Properties

Label 546.2.o.a.307.2
Level $546$
Weight $2$
Character 546.307
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 307.2
Root \(-2.73923i\) of defining polynomial
Character \(\chi\) \(=\) 546.307
Dual form 546.2.o.a.265.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} -1.00000i q^{3} +1.00000i q^{4} +(0.0951965 - 0.0951965i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-2.64404 + 0.0951965i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(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} +(-2.64404 + 0.0951965i) 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} +(0.0951965 + 2.64404i) 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} +(-0.0951965 - 2.64404i) 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} +(2.64404 - 0.0951965i) 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} +(0.355962 - 0.0128161i) 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} +(-2.64404 + 0.0951965i) 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} +(-5.57367 - 7.74172i) 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} +(-5.29289 - 4.58097i) q^{98} +(3.64404 - 3.64404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{5} - 8q^{9} + O(q^{10}) \) \( 8q - 4q^{5} - 8q^{9} + 4q^{10} - 8q^{11} + 8q^{12} + 16q^{13} + 4q^{15} - 8q^{16} - 12q^{17} + 4q^{19} - 4q^{20} - 4q^{21} + 4q^{22} + 4q^{28} - 12q^{29} + 20q^{31} + 8q^{33} - 24q^{34} + 32q^{35} - 8q^{37} + 12q^{38} + 24q^{39} + 16q^{41} + 4q^{42} - 8q^{44} + 4q^{45} - 20q^{46} - 16q^{47} - 4q^{49} + 24q^{50} - 24q^{52} - 24q^{53} - 4q^{56} - 4q^{57} - 16q^{58} + 28q^{59} - 4q^{60} - 20q^{65} + 8q^{67} - 20q^{69} + 24q^{70} + 52q^{71} - 8q^{73} - 4q^{74} - 20q^{75} + 4q^{76} + 32q^{77} - 48q^{79} + 4q^{80} + 8q^{81} + 40q^{82} + 32q^{83} + 20q^{85} - 20q^{86} + 4q^{89} - 4q^{90} + 12q^{91} + 20q^{92} - 20q^{93} - 36q^{97} - 48q^{98} + 8q^{99} + O(q^{100}) \)

Character values

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

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

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 \(-0.740416\pi\)
0.728073 + 0.685500i \(0.240416\pi\)
\(6\) −0.707107 + 0.707107i −0.288675 + 0.288675i
\(7\) −2.64404 + 0.0951965i −0.999352 + 0.0359809i
\(8\) 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 −0.104158 + 0.994561i \(0.533215\pi\)
−0.994561 + 0.104158i \(0.966785\pi\)
\(12\) 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 \(-0.241651\pi\)
0.725409 + 0.688318i \(0.241651\pi\)
\(18\) 0.707107 + 0.707107i 0.166667 + 0.166667i
\(19\) −4.19288 + 4.19288i −0.961913 + 0.961913i −0.999301 0.0373882i \(-0.988096\pi\)
0.0373882 + 0.999301i \(0.488096\pi\)
\(20\) 0.0951965 + 0.0951965i 0.0212866 + 0.0212866i
\(21\) 0.0951965 + 2.64404i 0.0207736 + 0.576976i
\(22\) 5.15345 1.09872
\(23\) 4.69380i 0.978725i −0.872081 0.489362i \(-0.837230\pi\)
0.872081 0.489362i \(-0.162770\pi\)
\(24\) −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
\(28\) −0.0951965 2.64404i −0.0179904 0.499676i
\(29\) −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 \(-0.779928\pi\)
0.637598 + 0.770369i \(0.279928\pi\)
\(32\) 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 −0.982266 0.187491i \(-0.939965\pi\)
0.187491 + 0.982266i \(0.439965\pi\)
\(38\) 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 \(-0.640820\pi\)
0.903727 + 0.428110i \(0.140820\pi\)
\(42\) 1.80230 1.93693i 0.278101 0.298875i
\(43\) 8.78467i 1.33965i 0.742519 + 0.669825i \(0.233631\pi\)
−0.742519 + 0.669825i \(0.766369\pi\)
\(44\) −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 \(-0.139864\pi\)
−0.425393 + 0.905009i \(0.639864\pi\)
\(48\) 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 \(-0.211632\pi\)
−0.616950 + 0.787003i \(0.711632\pi\)
\(60\) 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
\(63\) 2.64404 0.0951965i 0.333117 0.0119936i
\(64\) 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 0.704326 0.709877i \(-0.251249\pi\)
−0.709877 + 0.704326i \(0.751249\pi\)
\(68\) 5.98188i 0.725409i
\(69\) −4.69380 −0.565067
\(70\) 0.355962 0.0128161i 0.0425456 0.00153182i
\(71\) 8.69380 + 8.69380i 1.03176 + 1.03176i 0.999479 + 0.0322854i \(0.0102786\pi\)
0.0322854 + 0.999479i \(0.489721\pi\)
\(72\) −0.707107 + 0.707107i −0.0833333 + 0.0833333i
\(73\) −4.83443 4.83443i −0.565827 0.565827i 0.365129 0.930957i \(-0.381025\pi\)
−0.930957 + 0.365129i \(0.881025\pi\)
\(74\) 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 \(-0.781876\pi\)
0.632872 + 0.774257i \(0.281876\pi\)
\(84\) −2.64404 + 0.0951965i −0.288488 + 0.0103868i
\(85\) 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 \(-0.492784\pi\)
−0.999743 + 0.0226684i \(0.992784\pi\)
\(90\) 0.134628 0.0141910
\(91\) −5.57367 7.74172i −0.584279 0.811553i
\(92\) 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 −0.0128974 + 0.999917i \(0.504105\pi\)
−0.999917 + 0.0128974i \(0.995895\pi\)
\(98\) −5.29289 4.58097i −0.534663 0.462748i
\(99\) 3.64404 3.64404i 0.366240 0.366240i
\(100\) −4.98188 −0.498188
\(101\) −3.09271 −0.307736 −0.153868 0.988091i \(-0.549173\pi\)
−0.153868 + 0.988091i \(0.549173\pi\)
\(102\) −4.22982 + 4.22982i −0.418815 + 0.418815i
\(103\) −8.31301 −0.819106 −0.409553 0.912286i \(-0.634315\pi\)
−0.409553 + 0.912286i \(0.634315\pi\)
\(104\) 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 0.996110 + 0.0881221i \(0.0280866\pi\)
0.0881221 + 0.996110i \(0.471913\pi\)
\(110\) 0.490590 0.490590i 0.0467759 0.0467759i
\(111\) 4.83443 + 4.83443i 0.458864 + 0.458864i
\(112\) 2.64404 0.0951965i 0.249838 0.00899522i
\(113\) −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
\(119\) −15.8163 + 0.569453i −1.44988 + 0.0522017i
\(120\) −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 \(-0.967727\pi\)
0.994865 0.101215i \(-0.0322729\pi\)
\(128\) −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 −0.621040 0.783779i \(-0.713290\pi\)
0.783779 + 0.621040i \(0.213290\pi\)
\(138\) 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 0.284806 0.958585i \(-0.408071\pi\)
−0.958585 + 0.284806i \(0.908071\pi\)
\(150\) −3.52272 3.52272i −0.287629 0.287629i
\(151\) 13.6713 13.6713i 1.11256 1.11256i 0.119755 0.992803i \(-0.461789\pi\)
0.992803 0.119755i \(-0.0382110\pi\)
\(152\) 5.92963i 0.480956i
\(153\) −5.98188 −0.483606
\(154\) −13.6259 + 0.490590i −1.09801 + 0.0395329i
\(155\) 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
\(161\) 0.446833 + 12.4106i 0.0352154 + 0.978091i
\(162\) −0.707107 0.707107i −0.0555556 0.0555556i
\(163\) 8.72111 8.72111i 0.683090 0.683090i −0.277605 0.960695i \(-0.589541\pi\)
0.960695 + 0.277605i \(0.0895407\pi\)
\(164\) 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 −0.999530 0.0306531i \(-0.990241\pi\)
−0.0306531 0.999530i \(-0.509759\pi\)
\(168\) 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 \(-0.381312\pi\)
0.364290 + 0.931286i \(0.381312\pi\)
\(174\) 3.24864 3.24864i 0.246279 0.246279i
\(175\) −0.474257 13.1723i −0.0358504 0.995730i
\(176\) 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 \(0.0831088\pi\)
−0.966108 + 0.258138i \(0.916891\pi\)
\(180\) −0.0951965 0.0951965i −0.00709552 0.00709552i
\(181\) 22.3445 1.66086 0.830428 0.557126i \(-0.188096\pi\)
0.830428 + 0.557126i \(0.188096\pi\)
\(182\) −1.53305 + 9.41540i −0.113637 + 0.697916i
\(183\) −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
\(189\) −0.0951965 2.64404i −0.00692452 0.192325i
\(190\) 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 −0.0275533 + 0.999620i \(0.508772\pi\)
−0.999620 + 0.0275533i \(0.991228\pi\)
\(194\) 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 0.481247 0.876585i \(-0.340184\pi\)
−0.876585 + 0.481247i \(0.840184\pi\)
\(198\) −5.15345 −0.366240
\(199\) 9.16546 0.649722 0.324861 0.945762i \(-0.394682\pi\)
0.324861 + 0.945762i \(0.394682\pi\)
\(200\) 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
\(203\) 12.1474 0.437359i 0.852583 0.0306966i
\(204\) 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
\(210\) −0.0128161 0.355962i −0.000884396 0.0245637i
\(211\) 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 0.349052 0.937104i \(-0.386504\pi\)
0.937104 0.349052i \(-0.113496\pi\)
\(224\) −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 \(-0.940098\pi\)
0.187080 + 0.982345i \(0.440098\pi\)
\(228\) −4.19288 + 4.19288i −0.277680 + 0.277680i
\(229\) −8.98188 8.98188i −0.593539 0.593539i 0.345047 0.938586i \(-0.387863\pi\)
−0.938586 + 0.345047i \(0.887863\pi\)
\(230\) 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 \(0.141717\pi\)
−0.902517 + 0.430655i \(0.858283\pi\)
\(234\) −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 0.990026 + 0.140884i \(0.0449944\pi\)
0.140884 + 0.990026i \(0.455006\pi\)
\(240\) 0.0951965 + 0.0951965i 0.00614490 + 0.00614490i
\(241\) −5.69380 5.69380i −0.366770 0.366770i 0.499528 0.866298i \(-0.333507\pi\)
−0.866298 + 0.499528i \(0.833507\pi\)
\(242\) −11.0012 + 11.0012i −0.707183 + 0.707183i
\(243\) 1.00000i 0.0641500i
\(244\) 5.98188 0.382950
\(245\) 0.616727 0.712572i 0.0394013 0.0455246i
\(246\) 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 \(-0.628627\pi\)
−0.393187 + 0.919459i \(0.628627\pi\)
\(252\) 0.0951965 + 2.64404i 0.00599681 + 0.166559i
\(253\) 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 \(-0.0496089\pi\)
0.987880 + 0.155221i \(0.0496089\pi\)
\(258\) −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
\(266\) −15.6782 + 0.564480i −0.961290 + 0.0346105i
\(267\) −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 \(-0.393597\pi\)
−0.944649 + 0.328084i \(0.893597\pi\)
\(272\) −5.98188 −0.362704
\(273\) −7.74172 + 5.57367i −0.468550 + 0.337334i
\(274\) −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 \(-0.989549\pi\)
0.999461 0.0328273i \(-0.0104511\pi\)
\(278\) 0.506923 0.506923i 0.0304032 0.0304032i
\(279\) 0.739235 0.739235i 0.0442568 0.0442568i
\(280\) 0.0128161 + 0.355962i 0.000765910 + 0.0212728i
\(281\) −22.6284 + 22.6284i −1.34990 + 1.34990i −0.464130 + 0.885767i \(0.653633\pi\)
−0.885767 + 0.464130i \(0.846367\pi\)
\(282\) −4.65004 −0.276906
\(283\) 30.7167 1.82592 0.912958 0.408053i \(-0.133792\pi\)
0.912958 + 0.408053i \(0.133792\pi\)
\(284\) −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 \(-0.0274322\pi\)
−0.0860741 + 0.996289i \(0.527432\pi\)
\(294\) −4.58097 + 5.29289i −0.267168 + 0.308688i
\(295\) 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
\(301\) −0.836269 23.2270i −0.0482018 1.33878i
\(302\) −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 0.894522 + 0.447024i \(0.147516\pi\)
0.447024 + 0.894522i \(0.352484\pi\)
\(308\) 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 \(-0.913253\pi\)
−0.963095 + 0.269162i \(0.913253\pi\)
\(312\) 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 0.990210 0.139585i \(-0.0445767\pi\)
−0.139585 + 0.990210i \(0.544577\pi\)
\(318\) −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 0.930126 0.367241i \(-0.119697\pi\)
−0.367241 + 0.930126i \(0.619697\pi\)
\(332\) −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
\(336\) −0.0951965 2.64404i −0.00519339 0.144244i
\(337\) 4.59428i 0.250266i 0.992140 + 0.125133i \(0.0399358\pi\)
−0.992140 + 0.125133i \(0.960064\pi\)
\(338\) 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
\(343\) −18.4124 + 1.99567i −0.994177 + 0.107756i
\(344\) 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 \(-0.266704\pi\)
−0.743222 + 0.669044i \(0.766704\pi\)
\(350\) −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 \(-0.698133\pi\)
0.812450 + 0.583030i \(0.198133\pi\)
\(354\) −1.84725 −0.0981801
\(355\) 1.65524 0.0878509
\(356\) 9.21770 9.21770i 0.488537 0.488537i
\(357\) 0.569453 + 15.8163i 0.0301387 + 0.837088i
\(358\) 4.88419 4.88419i 0.258138 0.258138i
\(359\) 0.213491 0.213491i 0.0112676 0.0112676i −0.701451 0.712718i \(-0.747464\pi\)
0.712718 + 0.701451i \(0.247464\pi\)
\(360\) 0.134628i 0.00709552i
\(361\) 16.1605i 0.850552i
\(362\) −15.8000 15.8000i −0.830428 0.830428i
\(363\) −15.5580 −0.816585
\(364\) 7.74172 5.57367i 0.405776 0.292139i
\(365\) −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
\(371\) −2.90232 + 0.104496i −0.150681 + 0.00542514i
\(372\) −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 0.496779 0.867877i \(-0.334516\pi\)
−0.867877 + 0.496779i \(0.834516\pi\)
\(380\) −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 \(-0.680734\pi\)
0.843090 + 0.537773i \(0.180734\pi\)
\(384\) 0.707107 + 0.707107i 0.0360844 + 0.0360844i
\(385\) −0.0660472 1.83443i −0.00336608 0.0934913i
\(386\) 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 \(-0.780863\pi\)
0.772239 0.635333i \(-0.219137\pi\)
\(390\) −0.403884 + 0.269256i −0.0204515 + 0.0136343i
\(391\) 28.0777i 1.41995i
\(392\) 4.58097 5.29289i 0.231374 0.267331i
\(393\) −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 \(-0.166746\pi\)
−0.500215 + 0.865901i \(0.666746\pi\)
\(398\) −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 −0.371772 0.928324i \(-0.621250\pi\)
0.928324 + 0.371772i \(0.121250\pi\)
\(402\) 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 \(-0.579432\pi\)
0.969025 + 0.246962i \(0.0794324\pi\)
\(410\) −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 0.345508 0.938416i \(-0.387707\pi\)
−0.938416 + 0.345508i \(0.887707\pi\)
\(422\) −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
\(427\) 0.569453 + 15.8163i 0.0275578 + 0.765405i
\(428\) 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 0.833045 0.553206i \(-0.186596\pi\)
−0.553206 + 0.833045i \(0.686596\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 30.1229 1.44761 0.723806 0.690003i \(-0.242391\pi\)
0.723806 + 0.690003i \(0.242391\pi\)
\(434\) −2.76417 + 0.0995218i −0.132684 + 0.00477720i
\(435\) 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 \(-0.566240\pi\)
−0.206601 + 0.978425i \(0.566240\pi\)
\(440\) 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
\(448\) 0.0951965 + 2.64404i 0.00449761 + 0.124919i
\(449\) 2.29056 2.29056i 0.108098 0.108098i −0.650989 0.759087i \(-0.725646\pi\)
0.759087 + 0.650989i \(0.225646\pi\)
\(450\) −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
\(455\) −1.26758 0.206391i −0.0594250 0.00967577i
\(456\) 5.92963 0.277680
\(457\) 9.79829 + 9.79829i 0.458345 + 0.458345i 0.898112 0.439767i \(-0.144939\pi\)
−0.439767 + 0.898112i \(0.644939\pi\)
\(458\) 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 \(-0.831766\pi\)
0.504257 + 0.863553i \(0.331766\pi\)
\(462\) 0.490590 + 13.6259i 0.0228243 + 0.633935i
\(463\) 10.0521 10.0521i 0.467162 0.467162i −0.433832 0.900994i \(-0.642839\pi\)
0.900994 + 0.433832i \(0.142839\pi\)
\(464\) 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 \(-0.571577\pi\)
−0.222976 + 0.974824i \(0.571577\pi\)
\(468\) 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
\(476\) −0.569453 15.8163i −0.0261008 0.724939i
\(477\) −1.09768 −0.0502595
\(478\) 24.7253i 1.13091i
\(479\) 10.2288 + 10.2288i 0.467368 + 0.467368i 0.901061 0.433693i \(-0.142790\pi\)
−0.433693 + 0.901061i \(0.642790\pi\)
\(480\) 0.134628i 0.00614490i
\(481\) −24.1722 4.83443i −1.10216 0.220431i
\(482\) 8.05225i 0.366770i
\(483\) 12.4106 0.446833i 0.564701 0.0203316i
\(484\) 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 0.730644 0.682758i \(-0.239220\pi\)
−0.682758 + 0.730644i \(0.739220\pi\)
\(488\) −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 \(-0.991400\pi\)
0.999635 0.0270146i \(-0.00860005\pi\)
\(492\) 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 0.608310 0.793699i \(-0.291848\pi\)
−0.793699 + 0.608310i \(0.791848\pi\)
\(500\) −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 \(-0.675158\pi\)
0.852380 + 0.522922i \(0.175158\pi\)
\(510\) 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
\(518\) −18.0771 + 0.650850i −0.794261 + 0.0285967i
\(519\) 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
\(525\) −13.1723 + 0.474257i −0.574885 + 0.0206983i
\(526\) −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
\(539\) −23.6078 + 27.2767i −1.01686 + 1.17489i
\(540\) −0.0951965 + 0.0951965i −0.00409660 + 0.00409660i
\(541\) −4.11753 + 4.11753i −0.177027 + 0.177027i −0.790058 0.613032i \(-0.789950\pi\)
0.613032 + 0.790058i \(0.289950\pi\)
\(542\) 14.3542i 0.616564i
\(543\) 22.3445i 0.958896i
\(544\) 4.22982 + 4.22982i 0.181352 + 0.181352i
\(545\) 2.15519 0.0923183
\(546\) 9.41540 + 1.53305i 0.402942 + 0.0656084i
\(547\) −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
\(553\) 30.6126 1.10218i 1.30178 0.0468696i
\(554\) −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 −0.879236 0.476386i \(-0.841947\pi\)
0.476386 + 0.879236i \(0.341947\pi\)
\(558\) −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 \(-0.387937\pi\)
0.344829 + 0.938665i \(0.387937\pi\)
\(564\) 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
\(567\) −2.64404 + 0.0951965i −0.111039 + 0.00399788i
\(568\) 12.2949 0.515882
\(569\) 26.8760i 1.12670i 0.826218 + 0.563351i \(0.190488\pi\)
−0.826218 + 0.563351i \(0.809512\pi\)
\(570\) −0.564480 0.564480i −0.0236434 0.0236434i
\(571\) 26.1591i 1.09472i 0.836896 + 0.547362i \(0.184368\pi\)
−0.836896 + 0.547362i \(0.815632\pi\)
\(572\) 3.64404 18.2202i 0.152365 0.761824i
\(573\) 12.0315i 0.502624i
\(574\) 11.3876 0.410001i 0.475309 0.0171131i
\(575\) 23.3839 0.975177
\(576\) 1.00000i 0.0416667i
\(577\) 3.83454 3.83454i 0.159634 0.159634i −0.622770 0.782405i \(-0.713993\pi\)
0.782405 + 0.622770i \(0.213993\pi\)
\(578\) −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 \(-0.900047\pi\)
0.308877 + 0.951102i \(0.400047\pi\)
\(588\) 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 \(-0.253250\pi\)
−0.714290 + 0.699850i \(0.753250\pi\)
\(594\) 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
\(609\) −0.437359 12.1474i −0.0177227 0.492239i
\(610\) 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 −0.965804 0.259274i \(-0.916517\pi\)
−0.259274 0.965804i \(-0.583483\pi\)
\(614\) 33.2422i 1.34155i
\(615\) −0.579829 −0.0233810
\(616\) −0.490590 13.6259i −0.0197664 0.549004i
\(617\) −22.7622 22.7622i −0.916372 0.916372i 0.0803909 0.996763i \(-0.474383\pi\)
−0.996763 + 0.0803909i \(0.974383\pi\)
\(618\) 5.87819 5.87819i 0.236455 0.236455i
\(619\) −9.96126 9.96126i −0.400377 0.400377i 0.477989 0.878366i \(-0.341366\pi\)
−0.878366 + 0.477989i \(0.841366\pi\)
\(620\) −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
\(630\) −0.355962 + 0.0128161i −0.0141819 + 0.000510606i
\(631\) 8.24750 8.24750i 0.328328 0.328328i −0.523623 0.851950i \(-0.675420\pi\)
0.851950 + 0.523623i \(0.175420\pi\)
\(632\) −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
\(637\) 15.4740 + 19.9388i 0.613101 + 0.790005i
\(638\) −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 \(-0.817649\pi\)
0.840347 0.542049i \(-0.182351\pi\)
\(642\) 13.4046 13.4046i 0.529037 0.529037i
\(643\) 27.7346 27.7346i 1.09375 1.09375i 0.0986217 0.995125i \(-0.468557\pi\)
0.995125 0.0986217i \(-0.0314434\pi\)
\(644\) −12.4106 + 0.446833i −0.489046 + 0.0176077i
\(645\) 0.836269 0.836269i 0.0329281 0.0329281i
\(646\) 35.4703 1.39556
\(647\) −14.6620 −0.576425 −0.288212 0.957567i \(-0.593061\pi\)
−0.288212 + 0.957567i \(0.593061\pi\)
\(648\) 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
\(658\) 0.442668 + 12.2949i 0.0172570 + 0.479305i
\(659\) 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 0.975284 + 0.220956i \(0.0709178\pi\)
0.220956 + 0.975284i \(0.429082\pi\)
\(662\) 14.4827i 0.562885i
\(663\) 17.9456 11.9638i 0.696950 0.464634i
\(664\) 1.82161i 0.0706924i
\(665\) −0.0759948 2.11072i −0.00294695 0.0818503i
\(666\) −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 \(0.316831\pi\)
−0.544206 + 0.838952i \(0.683169\pi\)
\(674\) 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 −0.453165 0.891427i \(-0.649705\pi\)
0.891427 + 0.453165i \(0.149705\pi\)
\(684\) 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 \(-0.763281\pi\)
0.676996 + 0.735987i \(0.263281\pi\)
\(692\) 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
\(700\) 13.1723 0.474257i 0.497865 0.0179252i
\(701\) 8.43541i 0.318601i 0.987230 + 0.159300i \(0.0509239\pi\)
−0.987230 + 0.159300i \(0.949076\pi\)
\(702\) 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
\(707\) 8.17724 0.294415i 0.307537 0.0110726i
\(708\) 1.30620 + 1.30620i 0.0490900 + 0.0490900i
\(709\) −19.8616 + 19.8616i −0.745917 + 0.745917i −0.973710 0.227793i \(-0.926849\pi\)
0.227793 + 0.973710i \(0.426849\pi\)
\(710\) −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 \(-0.480877\pi\)
0.0600397 + 0.998196i \(0.480877\pi\)
\(720\) 0.0951965 0.0951965i 0.00354776 0.00354776i
\(721\) 21.9799 0.791369i 0.818575 0.0294721i
\(722\) −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 \(-0.420061\pi\)
0.248503 + 0.968631i \(0.420061\pi\)
\(728\) −9.41540 1.53305i −0.348958 0.0568185i
\(729\) −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 −0.0605789 + 0.998163i \(0.519295\pi\)
−0.998163 + 0.0605789i \(0.980705\pi\)
\(734\) 0.776179 0.776179i 0.0286493 0.0286493i
\(735\) −0.712572 0.616727i −0.0262836 0.0227483i
\(736\) 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 −0.593094 0.805133i \(-0.702094\pi\)
0.805133 + 0.593094i \(0.202094\pi\)
\(740\) −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 0.930826 0.365462i \(-0.119089\pi\)
−0.365462 + 0.930826i \(0.619089\pi\)
\(744\) 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
\(749\) 50.1229 1.80463i 1.83145 0.0659399i
\(750\) −1.34384 −0.0490701
\(751\) 4.11812i 0.150272i −0.997173 0.0751362i \(-0.976061\pi\)
0.997173 0.0751362i \(-0.0239391\pi\)
\(752\) −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
\(756\) 2.64404 0.0951965i 0.0961627 0.00346226i
\(757\) −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 \(-0.0678431\pi\)
−0.211525 + 0.977372i \(0.567843\pi\)
\(762\) 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 \(-0.767276\pi\)
0.667706 + 0.744425i \(0.267276\pi\)
\(770\) −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 \(-0.720624\pi\)
0.769263 + 0.638933i \(0.220624\pi\)
\(774\) −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