Properties

Label 475.2.j.c.349.1
Level $475$
Weight $2$
Character 475.349
Analytic conductor $3.793$
Analytic rank $0$
Dimension $16$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [475,2,Mod(49,475)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(475, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("475.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.j (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: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.1387535264013605949997056.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 11x^{14} + 82x^{12} - 337x^{10} + 1006x^{8} - 1596x^{6} + 1765x^{4} - 414x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 349.1
Root \(-0.426014 - 0.245959i\) of defining polynomial
Character \(\chi\) \(=\) 475.349
Dual form 475.2.j.c.49.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} +O(q^{10})\) \(q+(-2.38851 + 1.37901i) q^{2} +(1.29204 - 0.745959i) q^{3} +(2.80333 - 4.85550i) q^{4} +(-2.05737 + 3.56347i) q^{6} +2.84864i q^{7} +9.94721i q^{8} +(-0.387090 + 0.670459i) q^{9} -0.864801 q^{11} -8.36467i q^{12} +(-0.557098 - 0.321640i) q^{13} +(-3.92829 - 6.80401i) q^{14} +(-8.11063 - 14.0480i) q^{16} +(-3.24054 + 1.87093i) q^{17} -2.13520i q^{18} +(3.36069 + 2.77592i) q^{19} +(2.12497 + 3.68055i) q^{21} +(2.06559 - 1.19257i) q^{22} +(-0.361531 - 0.208730i) q^{23} +(7.42021 + 12.8522i) q^{24} +1.77418 q^{26} +5.63077i q^{27} +(13.8316 + 7.98566i) q^{28} +(-4.85261 + 8.40497i) q^{29} +4.93349 q^{31} +(21.5156 + 12.4220i) q^{32} +(-1.11736 + 0.645106i) q^{33} +(5.16005 - 8.93746i) q^{34} +(2.17028 + 3.75903i) q^{36} -6.36467i q^{37} +(-11.8551 - 1.99589i) q^{38} -0.959723 q^{39} +(2.00686 + 3.47598i) q^{41} +(-10.1510 - 5.86069i) q^{42} +(-1.78254 + 1.02915i) q^{43} +(-2.42432 + 4.19904i) q^{44} +1.15136 q^{46} +(-3.42423 - 1.97698i) q^{47} +(-20.9585 - 12.1004i) q^{48} -1.11474 q^{49} +(-2.79127 + 4.83462i) q^{51} +(-3.12345 + 1.80333i) q^{52} +(9.51544 + 5.49374i) q^{53} +(-7.76487 - 13.4492i) q^{54} -28.3360 q^{56} +(6.41287 + 1.07966i) q^{57} -26.7672i q^{58} +(1.22980 + 2.13007i) q^{59} +(-3.16740 + 5.48609i) q^{61} +(-11.7837 + 6.80333i) q^{62} +(-1.90989 - 1.10268i) q^{63} -36.0778 q^{64} +(1.77921 - 3.08169i) q^{66} +(-2.19295 - 1.26610i) q^{67} +20.9793i q^{68} -0.622817 q^{69} +(0.891065 + 1.54337i) q^{71} +(-6.66920 - 3.85046i) q^{72} +(-6.17554 + 3.56545i) q^{73} +(8.77693 + 15.2021i) q^{74} +(22.8996 - 8.53606i) q^{76} -2.46350i q^{77} +(2.29231 - 1.32347i) q^{78} +(0.912262 + 1.58008i) q^{79} +(3.03905 + 5.26380i) q^{81} +(-9.58681 - 5.53495i) q^{82} -7.43913i q^{83} +23.8279 q^{84} +(2.83841 - 4.91626i) q^{86} +14.4794i q^{87} -8.60235i q^{88} +(2.22294 - 3.85024i) q^{89} +(0.916237 - 1.58697i) q^{91} +(-2.02698 + 1.17028i) q^{92} +(6.37427 - 3.68018i) q^{93} +10.9051 q^{94} +37.0653 q^{96} +(9.39996 - 5.42707i) q^{97} +(2.66256 - 1.53723i) q^{98} +(0.334755 - 0.579813i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{4} - 4 q^{6} + 2 q^{9} - 8 q^{11} - 2 q^{14} - 14 q^{16} - 10 q^{19} + 8 q^{21} + 46 q^{24} + 12 q^{26} - 2 q^{29} + 30 q^{34} + 14 q^{36} - 60 q^{39} + 16 q^{41} - 24 q^{44} + 48 q^{46} + 40 q^{49} - 44 q^{51} - 68 q^{54} - 164 q^{56} - 10 q^{59} - 224 q^{64} + 62 q^{66} + 36 q^{69} - 40 q^{71} + 50 q^{74} + 126 q^{76} + 34 q^{79} - 24 q^{81} + 80 q^{84} - 16 q^{86} + 22 q^{89} - 12 q^{91} + 124 q^{94} + 84 q^{96} + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38851 + 1.37901i −1.68893 + 0.975106i −0.733597 + 0.679585i \(0.762160\pi\)
−0.955336 + 0.295521i \(0.904507\pi\)
\(3\) 1.29204 0.745959i 0.745959 0.430680i −0.0782728 0.996932i \(-0.524941\pi\)
0.824232 + 0.566252i \(0.191607\pi\)
\(4\) 2.80333 4.85550i 1.40166 2.42775i
\(5\) 0 0
\(6\) −2.05737 + 3.56347i −0.839917 + 1.45478i
\(7\) 2.84864i 1.07668i 0.842727 + 0.538342i \(0.180949\pi\)
−0.842727 + 0.538342i \(0.819051\pi\)
\(8\) 9.94721i 3.51687i
\(9\) −0.387090 + 0.670459i −0.129030 + 0.223486i
\(10\) 0 0
\(11\) −0.864801 −0.260747 −0.130374 0.991465i \(-0.541618\pi\)
−0.130374 + 0.991465i \(0.541618\pi\)
\(12\) 8.36467i 2.41467i
\(13\) −0.557098 0.321640i −0.154511 0.0892070i 0.420751 0.907176i \(-0.361767\pi\)
−0.575262 + 0.817969i \(0.695100\pi\)
\(14\) −3.92829 6.80401i −1.04988 1.81845i
\(15\) 0 0
\(16\) −8.11063 14.0480i −2.02766 3.51201i
\(17\) −3.24054 + 1.87093i −0.785946 + 0.453766i −0.838534 0.544850i \(-0.816587\pi\)
0.0525872 + 0.998616i \(0.483253\pi\)
\(18\) 2.13520i 0.503271i
\(19\) 3.36069 + 2.77592i 0.770996 + 0.636840i
\(20\) 0 0
\(21\) 2.12497 + 3.68055i 0.463706 + 0.803162i
\(22\) 2.06559 1.19257i 0.440385 0.254256i
\(23\) −0.361531 0.208730i −0.0753845 0.0435233i 0.461834 0.886966i \(-0.347192\pi\)
−0.537218 + 0.843443i \(0.680525\pi\)
\(24\) 7.42021 + 12.8522i 1.51464 + 2.62344i
\(25\) 0 0
\(26\) 1.77418 0.347945
\(27\) 5.63077i 1.08364i
\(28\) 13.8316 + 7.98566i 2.61392 + 1.50915i
\(29\) −4.85261 + 8.40497i −0.901108 + 1.56076i −0.0750490 + 0.997180i \(0.523911\pi\)
−0.826059 + 0.563584i \(0.809422\pi\)
\(30\) 0 0
\(31\) 4.93349 0.886081 0.443041 0.896501i \(-0.353900\pi\)
0.443041 + 0.896501i \(0.353900\pi\)
\(32\) 21.5156 + 12.4220i 3.80346 + 2.19593i
\(33\) −1.11736 + 0.645106i −0.194507 + 0.112299i
\(34\) 5.16005 8.93746i 0.884941 1.53276i
\(35\) 0 0
\(36\) 2.17028 + 3.75903i 0.361713 + 0.626505i
\(37\) 6.36467i 1.04635i −0.852227 0.523173i \(-0.824748\pi\)
0.852227 0.523173i \(-0.175252\pi\)
\(38\) −11.8551 1.99589i −1.92315 0.323777i
\(39\) −0.959723 −0.153679
\(40\) 0 0
\(41\) 2.00686 + 3.47598i 0.313419 + 0.542857i 0.979100 0.203379i \(-0.0651924\pi\)
−0.665681 + 0.746236i \(0.731859\pi\)
\(42\) −10.1510 5.86069i −1.56634 0.904325i
\(43\) −1.78254 + 1.02915i −0.271834 + 0.156944i −0.629721 0.776821i \(-0.716831\pi\)
0.357887 + 0.933765i \(0.383497\pi\)
\(44\) −2.42432 + 4.19904i −0.365480 + 0.633030i
\(45\) 0 0
\(46\) 1.15136 0.169759
\(47\) −3.42423 1.97698i −0.499475 0.288372i 0.229022 0.973421i \(-0.426447\pi\)
−0.728497 + 0.685049i \(0.759781\pi\)
\(48\) −20.9585 12.1004i −3.02510 1.74654i
\(49\) −1.11474 −0.159248
\(50\) 0 0
\(51\) −2.79127 + 4.83462i −0.390856 + 0.676982i
\(52\) −3.12345 + 1.80333i −0.433145 + 0.250076i
\(53\) 9.51544 + 5.49374i 1.30705 + 0.754624i 0.981602 0.190937i \(-0.0611528\pi\)
0.325444 + 0.945561i \(0.394486\pi\)
\(54\) −7.76487 13.4492i −1.05667 1.83020i
\(55\) 0 0
\(56\) −28.3360 −3.78656
\(57\) 6.41287 + 1.07966i 0.849406 + 0.143004i
\(58\) 26.7672i 3.51470i
\(59\) 1.22980 + 2.13007i 0.160106 + 0.277311i 0.934906 0.354894i \(-0.115483\pi\)
−0.774801 + 0.632206i \(0.782150\pi\)
\(60\) 0 0
\(61\) −3.16740 + 5.48609i −0.405543 + 0.702422i −0.994385 0.105827i \(-0.966251\pi\)
0.588841 + 0.808249i \(0.299584\pi\)
\(62\) −11.7837 + 6.80333i −1.49653 + 0.864023i
\(63\) −1.90989 1.10268i −0.240624 0.138924i
\(64\) −36.0778 −4.50973
\(65\) 0 0
\(66\) 1.77921 3.08169i 0.219006 0.379329i
\(67\) −2.19295 1.26610i −0.267911 0.154678i 0.360027 0.932942i \(-0.382767\pi\)
−0.627938 + 0.778263i \(0.716101\pi\)
\(68\) 20.9793i 2.54411i
\(69\) −0.622817 −0.0749783
\(70\) 0 0
\(71\) 0.891065 + 1.54337i 0.105750 + 0.183164i 0.914044 0.405614i \(-0.132942\pi\)
−0.808294 + 0.588779i \(0.799609\pi\)
\(72\) −6.66920 3.85046i −0.785972 0.453781i
\(73\) −6.17554 + 3.56545i −0.722792 + 0.417304i −0.815780 0.578363i \(-0.803692\pi\)
0.0929873 + 0.995667i \(0.470358\pi\)
\(74\) 8.77693 + 15.2021i 1.02030 + 1.76721i
\(75\) 0 0
\(76\) 22.8996 8.53606i 2.62677 0.979153i
\(77\) 2.46350i 0.280742i
\(78\) 2.29231 1.32347i 0.259553 0.149853i
\(79\) 0.912262 + 1.58008i 0.102637 + 0.177773i 0.912771 0.408473i \(-0.133939\pi\)
−0.810133 + 0.586246i \(0.800605\pi\)
\(80\) 0 0
\(81\) 3.03905 + 5.26380i 0.337673 + 0.584866i
\(82\) −9.58681 5.53495i −1.05869 0.611233i
\(83\) 7.43913i 0.816550i −0.912859 0.408275i \(-0.866130\pi\)
0.912859 0.408275i \(-0.133870\pi\)
\(84\) 23.8279 2.59984
\(85\) 0 0
\(86\) 2.83841 4.91626i 0.306073 0.530134i
\(87\) 14.4794i 1.55236i
\(88\) 8.60235i 0.917014i
\(89\) 2.22294 3.85024i 0.235631 0.408125i −0.723825 0.689984i \(-0.757618\pi\)
0.959456 + 0.281859i \(0.0909510\pi\)
\(90\) 0 0
\(91\) 0.916237 1.58697i 0.0960478 0.166360i
\(92\) −2.02698 + 1.17028i −0.211327 + 0.122010i
\(93\) 6.37427 3.68018i 0.660981 0.381617i
\(94\) 10.9051 1.12477
\(95\) 0 0
\(96\) 37.0653 3.78296
\(97\) 9.39996 5.42707i 0.954422 0.551036i 0.0599699 0.998200i \(-0.480900\pi\)
0.894452 + 0.447165i \(0.147566\pi\)
\(98\) 2.66256 1.53723i 0.268959 0.155284i
\(99\) 0.334755 0.579813i 0.0336442 0.0582734i
\(100\) 0 0
\(101\) 2.64799 4.58645i 0.263485 0.456369i −0.703681 0.710516i \(-0.748461\pi\)
0.967166 + 0.254147i \(0.0817948\pi\)
\(102\) 15.3967i 1.52450i
\(103\) 0.385134i 0.0379484i −0.999820 0.0189742i \(-0.993960\pi\)
0.999820 0.0189742i \(-0.00604004\pi\)
\(104\) 3.19943 5.54157i 0.313729 0.543395i
\(105\) 0 0
\(106\) −30.3037 −2.94335
\(107\) 6.43336i 0.621937i 0.950420 + 0.310968i \(0.100653\pi\)
−0.950420 + 0.310968i \(0.899347\pi\)
\(108\) 27.3402 + 15.7849i 2.63081 + 1.51890i
\(109\) 3.28441 + 5.68877i 0.314590 + 0.544885i 0.979350 0.202171i \(-0.0647998\pi\)
−0.664761 + 0.747056i \(0.731466\pi\)
\(110\) 0 0
\(111\) −4.74778 8.22340i −0.450640 0.780531i
\(112\) 40.0177 23.1042i 3.78132 2.18315i
\(113\) 0.294513i 0.0277054i 0.999904 + 0.0138527i \(0.00440960\pi\)
−0.999904 + 0.0138527i \(0.995590\pi\)
\(114\) −16.8061 + 6.26463i −1.57403 + 0.586736i
\(115\) 0 0
\(116\) 27.2069 + 47.1238i 2.52610 + 4.37533i
\(117\) 0.431294 0.249007i 0.0398731 0.0230207i
\(118\) −5.87477 3.39180i −0.540816 0.312240i
\(119\) −5.32959 9.23112i −0.488563 0.846216i
\(120\) 0 0
\(121\) −10.2521 −0.932011
\(122\) 17.4715i 1.58179i
\(123\) 5.18588 + 2.99407i 0.467595 + 0.269966i
\(124\) 13.8302 23.9546i 1.24199 2.15119i
\(125\) 0 0
\(126\) 6.08241 0.541864
\(127\) 7.65127 + 4.41746i 0.678940 + 0.391986i 0.799456 0.600725i \(-0.205121\pi\)
−0.120516 + 0.992711i \(0.538455\pi\)
\(128\) 43.1412 24.9076i 3.81318 2.20154i
\(129\) −1.53540 + 2.65940i −0.135185 + 0.234147i
\(130\) 0 0
\(131\) −10.4564 18.1110i −0.913578 1.58236i −0.808969 0.587851i \(-0.799974\pi\)
−0.104609 0.994513i \(-0.533359\pi\)
\(132\) 7.23377i 0.629619i
\(133\) −7.90759 + 9.57340i −0.685675 + 0.830119i
\(134\) 6.98384 0.603312
\(135\) 0 0
\(136\) −18.6105 32.2343i −1.59584 2.76407i
\(137\) 4.51613 + 2.60739i 0.385839 + 0.222764i 0.680356 0.732882i \(-0.261825\pi\)
−0.294517 + 0.955646i \(0.595159\pi\)
\(138\) 1.48761 0.858870i 0.126633 0.0731118i
\(139\) −5.36192 + 9.28711i −0.454792 + 0.787723i −0.998676 0.0514375i \(-0.983620\pi\)
0.543884 + 0.839160i \(0.316953\pi\)
\(140\) 0 0
\(141\) −5.89898 −0.496784
\(142\) −4.25664 2.45757i −0.357209 0.206235i
\(143\) 0.481778 + 0.278155i 0.0402883 + 0.0232605i
\(144\) 12.5582 1.04651
\(145\) 0 0
\(146\) 9.83357 17.0322i 0.813832 1.40960i
\(147\) −1.44028 + 0.831547i −0.118792 + 0.0685848i
\(148\) −30.9037 17.8423i −2.54027 1.46662i
\(149\) −7.45578 12.9138i −0.610801 1.05794i −0.991106 0.133078i \(-0.957514\pi\)
0.380304 0.924861i \(-0.375819\pi\)
\(150\) 0 0
\(151\) 21.4589 1.74630 0.873152 0.487448i \(-0.162072\pi\)
0.873152 + 0.487448i \(0.162072\pi\)
\(152\) −27.6127 + 33.4295i −2.23968 + 2.71149i
\(153\) 2.89687i 0.234198i
\(154\) 3.39719 + 5.88411i 0.273753 + 0.474155i
\(155\) 0 0
\(156\) −2.69042 + 4.65994i −0.215406 + 0.373094i
\(157\) 2.10546 1.21559i 0.168034 0.0970145i −0.413624 0.910448i \(-0.635737\pi\)
0.581659 + 0.813433i \(0.302404\pi\)
\(158\) −4.35790 2.51603i −0.346696 0.200165i
\(159\) 16.3924 1.30000
\(160\) 0 0
\(161\) 0.594597 1.02987i 0.0468608 0.0811653i
\(162\) −14.5176 8.38176i −1.14061 0.658533i
\(163\) 17.8175i 1.39558i 0.716305 + 0.697788i \(0.245832\pi\)
−0.716305 + 0.697788i \(0.754168\pi\)
\(164\) 22.5035 1.75723
\(165\) 0 0
\(166\) 10.2586 + 17.7684i 0.796223 + 1.37910i
\(167\) −0.351258 0.202799i −0.0271812 0.0156931i 0.486348 0.873765i \(-0.338329\pi\)
−0.513529 + 0.858072i \(0.671662\pi\)
\(168\) −36.6112 + 21.1375i −2.82462 + 1.63079i
\(169\) −6.29309 10.9000i −0.484084 0.838458i
\(170\) 0 0
\(171\) −3.16203 + 1.17868i −0.241807 + 0.0901358i
\(172\) 11.5401i 0.879928i
\(173\) 15.6067 9.01051i 1.18655 0.685056i 0.229031 0.973419i \(-0.426444\pi\)
0.957521 + 0.288363i \(0.0931109\pi\)
\(174\) −19.9672 34.5842i −1.51371 2.62182i
\(175\) 0 0
\(176\) 7.01408 + 12.1487i 0.528706 + 0.915746i
\(177\) 3.17789 + 1.83476i 0.238865 + 0.137909i
\(178\) 12.2618i 0.919061i
\(179\) −20.1523 −1.50625 −0.753127 0.657875i \(-0.771455\pi\)
−0.753127 + 0.657875i \(0.771455\pi\)
\(180\) 0 0
\(181\) 8.55541 14.8184i 0.635919 1.10144i −0.350401 0.936600i \(-0.613955\pi\)
0.986320 0.164844i \(-0.0527120\pi\)
\(182\) 5.05399i 0.374627i
\(183\) 9.45099i 0.698637i
\(184\) 2.07628 3.59623i 0.153066 0.265117i
\(185\) 0 0
\(186\) −10.1500 + 17.5803i −0.744235 + 1.28905i
\(187\) 2.80242 1.61798i 0.204933 0.118318i
\(188\) −19.1985 + 11.0842i −1.40019 + 0.808401i
\(189\) −16.0400 −1.16674
\(190\) 0 0
\(191\) 5.28080 0.382105 0.191053 0.981580i \(-0.438810\pi\)
0.191053 + 0.981580i \(0.438810\pi\)
\(192\) −46.6140 + 26.9126i −3.36408 + 1.94225i
\(193\) 15.5916 9.00182i 1.12231 0.647966i 0.180320 0.983608i \(-0.442287\pi\)
0.941989 + 0.335642i \(0.108953\pi\)
\(194\) −14.9679 + 25.9252i −1.07464 + 1.86132i
\(195\) 0 0
\(196\) −3.12497 + 5.41260i −0.223212 + 0.386614i
\(197\) 8.07785i 0.575523i −0.957702 0.287761i \(-0.907089\pi\)
0.957702 0.287761i \(-0.0929110\pi\)
\(198\) 1.84652i 0.131227i
\(199\) 0.701872 1.21568i 0.0497544 0.0861771i −0.840076 0.542469i \(-0.817489\pi\)
0.889830 + 0.456292i \(0.150823\pi\)
\(200\) 0 0
\(201\) −3.77783 −0.266468
\(202\) 14.6064i 1.02770i
\(203\) −23.9427 13.8233i −1.68045 0.970208i
\(204\) 15.6497 + 27.1060i 1.09570 + 1.89780i
\(205\) 0 0
\(206\) 0.531103 + 0.919897i 0.0370037 + 0.0640923i
\(207\) 0.279890 0.161595i 0.0194537 0.0112316i
\(208\) 10.4348i 0.723525i
\(209\) −2.90633 2.40062i −0.201035 0.166054i
\(210\) 0 0
\(211\) −9.45817 16.3820i −0.651128 1.12779i −0.982850 0.184409i \(-0.940963\pi\)
0.331722 0.943377i \(-0.392370\pi\)
\(212\) 53.3498 30.8015i 3.66408 2.11546i
\(213\) 2.30258 + 1.32940i 0.157770 + 0.0910888i
\(214\) −8.87166 15.3662i −0.606454 1.05041i
\(215\) 0 0
\(216\) −56.0104 −3.81103
\(217\) 14.0537i 0.954030i
\(218\) −15.6897 9.05846i −1.06264 0.613516i
\(219\) −5.31936 + 9.21340i −0.359449 + 0.622584i
\(220\) 0 0
\(221\) 2.40706 0.161917
\(222\) 22.6803 + 13.0945i 1.52220 + 0.878843i
\(223\) −13.9846 + 8.07400i −0.936477 + 0.540675i −0.888854 0.458190i \(-0.848498\pi\)
−0.0476227 + 0.998865i \(0.515165\pi\)
\(224\) −35.3859 + 61.2901i −2.36432 + 4.09512i
\(225\) 0 0
\(226\) −0.406136 0.703448i −0.0270157 0.0467926i
\(227\) 26.3186i 1.74683i −0.486978 0.873414i \(-0.661901\pi\)
0.486978 0.873414i \(-0.338099\pi\)
\(228\) 23.2197 28.1111i 1.53776 1.86170i
\(229\) 13.3323 0.881026 0.440513 0.897746i \(-0.354797\pi\)
0.440513 + 0.897746i \(0.354797\pi\)
\(230\) 0 0
\(231\) −1.83767 3.18294i −0.120910 0.209422i
\(232\) −83.6060 48.2700i −5.48900 3.16908i
\(233\) 21.9186 12.6547i 1.43594 0.829038i 0.438372 0.898794i \(-0.355555\pi\)
0.997564 + 0.0697556i \(0.0222220\pi\)
\(234\) −0.686767 + 1.18951i −0.0448953 + 0.0777610i
\(235\) 0 0
\(236\) 13.7901 0.897658
\(237\) 2.35736 + 1.36102i 0.153127 + 0.0884077i
\(238\) 25.4596 + 14.6991i 1.65030 + 0.952801i
\(239\) 23.5500 1.52332 0.761660 0.647977i \(-0.224385\pi\)
0.761660 + 0.647977i \(0.224385\pi\)
\(240\) 0 0
\(241\) −4.19208 + 7.26089i −0.270035 + 0.467715i −0.968871 0.247568i \(-0.920369\pi\)
0.698835 + 0.715283i \(0.253702\pi\)
\(242\) 24.4873 14.1378i 1.57410 0.908809i
\(243\) −6.77601 3.91213i −0.434681 0.250963i
\(244\) 17.7585 + 30.7586i 1.13687 + 1.96912i
\(245\) 0 0
\(246\) −16.5154 −1.05298
\(247\) −0.979387 2.62739i −0.0623169 0.167177i
\(248\) 49.0745i 3.11623i
\(249\) −5.54929 9.61165i −0.351672 0.609113i
\(250\) 0 0
\(251\) −9.12391 + 15.8031i −0.575896 + 0.997481i 0.420048 + 0.907502i \(0.362013\pi\)
−0.995944 + 0.0899792i \(0.971320\pi\)
\(252\) −10.7081 + 6.18233i −0.674548 + 0.389450i
\(253\) 0.312652 + 0.180510i 0.0196563 + 0.0113486i
\(254\) −24.3669 −1.52891
\(255\) 0 0
\(256\) −32.6176 + 56.4954i −2.03860 + 3.53096i
\(257\) 12.2108 + 7.04989i 0.761687 + 0.439760i 0.829901 0.557911i \(-0.188397\pi\)
−0.0682144 + 0.997671i \(0.521730\pi\)
\(258\) 8.46934i 0.527278i
\(259\) 18.1306 1.12658
\(260\) 0 0
\(261\) −3.75679 6.50696i −0.232540 0.402770i
\(262\) 49.9504 + 28.8389i 3.08595 + 1.78167i
\(263\) −5.55184 + 3.20536i −0.342341 + 0.197651i −0.661307 0.750116i \(-0.729998\pi\)
0.318966 + 0.947766i \(0.396665\pi\)
\(264\) −6.41700 11.1146i −0.394939 0.684055i
\(265\) 0 0
\(266\) 5.68558 33.7708i 0.348605 2.07062i
\(267\) 6.63288i 0.405926i
\(268\) −12.2951 + 7.09857i −0.751042 + 0.433614i
\(269\) 8.99557 + 15.5808i 0.548469 + 0.949977i 0.998380 + 0.0569032i \(0.0181226\pi\)
−0.449910 + 0.893074i \(0.648544\pi\)
\(270\) 0 0
\(271\) −5.94095 10.2900i −0.360887 0.625075i 0.627220 0.778842i \(-0.284193\pi\)
−0.988107 + 0.153767i \(0.950859\pi\)
\(272\) 52.5656 + 30.3488i 3.18726 + 1.84017i
\(273\) 2.73390i 0.165463i
\(274\) −14.3824 −0.868874
\(275\) 0 0
\(276\) −1.74596 + 3.02409i −0.105094 + 0.182029i
\(277\) 23.6240i 1.41943i −0.704489 0.709715i \(-0.748824\pi\)
0.704489 0.709715i \(-0.251176\pi\)
\(278\) 29.5765i 1.77388i
\(279\) −1.90970 + 3.30770i −0.114331 + 0.198027i
\(280\) 0 0
\(281\) −6.90465 + 11.9592i −0.411897 + 0.713426i −0.995097 0.0989020i \(-0.968467\pi\)
0.583200 + 0.812328i \(0.301800\pi\)
\(282\) 14.0898 8.13474i 0.839035 0.484417i
\(283\) −10.1822 + 5.87868i −0.605268 + 0.349451i −0.771111 0.636701i \(-0.780299\pi\)
0.165843 + 0.986152i \(0.446965\pi\)
\(284\) 9.99179 0.592904
\(285\) 0 0
\(286\) −1.53431 −0.0907257
\(287\) −9.90181 + 5.71681i −0.584485 + 0.337453i
\(288\) −16.6569 + 9.61689i −0.981519 + 0.566680i
\(289\) −1.49927 + 2.59681i −0.0881922 + 0.152753i
\(290\) 0 0
\(291\) 8.09675 14.0240i 0.474640 0.822100i
\(292\) 39.9805i 2.33968i
\(293\) 27.0576i 1.58072i −0.612640 0.790362i \(-0.709892\pi\)
0.612640 0.790362i \(-0.290108\pi\)
\(294\) 2.29342 3.97232i 0.133755 0.231670i
\(295\) 0 0
\(296\) 63.3107 3.67986
\(297\) 4.86949i 0.282557i
\(298\) 35.6165 + 20.5632i 2.06321 + 1.19119i
\(299\) 0.134272 + 0.232566i 0.00776516 + 0.0134497i
\(300\) 0 0
\(301\) −2.93167 5.07780i −0.168979 0.292679i
\(302\) −51.2549 + 29.5921i −2.94939 + 1.70283i
\(303\) 7.90117i 0.453910i
\(304\) 11.7388 69.7256i 0.673269 3.99904i
\(305\) 0 0
\(306\) 3.99480 + 6.91920i 0.228368 + 0.395544i
\(307\) −7.65414 + 4.41912i −0.436845 + 0.252212i −0.702258 0.711922i \(-0.747825\pi\)
0.265414 + 0.964135i \(0.414492\pi\)
\(308\) −11.9616 6.90601i −0.681573 0.393506i
\(309\) −0.287294 0.497608i −0.0163436 0.0283080i
\(310\) 0 0
\(311\) −0.651493 −0.0369428 −0.0184714 0.999829i \(-0.505880\pi\)
−0.0184714 + 0.999829i \(0.505880\pi\)
\(312\) 9.54656i 0.540468i
\(313\) 2.56825 + 1.48278i 0.145166 + 0.0838116i 0.570824 0.821073i \(-0.306624\pi\)
−0.425658 + 0.904884i \(0.639957\pi\)
\(314\) −3.35261 + 5.80690i −0.189199 + 0.327702i
\(315\) 0 0
\(316\) 10.2295 0.575453
\(317\) −8.98921 5.18993i −0.504885 0.291495i 0.225844 0.974164i \(-0.427486\pi\)
−0.730728 + 0.682668i \(0.760819\pi\)
\(318\) −39.1535 + 22.6053i −2.19562 + 1.26764i
\(319\) 4.19654 7.26862i 0.234961 0.406965i
\(320\) 0 0
\(321\) 4.79903 + 8.31216i 0.267856 + 0.463939i
\(322\) 3.27981i 0.182777i
\(323\) −16.0840 2.70787i −0.894938 0.150670i
\(324\) 34.0778 1.89321
\(325\) 0 0
\(326\) −24.5705 42.5574i −1.36083 2.35703i
\(327\) 8.48718 + 4.90007i 0.469342 + 0.270975i
\(328\) −34.5763 + 19.9626i −1.90916 + 1.10225i
\(329\) 5.63170 9.75438i 0.310485 0.537776i
\(330\) 0 0
\(331\) 15.0922 0.829543 0.414772 0.909926i \(-0.363861\pi\)
0.414772 + 0.909926i \(0.363861\pi\)
\(332\) −36.1207 20.8543i −1.98238 1.14453i
\(333\) 4.26725 + 2.46370i 0.233844 + 0.135010i
\(334\) 1.11865 0.0612096
\(335\) 0 0
\(336\) 34.4696 59.7032i 1.88047 3.25708i
\(337\) −13.6810 + 7.89872i −0.745251 + 0.430271i −0.823975 0.566626i \(-0.808249\pi\)
0.0787246 + 0.996896i \(0.474915\pi\)
\(338\) 30.0623 + 17.3565i 1.63517 + 0.944067i
\(339\) 0.219695 + 0.380522i 0.0119322 + 0.0206671i
\(340\) 0 0
\(341\) −4.26649 −0.231043
\(342\) 5.92714 7.17575i 0.320503 0.388020i
\(343\) 16.7650i 0.905224i
\(344\) −10.2371 17.7313i −0.551950 0.956005i
\(345\) 0 0
\(346\) −24.8511 + 43.0434i −1.33600 + 2.31403i
\(347\) 18.4915 10.6761i 0.992676 0.573122i 0.0866031 0.996243i \(-0.472399\pi\)
0.906073 + 0.423121i \(0.139065\pi\)
\(348\) 70.3048 + 40.5905i 3.76873 + 2.17588i
\(349\) 32.3897 1.73378 0.866891 0.498497i \(-0.166115\pi\)
0.866891 + 0.498497i \(0.166115\pi\)
\(350\) 0 0
\(351\) 1.81108 3.13689i 0.0966685 0.167435i
\(352\) −18.6067 10.7426i −0.991741 0.572582i
\(353\) 0.730583i 0.0388850i 0.999811 + 0.0194425i \(0.00618913\pi\)
−0.999811 + 0.0194425i \(0.993811\pi\)
\(354\) −10.1206 −0.537902
\(355\) 0 0
\(356\) −12.4632 21.5870i −0.660551 1.14411i
\(357\) −13.7721 7.95132i −0.728896 0.420828i
\(358\) 48.1340 27.7902i 2.54396 1.46876i
\(359\) −13.4248 23.2524i −0.708533 1.22722i −0.965401 0.260769i \(-0.916024\pi\)
0.256868 0.966447i \(-0.417309\pi\)
\(360\) 0 0
\(361\) 3.58853 + 18.6580i 0.188870 + 0.982002i
\(362\) 47.1919i 2.48035i
\(363\) −13.2461 + 7.64766i −0.695242 + 0.401398i
\(364\) −5.13702 8.89759i −0.269253 0.466360i
\(365\) 0 0
\(366\) −13.0330 22.5738i −0.681245 1.17995i
\(367\) −19.8877 11.4822i −1.03813 0.599364i −0.118826 0.992915i \(-0.537913\pi\)
−0.919303 + 0.393551i \(0.871246\pi\)
\(368\) 6.77173i 0.353001i
\(369\) −3.10734 −0.161761
\(370\) 0 0
\(371\) −15.6497 + 27.1060i −0.812491 + 1.40728i
\(372\) 41.2670i 2.13960i
\(373\) 29.5305i 1.52903i 0.644606 + 0.764515i \(0.277021\pi\)
−0.644606 + 0.764515i \(0.722979\pi\)
\(374\) −4.46241 + 7.72912i −0.230746 + 0.399663i
\(375\) 0 0
\(376\) 19.6654 34.0615i 1.01417 1.75659i
\(377\) 5.40676 3.12159i 0.278462 0.160770i
\(378\) 38.3118 22.1193i 1.97054 1.13769i
\(379\) −17.5117 −0.899517 −0.449759 0.893150i \(-0.648490\pi\)
−0.449759 + 0.893150i \(0.648490\pi\)
\(380\) 0 0
\(381\) 13.1810 0.675282
\(382\) −12.6132 + 7.28226i −0.645350 + 0.372593i
\(383\) 7.02045 4.05326i 0.358728 0.207112i −0.309794 0.950804i \(-0.600260\pi\)
0.668523 + 0.743692i \(0.266927\pi\)
\(384\) 37.1601 64.3631i 1.89632 3.28452i
\(385\) 0 0
\(386\) −24.8272 + 43.0019i −1.26367 + 2.18874i
\(387\) 1.59349i 0.0810016i
\(388\) 60.8554i 3.08947i
\(389\) 8.65392 14.9890i 0.438771 0.759974i −0.558824 0.829286i \(-0.688747\pi\)
0.997595 + 0.0693125i \(0.0220805\pi\)
\(390\) 0 0
\(391\) 1.56208 0.0789976
\(392\) 11.0885i 0.560054i
\(393\) −27.0201 15.6001i −1.36298 0.786920i
\(394\) 11.1394 + 19.2940i 0.561196 + 0.972019i
\(395\) 0 0
\(396\) −1.87686 3.25081i −0.0943156 0.163359i
\(397\) 9.86354 5.69472i 0.495037 0.285810i −0.231625 0.972805i \(-0.574404\pi\)
0.726662 + 0.686996i \(0.241071\pi\)
\(398\) 3.87155i 0.194063i
\(399\) −3.07555 + 18.2679i −0.153970 + 0.914541i
\(400\) 0 0
\(401\) 4.46930 + 7.74106i 0.223186 + 0.386570i 0.955774 0.294103i \(-0.0950208\pi\)
−0.732587 + 0.680673i \(0.761687\pi\)
\(402\) 9.02339 5.20966i 0.450046 0.259834i
\(403\) −2.74844 1.58681i −0.136909 0.0790447i
\(404\) −14.8464 25.7146i −0.738634 1.27935i
\(405\) 0 0
\(406\) 76.2500 3.78422
\(407\) 5.50417i 0.272832i
\(408\) −48.0910 27.7653i −2.38086 1.37459i
\(409\) −3.27235 + 5.66788i −0.161808 + 0.280259i −0.935517 0.353282i \(-0.885066\pi\)
0.773709 + 0.633541i \(0.218399\pi\)
\(410\) 0 0
\(411\) 7.78001 0.383760
\(412\) −1.87002 1.07966i −0.0921293 0.0531909i
\(413\) −6.06780 + 3.50324i −0.298577 + 0.172383i
\(414\) −0.445681 + 0.771941i −0.0219040 + 0.0379389i
\(415\) 0 0
\(416\) −7.99086 13.8406i −0.391784 0.678590i
\(417\) 15.9991i 0.783479i
\(418\) 10.2523 + 1.72605i 0.501455 + 0.0844239i
\(419\) −21.8441 −1.06715 −0.533576 0.845752i \(-0.679152\pi\)
−0.533576 + 0.845752i \(0.679152\pi\)
\(420\) 0 0
\(421\) 14.6717 + 25.4121i 0.715054 + 1.23851i 0.962939 + 0.269720i \(0.0869311\pi\)
−0.247885 + 0.968789i \(0.579736\pi\)
\(422\) 45.1819 + 26.0858i 2.19942 + 1.26984i
\(423\) 2.65097 1.53054i 0.128894 0.0744172i
\(424\) −54.6474 + 94.6521i −2.65391 + 4.59671i
\(425\) 0 0
\(426\) −7.33299 −0.355285
\(427\) −15.6279 9.02276i −0.756286 0.436642i
\(428\) 31.2372 + 18.0348i 1.50991 + 0.871746i
\(429\) 0.829969 0.0400713
\(430\) 0 0
\(431\) 6.44336 11.1602i 0.310366 0.537570i −0.668076 0.744093i \(-0.732882\pi\)
0.978442 + 0.206524i \(0.0662151\pi\)
\(432\) 79.1011 45.6691i 3.80576 2.19725i
\(433\) 11.9883 + 6.92144i 0.576120 + 0.332623i 0.759590 0.650402i \(-0.225400\pi\)
−0.183470 + 0.983025i \(0.558733\pi\)
\(434\) −19.3802 33.5675i −0.930280 1.61129i
\(435\) 0 0
\(436\) 36.8291 1.76379
\(437\) −0.635578 1.70506i −0.0304038 0.0815641i
\(438\) 29.3418i 1.40200i
\(439\) −0.0354040 0.0613216i −0.00168974 0.00292672i 0.865179 0.501463i \(-0.167205\pi\)
−0.866869 + 0.498536i \(0.833871\pi\)
\(440\) 0 0
\(441\) 0.431503 0.747384i 0.0205477 0.0355897i
\(442\) −5.74930 + 3.31936i −0.273466 + 0.157886i
\(443\) 3.28149 + 1.89457i 0.155908 + 0.0900137i 0.575924 0.817503i \(-0.304642\pi\)
−0.420016 + 0.907517i \(0.637976\pi\)
\(444\) −53.2384 −2.52658
\(445\) 0 0
\(446\) 22.2682 38.5697i 1.05443 1.82633i
\(447\) −19.2663 11.1234i −0.911266 0.526120i
\(448\) 102.773i 4.85555i
\(449\) 26.5765 1.25422 0.627112 0.778929i \(-0.284237\pi\)
0.627112 + 0.778929i \(0.284237\pi\)
\(450\) 0 0
\(451\) −1.73553 3.00603i −0.0817230 0.141548i
\(452\) 1.43001 + 0.825616i 0.0672620 + 0.0388337i
\(453\) 27.7258 16.0075i 1.30267 0.752098i
\(454\) 36.2936 + 62.8624i 1.70334 + 2.95028i
\(455\) 0 0
\(456\) −10.7396 + 63.7902i −0.502927 + 2.98725i
\(457\) 33.1523i 1.55080i 0.631471 + 0.775400i \(0.282452\pi\)
−0.631471 + 0.775400i \(0.717548\pi\)
\(458\) −31.8445 + 18.3854i −1.48799 + 0.859094i
\(459\) −10.5348 18.2467i −0.491720 0.851684i
\(460\) 0 0
\(461\) 9.62679 + 16.6741i 0.448364 + 0.776590i 0.998280 0.0586304i \(-0.0186734\pi\)
−0.549915 + 0.835220i \(0.685340\pi\)
\(462\) 8.77861 + 5.06833i 0.408418 + 0.235800i
\(463\) 39.1713i 1.82044i 0.414120 + 0.910222i \(0.364089\pi\)
−0.414120 + 0.910222i \(0.635911\pi\)
\(464\) 157.431 7.30855
\(465\) 0 0
\(466\) −34.9019 + 60.4519i −1.61680 + 2.80038i
\(467\) 39.0650i 1.80771i 0.427836 + 0.903856i \(0.359276\pi\)
−0.427836 + 0.903856i \(0.640724\pi\)
\(468\) 2.79220i 0.129069i
\(469\) 3.60665 6.24691i 0.166540 0.288455i
\(470\) 0 0
\(471\) 1.81356 3.14118i 0.0835644 0.144738i
\(472\) −21.1882 + 12.2330i −0.975268 + 0.563071i
\(473\) 1.54154 0.890007i 0.0708800 0.0409226i
\(474\) −7.50743 −0.344828
\(475\) 0 0
\(476\) −59.7623 −2.73920
\(477\) −7.36666 + 4.25314i −0.337296 + 0.194738i
\(478\) −56.2493 + 32.4756i −2.57279 + 1.48540i
\(479\) −12.3775 + 21.4385i −0.565543 + 0.979550i 0.431455 + 0.902134i \(0.358000\pi\)
−0.996999 + 0.0774158i \(0.975333\pi\)
\(480\) 0 0
\(481\) −2.04714 + 3.54574i −0.0933413 + 0.161672i
\(482\) 23.1236i 1.05325i
\(483\) 1.77418i 0.0807280i
\(484\) −28.7400 + 49.7792i −1.30637 + 2.26269i
\(485\) 0 0
\(486\) 21.5794 0.978863
\(487\) 21.8871i 0.991797i −0.868380 0.495899i \(-0.834839\pi\)
0.868380 0.495899i \(-0.165161\pi\)
\(488\) −54.5713 31.5067i −2.47033 1.42624i
\(489\) 13.2911 + 23.0209i 0.601046 + 1.04104i
\(490\) 0 0
\(491\) −4.69777 8.13677i −0.212007 0.367207i 0.740335 0.672238i \(-0.234667\pi\)
−0.952343 + 0.305030i \(0.901333\pi\)
\(492\) 29.0754 16.7867i 1.31082 0.756803i
\(493\) 36.3155i 1.63557i
\(494\) 5.96247 + 4.92498i 0.268264 + 0.221585i
\(495\) 0 0
\(496\) −40.0137 69.3058i −1.79667 3.11192i
\(497\) −4.39650 + 2.53832i −0.197210 + 0.113859i
\(498\) 26.5091 + 15.3050i 1.18790 + 0.685834i
\(499\) 12.4558 + 21.5740i 0.557596 + 0.965785i 0.997696 + 0.0678367i \(0.0216097\pi\)
−0.440100 + 0.897949i \(0.645057\pi\)
\(500\) 0 0
\(501\) −0.605119 −0.0270347
\(502\) 50.3278i 2.24624i
\(503\) 27.1222 + 15.6590i 1.20932 + 0.698200i 0.962610 0.270890i \(-0.0873181\pi\)
0.246707 + 0.969090i \(0.420651\pi\)
\(504\) 10.9686 18.9981i 0.488579 0.846244i
\(505\) 0 0
\(506\) −0.995699 −0.0442642
\(507\) −16.2619 9.38878i −0.722214 0.416971i
\(508\) 42.8980 24.7672i 1.90329 1.09887i
\(509\) −4.83310 + 8.37117i −0.214223 + 0.371045i −0.953032 0.302870i \(-0.902055\pi\)
0.738809 + 0.673915i \(0.235389\pi\)
\(510\) 0 0
\(511\) −10.1567 17.5919i −0.449305 0.778219i
\(512\) 80.2896i 3.54833i
\(513\) −15.6306 + 18.9233i −0.690106 + 0.835484i
\(514\) −38.8874 −1.71525
\(515\) 0 0
\(516\) 8.60848 + 14.9103i 0.378967 + 0.656390i
\(517\) 2.96127 + 1.70969i 0.130237 + 0.0751922i
\(518\) −43.3052 + 25.0023i −1.90272 + 1.09854i
\(519\) 13.4429 23.2839i 0.590080 1.02205i
\(520\) 0 0
\(521\) −0.982633 −0.0430499 −0.0215250 0.999768i \(-0.506852\pi\)
−0.0215250 + 0.999768i \(0.506852\pi\)
\(522\) 17.9463 + 10.3613i 0.785488 + 0.453502i
\(523\) −34.3993 19.8604i −1.50418 0.868436i −0.999988 0.00484172i \(-0.998459\pi\)
−0.504187 0.863594i \(-0.668208\pi\)
\(524\) −117.251 −5.12212
\(525\) 0 0
\(526\) 8.84043 15.3121i 0.385461 0.667638i
\(527\) −15.9872 + 9.23020i −0.696413 + 0.402074i
\(528\) 18.1249 + 10.4644i 0.788786 + 0.455406i
\(529\) −11.4129 19.7677i −0.496211 0.859463i
\(530\) 0 0
\(531\) −1.90417 −0.0826337
\(532\) 24.3161 + 65.2327i 1.05424 + 2.82820i
\(533\) 2.58195i 0.111837i
\(534\) 9.14680 + 15.8427i 0.395821 + 0.685582i
\(535\) 0 0
\(536\) 12.5941 21.8137i 0.543984 0.942208i
\(537\) −26.0376 + 15.0328i −1.12360 + 0.648713i
\(538\) −42.9720 24.8099i −1.85266 1.06963i
\(539\) 0.964024 0.0415234
\(540\) 0 0
\(541\) −15.3887 + 26.6541i −0.661614 + 1.14595i 0.318577 + 0.947897i \(0.396795\pi\)
−0.980191 + 0.198052i \(0.936538\pi\)
\(542\) 28.3801 + 16.3852i 1.21903 + 0.703807i
\(543\) 25.5280i 1.09551i
\(544\) −92.9629 −3.98575
\(545\) 0 0
\(546\) 3.77007 + 6.52996i 0.161344 + 0.279456i
\(547\) −15.4722 8.93287i −0.661543 0.381942i 0.131322 0.991340i \(-0.458078\pi\)
−0.792865 + 0.609398i \(0.791411\pi\)
\(548\) 25.3203 14.6187i 1.08163 0.624480i
\(549\) −2.45213 4.24722i −0.104654 0.181267i
\(550\) 0 0
\(551\) −39.6397 + 14.7761i −1.68871 + 0.629482i
\(552\) 6.19529i 0.263689i
\(553\) −4.50109 + 2.59870i −0.191406 + 0.110508i
\(554\) 32.5777 + 56.4263i 1.38409 + 2.39732i
\(555\) 0 0
\(556\) 30.0624 + 52.0696i 1.27493 + 2.20824i
\(557\) −9.22971 5.32878i −0.391075 0.225787i 0.291551 0.956555i \(-0.405829\pi\)
−0.682626 + 0.730768i \(0.739162\pi\)
\(558\) 10.5340i 0.445939i
\(559\) 1.32406 0.0560019
\(560\) 0 0
\(561\) 2.41389 4.18098i 0.101915 0.176521i
\(562\) 38.0863i 1.60657i
\(563\) 7.75961i 0.327029i 0.986541 + 0.163514i \(0.0522830\pi\)
−0.986541 + 0.163514i \(0.947717\pi\)
\(564\) −16.5368 + 28.6425i −0.696324 + 1.20607i
\(565\) 0 0
\(566\) 16.2135 28.0826i 0.681504 1.18040i
\(567\) −14.9946 + 8.65716i −0.629716 + 0.363567i
\(568\) −15.3522 + 8.86361i −0.644165 + 0.371909i
\(569\) −5.72754 −0.240111 −0.120056 0.992767i \(-0.538307\pi\)
−0.120056 + 0.992767i \(0.538307\pi\)
\(570\) 0 0
\(571\) −20.8347 −0.871903 −0.435952 0.899970i \(-0.643588\pi\)
−0.435952 + 0.899970i \(0.643588\pi\)
\(572\) 2.70116 1.55952i 0.112941 0.0652067i
\(573\) 6.82300 3.93926i 0.285035 0.164565i
\(574\) 15.7671 27.3093i 0.658104 1.13987i
\(575\) 0 0
\(576\) 13.9654 24.1887i 0.581890 1.00786i
\(577\) 5.11190i 0.212811i 0.994323 + 0.106406i \(0.0339342\pi\)
−0.994323 + 0.106406i \(0.966066\pi\)
\(578\) 8.27001i 0.343987i
\(579\) 13.4300 23.2614i 0.558131 0.966712i
\(580\) 0 0
\(581\) 21.1914 0.879167
\(582\) 44.6619i 1.85130i
\(583\) −8.22896 4.75099i −0.340809 0.196766i
\(584\) −35.4663 61.4294i −1.46760 2.54197i
\(585\) 0 0
\(586\) 37.3127 + 64.6275i 1.54137 + 2.66974i
\(587\) 9.23984 5.33462i 0.381369 0.220184i −0.297045 0.954864i \(-0.596001\pi\)
0.678414 + 0.734680i \(0.262668\pi\)
\(588\) 9.32439i 0.384531i
\(589\) 16.5800 + 13.6950i 0.683165 + 0.564292i
\(590\) 0 0
\(591\) −6.02574 10.4369i −0.247866 0.429316i
\(592\) −89.4110 + 51.6215i −3.67477 + 2.12163i
\(593\) 14.7247 + 8.50133i 0.604673 + 0.349108i 0.770878 0.636983i \(-0.219818\pi\)
−0.166205 + 0.986091i \(0.553151\pi\)
\(594\) 6.71507 + 11.6308i 0.275523 + 0.477219i
\(595\) 0 0
\(596\) −83.6040 −3.42455
\(597\) 2.09427i 0.0857128i
\(598\) −0.641421 0.370325i −0.0262297 0.0151437i
\(599\) 14.3375 24.8334i 0.585816 1.01466i −0.408957 0.912554i \(-0.634107\pi\)
0.994773 0.102110i \(-0.0325592\pi\)
\(600\) 0 0
\(601\) 27.4370 1.11918 0.559590 0.828770i \(-0.310959\pi\)
0.559590 + 0.828770i \(0.310959\pi\)
\(602\) 14.0046 + 8.08559i 0.570787 + 0.329544i
\(603\) 1.69773 0.980187i 0.0691371 0.0399163i
\(604\) 60.1564 104.194i 2.44773 4.23959i
\(605\) 0 0
\(606\) 10.8958 + 18.8720i 0.442611 + 0.766624i
\(607\) 17.7547i 0.720639i 0.932829 + 0.360320i \(0.117332\pi\)
−0.932829 + 0.360320i \(0.882668\pi\)
\(608\) 37.8248 + 101.472i 1.53400 + 4.11524i
\(609\) −41.2466 −1.67140
\(610\) 0 0
\(611\) 1.27175 + 2.20274i 0.0514496 + 0.0891133i
\(612\) −14.0657 8.12086i −0.568574 0.328266i
\(613\) 29.9983 17.3196i 1.21162 0.699530i 0.248509 0.968629i \(-0.420059\pi\)
0.963112 + 0.269099i \(0.0867260\pi\)
\(614\) 12.1880 21.1102i 0.491868 0.851940i
\(615\) 0 0
\(616\) 24.5050 0.987334
\(617\) 3.86740 + 2.23284i 0.155696 + 0.0898909i 0.575824 0.817574i \(-0.304681\pi\)
−0.420128 + 0.907465i \(0.638015\pi\)
\(618\) 1.37241 + 0.792362i 0.0552065 + 0.0318735i
\(619\) 17.9112 0.719913 0.359957 0.932969i \(-0.382791\pi\)
0.359957 + 0.932969i \(0.382791\pi\)
\(620\) 0 0
\(621\) 1.17531 2.03570i 0.0471636 0.0816898i
\(622\) 1.55610 0.898414i 0.0623939 0.0360231i
\(623\) 10.9679 + 6.33234i 0.439421 + 0.253700i
\(624\) 7.78396 + 13.4822i 0.311608 + 0.539720i
\(625\) 0 0
\(626\) −8.17906 −0.326901
\(627\) −5.54586 0.933688i −0.221480 0.0372879i
\(628\) 13.6308i 0.543927i
\(629\) 11.9078 + 20.6250i 0.474796 + 0.822371i
\(630\) 0 0
\(631\) −2.48440 + 4.30311i −0.0989026 + 0.171304i −0.911231 0.411896i \(-0.864867\pi\)
0.812328 + 0.583201i \(0.198200\pi\)
\(632\) −15.7174 + 9.07446i −0.625205 + 0.360963i
\(633\) −24.4407 14.1108i −0.971429 0.560855i
\(634\) 28.6278 1.13696
\(635\) 0 0
\(636\) 45.9534 79.5935i 1.82217 3.15609i
\(637\) 0.621016 + 0.358544i 0.0246056 + 0.0142060i
\(638\) 23.1483i 0.916449i
\(639\) −1.37969 −0.0545796
\(640\) 0 0
\(641\) 18.9760 + 32.8675i 0.749508 + 1.29819i 0.948059 + 0.318096i \(0.103043\pi\)
−0.198550 + 0.980091i \(0.563623\pi\)
\(642\) −22.9251 13.2358i −0.904780 0.522375i
\(643\) 30.5276 17.6251i 1.20389 0.695067i 0.242473 0.970158i \(-0.422042\pi\)
0.961418 + 0.275092i \(0.0887082\pi\)
\(644\) −3.33370 5.77413i −0.131366 0.227533i
\(645\) 0 0
\(646\) 42.1510 15.7122i 1.65841 0.618188i
\(647\) 35.5219i 1.39651i −0.715850 0.698254i \(-0.753960\pi\)
0.715850 0.698254i \(-0.246040\pi\)
\(648\) −52.3601 + 30.2301i −2.05690 + 1.18755i
\(649\) −1.06353 1.84209i −0.0417471 0.0723082i
\(650\) 0 0
\(651\) 10.4835 + 18.1580i 0.410881 + 0.711667i
\(652\) 86.5130 + 49.9483i 3.38811 + 1.95613i
\(653\) 8.02411i 0.314008i 0.987598 + 0.157004i \(0.0501835\pi\)
−0.987598 + 0.157004i \(0.949816\pi\)
\(654\) −27.0290 −1.05692
\(655\) 0 0
\(656\) 32.5538 56.3848i 1.27101 2.20146i
\(657\) 5.52059i 0.215379i
\(658\) 31.0646i 1.21102i
\(659\) −23.6098 + 40.8933i −0.919706 + 1.59298i −0.119844 + 0.992793i \(0.538240\pi\)
−0.799861 + 0.600185i \(0.795094\pi\)
\(660\) 0 0
\(661\) 13.0580 22.6171i 0.507896 0.879702i −0.492062 0.870560i \(-0.663757\pi\)
0.999958 0.00914181i \(-0.00290997\pi\)
\(662\) −36.0479 + 20.8123i −1.40104 + 0.808892i
\(663\) 3.11002 1.79557i 0.120783 0.0697342i
\(664\) 73.9986 2.87170
\(665\) 0 0
\(666\) −13.5898 −0.526596
\(667\) 3.50874 2.02577i 0.135859 0.0784383i
\(668\) −1.96938 + 1.13702i −0.0761978 + 0.0439928i
\(669\) −12.0458 + 20.8639i −0.465716 + 0.806643i
\(670\) 0 0
\(671\) 2.73917 4.74437i 0.105744 0.183154i
\(672\) 105.586i 4.07306i
\(673\) 15.3820i 0.592931i 0.955044 + 0.296466i \(0.0958080\pi\)
−0.955044 + 0.296466i \(0.904192\pi\)
\(674\) 21.7848 37.7324i 0.839119 1.45340i
\(675\) 0 0
\(676\) −70.5664 −2.71409
\(677\) 24.4763i 0.940701i −0.882480 0.470350i \(-0.844128\pi\)
0.882480 0.470350i \(-0.155872\pi\)
\(678\) −1.04949 0.605921i −0.0403053 0.0232703i
\(679\) 15.4598 + 26.7771i 0.593291 + 1.02761i
\(680\) 0 0
\(681\) −19.6326 34.0047i −0.752324 1.30306i
\(682\) 10.1906 5.88352i 0.390217 0.225292i
\(683\) 17.8502i 0.683018i −0.939879 0.341509i \(-0.889062\pi\)
0.939879 0.341509i \(-0.110938\pi\)
\(684\) −3.14113 + 18.6575i −0.120104 + 0.713386i
\(685\) 0 0
\(686\) −23.1191 40.0434i −0.882689 1.52886i
\(687\) 17.2259 9.94538i 0.657210 0.379440i
\(688\) 28.9150 + 16.6941i 1.10237 + 0.636455i
\(689\) −3.53402 6.12110i −0.134635 0.233195i
\(690\) 0 0
\(691\) −9.27242 −0.352739 −0.176370 0.984324i \(-0.556435\pi\)
−0.176370 + 0.984324i \(0.556435\pi\)
\(692\) 101.038i 3.84087i
\(693\) 1.65168 + 0.953597i 0.0627421 + 0.0362241i
\(694\) −29.4448 + 50.9999i −1.11771 + 1.93593i
\(695\) 0 0
\(696\) −144.030 −5.45943
\(697\) −13.0066 7.50937i −0.492660 0.284438i
\(698\) −77.3633 + 44.6657i −2.92824 + 1.69062i
\(699\) 18.8798 32.7008i 0.714100 1.23686i
\(700\) 0 0
\(701\) 3.84453 + 6.65892i 0.145206 + 0.251504i 0.929450 0.368949i \(-0.120282\pi\)
−0.784244 + 0.620453i \(0.786949\pi\)
\(702\) 9.98999i 0.377048i
\(703\) 17.6678 21.3897i 0.666354 0.806728i
\(704\) 31.2001 1.17590
\(705\) 0 0
\(706\) −1.00748 1.74501i −0.0379170 0.0656742i
\(707\) 13.0651 + 7.54316i 0.491365 + 0.283690i
\(708\) 17.8173 10.2868i 0.669616 0.386603i
\(709\) 12.2187 21.1635i 0.458885 0.794812i −0.540018 0.841654i \(-0.681582\pi\)
0.998902 + 0.0468421i \(0.0149158\pi\)
\(710\) 0 0
\(711\) −1.41251 −0.0529732
\(712\) 38.2992 + 22.1120i 1.43532 + 0.828683i
\(713\) −1.78361 1.02977i −0.0667968 0.0385652i
\(714\) 43.8597 1.64141
\(715\) 0 0
\(716\) −56.4935 + 97.8496i −2.11126 + 3.65681i
\(717\) 30.4275 17.5673i 1.13633 0.656063i
\(718\) 64.1305 + 37.0258i 2.39333 + 1.38179i
\(719\) −11.0563 19.1501i −0.412331 0.714178i 0.582813 0.812606i \(-0.301952\pi\)
−0.995144 + 0.0984282i \(0.968619\pi\)
\(720\) 0 0
\(721\) 1.09711 0.0408584
\(722\) −34.3008 39.6163i −1.27655 1.47437i
\(723\) 12.5085i 0.465195i
\(724\) −47.9672 83.0817i −1.78269 3.08771i
\(725\) 0 0
\(726\) 21.0924 36.5331i 0.782812 1.35587i
\(727\) 25.1575 14.5247i 0.933042 0.538692i 0.0452694 0.998975i \(-0.485585\pi\)
0.887772 + 0.460283i \(0.152252\pi\)
\(728\) 15.7859 + 9.11400i 0.585065 + 0.337787i
\(729\) −29.9075 −1.10768
\(730\) 0 0
\(731\) 3.85092 6.66999i 0.142431 0.246698i
\(732\) 45.8893 + 26.4942i 1.69612 + 0.979254i
\(733\) 14.5428i 0.537151i 0.963259 + 0.268576i \(0.0865529\pi\)
−0.963259 + 0.268576i \(0.913447\pi\)
\(734\) 63.3360 2.33777
\(735\) 0 0
\(736\) −5.18571 8.98191i −0.191148 0.331078i
\(737\) 1.89646 + 1.09492i 0.0698570 + 0.0403320i
\(738\) 7.42191 4.28504i 0.273204 0.157735i
\(739\) −2.37798 4.11878i −0.0874754 0.151512i 0.818968 0.573839i \(-0.194547\pi\)
−0.906443 + 0.422327i \(0.861213\pi\)
\(740\) 0 0
\(741\) −3.22533 2.66411i −0.118486 0.0978687i
\(742\) 86.3242i 3.16906i
\(743\) 5.08968 2.93853i 0.186722 0.107804i −0.403725 0.914880i \(-0.632285\pi\)
0.590447 + 0.807076i \(0.298951\pi\)
\(744\) 36.6076 + 63.4062i 1.34210 + 2.32458i
\(745\) 0 0
\(746\) −40.7228 70.5339i −1.49097 2.58243i
\(747\) 4.98763 + 2.87961i 0.182488 + 0.105359i
\(748\) 18.1429i 0.663370i
\(749\) −18.3263 −0.669629
\(750\) 0 0
\(751\) −0.810481 + 1.40379i −0.0295749 + 0.0512252i −0.880434 0.474169i \(-0.842749\pi\)
0.850859 + 0.525394i \(0.176082\pi\)
\(752\) 64.1382i 2.33888i
\(753\) 27.2243i 0.992107i
\(754\) −8.60941 + 14.9119i −0.313536 + 0.543060i
\(755\) 0 0
\(756\) −44.9654 + 77.8824i −1.63538 + 2.83255i
\(757\) 24.3470 14.0567i 0.884907 0.510901i 0.0126336 0.999920i \(-0.495978\pi\)
0.872273 + 0.489019i \(0.162645\pi\)
\(758\) 41.8270 24.1488i 1.51922 0.877125i
\(759\) 0.538612 0.0195504
\(760\) 0 0
\(761\) 20.1663 0.731027 0.365514 0.930806i \(-0.380893\pi\)
0.365514 + 0.930806i \(0.380893\pi\)
\(762\) −31.4829 + 18.1767i −1.14051 + 0.658472i
\(763\) −16.2052 + 9.35610i −0.586669 + 0.338713i
\(764\) 14.8038 25.6409i 0.535583 0.927656i
\(765\) 0 0
\(766\) −11.1790 + 19.3625i −0.403912 + 0.699597i
\(767\) 1.58221i 0.0571303i
\(768\) 97.3257i 3.51194i
\(769\) 22.6524 39.2350i 0.816865 1.41485i −0.0911160 0.995840i \(-0.529043\pi\)
0.907981 0.419011i \(-0.137623\pi\)
\(770\) 0 0
\(771\) 21.0357 0.757583
\(772\) 100.940i 3.63292i
\(773\) 17.4731 + 10.0881i 0.628462 + 0.362843i 0.780156 0.625585i \(-0.215139\pi\)
−0.151694 + 0.988428i \(0.548473\pi\)
\(774\) 2.19744 + 3.80607i 0.0789852 + 0.136806i
\(775\) 0 0
\(776\) 53.9842 + 93.5034i 1.93792 + 3.35658i
\(777\) 23.4255 13.5247i 0.840385 0.485196i
\(778\) 47.7353i 1.71139i