Properties

Label 169.2.c.b.146.2
Level $169$
Weight $2$
Character 169.146
Analytic conductor $1.349$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(22,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.34947179416\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.2
Root \(0.900969 + 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.2.c.b.22.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.277479 - 0.480608i) q^{2} +(-0.400969 - 0.694498i) q^{3} +(0.846011 - 1.46533i) q^{4} +2.80194 q^{5} +(-0.222521 + 0.385418i) q^{6} +(-1.34601 + 2.33136i) q^{7} -2.04892 q^{8} +(1.17845 - 2.04113i) q^{9} +O(q^{10})\) \(q+(-0.277479 - 0.480608i) q^{2} +(-0.400969 - 0.694498i) q^{3} +(0.846011 - 1.46533i) q^{4} +2.80194 q^{5} +(-0.222521 + 0.385418i) q^{6} +(-1.34601 + 2.33136i) q^{7} -2.04892 q^{8} +(1.17845 - 2.04113i) q^{9} +(-0.777479 - 1.34663i) q^{10} +(-0.599031 - 1.03755i) q^{11} -1.35690 q^{12} +1.49396 q^{14} +(-1.12349 - 1.94594i) q^{15} +(-1.12349 - 1.94594i) q^{16} +(-0.568532 + 0.984726i) q^{17} -1.30798 q^{18} +(0.969501 - 1.67922i) q^{19} +(2.37047 - 4.10577i) q^{20} +2.15883 q^{21} +(-0.332437 + 0.575798i) q^{22} +(2.30194 + 3.98707i) q^{23} +(0.821552 + 1.42297i) q^{24} +2.85086 q^{25} -4.29590 q^{27} +(2.27748 + 3.94471i) q^{28} +(3.94989 + 6.84140i) q^{29} +(-0.623490 + 1.07992i) q^{30} -5.89977 q^{31} +(-2.67241 + 4.62874i) q^{32} +(-0.480386 + 0.832052i) q^{33} +0.631023 q^{34} +(-3.77144 + 6.53232i) q^{35} +(-1.99396 - 3.45364i) q^{36} +(0.475541 + 0.823662i) q^{37} -1.07606 q^{38} -5.74094 q^{40} +(1.65883 + 2.87318i) q^{41} +(-0.599031 - 1.03755i) q^{42} +(-3.57942 + 6.19973i) q^{43} -2.02715 q^{44} +(3.30194 - 5.71912i) q^{45} +(1.27748 - 2.21266i) q^{46} +7.69202 q^{47} +(-0.900969 + 1.56052i) q^{48} +(-0.123490 - 0.213891i) q^{49} +(-0.791053 - 1.37014i) q^{50} +0.911854 q^{51} +5.87263 q^{53} +(1.19202 + 2.06464i) q^{54} +(-1.67845 - 2.90716i) q^{55} +(2.75786 - 4.77676i) q^{56} -1.55496 q^{57} +(2.19202 - 3.79669i) q^{58} +(-0.00604079 + 0.0104630i) q^{59} -3.80194 q^{60} +(4.01842 - 6.96010i) q^{61} +(1.63706 + 2.83548i) q^{62} +(3.17241 + 5.49477i) q^{63} -1.52781 q^{64} +0.533188 q^{66} +(-4.62833 - 8.01651i) q^{67} +(0.961968 + 1.66618i) q^{68} +(1.84601 - 3.19738i) q^{69} +4.18598 q^{70} +(-6.87047 + 11.9000i) q^{71} +(-2.41454 + 4.18211i) q^{72} -12.8170 q^{73} +(0.263906 - 0.457098i) q^{74} +(-1.14310 - 1.97991i) q^{75} +(-1.64042 - 2.84128i) q^{76} +3.22521 q^{77} +0.807315 q^{79} +(-3.14795 - 5.45241i) q^{80} +(-1.81282 - 3.13990i) q^{81} +(0.920583 - 1.59450i) q^{82} +16.3327 q^{83} +(1.82640 - 3.16341i) q^{84} +(-1.59299 + 2.75914i) q^{85} +3.97285 q^{86} +(3.16756 - 5.48638i) q^{87} +(1.22737 + 2.12586i) q^{88} +(-7.36443 - 12.7556i) q^{89} -3.66487 q^{90} +7.78986 q^{92} +(2.36563 + 4.09738i) q^{93} +(-2.13437 - 3.69685i) q^{94} +(2.71648 - 4.70508i) q^{95} +4.28621 q^{96} +(1.56584 - 2.71212i) q^{97} +(-0.0685317 + 0.118700i) q^{98} -2.82371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{2} + 2 q^{3} + 8 q^{5} - q^{6} - 3 q^{7} + 6 q^{8} + 3 q^{9} - 5 q^{10} - 8 q^{11} - 10 q^{14} - 2 q^{15} - 2 q^{16} + 2 q^{17} - 18 q^{18} - 4 q^{19} - 4 q^{21} - 3 q^{22} + 5 q^{23} + 9 q^{24} - 10 q^{25} + 2 q^{27} + 14 q^{28} + q^{29} + q^{30} + 10 q^{31} + 7 q^{32} + 10 q^{33} - 26 q^{34} - 4 q^{35} + 7 q^{36} + 12 q^{37} + 24 q^{38} - 6 q^{40} - 7 q^{41} - 8 q^{42} - 13 q^{43} + 11 q^{45} + 8 q^{46} + 36 q^{47} - q^{48} + 4 q^{49} + q^{50} - 2 q^{51} + 2 q^{53} - 3 q^{54} - 6 q^{55} + 4 q^{56} - 10 q^{57} + 3 q^{58} - 19 q^{59} - 14 q^{60} - 4 q^{61} - q^{62} - 4 q^{63} - 22 q^{64} + 10 q^{66} - q^{67} + 21 q^{68} + 6 q^{69} - 4 q^{70} - 27 q^{71} - 4 q^{72} - 18 q^{73} + 8 q^{74} - 15 q^{75} - 21 q^{76} + 16 q^{77} - 10 q^{79} - 5 q^{80} + q^{81} + 14 q^{82} + 14 q^{83} - 7 q^{84} + 5 q^{85} + 36 q^{86} + 18 q^{87} - 15 q^{88} - 11 q^{89} - 24 q^{90} + 22 q^{93} - 5 q^{94} - 3 q^{95} + 42 q^{96} + 7 q^{97} + 5 q^{98} - 2 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.277479 0.480608i −0.196207 0.339841i 0.751088 0.660202i \(-0.229529\pi\)
−0.947296 + 0.320361i \(0.896196\pi\)
\(3\) −0.400969 0.694498i −0.231499 0.400969i 0.726750 0.686902i \(-0.241030\pi\)
−0.958250 + 0.285933i \(0.907696\pi\)
\(4\) 0.846011 1.46533i 0.423005 0.732667i
\(5\) 2.80194 1.25306 0.626532 0.779395i \(-0.284474\pi\)
0.626532 + 0.779395i \(0.284474\pi\)
\(6\) −0.222521 + 0.385418i −0.0908438 + 0.157346i
\(7\) −1.34601 + 2.33136i −0.508744 + 0.881171i 0.491204 + 0.871044i \(0.336557\pi\)
−0.999949 + 0.0101266i \(0.996777\pi\)
\(8\) −2.04892 −0.724402
\(9\) 1.17845 2.04113i 0.392816 0.680377i
\(10\) −0.777479 1.34663i −0.245860 0.425843i
\(11\) −0.599031 1.03755i −0.180615 0.312834i 0.761475 0.648194i \(-0.224475\pi\)
−0.942090 + 0.335360i \(0.891142\pi\)
\(12\) −1.35690 −0.391702
\(13\) 0 0
\(14\) 1.49396 0.399277
\(15\) −1.12349 1.94594i −0.290084 0.502440i
\(16\) −1.12349 1.94594i −0.280872 0.486485i
\(17\) −0.568532 + 0.984726i −0.137889 + 0.238831i −0.926697 0.375808i \(-0.877365\pi\)
0.788808 + 0.614639i \(0.210698\pi\)
\(18\) −1.30798 −0.308293
\(19\) 0.969501 1.67922i 0.222419 0.385240i −0.733123 0.680096i \(-0.761938\pi\)
0.955542 + 0.294855i \(0.0952715\pi\)
\(20\) 2.37047 4.10577i 0.530053 0.918079i
\(21\) 2.15883 0.471096
\(22\) −0.332437 + 0.575798i −0.0708758 + 0.122761i
\(23\) 2.30194 + 3.98707i 0.479987 + 0.831362i 0.999736 0.0229566i \(-0.00730797\pi\)
−0.519749 + 0.854319i \(0.673975\pi\)
\(24\) 0.821552 + 1.42297i 0.167699 + 0.290463i
\(25\) 2.85086 0.570171
\(26\) 0 0
\(27\) −4.29590 −0.826746
\(28\) 2.27748 + 3.94471i 0.430403 + 0.745480i
\(29\) 3.94989 + 6.84140i 0.733475 + 1.27042i 0.955389 + 0.295350i \(0.0954364\pi\)
−0.221914 + 0.975066i \(0.571230\pi\)
\(30\) −0.623490 + 1.07992i −0.113833 + 0.197165i
\(31\) −5.89977 −1.05963 −0.529815 0.848113i \(-0.677739\pi\)
−0.529815 + 0.848113i \(0.677739\pi\)
\(32\) −2.67241 + 4.62874i −0.472419 + 0.818254i
\(33\) −0.480386 + 0.832052i −0.0836244 + 0.144842i
\(34\) 0.631023 0.108219
\(35\) −3.77144 + 6.53232i −0.637489 + 1.10416i
\(36\) −1.99396 3.45364i −0.332327 0.575606i
\(37\) 0.475541 + 0.823662i 0.0781785 + 0.135409i 0.902464 0.430765i \(-0.141756\pi\)
−0.824286 + 0.566174i \(0.808423\pi\)
\(38\) −1.07606 −0.174561
\(39\) 0 0
\(40\) −5.74094 −0.907722
\(41\) 1.65883 + 2.87318i 0.259066 + 0.448716i 0.965992 0.258572i \(-0.0832519\pi\)
−0.706926 + 0.707288i \(0.749919\pi\)
\(42\) −0.599031 1.03755i −0.0924325 0.160098i
\(43\) −3.57942 + 6.19973i −0.545856 + 0.945450i 0.452697 + 0.891665i \(0.350462\pi\)
−0.998553 + 0.0537856i \(0.982871\pi\)
\(44\) −2.02715 −0.305604
\(45\) 3.30194 5.71912i 0.492224 0.852557i
\(46\) 1.27748 2.21266i 0.188354 0.326239i
\(47\) 7.69202 1.12200 0.560998 0.827817i \(-0.310417\pi\)
0.560998 + 0.827817i \(0.310417\pi\)
\(48\) −0.900969 + 1.56052i −0.130044 + 0.225242i
\(49\) −0.123490 0.213891i −0.0176414 0.0305558i
\(50\) −0.791053 1.37014i −0.111872 0.193768i
\(51\) 0.911854 0.127685
\(52\) 0 0
\(53\) 5.87263 0.806667 0.403334 0.915053i \(-0.367851\pi\)
0.403334 + 0.915053i \(0.367851\pi\)
\(54\) 1.19202 + 2.06464i 0.162214 + 0.280962i
\(55\) −1.67845 2.90716i −0.226322 0.392001i
\(56\) 2.75786 4.77676i 0.368535 0.638322i
\(57\) −1.55496 −0.205959
\(58\) 2.19202 3.79669i 0.287827 0.498530i
\(59\) −0.00604079 + 0.0104630i −0.000786444 + 0.00136216i −0.866418 0.499319i \(-0.833584\pi\)
0.865632 + 0.500681i \(0.166917\pi\)
\(60\) −3.80194 −0.490828
\(61\) 4.01842 6.96010i 0.514506 0.891150i −0.485353 0.874318i \(-0.661309\pi\)
0.999858 0.0168315i \(-0.00535789\pi\)
\(62\) 1.63706 + 2.83548i 0.207907 + 0.360106i
\(63\) 3.17241 + 5.49477i 0.399686 + 0.692276i
\(64\) −1.52781 −0.190976
\(65\) 0 0
\(66\) 0.533188 0.0656309
\(67\) −4.62833 8.01651i −0.565441 0.979373i −0.997009 0.0772919i \(-0.975373\pi\)
0.431567 0.902081i \(-0.357961\pi\)
\(68\) 0.961968 + 1.66618i 0.116656 + 0.202054i
\(69\) 1.84601 3.19738i 0.222234 0.384920i
\(70\) 4.18598 0.500320
\(71\) −6.87047 + 11.9000i −0.815375 + 1.41227i 0.0936838 + 0.995602i \(0.470136\pi\)
−0.909059 + 0.416668i \(0.863198\pi\)
\(72\) −2.41454 + 4.18211i −0.284557 + 0.492866i
\(73\) −12.8170 −1.50012 −0.750058 0.661372i \(-0.769975\pi\)
−0.750058 + 0.661372i \(0.769975\pi\)
\(74\) 0.263906 0.457098i 0.0306784 0.0531365i
\(75\) −1.14310 1.97991i −0.131994 0.228621i
\(76\) −1.64042 2.84128i −0.188169 0.325918i
\(77\) 3.22521 0.367547
\(78\) 0 0
\(79\) 0.807315 0.0908300 0.0454150 0.998968i \(-0.485539\pi\)
0.0454150 + 0.998968i \(0.485539\pi\)
\(80\) −3.14795 5.45241i −0.351951 0.609598i
\(81\) −1.81282 3.13990i −0.201425 0.348878i
\(82\) 0.920583 1.59450i 0.101661 0.176083i
\(83\) 16.3327 1.79275 0.896375 0.443296i \(-0.146191\pi\)
0.896375 + 0.443296i \(0.146191\pi\)
\(84\) 1.82640 3.16341i 0.199276 0.345156i
\(85\) −1.59299 + 2.75914i −0.172784 + 0.299271i
\(86\) 3.97285 0.428404
\(87\) 3.16756 5.48638i 0.339598 0.588202i
\(88\) 1.22737 + 2.12586i 0.130838 + 0.226617i
\(89\) −7.36443 12.7556i −0.780628 1.35209i −0.931576 0.363546i \(-0.881566\pi\)
0.150949 0.988542i \(-0.451767\pi\)
\(90\) −3.66487 −0.386312
\(91\) 0 0
\(92\) 7.78986 0.812149
\(93\) 2.36563 + 4.09738i 0.245304 + 0.424879i
\(94\) −2.13437 3.69685i −0.220144 0.381301i
\(95\) 2.71648 4.70508i 0.278705 0.482731i
\(96\) 4.28621 0.437459
\(97\) 1.56584 2.71212i 0.158987 0.275374i −0.775516 0.631327i \(-0.782510\pi\)
0.934504 + 0.355953i \(0.115844\pi\)
\(98\) −0.0685317 + 0.118700i −0.00692274 + 0.0119905i
\(99\) −2.82371 −0.283793
\(100\) 2.41185 4.17745i 0.241185 0.417745i
\(101\) −2.64526 4.58172i −0.263213 0.455899i 0.703881 0.710318i \(-0.251449\pi\)
−0.967094 + 0.254420i \(0.918116\pi\)
\(102\) −0.253020 0.438244i −0.0250528 0.0433926i
\(103\) −13.5308 −1.33323 −0.666614 0.745403i \(-0.732257\pi\)
−0.666614 + 0.745403i \(0.732257\pi\)
\(104\) 0 0
\(105\) 6.04892 0.590314
\(106\) −1.62953 2.82243i −0.158274 0.274139i
\(107\) −2.81551 4.87661i −0.272186 0.471440i 0.697236 0.716842i \(-0.254413\pi\)
−0.969421 + 0.245403i \(0.921080\pi\)
\(108\) −3.63437 + 6.29492i −0.349718 + 0.605729i
\(109\) −4.17629 −0.400016 −0.200008 0.979794i \(-0.564097\pi\)
−0.200008 + 0.979794i \(0.564097\pi\)
\(110\) −0.931468 + 1.61335i −0.0888120 + 0.153827i
\(111\) 0.381355 0.660525i 0.0361966 0.0626943i
\(112\) 6.04892 0.571569
\(113\) −3.82155 + 6.61912i −0.359501 + 0.622675i −0.987878 0.155235i \(-0.950387\pi\)
0.628376 + 0.777910i \(0.283720\pi\)
\(114\) 0.431468 + 0.747325i 0.0404107 + 0.0699934i
\(115\) 6.44989 + 11.1715i 0.601455 + 1.04175i
\(116\) 13.3666 1.24106
\(117\) 0 0
\(118\) 0.00670477 0.000617224
\(119\) −1.53050 2.65090i −0.140301 0.243008i
\(120\) 2.30194 + 3.98707i 0.210137 + 0.363968i
\(121\) 4.78232 8.28323i 0.434757 0.753021i
\(122\) −4.46011 −0.403799
\(123\) 1.33028 2.30411i 0.119947 0.207755i
\(124\) −4.99127 + 8.64513i −0.448229 + 0.776356i
\(125\) −6.02177 −0.538604
\(126\) 1.76055 3.04937i 0.156843 0.271659i
\(127\) −3.38889 5.86972i −0.300715 0.520854i 0.675583 0.737284i \(-0.263892\pi\)
−0.976298 + 0.216430i \(0.930559\pi\)
\(128\) 5.76875 + 9.99177i 0.509890 + 0.883156i
\(129\) 5.74094 0.505461
\(130\) 0 0
\(131\) −13.6799 −1.19522 −0.597611 0.801786i \(-0.703883\pi\)
−0.597611 + 0.801786i \(0.703883\pi\)
\(132\) 0.812823 + 1.40785i 0.0707471 + 0.122538i
\(133\) 2.60992 + 4.52051i 0.226308 + 0.391978i
\(134\) −2.56853 + 4.44883i −0.221887 + 0.384320i
\(135\) −12.0368 −1.03597
\(136\) 1.16487 2.01762i 0.0998872 0.173010i
\(137\) 6.49396 11.2479i 0.554816 0.960970i −0.443101 0.896471i \(-0.646122\pi\)
0.997918 0.0644987i \(-0.0205448\pi\)
\(138\) −2.04892 −0.174415
\(139\) −6.02326 + 10.4326i −0.510886 + 0.884881i 0.489034 + 0.872265i \(0.337349\pi\)
−0.999920 + 0.0126165i \(0.995984\pi\)
\(140\) 6.38135 + 11.0528i 0.539323 + 0.934135i
\(141\) −3.08426 5.34210i −0.259742 0.449886i
\(142\) 7.62565 0.639930
\(143\) 0 0
\(144\) −5.29590 −0.441325
\(145\) 11.0673 + 19.1692i 0.919092 + 1.59191i
\(146\) 3.55645 + 6.15995i 0.294334 + 0.509801i
\(147\) −0.0990311 + 0.171527i −0.00816795 + 0.0141473i
\(148\) 1.60925 0.132280
\(149\) −0.370469 + 0.641672i −0.0303500 + 0.0525678i −0.880801 0.473486i \(-0.842996\pi\)
0.850451 + 0.526054i \(0.176329\pi\)
\(150\) −0.634375 + 1.09877i −0.0517965 + 0.0897142i
\(151\) 19.0737 1.55219 0.776097 0.630614i \(-0.217197\pi\)
0.776097 + 0.630614i \(0.217197\pi\)
\(152\) −1.98643 + 3.44059i −0.161120 + 0.279069i
\(153\) 1.33997 + 2.32090i 0.108330 + 0.187633i
\(154\) −0.894928 1.55006i −0.0721154 0.124907i
\(155\) −16.5308 −1.32779
\(156\) 0 0
\(157\) −4.02177 −0.320972 −0.160486 0.987038i \(-0.551306\pi\)
−0.160486 + 0.987038i \(0.551306\pi\)
\(158\) −0.224013 0.388002i −0.0178215 0.0308678i
\(159\) −2.35474 4.07853i −0.186743 0.323448i
\(160\) −7.48792 + 12.9695i −0.591972 + 1.02533i
\(161\) −12.3937 −0.976763
\(162\) −1.00604 + 1.74251i −0.0790420 + 0.136905i
\(163\) 7.56853 13.1091i 0.592813 1.02678i −0.401038 0.916061i \(-0.631351\pi\)
0.993852 0.110721i \(-0.0353161\pi\)
\(164\) 5.61356 0.438346
\(165\) −1.34601 + 2.33136i −0.104787 + 0.181496i
\(166\) −4.53199 7.84964i −0.351751 0.609250i
\(167\) −3.13169 5.42424i −0.242337 0.419740i 0.719042 0.694966i \(-0.244581\pi\)
−0.961380 + 0.275226i \(0.911247\pi\)
\(168\) −4.42327 −0.341263
\(169\) 0 0
\(170\) 1.76809 0.135606
\(171\) −2.28501 3.95776i −0.174739 0.302657i
\(172\) 6.05645 + 10.4901i 0.461800 + 0.799861i
\(173\) −8.19567 + 14.1953i −0.623105 + 1.07925i 0.365799 + 0.930694i \(0.380796\pi\)
−0.988904 + 0.148556i \(0.952538\pi\)
\(174\) −3.51573 −0.266527
\(175\) −3.83728 + 6.64637i −0.290071 + 0.502418i
\(176\) −1.34601 + 2.33136i −0.101459 + 0.175733i
\(177\) 0.00968868 0.000728246
\(178\) −4.08695 + 7.07880i −0.306330 + 0.530579i
\(179\) 1.22737 + 2.12586i 0.0917376 + 0.158894i 0.908242 0.418445i \(-0.137425\pi\)
−0.816505 + 0.577339i \(0.804091\pi\)
\(180\) −5.58695 9.67688i −0.416427 0.721272i
\(181\) 11.8073 0.877631 0.438815 0.898577i \(-0.355398\pi\)
0.438815 + 0.898577i \(0.355398\pi\)
\(182\) 0 0
\(183\) −6.44504 −0.476431
\(184\) −4.71648 8.16918i −0.347704 0.602240i
\(185\) 1.33244 + 2.30785i 0.0979627 + 0.169676i
\(186\) 1.31282 2.27388i 0.0962608 0.166729i
\(187\) 1.36227 0.0996192
\(188\) 6.50753 11.2714i 0.474611 0.822050i
\(189\) 5.78232 10.0153i 0.420602 0.728504i
\(190\) −3.01507 −0.218736
\(191\) 4.49665 7.78842i 0.325366 0.563550i −0.656220 0.754569i \(-0.727846\pi\)
0.981586 + 0.191019i \(0.0611792\pi\)
\(192\) 0.612605 + 1.06106i 0.0442109 + 0.0765756i
\(193\) 6.76271 + 11.7134i 0.486790 + 0.843146i 0.999885 0.0151865i \(-0.00483420\pi\)
−0.513094 + 0.858332i \(0.671501\pi\)
\(194\) −1.73795 −0.124778
\(195\) 0 0
\(196\) −0.417895 −0.0298496
\(197\) 6.48792 + 11.2374i 0.462245 + 0.800632i 0.999072 0.0430602i \(-0.0137107\pi\)
−0.536827 + 0.843692i \(0.680377\pi\)
\(198\) 0.783520 + 1.35710i 0.0556823 + 0.0964446i
\(199\) 6.79321 11.7662i 0.481558 0.834083i −0.518218 0.855248i \(-0.673404\pi\)
0.999776 + 0.0211659i \(0.00673782\pi\)
\(200\) −5.84117 −0.413033
\(201\) −3.71164 + 6.42874i −0.261799 + 0.453448i
\(202\) −1.46801 + 2.54267i −0.103289 + 0.178901i
\(203\) −21.2664 −1.49261
\(204\) 0.771438 1.33617i 0.0540115 0.0935506i
\(205\) 4.64795 + 8.05048i 0.324627 + 0.562270i
\(206\) 3.75451 + 6.50301i 0.261589 + 0.453086i
\(207\) 10.8509 0.754187
\(208\) 0 0
\(209\) −2.32304 −0.160688
\(210\) −1.67845 2.90716i −0.115824 0.200613i
\(211\) −5.23005 9.05872i −0.360052 0.623628i 0.627917 0.778280i \(-0.283908\pi\)
−0.987969 + 0.154652i \(0.950574\pi\)
\(212\) 4.96830 8.60536i 0.341225 0.591018i
\(213\) 11.0194 0.755035
\(214\) −1.56249 + 2.70631i −0.106810 + 0.185000i
\(215\) −10.0293 + 17.3713i −0.683993 + 1.18471i
\(216\) 8.80194 0.598896
\(217\) 7.94116 13.7545i 0.539081 0.933715i
\(218\) 1.15883 + 2.00716i 0.0784861 + 0.135942i
\(219\) 5.13922 + 8.90139i 0.347276 + 0.601500i
\(220\) −5.67994 −0.382941
\(221\) 0 0
\(222\) −0.423272 −0.0284081
\(223\) −5.70291 9.87772i −0.381895 0.661461i 0.609438 0.792834i \(-0.291395\pi\)
−0.991333 + 0.131372i \(0.958062\pi\)
\(224\) −7.19418 12.4607i −0.480681 0.832564i
\(225\) 3.35958 5.81897i 0.223972 0.387931i
\(226\) 4.24160 0.282147
\(227\) 5.32036 9.21513i 0.353124 0.611629i −0.633671 0.773603i \(-0.718453\pi\)
0.986795 + 0.161973i \(0.0517859\pi\)
\(228\) −1.31551 + 2.27853i −0.0871219 + 0.150899i
\(229\) 1.13946 0.0752974 0.0376487 0.999291i \(-0.488013\pi\)
0.0376487 + 0.999291i \(0.488013\pi\)
\(230\) 3.57942 6.19973i 0.236020 0.408798i
\(231\) −1.29321 2.23990i −0.0850869 0.147375i
\(232\) −8.09299 14.0175i −0.531331 0.920292i
\(233\) −10.8509 −0.710863 −0.355432 0.934702i \(-0.615666\pi\)
−0.355432 + 0.934702i \(0.615666\pi\)
\(234\) 0 0
\(235\) 21.5526 1.40593
\(236\) 0.0102212 + 0.0177036i 0.000665340 + 0.00115240i
\(237\) −0.323708 0.560679i −0.0210271 0.0364200i
\(238\) −0.849363 + 1.47114i −0.0550560 + 0.0953598i
\(239\) 11.9293 0.771643 0.385822 0.922573i \(-0.373918\pi\)
0.385822 + 0.922573i \(0.373918\pi\)
\(240\) −2.52446 + 4.37249i −0.162953 + 0.282243i
\(241\) −1.82424 + 3.15968i −0.117510 + 0.203533i −0.918780 0.394770i \(-0.870824\pi\)
0.801271 + 0.598302i \(0.204158\pi\)
\(242\) −5.30798 −0.341210
\(243\) −7.89762 + 13.6791i −0.506632 + 0.877513i
\(244\) −6.79925 11.7766i −0.435277 0.753922i
\(245\) −0.346011 0.599308i −0.0221058 0.0382884i
\(246\) −1.47650 −0.0941383
\(247\) 0 0
\(248\) 12.0881 0.767598
\(249\) −6.54892 11.3431i −0.415021 0.718837i
\(250\) 1.67092 + 2.89411i 0.105678 + 0.183040i
\(251\) −0.686645 + 1.18930i −0.0433406 + 0.0750682i −0.886882 0.461996i \(-0.847133\pi\)
0.843541 + 0.537064i \(0.180467\pi\)
\(252\) 10.7356 0.676277
\(253\) 2.75786 4.77676i 0.173385 0.300312i
\(254\) −1.88069 + 3.25745i −0.118005 + 0.204391i
\(255\) 2.55496 0.159998
\(256\) 1.67360 2.89877i 0.104600 0.181173i
\(257\) −14.7180 25.4923i −0.918082 1.59016i −0.802325 0.596887i \(-0.796404\pi\)
−0.115756 0.993278i \(-0.536929\pi\)
\(258\) −1.59299 2.75914i −0.0991752 0.171777i
\(259\) −2.56033 −0.159091
\(260\) 0 0
\(261\) 18.6189 1.15248
\(262\) 3.79590 + 6.57469i 0.234511 + 0.406185i
\(263\) −5.34817 9.26330i −0.329782 0.571199i 0.652686 0.757628i \(-0.273642\pi\)
−0.982468 + 0.186429i \(0.940309\pi\)
\(264\) 0.984271 1.70481i 0.0605777 0.104924i
\(265\) 16.4547 1.01081
\(266\) 1.44839 2.50869i 0.0888067 0.153818i
\(267\) −5.90581 + 10.2292i −0.361430 + 0.626015i
\(268\) −15.6625 −0.956738
\(269\) 5.09299 8.82132i 0.310525 0.537845i −0.667951 0.744205i \(-0.732828\pi\)
0.978476 + 0.206360i \(0.0661618\pi\)
\(270\) 3.33997 + 5.78500i 0.203264 + 0.352064i
\(271\) −14.7262 25.5065i −0.894551 1.54941i −0.834359 0.551221i \(-0.814162\pi\)
−0.0601918 0.998187i \(-0.519171\pi\)
\(272\) 2.55496 0.154917
\(273\) 0 0
\(274\) −7.20775 −0.435436
\(275\) −1.70775 2.95791i −0.102981 0.178369i
\(276\) −3.12349 5.41004i −0.188012 0.325646i
\(277\) 5.12229 8.87207i 0.307769 0.533071i −0.670105 0.742266i \(-0.733751\pi\)
0.977874 + 0.209195i \(0.0670843\pi\)
\(278\) 6.68532 0.400959
\(279\) −6.95257 + 12.0422i −0.416240 + 0.720948i
\(280\) 7.72737 13.3842i 0.461798 0.799858i
\(281\) 11.5646 0.689889 0.344944 0.938623i \(-0.387898\pi\)
0.344944 + 0.938623i \(0.387898\pi\)
\(282\) −1.71164 + 2.96464i −0.101926 + 0.176542i
\(283\) 15.3545 + 26.5948i 0.912730 + 1.58090i 0.810191 + 0.586167i \(0.199364\pi\)
0.102540 + 0.994729i \(0.467303\pi\)
\(284\) 11.6250 + 20.1351i 0.689816 + 1.19480i
\(285\) −4.35690 −0.258080
\(286\) 0 0
\(287\) −8.93123 −0.527194
\(288\) 6.29859 + 10.9095i 0.371148 + 0.642847i
\(289\) 7.85354 + 13.6027i 0.461973 + 0.800161i
\(290\) 6.14191 10.6381i 0.360665 0.624691i
\(291\) −2.51142 −0.147222
\(292\) −10.8433 + 18.7812i −0.634557 + 1.09909i
\(293\) −9.30409 + 16.1152i −0.543551 + 0.941458i 0.455146 + 0.890417i \(0.349587\pi\)
−0.998697 + 0.0510409i \(0.983746\pi\)
\(294\) 0.109916 0.00641045
\(295\) −0.0169259 + 0.0293166i −0.000985465 + 0.00170688i
\(296\) −0.974345 1.68761i −0.0566326 0.0980906i
\(297\) 2.57338 + 4.45722i 0.149322 + 0.258634i
\(298\) 0.411190 0.0238196
\(299\) 0 0
\(300\) −3.86831 −0.223337
\(301\) −9.63587 16.6898i −0.555402 0.961985i
\(302\) −5.29254 9.16696i −0.304552 0.527499i
\(303\) −2.12133 + 3.67426i −0.121867 + 0.211081i
\(304\) −4.35690 −0.249885
\(305\) 11.2594 19.5018i 0.644709 1.11667i
\(306\) 0.743627 1.28800i 0.0425103 0.0736301i
\(307\) −8.94438 −0.510483 −0.255241 0.966877i \(-0.582155\pi\)
−0.255241 + 0.966877i \(0.582155\pi\)
\(308\) 2.72856 4.72601i 0.155474 0.269289i
\(309\) 5.42543 + 9.39712i 0.308642 + 0.534583i
\(310\) 4.58695 + 7.94483i 0.260521 + 0.451236i
\(311\) 21.0398 1.19306 0.596529 0.802591i \(-0.296546\pi\)
0.596529 + 0.802591i \(0.296546\pi\)
\(312\) 0 0
\(313\) −7.12737 −0.402863 −0.201432 0.979503i \(-0.564559\pi\)
−0.201432 + 0.979503i \(0.564559\pi\)
\(314\) 1.11596 + 1.93289i 0.0629771 + 0.109080i
\(315\) 8.88889 + 15.3960i 0.500832 + 0.867467i
\(316\) 0.682997 1.18299i 0.0384216 0.0665481i
\(317\) −23.9651 −1.34601 −0.673007 0.739636i \(-0.734997\pi\)
−0.673007 + 0.739636i \(0.734997\pi\)
\(318\) −1.30678 + 2.26341i −0.0732807 + 0.126926i
\(319\) 4.73221 8.19643i 0.264953 0.458912i
\(320\) −4.28083 −0.239306
\(321\) −2.25786 + 3.91074i −0.126022 + 0.218276i
\(322\) 3.43900 + 5.95652i 0.191648 + 0.331944i
\(323\) 1.10238 + 1.90938i 0.0613383 + 0.106241i
\(324\) −6.13467 −0.340815
\(325\) 0 0
\(326\) −8.40044 −0.465257
\(327\) 1.67456 + 2.90043i 0.0926035 + 0.160394i
\(328\) −3.39881 5.88692i −0.187668 0.325051i
\(329\) −10.3535 + 17.9329i −0.570809 + 0.988671i
\(330\) 1.49396 0.0822397
\(331\) 1.44773 2.50754i 0.0795745 0.137827i −0.823492 0.567328i \(-0.807977\pi\)
0.903066 + 0.429501i \(0.141311\pi\)
\(332\) 13.8177 23.9329i 0.758343 1.31349i
\(333\) 2.24160 0.122839
\(334\) −1.73795 + 3.01023i −0.0950967 + 0.164712i
\(335\) −12.9683 22.4618i −0.708534 1.22722i
\(336\) −2.42543 4.20096i −0.132318 0.229181i
\(337\) −3.10560 −0.169173 −0.0845865 0.996416i \(-0.526957\pi\)
−0.0845865 + 0.996416i \(0.526957\pi\)
\(338\) 0 0
\(339\) 6.12929 0.332898
\(340\) 2.69537 + 4.66852i 0.146177 + 0.253186i
\(341\) 3.53415 + 6.12132i 0.191385 + 0.331488i
\(342\) −1.26809 + 2.19639i −0.0685702 + 0.118767i
\(343\) −18.1793 −0.981589
\(344\) 7.33393 12.7027i 0.395419 0.684886i
\(345\) 5.17241 8.95887i 0.278473 0.482329i
\(346\) 9.09651 0.489031
\(347\) 5.68933 9.85421i 0.305419 0.529002i −0.671935 0.740610i \(-0.734537\pi\)
0.977355 + 0.211608i \(0.0678700\pi\)
\(348\) −5.35958 9.28307i −0.287304 0.497625i
\(349\) −1.67360 2.89877i −0.0895859 0.155167i 0.817750 0.575573i \(-0.195221\pi\)
−0.907336 + 0.420406i \(0.861888\pi\)
\(350\) 4.25906 0.227656
\(351\) 0 0
\(352\) 6.40342 0.341303
\(353\) 0.318864 + 0.552288i 0.0169714 + 0.0293953i 0.874386 0.485230i \(-0.161264\pi\)
−0.857415 + 0.514626i \(0.827931\pi\)
\(354\) −0.00268841 0.00465646i −0.000142887 0.000247488i
\(355\) −19.2506 + 33.3431i −1.02172 + 1.76967i
\(356\) −24.9215 −1.32084
\(357\) −1.22737 + 2.12586i −0.0649591 + 0.112512i
\(358\) 0.681136 1.17976i 0.0359992 0.0623524i
\(359\) 21.4590 1.13256 0.566282 0.824211i \(-0.308381\pi\)
0.566282 + 0.824211i \(0.308381\pi\)
\(360\) −6.76540 + 11.7180i −0.356568 + 0.617593i
\(361\) 7.62014 + 13.1985i 0.401060 + 0.694656i
\(362\) −3.27628 5.67469i −0.172198 0.298255i
\(363\) −7.67025 −0.402584
\(364\) 0 0
\(365\) −35.9124 −1.87974
\(366\) 1.78836 + 3.09754i 0.0934793 + 0.161911i
\(367\) 4.69351 + 8.12940i 0.244999 + 0.424351i 0.962131 0.272586i \(-0.0878789\pi\)
−0.717132 + 0.696937i \(0.754546\pi\)
\(368\) 5.17241 8.95887i 0.269630 0.467013i
\(369\) 7.81940 0.407062
\(370\) 0.739447 1.28076i 0.0384420 0.0665835i
\(371\) −7.90462 + 13.6912i −0.410387 + 0.710812i
\(372\) 8.00538 0.415059
\(373\) −13.8632 + 24.0118i −0.717811 + 1.24329i 0.244054 + 0.969762i \(0.421522\pi\)
−0.961865 + 0.273523i \(0.911811\pi\)
\(374\) −0.378002 0.654719i −0.0195460 0.0338547i
\(375\) 2.41454 + 4.18211i 0.124686 + 0.215963i
\(376\) −15.7603 −0.812776
\(377\) 0 0
\(378\) −6.41789 −0.330101
\(379\) 17.9351 + 31.0645i 0.921265 + 1.59568i 0.797460 + 0.603371i \(0.206176\pi\)
0.123805 + 0.992307i \(0.460490\pi\)
\(380\) −4.59634 7.96110i −0.235787 0.408396i
\(381\) −2.71768 + 4.70715i −0.139231 + 0.241155i
\(382\) −4.99090 −0.255357
\(383\) 2.42758 4.20470i 0.124044 0.214850i −0.797315 0.603563i \(-0.793747\pi\)
0.921359 + 0.388713i \(0.127080\pi\)
\(384\) 4.62618 8.01278i 0.236079 0.408900i
\(385\) 9.03684 0.460560
\(386\) 3.75302 6.50042i 0.191024 0.330863i
\(387\) 8.43631 + 14.6121i 0.428842 + 0.742776i
\(388\) −2.64944 4.58897i −0.134505 0.232969i
\(389\) 2.38537 0.120943 0.0604716 0.998170i \(-0.480740\pi\)
0.0604716 + 0.998170i \(0.480740\pi\)
\(390\) 0 0
\(391\) −5.23490 −0.264740
\(392\) 0.253020 + 0.438244i 0.0127795 + 0.0221347i
\(393\) 5.48523 + 9.50070i 0.276693 + 0.479247i
\(394\) 3.60052 6.23629i 0.181392 0.314180i
\(395\) 2.26205 0.113816
\(396\) −2.38889 + 4.13767i −0.120046 + 0.207926i
\(397\) −7.63318 + 13.2211i −0.383098 + 0.663546i −0.991503 0.130081i \(-0.958476\pi\)
0.608405 + 0.793627i \(0.291810\pi\)
\(398\) −7.53989 −0.377941
\(399\) 2.09299 3.62517i 0.104781 0.181485i
\(400\) −3.20291 5.54760i −0.160145 0.277380i
\(401\) 6.37920 + 11.0491i 0.318562 + 0.551766i 0.980188 0.198068i \(-0.0634668\pi\)
−0.661626 + 0.749834i \(0.730133\pi\)
\(402\) 4.11960 0.205467
\(403\) 0 0
\(404\) −8.95167 −0.445362
\(405\) −5.07942 8.79781i −0.252398 0.437167i
\(406\) 5.90097 + 10.2208i 0.292860 + 0.507249i
\(407\) 0.569728 0.986798i 0.0282404 0.0489138i
\(408\) −1.86831 −0.0924953
\(409\) −12.6794 + 21.9614i −0.626956 + 1.08592i 0.361203 + 0.932487i \(0.382366\pi\)
−0.988159 + 0.153433i \(0.950967\pi\)
\(410\) 2.57942 4.46768i 0.127388 0.220643i
\(411\) −10.4155 −0.513759
\(412\) −11.4472 + 19.8271i −0.563963 + 0.976812i
\(413\) −0.0162619 0.0281665i −0.000800198 0.00138598i
\(414\) −3.01089 5.21501i −0.147977 0.256304i
\(415\) 45.7633 2.24643
\(416\) 0 0
\(417\) 9.66056 0.473080
\(418\) 0.644596 + 1.11647i 0.0315282 + 0.0546085i
\(419\) 5.83363 + 10.1041i 0.284992 + 0.493620i 0.972607 0.232455i \(-0.0746758\pi\)
−0.687616 + 0.726075i \(0.741343\pi\)
\(420\) 5.11745 8.86368i 0.249706 0.432503i
\(421\) 8.29291 0.404172 0.202086 0.979368i \(-0.435228\pi\)
0.202086 + 0.979368i \(0.435228\pi\)
\(422\) −2.90246 + 5.02721i −0.141290 + 0.244721i
\(423\) 9.06465 15.7004i 0.440738 0.763381i
\(424\) −12.0325 −0.584351
\(425\) −1.62080 + 2.80731i −0.0786204 + 0.136175i
\(426\) −3.05765 5.29600i −0.148143 0.256592i
\(427\) 10.8177 + 18.7367i 0.523504 + 0.906735i
\(428\) −9.52781 −0.460544
\(429\) 0 0
\(430\) 11.1317 0.536818
\(431\) 0.466148 + 0.807392i 0.0224536 + 0.0388907i 0.877034 0.480429i \(-0.159519\pi\)
−0.854580 + 0.519319i \(0.826186\pi\)
\(432\) 4.82640 + 8.35956i 0.232210 + 0.402200i
\(433\) 6.67510 11.5616i 0.320785 0.555615i −0.659866 0.751384i \(-0.729387\pi\)
0.980650 + 0.195768i \(0.0627201\pi\)
\(434\) −8.81402 −0.423086
\(435\) 8.87531 15.3725i 0.425539 0.737055i
\(436\) −3.53319 + 6.11966i −0.169209 + 0.293079i
\(437\) 8.92692 0.427032
\(438\) 2.85205 4.93990i 0.136276 0.236037i
\(439\) −6.99612 12.1176i −0.333906 0.578343i 0.649368 0.760475i \(-0.275034\pi\)
−0.983274 + 0.182132i \(0.941700\pi\)
\(440\) 3.43900 + 5.95652i 0.163948 + 0.283966i
\(441\) −0.582105 −0.0277193
\(442\) 0 0
\(443\) 23.7017 1.12610 0.563051 0.826422i \(-0.309627\pi\)
0.563051 + 0.826422i \(0.309627\pi\)
\(444\) −0.645260 1.11762i −0.0306227 0.0530401i
\(445\) −20.6347 35.7403i −0.978177 1.69425i
\(446\) −3.16487 + 5.48172i −0.149861 + 0.259567i
\(447\) 0.594187 0.0281041
\(448\) 2.05645 3.56188i 0.0971581 0.168283i
\(449\) −6.29321 + 10.9002i −0.296995 + 0.514410i −0.975447 0.220234i \(-0.929318\pi\)
0.678452 + 0.734645i \(0.262651\pi\)
\(450\) −3.72886 −0.175780
\(451\) 1.98739 3.44225i 0.0935823 0.162089i
\(452\) 6.46615 + 11.1997i 0.304142 + 0.526789i
\(453\) −7.64795 13.2466i −0.359332 0.622381i
\(454\) −5.90515 −0.277142
\(455\) 0 0
\(456\) 3.18598 0.149197
\(457\) −16.8192 29.1316i −0.786767 1.36272i −0.927938 0.372735i \(-0.878420\pi\)
0.141171 0.989985i \(-0.454913\pi\)
\(458\) −0.316175 0.547632i −0.0147739 0.0255891i
\(459\) 2.44235 4.23028i 0.113999 0.197453i
\(460\) 21.8267 1.01767
\(461\) −0.701415 + 1.21489i −0.0326681 + 0.0565829i −0.881897 0.471442i \(-0.843734\pi\)
0.849229 + 0.528025i \(0.177067\pi\)
\(462\) −0.717677 + 1.24305i −0.0333893 + 0.0578320i
\(463\) 15.2010 0.706453 0.353226 0.935538i \(-0.385085\pi\)
0.353226 + 0.935538i \(0.385085\pi\)
\(464\) 8.87531 15.3725i 0.412026 0.713650i
\(465\) 6.62833 + 11.4806i 0.307382 + 0.532401i
\(466\) 3.01089 + 5.21501i 0.139477 + 0.241580i
\(467\) −39.3414 −1.82050 −0.910250 0.414058i \(-0.864111\pi\)
−0.910250 + 0.414058i \(0.864111\pi\)
\(468\) 0 0
\(469\) 24.9191 1.15066
\(470\) −5.98039 10.3583i −0.275855 0.477794i
\(471\) 1.61260 + 2.79311i 0.0743049 + 0.128700i
\(472\) 0.0123771 0.0214377i 0.000569701 0.000986752i
\(473\) 8.57673 0.394358
\(474\) −0.179644 + 0.311153i −0.00825134 + 0.0142917i
\(475\) 2.76391 4.78722i 0.126817 0.219653i
\(476\) −5.17928 −0.237392
\(477\) 6.92058 11.9868i 0.316872 0.548838i
\(478\) −3.31013 5.73332i −0.151402 0.262236i
\(479\) −11.1845 19.3721i −0.511032 0.885134i −0.999918 0.0127862i \(-0.995930\pi\)
0.488886 0.872348i \(-0.337403\pi\)
\(480\) 12.0097 0.548165
\(481\) 0 0
\(482\) 2.02475 0.0922250
\(483\) 4.96950 + 8.60743i 0.226120 + 0.391652i
\(484\) −8.09179 14.0154i −0.367809 0.637064i
\(485\) 4.38740 7.59919i 0.199221 0.345062i
\(486\) 8.76569 0.397620
\(487\) 11.4602 19.8497i 0.519313 0.899476i −0.480435 0.877030i \(-0.659521\pi\)
0.999748 0.0224462i \(-0.00714544\pi\)
\(488\) −8.23341 + 14.2607i −0.372709 + 0.645551i
\(489\) −12.1390 −0.548944
\(490\) −0.192021 + 0.332591i −0.00867465 + 0.0150249i
\(491\) −0.921780 1.59657i −0.0415993 0.0720522i 0.844476 0.535593i \(-0.179912\pi\)
−0.886075 + 0.463541i \(0.846579\pi\)
\(492\) −2.25086 3.89861i −0.101477 0.175763i
\(493\) −8.98254 −0.404553
\(494\) 0 0
\(495\) −7.91185 −0.355611
\(496\) 6.62833 + 11.4806i 0.297621 + 0.515495i
\(497\) −18.4955 32.0351i −0.829634 1.43697i
\(498\) −3.63437 + 6.29492i −0.162860 + 0.282082i
\(499\) 12.0344 0.538736 0.269368 0.963037i \(-0.413185\pi\)
0.269368 + 0.963037i \(0.413185\pi\)
\(500\) −5.09448 + 8.82390i −0.227832 + 0.394617i
\(501\) −2.51142 + 4.34990i −0.112202 + 0.194339i
\(502\) 0.762118 0.0340150
\(503\) 15.2528 26.4186i 0.680088 1.17795i −0.294866 0.955539i \(-0.595275\pi\)
0.974954 0.222408i \(-0.0713918\pi\)
\(504\) −6.50000 11.2583i −0.289533 0.501486i
\(505\) −7.41185 12.8377i −0.329823 0.571270i
\(506\) −3.06100 −0.136078
\(507\) 0 0
\(508\) −11.4681 −0.508816
\(509\) −0.755709 1.30893i −0.0334962 0.0580171i 0.848791 0.528728i \(-0.177331\pi\)
−0.882288 + 0.470711i \(0.843998\pi\)
\(510\) −0.708947 1.22793i −0.0313927 0.0543738i
\(511\) 17.2518 29.8810i 0.763176 1.32186i
\(512\) 21.2174 0.937687
\(513\) −4.16487 + 7.21377i −0.183884 + 0.318496i
\(514\) −8.16786 + 14.1471i −0.360269 + 0.624004i
\(515\) −37.9124 −1.67062
\(516\) 4.85690 8.41239i 0.213813 0.370335i
\(517\) −4.60776 7.98088i −0.202649 0.350998i
\(518\) 0.710439 + 1.23052i 0.0312149 + 0.0540658i
\(519\) 13.1448 0.576994
\(520\) 0 0
\(521\) −5.64012 −0.247098 −0.123549 0.992338i \(-0.539428\pi\)
−0.123549 + 0.992338i \(0.539428\pi\)
\(522\) −5.16637 8.94841i −0.226126 0.391661i
\(523\) 15.8753 + 27.4968i 0.694179 + 1.20235i 0.970457 + 0.241275i \(0.0775657\pi\)
−0.276278 + 0.961078i \(0.589101\pi\)
\(524\) −11.5734 + 20.0457i −0.505585 + 0.875699i
\(525\) 6.15452 0.268605
\(526\) −2.96801 + 5.14074i −0.129411 + 0.224147i
\(527\) 3.35421 5.80966i 0.146112 0.253073i
\(528\) 2.15883 0.0939512
\(529\) 0.902165 1.56260i 0.0392246 0.0679390i
\(530\) −4.56584 7.90827i −0.198328 0.343513i
\(531\) 0.0142375 + 0.0246601i 0.000617856 + 0.00107016i
\(532\) 8.83207 0.382919
\(533\) 0 0
\(534\) 6.55496 0.283661
\(535\) −7.88889 13.6640i −0.341066 0.590744i
\(536\) 9.48307 + 16.4252i 0.409606 + 0.709459i
\(537\) 0.984271 1.70481i 0.0424744 0.0735678i
\(538\) −5.65279 −0.243709
\(539\) −0.147948 + 0.256254i −0.00637259 + 0.0110377i
\(540\) −10.1833 + 17.6380i −0.438219 + 0.759018i
\(541\) −24.3297 −1.04602 −0.523009 0.852327i \(-0.675191\pi\)
−0.523009 + 0.852327i \(0.675191\pi\)
\(542\) −8.17241 + 14.1550i −0.351035 + 0.608010i
\(543\) −4.73437 8.20016i −0.203171 0.351903i
\(544\) −3.03870 5.26318i −0.130283 0.225657i
\(545\) −11.7017 −0.501246
\(546\) 0 0
\(547\) −8.18896 −0.350135 −0.175067 0.984556i \(-0.556014\pi\)
−0.175067 + 0.984556i \(0.556014\pi\)
\(548\) −10.9879 19.0316i −0.469381 0.812991i
\(549\) −9.47099 16.4042i −0.404212 0.700116i
\(550\) −0.947730 + 1.64152i −0.0404114 + 0.0699945i
\(551\) 15.3177 0.652555
\(552\) −3.78232 + 6.55118i −0.160986 + 0.278837i
\(553\) −1.08665 + 1.88214i −0.0462092 + 0.0800367i
\(554\) −5.68532 −0.241546
\(555\) 1.06853 1.85075i 0.0453566 0.0785600i
\(556\) 10.1915 + 17.6522i 0.432215 + 0.748619i
\(557\) 12.6664 + 21.9388i 0.536691 + 0.929576i 0.999079 + 0.0428988i \(0.0136593\pi\)
−0.462388 + 0.886678i \(0.653007\pi\)
\(558\) 7.71678 0.326677
\(559\) 0 0
\(560\) 16.9487 0.716213
\(561\) −0.546229 0.946096i −0.0230618 0.0399442i
\(562\) −3.20895 5.55806i −0.135361 0.234453i
\(563\) 12.6969 21.9916i 0.535109 0.926836i −0.464049 0.885810i \(-0.653604\pi\)
0.999158 0.0410266i \(-0.0130628\pi\)
\(564\) −10.4373 −0.439488
\(565\) −10.7078 + 18.5464i −0.450478 + 0.780252i
\(566\) 8.52111 14.7590i 0.358169 0.620367i
\(567\) 9.76032 0.409895
\(568\) 14.0770 24.3821i 0.590659 1.02305i
\(569\) 15.5673 + 26.9634i 0.652617 + 1.13037i 0.982486 + 0.186338i \(0.0596621\pi\)
−0.329869 + 0.944027i \(0.607005\pi\)
\(570\) 1.20895 + 2.09396i 0.0506372 + 0.0877063i
\(571\) −20.5090 −0.858276 −0.429138 0.903239i \(-0.641183\pi\)
−0.429138 + 0.903239i \(0.641183\pi\)
\(572\) 0 0
\(573\) −7.21206 −0.301288
\(574\) 2.47823 + 4.29242i 0.103439 + 0.179162i
\(575\) 6.56249 + 11.3666i 0.273675 + 0.474019i
\(576\) −1.80045 + 3.11846i −0.0750186 + 0.129936i
\(577\) −15.6890 −0.653143 −0.326572 0.945172i \(-0.605893\pi\)
−0.326572 + 0.945172i \(0.605893\pi\)
\(578\) 4.35839 7.54895i 0.181285 0.313995i
\(579\) 5.42327 9.39338i 0.225383 0.390376i
\(580\) 37.4523 1.55512
\(581\) −21.9840 + 38.0775i −0.912051 + 1.57972i
\(582\) 0.696866 + 1.20701i 0.0288860 + 0.0500320i
\(583\) −3.51789 6.09316i −0.145696 0.252353i
\(584\) 26.2610 1.08669
\(585\) 0 0
\(586\) 10.3268 0.426595
\(587\) 15.2843 + 26.4733i 0.630853 + 1.09267i 0.987378 + 0.158383i \(0.0506281\pi\)
−0.356525 + 0.934286i \(0.616039\pi\)
\(588\) 0.167563 + 0.290227i 0.00691017 + 0.0119688i
\(589\) −5.71983 + 9.90704i −0.235682 + 0.408212i
\(590\) 0.0187864 0.000773422
\(591\) 5.20291 9.01170i 0.214019 0.370692i
\(592\) 1.06853 1.85075i 0.0439164 0.0760654i
\(593\) 29.6883 1.21915 0.609576 0.792727i \(-0.291340\pi\)
0.609576 + 0.792727i \(0.291340\pi\)
\(594\) 1.42812 2.47357i 0.0585963 0.101492i
\(595\) −4.28836 7.42766i −0.175806 0.304505i
\(596\) 0.626842 + 1.08572i 0.0256765 + 0.0444729i
\(597\) −10.8955 −0.445922
\(598\) 0 0
\(599\) 24.2325 0.990113 0.495057 0.868861i \(-0.335147\pi\)
0.495057 + 0.868861i \(0.335147\pi\)
\(600\) 2.34213 + 4.05668i 0.0956169 + 0.165613i
\(601\) −8.24094 14.2737i −0.336155 0.582237i 0.647551 0.762022i \(-0.275793\pi\)
−0.983706 + 0.179785i \(0.942460\pi\)
\(602\) −5.34750 + 9.26215i −0.217948 + 0.377497i
\(603\) −21.8170 −0.888457
\(604\) 16.1365 27.9493i 0.656586 1.13724i
\(605\) 13.3998 23.2091i 0.544778 0.943584i
\(606\) 2.35450 0.0956451
\(607\) −0.715948 + 1.24006i −0.0290594 + 0.0503324i −0.880189 0.474623i \(-0.842585\pi\)
0.851130 + 0.524955i \(0.175918\pi\)
\(608\) 5.18180 + 8.97514i 0.210150 + 0.363990i
\(609\) 8.52715 + 14.7695i 0.345537 + 0.598488i
\(610\) −12.4969 −0.505986
\(611\) 0 0
\(612\) 4.53452 0.183297
\(613\) 1.92423 + 3.33287i 0.0777190 + 0.134613i 0.902265 0.431181i \(-0.141903\pi\)
−0.824546 + 0.565794i \(0.808570\pi\)
\(614\) 2.48188 + 4.29874i 0.100160 + 0.173483i
\(615\) 3.72737 6.45599i 0.150302 0.260330i
\(616\) −6.60819 −0.266251
\(617\) −7.51938 + 13.0239i −0.302719 + 0.524324i −0.976751 0.214378i \(-0.931228\pi\)
0.674032 + 0.738702i \(0.264561\pi\)
\(618\) 3.01089 5.21501i 0.121116 0.209778i
\(619\) −12.8170 −0.515159 −0.257579 0.966257i \(-0.582925\pi\)
−0.257579 + 0.966257i \(0.582925\pi\)
\(620\) −13.9852 + 24.2231i −0.561660 + 0.972824i
\(621\) −9.88889 17.1281i −0.396827 0.687325i
\(622\) −5.83811 10.1119i −0.234087 0.405450i
\(623\) 39.6504 1.58856
\(624\) 0 0
\(625\) −31.1269 −1.24508
\(626\) 1.97770 + 3.42547i 0.0790447 + 0.136909i
\(627\) 0.931468 + 1.61335i 0.0371993 + 0.0644310i
\(628\) −3.40246 + 5.89324i −0.135773 + 0.235166i
\(629\) −1.08144 −0.0431199
\(630\) 4.93296 8.54414i 0.196534 0.340407i
\(631\) 12.8758 22.3016i 0.512579 0.887813i −0.487314 0.873227i \(-0.662023\pi\)
0.999894 0.0145868i \(-0.00464329\pi\)
\(632\) −1.65412 −0.0657974
\(633\) −4.19418 + 7.26453i −0.166704 + 0.288739i
\(634\) 6.64981 + 11.5178i 0.264098 + 0.457431i
\(635\) −9.49545 16.4466i −0.376815 0.652664i
\(636\) −7.96854 −0.315973
\(637\) 0 0
\(638\) −5.25236 −0.207943
\(639\) 16.1930 + 28.0471i 0.640584 + 1.10952i
\(640\) 16.1637 + 27.9963i 0.638925 + 1.10665i
\(641\) −12.2286 + 21.1805i −0.482999 + 0.836579i −0.999809 0.0195209i \(-0.993786\pi\)
0.516810 + 0.856100i \(0.327119\pi\)
\(642\) 2.50604 0.0989055
\(643\) −4.98672 + 8.63726i −0.196657 + 0.340620i −0.947442 0.319926i \(-0.896342\pi\)
0.750785 + 0.660546i \(0.229675\pi\)
\(644\) −10.4852 + 18.1610i −0.413176 + 0.715642i
\(645\) 16.0858 0.633376
\(646\) 0.611777 1.05963i 0.0240700 0.0416905i
\(647\) −5.92154 10.2564i −0.232800 0.403221i 0.725831 0.687873i \(-0.241455\pi\)
−0.958631 + 0.284652i \(0.908122\pi\)
\(648\) 3.71432 + 6.43340i 0.145912 + 0.252728i
\(649\) 0.0144745 0.000568173
\(650\) 0 0
\(651\) −12.7366 −0.499188
\(652\) −12.8061 22.1808i −0.501526 0.868669i
\(653\) 3.73705 + 6.47277i 0.146242 + 0.253299i 0.929836 0.367975i \(-0.119949\pi\)
−0.783593 + 0.621274i \(0.786615\pi\)
\(654\) 0.929312 1.60962i 0.0363390 0.0629410i
\(655\) −38.3303 −1.49769
\(656\) 3.72737 6.45599i 0.145529 0.252064i
\(657\) −15.1042 + 26.1612i −0.589270 + 1.02065i
\(658\) 11.4916 0.447988
\(659\) −17.0869 + 29.5955i −0.665613 + 1.15288i 0.313506 + 0.949586i \(0.398497\pi\)
−0.979119 + 0.203289i \(0.934837\pi\)
\(660\) 2.27748 + 3.94471i 0.0886508 + 0.153548i
\(661\) 16.8044 + 29.1061i 0.653615 + 1.13209i 0.982239 + 0.187634i \(0.0600817\pi\)
−0.328624 + 0.944461i \(0.606585\pi\)
\(662\) −1.60686 −0.0624524
\(663\) 0 0
\(664\) −33.4644 −1.29867
\(665\) 7.31282 + 12.6662i 0.283579 + 0.491173i
\(666\) −0.621998 1.07733i −0.0241019 0.0417458i
\(667\) −18.1848 + 31.4970i −0.704118 + 1.21957i
\(668\) −10.5978 −0.410040
\(669\) −4.57338 + 7.92132i −0.176817 + 0.306256i
\(670\) −7.19687 + 12.4653i −0.278039 + 0.481578i
\(671\) −9.62863 −0.371709
\(672\) −5.76928 + 9.99269i −0.222555 + 0.385476i
\(673\) −24.0160 41.5970i −0.925750 1.60345i −0.790351 0.612654i \(-0.790102\pi\)
−0.135399 0.990791i \(-0.543232\pi\)
\(674\) 0.861740 + 1.49258i 0.0331930 + 0.0574919i
\(675\) −12.2470 −0.471386
\(676\) 0 0
\(677\) −33.6582 −1.29359 −0.646794 0.762665i \(-0.723891\pi\)
−0.646794 + 0.762665i \(0.723891\pi\)
\(678\) −1.70075 2.94579i −0.0653169 0.113132i
\(679\) 4.21528 + 7.30109i 0.161768 + 0.280190i
\(680\) 3.26391 5.65325i 0.125165 0.216792i
\(681\) −8.53319 −0.326992
\(682\) 1.96130 3.39708i 0.0751022 0.130081i
\(683\) 7.95204 13.7733i 0.304276 0.527022i −0.672824 0.739803i \(-0.734919\pi\)
0.977100 + 0.212781i \(0.0682520\pi\)
\(684\) −7.73258 −0.295663
\(685\) 18.1957 31.5158i 0.695221 1.20416i
\(686\) 5.04437 + 8.73710i 0.192595 + 0.333584i
\(687\) −0.456886 0.791351i −0.0174313 0.0301919i
\(688\) 16.0858 0.613264
\(689\) 0 0
\(690\) −5.74094 −0.218554
\(691\) 16.5951 + 28.7436i 0.631309 + 1.09346i 0.987284 + 0.158964i \(0.0508154\pi\)
−0.355975 + 0.934495i \(0.615851\pi\)
\(692\) 13.8672 + 24.0188i 0.527154 + 0.913057i
\(693\) 3.80074 6.58308i 0.144378 0.250070i
\(694\) −6.31468 −0.239702
\(695\) −16.8768 + 29.2315i −0.640174 + 1.10881i
\(696\) −6.49007 + 11.2411i −0.246006 + 0.426094i
\(697\) −3.77240 −0.142890
\(698\) −0.928780 + 1.60869i −0.0351548 + 0.0608900i
\(699\) 4.35086 + 7.53590i 0.164564 + 0.285034i
\(700\) 6.49276 + 11.2458i 0.245403 + 0.425051i
\(701\) −14.9129 −0.563253 −0.281627 0.959524i \(-0.590874\pi\)
−0.281627 + 0.959524i \(0.590874\pi\)
\(702\) 0 0
\(703\) 1.84415 0.0695534
\(704\) 0.915206 + 1.58518i 0.0344931 + 0.0597439i
\(705\) −8.64191 14.9682i −0.325473 0.563736i
\(706\) 0.176956 0.306497i 0.00665983 0.0115352i
\(707\) 14.2422 0.535633
\(708\) 0.00819673 0.0141971i 0.000308052 0.000533561i
\(709\) 19.2156 33.2824i 0.721656 1.24995i −0.238679 0.971098i \(-0.576714\pi\)
0.960336 0.278847i \(-0.0899522\pi\)
\(710\) 21.3666 0.801874
\(711\) 0.951378 1.64784i 0.0356795 0.0617987i
\(712\) 15.0891 + 26.1351i 0.565488 + 0.979454i
\(713\) −13.5809 23.5228i −0.508609 0.880937i
\(714\) 1.36227 0.0509818
\(715\) 0 0
\(716\) 4.15346 0.155222
\(717\) −4.78328 8.28489i −0.178635 0.309405i
\(718\) −5.95444 10.3134i −0.222218 0.384892i
\(719\) 5.71864 9.90497i 0.213269 0.369393i −0.739467 0.673193i \(-0.764922\pi\)
0.952736 + 0.303800i \(0.0982555\pi\)
\(720\) −14.8388 −0.553008
\(721\) 18.2126 31.5451i 0.678272 1.17480i
\(722\) 4.22886 7.32460i 0.157382 0.272593i
\(723\) 2.92585 0.108814
\(724\) 9.98911 17.3017i 0.371243 0.643011i
\(725\) 11.2606 + 19.5039i 0.418206 + 0.724355i
\(726\) 2.12833 + 3.68638i 0.0789899 + 0.136815i
\(727\) 3.63640 0.134867 0.0674333 0.997724i \(-0.478519\pi\)
0.0674333 + 0.997724i \(0.478519\pi\)
\(728\) 0 0
\(729\) 1.78986 0.0662910
\(730\) 9.96495 + 17.2598i 0.368819 + 0.638814i
\(731\) −4.07002 7.04949i −0.150535 0.260735i
\(732\) −5.45257 + 9.44414i −0.201533 + 0.349065i
\(733\) 3.52217 0.130094 0.0650472 0.997882i \(-0.479280\pi\)
0.0650472 + 0.997882i \(0.479280\pi\)
\(734\) 2.60470 4.51148i 0.0961414 0.166522i
\(735\) −0.277479 + 0.480608i −0.0102350 + 0.0177275i
\(736\) −24.6069 −0.907021
\(737\) −5.54503 + 9.60428i −0.204254 + 0.353778i
\(738\) −2.16972 3.75806i −0.0798685 0.138336i
\(739\) 0.210144 + 0.363980i 0.00773027 + 0.0133892i 0.869865 0.493290i \(-0.164206\pi\)
−0.862134 + 0.506680i \(0.830873\pi\)
\(740\) 4.50902 0.165755
\(741\) 0 0
\(742\) 8.77346 0.322084
\(743\) −12.6811 21.9644i −0.465226 0.805795i 0.533986 0.845493i \(-0.320694\pi\)
−0.999212 + 0.0396987i \(0.987360\pi\)
\(744\) −4.84697 8.39520i −0.177699 0.307783i
\(745\) −1.03803 + 1.79792i −0.0380306 + 0.0658709i
\(746\) 15.3870 0.563359
\(747\) 19.2473 33.3373i 0.704221 1.21975i
\(748\) 1.15250 1.99618i 0.0421395 0.0729877i
\(749\) 15.1588 0.553892
\(750\) 1.33997 2.32090i 0.0489288 0.0847471i
\(751\) −0.325437 0.563673i −0.0118754 0.0205687i 0.860027 0.510249i \(-0.170447\pi\)
−0.871902 + 0.489680i \(0.837113\pi\)
\(752\) −8.64191 14.9682i −0.315138 0.545835i
\(753\) 1.10129 0.0401333
\(754\) 0 0
\(755\) 53.4432 1.94500
\(756\) −9.78382 16.9461i −0.355834 0.616322i
\(757\) 8.39546 + 14.5414i 0.305138 + 0.528515i 0.977292 0.211897i \(-0.0679640\pi\)
−0.672154 + 0.740411i \(0.734631\pi\)
\(758\) 9.95324 17.2395i 0.361518 0.626167i
\(759\) −4.42327 −0.160555
\(760\) −5.56584 + 9.64032i −0.201894 + 0.349691i
\(761\) 15.4611 26.7794i 0.560463 0.970751i −0.436993 0.899465i \(-0.643956\pi\)
0.997456 0.0712857i \(-0.0227102\pi\)
\(762\) 3.01639 0.109272
\(763\) 5.62133 9.73644i 0.203506 0.352483i
\(764\) −7.60842 13.1782i −0.275263 0.476770i
\(765\) 3.75451 + 6.50301i 0.135745 + 0.235117i
\(766\) −2.69441 −0.0973531
\(767\) 0 0
\(768\) −2.68425 −0.0968596
\(769\) −21.8845 37.9050i −0.789174 1.36689i −0.926473 0.376360i \(-0.877176\pi\)
0.137299 0.990530i \(-0.456158\pi\)
\(770\) −2.50753 4.34317i −0.0903652 0.156517i
\(771\) −11.8029 + 20.4432i −0.425071 + 0.736245i
\(772\) 22.8853 0.823660
\(773\) −21.2104 + 36.7376i −0.762886 + 1.32136i 0.178470 + 0.983945i \(0.442885\pi\)
−0.941357 + 0.337413i \(0.890448\pi\)
\(774\) 4.68180