Properties

Label 1470.2.n.j.79.5
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $12$
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] = [1470,2,Mod(79,1470)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1470, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1470.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.n (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.7652750400000000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 18 x^{10} - 14 x^{9} + 21 x^{8} - 108 x^{7} + 368 x^{6} - 216 x^{5} + 84 x^{4} - 112 x^{3} + 288 x^{2} - 192 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.5
Root \(-1.45845 - 1.45845i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.j.949.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.806615 - 2.08551i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.806615 - 2.08551i) q^{5} -1.00000 q^{6} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.74131 - 1.40280i) q^{10} +(-3.05362 - 5.28903i) q^{11} +(-0.866025 - 0.500000i) q^{12} -1.68842i q^{13} +(0.344208 + 2.20942i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-5.92159 + 3.41883i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-0.844208 + 1.46221i) q^{19} +(2.20942 - 0.344208i) q^{20} -6.10725i q^{22} +(-2.00189 - 1.15579i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-3.69874 - 3.36441i) q^{25} +(0.844208 - 1.46221i) q^{26} +1.00000i q^{27} -8.41883 q^{29} +(-0.806615 + 2.08551i) q^{30} +(-0.344208 - 0.596186i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(5.28903 + 3.05362i) q^{33} -6.83767 q^{34} +1.00000 q^{36} +(2.00189 + 1.15579i) q^{37} +(-1.46221 + 0.844208i) q^{38} +(0.844208 + 1.46221i) q^{39} +(2.08551 + 0.806615i) q^{40} -5.14925 q^{41} -2.00000i q^{43} +(3.05362 - 5.28903i) q^{44} +(-1.40280 - 1.74131i) q^{45} +(-1.15579 - 2.00189i) q^{46} +(2.65458 + 1.53263i) q^{47} -1.00000i q^{48} +(-1.52100 - 4.76304i) q^{50} +(3.41883 - 5.92159i) q^{51} +(1.46221 - 0.844208i) q^{52} +(-9.05935 + 5.23042i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-13.4935 + 2.10217i) q^{55} -1.68842i q^{57} +(-7.29092 - 4.20942i) q^{58} +(3.52100 + 6.09855i) q^{59} +(-1.74131 + 1.40280i) q^{60} +(4.73042 - 8.19332i) q^{61} -0.688417i q^{62} -1.00000 q^{64} +(-3.52122 - 1.36190i) q^{65} +(3.05362 + 5.28903i) q^{66} +(10.5781 - 6.10725i) q^{67} +(-5.92159 - 3.41883i) q^{68} +2.31158 q^{69} +6.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(1.15579 + 2.00189i) q^{74} +(4.88541 + 1.06430i) q^{75} -1.68842 q^{76} +1.68842i q^{78} +(3.65579 - 6.33202i) q^{79} +(1.40280 + 1.74131i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.45938 - 2.57462i) q^{82} -13.5261i q^{83} +(2.35358 + 15.1072i) q^{85} +(1.00000 - 1.73205i) q^{86} +(7.29092 - 4.20942i) q^{87} +(5.28903 - 3.05362i) q^{88} +(6.10725 - 10.5781i) q^{89} +(-0.344208 - 2.20942i) q^{90} -2.31158i q^{92} +(0.596186 + 0.344208i) q^{93} +(1.53263 + 2.65458i) q^{94} +(2.36851 + 2.94005i) q^{95} +(0.500000 - 0.866025i) q^{96} -4.95800i q^{97} -6.10725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 6 q^{4} - 12 q^{6} + 6 q^{9} - 6 q^{11} - 6 q^{16} - 6 q^{19} - 6 q^{24} + 6 q^{26} - 48 q^{29} + 24 q^{34} + 12 q^{36} + 6 q^{39} + 36 q^{41} + 6 q^{44} - 18 q^{46} - 12 q^{51} - 6 q^{54} - 60 q^{55} + 24 q^{59} + 12 q^{61} - 12 q^{64} - 30 q^{65} + 6 q^{66} + 36 q^{69} + 72 q^{71} + 18 q^{74} - 12 q^{76} + 48 q^{79} - 6 q^{81} + 12 q^{86} + 12 q^{89} + 6 q^{94} + 6 q^{96} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

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
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.806615 2.08551i 0.360729 0.932671i
\(6\) −1.00000 −0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 1.74131 1.40280i 0.550649 0.443605i
\(11\) −3.05362 5.28903i −0.920703 1.59470i −0.798331 0.602219i \(-0.794283\pi\)
−0.122372 0.992484i \(-0.539050\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 1.68842i 0.468283i −0.972203 0.234141i \(-0.924772\pi\)
0.972203 0.234141i \(-0.0752278\pi\)
\(14\) 0 0
\(15\) 0.344208 + 2.20942i 0.0888742 + 0.570469i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.92159 + 3.41883i −1.43620 + 0.829189i −0.997583 0.0694868i \(-0.977864\pi\)
−0.438614 + 0.898675i \(0.644530\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −0.844208 + 1.46221i −0.193675 + 0.335454i −0.946465 0.322806i \(-0.895374\pi\)
0.752791 + 0.658260i \(0.228707\pi\)
\(20\) 2.20942 0.344208i 0.494041 0.0769673i
\(21\) 0 0
\(22\) 6.10725i 1.30207i
\(23\) −2.00189 1.15579i −0.417423 0.240999i 0.276551 0.960999i \(-0.410808\pi\)
−0.693974 + 0.720000i \(0.744142\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) −3.69874 3.36441i −0.739749 0.672883i
\(26\) 0.844208 1.46221i 0.165563 0.286763i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) −8.41883 −1.56334 −0.781669 0.623694i \(-0.785631\pi\)
−0.781669 + 0.623694i \(0.785631\pi\)
\(30\) −0.806615 + 2.08551i −0.147267 + 0.380761i
\(31\) −0.344208 0.596186i −0.0618217 0.107078i 0.833458 0.552583i \(-0.186358\pi\)
−0.895280 + 0.445504i \(0.853024\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 5.28903 + 3.05362i 0.920703 + 0.531568i
\(34\) −6.83767 −1.17265
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.00189 + 1.15579i 0.329109 + 0.190011i 0.655445 0.755243i \(-0.272481\pi\)
−0.326337 + 0.945254i \(0.605814\pi\)
\(38\) −1.46221 + 0.844208i −0.237202 + 0.136949i
\(39\) 0.844208 + 1.46221i 0.135182 + 0.234141i
\(40\) 2.08551 + 0.806615i 0.329749 + 0.127537i
\(41\) −5.14925 −0.804178 −0.402089 0.915601i \(-0.631716\pi\)
−0.402089 + 0.915601i \(0.631716\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 3.05362 5.28903i 0.460351 0.797352i
\(45\) −1.40280 1.74131i −0.209117 0.259579i
\(46\) −1.15579 2.00189i −0.170412 0.295163i
\(47\) 2.65458 + 1.53263i 0.387211 + 0.223556i 0.680951 0.732329i \(-0.261567\pi\)
−0.293740 + 0.955885i \(0.594900\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) −1.52100 4.76304i −0.215102 0.673596i
\(51\) 3.41883 5.92159i 0.478732 0.829189i
\(52\) 1.46221 0.844208i 0.202772 0.117071i
\(53\) −9.05935 + 5.23042i −1.24440 + 0.718453i −0.969986 0.243160i \(-0.921816\pi\)
−0.274411 + 0.961613i \(0.588483\pi\)
\(54\) −0.500000 + 0.866025i −0.0680414 + 0.117851i
\(55\) −13.4935 + 2.10217i −1.81946 + 0.283456i
\(56\) 0 0
\(57\) 1.68842i 0.223636i
\(58\) −7.29092 4.20942i −0.957345 0.552723i
\(59\) 3.52100 + 6.09855i 0.458395 + 0.793964i 0.998876 0.0473925i \(-0.0150911\pi\)
−0.540481 + 0.841356i \(0.681758\pi\)
\(60\) −1.74131 + 1.40280i −0.224802 + 0.181101i
\(61\) 4.73042 8.19332i 0.605668 1.04905i −0.386278 0.922382i \(-0.626239\pi\)
0.991946 0.126665i \(-0.0404272\pi\)
\(62\) 0.688417i 0.0874290i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −3.52122 1.36190i −0.436753 0.168923i
\(66\) 3.05362 + 5.28903i 0.375875 + 0.651035i
\(67\) 10.5781 6.10725i 1.29232 0.746119i 0.313252 0.949670i \(-0.398582\pi\)
0.979064 + 0.203551i \(0.0652482\pi\)
\(68\) −5.92159 3.41883i −0.718098 0.414594i
\(69\) 2.31158 0.278282
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) −3.46410 + 2.00000i −0.405442 + 0.234082i −0.688830 0.724923i \(-0.741875\pi\)
0.283387 + 0.959006i \(0.408542\pi\)
\(74\) 1.15579 + 2.00189i 0.134358 + 0.232715i
\(75\) 4.88541 + 1.06430i 0.564119 + 0.122894i
\(76\) −1.68842 −0.193675
\(77\) 0 0
\(78\) 1.68842i 0.191176i
\(79\) 3.65579 6.33202i 0.411309 0.712408i −0.583724 0.811952i \(-0.698405\pi\)
0.995033 + 0.0995443i \(0.0317385\pi\)
\(80\) 1.40280 + 1.74131i 0.156838 + 0.194684i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −4.45938 2.57462i −0.492456 0.284320i
\(83\) 13.5261i 1.48468i −0.670023 0.742340i \(-0.733716\pi\)
0.670023 0.742340i \(-0.266284\pi\)
\(84\) 0 0
\(85\) 2.35358 + 15.1072i 0.255282 + 1.63861i
\(86\) 1.00000 1.73205i 0.107833 0.186772i
\(87\) 7.29092 4.20942i 0.781669 0.451297i
\(88\) 5.28903 3.05362i 0.563813 0.325517i
\(89\) 6.10725 10.5781i 0.647367 1.12127i −0.336382 0.941726i \(-0.609203\pi\)
0.983749 0.179547i \(-0.0574633\pi\)
\(90\) −0.344208 2.20942i −0.0362828 0.232893i
\(91\) 0 0
\(92\) 2.31158i 0.240999i
\(93\) 0.596186 + 0.344208i 0.0618217 + 0.0356928i
\(94\) 1.53263 + 2.65458i 0.158078 + 0.273800i
\(95\) 2.36851 + 2.94005i 0.243004 + 0.301643i
\(96\) 0.500000 0.866025i 0.0510310 0.0883883i
\(97\) 4.95800i 0.503409i −0.967804 0.251704i \(-0.919009\pi\)
0.967804 0.251704i \(-0.0809911\pi\)
\(98\) 0 0
\(99\) −6.10725 −0.613802
\(100\) 1.06430 4.88541i 0.106430 0.488541i
\(101\) −4.00000 6.92820i −0.398015 0.689382i 0.595466 0.803380i \(-0.296967\pi\)
−0.993481 + 0.113998i \(0.963634\pi\)
\(102\) 5.92159 3.41883i 0.586325 0.338515i
\(103\) 0.725439 + 0.418833i 0.0714797 + 0.0412688i 0.535314 0.844653i \(-0.320193\pi\)
−0.463834 + 0.885922i \(0.653527\pi\)
\(104\) 1.68842 0.165563
\(105\) 0 0
\(106\) −10.4608 −1.01605
\(107\) 13.4460 + 7.76304i 1.29987 + 0.750482i 0.980382 0.197108i \(-0.0631550\pi\)
0.319490 + 0.947590i \(0.396488\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −5.83767 10.1111i −0.559147 0.968471i −0.997568 0.0697012i \(-0.977795\pi\)
0.438421 0.898770i \(-0.355538\pi\)
\(110\) −12.7368 4.92620i −1.21440 0.469695i
\(111\) −2.31158 −0.219406
\(112\) 0 0
\(113\) 3.37683i 0.317666i −0.987305 0.158833i \(-0.949227\pi\)
0.987305 0.158833i \(-0.0507731\pi\)
\(114\) 0.844208 1.46221i 0.0790674 0.136949i
\(115\) −4.02517 + 3.24269i −0.375349 + 0.302383i
\(116\) −4.20942 7.29092i −0.390834 0.676945i
\(117\) −1.46221 0.844208i −0.135182 0.0780471i
\(118\) 7.04200i 0.648269i
\(119\) 0 0
\(120\) −2.20942 + 0.344208i −0.201691 + 0.0314218i
\(121\) −13.1492 + 22.7752i −1.19539 + 2.07047i
\(122\) 8.19332 4.73042i 0.741788 0.428272i
\(123\) 4.45938 2.57462i 0.402089 0.232146i
\(124\) 0.344208 0.596186i 0.0309108 0.0535391i
\(125\) −10.0000 + 5.00000i −0.894427 + 0.447214i
\(126\) 0 0
\(127\) 4.94491i 0.438790i 0.975636 + 0.219395i \(0.0704084\pi\)
−0.975636 + 0.219395i \(0.929592\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 1.00000 + 1.73205i 0.0880451 + 0.152499i
\(130\) −2.36851 2.94005i −0.207732 0.257860i
\(131\) −3.36521 + 5.82871i −0.294020 + 0.509257i −0.974756 0.223271i \(-0.928326\pi\)
0.680737 + 0.732528i \(0.261660\pi\)
\(132\) 6.10725i 0.531568i
\(133\) 0 0
\(134\) 12.2145 1.05517
\(135\) 2.08551 + 0.806615i 0.179493 + 0.0694224i
\(136\) −3.41883 5.92159i −0.293162 0.507772i
\(137\) −16.4997 + 9.52608i −1.40966 + 0.813868i −0.995355 0.0962697i \(-0.969309\pi\)
−0.414306 + 0.910138i \(0.635976\pi\)
\(138\) 2.00189 + 1.15579i 0.170412 + 0.0983875i
\(139\) 13.3768 1.13461 0.567304 0.823508i \(-0.307986\pi\)
0.567304 + 0.823508i \(0.307986\pi\)
\(140\) 0 0
\(141\) −3.06525 −0.258141
\(142\) 5.19615 + 3.00000i 0.436051 + 0.251754i
\(143\) −8.93009 + 5.15579i −0.746772 + 0.431149i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −6.79076 + 17.5576i −0.563942 + 1.45808i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) 2.31158i 0.190011i
\(149\) 6.31158 10.9320i 0.517065 0.895583i −0.482739 0.875765i \(-0.660358\pi\)
0.999804 0.0198184i \(-0.00630881\pi\)
\(150\) 3.69874 + 3.36441i 0.302001 + 0.274703i
\(151\) −0.967375 1.67554i −0.0787238 0.136354i 0.823976 0.566625i \(-0.191751\pi\)
−0.902700 + 0.430271i \(0.858418\pi\)
\(152\) −1.46221 0.844208i −0.118601 0.0684743i
\(153\) 6.83767i 0.552792i
\(154\) 0 0
\(155\) −1.52100 + 0.236959i −0.122170 + 0.0190330i
\(156\) −0.844208 + 1.46221i −0.0675908 + 0.117071i
\(157\) 14.8517 8.57462i 1.18529 0.684330i 0.228060 0.973647i \(-0.426762\pi\)
0.957233 + 0.289317i \(0.0934283\pi\)
\(158\) 6.33202 3.65579i 0.503748 0.290839i
\(159\) 5.23042 9.05935i 0.414799 0.718453i
\(160\) 0.344208 + 2.20942i 0.0272121 + 0.174670i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) −0.466934 0.269584i −0.0365731 0.0211155i 0.481602 0.876390i \(-0.340055\pi\)
−0.518175 + 0.855275i \(0.673388\pi\)
\(164\) −2.57462 4.45938i −0.201044 0.348219i
\(165\) 10.6346 8.56726i 0.827902 0.666960i
\(166\) 6.76304 11.7139i 0.524914 0.909177i
\(167\) 3.14925i 0.243696i −0.992549 0.121848i \(-0.961118\pi\)
0.992549 0.121848i \(-0.0388821\pi\)
\(168\) 0 0
\(169\) 10.1492 0.780711
\(170\) −5.51536 + 14.2601i −0.423009 + 1.09370i
\(171\) 0.844208 + 1.46221i 0.0645582 + 0.111818i
\(172\) 1.73205 1.00000i 0.132068 0.0762493i
\(173\) −9.11585 5.26304i −0.693066 0.400142i 0.111694 0.993743i \(-0.464372\pi\)
−0.804759 + 0.593601i \(0.797706\pi\)
\(174\) 8.41883 0.638230
\(175\) 0 0
\(176\) 6.10725 0.460351
\(177\) −6.09855 3.52100i −0.458395 0.264655i
\(178\) 10.5781 6.10725i 0.792860 0.457758i
\(179\) 2.46737 + 4.27362i 0.184420 + 0.319425i 0.943381 0.331711i \(-0.107626\pi\)
−0.758961 + 0.651136i \(0.774293\pi\)
\(180\) 0.806615 2.08551i 0.0601215 0.155445i
\(181\) −6.13050 −0.455677 −0.227838 0.973699i \(-0.573166\pi\)
−0.227838 + 0.973699i \(0.573166\pi\)
\(182\) 0 0
\(183\) 9.46083i 0.699365i
\(184\) 1.15579 2.00189i 0.0852061 0.147581i
\(185\) 4.02517 3.24269i 0.295937 0.238407i
\(186\) 0.344208 + 0.596186i 0.0252386 + 0.0437145i
\(187\) 36.1646 + 20.8797i 2.64462 + 1.52687i
\(188\) 3.06525i 0.223556i
\(189\) 0 0
\(190\) 0.581167 + 3.73042i 0.0421623 + 0.270633i
\(191\) 7.46083 12.9225i 0.539847 0.935042i −0.459065 0.888403i \(-0.651815\pi\)
0.998912 0.0466394i \(-0.0148512\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −4.83343 + 2.79058i −0.347918 + 0.200871i −0.663768 0.747939i \(-0.731044\pi\)
0.315850 + 0.948809i \(0.397710\pi\)
\(194\) 2.47900 4.29375i 0.177982 0.308274i
\(195\) 3.73042 0.581167i 0.267141 0.0416183i
\(196\) 0 0
\(197\) 14.5261i 1.03494i −0.855701 0.517470i \(-0.826874\pi\)
0.855701 0.517470i \(-0.173126\pi\)
\(198\) −5.28903 3.05362i −0.375875 0.217012i
\(199\) 4.31158 + 7.46788i 0.305640 + 0.529384i 0.977404 0.211382i \(-0.0677963\pi\)
−0.671764 + 0.740766i \(0.734463\pi\)
\(200\) 3.36441 3.69874i 0.237900 0.261541i
\(201\) −6.10725 + 10.5781i −0.430772 + 0.746119i
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 6.83767 0.478732
\(205\) −4.15346 + 10.7388i −0.290090 + 0.750033i
\(206\) 0.418833 + 0.725439i 0.0291815 + 0.0505438i
\(207\) −2.00189 + 1.15579i −0.139141 + 0.0803331i
\(208\) 1.46221 + 0.844208i 0.101386 + 0.0585353i
\(209\) 10.3116 0.713267
\(210\) 0 0
\(211\) −7.68842 −0.529292 −0.264646 0.964346i \(-0.585255\pi\)
−0.264646 + 0.964346i \(0.585255\pi\)
\(212\) −9.05935 5.23042i −0.622198 0.359226i
\(213\) −5.19615 + 3.00000i −0.356034 + 0.205557i
\(214\) 7.76304 + 13.4460i 0.530671 + 0.919148i
\(215\) −4.17103 1.61323i −0.284462 0.110021i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 11.6753i 0.790753i
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) −8.56726 10.6346i −0.577604 0.716984i
\(221\) 5.77241 + 9.99812i 0.388295 + 0.672546i
\(222\) −2.00189 1.15579i −0.134358 0.0775717i
\(223\) 11.1725i 0.748166i 0.927395 + 0.374083i \(0.122042\pi\)
−0.927395 + 0.374083i \(0.877958\pi\)
\(224\) 0 0
\(225\) −4.76304 + 1.52100i −0.317536 + 0.101400i
\(226\) 1.68842 2.92442i 0.112312 0.194530i
\(227\) 3.33485 1.92538i 0.221342 0.127792i −0.385230 0.922821i \(-0.625878\pi\)
0.606571 + 0.795029i \(0.292544\pi\)
\(228\) 1.46221 0.844208i 0.0968373 0.0559091i
\(229\) −2.83767 + 4.91498i −0.187518 + 0.324791i −0.944422 0.328735i \(-0.893378\pi\)
0.756904 + 0.653526i \(0.226711\pi\)
\(230\) −5.10725 + 0.795666i −0.336762 + 0.0524647i
\(231\) 0 0
\(232\) 8.41883i 0.552723i
\(233\) 9.92537 + 5.73042i 0.650233 + 0.375412i 0.788545 0.614977i \(-0.210835\pi\)
−0.138313 + 0.990389i \(0.544168\pi\)
\(234\) −0.844208 1.46221i −0.0551876 0.0955878i
\(235\) 5.33754 4.29994i 0.348183 0.280497i
\(236\) −3.52100 + 6.09855i −0.229198 + 0.396982i
\(237\) 7.31158i 0.474938i
\(238\) 0 0
\(239\) −15.4608 −1.00008 −0.500039 0.866003i \(-0.666681\pi\)
−0.500039 + 0.866003i \(0.666681\pi\)
\(240\) −2.08551 0.806615i −0.134619 0.0520668i
\(241\) 2.18842 + 3.79045i 0.140968 + 0.244164i 0.927862 0.372925i \(-0.121645\pi\)
−0.786893 + 0.617089i \(0.788312\pi\)
\(242\) −22.7752 + 13.1492i −1.46404 + 0.845266i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) 9.46083 0.605668
\(245\) 0 0
\(246\) 5.14925 0.328304
\(247\) 2.46882 + 1.42538i 0.157087 + 0.0906945i
\(248\) 0.596186 0.344208i 0.0378579 0.0218573i
\(249\) 6.76304 + 11.7139i 0.428590 + 0.742340i
\(250\) −11.1603 0.669873i −0.705836 0.0423665i
\(251\) 26.5362 1.67495 0.837477 0.546473i \(-0.184030\pi\)
0.837477 + 0.546473i \(0.184030\pi\)
\(252\) 0 0
\(253\) 14.1174i 0.887554i
\(254\) −2.47246 + 4.28242i −0.155136 + 0.268703i
\(255\) −9.59189 11.9065i −0.600667 0.745612i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −19.4241 11.2145i −1.21164 0.699541i −0.248524 0.968626i \(-0.579946\pi\)
−0.963117 + 0.269084i \(0.913279\pi\)
\(258\) 2.00000i 0.124515i
\(259\) 0 0
\(260\) −0.581167 3.73042i −0.0360425 0.231351i
\(261\) −4.20942 + 7.29092i −0.260556 + 0.451297i
\(262\) −5.82871 + 3.36521i −0.360099 + 0.207903i
\(263\) −16.9666 + 9.79567i −1.04620 + 0.604027i −0.921584 0.388178i \(-0.873105\pi\)
−0.124620 + 0.992204i \(0.539771\pi\)
\(264\) −3.05362 + 5.28903i −0.187938 + 0.325517i
\(265\) 3.60071 + 23.1123i 0.221190 + 1.41978i
\(266\) 0 0
\(267\) 12.2145i 0.747515i
\(268\) 10.5781 + 6.10725i 0.646158 + 0.373060i
\(269\) 3.47900 + 6.02581i 0.212118 + 0.367400i 0.952377 0.304922i \(-0.0986304\pi\)
−0.740259 + 0.672322i \(0.765297\pi\)
\(270\) 1.40280 + 1.74131i 0.0853718 + 0.105973i
\(271\) −14.1819 + 24.5637i −0.861487 + 1.49214i 0.00900561 + 0.999959i \(0.497133\pi\)
−0.870493 + 0.492181i \(0.836200\pi\)
\(272\) 6.83767i 0.414594i
\(273\) 0 0
\(274\) −19.0522 −1.15098
\(275\) −6.49992 + 29.8364i −0.391960 + 1.79921i
\(276\) 1.15579 + 2.00189i 0.0695705 + 0.120500i
\(277\) −4.37530 + 2.52608i −0.262886 + 0.151778i −0.625651 0.780103i \(-0.715166\pi\)
0.362764 + 0.931881i \(0.381833\pi\)
\(278\) 11.5847 + 6.68842i 0.694803 + 0.401145i
\(279\) −0.688417 −0.0412144
\(280\) 0 0
\(281\) 7.68842 0.458652 0.229326 0.973350i \(-0.426348\pi\)
0.229326 + 0.973350i \(0.426348\pi\)
\(282\) −2.65458 1.53263i −0.158078 0.0912665i
\(283\) −15.9600 + 9.21450i −0.948722 + 0.547745i −0.892684 0.450683i \(-0.851180\pi\)
−0.0560386 + 0.998429i \(0.517847\pi\)
\(284\) 3.00000 + 5.19615i 0.178017 + 0.308335i
\(285\) −3.52122 1.36190i −0.208579 0.0806721i
\(286\) −10.3116 −0.609737
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 14.8768 25.7674i 0.875108 1.51573i
\(290\) −14.6598 + 11.8100i −0.860851 + 0.693504i
\(291\) 2.47900 + 4.29375i 0.145322 + 0.251704i
\(292\) −3.46410 2.00000i −0.202721 0.117041i
\(293\) 1.83767i 0.107358i 0.998558 + 0.0536788i \(0.0170947\pi\)
−0.998558 + 0.0536788i \(0.982905\pi\)
\(294\) 0 0
\(295\) 15.5587 2.42392i 0.905863 0.141126i
\(296\) −1.15579 + 2.00189i −0.0671790 + 0.116357i
\(297\) 5.28903 3.05362i 0.306901 0.177189i
\(298\) 10.9320 6.31158i 0.633273 0.365620i
\(299\) −1.95146 + 3.38002i −0.112856 + 0.195472i
\(300\) 1.52100 + 4.76304i 0.0878149 + 0.274994i
\(301\) 0 0
\(302\) 1.93475i 0.111332i
\(303\) 6.92820 + 4.00000i 0.398015 + 0.229794i
\(304\) −0.844208 1.46221i −0.0484187 0.0838636i
\(305\) −13.2717 16.4742i −0.759933 0.943310i
\(306\) −3.41883 + 5.92159i −0.195442 + 0.338515i
\(307\) 16.0840i 0.917962i −0.888446 0.458981i \(-0.848215\pi\)
0.888446 0.458981i \(-0.151785\pi\)
\(308\) 0 0
\(309\) −0.837665 −0.0476531
\(310\) −1.43570 0.555287i −0.0815425 0.0315382i
\(311\) −7.68842 13.3167i −0.435970 0.755122i 0.561404 0.827542i \(-0.310261\pi\)
−0.997374 + 0.0724194i \(0.976928\pi\)
\(312\) −1.46221 + 0.844208i −0.0827814 + 0.0477939i
\(313\) −19.4153 11.2094i −1.09742 0.633594i −0.161875 0.986811i \(-0.551754\pi\)
−0.935541 + 0.353218i \(0.885088\pi\)
\(314\) 17.1492 0.967788
\(315\) 0 0
\(316\) 7.31158 0.411309
\(317\) −8.71676 5.03263i −0.489582 0.282660i 0.234819 0.972039i \(-0.424550\pi\)
−0.724401 + 0.689379i \(0.757884\pi\)
\(318\) 9.05935 5.23042i 0.508023 0.293307i
\(319\) 25.7080 + 44.5275i 1.43937 + 2.49306i
\(320\) −0.806615 + 2.08551i −0.0450911 + 0.116584i
\(321\) −15.5261 −0.866581
\(322\) 0 0
\(323\) 11.5448i 0.642371i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −5.68053 + 6.24502i −0.315099 + 0.346412i
\(326\) −0.269584 0.466934i −0.0149309 0.0258611i
\(327\) 10.1111 + 5.83767i 0.559147 + 0.322824i
\(328\) 5.14925i 0.284320i
\(329\) 0 0
\(330\) 13.4935 2.10217i 0.742790 0.115720i
\(331\) −11.6399 + 20.1609i −0.639785 + 1.10814i 0.345694 + 0.938347i \(0.387643\pi\)
−0.985480 + 0.169794i \(0.945690\pi\)
\(332\) 11.7139 6.76304i 0.642885 0.371170i
\(333\) 2.00189 1.15579i 0.109703 0.0633370i
\(334\) 1.57462 2.72733i 0.0861596 0.149233i
\(335\) −4.20433 26.9869i −0.229707 1.47445i
\(336\) 0 0
\(337\) 5.17250i 0.281764i 0.990026 + 0.140882i \(0.0449938\pi\)
−0.990026 + 0.140882i \(0.955006\pi\)
\(338\) 8.78951 + 5.07462i 0.478086 + 0.276023i
\(339\) 1.68842 + 2.92442i 0.0917022 + 0.158833i
\(340\) −11.9065 + 9.59189i −0.645719 + 0.520193i
\(341\) −2.10217 + 3.64106i −0.113839 + 0.197174i
\(342\) 1.68842i 0.0912991i
\(343\) 0 0
\(344\) 2.00000 0.107833
\(345\) 1.86456 4.82084i 0.100384 0.259545i
\(346\) −5.26304 9.11585i −0.282943 0.490071i
\(347\) 8.37908 4.83767i 0.449813 0.259699i −0.257938 0.966161i \(-0.583043\pi\)
0.707751 + 0.706462i \(0.249710\pi\)
\(348\) 7.29092 + 4.20942i 0.390834 + 0.225648i
\(349\) 28.2985 1.51478 0.757392 0.652961i \(-0.226473\pi\)
0.757392 + 0.652961i \(0.226473\pi\)
\(350\) 0 0
\(351\) 1.68842 0.0901210
\(352\) 5.28903 + 3.05362i 0.281906 + 0.162759i
\(353\) −15.3073 + 8.83767i −0.814725 + 0.470381i −0.848594 0.529045i \(-0.822550\pi\)
0.0338693 + 0.999426i \(0.489217\pi\)
\(354\) −3.52100 6.09855i −0.187139 0.324134i
\(355\) 4.83969 12.5131i 0.256864 0.664126i
\(356\) 12.2145 0.647367
\(357\) 0 0
\(358\) 4.93475i 0.260810i
\(359\) −2.41883 + 4.18954i −0.127661 + 0.221116i −0.922770 0.385351i \(-0.874080\pi\)
0.795109 + 0.606467i \(0.207414\pi\)
\(360\) 1.74131 1.40280i 0.0917749 0.0739341i
\(361\) 8.07462 + 13.9857i 0.424980 + 0.736087i
\(362\) −5.30917 3.06525i −0.279044 0.161106i
\(363\) 26.2985i 1.38031i
\(364\) 0 0
\(365\) 1.37683 + 8.83767i 0.0720668 + 0.462585i
\(366\) −4.73042 + 8.19332i −0.247263 + 0.428272i
\(367\) −9.22007 + 5.32321i −0.481284 + 0.277869i −0.720951 0.692986i \(-0.756295\pi\)
0.239668 + 0.970855i \(0.422962\pi\)
\(368\) 2.00189 1.15579i 0.104356 0.0602498i
\(369\) −2.57462 + 4.45938i −0.134030 + 0.232146i
\(370\) 5.10725 0.795666i 0.265513 0.0413647i
\(371\) 0 0
\(372\) 0.688417i 0.0356928i
\(373\) −30.0749 17.3637i −1.55722 0.899061i −0.997521 0.0703638i \(-0.977584\pi\)
−0.559698 0.828697i \(-0.689083\pi\)
\(374\) 20.8797 + 36.1646i 1.07966 + 1.87003i
\(375\) 6.16025 9.33013i 0.318114 0.481806i
\(376\) −1.53263 + 2.65458i −0.0790391 + 0.136900i
\(377\) 14.2145i 0.732084i
\(378\) 0 0
\(379\) 19.4477 0.998964 0.499482 0.866324i \(-0.333524\pi\)
0.499482 + 0.866324i \(0.333524\pi\)
\(380\) −1.36190 + 3.52122i −0.0698641 + 0.180635i
\(381\) −2.47246 4.28242i −0.126668 0.219395i
\(382\) 12.9225 7.46083i 0.661175 0.381729i
\(383\) −0.736772 0.425376i −0.0376473 0.0217357i 0.481058 0.876689i \(-0.340253\pi\)
−0.518706 + 0.854953i \(0.673586\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −5.58117 −0.284074
\(387\) −1.73205 1.00000i −0.0880451 0.0508329i
\(388\) 4.29375 2.47900i 0.217982 0.125852i
\(389\) 13.1492 + 22.7752i 0.666693 + 1.15475i 0.978823 + 0.204707i \(0.0656243\pi\)
−0.312130 + 0.950039i \(0.601042\pi\)
\(390\) 3.52122 + 1.36190i 0.178304 + 0.0689626i
\(391\) 15.8058 0.799335
\(392\) 0 0
\(393\) 6.73042i 0.339505i
\(394\) 7.26304 12.5800i 0.365907 0.633769i
\(395\) −10.2567 12.7317i −0.516071 0.640602i
\(396\) −3.05362 5.28903i −0.153450 0.265784i
\(397\) 1.47354 + 0.850752i 0.0739551 + 0.0426980i 0.536522 0.843887i \(-0.319738\pi\)
−0.462566 + 0.886585i \(0.653071\pi\)
\(398\) 8.62317i 0.432240i
\(399\) 0 0
\(400\) 4.76304 1.52100i 0.238152 0.0760500i
\(401\) −1.50937 + 2.61431i −0.0753745 + 0.130553i −0.901249 0.433301i \(-0.857349\pi\)
0.825875 + 0.563854i \(0.190682\pi\)
\(402\) −10.5781 + 6.10725i −0.527586 + 0.304602i
\(403\) −1.00661 + 0.581167i −0.0501429 + 0.0289500i
\(404\) 4.00000 6.92820i 0.199007 0.344691i
\(405\) −2.20942 + 0.344208i −0.109787 + 0.0171039i
\(406\) 0 0
\(407\) 14.1174i 0.699774i
\(408\) 5.92159 + 3.41883i 0.293162 + 0.169257i
\(409\) 2.07462 + 3.59335i 0.102584 + 0.177680i 0.912748 0.408522i \(-0.133956\pi\)
−0.810165 + 0.586202i \(0.800622\pi\)
\(410\) −8.96642 + 7.22337i −0.442820 + 0.356737i
\(411\) 9.52608 16.4997i 0.469887 0.813868i
\(412\) 0.837665i 0.0412688i
\(413\) 0 0
\(414\) −2.31158 −0.113608
\(415\) −28.2088 10.9103i −1.38472 0.535568i
\(416\) 0.844208 + 1.46221i 0.0413907 + 0.0716908i
\(417\) −11.5847 + 6.68842i −0.567304 + 0.327533i
\(418\) 8.93009 + 5.15579i 0.436785 + 0.252178i
\(419\) 13.8189 0.675098 0.337549 0.941308i \(-0.390402\pi\)
0.337549 + 0.941308i \(0.390402\pi\)
\(420\) 0 0
\(421\) 25.2667 1.23142 0.615711 0.787972i \(-0.288869\pi\)
0.615711 + 0.787972i \(0.288869\pi\)
\(422\) −6.65836 3.84421i −0.324124 0.187133i
\(423\) 2.65458 1.53263i 0.129070 0.0745188i
\(424\) −5.23042 9.05935i −0.254011 0.439961i
\(425\) 33.4048 + 7.27730i 1.62037 + 0.353001i
\(426\) −6.00000 −0.290701
\(427\) 0 0
\(428\) 15.5261i 0.750482i
\(429\) 5.15579 8.93009i 0.248924 0.431149i
\(430\) −2.80560 3.48261i −0.135298 0.167947i
\(431\) −9.77241 16.9263i −0.470721 0.815312i 0.528719 0.848797i \(-0.322673\pi\)
−0.999439 + 0.0334851i \(0.989339\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 14.7537i 0.709016i 0.935053 + 0.354508i \(0.115352\pi\)
−0.935053 + 0.354508i \(0.884648\pi\)
\(434\) 0 0
\(435\) −2.89783 18.6007i −0.138940 0.891836i
\(436\) 5.83767 10.1111i 0.279573 0.484235i
\(437\) 3.38002 1.95146i 0.161688 0.0933509i
\(438\) 3.46410 2.00000i 0.165521 0.0955637i
\(439\) 7.96737 13.7999i 0.380262 0.658633i −0.610838 0.791756i \(-0.709167\pi\)
0.991100 + 0.133123i \(0.0425005\pi\)
\(440\) −2.10217 13.4935i −0.100217 0.643275i
\(441\) 0 0
\(442\) 11.5448i 0.549132i
\(443\) −18.9006 10.9123i −0.897997 0.518459i −0.0214469 0.999770i \(-0.506827\pi\)
−0.876550 + 0.481311i \(0.840161\pi\)
\(444\) −1.15579 2.00189i −0.0548514 0.0950055i
\(445\) −17.1345 21.2692i −0.812254 1.00826i
\(446\) −5.58625 + 9.67567i −0.264517 + 0.458156i
\(447\) 12.6232i 0.597055i
\(448\) 0 0
\(449\) 11.3637 0.536288 0.268144 0.963379i \(-0.413590\pi\)
0.268144 + 0.963379i \(0.413590\pi\)
\(450\) −4.88541 1.06430i −0.230301 0.0501714i
\(451\) 15.7239 + 27.2345i 0.740408 + 1.28242i
\(452\) 2.92442 1.68842i 0.137553 0.0794164i
\(453\) 1.67554 + 0.967375i 0.0787238 + 0.0454512i
\(454\) 3.85075 0.180725
\(455\) 0 0
\(456\) 1.68842 0.0790674
\(457\) 5.55887 + 3.20942i 0.260033 + 0.150130i 0.624350 0.781145i \(-0.285364\pi\)
−0.364317 + 0.931275i \(0.618697\pi\)
\(458\) −4.91498 + 2.83767i −0.229662 + 0.132595i
\(459\) −3.41883 5.92159i −0.159577 0.276396i
\(460\) −4.82084 1.86456i −0.224773 0.0869354i
\(461\) −1.50733 −0.0702036 −0.0351018 0.999384i \(-0.511176\pi\)
−0.0351018 + 0.999384i \(0.511176\pi\)
\(462\) 0 0
\(463\) 24.1174i 1.12083i −0.828211 0.560416i \(-0.810641\pi\)
0.828211 0.560416i \(-0.189359\pi\)
\(464\) 4.20942 7.29092i 0.195417 0.338473i
\(465\) 1.19874 0.965712i 0.0555905 0.0447838i
\(466\) 5.73042 + 9.92537i 0.265456 + 0.459784i
\(467\) −20.3904 11.7724i −0.943556 0.544762i −0.0524828 0.998622i \(-0.516713\pi\)
−0.891073 + 0.453859i \(0.850047\pi\)
\(468\) 1.68842i 0.0780471i
\(469\) 0 0
\(470\) 6.77241 1.05509i 0.312388 0.0486674i
\(471\) −8.57462 + 14.8517i −0.395098 + 0.684330i
\(472\) −6.09855 + 3.52100i −0.280709 + 0.162067i
\(473\) −10.5781 + 6.10725i −0.486380 + 0.280812i
\(474\) −3.65579 + 6.33202i −0.167916 + 0.290839i
\(475\) 8.04200 2.56808i 0.368992 0.117832i
\(476\) 0 0
\(477\) 10.4608i 0.478969i
\(478\) −13.3895 7.73042i −0.612420 0.353581i
\(479\) −14.9869 25.9581i −0.684770 1.18606i −0.973509 0.228648i \(-0.926570\pi\)
0.288740 0.957408i \(-0.406764\pi\)
\(480\) −1.40280 1.74131i −0.0640288 0.0794794i
\(481\) 1.95146 3.38002i 0.0889788 0.154116i
\(482\) 4.37683i 0.199359i
\(483\) 0 0
\(484\) −26.2985 −1.19539
\(485\) −10.3400 3.99920i −0.469515 0.181594i
\(486\) 0.500000 + 0.866025i 0.0226805 + 0.0392837i
\(487\) 26.4162 15.2514i 1.19703 0.691108i 0.237141 0.971475i \(-0.423790\pi\)
0.959893 + 0.280368i \(0.0904564\pi\)
\(488\) 8.19332 + 4.73042i 0.370894 + 0.214136i
\(489\) 0.539168 0.0243820
\(490\) 0 0
\(491\) −3.87966 −0.175087 −0.0875434 0.996161i \(-0.527902\pi\)
−0.0875434 + 0.996161i \(0.527902\pi\)
\(492\) 4.45938 + 2.57462i 0.201044 + 0.116073i
\(493\) 49.8529 28.7826i 2.24526 1.29630i
\(494\) 1.42538 + 2.46882i 0.0641307 + 0.111078i
\(495\) −4.92620 + 12.7368i −0.221416 + 0.572475i
\(496\) 0.688417 0.0309108
\(497\) 0 0
\(498\) 13.5261i 0.606118i
\(499\) 4.68842 8.12058i 0.209882 0.363527i −0.741795 0.670627i \(-0.766025\pi\)
0.951677 + 0.307100i \(0.0993586\pi\)
\(500\) −9.33013 6.16025i −0.417256 0.275495i
\(501\) 1.57462 + 2.72733i 0.0703490 + 0.121848i
\(502\) 22.9811 + 13.2681i 1.02570 + 0.592185i
\(503\) 14.2145i 0.633793i −0.948460 0.316897i \(-0.897359\pi\)
0.948460 0.316897i \(-0.102641\pi\)
\(504\) 0 0
\(505\) −17.6753 + 2.75367i −0.786542 + 0.122537i
\(506\) −7.05871 + 12.2260i −0.313798 + 0.543514i
\(507\) −8.78951 + 5.07462i −0.390356 + 0.225372i
\(508\) −4.28242 + 2.47246i −0.190002 + 0.109698i
\(509\) −15.9818 + 27.6813i −0.708382 + 1.22695i 0.257075 + 0.966392i \(0.417241\pi\)
−0.965457 + 0.260562i \(0.916092\pi\)
\(510\) −2.35358 15.1072i −0.104218 0.668960i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) −1.46221 0.844208i −0.0645582 0.0372727i
\(514\) −11.2145 19.4241i −0.494650 0.856760i
\(515\) 1.45863 1.17508i 0.0642750 0.0517801i
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) 18.7203i 0.823316i
\(518\) 0 0
\(519\) 10.5261 0.462044
\(520\) 1.36190 3.52122i 0.0597234 0.154416i
\(521\) −18.1007 31.3513i −0.793006 1.37353i −0.924097 0.382157i \(-0.875181\pi\)
0.131091 0.991370i \(-0.458152\pi\)
\(522\) −7.29092 + 4.20942i −0.319115 + 0.184241i
\(523\) −32.0154 18.4841i −1.39993 0.808253i −0.405549 0.914073i \(-0.632920\pi\)
−0.994385 + 0.105821i \(0.966253\pi\)
\(524\) −6.73042 −0.294020
\(525\) 0 0
\(526\) −19.5913 −0.854223
\(527\) 4.07652 + 2.35358i 0.177576 + 0.102524i
\(528\) −5.28903 + 3.05362i −0.230176 + 0.132892i
\(529\) −8.82829 15.2910i −0.383839 0.664828i
\(530\) −8.43786 + 21.8162i −0.366517 + 0.947636i
\(531\) 7.04200 0.305597
\(532\) 0 0
\(533\) 8.69408i 0.376582i
\(534\) −6.10725 + 10.5781i −0.264287 + 0.457758i
\(535\) 27.0357 21.7800i 1.16885 0.941632i
\(536\) 6.10725 + 10.5781i 0.263793 + 0.456903i
\(537\) −4.27362 2.46737i −0.184420 0.106475i
\(538\) 6.95800i 0.299981i
\(539\) 0 0
\(540\) 0.344208 + 2.20942i 0.0148124 + 0.0950781i
\(541\) 8.63333 14.9534i 0.371176 0.642896i −0.618571 0.785729i \(-0.712288\pi\)
0.989747 + 0.142834i \(0.0456213\pi\)
\(542\) −24.5637 + 14.1819i −1.05510 + 0.609164i
\(543\) 5.30917 3.06525i 0.227838 0.131542i
\(544\) 3.41883 5.92159i 0.146581 0.253886i
\(545\) −25.7957 + 4.01875i −1.10496 + 0.172144i
\(546\) 0 0
\(547\) 39.4347i 1.68610i −0.537832 0.843052i \(-0.680756\pi\)
0.537832 0.843052i \(-0.319244\pi\)
\(548\) −16.4997 9.52608i −0.704830 0.406934i
\(549\) −4.73042 8.19332i −0.201889 0.349682i
\(550\) −20.5473 + 22.5892i −0.876141 + 0.963205i
\(551\) 7.10725 12.3101i 0.302779 0.524429i
\(552\) 2.31158i 0.0983875i
\(553\) 0 0
\(554\) −5.05216 −0.214646
\(555\) −1.86456 + 4.82084i −0.0791461 + 0.204633i
\(556\) 6.68842 + 11.5847i 0.283652 + 0.491300i
\(557\) 28.4834 16.4449i 1.20688 0.696793i 0.244805 0.969572i \(-0.421276\pi\)
0.962077 + 0.272779i \(0.0879428\pi\)
\(558\) −0.596186 0.344208i −0.0252386 0.0145715i
\(559\) −3.37683 −0.142825
\(560\) 0 0
\(561\) −41.7593 −1.76308
\(562\) 6.65836 + 3.84421i 0.280866 + 0.162158i
\(563\) 30.4853 17.6007i 1.28480 0.741781i 0.307081 0.951684i \(-0.400648\pi\)
0.977722 + 0.209902i \(0.0673146\pi\)
\(564\) −1.53263 2.65458i −0.0645352 0.111778i
\(565\) −7.04244 2.72380i −0.296278 0.114591i
\(566\) −18.4290 −0.774629
\(567\) 0 0
\(568\) 6.00000i 0.251754i
\(569\) 8.74712 15.1505i 0.366699 0.635140i −0.622349 0.782740i \(-0.713821\pi\)
0.989047 + 0.147600i \(0.0471547\pi\)
\(570\) −2.36851 2.94005i −0.0992061 0.123145i
\(571\) −4.41883 7.65364i −0.184922 0.320295i 0.758628 0.651524i \(-0.225870\pi\)
−0.943550 + 0.331229i \(0.892537\pi\)
\(572\) −8.93009 5.15579i −0.373386 0.215574i
\(573\) 14.9217i 0.623361i
\(574\) 0 0
\(575\) 3.51592 + 11.0102i 0.146624 + 0.459156i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −34.9083 + 20.1543i −1.45325 + 0.839036i −0.998664 0.0516659i \(-0.983547\pi\)
−0.454588 + 0.890702i \(0.650214\pi\)
\(578\) 25.7674 14.8768i 1.07178 0.618795i
\(579\) 2.79058 4.83343i 0.115973 0.200871i
\(580\) −18.6007 + 2.89783i −0.772352 + 0.120326i
\(581\) 0 0
\(582\) 4.95800i 0.205516i
\(583\) 55.3277 + 31.9435i 2.29144 + 1.32296i
\(584\) −2.00000 3.46410i −0.0827606 0.143346i
\(585\) −2.94005 + 2.36851i −0.121556 + 0.0979260i
\(586\) −0.918833 + 1.59146i −0.0379566 + 0.0657428i
\(587\) 36.1492i 1.49204i 0.665924 + 0.746020i \(0.268037\pi\)
−0.665924 + 0.746020i \(0.731963\pi\)
\(588\) 0 0
\(589\) 1.16233 0.0478932
\(590\) 14.6862 + 5.68018i 0.604621 + 0.233849i
\(591\) 7.26304 + 12.5800i 0.298762 + 0.517470i
\(592\) −2.00189 + 1.15579i −0.0822772 + 0.0475027i
\(593\) −3.53685 2.04200i −0.145241 0.0838548i 0.425619 0.904903i \(-0.360057\pi\)
−0.570859 + 0.821048i \(0.693390\pi\)
\(594\) 6.10725 0.250583
\(595\) 0 0
\(596\) 12.6232 0.517065
\(597\) −7.46788 4.31158i −0.305640 0.176461i
\(598\) −3.38002 + 1.95146i −0.138219 + 0.0798011i
\(599\) −9.87966 17.1121i −0.403672 0.699181i 0.590494 0.807042i \(-0.298933\pi\)
−0.994166 + 0.107862i \(0.965600\pi\)
\(600\) −1.06430 + 4.88541i −0.0434497 + 0.199446i
\(601\) −3.72025 −0.151752 −0.0758761 0.997117i \(-0.524175\pi\)
−0.0758761 + 0.997117i \(0.524175\pi\)
\(602\) 0 0
\(603\) 12.2145i 0.497413i
\(604\) 0.967375 1.67554i 0.0393619 0.0681768i
\(605\) 36.8916 + 45.7937i 1.49986 + 1.86178i
\(606\) 4.00000 + 6.92820i 0.162489 + 0.281439i
\(607\) −9.73708 5.62171i −0.395216 0.228178i 0.289202 0.957268i \(-0.406610\pi\)
−0.684418 + 0.729090i \(0.739943\pi\)
\(608\) 1.68842i 0.0684743i
\(609\) 0 0
\(610\) −3.25650 20.9029i −0.131852 0.846334i
\(611\) 2.58771 4.48205i 0.104688 0.181324i
\(612\) −5.92159 + 3.41883i −0.239366 + 0.138198i
\(613\) −23.3262 + 13.4674i −0.942135 + 0.543942i −0.890629 0.454731i \(-0.849736\pi\)
−0.0515063 + 0.998673i \(0.516402\pi\)
\(614\) 8.04200 13.9292i 0.324549 0.562135i
\(615\) −1.77241 11.3768i −0.0714707 0.458758i
\(616\) 0 0
\(617\) 33.4608i 1.34708i 0.739150 + 0.673541i \(0.235228\pi\)
−0.739150 + 0.673541i \(0.764772\pi\)
\(618\) −0.725439 0.418833i −0.0291815 0.0168479i
\(619\) 17.4355 + 30.1992i 0.700794 + 1.21381i 0.968188 + 0.250223i \(0.0805039\pi\)
−0.267395 + 0.963587i \(0.586163\pi\)
\(620\) −0.965712 1.19874i −0.0387839 0.0481427i
\(621\) 1.15579 2.00189i 0.0463803 0.0803331i
\(622\) 15.3768i 0.616555i
\(623\) 0 0
\(624\) −1.68842 −0.0675908
\(625\) 2.36143 + 24.8882i 0.0944570 + 0.995529i
\(626\) −11.2094 19.4153i −0.448018 0.775991i
\(627\) −8.93009 + 5.15579i −0.356634 + 0.205902i
\(628\) 14.8517 + 8.57462i 0.592647 + 0.342165i
\(629\) −15.8058 −0.630220
\(630\) 0 0
\(631\) −10.4942 −0.417769 −0.208885 0.977940i \(-0.566983\pi\)
−0.208885 + 0.977940i \(0.566983\pi\)
\(632\) 6.33202 + 3.65579i 0.251874 + 0.145420i
\(633\) 6.65836 3.84421i 0.264646 0.152794i
\(634\) −5.03263 8.71676i −0.199871 0.346187i
\(635\) 10.3127 + 3.98864i 0.409247 + 0.158284i
\(636\) 10.4608 0.414799
\(637\) 0 0
\(638\) 51.4159i 2.03558i
\(639\) 3.00000 5.19615i 0.118678 0.205557i
\(640\) −1.74131 + 1.40280i −0.0688312 + 0.0554506i
\(641\) −3.88621 6.73111i −0.153496 0.265863i 0.779014 0.627006i \(-0.215720\pi\)
−0.932510 + 0.361143i \(0.882387\pi\)
\(642\) −13.4460 7.76304i −0.530671 0.306383i
\(643\) 21.7218i 0.856626i −0.903631 0.428313i \(-0.859108\pi\)
0.903631 0.428313i \(-0.140892\pi\)
\(644\) 0 0
\(645\) 4.41883 0.688417i 0.173991 0.0271064i
\(646\) 5.77241 9.99812i 0.227113 0.393371i
\(647\) −8.27740 + 4.77896i −0.325418 + 0.187880i −0.653805 0.756663i \(-0.726828\pi\)
0.328387 + 0.944543i \(0.393495\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 21.5036 37.2454i 0.844091 1.46201i
\(650\) −8.04200 + 2.56808i −0.315433 + 0.100728i
\(651\) 0 0
\(652\) 0.539168i 0.0211155i
\(653\) 43.5322 + 25.1333i 1.70355 + 0.983543i 0.942110 + 0.335304i \(0.108839\pi\)
0.761437 + 0.648239i \(0.224494\pi\)
\(654\) 5.83767 + 10.1111i 0.228271 + 0.395377i
\(655\) 9.44144 + 11.7197i 0.368907 + 0.457927i
\(656\) 2.57462 4.45938i 0.100522 0.174110i
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) −11.1623 −0.434823 −0.217411 0.976080i \(-0.569761\pi\)
−0.217411 + 0.976080i \(0.569761\pi\)
\(660\) 12.7368 + 4.92620i 0.495778 + 0.191752i
\(661\) 7.17250 + 12.4231i 0.278978 + 0.483204i 0.971131 0.238547i \(-0.0766710\pi\)
−0.692153 + 0.721751i \(0.743338\pi\)
\(662\) −20.1609 + 11.6399i −0.783574 + 0.452397i
\(663\) −9.99812 5.77241i −0.388295 0.224182i
\(664\) 13.5261 0.524914
\(665\) 0 0
\(666\) 2.31158 0.0895720
\(667\) 16.8536 + 9.73042i 0.652573 + 0.376763i
\(668\) 2.72733 1.57462i 0.105524 0.0609240i
\(669\) −5.58625 9.67567i −0.215977 0.374083i
\(670\) 9.85240 25.4735i 0.380631 0.984128i
\(671\) −57.7797 −2.23056
\(672\) 0 0
\(673\) 30.8013i 1.18730i −0.804722 0.593652i \(-0.797686\pi\)
0.804722 0.593652i \(-0.202314\pi\)
\(674\) −2.58625 + 4.47952i −0.0996186 + 0.172545i
\(675\) 3.36441 3.69874i 0.129496 0.142365i
\(676\) 5.07462 + 8.78951i 0.195178 + 0.338058i
\(677\) −12.2649 7.08117i −0.471380 0.272151i 0.245437 0.969412i \(-0.421068\pi\)
−0.716817 + 0.697261i \(0.754402\pi\)
\(678\) 3.37683i 0.129687i
\(679\) 0 0
\(680\) −15.1072 + 2.35358i −0.579337 + 0.0902558i
\(681\) −1.92538 + 3.33485i −0.0737806 + 0.127792i
\(682\) −3.64106 + 2.10217i −0.139423 + 0.0804961i
\(683\) 26.5946 15.3544i 1.01761 0.587519i 0.104201 0.994556i \(-0.466771\pi\)
0.913411 + 0.407037i \(0.133438\pi\)
\(684\) −0.844208 + 1.46221i −0.0322791 + 0.0559091i
\(685\) 6.55792 + 42.0942i 0.250565 + 1.60834i
\(686\) 0 0
\(687\) 5.67533i 0.216527i
\(688\) 1.73205 + 1.00000i 0.0660338 + 0.0381246i
\(689\) 8.83112 + 15.2960i 0.336439 + 0.582729i
\(690\) 4.02517 3.24269i 0.153236 0.123447i
\(691\) −19.6753 + 34.0787i −0.748485 + 1.29641i 0.200064 + 0.979783i \(0.435885\pi\)
−0.948549 + 0.316631i \(0.897448\pi\)
\(692\) 10.5261i 0.400142i
\(693\) 0 0
\(694\) 9.67533 0.367271
\(695\) 10.7900 27.8976i 0.409286 1.05822i
\(696\) 4.20942 + 7.29092i 0.159558 + 0.276362i
\(697\) 30.4917 17.6044i 1.15496 0.666815i
\(698\) 24.5072 + 14.1492i 0.927612 + 0.535557i
\(699\) −11.4608 −0.433488
\(700\) 0 0
\(701\) −3.79567 −0.143360 −0.0716802 0.997428i \(-0.522836\pi\)
−0.0716802 + 0.997428i \(0.522836\pi\)
\(702\) 1.46221 + 0.844208i 0.0551876 + 0.0318626i
\(703\) −3.38002 + 1.95146i −0.127480 + 0.0736006i
\(704\) 3.05362 + 5.28903i 0.115088 + 0.199338i
\(705\) −2.47248 + 6.39263i −0.0931189 + 0.240760i
\(706\) −17.6753 −0.665220
\(707\) 0 0
\(708\) 7.04200i 0.264655i
\(709\) −10.2797 + 17.8050i −0.386064 + 0.668683i −0.991916 0.126895i \(-0.959499\pi\)
0.605852 + 0.795577i \(0.292832\pi\)
\(710\) 10.4478 8.41681i 0.392100 0.315877i
\(711\) −3.65579 6.33202i −0.137103 0.237469i
\(712\) 10.5781 + 6.10725i 0.396430 + 0.228879i
\(713\) 1.59133i 0.0595959i
\(714\) 0 0
\(715\) 3.54933 + 22.7826i 0.132738 + 0.852020i
\(716\) −2.46737 + 4.27362i −0.0922101 + 0.159713i
\(717\) 13.3895 7.73042i 0.500039 0.288698i
\(718\) −4.18954 + 2.41883i −0.156352 + 0.0902700i
\(719\) 12.4057 21.4874i 0.462656 0.801344i −0.536436 0.843941i \(-0.680230\pi\)
0.999092 + 0.0425968i \(0.0135631\pi\)
\(720\) 2.20942 0.344208i 0.0823401 0.0128279i
\(721\) 0 0
\(722\) 16.1492i 0.601013i
\(723\) −3.79045 2.18842i −0.140968 0.0813881i
\(724\) −3.06525 5.30917i −0.113919 0.197314i
\(725\) 31.1391 + 28.3244i 1.15648 + 1.05194i
\(726\) 13.1492 22.7752i 0.488014 0.845266i
\(727\) 39.2899i 1.45718i −0.684949 0.728591i \(-0.740175\pi\)
0.684949 0.728591i \(-0.259825\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −3.22646 + 8.34206i −0.119417 + 0.308753i
\(731\) 6.83767 + 11.8432i 0.252900 + 0.438036i
\(732\) −8.19332 + 4.73042i −0.302834 + 0.174841i
\(733\) −7.81046 4.50937i −0.288486 0.166558i 0.348773 0.937207i \(-0.386598\pi\)
−0.637259 + 0.770650i \(0.719932\pi\)
\(734\) −10.6464 −0.392966
\(735\) 0 0
\(736\) 2.31158 0.0852061
\(737\) −64.6029 37.2985i −2.37968 1.37391i
\(738\) −4.45938 + 2.57462i −0.164152 + 0.0947732i
\(739\) −7.03546 12.1858i −0.258803 0.448261i 0.707118 0.707095i \(-0.249995\pi\)
−0.965922 + 0.258835i \(0.916662\pi\)
\(740\) 4.82084 + 1.86456i 0.177218 + 0.0685425i
\(741\) −2.85075 −0.104725
\(742\) 0 0
\(743\) 39.1492i 1.43625i −0.695916 0.718123i \(-0.745001\pi\)
0.695916 0.718123i \(-0.254999\pi\)
\(744\) −0.344208 + 0.596186i −0.0126193 + 0.0218573i
\(745\) −17.7078 21.9808i −0.648763 0.805314i
\(746\) −17.3637 30.0749i −0.635732 1.10112i
\(747\) −11.7139 6.76304i −0.428590 0.247447i
\(748\) 41.7593i 1.52687i
\(749\) 0 0
\(750\) 10.0000 5.00000i 0.365148 0.182574i
\(751\) 19.6427 34.0222i 0.716773 1.24149i −0.245499 0.969397i \(-0.578952\pi\)
0.962272 0.272090i \(-0.0877147\pi\)
\(752\) −2.65458 + 1.53263i −0.0968028 + 0.0558891i
\(753\) −22.9811 + 13.2681i −0.837477 + 0.483517i
\(754\) −7.10725 + 12.3101i −0.258831 + 0.448308i
\(755\) −4.27467 + 0.665957i −0.155571 + 0.0242367i
\(756\) 0 0
\(757\) 28.9217i 1.05118i 0.850739 + 0.525588i \(0.176155\pi\)
−0.850739 + 0.525588i \(0.823845\pi\)
\(758\) 16.8422 + 9.72387i 0.611738 + 0.353187i
\(759\) −7.05871 12.2260i −0.256215 0.443777i
\(760\) −2.94005 + 2.36851i −0.106647 + 0.0859150i
\(761\) 7.77896 13.4736i 0.281987 0.488416i −0.689887 0.723917i \(-0.742340\pi\)
0.971874 + 0.235501i \(0.0756732\pi\)
\(762\) 4.94491i 0.179135i
\(763\) 0 0
\(764\) 14.9217 0.539847
\(765\) 14.2601 + 5.51536i 0.515573 + 0.199408i
\(766\) −0.425376 0.736772i −0.0153695 0.0266207i
\(767\) 10.2969 5.94491i 0.371799 0.214658i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) −4.05216 −0.146125 −0.0730624 0.997327i \(-0.523277\pi\)
−0.0730624 + 0.997327i \(0.523277\pi\)
\(770\) 0 0
\(771\) 22.4290 0.807761
\(772\) −4.83343 2.79058i −0.173959 0.100435i
\(773\) 18.5743 10.7239i 0.668071 0.385711i −0.127274 0.991868i \(-0.540623\pi\)
0.795345 + 0.606157i \(0.207290\pi\)
\(774\) −1.00000 1.73205i −0.0359443 0.0622573i
\(775\) −0.732680 + 3.36320i −0.0263186 + 0.120810i
\(776\) 4.95800 0.177982
\(777\) 0 0
\(778\) 26.2985i 0.942847i
\(779\) 4.34704 7.52929i 0.155749 0.269765i
\(780\) 2.36851 + 2.94005i 0.0848064 + 0.105271i
\(781\) −18.3217 31.7342i −0.655604 1.13554i
\(782\) 13.6883 + 7.90292i 0.489491 + 0.282608i
\(783\) 8.41883i 0.300865i
\(784\) 0 0
\(785\) −5.90292 37.8898i −0.210684 1.35235i
\(786\) 3.36521 5.82871i 0.120033 0.207903i
\(787\) −3.74527 + 2.16233i −0.133505 + 0.0770789i −0.565265 0.824910i \(-0.691226\pi\)
0.431760 + 0.901988i \(0.357893\pi\)
\(788\) 12.5800 7.26304i 0.448142 0.258735i
\(789\) 9.79567 16.9666i 0.348735 0.604027i
\(790\) −2.51671 16.1543i −0.0895405 0.574745i
\(791\) 0 0
\(792\) 6.10725i 0.217012i
\(793\) −13.8337 7.98691i −0.491251 0.283624i
\(794\) 0.850752 + 1.47354i 0.0301920 + 0.0522941i
\(795\) −14.6745 18.2155i −0.520450 0.646038i
\(796\) −4.31158 + 7.46788i −0.152820 + 0.264692i
\(797\) 41.1549i 1.45778i 0.684630 + 0.728891i \(0.259964\pi\)
−0.684630 + 0.728891i \(0.740036\pi\)
\(798\) 0 0
\(799\) −20.9592 −0.741482
\(800\) 4.88541 + 1.06430i 0.172725 + 0.0376286i
\(801\) −6.10725 10.5781i −0.215789 0.373758i
\(802\) −2.61431 + 1.50937i −0.0923146 + 0.0532978i
\(803\) 21.1561 + 12.2145i 0.746584 + 0.431040i
\(804\) −12.2145 −0.430772
\(805\) 0 0
\(806\) −1.16233 −0.0409415
\(807\) −6.02581 3.47900i −0.212118 0.122467i
\(808\) 6.92820 4.00000i 0.243733 0.140720i
\(809\) −8.88621 15.3914i −0.312422 0.541131i 0.666464 0.745537i \(-0.267807\pi\)
−0.978886 + 0.204406i \(0.934474\pi\)
\(810\) −2.08551 0.806615i −0.0732775 0.0283416i
\(811\) −47.1231 −1.65472 −0.827358 0.561676i \(-0.810157\pi\)
−0.827358 + 0.561676i \(0.810157\pi\)
\(812\) 0 0
\(813\) 28.3637i 0.994760i
\(814\) 7.05871 12.2260i 0.247408 0.428522i
\(815\) −0.938857 + 0.756346i −0.0328867 + 0.0264937i
\(816\) 3.41883 + 5.92159i 0.119683 + 0.207297i
\(817\) 2.92442 + 1.68842i 0.102313 + 0.0590702i
\(818\) 4.14925i 0.145075i
\(819\) 0 0
\(820\) −11.3768 + 1.77241i −0.397296 + 0.0618954i
\(821\) −2.85583 + 4.94645i −0.0996693 + 0.172632i −0.911548 0.411194i \(-0.865112\pi\)
0.811878 + 0.583826i \(0.198445\pi\)
\(822\) 16.4997 9.52608i 0.575492 0.332260i
\(823\) −26.2795 + 15.1725i −0.916047 + 0.528880i −0.882372 0.470553i \(-0.844055\pi\)
−0.0336753 + 0.999433i \(0.510721\pi\)
\(824\) −0.418833 + 0.725439i −0.0145907 + 0.0252719i
\(825\) −9.28912 29.0891i −0.323406 1.01275i
\(826\) 0 0
\(827\) 27.2014i 0.945886i 0.881093 + 0.472943i \(0.156808\pi\)
−0.881093 + 0.472943i \(0.843192\pi\)
\(828\) −2.00189 1.15579i −0.0695705 0.0401665i
\(829\) −5.41883 9.38569i −0.188204 0.325979i 0.756448 0.654054i \(-0.226933\pi\)
−0.944651 + 0.328076i \(0.893600\pi\)
\(830\) −18.9744 23.5531i −0.658611 0.817538i
\(831\) 2.52608 4.37530i 0.0876288 0.151778i
\(832\) 1.68842i 0.0585353i
\(833\) 0 0
\(834\) −13.3768 −0.463202
\(835\) −6.56780 2.54023i −0.227288 0.0879083i
\(836\) 5.15579 + 8.93009i 0.178317 + 0.308854i
\(837\) 0.596186 0.344208i 0.0206072 0.0118976i
\(838\) 11.9675 + 6.90946i 0.413412 + 0.238683i
\(839\) −1.59133 −0.0549389 −0.0274695 0.999623i \(-0.508745\pi\)
−0.0274695 + 0.999623i \(0.508745\pi\)
\(840\) 0 0
\(841\) 41.8767 1.44403
\(842\) 21.8816 + 12.6333i 0.754089 + 0.435373i
\(843\) −6.65836 + 3.84421i −0.229326 + 0.132402i
\(844\) −3.84421 6.65836i −0.132323 0.229190i
\(845\) 8.18654 21.1664i 0.281625 0.728147i
\(846\) 3.06525 0.105385
\(847\) 0 0
\(848\) 10.4608i 0.359226i
\(849\) 9.21450 15.9600i 0.316241 0.547745i
\(850\) 25.2908 + 23.0047i 0.867467 + 0.789056i
\(851\) −2.67171 4.62753i −0.0915850 0.158630i
\(852\) −5.19615 3.00000i −0.178017 0.102778i
\(853\) 29.9869i 1.02673i 0.858170 + 0.513366i \(0.171602\pi\)
−0.858170 + 0.513366i \(0.828398\pi\)
\(854\) 0 0
\(855\) 3.73042 0.581167i 0.127578 0.0198755i
\(856\) −7.76304 + 13.4460i −0.265335 + 0.459574i
\(857\) 32.0478 18.5028i 1.09473 0.632045i 0.159901 0.987133i \(-0.448883\pi\)
0.934833 + 0.355088i \(0.115549\pi\)
\(858\) 8.93009 5.15579i 0.304868 0.176016i
\(859\) −13.8797 + 24.0403i −0.473568 + 0.820244i −0.999542 0.0302567i \(-0.990368\pi\)
0.525974 + 0.850501i \(0.323701\pi\)
\(860\) −0.688417 4.41883i −0.0234748 0.150681i
\(861\) 0 0
\(862\) 19.5448i 0.665700i
\(863\) 3.12152 + 1.80221i 0.106258 + 0.0613479i 0.552187 0.833720i \(-0.313793\pi\)
−0.445929 + 0.895068i \(0.647127\pi\)
\(864\) −0.500000 0.866025i −0.0170103 0.0294628i
\(865\) −18.3291 + 14.7660i −0.623209 + 0.502059i
\(866\) −7.37683 + 12.7771i −0.250675 + 0.434182i
\(867\) 29.7537i 1.01049i
\(868\) 0 0
\(869\) −44.6537 −1.51477
\(870\) 6.79076 17.5576i 0.230228 0.595258i
\(871\) −10.3116 17.8602i −0.349395 0.605169i
\(872\) 10.1111 5.83767i 0.342406 0.197688i
\(873\) −4.29375 2.47900i −0.145322 0.0839015i
\(874\) 3.90292 0.132018
\(875\) 0 0
\(876\) 4.00000 0.135147
\(877\) −10.4764 6.04854i −0.353762 0.204245i 0.312579 0.949892i \(-0.398807\pi\)
−0.666341 + 0.745647i \(0.732141\pi\)
\(878\) 13.7999 7.96737i 0.465724 0.268886i
\(879\) −0.918833 1.59146i −0.0309915 0.0536788i
\(880\) 4.92620 12.7368i 0.166062 0.429356i
\(881\) 44.7406 1.50735 0.753674 0.657248i \(-0.228280\pi\)
0.753674 + 0.657248i \(0.228280\pi\)
\(882\) 0 0
\(883\) 36.5970i 1.23159i 0.787908 + 0.615793i \(0.211164\pi\)
−0.787908 + 0.615793i \(0.788836\pi\)
\(884\) −5.77241 + 9.99812i −0.194147 + 0.336273i
\(885\) −12.2623 + 9.87853i −0.412192 + 0.332063i
\(886\) −10.9123 18.9006i −0.366606 0.634979i
\(887\) 48.5475 + 28.0289i 1.63007 + 0.941119i 0.984071 + 0.177777i \(0.0568905\pi\)
0.645995 + 0.763342i \(0.276443\pi\)
\(888\) 2.31158i 0.0775717i
\(889\) 0 0
\(890\) −4.20433 26.9869i −0.140930 0.904603i
\(891\) −3.05362 + 5.28903i −0.102300 + 0.177189i
\(892\) −9.67567 + 5.58625i −0.323965 + 0.187041i
\(893\) −4.48205 + 2.58771i −0.149986 + 0.0865944i
\(894\) −6.31158 + 10.9320i −0.211091 + 0.365620i
\(895\) 10.9029 1.69858i 0.364444 0.0567773i
\(896\) 0 0
\(897\) 3.90292i 0.130315i
\(898\) 9.84129 + 5.68187i 0.328408 + 0.189607i
\(899\) 2.89783 + 5.01919i 0.0966481 + 0.167400i
\(900\) −3.69874 3.36441i −0.123291 0.112147i
\(901\) 35.7638 61.9448i 1.19147 2.06368i
\(902\) 31.4477i 1.04710i
\(903\) 0 0
\(904\) 3.37683 0.112312
\(905\) −4.94495 + 12.7853i −0.164376 + 0.424996i
\(906\) 0.967375 + 1.67554i 0.0321389 + 0.0556662i
\(907\) −16.1457 + 9.32175i −0.536111 + 0.309524i −0.743501 0.668735i \(-0.766836\pi\)
0.207391 + 0.978258i \(0.433503\pi\)
\(908\) 3.33485 + 1.92538i 0.110671 + 0.0638958i
\(909\) −8.00000 −0.265343
\(910\) 0 0
\(911\) −6.00000 −0.198789 −0.0993944 0.995048i \(-0.531691\pi\)
−0.0993944 + 0.995048i \(0.531691\pi\)
\(912\) 1.46221 + 0.844208i 0.0484187 + 0.0279545i
\(913\) −71.5399 + 41.3036i −2.36763 + 1.36695i
\(914\) 3.20942 + 5.55887i 0.106158 + 0.183871i
\(915\) 19.7307 + 7.63125i 0.652277 + 0.252281i
\(916\) −5.67533 −0.187518
\(917\) 0 0
\(918\) 6.83767i 0.225677i
\(919\) −19.4608 + 33.7071i −0.641954 + 1.11190i 0.343043 + 0.939320i \(0.388542\pi\)
−0.984996 + 0.172576i \(0.944791\pi\)
\(920\) −3.24269 4.02517i −0.106908 0.132706i
\(921\) 8.04200 + 13.9292i 0.264993 + 0.458981i
\(922\) −1.30539 0.753667i −0.0429907 0.0248207i
\(923\) 10.1305i 0.333450i
\(924\) 0 0
\(925\) −3.51592 11.0102i −0.115603 0.362012i
\(926\) 12.0587 20.8863i 0.396274 0.686366i
\(927\) 0.725439 0.418833i 0.0238266 0.0137563i
\(928\) 7.29092 4.20942i 0.239336 0.138181i
\(929\) −6.86746 + 11.8948i −0.225314 + 0.390255i −0.956414 0.292015i \(-0.905674\pi\)
0.731100 + 0.682271i \(0.239007\pi\)
\(930\) 1.52100 0.236959i 0.0498755 0.00777019i
\(931\) 0 0
\(932\) 11.4608i 0.375412i
\(933\) 13.3167 + 7.68842i 0.435970 + 0.251707i
\(934\) −11.7724 20.3904i −0.385205 0.667195i
\(935\) 72.7158 58.5800i 2.37806 1.91577i
\(936\) 0.844208 1.46221i 0.0275938 0.0477939i
\(937\) 20.7435i 0.677661i −0.940847 0.338830i \(-0.889969\pi\)
0.940847 0.338830i \(-0.110031\pi\)
\(938\) 0 0
\(939\) 22.4188 0.731611
\(940\) 6.39263 + 2.47248i 0.208504 + 0.0806433i
\(941\) 6.54425 + 11.3350i 0.213336 + 0.369510i 0.952757 0.303735i \(-0.0982336\pi\)
−0.739420 + 0.673244i \(0.764900\pi\)
\(942\) −14.8517 + 8.57462i −0.483894 + 0.279376i
\(943\) 10.3082 + 5.95146i 0.335682 + 0.193806i
\(944\) −7.04200 −0.229198
\(945\) 0 0
\(946\) −12.2145 −0.397128
\(947\) 17.5465 + 10.1305i 0.570186 + 0.329197i 0.757224 0.653156i \(-0.226555\pi\)
−0.187038 + 0.982353i \(0.559889\pi\)
\(948\) −6.33202 + 3.65579i −0.205654 + 0.118735i
\(949\) 3.37683 + 5.84885i 0.109617 + 0.189862i
\(950\) 8.24862 + 1.79698i 0.267620 + 0.0583016i
\(951\) 10.0653 0.326388
\(952\) 0 0
\(953\) 1.65500i 0.0536107i 0.999641 + 0.0268053i \(0.00853343\pi\)
−0.999641 + 0.0268053i \(0.991467\pi\)
\(954\) −5.23042 + 9.05935i −0.169341 + 0.293307i
\(955\) −20.9321 25.9832i −0.677348 0.840796i
\(956\) −7.73042 13.3895i −0.250020 0.433047i
\(957\) −44.5275 25.7080i −1.43937 0.831020i
\(958\) 29.9738i 0.968410i
\(959\) 0 0
\(960\) −0.344208 2.20942i −0.0111093 0.0713086i
\(961\) 15.2630 26.4364i 0.492356 0.852786i
\(962\) 3.38002 1.95146i 0.108976 0.0629175i
\(963\) 13.4460 7.76304i 0.433291 0.250161i
\(964\) −2.18842 + 3.79045i −0.0704842 + 0.122082i
\(965\) 1.92108 + 12.3311i 0.0618419 + 0.396953i
\(966\) 0 0
\(967\) 15.3405i 0.493317i 0.969102 + 0.246659i \(0.0793326\pi\)
−0.969102 + 0.246659i \(0.920667\pi\)
\(968\) −22.7752 13.1492i −0.732022 0.422633i
\(969\) 5.77241 + 9.99812i 0.185437 + 0.321186i
\(970\) −6.95509 8.63340i −0.223315 0.277202i
\(971\) 23.5565 40.8010i 0.755963 1.30937i −0.188932 0.981990i \(-0.560502\pi\)
0.944894 0.327375i \(-0.106164\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) 30.5028 0.977374
\(975\) 1.79698 8.24862i 0.0575493 0.264167i
\(976\) 4.73042 + 8.19332i 0.151417 + 0.262262i
\(977\) −25.8854 + 14.9449i −0.828146 + 0.478130i −0.853217 0.521555i \(-0.825352\pi\)
0.0250716 + 0.999686i \(0.492019\pi\)
\(978\) 0.466934 + 0.269584i 0.0149309 + 0.00862035i
\(979\) −74.5970 −2.38413
\(980\) 0 0
\(981\) −11.6753 −0.372765
\(982\) −3.35989 1.93983i −0.107218 0.0619025i
\(983\) −4.45938 + 2.57462i −0.142232 + 0.0821178i −0.569427 0.822042i \(-0.692835\pi\)
0.427195 + 0.904159i \(0.359502\pi\)
\(984\) 2.57462 + 4.45938i 0.0820760 + 0.142160i
\(985\) −30.2944 11.7170i −0.965259 0.373333i
\(986\) 57.5652 1.83325
\(987\) 0 0
\(988\) 2.85075i 0.0906945i
\(989\) −2.31158 + 4.00378i −0.0735041 + 0.127313i
\(990\) −10.6346 + 8.56726i −0.337990 + 0.272285i
\(991\) −3.40946 5.90536i −0.108305 0.187590i 0.806779 0.590854i \(-0.201209\pi\)
−0.915084 + 0.403264i \(0.867876\pi\)
\(992\) 0.596186 + 0.344208i 0.0189289 + 0.0109286i
\(993\) 23.2797i 0.738761i
\(994\) 0 0
\(995\) 19.0522 2.96817i 0.603994 0.0940972i
\(996\) −6.76304 + 11.7139i −0.214295 + 0.371170i
\(997\) 44.6567 25.7826i 1.41429 0.816543i 0.418504 0.908215i \(-0.362555\pi\)
0.995789 + 0.0916725i \(0.0292213\pi\)
\(998\) 8.12058 4.68842i 0.257052 0.148409i
\(999\) −1.15579 + 2.00189i −0.0365676 + 0.0633370i
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 1470.2.n.j.79.5 12
5.4 even 2 inner 1470.2.n.j.79.3 12
7.2 even 3 1470.2.g.h.589.1 6
7.3 odd 6 210.2.n.b.109.1 yes 12
7.4 even 3 inner 1470.2.n.j.949.3 12
7.5 odd 6 1470.2.g.i.589.3 6
7.6 odd 2 210.2.n.b.79.5 yes 12
21.17 even 6 630.2.u.f.109.6 12
21.20 even 2 630.2.u.f.289.2 12
28.3 even 6 1680.2.di.c.529.4 12
28.27 even 2 1680.2.di.c.289.2 12
35.2 odd 12 7350.2.a.dp.1.3 3
35.3 even 12 1050.2.i.v.151.3 6
35.4 even 6 inner 1470.2.n.j.949.5 12
35.9 even 6 1470.2.g.h.589.4 6
35.12 even 12 7350.2.a.dq.1.3 3
35.13 even 4 1050.2.i.v.751.3 6
35.17 even 12 1050.2.i.u.151.1 6
35.19 odd 6 1470.2.g.i.589.6 6
35.23 odd 12 7350.2.a.do.1.3 3
35.24 odd 6 210.2.n.b.109.5 yes 12
35.27 even 4 1050.2.i.u.751.1 6
35.33 even 12 7350.2.a.dn.1.3 3
35.34 odd 2 210.2.n.b.79.1 12
105.59 even 6 630.2.u.f.109.2 12
105.104 even 2 630.2.u.f.289.6 12
140.59 even 6 1680.2.di.c.529.2 12
140.139 even 2 1680.2.di.c.289.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.b.79.1 12 35.34 odd 2
210.2.n.b.79.5 yes 12 7.6 odd 2
210.2.n.b.109.1 yes 12 7.3 odd 6
210.2.n.b.109.5 yes 12 35.24 odd 6
630.2.u.f.109.2 12 105.59 even 6
630.2.u.f.109.6 12 21.17 even 6
630.2.u.f.289.2 12 21.20 even 2
630.2.u.f.289.6 12 105.104 even 2
1050.2.i.u.151.1 6 35.17 even 12
1050.2.i.u.751.1 6 35.27 even 4
1050.2.i.v.151.3 6 35.3 even 12
1050.2.i.v.751.3 6 35.13 even 4
1470.2.g.h.589.1 6 7.2 even 3
1470.2.g.h.589.4 6 35.9 even 6
1470.2.g.i.589.3 6 7.5 odd 6
1470.2.g.i.589.6 6 35.19 odd 6
1470.2.n.j.79.3 12 5.4 even 2 inner
1470.2.n.j.79.5 12 1.1 even 1 trivial
1470.2.n.j.949.3 12 7.4 even 3 inner
1470.2.n.j.949.5 12 35.4 even 6 inner
1680.2.di.c.289.2 12 28.27 even 2
1680.2.di.c.289.4 12 140.139 even 2
1680.2.di.c.529.2 12 140.59 even 6
1680.2.di.c.529.4 12 28.3 even 6
7350.2.a.dn.1.3 3 35.33 even 12
7350.2.a.do.1.3 3 35.23 odd 12
7350.2.a.dp.1.3 3 35.2 odd 12
7350.2.a.dq.1.3 3 35.12 even 12