Properties

Label 507.2.j.g.361.3
Level $507$
Weight $2$
Character 507.361
Analytic conductor $4.048$
Analytic rank $0$
Dimension $8$
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] = [507,2,Mod(316,507)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(507, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("507.316");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.j (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: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.1731891456.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.3
Root \(1.35234 - 0.780776i\) of defining polynomial
Character \(\chi\) \(=\) 507.361
Dual form 507.2.j.g.316.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.35234 - 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} +3.56155i q^{5} +(-1.35234 - 0.780776i) q^{6} +(-0.486319 - 0.280776i) q^{7} +2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.35234 - 0.780776i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.219224 - 0.379706i) q^{4} +3.56155i q^{5} +(-1.35234 - 0.780776i) q^{6} +(-0.486319 - 0.280776i) q^{7} +2.43845i q^{8} +(-0.500000 + 0.866025i) q^{9} +(2.78078 + 4.81645i) q^{10} +(-1.73205 + 1.00000i) q^{11} -0.438447 q^{12} -0.876894 q^{14} +(3.08440 - 1.78078i) q^{15} +(2.34233 + 4.05703i) q^{16} +(-0.780776 + 1.35234i) q^{17} +1.56155i q^{18} +(6.16879 + 3.56155i) q^{19} +(1.35234 + 0.780776i) q^{20} +0.561553i q^{21} +(-1.56155 + 2.70469i) q^{22} +(1.00000 + 1.73205i) q^{23} +(2.11176 - 1.21922i) q^{24} -7.68466 q^{25} +1.00000 q^{27} +(-0.213225 + 0.123106i) q^{28} +(-3.34233 - 5.78908i) q^{29} +(2.78078 - 4.81645i) q^{30} -2.56155i q^{31} +(2.11176 + 1.21922i) q^{32} +(1.73205 + 1.00000i) q^{33} +2.43845i q^{34} +(1.00000 - 1.73205i) q^{35} +(0.219224 + 0.379706i) q^{36} +(6.54850 - 3.78078i) q^{37} +11.1231 q^{38} -8.68466 q^{40} +(1.35234 - 0.780776i) q^{41} +(0.438447 + 0.759413i) q^{42} +(2.28078 - 3.95042i) q^{43} +0.876894i q^{44} +(-3.08440 - 1.78078i) q^{45} +(2.70469 + 1.56155i) q^{46} +8.24621i q^{47} +(2.34233 - 4.05703i) q^{48} +(-3.34233 - 5.78908i) q^{49} +(-10.3923 + 6.00000i) q^{50} +1.56155 q^{51} -0.684658 q^{53} +(1.35234 - 0.780776i) q^{54} +(-3.56155 - 6.16879i) q^{55} +(0.684658 - 1.18586i) q^{56} -7.12311i q^{57} +(-9.03996 - 5.21922i) q^{58} +(2.49146 + 1.43845i) q^{59} -1.56155i q^{60} +(-1.93845 + 3.35749i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(0.486319 - 0.280776i) q^{63} -5.56155 q^{64} +3.12311 q^{66} +(-3.95042 + 2.28078i) q^{67} +(0.342329 + 0.592932i) q^{68} +(1.00000 - 1.73205i) q^{69} -3.12311i q^{70} +(12.1244 + 7.00000i) q^{71} +(-2.11176 - 1.21922i) q^{72} -10.1231i q^{73} +(5.90388 - 10.2258i) q^{74} +(3.84233 + 6.65511i) q^{75} +(2.70469 - 1.56155i) q^{76} +1.12311 q^{77} +5.43845 q^{79} +(-14.4493 + 8.34233i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.21922 - 2.11176i) q^{82} +0.876894i q^{83} +(0.213225 + 0.123106i) q^{84} +(-4.81645 - 2.78078i) q^{85} -7.12311i q^{86} +(-3.34233 + 5.78908i) q^{87} +(-2.43845 - 4.22351i) q^{88} +(4.22351 - 2.43845i) q^{89} -5.56155 q^{90} +0.876894 q^{92} +(-2.21837 + 1.28078i) q^{93} +(6.43845 + 11.1517i) q^{94} +(-12.6847 + 21.9705i) q^{95} -2.43845i q^{96} +(-7.41452 - 4.28078i) q^{97} +(-9.03996 - 5.21922i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{3} + 10 q^{4} - 4 q^{9} + 14 q^{10} - 20 q^{12} - 40 q^{14} - 6 q^{16} + 2 q^{17} + 4 q^{22} + 8 q^{23} - 12 q^{25} + 8 q^{27} - 2 q^{29} + 14 q^{30} + 8 q^{35} + 10 q^{36} + 56 q^{38} - 20 q^{40} + 20 q^{42} + 10 q^{43} - 6 q^{48} - 2 q^{49} - 4 q^{51} + 44 q^{53} - 12 q^{55} - 44 q^{56} - 32 q^{61} - 16 q^{62} - 28 q^{64} - 8 q^{66} - 22 q^{68} + 8 q^{69} + 6 q^{74} + 6 q^{75} - 24 q^{77} + 60 q^{79} - 4 q^{81} + 18 q^{82} - 2 q^{87} - 36 q^{88} - 28 q^{90} + 40 q^{92} + 68 q^{94} - 52 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35234 0.780776i 0.956252 0.552092i 0.0612344 0.998123i \(-0.480496\pi\)
0.895017 + 0.446031i \(0.147163\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.219224 0.379706i 0.109612 0.189853i
\(5\) 3.56155i 1.59277i 0.604787 + 0.796387i \(0.293258\pi\)
−0.604787 + 0.796387i \(0.706742\pi\)
\(6\) −1.35234 0.780776i −0.552092 0.318751i
\(7\) −0.486319 0.280776i −0.183811 0.106124i 0.405271 0.914197i \(-0.367177\pi\)
−0.589082 + 0.808073i \(0.700511\pi\)
\(8\) 2.43845i 0.862121i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 2.78078 + 4.81645i 0.879359 + 1.52309i
\(11\) −1.73205 + 1.00000i −0.522233 + 0.301511i −0.737848 0.674967i \(-0.764158\pi\)
0.215615 + 0.976478i \(0.430824\pi\)
\(12\) −0.438447 −0.126569
\(13\) 0 0
\(14\) −0.876894 −0.234360
\(15\) 3.08440 1.78078i 0.796387 0.459794i
\(16\) 2.34233 + 4.05703i 0.585582 + 1.01426i
\(17\) −0.780776 + 1.35234i −0.189366 + 0.327992i −0.945039 0.326957i \(-0.893977\pi\)
0.755673 + 0.654949i \(0.227310\pi\)
\(18\) 1.56155i 0.368062i
\(19\) 6.16879 + 3.56155i 1.41522 + 0.817076i 0.995874 0.0907512i \(-0.0289268\pi\)
0.419344 + 0.907827i \(0.362260\pi\)
\(20\) 1.35234 + 0.780776i 0.302393 + 0.174587i
\(21\) 0.561553i 0.122541i
\(22\) −1.56155 + 2.70469i −0.332924 + 0.576642i
\(23\) 1.00000 + 1.73205i 0.208514 + 0.361158i 0.951247 0.308431i \(-0.0998038\pi\)
−0.742732 + 0.669588i \(0.766471\pi\)
\(24\) 2.11176 1.21922i 0.431061 0.248873i
\(25\) −7.68466 −1.53693
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) −0.213225 + 0.123106i −0.0402958 + 0.0232648i
\(29\) −3.34233 5.78908i −0.620655 1.07501i −0.989364 0.145461i \(-0.953533\pi\)
0.368709 0.929545i \(-0.379800\pi\)
\(30\) 2.78078 4.81645i 0.507698 0.879359i
\(31\) 2.56155i 0.460068i −0.973183 0.230034i \(-0.926116\pi\)
0.973183 0.230034i \(-0.0738838\pi\)
\(32\) 2.11176 + 1.21922i 0.373309 + 0.215530i
\(33\) 1.73205 + 1.00000i 0.301511 + 0.174078i
\(34\) 2.43845i 0.418190i
\(35\) 1.00000 1.73205i 0.169031 0.292770i
\(36\) 0.219224 + 0.379706i 0.0365373 + 0.0632844i
\(37\) 6.54850 3.78078i 1.07657 0.621556i 0.146598 0.989196i \(-0.453168\pi\)
0.929968 + 0.367640i \(0.119834\pi\)
\(38\) 11.1231 1.80441
\(39\) 0 0
\(40\) −8.68466 −1.37317
\(41\) 1.35234 0.780776i 0.211201 0.121937i −0.390669 0.920531i \(-0.627756\pi\)
0.601869 + 0.798595i \(0.294423\pi\)
\(42\) 0.438447 + 0.759413i 0.0676539 + 0.117180i
\(43\) 2.28078 3.95042i 0.347815 0.602433i −0.638046 0.769998i \(-0.720257\pi\)
0.985861 + 0.167565i \(0.0535903\pi\)
\(44\) 0.876894i 0.132197i
\(45\) −3.08440 1.78078i −0.459794 0.265462i
\(46\) 2.70469 + 1.56155i 0.398785 + 0.230238i
\(47\) 8.24621i 1.20283i 0.798935 + 0.601417i \(0.205397\pi\)
−0.798935 + 0.601417i \(0.794603\pi\)
\(48\) 2.34233 4.05703i 0.338086 0.585582i
\(49\) −3.34233 5.78908i −0.477476 0.827012i
\(50\) −10.3923 + 6.00000i −1.46969 + 0.848528i
\(51\) 1.56155 0.218661
\(52\) 0 0
\(53\) −0.684658 −0.0940451 −0.0470225 0.998894i \(-0.514973\pi\)
−0.0470225 + 0.998894i \(0.514973\pi\)
\(54\) 1.35234 0.780776i 0.184031 0.106250i
\(55\) −3.56155 6.16879i −0.480240 0.831800i
\(56\) 0.684658 1.18586i 0.0914913 0.158468i
\(57\) 7.12311i 0.943478i
\(58\) −9.03996 5.21922i −1.18700 0.685318i
\(59\) 2.49146 + 1.43845i 0.324361 + 0.187270i 0.653335 0.757069i \(-0.273369\pi\)
−0.328974 + 0.944339i \(0.606703\pi\)
\(60\) 1.56155i 0.201596i
\(61\) −1.93845 + 3.35749i −0.248193 + 0.429882i −0.963024 0.269414i \(-0.913170\pi\)
0.714832 + 0.699297i \(0.246503\pi\)
\(62\) −2.00000 3.46410i −0.254000 0.439941i
\(63\) 0.486319 0.280776i 0.0612704 0.0353745i
\(64\) −5.56155 −0.695194
\(65\) 0 0
\(66\) 3.12311 0.384428
\(67\) −3.95042 + 2.28078i −0.482621 + 0.278641i −0.721508 0.692406i \(-0.756551\pi\)
0.238887 + 0.971047i \(0.423217\pi\)
\(68\) 0.342329 + 0.592932i 0.0415135 + 0.0719035i
\(69\) 1.00000 1.73205i 0.120386 0.208514i
\(70\) 3.12311i 0.373283i
\(71\) 12.1244 + 7.00000i 1.43890 + 0.830747i 0.997773 0.0666994i \(-0.0212469\pi\)
0.441123 + 0.897447i \(0.354580\pi\)
\(72\) −2.11176 1.21922i −0.248873 0.143687i
\(73\) 10.1231i 1.18482i −0.805637 0.592410i \(-0.798177\pi\)
0.805637 0.592410i \(-0.201823\pi\)
\(74\) 5.90388 10.2258i 0.686312 1.18873i
\(75\) 3.84233 + 6.65511i 0.443674 + 0.768466i
\(76\) 2.70469 1.56155i 0.310249 0.179122i
\(77\) 1.12311 0.127990
\(78\) 0 0
\(79\) 5.43845 0.611873 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(80\) −14.4493 + 8.34233i −1.61549 + 0.932701i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.21922 2.11176i 0.134641 0.233205i
\(83\) 0.876894i 0.0962517i 0.998841 + 0.0481258i \(0.0153248\pi\)
−0.998841 + 0.0481258i \(0.984675\pi\)
\(84\) 0.213225 + 0.123106i 0.0232648 + 0.0134319i
\(85\) −4.81645 2.78078i −0.522417 0.301618i
\(86\) 7.12311i 0.768104i
\(87\) −3.34233 + 5.78908i −0.358335 + 0.620655i
\(88\) −2.43845 4.22351i −0.259939 0.450228i
\(89\) 4.22351 2.43845i 0.447692 0.258475i −0.259163 0.965834i \(-0.583447\pi\)
0.706855 + 0.707359i \(0.250113\pi\)
\(90\) −5.56155 −0.586239
\(91\) 0 0
\(92\) 0.876894 0.0914226
\(93\) −2.21837 + 1.28078i −0.230034 + 0.132810i
\(94\) 6.43845 + 11.1517i 0.664075 + 1.15021i
\(95\) −12.6847 + 21.9705i −1.30142 + 2.25412i
\(96\) 2.43845i 0.248873i
\(97\) −7.41452 4.28078i −0.752831 0.434647i 0.0738851 0.997267i \(-0.476460\pi\)
−0.826716 + 0.562620i \(0.809794\pi\)
\(98\) −9.03996 5.21922i −0.913174 0.527221i
\(99\) 2.00000i 0.201008i
\(100\) −1.68466 + 2.91791i −0.168466 + 0.291791i
\(101\) −3.78078 6.54850i −0.376201 0.651600i 0.614305 0.789069i \(-0.289437\pi\)
−0.990506 + 0.137469i \(0.956103\pi\)
\(102\) 2.11176 1.21922i 0.209095 0.120721i
\(103\) 3.43845 0.338800 0.169400 0.985547i \(-0.445817\pi\)
0.169400 + 0.985547i \(0.445817\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) −0.925894 + 0.534565i −0.0899308 + 0.0519216i
\(107\) 4.12311 + 7.14143i 0.398596 + 0.690388i 0.993553 0.113369i \(-0.0361644\pi\)
−0.594957 + 0.803757i \(0.702831\pi\)
\(108\) 0.219224 0.379706i 0.0210948 0.0365373i
\(109\) 2.80776i 0.268935i 0.990918 + 0.134468i \(0.0429324\pi\)
−0.990918 + 0.134468i \(0.957068\pi\)
\(110\) −9.63289 5.56155i −0.918460 0.530273i
\(111\) −6.54850 3.78078i −0.621556 0.358855i
\(112\) 2.63068i 0.248576i
\(113\) −2.90388 + 5.02967i −0.273174 + 0.473152i −0.969673 0.244406i \(-0.921407\pi\)
0.696499 + 0.717558i \(0.254740\pi\)
\(114\) −5.56155 9.63289i −0.520887 0.902203i
\(115\) −6.16879 + 3.56155i −0.575243 + 0.332117i
\(116\) −2.93087 −0.272124
\(117\) 0 0
\(118\) 4.49242 0.413561
\(119\) 0.759413 0.438447i 0.0696153 0.0401924i
\(120\) 4.34233 + 7.52113i 0.396399 + 0.686583i
\(121\) −3.50000 + 6.06218i −0.318182 + 0.551107i
\(122\) 6.05398i 0.548101i
\(123\) −1.35234 0.780776i −0.121937 0.0704002i
\(124\) −0.972638 0.561553i −0.0873455 0.0504289i
\(125\) 9.56155i 0.855211i
\(126\) 0.438447 0.759413i 0.0390600 0.0676539i
\(127\) 2.71922 + 4.70983i 0.241292 + 0.417930i 0.961083 0.276261i \(-0.0890955\pi\)
−0.719791 + 0.694191i \(0.755762\pi\)
\(128\) −11.7446 + 6.78078i −1.03809 + 0.599342i
\(129\) −4.56155 −0.401622
\(130\) 0 0
\(131\) 7.36932 0.643860 0.321930 0.946763i \(-0.395668\pi\)
0.321930 + 0.946763i \(0.395668\pi\)
\(132\) 0.759413 0.438447i 0.0660984 0.0381619i
\(133\) −2.00000 3.46410i −0.173422 0.300376i
\(134\) −3.56155 + 6.16879i −0.307671 + 0.532902i
\(135\) 3.56155i 0.306530i
\(136\) −3.29762 1.90388i −0.282769 0.163257i
\(137\) 4.81645 + 2.78078i 0.411497 + 0.237578i 0.691433 0.722441i \(-0.256980\pi\)
−0.279936 + 0.960019i \(0.590313\pi\)
\(138\) 3.12311i 0.265856i
\(139\) 8.96543 15.5286i 0.760438 1.31712i −0.182187 0.983264i \(-0.558318\pi\)
0.942625 0.333854i \(-0.108349\pi\)
\(140\) −0.438447 0.759413i −0.0370556 0.0641821i
\(141\) 7.14143 4.12311i 0.601417 0.347228i
\(142\) 21.8617 1.83460
\(143\) 0 0
\(144\) −4.68466 −0.390388
\(145\) 20.6181 11.9039i 1.71224 0.988564i
\(146\) −7.90388 13.6899i −0.654130 1.13299i
\(147\) −3.34233 + 5.78908i −0.275671 + 0.477476i
\(148\) 3.31534i 0.272519i
\(149\) −2.11176 1.21922i −0.173002 0.0998827i 0.410999 0.911636i \(-0.365180\pi\)
−0.584001 + 0.811753i \(0.698513\pi\)
\(150\) 10.3923 + 6.00000i 0.848528 + 0.489898i
\(151\) 9.36932i 0.762464i −0.924479 0.381232i \(-0.875500\pi\)
0.924479 0.381232i \(-0.124500\pi\)
\(152\) −8.68466 + 15.0423i −0.704419 + 1.22009i
\(153\) −0.780776 1.35234i −0.0631220 0.109331i
\(154\) 1.51883 0.876894i 0.122390 0.0706622i
\(155\) 9.12311 0.732785
\(156\) 0 0
\(157\) 20.3693 1.62565 0.812824 0.582509i \(-0.197929\pi\)
0.812824 + 0.582509i \(0.197929\pi\)
\(158\) 7.35465 4.24621i 0.585105 0.337810i
\(159\) 0.342329 + 0.592932i 0.0271485 + 0.0470225i
\(160\) −4.34233 + 7.52113i −0.343291 + 0.594598i
\(161\) 1.12311i 0.0885131i
\(162\) −1.35234 0.780776i −0.106250 0.0613436i
\(163\) 4.16365 + 2.40388i 0.326122 + 0.188287i 0.654118 0.756393i \(-0.273040\pi\)
−0.327996 + 0.944679i \(0.606373\pi\)
\(164\) 0.684658i 0.0534628i
\(165\) −3.56155 + 6.16879i −0.277267 + 0.480240i
\(166\) 0.684658 + 1.18586i 0.0531398 + 0.0920408i
\(167\) 8.87348 5.12311i 0.686650 0.396438i −0.115706 0.993284i \(-0.536913\pi\)
0.802356 + 0.596846i \(0.203580\pi\)
\(168\) −1.36932 −0.105645
\(169\) 0 0
\(170\) −8.68466 −0.666083
\(171\) −6.16879 + 3.56155i −0.471739 + 0.272359i
\(172\) −1.00000 1.73205i −0.0762493 0.132068i
\(173\) 10.1231 17.5337i 0.769645 1.33307i −0.168110 0.985768i \(-0.553766\pi\)
0.937755 0.347297i \(-0.112900\pi\)
\(174\) 10.4384i 0.791337i
\(175\) 3.73720 + 2.15767i 0.282505 + 0.163105i
\(176\) −8.11407 4.68466i −0.611621 0.353119i
\(177\) 2.87689i 0.216241i
\(178\) 3.80776 6.59524i 0.285404 0.494334i
\(179\) −2.43845 4.22351i −0.182258 0.315680i 0.760391 0.649466i \(-0.225007\pi\)
−0.942649 + 0.333785i \(0.891674\pi\)
\(180\) −1.35234 + 0.780776i −0.100798 + 0.0581956i
\(181\) 2.68466 0.199549 0.0997745 0.995010i \(-0.468188\pi\)
0.0997745 + 0.995010i \(0.468188\pi\)
\(182\) 0 0
\(183\) 3.87689 0.286588
\(184\) −4.22351 + 2.43845i −0.311362 + 0.179765i
\(185\) 13.4654 + 23.3228i 0.989998 + 1.71473i
\(186\) −2.00000 + 3.46410i −0.146647 + 0.254000i
\(187\) 3.12311i 0.228384i
\(188\) 3.13114 + 1.80776i 0.228362 + 0.131845i
\(189\) −0.486319 0.280776i −0.0353745 0.0204235i
\(190\) 39.6155i 2.87401i
\(191\) 4.56155 7.90084i 0.330062 0.571685i −0.652461 0.757822i \(-0.726264\pi\)
0.982524 + 0.186137i \(0.0595969\pi\)
\(192\) 2.78078 + 4.81645i 0.200685 + 0.347597i
\(193\) −11.6848 + 6.74621i −0.841089 + 0.485603i −0.857634 0.514260i \(-0.828067\pi\)
0.0165453 + 0.999863i \(0.494733\pi\)
\(194\) −13.3693 −0.959861
\(195\) 0 0
\(196\) −2.93087 −0.209348
\(197\) −11.5782 + 6.68466i −0.824910 + 0.476262i −0.852107 0.523368i \(-0.824675\pi\)
0.0271965 + 0.999630i \(0.491342\pi\)
\(198\) −1.56155 2.70469i −0.110975 0.192214i
\(199\) 11.0885 19.2059i 0.786046 1.36147i −0.142327 0.989820i \(-0.545458\pi\)
0.928372 0.371651i \(-0.121208\pi\)
\(200\) 18.7386i 1.32502i
\(201\) 3.95042 + 2.28078i 0.278641 + 0.160874i
\(202\) −10.2258 5.90388i −0.719486 0.415396i
\(203\) 3.75379i 0.263464i
\(204\) 0.342329 0.592932i 0.0239678 0.0415135i
\(205\) 2.78078 + 4.81645i 0.194218 + 0.336395i
\(206\) 4.64996 2.68466i 0.323978 0.187049i
\(207\) −2.00000 −0.139010
\(208\) 0 0
\(209\) −14.2462 −0.985431
\(210\) −2.70469 + 1.56155i −0.186641 + 0.107757i
\(211\) −9.84233 17.0474i −0.677574 1.17359i −0.975709 0.219069i \(-0.929698\pi\)
0.298136 0.954524i \(-0.403635\pi\)
\(212\) −0.150093 + 0.259969i −0.0103084 + 0.0178548i
\(213\) 14.0000i 0.959264i
\(214\) 11.1517 + 6.43845i 0.762316 + 0.440123i
\(215\) 14.0696 + 8.12311i 0.959541 + 0.553991i
\(216\) 2.43845i 0.165915i
\(217\) −0.719224 + 1.24573i −0.0488241 + 0.0845658i
\(218\) 2.19224 + 3.79706i 0.148477 + 0.257170i
\(219\) −8.76687 + 5.06155i −0.592410 + 0.342028i
\(220\) −3.12311 −0.210560
\(221\) 0 0
\(222\) −11.8078 −0.792485
\(223\) −6.92820 + 4.00000i −0.463947 + 0.267860i −0.713702 0.700449i \(-0.752983\pi\)
0.249756 + 0.968309i \(0.419650\pi\)
\(224\) −0.684658 1.18586i −0.0457457 0.0792338i
\(225\) 3.84233 6.65511i 0.256155 0.443674i
\(226\) 9.06913i 0.603270i
\(227\) 6.16879 + 3.56155i 0.409437 + 0.236389i 0.690548 0.723287i \(-0.257370\pi\)
−0.281111 + 0.959675i \(0.590703\pi\)
\(228\) −2.70469 1.56155i −0.179122 0.103416i
\(229\) 16.2462i 1.07358i −0.843716 0.536790i \(-0.819637\pi\)
0.843716 0.536790i \(-0.180363\pi\)
\(230\) −5.56155 + 9.63289i −0.366718 + 0.635174i
\(231\) −0.561553 0.972638i −0.0369475 0.0639949i
\(232\) 14.1164 8.15009i 0.926785 0.535080i
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) −29.3693 −1.91584
\(236\) 1.09238 0.630683i 0.0711076 0.0410540i
\(237\) −2.71922 4.70983i −0.176633 0.305937i
\(238\) 0.684658 1.18586i 0.0443798 0.0768681i
\(239\) 25.3693i 1.64100i 0.571643 + 0.820502i \(0.306306\pi\)
−0.571643 + 0.820502i \(0.693694\pi\)
\(240\) 14.4493 + 8.34233i 0.932701 + 0.538495i
\(241\) 15.4220 + 8.90388i 0.993417 + 0.573549i 0.906294 0.422648i \(-0.138899\pi\)
0.0871229 + 0.996198i \(0.472233\pi\)
\(242\) 10.9309i 0.702663i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.849907 + 1.47208i 0.0544097 + 0.0942404i
\(245\) 20.6181 11.9039i 1.31724 0.760511i
\(246\) −2.43845 −0.155470
\(247\) 0 0
\(248\) 6.24621 0.396635
\(249\) 0.759413 0.438447i 0.0481258 0.0277855i
\(250\) −7.46543 12.9305i −0.472156 0.817797i
\(251\) 9.36932 16.2281i 0.591386 1.02431i −0.402660 0.915350i \(-0.631914\pi\)
0.994046 0.108961i \(-0.0347524\pi\)
\(252\) 0.246211i 0.0155099i
\(253\) −3.46410 2.00000i −0.217786 0.125739i
\(254\) 7.35465 + 4.24621i 0.461472 + 0.266431i
\(255\) 5.56155i 0.348278i
\(256\) −5.02699 + 8.70700i −0.314187 + 0.544187i
\(257\) 14.5885 + 25.2681i 0.910008 + 1.57618i 0.814050 + 0.580795i \(0.197258\pi\)
0.0959583 + 0.995385i \(0.469408\pi\)
\(258\) −6.16879 + 3.56155i −0.384052 + 0.221733i
\(259\) −4.24621 −0.263847
\(260\) 0 0
\(261\) 6.68466 0.413770
\(262\) 9.96585 5.75379i 0.615693 0.355470i
\(263\) −4.68466 8.11407i −0.288868 0.500335i 0.684672 0.728852i \(-0.259946\pi\)
−0.973540 + 0.228517i \(0.926612\pi\)
\(264\) −2.43845 + 4.22351i −0.150076 + 0.259939i
\(265\) 2.43845i 0.149793i
\(266\) −5.40938 3.12311i −0.331670 0.191490i
\(267\) −4.22351 2.43845i −0.258475 0.149231i
\(268\) 2.00000i 0.122169i
\(269\) 10.6847 18.5064i 0.651455 1.12835i −0.331315 0.943520i \(-0.607492\pi\)
0.982770 0.184833i \(-0.0591745\pi\)
\(270\) 2.78078 + 4.81645i 0.169233 + 0.293120i
\(271\) −25.9209 + 14.9654i −1.57458 + 0.909085i −0.578986 + 0.815337i \(0.696551\pi\)
−0.995596 + 0.0937481i \(0.970115\pi\)
\(272\) −7.31534 −0.443558
\(273\) 0 0
\(274\) 8.68466 0.524659
\(275\) 13.3102 7.68466i 0.802636 0.463402i
\(276\) −0.438447 0.759413i −0.0263914 0.0457113i
\(277\) 2.65767 4.60322i 0.159684 0.276581i −0.775071 0.631874i \(-0.782286\pi\)
0.934755 + 0.355294i \(0.115619\pi\)
\(278\) 28.0000i 1.67933i
\(279\) 2.21837 + 1.28078i 0.132810 + 0.0766781i
\(280\) 4.22351 + 2.43845i 0.252403 + 0.145725i
\(281\) 17.8078i 1.06232i 0.847271 + 0.531161i \(0.178244\pi\)
−0.847271 + 0.531161i \(0.821756\pi\)
\(282\) 6.43845 11.1517i 0.383404 0.664075i
\(283\) −6.84233 11.8513i −0.406734 0.704484i 0.587787 0.809015i \(-0.299999\pi\)
−0.994522 + 0.104531i \(0.966666\pi\)
\(284\) 5.31589 3.06913i 0.315440 0.182119i
\(285\) 25.3693 1.50275
\(286\) 0 0
\(287\) −0.876894 −0.0517614
\(288\) −2.11176 + 1.21922i −0.124436 + 0.0718434i
\(289\) 7.28078 + 12.6107i 0.428281 + 0.741804i
\(290\) 18.5885 32.1963i 1.09156 1.89063i
\(291\) 8.56155i 0.501887i
\(292\) −3.84381 2.21922i −0.224942 0.129870i
\(293\) −17.7002 10.2192i −1.03406 0.597013i −0.115913 0.993259i \(-0.536979\pi\)
−0.918144 + 0.396246i \(0.870313\pi\)
\(294\) 10.4384i 0.608783i
\(295\) −5.12311 + 8.87348i −0.298279 + 0.516634i
\(296\) 9.21922 + 15.9682i 0.535856 + 0.928131i
\(297\) −1.73205 + 1.00000i −0.100504 + 0.0580259i
\(298\) −3.80776 −0.220578
\(299\) 0 0
\(300\) 3.36932 0.194528
\(301\) −2.21837 + 1.28078i −0.127865 + 0.0738227i
\(302\) −7.31534 12.6705i −0.420951 0.729108i
\(303\) −3.78078 + 6.54850i −0.217200 + 0.376201i
\(304\) 33.3693i 1.91386i
\(305\) −11.9579 6.90388i −0.684706 0.395315i
\(306\) −2.11176 1.21922i −0.120721 0.0696984i
\(307\) 30.8078i 1.75829i 0.476553 + 0.879146i \(0.341886\pi\)
−0.476553 + 0.879146i \(0.658114\pi\)
\(308\) 0.246211 0.426450i 0.0140292 0.0242993i
\(309\) −1.71922 2.97778i −0.0978032 0.169400i
\(310\) 12.3376 7.12311i 0.700728 0.404565i
\(311\) 19.1231 1.08437 0.542186 0.840259i \(-0.317597\pi\)
0.542186 + 0.840259i \(0.317597\pi\)
\(312\) 0 0
\(313\) −13.6847 −0.773503 −0.386751 0.922184i \(-0.626403\pi\)
−0.386751 + 0.922184i \(0.626403\pi\)
\(314\) 27.5463 15.9039i 1.55453 0.897508i
\(315\) 1.00000 + 1.73205i 0.0563436 + 0.0975900i
\(316\) 1.19224 2.06501i 0.0670685 0.116166i
\(317\) 14.0540i 0.789350i −0.918821 0.394675i \(-0.870857\pi\)
0.918821 0.394675i \(-0.129143\pi\)
\(318\) 0.925894 + 0.534565i 0.0519216 + 0.0299769i
\(319\) 11.5782 + 6.68466i 0.648253 + 0.374269i
\(320\) 19.8078i 1.10729i
\(321\) 4.12311 7.14143i 0.230129 0.398596i
\(322\) −0.876894 1.51883i −0.0488674 0.0846408i
\(323\) −9.63289 + 5.56155i −0.535988 + 0.309453i
\(324\) −0.438447 −0.0243582
\(325\) 0 0
\(326\) 7.50758 0.415806
\(327\) 2.43160 1.40388i 0.134468 0.0776349i
\(328\) 1.90388 + 3.29762i 0.105124 + 0.182081i
\(329\) 2.31534 4.01029i 0.127649 0.221094i
\(330\) 11.1231i 0.612307i
\(331\) −2.76456 1.59612i −0.151954 0.0877306i 0.422095 0.906552i \(-0.361295\pi\)
−0.574049 + 0.818821i \(0.694628\pi\)
\(332\) 0.332962 + 0.192236i 0.0182737 + 0.0105503i
\(333\) 7.56155i 0.414371i
\(334\) 8.00000 13.8564i 0.437741 0.758189i
\(335\) −8.12311 14.0696i −0.443813 0.768706i
\(336\) −2.27824 + 1.31534i −0.124288 + 0.0717578i
\(337\) 6.12311 0.333547 0.166773 0.985995i \(-0.446665\pi\)
0.166773 + 0.985995i \(0.446665\pi\)
\(338\) 0 0
\(339\) 5.80776 0.315434
\(340\) −2.11176 + 1.21922i −0.114526 + 0.0661217i
\(341\) 2.56155 + 4.43674i 0.138716 + 0.240263i
\(342\) −5.56155 + 9.63289i −0.300734 + 0.520887i
\(343\) 7.68466i 0.414933i
\(344\) 9.63289 + 5.56155i 0.519371 + 0.299859i
\(345\) 6.16879 + 3.56155i 0.332117 + 0.191748i
\(346\) 31.6155i 1.69966i
\(347\) −13.8078 + 23.9157i −0.741240 + 1.28386i 0.210692 + 0.977553i \(0.432428\pi\)
−0.951931 + 0.306312i \(0.900905\pi\)
\(348\) 1.46543 + 2.53821i 0.0785556 + 0.136062i
\(349\) 5.89570 3.40388i 0.315589 0.182206i −0.333836 0.942631i \(-0.608343\pi\)
0.649425 + 0.760426i \(0.275010\pi\)
\(350\) 6.73863 0.360195
\(351\) 0 0
\(352\) −4.87689 −0.259939
\(353\) −4.60322 + 2.65767i −0.245005 + 0.141454i −0.617475 0.786591i \(-0.711844\pi\)
0.372470 + 0.928044i \(0.378511\pi\)
\(354\) −2.24621 3.89055i −0.119385 0.206781i
\(355\) −24.9309 + 43.1815i −1.32319 + 2.29184i
\(356\) 2.13826i 0.113328i
\(357\) −0.759413 0.438447i −0.0401924 0.0232051i
\(358\) −6.59524 3.80776i −0.348569 0.201247i
\(359\) 9.36932i 0.494494i −0.968953 0.247247i \(-0.920474\pi\)
0.968953 0.247247i \(-0.0795258\pi\)
\(360\) 4.34233 7.52113i 0.228861 0.396399i
\(361\) 15.8693 + 27.4865i 0.835227 + 1.44666i
\(362\) 3.63058 2.09612i 0.190819 0.110170i
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) 36.0540 1.88715
\(366\) 5.24290 3.02699i 0.274051 0.158223i
\(367\) 8.52699 + 14.7692i 0.445105 + 0.770945i 0.998060 0.0622668i \(-0.0198330\pi\)
−0.552954 + 0.833212i \(0.686500\pi\)
\(368\) −4.68466 + 8.11407i −0.244205 + 0.422975i
\(369\) 1.56155i 0.0812912i
\(370\) 36.4198 + 21.0270i 1.89338 + 1.09314i
\(371\) 0.332962 + 0.192236i 0.0172865 + 0.00998039i
\(372\) 1.12311i 0.0582303i
\(373\) −14.1847 + 24.5685i −0.734454 + 1.27211i 0.220509 + 0.975385i \(0.429228\pi\)
−0.954963 + 0.296726i \(0.904105\pi\)
\(374\) −2.43845 4.22351i −0.126089 0.218393i
\(375\) −8.28055 + 4.78078i −0.427606 + 0.246878i
\(376\) −20.1080 −1.03699
\(377\) 0 0
\(378\) −0.876894 −0.0451026
\(379\) −20.5115 + 11.8423i −1.05361 + 0.608300i −0.923657 0.383221i \(-0.874815\pi\)
−0.129949 + 0.991521i \(0.541481\pi\)
\(380\) 5.56155 + 9.63289i 0.285302 + 0.494157i
\(381\) 2.71922 4.70983i 0.139310 0.241292i
\(382\) 14.2462i 0.728900i
\(383\) −19.6922 11.3693i −1.00623 0.580945i −0.0961417 0.995368i \(-0.530650\pi\)
−0.910085 + 0.414423i \(0.863984\pi\)
\(384\) 11.7446 + 6.78078i 0.599342 + 0.346030i
\(385\) 4.00000i 0.203859i
\(386\) −10.5346 + 18.2464i −0.536195 + 0.928717i
\(387\) 2.28078 + 3.95042i 0.115938 + 0.200811i
\(388\) −3.25088 + 1.87689i −0.165038 + 0.0952849i
\(389\) −34.0540 −1.72661 −0.863303 0.504687i \(-0.831608\pi\)
−0.863303 + 0.504687i \(0.831608\pi\)
\(390\) 0 0
\(391\) −3.12311 −0.157942
\(392\) 14.1164 8.15009i 0.712985 0.411642i
\(393\) −3.68466 6.38202i −0.185866 0.321930i
\(394\) −10.4384 + 18.0799i −0.525881 + 0.910853i
\(395\) 19.3693i 0.974576i
\(396\) −0.759413 0.438447i −0.0381619 0.0220328i
\(397\) −21.6974 12.5270i −1.08896 0.628711i −0.155661 0.987811i \(-0.549751\pi\)
−0.933299 + 0.359099i \(0.883084\pi\)
\(398\) 34.6307i 1.73588i
\(399\) −2.00000 + 3.46410i −0.100125 + 0.173422i
\(400\) −18.0000 31.1769i −0.900000 1.55885i
\(401\) 12.5041 7.21922i 0.624423 0.360511i −0.154166 0.988045i \(-0.549269\pi\)
0.778589 + 0.627534i \(0.215936\pi\)
\(402\) 7.12311 0.355268
\(403\) 0 0
\(404\) −3.31534 −0.164944
\(405\) 3.08440 1.78078i 0.153265 0.0884875i
\(406\) 2.93087 + 5.07642i 0.145457 + 0.251938i
\(407\) −7.56155 + 13.0970i −0.374812 + 0.649194i
\(408\) 3.80776i 0.188512i
\(409\) 5.51599 + 3.18466i 0.272748 + 0.157471i 0.630136 0.776485i \(-0.282999\pi\)
−0.357388 + 0.933956i \(0.616333\pi\)
\(410\) 7.52113 + 4.34233i 0.371442 + 0.214452i
\(411\) 5.56155i 0.274331i
\(412\) 0.753789 1.30560i 0.0371365 0.0643223i
\(413\) −0.807764 1.39909i −0.0397475 0.0688446i
\(414\) −2.70469 + 1.56155i −0.132928 + 0.0767461i
\(415\) −3.12311 −0.153307
\(416\) 0 0
\(417\) −17.9309 −0.878078
\(418\) −19.2658 + 11.1231i −0.942320 + 0.544049i
\(419\) 17.1231 + 29.6581i 0.836518 + 1.44889i 0.892788 + 0.450477i \(0.148746\pi\)
−0.0562697 + 0.998416i \(0.517921\pi\)
\(420\) −0.438447 + 0.759413i −0.0213940 + 0.0370556i
\(421\) 31.2462i 1.52285i −0.648255 0.761424i \(-0.724501\pi\)
0.648255 0.761424i \(-0.275499\pi\)
\(422\) −26.6204 15.3693i −1.29586 0.748167i
\(423\) −7.14143 4.12311i −0.347228 0.200472i
\(424\) 1.66950i 0.0810783i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) −10.9309 18.9328i −0.529602 0.917298i
\(427\) 1.88541 1.08854i 0.0912413 0.0526782i
\(428\) 3.61553 0.174763
\(429\) 0 0
\(430\) 25.3693 1.22342
\(431\) 9.63289 5.56155i 0.464000 0.267891i −0.249725 0.968317i \(-0.580340\pi\)
0.713725 + 0.700426i \(0.247007\pi\)
\(432\) 2.34233 + 4.05703i 0.112695 + 0.195194i
\(433\) 4.37689 7.58100i 0.210340 0.364320i −0.741481 0.670974i \(-0.765876\pi\)
0.951821 + 0.306654i \(0.0992095\pi\)
\(434\) 2.24621i 0.107822i
\(435\) −20.6181 11.9039i −0.988564 0.570747i
\(436\) 1.06613 + 0.615528i 0.0510582 + 0.0294785i
\(437\) 14.2462i 0.681489i
\(438\) −7.90388 + 13.6899i −0.377662 + 0.654130i
\(439\) −6.84233 11.8513i −0.326567 0.565630i 0.655262 0.755402i \(-0.272558\pi\)
−0.981828 + 0.189772i \(0.939225\pi\)
\(440\) 15.0423 8.68466i 0.717112 0.414025i
\(441\) 6.68466 0.318317
\(442\) 0 0
\(443\) −34.7386 −1.65048 −0.825241 0.564781i \(-0.808961\pi\)
−0.825241 + 0.564781i \(0.808961\pi\)
\(444\) −2.87117 + 1.65767i −0.136260 + 0.0786696i
\(445\) 8.68466 + 15.0423i 0.411692 + 0.713072i
\(446\) −6.24621 + 10.8188i −0.295767 + 0.512283i
\(447\) 2.43845i 0.115335i
\(448\) 2.70469 + 1.56155i 0.127785 + 0.0737764i
\(449\) 7.14143 + 4.12311i 0.337025 + 0.194581i 0.658956 0.752182i \(-0.270998\pi\)
−0.321931 + 0.946763i \(0.604332\pi\)
\(450\) 12.0000i 0.565685i
\(451\) −1.56155 + 2.70469i −0.0735307 + 0.127359i
\(452\) 1.27320 + 2.20525i 0.0598862 + 0.103726i
\(453\) −8.11407 + 4.68466i −0.381232 + 0.220104i
\(454\) 11.1231 0.522033
\(455\) 0 0
\(456\) 17.3693 0.813393
\(457\) −10.9254 + 6.30776i −0.511067 + 0.295065i −0.733272 0.679935i \(-0.762008\pi\)
0.222205 + 0.975000i \(0.428675\pi\)
\(458\) −12.6847 21.9705i −0.592715 1.02661i
\(459\) −0.780776 + 1.35234i −0.0364435 + 0.0631220i
\(460\) 3.12311i 0.145616i
\(461\) −14.0229 8.09612i −0.653111 0.377074i 0.136536 0.990635i \(-0.456403\pi\)
−0.789647 + 0.613561i \(0.789736\pi\)
\(462\) −1.51883 0.876894i −0.0706622 0.0407968i
\(463\) 14.3153i 0.665290i −0.943052 0.332645i \(-0.892059\pi\)
0.943052 0.332645i \(-0.107941\pi\)
\(464\) 15.6577 27.1199i 0.726889 1.25901i
\(465\) −4.56155 7.90084i −0.211537 0.366393i
\(466\) −35.1610 + 20.3002i −1.62880 + 0.940388i
\(467\) 26.0000 1.20314 0.601568 0.798821i \(-0.294543\pi\)
0.601568 + 0.798821i \(0.294543\pi\)
\(468\) 0 0
\(469\) 2.56155 0.118282
\(470\) −39.7174 + 22.9309i −1.83203 + 1.05772i
\(471\) −10.1847 17.6403i −0.469284 0.812824i
\(472\) −3.50758 + 6.07530i −0.161449 + 0.279638i
\(473\) 9.12311i 0.419481i
\(474\) −7.35465 4.24621i −0.337810 0.195035i
\(475\) −47.4050 27.3693i −2.17509 1.25579i
\(476\) 0.384472i 0.0176222i
\(477\) 0.342329 0.592932i 0.0156742 0.0271485i
\(478\) 19.8078 + 34.3081i 0.905986 + 1.56921i
\(479\) 8.87348 5.12311i 0.405440 0.234081i −0.283389 0.959005i \(-0.591459\pi\)
0.688828 + 0.724924i \(0.258125\pi\)
\(480\) 8.68466 0.396399
\(481\) 0 0
\(482\) 27.8078 1.26661
\(483\) −0.972638 + 0.561553i −0.0442566 + 0.0255515i
\(484\) 1.53457 + 2.65794i 0.0697530 + 0.120816i
\(485\) 15.2462 26.4072i 0.692295 1.19909i
\(486\) 1.56155i 0.0708335i
\(487\) 6.16879 + 3.56155i 0.279535 + 0.161389i 0.633213 0.773978i \(-0.281736\pi\)
−0.353678 + 0.935367i \(0.615069\pi\)
\(488\) −8.18706 4.72680i −0.370611 0.213972i
\(489\) 4.80776i 0.217415i
\(490\) 18.5885 32.1963i 0.839745 1.45448i
\(491\) −18.1231 31.3901i −0.817884 1.41662i −0.907238 0.420617i \(-0.861814\pi\)
0.0893539 0.996000i \(-0.471520\pi\)
\(492\) −0.592932 + 0.342329i −0.0267314 + 0.0154334i
\(493\) 10.4384 0.470124
\(494\) 0 0
\(495\) 7.12311 0.320160
\(496\) 10.3923 6.00000i 0.466628 0.269408i
\(497\) −3.93087 6.80847i −0.176324 0.305401i
\(498\) 0.684658 1.18586i 0.0306803 0.0531398i
\(499\) 4.49242i 0.201108i −0.994932 0.100554i \(-0.967938\pi\)
0.994932 0.100554i \(-0.0320616\pi\)
\(500\) −3.63058 2.09612i −0.162365 0.0937412i
\(501\) −8.87348 5.12311i −0.396438 0.228883i
\(502\) 29.2614i 1.30600i
\(503\) 14.1231 24.4619i 0.629718 1.09070i −0.357890 0.933764i \(-0.616504\pi\)
0.987608 0.156940i \(-0.0501630\pi\)
\(504\) 0.684658 + 1.18586i 0.0304971 + 0.0528225i
\(505\) 23.3228 13.4654i 1.03785 0.599204i
\(506\) −6.24621 −0.277678
\(507\) 0 0
\(508\) 2.38447 0.105794
\(509\) 11.9579 6.90388i 0.530023 0.306009i −0.211003 0.977486i \(-0.567673\pi\)
0.741026 + 0.671476i \(0.234340\pi\)
\(510\) 4.34233 + 7.52113i 0.192282 + 0.333041i
\(511\) −2.84233 + 4.92306i −0.125737 + 0.217783i
\(512\) 11.4233i 0.504843i
\(513\) 6.16879 + 3.56155i 0.272359 + 0.157246i
\(514\) 39.4575 + 22.7808i 1.74039 + 1.00482i
\(515\) 12.2462i 0.539633i
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) −8.24621 14.2829i −0.362668 0.628159i
\(518\) −5.74234 + 3.31534i −0.252304 + 0.145668i
\(519\) −20.2462 −0.888710
\(520\) 0 0
\(521\) −9.06913 −0.397326 −0.198663 0.980068i \(-0.563660\pi\)
−0.198663 + 0.980068i \(0.563660\pi\)
\(522\) 9.03996 5.21922i 0.395668 0.228439i
\(523\) −16.9309 29.3251i −0.740335 1.28230i −0.952343 0.305030i \(-0.901333\pi\)
0.212007 0.977268i \(-0.432000\pi\)
\(524\) 1.61553 2.79818i 0.0705747 0.122239i
\(525\) 4.31534i 0.188337i
\(526\) −12.6705 7.31534i −0.552462 0.318964i
\(527\) 3.46410 + 2.00000i 0.150899 + 0.0871214i
\(528\) 9.36932i 0.407747i
\(529\) 9.50000 16.4545i 0.413043 0.715412i
\(530\) −1.90388 3.29762i −0.0826994 0.143239i
\(531\) −2.49146 + 1.43845i −0.108120 + 0.0624233i
\(532\) −1.75379 −0.0760364
\(533\) 0 0
\(534\) −7.61553 −0.329556
\(535\) −25.4346 + 14.6847i −1.09963 + 0.634873i
\(536\) −5.56155 9.63289i −0.240222 0.416078i
\(537\) −2.43845 + 4.22351i −0.105227 + 0.182258i
\(538\) 33.3693i 1.43865i
\(539\) 11.5782 + 6.68466i 0.498707 + 0.287929i
\(540\) 1.35234 + 0.780776i 0.0581956 + 0.0335993i
\(541\) 19.7386i 0.848630i 0.905515 + 0.424315i \(0.139485\pi\)
−0.905515 + 0.424315i \(0.860515\pi\)
\(542\) −23.3693 + 40.4768i −1.00380 + 1.73863i
\(543\) −1.34233 2.32498i −0.0576049 0.0997745i
\(544\) −3.29762 + 1.90388i −0.141384 + 0.0816283i
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) 3.93087 0.168072 0.0840359 0.996463i \(-0.473219\pi\)
0.0840359 + 0.996463i \(0.473219\pi\)
\(548\) 2.11176 1.21922i 0.0902098 0.0520827i
\(549\) −1.93845 3.35749i −0.0827309 0.143294i
\(550\) 12.0000 20.7846i 0.511682 0.886259i
\(551\) 47.6155i 2.02849i
\(552\) 4.22351 + 2.43845i 0.179765 + 0.103787i
\(553\) −2.64482 1.52699i −0.112469 0.0649341i
\(554\) 8.30019i 0.352641i
\(555\) 13.4654 23.3228i 0.571576 0.989998i
\(556\) −3.93087 6.80847i −0.166706 0.288743i
\(557\) −37.1792 + 21.4654i −1.57533 + 0.909520i −0.579837 + 0.814733i \(0.696884\pi\)
−0.995498 + 0.0947869i \(0.969783\pi\)
\(558\) 4.00000 0.169334
\(559\) 0 0
\(560\) 9.36932 0.395926
\(561\) −2.70469 + 1.56155i −0.114192 + 0.0659288i
\(562\) 13.9039 + 24.0822i 0.586500 + 1.01585i
\(563\) −11.6847 + 20.2384i −0.492450 + 0.852948i −0.999962 0.00869657i \(-0.997232\pi\)
0.507513 + 0.861644i \(0.330565\pi\)
\(564\) 3.61553i 0.152241i
\(565\) −17.9134 10.3423i −0.753624 0.435105i
\(566\) −18.5064 10.6847i −0.777881 0.449110i
\(567\) 0.561553i 0.0235830i
\(568\) −17.0691 + 29.5646i −0.716205 + 1.24050i
\(569\) −4.36932 7.56788i −0.183171 0.317262i 0.759787 0.650171i \(-0.225303\pi\)
−0.942959 + 0.332910i \(0.891970\pi\)
\(570\) 34.3081 19.8078i 1.43701 0.829656i
\(571\) 5.36932 0.224699 0.112349 0.993669i \(-0.464162\pi\)
0.112349 + 0.993669i \(0.464162\pi\)
\(572\) 0 0
\(573\) −9.12311 −0.381123
\(574\) −1.18586 + 0.684658i −0.0494970 + 0.0285771i
\(575\) −7.68466 13.3102i −0.320472 0.555074i
\(576\) 2.78078 4.81645i 0.115866 0.200685i
\(577\) 17.3153i 0.720847i 0.932789 + 0.360424i \(0.117368\pi\)
−0.932789 + 0.360424i \(0.882632\pi\)
\(578\) 19.6922 + 11.3693i 0.819089 + 0.472901i
\(579\) 11.6848 + 6.74621i 0.485603 + 0.280363i
\(580\) 10.4384i 0.433433i
\(581\) 0.246211 0.426450i 0.0102146 0.0176921i
\(582\) 6.68466 + 11.5782i 0.277088 + 0.479931i
\(583\) 1.18586 0.684658i 0.0491134 0.0283557i
\(584\) 24.6847 1.02146
\(585\) 0 0
\(586\) −31.9157 −1.31843
\(587\) −34.0948 + 19.6847i −1.40724 + 0.812473i −0.995122 0.0986556i \(-0.968546\pi\)
−0.412123 + 0.911128i \(0.635212\pi\)
\(588\) 1.46543 + 2.53821i 0.0604335 + 0.104674i
\(589\) 9.12311 15.8017i 0.375911 0.651097i
\(590\) 16.0000i 0.658710i
\(591\) 11.5782 + 6.68466i 0.476262 + 0.274970i
\(592\) 30.6775 + 17.7116i 1.26084 + 0.727944i
\(593\) 17.4233i 0.715489i −0.933820 0.357744i \(-0.883546\pi\)
0.933820 0.357744i \(-0.116454\pi\)
\(594\) −1.56155 + 2.70469i −0.0640713 + 0.110975i
\(595\) 1.56155 + 2.70469i 0.0640174 + 0.110881i
\(596\) −0.925894 + 0.534565i −0.0379261 + 0.0218966i
\(597\) −22.1771 −0.907648
\(598\) 0 0
\(599\) −41.6155 −1.70036 −0.850182 0.526489i \(-0.823508\pi\)
−0.850182 + 0.526489i \(0.823508\pi\)
\(600\) −16.2281 + 9.36932i −0.662511 + 0.382501i
\(601\) 3.53457 + 6.12205i 0.144178 + 0.249723i 0.929066 0.369914i \(-0.120613\pi\)
−0.784888 + 0.619638i \(0.787280\pi\)
\(602\) −2.00000 + 3.46410i −0.0815139 + 0.141186i
\(603\) 4.56155i 0.185761i
\(604\) −3.55759 2.05398i −0.144756 0.0835751i
\(605\) −21.5908 12.4654i −0.877789 0.506792i
\(606\) 11.8078i 0.479658i
\(607\) 8.00000 13.8564i 0.324710 0.562414i −0.656744 0.754114i \(-0.728067\pi\)
0.981454 + 0.191700i \(0.0614000\pi\)
\(608\) 8.68466 + 15.0423i 0.352209 + 0.610045i
\(609\) 3.25088 1.87689i 0.131732 0.0760556i
\(610\) −21.5616 −0.873002
\(611\) 0 0
\(612\) −0.684658 −0.0276757
\(613\) 30.1912 17.4309i 1.21941 0.704026i 0.254618 0.967042i \(-0.418050\pi\)
0.964792 + 0.263016i \(0.0847171\pi\)
\(614\) 24.0540 + 41.6627i 0.970739 + 1.68137i
\(615\) 2.78078 4.81645i 0.112132 0.194218i
\(616\) 2.73863i 0.110343i
\(617\) 8.49377 + 4.90388i 0.341946 + 0.197423i 0.661132 0.750269i \(-0.270076\pi\)
−0.319186 + 0.947692i \(0.603409\pi\)
\(618\) −4.64996 2.68466i −0.187049 0.107993i
\(619\) 29.3002i 1.17767i 0.808252 + 0.588837i \(0.200414\pi\)
−0.808252 + 0.588837i \(0.799586\pi\)
\(620\) 2.00000 3.46410i 0.0803219 0.139122i
\(621\) 1.00000 + 1.73205i 0.0401286 + 0.0695048i
\(622\) 25.8610 14.9309i 1.03693 0.598673i
\(623\) −2.73863 −0.109721
\(624\) 0 0
\(625\) −4.36932 −0.174773
\(626\) −18.5064 + 10.6847i −0.739663 + 0.427045i
\(627\) 7.12311 + 12.3376i 0.284469 + 0.492716i
\(628\) 4.46543 7.73436i 0.178190 0.308635i
\(629\) 11.8078i 0.470806i
\(630\) 2.70469 + 1.56155i 0.107757 + 0.0622138i
\(631\) 16.0748 + 9.28078i 0.639927 + 0.369462i 0.784586 0.620020i \(-0.212875\pi\)
−0.144660 + 0.989481i \(0.546209\pi\)
\(632\) 13.2614i 0.527509i
\(633\) −9.84233 + 17.0474i −0.391197 + 0.677574i
\(634\) −10.9730 19.0058i −0.435794 0.754817i
\(635\) −16.7743 + 9.68466i −0.665669 + 0.384324i
\(636\) 0.300187 0.0119032
\(637\) 0 0
\(638\) 20.8769 0.826524
\(639\) −12.1244 + 7.00000i −0.479632 + 0.276916i
\(640\) −24.1501 41.8292i −0.954616 1.65344i
\(641\) −9.58854 + 16.6078i −0.378725 + 0.655970i −0.990877 0.134770i \(-0.956971\pi\)
0.612152 + 0.790740i \(0.290304\pi\)
\(642\) 12.8769i 0.508210i
\(643\) −27.3200 15.7732i −1.07739 0.622034i −0.147202 0.989106i \(-0.547027\pi\)
−0.930192 + 0.367072i \(0.880360\pi\)
\(644\) −0.426450 0.246211i −0.0168045 0.00970208i
\(645\) 16.2462i 0.639694i
\(646\) −8.68466 + 15.0423i −0.341693 + 0.591830i
\(647\) −3.19224 5.52911i −0.125500 0.217372i 0.796428 0.604733i \(-0.206720\pi\)
−0.921928 + 0.387361i \(0.873387\pi\)
\(648\) 2.11176 1.21922i 0.0829577 0.0478956i
\(649\) −5.75379 −0.225856
\(650\) 0 0
\(651\) 1.43845 0.0563772
\(652\) 1.82554 1.05398i 0.0714936 0.0412769i
\(653\) −11.5616 20.0252i −0.452439 0.783647i 0.546098 0.837721i \(-0.316112\pi\)
−0.998537 + 0.0540745i \(0.982779\pi\)
\(654\) 2.19224 3.79706i 0.0857232 0.148477i
\(655\) 26.2462i 1.02552i
\(656\) 6.33527 + 3.65767i 0.247351 + 0.142808i
\(657\) 8.76687 + 5.06155i 0.342028 + 0.197470i
\(658\) 7.23106i 0.281896i
\(659\) 1.12311 1.94528i 0.0437500 0.0757772i −0.843321 0.537410i \(-0.819403\pi\)
0.887071 + 0.461633i \(0.152736\pi\)
\(660\) 1.56155 + 2.70469i 0.0607834 + 0.105280i
\(661\) 4.87631 2.81534i 0.189667 0.109504i −0.402160 0.915569i \(-0.631740\pi\)
0.591827 + 0.806065i \(0.298407\pi\)
\(662\) −4.98485 −0.193742
\(663\) 0 0
\(664\) −2.13826 −0.0829806
\(665\) 12.3376 7.12311i 0.478431 0.276222i
\(666\) 5.90388 + 10.2258i 0.228771 + 0.396243i
\(667\) 6.68466 11.5782i 0.258831 0.448308i
\(668\) 4.49242i 0.173817i
\(669\) 6.92820 + 4.00000i 0.267860 + 0.154649i
\(670\) −21.9705 12.6847i −0.848793 0.490051i
\(671\) 7.75379i 0.299332i
\(672\) −0.684658 + 1.18586i −0.0264113 + 0.0457457i
\(673\) −11.6231 20.1318i −0.448038 0.776024i 0.550220 0.835019i \(-0.314544\pi\)
−0.998258 + 0.0589952i \(0.981210\pi\)
\(674\) 8.28055 4.78078i 0.318955 0.184149i
\(675\) −7.68466 −0.295783
\(676\) 0 0
\(677\) −15.6155 −0.600153 −0.300077 0.953915i \(-0.597012\pi\)
−0.300077 + 0.953915i \(0.597012\pi\)
\(678\) 7.85410 4.53457i 0.301635 0.174149i
\(679\) 2.40388 + 4.16365i 0.0922525 + 0.159786i
\(680\) 6.78078 11.7446i 0.260031 0.450387i
\(681\) 7.12311i 0.272958i
\(682\) 6.92820 + 4.00000i 0.265295 + 0.153168i
\(683\) 33.0025 + 19.0540i 1.26280 + 0.729080i 0.973616 0.228192i \(-0.0732815\pi\)
0.289188 + 0.957272i \(0.406615\pi\)
\(684\) 3.12311i 0.119415i
\(685\) −9.90388 + 17.1540i −0.378408 + 0.655422i
\(686\) 6.00000 + 10.3923i 0.229081 + 0.396780i
\(687\) −14.0696 + 8.12311i −0.536790 + 0.309916i
\(688\) 21.3693 0.814698
\(689\) 0 0
\(690\) 11.1231 0.423449
\(691\) 44.4273 25.6501i 1.69009 0.975776i 0.735659 0.677352i \(-0.236872\pi\)
0.954433 0.298424i \(-0.0964609\pi\)
\(692\) −4.43845 7.68762i −0.168724 0.292239i
\(693\) −0.561553 + 0.972638i −0.0213316 + 0.0369475i
\(694\) 43.1231i 1.63693i
\(695\) 55.3059 + 31.9309i 2.09787 + 1.21121i
\(696\) −14.1164 8.15009i −0.535080 0.308928i
\(697\) 2.43845i 0.0923628i
\(698\) 5.31534 9.20644i 0.201189 0.348469i
\(699\) 13.0000 + 22.5167i 0.491705 + 0.851658i
\(700\) 1.63856 0.946025i 0.0619319 0.0357564i
\(701\) 5.36932 0.202796 0.101398 0.994846i \(-0.467668\pi\)
0.101398 + 0.994846i \(0.467668\pi\)
\(702\) 0 0
\(703\) 53.8617 2.03143
\(704\) 9.63289 5.56155i 0.363053 0.209609i
\(705\) 14.6847 + 25.4346i 0.553056 + 0.957921i
\(706\) −4.15009 + 7.18817i −0.156191 + 0.270530i
\(707\) 4.24621i 0.159695i
\(708\) −1.09238 0.630683i −0.0410540 0.0237025i
\(709\) 6.48863 + 3.74621i 0.243686 + 0.140692i 0.616869 0.787065i \(-0.288401\pi\)
−0.373184 + 0.927757i \(0.621734\pi\)
\(710\) 77.8617i 2.92210i
\(711\) −2.71922 + 4.70983i −0.101979 + 0.176633i
\(712\) 5.94602 + 10.2988i 0.222837 + 0.385964i
\(713\) 4.43674 2.56155i 0.166157 0.0959309i
\(714\) −1.36932 −0.0512454
\(715\) 0 0
\(716\) −2.13826 −0.0799106
\(717\) 21.9705 12.6847i 0.820502 0.473717i
\(718\) −7.31534 12.6705i −0.273006 0.472860i
\(719\) −11.6847 + 20.2384i −0.435764 + 0.754766i −0.997358 0.0726475i \(-0.976855\pi\)
0.561593 + 0.827413i \(0.310189\pi\)
\(720\) 16.6847i 0.621801i
\(721\) −1.67218 0.965435i −0.0622753 0.0359547i
\(722\) 42.9216 + 24.7808i 1.59738 + 0.922245i
\(723\) 17.8078i 0.662278i
\(724\) 0.588540 1.01938i 0.0218729 0.0378850i
\(725\) 25.6847 + 44.4871i 0.953904 + 1.65221i
\(726\) 9.46641 5.46543i 0.351331 0.202841i
\(727\) 38.6695 1.43417 0.717086 0.696984i \(-0.245475\pi\)
0.717086 + 0.696984i \(0.245475\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 48.7574 28.1501i 1.80459 1.04188i
\(731\) 3.56155 + 6.16879i 0.131729 + 0.228161i
\(732\) 0.849907 1.47208i 0.0314135 0.0544097i
\(733\) 20.5076i 0.757465i −0.925506 0.378732i \(-0.876360\pi\)
0.925506 0.378732i \(-0.123640\pi\)
\(734\) 23.0628 + 13.3153i 0.851265 + 0.491478i
\(735\) −20.6181 11.9039i −0.760511 0.439081i
\(736\) 4.87689i 0.179765i
\(737\) 4.56155 7.90084i 0.168027 0.291031i
\(738\) 1.21922 + 2.11176i 0.0448802 + 0.0777349i
\(739\) 8.87348 5.12311i 0.326416 0.188456i −0.327833 0.944736i \(-0.606318\pi\)
0.654249 + 0.756279i \(0.272985\pi\)
\(740\) 11.8078 0.434062
\(741\) 0 0
\(742\) 0.600373 0.0220404
\(743\) 10.9385 6.31534i 0.401294 0.231687i −0.285748 0.958305i \(-0.592242\pi\)
0.687042 + 0.726617i \(0.258909\pi\)
\(744\) −3.12311 5.40938i −0.114499 0.198317i
\(745\) 4.34233 7.52113i 0.159091 0.275553i
\(746\) 44.3002i 1.62195i
\(747\) −0.759413 0.438447i −0.0277855 0.0160419i
\(748\) −1.18586 0.684658i −0.0433595 0.0250336i
\(749\) 4.63068i 0.169201i
\(750\) −7.46543 + 12.9305i −0.272599 + 0.472156i
\(751\) 22.0540 + 38.1986i 0.804761 + 1.39389i 0.916452 + 0.400144i \(0.131040\pi\)
−0.111691 + 0.993743i \(0.535627\pi\)
\(752\) −33.4552 + 19.3153i −1.21998 + 0.704358i
\(753\) −18.7386 −0.682874
\(754\) 0 0
\(755\) 33.3693 1.21443
\(756\) −0.213225 + 0.123106i −0.00775493 + 0.00447731i
\(757\) −15.0000 25.9808i −0.545184 0.944287i −0.998595 0.0529853i \(-0.983126\pi\)
0.453411 0.891302i \(-0.350207\pi\)
\(758\) −18.4924 + 32.0298i −0.671675 + 1.16338i
\(759\) 4.00000i 0.145191i
\(760\) −53.5738 30.9309i −1.94333 1.12198i
\(761\) −8.11407 4.68466i −0.294135 0.169819i 0.345670 0.938356i \(-0.387652\pi\)
−0.639805 + 0.768537i \(0.720985\pi\)
\(762\) 8.49242i 0.307648i
\(763\) 0.788354 1.36547i 0.0285403 0.0494333i
\(764\) −2.00000 3.46410i −0.0723575 0.125327i
\(765\) 4.81645 2.78078i 0.174139 0.100539i
\(766\) −35.5076 −1.28294
\(767\) 0 0
\(768\) 10.0540 0.362792
\(769\) 15.5885 9.00000i 0.562134 0.324548i −0.191867 0.981421i \(-0.561454\pi\)
0.754002 + 0.656873i \(0.228121\pi\)
\(770\) 3.12311 + 5.40938i 0.112549 + 0.194940i
\(771\) 14.5885 25.2681i 0.525393 0.910008i
\(772\) 5.91571i 0.212911i
\(773\) −20.9978 12.1231i −0.755240 0.436038i 0.0723444 0.997380i \(-0.476952\pi\)
−0.827584 + 0.561342i \(0.810285\pi\)
\(774\) 6.16879 + 3.56155i 0.221733 + 0.128017i
\(775\) 19.6847i 0.707094i
\(776\) 10.4384 18.0799i 0.374718 0.649031i
\(777\) 2.12311 + 3.67733i 0.0761660 + 0.131923i
\(778\) −46.0527 + 26.5885i −1.65107 + 0.953245i
\(779\) 11.1231 0.398527
\(780\) 0 0
\(781\) −28.0000 −1.00192
\(782\) −4.22351 + 2.43845i −0.151033 + 0.0871987i
\(783\) −3.34233 5.78908i −0.119445 0.206885i
\(784\) 15.6577 27.1199i 0.559203 0.968567i
\(785\) 72.5464i 2.58929i
\(786\) −9.96585 5.75379i −0.355470 0.205231i
\(787\) −38.2585 22.0885i −1.36377 0.787371i −0.373644 0.927572i \(-0.621892\pi\)
−0.990123 + 0.140201i \(0.955225\pi\)
\(788\) 5.86174i 0.208816i
\(789\) −4.68466 + 8.11407i −0.166778 + 0.288868i
\(790\) 15.1231 + 26.1940i 0.538056 + 0.931940i
\(791\) 2.82443 1.63068i 0.100425 0.0579804i
\(792\) 4.87689 0.173293
\(793\) 0 0
\(794\) −39.1231 −1.38843
\(795\) −2.11176 + 1.21922i −0.0748963 + 0.0432414i
\(796\) −4.86174 8.42078i −0.172320 0.298467i
\(797\) −0.192236 + 0.332962i −0.00680935 + 0.0117941i −0.869410 0.494091i \(-0.835501\pi\)
0.862601 + 0.505885i \(0.168834\pi\)
\(798\) 6.24621i 0.221113i
\(799\) −11.1517 6.43845i −0.394519 0.227776i
\(800\) −16.2281 9.36932i −0.573751 0.331255i
\(801\) 4.87689i 0.172317i
\(802\) 11.2732 19.5258i 0.398070 0.689478i
\(803\) 10.1231 + 17.5337i 0.357237 + 0.618752i
\(804\) 1.73205 1.00000i 0.0610847 0.0352673i
\(805\) 4.00000 0.140981
\(806\) 0 0
\(807\) −21.3693 −0.752236
\(808\) 15.9682 9.21922i 0.561758 0.324331i
\(809\) 8.15009 + 14.1164i 0.286542 + 0.496305i 0.972982 0.230881i \(-0.0741609\pi\)
−0.686440 + 0.727187i \(0.740828\pi\)
\(810\) 2.78078 4.81645i 0.0977065 0.169233i
\(811\) 2.56155i 0.0899483i −0.998988 0.0449741i \(-0.985679\pi\)
0.998988 0.0449741i \(-0.0143205\pi\)
\(812\) 1.42534 + 0.822919i 0.0500195 + 0.0288788i
\(813\) 25.9209 + 14.9654i 0.909085 + 0.524861i
\(814\) 23.6155i 0.827724i
\(815\) −8.56155 + 14.8290i −0.299898 + 0.519439i
\(816\) 3.65767 + 6.33527i 0.128044 + 0.221779i
\(817\) 28.1393 16.2462i 0.984468 0.568383i
\(818\) 9.94602 0.347755
\(819\) 0 0
\(820\) 2.43845 0.0851543
\(821\) −5.62260 + 3.24621i −0.196230 + 0.113294i −0.594896 0.803803i \(-0.702807\pi\)
0.398666 + 0.917096i \(0.369473\pi\)
\(822\) −4.34233 7.52113i −0.151456 0.262330i
\(823\) 4.00000 6.92820i 0.139431 0.241502i −0.787850 0.615867i \(-0.788806\pi\)
0.927281 + 0.374365i \(0.122139\pi\)
\(824\) 8.38447i 0.292087i
\(825\) −13.3102 7.68466i −0.463402 0.267545i
\(826\) −2.18475 1.26137i −0.0760172 0.0438885i
\(827\) 14.7386i 0.512513i −0.966609 0.256256i \(-0.917511\pi\)
0.966609 0.256256i \(-0.0824891\pi\)
\(828\) −0.438447 + 0.759413i −0.0152371 + 0.0263914i
\(829\) 6.74621 + 11.6848i 0.234306 + 0.405829i 0.959071 0.283167i \(-0.0913850\pi\)
−0.724765 + 0.688996i \(0.758052\pi\)
\(830\) −4.22351 + 2.43845i −0.146600 + 0.0846397i
\(831\) −5.31534 −0.184387
\(832\) 0 0
\(833\) 10.4384 0.361671
\(834\) −24.2487 + 14.0000i −0.839664 + 0.484780i
\(835\) 18.2462 + 31.6034i 0.631436 + 1.09368i
\(836\) −3.12311 + 5.40938i −0.108015 + 0.187087i
\(837\) 2.56155i 0.0885402i
\(838\) 46.3127 + 26.7386i 1.59984 + 0.923671i
\(839\) −18.7196 10.8078i −0.646272 0.373125i 0.140754 0.990045i \(-0.455047\pi\)
−0.787027 + 0.616919i \(0.788381\pi\)
\(840\) 4.87689i 0.168269i
\(841\) −7.84233 + 13.5833i −0.270425 + 0.468390i
\(842\) −24.3963 42.2556i −0.840752 1.45623i
\(843\) 15.4220 8.90388i 0.531161 0.306666i
\(844\) −8.63068 −0.297080
\(845\) 0 0
\(846\) −12.8769 −0.442717
\(847\) 3.40423 1.96543i 0.116971 0.0675331i
\(848\) −1.60370 2.77768i −0.0550711 0.0953860i
\(849\) −6.84233 + 11.8513i −0.234828 + 0.406734i
\(850\) 18.7386i 0.642730i
\(851\) 13.0970 + 7.56155i 0.448959 + 0.259207i
\(852\) −5.31589 3.06913i −0.182119 0.105147i
\(853\) 2.12311i 0.0726938i 0.999339 + 0.0363469i \(0.0115721\pi\)
−0.999339 + 0.0363469i \(0.988428\pi\)
\(854\) 1.69981 2.94416i 0.0581664 0.100747i
\(855\) −12.6847 21.9705i −0.433806 0.751374i
\(856\) −17.4140 + 10.0540i −0.595198 + 0.343638i
\(857\) −35.5616 −1.21476 −0.607380 0.794412i \(-0.707779\pi\)
−0.607380 + 0.794412i \(0.707779\pi\)
\(858\) 0 0
\(859\) 24.5616 0.838029 0.419015 0.907979i \(-0.362376\pi\)
0.419015 + 0.907979i \(0.362376\pi\)
\(860\) 6.16879 3.56155i 0.210354 0.121448i
\(861\) 0.438447 + 0.759413i 0.0149422 + 0.0258807i
\(862\) 8.68466 15.0423i 0.295801 0.512342i
\(863\) 30.4924i 1.03797i −0.854782 0.518987i \(-0.826309\pi\)
0.854782 0.518987i \(-0.173691\pi\)
\(864\) 2.11176 + 1.21922i 0.0718434 + 0.0414788i
\(865\) 62.4473 + 36.0540i 2.12327 + 1.22587i
\(866\) 13.6695i 0.464509i
\(867\) 7.28078 12.6107i 0.247268 0.428281i
\(868\) 0.315342 + 0.546188i 0.0107034 + 0.0185388i
\(869\) −9.41967 + 5.43845i −0.319540 + 0.184487i
\(870\) −37.1771 −1.26042
\(871\) 0 0
\(872\) −6.84658 −0.231855
\(873\) 7.41452 4.28078i 0.250944 0.144882i
\(874\) 11.1231 + 19.2658i 0.376245 + 0.651675i
\(875\) −2.68466 + 4.64996i −0.0907580 + 0.157198i
\(876\) 4.43845i 0.149961i
\(877\) 20.4049 + 11.7808i 0.689025 + 0.397809i 0.803247 0.595647i \(-0.203104\pi\)
−0.114222 + 0.993455i \(0.536437\pi\)
\(878\) −18.5064 10.6847i −0.624560 0.360590i
\(879\) 20.4384i 0.689372i
\(880\) 16.6847 28.8987i 0.562440 0.974174i
\(881\) −4.53457 7.85410i −0.152773 0.264611i 0.779473 0.626436i \(-0.215487\pi\)
−0.932246 + 0.361825i \(0.882154\pi\)
\(882\) 9.03996 5.21922i 0.304391 0.175740i
\(883\) −8.80776 −0.296405 −0.148202 0.988957i \(-0.547349\pi\)
−0.148202 + 0.988957i \(0.547349\pi\)
\(884\) 0 0
\(885\) 10.2462 0.344423
\(886\) −46.9786 + 27.1231i −1.57828 + 0.911219i
\(887\) −12.3153 21.3308i −0.413509 0.716218i 0.581762 0.813359i \(-0.302364\pi\)
−0.995271 + 0.0971410i \(0.969030\pi\)
\(888\) 9.21922 15.9682i 0.309377 0.535856i
\(889\) 3.05398i 0.102427i
\(890\) 23.4893 + 13.5616i 0.787363 + 0.454584i
\(891\) 1.73205 + 1.00000i 0.0580259 + 0.0335013i
\(892\) 3.50758i 0.117442i
\(893\) −29.3693 + 50.8691i −0.982807 + 1.70227i
\(894\) 1.90388 + 3.29762i 0.0636753 + 0.110289i
\(895\) 15.0423 8.68466i 0.502808 0.290296i
\(896\) 7.61553 0.254417
\(897\) 0 0
\(898\) 12.8769 0.429708
\(899\) −14.8290 + 8.56155i −0.494576 + 0.285544i
\(900\) −1.68466 2.91791i −0.0561553 0.0972638i
\(901\) 0.534565 0.925894i 0.0178089 0.0308460i
\(902\) 4.87689i 0.162383i
\(903\) 2.21837 + 1.28078i 0.0738227 + 0.0426216i
\(904\) −12.2646 7.08096i −0.407914 0.235509i
\(905\) 9.56155i 0.317837i
\(906\) −7.31534 + 12.6705i −0.243036 + 0.420951i
\(907\) 14.0000 + 24.2487i 0.464862 + 0.805165i 0.999195 0.0401089i \(-0.0127705\pi\)
−0.534333 + 0.845274i \(0.679437\pi\)
\(908\) 2.70469 1.56155i 0.0897583 0.0518220i
\(909\) 7.56155 0.250801
\(910\) 0 0
\(911\) 38.7386 1.28347 0.641734 0.766927i \(-0.278215\pi\)
0.641734 + 0.766927i \(0.278215\pi\)
\(912\) 28.8987 16.6847i 0.956931 0.552484i
\(913\) −0.876894 1.51883i −0.0290210 0.0502658i
\(914\) −9.84991 + 17.0605i −0.325806 + 0.564312i
\(915\) 13.8078i 0.456471i
\(916\) −6.16879 3.56155i −0.203823 0.117677i
\(917\) −3.58384 2.06913i −0.118349 0.0683287i
\(918\) 2.43845i 0.0804807i
\(919\) −5.75379 + 9.96585i −0.189800 + 0.328743i −0.945183 0.326540i \(-0.894117\pi\)
0.755383 + 0.655283i \(0.227451\pi\)
\(920\) −8.68466 15.0423i −0.286325 0.495929i
\(921\) 26.6803 15.4039i 0.879146 0.507575i
\(922\) −25.2850 −0.832718
\(923\) 0 0
\(924\) −0.492423 −0.0161995
\(925\) −50.3230 + 29.0540i −1.65461 + 0.955289i
\(926\) −11.1771 19.3593i −0.367302 0.636185i
\(927\) −1.71922 + 2.97778i −0.0564667 + 0.0978032i
\(928\) 16.3002i 0.535080i
\(929\) −6.76172 3.90388i −0.221845 0.128082i 0.384959 0.922934i \(-0.374215\pi\)
−0.606804 + 0.794851i \(0.707549\pi\)
\(930\) −12.3376 7.12311i −0.404565 0.233576i
\(931\) 47.6155i 1.56054i
\(932\) −5.69981 + 9.87237i −0.186704 + 0.323380i
\(933\) −9.56155 16.5611i −0.313031 0.542186i
\(934\) 35.1610 20.3002i 1.15050 0.664242i
\(935\) 11.1231 0.363764
\(936\) 0 0
\(937\) −7.56155 −0.247025 −0.123513 0.992343i \(-0.539416\pi\)
−0.123513 + 0.992343i \(0.539416\pi\)
\(938\) 3.46410 2.00000i 0.113107 0.0653023i
\(939\) 6.84233 + 11.8513i 0.223291 + 0.386751i
\(940\) −6.43845 + 11.1517i −0.209999 + 0.363729i
\(941\) 30.4924i 0.994025i −0.867744 0.497012i \(-0.834430\pi\)
0.867744 0.497012i \(-0.165570\pi\)
\(942\) −27.5463 15.9039i −0.897508 0.518176i
\(943\) 2.70469 + 1.56155i 0.0880768 + 0.0508512i
\(944\) 13.4773i 0.438648i
\(945\) 1.00000 1.73205i 0.0325300 0.0563436i
\(946\) 7.12311 + 12.3376i 0.231592 + 0.401129i
\(947\) −33.5486 + 19.3693i −1.09018 + 0.629418i −0.933626 0.358250i \(-0.883373\pi\)
−0.156559 + 0.987669i \(0.550040\pi\)
\(948\) −2.38447 −0.0774440
\(949\) 0 0
\(950\) −85.4773 −2.77325
\(951\) −12.1711 + 7.02699i −0.394675 + 0.227866i
\(952\) 1.06913 + 1.85179i 0.0346507 + 0.0600168i
\(953\) 15.4924 26.8337i 0.501849 0.869228i −0.498149 0.867091i \(-0.665987\pi\)
0.999998 0.00213612i \(-0.000679948\pi\)
\(954\) 1.06913i 0.0346144i
\(955\) 28.1393 + 16.2462i 0.910565 + 0.525715i
\(956\) 9.63289 + 5.56155i 0.311550 + 0.179873i
\(957\) 13.3693i 0.432169i
\(958\) 8.00000 13.8564i 0.258468 0.447680i
\(959\) −1.56155 2.70469i −0.0504252 0.0873390i
\(960\) −17.1540 + 9.90388i −0.553644 + 0.319646i
\(961\) 24.4384 0.788337
\(962\) 0 0
\(963\) −8.24621 −0.265730
\(964\) 6.76172 3.90388i 0.217780 0.125736i
\(965\) −24.0270 41.6160i −0.773456 1.33967i
\(966\) −0.876894 + 1.51883i −0.0282136 + 0.0488674i
\(967\) 0.876894i 0.0281990i 0.999901 + 0.0140995i \(0.00448816\pi\)
−0.999901 + 0.0140995i \(0.995512\pi\)
\(968\) −14.7823 8.53457i −0.475121 0.274311i
\(969\) 9.63289 + 5.56155i 0.309453 + 0.178663i
\(970\) 47.6155i 1.52884i
\(971\) 6.49242 11.2452i 0.208352 0.360876i −0.742844 0.669465i \(-0.766523\pi\)
0.951195 + 0.308589i \(0.0998568\pi\)
\(972\) 0.219224 + 0.379706i 0.00703160 + 0.0121791i
\(973\) −8.72012 + 5.03457i −0.279554 + 0.161401i
\(974\) 11.1231 0.356407
\(975\) 0 0
\(976\) −18.1619 −0.581349
\(977\) −52.9809 + 30.5885i −1.69501 + 0.978614i −0.744652 + 0.667453i \(0.767385\pi\)
−0.950357 + 0.311162i \(0.899282\pi\)
\(978\) −3.75379 6.50175i −0.120033 0.207903i
\(979\) −4.87689 + 8.44703i −0.155866 + 0.269968i
\(980\) 10.4384i 0.333444i
\(981\) −2.43160 1.40388i −0.0776349 0.0448225i
\(982\) −49.0174 28.3002i −1.56421 0.903095i
\(983\) 13.6155i 0.434268i 0.976142 + 0.217134i \(0.0696708\pi\)
−0.976142 + 0.217134i \(0.930329\pi\)
\(984\) 1.90388 3.29762i 0.0606935 0.105124i
\(985\) −23.8078 41.2363i −0.758578 1.31390i
\(986\) 14.1164 8.15009i 0.449557 0.259552i
\(987\) −4.63068 −0.147396
\(988\) 0 0
\(989\) 9.12311 0.290098
\(990\) 9.63289 5.56155i 0.306153 0.176758i
\(991\) 25.1771 + 43.6080i 0.799776 + 1.38525i 0.919762 + 0.392478i \(0.128382\pi\)
−0.119985 + 0.992776i \(0.538285\pi\)
\(992\) 3.12311 5.40938i 0.0991587 0.171748i
\(993\) 3.19224i 0.101303i
\(994\) −10.6318 6.13826i −0.337220 0.194694i
\(995\) 68.4029 + 39.4924i 2.16852 + 1.25199i
\(996\) 0.384472i 0.0121825i
\(997\) 10.3078 17.8536i 0.326450 0.565428i −0.655355 0.755321i \(-0.727481\pi\)
0.981805 + 0.189893i \(0.0608141\pi\)
\(998\) −3.50758 6.07530i −0.111030 0.192310i
\(999\) 6.54850 3.78078i 0.207185 0.119618i
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 507.2.j.g.361.3 8
13.2 odd 12 507.2.a.d.1.2 2
13.3 even 3 507.2.b.d.337.3 4
13.4 even 6 inner 507.2.j.g.316.3 8
13.5 odd 4 507.2.e.g.484.1 4
13.6 odd 12 507.2.e.g.22.1 4
13.7 odd 12 39.2.e.b.22.2 yes 4
13.8 odd 4 39.2.e.b.16.2 4
13.9 even 3 inner 507.2.j.g.316.2 8
13.10 even 6 507.2.b.d.337.2 4
13.11 odd 12 507.2.a.g.1.1 2
13.12 even 2 inner 507.2.j.g.361.2 8
39.2 even 12 1521.2.a.m.1.1 2
39.8 even 4 117.2.g.c.55.1 4
39.11 even 12 1521.2.a.g.1.2 2
39.20 even 12 117.2.g.c.100.1 4
39.23 odd 6 1521.2.b.h.1351.3 4
39.29 odd 6 1521.2.b.h.1351.2 4
52.7 even 12 624.2.q.h.529.1 4
52.11 even 12 8112.2.a.bk.1.1 2
52.15 even 12 8112.2.a.bo.1.2 2
52.47 even 4 624.2.q.h.289.1 4
65.7 even 12 975.2.bb.i.724.3 8
65.8 even 4 975.2.bb.i.874.3 8
65.33 even 12 975.2.bb.i.724.2 8
65.34 odd 4 975.2.i.k.601.1 4
65.47 even 4 975.2.bb.i.874.2 8
65.59 odd 12 975.2.i.k.451.1 4
156.47 odd 4 1872.2.t.r.289.2 4
156.59 odd 12 1872.2.t.r.1153.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.2.e.b.16.2 4 13.8 odd 4
39.2.e.b.22.2 yes 4 13.7 odd 12
117.2.g.c.55.1 4 39.8 even 4
117.2.g.c.100.1 4 39.20 even 12
507.2.a.d.1.2 2 13.2 odd 12
507.2.a.g.1.1 2 13.11 odd 12
507.2.b.d.337.2 4 13.10 even 6
507.2.b.d.337.3 4 13.3 even 3
507.2.e.g.22.1 4 13.6 odd 12
507.2.e.g.484.1 4 13.5 odd 4
507.2.j.g.316.2 8 13.9 even 3 inner
507.2.j.g.316.3 8 13.4 even 6 inner
507.2.j.g.361.2 8 13.12 even 2 inner
507.2.j.g.361.3 8 1.1 even 1 trivial
624.2.q.h.289.1 4 52.47 even 4
624.2.q.h.529.1 4 52.7 even 12
975.2.i.k.451.1 4 65.59 odd 12
975.2.i.k.601.1 4 65.34 odd 4
975.2.bb.i.724.2 8 65.33 even 12
975.2.bb.i.724.3 8 65.7 even 12
975.2.bb.i.874.2 8 65.47 even 4
975.2.bb.i.874.3 8 65.8 even 4
1521.2.a.g.1.2 2 39.11 even 12
1521.2.a.m.1.1 2 39.2 even 12
1521.2.b.h.1351.2 4 39.29 odd 6
1521.2.b.h.1351.3 4 39.23 odd 6
1872.2.t.r.289.2 4 156.47 odd 4
1872.2.t.r.1153.2 4 156.59 odd 12
8112.2.a.bk.1.1 2 52.11 even 12
8112.2.a.bo.1.2 2 52.15 even 12