Properties

Label 245.2.e.i.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.i.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 \(-0.568416\pi\)
0.952740 0.303786i \(-0.0982508\pi\)
\(4\) −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 \(-0.281999\pi\)
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 −0.444874 0.895593i \(-0.646752\pi\)
0.998043 0.0625245i \(-0.0199152\pi\)
\(18\) −2.78078 + 4.81645i −0.655435 + 1.13525i
\(19\) −0.561553 0.972638i −0.128829 0.223138i 0.794394 0.607403i \(-0.207789\pi\)
−0.923223 + 0.384264i \(0.874455\pi\)
\(20\) 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 \(-0.578418\pi\)
−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 0.699803 0.714336i \(-0.253271\pi\)
−0.968534 + 0.248879i \(0.919938\pi\)
\(48\) 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 −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0.561553 0.972638i 0.0724962 0.125567i
\(61\) 4.68466 + 8.11407i 0.599809 + 1.03890i 0.992849 + 0.119378i \(0.0380901\pi\)
−0.393040 + 0.919521i \(0.628577\pi\)
\(62\) 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 −0.963107 0.269118i \(-0.913268\pi\)
0.714617 + 0.699516i \(0.246601\pi\)
\(74\) −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 \(-0.429548\pi\)
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 0.613177 0.789945i \(-0.289891\pi\)
−0.990701 + 0.136055i \(0.956558\pi\)
\(90\) 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 −0.872085 0.489354i \(-0.837233\pi\)
0.859836 + 0.510571i \(0.170566\pi\)
\(102\) −9.12311 + 15.8017i −0.903322 + 1.56460i
\(103\) −0.719224 1.24573i −0.0708672 0.122746i 0.828414 0.560116i \(-0.189243\pi\)
−0.899282 + 0.437370i \(0.855910\pi\)
\(104\) −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 0.993547 0.113425i \(-0.0361820\pi\)
−0.595002 + 0.803724i \(0.702849\pi\)
\(132\) −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 \(-0.594203\pi\)
−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 0.939791 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 −0.931151 0.364635i \(-0.881194\pi\)
0.781358 + 0.624083i \(0.214527\pi\)
\(158\) 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 \(-0.177488\pi\)
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 0.981606 0.190920i \(-0.0611470\pi\)
−0.656144 + 0.754636i \(0.727814\pi\)
\(174\) 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 \(-0.159101\pi\)
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 0.984706 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 \(-0.609474\pi\)
0.983901 0.178712i \(-0.0571930\pi\)
\(200\) 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 0.142395 + 0.989810i \(0.454520\pi\)
−0.928398 + 0.371587i \(0.878814\pi\)
\(228\) 0.630683 1.09238i 0.0417680 0.0723443i
\(229\) −9.56155 16.5611i −0.631845 1.09439i −0.987174 0.159647i \(-0.948965\pi\)
0.355329 0.934741i \(-0.384369\pi\)
\(230\) −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 −0.993027 0.117883i \(-0.962389\pi\)
0.598604 + 0.801045i \(0.295722\pi\)
\(242\) 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 −0.967933 0.251208i \(-0.919172\pi\)
0.266414 0.963859i \(-0.414161\pi\)
\(258\) −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 \(0.506539\pi\)
−0.855573 + 0.517683i \(0.826795\pi\)
\(270\) 1.12311 1.94528i 0.0683500 0.118386i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) 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 \(-0.584750\pi\)
0.967068 0.254518i \(-0.0819170\pi\)
\(284\) −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 −0.696909 0.717159i \(-0.745442\pi\)
0.969533 + 0.244962i \(0.0787754\pi\)
\(312\) −14.2462 + 24.6752i −0.806533 + 1.39696i
\(313\) −15.6501 27.1068i −0.884596 1.53216i −0.846176 0.532903i \(-0.821101\pi\)
−0.0384191 0.999262i \(-0.512232\pi\)
\(314\) 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 \(-0.705628\pi\)
−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 −0.598913 0.800814i \(-0.704400\pi\)
0.992982 + 0.118267i \(0.0377338\pi\)
\(354\) −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 −0.910096 0.414398i \(-0.863992\pi\)
0.813927 + 0.580967i \(0.197326\pi\)
\(368\) −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 0.966715 0.255857i \(-0.0823577\pi\)
−0.704936 + 0.709271i \(0.749024\pi\)
\(384\) −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 \(-0.966515\pi\)
0.406301 0.913739i \(-0.366818\pi\)
\(398\) −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 \(-0.606009\pi\)
0.981898 0.189410i \(-0.0606576\pi\)
\(410\) 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 −0.875589 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 \(-0.563491\pi\)
−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 0.989058 0.147525i \(-0.0471307\pi\)
−0.622290 + 0.782787i \(0.713797\pi\)
\(440\) −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 \(-0.536229\pi\)
−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 −0.990461 0.137791i \(-0.956000\pi\)
0.375900 0.926660i \(-0.377334\pi\)
\(468\) 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 −0.976091 0.217362i \(-0.930255\pi\)
0.676286 + 0.736639i \(0.263588\pi\)
\(480\) −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 \(-0.427932\pi\)
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 0.988347 + 0.152215i \(0.0486406\pi\)
−0.362352 + 0.932041i \(0.618026\pi\)
\(510\) 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 −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) 15.8078 27.3799i 0.691887 1.19838i
\(523\) −3.75379 6.50175i −0.164142 0.284302i 0.772208 0.635369i \(-0.219152\pi\)
−0.936350 + 0.351067i \(0.885819\pi\)
\(524\) −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 \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 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 −0.969303 0.245870i \(-0.920926\pi\)
0.697581 + 0.716506i \(0.254260\pi\)
\(578\) −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 0.999769 0.0215160i \(-0.00684929\pi\)
−0.518518 + 0.855067i \(0.673516\pi\)
\(594\) −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 \(-0.681698\pi\)
−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 0.911840 0.410546i \(-0.134662\pi\)
−0.811463 + 0.584403i \(0.801329\pi\)
\(608\) −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 \(-0.512200\pi\)
0.884548 0.466449i \(-0.154467\pi\)
\(620\) 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 \(-0.516084\pi\)
−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 −0.898439 0.439099i \(-0.855298\pi\)
0.829490 + 0.558521i \(0.188631\pi\)
\(648\) −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 −0.894795 0.446477i \(-0.852679\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(662\) −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 0.998954 0.0457351i \(-0.0145630\pi\)
−0.539085 + 0.842252i \(0.681230\pi\)
\(678\) 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 0.773885 0.633326i \(-0.218311\pi\)
−0.935419 + 0.353542i \(0.884977\pi\)
\(692\) −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 \(-0.790586\pi\)
−0.133892 0.990996i \(-0.542747\pi\)
\(720\) −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 0.913732 0.406318i \(-0.133188\pi\)
−0.808748 + 0.588156i \(0.799854\pi\)
\(734\) 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 \(-0.971460\pi\)
0.420446 0.907318i \(-0.361874\pi\)
\(762\) −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 −0.929415 0.369036i \(-0.879688\pi\)
0.784302 + 0.620379i \(0.213021\pi\)
\(774\) −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
\(784\)