Properties

Label 245.2.e.i.116.2
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 116.2
Root \(1.28078 + 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 245.116
Dual form 245.2.e.i.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.28078 + 2.21837i) q^{2} +(-0.780776 + 1.35234i) q^{3} +(-2.28078 + 3.95042i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 + 0.486319i) q^{9} +O(q^{10})\) \(q+(1.28078 + 2.21837i) q^{2} +(-0.780776 + 1.35234i) q^{3} +(-2.28078 + 3.95042i) q^{4} +(-0.500000 - 0.866025i) q^{5} -4.00000 q^{6} -6.56155 q^{8} +(0.280776 + 0.486319i) q^{9} +(1.28078 - 2.21837i) q^{10} +(0.780776 - 1.35234i) q^{11} +(-3.56155 - 6.16879i) q^{12} +0.438447 q^{13} +1.56155 q^{15} +(-3.84233 - 6.65511i) q^{16} +(0.219224 - 0.379706i) q^{17} +(-0.719224 + 1.24573i) q^{18} +(3.56155 + 6.16879i) q^{19} +4.56155 q^{20} +4.00000 q^{22} +(-1.56155 - 2.70469i) q^{23} +(5.12311 - 8.87348i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.561553 + 0.972638i) q^{26} -5.56155 q^{27} +6.68466 q^{29} +(2.00000 + 3.46410i) q^{30} +(3.28078 - 5.68247i) q^{32} +(1.21922 + 2.11176i) q^{33} +1.12311 q^{34} -2.56155 q^{36} +(-3.00000 - 5.19615i) q^{37} +(-9.12311 + 15.8017i) q^{38} +(-0.342329 + 0.592932i) q^{39} +(3.28078 + 5.68247i) q^{40} +5.12311 q^{41} +0.876894 q^{43} +(3.56155 + 6.16879i) q^{44} +(0.280776 - 0.486319i) q^{45} +(4.00000 - 6.92820i) q^{46} +(4.34233 + 7.52113i) q^{47} +12.0000 q^{48} -2.56155 q^{50} +(0.342329 + 0.592932i) q^{51} +(-1.00000 + 1.73205i) q^{52} +(2.56155 - 4.43674i) q^{53} +(-7.12311 - 12.3376i) q^{54} -1.56155 q^{55} -11.1231 q^{57} +(8.56155 + 14.8290i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-3.56155 + 6.16879i) q^{60} +(-7.68466 - 13.3102i) q^{61} +1.43845 q^{64} +(-0.219224 - 0.379706i) q^{65} +(-3.12311 + 5.40938i) q^{66} +(-5.12311 + 8.87348i) q^{67} +(1.00000 + 1.73205i) q^{68} +4.87689 q^{69} +8.00000 q^{71} +(-1.84233 - 3.19101i) q^{72} +(6.12311 - 10.6055i) q^{73} +(7.68466 - 13.3102i) q^{74} +(-0.780776 - 1.35234i) q^{75} -32.4924 q^{76} -1.75379 q^{78} +(1.21922 + 2.11176i) q^{79} +(-3.84233 + 6.65511i) q^{80} +(3.50000 - 6.06218i) q^{81} +(6.56155 + 11.3649i) q^{82} +4.00000 q^{83} -0.438447 q^{85} +(1.12311 + 1.94528i) q^{86} +(-5.21922 + 9.03996i) q^{87} +(-5.12311 + 8.87348i) q^{88} +(0.561553 + 0.972638i) q^{89} +1.43845 q^{90} +14.2462 q^{92} +(-11.1231 + 19.2658i) q^{94} +(3.56155 - 6.16879i) q^{95} +(5.12311 + 8.87348i) q^{96} +5.80776 q^{97} +0.876894 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28078 + 2.21837i 0.905646 + 1.56862i 0.820048 + 0.572295i \(0.193947\pi\)
0.0855975 + 0.996330i \(0.472720\pi\)
\(3\) −0.780776 + 1.35234i −0.450781 + 0.780776i −0.998435 0.0559290i \(-0.982188\pi\)
0.547653 + 0.836705i \(0.315521\pi\)
\(4\) −2.28078 + 3.95042i −1.14039 + 1.97521i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −4.00000 −1.63299
\(7\) 0 0
\(8\) −6.56155 −2.31986
\(9\) 0.280776 + 0.486319i 0.0935921 + 0.162106i
\(10\) 1.28078 2.21837i 0.405017 0.701510i
\(11\) 0.780776 1.35234i 0.235413 0.407747i −0.723980 0.689821i \(-0.757689\pi\)
0.959393 + 0.282074i \(0.0910224\pi\)
\(12\) −3.56155 6.16879i −1.02813 1.78078i
\(13\) 0.438447 0.121603 0.0608017 0.998150i \(-0.480634\pi\)
0.0608017 + 0.998150i \(0.480634\pi\)
\(14\) 0 0
\(15\) 1.56155 0.403191
\(16\) −3.84233 6.65511i −0.960582 1.66378i
\(17\) 0.219224 0.379706i 0.0531695 0.0920923i −0.838216 0.545339i \(-0.816401\pi\)
0.891385 + 0.453247i \(0.149734\pi\)
\(18\) −0.719224 + 1.24573i −0.169523 + 0.293622i
\(19\) 3.56155 + 6.16879i 0.817076 + 1.41522i 0.907827 + 0.419344i \(0.137740\pi\)
−0.0907512 + 0.995874i \(0.528927\pi\)
\(20\) 4.56155 1.01999
\(21\) 0 0
\(22\) 4.00000 0.852803
\(23\) −1.56155 2.70469i −0.325606 0.563967i 0.656029 0.754736i \(-0.272235\pi\)
−0.981635 + 0.190769i \(0.938902\pi\)
\(24\) 5.12311 8.87348i 1.04575 1.81129i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0.561553 + 0.972638i 0.110130 + 0.190750i
\(27\) −5.56155 −1.07032
\(28\) 0 0
\(29\) 6.68466 1.24131 0.620655 0.784084i \(-0.286867\pi\)
0.620655 + 0.784084i \(0.286867\pi\)
\(30\) 2.00000 + 3.46410i 0.365148 + 0.632456i
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 3.28078 5.68247i 0.579965 1.00453i
\(33\) 1.21922 + 2.11176i 0.212240 + 0.367610i
\(34\) 1.12311 0.192611
\(35\) 0 0
\(36\) −2.56155 −0.426925
\(37\) −3.00000 5.19615i −0.493197 0.854242i 0.506772 0.862080i \(-0.330838\pi\)
−0.999969 + 0.00783774i \(0.997505\pi\)
\(38\) −9.12311 + 15.8017i −1.47996 + 2.56337i
\(39\) −0.342329 + 0.592932i −0.0548165 + 0.0949450i
\(40\) 3.28078 + 5.68247i 0.518736 + 0.898478i
\(41\) 5.12311 0.800095 0.400047 0.916494i \(-0.368994\pi\)
0.400047 + 0.916494i \(0.368994\pi\)
\(42\) 0 0
\(43\) 0.876894 0.133725 0.0668626 0.997762i \(-0.478701\pi\)
0.0668626 + 0.997762i \(0.478701\pi\)
\(44\) 3.56155 + 6.16879i 0.536924 + 0.929980i
\(45\) 0.280776 0.486319i 0.0418557 0.0724962i
\(46\) 4.00000 6.92820i 0.589768 1.02151i
\(47\) 4.34233 + 7.52113i 0.633394 + 1.09707i 0.986853 + 0.161620i \(0.0516720\pi\)
−0.353459 + 0.935450i \(0.614995\pi\)
\(48\) 12.0000 1.73205
\(49\) 0 0
\(50\) −2.56155 −0.362258
\(51\) 0.342329 + 0.592932i 0.0479357 + 0.0830270i
\(52\) −1.00000 + 1.73205i −0.138675 + 0.240192i
\(53\) 2.56155 4.43674i 0.351856 0.609433i −0.634718 0.772744i \(-0.718884\pi\)
0.986575 + 0.163310i \(0.0522172\pi\)
\(54\) −7.12311 12.3376i −0.969332 1.67893i
\(55\) −1.56155 −0.210560
\(56\) 0 0
\(57\) −11.1231 −1.47329
\(58\) 8.56155 + 14.8290i 1.12419 + 1.94715i
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) −3.56155 + 6.16879i −0.459794 + 0.796387i
\(61\) −7.68466 13.3102i −0.983920 1.70420i −0.646642 0.762794i \(-0.723827\pi\)
−0.337278 0.941405i \(-0.609506\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.43845 0.179806
\(65\) −0.219224 0.379706i −0.0271913 0.0470968i
\(66\) −3.12311 + 5.40938i −0.384428 + 0.665848i
\(67\) −5.12311 + 8.87348i −0.625887 + 1.08407i 0.362482 + 0.931991i \(0.381930\pi\)
−0.988369 + 0.152077i \(0.951404\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 4.87689 0.587109
\(70\) 0 0
\(71\) 8.00000 0.949425 0.474713 0.880141i \(-0.342552\pi\)
0.474713 + 0.880141i \(0.342552\pi\)
\(72\) −1.84233 3.19101i −0.217121 0.376064i
\(73\) 6.12311 10.6055i 0.716655 1.24128i −0.245662 0.969355i \(-0.579005\pi\)
0.962318 0.271928i \(-0.0876612\pi\)
\(74\) 7.68466 13.3102i 0.893323 1.54728i
\(75\) −0.780776 1.35234i −0.0901563 0.156155i
\(76\) −32.4924 −3.72714
\(77\) 0 0
\(78\) −1.75379 −0.198577
\(79\) 1.21922 + 2.11176i 0.137173 + 0.237591i 0.926426 0.376478i \(-0.122865\pi\)
−0.789252 + 0.614069i \(0.789532\pi\)
\(80\) −3.84233 + 6.65511i −0.429585 + 0.744064i
\(81\) 3.50000 6.06218i 0.388889 0.673575i
\(82\) 6.56155 + 11.3649i 0.724602 + 1.25505i
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −0.438447 −0.0475563
\(86\) 1.12311 + 1.94528i 0.121108 + 0.209765i
\(87\) −5.21922 + 9.03996i −0.559560 + 0.969185i
\(88\) −5.12311 + 8.87348i −0.546125 + 0.945916i
\(89\) 0.561553 + 0.972638i 0.0595245 + 0.103099i 0.894252 0.447564i \(-0.147708\pi\)
−0.834728 + 0.550663i \(0.814375\pi\)
\(90\) 1.43845 0.151626
\(91\) 0 0
\(92\) 14.2462 1.48527
\(93\) 0 0
\(94\) −11.1231 + 19.2658i −1.14726 + 1.98711i
\(95\) 3.56155 6.16879i 0.365408 0.632905i
\(96\) 5.12311 + 8.87348i 0.522875 + 0.905646i
\(97\) 5.80776 0.589689 0.294845 0.955545i \(-0.404732\pi\)
0.294845 + 0.955545i \(0.404732\pi\)
\(98\) 0 0
\(99\) 0.876894 0.0881312
\(100\) −2.28078 3.95042i −0.228078 0.395042i
\(101\) 8.12311 14.0696i 0.808279 1.39998i −0.105776 0.994390i \(-0.533733\pi\)
0.914055 0.405591i \(-0.132934\pi\)
\(102\) −0.876894 + 1.51883i −0.0868255 + 0.150386i
\(103\) −2.78078 4.81645i −0.273998 0.474579i 0.695884 0.718154i \(-0.255013\pi\)
−0.969882 + 0.243576i \(0.921680\pi\)
\(104\) −2.87689 −0.282103
\(105\) 0 0
\(106\) 13.1231 1.27463
\(107\) −6.68466 11.5782i −0.646230 1.11930i −0.984016 0.178081i \(-0.943011\pi\)
0.337786 0.941223i \(-0.390322\pi\)
\(108\) 12.6847 21.9705i 1.22058 2.11411i
\(109\) −2.65767 + 4.60322i −0.254559 + 0.440909i −0.964776 0.263074i \(-0.915264\pi\)
0.710217 + 0.703983i \(0.248597\pi\)
\(110\) −2.00000 3.46410i −0.190693 0.330289i
\(111\) 9.36932 0.889296
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −14.2462 24.6752i −1.33428 2.31104i
\(115\) −1.56155 + 2.70469i −0.145616 + 0.252214i
\(116\) −15.2462 + 26.4072i −1.41558 + 2.45185i
\(117\) 0.123106 + 0.213225i 0.0113811 + 0.0197127i
\(118\) 10.2462 0.943240
\(119\) 0 0
\(120\) −10.2462 −0.935347
\(121\) 4.28078 + 7.41452i 0.389161 + 0.674047i
\(122\) 19.6847 34.0948i 1.78217 3.08680i
\(123\) −4.00000 + 6.92820i −0.360668 + 0.624695i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.24621 −0.554262 −0.277131 0.960832i \(-0.589384\pi\)
−0.277131 + 0.960832i \(0.589384\pi\)
\(128\) −4.71922 8.17394i −0.417124 0.722481i
\(129\) −0.684658 + 1.18586i −0.0602808 + 0.104409i
\(130\) 0.561553 0.972638i 0.0492514 0.0853060i
\(131\) 0.438447 + 0.759413i 0.0383073 + 0.0663502i 0.884543 0.466458i \(-0.154470\pi\)
−0.846236 + 0.532808i \(0.821137\pi\)
\(132\) −11.1231 −0.968142
\(133\) 0 0
\(134\) −26.2462 −2.26733
\(135\) 2.78078 + 4.81645i 0.239331 + 0.414534i
\(136\) −1.43845 + 2.49146i −0.123346 + 0.213641i
\(137\) 8.56155 14.8290i 0.731463 1.26693i −0.224795 0.974406i \(-0.572171\pi\)
0.956258 0.292525i \(-0.0944954\pi\)
\(138\) 6.24621 + 10.8188i 0.531713 + 0.920954i
\(139\) −15.1231 −1.28273 −0.641363 0.767238i \(-0.721631\pi\)
−0.641363 + 0.767238i \(0.721631\pi\)
\(140\) 0 0
\(141\) −13.5616 −1.14209
\(142\) 10.2462 + 17.7470i 0.859843 + 1.48929i
\(143\) 0.342329 0.592932i 0.0286270 0.0495834i
\(144\) 2.15767 3.73720i 0.179806 0.311433i
\(145\) −3.34233 5.78908i −0.277565 0.480757i
\(146\) 31.3693 2.59614
\(147\) 0 0
\(148\) 27.3693 2.24974
\(149\) −6.12311 10.6055i −0.501624 0.868839i −0.999998 0.00187666i \(-0.999403\pi\)
0.498374 0.866962i \(-0.333931\pi\)
\(150\) 2.00000 3.46410i 0.163299 0.282843i
\(151\) 3.46543 6.00231i 0.282013 0.488461i −0.689867 0.723936i \(-0.742331\pi\)
0.971880 + 0.235475i \(0.0756645\pi\)
\(152\) −23.3693 40.4768i −1.89550 3.28311i
\(153\) 0.246211 0.0199050
\(154\) 0 0
\(155\) 0 0
\(156\) −1.56155 2.70469i −0.125024 0.216548i
\(157\) −10.1231 + 17.5337i −0.807912 + 1.39934i 0.106396 + 0.994324i \(0.466069\pi\)
−0.914308 + 0.405020i \(0.867264\pi\)
\(158\) −3.12311 + 5.40938i −0.248461 + 0.430347i
\(159\) 4.00000 + 6.92820i 0.317221 + 0.549442i
\(160\) −6.56155 −0.518736
\(161\) 0 0
\(162\) 17.9309 1.40878
\(163\) 3.56155 + 6.16879i 0.278962 + 0.483177i 0.971127 0.238563i \(-0.0766762\pi\)
−0.692165 + 0.721739i \(0.743343\pi\)
\(164\) −11.6847 + 20.2384i −0.912419 + 1.58036i
\(165\) 1.21922 2.11176i 0.0949164 0.164400i
\(166\) 5.12311 + 8.87348i 0.397630 + 0.688716i
\(167\) −6.93087 −0.536327 −0.268163 0.963373i \(-0.586417\pi\)
−0.268163 + 0.963373i \(0.586417\pi\)
\(168\) 0 0
\(169\) −12.8078 −0.985213
\(170\) −0.561553 0.972638i −0.0430691 0.0745979i
\(171\) −2.00000 + 3.46410i −0.152944 + 0.264906i
\(172\) −2.00000 + 3.46410i −0.152499 + 0.264135i
\(173\) 2.21922 + 3.84381i 0.168724 + 0.292239i 0.937972 0.346712i \(-0.112702\pi\)
−0.769247 + 0.638951i \(0.779369\pi\)
\(174\) −26.7386 −2.02705
\(175\) 0 0
\(176\) −12.0000 −0.904534
\(177\) 3.12311 + 5.40938i 0.234747 + 0.406594i
\(178\) −1.43845 + 2.49146i −0.107816 + 0.186743i
\(179\) −10.0000 + 17.3205i −0.747435 + 1.29460i 0.201613 + 0.979465i \(0.435382\pi\)
−0.949048 + 0.315130i \(0.897952\pi\)
\(180\) 1.28078 + 2.21837i 0.0954634 + 0.165348i
\(181\) −17.6155 −1.30935 −0.654676 0.755910i \(-0.727195\pi\)
−0.654676 + 0.755910i \(0.727195\pi\)
\(182\) 0 0
\(183\) 24.0000 1.77413
\(184\) 10.2462 + 17.7470i 0.755361 + 1.30832i
\(185\) −3.00000 + 5.19615i −0.220564 + 0.382029i
\(186\) 0 0
\(187\) −0.342329 0.592932i −0.0250336 0.0433595i
\(188\) −39.6155 −2.88926
\(189\) 0 0
\(190\) 18.2462 1.32372
\(191\) 6.78078 + 11.7446i 0.490640 + 0.849813i 0.999942 0.0107748i \(-0.00342978\pi\)
−0.509302 + 0.860588i \(0.670096\pi\)
\(192\) −1.12311 + 1.94528i −0.0810532 + 0.140388i
\(193\) −9.68466 + 16.7743i −0.697117 + 1.20744i 0.272345 + 0.962200i \(0.412201\pi\)
−0.969462 + 0.245242i \(0.921132\pi\)
\(194\) 7.43845 + 12.8838i 0.534049 + 0.925001i
\(195\) 0.684658 0.0490294
\(196\) 0 0
\(197\) 1.12311 0.0800180 0.0400090 0.999199i \(-0.487261\pi\)
0.0400090 + 0.999199i \(0.487261\pi\)
\(198\) 1.12311 + 1.94528i 0.0798156 + 0.138245i
\(199\) 0.876894 1.51883i 0.0621614 0.107667i −0.833270 0.552866i \(-0.813534\pi\)
0.895431 + 0.445200i \(0.146867\pi\)
\(200\) 3.28078 5.68247i 0.231986 0.401811i
\(201\) −8.00000 13.8564i −0.564276 0.977356i
\(202\) 41.6155 2.92806
\(203\) 0 0
\(204\) −3.12311 −0.218661
\(205\) −2.56155 4.43674i −0.178907 0.309875i
\(206\) 7.12311 12.3376i 0.496290 0.859600i
\(207\) 0.876894 1.51883i 0.0609484 0.105566i
\(208\) −1.68466 2.91791i −0.116810 0.202321i
\(209\) 11.1231 0.769401
\(210\) 0 0
\(211\) 14.0540 0.967516 0.483758 0.875202i \(-0.339272\pi\)
0.483758 + 0.875202i \(0.339272\pi\)
\(212\) 11.6847 + 20.2384i 0.802506 + 1.38998i
\(213\) −6.24621 + 10.8188i −0.427983 + 0.741289i
\(214\) 17.1231 29.6581i 1.17051 2.02739i
\(215\) −0.438447 0.759413i −0.0299018 0.0517915i
\(216\) 36.4924 2.48299
\(217\) 0 0
\(218\) −13.6155 −0.922160
\(219\) 9.56155 + 16.5611i 0.646110 + 1.11910i
\(220\) 3.56155 6.16879i 0.240120 0.415900i
\(221\) 0.0961180 0.166481i 0.00646559 0.0111987i
\(222\) 12.0000 + 20.7846i 0.805387 + 1.39497i
\(223\) −2.43845 −0.163291 −0.0816453 0.996661i \(-0.526017\pi\)
−0.0816453 + 0.996661i \(0.526017\pi\)
\(224\) 0 0
\(225\) −0.561553 −0.0374369
\(226\) −17.9309 31.0572i −1.19274 2.06589i
\(227\) −5.65767 + 9.79937i −0.375513 + 0.650407i −0.990404 0.138205i \(-0.955867\pi\)
0.614891 + 0.788612i \(0.289200\pi\)
\(228\) 25.3693 43.9409i 1.68012 2.91006i
\(229\) −5.43845 9.41967i −0.359383 0.622469i 0.628475 0.777830i \(-0.283679\pi\)
−0.987858 + 0.155361i \(0.950346\pi\)
\(230\) −8.00000 −0.527504
\(231\) 0 0
\(232\) −43.8617 −2.87966
\(233\) −2.56155 4.43674i −0.167813 0.290660i 0.769838 0.638240i \(-0.220337\pi\)
−0.937651 + 0.347579i \(0.887004\pi\)
\(234\) −0.315342 + 0.546188i −0.0206145 + 0.0357054i
\(235\) 4.34233 7.52113i 0.283262 0.490625i
\(236\) 9.12311 + 15.8017i 0.593864 + 1.02860i
\(237\) −3.80776 −0.247341
\(238\) 0 0
\(239\) 19.8078 1.28126 0.640629 0.767851i \(-0.278674\pi\)
0.640629 + 0.767851i \(0.278674\pi\)
\(240\) −6.00000 10.3923i −0.387298 0.670820i
\(241\) 2.12311 3.67733i 0.136761 0.236877i −0.789508 0.613741i \(-0.789664\pi\)
0.926269 + 0.376863i \(0.122997\pi\)
\(242\) −10.9654 + 18.9927i −0.704885 + 1.22090i
\(243\) −2.87689 4.98293i −0.184553 0.319655i
\(244\) 70.1080 4.48820
\(245\) 0 0
\(246\) −20.4924 −1.30655
\(247\) 1.56155 + 2.70469i 0.0993592 + 0.172095i
\(248\) 0 0
\(249\) −3.12311 + 5.40938i −0.197919 + 0.342805i
\(250\) 1.28078 + 2.21837i 0.0810034 + 0.140302i
\(251\) −8.87689 −0.560305 −0.280152 0.959956i \(-0.590385\pi\)
−0.280152 + 0.959956i \(0.590385\pi\)
\(252\) 0 0
\(253\) −4.87689 −0.306608
\(254\) −8.00000 13.8564i −0.501965 0.869428i
\(255\) 0.342329 0.592932i 0.0214375 0.0371308i
\(256\) 13.5270 23.4294i 0.845437 1.46434i
\(257\) 5.24621 + 9.08670i 0.327250 + 0.566813i 0.981965 0.189062i \(-0.0605449\pi\)
−0.654715 + 0.755875i \(0.727212\pi\)
\(258\) −3.50758 −0.218372
\(259\) 0 0
\(260\) 2.00000 0.124035
\(261\) 1.87689 + 3.25088i 0.116177 + 0.201224i
\(262\) −1.12311 + 1.94528i −0.0693857 + 0.120180i
\(263\) 6.43845 11.1517i 0.397012 0.687644i −0.596344 0.802729i \(-0.703381\pi\)
0.993356 + 0.115085i \(0.0367139\pi\)
\(264\) −8.00000 13.8564i −0.492366 0.852803i
\(265\) −5.12311 −0.314710
\(266\) 0 0
\(267\) −1.75379 −0.107330
\(268\) −23.3693 40.4768i −1.42751 2.47252i
\(269\) 10.3693 17.9602i 0.632228 1.09505i −0.354867 0.934917i \(-0.615474\pi\)
0.987095 0.160135i \(-0.0511929\pi\)
\(270\) −7.12311 + 12.3376i −0.433498 + 0.750841i
\(271\) 8.00000 + 13.8564i 0.485965 + 0.841717i 0.999870 0.0161307i \(-0.00513477\pi\)
−0.513905 + 0.857847i \(0.671801\pi\)
\(272\) −3.36932 −0.204295
\(273\) 0 0
\(274\) 43.8617 2.64978
\(275\) 0.780776 + 1.35234i 0.0470826 + 0.0815494i
\(276\) −11.1231 + 19.2658i −0.669532 + 1.15966i
\(277\) 0.123106 0.213225i 0.00739670 0.0128115i −0.862303 0.506392i \(-0.830979\pi\)
0.869700 + 0.493581i \(0.164312\pi\)
\(278\) −19.3693 33.5486i −1.16169 2.01211i
\(279\) 0 0
\(280\) 0 0
\(281\) 12.4384 0.742016 0.371008 0.928630i \(-0.379012\pi\)
0.371008 + 0.928630i \(0.379012\pi\)
\(282\) −17.3693 30.0845i −1.03433 1.79151i
\(283\) 5.65767 9.79937i 0.336314 0.582512i −0.647423 0.762131i \(-0.724153\pi\)
0.983736 + 0.179619i \(0.0574865\pi\)
\(284\) −18.2462 + 31.6034i −1.08271 + 1.87531i
\(285\) 5.56155 + 9.63289i 0.329438 + 0.570603i
\(286\) 1.75379 0.103704
\(287\) 0 0
\(288\) 3.68466 0.217121
\(289\) 8.40388 + 14.5560i 0.494346 + 0.856232i
\(290\) 8.56155 14.8290i 0.502752 0.870791i
\(291\) −4.53457 + 7.85410i −0.265821 + 0.460415i
\(292\) 27.9309 + 48.3777i 1.63453 + 2.83109i
\(293\) −2.68466 −0.156839 −0.0784197 0.996920i \(-0.524987\pi\)
−0.0784197 + 0.996920i \(0.524987\pi\)
\(294\) 0 0
\(295\) −4.00000 −0.232889
\(296\) 19.6847 + 34.0948i 1.14415 + 1.98172i
\(297\) −4.34233 + 7.52113i −0.251967 + 0.436421i
\(298\) 15.6847 27.1666i 0.908588 1.57372i
\(299\) −0.684658 1.18586i −0.0395948 0.0685802i
\(300\) 7.12311 0.411253
\(301\) 0 0
\(302\) 17.7538 1.02162
\(303\) 12.6847 + 21.9705i 0.728715 + 1.26217i
\(304\) 27.3693 47.4050i 1.56974 2.71887i
\(305\) −7.68466 + 13.3102i −0.440022 + 0.762141i
\(306\) 0.315342 + 0.546188i 0.0180269 + 0.0312235i
\(307\) −19.3153 −1.10238 −0.551192 0.834378i \(-0.685827\pi\)
−0.551192 + 0.834378i \(0.685827\pi\)
\(308\) 0 0
\(309\) 8.68466 0.494053
\(310\) 0 0
\(311\) −15.8078 + 27.3799i −0.896376 + 1.55257i −0.0642838 + 0.997932i \(0.520476\pi\)
−0.832092 + 0.554637i \(0.812857\pi\)
\(312\) 2.24621 3.89055i 0.127167 0.220259i
\(313\) 11.1501 + 19.3125i 0.630241 + 1.09161i 0.987502 + 0.157604i \(0.0503771\pi\)
−0.357262 + 0.934004i \(0.616290\pi\)
\(314\) −51.8617 −2.92673
\(315\) 0 0
\(316\) −11.1231 −0.625724
\(317\) −5.24621 9.08670i −0.294657 0.510360i 0.680248 0.732982i \(-0.261872\pi\)
−0.974905 + 0.222622i \(0.928539\pi\)
\(318\) −10.2462 + 17.7470i −0.574579 + 0.995200i
\(319\) 5.21922 9.03996i 0.292220 0.506141i
\(320\) −0.719224 1.24573i −0.0402058 0.0696385i
\(321\) 20.8769 1.16523
\(322\) 0 0
\(323\) 3.12311 0.173774
\(324\) 15.9654 + 27.6529i 0.886969 + 1.53627i
\(325\) −0.219224 + 0.379706i −0.0121603 + 0.0210623i
\(326\) −9.12311 + 15.8017i −0.505282 + 0.875174i
\(327\) −4.15009 7.18817i −0.229501 0.397507i
\(328\) −33.6155 −1.85611
\(329\) 0 0
\(330\) 6.24621 0.343843
\(331\) −6.00000 10.3923i −0.329790 0.571213i 0.652680 0.757634i \(-0.273645\pi\)
−0.982470 + 0.186421i \(0.940311\pi\)
\(332\) −9.12311 + 15.8017i −0.500695 + 0.867230i
\(333\) 1.68466 2.91791i 0.0923187 0.159901i
\(334\) −8.87689 15.3752i −0.485722 0.841295i
\(335\) 10.2462 0.559810
\(336\) 0 0
\(337\) −1.50758 −0.0821230 −0.0410615 0.999157i \(-0.513074\pi\)
−0.0410615 + 0.999157i \(0.513074\pi\)
\(338\) −16.4039 28.4124i −0.892254 1.54543i
\(339\) 10.9309 18.9328i 0.593683 1.02829i
\(340\) 1.00000 1.73205i 0.0542326 0.0939336i
\(341\) 0 0
\(342\) −10.2462 −0.554052
\(343\) 0 0
\(344\) −5.75379 −0.310223
\(345\) −2.43845 4.22351i −0.131282 0.227386i
\(346\) −5.68466 + 9.84612i −0.305609 + 0.529331i
\(347\) −3.56155 + 6.16879i −0.191194 + 0.331158i −0.945646 0.325197i \(-0.894569\pi\)
0.754452 + 0.656355i \(0.227903\pi\)
\(348\) −23.8078 41.2363i −1.27623 2.21050i
\(349\) 10.4924 0.561646 0.280823 0.959760i \(-0.409393\pi\)
0.280823 + 0.959760i \(0.409393\pi\)
\(350\) 0 0
\(351\) −2.43845 −0.130155
\(352\) −5.12311 8.87348i −0.273062 0.472958i
\(353\) −2.90388 + 5.02967i −0.154558 + 0.267702i −0.932898 0.360141i \(-0.882729\pi\)
0.778340 + 0.627843i \(0.216062\pi\)
\(354\) −8.00000 + 13.8564i −0.425195 + 0.736460i
\(355\) −4.00000 6.92820i −0.212298 0.367711i
\(356\) −5.12311 −0.271524
\(357\) 0 0
\(358\) −51.2311 −2.70765
\(359\) −4.00000 6.92820i −0.211112 0.365657i 0.740951 0.671559i \(-0.234375\pi\)
−0.952063 + 0.305903i \(0.901042\pi\)
\(360\) −1.84233 + 3.19101i −0.0970993 + 0.168181i
\(361\) −15.8693 + 27.4865i −0.835227 + 1.44666i
\(362\) −22.5616 39.0778i −1.18581 2.05388i
\(363\) −13.3693 −0.701707
\(364\) 0 0
\(365\) −12.2462 −0.640996
\(366\) 30.7386 + 53.2409i 1.60673 + 2.78295i
\(367\) 4.34233 7.52113i 0.226668 0.392600i −0.730151 0.683286i \(-0.760550\pi\)
0.956818 + 0.290686i \(0.0938835\pi\)
\(368\) −12.0000 + 20.7846i −0.625543 + 1.08347i
\(369\) 1.43845 + 2.49146i 0.0748826 + 0.129700i
\(370\) −15.3693 −0.799013
\(371\) 0 0
\(372\) 0 0
\(373\) −2.31534 4.01029i −0.119884 0.207645i 0.799838 0.600216i \(-0.204919\pi\)
−0.919721 + 0.392572i \(0.871586\pi\)
\(374\) 0.876894 1.51883i 0.0453431 0.0785366i
\(375\) −0.780776 + 1.35234i −0.0403191 + 0.0698348i
\(376\) −28.4924 49.3503i −1.46938 2.54505i
\(377\) 2.93087 0.150947
\(378\) 0 0
\(379\) −16.4924 −0.847159 −0.423579 0.905859i \(-0.639227\pi\)
−0.423579 + 0.905859i \(0.639227\pi\)
\(380\) 16.2462 + 28.1393i 0.833413 + 1.44351i
\(381\) 4.87689 8.44703i 0.249851 0.432754i
\(382\) −17.3693 + 30.0845i −0.888692 + 1.53926i
\(383\) −3.12311 5.40938i −0.159583 0.276406i 0.775135 0.631795i \(-0.217682\pi\)
−0.934718 + 0.355389i \(0.884348\pi\)
\(384\) 14.7386 0.752128
\(385\) 0 0
\(386\) −49.6155 −2.52536
\(387\) 0.246211 + 0.426450i 0.0125156 + 0.0216777i
\(388\) −13.2462 + 22.9431i −0.672474 + 1.16476i
\(389\) 12.4654 21.5908i 0.632023 1.09470i −0.355115 0.934823i \(-0.615558\pi\)
0.987138 0.159873i \(-0.0511084\pi\)
\(390\) 0.876894 + 1.51883i 0.0444033 + 0.0769087i
\(391\) −1.36932 −0.0692493
\(392\) 0 0
\(393\) −1.36932 −0.0690729
\(394\) 1.43845 + 2.49146i 0.0724679 + 0.125518i
\(395\) 1.21922 2.11176i 0.0613458 0.106254i
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) −13.7808 23.8690i −0.691637 1.19795i −0.971301 0.237853i \(-0.923556\pi\)
0.279664 0.960098i \(-0.409777\pi\)
\(398\) 4.49242 0.225185
\(399\) 0 0
\(400\) 7.68466 0.384233
\(401\) −15.7808 27.3331i −0.788054 1.36495i −0.927157 0.374672i \(-0.877755\pi\)
0.139103 0.990278i \(-0.455578\pi\)
\(402\) 20.4924 35.4939i 1.02207 1.77028i
\(403\) 0 0
\(404\) 37.0540 + 64.1794i 1.84350 + 3.19304i
\(405\) −7.00000 −0.347833
\(406\) 0 0
\(407\) −9.36932 −0.464420
\(408\) −2.24621 3.89055i −0.111204 0.192611i
\(409\) −3.24621 + 5.62260i −0.160515 + 0.278020i −0.935053 0.354507i \(-0.884649\pi\)
0.774539 + 0.632527i \(0.217982\pi\)
\(410\) 6.56155 11.3649i 0.324052 0.561275i
\(411\) 13.3693 + 23.1563i 0.659460 + 1.14222i
\(412\) 25.3693 1.24986
\(413\) 0 0
\(414\) 4.49242 0.220791
\(415\) −2.00000 3.46410i −0.0981761 0.170046i
\(416\) 1.43845 2.49146i 0.0705257 0.122154i
\(417\) 11.8078 20.4516i 0.578229 1.00152i
\(418\) 14.2462 + 24.6752i 0.696805 + 1.20690i
\(419\) 26.2462 1.28221 0.641106 0.767453i \(-0.278476\pi\)
0.641106 + 0.767453i \(0.278476\pi\)
\(420\) 0 0
\(421\) −2.68466 −0.130842 −0.0654211 0.997858i \(-0.520839\pi\)
−0.0654211 + 0.997858i \(0.520839\pi\)
\(422\) 18.0000 + 31.1769i 0.876226 + 1.51767i
\(423\) −2.43845 + 4.22351i −0.118561 + 0.205354i
\(424\) −16.8078 + 29.1119i −0.816257 + 1.41380i
\(425\) 0.219224 + 0.379706i 0.0106339 + 0.0184185i
\(426\) −32.0000 −1.55041
\(427\) 0 0
\(428\) 60.9848 2.94781
\(429\) 0.534565 + 0.925894i 0.0258090 + 0.0447026i
\(430\) 1.12311 1.94528i 0.0541610 0.0938095i
\(431\) 9.90388 17.1540i 0.477053 0.826280i −0.522601 0.852577i \(-0.675038\pi\)
0.999654 + 0.0262970i \(0.00837156\pi\)
\(432\) 21.3693 + 37.0127i 1.02813 + 1.78078i
\(433\) 8.24621 0.396288 0.198144 0.980173i \(-0.436509\pi\)
0.198144 + 0.980173i \(0.436509\pi\)
\(434\) 0 0
\(435\) 10.4384 0.500485
\(436\) −12.1231 20.9978i −0.580591 1.00561i
\(437\) 11.1231 19.2658i 0.532090 0.921607i
\(438\) −24.4924 + 42.4221i −1.17029 + 2.02701i
\(439\) −4.68466 8.11407i −0.223587 0.387263i 0.732308 0.680974i \(-0.238443\pi\)
−0.955894 + 0.293710i \(0.905110\pi\)
\(440\) 10.2462 0.488469
\(441\) 0 0
\(442\) 0.492423 0.0234221
\(443\) 1.31534 + 2.27824i 0.0624938 + 0.108242i 0.895580 0.444901i \(-0.146761\pi\)
−0.833086 + 0.553144i \(0.813428\pi\)
\(444\) −21.3693 + 37.0127i −1.01414 + 1.75655i
\(445\) 0.561553 0.972638i 0.0266202 0.0461075i
\(446\) −3.12311 5.40938i −0.147883 0.256141i
\(447\) 19.1231 0.904492
\(448\) 0 0
\(449\) −1.80776 −0.0853137 −0.0426568 0.999090i \(-0.513582\pi\)
−0.0426568 + 0.999090i \(0.513582\pi\)
\(450\) −0.719224 1.24573i −0.0339045 0.0587244i
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 31.9309 55.3059i 1.50190 2.60137i
\(453\) 5.41146 + 9.37292i 0.254253 + 0.440378i
\(454\) −28.9848 −1.36033
\(455\) 0 0
\(456\) 72.9848 3.41783
\(457\) 8.56155 + 14.8290i 0.400493 + 0.693673i 0.993785 0.111313i \(-0.0355057\pi\)
−0.593293 + 0.804987i \(0.702172\pi\)
\(458\) 13.9309 24.1290i 0.650947 1.12747i
\(459\) −1.21922 + 2.11176i −0.0569085 + 0.0985684i
\(460\) −7.12311 12.3376i −0.332117 0.575243i
\(461\) −13.1231 −0.611204 −0.305602 0.952159i \(-0.598858\pi\)
−0.305602 + 0.952159i \(0.598858\pi\)
\(462\) 0 0
\(463\) 12.4924 0.580572 0.290286 0.956940i \(-0.406250\pi\)
0.290286 + 0.956940i \(0.406250\pi\)
\(464\) −25.6847 44.4871i −1.19238 2.06526i
\(465\) 0 0
\(466\) 6.56155 11.3649i 0.303958 0.526471i
\(467\) −11.2192 19.4323i −0.519164 0.899218i −0.999752 0.0222716i \(-0.992910\pi\)
0.480588 0.876946i \(-0.340423\pi\)
\(468\) −1.12311 −0.0519156
\(469\) 0 0
\(470\) 22.2462 1.02614
\(471\) −15.8078 27.3799i −0.728383 1.26160i
\(472\) −13.1231 + 22.7299i −0.604040 + 1.04623i
\(473\) 0.684658 1.18586i 0.0314806 0.0545260i
\(474\) −4.87689 8.44703i −0.224003 0.387985i
\(475\) −7.12311 −0.326831
\(476\) 0 0
\(477\) 2.87689 0.131724
\(478\) 25.3693 + 43.9409i 1.16037 + 2.00981i
\(479\) −2.43845 + 4.22351i −0.111415 + 0.192977i −0.916341 0.400398i \(-0.868872\pi\)
0.804926 + 0.593376i \(0.202205\pi\)
\(480\) 5.12311 8.87348i 0.233837 0.405017i
\(481\) −1.31534 2.27824i −0.0599744 0.103879i
\(482\) 10.8769 0.495429
\(483\) 0 0
\(484\) −39.0540 −1.77518
\(485\) −2.90388 5.02967i −0.131858 0.228386i
\(486\) 7.36932 12.7640i 0.334279 0.578988i
\(487\) 1.56155 2.70469i 0.0707607 0.122561i −0.828474 0.560027i \(-0.810791\pi\)
0.899235 + 0.437466i \(0.144124\pi\)
\(488\) 50.4233 + 87.3357i 2.28256 + 3.95350i
\(489\) −11.1231 −0.503004
\(490\) 0 0
\(491\) −41.1771 −1.85830 −0.929148 0.369708i \(-0.879458\pi\)
−0.929148 + 0.369708i \(0.879458\pi\)
\(492\) −18.2462 31.6034i −0.822603 1.42479i
\(493\) 1.46543 2.53821i 0.0659999 0.114315i
\(494\) −4.00000 + 6.92820i −0.179969 + 0.311715i
\(495\) −0.438447 0.759413i −0.0197067 0.0341331i
\(496\) 0 0
\(497\) 0 0
\(498\) −16.0000 −0.716977
\(499\) −20.5885 35.6604i −0.921670 1.59638i −0.796832 0.604202i \(-0.793492\pi\)
−0.124838 0.992177i \(-0.539841\pi\)
\(500\) −2.28078 + 3.95042i −0.101999 + 0.176668i
\(501\) 5.41146 9.37292i 0.241766 0.418751i
\(502\) −11.3693 19.6922i −0.507437 0.878907i
\(503\) 38.9309 1.73584 0.867921 0.496703i \(-0.165456\pi\)
0.867921 + 0.496703i \(0.165456\pi\)
\(504\) 0 0
\(505\) −16.2462 −0.722947
\(506\) −6.24621 10.8188i −0.277678 0.480952i
\(507\) 10.0000 17.3205i 0.444116 0.769231i
\(508\) 14.2462 24.6752i 0.632073 1.09478i
\(509\) 5.87689 + 10.1791i 0.260489 + 0.451180i 0.966372 0.257149i \(-0.0827830\pi\)
−0.705883 + 0.708328i \(0.749450\pi\)
\(510\) 1.75379 0.0776591
\(511\) 0 0
\(512\) 50.4233 2.22842
\(513\) −19.8078 34.3081i −0.874534 1.51474i
\(514\) −13.4384 + 23.2761i −0.592744 + 1.02666i
\(515\) −2.78078 + 4.81645i −0.122536 + 0.212238i
\(516\) −3.12311 5.40938i −0.137487 0.238135i
\(517\) 13.5616 0.596436
\(518\) 0 0
\(519\) −6.93087 −0.304231
\(520\) 1.43845 + 2.49146i 0.0630801 + 0.109258i
\(521\) −5.00000 + 8.66025i −0.219054 + 0.379413i −0.954519 0.298150i \(-0.903630\pi\)
0.735465 + 0.677563i \(0.236964\pi\)
\(522\) −4.80776 + 8.32729i −0.210430 + 0.364476i
\(523\) −20.2462 35.0675i −0.885305 1.53339i −0.845364 0.534191i \(-0.820616\pi\)
−0.0399413 0.999202i \(-0.512717\pi\)
\(524\) −4.00000 −0.174741
\(525\) 0 0
\(526\) 32.9848 1.43821
\(527\) 0 0
\(528\) 9.36932 16.2281i 0.407747 0.706239i
\(529\) 6.62311 11.4716i 0.287961 0.498763i
\(530\) −6.56155 11.3649i −0.285016 0.493662i
\(531\) 2.24621 0.0974773
\(532\) 0 0
\(533\) 2.24621 0.0972942
\(534\) −2.24621 3.89055i −0.0972031 0.168361i
\(535\) −6.68466 + 11.5782i −0.289003 + 0.500568i
\(536\) 33.6155 58.2238i 1.45197 2.51489i
\(537\) −15.6155 27.0469i −0.673860 1.16716i
\(538\) 53.1231 2.29030
\(539\) 0 0
\(540\) −25.3693 −1.09172
\(541\) 18.9039 + 32.7425i 0.812741 + 1.40771i 0.910938 + 0.412542i \(0.135359\pi\)
−0.0981971 + 0.995167i \(0.531308\pi\)
\(542\) −20.4924 + 35.4939i −0.880225 + 1.52459i
\(543\) 13.7538 23.8223i 0.590232 1.02231i
\(544\) −1.43845 2.49146i −0.0616729 0.106821i
\(545\) 5.31534 0.227684
\(546\) 0 0
\(547\) −2.24621 −0.0960411 −0.0480205 0.998846i \(-0.515291\pi\)
−0.0480205 + 0.998846i \(0.515291\pi\)
\(548\) 39.0540 + 67.6435i 1.66830 + 2.88959i
\(549\) 4.31534 7.47439i 0.184174 0.318999i
\(550\) −2.00000 + 3.46410i −0.0852803 + 0.147710i
\(551\) 23.8078 + 41.2363i 1.01424 + 1.75672i
\(552\) −32.0000 −1.36201
\(553\) 0 0
\(554\) 0.630683 0.0267952
\(555\) −4.68466 8.11407i −0.198853 0.344423i
\(556\) 34.4924 59.7426i 1.46280 2.53365i
\(557\) 6.56155 11.3649i 0.278022 0.481548i −0.692871 0.721061i \(-0.743655\pi\)
0.970893 + 0.239513i \(0.0769879\pi\)
\(558\) 0 0
\(559\) 0.384472 0.0162614
\(560\) 0 0
\(561\) 1.06913 0.0451387
\(562\) 15.9309 + 27.5931i 0.672003 + 1.16394i
\(563\) 14.0000 24.2487i 0.590030 1.02196i −0.404198 0.914671i \(-0.632449\pi\)
0.994228 0.107290i \(-0.0342173\pi\)
\(564\) 30.9309 53.5738i 1.30242 2.25587i
\(565\) 7.00000 + 12.1244i 0.294492 + 0.510075i
\(566\) 28.9848 1.21832
\(567\) 0 0
\(568\) −52.4924 −2.20253
\(569\) 15.4924 + 26.8337i 0.649476 + 1.12493i 0.983248 + 0.182272i \(0.0583451\pi\)
−0.333772 + 0.942654i \(0.608322\pi\)
\(570\) −14.2462 + 24.6752i −0.596708 + 1.03353i
\(571\) −20.2462 + 35.0675i −0.847278 + 1.46753i 0.0363509 + 0.999339i \(0.488427\pi\)
−0.883629 + 0.468189i \(0.844907\pi\)
\(572\) 1.56155 + 2.70469i 0.0652918 + 0.113089i
\(573\) −21.1771 −0.884685
\(574\) 0 0
\(575\) 3.12311 0.130243
\(576\) 0.403882 + 0.699544i 0.0168284 + 0.0291477i
\(577\) 12.0270 20.8314i 0.500690 0.867221i −0.499310 0.866424i \(-0.666413\pi\)
1.00000 0.000796982i \(-0.000253687\pi\)
\(578\) −21.5270 + 37.2858i −0.895405 + 1.55089i
\(579\) −15.1231 26.1940i −0.628495 1.08858i
\(580\) 30.4924 1.26613
\(581\) 0 0
\(582\) −23.2311 −0.962958
\(583\) −4.00000 6.92820i −0.165663 0.286937i
\(584\) −40.1771 + 69.5887i −1.66254 + 2.87960i
\(585\) 0.123106 0.213225i 0.00508979 0.00881578i
\(586\) −3.43845 5.95557i −0.142041 0.246022i
\(587\) −26.2462 −1.08330 −0.541649 0.840605i \(-0.682200\pi\)
−0.541649 + 0.840605i \(0.682200\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −5.12311 8.87348i −0.210915 0.365315i
\(591\) −0.876894 + 1.51883i −0.0360706 + 0.0624761i
\(592\) −23.0540 + 39.9307i −0.947513 + 1.64114i
\(593\) 13.7808 + 23.8690i 0.565909 + 0.980183i 0.996965 + 0.0778573i \(0.0248079\pi\)
−0.431056 + 0.902325i \(0.641859\pi\)
\(594\) −22.2462 −0.912773
\(595\) 0 0
\(596\) 55.8617 2.28819
\(597\) 1.36932 + 2.37173i 0.0560424 + 0.0970683i
\(598\) 1.75379 3.03765i 0.0717178 0.124219i
\(599\) 5.90388 10.2258i 0.241226 0.417816i −0.719838 0.694142i \(-0.755784\pi\)
0.961064 + 0.276327i \(0.0891171\pi\)
\(600\) 5.12311 + 8.87348i 0.209150 + 0.362258i
\(601\) 6.49242 0.264831 0.132416 0.991194i \(-0.457727\pi\)
0.132416 + 0.991194i \(0.457727\pi\)
\(602\) 0 0
\(603\) −5.75379 −0.234312
\(604\) 15.8078 + 27.3799i 0.643209 + 1.11407i
\(605\) 4.28078 7.41452i 0.174038 0.301443i
\(606\) −32.4924 + 56.2785i −1.31991 + 2.28616i
\(607\) 21.0270 + 36.4198i 0.853459 + 1.47823i 0.878067 + 0.478537i \(0.158833\pi\)
−0.0246081 + 0.999697i \(0.507834\pi\)
\(608\) 46.7386 1.89550
\(609\) 0 0
\(610\) −39.3693 −1.59402
\(611\) 1.90388 + 3.29762i 0.0770228 + 0.133407i
\(612\) −0.561553 + 0.972638i −0.0226994 + 0.0393166i
\(613\) −20.3693 + 35.2807i −0.822709 + 1.42497i 0.0809488 + 0.996718i \(0.474205\pi\)
−0.903658 + 0.428255i \(0.859128\pi\)
\(614\) −24.7386 42.8486i −0.998370 1.72923i
\(615\) 8.00000 0.322591
\(616\) 0 0
\(617\) 32.2462 1.29818 0.649092 0.760710i \(-0.275149\pi\)
0.649092 + 0.760710i \(0.275149\pi\)
\(618\) 11.1231 + 19.2658i 0.447437 + 0.774983i
\(619\) −16.0540 + 27.8063i −0.645264 + 1.11763i 0.338977 + 0.940795i \(0.389919\pi\)
−0.984241 + 0.176835i \(0.943414\pi\)
\(620\) 0 0
\(621\) 8.68466 + 15.0423i 0.348503 + 0.603625i
\(622\) −80.9848 −3.24720
\(623\) 0 0
\(624\) 5.26137 0.210623
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −28.5616 + 49.4701i −1.14155 + 1.97722i
\(627\) −8.68466 + 15.0423i −0.346832 + 0.600730i
\(628\) −46.1771 79.9811i −1.84267 3.19159i
\(629\) −2.63068 −0.104892
\(630\) 0 0
\(631\) −11.8078 −0.470060 −0.235030 0.971988i \(-0.575519\pi\)
−0.235030 + 0.971988i \(0.575519\pi\)
\(632\) −8.00000 13.8564i −0.318223 0.551178i
\(633\) −10.9730 + 19.0058i −0.436138 + 0.755413i
\(634\) 13.4384 23.2761i 0.533709 0.924411i
\(635\) 3.12311 + 5.40938i 0.123937 + 0.214665i
\(636\) −36.4924 −1.44702
\(637\) 0 0
\(638\) 26.7386 1.05859
\(639\) 2.24621 + 3.89055i 0.0888587 + 0.153908i
\(640\) −4.71922 + 8.17394i −0.186544 + 0.323103i
\(641\) −1.00000 + 1.73205i −0.0394976 + 0.0684119i −0.885098 0.465404i \(-0.845909\pi\)
0.845601 + 0.533816i \(0.179242\pi\)
\(642\) 26.7386 + 46.3127i 1.05529 + 1.82782i
\(643\) 1.56155 0.0615816 0.0307908 0.999526i \(-0.490197\pi\)
0.0307908 + 0.999526i \(0.490197\pi\)
\(644\) 0 0
\(645\) 1.36932 0.0539168
\(646\) 4.00000 + 6.92820i 0.157378 + 0.272587i
\(647\) −18.2462 + 31.6034i −0.717333 + 1.24246i 0.244720 + 0.969594i \(0.421304\pi\)
−0.962053 + 0.272863i \(0.912029\pi\)
\(648\) −22.9654 + 39.7773i −0.902167 + 1.56260i
\(649\) −3.12311 5.40938i −0.122593 0.212337i
\(650\) −1.12311 −0.0440518
\(651\) 0 0
\(652\) −32.4924 −1.27250
\(653\) 16.6155 + 28.7789i 0.650216 + 1.12621i 0.983070 + 0.183229i \(0.0586549\pi\)
−0.332854 + 0.942978i \(0.608012\pi\)
\(654\) 10.6307 18.4129i 0.415693 0.720001i
\(655\) 0.438447 0.759413i 0.0171315 0.0296727i
\(656\) −19.6847 34.0948i −0.768557 1.33118i
\(657\) 6.87689 0.268293
\(658\) 0 0
\(659\) 9.17708 0.357488 0.178744 0.983896i \(-0.442797\pi\)
0.178744 + 0.983896i \(0.442797\pi\)
\(660\) 5.56155 + 9.63289i 0.216483 + 0.374960i
\(661\) 2.56155 4.43674i 0.0996329 0.172569i −0.811900 0.583797i \(-0.801567\pi\)
0.911533 + 0.411228i \(0.134900\pi\)
\(662\) 15.3693 26.6204i 0.597345 1.03463i
\(663\) 0.150093 + 0.259969i 0.00582914 + 0.0100964i
\(664\) −26.2462 −1.01855
\(665\) 0 0
\(666\) 8.63068 0.334432
\(667\) −10.4384 18.0799i −0.404178 0.700057i
\(668\) 15.8078 27.3799i 0.611621 1.05936i
\(669\) 1.90388 3.29762i 0.0736083 0.127493i
\(670\) 13.1231 + 22.7299i 0.506990 + 0.878132i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 31.8617 1.22818 0.614090 0.789236i \(-0.289523\pi\)
0.614090 + 0.789236i \(0.289523\pi\)
\(674\) −1.93087 3.34436i −0.0743743 0.128820i
\(675\) 2.78078 4.81645i 0.107032 0.185385i
\(676\) 29.2116 50.5961i 1.12352 1.94600i
\(677\) −2.46543 4.27026i −0.0947544 0.164119i 0.814752 0.579810i \(-0.196873\pi\)
−0.909506 + 0.415691i \(0.863540\pi\)
\(678\) 56.0000 2.15067
\(679\) 0 0
\(680\) 2.87689 0.110324
\(681\) −8.83475 15.3022i −0.338548 0.586383i
\(682\) 0 0
\(683\) 3.36932 5.83583i 0.128923 0.223302i −0.794336 0.607478i \(-0.792181\pi\)
0.923260 + 0.384176i \(0.125515\pi\)
\(684\) −9.12311 15.8017i −0.348831 0.604192i
\(685\) −17.1231 −0.654240
\(686\) 0 0
\(687\) 16.9848 0.648012
\(688\) −3.36932 5.83583i −0.128454 0.222489i
\(689\) 1.12311 1.94528i 0.0427869 0.0741091i
\(690\) 6.24621 10.8188i 0.237789 0.411863i
\(691\) 12.2462 + 21.2111i 0.465868 + 0.806907i 0.999240 0.0389738i \(-0.0124089\pi\)
−0.533372 + 0.845881i \(0.679076\pi\)
\(692\) −20.2462 −0.769645
\(693\) 0 0
\(694\) −18.2462 −0.692617
\(695\) 7.56155 + 13.0970i 0.286826 + 0.496797i
\(696\) 34.2462 59.3162i 1.29810 2.24837i
\(697\) 1.12311 1.94528i 0.0425407 0.0736826i
\(698\) 13.4384 + 23.2761i 0.508653 + 0.881012i
\(699\) 8.00000 0.302588
\(700\) 0 0
\(701\) 28.9309 1.09270 0.546352 0.837556i \(-0.316016\pi\)
0.546352 + 0.837556i \(0.316016\pi\)
\(702\) −3.12311 5.40938i −0.117874 0.204164i
\(703\) 21.3693 37.0127i 0.805959 1.39596i
\(704\) 1.12311 1.94528i 0.0423286 0.0733153i
\(705\) 6.78078 + 11.7446i 0.255379 + 0.442329i
\(706\) −14.8769 −0.559899
\(707\) 0 0
\(708\) −28.4924 −1.07081
\(709\) −13.5885 23.5360i −0.510328 0.883915i −0.999928 0.0119675i \(-0.996191\pi\)
0.489600 0.871947i \(-0.337143\pi\)
\(710\) 10.2462 17.7470i 0.384533 0.666031i
\(711\) −0.684658 + 1.18586i −0.0256767 + 0.0444733i
\(712\) −3.68466 6.38202i −0.138088 0.239176i
\(713\) 0 0
\(714\) 0 0
\(715\) −0.684658 −0.0256048
\(716\) −45.6155 79.0084i −1.70473 2.95268i
\(717\) −15.4654 + 26.7869i −0.577567 + 1.00038i
\(718\) 10.2462 17.7470i 0.382385 0.662311i
\(719\) −4.19224 7.26117i −0.156344 0.270796i 0.777204 0.629249i \(-0.216638\pi\)
−0.933548 + 0.358453i \(0.883304\pi\)
\(720\) −4.31534 −0.160823
\(721\) 0 0
\(722\) −81.3002 −3.02568
\(723\) 3.31534 + 5.74234i 0.123299 + 0.213560i
\(724\) 40.1771 69.5887i 1.49317 2.58625i
\(725\) −3.34233 + 5.78908i −0.124131 + 0.215001i
\(726\) −17.1231 29.6581i −0.635498 1.10071i
\(727\) 52.4924 1.94684 0.973418 0.229035i \(-0.0735572\pi\)
0.973418 + 0.229035i \(0.0735572\pi\)
\(728\) 0 0
\(729\) 29.9848 1.11055
\(730\) −15.6847 27.1666i −0.580515 1.00548i
\(731\) 0.192236 0.332962i 0.00711010 0.0123151i
\(732\) −54.7386 + 94.8101i −2.02320 + 3.50428i
\(733\) −3.34233 5.78908i −0.123452 0.213825i 0.797675 0.603088i \(-0.206063\pi\)
−0.921127 + 0.389263i \(0.872730\pi\)
\(734\) 22.2462 0.821123
\(735\) 0 0
\(736\) −20.4924 −0.755361
\(737\) 8.00000 + 13.8564i 0.294684 + 0.510407i
\(738\) −3.68466 + 6.38202i −0.135634 + 0.234925i
\(739\) −17.4654 + 30.2510i −0.642476 + 1.11280i 0.342402 + 0.939554i \(0.388760\pi\)
−0.984878 + 0.173248i \(0.944574\pi\)
\(740\) −13.6847 23.7025i −0.503058 0.871322i
\(741\) −4.87689 −0.179157
\(742\) 0 0
\(743\) −32.9848 −1.21010 −0.605048 0.796189i \(-0.706846\pi\)
−0.605048 + 0.796189i \(0.706846\pi\)
\(744\) 0 0
\(745\) −6.12311 + 10.6055i −0.224333 + 0.388557i
\(746\) 5.93087 10.2726i 0.217145 0.376105i
\(747\) 1.12311 + 1.94528i 0.0410923 + 0.0711739i
\(748\) 3.12311 0.114192
\(749\) 0 0
\(750\) −4.00000 −0.146059
\(751\) −8.53457 14.7823i −0.311431 0.539414i 0.667242 0.744841i \(-0.267475\pi\)
−0.978672 + 0.205428i \(0.934142\pi\)
\(752\) 33.3693 57.7974i 1.21685 2.10765i
\(753\) 6.93087 12.0046i 0.252575 0.437473i
\(754\) 3.75379 + 6.50175i 0.136705 + 0.236780i
\(755\) −6.93087 −0.252240
\(756\) 0 0
\(757\) 39.3693 1.43090 0.715451 0.698663i \(-0.246221\pi\)
0.715451 + 0.698663i \(0.246221\pi\)
\(758\) −21.1231 36.5863i −0.767226 1.32887i
\(759\) 3.80776 6.59524i 0.138213 0.239392i
\(760\) −23.3693 + 40.4768i −0.847694 + 1.46825i
\(761\) −24.1231 41.7824i −0.874462 1.51461i −0.857335 0.514759i \(-0.827881\pi\)
−0.0171270 0.999853i \(-0.505452\pi\)
\(762\) 24.9848 0.905105
\(763\) 0 0
\(764\) −61.8617 −2.23808
\(765\) −0.123106 0.213225i −0.00445089 0.00770917i
\(766\) 8.00000 13.8564i 0.289052 0.500652i
\(767\) 0.876894 1.51883i 0.0316628 0.0548416i
\(768\) 21.1231 + 36.5863i 0.762214 + 1.32019i
\(769\) −42.4924 −1.53232 −0.766158 0.642652i \(-0.777834\pi\)
−0.766158 + 0.642652i \(0.777834\pi\)
\(770\) 0 0
\(771\) −16.3845 −0.590072
\(772\) −44.1771 76.5169i −1.58997 2.75391i
\(773\) −18.4654 + 31.9831i −0.664156 + 1.15035i 0.315358 + 0.948973i \(0.397875\pi\)
−0.979514 + 0.201378i \(0.935458\pi\)
\(774\) −0.630683 + 1.09238i −0.0226694 + 0.0392646i
\(775\) 0 0
\(776\) −38.1080 −1.36800
\(777\) 0 0
\(778\) 63.8617 2.28955
\(779\) 18.2462 + 31.6034i 0.653738 + 1.13231i
\(780\) −1.56155 + 2.70469i −0.0559126 + 0.0968434i
\(781\) 6.24621 10.8188i 0.223507 0.387125i
\(782\) −1.75379 3.03765i −0.0627154 0.108626i
\(783\) −37.1771 −1.32860
\(784\)