Properties

Label 99.3.l.a.53.4
Level $99$
Weight $3$
Character 99.53
Analytic conductor $2.698$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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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 53.4
Character \(\chi\) \(=\) 99.53
Dual form 99.3.l.a.71.4

$q$-expansion

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

Character values

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

\(n\) \(46\) \(56\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\) \(-1\)

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 0.234050 0.972225i \(-0.424802\pi\)
−0.382109 + 0.924117i \(0.624802\pi\)
\(3\) 0 0
\(4\) −3.15764 2.29416i −0.789410 0.573540i
\(5\) 5.65537 1.83754i 1.13107 0.367508i 0.317090 0.948396i \(-0.397294\pi\)
0.813984 + 0.580887i \(0.197294\pi\)
\(6\) 0 0
\(7\) −7.01499 5.09669i −1.00214 0.728099i −0.0395956 0.999216i \(-0.512607\pi\)
−0.962546 + 0.271117i \(0.912607\pi\)
\(8\) 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 −0.438601 0.898682i \(-0.644526\pi\)
0.883067 0.469246i \(-0.155474\pi\)
\(14\) 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 −0.0279257 0.999610i \(-0.508890\pi\)
0.564964 + 0.825116i \(0.308890\pi\)
\(18\) 0 0
\(19\) −4.66262 + 3.38759i −0.245401 + 0.178294i −0.703686 0.710511i \(-0.748464\pi\)
0.458285 + 0.888805i \(0.348464\pi\)
\(20\) −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 \(0.359367\pi\)
−0.427578 + 0.903979i \(0.640633\pi\)
\(24\) 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 −0.595805 0.803129i \(-0.703167\pi\)
0.947935 + 0.318464i \(0.103167\pi\)
\(30\) 0 0
\(31\) −4.22647 + 13.0077i −0.136338 + 0.419604i −0.995796 0.0916020i \(-0.970801\pi\)
0.859458 + 0.511206i \(0.170801\pi\)
\(32\) 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 0.663853 0.747863i \(-0.268920\pi\)
−0.506118 + 0.862464i \(0.668920\pi\)
\(38\) 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 0.997065 + 0.0765632i \(0.0243947\pi\)
−0.235294 + 0.971924i \(0.575605\pi\)
\(42\) 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 0.674763 0.738035i \(-0.264246\pi\)
−0.910426 + 0.413672i \(0.864246\pi\)
\(48\) 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 0.754403 0.656411i \(-0.227926\pi\)
0.224496 + 0.974475i \(0.427926\pi\)
\(54\) 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 −0.595909 0.803052i \(-0.703208\pi\)
0.947894 + 0.318586i \(0.103208\pi\)
\(60\) 0 0
\(61\) −36.4184 112.084i −0.597023 1.83745i −0.544387 0.838834i \(-0.683238\pi\)
−0.0526365 0.998614i \(-0.516762\pi\)
\(62\) 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 0.596883 0.802328i \(-0.296406\pi\)
0.954485 + 0.298258i \(0.0964057\pi\)
\(72\) 0 0
\(73\) 42.8336 + 31.1204i 0.586762 + 0.426307i 0.841156 0.540793i \(-0.181876\pi\)
−0.254394 + 0.967101i \(0.581876\pi\)
\(74\) −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 −0.946969 0.321325i \(-0.895872\pi\)
0.954984 + 0.296657i \(0.0958717\pi\)
\(80\) 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 −0.469438 0.882965i \(-0.655543\pi\)
0.139211 + 0.990263i \(0.455543\pi\)
\(84\) 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 \(0.273976\pi\)
−0.651891 + 0.758313i \(0.726024\pi\)
\(90\) 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 −0.965689 0.259701i \(-0.916376\pi\)
0.933907 + 0.357515i \(0.116376\pi\)
\(98\) 8.15330i 0.0831970i
\(99\) 0 0
\(100\) −40.4347 −0.404347
\(101\) −163.987 53.2825i −1.62363 0.527550i −0.650837 0.759218i \(-0.725582\pi\)
−0.972795 + 0.231668i \(0.925582\pi\)
\(102\) 0 0
\(103\) 91.9355 + 66.7951i 0.892578 + 0.648496i 0.936549 0.350537i \(-0.114001\pi\)
−0.0439711 + 0.999033i \(0.514001\pi\)
\(104\) 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 0.516968 0.856005i \(-0.327061\pi\)
−0.973861 + 0.227146i \(0.927061\pi\)
\(108\) 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 0.986566 0.163363i \(-0.0522342\pi\)
−0.460233 + 0.887798i \(0.652234\pi\)
\(114\) 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 0.980885 + 0.194587i \(0.0623366\pi\)
−0.679178 + 0.733974i \(0.737663\pi\)
\(128\) −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 \(-0.935706\pi\)
0.979670 0.200614i \(-0.0642935\pi\)
\(132\) 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 0.162060 0.986781i \(-0.448186\pi\)
0.711125 + 0.703066i \(0.248186\pi\)
\(138\) 0 0
\(139\) −43.4005 31.5323i −0.312234 0.226851i 0.420620 0.907237i \(-0.361812\pi\)
−0.732855 + 0.680385i \(0.761812\pi\)
\(140\) 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 −0.322509 0.946566i \(-0.604526\pi\)
0.295462 + 0.955354i \(0.404526\pi\)
\(150\) 0 0
\(151\) −76.3610 + 55.4795i −0.505702 + 0.367414i −0.811191 0.584782i \(-0.801180\pi\)
0.305489 + 0.952196i \(0.401180\pi\)
\(152\) −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 −0.134632 0.990896i \(-0.542985\pi\)
0.900794 + 0.434247i \(0.142985\pi\)
\(158\) −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 −0.999584 0.0288552i \(-0.990814\pi\)
0.825641 + 0.564196i \(0.190814\pi\)
\(164\) 207.393i 1.26459i
\(165\) 0 0
\(166\) 8.97310 0.0540548
\(167\) −13.5693 4.40895i −0.0812536 0.0264009i 0.268108 0.963389i \(-0.413602\pi\)
−0.349362 + 0.936988i \(0.613602\pi\)
\(168\) 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 0.994208 + 0.107476i \(0.0342770\pi\)
−0.205011 + 0.978760i \(0.565723\pi\)
\(174\) 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 0.505157 0.863027i \(-0.331434\pi\)
−0.976890 + 0.213743i \(0.931434\pi\)
\(180\) 0 0
\(181\) −74.0732 227.974i −0.409244 1.25952i −0.917299 0.398199i \(-0.869635\pi\)
0.508055 0.861324i \(-0.330365\pi\)
\(182\) 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 −0.862853 0.505455i \(-0.831325\pi\)
0.747352 + 0.664428i \(0.231325\pi\)
\(192\) 0 0
\(193\) 62.9072 + 193.608i 0.325944 + 1.00315i 0.971013 + 0.239028i \(0.0768288\pi\)
−0.645069 + 0.764125i \(0.723171\pi\)
\(194\) 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 \(0.177481\pi\)
−0.848541 + 0.529129i \(0.822519\pi\)
\(198\) 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 −0.821740 0.569863i \(-0.806996\pi\)
0.999758 + 0.0219776i \(0.00699627\pi\)
\(212\) −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 −0.449853 0.893103i \(-0.648524\pi\)
0.710379 + 0.703820i \(0.248524\pi\)
\(224\) −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 −0.996243 0.0865981i \(-0.972400\pi\)
0.390216 + 0.920723i \(0.372400\pi\)
\(228\) 0 0
\(229\) 21.0536 64.7964i 0.0919372 0.282954i −0.894506 0.447056i \(-0.852473\pi\)
0.986443 + 0.164102i \(0.0524726\pi\)
\(230\) 76.9889i 0.334735i
\(231\) 0 0
\(232\) 42.7498 0.184267
\(233\) −101.511 32.9829i −0.435669 0.141558i 0.0829673 0.996552i \(-0.473560\pi\)
−0.518637 + 0.854995i \(0.673560\pi\)
\(234\) 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 −0.982206 0.187806i \(-0.939862\pi\)
0.124904 0.992169i \(-0.460138\pi\)
\(240\) 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 0.818507 0.574497i \(-0.194802\pi\)
0.324506 + 0.945884i \(0.394802\pi\)
\(252\) 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 −0.825800 0.563963i \(-0.809276\pi\)
0.791547 + 0.611108i \(0.209276\pi\)
\(258\) 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 \(0.352691\pi\)
−0.446443 + 0.894812i \(0.647309\pi\)
\(264\) 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 0.0663343 0.997797i \(-0.478870\pi\)
0.640156 + 0.768245i \(0.278870\pi\)
\(270\) 0 0
\(271\) 70.6026 + 51.2958i 0.260526 + 0.189283i 0.710379 0.703819i \(-0.248524\pi\)
−0.449853 + 0.893103i \(0.648524\pi\)
\(272\) 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 0.633504 + 0.773739i \(0.281616\pi\)
−0.967308 + 0.253604i \(0.918384\pi\)
\(278\) 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 −0.767245 0.641354i \(-0.778373\pi\)
−0.243735 + 0.969842i \(0.578373\pi\)
\(282\) 0 0
\(283\) 165.458 120.212i 0.584656 0.424777i −0.255744 0.966745i \(-0.582320\pi\)
0.840400 + 0.541967i \(0.182320\pi\)
\(284\) −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 −0.693304 0.720645i \(-0.743846\pi\)
0.899617 + 0.436680i \(0.143846\pi\)
\(294\) 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 0.920205 0.391437i \(-0.128022\pi\)
−0.656638 + 0.754206i \(0.728022\pi\)
\(312\) 0 0
\(313\) −69.8621 215.013i −0.223201 0.686943i −0.998469 0.0553107i \(-0.982385\pi\)
0.775268 0.631633i \(-0.217615\pi\)
\(314\) −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 0.785259 0.619167i \(-0.212530\pi\)
0.271350 + 0.962481i \(0.412530\pi\)
\(318\) 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 −0.266542 0.963823i \(-0.585881\pi\)
−0.999016 + 0.0443415i \(0.985881\pi\)
\(338\) 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 −0.130749 0.991416i \(-0.541738\pi\)
0.476961 + 0.878924i \(0.341738\pi\)
\(348\) 0 0
\(349\) 365.235 265.359i 1.04652 0.760340i 0.0749713 0.997186i \(-0.476113\pi\)
0.971547 + 0.236845i \(0.0761135\pi\)
\(350\) 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 \(0.0661708\pi\)
−0.978470 + 0.206388i \(0.933829\pi\)
\(354\) 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 −0.297187 0.954819i \(-0.596048\pi\)
0.999923 0.0124137i \(-0.00395151\pi\)
\(360\) 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 0.432260 0.901749i \(-0.357716\pi\)
−0.724038 + 0.689760i \(0.757716\pi\)
\(368\) −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 −0.999124 0.0418592i \(-0.986672\pi\)
0.783704 0.621135i \(-0.213328\pi\)
\(380\) 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 0.587479 0.809240i \(-0.300121\pi\)
−0.000379005 1.00000i \(0.500121\pi\)
\(384\) 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 0.223617 + 0.974677i \(0.428213\pi\)
−0.996074 + 0.0885193i \(0.971787\pi\)
\(390\) 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 −0.564551 0.825398i \(-0.690951\pi\)
0.0284257 + 0.999596i \(0.490951\pi\)
\(402\) 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 −0.995945 0.0899593i \(-0.971326\pi\)
0.858614 + 0.512623i \(0.171326\pi\)
\(410\) −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 \(0.0657656\pi\)
−0.978732 + 0.205142i \(0.934234\pi\)
\(420\) 0 0
\(421\) 97.7668 71.0318i 0.232225 0.168722i −0.465587 0.885002i \(-0.654157\pi\)
0.697813 + 0.716280i \(0.254157\pi\)
\(422\) −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 0.781331 0.624117i \(-0.214541\pi\)
0.265263 + 0.964176i \(0.414541\pi\)
\(432\) 0 0
\(433\) −205.673 149.430i −0.474996 0.345105i 0.324389 0.945924i \(-0.394841\pi\)
−0.799385 + 0.600819i \(0.794841\pi\)
\(434\) −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 −0.999973 0.00736244i \(-0.997656\pi\)
0.302007 0.953306i \(-0.402344\pi\)
\(444\) 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 −0.327452 0.944868i \(-0.606190\pi\)
−0.820293 + 0.571943i \(0.806190\pi\)
\(450\) 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 0.983878 0.178839i \(-0.0572340\pi\)
−0.901093 + 0.433626i \(0.857234\pi\)
\(458\) −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 \(0.108528\pi\)
−0.942438 + 0.334382i \(0.891472\pi\)
\(462\) 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 −0.417749 0.908562i \(-0.637181\pi\)
0.196073 + 0.980589i \(0.437181\pi\)
\(468\) 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 0.00729665 0.999973i \(-0.497677\pi\)
0.593673 + 0.804707i \(0.297677\pi\)
\(480\) 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 −0.902304 0.431101i \(-0.858125\pi\)
0.131174 + 0.991359i \(0.458125\pi\)
\(488\) 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 −0.964552 0.263892i \(-0.914994\pi\)
0.549039 + 0.835797i \(0.314994\pi\)
\(492\) 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 0.154356 0.988015i \(-0.450670\pi\)
−0.891960 + 0.452115i \(0.850670\pi\)
\(500\) 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 0.979332 0.202260i \(-0.0648287\pi\)
−0.494991 + 0.868898i \(0.664829\pi\)
\(504\) 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 0.713571 0.700583i \(-0.247077\pi\)
−0.886800 + 0.462154i \(0.847077\pi\)
\(510\) 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 −0.487850 0.872927i \(-0.662219\pi\)
0.980957 + 0.194224i \(0.0622187\pi\)
\(522\) 0 0
\(523\) −126.781 390.193i −0.242412 0.746067i −0.996051 0.0887790i \(-0.971703\pi\)
0.753639 0.657288i \(-0.228297\pi\)
\(524\) −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 0.700857 + 0.713302i \(0.252801\pi\)
−0.986274 + 0.165119i \(0.947199\pi\)
\(542\) −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 0.0606867 0.998157i \(-0.480671\pi\)
0.968057 + 0.250731i \(0.0806709\pi\)
\(548\) −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 −0.974031 0.226414i \(-0.927300\pi\)
0.516325 + 0.856393i \(0.327300\pi\)
\(558\) 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 −0.320343 0.947302i \(-0.603798\pi\)
−0.815973 + 0.578091i \(0.803798\pi\)
\(564\) 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 0.430359 0.902658i \(-0.358387\pi\)
−0.991467 + 0.130359i \(0.958387\pi\)
\(570\) 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 0.979997 0.199014i \(-0.0637738\pi\)
−0.909811 + 0.415022i \(0.863774\pi\)
\(578\) 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 −0.870679 0.491851i \(-0.836320\pi\)
0.736833 + 0.676075i \(0.236320\pi\)
\(588\) 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 \(0.0441585\pi\)
−0.990393 + 0.138283i \(0.955841\pi\)
\(594\) 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 −0.342805 0.939406i \(-0.611377\pi\)
0.274834 + 0.961492i \(0.411377\pi\)
\(600\) 0 0
\(601\) 252.000 + 183.089i 0.419301 + 0.304640i 0.777356 0.629060i \(-0.216560\pi\)
−0.358056 + 0.933700i \(0.616560\pi\)
\(602\) 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 −0.0685637 0.997647i \(-0.521842\pi\)
0.641871 0.766812i \(-0.278158\pi\)
\(608\) 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 −0.851571 0.524240i \(-0.824350\pi\)
0.235432 + 0.971891i \(0.424350\pi\)
\(614\) −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 \(0.0337644\pi\)
−0.994379 + 0.105875i \(0.966236\pi\)
\(618\) 0 0
\(619\) −887.453 + 644.773i −1.43369 + 1.04164i −0.444374 + 0.895841i \(0.646574\pi\)
−0.989315 + 0.145794i \(0.953426\pi\)
\(620\) 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 0.974366 + 0.224967i \(0.0722274\pi\)
0.515052 + 0.857159i \(0.327773\pi\)
\(632\) 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 0.593208 0.805049i \(-0.297861\pi\)
−0.948958 + 0.315401i \(0.897861\pi\)
\(642\) 0 0
\(643\) −35.6219 109.633i −0.0553995 0.170502i 0.919528 0.393024i \(-0.128571\pi\)
−0.974928 + 0.222522i \(0.928571\pi\)
\(644\) −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 0.440121 0.897939i \(-0.354936\pi\)
−0.171730 + 0.985144i \(0.554936\pi\)
\(648\) 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 −0.813855 0.581068i \(-0.802635\pi\)
0.804123 + 0.594463i \(0.202635\pi\)
\(654\) 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 \(-0.768779\pi\)
0.747569 0.664184i \(-0.231221\pi\)
\(660\) 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 −0.973777 0.227503i \(-0.926944\pi\)
0.921525 + 0.388318i \(0.126944\pi\)
\(674\) 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 −0.839293 0.543680i \(-0.817031\pi\)
−0.359435 + 0.933170i \(0.617031\pi\)
\(678\) 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 \(0.0452987\pi\)
−0.989891 + 0.141830i \(0.954701\pi\)
\(684\) 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 −0.991619 0.129197i \(-0.958760\pi\)
0.878177 + 0.478336i \(0.158760\pi\)
\(692\) 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 0.949123 + 0.314906i \(0.101973\pi\)
0.00619790 + 0.999981i \(0.498027\pi\)
\(702\) 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 0.998889 0.0471157i \(-0.0150029\pi\)
−0.835812 + 0.549015i \(0.815003\pi\)
\(710\) −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 −0.378028 0.925794i \(-0.623398\pi\)
0.997300 + 0.0734400i \(0.0233977\pi\)
\(720\) 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 −0.970806 0.239865i \(-0.922897\pi\)
−0.528121 0.849169i \(-0.677103\pi\)
\(734\) 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 −0.631688 0.775223i \(-0.717638\pi\)
0.966711 0.255871i \(-0.0823623\pi\)
\(740\) −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 0.325010 0.945711i \(-0.394632\pi\)
0.818813 + 0.574060i \(0.194632\pi\)
\(744\) 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 −0.780732 0.624867i \(-0.785153\pi\)
0.353024 + 0.935614i \(0.385153\pi\)
\(752\) 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 −0.753983 0.656894i \(-0.771870\pi\)
0.996098 0.0882586i \(-0.0281302\pi\)
\(758\) 82.2622i 0.108525i
\(759\) 0 0
\(760\) −84.3296 −0.110960
\(761\) 389.495 + 126.555i 0.511820 + 0.166301i 0.553530 0.832829i \(-0.313280\pi\)
−0.0417096 + 0.999130i \(0.513280\pi\)
\(762\) 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 0.454207 0.890896i \(-0.349923\pi\)
−0.987650 + 0.156674i \(0.949923\pi\)
\(774\) 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 + 1463.80i 0.604341 + 1.85997i 0.501261 + 0.865296i \(0.332870\pi\)
0.103080 + 0.994673i \(0.467130\pi\)