Properties

Label 1470.2.n.k.79.3
Level $1470$
Weight $2$
Character 1470.79
Analytic conductor $11.738$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 18x^{14} + 227x^{12} - 1394x^{10} + 6177x^{8} - 14768x^{6} + 24768x^{4} - 11264x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.3
Root \(2.73710 + 1.58027i\) of defining polynomial
Character \(\chi\) \(=\) 1470.79
Dual form 1470.2.n.k.949.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.506647 + 2.17791i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.506647 + 2.17791i) q^{5} +1.00000 q^{6} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.650187 - 2.13945i) q^{10} +(-2.23483 - 3.87084i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.88388i q^{13} +(-1.52773 - 1.63280i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(6.69895 - 3.86764i) q^{17} +(-0.866025 + 0.500000i) q^{18} +(3.30913 - 5.73159i) q^{19} +(-1.63280 + 1.52773i) q^{20} +4.46967i q^{22} +(-2.26749 - 1.30913i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-4.48662 + 2.20687i) q^{25} +(2.94194 - 5.09559i) q^{26} +1.00000i q^{27} +8.17246 q^{29} +(0.506647 + 2.17791i) q^{30} +(-4.23483 - 7.33495i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.87084 + 2.23483i) q^{33} -7.73528 q^{34} +1.00000 q^{36} +(2.76019 + 1.59359i) q^{37} +(-5.73159 + 3.30913i) q^{38} +(-2.94194 - 5.09559i) q^{39} +(2.17791 - 0.506647i) q^{40} +3.56282 q^{41} +1.43108i q^{43} +(2.23483 - 3.87084i) q^{44} +(2.13945 + 0.650187i) q^{45} +(1.30913 + 2.26749i) q^{46} +(5.88094 + 3.39536i) q^{47} -1.00000i q^{48} +(4.98896 + 0.332104i) q^{50} +(-3.86764 + 6.69895i) q^{51} +(-5.09559 + 2.94194i) q^{52} +(-1.19661 + 0.690865i) q^{53} +(0.500000 - 0.866025i) q^{54} +(7.29809 - 6.82843i) q^{55} +6.61827i q^{57} +(-7.07756 - 4.08623i) q^{58} +(2.33210 + 4.03932i) q^{59} +(0.650187 - 2.13945i) q^{60} +(-4.89841 + 8.48430i) q^{61} +8.46967i q^{62} -1.00000 q^{64} +(-12.8146 + 2.98105i) q^{65} +(-2.23483 - 3.87084i) q^{66} +(-1.60336 + 0.925698i) q^{67} +(6.69895 + 3.86764i) q^{68} +2.61827 q^{69} +2.02386 q^{71} +(-0.866025 - 0.500000i) q^{72} +(3.47871 - 2.00843i) q^{73} +(-1.59359 - 2.76019i) q^{74} +(2.78209 - 4.15451i) q^{75} +6.61827 q^{76} +5.88388i q^{78} +(-3.49264 + 6.04942i) q^{79} +(-2.13945 - 0.650187i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.08549 - 1.78141i) q^{82} +5.35965i q^{83} +(11.8174 + 12.6302i) q^{85} +(0.715541 - 1.23935i) q^{86} +(-7.07756 + 4.08623i) q^{87} +(-3.87084 + 2.23483i) q^{88} +(7.19562 - 12.4632i) q^{89} +(-1.52773 - 1.63280i) q^{90} -2.61827i q^{92} +(7.33495 + 4.23483i) q^{93} +(-3.39536 - 5.88094i) q^{94} +(14.1595 + 4.30312i) q^{95} +(-0.500000 + 0.866025i) q^{96} +7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 4 q^{5} + 16 q^{6} + 8 q^{9} - 8 q^{16} + 24 q^{19} - 8 q^{20} + 8 q^{24} - 4 q^{25} + 32 q^{29} - 4 q^{30} - 32 q^{31} - 16 q^{34} + 16 q^{36} + 48 q^{41} + 4 q^{45} - 8 q^{46} - 8 q^{50} - 8 q^{51} + 8 q^{54} + 40 q^{59} - 24 q^{61} - 16 q^{64} - 28 q^{65} - 16 q^{69} - 80 q^{71} - 16 q^{74} - 4 q^{75} + 48 q^{76} - 16 q^{79} - 4 q^{80} - 8 q^{81} + 56 q^{85} - 8 q^{86} + 88 q^{89} + 24 q^{94} - 24 q^{95} - 8 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.506647 + 2.17791i 0.226580 + 0.973993i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0.650187 2.13945i 0.205607 0.676554i
\(11\) −2.23483 3.87084i −0.673828 1.16710i −0.976810 0.214107i \(-0.931316\pi\)
0.302983 0.952996i \(-0.402018\pi\)
\(12\) −0.866025 0.500000i −0.250000 0.144338i
\(13\) 5.88388i 1.63189i 0.578126 + 0.815947i \(0.303784\pi\)
−0.578126 + 0.815947i \(0.696216\pi\)
\(14\) 0 0
\(15\) −1.52773 1.63280i −0.394457 0.421588i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 6.69895 3.86764i 1.62473 0.938040i 0.639103 0.769121i \(-0.279306\pi\)
0.985630 0.168919i \(-0.0540276\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 3.30913 5.73159i 0.759168 1.31492i −0.184108 0.982906i \(-0.558940\pi\)
0.943276 0.332011i \(-0.107727\pi\)
\(20\) −1.63280 + 1.52773i −0.365106 + 0.341610i
\(21\) 0 0
\(22\) 4.46967i 0.952936i
\(23\) −2.26749 1.30913i −0.472804 0.272974i 0.244609 0.969622i \(-0.421340\pi\)
−0.717413 + 0.696648i \(0.754674\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −4.48662 + 2.20687i −0.897323 + 0.441374i
\(26\) 2.94194 5.09559i 0.576962 0.999327i
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 8.17246 1.51759 0.758794 0.651331i \(-0.225789\pi\)
0.758794 + 0.651331i \(0.225789\pi\)
\(30\) 0.506647 + 2.17791i 0.0925007 + 0.397631i
\(31\) −4.23483 7.33495i −0.760598 1.31740i −0.942542 0.334086i \(-0.891572\pi\)
0.181944 0.983309i \(-0.441761\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 3.87084 + 2.23483i 0.673828 + 0.389035i
\(34\) −7.73528 −1.32659
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 2.76019 + 1.59359i 0.453772 + 0.261985i 0.709422 0.704784i \(-0.248956\pi\)
−0.255650 + 0.966769i \(0.582289\pi\)
\(38\) −5.73159 + 3.30913i −0.929787 + 0.536813i
\(39\) −2.94194 5.09559i −0.471087 0.815947i
\(40\) 2.17791 0.506647i 0.344358 0.0801080i
\(41\) 3.56282 0.556419 0.278209 0.960520i \(-0.410259\pi\)
0.278209 + 0.960520i \(0.410259\pi\)
\(42\) 0 0
\(43\) 1.43108i 0.218238i 0.994029 + 0.109119i \(0.0348029\pi\)
−0.994029 + 0.109119i \(0.965197\pi\)
\(44\) 2.23483 3.87084i 0.336914 0.583552i
\(45\) 2.13945 + 0.650187i 0.318931 + 0.0969242i
\(46\) 1.30913 + 2.26749i 0.193021 + 0.334323i
\(47\) 5.88094 + 3.39536i 0.857824 + 0.495265i 0.863283 0.504720i \(-0.168404\pi\)
−0.00545912 + 0.999985i \(0.501738\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.98896 + 0.332104i 0.705545 + 0.0469666i
\(51\) −3.86764 + 6.69895i −0.541578 + 0.938040i
\(52\) −5.09559 + 2.94194i −0.706631 + 0.407974i
\(53\) −1.19661 + 0.690865i −0.164367 + 0.0948976i −0.579927 0.814668i \(-0.696919\pi\)
0.415560 + 0.909566i \(0.363586\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 7.29809 6.82843i 0.984075 0.920745i
\(56\) 0 0
\(57\) 6.61827i 0.876611i
\(58\) −7.07756 4.08623i −0.929329 0.536548i
\(59\) 2.33210 + 4.03932i 0.303614 + 0.525875i 0.976952 0.213460i \(-0.0684733\pi\)
−0.673338 + 0.739335i \(0.735140\pi\)
\(60\) 0.650187 2.13945i 0.0839388 0.276202i
\(61\) −4.89841 + 8.48430i −0.627178 + 1.08630i 0.360938 + 0.932590i \(0.382457\pi\)
−0.988115 + 0.153714i \(0.950877\pi\)
\(62\) 8.46967i 1.07565i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −12.8146 + 2.98105i −1.58945 + 0.369754i
\(66\) −2.23483 3.87084i −0.275089 0.476468i
\(67\) −1.60336 + 0.925698i −0.195881 + 0.113092i −0.594733 0.803923i \(-0.702742\pi\)
0.398852 + 0.917015i \(0.369409\pi\)
\(68\) 6.69895 + 3.86764i 0.812366 + 0.469020i
\(69\) 2.61827 0.315203
\(70\) 0 0
\(71\) 2.02386 0.240187 0.120094 0.992763i \(-0.461680\pi\)
0.120094 + 0.992763i \(0.461680\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 3.47871 2.00843i 0.407152 0.235069i −0.282413 0.959293i \(-0.591135\pi\)
0.689565 + 0.724223i \(0.257802\pi\)
\(74\) −1.59359 2.76019i −0.185252 0.320865i
\(75\) 2.78209 4.15451i 0.321248 0.479722i
\(76\) 6.61827 0.759168
\(77\) 0 0
\(78\) 5.88388i 0.666218i
\(79\) −3.49264 + 6.04942i −0.392952 + 0.680613i −0.992837 0.119473i \(-0.961880\pi\)
0.599885 + 0.800086i \(0.295213\pi\)
\(80\) −2.13945 0.650187i −0.239198 0.0726932i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −3.08549 1.78141i −0.340735 0.196724i
\(83\) 5.35965i 0.588298i 0.955760 + 0.294149i \(0.0950361\pi\)
−0.955760 + 0.294149i \(0.904964\pi\)
\(84\) 0 0
\(85\) 11.8174 + 12.6302i 1.28178 + 1.36994i
\(86\) 0.715541 1.23935i 0.0771588 0.133643i
\(87\) −7.07756 + 4.08623i −0.758794 + 0.438090i
\(88\) −3.87084 + 2.23483i −0.412633 + 0.238234i
\(89\) 7.19562 12.4632i 0.762734 1.32109i −0.178702 0.983903i \(-0.557190\pi\)
0.941436 0.337191i \(-0.109477\pi\)
\(90\) −1.52773 1.63280i −0.161036 0.172113i
\(91\) 0 0
\(92\) 2.61827i 0.272974i
\(93\) 7.33495 + 4.23483i 0.760598 + 0.439132i
\(94\) −3.39536 5.88094i −0.350205 0.606573i
\(95\) 14.1595 + 4.30312i 1.45273 + 0.441490i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 7.71966i 0.783813i 0.920005 + 0.391906i \(0.128184\pi\)
−0.920005 + 0.391906i \(0.871816\pi\)
\(98\) 0 0
\(99\) −4.46967 −0.449218
\(100\) −4.15451 2.78209i −0.415451 0.278209i
\(101\) 6.67722 + 11.5653i 0.664408 + 1.15079i 0.979446 + 0.201709i \(0.0646495\pi\)
−0.315038 + 0.949079i \(0.602017\pi\)
\(102\) 6.69895 3.86764i 0.663294 0.382953i
\(103\) 8.10569 + 4.67982i 0.798678 + 0.461117i 0.843009 0.537900i \(-0.180782\pi\)
−0.0443310 + 0.999017i \(0.514116\pi\)
\(104\) 5.88388 0.576962
\(105\) 0 0
\(106\) 1.38173 0.134205
\(107\) 9.54057 + 5.50825i 0.922322 + 0.532503i 0.884375 0.466777i \(-0.154585\pi\)
0.0379467 + 0.999280i \(0.487918\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −2.34772 4.06637i −0.224871 0.389488i 0.731410 0.681938i \(-0.238863\pi\)
−0.956281 + 0.292451i \(0.905529\pi\)
\(110\) −9.73455 + 2.26454i −0.928153 + 0.215916i
\(111\) −3.18719 −0.302514
\(112\) 0 0
\(113\) 12.5723i 1.18271i −0.806413 0.591353i \(-0.798594\pi\)
0.806413 0.591353i \(-0.201406\pi\)
\(114\) 3.30913 5.73159i 0.309929 0.536813i
\(115\) 1.70237 5.60166i 0.158746 0.522358i
\(116\) 4.08623 + 7.07756i 0.379397 + 0.657135i
\(117\) 5.09559 + 2.94194i 0.471087 + 0.271982i
\(118\) 4.66421i 0.429375i
\(119\) 0 0
\(120\) −1.63280 + 1.52773i −0.149054 + 0.139462i
\(121\) −4.48896 + 7.77510i −0.408087 + 0.706828i
\(122\) 8.48430 4.89841i 0.768133 0.443482i
\(123\) −3.08549 + 1.78141i −0.278209 + 0.160624i
\(124\) 4.23483 7.33495i 0.380299 0.658698i
\(125\) −7.07950 8.65336i −0.633210 0.773980i
\(126\) 0 0
\(127\) 6.59619i 0.585317i 0.956217 + 0.292658i \(0.0945399\pi\)
−0.956217 + 0.292658i \(0.905460\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −0.715541 1.23935i −0.0629999 0.109119i
\(130\) 12.5883 + 3.82562i 1.10407 + 0.335529i
\(131\) 1.16053 2.01010i 0.101396 0.175623i −0.810864 0.585235i \(-0.801002\pi\)
0.912260 + 0.409611i \(0.134336\pi\)
\(132\) 4.46967i 0.389035i
\(133\) 0 0
\(134\) 1.85140 0.159936
\(135\) −2.17791 + 0.506647i −0.187445 + 0.0436053i
\(136\) −3.86764 6.69895i −0.331647 0.574430i
\(137\) 12.3626 7.13756i 1.05621 0.609803i 0.131828 0.991273i \(-0.457915\pi\)
0.924381 + 0.381469i \(0.124582\pi\)
\(138\) −2.26749 1.30913i −0.193021 0.111441i
\(139\) 14.9632 1.26916 0.634581 0.772857i \(-0.281173\pi\)
0.634581 + 0.772857i \(0.281173\pi\)
\(140\) 0 0
\(141\) −6.79073 −0.571883
\(142\) −1.75271 1.01193i −0.147084 0.0849191i
\(143\) 22.7756 13.1495i 1.90459 1.09962i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) 4.14055 + 17.7989i 0.343854 + 1.47812i
\(146\) −4.01687 −0.332438
\(147\) 0 0
\(148\) 3.18719i 0.261985i
\(149\) 5.58255 9.66926i 0.457341 0.792137i −0.541479 0.840714i \(-0.682135\pi\)
0.998819 + 0.0485773i \(0.0154687\pi\)
\(150\) −4.48662 + 2.20687i −0.366331 + 0.180190i
\(151\) −0.332104 0.575221i −0.0270263 0.0468109i 0.852196 0.523223i \(-0.175270\pi\)
−0.879222 + 0.476412i \(0.841937\pi\)
\(152\) −5.73159 3.30913i −0.464893 0.268406i
\(153\) 7.73528i 0.625360i
\(154\) 0 0
\(155\) 13.8293 12.9393i 1.11080 1.03931i
\(156\) 2.94194 5.09559i 0.235544 0.407974i
\(157\) 6.99907 4.04092i 0.558587 0.322500i −0.193991 0.981003i \(-0.562143\pi\)
0.752578 + 0.658503i \(0.228810\pi\)
\(158\) 6.04942 3.49264i 0.481266 0.277859i
\(159\) 0.690865 1.19661i 0.0547892 0.0948976i
\(160\) 1.52773 + 1.63280i 0.120777 + 0.129085i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 0.724575 + 0.418334i 0.0567531 + 0.0327664i 0.528108 0.849177i \(-0.322902\pi\)
−0.471355 + 0.881944i \(0.656235\pi\)
\(164\) 1.78141 + 3.08549i 0.139105 + 0.240936i
\(165\) −2.90612 + 9.56264i −0.226241 + 0.744450i
\(166\) 2.67982 4.64159i 0.207995 0.360257i
\(167\) 2.66762i 0.206427i −0.994659 0.103213i \(-0.967088\pi\)
0.994659 0.103213i \(-0.0329125\pi\)
\(168\) 0 0
\(169\) −21.6200 −1.66308
\(170\) −3.91906 16.8468i −0.300578 1.29209i
\(171\) −3.30913 5.73159i −0.253056 0.438306i
\(172\) −1.23935 + 0.715541i −0.0944998 + 0.0545595i
\(173\) −0.560613 0.323670i −0.0426226 0.0246082i 0.478537 0.878067i \(-0.341167\pi\)
−0.521160 + 0.853459i \(0.674500\pi\)
\(174\) 8.17246 0.619553
\(175\) 0 0
\(176\) 4.46967 0.336914
\(177\) −4.03932 2.33210i −0.303614 0.175292i
\(178\) −12.4632 + 7.19562i −0.934155 + 0.539335i
\(179\) −12.8687 22.2893i −0.961853 1.66598i −0.717842 0.696206i \(-0.754870\pi\)
−0.244011 0.969772i \(-0.578463\pi\)
\(180\) 0.506647 + 2.17791i 0.0377633 + 0.162332i
\(181\) 7.42245 0.551707 0.275853 0.961200i \(-0.411040\pi\)
0.275853 + 0.961200i \(0.411040\pi\)
\(182\) 0 0
\(183\) 9.79683i 0.724203i
\(184\) −1.30913 + 2.26749i −0.0965107 + 0.167161i
\(185\) −2.07227 + 6.81884i −0.152356 + 0.501331i
\(186\) −4.23483 7.33495i −0.310513 0.537824i
\(187\) −29.9421 17.2871i −2.18958 1.26415i
\(188\) 6.79073i 0.495265i
\(189\) 0 0
\(190\) −10.1109 10.8063i −0.733522 0.783975i
\(191\) 0.542261 0.939224i 0.0392367 0.0679599i −0.845740 0.533595i \(-0.820841\pi\)
0.884977 + 0.465635i \(0.154174\pi\)
\(192\) 0.866025 0.500000i 0.0625000 0.0360844i
\(193\) −7.74169 + 4.46967i −0.557259 + 0.321734i −0.752045 0.659112i \(-0.770932\pi\)
0.194786 + 0.980846i \(0.437599\pi\)
\(194\) 3.85983 6.68542i 0.277120 0.479985i
\(195\) 9.60723 8.98896i 0.687988 0.643713i
\(196\) 0 0
\(197\) 7.45890i 0.531425i 0.964052 + 0.265712i \(0.0856071\pi\)
−0.964052 + 0.265712i \(0.914393\pi\)
\(198\) 3.87084 + 2.23483i 0.275089 + 0.158823i
\(199\) 12.9147 + 22.3688i 0.915496 + 1.58569i 0.806174 + 0.591679i \(0.201535\pi\)
0.109322 + 0.994006i \(0.465132\pi\)
\(200\) 2.20687 + 4.48662i 0.156049 + 0.317252i
\(201\) 0.925698 1.60336i 0.0652937 0.113092i
\(202\) 13.3544i 0.939615i
\(203\) 0 0
\(204\) −7.73528 −0.541578
\(205\) 1.80509 + 7.75951i 0.126073 + 0.541948i
\(206\) −4.67982 8.10569i −0.326059 0.564750i
\(207\) −2.26749 + 1.30913i −0.157601 + 0.0909912i
\(208\) −5.09559 2.94194i −0.353316 0.203987i
\(209\) −29.5815 −2.04619
\(210\) 0 0
\(211\) 5.53375 0.380959 0.190479 0.981691i \(-0.438996\pi\)
0.190479 + 0.981691i \(0.438996\pi\)
\(212\) −1.19661 0.690865i −0.0821837 0.0474488i
\(213\) −1.75271 + 1.01193i −0.120094 + 0.0693361i
\(214\) −5.50825 9.54057i −0.376536 0.652180i
\(215\) −3.11677 + 0.725054i −0.212562 + 0.0494483i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 4.69544i 0.318015i
\(219\) −2.00843 + 3.47871i −0.135717 + 0.235069i
\(220\) 9.56264 + 2.90612i 0.644713 + 0.195931i
\(221\) 22.7567 + 39.4158i 1.53078 + 2.65139i
\(222\) 2.76019 + 1.59359i 0.185252 + 0.106955i
\(223\) 3.28248i 0.219811i −0.993942 0.109906i \(-0.964945\pi\)
0.993942 0.109906i \(-0.0350548\pi\)
\(224\) 0 0
\(225\) −0.332104 + 4.98896i −0.0221403 + 0.332597i
\(226\) −6.28617 + 10.8880i −0.418150 + 0.724256i
\(227\) 3.82810 2.21016i 0.254080 0.146693i −0.367551 0.930003i \(-0.619804\pi\)
0.621631 + 0.783310i \(0.286470\pi\)
\(228\) −5.73159 + 3.30913i −0.379584 + 0.219153i
\(229\) −3.98635 + 6.90456i −0.263426 + 0.456266i −0.967150 0.254207i \(-0.918186\pi\)
0.703724 + 0.710473i \(0.251519\pi\)
\(230\) −4.27512 + 4.00000i −0.281893 + 0.263752i
\(231\) 0 0
\(232\) 8.17246i 0.536548i
\(233\) −15.5502 8.97792i −1.01873 0.588163i −0.104993 0.994473i \(-0.533482\pi\)
−0.913735 + 0.406310i \(0.866815\pi\)
\(234\) −2.94194 5.09559i −0.192321 0.333109i
\(235\) −4.41525 + 14.5284i −0.288019 + 0.947731i
\(236\) −2.33210 + 4.03932i −0.151807 + 0.262938i
\(237\) 6.98527i 0.453742i
\(238\) 0 0
\(239\) −5.41296 −0.350135 −0.175068 0.984556i \(-0.556014\pi\)
−0.175068 + 0.984556i \(0.556014\pi\)
\(240\) 2.17791 0.506647i 0.140584 0.0327039i
\(241\) 2.34835 + 4.06745i 0.151270 + 0.262008i 0.931695 0.363242i \(-0.118330\pi\)
−0.780424 + 0.625250i \(0.784997\pi\)
\(242\) 7.77510 4.48896i 0.499803 0.288561i
\(243\) 0.866025 + 0.500000i 0.0555556 + 0.0320750i
\(244\) −9.79683 −0.627178
\(245\) 0 0
\(246\) 3.56282 0.227157
\(247\) 33.7240 + 19.4706i 2.14581 + 1.23888i
\(248\) −7.33495 + 4.23483i −0.465770 + 0.268912i
\(249\) −2.67982 4.64159i −0.169827 0.294149i
\(250\) 1.80435 + 11.0338i 0.114117 + 0.697838i
\(251\) 7.73402 0.488167 0.244084 0.969754i \(-0.421513\pi\)
0.244084 + 0.969754i \(0.421513\pi\)
\(252\) 0 0
\(253\) 11.7028i 0.735748i
\(254\) 3.29809 5.71247i 0.206941 0.358432i
\(255\) −16.5493 5.02938i −1.03635 0.314952i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.16430 + 0.672210i 0.0726271 + 0.0419313i 0.535874 0.844298i \(-0.319982\pi\)
−0.463247 + 0.886229i \(0.653316\pi\)
\(258\) 1.43108i 0.0890953i
\(259\) 0 0
\(260\) −8.98896 9.60723i −0.557472 0.595815i
\(261\) 4.08623 7.07756i 0.252931 0.438090i
\(262\) −2.01010 + 1.16053i −0.124184 + 0.0716979i
\(263\) −3.78193 + 2.18350i −0.233204 + 0.134640i −0.612049 0.790820i \(-0.709655\pi\)
0.378845 + 0.925460i \(0.376321\pi\)
\(264\) 2.23483 3.87084i 0.137544 0.238234i
\(265\) −2.11091 2.25610i −0.129672 0.138591i
\(266\) 0 0
\(267\) 14.3912i 0.880730i
\(268\) −1.60336 0.925698i −0.0979406 0.0565460i
\(269\) 11.5336 + 19.9767i 0.703213 + 1.21800i 0.967333 + 0.253511i \(0.0815854\pi\)
−0.264119 + 0.964490i \(0.585081\pi\)
\(270\) 2.13945 + 0.650187i 0.130203 + 0.0395691i
\(271\) −7.36047 + 12.7487i −0.447117 + 0.774429i −0.998197 0.0600236i \(-0.980882\pi\)
0.551080 + 0.834452i \(0.314216\pi\)
\(272\) 7.73528i 0.469020i
\(273\) 0 0
\(274\) −14.2751 −0.862392
\(275\) 18.5693 + 12.4350i 1.11977 + 0.749860i
\(276\) 1.30913 + 2.26749i 0.0788007 + 0.136487i
\(277\) 2.78085 1.60552i 0.167085 0.0964665i −0.414126 0.910220i \(-0.635913\pi\)
0.581211 + 0.813753i \(0.302579\pi\)
\(278\) −12.9585 7.48159i −0.777199 0.448716i
\(279\) −8.46967 −0.507066
\(280\) 0 0
\(281\) −7.72488 −0.460827 −0.230414 0.973093i \(-0.574008\pi\)
−0.230414 + 0.973093i \(0.574008\pi\)
\(282\) 5.88094 + 3.39536i 0.350205 + 0.202191i
\(283\) −25.5992 + 14.7797i −1.52171 + 0.878561i −0.522041 + 0.852920i \(0.674829\pi\)
−0.999671 + 0.0256411i \(0.991837\pi\)
\(284\) 1.01193 + 1.75271i 0.0600469 + 0.104004i
\(285\) −14.4140 + 3.35313i −0.853813 + 0.198622i
\(286\) −26.2990 −1.55509
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 21.4172 37.0958i 1.25984 2.18210i
\(290\) 5.31363 17.4846i 0.312027 1.02673i
\(291\) −3.85983 6.68542i −0.226267 0.391906i
\(292\) 3.47871 + 2.00843i 0.203576 + 0.117535i
\(293\) 1.17679i 0.0687487i 0.999409 + 0.0343743i \(0.0109438\pi\)
−0.999409 + 0.0343743i \(0.989056\pi\)
\(294\) 0 0
\(295\) −7.61574 + 7.12563i −0.443406 + 0.414870i
\(296\) 1.59359 2.76019i 0.0926258 0.160433i
\(297\) 3.87084 2.23483i 0.224609 0.129678i
\(298\) −9.66926 + 5.58255i −0.560125 + 0.323389i
\(299\) 7.70279 13.3416i 0.445464 0.771566i
\(300\) 4.98896 + 0.332104i 0.288038 + 0.0191740i
\(301\) 0 0
\(302\) 0.664208i 0.0382209i
\(303\) −11.5653 6.67722i −0.664408 0.383596i
\(304\) 3.30913 + 5.73159i 0.189792 + 0.328729i
\(305\) −20.9599 6.36978i −1.20016 0.364732i
\(306\) −3.86764 + 6.69895i −0.221098 + 0.382953i
\(307\) 20.3761i 1.16293i −0.813572 0.581464i \(-0.802480\pi\)
0.813572 0.581464i \(-0.197520\pi\)
\(308\) 0 0
\(309\) −9.35965 −0.532452
\(310\) −18.4462 + 4.29113i −1.04767 + 0.243720i
\(311\) 9.44670 + 16.3622i 0.535673 + 0.927813i 0.999130 + 0.0416937i \(0.0132754\pi\)
−0.463457 + 0.886119i \(0.653391\pi\)
\(312\) −5.09559 + 2.94194i −0.288481 + 0.166555i
\(313\) −14.2763 8.24245i −0.806946 0.465891i 0.0389480 0.999241i \(-0.487599\pi\)
−0.845894 + 0.533351i \(0.820933\pi\)
\(314\) −8.08184 −0.456084
\(315\) 0 0
\(316\) −6.98527 −0.392952
\(317\) −8.93830 5.16053i −0.502025 0.289844i 0.227524 0.973772i \(-0.426937\pi\)
−0.729549 + 0.683928i \(0.760270\pi\)
\(318\) −1.19661 + 0.690865i −0.0671027 + 0.0387418i
\(319\) −18.2641 31.6343i −1.02259 1.77118i
\(320\) −0.506647 2.17791i −0.0283224 0.121749i
\(321\) −11.0165 −0.614881
\(322\) 0 0
\(323\) 51.1941i 2.84852i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −12.9849 26.3987i −0.720275 1.46434i
\(326\) −0.418334 0.724575i −0.0231694 0.0401305i
\(327\) 4.06637 + 2.34772i 0.224871 + 0.129829i
\(328\) 3.56282i 0.196724i
\(329\) 0 0
\(330\) 7.29809 6.82843i 0.401747 0.375893i
\(331\) 9.59530 16.6195i 0.527405 0.913493i −0.472084 0.881553i \(-0.656498\pi\)
0.999490 0.0319396i \(-0.0101684\pi\)
\(332\) −4.64159 + 2.67982i −0.254740 + 0.147074i
\(333\) 2.76019 1.59359i 0.151257 0.0873284i
\(334\) −1.33381 + 2.31023i −0.0729829 + 0.126410i
\(335\) −2.82843 3.02297i −0.154533 0.165162i
\(336\) 0 0
\(337\) 27.6035i 1.50366i −0.659357 0.751830i \(-0.729171\pi\)
0.659357 0.751830i \(-0.270829\pi\)
\(338\) 18.7235 + 10.8100i 1.01842 + 0.587988i
\(339\) 6.28617 + 10.8880i 0.341418 + 0.591353i
\(340\) −5.02938 + 16.5493i −0.272756 + 0.897509i
\(341\) −18.9283 + 32.7848i −1.02502 + 1.77539i
\(342\) 6.61827i 0.357875i
\(343\) 0 0
\(344\) 1.43108 0.0771588
\(345\) 1.32654 + 5.70237i 0.0714185 + 0.307005i
\(346\) 0.323670 + 0.560613i 0.0174006 + 0.0301387i
\(347\) −17.6463 + 10.1881i −0.947301 + 0.546924i −0.892241 0.451559i \(-0.850868\pi\)
−0.0550595 + 0.998483i \(0.517535\pi\)
\(348\) −7.07756 4.08623i −0.379397 0.219045i
\(349\) 17.8281 0.954314 0.477157 0.878818i \(-0.341667\pi\)
0.477157 + 0.878818i \(0.341667\pi\)
\(350\) 0 0
\(351\) −5.88388 −0.314058
\(352\) −3.87084 2.23483i −0.206317 0.119117i
\(353\) 3.04275 1.75673i 0.161949 0.0935014i −0.416835 0.908982i \(-0.636861\pi\)
0.578784 + 0.815481i \(0.303527\pi\)
\(354\) 2.33210 + 4.03932i 0.123950 + 0.214688i
\(355\) 1.02538 + 4.40778i 0.0544216 + 0.233941i
\(356\) 14.3912 0.762734
\(357\) 0 0
\(358\) 25.7374i 1.36027i
\(359\) −1.09898 + 1.90349i −0.0580018 + 0.100462i −0.893568 0.448927i \(-0.851806\pi\)
0.835567 + 0.549389i \(0.185140\pi\)
\(360\) 0.650187 2.13945i 0.0342679 0.112759i
\(361\) −12.4007 21.4787i −0.652671 1.13046i
\(362\) −6.42803 3.71123i −0.337850 0.195058i
\(363\) 8.97792i 0.471218i
\(364\) 0 0
\(365\) 6.13668 + 6.55876i 0.321208 + 0.343301i
\(366\) −4.89841 + 8.48430i −0.256044 + 0.443482i
\(367\) −24.9173 + 14.3860i −1.30067 + 0.750945i −0.980520 0.196421i \(-0.937068\pi\)
−0.320155 + 0.947365i \(0.603735\pi\)
\(368\) 2.26749 1.30913i 0.118201 0.0682434i
\(369\) 1.78141 3.08549i 0.0927364 0.160624i
\(370\) 5.20406 4.86915i 0.270546 0.253135i
\(371\) 0 0
\(372\) 8.46967i 0.439132i
\(373\) −12.6171 7.28446i −0.653286 0.377175i 0.136428 0.990650i \(-0.456438\pi\)
−0.789714 + 0.613475i \(0.789771\pi\)
\(374\) 17.2871 + 29.9421i 0.893892 + 1.54827i
\(375\) 10.4577 + 3.95428i 0.540034 + 0.204198i
\(376\) 3.39536 5.88094i 0.175103 0.303287i
\(377\) 48.0858i 2.47654i
\(378\) 0 0
\(379\) 30.7868 1.58141 0.790705 0.612197i \(-0.209714\pi\)
0.790705 + 0.612197i \(0.209714\pi\)
\(380\) 3.35313 + 14.4140i 0.172012 + 0.739424i
\(381\) −3.29809 5.71247i −0.168966 0.292658i
\(382\) −0.939224 + 0.542261i −0.0480549 + 0.0277445i
\(383\) −20.2139 11.6705i −1.03288 0.596334i −0.115072 0.993357i \(-0.536710\pi\)
−0.917809 + 0.397023i \(0.870043\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 8.93933 0.455000
\(387\) 1.23935 + 0.715541i 0.0629999 + 0.0363730i
\(388\) −6.68542 + 3.85983i −0.339401 + 0.195953i
\(389\) −0.609209 1.05518i −0.0308881 0.0534998i 0.850168 0.526511i \(-0.176500\pi\)
−0.881056 + 0.473012i \(0.843167\pi\)
\(390\) −12.8146 + 2.98105i −0.648892 + 0.150951i
\(391\) −20.2530 −1.02424
\(392\) 0 0
\(393\) 2.32106i 0.117082i
\(394\) 3.72945 6.45960i 0.187887 0.325430i
\(395\) −14.9447 4.54174i −0.751947 0.228520i
\(396\) −2.23483 3.87084i −0.112305 0.194517i
\(397\) 7.27977 + 4.20298i 0.365361 + 0.210941i 0.671430 0.741068i \(-0.265680\pi\)
−0.306069 + 0.952009i \(0.599014\pi\)
\(398\) 25.8293i 1.29471i
\(399\) 0 0
\(400\) 0.332104 4.98896i 0.0166052 0.249448i
\(401\) 0.332104 0.575221i 0.0165845 0.0287252i −0.857614 0.514294i \(-0.828054\pi\)
0.874199 + 0.485569i \(0.161387\pi\)
\(402\) −1.60336 + 0.925698i −0.0799681 + 0.0461696i
\(403\) 43.1579 24.9172i 2.14985 1.24122i
\(404\) −6.67722 + 11.5653i −0.332204 + 0.575394i
\(405\) 1.63280 1.52773i 0.0811347 0.0759133i
\(406\) 0 0
\(407\) 14.2457i 0.706131i
\(408\) 6.69895 + 3.86764i 0.331647 + 0.191477i
\(409\) −3.69238 6.39539i −0.182576 0.316231i 0.760181 0.649712i \(-0.225110\pi\)
−0.942757 + 0.333480i \(0.891777\pi\)
\(410\) 2.31650 7.62248i 0.114404 0.376447i
\(411\) −7.13756 + 12.3626i −0.352070 + 0.609803i
\(412\) 9.35965i 0.461117i
\(413\) 0 0
\(414\) 2.61827 0.128681
\(415\) −11.6728 + 2.71545i −0.572998 + 0.133296i
\(416\) 2.94194 + 5.09559i 0.144240 + 0.249832i
\(417\) −12.9585 + 7.48159i −0.634581 + 0.366375i
\(418\) 25.6183 + 14.7907i 1.25303 + 0.723438i
\(419\) −18.6274 −0.910009 −0.455004 0.890489i \(-0.650362\pi\)
−0.455004 + 0.890489i \(0.650362\pi\)
\(420\) 0 0
\(421\) −13.5043 −0.658159 −0.329079 0.944302i \(-0.606738\pi\)
−0.329079 + 0.944302i \(0.606738\pi\)
\(422\) −4.79237 2.76687i −0.233289 0.134689i
\(423\) 5.88094 3.39536i 0.285941 0.165088i
\(424\) 0.690865 + 1.19661i 0.0335514 + 0.0581127i
\(425\) −21.5202 + 32.1363i −1.04388 + 1.55884i
\(426\) 2.02386 0.0980561
\(427\) 0 0
\(428\) 11.0165i 0.532503i
\(429\) −13.1495 + 22.7756i −0.634863 + 1.09962i
\(430\) 3.06173 + 0.930471i 0.147650 + 0.0448713i
\(431\) 15.8404 + 27.4363i 0.763003 + 1.32156i 0.941296 + 0.337583i \(0.109609\pi\)
−0.178293 + 0.983977i \(0.557057\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 25.3184i 1.21672i 0.793660 + 0.608362i \(0.208173\pi\)
−0.793660 + 0.608362i \(0.791827\pi\)
\(434\) 0 0
\(435\) −12.4853 13.3440i −0.598623 0.639797i
\(436\) 2.34772 4.06637i 0.112435 0.194744i
\(437\) −15.0068 + 8.66421i −0.717875 + 0.414465i
\(438\) 3.47871 2.00843i 0.166219 0.0959667i
\(439\) 16.4073 28.4183i 0.783077 1.35633i −0.147064 0.989127i \(-0.546982\pi\)
0.930141 0.367203i \(-0.119684\pi\)
\(440\) −6.82843 7.29809i −0.325532 0.347923i
\(441\) 0 0
\(442\) 45.5134i 2.16485i
\(443\) 14.4125 + 8.32106i 0.684759 + 0.395346i 0.801646 0.597800i \(-0.203958\pi\)
−0.116887 + 0.993145i \(0.537291\pi\)
\(444\) −1.59359 2.76019i −0.0756286 0.130993i
\(445\) 30.7894 + 9.35701i 1.45956 + 0.443565i
\(446\) −1.64124 + 2.84271i −0.0777149 + 0.134606i
\(447\) 11.1651i 0.528091i
\(448\) 0 0
\(449\) −20.1759 −0.952158 −0.476079 0.879402i \(-0.657942\pi\)
−0.476079 + 0.879402i \(0.657942\pi\)
\(450\) 2.78209 4.15451i 0.131149 0.195846i
\(451\) −7.96230 13.7911i −0.374930 0.649398i
\(452\) 10.8880 6.28617i 0.512126 0.295676i
\(453\) 0.575221 + 0.332104i 0.0270263 + 0.0156036i
\(454\) −4.42031 −0.207456
\(455\) 0 0
\(456\) 6.61827 0.309929
\(457\) 30.6680 + 17.7062i 1.43459 + 0.828261i 0.997466 0.0711396i \(-0.0226636\pi\)
0.437124 + 0.899401i \(0.355997\pi\)
\(458\) 6.90456 3.98635i 0.322629 0.186270i
\(459\) 3.86764 + 6.69895i 0.180526 + 0.312680i
\(460\) 5.70237 1.32654i 0.265874 0.0618502i
\(461\) −12.5940 −0.586562 −0.293281 0.956026i \(-0.594747\pi\)
−0.293281 + 0.956026i \(0.594747\pi\)
\(462\) 0 0
\(463\) 32.5061i 1.51069i −0.655330 0.755343i \(-0.727470\pi\)
0.655330 0.755343i \(-0.272530\pi\)
\(464\) −4.08623 + 7.07756i −0.189698 + 0.328567i
\(465\) −5.50687 + 18.1204i −0.255375 + 0.840316i
\(466\) 8.97792 + 15.5502i 0.415894 + 0.720349i
\(467\) −7.97203 4.60265i −0.368902 0.212985i 0.304077 0.952648i \(-0.401652\pi\)
−0.672979 + 0.739662i \(0.734985\pi\)
\(468\) 5.88388i 0.271982i
\(469\) 0 0
\(470\) 11.0879 10.3744i 0.511448 0.478534i
\(471\) −4.04092 + 6.99907i −0.186196 + 0.322500i
\(472\) 4.03932 2.33210i 0.185925 0.107344i
\(473\) 5.53950 3.19823i 0.254706 0.147055i
\(474\) −3.49264 + 6.04942i −0.160422 + 0.277859i
\(475\) −2.19796 + 33.0183i −0.100849 + 1.51498i
\(476\) 0 0
\(477\) 1.38173i 0.0632651i
\(478\) 4.68776 + 2.70648i 0.214413 + 0.123792i
\(479\) −19.7457 34.2005i −0.902203 1.56266i −0.824628 0.565675i \(-0.808616\pi\)
−0.0775746 0.996987i \(-0.524718\pi\)
\(480\) −2.13945 0.650187i −0.0976522 0.0296769i
\(481\) −9.37652 + 16.2406i −0.427532 + 0.740508i
\(482\) 4.69669i 0.213928i
\(483\) 0 0
\(484\) −8.97792 −0.408087
\(485\) −16.8128 + 3.91115i −0.763428 + 0.177596i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) −25.3466 + 14.6339i −1.14857 + 0.663125i −0.948537 0.316666i \(-0.897437\pi\)
−0.200028 + 0.979790i \(0.564103\pi\)
\(488\) 8.48430 + 4.89841i 0.384066 + 0.221741i
\(489\) −0.836668 −0.0378354
\(490\) 0 0
\(491\) 15.3631 0.693325 0.346663 0.937990i \(-0.387315\pi\)
0.346663 + 0.937990i \(0.387315\pi\)
\(492\) −3.08549 1.78141i −0.139105 0.0803121i
\(493\) 54.7469 31.6081i 2.46567 1.42356i
\(494\) −19.4706 33.7240i −0.876022 1.51731i
\(495\) −2.26454 9.73455i −0.101784 0.437535i
\(496\) 8.46967 0.380299
\(497\) 0 0
\(498\) 5.35965i 0.240172i
\(499\) 10.2751 17.7970i 0.459978 0.796705i −0.538981 0.842318i \(-0.681191\pi\)
0.998959 + 0.0456128i \(0.0145241\pi\)
\(500\) 3.95428 10.4577i 0.176841 0.467683i
\(501\) 1.33381 + 2.31023i 0.0595903 + 0.103213i
\(502\) −6.69786 3.86701i −0.298940 0.172593i
\(503\) 20.4788i 0.913105i −0.889696 0.456553i \(-0.849084\pi\)
0.889696 0.456553i \(-0.150916\pi\)
\(504\) 0 0
\(505\) −21.8052 + 20.4019i −0.970318 + 0.907873i
\(506\) 5.85140 10.1349i 0.260126 0.450552i
\(507\) 18.7235 10.8100i 0.831540 0.480090i
\(508\) −5.71247 + 3.29809i −0.253450 + 0.146329i
\(509\) 6.03509 10.4531i 0.267501 0.463325i −0.700715 0.713441i \(-0.747136\pi\)
0.968216 + 0.250116i \(0.0804689\pi\)
\(510\) 11.8174 + 12.6302i 0.523283 + 0.559275i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 5.73159 + 3.30913i 0.253056 + 0.146102i
\(514\) −0.672210 1.16430i −0.0296499 0.0513551i
\(515\) −6.08552 + 20.0245i −0.268160 + 0.882386i
\(516\) 0.715541 1.23935i 0.0314999 0.0545595i
\(517\) 30.3523i 1.33489i
\(518\) 0 0
\(519\) 0.647340 0.0284151
\(520\) 2.98105 + 12.8146i 0.130728 + 0.561957i
\(521\) −7.35247 12.7348i −0.322117 0.557924i 0.658807 0.752312i \(-0.271061\pi\)
−0.980925 + 0.194388i \(0.937728\pi\)
\(522\) −7.07756 + 4.08623i −0.309776 + 0.178849i
\(523\) 5.58081 + 3.22208i 0.244032 + 0.140892i 0.617028 0.786941i \(-0.288336\pi\)
−0.372996 + 0.927833i \(0.621670\pi\)
\(524\) 2.32106 0.101396
\(525\) 0 0
\(526\) 4.36700 0.190410
\(527\) −56.7378 32.7576i −2.47154 1.42694i
\(528\) −3.87084 + 2.23483i −0.168457 + 0.0972586i
\(529\) −8.07233 13.9817i −0.350971 0.607899i
\(530\) 0.700050 + 3.00929i 0.0304082 + 0.130715i
\(531\) 4.66421 0.202409
\(532\) 0 0
\(533\) 20.9632i 0.908016i
\(534\) 7.19562 12.4632i 0.311385 0.539335i
\(535\) −7.16279 + 23.5693i −0.309674 + 1.01899i
\(536\) 0.925698 + 1.60336i 0.0399841 + 0.0692544i
\(537\) 22.2893 + 12.8687i 0.961853 + 0.555326i
\(538\) 23.0671i 0.994494i
\(539\) 0 0
\(540\) −1.52773 1.63280i −0.0657429 0.0702647i
\(541\) 5.79073 10.0298i 0.248963 0.431216i −0.714275 0.699865i \(-0.753244\pi\)
0.963238 + 0.268648i \(0.0865769\pi\)
\(542\) 12.7487 7.36047i 0.547604 0.316159i
\(543\) −6.42803 + 3.71123i −0.275853 + 0.159264i
\(544\) 3.86764 6.69895i 0.165824 0.287215i
\(545\) 7.66674 7.17335i 0.328407 0.307272i
\(546\) 0 0
\(547\) 19.2656i 0.823737i 0.911243 + 0.411868i \(0.135124\pi\)
−0.911243 + 0.411868i \(0.864876\pi\)
\(548\) 12.3626 + 7.13756i 0.528105 + 0.304902i
\(549\) 4.89841 + 8.48430i 0.209059 + 0.362101i
\(550\) −9.86397 20.0537i −0.420601 0.855092i
\(551\) 27.0438 46.8412i 1.15210 1.99550i
\(552\) 2.61827i 0.111441i
\(553\) 0 0
\(554\) −3.21104 −0.136424
\(555\) −1.61478 6.94142i −0.0685436 0.294647i
\(556\) 7.48159 + 12.9585i 0.317290 + 0.549563i
\(557\) 18.2215 10.5202i 0.772069 0.445754i −0.0615432 0.998104i \(-0.519602\pi\)
0.833612 + 0.552350i \(0.186269\pi\)
\(558\) 7.33495 + 4.23483i 0.310513 + 0.179275i
\(559\) −8.42031 −0.356141
\(560\) 0 0
\(561\) 34.5741 1.45972
\(562\) 6.68994 + 3.86244i 0.282198 + 0.162927i
\(563\) −3.12714 + 1.80546i −0.131793 + 0.0760910i −0.564447 0.825469i \(-0.690911\pi\)
0.432654 + 0.901560i \(0.357577\pi\)
\(564\) −3.39536 5.88094i −0.142971 0.247632i
\(565\) 27.3815 6.36974i 1.15195 0.267977i
\(566\) 29.5594 1.24247
\(567\) 0 0
\(568\) 2.02386i 0.0849191i
\(569\) 16.6072 28.7646i 0.696211 1.20587i −0.273559 0.961855i \(-0.588201\pi\)
0.969771 0.244018i \(-0.0784656\pi\)
\(570\) 14.1595 + 4.30312i 0.593075 + 0.180238i
\(571\) 16.0888 + 27.8667i 0.673296 + 1.16618i 0.976964 + 0.213405i \(0.0684555\pi\)
−0.303667 + 0.952778i \(0.598211\pi\)
\(572\) 22.7756 + 13.1495i 0.952295 + 0.549808i
\(573\) 1.08452i 0.0453066i
\(574\) 0 0
\(575\) 13.0624 + 0.869539i 0.544741 + 0.0362623i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −29.6096 + 17.0951i −1.23266 + 0.711679i −0.967585 0.252547i \(-0.918732\pi\)
−0.265080 + 0.964226i \(0.585398\pi\)
\(578\) −37.0958 + 21.4172i −1.54298 + 0.890840i
\(579\) 4.46967 7.74169i 0.185753 0.321734i
\(580\) −13.3440 + 12.4853i −0.554081 + 0.518423i
\(581\) 0 0
\(582\) 7.71966i 0.319990i
\(583\) 5.34846 + 3.08794i 0.221511 + 0.127889i
\(584\) −2.00843 3.47871i −0.0831096 0.143950i
\(585\) −3.82562 + 12.5883i −0.158170 + 0.520461i
\(586\) 0.588394 1.01913i 0.0243063 0.0420998i
\(587\) 34.5962i 1.42794i −0.700178 0.713969i \(-0.746896\pi\)
0.700178 0.713969i \(-0.253104\pi\)
\(588\) 0 0
\(589\) −56.0545 −2.30969
\(590\) 10.1582 2.36311i 0.418208 0.0972877i
\(591\) −3.72945 6.45960i −0.153409 0.265712i
\(592\) −2.76019 + 1.59359i −0.113443 + 0.0654963i
\(593\) 28.6520 + 16.5422i 1.17660 + 0.679309i 0.955225 0.295881i \(-0.0956131\pi\)
0.221372 + 0.975189i \(0.428946\pi\)
\(594\) −4.46967 −0.183393
\(595\) 0 0
\(596\) 11.1651 0.457341
\(597\) −22.3688 12.9147i −0.915496 0.528562i
\(598\) −13.3416 + 7.70279i −0.545580 + 0.314991i
\(599\) 3.03742 + 5.26097i 0.124106 + 0.214958i 0.921383 0.388656i \(-0.127060\pi\)
−0.797277 + 0.603613i \(0.793727\pi\)
\(600\) −4.15451 2.78209i −0.169607 0.113578i
\(601\) −11.7469 −0.479167 −0.239584 0.970876i \(-0.577011\pi\)
−0.239584 + 0.970876i \(0.577011\pi\)
\(602\) 0 0
\(603\) 1.85140i 0.0753947i
\(604\) 0.332104 0.575221i 0.0135131 0.0234054i
\(605\) −19.2078 5.83733i −0.780909 0.237321i
\(606\) 6.67722 + 11.5653i 0.271243 + 0.469807i
\(607\) −39.6796 22.9090i −1.61054 0.929848i −0.989244 0.146275i \(-0.953271\pi\)
−0.621300 0.783573i \(-0.713395\pi\)
\(608\) 6.61827i 0.268406i
\(609\) 0 0
\(610\) 14.9669 + 15.9963i 0.605991 + 0.647672i
\(611\) −19.9779 + 34.6028i −0.808220 + 1.39988i
\(612\) 6.69895 3.86764i 0.270789 0.156340i
\(613\) 29.6626 17.1257i 1.19806 0.691701i 0.237938 0.971280i \(-0.423528\pi\)
0.960122 + 0.279580i \(0.0901952\pi\)
\(614\) −10.1881 + 17.6463i −0.411157 + 0.712145i
\(615\) −5.44301 5.81739i −0.219483 0.234580i
\(616\) 0 0
\(617\) 38.8106i 1.56246i 0.624245 + 0.781228i \(0.285407\pi\)
−0.624245 + 0.781228i \(0.714593\pi\)
\(618\) 8.10569 + 4.67982i 0.326059 + 0.188250i
\(619\) −2.13756 3.70237i −0.0859159 0.148811i 0.819865 0.572557i \(-0.194048\pi\)
−0.905781 + 0.423746i \(0.860715\pi\)
\(620\) 18.1204 + 5.50687i 0.727735 + 0.221161i
\(621\) 1.30913 2.26749i 0.0525338 0.0909912i
\(622\) 18.8934i 0.757556i
\(623\) 0 0
\(624\) 5.88388 0.235544
\(625\) 15.2595 19.8027i 0.610379 0.792110i
\(626\) 8.24245 + 14.2763i 0.329434 + 0.570597i
\(627\) 25.6183 14.7907i 1.02310 0.590685i
\(628\) 6.99907 + 4.04092i 0.279293 + 0.161250i
\(629\) 24.6538 0.983011
\(630\) 0 0
\(631\) 36.8419 1.46665 0.733326 0.679878i \(-0.237967\pi\)
0.733326 + 0.679878i \(0.237967\pi\)
\(632\) 6.04942 + 3.49264i 0.240633 + 0.138930i
\(633\) −4.79237 + 2.76687i −0.190479 + 0.109973i
\(634\) 5.16053 + 8.93830i 0.204951 + 0.354985i
\(635\) −14.3659 + 3.34194i −0.570094 + 0.132621i
\(636\) 1.38173 0.0547892
\(637\) 0 0
\(638\) 36.5282i 1.44616i
\(639\) 1.01193 1.75271i 0.0400312 0.0693361i
\(640\) −0.650187 + 2.13945i −0.0257009 + 0.0845693i
\(641\) −24.9521 43.2184i −0.985551 1.70702i −0.639464 0.768821i \(-0.720844\pi\)
−0.346086 0.938203i \(-0.612490\pi\)
\(642\) 9.54057 + 5.50825i 0.376536 + 0.217393i
\(643\) 29.0091i 1.14401i 0.820251 + 0.572004i \(0.193834\pi\)
−0.820251 + 0.572004i \(0.806166\pi\)
\(644\) 0 0
\(645\) 2.33668 2.18630i 0.0920066 0.0860855i
\(646\) −25.5971 + 44.3354i −1.00710 + 1.74435i
\(647\) −4.28102 + 2.47165i −0.168304 + 0.0971705i −0.581786 0.813342i \(-0.697646\pi\)
0.413482 + 0.910512i \(0.364313\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 10.4237 18.0544i 0.409167 0.708698i
\(650\) −1.95406 + 29.3544i −0.0766446 + 1.15138i
\(651\) 0 0
\(652\) 0.836668i 0.0327664i
\(653\) −8.14548 4.70279i −0.318757 0.184035i 0.332081 0.943251i \(-0.392249\pi\)
−0.650838 + 0.759216i \(0.725582\pi\)
\(654\) −2.34772 4.06637i −0.0918031 0.159008i
\(655\) 4.96580 + 1.50913i 0.194030 + 0.0589664i
\(656\) −1.78141 + 3.08549i −0.0695523 + 0.120468i
\(657\) 4.01687i 0.156713i
\(658\) 0 0
\(659\) −13.4090 −0.522340 −0.261170 0.965293i \(-0.584108\pi\)
−0.261170 + 0.965293i \(0.584108\pi\)
\(660\) −9.73455 + 2.26454i −0.378917 + 0.0881473i
\(661\) −6.62545 11.4756i −0.257700 0.446350i 0.707925 0.706287i \(-0.249631\pi\)
−0.965625 + 0.259938i \(0.916298\pi\)
\(662\) −16.6195 + 9.59530i −0.645937 + 0.372932i
\(663\) −39.4158 22.7567i −1.53078 0.883798i
\(664\) 5.35965 0.207995
\(665\) 0 0
\(666\) −3.18719 −0.123501
\(667\) −18.5310 10.6989i −0.717521 0.414261i
\(668\) 2.31023 1.33381i 0.0893854 0.0516067i
\(669\) 1.64124 + 2.84271i 0.0634540 + 0.109906i
\(670\) 0.938005 + 4.03218i 0.0362383 + 0.155777i
\(671\) 43.7886 1.69044
\(672\) 0 0
\(673\) 21.8236i 0.841237i 0.907238 + 0.420619i \(0.138187\pi\)
−0.907238 + 0.420619i \(0.861813\pi\)
\(674\) −13.8018 + 23.9054i −0.531624 + 0.920800i
\(675\) −2.20687 4.48662i −0.0849424 0.172690i
\(676\) −10.8100 18.7235i −0.415770 0.720135i
\(677\) 35.5566 + 20.5286i 1.36655 + 0.788979i 0.990486 0.137614i \(-0.0439435\pi\)
0.376065 + 0.926593i \(0.377277\pi\)
\(678\) 12.5723i 0.482837i
\(679\) 0 0
\(680\) 12.6302 11.8174i 0.484346 0.453176i
\(681\) −2.21016 + 3.82810i −0.0846934 + 0.146693i
\(682\) 32.7848 18.9283i 1.25539 0.724802i
\(683\) 26.9024 15.5321i 1.02939 0.594320i 0.112581 0.993643i \(-0.464088\pi\)
0.916810 + 0.399323i \(0.130755\pi\)
\(684\) 3.30913 5.73159i 0.126528 0.219153i
\(685\) 21.8085 + 23.3085i 0.833259 + 0.890572i
\(686\) 0 0
\(687\) 7.97270i 0.304178i
\(688\) −1.23935 0.715541i −0.0472499 0.0272797i
\(689\) −4.06497 7.04073i −0.154863 0.268230i
\(690\) 1.70237 5.60166i 0.0648080 0.213252i
\(691\) 16.0006 27.7139i 0.608692 1.05429i −0.382764 0.923846i \(-0.625028\pi\)
0.991456 0.130439i \(-0.0416388\pi\)
\(692\) 0.647340i 0.0246082i
\(693\) 0 0
\(694\) 20.3761 0.773468
\(695\) 7.58106 + 32.5885i 0.287566 + 1.23615i
\(696\) 4.08623 + 7.07756i 0.154888 + 0.268274i
\(697\) 23.8671 13.7797i 0.904032 0.521943i
\(698\) −15.4396 8.91403i −0.584396 0.337401i
\(699\) 17.9558 0.679152
\(700\) 0 0
\(701\) −45.4635 −1.71713 −0.858567 0.512701i \(-0.828645\pi\)
−0.858567 + 0.512701i \(0.828645\pi\)
\(702\) 5.09559 + 2.94194i 0.192321 + 0.111036i
\(703\) 18.2677 10.5468i 0.688978 0.397781i
\(704\) 2.23483 + 3.87084i 0.0842284 + 0.145888i
\(705\) −3.44050 14.7896i −0.129577 0.557009i
\(706\) −3.51347 −0.132231
\(707\) 0 0
\(708\) 4.66421i 0.175292i
\(709\) −23.8798 + 41.3611i −0.896826 + 1.55335i −0.0652969 + 0.997866i \(0.520799\pi\)
−0.831529 + 0.555482i \(0.812534\pi\)
\(710\) 1.31589 4.32994i 0.0493843 0.162500i
\(711\) 3.49264 + 6.04942i 0.130984 + 0.226871i
\(712\) −12.4632 7.19562i −0.467078 0.269667i
\(713\) 22.1759i 0.830493i
\(714\) 0 0
\(715\) 40.1776 + 42.9411i 1.50256 + 1.60591i
\(716\) 12.8687 22.2893i 0.480927 0.832989i
\(717\) 4.68776 2.70648i 0.175068 0.101075i
\(718\) 1.90349 1.09898i 0.0710374 0.0410135i
\(719\) 6.58057 11.3979i 0.245414 0.425069i −0.716834 0.697244i \(-0.754409\pi\)
0.962248 + 0.272175i \(0.0877428\pi\)
\(720\) −1.63280 + 1.52773i −0.0608510 + 0.0569350i
\(721\) 0 0
\(722\) 24.8015i 0.923016i
\(723\) −4.06745 2.34835i −0.151270 0.0873359i
\(724\) 3.71123 + 6.42803i 0.137927 + 0.238896i
\(725\) −36.6667 + 18.0355i −1.36177 + 0.669823i
\(726\) −4.48896 + 7.77510i −0.166601 + 0.288561i
\(727\) 8.17082i 0.303039i 0.988454 + 0.151519i \(0.0484166\pi\)
−0.988454 + 0.151519i \(0.951583\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −2.03514 8.74839i −0.0753238 0.323793i
\(731\) 5.53491 + 9.58674i 0.204716 + 0.354578i
\(732\) 8.48430 4.89841i 0.313589 0.181051i
\(733\) −1.74512 1.00755i −0.0644576 0.0372146i 0.467425 0.884033i \(-0.345182\pi\)
−0.531882 + 0.846818i \(0.678515\pi\)
\(734\) 28.7721 1.06200
\(735\) 0 0
\(736\) −2.61827 −0.0965107
\(737\) 7.16647 + 4.13756i 0.263980 + 0.152409i
\(738\) −3.08549 + 1.78141i −0.113578 + 0.0655746i
\(739\) −1.91295 3.31333i −0.0703690 0.121883i 0.828694 0.559702i \(-0.189084\pi\)
−0.899063 + 0.437819i \(0.855751\pi\)
\(740\) −6.94142 + 1.61478i −0.255172 + 0.0593605i
\(741\) −38.9411 −1.43054
\(742\) 0 0
\(743\) 36.6654i 1.34512i 0.740041 + 0.672562i \(0.234806\pi\)
−0.740041 + 0.672562i \(0.765194\pi\)
\(744\) 4.23483 7.33495i 0.155257 0.268912i
\(745\) 23.8872 + 7.25941i 0.875160 + 0.265964i
\(746\) 7.28446 + 12.6171i 0.266703 + 0.461943i
\(747\) 4.64159 + 2.67982i 0.169827 + 0.0980496i
\(748\) 34.5741i 1.26415i
\(749\) 0 0
\(750\) −7.07950 8.65336i −0.258507 0.315976i
\(751\) 10.2329 17.7238i 0.373402 0.646751i −0.616684 0.787210i \(-0.711525\pi\)
0.990086 + 0.140459i \(0.0448579\pi\)
\(752\) −5.88094 + 3.39536i −0.214456 + 0.123816i
\(753\) −6.69786 + 3.86701i −0.244084 + 0.140922i
\(754\) 24.0429 41.6435i 0.875590 1.51657i
\(755\) 1.08452 1.01473i 0.0394698 0.0369298i
\(756\) 0 0
\(757\) 37.9575i 1.37959i −0.724006 0.689794i \(-0.757701\pi\)
0.724006 0.689794i \(-0.242299\pi\)
\(758\) −26.6621 15.3934i −0.968412 0.559113i
\(759\) −5.85140 10.1349i −0.212392 0.367874i
\(760\) 4.30312 14.1595i 0.156090 0.513618i
\(761\) 17.3065 29.9758i 0.627361 1.08662i −0.360718 0.932675i \(-0.617468\pi\)
0.988079 0.153946i \(-0.0491983\pi\)
\(762\) 6.59619i 0.238955i
\(763\) 0 0
\(764\) 1.08452 0.0392367
\(765\) 16.8468 3.91906i 0.609096 0.141694i
\(766\) 11.6705 + 20.2139i 0.421672 + 0.730357i
\(767\) −23.7669 + 13.7218i −0.858173 + 0.495466i
\(768\) 0.866025 + 0.500000i 0.0312500 + 0.0180422i
\(769\) 1.48961 0.0537167 0.0268584 0.999639i \(-0.491450\pi\)
0.0268584 + 0.999639i \(0.491450\pi\)
\(770\) 0 0
\(771\) −1.34442 −0.0484181
\(772\) −7.74169 4.46967i −0.278629 0.160867i
\(773\) −0.859321 + 0.496129i −0.0309076 + 0.0178445i −0.515374 0.856965i \(-0.672347\pi\)
0.484467 + 0.874810i \(0.339014\pi\)
\(774\) −0.715541 1.23935i −0.0257196 0.0445476i
\(775\) 35.1873 + 23.5634i 1.26397 + 0.846421i
\(776\) 7.71966 0.277120
\(777\) 0 0
\(778\) 1.21842i 0.0436824i
\(779\) 11.7898 20.4206i 0.422415 0.731644i
\(780\) 12.5883 + 3.82562i 0.450733 + 0.136979i
\(781\) −4.52298 7.83403i −0.161845 0.280324i
\(782\) 17.5396 + 10.1265i 0.627217 + 0.362124i
\(783\) 8.17246i 0.292060i
\(784\) 0 0
\(785\) 12.3468 + 13.1961i 0.440677 + 0.470988i
\(786\) 1.16053 2.01010i 0.0413948 0.0716979i
\(787\) −8.87786 + 5.12563i −0.316461 + 0.182709i −0.649814 0.760093i \(-0.725153\pi\)
0.333353 + 0.942802i \(0.391820\pi\)
\(788\) −6.45960 + 3.72945i −0.230114 + 0.132856i
\(789\) 2.18350 3.78193i 0.0777347 0.134640i
\(790\) 10.6716 + 11.4056i 0.379678 + 0.405793i
\(791\) 0 0
\(792\) 4.46967i 0.158823i
\(793\) −49.9206 28.8217i −1.77273 1.02349i
\(794\) −4.20298 7.27977i −0.149158 0.258349i
\(795\) 2.95615 + 0.898384i 0.104844 + 0.0318624i
\(796\) −12.9147 + 22.3688i −0.457748 + 0.792843i
\(797\) 32.6811i 1.15762i −0.815461 0.578812i \(-0.803517\pi\)
0.815461 0.578812i \(-0.196483\pi\)
\(798\) 0 0
\(799\) 52.5282 1.85831
\(800\) −2.78209 + 4.15451i −0.0983617 + 0.146884i
\(801\) −7.19562 12.4632i −0.254245 0.440365i
\(802\) −0.575221 + 0.332104i −0.0203118 + 0.0117270i
\(803\) −15.5487 8.97703i −0.548701 0.316793i
\(804\) 1.85140 0.0652937
\(805\) 0 0
\(806\) −49.8345 −1.75535
\(807\) −19.9767 11.5336i −0.703213 0.406000i
\(808\) 11.5653 6.67722i 0.406865 0.234904i
\(809\) 11.2258 + 19.4436i 0.394677 + 0.683601i 0.993060 0.117610i \(-0.0375231\pi\)
−0.598383 + 0.801210i \(0.704190\pi\)
\(810\) −2.17791 + 0.506647i −0.0765241 + 0.0178018i
\(811\) 37.6581 1.32235 0.661177 0.750230i \(-0.270057\pi\)
0.661177 + 0.750230i \(0.270057\pi\)
\(812\) 0 0
\(813\) 14.7209i 0.516286i
\(814\) −7.12283 + 12.3371i −0.249655 + 0.432415i
\(815\) −0.543991 + 1.79001i −0.0190552 + 0.0627013i
\(816\) −3.86764 6.69895i −0.135394 0.234510i
\(817\) 8.20237 + 4.73564i 0.286965 + 0.165679i
\(818\) 7.38476i 0.258202i
\(819\) 0 0
\(820\) −5.81739 + 5.44301i −0.203152 + 0.190078i
\(821\) 10.7419 18.6056i 0.374896 0.649338i −0.615416 0.788203i \(-0.711012\pi\)
0.990311 + 0.138864i \(0.0443452\pi\)
\(822\) 12.3626 7.13756i 0.431196 0.248951i
\(823\) −16.1190 + 9.30633i −0.561875 + 0.324398i −0.753898 0.656992i \(-0.771829\pi\)
0.192023 + 0.981390i \(0.438495\pi\)
\(824\) 4.67982 8.10569i 0.163029 0.282375i
\(825\) −22.2990 1.48440i −0.776351 0.0516800i
\(826\) 0 0
\(827\) 18.4254i 0.640713i 0.947297 + 0.320356i \(0.103803\pi\)
−0.947297 + 0.320356i \(0.896197\pi\)
\(828\) −2.26749 1.30913i −0.0788007 0.0454956i
\(829\) 16.0188 + 27.7454i 0.556357 + 0.963639i 0.997797 + 0.0663478i \(0.0211347\pi\)
−0.441439 + 0.897291i \(0.645532\pi\)
\(830\) 11.4667 + 3.48478i 0.398015 + 0.120958i
\(831\) −1.60552 + 2.78085i −0.0556949 + 0.0964665i
\(832\) 5.88388i 0.203987i
\(833\) 0 0
\(834\) 14.9632 0.518133
\(835\) 5.80985 1.35154i 0.201058 0.0467721i
\(836\) −14.7907 25.6183i −0.511548 0.886027i
\(837\) 7.33495 4.23483i 0.253533 0.146377i
\(838\) 16.1318 + 9.31371i 0.557264 + 0.321737i
\(839\) −8.45154 −0.291780 −0.145890 0.989301i \(-0.546605\pi\)
−0.145890 + 0.989301i \(0.546605\pi\)
\(840\) 0 0
\(841\) 37.7891 1.30307
\(842\) 11.6951 + 6.75214i 0.403038 + 0.232694i
\(843\) 6.68994 3.86244i 0.230414 0.133029i
\(844\) 2.76687 + 4.79237i 0.0952397 + 0.164960i
\(845\) −10.9537 47.0866i −0.376820 1.61983i
\(846\) −6.79073 −0.233470
\(847\) 0 0
\(848\) 1.38173i 0.0474488i
\(849\) 14.7797 25.5992i 0.507238 0.878561i
\(850\) 34.7052 17.0707i 1.19038 0.585521i
\(851\) −4.17246 7.22691i −0.143030 0.247735i
\(852\) −1.75271 1.01193i −0.0600469 0.0346681i
\(853\) 50.6270i 1.73344i 0.498798 + 0.866718i \(0.333775\pi\)
−0.498798 + 0.866718i \(0.666225\pi\)
\(854\) 0 0
\(855\) 10.8063 10.1109i 0.369569 0.345786i
\(856\) 5.50825 9.54057i 0.188268 0.326090i
\(857\) −10.3934 + 6.00063i −0.355031 + 0.204978i −0.666899 0.745148i \(-0.732379\pi\)
0.311868 + 0.950126i \(0.399045\pi\)
\(858\) 22.7756 13.1495i 0.777546 0.448916i
\(859\) −17.8560 + 30.9274i −0.609238 + 1.05523i 0.382128 + 0.924109i \(0.375191\pi\)
−0.991366 + 0.131122i \(0.958142\pi\)
\(860\) −2.18630 2.33668i −0.0745523 0.0796801i
\(861\) 0 0
\(862\) 31.6807i 1.07905i
\(863\) −1.11219 0.642125i −0.0378595 0.0218582i 0.480951 0.876748i \(-0.340292\pi\)
−0.518810 + 0.854889i \(0.673625\pi\)
\(864\) 0.500000 + 0.866025i 0.0170103 + 0.0294628i
\(865\) 0.420892 1.38495i 0.0143108 0.0470898i
\(866\) 12.6592 21.9264i 0.430177 0.745088i
\(867\) 42.8345i 1.45474i
\(868\) 0 0
\(869\) 31.2218 1.05913
\(870\) 4.14055 + 17.7989i 0.140378 + 0.603440i
\(871\) −5.44670 9.43396i −0.184554 0.319657i
\(872\) −4.06637 + 2.34772i −0.137705 + 0.0795038i
\(873\) 6.68542 + 3.85983i 0.226267 + 0.130635i
\(874\) 17.3284 0.586142
\(875\) 0 0
\(876\) −4.01687 −0.135717
\(877\) −33.2122 19.1751i −1.12150 0.647496i −0.179713 0.983719i \(-0.557517\pi\)
−0.941782 + 0.336224i \(0.890850\pi\)
\(878\) −28.4183 + 16.4073i −0.959070 + 0.553719i
\(879\) −0.588394 1.01913i −0.0198460 0.0343743i
\(880\) 2.26454 + 9.73455i 0.0763378 + 0.328152i
\(881\) 0.389472 0.0131216 0.00656082 0.999978i \(-0.497912\pi\)
0.00656082 + 0.999978i \(0.497912\pi\)
\(882\) 0 0
\(883\) 18.5412i 0.623962i 0.950088 + 0.311981i \(0.100993\pi\)
−0.950088 + 0.311981i \(0.899007\pi\)
\(884\) −22.7567 + 39.4158i −0.765391 + 1.32570i
\(885\) 3.03261 9.97885i 0.101940 0.335435i
\(886\) −8.32106 14.4125i −0.279552 0.484198i
\(887\) 36.7893 + 21.2403i 1.23526 + 0.713179i 0.968122 0.250478i \(-0.0805879\pi\)
0.267140 + 0.963658i \(0.413921\pi\)
\(888\) 3.18719i 0.106955i
\(889\) 0 0
\(890\) −21.9859 23.4981i −0.736968 0.787658i
\(891\) −2.23483 + 3.87084i −0.0748697 + 0.129678i
\(892\) 2.84271 1.64124i 0.0951810 0.0549528i
\(893\) 38.9217 22.4714i 1.30246 0.751978i
\(894\) 5.58255 9.66926i 0.186708 0.323389i
\(895\) 42.0242 39.3198i 1.40471 1.31431i
\(896\) 0 0
\(897\) 15.4056i 0.514378i
\(898\) 17.4728 + 10.0879i 0.583075 + 0.336639i
\(899\) −34.6090 59.9445i −1.15427 1.99926i
\(900\) −4.48662 + 2.20687i −0.149554 + 0.0735623i
\(901\) −5.34403 + 9.25613i −0.178036 + 0.308367i
\(902\) 15.9246i 0.530231i
\(903\) 0 0
\(904\) −12.5723 −0.418150
\(905\) 3.76057 + 16.1655i 0.125005 + 0.537358i
\(906\) −0.332104 0.575221i −0.0110334 0.0191105i
\(907\) −35.6531 + 20.5843i −1.18384 + 0.683491i −0.956900 0.290417i \(-0.906206\pi\)
−0.226941 + 0.973908i \(0.572873\pi\)
\(908\) 3.82810 + 2.21016i 0.127040 + 0.0733466i
\(909\) 13.3544 0.442939
\(910\) 0 0
\(911\) −25.1703 −0.833929 −0.416964 0.908923i \(-0.636906\pi\)
−0.416964 + 0.908923i \(0.636906\pi\)
\(912\) −5.73159 3.30913i −0.189792 0.109576i
\(913\) 20.7464 11.9779i 0.686604 0.396411i
\(914\) −17.7062 30.6680i −0.585669 1.01441i
\(915\) 21.3367 4.96354i 0.705368 0.164090i
\(916\) −7.97270 −0.263426
\(917\) 0 0
\(918\) 7.73528i 0.255302i
\(919\) −2.51841 + 4.36201i −0.0830745 + 0.143889i −0.904569 0.426327i \(-0.859807\pi\)
0.821495 + 0.570216i \(0.193141\pi\)
\(920\) −5.60166 1.70237i −0.184681 0.0561253i
\(921\) 10.1881 + 17.6463i 0.335708 + 0.581464i
\(922\) 10.9067 + 6.29701i 0.359195 + 0.207381i
\(923\) 11.9081i 0.391961i
\(924\) 0 0
\(925\) −15.9007 1.05848i −0.522813 0.0348026i
\(926\) −16.2530 + 28.1511i −0.534108 + 0.925102i
\(927\) 8.10569 4.67982i 0.266226 0.153706i
\(928\) 7.07756 4.08623i 0.232332 0.134137i
\(929\) −7.14231 + 12.3708i −0.234332 + 0.405874i −0.959078 0.283141i \(-0.908623\pi\)
0.724747 + 0.689015i \(0.241957\pi\)
\(930\) 13.8293 12.9393i 0.453481 0.424297i
\(931\) 0 0
\(932\) 17.9558i 0.588163i
\(933\) −16.3622 9.44670i −0.535673 0.309271i
\(934\) 4.60265 + 7.97203i 0.150603 + 0.260853i
\(935\) 22.4796 73.9696i 0.735163 2.41907i
\(936\) 2.94194 5.09559i 0.0961603 0.166555i
\(937\) 19.8403i 0.648153i −0.946031 0.324077i \(-0.894946\pi\)
0.946031 0.324077i \(-0.105054\pi\)
\(938\) 0 0
\(939\) 16.4849 0.537964
\(940\) −14.7896 + 3.44050i −0.482384 + 0.112217i
\(941\) −7.95271 13.7745i −0.259251 0.449036i 0.706791 0.707423i \(-0.250142\pi\)
−0.966041 + 0.258387i \(0.916809\pi\)
\(942\) 6.99907 4.04092i 0.228042 0.131660i
\(943\) −8.07865 4.66421i −0.263077 0.151888i
\(944\) −4.66421 −0.151807
\(945\) 0 0
\(946\) −6.39646 −0.207967
\(947\) −8.27760 4.77908i −0.268986 0.155299i 0.359441 0.933168i \(-0.382967\pi\)
−0.628427 + 0.777869i \(0.716301\pi\)
\(948\) 6.04942 3.49264i 0.196476 0.113436i
\(949\) 11.8174 + 20.4683i 0.383609 + 0.664430i
\(950\) 18.4126 27.4957i 0.597384 0.892078i
\(951\) 10.3211 0.334683
\(952\) 0 0
\(953\) 23.7505i 0.769354i −0.923051 0.384677i \(-0.874313\pi\)
0.923051 0.384677i \(-0.125687\pi\)
\(954\) 0.690865 1.19661i 0.0223676 0.0387418i
\(955\) 2.32029 + 0.705143i 0.0750827 + 0.0228179i
\(956\) −2.70648 4.68776i −0.0875338 0.151613i
\(957\) 31.6343 + 18.2641i 1.02259 + 0.590394i
\(958\) 39.4914i 1.27591i
\(959\) 0 0
\(960\) 1.52773 + 1.63280i 0.0493072 + 0.0526986i
\(961\) −20.3676 + 35.2778i −0.657020 + 1.13799i
\(962\) 16.2406 9.37652i 0.523618 0.302311i
\(963\) 9.54057 5.50825i 0.307441 0.177501i
\(964\) −2.34835 + 4.06745i −0.0756351 + 0.131004i
\(965\) −13.6569 14.5962i −0.439630 0.469868i
\(966\) 0 0
\(967\) 56.9706i 1.83205i −0.401121 0.916025i \(-0.631379\pi\)
0.401121 0.916025i \(-0.368621\pi\)
\(968\) 7.77510 + 4.48896i 0.249901 + 0.144281i
\(969\) 25.5971 + 44.3354i 0.822296 + 1.42426i
\(970\) 16.5158 + 5.01923i 0.530292 + 0.161158i
\(971\) −16.5429 + 28.6531i −0.530886 + 0.919522i 0.468464 + 0.883482i \(0.344807\pi\)
−0.999350 + 0.0360392i \(0.988526\pi\)
\(972\) 1.00000i 0.0320750i
\(973\) 0 0
\(974\) 29.2678 0.937800
\(975\) 24.4447 + 16.3695i 0.782855 + 0.524243i
\(976\) −4.89841 8.48430i −0.156794 0.271576i
\(977\) −21.3152 + 12.3063i −0.681934 + 0.393715i −0.800583 0.599222i \(-0.795477\pi\)
0.118650 + 0.992936i \(0.462143\pi\)
\(978\) 0.724575 + 0.418334i 0.0231694 + 0.0133768i
\(979\) −64.3241 −2.05581
\(980\) 0 0
\(981\) −4.69544 −0.149914
\(982\) −13.3048 7.68153i −0.424573 0.245127i
\(983\) −36.7893 + 21.2403i −1.17340 + 0.677460i −0.954477 0.298283i \(-0.903586\pi\)
−0.218918 + 0.975743i \(0.570253\pi\)
\(984\) 1.78141 + 3.08549i 0.0567892 + 0.0983618i
\(985\) −16.2448 + 3.77903i −0.517604 + 0.120410i
\(986\) −63.2162 −2.01321
\(987\) 0 0
\(988\) 38.9411i 1.23888i
\(989\) 1.87348 3.24496i 0.0595732 0.103184i
\(990\) −2.90612 + 9.56264i −0.0923626 + 0.303921i
\(991\) 0.419154 + 0.725996i 0.0133149 + 0.0230620i 0.872606 0.488425i \(-0.162428\pi\)
−0.859291 + 0.511487i \(0.829095\pi\)
\(992\) −7.33495 4.23483i −0.232885 0.134456i
\(993\) 19.1906i 0.608995i
\(994\) 0 0
\(995\) −42.1742 + 39.4601i −1.33701 + 1.25097i
\(996\) 2.67982 4.64159i 0.0849135 0.147074i
\(997\) −27.3612 + 15.7970i −0.866539 + 0.500297i −0.866197 0.499703i \(-0.833442\pi\)
−0.000342701 1.00000i \(0.500109\pi\)
\(998\) −17.7970 + 10.2751i −0.563355 + 0.325253i
\(999\) −1.59359 + 2.76019i −0.0504191 + 0.0873284i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 1470.2.n.k.79.3 16
5.4 even 2 inner 1470.2.n.k.79.5 16
7.2 even 3 1470.2.g.k.589.7 yes 8
7.3 odd 6 1470.2.n.l.949.8 16
7.4 even 3 inner 1470.2.n.k.949.5 16
7.5 odd 6 1470.2.g.j.589.6 yes 8
7.6 odd 2 1470.2.n.l.79.2 16
35.2 odd 12 7350.2.a.dr.1.4 4
35.4 even 6 inner 1470.2.n.k.949.3 16
35.9 even 6 1470.2.g.k.589.3 yes 8
35.12 even 12 7350.2.a.ds.1.4 4
35.19 odd 6 1470.2.g.j.589.2 8
35.23 odd 12 7350.2.a.du.1.4 4
35.24 odd 6 1470.2.n.l.949.2 16
35.33 even 12 7350.2.a.dt.1.4 4
35.34 odd 2 1470.2.n.l.79.8 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1470.2.g.j.589.2 8 35.19 odd 6
1470.2.g.j.589.6 yes 8 7.5 odd 6
1470.2.g.k.589.3 yes 8 35.9 even 6
1470.2.g.k.589.7 yes 8 7.2 even 3
1470.2.n.k.79.3 16 1.1 even 1 trivial
1470.2.n.k.79.5 16 5.4 even 2 inner
1470.2.n.k.949.3 16 35.4 even 6 inner
1470.2.n.k.949.5 16 7.4 even 3 inner
1470.2.n.l.79.2 16 7.6 odd 2
1470.2.n.l.79.8 16 35.34 odd 2
1470.2.n.l.949.2 16 35.24 odd 6
1470.2.n.l.949.8 16 7.3 odd 6
7350.2.a.dr.1.4 4 35.2 odd 12
7350.2.a.ds.1.4 4 35.12 even 12
7350.2.a.dt.1.4 4 35.33 even 12
7350.2.a.du.1.4 4 35.23 odd 12