Properties

Label 576.2.bd.a.37.6
Level $576$
Weight $2$
Character 576.37
Analytic conductor $4.599$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bd (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(7\) over \(\Q(\zeta_{16})\)
Twist minimal: no (minimal twist has level 64)
Sato-Tate group: $\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label 37.6
Character \(\chi\) \(=\) 576.37
Dual form 576.2.bd.a.109.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.919278 - 1.07468i) q^{2} +(-0.309855 - 1.97585i) q^{4} +(-0.509835 + 2.56311i) q^{5} +(-1.78664 + 4.31333i) q^{7} +(-2.40824 - 1.48336i) q^{8} +O(q^{10})\) \(q+(0.919278 - 1.07468i) q^{2} +(-0.309855 - 1.97585i) q^{4} +(-0.509835 + 2.56311i) q^{5} +(-1.78664 + 4.31333i) q^{7} +(-2.40824 - 1.48336i) q^{8} +(2.28583 + 2.90412i) q^{10} +(0.337256 - 0.225347i) q^{11} +(0.558477 + 2.80765i) q^{13} +(2.99301 + 5.88521i) q^{14} +(-3.80798 + 1.22446i) q^{16} +(-2.50296 + 2.50296i) q^{17} +(-2.54690 + 0.506609i) q^{19} +(5.22231 + 0.213164i) q^{20} +(0.0678568 - 0.569597i) q^{22} +(2.78551 - 1.15380i) q^{23} +(-1.69022 - 0.700112i) q^{25} +(3.53071 + 1.98083i) q^{26} +(9.07610 + 2.19363i) q^{28} +(4.40189 + 2.94125i) q^{29} -0.289905i q^{31} +(-2.18470 + 5.21796i) q^{32} +(0.388954 + 4.99079i) q^{34} +(-10.1447 - 6.77845i) q^{35} +(1.93303 + 0.384503i) q^{37} +(-1.79687 + 3.20280i) q^{38} +(5.02983 - 5.41633i) q^{40} +(5.97284 - 2.47403i) q^{41} +(-3.47301 - 5.19772i) q^{43} +(-0.549753 - 0.596542i) q^{44} +(1.32070 - 4.05418i) q^{46} +(-0.140633 + 0.140633i) q^{47} +(-10.4630 - 10.4630i) q^{49} +(-2.30617 + 1.17284i) q^{50} +(5.37446 - 1.97343i) q^{52} +(-0.438386 + 0.292920i) q^{53} +(0.405645 + 0.979314i) q^{55} +(10.7009 - 7.73731i) q^{56} +(7.20745 - 2.02678i) q^{58} +(1.05758 - 5.31680i) q^{59} +(4.77369 - 7.14433i) q^{61} +(-0.311554 - 0.266504i) q^{62} +(3.59927 + 7.14460i) q^{64} -7.48106 q^{65} +(2.53466 - 3.79339i) q^{67} +(5.72104 + 4.16993i) q^{68} +(-16.6104 + 4.67094i) q^{70} +(-5.35506 + 12.9282i) q^{71} +(5.89360 + 14.2284i) q^{73} +(2.19020 - 1.72391i) q^{74} +(1.79015 + 4.87532i) q^{76} +(0.369442 + 1.85731i) q^{77} +(-4.17941 - 4.17941i) q^{79} +(-1.19698 - 10.3846i) q^{80} +(2.83192 - 8.69319i) q^{82} +(-7.83362 + 1.55820i) q^{83} +(-5.13928 - 7.69148i) q^{85} +(-8.77852 - 1.04580i) q^{86} +(-1.14646 + 0.0424176i) q^{88} +(6.46701 + 2.67872i) q^{89} +(-13.1081 - 2.60737i) q^{91} +(-3.14284 - 5.14625i) q^{92} +(0.0218540 + 0.280416i) q^{94} -6.78627i q^{95} +16.2429i q^{97} +(-20.8627 + 1.62592i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} + O(q^{10}) \) \( 56q + 8q^{2} - 8q^{4} + 8q^{5} - 8q^{7} + 8q^{8} - 8q^{10} + 8q^{11} - 8q^{13} + 8q^{14} - 8q^{16} + 8q^{17} - 8q^{19} + 8q^{20} + 8q^{23} - 8q^{25} - 32q^{26} + 32q^{28} + 8q^{29} - 32q^{32} + 32q^{34} + 8q^{35} - 8q^{37} - 32q^{38} + 32q^{40} + 8q^{41} - 8q^{43} - 8q^{46} + 8q^{47} - 8q^{49} + 32q^{50} - 56q^{52} + 8q^{53} + 56q^{55} + 64q^{56} - 80q^{58} - 56q^{59} - 8q^{61} + 40q^{62} - 104q^{64} + 16q^{65} + 72q^{67} + 56q^{68} - 104q^{70} - 56q^{71} - 8q^{73} + 64q^{74} - 72q^{76} + 8q^{77} + 24q^{79} - 32q^{80} + 72q^{82} + 8q^{83} - 8q^{85} - 96q^{86} + 72q^{88} + 8q^{89} - 8q^{91} - 144q^{92} + 88q^{94} - 128q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{9}{16}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.919278 1.07468i 0.650028 0.759910i
\(3\) 0 0
\(4\) −0.309855 1.97585i −0.154928 0.987926i
\(5\) −0.509835 + 2.56311i −0.228005 + 1.14626i 0.681901 + 0.731445i \(0.261154\pi\)
−0.909906 + 0.414814i \(0.863846\pi\)
\(6\) 0 0
\(7\) −1.78664 + 4.31333i −0.675287 + 1.63029i 0.0972076 + 0.995264i \(0.469009\pi\)
−0.772494 + 0.635022i \(0.780991\pi\)
\(8\) −2.40824 1.48336i −0.851442 0.524448i
\(9\) 0 0
\(10\) 2.28583 + 2.90412i 0.722844 + 0.918364i
\(11\) 0.337256 0.225347i 0.101686 0.0679447i −0.503687 0.863886i \(-0.668024\pi\)
0.605374 + 0.795941i \(0.293024\pi\)
\(12\) 0 0
\(13\) 0.558477 + 2.80765i 0.154894 + 0.778703i 0.977639 + 0.210292i \(0.0674415\pi\)
−0.822745 + 0.568411i \(0.807559\pi\)
\(14\) 2.99301 + 5.88521i 0.799916 + 1.57289i
\(15\) 0 0
\(16\) −3.80798 + 1.22446i −0.951995 + 0.306114i
\(17\) −2.50296 + 2.50296i −0.607058 + 0.607058i −0.942176 0.335118i \(-0.891224\pi\)
0.335118 + 0.942176i \(0.391224\pi\)
\(18\) 0 0
\(19\) −2.54690 + 0.506609i −0.584298 + 0.116224i −0.478384 0.878151i \(-0.658777\pi\)
−0.105915 + 0.994375i \(0.533777\pi\)
\(20\) 5.22231 + 0.213164i 1.16774 + 0.0476650i
\(21\) 0 0
\(22\) 0.0678568 0.569597i 0.0144671 0.121438i
\(23\) 2.78551 1.15380i 0.580820 0.240583i −0.0728759 0.997341i \(-0.523218\pi\)
0.653696 + 0.756758i \(0.273218\pi\)
\(24\) 0 0
\(25\) −1.69022 0.700112i −0.338044 0.140022i
\(26\) 3.53071 + 1.98083i 0.692429 + 0.388473i
\(27\) 0 0
\(28\) 9.07610 + 2.19363i 1.71522 + 0.414557i
\(29\) 4.40189 + 2.94125i 0.817410 + 0.546176i 0.892525 0.450999i \(-0.148932\pi\)
−0.0751143 + 0.997175i \(0.523932\pi\)
\(30\) 0 0
\(31\) 0.289905i 0.0520685i −0.999661 0.0260343i \(-0.991712\pi\)
0.999661 0.0260343i \(-0.00828790\pi\)
\(32\) −2.18470 + 5.21796i −0.386204 + 0.922413i
\(33\) 0 0
\(34\) 0.388954 + 4.99079i 0.0667051 + 0.855914i
\(35\) −10.1447 6.77845i −1.71476 1.14577i
\(36\) 0 0
\(37\) 1.93303 + 0.384503i 0.317787 + 0.0632119i 0.351407 0.936223i \(-0.385703\pi\)
−0.0336194 + 0.999435i \(0.510703\pi\)
\(38\) −1.79687 + 3.20280i −0.291490 + 0.519563i
\(39\) 0 0
\(40\) 5.02983 5.41633i 0.795287 0.856397i
\(41\) 5.97284 2.47403i 0.932801 0.386379i 0.136061 0.990700i \(-0.456556\pi\)
0.796741 + 0.604321i \(0.206556\pi\)
\(42\) 0 0
\(43\) −3.47301 5.19772i −0.529628 0.792645i 0.466124 0.884720i \(-0.345650\pi\)
−0.995752 + 0.0920747i \(0.970650\pi\)
\(44\) −0.549753 0.596542i −0.0828783 0.0899321i
\(45\) 0 0
\(46\) 1.32070 4.05418i 0.194727 0.597757i
\(47\) −0.140633 + 0.140633i −0.0205135 + 0.0205135i −0.717289 0.696776i \(-0.754617\pi\)
0.696776 + 0.717289i \(0.254617\pi\)
\(48\) 0 0
\(49\) −10.4630 10.4630i −1.49471 1.49471i
\(50\) −2.30617 + 1.17284i −0.326142 + 0.165865i
\(51\) 0 0
\(52\) 5.37446 1.97343i 0.745303 0.273666i
\(53\) −0.438386 + 0.292920i −0.0602169 + 0.0402356i −0.585314 0.810806i \(-0.699029\pi\)
0.525097 + 0.851042i \(0.324029\pi\)
\(54\) 0 0
\(55\) 0.405645 + 0.979314i 0.0546972 + 0.132051i
\(56\) 10.7009 7.73731i 1.42997 1.03394i
\(57\) 0 0
\(58\) 7.20745 2.02678i 0.946384 0.266129i
\(59\) 1.05758 5.31680i 0.137685 0.692189i −0.848850 0.528635i \(-0.822704\pi\)
0.986534 0.163554i \(-0.0522958\pi\)
\(60\) 0 0
\(61\) 4.77369 7.14433i 0.611209 0.914738i −0.388770 0.921335i \(-0.627100\pi\)
0.999978 + 0.00659665i \(0.00209980\pi\)
\(62\) −0.311554 0.266504i −0.0395674 0.0338460i
\(63\) 0 0
\(64\) 3.59927 + 7.14460i 0.449908 + 0.893075i
\(65\) −7.48106 −0.927912
\(66\) 0 0
\(67\) 2.53466 3.79339i 0.309658 0.463436i −0.643700 0.765278i \(-0.722601\pi\)
0.953358 + 0.301842i \(0.0976014\pi\)
\(68\) 5.72104 + 4.16993i 0.693778 + 0.505678i
\(69\) 0 0
\(70\) −16.6104 + 4.67094i −1.98532 + 0.558285i
\(71\) −5.35506 + 12.9282i −0.635528 + 1.53430i 0.197050 + 0.980393i \(0.436864\pi\)
−0.832578 + 0.553907i \(0.813136\pi\)
\(72\) 0 0
\(73\) 5.89360 + 14.2284i 0.689794 + 1.66531i 0.745196 + 0.666846i \(0.232356\pi\)
−0.0554020 + 0.998464i \(0.517644\pi\)
\(74\) 2.19020 1.72391i 0.254606 0.200401i
\(75\) 0 0
\(76\) 1.79015 + 4.87532i 0.205345 + 0.559237i
\(77\) 0.369442 + 1.85731i 0.0421018 + 0.211660i
\(78\) 0 0
\(79\) −4.17941 4.17941i −0.470220 0.470220i 0.431765 0.901986i \(-0.357891\pi\)
−0.901986 + 0.431765i \(0.857891\pi\)
\(80\) −1.19698 10.3846i −0.133826 1.16103i
\(81\) 0 0
\(82\) 2.83192 8.69319i 0.312733 0.960003i
\(83\) −7.83362 + 1.55820i −0.859851 + 0.171035i −0.605274 0.796017i \(-0.706936\pi\)
−0.254578 + 0.967052i \(0.581936\pi\)
\(84\) 0 0
\(85\) −5.13928 7.69148i −0.557433 0.834258i
\(86\) −8.77852 1.04580i −0.946612 0.112771i
\(87\) 0 0
\(88\) −1.14646 + 0.0424176i −0.122214 + 0.00452173i
\(89\) 6.46701 + 2.67872i 0.685501 + 0.283944i 0.698125 0.715976i \(-0.254018\pi\)
−0.0126231 + 0.999920i \(0.504018\pi\)
\(90\) 0 0
\(91\) −13.1081 2.60737i −1.37411 0.273327i
\(92\) −3.14284 5.14625i −0.327664 0.536534i
\(93\) 0 0
\(94\) 0.0218540 + 0.280416i 0.00225407 + 0.0289227i
\(95\) 6.78627i 0.696257i
\(96\) 0 0
\(97\) 16.2429i 1.64922i 0.565702 + 0.824610i \(0.308605\pi\)
−0.565702 + 0.824610i \(0.691395\pi\)
\(98\) −20.8627 + 1.62592i −2.10745 + 0.164243i
\(99\) 0 0
\(100\) −0.859594 + 3.55656i −0.0859594 + 0.355656i
\(101\) 15.3251 + 3.04834i 1.52490 + 0.303321i 0.885166 0.465275i \(-0.154045\pi\)
0.639734 + 0.768597i \(0.279045\pi\)
\(102\) 0 0
\(103\) 1.43693 + 0.595196i 0.141585 + 0.0586464i 0.452351 0.891840i \(-0.350586\pi\)
−0.310766 + 0.950486i \(0.600586\pi\)
\(104\) 2.81982 7.58993i 0.276506 0.744254i
\(105\) 0 0
\(106\) −0.0882045 + 0.740397i −0.00856718 + 0.0719137i
\(107\) 2.12845 + 3.18545i 0.205765 + 0.307949i 0.919971 0.391986i \(-0.128212\pi\)
−0.714206 + 0.699936i \(0.753212\pi\)
\(108\) 0 0
\(109\) −2.80639 + 0.558226i −0.268803 + 0.0534683i −0.327652 0.944799i \(-0.606257\pi\)
0.0588482 + 0.998267i \(0.481257\pi\)
\(110\) 1.42535 + 0.464325i 0.135901 + 0.0442716i
\(111\) 0 0
\(112\) 1.52201 18.6127i 0.143816 1.75874i
\(113\) −8.29968 8.29968i −0.780769 0.780769i 0.199192 0.979960i \(-0.436168\pi\)
−0.979960 + 0.199192i \(0.936168\pi\)
\(114\) 0 0
\(115\) 1.53716 + 7.72783i 0.143341 + 0.720624i
\(116\) 4.44752 9.60884i 0.412942 0.892158i
\(117\) 0 0
\(118\) −4.74163 6.02417i −0.436502 0.554570i
\(119\) −6.32421 15.2680i −0.579740 1.39962i
\(120\) 0 0
\(121\) −4.14656 + 10.0107i −0.376960 + 0.910061i
\(122\) −3.28949 11.6978i −0.297817 1.05907i
\(123\) 0 0
\(124\) −0.572810 + 0.0898286i −0.0514398 + 0.00806685i
\(125\) −4.60324 + 6.88923i −0.411726 + 0.616191i
\(126\) 0 0
\(127\) −7.21464 −0.640196 −0.320098 0.947384i \(-0.603716\pi\)
−0.320098 + 0.947384i \(0.603716\pi\)
\(128\) 10.9869 + 2.69983i 0.971110 + 0.238634i
\(129\) 0 0
\(130\) −6.87718 + 8.03971i −0.603168 + 0.705130i
\(131\) 6.24500 9.34631i 0.545628 0.816591i −0.451504 0.892269i \(-0.649112\pi\)
0.997132 + 0.0756785i \(0.0241123\pi\)
\(132\) 0 0
\(133\) 2.36522 11.8907i 0.205090 1.03106i
\(134\) −1.74660 6.21112i −0.150884 0.536559i
\(135\) 0 0
\(136\) 9.74055 2.31494i 0.835245 0.198504i
\(137\) 4.59287 + 11.0882i 0.392395 + 0.947326i 0.989417 + 0.145101i \(0.0463506\pi\)
−0.597022 + 0.802225i \(0.703649\pi\)
\(138\) 0 0
\(139\) 13.1247 8.76967i 1.11323 0.743834i 0.143895 0.989593i \(-0.454037\pi\)
0.969331 + 0.245759i \(0.0790372\pi\)
\(140\) −10.2498 + 22.1447i −0.866269 + 1.87157i
\(141\) 0 0
\(142\) 8.97089 + 17.6396i 0.752820 + 1.48028i
\(143\) 0.821045 + 0.821045i 0.0686593 + 0.0686593i
\(144\) 0 0
\(145\) −9.78299 + 9.78299i −0.812433 + 0.812433i
\(146\) 20.7088 + 6.74616i 1.71387 + 0.558316i
\(147\) 0 0
\(148\) 0.160762 3.93851i 0.0132146 0.323744i
\(149\) −10.8556 16.2465i −0.889324 1.33097i −0.943133 0.332416i \(-0.892136\pi\)
0.0538088 0.998551i \(-0.482864\pi\)
\(150\) 0 0
\(151\) 12.4999 5.17764i 1.01723 0.421351i 0.189143 0.981950i \(-0.439429\pi\)
0.828087 + 0.560599i \(0.189429\pi\)
\(152\) 6.88503 + 2.55794i 0.558450 + 0.207476i
\(153\) 0 0
\(154\) 2.33562 + 1.31035i 0.188210 + 0.105591i
\(155\) 0.743060 + 0.147804i 0.0596840 + 0.0118719i
\(156\) 0 0
\(157\) 8.26557 + 5.52287i 0.659664 + 0.440773i 0.839820 0.542865i \(-0.182660\pi\)
−0.180156 + 0.983638i \(0.557660\pi\)
\(158\) −8.33355 + 0.649469i −0.662982 + 0.0516690i
\(159\) 0 0
\(160\) −12.2604 8.25993i −0.969268 0.653005i
\(161\) 14.0763i 1.10936i
\(162\) 0 0
\(163\) −16.9295 11.3119i −1.32602 0.886017i −0.327746 0.944766i \(-0.606289\pi\)
−0.998273 + 0.0587489i \(0.981289\pi\)
\(164\) −6.73904 11.0349i −0.526231 0.861678i
\(165\) 0 0
\(166\) −5.52671 + 9.85102i −0.428956 + 0.764588i
\(167\) 6.10786 + 2.52996i 0.472640 + 0.195774i 0.606272 0.795257i \(-0.292664\pi\)
−0.133632 + 0.991031i \(0.542664\pi\)
\(168\) 0 0
\(169\) 4.43942 1.83887i 0.341494 0.141451i
\(170\) −12.9903 1.54755i −0.996308 0.118691i
\(171\) 0 0
\(172\) −9.19379 + 8.47268i −0.701020 + 0.646036i
\(173\) 2.36420 0.470269i 0.179747 0.0357539i −0.104396 0.994536i \(-0.533291\pi\)
0.284143 + 0.958782i \(0.408291\pi\)
\(174\) 0 0
\(175\) 6.03963 6.03963i 0.456553 0.456553i
\(176\) −1.00833 + 1.27107i −0.0760061 + 0.0958106i
\(177\) 0 0
\(178\) 8.82374 4.48744i 0.661367 0.336348i
\(179\) −2.21659 11.1436i −0.165676 0.832910i −0.970816 0.239825i \(-0.922910\pi\)
0.805140 0.593085i \(-0.202090\pi\)
\(180\) 0 0
\(181\) 16.6040 11.0944i 1.23417 0.824644i 0.244727 0.969592i \(-0.421302\pi\)
0.989439 + 0.144948i \(0.0463016\pi\)
\(182\) −14.8521 + 11.6901i −1.10091 + 0.866527i
\(183\) 0 0
\(184\) −8.41969 1.35330i −0.620708 0.0997669i
\(185\) −1.97105 + 4.75853i −0.144914 + 0.349854i
\(186\) 0 0
\(187\) −0.280103 + 1.40817i −0.0204832 + 0.102976i
\(188\) 0.321446 + 0.234294i 0.0234439 + 0.0170877i
\(189\) 0 0
\(190\) −7.29304 6.23847i −0.529093 0.452586i
\(191\) −6.26580 −0.453378 −0.226689 0.973967i \(-0.572790\pi\)
−0.226689 + 0.973967i \(0.572790\pi\)
\(192\) 0 0
\(193\) 10.7005 0.770241 0.385120 0.922866i \(-0.374160\pi\)
0.385120 + 0.922866i \(0.374160\pi\)
\(194\) 17.4559 + 14.9318i 1.25326 + 1.07204i
\(195\) 0 0
\(196\) −17.4313 + 23.9153i −1.24509 + 1.70824i
\(197\) 0.0517041 0.259934i 0.00368377 0.0185195i −0.978900 0.204341i \(-0.934495\pi\)
0.982583 + 0.185822i \(0.0594947\pi\)
\(198\) 0 0
\(199\) 0.892313 2.15423i 0.0632544 0.152710i −0.889092 0.457729i \(-0.848663\pi\)
0.952346 + 0.305019i \(0.0986630\pi\)
\(200\) 3.03194 + 4.19325i 0.214390 + 0.296507i
\(201\) 0 0
\(202\) 17.3640 13.6672i 1.22172 0.961620i
\(203\) −20.5512 + 13.7319i −1.44241 + 0.963787i
\(204\) 0 0
\(205\) 3.29606 + 16.5704i 0.230207 + 1.15733i
\(206\) 1.96058 0.997083i 0.136600 0.0694701i
\(207\) 0 0
\(208\) −5.56451 10.0077i −0.385830 0.693906i
\(209\) −0.744792 + 0.744792i −0.0515184 + 0.0515184i
\(210\) 0 0
\(211\) 13.1481 2.61531i 0.905149 0.180045i 0.279496 0.960147i \(-0.409833\pi\)
0.625653 + 0.780101i \(0.284833\pi\)
\(212\) 0.714602 + 0.775422i 0.0490791 + 0.0532562i
\(213\) 0 0
\(214\) 5.37996 + 0.640922i 0.367767 + 0.0438125i
\(215\) 15.0930 6.25173i 1.02933 0.426364i
\(216\) 0 0
\(217\) 1.25046 + 0.517956i 0.0848866 + 0.0351612i
\(218\) −1.97994 + 3.52912i −0.134099 + 0.239022i
\(219\) 0 0
\(220\) 1.80929 1.10494i 0.121982 0.0744950i
\(221\) −8.42530 5.62960i −0.566747 0.378688i
\(222\) 0 0
\(223\) 26.8359i 1.79706i 0.438907 + 0.898532i \(0.355366\pi\)
−0.438907 + 0.898532i \(0.644634\pi\)
\(224\) −18.6035 18.7459i −1.24300 1.25252i
\(225\) 0 0
\(226\) −16.5492 + 1.28975i −1.10084 + 0.0857928i
\(227\) 1.92112 + 1.28365i 0.127509 + 0.0851989i 0.617689 0.786422i \(-0.288069\pi\)
−0.490180 + 0.871621i \(0.663069\pi\)
\(228\) 0 0
\(229\) −9.00910 1.79202i −0.595338 0.118420i −0.111781 0.993733i \(-0.535656\pi\)
−0.483557 + 0.875313i \(0.660656\pi\)
\(230\) 9.71799 + 5.45208i 0.640785 + 0.359499i
\(231\) 0 0
\(232\) −6.23788 13.6128i −0.409537 0.893727i
\(233\) 16.3550 6.77448i 1.07145 0.443811i 0.223951 0.974600i \(-0.428104\pi\)
0.847504 + 0.530789i \(0.178104\pi\)
\(234\) 0 0
\(235\) −0.288759 0.432158i −0.0188366 0.0281909i
\(236\) −10.8329 0.442178i −0.705162 0.0287833i
\(237\) 0 0
\(238\) −22.2219 7.23906i −1.44043 0.469239i
\(239\) 2.35012 2.35012i 0.152017 0.152017i −0.627001 0.779018i \(-0.715718\pi\)
0.779018 + 0.627001i \(0.215718\pi\)
\(240\) 0 0
\(241\) −8.40368 8.40368i −0.541329 0.541329i 0.382590 0.923918i \(-0.375032\pi\)
−0.923918 + 0.382590i \(0.875032\pi\)
\(242\) 6.94639 + 13.6588i 0.446531 + 0.878021i
\(243\) 0 0
\(244\) −15.5953 7.21840i −0.998387 0.462111i
\(245\) 32.1522 21.4834i 2.05413 1.37253i
\(246\) 0 0
\(247\) −2.84477 6.86787i −0.181008 0.436992i
\(248\) −0.430035 + 0.698162i −0.0273072 + 0.0443333i
\(249\) 0 0
\(250\) 3.17203 + 11.2801i 0.200617 + 0.713416i
\(251\) −2.69294 + 13.5383i −0.169977 + 0.854531i 0.797839 + 0.602871i \(0.205977\pi\)
−0.967816 + 0.251660i \(0.919023\pi\)
\(252\) 0 0
\(253\) 0.679425 1.01683i 0.0427151 0.0639276i
\(254\) −6.63226 + 7.75340i −0.416145 + 0.486492i
\(255\) 0 0
\(256\) 13.0014 9.32541i 0.812588 0.582838i
\(257\) 8.71882 0.543865 0.271933 0.962316i \(-0.412337\pi\)
0.271933 + 0.962316i \(0.412337\pi\)
\(258\) 0 0
\(259\) −5.11211 + 7.65081i −0.317651 + 0.475398i
\(260\) 2.31805 + 14.7815i 0.143759 + 0.916708i
\(261\) 0 0
\(262\) −4.30335 15.3032i −0.265862 0.945435i
\(263\) 2.14234 5.17205i 0.132102 0.318923i −0.843963 0.536401i \(-0.819783\pi\)
0.976065 + 0.217479i \(0.0697833\pi\)
\(264\) 0 0
\(265\) −0.527283 1.27297i −0.0323907 0.0781981i
\(266\) −10.6044 13.4727i −0.650197 0.826067i
\(267\) 0 0
\(268\) −8.28056 3.83272i −0.505815 0.234120i
\(269\) 0.259937 + 1.30679i 0.0158487 + 0.0796766i 0.987900 0.155091i \(-0.0495671\pi\)
−0.972052 + 0.234768i \(0.924567\pi\)
\(270\) 0 0
\(271\) 21.0223 + 21.0223i 1.27701 + 1.27701i 0.942331 + 0.334682i \(0.108629\pi\)
0.334682 + 0.942331i \(0.391371\pi\)
\(272\) 6.46646 12.5960i 0.392087 0.763745i
\(273\) 0 0
\(274\) 16.1383 + 5.25726i 0.974950 + 0.317603i
\(275\) −0.727804 + 0.144769i −0.0438882 + 0.00872991i
\(276\) 0 0
\(277\) 7.36491 + 11.0224i 0.442515 + 0.662270i 0.983944 0.178476i \(-0.0571167\pi\)
−0.541430 + 0.840746i \(0.682117\pi\)
\(278\) 2.64074 22.1666i 0.158381 1.32946i
\(279\) 0 0
\(280\) 14.3759 + 31.3724i 0.859125 + 1.87486i
\(281\) −16.4892 6.83006i −0.983664 0.407447i −0.167883 0.985807i \(-0.553693\pi\)
−0.815782 + 0.578360i \(0.803693\pi\)
\(282\) 0 0
\(283\) 5.71735 + 1.13725i 0.339861 + 0.0676026i 0.362070 0.932151i \(-0.382070\pi\)
−0.0222092 + 0.999753i \(0.507070\pi\)
\(284\) 27.2036 + 6.57491i 1.61424 + 0.390149i
\(285\) 0 0
\(286\) 1.63713 0.127588i 0.0968053 0.00754445i
\(287\) 30.1831i 1.78165i
\(288\) 0 0
\(289\) 4.47035i 0.262962i
\(290\) 1.52025 + 19.5068i 0.0892722 + 1.14548i
\(291\) 0 0
\(292\) 26.2871 16.0536i 1.53833 0.939468i
\(293\) 0.815583 + 0.162230i 0.0476469 + 0.00947755i 0.218856 0.975757i \(-0.429767\pi\)
−0.171209 + 0.985235i \(0.554767\pi\)
\(294\) 0 0
\(295\) 13.0884 + 5.42138i 0.762035 + 0.315645i
\(296\) −4.08484 3.79336i −0.237426 0.220484i
\(297\) 0 0
\(298\) −27.4390 3.26885i −1.58950 0.189359i
\(299\) 4.79511 + 7.17638i 0.277308 + 0.415021i
\(300\) 0 0
\(301\) 28.6245 5.69377i 1.64989 0.328183i
\(302\) 5.92663 18.1931i 0.341039 1.04689i
\(303\) 0 0
\(304\) 9.07821 5.04772i 0.520671 0.289507i
\(305\) 15.8779 + 15.8779i 0.909168 + 0.909168i
\(306\) 0 0
\(307\) −1.18896 5.97730i −0.0678574 0.341142i 0.931910 0.362688i \(-0.118141\pi\)
−0.999768 + 0.0215462i \(0.993141\pi\)
\(308\) 3.55529 1.30546i 0.202582 0.0743854i
\(309\) 0 0
\(310\) 0.841920 0.662675i 0.0478178 0.0376374i
\(311\) −0.557543 1.34603i −0.0316154 0.0763262i 0.907283 0.420520i \(-0.138152\pi\)
−0.938899 + 0.344194i \(0.888152\pi\)
\(312\) 0 0
\(313\) 6.66243 16.0845i 0.376583 0.909151i −0.616019 0.787732i \(-0.711255\pi\)
0.992601 0.121419i \(-0.0387446\pi\)
\(314\) 13.5337 3.80574i 0.763748 0.214771i
\(315\) 0 0
\(316\) −6.96288 + 9.55291i −0.391693 + 0.537393i
\(317\) 0.843312 1.26210i 0.0473651 0.0708869i −0.807031 0.590509i \(-0.798927\pi\)
0.854396 + 0.519622i \(0.173927\pi\)
\(318\) 0 0
\(319\) 2.14736 0.120229
\(320\) −20.1474 + 5.58276i −1.12628 + 0.312086i
\(321\) 0 0
\(322\) 15.1274 + 12.9400i 0.843018 + 0.721118i
\(323\) 5.10677 7.64282i 0.284148 0.425258i
\(324\) 0 0
\(325\) 1.02172 5.13654i 0.0566749 0.284924i
\(326\) −27.7195 + 7.79490i −1.53524 + 0.431719i
\(327\) 0 0
\(328\) −18.0539 2.90183i −0.996862 0.160227i
\(329\) −0.355337 0.857858i −0.0195903 0.0472953i
\(330\) 0 0
\(331\) −27.1506 + 18.1415i −1.49233 + 0.997145i −0.501047 + 0.865420i \(0.667052\pi\)
−0.991286 + 0.131726i \(0.957948\pi\)
\(332\) 5.50607 + 14.9953i 0.302185 + 0.822971i
\(333\) 0 0
\(334\) 8.33370 4.23823i 0.456000 0.231906i
\(335\) 8.43063 + 8.43063i 0.460615 + 0.460615i
\(336\) 0 0
\(337\) 16.9423 16.9423i 0.922905 0.922905i −0.0743291 0.997234i \(-0.523682\pi\)
0.997234 + 0.0743291i \(0.0236815\pi\)
\(338\) 2.10487 6.46136i 0.114490 0.351452i
\(339\) 0 0
\(340\) −13.6048 + 12.5377i −0.737823 + 0.679952i
\(341\) −0.0653293 0.0977721i −0.00353778 0.00529466i
\(342\) 0 0
\(343\) 33.6307 13.9303i 1.81588 0.752164i
\(344\) 0.653732 + 17.6691i 0.0352469 + 0.952654i
\(345\) 0 0
\(346\) 1.66797 2.97306i 0.0896707 0.159832i
\(347\) 18.8803 + 3.75552i 1.01355 + 0.201607i 0.673803 0.738911i \(-0.264660\pi\)
0.339744 + 0.940518i \(0.389660\pi\)
\(348\) 0 0
\(349\) −19.9458 13.3274i −1.06768 0.713398i −0.107899 0.994162i \(-0.534412\pi\)
−0.959777 + 0.280764i \(0.909412\pi\)
\(350\) −0.938542 12.0427i −0.0501672 0.643711i
\(351\) 0 0
\(352\) 0.439049 + 2.25210i 0.0234014 + 0.120037i
\(353\) 5.30693i 0.282459i −0.989977 0.141230i \(-0.954894\pi\)
0.989977 0.141230i \(-0.0451056\pi\)
\(354\) 0 0
\(355\) −30.4064 20.3169i −1.61380 1.07831i
\(356\) 3.28892 13.6079i 0.174312 0.721215i
\(357\) 0 0
\(358\) −14.0134 7.86192i −0.740631 0.415516i
\(359\) 29.2567 + 12.1185i 1.54411 + 0.639591i 0.982239 0.187634i \(-0.0600819\pi\)
0.561871 + 0.827225i \(0.310082\pi\)
\(360\) 0 0
\(361\) −11.3237 + 4.69042i −0.595983 + 0.246864i
\(362\) 3.34078 28.0428i 0.175587 1.47390i
\(363\) 0 0
\(364\) −1.09015 + 26.7076i −0.0571395 + 1.39986i
\(365\) −39.4738 + 7.85183i −2.06615 + 0.410983i
\(366\) 0 0
\(367\) −10.7708 + 10.7708i −0.562232 + 0.562232i −0.929941 0.367709i \(-0.880142\pi\)
0.367709 + 0.929941i \(0.380142\pi\)
\(368\) −9.19440 + 7.80437i −0.479291 + 0.406831i
\(369\) 0 0
\(370\) 3.30194 + 6.49265i 0.171659 + 0.337537i
\(371\) −0.480223 2.41425i −0.0249319 0.125341i
\(372\) 0 0
\(373\) −7.80692 + 5.21641i −0.404227 + 0.270096i −0.741020 0.671483i \(-0.765658\pi\)
0.336793 + 0.941579i \(0.390658\pi\)
\(374\) 1.25584 + 1.59552i 0.0649378 + 0.0825025i
\(375\) 0 0
\(376\) 0.547289 0.130069i 0.0282243 0.00670778i
\(377\) −5.79965 + 14.0016i −0.298697 + 0.721119i
\(378\) 0 0
\(379\) 2.74905 13.8204i 0.141209 0.709906i −0.843697 0.536819i \(-0.819626\pi\)
0.984907 0.173087i \(-0.0553742\pi\)
\(380\) −13.4087 + 2.10276i −0.687850 + 0.107869i
\(381\) 0 0
\(382\) −5.76002 + 6.73371i −0.294708 + 0.344526i
\(383\) −15.8956 −0.812226 −0.406113 0.913823i \(-0.633116\pi\)
−0.406113 + 0.913823i \(0.633116\pi\)
\(384\) 0 0
\(385\) −4.94885 −0.252217
\(386\) 9.83676 11.4996i 0.500678 0.585314i
\(387\) 0 0
\(388\) 32.0936 5.03296i 1.62931 0.255510i
\(389\) 2.40830 12.1074i 0.122106 0.613867i −0.870468 0.492225i \(-0.836184\pi\)
0.992574 0.121643i \(-0.0388162\pi\)
\(390\) 0 0
\(391\) −4.08412 + 9.85995i −0.206543 + 0.498639i
\(392\) 9.67701 + 40.7179i 0.488763 + 2.05656i
\(393\) 0 0
\(394\) −0.231814 0.294517i −0.0116786 0.0148375i
\(395\) 12.8431 8.58149i 0.646207 0.431782i
\(396\) 0 0
\(397\) −0.557626 2.80338i −0.0279864 0.140697i 0.964266 0.264937i \(-0.0853510\pi\)
−0.992252 + 0.124239i \(0.960351\pi\)
\(398\) −1.49482 2.93929i −0.0749285 0.147333i
\(399\) 0 0
\(400\) 7.29358 + 0.596412i 0.364679 + 0.0298206i
\(401\) −12.5125 + 12.5125i −0.624843 + 0.624843i −0.946766 0.321923i \(-0.895671\pi\)
0.321923 + 0.946766i \(0.395671\pi\)
\(402\) 0 0
\(403\) 0.813953 0.161905i 0.0405459 0.00806508i
\(404\) 1.27453 31.2246i 0.0634100 1.55348i
\(405\) 0 0
\(406\) −4.13496 + 34.7092i −0.205214 + 1.72259i
\(407\) 0.738570 0.305926i 0.0366096 0.0151642i
\(408\) 0 0
\(409\) −9.49266 3.93199i −0.469382 0.194424i 0.135439 0.990786i \(-0.456755\pi\)
−0.604821 + 0.796361i \(0.706755\pi\)
\(410\) 20.8378 + 11.6906i 1.02911 + 0.577359i
\(411\) 0 0
\(412\) 0.730779 3.02359i 0.0360029 0.148961i
\(413\) 21.0436 + 14.0609i 1.03549 + 0.691891i
\(414\) 0 0
\(415\) 20.8729i 1.02461i
\(416\) −15.8703 3.21977i −0.778106 0.157862i
\(417\) 0 0
\(418\) 0.115739 + 1.48508i 0.00566097 + 0.0726377i
\(419\) −7.10316 4.74618i −0.347012 0.231866i 0.369834 0.929098i \(-0.379415\pi\)
−0.716846 + 0.697232i \(0.754415\pi\)
\(420\) 0 0
\(421\) −5.75098 1.14394i −0.280286 0.0557523i 0.0529457 0.998597i \(-0.483139\pi\)
−0.333231 + 0.942845i \(0.608139\pi\)
\(422\) 9.27611 16.5341i 0.451554 0.804867i
\(423\) 0 0
\(424\) 1.49025 0.0551370i 0.0723727 0.00267769i
\(425\) 5.98291 2.47820i 0.290214 0.120210i
\(426\) 0 0
\(427\) 22.2870 + 33.3549i 1.07854 + 1.61416i
\(428\) 5.63447 5.19253i 0.272352 0.250990i
\(429\) 0 0
\(430\) 7.15609 21.9672i 0.345097 1.05935i
\(431\) −26.6006 + 26.6006i −1.28131 + 1.28131i −0.341384 + 0.939924i \(0.610896\pi\)
−0.939924 + 0.341384i \(0.889104\pi\)
\(432\) 0 0
\(433\) 1.87012 + 1.87012i 0.0898724 + 0.0898724i 0.750614 0.660741i \(-0.229758\pi\)
−0.660741 + 0.750614i \(0.729758\pi\)
\(434\) 1.70615 0.867690i 0.0818980 0.0416504i
\(435\) 0 0
\(436\) 1.97255 + 5.37204i 0.0944678 + 0.257274i
\(437\) −6.50989 + 4.34977i −0.311410 + 0.208078i
\(438\) 0 0
\(439\) 3.81047 + 9.19929i 0.181864 + 0.439058i 0.988351 0.152194i \(-0.0486338\pi\)
−0.806487 + 0.591252i \(0.798634\pi\)
\(440\) 0.475787 2.96014i 0.0226822 0.141119i
\(441\) 0 0
\(442\) −13.7952 + 3.87929i −0.656170 + 0.184519i
\(443\) 2.30288 11.5774i 0.109413 0.550057i −0.886728 0.462292i \(-0.847027\pi\)
0.996141 0.0877657i \(-0.0279727\pi\)
\(444\) 0 0
\(445\) −10.1630 + 15.2100i −0.481771 + 0.721021i
\(446\) 28.8399 + 24.6697i 1.36561 + 1.16814i
\(447\) 0 0
\(448\) −37.2476 + 2.76000i −1.75978 + 0.130398i
\(449\) −34.7985 −1.64224 −0.821122 0.570753i \(-0.806651\pi\)
−0.821122 + 0.570753i \(0.806651\pi\)
\(450\) 0 0
\(451\) 1.45686 2.18034i 0.0686008 0.102668i
\(452\) −13.8272 + 18.9706i −0.650379 + 0.892304i
\(453\) 0 0
\(454\) 3.14555 0.884548i 0.147628 0.0415139i
\(455\) 13.3660 32.2683i 0.626606 1.51276i
\(456\) 0 0
\(457\) −9.80367 23.6682i −0.458596 1.10715i −0.968966 0.247195i \(-0.920491\pi\)
0.510369 0.859955i \(-0.329509\pi\)
\(458\) −10.2077 + 8.03450i −0.476975 + 0.375427i
\(459\) 0 0
\(460\) 14.7927 5.43171i 0.689716 0.253255i
\(461\) 7.22385 + 36.3168i 0.336448 + 1.69144i 0.664911 + 0.746923i \(0.268470\pi\)
−0.328463 + 0.944517i \(0.606530\pi\)
\(462\) 0 0
\(463\) 20.4267 + 20.4267i 0.949309 + 0.949309i 0.998776 0.0494671i \(-0.0157523\pi\)
−0.0494671 + 0.998776i \(0.515752\pi\)
\(464\) −20.3637 5.81029i −0.945362 0.269736i
\(465\) 0 0
\(466\) 7.75447 23.8040i 0.359219 1.10270i
\(467\) 13.6740 2.71993i 0.632758 0.125863i 0.131718 0.991287i \(-0.457951\pi\)
0.501041 + 0.865424i \(0.332951\pi\)
\(468\) 0 0
\(469\) 11.8336 + 17.7103i 0.546426 + 0.817784i
\(470\) −0.729880 0.0869515i −0.0336669 0.00401078i
\(471\) 0 0
\(472\) −10.4337 + 11.2354i −0.480248 + 0.517150i
\(473\) −2.34258 0.970329i −0.107712 0.0446158i
\(474\) 0 0
\(475\) 4.65950 + 0.926832i 0.213792 + 0.0425260i
\(476\) −28.2077 + 17.2266i −1.29290 + 0.789579i
\(477\) 0 0
\(478\) −0.365203 4.68603i −0.0167040 0.214334i
\(479\) 12.6579i 0.578354i −0.957276 0.289177i \(-0.906618\pi\)
0.957276 0.289177i \(-0.0933816\pi\)
\(480\) 0 0
\(481\) 5.64200i 0.257253i
\(482\) −16.7566 + 1.30591i −0.763240 + 0.0594826i
\(483\) 0 0
\(484\) 21.0644 + 5.09112i 0.957475 + 0.231415i
\(485\) −41.6325 8.28121i −1.89043 0.376030i
\(486\) 0 0
\(487\) 11.3843 + 4.71555i 0.515874 + 0.213682i 0.625404 0.780302i \(-0.284934\pi\)
−0.109529 + 0.993984i \(0.534934\pi\)
\(488\) −22.0939 + 10.1242i −1.00014 + 0.458300i
\(489\) 0 0
\(490\) 6.46912 54.3025i 0.292245 2.45314i
\(491\) 17.7122 + 26.5081i 0.799339 + 1.19629i 0.977217 + 0.212242i \(0.0680767\pi\)
−0.177878 + 0.984052i \(0.556923\pi\)
\(492\) 0 0
\(493\) −18.3796 + 3.65593i −0.827776 + 0.164655i
\(494\) −9.99587 3.25629i −0.449735 0.146507i
\(495\) 0 0
\(496\) 0.354976 + 1.10395i 0.0159389 + 0.0495690i
\(497\) −46.1963 46.1963i −2.07219 2.07219i
\(498\) 0 0
\(499\) −7.59034 38.1592i −0.339790 1.70824i −0.651992 0.758226i \(-0.726067\pi\)
0.312202 0.950016i \(-0.398933\pi\)
\(500\) 15.0384 + 6.96065i 0.672539 + 0.311290i
\(501\) 0 0
\(502\) 12.0737 + 15.3395i 0.538877 + 0.684636i
\(503\) −2.13613 5.15707i −0.0952452 0.229942i 0.869075 0.494680i \(-0.164715\pi\)
−0.964320 + 0.264738i \(0.914715\pi\)
\(504\) 0 0
\(505\) −15.6265 + 37.7257i −0.695370 + 1.67877i
\(506\) −0.468183 1.66491i −0.0208133 0.0740144i
\(507\) 0 0
\(508\) 2.23549 + 14.2551i 0.0991840 + 0.632466i
\(509\) 18.2483 27.3106i 0.808843 1.21052i −0.165668 0.986182i \(-0.552978\pi\)
0.974511 0.224338i \(-0.0720219\pi\)
\(510\) 0 0
\(511\) −71.9016 −3.18074
\(512\) 1.93013 22.5449i 0.0853006 0.996355i
\(513\) 0 0
\(514\) 8.01502 9.36991i 0.353528 0.413289i
\(515\) −2.25815 + 3.37956i −0.0995061 + 0.148921i
\(516\) 0 0
\(517\) −0.0157381 + 0.0791206i −0.000692159 + 0.00347972i
\(518\) 3.52269 + 12.5271i 0.154778 + 0.550408i
\(519\) 0 0
\(520\) 18.0162 + 11.0971i 0.790063 + 0.486642i
\(521\) −8.78528 21.2095i −0.384890 0.929207i −0.991004 0.133829i \(-0.957273\pi\)
0.606114 0.795378i \(-0.292727\pi\)
\(522\) 0 0
\(523\) −6.37316 + 4.25841i −0.278679 + 0.186207i −0.687053 0.726607i \(-0.741096\pi\)
0.408374 + 0.912815i \(0.366096\pi\)
\(524\) −20.4020 9.44320i −0.891264 0.412528i
\(525\) 0 0
\(526\) −3.58888 7.05687i −0.156483 0.307694i
\(527\) 0.725622 + 0.725622i 0.0316086 + 0.0316086i
\(528\) 0 0
\(529\) −9.83562 + 9.83562i −0.427636 + 0.427636i
\(530\) −1.85275 0.603558i −0.0804784 0.0262169i
\(531\) 0 0
\(532\) −24.2272 0.988907i −1.05038 0.0428745i
\(533\) 10.2819 + 15.3880i 0.445359 + 0.666527i
\(534\) 0 0
\(535\) −9.24983 + 3.83140i −0.399905 + 0.165646i
\(536\) −11.7311 + 5.37558i −0.506705 + 0.232190i
\(537\) 0 0
\(538\) 1.64333 + 0.921959i 0.0708492 + 0.0397485i
\(539\) −5.88651 1.17090i −0.253550 0.0504342i
\(540\) 0 0
\(541\) −30.0903 20.1057i −1.29368 0.864412i −0.297763 0.954640i \(-0.596241\pi\)
−0.995921 + 0.0902276i \(0.971241\pi\)
\(542\) 41.9175 3.26681i 1.80051 0.140321i
\(543\) 0 0
\(544\) −7.59213 18.5286i −0.325510 0.794406i
\(545\) 7.47770i 0.320309i
\(546\) 0 0
\(547\) 9.47625 + 6.33183i 0.405175 + 0.270729i 0.741415 0.671047i \(-0.234155\pi\)
−0.336239 + 0.941777i \(0.609155\pi\)
\(548\) 20.4854 12.5105i 0.875095 0.534424i
\(549\) 0 0
\(550\) −0.513474 + 0.915236i −0.0218946 + 0.0390258i
\(551\) −12.7012 5.26102i −0.541090 0.224127i
\(552\) 0 0
\(553\) 25.4943 10.5601i 1.08413 0.449060i
\(554\) 18.6159 + 2.21773i 0.790913 + 0.0942225i
\(555\) 0 0
\(556\) −21.3943 23.2152i −0.907322 0.984544i
\(557\) 31.7111 6.30773i 1.34364 0.267267i 0.529686 0.848194i \(-0.322310\pi\)
0.813956 + 0.580927i \(0.197310\pi\)
\(558\) 0 0
\(559\) 12.6538 12.6538i 0.535199 0.535199i
\(560\) 46.9306 + 13.3905i 1.98318 + 0.565852i
\(561\) 0 0
\(562\) −22.4983 + 11.4418i −0.949033 + 0.482645i
\(563\) −8.24892 41.4701i −0.347650 1.74776i −0.619108 0.785306i \(-0.712506\pi\)
0.271457 0.962451i \(-0.412494\pi\)
\(564\) 0 0
\(565\) 25.5045 17.0416i 1.07298 0.716944i
\(566\) 6.47801 5.09885i 0.272291 0.214320i
\(567\) 0 0
\(568\) 32.0736 23.1909i 1.34578 0.973067i
\(569\) −12.0106 + 28.9961i −0.503509 + 1.21558i 0.444051 + 0.896001i \(0.353541\pi\)
−0.947560 + 0.319577i \(0.896459\pi\)
\(570\) 0 0
\(571\) 0.546501 2.74744i 0.0228703 0.114977i −0.967664 0.252243i \(-0.918832\pi\)
0.990534 + 0.137266i \(0.0438316\pi\)
\(572\) 1.36786 1.87667i 0.0571930 0.0784675i
\(573\) 0 0
\(574\) 32.4370 + 27.7466i 1.35389 + 1.15812i
\(575\) −5.51591 −0.230030
\(576\) 0 0
\(577\) −24.8273 −1.03357 −0.516787 0.856114i \(-0.672872\pi\)
−0.516787 + 0.856114i \(0.672872\pi\)
\(578\) 4.80418 + 4.10950i 0.199827 + 0.170932i
\(579\) 0 0
\(580\) 22.3610 + 16.2984i 0.928492 + 0.676755i
\(581\) 7.27481 36.5729i 0.301810 1.51730i
\(582\) 0 0
\(583\) −0.0818394 + 0.197578i −0.00338944 + 0.00818283i
\(584\) 6.91269 43.0078i 0.286049 1.77968i
\(585\) 0 0
\(586\) 0.924092 0.727353i 0.0381739 0.0300467i
\(587\) 8.37191 5.59393i 0.345546 0.230886i −0.370671 0.928764i \(-0.620872\pi\)
0.716217 + 0.697878i \(0.245872\pi\)
\(588\) 0 0
\(589\) 0.146869 + 0.738359i 0.00605162 + 0.0304236i
\(590\) 17.8581 9.08200i 0.735206 0.373900i
\(591\) 0 0
\(592\) −7.83173 + 0.902726i −0.321882 + 0.0371018i
\(593\) 28.3397 28.3397i 1.16377 1.16377i 0.180131 0.983643i \(-0.442348\pi\)
0.983643 0.180131i \(-0.0576523\pi\)
\(594\) 0 0
\(595\) 42.3579 8.42552i 1.73651 0.345412i
\(596\) −28.7371 + 26.4831i −1.17712 + 1.08479i
\(597\) 0 0
\(598\) 12.1203 + 1.44391i 0.495637 + 0.0590458i
\(599\) 4.40247 1.82356i 0.179880 0.0745087i −0.290926 0.956746i \(-0.593963\pi\)
0.470806 + 0.882237i \(0.343963\pi\)
\(600\) 0 0
\(601\) −2.66779 1.10504i −0.108822 0.0450754i 0.327608 0.944814i \(-0.393757\pi\)
−0.436430 + 0.899738i \(0.643757\pi\)
\(602\) 20.1949 35.9962i 0.823084 1.46710i
\(603\) 0 0
\(604\) −14.1034 23.0937i −0.573860 0.939669i
\(605\) −23.5444 15.7319i −0.957217 0.639592i
\(606\) 0 0
\(607\) 46.5933i 1.89116i −0.325386 0.945581i \(-0.605494\pi\)
0.325386 0.945581i \(-0.394506\pi\)
\(608\) 2.92074 14.3964i 0.118452 0.583851i
\(609\) 0 0
\(610\) 31.6599 2.46739i 1.28187 0.0999017i
\(611\) −0.473389 0.316309i −0.0191513 0.0127965i
\(612\) 0 0
\(613\) −18.2485 3.62984i −0.737048 0.146608i −0.187729 0.982221i \(-0.560113\pi\)
−0.549319 + 0.835613i \(0.685113\pi\)
\(614\) −7.51664 4.21705i −0.303347 0.170186i
\(615\) 0 0
\(616\) 1.86536 5.02087i 0.0751574 0.202296i
\(617\) 26.6169 11.0251i 1.07155 0.443852i 0.224016 0.974586i \(-0.428083\pi\)
0.847539 + 0.530733i \(0.178083\pi\)
\(618\) 0 0
\(619\) 6.76585 + 10.1258i 0.271942 + 0.406990i 0.942154 0.335179i \(-0.108797\pi\)
−0.670212 + 0.742170i \(0.733797\pi\)
\(620\) 0.0617974 1.51397i 0.00248184 0.0608027i
\(621\) 0 0
\(622\) −1.95908 0.638196i −0.0785519 0.0255893i
\(623\) −23.1084 + 23.1084i −0.925820 + 0.925820i
\(624\) 0 0
\(625\) −21.7792 21.7792i −0.871167 0.871167i
\(626\) −11.1610 21.9461i −0.446084 0.877143i
\(627\) 0 0
\(628\) 8.35125 18.0428i 0.333251 0.719987i
\(629\) −5.80069 + 3.87590i −0.231289 + 0.154542i
\(630\) 0 0
\(631\) 0.364096 + 0.879005i 0.0144944 + 0.0349926i 0.930961 0.365118i \(-0.118972\pi\)
−0.916467 + 0.400111i \(0.868972\pi\)
\(632\) 3.86545 + 16.2646i 0.153759 + 0.646972i
\(633\) 0 0
\(634\) −0.581115 2.06651i −0.0230790 0.0820717i
\(635\) 3.67828 18.4919i 0.145968 0.733831i
\(636\) 0 0
\(637\) 23.5331 35.2198i 0.932416 1.39546i
\(638\) 1.97402 2.30772i 0.0781523 0.0913634i
\(639\) 0 0
\(640\) −12.5215 + 26.7841i −0.494954 + 1.05873i
\(641\) −23.8243 −0.941002 −0.470501 0.882399i \(-0.655927\pi\)
−0.470501 + 0.882399i \(0.655927\pi\)
\(642\) 0 0
\(643\) −25.7461 + 38.5318i −1.01533 + 1.51954i −0.169895 + 0.985462i \(0.554343\pi\)
−0.845432 + 0.534083i \(0.820657\pi\)
\(644\) 27.8126 4.36160i 1.09597 0.171871i
\(645\) 0 0
\(646\) −3.51901 12.5140i −0.138454 0.492356i
\(647\) −13.2165 + 31.9073i −0.519592 + 1.25441i 0.418561 + 0.908188i \(0.362534\pi\)
−0.938154 + 0.346219i \(0.887466\pi\)
\(648\) 0 0
\(649\) −0.841451 2.03144i −0.0330298 0.0797411i
\(650\) −4.58087 5.81993i −0.179677 0.228277i
\(651\) 0 0
\(652\) −17.1050 + 36.9552i −0.669882 + 1.44728i
\(653\) −2.10914 10.6034i −0.0825371 0.414942i −0.999859 0.0167955i \(-0.994654\pi\)
0.917322 0.398146i \(-0.130346\pi\)
\(654\) 0 0
\(655\) 20.7717 + 20.7717i 0.811618 + 0.811618i
\(656\) −19.7151 + 16.7346i −0.769746 + 0.653374i
\(657\) 0 0
\(658\) −1.24857 0.406739i −0.0486744 0.0158563i
\(659\) −19.8824 + 3.95485i −0.774508 + 0.154059i −0.566493 0.824067i \(-0.691700\pi\)
−0.208015 + 0.978126i \(0.566700\pi\)
\(660\) 0 0
\(661\) 1.28231 + 1.91911i 0.0498760 + 0.0746447i 0.855570 0.517688i \(-0.173207\pi\)
−0.805694 + 0.592333i \(0.798207\pi\)
\(662\) −5.46279 + 45.8552i −0.212317 + 1.78221i
\(663\) 0 0
\(664\) 21.1766 + 7.86757i 0.821813 + 0.305321i
\(665\) 29.2714 + 12.1246i 1.13510 + 0.470173i
\(666\) 0 0
\(667\) 15.6551 + 3.11400i 0.606169 + 0.120574i
\(668\) 3.10627 12.8521i 0.120185 0.497264i
\(669\) 0 0
\(670\) 16.8103 1.31010i 0.649438 0.0506135i
\(671\) 3.48520i 0.134545i
\(672\) 0 0
\(673\) 9.14126i 0.352370i −0.984357 0.176185i \(-0.943624\pi\)
0.984357 0.176185i \(-0.0563756\pi\)
\(674\) −2.63279 33.7821i −0.101411 1.30124i
\(675\) 0 0
\(676\) −5.00890 8.20185i −0.192650 0.315456i
\(677\) −41.3684 8.22868i −1.58992 0.316254i −0.680695 0.732567i \(-0.738322\pi\)
−0.909221 + 0.416313i \(0.863322\pi\)
\(678\) 0 0
\(679\) −70.0611 29.0203i −2.68870 1.11370i
\(680\) 0.967379 + 26.1464i 0.0370973 + 1.00267i
\(681\) 0 0
\(682\) −0.165129 0.0196720i −0.00632312 0.000753281i
\(683\) 17.8505 + 26.7151i 0.683029 + 1.02223i 0.997339 + 0.0729051i \(0.0232270\pi\)
−0.314310 + 0.949321i \(0.601773\pi\)
\(684\) 0 0
\(685\) −30.7618 + 6.11891i −1.17535 + 0.233791i
\(686\) 15.9454 48.9478i 0.608798 1.86884i
\(687\) 0 0
\(688\) 19.5895 + 15.5403i 0.746843 + 0.592467i
\(689\) −1.06725 1.06725i −0.0406588 0.0406588i
\(690\) 0 0
\(691\) 3.87095 + 19.4606i 0.147258 + 0.740315i 0.981882 + 0.189495i \(0.0606850\pi\)
−0.834624 + 0.550820i \(0.814315\pi\)
\(692\) −1.66174 4.52559i −0.0631699 0.172037i
\(693\) 0 0
\(694\) 21.3922 16.8378i 0.812037 0.639154i
\(695\) 15.7862 + 38.1113i 0.598805 + 1.44564i
\(696\) 0 0
\(697\) −8.75739 + 21.1422i −0.331710 + 0.800819i
\(698\) −32.6584 + 9.18373i −1.23614 + 0.347609i
\(699\) 0 0
\(700\) −13.8048 10.0620i −0.521773 0.380308i
\(701\) −15.9568 + 23.8811i −0.602681 + 0.901976i −0.999876 0.0157585i \(-0.994984\pi\)
0.397195 + 0.917734i \(0.369984\pi\)
\(702\) 0 0
\(703\) −5.11801 −0.193029
\(704\) 2.82389 + 1.59847i 0.106429 + 0.0602447i
\(705\) 0 0
\(706\) −5.70323 4.87854i −0.214644 0.183606i
\(707\) −40.5289 + 60.6557i −1.52424 + 2.28119i
\(708\) 0 0
\(709\) 3.15652 15.8689i 0.118546 0.595969i −0.875149 0.483853i \(-0.839237\pi\)
0.993695 0.112116i \(-0.0357629\pi\)
\(710\) −49.7860 + 14.0001i −1.86843 + 0.525415i
\(711\) 0 0
\(712\) −11.6006 16.0439i −0.434751 0.601272i
\(713\) −0.334492 0.807535i −0.0125268 0.0302424i
\(714\) 0 0
\(715\) −2.52303 + 1.68583i −0.0943560 + 0.0630466i
\(716\) −21.3312 + 7.83256i −0.797185 + 0.292716i
\(717\) 0 0
\(718\) 39.9185 20.3012i 1.48975 0.757633i
\(719\) −15.3302 15.3302i −0.571719 0.571719i 0.360889 0.932609i \(-0.382473\pi\)
−0.932609 + 0.360889i \(0.882473\pi\)
\(720\) 0 0
\(721\) −5.13455 + 5.13455i −0.191221 + 0.191221i
\(722\) −5.36893 + 16.4811i −0.199811 + 0.613362i
\(723\) 0 0
\(724\) −27.0658 29.3694i −1.00589 1.09150i
\(725\) −5.38095 8.05317i −0.199844 0.299087i
\(726\) 0 0
\(727\) −29.8242 + 12.3536i −1.10612 + 0.458169i −0.859599 0.510969i \(-0.829287\pi\)
−0.246519 + 0.969138i \(0.579287\pi\)
\(728\) 27.6999 + 25.7233i 1.02663 + 0.953369i
\(729\) 0 0
\(730\) −27.8492 + 49.6395i −1.03075 + 1.83724i
\(731\) 21.7025 + 4.31690i 0.802696 + 0.159666i
\(732\) 0 0
\(733\) 25.9985 + 17.3717i 0.960278 + 0.641637i 0.933718 0.358010i \(-0.116545\pi\)
0.0265602 + 0.999647i \(0.491545\pi\)
\(734\) 1.67376 + 21.4765i 0.0617795 + 0.792713i
\(735\) 0 0
\(736\) −0.0650434 + 17.0554i −0.00239753 + 0.628670i
\(737\) 1.85052i 0.0681648i
\(738\) 0 0
\(739\) 2.73845 + 1.82977i 0.100735 + 0.0673092i 0.604918 0.796288i \(-0.293206\pi\)
−0.504182 + 0.863597i \(0.668206\pi\)
\(740\) 10.0129 + 2.42004i 0.368081 + 0.0889625i
\(741\) 0 0
\(742\) −3.03599 1.70328i −0.111455 0.0625293i
\(743\) −2.57199 1.06535i −0.0943570 0.0390840i 0.335006 0.942216i \(-0.391262\pi\)
−0.429363 + 0.903132i \(0.641262\pi\)
\(744\) 0 0
\(745\) 47.1762 19.5410i 1.72840 0.715928i
\(746\) −1.57077 + 13.1852i −0.0575101 + 0.482746i
\(747\) 0 0
\(748\) 2.86913 + 0.117112i 0.104906 + 0.00428205i
\(749\) −17.5427 + 3.48946i −0.640996 + 0.127502i
\(750\) 0 0
\(751\) −10.0944 + 10.0944i −0.368350 + 0.368350i −0.866875 0.498525i \(-0.833875\pi\)
0.498525 + 0.866875i \(0.333875\pi\)
\(752\) 0.363329 0.707727i 0.0132492 0.0258082i
\(753\) 0 0
\(754\) 9.71568 + 19.1041i 0.353824 + 0.695730i
\(755\) 6.89798 + 34.6785i 0.251043 + 1.26208i
\(756\) 0 0
\(757\) 0.275639 0.184176i 0.0100183 0.00669400i −0.550551 0.834802i \(-0.685582\pi\)
0.560569 + 0.828108i \(0.310582\pi\)
\(758\) −12.3253 15.6591i −0.447675 0.568765i
\(759\) 0 0
\(760\) −10.0665 + 16.3430i −0.365151 + 0.592823i
\(761\) 14.0734 33.9761i 0.510160 1.23163i −0.433631 0.901091i \(-0.642768\pi\)
0.943791 0.330544i \(-0.107232\pi\)
\(762\) 0 0
\(763\) 2.60620 13.1022i 0.0943507 0.474333i
\(764\) 1.94149 + 12.3803i 0.0702407 + 0.447903i
\(765\) 0 0
\(766\) −14.6125 + 17.0826i −0.527970 + 0.617219i
\(767\) 15.5184 0.560336
\(768\) 0 0
\(769\) 10.1509 0.366049 0.183025 0.983108i \(-0.441411\pi\)
0.183025 + 0.983108i \(0.441411\pi\)
\(770\) −4.54937 + 5.31840i −0.163948 + 0.191662i
\(771\) 0 0
\(772\) −3.31561 21.1426i −0.119332 0.760941i
\(773\) −1.32796 + 6.67611i −0.0477634 + 0.240123i −0.997291 0.0735616i \(-0.976563\pi\)
0.949527 + 0.313685i \(0.101563\pi\)
\(774\) 0 0
\(775\) −0.202966 + 0.490003i −0.00729076 + 0.0176014i
\(776\) 24.0942 39.1169i 0.864930 1.40422i
\(777\) 0 0
\(778\) −10.7976 13.7182i −0.387112 0.491820i
\(779\) −13.9589 + 9.32701i −0.500128 + 0.334175i
\(780\) 0 0
\(781\) 1.10732 + 5.56687i 0.0396230 + 0.199198i
\(782\) 6.84180 + 13.4531i 0.244662 + 0.481083i
\(783\) 0 0
\(784\) 52.6543 + 27.0314i 1.88051 + 0.965407i
\(785\) −18.3698 + 18.3698i −0.655647 + 0.655647i
\(786\) 0 0
\(787\) −1.70358 + 0.338863i −0.0607260 + 0.0120792i −0.225360 0.974276i \(-0.572356\pi\)
0.164634 + 0.986355i \(0.447356\pi\)
\(788\) −0.529612 0.0216177i