Properties

Label 273.2.p.f.34.3
Level $273$
Weight $2$
Character 273.34
Analytic conductor $2.180$
Analytic rank $0$
Dimension $12$
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] = [273,2,Mod(34,273)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(273, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("273.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.p (of order \(4\), 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: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 60x^{8} - 8x^{7} + 80x^{5} + 320x^{4} + 160x^{3} + 32x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 34.3
Root \(1.85068 - 1.85068i\) of defining polynomial
Character \(\chi\) \(=\) 273.34
Dual form 273.2.p.f.265.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.786556 - 0.786556i) q^{2} +1.00000i q^{3} -0.762660i q^{4} +(2.85068 - 2.85068i) q^{5} +(0.786556 - 0.786556i) q^{6} +(-1.83993 - 1.90123i) q^{7} +(-2.17299 + 2.17299i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.786556 - 0.786556i) q^{2} +1.00000i q^{3} -0.762660i q^{4} +(2.85068 - 2.85068i) q^{5} +(0.786556 - 0.786556i) q^{6} +(-1.83993 - 1.90123i) q^{7} +(-2.17299 + 2.17299i) q^{8} -1.00000 q^{9} -4.48443 q^{10} +(-1.37164 + 1.37164i) q^{11} +0.762660 q^{12} +(2.79665 - 2.27569i) q^{13} +(-0.0482190 + 2.94263i) q^{14} +(2.85068 + 2.85068i) q^{15} +1.89303 q^{16} -3.67985 q^{17} +(0.786556 + 0.786556i) q^{18} +(1.10886 - 1.10886i) q^{19} +(-2.17410 - 2.17410i) q^{20} +(1.90123 - 1.83993i) q^{21} +2.15774 q^{22} +0.653796i q^{23} +(-2.17299 - 2.17299i) q^{24} -11.2527i q^{25} +(-3.98968 - 0.409765i) q^{26} -1.00000i q^{27} +(-1.44999 + 1.40324i) q^{28} -1.78095 q^{29} -4.48443i q^{30} +(5.70136 - 5.70136i) q^{31} +(2.85700 + 2.85700i) q^{32} +(-1.37164 - 1.37164i) q^{33} +(2.89441 + 2.89441i) q^{34} +(-10.6648 - 0.174758i) q^{35} +0.762660i q^{36} +(3.46293 - 3.46293i) q^{37} -1.74437 q^{38} +(2.27569 + 2.79665i) q^{39} +12.3890i q^{40} +(2.67464 - 2.67464i) q^{41} +(-2.94263 - 0.0482190i) q^{42} +11.0076i q^{43} +(1.04609 + 1.04609i) q^{44} +(-2.85068 + 2.85068i) q^{45} +(0.514247 - 0.514247i) q^{46} +(3.84609 + 3.84609i) q^{47} +1.89303i q^{48} +(-0.229348 + 6.99624i) q^{49} +(-8.85090 + 8.85090i) q^{50} -3.67985i q^{51} +(-1.73558 - 2.13289i) q^{52} -0.919315 q^{53} +(-0.786556 + 0.786556i) q^{54} +7.82021i q^{55} +(8.12948 + 0.133213i) q^{56} +(1.10886 + 1.10886i) q^{57} +(1.40082 + 1.40082i) q^{58} +(8.69367 + 8.69367i) q^{59} +(2.17410 - 2.17410i) q^{60} -5.92939i q^{61} -8.96887 q^{62} +(1.83993 + 1.90123i) q^{63} -8.28044i q^{64} +(1.48509 - 14.4596i) q^{65} +2.15774i q^{66} +(-8.44464 - 8.44464i) q^{67} +2.80648i q^{68} -0.653796 q^{69} +(8.25103 + 8.52594i) q^{70} +(8.55531 + 8.55531i) q^{71} +(2.17299 - 2.17299i) q^{72} +(6.74551 + 6.74551i) q^{73} -5.44757 q^{74} +11.2527 q^{75} +(-0.845686 - 0.845686i) q^{76} +(5.13152 + 0.0840870i) q^{77} +(0.409765 - 3.98968i) q^{78} +9.87363 q^{79} +(5.39642 - 5.39642i) q^{80} +1.00000 q^{81} -4.20751 q^{82} +(-8.71517 + 8.71517i) q^{83} +(-1.40324 - 1.44999i) q^{84} +(-10.4901 + 10.4901i) q^{85} +(8.65811 - 8.65811i) q^{86} -1.78095i q^{87} -5.96111i q^{88} +(-4.94580 - 4.94580i) q^{89} +4.48443 q^{90} +(-9.47223 - 1.12998i) q^{91} +0.498624 q^{92} +(5.70136 + 5.70136i) q^{93} -6.05033i q^{94} -6.32203i q^{95} +(-2.85700 + 2.85700i) q^{96} +(-0.857049 + 0.857049i) q^{97} +(5.68333 - 5.32254i) q^{98} +(1.37164 - 1.37164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{5} - 4 q^{7} - 12 q^{9} - 4 q^{11} - 28 q^{12} + 12 q^{15} - 36 q^{16} - 8 q^{17} + 8 q^{20} + 12 q^{21} + 32 q^{22} + 4 q^{26} + 12 q^{28} - 8 q^{29} + 24 q^{31} + 20 q^{32} - 4 q^{33} - 20 q^{35} - 4 q^{37} + 40 q^{38} - 16 q^{39} - 20 q^{41} + 8 q^{44} - 12 q^{45} + 20 q^{46} + 32 q^{47} + 20 q^{50} - 56 q^{52} - 16 q^{53} - 20 q^{56} + 8 q^{59} - 8 q^{60} + 4 q^{63} - 16 q^{65} - 32 q^{67} + 16 q^{69} - 20 q^{70} - 12 q^{71} - 32 q^{73} - 64 q^{74} + 4 q^{75} - 12 q^{77} + 16 q^{78} + 24 q^{79} - 4 q^{80} + 12 q^{81} + 28 q^{84} - 32 q^{85} + 4 q^{89} + 32 q^{91} + 112 q^{92} + 24 q^{93} - 20 q^{96} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.786556 0.786556i −0.556179 0.556179i 0.372038 0.928217i \(-0.378659\pi\)
−0.928217 + 0.372038i \(0.878659\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 0.762660i 0.381330i
\(5\) 2.85068 2.85068i 1.27486 1.27486i 0.331356 0.943506i \(-0.392494\pi\)
0.943506 0.331356i \(-0.107506\pi\)
\(6\) 0.786556 0.786556i 0.321110 0.321110i
\(7\) −1.83993 1.90123i −0.695427 0.718597i
\(8\) −2.17299 + 2.17299i −0.768267 + 0.768267i
\(9\) −1.00000 −0.333333
\(10\) −4.48443 −1.41810
\(11\) −1.37164 + 1.37164i −0.413565 + 0.413565i −0.882978 0.469414i \(-0.844465\pi\)
0.469414 + 0.882978i \(0.344465\pi\)
\(12\) 0.762660 0.220161
\(13\) 2.79665 2.27569i 0.775651 0.631162i
\(14\) −0.0482190 + 2.94263i −0.0128871 + 0.786450i
\(15\) 2.85068 + 2.85068i 0.736042 + 0.736042i
\(16\) 1.89303 0.473257
\(17\) −3.67985 −0.892495 −0.446248 0.894910i \(-0.647240\pi\)
−0.446248 + 0.894910i \(0.647240\pi\)
\(18\) 0.786556 + 0.786556i 0.185393 + 0.185393i
\(19\) 1.10886 1.10886i 0.254391 0.254391i −0.568377 0.822768i \(-0.692429\pi\)
0.822768 + 0.568377i \(0.192429\pi\)
\(20\) −2.17410 2.17410i −0.486143 0.486143i
\(21\) 1.90123 1.83993i 0.414882 0.401505i
\(22\) 2.15774 0.460032
\(23\) 0.653796i 0.136326i 0.997674 + 0.0681630i \(0.0217138\pi\)
−0.997674 + 0.0681630i \(0.978286\pi\)
\(24\) −2.17299 2.17299i −0.443559 0.443559i
\(25\) 11.2527i 2.25055i
\(26\) −3.98968 0.409765i −0.782440 0.0803616i
\(27\) 1.00000i 0.192450i
\(28\) −1.44999 + 1.40324i −0.274023 + 0.265187i
\(29\) −1.78095 −0.330715 −0.165357 0.986234i \(-0.552878\pi\)
−0.165357 + 0.986234i \(0.552878\pi\)
\(30\) 4.48443i 0.818742i
\(31\) 5.70136 5.70136i 1.02399 1.02399i 0.0242888 0.999705i \(-0.492268\pi\)
0.999705 0.0242888i \(-0.00773213\pi\)
\(32\) 2.85700 + 2.85700i 0.505051 + 0.505051i
\(33\) −1.37164 1.37164i −0.238772 0.238772i
\(34\) 2.89441 + 2.89441i 0.496387 + 0.496387i
\(35\) −10.6648 0.174758i −1.80269 0.0295395i
\(36\) 0.762660i 0.127110i
\(37\) 3.46293 3.46293i 0.569302 0.569302i −0.362631 0.931933i \(-0.618121\pi\)
0.931933 + 0.362631i \(0.118121\pi\)
\(38\) −1.74437 −0.282974
\(39\) 2.27569 + 2.79665i 0.364402 + 0.447822i
\(40\) 12.3890i 1.95887i
\(41\) 2.67464 2.67464i 0.417709 0.417709i −0.466704 0.884413i \(-0.654559\pi\)
0.884413 + 0.466704i \(0.154559\pi\)
\(42\) −2.94263 0.0482190i −0.454057 0.00744035i
\(43\) 11.0076i 1.67865i 0.543632 + 0.839324i \(0.317049\pi\)
−0.543632 + 0.839324i \(0.682951\pi\)
\(44\) 1.04609 + 1.04609i 0.157705 + 0.157705i
\(45\) −2.85068 + 2.85068i −0.424954 + 0.424954i
\(46\) 0.514247 0.514247i 0.0758216 0.0758216i
\(47\) 3.84609 + 3.84609i 0.561010 + 0.561010i 0.929594 0.368585i \(-0.120158\pi\)
−0.368585 + 0.929594i \(0.620158\pi\)
\(48\) 1.89303i 0.273235i
\(49\) −0.229348 + 6.99624i −0.0327640 + 0.999463i
\(50\) −8.85090 + 8.85090i −1.25171 + 1.25171i
\(51\) 3.67985i 0.515282i
\(52\) −1.73558 2.13289i −0.240681 0.295779i
\(53\) −0.919315 −0.126278 −0.0631388 0.998005i \(-0.520111\pi\)
−0.0631388 + 0.998005i \(0.520111\pi\)
\(54\) −0.786556 + 0.786556i −0.107037 + 0.107037i
\(55\) 7.82021i 1.05448i
\(56\) 8.12948 + 0.133213i 1.08635 + 0.0178013i
\(57\) 1.10886 + 1.10886i 0.146873 + 0.146873i
\(58\) 1.40082 + 1.40082i 0.183937 + 0.183937i
\(59\) 8.69367 + 8.69367i 1.13182 + 1.13182i 0.989875 + 0.141944i \(0.0453354\pi\)
0.141944 + 0.989875i \(0.454665\pi\)
\(60\) 2.17410 2.17410i 0.280675 0.280675i
\(61\) 5.92939i 0.759180i −0.925155 0.379590i \(-0.876065\pi\)
0.925155 0.379590i \(-0.123935\pi\)
\(62\) −8.96887 −1.13905
\(63\) 1.83993 + 1.90123i 0.231809 + 0.239532i
\(64\) 8.28044i 1.03505i
\(65\) 1.48509 14.4596i 0.184203 1.79349i
\(66\) 2.15774i 0.265600i
\(67\) −8.44464 8.44464i −1.03168 1.03168i −0.999482 0.0321948i \(-0.989750\pi\)
−0.0321948 0.999482i \(-0.510250\pi\)
\(68\) 2.80648i 0.340335i
\(69\) −0.653796 −0.0787078
\(70\) 8.25103 + 8.52594i 0.986186 + 1.01904i
\(71\) 8.55531 + 8.55531i 1.01533 + 1.01533i 0.999881 + 0.0154474i \(0.00491724\pi\)
0.0154474 + 0.999881i \(0.495083\pi\)
\(72\) 2.17299 2.17299i 0.256089 0.256089i
\(73\) 6.74551 + 6.74551i 0.789503 + 0.789503i 0.981413 0.191910i \(-0.0614681\pi\)
−0.191910 + 0.981413i \(0.561468\pi\)
\(74\) −5.44757 −0.633268
\(75\) 11.2527 1.29935
\(76\) −0.845686 0.845686i −0.0970069 0.0970069i
\(77\) 5.13152 + 0.0840870i 0.584791 + 0.00958260i
\(78\) 0.409765 3.98968i 0.0463968 0.451742i
\(79\) 9.87363 1.11087 0.555435 0.831560i \(-0.312552\pi\)
0.555435 + 0.831560i \(0.312552\pi\)
\(80\) 5.39642 5.39642i 0.603338 0.603338i
\(81\) 1.00000 0.111111
\(82\) −4.20751 −0.464642
\(83\) −8.71517 + 8.71517i −0.956614 + 0.956614i −0.999097 0.0424828i \(-0.986473\pi\)
0.0424828 + 0.999097i \(0.486473\pi\)
\(84\) −1.40324 1.44999i −0.153106 0.158207i
\(85\) −10.4901 + 10.4901i −1.13781 + 1.13781i
\(86\) 8.65811 8.65811i 0.933629 0.933629i
\(87\) 1.78095i 0.190938i
\(88\) 5.96111i 0.635456i
\(89\) −4.94580 4.94580i −0.524254 0.524254i 0.394600 0.918853i \(-0.370883\pi\)
−0.918853 + 0.394600i \(0.870883\pi\)
\(90\) 4.48443 0.472701
\(91\) −9.47223 1.12998i −0.992960 0.118454i
\(92\) 0.498624 0.0519852
\(93\) 5.70136 + 5.70136i 0.591203 + 0.591203i
\(94\) 6.05033i 0.624043i
\(95\) 6.32203i 0.648626i
\(96\) −2.85700 + 2.85700i −0.291591 + 0.291591i
\(97\) −0.857049 + 0.857049i −0.0870201 + 0.0870201i −0.749277 0.662257i \(-0.769599\pi\)
0.662257 + 0.749277i \(0.269599\pi\)
\(98\) 5.68333 5.32254i 0.574103 0.537658i
\(99\) 1.37164 1.37164i 0.137855 0.137855i
\(100\) −8.58201 −0.858201
\(101\) 7.21984 0.718401 0.359200 0.933260i \(-0.383049\pi\)
0.359200 + 0.933260i \(0.383049\pi\)
\(102\) −2.89441 + 2.89441i −0.286589 + 0.286589i
\(103\) −12.1497 −1.19715 −0.598575 0.801067i \(-0.704266\pi\)
−0.598575 + 0.801067i \(0.704266\pi\)
\(104\) −1.13204 + 11.0221i −0.111006 + 1.08081i
\(105\) 0.174758 10.6648i 0.0170546 1.04078i
\(106\) 0.723093 + 0.723093i 0.0702330 + 0.0702330i
\(107\) −14.3968 −1.39180 −0.695898 0.718141i \(-0.744993\pi\)
−0.695898 + 0.718141i \(0.744993\pi\)
\(108\) −0.762660 −0.0733870
\(109\) 11.6047 + 11.6047i 1.11153 + 1.11153i 0.992944 + 0.118583i \(0.0378353\pi\)
0.118583 + 0.992944i \(0.462165\pi\)
\(110\) 6.15103 6.15103i 0.586477 0.586477i
\(111\) 3.46293 + 3.46293i 0.328687 + 0.328687i
\(112\) −3.48303 3.59908i −0.329116 0.340081i
\(113\) 8.39121 0.789378 0.394689 0.918815i \(-0.370852\pi\)
0.394689 + 0.918815i \(0.370852\pi\)
\(114\) 1.74437i 0.163375i
\(115\) 1.86376 + 1.86376i 0.173797 + 0.173797i
\(116\) 1.35826i 0.126112i
\(117\) −2.79665 + 2.27569i −0.258550 + 0.210387i
\(118\) 13.6761i 1.25899i
\(119\) 6.77065 + 6.99624i 0.620665 + 0.641344i
\(120\) −12.3890 −1.13095
\(121\) 7.23721i 0.657928i
\(122\) −4.66379 + 4.66379i −0.422240 + 0.422240i
\(123\) 2.67464 + 2.67464i 0.241164 + 0.241164i
\(124\) −4.34820 4.34820i −0.390480 0.390480i
\(125\) −17.8245 17.8245i −1.59427 1.59427i
\(126\) 0.0482190 2.94263i 0.00429569 0.262150i
\(127\) 1.87363i 0.166258i 0.996539 + 0.0831291i \(0.0264914\pi\)
−0.996539 + 0.0831291i \(0.973509\pi\)
\(128\) −0.799026 + 0.799026i −0.0706246 + 0.0706246i
\(129\) −11.0076 −0.969168
\(130\) −12.5414 + 10.2052i −1.09995 + 0.895053i
\(131\) 15.5987i 1.36287i −0.731880 0.681433i \(-0.761357\pi\)
0.731880 0.681433i \(-0.238643\pi\)
\(132\) −1.04609 + 1.04609i −0.0910509 + 0.0910509i
\(133\) −4.14843 0.0679778i −0.359715 0.00589442i
\(134\) 13.2844i 1.14759i
\(135\) −2.85068 2.85068i −0.245347 0.245347i
\(136\) 7.99627 7.99627i 0.685674 0.685674i
\(137\) 11.6472 11.6472i 0.995087 0.995087i −0.00490102 0.999988i \(-0.501560\pi\)
0.999988 + 0.00490102i \(0.00156005\pi\)
\(138\) 0.514247 + 0.514247i 0.0437756 + 0.0437756i
\(139\) 2.12226i 0.180008i 0.995941 + 0.0900039i \(0.0286880\pi\)
−0.995941 + 0.0900039i \(0.971312\pi\)
\(140\) −0.133281 + 8.13364i −0.0112643 + 0.687418i
\(141\) −3.84609 + 3.84609i −0.323899 + 0.323899i
\(142\) 13.4584i 1.12941i
\(143\) −0.714571 + 6.95742i −0.0597555 + 0.581809i
\(144\) −1.89303 −0.157752
\(145\) −5.07693 + 5.07693i −0.421616 + 0.421616i
\(146\) 10.6114i 0.878209i
\(147\) −6.99624 0.229348i −0.577040 0.0189163i
\(148\) −2.64104 2.64104i −0.217092 0.217092i
\(149\) −0.409314 0.409314i −0.0335323 0.0335323i 0.690142 0.723674i \(-0.257548\pi\)
−0.723674 + 0.690142i \(0.757548\pi\)
\(150\) −8.85090 8.85090i −0.722673 0.722673i
\(151\) 1.06906 1.06906i 0.0869993 0.0869993i −0.662268 0.749267i \(-0.730406\pi\)
0.749267 + 0.662268i \(0.230406\pi\)
\(152\) 4.81909i 0.390880i
\(153\) 3.67985 0.297498
\(154\) −3.97008 4.10236i −0.319919 0.330578i
\(155\) 32.5055i 2.61090i
\(156\) 2.13289 1.73558i 0.170768 0.138957i
\(157\) 0.372554i 0.0297330i −0.999889 0.0148665i \(-0.995268\pi\)
0.999889 0.0148665i \(-0.00473233\pi\)
\(158\) −7.76616 7.76616i −0.617843 0.617843i
\(159\) 0.919315i 0.0729064i
\(160\) 16.2888 1.28774
\(161\) 1.24302 1.20294i 0.0979635 0.0948047i
\(162\) −0.786556 0.786556i −0.0617977 0.0617977i
\(163\) 4.28689 4.28689i 0.335775 0.335775i −0.518999 0.854775i \(-0.673695\pi\)
0.854775 + 0.518999i \(0.173695\pi\)
\(164\) −2.03984 2.03984i −0.159285 0.159285i
\(165\) −7.82021 −0.608802
\(166\) 13.7099 1.06410
\(167\) 0.407205 + 0.407205i 0.0315104 + 0.0315104i 0.722686 0.691176i \(-0.242907\pi\)
−0.691176 + 0.722686i \(0.742907\pi\)
\(168\) −0.133213 + 8.12948i −0.0102776 + 0.627203i
\(169\) 2.64249 12.7286i 0.203269 0.979123i
\(170\) 16.5021 1.26565
\(171\) −1.10886 + 1.10886i −0.0847969 + 0.0847969i
\(172\) 8.39508 0.640119
\(173\) −23.8232 −1.81124 −0.905622 0.424085i \(-0.860596\pi\)
−0.905622 + 0.424085i \(0.860596\pi\)
\(174\) −1.40082 + 1.40082i −0.106196 + 0.106196i
\(175\) −21.3940 + 20.7042i −1.61724 + 1.56509i
\(176\) −2.59655 + 2.59655i −0.195723 + 0.195723i
\(177\) −8.69367 + 8.69367i −0.653456 + 0.653456i
\(178\) 7.78029i 0.583157i
\(179\) 0.227613i 0.0170126i −0.999964 0.00850628i \(-0.997292\pi\)
0.999964 0.00850628i \(-0.00270767\pi\)
\(180\) 2.17410 + 2.17410i 0.162048 + 0.162048i
\(181\) 20.5214 1.52535 0.762674 0.646784i \(-0.223886\pi\)
0.762674 + 0.646784i \(0.223886\pi\)
\(182\) 6.56165 + 8.33923i 0.486382 + 0.618145i
\(183\) 5.92939 0.438313
\(184\) −1.42069 1.42069i −0.104735 0.104735i
\(185\) 19.7434i 1.45156i
\(186\) 8.96887i 0.657629i
\(187\) 5.04743 5.04743i 0.369105 0.369105i
\(188\) 2.93326 2.93326i 0.213930 0.213930i
\(189\) −1.90123 + 1.83993i −0.138294 + 0.133835i
\(190\) −4.97263 + 4.97263i −0.360752 + 0.360752i
\(191\) 0.119527 0.00864867 0.00432433 0.999991i \(-0.498624\pi\)
0.00432433 + 0.999991i \(0.498624\pi\)
\(192\) 8.28044 0.597589
\(193\) −8.53068 + 8.53068i −0.614051 + 0.614051i −0.943999 0.329948i \(-0.892969\pi\)
0.329948 + 0.943999i \(0.392969\pi\)
\(194\) 1.34823 0.0967975
\(195\) 14.4596 + 1.48509i 1.03547 + 0.106350i
\(196\) 5.33576 + 0.174914i 0.381125 + 0.0124939i
\(197\) 14.3031 + 14.3031i 1.01906 + 1.01906i 0.999815 + 0.0192413i \(0.00612508\pi\)
0.0192413 + 0.999815i \(0.493875\pi\)
\(198\) −2.15774 −0.153344
\(199\) −2.32628 −0.164905 −0.0824527 0.996595i \(-0.526275\pi\)
−0.0824527 + 0.996595i \(0.526275\pi\)
\(200\) 24.4520 + 24.4520i 1.72902 + 1.72902i
\(201\) 8.44464 8.44464i 0.595639 0.595639i
\(202\) −5.67880 5.67880i −0.399559 0.399559i
\(203\) 3.27682 + 3.38600i 0.229988 + 0.237651i
\(204\) −2.80648 −0.196493
\(205\) 15.2491i 1.06504i
\(206\) 9.55646 + 9.55646i 0.665830 + 0.665830i
\(207\) 0.653796i 0.0454420i
\(208\) 5.29414 4.30794i 0.367082 0.298702i
\(209\) 3.04192i 0.210414i
\(210\) −8.52594 + 8.25103i −0.588346 + 0.569375i
\(211\) −9.48119 −0.652712 −0.326356 0.945247i \(-0.605821\pi\)
−0.326356 + 0.945247i \(0.605821\pi\)
\(212\) 0.701125i 0.0481535i
\(213\) −8.55531 + 8.55531i −0.586200 + 0.586200i
\(214\) 11.3239 + 11.3239i 0.774087 + 0.774087i
\(215\) 31.3792 + 31.3792i 2.14004 + 2.14004i
\(216\) 2.17299 + 2.17299i 0.147853 + 0.147853i
\(217\) −21.3297 0.349516i −1.44795 0.0237267i
\(218\) 18.2555i 1.23642i
\(219\) −6.74551 + 6.74551i −0.455820 + 0.455820i
\(220\) 5.96416 0.402104
\(221\) −10.2913 + 8.37419i −0.692265 + 0.563309i
\(222\) 5.44757i 0.365617i
\(223\) −3.56512 + 3.56512i −0.238738 + 0.238738i −0.816327 0.577589i \(-0.803993\pi\)
0.577589 + 0.816327i \(0.303993\pi\)
\(224\) 0.175145 10.6885i 0.0117024 0.714154i
\(225\) 11.2527i 0.750182i
\(226\) −6.60015 6.60015i −0.439036 0.439036i
\(227\) −1.89144 + 1.89144i −0.125539 + 0.125539i −0.767085 0.641546i \(-0.778293\pi\)
0.641546 + 0.767085i \(0.278293\pi\)
\(228\) 0.845686 0.845686i 0.0560069 0.0560069i
\(229\) −8.57080 8.57080i −0.566374 0.566374i 0.364737 0.931111i \(-0.381159\pi\)
−0.931111 + 0.364737i \(0.881159\pi\)
\(230\) 2.93191i 0.193324i
\(231\) −0.0840870 + 5.13152i −0.00553252 + 0.337629i
\(232\) 3.86999 3.86999i 0.254077 0.254077i
\(233\) 3.54231i 0.232064i −0.993245 0.116032i \(-0.962982\pi\)
0.993245 0.116032i \(-0.0370176\pi\)
\(234\) 3.98968 + 0.409765i 0.260813 + 0.0267872i
\(235\) 21.9279 1.43042
\(236\) 6.63031 6.63031i 0.431597 0.431597i
\(237\) 9.87363i 0.641361i
\(238\) 0.177439 10.8284i 0.0115016 0.701903i
\(239\) −17.2035 17.2035i −1.11280 1.11280i −0.992770 0.120029i \(-0.961701\pi\)
−0.120029 0.992770i \(-0.538299\pi\)
\(240\) 5.39642 + 5.39642i 0.348337 + 0.348337i
\(241\) −6.62291 6.62291i −0.426619 0.426619i 0.460856 0.887475i \(-0.347542\pi\)
−0.887475 + 0.460856i \(0.847542\pi\)
\(242\) 5.69247 5.69247i 0.365926 0.365926i
\(243\) 1.00000i 0.0641500i
\(244\) −4.52211 −0.289498
\(245\) 19.2902 + 20.5978i 1.23241 + 1.31595i
\(246\) 4.20751i 0.268261i
\(247\) 0.577675 5.62453i 0.0367566 0.357880i
\(248\) 24.7779i 1.57340i
\(249\) −8.71517 8.71517i −0.552302 0.552302i
\(250\) 28.0400i 1.77340i
\(251\) 7.62601 0.481349 0.240675 0.970606i \(-0.422631\pi\)
0.240675 + 0.970606i \(0.422631\pi\)
\(252\) 1.44999 1.40324i 0.0913409 0.0883957i
\(253\) −0.896773 0.896773i −0.0563796 0.0563796i
\(254\) 1.47372 1.47372i 0.0924693 0.0924693i
\(255\) −10.4901 10.4901i −0.656914 0.656914i
\(256\) −15.3039 −0.956495
\(257\) −19.9162 −1.24234 −0.621170 0.783676i \(-0.713342\pi\)
−0.621170 + 0.783676i \(0.713342\pi\)
\(258\) 8.65811 + 8.65811i 0.539031 + 0.539031i
\(259\) −12.9554 0.212291i −0.805007 0.0131911i
\(260\) −11.0278 1.13262i −0.683913 0.0702422i
\(261\) 1.78095 0.110238
\(262\) −12.2693 + 12.2693i −0.757998 + 0.757998i
\(263\) 0.224683 0.0138545 0.00692727 0.999976i \(-0.497795\pi\)
0.00692727 + 0.999976i \(0.497795\pi\)
\(264\) 5.96111 0.366881
\(265\) −2.62067 + 2.62067i −0.160987 + 0.160987i
\(266\) 3.20950 + 3.31644i 0.196787 + 0.203344i
\(267\) 4.94580 4.94580i 0.302678 0.302678i
\(268\) −6.44039 + 6.44039i −0.393409 + 0.393409i
\(269\) 11.2518i 0.686034i 0.939329 + 0.343017i \(0.111449\pi\)
−0.939329 + 0.343017i \(0.888551\pi\)
\(270\) 4.48443i 0.272914i
\(271\) −9.55246 9.55246i −0.580271 0.580271i 0.354707 0.934978i \(-0.384581\pi\)
−0.934978 + 0.354707i \(0.884581\pi\)
\(272\) −6.96607 −0.422380
\(273\) 1.12998 9.47223i 0.0683893 0.573285i
\(274\) −18.3223 −1.10689
\(275\) 15.4347 + 15.4347i 0.930747 + 0.930747i
\(276\) 0.498624i 0.0300137i
\(277\) 23.8151i 1.43091i 0.698658 + 0.715456i \(0.253781\pi\)
−0.698658 + 0.715456i \(0.746219\pi\)
\(278\) 1.66928 1.66928i 0.100117 0.100117i
\(279\) −5.70136 + 5.70136i −0.341331 + 0.341331i
\(280\) 23.5543 22.7948i 1.40764 1.36225i
\(281\) 0.540489 0.540489i 0.0322429 0.0322429i −0.690802 0.723044i \(-0.742742\pi\)
0.723044 + 0.690802i \(0.242742\pi\)
\(282\) 6.05033 0.360292
\(283\) −6.04531 −0.359356 −0.179678 0.983725i \(-0.557506\pi\)
−0.179678 + 0.983725i \(0.557506\pi\)
\(284\) 6.52479 6.52479i 0.387175 0.387175i
\(285\) 6.32203 0.374485
\(286\) 6.03445 4.91035i 0.356824 0.290355i
\(287\) −10.0063 0.163966i −0.590650 0.00967862i
\(288\) −2.85700 2.85700i −0.168350 0.168350i
\(289\) −3.45870 −0.203453
\(290\) 7.98657 0.468988
\(291\) −0.857049 0.857049i −0.0502411 0.0502411i
\(292\) 5.14454 5.14454i 0.301061 0.301061i
\(293\) −15.4775 15.4775i −0.904204 0.904204i 0.0915927 0.995797i \(-0.470804\pi\)
−0.995797 + 0.0915927i \(0.970804\pi\)
\(294\) 5.32254 + 5.68333i 0.310417 + 0.331458i
\(295\) 49.5657 2.88583
\(296\) 15.0498i 0.874752i
\(297\) 1.37164 + 1.37164i 0.0795906 + 0.0795906i
\(298\) 0.643897i 0.0373000i
\(299\) 1.48784 + 1.82844i 0.0860438 + 0.105741i
\(300\) 8.58201i 0.495483i
\(301\) 20.9280 20.2532i 1.20627 1.16738i
\(302\) −1.68176 −0.0967743
\(303\) 7.21984i 0.414769i
\(304\) 2.09911 2.09911i 0.120392 0.120392i
\(305\) −16.9028 16.9028i −0.967850 0.967850i
\(306\) −2.89441 2.89441i −0.165462 0.165462i
\(307\) 23.2206 + 23.2206i 1.32527 + 1.32527i 0.909446 + 0.415821i \(0.136506\pi\)
0.415821 + 0.909446i \(0.363494\pi\)
\(308\) 0.0641298 3.91360i 0.00365413 0.222998i
\(309\) 12.1497i 0.691175i
\(310\) −25.5674 + 25.5674i −1.45213 + 1.45213i
\(311\) −6.55258 −0.371563 −0.185781 0.982591i \(-0.559482\pi\)
−0.185781 + 0.982591i \(0.559482\pi\)
\(312\) −11.0221 1.13204i −0.624005 0.0640893i
\(313\) 27.9268i 1.57852i 0.614062 + 0.789258i \(0.289535\pi\)
−0.614062 + 0.789258i \(0.710465\pi\)
\(314\) −0.293034 + 0.293034i −0.0165369 + 0.0165369i
\(315\) 10.6648 + 0.174758i 0.600895 + 0.00984649i
\(316\) 7.53023i 0.423608i
\(317\) 5.67885 + 5.67885i 0.318956 + 0.318956i 0.848366 0.529410i \(-0.177587\pi\)
−0.529410 + 0.848366i \(0.677587\pi\)
\(318\) −0.723093 + 0.723093i −0.0405490 + 0.0405490i
\(319\) 2.44283 2.44283i 0.136772 0.136772i
\(320\) −23.6049 23.6049i −1.31955 1.31955i
\(321\) 14.3968i 0.803553i
\(322\) −1.92388 0.0315254i −0.107214 0.00175684i
\(323\) −4.08045 + 4.08045i −0.227043 + 0.227043i
\(324\) 0.762660i 0.0423700i
\(325\) −25.6077 31.4699i −1.42046 1.74564i
\(326\) −6.74376 −0.373502
\(327\) −11.6047 + 11.6047i −0.641741 + 0.641741i
\(328\) 11.6239i 0.641824i
\(329\) 0.235780 14.3888i 0.0129990 0.793281i
\(330\) 6.15103 + 6.15103i 0.338603 + 0.338603i
\(331\) −4.44838 4.44838i −0.244505 0.244505i 0.574206 0.818711i \(-0.305311\pi\)
−0.818711 + 0.574206i \(0.805311\pi\)
\(332\) 6.64671 + 6.64671i 0.364786 + 0.364786i
\(333\) −3.46293 + 3.46293i −0.189767 + 0.189767i
\(334\) 0.640578i 0.0350509i
\(335\) −48.1459 −2.63049
\(336\) 3.59908 3.48303i 0.196346 0.190015i
\(337\) 9.53772i 0.519552i 0.965669 + 0.259776i \(0.0836488\pi\)
−0.965669 + 0.259776i \(0.916351\pi\)
\(338\) −12.0902 + 7.93329i −0.657621 + 0.431514i
\(339\) 8.39121i 0.455748i
\(340\) 8.00036 + 8.00036i 0.433880 + 0.433880i
\(341\) 15.6404i 0.846976i
\(342\) 1.74437 0.0943245
\(343\) 13.7234 12.4365i 0.740996 0.671509i
\(344\) −23.9194 23.9194i −1.28965 1.28965i
\(345\) −1.86376 + 1.86376i −0.100342 + 0.100342i
\(346\) 18.7383 + 18.7383i 1.00738 + 1.00738i
\(347\) −2.22056 −0.119206 −0.0596029 0.998222i \(-0.518983\pi\)
−0.0596029 + 0.998222i \(0.518983\pi\)
\(348\) −1.35826 −0.0728105
\(349\) −7.80156 7.80156i −0.417608 0.417608i 0.466771 0.884378i \(-0.345417\pi\)
−0.884378 + 0.466771i \(0.845417\pi\)
\(350\) 33.1126 + 0.542595i 1.76994 + 0.0290029i
\(351\) −2.27569 2.79665i −0.121467 0.149274i
\(352\) −7.83755 −0.417743
\(353\) 20.7785 20.7785i 1.10593 1.10593i 0.112246 0.993680i \(-0.464195\pi\)
0.993680 0.112246i \(-0.0358046\pi\)
\(354\) 13.6761 0.726877
\(355\) 48.7768 2.58881
\(356\) −3.77196 + 3.77196i −0.199914 + 0.199914i
\(357\) −6.99624 + 6.77065i −0.370280 + 0.358341i
\(358\) −0.179030 + 0.179030i −0.00946203 + 0.00946203i
\(359\) −20.4570 + 20.4570i −1.07968 + 1.07968i −0.0831407 + 0.996538i \(0.526495\pi\)
−0.996538 + 0.0831407i \(0.973505\pi\)
\(360\) 12.3890i 0.652956i
\(361\) 16.5408i 0.870571i
\(362\) −16.1413 16.1413i −0.848366 0.848366i
\(363\) −7.23721 −0.379855
\(364\) −0.861788 + 7.22409i −0.0451700 + 0.378645i
\(365\) 38.4586 2.01301
\(366\) −4.66379 4.66379i −0.243780 0.243780i
\(367\) 8.38088i 0.437478i −0.975783 0.218739i \(-0.929806\pi\)
0.975783 0.218739i \(-0.0701944\pi\)
\(368\) 1.23766i 0.0645173i
\(369\) −2.67464 + 2.67464i −0.139236 + 0.139236i
\(370\) −15.5293 + 15.5293i −0.807329 + 0.807329i
\(371\) 1.69147 + 1.74783i 0.0878168 + 0.0907428i
\(372\) 4.34820 4.34820i 0.225444 0.225444i
\(373\) −0.652524 −0.0337864 −0.0168932 0.999857i \(-0.505378\pi\)
−0.0168932 + 0.999857i \(0.505378\pi\)
\(374\) −7.94017 −0.410576
\(375\) 17.8245 17.8245i 0.920454 0.920454i
\(376\) −16.7150 −0.862010
\(377\) −4.98070 + 4.05290i −0.256519 + 0.208735i
\(378\) 2.94263 + 0.0482190i 0.151352 + 0.00248012i
\(379\) 16.5305 + 16.5305i 0.849115 + 0.849115i 0.990023 0.140907i \(-0.0450020\pi\)
−0.140907 + 0.990023i \(0.545002\pi\)
\(380\) −4.82156 −0.247341
\(381\) −1.87363 −0.0959892
\(382\) −0.0940146 0.0940146i −0.00481021 0.00481021i
\(383\) 13.9994 13.9994i 0.715335 0.715335i −0.252311 0.967646i \(-0.581191\pi\)
0.967646 + 0.252311i \(0.0811907\pi\)
\(384\) −0.799026 0.799026i −0.0407751 0.0407751i
\(385\) 14.8680 14.3886i 0.757744 0.733311i
\(386\) 13.4197 0.683045
\(387\) 11.0076i 0.559549i
\(388\) 0.653637 + 0.653637i 0.0331834 + 0.0331834i
\(389\) 17.3926i 0.881838i 0.897547 + 0.440919i \(0.145347\pi\)
−0.897547 + 0.440919i \(0.854653\pi\)
\(390\) −10.2052 12.5414i −0.516759 0.635058i
\(391\) 2.40587i 0.121670i
\(392\) −14.7044 15.7011i −0.742683 0.793026i
\(393\) 15.5987 0.786851
\(394\) 22.5004i 1.13356i
\(395\) 28.1466 28.1466i 1.41621 1.41621i
\(396\) −1.04609 1.04609i −0.0525682 0.0525682i
\(397\) −16.2242 16.2242i −0.814268 0.814268i 0.171002 0.985271i \(-0.445299\pi\)
−0.985271 + 0.171002i \(0.945299\pi\)
\(398\) 1.82975 + 1.82975i 0.0917168 + 0.0917168i
\(399\) 0.0679778 4.14843i 0.00340314 0.207681i
\(400\) 21.3017i 1.06509i
\(401\) −7.53850 + 7.53850i −0.376454 + 0.376454i −0.869821 0.493367i \(-0.835766\pi\)
0.493367 + 0.869821i \(0.335766\pi\)
\(402\) −13.2844 −0.662563
\(403\) 2.97019 28.9192i 0.147956 1.44057i
\(404\) 5.50628i 0.273948i
\(405\) 2.85068 2.85068i 0.141651 0.141651i
\(406\) 0.0858758 5.24068i 0.00426194 0.260091i
\(407\) 9.49978i 0.470887i
\(408\) 7.99627 + 7.99627i 0.395874 + 0.395874i
\(409\) −2.07779 + 2.07779i −0.102740 + 0.102740i −0.756608 0.653868i \(-0.773145\pi\)
0.653868 + 0.756608i \(0.273145\pi\)
\(410\) −11.9943 + 11.9943i −0.592354 + 0.592354i
\(411\) 11.6472 + 11.6472i 0.574514 + 0.574514i
\(412\) 9.26613i 0.456509i
\(413\) 0.532956 32.5244i 0.0262251 1.60042i
\(414\) −0.514247 + 0.514247i −0.0252739 + 0.0252739i
\(415\) 49.6883i 2.43910i
\(416\) 14.4917 + 1.48839i 0.710512 + 0.0729742i
\(417\) −2.12226 −0.103928
\(418\) 2.39264 2.39264i 0.117028 0.117028i
\(419\) 17.6403i 0.861784i −0.902403 0.430892i \(-0.858199\pi\)
0.902403 0.430892i \(-0.141801\pi\)
\(420\) −8.13364 0.133281i −0.396881 0.00650344i
\(421\) −22.6337 22.6337i −1.10310 1.10310i −0.994035 0.109062i \(-0.965215\pi\)
−0.109062 0.994035i \(-0.534785\pi\)
\(422\) 7.45748 + 7.45748i 0.363025 + 0.363025i
\(423\) −3.84609 3.84609i −0.187003 0.187003i
\(424\) 1.99766 1.99766i 0.0970149 0.0970149i
\(425\) 41.4084i 2.00860i
\(426\) 13.4584 0.652064
\(427\) −11.2731 + 10.9096i −0.545545 + 0.527954i
\(428\) 10.9799i 0.530734i
\(429\) −6.95742 0.714571i −0.335907 0.0344998i
\(430\) 49.3630i 2.38050i
\(431\) −13.0173 13.0173i −0.627023 0.627023i 0.320295 0.947318i \(-0.396218\pi\)
−0.947318 + 0.320295i \(0.896218\pi\)
\(432\) 1.89303i 0.0910784i
\(433\) −0.894979 −0.0430099 −0.0215050 0.999769i \(-0.506846\pi\)
−0.0215050 + 0.999769i \(0.506846\pi\)
\(434\) 16.5021 + 17.0519i 0.792124 + 0.818516i
\(435\) −5.07693 5.07693i −0.243420 0.243420i
\(436\) 8.85043 8.85043i 0.423859 0.423859i
\(437\) 0.724971 + 0.724971i 0.0346801 + 0.0346801i
\(438\) 10.6114 0.507034
\(439\) 12.4360 0.593539 0.296770 0.954949i \(-0.404091\pi\)
0.296770 + 0.954949i \(0.404091\pi\)
\(440\) −16.9932 16.9932i −0.810119 0.810119i
\(441\) 0.229348 6.99624i 0.0109213 0.333154i
\(442\) 14.6814 + 1.50788i 0.698324 + 0.0717223i
\(443\) −13.4521 −0.639129 −0.319565 0.947564i \(-0.603537\pi\)
−0.319565 + 0.947564i \(0.603537\pi\)
\(444\) 2.64104 2.64104i 0.125338 0.125338i
\(445\) −28.1978 −1.33670
\(446\) 5.60833 0.265562
\(447\) 0.409314 0.409314i 0.0193599 0.0193599i
\(448\) −15.7430 + 15.2354i −0.743787 + 0.719804i
\(449\) −13.7721 + 13.7721i −0.649945 + 0.649945i −0.952980 0.303034i \(-0.902000\pi\)
0.303034 + 0.952980i \(0.402000\pi\)
\(450\) 8.85090 8.85090i 0.417235 0.417235i
\(451\) 7.33729i 0.345500i
\(452\) 6.39964i 0.301014i
\(453\) 1.06906 + 1.06906i 0.0502290 + 0.0502290i
\(454\) 2.97544 0.139645
\(455\) −30.2235 + 23.7811i −1.41690 + 1.11487i
\(456\) −4.81909 −0.225675
\(457\) 15.6164 + 15.6164i 0.730505 + 0.730505i 0.970720 0.240214i \(-0.0772177\pi\)
−0.240214 + 0.970720i \(0.577218\pi\)
\(458\) 13.4828i 0.630011i
\(459\) 3.67985i 0.171761i
\(460\) 1.42142 1.42142i 0.0662740 0.0662740i
\(461\) 9.65686 9.65686i 0.449765 0.449765i −0.445511 0.895276i \(-0.646978\pi\)
0.895276 + 0.445511i \(0.146978\pi\)
\(462\) 4.10236 3.97008i 0.190859 0.184705i
\(463\) −9.70922 + 9.70922i −0.451226 + 0.451226i −0.895761 0.444536i \(-0.853369\pi\)
0.444536 + 0.895761i \(0.353369\pi\)
\(464\) −3.37140 −0.156513
\(465\) 32.5055 1.50740
\(466\) −2.78622 + 2.78622i −0.129069 + 0.129069i
\(467\) −15.6220 −0.722898 −0.361449 0.932392i \(-0.617718\pi\)
−0.361449 + 0.932392i \(0.617718\pi\)
\(468\) 1.73558 + 2.13289i 0.0802270 + 0.0985930i
\(469\) −0.517690 + 31.5927i −0.0239047 + 1.45881i
\(470\) −17.2475 17.2475i −0.795569 0.795569i
\(471\) 0.372554 0.0171664
\(472\) −37.7824 −1.73908
\(473\) −15.0985 15.0985i −0.694230 0.694230i
\(474\) 7.76616 7.76616i 0.356712 0.356712i
\(475\) −12.4777 12.4777i −0.572518 0.572518i
\(476\) 5.33576 5.16371i 0.244564 0.236678i
\(477\) 0.919315 0.0420925
\(478\) 27.0630i 1.23783i
\(479\) −7.85952 7.85952i −0.359110 0.359110i 0.504375 0.863485i \(-0.331723\pi\)
−0.863485 + 0.504375i \(0.831723\pi\)
\(480\) 16.2888i 0.743477i
\(481\) 1.80405 17.5651i 0.0822577 0.800902i
\(482\) 10.4186i 0.474553i
\(483\) 1.20294 + 1.24302i 0.0547355 + 0.0565592i
\(484\) 5.51953 0.250888
\(485\) 4.88634i 0.221877i
\(486\) 0.786556 0.786556i 0.0356789 0.0356789i
\(487\) −26.4643 26.4643i −1.19921 1.19921i −0.974403 0.224807i \(-0.927825\pi\)
−0.224807 0.974403i \(-0.572175\pi\)
\(488\) 12.8845 + 12.8845i 0.583253 + 0.583253i
\(489\) 4.28689 + 4.28689i 0.193860 + 0.193860i
\(490\) 1.02849 31.3742i 0.0464627 1.41734i
\(491\) 41.4045i 1.86856i 0.356543 + 0.934279i \(0.383955\pi\)
−0.356543 + 0.934279i \(0.616045\pi\)
\(492\) 2.03984 2.03984i 0.0919632 0.0919632i
\(493\) 6.55365 0.295161
\(494\) −4.87838 + 3.96963i −0.219489 + 0.178602i
\(495\) 7.82021i 0.351492i
\(496\) 10.7928 10.7928i 0.484613 0.484613i
\(497\) 0.524474 32.0067i 0.0235259 1.43570i
\(498\) 13.7099i 0.614357i
\(499\) 17.1634 + 17.1634i 0.768340 + 0.768340i 0.977814 0.209474i \(-0.0671751\pi\)
−0.209474 + 0.977814i \(0.567175\pi\)
\(500\) −13.5941 + 13.5941i −0.607945 + 0.607945i
\(501\) −0.407205 + 0.407205i −0.0181926 + 0.0181926i
\(502\) −5.99828 5.99828i −0.267716 0.267716i
\(503\) 9.14068i 0.407563i −0.979016 0.203781i \(-0.934677\pi\)
0.979016 0.203781i \(-0.0653232\pi\)
\(504\) −8.12948 0.133213i −0.362116 0.00593376i
\(505\) 20.5814 20.5814i 0.915862 0.915862i
\(506\) 1.41072i 0.0627143i
\(507\) 12.7286 + 2.64249i 0.565297 + 0.117357i
\(508\) 1.42895 0.0633992
\(509\) −5.44750 + 5.44750i −0.241456 + 0.241456i −0.817452 0.575996i \(-0.804614\pi\)
0.575996 + 0.817452i \(0.304614\pi\)
\(510\) 16.5021i 0.730723i
\(511\) 0.413527 25.2360i 0.0182933 1.11638i
\(512\) 13.6354 + 13.6354i 0.602607 + 0.602607i
\(513\) −1.10886 1.10886i −0.0489575 0.0489575i
\(514\) 15.6652 + 15.6652i 0.690964 + 0.690964i
\(515\) −34.6350 + 34.6350i −1.52620 + 1.52620i
\(516\) 8.39508i 0.369573i
\(517\) −10.5509 −0.464028
\(518\) 10.0231 + 10.3571i 0.440391 + 0.455064i
\(519\) 23.8232i 1.04572i
\(520\) 28.1934 + 34.6476i 1.23636 + 1.51940i
\(521\) 11.4764i 0.502791i 0.967885 + 0.251395i \(0.0808894\pi\)
−0.967885 + 0.251395i \(0.919111\pi\)
\(522\) −1.40082 1.40082i −0.0613122 0.0613122i
\(523\) 10.4153i 0.455431i −0.973728 0.227715i \(-0.926874\pi\)
0.973728 0.227715i \(-0.0731256\pi\)
\(524\) −11.8965 −0.519702
\(525\) −20.7042 21.3940i −0.903605 0.933712i
\(526\) −0.176726 0.176726i −0.00770560 0.00770560i
\(527\) −20.9801 + 20.9801i −0.913909 + 0.913909i
\(528\) −2.59655 2.59655i −0.113000 0.113000i
\(529\) 22.5726 0.981415
\(530\) 4.12261 0.179075
\(531\) −8.69367 8.69367i −0.377273 0.377273i
\(532\) −0.0518439 + 3.16384i −0.00224772 + 0.137170i
\(533\) 1.39339 13.5667i 0.0603542 0.587638i
\(534\) −7.78029 −0.336686
\(535\) −41.0408 + 41.0408i −1.77435 + 1.77435i
\(536\) 36.7002 1.58521
\(537\) 0.227613 0.00982221
\(538\) 8.85016 8.85016i 0.381558 0.381558i
\(539\) −9.28174 9.91090i −0.399793 0.426893i
\(540\) −2.17410 + 2.17410i −0.0935583 + 0.0935583i
\(541\) 30.0820 30.0820i 1.29333 1.29333i 0.360610 0.932717i \(-0.382568\pi\)
0.932717 0.360610i \(-0.117432\pi\)
\(542\) 15.0271i 0.645469i
\(543\) 20.5214i 0.880660i
\(544\) −10.5133 10.5133i −0.450755 0.450755i
\(545\) 66.1625 2.83409
\(546\) −8.33923 + 6.56165i −0.356886 + 0.280813i
\(547\) −4.22100 −0.180477 −0.0902384 0.995920i \(-0.528763\pi\)
−0.0902384 + 0.995920i \(0.528763\pi\)
\(548\) −8.88285 8.88285i −0.379457 0.379457i
\(549\) 5.92939i 0.253060i
\(550\) 24.2805i 1.03532i
\(551\) −1.97484 + 1.97484i −0.0841308 + 0.0841308i
\(552\) 1.42069 1.42069i 0.0604686 0.0604686i
\(553\) −18.1668 18.7720i −0.772529 0.798269i
\(554\) 18.7319 18.7319i 0.795843 0.795843i
\(555\) 19.7434 0.838060
\(556\) 1.61856 0.0686424
\(557\) 24.4288 24.4288i 1.03508 1.03508i 0.0357207 0.999362i \(-0.488627\pi\)
0.999362 0.0357207i \(-0.0113727\pi\)
\(558\) 8.96887 0.379682
\(559\) 25.0499 + 30.7845i 1.05950 + 1.30204i
\(560\) −20.1888 0.330822i −0.853134 0.0139798i
\(561\) 5.04743 + 5.04743i 0.213103 + 0.213103i
\(562\) −0.850249 −0.0358656
\(563\) −7.55703 −0.318491 −0.159245 0.987239i \(-0.550906\pi\)
−0.159245 + 0.987239i \(0.550906\pi\)
\(564\) 2.93326 + 2.93326i 0.123512 + 0.123512i
\(565\) 23.9206 23.9206i 1.00635 1.00635i
\(566\) 4.75497 + 4.75497i 0.199866 + 0.199866i
\(567\) −1.83993 1.90123i −0.0772696 0.0798441i
\(568\) −37.1811 −1.56009
\(569\) 30.8175i 1.29193i −0.763365 0.645967i \(-0.776454\pi\)
0.763365 0.645967i \(-0.223546\pi\)
\(570\) −4.97263 4.97263i −0.208280 0.208280i
\(571\) 21.7092i 0.908500i −0.890874 0.454250i \(-0.849907\pi\)
0.890874 0.454250i \(-0.150093\pi\)
\(572\) 5.30615 + 0.544975i 0.221861 + 0.0227866i
\(573\) 0.119527i 0.00499331i
\(574\) 7.74151 + 7.99944i 0.323124 + 0.333890i
\(575\) 7.35700 0.306808
\(576\) 8.28044i 0.345018i
\(577\) −25.9426 + 25.9426i −1.08000 + 1.08000i −0.0834969 + 0.996508i \(0.526609\pi\)
−0.996508 + 0.0834969i \(0.973391\pi\)
\(578\) 2.72046 + 2.72046i 0.113156 + 0.113156i
\(579\) −8.53068 8.53068i −0.354523 0.354523i
\(580\) 3.87197 + 3.87197i 0.160775 + 0.160775i
\(581\) 32.6048 + 0.534275i 1.35268 + 0.0221654i
\(582\) 1.34823i 0.0558861i
\(583\) 1.26097 1.26097i 0.0522240 0.0522240i
\(584\) −29.3158 −1.21310
\(585\) −1.48509 + 14.4596i −0.0614011 + 0.597831i
\(586\) 24.3478i 1.00580i
\(587\) 9.91583 9.91583i 0.409270 0.409270i −0.472214 0.881484i \(-0.656545\pi\)
0.881484 + 0.472214i \(0.156545\pi\)
\(588\) −0.174914 + 5.33576i −0.00721335 + 0.220043i
\(589\) 12.6441i 0.520989i
\(590\) −38.9862 38.9862i −1.60504 1.60504i
\(591\) −14.3031 + 14.3031i −0.588352 + 0.588352i
\(592\) 6.55543 6.55543i 0.269426 0.269426i
\(593\) −14.3032 14.3032i −0.587360 0.587360i 0.349555 0.936916i \(-0.386333\pi\)
−0.936916 + 0.349555i \(0.886333\pi\)
\(594\) 2.15774i 0.0885332i
\(595\) 39.2450 + 0.643083i 1.60889 + 0.0263638i
\(596\) −0.312168 + 0.312168i −0.0127869 + 0.0127869i
\(597\) 2.32628i 0.0952081i
\(598\) 0.267903 2.60844i 0.0109554 0.106667i
\(599\) 12.3813 0.505886 0.252943 0.967481i \(-0.418601\pi\)
0.252943 + 0.967481i \(0.418601\pi\)
\(600\) −24.4520 + 24.4520i −0.998250 + 0.998250i
\(601\) 32.7835i 1.33727i 0.743592 + 0.668634i \(0.233121\pi\)
−0.743592 + 0.668634i \(0.766879\pi\)
\(602\) −32.3914 0.530777i −1.32017 0.0216328i
\(603\) 8.44464 + 8.44464i 0.343892 + 0.343892i
\(604\) −0.815333 0.815333i −0.0331754 0.0331754i
\(605\) 20.6310 + 20.6310i 0.838768 + 0.838768i
\(606\) 5.67880 5.67880i 0.230686 0.230686i
\(607\) 26.5960i 1.07950i 0.841826 + 0.539749i \(0.181481\pi\)
−0.841826 + 0.539749i \(0.818519\pi\)
\(608\) 6.33605 0.256961
\(609\) −3.38600 + 3.27682i −0.137208 + 0.132784i
\(610\) 26.5899i 1.07660i
\(611\) 19.5087 + 2.00366i 0.789236 + 0.0810596i
\(612\) 2.80648i 0.113445i
\(613\) 10.6735 + 10.6735i 0.431099 + 0.431099i 0.889002 0.457903i \(-0.151399\pi\)
−0.457903 + 0.889002i \(0.651399\pi\)
\(614\) 36.5285i 1.47417i
\(615\) 15.2491 0.614903
\(616\) −11.3334 + 10.9680i −0.456637 + 0.441913i
\(617\) 25.3375 + 25.3375i 1.02005 + 1.02005i 0.999795 + 0.0202541i \(0.00644752\pi\)
0.0202541 + 0.999795i \(0.493552\pi\)
\(618\) −9.55646 + 9.55646i −0.384417 + 0.384417i
\(619\) 20.2261 + 20.2261i 0.812955 + 0.812955i 0.985076 0.172121i \(-0.0550620\pi\)
−0.172121 + 0.985076i \(0.555062\pi\)
\(620\) −24.7906 −0.995615
\(621\) 0.653796 0.0262359
\(622\) 5.15397 + 5.15397i 0.206655 + 0.206655i
\(623\) −0.303197 + 18.5030i −0.0121473 + 0.741307i
\(624\) 4.30794 + 5.29414i 0.172456 + 0.211935i
\(625\) −45.3603 −1.81441
\(626\) 21.9660 21.9660i 0.877937 0.877937i
\(627\) −3.04192 −0.121483
\(628\) −0.284132 −0.0113381
\(629\) −12.7431 + 12.7431i −0.508099 + 0.508099i
\(630\) −8.25103 8.52594i −0.328729 0.339682i
\(631\) 6.74447 6.74447i 0.268493 0.268493i −0.560000 0.828493i \(-0.689199\pi\)
0.828493 + 0.560000i \(0.189199\pi\)
\(632\) −21.4553 + 21.4553i −0.853445 + 0.853445i
\(633\) 9.48119i 0.376843i
\(634\) 8.93346i 0.354793i
\(635\) 5.34113 + 5.34113i 0.211956 + 0.211956i
\(636\) −0.701125 −0.0278014
\(637\) 15.2799 + 20.0880i 0.605410 + 0.795914i
\(638\) −3.84284 −0.152139
\(639\) −8.55531 8.55531i −0.338443 0.338443i
\(640\) 4.55553i 0.180073i
\(641\) 42.7458i 1.68836i 0.536062 + 0.844179i \(0.319911\pi\)
−0.536062 + 0.844179i \(0.680089\pi\)
\(642\) −11.3239 + 11.3239i −0.446919 + 0.446919i
\(643\) 24.5416 24.5416i 0.967827 0.967827i −0.0316713 0.999498i \(-0.510083\pi\)
0.999498 + 0.0316713i \(0.0100830\pi\)
\(644\) −0.917432 0.948000i −0.0361519 0.0373564i
\(645\) −31.3792 + 31.3792i −1.23556 + 1.23556i
\(646\) 6.41901 0.252553
\(647\) 32.2371 1.26737 0.633685 0.773591i \(-0.281541\pi\)
0.633685 + 0.773591i \(0.281541\pi\)
\(648\) −2.17299 + 2.17299i −0.0853630 + 0.0853630i
\(649\) −23.8492 −0.936161
\(650\) −4.61098 + 44.8947i −0.180857 + 1.76092i
\(651\) 0.349516 21.3297i 0.0136986 0.835975i
\(652\) −3.26944 3.26944i −0.128041 0.128041i
\(653\) 33.3640 1.30563 0.652817 0.757516i \(-0.273587\pi\)
0.652817 + 0.757516i \(0.273587\pi\)
\(654\) 18.2555 0.713845
\(655\) −44.4669 44.4669i −1.73747 1.73747i
\(656\) 5.06318 5.06318i 0.197684 0.197684i
\(657\) −6.74551 6.74551i −0.263168 0.263168i
\(658\) −11.5031 + 11.1321i −0.448436 + 0.433976i
\(659\) −6.27743 −0.244534 −0.122267 0.992497i \(-0.539016\pi\)
−0.122267 + 0.992497i \(0.539016\pi\)
\(660\) 5.96416i 0.232155i
\(661\) 27.2446 + 27.2446i 1.05969 + 1.05969i 0.998101 + 0.0615924i \(0.0196179\pi\)
0.0615924 + 0.998101i \(0.480382\pi\)
\(662\) 6.99780i 0.271977i
\(663\) −8.37419 10.2913i −0.325227 0.399679i
\(664\) 37.8759i 1.46987i
\(665\) −12.0196 + 11.6321i −0.466101 + 0.451072i
\(666\) 5.44757 0.211089
\(667\) 1.16438i 0.0450850i
\(668\) 0.310559 0.310559i 0.0120159 0.0120159i
\(669\) −3.56512 3.56512i −0.137835 0.137835i
\(670\) 37.8694 + 37.8694i 1.46302 + 1.46302i
\(671\) 8.13298 + 8.13298i 0.313970 + 0.313970i
\(672\) 10.6885 + 0.175145i 0.412317 + 0.00675638i
\(673\) 0.229492i 0.00884627i −0.999990 0.00442313i \(-0.998592\pi\)
0.999990 0.00442313i \(-0.00140793\pi\)
\(674\) 7.50194 7.50194i 0.288964 0.288964i
\(675\) −11.2527 −0.433118
\(676\) −9.70760 2.01532i −0.373369 0.0775124i
\(677\) 4.51279i 0.173441i 0.996233 + 0.0867204i \(0.0276387\pi\)
−0.996233 + 0.0867204i \(0.972361\pi\)
\(678\) 6.60015 6.60015i 0.253477 0.253477i
\(679\) 3.20635 + 0.0525405i 0.123049 + 0.00201632i
\(680\) 45.5896i 1.74828i
\(681\) −1.89144 1.89144i −0.0724801 0.0724801i
\(682\) 12.3021 12.3021i 0.471070 0.471070i
\(683\) 15.0159 15.0159i 0.574568 0.574568i −0.358833 0.933402i \(-0.616825\pi\)
0.933402 + 0.358833i \(0.116825\pi\)
\(684\) 0.845686 + 0.845686i 0.0323356 + 0.0323356i
\(685\) 66.4048i 2.53720i
\(686\) −20.5763 1.01224i −0.785606 0.0386474i
\(687\) 8.57080 8.57080i 0.326996 0.326996i
\(688\) 20.8378i 0.794432i
\(689\) −2.57100 + 2.09207i −0.0979474 + 0.0797017i
\(690\) 2.93191 0.111616
\(691\) 13.7088 13.7088i 0.521506 0.521506i −0.396520 0.918026i \(-0.629782\pi\)
0.918026 + 0.396520i \(0.129782\pi\)
\(692\) 18.1690i 0.690682i
\(693\) −5.13152 0.0840870i −0.194930 0.00319420i
\(694\) 1.74659 + 1.74659i 0.0662998 + 0.0662998i
\(695\) 6.04988 + 6.04988i 0.229485 + 0.229485i
\(696\) 3.86999 + 3.86999i 0.146692 + 0.146692i
\(697\) −9.84229 + 9.84229i −0.372803 + 0.372803i
\(698\) 12.2727i 0.464529i
\(699\) 3.54231 0.133982
\(700\) 15.7903 + 16.3164i 0.596816 + 0.616701i
\(701\) 24.9025i 0.940553i 0.882519 + 0.470277i \(0.155846\pi\)
−0.882519 + 0.470277i \(0.844154\pi\)
\(702\) −0.409765 + 3.98968i −0.0154656 + 0.150581i
\(703\) 7.67983i 0.289650i
\(704\) 11.3578 + 11.3578i 0.428062 + 0.428062i
\(705\) 21.9279i 0.825853i
\(706\) −32.6869 −1.23019
\(707\) −13.2840 13.7266i −0.499595 0.516241i
\(708\) 6.63031 + 6.63031i 0.249182 + 0.249182i
\(709\) −26.6069 + 26.6069i −0.999245 + 0.999245i −1.00000 0.000754806i \(-0.999760\pi\)
0.000754806 1.00000i \(0.499760\pi\)
\(710\) −38.3657 38.3657i −1.43984 1.43984i
\(711\) −9.87363 −0.370290
\(712\) 21.4943 0.805533
\(713\) 3.72753 + 3.72753i 0.139597 + 0.139597i
\(714\) 10.8284 + 0.177439i 0.405244 + 0.00664048i
\(715\) 17.7963 + 21.8704i 0.665546 + 0.817906i
\(716\) −0.173591 −0.00648740
\(717\) 17.2035 17.2035i 0.642475 0.642475i
\(718\) 32.1811 1.20099
\(719\) −11.7193 −0.437054 −0.218527 0.975831i \(-0.570125\pi\)
−0.218527 + 0.975831i \(0.570125\pi\)
\(720\) −5.39642 + 5.39642i −0.201113 + 0.201113i
\(721\) 22.3546 + 23.0995i 0.832530 + 0.860269i
\(722\) 13.0103 13.0103i 0.484193 0.484193i
\(723\) 6.62291 6.62291i 0.246309 0.246309i
\(724\) 15.6509i 0.581661i
\(725\) 20.0406i 0.744289i
\(726\) 5.69247 + 5.69247i 0.211267 + 0.211267i
\(727\) −1.29408 −0.0479949 −0.0239975 0.999712i \(-0.507639\pi\)
−0.0239975 + 0.999712i \(0.507639\pi\)
\(728\) 23.0384 18.1276i 0.853862 0.671854i
\(729\) −1.00000 −0.0370370
\(730\) −30.2498 30.2498i −1.11960 1.11960i
\(731\) 40.5064i 1.49818i
\(732\) 4.52211i 0.167142i
\(733\) −9.51083 + 9.51083i −0.351291 + 0.351291i −0.860590 0.509299i \(-0.829905\pi\)
0.509299 + 0.860590i \(0.329905\pi\)
\(734\) −6.59203 + 6.59203i −0.243316 + 0.243316i
\(735\) −20.5978 + 19.2902i −0.759762 + 0.711531i
\(736\) −1.86790 + 1.86790i −0.0688516 + 0.0688516i
\(737\) 23.1660 0.853330
\(738\) 4.20751 0.154881
\(739\) 13.5044 13.5044i 0.496766 0.496766i −0.413663 0.910430i \(-0.635751\pi\)
0.910430 + 0.413663i \(0.135751\pi\)
\(740\) −15.0575 −0.553525
\(741\) 5.62453 + 0.577675i 0.206622 + 0.0212214i
\(742\) 0.0443284 2.70520i 0.00162735 0.0993111i
\(743\) −27.2778 27.2778i −1.00073 1.00073i −1.00000 0.000725386i \(-0.999769\pi\)
−0.000725386 1.00000i \(-0.500231\pi\)
\(744\) −24.7779 −0.908403
\(745\) −2.33365 −0.0854982
\(746\) 0.513246 + 0.513246i 0.0187913 + 0.0187913i
\(747\) 8.71517 8.71517i 0.318871 0.318871i
\(748\) −3.84947 3.84947i −0.140751 0.140751i
\(749\) 26.4891 + 27.3717i 0.967891 + 1.00014i
\(750\) −28.0400 −1.02387
\(751\) 17.3413i 0.632792i −0.948627 0.316396i \(-0.897527\pi\)
0.948627 0.316396i \(-0.102473\pi\)
\(752\) 7.28076 + 7.28076i 0.265502 + 0.265502i
\(753\) 7.62601i 0.277907i
\(754\) 7.10543 + 0.729773i 0.258764 + 0.0265768i
\(755\) 6.09512i 0.221824i
\(756\) 1.40324 + 1.44999i 0.0510353 + 0.0527357i
\(757\) 14.0722 0.511464 0.255732 0.966748i \(-0.417684\pi\)
0.255732 + 0.966748i \(0.417684\pi\)
\(758\) 26.0043i 0.944520i
\(759\) 0.896773 0.896773i 0.0325508 0.0325508i
\(760\) 13.7377 + 13.7377i 0.498318 + 0.498318i
\(761\) 17.8688 + 17.8688i 0.647742 + 0.647742i 0.952447 0.304705i \(-0.0985579\pi\)
−0.304705 + 0.952447i \(0.598558\pi\)
\(762\) 1.47372 + 1.47372i 0.0533872 + 0.0533872i
\(763\) 0.711413 43.4149i 0.0257549 1.57173i
\(764\) 0.0911585i 0.00329800i
\(765\) 10.4901 10.4901i 0.379269 0.379269i
\(766\) −22.0226 −0.795708
\(767\) 44.0972 + 4.52907i 1.59226 + 0.163535i
\(768\) 15.3039i 0.552233i
\(769\) −24.0788 + 24.0788i −0.868302 + 0.868302i −0.992284 0.123982i \(-0.960433\pi\)
0.123982 + 0.992284i \(0.460433\pi\)
\(770\) −23.0119 0.377082i −0.829293 0.0135891i
\(771\) 19.9162i 0.717266i
\(772\) 6.50601 + 6.50601i 0.234156 + 0.234156i
\(773\) 16.3658 16.3658i 0.588636 0.588636i −0.348626 0.937262i \(-0.613352\pi\)
0.937262 + 0.348626i \(0.113352\pi\)
\(774\) −8.65811 + 8.65811i −0.311210 + 0.311210i
\(775\) −64.1558 64.1558i −2.30455 2.30455i
\(776\) 3.72471i 0.133709i
\(777\) 0.212291 12.9554i 0.00761591 0.464771i
\(778\) 13.6802 13.6802i 0.490460 0.490460i
\(779\) 5.93163i 0.212523i
\(780\) 1.13262 11.0278i 0.0405544 0.394857i
\(781\) −23.4696 −0.839808
\(782\) −1.89235 + 1.89235i −0.0676704 + 0.0676704i
\(783\) 1.78095i 0.0636461i
\(784\) −0.434162 + 13.2441i −0.0155058 + 0.473003i
\(785\) −1.06203 1.06203i −0.0379055 0.0379055i
\(786\) −12.2693 12.2693i −0.437630 0.437630i
\(787\) −9.35789 9.35789i −0.333573 0.333573i 0.520369 0.853942i \(-0.325794\pi\)
−0.853942 + 0.520369i \(0.825794\pi\)
\(788\) 10.9084 10.9084i 0.388597 0.388597i
\(789\) 0.224683i 0.00799892i
\(790\) −44.2777 −1.57533
\(791\) −15.4392 15.9536i −0.548955 0.567245i
\(792\) 5.96111i 0.211819i
\(793\) −13.4934 16.5824i −0.479166 0.588859i
\(794\) 25.5224i 0.905758i
\(795\) −2.62067 2.62067i −0.0929456 0.0929456i
\(796\) 1.77416i 0.0628834i
\(797\) 8.50189 0.301152 0.150576 0.988598i \(-0.451887\pi\)
0.150576 + 0.988598i \(0.451887\pi\)
\(798\) −3.31644 + 3.20950i −0.117401 + 0.113615i
\(799\) −14.1530 14.1530i −0.500698 0.500698i
\(800\) 32.1490 32.1490i 1.13664 1.13664i
\(801\) 4.94580 + 4.94580i 0.174751 + 0.174751i
\(802\) 11.8589 0.418752
\(803\) −18.5048 −0.653021
\(804\) −6.44039 6.44039i −0.227135 0.227135i
\(805\) 0.114256 6.97263i 0.00402700 0.245753i
\(806\) −25.0828 + 20.4103i −0.883503 + 0.718924i
\(807\) −11.2518 −0.396082
\(808\) −15.6886 + 15.6886i −0.551923 + 0.551923i
\(809\) 4.57041 0.160687 0.0803434 0.996767i \(-0.474398\pi\)
0.0803434 + 0.996767i \(0.474398\pi\)
\(810\) −4.48443 −0.157567
\(811\) −29.0467 + 29.0467i −1.01997 + 1.01997i −0.0201724 + 0.999797i \(0.506422\pi\)
−0.999797 + 0.0201724i \(0.993578\pi\)
\(812\) 2.58237 2.49910i 0.0906234 0.0877013i
\(813\) 9.55246 9.55246i 0.335019 0.335019i
\(814\) 7.47211 7.47211i 0.261897 0.261897i
\(815\) 24.4411i 0.856135i
\(816\) 6.96607i 0.243861i
\(817\) 12.2060 + 12.2060i 0.427033 + 0.427033i
\(818\) 3.26859 0.114284
\(819\) 9.47223 + 1.12998i 0.330987 + 0.0394846i
\(820\) −11.6299 −0.406133
\(821\) 24.7896 + 24.7896i 0.865163 + 0.865163i 0.991932 0.126769i \(-0.0404606\pi\)
−0.126769 + 0.991932i \(0.540461\pi\)
\(822\) 18.3223i 0.639065i
\(823\) 29.6585i 1.03383i 0.856036 + 0.516916i \(0.172920\pi\)
−0.856036 + 0.516916i \(0.827080\pi\)
\(824\) 26.4012 26.4012i 0.919731 0.919731i
\(825\) −15.4347 + 15.4347i −0.537367 + 0.537367i
\(826\) −26.0014 + 25.1630i −0.904705 + 0.875533i
\(827\) 28.6388 28.6388i 0.995870 0.995870i −0.00412144 0.999992i \(-0.501312\pi\)
0.999992 + 0.00412144i \(0.00131190\pi\)
\(828\) −0.498624 −0.0173284
\(829\) 11.4568 0.397912 0.198956 0.980008i \(-0.436245\pi\)
0.198956 + 0.980008i \(0.436245\pi\)
\(830\) 39.0826 39.0826i 1.35658 1.35658i
\(831\) −23.8151 −0.826138
\(832\) −18.8437 23.1575i −0.653287 0.802841i
\(833\) 0.843965 25.7451i 0.0292417 0.892016i
\(834\) 1.66928 + 1.66928i 0.0578023 + 0.0578023i
\(835\) 2.32162 0.0803429
\(836\) 2.31995 0.0802373
\(837\) −5.70136 5.70136i −0.197068 0.197068i
\(838\) −13.8751 + 13.8751i −0.479306 + 0.479306i
\(839\) −22.2494 22.2494i −0.768133 0.768133i 0.209644 0.977778i \(-0.432769\pi\)
−0.977778 + 0.209644i \(0.932769\pi\)
\(840\) 22.7948 + 23.5543i 0.786495 + 0.812700i
\(841\) −25.8282 −0.890628
\(842\) 35.6053i 1.22704i
\(843\) 0.540489 + 0.540489i 0.0186154 + 0.0186154i
\(844\) 7.23093i 0.248899i
\(845\) −28.7522 43.8180i −0.989107 1.50739i
\(846\) 6.05033i 0.208014i
\(847\) 13.7596 13.3159i 0.472785 0.457541i
\(848\) −1.74029 −0.0597618
\(849\) 6.04531i 0.207474i
\(850\) 32.5700 32.5700i 1.11714 1.11714i
\(851\) 2.26405 + 2.26405i 0.0776107 + 0.0776107i
\(852\) 6.52479 + 6.52479i 0.223536 + 0.223536i
\(853\) −7.32728 7.32728i −0.250881 0.250881i 0.570451 0.821332i \(-0.306769\pi\)
−0.821332 + 0.570451i \(0.806769\pi\)
\(854\) 17.4480 + 0.285909i 0.597057 + 0.00978360i
\(855\) 6.32203i 0.216209i
\(856\) 31.2841 31.2841i 1.06927 1.06927i
\(857\) 17.5648 0.600004 0.300002 0.953939i \(-0.403013\pi\)
0.300002 + 0.953939i \(0.403013\pi\)
\(858\) 4.91035 + 6.03445i 0.167636 + 0.206013i
\(859\) 17.1020i 0.583514i −0.956492 0.291757i \(-0.905760\pi\)
0.956492 0.291757i \(-0.0942399\pi\)
\(860\) 23.9317 23.9317i 0.816063 0.816063i
\(861\) 0.163966 10.0063i 0.00558795 0.341012i
\(862\) 20.4777i 0.697474i
\(863\) −16.9381 16.9381i −0.576579 0.576579i 0.357380 0.933959i \(-0.383670\pi\)
−0.933959 + 0.357380i \(0.883670\pi\)
\(864\) 2.85700 2.85700i 0.0971971 0.0971971i
\(865\) −67.9123 + 67.9123i −2.30909 + 2.30909i
\(866\) 0.703951 + 0.703951i 0.0239212 + 0.0239212i
\(867\) 3.45870i 0.117463i
\(868\) −0.266562 + 16.2673i −0.00904770 + 0.552148i
\(869\) −13.5431 + 13.5431i −0.459417 + 0.459417i
\(870\) 7.98657i 0.270770i
\(871\) −42.8340 4.39933i −1.45138 0.149066i
\(872\) −50.4336 −1.70790
\(873\) 0.857049 0.857049i 0.0290067 0.0290067i
\(874\) 1.14046i 0.0385766i
\(875\) −1.09271 + 66.6843i −0.0369405 + 2.25434i
\(876\) 5.14454 + 5.14454i 0.173818 + 0.173818i
\(877\) −7.32085 7.32085i −0.247208 0.247208i 0.572616 0.819824i \(-0.305929\pi\)
−0.819824 + 0.572616i \(0.805929\pi\)
\(878\) −9.78163 9.78163i −0.330114 0.330114i
\(879\) 15.4775 15.4775i 0.522042 0.522042i
\(880\) 14.8039i 0.499039i
\(881\) −40.4345 −1.36227 −0.681136 0.732157i \(-0.738514\pi\)
−0.681136 + 0.732157i \(0.738514\pi\)
\(882\) −5.68333 + 5.32254i −0.191368 + 0.179219i
\(883\) 19.4706i 0.655238i 0.944810 + 0.327619i \(0.106246\pi\)
−0.944810 + 0.327619i \(0.893754\pi\)
\(884\) 6.38666 + 7.84873i 0.214807 + 0.263981i
\(885\) 49.5657i 1.66613i
\(886\) 10.5808 + 10.5808i 0.355470 + 0.355470i
\(887\) 31.1044i 1.04438i 0.852828 + 0.522192i \(0.174886\pi\)
−0.852828 + 0.522192i \(0.825114\pi\)
\(888\) −15.0498 −0.505038
\(889\) 3.56221 3.44735i 0.119473 0.115620i
\(890\) 22.1791 + 22.1791i 0.743445 + 0.743445i
\(891\) −1.37164 + 1.37164i −0.0459517 + 0.0459517i
\(892\) 2.71897 + 2.71897i 0.0910380 + 0.0910380i
\(893\) 8.52958 0.285431
\(894\) −0.643897 −0.0215351
\(895\) −0.648850 0.648850i −0.0216887 0.0216887i
\(896\) 2.98928 + 0.0489835i 0.0998648 + 0.00163642i
\(897\) −1.82844 + 1.48784i −0.0610498 + 0.0496774i
\(898\) 21.6650 0.722972
\(899\) −10.1539 + 10.1539i −0.338650 + 0.338650i
\(900\) 8.58201 0.286067
\(901\) 3.38294 0.112702
\(902\) 5.77119 5.77119i 0.192160 0.192160i
\(903\) 20.2532 + 20.9280i 0.673985 + 0.696441i
\(904\) −18.2340 + 18.2340i −0.606453 + 0.606453i
\(905\) 58.5000 58.5000i 1.94461 1.94461i
\(906\) 1.68176i 0.0558727i
\(907\) 1.02572i 0.0340584i −0.999855 0.0170292i \(-0.994579\pi\)
0.999855 0.0170292i \(-0.00542082\pi\)
\(908\) 1.44253 + 1.44253i 0.0478719 + 0.0478719i
\(909\) −7.21984 −0.239467
\(910\) 42.4776 + 5.06730i 1.40812 + 0.167979i
\(911\) −41.0344 −1.35953 −0.679766 0.733429i \(-0.737919\pi\)
−0.679766 + 0.733429i \(0.737919\pi\)
\(912\) 2.09911 + 2.09911i 0.0695085 + 0.0695085i
\(913\) 23.9082i 0.791244i
\(914\) 24.5664i 0.812583i
\(915\) 16.9028 16.9028i 0.558788 0.558788i
\(916\) −6.53661 + 6.53661i −0.215976 + 0.215976i
\(917\) −29.6567 + 28.7005i −0.979352 + 0.947773i
\(918\) 2.89441 2.89441i 0.0955297 0.0955297i
\(919\) −15.4977 −0.511222 −0.255611 0.966780i \(-0.582277\pi\)
−0.255611 + 0.966780i \(0.582277\pi\)
\(920\) −8.09986 −0.267045
\(921\) −23.2206 + 23.2206i −0.765144 + 0.765144i
\(922\) −15.1913 −0.500299
\(923\) 43.3954 + 4.45699i 1.42838 + 0.146703i
\(924\) 3.91360 + 0.0641298i 0.128748 + 0.00210971i
\(925\) −38.9674 38.9674i −1.28124 1.28124i
\(926\) 15.2737 0.501924
\(927\) 12.1497 0.399050
\(928\) −5.08818 5.08818i −0.167028 0.167028i
\(929\) 23.0704 23.0704i 0.756914 0.756914i −0.218845 0.975760i \(-0.570229\pi\)
0.975760 + 0.218845i \(0.0702290\pi\)
\(930\) −25.5674 25.5674i −0.838387 0.838387i
\(931\) 7.50356 + 8.01219i 0.245919 + 0.262589i
\(932\) −2.70158 −0.0884932
\(933\) 6.55258i 0.214522i
\(934\) 12.2875 + 12.2875i 0.402061 + 0.402061i
\(935\) 28.7772i 0.941115i
\(936\) 1.13204 11.0221i 0.0370020 0.360269i
\(937\) 23.9494i 0.782391i 0.920308 + 0.391196i \(0.127938\pi\)
−0.920308 + 0.391196i \(0.872062\pi\)
\(938\) 25.2566 24.4422i 0.824657 0.798067i
\(939\) −27.9268 −0.911357
\(940\) 16.7235i 0.545462i
\(941\) −35.7947 + 35.7947i −1.16687 + 1.16687i −0.183935 + 0.982938i \(0.558884\pi\)
−0.982938 + 0.183935i \(0.941116\pi\)
\(942\) −0.293034 0.293034i −0.00954758 0.00954758i
\(943\) 1.74867 + 1.74867i 0.0569446 + 0.0569446i
\(944\) 16.4574 + 16.4574i 0.535642 + 0.535642i
\(945\) −0.174758 + 10.6648i −0.00568487 + 0.346927i
\(946\) 23.7516i 0.772232i
\(947\) 24.7804 24.7804i 0.805256 0.805256i −0.178656 0.983912i \(-0.557175\pi\)
0.983912 + 0.178656i \(0.0571748\pi\)
\(948\) 7.53023 0.244570
\(949\) 34.2155 + 3.51415i 1.11068 + 0.114074i
\(950\) 19.6289i 0.636845i
\(951\) −5.67885 + 5.67885i −0.184149 + 0.184149i
\(952\) −29.9153 0.490203i −0.969559 0.0158876i
\(953\) 45.1262i 1.46178i −0.682494 0.730891i \(-0.739105\pi\)
0.682494 0.730891i \(-0.260895\pi\)
\(954\) −0.723093 0.723093i −0.0234110 0.0234110i
\(955\) 0.340733 0.340733i 0.0110259 0.0110259i
\(956\) −13.1204 + 13.1204i −0.424344 + 0.424344i
\(957\) 2.44283 + 2.44283i 0.0789654 + 0.0789654i
\(958\) 12.3639i 0.399459i
\(959\) −43.5740 0.714019i −1.40708 0.0230569i
\(960\) 23.6049 23.6049i 0.761844 0.761844i
\(961\) 34.0109i 1.09713i
\(962\) −15.2350 + 12.3970i −0.491195 + 0.399695i
\(963\) 14.3968 0.463932
\(964\) −5.05103 + 5.05103i −0.162683 + 0.162683i
\(965\) 48.6364i 1.56566i
\(966\) 0.0315254 1.92388i 0.00101431 0.0618998i
\(967\) 14.6545 + 14.6545i 0.471257 + 0.471257i 0.902321 0.431065i \(-0.141862\pi\)
−0.431065 + 0.902321i \(0.641862\pi\)
\(968\) −15.7264 15.7264i −0.505464 0.505464i
\(969\) −4.08045 4.08045i −0.131083 0.131083i
\(970\) 3.84338 3.84338i 0.123403 0.123403i
\(971\) 44.5224i 1.42879i 0.699742 + 0.714396i \(0.253298\pi\)
−0.699742 + 0.714396i \(0.746702\pi\)
\(972\) 0.762660 0.0244623
\(973\) 4.03491 3.90480i 0.129353 0.125182i
\(974\) 41.6312i 1.33395i
\(975\) 31.4699 25.6077i 1.00784 0.820103i
\(976\) 11.2245i 0.359287i
\(977\) −0.515539 0.515539i −0.0164935 0.0164935i 0.698812 0.715305i \(-0.253712\pi\)
−0.715305 + 0.698812i \(0.753712\pi\)
\(978\) 6.74376i 0.215642i
\(979\) 13.5677 0.433626
\(980\) 15.7091 14.7119i 0.501810 0.469954i
\(981\) −11.6047 11.6047i −0.370509 0.370509i
\(982\) 32.5669 32.5669i 1.03925 1.03925i
\(983\) −16.5350 16.5350i −0.527386 0.527386i 0.392406 0.919792i \(-0.371643\pi\)
−0.919792 + 0.392406i \(0.871643\pi\)
\(984\) −11.6239 −0.370557
\(985\) 81.5473 2.59831
\(986\) −5.15481 5.15481i −0.164163 0.164163i
\(987\) 14.3888 + 0.235780i 0.458001 + 0.00750498i
\(988\) −4.28961 0.440570i −0.136471 0.0140164i
\(989\) −7.19675 −0.228843
\(990\) −6.15103 + 6.15103i −0.195492 + 0.195492i
\(991\) −35.2705 −1.12040 −0.560202 0.828356i \(-0.689277\pi\)
−0.560202 + 0.828356i \(0.689277\pi\)
\(992\) 32.5775 1.03434
\(993\) 4.44838 4.44838i 0.141165 0.141165i
\(994\) −25.5876 + 24.7625i −0.811589 + 0.785420i
\(995\) −6.63146 + 6.63146i −0.210232 + 0.210232i
\(996\) −6.64671 + 6.64671i −0.210609 + 0.210609i
\(997\) 60.2109i 1.90690i 0.301554 + 0.953449i \(0.402495\pi\)
−0.301554 + 0.953449i \(0.597505\pi\)
\(998\) 27.0000i 0.854669i
\(999\) −3.46293 3.46293i −0.109562 0.109562i
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 273.2.p.f.34.3 yes 12
3.2 odd 2 819.2.y.f.307.4 12
7.6 odd 2 273.2.p.e.34.3 12
13.5 odd 4 273.2.p.e.265.3 yes 12
21.20 even 2 819.2.y.g.307.4 12
39.5 even 4 819.2.y.g.811.4 12
91.83 even 4 inner 273.2.p.f.265.3 yes 12
273.83 odd 4 819.2.y.f.811.4 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
273.2.p.e.34.3 12 7.6 odd 2
273.2.p.e.265.3 yes 12 13.5 odd 4
273.2.p.f.34.3 yes 12 1.1 even 1 trivial
273.2.p.f.265.3 yes 12 91.83 even 4 inner
819.2.y.f.307.4 12 3.2 odd 2
819.2.y.f.811.4 12 273.83 odd 4
819.2.y.g.307.4 12 21.20 even 2
819.2.y.g.811.4 12 39.5 even 4