Properties

Label 99.3.l.a.71.4
Level $99$
Weight $3$
Character 99.71
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 99 = 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 99.l (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.69755461717\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 71.4
Character \(\chi\) \(=\) 99.71
Dual form 99.3.l.a.53.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.296118 + 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(5.65537 + 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(1.44634 - 1.99072i) q^{8} +O(q^{10})\) \(q+(-0.296118 + 0.0962144i) q^{2} +(-3.15764 + 2.29416i) q^{4} +(5.65537 + 1.83754i) q^{5} +(-7.01499 + 5.09669i) q^{7} +(1.44634 - 1.99072i) q^{8} -1.85145 q^{10} +(0.122358 + 10.9993i) q^{11} +(5.77807 + 17.7831i) q^{13} +(1.58689 - 2.18416i) q^{14} +(4.58769 - 14.1195i) q^{16} +(9.12965 + 2.96640i) q^{17} +(-4.66262 - 3.38759i) q^{19} +(-22.0732 + 7.17203i) q^{20} +(-1.09453 - 3.24532i) q^{22} -41.5830i q^{23} +(8.38122 + 6.08931i) q^{25} +(-3.42197 - 4.70994i) q^{26} +(10.4582 - 32.1870i) q^{28} +(10.2118 + 14.0553i) q^{29} +(-4.22647 - 13.0077i) q^{31} +14.4651i q^{32} -2.98886 q^{34} +(-49.0378 + 15.9333i) q^{35} +(5.83617 - 4.24023i) q^{37} +(1.70662 + 0.554514i) q^{38} +(11.8376 - 8.60055i) q^{40} +(31.2326 - 42.9880i) q^{41} +43.3682 q^{43} +(-25.6206 - 34.4512i) q^{44} +(4.00089 + 12.3135i) q^{46} +(-11.0762 + 15.2451i) q^{47} +(8.09204 - 24.9047i) q^{49} +(-3.06770 - 0.996758i) q^{50} +(-59.0422 - 42.8967i) q^{52} +(51.8817 - 16.8574i) q^{53} +(-19.5197 + 62.4300i) q^{55} +21.3365i q^{56} +(-4.37620 - 3.17949i) q^{58} +(20.7671 + 28.5835i) q^{59} +(-36.4184 + 112.084i) q^{61} +(2.50306 + 3.44517i) q^{62} +(16.9590 + 52.1945i) q^{64} +111.187i q^{65} -91.5111 q^{67} +(-35.6335 + 11.5780i) q^{68} +(12.9879 - 9.43628i) q^{70} +(110.147 + 35.7890i) q^{71} +(42.8336 - 31.1204i) q^{73} +(-1.32022 + 1.81713i) q^{74} +22.4946 q^{76} +(-56.9185 - 76.5365i) q^{77} +(0.633214 + 1.94883i) q^{79} +(51.8902 - 71.4207i) q^{80} +(-5.11246 + 15.7345i) q^{82} +(-27.4089 - 8.90568i) q^{83} +(46.1806 + 33.5522i) q^{85} +(-12.8421 + 4.17265i) q^{86} +(22.0736 + 15.6652i) q^{88} -134.980i q^{89} +(-131.168 - 95.2991i) q^{91} +(95.3981 + 131.304i) q^{92} +(1.81306 - 5.58001i) q^{94} +(-20.1440 - 27.7259i) q^{95} +(-3.08284 - 9.48799i) q^{97} +8.15330i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.296118 + 0.0962144i −0.148059 + 0.0481072i −0.382109 0.924117i \(-0.624802\pi\)
0.234050 + 0.972225i \(0.424802\pi\)
\(3\) 0 0
\(4\) −3.15764 + 2.29416i −0.789410 + 0.573540i
\(5\) 5.65537 + 1.83754i 1.13107 + 0.367508i 0.813984 0.580887i \(-0.197294\pi\)
0.317090 + 0.948396i \(0.397294\pi\)
\(6\) 0 0
\(7\) −7.01499 + 5.09669i −1.00214 + 0.728099i −0.962546 0.271117i \(-0.912607\pi\)
−0.0395956 + 0.999216i \(0.512607\pi\)
\(8\) 1.44634 1.99072i 0.180793 0.248840i
\(9\) 0 0
\(10\) −1.85145 −0.185145
\(11\) 0.122358 + 10.9993i 0.0111235 + 0.999938i
\(12\) 0 0
\(13\) 5.77807 + 17.7831i 0.444467 + 1.36793i 0.883067 + 0.469246i \(0.155474\pi\)
−0.438601 + 0.898682i \(0.644526\pi\)
\(14\) 1.58689 2.18416i 0.113349 0.156012i
\(15\) 0 0
\(16\) 4.58769 14.1195i 0.286731 0.882467i
\(17\) 9.12965 + 2.96640i 0.537038 + 0.174494i 0.564964 0.825116i \(-0.308890\pi\)
−0.0279257 + 0.999610i \(0.508890\pi\)
\(18\) 0 0
\(19\) −4.66262 3.38759i −0.245401 0.178294i 0.458285 0.888805i \(-0.348464\pi\)
−0.703686 + 0.710511i \(0.748464\pi\)
\(20\) −22.0732 + 7.17203i −1.10366 + 0.358601i
\(21\) 0 0
\(22\) −1.09453 3.24532i −0.0497512 0.147514i
\(23\) 41.5830i 1.80796i −0.427578 0.903979i \(-0.640633\pi\)
0.427578 0.903979i \(-0.359367\pi\)
\(24\) 0 0
\(25\) 8.38122 + 6.08931i 0.335249 + 0.243572i
\(26\) −3.42197 4.70994i −0.131614 0.181152i
\(27\) 0 0
\(28\) 10.4582 32.1870i 0.373507 1.14954i
\(29\) 10.2118 + 14.0553i 0.352129 + 0.484665i 0.947935 0.318464i \(-0.103167\pi\)
−0.595805 + 0.803129i \(0.703167\pi\)
\(30\) 0 0
\(31\) −4.22647 13.0077i −0.136338 0.419604i 0.859458 0.511206i \(-0.170801\pi\)
−0.995796 + 0.0916020i \(0.970801\pi\)
\(32\) 14.4651i 0.452034i
\(33\) 0 0
\(34\) −2.98886 −0.0879076
\(35\) −49.0378 + 15.9333i −1.40108 + 0.455238i
\(36\) 0 0
\(37\) 5.83617 4.24023i 0.157734 0.114601i −0.506118 0.862464i \(-0.668920\pi\)
0.663853 + 0.747863i \(0.268920\pi\)
\(38\) 1.70662 + 0.554514i 0.0449110 + 0.0145925i
\(39\) 0 0
\(40\) 11.8376 8.60055i 0.295941 0.215014i
\(41\) 31.2326 42.9880i 0.761771 1.04849i −0.235294 0.971924i \(-0.575605\pi\)
0.997065 0.0765632i \(-0.0243947\pi\)
\(42\) 0 0
\(43\) 43.3682 1.00856 0.504282 0.863539i \(-0.331757\pi\)
0.504282 + 0.863539i \(0.331757\pi\)
\(44\) −25.6206 34.4512i −0.582285 0.782981i
\(45\) 0 0
\(46\) 4.00089 + 12.3135i 0.0869758 + 0.267684i
\(47\) −11.0762 + 15.2451i −0.235663 + 0.324363i −0.910426 0.413672i \(-0.864246\pi\)
0.674763 + 0.738035i \(0.264246\pi\)
\(48\) 0 0
\(49\) 8.09204 24.9047i 0.165144 0.508260i
\(50\) −3.06770 0.996758i −0.0613541 0.0199352i
\(51\) 0 0
\(52\) −59.0422 42.8967i −1.13543 0.824937i
\(53\) 51.8817 16.8574i 0.978899 0.318064i 0.224496 0.974475i \(-0.427926\pi\)
0.754403 + 0.656411i \(0.227926\pi\)
\(54\) 0 0
\(55\) −19.5197 + 62.4300i −0.354904 + 1.13509i
\(56\) 21.3365i 0.381008i
\(57\) 0 0
\(58\) −4.37620 3.17949i −0.0754517 0.0548189i
\(59\) 20.7671 + 28.5835i 0.351985 + 0.484466i 0.947894 0.318586i \(-0.103208\pi\)
−0.595909 + 0.803052i \(0.703208\pi\)
\(60\) 0 0
\(61\) −36.4184 + 112.084i −0.597023 + 1.83745i −0.0526365 + 0.998614i \(0.516762\pi\)
−0.544387 + 0.838834i \(0.683238\pi\)
\(62\) 2.50306 + 3.44517i 0.0403720 + 0.0555673i
\(63\) 0 0
\(64\) 16.9590 + 52.1945i 0.264985 + 0.815539i
\(65\) 111.187i 1.71057i
\(66\) 0 0
\(67\) −91.5111 −1.36584 −0.682919 0.730494i \(-0.739290\pi\)
−0.682919 + 0.730494i \(0.739290\pi\)
\(68\) −35.6335 + 11.5780i −0.524022 + 0.170265i
\(69\) 0 0
\(70\) 12.9879 9.43628i 0.185542 0.134804i
\(71\) 110.147 + 35.7890i 1.55137 + 0.504070i 0.954485 0.298258i \(-0.0964057\pi\)
0.596883 + 0.802328i \(0.296406\pi\)
\(72\) 0 0
\(73\) 42.8336 31.1204i 0.586762 0.426307i −0.254394 0.967101i \(-0.581876\pi\)
0.841156 + 0.540793i \(0.181876\pi\)
\(74\) −1.32022 + 1.81713i −0.0178408 + 0.0245558i
\(75\) 0 0
\(76\) 22.4946 0.295981
\(77\) −56.9185 76.5365i −0.739201 0.993981i
\(78\) 0 0
\(79\) 0.633214 + 1.94883i 0.00801537 + 0.0246688i 0.954984 0.296657i \(-0.0958717\pi\)
−0.946969 + 0.321325i \(0.895872\pi\)
\(80\) 51.8902 71.4207i 0.648627 0.892759i
\(81\) 0 0
\(82\) −5.11246 + 15.7345i −0.0623470 + 0.191884i
\(83\) −27.4089 8.90568i −0.330227 0.107297i 0.139211 0.990263i \(-0.455543\pi\)
−0.469438 + 0.882965i \(0.655543\pi\)
\(84\) 0 0
\(85\) 46.1806 + 33.5522i 0.543302 + 0.394732i
\(86\) −12.8421 + 4.17265i −0.149327 + 0.0485192i
\(87\) 0 0
\(88\) 22.0736 + 15.6652i 0.250836 + 0.178014i
\(89\) 134.980i 1.51663i −0.651891 0.758313i \(-0.726024\pi\)
0.651891 0.758313i \(-0.273976\pi\)
\(90\) 0 0
\(91\) −131.168 95.2991i −1.44141 1.04724i
\(92\) 95.3981 + 131.304i 1.03694 + 1.42722i
\(93\) 0 0
\(94\) 1.81306 5.58001i 0.0192878 0.0593619i
\(95\) −20.1440 27.7259i −0.212042 0.291851i
\(96\) 0 0
\(97\) −3.08284 9.48799i −0.0317818 0.0978144i 0.933907 0.357515i \(-0.116376\pi\)
−0.965689 + 0.259701i \(0.916376\pi\)
\(98\) 8.15330i 0.0831970i
\(99\) 0 0
\(100\) −40.4347 −0.404347
\(101\) −163.987 + 53.2825i −1.62363 + 0.527550i −0.972795 0.231668i \(-0.925582\pi\)
−0.650837 + 0.759218i \(0.725582\pi\)
\(102\) 0 0
\(103\) 91.9355 66.7951i 0.892578 0.648496i −0.0439711 0.999033i \(-0.514001\pi\)
0.936549 + 0.350537i \(0.114001\pi\)
\(104\) 43.7582 + 14.2179i 0.420752 + 0.136711i
\(105\) 0 0
\(106\) −13.7411 + 9.98353i −0.129633 + 0.0941842i
\(107\) −48.8875 + 67.2879i −0.456893 + 0.628859i −0.973861 0.227146i \(-0.927061\pi\)
0.516968 + 0.856005i \(0.327061\pi\)
\(108\) 0 0
\(109\) 125.432 1.15075 0.575377 0.817888i \(-0.304855\pi\)
0.575377 + 0.817888i \(0.304855\pi\)
\(110\) −0.226540 20.3647i −0.00205945 0.185134i
\(111\) 0 0
\(112\) 39.7799 + 122.430i 0.355178 + 1.09313i
\(113\) 59.4756 81.8612i 0.526333 0.724435i −0.460233 0.887798i \(-0.652234\pi\)
0.986566 + 0.163363i \(0.0522342\pi\)
\(114\) 0 0
\(115\) 76.4105 235.167i 0.664439 2.04493i
\(116\) −64.4901 20.9541i −0.555949 0.180639i
\(117\) 0 0
\(118\) −8.89966 6.46598i −0.0754208 0.0547964i
\(119\) −79.1632 + 25.7217i −0.665237 + 0.216149i
\(120\) 0 0
\(121\) −120.970 + 2.69171i −0.999753 + 0.0222455i
\(122\) 36.6941i 0.300771i
\(123\) 0 0
\(124\) 43.1875 + 31.3775i 0.348286 + 0.253045i
\(125\) −51.1707 70.4305i −0.409366 0.563444i
\(126\) 0 0
\(127\) 38.3169 117.927i 0.301708 0.928561i −0.679178 0.733974i \(-0.737663\pi\)
0.980885 0.194587i \(-0.0623366\pi\)
\(128\) −44.0532 60.6340i −0.344166 0.473703i
\(129\) 0 0
\(130\) −10.6978 32.9245i −0.0822909 0.253265i
\(131\) 52.5607i 0.401227i 0.979670 + 0.200614i \(0.0642935\pi\)
−0.979670 + 0.200614i \(0.935706\pi\)
\(132\) 0 0
\(133\) 49.9738 0.375743
\(134\) 27.0980 8.80469i 0.202224 0.0657066i
\(135\) 0 0
\(136\) 19.1099 13.8841i 0.140514 0.102089i
\(137\) 119.626 + 38.8689i 0.873185 + 0.283715i 0.711125 0.703066i \(-0.248186\pi\)
0.162060 + 0.986781i \(0.448186\pi\)
\(138\) 0 0
\(139\) −43.4005 + 31.5323i −0.312234 + 0.226851i −0.732855 0.680385i \(-0.761812\pi\)
0.420620 + 0.907237i \(0.361812\pi\)
\(140\) 118.290 162.812i 0.844928 1.16294i
\(141\) 0 0
\(142\) −36.0599 −0.253943
\(143\) −194.895 + 65.7307i −1.36290 + 0.459655i
\(144\) 0 0
\(145\) 31.9241 + 98.2523i 0.220166 + 0.677602i
\(146\) −9.68955 + 13.3365i −0.0663668 + 0.0913460i
\(147\) 0 0
\(148\) −8.70077 + 26.7782i −0.0587890 + 0.180934i
\(149\) −4.02993 1.30940i −0.0270465 0.00878795i 0.295462 0.955354i \(-0.404526\pi\)
−0.322509 + 0.946566i \(0.604526\pi\)
\(150\) 0 0
\(151\) −76.3610 55.4795i −0.505702 0.367414i 0.305489 0.952196i \(-0.401180\pi\)
−0.811191 + 0.584782i \(0.801180\pi\)
\(152\) −13.4875 + 4.38236i −0.0887336 + 0.0288313i
\(153\) 0 0
\(154\) 24.2185 + 17.1874i 0.157263 + 0.111607i
\(155\) 81.3299i 0.524709i
\(156\) 0 0
\(157\) 120.287 + 87.3939i 0.766162 + 0.556649i 0.900794 0.434247i \(-0.142985\pi\)
−0.134632 + 0.990896i \(0.542985\pi\)
\(158\) −0.375011 0.516159i −0.00237349 0.00326683i
\(159\) 0 0
\(160\) −26.5802 + 81.8054i −0.166126 + 0.511284i
\(161\) 211.936 + 291.705i 1.31637 + 1.81183i
\(162\) 0 0
\(163\) −28.3527 87.2606i −0.173943 0.535341i 0.825641 0.564196i \(-0.190814\pi\)
−0.999584 + 0.0288552i \(0.990814\pi\)
\(164\) 207.393i 1.26459i
\(165\) 0 0
\(166\) 8.97310 0.0540548
\(167\) −13.5693 + 4.40895i −0.0812536 + 0.0264009i −0.349362 0.936988i \(-0.613602\pi\)
0.268108 + 0.963389i \(0.413602\pi\)
\(168\) 0 0
\(169\) −146.127 + 106.168i −0.864660 + 0.628212i
\(170\) −16.9031 5.49215i −0.0994300 0.0323068i
\(171\) 0 0
\(172\) −136.941 + 99.4936i −0.796170 + 0.578451i
\(173\) 136.531 187.919i 0.789197 1.08624i −0.205011 0.978760i \(-0.565723\pi\)
0.994208 0.107476i \(-0.0342770\pi\)
\(174\) 0 0
\(175\) −89.8295 −0.513312
\(176\) 155.866 + 48.7339i 0.885601 + 0.276897i
\(177\) 0 0
\(178\) 12.9870 + 39.9698i 0.0729606 + 0.224550i
\(179\) −84.4401 + 116.222i −0.471733 + 0.649284i −0.976890 0.213743i \(-0.931434\pi\)
0.505157 + 0.863027i \(0.331434\pi\)
\(180\) 0 0
\(181\) −74.0732 + 227.974i −0.409244 + 1.25952i 0.508055 + 0.861324i \(0.330365\pi\)
−0.917299 + 0.398199i \(0.869635\pi\)
\(182\) 48.0103 + 15.5995i 0.263793 + 0.0857114i
\(183\) 0 0
\(184\) −82.7802 60.1433i −0.449892 0.326866i
\(185\) 40.7973 13.2558i 0.220526 0.0716532i
\(186\) 0 0
\(187\) −31.5113 + 100.783i −0.168510 + 0.538946i
\(188\) 73.5489i 0.391218i
\(189\) 0 0
\(190\) 8.63262 + 6.27197i 0.0454349 + 0.0330104i
\(191\) −22.0606 30.3638i −0.115501 0.158973i 0.747352 0.664428i \(-0.231325\pi\)
−0.862853 + 0.505455i \(0.831325\pi\)
\(192\) 0 0
\(193\) 62.9072 193.608i 0.325944 1.00315i −0.645069 0.764125i \(-0.723171\pi\)
0.971013 0.239028i \(-0.0768288\pi\)
\(194\) 1.82576 + 2.51295i 0.00941115 + 0.0129533i
\(195\) 0 0
\(196\) 31.5837 + 97.2047i 0.161141 + 0.495942i
\(197\) 208.477i 1.05826i −0.848541 0.529129i \(-0.822519\pi\)
0.848541 0.529129i \(-0.177481\pi\)
\(198\) 0 0
\(199\) −249.874 −1.25565 −0.627825 0.778355i \(-0.716055\pi\)
−0.627825 + 0.778355i \(0.716055\pi\)
\(200\) 24.2442 7.87743i 0.121221 0.0393872i
\(201\) 0 0
\(202\) 43.4328 31.5558i 0.215014 0.156217i
\(203\) −143.271 46.5515i −0.705767 0.229318i
\(204\) 0 0
\(205\) 255.624 185.722i 1.24695 0.905960i
\(206\) −20.7971 + 28.6247i −0.100957 + 0.138955i
\(207\) 0 0
\(208\) 277.595 1.33459
\(209\) 36.6907 51.7002i 0.175554 0.247369i
\(210\) 0 0
\(211\) 37.5620 + 115.604i 0.178019 + 0.547885i 0.999758 0.0219776i \(-0.00699627\pi\)
−0.821740 + 0.569863i \(0.806996\pi\)
\(212\) −125.150 + 172.254i −0.590331 + 0.812520i
\(213\) 0 0
\(214\) 8.00238 24.6288i 0.0373943 0.115088i
\(215\) 245.263 + 79.6909i 1.14076 + 0.370655i
\(216\) 0 0
\(217\) 95.9451 + 69.7082i 0.442143 + 0.321236i
\(218\) −37.1427 + 12.0684i −0.170379 + 0.0553595i
\(219\) 0 0
\(220\) −81.5883 241.913i −0.370856 1.09960i
\(221\) 179.493i 0.812186i
\(222\) 0 0
\(223\) 58.0972 + 42.2101i 0.260526 + 0.189283i 0.710379 0.703820i \(-0.248524\pi\)
−0.449853 + 0.893103i \(0.648524\pi\)
\(224\) −73.7241 101.473i −0.329125 0.453002i
\(225\) 0 0
\(226\) −9.73555 + 29.9629i −0.0430776 + 0.132579i
\(227\) −137.568 189.346i −0.606028 0.834125i 0.390216 0.920723i \(-0.372400\pi\)
−0.996243 + 0.0865981i \(0.972400\pi\)
\(228\) 0 0
\(229\) 21.0536 + 64.7964i 0.0919372 + 0.282954i 0.986443 0.164102i \(-0.0524726\pi\)
−0.894506 + 0.447056i \(0.852473\pi\)
\(230\) 76.9889i 0.334735i
\(231\) 0 0
\(232\) 42.7498 0.184267
\(233\) −101.511 + 32.9829i −0.435669 + 0.141558i −0.518637 0.854995i \(-0.673560\pi\)
0.0829673 + 0.996552i \(0.473560\pi\)
\(234\) 0 0
\(235\) −90.6533 + 65.8635i −0.385759 + 0.280270i
\(236\) −131.150 42.6133i −0.555721 0.180565i
\(237\) 0 0
\(238\) 20.9668 15.2333i 0.0880959 0.0640054i
\(239\) −204.895 + 282.014i −0.857302 + 1.17997i 0.124904 + 0.992169i \(0.460138\pi\)
−0.982206 + 0.187806i \(0.939862\pi\)
\(240\) 0 0
\(241\) −377.429 −1.56609 −0.783047 0.621962i \(-0.786336\pi\)
−0.783047 + 0.621962i \(0.786336\pi\)
\(242\) 35.5624 12.4361i 0.146952 0.0513889i
\(243\) 0 0
\(244\) −142.143 437.472i −0.582554 1.79292i
\(245\) 91.5270 125.976i 0.373580 0.514188i
\(246\) 0 0
\(247\) 33.3009 102.489i 0.134821 0.414937i
\(248\) −32.0077 10.3999i −0.129063 0.0419352i
\(249\) 0 0
\(250\) 21.9290 + 15.9323i 0.0877159 + 0.0637293i
\(251\) 286.896 93.2182i 1.14301 0.371387i 0.324506 0.945884i \(-0.394802\pi\)
0.818507 + 0.574497i \(0.194802\pi\)
\(252\) 0 0
\(253\) 457.385 5.08802i 1.80785 0.0201107i
\(254\) 38.6069i 0.151996i
\(255\) 0 0
\(256\) −158.718 115.316i −0.619994 0.450452i
\(257\) −8.80297 12.1162i −0.0342528 0.0471449i 0.791547 0.611108i \(-0.209276\pi\)
−0.825800 + 0.563963i \(0.809276\pi\)
\(258\) 0 0
\(259\) −19.3296 + 59.4903i −0.0746316 + 0.229692i
\(260\) −255.081 351.089i −0.981082 1.35034i
\(261\) 0 0
\(262\) −5.05710 15.5642i −0.0193019 0.0594052i
\(263\) 470.671i 1.78962i −0.446443 0.894812i \(-0.647309\pi\)
0.446443 0.894812i \(-0.352691\pi\)
\(264\) 0 0
\(265\) 324.386 1.22410
\(266\) −14.7981 + 4.80820i −0.0556320 + 0.0180759i
\(267\) 0 0
\(268\) 288.959 209.941i 1.07821 0.783362i
\(269\) 190.046 + 61.7497i 0.706491 + 0.229553i 0.640156 0.768245i \(-0.278870\pi\)
0.0663343 + 0.997797i \(0.478870\pi\)
\(270\) 0 0
\(271\) 70.6026 51.2958i 0.260526 0.189283i −0.449853 0.893103i \(-0.648524\pi\)
0.710379 + 0.703819i \(0.248524\pi\)
\(272\) 83.7680 115.297i 0.307971 0.423885i
\(273\) 0 0
\(274\) −39.1632 −0.142931
\(275\) −65.9528 + 92.9328i −0.239828 + 0.337937i
\(276\) 0 0
\(277\) −92.4637 284.574i −0.333804 1.02734i −0.967308 0.253604i \(-0.918384\pi\)
0.633504 0.773739i \(-0.281616\pi\)
\(278\) 9.81780 13.5130i 0.0353158 0.0486080i
\(279\) 0 0
\(280\) −39.2066 + 120.666i −0.140024 + 0.430949i
\(281\) −284.085 92.3049i −1.01098 0.328487i −0.243735 0.969842i \(-0.578373\pi\)
−0.767245 + 0.641354i \(0.778373\pi\)
\(282\) 0 0
\(283\) 165.458 + 120.212i 0.584656 + 0.424777i 0.840400 0.541967i \(-0.182320\pi\)
−0.255744 + 0.966745i \(0.582320\pi\)
\(284\) −429.911 + 139.686i −1.51377 + 0.491854i
\(285\) 0 0
\(286\) 51.3875 38.2157i 0.179676 0.133621i
\(287\) 460.743i 1.60538i
\(288\) 0 0
\(289\) −159.255 115.706i −0.551055 0.400365i
\(290\) −18.9066 26.0227i −0.0651951 0.0897333i
\(291\) 0 0
\(292\) −63.8579 + 196.534i −0.218691 + 0.673063i
\(293\) 60.4497 + 83.2019i 0.206313 + 0.283965i 0.899617 0.436680i \(-0.143846\pi\)
−0.693304 + 0.720645i \(0.743846\pi\)
\(294\) 0 0
\(295\) 64.9224 + 199.811i 0.220076 + 0.677324i
\(296\) 17.7510i 0.0599697i
\(297\) 0 0
\(298\) 1.31932 0.00442724
\(299\) 739.473 240.270i 2.47316 0.803577i
\(300\) 0 0
\(301\) −304.228 + 221.035i −1.01072 + 0.734334i
\(302\) 27.9497 + 9.08142i 0.0925488 + 0.0300709i
\(303\) 0 0
\(304\) −69.2217 + 50.2925i −0.227703 + 0.165436i
\(305\) −411.919 + 566.958i −1.35055 + 1.85888i
\(306\) 0 0
\(307\) 39.5643 0.128874 0.0644369 0.997922i \(-0.479475\pi\)
0.0644369 + 0.997922i \(0.479475\pi\)
\(308\) 355.315 + 111.095i 1.15362 + 0.360697i
\(309\) 0 0
\(310\) 7.82510 + 24.0832i 0.0252423 + 0.0776877i
\(311\) 81.9693 112.821i 0.263567 0.362769i −0.656638 0.754206i \(-0.728022\pi\)
0.920205 + 0.391437i \(0.128022\pi\)
\(312\) 0 0
\(313\) −69.8621 + 215.013i −0.223201 + 0.686943i 0.775268 + 0.631633i \(0.217615\pi\)
−0.998469 + 0.0553107i \(0.982385\pi\)
\(314\) −44.0278 14.3055i −0.140216 0.0455589i
\(315\) 0 0
\(316\) −6.47039 4.70102i −0.0204759 0.0148766i
\(317\) 334.945 108.830i 1.05661 0.343313i 0.271350 0.962481i \(-0.412530\pi\)
0.785259 + 0.619167i \(0.212530\pi\)
\(318\) 0 0
\(319\) −153.349 + 114.042i −0.480718 + 0.357499i
\(320\) 326.342i 1.01982i
\(321\) 0 0
\(322\) −90.8241 65.9876i −0.282062 0.204930i
\(323\) −32.5191 44.7587i −0.100678 0.138572i
\(324\) 0 0
\(325\) −59.8594 + 184.228i −0.184183 + 0.566856i
\(326\) 16.7914 + 23.1114i 0.0515075 + 0.0708940i
\(327\) 0 0
\(328\) −40.4040 124.351i −0.123183 0.379118i
\(329\) 163.396i 0.496644i
\(330\) 0 0
\(331\) −84.8580 −0.256369 −0.128184 0.991750i \(-0.540915\pi\)
−0.128184 + 0.991750i \(0.540915\pi\)
\(332\) 106.978 34.7594i 0.322224 0.104697i
\(333\) 0 0
\(334\) 3.59392 2.61113i 0.0107602 0.00781776i
\(335\) −517.529 168.155i −1.54486 0.501956i
\(336\) 0 0
\(337\) −426.493 + 309.865i −1.26556 + 0.919482i −0.999016 0.0443415i \(-0.985881\pi\)
−0.266542 + 0.963823i \(0.585881\pi\)
\(338\) 33.0560 45.4977i 0.0977989 0.134609i
\(339\) 0 0
\(340\) −222.796 −0.655282
\(341\) 142.559 48.0799i 0.418062 0.140997i
\(342\) 0 0
\(343\) −61.1288 188.135i −0.178218 0.548499i
\(344\) 62.7254 86.3341i 0.182341 0.250971i
\(345\) 0 0
\(346\) −22.3487 + 68.7823i −0.0645917 + 0.198793i
\(347\) 120.136 + 39.0345i 0.346212 + 0.112491i 0.476961 0.878924i \(-0.341738\pi\)
−0.130749 + 0.991416i \(0.541738\pi\)
\(348\) 0 0
\(349\) 365.235 + 265.359i 1.04652 + 0.760340i 0.971547 0.236845i \(-0.0761135\pi\)
0.0749713 + 0.997186i \(0.476113\pi\)
\(350\) 26.6001 8.64290i 0.0760003 0.0246940i
\(351\) 0 0
\(352\) −159.106 + 1.76992i −0.452006 + 0.00502818i
\(353\) 145.710i 0.412775i −0.978470 0.206388i \(-0.933829\pi\)
0.978470 0.206388i \(-0.0661708\pi\)
\(354\) 0 0
\(355\) 557.159 + 404.800i 1.56946 + 1.14028i
\(356\) 309.665 + 426.217i 0.869845 + 1.19724i
\(357\) 0 0
\(358\) 13.8220 42.5397i 0.0386089 0.118826i
\(359\) 252.282 + 347.237i 0.702736 + 0.967233i 0.999923 + 0.0124137i \(0.00395151\pi\)
−0.297187 + 0.954819i \(0.596048\pi\)
\(360\) 0 0
\(361\) −101.291 311.741i −0.280584 0.863549i
\(362\) 74.6339i 0.206171i
\(363\) 0 0
\(364\) 632.812 1.73850
\(365\) 299.425 97.2891i 0.820342 0.266545i
\(366\) 0 0
\(367\) −107.083 + 77.8000i −0.291778 + 0.211989i −0.724038 0.689760i \(-0.757716\pi\)
0.432260 + 0.901749i \(0.357716\pi\)
\(368\) −587.130 190.770i −1.59546 0.518397i
\(369\) 0 0
\(370\) −10.8054 + 7.85058i −0.0292038 + 0.0212178i
\(371\) −278.033 + 382.679i −0.749414 + 1.03148i
\(372\) 0 0
\(373\) −478.180 −1.28198 −0.640992 0.767547i \(-0.721477\pi\)
−0.640992 + 0.767547i \(0.721477\pi\)
\(374\) −0.365711 32.8754i −0.000977837 0.0879022i
\(375\) 0 0
\(376\) 14.3287 + 44.0992i 0.0381082 + 0.117285i
\(377\) −190.942 + 262.809i −0.506476 + 0.697105i
\(378\) 0 0
\(379\) −81.6441 + 251.275i −0.215420 + 0.662994i 0.783704 + 0.621135i \(0.213328\pi\)
−0.999124 + 0.0418592i \(0.986672\pi\)
\(380\) 127.215 + 41.3347i 0.334777 + 0.108775i
\(381\) 0 0
\(382\) 9.45396 + 6.86871i 0.0247486 + 0.0179809i
\(383\) 224.859 73.0612i 0.587100 0.190760i −0.000379005 1.00000i \(-0.500121\pi\)
0.587479 + 0.809240i \(0.300121\pi\)
\(384\) 0 0
\(385\) −181.256 537.432i −0.470795 1.39593i
\(386\) 63.3834i 0.164206i
\(387\) 0 0
\(388\) 31.5015 + 22.8871i 0.0811893 + 0.0589875i
\(389\) −300.486 413.583i −0.772457 1.06320i −0.996074 0.0885193i \(-0.971787\pi\)
0.223617 0.974677i \(-0.428213\pi\)
\(390\) 0 0
\(391\) 123.352 379.638i 0.315478 0.970942i
\(392\) −37.8745 52.1298i −0.0966187 0.132984i
\(393\) 0 0
\(394\) 20.0585 + 61.7336i 0.0509098 + 0.156684i
\(395\) 12.1849i 0.0308479i
\(396\) 0 0
\(397\) 389.224 0.980413 0.490207 0.871606i \(-0.336921\pi\)
0.490207 + 0.871606i \(0.336921\pi\)
\(398\) 73.9921 24.0415i 0.185910 0.0604058i
\(399\) 0 0
\(400\) 124.428 90.4024i 0.311071 0.226006i
\(401\) −214.986 69.8532i −0.536125 0.174198i 0.0284257 0.999596i \(-0.490951\pi\)
−0.564551 + 0.825398i \(0.690951\pi\)
\(402\) 0 0
\(403\) 206.897 150.319i 0.513391 0.373000i
\(404\) 395.573 544.459i 0.979140 1.34767i
\(405\) 0 0
\(406\) 46.9039 0.115527
\(407\) 47.3537 + 63.6751i 0.116348 + 0.156450i
\(408\) 0 0
\(409\) −56.1688 172.870i −0.137332 0.422664i 0.858614 0.512623i \(-0.171326\pi\)
−0.995945 + 0.0899593i \(0.971326\pi\)
\(410\) −57.8256 + 79.5902i −0.141038 + 0.194122i
\(411\) 0 0
\(412\) −137.061 + 421.829i −0.332672 + 1.02386i
\(413\) −291.363 94.6694i −0.705478 0.229224i
\(414\) 0 0
\(415\) −138.643 100.730i −0.334079 0.242722i
\(416\) −257.234 + 83.5803i −0.618350 + 0.200914i
\(417\) 0 0
\(418\) −5.89046 + 18.8395i −0.0140920 + 0.0450706i
\(419\) 171.909i 0.410284i −0.978732 0.205142i \(-0.934234\pi\)
0.978732 0.205142i \(-0.0657656\pi\)
\(420\) 0 0
\(421\) 97.7668 + 71.0318i 0.232225 + 0.168722i 0.697813 0.716280i \(-0.254157\pi\)
−0.465587 + 0.885002i \(0.654157\pi\)
\(422\) −22.2455 30.6183i −0.0527145 0.0725552i
\(423\) 0 0
\(424\) 41.4804 127.663i 0.0978311 0.301093i
\(425\) 58.4542 + 80.4553i 0.137539 + 0.189307i
\(426\) 0 0
\(427\) −315.784 971.884i −0.739542 2.27608i
\(428\) 324.627i 0.758473i
\(429\) 0 0
\(430\) −80.2942 −0.186731
\(431\) 451.082 146.565i 1.04659 0.340059i 0.265263 0.964176i \(-0.414541\pi\)
0.781331 + 0.624117i \(0.214541\pi\)
\(432\) 0 0
\(433\) −205.673 + 149.430i −0.474996 + 0.345105i −0.799385 0.600819i \(-0.794841\pi\)
0.324389 + 0.945924i \(0.394841\pi\)
\(434\) −35.1179 11.4105i −0.0809169 0.0262915i
\(435\) 0 0
\(436\) −396.070 + 287.761i −0.908416 + 0.660003i
\(437\) −140.866 + 193.886i −0.322349 + 0.443675i
\(438\) 0 0
\(439\) 515.246 1.17368 0.586841 0.809703i \(-0.300372\pi\)
0.586841 + 0.809703i \(0.300372\pi\)
\(440\) 96.0486 + 129.154i 0.218292 + 0.293531i
\(441\) 0 0
\(442\) −17.2698 53.1511i −0.0390720 0.120251i
\(443\) −309.199 + 425.576i −0.697966 + 0.960668i 0.302007 + 0.953306i \(0.402344\pi\)
−0.999973 + 0.00736244i \(0.997656\pi\)
\(444\) 0 0
\(445\) 248.031 763.360i 0.557372 1.71542i
\(446\) −21.2648 6.90936i −0.0476790 0.0154918i
\(447\) 0 0
\(448\) −384.987 279.709i −0.859345 0.624351i
\(449\) −515.338 + 167.443i −1.14775 + 0.372925i −0.820293 0.571943i \(-0.806190\pi\)
−0.327452 + 0.944868i \(0.606190\pi\)
\(450\) 0 0
\(451\) 476.660 + 338.277i 1.05690 + 0.750061i
\(452\) 394.935i 0.873749i
\(453\) 0 0
\(454\) 58.9542 + 42.8328i 0.129855 + 0.0943453i
\(455\) −566.687 779.978i −1.24547 1.71424i
\(456\) 0 0
\(457\) 37.8329 116.438i 0.0827854 0.254787i −0.901093 0.433626i \(-0.857234\pi\)
0.983878 + 0.178839i \(0.0572340\pi\)
\(458\) −12.4687 17.1617i −0.0272242 0.0374709i
\(459\) 0 0
\(460\) 298.235 + 917.871i 0.648336 + 1.99537i
\(461\) 308.300i 0.668764i −0.942438 0.334382i \(-0.891472\pi\)
0.942438 0.334382i \(-0.108528\pi\)
\(462\) 0 0
\(463\) 369.654 0.798389 0.399195 0.916866i \(-0.369290\pi\)
0.399195 + 0.916866i \(0.369290\pi\)
\(464\) 245.301 79.7032i 0.528667 0.171774i
\(465\) 0 0
\(466\) 26.8857 19.5336i 0.0576947 0.0419177i
\(467\) −103.523 33.6365i −0.221676 0.0720269i 0.196073 0.980589i \(-0.437181\pi\)
−0.417749 + 0.908562i \(0.637181\pi\)
\(468\) 0 0
\(469\) 641.950 466.404i 1.36876 0.994465i
\(470\) 20.5070 28.2255i 0.0436319 0.0600542i
\(471\) 0 0
\(472\) 86.9382 0.184191
\(473\) 5.30645 + 477.021i 0.0112187 + 1.00850i
\(474\) 0 0
\(475\) −18.4503 56.7843i −0.0388428 0.119546i
\(476\) 190.959 262.833i 0.401175 0.552170i
\(477\) 0 0
\(478\) 33.5392 103.223i 0.0701658 0.215948i
\(479\) 287.864 + 93.5328i 0.600969 + 0.195267i 0.593673 0.804707i \(-0.297677\pi\)
0.00729665 + 0.999973i \(0.497677\pi\)
\(480\) 0 0
\(481\) 109.126 + 79.2847i 0.226873 + 0.164833i
\(482\) 111.763 36.3141i 0.231874 0.0753404i
\(483\) 0 0
\(484\) 375.805 286.024i 0.776456 0.590959i
\(485\) 59.3229i 0.122315i
\(486\) 0 0
\(487\) −375.540 272.846i −0.771130 0.560258i 0.131174 0.991359i \(-0.458125\pi\)
−0.902304 + 0.431101i \(0.858125\pi\)
\(488\) 170.455 + 234.611i 0.349293 + 0.480761i
\(489\) 0 0
\(490\) −14.9820 + 46.1099i −0.0305756 + 0.0941019i
\(491\) −204.017 280.805i −0.415513 0.571905i 0.549039 0.835797i \(-0.314994\pi\)
−0.964552 + 0.263892i \(0.914994\pi\)
\(492\) 0 0
\(493\) 51.5361 + 158.612i 0.104536 + 0.321728i
\(494\) 33.5530i 0.0679210i
\(495\) 0 0
\(496\) −203.052 −0.409379
\(497\) −955.087 + 310.326i −1.92170 + 0.624399i
\(498\) 0 0
\(499\) −368.064 + 267.414i −0.737603 + 0.535900i −0.891960 0.452115i \(-0.850670\pi\)
0.154356 + 0.988015i \(0.450670\pi\)
\(500\) 323.157 + 105.000i 0.646315 + 0.210000i
\(501\) 0 0
\(502\) −75.9860 + 55.2071i −0.151367 + 0.109974i
\(503\) 243.623 335.319i 0.484341 0.666638i −0.494991 0.868898i \(-0.664829\pi\)
0.979332 + 0.202260i \(0.0648287\pi\)
\(504\) 0 0
\(505\) −1025.31 −2.03033
\(506\) −134.950 + 45.5137i −0.266700 + 0.0899480i
\(507\) 0 0
\(508\) 149.553 + 460.277i 0.294396 + 0.906056i
\(509\) −88.1735 + 121.360i −0.173229 + 0.238429i −0.886800 0.462154i \(-0.847077\pi\)
0.713571 + 0.700583i \(0.247077\pi\)
\(510\) 0 0
\(511\) −141.866 + 436.619i −0.277625 + 0.854441i
\(512\) 343.213 + 111.517i 0.670337 + 0.217806i
\(513\) 0 0
\(514\) 3.77247 + 2.74086i 0.00733943 + 0.00533241i
\(515\) 642.668 208.815i 1.24790 0.405467i
\(516\) 0 0
\(517\) −169.040 119.965i −0.326964 0.232041i
\(518\) 19.4759i 0.0375983i
\(519\) 0 0
\(520\) 221.343 + 160.815i 0.425659 + 0.309260i
\(521\) 256.909 + 353.605i 0.493107 + 0.678704i 0.980957 0.194224i \(-0.0622187\pi\)
−0.487850 + 0.872927i \(0.662219\pi\)
\(522\) 0 0
\(523\) −126.781 + 390.193i −0.242412 + 0.746067i 0.753639 + 0.657288i \(0.228297\pi\)
−0.996051 + 0.0887790i \(0.971703\pi\)
\(524\) −120.583 165.968i −0.230120 0.316733i
\(525\) 0 0
\(526\) 45.2854 + 139.374i 0.0860938 + 0.264970i
\(527\) 131.293i 0.249134i
\(528\) 0 0
\(529\) −1200.15 −2.26871
\(530\) −96.0564 + 31.2106i −0.181238 + 0.0588879i
\(531\) 0 0
\(532\) −157.799 + 114.648i −0.296615 + 0.215504i
\(533\) 944.922 + 307.024i 1.77284 + 0.576030i
\(534\) 0 0
\(535\) −400.121 + 290.705i −0.747890 + 0.543374i
\(536\) −132.357 + 182.173i −0.246934 + 0.339875i
\(537\) 0 0
\(538\) −62.2171 −0.115645
\(539\) 274.925 + 85.9597i 0.510066 + 0.159480i
\(540\) 0 0
\(541\) −154.410 475.226i −0.285416 0.878421i −0.986274 0.165119i \(-0.947199\pi\)
0.700857 0.713302i \(-0.252801\pi\)
\(542\) −15.9713 + 21.9826i −0.0294673 + 0.0405583i
\(543\) 0 0
\(544\) −42.9093 + 132.061i −0.0788773 + 0.242759i
\(545\) 709.365 + 230.487i 1.30159 + 0.422911i
\(546\) 0 0
\(547\) 562.723 + 408.842i 1.02874 + 0.747426i 0.968057 0.250731i \(-0.0806709\pi\)
0.0606867 + 0.998157i \(0.480671\pi\)
\(548\) −466.908 + 151.708i −0.852022 + 0.276839i
\(549\) 0 0
\(550\) 10.5883 33.8646i 0.0192515 0.0615720i
\(551\) 100.128i 0.181720i
\(552\) 0 0
\(553\) −14.3746 10.4437i −0.0259938 0.0188856i
\(554\) 54.7602 + 75.3710i 0.0988452 + 0.136049i
\(555\) 0 0
\(556\) 64.7031 199.136i 0.116372 0.358157i
\(557\) −254.943 350.898i −0.457707 0.629979i 0.516325 0.856393i \(-0.327300\pi\)
−0.974031 + 0.226414i \(0.927300\pi\)
\(558\) 0 0
\(559\) 250.585 + 771.220i 0.448273 + 1.37964i
\(560\) 765.484i 1.36694i
\(561\) 0 0
\(562\) 93.0037 0.165487
\(563\) −639.745 + 207.866i −1.13632 + 0.369211i −0.815973 0.578091i \(-0.803798\pi\)
−0.320343 + 0.947302i \(0.603798\pi\)
\(564\) 0 0
\(565\) 486.780 353.666i 0.861557 0.625958i
\(566\) −60.5610 19.6775i −0.106998 0.0347658i
\(567\) 0 0
\(568\) 230.556 167.509i 0.405909 0.294910i
\(569\) −319.271 + 439.438i −0.561108 + 0.772299i −0.991467 0.130359i \(-0.958387\pi\)
0.430359 + 0.902658i \(0.358387\pi\)
\(570\) 0 0
\(571\) 607.861 1.06456 0.532278 0.846570i \(-0.321336\pi\)
0.532278 + 0.846570i \(0.321336\pi\)
\(572\) 464.610 654.673i 0.812256 1.14453i
\(573\) 0 0
\(574\) −44.3301 136.434i −0.0772302 0.237690i
\(575\) 253.212 348.516i 0.440369 0.606115i
\(576\) 0 0
\(577\) 40.4970 124.637i 0.0701854 0.216009i −0.909811 0.415022i \(-0.863774\pi\)
0.979997 + 0.199014i \(0.0637738\pi\)
\(578\) 58.2907 + 18.9398i 0.100849 + 0.0327678i
\(579\) 0 0
\(580\) −326.211 237.006i −0.562433 0.408632i
\(581\) 237.663 77.2212i 0.409058 0.132911i
\(582\) 0 0
\(583\) 191.768 + 568.600i 0.328933 + 0.975301i
\(584\) 130.281i 0.223083i
\(585\) 0 0
\(586\) −25.9054 18.8214i −0.0442072 0.0321184i
\(587\) −78.5679 108.139i −0.133846 0.184224i 0.736833 0.676075i \(-0.236320\pi\)
−0.870679 + 0.491851i \(0.836320\pi\)
\(588\) 0 0
\(589\) −24.3585 + 74.9677i −0.0413557 + 0.127280i
\(590\) −38.4493 52.9210i −0.0651684 0.0896966i
\(591\) 0 0
\(592\) −33.0952 101.857i −0.0559040 0.172055i
\(593\) 164.004i 0.276567i −0.990393 0.138283i \(-0.955841\pi\)
0.990393 0.138283i \(-0.0441585\pi\)
\(594\) 0 0
\(595\) −494.962 −0.831869
\(596\) 15.7291 5.11068i 0.0263910 0.00857497i
\(597\) 0 0
\(598\) −195.854 + 142.296i −0.327514 + 0.237953i
\(599\) −40.7149 13.2291i −0.0679714 0.0220852i 0.274834 0.961492i \(-0.411377\pi\)
−0.342805 + 0.939406i \(0.611377\pi\)
\(600\) 0 0
\(601\) 252.000 183.089i 0.419301 0.304640i −0.358056 0.933700i \(-0.616560\pi\)
0.777356 + 0.629060i \(0.216560\pi\)
\(602\) 68.8205 94.7233i 0.114320 0.157348i
\(603\) 0 0
\(604\) 368.399 0.609933
\(605\) −689.076 207.065i −1.13897 0.342256i
\(606\) 0 0
\(607\) 347.998 + 1071.03i 0.573308 + 1.76446i 0.641871 + 0.766812i \(0.278158\pi\)
−0.0685637 + 0.997647i \(0.521842\pi\)
\(608\) 49.0019 67.4453i 0.0805952 0.110930i
\(609\) 0 0
\(610\) 67.4269 207.519i 0.110536 0.340195i
\(611\) −335.103 108.881i −0.548450 0.178202i
\(612\) 0 0
\(613\) −377.693 274.410i −0.616139 0.447651i 0.235432 0.971891i \(-0.424350\pi\)
−0.851571 + 0.524240i \(0.824350\pi\)
\(614\) −11.7157 + 3.80665i −0.0190809 + 0.00619976i
\(615\) 0 0
\(616\) −234.687 + 2.61069i −0.380985 + 0.00423813i
\(617\) 130.650i 0.211750i −0.994379 0.105875i \(-0.966236\pi\)
0.994379 0.105875i \(-0.0337644\pi\)
\(618\) 0 0
\(619\) −887.453 644.773i −1.43369 1.04164i −0.989315 0.145794i \(-0.953426\pi\)
−0.444374 0.895841i \(-0.646574\pi\)
\(620\) 186.584 + 256.810i 0.300941 + 0.414210i
\(621\) 0 0
\(622\) −13.4175 + 41.2949i −0.0215716 + 0.0663905i
\(623\) 687.950 + 946.881i 1.10425 + 1.51987i
\(624\) 0 0
\(625\) −240.004 738.656i −0.384006 1.18185i
\(626\) 70.3909i 0.112446i
\(627\) 0 0
\(628\) −580.320 −0.924076
\(629\) 65.8604 21.3993i 0.104707 0.0340212i
\(630\) 0 0
\(631\) 939.823 682.821i 1.48942 1.08213i 0.515052 0.857159i \(-0.327773\pi\)
0.974366 0.224967i \(-0.0722274\pi\)
\(632\) 4.79543 + 1.55813i 0.00758770 + 0.00246539i
\(633\) 0 0
\(634\) −88.7121 + 64.4531i −0.139924 + 0.101661i
\(635\) 433.392 596.513i 0.682507 0.939391i
\(636\) 0 0
\(637\) 489.639 0.768664
\(638\) 34.4368 48.5242i 0.0539762 0.0760568i
\(639\) 0 0
\(640\) −137.720 423.857i −0.215187 0.662277i
\(641\) −228.036 + 313.864i −0.355750 + 0.489648i −0.948958 0.315401i \(-0.897861\pi\)
0.593208 + 0.805049i \(0.297861\pi\)
\(642\) 0 0
\(643\) −35.6219 + 109.633i −0.0553995 + 0.170502i −0.974928 0.222522i \(-0.928571\pi\)
0.919528 + 0.393024i \(0.128571\pi\)
\(644\) −1338.43 434.883i −2.07831 0.675285i
\(645\) 0 0
\(646\) 13.9359 + 10.1250i 0.0215726 + 0.0156734i
\(647\) 173.649 56.4219i 0.268391 0.0872054i −0.171730 0.985144i \(-0.554936\pi\)
0.440121 + 0.897939i \(0.354936\pi\)
\(648\) 0 0
\(649\) −311.858 + 231.922i −0.480521 + 0.357352i
\(650\) 60.3125i 0.0927885i
\(651\) 0 0
\(652\) 289.717 + 210.492i 0.444352 + 0.322840i
\(653\) −6.35509 8.74703i −0.00973214 0.0133951i 0.804123 0.594463i \(-0.202635\pi\)
−0.813855 + 0.581068i \(0.802635\pi\)
\(654\) 0 0
\(655\) −96.5825 + 297.250i −0.147454 + 0.453817i
\(656\) −463.682 638.203i −0.706832 0.972871i
\(657\) 0 0
\(658\) 15.7210 + 48.3844i 0.0238921 + 0.0735325i
\(659\) 875.394i 1.32837i 0.747569 + 0.664184i \(0.231221\pi\)
−0.747569 + 0.664184i \(0.768779\pi\)
\(660\) 0 0
\(661\) 1015.92 1.53695 0.768475 0.639880i \(-0.221016\pi\)
0.768475 + 0.639880i \(0.221016\pi\)
\(662\) 25.1279 8.16456i 0.0379576 0.0123332i
\(663\) 0 0
\(664\) −57.3714 + 41.6827i −0.0864027 + 0.0627752i
\(665\) 282.620 + 91.8289i 0.424993 + 0.138089i
\(666\) 0 0
\(667\) 584.461 424.636i 0.876253 0.636635i
\(668\) 32.7323 45.0521i 0.0490004 0.0674433i
\(669\) 0 0
\(670\) 169.428 0.252878
\(671\) −1237.31 386.863i −1.84398 0.576547i
\(672\) 0 0
\(673\) −35.1655 108.228i −0.0522519 0.160815i 0.921525 0.388318i \(-0.126944\pi\)
−0.973777 + 0.227503i \(0.926944\pi\)
\(674\) 96.4786 132.791i 0.143143 0.197020i
\(675\) 0 0
\(676\) 217.852 670.479i 0.322266 0.991834i
\(677\) −811.539 263.685i −1.19873 0.389490i −0.359435 0.933170i \(-0.617031\pi\)
−0.839293 + 0.543680i \(0.817031\pi\)
\(678\) 0 0
\(679\) 69.9835 + 50.8460i 0.103068 + 0.0748836i
\(680\) 133.586 43.4048i 0.196450 0.0638305i
\(681\) 0 0
\(682\) −37.5883 + 27.9535i −0.0551148 + 0.0409876i
\(683\) 193.740i 0.283661i −0.989891 0.141830i \(-0.954701\pi\)
0.989891 0.141830i \(-0.0452987\pi\)
\(684\) 0 0
\(685\) 605.108 + 439.636i 0.883369 + 0.641805i
\(686\) 36.2026 + 49.8286i 0.0527735 + 0.0726365i
\(687\) 0 0
\(688\) 198.960 612.336i 0.289186 0.890024i
\(689\) 599.551 + 825.212i 0.870176 + 1.19769i
\(690\) 0 0
\(691\) −78.3885 241.255i −0.113442 0.349139i 0.878177 0.478336i \(-0.158760\pi\)
−0.991619 + 0.129197i \(0.958760\pi\)
\(692\) 906.604i 1.31012i
\(693\) 0 0
\(694\) −39.3300 −0.0566714
\(695\) −303.388 + 98.5768i −0.436530 + 0.141837i
\(696\) 0 0
\(697\) 412.662 299.817i 0.592055 0.430153i
\(698\) −133.684 43.4365i −0.191524 0.0622300i
\(699\) 0 0
\(700\) 283.649 206.083i 0.405213 0.294405i
\(701\) 669.680 921.735i 0.955321 1.31489i 0.00619790 0.999981i \(-0.498027\pi\)
0.949123 0.314906i \(-0.101973\pi\)
\(702\) 0 0
\(703\) −41.5761 −0.0591409
\(704\) −572.029 + 192.924i −0.812541 + 0.274040i
\(705\) 0 0
\(706\) 14.0194 + 43.1472i 0.0198575 + 0.0611150i
\(707\) 878.802 1209.57i 1.24300 1.71084i
\(708\) 0 0
\(709\) 115.622 355.847i 0.163077 0.501899i −0.835812 0.549015i \(-0.815003\pi\)
0.998889 + 0.0471157i \(0.0150029\pi\)
\(710\) −203.932 66.2615i −0.287228 0.0933261i
\(711\) 0 0
\(712\) −268.707 195.227i −0.377397 0.274195i
\(713\) −540.901 + 175.749i −0.758627 + 0.246493i
\(714\) 0 0
\(715\) −1222.98 + 13.6047i −1.71047 + 0.0190275i
\(716\) 560.706i 0.783109i
\(717\) 0 0
\(718\) −108.114 78.5497i −0.150577 0.109401i
\(719\) 445.256 + 612.843i 0.619272 + 0.852354i 0.997300 0.0734400i \(-0.0233977\pi\)
−0.378028 + 0.925794i \(0.623398\pi\)
\(720\) 0 0
\(721\) −304.493 + 937.134i −0.422321 + 1.29977i
\(722\) 59.9880 + 82.5664i 0.0830859 + 0.114358i
\(723\) 0 0
\(724\) −289.112 889.794i −0.399326 1.22900i
\(725\) 179.983i 0.248252i
\(726\) 0 0
\(727\) 845.080 1.16242 0.581211 0.813753i \(-0.302579\pi\)
0.581211 + 0.813753i \(0.302579\pi\)
\(728\) −379.428 + 123.284i −0.521192 + 0.169346i
\(729\) 0 0
\(730\) −79.3044 + 57.6180i −0.108636 + 0.0789288i
\(731\) 395.937 + 128.648i 0.541637 + 0.175989i
\(732\) 0 0
\(733\) −1098.71 + 798.262i −1.49893 + 1.08903i −0.528121 + 0.849169i \(0.677103\pi\)
−0.970806 + 0.239865i \(0.922897\pi\)
\(734\) 24.2235 33.3408i 0.0330021 0.0454235i
\(735\) 0 0
\(736\) 601.502 0.817258
\(737\) −11.1971 1006.56i −0.0151928 1.36575i
\(738\) 0 0
\(739\) 247.582 + 761.978i 0.335023 + 1.03109i 0.966711 + 0.255871i \(0.0823623\pi\)
−0.631688 + 0.775223i \(0.717638\pi\)
\(740\) −98.4122 + 135.453i −0.132989 + 0.183044i
\(741\) 0 0
\(742\) 45.5111 140.069i 0.0613357 0.188772i
\(743\) 849.861 + 276.136i 1.14382 + 0.371651i 0.818813 0.574060i \(-0.194632\pi\)
0.325010 + 0.945711i \(0.394632\pi\)
\(744\) 0 0
\(745\) −20.3847 14.8103i −0.0273620 0.0198796i
\(746\) 141.598 46.0078i 0.189809 0.0616727i
\(747\) 0 0
\(748\) −131.711 390.528i −0.176084 0.522096i
\(749\) 721.189i 0.962868i
\(750\) 0 0
\(751\) −321.208 233.372i −0.427708 0.310748i 0.353024 0.935614i \(-0.385153\pi\)
−0.780732 + 0.624867i \(0.785153\pi\)
\(752\) 164.438 + 226.329i 0.218667 + 0.300970i
\(753\) 0 0
\(754\) 31.2552 96.1936i 0.0414525 0.127578i
\(755\) −329.904 454.073i −0.436958 0.601422i
\(756\) 0 0
\(757\) 183.281 + 564.081i 0.242115 + 0.745153i 0.996098 + 0.0882586i \(0.0281302\pi\)
−0.753983 + 0.656894i \(0.771870\pi\)
\(758\) 82.2622i 0.108525i
\(759\) 0 0
\(760\) −84.3296 −0.110960
\(761\) 389.495 126.555i 0.511820 0.166301i −0.0417096 0.999130i \(-0.513280\pi\)
0.553530 + 0.832829i \(0.313280\pi\)
\(762\) 0 0
\(763\) −879.906 + 639.289i −1.15322 + 0.837862i
\(764\) 139.319 + 45.2674i 0.182354 + 0.0592506i
\(765\) 0 0
\(766\) −59.5552 + 43.2694i −0.0777483 + 0.0564874i
\(767\) −388.308 + 534.461i −0.506269 + 0.696820i
\(768\) 0 0
\(769\) 119.029 0.154784 0.0773921 0.997001i \(-0.475341\pi\)
0.0773921 + 0.997001i \(0.475341\pi\)
\(770\) 105.382 + 141.704i 0.136859 + 0.184031i
\(771\) 0 0
\(772\) 245.530 + 755.665i 0.318045 + 0.978841i
\(773\) −412.352 + 567.554i −0.533444 + 0.734222i −0.987650 0.156674i \(-0.949923\pi\)
0.454207 + 0.890896i \(0.349923\pi\)
\(774\) 0 0
\(775\) 43.7852 134.757i 0.0564970 0.173880i
\(776\) −23.3468 7.58583i −0.0300861 0.00977556i
\(777\) 0 0
\(778\) 128.772 + 93.5582i 0.165516 + 0.120255i
\(779\) −291.252 + 94.6334i −0.373879 + 0.121481i
\(780\) 0 0
\(781\) −380.177 + 1215.92i −0.486782 + 1.55688i
\(782\) 124.286i 0.158933i
\(783\) 0 0
\(784\) −314.518 228.511i −0.401171 0.291468i
\(785\) 519.680 + 715.278i 0.662012 + 0.911182i
\(786\) 0 0
\(787\) 475.616