Properties

Label 245.2.e.h.116.1
Level $245$
Weight $2$
Character 245.116
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 116.1
Root \(-0.780776 - 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.2.e.h.226.1

$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 −0.998123 0.0612344i \(-0.980496\pi\)
0.446031 0.895017i \(-0.352837\pi\)
\(3\) −1.28078 + 2.21837i −0.739457 + 1.28078i 0.213284 + 0.976990i \(0.431584\pi\)
−0.952740 + 0.303786i \(0.901749\pi\)
\(4\) −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 −0.991931 0.126782i \(-0.959535\pi\)
0.605762 + 0.795646i \(0.292868\pi\)
\(12\) −0.561553 0.972638i −0.162106 0.280776i
\(13\) −4.56155 −1.26515 −0.632574 0.774500i \(-0.718001\pi\)
−0.632574 + 0.774500i \(0.718001\pi\)
\(14\) 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 0.444874 + 0.895593i \(0.353248\pi\)
−0.998043 + 0.0625245i \(0.980085\pi\)
\(18\) −2.78078 + 4.81645i −0.655435 + 1.13525i
\(19\) 0.561553 + 0.972638i 0.128829 + 0.223138i 0.923223 0.384264i \(-0.125545\pi\)
−0.794394 + 0.607403i \(0.792211\pi\)
\(20\) −0.438447 −0.0980398
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) 2.56155 + 4.43674i 0.534121 + 0.925124i 0.999205 + 0.0398580i \(0.0126905\pi\)
−0.465085 + 0.885266i \(0.653976\pi\)
\(24\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 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 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) 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 \(-0.421582\pi\)
0.243874 + 0.969807i \(0.421582\pi\)
\(42\) 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 \(-0.0800623\pi\)
−0.699803 + 0.714336i \(0.746729\pi\)
\(48\) −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 −0.953116 0.302604i \(-0.902144\pi\)
0.738621 + 0.674121i \(0.235477\pi\)
\(54\) −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 \(-0.917180\pi\)
0.705965 + 0.708247i \(0.250514\pi\)
\(60\) 0.561553 0.972638i 0.0724962 0.125567i
\(61\) −4.68466 8.11407i −0.599809 1.03890i −0.992849 0.119378i \(-0.961910\pi\)
0.393040 0.919521i \(-0.371423\pi\)
\(62\) 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 −0.609736 0.792605i \(-0.708724\pi\)
0.991284 + 0.131744i \(0.0420577\pi\)
\(68\) −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 \(-0.753399\pi\)
0.963107 + 0.269118i \(0.0867321\pi\)
\(74\) −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 0.989428 0.145028i \(-0.0463271\pi\)
−0.620311 + 0.784356i \(0.712994\pi\)
\(80\) −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 \(-0.570452\pi\)
−0.219529 + 0.975606i \(0.570452\pi\)
\(84\) 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 \(-0.0434423\pi\)
−0.613177 + 0.789945i \(0.710109\pi\)
\(90\) −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 \(-0.229210\pi\)
0.751750 + 0.659448i \(0.229210\pi\)
\(98\) 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 \(-0.829434\pi\)
0.872085 + 0.489354i \(0.162767\pi\)
\(102\) −9.12311 + 15.8017i −0.903322 + 1.56460i
\(103\) 0.719224 + 1.24573i 0.0708672 + 0.122746i 0.899282 0.437370i \(-0.144090\pi\)
−0.828414 + 0.560116i \(0.810757\pi\)
\(104\) 11.1231 1.09071
\(105\) 0 0
\(106\) 4.87689 0.473686
\(107\) 5.68466 + 9.84612i 0.549557 + 0.951860i 0.998305 + 0.0582018i \(0.0185367\pi\)
−0.448748 + 0.893658i \(0.648130\pi\)
\(108\) −0.315342 + 0.546188i −0.0303438 + 0.0525569i
\(109\) −8.84233 + 15.3154i −0.846942 + 1.46695i 0.0369828 + 0.999316i \(0.488225\pi\)
−0.883924 + 0.467630i \(0.845108\pi\)
\(110\) 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 \(-0.297151\pi\)
−0.993547 + 0.113425i \(0.963818\pi\)
\(132\) 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 −0.611744 0.791056i \(-0.709532\pi\)
0.990946 + 0.134258i \(0.0428652\pi\)
\(138\) 10.2462 + 17.7470i 0.872215 + 1.51072i
\(139\) 6.87689 0.583291 0.291645 0.956527i \(-0.405797\pi\)
0.291645 + 0.956527i \(0.405797\pi\)
\(140\) 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 0.939791 0.341750i \(-0.111020\pi\)
−0.765859 + 0.643008i \(0.777686\pi\)
\(150\) −2.00000 + 3.46410i −0.163299 + 0.282843i
\(151\) −10.9654 + 18.9927i −0.892354 + 1.54560i −0.0553094 + 0.998469i \(0.517615\pi\)
−0.837045 + 0.547134i \(0.815719\pi\)
\(152\) −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 \(-0.785473\pi\)
0.931151 + 0.364635i \(0.118806\pi\)
\(158\) 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 0.843195 0.537608i \(-0.180672\pi\)
−0.887179 + 0.461425i \(0.847338\pi\)
\(164\) −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 \(-0.822512\pi\)
−0.848531 + 0.529146i \(0.822512\pi\)
\(168\) 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 \(-0.272186\pi\)
−0.981606 + 0.190920i \(0.938853\pi\)
\(174\) −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 0.201613 + 0.979465i \(0.435382\pi\)
−0.949048 + 0.315130i \(0.897952\pi\)
\(180\) 0.780776 + 1.35234i 0.0581956 + 0.100798i
\(181\) −23.6155 −1.75533 −0.877664 0.479276i \(-0.840899\pi\)
−0.877664 + 0.479276i \(0.840899\pi\)
\(182\) 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 0.984706 0.174224i \(-0.0557415\pi\)
−0.643235 + 0.765669i \(0.722408\pi\)
\(192\) −7.12311 + 12.3376i −0.514066 + 0.890388i
\(193\) 2.68466 4.64996i 0.193246 0.334712i −0.753078 0.657931i \(-0.771432\pi\)
0.946324 + 0.323219i \(0.104765\pi\)
\(194\) −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 0.337182 + 0.941440i \(0.390526\pi\)
−0.983901 + 0.178712i \(0.942807\pi\)
\(200\) 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 \(-0.429493\pi\)
0.219697 + 0.975568i \(0.429493\pi\)
\(224\) 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 −0.142395 0.989810i \(-0.545480\pi\)
0.928398 0.371587i \(-0.121186\pi\)
\(228\) 0.630683 1.09238i 0.0417680 0.0723443i
\(229\) 9.56155 + 16.5611i 0.631845 + 1.09439i 0.987174 + 0.159647i \(0.0510355\pi\)
−0.355329 + 0.934741i \(0.615631\pi\)
\(230\) 8.00000 0.527504
\(231\) 0 0
\(232\) 13.8617 0.910068
\(233\) 1.56155 + 2.70469i 0.102301 + 0.177190i 0.912632 0.408782i \(-0.134046\pi\)
−0.810331 + 0.585972i \(0.800713\pi\)
\(234\) 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 \(-0.704278\pi\)
0.993027 + 0.117883i \(0.0376108\pi\)
\(242\) 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 \(-0.318273\pi\)
0.540400 + 0.841408i \(0.318273\pi\)
\(252\) 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 0.967933 + 0.251208i \(0.0808280\pi\)
−0.266414 + 0.963859i \(0.585839\pi\)
\(258\) 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 −0.331566 0.943432i \(-0.607577\pi\)
0.982819 0.184572i \(-0.0590898\pi\)
\(264\) 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 0.0205400 0.999789i \(-0.493461\pi\)
0.855573 0.517683i \(-0.173205\pi\)
\(270\) 1.12311 1.94528i 0.0683500 0.118386i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) −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 −0.999906 0.0137211i \(-0.995632\pi\)
0.511836 + 0.859083i \(0.328966\pi\)
\(278\) −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 0.263115 + 0.964765i \(0.415250\pi\)
−0.967068 + 0.254518i \(0.918083\pi\)
\(284\) −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 \(-0.591294\pi\)
−0.282892 + 0.959152i \(0.591294\pi\)
\(294\) 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 \(-0.140491\pi\)
0.904169 + 0.427174i \(0.140491\pi\)
\(308\) 0 0
\(309\) −3.68466 −0.209613
\(310\) 0 0
\(311\) −4.80776 + 8.32729i −0.272623 + 0.472197i −0.969533 0.244962i \(-0.921225\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(312\) −14.2462 + 24.6752i −0.806533 + 1.39696i
\(313\) 15.6501 + 27.1068i 0.884596 + 1.53216i 0.846176 + 0.532903i \(0.178899\pi\)
0.0384191 + 0.999262i \(0.487768\pi\)
\(314\) −5.86174 −0.330797
\(315\) 0 0
\(316\) −2.87689 −0.161838
\(317\) 11.2462 + 19.4790i 0.631650 + 1.09405i 0.987214 + 0.159398i \(0.0509554\pi\)
−0.355564 + 0.934652i \(0.615711\pi\)
\(318\) −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 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) 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 −0.850559 0.525880i \(-0.823736\pi\)
0.880705 + 0.473666i \(0.157070\pi\)
\(348\) 3.19224 + 5.52911i 0.171122 + 0.296392i
\(349\) 22.4924 1.20399 0.601996 0.798499i \(-0.294372\pi\)
0.601996 + 0.798499i \(0.294372\pi\)
\(350\) 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 \(-0.962266\pi\)
0.598913 + 0.800814i \(0.295600\pi\)
\(354\) −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 0.740951 0.671559i \(-0.234375\pi\)
−0.952063 + 0.305903i \(0.901042\pi\)
\(360\) −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 \(-0.802674\pi\)
0.910096 + 0.414398i \(0.136008\pi\)
\(368\) −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 −0.942674 0.333715i \(-0.891698\pi\)
0.182331 0.983237i \(-0.441636\pi\)
\(374\) −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 \(-0.250976\pi\)
−0.966715 + 0.255857i \(0.917642\pi\)
\(384\) 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 −0.911540 0.411210i \(-0.865106\pi\)
0.811889 + 0.583812i \(0.198439\pi\)
\(390\) −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 0.994472 + 0.105003i \(0.0334851\pi\)
−0.406301 + 0.913739i \(0.633182\pi\)
\(398\) 28.4924 1.42820
\(399\) 0 0
\(400\) −4.68466 −0.234233
\(401\) −13.7192 23.7624i −0.685105 1.18664i −0.973404 0.229097i \(-0.926423\pi\)
0.288298 0.957541i \(-0.406911\pi\)
\(402\) 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 0.326915 + 0.945054i \(0.393991\pi\)
−0.981898 + 0.189410i \(0.939342\pi\)
\(410\) 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 \(-0.576574\pi\)
−0.238252 + 0.971203i \(0.576574\pi\)
\(420\) 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 −0.875589 0.483057i \(-0.839526\pi\)
0.856134 + 0.516753i \(0.172860\pi\)
\(432\) 3.36932 + 5.83583i 0.162106 + 0.280776i
\(433\) 8.24621 0.396288 0.198144 0.980173i \(-0.436509\pi\)
0.198144 + 0.980173i \(0.436509\pi\)
\(434\) 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 \(-0.286203\pi\)
−0.989058 + 0.147525i \(0.952869\pi\)
\(440\) 6.24621 0.297776
\(441\) 0 0
\(442\) −32.4924 −1.54551
\(443\) 13.6847 + 23.7025i 0.650178 + 1.12614i 0.983080 + 0.183179i \(0.0586389\pi\)
−0.332902 + 0.942962i \(0.608028\pi\)
\(444\) −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 0.950965 0.309299i \(-0.100094\pi\)
−0.743343 + 0.668910i \(0.766761\pi\)
\(458\) 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 \(-0.463771\pi\)
0.113570 + 0.993530i \(0.463771\pi\)
\(462\) 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 0.990461 + 0.137791i \(0.0440002\pi\)
−0.375900 + 0.926660i \(0.622666\pi\)
\(468\) −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 \(-0.736412\pi\)
0.976091 + 0.217362i \(0.0697450\pi\)
\(480\) −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 −0.918209 0.396096i \(-0.870365\pi\)
0.802134 + 0.597144i \(0.203698\pi\)
\(488\) 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 0.908980 0.416840i \(-0.136862\pi\)
−0.815484 + 0.578780i \(0.803529\pi\)
\(500\) 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 \(-0.572068\pi\)
−0.224480 + 0.974479i \(0.572068\pi\)
\(504\) 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 −0.988347 0.152215i \(-0.951359\pi\)
0.362352 0.932041i \(-0.381974\pi\)
\(510\) −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 \(-0.763036\pi\)
0.954519 + 0.298150i \(0.0963696\pi\)
\(522\) 15.8078 27.3799i 0.691887 1.19838i
\(523\) 3.75379 + 6.50175i 0.164142 + 0.284302i 0.936350 0.351067i \(-0.114181\pi\)
−0.772208 + 0.635369i \(0.780848\pi\)
\(524\) 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 0.989499 0.144538i \(-0.0461696\pi\)
−0.619923 + 0.784662i \(0.712836\pi\)
\(542\) −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 −0.809730 0.586802i \(-0.800387\pi\)
0.913051 + 0.407846i \(0.133720\pi\)
\(558\) 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 0.404198 + 0.914671i \(0.367551\pi\)
−0.994228 + 0.107290i \(0.965783\pi\)
\(564\) 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 −0.955456 0.295133i \(-0.904636\pi\)
0.222136 0.975016i \(-0.428697\pi\)
\(570\) −2.24621 + 3.89055i −0.0940834 + 0.162957i
\(571\) −3.75379 + 6.50175i −0.157091 + 0.272090i −0.933819 0.357747i \(-0.883545\pi\)
0.776727 + 0.629837i \(0.216878\pi\)
\(572\) 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 \(-0.745740\pi\)
0.969303 + 0.245870i \(0.0790735\pi\)
\(578\) −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 \(-0.435486\pi\)
0.201291 + 0.979531i \(0.435486\pi\)
\(588\) 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 \(-0.326484\pi\)
−0.999769 + 0.0215160i \(0.993151\pi\)
\(594\) 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 −0.941859 0.336008i \(-0.890923\pi\)
0.761921 + 0.647670i \(0.224256\pi\)
\(600\) 3.12311 + 5.40938i 0.127500 + 0.220837i
\(601\) 26.4924 1.08065 0.540324 0.841457i \(-0.318302\pi\)
0.540324 + 0.841457i \(0.318302\pi\)
\(602\) 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 \(-0.198671\pi\)
−0.911840 + 0.410546i \(0.865338\pi\)
\(608\) 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 −0.764196 0.644984i \(-0.776864\pi\)
0.940671 + 0.339321i \(0.110197\pi\)
\(614\) −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 0.0383174 + 0.999266i \(0.487800\pi\)
−0.884548 + 0.466449i \(0.845533\pi\)
\(620\) 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 −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 22.7386 + 39.3845i 0.897422 + 1.55438i
\(643\) 2.56155 0.101018 0.0505089 0.998724i \(-0.483916\pi\)
0.0505089 + 0.998724i \(0.483916\pi\)
\(644\) 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 \(-0.811369\pi\)
0.898439 + 0.439099i \(0.144702\pi\)
\(648\) −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 −0.714167 0.699976i \(-0.753194\pi\)
−0.249113 0.968474i \(-0.580139\pi\)
\(654\) −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 \(-0.813988\pi\)
0.894795 + 0.446477i \(0.147321\pi\)
\(662\) −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 \(-0.318770\pi\)
−0.998954 + 0.0457351i \(0.985437\pi\)
\(678\) −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 0.0897175 + 0.995967i \(0.471404\pi\)
−0.907392 + 0.420286i \(0.861930\pi\)
\(684\) 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 \(-0.115023\pi\)
−0.773885 + 0.633326i \(0.781689\pi\)
\(692\) 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 0.984679 0.174374i \(-0.0557902\pi\)
−0.643352 + 0.765570i \(0.722457\pi\)
\(710\) 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 0.791282 + 0.611451i \(0.209414\pi\)
0.133892 + 0.990996i \(0.457253\pi\)
\(720\) 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 \(-0.617820\pi\)
−0.361748 + 0.932276i \(0.617820\pi\)
\(728\) 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 \(-0.200146\pi\)
−0.913732 + 0.406318i \(0.866812\pi\)
\(734\) −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 −0.916427 0.400202i \(-0.868940\pi\)
0.804799 + 0.593548i \(0.202273\pi\)
\(740\) 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 −0.891547 0.452928i \(-0.850380\pi\)
0.0535265 0.998566i \(-0.482954\pi\)
\(752\) −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 0.995983 + 0.0895418i \(0.0285403\pi\)
−0.420446 + 0.907318i \(0.638126\pi\)
\(762\) 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 \(-0.445163\pi\)
0.171426 + 0.985197i \(0.445163\pi\)
\(770\) 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 \(-0.786979\pi\)
0.929415 + 0.369036i \(0.120312\pi\)
\(774\) −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
\(784\) 0