Properties

Label 546.2.o.d.265.1
Level $546$
Weight $2$
Character 546.265
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.7442857984.4
Defining polynomial: \(x^{8} + 26 x^{6} + 205 x^{4} + 540 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 265.1
Root \(-3.73923i\) of defining polynomial
Character \(\chi\) \(=\) 546.265
Dual form 546.2.o.d.307.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-0.0951965 - 0.0951965i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.0951965 - 2.64404i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{3} -1.00000i q^{4} +(-0.0951965 - 0.0951965i) q^{5} +(0.707107 + 0.707107i) q^{6} +(-0.0951965 - 2.64404i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +0.134628 q^{10} +(-3.64404 - 3.64404i) q^{11} -1.00000 q^{12} +(-2.00000 + 3.00000i) q^{13} +(1.93693 + 1.80230i) q^{14} +(-0.0951965 + 0.0951965i) q^{15} -1.00000 q^{16} -5.98188 q^{17} +(0.707107 - 0.707107i) q^{18} +(4.19288 + 4.19288i) q^{19} +(-0.0951965 + 0.0951965i) q^{20} +(-2.64404 + 0.0951965i) q^{21} +5.15345 q^{22} +4.69380i q^{23} +(0.707107 - 0.707107i) q^{24} -4.98188i q^{25} +(-0.707107 - 3.53553i) q^{26} +1.00000i q^{27} +(-2.64404 + 0.0951965i) q^{28} -4.59428 q^{29} -0.134628i q^{30} +(0.739235 + 0.739235i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-3.64404 + 3.64404i) q^{33} +(4.22982 - 4.22982i) q^{34} +(-0.242641 + 0.260765i) q^{35} +1.00000i q^{36} +(-4.83443 - 4.83443i) q^{37} -5.92963 q^{38} +(3.00000 + 2.00000i) q^{39} -0.134628i q^{40} +(-3.04544 - 3.04544i) q^{41} +(1.80230 - 1.93693i) q^{42} -8.78467i q^{43} +(-3.64404 + 3.64404i) q^{44} +(0.0951965 + 0.0951965i) q^{45} +(-3.31902 - 3.31902i) q^{46} +(-3.28808 + 3.28808i) q^{47} +1.00000i q^{48} +(-6.98188 + 0.503406i) q^{49} +(3.52272 + 3.52272i) q^{50} +5.98188i q^{51} +(3.00000 + 2.00000i) q^{52} +1.09768 q^{53} +(-0.707107 - 0.707107i) q^{54} +0.693799i q^{55} +(1.80230 - 1.93693i) q^{56} +(4.19288 - 4.19288i) q^{57} +(3.24864 - 3.24864i) q^{58} +(-1.30620 + 1.30620i) q^{59} +(0.0951965 + 0.0951965i) q^{60} -5.98188i q^{61} -1.04544 q^{62} +(0.0951965 + 2.64404i) q^{63} +1.00000i q^{64} +(0.475982 - 0.0951965i) q^{65} -5.15345i q^{66} +(-0.0454356 + 0.0454356i) q^{67} +5.98188i q^{68} +4.69380 q^{69} +(-0.0128161 - 0.355962i) q^{70} +(8.69380 - 8.69380i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(4.83443 - 4.83443i) q^{73} +6.83692 q^{74} -4.98188 q^{75} +(4.19288 - 4.19288i) q^{76} +(-9.28808 + 9.98188i) q^{77} +(-3.53553 + 0.707107i) q^{78} -11.5780 q^{79} +(0.0951965 + 0.0951965i) q^{80} +1.00000 q^{81} +4.30690 q^{82} +(1.28808 + 1.28808i) q^{83} +(0.0951965 + 2.64404i) q^{84} +(0.569453 + 0.569453i) q^{85} +(6.21170 + 6.21170i) q^{86} +4.59428i q^{87} -5.15345i q^{88} +(9.21770 - 9.21770i) q^{89} -0.134628 q^{90} +(8.12251 + 5.00249i) q^{91} +4.69380 q^{92} +(0.739235 - 0.739235i) q^{93} -4.65004i q^{94} -0.798295i q^{95} +(-0.707107 - 0.707107i) q^{96} +(9.97506 + 9.97506i) q^{97} +(4.58097 - 5.29289i) q^{98} +(3.64404 + 3.64404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} + O(q^{10}) \) \( 8q + 4q^{5} + 4q^{7} - 8q^{9} - 4q^{10} - 8q^{11} - 8q^{12} - 16q^{13} + 4q^{15} - 8q^{16} + 12q^{17} - 4q^{19} + 4q^{20} + 4q^{22} - 12q^{29} - 20q^{31} - 8q^{33} + 24q^{34} + 32q^{35} - 8q^{37} - 12q^{38} + 24q^{39} - 16q^{41} + 4q^{42} - 8q^{44} - 4q^{45} - 20q^{46} + 16q^{47} + 4q^{49} + 24q^{50} + 24q^{52} - 24q^{53} + 4q^{56} - 4q^{57} - 16q^{58} - 28q^{59} - 4q^{60} - 4q^{63} - 20q^{65} + 8q^{67} + 20q^{69} + 24q^{70} + 52q^{71} + 8q^{73} - 4q^{74} + 20q^{75} - 4q^{76} - 32q^{77} - 48q^{79} - 4q^{80} + 8q^{81} - 40q^{82} - 32q^{83} - 4q^{84} + 20q^{85} - 20q^{86} - 4q^{89} + 4q^{90} - 8q^{91} + 20q^{92} - 20q^{93} + 36q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.00000i 0.577350i
\(4\) 1.00000i 0.500000i
\(5\) −0.0951965 0.0951965i −0.0425731 0.0425731i 0.685500 0.728073i \(-0.259584\pi\)
−0.728073 + 0.685500i \(0.759584\pi\)
\(6\) 0.707107 + 0.707107i 0.288675 + 0.288675i
\(7\) −0.0951965 2.64404i −0.0359809 0.999352i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −1.00000 −0.333333
\(10\) 0.134628 0.0425731
\(11\) −3.64404 3.64404i −1.09872 1.09872i −0.994561 0.104158i \(-0.966785\pi\)
−0.104158 0.994561i \(-0.533215\pi\)
\(12\) −1.00000 −0.288675
\(13\) −2.00000 + 3.00000i −0.554700 + 0.832050i
\(14\) 1.93693 + 1.80230i 0.517667 + 0.481686i
\(15\) −0.0951965 + 0.0951965i −0.0245796 + 0.0245796i
\(16\) −1.00000 −0.250000
\(17\) −5.98188 −1.45082 −0.725409 0.688318i \(-0.758349\pi\)
−0.725409 + 0.688318i \(0.758349\pi\)
\(18\) 0.707107 0.707107i 0.166667 0.166667i
\(19\) 4.19288 + 4.19288i 0.961913 + 0.961913i 0.999301 0.0373882i \(-0.0119038\pi\)
−0.0373882 + 0.999301i \(0.511904\pi\)
\(20\) −0.0951965 + 0.0951965i −0.0212866 + 0.0212866i
\(21\) −2.64404 + 0.0951965i −0.576976 + 0.0207736i
\(22\) 5.15345 1.09872
\(23\) 4.69380i 0.978725i 0.872081 + 0.489362i \(0.162770\pi\)
−0.872081 + 0.489362i \(0.837230\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 4.98188i 0.996375i
\(26\) −0.707107 3.53553i −0.138675 0.693375i
\(27\) 1.00000i 0.192450i
\(28\) −2.64404 + 0.0951965i −0.499676 + 0.0179904i
\(29\) −4.59428 −0.853136 −0.426568 0.904456i \(-0.640277\pi\)
−0.426568 + 0.904456i \(0.640277\pi\)
\(30\) 0.134628i 0.0245796i
\(31\) 0.739235 + 0.739235i 0.132770 + 0.132770i 0.770369 0.637598i \(-0.220072\pi\)
−0.637598 + 0.770369i \(0.720072\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −3.64404 + 3.64404i −0.634346 + 0.634346i
\(34\) 4.22982 4.22982i 0.725409 0.725409i
\(35\) −0.242641 + 0.260765i −0.0410138 + 0.0440774i
\(36\) 1.00000i 0.166667i
\(37\) −4.83443 4.83443i −0.794776 0.794776i 0.187491 0.982266i \(-0.439965\pi\)
−0.982266 + 0.187491i \(0.939965\pi\)
\(38\) −5.92963 −0.961913
\(39\) 3.00000 + 2.00000i 0.480384 + 0.320256i
\(40\) 0.134628i 0.0212866i
\(41\) −3.04544 3.04544i −0.475617 0.475617i 0.428110 0.903727i \(-0.359180\pi\)
−0.903727 + 0.428110i \(0.859180\pi\)
\(42\) 1.80230 1.93693i 0.278101 0.298875i
\(43\) 8.78467i 1.33965i −0.742519 0.669825i \(-0.766369\pi\)
0.742519 0.669825i \(-0.233631\pi\)
\(44\) −3.64404 + 3.64404i −0.549359 + 0.549359i
\(45\) 0.0951965 + 0.0951965i 0.0141910 + 0.0141910i
\(46\) −3.31902 3.31902i −0.489362 0.489362i
\(47\) −3.28808 + 3.28808i −0.479615 + 0.479615i −0.905009 0.425393i \(-0.860136\pi\)
0.425393 + 0.905009i \(0.360136\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −6.98188 + 0.503406i −0.997411 + 0.0719152i
\(50\) 3.52272 + 3.52272i 0.498188 + 0.498188i
\(51\) 5.98188i 0.837630i
\(52\) 3.00000 + 2.00000i 0.416025 + 0.277350i
\(53\) 1.09768 0.150778 0.0753892 0.997154i \(-0.475980\pi\)
0.0753892 + 0.997154i \(0.475980\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 0.693799i 0.0935518i
\(56\) 1.80230 1.93693i 0.240843 0.258833i
\(57\) 4.19288 4.19288i 0.555360 0.555360i
\(58\) 3.24864 3.24864i 0.426568 0.426568i
\(59\) −1.30620 + 1.30620i −0.170053 + 0.170053i −0.787003 0.616950i \(-0.788368\pi\)
0.616950 + 0.787003i \(0.288368\pi\)
\(60\) 0.0951965 + 0.0951965i 0.0122898 + 0.0122898i
\(61\) 5.98188i 0.765901i −0.923769 0.382950i \(-0.874908\pi\)
0.923769 0.382950i \(-0.125092\pi\)
\(62\) −1.04544 −0.132770
\(63\) 0.0951965 + 2.64404i 0.0119936 + 0.333117i
\(64\) 1.00000i 0.125000i
\(65\) 0.475982 0.0951965i 0.0590383 0.0118077i
\(66\) 5.15345i 0.634346i
\(67\) −0.0454356 + 0.0454356i −0.00555084 + 0.00555084i −0.709877 0.704326i \(-0.751249\pi\)
0.704326 + 0.709877i \(0.251249\pi\)
\(68\) 5.98188i 0.725409i
\(69\) 4.69380 0.565067
\(70\) −0.0128161 0.355962i −0.00153182 0.0425456i
\(71\) 8.69380 8.69380i 1.03176 1.03176i 0.0322854 0.999479i \(-0.489721\pi\)
0.999479 0.0322854i \(-0.0102786\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 4.83443 4.83443i 0.565827 0.565827i −0.365129 0.930957i \(-0.618975\pi\)
0.930957 + 0.365129i \(0.118975\pi\)
\(74\) 6.83692 0.794776
\(75\) −4.98188 −0.575257
\(76\) 4.19288 4.19288i 0.480956 0.480956i
\(77\) −9.28808 + 9.98188i −1.05847 + 1.13754i
\(78\) −3.53553 + 0.707107i −0.400320 + 0.0800641i
\(79\) −11.5780 −1.30263 −0.651313 0.758809i \(-0.725781\pi\)
−0.651313 + 0.758809i \(0.725781\pi\)
\(80\) 0.0951965 + 0.0951965i 0.0106433 + 0.0106433i
\(81\) 1.00000 0.111111
\(82\) 4.30690 0.475617
\(83\) 1.28808 + 1.28808i 0.141385 + 0.141385i 0.774257 0.632872i \(-0.218124\pi\)
−0.632872 + 0.774257i \(0.718124\pi\)
\(84\) 0.0951965 + 2.64404i 0.0103868 + 0.288488i
\(85\) 0.569453 + 0.569453i 0.0617659 + 0.0617659i
\(86\) 6.21170 + 6.21170i 0.669825 + 0.669825i
\(87\) 4.59428i 0.492558i
\(88\) 5.15345i 0.549359i
\(89\) 9.21770 9.21770i 0.977075 0.977075i −0.0226684 0.999743i \(-0.507216\pi\)
0.999743 + 0.0226684i \(0.00721619\pi\)
\(90\) −0.134628 −0.0141910
\(91\) 8.12251 + 5.00249i 0.851470 + 0.524403i
\(92\) 4.69380 0.489362
\(93\) 0.739235 0.739235i 0.0766551 0.0766551i
\(94\) 4.65004i 0.479615i
\(95\) 0.798295i 0.0819033i
\(96\) −0.707107 0.707107i −0.0721688 0.0721688i
\(97\) 9.97506 + 9.97506i 1.01281 + 1.01281i 0.999917 + 0.0128974i \(0.00410548\pi\)
0.0128974 + 0.999917i \(0.495895\pi\)
\(98\) 4.58097 5.29289i 0.462748 0.534663i
\(99\) 3.64404 + 3.64404i 0.366240 + 0.366240i
\(100\) −4.98188 −0.498188
\(101\) 3.09271 0.307736 0.153868 0.988091i \(-0.450827\pi\)
0.153868 + 0.988091i \(0.450827\pi\)
\(102\) −4.22982 4.22982i −0.418815 0.418815i
\(103\) 8.31301 0.819106 0.409553 0.912286i \(-0.365685\pi\)
0.409553 + 0.912286i \(0.365685\pi\)
\(104\) −3.53553 + 0.707107i −0.346688 + 0.0693375i
\(105\) 0.260765 + 0.242641i 0.0254481 + 0.0236793i
\(106\) −0.776179 + 0.776179i −0.0753892 + 0.0753892i
\(107\) −18.9569 −1.83264 −0.916318 0.400451i \(-0.868853\pi\)
−0.916318 + 0.400451i \(0.868853\pi\)
\(108\) 1.00000 0.0962250
\(109\) 11.3197 11.3197i 1.08423 1.08423i 0.0881221 0.996110i \(-0.471913\pi\)
0.996110 0.0881221i \(-0.0280866\pi\)
\(110\) −0.490590 0.490590i −0.0467759 0.0467759i
\(111\) −4.83443 + 4.83443i −0.458864 + 0.458864i
\(112\) 0.0951965 + 2.64404i 0.00899522 + 0.249838i
\(113\) −0.716898 −0.0674400 −0.0337200 0.999431i \(-0.510735\pi\)
−0.0337200 + 0.999431i \(0.510735\pi\)
\(114\) 5.92963i 0.555360i
\(115\) 0.446833 0.446833i 0.0416674 0.0416674i
\(116\) 4.59428i 0.426568i
\(117\) 2.00000 3.00000i 0.184900 0.277350i
\(118\) 1.84725i 0.170053i
\(119\) 0.569453 + 15.8163i 0.0522017 + 1.44988i
\(120\) −0.134628 −0.0122898
\(121\) 15.5580i 1.41437i
\(122\) 4.22982 + 4.22982i 0.382950 + 0.382950i
\(123\) −3.04544 + 3.04544i −0.274598 + 0.274598i
\(124\) 0.739235 0.739235i 0.0663852 0.0663852i
\(125\) −0.950239 + 0.950239i −0.0849920 + 0.0849920i
\(126\) −1.93693 1.80230i −0.172556 0.160562i
\(127\) 2.28126i 0.202429i 0.994865 + 0.101215i \(0.0322729\pi\)
−0.994865 + 0.101215i \(0.967727\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −8.78467 −0.773447
\(130\) −0.269256 + 0.403884i −0.0236153 + 0.0354230i
\(131\) 7.79148i 0.680745i −0.940291 0.340372i \(-0.889447\pi\)
0.940291 0.340372i \(-0.110553\pi\)
\(132\) 3.64404 + 3.64404i 0.317173 + 0.317173i
\(133\) 10.6870 11.4853i 0.926679 0.995900i
\(134\) 0.0642556i 0.00555084i
\(135\) 0.0951965 0.0951965i 0.00819321 0.00819321i
\(136\) −4.22982 4.22982i −0.362704 0.362704i
\(137\) 1.90480 + 1.90480i 0.162738 + 0.162738i 0.783779 0.621040i \(-0.213290\pi\)
−0.621040 + 0.783779i \(0.713290\pi\)
\(138\) −3.31902 + 3.31902i −0.282533 + 0.282533i
\(139\) 0.716898i 0.0608065i 0.999538 + 0.0304032i \(0.00967914\pi\)
−0.999538 + 0.0304032i \(0.990321\pi\)
\(140\) 0.260765 + 0.242641i 0.0220387 + 0.0205069i
\(141\) 3.28808 + 3.28808i 0.276906 + 0.276906i
\(142\) 12.2949i 1.03176i
\(143\) 18.2202 3.64404i 1.52365 0.304730i
\(144\) 1.00000 0.0833333
\(145\) 0.437359 + 0.437359i 0.0363207 + 0.0363207i
\(146\) 6.83692i 0.565827i
\(147\) 0.503406 + 6.98188i 0.0415202 + 0.575855i
\(148\) −4.83443 + 4.83443i −0.397388 + 0.397388i
\(149\) −8.22452 + 8.22452i −0.673779 + 0.673779i −0.958585 0.284806i \(-0.908071\pi\)
0.284806 + 0.958585i \(0.408071\pi\)
\(150\) 3.52272 3.52272i 0.287629 0.287629i
\(151\) 13.6713 + 13.6713i 1.11256 + 1.11256i 0.992803 + 0.119755i \(0.0382110\pi\)
0.119755 + 0.992803i \(0.461789\pi\)
\(152\) 5.92963i 0.480956i
\(153\) 5.98188 0.483606
\(154\) −0.490590 13.6259i −0.0395329 1.09801i
\(155\) 0.140745i 0.0113049i
\(156\) 2.00000 3.00000i 0.160128 0.240192i
\(157\) 12.3627i 0.986648i 0.869846 + 0.493324i \(0.164218\pi\)
−0.869846 + 0.493324i \(0.835782\pi\)
\(158\) 8.18688 8.18688i 0.651313 0.651313i
\(159\) 1.09768i 0.0870520i
\(160\) −0.134628 −0.0106433
\(161\) 12.4106 0.446833i 0.978091 0.0352154i
\(162\) −0.707107 + 0.707107i −0.0555556 + 0.0555556i
\(163\) 8.72111 + 8.72111i 0.683090 + 0.683090i 0.960695 0.277605i \(-0.0895407\pi\)
−0.277605 + 0.960695i \(0.589541\pi\)
\(164\) −3.04544 + 3.04544i −0.237809 + 0.237809i
\(165\) 0.693799 0.0540122
\(166\) −1.82161 −0.141385
\(167\) 13.3129 13.3129i 1.03018 1.03018i 0.0306531 0.999530i \(-0.490241\pi\)
0.999530 0.0306531i \(-0.00975870\pi\)
\(168\) −1.93693 1.80230i −0.149437 0.139051i
\(169\) −5.00000 12.0000i −0.384615 0.923077i
\(170\) −0.805329 −0.0617659
\(171\) −4.19288 4.19288i −0.320638 0.320638i
\(172\) −8.78467 −0.669825
\(173\) −9.58296 −0.728579 −0.364290 0.931286i \(-0.618688\pi\)
−0.364290 + 0.931286i \(0.618688\pi\)
\(174\) −3.24864 3.24864i −0.246279 0.246279i
\(175\) −13.1723 + 0.474257i −0.995730 + 0.0358504i
\(176\) 3.64404 + 3.64404i 0.274680 + 0.274680i
\(177\) 1.30620 + 1.30620i 0.0981801 + 0.0981801i
\(178\) 13.0358i 0.977075i
\(179\) 6.90729i 0.516275i −0.966108 0.258138i \(-0.916891\pi\)
0.966108 0.258138i \(-0.0831088\pi\)
\(180\) 0.0951965 0.0951965i 0.00709552 0.00709552i
\(181\) −22.3445 −1.66086 −0.830428 0.557126i \(-0.811904\pi\)
−0.830428 + 0.557126i \(0.811904\pi\)
\(182\) −9.28077 + 2.20619i −0.687937 + 0.163534i
\(183\) −5.98188 −0.442193
\(184\) −3.31902 + 3.31902i −0.244681 + 0.244681i
\(185\) 0.920441i 0.0676722i
\(186\) 1.04544i 0.0766551i
\(187\) 21.7982 + 21.7982i 1.59404 + 1.59404i
\(188\) 3.28808 + 3.28808i 0.239808 + 0.239808i
\(189\) 2.64404 0.0951965i 0.192325 0.00692452i
\(190\) 0.564480 + 0.564480i 0.0409516 + 0.0409516i
\(191\) 12.0315 0.870570 0.435285 0.900293i \(-0.356648\pi\)
0.435285 + 0.900293i \(0.356648\pi\)
\(192\) 1.00000 0.0721688
\(193\) −14.2700 14.2700i −1.02717 1.02717i −0.999620 0.0275533i \(-0.991228\pi\)
−0.0275533 0.999620i \(-0.508772\pi\)
\(194\) −14.1069 −1.01281
\(195\) −0.0951965 0.475982i −0.00681716 0.0340858i
\(196\) 0.503406 + 6.98188i 0.0359576 + 0.498705i
\(197\) −5.54884 + 5.54884i −0.395339 + 0.395339i −0.876585 0.481247i \(-0.840184\pi\)
0.481247 + 0.876585i \(0.340184\pi\)
\(198\) −5.15345 −0.366240
\(199\) −9.16546 −0.649722 −0.324861 0.945762i \(-0.605318\pi\)
−0.324861 + 0.945762i \(0.605318\pi\)
\(200\) 3.52272 3.52272i 0.249094 0.249094i
\(201\) 0.0454356 + 0.0454356i 0.00320478 + 0.00320478i
\(202\) −2.18688 + 2.18688i −0.153868 + 0.153868i
\(203\) 0.437359 + 12.1474i 0.0306966 + 0.852583i
\(204\) 5.98188 0.418815
\(205\) 0.579829i 0.0404970i
\(206\) −5.87819 + 5.87819i −0.409553 + 0.409553i
\(207\) 4.69380i 0.326242i
\(208\) 2.00000 3.00000i 0.138675 0.208013i
\(209\) 30.5580i 2.11374i
\(210\) −0.355962 + 0.0128161i −0.0245637 + 0.000884396i
\(211\) 0.784670 0.0540189 0.0270095 0.999635i \(-0.491402\pi\)
0.0270095 + 0.999635i \(0.491402\pi\)
\(212\) 1.09768i 0.0753892i
\(213\) −8.69380 8.69380i −0.595689 0.595689i
\(214\) 13.4046 13.4046i 0.916318 0.916318i
\(215\) −0.836269 + 0.836269i −0.0570331 + 0.0570331i
\(216\) −0.707107 + 0.707107i −0.0481125 + 0.0481125i
\(217\) 1.88419 2.02494i 0.127907 0.137462i
\(218\) 16.0085i 1.08423i
\(219\) −4.83443 4.83443i −0.326681 0.326681i
\(220\) 0.693799 0.0467759
\(221\) 11.9638 17.9456i 0.804769 1.20715i
\(222\) 6.83692i 0.458864i
\(223\) −19.2064 19.2064i −1.28616 1.28616i −0.937104 0.349052i \(-0.886504\pi\)
−0.349052 0.937104i \(-0.613496\pi\)
\(224\) −1.93693 1.80230i −0.129417 0.120421i
\(225\) 4.98188i 0.332125i
\(226\) 0.506923 0.506923i 0.0337200 0.0337200i
\(227\) 11.9819 + 11.9819i 0.795265 + 0.795265i 0.982345 0.187080i \(-0.0599023\pi\)
−0.187080 + 0.982345i \(0.559902\pi\)
\(228\) −4.19288 4.19288i −0.277680 0.277680i
\(229\) 8.98188 8.98188i 0.593539 0.593539i −0.345047 0.938586i \(-0.612137\pi\)
0.938586 + 0.345047i \(0.112137\pi\)
\(230\) 0.631917i 0.0416674i
\(231\) 9.98188 + 9.28808i 0.656759 + 0.611111i
\(232\) −3.24864 3.24864i −0.213284 0.213284i
\(233\) 13.1473i 0.861310i −0.902517 0.430655i \(-0.858283\pi\)
0.902517 0.430655i \(-0.141717\pi\)
\(234\) 0.707107 + 3.53553i 0.0462250 + 0.231125i
\(235\) 0.626026 0.0408375
\(236\) 1.30620 + 1.30620i 0.0850264 + 0.0850264i
\(237\) 11.5780i 0.752071i
\(238\) −11.5865 10.7812i −0.751040 0.698838i
\(239\) 17.4834 17.4834i 1.13091 1.13091i 0.140884 0.990026i \(-0.455006\pi\)
0.990026 0.140884i \(-0.0449944\pi\)
\(240\) 0.0951965 0.0951965i 0.00614490 0.00614490i
\(241\) 5.69380 5.69380i 0.366770 0.366770i −0.499528 0.866298i \(-0.666493\pi\)
0.866298 + 0.499528i \(0.166493\pi\)
\(242\) −11.0012 11.0012i −0.707183 0.707183i
\(243\) 1.00000i 0.0641500i
\(244\) −5.98188 −0.382950
\(245\) 0.712572 + 0.616727i 0.0455246 + 0.0394013i
\(246\) 4.30690i 0.274598i
\(247\) −20.9644 + 4.19288i −1.33393 + 0.266787i
\(248\) 1.04544i 0.0663852i
\(249\) 1.28808 1.28808i 0.0816285 0.0816285i
\(250\) 1.34384i 0.0849920i
\(251\) 12.4585 0.786374 0.393187 0.919459i \(-0.371373\pi\)
0.393187 + 0.919459i \(0.371373\pi\)
\(252\) 2.64404 0.0951965i 0.166559 0.00599681i
\(253\) 17.1044 17.1044i 1.07534 1.07534i
\(254\) −1.61310 1.61310i −0.101215 0.101215i
\(255\) 0.569453 0.569453i 0.0356605 0.0356605i
\(256\) 1.00000 0.0625000
\(257\) −31.6738 −1.97576 −0.987880 0.155221i \(-0.950391\pi\)
−0.987880 + 0.155221i \(0.950391\pi\)
\(258\) 6.21170 6.21170i 0.386724 0.386724i
\(259\) −12.3222 + 13.2426i −0.765664 + 0.822858i
\(260\) −0.0951965 0.475982i −0.00590383 0.0295192i
\(261\) 4.59428 0.284379
\(262\) 5.50941 + 5.50941i 0.340372 + 0.340372i
\(263\) 23.4422 1.44551 0.722755 0.691105i \(-0.242876\pi\)
0.722755 + 0.691105i \(0.242876\pi\)
\(264\) −5.15345 −0.317173
\(265\) −0.104496 0.104496i −0.00641911 0.00641911i
\(266\) 0.564480 + 15.6782i 0.0346105 + 0.961290i
\(267\) −9.21770 9.21770i −0.564114 0.564114i
\(268\) 0.0454356 + 0.0454356i 0.00277542 + 0.00277542i
\(269\) 16.2813i 0.992686i −0.868126 0.496343i \(-0.834676\pi\)
0.868126 0.496343i \(-0.165324\pi\)
\(270\) 0.134628i 0.00819321i
\(271\) 10.1499 10.1499i 0.616564 0.616564i −0.328084 0.944649i \(-0.606403\pi\)
0.944649 + 0.328084i \(0.106403\pi\)
\(272\) 5.98188 0.362704
\(273\) 5.00249 8.12251i 0.302764 0.491597i
\(274\) −2.69380 −0.162738
\(275\) −18.1541 + 18.1541i −1.09474 + 1.09474i
\(276\) 4.69380i 0.282533i
\(277\) 1.09271i 0.0656546i 0.999461 + 0.0328273i \(0.0104511\pi\)
−0.999461 + 0.0328273i \(0.989549\pi\)
\(278\) −0.506923 0.506923i −0.0304032 0.0304032i
\(279\) −0.739235 0.739235i −0.0442568 0.0442568i
\(280\) −0.355962 + 0.0128161i −0.0212728 + 0.000765910i
\(281\) −22.6284 22.6284i −1.34990 1.34990i −0.885767 0.464130i \(-0.846367\pi\)
−0.464130 0.885767i \(-0.653633\pi\)
\(282\) −4.65004 −0.276906
\(283\) −30.7167 −1.82592 −0.912958 0.408053i \(-0.866208\pi\)
−0.912958 + 0.408053i \(0.866208\pi\)
\(284\) −8.69380 8.69380i −0.515882 0.515882i
\(285\) −0.798295 −0.0472869
\(286\) −10.3069 + 15.4603i −0.609460 + 0.914189i
\(287\) −7.76233 + 8.34216i −0.458196 + 0.492422i
\(288\) −0.707107 + 0.707107i −0.0416667 + 0.0416667i
\(289\) 18.7828 1.10487
\(290\) −0.618519 −0.0363207
\(291\) 9.97506 9.97506i 0.584749 0.584749i
\(292\) −4.83443 4.83443i −0.282914 0.282914i
\(293\) −15.5804 + 15.5804i −0.910215 + 0.910215i −0.996289 0.0860741i \(-0.972568\pi\)
0.0860741 + 0.996289i \(0.472568\pi\)
\(294\) −5.29289 4.58097i −0.308688 0.267168i
\(295\) 0.248691 0.0144794
\(296\) 6.83692i 0.397388i
\(297\) 3.64404 3.64404i 0.211449 0.211449i
\(298\) 11.6312i 0.673779i
\(299\) −14.0814 9.38760i −0.814348 0.542899i
\(300\) 4.98188i 0.287629i
\(301\) −23.2270 + 0.836269i −1.33878 + 0.0482018i
\(302\) −19.3342 −1.11256
\(303\) 3.09271i 0.177672i
\(304\) −4.19288 4.19288i −0.240478 0.240478i
\(305\) −0.569453 + 0.569453i −0.0326068 + 0.0326068i
\(306\) −4.22982 + 4.22982i −0.241803 + 0.241803i
\(307\) −23.5058 + 23.5058i −1.34155 + 1.34155i −0.447024 + 0.894522i \(0.647516\pi\)
−0.894522 + 0.447024i \(0.852484\pi\)
\(308\) 9.98188 + 9.28808i 0.568770 + 0.529237i
\(309\) 8.31301i 0.472911i
\(310\) 0.0995218 + 0.0995218i 0.00565246 + 0.00565246i
\(311\) 33.9687 1.92619 0.963095 0.269162i \(-0.0867468\pi\)
0.963095 + 0.269162i \(0.0867468\pi\)
\(312\) 0.707107 + 3.53553i 0.0400320 + 0.200160i
\(313\) 29.8779i 1.68880i 0.535716 + 0.844398i \(0.320042\pi\)
−0.535716 + 0.844398i \(0.679958\pi\)
\(314\) −8.74172 8.74172i −0.493324 0.493324i
\(315\) 0.242641 0.260765i 0.0136713 0.0146925i
\(316\) 11.5780i 0.651313i
\(317\) 15.1450 15.1450i 0.850626 0.850626i −0.139585 0.990210i \(-0.544577\pi\)
0.990210 + 0.139585i \(0.0445767\pi\)
\(318\) 0.776179 + 0.776179i 0.0435260 + 0.0435260i
\(319\) 16.7417 + 16.7417i 0.937356 + 0.937356i
\(320\) 0.0951965 0.0951965i 0.00532164 0.00532164i
\(321\) 18.9569i 1.05807i
\(322\) −8.45965 + 9.09157i −0.471438 + 0.506653i
\(323\) −25.0813 25.0813i −1.39556 1.39556i
\(324\) 1.00000i 0.0555556i
\(325\) 14.9456 + 9.96375i 0.829034 + 0.552689i
\(326\) −12.3335 −0.683090
\(327\) −11.3197 11.3197i −0.625982 0.625982i
\(328\) 4.30690i 0.237809i
\(329\) 9.00681 + 8.38079i 0.496562 + 0.462048i
\(330\) −0.490590 + 0.490590i −0.0270061 + 0.0270061i
\(331\) 10.2408 10.2408i 0.562885 0.562885i −0.367241 0.930126i \(-0.619697\pi\)
0.930126 + 0.367241i \(0.119697\pi\)
\(332\) 1.28808 1.28808i 0.0706924 0.0706924i
\(333\) 4.83443 + 4.83443i 0.264925 + 0.264925i
\(334\) 18.8273i 1.03018i
\(335\) 0.00865061 0.000472633
\(336\) 2.64404 0.0951965i 0.144244 0.00519339i
\(337\) 4.59428i 0.250266i −0.992140 0.125133i \(-0.960064\pi\)
0.992140 0.125133i \(-0.0399358\pi\)
\(338\) 12.0208 + 4.94975i 0.653846 + 0.269231i
\(339\) 0.716898i 0.0389365i
\(340\) 0.569453 0.569453i 0.0308829 0.0308829i
\(341\) 5.38760i 0.291755i
\(342\) 5.92963 0.320638
\(343\) 1.99567 + 18.4124i 0.107756 + 0.994177i
\(344\) 6.21170 6.21170i 0.334912 0.334912i
\(345\) −0.446833 0.446833i −0.0240567 0.0240567i
\(346\) 6.77618 6.77618i 0.364290 0.364290i
\(347\) −12.2500 −0.657614 −0.328807 0.944397i \(-0.606647\pi\)
−0.328807 + 0.944397i \(0.606647\pi\)
\(348\) 4.59428 0.246279
\(349\) 1.38576 1.38576i 0.0741780 0.0741780i −0.669044 0.743222i \(-0.733296\pi\)
0.743222 + 0.669044i \(0.233296\pi\)
\(350\) 8.97885 9.64955i 0.479940 0.515790i
\(351\) −3.00000 2.00000i −0.160128 0.106752i
\(352\) −5.15345 −0.274680
\(353\) −4.31041 4.31041i −0.229420 0.229420i 0.583030 0.812450i \(-0.301867\pi\)
−0.812450 + 0.583030i \(0.801867\pi\)
\(354\) −1.84725 −0.0981801
\(355\) −1.65524 −0.0878509
\(356\) −9.21770 9.21770i −0.488537 0.488537i
\(357\) 15.8163 0.569453i 0.837088 0.0301387i
\(358\) 4.88419 + 4.88419i 0.258138 + 0.258138i
\(359\) 0.213491 + 0.213491i 0.0112676 + 0.0112676i 0.712718 0.701451i \(-0.247464\pi\)
−0.701451 + 0.712718i \(0.747464\pi\)
\(360\) 0.134628i 0.00709552i
\(361\) 16.1605i 0.850552i
\(362\) 15.8000 15.8000i 0.830428 0.830428i
\(363\) 15.5580 0.816585
\(364\) 5.00249 8.12251i 0.262202 0.425735i
\(365\) −0.920441 −0.0481781
\(366\) 4.22982 4.22982i 0.221096 0.221096i
\(367\) 1.09768i 0.0572986i 0.999590 + 0.0286493i \(0.00912060\pi\)
−0.999590 + 0.0286493i \(0.990879\pi\)
\(368\) 4.69380i 0.244681i
\(369\) 3.04544 + 3.04544i 0.158539 + 0.158539i
\(370\) −0.650850 0.650850i −0.0338361 0.0338361i
\(371\) −0.104496 2.90232i −0.00542514 0.150681i
\(372\) −0.739235 0.739235i −0.0383275 0.0383275i
\(373\) 21.0565 1.09026 0.545131 0.838351i \(-0.316480\pi\)
0.545131 + 0.838351i \(0.316480\pi\)
\(374\) −30.8273 −1.59404
\(375\) 0.950239 + 0.950239i 0.0490701 + 0.0490701i
\(376\) −4.65004 −0.239808
\(377\) 9.18855 13.7828i 0.473235 0.709852i
\(378\) −1.80230 + 1.93693i −0.0927005 + 0.0996250i
\(379\) −7.22452 + 7.22452i −0.371098 + 0.371098i −0.867877 0.496779i \(-0.834516\pi\)
0.496779 + 0.867877i \(0.334516\pi\)
\(380\) −0.798295 −0.0409516
\(381\) 2.28126 0.116873
\(382\) −8.50757 + 8.50757i −0.435285 + 0.435285i
\(383\) −5.97518 5.97518i −0.305317 0.305317i 0.537773 0.843090i \(-0.319266\pi\)
−0.843090 + 0.537773i \(0.819266\pi\)
\(384\) −0.707107 + 0.707107i −0.0360844 + 0.0360844i
\(385\) 1.83443 0.0660472i 0.0934913 0.00336608i
\(386\) 20.1808 1.02717
\(387\) 8.78467i 0.446550i
\(388\) 9.97506 9.97506i 0.506407 0.506407i
\(389\) 25.0614i 1.27067i 0.772239 + 0.635333i \(0.219137\pi\)
−0.772239 + 0.635333i \(0.780863\pi\)
\(390\) 0.403884 + 0.269256i 0.0204515 + 0.0136343i
\(391\) 28.0777i 1.41995i
\(392\) −5.29289 4.58097i −0.267331 0.231374i
\(393\) −7.79148 −0.393028
\(394\) 7.84725i 0.395339i
\(395\) 1.10218 + 1.10218i 0.0554569 + 0.0554569i
\(396\) 3.64404 3.64404i 0.183120 0.183120i
\(397\) −7.28624 + 7.28624i −0.365686 + 0.365686i −0.865901 0.500215i \(-0.833254\pi\)
0.500215 + 0.865901i \(0.333254\pi\)
\(398\) 6.48096 6.48096i 0.324861 0.324861i
\(399\) −11.4853 10.6870i −0.574983 0.535019i
\(400\) 4.98188i 0.249094i
\(401\) 11.1450 + 11.1450i 0.556553 + 0.556553i 0.928324 0.371772i \(-0.121250\pi\)
−0.371772 + 0.928324i \(0.621250\pi\)
\(402\) −0.0642556 −0.00320478
\(403\) −3.69617 + 0.739235i −0.184119 + 0.0368239i
\(404\) 3.09271i 0.153868i
\(405\) −0.0951965 0.0951965i −0.00473035 0.00473035i
\(406\) −8.89880 8.28028i −0.441640 0.410943i
\(407\) 35.2337i 1.74647i
\(408\) −4.22982 + 4.22982i −0.209408 + 0.209408i
\(409\) −14.6028 14.6028i −0.722063 0.722063i 0.246962 0.969025i \(-0.420568\pi\)
−0.969025 + 0.246962i \(0.920568\pi\)
\(410\) −0.410001 0.410001i −0.0202485 0.0202485i
\(411\) 1.90480 1.90480i 0.0939570 0.0939570i
\(412\) 8.31301i 0.409553i
\(413\) 3.57799 + 3.32930i 0.176061 + 0.163824i
\(414\) 3.31902 + 3.31902i 0.163121 + 0.163121i
\(415\) 0.245241i 0.0120384i
\(416\) 0.707107 + 3.53553i 0.0346688 + 0.173344i
\(417\) 0.716898 0.0351066
\(418\) 21.6078 + 21.6078i 1.05687 + 1.05687i
\(419\) 16.5630i 0.809156i 0.914504 + 0.404578i \(0.132582\pi\)
−0.914504 + 0.404578i \(0.867418\pi\)
\(420\) 0.242641 0.260765i 0.0118397 0.0127240i
\(421\) −12.1655 + 12.1655i −0.592908 + 0.592908i −0.938416 0.345508i \(-0.887707\pi\)
0.345508 + 0.938416i \(0.387707\pi\)
\(422\) −0.554846 + 0.554846i −0.0270095 + 0.0270095i
\(423\) 3.28808 3.28808i 0.159872 0.159872i
\(424\) 0.776179 + 0.776179i 0.0376946 + 0.0376946i
\(425\) 29.8010i 1.44556i
\(426\) 12.2949 0.595689
\(427\) −15.8163 + 0.569453i −0.765405 + 0.0275578i
\(428\) 18.9569i 0.916318i
\(429\) −3.64404 18.2202i −0.175936 0.879679i
\(430\) 1.18266i 0.0570331i
\(431\) 5.80961 5.80961i 0.279839 0.279839i −0.553206 0.833045i \(-0.686596\pi\)
0.833045 + 0.553206i \(0.186596\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) −30.1229 −1.44761 −0.723806 0.690003i \(-0.757609\pi\)
−0.723806 + 0.690003i \(0.757609\pi\)
\(434\) 0.0995218 + 2.76417i 0.00477720 + 0.132684i
\(435\) 0.437359 0.437359i 0.0209698 0.0209698i
\(436\) −11.3197 11.3197i −0.542116 0.542116i
\(437\) −19.6805 + 19.6805i −0.941448 + 0.941448i
\(438\) 6.83692 0.326681
\(439\) 8.65755 0.413202 0.206601 0.978425i \(-0.433760\pi\)
0.206601 + 0.978425i \(0.433760\pi\)
\(440\) −0.490590 + 0.490590i −0.0233880 + 0.0233880i
\(441\) 6.98188 0.503406i 0.332470 0.0239717i
\(442\) 4.22982 + 21.1491i 0.201192 + 1.00596i
\(443\) 15.3839 0.730912 0.365456 0.930829i \(-0.380913\pi\)
0.365456 + 0.930829i \(0.380913\pi\)
\(444\) 4.83443 + 4.83443i 0.229432 + 0.229432i
\(445\) −1.75499 −0.0831943
\(446\) 27.1619 1.28616
\(447\) 8.22452 + 8.22452i 0.389006 + 0.389006i
\(448\) 2.64404 0.0951965i 0.124919 0.00449761i
\(449\) 2.29056 + 2.29056i 0.108098 + 0.108098i 0.759087 0.650989i \(-0.225646\pi\)
−0.650989 + 0.759087i \(0.725646\pi\)
\(450\) −3.52272 3.52272i −0.166063 0.166063i
\(451\) 22.1954i 1.04514i
\(452\) 0.716898i 0.0337200i
\(453\) 13.6713 13.6713i 0.642336 0.642336i
\(454\) −16.9449 −0.795265
\(455\) −0.297015 1.24945i −0.0139243 0.0585753i
\(456\) 5.92963 0.277680
\(457\) 9.79829 9.79829i 0.458345 0.458345i −0.439767 0.898112i \(-0.644939\pi\)
0.898112 + 0.439767i \(0.144939\pi\)
\(458\) 12.7023i 0.593539i
\(459\) 5.98188i 0.279210i
\(460\) −0.446833 0.446833i −0.0208337 0.0208337i
\(461\) 7.71441 + 7.71441i 0.359296 + 0.359296i 0.863553 0.504257i \(-0.168234\pi\)
−0.504257 + 0.863553i \(0.668234\pi\)
\(462\) −13.6259 + 0.490590i −0.633935 + 0.0228243i
\(463\) 10.0521 + 10.0521i 0.467162 + 0.467162i 0.900994 0.433832i \(-0.142839\pi\)
−0.433832 + 0.900994i \(0.642839\pi\)
\(464\) 4.59428 0.213284
\(465\) −0.140745 −0.00652689
\(466\) 9.29657 + 9.29657i 0.430655 + 0.430655i
\(467\) 9.63711 0.445952 0.222976 0.974824i \(-0.428423\pi\)
0.222976 + 0.974824i \(0.428423\pi\)
\(468\) −3.00000 2.00000i −0.138675 0.0924500i
\(469\) 0.124459 + 0.115808i 0.00574697 + 0.00534752i
\(470\) −0.442668 + 0.442668i −0.0204187 + 0.0204187i
\(471\) 12.3627 0.569641
\(472\) −1.84725 −0.0850264
\(473\) −32.0117 + 32.0117i −1.47190 + 1.47190i
\(474\) −8.18688 8.18688i −0.376036 0.376036i
\(475\) 20.8884 20.8884i 0.958426 0.958426i
\(476\) 15.8163 0.569453i 0.724939 0.0261008i
\(477\) −1.09768 −0.0502595
\(478\) 24.7253i 1.13091i
\(479\) −10.2288 + 10.2288i −0.467368 + 0.467368i −0.901061 0.433693i \(-0.857210\pi\)
0.433693 + 0.901061i \(0.357210\pi\)
\(480\) 0.134628i 0.00614490i
\(481\) 24.1722 4.83443i 1.10216 0.220431i
\(482\) 8.05225i 0.366770i
\(483\) −0.446833 12.4106i −0.0203316 0.564701i
\(484\) 15.5580 0.707183
\(485\) 1.89918i 0.0862374i
\(486\) 0.707107 + 0.707107i 0.0320750 + 0.0320750i
\(487\) 1.05675 1.05675i 0.0478858 0.0478858i −0.682758 0.730644i \(-0.739220\pi\)
0.730644 + 0.682758i \(0.239220\pi\)
\(488\) 4.22982 4.22982i 0.191475 0.191475i
\(489\) 8.72111 8.72111i 0.394382 0.394382i
\(490\) −0.939957 + 0.0677726i −0.0424629 + 0.00306165i
\(491\) 1.19721i 0.0540291i 0.999635 + 0.0270146i \(0.00860005\pi\)
−0.999635 + 0.0270146i \(0.991400\pi\)
\(492\) 3.04544 + 3.04544i 0.137299 + 0.137299i
\(493\) 27.4824 1.23774
\(494\) 11.8593 17.7889i 0.533573 0.800360i
\(495\) 0.693799i 0.0311839i
\(496\) −0.739235 0.739235i −0.0331926 0.0331926i
\(497\) −23.8144 22.1591i −1.06822 0.993972i
\(498\) 1.82161i 0.0816285i
\(499\) −4.14128 + 4.14128i −0.185389 + 0.185389i −0.793699 0.608310i \(-0.791848\pi\)
0.608310 + 0.793699i \(0.291848\pi\)
\(500\) 0.950239 + 0.950239i 0.0424960 + 0.0424960i
\(501\) −13.3129 13.3129i −0.594777 0.594777i
\(502\) −8.80949 + 8.80949i −0.393187 + 0.393187i
\(503\) 12.0000i 0.535054i −0.963550 0.267527i \(-0.913794\pi\)
0.963550 0.267527i \(-0.0862064\pi\)
\(504\) −1.80230 + 1.93693i −0.0802810 + 0.0862778i
\(505\) −0.294415 0.294415i −0.0131013 0.0131013i
\(506\) 24.1892i 1.07534i
\(507\) −12.0000 + 5.00000i −0.532939 + 0.222058i
\(508\) 2.28126 0.101215
\(509\) −7.43292 7.43292i −0.329458 0.329458i 0.522922 0.852380i \(-0.324842\pi\)
−0.852380 + 0.522922i \(0.824842\pi\)
\(510\) 0.805329i 0.0356605i
\(511\) −13.2426 12.3222i −0.585820 0.545102i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.19288 + 4.19288i −0.185120 + 0.185120i
\(514\) 22.3968 22.3968i 0.987880 0.987880i
\(515\) −0.791369 0.791369i −0.0348719 0.0348719i
\(516\) 8.78467i 0.386724i
\(517\) 23.9638 1.05392
\(518\) −0.650850 18.0771i −0.0285967 0.794261i
\(519\) 9.58296i 0.420645i
\(520\) 0.403884 + 0.269256i 0.0177115 + 0.0118077i
\(521\) 32.0002i 1.40196i −0.713183 0.700978i \(-0.752747\pi\)
0.713183 0.700978i \(-0.247253\pi\)
\(522\) −3.24864 + 3.24864i −0.142189 + 0.142189i
\(523\) 1.89550i 0.0828846i −0.999141 0.0414423i \(-0.986805\pi\)
0.999141 0.0414423i \(-0.0131953\pi\)
\(524\) −7.79148 −0.340372
\(525\) 0.474257 + 13.1723i 0.0206983 + 0.574885i
\(526\) −16.5762 + 16.5762i −0.722755 + 0.722755i
\(527\) −4.42201 4.42201i −0.192626 0.192626i
\(528\) 3.64404 3.64404i 0.158586 0.158586i
\(529\) 0.968251 0.0420979
\(530\) 0.147779 0.00641911
\(531\) 1.30620 1.30620i 0.0566843 0.0566843i
\(532\) −11.4853 10.6870i −0.497950 0.463340i
\(533\) 15.2272 3.04544i 0.659562 0.131912i
\(534\) 13.0358 0.564114
\(535\) 1.80463 + 1.80463i 0.0780211 + 0.0780211i
\(536\) −0.0642556 −0.00277542
\(537\) −6.90729 −0.298072
\(538\) 11.5126 + 11.5126i 0.496343 + 0.496343i
\(539\) 27.2767 + 23.6078i 1.17489 + 1.01686i
\(540\) −0.0951965 0.0951965i −0.00409660 0.00409660i
\(541\) −4.11753 4.11753i −0.177027 0.177027i 0.613032 0.790058i \(-0.289950\pi\)
−0.790058 + 0.613032i \(0.789950\pi\)
\(542\) 14.3542i 0.616564i
\(543\) 22.3445i 0.958896i
\(544\) −4.22982 + 4.22982i −0.181352 + 0.181352i
\(545\) −2.15519 −0.0923183
\(546\) 2.20619 + 9.28077i 0.0944161 + 0.397180i
\(547\) −44.5000 −1.90268 −0.951341 0.308141i \(-0.900293\pi\)
−0.951341 + 0.308141i \(0.900293\pi\)
\(548\) 1.90480 1.90480i 0.0813692 0.0813692i
\(549\) 5.98188i 0.255300i
\(550\) 25.6738i 1.09474i
\(551\) −19.2633 19.2633i −0.820642 0.820642i
\(552\) 3.31902 + 3.31902i 0.141267 + 0.141267i
\(553\) 1.10218 + 30.6126i 0.0468696 + 1.30178i
\(554\) −0.772662 0.772662i −0.0328273 0.0328273i
\(555\) 0.920441 0.0390706
\(556\) 0.716898 0.0304032
\(557\) −9.50762 9.50762i −0.402851 0.402851i 0.476386 0.879236i \(-0.341947\pi\)
−0.879236 + 0.476386i \(0.841947\pi\)
\(558\) 1.04544 0.0442568
\(559\) 26.3540 + 17.5693i 1.11466 + 0.743104i
\(560\) 0.242641 0.260765i 0.0102534 0.0110194i
\(561\) 21.7982 21.7982i 0.920320 0.920320i
\(562\) 32.0014 1.34990
\(563\) −16.3640 −0.689659 −0.344829 0.938665i \(-0.612063\pi\)
−0.344829 + 0.938665i \(0.612063\pi\)
\(564\) 3.28808 3.28808i 0.138453 0.138453i
\(565\) 0.0682461 + 0.0682461i 0.00287114 + 0.00287114i
\(566\) 21.7200 21.7200i 0.912958 0.912958i
\(567\) −0.0951965 2.64404i −0.00399788 0.111039i
\(568\) 12.2949 0.515882
\(569\) 26.8760i 1.12670i −0.826218 0.563351i \(-0.809512\pi\)
0.826218 0.563351i \(-0.190488\pi\)
\(570\) 0.564480 0.564480i 0.0236434 0.0236434i
\(571\) 26.1591i 1.09472i −0.836896 0.547362i \(-0.815632\pi\)
0.836896 0.547362i \(-0.184368\pi\)
\(572\) −3.64404 18.2202i −0.152365 0.761824i
\(573\) 12.0315i 0.502624i
\(574\) −0.410001 11.3876i −0.0171131 0.475309i
\(575\) 23.3839 0.975177
\(576\) 1.00000i 0.0416667i
\(577\) −3.83454 3.83454i −0.159634 0.159634i 0.622770 0.782405i \(-0.286007\pi\)
−0.782405 + 0.622770i \(0.786007\pi\)
\(578\) −13.2815 + 13.2815i −0.552436 + 0.552436i
\(579\) −14.2700 + 14.2700i −0.593039 + 0.593039i
\(580\) 0.437359 0.437359i 0.0181603 0.0181603i
\(581\) 3.28310 3.52834i 0.136206 0.146380i
\(582\) 14.1069i 0.584749i
\(583\) −4.00000 4.00000i −0.165663 0.165663i
\(584\) 6.83692 0.282914
\(585\) −0.475982 + 0.0951965i −0.0196794 + 0.00393589i
\(586\) 22.0340i 0.910215i
\(587\) 15.5599 + 15.5599i 0.642224 + 0.642224i 0.951102 0.308877i \(-0.0999533\pi\)
−0.308877 + 0.951102i \(0.599953\pi\)
\(588\) 6.98188 0.503406i 0.287928 0.0207601i
\(589\) 6.19904i 0.255427i
\(590\) −0.175851 + 0.175851i −0.00723969 + 0.00723969i
\(591\) 5.54884 + 5.54884i 0.228249 + 0.228249i
\(592\) 4.83443 + 4.83443i 0.198694 + 0.198694i
\(593\) 0.351637 0.351637i 0.0144400 0.0144400i −0.699850 0.714290i \(-0.746750\pi\)
0.714290 + 0.699850i \(0.246750\pi\)
\(594\) 5.15345i 0.211449i
\(595\) 1.45145 1.55987i 0.0595035 0.0639483i
\(596\) 8.22452 + 8.22452i 0.336889 + 0.336889i
\(597\) 9.16546i 0.375117i
\(598\) 16.5951 3.31902i 0.678624 0.135725i
\(599\) 34.9302 1.42721 0.713604 0.700549i \(-0.247062\pi\)
0.713604 + 0.700549i \(0.247062\pi\)
\(600\) −3.52272 3.52272i −0.143814 0.143814i
\(601\) 0.993188i 0.0405130i −0.999795 0.0202565i \(-0.993552\pi\)
0.999795 0.0202565i \(-0.00644828\pi\)
\(602\) 15.8326 17.0153i 0.645290 0.693492i
\(603\) 0.0454356 0.0454356i 0.00185028 0.00185028i
\(604\) 13.6713 13.6713i 0.556279 0.556279i
\(605\) 1.48107 1.48107i 0.0602140 0.0602140i
\(606\) 2.18688 + 2.18688i 0.0888358 + 0.0888358i
\(607\) 20.6029i 0.836247i 0.908390 + 0.418124i \(0.137312\pi\)
−0.908390 + 0.418124i \(0.862688\pi\)
\(608\) 5.92963 0.240478
\(609\) 12.1474 0.437359i 0.492239 0.0177227i
\(610\) 0.805329i 0.0326068i
\(611\) −3.28808 16.4404i −0.133021 0.665107i
\(612\) 5.98188i 0.241803i
\(613\) −30.3315 + 30.3315i −1.22508 + 1.22508i −0.259274 + 0.965804i \(0.583483\pi\)
−0.965804 + 0.259274i \(0.916517\pi\)
\(614\) 33.2422i 1.34155i
\(615\) 0.579829 0.0233810
\(616\) −13.6259 + 0.490590i −0.549004 + 0.0197664i
\(617\) −22.7622 + 22.7622i −0.916372 + 0.916372i −0.996763 0.0803909i \(-0.974383\pi\)
0.0803909 + 0.996763i \(0.474383\pi\)
\(618\) 5.87819 + 5.87819i 0.236455 + 0.236455i
\(619\) 9.96126 9.96126i 0.400377 0.400377i −0.477989 0.878366i \(-0.658634\pi\)
0.878366 + 0.477989i \(0.158634\pi\)
\(620\) −0.140745 −0.00565246
\(621\) −4.69380 −0.188356
\(622\) −24.0195 + 24.0195i −0.963095 + 0.963095i
\(623\) −25.2495 23.4945i −1.01160 0.941286i
\(624\) −3.00000 2.00000i −0.120096 0.0800641i
\(625\) −24.7285 −0.989138
\(626\) −21.1268 21.1268i −0.844398 0.844398i
\(627\) −30.5580 −1.22037
\(628\) 12.3627 0.493324
\(629\) 28.9190 + 28.9190i 1.15307 + 1.15307i
\(630\) 0.0128161 + 0.355962i 0.000510606 + 0.0141819i
\(631\) 8.24750 + 8.24750i 0.328328 + 0.328328i 0.851950 0.523623i \(-0.175420\pi\)
−0.523623 + 0.851950i \(0.675420\pi\)
\(632\) −8.18688 8.18688i −0.325656 0.325656i
\(633\) 0.784670i 0.0311878i
\(634\) 21.4182i 0.850626i
\(635\) 0.217168 0.217168i 0.00861806 0.00861806i
\(636\) −1.09768 −0.0435260
\(637\) 12.4535 21.9524i 0.493427 0.869787i
\(638\) −23.6764 −0.937356
\(639\) −8.69380 + 8.69380i −0.343921 + 0.343921i
\(640\) 0.134628i 0.00532164i
\(641\) 27.4472i 1.08410i 0.840347 + 0.542049i \(0.182351\pi\)
−0.840347 + 0.542049i \(0.817649\pi\)
\(642\) −13.4046 13.4046i −0.529037 0.529037i
\(643\) −27.7346 27.7346i −1.09375 1.09375i −0.995125 0.0986217i \(-0.968557\pi\)
−0.0986217 0.995125i \(-0.531443\pi\)
\(644\) −0.446833 12.4106i −0.0176077 0.489046i
\(645\) 0.836269 + 0.836269i 0.0329281 + 0.0329281i
\(646\) 35.4703 1.39556
\(647\) 14.6620 0.576425 0.288212 0.957567i \(-0.406939\pi\)
0.288212 + 0.957567i \(0.406939\pi\)
\(648\) 0.707107 + 0.707107i 0.0277778 + 0.0277778i
\(649\) 9.51969 0.373681
\(650\) −17.6136 + 3.52272i −0.690862 + 0.138172i
\(651\) −2.02494 1.88419i −0.0793635 0.0738473i
\(652\) 8.72111 8.72111i 0.341545 0.341545i
\(653\) 15.7965 0.618163 0.309082 0.951036i \(-0.399978\pi\)
0.309082 + 0.951036i \(0.399978\pi\)
\(654\) 16.0085 0.625982
\(655\) −0.741721 + 0.741721i −0.0289815 + 0.0289815i
\(656\) 3.04544 + 3.04544i 0.118904 + 0.118904i
\(657\) −4.83443 + 4.83443i −0.188609 + 0.188609i
\(658\) −12.2949 + 0.442668i −0.479305 + 0.0172570i
\(659\) 8.06825 0.314294 0.157147 0.987575i \(-0.449770\pi\)
0.157147 + 0.987575i \(0.449770\pi\)
\(660\) 0.693799i 0.0270061i
\(661\) −30.7552 + 30.7552i −1.19624 + 1.19624i −0.220956 + 0.975284i \(0.570918\pi\)
−0.975284 + 0.220956i \(0.929082\pi\)
\(662\) 14.4827i 0.562885i
\(663\) −17.9456 11.9638i −0.696950 0.464634i
\(664\) 1.82161i 0.0706924i
\(665\) −2.11072 + 0.0759948i −0.0818503 + 0.00294695i
\(666\) −6.83692 −0.264925
\(667\) 21.5646i 0.834985i
\(668\) −13.3129 13.3129i −0.515092 0.515092i
\(669\) −19.2064 + 19.2064i −0.742562 + 0.742562i
\(670\) −0.00611691 + 0.00611691i −0.000236317 + 0.000236317i
\(671\) −21.7982 + 21.7982i −0.841509 + 0.841509i
\(672\) −1.80230 + 1.93693i −0.0695254 + 0.0747187i
\(673\) 43.5286i 1.67790i −0.544206 0.838952i \(-0.683169\pi\)
0.544206 0.838952i \(-0.316831\pi\)
\(674\) 3.24864 + 3.24864i 0.125133 + 0.125133i
\(675\) 4.98188 0.191752
\(676\) −12.0000 + 5.00000i −0.461538 + 0.192308i
\(677\) 13.3826i 0.514336i 0.966367 + 0.257168i \(0.0827894\pi\)
−0.966367 + 0.257168i \(0.917211\pi\)
\(678\) −0.506923 0.506923i −0.0194683 0.0194683i
\(679\) 25.4249 27.3240i 0.975716 1.04860i
\(680\) 0.805329i 0.0308829i
\(681\) 11.9819 11.9819i 0.459146 0.459146i
\(682\) 3.80961 + 3.80961i 0.145877 + 0.145877i
\(683\) 11.4536 + 11.4536i 0.438262 + 0.438262i 0.891427 0.453165i \(-0.149705\pi\)
−0.453165 + 0.891427i \(0.649705\pi\)
\(684\) −4.19288 + 4.19288i −0.160319 + 0.160319i
\(685\) 0.362661i 0.0138566i
\(686\) −14.4307 11.6084i −0.550967 0.443211i
\(687\) −8.98188 8.98188i −0.342680 0.342680i
\(688\) 8.78467i 0.334912i
\(689\) −2.19537 + 3.29305i −0.0836368 + 0.125455i
\(690\) 0.631917 0.0240567
\(691\) 1.55068 + 1.55068i 0.0589907 + 0.0589907i 0.735987 0.676996i \(-0.236719\pi\)
−0.676996 + 0.735987i \(0.736719\pi\)
\(692\) 9.58296i 0.364290i
\(693\) 9.28808 9.98188i 0.352825 0.379180i
\(694\) 8.66205 8.66205i 0.328807 0.328807i
\(695\) 0.0682461 0.0682461i 0.00258872 0.00258872i
\(696\) −3.24864 + 3.24864i −0.123140 + 0.123140i
\(697\) 18.2174 + 18.2174i 0.690034 + 0.690034i
\(698\) 1.95976i 0.0741780i
\(699\) −13.1473 −0.497278
\(700\) 0.474257 + 13.1723i 0.0179252 + 0.497865i
\(701\) 8.43541i 0.318601i −0.987230 0.159300i \(-0.949076\pi\)
0.987230 0.159300i \(-0.0509239\pi\)
\(702\) 3.53553 0.707107i 0.133440 0.0266880i
\(703\) 40.5404i 1.52901i
\(704\) 3.64404 3.64404i 0.137340 0.137340i
\(705\) 0.626026i 0.0235775i
\(706\) 6.09584 0.229420
\(707\) −0.294415 8.17724i −0.0110726 0.307537i
\(708\) 1.30620 1.30620i 0.0490900 0.0490900i
\(709\) −19.8616 19.8616i −0.745917 0.745917i 0.227793 0.973710i \(-0.426849\pi\)
−0.973710 + 0.227793i \(0.926849\pi\)
\(710\) 1.17043 1.17043i 0.0439254 0.0439254i
\(711\) 11.5780 0.434209
\(712\) 13.0358 0.488537
\(713\) −3.46982 + 3.46982i −0.129946 + 0.129946i
\(714\) −10.7812 + 11.5865i −0.403475 + 0.433613i
\(715\) −2.08140 1.38760i −0.0778398 0.0518932i
\(716\) −6.90729 −0.258138
\(717\) −17.4834 17.4834i −0.652931 0.652931i
\(718\) −0.301922 −0.0112676
\(719\) −3.21983 −0.120079 −0.0600397 0.998196i \(-0.519123\pi\)
−0.0600397 + 0.998196i \(0.519123\pi\)
\(720\) −0.0951965 0.0951965i −0.00354776 0.00354776i
\(721\) −0.791369 21.9799i −0.0294721 0.818575i
\(722\) −11.4272 11.4272i −0.425276 0.425276i
\(723\) −5.69380 5.69380i −0.211755 0.211755i
\(724\) 22.3445i 0.830428i
\(725\) 22.8881i 0.850043i
\(726\) −11.0012 + 11.0012i −0.408292 + 0.408292i
\(727\) −13.4007 −0.497006 −0.248503 0.968631i \(-0.579939\pi\)
−0.248503 + 0.968631i \(0.579939\pi\)
\(728\) 2.20619 + 9.28077i 0.0817668 + 0.343968i
\(729\) −1.00000 −0.0370370
\(730\) 0.650850 0.650850i 0.0240891 0.0240891i
\(731\) 52.5488i 1.94359i
\(732\) 5.98188i 0.221096i
\(733\) 28.6644 + 28.6644i 1.05874 + 1.05874i 0.998163 + 0.0605789i \(0.0192947\pi\)
0.0605789 + 0.998163i \(0.480705\pi\)
\(734\) −0.776179 0.776179i −0.0286493 0.0286493i
\(735\) 0.616727 0.712572i 0.0227483 0.0262836i
\(736\) 3.31902 + 3.31902i 0.122341 + 0.122341i
\(737\) 0.331138 0.0121976
\(738\) −4.30690 −0.158539
\(739\) 5.76417 + 5.76417i 0.212038 + 0.212038i 0.805133 0.593094i \(-0.202094\pi\)
−0.593094 + 0.805133i \(0.702094\pi\)
\(740\) 0.920441 0.0338361
\(741\) 4.19288 + 20.9644i 0.154029 + 0.770146i
\(742\) 2.12614 + 1.97836i 0.0780530 + 0.0726278i
\(743\) 15.4107 15.4107i 0.565364 0.565364i −0.365462 0.930826i \(-0.619089\pi\)
0.930826 + 0.365462i \(0.119089\pi\)
\(744\) 1.04544 0.0383275
\(745\) 1.56589 0.0573698
\(746\) −14.8892 + 14.8892i −0.545131 + 0.545131i
\(747\) −1.28808 1.28808i −0.0471282 0.0471282i
\(748\) 21.7982 21.7982i 0.797020 0.797020i
\(749\) 1.80463 + 50.1229i 0.0659399 + 1.83145i
\(750\) −1.34384 −0.0490701
\(751\) 4.11812i 0.150272i 0.997173 + 0.0751362i \(0.0239391\pi\)
−0.997173 + 0.0751362i \(0.976061\pi\)
\(752\) 3.28808 3.28808i 0.119904 0.119904i
\(753\) 12.4585i 0.454013i
\(754\) 3.24864 + 16.2432i 0.118309 + 0.591543i
\(755\) 2.60293i 0.0947302i
\(756\) −0.0951965 2.64404i −0.00346226 0.0961627i
\(757\) −18.1229 −0.658687 −0.329343 0.944210i \(-0.606827\pi\)
−0.329343 + 0.944210i \(0.606827\pi\)
\(758\) 10.2170i 0.371098i
\(759\) −17.1044 17.1044i −0.620850 0.620850i
\(760\) 0.564480 0.564480i 0.0204758 0.0204758i
\(761\) −21.1268 + 21.1268i −0.765847 + 0.765847i −0.977372 0.211525i \(-0.932157\pi\)
0.211525 + 0.977372i \(0.432157\pi\)
\(762\) −1.61310 + 1.61310i −0.0584363 + 0.0584363i
\(763\) −31.0073 28.8522i −1.12254 1.04452i
\(764\) 12.0315i 0.435285i
\(765\) −0.569453 0.569453i −0.0205886 0.0205886i
\(766\) 8.45018 0.305317
\(767\) −1.30620 6.53100i −0.0471642 0.235821i
\(768\) 1.00000i 0.0360844i
\(769\) 2.12748 + 2.12748i 0.0767189 + 0.0767189i 0.744425 0.667706i \(-0.232724\pi\)
−0.667706 + 0.744425i \(0.732724\pi\)
\(770\) −1.25044 + 1.34384i −0.0450626 + 0.0484287i
\(771\) 31.6738i 1.14071i
\(772\) −14.2700 + 14.2700i −0.513587 + 0.513587i
\(773\) −3.62354 3.62354i −0.130330 0.130330i 0.638933 0.769263i \(-0.279376\pi\)
−0.769263 + 0.638933i \(0.779376\pi\)
\(774\) −6.21170 6.21170i −0.223275 0.223275i
\(775\) 3.68277 3.68277i 0.132289 0.132289i
\(776\) 14.1069i 0.506407i
\(777\) 13.2426 + 12.3222i 0.475077 + 0.442056i
\(778\) −17.7211