Properties

Label 690.2.j.a.367.6
Level $690$
Weight $2$
Character 690.367
Analytic conductor $5.510$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 367.6
Character \(\chi\) \(=\) 690.367
Dual form 690.2.j.a.643.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(1.05927 - 1.05927i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.13084 - 0.677875i) q^{5} -1.00000 q^{6} +(1.05927 - 1.05927i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(-1.98606 - 1.02740i) q^{10} -2.05480i q^{11} +(0.707107 + 0.707107i) q^{12} +(2.75307 - 2.75307i) q^{13} -1.49804 q^{14} +(1.02740 - 1.98606i) q^{15} -1.00000 q^{16} +(-4.76291 + 4.76291i) q^{17} +(-0.707107 + 0.707107i) q^{18} -1.85358 q^{19} +(0.677875 + 2.13084i) q^{20} -1.49804i q^{21} +(-1.45297 + 1.45297i) q^{22} +(2.97121 + 3.76456i) q^{23} -1.00000i q^{24} +(4.08097 - 2.88889i) q^{25} -3.89342 q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.05927 + 1.05927i) q^{28} -7.96345i q^{29} +(-2.13084 + 0.677875i) q^{30} +10.3127 q^{31} +(0.707107 + 0.707107i) q^{32} +(-1.45297 - 1.45297i) q^{33} +6.73577 q^{34} +(1.53909 - 2.97520i) q^{35} +1.00000 q^{36} +(-2.66303 + 2.66303i) q^{37} +(1.31068 + 1.31068i) q^{38} -3.89342i q^{39} +(1.02740 - 1.98606i) q^{40} -8.60620 q^{41} +(-1.05927 + 1.05927i) q^{42} +(-1.45989 - 1.45989i) q^{43} +2.05480 q^{44} +(-0.677875 - 2.13084i) q^{45} +(0.560984 - 4.76291i) q^{46} +(1.89984 + 1.89984i) q^{47} +(-0.707107 + 0.707107i) q^{48} +4.75588i q^{49} +(-4.92843 - 0.842929i) q^{50} +6.73577i q^{51} +(2.75307 + 2.75307i) q^{52} +(-3.57151 - 3.57151i) q^{53} +1.00000i q^{54} +(-1.39290 - 4.37846i) q^{55} -1.49804i q^{56} +(-1.31068 + 1.31068i) q^{57} +(-5.63101 + 5.63101i) q^{58} -3.82027i q^{59} +(1.98606 + 1.02740i) q^{60} -2.76364i q^{61} +(-7.29215 - 7.29215i) q^{62} +(-1.05927 - 1.05927i) q^{63} -1.00000i q^{64} +(4.00011 - 7.73258i) q^{65} +2.05480i q^{66} +(-7.21961 + 7.21961i) q^{67} +(-4.76291 - 4.76291i) q^{68} +(4.76291 + 0.560984i) q^{69} +(-3.19208 + 1.01548i) q^{70} +0.620733 q^{71} +(-0.707107 - 0.707107i) q^{72} +(4.77136 - 4.77136i) q^{73} +3.76610 q^{74} +(0.842929 - 4.92843i) q^{75} -1.85358i q^{76} +(-2.17660 - 2.17660i) q^{77} +(-2.75307 + 2.75307i) q^{78} +16.3891 q^{79} +(-2.13084 + 0.677875i) q^{80} -1.00000 q^{81} +(6.08551 + 6.08551i) q^{82} +(-5.71805 - 5.71805i) q^{83} +1.49804 q^{84} +(-6.92035 + 13.3777i) q^{85} +2.06459i q^{86} +(-5.63101 - 5.63101i) q^{87} +(-1.45297 - 1.45297i) q^{88} -0.705848 q^{89} +(-1.02740 + 1.98606i) q^{90} -5.83250i q^{91} +(-3.76456 + 2.97121i) q^{92} +(7.29215 - 7.29215i) q^{93} -2.68677i q^{94} +(-3.94968 + 1.25650i) q^{95} +1.00000 q^{96} +(-0.564967 + 0.564967i) q^{97} +(3.36292 - 3.36292i) q^{98} -2.05480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 24q^{6} + O(q^{10}) \) \( 24q - 24q^{6} - 24q^{16} - 8q^{23} - 16q^{25} - 16q^{26} + 16q^{31} - 16q^{35} + 24q^{36} - 8q^{46} - 8q^{47} + 24q^{50} + 24q^{55} + 16q^{58} - 56q^{62} - 32q^{70} - 16q^{71} - 48q^{73} - 24q^{81} + 24q^{82} + 16q^{87} - 8q^{92} + 56q^{93} + 24q^{95} + 24q^{96} - 32q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 0.707107i −0.500000 0.500000i
\(3\) 0.707107 0.707107i 0.408248 0.408248i
\(4\) 1.00000i 0.500000i
\(5\) 2.13084 0.677875i 0.952941 0.303155i
\(6\) −1.00000 −0.408248
\(7\) 1.05927 1.05927i 0.400368 0.400368i −0.477995 0.878363i \(-0.658636\pi\)
0.878363 + 0.477995i \(0.158636\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) 1.00000i 0.333333i
\(10\) −1.98606 1.02740i −0.628048 0.324893i
\(11\) 2.05480i 0.619547i −0.950810 0.309773i \(-0.899747\pi\)
0.950810 0.309773i \(-0.100253\pi\)
\(12\) 0.707107 + 0.707107i 0.204124 + 0.204124i
\(13\) 2.75307 2.75307i 0.763563 0.763563i −0.213401 0.976965i \(-0.568454\pi\)
0.976965 + 0.213401i \(0.0684542\pi\)
\(14\) −1.49804 −0.400368
\(15\) 1.02740 1.98606i 0.265274 0.512799i
\(16\) −1.00000 −0.250000
\(17\) −4.76291 + 4.76291i −1.15517 + 1.15517i −0.169675 + 0.985500i \(0.554272\pi\)
−0.985500 + 0.169675i \(0.945728\pi\)
\(18\) −0.707107 + 0.707107i −0.166667 + 0.166667i
\(19\) −1.85358 −0.425240 −0.212620 0.977135i \(-0.568200\pi\)
−0.212620 + 0.977135i \(0.568200\pi\)
\(20\) 0.677875 + 2.13084i 0.151577 + 0.476471i
\(21\) 1.49804i 0.326899i
\(22\) −1.45297 + 1.45297i −0.309773 + 0.309773i
\(23\) 2.97121 + 3.76456i 0.619540 + 0.784965i
\(24\) 1.00000i 0.204124i
\(25\) 4.08097 2.88889i 0.816194 0.577778i
\(26\) −3.89342 −0.763563
\(27\) −0.707107 0.707107i −0.136083 0.136083i
\(28\) 1.05927 + 1.05927i 0.200184 + 0.200184i
\(29\) 7.96345i 1.47877i −0.673280 0.739387i \(-0.735115\pi\)
0.673280 0.739387i \(-0.264885\pi\)
\(30\) −2.13084 + 0.677875i −0.389037 + 0.123762i
\(31\) 10.3127 1.85221 0.926105 0.377267i \(-0.123136\pi\)
0.926105 + 0.377267i \(0.123136\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −1.45297 1.45297i −0.252929 0.252929i
\(34\) 6.73577 1.15517
\(35\) 1.53909 2.97520i 0.260153 0.502900i
\(36\) 1.00000 0.166667
\(37\) −2.66303 + 2.66303i −0.437800 + 0.437800i −0.891271 0.453471i \(-0.850185\pi\)
0.453471 + 0.891271i \(0.350185\pi\)
\(38\) 1.31068 + 1.31068i 0.212620 + 0.212620i
\(39\) 3.89342i 0.623447i
\(40\) 1.02740 1.98606i 0.162447 0.314024i
\(41\) −8.60620 −1.34406 −0.672032 0.740522i \(-0.734578\pi\)
−0.672032 + 0.740522i \(0.734578\pi\)
\(42\) −1.05927 + 1.05927i −0.163449 + 0.163449i
\(43\) −1.45989 1.45989i −0.222630 0.222630i 0.586975 0.809605i \(-0.300319\pi\)
−0.809605 + 0.586975i \(0.800319\pi\)
\(44\) 2.05480 0.309773
\(45\) −0.677875 2.13084i −0.101052 0.317647i
\(46\) 0.560984 4.76291i 0.0827126 0.702253i
\(47\) 1.89984 + 1.89984i 0.277120 + 0.277120i 0.831958 0.554838i \(-0.187220\pi\)
−0.554838 + 0.831958i \(0.687220\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 4.75588i 0.679412i
\(50\) −4.92843 0.842929i −0.696986 0.119208i
\(51\) 6.73577i 0.943196i
\(52\) 2.75307 + 2.75307i 0.381782 + 0.381782i
\(53\) −3.57151 3.57151i −0.490585 0.490585i 0.417906 0.908490i \(-0.362764\pi\)
−0.908490 + 0.417906i \(0.862764\pi\)
\(54\) 1.00000i 0.136083i
\(55\) −1.39290 4.37846i −0.187819 0.590392i
\(56\) 1.49804i 0.200184i
\(57\) −1.31068 + 1.31068i −0.173604 + 0.173604i
\(58\) −5.63101 + 5.63101i −0.739387 + 0.739387i
\(59\) 3.82027i 0.497357i −0.968586 0.248679i \(-0.920004\pi\)
0.968586 0.248679i \(-0.0799963\pi\)
\(60\) 1.98606 + 1.02740i 0.256400 + 0.132637i
\(61\) 2.76364i 0.353848i −0.984224 0.176924i \(-0.943385\pi\)
0.984224 0.176924i \(-0.0566148\pi\)
\(62\) −7.29215 7.29215i −0.926105 0.926105i
\(63\) −1.05927 1.05927i −0.133456 0.133456i
\(64\) 1.00000i 0.125000i
\(65\) 4.00011 7.73258i 0.496153 0.959109i
\(66\) 2.05480i 0.252929i
\(67\) −7.21961 + 7.21961i −0.882015 + 0.882015i −0.993739 0.111724i \(-0.964363\pi\)
0.111724 + 0.993739i \(0.464363\pi\)
\(68\) −4.76291 4.76291i −0.577587 0.577587i
\(69\) 4.76291 + 0.560984i 0.573387 + 0.0675345i
\(70\) −3.19208 + 1.01548i −0.381527 + 0.121373i
\(71\) 0.620733 0.0736675 0.0368337 0.999321i \(-0.488273\pi\)
0.0368337 + 0.999321i \(0.488273\pi\)
\(72\) −0.707107 0.707107i −0.0833333 0.0833333i
\(73\) 4.77136 4.77136i 0.558446 0.558446i −0.370419 0.928865i \(-0.620786\pi\)
0.928865 + 0.370419i \(0.120786\pi\)
\(74\) 3.76610 0.437800
\(75\) 0.842929 4.92843i 0.0973331 0.569087i
\(76\) 1.85358i 0.212620i
\(77\) −2.17660 2.17660i −0.248047 0.248047i
\(78\) −2.75307 + 2.75307i −0.311723 + 0.311723i
\(79\) 16.3891 1.84391 0.921957 0.387292i \(-0.126589\pi\)
0.921957 + 0.387292i \(0.126589\pi\)
\(80\) −2.13084 + 0.677875i −0.238235 + 0.0757887i
\(81\) −1.00000 −0.111111
\(82\) 6.08551 + 6.08551i 0.672032 + 0.672032i
\(83\) −5.71805 5.71805i −0.627637 0.627637i 0.319836 0.947473i \(-0.396372\pi\)
−0.947473 + 0.319836i \(0.896372\pi\)
\(84\) 1.49804 0.163449
\(85\) −6.92035 + 13.3777i −0.750617 + 1.45101i
\(86\) 2.06459i 0.222630i
\(87\) −5.63101 5.63101i −0.603707 0.603707i
\(88\) −1.45297 1.45297i −0.154887 0.154887i
\(89\) −0.705848 −0.0748197 −0.0374099 0.999300i \(-0.511911\pi\)
−0.0374099 + 0.999300i \(0.511911\pi\)
\(90\) −1.02740 + 1.98606i −0.108298 + 0.209349i
\(91\) 5.83250i 0.611412i
\(92\) −3.76456 + 2.97121i −0.392483 + 0.309770i
\(93\) 7.29215 7.29215i 0.756161 0.756161i
\(94\) 2.68677i 0.277120i
\(95\) −3.94968 + 1.25650i −0.405229 + 0.128914i
\(96\) 1.00000 0.102062
\(97\) −0.564967 + 0.564967i −0.0573637 + 0.0573637i −0.735207 0.677843i \(-0.762915\pi\)
0.677843 + 0.735207i \(0.262915\pi\)
\(98\) 3.36292 3.36292i 0.339706 0.339706i
\(99\) −2.05480 −0.206516
\(100\) 2.88889 + 4.08097i 0.288889 + 0.408097i
\(101\) −14.5606 −1.44883 −0.724416 0.689363i \(-0.757890\pi\)
−0.724416 + 0.689363i \(0.757890\pi\)
\(102\) 4.76291 4.76291i 0.471598 0.471598i
\(103\) 4.76419 + 4.76419i 0.469430 + 0.469430i 0.901730 0.432300i \(-0.142298\pi\)
−0.432300 + 0.901730i \(0.642298\pi\)
\(104\) 3.89342i 0.381782i
\(105\) −1.01548 3.19208i −0.0991010 0.311515i
\(106\) 5.05088i 0.490585i
\(107\) −11.8110 + 11.8110i −1.14181 + 1.14181i −0.153689 + 0.988119i \(0.549115\pi\)
−0.988119 + 0.153689i \(0.950885\pi\)
\(108\) 0.707107 0.707107i 0.0680414 0.0680414i
\(109\) −2.85379 −0.273343 −0.136672 0.990616i \(-0.543641\pi\)
−0.136672 + 0.990616i \(0.543641\pi\)
\(110\) −2.11111 + 4.08097i −0.201287 + 0.389105i
\(111\) 3.76610i 0.357462i
\(112\) −1.05927 + 1.05927i −0.100092 + 0.100092i
\(113\) 6.25116 + 6.25116i 0.588060 + 0.588060i 0.937106 0.349046i \(-0.113494\pi\)
−0.349046 + 0.937106i \(0.613494\pi\)
\(114\) 1.85358 0.173604
\(115\) 8.88308 + 6.00757i 0.828351 + 0.560209i
\(116\) 7.96345 0.739387
\(117\) −2.75307 2.75307i −0.254521 0.254521i
\(118\) −2.70134 + 2.70134i −0.248679 + 0.248679i
\(119\) 10.0904i 0.924989i
\(120\) −0.677875 2.13084i −0.0618812 0.194518i
\(121\) 6.77778 0.616162
\(122\) −1.95419 + 1.95419i −0.176924 + 0.176924i
\(123\) −6.08551 + 6.08551i −0.548712 + 0.548712i
\(124\) 10.3127i 0.926105i
\(125\) 6.73760 8.92215i 0.602629 0.798022i
\(126\) 1.49804i 0.133456i
\(127\) 5.96063 + 5.96063i 0.528920 + 0.528920i 0.920250 0.391330i \(-0.127985\pi\)
−0.391330 + 0.920250i \(0.627985\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) −2.06459 −0.181777
\(130\) −8.29627 + 2.63925i −0.727631 + 0.231478i
\(131\) 19.3136 1.68744 0.843718 0.536787i \(-0.180362\pi\)
0.843718 + 0.536787i \(0.180362\pi\)
\(132\) 1.45297 1.45297i 0.126464 0.126464i
\(133\) −1.96345 + 1.96345i −0.170252 + 0.170252i
\(134\) 10.2101 0.882015
\(135\) −1.98606 1.02740i −0.170933 0.0884247i
\(136\) 6.73577i 0.577587i
\(137\) −11.2806 + 11.2806i −0.963769 + 0.963769i −0.999366 0.0355976i \(-0.988667\pi\)
0.0355976 + 0.999366i \(0.488667\pi\)
\(138\) −2.97121 3.76456i −0.252926 0.320461i
\(139\) 5.76656i 0.489113i 0.969635 + 0.244557i \(0.0786424\pi\)
−0.969635 + 0.244557i \(0.921358\pi\)
\(140\) 2.97520 + 1.53909i 0.251450 + 0.130077i
\(141\) 2.68677 0.226267
\(142\) −0.438925 0.438925i −0.0368337 0.0368337i
\(143\) −5.65701 5.65701i −0.473063 0.473063i
\(144\) 1.00000i 0.0833333i
\(145\) −5.39822 16.9688i −0.448298 1.40919i
\(146\) −6.74773 −0.558446
\(147\) 3.36292 + 3.36292i 0.277369 + 0.277369i
\(148\) −2.66303 2.66303i −0.218900 0.218900i
\(149\) 19.0202 1.55820 0.779100 0.626900i \(-0.215677\pi\)
0.779100 + 0.626900i \(0.215677\pi\)
\(150\) −4.08097 + 2.88889i −0.333210 + 0.235877i
\(151\) −8.07922 −0.657478 −0.328739 0.944421i \(-0.606624\pi\)
−0.328739 + 0.944421i \(0.606624\pi\)
\(152\) −1.31068 + 1.31068i −0.106310 + 0.106310i
\(153\) 4.76291 + 4.76291i 0.385058 + 0.385058i
\(154\) 3.07818i 0.248047i
\(155\) 21.9747 6.99070i 1.76505 0.561506i
\(156\) 3.89342 0.311723
\(157\) 5.10732 5.10732i 0.407609 0.407609i −0.473295 0.880904i \(-0.656936\pi\)
0.880904 + 0.473295i \(0.156936\pi\)
\(158\) −11.5888 11.5888i −0.921957 0.921957i
\(159\) −5.05088 −0.400561
\(160\) 1.98606 + 1.02740i 0.157012 + 0.0812233i
\(161\) 7.13502 + 0.840376i 0.562318 + 0.0662309i
\(162\) 0.707107 + 0.707107i 0.0555556 + 0.0555556i
\(163\) 3.50613 3.50613i 0.274621 0.274621i −0.556336 0.830957i \(-0.687793\pi\)
0.830957 + 0.556336i \(0.187793\pi\)
\(164\) 8.60620i 0.672032i
\(165\) −4.08097 2.11111i −0.317703 0.164350i
\(166\) 8.08654i 0.627637i
\(167\) 14.5151 + 14.5151i 1.12321 + 1.12321i 0.991255 + 0.131958i \(0.0421263\pi\)
0.131958 + 0.991255i \(0.457874\pi\)
\(168\) −1.05927 1.05927i −0.0817247 0.0817247i
\(169\) 2.15875i 0.166057i
\(170\) 14.3529 4.56601i 1.10081 0.350197i
\(171\) 1.85358i 0.141747i
\(172\) 1.45989 1.45989i 0.111315 0.111315i
\(173\) −17.0914 + 17.0914i −1.29943 + 1.29943i −0.370665 + 0.928767i \(0.620870\pi\)
−0.928767 + 0.370665i \(0.879130\pi\)
\(174\) 7.96345i 0.603707i
\(175\) 1.26274 7.38298i 0.0954542 0.558101i
\(176\) 2.05480i 0.154887i
\(177\) −2.70134 2.70134i −0.203045 0.203045i
\(178\) 0.499110 + 0.499110i 0.0374099 + 0.0374099i
\(179\) 19.5452i 1.46088i 0.682979 + 0.730438i \(0.260684\pi\)
−0.682979 + 0.730438i \(0.739316\pi\)
\(180\) 2.13084 0.677875i 0.158824 0.0505258i
\(181\) 25.0126i 1.85917i 0.368607 + 0.929585i \(0.379835\pi\)
−0.368607 + 0.929585i \(0.620165\pi\)
\(182\) −4.12420 + 4.12420i −0.305706 + 0.305706i
\(183\) −1.95419 1.95419i −0.144458 0.144458i
\(184\) 4.76291 + 0.560984i 0.351126 + 0.0413563i
\(185\) −3.86930 + 7.47970i −0.284476 + 0.549919i
\(186\) −10.3127 −0.756161
\(187\) 9.78685 + 9.78685i 0.715685 + 0.715685i
\(188\) −1.89984 + 1.89984i −0.138560 + 0.138560i
\(189\) −1.49804 −0.108966
\(190\) 3.68132 + 1.90437i 0.267071 + 0.138158i
\(191\) 10.7049i 0.774582i −0.921958 0.387291i \(-0.873411\pi\)
0.921958 0.387291i \(-0.126589\pi\)
\(192\) −0.707107 0.707107i −0.0510310 0.0510310i
\(193\) −7.17660 + 7.17660i −0.516583 + 0.516583i −0.916536 0.399953i \(-0.869027\pi\)
0.399953 + 0.916536i \(0.369027\pi\)
\(194\) 0.798984 0.0573637
\(195\) −2.63925 8.29627i −0.189001 0.594108i
\(196\) −4.75588 −0.339706
\(197\) 2.71278 + 2.71278i 0.193278 + 0.193278i 0.797111 0.603833i \(-0.206361\pi\)
−0.603833 + 0.797111i \(0.706361\pi\)
\(198\) 1.45297 + 1.45297i 0.103258 + 0.103258i
\(199\) 19.3755 1.37350 0.686748 0.726896i \(-0.259038\pi\)
0.686748 + 0.726896i \(0.259038\pi\)
\(200\) 0.842929 4.92843i 0.0596041 0.348493i
\(201\) 10.2101i 0.720163i
\(202\) 10.2959 + 10.2959i 0.724416 + 0.724416i
\(203\) −8.43546 8.43546i −0.592053 0.592053i
\(204\) −6.73577 −0.471598
\(205\) −18.3385 + 5.83393i −1.28081 + 0.407459i
\(206\) 6.73758i 0.469430i
\(207\) 3.76456 2.97121i 0.261655 0.206513i
\(208\) −2.75307 + 2.75307i −0.190891 + 0.190891i
\(209\) 3.80874i 0.263456i
\(210\) −1.53909 + 2.97520i −0.106207 + 0.205308i
\(211\) −9.81831 −0.675921 −0.337960 0.941160i \(-0.609737\pi\)
−0.337960 + 0.941160i \(0.609737\pi\)
\(212\) 3.57151 3.57151i 0.245292 0.245292i
\(213\) 0.438925 0.438925i 0.0300746 0.0300746i
\(214\) 16.7032 1.14181
\(215\) −4.10040 2.12116i −0.279645 0.144662i
\(216\) −1.00000 −0.0680414
\(217\) 10.9239 10.9239i 0.741564 0.741564i
\(218\) 2.01793 + 2.01793i 0.136672 + 0.136672i
\(219\) 6.74773i 0.455969i
\(220\) 4.37846 1.39290i 0.295196 0.0939094i
\(221\) 26.2252i 1.76410i
\(222\) 2.66303 2.66303i 0.178731 0.178731i
\(223\) −11.7320 + 11.7320i −0.785633 + 0.785633i −0.980775 0.195142i \(-0.937483\pi\)
0.195142 + 0.980775i \(0.437483\pi\)
\(224\) 1.49804 0.100092
\(225\) −2.88889 4.08097i −0.192593 0.272065i
\(226\) 8.84048i 0.588060i
\(227\) −7.21427 + 7.21427i −0.478828 + 0.478828i −0.904757 0.425929i \(-0.859947\pi\)
0.425929 + 0.904757i \(0.359947\pi\)
\(228\) −1.31068 1.31068i −0.0868018 0.0868018i
\(229\) −26.7216 −1.76582 −0.882908 0.469547i \(-0.844417\pi\)
−0.882908 + 0.469547i \(0.844417\pi\)
\(230\) −2.03329 10.5293i −0.134071 0.694280i
\(231\) −3.07818 −0.202529
\(232\) −5.63101 5.63101i −0.369694 0.369694i
\(233\) 7.66479 7.66479i 0.502137 0.502137i −0.409965 0.912101i \(-0.634459\pi\)
0.912101 + 0.409965i \(0.134459\pi\)
\(234\) 3.89342i 0.254521i
\(235\) 5.33610 + 2.76040i 0.348089 + 0.180069i
\(236\) 3.82027 0.248679
\(237\) 11.5888 11.5888i 0.752775 0.752775i
\(238\) 7.13502 7.13502i 0.462495 0.462495i
\(239\) 5.19806i 0.336235i 0.985767 + 0.168117i \(0.0537688\pi\)
−0.985767 + 0.168117i \(0.946231\pi\)
\(240\) −1.02740 + 1.98606i −0.0663185 + 0.128200i
\(241\) 26.1013i 1.68134i −0.541551 0.840668i \(-0.682163\pi\)
0.541551 0.840668i \(-0.317837\pi\)
\(242\) −4.79261 4.79261i −0.308081 0.308081i
\(243\) −0.707107 + 0.707107i −0.0453609 + 0.0453609i
\(244\) 2.76364 0.176924
\(245\) 3.22389 + 10.1340i 0.205967 + 0.647439i
\(246\) 8.60620 0.548712
\(247\) −5.10303 + 5.10303i −0.324698 + 0.324698i
\(248\) 7.29215 7.29215i 0.463052 0.463052i
\(249\) −8.08654 −0.512464
\(250\) −11.0731 + 1.54471i −0.700325 + 0.0976963i
\(251\) 4.77728i 0.301539i 0.988569 + 0.150770i \(0.0481752\pi\)
−0.988569 + 0.150770i \(0.951825\pi\)
\(252\) 1.05927 1.05927i 0.0667279 0.0667279i
\(253\) 7.73544 6.10525i 0.486323 0.383834i
\(254\) 8.42961i 0.528920i
\(255\) 4.56601 + 14.3529i 0.285935 + 0.898811i
\(256\) 1.00000 0.0625000
\(257\) 3.06500 + 3.06500i 0.191189 + 0.191189i 0.796210 0.605021i \(-0.206835\pi\)
−0.605021 + 0.796210i \(0.706835\pi\)
\(258\) 1.45989 + 1.45989i 0.0908885 + 0.0908885i
\(259\) 5.64176i 0.350562i
\(260\) 7.73258 + 4.00011i 0.479554 + 0.248076i
\(261\) −7.96345 −0.492925
\(262\) −13.6568 13.6568i −0.843718 0.843718i
\(263\) −3.15317 3.15317i −0.194433 0.194433i 0.603176 0.797608i \(-0.293902\pi\)
−0.797608 + 0.603176i \(0.793902\pi\)
\(264\) −2.05480 −0.126464
\(265\) −10.0314 5.18929i −0.616222 0.318775i
\(266\) 2.77673 0.170252
\(267\) −0.499110 + 0.499110i −0.0305450 + 0.0305450i
\(268\) −7.21961 7.21961i −0.441008 0.441008i
\(269\) 14.0173i 0.854649i −0.904098 0.427325i \(-0.859456\pi\)
0.904098 0.427325i \(-0.140544\pi\)
\(270\) 0.677875 + 2.13084i 0.0412542 + 0.129679i
\(271\) 0.314270 0.0190906 0.00954528 0.999954i \(-0.496962\pi\)
0.00954528 + 0.999954i \(0.496962\pi\)
\(272\) 4.76291 4.76291i 0.288794 0.288794i
\(273\) −4.12420 4.12420i −0.249608 0.249608i
\(274\) 15.9532 0.963769
\(275\) −5.93610 8.38560i −0.357960 0.505671i
\(276\) −0.560984 + 4.76291i −0.0337673 + 0.286693i
\(277\) −13.1608 13.1608i −0.790754 0.790754i 0.190862 0.981617i \(-0.438872\pi\)
−0.981617 + 0.190862i \(0.938872\pi\)
\(278\) 4.07757 4.07757i 0.244557 0.244557i
\(279\) 10.3127i 0.617403i
\(280\) −1.01548 3.19208i −0.0606867 0.190763i
\(281\) 11.4727i 0.684403i 0.939627 + 0.342201i \(0.111173\pi\)
−0.939627 + 0.342201i \(0.888827\pi\)
\(282\) −1.89984 1.89984i −0.113134 0.113134i
\(283\) 3.63921 + 3.63921i 0.216329 + 0.216329i 0.806949 0.590621i \(-0.201117\pi\)
−0.590621 + 0.806949i \(0.701117\pi\)
\(284\) 0.620733i 0.0368337i
\(285\) −1.90437 + 3.68132i −0.112805 + 0.218063i
\(286\) 8.00023i 0.473063i
\(287\) −9.11632 + 9.11632i −0.538119 + 0.538119i
\(288\) 0.707107 0.707107i 0.0416667 0.0416667i
\(289\) 28.3706i 1.66886i
\(290\) −8.18166 + 15.8159i −0.480444 + 0.928742i
\(291\) 0.798984i 0.0468373i
\(292\) 4.77136 + 4.77136i 0.279223 + 0.279223i
\(293\) −3.00016 3.00016i −0.175271 0.175271i 0.614020 0.789291i \(-0.289552\pi\)
−0.789291 + 0.614020i \(0.789552\pi\)
\(294\) 4.75588i 0.277369i
\(295\) −2.58967 8.14040i −0.150776 0.473952i
\(296\) 3.76610i 0.218900i
\(297\) −1.45297 + 1.45297i −0.0843097 + 0.0843097i
\(298\) −13.4493 13.4493i −0.779100 0.779100i
\(299\) 18.5440 + 2.18415i 1.07243 + 0.126313i
\(300\) 4.92843 + 0.842929i 0.284543 + 0.0486665i
\(301\) −3.09283 −0.178268
\(302\) 5.71287 + 5.71287i 0.328739 + 0.328739i
\(303\) −10.2959 + 10.2959i −0.591483 + 0.591483i
\(304\) 1.85358 0.106310
\(305\) −1.87341 5.88889i −0.107271 0.337197i
\(306\) 6.73577i 0.385058i
\(307\) −14.9088 14.9088i −0.850891 0.850891i 0.139352 0.990243i \(-0.455498\pi\)
−0.990243 + 0.139352i \(0.955498\pi\)
\(308\) 2.17660 2.17660i 0.124023 0.124023i
\(309\) 6.73758 0.383288
\(310\) −20.4816 10.5953i −1.16328 0.601770i
\(311\) 10.4912 0.594903 0.297451 0.954737i \(-0.403863\pi\)
0.297451 + 0.954737i \(0.403863\pi\)
\(312\) −2.75307 2.75307i −0.155862 0.155862i
\(313\) 13.7256 + 13.7256i 0.775815 + 0.775815i 0.979116 0.203301i \(-0.0651671\pi\)
−0.203301 + 0.979116i \(0.565167\pi\)
\(314\) −7.22285 −0.407609
\(315\) −2.97520 1.53909i −0.167633 0.0867178i
\(316\) 16.3891i 0.921957i
\(317\) −8.37263 8.37263i −0.470254 0.470254i 0.431743 0.901997i \(-0.357899\pi\)
−0.901997 + 0.431743i \(0.857899\pi\)
\(318\) 3.57151 + 3.57151i 0.200280 + 0.200280i
\(319\) −16.3633 −0.916170
\(320\) −0.677875 2.13084i −0.0378944 0.119118i
\(321\) 16.7032i 0.932283i
\(322\) −4.45099 5.63946i −0.248044 0.314275i
\(323\) 8.82843 8.82843i 0.491227 0.491227i
\(324\) 1.00000i 0.0555556i
\(325\) 3.28188 19.1885i 0.182046 1.06439i
\(326\) −4.95842 −0.274621
\(327\) −2.01793 + 2.01793i −0.111592 + 0.111592i
\(328\) −6.08551 + 6.08551i −0.336016 + 0.336016i
\(329\) 4.02489 0.221899
\(330\) 1.39290 + 4.37846i 0.0766767 + 0.241026i
\(331\) 14.8469 0.816059 0.408029 0.912969i \(-0.366216\pi\)
0.408029 + 0.912969i \(0.366216\pi\)
\(332\) 5.71805 5.71805i 0.313819 0.313819i
\(333\) 2.66303 + 2.66303i 0.145933 + 0.145933i
\(334\) 20.5275i 1.12321i
\(335\) −10.4898 + 20.2778i −0.573122 + 1.10790i
\(336\) 1.49804i 0.0817247i
\(337\) 0.402707 0.402707i 0.0219369 0.0219369i −0.696053 0.717990i \(-0.745062\pi\)
0.717990 + 0.696053i \(0.245062\pi\)
\(338\) −1.52646 + 1.52646i −0.0830287 + 0.0830287i
\(339\) 8.84048 0.480149
\(340\) −13.3777 6.92035i −0.725505 0.375308i
\(341\) 21.1905i 1.14753i
\(342\) 1.31068 1.31068i 0.0708734 0.0708734i
\(343\) 12.4527 + 12.4527i 0.672382 + 0.672382i
\(344\) −2.06459 −0.111315
\(345\) 10.5293 2.03329i 0.566877 0.109469i
\(346\) 24.1708 1.29943
\(347\) 10.0204 + 10.0204i 0.537924 + 0.537924i 0.922919 0.384995i \(-0.125797\pi\)
−0.384995 + 0.922919i \(0.625797\pi\)
\(348\) 5.63101 5.63101i 0.301854 0.301854i
\(349\) 21.1479i 1.13202i −0.824398 0.566010i \(-0.808486\pi\)
0.824398 0.566010i \(-0.191514\pi\)
\(350\) −6.11345 + 4.32767i −0.326778 + 0.231323i
\(351\) −3.89342 −0.207816
\(352\) 1.45297 1.45297i 0.0774434 0.0774434i
\(353\) −5.85206 + 5.85206i −0.311474 + 0.311474i −0.845480 0.534006i \(-0.820686\pi\)
0.534006 + 0.845480i \(0.320686\pi\)
\(354\) 3.82027i 0.203045i
\(355\) 1.32268 0.420780i 0.0702008 0.0223327i
\(356\) 0.705848i 0.0374099i
\(357\) 7.13502 + 7.13502i 0.377625 + 0.377625i
\(358\) 13.8205 13.8205i 0.730438 0.730438i
\(359\) −7.29231 −0.384874 −0.192437 0.981309i \(-0.561639\pi\)
−0.192437 + 0.981309i \(0.561639\pi\)
\(360\) −1.98606 1.02740i −0.104675 0.0541489i
\(361\) −15.5642 −0.819171
\(362\) 17.6866 17.6866i 0.929585 0.929585i
\(363\) 4.79261 4.79261i 0.251547 0.251547i
\(364\) 5.83250 0.305706
\(365\) 6.93263 13.4014i 0.362871 0.701462i
\(366\) 2.76364i 0.144458i
\(367\) −4.42844 + 4.42844i −0.231162 + 0.231162i −0.813178 0.582015i \(-0.802264\pi\)
0.582015 + 0.813178i \(0.302264\pi\)
\(368\) −2.97121 3.76456i −0.154885 0.196241i
\(369\) 8.60620i 0.448021i
\(370\) 8.02495 2.55294i 0.417197 0.132721i
\(371\) −7.56641 −0.392829
\(372\) 7.29215 + 7.29215i 0.378081 + 0.378081i
\(373\) 16.7491 + 16.7491i 0.867237 + 0.867237i 0.992166 0.124929i \(-0.0398703\pi\)
−0.124929 + 0.992166i \(0.539870\pi\)
\(374\) 13.8407i 0.715685i
\(375\) −1.54471 11.0731i −0.0797687 0.571813i
\(376\) 2.68677 0.138560
\(377\) −21.9239 21.9239i −1.12914 1.12914i
\(378\) 1.05927 + 1.05927i 0.0544831 + 0.0544831i
\(379\) −19.1753 −0.984968 −0.492484 0.870322i \(-0.663911\pi\)
−0.492484 + 0.870322i \(0.663911\pi\)
\(380\) −1.25650 3.94968i −0.0644568 0.202614i
\(381\) 8.42961 0.431862
\(382\) −7.56953 + 7.56953i −0.387291 + 0.387291i
\(383\) 6.51953 + 6.51953i 0.333132 + 0.333132i 0.853775 0.520643i \(-0.174308\pi\)
−0.520643 + 0.853775i \(0.674308\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −6.11345 3.16253i −0.311570 0.161177i
\(386\) 10.1492 0.516583
\(387\) −1.45989 + 1.45989i −0.0742102 + 0.0742102i
\(388\) −0.564967 0.564967i −0.0286818 0.0286818i
\(389\) −33.2608 −1.68639 −0.843195 0.537608i \(-0.819328\pi\)
−0.843195 + 0.537608i \(0.819328\pi\)
\(390\) −4.00011 + 7.73258i −0.202554 + 0.391555i
\(391\) −32.0819 3.77866i −1.62245 0.191095i
\(392\) 3.36292 + 3.36292i 0.169853 + 0.169853i
\(393\) 13.6568 13.6568i 0.688893 0.688893i
\(394\) 3.83645i 0.193278i
\(395\) 34.9225 11.1097i 1.75714 0.558992i
\(396\) 2.05480i 0.103258i
\(397\) −13.0410 13.0410i −0.654510 0.654510i 0.299566 0.954076i \(-0.403158\pi\)
−0.954076 + 0.299566i \(0.903158\pi\)
\(398\) −13.7006 13.7006i −0.686748 0.686748i
\(399\) 2.77673i 0.139010i
\(400\) −4.08097 + 2.88889i −0.204049 + 0.144444i
\(401\) 36.5844i 1.82694i −0.406911 0.913468i \(-0.633394\pi\)
0.406911 0.913468i \(-0.366606\pi\)
\(402\) 7.21961 7.21961i 0.360081 0.360081i
\(403\) 28.3914 28.3914i 1.41428 1.41428i
\(404\) 14.5606i 0.724416i
\(405\) −2.13084 + 0.677875i −0.105882 + 0.0336839i
\(406\) 11.9295i 0.592053i
\(407\) 5.47201 + 5.47201i 0.271237 + 0.271237i
\(408\) 4.76291 + 4.76291i 0.235799 + 0.235799i
\(409\) 2.61805i 0.129454i 0.997903 + 0.0647271i \(0.0206177\pi\)
−0.997903 + 0.0647271i \(0.979382\pi\)
\(410\) 17.0925 + 8.84204i 0.844136 + 0.436677i
\(411\) 15.9532i 0.786914i
\(412\) −4.76419 + 4.76419i −0.234715 + 0.234715i
\(413\) −4.04671 4.04671i −0.199126 0.199126i
\(414\) −4.76291 0.560984i −0.234084 0.0275709i
\(415\) −16.0604 8.30813i −0.788373 0.407830i
\(416\) 3.89342 0.190891
\(417\) 4.07757 + 4.07757i 0.199680 + 0.199680i
\(418\) 2.69319 2.69319i 0.131728 0.131728i
\(419\) 5.34180 0.260964 0.130482 0.991451i \(-0.458348\pi\)
0.130482 + 0.991451i \(0.458348\pi\)
\(420\) 3.19208 1.01548i 0.155758 0.0495505i
\(421\) 22.4150i 1.09244i −0.837642 0.546220i \(-0.816066\pi\)
0.837642 0.546220i \(-0.183934\pi\)
\(422\) 6.94260 + 6.94260i 0.337960 + 0.337960i
\(423\) 1.89984 1.89984i 0.0923732 0.0923732i
\(424\) −5.05088 −0.245292
\(425\) −5.67778 + 33.1968i −0.275413 + 1.61028i
\(426\) −0.620733 −0.0300746
\(427\) −2.92745 2.92745i −0.141669 0.141669i
\(428\) −11.8110 11.8110i −0.570904 0.570904i
\(429\) −8.00023 −0.386255
\(430\) 1.39953 + 4.39931i 0.0674915 + 0.212154i
\(431\) 30.2418i 1.45670i −0.685207 0.728348i \(-0.740288\pi\)
0.685207 0.728348i \(-0.259712\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) 11.9248 + 11.9248i 0.573067 + 0.573067i 0.932984 0.359917i \(-0.117195\pi\)
−0.359917 + 0.932984i \(0.617195\pi\)
\(434\) −15.4488 −0.741564
\(435\) −15.8159 8.18166i −0.758314 0.392281i
\(436\) 2.85379i 0.136672i
\(437\) −5.50737 6.97791i −0.263453 0.333799i
\(438\) −4.77136 + 4.77136i −0.227985 + 0.227985i
\(439\) 6.91115i 0.329851i 0.986306 + 0.164926i \(0.0527384\pi\)
−0.986306 + 0.164926i \(0.947262\pi\)
\(440\) −4.08097 2.11111i −0.194553 0.100643i
\(441\) 4.75588 0.226471
\(442\) 18.5440 18.5440i 0.882049 0.882049i
\(443\) −10.1194 + 10.1194i −0.480789 + 0.480789i −0.905384 0.424594i \(-0.860417\pi\)
0.424594 + 0.905384i \(0.360417\pi\)
\(444\) −3.76610 −0.178731
\(445\) −1.50405 + 0.478477i −0.0712988 + 0.0226820i
\(446\) 16.5915 0.785633
\(447\) 13.4493 13.4493i 0.636132 0.636132i
\(448\) −1.05927 1.05927i −0.0500459 0.0500459i
\(449\) 31.3177i 1.47798i 0.673719 + 0.738988i \(0.264696\pi\)
−0.673719 + 0.738988i \(0.735304\pi\)
\(450\) −0.842929 + 4.92843i −0.0397361 + 0.232329i
\(451\) 17.6841i 0.832710i
\(452\) −6.25116 + 6.25116i −0.294030 + 0.294030i
\(453\) −5.71287 + 5.71287i −0.268414 + 0.268414i
\(454\) 10.2025 0.478828
\(455\) −3.95370 12.4281i −0.185353 0.582640i
\(456\) 1.85358i 0.0868018i
\(457\) 9.94629 9.94629i 0.465268 0.465268i −0.435110 0.900378i \(-0.643290\pi\)
0.900378 + 0.435110i \(0.143290\pi\)
\(458\) 18.8950 + 18.8950i 0.882908 + 0.882908i
\(459\) 6.73577 0.314399
\(460\) −6.00757 + 8.88308i −0.280105 + 0.414176i
\(461\) −34.8508 −1.62317 −0.811583 0.584237i \(-0.801394\pi\)
−0.811583 + 0.584237i \(0.801394\pi\)
\(462\) 2.17660 + 2.17660i 0.101265 + 0.101265i
\(463\) −15.4230 + 15.4230i −0.716766 + 0.716766i −0.967942 0.251175i \(-0.919183\pi\)
0.251175 + 0.967942i \(0.419183\pi\)
\(464\) 7.96345i 0.369694i
\(465\) 10.5953 20.4816i 0.491343 0.949811i
\(466\) −10.8396 −0.502137
\(467\) 21.1172 21.1172i 0.977189 0.977189i −0.0225568 0.999746i \(-0.507181\pi\)
0.999746 + 0.0225568i \(0.00718066\pi\)
\(468\) 2.75307 2.75307i 0.127261 0.127261i
\(469\) 15.2951i 0.706261i
\(470\) −1.82130 5.72509i −0.0840102 0.264079i
\(471\) 7.22285i 0.332811i
\(472\) −2.70134 2.70134i −0.124339 0.124339i
\(473\) −2.99978 + 2.99978i −0.137930 + 0.137930i
\(474\) −16.3891 −0.752775
\(475\) −7.56440 + 5.35478i −0.347079 + 0.245694i
\(476\) −10.0904 −0.462495
\(477\) −3.57151 + 3.57151i −0.163528 + 0.163528i
\(478\) 3.67559 3.67559i 0.168117 0.168117i
\(479\) 41.0169 1.87411 0.937056 0.349180i \(-0.113540\pi\)
0.937056 + 0.349180i \(0.113540\pi\)
\(480\) 2.13084 0.677875i 0.0972592 0.0309406i
\(481\) 14.6630i 0.668575i
\(482\) −18.4564 + 18.4564i −0.840668 + 0.840668i
\(483\) 5.63946 4.45099i 0.256604 0.202527i
\(484\) 6.77778i 0.308081i
\(485\) −0.820878 + 1.58683i −0.0372741 + 0.0720543i
\(486\) 1.00000 0.0453609
\(487\) 4.93023 + 4.93023i 0.223410 + 0.223410i 0.809933 0.586523i \(-0.199504\pi\)
−0.586523 + 0.809933i \(0.699504\pi\)
\(488\) −1.95419 1.95419i −0.0884621 0.0884621i
\(489\) 4.95842i 0.224227i
\(490\) 4.88620 9.44548i 0.220736 0.426703i
\(491\) 23.7765 1.07302 0.536509 0.843895i \(-0.319743\pi\)
0.536509 + 0.843895i \(0.319743\pi\)
\(492\) −6.08551 6.08551i −0.274356 0.274356i
\(493\) 37.9292 + 37.9292i 1.70824 + 1.70824i
\(494\) 7.21677 0.324698
\(495\) −4.37846 + 1.39290i −0.196797 + 0.0626062i
\(496\) −10.3127 −0.463052
\(497\) 0.657526 0.657526i 0.0294941 0.0294941i
\(498\) 5.71805 + 5.71805i 0.256232 + 0.256232i
\(499\) 17.9066i 0.801610i −0.916163 0.400805i \(-0.868731\pi\)
0.916163 0.400805i \(-0.131269\pi\)
\(500\) 8.92215 + 6.73760i 0.399011 + 0.301314i
\(501\) 20.5275 0.917100
\(502\) 3.37805 3.37805i 0.150770 0.150770i
\(503\) 8.64630 + 8.64630i 0.385519 + 0.385519i 0.873086 0.487567i \(-0.162115\pi\)
−0.487567 + 0.873086i \(0.662115\pi\)
\(504\) −1.49804 −0.0667279
\(505\) −31.0263 + 9.87026i −1.38065 + 0.439221i
\(506\) −9.78685 1.15271i −0.435078 0.0512443i
\(507\) −1.52646 1.52646i −0.0677927 0.0677927i
\(508\) −5.96063 + 5.96063i −0.264460 + 0.264460i
\(509\) 13.9217i 0.617070i −0.951213 0.308535i \(-0.900161\pi\)
0.951213 0.308535i \(-0.0998388\pi\)
\(510\) 6.92035 13.3777i 0.306438 0.592373i
\(511\) 10.1084i 0.447167i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 1.31068 + 1.31068i 0.0578679 + 0.0578679i
\(514\) 4.33456i 0.191189i
\(515\) 13.3813 + 6.92221i 0.589649 + 0.305029i
\(516\) 2.06459i 0.0908885i
\(517\) 3.90379 3.90379i 0.171689 0.171689i
\(518\) 3.98932 3.98932i 0.175281 0.175281i
\(519\) 24.1708i 1.06098i
\(520\) −2.63925 8.29627i −0.115739 0.363815i
\(521\) 1.76029i 0.0771199i 0.999256 + 0.0385600i \(0.0122771\pi\)
−0.999256 + 0.0385600i \(0.987723\pi\)
\(522\) 5.63101 + 5.63101i 0.246462 + 0.246462i
\(523\) −28.5430 28.5430i −1.24810 1.24810i −0.956559 0.291540i \(-0.905832\pi\)
−0.291540 0.956559i \(-0.594168\pi\)
\(524\) 19.3136i 0.843718i
\(525\) −4.32767 6.11345i −0.188875 0.266813i
\(526\) 4.45926i 0.194433i
\(527\) −49.1183 + 49.1183i −2.13963 + 2.13963i
\(528\) 1.45297 + 1.45297i 0.0632322 + 0.0632322i
\(529\) −5.34383 + 22.3706i −0.232341 + 0.972635i
\(530\) 3.42387 + 10.7626i 0.148723 + 0.467499i
\(531\) −3.82027 −0.165786
\(532\) −1.96345 1.96345i −0.0851262 0.0851262i
\(533\) −23.6935 + 23.6935i −1.02628 + 1.02628i
\(534\) 0.705848 0.0305450
\(535\) −17.1609 + 33.1736i −0.741932 + 1.43422i
\(536\) 10.2101i 0.441008i
\(537\) 13.8205 + 13.8205i 0.596400 + 0.596400i
\(538\) −9.91172 + 9.91172i −0.427325 + 0.427325i
\(539\) 9.77241 0.420927
\(540\) 1.02740 1.98606i 0.0442124 0.0854665i
\(541\) 31.2095 1.34180 0.670900 0.741548i \(-0.265908\pi\)
0.670900 + 0.741548i \(0.265908\pi\)
\(542\) −0.222223 0.222223i −0.00954528 0.00954528i
\(543\) 17.6866 + 17.6866i 0.759003 + 0.759003i
\(544\) −6.73577 −0.288794
\(545\) −6.08097 + 1.93451i −0.260480 + 0.0828654i
\(546\) 5.83250i 0.249608i
\(547\) −7.93990 7.93990i −0.339486 0.339486i 0.516688 0.856174i \(-0.327165\pi\)
−0.856174 + 0.516688i \(0.827165\pi\)
\(548\) −11.2806 11.2806i −0.481884 0.481884i
\(549\) −2.76364 −0.117949
\(550\) −1.73206 + 10.1270i −0.0738551 + 0.431816i
\(551\) 14.7609i 0.628834i
\(552\) 3.76456 2.97121i 0.160230 0.126463i
\(553\) 17.3605 17.3605i 0.738243 0.738243i
\(554\) 18.6121i 0.790754i
\(555\) 2.55294 + 8.02495i 0.108366 + 0.340640i
\(556\) −5.76656 −0.244557
\(557\) −11.9125 + 11.9125i −0.504749 + 0.504749i −0.912910 0.408161i \(-0.866170\pi\)
0.408161 + 0.912910i \(0.366170\pi\)
\(558\) −7.29215 + 7.29215i −0.308702 + 0.308702i
\(559\) −8.03832 −0.339985
\(560\) −1.53909 + 2.97520i −0.0650383 + 0.125725i
\(561\) 13.8407 0.584354
\(562\) 8.11241 8.11241i 0.342201 0.342201i
\(563\) −9.93961 9.93961i −0.418905 0.418905i 0.465921 0.884826i \(-0.345723\pi\)
−0.884826 + 0.465921i \(0.845723\pi\)
\(564\) 2.68677i 0.113134i
\(565\) 17.5577 + 9.08273i 0.738660 + 0.382113i
\(566\) 5.14662i 0.216329i
\(567\) −1.05927 + 1.05927i −0.0444853 + 0.0444853i
\(568\) 0.438925 0.438925i 0.0184169 0.0184169i
\(569\) −21.8062 −0.914164 −0.457082 0.889425i \(-0.651105\pi\)
−0.457082 + 0.889425i \(0.651105\pi\)
\(570\) 3.94968 1.25650i 0.165434 0.0526288i
\(571\) 4.43149i 0.185452i −0.995692 0.0927260i \(-0.970442\pi\)
0.995692 0.0927260i \(-0.0295580\pi\)
\(572\) 5.65701 5.65701i 0.236532 0.236532i
\(573\) −7.56953 7.56953i −0.316222 0.316222i
\(574\) 12.8924 0.538119
\(575\) 23.0008 + 6.77957i 0.959200 + 0.282728i
\(576\) −1.00000 −0.0416667
\(577\) 4.31029 + 4.31029i 0.179440 + 0.179440i 0.791112 0.611672i \(-0.209503\pi\)
−0.611672 + 0.791112i \(0.709503\pi\)
\(578\) −20.0610 + 20.0610i −0.834429 + 0.834429i
\(579\) 10.1492i 0.421788i
\(580\) 16.9688 5.39822i 0.704593 0.224149i
\(581\) −12.1139 −0.502571
\(582\) 0.564967 0.564967i 0.0234186 0.0234186i
\(583\) −7.33876 + 7.33876i −0.303940 + 0.303940i
\(584\) 6.74773i 0.279223i
\(585\) −7.73258 4.00011i −0.319703 0.165384i
\(586\) 4.24286i 0.175271i
\(587\) 6.29354 + 6.29354i 0.259762 + 0.259762i 0.824957 0.565195i \(-0.191199\pi\)
−0.565195 + 0.824957i \(0.691199\pi\)
\(588\) −3.36292 + 3.36292i −0.138684 + 0.138684i
\(589\) −19.1153 −0.787634
\(590\) −3.92496 + 7.58730i −0.161588 + 0.312364i
\(591\) 3.83645 0.157811
\(592\) 2.66303 2.66303i 0.109450 0.109450i
\(593\) 21.5701 21.5701i 0.885777 0.885777i −0.108337 0.994114i \(-0.534553\pi\)
0.994114 + 0.108337i \(0.0345526\pi\)
\(594\) 2.05480 0.0843097
\(595\) 6.84006 + 21.5011i 0.280415 + 0.881460i
\(596\) 19.0202i 0.779100i
\(597\) 13.7006 13.7006i 0.560727 0.560727i
\(598\) −11.5682 14.6570i −0.473058 0.599370i
\(599\) 7.58866i 0.310064i 0.987909 + 0.155032i \(0.0495481\pi\)
−0.987909 + 0.155032i \(0.950452\pi\)
\(600\) −2.88889 4.08097i −0.117938 0.166605i
\(601\) −21.0502 −0.858656 −0.429328 0.903149i \(-0.641250\pi\)
−0.429328 + 0.903149i \(0.641250\pi\)
\(602\) 2.18696 + 2.18696i 0.0891340 + 0.0891340i
\(603\) 7.21961 + 7.21961i 0.294005 + 0.294005i
\(604\) 8.07922i 0.328739i
\(605\) 14.4424 4.59449i 0.587166 0.186792i
\(606\) 14.5606 0.591483
\(607\) −4.94638 4.94638i −0.200767 0.200767i 0.599561 0.800329i \(-0.295342\pi\)
−0.800329 + 0.599561i \(0.795342\pi\)
\(608\) −1.31068 1.31068i −0.0531550 0.0531550i
\(609\) −11.9295 −0.483410
\(610\) −2.83938 + 5.48877i −0.114963 + 0.222234i
\(611\) 10.4608 0.423197
\(612\) −4.76291 + 4.76291i −0.192529 + 0.192529i
\(613\) −3.74955 3.74955i −0.151443 0.151443i 0.627319 0.778762i \(-0.284152\pi\)
−0.778762 + 0.627319i \(0.784152\pi\)
\(614\) 21.0842i 0.850891i
\(615\) −8.84204 + 17.0925i −0.356545 + 0.689235i
\(616\) −3.07818 −0.124023
\(617\) 19.0364 19.0364i 0.766378 0.766378i −0.211089 0.977467i \(-0.567701\pi\)
0.977467 + 0.211089i \(0.0677011\pi\)
\(618\) −4.76419 4.76419i −0.191644 0.191644i
\(619\) −46.6096 −1.87340 −0.936700 0.350134i \(-0.886136\pi\)
−0.936700 + 0.350134i \(0.886136\pi\)
\(620\) 6.99070 + 21.9747i 0.280753 + 0.882523i
\(621\) 0.560984 4.76291i 0.0225115 0.191129i
\(622\) −7.41842 7.41842i −0.297451 0.297451i
\(623\) −0.747686 + 0.747686i −0.0299554 + 0.0299554i
\(624\) 3.89342i 0.155862i
\(625\) 8.30864 23.5789i 0.332346 0.943158i
\(626\) 19.4109i 0.775815i
\(627\) 2.69319 + 2.69319i 0.107556 + 0.107556i
\(628\) 5.10732 + 5.10732i 0.203804 + 0.203804i
\(629\) 25.3676i 1.01147i
\(630\) 1.01548 + 3.19208i 0.0404578 + 0.127176i
\(631\) 17.2332i 0.686042i −0.939328 0.343021i \(-0.888550\pi\)
0.939328 0.343021i \(-0.111450\pi\)
\(632\) 11.5888 11.5888i 0.460979 0.460979i
\(633\) −6.94260 + 6.94260i −0.275943 + 0.275943i
\(634\) 11.8407i 0.470254i
\(635\) 16.7417 + 8.66060i 0.664375 + 0.343685i
\(636\) 5.05088i 0.200280i
\(637\) 13.0933 + 13.0933i 0.518774 + 0.518774i
\(638\) 11.5706 + 11.5706i 0.458085 + 0.458085i
\(639\) 0.620733i 0.0245558i
\(640\) −1.02740 + 1.98606i −0.0406116 + 0.0785060i
\(641\) 37.3431i 1.47496i −0.675367 0.737482i \(-0.736015\pi\)
0.675367 0.737482i \(-0.263985\pi\)
\(642\) 11.8110 11.8110i 0.466141 0.466141i
\(643\) 9.61594 + 9.61594i 0.379215 + 0.379215i 0.870819 0.491604i \(-0.163589\pi\)
−0.491604 + 0.870819i \(0.663589\pi\)
\(644\) −0.840376 + 7.13502i −0.0331154 + 0.281159i
\(645\) −4.39931 + 1.39953i −0.173223 + 0.0551066i
\(646\) −12.4853 −0.491227
\(647\) 31.9140 + 31.9140i 1.25467 + 1.25467i 0.953604 + 0.301064i \(0.0973416\pi\)
0.301064 + 0.953604i \(0.402658\pi\)
\(648\) −0.707107 + 0.707107i −0.0277778 + 0.0277778i
\(649\) −7.84992 −0.308136
\(650\) −15.8889 + 11.2477i −0.623216 + 0.441170i
\(651\) 15.4488i 0.605485i
\(652\) 3.50613 + 3.50613i 0.137311 + 0.137311i
\(653\) 12.0188 12.0188i 0.470332 0.470332i −0.431690 0.902022i \(-0.642082\pi\)
0.902022 + 0.431690i \(0.142082\pi\)
\(654\) 2.85379 0.111592
\(655\) 41.1542 13.0922i 1.60803 0.511554i
\(656\) 8.60620 0.336016
\(657\) −4.77136 4.77136i −0.186149 0.186149i
\(658\) −2.84603 2.84603i −0.110950 0.110950i
\(659\) 5.65904 0.220445 0.110222 0.993907i \(-0.464844\pi\)
0.110222 + 0.993907i \(0.464844\pi\)
\(660\) 2.11111 4.08097i 0.0821749 0.158852i
\(661\) 21.4115i 0.832811i −0.909179 0.416406i \(-0.863290\pi\)
0.909179 0.416406i \(-0.136710\pi\)
\(662\) −10.4983 10.4983i −0.408029 0.408029i
\(663\) 18.5440 + 18.5440i 0.720190 + 0.720190i
\(664\) −8.08654 −0.313819
\(665\) −2.85282 + 5.51476i −0.110628 + 0.213853i
\(666\) 3.76610i 0.145933i
\(667\) 29.9789 23.6611i 1.16079 0.916160i
\(668\) −14.5151 + 14.5151i −0.561606 + 0.561606i
\(669\) 16.5915i 0.641466i
\(670\) 21.7560 6.92115i 0.840509 0.267387i
\(671\) −5.67875 −0.219226
\(672\) 1.05927 1.05927i 0.0408623 0.0408623i
\(673\) 0.273515 0.273515i 0.0105432 0.0105432i −0.701816 0.712359i \(-0.747627\pi\)
0.712359 + 0.701816i \(0.247627\pi\)
\(674\) −0.569514 −0.0219369
\(675\) −4.92843 0.842929i −0.189696 0.0324444i
\(676\) 2.15875 0.0830287
\(677\) −3.62366 + 3.62366i −0.139268 + 0.139268i −0.773304 0.634035i \(-0.781397\pi\)
0.634035 + 0.773304i \(0.281397\pi\)
\(678\) −6.25116 6.25116i −0.240074 0.240074i
\(679\) 1.19691i 0.0459331i
\(680\) 4.56601 + 14.3529i 0.175099 + 0.550407i
\(681\) 10.2025i 0.390962i
\(682\) −14.9840 + 14.9840i −0.573765 + 0.573765i
\(683\) 22.0303 22.0303i 0.842968 0.842968i −0.146276 0.989244i \(-0.546729\pi\)
0.989244 + 0.146276i \(0.0467288\pi\)
\(684\) −1.85358 −0.0708734
\(685\) −16.3904 + 31.6841i −0.626244 + 1.21059i
\(686\) 17.6108i 0.672382i
\(687\) −18.8950 + 18.8950i −0.720891 + 0.720891i
\(688\) 1.45989 + 1.45989i 0.0556576 + 0.0556576i
\(689\) −19.6652 −0.749185
\(690\) −8.88308 6.00757i −0.338173 0.228704i
\(691\) 11.8861 0.452167 0.226083 0.974108i \(-0.427408\pi\)
0.226083 + 0.974108i \(0.427408\pi\)
\(692\) −17.0914 17.0914i −0.649716 0.649716i
\(693\) −2.17660 + 2.17660i −0.0826822 + 0.0826822i
\(694\) 14.1710i 0.537924i
\(695\) 3.90901 + 12.2876i 0.148277 + 0.466096i
\(696\) −7.96345 −0.301854
\(697\) 40.9906 40.9906i 1.55263 1.55263i
\(698\) −14.9538 + 14.9538i −0.566010 + 0.566010i
\(699\) 10.8396i 0.409993i
\(700\) 7.38298 + 1.26274i 0.279051 + 0.0477271i
\(701\) 18.1192i 0.684353i 0.939636 + 0.342177i \(0.111164\pi\)
−0.939636 + 0.342177i \(0.888836\pi\)
\(702\) 2.75307 + 2.75307i 0.103908 + 0.103908i
\(703\) 4.93614 4.93614i 0.186170 0.186170i
\(704\) −2.05480 −0.0774434
\(705\) 5.72509 1.82130i 0.215619 0.0685940i
\(706\) 8.27607 0.311474
\(707\) −15.4236 + 15.4236i −0.580065 + 0.580065i
\(708\) 2.70134 2.70134i 0.101523 0.101523i
\(709\) −27.9725 −1.05053 −0.525266 0.850938i \(-0.676034\pi\)
−0.525266 + 0.850938i \(0.676034\pi\)
\(710\) −1.23282 0.637743i −0.0462667 0.0239341i
\(711\) 16.3891i 0.614638i
\(712\) −0.499110 + 0.499110i −0.0187049 + 0.0187049i
\(713\) 30.6411 + 38.8226i 1.14752 + 1.45392i
\(714\) 10.0904i 0.377625i
\(715\) −15.8889 8.21945i −0.594213 0.307390i
\(716\) −19.5452 −0.730438
\(717\) 3.67559 + 3.67559i 0.137267 + 0.137267i
\(718\) 5.15644 + 5.15644i 0.192437 + 0.192437i
\(719\) 30.4764i 1.13658i −0.822829 0.568289i \(-0.807606\pi\)
0.822829 0.568289i \(-0.192394\pi\)
\(720\) 0.677875 + 2.13084i 0.0252629 + 0.0794118i
\(721\) 10.0932 0.375889
\(722\) 11.0056 + 11.0056i 0.409585 + 0.409585i
\(723\) −18.4564 18.4564i −0.686402 0.686402i
\(724\) −25.0126 −0.929585
\(725\) −23.0055 32.4986i −0.854403 1.20697i
\(726\) −6.77778 −0.251547
\(727\) −34.3280 + 34.3280i −1.27316 + 1.27316i −0.328732 + 0.944423i \(0.606621\pi\)
−0.944423 + 0.328732i \(0.893379\pi\)
\(728\) −4.12420 4.12420i −0.152853 0.152853i
\(729\) 1.00000i 0.0370370i
\(730\) −14.3783 + 4.57412i −0.532166 + 0.169296i
\(731\) 13.9066 0.514354
\(732\) 1.95419 1.95419i 0.0722290 0.0722290i
\(733\) 21.2431 + 21.2431i 0.784630 + 0.784630i 0.980608 0.195978i \(-0.0627881\pi\)
−0.195978 + 0.980608i \(0.562788\pi\)
\(734\) 6.26275 0.231162
\(735\) 9.44548 + 4.88620i 0.348402 + 0.180230i
\(736\) −0.560984 + 4.76291i −0.0206781 + 0.175563i
\(737\) 14.8349 + 14.8349i 0.546450 + 0.546450i
\(738\) 6.08551 6.08551i 0.224011 0.224011i
\(739\) 13.7089i 0.504289i −0.967690 0.252144i \(-0.918864\pi\)
0.967690 0.252144i \(-0.0811358\pi\)
\(740\) −7.47970 3.86930i −0.274959 0.142238i
\(741\) 7.21677i 0.265115i
\(742\) 5.35026 + 5.35026i 0.196414 + 0.196414i
\(743\) −4.39312 4.39312i −0.161168 0.161168i 0.621916 0.783084i \(-0.286355\pi\)
−0.783084 + 0.621916i \(0.786355\pi\)
\(744\) 10.3127i 0.378081i
\(745\) 40.5291 12.8934i 1.48487 0.472376i
\(746\) 23.6868i 0.867237i
\(747\) −5.71805 + 5.71805i −0.209212 + 0.209212i
\(748\) −9.78685 + 9.78685i −0.357843 + 0.357843i
\(749\) 25.0221i 0.914286i
\(750\) −6.73760 + 8.92215i −0.246022 + 0.325791i
\(751\) 34.4080i 1.25557i −0.778388 0.627783i \(-0.783962\pi\)
0.778388 0.627783i \(-0.216038\pi\)
\(752\) −1.89984 1.89984i −0.0692799 0.0692799i
\(753\) 3.37805 + 3.37805i 0.123103 + 0.123103i
\(754\) 31.0051i 1.12914i
\(755\) −17.2155 + 5.47670i −0.626538 + 0.199318i
\(756\) 1.49804i 0.0544831i
\(757\) 14.8002 14.8002i 0.537924 0.537924i −0.384995 0.922919i \(-0.625797\pi\)
0.922919 + 0.384995i \(0.125797\pi\)
\(758\) 13.5590 + 13.5590i 0.492484 + 0.492484i
\(759\) 1.15271 9.78685i 0.0418408 0.355240i
\(760\) −1.90437 + 3.68132i −0.0690788 + 0.133536i
\(761\) −25.2096 −0.913849 −0.456924 0.889506i \(-0.651049\pi\)
−0.456924 + 0.889506i \(0.651049\pi\)
\(762\) −5.96063 5.96063i −0.215931 0.215931i
\(763\) −3.02294 + 3.02294i −0.109438 + 0.109438i
\(764\) 10.7049 0.387291
\(765\) 13.3777 + 6.92035i 0.483670 + 0.250206i
\(766\) 9.22000i 0.333132i
\(767\) −10.5175 10.5175i −0.379764 0.379764i
\(768\) 0.707107 0.707107i 0.0255155 0.0255155i
\(769\) 7.92654 0.285838 0.142919 0.989734i \(-0.454351\pi\)
0.142919 + 0.989734i \(0.454351\pi\)
\(770\) 2.08662 + 6.55911i 0.0751965 + 0.236374i
\(771\) 4.33456 0.156105
\(772\) −7.17660 7.17660i −0.258291 0.258291i
\(773\) −36.0701 36.0701i −1.29735 1.29735i −0.930136 0.367215i \(-0.880311\pi\)
−0.367215 0.930136i \(-0.619689\pi\)
\(774\) 2.06459 0.0742102
\(775\) 42.0857 29.7921i 1.51176 1.07017i
\(776\) 0.798984i 0.0286818i
\(777\) 3.98932 + 3.98932i 0.143116 + 0.143116i
\(778\) 23.5189 + 23.5189i 0.843195 + 0.843195i
\(779\) 15.9523 0.571550
\(780\) 8.29627 2.63925i 0.297054