Properties

Label 637.2.h.c.165.2
Level $637$
Weight $2$
Character 637.165
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
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] = [637,2,Mod(165,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), 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: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.c.471.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.414214 q^{2} +(0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(-0.914214 - 1.58346i) q^{5} +(0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+0.414214 q^{2} +(0.707107 + 1.22474i) q^{3} -1.82843 q^{4} +(-0.914214 - 1.58346i) q^{5} +(0.292893 + 0.507306i) q^{6} -1.58579 q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.378680 - 0.655892i) q^{10} +(-0.292893 - 0.507306i) q^{11} +(-1.29289 - 2.23936i) q^{12} +(3.50000 + 0.866025i) q^{13} +(1.29289 - 2.23936i) q^{15} +3.00000 q^{16} +5.82843 q^{17} +(0.207107 - 0.358719i) q^{18} +(3.00000 - 5.19615i) q^{19} +(1.67157 + 2.89525i) q^{20} +(-0.121320 - 0.210133i) q^{22} -1.41421 q^{23} +(-1.12132 - 1.94218i) q^{24} +(0.828427 - 1.43488i) q^{25} +(1.44975 + 0.358719i) q^{26} +5.65685 q^{27} +(-2.08579 + 3.61269i) q^{29} +(0.535534 - 0.927572i) q^{30} +(1.29289 - 2.23936i) q^{31} +4.41421 q^{32} +(0.414214 - 0.717439i) q^{33} +2.41421 q^{34} +(-0.914214 + 1.58346i) q^{36} -9.48528 q^{37} +(1.24264 - 2.15232i) q^{38} +(1.41421 + 4.89898i) q^{39} +(1.44975 + 2.51104i) q^{40} +(0.0857864 - 0.148586i) q^{41} +(-1.70711 - 2.95680i) q^{43} +(0.535534 + 0.927572i) q^{44} -1.82843 q^{45} -0.585786 q^{46} +(-1.82843 - 3.16693i) q^{47} +(2.12132 + 3.67423i) q^{48} +(0.343146 - 0.594346i) q^{50} +(4.12132 + 7.13834i) q^{51} +(-6.39949 - 1.58346i) q^{52} +(1.50000 - 2.59808i) q^{53} +2.34315 q^{54} +(-0.535534 + 0.927572i) q^{55} +8.48528 q^{57} +(-0.863961 + 1.49642i) q^{58} +10.2426 q^{59} +(-2.36396 + 4.09450i) q^{60} +(2.08579 - 3.61269i) q^{61} +(0.535534 - 0.927572i) q^{62} -4.17157 q^{64} +(-1.82843 - 6.33386i) q^{65} +(0.171573 - 0.297173i) q^{66} +(-2.12132 - 3.67423i) q^{67} -10.6569 q^{68} +(-1.00000 - 1.73205i) q^{69} +(5.82843 + 10.0951i) q^{71} +(-0.792893 + 1.37333i) q^{72} +(-5.32843 + 9.22911i) q^{73} -3.92893 q^{74} +2.34315 q^{75} +(-5.48528 + 9.50079i) q^{76} +(0.585786 + 2.02922i) q^{78} +(-0.878680 - 1.52192i) q^{79} +(-2.74264 - 4.75039i) q^{80} +(2.50000 + 4.33013i) q^{81} +(0.0355339 - 0.0615465i) q^{82} -1.07107 q^{83} +(-5.32843 - 9.22911i) q^{85} +(-0.707107 - 1.22474i) q^{86} -5.89949 q^{87} +(0.464466 + 0.804479i) q^{88} -15.3137 q^{89} -0.757359 q^{90} +2.58579 q^{92} +3.65685 q^{93} +(-0.757359 - 1.31178i) q^{94} -10.9706 q^{95} +(3.12132 + 5.40629i) q^{96} +(-5.41421 - 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{2} + 4 q^{4} + 2 q^{5} + 4 q^{6} - 12 q^{8} + 2 q^{9} - 10 q^{10} - 4 q^{11} - 8 q^{12} + 14 q^{13} + 8 q^{15} + 12 q^{16} + 12 q^{17} - 2 q^{18} + 12 q^{19} + 18 q^{20} + 8 q^{22} + 4 q^{24} - 8 q^{25} - 14 q^{26} - 14 q^{29} - 12 q^{30} + 8 q^{31} + 12 q^{32} - 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 12 q^{38} - 14 q^{40} + 6 q^{41} - 4 q^{43} - 12 q^{44} + 4 q^{45} - 8 q^{46} + 4 q^{47} + 24 q^{50} + 8 q^{51} + 14 q^{52} + 6 q^{53} + 32 q^{54} + 12 q^{55} + 22 q^{58} + 24 q^{59} + 16 q^{60} + 14 q^{61} - 12 q^{62} - 28 q^{64} + 4 q^{65} + 12 q^{66} - 20 q^{68} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 10 q^{73} - 44 q^{74} + 32 q^{75} + 12 q^{76} + 8 q^{78} - 12 q^{79} + 6 q^{80} + 10 q^{81} - 14 q^{82} + 24 q^{83} - 10 q^{85} + 16 q^{87} + 16 q^{88} - 16 q^{89} - 20 q^{90} + 16 q^{92} - 8 q^{93} - 20 q^{94} + 24 q^{95} + 4 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.414214 0.292893 0.146447 0.989219i \(-0.453216\pi\)
0.146447 + 0.989219i \(0.453216\pi\)
\(3\) 0.707107 + 1.22474i 0.408248 + 0.707107i 0.994694 0.102882i \(-0.0328064\pi\)
−0.586445 + 0.809989i \(0.699473\pi\)
\(4\) −1.82843 −0.914214
\(5\) −0.914214 1.58346i −0.408849 0.708147i 0.585912 0.810374i \(-0.300736\pi\)
−0.994761 + 0.102228i \(0.967403\pi\)
\(6\) 0.292893 + 0.507306i 0.119573 + 0.207107i
\(7\) 0 0
\(8\) −1.58579 −0.560660
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −0.378680 0.655892i −0.119749 0.207411i
\(11\) −0.292893 0.507306i −0.0883106 0.152958i 0.818487 0.574526i \(-0.194813\pi\)
−0.906797 + 0.421567i \(0.861480\pi\)
\(12\) −1.29289 2.23936i −0.373226 0.646447i
\(13\) 3.50000 + 0.866025i 0.970725 + 0.240192i
\(14\) 0 0
\(15\) 1.29289 2.23936i 0.333824 0.578199i
\(16\) 3.00000 0.750000
\(17\) 5.82843 1.41360 0.706801 0.707413i \(-0.250138\pi\)
0.706801 + 0.707413i \(0.250138\pi\)
\(18\) 0.207107 0.358719i 0.0488155 0.0845510i
\(19\) 3.00000 5.19615i 0.688247 1.19208i −0.284157 0.958778i \(-0.591714\pi\)
0.972404 0.233301i \(-0.0749529\pi\)
\(20\) 1.67157 + 2.89525i 0.373775 + 0.647397i
\(21\) 0 0
\(22\) −0.121320 0.210133i −0.0258656 0.0448005i
\(23\) −1.41421 −0.294884 −0.147442 0.989071i \(-0.547104\pi\)
−0.147442 + 0.989071i \(0.547104\pi\)
\(24\) −1.12132 1.94218i −0.228889 0.396447i
\(25\) 0.828427 1.43488i 0.165685 0.286976i
\(26\) 1.44975 + 0.358719i 0.284319 + 0.0703507i
\(27\) 5.65685 1.08866
\(28\) 0 0
\(29\) −2.08579 + 3.61269i −0.387321 + 0.670859i −0.992088 0.125543i \(-0.959933\pi\)
0.604767 + 0.796402i \(0.293266\pi\)
\(30\) 0.535534 0.927572i 0.0977747 0.169351i
\(31\) 1.29289 2.23936i 0.232210 0.402200i −0.726248 0.687433i \(-0.758738\pi\)
0.958458 + 0.285233i \(0.0920709\pi\)
\(32\) 4.41421 0.780330
\(33\) 0.414214 0.717439i 0.0721053 0.124890i
\(34\) 2.41421 0.414034
\(35\) 0 0
\(36\) −0.914214 + 1.58346i −0.152369 + 0.263911i
\(37\) −9.48528 −1.55937 −0.779685 0.626172i \(-0.784621\pi\)
−0.779685 + 0.626172i \(0.784621\pi\)
\(38\) 1.24264 2.15232i 0.201583 0.349152i
\(39\) 1.41421 + 4.89898i 0.226455 + 0.784465i
\(40\) 1.44975 + 2.51104i 0.229225 + 0.397030i
\(41\) 0.0857864 0.148586i 0.0133976 0.0232053i −0.859249 0.511558i \(-0.829069\pi\)
0.872646 + 0.488352i \(0.162402\pi\)
\(42\) 0 0
\(43\) −1.70711 2.95680i −0.260331 0.450907i 0.705999 0.708213i \(-0.250498\pi\)
−0.966330 + 0.257306i \(0.917165\pi\)
\(44\) 0.535534 + 0.927572i 0.0807348 + 0.139837i
\(45\) −1.82843 −0.272566
\(46\) −0.585786 −0.0863695
\(47\) −1.82843 3.16693i −0.266704 0.461944i 0.701305 0.712861i \(-0.252601\pi\)
−0.968009 + 0.250917i \(0.919268\pi\)
\(48\) 2.12132 + 3.67423i 0.306186 + 0.530330i
\(49\) 0 0
\(50\) 0.343146 0.594346i 0.0485281 0.0840532i
\(51\) 4.12132 + 7.13834i 0.577100 + 0.999567i
\(52\) −6.39949 1.58346i −0.887450 0.219587i
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 2.34315 0.318862
\(55\) −0.535534 + 0.927572i −0.0722114 + 0.125074i
\(56\) 0 0
\(57\) 8.48528 1.12390
\(58\) −0.863961 + 1.49642i −0.113444 + 0.196490i
\(59\) 10.2426 1.33348 0.666739 0.745291i \(-0.267690\pi\)
0.666739 + 0.745291i \(0.267690\pi\)
\(60\) −2.36396 + 4.09450i −0.305186 + 0.528598i
\(61\) 2.08579 3.61269i 0.267058 0.462557i −0.701043 0.713119i \(-0.747282\pi\)
0.968101 + 0.250562i \(0.0806153\pi\)
\(62\) 0.535534 0.927572i 0.0680129 0.117802i
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) −1.82843 6.33386i −0.226788 0.785618i
\(66\) 0.171573 0.297173i 0.0211192 0.0365795i
\(67\) −2.12132 3.67423i −0.259161 0.448879i 0.706857 0.707357i \(-0.250113\pi\)
−0.966017 + 0.258478i \(0.916779\pi\)
\(68\) −10.6569 −1.29233
\(69\) −1.00000 1.73205i −0.120386 0.208514i
\(70\) 0 0
\(71\) 5.82843 + 10.0951i 0.691707 + 1.19807i 0.971278 + 0.237947i \(0.0764744\pi\)
−0.279571 + 0.960125i \(0.590192\pi\)
\(72\) −0.792893 + 1.37333i −0.0934434 + 0.161849i
\(73\) −5.32843 + 9.22911i −0.623645 + 1.08019i 0.365156 + 0.930946i \(0.381016\pi\)
−0.988801 + 0.149239i \(0.952318\pi\)
\(74\) −3.92893 −0.456729
\(75\) 2.34315 0.270563
\(76\) −5.48528 + 9.50079i −0.629205 + 1.08981i
\(77\) 0 0
\(78\) 0.585786 + 2.02922i 0.0663273 + 0.229764i
\(79\) −0.878680 1.52192i −0.0988592 0.171229i 0.812354 0.583165i \(-0.198186\pi\)
−0.911213 + 0.411936i \(0.864853\pi\)
\(80\) −2.74264 4.75039i −0.306637 0.531110i
\(81\) 2.50000 + 4.33013i 0.277778 + 0.481125i
\(82\) 0.0355339 0.0615465i 0.00392406 0.00679668i
\(83\) −1.07107 −0.117565 −0.0587825 0.998271i \(-0.518722\pi\)
−0.0587825 + 0.998271i \(0.518722\pi\)
\(84\) 0 0
\(85\) −5.32843 9.22911i −0.577949 1.00104i
\(86\) −0.707107 1.22474i −0.0762493 0.132068i
\(87\) −5.89949 −0.632492
\(88\) 0.464466 + 0.804479i 0.0495123 + 0.0857577i
\(89\) −15.3137 −1.62325 −0.811625 0.584179i \(-0.801417\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(90\) −0.757359 −0.0798327
\(91\) 0 0
\(92\) 2.58579 0.269587
\(93\) 3.65685 0.379198
\(94\) −0.757359 1.31178i −0.0781156 0.135300i
\(95\) −10.9706 −1.12556
\(96\) 3.12132 + 5.40629i 0.318568 + 0.551777i
\(97\) −5.41421 9.37769i −0.549730 0.952160i −0.998293 0.0584091i \(-0.981397\pi\)
0.448563 0.893751i \(-0.351936\pi\)
\(98\) 0 0
\(99\) −0.585786 −0.0588738
\(100\) −1.51472 + 2.62357i −0.151472 + 0.262357i
\(101\) 7.32843 + 12.6932i 0.729206 + 1.26302i 0.957219 + 0.289363i \(0.0934436\pi\)
−0.228014 + 0.973658i \(0.573223\pi\)
\(102\) 1.70711 + 2.95680i 0.169029 + 0.292766i
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) −5.55025 1.37333i −0.544247 0.134666i
\(105\) 0 0
\(106\) 0.621320 1.07616i 0.0603480 0.104526i
\(107\) 17.3137 1.67378 0.836890 0.547372i \(-0.184372\pi\)
0.836890 + 0.547372i \(0.184372\pi\)
\(108\) −10.3431 −0.995270
\(109\) 6.82843 11.8272i 0.654045 1.13284i −0.328088 0.944647i \(-0.606404\pi\)
0.982132 0.188191i \(-0.0602625\pi\)
\(110\) −0.221825 + 0.384213i −0.0211502 + 0.0366333i
\(111\) −6.70711 11.6170i −0.636610 1.10264i
\(112\) 0 0
\(113\) −10.1569 17.5922i −0.955476 1.65493i −0.733274 0.679933i \(-0.762009\pi\)
−0.222202 0.975001i \(-0.571325\pi\)
\(114\) 3.51472 0.329184
\(115\) 1.29289 + 2.23936i 0.120563 + 0.208821i
\(116\) 3.81371 6.60554i 0.354094 0.613309i
\(117\) 2.50000 2.59808i 0.231125 0.240192i
\(118\) 4.24264 0.390567
\(119\) 0 0
\(120\) −2.05025 + 3.55114i −0.187162 + 0.324173i
\(121\) 5.32843 9.22911i 0.484402 0.839010i
\(122\) 0.863961 1.49642i 0.0782194 0.135480i
\(123\) 0.242641 0.0218782
\(124\) −2.36396 + 4.09450i −0.212290 + 0.367697i
\(125\) −12.1716 −1.08866
\(126\) 0 0
\(127\) −6.65685 + 11.5300i −0.590700 + 1.02312i 0.403438 + 0.915007i \(0.367815\pi\)
−0.994138 + 0.108116i \(0.965518\pi\)
\(128\) −10.5563 −0.933058
\(129\) 2.41421 4.18154i 0.212560 0.368164i
\(130\) −0.757359 2.62357i −0.0664248 0.230102i
\(131\) 10.6569 + 18.4582i 0.931094 + 1.61270i 0.781456 + 0.623961i \(0.214477\pi\)
0.149638 + 0.988741i \(0.452189\pi\)
\(132\) −0.757359 + 1.31178i −0.0659197 + 0.114176i
\(133\) 0 0
\(134\) −0.878680 1.52192i −0.0759064 0.131474i
\(135\) −5.17157 8.95743i −0.445098 0.770933i
\(136\) −9.24264 −0.792550
\(137\) −0.171573 −0.0146585 −0.00732923 0.999973i \(-0.502333\pi\)
−0.00732923 + 0.999973i \(0.502333\pi\)
\(138\) −0.414214 0.717439i −0.0352602 0.0610725i
\(139\) −5.94975 10.3053i −0.504651 0.874081i −0.999986 0.00537886i \(-0.998288\pi\)
0.495335 0.868702i \(-0.335045\pi\)
\(140\) 0 0
\(141\) 2.58579 4.47871i 0.217763 0.377176i
\(142\) 2.41421 + 4.18154i 0.202596 + 0.350907i
\(143\) −0.585786 2.02922i −0.0489859 0.169692i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) 7.62742 0.633423
\(146\) −2.20711 + 3.82282i −0.182661 + 0.316379i
\(147\) 0 0
\(148\) 17.3431 1.42560
\(149\) −1.50000 + 2.59808i −0.122885 + 0.212843i −0.920904 0.389789i \(-0.872548\pi\)
0.798019 + 0.602632i \(0.205881\pi\)
\(150\) 0.970563 0.0792461
\(151\) −7.48528 + 12.9649i −0.609144 + 1.05507i 0.382238 + 0.924064i \(0.375153\pi\)
−0.991382 + 0.131004i \(0.958180\pi\)
\(152\) −4.75736 + 8.23999i −0.385873 + 0.668351i
\(153\) 2.91421 5.04757i 0.235600 0.408072i
\(154\) 0 0
\(155\) −4.72792 −0.379756
\(156\) −2.58579 8.95743i −0.207029 0.717168i
\(157\) 2.74264 4.75039i 0.218887 0.379123i −0.735581 0.677436i \(-0.763091\pi\)
0.954468 + 0.298314i \(0.0964242\pi\)
\(158\) −0.363961 0.630399i −0.0289552 0.0501519i
\(159\) 4.24264 0.336463
\(160\) −4.03553 6.98975i −0.319037 0.552588i
\(161\) 0 0
\(162\) 1.03553 + 1.79360i 0.0813592 + 0.140918i
\(163\) −6.29289 + 10.8996i −0.492897 + 0.853723i −0.999967 0.00818201i \(-0.997396\pi\)
0.507069 + 0.861905i \(0.330729\pi\)
\(164\) −0.156854 + 0.271680i −0.0122483 + 0.0212146i
\(165\) −1.51472 −0.117921
\(166\) −0.443651 −0.0344340
\(167\) 3.36396 5.82655i 0.260311 0.450872i −0.706013 0.708198i \(-0.749508\pi\)
0.966325 + 0.257326i \(0.0828415\pi\)
\(168\) 0 0
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) −2.20711 3.82282i −0.169277 0.293197i
\(171\) −3.00000 5.19615i −0.229416 0.397360i
\(172\) 3.12132 + 5.40629i 0.237998 + 0.412225i
\(173\) −5.07107 + 8.78335i −0.385546 + 0.667786i −0.991845 0.127452i \(-0.959320\pi\)
0.606299 + 0.795237i \(0.292654\pi\)
\(174\) −2.44365 −0.185253
\(175\) 0 0
\(176\) −0.878680 1.52192i −0.0662330 0.114719i
\(177\) 7.24264 + 12.5446i 0.544390 + 0.942912i
\(178\) −6.34315 −0.475439
\(179\) 2.82843 + 4.89898i 0.211407 + 0.366167i 0.952155 0.305616i \(-0.0988623\pi\)
−0.740748 + 0.671783i \(0.765529\pi\)
\(180\) 3.34315 0.249183
\(181\) −9.14214 −0.679530 −0.339765 0.940510i \(-0.610347\pi\)
−0.339765 + 0.940510i \(0.610347\pi\)
\(182\) 0 0
\(183\) 5.89949 0.436103
\(184\) 2.24264 0.165330
\(185\) 8.67157 + 15.0196i 0.637547 + 1.10426i
\(186\) 1.51472 0.111065
\(187\) −1.70711 2.95680i −0.124836 0.216222i
\(188\) 3.34315 + 5.79050i 0.243824 + 0.422315i
\(189\) 0 0
\(190\) −4.54416 −0.329668
\(191\) −8.12132 + 14.0665i −0.587638 + 1.01782i 0.406903 + 0.913471i \(0.366609\pi\)
−0.994541 + 0.104348i \(0.966725\pi\)
\(192\) −2.94975 5.10911i −0.212880 0.368718i
\(193\) −3.57107 6.18527i −0.257051 0.445226i 0.708400 0.705812i \(-0.249418\pi\)
−0.965451 + 0.260586i \(0.916084\pi\)
\(194\) −2.24264 3.88437i −0.161012 0.278881i
\(195\) 6.46447 6.71807i 0.462930 0.481091i
\(196\) 0 0
\(197\) −7.41421 + 12.8418i −0.528241 + 0.914940i 0.471217 + 0.882017i \(0.343815\pi\)
−0.999458 + 0.0329227i \(0.989518\pi\)
\(198\) −0.242641 −0.0172437
\(199\) 14.9706 1.06124 0.530618 0.847611i \(-0.321960\pi\)
0.530618 + 0.847611i \(0.321960\pi\)
\(200\) −1.31371 + 2.27541i −0.0928932 + 0.160896i
\(201\) 3.00000 5.19615i 0.211604 0.366508i
\(202\) 3.03553 + 5.25770i 0.213579 + 0.369930i
\(203\) 0 0
\(204\) −7.53553 13.0519i −0.527593 0.913818i
\(205\) −0.313708 −0.0219104
\(206\) 2.89949 + 5.02207i 0.202017 + 0.349904i
\(207\) −0.707107 + 1.22474i −0.0491473 + 0.0851257i
\(208\) 10.5000 + 2.59808i 0.728044 + 0.180144i
\(209\) −3.51472 −0.243118
\(210\) 0 0
\(211\) −12.3640 + 21.4150i −0.851170 + 1.47427i 0.0289828 + 0.999580i \(0.490773\pi\)
−0.880153 + 0.474690i \(0.842560\pi\)
\(212\) −2.74264 + 4.75039i −0.188365 + 0.326258i
\(213\) −8.24264 + 14.2767i −0.564776 + 0.978221i
\(214\) 7.17157 0.490239
\(215\) −3.12132 + 5.40629i −0.212872 + 0.368706i
\(216\) −8.97056 −0.610369
\(217\) 0 0
\(218\) 2.82843 4.89898i 0.191565 0.331801i
\(219\) −15.0711 −1.01841
\(220\) 0.979185 1.69600i 0.0660166 0.114344i
\(221\) 20.3995 + 5.04757i 1.37222 + 0.339536i
\(222\) −2.77817 4.81194i −0.186459 0.322956i
\(223\) 1.00000 1.73205i 0.0669650 0.115987i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440884i \(0.145335\pi\)
\(224\) 0 0
\(225\) −0.828427 1.43488i −0.0552285 0.0956585i
\(226\) −4.20711 7.28692i −0.279853 0.484719i
\(227\) −5.89949 −0.391563 −0.195782 0.980648i \(-0.562724\pi\)
−0.195782 + 0.980648i \(0.562724\pi\)
\(228\) −15.5147 −1.02749
\(229\) −6.24264 10.8126i −0.412525 0.714515i 0.582640 0.812730i \(-0.302020\pi\)
−0.995165 + 0.0982157i \(0.968686\pi\)
\(230\) 0.535534 + 0.927572i 0.0353121 + 0.0611623i
\(231\) 0 0
\(232\) 3.30761 5.72895i 0.217155 0.376124i
\(233\) −1.41421 2.44949i −0.0926482 0.160471i 0.815976 0.578085i \(-0.196200\pi\)
−0.908625 + 0.417614i \(0.862867\pi\)
\(234\) 1.03553 1.07616i 0.0676950 0.0703507i
\(235\) −3.34315 + 5.79050i −0.218083 + 0.377730i
\(236\) −18.7279 −1.21908
\(237\) 1.24264 2.15232i 0.0807182 0.139808i
\(238\) 0 0
\(239\) 24.3848 1.57732 0.788660 0.614830i \(-0.210775\pi\)
0.788660 + 0.614830i \(0.210775\pi\)
\(240\) 3.87868 6.71807i 0.250368 0.433650i
\(241\) −15.4853 −0.997495 −0.498747 0.866747i \(-0.666206\pi\)
−0.498747 + 0.866747i \(0.666206\pi\)
\(242\) 2.20711 3.82282i 0.141878 0.245740i
\(243\) 4.94975 8.57321i 0.317526 0.549972i
\(244\) −3.81371 + 6.60554i −0.244148 + 0.422876i
\(245\) 0 0
\(246\) 0.100505 0.00640797
\(247\) 15.0000 15.5885i 0.954427 0.991870i
\(248\) −2.05025 + 3.55114i −0.130191 + 0.225498i
\(249\) −0.757359 1.31178i −0.0479957 0.0831310i
\(250\) −5.04163 −0.318861
\(251\) 11.4853 + 19.8931i 0.724945 + 1.25564i 0.958997 + 0.283417i \(0.0914680\pi\)
−0.234052 + 0.972224i \(0.575199\pi\)
\(252\) 0 0
\(253\) 0.414214 + 0.717439i 0.0260414 + 0.0451050i
\(254\) −2.75736 + 4.77589i −0.173012 + 0.299666i
\(255\) 7.53553 13.0519i 0.471893 0.817343i
\(256\) 3.97056 0.248160
\(257\) −15.0000 −0.935674 −0.467837 0.883815i \(-0.654967\pi\)
−0.467837 + 0.883815i \(0.654967\pi\)
\(258\) 1.00000 1.73205i 0.0622573 0.107833i
\(259\) 0 0
\(260\) 3.34315 + 11.5810i 0.207333 + 0.718223i
\(261\) 2.08579 + 3.61269i 0.129107 + 0.223620i
\(262\) 4.41421 + 7.64564i 0.272711 + 0.472349i
\(263\) 3.36396 + 5.82655i 0.207431 + 0.359281i 0.950904 0.309485i \(-0.100157\pi\)
−0.743474 + 0.668765i \(0.766823\pi\)
\(264\) −0.656854 + 1.13770i −0.0404266 + 0.0700209i
\(265\) −5.48528 −0.336958
\(266\) 0 0
\(267\) −10.8284 18.7554i −0.662689 1.14781i
\(268\) 3.87868 + 6.71807i 0.236928 + 0.410371i
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −2.14214 3.71029i −0.130366 0.225801i
\(271\) 21.0711 1.27998 0.639988 0.768385i \(-0.278939\pi\)
0.639988 + 0.768385i \(0.278939\pi\)
\(272\) 17.4853 1.06020
\(273\) 0 0
\(274\) −0.0710678 −0.00429336
\(275\) −0.970563 −0.0585271
\(276\) 1.82843 + 3.16693i 0.110058 + 0.190627i
\(277\) 1.97056 0.118400 0.0591998 0.998246i \(-0.481145\pi\)
0.0591998 + 0.998246i \(0.481145\pi\)
\(278\) −2.46447 4.26858i −0.147809 0.256012i
\(279\) −1.29289 2.23936i −0.0774035 0.134067i
\(280\) 0 0
\(281\) −17.4853 −1.04308 −0.521542 0.853225i \(-0.674643\pi\)
−0.521542 + 0.853225i \(0.674643\pi\)
\(282\) 1.07107 1.85514i 0.0637812 0.110472i
\(283\) −9.94975 17.2335i −0.591451 1.02442i −0.994037 0.109041i \(-0.965222\pi\)
0.402586 0.915382i \(-0.368111\pi\)
\(284\) −10.6569 18.4582i −0.632368 1.09529i
\(285\) −7.75736 13.4361i −0.459506 0.795888i
\(286\) −0.242641 0.840532i −0.0143476 0.0497017i
\(287\) 0 0
\(288\) 2.20711 3.82282i 0.130055 0.225262i
\(289\) 16.9706 0.998268
\(290\) 3.15938 0.185525
\(291\) 7.65685 13.2621i 0.448853 0.777436i
\(292\) 9.74264 16.8747i 0.570145 0.987520i
\(293\) 14.2279 + 24.6435i 0.831204 + 1.43969i 0.897084 + 0.441860i \(0.145681\pi\)
−0.0658799 + 0.997828i \(0.520985\pi\)
\(294\) 0 0
\(295\) −9.36396 16.2189i −0.545191 0.944298i
\(296\) 15.0416 0.874277
\(297\) −1.65685 2.86976i −0.0961404 0.166520i
\(298\) −0.621320 + 1.07616i −0.0359921 + 0.0623402i
\(299\) −4.94975 1.22474i −0.286251 0.0708288i
\(300\) −4.28427 −0.247353
\(301\) 0 0
\(302\) −3.10051 + 5.37023i −0.178414 + 0.309022i
\(303\) −10.3640 + 17.9509i −0.595394 + 1.03125i
\(304\) 9.00000 15.5885i 0.516185 0.894059i
\(305\) −7.62742 −0.436745
\(306\) 1.20711 2.09077i 0.0690057 0.119521i
\(307\) 32.7279 1.86788 0.933941 0.357428i \(-0.116346\pi\)
0.933941 + 0.357428i \(0.116346\pi\)
\(308\) 0 0
\(309\) −9.89949 + 17.1464i −0.563163 + 0.975426i
\(310\) −1.95837 −0.111228
\(311\) −6.46447 + 11.1968i −0.366566 + 0.634911i −0.989026 0.147740i \(-0.952800\pi\)
0.622460 + 0.782652i \(0.286133\pi\)
\(312\) −2.24264 7.76874i −0.126965 0.439818i
\(313\) −7.00000 12.1244i −0.395663 0.685309i 0.597522 0.801852i \(-0.296152\pi\)
−0.993186 + 0.116543i \(0.962819\pi\)
\(314\) 1.13604 1.96768i 0.0641104 0.111042i
\(315\) 0 0
\(316\) 1.60660 + 2.78272i 0.0903784 + 0.156540i
\(317\) −16.3284 28.2817i −0.917096 1.58846i −0.803804 0.594895i \(-0.797194\pi\)
−0.113292 0.993562i \(-0.536140\pi\)
\(318\) 1.75736 0.0985478
\(319\) 2.44365 0.136818
\(320\) 3.81371 + 6.60554i 0.213193 + 0.369261i
\(321\) 12.2426 + 21.2049i 0.683318 + 1.18354i
\(322\) 0 0
\(323\) 17.4853 30.2854i 0.972907 1.68512i
\(324\) −4.57107 7.91732i −0.253948 0.439851i
\(325\) 4.14214 4.30463i 0.229764 0.238778i
\(326\) −2.60660 + 4.51477i −0.144366 + 0.250050i
\(327\) 19.3137 1.06805
\(328\) −0.136039 + 0.235626i −0.00751150 + 0.0130103i
\(329\) 0 0
\(330\) −0.627417 −0.0345382
\(331\) 12.4350 21.5381i 0.683491 1.18384i −0.290417 0.956900i \(-0.593794\pi\)
0.973908 0.226941i \(-0.0728725\pi\)
\(332\) 1.95837 0.107479
\(333\) −4.74264 + 8.21449i −0.259895 + 0.450152i
\(334\) 1.39340 2.41344i 0.0762434 0.132057i
\(335\) −3.87868 + 6.71807i −0.211915 + 0.367047i
\(336\) 0 0
\(337\) −3.48528 −0.189855 −0.0949277 0.995484i \(-0.530262\pi\)
−0.0949277 + 0.995484i \(0.530262\pi\)
\(338\) 4.76346 + 2.51104i 0.259098 + 0.136582i
\(339\) 14.3640 24.8791i 0.780143 1.35125i
\(340\) 9.74264 + 16.8747i 0.528369 + 0.915162i
\(341\) −1.51472 −0.0820266
\(342\) −1.24264 2.15232i −0.0671943 0.116384i
\(343\) 0 0
\(344\) 2.70711 + 4.68885i 0.145957 + 0.252806i
\(345\) −1.82843 + 3.16693i −0.0984392 + 0.170502i
\(346\) −2.10051 + 3.63818i −0.112924 + 0.195590i
\(347\) −6.10051 −0.327492 −0.163746 0.986503i \(-0.552358\pi\)
−0.163746 + 0.986503i \(0.552358\pi\)
\(348\) 10.7868 0.578233
\(349\) 4.65685 8.06591i 0.249276 0.431758i −0.714049 0.700095i \(-0.753141\pi\)
0.963325 + 0.268337i \(0.0864741\pi\)
\(350\) 0 0
\(351\) 19.7990 + 4.89898i 1.05679 + 0.261488i
\(352\) −1.29289 2.23936i −0.0689114 0.119358i
\(353\) 2.91421 + 5.04757i 0.155108 + 0.268655i 0.933098 0.359621i \(-0.117094\pi\)
−0.777990 + 0.628276i \(0.783761\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) 10.6569 18.4582i 0.565607 0.979660i
\(356\) 28.0000 1.48400
\(357\) 0 0
\(358\) 1.17157 + 2.02922i 0.0619196 + 0.107248i
\(359\) 8.48528 + 14.6969i 0.447836 + 0.775675i 0.998245 0.0592205i \(-0.0188615\pi\)
−0.550409 + 0.834895i \(0.685528\pi\)
\(360\) 2.89949 0.152817
\(361\) −8.50000 14.7224i −0.447368 0.774865i
\(362\) −3.78680 −0.199030
\(363\) 15.0711 0.791026
\(364\) 0 0
\(365\) 19.4853 1.01991
\(366\) 2.44365 0.127732
\(367\) −14.3640 24.8791i −0.749793 1.29868i −0.947922 0.318503i \(-0.896820\pi\)
0.198129 0.980176i \(-0.436513\pi\)
\(368\) −4.24264 −0.221163
\(369\) −0.0857864 0.148586i −0.00446586 0.00773510i
\(370\) 3.59188 + 6.22132i 0.186733 + 0.323431i
\(371\) 0 0
\(372\) −6.68629 −0.346668
\(373\) −13.2279 + 22.9114i −0.684916 + 1.18631i 0.288547 + 0.957466i \(0.406828\pi\)
−0.973463 + 0.228843i \(0.926506\pi\)
\(374\) −0.707107 1.22474i −0.0365636 0.0633300i
\(375\) −8.60660 14.9071i −0.444443 0.769798i
\(376\) 2.89949 + 5.02207i 0.149530 + 0.258994i
\(377\) −10.4289 + 10.8381i −0.537117 + 0.558189i
\(378\) 0 0
\(379\) 0.121320 0.210133i 0.00623181 0.0107938i −0.862893 0.505387i \(-0.831350\pi\)
0.869124 + 0.494593i \(0.164683\pi\)
\(380\) 20.0589 1.02900
\(381\) −18.8284 −0.964610
\(382\) −3.36396 + 5.82655i −0.172115 + 0.298112i
\(383\) −17.0208 + 29.4809i −0.869723 + 1.50640i −0.00744324 + 0.999972i \(0.502369\pi\)
−0.862280 + 0.506432i \(0.830964\pi\)
\(384\) −7.46447 12.9288i −0.380919 0.659772i
\(385\) 0 0
\(386\) −1.47918 2.56202i −0.0752885 0.130404i
\(387\) −3.41421 −0.173554
\(388\) 9.89949 + 17.1464i 0.502571 + 0.870478i
\(389\) −13.5711 + 23.5058i −0.688080 + 1.19179i 0.284378 + 0.958712i \(0.408213\pi\)
−0.972458 + 0.233078i \(0.925120\pi\)
\(390\) 2.67767 2.78272i 0.135589 0.140908i
\(391\) −8.24264 −0.416848
\(392\) 0 0
\(393\) −15.0711 + 26.1039i −0.760235 + 1.31677i
\(394\) −3.07107 + 5.31925i −0.154718 + 0.267980i
\(395\) −1.60660 + 2.78272i −0.0808369 + 0.140014i
\(396\) 1.07107 0.0538232
\(397\) 3.31371 5.73951i 0.166310 0.288058i −0.770810 0.637066i \(-0.780148\pi\)
0.937120 + 0.349008i \(0.113481\pi\)
\(398\) 6.20101 0.310829
\(399\) 0 0
\(400\) 2.48528 4.30463i 0.124264 0.215232i
\(401\) 8.79899 0.439401 0.219700 0.975567i \(-0.429492\pi\)
0.219700 + 0.975567i \(0.429492\pi\)
\(402\) 1.24264 2.15232i 0.0619773 0.107348i
\(403\) 6.46447 6.71807i 0.322018 0.334651i
\(404\) −13.3995 23.2086i −0.666650 1.15467i
\(405\) 4.57107 7.91732i 0.227138 0.393415i
\(406\) 0 0
\(407\) 2.77817 + 4.81194i 0.137709 + 0.238519i
\(408\) −6.53553 11.3199i −0.323557 0.560417i
\(409\) 21.9706 1.08637 0.543187 0.839612i \(-0.317217\pi\)
0.543187 + 0.839612i \(0.317217\pi\)
\(410\) −0.129942 −0.00641739
\(411\) −0.121320 0.210133i −0.00598429 0.0103651i
\(412\) −12.7990 22.1685i −0.630561 1.09216i
\(413\) 0 0
\(414\) −0.292893 + 0.507306i −0.0143949 + 0.0249327i
\(415\) 0.979185 + 1.69600i 0.0480663 + 0.0832533i
\(416\) 15.4497 + 3.82282i 0.757486 + 0.187429i
\(417\) 8.41421 14.5738i 0.412046 0.713684i
\(418\) −1.45584 −0.0712077
\(419\) −5.77817 + 10.0081i −0.282282 + 0.488927i −0.971946 0.235202i \(-0.924425\pi\)
0.689664 + 0.724129i \(0.257758\pi\)
\(420\) 0 0
\(421\) 21.4853 1.04713 0.523564 0.851986i \(-0.324602\pi\)
0.523564 + 0.851986i \(0.324602\pi\)
\(422\) −5.12132 + 8.87039i −0.249302 + 0.431804i
\(423\) −3.65685 −0.177802
\(424\) −2.37868 + 4.11999i −0.115519 + 0.200085i
\(425\) 4.82843 8.36308i 0.234213 0.405669i
\(426\) −3.41421 + 5.91359i −0.165419 + 0.286514i
\(427\) 0 0
\(428\) −31.6569 −1.53019
\(429\) 2.07107 2.15232i 0.0999921 0.103915i
\(430\) −1.29289 + 2.23936i −0.0623488 + 0.107991i
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 16.9706 0.816497
\(433\) 8.74264 + 15.1427i 0.420144 + 0.727712i 0.995953 0.0898728i \(-0.0286461\pi\)
−0.575809 + 0.817584i \(0.695313\pi\)
\(434\) 0 0
\(435\) 5.39340 + 9.34164i 0.258594 + 0.447897i
\(436\) −12.4853 + 21.6251i −0.597937 + 1.03566i
\(437\) −4.24264 + 7.34847i −0.202953 + 0.351525i
\(438\) −6.24264 −0.298285
\(439\) 1.27208 0.0607130 0.0303565 0.999539i \(-0.490336\pi\)
0.0303565 + 0.999539i \(0.490336\pi\)
\(440\) 0.849242 1.47093i 0.0404860 0.0701239i
\(441\) 0 0
\(442\) 8.44975 + 2.09077i 0.401914 + 0.0994478i
\(443\) −12.8284 22.2195i −0.609497 1.05568i −0.991323 0.131446i \(-0.958038\pi\)
0.381826 0.924234i \(-0.375295\pi\)
\(444\) 12.2635 + 21.2409i 0.581998 + 1.00805i
\(445\) 14.0000 + 24.2487i 0.663664 + 1.14950i
\(446\) 0.414214 0.717439i 0.0196136 0.0339717i
\(447\) −4.24264 −0.200670
\(448\) 0 0
\(449\) −16.2426 28.1331i −0.766538 1.32768i −0.939430 0.342741i \(-0.888645\pi\)
0.172892 0.984941i \(-0.444689\pi\)
\(450\) −0.343146 0.594346i −0.0161760 0.0280177i
\(451\) −0.100505 −0.00473260
\(452\) 18.5711 + 32.1660i 0.873510 + 1.51296i
\(453\) −21.1716 −0.994727
\(454\) −2.44365 −0.114686
\(455\) 0 0
\(456\) −13.4558 −0.630128
\(457\) −25.0000 −1.16945 −0.584725 0.811231i \(-0.698798\pi\)
−0.584725 + 0.811231i \(0.698798\pi\)
\(458\) −2.58579 4.47871i −0.120826 0.209277i
\(459\) 32.9706 1.53893
\(460\) −2.36396 4.09450i −0.110220 0.190907i
\(461\) 0.671573 + 1.16320i 0.0312783 + 0.0541755i 0.881241 0.472668i \(-0.156709\pi\)
−0.849963 + 0.526843i \(0.823376\pi\)
\(462\) 0 0
\(463\) 6.72792 0.312673 0.156337 0.987704i \(-0.450032\pi\)
0.156337 + 0.987704i \(0.450032\pi\)
\(464\) −6.25736 + 10.8381i −0.290491 + 0.503145i
\(465\) −3.34315 5.79050i −0.155035 0.268528i
\(466\) −0.585786 1.01461i −0.0271360 0.0470010i
\(467\) 5.70711 + 9.88500i 0.264093 + 0.457423i 0.967326 0.253537i \(-0.0815939\pi\)
−0.703232 + 0.710960i \(0.748261\pi\)
\(468\) −4.57107 + 4.75039i −0.211298 + 0.219587i
\(469\) 0 0
\(470\) −1.38478 + 2.39850i −0.0638750 + 0.110635i
\(471\) 7.75736 0.357440
\(472\) −16.2426 −0.747628
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0.514719 0.891519i 0.0236418 0.0409488i
\(475\) −4.97056 8.60927i −0.228065 0.395020i
\(476\) 0 0
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) 10.1005 0.461986
\(479\) −0.807612 1.39882i −0.0369007 0.0639139i 0.846985 0.531616i \(-0.178415\pi\)
−0.883886 + 0.467703i \(0.845082\pi\)
\(480\) 5.70711 9.88500i 0.260493 0.451186i
\(481\) −33.1985 8.21449i −1.51372 0.374549i
\(482\) −6.41421 −0.292159
\(483\) 0 0
\(484\) −9.74264 + 16.8747i −0.442847 + 0.767034i
\(485\) −9.89949 + 17.1464i −0.449513 + 0.778579i
\(486\) 2.05025 3.55114i 0.0930013 0.161083i
\(487\) −12.9706 −0.587752 −0.293876 0.955844i \(-0.594945\pi\)
−0.293876 + 0.955844i \(0.594945\pi\)
\(488\) −3.30761 + 5.72895i −0.149729 + 0.259337i
\(489\) −17.7990 −0.804898
\(490\) 0 0
\(491\) −6.34315 + 10.9867i −0.286262 + 0.495821i −0.972914 0.231165i \(-0.925746\pi\)
0.686652 + 0.726986i \(0.259079\pi\)
\(492\) −0.443651 −0.0200013
\(493\) −12.1569 + 21.0563i −0.547517 + 0.948328i
\(494\) 6.21320 6.45695i 0.279545 0.290512i
\(495\) 0.535534 + 0.927572i 0.0240705 + 0.0416913i
\(496\) 3.87868 6.71807i 0.174158 0.301650i
\(497\) 0 0
\(498\) −0.313708 0.543359i −0.0140576 0.0243485i
\(499\) −10.0208 17.3566i −0.448593 0.776986i 0.549701 0.835361i \(-0.314741\pi\)
−0.998295 + 0.0583748i \(0.981408\pi\)
\(500\) 22.2548 0.995266
\(501\) 9.51472 0.425086
\(502\) 4.75736 + 8.23999i 0.212331 + 0.367769i
\(503\) −1.22183 2.11626i −0.0544785 0.0943595i 0.837500 0.546437i \(-0.184016\pi\)
−0.891979 + 0.452078i \(0.850683\pi\)
\(504\) 0 0
\(505\) 13.3995 23.2086i 0.596270 1.03277i
\(506\) 0.171573 + 0.297173i 0.00762734 + 0.0132109i
\(507\) 0.707107 + 18.3712i 0.0314037 + 0.815892i
\(508\) 12.1716 21.0818i 0.540026 0.935353i
\(509\) −4.65685 −0.206411 −0.103206 0.994660i \(-0.532910\pi\)
−0.103206 + 0.994660i \(0.532910\pi\)
\(510\) 3.12132 5.40629i 0.138214 0.239394i
\(511\) 0 0
\(512\) 22.7574 1.00574
\(513\) 16.9706 29.3939i 0.749269 1.29777i
\(514\) −6.21320 −0.274053
\(515\) 12.7990 22.1685i 0.563991 0.976861i
\(516\) −4.41421 + 7.64564i −0.194325 + 0.336581i
\(517\) −1.07107 + 1.85514i −0.0471055 + 0.0815891i
\(518\) 0 0
\(519\) −14.3431 −0.629594
\(520\) 2.89949 + 10.0441i 0.127151 + 0.440465i
\(521\) −12.3284 + 21.3535i −0.540118 + 0.935512i 0.458779 + 0.888551i \(0.348287\pi\)
−0.998897 + 0.0469615i \(0.985046\pi\)
\(522\) 0.863961 + 1.49642i 0.0378145 + 0.0654967i
\(523\) 16.9706 0.742071 0.371035 0.928619i \(-0.379003\pi\)
0.371035 + 0.928619i \(0.379003\pi\)
\(524\) −19.4853 33.7495i −0.851218 1.47435i
\(525\) 0 0
\(526\) 1.39340 + 2.41344i 0.0607551 + 0.105231i
\(527\) 7.53553 13.0519i 0.328253 0.568551i
\(528\) 1.24264 2.15232i 0.0540790 0.0936676i
\(529\) −21.0000 −0.913043
\(530\) −2.27208 −0.0986928
\(531\) 5.12132 8.87039i 0.222246 0.384942i
\(532\) 0 0
\(533\) 0.428932 0.445759i 0.0185791 0.0193080i
\(534\) −4.48528 7.76874i −0.194097 0.336186i
\(535\) −15.8284 27.4156i −0.684323 1.18528i
\(536\) 3.36396 + 5.82655i 0.145301 + 0.251669i
\(537\) −4.00000 + 6.92820i −0.172613 + 0.298974i
\(538\) 7.45584 0.321444
\(539\) 0 0
\(540\) 9.45584 + 16.3780i 0.406915 + 0.704797i
\(541\) 5.74264 + 9.94655i 0.246895 + 0.427635i 0.962663 0.270703i \(-0.0872563\pi\)
−0.715767 + 0.698339i \(0.753923\pi\)
\(542\) 8.72792 0.374896
\(543\) −6.46447 11.1968i −0.277417 0.480500i
\(544\) 25.7279 1.10308
\(545\) −24.9706 −1.06962
\(546\) 0 0
\(547\) 0.928932 0.0397183 0.0198591 0.999803i \(-0.493678\pi\)
0.0198591 + 0.999803i \(0.493678\pi\)
\(548\) 0.313708 0.0134010
\(549\) −2.08579 3.61269i −0.0890192 0.154186i
\(550\) −0.402020 −0.0171422
\(551\) 12.5147 + 21.6761i 0.533145 + 0.923434i
\(552\) 1.58579 + 2.74666i 0.0674956 + 0.116906i
\(553\) 0 0
\(554\) 0.816234 0.0346785
\(555\) −12.2635 + 21.2409i −0.520555 + 0.901627i
\(556\) 10.8787 + 18.8424i 0.461359 + 0.799097i
\(557\) −6.15685 10.6640i −0.260874 0.451848i 0.705600 0.708610i \(-0.250677\pi\)
−0.966474 + 0.256763i \(0.917344\pi\)
\(558\) −0.535534 0.927572i −0.0226710 0.0392673i
\(559\) −3.41421 11.8272i −0.144406 0.500237i
\(560\) 0 0
\(561\) 2.41421 4.18154i 0.101928 0.176545i
\(562\) −7.24264 −0.305512
\(563\) −0.100505 −0.00423578 −0.00211789 0.999998i \(-0.500674\pi\)
−0.00211789 + 0.999998i \(0.500674\pi\)
\(564\) −4.72792 + 8.18900i −0.199081 + 0.344819i
\(565\) −18.5711 + 32.1660i −0.781291 + 1.35324i
\(566\) −4.12132 7.13834i −0.173232 0.300047i
\(567\) 0 0
\(568\) −9.24264 16.0087i −0.387813 0.671711i
\(569\) 18.8284 0.789329 0.394664 0.918825i \(-0.370861\pi\)
0.394664 + 0.918825i \(0.370861\pi\)
\(570\) −3.21320 5.56543i −0.134586 0.233110i
\(571\) −14.4853 + 25.0892i −0.606190 + 1.04995i 0.385672 + 0.922636i \(0.373970\pi\)
−0.991862 + 0.127316i \(0.959364\pi\)
\(572\) 1.07107 + 3.71029i 0.0447836 + 0.155135i
\(573\) −22.9706 −0.959609
\(574\) 0 0
\(575\) −1.17157 + 2.02922i −0.0488580 + 0.0846245i
\(576\) −2.08579 + 3.61269i −0.0869078 + 0.150529i
\(577\) −6.84315 + 11.8527i −0.284884 + 0.493433i −0.972581 0.232564i \(-0.925288\pi\)
0.687697 + 0.725998i \(0.258622\pi\)
\(578\) 7.02944 0.292386
\(579\) 5.05025 8.74729i 0.209881 0.363525i
\(580\) −13.9462 −0.579083
\(581\) 0 0
\(582\) 3.17157 5.49333i 0.131466 0.227706i
\(583\) −1.75736 −0.0727824
\(584\) 8.44975 14.6354i 0.349653 0.605617i
\(585\) −6.39949 1.58346i −0.264587 0.0654682i
\(586\) 5.89340 + 10.2077i 0.243454 + 0.421675i
\(587\) −14.8284 + 25.6836i −0.612035 + 1.06008i 0.378862 + 0.925453i \(0.376315\pi\)
−0.990897 + 0.134622i \(0.957018\pi\)
\(588\) 0 0
\(589\) −7.75736 13.4361i −0.319636 0.553627i
\(590\) −3.87868 6.71807i −0.159683 0.276579i
\(591\) −20.9706 −0.862614
\(592\) −28.4558 −1.16953
\(593\) 12.6421 + 21.8968i 0.519150 + 0.899195i 0.999752 + 0.0222559i \(0.00708484\pi\)
−0.480602 + 0.876939i \(0.659582\pi\)
\(594\) −0.686292 1.18869i −0.0281589 0.0487726i
\(595\) 0 0
\(596\) 2.74264 4.75039i 0.112343 0.194584i
\(597\) 10.5858 + 18.3351i 0.433247 + 0.750407i
\(598\) −2.05025 0.507306i −0.0838411 0.0207453i
\(599\) −14.1716 + 24.5459i −0.579035 + 1.00292i 0.416556 + 0.909110i \(0.363237\pi\)
−0.995590 + 0.0938074i \(0.970096\pi\)
\(600\) −3.71573 −0.151694
\(601\) 15.4706 26.7958i 0.631057 1.09302i −0.356278 0.934380i \(-0.615955\pi\)
0.987336 0.158644i \(-0.0507121\pi\)
\(602\) 0 0
\(603\) −4.24264 −0.172774
\(604\) 13.6863 23.7054i 0.556887 0.964557i
\(605\) −19.4853 −0.792189
\(606\) −4.29289 + 7.43551i −0.174387 + 0.302047i
\(607\) −16.1716 + 28.0100i −0.656384 + 1.13689i 0.325161 + 0.945659i \(0.394581\pi\)
−0.981545 + 0.191232i \(0.938752\pi\)
\(608\) 13.2426 22.9369i 0.537060 0.930215i
\(609\) 0 0
\(610\) −3.15938 −0.127920
\(611\) −3.65685 12.6677i −0.147940 0.512481i
\(612\) −5.32843 + 9.22911i −0.215389 + 0.373065i
\(613\) 7.39949 + 12.8163i 0.298863 + 0.517646i 0.975876 0.218325i \(-0.0700594\pi\)
−0.677013 + 0.735971i \(0.736726\pi\)
\(614\) 13.5563 0.547090
\(615\) −0.221825 0.384213i −0.00894486 0.0154930i
\(616\) 0 0
\(617\) 15.5711 + 26.9699i 0.626868 + 1.08577i 0.988177 + 0.153320i \(0.0489966\pi\)
−0.361309 + 0.932446i \(0.617670\pi\)
\(618\) −4.10051 + 7.10228i −0.164947 + 0.285696i
\(619\) 20.7782 35.9889i 0.835145 1.44651i −0.0587667 0.998272i \(-0.518717\pi\)
0.893912 0.448242i \(-0.147950\pi\)
\(620\) 8.64466 0.347178
\(621\) −8.00000 −0.321029
\(622\) −2.67767 + 4.63786i −0.107365 + 0.185961i
\(623\) 0 0
\(624\) 4.24264 + 14.6969i 0.169842 + 0.588348i
\(625\) 6.98528 + 12.0989i 0.279411 + 0.483954i
\(626\) −2.89949 5.02207i −0.115887 0.200722i
\(627\) −2.48528 4.30463i −0.0992526 0.171911i
\(628\) −5.01472 + 8.68575i −0.200109 + 0.346599i
\(629\) −55.2843 −2.20433
\(630\) 0 0
\(631\) −12.1421 21.0308i −0.483371 0.837223i 0.516447 0.856319i \(-0.327254\pi\)
−0.999818 + 0.0190965i \(0.993921\pi\)
\(632\) 1.39340 + 2.41344i 0.0554264 + 0.0960014i
\(633\) −34.9706 −1.38996
\(634\) −6.76346 11.7146i −0.268611 0.465248i
\(635\) 24.3431 0.966028
\(636\) −7.75736 −0.307599
\(637\) 0 0
\(638\) 1.01219 0.0400731
\(639\) 11.6569 0.461138
\(640\) 9.65076 + 16.7156i 0.381480 + 0.660742i
\(641\) −14.7990 −0.584525 −0.292262 0.956338i \(-0.594408\pi\)
−0.292262 + 0.956338i \(0.594408\pi\)
\(642\) 5.07107 + 8.78335i 0.200139 + 0.346651i
\(643\) 7.51472 + 13.0159i 0.296352 + 0.513296i 0.975298 0.220891i \(-0.0708967\pi\)
−0.678947 + 0.734187i \(0.737563\pi\)
\(644\) 0 0
\(645\) −8.82843 −0.347619
\(646\) 7.24264 12.5446i 0.284958 0.493562i
\(647\) −8.65685 14.9941i −0.340336 0.589479i 0.644159 0.764892i \(-0.277207\pi\)
−0.984495 + 0.175412i \(0.943874\pi\)
\(648\) −3.96447 6.86666i −0.155739 0.269748i
\(649\) −3.00000 5.19615i −0.117760 0.203967i
\(650\) 1.71573 1.78304i 0.0672964 0.0699365i
\(651\) 0 0
\(652\) 11.5061 19.9291i 0.450614 0.780486i
\(653\) 26.1421 1.02302 0.511510 0.859277i \(-0.329086\pi\)
0.511510 + 0.859277i \(0.329086\pi\)
\(654\) 8.00000 0.312825
\(655\) 19.4853 33.7495i 0.761353 1.31870i
\(656\) 0.257359 0.445759i 0.0100482 0.0174040i
\(657\) 5.32843 + 9.22911i 0.207882 + 0.360062i
\(658\) 0 0
\(659\) 7.65685 + 13.2621i 0.298269 + 0.516617i 0.975740 0.218933i \(-0.0702575\pi\)
−0.677471 + 0.735549i \(0.736924\pi\)
\(660\) 2.76955 0.107805
\(661\) −16.5711 28.7019i −0.644540 1.11638i −0.984408 0.175903i \(-0.943716\pi\)
0.339868 0.940473i \(-0.389618\pi\)
\(662\) 5.15076 8.92137i 0.200190 0.346739i
\(663\) 8.24264 + 28.5533i 0.320118 + 1.10892i
\(664\) 1.69848 0.0659140
\(665\) 0 0
\(666\) −1.96447 + 3.40256i −0.0761215 + 0.131846i
\(667\) 2.94975 5.10911i 0.114215 0.197826i
\(668\) −6.15076 + 10.6534i −0.237980 + 0.412193i
\(669\) 2.82843 0.109353
\(670\) −1.60660 + 2.78272i −0.0620684 + 0.107506i
\(671\) −2.44365 −0.0943361
\(672\) 0 0
\(673\) −7.25736 + 12.5701i −0.279751 + 0.484542i −0.971323 0.237765i \(-0.923585\pi\)
0.691572 + 0.722308i \(0.256918\pi\)
\(674\) −1.44365 −0.0556074
\(675\) 4.68629 8.11689i 0.180375 0.312419i
\(676\) −21.0269 11.0843i −0.808727 0.426317i
\(677\) −8.82843 15.2913i −0.339304 0.587692i 0.644998 0.764184i \(-0.276858\pi\)
−0.984302 + 0.176492i \(0.943525\pi\)
\(678\) 5.94975 10.3053i 0.228499 0.395771i
\(679\) 0 0
\(680\) 8.44975 + 14.6354i 0.324033 + 0.561242i
\(681\) −4.17157 7.22538i −0.159855 0.276877i
\(682\) −0.627417 −0.0240250
\(683\) 5.31371 0.203323 0.101662 0.994819i \(-0.467584\pi\)
0.101662 + 0.994819i \(0.467584\pi\)
\(684\) 5.48528 + 9.50079i 0.209735 + 0.363272i
\(685\) 0.156854 + 0.271680i 0.00599309 + 0.0103803i
\(686\) 0 0
\(687\) 8.82843 15.2913i 0.336826 0.583399i
\(688\) −5.12132 8.87039i −0.195249 0.338180i
\(689\) 7.50000 7.79423i 0.285727 0.296936i
\(690\) −0.757359 + 1.31178i −0.0288322 + 0.0499388i
\(691\) −29.9411 −1.13901 −0.569507 0.821986i \(-0.692866\pi\)
−0.569507 + 0.821986i \(0.692866\pi\)
\(692\) 9.27208 16.0597i 0.352472 0.610499i
\(693\) 0 0
\(694\) −2.52691 −0.0959203
\(695\) −10.8787 + 18.8424i −0.412652 + 0.714734i
\(696\) 9.35534 0.354613
\(697\) 0.500000 0.866025i 0.0189389 0.0328031i
\(698\) 1.92893 3.34101i 0.0730112 0.126459i
\(699\) 2.00000 3.46410i 0.0756469 0.131024i
\(700\) 0 0
\(701\) 13.8579 0.523404 0.261702 0.965149i \(-0.415716\pi\)
0.261702 + 0.965149i \(0.415716\pi\)
\(702\) 8.20101 + 2.02922i 0.309527 + 0.0765881i
\(703\) −28.4558 + 49.2870i −1.07323 + 1.85889i
\(704\) 1.22183 + 2.11626i 0.0460493 + 0.0797597i
\(705\) −9.45584 −0.356128
\(706\) 1.20711 + 2.09077i 0.0454301 + 0.0786872i
\(707\) 0 0
\(708\) −13.2426 22.9369i −0.497689 0.862022i
\(709\) −8.81371 + 15.2658i −0.331006 + 0.573319i −0.982709 0.185155i \(-0.940721\pi\)
0.651704 + 0.758474i \(0.274055\pi\)
\(710\) 4.41421 7.64564i 0.165662 0.286936i
\(711\) −1.75736 −0.0659061
\(712\) 24.2843 0.910092
\(713\) −1.82843 + 3.16693i −0.0684751 + 0.118602i
\(714\) 0 0
\(715\) −2.67767 + 2.78272i −0.100139 + 0.104068i
\(716\) −5.17157 8.95743i −0.193271 0.334755i
\(717\) 17.2426 + 29.8651i 0.643938 + 1.11533i
\(718\) 3.51472 + 6.08767i 0.131168 + 0.227190i
\(719\) 0.192388 0.333226i 0.00717487 0.0124272i −0.862416 0.506201i \(-0.831049\pi\)
0.869591 + 0.493774i \(0.164383\pi\)
\(720\) −5.48528 −0.204424
\(721\) 0 0
\(722\) −3.52082 6.09823i −0.131031 0.226953i
\(723\) −10.9497 18.9655i −0.407225 0.705335i
\(724\) 16.7157 0.621235
\(725\) 3.45584 + 5.98570i 0.128347 + 0.222303i
\(726\) 6.24264 0.231686
\(727\) −24.9706 −0.926107 −0.463053 0.886330i \(-0.653246\pi\)
−0.463053 + 0.886330i \(0.653246\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) 8.07107 0.298724
\(731\) −9.94975 17.2335i −0.368005 0.637403i
\(732\) −10.7868 −0.398691
\(733\) −10.5000 18.1865i −0.387826 0.671735i 0.604331 0.796734i \(-0.293441\pi\)
−0.992157 + 0.124999i \(0.960107\pi\)
\(734\) −5.94975 10.3053i −0.219609 0.380374i
\(735\) 0 0
\(736\) −6.24264 −0.230107
\(737\) −1.24264 + 2.15232i −0.0457733 + 0.0792816i
\(738\) −0.0355339 0.0615465i −0.00130802 0.00226556i
\(739\) 10.1421 + 17.5667i 0.373084 + 0.646201i 0.990038 0.140798i \(-0.0449668\pi\)
−0.616954 + 0.786999i \(0.711633\pi\)
\(740\) −15.8553 27.4623i −0.582854 1.00953i
\(741\) 29.6985 + 7.34847i 1.09100 + 0.269953i
\(742\) 0 0
\(743\) −15.7990 + 27.3647i −0.579609 + 1.00391i 0.415915 + 0.909403i \(0.363461\pi\)
−0.995524 + 0.0945084i \(0.969872\pi\)
\(744\) −5.79899 −0.212601
\(745\) 5.48528 0.200965
\(746\) −5.47918 + 9.49023i −0.200607 + 0.347462i
\(747\) −0.535534 + 0.927572i −0.0195942 + 0.0339381i
\(748\) 3.12132 + 5.40629i 0.114127 + 0.197673i
\(749\) 0 0
\(750\) −3.56497 6.17471i −0.130174 0.225469i
\(751\) −17.5563 −0.640640 −0.320320 0.947309i \(-0.603790\pi\)
−0.320320 + 0.947309i \(0.603790\pi\)
\(752\) −5.48528 9.50079i −0.200028 0.346458i
\(753\) −16.2426 + 28.1331i −0.591915 + 1.02523i
\(754\) −4.31981 + 4.48927i −0.157318 + 0.163490i
\(755\) 27.3726 0.996190
\(756\) 0 0
\(757\) −14.7279 + 25.5095i −0.535295 + 0.927159i 0.463854 + 0.885912i \(0.346466\pi\)
−0.999149 + 0.0412470i \(0.986867\pi\)
\(758\) 0.0502525 0.0870399i 0.00182525 0.00316143i
\(759\) −0.585786 + 1.01461i −0.0212627 + 0.0368281i
\(760\) 17.3970 0.631054
\(761\) 8.92893 15.4654i 0.323674 0.560619i −0.657569 0.753394i \(-0.728415\pi\)
0.981243 + 0.192775i \(0.0617487\pi\)
\(762\) −7.79899 −0.282528
\(763\) 0 0
\(764\) 14.8492 25.7196i 0.537227 0.930504i
\(765\) −10.6569 −0.385299
\(766\) −7.05025 + 12.2114i −0.254736 + 0.441216i
\(767\) 35.8492 + 8.87039i 1.29444 + 0.320291i
\(768\) 2.80761 + 4.86293i 0.101311 + 0.175476i
\(769\) −24.7279 + 42.8300i −0.891712 + 1.54449i −0.0538894 + 0.998547i \(0.517162\pi\)
−0.837822 + 0.545943i \(0.816172\pi\)
\(770\) 0 0
\(771\) −10.6066 18.3712i −0.381987 0.661622i
\(772\) 6.52944 + 11.3093i 0.235000 + 0.407031i
\(773\) −6.34315 −0.228147 −0.114074 0.993472i \(-0.536390\pi\)
−0.114074 + 0.993472i \(0.536390\pi\)
\(774\) −1.41421 −0.0508329
\(775\) −2.14214 3.71029i −0.0769478 0.133277i
\(776\) 8.58579 + 14.8710i 0.308212 + 0.533838i
\(777\) 0 0
\(778\) −5.62132 + 9.73641i −0.201534 + 0.349067i
\(779\) −0.514719 0.891519i −0.0184417 0.0319420i
\(780\) −11.8198 + 12.2835i −0.423217 + 0.439820i
\(781\) 3.41421 5.91359i 0.122170 0.211605i
\(782\) −3.41421 −0.122092
\(783\) −11.7990 + 20.4364i −0.421661 + 0.730339i
\(784\) 0 0
\(785\) −10.0294 −0.357966
\(786\) −6.24264 + 10.8126i −0.222668 + 0.385672i
\(787\) 13.8995 0.495463 0.247732 0.968829i \(-0.420315\pi\)
0.247732 + 0.968829i \(0.420315\pi\)
\(788\) 13.5563 23.4803i 0.482925 0.836451i
\(789\) −4.75736 + 8.23999i −0.169366 + 0.293351i
\(790\) −0.665476 + 1.15264i −0.0236766 + 0.0410090i
\(791\) 0 0
\(792\) 0.928932 0.0330082
\(793\) 10.4289 10.8381i 0.370342 0.384871i
\(794\) 1.37258 2.37738i 0.0487111 0.0843702i
\(795\) −3.87868 6.71807i −0.137563 0.238265i
\(796\) −27.3726 −0.970195
\(797\) −9.07107 15.7116i −0.321314 0.556532i 0.659446 0.751752i \(-0.270791\pi\)
−0.980759 + 0.195221i \(0.937458\pi\)
\(798\) 0 0
\(799\) −10.6569 18.4582i −0.377012 0.653005i
\(800\) 3.65685 6.33386i 0.129289 0.223936i
\(801\) −7.65685 + 13.2621i −0.270542 + 0.468592i
\(802\) 3.64466 0.128697
\(803\) 6.24264 0.220298
\(804\) −5.48528 + 9.50079i −0.193451 + 0.335067i
\(805\) 0 0
\(806\) 2.67767 2.78272i 0.0943169 0.0980170i
\(807\) 12.7279 + 22.0454i 0.448044 + 0.776035i
\(808\) −11.6213 20.1287i −0.408837 0.708126i
\(809\) −17.5711 30.4340i −0.617766 1.07000i −0.989892 0.141820i \(-0.954705\pi\)
0.372127 0.928182i \(-0.378629\pi\)
\(810\) 1.89340 3.27946i 0.0665272 0.115229i
\(811\) 42.1838 1.48127 0.740636 0.671906i \(-0.234524\pi\)
0.740636 + 0.671906i \(0.234524\pi\)
\(812\) 0 0
\(813\) 14.8995 + 25.8067i 0.522548 + 0.905080i
\(814\) 1.15076 + 1.99317i 0.0403340 + 0.0698606i
\(815\) 23.0122 0.806082
\(816\) 12.3640 + 21.4150i 0.432825 + 0.749675i
\(817\) −20.4853 −0.716689
\(818\) 9.10051 0.318192
\(819\) 0 0
\(820\) 0.573593 0.0200307
\(821\) −39.9411 −1.39395 −0.696977 0.717093i \(-0.745472\pi\)
−0.696977 + 0.717093i \(0.745472\pi\)
\(822\) −0.0502525 0.0870399i −0.00175276 0.00303587i
\(823\) 19.3137 0.673234 0.336617 0.941642i \(-0.390717\pi\)
0.336617 + 0.941642i \(0.390717\pi\)
\(824\) −11.1005 19.2266i −0.386704 0.669792i
\(825\) −0.686292 1.18869i −0.0238936 0.0413849i
\(826\) 0 0
\(827\) −52.6690 −1.83148 −0.915741 0.401769i \(-0.868396\pi\)
−0.915741 + 0.401769i \(0.868396\pi\)
\(828\) 1.29289 2.23936i 0.0449311 0.0778230i
\(829\) 23.1569 + 40.1088i 0.804271 + 1.39304i 0.916782 + 0.399387i \(0.130777\pi\)
−0.112511 + 0.993650i \(0.535889\pi\)
\(830\) 0.405592 + 0.702505i 0.0140783 + 0.0243843i
\(831\) 1.39340 + 2.41344i 0.0483365 + 0.0837212i
\(832\) −14.6005 3.61269i −0.506181 0.125247i
\(833\) 0 0
\(834\) 3.48528 6.03668i 0.120685 0.209033i
\(835\) −12.3015 −0.425711
\(836\) 6.42641 0.222262
\(837\) 7.31371 12.6677i 0.252799 0.437860i
\(838\) −2.39340 + 4.14549i −0.0826786 + 0.143203i
\(839\) −20.7990 36.0249i −0.718061 1.24372i −0.961767 0.273869i \(-0.911697\pi\)
0.243706 0.969849i \(-0.421637\pi\)
\(840\) 0 0
\(841\) 5.79899 + 10.0441i 0.199965 + 0.346350i
\(842\) 8.89949 0.306697
\(843\) −12.3640 21.4150i −0.425837 0.737572i
\(844\) 22.6066 39.1558i 0.778151 1.34780i
\(845\) −0.914214 23.7520i −0.0314499 0.817092i
\(846\) −1.51472 −0.0520771
\(847\) 0 0
\(848\) 4.50000 7.79423i 0.154531 0.267655i
\(849\) 14.0711 24.3718i 0.482918 0.836438i
\(850\) 2.00000 3.46410i 0.0685994 0.118818i
\(851\) 13.4142 0.459833
\(852\) 15.0711 26.1039i 0.516326 0.894303i
\(853\) 35.0000 1.19838 0.599189 0.800608i \(-0.295490\pi\)
0.599189 + 0.800608i \(0.295490\pi\)
\(854\) 0 0
\(855\) −5.48528 + 9.50079i −0.187593 + 0.324920i
\(856\) −27.4558 −0.938421
\(857\) 0.600505 1.04011i 0.0205129 0.0355293i −0.855587 0.517659i \(-0.826803\pi\)
0.876100 + 0.482130i \(0.160137\pi\)
\(858\) 0.857864 0.891519i 0.0292870 0.0304360i
\(859\) −6.46447 11.1968i −0.220565 0.382029i 0.734415 0.678701i \(-0.237457\pi\)
−0.954980 + 0.296672i \(0.904123\pi\)
\(860\) 5.70711 9.88500i 0.194611 0.337076i
\(861\) 0 0
\(862\) −2.48528 4.30463i −0.0846490 0.146616i
\(863\) 10.0919 + 17.4797i 0.343532 + 0.595014i 0.985086 0.172063i \(-0.0550434\pi\)
−0.641554 + 0.767078i \(0.721710\pi\)
\(864\) 24.9706 0.849516
\(865\) 18.5442 0.630520
\(866\) 3.62132 + 6.27231i 0.123057 + 0.213142i
\(867\) 12.0000 + 20.7846i 0.407541 + 0.705882i
\(868\) 0 0
\(869\) −0.514719 + 0.891519i −0.0174606 + 0.0302427i
\(870\) 2.23402 + 3.86943i 0.0757403 + 0.131186i
\(871\) −4.24264 14.6969i −0.143756 0.497987i
\(872\) −10.8284 + 18.7554i −0.366697 + 0.635138i
\(873\) −10.8284 −0.366487
\(874\) −1.75736 + 3.04384i −0.0594436 + 0.102959i
\(875\) 0 0
\(876\) 27.5563 0.931043
\(877\) −8.50000 + 14.7224i −0.287025 + 0.497141i −0.973098 0.230391i \(-0.925999\pi\)
0.686074 + 0.727532i \(0.259333\pi\)
\(878\) 0.526912 0.0177824
\(879\) −20.1213 + 34.8511i −0.678675 + 1.17550i
\(880\) −1.60660 + 2.78272i −0.0541585 + 0.0938053i
\(881\) 2.22792 3.85887i 0.0750606 0.130009i −0.826052 0.563594i \(-0.809418\pi\)
0.901113 + 0.433585i \(0.142752\pi\)
\(882\) 0 0
\(883\) 56.0416 1.88595 0.942976 0.332862i \(-0.108014\pi\)
0.942976 + 0.332862i \(0.108014\pi\)
\(884\) −37.2990 9.22911i −1.25450 0.310408i
\(885\) 13.2426 22.9369i 0.445146 0.771016i
\(886\) −5.31371 9.20361i −0.178518 0.309201i
\(887\) 34.6274 1.16267 0.581337 0.813663i \(-0.302530\pi\)
0.581337 + 0.813663i \(0.302530\pi\)
\(888\) 10.6360 + 18.4222i 0.356922 + 0.618207i
\(889\) 0 0
\(890\) 5.79899 + 10.0441i 0.194383 + 0.336681i
\(891\) 1.46447 2.53653i 0.0490615 0.0849769i
\(892\) −1.82843 + 3.16693i −0.0612203 + 0.106037i
\(893\) −21.9411 −0.734232
\(894\) −1.75736 −0.0587749
\(895\) 5.17157 8.95743i 0.172867 0.299414i
\(896\) 0 0
\(897\) −2.00000 6.92820i −0.0667781 0.231326i
\(898\) −6.72792 11.6531i −0.224514 0.388869i
\(899\) 5.39340 + 9.34164i 0.179880 + 0.311561i
\(900\) 1.51472 + 2.62357i 0.0504906 + 0.0874523i
\(901\) 8.74264 15.1427i 0.291260 0.504476i
\(902\) −0.0416306 −0.00138615
\(903\) 0 0
\(904\) 16.1066 + 27.8975i 0.535698 + 0.927855i
\(905\) 8.35786 + 14.4762i 0.277825 + 0.481207i
\(906\) −8.76955 −0.291349
\(907\) 3.36396 + 5.82655i 0.111698 + 0.193467i 0.916455 0.400137i \(-0.131038\pi\)
−0.804757 + 0.593605i \(0.797704\pi\)
\(908\) 10.7868 0.357972
\(909\) 14.6569 0.486137
\(910\) 0 0
\(911\) −29.6569 −0.982575 −0.491288 0.870997i \(-0.663474\pi\)
−0.491288 + 0.870997i \(0.663474\pi\)
\(912\) 25.4558 0.842927
\(913\) 0.313708 + 0.543359i 0.0103822 + 0.0179826i
\(914\) −10.3553 −0.342524
\(915\) −5.39340 9.34164i −0.178300 0.308825i
\(916\) 11.4142 + 19.7700i 0.377136 + 0.653219i
\(917\) 0 0
\(918\) 13.6569 0.450743
\(919\) −1.34315 + 2.32640i −0.0443063 + 0.0767407i −0.887328 0.461139i \(-0.847441\pi\)
0.843022 + 0.537879i \(0.180774\pi\)
\(920\) −2.05025 3.55114i −0.0675948 0.117078i
\(921\) 23.1421 + 40.0834i 0.762559 + 1.32079i
\(922\) 0.278175 + 0.481813i 0.00916119 + 0.0158677i
\(923\) 11.6569 + 40.3805i 0.383690 + 1.32914i
\(924\) 0 0
\(925\) −7.85786 + 13.6102i −0.258365 + 0.447501i
\(926\) 2.78680 0.0915798
\(927\) 14.0000 0.459820
\(928\) −9.20711 + 15.9472i −0.302238 + 0.523492i
\(929\) 24.4706 42.3843i 0.802853 1.39058i −0.114878 0.993380i \(-0.536648\pi\)
0.917731 0.397203i \(-0.130019\pi\)
\(930\) −1.38478 2.39850i −0.0454086 0.0786500i
\(931\) 0 0
\(932\) 2.58579 + 4.47871i 0.0847003 + 0.146705i
\(933\) −18.2843 −0.598600
\(934\) 2.36396 + 4.09450i 0.0773512 + 0.133976i
\(935\) −3.12132 + 5.40629i −0.102078 + 0.176804i
\(936\) −3.96447 + 4.11999i −0.129583 + 0.134666i
\(937\) 37.1421 1.21338 0.606690 0.794938i \(-0.292497\pi\)
0.606690 + 0.794938i \(0.292497\pi\)
\(938\) 0 0
\(939\) 9.89949 17.1464i 0.323058 0.559553i
\(940\) 6.11270 10.5875i 0.199374 0.345326i
\(941\) 26.4853 45.8739i 0.863395 1.49544i −0.00523607 0.999986i \(-0.501667\pi\)
0.868632 0.495459i \(-0.165000\pi\)
\(942\) 3.21320 0.104692
\(943\) −0.121320 + 0.210133i −0.00395073 + 0.00684287i
\(944\) 30.7279 1.00011
\(945\) 0 0
\(946\) −0.414214 + 0.717439i −0.0134672 + 0.0233260i
\(947\) 21.4142 0.695868 0.347934 0.937519i \(-0.386883\pi\)
0.347934 + 0.937519i \(0.386883\pi\)
\(948\) −2.27208 + 3.93535i −0.0737937 + 0.127814i
\(949\) −26.6421 + 27.6873i −0.864840 + 0.898768i
\(950\) −2.05887 3.56608i −0.0667987 0.115699i
\(951\) 23.0919 39.9963i 0.748806 1.29697i
\(952\) 0 0
\(953\) −3.31371 5.73951i −0.107342 0.185921i 0.807351 0.590072i \(-0.200900\pi\)
−0.914692 + 0.404151i \(0.867567\pi\)
\(954\) −0.621320 1.07616i −0.0201160 0.0348419i
\(955\) 29.6985 0.961020
\(956\) −44.5858 −1.44201
\(957\) 1.72792 + 2.99285i 0.0558558 + 0.0967451i
\(958\) −0.334524 0.579412i −0.0108080 0.0187200i
\(959\) 0 0
\(960\) −5.39340 + 9.34164i −0.174071 + 0.301500i
\(961\) 12.1569 + 21.0563i 0.392157 + 0.679235i
\(962\) −13.7513 3.40256i −0.443359 0.109703i
\(963\) 8.65685 14.9941i 0.278963 0.483178i
\(964\) 28.3137 0.911923
\(965\) −6.52944 + 11.3093i −0.210190 + 0.364060i
\(966\) 0 0
\(967\) −19.7574 −0.635354 −0.317677 0.948199i \(-0.602903\pi\)
−0.317677 + 0.948199i \(0.602903\pi\)
\(968\) −8.44975 + 14.6354i −0.271585 + 0.470399i
\(969\) 49.4558 1.58875
\(970\) −4.10051 + 7.10228i −0.131659 + 0.228041i
\(971\) 25.8284 44.7361i 0.828874 1.43565i −0.0700488 0.997544i \(-0.522315\pi\)
0.898922 0.438108i \(-0.144351\pi\)
\(972\) −9.05025 + 15.6755i −0.290287 + 0.502792i
\(973\) 0 0
\(974\) −5.37258 −0.172149
\(975\) 8.20101 + 2.02922i 0.262643 + 0.0649872i
\(976\) 6.25736 10.8381i 0.200293 0.346918i
\(977\) −15.2990 26.4986i −0.489458 0.847766i 0.510468 0.859897i \(-0.329472\pi\)
−0.999926 + 0.0121303i \(0.996139\pi\)
\(978\) −7.37258 −0.235749
\(979\) 4.48528 + 7.76874i 0.143350 + 0.248290i
\(980\) 0 0
\(981\) −6.82843 11.8272i −0.218015 0.377613i
\(982\) −2.62742 + 4.55082i −0.0838442 + 0.145222i
\(983\) −21.0000 + 36.3731i −0.669796 + 1.16012i 0.308165 + 0.951333i \(0.400285\pi\)
−0.977961 + 0.208788i \(0.933048\pi\)
\(984\) −0.384776 −0.0122662
\(985\) 27.1127 0.863882
\(986\) −5.03553 + 8.72180i −0.160364 + 0.277759i
\(987\) 0 0
\(988\) −27.4264 + 28.5024i −0.872550 + 0.906781i
\(989\) 2.41421 + 4.18154i 0.0767675 + 0.132965i
\(990\) 0.221825 + 0.384213i 0.00705007 + 0.0122111i
\(991\) −9.87868 17.1104i −0.313807 0.543529i 0.665376 0.746508i \(-0.268271\pi\)
−0.979183 + 0.202979i \(0.934938\pi\)
\(992\) 5.70711 9.88500i 0.181201 0.313849i
\(993\) 35.1716 1.11614
\(994\) 0 0
\(995\) −13.6863 23.7054i −0.433885 0.751510i
\(996\) 1.38478 + 2.39850i 0.0438783 + 0.0759995i
\(997\) −13.9706 −0.442452 −0.221226 0.975223i \(-0.571006\pi\)
−0.221226 + 0.975223i \(0.571006\pi\)
\(998\) −4.15076 7.18932i −0.131390 0.227574i
\(999\) −53.6569 −1.69763
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 637.2.h.c.165.2 4
7.2 even 3 637.2.g.g.373.1 4
7.3 odd 6 637.2.f.f.295.1 yes 4
7.4 even 3 637.2.f.e.295.1 4
7.5 odd 6 637.2.g.f.373.1 4
7.6 odd 2 637.2.h.b.165.2 4
13.3 even 3 637.2.g.g.263.1 4
91.3 odd 6 637.2.f.f.393.1 yes 4
91.4 even 6 8281.2.a.y.1.1 2
91.16 even 3 inner 637.2.h.c.471.2 4
91.17 odd 6 8281.2.a.x.1.1 2
91.55 odd 6 637.2.g.f.263.1 4
91.68 odd 6 637.2.h.b.471.2 4
91.74 even 3 8281.2.a.o.1.2 2
91.81 even 3 637.2.f.e.393.1 yes 4
91.87 odd 6 8281.2.a.p.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.e.295.1 4 7.4 even 3
637.2.f.e.393.1 yes 4 91.81 even 3
637.2.f.f.295.1 yes 4 7.3 odd 6
637.2.f.f.393.1 yes 4 91.3 odd 6
637.2.g.f.263.1 4 91.55 odd 6
637.2.g.f.373.1 4 7.5 odd 6
637.2.g.g.263.1 4 13.3 even 3
637.2.g.g.373.1 4 7.2 even 3
637.2.h.b.165.2 4 7.6 odd 2
637.2.h.b.471.2 4 91.68 odd 6
637.2.h.c.165.2 4 1.1 even 1 trivial
637.2.h.c.471.2 4 91.16 even 3 inner
8281.2.a.o.1.2 2 91.74 even 3
8281.2.a.p.1.2 2 91.87 odd 6
8281.2.a.x.1.1 2 91.17 odd 6
8281.2.a.y.1.1 2 91.4 even 6