Properties

Label 169.2.e.b.23.4
Level $169$
Weight $2$
Character 169.23
Analytic conductor $1.349$
Analytic rank $0$
Dimension $12$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,2,Mod(23,169)]
 
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([5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), 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: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.17213603549184.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 23.4
Root \(0.385418 + 0.222521i\) of defining polynomial
Character \(\chi\) \(=\) 169.23
Dual form 169.2.e.b.147.4

$q$-expansion

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

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.480608 0.277479i 0.339841 0.196207i −0.320361 0.947296i \(-0.603804\pi\)
0.660202 + 0.751088i \(0.270471\pi\)
\(3\) −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
\(5\) 2.80194i 1.25306i 0.779395 + 0.626532i \(0.215526\pi\)
−0.779395 + 0.626532i \(0.784474\pi\)
\(6\) −0.385418 0.222521i −0.157346 0.0908438i
\(7\) 2.33136 + 1.34601i 0.881171 + 0.508744i 0.871044 0.491204i \(-0.163443\pi\)
0.0101266 + 0.999949i \(0.496777\pi\)
\(8\) 2.04892i 0.724402i
\(9\) 1.17845 2.04113i 0.392816 0.680377i
\(10\) 0.777479 + 1.34663i 0.245860 + 0.425843i
\(11\) −1.03755 + 0.599031i −0.312834 + 0.180615i −0.648194 0.761475i \(-0.724475\pi\)
0.335360 + 0.942090i \(0.391142\pi\)
\(12\) 1.35690 0.391702
\(13\) 0 0
\(14\) 1.49396 0.399277
\(15\) 1.94594 1.12349i 0.502440 0.290084i
\(16\) −1.12349 1.94594i −0.280872 0.486485i
\(17\) 0.568532 0.984726i 0.137889 0.238831i −0.788808 0.614639i \(-0.789302\pi\)
0.926697 + 0.375808i \(0.122635\pi\)
\(18\) 1.30798i 0.308293i
\(19\) 1.67922 + 0.969501i 0.385240 + 0.222419i 0.680096 0.733123i \(-0.261938\pi\)
−0.294855 + 0.955542i \(0.595271\pi\)
\(20\) −4.10577 2.37047i −0.918079 0.530053i
\(21\) 2.15883i 0.471096i
\(22\) −0.332437 + 0.575798i −0.0708758 + 0.122761i
\(23\) −2.30194 3.98707i −0.479987 0.831362i 0.519749 0.854319i \(-0.326025\pi\)
−0.999736 + 0.0229566i \(0.992692\pi\)
\(24\) 1.42297 0.821552i 0.290463 0.167699i
\(25\) −2.85086 −0.570171
\(26\) 0 0
\(27\) −4.29590 −0.826746
\(28\) −3.94471 + 2.27748i −0.745480 + 0.430403i
\(29\) 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
\(31\) 5.89977i 1.05963i −0.848113 0.529815i \(-0.822261\pi\)
0.848113 0.529815i \(-0.177739\pi\)
\(32\) −4.62874 2.67241i −0.818254 0.472419i
\(33\) 0.832052 + 0.480386i 0.144842 + 0.0836244i
\(34\) 0.631023i 0.108219i
\(35\) −3.77144 + 6.53232i −0.637489 + 1.10416i
\(36\) 1.99396 + 3.45364i 0.332327 + 0.575606i
\(37\) 0.823662 0.475541i 0.135409 0.0781785i −0.430765 0.902464i \(-0.641756\pi\)
0.566174 + 0.824286i \(0.308423\pi\)
\(38\) 1.07606 0.174561
\(39\) 0 0
\(40\) −5.74094 −0.907722
\(41\) −2.87318 + 1.65883i −0.448716 + 0.259066i −0.707288 0.706926i \(-0.750081\pi\)
0.258572 + 0.965992i \(0.416748\pi\)
\(42\) −0.599031 1.03755i −0.0924325 0.160098i
\(43\) 3.57942 6.19973i 0.545856 0.945450i −0.452697 0.891665i \(-0.649538\pi\)
0.998553 0.0537856i \(-0.0171288\pi\)
\(44\) 2.02715i 0.305604i
\(45\) 5.71912 + 3.30194i 0.852557 + 0.492224i
\(46\) −2.21266 1.27748i −0.326239 0.188354i
\(47\) 7.69202i 1.12200i −0.827817 0.560998i \(-0.810417\pi\)
0.827817 0.560998i \(-0.189583\pi\)
\(48\) −0.900969 + 1.56052i −0.130044 + 0.225242i
\(49\) 0.123490 + 0.213891i 0.0176414 + 0.0305558i
\(50\) −1.37014 + 0.791053i −0.193768 + 0.111872i
\(51\) −0.911854 −0.127685
\(52\) 0 0
\(53\) 5.87263 0.806667 0.403334 0.915053i \(-0.367851\pi\)
0.403334 + 0.915053i \(0.367851\pi\)
\(54\) −2.06464 + 1.19202i −0.280962 + 0.162214i
\(55\) −1.67845 2.90716i −0.226322 0.392001i
\(56\) −2.75786 + 4.77676i −0.368535 + 0.638322i
\(57\) 1.55496i 0.205959i
\(58\) 3.79669 + 2.19202i 0.498530 + 0.287827i
\(59\) 0.0104630 + 0.00604079i 0.00136216 + 0.000786444i 0.500681 0.865632i \(-0.333083\pi\)
−0.499319 + 0.866418i \(0.666416\pi\)
\(60\) 3.80194i 0.490828i
\(61\) 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
\(63\) 5.49477 3.17241i 0.692276 0.399686i
\(64\) 1.52781 0.190976
\(65\) 0 0
\(66\) 0.533188 0.0656309
\(67\) 8.01651 4.62833i 0.979373 0.565441i 0.0772919 0.997009i \(-0.475373\pi\)
0.902081 + 0.431567i \(0.142039\pi\)
\(68\) 0.961968 + 1.66618i 0.116656 + 0.202054i
\(69\) −1.84601 + 3.19738i −0.222234 + 0.384920i
\(70\) 4.18598i 0.500320i
\(71\) −11.9000 6.87047i −1.41227 0.815375i −0.416668 0.909059i \(-0.636802\pi\)
−0.995602 + 0.0936838i \(0.970136\pi\)
\(72\) 4.18211 + 2.41454i 0.492866 + 0.284557i
\(73\) 12.8170i 1.50012i 0.661372 + 0.750058i \(0.269975\pi\)
−0.661372 + 0.750058i \(0.730025\pi\)
\(74\) 0.263906 0.457098i 0.0306784 0.0531365i
\(75\) 1.14310 + 1.97991i 0.131994 + 0.228621i
\(76\) −2.84128 + 1.64042i −0.325918 + 0.188169i
\(77\) −3.22521 −0.367547
\(78\) 0 0
\(79\) 0.807315 0.0908300 0.0454150 0.998968i \(-0.485539\pi\)
0.0454150 + 0.998968i \(0.485539\pi\)
\(80\) 5.45241 3.14795i 0.609598 0.351951i
\(81\) −1.81282 3.13990i −0.201425 0.348878i
\(82\) −0.920583 + 1.59450i −0.101661 + 0.176083i
\(83\) 16.3327i 1.79275i 0.443296 + 0.896375i \(0.353809\pi\)
−0.443296 + 0.896375i \(0.646191\pi\)
\(84\) 3.16341 + 1.82640i 0.345156 + 0.199276i
\(85\) 2.75914 + 1.59299i 0.299271 + 0.172784i
\(86\) 3.97285i 0.428404i
\(87\) 3.16756 5.48638i 0.339598 0.588202i
\(88\) −1.22737 2.12586i −0.130838 0.226617i
\(89\) −12.7556 + 7.36443i −1.35209 + 0.780628i −0.988542 0.150949i \(-0.951767\pi\)
−0.363546 + 0.931576i \(0.618434\pi\)
\(90\) 3.66487 0.386312
\(91\) 0 0
\(92\) 7.78986 0.812149
\(93\) −4.09738 + 2.36563i −0.424879 + 0.245304i
\(94\) −2.13437 3.69685i −0.220144 0.381301i
\(95\) −2.71648 + 4.70508i −0.278705 + 0.482731i
\(96\) 4.28621i 0.437459i
\(97\) 2.71212 + 1.56584i 0.275374 + 0.158987i 0.631327 0.775516i \(-0.282510\pi\)
−0.355953 + 0.934504i \(0.615844\pi\)
\(98\) 0.118700 + 0.0685317i 0.0119905 + 0.00692274i
\(99\) 2.82371i 0.283793i
\(100\) 2.41185 4.17745i 0.241185 0.417745i
\(101\) 2.64526 + 4.58172i 0.263213 + 0.455899i 0.967094 0.254420i \(-0.0818844\pi\)
−0.703881 + 0.710318i \(0.748551\pi\)
\(102\) −0.438244 + 0.253020i −0.0433926 + 0.0250528i
\(103\) 13.5308 1.33323 0.666614 0.745403i \(-0.267743\pi\)
0.666614 + 0.745403i \(0.267743\pi\)
\(104\) 0 0
\(105\) 6.04892 0.590314
\(106\) 2.82243 1.62953i 0.274139 0.158274i
\(107\) −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
\(109\) 4.17629i 0.400016i −0.979794 0.200008i \(-0.935903\pi\)
0.979794 0.200008i \(-0.0640969\pi\)
\(110\) −1.61335 0.931468i −0.153827 0.0888120i
\(111\) −0.660525 0.381355i −0.0626943 0.0361966i
\(112\) 6.04892i 0.571569i
\(113\) −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
\(115\) 11.1715 6.44989i 1.04175 0.601455i
\(116\) −13.3666 −1.24106
\(117\) 0 0
\(118\) 0.00670477 0.000617224
\(119\) 2.65090 1.53050i 0.243008 0.140301i
\(120\) 2.30194 + 3.98707i 0.210137 + 0.363968i
\(121\) −4.78232 + 8.28323i −0.434757 + 0.753021i
\(122\) 4.46011i 0.403799i
\(123\) 2.30411 + 1.33028i 0.207755 + 0.119947i
\(124\) 8.64513 + 4.99127i 0.776356 + 0.448229i
\(125\) 6.02177i 0.538604i
\(126\) 1.76055 3.04937i 0.156843 0.271659i
\(127\) 3.38889 + 5.86972i 0.300715 + 0.520854i 0.976298 0.216430i \(-0.0694413\pi\)
−0.675583 + 0.737284i \(0.736108\pi\)
\(128\) 9.99177 5.76875i 0.883156 0.509890i
\(129\) −5.74094 −0.505461
\(130\) 0 0
\(131\) −13.6799 −1.19522 −0.597611 0.801786i \(-0.703883\pi\)
−0.597611 + 0.801786i \(0.703883\pi\)
\(132\) −1.40785 + 0.812823i −0.122538 + 0.0707471i
\(133\) 2.60992 + 4.52051i 0.226308 + 0.391978i
\(134\) 2.56853 4.44883i 0.221887 0.384320i
\(135\) 12.0368i 1.03597i
\(136\) 2.01762 + 1.16487i 0.173010 + 0.0998872i
\(137\) −11.2479 6.49396i −0.960970 0.554816i −0.0644987 0.997918i \(-0.520545\pi\)
−0.896471 + 0.443101i \(0.853878\pi\)
\(138\) 2.04892i 0.174415i
\(139\) −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
\(141\) −5.34210 + 3.08426i −0.449886 + 0.259742i
\(142\) −7.62565 −0.639930
\(143\) 0 0
\(144\) −5.29590 −0.441325
\(145\) −19.1692 + 11.0673i −1.59191 + 0.919092i
\(146\) 3.55645 + 6.15995i 0.294334 + 0.509801i
\(147\) 0.0990311 0.171527i 0.00816795 0.0141473i
\(148\) 1.60925i 0.132280i
\(149\) −0.641672 0.370469i −0.0525678 0.0303500i 0.473486 0.880801i \(-0.342996\pi\)
−0.526054 + 0.850451i \(0.676329\pi\)
\(150\) 1.09877 + 0.634375i 0.0897142 + 0.0517965i
\(151\) 19.0737i 1.55219i −0.630614 0.776097i \(-0.717197\pi\)
0.630614 0.776097i \(-0.282803\pi\)
\(152\) −1.98643 + 3.44059i −0.161120 + 0.279069i
\(153\) −1.33997 2.32090i −0.108330 0.187633i
\(154\) −1.55006 + 0.894928i −0.124907 + 0.0721154i
\(155\) 16.5308 1.32779
\(156\) 0 0
\(157\) −4.02177 −0.320972 −0.160486 0.987038i \(-0.551306\pi\)
−0.160486 + 0.987038i \(0.551306\pi\)
\(158\) 0.388002 0.224013i 0.0308678 0.0178215i
\(159\) −2.35474 4.07853i −0.186743 0.323448i
\(160\) 7.48792 12.9695i 0.591972 1.02533i
\(161\) 12.3937i 0.976763i
\(162\) −1.74251 1.00604i −0.136905 0.0790420i
\(163\) −13.1091 7.56853i −1.02678 0.592813i −0.110721 0.993852i \(-0.535316\pi\)
−0.916061 + 0.401038i \(0.868649\pi\)
\(164\) 5.61356i 0.438346i
\(165\) −1.34601 + 2.33136i −0.104787 + 0.181496i
\(166\) 4.53199 + 7.84964i 0.351751 + 0.609250i
\(167\) −5.42424 + 3.13169i −0.419740 + 0.242337i −0.694966 0.719042i \(-0.744581\pi\)
0.275226 + 0.961380i \(0.411247\pi\)
\(168\) 4.42327 0.341263
\(169\) 0 0
\(170\) 1.76809 0.135606
\(171\) 3.95776 2.28501i 0.302657 0.174739i
\(172\) 6.05645 + 10.4901i 0.461800 + 0.799861i
\(173\) 8.19567 14.1953i 0.623105 1.07925i −0.365799 0.930694i \(-0.619204\pi\)
0.988904 0.148556i \(-0.0474625\pi\)
\(174\) 3.51573i 0.266527i
\(175\) −6.64637 3.83728i −0.502418 0.290071i
\(176\) 2.33136 + 1.34601i 0.175733 + 0.101459i
\(177\) 0.00968868i 0.000728246i
\(178\) −4.08695 + 7.07880i −0.306330 + 0.530579i
\(179\) −1.22737 2.12586i −0.0917376 0.158894i 0.816505 0.577339i \(-0.195909\pi\)
−0.908242 + 0.418445i \(0.862575\pi\)
\(180\) −9.67688 + 5.58695i −0.721272 + 0.416427i
\(181\) −11.8073 −0.877631 −0.438815 0.898577i \(-0.644602\pi\)
−0.438815 + 0.898577i \(0.644602\pi\)
\(182\) 0 0
\(183\) −6.44504 −0.476431
\(184\) 8.16918 4.71648i 0.602240 0.347704i
\(185\) 1.33244 + 2.30785i 0.0979627 + 0.169676i
\(186\) −1.31282 + 2.27388i −0.0962608 + 0.166729i
\(187\) 1.36227i 0.0996192i
\(188\) 11.2714 + 6.50753i 0.822050 + 0.474611i
\(189\) −10.0153 5.78232i −0.728504 0.420602i
\(190\) 3.01507i 0.218736i
\(191\) 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
\(193\) 11.7134 6.76271i 0.843146 0.486790i −0.0151865 0.999885i \(-0.504834\pi\)
0.858332 + 0.513094i \(0.171501\pi\)
\(194\) 1.73795 0.124778
\(195\) 0 0
\(196\) −0.417895 −0.0298496
\(197\) −11.2374 + 6.48792i −0.800632 + 0.462245i −0.843692 0.536827i \(-0.819623\pi\)
0.0430602 + 0.999072i \(0.486289\pi\)
\(198\) 0.783520 + 1.35710i 0.0556823 + 0.0964446i
\(199\) −6.79321 + 11.7662i −0.481558 + 0.834083i −0.999776 0.0211659i \(-0.993262\pi\)
0.518218 + 0.855248i \(0.326596\pi\)
\(200\) 5.84117i 0.413033i
\(201\) −6.42874 3.71164i −0.453448 0.261799i
\(202\) 2.54267 + 1.46801i 0.178901 + 0.103289i
\(203\) 21.2664i 1.49261i
\(204\) 0.771438 1.33617i 0.0540115 0.0935506i
\(205\) −4.64795 8.05048i −0.324627 0.562270i
\(206\) 6.50301 3.75451i 0.453086 0.261589i
\(207\) −10.8509 −0.754187
\(208\) 0 0
\(209\) −2.32304 −0.160688
\(210\) 2.90716 1.67845i 0.200613 0.115824i
\(211\) −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
\(213\) 11.0194i 0.755035i
\(214\) −2.70631 1.56249i −0.185000 0.106810i
\(215\) 17.3713 + 10.0293i 1.18471 + 0.683993i
\(216\) 8.80194i 0.598896i
\(217\) 7.94116 13.7545i 0.539081 0.933715i
\(218\) −1.15883 2.00716i −0.0784861 0.135942i
\(219\) 8.90139 5.13922i 0.601500 0.347276i
\(220\) 5.67994 0.382941
\(221\) 0 0
\(222\) −0.423272 −0.0284081
\(223\) 9.87772 5.70291i 0.661461 0.381895i −0.131372 0.991333i \(-0.541938\pi\)
0.792834 + 0.609438i \(0.208605\pi\)
\(224\) −7.19418 12.4607i −0.480681 0.832564i
\(225\) −3.35958 + 5.81897i −0.223972 + 0.387931i
\(226\) 4.24160i 0.282147i
\(227\) 9.21513 + 5.32036i 0.611629 + 0.353124i 0.773603 0.633671i \(-0.218453\pi\)
−0.161973 + 0.986795i \(0.551786\pi\)
\(228\) 2.27853 + 1.31551i 0.150899 + 0.0871219i
\(229\) 1.13946i 0.0752974i −0.999291 0.0376487i \(-0.988013\pi\)
0.999291 0.0376487i \(-0.0119868\pi\)
\(230\) 3.57942 6.19973i 0.236020 0.408798i
\(231\) 1.29321 + 2.23990i 0.0850869 + 0.147375i
\(232\) −14.0175 + 8.09299i −0.920292 + 0.531331i
\(233\) 10.8509 0.710863 0.355432 0.934702i \(-0.384334\pi\)
0.355432 + 0.934702i \(0.384334\pi\)
\(234\) 0 0
\(235\) 21.5526 1.40593
\(236\) −0.0177036 + 0.0102212i −0.00115240 + 0.000665340i
\(237\) −0.323708 0.560679i −0.0210271 0.0364200i
\(238\) 0.849363 1.47114i 0.0550560 0.0953598i
\(239\) 11.9293i 0.771643i 0.922573 + 0.385822i \(0.126082\pi\)
−0.922573 + 0.385822i \(0.873918\pi\)
\(240\) −4.37249 2.52446i −0.282243 0.162953i
\(241\) 3.15968 + 1.82424i 0.203533 + 0.117510i 0.598302 0.801271i \(-0.295842\pi\)
−0.394770 + 0.918780i \(0.629176\pi\)
\(242\) 5.30798i 0.341210i
\(243\) −7.89762 + 13.6791i −0.506632 + 0.877513i
\(244\) 6.79925 + 11.7766i 0.435277 + 0.753922i
\(245\) −0.599308 + 0.346011i −0.0382884 + 0.0221058i
\(246\) 1.47650 0.0941383
\(247\) 0 0
\(248\) 12.0881 0.767598
\(249\) 11.3431 6.54892i 0.718837 0.415021i
\(250\) 1.67092 + 2.89411i 0.105678 + 0.183040i
\(251\) 0.686645 1.18930i 0.0433406 0.0750682i −0.843541 0.537064i \(-0.819533\pi\)
0.886882 + 0.461996i \(0.152867\pi\)
\(252\) 10.7356i 0.676277i
\(253\) 4.77676 + 2.75786i 0.300312 + 0.173385i
\(254\) 3.25745 + 1.88069i 0.204391 + 0.118005i
\(255\) 2.55496i 0.159998i
\(256\) 1.67360 2.89877i 0.104600 0.181173i
\(257\) 14.7180 + 25.4923i 0.918082 + 1.59016i 0.802325 + 0.596887i \(0.203596\pi\)
0.115756 + 0.993278i \(0.463071\pi\)
\(258\) −2.75914 + 1.59299i −0.171777 + 0.0991752i
\(259\) 2.56033 0.159091
\(260\) 0 0
\(261\) 18.6189 1.15248
\(262\) −6.57469 + 3.79590i −0.406185 + 0.234511i
\(263\) −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
\(265\) 16.4547i 1.01081i
\(266\) 2.50869 + 1.44839i 0.153818 + 0.0888067i
\(267\) 10.2292 + 5.90581i 0.626015 + 0.361430i
\(268\) 15.6625i 0.956738i
\(269\) 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
\(271\) −25.5065 + 14.7262i −1.54941 + 0.894551i −0.551221 + 0.834359i \(0.685838\pi\)
−0.998187 + 0.0601918i \(0.980829\pi\)
\(272\) −2.55496 −0.154917
\(273\) 0 0
\(274\) −7.20775 −0.435436
\(275\) 2.95791 1.70775i 0.178369 0.102981i
\(276\) −3.12349 5.41004i −0.188012 0.325646i
\(277\) −5.12229 + 8.87207i −0.307769 + 0.533071i −0.977874 0.209195i \(-0.932916\pi\)
0.670105 + 0.742266i \(0.266249\pi\)
\(278\) 6.68532i 0.400959i
\(279\) −12.0422 6.95257i −0.720948 0.416240i
\(280\) −13.3842 7.72737i −0.799858 0.461798i
\(281\) 11.5646i 0.689889i −0.938623 0.344944i \(-0.887898\pi\)
0.938623 0.344944i \(-0.112102\pi\)
\(282\) −1.71164 + 2.96464i −0.101926 + 0.176542i
\(283\) −15.3545 26.5948i −0.912730 1.58090i −0.810191 0.586167i \(-0.800636\pi\)
−0.102540 0.994729i \(-0.532697\pi\)
\(284\) 20.1351 11.6250i 1.19480 0.689816i
\(285\) 4.35690 0.258080
\(286\) 0 0
\(287\) −8.93123 −0.527194
\(288\) −10.9095 + 6.29859i −0.642847 + 0.371148i
\(289\) 7.85354 + 13.6027i 0.461973 + 0.800161i
\(290\) −6.14191 + 10.6381i −0.360665 + 0.624691i
\(291\) 2.51142i 0.147222i
\(292\) −18.7812 10.8433i −1.09909 0.634557i
\(293\) 16.1152 + 9.30409i 0.941458 + 0.543551i 0.890417 0.455146i \(-0.150413\pi\)
0.0510409 + 0.998697i \(0.483746\pi\)
\(294\) 0.109916i 0.00641045i
\(295\) −0.0169259 + 0.0293166i −0.000985465 + 0.00170688i
\(296\) 0.974345 + 1.68761i 0.0566326 + 0.0980906i
\(297\) 4.45722 2.57338i 0.258634 0.149322i
\(298\) −0.411190 −0.0238196
\(299\) 0 0
\(300\) −3.86831 −0.223337
\(301\) 16.6898 9.63587i 0.961985 0.555402i
\(302\) −5.29254 9.16696i −0.304552 0.527499i
\(303\) 2.12133 3.67426i 0.121867 0.211081i
\(304\) 4.35690i 0.249885i
\(305\) 19.5018 + 11.2594i 1.11667 + 0.644709i
\(306\) −1.28800 0.743627i −0.0736301 0.0425103i
\(307\) 8.94438i 0.510483i 0.966877 + 0.255241i \(0.0821549\pi\)
−0.966877 + 0.255241i \(0.917845\pi\)
\(308\) 2.72856 4.72601i 0.155474 0.269289i
\(309\) −5.42543 9.39712i −0.308642 0.534583i
\(310\) 7.94483 4.58695i 0.451236 0.260521i
\(311\) −21.0398 −1.19306 −0.596529 0.802591i \(-0.703454\pi\)
−0.596529 + 0.802591i \(0.703454\pi\)
\(312\) 0 0
\(313\) −7.12737 −0.402863 −0.201432 0.979503i \(-0.564559\pi\)
−0.201432 + 0.979503i \(0.564559\pi\)
\(314\) −1.93289 + 1.11596i −0.109080 + 0.0629771i
\(315\) 8.88889 + 15.3960i 0.500832 + 0.867467i
\(316\) −0.682997 + 1.18299i −0.0384216 + 0.0665481i
\(317\) 23.9651i 1.34601i −0.739636 0.673007i \(-0.765003\pi\)
0.739636 0.673007i \(-0.234997\pi\)
\(318\) −2.26341 1.30678i −0.126926 0.0732807i
\(319\) −8.19643 4.73221i −0.458912 0.264953i
\(320\) 4.28083i 0.239306i
\(321\) −2.25786 + 3.91074i −0.126022 + 0.218276i
\(322\) −3.43900 5.95652i −0.191648 0.331944i
\(323\) 1.90938 1.10238i 0.106241 0.0613383i
\(324\) 6.13467 0.340815
\(325\) 0 0
\(326\) −8.40044 −0.465257
\(327\) −2.90043 + 1.67456i −0.160394 + 0.0926035i
\(328\) −3.39881 5.88692i −0.187668 0.325051i
\(329\) 10.3535 17.9329i 0.570809 0.988671i
\(330\) 1.49396i 0.0822397i
\(331\) 2.50754 + 1.44773i 0.137827 + 0.0795745i 0.567328 0.823492i \(-0.307977\pi\)
−0.429501 + 0.903066i \(0.641311\pi\)
\(332\) −23.9329 13.8177i −1.31349 0.758343i
\(333\) 2.24160i 0.122839i
\(334\) −1.73795 + 3.01023i −0.0950967 + 0.164712i
\(335\) 12.9683 + 22.4618i 0.708534 + 1.22722i
\(336\) −4.20096 + 2.42543i −0.229181 + 0.132318i
\(337\) 3.10560 0.169173 0.0845865 0.996416i \(-0.473043\pi\)
0.0845865 + 0.996416i \(0.473043\pi\)
\(338\) 0 0
\(339\) 6.12929 0.332898
\(340\) −4.66852 + 2.69537i −0.253186 + 0.146177i
\(341\) 3.53415 + 6.12132i 0.191385 + 0.331488i
\(342\) 1.26809 2.19639i 0.0685702 0.118767i
\(343\) 18.1793i 0.981589i
\(344\) 12.7027 + 7.33393i 0.684886 + 0.395419i
\(345\) −8.95887 5.17241i −0.482329 0.278473i
\(346\) 9.09651i 0.489031i
\(347\) 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
\(349\) −2.89877 + 1.67360i −0.155167 + 0.0895859i −0.575573 0.817750i \(-0.695221\pi\)
0.420406 + 0.907336i \(0.361888\pi\)
\(350\) −4.25906 −0.227656
\(351\) 0 0
\(352\) 6.40342 0.341303
\(353\) −0.552288 + 0.318864i −0.0293953 + 0.0169714i −0.514626 0.857415i \(-0.672069\pi\)
0.485230 + 0.874386i \(0.338736\pi\)
\(354\) −0.00268841 0.00465646i −0.000142887 0.000247488i
\(355\) 19.2506 33.3431i 1.02172 1.76967i
\(356\) 24.9215i 1.32084i
\(357\) −2.12586 1.22737i −0.112512 0.0649591i
\(358\) −1.17976 0.681136i −0.0623524 0.0359992i
\(359\) 21.4590i 1.13256i −0.824211 0.566282i \(-0.808381\pi\)
0.824211 0.566282i \(-0.191619\pi\)
\(360\) −6.76540 + 11.7180i −0.356568 + 0.617593i
\(361\) −7.62014 13.1985i −0.401060 0.694656i
\(362\) −5.67469 + 3.27628i −0.298255 + 0.172198i
\(363\) 7.67025 0.402584
\(364\) 0 0
\(365\) −35.9124 −1.87974
\(366\) −3.09754 + 1.78836i −0.161911 + 0.0934793i
\(367\) 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
\(369\) 7.81940i 0.407062i
\(370\) 1.28076 + 0.739447i 0.0665835 + 0.0384420i
\(371\) 13.6912 + 7.90462i 0.710812 + 0.410387i
\(372\) 8.00538i 0.415059i
\(373\) −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
\(375\) 4.18211 2.41454i 0.215963 0.124686i
\(376\) 15.7603 0.812776
\(377\) 0 0
\(378\) −6.41789 −0.330101
\(379\) −31.0645 + 17.9351i −1.59568 + 0.921265i −0.603371 + 0.797460i \(0.706176\pi\)
−0.992307 + 0.123805i \(0.960490\pi\)
\(380\) −4.59634 7.96110i −0.235787 0.408396i
\(381\) 2.71768 4.70715i 0.139231 0.241155i
\(382\) 4.99090i 0.255357i
\(383\) 4.20470 + 2.42758i 0.214850 + 0.124044i 0.603563 0.797315i \(-0.293747\pi\)
−0.388713 + 0.921359i \(0.627080\pi\)
\(384\) −8.01278 4.62618i −0.408900 0.236079i
\(385\) 9.03684i 0.460560i
\(386\) 3.75302 6.50042i 0.191024 0.330863i
\(387\) −8.43631 14.6121i −0.428842 0.742776i
\(388\) −4.58897 + 2.64944i −0.232969 + 0.134505i
\(389\) −2.38537 −0.120943 −0.0604716 0.998170i \(-0.519260\pi\)
−0.0604716 + 0.998170i \(0.519260\pi\)
\(390\) 0 0
\(391\) −5.23490 −0.264740
\(392\) −0.438244 + 0.253020i −0.0221347 + 0.0127795i
\(393\) 5.48523 + 9.50070i 0.276693 + 0.479247i
\(394\) −3.60052 + 6.23629i −0.181392 + 0.314180i
\(395\) 2.26205i 0.113816i
\(396\) −4.13767 2.38889i −0.207926 0.120046i
\(397\) 13.2211 + 7.63318i 0.663546 + 0.383098i 0.793627 0.608405i \(-0.208190\pi\)
−0.130081 + 0.991503i \(0.541524\pi\)
\(398\) 7.53989i 0.377941i
\(399\) 2.09299 3.62517i 0.104781 0.181485i
\(400\) 3.20291 + 5.54760i 0.160145 + 0.277380i
\(401\) 11.0491 6.37920i 0.551766 0.318562i −0.198068 0.980188i \(-0.563467\pi\)
0.749834 + 0.661626i \(0.230133\pi\)
\(402\) −4.11960 −0.205467
\(403\) 0 0
\(404\) −8.95167 −0.445362
\(405\) 8.79781 5.07942i 0.437167 0.252398i
\(406\) 5.90097 + 10.2208i 0.292860 + 0.507249i
\(407\) −0.569728 + 0.986798i −0.0282404 + 0.0489138i
\(408\) 1.86831i 0.0924953i
\(409\) −21.9614 12.6794i −1.08592 0.626956i −0.153433 0.988159i \(-0.549033\pi\)
−0.932487 + 0.361203i \(0.882366\pi\)
\(410\) −4.46768 2.57942i −0.220643 0.127388i
\(411\) 10.4155i 0.513759i
\(412\) −11.4472 + 19.8271i −0.563963 + 0.976812i
\(413\) 0.0162619 + 0.0281665i 0.000800198 + 0.00138598i
\(414\) −5.21501 + 3.01089i −0.256304 + 0.147977i
\(415\) −45.7633 −2.24643
\(416\) 0 0
\(417\) 9.66056 0.473080
\(418\) −1.11647 + 0.644596i −0.0546085 + 0.0315282i
\(419\) 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
\(421\) 8.29291i 0.404172i 0.979368 + 0.202086i \(0.0647720\pi\)
−0.979368 + 0.202086i \(0.935228\pi\)
\(422\) −5.02721 2.90246i −0.244721 0.141290i
\(423\) −15.7004 9.06465i −0.763381 0.440738i
\(424\) 12.0325i 0.584351i
\(425\) −1.62080 + 2.80731i −0.0786204 + 0.136175i
\(426\) 3.05765 + 5.29600i 0.148143 + 0.256592i
\(427\) 18.7367 10.8177i 0.906735 0.523504i
\(428\) 9.52781 0.460544
\(429\) 0 0
\(430\) 11.1317 0.536818
\(431\) −0.807392 + 0.466148i −0.0388907 + 0.0224536i −0.519319 0.854580i \(-0.673814\pi\)
0.480429 + 0.877034i \(0.340481\pi\)
\(432\) 4.82640 + 8.35956i 0.232210 + 0.402200i
\(433\) −6.67510 + 11.5616i −0.320785 + 0.555615i −0.980650 0.195768i \(-0.937280\pi\)
0.659866 + 0.751384i \(0.270613\pi\)
\(434\) 8.81402i 0.423086i
\(435\) 15.3725 + 8.87531i 0.737055 + 0.425539i
\(436\) 6.11966 + 3.53319i 0.293079 + 0.169209i
\(437\) 8.92692i 0.427032i
\(438\) 2.85205 4.93990i 0.136276 0.236037i
\(439\) 6.99612 + 12.1176i 0.333906 + 0.578343i 0.983274 0.182132i \(-0.0582997\pi\)
−0.649368 + 0.760475i \(0.724966\pi\)
\(440\) 5.95652 3.43900i 0.283966 0.163948i
\(441\) 0.582105 0.0277193
\(442\) 0 0
\(443\) 23.7017 1.12610 0.563051 0.826422i \(-0.309627\pi\)
0.563051 + 0.826422i \(0.309627\pi\)
\(444\) 1.11762 0.645260i 0.0530401 0.0306227i
\(445\) −20.6347 35.7403i −0.978177 1.69425i
\(446\) 3.16487 5.48172i 0.149861 0.259567i
\(447\) 0.594187i 0.0281041i
\(448\) 3.56188 + 2.05645i 0.168283 + 0.0971581i
\(449\) 10.9002 + 6.29321i 0.514410 + 0.296995i 0.734645 0.678452i \(-0.237349\pi\)
−0.220234 + 0.975447i \(0.570682\pi\)
\(450\) 3.72886i 0.175780i
\(451\) 1.98739 3.44225i 0.0935823 0.162089i
\(452\) −6.46615 11.1997i −0.304142 0.526789i
\(453\) −13.2466 + 7.64795i −0.622381 + 0.359332i
\(454\) 5.90515 0.277142
\(455\) 0 0
\(456\) 3.18598 0.149197
\(457\) 29.1316 16.8192i 1.36272 0.786767i 0.372735 0.927938i \(-0.378420\pi\)
0.989985 + 0.141171i \(0.0450866\pi\)
\(458\) −0.316175 0.547632i −0.0147739 0.0255891i
\(459\) −2.44235 + 4.23028i −0.113999 + 0.197453i
\(460\) 21.8267i 1.01767i
\(461\) −1.21489 0.701415i −0.0565829 0.0326681i 0.471442 0.881897i \(-0.343734\pi\)
−0.528025 + 0.849229i \(0.677067\pi\)
\(462\) 1.24305 + 0.717677i 0.0578320 + 0.0333893i
\(463\) 15.2010i 0.706453i −0.935538 0.353226i \(-0.885085\pi\)
0.935538 0.353226i \(-0.114915\pi\)
\(464\) 8.87531 15.3725i 0.412026 0.713650i
\(465\) −6.62833 11.4806i −0.307382 0.532401i
\(466\) 5.21501 3.01089i 0.241580 0.139477i
\(467\) 39.3414 1.82050 0.910250 0.414058i \(-0.135889\pi\)
0.910250 + 0.414058i \(0.135889\pi\)
\(468\) 0 0
\(469\) 24.9191 1.15066
\(470\) 10.3583 5.98039i 0.477794 0.275855i
\(471\) 1.61260 + 2.79311i 0.0743049 + 0.128700i
\(472\) −0.0123771 + 0.0214377i −0.000569701 + 0.000986752i
\(473\) 8.57673i 0.394358i
\(474\) −0.311153 0.179644i −0.0142917 0.00825134i
\(475\) −4.78722 2.76391i −0.219653 0.126817i
\(476\) 5.17928i 0.237392i
\(477\) 6.92058 11.9868i 0.316872 0.548838i
\(478\) 3.31013 + 5.73332i 0.151402 + 0.262236i
\(479\) −19.3721 + 11.1845i −0.885134 + 0.511032i −0.872348 0.488886i \(-0.837403\pi\)
−0.0127862 + 0.999918i \(0.504070\pi\)
\(480\) −12.0097 −0.548165
\(481\) 0 0
\(482\) 2.02475 0.0922250
\(483\) −8.60743 + 4.96950i −0.391652 + 0.226120i
\(484\) −8.09179 14.0154i −0.367809 0.637064i
\(485\) −4.38740 + 7.59919i −0.199221 + 0.345062i
\(486\) 8.76569i 0.397620i
\(487\) 19.8497 + 11.4602i 0.899476 + 0.519313i 0.877030 0.480435i \(-0.159521\pi\)
0.0224462 + 0.999748i \(0.492855\pi\)
\(488\) 14.2607 + 8.23341i 0.645551 + 0.372709i
\(489\) 12.1390i 0.548944i
\(490\) −0.192021 + 0.332591i −0.00867465 + 0.0150249i
\(491\) 0.921780 + 1.59657i 0.0415993 + 0.0720522i 0.886075 0.463541i \(-0.153421\pi\)
−0.844476 + 0.535593i \(0.820088\pi\)
\(492\) −3.89861 + 2.25086i −0.175763 + 0.101477i
\(493\) 8.98254 0.404553
\(494\) 0 0
\(495\) −7.91185 −0.355611
\(496\) −11.4806 + 6.62833i −0.515495 + 0.297621i
\(497\) −18.4955 32.0351i −0.829634 1.43697i
\(498\) 3.63437 6.29492i 0.162860 0.282082i
\(499\) 12.0344i 0.538736i 0.963037 + 0.269368i \(0.0868147\pi\)
−0.963037 + 0.269368i \(0.913185\pi\)
\(500\) −8.82390 5.09448i −0.394617 0.227832i
\(501\) 4.34990 + 2.51142i 0.194339 + 0.112202i
\(502\) 0.762118i 0.0340150i
\(503\) 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
\(505\) −12.8377 + 7.41185i −0.571270 + 0.329823i
\(506\) 3.06100 0.136078
\(507\) 0 0
\(508\) −11.4681 −0.508816
\(509\) 1.30893 0.755709i 0.0580171 0.0334962i −0.470711 0.882288i \(-0.656002\pi\)
0.528728 + 0.848791i \(0.322669\pi\)
\(510\) −0.708947 1.22793i −0.0313927 0.0543738i
\(511\) −17.2518 + 29.8810i −0.763176 + 1.32186i
\(512\) 21.2174i 0.937687i
\(513\) −7.21377 4.16487i −0.318496 0.183884i
\(514\) 14.1471 + 8.16786i 0.624004 + 0.360269i
\(515\) 37.9124i 1.67062i
\(516\) 4.85690 8.41239i 0.213813 0.370335i
\(517\) 4.60776 + 7.98088i 0.202649 + 0.350998i
\(518\) 1.23052 0.710439i 0.0540658 0.0312149i
\(519\) −13.1448 −0.576994
\(520\) 0 0
\(521\) −5.64012 −0.247098 −0.123549 0.992338i \(-0.539428\pi\)
−0.123549 + 0.992338i \(0.539428\pi\)
\(522\) 8.94841 5.16637i 0.391661 0.226126i
\(523\) 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
\(525\) 6.15452i 0.268605i
\(526\) −5.14074 2.96801i −0.224147 0.129411i
\(527\) −5.80966 3.35421i −0.253073 0.146112i
\(528\) 2.15883i 0.0939512i
\(529\) 0.902165 1.56260i 0.0392246 0.0679390i
\(530\) 4.56584 + 7.90827i 0.198328 + 0.343513i
\(531\) 0.0246601 0.0142375i 0.00107016 0.000617856i
\(532\) −8.83207 −0.382919
\(533\) 0 0
\(534\) 6.55496 0.283661
\(535\) 13.6640 7.88889i 0.590744 0.341066i
\(536\) 9.48307 + 16.4252i 0.409606 + 0.709459i
\(537\) −0.984271 + 1.70481i −0.0424744 + 0.0735678i
\(538\) 5.65279i 0.243709i
\(539\) −0.256254 0.147948i −0.0110377 0.00637259i
\(540\) 17.6380 + 10.1833i 0.759018 + 0.438219i
\(541\) 24.3297i 1.04602i 0.852327 + 0.523009i \(0.175191\pi\)
−0.852327 + 0.523009i \(0.824809\pi\)
\(542\) −8.17241 + 14.1550i −0.351035 + 0.608010i
\(543\) 4.73437 + 8.20016i 0.203171 + 0.351903i
\(544\) −5.26318 + 3.03870i −0.225657 + 0.130283i
\(545\) 11.7017 0.501246
\(546\) 0 0
\(547\) −8.18896 −0.350135 −0.175067 0.984556i \(-0.556014\pi\)
−0.175067 + 0.984556i \(0.556014\pi\)
\(548\) 19.0316 10.9879i 0.812991 0.469381i
\(549\) −9.47099 16.4042i −0.404212 0.700116i
\(550\) 0.947730 1.64152i 0.0404114 0.0699945i
\(551\) 15.3177i 0.652555i
\(552\) −6.55118 3.78232i −0.278837 0.160986i
\(553\) 1.88214 + 1.08665i 0.0800367 + 0.0462092i
\(554\) 5.68532i 0.241546i
\(555\) 1.06853 1.85075i 0.0453566 0.0785600i
\(556\) −10.1915 17.6522i −0.432215 0.748619i
\(557\) 21.9388 12.6664i 0.929576 0.536691i 0.0428988 0.999079i \(-0.486341\pi\)
0.886678 + 0.462388i \(0.153007\pi\)
\(558\) −7.71678 −0.326677
\(559\) 0 0
\(560\) 16.9487 0.716213
\(561\) 0.946096 0.546229i 0.0399442 0.0230618i
\(562\) −3.20895 5.55806i −0.135361 0.234453i
\(563\) −12.6969 + 21.9916i −0.535109 + 0.926836i 0.464049 + 0.885810i \(0.346396\pi\)
−0.999158 + 0.0410266i \(0.986937\pi\)
\(564\) 10.4373i 0.439488i
\(565\) −18.5464 10.7078i −0.780252 0.450478i
\(566\) −14.7590 8.52111i −0.620367 0.358169i
\(567\) 9.76032i 0.409895i
\(568\) 14.0770 24.3821i 0.590659 1.02305i
\(569\) −15.5673 26.9634i −0.652617 1.13037i −0.982486 0.186338i \(-0.940338\pi\)
0.329869 0.944027i \(-0.392995\pi\)
\(570\) 2.09396 1.20895i 0.0877063 0.0506372i
\(571\) 20.5090 0.858276 0.429138 0.903239i \(-0.358817\pi\)
0.429138 + 0.903239i \(0.358817\pi\)
\(572\) 0 0
\(573\) −7.21206 −0.301288
\(574\) −4.29242 + 2.47823i −0.179162 + 0.103439i
\(575\) 6.56249 + 11.3666i 0.273675 + 0.474019i
\(576\) 1.80045 3.11846i 0.0750186 0.129936i
\(577\) 15.6890i 0.653143i −0.945172 0.326572i \(-0.894107\pi\)
0.945172 0.326572i \(-0.105893\pi\)
\(578\) 7.54895 + 4.35839i 0.313995 + 0.181285i
\(579\) −9.39338 5.42327i −0.390376 0.225383i
\(580\) 37.4523i 1.55512i
\(581\) −21.9840 + 38.0775i −0.912051 + 1.57972i
\(582\) −0.696866 1.20701i −0.0288860 0.0500320i
\(583\) −6.09316 + 3.51789i −0.252353 + 0.145696i
\(584\) −26.2610 −1.08669
\(585\) 0 0
\(586\) 10.3268 0.426595
\(587\) −26.4733 + 15.2843i −1.09267 + 0.630853i −0.934286 0.356525i \(-0.883961\pi\)
−0.158383 + 0.987378i \(0.550628\pi\)
\(588\) 0.167563 + 0.290227i 0.00691017 + 0.0119688i
\(589\) 5.71983 9.90704i 0.235682 0.408212i
\(590\) 0.0187864i 0.000773422i
\(591\) 9.01170 + 5.20291i 0.370692 + 0.214019i
\(592\) −1.85075 1.06853i −0.0760654 0.0439164i
\(593\) 29.6883i 1.21915i −0.792727 0.609576i \(-0.791340\pi\)
0.792727 0.609576i \(-0.208660\pi\)
\(594\) 1.42812 2.47357i 0.0585963 0.101492i
\(595\) 4.28836 + 7.42766i 0.175806 + 0.304505i
\(596\) 1.08572 0.626842i 0.0444729 0.0256765i
\(597\) 10.8955 0.445922
\(598\) 0 0
\(599\) 24.2325 0.990113 0.495057 0.868861i \(-0.335147\pi\)
0.495057 + 0.868861i \(0.335147\pi\)
\(600\) −4.05668 + 2.34213i −0.165613 + 0.0956169i
\(601\) −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
\(603\) 21.8170i 0.888457i
\(604\) 27.9493 + 16.1365i 1.13724 + 0.656586i
\(605\) −23.2091 13.3998i −0.943584 0.544778i
\(606\) 2.35450i 0.0956451i
\(607\) −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
\(609\) 14.7695 8.52715i 0.598488 0.345537i
\(610\) 12.4969 0.505986
\(611\) 0 0
\(612\) 4.53452 0.183297
\(613\) −3.33287 + 1.92423i −0.134613 + 0.0777190i −0.565794 0.824546i \(-0.691430\pi\)
0.431181 + 0.902265i \(0.358097\pi\)
\(614\) 2.48188 + 4.29874i 0.100160 + 0.173483i
\(615\) −3.72737 + 6.45599i −0.150302 + 0.260330i
\(616\) 6.60819i 0.266251i
\(617\) −13.0239 7.51938i −0.524324 0.302719i 0.214378 0.976751i \(-0.431228\pi\)
−0.738702 + 0.674032i \(0.764561\pi\)
\(618\) −5.21501 3.01089i −0.209778 0.121116i
\(619\) 12.8170i 0.515159i 0.966257 + 0.257579i \(0.0829249\pi\)
−0.966257 + 0.257579i \(0.917075\pi\)
\(620\) −13.9852 + 24.2231i −0.561660 + 0.972824i
\(621\) 9.88889 + 17.1281i 0.396827 + 0.687325i
\(622\) −10.1119 + 5.83811i −0.405450 + 0.234087i
\(623\) −39.6504 −1.58856
\(624\) 0 0
\(625\) −31.1269 −1.24508
\(626\) −3.42547 + 1.97770i −0.136909 + 0.0790447i
\(627\) 0.931468 + 1.61335i 0.0371993 + 0.0644310i
\(628\) 3.40246 5.89324i 0.135773 0.235166i
\(629\) 1.08144i 0.0431199i
\(630\) 8.54414 + 4.93296i 0.340407 + 0.196534i
\(631\) −22.3016 12.8758i −0.887813 0.512579i −0.0145868 0.999894i \(-0.504643\pi\)
−0.873227 + 0.487314i \(0.837977\pi\)
\(632\) 1.65412i 0.0657974i
\(633\) −4.19418 + 7.26453i −0.166704 + 0.288739i
\(634\) −6.64981 11.5178i −0.264098 0.457431i
\(635\) −16.4466 + 9.49545i −0.652664 + 0.376815i
\(636\) 7.96854 0.315973
\(637\) 0 0
\(638\) −5.25236 −0.207943
\(639\) −28.0471 + 16.1930i −1.10952 + 0.640584i
\(640\) 16.1637 + 27.9963i 0.638925 + 1.10665i
\(641\) 12.2286 21.1805i 0.482999 0.836579i −0.516810 0.856100i \(-0.672881\pi\)
0.999809 + 0.0195209i \(0.00621408\pi\)
\(642\) 2.50604i 0.0989055i
\(643\) −8.63726 4.98672i −0.340620 0.196657i 0.319926 0.947442i \(-0.396342\pi\)
−0.660546 + 0.750785i \(0.729675\pi\)
\(644\) 18.1610 + 10.4852i 0.715642 + 0.413176i
\(645\) 16.0858i 0.633376i
\(646\) 0.611777 1.05963i 0.0240700 0.0416905i
\(647\) 5.92154 + 10.2564i 0.232800 + 0.403221i 0.958631 0.284652i \(-0.0918780\pi\)
−0.725831 + 0.687873i \(0.758545\pi\)
\(648\) 6.43340 3.71432i 0.252728 0.145912i
\(649\) −0.0144745 −0.000568173
\(650\) 0 0
\(651\) −12.7366 −0.499188
\(652\) 22.1808 12.8061i 0.868669 0.501526i
\(653\) 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
\(655\) 38.3303i 1.49769i
\(656\) 6.45599 + 3.72737i 0.252064 + 0.145529i
\(657\) 26.1612 + 15.1042i 1.02065 + 0.589270i
\(658\) 11.4916i 0.447988i
\(659\) −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
\(661\) 29.1061 16.8044i 1.13209 0.653615i 0.187634 0.982239i \(-0.439918\pi\)
0.944461 + 0.328624i \(0.106585\pi\)
\(662\) 1.60686 0.0624524
\(663\) 0 0
\(664\) −33.4644 −1.29867
\(665\) −12.6662 + 7.31282i −0.491173 + 0.283579i
\(666\) −0.621998 1.07733i −0.0241019 0.0417458i
\(667\) 18.1848 31.4970i 0.704118 1.21957i
\(668\) 10.5978i 0.410040i
\(669\) −7.92132 4.57338i −0.306256 0.176817i
\(670\) 12.4653 + 7.19687i 0.481578 + 0.278039i
\(671\) 9.62863i 0.371709i
\(672\) −5.76928 + 9.99269i −0.222555 + 0.385476i
\(673\) 24.0160 + 41.5970i 0.925750 + 1.60345i 0.790351 + 0.612654i \(0.209898\pi\)
0.135399 + 0.990791i \(0.456768\pi\)
\(674\) 1.49258 0.861740i 0.0574919 0.0331930i
\(675\) 12.2470 0.471386
\(676\) 0 0
\(677\) −33.6582 −1.29359 −0.646794 0.762665i \(-0.723891\pi\)
−0.646794 + 0.762665i \(0.723891\pi\)
\(678\) 2.94579 1.70075i 0.113132 0.0653169i
\(679\) 4.21528 + 7.30109i 0.161768 + 0.280190i
\(680\) −3.26391 + 5.65325i −0.125165 + 0.216792i
\(681\) 8.53319i 0.326992i
\(682\) 3.39708 + 1.96130i 0.130081 + 0.0751022i
\(683\) −13.7733 7.95204i −0.527022 0.304276i 0.212781 0.977100i \(-0.431748\pi\)
−0.739803 + 0.672824i \(0.765081\pi\)
\(684\) 7.73258i 0.295663i
\(685\) 18.1957 31.5158i 0.695221 1.20416i
\(686\) −5.04437 8.73710i −0.192595 0.333584i
\(687\) −0.791351 + 0.456886i −0.0301919 + 0.0174313i
\(688\) −16.0858 −0.613264
\(689\) 0 0
\(690\) −5.74094 −0.218554
\(691\) −28.7436 + 16.5951i −1.09346 + 0.631309i −0.934495 0.355975i \(-0.884149\pi\)
−0.158964 + 0.987284i \(0.550815\pi\)
\(692\) 13.8672 + 24.0188i 0.527154 + 0.913057i
\(693\) −3.80074 + 6.58308i −0.144378 + 0.250070i
\(694\) 6.31468i 0.239702i
\(695\) −29.2315 16.8768i −1.10881 0.640174i
\(696\) 11.2411 + 6.49007i 0.426094 + 0.246006i
\(697\) 3.77240i 0.142890i
\(698\) −0.928780 + 1.60869i −0.0351548 + 0.0608900i
\(699\) −4.35086 7.53590i −0.164564 0.285034i
\(700\) 11.2458 6.49276i 0.425051 0.245403i
\(701\) 14.9129 0.563253 0.281627 0.959524i \(-0.409126\pi\)
0.281627 + 0.959524i \(0.409126\pi\)
\(702\) 0 0
\(703\) 1.84415 0.0695534
\(704\) −1.58518 + 0.915206i −0.0597439 + 0.0344931i
\(705\) −8.64191 14.9682i −0.325473 0.563736i
\(706\) −0.176956 + 0.306497i −0.00665983 + 0.0115352i
\(707\) 14.2422i 0.535633i
\(708\) 0.0141971 + 0.00819673i 0.000533561 + 0.000308052i
\(709\) −33.2824 19.2156i −1.24995 0.721656i −0.278847 0.960336i \(-0.589952\pi\)
−0.971098 + 0.238679i \(0.923286\pi\)
\(710\) 21.3666i 0.801874i
\(711\) 0.951378 1.64784i 0.0356795 0.0617987i
\(712\) −15.0891 26.1351i −0.565488 0.979454i
\(713\) −23.5228 + 13.5809i −0.880937 + 0.508609i
\(714\) −1.36227 −0.0509818
\(715\) 0 0
\(716\) 4.15346 0.155222
\(717\) 8.28489 4.78328i 0.309405 0.178635i
\(718\) −5.95444 10.3134i −0.222218 0.384892i
\(719\) −5.71864 + 9.90497i −0.213269 + 0.369393i −0.952736 0.303800i \(-0.901744\pi\)
0.739467 + 0.673193i \(0.235078\pi\)
\(720\) 14.8388i 0.553008i
\(721\) 31.5451 + 18.2126i 1.17480 + 0.678272i
\(722\) −7.32460 4.22886i −0.272593 0.157382i
\(723\) 2.92585i 0.108814i
\(724\) 9.98911 17.3017i 0.371243 0.643011i
\(725\) −11.2606 19.5039i −0.418206 0.724355i
\(726\) 3.68638 2.12833i 0.136815 0.0789899i
\(727\) −3.63640 −0.134867 −0.0674333 0.997724i \(-0.521481\pi\)
−0.0674333 + 0.997724i \(0.521481\pi\)
\(728\) 0 0
\(729\) 1.78986 0.0662910
\(730\) −17.2598 + 9.96495i −0.638814 + 0.368819i
\(731\) −4.07002 7.04949i −0.150535 0.260735i
\(732\) 5.45257 9.44414i 0.201533 0.349065i
\(733\) 3.52217i 0.130094i 0.997882 + 0.0650472i \(0.0207198\pi\)
−0.997882 + 0.0650472i \(0.979280\pi\)
\(734\) 4.51148 + 2.60470i 0.166522 + 0.0961414i
\(735\) 0.480608 + 0.277479i 0.0177275 + 0.0102350i
\(736\) 24.6069i 0.907021i
\(737\) −5.54503 + 9.60428i −0.204254 + 0.353778i
\(738\) 2.16972 + 3.75806i 0.0798685 + 0.138336i
\(739\) 0.363980 0.210144i 0.0133892 0.00773027i −0.493290 0.869865i \(-0.664206\pi\)
0.506680 + 0.862134i \(0.330873\pi\)
\(740\) −4.50902 −0.165755
\(741\) 0 0
\(742\) 8.77346 0.322084
\(743\) 21.9644 12.6811i 0.805795 0.465226i −0.0396987 0.999212i \(-0.512640\pi\)
0.845493 + 0.533986i \(0.179306\pi\)
\(744\) −4.84697 8.39520i −0.177699 0.307783i
\(745\) 1.03803 1.79792i 0.0380306 0.0658709i
\(746\) 15.3870i 0.563359i
\(747\) 33.3373 + 19.2473i 1.21975 + 0.704221i
\(748\) −1.99618 1.15250i −0.0729877 0.0421395i
\(749\) 15.1588i 0.553892i
\(750\) 1.33997 2.32090i 0.0489288 0.0847471i
\(751\) 0.325437 + 0.563673i 0.0118754 + 0.0205687i 0.871902 0.489680i \(-0.162887\pi\)
−0.860027 + 0.510249i \(0.829553\pi\)
\(752\) −14.9682 + 8.64191i −0.545835 + 0.315138i
\(753\) −1.10129 −0.0401333
\(754\) 0 0
\(755\) 53.4432 1.94500
\(756\) 16.9461 9.78382i 0.616322 0.355834i
\(757\) 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
\(759\) 4.42327i 0.160555i
\(760\) −9.64032 5.56584i −0.349691 0.201894i
\(761\) −26.7794 15.4611i −0.970751 0.560463i −0.0712857 0.997456i \(-0.522710\pi\)
−0.899465 + 0.436993i \(0.856044\pi\)
\(762\) 3.01639i 0.109272i
\(763\) 5.62133 9.73644i 0.203506 0.352483i
\(764\) 7.60842 + 13.1782i 0.275263 + 0.476770i
\(765\) 6.50301 3.75451i 0.235117 0.135745i
\(766\) 2.69441 0.0973531
\(767\) 0 0
\(768\) −2.68425 −0.0968596
\(769\) 37.9050 21.8845i 1.36689 0.789174i 0.376360 0.926473i \(-0.377176\pi\)
0.990530 + 0.137299i \(0.0438422\pi\)
\(770\) −2.50753 4.34317i −0.0903652 0.156517i
\(771\) 11.8029 20.4432i 0.425071 0.736245i
\(772\) 22.8853i 0.823660i
\(773\) −36.7376 21.2104i −1.32136 0.762886i −0.337413 0.941357i \(-0.609552\pi\)
−0.983945 + 0.178470i \(0.942885\pi\)