Properties

Label 245.2.e.i.226.1
Level $245$
Weight $2$
Character 245.226
Analytic conductor $1.956$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 245 = 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 245.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.95633484952\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.780776 + 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 245.226
Dual form 245.2.e.i.116.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.780776 + 1.35234i) q^{2} +(1.28078 + 2.21837i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 + 3.08440i) q^{9} +O(q^{10})\) \(q+(-0.780776 + 1.35234i) q^{2} +(1.28078 + 2.21837i) q^{3} +(-0.219224 - 0.379706i) q^{4} +(-0.500000 + 0.866025i) q^{5} -4.00000 q^{6} -2.43845 q^{8} +(-1.78078 + 3.08440i) q^{9} +(-0.780776 - 1.35234i) q^{10} +(-1.28078 - 2.21837i) q^{11} +(0.561553 - 0.972638i) q^{12} +4.56155 q^{13} -2.56155 q^{15} +(2.34233 - 4.05703i) q^{16} +(2.28078 + 3.95042i) q^{17} +(-2.78078 - 4.81645i) q^{18} +(-0.561553 + 0.972638i) q^{19} +0.438447 q^{20} +4.00000 q^{22} +(2.56155 - 4.43674i) q^{23} +(-3.12311 - 5.40938i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-3.56155 + 6.16879i) q^{26} -1.43845 q^{27} -5.68466 q^{29} +(2.00000 - 3.46410i) q^{30} +(1.21922 + 2.11176i) q^{32} +(3.28078 - 5.68247i) q^{33} -7.12311 q^{34} +1.56155 q^{36} +(-3.00000 + 5.19615i) q^{37} +(-0.876894 - 1.51883i) q^{38} +(5.84233 + 10.1192i) q^{39} +(1.21922 - 2.11176i) q^{40} -3.12311 q^{41} +9.12311 q^{43} +(-0.561553 + 0.972638i) q^{44} +(-1.78078 - 3.08440i) q^{45} +(4.00000 + 6.92820i) q^{46} +(-1.84233 + 3.19101i) q^{47} +12.0000 q^{48} +1.56155 q^{50} +(-5.84233 + 10.1192i) q^{51} +(-1.00000 - 1.73205i) q^{52} +(-1.56155 - 2.70469i) q^{53} +(1.12311 - 1.94528i) q^{54} +2.56155 q^{55} -2.87689 q^{57} +(4.43845 - 7.68762i) q^{58} +(2.00000 + 3.46410i) q^{59} +(0.561553 + 0.972638i) q^{60} +(4.68466 - 8.11407i) q^{61} +5.56155 q^{64} +(-2.28078 + 3.95042i) q^{65} +(5.12311 + 8.87348i) q^{66} +(3.12311 + 5.40938i) q^{67} +(1.00000 - 1.73205i) q^{68} +13.1231 q^{69} +8.00000 q^{71} +(4.34233 - 7.52113i) q^{72} +(-2.12311 - 3.67733i) q^{73} +(-4.68466 - 8.11407i) q^{74} +(1.28078 - 2.21837i) q^{75} +0.492423 q^{76} -18.2462 q^{78} +(3.28078 - 5.68247i) q^{79} +(2.34233 + 4.05703i) q^{80} +(3.50000 + 6.06218i) q^{81} +(2.43845 - 4.22351i) q^{82} +4.00000 q^{83} -4.56155 q^{85} +(-7.12311 + 12.3376i) q^{86} +(-7.28078 - 12.6107i) q^{87} +(3.12311 + 5.40938i) q^{88} +(-3.56155 + 6.16879i) q^{89} +5.56155 q^{90} -2.24621 q^{92} +(-2.87689 - 4.98293i) q^{94} +(-0.561553 - 0.972638i) q^{95} +(-3.12311 + 5.40938i) q^{96} -14.8078 q^{97} +9.12311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} + q^{3} - 5q^{4} - 2q^{5} - 16q^{6} - 18q^{8} - 3q^{9} + O(q^{10}) \) \( 4q + q^{2} + q^{3} - 5q^{4} - 2q^{5} - 16q^{6} - 18q^{8} - 3q^{9} + q^{10} - q^{11} - 6q^{12} + 10q^{13} - 2q^{15} - 3q^{16} + 5q^{17} - 7q^{18} + 6q^{19} + 10q^{20} + 16q^{22} + 2q^{23} + 4q^{24} - 2q^{25} - 6q^{26} - 14q^{27} + 2q^{29} + 8q^{30} + 9q^{32} + 9q^{33} - 12q^{34} - 2q^{36} - 12q^{37} - 20q^{38} + 11q^{39} + 9q^{40} + 4q^{41} + 20q^{43} + 6q^{44} - 3q^{45} + 16q^{46} + 5q^{47} + 48q^{48} - 2q^{50} - 11q^{51} - 4q^{52} + 2q^{53} - 12q^{54} + 2q^{55} - 28q^{57} + 26q^{58} + 8q^{59} - 6q^{60} - 6q^{61} + 14q^{64} - 5q^{65} + 4q^{66} - 4q^{67} + 4q^{68} + 36q^{69} + 32q^{71} + 5q^{72} + 8q^{73} + 6q^{74} + q^{75} - 64q^{76} - 40q^{78} + 9q^{79} - 3q^{80} + 14q^{81} + 18q^{82} + 16q^{83} - 10q^{85} - 12q^{86} - 25q^{87} - 4q^{88} - 6q^{89} + 14q^{90} + 24q^{92} - 28q^{94} + 6q^{95} + 4q^{96} - 18q^{97} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 + 1.35234i −0.552092 + 0.956252i 0.446031 + 0.895017i \(0.352837\pi\)
−0.998123 + 0.0612344i \(0.980496\pi\)
\(3\) 1.28078 + 2.21837i 0.739457 + 1.28078i 0.952740 + 0.303786i \(0.0982508\pi\)
−0.213284 + 0.976990i \(0.568416\pi\)
\(4\) −0.219224 0.379706i −0.109612 0.189853i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −4.00000 −1.63299
\(7\) 0 0
\(8\) −2.43845 −0.862121
\(9\) −1.78078 + 3.08440i −0.593592 + 1.02813i
\(10\) −0.780776 1.35234i −0.246903 0.427649i
\(11\) −1.28078 2.21837i −0.386169 0.668864i 0.605762 0.795646i \(-0.292868\pi\)
−0.991931 + 0.126782i \(0.959535\pi\)
\(12\) 0.561553 0.972638i 0.162106 0.280776i
\(13\) 4.56155 1.26515 0.632574 0.774500i \(-0.281999\pi\)
0.632574 + 0.774500i \(0.281999\pi\)
\(14\) 0 0
\(15\) −2.56155 −0.661390
\(16\) 2.34233 4.05703i 0.585582 1.01426i
\(17\) 2.28078 + 3.95042i 0.553170 + 0.958118i 0.998043 + 0.0625245i \(0.0199152\pi\)
−0.444874 + 0.895593i \(0.646752\pi\)
\(18\) −2.78078 4.81645i −0.655435 1.13525i
\(19\) −0.561553 + 0.972638i −0.128829 + 0.223138i −0.923223 0.384264i \(-0.874455\pi\)
0.794394 + 0.607403i \(0.207789\pi\)
\(20\) 0.438447 0.0980398
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 2.56155 4.43674i 0.534121 0.925124i −0.465085 0.885266i \(-0.653976\pi\)
0.999205 0.0398580i \(-0.0126905\pi\)
\(24\) −3.12311 5.40938i −0.637501 1.10418i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −3.56155 + 6.16879i −0.698478 + 1.20980i
\(27\) −1.43845 −0.276829
\(28\) 0 0
\(29\) −5.68466 −1.05561 −0.527807 0.849364i \(-0.676986\pi\)
−0.527807 + 0.849364i \(0.676986\pi\)
\(30\) 2.00000 3.46410i 0.365148 0.632456i
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 1.21922 + 2.11176i 0.215530 + 0.373309i
\(33\) 3.28078 5.68247i 0.571110 0.989191i
\(34\) −7.12311 −1.22160
\(35\) 0 0
\(36\) 1.56155 0.260259
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) −0.876894 1.51883i −0.142251 0.246386i
\(39\) 5.84233 + 10.1192i 0.935521 + 1.62037i
\(40\) 1.21922 2.11176i 0.192776 0.333898i
\(41\) −3.12311 −0.487747 −0.243874 0.969807i \(-0.578418\pi\)
−0.243874 + 0.969807i \(0.578418\pi\)
\(42\) 0 0
\(43\) 9.12311 1.39126 0.695630 0.718400i \(-0.255125\pi\)
0.695630 + 0.718400i \(0.255125\pi\)
\(44\) −0.561553 + 0.972638i −0.0846573 + 0.146631i
\(45\) −1.78078 3.08440i −0.265462 0.459794i
\(46\) 4.00000 + 6.92820i 0.589768 + 1.02151i
\(47\) −1.84233 + 3.19101i −0.268731 + 0.465456i −0.968534 0.248879i \(-0.919938\pi\)
0.699803 + 0.714336i \(0.253271\pi\)
\(48\) 12.0000 1.73205
\(49\) 0 0
\(50\) 1.56155 0.220837
\(51\) −5.84233 + 10.1192i −0.818090 + 1.41697i
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) −1.56155 2.70469i −0.214496 0.371518i 0.738621 0.674121i \(-0.235477\pi\)
−0.953116 + 0.302604i \(0.902144\pi\)
\(54\) 1.12311 1.94528i 0.152835 0.264719i
\(55\) 2.56155 0.345400
\(56\) 0 0
\(57\) −2.87689 −0.381054
\(58\) 4.43845 7.68762i 0.582797 1.00943i
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0.561553 + 0.972638i 0.0724962 + 0.125567i
\(61\) 4.68466 8.11407i 0.599809 1.03890i −0.393040 0.919521i \(-0.628577\pi\)
0.992849 0.119378i \(-0.0380901\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 5.56155 0.695194
\(65\) −2.28078 + 3.95042i −0.282895 + 0.489989i
\(66\) 5.12311 + 8.87348i 0.630611 + 1.09225i
\(67\) 3.12311 + 5.40938i 0.381548 + 0.660861i 0.991284 0.131744i \(-0.0420577\pi\)
−0.609736 + 0.792605i \(0.708724\pi\)
\(68\) 1.00000 1.73205i 0.121268 0.210042i
\(69\) 13.1231 1.57984
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) 4.34233 7.52113i 0.511748 0.886374i
\(73\) −2.12311 3.67733i −0.248491 0.430399i 0.714617 0.699516i \(-0.246601\pi\)
−0.963107 + 0.269118i \(0.913268\pi\)
\(74\) −4.68466 8.11407i −0.544580 0.943241i
\(75\) 1.28078 2.21837i 0.147891 0.256155i
\(76\) 0.492423 0.0564847
\(77\) 0 0
\(78\) −18.2462 −2.06598
\(79\) 3.28078 5.68247i 0.369116 0.639328i −0.620311 0.784356i \(-0.712994\pi\)
0.989428 + 0.145028i \(0.0463271\pi\)
\(80\) 2.34233 + 4.05703i 0.261880 + 0.453590i
\(81\) 3.50000 + 6.06218i 0.388889 + 0.673575i
\(82\) 2.43845 4.22351i 0.269281 0.466409i
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −4.56155 −0.494770
\(86\) −7.12311 + 12.3376i −0.768104 + 1.33040i
\(87\) −7.28078 12.6107i −0.780581 1.35201i
\(88\) 3.12311 + 5.40938i 0.332924 + 0.576642i
\(89\) −3.56155 + 6.16879i −0.377524 + 0.653890i −0.990701 0.136055i \(-0.956558\pi\)
0.613177 + 0.789945i \(0.289891\pi\)
\(90\) 5.56155 0.586239
\(91\) 0 0
\(92\) −2.24621 −0.234184
\(93\) 0 0
\(94\) −2.87689 4.98293i −0.296729 0.513950i
\(95\) −0.561553 0.972638i −0.0576141 0.0997906i
\(96\) −3.12311 + 5.40938i −0.318751 + 0.552092i
\(97\) −14.8078 −1.50350 −0.751750 0.659448i \(-0.770790\pi\)
−0.751750 + 0.659448i \(0.770790\pi\)
\(98\) 0 0
\(99\) 9.12311 0.916907
\(100\) −0.219224 + 0.379706i −0.0219224 + 0.0379706i
\(101\) −0.123106 0.213225i −0.0122495 0.0212167i 0.859836 0.510571i \(-0.170566\pi\)
−0.872085 + 0.489354i \(0.837233\pi\)
\(102\) −9.12311 15.8017i −0.903322 1.56460i
\(103\) −0.719224 + 1.24573i −0.0708672 + 0.122746i −0.899282 0.437370i \(-0.855910\pi\)
0.828414 + 0.560116i \(0.189243\pi\)
\(104\) −11.1231 −1.09071
\(105\) 0 0
\(106\) 4.87689 0.473686
\(107\) 5.68466 9.84612i 0.549557 0.951860i −0.448748 0.893658i \(-0.648130\pi\)
0.998305 0.0582018i \(-0.0185367\pi\)
\(108\) 0.315342 + 0.546188i 0.0303438 + 0.0525569i
\(109\) −8.84233 15.3154i −0.846942 1.46695i −0.883924 0.467630i \(-0.845108\pi\)
0.0369828 0.999316i \(-0.488225\pi\)
\(110\) −2.00000 + 3.46410i −0.190693 + 0.330289i
\(111\) −15.3693 −1.45879
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 2.24621 3.89055i 0.210377 0.364384i
\(115\) 2.56155 + 4.43674i 0.238866 + 0.413728i
\(116\) 1.24621 + 2.15850i 0.115708 + 0.200412i
\(117\) −8.12311 + 14.0696i −0.750981 + 1.30074i
\(118\) −6.24621 −0.575010
\(119\) 0 0
\(120\) 6.24621 0.570198
\(121\) 2.21922 3.84381i 0.201748 0.349437i
\(122\) 7.31534 + 12.6705i 0.662300 + 1.14714i
\(123\) −4.00000 6.92820i −0.360668 0.624695i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.2462 0.909204 0.454602 0.890695i \(-0.349781\pi\)
0.454602 + 0.890695i \(0.349781\pi\)
\(128\) −6.78078 + 11.7446i −0.599342 + 1.03809i
\(129\) 11.6847 + 20.2384i 1.02878 + 1.78189i
\(130\) −3.56155 6.16879i −0.312369 0.541039i
\(131\) 4.56155 7.90084i 0.398545 0.690300i −0.595002 0.803724i \(-0.702849\pi\)
0.993547 + 0.113425i \(0.0361820\pi\)
\(132\) −2.87689 −0.250402
\(133\) 0 0
\(134\) −9.75379 −0.842599
\(135\) 0.719224 1.24573i 0.0619009 0.107216i
\(136\) −5.56155 9.63289i −0.476899 0.826014i
\(137\) 4.43845 + 7.68762i 0.379202 + 0.656797i 0.990946 0.134258i \(-0.0428652\pi\)
−0.611744 + 0.791056i \(0.709532\pi\)
\(138\) −10.2462 + 17.7470i −0.872215 + 1.51072i
\(139\) −6.87689 −0.583291 −0.291645 0.956527i \(-0.594203\pi\)
−0.291645 + 0.956527i \(0.594203\pi\)
\(140\) 0 0
\(141\) −9.43845 −0.794861
\(142\) −6.24621 + 10.8188i −0.524170 + 0.907890i
\(143\) −5.84233 10.1192i −0.488560 0.846211i
\(144\) 8.34233 + 14.4493i 0.695194 + 1.20411i
\(145\) 2.84233 4.92306i 0.236043 0.408838i
\(146\) 6.63068 0.548759
\(147\) 0 0
\(148\) 2.63068 0.216241
\(149\) 2.12311 3.67733i 0.173932 0.301258i −0.765859 0.643008i \(-0.777686\pi\)
0.939791 + 0.341750i \(0.111020\pi\)
\(150\) 2.00000 + 3.46410i 0.163299 + 0.282843i
\(151\) −10.9654 18.9927i −0.892354 1.54560i −0.837045 0.547134i \(-0.815719\pi\)
−0.0553094 0.998469i \(-0.517615\pi\)
\(152\) 1.36932 2.37173i 0.111066 0.192372i
\(153\) −16.2462 −1.31343
\(154\) 0 0
\(155\) 0 0
\(156\) 2.56155 4.43674i 0.205088 0.355223i
\(157\) −1.87689 3.25088i −0.149792 0.259448i 0.781358 0.624083i \(-0.214527\pi\)
−0.931151 + 0.364635i \(0.881194\pi\)
\(158\) 5.12311 + 8.87348i 0.407572 + 0.705936i
\(159\) 4.00000 6.92820i 0.317221 0.549442i
\(160\) −2.43845 −0.192776
\(161\) 0 0
\(162\) −10.9309 −0.858810
\(163\) −0.561553 + 0.972638i −0.0439842 + 0.0761829i −0.887179 0.461425i \(-0.847338\pi\)
0.843195 + 0.537608i \(0.180672\pi\)
\(164\) 0.684658 + 1.18586i 0.0534628 + 0.0926004i
\(165\) 3.28078 + 5.68247i 0.255408 + 0.442380i
\(166\) −3.12311 + 5.40938i −0.242400 + 0.419849i
\(167\) 21.9309 1.69706 0.848531 0.529146i \(-0.177488\pi\)
0.848531 + 0.529146i \(0.177488\pi\)
\(168\) 0 0
\(169\) 7.80776 0.600597
\(170\) 3.56155 6.16879i 0.273159 0.473125i
\(171\) −2.00000 3.46410i −0.152944 0.264906i
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 4.28078 7.41452i 0.325461 0.563716i −0.656144 0.754636i \(-0.727814\pi\)
0.981606 + 0.190920i \(0.0611470\pi\)
\(174\) 22.7386 1.72381
\(175\) 0 0
\(176\) −12.0000 −0.904534
\(177\) −5.12311 + 8.87348i −0.385076 + 0.666972i
\(178\) −5.56155 9.63289i −0.416856 0.722016i
\(179\) −10.0000 17.3205i −0.747435 1.29460i −0.949048 0.315130i \(-0.897952\pi\)
0.201613 0.979465i \(-0.435382\pi\)
\(180\) −0.780776 + 1.35234i −0.0581956 + 0.100798i
\(181\) 23.6155 1.75533 0.877664 0.479276i \(-0.159101\pi\)
0.877664 + 0.479276i \(0.159101\pi\)
\(182\) 0 0
\(183\) 24.0000 1.77413
\(184\) −6.24621 + 10.8188i −0.460477 + 0.797569i
\(185\) −3.00000 5.19615i −0.220564 0.382029i
\(186\) 0 0
\(187\) 5.84233 10.1192i 0.427233 0.739990i
\(188\) 1.61553 0.117824
\(189\) 0 0
\(190\) 1.75379 0.127233
\(191\) 4.71922 8.17394i 0.341471 0.591445i −0.643235 0.765669i \(-0.722408\pi\)
0.984706 + 0.174224i \(0.0557415\pi\)
\(192\) 7.12311 + 12.3376i 0.514066 + 0.890388i
\(193\) 2.68466 + 4.64996i 0.193246 + 0.334712i 0.946324 0.323219i \(-0.104765\pi\)
−0.753078 + 0.657931i \(0.771432\pi\)
\(194\) 11.5616 20.0252i 0.830071 1.43773i
\(195\) −11.6847 −0.836756
\(196\) 0 0
\(197\) −7.12311 −0.507500 −0.253750 0.967270i \(-0.581664\pi\)
−0.253750 + 0.967270i \(0.581664\pi\)
\(198\) −7.12311 + 12.3376i −0.506217 + 0.876794i
\(199\) 9.12311 + 15.8017i 0.646720 + 1.12015i 0.983901 + 0.178712i \(0.0571930\pi\)
−0.337182 + 0.941440i \(0.609474\pi\)
\(200\) 1.21922 + 2.11176i 0.0862121 + 0.149324i
\(201\) −8.00000 + 13.8564i −0.564276 + 0.977356i
\(202\) 0.384472 0.0270513
\(203\) 0 0
\(204\) 5.12311 0.358689
\(205\) 1.56155 2.70469i 0.109064 0.188904i
\(206\) −1.12311 1.94528i −0.0782505 0.135534i
\(207\) 9.12311 + 15.8017i 0.634100 + 1.09829i
\(208\) 10.6847 18.5064i 0.740848 1.28319i
\(209\) 2.87689 0.198999
\(210\) 0 0
\(211\) −23.0540 −1.58710 −0.793551 0.608504i \(-0.791770\pi\)
−0.793551 + 0.608504i \(0.791770\pi\)
\(212\) −0.684658 + 1.18586i −0.0470225 + 0.0814454i
\(213\) 10.2462 + 17.7470i 0.702059 + 1.21600i
\(214\) 8.87689 + 15.3752i 0.606812 + 1.05103i
\(215\) −4.56155 + 7.90084i −0.311095 + 0.538833i
\(216\) 3.50758 0.238660
\(217\) 0 0
\(218\) 27.6155 1.87036
\(219\) 5.43845 9.41967i 0.367496 0.636522i
\(220\) −0.561553 0.972638i −0.0378599 0.0655752i
\(221\) 10.4039 + 18.0201i 0.699841 + 1.21216i
\(222\) 12.0000 20.7846i 0.805387 1.39497i
\(223\) −6.56155 −0.439394 −0.219697 0.975568i \(-0.570507\pi\)
−0.219697 + 0.975568i \(0.570507\pi\)
\(224\) 0 0
\(225\) 3.56155 0.237437
\(226\) 10.9309 18.9328i 0.727111 1.25939i
\(227\) −11.8423 20.5115i −0.786003 1.36140i −0.928398 0.371587i \(-0.878814\pi\)
0.142395 0.989810i \(-0.454520\pi\)
\(228\) 0.630683 + 1.09238i 0.0417680 + 0.0723443i
\(229\) −9.56155 + 16.5611i −0.631845 + 1.09439i 0.355329 + 0.934741i \(0.384369\pi\)
−0.987174 + 0.159647i \(0.948965\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) 13.8617 0.910068
\(233\) 1.56155 2.70469i 0.102301 0.177190i −0.810331 0.585972i \(-0.800713\pi\)
0.912632 + 0.408782i \(0.134046\pi\)
\(234\) −12.6847 21.9705i −0.829222 1.43625i
\(235\) −1.84233 3.19101i −0.120180 0.208158i
\(236\) 0.876894 1.51883i 0.0570810 0.0988671i
\(237\) 16.8078 1.09178
\(238\) 0 0
\(239\) −0.807764 −0.0522499 −0.0261250 0.999659i \(-0.508317\pi\)
−0.0261250 + 0.999659i \(0.508317\pi\)
\(240\) −6.00000 + 10.3923i −0.387298 + 0.670820i
\(241\) −6.12311 10.6055i −0.394424 0.683162i 0.598604 0.801045i \(-0.295722\pi\)
−0.993027 + 0.117883i \(0.962389\pi\)
\(242\) 3.46543 + 6.00231i 0.222767 + 0.385843i
\(243\) −11.1231 + 19.2658i −0.713548 + 1.23590i
\(244\) −4.10795 −0.262985
\(245\) 0 0
\(246\) 12.4924 0.796488
\(247\) −2.56155 + 4.43674i −0.162988 + 0.282303i
\(248\) 0 0
\(249\) 5.12311 + 8.87348i 0.324664 + 0.562334i
\(250\) −0.780776 + 1.35234i −0.0493806 + 0.0855298i
\(251\) −17.1231 −1.08080 −0.540400 0.841408i \(-0.681727\pi\)
−0.540400 + 0.841408i \(0.681727\pi\)
\(252\) 0 0
\(253\) −13.1231 −0.825043
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) −5.84233 10.1192i −0.365861 0.633690i
\(256\) −5.02699 8.70700i −0.314187 0.544187i
\(257\) −11.2462 + 19.4790i −0.701519 + 1.21507i 0.266414 + 0.963859i \(0.414161\pi\)
−0.967933 + 0.251208i \(0.919172\pi\)
\(258\) −36.4924 −2.27192
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 10.1231 17.5337i 0.626605 1.08531i
\(262\) 7.12311 + 12.3376i 0.440067 + 0.762218i
\(263\) 10.5616 + 18.2931i 0.651253 + 1.12800i 0.982819 + 0.184572i \(0.0590898\pi\)
−0.331566 + 0.943432i \(0.607577\pi\)
\(264\) −8.00000 + 13.8564i −0.492366 + 0.852803i
\(265\) 3.12311 0.191851
\(266\) 0 0
\(267\) −18.2462 −1.11665
\(268\) 1.36932 2.37173i 0.0836443 0.144876i
\(269\) −14.3693 24.8884i −0.876113 1.51747i −0.855573 0.517683i \(-0.826795\pi\)
−0.0205400 0.999789i \(-0.506539\pi\)
\(270\) 1.12311 + 1.94528i 0.0683500 + 0.118386i
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 21.3693 1.29571
\(273\) 0 0
\(274\) −13.8617 −0.837418
\(275\) −1.28078 + 2.21837i −0.0772337 + 0.133773i
\(276\) −2.87689 4.98293i −0.173169 0.299937i
\(277\) −8.12311 14.0696i −0.488070 0.845362i 0.511836 0.859083i \(-0.328966\pi\)
−0.999906 + 0.0137211i \(0.995632\pi\)
\(278\) 5.36932 9.29993i 0.322030 0.557773i
\(279\) 0 0
\(280\) 0 0
\(281\) 16.5616 0.987979 0.493990 0.869468i \(-0.335538\pi\)
0.493990 + 0.869468i \(0.335538\pi\)
\(282\) 7.36932 12.7640i 0.438836 0.760087i
\(283\) 11.8423 + 20.5115i 0.703953 + 1.21928i 0.967068 + 0.254518i \(0.0819170\pi\)
−0.263115 + 0.964765i \(0.584750\pi\)
\(284\) −1.75379 3.03765i −0.104068 0.180251i
\(285\) 1.43845 2.49146i 0.0852063 0.147582i
\(286\) 18.2462 1.07892
\(287\) 0 0
\(288\) −8.68466 −0.511748
\(289\) −1.90388 + 3.29762i −0.111993 + 0.193978i
\(290\) 4.43845 + 7.68762i 0.260635 + 0.451432i
\(291\) −18.9654 32.8491i −1.11177 1.92565i
\(292\) −0.930870 + 1.61231i −0.0544750 + 0.0943535i
\(293\) 9.68466 0.565784 0.282892 0.959152i \(-0.408706\pi\)
0.282892 + 0.959152i \(0.408706\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 7.31534 12.6705i 0.425196 0.736460i
\(297\) 1.84233 + 3.19101i 0.106903 + 0.185161i
\(298\) 3.31534 + 5.74234i 0.192053 + 0.332645i
\(299\) 11.6847 20.2384i 0.675741 1.17042i
\(300\) −1.12311 −0.0648425
\(301\) 0 0
\(302\) 34.2462 1.97065
\(303\) 0.315342 0.546188i 0.0181159 0.0313777i
\(304\) 2.63068 + 4.55648i 0.150880 + 0.261332i
\(305\) 4.68466 + 8.11407i 0.268243 + 0.464610i
\(306\) 12.6847 21.9705i 0.725134 1.25597i
\(307\) −31.6847 −1.80834 −0.904169 0.427174i \(-0.859509\pi\)
−0.904169 + 0.427174i \(0.859509\pi\)
\(308\) 0 0
\(309\) −3.68466 −0.209613
\(310\) 0 0
\(311\) 4.80776 + 8.32729i 0.272623 + 0.472197i 0.969533 0.244962i \(-0.0787754\pi\)
−0.696909 + 0.717159i \(0.745442\pi\)
\(312\) −14.2462 24.6752i −0.806533 1.39696i
\(313\) −15.6501 + 27.1068i −0.884596 + 1.53216i −0.0384191 + 0.999262i \(0.512232\pi\)
−0.846176 + 0.532903i \(0.821101\pi\)
\(314\) 5.86174 0.330797
\(315\) 0 0
\(316\) −2.87689 −0.161838
\(317\) 11.2462 19.4790i 0.631650 1.09405i −0.355564 0.934652i \(-0.615711\pi\)
0.987214 0.159398i \(-0.0509554\pi\)
\(318\) 6.24621 + 10.8188i 0.350270 + 0.606686i
\(319\) 7.28078 + 12.6107i 0.407645 + 0.706062i
\(320\) −2.78078 + 4.81645i −0.155450 + 0.269248i
\(321\) 29.1231 1.62549
\(322\) 0 0
\(323\) −5.12311 −0.285057
\(324\) 1.53457 2.65794i 0.0852536 0.147664i
\(325\) −2.28078 3.95042i −0.126515 0.219130i
\(326\) −0.876894 1.51883i −0.0485667 0.0841200i
\(327\) 22.6501 39.2311i 1.25255 2.16949i
\(328\) 7.61553 0.420497
\(329\) 0 0
\(330\) −10.2462 −0.564035
\(331\) −6.00000 + 10.3923i −0.329790 + 0.571213i −0.982470 0.186421i \(-0.940311\pi\)
0.652680 + 0.757634i \(0.273645\pi\)
\(332\) −0.876894 1.51883i −0.0481258 0.0833564i
\(333\) −10.6847 18.5064i −0.585516 1.01414i
\(334\) −17.1231 + 29.6581i −0.936935 + 1.62282i
\(335\) −6.24621 −0.341267
\(336\) 0 0
\(337\) −34.4924 −1.87892 −0.939461 0.342656i \(-0.888674\pi\)
−0.939461 + 0.342656i \(0.888674\pi\)
\(338\) −6.09612 + 10.5588i −0.331585 + 0.574322i
\(339\) −17.9309 31.0572i −0.973871 1.68679i
\(340\) 1.00000 + 1.73205i 0.0542326 + 0.0939336i
\(341\) 0 0
\(342\) 6.24621 0.337756
\(343\) 0 0
\(344\) −22.2462 −1.19944
\(345\) −6.56155 + 11.3649i −0.353262 + 0.611868i
\(346\) 6.68466 + 11.5782i 0.359369 + 0.622446i
\(347\) 0.561553 + 0.972638i 0.0301457 + 0.0522139i 0.880705 0.473666i \(-0.157070\pi\)
−0.850559 + 0.525880i \(0.823736\pi\)
\(348\) −3.19224 + 5.52911i −0.171122 + 0.296392i
\(349\) −22.4924 −1.20399 −0.601996 0.798499i \(-0.705628\pi\)
−0.601996 + 0.798499i \(0.705628\pi\)
\(350\) 0 0
\(351\) −6.56155 −0.350230
\(352\) 3.12311 5.40938i 0.166462 0.288321i
\(353\) 7.40388 + 12.8239i 0.394069 + 0.682547i 0.992982 0.118267i \(-0.0377338\pi\)
−0.598913 + 0.800814i \(0.704400\pi\)
\(354\) −8.00000 13.8564i −0.425195 0.736460i
\(355\) −4.00000 + 6.92820i −0.212298 + 0.367711i
\(356\) 3.12311 0.165524
\(357\) 0 0
\(358\) 31.2311 1.65061
\(359\) −4.00000 + 6.92820i −0.211112 + 0.365657i −0.952063 0.305903i \(-0.901042\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(360\) 4.34233 + 7.52113i 0.228861 + 0.396399i
\(361\) 8.86932 + 15.3621i 0.466806 + 0.808532i
\(362\) −18.4384 + 31.9363i −0.969103 + 1.67854i
\(363\) 11.3693 0.596734
\(364\) 0 0
\(365\) 4.24621 0.222257
\(366\) −18.7386 + 32.4563i −0.979484 + 1.69652i
\(367\) −1.84233 3.19101i −0.0961688 0.166569i 0.813927 0.580967i \(-0.197326\pi\)
−0.910096 + 0.414398i \(0.863992\pi\)
\(368\) −12.0000 20.7846i −0.625543 1.08347i
\(369\) 5.56155 9.63289i 0.289523 0.501468i
\(370\) 9.36932 0.487088
\(371\) 0 0
\(372\) 0 0
\(373\) −14.6847 + 25.4346i −0.760343 + 1.31695i 0.182331 + 0.983237i \(0.441636\pi\)
−0.942674 + 0.333715i \(0.891698\pi\)
\(374\) 9.12311 + 15.8017i 0.471745 + 0.817086i
\(375\) 1.28078 + 2.21837i 0.0661390 + 0.114556i
\(376\) 4.49242 7.78110i 0.231679 0.401280i
\(377\) −25.9309 −1.33551
\(378\) 0 0
\(379\) 16.4924 0.847159 0.423579 0.905859i \(-0.360773\pi\)
0.423579 + 0.905859i \(0.360773\pi\)
\(380\) −0.246211 + 0.426450i −0.0126304 + 0.0218764i
\(381\) 13.1231 + 22.7299i 0.672317 + 1.16449i
\(382\) 7.36932 + 12.7640i 0.377047 + 0.653065i
\(383\) 5.12311 8.87348i 0.261778 0.453414i −0.704936 0.709271i \(-0.749024\pi\)
0.966715 + 0.255857i \(0.0823577\pi\)
\(384\) −34.7386 −1.77275
\(385\) 0 0
\(386\) −8.38447 −0.426758
\(387\) −16.2462 + 28.1393i −0.825841 + 1.43040i
\(388\) 3.24621 + 5.62260i 0.164801 + 0.285444i
\(389\) −1.96543 3.40423i −0.0996515 0.172601i 0.811889 0.583812i \(-0.198439\pi\)
−0.911540 + 0.411210i \(0.865106\pi\)
\(390\) 9.12311 15.8017i 0.461966 0.800149i
\(391\) 23.3693 1.18184
\(392\) 0 0
\(393\) 23.3693 1.17883
\(394\) 5.56155 9.63289i 0.280187 0.485298i
\(395\) 3.28078 + 5.68247i 0.165074 + 0.285916i
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) −11.7192 + 20.2983i −0.588171 + 1.01874i 0.406301 + 0.913739i \(0.366818\pi\)
−0.994472 + 0.105003i \(0.966515\pi\)
\(398\) −28.4924 −1.42820
\(399\) 0 0
\(400\) −4.68466 −0.234233
\(401\) −13.7192 + 23.7624i −0.685105 + 1.18664i 0.288298 + 0.957541i \(0.406911\pi\)
−0.973404 + 0.229097i \(0.926423\pi\)
\(402\) −12.4924 21.6375i −0.623065 1.07918i
\(403\) 0 0
\(404\) −0.0539753 + 0.0934880i −0.00268537 + 0.00465120i
\(405\) −7.00000 −0.347833
\(406\) 0 0
\(407\) 15.3693 0.761829
\(408\) 14.2462 24.6752i 0.705293 1.22160i
\(409\) 13.2462 + 22.9431i 0.654983 + 1.13446i 0.981898 + 0.189410i \(0.0606576\pi\)
−0.326915 + 0.945054i \(0.606009\pi\)
\(410\) 2.43845 + 4.22351i 0.120426 + 0.208585i
\(411\) −11.3693 + 19.6922i −0.560807 + 0.971346i
\(412\) 0.630683 0.0310715
\(413\) 0 0
\(414\) −28.4924 −1.40033
\(415\) −2.00000 + 3.46410i −0.0981761 + 0.170046i
\(416\) 5.56155 + 9.63289i 0.272678 + 0.472291i
\(417\) −8.80776 15.2555i −0.431318 0.747065i
\(418\) −2.24621 + 3.89055i −0.109866 + 0.190293i
\(419\) 9.75379 0.476504 0.238252 0.971203i \(-0.423426\pi\)
0.238252 + 0.971203i \(0.423426\pi\)
\(420\) 0 0
\(421\) 9.68466 0.472001 0.236001 0.971753i \(-0.424163\pi\)
0.236001 + 0.971753i \(0.424163\pi\)
\(422\) 18.0000 31.1769i 0.876226 1.51767i
\(423\) −6.56155 11.3649i −0.319034 0.552582i
\(424\) 3.80776 + 6.59524i 0.184921 + 0.320293i
\(425\) 2.28078 3.95042i 0.110634 0.191624i
\(426\) −32.0000 −1.55041
\(427\) 0 0
\(428\) −4.98485 −0.240952
\(429\) 14.9654 25.9209i 0.722538 1.25147i
\(430\) −7.12311 12.3376i −0.343507 0.594971i
\(431\) −0.403882 0.699544i −0.0194543 0.0336959i 0.856134 0.516753i \(-0.172860\pi\)
−0.875589 + 0.483057i \(0.839526\pi\)
\(432\) −3.36932 + 5.83583i −0.162106 + 0.280776i
\(433\) −8.24621 −0.396288 −0.198144 0.980173i \(-0.563491\pi\)
−0.198144 + 0.980173i \(0.563491\pi\)
\(434\) 0 0
\(435\) 14.5616 0.698173
\(436\) −3.87689 + 6.71498i −0.185670 + 0.321589i
\(437\) 2.87689 + 4.98293i 0.137621 + 0.238366i
\(438\) 8.49242 + 14.7093i 0.405784 + 0.702838i
\(439\) 7.68466 13.3102i 0.366769 0.635262i −0.622290 0.782787i \(-0.713797\pi\)
0.989058 + 0.147525i \(0.0471307\pi\)
\(440\) −6.24621 −0.297776
\(441\) 0 0
\(442\) −32.4924 −1.54551
\(443\) 13.6847 23.7025i 0.650178 1.12614i −0.332902 0.942962i \(-0.608028\pi\)
0.983080 0.183179i \(-0.0586389\pi\)
\(444\) 3.36932 + 5.83583i 0.159901 + 0.276956i
\(445\) −3.56155 6.16879i −0.168834 0.292429i
\(446\) 5.12311 8.87348i 0.242586 0.420171i
\(447\) 10.8769 0.514459
\(448\) 0 0
\(449\) 18.8078 0.887593 0.443797 0.896128i \(-0.353631\pi\)
0.443797 + 0.896128i \(0.353631\pi\)
\(450\) −2.78078 + 4.81645i −0.131087 + 0.227049i
\(451\) 4.00000 + 6.92820i 0.188353 + 0.326236i
\(452\) 3.06913 + 5.31589i 0.144360 + 0.250038i
\(453\) 28.0885 48.6508i 1.31971 2.28581i
\(454\) 36.9848 1.73578
\(455\) 0 0
\(456\) 7.01515 0.328515
\(457\) 4.43845 7.68762i 0.207622 0.359612i −0.743343 0.668910i \(-0.766761\pi\)
0.950965 + 0.309299i \(0.100094\pi\)
\(458\) −14.9309 25.8610i −0.697674 1.20841i
\(459\) −3.28078 5.68247i −0.153134 0.265235i
\(460\) 1.12311 1.94528i 0.0523651 0.0906990i
\(461\) −4.87689 −0.227140 −0.113570 0.993530i \(-0.536229\pi\)
−0.113570 + 0.993530i \(0.536229\pi\)
\(462\) 0 0
\(463\) −20.4924 −0.952364 −0.476182 0.879347i \(-0.657980\pi\)
−0.476182 + 0.879347i \(0.657980\pi\)
\(464\) −13.3153 + 23.0628i −0.618149 + 1.07067i
\(465\) 0 0
\(466\) 2.43845 + 4.22351i 0.112959 + 0.195651i
\(467\) −13.2808 + 23.0030i −0.614561 + 1.06445i 0.375900 + 0.926660i \(0.377334\pi\)
−0.990461 + 0.137791i \(0.956000\pi\)
\(468\) 7.12311 0.329266
\(469\) 0 0
\(470\) 5.75379 0.265402
\(471\) 4.80776 8.32729i 0.221530 0.383701i
\(472\) −4.87689 8.44703i −0.224477 0.388806i
\(473\) −11.6847 20.2384i −0.537261 0.930564i
\(474\) −13.1231 + 22.7299i −0.602764 + 1.04402i
\(475\) 1.12311 0.0515316
\(476\) 0 0
\(477\) 11.1231 0.509292
\(478\) 0.630683 1.09238i 0.0288468 0.0499641i
\(479\) −6.56155 11.3649i −0.299805 0.519277i 0.676286 0.736639i \(-0.263588\pi\)
−0.976091 + 0.217362i \(0.930255\pi\)
\(480\) −3.12311 5.40938i −0.142550 0.246903i
\(481\) −13.6847 + 23.7025i −0.623967 + 1.08074i
\(482\) 19.1231 0.871034
\(483\) 0 0
\(484\) −1.94602 −0.0884557
\(485\) 7.40388 12.8239i 0.336193 0.582303i
\(486\) −17.3693 30.0845i −0.787888 1.36466i
\(487\) −2.56155 4.43674i −0.116075 0.201048i 0.802134 0.597144i \(-0.203698\pi\)
−0.918209 + 0.396096i \(0.870365\pi\)
\(488\) −11.4233 + 19.7857i −0.517108 + 0.895658i
\(489\) −2.87689 −0.130098
\(490\) 0 0
\(491\) 4.17708 0.188509 0.0942545 0.995548i \(-0.469953\pi\)
0.0942545 + 0.995548i \(0.469953\pi\)
\(492\) −1.75379 + 3.03765i −0.0790669 + 0.136948i
\(493\) −12.9654 22.4568i −0.583934 1.01140i
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) −4.56155 + 7.90084i −0.205027 + 0.355116i
\(496\) 0 0
\(497\) 0 0
\(498\) −16.0000 −0.716977
\(499\) 2.08854 3.61746i 0.0934959 0.161940i −0.815484 0.578780i \(-0.803529\pi\)
0.908980 + 0.416840i \(0.136862\pi\)
\(500\) −0.219224 0.379706i −0.00980398 0.0169810i
\(501\) 28.0885 + 48.6508i 1.25490 + 2.17356i
\(502\) 13.3693 23.1563i 0.596702 1.03352i
\(503\) 10.0691 0.448960 0.224480 0.974479i \(-0.427932\pi\)
0.224480 + 0.974479i \(0.427932\pi\)
\(504\) 0 0
\(505\) 0.246211 0.0109563
\(506\) 10.2462 17.7470i 0.455500 0.788949i
\(507\) 10.0000 + 17.3205i 0.444116 + 0.769231i
\(508\) −2.24621 3.89055i −0.0996595 0.172615i
\(509\) 14.1231 24.4619i 0.625996 1.08426i −0.362352 0.932041i \(-0.618026\pi\)
0.988347 0.152215i \(-0.0486406\pi\)
\(510\) 18.2462 0.807956
\(511\) 0 0
\(512\) −11.4233 −0.504843
\(513\) 0.807764 1.39909i 0.0356637 0.0617713i
\(514\) −17.5616 30.4175i −0.774607 1.34166i
\(515\) −0.719224 1.24573i −0.0316928 0.0548935i
\(516\) 5.12311 8.87348i 0.225532 0.390633i
\(517\) 9.43845 0.415102
\(518\) 0 0
\(519\) 21.9309 0.962658
\(520\) 5.56155 9.63289i 0.243890 0.422430i
\(521\) −5.00000 8.66025i −0.219054 0.379413i 0.735465 0.677563i \(-0.236964\pi\)
−0.954519 + 0.298150i \(0.903630\pi\)
\(522\) 15.8078 + 27.3799i 0.691887 + 1.19838i
\(523\) −3.75379 + 6.50175i −0.164142 + 0.284302i −0.936350 0.351067i \(-0.885819\pi\)
0.772208 + 0.635369i \(0.219152\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) −32.9848 −1.43821
\(527\) 0 0
\(528\) −15.3693 26.6204i −0.668864 1.15851i
\(529\) −1.62311 2.81130i −0.0705698 0.122230i
\(530\) −2.43845 + 4.22351i −0.105919 + 0.183458i
\(531\) −14.2462 −0.618233
\(532\) 0 0
\(533\) −14.2462 −0.617072
\(534\) 14.2462 24.6752i 0.616494 1.06780i
\(535\) 5.68466 + 9.84612i 0.245769 + 0.425685i
\(536\) −7.61553 13.1905i −0.328941 0.569742i
\(537\) 25.6155 44.3674i 1.10539 1.91459i
\(538\) 44.8769 1.93478
\(539\) 0 0
\(540\) −0.630683 −0.0271403
\(541\) 8.59612 14.8889i 0.369576 0.640124i −0.619923 0.784662i \(-0.712836\pi\)
0.989499 + 0.144538i \(0.0461696\pi\)
\(542\) 12.4924 + 21.6375i 0.536595 + 0.929411i
\(543\) 30.2462 + 52.3880i 1.29799 + 2.24818i
\(544\) −5.56155 + 9.63289i −0.238450 + 0.413007i
\(545\) 17.6847 0.757528
\(546\) 0 0
\(547\) 14.2462 0.609124 0.304562 0.952493i \(-0.401490\pi\)
0.304562 + 0.952493i \(0.401490\pi\)
\(548\) 1.94602 3.37061i 0.0831301 0.143985i
\(549\) 16.6847 + 28.8987i 0.712084 + 1.23337i
\(550\) −2.00000 3.46410i −0.0852803 0.147710i
\(551\) 3.19224 5.52911i 0.135994 0.235548i
\(552\) −32.0000 −1.36201
\(553\) 0 0
\(554\) 25.3693 1.07784
\(555\) 7.68466 13.3102i 0.326196 0.564987i
\(556\) 1.50758 + 2.61120i 0.0639355 + 0.110740i
\(557\) 2.43845 + 4.22351i 0.103320 + 0.178956i 0.913051 0.407846i \(-0.133720\pi\)
−0.809730 + 0.586802i \(0.800387\pi\)
\(558\) 0 0
\(559\) 41.6155 1.76015
\(560\) 0 0
\(561\) 29.9309 1.26368
\(562\) −12.9309 + 22.3969i −0.545456 + 0.944757i
\(563\) 14.0000 + 24.2487i 0.590030 + 1.02196i 0.994228 + 0.107290i \(0.0342173\pi\)
−0.404198 + 0.914671i \(0.632449\pi\)
\(564\) 2.06913 + 3.58384i 0.0871261 + 0.150907i
\(565\) 7.00000 12.1244i 0.294492 0.510075i
\(566\) −36.9848 −1.55459
\(567\) 0 0
\(568\) −19.5076 −0.818520
\(569\) −17.4924 + 30.2978i −0.733320 + 1.27015i 0.222136 + 0.975016i \(0.428697\pi\)
−0.955456 + 0.295133i \(0.904636\pi\)
\(570\) 2.24621 + 3.89055i 0.0940834 + 0.162957i
\(571\) −3.75379 6.50175i −0.157091 0.272090i 0.776727 0.629837i \(-0.216878\pi\)
−0.933819 + 0.357747i \(0.883545\pi\)
\(572\) −2.56155 + 4.43674i −0.107104 + 0.185509i
\(573\) 24.1771 1.01001
\(574\) 0 0
\(575\) −5.12311 −0.213648
\(576\) −9.90388 + 17.1540i −0.412662 + 0.714751i
\(577\) −6.52699 11.3051i −0.271722 0.470636i 0.697581 0.716506i \(-0.254260\pi\)
−0.969303 + 0.245870i \(0.920926\pi\)
\(578\) −2.97301 5.14941i −0.123661 0.214187i
\(579\) −6.87689 + 11.9111i −0.285794 + 0.495010i
\(580\) −2.49242 −0.103492
\(581\) 0 0
\(582\) 59.2311 2.45521
\(583\) −4.00000 + 6.92820i −0.165663 + 0.286937i
\(584\) 5.17708 + 8.96697i 0.214229 + 0.371056i
\(585\) −8.12311 14.0696i −0.335849 0.581708i
\(586\) −7.56155 + 13.0970i −0.312365 + 0.541032i
\(587\) −9.75379 −0.402582 −0.201291 0.979531i \(-0.564514\pi\)
−0.201291 + 0.979531i \(0.564514\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 3.12311 5.40938i 0.128576 0.222701i
\(591\) −9.12311 15.8017i −0.375274 0.649994i
\(592\) 14.0540 + 24.3422i 0.577615 + 1.00046i
\(593\) 11.7192 20.2983i 0.481251 0.833551i −0.518518 0.855067i \(-0.673516\pi\)
0.999769 + 0.0215160i \(0.00684929\pi\)
\(594\) −5.75379 −0.236081
\(595\) 0 0
\(596\) −1.86174 −0.0762598
\(597\) −23.3693 + 40.4768i −0.956442 + 1.65661i
\(598\) 18.2462 + 31.6034i 0.746143 + 1.29236i
\(599\) −4.40388 7.62775i −0.179938 0.311661i 0.761921 0.647670i \(-0.224256\pi\)
−0.941859 + 0.336008i \(0.890923\pi\)
\(600\) −3.12311 + 5.40938i −0.127500 + 0.220837i
\(601\) −26.4924 −1.08065 −0.540324 0.841457i \(-0.681698\pi\)
−0.540324 + 0.841457i \(0.681698\pi\)
\(602\) 0 0
\(603\) −22.2462 −0.905936
\(604\) −4.80776 + 8.32729i −0.195625 + 0.338833i
\(605\) 2.21922 + 3.84381i 0.0902243 + 0.156273i
\(606\) 0.492423 + 0.852901i 0.0200033 + 0.0346467i
\(607\) 2.47301 4.28338i 0.100376 0.173857i −0.811463 0.584403i \(-0.801329\pi\)
0.911840 + 0.410546i \(0.134662\pi\)
\(608\) −2.73863 −0.111066
\(609\) 0 0
\(610\) −14.6307 −0.592379
\(611\) −8.40388 + 14.5560i −0.339985 + 0.588871i
\(612\) 3.56155 + 6.16879i 0.143967 + 0.249359i
\(613\) 4.36932 + 7.56788i 0.176475 + 0.305664i 0.940671 0.339321i \(-0.110197\pi\)
−0.764196 + 0.644984i \(0.776864\pi\)
\(614\) 24.7386 42.8486i 0.998370 1.72923i
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) 15.7538 0.634224 0.317112 0.948388i \(-0.397287\pi\)
0.317112 + 0.948388i \(0.397287\pi\)
\(618\) 2.87689 4.98293i 0.115726 0.200443i
\(619\) 21.0540 + 36.4666i 0.846231 + 1.46571i 0.884548 + 0.466449i \(0.154467\pi\)
−0.0383174 + 0.999266i \(0.512200\pi\)
\(620\) 0 0
\(621\) −3.68466 + 6.38202i −0.147860 + 0.256101i
\(622\) −15.0152 −0.602053
\(623\) 0 0
\(624\) 54.7386 2.19130
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −24.4384 42.3286i −0.976757 1.69179i
\(627\) 3.68466 + 6.38202i 0.147151 + 0.254873i
\(628\) −0.822919 + 1.42534i −0.0328380 + 0.0568772i
\(629\) −27.3693 −1.09129
\(630\) 0 0
\(631\) 8.80776 0.350632 0.175316 0.984512i \(-0.443905\pi\)
0.175316 + 0.984512i \(0.443905\pi\)
\(632\) −8.00000 + 13.8564i −0.318223 + 0.551178i
\(633\) −29.5270 51.1422i −1.17359 2.03272i
\(634\) 17.5616 + 30.4175i 0.697458 + 1.20803i
\(635\) −5.12311 + 8.87348i −0.203304 + 0.352133i
\(636\) −3.50758 −0.139084
\(637\) 0 0
\(638\) −22.7386 −0.900231
\(639\) −14.2462 + 24.6752i −0.563571 + 0.976134i
\(640\) −6.78078 11.7446i −0.268034 0.464248i
\(641\) −1.00000 1.73205i −0.0394976 0.0684119i 0.845601 0.533816i \(-0.179242\pi\)
−0.885098 + 0.465404i \(0.845909\pi\)
\(642\) −22.7386 + 39.3845i −0.897422 + 1.55438i
\(643\) −2.56155 −0.101018 −0.0505089 0.998724i \(-0.516084\pi\)
−0.0505089 + 0.998724i \(0.516084\pi\)
\(644\) 0 0
\(645\) −23.3693 −0.920166
\(646\) 4.00000 6.92820i 0.157378 0.272587i
\(647\) −1.75379 3.03765i −0.0689486 0.119422i 0.829490 0.558521i \(-0.188631\pi\)
−0.898439 + 0.439099i \(0.855298\pi\)
\(648\) −8.53457 14.7823i −0.335269 0.580704i
\(649\) 5.12311 8.87348i 0.201099 0.348315i
\(650\) 7.12311 0.279391
\(651\) 0 0
\(652\) 0.492423 0.0192848
\(653\) −24.6155 + 42.6353i −0.963280 + 1.66845i −0.249113 + 0.968474i \(0.580139\pi\)
−0.714167 + 0.699976i \(0.753194\pi\)
\(654\) 35.3693 + 61.2615i 1.38305 + 2.39551i
\(655\) 4.56155 + 7.90084i 0.178235 + 0.308711i
\(656\) −7.31534 + 12.6705i −0.285616 + 0.494702i
\(657\) 15.1231 0.590009
\(658\) 0 0
\(659\) −36.1771 −1.40926 −0.704629 0.709575i \(-0.748887\pi\)
−0.704629 + 0.709575i \(0.748887\pi\)
\(660\) 1.43845 2.49146i 0.0559915 0.0969801i
\(661\) −1.56155 2.70469i −0.0607374 0.105200i 0.834058 0.551677i \(-0.186012\pi\)
−0.894795 + 0.446477i \(0.852679\pi\)
\(662\) −9.36932 16.2281i −0.364149 0.630724i
\(663\) −26.6501 + 46.1593i −1.03500 + 1.79268i
\(664\) −9.75379 −0.378520
\(665\) 0 0
\(666\) 33.3693 1.29303
\(667\) −14.5616 + 25.2213i −0.563826 + 0.976575i
\(668\) −4.80776 8.32729i −0.186018 0.322193i
\(669\) −8.40388 14.5560i −0.324913 0.562766i
\(670\) 4.87689 8.44703i 0.188411 0.326337i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −25.8617 −0.996897 −0.498448 0.866919i \(-0.666097\pi\)
−0.498448 + 0.866919i \(0.666097\pi\)
\(674\) 26.9309 46.6456i 1.03734 1.79672i
\(675\) 0.719224 + 1.24573i 0.0276829 + 0.0479482i
\(676\) −1.71165 2.96466i −0.0658325 0.114025i
\(677\) 11.9654 20.7247i 0.459869 0.796517i −0.539085 0.842252i \(-0.681230\pi\)
0.998954 + 0.0457351i \(0.0145630\pi\)
\(678\) 56.0000 2.15067
\(679\) 0 0
\(680\) 11.1231 0.426552
\(681\) 30.3348 52.5413i 1.16243 2.01339i
\(682\) 0 0
\(683\) −21.3693 37.0127i −0.817674 1.41625i −0.907392 0.420286i \(-0.861930\pi\)
0.0897175 0.995967i \(-0.471404\pi\)
\(684\) −0.876894 + 1.51883i −0.0335289 + 0.0580737i
\(685\) −8.87689 −0.339169
\(686\) 0 0
\(687\) −48.9848 −1.86889
\(688\) 21.3693 37.0127i 0.814698 1.41110i
\(689\) −7.12311 12.3376i −0.271369 0.470024i
\(690\) −10.2462 17.7470i −0.390067 0.675615i
\(691\) −4.24621 + 7.35465i −0.161533 + 0.279784i −0.935419 0.353542i \(-0.884977\pi\)
0.773885 + 0.633326i \(0.218311\pi\)
\(692\) −3.75379 −0.142698
\(693\) 0 0
\(694\) −1.75379 −0.0665729
\(695\) 3.43845 5.95557i 0.130428 0.225907i
\(696\) 17.7538 + 30.7505i 0.672956 + 1.16559i
\(697\) −7.12311 12.3376i −0.269807 0.467319i
\(698\) 17.5616 30.4175i 0.664715 1.15132i
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) 0.0691303 0.00261102 0.00130551 0.999999i \(-0.499584\pi\)
0.00130551 + 0.999999i \(0.499584\pi\)
\(702\) 5.12311 8.87348i 0.193359 0.334908i
\(703\) −3.36932 5.83583i −0.127076 0.220102i
\(704\) −7.12311 12.3376i −0.268462 0.464990i
\(705\) 4.71922 8.17394i 0.177736 0.307848i
\(706\) −23.1231 −0.870250
\(707\) 0 0
\(708\) 4.49242 0.168836
\(709\) 9.08854 15.7418i 0.341327 0.591196i −0.643352 0.765570i \(-0.722457\pi\)
0.984679 + 0.174374i \(0.0557902\pi\)
\(710\) −6.24621 10.8188i −0.234416 0.406021i
\(711\) 11.6847 + 20.2384i 0.438209 + 0.759000i
\(712\) 8.68466 15.0423i 0.325471 0.563733i
\(713\) 0 0
\(714\) 0 0
\(715\) 11.6847 0.436981
\(716\) −4.38447 + 7.59413i −0.163855 + 0.283806i
\(717\) −1.03457 1.79192i −0.0386365 0.0669205i
\(718\) −6.24621 10.8188i −0.233107 0.403752i
\(719\) −24.8078 + 42.9683i −0.925173 + 1.60245i −0.133892 + 0.990996i \(0.542747\pi\)
−0.791282 + 0.611451i \(0.790586\pi\)
\(720\) −16.6847 −0.621801
\(721\) 0 0
\(722\) −27.6998 −1.03088
\(723\) 15.6847 27.1666i 0.583319 1.01034i
\(724\) −5.17708 8.96697i −0.192405 0.333255i
\(725\) 2.84233 + 4.92306i 0.105561 + 0.182838i
\(726\) −8.87689 + 15.3752i −0.329452 + 0.570628i
\(727\) 19.5076 0.723496 0.361748 0.932276i \(-0.382180\pi\)
0.361748 + 0.932276i \(0.382180\pi\)
\(728\) 0 0
\(729\) −35.9848 −1.33277
\(730\) −3.31534 + 5.74234i −0.122706 + 0.212534i
\(731\) 20.8078 + 36.0401i 0.769603 + 1.33299i
\(732\) −5.26137 9.11295i −0.194466 0.336824i
\(733\) 2.84233 4.92306i 0.104984 0.181837i −0.808748 0.588156i \(-0.799854\pi\)
0.913732 + 0.406318i \(0.133188\pi\)
\(734\) 5.75379 0.212376
\(735\) 0 0
\(736\) 12.4924 0.460477
\(737\) 8.00000 13.8564i 0.294684 0.510407i
\(738\) 8.68466 + 15.0423i 0.319687 + 0.553714i
\(739\) −3.03457 5.25602i −0.111628 0.193346i 0.804799 0.593548i \(-0.202273\pi\)
−0.916427 + 0.400202i \(0.868940\pi\)
\(740\) −1.31534 + 2.27824i −0.0483529 + 0.0837497i
\(741\) −13.1231 −0.482089
\(742\) 0 0
\(743\) 32.9848 1.21010 0.605048 0.796189i \(-0.293154\pi\)
0.605048 + 0.796189i \(0.293154\pi\)
\(744\) 0 0
\(745\) 2.12311 + 3.67733i 0.0777846 + 0.134727i
\(746\) −22.9309 39.7174i −0.839559 1.45416i
\(747\) −7.12311 + 12.3376i −0.260621 + 0.451408i
\(748\) −5.12311 −0.187319
\(749\) 0 0
\(750\) −4.00000 −0.146059
\(751\) −22.9654 + 39.7773i −0.838021 + 1.45149i 0.0535265 + 0.998566i \(0.482954\pi\)
−0.891547 + 0.452928i \(0.850380\pi\)
\(752\) 8.63068 + 14.9488i 0.314729 + 0.545126i
\(753\) −21.9309 37.9854i −0.799205 1.38426i
\(754\) 20.2462 35.0675i 0.737324 1.27708i
\(755\) 21.9309 0.798146
\(756\) 0 0
\(757\) 14.6307 0.531761 0.265881 0.964006i \(-0.414337\pi\)
0.265881 + 0.964006i \(0.414337\pi\)
\(758\) −12.8769 + 22.3034i −0.467710 + 0.810097i
\(759\) −16.8078 29.1119i −0.610083 1.05670i
\(760\) 1.36932 + 2.37173i 0.0496703 + 0.0860316i
\(761\) −15.8769 + 27.4996i −0.575537 + 0.996859i 0.420446 + 0.907318i \(0.361874\pi\)
−0.995983 + 0.0895418i \(0.971460\pi\)
\(762\) −40.9848 −1.48472
\(763\) 0 0
\(764\) −4.13826 −0.149717
\(765\) 8.12311 14.0696i 0.293692 0.508689i
\(766\) 8.00000 + 13.8564i 0.289052 + 0.500652i
\(767\) 9.12311 + 15.8017i 0.329416 + 0.570566i
\(768\) 12.8769 22.3034i 0.464655 0.804806i
\(769\) −9.50758 −0.342852 −0.171426 0.985197i \(-0.554837\pi\)
−0.171426 + 0.985197i \(0.554837\pi\)
\(770\) 0 0
\(771\) −57.6155 −2.07497
\(772\) 1.17708 2.03876i 0.0423641 0.0733767i
\(773\) −4.03457 6.98807i −0.145113 0.251343i 0.784302 0.620379i \(-0.213021\pi\)
−0.929415 + 0.369036i \(0.879688\pi\)
\(774\) −25.3693 43.9409i −0.911881 1.57942i
\(775\) 0 0
\(776\) 36.1080 1.29620
\(777\) 0 0
\(778\) 6.13826 0.220067
\(779\) 1.75379 3.03765i 0.0628360 0.108835i
\(780\) 2.56155 + 4.43674i 0.0917183 + 0.158861i
\(781\) −10.2462 17.7470i −0.366638 0.635036i
\(782\) −18.2462 + 31.6034i −0.652483 + 1.13013i
\(783\) 8.17708 0.292225
\(784\)