Properties

Label 95.2.e.c.11.2
Level $95$
Weight $2$
Character 95.11
Analytic conductor $0.759$
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] = [95,2,Mod(11,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.11");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.e (of order \(3\), degree \(2\), 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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.2
Root \(0.689667 - 1.19454i\) of defining polynomial
Character \(\chi\) \(=\) 95.11
Dual form 95.2.e.c.26.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.548719 + 0.950409i) q^{2} +(0.189667 - 0.328513i) q^{3} +(0.397815 + 0.689035i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.208148 + 0.360522i) q^{6} +1.89307 q^{7} -3.06803 q^{8} +(1.42805 + 2.47346i) q^{9} +O(q^{10})\) \(q+(-0.548719 + 0.950409i) q^{2} +(0.189667 - 0.328513i) q^{3} +(0.397815 + 0.689035i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.208148 + 0.360522i) q^{6} +1.89307 q^{7} -3.06803 q^{8} +(1.42805 + 2.47346i) q^{9} +(-0.548719 - 0.950409i) q^{10} +0.134400 q^{11} +0.301809 q^{12} +(-1.75687 - 3.04298i) q^{13} +(-1.03876 + 1.79919i) q^{14} +(0.189667 + 0.328513i) q^{15} +(0.887858 - 1.53781i) q^{16} +(0.830615 - 1.43867i) q^{17} -3.13440 q^{18} +(2.10596 - 3.81640i) q^{19} -0.795629 q^{20} +(0.359052 - 0.621897i) q^{21} +(-0.0737478 + 0.127735i) q^{22} +(-2.68492 - 4.65042i) q^{23} +(-0.581904 + 1.00789i) q^{24} +(-0.500000 - 0.866025i) q^{25} +3.85611 q^{26} +2.22142 q^{27} +(0.753090 + 1.30439i) q^{28} +(-2.48530 - 4.30466i) q^{29} -0.416295 q^{30} +6.56472 q^{31} +(-2.09366 - 3.62633i) q^{32} +(0.0254912 - 0.0441521i) q^{33} +(0.911548 + 1.57885i) q^{34} +(-0.946534 + 1.63944i) q^{35} +(-1.13620 + 1.96796i) q^{36} -1.69819 q^{37} +(2.47156 + 4.09566i) q^{38} -1.33288 q^{39} +(1.53402 - 2.65699i) q^{40} +(-5.31637 + 9.20823i) q^{41} +(0.394038 + 0.682493i) q^{42} +(-4.25392 + 7.36801i) q^{43} +(0.0534662 + 0.0926063i) q^{44} -2.85611 q^{45} +5.89307 q^{46} +(5.55771 + 9.62623i) q^{47} +(-0.336794 - 0.583345i) q^{48} -3.41630 q^{49} +1.09744 q^{50} +(-0.315080 - 0.545735i) q^{51} +(1.39781 - 2.42109i) q^{52} +(0.132424 + 0.229365i) q^{53} +(-1.21894 + 2.11126i) q^{54} +(-0.0672000 + 0.116394i) q^{55} -5.80799 q^{56} +(-0.854305 - 1.41568i) q^{57} +5.45492 q^{58} +(3.44833 - 5.97269i) q^{59} +(-0.150905 + 0.261374i) q^{60} +(-4.58794 - 7.94655i) q^{61} +(-3.60219 + 6.23917i) q^{62} +(2.70340 + 4.68243i) q^{63} +8.14676 q^{64} +3.51373 q^{65} +(0.0279750 + 0.0484542i) q^{66} +(1.47677 + 2.55784i) q^{67} +1.32172 q^{68} -2.03696 q^{69} +(-1.03876 - 1.79919i) q^{70} +(-0.664176 + 1.15039i) q^{71} +(-4.38131 - 7.58865i) q^{72} +(3.17119 - 5.49266i) q^{73} +(0.931830 - 1.61398i) q^{74} -0.379334 q^{75} +(3.46742 - 0.0671384i) q^{76} +0.254428 q^{77} +(0.731376 - 1.26678i) q^{78} +(0.733639 - 1.27070i) q^{79} +(0.887858 + 1.53781i) q^{80} +(-3.86283 + 6.69062i) q^{81} +(-5.83439 - 10.1055i) q^{82} +7.44736 q^{83} +0.571345 q^{84} +(0.830615 + 1.43867i) q^{85} +(-4.66842 - 8.08593i) q^{86} -1.88551 q^{87} -0.412343 q^{88} +(-4.86804 - 8.43169i) q^{89} +(1.56720 - 2.71447i) q^{90} +(-3.32587 - 5.76057i) q^{91} +(2.13620 - 3.70001i) q^{92} +(1.24511 - 2.15659i) q^{93} -12.1985 q^{94} +(2.25212 + 3.73202i) q^{95} -1.58839 q^{96} +(-8.73447 + 15.1285i) q^{97} +(1.87459 - 3.24688i) q^{98} +(0.191930 + 0.332433i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 3 q^{3} - 5 q^{4} - 4 q^{5} - 2 q^{6} - 8 q^{7} + 24 q^{8} - q^{9} - q^{10} - 4 q^{11} + 12 q^{12} - 7 q^{13} + q^{14} - 3 q^{15} - 7 q^{16} + q^{17} - 20 q^{18} + 5 q^{19} + 10 q^{20} + 4 q^{21} - 2 q^{22} - 2 q^{23} - 23 q^{24} - 4 q^{25} + 6 q^{26} + 24 q^{27} + 19 q^{28} + q^{29} + 4 q^{30} - 30 q^{32} - 19 q^{33} - 15 q^{34} + 4 q^{35} + 7 q^{36} - 4 q^{37} + 13 q^{38} + 30 q^{39} - 12 q^{40} + 8 q^{41} + 15 q^{42} - q^{43} + 12 q^{44} + 2 q^{45} + 24 q^{46} + 12 q^{47} - 23 q^{48} - 20 q^{49} + 2 q^{50} - 22 q^{51} + 3 q^{52} + 5 q^{53} + 34 q^{54} + 2 q^{55} - 82 q^{56} + 7 q^{57} - 54 q^{58} + 5 q^{59} - 6 q^{60} - 37 q^{62} + 3 q^{63} + 112 q^{64} + 14 q^{65} + 31 q^{66} - 4 q^{67} + 32 q^{68} - 18 q^{69} + q^{70} - 20 q^{71} - 17 q^{72} + 20 q^{73} - 25 q^{74} + 6 q^{75} + 63 q^{76} + 28 q^{77} + 18 q^{78} - 17 q^{79} - 7 q^{80} - 12 q^{81} - 21 q^{82} + 2 q^{83} - 40 q^{84} + q^{85} - 8 q^{86} - 32 q^{87} - 14 q^{88} - 11 q^{89} + 10 q^{90} - 6 q^{91} + q^{92} + 8 q^{93} - 62 q^{94} - 4 q^{95} + 42 q^{96} - q^{97} - 9 q^{98} - 38 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.548719 + 0.950409i −0.388003 + 0.672041i −0.992181 0.124809i \(-0.960168\pi\)
0.604178 + 0.796850i \(0.293502\pi\)
\(3\) 0.189667 0.328513i 0.109504 0.189667i −0.806065 0.591827i \(-0.798407\pi\)
0.915570 + 0.402160i \(0.131740\pi\)
\(4\) 0.397815 + 0.689035i 0.198907 + 0.344518i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0.208148 + 0.360522i 0.0849759 + 0.147183i
\(7\) 1.89307 0.715512 0.357756 0.933815i \(-0.383542\pi\)
0.357756 + 0.933815i \(0.383542\pi\)
\(8\) −3.06803 −1.08471
\(9\) 1.42805 + 2.47346i 0.476018 + 0.824487i
\(10\) −0.548719 0.950409i −0.173520 0.300546i
\(11\) 0.134400 0.0405231 0.0202615 0.999795i \(-0.493550\pi\)
0.0202615 + 0.999795i \(0.493550\pi\)
\(12\) 0.301809 0.0871248
\(13\) −1.75687 3.04298i −0.487267 0.843972i 0.512626 0.858612i \(-0.328673\pi\)
−0.999893 + 0.0146407i \(0.995340\pi\)
\(14\) −1.03876 + 1.79919i −0.277621 + 0.480854i
\(15\) 0.189667 + 0.328513i 0.0489718 + 0.0848216i
\(16\) 0.887858 1.53781i 0.221964 0.384454i
\(17\) 0.830615 1.43867i 0.201454 0.348928i −0.747543 0.664213i \(-0.768767\pi\)
0.948997 + 0.315285i \(0.102100\pi\)
\(18\) −3.13440 −0.738785
\(19\) 2.10596 3.81640i 0.483141 0.875543i
\(20\) −0.795629 −0.177908
\(21\) 0.359052 0.621897i 0.0783516 0.135709i
\(22\) −0.0737478 + 0.127735i −0.0157231 + 0.0272332i
\(23\) −2.68492 4.65042i −0.559844 0.969679i −0.997509 0.0705407i \(-0.977528\pi\)
0.437664 0.899138i \(-0.355806\pi\)
\(24\) −0.581904 + 1.00789i −0.118781 + 0.205734i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 3.85611 0.756245
\(27\) 2.22142 0.427512
\(28\) 0.753090 + 1.30439i 0.142321 + 0.246507i
\(29\) −2.48530 4.30466i −0.461508 0.799355i 0.537528 0.843246i \(-0.319358\pi\)
−0.999036 + 0.0438905i \(0.986025\pi\)
\(30\) −0.416295 −0.0760048
\(31\) 6.56472 1.17906 0.589529 0.807747i \(-0.299313\pi\)
0.589529 + 0.807747i \(0.299313\pi\)
\(32\) −2.09366 3.62633i −0.370111 0.641050i
\(33\) 0.0254912 0.0441521i 0.00443745 0.00768589i
\(34\) 0.911548 + 1.57885i 0.156329 + 0.270770i
\(35\) −0.946534 + 1.63944i −0.159993 + 0.277117i
\(36\) −1.13620 + 1.96796i −0.189367 + 0.327993i
\(37\) −1.69819 −0.279181 −0.139590 0.990209i \(-0.544579\pi\)
−0.139590 + 0.990209i \(0.544579\pi\)
\(38\) 2.47156 + 4.09566i 0.400940 + 0.664404i
\(39\) −1.33288 −0.213431
\(40\) 1.53402 2.65699i 0.242549 0.420107i
\(41\) −5.31637 + 9.20823i −0.830278 + 1.43808i 0.0675398 + 0.997717i \(0.478485\pi\)
−0.897818 + 0.440367i \(0.854848\pi\)
\(42\) 0.394038 + 0.682493i 0.0608013 + 0.105311i
\(43\) −4.25392 + 7.36801i −0.648717 + 1.12361i 0.334713 + 0.942320i \(0.391361\pi\)
−0.983430 + 0.181290i \(0.941973\pi\)
\(44\) 0.0534662 + 0.0926063i 0.00806034 + 0.0139609i
\(45\) −2.85611 −0.425763
\(46\) 5.89307 0.868885
\(47\) 5.55771 + 9.62623i 0.810675 + 1.40413i 0.912392 + 0.409316i \(0.134233\pi\)
−0.101718 + 0.994813i \(0.532434\pi\)
\(48\) −0.336794 0.583345i −0.0486121 0.0841986i
\(49\) −3.41630 −0.488042
\(50\) 1.09744 0.155201
\(51\) −0.315080 0.545735i −0.0441201 0.0764182i
\(52\) 1.39781 2.42109i 0.193842 0.335744i
\(53\) 0.132424 + 0.229365i 0.0181898 + 0.0315057i 0.874977 0.484164i \(-0.160876\pi\)
−0.856787 + 0.515670i \(0.827543\pi\)
\(54\) −1.21894 + 2.11126i −0.165876 + 0.287306i
\(55\) −0.0672000 + 0.116394i −0.00906124 + 0.0156945i
\(56\) −5.80799 −0.776125
\(57\) −0.854305 1.41568i −0.113155 0.187511i
\(58\) 5.45492 0.716266
\(59\) 3.44833 5.97269i 0.448935 0.777578i −0.549382 0.835571i \(-0.685137\pi\)
0.998317 + 0.0579932i \(0.0184702\pi\)
\(60\) −0.150905 + 0.261374i −0.0194817 + 0.0337433i
\(61\) −4.58794 7.94655i −0.587426 1.01745i −0.994568 0.104087i \(-0.966808\pi\)
0.407142 0.913365i \(-0.366525\pi\)
\(62\) −3.60219 + 6.23917i −0.457478 + 0.792375i
\(63\) 2.70340 + 4.68243i 0.340596 + 0.589930i
\(64\) 8.14676 1.01834
\(65\) 3.51373 0.435825
\(66\) 0.0279750 + 0.0484542i 0.00344349 + 0.00596430i
\(67\) 1.47677 + 2.55784i 0.180416 + 0.312490i 0.942022 0.335550i \(-0.108922\pi\)
−0.761606 + 0.648040i \(0.775589\pi\)
\(68\) 1.32172 0.160282
\(69\) −2.03696 −0.245221
\(70\) −1.03876 1.79919i −0.124156 0.215044i
\(71\) −0.664176 + 1.15039i −0.0788232 + 0.136526i −0.902742 0.430181i \(-0.858450\pi\)
0.823919 + 0.566707i \(0.191783\pi\)
\(72\) −4.38131 7.58865i −0.516342 0.894331i
\(73\) 3.17119 5.49266i 0.371159 0.642867i −0.618585 0.785718i \(-0.712294\pi\)
0.989744 + 0.142851i \(0.0456271\pi\)
\(74\) 0.931830 1.61398i 0.108323 0.187621i
\(75\) −0.379334 −0.0438017
\(76\) 3.46742 0.0671384i 0.397740 0.00770130i
\(77\) 0.254428 0.0289948
\(78\) 0.731376 1.26678i 0.0828120 0.143435i
\(79\) 0.733639 1.27070i 0.0825408 0.142965i −0.821800 0.569776i \(-0.807030\pi\)
0.904341 + 0.426811i \(0.140363\pi\)
\(80\) 0.887858 + 1.53781i 0.0992655 + 0.171933i
\(81\) −3.86283 + 6.69062i −0.429203 + 0.743402i
\(82\) −5.83439 10.1055i −0.644301 1.11596i
\(83\) 7.44736 0.817454 0.408727 0.912657i \(-0.365973\pi\)
0.408727 + 0.912657i \(0.365973\pi\)
\(84\) 0.571345 0.0623388
\(85\) 0.830615 + 1.43867i 0.0900928 + 0.156045i
\(86\) −4.66842 8.08593i −0.503408 0.871929i
\(87\) −1.88551 −0.202148
\(88\) −0.412343 −0.0439559
\(89\) −4.86804 8.43169i −0.516011 0.893757i −0.999827 0.0185878i \(-0.994083\pi\)
0.483816 0.875170i \(-0.339250\pi\)
\(90\) 1.56720 2.71447i 0.165197 0.286130i
\(91\) −3.32587 5.76057i −0.348646 0.603872i
\(92\) 2.13620 3.70001i 0.222714 0.385753i
\(93\) 1.24511 2.15659i 0.129112 0.223628i
\(94\) −12.1985 −1.25818
\(95\) 2.25212 + 3.73202i 0.231063 + 0.382897i
\(96\) −1.58839 −0.162115
\(97\) −8.73447 + 15.1285i −0.886851 + 1.53607i −0.0432737 + 0.999063i \(0.513779\pi\)
−0.843577 + 0.537008i \(0.819555\pi\)
\(98\) 1.87459 3.24688i 0.189362 0.327984i
\(99\) 0.191930 + 0.332433i 0.0192897 + 0.0334108i
\(100\) 0.397815 0.689035i 0.0397815 0.0689035i
\(101\) −2.69865 4.67420i −0.268526 0.465101i 0.699955 0.714187i \(-0.253203\pi\)
−0.968481 + 0.249086i \(0.919870\pi\)
\(102\) 0.691562 0.0684749
\(103\) 2.14750 0.211599 0.105800 0.994387i \(-0.466260\pi\)
0.105800 + 0.994387i \(0.466260\pi\)
\(104\) 5.39012 + 9.33596i 0.528545 + 0.915467i
\(105\) 0.359052 + 0.621897i 0.0350399 + 0.0606909i
\(106\) −0.290654 −0.0282308
\(107\) −1.00093 −0.0967631 −0.0483815 0.998829i \(-0.515406\pi\)
−0.0483815 + 0.998829i \(0.515406\pi\)
\(108\) 0.883713 + 1.53064i 0.0850353 + 0.147285i
\(109\) −8.13145 + 14.0841i −0.778852 + 1.34901i 0.153752 + 0.988109i \(0.450864\pi\)
−0.932604 + 0.360902i \(0.882469\pi\)
\(110\) −0.0737478 0.127735i −0.00703158 0.0121790i
\(111\) −0.322091 + 0.557877i −0.0305715 + 0.0529514i
\(112\) 1.68077 2.91119i 0.158818 0.275081i
\(113\) 0.843010 0.0793037 0.0396519 0.999214i \(-0.487375\pi\)
0.0396519 + 0.999214i \(0.487375\pi\)
\(114\) 1.81425 0.0351287i 0.169920 0.00329010i
\(115\) 5.36984 0.500740
\(116\) 1.97737 3.42491i 0.183595 0.317995i
\(117\) 5.01780 8.69108i 0.463896 0.803491i
\(118\) 3.78433 + 6.55466i 0.348376 + 0.603405i
\(119\) 1.57241 2.72349i 0.144143 0.249662i
\(120\) −0.581904 1.00789i −0.0531203 0.0920071i
\(121\) −10.9819 −0.998358
\(122\) 10.0700 0.911692
\(123\) 2.01668 + 3.49299i 0.181838 + 0.314953i
\(124\) 2.61154 + 4.52332i 0.234523 + 0.406206i
\(125\) 1.00000 0.0894427
\(126\) −5.93363 −0.528610
\(127\) −9.36984 16.2290i −0.831439 1.44009i −0.896897 0.442239i \(-0.854184\pi\)
0.0654584 0.997855i \(-0.479149\pi\)
\(128\) −0.282960 + 0.490101i −0.0250104 + 0.0433193i
\(129\) 1.61366 + 2.79493i 0.142074 + 0.246080i
\(130\) −1.92805 + 3.33949i −0.169101 + 0.292892i
\(131\) −1.44322 + 2.49973i −0.126095 + 0.218402i −0.922160 0.386808i \(-0.873578\pi\)
0.796066 + 0.605210i \(0.206911\pi\)
\(132\) 0.0405631 0.00353057
\(133\) 3.98673 7.22471i 0.345693 0.626461i
\(134\) −3.24133 −0.280008
\(135\) −1.11071 + 1.92381i −0.0955946 + 0.165575i
\(136\) −2.54835 + 4.41387i −0.218519 + 0.378487i
\(137\) 9.41579 + 16.3086i 0.804445 + 1.39334i 0.916665 + 0.399656i \(0.130871\pi\)
−0.112220 + 0.993683i \(0.535796\pi\)
\(138\) 1.11772 1.93595i 0.0951466 0.164799i
\(139\) 9.08974 + 15.7439i 0.770982 + 1.33538i 0.937025 + 0.349262i \(0.113568\pi\)
−0.166043 + 0.986118i \(0.553099\pi\)
\(140\) −1.50618 −0.127295
\(141\) 4.21645 0.355089
\(142\) −0.728892 1.26248i −0.0611672 0.105945i
\(143\) −0.236123 0.408977i −0.0197456 0.0342003i
\(144\) 5.07163 0.422636
\(145\) 4.97059 0.412785
\(146\) 3.48018 + 6.02785i 0.288022 + 0.498868i
\(147\) −0.647958 + 1.12230i −0.0534427 + 0.0925655i
\(148\) −0.675565 1.17011i −0.0555311 0.0961827i
\(149\) 11.1272 19.2728i 0.911573 1.57889i 0.0997308 0.995014i \(-0.468202\pi\)
0.811842 0.583877i \(-0.198465\pi\)
\(150\) 0.208148 0.360522i 0.0169952 0.0294365i
\(151\) 3.33482 0.271384 0.135692 0.990751i \(-0.456674\pi\)
0.135692 + 0.990751i \(0.456674\pi\)
\(152\) −6.46116 + 11.7088i −0.524069 + 0.949712i
\(153\) 4.74465 0.383582
\(154\) −0.139610 + 0.241811i −0.0112501 + 0.0194857i
\(155\) −3.28236 + 5.68521i −0.263645 + 0.456647i
\(156\) −0.530238 0.918400i −0.0424530 0.0735308i
\(157\) −3.63145 + 6.28986i −0.289822 + 0.501986i −0.973767 0.227548i \(-0.926929\pi\)
0.683945 + 0.729533i \(0.260263\pi\)
\(158\) 0.805123 + 1.39451i 0.0640522 + 0.110942i
\(159\) 0.100466 0.00796744
\(160\) 4.18732 0.331037
\(161\) −5.08273 8.80355i −0.400576 0.693817i
\(162\) −4.23922 7.34254i −0.333064 0.576884i
\(163\) −19.7783 −1.54916 −0.774578 0.632478i \(-0.782038\pi\)
−0.774578 + 0.632478i \(0.782038\pi\)
\(164\) −8.45972 −0.660593
\(165\) 0.0254912 + 0.0441521i 0.00198449 + 0.00343723i
\(166\) −4.08651 + 7.07805i −0.317175 + 0.549363i
\(167\) 1.70160 + 2.94726i 0.131674 + 0.228066i 0.924322 0.381614i \(-0.124632\pi\)
−0.792648 + 0.609679i \(0.791298\pi\)
\(168\) −1.10158 + 1.90800i −0.0849890 + 0.147205i
\(169\) 0.326838 0.566100i 0.0251414 0.0435461i
\(170\) −1.82310 −0.139825
\(171\) 12.4471 0.241010i 0.951857 0.0184305i
\(172\) −6.76909 −0.516138
\(173\) 5.29286 9.16750i 0.402409 0.696992i −0.591607 0.806226i \(-0.701506\pi\)
0.994016 + 0.109234i \(0.0348398\pi\)
\(174\) 1.03462 1.79201i 0.0784341 0.135852i
\(175\) −0.946534 1.63944i −0.0715512 0.123930i
\(176\) 0.119328 0.206682i 0.00899469 0.0155793i
\(177\) −1.30807 2.26564i −0.0983205 0.170296i
\(178\) 10.6847 0.800855
\(179\) −14.6024 −1.09144 −0.545718 0.837969i \(-0.683743\pi\)
−0.545718 + 0.837969i \(0.683743\pi\)
\(180\) −1.13620 1.96796i −0.0846874 0.146683i
\(181\) 2.71630 + 4.70478i 0.201901 + 0.349703i 0.949141 0.314851i \(-0.101955\pi\)
−0.747240 + 0.664555i \(0.768621\pi\)
\(182\) 7.29987 0.541102
\(183\) −3.48072 −0.257303
\(184\) 8.23742 + 14.2676i 0.607270 + 1.05182i
\(185\) 0.849095 1.47068i 0.0624267 0.108126i
\(186\) 1.36643 + 2.36673i 0.100192 + 0.173537i
\(187\) 0.111635 0.193357i 0.00816353 0.0141396i
\(188\) −4.42187 + 7.65891i −0.322498 + 0.558583i
\(189\) 4.20530 0.305890
\(190\) −4.78273 + 0.0926063i −0.346975 + 0.00671836i
\(191\) 20.4758 1.48157 0.740787 0.671740i \(-0.234453\pi\)
0.740787 + 0.671740i \(0.234453\pi\)
\(192\) 1.54517 2.67631i 0.111513 0.193146i
\(193\) −5.51176 + 9.54664i −0.396745 + 0.687182i −0.993322 0.115373i \(-0.963194\pi\)
0.596577 + 0.802556i \(0.296527\pi\)
\(194\) −9.58554 16.6026i −0.688202 1.19200i
\(195\) 0.666439 1.15431i 0.0477247 0.0826616i
\(196\) −1.35905 2.35395i −0.0970752 0.168139i
\(197\) −19.8532 −1.41448 −0.707242 0.706971i \(-0.750061\pi\)
−0.707242 + 0.706971i \(0.750061\pi\)
\(198\) −0.421263 −0.0299379
\(199\) −10.5013 18.1888i −0.744417 1.28937i −0.950467 0.310826i \(-0.899394\pi\)
0.206050 0.978542i \(-0.433939\pi\)
\(200\) 1.53402 + 2.65699i 0.108471 + 0.187878i
\(201\) 1.12038 0.0790254
\(202\) 5.92321 0.416756
\(203\) −4.70483 8.14901i −0.330215 0.571948i
\(204\) 0.250687 0.434203i 0.0175516 0.0304003i
\(205\) −5.31637 9.20823i −0.371312 0.643131i
\(206\) −1.17837 + 2.04100i −0.0821011 + 0.142203i
\(207\) 7.66842 13.2821i 0.532992 0.923169i
\(208\) −6.23939 −0.432624
\(209\) 0.283041 0.512924i 0.0195784 0.0354797i
\(210\) −0.788075 −0.0543824
\(211\) 6.41284 11.1074i 0.441478 0.764663i −0.556321 0.830967i \(-0.687788\pi\)
0.997799 + 0.0663046i \(0.0211209\pi\)
\(212\) −0.105360 + 0.182489i −0.00723617 + 0.0125334i
\(213\) 0.251944 + 0.436380i 0.0172629 + 0.0299003i
\(214\) 0.549227 0.951289i 0.0375444 0.0650288i
\(215\) −4.25392 7.36801i −0.290115 0.502494i
\(216\) −6.81538 −0.463728
\(217\) 12.4275 0.843630
\(218\) −8.92377 15.4564i −0.604394 1.04684i
\(219\) −1.20294 2.08355i −0.0812870 0.140793i
\(220\) −0.106932 −0.00720939
\(221\) −5.83712 −0.392647
\(222\) −0.353475 0.612236i −0.0237237 0.0410906i
\(223\) −10.1972 + 17.6621i −0.682856 + 1.18274i 0.291249 + 0.956647i \(0.405929\pi\)
−0.974105 + 0.226095i \(0.927404\pi\)
\(224\) −3.96344 6.86488i −0.264819 0.458679i
\(225\) 1.42805 2.47346i 0.0952035 0.164897i
\(226\) −0.462576 + 0.801205i −0.0307701 + 0.0532954i
\(227\) 25.4172 1.68700 0.843500 0.537129i \(-0.180491\pi\)
0.843500 + 0.537129i \(0.180491\pi\)
\(228\) 0.635598 1.15182i 0.0420935 0.0762814i
\(229\) 2.21553 0.146406 0.0732030 0.997317i \(-0.476678\pi\)
0.0732030 + 0.997317i \(0.476678\pi\)
\(230\) −2.94653 + 5.10355i −0.194289 + 0.336518i
\(231\) 0.0482566 0.0835829i 0.00317505 0.00549935i
\(232\) 7.62496 + 13.2068i 0.500603 + 0.867071i
\(233\) 7.07882 12.2609i 0.463749 0.803236i −0.535395 0.844602i \(-0.679837\pi\)
0.999144 + 0.0413652i \(0.0131707\pi\)
\(234\) 5.50672 + 9.53792i 0.359986 + 0.623514i
\(235\) −11.1154 −0.725089
\(236\) 5.48719 0.357186
\(237\) −0.278294 0.482019i −0.0180771 0.0313105i
\(238\) 1.72562 + 2.98887i 0.111855 + 0.193739i
\(239\) 3.01476 0.195008 0.0975042 0.995235i \(-0.468914\pi\)
0.0975042 + 0.995235i \(0.468914\pi\)
\(240\) 0.673589 0.0434800
\(241\) 11.8896 + 20.5934i 0.765877 + 1.32654i 0.939781 + 0.341776i \(0.111028\pi\)
−0.173904 + 0.984763i \(0.555638\pi\)
\(242\) 6.02600 10.4373i 0.387366 0.670937i
\(243\) 4.79743 + 8.30939i 0.307755 + 0.533048i
\(244\) 3.65030 6.32251i 0.233687 0.404757i
\(245\) 1.70815 2.95860i 0.109130 0.189018i
\(246\) −4.42636 −0.282215
\(247\) −15.3131 + 0.296503i −0.974352 + 0.0188660i
\(248\) −20.1407 −1.27894
\(249\) 1.41252 2.44655i 0.0895147 0.155044i
\(250\) −0.548719 + 0.950409i −0.0347040 + 0.0601092i
\(251\) −8.59495 14.8869i −0.542509 0.939653i −0.998759 0.0498012i \(-0.984141\pi\)
0.456250 0.889851i \(-0.349192\pi\)
\(252\) −2.15090 + 3.72548i −0.135494 + 0.234683i
\(253\) −0.360853 0.625016i −0.0226866 0.0392944i
\(254\) 20.5656 1.29040
\(255\) 0.630160 0.0394622
\(256\) 7.83623 + 13.5727i 0.489764 + 0.848297i
\(257\) 9.77143 + 16.9246i 0.609525 + 1.05573i 0.991319 + 0.131481i \(0.0419732\pi\)
−0.381794 + 0.924248i \(0.624693\pi\)
\(258\) −3.54178 −0.220501
\(259\) −3.21479 −0.199757
\(260\) 1.39781 + 2.42109i 0.0866888 + 0.150149i
\(261\) 7.09827 12.2946i 0.439372 0.761014i
\(262\) −1.58384 2.74330i −0.0978502 0.169482i
\(263\) −4.40680 + 7.63280i −0.271735 + 0.470659i −0.969306 0.245857i \(-0.920931\pi\)
0.697571 + 0.716515i \(0.254264\pi\)
\(264\) −0.0782078 + 0.135460i −0.00481336 + 0.00833698i
\(265\) −0.264847 −0.0162694
\(266\) 4.67883 + 7.75336i 0.286878 + 0.475389i
\(267\) −3.69322 −0.226022
\(268\) −1.17496 + 2.03510i −0.0717723 + 0.124313i
\(269\) −0.144181 + 0.249729i −0.00879088 + 0.0152263i −0.870387 0.492368i \(-0.836132\pi\)
0.861596 + 0.507594i \(0.169465\pi\)
\(270\) −1.21894 2.11126i −0.0741820 0.128487i
\(271\) 12.4356 21.5391i 0.755409 1.30841i −0.189761 0.981830i \(-0.560771\pi\)
0.945171 0.326577i \(-0.105895\pi\)
\(272\) −1.47494 2.55466i −0.0894311 0.154899i
\(273\) −2.52323 −0.152713
\(274\) −20.6665 −1.24851
\(275\) −0.0672000 0.116394i −0.00405231 0.00701881i
\(276\) −0.810333 1.40354i −0.0487763 0.0844831i
\(277\) −4.40486 −0.264662 −0.132331 0.991206i \(-0.542246\pi\)
−0.132331 + 0.991206i \(0.542246\pi\)
\(278\) −19.9509 −1.19657
\(279\) 9.37476 + 16.2376i 0.561252 + 0.972118i
\(280\) 2.90399 5.02987i 0.173547 0.300592i
\(281\) 16.3607 + 28.3376i 0.975998 + 1.69048i 0.676600 + 0.736350i \(0.263452\pi\)
0.299398 + 0.954128i \(0.403214\pi\)
\(282\) −2.31365 + 4.00736i −0.137776 + 0.238635i
\(283\) 0.664463 1.15088i 0.0394982 0.0684129i −0.845600 0.533816i \(-0.820757\pi\)
0.885099 + 0.465403i \(0.154091\pi\)
\(284\) −1.05688 −0.0627140
\(285\) 1.65317 0.0320097i 0.0979252 0.00189609i
\(286\) 0.518260 0.0306454
\(287\) −10.0643 + 17.4318i −0.594074 + 1.02897i
\(288\) 5.97972 10.3572i 0.352358 0.610302i
\(289\) 7.12016 + 12.3325i 0.418833 + 0.725440i
\(290\) −2.72746 + 4.72410i −0.160162 + 0.277409i
\(291\) 3.31328 + 5.73877i 0.194228 + 0.336413i
\(292\) 5.04618 0.295305
\(293\) −7.72365 −0.451220 −0.225610 0.974218i \(-0.572438\pi\)
−0.225610 + 0.974218i \(0.572438\pi\)
\(294\) −0.711094 1.23165i −0.0414718 0.0718313i
\(295\) 3.44833 + 5.97269i 0.200770 + 0.347743i
\(296\) 5.21010 0.302831
\(297\) 0.298558 0.0173241
\(298\) 12.2114 + 21.1507i 0.707386 + 1.22523i
\(299\) −9.43409 + 16.3403i −0.545588 + 0.944986i
\(300\) −0.150905 0.261374i −0.00871248 0.0150905i
\(301\) −8.05296 + 13.9481i −0.464165 + 0.803957i
\(302\) −1.82988 + 3.16944i −0.105298 + 0.182381i
\(303\) −2.04738 −0.117619
\(304\) −3.99912 6.62700i −0.229366 0.380085i
\(305\) 9.17589 0.525410
\(306\) −2.60348 + 4.50936i −0.148831 + 0.257783i
\(307\) 4.55001 7.88085i 0.259683 0.449784i −0.706474 0.707739i \(-0.749715\pi\)
0.966157 + 0.257955i \(0.0830486\pi\)
\(308\) 0.101215 + 0.175310i 0.00576727 + 0.00998921i
\(309\) 0.407309 0.705480i 0.0231710 0.0401333i
\(310\) −3.60219 6.23917i −0.204590 0.354361i
\(311\) −12.4569 −0.706364 −0.353182 0.935555i \(-0.614900\pi\)
−0.353182 + 0.935555i \(0.614900\pi\)
\(312\) 4.08931 0.231512
\(313\) −1.02277 1.77148i −0.0578101 0.100130i 0.835672 0.549229i \(-0.185078\pi\)
−0.893482 + 0.449099i \(0.851745\pi\)
\(314\) −3.98530 6.90274i −0.224903 0.389544i
\(315\) −5.40680 −0.304639
\(316\) 1.16741 0.0656719
\(317\) −11.7856 20.4133i −0.661947 1.14653i −0.980103 0.198487i \(-0.936397\pi\)
0.318157 0.948038i \(-0.396936\pi\)
\(318\) −0.0551274 + 0.0954834i −0.00309139 + 0.00535445i
\(319\) −0.334024 0.578546i −0.0187017 0.0323923i
\(320\) −4.07338 + 7.05530i −0.227709 + 0.394403i
\(321\) −0.189842 + 0.328817i −0.0105960 + 0.0183528i
\(322\) 11.1560 0.621698
\(323\) −3.74129 6.19974i −0.208171 0.344963i
\(324\) −6.14676 −0.341487
\(325\) −1.75687 + 3.04298i −0.0974534 + 0.168794i
\(326\) 10.8527 18.7975i 0.601077 1.04110i
\(327\) 3.08454 + 5.34257i 0.170575 + 0.295445i
\(328\) 16.3108 28.2511i 0.900613 1.55991i
\(329\) 10.5211 + 18.2231i 0.580048 + 1.00467i
\(330\) −0.0559501 −0.00307995
\(331\) −18.7175 −1.02881 −0.514403 0.857549i \(-0.671986\pi\)
−0.514403 + 0.857549i \(0.671986\pi\)
\(332\) 2.96267 + 5.13150i 0.162598 + 0.281627i
\(333\) −2.42511 4.20041i −0.132895 0.230181i
\(334\) −3.73480 −0.204359
\(335\) −2.95354 −0.161369
\(336\) −0.637575 1.10431i −0.0347826 0.0602451i
\(337\) 16.3440 28.3087i 0.890316 1.54207i 0.0508197 0.998708i \(-0.483817\pi\)
0.839497 0.543365i \(-0.182850\pi\)
\(338\) 0.358684 + 0.621259i 0.0195098 + 0.0337921i
\(339\) 0.159891 0.276940i 0.00868409 0.0150413i
\(340\) −0.660861 + 1.14465i −0.0358402 + 0.0620771i
\(341\) 0.882297 0.0477791
\(342\) −6.60093 + 11.9621i −0.356937 + 0.646838i
\(343\) −19.7188 −1.06471
\(344\) 13.0512 22.6053i 0.703671 1.21879i
\(345\) 1.01848 1.76406i 0.0548332 0.0949738i
\(346\) 5.80859 + 10.0608i 0.312271 + 0.540870i
\(347\) 1.28333 2.22279i 0.0688927 0.119326i −0.829521 0.558475i \(-0.811387\pi\)
0.898414 + 0.439149i \(0.144720\pi\)
\(348\) −0.750085 1.29919i −0.0402088 0.0696436i
\(349\) 16.6195 0.889619 0.444810 0.895625i \(-0.353271\pi\)
0.444810 + 0.895625i \(0.353271\pi\)
\(350\) 2.07752 0.111048
\(351\) −3.90274 6.75974i −0.208313 0.360808i
\(352\) −0.281388 0.487378i −0.0149980 0.0259773i
\(353\) 28.3629 1.50961 0.754803 0.655951i \(-0.227732\pi\)
0.754803 + 0.655951i \(0.227732\pi\)
\(354\) 2.87105 0.152595
\(355\) −0.664176 1.15039i −0.0352508 0.0610562i
\(356\) 3.87315 6.70850i 0.205277 0.355550i
\(357\) −0.596468 1.03311i −0.0315684 0.0546781i
\(358\) 8.01262 13.8783i 0.423480 0.733489i
\(359\) −8.69427 + 15.0589i −0.458866 + 0.794780i −0.998901 0.0468628i \(-0.985078\pi\)
0.540035 + 0.841643i \(0.318411\pi\)
\(360\) 8.76262 0.461831
\(361\) −10.1298 16.0744i −0.533150 0.846021i
\(362\) −5.96195 −0.313353
\(363\) −2.08291 + 3.60771i −0.109324 + 0.189355i
\(364\) 2.64616 4.58328i 0.138696 0.240229i
\(365\) 3.17119 + 5.49266i 0.165987 + 0.287499i
\(366\) 1.90994 3.30811i 0.0998342 0.172918i
\(367\) −12.9024 22.3477i −0.673501 1.16654i −0.976905 0.213676i \(-0.931456\pi\)
0.303404 0.952862i \(-0.401877\pi\)
\(368\) −9.53531 −0.497062
\(369\) −30.3683 −1.58091
\(370\) 0.931830 + 1.61398i 0.0484435 + 0.0839067i
\(371\) 0.250687 + 0.434203i 0.0130150 + 0.0225427i
\(372\) 1.98129 0.102725
\(373\) 27.0663 1.40144 0.700719 0.713437i \(-0.252862\pi\)
0.700719 + 0.713437i \(0.252862\pi\)
\(374\) 0.122512 + 0.212197i 0.00633495 + 0.0109724i
\(375\) 0.189667 0.328513i 0.00979436 0.0169643i
\(376\) −17.0512 29.5336i −0.879349 1.52308i
\(377\) −8.73267 + 15.1254i −0.449755 + 0.778999i
\(378\) −2.30753 + 3.99675i −0.118686 + 0.205571i
\(379\) 12.4028 0.637092 0.318546 0.947907i \(-0.396806\pi\)
0.318546 + 0.947907i \(0.396806\pi\)
\(380\) −1.67557 + 3.03644i −0.0859547 + 0.155766i
\(381\) −7.10859 −0.364184
\(382\) −11.2354 + 19.4604i −0.574855 + 0.995678i
\(383\) 2.67971 4.64139i 0.136927 0.237164i −0.789405 0.613873i \(-0.789611\pi\)
0.926332 + 0.376709i \(0.122944\pi\)
\(384\) 0.107336 + 0.185912i 0.00547749 + 0.00948728i
\(385\) −0.127214 + 0.220341i −0.00648343 + 0.0112296i
\(386\) −6.04881 10.4769i −0.307877 0.533258i
\(387\) −24.2993 −1.23520
\(388\) −13.8988 −0.705605
\(389\) −4.28467 7.42126i −0.217241 0.376273i 0.736722 0.676195i \(-0.236372\pi\)
−0.953964 + 0.299923i \(0.903039\pi\)
\(390\) 0.731376 + 1.26678i 0.0370346 + 0.0641459i
\(391\) −8.92053 −0.451131
\(392\) 10.4813 0.529386
\(393\) 0.547462 + 0.948232i 0.0276158 + 0.0478320i
\(394\) 10.8939 18.8687i 0.548824 0.950592i
\(395\) 0.733639 + 1.27070i 0.0369134 + 0.0639359i
\(396\) −0.152705 + 0.264493i −0.00767373 + 0.0132913i
\(397\) 5.32227 9.21844i 0.267117 0.462660i −0.700999 0.713162i \(-0.747262\pi\)
0.968116 + 0.250502i \(0.0805957\pi\)
\(398\) 23.0490 1.15534
\(399\) −1.61726 2.67998i −0.0809641 0.134167i
\(400\) −1.77572 −0.0887858
\(401\) −3.82604 + 6.62690i −0.191063 + 0.330932i −0.945603 0.325323i \(-0.894527\pi\)
0.754539 + 0.656255i \(0.227860\pi\)
\(402\) −0.614773 + 1.06482i −0.0306621 + 0.0531083i
\(403\) −11.5333 19.9763i −0.574516 0.995091i
\(404\) 2.14713 3.71893i 0.106824 0.185024i
\(405\) −3.86283 6.69062i −0.191946 0.332459i
\(406\) 10.3265 0.512497
\(407\) −0.228237 −0.0113133
\(408\) 0.966676 + 1.67433i 0.0478576 + 0.0828918i
\(409\) 8.84435 + 15.3189i 0.437325 + 0.757469i 0.997482 0.0709173i \(-0.0225927\pi\)
−0.560157 + 0.828386i \(0.689259\pi\)
\(410\) 11.6688 0.576280
\(411\) 7.14345 0.352361
\(412\) 0.854305 + 1.47970i 0.0420886 + 0.0728996i
\(413\) 6.52793 11.3067i 0.321218 0.556367i
\(414\) 8.41561 + 14.5763i 0.413605 + 0.716384i
\(415\) −3.72368 + 6.44961i −0.182788 + 0.316599i
\(416\) −7.35657 + 12.7420i −0.360685 + 0.624726i
\(417\) 6.89609 0.337703
\(418\) 0.332178 + 0.550456i 0.0162473 + 0.0269237i
\(419\) 1.18732 0.0580045 0.0290023 0.999579i \(-0.490767\pi\)
0.0290023 + 0.999579i \(0.490767\pi\)
\(420\) −0.285672 + 0.494799i −0.0139394 + 0.0241437i
\(421\) −16.6836 + 28.8969i −0.813111 + 1.40835i 0.0975661 + 0.995229i \(0.468894\pi\)
−0.910677 + 0.413120i \(0.864439\pi\)
\(422\) 7.03770 + 12.1896i 0.342590 + 0.593383i
\(423\) −15.8734 + 27.4935i −0.771791 + 1.33678i
\(424\) −0.406280 0.703698i −0.0197307 0.0341746i
\(425\) −1.66123 −0.0805815
\(426\) −0.552987 −0.0267923
\(427\) −8.68529 15.0434i −0.420311 0.727999i
\(428\) −0.398183 0.689673i −0.0192469 0.0333366i
\(429\) −0.179139 −0.00864890
\(430\) 9.33683 0.450262
\(431\) 3.08799 + 5.34855i 0.148743 + 0.257631i 0.930763 0.365623i \(-0.119144\pi\)
−0.782020 + 0.623253i \(0.785811\pi\)
\(432\) 1.97230 3.41613i 0.0948925 0.164359i
\(433\) 9.27761 + 16.0693i 0.445854 + 0.772241i 0.998111 0.0614325i \(-0.0195669\pi\)
−0.552258 + 0.833673i \(0.686234\pi\)
\(434\) −6.81918 + 11.8112i −0.327331 + 0.566954i
\(435\) 0.942757 1.63290i 0.0452017 0.0782917i
\(436\) −12.9392 −0.619677
\(437\) −23.4022 + 0.453129i −1.11948 + 0.0216761i
\(438\) 2.64030 0.126158
\(439\) 0.113656 0.196858i 0.00542450 0.00939550i −0.863300 0.504690i \(-0.831607\pi\)
0.868725 + 0.495295i \(0.164940\pi\)
\(440\) 0.206172 0.357100i 0.00982884 0.0170241i
\(441\) −4.87865 8.45007i −0.232317 0.402384i
\(442\) 3.20294 5.54765i 0.152348 0.263875i
\(443\) 17.4913 + 30.2959i 0.831038 + 1.43940i 0.897216 + 0.441593i \(0.145586\pi\)
−0.0661770 + 0.997808i \(0.521080\pi\)
\(444\) −0.512529 −0.0243236
\(445\) 9.73608 0.461534
\(446\) −11.1908 19.3831i −0.529901 0.917815i
\(447\) −4.22091 7.31083i −0.199642 0.345791i
\(448\) 15.4224 0.728638
\(449\) −16.9509 −0.799961 −0.399980 0.916524i \(-0.630983\pi\)
−0.399980 + 0.916524i \(0.630983\pi\)
\(450\) 1.56720 + 2.71447i 0.0738785 + 0.127961i
\(451\) −0.714520 + 1.23759i −0.0336454 + 0.0582756i
\(452\) 0.335362 + 0.580864i 0.0157741 + 0.0273215i
\(453\) 0.632505 1.09553i 0.0297177 0.0514725i
\(454\) −13.9469 + 24.1568i −0.654561 + 1.13373i
\(455\) 6.65174 0.311838
\(456\) 2.62103 + 4.34335i 0.122741 + 0.203396i
\(457\) 1.60241 0.0749578 0.0374789 0.999297i \(-0.488067\pi\)
0.0374789 + 0.999297i \(0.488067\pi\)
\(458\) −1.21570 + 2.10566i −0.0568060 + 0.0983909i
\(459\) 1.84514 3.19588i 0.0861239 0.149171i
\(460\) 2.13620 + 3.70001i 0.0996009 + 0.172514i
\(461\) 4.37081 7.57046i 0.203569 0.352592i −0.746107 0.665826i \(-0.768079\pi\)
0.949676 + 0.313234i \(0.101413\pi\)
\(462\) 0.0529586 + 0.0917270i 0.00246386 + 0.00426753i
\(463\) 21.1886 0.984718 0.492359 0.870392i \(-0.336135\pi\)
0.492359 + 0.870392i \(0.336135\pi\)
\(464\) −8.82636 −0.409753
\(465\) 1.24511 + 2.15659i 0.0577406 + 0.100010i
\(466\) 7.76857 + 13.4556i 0.359872 + 0.623316i
\(467\) 20.4516 0.946388 0.473194 0.880958i \(-0.343101\pi\)
0.473194 + 0.880958i \(0.343101\pi\)
\(468\) 7.98461 0.369089
\(469\) 2.79563 + 4.84217i 0.129090 + 0.223591i
\(470\) 6.09924 10.5642i 0.281337 0.487290i
\(471\) 1.37753 + 2.38596i 0.0634734 + 0.109939i
\(472\) −10.5796 + 18.3244i −0.486965 + 0.843449i
\(473\) −0.571727 + 0.990259i −0.0262880 + 0.0455322i
\(474\) 0.610821 0.0280559
\(475\) −4.35808 + 0.0843840i −0.199963 + 0.00387180i
\(476\) 2.50211 0.114684
\(477\) −0.378216 + 0.655090i −0.0173173 + 0.0299945i
\(478\) −1.65425 + 2.86525i −0.0756639 + 0.131054i
\(479\) −11.7746 20.3942i −0.537994 0.931833i −0.999012 0.0444419i \(-0.985849\pi\)
0.461018 0.887391i \(-0.347484\pi\)
\(480\) 0.794197 1.37559i 0.0362499 0.0627867i
\(481\) 2.98350 + 5.16757i 0.136036 + 0.235621i
\(482\) −26.0962 −1.18865
\(483\) −3.85611 −0.175459
\(484\) −4.36877 7.56694i −0.198581 0.343952i
\(485\) −8.73447 15.1285i −0.396612 0.686952i
\(486\) −10.5298 −0.477640
\(487\) 36.0392 1.63309 0.816546 0.577280i \(-0.195886\pi\)
0.816546 + 0.577280i \(0.195886\pi\)
\(488\) 14.0760 + 24.3803i 0.637188 + 1.10364i
\(489\) −3.75129 + 6.49742i −0.169639 + 0.293824i
\(490\) 1.87459 + 3.24688i 0.0846852 + 0.146679i
\(491\) −10.0297 + 17.3720i −0.452635 + 0.783988i −0.998549 0.0538541i \(-0.982849\pi\)
0.545913 + 0.837842i \(0.316183\pi\)
\(492\) −1.60453 + 2.77913i −0.0723378 + 0.125293i
\(493\) −8.25729 −0.371890
\(494\) 8.12081 14.7164i 0.365373 0.662124i
\(495\) −0.383860 −0.0172532
\(496\) 5.82853 10.0953i 0.261709 0.453293i
\(497\) −1.25733 + 2.17776i −0.0563989 + 0.0976858i
\(498\) 1.55015 + 2.68494i 0.0694640 + 0.120315i
\(499\) 18.4364 31.9328i 0.825328 1.42951i −0.0763399 0.997082i \(-0.524323\pi\)
0.901668 0.432429i \(-0.142343\pi\)
\(500\) 0.397815 + 0.689035i 0.0177908 + 0.0308146i
\(501\) 1.29095 0.0576753
\(502\) 18.8649 0.841980
\(503\) 10.8244 + 18.7483i 0.482634 + 0.835947i 0.999801 0.0199377i \(-0.00634678\pi\)
−0.517167 + 0.855884i \(0.673013\pi\)
\(504\) −8.29412 14.3658i −0.369449 0.639905i
\(505\) 5.39731 0.240177
\(506\) 0.792028 0.0352099
\(507\) −0.123981 0.214741i −0.00550617 0.00953697i
\(508\) 7.45492 12.9123i 0.330759 0.572891i
\(509\) 18.2279 + 31.5717i 0.807938 + 1.39939i 0.914289 + 0.405062i \(0.132750\pi\)
−0.106351 + 0.994329i \(0.533917\pi\)
\(510\) −0.345781 + 0.598910i −0.0153114 + 0.0265202i
\(511\) 6.00327 10.3980i 0.265569 0.459979i
\(512\) −18.3314 −0.810141
\(513\) 4.67822 8.47783i 0.206549 0.374305i
\(514\) −21.4471 −0.945990
\(515\) −1.07375 + 1.85979i −0.0473150 + 0.0819520i
\(516\) −1.28387 + 2.22373i −0.0565193 + 0.0978943i
\(517\) 0.746955 + 1.29376i 0.0328511 + 0.0568997i
\(518\) 1.76402 3.05537i 0.0775065 0.134245i
\(519\) −2.00776 3.47754i −0.0881309 0.152647i
\(520\) −10.7802 −0.472745
\(521\) −22.6092 −0.990528 −0.495264 0.868742i \(-0.664929\pi\)
−0.495264 + 0.868742i \(0.664929\pi\)
\(522\) 7.78991 + 13.4925i 0.340955 + 0.590552i
\(523\) −0.266456 0.461515i −0.0116513 0.0201806i 0.860141 0.510056i \(-0.170375\pi\)
−0.871792 + 0.489876i \(0.837042\pi\)
\(524\) −2.29654 −0.100325
\(525\) −0.718104 −0.0313406
\(526\) −4.83619 8.37653i −0.210868 0.365234i
\(527\) 5.45275 9.44444i 0.237525 0.411406i
\(528\) −0.0452651 0.0784015i −0.00196991 0.00341199i
\(529\) −2.91759 + 5.05341i −0.126852 + 0.219714i
\(530\) 0.145327 0.251713i 0.00631259 0.0109337i
\(531\) 19.6976 0.854804
\(532\) 6.56406 0.127098i 0.284588 0.00551038i
\(533\) 37.3606 1.61827
\(534\) 2.02654 3.51007i 0.0876971 0.151896i
\(535\) 0.500463 0.866827i 0.0216369 0.0374762i
\(536\) −4.53078 7.84754i −0.195700 0.338962i
\(537\) −2.76959 + 4.79708i −0.119517 + 0.207009i
\(538\) −0.158230 0.274062i −0.00682178 0.0118157i
\(539\) −0.459150 −0.0197770
\(540\) −1.76743 −0.0760579
\(541\) −2.50820 4.34433i −0.107836 0.186777i 0.807057 0.590473i \(-0.201059\pi\)
−0.914893 + 0.403696i \(0.867725\pi\)
\(542\) 13.6473 + 23.6378i 0.586202 + 1.01533i
\(543\) 2.06077 0.0884362
\(544\) −6.95610 −0.298240
\(545\) −8.13145 14.0841i −0.348313 0.603296i
\(546\) 1.38454 2.39810i 0.0592530 0.102629i
\(547\) −11.3149 19.5981i −0.483792 0.837952i 0.516035 0.856568i \(-0.327408\pi\)
−0.999827 + 0.0186154i \(0.994074\pi\)
\(548\) −7.49148 + 12.9756i −0.320020 + 0.554291i
\(549\) 13.1037 22.6962i 0.559250 0.968650i
\(550\) 0.147496 0.00628923
\(551\) −21.6622 + 0.419439i −0.922843 + 0.0178687i
\(552\) 6.24946 0.265995
\(553\) 1.38883 2.40552i 0.0590590 0.102293i
\(554\) 2.41703 4.18642i 0.102690 0.177864i
\(555\) −0.322091 0.557877i −0.0136720 0.0236806i
\(556\) −7.23207 + 12.5263i −0.306708 + 0.531234i
\(557\) −17.6277 30.5321i −0.746910 1.29369i −0.949297 0.314381i \(-0.898203\pi\)
0.202387 0.979306i \(-0.435130\pi\)
\(558\) −20.5764 −0.871070
\(559\) 29.8943 1.26439
\(560\) 1.68077 + 2.91119i 0.0710257 + 0.123020i
\(561\) −0.0423468 0.0733467i −0.00178788 0.00309670i
\(562\) −35.9097 −1.51476
\(563\) −24.6295 −1.03801 −0.519005 0.854771i \(-0.673698\pi\)
−0.519005 + 0.854771i \(0.673698\pi\)
\(564\) 1.67737 + 2.90528i 0.0706298 + 0.122334i
\(565\) −0.421505 + 0.730068i −0.0177329 + 0.0307142i
\(566\) 0.729207 + 1.26302i 0.0306509 + 0.0530888i
\(567\) −7.31260 + 12.6658i −0.307100 + 0.531913i
\(568\) 2.03771 3.52942i 0.0855005 0.148091i
\(569\) −20.0193 −0.839252 −0.419626 0.907697i \(-0.637839\pi\)
−0.419626 + 0.907697i \(0.637839\pi\)
\(570\) −0.876702 + 1.58875i −0.0367210 + 0.0665454i
\(571\) −16.6121 −0.695195 −0.347597 0.937644i \(-0.613002\pi\)
−0.347597 + 0.937644i \(0.613002\pi\)
\(572\) 0.187866 0.325394i 0.00785508 0.0136054i
\(573\) 3.88357 6.72655i 0.162239 0.281006i
\(574\) −11.0449 19.1303i −0.461005 0.798484i
\(575\) −2.68492 + 4.65042i −0.111969 + 0.193936i
\(576\) 11.6340 + 20.1507i 0.484750 + 0.839612i
\(577\) 12.4486 0.518244 0.259122 0.965845i \(-0.416567\pi\)
0.259122 + 0.965845i \(0.416567\pi\)
\(578\) −15.6279 −0.650034
\(579\) 2.09080 + 3.62136i 0.0868905 + 0.150499i
\(580\) 1.97737 + 3.42491i 0.0821060 + 0.142212i
\(581\) 14.0984 0.584899
\(582\) −7.27224 −0.301444
\(583\) 0.0177977 + 0.0308266i 0.000737107 + 0.00127671i
\(584\) −9.72930 + 16.8516i −0.402601 + 0.697326i
\(585\) 5.01780 + 8.69108i 0.207460 + 0.359332i
\(586\) 4.23811 7.34063i 0.175075 0.303238i
\(587\) −2.25572 + 3.90702i −0.0931036 + 0.161260i −0.908816 0.417198i \(-0.863012\pi\)
0.815712 + 0.578458i \(0.196345\pi\)
\(588\) −1.03107 −0.0425206
\(589\) 13.8250 25.0536i 0.569651 1.03232i
\(590\) −7.56867 −0.311597
\(591\) −3.76550 + 6.52204i −0.154892 + 0.268281i
\(592\) −1.50775 + 2.61150i −0.0619682 + 0.107332i
\(593\) −9.80411 16.9812i −0.402606 0.697335i 0.591433 0.806354i \(-0.298562\pi\)
−0.994040 + 0.109019i \(0.965229\pi\)
\(594\) −0.163825 + 0.283753i −0.00672181 + 0.0116425i
\(595\) 1.57241 + 2.72349i 0.0644625 + 0.111652i
\(596\) 17.7062 0.725274
\(597\) −7.96699 −0.326067
\(598\) −10.3533 17.9325i −0.423379 0.733315i
\(599\) −5.38795 9.33221i −0.220146 0.381304i 0.734706 0.678385i \(-0.237320\pi\)
−0.954852 + 0.297082i \(0.903987\pi\)
\(600\) 1.16381 0.0475122
\(601\) 15.0244 0.612860 0.306430 0.951893i \(-0.400866\pi\)
0.306430 + 0.951893i \(0.400866\pi\)
\(602\) −8.83763 15.3072i −0.360195 0.623876i
\(603\) −4.21782 + 7.30547i −0.171763 + 0.297502i
\(604\) 1.32664 + 2.29781i 0.0539802 + 0.0934964i
\(605\) 5.49097 9.51064i 0.223240 0.386662i
\(606\) 1.12344 1.94585i 0.0456365 0.0790448i
\(607\) 25.1901 1.02243 0.511217 0.859452i \(-0.329195\pi\)
0.511217 + 0.859452i \(0.329195\pi\)
\(608\) −18.2487 + 0.353343i −0.740082 + 0.0143300i
\(609\) −3.56940 −0.144640
\(610\) −5.03499 + 8.72085i −0.203861 + 0.353097i
\(611\) 19.5283 33.8240i 0.790030 1.36837i
\(612\) 1.88749 + 3.26923i 0.0762973 + 0.132151i
\(613\) −8.11753 + 14.0600i −0.327864 + 0.567877i −0.982088 0.188424i \(-0.939662\pi\)
0.654224 + 0.756301i \(0.272995\pi\)
\(614\) 4.99336 + 8.64875i 0.201516 + 0.349035i
\(615\) −4.03336 −0.162641
\(616\) −0.780593 −0.0314510
\(617\) −3.25913 5.64498i −0.131208 0.227258i 0.792935 0.609307i \(-0.208552\pi\)
−0.924142 + 0.382048i \(0.875219\pi\)
\(618\) 0.446996 + 0.774220i 0.0179808 + 0.0311437i
\(619\) −4.39112 −0.176494 −0.0882470 0.996099i \(-0.528126\pi\)
−0.0882470 + 0.996099i \(0.528126\pi\)
\(620\) −5.22308 −0.209764
\(621\) −5.96433 10.3305i −0.239340 0.414550i
\(622\) 6.83532 11.8391i 0.274071 0.474705i
\(623\) −9.21553 15.9618i −0.369212 0.639494i
\(624\) −1.18341 + 2.04972i −0.0473742 + 0.0820545i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 2.24484 0.0897220
\(627\) −0.114819 0.190267i −0.00458541 0.00759855i
\(628\) −5.77858 −0.230590
\(629\) −1.41054 + 2.44313i −0.0562420 + 0.0974140i
\(630\) 2.96682 5.13867i 0.118201 0.204730i
\(631\) 17.3104 + 29.9826i 0.689118 + 1.19359i 0.972124 + 0.234469i \(0.0753350\pi\)
−0.283006 + 0.959118i \(0.591332\pi\)
\(632\) −2.25083 + 3.89855i −0.0895331 + 0.155076i
\(633\) −2.43261 4.21340i −0.0966875 0.167468i
\(634\) 25.8680 1.02735
\(635\) 18.7397 0.743661
\(636\) 0.0399667 + 0.0692243i 0.00158478 + 0.00274492i
\(637\) 6.00198 + 10.3957i 0.237807 + 0.411894i
\(638\) 0.733141 0.0290253
\(639\) −3.79391 −0.150085
\(640\) −0.282960 0.490101i −0.0111850 0.0193730i
\(641\) −3.70621 + 6.41934i −0.146386 + 0.253549i −0.929889 0.367839i \(-0.880098\pi\)
0.783503 + 0.621388i \(0.213431\pi\)
\(642\) −0.208340 0.360856i −0.00822253 0.0142418i
\(643\) 8.27294 14.3292i 0.326253 0.565087i −0.655512 0.755185i \(-0.727547\pi\)
0.981765 + 0.190098i \(0.0608805\pi\)
\(644\) 4.04397 7.00437i 0.159355 0.276011i
\(645\) −3.22731 −0.127075
\(646\) 7.94520 0.153840i 0.312600 0.00605276i
\(647\) 29.4822 1.15907 0.579533 0.814949i \(-0.303235\pi\)
0.579533 + 0.814949i \(0.303235\pi\)
\(648\) 11.8513 20.5270i 0.465562 0.806377i
\(649\) 0.463456 0.802729i 0.0181922 0.0315099i
\(650\) −1.92805 3.33949i −0.0756245 0.130985i
\(651\) 2.35708 4.08258i 0.0923811 0.160009i
\(652\) −7.86810 13.6279i −0.308138 0.533712i
\(653\) 6.57421 0.257269 0.128634 0.991692i \(-0.458941\pi\)
0.128634 + 0.991692i \(0.458941\pi\)
\(654\) −6.77017 −0.264735
\(655\) −1.44322 2.49973i −0.0563912 0.0976725i
\(656\) 9.44037 + 16.3512i 0.368584 + 0.638407i
\(657\) 18.1145 0.706713
\(658\) −23.0925 −0.900241
\(659\) 13.1685 + 22.8085i 0.512972 + 0.888494i 0.999887 + 0.0150445i \(0.00478898\pi\)
−0.486915 + 0.873450i \(0.661878\pi\)
\(660\) −0.0202816 + 0.0351287i −0.000789458 + 0.00136738i
\(661\) −1.89210 3.27721i −0.0735941 0.127469i 0.826880 0.562378i \(-0.190114\pi\)
−0.900474 + 0.434910i \(0.856780\pi\)
\(662\) 10.2706 17.7893i 0.399180 0.691399i
\(663\) −1.10711 + 1.91757i −0.0429965 + 0.0744721i
\(664\) −22.8487 −0.886703
\(665\) 4.26341 + 7.06496i 0.165328 + 0.273967i
\(666\) 5.32281 0.206255
\(667\) −13.3456 + 23.1153i −0.516745 + 0.895029i
\(668\) −1.35384 + 2.34492i −0.0523817 + 0.0907278i
\(669\) 3.86815 + 6.69983i 0.149551 + 0.259031i
\(670\) 1.62067 2.80708i 0.0626118 0.108447i
\(671\) −0.616619 1.06802i −0.0238043 0.0412303i
\(672\) −3.00694 −0.115995
\(673\) −21.0431 −0.811150 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(674\) 17.9366 + 31.0670i 0.690891 + 1.19666i
\(675\) −1.11071 1.92381i −0.0427512 0.0740473i
\(676\) 0.520083 0.0200032
\(677\) −15.2744 −0.587043 −0.293522 0.955952i \(-0.594827\pi\)
−0.293522 + 0.955952i \(0.594827\pi\)
\(678\) 0.175471 + 0.303924i 0.00673891 + 0.0116721i
\(679\) −16.5349 + 28.6394i −0.634553 + 1.09908i
\(680\) −2.54835 4.41387i −0.0977248 0.169264i
\(681\) 4.82081 8.34988i 0.184734 0.319968i
\(682\) −0.484133 + 0.838544i −0.0185384 + 0.0321095i
\(683\) −8.60225 −0.329156 −0.164578 0.986364i \(-0.552626\pi\)
−0.164578 + 0.986364i \(0.552626\pi\)
\(684\) 5.11772 + 8.48064i 0.195681 + 0.324265i
\(685\) −18.8316 −0.719518
\(686\) 10.8201 18.7409i 0.413112 0.715530i
\(687\) 0.420212 0.727828i 0.0160321 0.0277684i
\(688\) 7.55375 + 13.0835i 0.287984 + 0.498803i
\(689\) 0.465302 0.805926i 0.0177266 0.0307033i
\(690\) 1.11772 + 1.93595i 0.0425509 + 0.0737003i
\(691\) 34.1079 1.29753 0.648763 0.760990i \(-0.275286\pi\)
0.648763 + 0.760990i \(0.275286\pi\)
\(692\) 8.42231 0.320168
\(693\) 0.363337 + 0.629318i 0.0138020 + 0.0239058i
\(694\) 1.40837 + 2.43937i 0.0534611 + 0.0925974i
\(695\) −18.1795 −0.689587
\(696\) 5.78481 0.219273
\(697\) 8.83172 + 15.2970i 0.334525 + 0.579414i
\(698\) −9.11942 + 15.7953i −0.345175 + 0.597861i
\(699\) −2.68523 4.65096i −0.101565 0.175916i
\(700\) 0.753090 1.30439i 0.0284641 0.0493013i
\(701\) −5.36463 + 9.29181i −0.202619 + 0.350947i −0.949372 0.314155i \(-0.898279\pi\)
0.746752 + 0.665102i \(0.231612\pi\)
\(702\) 8.56603 0.323304
\(703\) −3.57633 + 6.48098i −0.134884 + 0.244435i
\(704\) 1.09492 0.0412665
\(705\) −2.10823 + 3.65155i −0.0794004 + 0.137525i
\(706\) −15.5633 + 26.9564i −0.585732 + 1.01452i
\(707\) −5.10873 8.84859i −0.192134 0.332785i
\(708\) 1.04074 1.80261i 0.0391134 0.0677463i
\(709\) 14.4238 + 24.9828i 0.541697 + 0.938247i 0.998807 + 0.0488369i \(0.0155514\pi\)
−0.457109 + 0.889410i \(0.651115\pi\)
\(710\) 1.45778 0.0547096
\(711\) 4.19070 0.157164
\(712\) 14.9353 + 25.8687i 0.559724 + 0.969470i
\(713\) −17.6257 30.5287i −0.660089 1.14331i
\(714\) 1.30917 0.0489946
\(715\) 0.472245 0.0176610
\(716\) −5.80905 10.0616i −0.217095 0.376019i
\(717\) 0.571800 0.990386i 0.0213542 0.0369866i
\(718\) −9.54143 16.5262i −0.356083 0.616754i
\(719\) 10.0278 17.3686i 0.373972 0.647739i −0.616200 0.787589i \(-0.711329\pi\)
0.990173 + 0.139851i \(0.0446622\pi\)
\(720\) −2.53582 + 4.39216i −0.0945043 + 0.163686i
\(721\) 4.06535 0.151402
\(722\) 20.8357 0.807171i 0.775424 0.0300398i
\(723\) 9.02026 0.335467
\(724\) −2.16117 + 3.74326i −0.0803193 + 0.139117i
\(725\) −2.48530 + 4.30466i −0.0923016 + 0.159871i
\(726\) −2.28587 3.95923i −0.0848364 0.146941i
\(727\) 0.390261 0.675951i 0.0144740 0.0250697i −0.858698 0.512482i \(-0.828726\pi\)
0.873172 + 0.487413i \(0.162059\pi\)
\(728\) 10.2039 + 17.6736i 0.378180 + 0.655028i
\(729\) −19.5373 −0.723604
\(730\) −6.96036 −0.257615
\(731\) 7.06674 + 12.2399i 0.261373 + 0.452711i
\(732\) −1.38468 2.39834i −0.0511794 0.0886452i
\(733\) −26.8391 −0.991326 −0.495663 0.868515i \(-0.665075\pi\)
−0.495663 + 0.868515i \(0.665075\pi\)
\(734\) 28.3192 1.04528
\(735\) −0.647958 1.12230i −0.0239003 0.0413965i
\(736\) −11.2426 + 19.4728i −0.414409 + 0.717777i
\(737\) 0.198478 + 0.343774i 0.00731103 + 0.0126631i
\(738\) 16.6636 28.8623i 0.613397 1.06243i
\(739\) −10.3265 + 17.8861i −0.379867 + 0.657949i −0.991043 0.133546i \(-0.957364\pi\)
0.611175 + 0.791495i \(0.290697\pi\)
\(740\) 1.35113 0.0496685
\(741\) −2.80699 + 5.08680i −0.103117 + 0.186868i
\(742\) −0.550227 −0.0201995
\(743\) −0.736585 + 1.27580i −0.0270227 + 0.0468047i −0.879220 0.476415i \(-0.841936\pi\)
0.852198 + 0.523220i \(0.175269\pi\)
\(744\) −3.82003 + 6.61649i −0.140049 + 0.242572i
\(745\) 11.1272 + 19.2728i 0.407668 + 0.706102i
\(746\) −14.8518 + 25.7240i −0.543762 + 0.941824i
\(747\) 10.6352 + 18.4208i 0.389123 + 0.673980i
\(748\) 0.177639 0.00649514
\(749\) −1.89482 −0.0692352
\(750\) 0.208148 + 0.360522i 0.00760048 + 0.0131644i
\(751\) −7.78121 13.4775i −0.283940 0.491799i 0.688411 0.725321i \(-0.258308\pi\)
−0.972352 + 0.233521i \(0.924975\pi\)
\(752\) 19.7378 0.719764
\(753\) −6.52071 −0.237628
\(754\) −9.58356 16.5992i −0.349013 0.604508i
\(755\) −1.66741 + 2.88804i −0.0606832 + 0.105106i
\(756\) 1.67293 + 2.89760i 0.0608438 + 0.105385i
\(757\) −10.0878 + 17.4726i −0.366647 + 0.635052i −0.989039 0.147654i \(-0.952828\pi\)
0.622392 + 0.782706i \(0.286161\pi\)
\(758\) −6.80568 + 11.7878i −0.247193 + 0.428152i
\(759\) −0.273767 −0.00993713
\(760\) −6.90957 11.4499i −0.250637 0.415333i
\(761\) −15.1076 −0.547649 −0.273825 0.961780i \(-0.588289\pi\)
−0.273825 + 0.961780i \(0.588289\pi\)
\(762\) 3.90062 6.75607i 0.141305 0.244747i
\(763\) −15.3934 + 26.6621i −0.557278 + 0.965234i
\(764\) 8.14556 + 14.1085i 0.294696 + 0.510428i
\(765\) −2.37232 + 4.10898i −0.0857715 + 0.148561i
\(766\) 2.94082 + 5.09364i 0.106256 + 0.184041i
\(767\) −24.2331 −0.875005
\(768\) 5.94509 0.214525
\(769\) −25.8290 44.7372i −0.931418 1.61326i −0.780900 0.624656i \(-0.785239\pi\)
−0.150518 0.988607i \(-0.548094\pi\)
\(770\) −0.139610 0.241811i −0.00503118 0.00871426i
\(771\) 7.41327 0.266982
\(772\) −8.77063 −0.315662
\(773\) −15.0779 26.1157i −0.542314 0.939316i −0.998771 0.0495699i \(-0.984215\pi\)
0.456457 0.889746i \(-0.349118\pi\)
\(774\) 13.3335 23.0943i 0.479262 0.830107i
\(775\) −3.28236 5.68521i −0.117906 0.204219i
\(776\) 26.7976 46.4148i 0.961978 1.66620i
\(777\) −0.609739 + 1.05610i −0.0218743 + 0.0378874i
\(778\) 9.40431 0.337161
\(779\) 23.9462 + 39.6816i 0.857962 + 1.42174i
\(780\) 1.06048 0.0379712
\(781\) −0.0892652 + 0.154612i −0.00319416 + 0.00553244i
\(782\) 4.89487 8.47816i 0.175040 0.303178i
\(783\) −5.52088 9.56245i −0.197300 0.341734i
\(784\) −3.03318 + 5.25363i −0.108328 + 0.187630i
\(785\) −3.63145 6.28986i −0.129612 0.224495i
\(786\) −1.20161 −0.0428601
\(787\) 43.0969 1.53624 0.768119 0.640307i \(-0.221193\pi\)
0.768119 + 0.640307i \(0.221193\pi\)
\(788\) −7.89791 13.6796i −0.281351 0.487315i
\(789\) 1.67165 + 2.89538i 0.0595123 + 0.103078i
\(790\) −1.61025 −0.0572900
\(791\) 1.59588 0.0567428
\(792\) −0.588848 1.01991i −0.0209238 0.0362411i
\(793\) −16.1208 + 27.9221i −0.572467 + 0.991542i
\(794\) 5.84086 + 10.1167i 0.207284 + 0.359027i
\(795\) −0.0502328 + 0.0870057i −0.00178157 + 0.00308578i
\(796\) 8.35514 14.4715i 0.296140 0.512929i
\(797\) −50.5062 −1.78902 −0.894510 0.447048i \(-0.852475\pi\)
−0.894510 + 0.447048i \(0.852475\pi\)
\(798\) 3.43450 0.0665010i 0.121580 0.00235411i
\(799\) 18.4652 0.653253
\(800\) −2.09366 + 3.62633i −0.0740221 + 0.128210i
\(801\) 13.9036 24.0818i 0.491261 0.850889i
\(802\) −4.19885 7.27261i −0.148266 0.256805i
\(803\) 0.426207 0.738212i 0.0150405 0.0260509i
\(804\) 0.445703 + 0.771981i 0.0157187 + 0.0272257i
\(805\) 10.1655 0.358286
\(806\) 25.3142 0.891656
\(807\) 0.0546928 + 0.0947307i 0.00192528 + 0.00333468i
\(808\) 8.27955 + 14.3406i 0.291274 + 0.504501i
\(809\) −30.0872 −1.05781 −0.528905 0.848681i \(-0.677397\pi\)
−0.528905 + 0.848681i \(0.677397\pi\)
\(810\) 8.47843 0.297902
\(811\) −11.4755 19.8761i −0.402958 0.697944i 0.591123 0.806581i \(-0.298685\pi\)
−0.994081 + 0.108637i \(0.965351\pi\)
\(812\) 3.74330 6.48359i 0.131364 0.227529i
\(813\) −4.71725 8.17051i −0.165441 0.286552i
\(814\) 0.125238 0.216918i 0.00438958 0.00760298i
\(815\) 9.88915 17.1285i 0.346402 0.599986i
\(816\) −1.11899 −0.0391723
\(817\) 19.1607 + 31.7514i 0.670347 + 1.11084i
\(818\) −19.4123 −0.678734
\(819\) 9.49903 16.4528i 0.331923 0.574907i
\(820\) 4.22986 7.32634i 0.147713 0.255847i
\(821\) 19.0403 + 32.9788i 0.664513 + 1.15097i 0.979417 + 0.201846i \(0.0646941\pi\)
−0.314905 + 0.949123i \(0.601973\pi\)
\(822\) −3.91975 + 6.78921i −0.136717 + 0.236801i
\(823\) −26.8966 46.5862i −0.937556 1.62389i −0.770012 0.638030i \(-0.779750\pi\)
−0.167544 0.985865i \(-0.553584\pi\)
\(824\) −6.58858 −0.229524
\(825\) −0.0509824 −0.00177498
\(826\) 7.16400 + 12.4084i 0.249267 + 0.431744i
\(827\) −16.2046 28.0672i −0.563490 0.975993i −0.997188 0.0749347i \(-0.976125\pi\)
0.433699 0.901058i \(-0.357208\pi\)
\(828\) 12.2024 0.424064
\(829\) −18.5305 −0.643592 −0.321796 0.946809i \(-0.604287\pi\)
−0.321796 + 0.946809i \(0.604287\pi\)
\(830\) −4.08651 7.07805i −0.141845 0.245683i
\(831\) −0.835456 + 1.44705i −0.0289817 + 0.0501977i
\(832\) −14.3128 24.7904i −0.496206 0.859454i
\(833\) −2.83763 + 4.91491i −0.0983179 + 0.170292i
\(834\) −3.78402 + 6.55411i −0.131030 + 0.226950i
\(835\) −3.40320 −0.117773
\(836\) 0.466021 0.00902339i 0.0161177 0.000312081i
\(837\) 14.5830 0.504062
\(838\) −0.651507 + 1.12844i −0.0225059 + 0.0389814i
\(839\) −0.413304 + 0.715864i −0.0142688 + 0.0247144i −0.873072 0.487592i \(-0.837875\pi\)
0.858803 + 0.512306i \(0.171209\pi\)
\(840\) −1.10158 1.90800i −0.0380082 0.0658322i
\(841\) 2.14661 3.71803i 0.0740209 0.128208i
\(842\) −18.3093 31.7126i −0.630979 1.09289i
\(843\) 12.4123 0.427504
\(844\) 10.2045 0.351253
\(845\) 0.326838 + 0.566100i 0.0112436 + 0.0194744i
\(846\) −17.4201 30.1725i −0.598914 1.03735i
\(847\) −20.7895 −0.714337
\(848\) 0.470294 0.0161500
\(849\) −0.252053 0.436569i −0.00865044 0.0149830i
\(850\) 0.911548 1.57885i 0.0312658 0.0541540i
\(851\) 4.55951 + 7.89730i 0.156298 + 0.270716i
\(852\) −0.200454 + 0.347197i −0.00686745 + 0.0118948i
\(853\) 3.67469 6.36475i 0.125819 0.217925i −0.796234 0.604989i \(-0.793177\pi\)
0.922053 + 0.387064i \(0.126511\pi\)
\(854\) 19.0631 0.652327
\(855\) −6.01485 + 10.9000i −0.205704 + 0.372774i
\(856\) 3.07087 0.104960
\(857\) 22.6748 39.2739i 0.774556 1.34157i −0.160488 0.987038i \(-0.551307\pi\)
0.935044 0.354532i \(-0.115360\pi\)
\(858\) 0.0982968 0.170255i 0.00335580 0.00581241i
\(859\) −14.8143 25.6590i −0.505456 0.875475i −0.999980 0.00631148i \(-0.997991\pi\)
0.494524 0.869164i \(-0.335342\pi\)
\(860\) 3.38454 5.86220i 0.115412 0.199899i
\(861\) 3.81771 + 6.61247i 0.130107 + 0.225352i
\(862\) −6.77775 −0.230851
\(863\) 41.0807 1.39840 0.699201 0.714925i \(-0.253539\pi\)
0.699201 + 0.714925i \(0.253539\pi\)
\(864\) −4.65090 8.05559i −0.158227 0.274057i
\(865\) 5.29286 + 9.16750i 0.179963 + 0.311704i
\(866\) −20.3632 −0.691970
\(867\) 5.40183 0.183456
\(868\) 4.94382 + 8.56295i 0.167804 + 0.290645i
\(869\) 0.0986010 0.170782i 0.00334481 0.00579338i
\(870\) 1.03462 + 1.79201i 0.0350768 + 0.0607548i
\(871\) 5.18898 8.98758i 0.175822 0.304533i
\(872\) 24.9475 43.2104i 0.844831 1.46329i
\(873\) −49.8931 −1.68863
\(874\) 12.4106 22.4903i 0.419794 0.760746i
\(875\) 1.89307 0.0639974
\(876\) 0.957093 1.65773i 0.0323372 0.0560096i
\(877\) −27.3154 + 47.3116i −0.922374 + 1.59760i −0.126643 + 0.991948i \(0.540420\pi\)
−0.795731 + 0.605650i \(0.792913\pi\)
\(878\) 0.124730 + 0.216039i 0.00420944 + 0.00729097i
\(879\) −1.46492 + 2.53732i −0.0494105 + 0.0855815i
\(880\) 0.119328 + 0.206682i 0.00402255 + 0.00696726i
\(881\) −15.4805 −0.521552 −0.260776 0.965399i \(-0.583978\pi\)
−0.260776 + 0.965399i \(0.583978\pi\)
\(882\) 10.7080 0.360558
\(883\) 22.6747 + 39.2738i 0.763066 + 1.32167i 0.941263 + 0.337674i \(0.109640\pi\)
−0.178197 + 0.983995i \(0.557027\pi\)
\(884\) −2.32209 4.02198i −0.0781004 0.135274i
\(885\) 2.61614 0.0879406
\(886\) −38.3913 −1.28978
\(887\) 15.5700 + 26.9680i 0.522788 + 0.905496i 0.999648 + 0.0265165i \(0.00844145\pi\)
−0.476860 + 0.878979i \(0.658225\pi\)
\(888\) 0.988184 1.71158i 0.0331613 0.0574370i
\(889\) −17.7377 30.7227i −0.594905 1.03041i
\(890\) −5.34237 + 9.25326i −0.179077 + 0.310170i
\(891\) −0.519164 + 0.899218i −0.0173926 + 0.0301249i
\(892\) −16.2264 −0.543301
\(893\) 48.4419 0.937963i 1.62105 0.0313877i
\(894\) 9.26438 0.309847
\(895\) 7.30121 12.6461i 0.244052 0.422711i
\(896\) −0.535663 + 0.927795i −0.0178952 + 0.0309955i
\(897\) 3.57867 + 6.19844i 0.119488 + 0.206960i
\(898\) 9.30127 16.1103i 0.310387 0.537606i
\(899\) −16.3153 28.2589i −0.544145 0.942486i
\(900\) 2.27240 0.0757467
\(901\) 0.439972 0.0146576
\(902\) −0.784142 1.35817i −0.0261091 0.0452222i
\(903\) 3.05476 + 5.29100i 0.101656 + 0.176073i
\(904\) −2.58638 −0.0860218
\(905\) −5.43261 −0.180586
\(906\) 0.694135 + 1.20228i 0.0230611 + 0.0399430i
\(907\) −21.7707 + 37.7080i −0.722886 + 1.25207i 0.236952 + 0.971521i \(0.423851\pi\)
−0.959838 + 0.280554i \(0.909482\pi\)
\(908\) 10.1113 + 17.5134i 0.335557 + 0.581201i
\(909\) 7.70764 13.3500i 0.255646 0.442792i
\(910\) −3.64993 + 6.32187i −0.120994 + 0.209568i
\(911\) 5.72789 0.189774 0.0948868 0.995488i \(-0.469751\pi\)
0.0948868 + 0.995488i \(0.469751\pi\)
\(912\) −2.93556 + 0.0568401i −0.0972060 + 0.00188217i
\(913\) 1.00093 0.0331258
\(914\) −0.879275 + 1.52295i −0.0290838 + 0.0503747i
\(915\) 1.74036 3.01440i 0.0575346 0.0996529i
\(916\) 0.881369 + 1.52658i 0.0291212 + 0.0504395i
\(917\) −2.73211 + 4.73216i −0.0902223 + 0.156270i
\(918\) 2.02493 + 3.50728i 0.0668327 + 0.115758i
\(919\) 7.93860 0.261870 0.130935 0.991391i \(-0.458202\pi\)
0.130935 + 0.991391i \(0.458202\pi\)
\(920\) −16.4748 −0.543159
\(921\) −1.72597 2.98947i −0.0568728 0.0985065i
\(922\) 4.79669 + 8.30812i 0.157971 + 0.273613i
\(923\) 4.66747 0.153632
\(924\) 0.0767887 0.00252616
\(925\) 0.849095 + 1.47068i 0.0279181 + 0.0483555i
\(926\) −11.6266 + 20.1378i −0.382073 + 0.661771i
\(927\) 3.06674 + 5.31174i 0.100725 + 0.174461i
\(928\) −10.4067 + 18.0250i −0.341618 + 0.591700i
\(929\) 14.4784 25.0772i 0.475019 0.822758i −0.524571 0.851366i \(-0.675774\pi\)
0.999591 + 0.0286089i \(0.00910773\pi\)
\(930\) −2.73286 −0.0896141
\(931\) −7.19459 + 13.0380i −0.235793 + 0.427302i
\(932\) 11.2642 0.368972
\(933\) −2.36265 + 4.09224i −0.0773498 + 0.133974i
\(934\) −11.2222 + 19.4374i −0.367201 + 0.636011i
\(935\) 0.111635 + 0.193357i 0.00365084 + 0.00632344i
\(936\) −15.3948 + 26.6645i −0.503193 + 0.871556i
\(937\) 7.34080 + 12.7146i 0.239813 + 0.415369i 0.960661 0.277725i \(-0.0895804\pi\)
−0.720847 + 0.693094i \(0.756247\pi\)
\(938\) −6.13606 −0.200349
\(939\) −0.775939 −0.0253218
\(940\) −4.42187 7.65891i −0.144226 0.249806i
\(941\) 0.0773773 + 0.134021i 0.00252243 + 0.00436897i 0.867284 0.497814i \(-0.165864\pi\)
−0.864761 + 0.502183i \(0.832530\pi\)
\(942\) −3.02352 −0.0985114
\(943\) 57.0961 1.85931
\(944\) −6.12326 10.6058i −0.199295 0.345189i
\(945\) −2.10265 + 3.64189i −0.0683991 + 0.118471i
\(946\) −0.627435 1.08675i −0.0203997 0.0353332i
\(947\) 3.75904 6.51084i 0.122152 0.211574i −0.798464 0.602043i \(-0.794354\pi\)
0.920616 + 0.390469i \(0.127687\pi\)
\(948\) 0.221419 0.383509i 0.00719135 0.0124558i
\(949\) −22.2854 −0.723415
\(950\) 2.31116 4.18827i 0.0749841 0.135885i
\(951\) −8.94137 −0.289944
\(952\) −4.82420 + 8.35576i −0.156353 + 0.270812i
\(953\) −11.3372 + 19.6365i −0.367247 + 0.636090i −0.989134 0.147017i \(-0.953033\pi\)
0.621887 + 0.783107i \(0.286366\pi\)
\(954\) −0.415069 0.718920i −0.0134384 0.0232759i
\(955\) −10.2379 + 17.7325i −0.331290 + 0.573811i
\(956\) 1.19931 + 2.07727i 0.0387886 + 0.0671838i
\(957\) −0.253413 −0.00819167
\(958\) 25.8437 0.834973
\(959\) 17.8247 + 30.8733i 0.575590 + 0.996952i
\(960\) 1.54517 + 2.67631i 0.0498702 + 0.0863777i
\(961\) 12.0955 0.390177
\(962\) −6.54840 −0.211129
\(963\) −1.42937 2.47575i −0.0460609 0.0797799i
\(964\) −9.45972 + 16.3847i −0.304677 + 0.527716i
\(965\) −5.51176 9.54664i −0.177430 0.307317i
\(966\) 2.11592 3.66488i 0.0680786 0.117916i
\(967\) −14.4172 + 24.9714i −0.463627 + 0.803025i −0.999138 0.0415030i \(-0.986785\pi\)
0.535512 + 0.844528i \(0.320119\pi\)
\(968\) 33.6929 1.08293
\(969\) −2.74629 + 0.0531755i −0.0882236 + 0.00170824i
\(970\) 19.1711 0.615546
\(971\) −13.1831 + 22.8338i −0.423065 + 0.732770i −0.996238 0.0866647i \(-0.972379\pi\)
0.573173 + 0.819435i \(0.305712\pi\)
\(972\) −3.81698 + 6.61120i −0.122430 + 0.212054i
\(973\) 17.2075 + 29.8043i 0.551647 + 0.955481i
\(974\) −19.7754 + 34.2520i −0.633645 + 1.09750i
\(975\) 0.666439 + 1.15431i 0.0213431 + 0.0369674i
\(976\) −16.2938 −0.521551
\(977\) 4.59218 0.146917 0.0734585 0.997298i \(-0.476596\pi\)
0.0734585 + 0.997298i \(0.476596\pi\)
\(978\) −4.11681 7.13052i −0.131641 0.228009i
\(979\) −0.654264 1.13322i −0.0209104 0.0362178i
\(980\) 2.71810 0.0868267
\(981\) −46.4486 −1.48299
\(982\) −11.0070 19.0647i −0.351248 0.608379i
\(983\) −3.45737 + 5.98833i −0.110273 + 0.190998i −0.915880 0.401452i \(-0.868506\pi\)
0.805607 + 0.592450i \(0.201839\pi\)
\(984\) −6.18724 10.7166i −0.197242 0.341633i
\(985\) 9.92662 17.1934i 0.316288 0.547828i
\(986\) 4.53094 7.84781i 0.144294 0.249925i
\(987\) 7.98203 0.254071
\(988\) −6.29609 10.4333i −0.200305 0.331929i
\(989\) 45.6857 1.45272
\(990\) 0.210632 0.364825i 0.00669431 0.0115949i
\(991\) 19.0035 32.9150i 0.603666 1.04558i −0.388594 0.921409i \(-0.627039\pi\)
0.992261 0.124172i \(-0.0396274\pi\)
\(992\) −13.7443 23.8058i −0.436382 0.755835i
\(993\) −3.55009 + 6.14893i −0.112659 + 0.195130i
\(994\) −1.37984 2.38996i −0.0437659 0.0758048i
\(995\) 21.0026 0.665827
\(996\) 2.24768 0.0712205
\(997\) −8.11326 14.0526i −0.256950 0.445050i 0.708474 0.705737i \(-0.249384\pi\)
−0.965423 + 0.260688i \(0.916051\pi\)
\(998\) 20.2329 + 35.0443i 0.640460 + 1.10931i
\(999\) −3.77239 −0.119353
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 95.2.e.c.11.2 8
3.2 odd 2 855.2.k.h.676.3 8
4.3 odd 2 1520.2.q.o.961.2 8
5.2 odd 4 475.2.j.c.49.4 16
5.3 odd 4 475.2.j.c.49.5 16
5.4 even 2 475.2.e.e.201.3 8
19.7 even 3 inner 95.2.e.c.26.2 yes 8
19.8 odd 6 1805.2.a.i.1.2 4
19.11 even 3 1805.2.a.o.1.3 4
57.26 odd 6 855.2.k.h.406.3 8
76.7 odd 6 1520.2.q.o.881.2 8
95.7 odd 12 475.2.j.c.349.5 16
95.49 even 6 9025.2.a.bg.1.2 4
95.64 even 6 475.2.e.e.26.3 8
95.83 odd 12 475.2.j.c.349.4 16
95.84 odd 6 9025.2.a.bp.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
95.2.e.c.11.2 8 1.1 even 1 trivial
95.2.e.c.26.2 yes 8 19.7 even 3 inner
475.2.e.e.26.3 8 95.64 even 6
475.2.e.e.201.3 8 5.4 even 2
475.2.j.c.49.4 16 5.2 odd 4
475.2.j.c.49.5 16 5.3 odd 4
475.2.j.c.349.4 16 95.83 odd 12
475.2.j.c.349.5 16 95.7 odd 12
855.2.k.h.406.3 8 57.26 odd 6
855.2.k.h.676.3 8 3.2 odd 2
1520.2.q.o.881.2 8 76.7 odd 6
1520.2.q.o.961.2 8 4.3 odd 2
1805.2.a.i.1.2 4 19.8 odd 6
1805.2.a.o.1.3 4 19.11 even 3
9025.2.a.bg.1.2 4 95.49 even 6
9025.2.a.bp.1.3 4 95.84 odd 6