
0.143536 + 0.989645i \(0.454153\pi\)
\(158\) 3.82860 4.80091i 0.304587 0.381940i
\(159\) 0 0
\(160\) −6.74140 + 8.45345i −0.532955 + 0.668304i
\(161\) −4.72569 0.419263i −0.372436 0.0330426i
\(162\) 0 0
\(163\) 3.52731 1.69866i 0.276280 0.133050i −0.290613 0.956841i \(-0.593859\pi\)
0.566894 + 0.823791i \(0.308145\pi\)
\(164\) −1.81243 + 7.94079i −0.141527 + 0.620071i
\(165\) 0 0
\(166\) 1.60940 0.124914
\(167\) 0.794789 3.48220i 0.0615026 0.269461i −0.934822 0.355116i \(-0.884441\pi\)
0.996325 + 0.0856555i \(0.0272984\pi\)
\(168\) 0 0
\(169\) −5.18076 22.6984i −0.398520 1.74603i
\(170\) 1.57222 + 6.88834i 0.120584 + 0.528312i
\(171\) 0 0
\(172\) 6.49733 + 8.14739i 0.495416 + 0.621233i
\(173\) −0.434931 1.90556i −0.0330672 0.144877i 0.955699 0.294344i \(-0.0951012\pi\)
−0.988767 + 0.149468i \(0.952244\pi\)
\(174\) 0 0
\(175\) −3.89037 + 1.46572i −0.294084 + 0.110798i
\(176\) 0.452357 1.98191i 0.0340977 0.149392i
\(177\) 0 0
\(178\) 3.83977 0.287803
\(179\) −2.17788 + 9.54190i −0.162782 + 0.713195i 0.825980 + 0.563699i \(0.190622\pi\)
−0.988762 + 0.149496i \(0.952235\pi\)
\(180\) 0 0
\(181\) 7.30729 + 9.16305i 0.543146 + 0.681084i 0.975343 0.220696i \(-0.0708327\pi\)
−0.432196 + 0.901779i \(0.642261\pi\)
\(182\) −12.6012 1.11798i −0.934065 0.0828702i
\(183\) 0 0
\(184\) −1.06738 + 4.67652i −0.0786886 + 0.344757i
\(185\) 2.83252 3.55187i 0.208251 0.261139i
\(186\) 0 0
\(187\) −9.88699 12.3979i −0.723009 0.906624i
\(188\) −9.97603 4.80420i −0.727577 0.350382i
\(189\) 0 0
\(190\) −4.76559 + 2.29499i −0.345733 + 0.166496i
\(191\) −7.94952 3.82829i −0.575207 0.277005i 0.123580 0.992335i \(-0.460562\pi\)
−0.698787 + 0.715329i \(0.746277\pi\)
\(192\) 0 0
\(193\) −7.40229 3.56475i −0.532828 0.256597i 0.148067 0.988977i \(-0.452695\pi\)
−0.680895 + 0.732381i \(0.738409\pi\)
\(194\) −5.67120 + 7.11146i −0.407168 + 0.510573i
\(195\) 0 0
\(196\) 3.74628 8.82690i 0.267591 0.630493i
\(197\) −7.29570 −0.519797 −0.259898 0.965636i \(-0.583689\pi\)
−0.259898 + 0.965636i \(0.583689\pi\)
\(198\) 0 0
\(199\) 1.25737 + 0.605517i 0.0891326 + 0.0429240i 0.477919 0.878404i \(-0.341391\pi\)
−0.388786 + 0.921328i \(0.627106\pi\)
\(200\) 0.935333 + 4.09796i 0.0661381 + 0.289770i
\(201\) 0 0
\(202\) 12.4148 5.97866i 0.873503 0.420657i
\(203\) −15.9561 9.50585i −1.11990 0.667180i
\(204\) 0 0
\(205\) −6.86450 8.60781i −0.479438 0.601196i
\(206\) −7.31044 + 3.52052i −0.509343 + 0.245287i
\(207\) 0 0
\(208\) 0.825946 3.61871i 0.0572691 0.250912i
\(209\) 7.40166 9.28139i 0.511984 0.642007i
\(210\) 0 0
\(211\) 5.92398 + 7.42844i 0.407824 + 0.511395i 0.942748 0.333505i \(-0.108231\pi\)
−0.534925 + 0.844900i \(0.679660\pi\)
\(212\) −14.4808 + 6.97357i −0.994543 + 0.478947i
\(213\) 0 0
\(214\) −13.5630 −0.927144
\(215\) −14.0862 −0.960671
\(216\) 0 0
\(217\) −6.12877 + 18.9443i −0.416048 + 1.28603i
\(218\) −1.56851 6.87207i −0.106233 0.465435i
\(219\) 0 0
\(220\) 5.21728 + 6.54226i 0.351749 + 0.441079i
\(221\) −18.0524 22.6370i −1.21433 1.52273i
\(222\) 0 0
\(223\) −5.37217 23.5370i −0.359747 1.57616i −0.753823 0.657078i \(-0.771792\pi\)
0.394076 0.919078i \(-0.371065\pi\)
\(224\) −13.2724 7.90702i −0.886801 0.528310i
\(225\) 0 0
\(226\) 13.2562 0.881791
\(227\) −9.47947 −0.629174 −0.314587 0.949229i \(-0.601866\pi\)
−0.314587 + 0.949229i \(0.601866\pi\)
\(228\) 0 0
\(229\) 10.1328 4.87968i 0.669591 0.322458i −0.0680200 0.997684i \(-0.521668\pi\)
0.737611 + 0.675226i \(0.235954\pi\)
\(230\) −1.64336 2.06070i −0.108360 0.135879i
\(231\) 0 0
\(232\) −11.7084 + 14.6818i −0.768691 + 0.963908i
\(233\) −0.959744 + 4.20491i −0.0628749 + 0.275473i −0.996587 0.0825525i \(-0.973693\pi\)
0.933712 + 0.358026i \(0.116550\pi\)
\(234\) 0 0
\(235\) 13.4849 6.49396i 0.879655 0.423619i
\(236\) 0.819438 + 1.02754i 0.0533409 + 0.0668873i
\(237\) 0 0
\(238\) −9.44724 + 3.55932i −0.612374 + 0.230716i
\(239\) 15.8586 7.63710i 1.02581 0.494003i 0.156189 0.987727i \(-0.450079\pi\)
0.869619 + 0.493724i \(0.164365\pi\)
\(240\) 0 0
\(241\) −0.628797 2.75494i −0.0405044 0.177461i 0.950630 0.310328i \(-0.100439\pi\)
−0.991134 + 0.132867i \(0.957582\pi\)
\(242\) −0.0836210 0.0402697i −0.00537536 0.00258864i
\(243\) 0 0
\(244\) −8.67102 −0.555105
\(245\) 6.17114 + 11.3983i 0.394260 + 0.728214i
\(246\) 0 0
\(247\) 13.5145 16.9466i 0.859906 1.07829i
\(248\) 18.1379 + 8.73473i 1.15176 + 0.554656i
\(249\) 0 0
\(250\) −8.70253 4.19092i −0.550397 0.265057i
\(251\) −0.949894 + 0.457445i −0.0599568 + 0.0288737i −0.463622 0.886033i \(-0.653450\pi\)
0.403665 + 0.914907i \(0.367736\pi\)
\(252\) 0 0
\(253\) 5.32972 + 2.56666i 0.335077 + 0.161364i
\(254\) −4.58410 5.74827i −0.287632 0.360679i
\(255\) 0 0
\(256\) −8.68647 + 10.8925i −0.542904 + 0.680780i
\(257\) −6.47732 + 28.3790i −0.404044 + 1.77023i 0.206698 + 0.978405i \(0.433728\pi\)
−0.610743 + 0.791829i \(0.709129\pi\)
\(258\) 0 0
\(259\) 5.57665 + 3.32228i 0.346516 + 0.206436i
\(260\) 9.52608 + 11.9453i 0.590782 + 0.740818i
\(261\) 0 0
\(262\) −1.03937 + 4.55377i −0.0642125 + 0.281333i
\(263\) 27.0814 1.66991 0.834954 0.550320i \(-0.185494\pi\)
0.834954 + 0.550320i \(0.185494\pi\)
\(264\) 0 0
\(265\) 4.83438 21.1808i 0.296974 1.30113i
\(266\) −4.17156 6.30220i −0.255775 0.386413i
\(267\) 0 0
\(268\) 2.32645 + 10.1928i 0.142110 + 0.622627i
\(269\) −12.0295 15.0845i −0.733450 0.919717i 0.265565 0.964093i \(-0.414442\pi\)
−0.999015 + 0.0443759i \(0.985870\pi\)
\(270\) 0 0
\(271\) −3.97657 17.4225i −0.241560 1.05834i −0.939598 0.342281i \(-0.888800\pi\)
0.698038 0.716061i \(-0.254057\pi\)
\(272\) −0.659120 2.88779i −0.0399650 0.175098i
\(273\) 0 0
\(274\) −0.924145 + 4.04895i −0.0558297 + 0.244606i
\(275\) 5.18370 0.312589
\(276\) 0 0
\(277\) −5.88358 + 25.7777i −0.353510 + 1.54883i 0.415500 + 0.909593i \(0.363606\pi\)
−0.769011 + 0.639236i \(0.779251\pi\)
\(278\) −5.89796 + 2.84031i −0.353736 + 0.170350i
\(279\) 0 0
\(280\) 12.2637 4.62044i 0.732895 0.276124i
\(281\) −4.51391 + 5.66027i −0.269278 + 0.337663i −0.898024 0.439947i \(-0.854997\pi\)
0.628746 + 0.777611i \(0.283569\pi\)
\(282\) 0 0
\(283\) −1.97448 + 2.47592i −0.117371 + 0.147178i −0.837046 0.547133i \(-0.815719\pi\)
0.719675 + 0.694311i \(0.244291\pi\)
\(284\) 3.81759 1.83845i 0.226532 0.109092i
\(285\) 0 0
\(286\) 14.2119 + 6.84409i 0.840367 + 0.404699i
\(287\) 10.8569 11.3843i 0.640860 0.671996i
\(288\) 0 0
\(289\) −5.50099 2.64914i −0.323587 0.155832i
\(290\) −2.29609 10.0598i −0.134831 0.590734i
\(291\) 0 0
\(292\) −1.77559 + 2.22652i −0.103909 + 0.130297i
\(293\) −28.7842 −1.68159 −0.840797 0.541351i \(-0.817913\pi\)
−0.840797 + 0.541351i \(0.817913\pi\)
\(294\) 0 0
\(295\) −1.77654 −0.103434
\(296\) 4.09205 5.13127i 0.237846 0.298249i
\(297\) 0 0
\(298\) −1.99203 8.72766i −0.115395 0.505580i
\(299\) 9.73139 + 4.68639i 0.562781 + 0.271021i
\(300\) 0 0
\(301\) −2.72707 19.9414i −0.157186 1.14940i
\(302\) 14.8279 + 7.14075i 0.853251 + 0.410904i
\(303\) 0 0
\(304\) 1.99788 0.962126i 0.114586 0.0551817i
\(305\) 7.30783 9.16373i 0.418445 0.524713i
\(306\) 0 0
\(307\) −10.6637 + 13.3718i −0.608608 + 0.763171i −0.986692 0.162601i \(-0.948012\pi\)
0.378084 + 0.925771i \(0.376583\pi\)
\(308\) −8.25162 + 8.65251i −0.470180 + 0.493023i
\(309\) 0 0
\(310\) −9.96640 + 4.79956i −0.566053 + 0.272597i
\(311\) −1.22057 + 5.34767i −0.0692122 + 0.303238i −0.997672 0.0681944i \(-0.978276\pi\)
0.928460 + 0.371433i \(0.121133\pi\)
\(312\) 0 0
\(313\) −17.8174 −1.00710 −0.503549 0.863967i \(-0.667973\pi\)
−0.503549 + 0.863967i \(0.667973\pi\)
\(314\) 1.32829 5.81961i 0.0749596 0.328419i
\(315\) 0 0
\(316\) −2.35796 10.3309i −0.132646 0.581159i
\(317\) 3.86268 + 16.9235i 0.216950 + 0.950520i 0.959717 + 0.280970i \(0.0906560\pi\)
−0.742767 + 0.669550i \(0.766487\pi\)
\(318\) 0 0
\(319\) 14.4391 + 18.1061i 0.808435 + 1.01375i
\(320\) −1.40210 6.14299i −0.0783796 0.343404i
\(321\) 0 0
\(322\) 2.59912 2.72540i 0.144843 0.151880i
\(323\) 3.84905 16.8638i 0.214167 0.938327i
\(324\) 0 0
\(325\) 9.46478 0.525012
\(326\) −0.691551 + 3.02988i −0.0383015 + 0.167810i
\(327\) 0 0
\(328\) −9.91692 12.4354i −0.547570 0.686631i
\(329\) 11.8040 + 17.8329i 0.650773 + 0.983158i
\(330\) 0 0
\(331\) −4.01232 + 17.5791i −0.220537 + 0.966236i 0.736538 + 0.676396i \(0.236459\pi\)
−0.957075 + 0.289840i \(0.906398\pi\)
\(332\) 1.73160 2.17136i 0.0950341 0.119169i
\(333\) 0 0
\(334\) 1.76779 + 2.21674i 0.0967291 + 0.121294i
\(335\) −12.7327 6.13175i −0.695662 0.335013i
\(336\) 0 0
\(337\) −17.1186 + 8.24390i −0.932511 + 0.449074i −0.837521 0.546404i \(-0.815996\pi\)
−0.0949899 + 0.995478i \(0.530282\pi\)
\(338\) 16.6515 + 8.01892i 0.905719 + 0.436172i
\(339\) 0 0
\(340\) 10.9852 + 5.29019i 0.595755 + 0.286901i
\(341\) 15.4793 19.4104i 0.838249 1.05113i
\(342\) 0 0
\(343\) −14.9416 + 10.9430i −0.806769 + 0.590867i
\(344\) −20.3499 −1.09719
\(345\) 0 0
\(346\) 1.39791 + 0.673197i 0.0751520 + 0.0361913i
\(347\) 5.49342 + 24.0682i 0.294902 + 1.29205i 0.877613 + 0.479370i \(0.159135\pi\)
−0.582711 + 0.812680i \(0.698008\pi\)
\(348\) 0 0
\(349\) −21.0536 + 10.1389i −1.12697 + 0.542722i −0.902040 0.431652i \(-0.857931\pi\)
−0.224933 + 0.974374i \(0.572216\pi\)
\(350\) 1.01581 3.13992i 0.0542973 0.167836i
\(351\) 0 0
\(352\) 12.0105 + 15.0607i 0.640164 + 0.802741i
\(353\) −9.74754 + 4.69417i −0.518809 + 0.249845i −0.674916 0.737895i \(-0.735820\pi\)
0.156106 + 0.987740i \(0.450106\pi\)
\(354\) 0 0
\(355\) −1.27450 + 5.58394i −0.0676433 + 0.296365i
\(356\) 4.13133 5.18052i 0.218960 0.274567i
\(357\) 0 0
\(358\) −4.84408 6.07429i −0.256018 0.321036i
\(359\) 5.60658 2.69999i 0.295904 0.142500i −0.280042 0.959988i \(-0.590348\pi\)
0.575946 + 0.817488i \(0.304634\pi\)
\(360\) 0 0
\(361\) −6.05065 −0.318455
\(362\) −9.30351 −0.488981
\(363\) 0 0
\(364\) −15.0664 + 15.7984i −0.789694 + 0.828060i
\(365\) −0.856591 3.75297i −0.0448360 0.196439i
\(366\) 0 0
\(367\) 4.43146 + 5.55687i 0.231320 + 0.290066i 0.883922 0.467635i \(-0.154894\pi\)
−0.652601 + 0.757701i \(0.726322\pi\)
\(368\) 0.688942 + 0.863906i 0.0359136 + 0.0450342i
\(369\) 0 0
\(370\) 0.802482 + 3.51590i 0.0417190 + 0.182783i
\(371\) 30.9210 + 2.74331i 1.60534 + 0.142426i
\(372\) 0 0
\(373\) 18.6719 0.966797 0.483398 0.875401i \(-0.339402\pi\)
0.483398 + 0.875401i \(0.339402\pi\)
\(374\) 12.5879 0.650907
\(375\) 0 0
\(376\) 19.4811 9.38161i 1.00466 0.483820i
\(377\) 26.3640 + 33.0594i 1.35781 + 1.70264i
\(378\) 0 0
\(379\) 13.9657 17.5124i 0.717370 0.899553i −0.280816 0.959762i \(-0.590605\pi\)
0.998186 + 0.0602084i \(0.0191765\pi\)
\(380\) −2.03111 + 8.89887i −0.104194 + 0.456503i
\(381\) 0 0
\(382\) 6.31046 3.03896i 0.322871 0.155486i
\(383\) −11.0617 13.8709i −0.565226 0.708770i 0.414289 0.910146i \(-0.364030\pi\)
−0.979514 + 0.201375i \(0.935459\pi\)
\(384\) 0 0
\(385\) −2.18981 16.0127i −0.111603 0.816084i
\(386\) 5.87605 2.82976i 0.299083 0.144031i
\(387\) 0 0
\(388\) 3.49278 + 15.3029i 0.177319 + 0.776886i
\(389\) −31.7739 15.3015i −1.61100 0.775818i −0.611126 0.791534i \(-0.709283\pi\)
−0.999876 + 0.0157159i \(0.994997\pi\)
\(390\) 0 0
\(391\) 8.61941 0.435902
\(392\) 8.91524 + 16.4668i 0.450288 + 0.831700i
\(393\) 0 0
\(394\) 3.61090 4.52793i 0.181915 0.228114i
\(395\) 12.9052 + 6.21481i 0.649330 + 0.312701i
\(396\) 0 0
\(397\) 14.7510 + 7.10371i 0.740332 + 0.356525i 0.765738 0.643152i \(-0.222374\pi\)
−0.0254064 + 0.999677i \(0.508088\pi\)
\(398\) −0.998120 + 0.480669i −0.0500312 + 0.0240938i
\(399\) 0 0
\(400\) 0.872386 + 0.420119i 0.0436193 + 0.0210059i
\(401\) −15.0216 18.8365i −0.750142 0.940648i 0.249474 0.968382i \(-0.419742\pi\)
−0.999615 + 0.0277336i \(0.991171\pi\)
\(402\) 0 0
\(403\) 28.2632 35.4409i 1.40789 1.76544i
\(404\) 5.29123 23.1824i 0.263248 1.15337i
\(405\) 0 0
\(406\) 13.7969 5.19808i 0.684728 0.257976i
\(407\) −5.04645 6.32805i −0.250143 0.313670i
\(408\) 0 0
\(409\) 0.296490 1.29901i 0.0146605 0.0642317i −0.967069 0.254516i \(-0.918084\pi\)
0.981729 + 0.190284i \(0.0609410\pi\)
\(410\) 8.73976 0.431626
\(411\) 0 0
\(412\) −3.11573 + 13.6509i −0.153501 + 0.672532i
\(413\) −0.343936 2.51499i −0.0169240 0.123755i
\(414\) 0 0
\(415\) 0.835370 + 3.65999i 0.0410067 + 0.179662i
\(416\) 21.9297 + 27.4990i 1.07519 + 1.34825i
\(417\) 0 0
\(418\) 2.09696 + 9.18739i 0.102566 + 0.449370i
\(419\) 4.50536 + 19.7393i 0.220101 + 0.964328i 0.957401 + 0.288762i \(0.0932435\pi\)
−0.737300 + 0.675566i \(0.763899\pi\)
\(420\) 0 0
\(421\) 4.06152 17.7947i 0.197946 0.867260i −0.774210 0.632928i \(-0.781853\pi\)
0.972157 0.234332i \(-0.0752901\pi\)
\(422\) −7.54231 −0.367154
\(423\) 0 0
\(424\) 6.98407 30.5992i 0.339177 1.48603i
\(425\) 6.80508 3.27715i 0.330095 0.158965i
\(426\) 0 0
\(427\) 14.3876 + 8.57138i 0.696265 + 0.414798i
\(428\) −14.5928 + 18.2988i −0.705370 + 0.884506i
\(429\) 0 0
\(430\) 6.97177 8.74232i 0.336209 0.421592i
\(431\) −4.37009 + 2.10452i −0.210500 + 0.101371i −0.536163 0.844115i \(-0.680127\pi\)
0.325663 + 0.945486i \(0.394412\pi\)
\(432\) 0 0
\(433\) −19.3356 9.31154i −0.929210 0.447484i −0.0928597 0.995679i \(-0.529601\pi\)
−0.836350 + 0.548195i \(0.815315\pi\)
\(434\) −8.72408 13.1799i −0.418769 0.632657i
\(435\) 0 0
\(436\) −10.9592 5.27769i −0.524852 0.252755i
\(437\) 1.43586 + 6.29093i 0.0686867 + 0.300936i
\(438\) 0 0
\(439\) −5.74661 + 7.20602i −0.274271 + 0.343925i −0.899821 0.436259i \(-0.856303\pi\)
0.625550 + 0.780184i \(0.284874\pi\)
\(440\) −16.3407 −0.779012
\(441\) 0 0
\(442\) 22.9840 1.09324
\(443\) 18.7955 23.5688i 0.893002 1.11979i −0.0991904 0.995068i \(-0.531625\pi\)
0.992192 0.124720i \(-0.0398033\pi\)
\(444\) 0 0
\(445\) 1.99306 + 8.73216i 0.0944800 + 0.413944i
\(446\) 17.2667 + 8.31519i 0.817601 + 0.393736i
\(447\) 0 0
\(448\) 8.42500 3.17418i 0.398044 0.149966i
\(449\) 2.43196 + 1.17117i 0.114771 + 0.0552708i 0.490388 0.871504i \(-0.336855\pi\)
−0.375617 + 0.926775i \(0.622569\pi\)
\(450\) 0 0
\(451\) −17.6727 + 8.51070i −0.832173 + 0.400753i
\(452\) 14.2628 17.8850i 0.670865 0.841239i
\(453\) 0 0
\(454\) 4.69173 5.88324i 0.220194 0.276114i
\(455\) −3.99831 29.2372i −0.187443 1.37066i
\(456\) 0 0
\(457\) 5.31029 2.55730i 0.248405 0.119626i −0.305539 0.952180i \(-0.598837\pi\)
0.553944 + 0.832554i \(0.313122\pi\)
\(458\) −1.98659 + 8.70382i −0.0928273 + 0.406703i
\(459\) 0 0
\(460\) −4.54838 −0.212070
\(461\) 4.52727 19.8353i 0.210856 0.923820i −0.753131 0.657871i \(-0.771457\pi\)
0.963987 0.265950i \(-0.0856855\pi\)
\(462\) 0 0
\(463\) 5.03725 + 22.0697i 0.234101 + 1.02566i 0.946199 + 0.323584i \(0.104888\pi\)
−0.712098 + 0.702080i \(0.752255\pi\)
\(464\) 0.962589 + 4.21738i 0.0446871 + 0.195787i
\(465\) 0 0
\(466\) −2.13468 2.67681i −0.0988874 0.124001i
\(467\) −5.09404 22.3184i −0.235724 1.03277i −0.944802 0.327643i \(-0.893746\pi\)
0.709078 0.705130i \(-0.249112\pi\)
\(468\) 0 0
\(469\) 6.21550 19.2124i 0.287005 0.887147i
\(470\) −2.64379 + 11.5832i −0.121949 + 0.534293i
\(471\) 0 0
\(472\) −2.56651 −0.118133
\(473\) −5.58441 + 24.4669i −0.256771 + 1.12499i
\(474\) 0 0
\(475\) 3.52547 + 4.42081i 0.161760 + 0.202840i
\(476\) −5.36244 + 16.5756i −0.245787 + 0.759740i
\(477\) 0 0
\(478\) −3.10918 + 13.6222i −0.142211 + 0.623065i
\(479\) 3.24393 4.06776i 0.148219 0.185861i −0.702179 0.712000i \(-0.747790\pi\)
0.850398 + 0.526139i \(0.176361\pi\)
\(480\) 0 0
\(481\) −9.21417 11.5542i −0.420130 0.526827i
\(482\) 2.02101 + 0.973268i 0.0920546 + 0.0443312i
\(483\) 0 0
\(484\) −0.144301 + 0.0694918i −0.00655915 + 0.00315872i
\(485\) −19.1161 9.20583i −0.868017 0.418015i
\(486\) 0 0
\(487\) −29.0767 14.0026i −1.31759 0.634519i −0.362821 0.931859i \(-0.618186\pi\)
−0.954772 + 0.297339i \(0.903901\pi\)
\(488\) 10.5574 13.2385i 0.477910 0.599280i
\(489\) 0 0
\(490\) −10.1285 1.81146i −0.457558 0.0818333i
\(491\) 27.8108 1.25508 0.627541 0.778583i \(-0.284061\pi\)
0.627541 + 0.778583i \(0.284061\pi\)
\(492\) 0 0
\(493\) 30.4021 + 14.6409i 1.36924 + 0.659393i
\(494\) 3.82878 + 16.7750i 0.172265 + 0.754743i
\(495\) 0 0
\(496\) 4.17820 2.01212i 0.187607 0.0903467i
\(497\) −8.15175 0.723224i −0.365656 0.0324410i
\(498\) 0 0
\(499\) −19.9403 25.0043i −0.892649 1.11935i −0.992242 0.124318i \(-0.960326\pi\)
0.0995934 0.995028i \(-0.468246\pi\)
\(500\) −15.0176 + 7.23210i −0.671608 + 0.323429i
\(501\) 0 0
\(502\) 0.186233 0.815939i 0.00831198 0.0364172i
\(503\) −8.92014 + 11.1855i −0.397729 + 0.498737i −0.939861 0.341557i \(-0.889046\pi\)
0.542132 + 0.840293i \(0.317617\pi\)
\(504\) 0 0
\(505\) 20.0403 + 25.1297i 0.891780 + 1.11826i
\(506\) −4.23082 + 2.03745i −0.188083 + 0.0905759i
\(507\) 0 0
\(508\) −12.6876 −0.562921
\(509\) −13.2013 −0.585136 −0.292568 0.956245i \(-0.594510\pi\)
−0.292568 + 0.956245i \(0.594510\pi\)
\(510\) 0 0
\(511\) 5.14713 1.93922i 0.227696 0.0857860i
\(512\) 1.53430 + 6.72221i 0.0678071 + 0.297082i
\(513\) 0 0
\(514\) −14.4070 18.0658i −0.635466 0.796849i
\(515\) −11.8007 14.7976i −0.520000 0.652059i
\(516\) 0 0
\(517\) −5.93362 25.9969i −0.260960 1.14334i
\(518\) −4.82200 + 1.81672i −0.211866 + 0.0798222i
\(519\) 0 0
\(520\) −29.8360 −1.30840
\(521\) 26.2490 1.14999 0.574996 0.818156i \(-0.305004\pi\)
0.574996 + 0.818156i \(0.305004\pi\)
\(522\) 0 0
\(523\) −8.81908 + 4.24705i −0.385631 + 0.185710i −0.616647 0.787240i \(-0.711509\pi\)
0.231016 + 0.972950i \(0.425795\pi\)
\(524\) 5.02555 + 6.30184i 0.219542 + 0.275297i
\(525\) 0 0
\(526\) −13.4035 + 16.8075i −0.584422 + 0.732842i
\(527\) 8.04961 35.2677i 0.350647 1.53628i
\(528\) 0 0
\(529\) 17.8253 8.58421i 0.775013 0.373226i
\(530\) 10.7527 + 13.4835i 0.467070 + 0.585687i
\(531\) 0 0
\(532\) −12.9911 1.15257i −0.563235 0.0499702i
\(533\) −32.2680 + 15.5395i −1.39768 + 0.673088i
\(534\) 0 0
\(535\) −7.03994 30.8440i −0.304363 1.33350i
\(536\) −18.3945 8.85834i −0.794522 0.382622i
\(537\) 0 0
\(538\) 15.3157 0.660307
\(539\) 22.2448 6.20008i 0.958150 0.267057i
\(540\) 0 0
\(541\) −13.2505 + 16.6156i −0.569684 + 0.714361i −0.980315 0.197441i \(-0.936737\pi\)
0.410631 + 0.911802i \(0.365308\pi\)
\(542\) 12.7811 + 6.15505i 0.548995 + 0.264382i
\(543\) 0 0
\(544\) 25.2887 + 12.1784i 1.08424 + 0.522144i
\(545\) 14.8139 7.13399i 0.634557 0.305586i
\(546\) 0 0
\(547\) 5.91812 + 2.85002i 0.253040 + 0.121858i 0.556105 0.831112i \(-0.312295\pi\)
−0.303064 + 0.952970i \(0.598010\pi\)
\(548\) 4.46842 + 5.60322i 0.190881 + 0.239358i
\(549\) 0 0
\(550\) −2.56560 + 3.21716i −0.109398 + 0.137180i
\(551\) −5.62121 + 24.6281i −0.239472 + 1.04919i
\(552\) 0 0
\(553\) −6.29969 + 19.4727i −0.267890 + 0.828062i
\(554\) −13.0864 16.4098i −0.555988 0.697187i
\(555\) 0 0
\(556\) −2.51373 + 11.0134i −0.106606 + 0.467071i
\(557\) −27.6602 −1.17200 −0.586001 0.810310i \(-0.699299\pi\)
−0.586001 + 0.810310i \(0.699299\pi\)
\(558\) 0 0
\(559\) −10.1964 + 44.6734i −0.431262 + 1.88948i
\(560\) 0.929237 2.87232i 0.0392674 0.121378i
\(561\) 0 0
\(562\) −1.27884 5.60294i −0.0539444 0.236346i
\(563\) 19.3807 + 24.3027i 0.816801 + 1.02424i 0.999159 + 0.0410037i \(0.0130555\pi\)
−0.182358 + 0.983232i \(0.558373\pi\)
\(564\) 0 0
\(565\) 6.88073 + 30.1465i 0.289475 + 1.26827i
\(566\) −0.559390 2.45085i −0.0235129 0.103017i
\(567\) 0 0
\(568\) −1.84122 + 8.06693i −0.0772560 + 0.338481i
\(569\) −24.2804 −1.01789 −0.508943 0.860800i \(-0.669963\pi\)
−0.508943 + 0.860800i \(0.669963\pi\)
\(570\) 0 0
\(571\) −7.61681 + 33.3714i −0.318754 + 1.39655i 0.520987 + 0.853564i \(0.325564\pi\)
−0.839741 + 0.542987i \(0.817293\pi\)
\(572\) 24.5249 11.8106i 1.02544 0.493824i
\(573\) 0 0
\(574\) 1.69201 + 12.3726i 0.0706230 + 0.516423i
\(575\) −1.75676 + 2.20291i −0.0732619 + 0.0918676i
\(576\) 0 0
\(577\) 6.82975 8.56423i 0.284326 0.356534i −0.619074 0.785333i \(-0.712492\pi\)
0.903400 + 0.428799i \(0.141063\pi\)
\(578\) 4.36677 2.10293i 0.181634 0.0874702i
\(579\) 0 0
\(580\) −16.0429 7.72586i −0.666146 0.320799i
\(581\) −5.01962 + 1.89118i −0.208249 + 0.0784593i
\(582\) 0 0
\(583\) −34.8733 16.7941i −1.44430 0.695539i
\(584\) −1.23749 5.42179i −0.0512076 0.224355i
\(585\) 0 0
\(586\) 14.2464 17.8644i 0.588512 0.737971i
\(587\) 3.78119 0.156067 0.0780333 0.996951i \(-0.475136\pi\)
0.0780333 + 0.996951i \(0.475136\pi\)
\(588\) 0 0
\(589\) 27.0813 1.11586
\(590\) 0.879274 1.10258i 0.0361991 0.0453923i
\(591\) 0 0
\(592\) −0.336423 1.47397i −0.0138269 0.0605797i
\(593\) 2.44453 + 1.17722i 0.100385 + 0.0483428i 0.483402 0.875398i \(-0.339401\pi\)
−0.383017 + 0.923741i \(0.625115\pi\)
\(594\) 0 0
\(595\) −12.9980 19.6368i −0.532867 0.805031i
\(596\) −13.9184 6.70276i −0.570121 0.274556i
\(597\) 0 0
\(598\) −7.72493 + 3.72013i −0.315896 + 0.152127i
\(599\) −6.68170 + 8.37858i −0.273007 + 0.342340i −0.899367 0.437194i \(-0.855972\pi\)
0.626361 + 0.779533i \(0.284544\pi\)
\(600\) 0 0
\(601\) −29.9684 + 37.5791i −1.22244 + 1.53289i −0.456860 + 0.889539i \(0.651026\pi\)
−0.765575 + 0.643347i \(0.777545\pi\)
\(602\) 13.7260 + 8.17722i 0.559429 + 0.333279i
\(603\) 0 0
\(604\) 25.5879 12.3225i 1.04116 0.501395i
\(605\) 0.0481748 0.211068i 0.00195858 0.00858112i
\(606\) 0 0
\(607\) 34.5262 1.40138 0.700688 0.713468i \(-0.252876\pi\)
0.700688 + 0.713468i \(0.252876\pi\)
\(608\) −4.67576 + 20.4858i −0.189627 + 0.830811i
\(609\) 0 0
\(610\) 2.07038 + 9.07092i 0.0838272 + 0.367271i
\(611\) −10.8340 47.4670i −0.438298 1.92031i
\(612\) 0 0
\(613\) −21.7059 27.2183i −0.876691 1.09934i −0.994336 0.106280i \(-0.966106\pi\)
0.117645 0.993056i \(-0.462465\pi\)
\(614\) −3.02112 13.2364i −0.121923 0.534178i
\(615\) 0 0
\(616\) −3.16354 23.1330i −0.127463 0.932057i
\(617\) −6.17548 + 27.0565i −0.248615 + 1.08925i 0.684312 + 0.729189i \(0.260103\pi\)
−0.932927 + 0.360065i \(0.882754\pi\)
\(618\) 0 0
\(619\) 0.727486 0.0292401 0.0146201 0.999893i \(-0.495346\pi\)
0.0146201 + 0.999893i \(0.495346\pi\)
\(620\) −4.24771 + 18.6104i −0.170592 + 0.747412i
\(621\) 0 0
\(622\) −2.71482 3.40428i −0.108854 0.136499i
\(623\) −11.9760 + 4.51205i −0.479808 + 0.180771i
\(624\) 0 0
\(625\) 3.26535 14.3064i 0.130614 0.572258i
\(626\) 8.81847 11.0580i 0.352457 0.441967i
\(627\) 0 0
\(628\) −6.42252 8.05359i −0.256286 0.321373i
\(629\) −10.6255 5.11697i −0.423667 0.204027i
\(630\) 0 0
\(631\) −26.5841 + 12.8022i −1.05829 + 0.509648i −0.880317 0.474387i \(-0.842670\pi\)
−0.177978 + 0.984034i \(0.556956\pi\)
\(632\) 18.6437 + 8.97833i 0.741606 + 0.357139i
\(633\) 0 0
\(634\) −12.4150 5.97877i −0.493064 0.237447i
\(635\) 10.6929 13.4085i 0.424337 0.532101i
\(636\) 0 0
\(637\) 40.6161 11.3206i 1.60927 0.448537i
\(638\) −18.3836 −0.727814
\(639\) 0 0
\(640\) −14.9767 7.21242i −0.592008 0.285096i
\(641\) 1.51293 + 6.62858i 0.0597572 + 0.261813i 0.995978 0.0895992i \(-0.0285586\pi\)
−0.936221 + 0.351413i \(0.885701\pi\)
\(642\) 0 0
\(643\) 7.16064 3.44838i 0.282388 0.135991i −0.287329 0.957832i \(-0.592767\pi\)
0.569717 + 0.821841i \(0.307053\pi\)
\(644\) −0.880562 6.43901i −0.0346990 0.253733i
\(645\) 0 0
\(646\) 8.56115 + 10.7353i 0.336834 + 0.422376i
\(647\) 7.46060 3.59283i 0.293306 0.141249i −0.281444 0.959578i \(-0.590813\pi\)
0.574750 + 0.818329i \(0.305099\pi\)
\(648\) 0 0
\(649\) −0.704301 + 3.08575i −0.0276462 + 0.121126i
\(650\) −4.68446 + 5.87413i −0.183740 + 0.230402i
\(651\) 0 0
\(652\) 3.34378 + 4.19297i 0.130953 + 0.164209i
\(653\) 15.5558 7.49130i 0.608747 0.293157i −0.104001 0.994577i \(-0.533165\pi\)
0.712748 + 0.701420i \(0.247450\pi\)
\(654\) 0 0
\(655\) −10.8954 −0.425718
\(656\) −3.66396 −0.143054
\(657\) 0 0
\(658\) −16.9098 1.50024i −0.659214 0.0584855i
\(659\) 0.699457 + 3.06452i 0.0272470 + 0.119377i 0.986723 0.162415i \(-0.0519284\pi\)
−0.959476 + 0.281792i \(0.909071\pi\)
\(660\) 0 0
\(661\) −13.6441 17.1091i −0.530693 0.665468i 0.442148 0.896942i \(-0.354217\pi\)
−0.972841 + 0.231474i \(0.925645\pi\)
\(662\) −8.92429 11.1907i −0.346852 0.434939i
\(663\) 0 0
\(664\) 1.20683 + 5.28747i 0.0468341 + 0.205194i
\(665\) 12.1668 12.7579i 0.471807 0.494730i
\(666\) 0 0
\(667\) −12.5879 −0.487406
\(668\) 4.89278 0.189308
\(669\) 0 0
\(670\) 10.1074 4.86748i 0.390484 0.188047i
\(671\) −13.0197 16.3262i −0.502620 0.630265i
\(672\) 0 0
\(673\) 6.21700 7.79587i 0.239648 0.300509i −0.647434 0.762122i \(-0.724158\pi\)
0.887081 + 0.461613i \(0.152729\pi\)
\(674\) 3.35622 14.7045i 0.129277 0.566398i
\(675\) 0 0
\(676\) 28.7347 13.8379i 1.10518 0.532228i
\(677\) 21.2670 + 26.6680i 0.817358 + 1.02493i 0.999135 + 0.0415945i \(0.0132437\pi\)
−0.181777 + 0.983340i \(0.558185\pi\)
\(678\) 0 0
\(679\) 9.33156 28.8443i 0.358112 1.10694i
\(680\) −21.4518 + 10.3306i −0.822639 + 0.396162i
\(681\) 0 0
\(682\) 4.38543 + 19.2138i 0.167927 + 0.735735i
\(683\) −30.9267 14.8935i −1.18338 0.569884i −0.264483 0.964390i \(-0.585201\pi\)
−0.918893 + 0.394507i \(0.870915\pi\)
\(684\) 0 0
\(685\) −9.68753 −0.370142
\(686\) 0.603563 14.6893i 0.0230441 0.560839i
\(687\) 0 0
\(688\) −2.92277 + 3.66503i −0.111429 + 0.139728i
\(689\) −63.6741 30.6638i −2.42579 1.16820i
\(690\) 0 0
\(691\) 16.1610 + 7.78271i 0.614792 + 0.296068i 0.715245 0.698874i \(-0.246315\pi\)
−0.100453 + 0.994942i \(0.532029\pi\)
\(692\) 2.41231 1.16171i 0.0917024 0.0441616i
\(693\) 0 0
\(694\) −17.6564 8.50286i −0.670226 0.322764i
\(695\) −9.52062 11.9385i −0.361138 0.452852i
\(696\) 0 0
\(697\) −17.8199 + 22.3454i −0.674976 + 0.846393i
\(698\) 4.12769 18.0846i 0.156235 0.684512i
\(699\) 0 0
\(700\) −3.14336 4.74884i −0.118808 0.179489i
\(701\) 28.5937 + 35.8553i 1.07997 + 1.35424i 0.930843 + 0.365419i \(0.119074\pi\)
0.149125 + 0.988818i \(0.452354\pi\)
\(702\) 0 0
\(703\) 1.96461 8.60750i 0.0740965 0.324638i
\(704\) −11.2259 −0.423091
\(705\) 0 0
\(706\) 1.91107 8.37294i 0.0719240 0.315120i
\(707\) −31.6956 + 33.2355i −1.19203 + 1.24995i
\(708\) 0 0
\(709\) 8.87092 + 38.8660i 0.333154 + 1.45964i 0.812985 + 0.582284i \(0.197841\pi\)
−0.479831 + 0.877361i \(0.659302\pi\)
\(710\) −2.83477 3.55468i −0.106387 0.133405i
\(711\) 0 0
\(712\) 2.87931 + 12.6151i 0.107907 + 0.472769i
\(713\) 3.00286 + 13.1564i 0.112458 + 0.492710i
\(714\) 0 0
\(715\) −8.18760 + 35.8722i −0.306199 + 1.34155i
\(716\) −13.4072 −0.501050
\(717\) 0 0
\(718\) −1.09921 + 4.81594i −0.0410220 + 0.179729i
\(719\) −5.13597 + 2.47335i −0.191539 + 0.0922405i −0.527195 0.849744i \(-0.676756\pi\)
0.335656 + 0.941985i \(0.391042\pi\)
\(720\) 0 0
\(721\) 18.6639 19.5707i 0.695080 0.728849i
\(722\) 2.99469 3.75522i 0.111451 0.139755i
\(723\) 0 0
\(724\) −10.0099 + 12.5521i −0.372016 + 0.466494i
\(725\) −9.93824 + 4.78600i −0.369097 + 0.177748i
\(726\) 0 0
\(727\) 36.9522 + 17.7952i 1.37048 + 0.659989i 0.966947 0.254976i \(-0.0820675\pi\)
0.403534 + 0.914965i \(0.367782\pi\)
\(728\) −5.77622 42.2380i −0.214081 1.56544i
\(729\) 0 0
\(730\) 2.75316 + 1.32585i 0.101899 + 0.0490721i
\(731\) 8.13692 + 35.6502i 0.300955 + 1.31857i
\(732\) 0 0
\(733\) 14.6636 18.3875i 0.541611 0.679159i −0.433429 0.901188i \(-0.642697\pi\)
0.975040 + 0.222029i \(0.0712680\pi\)
\(734\) −5.64205 −0.208252
\(735\) 0 0
\(736\) −10.4707 −0.385955
\(737\) −15.6983 + 19.6851i −0.578255 + 0.725108i
\(738\) 0 0
\(739\) 8.89968 + 38.9920i 0.327380 + 1.43435i 0.824105 + 0.566437i \(0.191679\pi\)
−0.496725 + 0.867908i \(0.665464\pi\)
\(740\) 5.60698 + 2.70018i 0.206117 + 0.0992606i
\(741\) 0 0
\(742\) −17.0065 + 17.8327i −0.624328 + 0.654660i
\(743\) 12.8125 + 6.17017i 0.470045 + 0.226362i 0.653884 0.756595i \(-0.273138\pi\)
−0.183839 + 0.982956i \(0.558853\pi\)
\(744\) 0 0
\(745\) 18.8139 9.06030i 0.689288 0.331944i
\(746\) −9.24142 + 11.5884i −0.338352 + 0.424281i
\(747\) 0 0
\(748\) 13.5438 16.9833i 0.495209 0.620972i
\(749\) 42.3020 15.9376i 1.54568 0.582347i
\(750\) 0 0
\(751\) 34.1167 16.4297i 1.24494 0.599530i 0.308787 0.951131i \(-0.400077\pi\)
0.936150 + 0.351601i \(0.114363\pi\)
\(752\) 1.10835 4.85601i 0.0404175 0.177081i
\(753\) 0 0
\(754\) −33.5661 −1.22241
\(755\) −8.54250 + 37.4271i −0.310893 + 1.36211i
\(756\) 0 0
\(757\) −8.93459 39.1450i −0.324733 1.42275i −0.829023 0.559214i \(-0.811103\pi\)
0.504290 0.863534i \(-0.331754\pi\)
\(758\) 3.95662 + 17.3351i 0.143711 + 0.629638i
\(759\) 0 0
\(760\) −11.1134 13.9358i −0.403126 0.505505i
\(761\) 4.39271 + 19.2457i 0.159236 + 0.697656i 0.990004 + 0.141038i \(0.0450441\pi\)
−0.830769 + 0.556618i \(0.812099\pi\)
\(762\) 0 0
\(763\) 12.9673 + 19.5904i 0.469448 + 0.709221i
\(764\) 2.68953 11.7836i 0.0973039 0.426316i
\(765\) 0 0
\(766\) 14.0835 0.508859
\(767\) −1.28596 + 5.63418i −0.0464335 + 0.203438i
\(768\) 0 0
\(769\) 3.09928 + 3.88637i 0.111763 + 0.140146i 0.834566 0.550907i \(-0.185718\pi\)
−0.722804 + 0.691054i \(0.757147\pi\)
\(770\) 11.0218 + 6.56621i 0.397198 + 0.236630i
\(771\) 0 0
\(772\) 2.50439 10.9725i 0.0901350 0.394907i
\(773\) 27.2513 34.1720i 0.980161 1.22908i 0.00675910 0.999977i \(-0.497848\pi\)
0.973402 0.229105i \(-0.0735801\pi\)
\(774\) 0 0
\(775\) 7.37291 + 9.24533i 0.264843 + 0.332102i
\(776\) −27.6164 13.2993i −0.991370 0.477419i
\(777\) 0 0
\(778\) 25.2227 12.1466i 0.904276 0.435476i
\(779\) −19.2775 9.28354i −0.690687 0.332617i
\(780\) 0 0
\(781\) 9.19370 + 4.42745i 0.328976 + 0.158427i
\(782\) −4.26606 + 5.34947i −0.152554 + 0.191297i
\(783\) 0 0
\(784\) 4.24615 + 0.759415i 0.151648 + 0.0271220i
\(785\) 13.9240 0.496970
\(786\) 0 0
\(787\) −43.0879 20.7500i −1.53592 0.739659i −0.541064 0.840982i \(-0.681978\pi\)
−0.994854 + 0.101323i \(0.967692\pi\)
\(788\) −2.22389 9.74348i −0.0792227 0.347097i
\(789\) 0 0
\(790\) −10.2443 + 4.93341i −0.364477 + 0.175523i
\(791\) −41.3453 + 15.5772i −1.47007 + 0.553860i
\(792\) 0 0
\(793\) −23.7723 29.8095i −0.844179 1.05857i
\(794\) −11.7096 + 5.63904i −0.415558 + 0.200122i
\(795\) 0 0
\(796\) −0.425402 + 1.86381i −0.0150780 + 0.0660608i
\(797\) −0.921132 + 1.15506i −0.0326282 + 0.0409145i −0.797878 0.602819i \(-0.794044\pi\)
0.765250 + 0.643734i \(0.222615\pi\)
\(798\) 0 0
\(799\) −24.2249 30.3770i −0.857014 1.07466i
\(800\) −8.26669 + 3.98103i −0.292272 + 0.140751i
\(801\) 0 0
\(802\) 19.1252 0.675334
\(803\) −6.85827 −0.242023
\(804\) 0 0
\(805\) 7.54701 + 4.49612i 0.265997 + 0.158467i
\(806\) 8.00723 + 35.0819i 0.282043 + 1.23571i
\(807\) 0 0
\(808\) 28.9515 + 36.3040i 1.01851 + 1.27717i
\(809\) −33.1446 41.5620i −1.16530 1.46124i −0.860956 0.508679i \(-0.830134\pi\)
−0.304344 0.952562i \(-0.598437\pi\)
\(810\) 0 0
\(811\) 0.512939 + 2.24733i 0.0180117 + 0.0789145i 0.983135 0.182881i \(-0.0585424\pi\)
−0.965123 + 0.261796i \(0.915685\pi\)
\(812\) 7.83138 24.2072i 0.274828 0.849506i
\(813\) 0 0
\(814\) 6.42505 0.225198
\(815\) −7.24932 −0.253933
\(816\) 0 0
\(817\) −24.6640 + 11.8776i −0.862885 + 0.415544i
\(818\) 0.659459 + 0.826936i 0.0230574 + 0.0289131i
\(819\) 0 0
\(820\) 9.40338 11.7915i 0.328380 0.411776i
\(821\) −7.62373 + 33.4018i −0.266070 + 1.16573i 0.648472 + 0.761238i \(0.275408\pi\)
−0.914542 + 0.404491i \(0.867449\pi\)
\(822\) 0 0
\(823\) −16.7611 + 8.07174i −0.584257 + 0.281363i −0.702572 0.711613i \(-0.747965\pi\)
0.118315 + 0.992976i \(0.462251\pi\)
\(824\) −17.0480 21.3776i −0.593897 0.744723i
\(825\) 0 0
\(826\) 1.73111 + 1.03130i 0.0602330 + 0.0358837i
\(827\) 28.9585 13.9457i 1.00699 0.484938i 0.143682 0.989624i \(-0.454106\pi\)
0.863303 + 0.504685i \(0.168392\pi\)
\(828\) 0 0
\(829\) 0.788686 + 3.45546i 0.0273922 + 0.120013i 0.986776 0.162093i \(-0.0518243\pi\)
−0.959383 + 0.282106i \(0.908967\pi\)
\(830\) −2.68496 1.29301i −0.0931962 0.0448809i
\(831\) 0 0
\(832\) −20.4970 −0.710605
\(833\) 25.2828 22.2026i 0.875998 0.769273i
\(834\) 0 0
\(835\) −4.12358 + 5.17080i −0.142702 + 0.178943i
\(836\) 14.6516 + 7.05583i 0.506736 + 0.244031i
\(837\) 0 0
\(838\) −14.4807 6.97352i −0.500226 0.240896i
\(839\) −11.7611 + 5.66385i −0.406039 + 0.195538i −0.625744 0.780028i \(-0.715205\pi\)
0.219706 + 0.975566i \(0.429490\pi\)
\(840\) 0 0
\(841\) −18.2716 8.79915i −0.630056 0.303419i
\(842\) 9.03373 + 11.3279i 0.311323 + 0.390387i
\(843\) 0 0
\(844\) −8.11501 + 10.1759i −0.279330 + 0.350269i
\(845\) −9.59305 + 42.0299i −0.330011 + 1.44587i
\(846\) 0 0
\(847\) 0.308129 + 0.0273372i 0.0105874 + 0.000939316i
\(848\) −4.50786 5.65268i −0.154801 0.194114i
\(849\) 0 0
\(850\) −1.33418 + 5.84542i −0.0457619 + 0.200496i
\(851\) 4.39946 0.150812
\(852\) 0 0
\(853\) 2.07156 9.07611i 0.0709289 0.310760i −0.927002 0.375057i \(-0.877623\pi\)
0.997931 + 0.0642967i \(0.0204804\pi\)
\(854\) −12.4406 + 4.68709i −0.425709 + 0.160389i
\(855\) 0 0
\(856\) −10.1704 44.5593i −0.347616 1.52300i
\(857\) 22.3451 + 28.0199i 0.763296 + 0.957143i 0.999895 0.0144646i \(-0.00460439\pi\)
−0.236600 + 0.971607i \(0.576033\pi\)
\(858\) 0 0
\(859\) −2.49122 10.9147i −0.0849992 0.372406i 0.914482 0.404628i \(-0.132599\pi\)
−0.999481 + 0.0322218i \(0.989742\pi\)
\(860\) −4.29378 18.8123i −0.146417 0.641493i
\(861\) 0 0
\(862\) 0.856784 3.75381i 0.0291822 0.127855i
\(863\) 18.2005 0.619551 0.309776 0.950810i \(-0.399746\pi\)
0.309776 + 0.950810i \(0.399746\pi\)
\(864\) 0 0
\(865\) −0.805348 + 3.52846i −0.0273826 + 0.119971i
\(866\) 15.3489 7.39165i 0.521577 0.251178i
\(867\) 0 0
\(868\) −27.1686 2.41039i −0.922161 0.0818141i
\(869\) 15.9109 19.9517i 0.539742 0.676815i
\(870\) 0 0
\(871\) −28.6631 + 35.9424i −0.971212 + 1.21786i
\(872\) 21.4011 10.3062i 0.724733 0.349013i
\(873\) 0 0
\(874\) −4.61501 2.22247i −0.156105 0.0751761i
\(875\) 32.0673 + 2.84501i 1.08407 + 0.0961790i
\(876\) 0 0
\(877\) 32.5063 + 15.6542i 1.09766 + 0.528605i 0.892922 0.450212i \(-0.148652\pi\)
0.204738 + 0.978817i \(0.434366\pi\)
\(878\) −1.62807 7.13304i −0.0549447 0.240728i
\(879\) 0 0
\(880\) −2.34695 + 2.94298i −0.0791156 + 0.0992078i
\(881\) 46.6618 1.57208 0.786038 0.618178i \(-0.212129\pi\)
0.786038 + 0.618178i \(0.212129\pi\)
\(882\) 0 0
\(883\) −28.4556 −0.957608 −0.478804 0.877922i \(-0.658930\pi\)
−0.478804 + 0.877922i \(0.658930\pi\)
\(884\) 24.7292 31.0094i 0.831732 1.04296i
\(885\) 0 0
\(886\) 5.32495 + 23.3301i 0.178895 + 0.783791i
\(887\) 45.1380 + 21.7373i 1.51558 + 0.729867i 0.992481 0.122402i \(-0.0390597\pi\)
0.523104 + 0.852269i \(0.324774\pi\)
\(888\) 0 0
\(889\) 21.0522 + 12.5418i 0.706068 + 0.420639i
\(890\) −6.40588 3.08491i −0.214726 0.103406i
\(891\) 0 0
\(892\) 29.7964 14.3492i 0.997657 0.480446i
\(893\) 18.1354 22.7410i 0.606877 0.760999i
\(894\) 0 0
\(895\) 11.2994 14.1690i 0.377697 0.473617i
\(896\) 7.31093 22.5984i 0.244241 0.754961i
\(897\) 0 0
\(898\) −1.93053 + 0.929692i −0.0644225 + 0.0310242i
\(899\) −11.7558 + 51.5054i −0.392077 + 1.71780i
\(900\) 0 0
\(901\) −56.3983 −1.87890
\(902\) 3.46484 15.1804i 0.115366 0.505453i
\(903\) 0 0
\(904\) 9.94036 + 43.5516i 0.330612 + 1.44850i
\(905\) −4.82904 21.1574i −0.160523 0.703297i
\(906\) 0 0
\(907\) −16.5869 20.7994i −0.550760 0.690631i 0.426059 0.904695i \(-0.359901\pi\)
−0.976820 + 0.214064i \(0.931330\pi\)
\(908\) −2.88955 12.6599i −0.0958930 0.420135i
\(909\) 0 0
\(910\) 20.1244 + 11.9891i 0.667117 + 0.397434i
\(911\) 5.34722 23.4277i 0.177161 0.776194i −0.805771 0.592227i \(-0.798249\pi\)
0.982932 0.183967i \(-0.0588940\pi\)
\(912\) 0 0
\(913\) 6.68837 0.221353
\(914\) −1.04112 + 4.56143i −0.0344371 + 0.150879i
\(915\) 0 0
\(916\) 9.60554 + 12.0450i 0.317376 + 0.397977i
\(917\) −2.10933 15.4243i −0.0696564 0.509354i
\(918\) 0 0
\(919\) 8.43676 36.9639i 0.278303 1.21933i −0.621635 0.783307i \(-0.713531\pi\)
0.899938 0.436018i \(-0.143612\pi\)
\(920\) 5.53787 6.94427i 0.182578 0.228946i
\(921\) 0 0
\(922\) 10.0697 + 12.6269i 0.331626 + 0.415846i
\(923\) 16.7865 + 8.08396i 0.552535 + 0.266087i
\(924\) 0 0
\(925\) 3.47340 1.67270i 0.114205 0.0549981i
\(926\) −16.1902 7.79680i −0.532043 0.256219i
\(927\) 0 0
\(928\) −36.9320 17.7855i −1.21235 0.583838i
\(929\) −11.5246 + 14.4513i −0.378108 + 0.474133i −0.934078 0.357070i \(-0.883776\pi\)
0.555969 + 0.831203i \(0.312347\pi\)
\(930\) 0 0
\(931\) 20.4164 + 14.7542i 0.669122 + 0.483550i
\(932\) −5.90826 −0.193531
\(933\) 0 0
\(934\) 16.3727 + 7.88468i 0.535732 + 0.257995i
\(935\) 6.53385 + 28.6267i 0.213680 + 0.936192i
\(936\) 0 0
\(937\) 22.3567 10.7664i 0.730362 0.351724i −0.0314645 0.999505i \(-0.510017\pi\)
0.761827 + 0.647781i \(0.224303\pi\)
\(938\) 8.84753 + 13.3664i 0.288882 + 0.436430i
\(939\) 0 0
\(940\) 12.7832 + 16.0297i 0.416943 + 0.522830i
\(941\) 37.5720 18.0937i 1.22481 0.589838i 0.294163 0.955755i \(-0.404959\pi\)
0.930647 + 0.365917i \(0.119245\pi\)
\(942\) 0 0
\(943\) 2.37250 10.3946i 0.0772591 0.338494i
\(944\) −0.368617 + 0.462231i −0.0119975 + 0.0150443i
\(945\) 0 0
\(946\) −12.4210 15.5754i −0.403840 0.506400i
\(947\) 25.7420 12.3967i 0.836504 0.402839i 0.0339536 0.999423i \(-0.489190\pi\)
0.802550 + 0.596584i \(0.203476\pi\)
\(948\) 0 0
\(949\) −12.5223 −0.406492
\(950\) −4.48857 −0.145628
\(951\) 0 0
\(952\) −18.7778 28.3686i −0.608592 0.919433i
\(953\) 11.2018 + 49.0784i 0.362863 + 1.58981i 0.745890 + 0.666069i \(0.232024\pi\)
−0.383028 + 0.923737i \(0.625119\pi\)
\(954\) 0 0
\(955\) 10.1865 + 12.7734i 0.329627 + 0.413339i
\(956\) 15.0335 + 18.8514i 0.486217 + 0.609697i
\(957\) 0 0
\(958\) 0.919037 + 4.02656i 0.0296927 + 0.130092i
\(959\) −1.87549 13.7143i −0.0605629 0.442859i
\(960\) 0 0
\(961\) 25.6357 0.826958
\(962\) 11.7313 0.378233
\(963\) 0 0
\(964\) 3.48758 1.67953i 0.112327 0.0540940i
\(965\) 9.48526 + 11.8941i 0.305341 + 0.382886i
\(966\) 0 0
\(967\) 16.6082 20.8261i 0.534085 0.669721i −0.439448 0.898268i \(-0.644826\pi\)
0.973533 + 0.228547i \(0.0733974\pi\)
\(968\) 0.0695965 0.304922i 0.00223692 0.00980057i
\(969\) 0 0
\(970\) 15.1747 7.30773i 0.487229 0.234637i
\(971\) 12.9670 + 16.2601i 0.416130 + 0.521810i 0.945078 0.326844i \(-0.105985\pi\)
−0.528949 + 0.848654i \(0.677414\pi\)
\(972\) 0 0
\(973\) 15.0578 15.7893i 0.482730 0.506183i
\(974\) 23.0816 11.1155i 0.739582 0.356164i
\(975\) 0 0
\(976\) −0.867962 3.80279i −0.0277828 0.121724i
\(977\) 8.50378 + 4.09521i 0.272060 + 0.131017i 0.564940 0.825132i \(-0.308899\pi\)
−0.292880 + 0.956149i \(0.594614\pi\)
\(978\) 0 0
\(979\) 15.9574 0.510000
\(980\) −13.3415 + 11.7161i −0.426179 + 0.374257i
\(981\) 0 0
\(982\) −13.7646 + 17.2602i −0.439244 + 0.550795i
\(983\) −53.6021 25.8134i −1.70964 0.823319i −0.991902 0.127007i \(-0.959463\pi\)
−0.717739 0.696313i \(-0.754823\pi\)
\(984\) 0 0
\(985\) 12.1714 + 5.86143i 0.387813 + 0.186761i
\(986\) −24.1337 + 11.6222i −0.768573 + 0.370125i
\(987\) 0 0
\(988\) 26.7519 + 12.8830i 0.851092 + 0.409864i
\(989\) −8.50508 10.6650i −0.270446 0.339128i
\(990\) 0 0
\(991\) −15.1927 + 19.0510i −0.482611 + 0.605175i −0.962209 0.272314i \(-0.912211\pi\)
0.479598 + 0.877488i \(0.340783\pi\)
\(992\) −9.77853 + 42.8425i −0.310469 + 1.36025i
\(993\) 0 0
\(994\) 4.48345 4.70128i 0.142206 0.149115i
\(995\) −1.61119 2.02037i −0.0510781 0.0640499i
\(996\) 0 0
\(997\) −2.60136 + 11.3973i −0.0823860 + 0.360957i −0.999270 0.0381966i \(-0.987839\pi\)
0.916884 + 0.399153i \(0.130696\pi\)
\(998\) 25.3876 0.803630
\(999\) 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 441.2.u.d.190.3 36
3.2 odd 2 147.2.i.b.43.4 36
49.8 even 7 inner 441.2.u.d.253.3 36
147.8 odd 14 147.2.i.b.106.4 yes 36
147.20 even 14 7203.2.a.g.1.11 18
147.29 odd 14 7203.2.a.h.1.11 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
147.2.i.b.43.4 36 3.2 odd 2
147.2.i.b.106.4 yes 36 147.8 odd 14
441.2.u.d.190.3 36 1.1 even 1 trivial
441.2.u.d.253.3 36 49.8 even 7 inner
7203.2.a.g.1.11 18 147.20 even 14
7203.2.a.h.1.11 18 147.29 odd 14