Properties

Label 490.2.g.c.97.5
Level $490$
Weight $2$
Character 490.97
Analytic conductor $3.913$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 10 x^{14} + 61 x^{12} + 266 x^{10} + 852 x^{8} + 1438 x^{6} + 1933 x^{4} + 3038 x^{2} + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 97.5
Root \(-0.144868 + 1.25092i\) of defining polynomial
Character \(\chi\) \(=\) 490.97
Dual form 490.2.g.c.293.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.42962 - 1.42962i) q^{3} +1.00000i q^{4} +(-0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.08763i q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(-1.42962 - 1.42962i) q^{3} +1.00000i q^{4} +(-0.204875 - 2.22666i) q^{5} -2.02179i q^{6} +(-0.707107 + 0.707107i) q^{8} +1.08763i q^{9} +(1.42962 - 1.71936i) q^{10} -4.03997 q^{11} +(1.42962 - 1.42962i) q^{12} +(-0.204875 - 0.204875i) q^{13} +(-2.89039 + 3.47617i) q^{15} -1.00000 q^{16} +(-1.44231 + 1.44231i) q^{17} +(-0.769067 + 0.769067i) q^{18} -6.20333 q^{19} +(2.22666 - 0.204875i) q^{20} +(-2.85669 - 2.85669i) q^{22} +(3.20895 - 3.20895i) q^{23} +2.02179 q^{24} +(-4.91605 + 0.912375i) q^{25} -0.289737i q^{26} +(-2.73397 + 2.73397i) q^{27} -7.15869i q^{29} +(-4.50184 + 0.414214i) q^{30} -7.31256i q^{31} +(-0.707107 - 0.707107i) q^{32} +(5.77563 + 5.77563i) q^{33} -2.03974 q^{34} -1.08763 q^{36} +(3.27091 + 3.27091i) q^{37} +(-4.38642 - 4.38642i) q^{38} +0.585786i q^{39} +(1.71936 + 1.42962i) q^{40} -2.58745i q^{41} +(-4.97801 + 4.97801i) q^{43} -4.03997i q^{44} +(2.42177 - 0.222827i) q^{45} +4.53813 q^{46} +(0.222827 - 0.222827i) q^{47} +(1.42962 + 1.42962i) q^{48} +(-4.12132 - 2.83103i) q^{50} +4.12392 q^{51} +(0.204875 - 0.204875i) q^{52} +(5.85669 - 5.85669i) q^{53} -3.86642 q^{54} +(0.827689 + 8.99566i) q^{55} +(8.86840 + 8.86840i) q^{57} +(5.06196 - 5.06196i) q^{58} +0.855404 q^{59} +(-3.47617 - 2.89039i) q^{60} -6.92077i q^{61} +(5.17076 - 5.17076i) q^{62} -1.00000i q^{64} +(-0.414214 + 0.498161i) q^{65} +8.16797i q^{66} +(-2.23353 - 2.23353i) q^{67} +(-1.44231 - 1.44231i) q^{68} -9.17514 q^{69} +7.12240 q^{71} +(-0.769067 - 0.769067i) q^{72} +(8.15002 + 8.15002i) q^{73} +4.62576i q^{74} +(8.33243 + 5.72374i) q^{75} -6.20333i q^{76} +(-0.414214 + 0.414214i) q^{78} +5.07627i q^{79} +(0.204875 + 2.22666i) q^{80} +11.0799 q^{81} +(1.82961 - 1.82961i) q^{82} +(3.85372 + 3.85372i) q^{83} +(3.50704 + 2.91605i) q^{85} -7.03997 q^{86} +(-10.2342 + 10.2342i) q^{87} +(2.85669 - 2.85669i) q^{88} -3.07230 q^{89} +(1.87002 + 1.55489i) q^{90} +(3.20895 + 3.20895i) q^{92} +(-10.4542 + 10.4542i) q^{93} +0.315125 q^{94} +(1.27091 + 13.8127i) q^{95} +2.02179i q^{96} +(6.63103 - 6.63103i) q^{97} -4.39398i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + O(q^{10}) \) \( 16 q + 24 q^{11} + 16 q^{15} - 16 q^{16} + 16 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{25} - 40 q^{30} - 8 q^{36} - 8 q^{37} - 8 q^{43} + 16 q^{46} - 32 q^{50} + 32 q^{51} + 56 q^{53} + 8 q^{57} + 64 q^{58} - 16 q^{60} + 16 q^{65} - 64 q^{67} + 16 q^{71} + 16 q^{72} + 16 q^{78} + 24 q^{85} - 24 q^{86} + 8 q^{88} + 8 q^{92} - 56 q^{93} - 40 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) −1.42962 1.42962i −0.825391 0.825391i 0.161484 0.986875i \(-0.448372\pi\)
−0.986875 + 0.161484i \(0.948372\pi\)
\(4\) 1.00000i 0.500000i
\(5\) −0.204875 2.22666i −0.0916228 0.995794i
\(6\) 2.02179i 0.825391i
\(7\) 0 0
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 1.08763i 0.362542i
\(10\) 1.42962 1.71936i 0.452085 0.543708i
\(11\) −4.03997 −1.21810 −0.609049 0.793133i \(-0.708449\pi\)
−0.609049 + 0.793133i \(0.708449\pi\)
\(12\) 1.42962 1.42962i 0.412696 0.412696i
\(13\) −0.204875 0.204875i −0.0568221 0.0568221i 0.678125 0.734947i \(-0.262793\pi\)
−0.734947 + 0.678125i \(0.762793\pi\)
\(14\) 0 0
\(15\) −2.89039 + 3.47617i −0.746295 + 0.897544i
\(16\) −1.00000 −0.250000
\(17\) −1.44231 + 1.44231i −0.349813 + 0.349813i −0.860040 0.510227i \(-0.829561\pi\)
0.510227 + 0.860040i \(0.329561\pi\)
\(18\) −0.769067 + 0.769067i −0.181271 + 0.181271i
\(19\) −6.20333 −1.42314 −0.711571 0.702615i \(-0.752016\pi\)
−0.711571 + 0.702615i \(0.752016\pi\)
\(20\) 2.22666 0.204875i 0.497897 0.0458114i
\(21\) 0 0
\(22\) −2.85669 2.85669i −0.609049 0.609049i
\(23\) 3.20895 3.20895i 0.669111 0.669111i −0.288399 0.957510i \(-0.593123\pi\)
0.957510 + 0.288399i \(0.0931229\pi\)
\(24\) 2.02179 0.412696
\(25\) −4.91605 + 0.912375i −0.983211 + 0.182475i
\(26\) 0.289737i 0.0568221i
\(27\) −2.73397 + 2.73397i −0.526152 + 0.526152i
\(28\) 0 0
\(29\) 7.15869i 1.32934i −0.747139 0.664668i \(-0.768573\pi\)
0.747139 0.664668i \(-0.231427\pi\)
\(30\) −4.50184 + 0.414214i −0.821920 + 0.0756247i
\(31\) 7.31256i 1.31338i −0.754163 0.656688i \(-0.771957\pi\)
0.754163 0.656688i \(-0.228043\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) 5.77563 + 5.77563i 1.00541 + 1.00541i
\(34\) −2.03974 −0.349813
\(35\) 0 0
\(36\) −1.08763 −0.181271
\(37\) 3.27091 + 3.27091i 0.537734 + 0.537734i 0.922863 0.385129i \(-0.125843\pi\)
−0.385129 + 0.922863i \(0.625843\pi\)
\(38\) −4.38642 4.38642i −0.711571 0.711571i
\(39\) 0.585786i 0.0938009i
\(40\) 1.71936 + 1.42962i 0.271854 + 0.226043i
\(41\) 2.58745i 0.404093i −0.979376 0.202046i \(-0.935241\pi\)
0.979376 0.202046i \(-0.0647591\pi\)
\(42\) 0 0
\(43\) −4.97801 + 4.97801i −0.759140 + 0.759140i −0.976166 0.217026i \(-0.930364\pi\)
0.217026 + 0.976166i \(0.430364\pi\)
\(44\) 4.03997i 0.609049i
\(45\) 2.42177 0.222827i 0.361017 0.0332171i
\(46\) 4.53813 0.669111
\(47\) 0.222827 0.222827i 0.0325027 0.0325027i −0.690669 0.723171i \(-0.742684\pi\)
0.723171 + 0.690669i \(0.242684\pi\)
\(48\) 1.42962 + 1.42962i 0.206348 + 0.206348i
\(49\) 0 0
\(50\) −4.12132 2.83103i −0.582843 0.400368i
\(51\) 4.12392 0.577464
\(52\) 0.204875 0.204875i 0.0284110 0.0284110i
\(53\) 5.85669 5.85669i 0.804479 0.804479i −0.179313 0.983792i \(-0.557388\pi\)
0.983792 + 0.179313i \(0.0573876\pi\)
\(54\) −3.86642 −0.526152
\(55\) 0.827689 + 8.99566i 0.111606 + 1.21297i
\(56\) 0 0
\(57\) 8.86840 + 8.86840i 1.17465 + 1.17465i
\(58\) 5.06196 5.06196i 0.664668 0.664668i
\(59\) 0.855404 0.111364 0.0556821 0.998449i \(-0.482267\pi\)
0.0556821 + 0.998449i \(0.482267\pi\)
\(60\) −3.47617 2.89039i −0.448772 0.373147i
\(61\) 6.92077i 0.886113i −0.896494 0.443057i \(-0.853894\pi\)
0.896494 0.443057i \(-0.146106\pi\)
\(62\) 5.17076 5.17076i 0.656688 0.656688i
\(63\) 0 0
\(64\) 1.00000i 0.125000i
\(65\) −0.414214 + 0.498161i −0.0513769 + 0.0617893i
\(66\) 8.16797i 1.00541i
\(67\) −2.23353 2.23353i −0.272870 0.272870i 0.557385 0.830254i \(-0.311805\pi\)
−0.830254 + 0.557385i \(0.811805\pi\)
\(68\) −1.44231 1.44231i −0.174906 0.174906i
\(69\) −9.17514 −1.10456
\(70\) 0 0
\(71\) 7.12240 0.845273 0.422637 0.906299i \(-0.361105\pi\)
0.422637 + 0.906299i \(0.361105\pi\)
\(72\) −0.769067 0.769067i −0.0906355 0.0906355i
\(73\) 8.15002 + 8.15002i 0.953887 + 0.953887i 0.998983 0.0450954i \(-0.0143592\pi\)
−0.0450954 + 0.998983i \(0.514359\pi\)
\(74\) 4.62576i 0.537734i
\(75\) 8.33243 + 5.72374i 0.962147 + 0.660920i
\(76\) 6.20333i 0.711571i
\(77\) 0 0
\(78\) −0.414214 + 0.414214i −0.0469005 + 0.0469005i
\(79\) 5.07627i 0.571125i 0.958360 + 0.285562i \(0.0921804\pi\)
−0.958360 + 0.285562i \(0.907820\pi\)
\(80\) 0.204875 + 2.22666i 0.0229057 + 0.248948i
\(81\) 11.0799 1.23111
\(82\) 1.82961 1.82961i 0.202046 0.202046i
\(83\) 3.85372 + 3.85372i 0.423001 + 0.423001i 0.886236 0.463235i \(-0.153311\pi\)
−0.463235 + 0.886236i \(0.653311\pi\)
\(84\) 0 0
\(85\) 3.50704 + 2.91605i 0.380392 + 0.316290i
\(86\) −7.03997 −0.759140
\(87\) −10.2342 + 10.2342i −1.09722 + 1.09722i
\(88\) 2.85669 2.85669i 0.304524 0.304524i
\(89\) −3.07230 −0.325664 −0.162832 0.986654i \(-0.552063\pi\)
−0.162832 + 0.986654i \(0.552063\pi\)
\(90\) 1.87002 + 1.55489i 0.197117 + 0.163900i
\(91\) 0 0
\(92\) 3.20895 + 3.20895i 0.334556 + 0.334556i
\(93\) −10.4542 + 10.4542i −1.08405 + 1.08405i
\(94\) 0.315125 0.0325027
\(95\) 1.27091 + 13.8127i 0.130392 + 1.41716i
\(96\) 2.02179i 0.206348i
\(97\) 6.63103 6.63103i 0.673279 0.673279i −0.285191 0.958471i \(-0.592057\pi\)
0.958471 + 0.285191i \(0.0920572\pi\)
\(98\) 0 0
\(99\) 4.39398i 0.441611i
\(100\) −0.912375 4.91605i −0.0912375 0.491605i
\(101\) 9.88844i 0.983936i 0.870613 + 0.491968i \(0.163722\pi\)
−0.870613 + 0.491968i \(0.836278\pi\)
\(102\) 2.91605 + 2.91605i 0.288732 + 0.288732i
\(103\) 3.02785 + 3.02785i 0.298343 + 0.298343i 0.840365 0.542022i \(-0.182341\pi\)
−0.542022 + 0.840365i \(0.682341\pi\)
\(104\) 0.289737 0.0284110
\(105\) 0 0
\(106\) 8.28261 0.804479
\(107\) −10.5161 10.5161i −1.01663 1.01663i −0.999859 0.0167751i \(-0.994660\pi\)
−0.0167751 0.999859i \(-0.505340\pi\)
\(108\) −2.73397 2.73397i −0.263076 0.263076i
\(109\) 13.2313i 1.26733i −0.773609 0.633664i \(-0.781550\pi\)
0.773609 0.633664i \(-0.218450\pi\)
\(110\) −5.77563 + 6.94616i −0.550684 + 0.662290i
\(111\) 9.35230i 0.887681i
\(112\) 0 0
\(113\) 9.75336 9.75336i 0.917519 0.917519i −0.0793296 0.996848i \(-0.525278\pi\)
0.996848 + 0.0793296i \(0.0252780\pi\)
\(114\) 12.5418i 1.17465i
\(115\) −7.80267 6.48781i −0.727603 0.604991i
\(116\) 7.15869 0.664668
\(117\) 0.222827 0.222827i 0.0206004 0.0206004i
\(118\) 0.604862 + 0.604862i 0.0556821 + 0.0556821i
\(119\) 0 0
\(120\) −0.414214 4.50184i −0.0378124 0.410960i
\(121\) 5.32139 0.483762
\(122\) 4.89372 4.89372i 0.443057 0.443057i
\(123\) −3.69908 + 3.69908i −0.333535 + 0.333535i
\(124\) 7.31256 0.656688
\(125\) 3.03873 + 10.7595i 0.271792 + 0.962356i
\(126\) 0 0
\(127\) −2.19984 2.19984i −0.195204 0.195204i 0.602736 0.797940i \(-0.294077\pi\)
−0.797940 + 0.602736i \(0.794077\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 14.2333 1.25317
\(130\) −0.645146 + 0.0593598i −0.0565831 + 0.00520620i
\(131\) 7.29876i 0.637695i −0.947806 0.318848i \(-0.896704\pi\)
0.947806 0.318848i \(-0.103296\pi\)
\(132\) −5.77563 + 5.77563i −0.502704 + 0.502704i
\(133\) 0 0
\(134\) 3.15869i 0.272870i
\(135\) 6.64775 + 5.52750i 0.572147 + 0.475732i
\(136\) 2.03974i 0.174906i
\(137\) 5.07627 + 5.07627i 0.433695 + 0.433695i 0.889883 0.456188i \(-0.150786\pi\)
−0.456188 + 0.889883i \(0.650786\pi\)
\(138\) −6.48781 6.48781i −0.552279 0.552279i
\(139\) −12.4172 −1.05321 −0.526605 0.850110i \(-0.676535\pi\)
−0.526605 + 0.850110i \(0.676535\pi\)
\(140\) 0 0
\(141\) −0.637116 −0.0536549
\(142\) 5.03630 + 5.03630i 0.422637 + 0.422637i
\(143\) 0.827689 + 0.827689i 0.0692148 + 0.0692148i
\(144\) 1.08763i 0.0906355i
\(145\) −15.9400 + 1.46664i −1.32374 + 0.121798i
\(146\) 11.5259i 0.953887i
\(147\) 0 0
\(148\) −3.27091 + 3.27091i −0.268867 + 0.268867i
\(149\) 23.9483i 1.96193i −0.194197 0.980963i \(-0.562210\pi\)
0.194197 0.980963i \(-0.437790\pi\)
\(150\) 1.84463 + 9.93921i 0.150613 + 0.811533i
\(151\) −3.54334 −0.288353 −0.144176 0.989552i \(-0.546053\pi\)
−0.144176 + 0.989552i \(0.546053\pi\)
\(152\) 4.38642 4.38642i 0.355785 0.355785i
\(153\) −1.56870 1.56870i −0.126822 0.126822i
\(154\) 0 0
\(155\) −16.2826 + 1.49816i −1.30785 + 0.120335i
\(156\) −0.585786 −0.0469005
\(157\) −4.32927 + 4.32927i −0.345513 + 0.345513i −0.858435 0.512922i \(-0.828563\pi\)
0.512922 + 0.858435i \(0.328563\pi\)
\(158\) −3.58946 + 3.58946i −0.285562 + 0.285562i
\(159\) −16.7457 −1.32802
\(160\) −1.42962 + 1.71936i −0.113021 + 0.135927i
\(161\) 0 0
\(162\) 7.83471 + 7.83471i 0.615553 + 0.615553i
\(163\) −11.7082 + 11.7082i −0.917056 + 0.917056i −0.996814 0.0797585i \(-0.974585\pi\)
0.0797585 + 0.996814i \(0.474585\pi\)
\(164\) 2.58745 0.202046
\(165\) 11.6771 14.0437i 0.909060 1.09330i
\(166\) 5.44998i 0.423001i
\(167\) 10.2873 10.2873i 0.796056 0.796056i −0.186415 0.982471i \(-0.559687\pi\)
0.982471 + 0.186415i \(0.0596869\pi\)
\(168\) 0 0
\(169\) 12.9161i 0.993543i
\(170\) 0.417892 + 4.54181i 0.0320508 + 0.348341i
\(171\) 6.74690i 0.515948i
\(172\) −4.97801 4.97801i −0.379570 0.379570i
\(173\) 5.49565 + 5.49565i 0.417827 + 0.417827i 0.884454 0.466627i \(-0.154531\pi\)
−0.466627 + 0.884454i \(0.654531\pi\)
\(174\) −14.4734 −1.09722
\(175\) 0 0
\(176\) 4.03997 0.304524
\(177\) −1.22290 1.22290i −0.0919190 0.0919190i
\(178\) −2.17245 2.17245i −0.162832 0.162832i
\(179\) 3.86472i 0.288863i 0.989515 + 0.144431i \(0.0461353\pi\)
−0.989515 + 0.144431i \(0.953865\pi\)
\(180\) 0.222827 + 2.42177i 0.0166086 + 0.180508i
\(181\) 6.99107i 0.519642i 0.965657 + 0.259821i \(0.0836636\pi\)
−0.965657 + 0.259821i \(0.916336\pi\)
\(182\) 0 0
\(183\) −9.89407 + 9.89407i −0.731390 + 0.731390i
\(184\) 4.53813i 0.334556i
\(185\) 6.61308 7.95333i 0.486203 0.584741i
\(186\) −14.7845 −1.08405
\(187\) 5.82691 5.82691i 0.426106 0.426106i
\(188\) 0.222827 + 0.222827i 0.0162513 + 0.0162513i
\(189\) 0 0
\(190\) −8.86840 + 10.6657i −0.643381 + 0.773774i
\(191\) 4.47442 0.323758 0.161879 0.986811i \(-0.448245\pi\)
0.161879 + 0.986811i \(0.448245\pi\)
\(192\) −1.42962 + 1.42962i −0.103174 + 0.103174i
\(193\) −14.1950 + 14.1950i −1.02178 + 1.02178i −0.0220201 + 0.999758i \(0.507010\pi\)
−0.999758 + 0.0220201i \(0.992990\pi\)
\(194\) 9.37769 0.673279
\(195\) 1.30435 0.120013i 0.0934064 0.00859431i
\(196\) 0 0
\(197\) −7.84901 7.84901i −0.559219 0.559219i 0.369866 0.929085i \(-0.379404\pi\)
−0.929085 + 0.369866i \(0.879404\pi\)
\(198\) 3.10701 3.10701i 0.220806 0.220806i
\(199\) −10.8021 −0.765737 −0.382869 0.923803i \(-0.625064\pi\)
−0.382869 + 0.923803i \(0.625064\pi\)
\(200\) 2.83103 4.12132i 0.200184 0.291421i
\(201\) 6.38621i 0.450448i
\(202\) −6.99218 + 6.99218i −0.491968 + 0.491968i
\(203\) 0 0
\(204\) 4.12392i 0.288732i
\(205\) −5.76139 + 0.530105i −0.402393 + 0.0370241i
\(206\) 4.28203i 0.298343i
\(207\) 3.49013 + 3.49013i 0.242581 + 0.242581i
\(208\) 0.204875 + 0.204875i 0.0142055 + 0.0142055i
\(209\) 25.0613 1.73353
\(210\) 0 0
\(211\) 7.56555 0.520834 0.260417 0.965496i \(-0.416140\pi\)
0.260417 + 0.965496i \(0.416140\pi\)
\(212\) 5.85669 + 5.85669i 0.402239 + 0.402239i
\(213\) −10.1823 10.1823i −0.697681 0.697681i
\(214\) 14.8721i 1.01663i
\(215\) 12.1042 + 10.0645i 0.825501 + 0.686392i
\(216\) 3.86642i 0.263076i
\(217\) 0 0
\(218\) 9.35593 9.35593i 0.633664 0.633664i
\(219\) 23.3028i 1.57466i
\(220\) −8.99566 + 0.827689i −0.606487 + 0.0558028i
\(221\) 0.590988 0.0397541
\(222\) 6.61308 6.61308i 0.443841 0.443841i
\(223\) −9.35230 9.35230i −0.626277 0.626277i 0.320853 0.947129i \(-0.396031\pi\)
−0.947129 + 0.320853i \(0.896031\pi\)
\(224\) 0 0
\(225\) −0.992322 5.34682i −0.0661548 0.356455i
\(226\) 13.7933 0.917519
\(227\) 11.4508 11.4508i 0.760014 0.760014i −0.216311 0.976325i \(-0.569402\pi\)
0.976325 + 0.216311i \(0.0694024\pi\)
\(228\) −8.86840 + 8.86840i −0.587324 + 0.587324i
\(229\) 11.7764 0.778207 0.389103 0.921194i \(-0.372785\pi\)
0.389103 + 0.921194i \(0.372785\pi\)
\(230\) −0.929750 10.1049i −0.0613059 0.666297i
\(231\) 0 0
\(232\) 5.06196 + 5.06196i 0.332334 + 0.332334i
\(233\) −4.04765 + 4.04765i −0.265170 + 0.265170i −0.827151 0.561980i \(-0.810040\pi\)
0.561980 + 0.827151i \(0.310040\pi\)
\(234\) 0.315125 0.0206004
\(235\) −0.541813 0.450509i −0.0353440 0.0293880i
\(236\) 0.855404i 0.0556821i
\(237\) 7.25713 7.25713i 0.471402 0.471402i
\(238\) 0 0
\(239\) 8.33794i 0.539337i 0.962953 + 0.269668i \(0.0869141\pi\)
−0.962953 + 0.269668i \(0.913086\pi\)
\(240\) 2.89039 3.47617i 0.186574 0.224386i
\(241\) 2.96438i 0.190953i −0.995432 0.0954763i \(-0.969563\pi\)
0.995432 0.0954763i \(-0.0304374\pi\)
\(242\) 3.76279 + 3.76279i 0.241881 + 0.241881i
\(243\) −7.63821 7.63821i −0.489991 0.489991i
\(244\) 6.92077 0.443057
\(245\) 0 0
\(246\) −5.23128 −0.333535
\(247\) 1.27091 + 1.27091i 0.0808658 + 0.0808658i
\(248\) 5.17076 + 5.17076i 0.328344 + 0.328344i
\(249\) 11.0187i 0.698283i
\(250\) −5.45939 + 9.75680i −0.345282 + 0.617074i
\(251\) 16.1800i 1.02127i −0.859796 0.510637i \(-0.829410\pi\)
0.859796 0.510637i \(-0.170590\pi\)
\(252\) 0 0
\(253\) −12.9641 + 12.9641i −0.815043 + 0.815043i
\(254\) 3.11104i 0.195204i
\(255\) −0.844888 9.18258i −0.0529089 0.575036i
\(256\) 1.00000 0.0625000
\(257\) 4.11867 4.11867i 0.256916 0.256916i −0.566883 0.823799i \(-0.691851\pi\)
0.823799 + 0.566883i \(0.191851\pi\)
\(258\) 10.0645 + 10.0645i 0.626587 + 0.626587i
\(259\) 0 0
\(260\) −0.498161 0.414214i −0.0308946 0.0256884i
\(261\) 7.78598 0.481940
\(262\) 5.16100 5.16100i 0.318848 0.318848i
\(263\) 1.22833 1.22833i 0.0757422 0.0757422i −0.668221 0.743963i \(-0.732944\pi\)
0.743963 + 0.668221i \(0.232944\pi\)
\(264\) −8.16797 −0.502704
\(265\) −14.2408 11.8410i −0.874803 0.727386i
\(266\) 0 0
\(267\) 4.39223 + 4.39223i 0.268800 + 0.268800i
\(268\) 2.23353 2.23353i 0.136435 0.136435i
\(269\) −3.78337 −0.230676 −0.115338 0.993326i \(-0.536795\pi\)
−0.115338 + 0.993326i \(0.536795\pi\)
\(270\) 0.792131 + 8.60920i 0.0482076 + 0.523939i
\(271\) 21.2498i 1.29083i −0.763831 0.645416i \(-0.776684\pi\)
0.763831 0.645416i \(-0.223316\pi\)
\(272\) 1.44231 1.44231i 0.0874531 0.0874531i
\(273\) 0 0
\(274\) 7.17893i 0.433695i
\(275\) 19.8607 3.68597i 1.19765 0.222272i
\(276\) 9.17514i 0.552279i
\(277\) −3.45787 3.45787i −0.207763 0.207763i 0.595553 0.803316i \(-0.296933\pi\)
−0.803316 + 0.595553i \(0.796933\pi\)
\(278\) −8.78027 8.78027i −0.526605 0.526605i
\(279\) 7.95333 0.476153
\(280\) 0 0
\(281\) −29.4776 −1.75849 −0.879243 0.476373i \(-0.841951\pi\)
−0.879243 + 0.476373i \(0.841951\pi\)
\(282\) −0.450509 0.450509i −0.0268274 0.0268274i
\(283\) 7.97872 + 7.97872i 0.474286 + 0.474286i 0.903298 0.429013i \(-0.141138\pi\)
−0.429013 + 0.903298i \(0.641138\pi\)
\(284\) 7.12240i 0.422637i
\(285\) 17.9300 21.5638i 1.06208 1.27733i
\(286\) 1.17053i 0.0692148i
\(287\) 0 0
\(288\) 0.769067 0.769067i 0.0453177 0.0453177i
\(289\) 12.8395i 0.755262i
\(290\) −12.3083 10.2342i −0.722771 0.600973i
\(291\) −18.9597 −1.11144
\(292\) −8.15002 + 8.15002i −0.476944 + 0.476944i
\(293\) 7.23407 + 7.23407i 0.422619 + 0.422619i 0.886105 0.463485i \(-0.153401\pi\)
−0.463485 + 0.886105i \(0.653401\pi\)
\(294\) 0 0
\(295\) −0.175251 1.90470i −0.0102035 0.110896i
\(296\) −4.62576 −0.268867
\(297\) 11.0452 11.0452i 0.640905 0.640905i
\(298\) 16.9340 16.9340i 0.980963 0.980963i
\(299\) −1.31486 −0.0760406
\(300\) −5.72374 + 8.33243i −0.330460 + 0.481073i
\(301\) 0 0
\(302\) −2.50552 2.50552i −0.144176 0.144176i
\(303\) 14.1367 14.1367i 0.812133 0.812133i
\(304\) 6.20333 0.355785
\(305\) −15.4102 + 1.41789i −0.882386 + 0.0811882i
\(306\) 2.21847i 0.126822i
\(307\) 1.07859 1.07859i 0.0615584 0.0615584i −0.675657 0.737216i \(-0.736140\pi\)
0.737216 + 0.675657i \(0.236140\pi\)
\(308\) 0 0
\(309\) 8.65735i 0.492500i
\(310\) −12.5729 10.4542i −0.714093 0.593758i
\(311\) 9.62824i 0.545967i 0.962019 + 0.272984i \(0.0880105\pi\)
−0.962019 + 0.272984i \(0.911990\pi\)
\(312\) −0.414214 0.414214i −0.0234502 0.0234502i
\(313\) 2.14023 + 2.14023i 0.120973 + 0.120973i 0.765001 0.644029i \(-0.222738\pi\)
−0.644029 + 0.765001i \(0.722738\pi\)
\(314\) −6.12251 −0.345513
\(315\) 0 0
\(316\) −5.07627 −0.285562
\(317\) 1.37792 + 1.37792i 0.0773916 + 0.0773916i 0.744743 0.667351i \(-0.232572\pi\)
−0.667351 + 0.744743i \(0.732572\pi\)
\(318\) −11.8410 11.8410i −0.664010 0.664010i
\(319\) 28.9209i 1.61926i
\(320\) −2.22666 + 0.204875i −0.124474 + 0.0114529i
\(321\) 30.0682i 1.67824i
\(322\) 0 0
\(323\) 8.94715 8.94715i 0.497833 0.497833i
\(324\) 11.0799i 0.615553i
\(325\) 1.19410 + 0.820253i 0.0662367 + 0.0454995i
\(326\) −16.5579 −0.917056
\(327\) −18.9157 + 18.9157i −1.04604 + 1.04604i
\(328\) 1.82961 + 1.82961i 0.101023 + 0.101023i
\(329\) 0 0
\(330\) 18.1873 1.67341i 1.00118 0.0921183i
\(331\) −28.8935 −1.58813 −0.794066 0.607832i \(-0.792039\pi\)
−0.794066 + 0.607832i \(0.792039\pi\)
\(332\) −3.85372 + 3.85372i −0.211500 + 0.211500i
\(333\) −3.55752 + 3.55752i −0.194951 + 0.194951i
\(334\) 14.5485 0.796056
\(335\) −4.51573 + 5.43092i −0.246721 + 0.296723i
\(336\) 0 0
\(337\) −0.823226 0.823226i −0.0448440 0.0448440i 0.684329 0.729173i \(-0.260095\pi\)
−0.729173 + 0.684329i \(0.760095\pi\)
\(338\) 9.13303 9.13303i 0.496771 0.496771i
\(339\) −27.8872 −1.51462
\(340\) −2.91605 + 3.50704i −0.158145 + 0.190196i
\(341\) 29.5426i 1.59982i
\(342\) 4.77078 4.77078i 0.257974 0.257974i
\(343\) 0 0
\(344\) 7.03997i 0.379570i
\(345\) 1.87976 + 20.4300i 0.101203 + 1.09991i
\(346\) 7.77203i 0.417827i
\(347\) −11.8116 11.8116i −0.634082 0.634082i 0.315007 0.949089i \(-0.397993\pi\)
−0.949089 + 0.315007i \(0.897993\pi\)
\(348\) −10.2342 10.2342i −0.548611 0.548611i
\(349\) −36.7146 −1.96529 −0.982644 0.185503i \(-0.940608\pi\)
−0.982644 + 0.185503i \(0.940608\pi\)
\(350\) 0 0
\(351\) 1.12024 0.0597942
\(352\) 2.85669 + 2.85669i 0.152262 + 0.152262i
\(353\) 10.0910 + 10.0910i 0.537089 + 0.537089i 0.922673 0.385584i \(-0.126000\pi\)
−0.385584 + 0.922673i \(0.626000\pi\)
\(354\) 1.72945i 0.0919190i
\(355\) −1.45920 15.8592i −0.0774463 0.841718i
\(356\) 3.07230i 0.162832i
\(357\) 0 0
\(358\) −2.73277 + 2.73277i −0.144431 + 0.144431i
\(359\) 27.0888i 1.42969i 0.699281 + 0.714847i \(0.253504\pi\)
−0.699281 + 0.714847i \(0.746496\pi\)
\(360\) −1.55489 + 1.87002i −0.0819499 + 0.0985585i
\(361\) 19.4813 1.02533
\(362\) −4.94343 + 4.94343i −0.259821 + 0.259821i
\(363\) −7.60756 7.60756i −0.399293 0.399293i
\(364\) 0 0
\(365\) 16.4776 19.8171i 0.862477 1.03727i
\(366\) −13.9923 −0.731390
\(367\) 16.0312 16.0312i 0.836821 0.836821i −0.151618 0.988439i \(-0.548448\pi\)
0.988439 + 0.151618i \(0.0484485\pi\)
\(368\) −3.20895 + 3.20895i −0.167278 + 0.167278i
\(369\) 2.81418 0.146500
\(370\) 10.3000 0.947702i 0.535472 0.0492687i
\(371\) 0 0
\(372\) −10.4542 10.4542i −0.542024 0.542024i
\(373\) −9.07627 + 9.07627i −0.469951 + 0.469951i −0.901899 0.431947i \(-0.857827\pi\)
0.431947 + 0.901899i \(0.357827\pi\)
\(374\) 8.24050 0.426106
\(375\) 11.0377 19.7262i 0.569986 1.01866i
\(376\) 0.315125i 0.0162513i
\(377\) −1.46664 + 1.46664i −0.0755356 + 0.0755356i
\(378\) 0 0
\(379\) 14.4739i 0.743476i 0.928338 + 0.371738i \(0.121238\pi\)
−0.928338 + 0.371738i \(0.878762\pi\)
\(380\) −13.8127 + 1.27091i −0.708578 + 0.0651961i
\(381\) 6.28987i 0.322240i
\(382\) 3.16389 + 3.16389i 0.161879 + 0.161879i
\(383\) 1.23855 + 1.23855i 0.0632870 + 0.0632870i 0.738042 0.674755i \(-0.235751\pi\)
−0.674755 + 0.738042i \(0.735751\pi\)
\(384\) −2.02179 −0.103174
\(385\) 0 0
\(386\) −20.0747 −1.02178
\(387\) −5.41421 5.41421i −0.275220 0.275220i
\(388\) 6.63103 + 6.63103i 0.336640 + 0.336640i
\(389\) 2.78230i 0.141068i −0.997509 0.0705341i \(-0.977530\pi\)
0.997509 0.0705341i \(-0.0224704\pi\)
\(390\) 1.00718 + 0.837452i 0.0510003 + 0.0424060i
\(391\) 9.25661i 0.468127i
\(392\) 0 0
\(393\) −10.4344 + 10.4344i −0.526348 + 0.526348i
\(394\) 11.1002i 0.559219i
\(395\) 11.3031 1.04000i 0.568723 0.0523281i
\(396\) 4.39398 0.220806
\(397\) −28.0495 + 28.0495i −1.40776 + 1.40776i −0.636421 + 0.771342i \(0.719586\pi\)
−0.771342 + 0.636421i \(0.780414\pi\)
\(398\) −7.63821 7.63821i −0.382869 0.382869i
\(399\) 0 0
\(400\) 4.91605 0.912375i 0.245803 0.0456187i
\(401\) −19.9706 −0.997282 −0.498641 0.866809i \(-0.666167\pi\)
−0.498641 + 0.866809i \(0.666167\pi\)
\(402\) −4.51573 + 4.51573i −0.225224 + 0.225224i
\(403\) −1.49816 + 1.49816i −0.0746287 + 0.0746287i
\(404\) −9.88844 −0.491968
\(405\) −2.27000 24.6713i −0.112797 1.22593i
\(406\) 0 0
\(407\) −13.2144 13.2144i −0.655012 0.655012i
\(408\) −2.91605 + 2.91605i −0.144366 + 0.144366i
\(409\) −15.3056 −0.756813 −0.378407 0.925639i \(-0.623528\pi\)
−0.378407 + 0.925639i \(0.623528\pi\)
\(410\) −4.44876 3.69908i −0.219708 0.182684i
\(411\) 14.5143i 0.715936i
\(412\) −3.02785 + 3.02785i −0.149172 + 0.149172i
\(413\) 0 0
\(414\) 4.93579i 0.242581i
\(415\) 7.79141 9.37047i 0.382465 0.459978i
\(416\) 0.289737i 0.0142055i
\(417\) 17.7518 + 17.7518i 0.869311 + 0.869311i
\(418\) 17.7210 + 17.7210i 0.866763 + 0.866763i
\(419\) 27.7027 1.35337 0.676684 0.736274i \(-0.263416\pi\)
0.676684 + 0.736274i \(0.263416\pi\)
\(420\) 0 0
\(421\) 33.0159 1.60910 0.804549 0.593887i \(-0.202407\pi\)
0.804549 + 0.593887i \(0.202407\pi\)
\(422\) 5.34965 + 5.34965i 0.260417 + 0.260417i
\(423\) 0.242352 + 0.242352i 0.0117836 + 0.0117836i
\(424\) 8.28261i 0.402239i
\(425\) 5.77456 8.40642i 0.280107 0.407771i
\(426\) 14.4000i 0.697681i
\(427\) 0 0
\(428\) 10.5161 10.5161i 0.508317 0.508317i
\(429\) 2.36656i 0.114259i
\(430\) 1.44231 + 15.6756i 0.0695546 + 0.755947i
\(431\) 23.9173 1.15205 0.576027 0.817431i \(-0.304602\pi\)
0.576027 + 0.817431i \(0.304602\pi\)
\(432\) 2.73397 2.73397i 0.131538 0.131538i
\(433\) 13.2515 + 13.2515i 0.636829 + 0.636829i 0.949772 0.312943i \(-0.101315\pi\)
−0.312943 + 0.949772i \(0.601315\pi\)
\(434\) 0 0
\(435\) 24.8849 + 20.6914i 1.19314 + 0.992077i
\(436\) 13.2313 0.633664
\(437\) −19.9061 + 19.9061i −0.952240 + 0.952240i
\(438\) 16.4776 16.4776i 0.787330 0.787330i
\(439\) −14.1077 −0.673322 −0.336661 0.941626i \(-0.609298\pi\)
−0.336661 + 0.941626i \(0.609298\pi\)
\(440\) −6.94616 5.77563i −0.331145 0.275342i
\(441\) 0 0
\(442\) 0.417892 + 0.417892i 0.0198771 + 0.0198771i
\(443\) 14.8941 14.8941i 0.707638 0.707638i −0.258400 0.966038i \(-0.583195\pi\)
0.966038 + 0.258400i \(0.0831951\pi\)
\(444\) 9.35230 0.443841
\(445\) 0.629438 + 6.84098i 0.0298382 + 0.324294i
\(446\) 13.2262i 0.626277i
\(447\) −34.2370 + 34.2370i −1.61936 + 1.61936i
\(448\) 0 0
\(449\) 31.3247i 1.47831i 0.673538 + 0.739153i \(0.264774\pi\)
−0.673538 + 0.739153i \(0.735226\pi\)
\(450\) 3.07910 4.48245i 0.145150 0.211305i
\(451\) 10.4532i 0.492224i
\(452\) 9.75336 + 9.75336i 0.458759 + 0.458759i
\(453\) 5.06562 + 5.06562i 0.238004 + 0.238004i
\(454\) 16.1938 0.760014
\(455\) 0 0
\(456\) −12.5418 −0.587324
\(457\) −2.02342 2.02342i −0.0946514 0.0946514i 0.658196 0.752847i \(-0.271320\pi\)
−0.752847 + 0.658196i \(0.771320\pi\)
\(458\) 8.32718 + 8.32718i 0.389103 + 0.389103i
\(459\) 7.88648i 0.368109i
\(460\) 6.48781 7.80267i 0.302496 0.363801i
\(461\) 3.02674i 0.140969i 0.997513 + 0.0704846i \(0.0224546\pi\)
−0.997513 + 0.0704846i \(0.977545\pi\)
\(462\) 0 0
\(463\) 19.2889 19.2889i 0.896431 0.896431i −0.0986876 0.995118i \(-0.531464\pi\)
0.995118 + 0.0986876i \(0.0314644\pi\)
\(464\) 7.15869i 0.332334i
\(465\) 25.4197 + 21.1361i 1.17881 + 0.980165i
\(466\) −5.72424 −0.265170
\(467\) 17.7688 17.7688i 0.822244 0.822244i −0.164185 0.986430i \(-0.552500\pi\)
0.986430 + 0.164185i \(0.0524995\pi\)
\(468\) 0.222827 + 0.222827i 0.0103002 + 0.0103002i
\(469\) 0 0
\(470\) −0.0645612 0.701677i −0.00297799 0.0323660i
\(471\) 12.3784 0.570367
\(472\) −0.604862 + 0.604862i −0.0278410 + 0.0278410i
\(473\) 20.1110 20.1110i 0.924707 0.924707i
\(474\) 10.2631 0.471402
\(475\) 30.4959 5.65976i 1.39925 0.259688i
\(476\) 0 0
\(477\) 6.36989 + 6.36989i 0.291657 + 0.291657i
\(478\) −5.89582 + 5.89582i −0.269668 + 0.269668i
\(479\) −8.28692 −0.378639 −0.189319 0.981916i \(-0.560628\pi\)
−0.189319 + 0.981916i \(0.560628\pi\)
\(480\) 4.50184 0.414214i 0.205480 0.0189062i
\(481\) 1.34025i 0.0611103i
\(482\) 2.09613 2.09613i 0.0954763 0.0954763i
\(483\) 0 0
\(484\) 5.32139i 0.241881i
\(485\) −16.1236 13.4065i −0.732135 0.608759i
\(486\) 10.8021i 0.489991i
\(487\) 7.55069 + 7.55069i 0.342155 + 0.342155i 0.857177 0.515022i \(-0.172216\pi\)
−0.515022 + 0.857177i \(0.672216\pi\)
\(488\) 4.89372 + 4.89372i 0.221528 + 0.221528i
\(489\) 33.4765 1.51386
\(490\) 0 0
\(491\) 25.7259 1.16100 0.580498 0.814262i \(-0.302858\pi\)
0.580498 + 0.814262i \(0.302858\pi\)
\(492\) −3.69908 3.69908i −0.166767 0.166767i
\(493\) 10.3251 + 10.3251i 0.465018 + 0.465018i
\(494\) 1.79733i 0.0808658i
\(495\) −9.78391 + 0.900216i −0.439754 + 0.0404617i
\(496\) 7.31256i 0.328344i
\(497\) 0 0
\(498\) 7.79141 7.79141i 0.349141 0.349141i
\(499\) 14.5988i 0.653532i 0.945105 + 0.326766i \(0.105959\pi\)
−0.945105 + 0.326766i \(0.894041\pi\)
\(500\) −10.7595 + 3.03873i −0.481178 + 0.135896i
\(501\) −29.4139 −1.31412
\(502\) 11.4410 11.4410i 0.510637 0.510637i
\(503\) −13.9891 13.9891i −0.623744 0.623744i 0.322743 0.946487i \(-0.395395\pi\)
−0.946487 + 0.322743i \(0.895395\pi\)
\(504\) 0 0
\(505\) 22.0182 2.02589i 0.979798 0.0901510i
\(506\) −18.3339 −0.815043
\(507\) −18.4650 + 18.4650i −0.820061 + 0.820061i
\(508\) 2.19984 2.19984i 0.0976020 0.0976020i
\(509\) 2.85767 0.126664 0.0633319 0.997993i \(-0.479827\pi\)
0.0633319 + 0.997993i \(0.479827\pi\)
\(510\) 5.89564 7.09049i 0.261063 0.313972i
\(511\) 0 0
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 16.9597 16.9597i 0.748789 0.748789i
\(514\) 5.82469 0.256916
\(515\) 6.12167 7.36233i 0.269753 0.324423i
\(516\) 14.2333i 0.626587i
\(517\) −0.900216 + 0.900216i −0.0395914 + 0.0395914i
\(518\) 0 0
\(519\) 15.7134i 0.689741i
\(520\) −0.0593598 0.645146i −0.00260310 0.0282915i
\(521\) 28.6269i 1.25417i −0.778951 0.627084i \(-0.784248\pi\)
0.778951 0.627084i \(-0.215752\pi\)
\(522\) 5.50552 + 5.50552i 0.240970 + 0.240970i
\(523\) 22.3326 + 22.3326i 0.976535 + 0.976535i 0.999731 0.0231958i \(-0.00738410\pi\)
−0.0231958 + 0.999731i \(0.507384\pi\)
\(524\) 7.29876 0.318848
\(525\) 0 0
\(526\) 1.73712 0.0757422
\(527\) 10.5470 + 10.5470i 0.459435 + 0.459435i
\(528\) −5.77563 5.77563i −0.251352 0.251352i
\(529\) 2.40533i 0.104580i
\(530\) −1.69690 18.4426i −0.0737086 0.801095i
\(531\) 0.930359i 0.0403742i
\(532\) 0 0
\(533\) −0.530105 + 0.530105i −0.0229614 + 0.0229614i
\(534\) 6.21155i 0.268800i
\(535\) −21.2614 + 25.5704i −0.919211 + 1.10551i
\(536\) 3.15869 0.136435
\(537\) 5.52508 5.52508i 0.238425 0.238425i
\(538\) −2.67525 2.67525i −0.115338 0.115338i
\(539\) 0 0
\(540\) −5.52750 + 6.64775i −0.237866 + 0.286073i
\(541\) 36.9989 1.59071 0.795353 0.606147i \(-0.207286\pi\)
0.795353 + 0.606147i \(0.207286\pi\)
\(542\) 15.0259 15.0259i 0.645416 0.645416i
\(543\) 9.99457 9.99457i 0.428908 0.428908i
\(544\) 2.03974 0.0874531
\(545\) −29.4616 + 2.71076i −1.26200 + 0.116116i
\(546\) 0 0
\(547\) −20.0765 20.0765i −0.858409 0.858409i 0.132742 0.991151i \(-0.457622\pi\)
−0.991151 + 0.132742i \(0.957622\pi\)
\(548\) −5.07627 + 5.07627i −0.216847 + 0.216847i
\(549\) 7.52720 0.321253
\(550\) 16.6500 + 11.4373i 0.709959 + 0.487687i
\(551\) 44.4077i 1.89183i
\(552\) 6.48781 6.48781i 0.276139 0.276139i
\(553\) 0 0
\(554\) 4.89016i 0.207763i
\(555\) −20.8244 + 1.91605i −0.883948 + 0.0813319i
\(556\) 12.4172i 0.526605i
\(557\) −18.1818 18.1818i −0.770386 0.770386i 0.207788 0.978174i \(-0.433374\pi\)
−0.978174 + 0.207788i \(0.933374\pi\)
\(558\) 5.62385 + 5.62385i 0.238077 + 0.238077i
\(559\) 2.03974 0.0862718
\(560\) 0 0
\(561\) −16.6605 −0.703408
\(562\) −20.8438 20.8438i −0.879243 0.879243i
\(563\) −3.79500 3.79500i −0.159940 0.159940i 0.622600 0.782540i \(-0.286076\pi\)
−0.782540 + 0.622600i \(0.786076\pi\)
\(564\) 0.637116i 0.0268274i
\(565\) −23.7157 19.7192i −0.997725 0.829594i
\(566\) 11.2836i 0.474286i
\(567\) 0 0
\(568\) −5.03630 + 5.03630i −0.211318 + 0.211318i
\(569\) 25.5003i 1.06903i −0.845159 0.534514i \(-0.820495\pi\)
0.845159 0.534514i \(-0.179505\pi\)
\(570\) 27.9264 2.56950i 1.16971 0.107625i
\(571\) 15.9047 0.665591 0.332795 0.942999i \(-0.392008\pi\)
0.332795 + 0.942999i \(0.392008\pi\)
\(572\) −0.827689 + 0.827689i −0.0346074 + 0.0346074i
\(573\) −6.39672 6.39672i −0.267227 0.267227i
\(574\) 0 0
\(575\) −12.8476 + 18.7031i −0.535781 + 0.779973i
\(576\) 1.08763 0.0453177
\(577\) −16.2985 + 16.2985i −0.678514 + 0.678514i −0.959664 0.281150i \(-0.909284\pi\)
0.281150 + 0.959664i \(0.409284\pi\)
\(578\) −9.07887 + 9.07887i −0.377631 + 0.377631i
\(579\) 40.5869 1.68673
\(580\) −1.46664 15.9400i −0.0608988 0.661872i
\(581\) 0 0
\(582\) −13.4065 13.4065i −0.555719 0.555719i
\(583\) −23.6609 + 23.6609i −0.979934 + 0.979934i
\(584\) −11.5259 −0.476944
\(585\) −0.541813 0.450509i −0.0224012 0.0186263i
\(586\) 10.2305i 0.422619i
\(587\) −28.2277 + 28.2277i −1.16508 + 1.16508i −0.181734 + 0.983348i \(0.558171\pi\)
−0.983348 + 0.181734i \(0.941829\pi\)
\(588\) 0 0
\(589\) 45.3622i 1.86912i
\(590\) 1.22290 1.47074i 0.0503461 0.0605496i
\(591\) 22.4422i 0.923149i
\(592\) −3.27091 3.27091i −0.134433 0.134433i
\(593\) −25.0523 25.0523i −1.02877 1.02877i −0.999574 0.0292000i \(-0.990704\pi\)
−0.0292000 0.999574i \(-0.509296\pi\)
\(594\) 15.6202 0.640905
\(595\) 0 0
\(596\) 23.9483 0.980963
\(597\) 15.4428 + 15.4428i 0.632033 + 0.632033i
\(598\) −0.929750 0.929750i −0.0380203 0.0380203i
\(599\) 16.7823i 0.685706i 0.939389 + 0.342853i \(0.111393\pi\)
−0.939389 + 0.342853i \(0.888607\pi\)
\(600\) −9.93921 + 1.84463i −0.405767 + 0.0753066i
\(601\) 1.73528i 0.0707833i 0.999374 + 0.0353917i \(0.0112679\pi\)
−0.999374 + 0.0353917i \(0.988732\pi\)
\(602\) 0 0
\(603\) 2.42925 2.42925i 0.0989266 0.0989266i
\(604\) 3.54334i 0.144176i
\(605\) −1.09022 11.8489i −0.0443237 0.481728i
\(606\) 19.9923 0.812133
\(607\) −27.8860 + 27.8860i −1.13186 + 1.13186i −0.141989 + 0.989868i \(0.545350\pi\)
−0.989868 + 0.141989i \(0.954650\pi\)
\(608\) 4.38642 + 4.38642i 0.177893 + 0.177893i
\(609\) 0 0
\(610\) −11.8993 9.89407i −0.481787 0.400599i
\(611\) −0.0913034 −0.00369374
\(612\) 1.56870 1.56870i 0.0634108 0.0634108i
\(613\) 0.241791 0.241791i 0.00976586 0.00976586i −0.702207 0.711973i \(-0.747802\pi\)
0.711973 + 0.702207i \(0.247802\pi\)
\(614\) 1.52536 0.0615584
\(615\) 8.99444 + 7.47875i 0.362691 + 0.301572i
\(616\) 0 0
\(617\) 11.1876 + 11.1876i 0.450397 + 0.450397i 0.895486 0.445089i \(-0.146828\pi\)
−0.445089 + 0.895486i \(0.646828\pi\)
\(618\) 6.12167 6.12167i 0.246250 0.246250i
\(619\) 36.5364 1.46852 0.734260 0.678868i \(-0.237529\pi\)
0.734260 + 0.678868i \(0.237529\pi\)
\(620\) −1.49816 16.2826i −0.0601676 0.653926i
\(621\) 17.5463i 0.704109i
\(622\) −6.80819 + 6.80819i −0.272984 + 0.272984i
\(623\) 0 0
\(624\) 0.585786i 0.0234502i
\(625\) 23.3351 8.97056i 0.933406 0.358823i
\(626\) 3.02674i 0.120973i
\(627\) −35.8281 35.8281i −1.43084 1.43084i
\(628\) −4.32927 4.32927i −0.172757 0.172757i
\(629\) −9.43535 −0.376212
\(630\) 0 0
\(631\) −35.8189 −1.42593 −0.712964 0.701201i \(-0.752648\pi\)
−0.712964 + 0.701201i \(0.752648\pi\)
\(632\) −3.58946 3.58946i −0.142781 0.142781i
\(633\) −10.8159 10.8159i −0.429892 0.429892i
\(634\) 1.94867i 0.0773916i
\(635\) −4.44761 + 5.34899i −0.176498 + 0.212268i
\(636\) 16.7457i 0.664010i
\(637\) 0 0
\(638\) −20.4502 + 20.4502i −0.809631 + 0.809631i
\(639\) 7.74650i 0.306447i
\(640\) −1.71936 1.42962i −0.0679635 0.0565107i
\(641\) −14.3315 −0.566059 −0.283029 0.959111i \(-0.591339\pi\)
−0.283029 + 0.959111i \(0.591339\pi\)
\(642\) −21.2614 + 21.2614i −0.839121 + 0.839121i
\(643\) −7.65201 7.65201i −0.301766 0.301766i 0.539939 0.841704i \(-0.318447\pi\)
−0.841704 + 0.539939i \(0.818447\pi\)
\(644\) 0 0
\(645\) −2.91605 31.6928i −0.114819 1.24790i
\(646\) 12.6532 0.497833
\(647\) 22.8742 22.8742i 0.899278 0.899278i −0.0960943 0.995372i \(-0.530635\pi\)
0.995372 + 0.0960943i \(0.0306350\pi\)
\(648\) −7.83471 + 7.83471i −0.307776 + 0.307776i
\(649\) −3.45581 −0.135652
\(650\) 0.264349 + 1.42436i 0.0103686 + 0.0558681i
\(651\) 0 0
\(652\) −11.7082 11.7082i −0.458528 0.458528i
\(653\) −0.362210 + 0.362210i −0.0141744 + 0.0141744i −0.714158 0.699984i \(-0.753190\pi\)
0.699984 + 0.714158i \(0.253190\pi\)
\(654\) −26.7508 −1.04604
\(655\) −16.2519 + 1.49533i −0.635013 + 0.0584275i
\(656\) 2.58745i 0.101023i
\(657\) −8.86417 + 8.86417i −0.345824 + 0.345824i
\(658\) 0 0
\(659\) 19.5542i 0.761723i 0.924632 + 0.380862i \(0.124373\pi\)
−0.924632 + 0.380862i \(0.875627\pi\)
\(660\) 14.0437 + 11.6771i 0.546648 + 0.454530i
\(661\) 39.2972i 1.52848i −0.644930 0.764242i \(-0.723113\pi\)
0.644930 0.764242i \(-0.276887\pi\)
\(662\) −20.4308 20.4308i −0.794066 0.794066i
\(663\) −0.844888 0.844888i −0.0328127 0.0328127i
\(664\) −5.44998 −0.211500
\(665\) 0 0
\(666\) −5.03109 −0.194951
\(667\) −22.9719 22.9719i −0.889474 0.889474i
\(668\) 10.2873 + 10.2873i 0.398028 + 0.398028i
\(669\) 26.7405i 1.03385i
\(670\) −7.03334 + 0.647137i −0.271722 + 0.0250011i
\(671\) 27.9597i 1.07937i
\(672\) 0 0
\(673\) 18.4813 18.4813i 0.712401 0.712401i −0.254636 0.967037i \(-0.581956\pi\)
0.967037 + 0.254636i \(0.0819556\pi\)
\(674\) 1.16422i 0.0448440i
\(675\) 10.9459 15.9347i 0.421309 0.613328i
\(676\) 12.9161 0.496771
\(677\) 29.1321 29.1321i 1.11964 1.11964i 0.127842 0.991795i \(-0.459195\pi\)
0.991795 0.127842i \(-0.0408049\pi\)
\(678\) −19.7192 19.7192i −0.757312 0.757312i
\(679\) 0 0
\(680\) −4.54181 + 0.417892i −0.174171 + 0.0160254i
\(681\) −32.7405 −1.25462
\(682\) −20.8898 + 20.8898i −0.799910 + 0.799910i
\(683\) −6.45442 + 6.45442i −0.246971 + 0.246971i −0.819726 0.572755i \(-0.805875\pi\)
0.572755 + 0.819726i \(0.305875\pi\)
\(684\) 6.74690 0.257974
\(685\) 10.2631 12.3431i 0.392134 0.471607i
\(686\) 0 0
\(687\) −16.8358 16.8358i −0.642325 0.642325i
\(688\) 4.97801 4.97801i 0.189785 0.189785i
\(689\) −2.39978 −0.0914243
\(690\) −13.1170 + 15.7753i −0.499354 + 0.600557i
\(691\) 48.4941i 1.84480i −0.386234 0.922401i \(-0.626224\pi\)
0.386234 0.922401i \(-0.373776\pi\)
\(692\) −5.49565 + 5.49565i −0.208913 + 0.208913i
\(693\) 0 0
\(694\) 16.7042i 0.634082i
\(695\) 2.54397 + 27.6489i 0.0964982 + 1.04878i
\(696\) 14.4734i 0.548611i
\(697\) 3.73192 + 3.73192i 0.141357 + 0.141357i
\(698\) −25.9611 25.9611i −0.982644 0.982644i
\(699\) 11.5732 0.437739
\(700\) 0 0
\(701\) −30.8898 −1.16669 −0.583347 0.812223i \(-0.698257\pi\)
−0.583347 + 0.812223i \(0.698257\pi\)
\(702\) 0.792131 + 0.792131i 0.0298971 + 0.0298971i
\(703\) −20.2905 20.2905i −0.765271 0.765271i
\(704\) 4.03997i 0.152262i
\(705\) 0.130529 + 1.41864i 0.00491601 + 0.0534292i
\(706\) 14.2708i 0.537089i
\(707\) 0 0
\(708\) 1.22290 1.22290i 0.0459595 0.0459595i
\(709\) 14.7055i 0.552278i 0.961118 + 0.276139i \(0.0890550\pi\)
−0.961118 + 0.276139i \(0.910945\pi\)
\(710\) 10.1823 12.2459i 0.382136 0.459582i
\(711\) −5.52108 −0.207057
\(712\) 2.17245 2.17245i 0.0814159 0.0814159i
\(713\) −23.4656 23.4656i −0.878795 0.878795i
\(714\) 0 0
\(715\) 1.67341 2.01256i 0.0625821 0.0752654i
\(716\) −3.86472 −0.144431
\(717\) 11.9201 11.9201i 0.445164 0.445164i
\(718\) −19.1547 + 19.1547i −0.714847 + 0.714847i
\(719\) 23.4720 0.875358 0.437679 0.899131i \(-0.355801\pi\)
0.437679 + 0.899131i \(0.355801\pi\)
\(720\) −2.42177 + 0.222827i −0.0902542 + 0.00830428i
\(721\) 0 0
\(722\) 13.7753 + 13.7753i 0.512665 + 0.512665i
\(723\) −4.23794 + 4.23794i −0.157611 + 0.157611i
\(724\) −6.99107 −0.259821
\(725\) 6.53141 + 35.1925i 0.242570 + 1.30702i
\(726\) 10.7587i 0.399293i
\(727\) 14.1380 14.1380i 0.524349 0.524349i −0.394533 0.918882i \(-0.629093\pi\)
0.918882 + 0.394533i \(0.129093\pi\)
\(728\) 0 0
\(729\) 11.4004i 0.422236i
\(730\) 25.6642 2.36136i 0.949875 0.0873979i
\(731\) 14.3597i 0.531113i
\(732\) −9.89407 9.89407i −0.365695 0.365695i
\(733\) −19.6123 19.6123i −0.724395 0.724395i 0.245102 0.969497i \(-0.421179\pi\)
−0.969497 + 0.245102i \(0.921179\pi\)
\(734\) 22.6715 0.836821
\(735\) 0 0
\(736\) −4.53813 −0.167278
\(737\) 9.02342 + 9.02342i 0.332382 + 0.332382i
\(738\) 1.98993 + 1.98993i 0.0732502 + 0.0732502i
\(739\) 13.5620i 0.498888i −0.968389 0.249444i \(-0.919752\pi\)
0.968389 0.249444i \(-0.0802479\pi\)
\(740\) 7.95333 + 6.61308i 0.292370 + 0.243102i
\(741\) 3.63383i 0.133492i
\(742\) 0 0
\(743\) 13.5961 13.5961i 0.498791 0.498791i −0.412270 0.911062i \(-0.635264\pi\)
0.911062 + 0.412270i \(0.135264\pi\)
\(744\) 14.7845i 0.542024i
\(745\) −53.3249 + 4.90642i −1.95367 + 0.179757i
\(746\) −12.8358 −0.469951
\(747\) −4.19141 + 4.19141i −0.153355 + 0.153355i
\(748\) 5.82691 + 5.82691i 0.213053 + 0.213053i
\(749\) 0 0
\(750\) 21.7534 6.14366i 0.794320 0.224335i
\(751\) 43.6619 1.59324 0.796622 0.604478i \(-0.206618\pi\)
0.796622 + 0.604478i \(0.206618\pi\)
\(752\) −0.222827 + 0.222827i −0.00812567 + 0.00812567i
\(753\) −23.1313 + 23.1313i −0.842951 + 0.842951i
\(754\) −2.07414 −0.0755356
\(755\) 0.725941 + 7.88981i 0.0264197 + 0.287140i
\(756\) 0 0
\(757\) 7.88896 + 7.88896i 0.286729 + 0.286729i 0.835785 0.549056i \(-0.185013\pi\)
−0.549056 + 0.835785i \(0.685013\pi\)
\(758\) −10.2346 + 10.2346i −0.371738 + 0.371738i
\(759\) 37.0673 1.34546
\(760\) −10.6657 8.86840i −0.386887 0.321691i
\(761\) 1.97365i 0.0715447i −0.999360 0.0357724i \(-0.988611\pi\)
0.999360 0.0357724i \(-0.0113891\pi\)
\(762\) −4.44761 + 4.44761i −0.161120 + 0.161120i
\(763\) 0 0
\(764\) 4.47442i 0.161879i
\(765\) −3.17157 + 3.81435i −0.114668 + 0.137908i
\(766\) 1.75158i 0.0632870i
\(767\) −0.175251 0.175251i −0.00632794 0.00632794i
\(768\) −1.42962 1.42962i −0.0515870 0.0515870i
\(769\) 17.4914 0.630756 0.315378 0.948966i \(-0.397869\pi\)
0.315378 + 0.948966i \(0.397869\pi\)
\(770\) 0 0
\(771\) −11.7763 −0.424112
\(772\) −14.1950 14.1950i −0.510889 0.510889i
\(773\) −31.6197 31.6197i −1.13728 1.13728i −0.988936 0.148345i \(-0.952605\pi\)
−0.148345 0.988936i \(-0.547395\pi\)
\(774\) 7.65685i 0.275220i
\(775\) 6.67180 + 35.9490i 0.239658 + 1.29132i
\(776\) 9.37769i 0.336640i
\(777\) 0 0
\(778\) 1.96738 1.96738i 0.0705341 0.0705341i
\(779\) 16.0508i 0.575081i
\(780\) 0.120013 + 1.30435i 0.00429715 + 0.0467032i
\(781\) −28.7743 −1.02963
\(782\) −6.54541 + 6.54541i −0.234064 + 0.234064i
\(783\) 19.5716 + 19.5716i 0.699433 + 0.699433i
\(784\) 0 0