Properties

Label 169.2.c.c.22.2
Level $169$
Weight $2$
Character 169.22
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 22.2
Root \(-0.623490 + 1.07992i\) of defining polynomial
Character \(\chi\) \(=\) 169.22
Dual form 169.2.c.c.146.2

$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

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

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 \(-0.770471\pi\)
0.947296 + 0.320361i \(0.103804\pi\)
\(3\) −0.400969 + 0.694498i −0.231499 + 0.400969i −0.958250 0.285933i \(-0.907696\pi\)
0.726750 + 0.686902i \(0.241030\pi\)
\(4\) 0.846011 + 1.46533i 0.423005 + 0.732667i
\(5\) −2.80194 −1.25306 −0.626532 0.779395i \(-0.715526\pi\)
−0.626532 + 0.779395i \(0.715526\pi\)
\(6\) 0.222521 + 0.385418i 0.0908438 + 0.157346i
\(7\) 1.34601 + 2.33136i 0.508744 + 0.881171i 0.999949 + 0.0101266i \(0.00322345\pi\)
−0.491204 + 0.871044i \(0.663443\pi\)
\(8\) 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 \(-0.775525\pi\)
0.942090 + 0.335360i \(0.108858\pi\)
\(12\) −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 0.788808 0.614639i \(-0.210698\pi\)
−0.926697 + 0.375808i \(0.877365\pi\)
\(18\) 1.30798 0.308293
\(19\) −0.969501 1.67922i −0.222419 0.385240i 0.733123 0.680096i \(-0.238062\pi\)
−0.955542 + 0.294855i \(0.904729\pi\)
\(20\) −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 −0.519749 0.854319i \(-0.673975\pi\)
0.999736 + 0.0229566i \(0.00730797\pi\)
\(24\) −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 −0.221914 0.975066i \(-0.571230\pi\)
0.955389 0.295350i \(-0.0954364\pi\)
\(30\) −0.623490 1.07992i −0.113833 0.197165i
\(31\) 5.89977 1.05963 0.529815 0.848113i \(-0.322261\pi\)
0.529815 + 0.848113i \(0.322261\pi\)
\(32\) 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 \(-0.858244\pi\)
0.824286 + 0.566174i \(0.191577\pi\)
\(38\) −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 \(-0.916748\pi\)
0.706926 + 0.707288i \(0.250081\pi\)
\(42\) −0.599031 + 1.03755i −0.0924325 + 0.160098i
\(43\) −3.57942 6.19973i −0.545856 0.945450i −0.998553 0.0537856i \(-0.982871\pi\)
0.452697 0.891665i \(-0.350462\pi\)
\(44\) 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 \(-0.689583\pi\)
−0.560998 + 0.827817i \(0.689583\pi\)
\(48\) −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 \(-0.166416\pi\)
−0.865632 + 0.500681i \(0.833083\pi\)
\(60\) 3.80194 0.490828
\(61\) 4.01842 + 6.96010i 0.514506 + 0.891150i 0.999858 + 0.0168315i \(0.00535789\pi\)
−0.485353 + 0.874318i \(0.661309\pi\)
\(62\) 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 −0.431567 0.902081i \(-0.642039\pi\)
0.997009 0.0772919i \(-0.0246273\pi\)
\(68\) 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 0.909059 + 0.416668i \(0.136802\pi\)
−0.0936838 + 0.995602i \(0.529864\pi\)
\(72\) 2.41454 + 4.18211i 0.284557 + 0.492866i
\(73\) 12.8170 1.50012 0.750058 0.661372i \(-0.230025\pi\)
0.750058 + 0.661372i \(0.230025\pi\)
\(74\) 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 \(-0.853809\pi\)
−0.896375 + 0.443296i \(0.853809\pi\)
\(84\) −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 −0.150949 0.988542i \(-0.548233\pi\)
0.931576 0.363546i \(-0.118434\pi\)
\(90\) −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 \(-0.217490\pi\)
−0.934504 + 0.355953i \(0.884156\pi\)
\(98\) 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 −0.967094 0.254420i \(-0.918116\pi\)
0.703881 + 0.710318i \(0.251449\pi\)
\(102\) 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 −0.969421 0.245403i \(-0.921080\pi\)
0.697236 + 0.716842i \(0.254413\pi\)
\(108\) −3.63437 6.29492i −0.349718 0.605729i
\(109\) 4.17629 0.400016 0.200008 0.979794i \(-0.435903\pi\)
0.200008 + 0.979794i \(0.435903\pi\)
\(110\) 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 0.628376 0.777910i \(-0.283720\pi\)
−0.987878 + 0.155235i \(0.950387\pi\)
\(114\) 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 −0.976298 0.216430i \(-0.930559\pi\)
0.675583 + 0.737284i \(0.263892\pi\)
\(128\) −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 −0.997918 0.0644987i \(-0.979455\pi\)
0.443101 0.896471i \(-0.353878\pi\)
\(138\) 2.04892 0.174415
\(139\) −6.02326 10.4326i −0.510886 0.884881i −0.999920 0.0126165i \(-0.995984\pi\)
0.489034 0.872265i \(-0.337349\pi\)
\(140\) 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 \(-0.157004\pi\)
−0.850451 + 0.526054i \(0.823671\pi\)
\(150\) 0.634375 + 1.09877i 0.0517965 + 0.0897142i
\(151\) −19.0737 −1.55219 −0.776097 0.630614i \(-0.782803\pi\)
−0.776097 + 0.630614i \(0.782803\pi\)
\(152\) −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 −0.993852 0.110721i \(-0.964684\pi\)
0.401038 0.916061i \(-0.368649\pi\)
\(164\) −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 \(-0.755419\pi\)
0.961380 + 0.275226i \(0.0887526\pi\)
\(168\) −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 −0.988904 0.148556i \(-0.952538\pi\)
0.365799 0.930694i \(-0.380796\pi\)
\(174\) 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 −0.816505 0.577339i \(-0.804091\pi\)
0.908242 + 0.418445i \(0.137425\pi\)
\(180\) 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 0.981586 0.191019i \(-0.0611792\pi\)
−0.656220 + 0.754569i \(0.727846\pi\)
\(192\) 0.612605 1.06106i 0.0442109 0.0765756i
\(193\) −6.76271 + 11.7134i −0.486790 + 0.843146i −0.999885 0.0151865i \(-0.995166\pi\)
0.513094 + 0.858332i \(0.328499\pi\)
\(194\) −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 \(-0.986289\pi\)
0.536827 + 0.843692i \(0.319623\pi\)
\(198\) 0.783520 1.35710i 0.0556823 0.0964446i
\(199\) 6.79321 + 11.7662i 0.481558 + 0.834083i 0.999776 0.0211659i \(-0.00673782\pi\)
−0.518218 + 0.855248i \(0.673404\pi\)
\(200\) 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 −0.987969 0.154652i \(-0.950574\pi\)
0.627917 + 0.778280i \(0.283908\pi\)
\(212\) 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 \(-0.708605\pi\)
0.991333 + 0.131372i \(0.0419383\pi\)
\(224\) −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 \(-0.281547\pi\)
−0.986795 + 0.161973i \(0.948214\pi\)
\(228\) 1.31551 + 2.27853i 0.0871219 + 0.150899i
\(229\) −1.13946 −0.0752974 −0.0376487 0.999291i \(-0.511987\pi\)
−0.0376487 + 0.999291i \(0.511987\pi\)
\(230\) 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 \(-0.626082\pi\)
−0.385822 + 0.922573i \(0.626082\pi\)
\(240\) 2.52446 + 4.37249i 0.162953 + 0.282243i
\(241\) 1.82424 + 3.15968i 0.117510 + 0.203533i 0.918780 0.394770i \(-0.129176\pi\)
−0.801271 + 0.598302i \(0.795842\pi\)
\(242\) 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 0.843541 0.537064i \(-0.180467\pi\)
−0.886882 + 0.461996i \(0.847133\pi\)
\(252\) −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 −0.115756 + 0.993278i \(0.536929\pi\)
−0.802325 + 0.596887i \(0.796404\pi\)
\(258\) 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 −0.982468 0.186429i \(-0.940309\pi\)
0.652686 + 0.757628i \(0.273642\pi\)
\(264\) 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 0.978476 0.206360i \(-0.0661618\pi\)
−0.667951 + 0.744205i \(0.732828\pi\)
\(270\) 3.33997 5.78500i 0.203264 0.352064i
\(271\) 14.7262 25.5065i 0.894551 1.54941i 0.0601918 0.998187i \(-0.480829\pi\)
0.834359 0.551221i \(-0.185838\pi\)
\(272\) 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 0.977874 0.209195i \(-0.0670843\pi\)
−0.670105 + 0.742266i \(0.733751\pi\)
\(278\) −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 \(-0.612102\pi\)
−0.344944 + 0.938623i \(0.612102\pi\)
\(282\) −1.71164 2.96464i −0.101926 0.176542i
\(283\) 15.3545 26.5948i 0.912730 1.58090i 0.102540 0.994729i \(-0.467303\pi\)
0.810191 0.586167i \(-0.199364\pi\)
\(284\) −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 0.998697 + 0.0510409i \(0.0162539\pi\)
−0.455146 + 0.890417i \(0.650413\pi\)
\(294\) −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 \(-0.417845\pi\)
0.255241 + 0.966877i \(0.417845\pi\)
\(308\) 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 \(-0.265003\pi\)
0.673007 + 0.739636i \(0.265003\pi\)
\(318\) 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 \(-0.192023\pi\)
−0.903066 + 0.429501i \(0.858689\pi\)
\(332\) −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 0.977355 0.211608i \(-0.0678700\pi\)
−0.671935 + 0.740610i \(0.734537\pi\)
\(348\) −5.35958 + 9.28307i −0.287304 + 0.497625i
\(349\) 1.67360 2.89877i 0.0895859 0.155167i −0.817750 0.575573i \(-0.804779\pi\)
0.907336 + 0.420406i \(0.138112\pi\)
\(350\) 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 \(-0.838736\pi\)
0.857415 + 0.514626i \(0.172069\pi\)
\(354\) −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 \(-0.691619\pi\)
−0.566282 + 0.824211i \(0.691619\pi\)
\(360\) −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 −0.717132 0.696937i \(-0.754546\pi\)
0.962131 + 0.272586i \(0.0878789\pi\)
\(368\) 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 −0.961865 0.273523i \(-0.911811\pi\)
0.244054 0.969762i \(-0.421522\pi\)
\(374\) −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 −0.123805 + 0.992307i \(0.539510\pi\)
−0.797460 + 0.603371i \(0.793824\pi\)
\(380\) −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 \(-0.206253\pi\)
−0.921359 + 0.388713i \(0.872920\pi\)
\(384\) −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 \(-0.0415237\pi\)
−0.608405 + 0.793627i \(0.708190\pi\)
\(398\) 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 \(-0.936533\pi\)
0.661626 + 0.749834i \(0.269867\pi\)
\(402\) 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 0.988159 + 0.153433i \(0.0490329\pi\)
−0.361203 + 0.932487i \(0.617634\pi\)
\(410\) −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 −0.687616 0.726075i \(-0.741343\pi\)
0.972607 + 0.232455i \(0.0746758\pi\)
\(420\) 5.11745 + 8.86368i 0.249706 + 0.432503i
\(421\) −8.29291 −0.404172 −0.202086 0.979368i \(-0.564772\pi\)
−0.202086 + 0.979368i \(0.564772\pi\)
\(422\) 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 \(-0.840481\pi\)
0.854580 + 0.519319i \(0.173814\pi\)
\(432\) 4.82640 8.35956i 0.232210 0.402200i
\(433\) 6.67510 + 11.5616i 0.320785 + 0.555615i 0.980650 0.195768i \(-0.0627201\pi\)
−0.659866 + 0.751384i \(0.729387\pi\)
\(434\) 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 −0.983274 0.182132i \(-0.941700\pi\)
0.649368 + 0.760475i \(0.275034\pi\)
\(440\) −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 \(-0.0706822\pi\)
−0.678452 + 0.734645i \(0.737349\pi\)
\(450\) 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 −0.141171 0.989985i \(-0.545087\pi\)
0.927938 0.372735i \(-0.121580\pi\)
\(458\) −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 \(-0.156266\pi\)
−0.849229 + 0.528025i \(0.822933\pi\)
\(462\) 0.717677 + 1.24305i 0.0333893 + 0.0578320i
\(463\) −15.2010 −0.706453 −0.353226 0.935538i \(-0.614915\pi\)
−0.353226 + 0.935538i \(0.614915\pi\)
\(464\) 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 −0.488886 0.872348i \(-0.662597\pi\)
0.999918 0.0127862i \(-0.00407010\pi\)
\(480\) 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 −0.999748 0.0224462i \(-0.992855\pi\)
0.480435 0.877030i \(-0.340479\pi\)
\(488\) 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 −0.886075 0.463541i \(-0.846579\pi\)
0.844476 + 0.535593i \(0.179912\pi\)
\(492\) 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 \(-0.586815\pi\)
−0.269368 + 0.963037i \(0.586815\pi\)
\(500\) 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 0.974954 + 0.222408i \(0.0713918\pi\)
−0.294866 + 0.955539i \(0.595275\pi\)
\(504\) −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 \(-0.822669\pi\)
0.882288 + 0.470711i \(0.156002\pi\)
\(510\) −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 −0.276278 0.961078i \(-0.589101\pi\)
0.970457 0.241275i \(-0.0775657\pi\)
\(524\) −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 \(-0.324809\pi\)
0.523009 + 0.852327i \(0.324809\pi\)
\(542\) −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 0.462388 + 0.886678i \(0.346993\pi\)
−0.999079 + 0.0428988i \(0.986341\pi\)
\(558\) 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 0.999158 + 0.0410266i \(0.0130628\pi\)
−0.464049 + 0.885810i \(0.653604\pi\)
\(564\) 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 −0.329869 0.944027i \(-0.607005\pi\)
0.982486 0.186338i \(-0.0596621\pi\)
\(570\) −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 \(-0.394107\pi\)
0.326572 + 0.945172i \(0.394107\pi\)
\(578\) −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 0.356525 + 0.934286i \(0.383961\pi\)
−0.987378 + 0.158383i \(0.949372\pi\)
\(588\) 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 \(-0.708660\pi\)
−0.609576 + 0.792727i \(0.708660\pi\)
\(594\) 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 −0.983706 0.179785i \(-0.942460\pi\)
0.647551 + 0.762022i \(0.275793\pi\)
\(602\) −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 0.851130 0.524955i \(-0.175918\pi\)
−0.880189 + 0.474623i \(0.842585\pi\)
\(608\) 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 \(-0.858097\pi\)
0.824546 + 0.565794i \(0.191430\pi\)
\(614\) 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 \(-0.0687724\pi\)
−0.674032 + 0.738702i \(0.735439\pi\)
\(618\) −3.01089 5.21501i −0.121116 0.209778i
\(619\) 12.8170 0.515159 0.257579 0.966257i \(-0.417075\pi\)
0.257579 + 0.966257i \(0.417075\pi\)
\(620\) −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 −0.999894 0.0145868i \(-0.995357\pi\)
0.487314 0.873227i \(-0.337977\pi\)
\(632\) 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 0.516810 0.856100i \(-0.327119\pi\)
−0.999809 + 0.0195209i \(0.993786\pi\)
\(642\) −2.50604 −0.0989055
\(643\) 4.98672 + 8.63726i 0.196657 + 0.340620i 0.947442 0.319926i \(-0.103658\pi\)
−0.750785 + 0.660546i \(0.770325\pi\)
\(644\) 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 −0.958631 0.284652i \(-0.908122\pi\)
0.725831 + 0.687873i \(0.241455\pi\)
\(648\) −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 −0.783593 0.621274i \(-0.786615\pi\)
0.929836 + 0.367975i \(0.119949\pi\)
\(654\) 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 −0.979119 0.203289i \(-0.934837\pi\)
0.313506 0.949586i \(-0.398497\pi\)
\(660\) 2.27748 3.94471i 0.0886508 0.153548i
\(661\) −16.8044 + 29.1061i −0.653615 + 1.13209i 0.328624 + 0.944461i \(0.393415\pi\)
−0.982239 + 0.187634i \(0.939918\pi\)
\(662\) −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 −0.135399 + 0.990791i \(0.543232\pi\)
−0.790351 + 0.612654i \(0.790102\pi\)
\(674\) −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 \(-0.265081\pi\)
−0.977100 + 0.212781i \(0.931748\pi\)
\(684\) 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 0.355975 + 0.934495i \(0.384149\pi\)
−0.987284 + 0.158964i \(0.949185\pi\)
\(692\) 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 −0.960336 0.278847i \(-0.910048\pi\)
0.238679 0.971098i \(-0.423286\pi\)
\(710\) −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 0.952736 0.303800i \(-0.0982555\pi\)
−0.739467 + 0.673193i \(0.764922\pi\)
\(720\) 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 \(-0.520720\pi\)
−0.0650472 + 0.997882i \(0.520720\pi\)
\(734\) −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 \(-0.835794\pi\)
0.862134 + 0.506680i \(0.169127\pi\)
\(740\) 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 \(-0.679306\pi\)
0.999212 + 0.0396987i \(0.0126398\pi\)
\(744\) −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 −0.871902 0.489680i \(-0.837113\pi\)
0.860027 + 0.510249i \(0.170447\pi\)
\(752\) 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 −0.672154 0.740411i \(-0.734631\pi\)
0.977292 + 0.211897i \(0.0679640\pi\)
\(758\) 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 −0.997456 0.0712857i \(-0.977290\pi\)
0.436993 0.899465i \(-0.356044\pi\)
\(762\) −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 −0.137299 0.990530i \(-0.543842\pi\)
0.926473 0.376360i \(-0.122824\pi\)
\(770\) −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 0.941357 + 0.337413i \(0.109552\pi\)
−0.178470 + 0.983945i