Properties

Label 637.2.g.f.373.1
Level $637$
Weight $2$
Character 637.373
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(263,637)]
 
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, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 637.373
Dual form 637.2.g.f.263.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.207107 - 0.358719i) q^{2} +1.41421 q^{3} +(0.914214 - 1.58346i) q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 - 0.507306i) q^{6} -1.58579 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.207107 - 0.358719i) q^{2} +1.41421 q^{3} +(0.914214 - 1.58346i) q^{4} +(0.914214 - 1.58346i) q^{5} +(-0.292893 - 0.507306i) q^{6} -1.58579 q^{8} -1.00000 q^{9} -0.757359 q^{10} +0.585786 q^{11} +(1.29289 - 2.23936i) q^{12} +(-3.50000 - 0.866025i) q^{13} +(1.29289 - 2.23936i) q^{15} +(-1.50000 - 2.59808i) q^{16} +(2.91421 - 5.04757i) q^{17} +(0.207107 + 0.358719i) q^{18} +6.00000 q^{19} +(-1.67157 - 2.89525i) q^{20} +(-0.121320 - 0.210133i) q^{22} +(0.707107 + 1.22474i) q^{23} -2.24264 q^{24} +(0.828427 + 1.43488i) q^{25} +(0.414214 + 1.43488i) q^{26} -5.65685 q^{27} +(-2.08579 + 3.61269i) q^{29} -1.07107 q^{30} +(-1.29289 - 2.23936i) q^{31} +(-2.20711 + 3.82282i) q^{32} +0.828427 q^{33} -2.41421 q^{34} +(-0.914214 + 1.58346i) q^{36} +(4.74264 + 8.21449i) q^{37} +(-1.24264 - 2.15232i) q^{38} +(-4.94975 - 1.22474i) 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} +(-0.914214 + 1.58346i) q^{45} +(0.292893 - 0.507306i) 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} +(-4.57107 + 4.75039i) q^{52} +(1.50000 + 2.59808i) q^{53} +(1.17157 + 2.02922i) q^{54} +(0.535534 - 0.927572i) q^{55} +8.48528 q^{57} +1.72792 q^{58} +(5.12132 - 8.87039i) q^{59} +(-2.36396 - 4.09450i) q^{60} +4.17157 q^{61} +(-0.535534 + 0.927572i) q^{62} -4.17157 q^{64} +(-4.57107 + 4.75039i) q^{65} +(-0.171573 - 0.297173i) q^{66} +4.24264 q^{67} +(-5.32843 - 9.22911i) q^{68} +(1.00000 + 1.73205i) q^{69} +(5.82843 + 10.0951i) q^{71} +1.58579 q^{72} +(5.32843 + 9.22911i) q^{73} +(1.96447 - 3.40256i) q^{74} +(1.17157 + 2.02922i) q^{75} +(5.48528 - 9.50079i) q^{76} +(0.585786 + 2.02922i) q^{78} +(-0.878680 + 1.52192i) q^{79} -5.48528 q^{80} -5.00000 q^{81} +0.0710678 q^{82} +1.07107 q^{83} +(-5.32843 - 9.22911i) q^{85} +(-0.707107 + 1.22474i) q^{86} +(-2.94975 + 5.10911i) q^{87} -0.928932 q^{88} +(-7.65685 - 13.2621i) q^{89} +0.757359 q^{90} +2.58579 q^{92} +(-1.82843 - 3.16693i) q^{93} -1.51472 q^{94} +(5.48528 - 9.50079i) q^{95} +(-3.12132 + 5.40629i) q^{96} +(5.41421 + 9.37769i) q^{97} -0.585786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{6} - 12 q^{8} - 4 q^{9} - 20 q^{10} + 8 q^{11} + 8 q^{12} - 14 q^{13} + 8 q^{15} - 6 q^{16} + 6 q^{17} - 2 q^{18} + 24 q^{19} - 18 q^{20} + 8 q^{22} + 8 q^{24} - 8 q^{25} - 4 q^{26} - 14 q^{29} + 24 q^{30} - 8 q^{31} - 6 q^{32} - 8 q^{33} - 4 q^{34} + 2 q^{36} + 2 q^{37} + 12 q^{38} + 14 q^{40} - 6 q^{41} - 4 q^{43} - 12 q^{44} + 2 q^{45} + 4 q^{46} - 4 q^{47} + 24 q^{50} + 8 q^{51} + 10 q^{52} + 6 q^{53} + 16 q^{54} - 12 q^{55} - 44 q^{58} + 12 q^{59} + 16 q^{60} + 28 q^{61} + 12 q^{62} - 28 q^{64} + 10 q^{65} - 12 q^{66} - 10 q^{68} + 4 q^{69} + 12 q^{71} + 12 q^{72} + 10 q^{73} + 22 q^{74} + 16 q^{75} - 12 q^{76} + 8 q^{78} - 12 q^{79} + 12 q^{80} - 20 q^{81} - 28 q^{82} - 24 q^{83} - 10 q^{85} + 8 q^{87} - 32 q^{88} - 8 q^{89} + 20 q^{90} + 16 q^{92} + 4 q^{93} - 40 q^{94} - 12 q^{95} - 4 q^{96} + 16 q^{97} - 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 0.358719i −0.146447 0.253653i 0.783465 0.621436i \(-0.213450\pi\)
−0.929912 + 0.367783i \(0.880117\pi\)
\(3\) 1.41421 0.816497 0.408248 0.912871i \(-0.366140\pi\)
0.408248 + 0.912871i \(0.366140\pi\)
\(4\) 0.914214 1.58346i 0.457107 0.791732i
\(5\) 0.914214 1.58346i 0.408849 0.708147i −0.585912 0.810374i \(-0.699264\pi\)
0.994761 + 0.102228i \(0.0325970\pi\)
\(6\) −0.292893 0.507306i −0.119573 0.207107i
\(7\) 0 0
\(8\) −1.58579 −0.560660
\(9\) −1.00000 −0.333333
\(10\) −0.757359 −0.239498
\(11\) 0.585786 0.176621 0.0883106 0.996093i \(-0.471853\pi\)
0.0883106 + 0.996093i \(0.471853\pi\)
\(12\) 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
\(16\) −1.50000 2.59808i −0.375000 0.649519i
\(17\) 2.91421 5.04757i 0.706801 1.22421i −0.259237 0.965814i \(-0.583471\pi\)
0.966038 0.258401i \(-0.0831955\pi\)
\(18\) 0.207107 + 0.358719i 0.0488155 + 0.0845510i
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) −1.67157 2.89525i −0.373775 0.647397i
\(21\) 0 0
\(22\) −0.121320 0.210133i −0.0258656 0.0448005i
\(23\) 0.707107 + 1.22474i 0.147442 + 0.255377i 0.930281 0.366847i \(-0.119563\pi\)
−0.782839 + 0.622224i \(0.786229\pi\)
\(24\) −2.24264 −0.457777
\(25\) 0.828427 + 1.43488i 0.165685 + 0.286976i
\(26\) 0.414214 + 1.43488i 0.0812340 + 0.281403i
\(27\) −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 \(0.293266\pi\)
\(30\) −1.07107 −0.195549
\(31\) −1.29289 2.23936i −0.232210 0.402200i 0.726248 0.687433i \(-0.241262\pi\)
−0.958458 + 0.285233i \(0.907929\pi\)
\(32\) −2.20711 + 3.82282i −0.390165 + 0.675786i
\(33\) 0.828427 0.144211
\(34\) −2.41421 −0.414034
\(35\) 0 0
\(36\) −0.914214 + 1.58346i −0.152369 + 0.263911i
\(37\) 4.74264 + 8.21449i 0.779685 + 1.35045i 0.932123 + 0.362142i \(0.117954\pi\)
−0.152438 + 0.988313i \(0.548712\pi\)
\(38\) −1.24264 2.15232i −0.201583 0.349152i
\(39\) −4.94975 1.22474i −0.792594 0.196116i
\(40\) −1.44975 + 2.51104i −0.229225 + 0.397030i
\(41\) −0.0857864 + 0.148586i −0.0133976 + 0.0232053i −0.872646 0.488352i \(-0.837598\pi\)
0.859249 + 0.511558i \(0.170931\pi\)
\(42\) 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
\(45\) −0.914214 + 1.58346i −0.136283 + 0.236049i
\(46\) 0.292893 0.507306i 0.0431847 0.0747982i
\(47\) 1.82843 3.16693i 0.266704 0.461944i −0.701305 0.712861i \(-0.747399\pi\)
0.968009 + 0.250917i \(0.0807322\pi\)
\(48\) −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
\(52\) −4.57107 + 4.75039i −0.633893 + 0.658761i
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 1.17157 + 2.02922i 0.159431 + 0.276142i
\(55\) 0.535534 0.927572i 0.0722114 0.125074i
\(56\) 0 0
\(57\) 8.48528 1.12390
\(58\) 1.72792 0.226887
\(59\) 5.12132 8.87039i 0.666739 1.15483i −0.312072 0.950059i \(-0.601023\pi\)
0.978811 0.204767i \(-0.0656438\pi\)
\(60\) −2.36396 4.09450i −0.305186 0.528598i
\(61\) 4.17157 0.534115 0.267058 0.963681i \(-0.413949\pi\)
0.267058 + 0.963681i \(0.413949\pi\)
\(62\) −0.535534 + 0.927572i −0.0680129 + 0.117802i
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) −4.57107 + 4.75039i −0.566971 + 0.589214i
\(66\) −0.171573 0.297173i −0.0211192 0.0365795i
\(67\) 4.24264 0.518321 0.259161 0.965834i \(-0.416554\pi\)
0.259161 + 0.965834i \(0.416554\pi\)
\(68\) −5.32843 9.22911i −0.646167 1.11919i
\(69\) 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 \(0.590192\pi\)
\(72\) 1.58579 0.186887
\(73\) 5.32843 + 9.22911i 0.623645 + 1.08019i 0.988801 + 0.149239i \(0.0476823\pi\)
−0.365156 + 0.930946i \(0.618984\pi\)
\(74\) 1.96447 3.40256i 0.228365 0.395539i
\(75\) 1.17157 + 2.02922i 0.135282 + 0.234315i
\(76\) 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 −0.911213 0.411936i \(-0.864853\pi\)
0.812354 + 0.583165i \(0.198186\pi\)
\(80\) −5.48528 −0.613273
\(81\) −5.00000 −0.555556
\(82\) 0.0710678 0.00784813
\(83\) 1.07107 0.117565 0.0587825 0.998271i \(-0.481278\pi\)
0.0587825 + 0.998271i \(0.481278\pi\)
\(84\) 0 0
\(85\) −5.32843 9.22911i −0.577949 1.00104i
\(86\) −0.707107 + 1.22474i −0.0762493 + 0.132068i
\(87\) −2.94975 + 5.10911i −0.316246 + 0.547754i
\(88\) −0.928932 −0.0990245
\(89\) −7.65685 13.2621i −0.811625 1.40578i −0.911726 0.410798i \(-0.865250\pi\)
0.100101 0.994977i \(-0.468083\pi\)
\(90\) 0.757359 0.0798327
\(91\) 0 0
\(92\) 2.58579 0.269587
\(93\) −1.82843 3.16693i −0.189599 0.328395i
\(94\) −1.51472 −0.156231
\(95\) 5.48528 9.50079i 0.562778 0.974760i
\(96\) −3.12132 + 5.40629i −0.318568 + 0.551777i
\(97\) 5.41421 + 9.37769i 0.549730 + 0.952160i 0.998293 + 0.0584091i \(0.0186028\pi\)
−0.448563 + 0.893751i \(0.648064\pi\)
\(98\) 0 0
\(99\) −0.585786 −0.0588738
\(100\) 3.02944 0.302944
\(101\) 14.6569 1.45841 0.729206 0.684295i \(-0.239890\pi\)
0.729206 + 0.684295i \(0.239890\pi\)
\(102\) −3.41421 −0.338058
\(103\) −7.00000 + 12.1244i −0.689730 + 1.19465i 0.282194 + 0.959357i \(0.408938\pi\)
−0.971925 + 0.235291i \(0.924396\pi\)
\(104\) 5.55025 + 1.37333i 0.544247 + 0.134666i
\(105\) 0 0
\(106\) 0.621320 1.07616i 0.0603480 0.104526i
\(107\) −8.65685 14.9941i −0.836890 1.44954i −0.892483 0.451082i \(-0.851038\pi\)
0.0555929 0.998454i \(-0.482295\pi\)
\(108\) −5.17157 + 8.95743i −0.497635 + 0.861929i
\(109\) 6.82843 + 11.8272i 0.654045 + 1.13284i 0.982132 + 0.188191i \(0.0602625\pi\)
−0.328088 + 0.944647i \(0.606404\pi\)
\(110\) −0.443651 −0.0423004
\(111\) 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 \(-0.571325\pi\)
\(114\) −1.75736 3.04384i −0.164592 0.285081i
\(115\) 2.58579 0.241126
\(116\) 3.81371 + 6.60554i 0.354094 + 0.613309i
\(117\) 3.50000 + 0.866025i 0.323575 + 0.0800641i
\(118\) −4.24264 −0.390567
\(119\) 0 0
\(120\) −2.05025 + 3.55114i −0.187162 + 0.324173i
\(121\) −10.6569 −0.968805
\(122\) −0.863961 1.49642i −0.0782194 0.135480i
\(123\) −0.121320 + 0.210133i −0.0109391 + 0.0189471i
\(124\) −4.72792 −0.424580
\(125\) 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 \(0.965518\pi\)
\(128\) 5.27817 + 9.14207i 0.466529 + 0.808052i
\(129\) −2.41421 4.18154i −0.212560 0.368164i
\(130\) 2.65076 + 0.655892i 0.232487 + 0.0575256i
\(131\) −10.6569 + 18.4582i −0.931094 + 1.61270i −0.149638 + 0.988741i \(0.547811\pi\)
−0.781456 + 0.623961i \(0.785523\pi\)
\(132\) 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
\(136\) −4.62132 + 8.00436i −0.396275 + 0.686368i
\(137\) 0.0857864 0.148586i 0.00732923 0.0126946i −0.862338 0.506334i \(-0.831000\pi\)
0.869667 + 0.493639i \(0.164334\pi\)
\(138\) 0.414214 0.717439i 0.0352602 0.0610725i
\(139\) 5.94975 + 10.3053i 0.504651 + 0.874081i 0.999986 + 0.00537886i \(0.00171215\pi\)
−0.495335 + 0.868702i \(0.664955\pi\)
\(140\) 0 0
\(141\) 2.58579 4.47871i 0.217763 0.377176i
\(142\) 2.41421 4.18154i 0.202596 0.350907i
\(143\) −2.05025 0.507306i −0.171451 0.0424231i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 3.81371 + 6.60554i 0.316711 + 0.548560i
\(146\) 2.20711 3.82282i 0.182661 0.316379i
\(147\) 0 0
\(148\) 17.3431 1.42560
\(149\) 3.00000 0.245770 0.122885 0.992421i \(-0.460785\pi\)
0.122885 + 0.992421i \(0.460785\pi\)
\(150\) 0.485281 0.840532i 0.0396231 0.0686292i
\(151\) −7.48528 12.9649i −0.609144 1.05507i −0.991382 0.131004i \(-0.958180\pi\)
0.382238 0.924064i \(-0.375153\pi\)
\(152\) −9.51472 −0.771746
\(153\) −2.91421 + 5.04757i −0.235600 + 0.408072i
\(154\) 0 0
\(155\) −4.72792 −0.379756
\(156\) −6.46447 + 6.71807i −0.517572 + 0.537876i
\(157\) −2.74264 4.75039i −0.218887 0.379123i 0.735581 0.677436i \(-0.236909\pi\)
−0.954468 + 0.298314i \(0.903576\pi\)
\(158\) 0.727922 0.0579104
\(159\) 2.12132 + 3.67423i 0.168232 + 0.291386i
\(160\) 4.03553 + 6.98975i 0.319037 + 0.552588i
\(161\) 0 0
\(162\) 1.03553 + 1.79360i 0.0813592 + 0.140918i
\(163\) 12.5858 0.985795 0.492897 0.870087i \(-0.335938\pi\)
0.492897 + 0.870087i \(0.335938\pi\)
\(164\) 0.156854 + 0.271680i 0.0122483 + 0.0212146i
\(165\) 0.757359 1.31178i 0.0589603 0.102122i
\(166\) −0.221825 0.384213i −0.0172170 0.0298207i
\(167\) −3.36396 + 5.82655i −0.260311 + 0.450872i −0.966325 0.257326i \(-0.917158\pi\)
0.706013 + 0.708198i \(0.250492\pi\)
\(168\) 0 0
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) −2.20711 + 3.82282i −0.169277 + 0.293197i
\(171\) −6.00000 −0.458831
\(172\) −6.24264 −0.475997
\(173\) −10.1421 −0.771092 −0.385546 0.922689i \(-0.625987\pi\)
−0.385546 + 0.922689i \(0.625987\pi\)
\(174\) 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
\(178\) −3.17157 + 5.49333i −0.237719 + 0.411742i
\(179\) −5.65685 −0.422813 −0.211407 0.977398i \(-0.567804\pi\)
−0.211407 + 0.977398i \(0.567804\pi\)
\(180\) 1.67157 + 2.89525i 0.124592 + 0.215799i
\(181\) 9.14214 0.679530 0.339765 0.940510i \(-0.389653\pi\)
0.339765 + 0.940510i \(0.389653\pi\)
\(182\) 0 0
\(183\) 5.89949 0.436103
\(184\) −1.12132 1.94218i −0.0826648 0.143180i
\(185\) 17.3431 1.27509
\(186\) −0.757359 + 1.31178i −0.0555323 + 0.0961847i
\(187\) 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
\(191\) 16.2426 1.17528 0.587638 0.809124i \(-0.300058\pi\)
0.587638 + 0.809124i \(0.300058\pi\)
\(192\) −5.89949 −0.425759
\(193\) 7.14214 0.514102 0.257051 0.966398i \(-0.417249\pi\)
0.257051 + 0.966398i \(0.417249\pi\)
\(194\) 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 \(0.989518\pi\)
\(198\) 0.121320 + 0.210133i 0.00862186 + 0.0149335i
\(199\) 7.48528 12.9649i 0.530618 0.919057i −0.468744 0.883334i \(-0.655293\pi\)
0.999362 0.0357226i \(-0.0113733\pi\)
\(200\) −1.31371 2.27541i −0.0928932 0.160896i
\(201\) 6.00000 0.423207
\(202\) −3.03553 5.25770i −0.213579 0.369930i
\(203\) 0 0
\(204\) −7.53553 13.0519i −0.527593 0.913818i
\(205\) 0.156854 + 0.271680i 0.0109552 + 0.0189749i
\(206\) 5.79899 0.404035
\(207\) −0.707107 1.22474i −0.0491473 0.0851257i
\(208\) 3.00000 + 10.3923i 0.208013 + 0.720577i
\(209\) 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 \(0.842560\pi\)
\(212\) 5.48528 0.376731
\(213\) 8.24264 + 14.2767i 0.564776 + 0.978221i
\(214\) −3.58579 + 6.21076i −0.245119 + 0.424559i
\(215\) −6.24264 −0.425745
\(216\) 8.97056 0.610369
\(217\) 0 0
\(218\) 2.82843 4.89898i 0.191565 0.331801i
\(219\) 7.53553 + 13.0519i 0.509204 + 0.881968i
\(220\) −0.979185 1.69600i −0.0660166 0.114344i
\(221\) −14.5711 + 15.1427i −0.980156 + 1.01861i
\(222\) 2.77817 4.81194i 0.186459 0.322956i
\(223\) −1.00000 + 1.73205i −0.0669650 + 0.115987i −0.897564 0.440884i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(224\) 0 0
\(225\) −0.828427 1.43488i −0.0552285 0.0956585i
\(226\) −4.20711 + 7.28692i −0.279853 + 0.484719i
\(227\) −2.94975 + 5.10911i −0.195782 + 0.339104i −0.947156 0.320772i \(-0.896058\pi\)
0.751375 + 0.659876i \(0.229391\pi\)
\(228\) 7.75736 13.4361i 0.513744 0.889830i
\(229\) 6.24264 10.8126i 0.412525 0.714515i −0.582640 0.812730i \(-0.697980\pi\)
0.995165 + 0.0982157i \(0.0313135\pi\)
\(230\) −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 −0.908625 0.417614i \(-0.862867\pi\)
0.815976 + 0.578085i \(0.196200\pi\)
\(234\) −0.414214 1.43488i −0.0270780 0.0938009i
\(235\) −3.34315 5.79050i −0.218083 0.377730i
\(236\) −9.36396 16.2189i −0.609542 1.05576i
\(237\) −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 \(0.210775\pi\)
\(240\) −7.75736 −0.500735
\(241\) −7.74264 + 13.4106i −0.498747 + 0.863856i −0.999999 0.00144585i \(-0.999540\pi\)
0.501252 + 0.865302i \(0.332873\pi\)
\(242\) 2.20711 + 3.82282i 0.141878 + 0.245740i
\(243\) 9.89949 0.635053
\(244\) 3.81371 6.60554i 0.244148 0.422876i
\(245\) 0 0
\(246\) 0.100505 0.00640797
\(247\) −21.0000 5.19615i −1.33620 0.330623i
\(248\) 2.05025 + 3.55114i 0.130191 + 0.225498i
\(249\) 1.51472 0.0959914
\(250\) −2.52082 4.36618i −0.159430 0.276141i
\(251\) −11.4853 19.8931i −0.724945 1.25564i −0.958997 0.283417i \(-0.908532\pi\)
0.234052 0.972224i \(-0.424801\pi\)
\(252\) 0 0
\(253\) 0.414214 + 0.717439i 0.0260414 + 0.0451050i
\(254\) 5.51472 0.346024
\(255\) −7.53553 13.0519i −0.471893 0.817343i
\(256\) −1.98528 + 3.43861i −0.124080 + 0.214913i
\(257\) −7.50000 12.9904i −0.467837 0.810318i 0.531487 0.847066i \(-0.321633\pi\)
−0.999325 + 0.0367485i \(0.988300\pi\)
\(258\) −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
\(262\) 8.82843 0.545422
\(263\) −6.72792 −0.414861 −0.207431 0.978250i \(-0.566510\pi\)
−0.207431 + 0.978250i \(0.566510\pi\)
\(264\) −1.31371 −0.0808532
\(265\) 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
\(269\) 9.00000 15.5885i 0.548740 0.950445i −0.449622 0.893219i \(-0.648441\pi\)
0.998361 0.0572259i \(-0.0182255\pi\)
\(270\) 4.28427 0.260732
\(271\) 10.5355 + 18.2481i 0.639988 + 1.10849i 0.985435 + 0.170054i \(0.0543941\pi\)
−0.345447 + 0.938438i \(0.612273\pi\)
\(272\) −17.4853 −1.06020
\(273\) 0 0
\(274\) −0.0710678 −0.00429336
\(275\) 0.485281 + 0.840532i 0.0292636 + 0.0506860i
\(276\) 3.65685 0.220117
\(277\) −0.985281 + 1.70656i −0.0591998 + 0.102537i −0.894106 0.447855i \(-0.852188\pi\)
0.834907 + 0.550392i \(0.185522\pi\)
\(278\) 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 \(0.674643\pi\)
\(282\) −2.14214 −0.127562
\(283\) −19.8995 −1.18290 −0.591451 0.806341i \(-0.701445\pi\)
−0.591451 + 0.806341i \(0.701445\pi\)
\(284\) 21.3137 1.26474
\(285\) 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
\(289\) −8.48528 14.6969i −0.499134 0.864526i
\(290\) 1.57969 2.73610i 0.0927626 0.160669i
\(291\) 7.65685 + 13.2621i 0.448853 + 0.777436i
\(292\) 19.4853 1.14029
\(293\) −14.2279 24.6435i −0.831204 1.43969i −0.897084 0.441860i \(-0.854319\pi\)
0.0658799 0.997828i \(-0.479015\pi\)
\(294\) 0 0
\(295\) −9.36396 16.2189i −0.545191 0.944298i
\(296\) −7.52082 13.0264i −0.437139 0.757146i
\(297\) −3.31371 −0.192281
\(298\) −0.621320 1.07616i −0.0359921 0.0623402i
\(299\) −1.41421 4.89898i −0.0817861 0.283315i
\(300\) 4.28427 0.247353
\(301\) 0 0
\(302\) −3.10051 + 5.37023i −0.178414 + 0.309022i
\(303\) 20.7279 1.19079
\(304\) −9.00000 15.5885i −0.516185 0.894059i
\(305\) 3.81371 6.60554i 0.218372 0.378232i
\(306\) 2.41421 0.138011
\(307\) −32.7279 −1.86788 −0.933941 0.357428i \(-0.883654\pi\)
−0.933941 + 0.357428i \(0.883654\pi\)
\(308\) 0 0
\(309\) −9.89949 + 17.1464i −0.563163 + 0.975426i
\(310\) 0.979185 + 1.69600i 0.0556140 + 0.0963262i
\(311\) 6.46447 + 11.1968i 0.366566 + 0.634911i 0.989026 0.147740i \(-0.0472000\pi\)
−0.622460 + 0.782652i \(0.713867\pi\)
\(312\) 7.84924 + 1.94218i 0.444376 + 0.109955i
\(313\) 7.00000 12.1244i 0.395663 0.685309i −0.597522 0.801852i \(-0.703848\pi\)
0.993186 + 0.116543i \(0.0371814\pi\)
\(314\) −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 −0.113292 + 0.993562i \(0.536140\pi\)
−0.803804 + 0.594895i \(0.797194\pi\)
\(318\) 0.878680 1.52192i 0.0492739 0.0853449i
\(319\) −1.22183 + 2.11626i −0.0684091 + 0.118488i
\(320\) −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
\(325\) −1.65685 5.73951i −0.0919057 0.318371i
\(326\) −2.60660 4.51477i −0.144366 0.250050i
\(327\) 9.65685 + 16.7262i 0.534025 + 0.924959i
\(328\) 0.136039 0.235626i 0.00751150 0.0130103i
\(329\) 0 0
\(330\) −0.627417 −0.0345382
\(331\) −24.8701 −1.36698 −0.683491 0.729959i \(-0.739539\pi\)
−0.683491 + 0.729959i \(0.739539\pi\)
\(332\) 0.979185 1.69600i 0.0537397 0.0930800i
\(333\) −4.74264 8.21449i −0.259895 0.450152i
\(334\) 2.78680 0.152487
\(335\) 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 \(0.530262\pi\)
\(338\) −0.207107 5.38079i −0.0112651 0.292677i
\(339\) −14.3640 24.8791i −0.780143 1.35125i
\(340\) −19.4853 −1.05674
\(341\) −0.757359 1.31178i −0.0410133 0.0710371i
\(342\) 1.24264 + 2.15232i 0.0671943 + 0.116384i
\(343\) 0 0
\(344\) 2.70711 + 4.68885i 0.145957 + 0.252806i
\(345\) 3.65685 0.196878
\(346\) 2.10051 + 3.63818i 0.112924 + 0.195590i
\(347\) 3.05025 5.28319i 0.163746 0.283617i −0.772463 0.635060i \(-0.780976\pi\)
0.936209 + 0.351443i \(0.114309\pi\)
\(348\) 5.39340 + 9.34164i 0.289116 + 0.500764i
\(349\) −4.65685 + 8.06591i −0.249276 + 0.431758i −0.963325 0.268337i \(-0.913526\pi\)
0.714049 + 0.700095i \(0.246859\pi\)
\(350\) 0 0
\(351\) 19.7990 + 4.89898i 1.05679 + 0.261488i
\(352\) −1.29289 + 2.23936i −0.0689114 + 0.119358i
\(353\) 5.82843 0.310216 0.155108 0.987898i \(-0.450427\pi\)
0.155108 + 0.987898i \(0.450427\pi\)
\(354\) −6.00000 −0.318896
\(355\) 21.3137 1.13121
\(356\) −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 −0.550409 0.834895i \(-0.685528\pi\)
0.998245 + 0.0592205i \(0.0188615\pi\)
\(360\) 1.44975 2.51104i 0.0764084 0.132343i
\(361\) 17.0000 0.894737
\(362\) −1.89340 3.27946i −0.0995148 0.172365i
\(363\) −15.0711 −0.791026
\(364\) 0 0
\(365\) 19.4853 1.01991
\(366\) −1.22183 2.11626i −0.0638658 0.110619i
\(367\) −28.7279 −1.49959 −0.749793 0.661673i \(-0.769847\pi\)
−0.749793 + 0.661673i \(0.769847\pi\)
\(368\) 2.12132 3.67423i 0.110581 0.191533i
\(369\) 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
\(373\) 26.4558 1.36983 0.684916 0.728622i \(-0.259839\pi\)
0.684916 + 0.728622i \(0.259839\pi\)
\(374\) −1.41421 −0.0731272
\(375\) 17.2132 0.888886
\(376\) −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 \(0.164683\pi\)
\(380\) −10.0294 17.3715i −0.514499 0.891139i
\(381\) −9.41421 + 16.3059i −0.482305 + 0.835376i
\(382\) −3.36396 5.82655i −0.172115 0.298112i
\(383\) −34.0416 −1.73945 −0.869723 0.493540i \(-0.835703\pi\)
−0.869723 + 0.493540i \(0.835703\pi\)
\(384\) 7.46447 + 12.9288i 0.380919 + 0.659772i
\(385\) 0 0
\(386\) −1.47918 2.56202i −0.0752885 0.130404i
\(387\) 1.70711 + 2.95680i 0.0867771 + 0.150302i
\(388\) 19.7990 1.00514
\(389\) −13.5711 23.5058i −0.688080 1.19179i −0.972458 0.233078i \(-0.925120\pi\)
0.284378 0.958712i \(-0.408213\pi\)
\(390\) 3.74874 + 0.927572i 0.189825 + 0.0469694i
\(391\) 8.24264 0.416848
\(392\) 0 0
\(393\) −15.0711 + 26.1039i −0.760235 + 1.31677i
\(394\) 6.14214 0.309436
\(395\) 1.60660 + 2.78272i 0.0808369 + 0.140014i
\(396\) −0.535534 + 0.927572i −0.0269116 + 0.0466122i
\(397\) 6.62742 0.332621 0.166310 0.986073i \(-0.446815\pi\)
0.166310 + 0.986073i \(0.446815\pi\)
\(398\) −6.20101 −0.310829
\(399\) 0 0
\(400\) 2.48528 4.30463i 0.124264 0.215232i
\(401\) −4.39949 7.62015i −0.219700 0.380532i 0.735016 0.678050i \(-0.237175\pi\)
−0.954716 + 0.297518i \(0.903841\pi\)
\(402\) −1.24264 2.15232i −0.0619773 0.107348i
\(403\) 2.58579 + 8.95743i 0.128807 + 0.446201i
\(404\) 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
\(409\) 10.9853 19.0271i 0.543187 0.940828i −0.455531 0.890220i \(-0.650551\pi\)
0.998719 0.0506081i \(-0.0161159\pi\)
\(410\) 0.0649712 0.112533i 0.00320870 0.00555763i
\(411\) 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
\(416\) 11.0355 11.4685i 0.541062 0.562288i
\(417\) 8.41421 + 14.5738i 0.412046 + 0.713684i
\(418\) −0.727922 1.26080i −0.0356038 0.0616676i
\(419\) 5.77817 10.0081i 0.282282 0.488927i −0.689664 0.724129i \(-0.742242\pi\)
0.971946 + 0.235202i \(0.0755752\pi\)
\(420\) 0 0
\(421\) 21.4853 1.04713 0.523564 0.851986i \(-0.324602\pi\)
0.523564 + 0.851986i \(0.324602\pi\)
\(422\) 10.2426 0.498604
\(423\) −1.82843 + 3.16693i −0.0889012 + 0.153981i
\(424\) −2.37868 4.11999i −0.115519 0.200085i
\(425\) 9.65685 0.468426
\(426\) 3.41421 5.91359i 0.165419 0.286514i
\(427\) 0 0
\(428\) −31.6569 −1.53019
\(429\) −2.89949 0.717439i −0.139989 0.0346383i
\(430\) 1.29289 + 2.23936i 0.0623488 + 0.107991i
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) 8.48528 + 14.6969i 0.408248 + 0.707107i
\(433\) −8.74264 15.1427i −0.420144 0.727712i 0.575809 0.817584i \(-0.304687\pi\)
−0.995953 + 0.0898728i \(0.971354\pi\)
\(434\) 0 0
\(435\) 5.39340 + 9.34164i 0.258594 + 0.447897i
\(436\) 24.9706 1.19587
\(437\) 4.24264 + 7.34847i 0.202953 + 0.351525i
\(438\) 3.12132 5.40629i 0.149142 0.258322i
\(439\) 0.636039 + 1.10165i 0.0303565 + 0.0525790i 0.880805 0.473480i \(-0.157002\pi\)
−0.850448 + 0.526059i \(0.823669\pi\)
\(440\) −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 0.381826 + 0.924234i \(0.375295\pi\)
−0.991323 + 0.131446i \(0.958038\pi\)
\(444\) 24.5269 1.16400
\(445\) −28.0000 −1.32733
\(446\) 0.828427 0.0392272
\(447\) 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
\(451\) −0.0502525 + 0.0870399i −0.00236630 + 0.00409855i
\(452\) −37.1421 −1.74702
\(453\) −10.5858 18.3351i −0.497364 0.861459i
\(454\) 2.44365 0.114686
\(455\) 0 0
\(456\) −13.4558 −0.630128
\(457\) 12.5000 + 21.6506i 0.584725 + 1.01277i 0.994910 + 0.100771i \(0.0321310\pi\)
−0.410184 + 0.912003i \(0.634536\pi\)
\(458\) −5.17157 −0.241652
\(459\) −16.4853 + 28.5533i −0.769467 + 1.33276i
\(460\) 2.36396 4.09450i 0.110220 0.190907i
\(461\) −0.671573 1.16320i −0.0312783 0.0541755i 0.849963 0.526843i \(-0.176624\pi\)
−0.881241 + 0.472668i \(0.843291\pi\)
\(462\) 0 0
\(463\) 6.72792 0.312673 0.156337 0.987704i \(-0.450032\pi\)
0.156337 + 0.987704i \(0.450032\pi\)
\(464\) 12.5147 0.580981
\(465\) −6.68629 −0.310069
\(466\) 1.17157 0.0542721
\(467\) −5.70711 + 9.88500i −0.264093 + 0.457423i −0.967326 0.253537i \(-0.918406\pi\)
0.703232 + 0.710960i \(0.251739\pi\)
\(468\) 4.57107 4.75039i 0.211298 0.219587i
\(469\) 0 0
\(470\) −1.38478 + 2.39850i −0.0638750 + 0.110635i
\(471\) −3.87868 6.71807i −0.178720 0.309552i
\(472\) −8.12132 + 14.0665i −0.373814 + 0.647465i
\(473\) −1.00000 1.73205i −0.0459800 0.0796398i
\(474\) 1.02944 0.0472836
\(475\) 4.97056 + 8.60927i 0.228065 + 0.395020i
\(476\) 0 0
\(477\) −1.50000 2.59808i −0.0686803 0.118958i
\(478\) −5.05025 8.74729i −0.230993 0.400092i
\(479\) −1.61522 −0.0738015 −0.0369007 0.999319i \(-0.511749\pi\)
−0.0369007 + 0.999319i \(0.511749\pi\)
\(480\) 5.70711 + 9.88500i 0.260493 + 0.451186i
\(481\) −9.48528 32.8580i −0.432492 1.49819i
\(482\) 6.41421 0.292159
\(483\) 0 0
\(484\) −9.74264 + 16.8747i −0.442847 + 0.767034i
\(485\) 19.7990 0.899026
\(486\) −2.05025 3.55114i −0.0930013 0.161083i
\(487\) 6.48528 11.2328i 0.293876 0.509008i −0.680847 0.732426i \(-0.738388\pi\)
0.974723 + 0.223418i \(0.0717213\pi\)
\(488\) −6.61522 −0.299457
\(489\) 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 \(0.259079\pi\)
\(492\) 0.221825 + 0.384213i 0.0100007 + 0.0173217i
\(493\) 12.1569 + 21.0563i 0.547517 + 0.948328i
\(494\) 2.48528 + 8.60927i 0.111818 + 0.387349i
\(495\) −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 −0.998295 0.0583748i \(-0.981408\pi\)
0.549701 + 0.835361i \(0.314741\pi\)
\(500\) 11.1274 19.2733i 0.497633 0.861926i
\(501\) −4.75736 + 8.23999i −0.212543 + 0.368136i
\(502\) −4.75736 + 8.23999i −0.212331 + 0.367769i
\(503\) 1.22183 + 2.11626i 0.0544785 + 0.0943595i 0.891979 0.452078i \(-0.149317\pi\)
−0.837500 + 0.546437i \(0.815984\pi\)
\(504\) 0 0
\(505\) 13.3995 23.2086i 0.596270 1.03277i
\(506\) 0.171573 0.297173i 0.00762734 0.0132109i
\(507\) 16.2635 + 8.57321i 0.722285 + 0.380750i
\(508\) 12.1716 + 21.0818i 0.540026 + 0.935353i
\(509\) −2.32843 4.03295i −0.103206 0.178758i 0.809798 0.586709i \(-0.199577\pi\)
−0.913004 + 0.407951i \(0.866243\pi\)
\(510\) −3.12132 + 5.40629i −0.138214 + 0.239394i
\(511\) 0 0
\(512\) 22.7574 1.00574
\(513\) −33.9411 −1.49854
\(514\) −3.10660 + 5.38079i −0.137026 + 0.237337i
\(515\) 12.7990 + 22.1685i 0.563991 + 0.976861i
\(516\) −8.82843 −0.388650
\(517\) 1.07107 1.85514i 0.0471055 0.0815891i
\(518\) 0 0
\(519\) −14.3431 −0.629594
\(520\) 7.24874 7.53311i 0.317878 0.330349i
\(521\) 12.3284 + 21.3535i 0.540118 + 0.935512i 0.998897 + 0.0469615i \(0.0149538\pi\)
−0.458779 + 0.888551i \(0.651713\pi\)
\(522\) −1.72792 −0.0756291
\(523\) 8.48528 + 14.6969i 0.371035 + 0.642652i 0.989725 0.142983i \(-0.0456695\pi\)
−0.618690 + 0.785635i \(0.712336\pi\)
\(524\) 19.4853 + 33.7495i 0.851218 + 1.47435i
\(525\) 0 0
\(526\) 1.39340 + 2.41344i 0.0607551 + 0.105231i
\(527\) −15.0711 −0.656506
\(528\) −1.24264 2.15232i −0.0540790 0.0936676i
\(529\) 10.5000 18.1865i 0.456522 0.790719i
\(530\) −1.13604 1.96768i −0.0493464 0.0854704i
\(531\) −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
\(535\) −31.6569 −1.36865
\(536\) −6.72792 −0.290602
\(537\) −8.00000 −0.345225
\(538\) −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 −0.715767 0.698339i \(-0.753923\pi\)
0.962663 + 0.270703i \(0.0872563\pi\)
\(542\) 4.36396 7.55860i 0.187448 0.324670i
\(543\) 12.9289 0.554834
\(544\) 12.8640 + 22.2810i 0.551538 + 0.955291i
\(545\) 24.9706 1.06962
\(546\) 0 0
\(547\) 0.928932 0.0397183 0.0198591 0.999803i \(-0.493678\pi\)
0.0198591 + 0.999803i \(0.493678\pi\)
\(548\) −0.156854 0.271680i −0.00670048 0.0116056i
\(549\) −4.17157 −0.178038
\(550\) 0.201010 0.348160i 0.00857110 0.0148456i
\(551\) −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
\(555\) 24.5269 1.04111
\(556\) 21.7574 0.922718
\(557\) 12.3137 0.521749 0.260874 0.965373i \(-0.415989\pi\)
0.260874 + 0.965373i \(0.415989\pi\)
\(558\) 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
\(562\) 3.62132 + 6.27231i 0.152756 + 0.264581i
\(563\) −0.0502525 + 0.0870399i −0.00211789 + 0.00366830i −0.867082 0.498165i \(-0.834007\pi\)
0.864965 + 0.501833i \(0.167341\pi\)
\(564\) −4.72792 8.18900i −0.199081 0.344819i
\(565\) −37.1421 −1.56258
\(566\) 4.12132 + 7.13834i 0.173232 + 0.300047i
\(567\) 0 0
\(568\) −9.24264 16.0087i −0.387813 0.671711i
\(569\) −9.41421 16.3059i −0.394664 0.683579i 0.598394 0.801202i \(-0.295806\pi\)
−0.993058 + 0.117623i \(0.962472\pi\)
\(570\) −6.42641 −0.269173
\(571\) −14.4853 25.0892i −0.606190 1.04995i −0.991862 0.127316i \(-0.959364\pi\)
0.385672 0.922636i \(-0.373970\pi\)
\(572\) −2.67767 + 2.78272i −0.111959 + 0.116351i
\(573\) 22.9706 0.959609
\(574\) 0 0
\(575\) −1.17157 + 2.02922i −0.0488580 + 0.0846245i
\(576\) 4.17157 0.173816
\(577\) 6.84315 + 11.8527i 0.284884 + 0.493433i 0.972581 0.232564i \(-0.0747116\pi\)
−0.687697 + 0.725998i \(0.741378\pi\)
\(578\) −3.51472 + 6.08767i −0.146193 + 0.253214i
\(579\) 10.1005 0.419763
\(580\) 13.9462 0.579083
\(581\) 0 0
\(582\) 3.17157 5.49333i 0.131466 0.227706i
\(583\) 0.878680 + 1.52192i 0.0363912 + 0.0630314i
\(584\) −8.44975 14.6354i −0.349653 0.605617i
\(585\) 4.57107 4.75039i 0.188990 0.196405i
\(586\) −5.89340 + 10.2077i −0.243454 + 0.421675i
\(587\) 14.8284 25.6836i 0.612035 1.06008i −0.378862 0.925453i \(-0.623685\pi\)
0.990897 0.134622i \(-0.0429821\pi\)
\(588\) 0 0
\(589\) −7.75736 13.4361i −0.319636 0.553627i
\(590\) −3.87868 + 6.71807i −0.159683 + 0.276579i
\(591\) −10.4853 + 18.1610i −0.431307 + 0.747045i
\(592\) 14.2279 24.6435i 0.584764 1.01284i
\(593\) −12.6421 + 21.8968i −0.519150 + 0.899195i 0.480602 + 0.876939i \(0.340418\pi\)
−0.999752 + 0.0222559i \(0.992915\pi\)
\(594\) 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
\(598\) −1.46447 + 1.52192i −0.0598865 + 0.0622358i
\(599\) −14.1716 24.5459i −0.579035 1.00292i −0.995590 0.0938074i \(-0.970096\pi\)
0.416556 0.909110i \(-0.363237\pi\)
\(600\) −1.85786 3.21792i −0.0758470 0.131371i
\(601\) −15.4706 + 26.7958i −0.631057 + 1.09302i 0.356278 + 0.934380i \(0.384045\pi\)
−0.987336 + 0.158644i \(0.949288\pi\)
\(602\) 0 0
\(603\) −4.24264 −0.172774
\(604\) −27.3726 −1.11377
\(605\) −9.74264 + 16.8747i −0.396095 + 0.686056i
\(606\) −4.29289 7.43551i −0.174387 0.302047i
\(607\) −32.3431 −1.31277 −0.656384 0.754427i \(-0.727915\pi\)
−0.656384 + 0.754427i \(0.727915\pi\)
\(608\) −13.2426 + 22.9369i −0.537060 + 0.930215i
\(609\) 0 0
\(610\) −3.15938 −0.127920
\(611\) −9.14214 + 9.50079i −0.369851 + 0.384361i
\(612\) 5.32843 + 9.22911i 0.215389 + 0.373065i
\(613\) −14.7990 −0.597726 −0.298863 0.954296i \(-0.596607\pi\)
−0.298863 + 0.954296i \(0.596607\pi\)
\(614\) 6.77817 + 11.7401i 0.273545 + 0.473794i
\(615\) 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 \(0.617670\pi\)
\(618\) 8.20101 0.329893
\(619\) −20.7782 35.9889i −0.835145 1.44651i −0.893912 0.448242i \(-0.852050\pi\)
0.0587667 0.998272i \(-0.481283\pi\)
\(620\) −4.32233 + 7.48650i −0.173589 + 0.300665i
\(621\) −4.00000 6.92820i −0.160514 0.278019i
\(622\) 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
\(626\) −5.79899 −0.231774
\(627\) 4.97056 0.198505
\(628\) −10.0294 −0.400218
\(629\) 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
\(633\) −17.4853 + 30.2854i −0.694978 + 1.20374i
\(634\) 13.5269 0.537222
\(635\) 12.1716 + 21.0818i 0.483014 + 0.836605i
\(636\) 7.75736 0.307599
\(637\) 0 0
\(638\) 1.01219 0.0400731
\(639\) −5.82843 10.0951i −0.230569 0.399357i
\(640\) 19.3015 0.762959
\(641\) 7.39949 12.8163i 0.292262 0.506213i −0.682082 0.731276i \(-0.738925\pi\)
0.974344 + 0.225062i \(0.0722586\pi\)
\(642\) −5.07107 + 8.78335i −0.200139 + 0.346651i
\(643\) −7.51472 13.0159i −0.296352 0.513296i 0.678947 0.734187i \(-0.262437\pi\)
−0.975298 + 0.220891i \(0.929103\pi\)
\(644\) 0 0
\(645\) −8.82843 −0.347619
\(646\) −14.4853 −0.569916
\(647\) −17.3137 −0.680672 −0.340336 0.940304i \(-0.610541\pi\)
−0.340336 + 0.940304i \(0.610541\pi\)
\(648\) 7.92893 0.311478
\(649\) 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
\(653\) −13.0711 22.6398i −0.511510 0.885962i −0.999911 0.0133425i \(-0.995753\pi\)
0.488401 0.872620i \(-0.337580\pi\)
\(654\) 4.00000 6.92820i 0.156412 0.270914i
\(655\) 19.4853 + 33.7495i 0.761353 + 1.31870i
\(656\) 0.514719 0.0200964
\(657\) −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 \(0.736924\pi\)
\(660\) −1.38478 2.39850i −0.0539023 0.0933616i
\(661\) −33.1421 −1.28908 −0.644540 0.764571i \(-0.722951\pi\)
−0.644540 + 0.764571i \(0.722951\pi\)
\(662\) 5.15076 + 8.92137i 0.200190 + 0.346739i
\(663\) −20.6066 + 21.4150i −0.800294 + 0.831690i
\(664\) −1.69848 −0.0659140
\(665\) 0 0
\(666\) −1.96447 + 3.40256i −0.0761215 + 0.131846i
\(667\) −5.89949 −0.228429
\(668\) 6.15076 + 10.6534i 0.237980 + 0.412193i
\(669\) −1.41421 + 2.44949i −0.0546767 + 0.0947027i
\(670\) −3.21320 −0.124137
\(671\) 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 \(0.256918\pi\)
\(674\) 0.721825 + 1.25024i 0.0278037 + 0.0481574i
\(675\) −4.68629 8.11689i −0.180375 0.312419i
\(676\) 20.1127 12.6677i 0.773565 0.487220i
\(677\) 8.82843 15.2913i 0.339304 0.587692i −0.644998 0.764184i \(-0.723142\pi\)
0.984302 + 0.176492i \(0.0564751\pi\)
\(678\) −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
\(682\) −0.313708 + 0.543359i −0.0120125 + 0.0208063i
\(683\) −2.65685 + 4.60181i −0.101662 + 0.176083i −0.912369 0.409368i \(-0.865749\pi\)
0.810708 + 0.585451i \(0.199083\pi\)
\(684\) −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
\(689\) −3.00000 10.3923i −0.114291 0.395915i
\(690\) −0.757359 1.31178i −0.0288322 0.0499388i
\(691\) −14.9706 25.9298i −0.569507 0.986415i −0.996615 0.0822143i \(-0.973801\pi\)
0.427108 0.904201i \(-0.359533\pi\)
\(692\) −9.27208 + 16.0597i −0.352472 + 0.610499i
\(693\) 0 0
\(694\) −2.52691 −0.0959203
\(695\) 21.7574 0.825304
\(696\) 4.67767 8.10196i 0.177307 0.307104i
\(697\) 0.500000 + 0.866025i 0.0189389 + 0.0328031i
\(698\) 3.85786 0.146022
\(699\) −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 \(0.415716\pi\)
\(702\) −2.34315 8.11689i −0.0884363 0.306352i
\(703\) 28.4558 + 49.2870i 1.07323 + 1.85889i
\(704\) −2.44365 −0.0920986
\(705\) −4.72792 8.18900i −0.178064 0.308416i
\(706\) −1.20711 2.09077i −0.0454301 0.0786872i
\(707\) 0 0
\(708\) −13.2426 22.9369i −0.497689 0.862022i
\(709\) 17.6274 0.662012 0.331006 0.943629i \(-0.392612\pi\)
0.331006 + 0.943629i \(0.392612\pi\)
\(710\) −4.41421 7.64564i −0.165662 0.286936i
\(711\) 0.878680 1.52192i 0.0329531 0.0570764i
\(712\) 12.1421 + 21.0308i 0.455046 + 0.788162i
\(713\) 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
\(717\) 34.4853 1.28788
\(718\) −7.02944 −0.262336
\(719\) 0.384776 0.0143497 0.00717487 0.999974i \(-0.497716\pi\)
0.00717487 + 0.999974i \(0.497716\pi\)
\(720\) 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
\(724\) 8.35786 14.4762i 0.310618 0.538005i
\(725\) −6.91169 −0.256694
\(726\) 3.12132 + 5.40629i 0.115843 + 0.200646i
\(727\) 24.9706 0.926107 0.463053 0.886330i \(-0.346754\pi\)
0.463053 + 0.886330i \(0.346754\pi\)
\(728\) 0 0
\(729\) 29.0000 1.07407
\(730\) −4.03553 6.98975i −0.149362 0.258702i
\(731\) −19.8995 −0.736009
\(732\) 5.39340 9.34164i 0.199346 0.345277i
\(733\) 10.5000 18.1865i 0.387826 0.671735i −0.604331 0.796734i \(-0.706559\pi\)
0.992157 + 0.124999i \(0.0398927\pi\)
\(734\) 5.94975 + 10.3053i 0.219609 + 0.380374i
\(735\) 0 0
\(736\) −6.24264 −0.230107
\(737\) 2.48528 0.0915465
\(738\) −0.0710678 −0.00261604
\(739\) −20.2843 −0.746169 −0.373084 0.927797i \(-0.621700\pi\)
−0.373084 + 0.927797i \(0.621700\pi\)
\(740\) 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 \(0.969872\pi\)
\(744\) 2.89949 + 5.02207i 0.106301 + 0.184118i
\(745\) 2.74264 4.75039i 0.100483 0.174041i
\(746\) −5.47918 9.49023i −0.200607 0.347462i
\(747\) −1.07107 −0.0391883
\(748\) −3.12132 5.40629i −0.114127 0.197673i
\(749\) 0 0
\(750\) −3.56497 6.17471i −0.130174 0.225469i
\(751\) 8.77817 + 15.2042i 0.320320 + 0.554811i 0.980554 0.196249i \(-0.0628762\pi\)
−0.660234 + 0.751060i \(0.729543\pi\)
\(752\) −10.9706 −0.400055
\(753\) −16.2426 28.1331i −0.591915 1.02523i
\(754\) −6.04773 1.49642i −0.220245 0.0544966i
\(755\) −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 \(0.986867\pi\)
\(758\) −0.100505 −0.00365051
\(759\) 0.585786 + 1.01461i 0.0212627 + 0.0368281i
\(760\) −8.69848 + 15.0662i −0.315527 + 0.546509i
\(761\) 17.8579 0.647347 0.323674 0.946169i \(-0.395082\pi\)
0.323674 + 0.946169i \(0.395082\pi\)
\(762\) 7.79899 0.282528
\(763\) 0 0
\(764\) 14.8492 25.7196i 0.537227 0.930504i
\(765\) 5.32843 + 9.22911i 0.192650 + 0.333679i
\(766\) 7.05025 + 12.2114i 0.254736 + 0.441216i
\(767\) −25.6066 + 26.6112i −0.924601 + 0.960873i
\(768\) −2.80761 + 4.86293i −0.101311 + 0.175476i
\(769\) 24.7279 42.8300i 0.891712 1.54449i 0.0538894 0.998547i \(-0.482838\pi\)
0.837822 0.545943i \(-0.183828\pi\)
\(770\) 0 0
\(771\) −10.6066 18.3712i −0.381987 0.661622i
\(772\) 6.52944 11.3093i 0.235000 0.407031i
\(773\) −3.17157 + 5.49333i −0.114074 + 0.197581i −0.917409 0.397946i \(-0.869723\pi\)
0.803335 + 0.595527i \(0.203057\pi\)
\(774\) 0.707107 1.22474i 0.0254164 0.0440225i
\(775\) 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
\(780\) 4.72792 + 16.3780i 0.169287 + 0.586427i
\(781\) 3.41421 + 5.91359i 0.122170 + 0.211605i
\(782\) −1.70711 2.95680i −0.0610460 0.105735i
\(783\) 11.7990 20.4364i 0.421661 0.730339i
\(784\) 0 0
\(785\) −10.0294 −0.357966
\(786\) 12.4853 0.445335
\(787\) 6.94975 12.0373i 0.247732 0.429084i −0.715164 0.698956i \(-0.753648\pi\)
0.962896 + 0.269872i \(0.0869815\pi\)
\(788\) 13.5563 + 23.4803i 0.482925 + 0.836451i
\(789\) −9.51472 −0.338733
\(790\) 0.665476 1.15264i 0.0236766 0.0410090i
\(791\) 0 0
\(792\) 0.928932 0.0330082
\(793\) −14.6005 3.61269i −0.518479 0.128290i
\(794\) −1.37258 2.37738i −0.0487111 0.0843702i
\(795\) 7.75736 0.275125
\(796\) −13.6863 23.7054i −0.485098 0.840214i
\(797\) 9.07107 + 15.7116i 0.321314 + 0.556532i 0.980759 0.195221i \(-0.0625423\pi\)
−0.659446 + 0.751752i \(0.729209\pi\)
\(798\) 0 0
\(799\) −10.6569 18.4582i −0.377012 0.653005i
\(800\) −7.31371 −0.258579
\(801\) 7.65685 + 13.2621i 0.270542 + 0.468592i
\(802\) −1.82233 + 3.15637i −0.0643487 + 0.111455i
\(803\) 3.12132 + 5.40629i 0.110149 + 0.190784i
\(804\) 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
\(808\) −23.2426 −0.817673
\(809\) 35.1421 1.23553 0.617766 0.786362i \(-0.288038\pi\)
0.617766 + 0.786362i \(0.288038\pi\)
\(810\) 3.78680 0.133054
\(811\) −42.1838 −1.48127 −0.740636 0.671906i \(-0.765476\pi\)
−0.740636 + 0.671906i \(0.765476\pi\)
\(812\) 0 0
\(813\) 14.8995 + 25.8067i 0.522548 + 0.905080i
\(814\) 1.15076 1.99317i 0.0403340 0.0698606i
\(815\) 11.5061 19.9291i 0.403041 0.698087i
\(816\) −24.7279 −0.865650
\(817\) −10.2426 17.7408i −0.358345 0.620671i
\(818\) −9.10051 −0.318192
\(819\) 0 0
\(820\) 0.573593 0.0200307
\(821\) 19.9706 + 34.5900i 0.696977 + 1.20720i 0.969510 + 0.245054i \(0.0788056\pi\)
−0.272532 + 0.962147i \(0.587861\pi\)
\(822\) −0.100505 −0.00350552
\(823\) −9.65685 + 16.7262i −0.336617 + 0.583037i −0.983794 0.179302i \(-0.942616\pi\)
0.647177 + 0.762340i \(0.275949\pi\)
\(824\) 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 \(0.868396\pi\)
\(828\) −2.58579 −0.0898623
\(829\) 46.3137 1.60854 0.804271 0.594263i \(-0.202556\pi\)
0.804271 + 0.594263i \(0.202556\pi\)
\(830\) −0.811183 −0.0281566
\(831\) −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
\(835\) 6.15076 + 10.6534i 0.212856 + 0.368677i
\(836\) 3.21320 5.56543i 0.111131 0.192484i
\(837\) 7.31371 + 12.6677i 0.252799 + 0.437860i
\(838\) −4.78680 −0.165357
\(839\) 20.7990 + 36.0249i 0.718061 + 1.24372i 0.961767 + 0.273869i \(0.0883034\pi\)
−0.243706 + 0.969849i \(0.578363\pi\)
\(840\) 0 0
\(841\) 5.79899 + 10.0441i 0.199965 + 0.346350i
\(842\) −4.44975 7.70719i −0.153348 0.265607i
\(843\) −24.7279 −0.851675
\(844\) 22.6066 + 39.1558i 0.778151 + 1.34780i
\(845\) 20.1127 12.6677i 0.691898 0.435783i
\(846\) 1.51472 0.0520771
\(847\) 0 0
\(848\) 4.50000 7.79423i 0.154531 0.267655i
\(849\) −28.1421 −0.965836
\(850\) −2.00000 3.46410i −0.0685994 0.118818i
\(851\) −6.70711 + 11.6170i −0.229917 + 0.398227i
\(852\) 30.1421 1.03265
\(853\) −35.0000 −1.19838 −0.599189 0.800608i \(-0.704510\pi\)
−0.599189 + 0.800608i \(0.704510\pi\)
\(854\) 0 0
\(855\) −5.48528 + 9.50079i −0.187593 + 0.324920i
\(856\) 13.7279 + 23.7775i 0.469211 + 0.812697i
\(857\) −0.600505 1.04011i −0.0205129 0.0355293i 0.855587 0.517659i \(-0.173197\pi\)
−0.876100 + 0.482130i \(0.839863\pi\)
\(858\) 0.343146 + 1.18869i 0.0117148 + 0.0405813i
\(859\) 6.46447 11.1968i 0.220565 0.382029i −0.734415 0.678701i \(-0.762543\pi\)
0.954980 + 0.296672i \(0.0958766\pi\)
\(860\) −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 −0.641554 0.767078i \(-0.721710\pi\)
0.985086 + 0.172063i \(0.0550434\pi\)
\(864\) 12.4853 21.6251i 0.424758 0.735702i
\(865\) −9.27208 + 16.0597i −0.315260 + 0.546047i
\(866\) −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
\(871\) −14.8492 3.67423i −0.503147 0.124497i
\(872\) −10.8284 18.7554i −0.366697 0.635138i
\(873\) −5.41421 9.37769i −0.183243 0.317387i
\(874\) 1.75736 3.04384i 0.0594436 0.102959i
\(875\) 0 0
\(876\) 27.5563 0.931043
\(877\) 17.0000 0.574049 0.287025 0.957923i \(-0.407334\pi\)
0.287025 + 0.957923i \(0.407334\pi\)
\(878\) 0.263456 0.456319i 0.00889121 0.0154000i
\(879\) −20.1213 34.8511i −0.678675 1.17550i
\(880\) −3.21320 −0.108317
\(881\) −2.22792 + 3.85887i −0.0750606 + 0.130009i −0.901113 0.433585i \(-0.857248\pi\)
0.826052 + 0.563594i \(0.190582\pi\)
\(882\) 0 0
\(883\) 56.0416 1.88595 0.942976 0.332862i \(-0.108014\pi\)
0.942976 + 0.332862i \(0.108014\pi\)
\(884\) 10.6569 + 36.9164i 0.358429 + 1.24163i
\(885\) −13.2426 22.9369i −0.445146 0.771016i
\(886\) 10.6274 0.357035
\(887\) 17.3137 + 29.9882i 0.581337 + 1.00691i 0.995321 + 0.0966217i \(0.0308037\pi\)
−0.413984 + 0.910284i \(0.635863\pi\)
\(888\) −10.6360 18.4222i −0.356922 0.618207i
\(889\) 0 0
\(890\) 5.79899 + 10.0441i 0.194383 + 0.336681i
\(891\) −2.92893 −0.0981229
\(892\) 1.82843 + 3.16693i 0.0612203 + 0.106037i
\(893\) 10.9706 19.0016i 0.367116 0.635863i
\(894\) −0.878680 1.52192i −0.0293874 0.0509005i
\(895\) −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
\(899\) 10.7868 0.359760
\(900\) −3.02944 −0.100981
\(901\) 17.4853 0.582519
\(902\) 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
\(906\) −4.38478 + 7.59466i −0.145674 + 0.252316i
\(907\) −6.72792 −0.223397 −0.111698 0.993742i \(-0.535629\pi\)
−0.111698 + 0.993742i \(0.535629\pi\)
\(908\) 5.39340 + 9.34164i 0.178986 + 0.310013i
\(909\) −14.6569 −0.486137
\(910\) 0 0
\(911\) −29.6569 −0.982575 −0.491288 0.870997i \(-0.663474\pi\)
−0.491288 + 0.870997i \(0.663474\pi\)
\(912\) −12.7279 22.0454i −0.421464 0.729996i
\(913\) 0.627417 0.0207645
\(914\) 5.17767 8.96799i 0.171262 0.296635i
\(915\) 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
\(919\) 2.68629 0.0886126 0.0443063 0.999018i \(-0.485892\pi\)
0.0443063 + 0.999018i \(0.485892\pi\)
\(920\) −4.10051 −0.135190
\(921\) −46.2843 −1.52512
\(922\) −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
\(926\) −1.39340 2.41344i −0.0457899 0.0793104i
\(927\) 7.00000 12.1244i 0.229910 0.398216i
\(928\) −9.20711 15.9472i −0.302238 0.523492i
\(929\) 48.9411 1.60571 0.802853 0.596177i \(-0.203314\pi\)
0.802853 + 0.596177i \(0.203314\pi\)
\(930\) 1.38478 + 2.39850i 0.0454086 + 0.0786500i
\(931\) 0 0
\(932\) 2.58579 + 4.47871i 0.0847003 + 0.146705i
\(933\) 9.14214 + 15.8346i 0.299300 + 0.518403i
\(934\) 4.72792 0.154702
\(935\) −3.12132 5.40629i −0.102078 0.176804i
\(936\) −5.55025 1.37333i −0.181416 0.0448887i
\(937\) −37.1421 −1.21338 −0.606690 0.794938i \(-0.707503\pi\)
−0.606690 + 0.794938i \(0.707503\pi\)
\(938\) 0 0
\(939\) 9.89949 17.1464i 0.323058 0.559553i
\(940\) −12.2254 −0.398748
\(941\) −26.4853 45.8739i −0.863395 1.49544i −0.868632 0.495459i \(-0.835000\pi\)
0.00523607 0.999986i \(-0.498333\pi\)
\(942\) −1.60660 + 2.78272i −0.0523459 + 0.0906658i
\(943\) −0.242641 −0.00790147
\(944\) −30.7279 −1.00011
\(945\) 0 0
\(946\) −0.414214 + 0.717439i −0.0134672 + 0.0233260i
\(947\) −10.7071 18.5453i −0.347934 0.602640i 0.637948 0.770079i \(-0.279783\pi\)
−0.985882 + 0.167440i \(0.946450\pi\)
\(948\) 2.27208 + 3.93535i 0.0737937 + 0.127814i
\(949\) −10.6569 36.9164i −0.345936 1.19836i
\(950\) 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
\(955\) 14.8492 25.7196i 0.480510 0.832268i
\(956\) 22.2929 38.6124i 0.721004 1.24882i
\(957\) −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
\(962\) −9.82233 + 10.2077i −0.316685 + 0.329108i
\(963\) 8.65685 + 14.9941i 0.278963 + 0.483178i
\(964\) 14.1569 + 24.5204i 0.455962 + 0.789749i
\(965\) 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 \(0.602903\pi\)
\(968\) 16.8995 0.543170
\(969\) 24.7279 42.8300i 0.794375 1.37590i
\(970\) −4.10051 7.10228i −0.131659 0.228041i
\(971\) 51.6569 1.65775 0.828874 0.559436i \(-0.188982\pi\)
0.828874 + 0.559436i \(0.188982\pi\)
\(972\) 9.05025 15.6755i 0.290287 0.502792i
\(973\) 0 0
\(974\) −5.37258 −0.172149
\(975\) −2.34315 8.11689i −0.0750407 0.259949i
\(976\) −6.25736 10.8381i −0.200293 0.346918i
\(977\) 30.5980 0.978916 0.489458 0.872027i \(-0.337195\pi\)
0.489458 + 0.872027i \(0.337195\pi\)
\(978\) −3.68629 6.38484i −0.117875 0.204165i
\(979\) −4.48528 7.76874i −0.143350 0.248290i
\(980\) 0 0
\(981\) −6.82843 11.8272i −0.218015 0.377613i
\(982\) 5.25483 0.167688
\(983\) 21.0000 + 36.3731i 0.669796 + 1.16012i 0.977961 + 0.208788i \(0.0669518\pi\)
−0.308165 + 0.951333i \(0.599715\pi\)
\(984\) 0.192388 0.333226i 0.00613311 0.0106229i
\(985\) 13.5563 + 23.4803i 0.431941 + 0.748144i
\(986\) 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
\(990\) 0.443651 0.0141001
\(991\) 19.7574 0.627613 0.313807 0.949487i \(-0.398396\pi\)
0.313807 + 0.949487i \(0.398396\pi\)
\(992\) 11.4142 0.362402
\(993\) −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
\(997\) −6.98528 + 12.0989i −0.221226 + 0.383175i −0.955181 0.296024i \(-0.904339\pi\)
0.733954 + 0.679199i \(0.237673\pi\)
\(998\) 8.30152 0.262780
\(999\) −26.8284 46.4682i −0.848814 1.47019i
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.g.f.373.1 4
7.2 even 3 637.2.f.f.295.1 yes 4
7.3 odd 6 637.2.h.c.165.2 4
7.4 even 3 637.2.h.b.165.2 4
7.5 odd 6 637.2.f.e.295.1 4
7.6 odd 2 637.2.g.g.373.1 4
13.3 even 3 637.2.h.b.471.2 4
91.3 odd 6 637.2.g.g.263.1 4
91.9 even 3 8281.2.a.p.1.2 2
91.16 even 3 637.2.f.f.393.1 yes 4
91.30 even 6 8281.2.a.x.1.1 2
91.55 odd 6 637.2.h.c.471.2 4
91.61 odd 6 8281.2.a.o.1.2 2
91.68 odd 6 637.2.f.e.393.1 yes 4
91.81 even 3 inner 637.2.g.f.263.1 4
91.82 odd 6 8281.2.a.y.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
637.2.f.e.295.1 4 7.5 odd 6
637.2.f.e.393.1 yes 4 91.68 odd 6
637.2.f.f.295.1 yes 4 7.2 even 3
637.2.f.f.393.1 yes 4 91.16 even 3
637.2.g.f.263.1 4 91.81 even 3 inner
637.2.g.f.373.1 4 1.1 even 1 trivial
637.2.g.g.263.1 4 91.3 odd 6
637.2.g.g.373.1 4 7.6 odd 2
637.2.h.b.165.2 4 7.4 even 3
637.2.h.b.471.2 4 13.3 even 3
637.2.h.c.165.2 4 7.3 odd 6
637.2.h.c.471.2 4 91.55 odd 6
8281.2.a.o.1.2 2 91.61 odd 6
8281.2.a.p.1.2 2 91.9 even 3
8281.2.a.x.1.1 2 91.30 even 6
8281.2.a.y.1.1 2 91.82 odd 6