Properties

Label 273.2.k.d.211.3
Level $273$
Weight $2$
Character 273.211
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.771147.1
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} + 6 x^{3} + 15 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.3
Root \(1.32555 + 2.29591i\) of defining polynomial
Character \(\chi\) \(=\) 273.211
Dual form 273.2.k.d.22.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(1.18860 + 2.05872i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.82555 + 3.16194i) q^{4} -4.02830 q^{5} +(-1.18860 + 2.05872i) q^{6} +(0.500000 - 0.866025i) q^{7} -3.92498 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.78804 - 8.29313i) q^{10} +(1.63695 + 2.83527i) q^{11} -3.65109 q^{12} +(0.910836 + 3.48861i) q^{13} +2.37720 q^{14} +(-2.01415 - 3.48861i) q^{15} +(-1.01415 - 1.75656i) q^{16} +(0.188601 - 0.326667i) q^{17} -2.37720 q^{18} +(1.77389 - 3.07247i) q^{19} +(7.35384 - 12.7372i) q^{20} +1.00000 q^{21} +(-3.89135 + 6.74002i) q^{22} +(-0.948344 - 1.64258i) q^{23} +(-1.96249 - 3.39914i) q^{24} +11.2272 q^{25} +(-6.09944 + 6.02172i) q^{26} -1.00000 q^{27} +(1.82555 + 3.16194i) q^{28} +(4.33969 + 7.51657i) q^{29} +(4.78804 - 8.29313i) q^{30} +6.33048 q^{31} +(-1.51415 + 2.62258i) q^{32} +(-1.63695 + 2.83527i) q^{33} +0.896688 q^{34} +(-2.01415 + 3.48861i) q^{35} +(-1.82555 - 3.16194i) q^{36} +(-2.01415 - 3.48861i) q^{37} +8.43380 q^{38} +(-2.56580 + 2.53311i) q^{39} +15.8110 q^{40} +(-3.75441 - 6.50282i) q^{41} +(1.18860 + 2.05872i) q^{42} +(4.32555 - 7.49207i) q^{43} -11.9533 q^{44} +(2.01415 - 3.48861i) q^{45} +(2.25441 - 3.90475i) q^{46} -12.1239 q^{47} +(1.01415 - 1.75656i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(13.3446 + 23.1136i) q^{50} +0.377203 q^{51} +(-12.6935 - 3.48861i) q^{52} +7.75441 q^{53} +(-1.18860 - 2.05872i) q^{54} +(-6.59410 - 11.4213i) q^{55} +(-1.96249 + 3.39914i) q^{56} +3.54778 q^{57} +(-10.3163 + 17.8684i) q^{58} +(1.05166 - 1.82152i) q^{59} +14.7077 q^{60} +(-3.87720 + 6.71551i) q^{61} +(7.52442 + 13.0327i) q^{62} +(0.500000 + 0.866025i) q^{63} -11.2555 q^{64} +(-3.66912 - 14.0531i) q^{65} -7.78270 q^{66} +(-2.79191 - 4.83574i) q^{67} +(0.688601 + 1.19269i) q^{68} +(0.948344 - 1.64258i) q^{69} -9.57608 q^{70} +(-1.99612 + 3.45739i) q^{71} +(1.96249 - 3.39914i) q^{72} +7.50106 q^{73} +(4.78804 - 8.29313i) q^{74} +(5.61359 + 9.72302i) q^{75} +(6.47664 + 11.2179i) q^{76} +3.27389 q^{77} +(-8.26468 - 2.27141i) q^{78} -1.16283 q^{79} +(4.08529 + 7.07593i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.92498 - 15.4585i) q^{82} +15.1805 q^{83} +(-1.82555 + 3.16194i) q^{84} +(-0.759742 + 1.31591i) q^{85} +20.5654 q^{86} +(-4.33969 + 7.51657i) q^{87} +(-6.42498 - 11.1284i) q^{88} +(-3.17939 - 5.50686i) q^{89} +9.57608 q^{90} +(3.47664 + 0.955496i) q^{91} +6.92498 q^{92} +(3.16524 + 5.48236i) q^{93} +(-14.4104 - 24.9596i) q^{94} +(-7.14576 + 12.3768i) q^{95} -3.02830 q^{96} +(-2.48585 + 4.30562i) q^{97} +(1.18860 - 2.05872i) q^{98} -3.27389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} - 13q^{10} + 8q^{11} - 8q^{12} + 4q^{14} + 6q^{16} - 4q^{17} - 4q^{18} + 7q^{19} + 13q^{20} + 6q^{21} - q^{22} - 9q^{23} - 3q^{24} + 22q^{25} - 26q^{26} - 6q^{27} + 4q^{28} + 7q^{29} + 13q^{30} - 14q^{31} + 3q^{32} - 8q^{33} + 12q^{34} - 4q^{36} - 8q^{38} + 26q^{40} - 2q^{41} + 2q^{42} + 19q^{43} - 30q^{44} - 7q^{46} - 34q^{47} - 6q^{48} - 3q^{49} + 16q^{50} - 8q^{51} - 26q^{52} + 26q^{53} - 2q^{54} - 3q^{56} + 14q^{57} - 22q^{58} + 3q^{59} + 26q^{60} - 13q^{61} + 17q^{62} + 3q^{63} + 2q^{64} - 2q^{66} - 5q^{67} - q^{68} + 9q^{69} - 26q^{70} - 8q^{71} + 3q^{72} - 4q^{73} + 13q^{74} + 11q^{75} + 18q^{76} + 16q^{77} - 13q^{78} - 2q^{79} + 26q^{80} - 3q^{81} + 36q^{82} + 4q^{83} - 4q^{84} - 13q^{85} + 34q^{86} - 7q^{87} - 21q^{88} + 19q^{89} + 26q^{90} + 24q^{92} - 7q^{93} - 7q^{94} + 6q^{96} - 27q^{97} + 2q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.18860 + 2.05872i 0.840468 + 1.45573i 0.889499 + 0.456936i \(0.151053\pi\)
−0.0490313 + 0.998797i \(0.515613\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −1.82555 + 3.16194i −0.912773 + 1.58097i
\(5\) −4.02830 −1.80151 −0.900754 0.434329i \(-0.856986\pi\)
−0.900754 + 0.434329i \(0.856986\pi\)
\(6\) −1.18860 + 2.05872i −0.485245 + 0.840468i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −3.92498 −1.38769
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −4.78804 8.29313i −1.51411 2.62252i
\(11\) 1.63695 + 2.83527i 0.493558 + 0.854867i 0.999972 0.00742317i \(-0.00236289\pi\)
−0.506415 + 0.862290i \(0.669030\pi\)
\(12\) −3.65109 −1.05398
\(13\) 0.910836 + 3.48861i 0.252620 + 0.967565i
\(14\) 2.37720 0.635334
\(15\) −2.01415 3.48861i −0.520051 0.900754i
\(16\) −1.01415 1.75656i −0.253537 0.439139i
\(17\) 0.188601 0.326667i 0.0457426 0.0792284i −0.842248 0.539091i \(-0.818768\pi\)
0.887990 + 0.459862i \(0.152101\pi\)
\(18\) −2.37720 −0.560312
\(19\) 1.77389 3.07247i 0.406958 0.704873i −0.587589 0.809160i \(-0.699923\pi\)
0.994547 + 0.104287i \(0.0332561\pi\)
\(20\) 7.35384 12.7372i 1.64437 2.84813i
\(21\) 1.00000 0.218218
\(22\) −3.89135 + 6.74002i −0.829639 + 1.43698i
\(23\) −0.948344 1.64258i −0.197743 0.342502i 0.750053 0.661378i \(-0.230028\pi\)
−0.947796 + 0.318876i \(0.896695\pi\)
\(24\) −1.96249 3.39914i −0.400592 0.693846i
\(25\) 11.2272 2.24543
\(26\) −6.09944 + 6.02172i −1.19620 + 1.18096i
\(27\) −1.00000 −0.192450
\(28\) 1.82555 + 3.16194i 0.344996 + 0.597550i
\(29\) 4.33969 + 7.51657i 0.805861 + 1.39579i 0.915708 + 0.401844i \(0.131631\pi\)
−0.109847 + 0.993948i \(0.535036\pi\)
\(30\) 4.78804 8.29313i 0.874172 1.51411i
\(31\) 6.33048 1.13699 0.568494 0.822687i \(-0.307526\pi\)
0.568494 + 0.822687i \(0.307526\pi\)
\(32\) −1.51415 + 2.62258i −0.267666 + 0.463611i
\(33\) −1.63695 + 2.83527i −0.284956 + 0.493558i
\(34\) 0.896688 0.153781
\(35\) −2.01415 + 3.48861i −0.340453 + 0.589682i
\(36\) −1.82555 3.16194i −0.304258 0.526990i
\(37\) −2.01415 3.48861i −0.331124 0.573523i 0.651609 0.758555i \(-0.274094\pi\)
−0.982733 + 0.185032i \(0.940761\pi\)
\(38\) 8.43380 1.36814
\(39\) −2.56580 + 2.53311i −0.410858 + 0.405622i
\(40\) 15.8110 2.49994
\(41\) −3.75441 6.50282i −0.586340 1.01557i −0.994707 0.102752i \(-0.967235\pi\)
0.408367 0.912818i \(-0.366098\pi\)
\(42\) 1.18860 + 2.05872i 0.183405 + 0.317667i
\(43\) 4.32555 7.49207i 0.659640 1.14253i −0.321069 0.947056i \(-0.604042\pi\)
0.980709 0.195474i \(-0.0626244\pi\)
\(44\) −11.9533 −1.80202
\(45\) 2.01415 3.48861i 0.300251 0.520051i
\(46\) 2.25441 3.90475i 0.332394 0.575723i
\(47\) −12.1239 −1.76845 −0.884223 0.467064i \(-0.845312\pi\)
−0.884223 + 0.467064i \(0.845312\pi\)
\(48\) 1.01415 1.75656i 0.146380 0.253537i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 13.3446 + 23.1136i 1.88722 + 3.26875i
\(51\) 0.377203 0.0528190
\(52\) −12.6935 3.48861i −1.76028 0.483783i
\(53\) 7.75441 1.06515 0.532575 0.846383i \(-0.321225\pi\)
0.532575 + 0.846383i \(0.321225\pi\)
\(54\) −1.18860 2.05872i −0.161748 0.280156i
\(55\) −6.59410 11.4213i −0.889148 1.54005i
\(56\) −1.96249 + 3.39914i −0.262249 + 0.454229i
\(57\) 3.54778 0.469915
\(58\) −10.3163 + 17.8684i −1.35460 + 2.34624i
\(59\) 1.05166 1.82152i 0.136914 0.237142i −0.789413 0.613862i \(-0.789615\pi\)
0.926327 + 0.376720i \(0.122948\pi\)
\(60\) 14.7077 1.89875
\(61\) −3.87720 + 6.71551i −0.496425 + 0.859833i −0.999991 0.00412320i \(-0.998688\pi\)
0.503567 + 0.863956i \(0.332021\pi\)
\(62\) 7.52442 + 13.0327i 0.955602 + 1.65515i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) −11.2555 −1.40693
\(65\) −3.66912 14.0531i −0.455098 1.74308i
\(66\) −7.78270 −0.957984
\(67\) −2.79191 4.83574i −0.341087 0.590779i 0.643548 0.765406i \(-0.277462\pi\)
−0.984635 + 0.174626i \(0.944128\pi\)
\(68\) 0.688601 + 1.19269i 0.0835052 + 0.144635i
\(69\) 0.948344 1.64258i 0.114167 0.197743i
\(70\) −9.57608 −1.14456
\(71\) −1.99612 + 3.45739i −0.236896 + 0.410317i −0.959822 0.280609i \(-0.909464\pi\)
0.722926 + 0.690926i \(0.242797\pi\)
\(72\) 1.96249 3.39914i 0.231282 0.400592i
\(73\) 7.50106 0.877933 0.438966 0.898503i \(-0.355345\pi\)
0.438966 + 0.898503i \(0.355345\pi\)
\(74\) 4.78804 8.29313i 0.556598 0.964056i
\(75\) 5.61359 + 9.72302i 0.648201 + 1.12272i
\(76\) 6.47664 + 11.2179i 0.742922 + 1.28678i
\(77\) 3.27389 0.373094
\(78\) −8.26468 2.27141i −0.935791 0.257186i
\(79\) −1.16283 −0.130828 −0.0654142 0.997858i \(-0.520837\pi\)
−0.0654142 + 0.997858i \(0.520837\pi\)
\(80\) 4.08529 + 7.07593i 0.456749 + 0.791113i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 8.92498 15.4585i 0.985600 1.70711i
\(83\) 15.1805 1.66627 0.833135 0.553069i \(-0.186543\pi\)
0.833135 + 0.553069i \(0.186543\pi\)
\(84\) −1.82555 + 3.16194i −0.199183 + 0.344996i
\(85\) −0.759742 + 1.31591i −0.0824056 + 0.142731i
\(86\) 20.5654 2.21762
\(87\) −4.33969 + 7.51657i −0.465264 + 0.805861i
\(88\) −6.42498 11.1284i −0.684906 1.18629i
\(89\) −3.17939 5.50686i −0.337015 0.583726i 0.646855 0.762613i \(-0.276084\pi\)
−0.983870 + 0.178886i \(0.942751\pi\)
\(90\) 9.57608 1.00941
\(91\) 3.47664 + 0.955496i 0.364451 + 0.100163i
\(92\) 6.92498 0.721979
\(93\) 3.16524 + 5.48236i 0.328220 + 0.568494i
\(94\) −14.4104 24.9596i −1.48632 2.57439i
\(95\) −7.14576 + 12.3768i −0.733139 + 1.26983i
\(96\) −3.02830 −0.309074
\(97\) −2.48585 + 4.30562i −0.252400 + 0.437170i −0.964186 0.265227i \(-0.914553\pi\)
0.711786 + 0.702396i \(0.247887\pi\)
\(98\) 1.18860 2.05872i 0.120067 0.207962i
\(99\) −3.27389 −0.329038
\(100\) −20.4957 + 35.4996i −2.04957 + 3.54996i
\(101\) −2.94834 5.10668i −0.293371 0.508134i 0.681233 0.732066i \(-0.261444\pi\)
−0.974605 + 0.223932i \(0.928111\pi\)
\(102\) 0.448344 + 0.776554i 0.0443927 + 0.0768903i
\(103\) 10.5654 1.04104 0.520520 0.853849i \(-0.325738\pi\)
0.520520 + 0.853849i \(0.325738\pi\)
\(104\) −3.57502 13.6927i −0.350559 1.34268i
\(105\) −4.02830 −0.393121
\(106\) 9.21690 + 15.9641i 0.895224 + 1.55057i
\(107\) 6.20275 + 10.7435i 0.599642 + 1.03861i 0.992874 + 0.119172i \(0.0380239\pi\)
−0.393231 + 0.919440i \(0.628643\pi\)
\(108\) 1.82555 3.16194i 0.175663 0.304258i
\(109\) −12.1316 −1.16200 −0.580999 0.813905i \(-0.697338\pi\)
−0.580999 + 0.813905i \(0.697338\pi\)
\(110\) 15.6755 27.1508i 1.49460 2.58873i
\(111\) 2.01415 3.48861i 0.191174 0.331124i
\(112\) −2.02830 −0.191656
\(113\) 5.33582 9.24191i 0.501952 0.869406i −0.498046 0.867151i \(-0.665949\pi\)
0.999997 0.00225510i \(-0.000717821\pi\)
\(114\) 4.21690 + 7.30388i 0.394949 + 0.684071i
\(115\) 3.82021 + 6.61680i 0.356236 + 0.617020i
\(116\) −31.6893 −2.94227
\(117\) −3.47664 0.955496i −0.321415 0.0883357i
\(118\) 5.00000 0.460287
\(119\) −0.188601 0.326667i −0.0172891 0.0299455i
\(120\) 7.90550 + 13.6927i 0.721670 + 1.24997i
\(121\) 0.140820 0.243908i 0.0128018 0.0221734i
\(122\) −18.4338 −1.66892
\(123\) 3.75441 6.50282i 0.338523 0.586340i
\(124\) −11.5566 + 20.0166i −1.03781 + 1.79754i
\(125\) −25.0849 −2.24366
\(126\) −1.18860 + 2.05872i −0.105889 + 0.183405i
\(127\) −3.66524 6.34838i −0.325238 0.563328i 0.656323 0.754480i \(-0.272111\pi\)
−0.981560 + 0.191152i \(0.938778\pi\)
\(128\) −10.3500 17.9267i −0.914817 1.58451i
\(129\) 8.65109 0.761686
\(130\) 24.5703 24.2573i 2.15496 2.12750i
\(131\) 11.4239 0.998113 0.499056 0.866570i \(-0.333680\pi\)
0.499056 + 0.866570i \(0.333680\pi\)
\(132\) −5.97664 10.3518i −0.520200 0.901012i
\(133\) −1.77389 3.07247i −0.153816 0.266417i
\(134\) 6.63695 11.4955i 0.573345 0.993062i
\(135\) 4.02830 0.346701
\(136\) −0.740258 + 1.28216i −0.0634766 + 0.109945i
\(137\) 1.59556 2.76359i 0.136318 0.236110i −0.789782 0.613387i \(-0.789806\pi\)
0.926100 + 0.377278i \(0.123140\pi\)
\(138\) 4.50881 0.383816
\(139\) −2.68860 + 4.65679i −0.228044 + 0.394984i −0.957228 0.289333i \(-0.906566\pi\)
0.729184 + 0.684317i \(0.239900\pi\)
\(140\) −7.35384 12.7372i −0.621513 1.07649i
\(141\) −6.06193 10.4996i −0.510507 0.884223i
\(142\) −9.49039 −0.796416
\(143\) −8.40016 + 8.29313i −0.702457 + 0.693506i
\(144\) 2.02830 0.169025
\(145\) −17.4816 30.2790i −1.45177 2.51453i
\(146\) 8.91577 + 15.4426i 0.737875 + 1.27804i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 14.7077 1.20896
\(149\) 5.01415 8.68476i 0.410775 0.711483i −0.584200 0.811610i \(-0.698592\pi\)
0.994975 + 0.100127i \(0.0319248\pi\)
\(150\) −13.3446 + 23.1136i −1.08958 + 1.88722i
\(151\) −9.71544 −0.790631 −0.395315 0.918545i \(-0.629365\pi\)
−0.395315 + 0.918545i \(0.629365\pi\)
\(152\) −6.96249 + 12.0594i −0.564733 + 0.978146i
\(153\) 0.188601 + 0.326667i 0.0152475 + 0.0264095i
\(154\) 3.89135 + 6.74002i 0.313574 + 0.543126i
\(155\) −25.5011 −2.04829
\(156\) −3.32555 12.7372i −0.266257 1.01979i
\(157\) 17.5761 1.40272 0.701362 0.712805i \(-0.252576\pi\)
0.701362 + 0.712805i \(0.252576\pi\)
\(158\) −1.38214 2.39394i −0.109957 0.190451i
\(159\) 3.87720 + 6.71551i 0.307482 + 0.532575i
\(160\) 6.09944 10.5645i 0.482203 0.835200i
\(161\) −1.89669 −0.149480
\(162\) 1.18860 2.05872i 0.0933853 0.161748i
\(163\) 2.74559 4.75551i 0.215052 0.372480i −0.738237 0.674541i \(-0.764341\pi\)
0.953289 + 0.302061i \(0.0976747\pi\)
\(164\) 27.4154 2.14078
\(165\) 6.59410 11.4213i 0.513350 0.889148i
\(166\) 18.0435 + 31.2523i 1.40045 + 2.42565i
\(167\) −2.21836 3.84231i −0.171662 0.297327i 0.767339 0.641241i \(-0.221580\pi\)
−0.939001 + 0.343914i \(0.888247\pi\)
\(168\) −3.92498 −0.302819
\(169\) −11.3408 + 6.35510i −0.872366 + 0.488854i
\(170\) −3.61212 −0.277037
\(171\) 1.77389 + 3.07247i 0.135653 + 0.234958i
\(172\) 15.7930 + 27.3542i 1.20420 + 2.08574i
\(173\) −11.0800 + 19.1910i −0.842393 + 1.45907i 0.0454728 + 0.998966i \(0.485521\pi\)
−0.887866 + 0.460102i \(0.847813\pi\)
\(174\) −20.6327 −1.56416
\(175\) 5.61359 9.72302i 0.424347 0.734991i
\(176\) 3.32021 5.75077i 0.250270 0.433481i
\(177\) 2.10331 0.158095
\(178\) 7.55805 13.0909i 0.566500 0.981207i
\(179\) 0.970242 + 1.68051i 0.0725193 + 0.125607i 0.900005 0.435880i \(-0.143563\pi\)
−0.827486 + 0.561487i \(0.810229\pi\)
\(180\) 7.35384 + 12.7372i 0.548123 + 0.949377i
\(181\) −8.50106 −0.631879 −0.315939 0.948779i \(-0.602320\pi\)
−0.315939 + 0.948779i \(0.602320\pi\)
\(182\) 2.16524 + 8.29313i 0.160498 + 0.614727i
\(183\) −7.75441 −0.573222
\(184\) 3.72223 + 6.44710i 0.274407 + 0.475286i
\(185\) 8.11359 + 14.0531i 0.596523 + 1.03321i
\(186\) −7.52442 + 13.0327i −0.551717 + 0.955602i
\(187\) 1.23492 0.0903064
\(188\) 22.1327 38.3349i 1.61419 2.79586i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) −33.9738 −2.46472
\(191\) −0.325547 + 0.563863i −0.0235557 + 0.0407997i −0.877563 0.479461i \(-0.840832\pi\)
0.854007 + 0.520261i \(0.174165\pi\)
\(192\) −5.62773 9.74752i −0.406147 0.703467i
\(193\) −9.53217 16.5102i −0.686141 1.18843i −0.973077 0.230481i \(-0.925970\pi\)
0.286936 0.957950i \(-0.407363\pi\)
\(194\) −11.8187 −0.848537
\(195\) 10.3358 10.2041i 0.740163 0.730732i
\(196\) 3.65109 0.260792
\(197\) −12.3549 21.3993i −0.880250 1.52464i −0.851062 0.525065i \(-0.824041\pi\)
−0.0291881 0.999574i \(-0.509292\pi\)
\(198\) −3.89135 6.74002i −0.276546 0.478992i
\(199\) −6.57220 + 11.3834i −0.465891 + 0.806947i −0.999241 0.0389475i \(-0.987599\pi\)
0.533350 + 0.845895i \(0.320933\pi\)
\(200\) −44.0665 −3.11597
\(201\) 2.79191 4.83574i 0.196926 0.341087i
\(202\) 7.00881 12.1396i 0.493138 0.854141i
\(203\) 8.67939 0.609174
\(204\) −0.688601 + 1.19269i −0.0482117 + 0.0835052i
\(205\) 15.1239 + 26.1953i 1.05630 + 1.82956i
\(206\) 12.5581 + 21.7512i 0.874961 + 1.51548i
\(207\) 1.89669 0.131829
\(208\) 5.20421 5.13790i 0.360847 0.356249i
\(209\) 11.6150 0.803430
\(210\) −4.78804 8.29313i −0.330406 0.572280i
\(211\) 9.79831 + 16.9712i 0.674544 + 1.16834i 0.976602 + 0.215054i \(0.0689929\pi\)
−0.302058 + 0.953289i \(0.597674\pi\)
\(212\) −14.1560 + 24.5190i −0.972240 + 1.68397i
\(213\) −3.99225 −0.273544
\(214\) −14.7452 + 25.5394i −1.00796 + 1.74584i
\(215\) −17.4246 + 30.1803i −1.18835 + 2.05828i
\(216\) 3.92498 0.267061
\(217\) 3.16524 5.48236i 0.214871 0.372167i
\(218\) −14.4196 24.9756i −0.976622 1.69156i
\(219\) 3.75053 + 6.49611i 0.253437 + 0.438966i
\(220\) 48.1514 3.24636
\(221\) 1.31140 + 0.360416i 0.0882142 + 0.0242442i
\(222\) 9.57608 0.642704
\(223\) 13.9338 + 24.1340i 0.933076 + 1.61613i 0.778029 + 0.628228i \(0.216219\pi\)
0.155046 + 0.987907i \(0.450447\pi\)
\(224\) 1.51415 + 2.62258i 0.101168 + 0.175229i
\(225\) −5.61359 + 9.72302i −0.374239 + 0.648201i
\(226\) 25.3687 1.68750
\(227\) −6.01521 + 10.4186i −0.399243 + 0.691510i −0.993633 0.112667i \(-0.964061\pi\)
0.594389 + 0.804177i \(0.297394\pi\)
\(228\) −6.47664 + 11.2179i −0.428926 + 0.742922i
\(229\) −9.19887 −0.607879 −0.303939 0.952691i \(-0.598302\pi\)
−0.303939 + 0.952691i \(0.598302\pi\)
\(230\) −9.08141 + 15.7295i −0.598811 + 1.03717i
\(231\) 1.63695 + 2.83527i 0.107703 + 0.186547i
\(232\) −17.0332 29.5024i −1.11829 1.93693i
\(233\) −12.4522 −0.815772 −0.407886 0.913033i \(-0.633734\pi\)
−0.407886 + 0.913033i \(0.633734\pi\)
\(234\) −2.16524 8.29313i −0.141546 0.542139i
\(235\) 48.8385 3.18587
\(236\) 3.83969 + 6.65055i 0.249943 + 0.432914i
\(237\) −0.581414 1.00704i −0.0377669 0.0654142i
\(238\) 0.448344 0.776554i 0.0290618 0.0503365i
\(239\) −3.24559 −0.209940 −0.104970 0.994475i \(-0.533475\pi\)
−0.104970 + 0.994475i \(0.533475\pi\)
\(240\) −4.08529 + 7.07593i −0.263704 + 0.456749i
\(241\) −4.71302 + 8.16319i −0.303592 + 0.525838i −0.976947 0.213482i \(-0.931519\pi\)
0.673354 + 0.739320i \(0.264853\pi\)
\(242\) 0.669517 0.0430382
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −14.1560 24.5190i −0.906247 1.56967i
\(245\) 2.01415 + 3.48861i 0.128679 + 0.222879i
\(246\) 17.8500 1.13807
\(247\) 12.3344 + 3.38989i 0.784816 + 0.215694i
\(248\) −24.8470 −1.57779
\(249\) 7.59023 + 13.1467i 0.481011 + 0.833135i
\(250\) −29.8159 51.6427i −1.88573 3.26617i
\(251\) 5.99466 10.3831i 0.378380 0.655373i −0.612447 0.790512i \(-0.709815\pi\)
0.990827 + 0.135139i \(0.0431480\pi\)
\(252\) −3.65109 −0.229997
\(253\) 3.10477 5.37763i 0.195195 0.338088i
\(254\) 8.71302 15.0914i 0.546704 0.946919i
\(255\) −1.51948 −0.0951538
\(256\) 13.3485 23.1203i 0.834282 1.44502i
\(257\) −7.29831 12.6410i −0.455256 0.788527i 0.543447 0.839444i \(-0.317119\pi\)
−0.998703 + 0.0509168i \(0.983786\pi\)
\(258\) 10.2827 + 17.8102i 0.640173 + 1.10881i
\(259\) −4.02830 −0.250306
\(260\) 51.1333 + 14.0531i 3.17115 + 0.871539i
\(261\) −8.67939 −0.537241
\(262\) 13.5785 + 23.5186i 0.838882 + 1.45299i
\(263\) −11.3266 19.6183i −0.698429 1.20971i −0.969011 0.247017i \(-0.920550\pi\)
0.270583 0.962697i \(-0.412784\pi\)
\(264\) 6.42498 11.1284i 0.395430 0.684906i
\(265\) −31.2370 −1.91888
\(266\) 4.21690 7.30388i 0.258555 0.447830i
\(267\) 3.17939 5.50686i 0.194575 0.337015i
\(268\) 20.3871 1.24534
\(269\) 13.9947 24.2395i 0.853270 1.47791i −0.0249713 0.999688i \(-0.507949\pi\)
0.878241 0.478218i \(-0.158717\pi\)
\(270\) 4.78804 + 8.29313i 0.291391 + 0.504704i
\(271\) 3.80365 + 6.58811i 0.231055 + 0.400199i 0.958119 0.286371i \(-0.0924489\pi\)
−0.727064 + 0.686570i \(0.759116\pi\)
\(272\) −0.765079 −0.0463897
\(273\) 0.910836 + 3.48861i 0.0551263 + 0.211140i
\(274\) 7.58595 0.458284
\(275\) 18.3783 + 31.8321i 1.10825 + 1.91955i
\(276\) 3.46249 + 5.99721i 0.208418 + 0.360990i
\(277\) 3.44447 5.96599i 0.206958 0.358462i −0.743797 0.668406i \(-0.766977\pi\)
0.950755 + 0.309944i \(0.100310\pi\)
\(278\) −12.7827 −0.766656
\(279\) −3.16524 + 5.48236i −0.189498 + 0.328220i
\(280\) 7.90550 13.6927i 0.472444 0.818297i
\(281\) 10.8062 0.644642 0.322321 0.946630i \(-0.395537\pi\)
0.322321 + 0.946630i \(0.395537\pi\)
\(282\) 14.4104 24.9596i 0.858129 1.48632i
\(283\) 3.81246 + 6.60337i 0.226627 + 0.392530i 0.956806 0.290726i \(-0.0938968\pi\)
−0.730179 + 0.683256i \(0.760563\pi\)
\(284\) −7.28804 12.6233i −0.432466 0.749052i
\(285\) −14.2915 −0.846556
\(286\) −27.0577 7.43634i −1.59995 0.439720i
\(287\) −7.50881 −0.443231
\(288\) −1.51415 2.62258i −0.0892220 0.154537i
\(289\) 8.42886 + 14.5992i 0.495815 + 0.858777i
\(290\) 41.5573 71.9793i 2.44033 4.22677i
\(291\) −4.97170 −0.291446
\(292\) −13.6935 + 23.7179i −0.801354 + 1.38799i
\(293\) 11.1458 19.3050i 0.651142 1.12781i −0.331704 0.943384i \(-0.607624\pi\)
0.982846 0.184428i \(-0.0590431\pi\)
\(294\) 2.37720 0.138641
\(295\) −4.23638 + 7.33763i −0.246652 + 0.427213i
\(296\) 7.90550 + 13.6927i 0.459498 + 0.795874i
\(297\) −1.63695 2.83527i −0.0949852 0.164519i
\(298\) 23.8393 1.38097
\(299\) 4.86653 4.80452i 0.281439 0.277853i
\(300\) −40.9914 −2.36664
\(301\) −4.32555 7.49207i −0.249320 0.431836i
\(302\) −11.5478 20.0013i −0.664500 1.15095i
\(303\) 2.94834 5.10668i 0.169378 0.293371i
\(304\) −7.19595 −0.412716
\(305\) 15.6185 27.0521i 0.894314 1.54900i
\(306\) −0.448344 + 0.776554i −0.0256301 + 0.0443927i
\(307\) −28.2448 −1.61202 −0.806008 0.591905i \(-0.798376\pi\)
−0.806008 + 0.591905i \(0.798376\pi\)
\(308\) −5.97664 + 10.3518i −0.340551 + 0.589851i
\(309\) 5.28270 + 9.14991i 0.300522 + 0.520520i
\(310\) −30.3106 52.4995i −1.72153 2.98177i
\(311\) −2.66177 −0.150935 −0.0754675 0.997148i \(-0.524045\pi\)
−0.0754675 + 0.997148i \(0.524045\pi\)
\(312\) 10.0707 9.94242i 0.570143 0.562879i
\(313\) −22.4826 −1.27079 −0.635397 0.772186i \(-0.719163\pi\)
−0.635397 + 0.772186i \(0.719163\pi\)
\(314\) 20.8910 + 36.1842i 1.17894 + 2.04199i
\(315\) −2.01415 3.48861i −0.113484 0.196561i
\(316\) 2.12280 3.67679i 0.119417 0.206836i
\(317\) 18.8315 1.05768 0.528842 0.848720i \(-0.322626\pi\)
0.528842 + 0.848720i \(0.322626\pi\)
\(318\) −9.21690 + 15.9641i −0.516858 + 0.895224i
\(319\) −14.2077 + 24.6084i −0.795478 + 1.37781i
\(320\) 45.3404 2.53460
\(321\) −6.20275 + 10.7435i −0.346204 + 0.599642i
\(322\) −2.25441 3.90475i −0.125633 0.217603i
\(323\) −0.669117 1.15894i −0.0372306 0.0644854i
\(324\) 3.65109 0.202839
\(325\) 10.2261 + 39.1672i 0.567242 + 2.17260i
\(326\) 13.0537 0.722976
\(327\) −6.06580 10.5063i −0.335440 0.580999i
\(328\) 14.7360 + 25.5235i 0.813659 + 1.40930i
\(329\) −6.06193 + 10.4996i −0.334205 + 0.578860i
\(330\) 31.3510 1.72582
\(331\) 8.91577 15.4426i 0.490055 0.848800i −0.509879 0.860246i \(-0.670310\pi\)
0.999934 + 0.0114455i \(0.00364329\pi\)
\(332\) −27.7126 + 47.9997i −1.52093 + 2.63432i
\(333\) 4.02830 0.220749
\(334\) 5.27349 9.13395i 0.288553 0.499788i
\(335\) 11.2467 + 19.4798i 0.614470 + 1.06429i
\(336\) −1.01415 1.75656i −0.0553263 0.0958280i
\(337\) 7.57608 0.412695 0.206348 0.978479i \(-0.433842\pi\)
0.206348 + 0.978479i \(0.433842\pi\)
\(338\) −26.5630 15.7937i −1.44484 0.859066i
\(339\) 10.6716 0.579604
\(340\) −2.77389 4.80452i −0.150435 0.260562i
\(341\) 10.3627 + 17.9486i 0.561169 + 0.971974i
\(342\) −4.21690 + 7.30388i −0.228024 + 0.394949i
\(343\) −1.00000 −0.0539949
\(344\) −16.9777 + 29.4062i −0.915376 + 1.58548i
\(345\) −3.82021 + 6.61680i −0.205673 + 0.356236i
\(346\) −52.6786 −2.83202
\(347\) −3.94407 + 6.83133i −0.211729 + 0.366725i −0.952256 0.305302i \(-0.901243\pi\)
0.740527 + 0.672027i \(0.234576\pi\)
\(348\) −15.8446 27.4437i −0.849361 1.47114i
\(349\) 5.86693 + 10.1618i 0.314050 + 0.543950i 0.979235 0.202728i \(-0.0649809\pi\)
−0.665185 + 0.746678i \(0.731648\pi\)
\(350\) 26.6893 1.42660
\(351\) −0.910836 3.48861i −0.0486168 0.186208i
\(352\) −9.91431 −0.528435
\(353\) 6.26855 + 10.8575i 0.333641 + 0.577884i 0.983223 0.182408i \(-0.0583892\pi\)
−0.649581 + 0.760292i \(0.725056\pi\)
\(354\) 2.50000 + 4.33013i 0.132874 + 0.230144i
\(355\) 8.04098 13.9274i 0.426771 0.739189i
\(356\) 23.2165 1.23047
\(357\) 0.188601 0.326667i 0.00998185 0.0172891i
\(358\) −2.30646 + 3.99491i −0.121900 + 0.211138i
\(359\) −5.01762 −0.264820 −0.132410 0.991195i \(-0.542272\pi\)
−0.132410 + 0.991195i \(0.542272\pi\)
\(360\) −7.90550 + 13.6927i −0.416656 + 0.721670i
\(361\) 3.20662 + 5.55404i 0.168770 + 0.292318i
\(362\) −10.1044 17.5013i −0.531074 0.919847i
\(363\) 0.281641 0.0147823
\(364\) −9.36799 + 9.24862i −0.491016 + 0.484760i
\(365\) −30.2165 −1.58160
\(366\) −9.21690 15.9641i −0.481775 0.834459i
\(367\) −11.8549 20.5333i −0.618821 1.07183i −0.989701 0.143149i \(-0.954277\pi\)
0.370880 0.928681i \(-0.379056\pi\)
\(368\) −1.92352 + 3.33164i −0.100271 + 0.173674i
\(369\) 7.50881 0.390893
\(370\) −19.2876 + 33.4072i −1.00272 + 1.73676i
\(371\) 3.87720 6.71551i 0.201294 0.348652i
\(372\) −23.1132 −1.19836
\(373\) 4.97664 8.61979i 0.257681 0.446316i −0.707940 0.706273i \(-0.750375\pi\)
0.965620 + 0.259957i \(0.0837084\pi\)
\(374\) 1.46783 + 2.54235i 0.0758996 + 0.131462i
\(375\) −12.5424 21.7242i −0.647689 1.12183i
\(376\) 47.5860 2.45406
\(377\) −22.2696 + 21.9859i −1.14694 + 1.13233i
\(378\) −2.37720 −0.122270
\(379\) 13.9250 + 24.1188i 0.715278 + 1.23890i 0.962852 + 0.270029i \(0.0870334\pi\)
−0.247574 + 0.968869i \(0.579633\pi\)
\(380\) −26.0898 45.1889i −1.33838 2.31814i
\(381\) 3.66524 6.34838i 0.187776 0.325238i
\(382\) −1.54778 −0.0791914
\(383\) 3.45222 5.97942i 0.176400 0.305534i −0.764245 0.644926i \(-0.776888\pi\)
0.940645 + 0.339392i \(0.110221\pi\)
\(384\) 10.3500 17.9267i 0.528170 0.914817i
\(385\) −13.1882 −0.672133
\(386\) 22.6599 39.2481i 1.15336 1.99768i
\(387\) 4.32555 + 7.49207i 0.219880 + 0.380843i
\(388\) −9.07608 15.7202i −0.460768 0.798074i
\(389\) −28.3764 −1.43874 −0.719370 0.694627i \(-0.755570\pi\)
−0.719370 + 0.694627i \(0.755570\pi\)
\(390\) 33.2926 + 9.14991i 1.68584 + 0.463324i
\(391\) −0.715436 −0.0361812
\(392\) 1.96249 + 3.39914i 0.0991208 + 0.171682i
\(393\) 5.71196 + 9.89341i 0.288130 + 0.499056i
\(394\) 29.3701 50.8705i 1.47964 2.56282i
\(395\) 4.68422 0.235689
\(396\) 5.97664 10.3518i 0.300337 0.520200i
\(397\) 2.38360 4.12852i 0.119630 0.207204i −0.799991 0.600011i \(-0.795163\pi\)
0.919621 + 0.392807i \(0.128496\pi\)
\(398\) −31.2469 −1.56627
\(399\) 1.77389 3.07247i 0.0888056 0.153816i
\(400\) −11.3860 19.7212i −0.569301 0.986058i
\(401\) 4.13307 + 7.15869i 0.206396 + 0.357488i 0.950577 0.310490i \(-0.100493\pi\)
−0.744181 + 0.667978i \(0.767160\pi\)
\(402\) 13.2739 0.662041
\(403\) 5.76603 + 22.0846i 0.287226 + 1.10011i
\(404\) 21.5294 1.07113
\(405\) 2.01415 + 3.48861i 0.100084 + 0.173350i
\(406\) 10.3163 + 17.8684i 0.511991 + 0.886795i
\(407\) 6.59410 11.4213i 0.326857 0.566134i
\(408\) −1.48052 −0.0732964
\(409\) −10.7169 + 18.5622i −0.529916 + 0.917842i 0.469474 + 0.882946i \(0.344443\pi\)
−0.999391 + 0.0348962i \(0.988890\pi\)
\(410\) −35.9525 + 62.2715i −1.77557 + 3.07537i
\(411\) 3.19112 0.157407
\(412\) −19.2876 + 33.4072i −0.950234 + 1.64585i
\(413\) −1.05166 1.82152i −0.0517486 0.0896312i
\(414\) 2.25441 + 3.90475i 0.110798 + 0.191908i
\(415\) −61.1514 −3.00180
\(416\) −10.5283 2.89353i −0.516192 0.141867i
\(417\) −5.37720 −0.263323
\(418\) 13.8057 + 23.9121i 0.675257 + 1.16958i
\(419\) 1.14576 + 1.98451i 0.0559739 + 0.0969496i 0.892655 0.450741i \(-0.148840\pi\)
−0.836681 + 0.547691i \(0.815507\pi\)
\(420\) 7.35384 12.7372i 0.358831 0.621513i
\(421\) 7.61292 0.371031 0.185516 0.982641i \(-0.440604\pi\)
0.185516 + 0.982641i \(0.440604\pi\)
\(422\) −23.2926 + 40.3439i −1.13386 + 1.96391i
\(423\) 6.06193 10.4996i 0.294741 0.510507i
\(424\) −30.4359 −1.47810
\(425\) 2.11746 3.66755i 0.102712 0.177902i
\(426\) −4.74519 8.21892i −0.229905 0.398208i
\(427\) 3.87720 + 6.71551i 0.187631 + 0.324986i
\(428\) −45.2936 −2.18935
\(429\) −11.3821 3.12819i −0.549535 0.151030i
\(430\) −82.8435 −3.99507
\(431\) −10.4314 18.0677i −0.502462 0.870290i −0.999996 0.00284520i \(-0.999094\pi\)
0.497534 0.867444i \(-0.334239\pi\)
\(432\) 1.01415 + 1.75656i 0.0487932 + 0.0845123i
\(433\) 11.6882 20.2446i 0.561699 0.972891i −0.435649 0.900116i \(-0.643481\pi\)
0.997348 0.0727749i \(-0.0231855\pi\)
\(434\) 15.0488 0.722368
\(435\) 17.4816 30.2790i 0.838177 1.45177i
\(436\) 22.1468 38.3594i 1.06064 1.83708i
\(437\) −6.72903 −0.321893
\(438\) −8.91577 + 15.4426i −0.426012 + 0.737875i
\(439\) −4.57754 7.92853i −0.218474 0.378408i 0.735868 0.677125i \(-0.236775\pi\)
−0.954342 + 0.298717i \(0.903441\pi\)
\(440\) 25.8817 + 44.8285i 1.23386 + 2.13711i
\(441\) 1.00000 0.0476190
\(442\) 0.816735 + 3.12819i 0.0388481 + 0.148793i
\(443\) 11.2632 0.535132 0.267566 0.963540i \(-0.413781\pi\)
0.267566 + 0.963540i \(0.413781\pi\)
\(444\) 7.35384 + 12.7372i 0.348998 + 0.604482i
\(445\) 12.8075 + 22.1833i 0.607135 + 1.05159i
\(446\) −33.1235 + 57.3715i −1.56844 + 2.71662i
\(447\) 10.0283 0.474322
\(448\) −5.62773 + 9.74752i −0.265885 + 0.460527i
\(449\) 16.8924 29.2585i 0.797202 1.38079i −0.124229 0.992254i \(-0.539646\pi\)
0.921431 0.388541i \(-0.127021\pi\)
\(450\) −26.6893 −1.25814
\(451\) 12.2915 21.2895i 0.578785 1.00248i
\(452\) 19.4816 + 33.7431i 0.916336 + 1.58714i
\(453\) −4.85772 8.41381i −0.228236 0.395315i
\(454\) −28.5987 −1.34221
\(455\) −14.0049 3.84902i −0.656562 0.180445i
\(456\) −13.9250 −0.652097
\(457\) −17.1472 29.6999i −0.802113 1.38930i −0.918223 0.396064i \(-0.870376\pi\)
0.116110 0.993236i \(-0.462958\pi\)
\(458\) −10.9338 18.9379i −0.510903 0.884909i
\(459\) −0.188601 + 0.326667i −0.00880316 + 0.0152475i
\(460\) −27.8959 −1.30065
\(461\) −9.66630 + 16.7425i −0.450205 + 0.779777i −0.998398 0.0565741i \(-0.981982\pi\)
0.548194 + 0.836351i \(0.315316\pi\)
\(462\) −3.89135 + 6.74002i −0.181042 + 0.313574i
\(463\) 6.29444 0.292527 0.146264 0.989246i \(-0.453275\pi\)
0.146264 + 0.989246i \(0.453275\pi\)
\(464\) 8.80219 15.2458i 0.408631 0.707770i
\(465\) −12.7505 22.0846i −0.591292 1.02415i
\(466\) −14.8007 25.6356i −0.685630 1.18755i
\(467\) 24.2293 1.12120 0.560599 0.828087i \(-0.310571\pi\)
0.560599 + 0.828087i \(0.310571\pi\)
\(468\) 9.36799 9.24862i 0.433036 0.427518i
\(469\) −5.58383 −0.257837
\(470\) 58.0495 + 100.545i 2.67762 + 4.63778i
\(471\) 8.78804 + 15.2213i 0.404931 + 0.701362i
\(472\) −4.12773 + 7.14944i −0.189994 + 0.329080i
\(473\) 28.3227 1.30228
\(474\) 1.38214 2.39394i 0.0634838 0.109957i
\(475\) 19.9158 34.4951i 0.913798 1.58275i
\(476\) 1.37720 0.0631240
\(477\) −3.87720 + 6.71551i −0.177525 + 0.307482i
\(478\) −3.85772 6.68176i −0.176448 0.305617i
\(479\) 16.8149 + 29.1242i 0.768291 + 1.33072i 0.938489 + 0.345309i \(0.112226\pi\)
−0.170198 + 0.985410i \(0.554441\pi\)
\(480\) 12.1989 0.556800
\(481\) 10.3358 10.2041i 0.471273 0.465268i
\(482\) −22.4076 −1.02064
\(483\) −0.948344 1.64258i −0.0431511 0.0747400i
\(484\) 0.514148 + 0.890531i 0.0233704 + 0.0404787i
\(485\) 10.0137 17.3443i 0.454701 0.787565i
\(486\) 2.37720 0.107832
\(487\) 3.96249 6.86324i 0.179558 0.311003i −0.762171 0.647375i \(-0.775867\pi\)
0.941729 + 0.336372i \(0.109200\pi\)
\(488\) 15.2180 26.3583i 0.688885 1.19318i
\(489\) 5.49119 0.248320
\(490\) −4.78804 + 8.29313i −0.216302 + 0.374645i
\(491\) −1.21584 2.10589i −0.0548699 0.0950375i 0.837286 0.546766i \(-0.184141\pi\)
−0.892156 + 0.451728i \(0.850808\pi\)
\(492\) 13.7077 + 23.7424i 0.617990 + 1.07039i
\(493\) 3.27389 0.147449
\(494\) 7.68180 + 29.4222i 0.345621 + 1.32377i
\(495\) 13.1882 0.592766
\(496\) −6.42005 11.1198i −0.288269 0.499296i
\(497\) 1.99612 + 3.45739i 0.0895384 + 0.155085i
\(498\) −18.0435 + 31.2523i −0.808549 + 1.40045i
\(499\) −18.5838 −0.831926 −0.415963 0.909381i \(-0.636555\pi\)
−0.415963 + 0.909381i \(0.636555\pi\)
\(500\) 45.7936 79.3169i 2.04795 3.54716i
\(501\) 2.21836 3.84231i 0.0991090 0.171662i
\(502\) 28.5011 1.27206
\(503\) 8.72717 15.1159i 0.389125 0.673985i −0.603207 0.797585i \(-0.706111\pi\)
0.992332 + 0.123600i \(0.0394440\pi\)
\(504\) −1.96249 3.39914i −0.0874163 0.151410i
\(505\) 11.8768 + 20.5712i 0.528511 + 0.915408i
\(506\) 14.7614 0.656222
\(507\) −11.1741 6.64383i −0.496257 0.295063i
\(508\) 26.7643 1.18747
\(509\) −1.38495 2.39881i −0.0613870 0.106325i 0.833699 0.552220i \(-0.186219\pi\)
−0.895086 + 0.445894i \(0.852886\pi\)
\(510\) −1.80606 3.12819i −0.0799738 0.138519i
\(511\) 3.75053 6.49611i 0.165914 0.287371i
\(512\) 22.0643 0.975115
\(513\) −1.77389 + 3.07247i −0.0783192 + 0.135653i
\(514\) 17.3496 30.0503i 0.765257 1.32546i
\(515\) −42.5606 −1.87544
\(516\) −15.7930 + 27.3542i −0.695247 + 1.20420i
\(517\) −19.8461 34.3744i −0.872830 1.51179i
\(518\) −4.78804 8.29313i −0.210374 0.364379i
\(519\) −22.1599 −0.972712
\(520\) 14.4012 + 55.1584i 0.631535 + 2.41885i
\(521\) −26.2816 −1.15142 −0.575710 0.817654i \(-0.695274\pi\)
−0.575710 + 0.817654i \(0.695274\pi\)
\(522\) −10.3163 17.8684i −0.451534 0.782079i
\(523\) −2.62521 4.54700i −0.114792 0.198826i 0.802904 0.596108i \(-0.203287\pi\)
−0.917697 + 0.397282i \(0.869954\pi\)
\(524\) −20.8549 + 36.1218i −0.911051 + 1.57799i
\(525\) 11.2272 0.489994
\(526\) 26.9256 46.6366i 1.17401 2.03345i
\(527\) 1.19394 2.06796i 0.0520088 0.0900818i
\(528\) 6.64042 0.288987
\(529\) 9.70129 16.8031i 0.421795 0.730571i
\(530\) −37.1284 64.3083i −1.61275 2.79337i
\(531\) 1.05166 + 1.82152i 0.0456380 + 0.0790473i
\(532\) 12.9533 0.561596
\(533\) 19.2661 19.0206i 0.834509 0.823876i
\(534\) 15.1161 0.654138
\(535\) −24.9865 43.2779i −1.08026 1.87107i
\(536\) 10.9582 + 18.9802i 0.473323 + 0.819819i
\(537\) −0.970242 + 1.68051i −0.0418690 + 0.0725193i
\(538\) 66.5363 2.86858
\(539\) 1.63695 2.83527i 0.0705082 0.122124i
\(540\) −7.35384 + 12.7372i −0.316459 + 0.548123i
\(541\) −0.111863 −0.00480937 −0.00240468 0.999997i \(-0.500765\pi\)
−0.00240468 + 0.999997i \(0.500765\pi\)
\(542\) −9.04204 + 15.6613i −0.388389 + 0.672710i
\(543\) −4.25053 7.36214i −0.182408 0.315939i
\(544\) 0.571141 + 0.989245i 0.0244875 + 0.0424135i
\(545\) 48.8697 2.09335
\(546\) −6.09944 + 6.02172i −0.261032 + 0.257706i
\(547\) −33.7515 −1.44311 −0.721555 0.692358i \(-0.756572\pi\)
−0.721555 + 0.692358i \(0.756572\pi\)
\(548\) 5.82555 + 10.0901i 0.248855 + 0.431030i
\(549\) −3.87720 6.71551i −0.165475 0.286611i
\(550\) −43.6889 + 75.6713i −1.86290 + 3.22664i
\(551\) 30.7926 1.31181
\(552\) −3.72223 + 6.44710i −0.158429 + 0.274407i
\(553\) −0.581414 + 1.00704i −0.0247242 + 0.0428236i
\(554\) 16.3764 0.695767
\(555\) −8.11359 + 14.0531i −0.344403 + 0.596523i
\(556\) −9.81633 17.0024i −0.416305 0.721062i
\(557\) −14.5073 25.1275i −0.614696 1.06468i −0.990438 0.137960i \(-0.955945\pi\)
0.375742 0.926724i \(-0.377388\pi\)
\(558\) −15.0488 −0.637068
\(559\) 30.0767 + 8.26609i 1.27211 + 0.349618i
\(560\) 8.17058 0.345270
\(561\) 0.617460 + 1.06947i 0.0260692 + 0.0451532i
\(562\) 12.8442 + 22.2469i 0.541801 + 0.938427i
\(563\) −0.715836 + 1.23986i −0.0301689 + 0.0522541i −0.880716 0.473645i \(-0.842938\pi\)
0.850547 + 0.525899i \(0.176271\pi\)
\(564\) 44.2653 1.86391
\(565\) −21.4943 + 37.2292i −0.904270 + 1.56624i
\(566\) −9.06299 + 15.6976i −0.380946 + 0.659818i
\(567\) −1.00000 −0.0419961
\(568\) 7.83476 13.5702i 0.328739 0.569393i
\(569\) 12.2505 + 21.2185i 0.513569 + 0.889528i 0.999876 + 0.0157396i \(0.00501028\pi\)
−0.486307 + 0.873788i \(0.661656\pi\)
\(570\) −16.9869 29.4222i −0.711503 1.23236i
\(571\) −47.3735 −1.98252 −0.991259 0.131929i \(-0.957883\pi\)
−0.991259 + 0.131929i \(0.957883\pi\)
\(572\) −10.8875 41.7003i −0.455228 1.74358i
\(573\) −0.651093 −0.0271998
\(574\) −8.92498 15.4585i −0.372522 0.645226i
\(575\) −10.6472 18.4415i −0.444020 0.769065i
\(576\) 5.62773 9.74752i 0.234489 0.406147i
\(577\) 27.4055 1.14091 0.570453 0.821330i \(-0.306768\pi\)
0.570453 + 0.821330i \(0.306768\pi\)
\(578\) −20.0371 + 34.7053i −0.833434 + 1.44355i
\(579\) 9.53217 16.5102i 0.396144 0.686141i
\(580\) 127.654 5.30053
\(581\) 7.59023 13.1467i 0.314896 0.545415i
\(582\) −5.90937 10.2353i −0.244951 0.424268i
\(583\) 12.6935 + 21.9859i 0.525713 + 0.910561i
\(584\) −29.4415 −1.21830
\(585\) 14.0049 + 3.84902i 0.579033 + 0.159138i
\(586\) 52.9914 2.18906
\(587\) −13.9479 24.1585i −0.575693 0.997130i −0.995966 0.0897321i \(-0.971399\pi\)
0.420273 0.907398i \(-0.361934\pi\)
\(588\) 1.82555 + 3.16194i 0.0752843 + 0.130396i
\(589\) 11.2296 19.4502i 0.462707 0.801432i
\(590\) −20.1415 −0.829212
\(591\) 12.3549 21.3993i 0.508213 0.880250i
\(592\) −4.08529 + 7.07593i −0.167904 + 0.290819i
\(593\) −16.6015 −0.681740 −0.340870 0.940110i \(-0.610722\pi\)
−0.340870 + 0.940110i \(0.610722\pi\)
\(594\) 3.89135 6.74002i 0.159664 0.276546i
\(595\) 0.759742 + 1.31591i 0.0311464 + 0.0539472i
\(596\) 18.3071 + 31.7089i 0.749889 + 1.29885i
\(597\) −13.1444 −0.537965
\(598\) 15.6755 + 4.30815i 0.641019 + 0.176173i
\(599\) 11.7913 0.481778 0.240889 0.970553i \(-0.422561\pi\)
0.240889 + 0.970553i \(0.422561\pi\)
\(600\) −22.0332 38.1627i −0.899503 1.55798i
\(601\) −6.91084 11.9699i −0.281899 0.488263i 0.689954 0.723854i \(-0.257631\pi\)
−0.971852 + 0.235590i \(0.924298\pi\)
\(602\) 10.2827 17.8102i 0.419092 0.725888i
\(603\) 5.58383 0.227391
\(604\) 17.7360 30.7196i 0.721667 1.24996i
\(605\) −0.567266 + 0.982533i −0.0230626 + 0.0399457i
\(606\) 14.0176 0.569427
\(607\) 10.5474 18.2686i 0.428105 0.741500i −0.568600 0.822614i \(-0.692515\pi\)
0.996705 + 0.0811147i \(0.0258480\pi\)
\(608\) 5.37187 + 9.30435i 0.217858 + 0.377341i
\(609\) 4.33969 + 7.51657i 0.175853 + 0.304587i
\(610\) 74.2568 3.00657
\(611\) −11.0428 42.2954i −0.446746 1.71109i
\(612\) −1.37720 −0.0556701
\(613\) −1.09691 1.89991i −0.0443039 0.0767367i 0.843023 0.537877i \(-0.180774\pi\)
−0.887327 + 0.461141i \(0.847440\pi\)
\(614\) −33.5718 58.1481i −1.35485 2.34666i
\(615\) −15.1239 + 26.1953i −0.609853 + 1.05630i
\(616\) −12.8500 −0.517740
\(617\) 3.17405 5.49762i 0.127783 0.221326i −0.795035 0.606564i \(-0.792547\pi\)
0.922817 + 0.385238i \(0.125881\pi\)
\(618\) −12.5581 + 21.7512i −0.505159 + 0.874961i
\(619\) −7.77203 −0.312384 −0.156192 0.987727i \(-0.549922\pi\)
−0.156192 + 0.987727i \(0.549922\pi\)
\(620\) 46.5534 80.6328i 1.86963 3.23829i
\(621\) 0.948344 + 1.64258i 0.0380557 + 0.0659145i
\(622\) −3.16378 5.47983i −0.126856 0.219721i
\(623\) −6.35878 −0.254759
\(624\) 7.05166 + 1.93803i 0.282292 + 0.0775833i
\(625\) 44.9135 1.79654
\(626\) −26.7229 46.2854i −1.06806 1.84994i
\(627\) 5.80752 + 10.0589i 0.231930 + 0.401715i
\(628\) −32.0860 + 55.5745i −1.28037 + 2.21766i
\(629\) −1.51948 −0.0605858
\(630\) 4.78804 8.29313i 0.190760 0.330406i
\(631\) −17.1312 + 29.6721i −0.681983 + 1.18123i 0.292392 + 0.956298i \(0.405549\pi\)
−0.974375 + 0.224930i \(0.927785\pi\)
\(632\) 4.56408 0.181549
\(633\) −9.79831 + 16.9712i −0.389448 + 0.674544i
\(634\) 22.3832 + 38.7688i 0.888950 + 1.53971i
\(635\) 14.7647 + 25.5732i 0.585918 + 1.01484i
\(636\) −28.3121 −1.12265
\(637\) 2.56580 2.53311i 0.101661 0.100365i
\(638\) −67.5491 −2.67429
\(639\) −1.99612 3.45739i −0.0789655 0.136772i
\(640\) 41.6927 + 72.2139i 1.64805 + 2.85451i
\(641\) 11.6093 20.1079i 0.458540 0.794215i −0.540344 0.841444i \(-0.681706\pi\)
0.998884 + 0.0472294i \(0.0150392\pi\)
\(642\) −29.4904 −1.16389
\(643\) −10.0400 + 17.3898i −0.395940 + 0.685788i −0.993221 0.116244i \(-0.962915\pi\)
0.597281 + 0.802032i \(0.296248\pi\)
\(644\) 3.46249 5.99721i 0.136441 0.236323i
\(645\) −34.8492 −1.37218
\(646\) 1.59063 2.75504i 0.0625823 0.108396i
\(647\) 8.26468 + 14.3148i 0.324918 + 0.562775i 0.981496 0.191484i \(-0.0613299\pi\)
−0.656578 + 0.754258i \(0.727997\pi\)
\(648\) 1.96249 + 3.39914i 0.0770940 + 0.133531i
\(649\) 6.88601 0.270300
\(650\) −68.4794 + 67.6068i −2.68598 + 2.65176i
\(651\) 6.33048 0.248111
\(652\) 10.0244 + 17.3628i 0.392587 + 0.679980i
\(653\) 0.463954 + 0.803591i 0.0181559 + 0.0314470i 0.874961 0.484194i \(-0.160887\pi\)
−0.856805 + 0.515641i \(0.827554\pi\)
\(654\) 14.4196 24.9756i 0.563853 0.976622i
\(655\) −46.0189 −1.79811
\(656\) −7.61505 + 13.1896i −0.297318 + 0.514969i
\(657\) −3.75053 + 6.49611i −0.146322 + 0.253437i
\(658\) −28.8209 −1.12355
\(659\) −16.1284 + 27.9352i −0.628273 + 1.08820i 0.359625 + 0.933097i \(0.382905\pi\)
−0.987898 + 0.155104i \(0.950429\pi\)
\(660\) 24.0757 + 41.7003i 0.937144 + 1.62318i
\(661\) 11.4285 + 19.7947i 0.444516 + 0.769923i 0.998018 0.0629238i \(-0.0200425\pi\)
−0.553503 + 0.832847i \(0.686709\pi\)
\(662\) 42.3892 1.64750
\(663\) 0.343570 + 1.31591i 0.0133431 + 0.0511058i
\(664\) −59.5830 −2.31227
\(665\) 7.14576 + 12.3768i 0.277101 + 0.479952i
\(666\) 4.78804 + 8.29313i 0.185533 + 0.321352i
\(667\) 8.23105 14.2566i 0.318707 0.552017i
\(668\) 16.1989 0.626753
\(669\) −13.9338 + 24.1340i −0.538712 + 0.933076i
\(670\) −26.7356 + 46.3074i −1.03289 + 1.78901i
\(671\) −25.3871 −0.980057
\(672\) −1.51415 + 2.62258i −0.0584095 + 0.101168i
\(673\) −0.542845 0.940235i −0.0209251 0.0362434i 0.855373 0.518012i \(-0.173328\pi\)
−0.876298 + 0.481769i \(0.839994\pi\)
\(674\) 9.00494 + 15.5970i 0.346857 + 0.600774i
\(675\) −11.2272 −0.432134
\(676\) 0.608649 47.4603i 0.0234096 1.82540i
\(677\) −8.60730 −0.330805 −0.165403 0.986226i \(-0.552892\pi\)
−0.165403 + 0.986226i \(0.552892\pi\)
\(678\) 12.6843 + 21.9699i 0.487139 + 0.843749i
\(679\) 2.48585 + 4.30562i 0.0953982 + 0.165235i
\(680\) 2.98198 5.16494i 0.114354 0.198066i
\(681\) −12.0304 −0.461007
\(682\) −24.6341 + 42.6676i −0.943290 + 1.63383i
\(683\) −16.7310 + 28.9790i −0.640196 + 1.10885i 0.345193 + 0.938532i \(0.387813\pi\)
−0.985389 + 0.170320i \(0.945520\pi\)
\(684\) −12.9533 −0.495281
\(685\) −6.42740 + 11.1326i −0.245578 + 0.425354i
\(686\) −1.18860 2.05872i −0.0453810 0.0786022i
\(687\) −4.59944 7.96646i −0.175479 0.303939i
\(688\) −17.5470 −0.668972
\(689\) 7.06299 + 27.0521i 0.269079 + 1.03060i
\(690\) −18.1628 −0.691447
\(691\) 2.34609 + 4.06355i 0.0892496 + 0.154585i 0.907194 0.420712i \(-0.138220\pi\)
−0.817945 + 0.575297i \(0.804886\pi\)
\(692\) −40.4539 70.0683i −1.53783 2.66360i
\(693\) −1.63695 + 2.83527i −0.0621824 + 0.107703i
\(694\) −18.7517 −0.711805
\(695\) 10.8305 18.7589i 0.410824 0.711567i
\(696\) 17.0332 29.5024i 0.645643 1.11829i
\(697\) −2.83235 −0.107283
\(698\) −13.9469 + 24.1567i −0.527897 + 0.914345i
\(699\) −6.22611 10.7839i −0.235493 0.407886i
\(700\) 20.4957 + 35.4996i 0.774666 + 1.34176i
\(701\) 41.4535 1.56568 0.782839 0.622224i \(-0.213771\pi\)
0.782839 + 0.622224i \(0.213771\pi\)
\(702\) 6.09944 6.02172i 0.230208 0.227275i
\(703\) −14.2915 −0.539015
\(704\) −18.4246 31.9123i −0.694403 1.20274i
\(705\) 24.4192 + 42.2954i 0.919682 + 1.59294i
\(706\) −14.9016 + 25.8104i −0.560830 + 0.971386i
\(707\) −5.89669 −0.221768
\(708\) −3.83969 + 6.65055i −0.144305 + 0.249943i
\(709\) −1.92111 + 3.32746i −0.0721488 + 0.124965i −0.899843 0.436214i \(-0.856319\pi\)
0.827694 + 0.561180i \(0.189652\pi\)
\(710\) 38.2301 1.43475
\(711\) 0.581414 1.00704i 0.0218047 0.0377669i
\(712\) 12.4791 + 21.6144i 0.467672 + 0.810032i
\(713\) −6.00347 10.3983i −0.224832 0.389420i
\(714\) 0.896688 0.0335577
\(715\) 33.8383 33.4072i 1.26548 1.24936i
\(716\) −7.08489 −0.264775
\(717\) −1.62280 2.81077i −0.0606045 0.104970i
\(718\) −5.96395 10.3299i −0.222573 0.385507i
\(719\) −4.45609 + 7.71818i −0.166184 + 0.287840i −0.937075 0.349128i \(-0.886478\pi\)
0.770891 + 0.636967i \(0.219811\pi\)
\(720\) −8.17058 −0.304499
\(721\) 5.28270 9.14991i 0.196738 0.340760i
\(722\) −7.62280 + 13.2031i −0.283691 + 0.491367i
\(723\) −9.42605 −0.350558
\(724\) 15.5191 26.8798i 0.576762 0.998981i
\(725\) 48.7225 + 84.3898i 1.80951 + 3.13416i
\(726\) 0.334758 + 0.579819i 0.0124241 + 0.0215191i
\(727\) 29.6815 1.10083 0.550413 0.834892i \(-0.314470\pi\)
0.550413 + 0.834892i \(0.314470\pi\)
\(728\) −13.6458 3.75031i −0.505745 0.138996i
\(729\) 1.00000 0.0370370
\(730\) −35.9154 62.2072i −1.32929 2.30239i
\(731\) −1.63161 2.82603i −0.0603472 0.104524i
\(732\) 14.1560 24.5190i 0.523222 0.906247i
\(733\) 5.30299 0.195870 0.0979352 0.995193i \(-0.468776\pi\)
0.0979352 + 0.995193i \(0.468776\pi\)
\(734\) 28.1815 48.8118i 1.04020 1.80168i
\(735\) −2.01415 + 3.48861i −0.0742930 + 0.128679i
\(736\) 5.74373 0.211717
\(737\) 9.14042 15.8317i 0.336692 0.583167i
\(738\) 8.92498 + 15.4585i 0.328533 + 0.569036i
\(739\) 10.4572 + 18.1123i 0.384673 + 0.666273i 0.991724 0.128390i \(-0.0409810\pi\)
−0.607051 + 0.794663i \(0.707648\pi\)
\(740\) −59.2469 −2.17796
\(741\) 3.23145 + 12.3768i 0.118710 + 0.454674i
\(742\) 18.4338 0.676726
\(743\) 0.159244 + 0.275818i 0.00584209 + 0.0101188i 0.868932 0.494932i \(-0.164807\pi\)
−0.863090 + 0.505051i \(0.831474\pi\)
\(744\) −12.4235 21.5182i −0.455468 0.788894i
\(745\) −20.1985 + 34.9848i −0.740015 + 1.28174i
\(746\) 23.6610 0.866290
\(747\) −7.59023 + 13.1467i −0.277712 + 0.481011i
\(748\) −2.25441 + 3.90475i −0.0824292 + 0.142772i
\(749\) 12.4055 0.453287
\(750\) 29.8159 51.6427i 1.08872 1.88573i
\(751\) −19.7940 34.2843i −0.722295 1.25105i −0.960078 0.279733i \(-0.909754\pi\)
0.237783 0.971318i \(-0.423579\pi\)
\(752\) 12.2954 + 21.2962i 0.448367 + 0.776594i
\(753\) 11.9893 0.436915
\(754\) −71.7324 19.7144i −2.61234 0.717958i
\(755\) 39.1367 1.42433
\(756\) −1.82555 3.16194i −0.0663945 0.114999i
\(757\) 5.12667 + 8.87966i 0.186332 + 0.322737i 0.944025 0.329875i \(-0.107007\pi\)
−0.757693 + 0.652612i \(0.773673\pi\)
\(758\) −33.1025 + 57.3352i −1.20234 + 2.08251i
\(759\) 6.20955 0.225392
\(760\) 28.0470 48.5788i 1.01737 1.76214i
\(761\) 8.73920 15.1367i 0.316796 0.548706i −0.663022 0.748600i \(-0.730726\pi\)
0.979818 + 0.199894i \(0.0640597\pi\)
\(762\) 17.4260 0.631279
\(763\) −6.06580 + 10.5063i −0.219597 + 0.380353i
\(764\) −1.18860 2.05872i −0.0430021 0.0744818i
\(765\) −0.759742 1.31591i −0.0274685 0.0475769i
\(766\) 16.4132 0.593035
\(767\) 7.31246 + 2.00971i 0.264038 + 0.0725663i
\(768\) 26.6970 0.963345
\(769\) −18.0283 31.2259i −0.650117 1.12604i −0.983094 0.183101i \(-0.941387\pi\)
0.332977 0.942935i \(-0.391947\pi\)
\(770\) −15.6755 27.1508i −0.564906 0.978446i
\(771\) 7.29831 12.6410i 0.262842 0.455256i
\(772\) 69.6057 2.50516
\(773\) 5.35918 9.28237i 0.192756 0.333864i −0.753406 0.657555i \(-0.771591\pi\)
0.946163 + 0.323691i \(0.104924\pi\)
\(774\) −10.2827 + 17.8102i −0.369604 + 0.640173i
\(775\) 71.0734 2.55303
\(776\) 9.75693 16.8995i 0.350253 0.606657i
\(777\) −2.01415 3.48861i −0.0722572 0.125153i
\(778\) −33.7282 58.4190i −1.20922 2.09442i