Properties

Label 250.2.d.d.101.2
Level $250$
Weight $2$
Character 250.101
Analytic conductor $1.996$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [250,2,Mod(51,250)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(250, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("250.51");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 250 = 2 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 250.d (of order \(5\), degree \(4\), 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: \(1.99626005053\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 101.2
Root \(-0.983224 - 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 250.101
Dual form 250.2.d.d.151.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(2.39991 + 1.74363i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.39991 + 1.74363i) q^{6} -1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.79224 + 5.51595i) q^{9} +O(q^{10})\) \(q+(-0.309017 + 0.951057i) q^{2} +(2.39991 + 1.74363i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-2.39991 + 1.74363i) q^{6} -1.83337 q^{7} +(0.809017 - 0.587785i) q^{8} +(1.79224 + 5.51595i) q^{9} +(-0.566541 + 1.74363i) q^{11} +(-0.916683 - 2.82126i) q^{12} +(0.747156 + 2.29951i) q^{13} +(0.566541 - 1.74363i) q^{14} +(0.309017 + 0.951057i) q^{16} +(2.25284 - 1.63679i) q^{17} -5.79981 q^{18} +(1.35294 - 0.982966i) q^{19} +(-4.39991 - 3.19672i) q^{21} +(-1.48322 - 1.07763i) q^{22} +(2.39991 - 7.38615i) q^{23} +2.96645 q^{24} -2.41785 q^{26} +(-2.56654 + 7.89900i) q^{27} +(1.48322 + 1.07763i) q^{28} +(-6.13597 - 4.45805i) q^{29} +(4.28304 - 3.11181i) q^{31} -1.00000 q^{32} +(-4.39991 + 3.19672i) q^{33} +(0.860510 + 2.64838i) q^{34} +(1.79224 - 5.51595i) q^{36} +(0.406315 + 1.25051i) q^{37} +(0.516776 + 1.59047i) q^{38} +(-2.21640 + 6.82138i) q^{39} +(1.08621 + 3.34301i) q^{41} +(4.39991 - 3.19672i) q^{42} +4.30550 q^{43} +(1.48322 - 1.07763i) q^{44} +(6.28304 + 4.56489i) q^{46} +(1.48322 + 1.07763i) q^{47} +(-0.916683 + 2.82126i) q^{48} -3.63877 q^{49} +8.26057 q^{51} +(0.747156 - 2.29951i) q^{52} +(-5.27267 - 3.83082i) q^{53} +(-6.71929 - 4.88185i) q^{54} +(-1.48322 + 1.07763i) q^{56} +4.96086 q^{57} +(6.13597 - 4.45805i) q^{58} +(-2.79981 - 8.61694i) q^{59} +(0.799717 - 2.46127i) q^{61} +(1.63597 + 5.03501i) q^{62} +(-3.28583 - 10.1128i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-1.68061 - 5.17240i) q^{66} +(7.68574 - 5.58402i) q^{67} -2.78467 q^{68} +(18.6383 - 13.5415i) q^{69} +(-0.247156 - 0.179569i) q^{71} +(4.69215 + 3.40904i) q^{72} +(-4.61920 + 14.2164i) q^{73} -1.31486 q^{74} -1.67232 q^{76} +(1.03868 - 3.19672i) q^{77} +(-5.80261 - 4.21584i) q^{78} +(2.79981 + 2.03418i) q^{79} +(-5.85599 + 4.25462i) q^{81} -3.51505 q^{82} +(-5.15555 + 3.74572i) q^{83} +(1.68061 + 5.17240i) q^{84} +(-1.33047 + 4.09478i) q^{86} +(-6.95256 - 21.3978i) q^{87} +(0.566541 + 1.74363i) q^{88} +(-1.02608 + 3.15794i) q^{89} +(-1.36981 - 4.21584i) q^{91} +(-6.28304 + 4.56489i) q^{92} +15.7047 q^{93} +(-1.48322 + 1.07763i) q^{94} +(-2.39991 - 1.74363i) q^{96} +(8.97214 + 6.51864i) q^{97} +(1.12444 - 3.46068i) q^{98} -10.6332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - 3 q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{11} - 2 q^{12} + 13 q^{13} - q^{14} - 2 q^{16} + 11 q^{17} - 14 q^{18} + 20 q^{19} - 19 q^{21} - q^{22} + 3 q^{23} + 2 q^{24} + 22 q^{26} - 15 q^{27} + q^{28} - 15 q^{29} - 9 q^{31} - 8 q^{32} - 19 q^{33} - q^{34} - q^{36} + 6 q^{37} + 15 q^{38} - 12 q^{39} - 9 q^{41} + 19 q^{42} - 12 q^{43} + q^{44} + 7 q^{46} + q^{47} - 2 q^{48} - 4 q^{49} + 26 q^{51} + 13 q^{52} - 7 q^{53} - 25 q^{54} - q^{56} + 15 q^{58} + 10 q^{59} + 6 q^{61} - 21 q^{62} + 8 q^{63} - 2 q^{64} - 26 q^{66} + 11 q^{67} - 24 q^{68} + 43 q^{69} - 9 q^{71} + 6 q^{72} + 8 q^{73} + 24 q^{74} - 10 q^{76} - 33 q^{77} - 23 q^{78} - 10 q^{79} - 17 q^{81} - 26 q^{82} - 27 q^{83} + 26 q^{84} - 23 q^{86} - q^{88} - 15 q^{89} + q^{91} - 7 q^{92} + 46 q^{93} - q^{94} - 3 q^{96} + 36 q^{97} + 19 q^{98} - 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/250\mathbb{Z}\right)^\times\).

\(n\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 + 0.951057i −0.218508 + 0.672499i
\(3\) 2.39991 + 1.74363i 1.38559 + 1.00669i 0.996333 + 0.0855571i \(0.0272670\pi\)
0.389254 + 0.921131i \(0.372733\pi\)
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0 0
\(6\) −2.39991 + 1.74363i −0.979758 + 0.711836i
\(7\) −1.83337 −0.692947 −0.346474 0.938060i \(-0.612621\pi\)
−0.346474 + 0.938060i \(0.612621\pi\)
\(8\) 0.809017 0.587785i 0.286031 0.207813i
\(9\) 1.79224 + 5.51595i 0.597414 + 1.83865i
\(10\) 0 0
\(11\) −0.566541 + 1.74363i −0.170819 + 0.525726i −0.999418 0.0341166i \(-0.989138\pi\)
0.828599 + 0.559842i \(0.189138\pi\)
\(12\) −0.916683 2.82126i −0.264624 0.814428i
\(13\) 0.747156 + 2.29951i 0.207224 + 0.637769i 0.999615 + 0.0277557i \(0.00883604\pi\)
−0.792391 + 0.610014i \(0.791164\pi\)
\(14\) 0.566541 1.74363i 0.151414 0.466006i
\(15\) 0 0
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 2.25284 1.63679i 0.546395 0.396979i −0.280060 0.959983i \(-0.590354\pi\)
0.826455 + 0.563003i \(0.190354\pi\)
\(18\) −5.79981 −1.36703
\(19\) 1.35294 0.982966i 0.310385 0.225508i −0.421677 0.906746i \(-0.638558\pi\)
0.732062 + 0.681238i \(0.238558\pi\)
\(20\) 0 0
\(21\) −4.39991 3.19672i −0.960138 0.697581i
\(22\) −1.48322 1.07763i −0.316224 0.229750i
\(23\) 2.39991 7.38615i 0.500415 1.54012i −0.307929 0.951409i \(-0.599636\pi\)
0.808344 0.588710i \(-0.200364\pi\)
\(24\) 2.96645 0.605524
\(25\) 0 0
\(26\) −2.41785 −0.474179
\(27\) −2.56654 + 7.89900i −0.493931 + 1.52016i
\(28\) 1.48322 + 1.07763i 0.280303 + 0.203652i
\(29\) −6.13597 4.45805i −1.13942 0.827838i −0.152383 0.988321i \(-0.548695\pi\)
−0.987039 + 0.160483i \(0.948695\pi\)
\(30\) 0 0
\(31\) 4.28304 3.11181i 0.769256 0.558897i −0.132479 0.991186i \(-0.542294\pi\)
0.901735 + 0.432288i \(0.142294\pi\)
\(32\) −1.00000 −0.176777
\(33\) −4.39991 + 3.19672i −0.765925 + 0.556477i
\(34\) 0.860510 + 2.64838i 0.147576 + 0.454193i
\(35\) 0 0
\(36\) 1.79224 5.51595i 0.298707 0.919325i
\(37\) 0.406315 + 1.25051i 0.0667977 + 0.205582i 0.978884 0.204416i \(-0.0655294\pi\)
−0.912086 + 0.409998i \(0.865529\pi\)
\(38\) 0.516776 + 1.59047i 0.0838321 + 0.258009i
\(39\) −2.21640 + 6.82138i −0.354908 + 1.09229i
\(40\) 0 0
\(41\) 1.08621 + 3.34301i 0.169637 + 0.522090i 0.999348 0.0361034i \(-0.0114946\pi\)
−0.829711 + 0.558194i \(0.811495\pi\)
\(42\) 4.39991 3.19672i 0.678920 0.493265i
\(43\) 4.30550 0.656583 0.328291 0.944576i \(-0.393527\pi\)
0.328291 + 0.944576i \(0.393527\pi\)
\(44\) 1.48322 1.07763i 0.223604 0.162458i
\(45\) 0 0
\(46\) 6.28304 + 4.56489i 0.926383 + 0.673057i
\(47\) 1.48322 + 1.07763i 0.216350 + 0.157188i 0.690682 0.723158i \(-0.257310\pi\)
−0.474332 + 0.880346i \(0.657310\pi\)
\(48\) −0.916683 + 2.82126i −0.132312 + 0.407214i
\(49\) −3.63877 −0.519824
\(50\) 0 0
\(51\) 8.26057 1.15671
\(52\) 0.747156 2.29951i 0.103612 0.318885i
\(53\) −5.27267 3.83082i −0.724257 0.526203i 0.163485 0.986546i \(-0.447727\pi\)
−0.887741 + 0.460342i \(0.847727\pi\)
\(54\) −6.71929 4.88185i −0.914380 0.664336i
\(55\) 0 0
\(56\) −1.48322 + 1.07763i −0.198204 + 0.144004i
\(57\) 4.96086 0.657082
\(58\) 6.13597 4.45805i 0.805693 0.585370i
\(59\) −2.79981 8.61694i −0.364505 1.12183i −0.950291 0.311364i \(-0.899214\pi\)
0.585786 0.810466i \(-0.300786\pi\)
\(60\) 0 0
\(61\) 0.799717 2.46127i 0.102393 0.315134i −0.886717 0.462313i \(-0.847019\pi\)
0.989110 + 0.147180i \(0.0470195\pi\)
\(62\) 1.63597 + 5.03501i 0.207769 + 0.639447i
\(63\) −3.28583 10.1128i −0.413976 1.27409i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) 0 0
\(66\) −1.68061 5.17240i −0.206869 0.636679i
\(67\) 7.68574 5.58402i 0.938963 0.682196i −0.00920814 0.999958i \(-0.502931\pi\)
0.948171 + 0.317761i \(0.102931\pi\)
\(68\) −2.78467 −0.337691
\(69\) 18.6383 13.5415i 2.24379 1.63021i
\(70\) 0 0
\(71\) −0.247156 0.179569i −0.0293320 0.0213110i 0.573023 0.819540i \(-0.305771\pi\)
−0.602355 + 0.798229i \(0.705771\pi\)
\(72\) 4.69215 + 3.40904i 0.552975 + 0.401760i
\(73\) −4.61920 + 14.2164i −0.540636 + 1.66391i 0.190509 + 0.981685i \(0.438986\pi\)
−0.731145 + 0.682222i \(0.761014\pi\)
\(74\) −1.31486 −0.152850
\(75\) 0 0
\(76\) −1.67232 −0.191829
\(77\) 1.03868 3.19672i 0.118368 0.364300i
\(78\) −5.80261 4.21584i −0.657016 0.477350i
\(79\) 2.79981 + 2.03418i 0.315004 + 0.228864i 0.734041 0.679106i \(-0.237632\pi\)
−0.419037 + 0.907969i \(0.637632\pi\)
\(80\) 0 0
\(81\) −5.85599 + 4.25462i −0.650665 + 0.472736i
\(82\) −3.51505 −0.388172
\(83\) −5.15555 + 3.74572i −0.565895 + 0.411147i −0.833612 0.552351i \(-0.813731\pi\)
0.267717 + 0.963498i \(0.413731\pi\)
\(84\) 1.68061 + 5.17240i 0.183370 + 0.564355i
\(85\) 0 0
\(86\) −1.33047 + 4.09478i −0.143469 + 0.441551i
\(87\) −6.95256 21.3978i −0.745393 2.29408i
\(88\) 0.566541 + 1.74363i 0.0603935 + 0.185872i
\(89\) −1.02608 + 3.15794i −0.108764 + 0.334741i −0.990595 0.136824i \(-0.956311\pi\)
0.881832 + 0.471565i \(0.156311\pi\)
\(90\) 0 0
\(91\) −1.36981 4.21584i −0.143595 0.441940i
\(92\) −6.28304 + 4.56489i −0.655052 + 0.475923i
\(93\) 15.7047 1.62851
\(94\) −1.48322 + 1.07763i −0.152983 + 0.111149i
\(95\) 0 0
\(96\) −2.39991 1.74363i −0.244939 0.177959i
\(97\) 8.97214 + 6.51864i 0.910982 + 0.661867i 0.941263 0.337674i \(-0.109640\pi\)
−0.0302807 + 0.999541i \(0.509640\pi\)
\(98\) 1.12444 3.46068i 0.113586 0.349581i
\(99\) −10.6332 −1.06867
\(100\) 0 0
\(101\) −13.1807 −1.31152 −0.655762 0.754968i \(-0.727653\pi\)
−0.655762 + 0.754968i \(0.727653\pi\)
\(102\) −2.55266 + 7.85627i −0.252751 + 0.777887i
\(103\) −2.13029 1.54774i −0.209903 0.152504i 0.477867 0.878432i \(-0.341410\pi\)
−0.687770 + 0.725929i \(0.741410\pi\)
\(104\) 1.95608 + 1.42118i 0.191809 + 0.139358i
\(105\) 0 0
\(106\) 5.27267 3.83082i 0.512127 0.372082i
\(107\) −18.8045 −1.81790 −0.908949 0.416908i \(-0.863114\pi\)
−0.908949 + 0.416908i \(0.863114\pi\)
\(108\) 6.71929 4.88185i 0.646564 0.469756i
\(109\) 3.18574 + 9.80470i 0.305139 + 0.939120i 0.979625 + 0.200833i \(0.0643649\pi\)
−0.674487 + 0.738287i \(0.735635\pi\)
\(110\) 0 0
\(111\) −1.20531 + 3.70957i −0.114403 + 0.352097i
\(112\) −0.566541 1.74363i −0.0535331 0.164758i
\(113\) −1.87160 5.76019i −0.176065 0.541873i 0.823615 0.567149i \(-0.191954\pi\)
−0.999681 + 0.0252760i \(0.991954\pi\)
\(114\) −1.53299 + 4.71806i −0.143578 + 0.441886i
\(115\) 0 0
\(116\) 2.34373 + 7.21327i 0.217610 + 0.669735i
\(117\) −11.3449 + 8.24255i −1.04884 + 0.762024i
\(118\) 9.06039 0.834076
\(119\) −4.13029 + 3.00083i −0.378623 + 0.275086i
\(120\) 0 0
\(121\) 6.17989 + 4.48996i 0.561809 + 0.408178i
\(122\) 2.09369 + 1.52115i 0.189553 + 0.137719i
\(123\) −3.22218 + 9.91686i −0.290535 + 0.894174i
\(124\) −5.29413 −0.475427
\(125\) 0 0
\(126\) 10.6332 0.947279
\(127\) −0.102986 + 0.316957i −0.00913850 + 0.0281254i −0.955522 0.294921i \(-0.904707\pi\)
0.946383 + 0.323046i \(0.104707\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 10.3328 + 7.50722i 0.909753 + 0.660974i
\(130\) 0 0
\(131\) 4.18910 3.04356i 0.366003 0.265917i −0.389548 0.921006i \(-0.627369\pi\)
0.755552 + 0.655089i \(0.227369\pi\)
\(132\) 5.43858 0.473368
\(133\) −2.48043 + 1.80214i −0.215080 + 0.156265i
\(134\) 2.93569 + 9.03513i 0.253605 + 0.780516i
\(135\) 0 0
\(136\) 0.860510 2.64838i 0.0737881 0.227096i
\(137\) 6.03299 + 18.5676i 0.515433 + 1.58634i 0.782493 + 0.622660i \(0.213948\pi\)
−0.267060 + 0.963680i \(0.586052\pi\)
\(138\) 7.11920 + 21.9106i 0.606026 + 1.86516i
\(139\) −2.45825 + 7.56572i −0.208506 + 0.641716i 0.791045 + 0.611758i \(0.209537\pi\)
−0.999551 + 0.0299582i \(0.990463\pi\)
\(140\) 0 0
\(141\) 1.68061 + 5.17240i 0.141533 + 0.435595i
\(142\) 0.247156 0.179569i 0.0207409 0.0150691i
\(143\) −4.43280 −0.370689
\(144\) −4.69215 + 3.40904i −0.391012 + 0.284087i
\(145\) 0 0
\(146\) −12.0932 8.78624i −1.00084 0.727154i
\(147\) −8.73271 6.34468i −0.720262 0.523301i
\(148\) 0.406315 1.25051i 0.0333989 0.102791i
\(149\) −1.67955 −0.137594 −0.0687969 0.997631i \(-0.521916\pi\)
−0.0687969 + 0.997631i \(0.521916\pi\)
\(150\) 0 0
\(151\) −21.2664 −1.73063 −0.865316 0.501227i \(-0.832882\pi\)
−0.865316 + 0.501227i \(0.832882\pi\)
\(152\) 0.516776 1.59047i 0.0419161 0.129004i
\(153\) 13.0661 + 9.49306i 1.05633 + 0.767468i
\(154\) 2.71929 + 1.97568i 0.219127 + 0.159205i
\(155\) 0 0
\(156\) 5.80261 4.21584i 0.464581 0.337538i
\(157\) −10.4514 −0.834113 −0.417056 0.908881i \(-0.636938\pi\)
−0.417056 + 0.908881i \(0.636938\pi\)
\(158\) −2.79981 + 2.03418i −0.222741 + 0.161831i
\(159\) −5.97437 18.3872i −0.473798 1.45820i
\(160\) 0 0
\(161\) −4.39991 + 13.5415i −0.346761 + 1.06722i
\(162\) −2.23679 6.88413i −0.175739 0.540868i
\(163\) −3.21706 9.90109i −0.251980 0.775513i −0.994410 0.105590i \(-0.966327\pi\)
0.742430 0.669923i \(-0.233673\pi\)
\(164\) 1.08621 3.34301i 0.0848187 0.261045i
\(165\) 0 0
\(166\) −1.96924 6.06071i −0.152843 0.470402i
\(167\) 1.71650 1.24711i 0.132826 0.0965041i −0.519388 0.854538i \(-0.673840\pi\)
0.652215 + 0.758034i \(0.273840\pi\)
\(168\) −5.43858 −0.419596
\(169\) 5.78772 4.20502i 0.445209 0.323463i
\(170\) 0 0
\(171\) 7.84678 + 5.70102i 0.600059 + 0.435968i
\(172\) −3.48322 2.53071i −0.265593 0.192965i
\(173\) 5.59774 17.2281i 0.425588 1.30983i −0.476841 0.878989i \(-0.658218\pi\)
0.902430 0.430837i \(-0.141782\pi\)
\(174\) 22.4990 1.70564
\(175\) 0 0
\(176\) −1.83337 −0.138195
\(177\) 8.30550 25.5617i 0.624280 1.92134i
\(178\) −2.68630 1.95171i −0.201347 0.146287i
\(179\) −8.54361 6.20730i −0.638579 0.463955i 0.220782 0.975323i \(-0.429139\pi\)
−0.859362 + 0.511368i \(0.829139\pi\)
\(180\) 0 0
\(181\) −14.6886 + 10.6719i −1.09180 + 0.793237i −0.979702 0.200460i \(-0.935756\pi\)
−0.112096 + 0.993697i \(0.535756\pi\)
\(182\) 4.43280 0.328581
\(183\) 6.21081 4.51242i 0.459116 0.333567i
\(184\) −2.39991 7.38615i −0.176923 0.544514i
\(185\) 0 0
\(186\) −4.85303 + 14.9361i −0.355842 + 1.09517i
\(187\) 1.57763 + 4.85544i 0.115368 + 0.355065i
\(188\) −0.566541 1.74363i −0.0413193 0.127168i
\(189\) 4.70541 14.4818i 0.342268 1.05339i
\(190\) 0 0
\(191\) −6.76906 20.8330i −0.489792 1.50742i −0.824919 0.565251i \(-0.808779\pi\)
0.335127 0.942173i \(-0.391221\pi\)
\(192\) 2.39991 1.74363i 0.173198 0.125836i
\(193\) −27.4248 −1.97408 −0.987041 0.160465i \(-0.948700\pi\)
−0.987041 + 0.160465i \(0.948700\pi\)
\(194\) −8.97214 + 6.51864i −0.644162 + 0.468011i
\(195\) 0 0
\(196\) 2.94383 + 2.13882i 0.210273 + 0.152773i
\(197\) −0.909110 0.660507i −0.0647714 0.0470592i 0.554928 0.831898i \(-0.312746\pi\)
−0.619700 + 0.784839i \(0.712746\pi\)
\(198\) 3.28583 10.1128i 0.233514 0.718682i
\(199\) 25.4992 1.80759 0.903794 0.427968i \(-0.140770\pi\)
0.903794 + 0.427968i \(0.140770\pi\)
\(200\) 0 0
\(201\) 28.1815 1.98777
\(202\) 4.07305 12.5355i 0.286579 0.881998i
\(203\) 11.2495 + 8.17323i 0.789559 + 0.573648i
\(204\) −6.68294 4.85544i −0.467900 0.339949i
\(205\) 0 0
\(206\) 2.13029 1.54774i 0.148424 0.107836i
\(207\) 45.0429 3.13070
\(208\) −1.95608 + 1.42118i −0.135630 + 0.0985408i
\(209\) 0.947439 + 2.91592i 0.0655358 + 0.201698i
\(210\) 0 0
\(211\) 6.58341 20.2617i 0.453221 1.39487i −0.419990 0.907529i \(-0.637967\pi\)
0.873211 0.487342i \(-0.162033\pi\)
\(212\) 2.01398 + 6.19839i 0.138321 + 0.425708i
\(213\) −0.280048 0.861899i −0.0191886 0.0590564i
\(214\) 5.81090 17.8841i 0.397225 1.22253i
\(215\) 0 0
\(216\) 2.56654 + 7.89900i 0.174631 + 0.537459i
\(217\) −7.85237 + 5.70508i −0.533054 + 0.387286i
\(218\) −10.3093 −0.698232
\(219\) −35.8739 + 26.0639i −2.42413 + 1.76124i
\(220\) 0 0
\(221\) 5.44703 + 3.95750i 0.366407 + 0.266210i
\(222\) −3.15555 2.29264i −0.211786 0.153872i
\(223\) −1.00280 + 3.08629i −0.0671522 + 0.206673i −0.979002 0.203851i \(-0.934654\pi\)
0.911850 + 0.410524i \(0.134654\pi\)
\(224\) 1.83337 0.122497
\(225\) 0 0
\(226\) 6.05662 0.402880
\(227\) −5.06085 + 15.5757i −0.335901 + 1.03380i 0.630376 + 0.776290i \(0.282901\pi\)
−0.966277 + 0.257506i \(0.917099\pi\)
\(228\) −4.01342 2.91592i −0.265795 0.193111i
\(229\) 4.11788 + 2.99181i 0.272117 + 0.197705i 0.715472 0.698642i \(-0.246212\pi\)
−0.443355 + 0.896346i \(0.646212\pi\)
\(230\) 0 0
\(231\) 8.06664 5.86076i 0.530746 0.385609i
\(232\) −7.58448 −0.497946
\(233\) −1.34536 + 0.977464i −0.0881378 + 0.0640358i −0.630981 0.775798i \(-0.717348\pi\)
0.542844 + 0.839834i \(0.317348\pi\)
\(234\) −4.33337 13.3367i −0.283281 0.871849i
\(235\) 0 0
\(236\) −2.79981 + 8.61694i −0.182252 + 0.560915i
\(237\) 3.17242 + 9.76370i 0.206071 + 0.634221i
\(238\) −1.57763 4.85544i −0.102263 0.314732i
\(239\) 3.95536 12.1733i 0.255851 0.787428i −0.737810 0.675009i \(-0.764140\pi\)
0.993661 0.112420i \(-0.0358601\pi\)
\(240\) 0 0
\(241\) 0.122209 + 0.376121i 0.00787219 + 0.0242281i 0.954915 0.296878i \(-0.0959454\pi\)
−0.947043 + 0.321106i \(0.895945\pi\)
\(242\) −6.17989 + 4.48996i −0.397259 + 0.288625i
\(243\) 3.44417 0.220944
\(244\) −2.09369 + 1.52115i −0.134034 + 0.0973817i
\(245\) 0 0
\(246\) −8.43579 6.12896i −0.537846 0.390768i
\(247\) 3.27120 + 2.37666i 0.208141 + 0.151223i
\(248\) 1.63597 5.03501i 0.103885 0.319724i
\(249\) −18.9040 −1.19799
\(250\) 0 0
\(251\) 9.36589 0.591170 0.295585 0.955316i \(-0.404485\pi\)
0.295585 + 0.955316i \(0.404485\pi\)
\(252\) −3.28583 + 10.1128i −0.206988 + 0.637044i
\(253\) 11.5191 + 8.36912i 0.724200 + 0.526162i
\(254\) −0.269620 0.195890i −0.0169175 0.0122913i
\(255\) 0 0
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 4.97926 0.310598 0.155299 0.987868i \(-0.450366\pi\)
0.155299 + 0.987868i \(0.450366\pi\)
\(258\) −10.3328 + 7.50722i −0.643292 + 0.467379i
\(259\) −0.744923 2.29264i −0.0462873 0.142458i
\(260\) 0 0
\(261\) 13.5932 41.8356i 0.841399 2.58956i
\(262\) 1.60009 + 4.92458i 0.0988541 + 0.304242i
\(263\) 6.12199 + 18.8416i 0.377498 + 1.16182i 0.941778 + 0.336236i \(0.109154\pi\)
−0.564279 + 0.825584i \(0.690846\pi\)
\(264\) −1.68061 + 5.17240i −0.103435 + 0.318339i
\(265\) 0 0
\(266\) −0.947439 2.91592i −0.0580912 0.178786i
\(267\) −7.96878 + 5.78966i −0.487681 + 0.354321i
\(268\) −9.50010 −0.580311
\(269\) −11.9685 + 8.69564i −0.729734 + 0.530183i −0.889479 0.456976i \(-0.848933\pi\)
0.159745 + 0.987158i \(0.448933\pi\)
\(270\) 0 0
\(271\) 10.1583 + 7.38047i 0.617075 + 0.448331i 0.851899 0.523707i \(-0.175451\pi\)
−0.234823 + 0.972038i \(0.575451\pi\)
\(272\) 2.25284 + 1.63679i 0.136599 + 0.0992448i
\(273\) 4.06347 12.5061i 0.245932 0.756902i
\(274\) −19.5232 −1.17944
\(275\) 0 0
\(276\) −23.0382 −1.38674
\(277\) 1.95664 6.02193i 0.117563 0.361823i −0.874910 0.484286i \(-0.839079\pi\)
0.992473 + 0.122463i \(0.0390794\pi\)
\(278\) −6.43579 4.67587i −0.385993 0.280440i
\(279\) 24.8408 + 18.0479i 1.48718 + 1.08050i
\(280\) 0 0
\(281\) 16.2525 11.8082i 0.969545 0.704416i 0.0141971 0.999899i \(-0.495481\pi\)
0.955348 + 0.295484i \(0.0954808\pi\)
\(282\) −5.43858 −0.323863
\(283\) 1.46981 1.06788i 0.0873709 0.0634787i −0.543242 0.839576i \(-0.682803\pi\)
0.630613 + 0.776097i \(0.282803\pi\)
\(284\) 0.0944052 + 0.290549i 0.00560192 + 0.0172409i
\(285\) 0 0
\(286\) 1.36981 4.21584i 0.0809986 0.249288i
\(287\) −1.99142 6.12896i −0.117550 0.361781i
\(288\) −1.79224 5.51595i −0.105609 0.325031i
\(289\) −2.85705 + 8.79311i −0.168062 + 0.517242i
\(290\) 0 0
\(291\) 10.1662 + 31.2882i 0.595951 + 1.83415i
\(292\) 12.0932 8.78624i 0.707702 0.514176i
\(293\) 6.85931 0.400725 0.200363 0.979722i \(-0.435788\pi\)
0.200363 + 0.979722i \(0.435788\pi\)
\(294\) 8.73271 6.34468i 0.509302 0.370030i
\(295\) 0 0
\(296\) 1.06375 + 0.772856i 0.0618290 + 0.0449214i
\(297\) −12.3189 8.95022i −0.714816 0.519344i
\(298\) 0.519009 1.59734i 0.0300654 0.0925317i
\(299\) 18.7776 1.08594
\(300\) 0 0
\(301\) −7.89356 −0.454977
\(302\) 6.57167 20.2255i 0.378157 1.16385i
\(303\) −31.6323 22.9822i −1.81723 1.32030i
\(304\) 1.35294 + 0.982966i 0.0775963 + 0.0563770i
\(305\) 0 0
\(306\) −13.0661 + 9.49306i −0.746938 + 0.542682i
\(307\) 2.89526 0.165241 0.0826206 0.996581i \(-0.473671\pi\)
0.0826206 + 0.996581i \(0.473671\pi\)
\(308\) −2.71929 + 1.97568i −0.154946 + 0.112575i
\(309\) −2.41379 7.42888i −0.137316 0.422614i
\(310\) 0 0
\(311\) −6.38090 + 19.6384i −0.361828 + 1.11359i 0.590116 + 0.807318i \(0.299082\pi\)
−0.951944 + 0.306272i \(0.900918\pi\)
\(312\) 2.21640 + 6.82138i 0.125479 + 0.386184i
\(313\) −5.07629 15.6232i −0.286929 0.883076i −0.985814 0.167842i \(-0.946320\pi\)
0.698885 0.715234i \(-0.253680\pi\)
\(314\) 3.22966 9.93987i 0.182260 0.560939i
\(315\) 0 0
\(316\) −1.06943 3.29138i −0.0601603 0.185154i
\(317\) 13.3535 9.70191i 0.750009 0.544914i −0.145820 0.989311i \(-0.546582\pi\)
0.895830 + 0.444397i \(0.146582\pi\)
\(318\) 19.3335 1.08417
\(319\) 11.2495 8.17323i 0.629850 0.457613i
\(320\) 0 0
\(321\) −45.1290 32.7881i −2.51885 1.83005i
\(322\) −11.5191 8.36912i −0.641935 0.466393i
\(323\) 1.43905 4.42894i 0.0800709 0.246433i
\(324\) 7.23840 0.402133
\(325\) 0 0
\(326\) 10.4106 0.576591
\(327\) −9.45033 + 29.0851i −0.522605 + 1.60841i
\(328\) 2.84373 + 2.06609i 0.157019 + 0.114081i
\(329\) −2.71929 1.97568i −0.149919 0.108923i
\(330\) 0 0
\(331\) −22.2245 + 16.1471i −1.22157 + 0.887522i −0.996229 0.0867577i \(-0.972349\pi\)
−0.225340 + 0.974280i \(0.572349\pi\)
\(332\) 6.37261 0.349742
\(333\) −6.16953 + 4.48242i −0.338088 + 0.245635i
\(334\) 0.655643 + 2.01786i 0.0358752 + 0.110413i
\(335\) 0 0
\(336\) 1.68061 5.17240i 0.0916851 0.282178i
\(337\) 0.848317 + 2.61085i 0.0462108 + 0.142222i 0.971500 0.237041i \(-0.0761775\pi\)
−0.925289 + 0.379263i \(0.876178\pi\)
\(338\) 2.21071 + 6.80387i 0.120247 + 0.370082i
\(339\) 5.55200 17.0873i 0.301543 0.928054i
\(340\) 0 0
\(341\) 2.99934 + 9.23102i 0.162423 + 0.499888i
\(342\) −7.84678 + 5.70102i −0.424305 + 0.308276i
\(343\) 19.5048 1.05316
\(344\) 3.48322 2.53071i 0.187803 0.136447i
\(345\) 0 0
\(346\) 14.6551 + 10.6475i 0.787862 + 0.572415i
\(347\) −17.2637 12.5428i −0.926762 0.673332i 0.0184361 0.999830i \(-0.494131\pi\)
−0.945198 + 0.326498i \(0.894131\pi\)
\(348\) −6.95256 + 21.3978i −0.372697 + 1.14704i
\(349\) −16.7650 −0.897411 −0.448705 0.893680i \(-0.648115\pi\)
−0.448705 + 0.893680i \(0.648115\pi\)
\(350\) 0 0
\(351\) −20.0814 −1.07187
\(352\) 0.566541 1.74363i 0.0301967 0.0929360i
\(353\) 2.41785 + 1.75667i 0.128689 + 0.0934981i 0.650268 0.759705i \(-0.274657\pi\)
−0.521579 + 0.853203i \(0.674657\pi\)
\(354\) 21.7441 + 15.7980i 1.15569 + 0.839654i
\(355\) 0 0
\(356\) 2.68630 1.95171i 0.142374 0.103441i
\(357\) −15.1447 −0.801540
\(358\) 8.54361 6.20730i 0.451544 0.328066i
\(359\) 2.07194 + 6.37678i 0.109353 + 0.336554i 0.990727 0.135865i \(-0.0433812\pi\)
−0.881375 + 0.472418i \(0.843381\pi\)
\(360\) 0 0
\(361\) −5.00711 + 15.4103i −0.263532 + 0.811068i
\(362\) −5.61056 17.2675i −0.294884 0.907561i
\(363\) 7.00233 + 21.5510i 0.367527 + 1.13113i
\(364\) −1.36981 + 4.21584i −0.0717976 + 0.220970i
\(365\) 0 0
\(366\) 2.37232 + 7.30124i 0.124003 + 0.381642i
\(367\) 3.24949 2.36089i 0.169622 0.123237i −0.499736 0.866178i \(-0.666570\pi\)
0.669357 + 0.742941i \(0.266570\pi\)
\(368\) 7.76626 0.404844
\(369\) −16.4931 + 11.9830i −0.858598 + 0.623808i
\(370\) 0 0
\(371\) 9.66673 + 7.02329i 0.501872 + 0.364631i
\(372\) −12.7054 9.23102i −0.658745 0.478606i
\(373\) −8.21467 + 25.2822i −0.425340 + 1.30906i 0.477329 + 0.878725i \(0.341605\pi\)
−0.902669 + 0.430336i \(0.858395\pi\)
\(374\) −5.10532 −0.263990
\(375\) 0 0
\(376\) 1.83337 0.0945486
\(377\) 5.66679 17.4406i 0.291855 0.898236i
\(378\) 12.3189 + 8.95022i 0.633617 + 0.460350i
\(379\) 12.6431 + 9.18578i 0.649435 + 0.471842i 0.863079 0.505070i \(-0.168533\pi\)
−0.213644 + 0.976912i \(0.568533\pi\)
\(380\) 0 0
\(381\) −0.799814 + 0.581099i −0.0409757 + 0.0297706i
\(382\) 21.9051 1.12076
\(383\) 10.8776 7.90306i 0.555821 0.403828i −0.274106 0.961699i \(-0.588382\pi\)
0.829927 + 0.557872i \(0.188382\pi\)
\(384\) 0.916683 + 2.82126i 0.0467793 + 0.143972i
\(385\) 0 0
\(386\) 8.47474 26.0826i 0.431353 1.32757i
\(387\) 7.71650 + 23.7489i 0.392252 + 1.20723i
\(388\) −3.42705 10.5474i −0.173982 0.535462i
\(389\) −7.75991 + 23.8826i −0.393443 + 1.21089i 0.536724 + 0.843758i \(0.319662\pi\)
−0.930167 + 0.367136i \(0.880338\pi\)
\(390\) 0 0
\(391\) −6.68294 20.5680i −0.337971 1.04017i
\(392\) −2.94383 + 2.13882i −0.148686 + 0.108026i
\(393\) 15.3603 0.774825
\(394\) 0.909110 0.660507i 0.0458003 0.0332759i
\(395\) 0 0
\(396\) 8.60242 + 6.25003i 0.432288 + 0.314076i
\(397\) 2.84628 + 2.06794i 0.142850 + 0.103787i 0.656915 0.753964i \(-0.271861\pi\)
−0.514065 + 0.857751i \(0.671861\pi\)
\(398\) −7.87968 + 24.2511i −0.394972 + 1.21560i
\(399\) −9.09507 −0.455323
\(400\) 0 0
\(401\) 29.8696 1.49161 0.745807 0.666162i \(-0.232064\pi\)
0.745807 + 0.666162i \(0.232064\pi\)
\(402\) −8.70858 + 26.8022i −0.434344 + 1.33677i
\(403\) 10.3557 + 7.52388i 0.515856 + 0.374791i
\(404\) 10.6634 + 7.74739i 0.530523 + 0.385447i
\(405\) 0 0
\(406\) −11.2495 + 8.17323i −0.558303 + 0.405631i
\(407\) −2.41062 −0.119490
\(408\) 6.68294 4.85544i 0.330855 0.240380i
\(409\) −11.9784 36.8656i −0.592291 1.82289i −0.567771 0.823186i \(-0.692194\pi\)
−0.0245200 0.999699i \(-0.507806\pi\)
\(410\) 0 0
\(411\) −17.8965 + 55.0799i −0.882772 + 2.71689i
\(412\) 0.813697 + 2.50430i 0.0400880 + 0.123378i
\(413\) 5.13308 + 15.7980i 0.252582 + 0.777369i
\(414\) −13.9190 + 42.8383i −0.684082 + 2.10539i
\(415\) 0 0
\(416\) −0.747156 2.29951i −0.0366323 0.112743i
\(417\) −19.0914 + 13.8707i −0.934911 + 0.679253i
\(418\) −3.06598 −0.149962
\(419\) 15.2988 11.1152i 0.747395 0.543014i −0.147624 0.989044i \(-0.547162\pi\)
0.895018 + 0.446030i \(0.147162\pi\)
\(420\) 0 0
\(421\) 17.8414 + 12.9625i 0.869536 + 0.631755i 0.930462 0.366388i \(-0.119406\pi\)
−0.0609265 + 0.998142i \(0.519406\pi\)
\(422\) 17.2356 + 12.5224i 0.839016 + 0.609581i
\(423\) −3.28583 + 10.1128i −0.159763 + 0.491699i
\(424\) −6.51738 −0.316512
\(425\) 0 0
\(426\) 0.906255 0.0439082
\(427\) −1.46617 + 4.51242i −0.0709531 + 0.218371i
\(428\) 15.2131 + 11.0530i 0.735355 + 0.534267i
\(429\) −10.6383 7.72918i −0.513622 0.373168i
\(430\) 0 0
\(431\) 7.44763 5.41102i 0.358740 0.260640i −0.393787 0.919202i \(-0.628835\pi\)
0.752526 + 0.658562i \(0.228835\pi\)
\(432\) −8.30550 −0.399599
\(433\) 28.1516 20.4533i 1.35288 0.982923i 0.354015 0.935240i \(-0.384816\pi\)
0.998862 0.0476837i \(-0.0151840\pi\)
\(434\) −2.99934 9.23102i −0.143973 0.443103i
\(435\) 0 0
\(436\) 3.18574 9.80470i 0.152569 0.469560i
\(437\) −4.01342 12.3520i −0.191988 0.590878i
\(438\) −13.7026 42.1723i −0.654736 2.01507i
\(439\) −2.58025 + 7.94118i −0.123148 + 0.379012i −0.993559 0.113314i \(-0.963853\pi\)
0.870411 + 0.492326i \(0.163853\pi\)
\(440\) 0 0
\(441\) −6.52155 20.0713i −0.310550 0.955775i
\(442\) −5.44703 + 3.95750i −0.259089 + 0.188239i
\(443\) 1.19887 0.0569599 0.0284799 0.999594i \(-0.490933\pi\)
0.0284799 + 0.999594i \(0.490933\pi\)
\(444\) 3.15555 2.29264i 0.149756 0.108804i
\(445\) 0 0
\(446\) −2.62535 1.90743i −0.124314 0.0903194i
\(447\) −4.03076 2.92852i −0.190648 0.138514i
\(448\) −0.566541 + 1.74363i −0.0267666 + 0.0823790i
\(449\) 32.7953 1.54771 0.773853 0.633365i \(-0.218327\pi\)
0.773853 + 0.633365i \(0.218327\pi\)
\(450\) 0 0
\(451\) −6.44437 −0.303453
\(452\) −1.87160 + 5.76019i −0.0880326 + 0.270936i
\(453\) −51.0373 37.0808i −2.39794 1.74221i
\(454\) −13.2495 9.62631i −0.621829 0.451785i
\(455\) 0 0
\(456\) 4.01342 2.91592i 0.187946 0.136550i
\(457\) −19.7884 −0.925664 −0.462832 0.886446i \(-0.653167\pi\)
−0.462832 + 0.886446i \(0.653167\pi\)
\(458\) −4.11788 + 2.99181i −0.192416 + 0.139798i
\(459\) 7.14697 + 21.9961i 0.333592 + 1.02669i
\(460\) 0 0
\(461\) 2.90468 8.93970i 0.135285 0.416363i −0.860350 0.509704i \(-0.829755\pi\)
0.995634 + 0.0933412i \(0.0297547\pi\)
\(462\) 3.08118 + 9.48290i 0.143350 + 0.441185i
\(463\) −5.47977 16.8650i −0.254666 0.783783i −0.993895 0.110328i \(-0.964810\pi\)
0.739229 0.673454i \(-0.235190\pi\)
\(464\) 2.34373 7.21327i 0.108805 0.334868i
\(465\) 0 0
\(466\) −0.513883 1.58157i −0.0238052 0.0732649i
\(467\) 17.6857 12.8494i 0.818398 0.594601i −0.0978549 0.995201i \(-0.531198\pi\)
0.916253 + 0.400599i \(0.131198\pi\)
\(468\) 14.0231 0.648216
\(469\) −14.0908 + 10.2375i −0.650651 + 0.472726i
\(470\) 0 0
\(471\) −25.0824 18.2234i −1.15574 0.839691i
\(472\) −7.33001 5.32556i −0.337391 0.245129i
\(473\) −2.43924 + 7.50722i −0.112157 + 0.345182i
\(474\) −10.2662 −0.471541
\(475\) 0 0
\(476\) 5.10532 0.234002
\(477\) 11.6807 35.9495i 0.534823 1.64602i
\(478\) 10.3553 + 7.52354i 0.473639 + 0.344119i
\(479\) 4.94352 + 3.59168i 0.225875 + 0.164108i 0.694967 0.719041i \(-0.255419\pi\)
−0.469092 + 0.883149i \(0.655419\pi\)
\(480\) 0 0
\(481\) −2.57198 + 1.86865i −0.117272 + 0.0852031i
\(482\) −0.395477 −0.0180135
\(483\) −34.1708 + 24.8266i −1.55483 + 1.12965i
\(484\) −2.36051 7.26490i −0.107296 0.330223i
\(485\) 0 0
\(486\) −1.06431 + 3.27560i −0.0482780 + 0.148584i
\(487\) −1.56421 4.81415i −0.0708812 0.218150i 0.909340 0.416053i \(-0.136587\pi\)
−0.980222 + 0.197903i \(0.936587\pi\)
\(488\) −0.799717 2.46127i −0.0362015 0.111417i
\(489\) 9.54324 29.3711i 0.431560 1.32821i
\(490\) 0 0
\(491\) 0.736165 + 2.26568i 0.0332227 + 0.102249i 0.966293 0.257446i \(-0.0828809\pi\)
−0.933070 + 0.359695i \(0.882881\pi\)
\(492\) 8.43579 6.12896i 0.380315 0.276315i
\(493\) −21.1203 −0.951209
\(494\) −3.27120 + 2.37666i −0.147178 + 0.106931i
\(495\) 0 0
\(496\) 4.28304 + 3.11181i 0.192314 + 0.139724i
\(497\) 0.453127 + 0.329216i 0.0203255 + 0.0147674i
\(498\) 5.84166 17.9788i 0.261771 0.805648i
\(499\) −0.0503313 −0.00225314 −0.00112657 0.999999i \(-0.500359\pi\)
−0.00112657 + 0.999999i \(0.500359\pi\)
\(500\) 0 0
\(501\) 6.29393 0.281192
\(502\) −2.89422 + 8.90749i −0.129175 + 0.397561i
\(503\) −4.37744 3.18040i −0.195181 0.141807i 0.485903 0.874013i \(-0.338491\pi\)
−0.681083 + 0.732206i \(0.738491\pi\)
\(504\) −8.60242 6.25003i −0.383182 0.278398i
\(505\) 0 0
\(506\) −11.5191 + 8.36912i −0.512087 + 0.372053i
\(507\) 21.2220 0.942502
\(508\) 0.269620 0.195890i 0.0119625 0.00869123i
\(509\) 5.85472 + 18.0190i 0.259506 + 0.798678i 0.992908 + 0.118883i \(0.0379312\pi\)
−0.733402 + 0.679795i \(0.762069\pi\)
\(510\) 0 0
\(511\) 8.46868 26.0639i 0.374632 1.15300i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) 4.29208 + 13.2097i 0.189500 + 0.583221i
\(514\) −1.53868 + 4.73556i −0.0678681 + 0.208877i
\(515\) 0 0
\(516\) −3.94678 12.1469i −0.173747 0.534739i
\(517\) −2.71929 + 1.97568i −0.119594 + 0.0868904i
\(518\) 2.41062 0.105917
\(519\) 43.4735 31.5854i 1.90828 1.38644i
\(520\) 0 0
\(521\) −31.0817 22.5822i −1.36171 0.989342i −0.998334 0.0577005i \(-0.981623\pi\)
−0.363379 0.931642i \(-0.618377\pi\)
\(522\) 35.5875 + 25.8558i 1.55762 + 1.13168i
\(523\) 3.79057 11.6662i 0.165750 0.510127i −0.833341 0.552760i \(-0.813575\pi\)
0.999091 + 0.0426332i \(0.0135747\pi\)
\(524\) −5.17801 −0.226202
\(525\) 0 0
\(526\) −19.8112 −0.863809
\(527\) 4.55565 14.0208i 0.198447 0.610757i
\(528\) −4.39991 3.19672i −0.191481 0.139119i
\(529\) −30.1883 21.9331i −1.31254 0.953613i
\(530\) 0 0
\(531\) 42.5127 30.8873i 1.84489 1.34039i
\(532\) 3.06598 0.132927
\(533\) −6.87572 + 4.99550i −0.297820 + 0.216379i
\(534\) −3.04380 9.36786i −0.131718 0.405387i
\(535\) 0 0
\(536\) 2.93569 9.03513i 0.126803 0.390258i
\(537\) −9.68061 29.7939i −0.417749 1.28570i
\(538\) −4.57157 14.0698i −0.197094 0.606594i
\(539\) 2.06151 6.34468i 0.0887957 0.273285i
\(540\) 0 0
\(541\) 12.9872 + 39.9704i 0.558362 + 1.71846i 0.686896 + 0.726756i \(0.258973\pi\)
−0.128534 + 0.991705i \(0.541027\pi\)
\(542\) −10.1583 + 7.38047i −0.436338 + 0.317018i
\(543\) −53.8593 −2.31132
\(544\) −2.25284 + 1.63679i −0.0965899 + 0.0701767i
\(545\) 0 0
\(546\) 10.6383 + 7.72918i 0.455277 + 0.330778i
\(547\) 15.6719 + 11.3863i 0.670080 + 0.486842i 0.870052 0.492960i \(-0.164085\pi\)
−0.199972 + 0.979802i \(0.564085\pi\)
\(548\) 6.03299 18.5676i 0.257717 0.793170i
\(549\) 15.0096 0.640592
\(550\) 0 0
\(551\) −12.6837 −0.540344
\(552\) 7.11920 21.9106i 0.303013 0.932579i
\(553\) −5.13308 3.72940i −0.218281 0.158590i
\(554\) 5.12256 + 3.72176i 0.217637 + 0.158122i
\(555\) 0 0
\(556\) 6.43579 4.67587i 0.272938 0.198301i
\(557\) −8.54685 −0.362142 −0.181071 0.983470i \(-0.557956\pi\)
−0.181071 + 0.983470i \(0.557956\pi\)
\(558\) −24.8408 + 18.0479i −1.05160 + 0.764029i
\(559\) 3.21688 + 9.90054i 0.136060 + 0.418748i
\(560\) 0 0
\(561\) −4.67995 + 14.4034i −0.197588 + 0.608113i
\(562\) 6.20792 + 19.1060i 0.261865 + 0.805938i
\(563\) 7.24949 + 22.3116i 0.305529 + 0.940323i 0.979479 + 0.201546i \(0.0645964\pi\)
−0.673950 + 0.738777i \(0.735404\pi\)
\(564\) 1.68061 5.17240i 0.0707667 0.217797i
\(565\) 0 0
\(566\) 0.561416 + 1.72786i 0.0235981 + 0.0726274i
\(567\) 10.7362 7.80028i 0.450877 0.327581i
\(568\) −0.305502 −0.0128186
\(569\) 5.74445 4.17359i 0.240820 0.174966i −0.460829 0.887489i \(-0.652448\pi\)
0.701649 + 0.712523i \(0.252448\pi\)
\(570\) 0 0
\(571\) 9.67745 + 7.03108i 0.404989 + 0.294241i 0.771570 0.636145i \(-0.219472\pi\)
−0.366581 + 0.930386i \(0.619472\pi\)
\(572\) 3.58621 + 2.60553i 0.149947 + 0.108943i
\(573\) 20.0801 61.8001i 0.838856 2.58173i
\(574\) 6.44437 0.268983
\(575\) 0 0
\(576\) 5.79981 0.241659
\(577\) −12.8457 + 39.5350i −0.534774 + 1.64587i 0.209362 + 0.977838i \(0.432861\pi\)
−0.744137 + 0.668027i \(0.767139\pi\)
\(578\) −7.47987 5.43444i −0.311121 0.226043i
\(579\) −65.8171 47.8189i −2.73526 1.98729i
\(580\) 0 0
\(581\) 9.45200 6.86728i 0.392135 0.284903i
\(582\) −32.8984 −1.36368
\(583\) 9.66673 7.02329i 0.400355 0.290875i
\(584\) 4.61920 + 14.2164i 0.191144 + 0.588280i
\(585\) 0 0
\(586\) −2.11964 + 6.52359i −0.0875617 + 0.269487i
\(587\) −5.91072 18.1913i −0.243962 0.750836i −0.995806 0.0914953i \(-0.970835\pi\)
0.751844 0.659341i \(-0.229165\pi\)
\(588\) 3.33560 + 10.2659i 0.137558 + 0.423359i
\(589\) 2.73588 8.42016i 0.112730 0.346947i
\(590\) 0 0
\(591\) −1.03010 3.17031i −0.0423725 0.130409i
\(592\) −1.06375 + 0.772856i −0.0437197 + 0.0317642i
\(593\) −0.538428 −0.0221106 −0.0110553 0.999939i \(-0.503519\pi\)
−0.0110553 + 0.999939i \(0.503519\pi\)
\(594\) 12.3189 8.95022i 0.505451 0.367232i
\(595\) 0 0
\(596\) 1.35878 + 0.987213i 0.0556579 + 0.0404378i
\(597\) 61.1956 + 44.4612i 2.50457 + 1.81968i
\(598\) −5.80261 + 17.8586i −0.237286 + 0.730292i
\(599\) −38.4209 −1.56983 −0.784917 0.619601i \(-0.787295\pi\)
−0.784917 + 0.619601i \(0.787295\pi\)
\(600\) 0 0
\(601\) 19.6034 0.799639 0.399820 0.916594i \(-0.369073\pi\)
0.399820 + 0.916594i \(0.369073\pi\)
\(602\) 2.43924 7.50722i 0.0994162 0.305971i
\(603\) 44.5759 + 32.3863i 1.81527 + 1.31887i
\(604\) 17.2048 + 12.5001i 0.700055 + 0.508620i
\(605\) 0 0
\(606\) 31.6323 22.9822i 1.28498 0.933590i
\(607\) 32.4415 1.31676 0.658381 0.752685i \(-0.271242\pi\)
0.658381 + 0.752685i \(0.271242\pi\)
\(608\) −1.35294 + 0.982966i −0.0548688 + 0.0398646i
\(609\) 12.7466 + 39.2300i 0.516518 + 1.58968i
\(610\) 0 0
\(611\) −1.36981 + 4.21584i −0.0554166 + 0.170555i
\(612\) −4.99080 15.3601i −0.201741 0.620895i
\(613\) 7.25273 + 22.3216i 0.292935 + 0.901561i 0.983907 + 0.178680i \(0.0571826\pi\)
−0.690972 + 0.722881i \(0.742817\pi\)
\(614\) −0.894685 + 2.75356i −0.0361065 + 0.111124i
\(615\) 0 0
\(616\) −1.03868 3.19672i −0.0418495 0.128799i
\(617\) 14.0876 10.2353i 0.567147 0.412056i −0.266921 0.963718i \(-0.586006\pi\)
0.834068 + 0.551662i \(0.186006\pi\)
\(618\) 7.81119 0.314212
\(619\) −10.1801 + 7.39624i −0.409171 + 0.297280i −0.773266 0.634082i \(-0.781378\pi\)
0.364095 + 0.931362i \(0.381378\pi\)
\(620\) 0 0
\(621\) 52.1838 + 37.9137i 2.09406 + 1.52143i
\(622\) −16.7054 12.1372i −0.669826 0.486657i
\(623\) 1.88117 5.78966i 0.0753676 0.231958i
\(624\) −7.17242 −0.287127
\(625\) 0 0
\(626\) 16.4272 0.656563
\(627\) −2.81053 + 8.64992i −0.112242 + 0.345445i
\(628\) 8.45536 + 6.14318i 0.337406 + 0.245140i
\(629\) 2.96218 + 2.15215i 0.118110 + 0.0858118i
\(630\) 0 0
\(631\) −33.7653 + 24.5319i −1.34418 + 0.976601i −0.344897 + 0.938640i \(0.612086\pi\)
−0.999279 + 0.0379610i \(0.987914\pi\)
\(632\) 3.46076 0.137662
\(633\) 51.1285 37.1470i 2.03218 1.47646i
\(634\) 5.10060 + 15.6980i 0.202571 + 0.623448i
\(635\) 0 0
\(636\) −5.97437 + 18.3872i −0.236899 + 0.729101i
\(637\) −2.71873 8.36739i −0.107720 0.331528i
\(638\) 4.29692 + 13.2246i 0.170117 + 0.523565i
\(639\) 0.547533 1.68513i 0.0216601 0.0666628i
\(640\) 0 0
\(641\) −4.44926 13.6934i −0.175735 0.540858i 0.823931 0.566690i \(-0.191776\pi\)
−0.999666 + 0.0258324i \(0.991776\pi\)
\(642\) 45.1290 32.7881i 1.78110 1.29404i
\(643\) −30.1666 −1.18966 −0.594828 0.803853i \(-0.702780\pi\)
−0.594828 + 0.803853i \(0.702780\pi\)
\(644\) 11.5191 8.36912i 0.453916 0.329790i
\(645\) 0 0
\(646\) 3.76748 + 2.73724i 0.148230 + 0.107695i
\(647\) −8.64660 6.28212i −0.339933 0.246976i 0.404701 0.914449i \(-0.367376\pi\)
−0.744633 + 0.667474i \(0.767376\pi\)
\(648\) −2.23679 + 6.88413i −0.0878693 + 0.270434i
\(649\) 16.6110 0.652039
\(650\) 0 0
\(651\) −28.7925 −1.12847
\(652\) −3.21706 + 9.90109i −0.125990 + 0.387757i
\(653\) 8.22432 + 5.97532i 0.321843 + 0.233832i 0.736961 0.675935i \(-0.236260\pi\)
−0.415119 + 0.909767i \(0.636260\pi\)
\(654\) −24.7413 17.9756i −0.967461 0.702902i
\(655\) 0 0
\(656\) −2.84373 + 2.06609i −0.111029 + 0.0806674i
\(657\) −86.6959 −3.38233
\(658\) 2.71929 1.97568i 0.106009 0.0770201i
\(659\) 9.61668 + 29.5971i 0.374613 + 1.15294i 0.943740 + 0.330689i \(0.107281\pi\)
−0.569127 + 0.822250i \(0.692719\pi\)
\(660\) 0 0
\(661\) 12.8131 39.4347i 0.498372 1.53383i −0.313262 0.949667i \(-0.601422\pi\)
0.811635 0.584165i \(-0.198578\pi\)
\(662\) −8.48901 26.1265i −0.329935 1.01543i
\(663\) 6.17194 + 18.9953i 0.239698 + 0.737715i
\(664\) −1.96924 + 6.06071i −0.0764215 + 0.235201i
\(665\) 0 0
\(666\) −2.35655 7.25271i −0.0913144 0.281037i
\(667\) −47.6536 + 34.6224i −1.84515 + 1.34058i
\(668\) −2.12171 −0.0820913
\(669\) −7.78797 + 5.65829i −0.301100 + 0.218762i
\(670\) 0 0
\(671\) 3.83849 + 2.78883i 0.148183 + 0.107661i
\(672\) 4.39991 + 3.19672i 0.169730 + 0.123316i
\(673\) −0.662831 + 2.03998i −0.0255503 + 0.0786356i −0.963019 0.269435i \(-0.913163\pi\)
0.937468 + 0.348071i \(0.113163\pi\)
\(674\) −2.74521 −0.105742
\(675\) 0 0
\(676\) −7.15401 −0.275154
\(677\) −12.8391 + 39.5147i −0.493446 + 1.51867i 0.325918 + 0.945398i \(0.394327\pi\)
−0.819364 + 0.573274i \(0.805673\pi\)
\(678\) 14.5353 + 10.5605i 0.558226 + 0.405575i
\(679\) −16.4492 11.9510i −0.631263 0.458639i
\(680\) 0 0
\(681\) −39.3039 + 28.5560i −1.50613 + 1.09427i
\(682\) −9.70607 −0.371665
\(683\) −23.3247 + 16.9464i −0.892495 + 0.648436i −0.936527 0.350595i \(-0.885980\pi\)
0.0440323 + 0.999030i \(0.485980\pi\)
\(684\) −2.99720 9.22445i −0.114601 0.352706i
\(685\) 0 0
\(686\) −6.02730 + 18.5501i −0.230123 + 0.708247i
\(687\) 4.66589 + 14.3601i 0.178015 + 0.547874i
\(688\) 1.33047 + 4.09478i 0.0507238 + 0.156112i
\(689\) 4.86950 14.9868i 0.185513 0.570951i
\(690\) 0 0
\(691\) −15.2050 46.7963i −0.578426 1.78021i −0.624204 0.781262i \(-0.714576\pi\)
0.0457774 0.998952i \(-0.485424\pi\)
\(692\) −14.6551 + 10.6475i −0.557103 + 0.404759i
\(693\) 19.4945 0.740535
\(694\) 17.2637 12.5428i 0.655319 0.476117i
\(695\) 0 0
\(696\) −18.2021 13.2246i −0.689947 0.501276i
\(697\) 7.91886 + 5.75339i 0.299948 + 0.217925i
\(698\) 5.18067 15.9445i 0.196091 0.603507i
\(699\) −4.93309 −0.186587
\(700\) 0 0
\(701\) −24.9783 −0.943419 −0.471709 0.881754i \(-0.656363\pi\)
−0.471709 + 0.881754i \(0.656363\pi\)
\(702\) 6.20551 19.0986i 0.234212 0.720830i
\(703\) 1.77893 + 1.29247i 0.0670935 + 0.0487462i
\(704\) 1.48322 + 1.07763i 0.0559011 + 0.0406145i
\(705\) 0 0
\(706\) −2.41785 + 1.75667i −0.0909969 + 0.0661131i
\(707\) 24.1650 0.908817
\(708\) −21.7441 + 15.7980i −0.817193 + 0.593725i
\(709\) 3.02602 + 9.31312i 0.113644 + 0.349762i 0.991662 0.128867i \(-0.0411340\pi\)
−0.878017 + 0.478629i \(0.841134\pi\)
\(710\) 0 0
\(711\) −6.20252 + 19.0894i −0.232613 + 0.715908i
\(712\) 1.02608 + 3.15794i 0.0384538 + 0.118349i
\(713\) −12.7054 39.1032i −0.475821 1.46443i
\(714\) 4.67995 14.4034i 0.175143 0.539034i
\(715\) 0 0
\(716\) 3.26337 + 10.0436i 0.121958 + 0.375348i
\(717\) 30.7184 22.3182i 1.14720 0.833488i
\(718\) −6.70494 −0.250226
\(719\) 6.94474 5.04565i 0.258995 0.188171i −0.450709 0.892671i \(-0.648829\pi\)
0.709704 + 0.704500i \(0.248829\pi\)
\(720\) 0 0
\(721\) 3.90559 + 2.83758i 0.145452 + 0.105677i
\(722\) −13.1088 9.52408i −0.487858 0.354450i
\(723\) −0.362527 + 1.11574i −0.0134825 + 0.0414950i
\(724\) 18.1561 0.674768
\(725\) 0 0
\(726\) −22.6600 −0.840992
\(727\) 7.42142 22.8408i 0.275245 0.847118i −0.713909 0.700238i \(-0.753077\pi\)
0.989154 0.146880i \(-0.0469230\pi\)
\(728\) −3.58621 2.60553i −0.132914 0.0965675i
\(729\) 25.8337 + 18.7693i 0.956802 + 0.695157i
\(730\) 0 0
\(731\) 9.69962 7.04719i 0.358754 0.260650i
\(732\) −7.67698 −0.283749
\(733\) −15.3787 + 11.1733i −0.568025 + 0.412695i −0.834387 0.551178i \(-0.814178\pi\)
0.266362 + 0.963873i \(0.414178\pi\)
\(734\) 1.24119 + 3.82000i 0.0458133 + 0.140999i
\(735\) 0 0
\(736\) −2.39991 + 7.38615i −0.0884617 + 0.272257i
\(737\) 5.38220 + 16.5647i 0.198256 + 0.610168i
\(738\) −6.29981 19.3888i −0.231899 0.713713i
\(739\) −6.42507 + 19.7743i −0.236350 + 0.727411i 0.760589 + 0.649233i \(0.224910\pi\)
−0.996939 + 0.0781776i \(0.975090\pi\)
\(740\) 0 0
\(741\) 3.70653 + 11.4075i 0.136163 + 0.419066i
\(742\) −9.66673 + 7.02329i −0.354877 + 0.257833i
\(743\) −6.53365 −0.239696 −0.119848 0.992792i \(-0.538241\pi\)
−0.119848 + 0.992792i \(0.538241\pi\)
\(744\) 12.7054 9.23102i 0.465803 0.338426i
\(745\) 0 0
\(746\) −21.5063 15.6252i −0.787401 0.572080i
\(747\) −29.9012 21.7245i −1.09403 0.794858i
\(748\) 1.57763 4.85544i 0.0576838 0.177533i
\(749\) 34.4755 1.25971
\(750\) 0 0
\(751\) 27.9879 1.02129 0.510646 0.859791i \(-0.329406\pi\)
0.510646 + 0.859791i \(0.329406\pi\)
\(752\) −0.566541 + 1.74363i −0.0206596 + 0.0635838i
\(753\) 22.4773 + 16.3307i 0.819117 + 0.595123i
\(754\) 14.8359 + 10.7789i 0.540290 + 0.392544i
\(755\) 0 0
\(756\) −12.3189 + 8.95022i −0.448035 + 0.325516i
\(757\) −4.48558 −0.163031 −0.0815156 0.996672i \(-0.525976\pi\)
−0.0815156 + 0.996672i \(0.525976\pi\)
\(758\) −12.6431 + 9.18578i −0.459220 + 0.333643i
\(759\) 13.0521 + 40.1702i 0.473761 + 1.45809i
\(760\) 0 0
\(761\) 0.138770 0.427091i 0.00503042 0.0154820i −0.948510 0.316748i \(-0.897409\pi\)
0.953540 + 0.301266i \(0.0974091\pi\)
\(762\) −0.305502 0.940237i −0.0110672 0.0340612i
\(763\) −5.84063 17.9756i −0.211445 0.650760i
\(764\) −6.76906 + 20.8330i −0.244896 + 0.753712i
\(765\) 0 0
\(766\) 4.15489 + 12.7874i 0.150122 + 0.462028i
\(767\) 17.7228 12.8764i 0.639935 0.464940i
\(768\) −2.96645 −0.107042
\(769\) −16.9783 + 12.3355i −0.612254 + 0.444829i −0.850207 0.526448i \(-0.823524\pi\)
0.237953 + 0.971277i \(0.423524\pi\)
\(770\) 0 0
\(771\) 11.9498 + 8.68202i 0.430360 + 0.312675i
\(772\) 22.1872 + 16.1199i 0.798533 + 0.580168i
\(773\) −10.8283 + 33.3262i −0.389468 + 1.19866i 0.543718 + 0.839268i \(0.317016\pi\)
−0.933187 + 0.359392i \(0.882984\pi\)
\(774\) −24.9711 −0.897568
\(775\) 0 0
\(776\) 11.0902 0.398114
\(777\) 2.20978 6.80099i 0.0792753 0.243984i
\(778\) −20.3157 14.7602i −0.728354 0.529180i
\(779\) 4.75564 + 3.45517i 0.170388 + 0.123794i
\(780\) 0 0
\(781\) 0.453127 0.329216i 0.0162142 0.0117803i
\(782\) 21.6265 0.773361
\(783\) 50.9623 37.0263i 1.82125 1.32321i
\(784\) −1.12444 3.46068i −0.0401586 0.123596i
\(785\) 0 0
\(786\) −4.74659 + 14.6085i −0.169305 + 0.521068i
\(787\) −12.1132 37.2807i −0.431790 1.32891i −0.896340 0.443367i \(-0.853784\pi\)
0.464550 0.885547i \(-0.346216\pi\)
\(788\) 0.347249 + 1.06872i 0.0123702 + 0.0380717i
\(789\) −18.1606 + 55.8925i −0.646534 + 1.98983i
\(790\) 0 0
\(791\) 3.43132 + 10.5605i 0.122004 + 0.375489i
\(792\) −8.60242 + 6.25003i −0.305674 + 0.222085i
\(793\) 6.25724 0.222201
\(794\) −2.84628 + 2.06794i −0.101011 + 0.0733884i
\(795\) 0 0
\(796\) −20.6293 14.9880i −0.731185 0.531237i
\(797\) −6.98479 5.07475i −0.247414 0.179757i 0.457166 0.889381i \(-0.348865\pi\)
−0.704580 + 0.709625i \(0.748865\pi\)
\(798\) 2.81053 8.64992i 0.0994917 0.306204i
\(799\) 5.10532 0.180613
\(800\) 0 0
\(801\) −19.2580 −0.680448
\(802\) −9.23020 + 28.4076i −0.325930 + 1.00311i
\(803\) −22.1713 16.1084i −0.782408 0.568453i
\(804\) −22.7993 16.5647i −0.804071 0.584192i
\(805\) 0 0
\(806\) −10.3557 + 7.52388i −0.364765 + 0.265017i
\(807\) −43.8854 −1.54484
\(808\) −10.6634 + 7.74739i −0.375136 + 0.272552i
\(809\) −14.1830 43.6508i −0.498648 1.53468i −0.811194 0.584778i \(-0.801182\pi\)
0.312546 0.949903i \(-0.398818\pi\)
\(810\) 0 0
\(811\) 12.1734 37.4660i 0.427467 1.31561i −0.473145 0.880984i \(-0.656881\pi\)
0.900612 0.434623i \(-0.143119\pi\)
\(812\) −4.29692 13.2246i −0.150792 0.464091i
\(813\) 11.5102 + 35.4249i 0.403682 + 1.24240i
\(814\) 0.744923 2.29264i 0.0261096 0.0803569i
\(815\) 0 0
\(816\) 2.55266 + 7.85627i 0.0893609 + 0.275025i
\(817\) 5.82507 4.23216i 0.203794 0.148065i
\(818\) 38.7628 1.35531
\(819\) 20.7993 15.1116i 0.726788 0.528042i
\(820\) 0 0
\(821\) −22.0672 16.0328i −0.770152 0.559548i 0.131855 0.991269i \(-0.457907\pi\)
−0.902007 + 0.431721i \(0.857907\pi\)
\(822\) −46.8538 34.0413i −1.63421 1.18733i
\(823\) −1.89701 + 5.83841i −0.0661258 + 0.203514i −0.978660 0.205486i \(-0.934122\pi\)
0.912534 + 0.409000i \(0.134122\pi\)
\(824\) −2.63318 −0.0917311
\(825\) 0 0
\(826\) −16.6110 −0.577971
\(827\) −13.6170 + 41.9087i −0.473508 + 1.45731i 0.374451 + 0.927247i \(0.377831\pi\)
−0.847959 + 0.530062i \(0.822169\pi\)
\(828\) −36.4404 26.4755i −1.26639 0.920088i
\(829\) −3.80236 2.76257i −0.132061 0.0959481i 0.519794 0.854292i \(-0.326009\pi\)
−0.651855 + 0.758344i \(0.726009\pi\)
\(830\) 0 0
\(831\) 15.1958 11.0404i 0.527136 0.382987i
\(832\) 2.41785 0.0838238
\(833\) −8.19758 + 5.95589i −0.284029 + 0.206359i
\(834\) −7.29228 22.4433i −0.252511 0.777149i
\(835\) 0 0
\(836\) 0.947439 2.91592i 0.0327679 0.100849i
\(837\) 13.5876 + 41.8183i 0.469656 + 1.44545i
\(838\) 5.84362 + 17.9848i 0.201864 + 0.621275i
\(839\) −14.2747 + 43.9331i −0.492819 + 1.51674i 0.327509 + 0.944848i \(0.393791\pi\)
−0.820328 + 0.571893i \(0.806209\pi\)
\(840\) 0 0
\(841\) 8.81451 + 27.1283i 0.303949 + 0.935458i
\(842\) −17.8414 + 12.9625i −0.614855 + 0.446718i
\(843\) 59.5937 2.05252
\(844\) −17.2356 + 12.5224i −0.593274 + 0.431039i
\(845\) 0 0
\(846\) −8.60242 6.25003i −0.295757 0.214880i
\(847\) −11.3300 8.23173i −0.389304 0.282846i
\(848\) 2.01398 6.19839i 0.0691604 0.212854i
\(849\) 5.38938 0.184963
\(850\) 0 0
\(851\) 10.2116 0.350048
\(852\) −0.280048 + 0.861899i −0.00959429 + 0.0295282i
\(853\) 10.2282 + 7.43121i 0.350206 + 0.254440i 0.748956 0.662620i \(-0.230556\pi\)
−0.398749 + 0.917060i \(0.630556\pi\)
\(854\) −3.83849 2.78883i −0.131350 0.0954317i
\(855\) 0 0
\(856\) −15.2131 + 11.0530i −0.519974 + 0.377783i
\(857\) 19.4162 0.663245 0.331623 0.943412i \(-0.392404\pi\)
0.331623 + 0.943412i \(0.392404\pi\)
\(858\) 10.6383 7.72918i 0.363186 0.263870i
\(859\) 2.88593 + 8.88197i 0.0984665 + 0.303049i 0.988142 0.153545i \(-0.0490691\pi\)
−0.889675 + 0.456594i \(0.849069\pi\)
\(860\) 0 0
\(861\) 5.90744 18.1812i 0.201325 0.619615i
\(862\) 2.84474 + 8.75521i 0.0968923 + 0.298204i
\(863\) 5.05071 + 15.5445i 0.171928 + 0.529141i 0.999480 0.0322489i \(-0.0102669\pi\)
−0.827552 + 0.561390i \(0.810267\pi\)
\(864\) 2.56654 7.89900i 0.0873155 0.268729i
\(865\) 0 0
\(866\) 10.7529 + 33.0941i 0.365400 + 1.12458i
\(867\) −22.1886 + 16.1210i −0.753565 + 0.547497i
\(868\) 9.70607 0.329445
\(869\) −5.13308 + 3.72940i −0.174128 + 0.126511i
\(870\) 0 0
\(871\) 18.5829 + 13.5013i 0.629659 + 0.457474i
\(872\) 8.34038 + 6.05964i 0.282441 + 0.205205i
\(873\) −19.8763 + 61.1728i −0.672709 + 2.07039i
\(874\) 12.9877 0.439315
\(875\) 0 0
\(876\) 44.3426 1.49820
\(877\) 10.9717 33.7673i 0.370487 1.14024i −0.575986 0.817459i \(-0.695382\pi\)
0.946473 0.322782i \(-0.104618\pi\)
\(878\) −6.75517 4.90792i −0.227976 0.165634i
\(879\) 16.4617 + 11.9601i 0.555240 + 0.403405i
\(880\) 0 0
\(881\) 25.5378 18.5543i 0.860390 0.625110i −0.0676008 0.997712i \(-0.521534\pi\)
0.927991 + 0.372602i \(0.121534\pi\)
\(882\) 21.1042 0.710615
\(883\) 28.2592 20.5315i 0.950997 0.690940i −4.54670e−5 1.00000i \(-0.500014\pi\)
0.951042 + 0.309060i \(0.100014\pi\)
\(884\) −2.08058 6.40337i −0.0699775 0.215369i
\(885\) 0 0
\(886\) −0.370470 + 1.14019i −0.0124462 + 0.0383054i
\(887\) 13.2668 + 40.8311i 0.445456 + 1.37097i 0.881982 + 0.471282i \(0.156209\pi\)
−0.436526 + 0.899692i \(0.643791\pi\)
\(888\) 1.20531 + 3.70957i 0.0404476 + 0.124485i
\(889\) 0.188810 0.581099i 0.00633250 0.0194894i
\(890\) 0 0
\(891\) −4.10085 12.6211i −0.137384 0.422823i
\(892\) 2.62535 1.90743i 0.0879033 0.0638655i
\(893\) 3.06598 0.102599
\(894\) 4.03076 2.92852i 0.134809 0.0979442i
\(895\) 0 0
\(896\) −1.48322 1.07763i −0.0495510 0.0360009i
\(897\) 45.0646 + 32.7413i 1.50466 + 1.09320i
\(898\) −10.1343 + 31.1902i −0.338186 + 1.04083i
\(899\) −40.1532 −1.33918
\(900\) 0 0
\(901\) −18.1487 −0.604622
\(902\) 1.99142 6.12896i 0.0663070 0.204072i
\(903\) −18.9438 13.7635i −0.630410 0.458020i
\(904\) −4.89991 3.55999i −0.162968 0.118404i
\(905\) 0 0
\(906\) 51.0373 37.0808i 1.69560 1.23193i
\(907\) 39.8259 1.32240 0.661199 0.750211i \(-0.270048\pi\)
0.661199 + 0.750211i \(0.270048\pi\)
\(908\) 13.2495 9.62631i 0.439700 0.319460i
\(909\) −23.6229 72.7038i −0.783522 2.41143i
\(910\) 0 0
\(911\) −0.522189 + 1.60713i −0.0173009 + 0.0532467i −0.959334 0.282273i \(-0.908912\pi\)
0.942033 + 0.335519i \(0.108912\pi\)
\(912\) 1.53299 + 4.71806i 0.0507623 + 0.156230i
\(913\) −3.61034 11.1115i −0.119485 0.367737i
\(914\) 6.11496 18.8199i 0.202265 0.622508i
\(915\) 0 0
\(916\) −1.57289 4.84085i −0.0519697 0.159946i
\(917\) −7.68015 + 5.57995i −0.253621 + 0.184266i
\(918\) −23.1281 −0.763340
\(919\) 24.2013 17.5833i 0.798327 0.580019i −0.112096 0.993697i \(-0.535756\pi\)
0.910423 + 0.413679i \(0.135756\pi\)
\(920\) 0 0
\(921\) 6.94836 + 5.04828i 0.228956 + 0.166346i
\(922\) 7.60456 + 5.52504i 0.250443 + 0.181957i
\(923\) 0.228257 0.702504i 0.00751318 0.0231232i
\(924\) −9.97091 −0.328019
\(925\) 0 0
\(926\) 17.7329 0.582739
\(927\) 4.71929 14.5245i 0.155002 0.477047i
\(928\) 6.13597 + 4.45805i 0.201423 + 0.146343i
\(929\) 12.8664 + 9.34795i 0.422131 + 0.306696i 0.778495 0.627651i \(-0.215983\pi\)
−0.356363 + 0.934347i \(0.615983\pi\)
\(930\) 0 0
\(931\) −4.92303 + 3.57679i −0.161346 + 0.117225i
\(932\) 1.66296 0.0544721
\(933\) −49.5557 + 36.0043i −1.62238 + 1.17873i
\(934\) 6.75535 + 20.7908i 0.221042 + 0.680297i
\(935\) 0 0
\(936\) −4.33337 + 13.3367i −0.141640 + 0.435925i
\(937\) −14.2973 44.0026i −0.467073 1.43750i −0.856357 0.516384i \(-0.827278\pi\)
0.389284 0.921118i \(-0.372722\pi\)
\(938\) −5.38220 16.5647i −0.175735 0.540856i
\(939\) 15.0585 46.3454i 0.491417 1.51243i
\(940\) 0 0
\(941\) −3.60650 11.0997i −0.117569 0.361839i 0.874906 0.484294i \(-0.160923\pi\)
−0.992474 + 0.122455i \(0.960923\pi\)
\(942\) 25.0824 18.2234i 0.817228 0.593751i
\(943\) 27.2988 0.888971
\(944\) 7.33001 5.32556i 0.238571 0.173332i
\(945\) 0 0
\(946\) −6.38602 4.63972i −0.207628 0.150850i
\(947\) −2.37336 1.72435i −0.0771238 0.0560337i 0.548555 0.836114i \(-0.315178\pi\)
−0.625679 + 0.780081i \(0.715178\pi\)
\(948\) 3.17242 9.76370i 0.103035 0.317110i
\(949\) −36.1421 −1.17322
\(950\) 0 0
\(951\) 48.9638 1.58776
\(952\) −1.57763 + 4.85544i −0.0511313 + 0.157366i
\(953\) −8.03924 5.84085i −0.260417 0.189204i 0.449914 0.893072i \(-0.351455\pi\)
−0.710331 + 0.703868i \(0.751455\pi\)
\(954\) 30.5805 + 22.2180i 0.990080 + 0.719335i
\(955\) 0 0
\(956\) −10.3553 + 7.52354i −0.334913 + 0.243329i
\(957\) 41.2488 1.33339
\(958\) −4.94352 + 3.59168i −0.159718 + 0.116042i
\(959\) −11.0607 34.0413i −0.357168 1.09925i
\(960\) 0 0
\(961\) −0.918471 + 2.82676i −0.0296281 + 0.0911859i
\(962\) −0.982407 3.02354i −0.0316741 0.0974828i
\(963\) −33.7021 103.725i −1.08604 3.34248i
\(964\) 0.122209 0.376121i 0.00393610 0.0121141i
\(965\) 0 0
\(966\) −13.0521 40.1702i −0.419944 1.29246i
\(967\) 36.7193 26.6781i 1.18081 0.857910i 0.188549 0.982064i \(-0.439621\pi\)
0.992263 + 0.124153i \(0.0396215\pi\)
\(968\) 7.63877 0.245519
\(969\) 11.1760 8.11987i 0.359026 0.260848i
\(970\) 0 0
\(971\) 3.78844 + 2.75246i 0.121577 + 0.0883307i 0.646912 0.762565i \(-0.276060\pi\)
−0.525335 + 0.850895i \(0.676060\pi\)
\(972\) −2.78640 2.02444i −0.0893737 0.0649338i
\(973\) 4.50688 13.8707i 0.144484 0.444675i
\(974\) 5.06189 0.162194
\(975\) 0 0
\(976\) 2.58794 0.0828379
\(977\) −0.991339 + 3.05103i −0.0317157 + 0.0976110i −0.965661 0.259804i \(-0.916342\pi\)
0.933946 + 0.357415i \(0.116342\pi\)
\(978\) 24.9845 + 18.1523i 0.798917 + 0.580447i
\(979\) −4.92498 3.57820i −0.157403 0.114360i
\(980\) 0 0
\(981\) −48.3726 + 35.1448i −1.54442 + 1.12209i
\(982\) −2.38228 −0.0760216
\(983\) 15.8337 11.5038i 0.505015 0.366915i −0.305914 0.952059i \(-0.598962\pi\)
0.810929 + 0.585144i \(0.198962\pi\)
\(984\) 3.22218 + 9.91686i 0.102719 + 0.316138i
\(985\) 0 0
\(986\) 6.52652 20.0866i 0.207847 0.639687i
\(987\) −3.08118 9.48290i −0.0980751 0.301844i
\(988\) −1.24949 3.84552i −0.0397514 0.122342i
\(989\) 10.3328 31.8011i 0.328564 1.01122i
\(990\) 0 0
\(991\) 13.9762 + 43.0144i 0.443969 + 1.36640i 0.883610 + 0.468223i \(0.155106\pi\)
−0.439641 + 0.898173i \(0.644894\pi\)
\(992\) −4.28304 + 3.11181i −0.135987 + 0.0988000i
\(993\) −81.4913 −2.58605
\(994\) −0.453127 + 0.329216i −0.0143723 + 0.0104421i
\(995\) 0 0
\(996\) 15.2937 + 11.1115i 0.484598 + 0.352081i
\(997\) −46.9808 34.1335i −1.48790 1.08102i −0.974904 0.222626i \(-0.928537\pi\)
−0.512991 0.858394i \(-0.671463\pi\)
\(998\) 0.0155532 0.0478679i 0.000492329 0.00151523i
\(999\) −10.9206 −0.345512
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 250.2.d.d.101.2 8
5.2 odd 4 250.2.e.c.149.2 16
5.3 odd 4 250.2.e.c.149.3 16
5.4 even 2 50.2.d.b.21.1 8
15.14 odd 2 450.2.h.e.271.1 8
20.19 odd 2 400.2.u.d.321.2 8
25.6 even 5 inner 250.2.d.d.151.2 8
25.8 odd 20 250.2.e.c.99.2 16
25.9 even 10 1250.2.a.l.1.4 4
25.12 odd 20 1250.2.b.e.1249.4 8
25.13 odd 20 1250.2.b.e.1249.5 8
25.16 even 5 1250.2.a.f.1.1 4
25.17 odd 20 250.2.e.c.99.3 16
25.19 even 10 50.2.d.b.31.1 yes 8
75.44 odd 10 450.2.h.e.181.1 8
100.19 odd 10 400.2.u.d.81.2 8
100.59 odd 10 10000.2.a.t.1.1 4
100.91 odd 10 10000.2.a.x.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.2.d.b.21.1 8 5.4 even 2
50.2.d.b.31.1 yes 8 25.19 even 10
250.2.d.d.101.2 8 1.1 even 1 trivial
250.2.d.d.151.2 8 25.6 even 5 inner
250.2.e.c.99.2 16 25.8 odd 20
250.2.e.c.99.3 16 25.17 odd 20
250.2.e.c.149.2 16 5.2 odd 4
250.2.e.c.149.3 16 5.3 odd 4
400.2.u.d.81.2 8 100.19 odd 10
400.2.u.d.321.2 8 20.19 odd 2
450.2.h.e.181.1 8 75.44 odd 10
450.2.h.e.271.1 8 15.14 odd 2
1250.2.a.f.1.1 4 25.16 even 5
1250.2.a.l.1.4 4 25.9 even 10
1250.2.b.e.1249.4 8 25.12 odd 20
1250.2.b.e.1249.5 8 25.13 odd 20
10000.2.a.t.1.1 4 100.59 odd 10
10000.2.a.x.1.4 4 100.91 odd 10